LMFDB - Embedded newform 210.4.u.a.73.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,4,Mod(73,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 2]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("210.73");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	210.u (of order $12$, degree $4$, 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:	$12.3904011012$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			73.8
Character	$\chi$	$=$	210.73
Dual form			210.4.u.a.187.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.93185 + 0.517638i) q^{2} +(0.776457 + 2.89778i) q^{3} +(3.46410 + 2.00000i) q^{4} +(-5.82019 + 9.54596i) q^{5} +6.00000i q^{6} +(-10.6715 - 15.1367i) q^{7} +(5.65685 + 5.65685i) q^{8} +(-7.79423 + 4.50000i) q^{9} +O(q^{10})$	\(q+(1.93185 + 0.517638i) q^{2} +(0.776457 + 2.89778i) q^{3} +(3.46410 + 2.00000i) q^{4} +(-5.82019 + 9.54596i) q^{5} +6.00000i q^{6} +(-10.6715 - 15.1367i) q^{7} +(5.65685 + 5.65685i) q^{8} +(-7.79423 + 4.50000i) q^{9} +(-16.1851 + 15.4286i) q^{10} +(-34.6217 + 59.9665i) q^{11} +(-3.10583 + 11.5911i) q^{12} +(29.8548 - 29.8548i) q^{13} +(-12.7805 - 34.7658i) q^{14} +(-32.1812 - 9.45358i) q^{15} +(8.00000 + 13.8564i) q^{16} +(-115.996 + 31.0809i) q^{17} +(-17.3867 + 4.65874i) q^{18} +(44.7717 + 77.5468i) q^{19} +(-39.2537 + 21.4278i) q^{20} +(35.5767 - 42.6767i) q^{21} +(-97.9249 + 97.9249i) q^{22} +(23.2125 - 86.6302i) q^{23} +(-12.0000 + 20.7846i) q^{24} +(-57.2508 - 111.119i) q^{25} +(73.1289 - 42.2210i) q^{26} +(-19.0919 - 19.0919i) q^{27} +(-6.69393 - 73.7780i) q^{28} +108.029i q^{29} +(-57.2758 - 34.9211i) q^{30} +(-181.737 - 104.926i) q^{31} +(8.28221 + 30.9096i) q^{32} +(-200.652 - 53.7645i) q^{33} -240.175 q^{34} +(206.604 - 13.7718i) q^{35} -36.0000 q^{36} +(236.958 + 63.4927i) q^{37} +(46.3511 + 172.985i) q^{38} +(109.693 + 63.3315i) q^{39} +(-86.9241 + 21.0762i) q^{40} +187.101i q^{41} +(90.8200 - 64.0292i) q^{42} +(341.737 + 341.737i) q^{43} +(-239.866 + 138.487i) q^{44} +(2.40706 - 100.594i) q^{45} +(89.6862 - 155.341i) q^{46} +(-34.5681 + 129.010i) q^{47} +(-33.9411 + 33.9411i) q^{48} +(-115.237 + 323.063i) q^{49} +(-53.0808 - 244.300i) q^{50} +(-180.131 - 311.996i) q^{51} +(163.129 - 43.7104i) q^{52} +(141.320 - 37.8665i) q^{53} +(-27.0000 - 46.7654i) q^{54} +(-370.933 - 679.513i) q^{55} +(25.2586 - 145.993i) q^{56} +(-189.950 + 189.950i) q^{57} +(-55.9201 + 208.696i) q^{58} +(177.224 - 306.962i) q^{59} +(-92.5718 - 97.1106i) q^{60} +(-2.31072 + 1.33410i) q^{61} +(-296.775 - 296.775i) q^{62} +(151.291 + 69.9567i) q^{63} +64.0000i q^{64} +(111.232 + 458.753i) q^{65} +(-359.799 - 207.730i) q^{66} +(153.821 + 574.067i) q^{67} +(-463.982 - 124.324i) q^{68} +269.058 q^{69} +(406.258 + 80.3413i) q^{70} +316.036 q^{71} +(-69.5467 - 18.6350i) q^{72} +(-30.0083 - 111.992i) q^{73} +(424.901 + 245.317i) q^{74} +(277.544 - 252.179i) q^{75} +358.173i q^{76} +(1277.16 - 115.877i) q^{77} +(179.129 + 179.129i) q^{78} +(926.378 - 534.844i) q^{79} +(-178.834 - 4.27921i) q^{80} +(40.5000 - 70.1481i) q^{81} +(-96.8505 + 361.451i) q^{82} +(-710.450 + 710.450i) q^{83} +(208.595 - 76.6830i) q^{84} +(378.419 - 1288.19i) q^{85} +(483.288 + 837.080i) q^{86} +(-313.045 + 83.8801i) q^{87} +(-535.071 + 143.372i) q^{88} +(245.877 + 425.872i) q^{89} +(56.7215 - 193.087i) q^{90} +(-770.497 - 133.306i) q^{91} +(253.671 - 253.671i) q^{92} +(162.941 - 608.104i) q^{93} +(-133.561 + 231.334i) q^{94} +(-1000.84 - 23.9484i) q^{95} +(-83.1384 + 48.0000i) q^{96} +(-217.897 - 217.897i) q^{97} +(-389.850 + 564.458i) q^{98} -623.190i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{5} - 36 q^{7}+O(q^{10}) $ 48 * q - 48 * q^5 - 36 * q^7	$ 48 q - 48 q^{5} - 36 q^{7} + 64 q^{10} - 28 q^{11} + 112 q^{13} - 128 q^{14} + 84 q^{15} + 384 q^{16} - 204 q^{17} + 104 q^{19} - 32 q^{20} - 96 q^{21} - 312 q^{22} - 464 q^{23} - 576 q^{24} - 884 q^{25} - 456 q^{26} - 224 q^{28} - 24 q^{30} + 528 q^{31} - 216 q^{33} - 448 q^{34} + 1256 q^{35} - 1728 q^{36} + 444 q^{37} + 296 q^{38} - 684 q^{39} + 192 q^{42} - 832 q^{43} + 36 q^{45} - 392 q^{46} - 1548 q^{47} - 436 q^{49} - 336 q^{51} + 224 q^{52} + 412 q^{53} - 1296 q^{54} + 1736 q^{55} + 64 q^{56} - 696 q^{57} - 3256 q^{58} + 296 q^{59} + 2592 q^{61} - 304 q^{62} + 792 q^{63} + 236 q^{65} + 652 q^{67} - 816 q^{68} - 1176 q^{69} - 296 q^{70} - 496 q^{71} + 1300 q^{73} - 528 q^{74} + 936 q^{75} + 5392 q^{77} + 672 q^{78} + 11724 q^{79} - 768 q^{80} + 1944 q^{81} - 96 q^{82} + 6272 q^{83} + 48 q^{84} + 128 q^{85} + 176 q^{86} - 3576 q^{87} - 576 q^{88} + 4448 q^{89} - 5856 q^{91} - 1184 q^{92} - 3360 q^{93} + 16 q^{94} + 4572 q^{95} - 4652 q^{97} + 2256 q^{98}+O(q^{100}) $ 48 * q - 48 * q^5 - 36 * q^7 + 64 * q^10 - 28 * q^11 + 112 * q^13 - 128 * q^14 + 84 * q^15 + 384 * q^16 - 204 * q^17 + 104 * q^19 - 32 * q^20 - 96 * q^21 - 312 * q^22 - 464 * q^23 - 576 * q^24 - 884 * q^25 - 456 * q^26 - 224 * q^28 - 24 * q^30 + 528 * q^31 - 216 * q^33 - 448 * q^34 + 1256 * q^35 - 1728 * q^36 + 444 * q^37 + 296 * q^38 - 684 * q^39 + 192 * q^42 - 832 * q^43 + 36 * q^45 - 392 * q^46 - 1548 * q^47 - 436 * q^49 - 336 * q^51 + 224 * q^52 + 412 * q^53 - 1296 * q^54 + 1736 * q^55 + 64 * q^56 - 696 * q^57 - 3256 * q^58 + 296 * q^59 + 2592 * q^61 - 304 * q^62 + 792 * q^63 + 236 * q^65 + 652 * q^67 - 816 * q^68 - 1176 * q^69 - 296 * q^70 - 496 * q^71 + 1300 * q^73 - 528 * q^74 + 936 * q^75 + 5392 * q^77 + 672 * q^78 + 11724 * q^79 - 768 * q^80 + 1944 * q^81 - 96 * q^82 + 6272 * q^83 + 48 * q^84 + 128 * q^85 + 176 * q^86 - 3576 * q^87 - 576 * q^88 + 4448 * q^89 - 5856 * q^91 - 1184 * q^92 - 3360 * q^93 + 16 * q^94 + 4572 * q^95 - 4652 * q^97 + 2256 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	1.93185	+	0.517638i	0.683013	+	0.183013i
$2$	1.93185	+	0.517638i	0.683013	+	0.183013i
$3$	0.776457	+	2.89778i	0.149429	+	0.557678i
$3$	0.776457	+	2.89778i	0.149429	+	0.557678i
$4$	3.46410	+	2.00000i	0.433013	+	0.250000i
$5$	−5.82019	+	9.54596i	−0.520574	+	0.853817i
$5$	−5.82019	+	9.54596i	−0.520574	+	0.853817i
$6$			6.00000i			0.408248i
$7$	−10.6715	−	15.1367i	−0.576208	−	0.817303i
$7$	−10.6715	−	15.1367i	−0.576208	−	0.817303i
$8$	5.65685	+	5.65685i	0.250000	+	0.250000i
$9$	−7.79423	+	4.50000i	−0.288675	+	0.166667i
$10$	−16.1851	+	15.4286i	−0.511818	+	0.487896i
$11$	−34.6217	+	59.9665i	−0.948984	+	1.64369i	−0.201414	+	0.979506i	$0.564553\pi$
$11$	−34.6217	+	59.9665i	−0.948984	+	1.64369i	−0.747571	+	0.664182i	$0.768780\pi$
$12$	−3.10583	+	11.5911i	−0.0747146	+	0.278839i
$13$	29.8548	−	29.8548i	0.636940	−	0.636940i	−0.312860	−	0.949799i	$-0.601287\pi$
$13$	29.8548	−	29.8548i	0.636940	−	0.636940i	0.949799	+	0.312860i	$0.101287\pi$
$14$	−12.7805	−	34.7658i	−0.243981	−	0.663682i
$15$	−32.1812	−	9.45358i	−0.553943	−	0.162727i
$16$	8.00000	+	13.8564i	0.125000	+	0.216506i
$17$	−115.996	+	31.0809i	−1.65489	+	0.443425i	−0.960975	−	0.276636i	$-0.910780\pi$
$17$	−115.996	+	31.0809i	−1.65489	+	0.443425i	−0.693911	+	0.720061i	$0.744114\pi$
$18$	−17.3867	+	4.65874i	−0.227671	+	0.0610042i
$19$	44.7717	+	77.5468i	0.540596	+	0.936340i	0.998870	+	0.0475290i	$0.0151347\pi$
$19$	44.7717	+	77.5468i	0.540596	+	0.936340i	−0.458274	+	0.888811i	$0.651532\pi$
$20$	−39.2537	+	21.4278i	−0.438869	+	0.239570i
$21$	35.5767	−	42.6767i	0.369689	−	0.443467i
$22$	−97.9249	+	97.9249i	−0.948984	+	0.948984i
$23$	23.2125	−	86.6302i	0.210441	−	0.785376i	−0.777281	−	0.629153i	$-0.783402\pi$
$23$	23.2125	−	86.6302i	0.210441	−	0.785376i	0.987722	−	0.156222i	$-0.0499316\pi$
$24$	−12.0000	+	20.7846i	−0.102062	+	0.176777i
$25$	−57.2508	−	111.119i	−0.458006	−	0.888949i
$26$	73.1289	−	42.2210i	0.551606	−	0.318470i
$27$	−19.0919	−	19.0919i	−0.136083	−	0.136083i
$28$	−6.69393	−	73.7780i	−0.0451798	−	0.497955i
$29$			108.029i			0.691742i	0.938282	+	0.345871i	$0.112417\pi$
$29$			108.029i			0.691742i	−0.938282	+	0.345871i	$0.887583\pi$
$30$	−57.2758	−	34.9211i	−0.348569	−	0.212523i
$31$	−181.737	−	104.926i	−1.05293	−	0.607911i	−0.129464	−	0.991584i	$-0.541326\pi$
$31$	−181.737	−	104.926i	−1.05293	−	0.607911i	−0.923469	+	0.383673i	$0.874659\pi$
$32$	8.28221	+	30.9096i	0.0457532	+	0.170753i
$33$	−200.652	−	53.7645i	−1.05845	−	0.283612i
$34$	−240.175			−1.21146
$35$	206.604	−	13.7718i	0.997786	−	0.0665100i
$36$	−36.0000			−0.166667
$37$	236.958	+	63.4927i	1.05286	+	0.282112i	0.743431	−	0.668813i	$-0.233197\pi$
$37$	236.958	+	63.4927i	1.05286	+	0.282112i	0.309424	+	0.950924i	$0.399864\pi$
$38$	46.3511	+	172.985i	0.197872	+	0.738468i
$39$	109.693	+	63.3315i	0.450384	+	0.260030i
$40$	−86.9241	+	21.0762i	−0.343598	+	0.0833108i
$41$			187.101i			0.712689i	0.934355	+	0.356344i	$0.115977\pi$
$41$			187.101i			0.712689i	−0.934355	+	0.356344i	$0.884023\pi$
$42$	90.8200	−	64.0292i	0.333663	−	0.235236i
$43$	341.737	+	341.737i	1.21196	+	1.21196i	0.970381	+	0.241580i	$0.0776658\pi$
$43$	341.737	+	341.737i	1.21196	+	1.21196i	0.241580	+	0.970381i	$0.422334\pi$
$44$	−239.866	+	138.487i	−0.821844	+	0.474492i
$45$	2.40706	−	100.594i	0.00797384	−	0.333238i
$46$	89.6862	−	155.341i	0.287467	−	0.497908i
$47$	−34.5681	+	129.010i	−0.107282	+	0.400384i	−0.998594	−	0.0530076i	$-0.983119\pi$
$47$	−34.5681	+	129.010i	−0.107282	+	0.400384i	0.891312	+	0.453391i	$0.149786\pi$
$48$	−33.9411	+	33.9411i	−0.102062	+	0.102062i
$49$	−115.237	+	323.063i	−0.335968	+	0.941873i
$50$	−53.0808	−	244.300i	−0.150135	−	0.690984i
$51$	−180.131	−	311.996i	−0.494577	−	0.856632i
$52$	163.129	−	43.7104i	0.435038	−	0.116568i
$53$	141.320	−	37.8665i	0.366260	−	0.0981391i	−0.0709950	−	0.997477i	$-0.522617\pi$
