LMFDB - Embedded newform 38.7.f.a.13.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,7,Mod(3,38)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([13]))

N = Newforms(chi, 7, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("38.3");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	38.f (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.74205517755$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			13.5
Character	$\chi$	$=$	38.13
Dual form			38.7.f.a.3.5

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.63616 - 4.33340i) q^{2} +(12.5750 - 34.5495i) q^{3} +(-5.55674 + 31.5138i) q^{4} +(-24.6848 - 139.995i) q^{5} +(-195.442 + 71.1350i) q^{6} +(136.699 - 236.770i) q^{7} +(156.767 - 90.5097i) q^{8} +(-477.093 - 400.329i) q^{9} +O(q^{10})$	\(q+(-3.63616 - 4.33340i) q^{2} +(12.5750 - 34.5495i) q^{3} +(-5.55674 + 31.5138i) q^{4} +(-24.6848 - 139.995i) q^{5} +(-195.442 + 71.1350i) q^{6} +(136.699 - 236.770i) q^{7} +(156.767 - 90.5097i) q^{8} +(-477.093 - 400.329i) q^{9} +(-516.895 + 616.012i) q^{10} +(154.353 + 267.347i) q^{11} +(1018.91 + 588.270i) q^{12} +(192.920 + 530.044i) q^{13} +(-1523.08 + 268.560i) q^{14} +(-5147.16 - 907.583i) q^{15} +(-962.245 - 350.229i) q^{16} +(-7404.65 + 6213.24i) q^{17} +3523.10i q^{18} +(571.576 - 6835.14i) q^{19} +4548.94 q^{20} +(-6461.31 - 7700.29i) q^{21} +(597.272 - 1640.99i) q^{22} +(-790.114 + 4480.96i) q^{23} +(-1155.72 - 6554.40i) q^{24} +(-4306.46 + 1567.42i) q^{25} +(1595.41 - 2763.32i) q^{26} +(3381.48 - 1952.30i) q^{27} +(6701.94 + 5623.60i) q^{28} +(7702.41 - 9179.37i) q^{29} +(14783.0 + 25604.8i) q^{30} +(34857.0 + 20124.7i) q^{31} +(1981.19 + 5443.28i) q^{32} +(11177.7 - 1970.93i) q^{33} +(53848.9 + 9495.02i) q^{34} +(-36521.0 - 13292.6i) q^{35} +(15267.0 - 12810.5i) q^{36} -83779.7i q^{37} +(-31697.8 + 22376.8i) q^{38} +20738.8 q^{39} +(-16540.6 - 19712.4i) q^{40} +(10334.6 - 28394.2i) q^{41} +(-9874.12 + 55998.9i) q^{42} +(-17549.1 - 99525.8i) q^{43} +(-9282.84 + 3378.68i) q^{44} +(-44266.9 + 76672.6i) q^{45} +(22290.8 - 12869.6i) q^{46} +(17452.2 + 14644.2i) q^{47} +(-24200.5 + 28841.0i) q^{48} +(21451.0 + 37154.3i) q^{49} +(22451.2 + 12962.2i) q^{50} +(121551. + 333959. i) q^{51} +(-17775.7 + 3134.34i) q^{52} +(-136542. - 24076.1i) q^{53} +(-20755.7 - 7554.45i) q^{54} +(33617.0 - 28208.0i) q^{55} -49490.5i q^{56} +(-228963. - 105700. i) q^{57} -67785.0 q^{58} +(-28663.2 - 34159.5i) q^{59} +(57202.9 - 157164. i) q^{60} +(36239.2 - 205523. i) q^{61} +(-39537.1 - 224226. i) q^{62} +(-160004. + 58236.8i) q^{63} +(16384.0 - 28377.9i) q^{64} +(69441.1 - 40091.9i) q^{65} +(-49184.8 - 41270.9i) q^{66} +(-269824. + 321564. i) q^{67} +(-154657. - 267874. i) q^{68} +(144879. + 83646.2i) q^{69} +(75194.0 + 206594. i) q^{70} +(128224. - 22609.3i) q^{71} +(-111026. - 19576.9i) q^{72} +(498363. + 181389. i) q^{73} +(-363051. + 304636. i) q^{74} +168497. i q^{75} +(212226. + 55993.7i) q^{76} +84399.9 q^{77} +(-75409.4 - 89869.4i) q^{78} +(-57206.4 + 157173. i) q^{79} +(-25277.3 + 143355. i) q^{80} +(-103769. - 588503. i) q^{81} +(-160622. + 58461.5i) q^{82} +(315134. - 545828. i) q^{83} +(278570. - 160832. i) q^{84} +(1.05260e6 + 883239. i) q^{85} +(-367474. + 437939. i) q^{86} +(-220285. - 381545. i) q^{87} +(48395.0 + 27940.9i) q^{88} +(259935. + 714166. i) q^{89} +(493214. - 86967.0i) q^{90} +(151871. + 26778.9i) q^{91} +(-136822. - 49799.1i) q^{92} +(1.13363e6 - 951225. i) q^{93} -128876. i q^{94} +(-970993. + 88706.8i) q^{95} +212976. q^{96} +(-253212. - 301767. i) q^{97} +(83005.1 - 228055. i) q^{98} +(33386.0 - 189342. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 30 q^{3} - 240 q^{6} + 432 q^{7} + 690 q^{9}+O(q^{10}) $ 60 * q + 30 * q^3 - 240 * q^6 + 432 * q^7 + 690 * q^9	\( 60 q + 30 q^{3} - 240 q^{6} + 432 q^{7} + 690 q^{9} - 3360 q^{11} + 9660 q^{13} + 2496 q^{14} - 37464 q^{15} + 7704 q^{17} + 46704 q^{19} + 21504 q^{20} + 78732 q^{21} - 20304 q^{22} - 54120 q^{23} + 7680 q^{24} - 41328 q^{25} - 25536 q^{26} - 124830 q^{27} + 65280 q^{28} - 21840 q^{29} + 30780 q^{31} - 54582 q^{33} - 70560 q^{34} - 56796 q^{35} - 22080 q^{36} + 52080 q^{38} + 496344 q^{39} + 83394 q^{41} + 38880 q^{42} - 294384 q^{43} - 8448 q^{44} - 391824 q^{45} + 738720 q^{46} + 639264 q^{47} + 61440 q^{48} - 85530 q^{49} - 689472 q^{50} - 215478 q^{51} - 456960 q^{52} - 1189428 q^{53} - 907200 q^{54} - 316512 q^{55} + 517776 q^{57} + 440640 q^{58} + 957390 q^{59} + 586752 q^{60} + 1390404 q^{61} + 978384 q^{62} + 2002152 q^{63} + 983040 q^{64} - 878940 q^{65} - 976992 q^{66} - 2920854 q^{67} - 78144 q^{68} - 2667600 q^{69} - 643392 q^{70} + 1585980 q^{71} + 706560 q^{72} + 1734648 q^{73} - 1167552 q^{74} - 411264 q^{76} - 1481400 q^{77} - 2170608 q^{78} + 4991952 q^{79} + 40002 q^{81} + 2299392 q^{82} - 30672 q^{83} + 1313280 q^{84} + 815976 q^{85} - 1424976 q^{86} - 125892 q^{87} - 6804636 q^{89} - 2283456 q^{90} - 3838704 q^{91} - 244992 q^{92} - 3271128 q^{93} - 4631640 q^{95} + 2112390 q^{97} + 7177728 q^{98} + 21467982 q^{99}+O(q^{100}) \) 60 * q + 30 * q^3 - 240 * q^6 + 432 * q^7 + 690 * q^9 - 3360 * q^11 + 9660 * q^13 + 2496 * q^14 - 37464 * q^15 + 7704 * q^17 + 46704 * q^19 + 21504 * q^20 + 78732 * q^21 - 20304 * q^22 - 54120 * q^23 + 7680 * q^24 - 41328 * q^25 - 25536 * q^26 - 124830 * q^27 + 65280 * q^28 - 21840 * q^29 + 30780 * q^31 - 54582 * q^33 - 70560 * q^34 - 56796 * q^35 - 22080 * q^36 + 52080 * q^38 + 496344 * q^39 + 83394 * q^41 + 38880 * q^42 - 294384 * q^43 - 8448 * q^44 - 391824 * q^45 + 738720 * q^46 + 639264 * q^47 + 61440 * q^48 - 85530 * q^49 - 689472 * q^50 - 215478 * q^51 - 456960 * q^52 - 1189428 * q^53 - 907200 * q^54 - 316512 * q^55 + 517776 * q^57 + 440640 * q^58 + 957390 * q^59 + 586752 * q^60 + 1390404 * q^61 + 978384 * q^62 + 2002152 * q^63 + 983040 * q^64 - 878940 * q^65 - 976992 * q^66 - 2920854 * q^67 - 78144 * q^68 - 2667600 * q^69 - 643392 * q^70 + 1585980 * q^71 + 706560 * q^72 + 1734648 * q^73 - 1167552 * q^74 - 411264 * q^76 - 1481400 * q^77 - 2170608 * q^78 + 4991952 * q^79 + 40002 * q^81 + 2299392 * q^82 - 30672 * q^83 + 1313280 * q^84 + 815976 * q^85 - 1424976 * q^86 - 125892 * q^87 - 6804636 * q^89 - 2283456 * q^90 - 3838704 * q^91 - 244992 * q^92 - 3271128 * q^93 - 4631640 * q^95 + 2112390 * q^97 + 7177728 * q^98 + 21467982 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{5}{18}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−3.63616	−	4.33340i	−0.454519	−	0.541675i
$2$	−3.63616	−	4.33340i	−0.454519	−	0.541675i
$3$	12.5750	−	34.5495i	0.465741	−	1.27961i	−0.455367	−	0.890304i	$-0.650492\pi$
$3$	12.5750	−	34.5495i	0.465741	−	1.27961i	0.921107	−	0.389308i	$-0.127286\pi$
$4$	−5.55674	+	31.5138i	−0.0868241	+	0.492404i
$5$	−24.6848	−	139.995i	−0.197479	−	1.11996i	−0.908844	−	0.417135i	$-0.863034\pi$
$5$	−24.6848	−	139.995i	−0.197479	−	1.11996i	0.711366	−	0.702822i	$-0.248077\pi$
$6$	−195.442	+	71.1350i	−0.904823	+	0.329329i
$7$	136.699	−	236.770i	0.398541	−	0.690293i	−0.595005	−	0.803722i	$-0.702850\pi$
$7$	136.699	−	236.770i	0.398541	−	0.690293i	0.993546	+	0.113429i	$0.0361834\pi$
$8$	156.767	−	90.5097i	0.306186	−	0.176777i
$9$	−477.093	−	400.329i	−0.654449	−	0.549148i
$10$	−516.895	+	616.012i	−0.516895	+	0.616012i
$11$	154.353	+	267.347i	0.115968	+	0.200862i	0.918166	−	0.396195i	$-0.129670\pi$
$11$	154.353	+	267.347i	0.115968	+	0.200862i	−0.802198	+	0.597057i	$0.796336\pi$
$12$	1018.91	+	588.270i	0.589649	+	0.340434i
$13$	192.920	+	530.044i	0.0878108	+	0.241258i	0.975823	−	0.218561i	$-0.0701363\pi$
$13$	192.920	+	530.044i	0.0878108	+	0.241258i	−0.888012	+	0.459819i	$0.847914\pi$
$14$	−1523.08	+	268.560i	−0.555059	+	0.0978719i
$15$	−5147.16	−	907.583i	−1.52508	−	0.268914i
$16$	−962.245	−	350.229i	−0.234923	−	0.0855050i
$17$	−7404.65	+	6213.24i	−1.50715	+	1.26465i	−0.638083	+	0.769968i	$0.720272\pi$
$17$	−7404.65	+	6213.24i	−1.50715	+	1.26465i	−0.869072	+	0.494685i	$0.835283\pi$
$18$			3523.10i			0.604097i
$19$	571.576	−	6835.14i	0.0833322	−	0.996522i
$19$	571.576	−	6835.14i	0.0833322	−	0.996522i
$20$	4548.94			0.568617
$21$	−6461.31	−	7700.29i	−0.697690	−	0.831475i
$22$	597.272	−	1640.99i	0.0560924	−	0.154113i
$23$	−790.114	+	4480.96i	−0.0649391	+	0.368288i	0.934969	+	0.354730i	$0.115427\pi$
$23$	−790.114	+	4480.96i	−0.0649391	+	0.368288i	−0.999908	+	0.0135585i	$0.995684\pi$
$24$	−1155.72	−	6554.40i	−0.0836022	−	0.474132i
$25$	−4306.46	+	1567.42i	−0.275613	+	0.100315i
$26$	1595.41	−	2763.32i	0.0907719	−	0.157221i
$27$	3381.48	−	1952.30i	0.171797	−	0.0991871i
$28$	6701.94	+	5623.60i	0.305300	+	0.256177i
$29$	7702.41	−	9179.37i	0.315815	−	0.376373i	−0.584662	−	0.811277i	$-0.698773\pi$
$29$	7702.41	−	9179.37i	0.315815	−	0.376373i	0.900477	+	0.434903i	$0.143217\pi$
$30$	14783.0	+	25604.8i	0.547517	+	0.948327i
$31$	34857.0	+	20124.7i	1.17005	+	0.675529i	0.953692	−	0.300785i	$-0.0972485\pi$
$31$	34857.0	+	20124.7i	1.17005	+	0.675529i	0.216359	+	0.976314i	$0.430582\pi$
$32$	1981.19	+	5443.28i	0.0604612	+	0.166116i
$33$	11177.7	−	1970.93i	0.311036	−	0.0548441i
$34$	53848.9	+	9495.02i	1.37006	+	0.241579i
$35$	−36521.0	−	13292.6i	−0.851801	−	0.310030i
$36$	15267.0	−	12810.5i	0.327225	−	0.274574i
$37$		−	83779.7i		−	1.65399i	−0.562208	−	0.826996i	$-0.690048\pi$
$37$		−	83779.7i		−	1.65399i	0.562208	−	0.826996i	$-0.309952\pi$
$38$	−31697.8	+	22376.8i	−0.577667	+	0.407800i
$39$	20738.8			0.349614
$40$	−16540.6	−	19712.4i	−0.258448	−	0.308006i
$41$	10334.6	−	28394.2i	0.149949	−	0.411982i	−0.841862	−	0.539692i	$-0.818541\pi$
$41$	10334.6	−	28394.2i	0.149949	−	0.411982i	0.991811	+	0.127711i	$0.0407629\pi$
$42$	−9874.12	+	55998.9i	−0.133276	+	0.755843i
$43$	−17549.1	−	99525.8i	−0.220724	−	1.25179i	−0.870693	−	0.491826i	$-0.836329\pi$
$43$	−17549.1	−	99525.8i	−0.220724	−	1.25179i	0.649970	−	0.759960i	$-0.274782\pi$
$44$	−9282.84	+	3378.68i	−0.108974	+	0.0396633i
$45$	−44266.9	+	76672.6i	−0.485782	+	0.841400i
$46$	22290.8	−	12869.6i	0.229009	−	0.132218i
$47$	17452.2	+	14644.2i	0.168096	+	0.141049i	0.722955	−	0.690895i	$-0.242783\pi$
$47$	17452.2	+	14644.2i	0.168096	+	0.141049i	−0.554859	+	0.831944i	$0.687228\pi$
$48$	−24200.5	+	28841.0i	−0.218827	+	0.260787i
$49$	21451.0	+	37154.3i	0.182331	+	0.315806i
$50$	22451.2	+	12962.2i	0.179610	+	0.103698i
$51$	121551.	+	333959.i	0.916322	+	2.51757i
$52$	−17775.7	+	3134.34i	−0.126421	+	0.0222914i
$53$	−136542.	−	24076.1i	−0.917149	−	0.161718i	−0.304901	−	0.952384i	$-0.598623\pi$
$53$	−136542.	−	24076.1i	−0.917149	−	0.161718i	−0.612248	+	0.790666i	$0.709735\pi$
$54$	−20755.7	−	7554.45i	−0.131812	−	0.0479758i
$55$	33617.0	−	28208.0i	0.202056	−	0.169545i
$56$		−	49490.5i		−	0.281811i
$57$	−228963.	−	105700.i	−1.23635	−	0.570754i
$58$	−67785.0			−0.347416
$59$	−28663.2	−	34159.5i	−0.139562	−	0.166324i	0.691736	−	0.722151i	$-0.256846\pi$
$59$	−28663.2	−	34159.5i	−0.139562	−	0.166324i	−0.831298	+	0.555827i	$0.812402\pi$
$60$	57202.9	−	157164.i	0.264828	−	0.727610i
$61$	36239.2	−	205523.i	0.159658	−	0.905463i	−0.794746	−	0.606943i	$-0.792396\pi$
$61$	36239.2	−	205523.i	0.159658	−	0.905463i	0.954403	−	0.298520i	$-0.0964931\pi$
$62$	−39537.1	−	224226.i	−0.165894	−	0.940829i
$63$	−160004.	+	58236.8i	−0.639897	+	0.232904i
$64$	16384.0	−	28377.9i	0.0625000	−	0.108253i
$65$	69441.1	−	40091.9i	0.252858	−	0.145988i
$66$	−49184.8	−	41270.9i	−0.171080	−	0.143553i
$67$	−269824.	+	321564.i	−0.897132	+	1.06916i	0.100113	+	0.994976i	$0.468080\pi$
$67$	−269824.	+	321564.i	−0.897132	+	1.06916i	−0.997245	+	0.0741837i	$0.976365\pi$
$68$	−154657.	−	267874.i	−0.491863	−	0.851931i
$69$	144879.	+	83646.2i	0.441021	+	0.254624i
$70$	75194.0	+	206594.i	0.219225	+	0.602315i
$71$	128224.	−	22609.3i	0.358256	−	0.0631703i	0.00837668	−	0.999965i	$-0.497334\pi$
$71$	128224.	−	22609.3i	0.358256	−	0.0631703i	0.349880	+	0.936795i	$0.386222\pi$
$72$	−111026.	−	19576.9i	−0.297460	−	0.0524502i
$73$	498363.	+	181389.i	1.28108	+	0.466276i	0.890790	−	0.454415i	$-0.150152\pi$
$73$	498363.	+	181389.i	1.28108	+	0.466276i	0.390293	+	0.920691i	$0.372374\pi$
$74$	−363051.	+	304636.i	−0.895927	+	0.751772i
$75$			168497.i			0.399399i
$76$	212226.	+	55993.7i	0.483456	+	0.127555i
$77$	84399.9			0.184871
$78$	−75409.4	−	89869.4i	−0.158906	−	0.189377i
$79$	−57206.4	+	157173.i	−0.116028	+	0.318785i	−0.984090	−	0.177672i	$-0.943144\pi$
$79$	−57206.4	+	157173.i	−0.116028	+	0.318785i	0.868062	+	0.496456i	$0.165366\pi$
$80$	−25277.3	+	143355.i	−0.0493697	+	0.279989i
$81$	−103769.	−	588503.i	−0.195260	−	1.10737i
$82$	−160622.	+	58461.5i	−0.291315	+	0.106030i
$83$	315134.	−	545828.i	0.551139	−	0.954601i	−0.447054	−	0.894507i	$-0.647527\pi$
$83$	315134.	−	545828.i	0.551139	−	0.954601i	0.998193	−	0.0600935i	$-0.0191399\pi$
$84$	278570.	−	160832.i	0.469998	−	0.271353i
$85$	1.05260e6	+	883239.i	1.71399	+	1.43821i
$86$	−367474.	+	437939.i	−0.577739	+	0.688522i
$87$	−220285.	−	381545.i	−0.334524	−	0.579413i
$88$	48395.0	+	27940.9i	0.0710154	+	0.0410008i
$89$	259935.	+	714166.i	0.368719	+	1.01305i	0.975849	+	0.218444i	$0.0700981\pi$
$89$	259935.	+	714166.i	0.368719	+	1.01305i	−0.607131	+	0.794602i	$0.707680\pi$
$90$	493214.	−	86967.0i	0.676563	−	0.119296i
$91$	151871.	+	26778.9i	0.201535	+	0.0355360i
$92$	−136822.	−	49799.1i	−0.175708	−	0.0639526i
$93$	1.13363e6	−	951225.i	1.40936	−	1.18259i
$94$		−	128876.i		−	0.155163i
$95$	−970993.	+	88706.8i	−1.13252	+	0.103463i
$96$	212976.			0.240723
$97$	−253212.	−	301767.i	−0.277440	−	0.330641i	0.609273	−	0.792961i	$-0.291462\pi$
$97$	−253212.	−	301767.i	−0.277440	−	0.330641i	−0.886713	+	0.462320i	$0.847017\pi$
$98$	83005.1	−	228055.i	0.0881914	−	0.242304i
$99$	33386.0	−	189342.i	0.0344080	−	0.195137i
$100$	−25465.6	−	144423.i	−0.0254656	−	0.144423i
$101$	−13897.0	+	5058.10i	−0.0134883	+	0.00490934i	−0.348755	−	0.937214i	$-0.613396\pi$
$101$	−13897.0	+	5058.10i	−0.0134883	+	0.00490934i	0.335267	+	0.942123i	$0.391173\pi$
$102$	1.00520e6	−	1.74106e6i	0.947222	−	1.64064i
$103$	−723035.	+	417445.i	−0.661680	+	0.382021i	−0.792917	−	0.609330i	$-0.791438\pi$
$103$	−723035.	+	417445.i	−0.661680	+	0.382021i	0.131237	+	0.991351i	$0.458105\pi$
$104$	78217.7	+	65632.5i	0.0695353	+	0.0583470i
$105$	−918503.	+	1.09463e6i	−0.793437	+	0.945582i
$106$	392158.	+	679238.i	0.329263	+	0.570301i
$107$	−1.80257e6	−	1.04072e6i	−1.47144	−	0.849535i	−0.471952	−	0.881624i	$-0.656451\pi$
$107$	−1.80257e6	−	1.04072e6i	−1.47144	−	0.849535i	−0.999485	+	0.0320892i	$0.989784\pi$
$108$	42734.4	+	117412.i	0.0339240	+	0.0932054i
$109$	2.23666e6	−	394383.i	1.72711	−	0.304536i	0.780080	−	0.625680i	$-0.215178\pi$
$109$	2.23666e6	−	394383.i	1.72711	−	0.304536i	0.947031	+	0.321143i	$0.104067\pi$
$110$	−244473.	−	43107.3i	−0.183676	−	0.0323871i
$111$	−2.89455e6	−	1.05353e6i	−2.11647	−	0.770332i
$112$	−214462.	+	179955.i	−0.152650	+	0.128088i
$113$			960838.i			0.665909i	0.942943	+	0.332954i	$0.108046\pi$
$113$			960838.i			0.665909i	−0.942943	+	0.332954i	$0.891954\pi$
$114$	374508.	+	1.37653e6i	0.252782	+	0.929119i
$115$	646814.			0.425291
$116$	246477.	+	293740.i	0.157907	+	0.188187i
$117$	120151.	−	330112.i	0.0750187	−	0.206112i
$118$	−43802.9	+	248418.i	−0.0266598	+	0.151195i
$119$	458900.	+	2.60255e6i	0.272318	+	1.54439i
$120$	−889052.	+	323588.i	−0.514498	+	0.187262i
$121$	838131.	−	1.45169e6i	0.473103	−	0.819438i
$122$	−1.02238e6	+	590274.i	−0.563034	+	0.325068i
$123$	−851048.	−	714114.i	−0.457339	−	0.383753i
$124$	−827898.	+	986650.i	−0.434222	+	0.517485i
$125$	−784845.	−	1.35939e6i	−0.401841	−	0.696009i
$126$	834165.	+	481605.i	0.417004	+	0.240757i
$127$	834691.	+	2.29329e6i	0.407488	+	1.11956i	0.958507	+	0.285071i	$0.0920171\pi$
$127$	834691.	+	2.29329e6i	0.407488	+	1.11956i	−0.551019	+	0.834493i	$0.685761\pi$
$128$	−182548.	+	32188.1i	−0.0870455	+	0.0153485i
$129$	−3.65925e6	−	645224.i	−1.70460	−	0.300567i
$130$	−426233.	−	155136.i	−0.194007	−	0.0706127i
$131$	−2.24878e6	+	1.88695e6i	−1.00031	+	0.839357i	−0.987027	−	0.160555i	$-0.948672\pi$
$131$	−2.24878e6	+	1.88695e6i	−1.00031	+	0.839357i	−0.0132799	+	0.999912i	$0.504227\pi$
$132$			363205.i			0.157917i
$133$	−1.54023e6	−	1.06969e6i	−0.654680	−	0.454678i
$134$	2.37459e6			0.986901
$135$	−356783.	−	425197.i	−0.145012	−	0.172818i
$136$	−598449.	+	1.64423e6i	−0.237909	+	0.653649i
$137$	763859.	−	4.33206e6i	0.297065	−	1.68474i	−0.361624	−	0.932324i	$-0.617778\pi$
$137$	763859.	−	4.33206e6i	0.297065	−	1.68474i	0.658689	−	0.752415i	$-0.271111\pi$
$138$	−164332.	−	931971.i	−0.0625294	−	0.354622i
$139$	4.35019e6	−	1.58334e6i	1.61981	−	0.589562i	0.636463	−	0.771307i	$-0.280397\pi$
$139$	4.35019e6	−	1.58334e6i	1.61981	−	0.589562i	0.983346	+	0.181745i	$0.0581745\pi$
$140$	621837.	−	1.07705e6i	0.226617	−	0.392512i
$141$	725410.	−	418816.i	0.258777	−	0.149405i
$142$	−564217.	−	473435.i	−0.197052	−	0.165346i
$143$	−111928.	+	133391.i	−0.0382764	+	0.0456160i
$144$	318874.	+	552306.i	0.106790	+	0.184966i
$145$	−1.47520e6	−	851704.i	−0.483889	−	0.279373i
$146$	−1.02609e6	−	2.81917e6i	−0.329707	−	0.905862i
$147$	1.55341e6	−	273908.i	0.489028	−	0.0862289i
$148$	2.64022e6	+	465542.i	0.814432	+	0.143606i
$149$	1.64029e6	+	597017.i	0.495864	+	0.180480i	0.577833	−	0.816155i	$-0.303899\pi$
$149$	1.64029e6	+	597017.i	0.495864	+	0.180480i	−0.0819690	+	0.996635i	$0.526121\pi$
$150$	730163.	−	612680.i	0.216345	−	0.181535i
$151$			6.64385e6i			1.92970i	0.262806	+	0.964849i	$0.415352\pi$
$151$			6.64385e6i			1.92970i	−0.262806	+	0.964849i	$0.584648\pi$
$152$	−529042.	−	1.12326e6i	−0.150647	−	0.319852i
$153$	6.02005e6			1.68084
$154$	−306891.	−	365739.i	−0.0840277	−	0.100140i
$155$	1.95691e6	−	5.37657e6i	0.525504	−	1.44381i
$156$	−115240.	+	653558.i	−0.0303549	+	0.172151i
$157$	−73480.1	−	416726.i	−0.0189876	−	0.107684i	0.973841	−	0.227231i	$-0.0729671\pi$
$157$	−73480.1	−	416726.i	−0.0189876	−	0.107684i	−0.992829	+	0.119546i	$0.961856\pi$
$158$	889107.	−	323608.i	0.225415	−	0.0820443i
$159$	−2.54884e6	+	4.41472e6i	−0.634090	+	1.09828i
$160$	713125.	−	411723.i	0.174103	−	0.100518i
$161$	952951.	+	799621.i	0.228346	+	0.191605i
$162$	−2.17290e6	+	2.58956e6i	−0.511087	+	0.609090i
$163$	3.06903e6	+	5.31572e6i	0.708661	+	1.22744i	0.965354	+	0.260944i	$0.0840339\pi$
$163$	3.06903e6	+	5.31572e6i	0.708661	+	1.22744i	−0.256693	+	0.966493i	$0.582633\pi$
$164$	837383.	+	483463.i	0.189842	+	0.109605i
$165$	−551840.	−	1.51617e6i	−0.122846	−	0.337517i
$166$	−3.51117e6	+	619114.i	−0.767587	+	0.135346i
$167$	98994.6	+	17455.4i	0.0212550	+	0.00374784i	0.184266	−	0.982876i	$-0.441009\pi$
$167$	98994.6	+	17455.4i	0.0212550	+	0.00374784i	−0.163011	+	0.986624i	$0.552120\pi$
$168$	−1.70987e6	−	622343.i	−0.360609	−	0.131251i
$169$	3.45382e6	−	2.89810e6i	0.715550	−	0.600417i
$170$		−	7.77294e6i		−	1.58212i
$171$	−3.00900e6	+	3.03218e6i	−0.601775	+	0.606411i
$172$	3.23396e6			0.635549
$173$	5.86281e6	+	6.98703e6i	1.13232	+	1.34944i	0.928892	+	0.370351i	$0.120762\pi$
$173$	5.86281e6	+	6.98703e6i	1.13232	+	1.34944i	0.203424	+	0.979091i	$0.434793\pi$
$174$	−852397.	+	2.34194e6i	−0.161806	+	0.444558i
$175$	−217571.	+	1.23391e6i	−0.0405964	+	0.230234i
$176$	−54892.8	−	311313.i	−0.0100688	−	0.0571030i
$177$	−1.54063e6	+	560745.i	−0.277830	+	0.101122i
$178$	2.14960e6	−	3.72322e6i	0.381152	−	0.660175i
$179$	7.88861e6	−	4.55449e6i	1.37544	−	0.794110i	0.383832	−	0.923403i	$-0.374604\pi$
$179$	7.88861e6	−	4.55449e6i	1.37544	−	0.794110i	0.991606	+	0.129293i	$0.0412707\pi$
$180$	−2.17027e6	−	1.82107e6i	−0.372131	−	0.312255i
$181$	−3.12824e6	+	3.72809e6i	−0.527551	+	0.628710i	−0.962349	−	0.271817i	$-0.912375\pi$
$181$	−3.12824e6	+	3.72809e6i	−0.527551	+	0.628710i	0.434798	+	0.900528i	$0.356820\pi$
$182$	−436182.	−	755490.i	−0.0723526	−	0.125318i
$183$	−6.64501e6	−	3.83650e6i	−1.08428	−	0.626011i
$184$	281706.	+	773981.i	0.0452213	+	0.124244i
$185$	−1.17287e7	+	2.06809e6i	−1.85240	+	0.326628i
$186$	−8.24408e6	−	1.45365e6i	−1.28116	−	0.225903i
$187$	−2.80402e6	−	1.02058e6i	−0.428802	−	0.156071i
$188$	−558471.	+	468613.i	−0.0840480	+	0.0705246i
$189$		−	1.06751e6i		−	0.158120i
$190$	3.91508e6	+	3.88515e6i	0.570795	+	0.566431i
$191$	−666840.			−0.0957021			−0.0478510	−	0.998854i	$-0.515237\pi$
$191$	−666840.			−0.0957021			−0.0478510	+	0.998854i	$0.515237\pi$
$192$	−774415.	−	922912.i	−0.109413	−	0.130394i
$193$	3.57029e6	−	9.80928e6i	0.496628	−	1.36447i	−0.397886	−	0.917435i	$-0.630256\pi$
$193$	3.57029e6	−	9.80928e6i	0.496628	−	1.36447i	0.894514	−	0.447040i	$-0.147522\pi$
$194$	−386957.	+	2.19454e6i	−0.0529978	+	0.300565i
$195$	−511933.	−	2.90331e6i	−0.0690413	−	0.391553i