$53$	141.320	−	37.8665i	0.366260	−	0.0981391i	0.437255	+	0.899338i	$0.355951\pi$
$54$	−27.0000	−	46.7654i	−0.0680414	−	0.117851i
$55$	−370.933	−	679.513i	−0.909393	−	1.66592i
$56$	25.2586	−	145.993i	0.0602737	−	0.348378i
$57$	−189.950	+	189.950i	−0.441395	+	0.441395i
$58$	−55.9201	+	208.696i	−0.126598	+	0.472469i
$59$	177.224	−	306.962i	0.391062	−	0.677339i	−0.601528	−	0.798852i	$-0.705441\pi$
$59$	177.224	−	306.962i	0.391062	−	0.677339i	0.992590	+	0.121513i	$0.0387745\pi$
$60$	−92.5718	−	97.1106i	−0.199183	−	0.208949i
$61$	−2.31072	+	1.33410i	−0.00485013	+	0.00280022i	−0.502423	−	0.864622i	$-0.667558\pi$
$61$	−2.31072	+	1.33410i	−0.00485013	+	0.00280022i	0.497573	+	0.867422i	$0.334225\pi$
$62$	−296.775	−	296.775i	−0.607911	−	0.607911i
$63$	151.291	+	69.9567i	0.302554	+	0.139900i
$64$			64.0000i			0.125000i
$65$	111.232	+	458.753i	0.212256	+	0.875404i
$66$	−359.799	−	207.730i	−0.671033	−	0.387421i
$67$	153.821	+	574.067i	0.280481	+	1.04677i	0.952079	+	0.305853i	$0.0989416\pi$
$67$	153.821	+	574.067i	0.280481	+	1.04677i	−0.671598	+	0.740916i	$0.734392\pi$
$68$	−463.982	−	124.324i	−0.827443	−	0.221713i
$69$	269.058			0.469432
$70$	406.258	+	80.3413i	0.693673	+	0.137180i
$71$	316.036			0.528261			0.264130	−	0.964487i	$-0.414915\pi$
$71$	316.036			0.528261			0.264130	+	0.964487i	$0.414915\pi$
$72$	−69.5467	−	18.6350i	−0.113835	−	0.0305021i
$73$	−30.0083	−	111.992i	−0.0481124	−	0.179558i	0.937688	−	0.347478i	$-0.112962\pi$
$73$	−30.0083	−	111.992i	−0.0481124	−	0.179558i	−0.985801	+	0.167920i	$0.946295\pi$
$74$	424.901	+	245.317i	0.667483	+	0.385372i
$75$	277.544	−	252.179i	0.427307	−	0.388255i
$76$			358.173i			0.540596i
$77$	1277.16	−	115.877i	1.89020	−	0.171500i
$78$	179.129	+	179.129i	0.260030	+	0.260030i
$79$	926.378	−	534.844i	1.31931	−	0.761705i	0.335694	−	0.941971i	$-0.391029\pi$
$79$	926.378	−	534.844i	1.31931	−	0.761705i	0.983618	+	0.180266i	$0.0576959\pi$
$80$	−178.834	−	4.27921i	−0.249928	−	0.00598038i
$81$	40.5000	−	70.1481i	0.0555556	−	0.0962250i
$82$	−96.8505	+	361.451i	−0.130431	+	0.486775i
$83$	−710.450	+	710.450i	−0.939542	+	0.939542i	−0.998274	−	0.0587315i	$-0.981294\pi$
$83$	−710.450	+	710.450i	−0.939542	+	0.939542i	0.0587315	+	0.998274i	$0.481294\pi$
$84$	208.595	−	76.6830i	0.270947	−	0.0996047i
$85$	378.419	−	1288.19i	0.482886	−	1.64380i
$86$	483.288	+	837.080i	0.605981	+	1.04959i
$87$	−313.045	+	83.8801i	−0.385769	+	0.103367i
$88$	−535.071	+	143.372i	−0.648168	+	0.173676i
$89$	245.877	+	425.872i	0.292842	+	0.507217i	0.974481	−	0.224472i	$-0.0720657\pi$
$89$	245.877	+	425.872i	0.292842	+	0.507217i	−0.681639	+	0.731689i	$0.738732\pi$
$90$	56.7215	−	193.087i	0.0664330	−	0.226146i
$91$	−770.497	−	133.306i	−0.887583	−	0.153563i
$92$	253.671	−	253.671i	0.287467	−	0.287467i
$93$	162.941	−	608.104i	0.181679	−	0.678037i
$94$	−133.561	+	231.334i	−0.146551	+	0.253833i
$95$	−1000.84	−	23.9484i	−1.08088	−	0.0258638i
$96$	−83.1384	+	48.0000i	−0.0883883	+	0.0510310i
$97$	−217.897	−	217.897i	−0.228084	−	0.228084i	0.583808	−	0.811892i	$-0.301562\pi$
$97$	−217.897	−	217.897i	−0.228084	−	0.228084i	−0.811892	+	0.583808i	$0.801562\pi$
$98$	−389.850	+	564.458i	−0.401845	+	0.581825i
$99$		−	623.190i		−	0.632656i
$100$	23.9147	−	499.428i	0.0239147	−	0.499428i
$101$	−196.009	−	113.166i	−0.193105	−	0.111489i	0.400330	−	0.916371i	$-0.368895\pi$
$101$	−196.009	−	113.166i	−0.193105	−	0.111489i	−0.593435	+	0.804882i	$0.702229\pi$
$102$	−186.485	−	695.973i	−0.181028	−	0.675604i
$103$	705.702	+	189.092i	0.675096	+	0.180891i	0.580049	−	0.814581i	$-0.303033\pi$
$103$	705.702	+	189.092i	0.675096	+	0.180891i	0.0950468	+	0.995473i	$0.469700\pi$
$104$	337.768			0.318470
$105$	200.327	+	588.000i	0.186190	+	0.546504i
$106$	292.610			0.268121
$107$	1969.83	+	527.815i	1.77973	+	0.476876i	0.990534	−	0.137269i	$-0.0438326\pi$
$107$	1969.83	+	527.815i	1.77973	+	0.476876i	0.789193	+	0.614146i	$0.210499\pi$
$108$	−27.9525	−	104.320i	−0.0249049	−	0.0929463i
$109$	−896.635	−	517.673i	−0.787909	−	0.454899i	0.0513170	−	0.998682i	$-0.483658\pi$
$109$	−896.635	−	517.673i	−0.787909	−	0.454899i	−0.839226	+	0.543783i	$0.816991\pi$
$110$	−364.846	−	1504.73i	−0.316243	−	1.30427i
$111$			735.951i			0.629309i
$112$	124.368	−	268.962i	0.104925	−	0.226916i
$113$	366.552	+	366.552i	0.305153	+	0.305153i	0.843026	−	0.537873i	$-0.180772\pi$
$113$	366.552	+	366.552i	0.305153	+	0.305153i	−0.537873	+	0.843026i	$0.680772\pi$
$114$	−465.281	+	268.630i	−0.382259	+	0.220698i
$115$	691.867	+	725.789i	0.561017	+	0.588524i
$116$	−216.059	+	374.224i	−0.172936	+	0.299533i
$117$	−98.3484	+	367.041i	−0.0777121	+	0.290025i
$118$	501.266	−	501.266i	0.391062	−	0.391062i
$119$	1708.31	+	1424.10i	1.31597	+	1.09704i
$120$	−128.567	−	235.522i	−0.0978041	−	0.179168i
$121$	−1731.82	−	2999.60i	−1.30114	−	2.25364i
$122$	−5.15455	+	1.38116i	−0.00382517	+	0.00102495i
$123$	−542.176	+	145.276i	−0.397450	+	0.106497i
$124$	−419.704	−	726.948i	−0.303956	−	0.526467i
$125$	1393.94	+	100.217i	0.997426	+	0.0717098i
$126$	256.060	+	213.460i	0.181045	+	0.150925i
$127$	754.300	−	754.300i	0.527034	−	0.527034i	−0.392653	−	0.919687i	$-0.628443\pi$
$127$	754.300	−	754.300i	0.527034	−	0.527034i	0.919687	+	0.392653i	$0.128443\pi$
$128$	−33.1288	+	123.639i	−0.0228766	+	0.0853766i
$129$	−724.933	+	1255.62i	−0.494781	+	0.856986i
$130$	−22.5841	+	943.820i	−0.0152366	+	0.636758i
$131$	−129.700	+	74.8822i	−0.0865032	+	0.0499426i	−0.542628	−	0.839973i	$-0.682571\pi$
$131$	−129.700	+	74.8822i	−0.0865032	+	0.0499426i	0.456124	+	0.889916i	$0.349237\pi$
$132$	−587.549	−	587.549i	−0.387421	−	0.387421i
$133$	696.018	−	1505.24i	0.453778	−	0.981358i
$134$			1188.64i			0.766288i
$135$	293.369	−	71.1320i	0.187031	−	0.0453487i
$136$	−831.990	−	480.350i	−0.524578	−	0.302865i
$137$	−550.276	−	2053.66i	−0.343163	−	1.28070i	−0.894744	−	0.446579i	$-0.852642\pi$
$137$	−550.276	−	2053.66i	−0.343163	−	1.28070i	0.551581	−	0.834121i	$-0.314025\pi$
$138$	519.781	+	139.275i	0.320628	+	0.0859121i
$139$	−1732.29			−1.05706			−0.528528	−	0.848916i	$-0.677256\pi$
$139$	−1732.29			−1.05706			−0.528528	+	0.848916i	$0.677256\pi$
$140$	743.242	+	365.502i	0.448681	+	0.220647i
$141$	−400.683			−0.239316
$142$	610.534	+	163.592i	0.360809	+	0.0966785i
$143$	756.663	+	2823.91i	0.442485	+	1.65138i
$144$	−124.708	−	72.0000i	−0.0721688	−	0.0416667i
$145$	−1031.24	−	628.751i	−0.590621	−	0.360103i
$146$		−	231.886i		−	0.131445i
$147$	−1025.64	−	83.0871i	−0.575465	−	0.0466184i
$148$	693.861	+	693.861i	0.385372	+	0.385372i
$149$	−394.294	+	227.645i	−0.216791	+	0.125164i	−0.604463	−	0.796633i	$-0.706612\pi$
$149$	−394.294	+	227.645i	−0.216791	+	0.125164i	0.387673	+	0.921797i	$0.373279\pi$
$150$	666.712	−	343.505i	0.362912	−	0.186980i
$151$	−1153.28	+	1997.55i	−0.621542	+	1.07654i	0.367656	+	0.929962i	$0.380160\pi$
$151$	−1153.28	+	1997.55i	−0.621542	+	1.07654i	−0.989199	+	0.146581i	$0.953173\pi$
$152$	−185.404	+	691.938i	−0.0989360	+	0.369234i
$153$	764.232	−	764.232i	0.403820	−	0.403820i
$154$	2527.26	+	437.248i	1.32242	+	0.228795i
$155$	2059.36	−	1124.17i	1.06717	−	0.582549i
$156$	253.326	+	438.773i	0.130015	+	0.225192i
$157$	−1640.13	+	439.471i	−0.833736	+	0.223399i	−0.650343	−	0.759641i	$-0.725375\pi$
$157$	−1640.13	+	439.471i	−0.833736	+	0.223399i	−0.183393	+	0.983040i	$0.558708\pi$
$158$	2066.48	−	553.712i	1.04051	−	0.278803i
$159$	219.458	+	380.112i	0.109460	+	0.189590i
$160$	−343.266	−	100.838i	−0.169610	−	0.0498248i
$161$	−1559.00	+	573.117i	−0.763147	+	0.280546i
$162$	114.551	−	114.551i	0.0555556	−	0.0555556i
$163$	−505.087	+	1885.01i	−0.242709	+	0.905801i	0.731813	+	0.681506i	$0.238675\pi$
$163$	−505.087	+	1885.01i	−0.242709	+	0.905801i	−0.974521	+	0.224295i	$0.927992\pi$
$164$	−374.202	+	648.136i	−0.178172	+	0.308603i
$165$	1681.06	−	1602.49i	0.793156	−	0.756085i
$166$	−1740.24	+	1004.73i	−0.813668	+	0.469771i
$167$	−1160.20	−	1160.20i	−0.537599	−	0.537599i	0.385224	−	0.922823i	$-0.374124\pi$
$167$	−1160.20	−	1160.20i	−0.537599	−	0.537599i	−0.922823	+	0.385224i	$0.874124\pi$
$168$	442.668	−	40.1636i	0.203289	−	0.0184446i
$169$			414.388i			0.188615i
$170$	1397.86	−	2292.70i	0.630654	−	1.03437i
$171$	−697.922	−	402.945i	−0.312113	−	0.180199i
$172$	500.337	+	1867.28i	0.221804	+	0.827785i
$173$	−2366.11	−	633.998i	−1.03984	−	0.278624i	−0.301793	−	0.953374i	$-0.597585\pi$
$173$	−2366.11	−	633.998i	−1.03984	−	0.278624i	−0.738047	+	0.674749i	$0.764252\pi$
$174$	−648.176			−0.282403
$175$	−1071.01	+	2052.39i	−0.462634	+	0.886550i
$176$	−1107.89			−0.474492
$177$	1027.11	+	275.214i	0.436173	+	0.116872i
$178$	254.551	+	949.996i	0.107188	+	0.400029i
$179$	1693.09	+	977.505i	0.706968	+	0.408168i	0.809938	−	0.586516i	$-0.199501\pi$
$179$	1693.09	+	977.505i	0.706968	+	0.408168i	−0.102969	+	0.994685i	$0.532834\pi$
$180$	209.527	−	343.655i	0.0867623	−	0.142303i
$181$		−	141.594i		−	0.0581468i	−0.999577	−	0.0290734i	$-0.990744\pi$
$181$		−	141.594i		−	0.0581468i	0.999577	−	0.0290734i	$-0.00925566\pi$
$182$	−1419.48	−	656.365i	−0.578126	−	0.267324i
$183$	−5.66009	−	5.66009i	−0.00228637	−	0.00228637i
$184$	621.364	−	358.745i	0.248954	−	0.143734i
$185$	−1985.24	+	1892.45i	−0.788960	+	0.752085i
$186$	629.555	−	1090.42i	0.248179	−	0.429858i
$187$	2152.15	−	8031.92i	0.841607	−	3.14092i
$188$	−377.767	+	377.767i	−0.146551	+	0.146551i
$189$	−85.2478	+	492.727i	−0.0328088	+	0.189633i
$190$	−1921.08	−	564.337i	−0.733524	−	0.215481i
$191$	−1342.35	−	2325.01i	−0.508527	−	0.880795i	−0.999951	−	0.00987445i	$-0.996857\pi$
$191$	−1342.35	−	2325.01i	−0.508527	−	0.880795i	0.491424	−	0.870920i	$-0.336477\pi$
$192$	−185.458	+	49.6933i	−0.0697097	+	0.0186787i