$196$	−1.29007e6	+	469548.i	−0.171335	+	0.0623608i
$197$	−2.83200e6	+	4.90516e6i	−0.370420	+	0.641585i	−0.989630	−	0.143640i	$-0.954119\pi$
$197$	−2.83200e6	+	4.90516e6i	−0.370420	+	0.641585i	0.619211	+	0.785225i	$0.287453\pi$
$198$	−941890.	+	543800.i	−0.121340	+	0.0700558i
$199$	−3.17961e6	−	2.66801e6i	−0.403473	−	0.338554i	0.418361	−	0.908281i	$-0.362605\pi$
$199$	−3.17961e6	−	2.66801e6i	−0.403473	−	0.338554i	−0.821834	+	0.569727i	$0.807049\pi$
$200$	−533245.	+	635497.i	−0.0666557	+	0.0794371i
$201$	7.71684e6	+	1.33660e7i	0.950279	+	1.64593i
$202$	72450.4	+	41829.3i	0.00878996	+	0.00507489i
$203$	−1.12049e6	−	3.07852e6i	−0.133943	−	0.368005i
$204$	−1.11998e7	+	1.97482e6i	−1.31922	+	0.232614i
$205$	−4.23014e6	−	745888.i	−0.491013	−	0.0865789i
$206$	4.43802e6	+	1.61531e6i	0.507678	+	0.184780i
$207$	2.17082e6	−	1.82153e6i	0.244744	−	0.205365i
$208$		−	577599.i		−	0.0641854i
$209$	1.91558e6	−	902216.i	0.209827	−	0.0988261i
$210$	8.08329e6			0.872831
$211$	3.05991e6	+	3.64666e6i	0.325733	+	0.388193i	0.903913	−	0.427716i	$-0.140682\pi$
$211$	3.05991e6	+	3.64666e6i	0.325733	+	0.388193i	−0.578181	+	0.815909i	$0.696237\pi$
$212$	1.51746e6	−	4.16919e6i	0.159261	−	0.437567i
$213$	831274.	−	4.71439e6i	0.0860212	−	0.487850i
$214$	2.04460e6	+	1.15955e7i	0.208625	+	1.18317i
$215$	−1.34999e7	+	4.91356e6i	−1.35836	+	0.494402i
$216$	353404.	−	612114.i	0.0350679	−	0.0607394i
$217$	9.52986e6	−	5.50207e6i	0.932626	−	0.538452i
$218$	−9.84186e6	−	8.25830e6i	−0.949965	−	0.797115i
$219$	1.25338e7	−	1.49372e7i	1.19331	−	1.42213i
$220$	702142.	+	1.21615e6i	0.0659412	+	0.114214i
$221$	−4.72180e6	−	2.72613e6i	−0.437452	−	0.252563i
$222$	5.95966e6	+	1.63740e7i	0.544707	+	1.49657i
$223$	−1.15758e7	+	2.04113e6i	−1.04385	+	0.184059i	−0.669181	−	0.743099i	$-0.733355\pi$
$223$	−1.15758e7	+	2.04113e6i	−1.04385	+	0.184059i	−0.374669	+	0.927158i	$0.622244\pi$
$224$	1.55964e6	+	275006.i	0.138765	+	0.0244680i
$225$	2.68207e6	+	976193.i	0.235463	+	0.0857014i
$226$	4.16370e6	−	3.49376e6i	0.360706	−	0.302669i
$227$			3.04583e6i			0.260392i	0.991488	+	0.130196i	$0.0415607\pi$
$227$			3.04583e6i			0.260392i	−0.991488	+	0.130196i	$0.958439\pi$
$228$	4.60329e6	−	6.62817e6i	0.388386	−	0.559229i
$229$	−1.40837e7			−1.17276			−0.586380	−	0.810036i	$-0.699448\pi$
$229$	−1.40837e7			−1.17276			−0.586380	+	0.810036i	$0.699448\pi$
$230$	−2.35192e6	−	2.80291e6i	−0.193303	−	0.230370i
$231$	1.06133e6	−	2.91598e6i	0.0861022	−	0.236564i
$232$	376664.	−	2.13617e6i	0.0301641	−	0.171069i
$233$	2.13831e6	+	1.21270e7i	0.169045	+	0.958703i	0.944795	+	0.327663i	$0.106261\pi$
$233$	2.13831e6	+	1.21270e7i	0.169045	+	0.958703i	−0.775750	+	0.631041i	$0.782628\pi$
$234$	−1.86740e6	+	679677.i	−0.145743	+	0.0530463i
$235$	1.61930e6	−	2.80471e6i	0.124774	−	0.216114i
$236$	1.23577e6	−	713472.i	0.0940160	−	0.0542802i
$237$	4.71090e6	+	3.95291e6i	0.353882	+	0.296942i
$238$	9.60926e6	−	1.14519e7i	0.712786	−	0.849465i
$239$	7.85992e6	+	1.36138e7i	0.575737	+	0.997206i	0.995961	+	0.0897859i	$0.0286183\pi$
$239$	7.85992e6	+	1.36138e7i	0.575737	+	0.997206i	−0.420224	+	0.907421i	$0.638048\pi$
$240$	4.63497e6	+	2.67600e6i	0.335284	+	0.193576i
$241$	47024.5	+	129199.i	0.00335949	+	0.00923013i	0.941361	−	0.337401i	$-0.109548\pi$
$241$	47024.5	+	129199.i	0.00335949	+	0.00923013i	−0.938002	+	0.346631i	$0.887326\pi$
$242$	−9.33831e6	+	1.64660e6i	−0.658904	+	0.116183i
$243$	−1.88342e7	−	3.32098e6i	−1.31259	−	0.231445i
$244$	6.27545e6	+	2.28408e6i	0.431991	+	0.157232i
$245$	4.67188e6	−	3.92017e6i	0.317683	−	0.266567i
$246$			6.28456e6i			0.422153i
$247$	3.73320e6	−	1.01568e6i	0.247737	−	0.0674008i
$248$	7.28592e6			0.477671
$249$	−1.48953e7	−	1.77515e7i	−0.964831	−	1.14984i
$250$	−3.03697e6	+	8.34401e6i	−0.194366	+	0.534017i
$251$	−1.62888e6	+	9.23786e6i	−0.103008	+	0.584185i	0.888990	+	0.457927i	$0.151408\pi$
$251$	−1.62888e6	+	9.23786e6i	−0.103008	+	0.584185i	−0.991997	+	0.126258i	$0.959703\pi$
$252$	−946164.	−	5.36596e6i	−0.0591241	−	0.335310i
$253$	−1.31993e6	+	480415.i	−0.0815059	+	0.0296657i
$254$	6.90270e6	−	1.19558e7i	0.421229	−	0.729590i
$255$	4.37520e7	−	2.52602e7i	2.63862	−	1.52341i
$256$	803256.	+	674012.i	0.0478778	+	0.0401742i
$257$	−1.76339e6	+	2.10153e6i	−0.103884	+	0.123804i	−0.815481	−	0.578783i	$-0.803528\pi$
$257$	−1.76339e6	+	2.10153e6i	−0.103884	+	0.123804i	0.711597	+	0.702588i	$0.247972\pi$
$258$	1.05096e7	+	1.82031e7i	0.611965	+	1.05995i
$259$	−1.98365e7	−	1.14526e7i	−1.14174	−	0.659183i
$260$	877582.	+	2.41114e6i	0.0499307	+	0.137184i
$261$	−7.34953e6	+	1.29592e6i	−0.413369	+	0.0728882i
$262$	1.63538e7	+	2.88362e6i	0.909318	+	0.160337i
$263$	1.32577e7	+	4.82541e6i	0.728787	+	0.265257i	0.679651	−	0.733535i	$-0.262131\pi$
$263$	1.32577e7	+	4.82541e6i	0.728787	+	0.265257i	0.0491359	+	0.998792i	$0.484353\pi$
$264$	1.57391e6	−	1.32067e6i	0.0855399	−	0.0717765i
$265$			1.97095e7i			1.05910i
$266$	965092.	+	1.05640e7i	0.0512771	+	0.561284i
$267$	2.79428e7			1.46803
$268$	−8.63437e6	−	1.02900e7i	−0.448566	−	0.534580i
$269$	−6.50270e6	+	1.78660e7i	−0.334070	+	0.917849i	0.652972	+	0.757382i	$0.273522\pi$
$269$	−6.50270e6	+	1.78660e7i	−0.334070	+	0.917849i	−0.987041	+	0.160466i	$0.948700\pi$
$270$	−545232.	+	3.09217e6i	−0.0277007	+	0.157098i
$271$	99609.5	+	564914.i	0.00500487	+	0.0283840i	0.987208	−	0.159438i	$-0.0509682\pi$
$271$	99609.5	+	564914.i	0.00500487	+	0.0283840i	−0.982203	+	0.187822i	$0.939857\pi$
$272$	9.30115e6	−	3.38534e6i	0.462200	−	0.168227i
$273$	2.83498e6	−	4.91032e6i	0.139335	−	0.241336i
$274$	−2.15501e7	+	1.24419e7i	−1.04760	+	0.604834i
$275$	−1.08376e6	−	909384.i	−0.0521117	−	0.0437269i
$276$	−3.44107e6	+	4.10091e6i	−0.163669	+	0.195053i
$277$	7.73716e6	+	1.34011e7i	0.364034	+	0.630526i	0.988621	−	0.150430i	$-0.0480658\pi$
$277$	7.73716e6	+	1.34011e7i	0.364034	+	0.630526i	−0.624587	+	0.780956i	$0.714732\pi$
$278$	−2.26792e7	−	1.30938e7i	−1.05559	−	0.609443i
$279$	−8.57354e6	−	2.35556e7i	−0.394773	−	1.08463i
$280$	−6.92840e6	+	1.22166e6i	−0.315616	+	0.0556516i
$281$	−1.92810e7	−	3.39977e6i	−0.868984	−	0.153225i	−0.278658	−	0.960390i	$-0.589890\pi$
$281$	−1.92810e7	−	3.39977e6i	−0.868984	−	0.153225i	−0.590326	+	0.807165i	$0.701001\pi$
$282$	−4.45260e6	−	1.62061e6i	−0.198548	−	0.0722657i
$283$	8.68005e6	−	7.28343e6i	0.382969	−	0.321349i	−0.430898	−	0.902401i	$-0.641803\pi$
$283$	8.68005e6	−	7.28343e6i	0.382969	−	0.321349i	0.813867	+	0.581052i	$0.197359\pi$
$284$			4.16646e6i			0.181892i
$285$	−9.14546e6	+	3.46628e7i	−0.395067	+	1.49737i
$286$	985023.			0.0421064
$287$	−5.31016e6	−	6.32841e6i	−0.224627	−	0.267700i
$288$	1.23389e6	−	3.39008e6i	0.0516534	−	0.141916i
$289$	1.20331e7	−	6.82429e7i	0.498520	−	2.82725i
$290$	1.67326e6	+	9.48954e6i	0.0686073	+	0.389091i
$291$	−1.36100e7	+	4.95365e6i	−0.552307	+	0.201023i
$292$	−8.48555e6	+	1.46974e7i	−0.340825	+	0.590326i
$293$	2.15577e7	−	1.24463e7i	0.857035	−	0.494809i	−0.00598315	−	0.999982i	$-0.501905\pi$
$293$	2.15577e7	−	1.24463e7i	0.857035	−	0.494809i	0.863018	+	0.505173i	$0.168571\pi$
$294$	−6.83539e6	−	5.73557e6i	−0.268981	−	0.225702i
$295$	−4.07460e6	+	4.85591e6i	−0.158715	+	0.189149i
$296$	−7.58287e6	−	1.31339e7i	−0.292387	−	0.506430i
$297$	1.04388e6	+	602687.i	0.0398458	+	0.0230050i
$298$	−3.37724e6	−	9.27889e6i	−0.127618	−	0.350629i
$299$	−2.52754e6	+	445673.i	−0.0945549	+	0.0166726i
$300$	−5.30997e6	−	936292.i	−0.196666	−	0.0346775i
$301$	−2.59637e7	−	9.45002e6i	−0.952067	−	0.346524i
$302$	2.87905e7	−	2.41581e7i	1.04527	−	0.877085i
$303$			543741.i			0.0195463i
$304$	−2.94386e6	+	6.37690e6i	−0.104784	+	0.226981i
$305$	−2.96667e7			−1.04561
$306$	−2.18898e7	−	2.60873e7i	−0.763973	−	0.910468i
$307$	−3.97741e6	+	1.09279e7i	−0.137463	+	0.377676i	−0.989254	−	0.146205i	$-0.953294\pi$
$307$	−3.97741e6	+	1.09279e7i	−0.137463	+	0.377676i	0.851791	+	0.523881i	$0.175516\pi$
$308$	−468988.	+	2.65977e6i	−0.0160513	+	0.0910314i
$309$	5.33035e6	+	3.02299e7i	0.180668	+	1.02462i
$310$	−3.04145e7	+	1.10700e7i	−1.02093	+	0.371587i
$311$	−1.48886e7	+	2.57878e7i	−0.494962	+	0.857299i	−0.999983	−	0.00580778i	$-0.998151\pi$
$311$	−1.48886e7	+	2.57878e7i	−0.494962	+	0.857299i	0.505021	+	0.863107i	$0.331485\pi$
$312$	3.25116e6	−	1.87706e6i	0.107047	−	0.0618036i
$313$	−1.17692e7	−	9.87553e6i	−0.383808	−	0.322053i	0.430387	−	0.902644i	$-0.358377\pi$
$313$	−1.17692e7	−	9.87553e6i	−0.383808	−	0.322053i	−0.814195	+	0.580591i	$0.802821\pi$
$314$	−1.53866e6	+	1.83370e6i	−0.0496996	+	0.0592297i
$315$	1.21025e7	+	2.09622e7i	0.387208	+	0.670664i
$316$	−4.63526e6	−	2.67617e6i	−0.146897	−	0.0848110i
$317$	1.69378e7	+	4.65363e7i	0.531716	+	1.46088i	0.857027	+	0.515271i	$0.172309\pi$
$317$	1.69378e7	+	4.65363e7i	0.531716	+	1.46088i	−0.325311	+	0.945607i	$0.605469\pi$
$318$	2.83987e7	−	5.00746e6i	0.883116	−	0.155717i
$319$	3.64297e6	+	642354.i	0.112223	+	0.0197880i
$320$	−4.37719e6	−	1.59317e6i	−0.133581	−	0.0486196i
$321$	−5.86237e7	+	4.91911e7i	−1.77238	+	1.48721i
$322$		−	7.03706e6i		−	0.210777i
$323$	3.82361e7	+	5.41632e7i	1.13466	+	1.60730i
$324$	1.91226e7			0.562228
$325$	−1.66161e6	−	1.98023e6i	−0.0484037	−	0.0576852i
$326$	1.18757e7	−	3.26281e7i	0.342772	−	0.941759i
$327$	1.45002e7	−	8.22349e7i	0.414698	−	2.35187i
$328$	−949814.	−	5.38667e6i	−0.0269164	−	0.152651i
$329$	5.85301e6	−	2.13032e6i	0.164358	−	0.0598215i
$330$	−4.56359e6	+	7.90437e6i	−0.126989	+	0.219951i
$331$	−8.30764e6	+	4.79642e6i	−0.229083	+	0.132261i	−0.610149	−	0.792287i	$-0.708890\pi$
$331$	−8.30764e6	+	4.79642e6i	−0.229083	+	0.132261i	0.381066	+	0.924548i	$0.375557\pi$
$332$	1.54500e7	+	1.29641e7i	0.422197	+	0.354265i
$333$	−3.35394e7	+	3.99707e7i	−0.908286	+	1.08245i
$334$	−284318.	−	492454.i	−0.00763072	−	0.0132168i
$335$	5.16778e7	+	2.98362e7i	1.37458	+	0.793613i
$336$	3.52050e6	+	9.67250e6i	0.0928083	+	0.254989i
$337$	6.94179e6	−	1.22402e6i	0.181377	−	0.0319816i	−0.0822220	−	0.996614i	$-0.526202\pi$
$337$	6.94179e6	−	1.22402e6i	0.181377	−	0.0319816i	0.263599	+	0.964632i	$0.415091\pi$
$338$	−2.51173e7	−	4.42885e6i	−0.650463	−	0.114694i
$339$	3.31965e7	+	1.20825e7i	0.852105	+	0.310141i
$340$	−3.36833e7	+	2.82636e7i	−0.856994	+	0.719103i
$341$			1.24252e7i			0.313358i
$342$	2.40809e7	+	2.01372e6i	0.601996	+	0.0503408i
$343$	4.38945e7			1.08775
$344$	−1.17592e7	−	1.40140e7i	−0.288869	−	0.344261i
$345$	8.13369e6	−	2.23471e7i	0.198075	−	0.544208i
$346$	8.95950e6	−	5.08118e7i	0.216299	−	1.22669i
$347$	−5.54360e6	−	3.14393e7i	−0.132679	−	0.752463i	−0.976448	−	0.215755i	$-0.930779\pi$
$347$	−5.54360e6	−	3.14393e7i	−0.132679	−	0.752463i	0.843768	−	0.536708i	$-0.180332\pi$
$348$	1.32480e7	−	4.82189e6i	0.314350	−	0.114414i
$349$	3.80754e7	−	6.59486e7i	0.895712	−	1.55142i	0.0627914	−	0.998027i	$-0.480000\pi$
$349$	3.80754e7	−	6.59486e7i	0.895712	−	1.55142i	0.832921	−	0.553392i	$-0.186667\pi$
$350$	6.13814e6	−	3.54386e6i	0.143164	−	0.0826556i
$351$	1.68716e6	+	1.41570e6i	0.0390153	+	0.0327378i
$352$	−1.14944e6	+	1.36985e6i	−0.0263548	+	0.0314084i
$353$	−2.27307e7	−	3.93707e7i	−0.516759	−	0.895053i	−0.999811	−	0.0194613i	$-0.993805\pi$
$353$	−2.27307e7	−	3.93707e7i	−0.516759	−	0.895053i	0.483051	−	0.875592i	$-0.339528\pi$
$354$	8.03192e6	+	4.63723e6i	0.181055	+	0.104532i
$355$	−6.33037e6	−	1.73925e7i	−0.141496	−	0.388757i
$356$	−2.39505e7	+	4.22312e6i	−0.530841	+	0.0936017i
$357$	9.56875e7	+	1.68723e7i	2.10306	+	0.370825i
$358$	−4.84206e7	−	1.76237e7i	−1.05531	−	0.384103i
$359$	5.66548e7	−	4.75390e7i	1.22448	−	1.02746i	0.225907	−	0.974149i	$-0.427465\pi$
$359$	5.66548e7	−	4.75390e7i	1.22448	−	1.02746i	0.998578	−	0.0533158i	$-0.0169790\pi$
$360$			1.60263e7i			0.343500i
$361$	−4.63925e7	−	7.81361e6i	−0.986111	−	0.166085i
$362$	2.75301e7			0.580339
$363$	−3.96155e7	−	4.72120e7i	−0.828220	−	0.987034i
$364$	−1.68781e6	+	4.63723e6i	−0.0349962	+	0.0961512i
$365$	1.30915e7	−	7.42457e7i	0.269223	−	1.52684i
$366$	7.53721e6	+	4.27456e7i	0.153733	+	0.871863i
$367$	8.18123e6	−	2.97772e6i	0.165509	−	0.0602402i	−0.257937	−	0.966162i	$-0.583043\pi$
$367$	8.18123e6	−	2.97772e6i	0.165509	−	0.0602402i	0.423446	+	0.905922i	$0.360820\pi$
$368$	2.32964e6	−	4.03506e6i	0.0467462	−	0.0809668i
$369$	−1.62976e7	+	9.40942e6i	−0.324373	+	0.187277i
$370$	5.16092e7	+	4.33053e7i	1.01888	+	0.854940i
$371$	−2.43658e7	+	2.90380e7i	−0.477154	+	0.568650i
$372$	2.36775e7	+	4.10106e7i	0.459946	+	0.796650i
$373$	−4.24170e7	−	2.44894e7i	−0.817359	−	0.471903i	0.0321456	−	0.999483i	$-0.489766\pi$
$373$	−4.24170e7	−	2.44894e7i	−0.817359	−	0.471903i	−0.849505	+	0.527581i	$0.823099\pi$
$374$	5.77328e6	+	1.58620e7i	0.110359	+	0.303209i
$375$	−5.68358e7	+	1.00217e7i	−1.07777	+	0.190041i
$376$	4.06138e6	+	716130.i	0.0764029	+	0.0134719i
$377$	6.35142e6	+	2.31173e6i	0.118535	+	0.0431432i
$378$	−4.62596e6	+	3.88164e6i	−0.0856499	+	0.0718688i
$379$			2.34953e7i			0.431582i	0.976440	+	0.215791i	$0.0692329\pi$
$379$			2.34953e7i			0.431582i	−0.976440	+	0.215791i	$0.930767\pi$
$380$	2.60006e6	−	3.10926e7i	0.0473841	−	0.566639i
$381$	8.97285e7			1.62239
$382$	2.42473e6	+	2.88968e6i	0.0434985	+	0.0518395i
$383$	−1.13887e7	+	3.12903e7i	−0.202712	+	0.556947i	−0.998839	−	0.0481835i	$-0.984657\pi$
$383$	−1.13887e7	+	3.12903e7i	−0.202712	+	0.556947i	0.796126	+	0.605130i	$0.206879\pi$
$384$	−1.18345e6	+	6.71170e6i	−0.0209006	+	0.118533i
$385$	−2.08340e6	−	1.18155e7i	−0.0365082	−	0.207048i
$386$	−5.54897e7	+	2.01966e7i	−0.964829	+	0.351169i
$387$	−3.14705e7	+	5.45085e7i	−0.542964	+	0.940441i
$388$	1.09169e7	−	6.30286e6i	0.186897	−	0.107905i
$389$	3.90526e7	+	3.27691e7i	0.663440	+	0.556692i	0.911116	−	0.412151i	$-0.135222\pi$
$389$	3.90526e7	+	3.27691e7i	0.663440	+	0.556692i	−0.247676	+	0.968843i	$0.579667\pi$
$390$	−1.07198e7	+	1.27753e7i	−0.180714	+	0.215366i
$391$	−2.19908e7	−	3.80891e7i	−0.367883	−	0.637193i
$392$	6.72564e6	+	3.88305e6i	0.111654	+	0.0644636i
$393$	3.69149e7	+	1.01423e8i	0.608168	+	1.67093i
$394$	3.15536e7	−	5.56375e6i	0.515894	−	0.0909660i
$395$	2.34156e7	+	4.12880e6i	0.379938	+	0.0669934i
$396$	5.78137e6	+	2.10424e6i	0.0930990	+	0.0338853i
$397$	−4.32889e7	+	3.63237e7i	−0.691839	+	0.580522i	−0.919439	−	0.393233i	$-0.871357\pi$
$397$	−4.32889e7	+	3.63237e7i	−0.691839	+	0.580522i	0.227600	+	0.973755i	$0.426912\pi$
$398$			2.34798e7i			0.372431i
$399$	−5.63257e7	+	3.97627e7i	−0.886723	+	0.625975i
$400$	4.69283e6			0.0733254
$401$	−2.93471e7	−	3.49745e7i	−0.455126	−	0.542398i	0.488869	−	0.872357i	$-0.337409\pi$
$401$	−2.93471e7	−	3.49745e7i	−0.455126	−	0.542398i	−0.943995	+	0.329959i	$0.892965\pi$
$402$	2.98604e7	−	8.20409e7i	0.459640	−	1.26285i
$403$	−3.94236e6	+	2.23582e7i	−0.0602339	+	0.341603i
$404$	−82178.0	−	466055.i	−0.00124627	−	0.00706794i
$405$	−7.98258e7	+	2.90542e7i	−1.20165	+	0.437365i
$406$	−9.26618e6	+	1.60495e7i	−0.138459	+	0.239819i
$407$	2.23983e7	−	1.29316e7i	0.332224	−	0.191810i
$408$	4.92817e7	+	4.13523e7i	0.725614	+	0.608862i
$409$	−2.44302e6	+	2.91148e6i	−0.0357073	+	0.0425543i	−0.783603	−	0.621262i	$-0.786620\pi$
$409$	−2.44302e6	+	2.91148e6i	−0.0357073	+	0.0425543i	0.747895	+	0.663817i	$0.231065\pi$
$410$	1.21492e7	+	2.10431e7i	0.176278	+	0.305322i
$411$	−1.40065e8	−	8.08666e7i	−2.01746	−	1.16478i
$412$	−9.13757e6	−	2.51053e7i	−0.130659	−	0.358982i
$413$	−1.20062e7	+	2.11702e6i	−0.170434	+	0.0300520i
$414$	−1.57869e7	−	2.78365e6i	−0.222482	−	0.0392295i
$415$	−8.41920e7	−	3.06434e7i	−1.17795	−	0.428739i
$416$	−2.50297e6	+	2.10024e6i	−0.0347676	+	0.0291735i
$417$		−	1.70208e8i		−	2.34731i
$418$	−1.08750e7	−	5.02039e6i	−0.148902	−	0.0687398i
$419$	2.58588e7			0.351533			0.175767	−	0.984432i	$-0.443760\pi$
$419$	2.58588e7			0.351533			0.175767	+	0.984432i	$0.443760\pi$
$420$	−2.93921e7	−	3.50281e7i	−0.396719	−	0.472791i
$421$	−2.42195e7	+	6.65424e7i	−0.324577	+	0.891768i	0.664881	+	0.746949i	$0.268482\pi$
$421$	−2.42195e7	+	6.65424e7i	−0.324577	+	0.891768i	−0.989458	+	0.144819i	$0.953740\pi$
$422$	4.67613e6	−	2.65196e7i	0.0622227	−	0.352883i
$423$	−2.46386e6	−	1.39733e7i	−0.0325533	−	0.184619i
$424$	−2.35845e7	+	8.58406e6i	−0.309406	+	0.112615i
$425$	2.21491e7	−	3.83633e7i	0.288528	−	0.499746i
$426$	−2.34520e7	+	1.35400e7i	−0.303355	+	0.175142i
$427$	−4.37079e7	−	3.66752e7i	−0.561404	−	0.471074i
$428$	4.28134e7	−	5.10231e7i	0.546070	−	0.650781i
$429$	3.20109e6	+	5.54445e6i	0.0405440	+	0.0702242i
$430$	7.03801e7	+	4.06340e7i	0.885206	+	0.511074i
$431$	1.28022e7	+	3.51736e7i	0.159901	+	0.439324i	0.993608	−	0.112882i	$-0.0360082\pi$
$431$	1.28022e7	+	3.51736e7i	0.159901	+	0.439324i	−0.833707	+	0.552207i	$0.813786\pi$
$432$	−3.93757e6	+	694299.i	−0.0488401	+	0.00861183i
$433$	−1.31143e7	−	2.31241e6i	−0.161541	−	0.0284840i	0.0922929	−	0.995732i	$-0.470580\pi$
$433$	−1.31143e7	−	2.31241e6i	−0.161541	−	0.0284840i	−0.253833	+	0.967248i	$0.581692\pi$
$434$	−5.84947e7	−	2.12903e7i	−0.715563	−	0.260444i
$435$	−4.79766e7	+	4.02571e7i	−0.582856	+	0.489074i
$436$			7.26772e7i			0.876877i
$437$	3.01764e7	+	7.96175e6i	0.361596	+	0.0954035i
$438$	−1.10304e8			−1.31271
$439$	4.83498e7	+	5.76211e7i	0.571481	+	0.681064i	0.971934	−	0.235253i	$-0.0755919\pi$
$439$	4.83498e7	+	5.76211e7i	0.571481	+	0.681064i	−0.400454	+	0.916317i	$0.631147\pi$
$440$	2.71695e6	−	7.46476e6i	0.0318951	−	0.0876310i
$441$	4.63978e6	−	2.63135e7i	0.0540981	−	0.306805i
$442$	5.35577e6	+	3.03741e7i	0.0620234	+	0.351752i
$443$	−8.19699e7	+	2.98346e7i	−0.942852	+	0.343170i	−0.767291	−	0.641299i	$-0.778396\pi$
$443$	−8.19699e7	+	2.98346e7i	−0.942852	+	0.343170i	−0.175560	+	0.984469i	$0.556174\pi$
$444$	4.92850e7	−	8.53642e7i	0.563075	−	0.975274i
$445$	9.35629e7	−	5.40186e7i	1.06175	−	0.613004i
$446$	5.09366e7	+	4.27409e7i	0.574151	+	0.481769i
$447$	4.12533e7	−	4.91638e7i	0.461888	−	0.550457i
$448$	−4.47937e6	−	7.75849e6i	−0.0498176	−	0.0862866i
$449$	4.11482e7	+	2.37569e7i	0.454581	+	0.262453i	0.709763	−	0.704440i	$-0.248802\pi$
$449$	4.11482e7	+	2.37569e7i	0.454581	+	0.262453i	−0.255182	+	0.966893i	$0.582135\pi$
$450$	−5.52218e6	−	1.51721e7i	−0.0606001	−	0.166497i
$451$	9.18629e6	−	1.61979e6i	0.100141	−	0.0176575i
$452$	−3.02797e7	−	5.33913e6i	−0.327896	−	0.0578169i
$453$	2.29542e8	+	8.35465e7i	2.46926	+	0.898739i
$454$	1.31988e7	−	1.10751e7i	0.141048	−	0.118353i
$455$		−	2.19221e7i		−	0.232728i
$456$	−4.54608e7	+	4.15316e6i	−0.479449	+	0.0438010i
$457$	5.19218e7			0.544003			0.272002	−	0.962297i	$-0.412314\pi$
$457$	5.19218e7			0.544003			0.272002	+	0.962297i	$0.412314\pi$
$458$	5.12104e7	+	6.10302e7i	0.533042	+	0.635255i
$459$	−1.29086e7	+	3.54661e7i	−0.133488	+	0.366754i
$460$	−3.59418e6	+	2.03836e7i	−0.0369255	+	0.209415i
$461$	−9.68053e6	−	5.49010e7i	−0.0988090	−	0.560374i	−0.993513	−	0.113715i	$-0.963725\pi$
$461$	−9.68053e6	−	5.49010e7i	−0.0988090	−	0.560374i	0.894704	−	0.446659i	$-0.147386\pi$
$462$	−1.64953e7	+	6.00378e6i	−0.167276	+	0.0608834i
$463$	2.00833e6	−	3.47853e6i	0.0202345	−	0.0350471i	−0.855731	−	0.517421i	$-0.826892\pi$
$463$	2.00833e6	−	3.47853e6i	0.0202345	−	0.0350471i	0.875965	+	0.482374i	$0.160225\pi$
$464$	−1.06265e7	+	6.13520e6i	−0.106374	+	0.0614151i
$465$	−1.61150e8	−	1.35221e8i	−1.60277	−	1.34488i
$466$	4.47758e7	−	5.33617e7i	0.442472	−	0.527317i
$467$	−2.86733e7	−	4.96635e7i	−0.281531	−	0.487626i	0.690231	−	0.723589i	$-0.257509\pi$
$467$	−2.86733e7	−	4.96635e7i	−0.281531	−	0.487626i	−0.971762	+	0.235963i	$0.924176\pi$
$468$	9.73546e6	+	5.62077e6i	0.0949771	+	0.0548350i
$469$	3.92520e7	+	1.07844e8i	0.380490	+	1.04539i
$470$	−1.80419e7	+	3.18128e6i	−0.173776	+	0.0306414i
$471$	−1.53217e7	−	2.70163e6i	−0.146637	−	0.0258561i
$472$	−7.58522e6	−	2.76079e6i	−0.0721343	−	0.0262547i
$473$	2.38992e7	−	2.00538e7i	0.225840	−	0.189502i
$474$		−	3.47876e7i		−	0.326655i
$475$	8.25209e6	+	3.03312e7i	0.0769987	+	0.283014i
$476$	−8.45663e7			−0.784109
$477$	5.55051e7	+	6.61484e7i	0.511420	+	0.609487i
$478$	3.04141e7	−	8.35620e7i	0.278478	−	0.765112i
$479$	−2.51051e7	+	1.42378e8i	−0.228431	+	1.29550i	0.627585	+	0.778548i	$0.284043\pi$
$479$	−2.51051e7	+	1.42378e8i	−0.228431	+	1.29550i	−0.856016	+	0.516949i	$0.827068\pi$
$480$	−5.25728e6	−	2.98155e7i	−0.0475377	−	0.269599i
$481$	4.44069e7	−	1.61628e7i	0.399039	−	0.145238i
$482$	388882.	−	673564.i	0.00347278	−	0.00601503i
$483$	3.96099e7	−	2.28688e7i	0.351530	−	0.202956i
$484$	4.10909e7	+	3.44794e7i	0.362418	+	0.304105i
$485$	−3.59952e7	+	4.28974e7i	−0.315515	+	0.376016i
$486$	5.40930e7	+	9.36917e7i	0.471229	+	0.816192i
$487$	1.79201e6	+	1.03462e6i	0.0155151	+	0.00895763i	0.507737	−	0.861512i	$-0.330482\pi$
$487$	1.79201e6	+	1.03462e6i	0.0155151	+	0.00895763i	−0.492222	+	0.870469i	$0.663815\pi$