$193$	−1317.40	+	352.997i	−0.491340	+	0.131654i	−0.495978	−	0.868335i	$-0.665190\pi$
$193$	−1317.40	+	352.997i	−0.491340	+	0.131654i	0.00463795	+	0.999989i	$0.498524\pi$
$194$	−308.153	−	533.737i	−0.114042	−	0.197526i
$195$	−1243.00	+	678.527i	−0.456476	+	0.249181i
$196$	−1045.32	+	888.647i	−0.380947	+	0.323851i
$197$	−2623.35	+	2623.35i	−0.948759	+	0.948759i	−0.998750	−	0.0499903i	$-0.984081\pi$
$197$	−2623.35	+	2623.35i	−0.948759	+	0.948759i	0.0499903	+	0.998750i	$0.484081\pi$
$198$	322.587	−	1203.91i	0.115784	−	0.432112i
$199$	−1677.42	+	2905.38i	−0.597535	+	1.03496i	0.395649	+	0.918402i	$0.370520\pi$
$199$	−1677.42	+	2905.38i	−0.597535	+	1.03496i	−0.993184	+	0.116559i	$0.962814\pi$
$200$	304.722	−	952.441i	0.107736	−	0.336739i
$201$	−1544.08	+	891.478i	−0.541847	+	0.312836i
$202$	−320.081	−	320.081i	−0.111489	−	0.111489i
$203$	1635.20	−	1152.84i	0.565363	−	0.398588i
$204$		−	1441.05i		−	0.494577i
$205$	−1786.06	−	1088.96i	−0.608506	−	0.371007i
$206$	1265.43	+	730.597i	0.427994	+	0.247102i
$207$	208.912	+	779.672i	0.0701469	+	0.261792i
$208$	652.518	+	174.842i	0.217519	+	0.0582840i
$209$	−6200.28			−2.05207
$210$	82.6305	+	1239.63i	0.0271526	+	0.407344i
$211$	−1376.38			−0.449070			−0.224535	−	0.974466i	$-0.572086\pi$
$211$	−1376.38			−0.449070			−0.224535	+	0.974466i	$0.572086\pi$
$212$	565.279	+	151.466i	0.183130	+	0.0490695i
$213$	245.388	+	915.801i	0.0789376	+	0.294599i
$214$	3532.20	+	2039.32i	1.12830	+	0.651425i
$215$	−5251.18	+	1273.23i	−1.66571	+	0.403878i
$216$		−	216.000i		−	0.0680414i
$217$	351.183	+	3870.61i	0.109861	+	1.21085i
$218$	−1464.20	−	1464.20i	−0.454899	−	0.454899i
$219$	301.229	−	173.915i	0.0929460	−	0.0536624i
$220$	74.0767	−	3095.77i	0.0227011	−	0.948713i
$221$	−2535.11	+	4390.93i	−0.771627	+	1.33650i
$222$	−380.956	+	1421.75i	−0.115172	+	0.429826i
$223$	1452.13	−	1452.13i	0.436062	−	0.436062i	−0.454622	−	0.890684i	$-0.650226\pi$
$223$	1452.13	−	1452.13i	0.436062	−	0.436062i	0.890684	+	0.454622i	$0.150226\pi$
$224$	379.485	−	455.218i	0.113194	−	0.135784i
$225$	946.260	+	608.455i	0.280373	+	0.180283i
$226$	518.382	+	897.865i	0.152576	+	0.264270i
$227$	3593.17	−	962.788i	1.05060	−	0.281509i	0.308103	−	0.951353i	$-0.400306\pi$
$227$	3593.17	−	962.788i	1.05060	−	0.281509i	0.742502	+	0.669844i	$0.233639\pi$
$228$	−1037.91	+	278.106i	−0.301478	+	0.0807809i
$229$	−623.924	−	1080.67i	−0.180044	−	0.311845i	0.761851	−	0.647752i	$-0.224291\pi$
$229$	−623.924	−	1080.67i	−0.180044	−	0.311845i	−0.941895	+	0.335907i	$0.890957\pi$
$230$	960.889	+	1760.25i	0.275474	+	0.504642i
$231$	1327.45	+	3610.95i	0.378093	+	1.02850i
$232$	−611.106	+	611.106i	−0.172936	+	0.172936i
$233$	917.961	−	3425.88i	0.258101	−	0.963248i	−0.708237	−	0.705974i	$-0.750509\pi$
$233$	917.961	−	3425.88i	0.258101	−	0.963248i	0.966339	−	0.257273i	$-0.0828240\pi$
$234$	−379.989	+	658.160i	−0.106157	+	0.183869i
$235$	−1030.33	−	1080.85i	−0.286006	−	0.300029i
$236$	1227.85	−	708.897i	0.338669	−	0.195531i
$237$	2269.15	+	2269.15i	0.621930	+	0.621930i
$238$	2563.03	+	3635.45i	0.698053	+	0.990130i
$239$			5118.27i			1.38524i	0.721300	+	0.692622i	$0.243545\pi$
$239$			5118.27i			1.38524i	−0.721300	+	0.692622i	$0.756455\pi$
$240$	−126.457	−	521.544i	−0.0340115	−	0.140273i
$241$	−1607.54	−	928.111i	−0.429670	−	0.248070i	0.269536	−	0.962990i	$-0.413130\pi$
$241$	−1607.54	−	928.111i	−0.429670	−	0.248070i	−0.699206	+	0.714920i	$0.746463\pi$
$242$	−1792.91	−	6691.24i	−0.476251	−	1.77739i
$243$	234.720	+	62.8930i	0.0619642	+	0.0166032i
$244$	−10.6728			−0.00280022
$245$	−2413.24	−	2980.33i	−0.629291	−	0.777170i
$246$	−1122.60			−0.290954
$247$	3651.79	+	978.494i	0.940720	+	0.252065i
$248$	−434.509	−	1621.61i	−0.111255	−	0.415211i
$249$	−2610.36	−	1507.09i	−0.664357	−	0.383567i
$250$	2641.02	+	915.164i	0.668131	+	0.231520i
$251$		−	7213.85i		−	1.81408i	−0.421044	−	0.907040i	$-0.638336\pi$
$251$		−	7213.85i		−	1.81408i	0.421044	−	0.907040i	$-0.361664\pi$
$252$	384.175	+	544.920i	0.0960347	+	0.136217i
$253$	4391.25	+	4391.25i	1.09121	+	1.09121i
$254$	1847.65	−	1066.74i	0.456425	−	0.263517i
$255$	4026.70	+	96.3524i	0.988870	+	0.0236620i
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	96.3591	−	359.617i	0.0233880	−	0.0872852i	−0.953245	−	0.302197i	$-0.902280\pi$
$257$	96.3591	−	359.617i	0.0233880	−	0.0872852i	0.976633	+	0.214912i	$0.0689465\pi$
$258$	−2050.42	+	2050.42i	−0.494781	+	0.494781i
$259$	−1567.64	−	4264.32i	−0.376093	−	1.02306i
$260$	−532.186	+	1811.63i	−0.126941	+	0.432125i
$261$	−486.132	−	842.005i	−0.115290	−	0.199689i
$262$	−289.322	+	77.5237i	−0.0682229	+	0.0182803i
$263$	5144.46	−	1378.45i	1.20616	−	0.323190i	0.400907	−	0.916119i	$-0.368695\pi$
$263$	5144.46	−	1378.45i	1.20616	−	0.323190i	0.805255	+	0.592928i	$0.202028\pi$
$264$	−830.920	−	1439.20i	−0.193711	−	0.335517i
$265$	−461.036	+	1569.42i	−0.106872	+	0.363807i
$266$	2123.77	−	2547.61i	0.489537	−	0.587233i
$267$	−1043.17	+	1043.17i	−0.239104	+	0.239104i
$268$	−615.284	+	2296.27i	−0.140240	+	0.523384i
$269$	−3320.24	+	5750.82i	−0.752560	+	1.30347i	0.194019	+	0.980998i	$0.437848\pi$
$269$	−3320.24	+	5750.82i	−0.752560	+	1.30347i	−0.946578	+	0.322474i	$0.895486\pi$
$270$	603.566	+	14.4423i	0.136044	+	0.00325531i
$271$	2172.50	−	1254.29i	0.486973	−	0.281154i	−0.236345	−	0.971669i	$-0.575949\pi$
$271$	2172.50	−	1254.29i	0.486973	−	0.281154i	0.723318	+	0.690515i	$0.242616\pi$
$272$	−1358.63	−	1358.63i	−0.302865	−	0.302865i
$273$	−211.968	−	2336.23i	−0.0469923	−	0.517932i
$274$		−	4252.21i		−	0.937538i
$275$	8645.51	+	413.983i	1.89580	+	0.0907786i
$276$	932.046	+	538.117i	0.203270	+	0.117358i
$277$	−523.152	−	1952.43i	−0.113477	−	0.423502i	0.885691	−	0.464274i	$-0.153685\pi$
$277$	−523.152	−	1952.43i	−0.113477	−	0.423502i	−0.999168	+	0.0407722i	$0.987018\pi$
$278$	−3346.52	−	896.698i	−0.721982	−	0.193455i
$279$	1888.67			0.405274
$280$	1246.64	+	1090.83i	0.266074	+	0.232819i
$281$	−3663.27			−0.777695			−0.388847	−	0.921302i	$-0.627127\pi$
$281$	−3663.27			−0.777695			−0.388847	+	0.921302i	$0.627127\pi$
$282$	−774.059	−	207.409i	−0.163456	−	0.0437979i
$283$	2066.95	+	7713.98i	0.434161	+	1.62031i	0.743065	+	0.669219i	$0.233371\pi$
$283$	2066.95	+	7713.98i	0.434161	+	1.62031i	−0.308904	+	0.951093i	$0.599962\pi$
$284$	1094.78	+	632.071i	0.228744	+	0.132065i
$285$	−707.711	−	2918.80i	−0.147092	−	0.606649i
$286$			5847.04i			1.20889i
$287$	2832.08	−	1996.65i	0.582483	−	0.410657i
$288$	−203.647	−	203.647i	−0.0416667	−	0.0416667i
$289$	8234.16	−	4754.00i	1.67599	−	0.967636i
$290$	−1666.74	−	1748.46i	−0.337498	−	0.354046i
$291$	462.230	−	800.606i	0.0931148	−	0.161280i
$292$	120.033	−	447.970i	0.0240562	−	0.0897789i
$293$	4245.41	−	4245.41i	0.846482	−	0.846482i	−0.143210	−	0.989692i	$-0.545742\pi$
$293$	4245.41	−	4245.41i	0.846482	−	0.846482i	0.989692	+	0.143210i	$0.0457425\pi$
$294$	−1938.38	−	691.422i	−0.384518	−	0.137158i
$295$	1898.76	+	3478.35i	0.374747	+	0.686500i
$296$	981.267	+	1699.61i	0.192686	+	0.333742i
$297$	1805.87	−	483.880i	0.352818	−	0.0945373i
$298$	−879.555	+	235.676i	−0.170977	+	0.0458132i
$299$	−1893.32	−	3279.33i	−0.366199	−	0.634275i
$300$	1465.80	−	318.485i	0.282093	−	0.0612924i
$301$	1525.90	−	8819.60i	0.292197	−	1.68888i
$302$	−3261.98	+	3261.98i	−0.621542	+	0.621542i
$303$	175.737	−	655.859i	0.0333195	−	0.124350i
$304$	−716.347	+	1240.75i	−0.135149	+	0.234085i
$305$	0.713610	−	29.8228i	0.000133971	−	0.00559884i
$306$	1871.98	−	1080.79i	0.349718	−	0.201910i
$307$	5455.44	+	5455.44i	1.01420	+	1.01420i	0.999898	+	0.0142985i	$0.00455150\pi$
$307$	5455.44	+	5455.44i	1.01420	+	1.01420i	0.0142985	+	0.999898i	$0.495449\pi$
$308$	4655.96	+	2152.91i	0.861357	+	0.398290i
$309$			2191.79i			0.403516i
$310$	4560.29	−	1105.72i	0.835507	−	0.202582i
$311$	3802.70	+	2195.49i	0.693348	+	0.400304i	0.804865	−	0.593458i	$-0.202238\pi$
$311$	3802.70	+	2195.49i	0.693348	+	0.400304i	−0.111517	+	0.993762i	$0.535571\pi$
$312$	262.262	+	978.776i	0.0475887	+	0.177604i
$313$	−3500.46	−	937.944i	−0.632132	−	0.169379i	−0.0714952	−	0.997441i	$-0.522777\pi$
$313$	−3500.46	−	937.944i	−0.632132	−	0.169379i	−0.560637	+	0.828062i	$0.689444\pi$
$314$	−3395.97			−0.610337
$315$	−1548.35	+	1037.06i	−0.276951	+	0.185497i
$316$	4278.76			0.761705
$317$	−2054.81	−	550.586i	−0.364069	−	0.0975520i	0.0721470	−	0.997394i	$-0.477015\pi$
$317$	−2054.81	−	550.586i	−0.364069	−	0.0975520i	−0.436216	+	0.899842i	$0.643682\pi$
$318$	227.199	+	847.919i	0.0400651	+	0.149525i
$319$	−6478.13	−	3740.15i	−1.13701	−	0.656453i
$320$	−610.942	−	372.492i	−0.106727	−	0.0650717i
$321$			6117.96i			1.06377i
$322$	−3308.43	+	300.176i	−0.572583	+	0.0519508i
$323$	−7603.54	−	7603.54i	−1.30982	−	1.30982i
$324$	280.592	−	162.000i	0.0481125	−	0.0277778i
$325$	−5026.63	−	1608.21i	−0.857929	−	0.274485i
$326$	−1951.51	+	3380.11i	−0.331546	+	0.574255i
$327$	803.901	−	3000.20i	0.135951	−	0.507374i
$328$	−1058.40	+	1058.40i	−0.178172	+	0.178172i
$329$	2321.67	−	853.487i	0.389052	−	0.143022i
$330$	4077.08	−	2225.60i	0.680109	−	0.371258i
$331$	4367.81	+	7565.27i	0.725307	+	1.25627i	0.958848	+	0.283921i	$0.0916354\pi$
$331$	4367.81	+	7565.27i	0.725307	+	1.25627i	−0.233541	+	0.972347i	$0.575031\pi$
$332$	−3881.97	+	1040.17i	−0.641719	+	0.171948i
$333$	−2132.62	+	571.434i	−0.350952	+	0.0940372i
$334$	−1640.77	−	2841.90i	−0.268800	−	0.465574i
$335$	−6375.29	−	1872.81i	−1.03976	−	0.305441i
$336$	875.959	+	151.552i	0.142225	+	0.0246066i
$337$	6819.39	−	6819.39i	1.10230	−	1.10230i	0.108171	−	0.994132i	$-0.465501\pi$
$337$	6819.39	−	6819.39i	1.10230	−	1.10230i	0.994132	−	0.108171i	$-0.0344993\pi$