$488$	−1.29207e7	−	3.54993e7i	−0.111180	−	0.305464i
$489$	2.22249e8	−	3.91885e7i	1.90070	−	0.335144i
$490$	−3.39754e7	−	5.99078e6i	−0.288786	−	0.0509208i
$491$	2.06873e8	+	7.52955e7i	1.74767	+	0.636099i	0.999620	−	0.0275480i	$-0.00876992\pi$
$491$	2.06873e8	+	7.52955e7i	1.74767	+	0.636099i	0.748046	+	0.663647i	$0.230992\pi$
$492$	2.72335e7	−	2.28516e7i	0.228670	−	0.191877i
$493$			1.15827e8i			0.966649i
$494$	−1.79758e7	−	1.24843e7i	−0.149110	−	0.103558i
$495$	−2.73309e7			−0.225340
$496$	−2.64927e7	−	3.15728e7i	−0.217111	−	0.258743i
$497$	1.21749e7	−	3.34503e7i	0.0991738	−	0.272478i
$498$	−2.27629e7	+	1.29095e8i	−0.184306	+	1.04525i
$499$	1.91640e7	+	1.08684e8i	0.154235	+	0.874713i	0.959481	+	0.281772i	$0.0909221\pi$
$499$	1.91640e7	+	1.08684e8i	0.154235	+	0.874713i	−0.805246	+	0.592941i	$0.797967\pi$
$500$	4.72009e7	−	1.71797e7i	0.377607	−	0.137438i
$501$	1.84793e6	−	3.20072e6i	0.0146951	−	0.0254527i
$502$	4.59542e7	−	2.65317e7i	0.363257	−	0.209727i
$503$	−1.09452e8	−	9.18414e7i	−0.860045	−	0.721663i	0.101933	−	0.994791i	$-0.467497\pi$
$503$	−1.09452e8	−	9.18414e7i	−0.860045	−	0.721663i	−0.961978	+	0.273128i	$0.911942\pi$
$504$	−1.98125e7	+	2.36116e7i	−0.154756	+	0.184431i
$505$	1.05115e6	+	1.82065e6i	0.00816190	+	0.0141368i
$506$	6.88130e6	+	3.97292e6i	0.0531152	+	0.0306661i
$507$	−5.66962e7	−	1.55772e8i	−0.435041	−	1.19527i
$508$	−7.69087e7	+	1.35611e7i	−0.586657	+	0.103443i
$509$	−2.28896e8	−	4.03605e7i	−1.73574	−	0.306058i	−0.785798	−	0.618483i	$-0.787747\pi$
$509$	−2.28896e8	−	4.03605e7i	−1.73574	−	0.306058i	−0.949942	+	0.312425i	$0.898859\pi$
$510$	−2.68552e8	−	9.77448e7i	−2.02450	−	0.736857i
$511$	1.11074e8	−	9.32018e7i	0.832431	−	0.698492i
$512$		−	5.93164e6i		−	0.0441942i
$513$	−1.14115e7	−	2.42288e7i	−0.0845259	−	0.179465i
$514$	1.55187e7			0.114279
$515$	7.62880e7	+	9.09165e7i	0.558515	+	0.665612i
$516$	4.06670e7	−	1.11732e8i	0.296001	−	0.813256i
$517$	−1.22127e6	+	6.92617e6i	−0.00883773	+	0.0501212i
$518$	2.24999e7	+	1.27603e8i	0.161879	+	0.918063i
$519$	3.15123e8	−	1.14696e8i	2.25413	−	0.820435i
$520$	7.25740e6	−	1.25702e7i	0.0516144	−	0.0893988i
$521$	−1.48742e8	+	8.58762e7i	−1.05177	+	0.607239i	−0.923144	−	0.384455i	$-0.874390\pi$
$521$	−1.48742e8	+	8.58762e7i	−1.05177	+	0.607239i	−0.128625	+	0.991693i	$0.541056\pi$
$522$	3.23398e7	+	2.71363e7i	0.227366	+	0.190783i
$523$	1.13339e7	−	1.35073e7i	0.0792275	−	0.0944197i	−0.724975	−	0.688776i	$-0.758149\pi$
$523$	1.13339e7	−	1.35073e7i	0.0792275	−	0.0944197i	0.804202	+	0.594356i	$0.202593\pi$
$524$	−4.69692e7	−	8.13530e7i	−0.326452	−	0.565431i
$525$	3.98950e7	+	2.30334e7i	0.275702	+	0.159177i
$526$	−2.72966e7	−	7.49969e7i	−0.187565	−	0.515331i
$527$	−3.83143e8	+	6.75585e7i	−2.61776	+	0.461581i
$528$	−1.14460e7	−	2.01824e6i	−0.0777591	−	0.0137110i
$529$	1.19654e8	+	4.35503e7i	0.808274	+	0.294188i
$530$	8.54093e7	−	7.16669e7i	0.573690	−	0.481383i
$531$			2.77720e7i			0.185491i
$532$	4.22688e7	−	4.25944e7i	0.280727	−	0.282890i
$533$	1.70439e7			0.112561
$534$	−1.01604e8	−	1.21087e8i	−0.667250	−	0.795197i
$535$	−1.01199e8	+	2.78041e8i	−0.660865	+	1.81571i
$536$	−1.31950e7	+	7.48324e7i	−0.0856868	+	0.485954i
$537$	−5.81563e7	−	3.29820e8i	−0.375555	−	2.12988i
$538$	1.01065e8	−	3.67848e7i	0.649017	−	0.236223i
$539$	−6.62206e6	+	1.14697e7i	−0.0422890	+	0.0732466i
$540$	1.53821e7	−	8.88089e6i	0.0976867	−	0.0563995i
$541$	2.44570e7	+	2.05218e7i	0.154458	+	0.129606i	0.716742	−	0.697339i	$-0.245633\pi$
$541$	2.44570e7	+	2.05218e7i	0.154458	+	0.129606i	−0.562284	+	0.826944i	$0.690077\pi$
$542$	2.08580e6	−	2.48576e6i	0.0131001	−	0.0156121i
$543$	8.94662e7	+	1.54960e8i	0.558804	+	0.967877i
$544$	−4.84905e7	−	2.79960e7i	−0.301203	−	0.173900i
$545$	−1.10423e8	−	3.03385e8i	−0.682135	−	1.87415i
$546$	−3.15868e7	+	5.56961e6i	−0.194056	+	0.0342174i
$547$	1.78000e8	+	3.13863e7i	1.08757	+	0.191769i	0.688563	−	0.725177i	$-0.258242\pi$
$547$	1.78000e8	+	3.13863e7i	1.08757	+	0.191769i	0.399012	+	0.916946i	$0.369353\pi$
$548$	1.32275e8	+	4.81443e7i	0.803780	+	0.292552i
$549$	−9.95662e7	+	8.35460e7i	−0.601721	+	0.504904i
$550$			8.00304e6i			0.0481024i
$551$	−5.83398e7	−	5.78938e7i	−0.348747	−	0.346080i
$552$	3.02832e7			0.180046
$553$	2.93939e7	+	3.50303e7i	0.173813	+	0.207142i
$554$	2.99391e7	−	8.22569e7i	0.176080	−	0.483774i
$555$	−7.60370e7	+	4.31227e8i	−0.444781	+	2.52248i
$556$	2.57242e7	+	1.45889e8i	0.149664	+	0.848788i
$557$	−3.88624e7	+	1.41447e7i	−0.224887	+	0.0818520i	−0.452006	−	0.892015i	$-0.649291\pi$
$557$	−3.88624e7	+	1.41447e7i	−0.224887	+	0.0818520i	0.227119	+	0.973867i	$0.427069\pi$
$558$	−7.09012e7	+	1.22805e8i	−0.408085	+	0.706825i
$559$	4.93675e7	−	2.85023e7i	0.282622	−	0.163172i
$560$	3.04867e7	+	2.55814e7i	0.173599	+	0.145667i
$561$	−7.05212e7	+	8.40439e7i	−0.399421	+	0.476012i
$562$	5.53763e7	+	9.59146e7i	0.311972	+	0.540351i
$563$	−9.35105e7	−	5.39883e7i	−0.524005	−	0.302534i	0.214567	−	0.976709i	$-0.431166\pi$
$563$	−9.35105e7	−	5.39883e7i	−0.524005	−	0.302534i	−0.738572	+	0.674175i	$0.764499\pi$
$564$	9.16758e6	+	2.51877e7i	0.0510996	+	0.140395i
$565$	1.34512e8	−	2.37181e7i	0.745789	−	0.131503i
$566$	−6.31241e7	−	1.11305e7i	−0.348133	−	0.0613853i
$567$	−1.53525e8	−	5.58786e7i	−0.842230	−	0.306547i
$568$	1.80550e7	−	1.51499e7i	0.0985261	−	0.0826732i
$569$		−	6.59347e7i		−	0.357913i	−0.983857	−	0.178956i	$-0.942728\pi$
$569$		−	6.59347e7i		−	0.357913i	0.983857	−	0.178956i	$-0.0572721\pi$
$570$	1.83462e8	−	8.64085e7i	0.990655	−	0.466586i
$571$	−3.18970e8			−1.71333			−0.856667	−	0.515870i	$-0.827469\pi$
$571$	−3.18970e8			−1.71333			−0.856667	+	0.515870i	$0.827469\pi$
$572$	−3.58170e6	−	4.26850e6i	−0.0191382	−	0.0228080i
$573$	−8.38551e6	+	2.30390e7i	−0.0445724	+	0.122462i
$574$	−8.11494e6	+	4.60221e7i	−0.0429091	+	0.243350i
$575$	−3.62097e6	−	2.05355e7i	−0.0190468	−	0.108020i
$576$	−1.91772e7	+	6.97993e6i	−0.100350	+	0.0365244i
$577$	−8.83027e7	+	1.52945e8i	−0.459671	+	0.796173i	−0.998943	−	0.0459583i	$-0.985366\pi$
$577$	−8.83027e7	+	1.52945e8i	−0.459671	+	0.796173i	0.539273	+	0.842131i	$0.318699\pi$
$578$	−3.39478e8	+	1.95998e8i	−1.75804	+	1.01500i
$579$	−2.94010e8	−	2.46704e8i	−1.51470	−	1.27098i
$580$	3.50378e7	−	4.17564e7i	0.179578	−	0.214012i
$581$	−8.61573e7	−	1.49229e8i	−0.439303	−	0.760894i
$582$	7.09544e7	+	4.09656e7i	0.359924	+	0.207802i
$583$	−1.46391e7	−	4.02205e7i	−0.0738767	−	0.202975i
$584$	9.45445e7	−	1.66708e7i	0.474677	−	0.0836983i
$585$	−4.91798e7	−	8.67173e6i	−0.245652	−	0.0433150i
$586$	−1.32322e8	−	4.81612e7i	−0.657565	−	0.239334i
$587$	2.11776e8	−	1.77701e8i	1.04704	−	0.878570i	0.0542600	−	0.998527i	$-0.482720\pi$
$587$	2.11776e8	−	1.77701e8i	1.04704	−	0.878570i	0.992779	+	0.119957i	$0.0382756\pi$
$588$			5.04759e7i			0.248286i
$589$	1.57479e8	−	2.26750e8i	0.770683	−	1.10969i
$590$	3.58585e7			0.174597
$591$	1.33859e8	+	1.59527e8i	0.648461	+	0.772806i
$592$	−2.93420e7	+	8.06166e7i	−0.141425	+	0.388561i
$593$	4.70703e7	−	2.66949e8i	0.225726	−	1.28016i	−0.635565	−	0.772047i	$-0.719233\pi$
$593$	4.70703e7	−	2.66949e8i	0.225726	−	1.28016i	0.861292	−	0.508111i	$-0.169656\pi$
$594$	−1.18404e6	−	6.71503e6i	−0.00564947	−	0.0320397i
$595$	3.53015e8	−	1.28487e8i	1.67588	−	0.609970i
$596$	−2.79290e7	+	4.83744e7i	−0.131922	+	0.228495i
$597$	−1.32162e8	+	7.63038e7i	−0.621132	+	0.358611i
$598$	1.11218e7	+	9.33230e6i	0.0520082	+	0.0436400i
$599$	−2.18949e7	+	2.60934e7i	−0.101874	+	0.121409i	−0.814572	−	0.580062i	$-0.803028\pi$
$599$	−2.18949e7	+	2.60934e7i	−0.101874	+	0.121409i	0.712698	+	0.701471i	$0.247473\pi$
$600$	1.52506e7	+	2.64148e7i	0.0706045	+	0.122291i
$601$	6.10673e7	+	3.52572e7i	0.281310	+	0.162415i	0.634016	−	0.773320i	$-0.281405\pi$
$601$	6.10673e7	+	3.52572e7i	0.281310	+	0.162415i	−0.352706	+	0.935734i	$0.614738\pi$
$602$	5.34574e7	+	1.46873e8i	0.245029	+	0.673213i
$603$	2.57462e8	−	4.53976e7i	1.17425	−	0.207053i
$604$	−2.09373e8	−	3.69182e7i	−0.950190	−	0.167544i
$605$	−2.23917e8	−	8.14992e7i	−1.01116	−	0.368033i
$606$	2.35625e6	−	1.97713e6i	0.0105877	−	0.00888416i
$607$		−	2.84658e8i		−	1.27279i	−0.771362	−	0.636396i	$-0.780424\pi$
$607$		−	2.84658e8i		−	1.27279i	0.771362	−	0.636396i	$-0.219576\pi$
$608$	3.83380e7	−	1.04305e7i	0.170576	−	0.0464081i
$609$	−1.20451e8			−0.533286
$610$	1.07873e8	+	1.28558e8i	0.475250	+	0.566380i
$611$	−4.39516e6	+	1.20756e7i	−0.0192686	+	0.0529402i
$612$	−3.34519e7	+	1.89715e8i	−0.145937	+	0.827651i
$613$	2.16030e7	+	1.22517e8i	0.0937851	+	0.531881i	0.995113	+	0.0987439i	$0.0314825\pi$
$613$	2.16030e7	+	1.22517e8i	0.0937851	+	0.531881i	−0.901328	+	0.433138i	$0.857406\pi$
$614$	6.18173e7	−	2.24996e7i	0.267057	−	0.0972010i
$615$	−7.89641e7	+	1.36770e8i	−0.339472	+	0.587984i
$616$	1.32311e7	−	7.63901e6i	0.0566051	−	0.0326810i
$617$	−7.60819e7	−	6.38403e7i	−0.323911	−	0.271794i	0.466302	−	0.884625i	$-0.345586\pi$
$617$	−7.60819e7	−	6.38403e7i	−0.323911	−	0.271794i	−0.790213	+	0.612832i	$0.790030\pi$
$618$	1.11616e8	−	1.33019e8i	0.472892	−	0.563571i
$619$	2.74391e7	+	4.75259e7i	0.115690	+	0.200382i	0.918056	−	0.396452i	$-0.129759\pi$
$619$	2.74391e7	+	4.75259e7i	0.115690	+	0.200382i	−0.802365	+	0.596834i	$0.796425\pi$
$620$	1.58562e8	+	9.15460e7i	0.665311	+	0.384118i
$621$	6.07642e6	+	1.66948e7i	0.0253731	+	0.0697119i
$622$	1.65886e8	−	2.92502e7i	0.689348	−	0.121551i
$623$	2.04626e8	+	3.60811e7i	0.846248	+	0.149216i
$624$	−1.99558e7	−	7.26331e6i	−0.0821324	−	0.0298938i
$625$	−2.25788e8	+	1.89458e8i	−0.924827	+	0.776022i
$626$			8.69096e7i			0.354279i
$627$	−7.08270e6	−	7.75278e7i	−0.0287340	−	0.314525i
$628$	1.35410e7			0.0546727
$629$	5.20543e8	+	6.20359e8i	2.09173	+	2.49282i
$630$	4.68309e7	−	1.28667e8i	0.187288	−	0.514571i
$631$	1.03193e7	−	5.85234e7i	0.0410734	−	0.232939i	−0.957360	−	0.288899i	$-0.906711\pi$
$631$	1.03193e7	−	5.85234e7i	0.0410734	−	0.232939i	0.998433	+	0.0559601i	$0.0178220\pi$
$632$	5.25761e6	+	2.98174e7i	0.0208275	+	0.118119i
$633$	1.64469e8	−	5.98617e7i	0.648444	−	0.236014i
$634$	1.40072e8	−	2.42612e8i	0.549646	−	0.952015i
$635$	3.00445e8	−	1.73462e8i	1.17339	−	0.677459i
$636$	−1.24962e8	−	1.04855e8i	−0.485741	−	0.407585i
$637$	−1.55551e7	+	1.85378e7i	−0.0601802	+	0.0717200i
$638$	−1.04628e7	−	1.81222e7i	−0.0402891	−	0.0697827i
$639$	−7.02259e7	−	4.05450e7i	−0.269150	−	0.155394i
$640$	9.01232e6	+	2.47611e7i	0.0343793	+	0.0944563i
$641$	7.62023e7	−	1.34365e7i	0.289330	−	0.0510168i	−0.0270992	−	0.999633i	$-0.508627\pi$
$641$	7.62023e7	−	1.34365e7i	0.289330	−	0.0510168i	0.316430	+	0.948616i	$0.397516\pi$
$642$	4.26329e8	+	7.51734e7i	1.61117	+	0.284092i
$643$	−2.18370e8	−	7.94802e7i	−0.821410	−	0.298969i	−0.103082	−	0.994673i	$-0.532870\pi$
$643$	−2.18370e8	−	7.94802e7i	−0.821410	−	0.298969i	−0.718329	+	0.695704i	$0.755093\pi$
$644$	−3.04944e7	+	2.55879e7i	−0.114173	+	0.0958024i
$645$			5.28203e8i			1.96844i
$646$	9.56786e7	−	3.62638e8i	0.354909	−	1.34517i
$647$	−1.10057e8			−0.406355			−0.203177	−	0.979142i	$-0.565127\pi$
$647$	−1.10057e8			−0.406355			−0.203177	+	0.979142i	$0.565127\pi$
$648$	−6.95328e7	−	8.28660e7i	−0.255543	−	0.304545i
$649$	4.70819e6	−	1.29356e7i	0.0172234	−	0.0473210i
$650$	−2.53925e6	+	1.44008e7i	−0.00924626	+	0.0524381i
$651$	−7.02559e7	−	3.98441e8i	−0.254648	−	1.44418i
$652$	−1.84573e8	+	6.71789e7i	−0.665924	+	0.242376i
$653$	1.34217e8	−	2.32471e8i	0.482024	−	0.834890i	−0.517763	−	0.855524i	$-0.673235\pi$
$653$	1.34217e8	−	2.32471e8i	0.482024	−	0.834890i	0.999787	+	0.0206339i	$0.00656846\pi$
$654$	−4.09082e8	+	2.36184e8i	−1.46244	+	0.844338i
$655$	3.19674e8	+	2.68238e8i	1.13758	+	0.954546i
$656$	−1.98889e7	+	2.37027e7i	−0.0704530	+	0.0839626i
$657$	−1.65150e8	−	2.86049e8i	−0.582349	−	1.00866i
$658$	−3.05140e7	−	1.76173e7i	−0.107108	−	0.0618388i
$659$	−9.33979e7	−	2.56609e8i	−0.326348	−	0.896634i	−0.989028	−	0.147731i	$-0.952803\pi$
$659$	−9.33979e7	−	2.56609e8i	−0.326348	−	0.896634i	0.662680	−	0.748903i	$-0.269419\pi$
$660$	5.08467e7	−	8.96565e6i	0.176861	−	0.0311853i
$661$	−3.91731e7	−	6.90728e6i	−0.135639	−	0.0239168i	0.105417	−	0.994428i	$-0.466382\pi$
$661$	−3.91731e7	−	6.90728e6i	−0.135639	−	0.0239168i	−0.241055	+	0.970511i	$0.577494\pi$
$662$	5.09927e7	+	1.85598e7i	0.175766	+	0.0639734i
$663$	−1.53563e8	+	1.28855e8i	−0.526923	+	0.442141i
$664$		−	1.14091e8i		−	0.389714i
$665$	−1.11731e8	+	2.42028e8i	−0.379935	+	0.823003i
$666$	2.95164e8			0.999172
$667$	3.50466e7	+	4.17669e7i	0.118105	+	0.140752i
$668$	−1.10017e6	+	3.02271e6i	−0.00369090	+	0.0101407i
$669$	−7.50461e7	+	4.25607e8i	−0.250640	+	1.42145i
$670$	−5.86163e7	−	3.32429e8i	−0.194892	−	1.10529i
$671$	6.05396e7	−	2.20346e7i	0.200388	−	0.0729354i
$672$	2.91137e7	−	5.04265e7i	0.0959379	−	0.166169i
$673$	3.36382e8	−	1.94210e8i	1.10354	−	0.637128i	0.166389	−	0.986060i	$-0.446789\pi$
$673$	3.36382e8	−	1.94210e8i	1.10354	−	0.637128i	0.937148	+	0.348933i	$0.113456\pi$
$674$	−3.05456e7	−	2.56308e7i	−0.0997629	−	0.0837110i
$675$	−1.15021e7	+	1.37077e7i	−0.0373996	+	0.0445711i
$676$	7.21383e7	+	1.24947e8i	0.233521	+	0.404470i
$677$	2.95868e8	+	1.70820e8i	0.953526	+	0.550519i	0.894175	−	0.447718i	$-0.147763\pi$
$677$	2.95868e8	+	1.70820e8i	0.953526	+	0.550519i	0.0593517	+	0.998237i	$0.481097\pi$
$678$	−6.83492e7	−	1.87788e8i	−0.219303	−	0.602529i
$679$	−1.06063e8	+	1.87018e7i	−0.338810	+	0.0597414i
$680$	2.44955e8	+	4.31922e7i	0.779041	+	0.137366i
$681$	1.05232e8	+	3.83013e7i	0.333201	+	0.121275i
$682$	5.38435e7	−	4.51801e7i	0.169738	−	0.142428i
$683$		−	6.12319e8i		−	1.92183i	−0.276838	−	0.960917i	$-0.589287\pi$
$683$		−	6.12319e8i		−	1.92183i	0.276838	−	0.960917i	$-0.410713\pi$
$684$	−7.88355e7	−	1.11674e8i	−0.246351	−	0.348967i
$685$	−6.25321e8			−1.94550
$686$	−1.59607e8	−	1.90212e8i	−0.494402	−	0.589205i
$687$	−1.77102e8	+	4.86584e8i	−0.546202	+	1.50068i
$688$	−1.79703e7	+	1.01914e8i	−0.0551809	+	0.312947i
$689$	−1.35804e7	−	7.70183e7i	−0.0415198	−	0.235470i
$690$	−1.26414e8	+	4.60111e7i	−0.384813	+	0.140060i
$691$	−1.01508e8	+	1.75816e8i	−0.307655	+	0.532875i	−0.977849	−	0.209312i	$-0.932878\pi$
$691$	−1.01508e8	+	1.75816e8i	−0.307655	+	0.532875i	0.670194	+	0.742186i	$0.266211\pi$
$692$	−2.52766e8	+	1.45935e8i	−0.762782	+	0.440393i
$693$	−4.02666e7	−	3.37877e7i	−0.120989	−	0.101522i
$694$	−1.16082e8	+	1.38341e8i	−0.347285	+	0.413878i
$695$	−3.29043e8	−	5.69919e8i	−0.980162	−	1.69769i
$696$	−6.90670e7	−	3.98759e7i	−0.204853	−	0.118272i
$697$	9.98955e7	+	2.74461e8i	0.295017	+	0.810554i
$698$	−4.24230e8	+	7.48032e7i	−1.24748	+	0.219965i
$699$	4.45870e8	+	7.86189e7i	1.30550	+	0.230195i
$700$	−3.76762e7	−	1.37130e7i	−0.109843	−	0.0399796i
$701$	−1.51401e8	+	1.27041e8i	−0.439516	+	0.368798i	−0.835528	−	0.549447i	$-0.814838\pi$
$701$	−1.51401e8	+	1.27041e8i	−0.439516	+	0.368798i	0.396012	+	0.918245i	$0.370394\pi$
$702$		−	1.24588e7i		−	0.0360136i
$703$	−5.72646e8	−	4.78864e7i	−1.64824	−	0.137831i
$704$	1.01157e7			0.0289919
$705$	−7.65386e7	−	9.12152e7i	−0.218430	−	0.260315i
$706$	−8.79567e7	+	2.41659e8i	−0.249951	+	0.686735i
$707$	−702106.	+	3.98184e6i	−0.00198675	+	0.0112674i
$708$	−9.11032e6	−	5.16672e7i	−0.0256705	−	0.145585i
$709$	−1.61477e8	+	5.87727e7i	−0.453076	+	0.164906i	−0.558471	−	0.829524i	$-0.688612\pi$
$709$	−1.61477e8	+	5.87727e7i	−0.453076	+	0.164906i	0.105395	+	0.994430i	$0.466389\pi$
$710$	−5.23507e7	+	9.06740e7i	−0.146267	+	0.253342i
$711$	9.02138e7	−	5.20850e7i	0.250995	−	0.144912i
$712$	1.05388e8	+	8.84313e7i	0.291979	+	0.245000i
$713$	−1.17719e8	+	1.40292e8i	−0.324772	+	0.387048i
$714$	−2.74820e8	−	4.76003e8i	−0.755013	−	1.30772i
$715$	2.14369e7	+	1.23766e7i	0.0586468	+	0.0338597i
$716$	9.96946e7	+	2.73909e8i	0.271602	+	0.746219i
$717$	5.69188e8	−	1.00363e8i	1.54418	−	0.272281i
$718$	−4.12011e8	−	7.26487e7i	−1.11310	−	0.196270i
$719$	3.15778e8	+	1.14934e8i	0.849561	+	0.309215i	0.729861	−	0.683595i	$-0.239585\pi$
$719$	3.15778e8	+	1.14934e8i	0.849561	+	0.309215i	0.119700	+	0.992810i	$0.461807\pi$
$720$	6.94486e7	−	5.82743e7i	0.186065	−	0.156127i
$721$			2.28258e8i			0.609004i
$722$	1.34831e8	+	2.29449e8i	0.358243	+	0.609641i
$723$	5.05510e6			0.0133756
$724$	−1.00104e8	−	1.19299e8i	−0.263775	−	0.314355i
$725$	−1.87821e7	+	5.16035e7i	−0.0492869	+	0.135415i
$726$	−6.05401e7	+	3.43340e8i	−0.158210	+	0.897253i
$727$	5.32699e7	+	3.02108e8i	0.138637	+	0.786248i	0.972258	+	0.233911i	$0.0751526\pi$
$727$	5.32699e7	+	3.02108e8i	0.138637	+	0.786248i	−0.833621	+	0.552337i	$0.813736\pi$
$728$	2.62321e7	−	9.54772e6i	0.0679892	−	0.0247460i
$729$	−1.33760e8	+	2.31679e8i	−0.345257	+	0.598003i
$730$	−3.69339e8	+	2.13238e8i	−0.949417	+	0.548146i
$731$	7.48323e8	+	6.27917e8i	1.91574	+	1.60750i
$732$	1.57827e8	−	1.88091e8i	0.402392	−	0.479552i
$733$	−3.39782e8	−	5.88520e8i	−0.862757	−	1.49434i	−0.869257	−	0.494360i	$-0.835402\pi$
$733$	−3.39782e8	−	5.88520e8i	−0.862757	−	1.49434i	0.00650012	−	0.999979i	$-0.497931\pi$
$734$	−4.26519e7	−	2.46251e7i	−0.107857	−	0.0622715i
$735$	−7.66913e7	−	2.10708e8i	−0.193145	−	0.530662i
$736$	−2.59565e7	+	4.57683e6i	−0.0651048	+	0.0114797i
$737$	−1.27617e8	−	2.25024e7i	−0.318792	−	0.0562116i
$738$	1.00035e8	+	3.64099e7i	0.248877	+	0.0905838i
$739$	−3.11526e7	+	2.61401e7i	−0.0771899	+	0.0647700i	−0.680566	−	0.732687i	$-0.738266\pi$
$739$	−3.11526e7	+	2.61401e7i	−0.0771899	+	0.0647700i	0.603376	+	0.797457i	$0.293822\pi$
$740$		−	3.81108e8i		−	0.940488i
$741$	1.18538e7	−	1.41752e8i	0.0291341	−	0.348398i
$742$	2.14431e8			0.524899
$743$	1.01196e8	+	1.20600e8i	0.246715	+	0.294023i	0.875163	−	0.483828i	$-0.160754\pi$
$743$	1.01196e8	+	1.20600e8i	0.246715	+	0.294023i	−0.628448	+	0.777852i	$0.716310\pi$
$744$	9.16204e7	−	2.51725e8i	0.222471	−	0.611234i
$745$	4.30889e7	−	2.44369e8i	0.104207	−	0.590987i
$746$	4.81121e7	+	2.72857e8i	0.115888	+	0.657232i
$747$	−3.68859e8	+	1.34254e8i	−0.884909	+	0.322081i
$748$	4.77437e7	−	8.26945e7i	0.114080	−	0.197593i
$749$	−4.92822e8	+	2.84531e8i	−1.17286	+	0.677148i
$750$	2.50092e8	+	2.09852e8i	0.592810	+	0.497427i
$751$	2.72704e8	−	3.24996e8i	0.643830	−	0.767287i	−0.341140	−	0.940013i	$-0.610813\pi$
$751$	2.72704e8	−	3.24996e8i	0.643830	−	0.767287i	0.984970	+	0.172726i	$0.0552574\pi$
$752$	−1.16645e7	−	2.02035e7i	−0.0274292	−	0.0475088i
$753$	2.98681e8	+	1.72443e8i	0.699555	+	0.403888i
$754$	−1.30771e7	−	3.59291e7i	−0.0305069	−	0.0838170i
$755$	9.30104e8	−	1.64002e8i	2.16118	−	0.381074i
$756$	3.36414e7	+	5.93189e6i	0.0778591	+	0.0137287i
$757$	4.75933e8	+	1.73226e8i	1.09713	+	0.399323i	0.826258	−	0.563292i	$-0.190465\pi$
$757$	4.75933e8	+	1.73226e8i	1.09713	+	0.399323i	0.270873	+	0.962615i	$0.412688\pi$
$758$	1.01814e8	−	8.54325e7i	0.233777	−	0.196162i
$759$			5.16442e7i			0.118113i
$760$	−1.44191e8	+	1.01791e8i	−0.328472	+	0.231882i
$761$	−4.85628e8			−1.10192			−0.550960	−	0.834532i	$-0.685738\pi$
$761$	−4.85628e8			−1.10192			−0.550960	+	0.834532i	$0.685738\pi$
$762$	−3.26267e8	−	3.88830e8i	−0.737408	−	0.878809i
$763$	2.12372e8	−	5.83486e8i	0.478105	−	1.31358i
$764$	3.70546e6	−	2.10147e7i	0.00830925	−	0.0471241i
$765$	−1.48604e8	−	8.42775e8i	−0.331930	−	1.88247i
$766$	1.77005e8	−	6.44245e7i	0.393821	−	0.143339i
$767$	1.25763e7	−	2.17828e7i	0.0278720	−	0.0482756i
$768$	3.33877e7	−	1.92764e7i	0.0737061	−	0.0425542i
$769$	−3.50744e8	−	2.94309e8i	−0.771277	−	0.647179i	0.169758	−	0.985486i	$-0.445701\pi$
$769$	−3.50744e8	−	2.94309e8i	−0.771277	−	0.647179i	−0.941036	+	0.338307i	$0.890146\pi$
$770$	−4.36259e7	+	5.19913e7i	−0.0955591	+	0.113883i
$771$	5.04322e7	+	8.73511e7i	0.110038	+	0.190592i
$772$	2.89289e8	+	1.67021e8i	0.628753	+	0.363011i
$773$	1.68370e8	+	4.62594e8i	0.364525	+	1.00152i	0.977410	+	0.211352i	$0.0677865\pi$
$773$	1.68370e8	+	4.62594e8i	0.364525	+	1.00152i	−0.612885	+	0.790172i	$0.709991\pi$
$774$	3.50639e8	−	6.18271e7i	0.756201	−	0.133339i
$775$	−1.81654e8	−	3.20305e7i	−0.390248	−	0.0688112i
$776$	−6.70082e7	−	2.43890e7i	−0.143398	−	0.0521926i
$777$	−6.45128e8	+	5.41326e8i	−1.37525	+	1.15397i
$778$		−	2.88384e8i		−	0.612396i
$779$	−1.88171e8	−	8.68682e7i	−0.398053	−	0.183759i
$780$	9.43393e7			0.198797
$781$	2.58363e7	+	3.07905e7i	0.0542347	+	0.0646344i
$782$	−8.50936e7	+	2.33793e8i	−0.177941	+	0.488890i
$783$	8.12467e6	−	4.60773e7i	0.0169247	−	0.0959846i
$784$	−7.62866e6	−	4.32643e7i	−0.0158307	−	0.0897803i
$785$	−5.65256e7	+	2.05736e7i	−0.116852	+	0.0425307i
$786$	3.05277e8	−	5.28756e8i	0.628676	−	1.08890i
$787$	−6.39495e8	+	3.69212e8i	−1.31194	+	0.757447i	−0.982417	−	0.186702i	$-0.940220\pi$
$787$	−6.39495e8	+	3.69212e8i	−1.31194	+	0.757447i	−0.329519	+	0.944149i	$0.606887\pi$