$338$	−214.503	+	800.536i	−0.0345190	+	0.128827i
$339$	−777.574	+	1346.80i	−0.124578	+	0.215776i
$340$	3887.25	−	3705.57i	0.620047	−	0.591067i
$341$	12584.1	−	7265.42i	1.99843	−	1.15380i
$342$	−1139.70	−	1139.70i	−0.180199	−	0.180199i
$343$	6119.84	−	1703.27i	0.963383	−	0.268128i
$344$			3866.31i			0.605981i
$345$	−1565.97	+	2568.42i	−0.244374	+	0.400809i
$346$	−4242.80	−	2449.58i	−0.659232	−	0.380608i
$347$	−31.2106	−	116.480i	−0.00482845	−	0.0180200i	0.963470	−	0.267818i	$-0.0863025\pi$
$347$	−31.2106	−	116.480i	−0.00482845	−	0.0180200i	−0.968298	+	0.249798i	$0.919636\pi$
$348$	−1252.18	−	335.520i	−0.192885	−	0.0516833i
$349$	4296.66			0.659012			0.329506	−	0.944153i	$-0.393118\pi$
$349$	4296.66			0.659012			0.329506	+	0.944153i	$0.393118\pi$
$350$	−3131.43	+	3410.52i	−0.478234	+	0.520857i
$351$	−1139.97			−0.173353
$352$	−2140.29	−	573.488i	−0.324084	−	0.0868381i
$353$	−2650.85	−	9893.12i	−0.399690	−	1.49167i	−0.813642	−	0.581366i	$-0.802518\pi$
$353$	−2650.85	−	9893.12i	−0.399690	−	1.49167i	0.413952	−	0.910299i	$-0.364148\pi$
$354$	1841.77	+	1063.35i	0.276522	+	0.159650i
$355$	−1839.39	+	3016.86i	−0.274999	+	0.451038i
$356$			1967.02i			0.292842i
$357$	−2800.31	+	6056.06i	−0.415149	+	0.897817i
$358$	2764.80	+	2764.80i	0.408168	+	0.408168i
$359$	3863.08	−	2230.35i	0.567927	−	0.327893i	−0.188394	−	0.982094i	$-0.560328\pi$
$359$	3863.08	−	2230.35i	0.567927	−	0.327893i	0.756321	+	0.654201i	$0.226995\pi$
$360$	582.663	−	555.431i	0.0853029	−	0.0813160i
$361$	−579.508	+	1003.74i	−0.0844887	+	0.146339i
$362$	73.2943	−	273.538i	0.0106416	−	0.0397150i
$363$	7347.49	−	7347.49i	1.06238	−	1.06238i
$364$	−2402.47	−	2002.78i	−0.345944	−	0.288390i
$365$	1243.73	+	365.359i	0.178356	+	0.0523939i
$366$	−8.00458	−	13.8643i	−0.00114319	−	0.00198006i
$367$	5284.53	−	1415.98i	0.751635	−	0.201400i	0.137392	−	0.990517i	$-0.456128\pi$
$367$	5284.53	−	1415.98i	0.751635	−	0.201400i	0.614243	+	0.789117i	$0.289461\pi$
$368$	1386.08	−	371.400i	0.196344	−	0.0526102i
$369$	−841.954	−	1458.31i	−0.118781	−	0.205735i
$370$	−4814.79	+	2628.30i	−0.676511	+	0.369294i
$371$	−2081.27	−	1735.02i	−0.291251	−	0.242797i
$372$	1780.65	−	1780.65i	0.248179	−	0.248179i
$373$	−561.628	+	2096.03i	−0.0779625	+	0.290960i	−0.993889	−	0.110387i	$-0.964791\pi$
$373$	−561.628	+	2096.03i	−0.0779625	+	0.290960i	0.915926	+	0.401347i	$0.131458\pi$
$374$	8315.25	−	14402.4i	1.14966	−	1.99126i
$375$	791.930	+	4117.16i	0.109054	+	0.566957i
$376$	−925.337	+	534.244i	−0.126917	+	0.0732753i
$377$	3225.19	+	3225.19i	0.440598	+	0.440598i
$378$	−419.740	+	907.748i	−0.0571141	+	0.123517i
$379$		−	1829.90i		−	0.248010i	−0.992282	−	0.124005i	$-0.960426\pi$
$379$		−	1829.90i		−	0.248010i	0.992282	−	0.124005i	$-0.0395738\pi$
$380$	−3419.11	−	2084.64i	−0.461570	−	0.281420i
$381$	2771.47	+	1600.11i	0.372669	+	0.215161i
$382$	−1389.70	−	5186.42i	−0.186134	−	0.694661i
$383$	−2641.09	−	707.678i	−0.352359	−	0.0944143i	0.0782980	−	0.996930i	$-0.475051\pi$
$383$	−2641.09	−	707.678i	−0.352359	−	0.0944143i	−0.430657	+	0.902516i	$0.641718\pi$
$384$	−384.000			−0.0510310
$385$	−6327.14	+	12866.1i	−0.837561	+	1.70317i
$386$	−2727.75			−0.359686
$387$	−4201.39	−	1125.76i	−0.551857	−	0.147870i
$388$	−319.024	−	1190.61i	−0.0417422	−	0.155784i
$389$	9531.33	+	5502.92i	1.24231	+	0.717247i	0.969564	−	0.244840i	$-0.0787353\pi$
$389$	9531.33	+	5502.92i	1.24231	+	0.717247i	0.272744	+	0.962087i	$0.412069\pi$
$390$	−2752.52	+	667.392i	−0.357382	+	0.0866531i
$391$			10770.2i			1.39302i
$392$	−2479.40	+	1175.64i	−0.319460	+	0.151476i
$393$	−317.698	−	317.698i	−0.0407780	−	0.0407780i
$394$	−6425.86	+	3709.97i	−0.821650	+	0.474380i
$395$	−286.089	+	11956.1i	−0.0364423	+	1.52297i
$396$	1246.38	−	2158.79i	0.158164	−	0.273948i
$397$	−3625.74	+	13531.5i	−0.458365	+	1.71064i	0.219637	+	0.975582i	$0.429513\pi$
$397$	−3625.74	+	13531.5i	−0.458365	+	1.71064i	−0.678002	+	0.735060i	$0.737154\pi$
$398$	−4744.47	+	4744.47i	−0.597535	+	0.597535i
$399$	4902.27	+	848.153i	0.615089	+	0.106418i
$400$	1081.70	−	1682.24i	0.135212	−	0.210280i
$401$	−3567.85	−	6179.70i	−0.444314	−	0.769575i	0.553690	−	0.832723i	$-0.313219\pi$
$401$	−3567.85	−	6179.70i	−0.444314	−	0.769575i	−0.998004	+	0.0631478i	$0.979886\pi$
$402$	−3444.40	+	922.926i	−0.427342	+	0.114506i
$403$	−8558.25	+	2293.18i	−1.05786	+	0.283452i
$404$	−452.663	−	784.036i	−0.0557447	−	0.0965526i
$405$	433.913	+	794.886i	0.0532378	+	0.0975265i
$406$	3755.72	−	1380.67i	0.459097	−	0.168772i
$407$	−12011.3	+	12011.3i	−1.46285	+	1.46285i
$408$	745.942	−	2783.89i	0.0905138	−	0.337802i
$409$	1873.99	−	3245.85i	0.226560	−	0.392413i	−0.730226	−	0.683205i	$-0.760585\pi$
$409$	1873.99	−	3245.85i	0.226560	−	0.392413i	0.956786	+	0.290792i	$0.0939188\pi$
$410$	−2886.71	−	3028.24i	−0.347718	−	0.364767i
$411$	5523.78	−	3189.16i	0.662939	−	0.382748i
$412$	2066.44	+	2066.44i	0.247102	+	0.247102i
$413$	−6537.63	+	593.164i	−0.778924	+	0.0706723i
$414$			1614.35i			0.191645i
$415$	−2646.98	−	10916.9i	−0.313096	−	1.29130i
$416$	1170.06	+	675.536i	0.137902	+	0.0796175i
$417$	−1345.05	−	5019.78i	−0.157955	−	0.589496i
$418$	−11978.0	−	3209.50i	−1.40159	−	0.375555i
$419$	−3049.10			−0.355509			−0.177754	−	0.984075i	$-0.556883\pi$
$419$	−3049.10			−0.355509			−0.177754	+	0.984075i	$0.556883\pi$
$420$	−482.048	+	2437.55i	−0.0560036	+	0.283191i
$421$	−8549.21			−0.989699			−0.494849	−	0.868979i	$-0.664777\pi$
$421$	−8549.21			−0.989699			−0.494849	+	0.868979i	$0.664777\pi$
$422$	−2658.96	−	712.466i	−0.306721	−	0.0821856i
$423$	−311.113	−	1161.09i	−0.0357608	−	0.133461i
$424$	1013.63	+	585.220i	0.116100	+	0.0670302i
$425$	10094.5	+	11109.9i	1.15213	+	1.26802i
$426$			1896.21i			0.215662i
$427$	44.8527	+	20.7398i	0.00508331	+	0.00235051i
$428$	5768.07	+	5768.07i	0.651425	+	0.651425i
$429$	−7595.53	+	4385.28i	−0.854815	+	0.493528i
$430$	−10803.6	−	258.512i	−1.21161	−	0.0289919i
$431$	2274.59	−	3939.71i	0.254207	−	0.440300i	−0.710473	−	0.703725i	$-0.751519\pi$
$431$	2274.59	−	3939.71i	0.254207	−	0.440300i	0.964680	+	0.263425i	$0.0848522\pi$
$432$	111.810	−	417.280i	0.0124524	−	0.0464731i
$433$	1016.76	−	1016.76i	0.112846	−	0.112846i	−0.648429	−	0.761275i	$-0.724574\pi$
$433$	1016.76	−	1016.76i	0.112846	−	0.112846i	0.761275	+	0.648429i	$0.224574\pi$
$434$	−1325.14	+	7659.23i	−0.146564	+	0.847131i
$435$	1021.26	−	3476.51i	0.112565	−	0.383186i
$436$	−2070.69	−	3586.54i	−0.227450	−	0.393954i
$437$	7757.16	−	2078.52i	0.849142	−	0.227527i
$438$	671.954	−	180.050i	0.0733042	−	0.0196418i
$439$	197.909	+	342.788i	0.0215164	+	0.0372674i	0.876583	−	0.481251i	$-0.159817\pi$
$439$	197.909	+	342.788i	0.0215164	+	0.0372674i	−0.855067	+	0.518518i	$0.826484\pi$
$440$	1745.59	−	5942.22i	0.189132	−	0.643828i
$441$	−555.598	−	3036.59i	−0.0599933	−	0.327890i
$442$	−7170.36	+	7170.36i	−0.771627	+	0.771627i
$443$	−3082.67	+	11504.7i	−0.330614	+	1.23387i	0.577932	+	0.816085i	$0.303860\pi$
$443$	−3082.67	+	11504.7i	−0.330614	+	1.23387i	−0.908546	+	0.417785i	$0.862807\pi$
$444$	−1471.90	+	2549.41i	−0.157327	+	0.272499i
$445$	−5496.41	−	131.520i	−0.585516	−	0.0140104i
$446$	3556.98	−	2053.62i	0.377641	−	0.218031i
$447$	−965.818	−	965.818i	−0.102196	−	0.102196i
$448$	968.746	−	682.978i	0.102163	−	0.0720260i
$449$			1102.47i			0.115877i	0.998320	+	0.0579384i	$0.0184527\pi$
$449$			1102.47i			0.115877i	−0.998320	+	0.0579384i	$0.981547\pi$
$450$	1513.07	+	1665.27i	0.158504	+	0.174447i
$451$	−11219.8	−	6477.74i	−1.17144	−	0.676330i
$452$	536.669	+	2002.88i	0.0558469	+	0.208423i
$453$	−6683.92	−	1790.95i	−0.693241	−	0.185753i
$454$	7439.85			0.769096
$455$	5756.97	−	6579.27i	0.593167	−	0.677892i
$456$	−2149.04			−0.220698
$457$	−2331.02	−	624.594i	−0.238600	−	0.0639328i	0.137537	−	0.990497i	$-0.456081\pi$
$457$	−2331.02	−	624.594i	−0.238600	−	0.0639328i	−0.376138	+	0.926564i	$0.622748\pi$
$458$	−645.934	−	2410.66i	−0.0659007	−	0.245945i
$459$	2807.97	+	1621.18i	0.285544	+	0.164859i
$460$	945.120	+	3897.94i	0.0957966	+	0.395092i
$461$		−	9823.08i		−	0.992422i	−0.868202	−	0.496211i	$-0.834724\pi$
$461$		−	9823.08i		−	0.992422i	0.868202	−	0.496211i	$-0.165276\pi$
$462$	695.265	+	7662.95i	0.0700144	+	0.771673i
$463$	4493.64	+	4493.64i	0.451052	+	0.451052i	0.895704	−	0.444652i	$-0.146672\pi$
$463$	4493.64	+	4493.64i	0.451052	+	0.451052i	−0.444652	+	0.895704i	$0.646672\pi$
$464$	−1496.90	+	864.234i	−0.149767	+	0.0864678i
$465$	4856.59	+	5094.71i	0.484342	+	0.508089i
$466$	3546.73	−	6143.12i	0.352573	−	0.610674i
$467$	−1696.08	+	6329.85i	−0.168062	+	0.627218i	0.829567	+	0.558407i	$0.188587\pi$
$467$	−1696.08	+	6329.85i	−0.168062	+	0.627218i	−0.997630	+	0.0688109i	$0.978079\pi$
$468$	−1074.77	+	1074.77i	−0.106157	+	0.106157i
$469$	7047.96	−	8454.51i	0.693912	−	0.832395i
$470$	−1430.96	−	2621.38i	−0.140437	−	0.257266i
$471$	−2546.98	−	4411.50i	−0.249169	−	0.431573i
$472$	2738.97	−	733.905i	0.267100	−	0.0715693i
$473$	−32324.2	+	8661.25i	−3.14222	+	0.841955i
$474$	3209.07	+	5558.27i	0.310965	+	0.538607i
$475$	6053.68	−	9414.59i	0.584762	−	0.909412i
$476$	3069.55	+	8349.86i	0.295573	+	0.804024i
$477$	−931.080	+	931.080i	−0.0893736	+	0.0893736i
$478$	−2649.41	+	9887.74i	−0.253517	+	0.946140i
$479$	−6960.14	+	12055.3i	−0.663919	+	1.14994i	0.315659	+	0.948873i	$0.397775\pi$
$479$	−6960.14	+	12055.3i	−0.663919	+	1.14994i	−0.979577	+	0.201068i	$0.935559\pi$
$480$	25.6753	−	1073.01i	0.00244148	−	0.102033i
$481$	8969.88	−	5178.76i	0.850294	−	0.490917i
$482$	−2625.09	−	2625.09i	−0.248070	−	0.248070i
$483$	−2871.26	−	4072.65i	−0.270491	−	0.383668i
$484$		−	13854.6i		−	1.30114i
$485$	3348.24	−	811.836i	0.313476	−	0.0760074i
$486$	420.888	+	243.000i	0.0392837	+	0.0226805i
$487$	759.975	+	2836.26i	0.0707141	+	0.263908i	0.992227	−	0.124438i	$-0.0397129\pi$
$487$	759.975	+	2836.26i	0.0707141	+	0.263908i	−0.921513	+	0.388347i	$0.873046\pi$
$488$	−20.6182	−	5.52463i	−0.00191259	−	0.000512476i
$489$	−5854.52			−0.541412
$490$	−3119.29	−	7006.75i	−0.287582	−	0.645985i
$491$	13442.6			1.23555			0.617774	−	0.786355i	$-0.288034\pi$
$491$	13442.6			1.23555			0.617774	+	0.786355i	$0.288034\pi$
$492$	−2168.71	−	581.103i	−0.198725	−	0.0532483i
$493$	−3357.65	−	12530.9i	−0.306736	−	1.14475i
$494$	6548.21	+	3780.61i	0.596392	+	0.344327i
$495$	5948.95	+	3627.08i	0.540172	+	0.329344i
$496$		−	3357.63i		−	0.303956i
$497$	−3372.58	−	4783.72i	−0.304388	−	0.431749i
$498$	−4262.70	−	4262.70i	−0.383567	−	0.383567i
$499$	−7451.51	+	4302.13i	−0.668488	+	0.385951i	−0.795503	−	0.605949i	$-0.792793\pi$
$499$	−7451.51	+	4302.13i	−0.668488	+	0.385951i	0.127016	+	0.991901i	$0.459460\pi$
$500$	4628.33	+	3135.05i	0.413970	+	0.280408i
$501$	2461.16	−	4262.85i	0.219474	−	0.380140i
$502$	3734.16	−	13936.1i	0.332000	−	1.23904i
$503$	4352.00	−	4352.00i	0.385778	−	0.385778i	−0.487401	−	0.873178i	$-0.662055\pi$
$503$	4352.00	−	4352.00i	0.385778	−	0.385778i	0.873178	+	0.487401i	$0.162055\pi$
$504$	460.098	+	1251.57i	0.0406635	+	0.110614i
$505$	2221.09	−	1212.45i	0.195717	−	0.106838i
$506$	6210.17	+	10756.3i	0.545604	+	0.945014i
$507$	−1200.80	+	321.754i	−0.105186	+	0.0281846i
$508$	4121.57	−	1104.37i	0.359971	−	0.0964539i
$509$	−2550.10	−	4416.90i	−0.222065	−	0.384628i	0.733370	−	0.679830i	$-0.237946\pi$
$509$	−2550.10	−	4416.90i	−0.222065	−	0.384628i	−0.955435	+	0.295202i	$0.904613\pi$
$510$	7729.12	+	2270.51i	0.671080	+	0.197137i
$511$	−1374.96	+	1649.36i	−0.119030	+	0.142785i
$512$	−362.039	+	362.039i	−0.0312500	+	0.0312500i
$513$	625.739	−	2335.29i	0.0538539	−	0.200986i
$514$	372.303	−	644.847i	0.0319486	−	0.0553366i
$515$	−5912.39	+	5636.05i	−0.505885	+	0.482241i
$516$	−5022.48	+	2899.73i	−0.428493	+	0.247391i
$517$	−6539.47	−	6539.47i	−0.556297	−	0.556297i
$518$	−821.067	−	9049.49i	−0.0696440	−	0.767590i
$519$		−	7348.74i		−	0.621530i
$520$	−1965.87	+	3224.32i	−0.165787	+	0.271915i
$521$	16191.9	+	9348.38i	1.36157	+	0.786103i	0.989833	−	0.142234i	$-0.0454286\pi$
$521$	16191.9	+	9348.38i	1.36157	+	0.786103i	0.371738	+	0.928338i	$0.378762\pi$
$522$	−503.281	−	1878.27i	−0.0421992	−	0.157490i
$523$	20642.2	+	5531.06i	1.72585	+	0.462441i	0.979221	−	0.202797i	$-0.0650033\pi$
$523$	20642.2	+	5531.06i	1.72585	+	0.462441i	0.746631	+	0.665238i	$0.231670\pi$
$524$	−599.057			−0.0499426
$525$	−6778.97	−	1509.96i	−0.563540	−	0.125524i
$526$	10651.9			0.882972
$527$	24341.9	+	6522.39i	2.01205	+	0.539126i
$528$	−860.232	−	3210.43i	−0.0709030	−	0.264614i
$529$	3570.96	+	2061.70i	0.293496	+	0.169450i
$530$	−1703.05	+	2793.25i	−0.139577	+	0.228926i
$531$			3190.04i			0.260708i
$532$	5421.55	−	3822.26i	0.441831	−	0.311496i
$533$	5585.85	+	5585.85i	0.453940	+	0.453940i
$534$	−2555.23	+	1475.26i	−0.207070	+	0.119552i
$535$	−16503.3	+	15732.0i	−1.33364	+	1.27131i
$536$	−2377.27	+	4117.56i	−0.191572	+	0.331812i
$537$	−1517.98	+	5665.18i	−0.121985	+	0.455253i
$538$	−9391.05	+	9391.05i	−0.752560	+	0.752560i
$539$	−15383.2	−	18095.3i	−1.22932	−	1.44605i
$540$	1158.52	+	340.329i	0.0923239	+	0.0271212i
$541$	−5254.94	−	9101.82i	−0.417611	−	0.723323i	0.578088	−	0.815975i	$-0.303799\pi$
$541$	−5254.94	−	9101.82i	−0.417611	−	0.723323i	−0.995699	+	0.0926513i	$0.970466\pi$
$542$	4846.21	−	1298.54i	0.384064	−	0.102910i
$543$	410.307	−	109.941i	0.0324272	−	0.00868883i
$544$	−1921.40	−	3327.96i	−0.151433	−	0.262289i
$545$	10160.3	−	5546.29i	0.798565	−	0.435921i
$546$	799.833	−	4622.98i	0.0626917	−	0.362354i
$547$	1483.85	−	1483.85i	0.115987	−	0.115987i	−0.646731	−	0.762718i	$-0.723864\pi$
$547$	1483.85	−	1483.85i	0.115987	−	0.115987i	0.762718	+	0.646731i	$0.223864\pi$
$548$	2201.11	−	8214.64i	0.171581	−	0.640350i
$549$	12.0069	−	20.7965i	0.000933407	−	0.00161671i
$550$	16487.6	+	5275.00i	1.27824	+	0.408958i
$551$	−8377.33	+	4836.65i	−0.647706	+	0.373953i
$552$	1522.02	+	1522.02i	0.117358	+	0.117358i
$553$	−17981.6	−	8314.66i	−1.38274	−	0.639377i
$554$		−	4042.61i		−	0.310025i
$555$	−7025.36	−	4283.37i	−0.537315	−	0.327602i
$556$	−6000.82	−	3464.57i	−0.457718	−	0.264264i
$557$	223.475	+	834.020i	0.0169999	+	0.0634444i	0.973905	−	0.226957i	$-0.0728778\pi$
$557$	223.475	+	834.020i	0.0169999	+	0.0634444i	−0.956905	+	0.290402i	$0.906211\pi$
$558$	3648.62	+	977.645i	0.276807	+	0.0741703i
$559$	20404.9			1.54389
$560$	1843.66	+	2752.62i	0.139123	+	0.207713i
$561$	24945.8			1.87738
$562$	−7076.89	−	1896.25i	−0.531175	−	0.142328i
$563$	−5282.41	−	19714.2i	−0.395430	−	1.47576i	−0.821047	−	0.570861i	$-0.806609\pi$
$563$	−5282.41	−	19714.2i	−0.395430	−	1.47576i	0.425617	−	0.904904i	$-0.360057\pi$
$564$	−1388.01	−	801.365i	−0.103627	−	0.0598290i
$565$	−5632.49	+	1365.69i	−0.419399	+	0.101690i
$566$			15972.2i			1.18615i
$567$	−1494.00	+	135.552i	−0.110657	+	0.0100399i
$568$	1787.77	+	1787.77i	0.132065	+	0.132065i
$569$	−4871.93	+	2812.81i	−0.358949	+	0.207239i	−0.668619	−	0.743605i	$-0.733114\pi$
$569$	−4871.93	+	2812.81i	−0.358949	+	0.207239i	0.309671	+	0.950844i	$0.399781\pi$
$570$	143.691	−	6005.03i	0.0105588	−	0.441269i
$571$	−10668.3	+	18478.1i	−0.781885	+	1.35426i	0.148957	+	0.988844i	$0.452408\pi$
$571$	−10668.3	+	18478.1i	−0.781885	+	1.35426i	−0.930842	+	0.365421i	$0.880925\pi$
$572$	−3026.65	+	11295.6i	−0.221243	+	0.825688i
$573$	5695.09	−	5695.09i	0.415211	−	0.415211i
$574$	6504.70	−	2391.24i	0.472998	−	0.173882i
$575$	−10955.2	+	2380.31i	−0.794542	+	0.172636i
$576$	−288.000	−	498.831i	−0.0208333	−	0.0360844i
$577$	12429.5	−	3330.47i	0.896786	−	0.240293i	0.219151	−	0.975691i	$-0.429671\pi$
$577$	12429.5	−	3330.47i	0.896786	−	0.240293i	0.677636	+	0.735398i	$0.263005\pi$
$578$	18368.0	−	4921.70i	1.32182	−	0.354179i
$579$	−2045.81	−	3543.45i	−0.146841	−	0.254336i
$580$	−2314.83	−	4240.54i	−0.165721	−	0.303584i
$581$	18335.4	+	3172.26i	1.30926	+	0.226519i
$582$	1307.38	−	1307.38i	0.0931148	−	0.0931148i
$583$	−2622.01	+	9785.46i	−0.186265	+	0.695150i
$584$	463.772	−	803.277i	0.0328614	−	0.0569175i
$585$	−2931.35	−	3075.08i	−0.207174	−	0.217331i
$586$	10399.1	−	6003.91i	0.733075	−	0.423241i
$587$	−14866.1	−	14866.1i	−1.04530	−	1.04530i	−0.998924	−	0.0463725i	$-0.985234\pi$
$587$	−14866.1	−	14866.1i	−1.04530	−	1.04530i	−0.0463725	−	0.998924i	$-0.514766\pi$
$588$	−3386.75	−	2339.10i	−0.237529	−	0.164053i
$589$		−	18790.8i		−	1.31454i
$590$	1867.60	+	7702.53i	0.130319	+	0.537472i
$591$	−9638.79	−	5564.96i	−0.670874	−	0.387329i
$592$	1015.88	+	3791.33i	0.0705279	+	0.263214i
$593$	11865.9	+	3179.47i	0.821712	+	0.220177i	0.645095	−	0.764103i	$-0.276818\pi$
$593$	11865.9	+	3179.47i	0.821712	+	0.220177i	0.176617	+	0.984280i	$0.443485\pi$
$594$	3739.14			0.258281
$595$	−23537.1	+	8018.91i	−1.62173	+	0.552510i
$596$	−1821.16			−0.125164
$597$	−9721.60	−	2604.90i	−0.666464	−	0.178578i
$598$	−1960.11	−	7315.22i	−0.134038	−	0.500237i
$599$	3166.71	+	1828.30i	0.216007	+	0.124712i	0.604100	−	0.796908i	$-0.293533\pi$
$599$	3166.71	+	1828.30i	0.216007	+	0.124712i	−0.388093	+	0.921620i	$0.626866\pi$
$600$	2996.57	+	143.488i	0.203891	+	0.00976312i
$601$		−	3574.89i		−	0.242633i	−0.992614	−	0.121317i	$-0.961288\pi$
$601$		−	3574.89i		−	0.242633i	0.992614	−	0.121317i	$-0.0387117\pi$
$602$	7513.17	−	16248.3i	0.508661	−	1.10005i
$603$	−3782.22	−	3782.22i	−0.255429	−	0.255429i
$604$	−7990.18	+	4613.14i	−0.538272	+	0.310771i
$605$	38713.6	+	926.353i	2.60154	+	0.0622506i
$606$	678.995	−	1176.05i	0.0455153	−	0.0788349i
$607$	−1074.46	+	4009.94i	−0.0718468	+	0.268136i	−0.992500	−	0.122246i	$-0.960990\pi$
$607$	−1074.46	+	4009.94i	−0.0718468	+	0.268136i	0.920653	+	0.390382i	$0.127657\pi$
$608$	−2026.14	+	2026.14i	−0.135149	+	0.135149i
$609$	4610.33	+	3843.32i	0.306765	+	0.255730i
$610$	16.8160	−	57.2438i	0.00111616	−	0.00379956i
$611$	2819.54	+	4883.58i	0.186688	+	0.323353i
$612$	4175.84	−	1118.91i	0.275814	−	0.0739042i
$613$	14277.7	−	3825.69i	0.940733	−	0.252069i	0.244308	−	0.969698i	$-0.421439\pi$
$613$	14277.7	−	3825.69i	0.940733	−	0.252069i	0.696426	+	0.717629i	$0.254773\pi$
$614$	7715.15	+	13363.0i	0.507098	+	0.878320i
$615$	1768.77	−	6021.13i	0.115974	−	0.394789i
$616$	7880.20	+	6569.20i	0.515426	+	0.429676i
$617$	−13747.3	+	13747.3i	−0.896997	+	0.896997i	−0.995169	−	0.0981723i	$-0.968700\pi$
$617$	−13747.3	+	13747.3i	−0.896997	+	0.896997i	0.0981723	+	0.995169i	$0.468700\pi$
$618$	−1134.55	+	4234.21i	−0.0738486	+	0.275607i
$619$	3813.61	−	6605.36i	0.247628	−	0.428904i	−0.715239	−	0.698880i	$-0.753682\pi$
$619$	3813.61	−	6605.36i	0.247628	−	0.428904i	0.962867	+	0.269975i	$0.0870156\pi$
$620$	9382.17	+	224.500i	0.607737	+	0.0145422i
$621$	−2097.10	+	1210.76i	−0.135513	+	0.0782387i
$622$	6209.78	+	6209.78i	0.400304	+	0.400304i
$623$	3822.39	−	8266.46i	0.245812	−	0.531603i
$624$			2026.61i			0.130015i
$625$	−9069.69	+	12723.3i	−0.580460	+	0.814288i
$626$	−6276.84	−	3623.94i	−0.400756	−	0.231377i
$627$	−4814.25	−	17967.0i	−0.306639	−	1.14439i
$628$	−6560.51	−	1757.88i	−0.416868	−	0.111699i
$629$	−29459.5			−1.86745
$630$	−3528.00	+	1201.96i	−0.223109	+	0.0760116i
$631$	15018.7			0.947523			0.473761	−	0.880653i	$-0.342896\pi$
$631$	15018.7			0.947523			0.473761	+	0.880653i	$0.342896\pi$
$632$	8265.92	+	2214.85i	0.520254	+	0.139402i
$633$	−1068.70	−	3988.44i	−0.0671042	−	0.250436i
$634$	−3684.59	−	2127.30i	−0.230810	−	0.133258i
$635$	2810.35	+	11590.7i	0.175630	+	0.724350i