$788$	−1.38844e8	−	1.16504e8i	−0.283758	−	0.238101i
$789$	3.33431e8	−	3.97368e8i	0.678852	−	0.809024i
$790$	−6.72509e7	−	1.16482e8i	−0.136401	−	0.236253i
$791$	2.27498e8	+	1.31346e8i	0.459672	+	0.265392i
$792$	−1.19034e7	−	3.27043e7i	−0.0239605	−	0.0658309i
$793$	1.15928e8	−	2.04412e7i	0.232470	−	0.0409907i
$794$	3.14810e8	+	5.55096e7i	0.628909	+	0.110894i
$795$	6.80955e8	+	2.47847e8i	1.35524	+	0.493268i
$796$	1.01748e8	−	8.53763e7i	0.201737	−	0.169277i
$797$		−	1.94384e8i		−	0.383960i	−0.981399	−	0.191980i	$-0.938509\pi$
$797$		−	1.94384e8i		−	0.383960i	0.981399	−	0.191980i	$-0.0614908\pi$
$798$	3.77117e8	+	9.94986e7i	0.742108	+	0.195798i
$799$	−2.20215e8			−0.431725
$800$	−1.70638e7	−	2.03359e7i	−0.0333278	−	0.0397186i
$801$	1.61888e8	−	4.44783e8i	0.315005	−	0.865468i
$802$	−4.48479e7	+	2.54345e8i	−0.0869399	+	0.493061i
$803$	2.84299e7	+	1.61234e8i	0.0549071	+	0.311394i
$804$	−4.64093e8	+	1.68916e8i	−0.892970	+	0.325015i
$805$	8.84192e7	−	1.53146e8i	0.169496	−	0.293575i
$806$	1.11222e8	−	6.42141e7i	0.212415	−	0.122638i
$807$	5.35491e8	+	4.49331e8i	1.01890	+	0.854959i
$808$	−1.72079e6	+	2.05076e6i	−0.00326207	+	0.00388759i
$809$	2.29037e8	+	3.96704e8i	0.432574	+	0.749239i	0.997094	−	0.0761797i	$-0.0242723\pi$
$809$	2.29037e8	+	3.96704e8i	0.432574	+	0.749239i	−0.564521	+	0.825419i	$0.690939\pi$
$810$	4.16162e8	+	2.40272e8i	0.783083	+	0.452113i
$811$	−4.77496e7	−	1.31191e8i	−0.0895173	−	0.245947i	0.886853	−	0.462052i	$-0.152887\pi$
$811$	−4.77496e7	−	1.31191e8i	−0.0895173	−	0.245947i	−0.976370	+	0.216105i	$0.930665\pi$
$812$	1.03242e8	−	1.82044e7i	0.192836	−	0.0340023i
$813$	2.07701e7	+	3.66233e6i	0.0386515	+	0.00681531i
$814$	−1.37482e8	−	5.00392e7i	−0.254901	−	0.0927764i
$815$	6.68414e8	−	5.60866e8i	1.23473	−	1.03606i
$816$		−	3.63921e8i		−	0.669787i
$817$	−6.90304e8	+	6.30640e7i	−1.26583	+	0.115642i
$818$	2.14998e7			0.0392803
$819$	−6.17362e7	−	7.35743e7i	−0.112380	−	0.133929i
$820$	4.70116e7	−	1.29163e8i	0.0852636	−	0.234260i
$821$	1.21058e8	−	6.86554e8i	0.218758	−	1.24064i	−0.655507	−	0.755189i	$-0.727545\pi$
$821$	1.21058e8	−	6.86554e8i	0.218758	−	1.24064i	0.874265	−	0.485449i	$-0.161344\pi$
$822$	1.58871e8	+	9.01002e8i	0.286041	+	1.62222i
$823$	4.74375e6	−	1.72658e6i	0.00850986	−	0.00309733i	−0.337762	−	0.941232i	$-0.609670\pi$
$823$	4.74375e6	−	1.72658e6i	0.00850986	−	0.00309733i	0.346272	+	0.938134i	$0.387448\pi$
$824$	−7.55655e7	+	1.30883e8i	−0.135065	+	0.233939i
$825$	−4.50471e7	+	2.60080e7i	−0.0802241	+	0.0463174i
$826$	5.28303e7	+	4.43299e7i	0.0937438	+	0.0786604i
$827$	−6.28587e8	+	7.49121e8i	−1.11135	+	1.32445i	−0.170598	+	0.985341i	$0.554570\pi$
$827$	−6.28587e8	+	7.49121e8i	−1.11135	+	1.32445i	−0.940747	+	0.339109i	$0.889874\pi$
$828$	4.53408e7	+	7.85326e7i	0.0798726	+	0.138343i
$829$	4.13903e8	+	2.38967e8i	0.726500	+	0.419445i	0.817140	−	0.576439i	$-0.195558\pi$
$829$	4.13903e8	+	2.38967e8i	0.726500	+	0.419445i	−0.0906406	+	0.995884i	$0.528891\pi$
$830$	1.73345e8	+	4.76262e8i	0.303164	+	0.832936i
$831$	5.60298e8	−	9.87957e7i	0.976374	−	0.172161i
$832$	1.82024e7	+	3.20957e6i	0.0316051	+	0.00557284i
$833$	−3.89686e8	−	1.41834e8i	−0.674186	−	0.245383i
$834$	−7.37578e8	+	6.18901e8i	−1.27148	+	1.06690i
$835$		−	1.42896e7i		−	0.0245449i
$836$	1.77879e7	+	6.53807e7i	0.0304443	+	0.111900i
$837$	1.57158e8			0.268015
$838$	−9.40267e7	−	1.12057e8i	−0.159779	−	0.190417i
$839$	−1.81053e8	+	4.97438e8i	−0.306562	+	0.842273i	0.686758	+	0.726886i	$0.259033\pi$
$839$	−1.81053e8	+	4.97438e8i	−0.306562	+	0.842273i	−0.993321	+	0.115387i	$0.963189\pi$
$840$	−4.49167e7	+	2.54736e8i	−0.0757828	+	0.429785i
$841$	7.83562e7	+	4.44380e8i	0.131730	+	0.747079i
$842$	3.76421e8	−	1.37006e8i	0.630576	−	0.229511i
$843$	−3.59920e8	+	6.23399e8i	−0.600790	+	1.04060i
$844$	−1.31923e8	+	7.61660e7i	−0.219429	+	0.126688i
$845$	−4.90976e8	−	4.11977e8i	−0.813748	−	0.682815i
$846$	−5.15927e7	+	6.14858e7i	−0.0852074	+	0.101546i
$847$	−2.29144e8	−	3.96889e8i	−0.377102	−	0.653159i
$848$	1.22955e8	+	7.09882e7i	0.201632	+	0.116412i
$849$	−1.42487e8	−	3.91481e8i	−0.232838	−	0.639717i
$850$	−2.46781e8	+	4.35141e7i	−0.401842	+	0.0708555i
$851$	3.75413e8	+	6.61955e7i	0.609146	+	0.107409i
$852$	1.43949e8	+	5.23933e7i	0.232751	+	0.0847143i
$853$	−4.96225e8	+	4.16382e8i	−0.799524	+	0.670881i	−0.948083	−	0.318023i	$-0.896981\pi$
$853$	−4.96225e8	+	4.16382e8i	−0.799524	+	0.670881i	0.148559	+	0.988904i	$0.452537\pi$
$854$			3.22761e8i			0.518211i
$855$	4.98766e8	+	3.46395e8i	0.797992	+	0.554208i
$856$	−3.76780e8			−0.600712
$857$	−5.10140e8	−	6.07962e8i	−0.810489	−	0.965903i	0.189383	−	0.981903i	$-0.439351\pi$
$857$	−5.10140e8	−	6.07962e8i	−0.810489	−	0.965903i	−0.999872	+	0.0159999i	$0.994907\pi$
$858$	1.23867e7	−	3.40321e7i	0.0196107	−	0.0538799i
$859$	1.83245e7	−	1.03923e8i	0.0289103	−	0.163958i	−0.966935	−	0.255025i	$-0.917916\pi$
$859$	1.83245e7	−	1.03923e8i	0.0289103	−	0.163958i	0.995845	+	0.0910663i	$0.0290275\pi$
$860$	−7.98297e7	−	4.52737e8i	−0.125507	−	0.711787i
$861$	−2.85419e8	+	1.03884e8i	−0.447170	+	0.162757i
$862$	1.05871e8	−	1.83374e8i	0.165293	−	0.286296i
$863$	4.45885e8	−	2.57432e8i	0.693730	−	0.400525i	−0.111278	−	0.993789i	$-0.535494\pi$
$863$	4.45885e8	−	2.57432e8i	0.693730	−	0.400525i	0.805008	+	0.593264i	$0.202161\pi$
$864$	1.73263e7	+	1.45385e7i	0.0268636	+	0.0225412i
$865$	8.33424e8	−	9.93236e8i	1.28771	−	1.53463i
$866$	3.76651e7	+	6.52378e7i	0.0579943	+	0.100449i
$867$	−2.20644e9	−	1.27389e9i	−3.38560	−	1.95468i
$868$	1.20436e8	+	3.30896e8i	0.184161	+	0.505979i
$869$	−5.08499e7	+	8.96620e6i	−0.0774873	+	0.0136631i
$870$	3.48901e8	+	6.15206e7i	0.529839	+	0.0934249i
$871$	−2.22498e8	−	8.09825e7i	−0.336721	−	0.122557i
$872$	3.14940e8	−	2.64266e8i	0.474983	−	0.398558i
$873$			2.45339e8i			0.368743i
$874$	−7.52246e7	−	1.59717e8i	−0.112675	−	0.239230i
$875$	−4.29152e8			−0.640600
$876$	4.01083e8	+	4.77992e8i	0.596653	+	0.711063i
$877$	−1.33426e8	+	3.66584e8i	−0.197806	+	0.543469i	−0.998449	−	0.0556735i	$-0.982269\pi$
$877$	−1.33426e8	+	3.66584e8i	−0.197806	+	0.543469i	0.800643	+	0.599142i	$0.204492\pi$
$878$	7.38878e7	−	4.19039e8i	0.109166	−	0.619114i
$879$	−1.58927e8	−	9.01319e8i	−0.234008	−	1.32713i
$880$	−4.22271e7	+	1.53694e7i	−0.0619645	+	0.0225532i
$881$	−1.64461e8	+	2.84854e8i	−0.240511	+	0.416577i	−0.960860	−	0.277035i	$-0.910648\pi$
$881$	−1.64461e8	+	2.84854e8i	−0.240511	+	0.416577i	0.720349	+	0.693612i	$0.243982\pi$
$882$	−1.30898e8	+	7.55740e7i	−0.190778	+	0.110145i
$883$	2.28387e8	+	1.91640e8i	0.331734	+	0.278358i	0.793406	−	0.608693i	$-0.208306\pi$
$883$	2.28387e8	+	1.91640e8i	0.331734	+	0.278358i	−0.461672	+	0.887051i	$0.652750\pi$
$884$	1.12149e8	−	1.33654e8i	0.162345	−	0.193475i
$885$	1.16532e8	+	2.01839e8i	0.168118	+	0.291189i
$886$	4.27341e8	+	2.46725e8i	0.614431	+	0.354742i
$887$	−2.49617e8	−	6.85818e8i	−0.357688	−	0.982738i	−0.979830	−	0.199834i	$-0.935960\pi$
$887$	−2.49617e8	−	6.85818e8i	−0.357688	−	0.982738i	0.622142	−	0.782904i	$-0.286263\pi$
$888$	−5.49125e8	+	9.68256e7i	−0.784210	+	0.138277i
$889$	6.57086e8	+	1.15862e8i	0.935227	+	0.164906i
$890$	−5.74294e8	−	2.09026e8i	−0.814637	−	0.296504i
$891$	1.41318e8	−	1.18580e8i	0.199785	−	0.167640i
$892$		−	3.76142e8i		−	0.529977i
$893$	1.10070e8	−	1.10918e8i	0.154566	−	0.155757i
$894$	−3.63050e8			−0.508106
$895$	−8.32333e8	−	9.91936e8i	−1.16099	−	1.38361i
$896$	−1.73330e7	+	4.76220e7i	−0.0240962	+	0.0662039i
$897$	−1.63860e7	+	9.29296e7i	−0.0227036	+	0.128759i
$898$	−4.66729e7	−	2.64695e8i	−0.0644520	−	0.365525i
$899$	4.53215e8	−	1.64957e8i	0.623771	−	0.227034i
$900$	−4.56671e7	+	7.90978e7i	−0.0626436	+	0.108502i
$901$	1.16064e9	−	6.70096e8i	1.58680	−	0.916141i
$902$	−4.04220e7	−	3.39181e7i	−0.0550805	−	0.0462181i
$903$	−6.52988e8	+	7.78200e8i	−0.886833	+	1.05689i
$904$	8.69651e7	+	1.50628e8i	0.117717	+	0.203892i
$905$	5.99133e8	+	3.45909e8i	0.808309	+	0.466677i
$906$	−4.72610e8	−	1.29849e9i	−0.635504	−	1.74603i
$907$	−1.36774e9	+	2.41169e8i	−1.83308	+	0.323221i	−0.980067	−	0.198669i	$-0.936338\pi$
$907$	−1.36774e9	+	2.41169e8i	−1.83308	+	0.323221i	−0.853012	+	0.521890i	$0.825227\pi$
$908$	−9.59857e7	−	1.69249e7i	−0.128218	−	0.0226083i
$909$	8.65507e6	+	3.15019e6i	0.0115234	+	0.00419416i
$910$	−9.49975e7	+	7.97123e7i	−0.126063	+	0.105779i
$911$			1.53396e8i			0.202889i	0.994841	+	0.101444i	$0.0323464\pi$
$911$			1.53396e8i			0.202889i	−0.994841	+	0.101444i	$0.967654\pi$
$912$	1.83300e8	+	1.81899e8i	0.241645	+	0.239797i
$913$	1.94568e8			0.255657
$914$	−1.88796e8	−	2.24998e8i	−0.247260	−	0.294673i
$915$	−3.73058e8	+	1.02497e9i	−0.486983	+	1.33797i
$916$	7.82593e7	−	4.43830e8i	0.101824	−	0.577472i
$917$	1.39367e8	+	7.90390e8i	0.180739	+	1.02502i
$918$	2.00626e8	−	7.30220e7i	0.259334	−	0.0943899i
$919$	−4.84684e8	+	8.39498e8i	−0.624471	+	1.08162i	0.364171	+	0.931332i	$0.381352\pi$
$919$	−4.84684e8	+	8.39498e8i	−0.624471	+	1.08162i	−0.988643	+	0.150284i	$0.951981\pi$
$920$	1.01399e8	−	5.85430e7i	0.130218	−	0.0751815i
$921$	3.27536e8	+	2.74836e8i	0.419257	+	0.351799i
$922$	−2.02708e8	+	2.41578e8i	−0.258630	+	0.308223i
$923$	3.67209e7	+	6.36025e7i	0.0466991	+	0.0808852i
$924$	8.59961e7	+	4.96499e7i	0.109009	+	0.0629365i
$925$	1.31318e8	+	3.60794e8i	0.165920	+	0.455862i
$926$	−2.23765e7	+	3.94557e6i	−0.0281811	+	0.00496909i
$927$	5.12070e8	+	9.02918e7i	0.642822	+	0.113347i
$928$	6.52258e7	+	2.37403e7i	0.0816161	+	0.0297058i
$929$	−1.73480e8	+	1.45567e8i	−0.216373	+	0.181559i	−0.744532	−	0.667587i	$-0.767327\pi$
$929$	−1.73480e8	+	1.45567e8i	−0.216373	+	0.181559i	0.528159	+	0.849146i	$0.322883\pi$
$930$			1.19001e9i			1.47946i
$931$	2.66216e8	−	1.25384e8i	0.329902	−	0.155380i
$932$	−3.94049e8			−0.486747
$933$	7.03731e8	+	8.38674e8i	0.866487	+	1.03264i
$934$	−1.10952e8	+	3.04837e8i	−0.136174	+	0.374134i
$935$	−7.36590e7	+	4.17741e8i	−0.0901138	+	0.511061i
$936$	−1.10426e7	−	6.26256e7i	−0.0134661	−	0.0763703i
$937$	8.14968e8	−	2.96624e8i	0.990653	−	0.360568i	0.204680	−	0.978829i	$-0.434385\pi$
$937$	8.14968e8	−	2.96624e8i	0.990653	−	0.360568i	0.785973	+	0.618261i	$0.212162\pi$
$938$	3.24605e8	−	5.62232e8i	0.393320	−	0.681251i
$939$	−4.89193e8	+	2.82435e8i	−0.590858	+	0.341132i
$940$	7.93890e7	+	6.66153e7i	0.0955822	+	0.0802030i