$636$			1755.66i			0.109460i
$637$	6204.58	+	13085.3i	0.385925	+	0.813908i
$638$	−10578.7	−	10578.7i	−0.656453	−	0.656453i
$639$	−2463.25	+	1422.16i	−0.152496	+	0.0880435i
$640$	−987.432	−	1035.85i	−0.0609870	−	0.0639772i
$641$	−10361.7	+	17947.0i	−0.638477	+	1.10587i	0.347290	+	0.937758i	$0.387102\pi$
$641$	−10361.7	+	17947.0i	−0.638477	+	1.10587i	−0.985767	+	0.168117i	$0.946232\pi$
$642$	−3166.89	+	11819.0i	−0.194684	+	0.726570i
$643$	−12728.4	+	12728.4i	−0.780650	+	0.780650i	−0.979940	−	0.199291i	$-0.936136\pi$
$643$	−12728.4	+	12728.4i	−0.780650	+	0.780650i	0.199291	+	0.979940i	$0.436136\pi$
$644$	−6546.78	−	1132.67i	−0.400589	−	0.0693069i
$645$	−7766.86	−	14228.1i	−0.474139	−	0.868577i
$646$	−10753.0	−	18624.8i	−0.654911	−	1.13434i
$647$	18104.1	−	4850.99i	1.10007	−	0.294764i	0.337279	−	0.941405i	$-0.390493\pi$
$647$	18104.1	−	4850.99i	1.10007	−	0.294764i	0.762794	+	0.646641i	$0.223827\pi$
$648$	625.920	−	167.715i	0.0379452	−	0.0101674i
$649$	12271.6	+	21255.0i	0.742223	+	1.28557i
$650$	−8878.23	−	5708.80i	−0.535743	−	0.344488i
$651$	−10943.5	+	4023.01i	−0.658847	+	0.242203i
$652$	−5519.70	+	5519.70i	−0.331546	+	0.331546i
$653$	−3577.46	+	13351.3i	−0.214390	+	0.800116i	0.771990	+	0.635635i	$0.219262\pi$
$653$	−3577.46	+	13351.3i	−0.214390	+	0.800116i	−0.986380	+	0.164481i	$0.947405\pi$
$654$	3106.04	−	5379.81i	0.185712	−	0.321662i
$655$	40.0546	−	1673.94i	0.00238941	−	0.0998567i
$656$	−2592.54	+	1496.81i	−0.154302	+	0.0890861i
$657$	737.857	+	737.857i	0.0438151	+	0.0438151i
$658$	4926.93	−	447.023i	0.291902	−	0.0264845i
$659$		−	14480.1i		−	0.855941i	−0.903793	−	0.427971i	$-0.859229\pi$
$659$		−	14480.1i		−	0.855941i	0.903793	−	0.427971i	$-0.140771\pi$
$660$	9028.37	−	2189.07i	0.532468	−	0.129105i
$661$	15981.5	+	9226.93i	0.940407	+	0.542944i	0.890088	−	0.455789i	$-0.150643\pi$
$661$	15981.5	+	9226.93i	0.940407	+	0.542944i	0.0503190	+	0.998733i	$0.483976\pi$
$662$	4521.89	+	16875.9i	0.265481	+	0.990788i
$663$	−14692.3	−	3936.80i	−0.860638	−	0.230607i
$664$	−8037.82			−0.469771
$665$	10318.0	+	15404.9i	0.601675	+	0.898312i
$666$	−4415.70			−0.256914
$667$	9358.59	+	2507.63i	0.543278	+	0.145571i
$668$	−1698.65	−	6339.46i	−0.0983874	−	0.367187i
$669$	5335.46	+	3080.43i	0.308342	+	0.178021i
$670$	−11346.7	−	6918.09i	−0.654270	−	0.398909i
$671$		−	184.755i		−	0.0106295i
$672$	1613.77	+	746.205i	0.0926379	+	0.0428355i
$673$	−163.644	−	163.644i	−0.00937299	−	0.00937299i	0.702405	−	0.711778i	$-0.252110\pi$
$673$	−163.644	−	163.644i	−0.00937299	−	0.00937299i	−0.711778	+	0.702405i	$0.752110\pi$
$674$	16704.0	−	9644.08i	0.954622	−	0.551151i
$675$	−1028.44	+	3214.49i	−0.0586439	+	0.183297i
$676$	−828.775	+	1435.48i	−0.0471538	+	0.0816728i
$677$	−3593.59	+	13411.5i	−0.204007	+	0.761366i	0.785742	+	0.618554i	$0.212281\pi$
$677$	−3593.59	+	13411.5i	−0.204007	+	0.761366i	−0.989750	+	0.142812i	$0.954385\pi$
$678$	−2199.31	+	2199.31i	−0.124578	+	0.124578i
$679$	−972.941	+	5623.53i	−0.0549898	+	0.317837i
$680$	9427.74	−	5146.42i	0.531673	−	0.290230i
$681$	5579.89	+	9664.65i	0.313982	+	0.543833i
$682$	28071.4	−	7521.71i	1.57611	−	0.422319i
$683$	18990.7	−	5088.55i	1.06392	−	0.285078i	0.315930	−	0.948783i	$-0.397684\pi$
$683$	18990.7	−	5088.55i	1.06392	−	0.285078i	0.747994	+	0.663705i	$0.231017\pi$
$684$	−1611.78	−	2791.69i	−0.0900994	−	0.156057i
$685$	22806.9	+	6699.77i	1.27213	+	0.373701i
$686$	12704.3	−	122.594i	0.707074	−	0.00682310i
$687$	2647.09	−	2647.09i	0.147005	−	0.147005i
$688$	−2001.35	+	7469.13i	−0.110902	+	0.413892i
$689$	3088.57	−	5349.57i	0.170777	−	0.295794i
$690$	−4354.74	+	4151.20i	−0.240264	+	0.229034i
$691$	5680.30	−	3279.52i	0.312719	−	0.180548i	−0.335424	−	0.942067i	$-0.608879\pi$
$691$	5680.30	−	3279.52i	0.312719	−	0.180548i	0.648143	+	0.761519i	$0.275546\pi$
$692$	−6928.46	−	6928.46i	−0.380608	−	0.380608i
$693$	−9433.02	+	6650.39i	−0.517072	+	0.364542i
$694$		−	241.177i		−	0.0131916i
$695$	10082.2	−	16536.4i	0.550275	−	0.902532i
$696$	−2245.35	−	1296.35i	−0.122284	−	0.0706007i
$697$	−5815.26	−	21702.9i	−0.316024	−	1.17942i
$698$	8300.52	+	2224.12i	0.450114	+	0.120608i
$699$	10640.2			0.575749
$700$	−7814.88	+	4967.67i	−0.421964	+	0.268229i
$701$	−13015.2			−0.701250			−0.350625	−	0.936516i	$-0.614031\pi$
$701$	−13015.2			−0.701250			−0.350625	+	0.936516i	$0.614031\pi$
$702$	−2202.25	−	590.090i	−0.118402	−	0.0317258i
$703$	5685.35	+	21218.0i	0.305017	+	1.13834i
$704$	−3837.86	−	2215.79i	−0.205461	−	0.118623i
$705$	2332.05	−	3824.90i	0.124582	−	0.204332i
$706$		−	20484.2i		−	1.09197i
$707$	378.762	+	4174.57i	0.0201482	+	0.222067i
$708$	3007.60	+	3007.60i	0.159650	+	0.159650i
$709$	−6180.87	+	3568.53i	−0.327401	+	0.189025i	−0.654687	−	0.755900i	$-0.727199\pi$
$709$	−6180.87	+	3568.53i	−0.327401	+	0.189025i	0.327286	+	0.944925i	$0.393866\pi$
$710$	−5115.07	+	4876.00i	−0.270373	+	0.257737i
$711$	−4813.60	+	8337.40i	−0.253902	+	0.439771i
$712$	−1018.20	+	3799.98i	−0.0535938	+	0.200015i
$713$	−13308.3	+	13308.3i	−0.699019	+	0.699019i
$714$	−8544.63	+	10249.9i	−0.447864	+	0.537243i
$715$	−31360.8	−	9212.59i	−1.64032	−	0.481862i
$716$	3910.02	+	6772.35i	0.204084	+	0.353484i
$717$	−14831.6	+	3974.12i	−0.772520	+	0.206996i
$718$	8617.42	−	2309.03i	0.447910	−	0.120017i
$719$	−6268.26	−	10856.9i	−0.325127	−	0.563137i	0.656411	−	0.754404i	$-0.272074\pi$
$719$	−6268.26	−	10856.9i	−0.325127	−	0.563137i	−0.981538	+	0.191267i	$0.938740\pi$
$720$	1413.13	−	771.401i	0.0731449	−	0.0399284i
$721$	−4668.69	−	12699.9i	−0.241153	−	0.655989i
$722$	−1639.10	+	1639.10i	−0.0844887	+	0.0844887i
$723$	1441.28	−	5378.92i	0.0741378	−	0.276686i
$724$	283.187	−	490.495i	0.0145367	−	0.0251783i
$725$	12004.1	−	6184.76i	0.614924	−	0.316822i
$726$	17997.6	−	10390.9i	0.920046	−	0.531189i
$727$	−20111.3	−	20111.3i	−1.02598	−	1.02598i	−0.999653	−	0.0263236i	$-0.991620\pi$
$727$	−20111.3	−	20111.3i	−1.02598	−	1.02598i	−0.0263236	−	0.999653i	$-0.508380\pi$
$728$	−3604.50	−	5112.68i	−0.183505	−	0.260286i
$729$			729.000i			0.0370370i
$730$	2213.58	+	1349.62i	0.112230	+	0.0684270i
$731$	−50261.4	−	29018.4i	−2.54307	−	1.46824i
$732$	−8.28695	−	30.9273i	−0.000418435	−	0.00156162i
$733$	16671.2	+	4467.03i	0.840060	+	0.225093i	0.653098	−	0.757274i	$-0.273469\pi$
$733$	16671.2	+	4467.03i	0.840060	+	0.225093i	0.186962	+	0.982367i	$0.440136\pi$
$734$	10941.9			0.550235
$735$	6762.57	−	9307.14i	0.339375	−	0.467073i
$736$	2869.96			0.143734
$737$	−39750.3	−	10651.1i	−1.98673	−	0.532344i
$738$	−871.654	−	3253.06i	−0.0434770	−	0.162258i
$739$	10080.4	+	5819.92i	0.501777	+	0.289701i	0.729447	−	0.684037i	$-0.239777\pi$
$739$	10080.4	+	5819.92i	0.501777	+	0.289701i	−0.227670	+	0.973738i	$0.573111\pi$
$740$	−10662.0	+	2585.17i	−0.529651	+	0.128423i
$741$			11341.8i			0.562284i
$742$	−3122.60	−	4429.14i	−0.154493	−	0.219136i
$743$	17280.8	+	17280.8i	0.853261	+	0.853261i	0.990533	−	0.137273i	$-0.0438336\pi$
$743$	17280.8	+	17280.8i	0.853261	+	0.853261i	−0.137273	+	0.990533i	$0.543834\pi$
$744$	4361.69	−	2518.22i	0.214929	−	0.124089i
$745$	121.768	−	5088.85i	0.00598823	−	0.250256i
$746$	−2169.97	+	3758.49i	−0.106499	+	0.184461i
$747$	2340.38	−	8734.43i	0.114632	−	0.427813i
$748$	23519.1	−	23519.1i	1.14966	−	1.14966i
$749$	−13031.8	−	35449.3i	−0.635741	−	1.72936i
$750$	−601.305	+	8363.67i	−0.0292754	+	0.407197i
$751$	−19582.8	−	33918.4i	−0.951513	−	1.64807i	−0.742153	−	0.670230i	$-0.766195\pi$
$751$	−19582.8	−	33918.4i	−0.951513	−	1.64807i	−0.209360	−	0.977839i	$-0.567138\pi$
$752$	−2064.16	+	553.090i	−0.100096	+	0.0268206i
$753$	20904.1	−	5601.24i	1.01167	−	0.271077i
$754$	4561.10	+	7900.06i	0.220299	+	0.381569i
$755$	−12356.2	−	22635.3i	−0.595612	−	1.09110i
$756$	−1280.76	+	1536.36i	−0.0616149	+	0.0739112i
$757$	22647.5	−	22647.5i	1.08737	−	1.08737i	0.0915681	−	0.995799i	$-0.470812\pi$
$757$	22647.5	−	22647.5i	1.08737	−	1.08737i	0.995799	−	0.0915681i	$-0.0291879\pi$
$758$	947.226	−	3535.10i	0.0453889	−	0.169394i
$759$	−9315.25	+	16134.5i	−0.445484	+	0.771601i
$760$	−5526.13	−	5797.07i	−0.263755	−	0.276687i
$761$	4375.97	−	2526.47i	0.208448	−	0.120347i	−0.392142	−	0.919905i	$-0.628266\pi$
$761$	4375.97	−	2526.47i	0.208448	−	0.120347i	0.600590	+	0.799557i	$0.294933\pi$
$762$	4525.80	+	4525.80i	0.215161	+	0.215161i
$763$	1732.63	+	19096.4i	0.0822090	+	0.906077i
$764$		−	10738.8i		−	0.508527i
$765$	2847.35	+	11743.3i	0.134570	+	0.555006i
$766$	−4735.88	−	2734.26i	−0.223387	−	0.128972i
$767$	−3873.27	−	14455.3i	−0.182341	−	0.680507i
$768$	−741.831	−	198.773i	−0.0348548	−	0.00933933i
$769$	18332.3			0.859660			0.429830	−	0.902910i	$-0.358573\pi$
$769$	18332.3			0.859660			0.429830	+	0.902910i	$0.358573\pi$
$770$	−18883.1	+	21580.3i	−0.883766	+	1.01000i
$771$	1116.91			0.0521718
$772$	−5269.61	−	1411.99i	−0.245670	−	0.0658271i
$773$	7078.71	+	26418.1i	0.329371	+	1.22923i	0.909845	+	0.414949i	$0.136201\pi$
$773$	7078.71	+	26418.1i	0.329371	+	1.22923i	−0.580474	+	0.814279i	$0.697133\pi$
$774$	−7533.72	−	4349.60i	−0.349863	−	0.201994i
$775$	−1254.63	+	26201.5i	−0.0581520	+	1.21443i
$776$		−	2465.23i		−	0.114042i
$777$	11139.8	−	7853.72i	0.514336	−	0.362613i
$778$	15564.6	+	15564.6i	0.717247	+	0.717247i
$779$	−14509.1	+	8376.82i	−0.667319	+	0.385277i
$780$	−5662.92	−	135.504i	−0.259955	−	0.00622030i
$781$	−10941.7	+	18951.5i	−0.501311	+	0.868297i
$782$	−5575.06	+	20806.4i	−0.254941	+	0.951451i
$783$	2062.48	−	2062.48i	0.0941342	−	0.0941342i
$784$	−5398.38	+	987.729i	−0.245918	+	0.0449949i
$785$	5350.68	−	18214.4i	0.243279	−	0.828153i
$786$	−449.293	−	778.198i	−0.0203890	−	0.0353148i
$787$	4946.80	−	1325.49i	0.224059	−	0.0600365i	−0.145043	−	0.989425i	$-0.546332\pi$
$787$	4946.80	−	1325.49i	0.224059	−	0.0600365i	0.369102	+	0.929389i	$0.379665\pi$
$788$	−14334.2	+	3840.84i	−0.648015	+	0.173635i
$789$	7988.90	+	13837.2i	0.360472	+	0.624356i
$790$	−6741.59	+	22949.2i	−0.303614	+	1.03354i
$791$	1636.70	−	9460.04i	0.0735707	−	0.425234i
$792$	3525.29	−	3525.29i	0.158164	−	0.158164i
$793$	−29.1569	+	108.815i	−0.00130567	+	0.00487281i
$794$	−14008.8	+	24264.0i	−0.626138	+	1.08450i
$795$	−4905.82	−	117.388i	−0.218857	−	0.00523689i
$796$	−11621.5	+	6709.70i	−0.517480	+	0.298767i
$797$	13264.9	+	13264.9i	0.589543	+	0.589543i	0.937508	−	0.347965i	$-0.113127\pi$
$797$	13264.9	+	13264.9i	0.589543	+	0.589543i	−0.347965	+	0.937508i	$0.613127\pi$
$798$	9031.42	+	4176.11i	0.400638	+	0.185254i
$799$		−	16039.0i		−	0.710161i
$800$	2960.47	−	2689.91i	0.130836	−	0.118878i
$801$	−3832.84	−	2212.89i	−0.169072	−	0.0976139i
$802$	−3693.71	−	13785.1i	−0.162630	−	0.606945i
$803$	7754.73	+	2077.87i	0.340795	+	0.0913157i
$804$	−7131.82			−0.312836
$805$	3602.75	−	18217.8i	0.157739	−	0.797633i
$806$	−17720.3			−0.774406
$807$	−19242.6	−	5156.05i	−0.839371	−	0.224909i
$808$	−468.632	−	1748.96i	−0.0204040	−	0.0761486i
$809$	8100.37	+	4676.75i	0.352032	+	0.203246i	0.665580	−	0.746327i	$-0.268184\pi$
$809$	8100.37	+	4676.75i	0.352032	+	0.203246i	−0.313548	+	0.949572i	$0.601518\pi$
$810$	426.792	+	1760.21i	0.0185135	+	0.0763550i
$811$			22138.6i			0.958558i	0.877663	+	0.479279i	$0.159102\pi$
$811$			22138.6i			0.958558i	−0.877663	+	0.479279i	$0.840898\pi$
$812$	7970.18	−	723.140i	0.344456	−	0.0312528i
$813$	5321.51	+	5321.51i	0.229561	+	0.229561i
$814$	−29421.6	+	16986.6i	−1.26686	+	0.731423i
$815$	−15054.5	−	15792.7i	−0.647040	−	0.678765i
$816$	2882.10	−	4991.94i	0.123644	−	0.214158i
$817$	−11200.5	+	41800.7i	−0.479626	+	1.78999i
$818$	5300.45	−	5300.45i	0.226560	−	0.226560i
$819$	6605.30	−	2428.22i	0.281817	−	0.103601i
$820$	−4009.16	−	7344.39i	−0.170739	−	0.312777i
$821$	13857.4	+	24001.7i	0.589071	+	1.02030i	0.994354	+	0.106110i	$0.0338394\pi$
$821$	13857.4	+	24001.7i	0.589071	+	1.02030i	−0.405284	+	0.914191i	$0.632827\pi$
$822$	12322.0	−	3301.66i	0.522844	−	0.140096i
$823$	−5304.80	+	1421.42i	−0.224683	+	0.0602035i	−0.369404	−	0.929269i	$-0.620438\pi$
$823$	−5304.80	+	1421.42i	−0.224683	+	0.0602035i	0.144721	+	0.989472i	$0.453771\pi$
$824$	2922.39	+	5061.72i	0.123551	+	0.213997i
$825$	5513.24	+	25374.2i	0.232662	+	1.07081i
$826$	−12936.8	−	2238.22i	−0.544949	−	0.0942829i
$827$	−20311.5	+	20311.5i	−0.854052	+	0.854052i	−0.990629	−	0.136578i	$-0.956390\pi$
$827$	−20311.5	+	20311.5i	−0.854052	+	0.854052i	0.136578	+	0.990629i	$0.456390\pi$
$828$	−835.649	+	3118.69i	−0.0350735	+	0.130896i
$829$	−8611.38	+	14915.3i	−0.360779	+	0.624887i	−0.988089	−	0.153882i	$-0.950822\pi$
$829$	−8611.38	+	14915.3i	−0.360779	+	0.624887i	0.627311	+	0.778769i	$0.284156\pi$
$830$	537.430	−	22460.0i	0.0224753	−	0.939273i
$831$	5251.50	−	3031.96i	0.219221	−	0.126567i
$832$	1910.70	+	1910.70i	0.0796175	+	0.0796175i
$833$	3325.91	−	41055.5i	0.138338	−	1.70767i
$834$		−	10393.7i		−	0.431541i
$835$	17827.8	−	4322.64i	0.738871	−	0.179151i
$836$	−21478.4	−	12400.6i	−0.888572	−	0.513017i
$837$	1466.47	+	5472.93i	0.0605598	+	0.226012i
$838$	−5890.40	−	1578.33i	−0.242817	−	0.0650626i
$839$	36300.3			1.49371			0.746857	−	0.664985i	$-0.231562\pi$
$839$	36300.3			1.49371			0.746857	+	0.664985i	$0.231562\pi$
$840$	−2193.01	+	4459.45i	−0.0900787	+	0.183173i
$841$	12718.7			0.521492
$842$	−16515.8	−	4425.40i	−0.675977	−	0.181127i
$843$	−2844.37	−	10615.3i	−0.116210	−	0.433703i
$844$	−4767.92	−	2752.76i	−0.194453	−	0.112268i
$845$	−3955.73	−	2411.81i	−0.161043	−	0.0981881i
$846$		−	2404.10i		−	0.0977004i
$847$	−26922.8	+	58224.3i	−1.09218	+	2.36199i
$848$	1655.25	+	1655.25i	0.0670302	+	0.0670302i
$849$	−20748.5	+	11979.1i	−0.838735	+	0.484244i
$850$	13750.2	+	26687.9i	0.554856	+	1.07693i
$851$	11000.8	−	19053.9i	0.443127	−	0.767519i
$852$	−981.553	+	3663.20i	−0.0394688	+	0.147300i
$853$	15891.6	−	15891.6i	0.637888	−	0.637888i	−0.312146	−	0.950034i	$-0.601048\pi$
$853$	15891.6	−	15891.6i	0.637888	−	0.637888i	0.950034	+	0.312146i	$0.101048\pi$
$854$	75.9131	+	63.2836i	0.00304179	+	0.00253574i
$855$	7908.53	−	4317.12i	0.316335	−	0.172681i
$856$	8157.28	+	14128.8i	0.325713	+	0.564151i
$857$	6180.45	−	1656.05i	0.246348	−	0.0660087i	−0.133532	−	0.991044i	$-0.542632\pi$
$857$	6180.45	−	1656.05i	0.246348	−	0.0660087i	0.379880	+	0.925036i	$0.375965\pi$
$858$	−16943.4	+	4539.98i	−0.674172	+	0.180644i
$859$	−12715.2	−	22023.4i	−0.505049	−	0.874770i	−0.999983	−	0.00583988i	$-0.998141\pi$
$859$	−12715.2	−	22023.4i	−0.505049	−	0.874770i	0.494934	−	0.868931i	$-0.335192\pi$
$860$	−20737.1	−	6091.74i	−0.822242	−	0.241543i
$861$	7984.84	+	6656.43i	0.316054	+	0.263473i
$862$	6433.52	−	6433.52i	0.254207	−	0.254207i
$863$	−5462.25	+	20385.4i	−0.215454	+	0.804087i	0.770552	+	0.637378i	$0.219981\pi$
$863$	−5462.25	+	20385.4i	−0.215454	+	0.804087i	−0.986006	+	0.166709i	$0.946686\pi$
$864$	432.000	−	748.246i	0.0170103	−	0.0294628i
$865$	19823.3	−	18896.8i	0.779207	−	0.742788i
$866$	2490.54	−	1437.92i	0.0977276	−	0.0564231i
$867$	20169.5	+	20169.5i	0.790072	+	0.790072i
$868$	−6524.69	+	14110.6i	−0.255141	+	0.551778i
$869$			74068.8i			2.89138i
$870$	3772.50	−	6187.46i	0.147011	−	0.241120i
$871$	21730.9	+	12546.4i	0.845378	+	0.488079i
$872$	−2143.74	−	8000.53i	−0.0832524	−	0.310702i
$873$	2678.88	+	717.804i	0.103856	+	0.0278281i
$874$	16061.6			0.621615
$875$	−13358.6	−	22169.1i	−0.516116	−	0.856519i
$876$	1391.32			0.0536624
$877$	−21691.0	−	5812.10i	−0.835182	−	0.223786i	−0.184209	−	0.982887i	$-0.558972\pi$
$877$	−21691.0	−	5812.10i	−0.835182	−	0.223786i	−0.650973	+	0.759101i	$0.725639\pi$
$878$	204.890	+	764.662i	0.00787553	+	0.0293919i
$879$	15598.6	+	9005.87i	0.598553	+	0.345575i
$880$	6448.15	−	10575.9i	0.247008	−	0.405129i
$881$		−	18198.9i		−	0.695954i	−0.937503	−	0.347977i	$-0.886869\pi$
$881$		−	18198.9i		−	0.695954i	0.937503	−	0.347977i	$-0.113131\pi$
$882$	498.523	−	6153.84i	0.0190319	−	0.234933i
$883$	−5256.92	−	5256.92i	−0.200350	−	0.200350i	0.599800	−	0.800150i	$-0.295247\pi$
$883$	−5256.92	−	5256.92i	−0.200350	−	0.200350i	−0.800150	+	0.599800i	$0.795247\pi$
$884$	−17563.7	+	10140.4i	−0.668249	+	0.385814i
$885$	−8605.18	+	8202.99i	−0.326847	+	0.311571i
$886$	−11910.5	+	20629.6i	−0.451628	+	0.782242i
$887$	6956.12	−	25960.6i	0.263319	−	0.982719i	−0.699953	−	0.714189i	$-0.746796\pi$
$887$	6956.12	−	25960.6i	0.263319	−	0.982719i	0.963271	−	0.268530i	$-0.0865378\pi$
$888$	−4163.17	+	4163.17i	−0.157327	+	0.157327i
$889$	−19467.1	−	3368.05i	−0.734427	−	0.127065i
$890$	−10550.2	−	3099.23i	−0.397351	−	0.116726i
$891$	2804.35	+	4857.29i	0.105443	+	0.182632i
$892$	7934.58	−	2126.06i	0.297836	−	0.0798048i
$893$	−11552.0	+	3095.34i	−0.432892	+	0.115993i
$894$	−1365.87	−	2365.76i	−0.0510980	−	0.0885044i
$895$	−19185.3	+	10472.9i	−0.716530	+	0.391140i
$896$	2225.01	−	817.952i	0.0829602	−	0.0304976i
$897$	8032.67	−	8032.67i	0.299000	−	0.299000i
$898$	−570.679	+	2129.80i	−0.0212069	+	0.0791453i
$899$	11335.1	−	19632.9i	0.420518	−	0.728358i
$900$	2061.03	+	4000.27i	0.0763344	+	0.148158i
$901$	−15215.5	+	8784.70i	−0.562601	+	0.324818i
$902$	−18321.8	−	18321.8i	−0.676330	−	0.676330i
$903$	26742.0	−	2426.32i	0.985514	−	0.0894164i
$904$			4147.06i			0.152576i
$905$	1351.65	+	824.102i	0.0496467	+	0.0302697i
$906$	−11985.3	−	6919.70i	−0.439497	−	0.253744i
$907$	−12098.5	−	45152.2i	−0.442915	−	1.65298i	−0.721384	−	0.692535i	$-0.756494\pi$
$907$	−12098.5	−	45152.2i	−0.442915	−	1.65298i	0.278469	−	0.960445i	$-0.410173\pi$
$908$	14372.7	+	3851.15i	0.525302	+	0.140754i
$909$	2036.99			0.0743262
$910$	14527.3	−	9730.15i	0.529203	−	0.354452i
$911$	−32412.1			−1.17877			−0.589386	−	0.807851i	$-0.700630\pi$
$911$	−32412.1			−1.17877			−0.589386	+	0.807851i	$0.700630\pi$
$912$	−4151.63	−	1112.43i	−0.150739	−	0.0403904i
$913$	−18006.2	−	67200.1i	−0.652704	−	2.43593i
$914$	−4179.86	−	2413.25i	−0.151267	−	0.0873338i
$915$	86.9738	−	21.0882i	0.00314237	−	0.000761918i
$916$		−	4991.40i		−	0.180044i
$917$	2517.56	+	1164.11i	0.0906621	+	0.0419219i
$918$	4585.39	+	4585.39i	0.164859	+	0.164859i
$919$	24160.6	−	13949.1i	0.867231	−	0.500696i	0.000804134	−	1.00000i	$-0.499744\pi$
$919$	24160.6	−	13949.1i	0.867231	−	0.500696i	0.866427	+	0.499303i	$0.166411\pi$
$920$	−191.893	+	8019.48i	−0.00687666	+	0.287385i
$921$	−11572.7	+	20044.6i	−0.414044	+	0.717145i
$922$	5084.80	−	18976.7i	0.181626	−	0.677837i
$923$	9435.17	−	9435.17i	0.336470	−	0.336470i
$924$	−2623.49	+	15163.6i	−0.0934052	+	0.539876i
$925$	−6510.81	−	29965.4i	−0.231431	−	1.06514i
$926$	6354.97	+	11007.1i	0.225526	+	0.390623i
$927$	−6351.32	+	1701.83i	−0.225032	+	0.0602972i
$928$	−3339.14	+	894.721i	−0.118117	+	0.0316494i
$929$	−406.471	−	704.028i	−0.0143551	−	0.0248637i	0.858759	−	0.512380i	$-0.171236\pi$
$929$	−406.471	−	704.028i	−0.0143551	−	0.0248637i	−0.873114	+	0.487517i	$0.837903\pi$
$930$	6744.99	+	12356.2i	0.237825	+	0.435672i
$931$	−30211.8	+	5527.79i	−1.06354	+	0.194593i
$932$	10031.7	−	10031.7i	0.352573	−	0.352573i
$933$	−3409.40	+	12724.1i	−0.119634	+	0.446482i
$934$	−6553.15	+	11350.4i	−0.229578	+	0.397640i
$935$	64146.5	+	67291.6i	2.24365	+	2.35366i
$936$	−2632.64	+	1519.96i	−0.0919343	+	0.0530783i
$937$	20893.2	+	20893.2i	0.728442	+	0.728442i	0.970309	−	0.241867i	$-0.0777598\pi$
$937$	20893.2	+	20893.2i	0.728442	+	0.728442i	−0.241867	+	0.970309i	$0.577760\pi$
$938$	17992.0	−	12684.6i	0.626289	−	0.441541i
$939$		−	10871.8i		−	0.377836i