$941$	3.88433e8	−	4.62916e8i	0.466173	−	0.555563i	−0.480819	−	0.876820i	$-0.659661\pi$
$941$	3.88433e8	−	4.62916e8i	0.466173	−	0.555563i	0.946992	+	0.321257i	$0.104105\pi$
$942$	4.40049e7	+	7.62187e7i	0.0526439	+	0.0911819i
$943$	1.19068e8	+	6.87438e7i	0.141990	+	0.0819782i
$944$	1.56174e7	+	4.29085e7i	0.0185649	+	0.0510067i
$945$	−1.49446e8	+	2.63514e7i	−0.177088	+	0.0312254i
$946$	−1.73802e8	−	3.06461e7i	−0.205297	−	0.0361994i
$947$	−9.79248e8	−	3.56417e8i	−1.15304	−	0.419671i	−0.306431	−	0.951893i	$-0.599135\pi$
$947$	−9.79248e8	−	3.56417e8i	−1.15304	−	0.419671i	−0.846605	+	0.532222i	$0.821357\pi$
$948$	−1.50749e8	+	1.26493e8i	−0.176941	+	0.148471i
$949$			2.99148e8i			0.350016i
$950$	1.01431e8	−	1.46048e8i	0.118304	−	0.170344i
$951$	1.82080e9			2.11700
$952$	3.07496e8	+	3.66460e8i	0.356393	+	0.424733i
$953$	−3.12186e8	+	8.57724e8i	−0.360691	+	0.990989i	0.618095	+	0.786103i	$0.287905\pi$
$953$	−3.12186e8	+	8.57724e8i	−0.360691	+	0.990989i	−0.978786	+	0.204886i	$0.934318\pi$
$954$	8.48224e7	−	4.81052e8i	0.0976935	−	0.554047i
$955$	1.64608e7	+	9.33540e7i	0.0188991	+	0.107182i
$956$	−4.72698e8	+	1.72048e8i	−0.541016	+	0.196914i
$957$	6.80034e7	−	1.17785e8i	0.0775880	−	0.134386i
$958$	7.08267e8	−	4.08918e8i	0.805565	−	0.465093i
$959$	−9.21284e8	−	7.73049e8i	−1.04457	−	0.876499i
$960$	−1.10086e8	+	1.31196e8i	−0.124429	+	0.148288i
$961$	3.66255e8	+	6.34372e8i	0.412680	+	0.714782i
$962$	−2.31510e8	−	1.33663e8i	−0.260043	−	0.150136i
$963$	4.43367e8	+	1.21814e9i	0.496461	+	1.36401i
$964$	−4.33286e6	+	764000.i	−0.00483663	+	0.000852829i
$965$	−1.46138e9	−	2.57681e8i	−1.62623	−	0.286748i
$966$	−2.43127e8	−	8.84911e7i	−0.269713	−	0.0981676i
$967$	5.19251e8	−	4.35703e8i	0.574245	−	0.481849i	−0.308806	−	0.951125i	$-0.599929\pi$
$967$	5.19251e8	−	4.35703e8i	0.574245	−	0.481849i	0.883052	+	0.469276i	$0.155485\pi$
$968$		−	3.03436e8i		−	0.334534i
$969$	2.35213e9	−	6.39936e8i	2.58518	−	0.703340i
$970$	3.16776e8			0.347086
$971$	6.21367e8	+	7.40516e8i	0.678719	+	0.808866i	0.989942	−	0.141471i	$-0.0451831\pi$
$971$	6.21367e8	+	7.40516e8i	0.678719	+	0.808866i	−0.311223	+	0.950337i	$0.600739\pi$
$972$	2.09314e8	−	5.75084e8i	0.227928	−	0.626228i
$973$	2.19781e8	−	1.24644e9i	0.238589	−	1.35311i
$974$	−2.03261e6	−	1.15275e7i	−0.00219977	−	0.0124755i
$975$	−8.93106e7	+	3.25064e7i	−0.0963583	+	0.0350716i
$976$	−1.06851e8	+	1.85071e8i	−0.114929	+	0.199063i
$977$	6.68630e7	−	3.86034e7i	0.0716972	−	0.0413944i	−0.463723	−	0.885980i	$-0.653487\pi$
$977$	6.68630e7	−	3.86034e7i	0.0716972	−	0.0413944i	0.535420	+	0.844586i	$0.320153\pi$
$978$	−9.77951e8	−	8.20598e8i	−1.04544	−	0.877231i
$979$	−1.50809e8	+	1.79727e8i	−0.160723	+	0.191542i
$980$	9.75793e7	+	1.69012e8i	0.103676	+	0.179573i
$981$	−1.22498e9	−	7.07241e8i	−1.29754	−	0.749136i
$982$	−4.25936e8	−	1.17025e9i	−0.449790	−	1.23579i
$983$	−1.04399e8	+	1.84084e7i	−0.109910	+	0.0193801i	−0.228333	−	0.973583i	$-0.573327\pi$
$983$	−1.04399e8	+	1.84084e7i	−0.109910	+	0.0193801i	0.118423	+	0.992963i	$0.462216\pi$
$984$	−1.98051e8	−	3.49217e7i	−0.207870	−	0.0366530i
$985$	7.56603e8	+	2.75381e8i	0.791698	+	0.288155i
$986$	5.01925e8	−	4.21165e8i	0.523610	−	0.439361i
$987$		−	2.29008e8i		−	0.238176i
$988$	1.12635e7	+	1.23291e8i	0.0116789	+	0.127838i
$989$	4.59837e8			0.475352
$990$	9.93795e7	+	1.18436e8i	0.102422	+	0.122061i
$991$	5.00484e8	−	1.37507e9i	0.514244	−	1.41287i	−0.362530	−	0.931972i	$-0.618087\pi$
$991$	5.00484e8	−	1.37507e9i	0.514244	−	1.41287i	0.876774	−	0.480903i	$-0.159691\pi$
$992$	−4.04860e7	+	2.29607e8i	−0.0414734	+	0.235207i
$993$	6.12454e7	+	3.47340e8i	0.0625498	+	0.354738i
$994$	−1.89223e8	+	6.88717e7i	−0.192671	+	0.0701264i
$995$	−2.95019e8	+	5.10988e8i	−0.299489	+	0.518730i
$996$	6.42188e8	−	3.70768e8i	0.649957	−	0.375253i
$997$	−1.23269e9	−	1.03435e9i	−1.24385	−	1.04371i	−0.997213	−	0.0746037i	$-0.976231\pi$
$997$	−1.23269e9	−	1.03435e9i	−1.24385	−	1.04371i	−0.246635	−	0.969109i	$-0.579325\pi$
$998$	4.01290e8	−	4.78239e8i	0.403707	−	0.481119i
$999$	−1.63563e8	−	2.83299e8i	−0.164055	−	0.284151i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.7.f.a.13.5	yes	60
19.3	odd	18	inner	38.7.f.a.3.5	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.7.f.a.3.5	✓	60	19.3	odd	18	inner
38.7.f.a.13.5	yes	60	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	38.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.63616 - 4.33340i) q^{2} +(12.5750 - 34.5495i) q^{3} +(-5.55674 + 31.5138i) q^{4} +(-24.6848 - 139.995i) q^{5} +(-195.442 + 71.1350i) q^{6} +(136.699 - 236.770i) q^{7} +(156.767 - 90.5097i) q^{8} +(-477.093 - 400.329i) q^{9} +O(q^{10})\)	\(q+(-3.63616 - 4.33340i) q^{2} +(12.5750 - 34.5495i) q^{3} +(-5.55674 + 31.5138i) q^{4} +(-24.6848 - 139.995i) q^{5} +(-195.442 + 71.1350i) q^{6} +(136.699 - 236.770i) q^{7} +(156.767 - 90.5097i) q^{8} +(-477.093 - 400.329i) q^{9} +(-516.895 + 616.012i) q^{10} +(154.353 + 267.347i) q^{11} +(1018.91 + 588.270i) q^{12} +(192.920 + 530.044i) q^{13} +(-1523.08 + 268.560i) q^{14} +(-5147.16 - 907.583i) q^{15} +(-962.245 - 350.229i) q^{16} +(-7404.65 + 6213.24i) q^{17} +3523.10i q^{18} +(571.576 - 6835.14i) q^{19} +4548.94 q^{20} +(-6461.31 - 7700.29i) q^{21} +(597.272 - 1640.99i) q^{22} +(-790.114 + 4480.96i) q^{23} +(-1155.72 - 6554.40i) q^{24} +(-4306.46 + 1567.42i) q^{25} +(1595.41 - 2763.32i) q^{26} +(3381.48 - 1952.30i) q^{27} +(6701.94 + 5623.60i) q^{28} +(7702.41 - 9179.37i) q^{29} +(14783.0 + 25604.8i) q^{30} +(34857.0 + 20124.7i) q^{31} +(1981.19 + 5443.28i) q^{32} +(11177.7 - 1970.93i) q^{33} +(53848.9 + 9495.02i) q^{34} +(-36521.0 - 13292.6i) q^{35} +(15267.0 - 12810.5i) q^{36} -83779.7i q^{37} +(-31697.8 + 22376.8i) q^{38} +20738.8 q^{39} +(-16540.6 - 19712.4i) q^{40} +(10334.6 - 28394.2i) q^{41} +(-9874.12 + 55998.9i) q^{42} +(-17549.1 - 99525.8i) q^{43} +(-9282.84 + 3378.68i) q^{44} +(-44266.9 + 76672.6i) q^{45} +(22290.8 - 12869.6i) q^{46} +(17452.2 + 14644.2i) q^{47} +(-24200.5 + 28841.0i) q^{48} +(21451.0 + 37154.3i) q^{49} +(22451.2 + 12962.2i) q^{50} +(121551. + 333959. i) q^{51} +(-17775.7 + 3134.34i) q^{52} +(-136542. - 24076.1i) q^{53} +(-20755.7 - 7554.45i) q^{54} +(33617.0 - 28208.0i) q^{55} -49490.5i q^{56} +(-228963. - 105700. i) q^{57} -67785.0 q^{58} +(-28663.2 - 34159.5i) q^{59} +(57202.9 - 157164. i) q^{60} +(36239.2 - 205523. i) q^{61} +(-39537.1 - 224226. i) q^{62} +(-160004. + 58236.8i) q^{63} +(16384.0 - 28377.9i) q^{64} +(69441.1 - 40091.9i) q^{65} +(-49184.8 - 41270.9i) q^{66} +(-269824. + 321564. i) q^{67} +(-154657. - 267874. i) q^{68} +(144879. + 83646.2i) q^{69} +(75194.0 + 206594. i) q^{70} +(128224. - 22609.3i) q^{71} +(-111026. - 19576.9i) q^{72} +(498363. + 181389. i) q^{73} +(-363051. + 304636. i) q^{74} +168497. i q^{75} +(212226. + 55993.7i) q^{76} +84399.9 q^{77} +(-75409.4 - 89869.4i) q^{78} +(-57206.4 + 157173. i) q^{79} +(-25277.3 + 143355. i) q^{80} +(-103769. - 588503. i) q^{81} +(-160622. + 58461.5i) q^{82} +(315134. - 545828. i) q^{83} +(278570. - 160832. i) q^{84} +(1.05260e6 + 883239. i) q^{85} +(-367474. + 437939. i) q^{86} +(-220285. - 381545. i) q^{87} +(48395.0 + 27940.9i) q^{88} +(259935. + 714166. i) q^{89} +(493214. - 86967.0i) q^{90} +(151871. + 26778.9i) q^{91} +(-136822. - 49799.1i) q^{92} +(1.13363e6 - 951225. i) q^{93} -128876. i q^{94} +(-970993. + 88706.8i) q^{95} +212976. q^{96} +(-253212. - 301767. i) q^{97} +(83005.1 - 228055. i) q^{98} +(33386.0 - 189342. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 30 q^{3} - 240 q^{6} + 432 q^{7} + 690 q^{9}+O(q^{10}) \) 60 * q + 30 * q^3 - 240 * q^6 + 432 * q^7 + 690 * q^9	\( 60 q + 30 q^{3} - 240 q^{6} + 432 q^{7} + 690 q^{9} - 3360 q^{11} + 9660 q^{13} + 2496 q^{14} - 37464 q^{15} + 7704 q^{17} + 46704 q^{19} + 21504 q^{20} + 78732 q^{21} - 20304 q^{22} - 54120 q^{23} + 7680 q^{24} - 41328 q^{25} - 25536 q^{26} - 124830 q^{27} + 65280 q^{28} - 21840 q^{29} + 30780 q^{31} - 54582 q^{33} - 70560 q^{34} - 56796 q^{35} - 22080 q^{36} + 52080 q^{38} + 496344 q^{39} + 83394 q^{41} + 38880 q^{42} - 294384 q^{43} - 8448 q^{44} - 391824 q^{45} + 738720 q^{46} + 639264 q^{47} + 61440 q^{48} - 85530 q^{49} - 689472 q^{50} - 215478 q^{51} - 456960 q^{52} - 1189428 q^{53} - 907200 q^{54} - 316512 q^{55} + 517776 q^{57} + 440640 q^{58} + 957390 q^{59} + 586752 q^{60} + 1390404 q^{61} + 978384 q^{62} + 2002152 q^{63} + 983040 q^{64} - 878940 q^{65} - 976992 q^{66} - 2920854 q^{67} - 78144 q^{68} - 2667600 q^{69} - 643392 q^{70} + 1585980 q^{71} + 706560 q^{72} + 1734648 q^{73} - 1167552 q^{74} - 411264 q^{76} - 1481400 q^{77} - 2170608 q^{78} + 4991952 q^{79} + 40002 q^{81} + 2299392 q^{82} - 30672 q^{83} + 1313280 q^{84} + 815976 q^{85} - 1424976 q^{86} - 125892 q^{87} - 6804636 q^{89} - 2283456 q^{90} - 3838704 q^{91} - 244992 q^{92} - 3271128 q^{93} - 4631640 q^{95} + 2112390 q^{97} + 7177728 q^{98} + 21467982 q^{99}+O(q^{100}) \) 60 * q + 30 * q^3 - 240 * q^6 + 432 * q^7 + 690 * q^9 - 3360 * q^11 + 9660 * q^13 + 2496 * q^14 - 37464 * q^15 + 7704 * q^17 + 46704 * q^19 + 21504 * q^20 + 78732 * q^21 - 20304 * q^22 - 54120 * q^23 + 7680 * q^24 - 41328 * q^25 - 25536 * q^26 - 124830 * q^27 + 65280 * q^28 - 21840 * q^29 + 30780 * q^31 - 54582 * q^33 - 70560 * q^34 - 56796 * q^35 - 22080 * q^36 + 52080 * q^38 + 496344 * q^39 + 83394 * q^41 + 38880 * q^42 - 294384 * q^43 - 8448 * q^44 - 391824 * q^45 + 738720 * q^46 + 639264 * q^47 + 61440 * q^48 - 85530 * q^49 - 689472 * q^50 - 215478 * q^51 - 456960 * q^52 - 1189428 * q^53 - 907200 * q^54 - 316512 * q^55 + 517776 * q^57 + 440640 * q^58 + 957390 * q^59 + 586752 * q^60 + 1390404 * q^61 + 978384 * q^62 + 2002152 * q^63 + 983040 * q^64 - 878940 * q^65 - 976992 * q^66 - 2920854 * q^67 - 78144 * q^68 - 2667600 * q^69 - 643392 * q^70 + 1585980 * q^71 + 706560 * q^72 + 1734648 * q^73 - 1167552 * q^74 - 411264 * q^76 - 1481400 * q^77 - 2170608 * q^78 + 4991952 * q^79 + 40002 * q^81 + 2299392 * q^82 - 30672 * q^83 + 1313280 * q^84 + 815976 * q^85 - 1424976 * q^86 - 125892 * q^87 - 6804636 * q^89 - 2283456 * q^90 - 3838704 * q^91 - 244992 * q^92 - 3271128 * q^93 - 4631640 * q^95 + 2112390 * q^97 + 7177728 * q^98 + 21467982 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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