$940$	−1407.47	−	5804.83i	−0.0488370	−	0.201418i
$941$	−39984.1	−	23084.8i	−1.38517	−	0.799727i	−0.392402	−	0.919794i	$-0.628356\pi$
$941$	−39984.1	−	23084.8i	−1.38517	−	0.799727i	−0.992766	+	0.120067i	$0.961689\pi$
$942$	−2636.83	−	9840.77i	−0.0912022	−	0.340371i
$943$	16208.6	+	4343.07i	0.559728	+	0.149979i
$944$	5671.18			0.195531
$945$	−4207.39	−	3681.54i	−0.144832	−	0.126731i
$946$	−66929.0			−2.30026
$947$	5640.19	+	1511.28i	0.193539	+	0.0518587i	0.354287	−	0.935137i	$-0.384724\pi$
$947$	5640.19	+	1511.28i	0.193539	+	0.0518587i	−0.160747	+	0.986996i	$0.551390\pi$
$948$	3322.27	+	12398.9i	0.113821	+	0.424786i
$949$	−4239.40	−	2447.62i	−0.145012	−	0.0837228i
$950$	16568.2	−	15054.0i	0.565834	−	0.514121i
$951$		−	6381.90i		−	0.217610i
$952$	1607.71	+	17719.6i	0.0547335	+	0.603252i
$953$	15842.4	+	15842.4i	0.538494	+	0.538494i	0.923087	−	0.384592i	$-0.125658\pi$
$953$	15842.4	+	15842.4i	0.538494	+	0.538494i	−0.384592	+	0.923087i	$0.625658\pi$
$954$	−2280.67	+	1316.75i	−0.0773998	+	0.0446868i
$955$	30007.2	+	718.022i	1.01676	+	0.0243295i
$956$	−10236.5	+	17730.2i	−0.346311	+	0.599829i
$957$	5808.14	−	21676.3i	0.196186	−	0.732178i
$958$	−19686.3	+	19686.3i	−0.663919	+	0.663919i
$959$	−25213.3	+	30245.0i	−0.848987	+	1.01842i
$960$	605.029	−	2059.60i	0.0203409	−	0.0692429i
$961$	7123.39	+	12338.1i	0.239112	+	0.414154i
$962$	20009.2	−	5361.45i	0.670605	−	0.179688i
$963$	−17728.5	+	4750.33i	−0.593242	+	0.158959i
$964$	−3712.44	−	6430.14i	−0.124035	−	0.214835i
$965$	4297.83	−	14630.4i	0.143370	−	0.488050i
$966$	−3438.70	−	9354.03i	−0.114532	−	0.311554i
$967$	26028.0	−	26028.0i	0.865569	−	0.865569i	−0.126409	−	0.991978i	$-0.540345\pi$
$967$	26028.0	−	26028.0i	0.865569	−	0.865569i	0.991978	+	0.126409i	$0.0403452\pi$
$968$	7171.65	−	26764.9i	0.238125	−	0.888696i
$969$	16129.6	−	27937.2i	0.534733	−	0.926184i
$970$	6888.55	+	164.832i	0.228018	+	0.00545611i
$971$	−8270.49	+	4774.97i	−0.273339	+	0.157813i	−0.630404	−	0.776267i	$-0.717111\pi$
$971$	−8270.49	+	4774.97i	−0.273339	+	0.157813i	0.357065	+	0.934080i	$0.383778\pi$
$972$	687.308	+	687.308i	0.0226805	+	0.0226805i
$973$	18486.2	+	26221.0i	0.609084	+	0.863934i
$974$			5872.63i			0.193194i
$975$	757.276	−	15814.8i	0.0248741	−	0.519464i
$976$	−36.9716	−	21.3455i	−0.00121253	−	0.000700055i
$977$	−2909.08	−	10856.8i	−0.0952608	−	0.355518i	0.901798	−	0.432158i	$-0.142248\pi$
$977$	−2909.08	−	10856.8i	−0.0952608	−	0.355518i	−0.997059	+	0.0766395i	$0.975581\pi$
$978$	−11310.1	−	3030.52i	−0.369792	−	0.0990854i
$979$	−34050.7			−1.11161
$980$	−2399.05	−	15150.7i	−0.0781987	−	0.493847i
$981$	9318.11			0.303266
$982$	25969.0	+	6958.38i	0.843896	+	0.226121i
$983$	2699.57	+	10074.9i	0.0875920	+	0.326898i	0.995792	−	0.0916378i	$-0.0292102\pi$
$983$	2699.57	+	10074.9i	0.0875920	+	0.326898i	−0.908200	+	0.418536i	$0.862544\pi$
$984$	−3888.82	−	2245.21i	−0.125987	−	0.0727385i
$985$	−9773.99	−	40310.7i	−0.316168	−	1.30397i
$986$		−	25945.9i		−	0.838018i
$987$	4275.90	+	6065.00i	0.137896	+	0.195594i
$988$	10693.2	+	10693.2i	0.344327	+	0.344327i
$989$	37537.2	−	21672.1i	1.20689	−	0.696799i
$990$	9614.97	+	10086.4i	0.308670	+	0.323805i
$991$	−14809.2	+	25650.3i	−0.474703	+	0.822210i	−0.999580	−	0.0289682i	$-0.990778\pi$
$991$	−14809.2	+	25650.3i	−0.474703	+	0.822210i	0.524877	+	0.851178i	$0.324111\pi$
$992$	1738.04	−	6486.44i	0.0556277	−	0.207606i
$993$	−18531.0	+	18531.0i	−0.592211	+	0.592211i
$994$	−4039.09	−	10987.2i	−0.128886	−	0.350597i
$995$	−17971.8	−	32922.5i	−0.572606	−	1.04896i
$996$	−6028.37	−	10441.4i	−0.191783	−	0.332178i
$997$	24527.8	−	6572.21i	0.779141	−	0.208770i	0.152735	−	0.988267i	$-0.451192\pi$
$997$	24527.8	−	6572.21i	0.779141	−	0.208770i	0.626406	+	0.779497i	$0.284525\pi$
$998$	−16622.2	+	4453.89i	−0.527220	+	0.141268i
$999$	−3311.78	−	5736.17i	−0.104885	−	0.181666i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.4.u.a.73.8	✓	48
5.2	odd	4		210.4.u.b.157.1	yes	48
7.5	odd	6		210.4.u.b.103.1	yes	48
35.12	even	12	inner	210.4.u.a.187.8	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.4.u.a.73.8	✓	48	1.1	even	1	trivial
210.4.u.a.187.8	yes	48	35.12	even	12	inner
210.4.u.b.103.1	yes	48	7.5	odd	6
210.4.u.b.157.1	yes	48	5.2	odd	4

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:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	210.u (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.93185 + 0.517638i) q^{2} +(0.776457 + 2.89778i) q^{3} +(3.46410 + 2.00000i) q^{4} +(-5.82019 + 9.54596i) q^{5} +6.00000i q^{6} +(-10.6715 - 15.1367i) q^{7} +(5.65685 + 5.65685i) q^{8} +(-7.79423 + 4.50000i) q^{9} +O(q^{10})\)	\(q+(1.93185 + 0.517638i) q^{2} +(0.776457 + 2.89778i) q^{3} +(3.46410 + 2.00000i) q^{4} +(-5.82019 + 9.54596i) q^{5} +6.00000i q^{6} +(-10.6715 - 15.1367i) q^{7} +(5.65685 + 5.65685i) q^{8} +(-7.79423 + 4.50000i) q^{9} +(-16.1851 + 15.4286i) q^{10} +(-34.6217 + 59.9665i) q^{11} +(-3.10583 + 11.5911i) q^{12} +(29.8548 - 29.8548i) q^{13} +(-12.7805 - 34.7658i) q^{14} +(-32.1812 - 9.45358i) q^{15} +(8.00000 + 13.8564i) q^{16} +(-115.996 + 31.0809i) q^{17} +(-17.3867 + 4.65874i) q^{18} +(44.7717 + 77.5468i) q^{19} +(-39.2537 + 21.4278i) q^{20} +(35.5767 - 42.6767i) q^{21} +(-97.9249 + 97.9249i) q^{22} +(23.2125 - 86.6302i) q^{23} +(-12.0000 + 20.7846i) q^{24} +(-57.2508 - 111.119i) q^{25} +(73.1289 - 42.2210i) q^{26} +(-19.0919 - 19.0919i) q^{27} +(-6.69393 - 73.7780i) q^{28} +108.029i q^{29} +(-57.2758 - 34.9211i) q^{30} +(-181.737 - 104.926i) q^{31} +(8.28221 + 30.9096i) q^{32} +(-200.652 - 53.7645i) q^{33} -240.175 q^{34} +(206.604 - 13.7718i) q^{35} -36.0000 q^{36} +(236.958 + 63.4927i) q^{37} +(46.3511 + 172.985i) q^{38} +(109.693 + 63.3315i) q^{39} +(-86.9241 + 21.0762i) q^{40} +187.101i q^{41} +(90.8200 - 64.0292i) q^{42} +(341.737 + 341.737i) q^{43} +(-239.866 + 138.487i) q^{44} +(2.40706 - 100.594i) q^{45} +(89.6862 - 155.341i) q^{46} +(-34.5681 + 129.010i) q^{47} +(-33.9411 + 33.9411i) q^{48} +(-115.237 + 323.063i) q^{49} +(-53.0808 - 244.300i) q^{50} +(-180.131 - 311.996i) q^{51} +(163.129 - 43.7104i) q^{52} +(141.320 - 37.8665i) q^{53} +(-27.0000 - 46.7654i) q^{54} +(-370.933 - 679.513i) q^{55} +(25.2586 - 145.993i) q^{56} +(-189.950 + 189.950i) q^{57} +(-55.9201 + 208.696i) q^{58} +(177.224 - 306.962i) q^{59} +(-92.5718 - 97.1106i) q^{60} +(-2.31072 + 1.33410i) q^{61} +(-296.775 - 296.775i) q^{62} +(151.291 + 69.9567i) q^{63} +64.0000i q^{64} +(111.232 + 458.753i) q^{65} +(-359.799 - 207.730i) q^{66} +(153.821 + 574.067i) q^{67} +(-463.982 - 124.324i) q^{68} +269.058 q^{69} +(406.258 + 80.3413i) q^{70} +316.036 q^{71} +(-69.5467 - 18.6350i) q^{72} +(-30.0083 - 111.992i) q^{73} +(424.901 + 245.317i) q^{74} +(277.544 - 252.179i) q^{75} +358.173i q^{76} +(1277.16 - 115.877i) q^{77} +(179.129 + 179.129i) q^{78} +(926.378 - 534.844i) q^{79} +(-178.834 - 4.27921i) q^{80} +(40.5000 - 70.1481i) q^{81} +(-96.8505 + 361.451i) q^{82} +(-710.450 + 710.450i) q^{83} +(208.595 - 76.6830i) q^{84} +(378.419 - 1288.19i) q^{85} +(483.288 + 837.080i) q^{86} +(-313.045 + 83.8801i) q^{87} +(-535.071 + 143.372i) q^{88} +(245.877 + 425.872i) q^{89} +(56.7215 - 193.087i) q^{90} +(-770.497 - 133.306i) q^{91} +(253.671 - 253.671i) q^{92} +(162.941 - 608.104i) q^{93} +(-133.561 + 231.334i) q^{94} +(-1000.84 - 23.9484i) q^{95} +(-83.1384 + 48.0000i) q^{96} +(-217.897 - 217.897i) q^{97} +(-389.850 + 564.458i) q^{98} -623.190i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{5} - 36 q^{7}+O(q^{10}) \) 48 * q - 48 * q^5 - 36 * q^7	\( 48 q - 48 q^{5} - 36 q^{7} + 64 q^{10} - 28 q^{11} + 112 q^{13} - 128 q^{14} + 84 q^{15} + 384 q^{16} - 204 q^{17} + 104 q^{19} - 32 q^{20} - 96 q^{21} - 312 q^{22} - 464 q^{23} - 576 q^{24} - 884 q^{25} - 456 q^{26} - 224 q^{28} - 24 q^{30} + 528 q^{31} - 216 q^{33} - 448 q^{34} + 1256 q^{35} - 1728 q^{36} + 444 q^{37} + 296 q^{38} - 684 q^{39} + 192 q^{42} - 832 q^{43} + 36 q^{45} - 392 q^{46} - 1548 q^{47} - 436 q^{49} - 336 q^{51} + 224 q^{52} + 412 q^{53} - 1296 q^{54} + 1736 q^{55} + 64 q^{56} - 696 q^{57} - 3256 q^{58} + 296 q^{59} + 2592 q^{61} - 304 q^{62} + 792 q^{63} + 236 q^{65} + 652 q^{67} - 816 q^{68} - 1176 q^{69} - 296 q^{70} - 496 q^{71} + 1300 q^{73} - 528 q^{74} + 936 q^{75} + 5392 q^{77} + 672 q^{78} + 11724 q^{79} - 768 q^{80} + 1944 q^{81} - 96 q^{82} + 6272 q^{83} + 48 q^{84} + 128 q^{85} + 176 q^{86} - 3576 q^{87} - 576 q^{88} + 4448 q^{89} - 5856 q^{91} - 1184 q^{92} - 3360 q^{93} + 16 q^{94} + 4572 q^{95} - 4652 q^{97} + 2256 q^{98}+O(q^{100}) \) 48 * q - 48 * q^5 - 36 * q^7 + 64 * q^10 - 28 * q^11 + 112 * q^13 - 128 * q^14 + 84 * q^15 + 384 * q^16 - 204 * q^17 + 104 * q^19 - 32 * q^20 - 96 * q^21 - 312 * q^22 - 464 * q^23 - 576 * q^24 - 884 * q^25 - 456 * q^26 - 224 * q^28 - 24 * q^30 + 528 * q^31 - 216 * q^33 - 448 * q^34 + 1256 * q^35 - 1728 * q^36 + 444 * q^37 + 296 * q^38 - 684 * q^39 + 192 * q^42 - 832 * q^43 + 36 * q^45 - 392 * q^46 - 1548 * q^47 - 436 * q^49 - 336 * q^51 + 224 * q^52 + 412 * q^53 - 1296 * q^54 + 1736 * q^55 + 64 * q^56 - 696 * q^57 - 3256 * q^58 + 296 * q^59 + 2592 * q^61 - 304 * q^62 + 792 * q^63 + 236 * q^65 + 652 * q^67 - 816 * q^68 - 1176 * q^69 - 296 * q^70 - 496 * q^71 + 1300 * q^73 - 528 * q^74 + 936 * q^75 + 5392 * q^77 + 672 * q^78 + 11724 * q^79 - 768 * q^80 + 1944 * q^81 - 96 * q^82 + 6272 * q^83 + 48 * q^84 + 128 * q^85 + 176 * q^86 - 3576 * q^87 - 576 * q^88 + 4448 * q^89 - 5856 * q^91 - 1184 * q^92 - 3360 * q^93 + 16 * q^94 + 4572 * q^95 - 4652 * q^97 + 2256 * q^98

Introduction

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