LMFDB - Embedded newform 37.9.d.a.6.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,9,Mod(6,37)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("37.6");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	37.d (of order $4$, degree $2$, 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:	$15.0730085723$
Analytic rank:	$0$
Dimension:	$50$
Relative dimension:	$25$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			6.12
Character	$\chi$	$=$	37.6
Dual form			37.9.d.a.31.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.21071 + 2.21071i) q^{2} -26.6774i q^{3} +246.226i q^{4} +(1.29434 + 1.29434i) q^{5} +(58.9759 + 58.9759i) q^{6} -2354.04 q^{7} +(-1110.28 - 1110.28i) q^{8} +5849.32 q^{9} +O(q^{10})$	\(q+(-2.21071 + 2.21071i) q^{2} -26.6774i q^{3} +246.226i q^{4} +(1.29434 + 1.29434i) q^{5} +(58.9759 + 58.9759i) q^{6} -2354.04 q^{7} +(-1110.28 - 1110.28i) q^{8} +5849.32 q^{9} -5.72281 q^{10} -51.6478i q^{11} +6568.65 q^{12} +(-10705.7 - 10705.7i) q^{13} +(5204.10 - 5204.10i) q^{14} +(34.5295 - 34.5295i) q^{15} -58124.7 q^{16} +(-81313.2 - 81313.2i) q^{17} +(-12931.1 + 12931.1i) q^{18} +(27781.5 + 27781.5i) q^{19} +(-318.699 + 318.699i) q^{20} +62799.5i q^{21} +(114.178 + 114.178i) q^{22} +(-370986. - 370986. i) q^{23} +(-29619.2 + 29619.2i) q^{24} -390622. i q^{25} +47334.6 q^{26} -331075. i q^{27} -579624. i q^{28} +(83232.4 - 83232.4i) q^{29} +152.670i q^{30} +(-904935. + 904935. i) q^{31} +(412727. - 412727. i) q^{32} -1377.83 q^{33} +359520. q^{34} +(-3046.92 - 3046.92i) q^{35} +1.44025e6i q^{36} +(-1.86081e6 + 223332. i) q^{37} -122834. q^{38} +(-285601. + 285601. i) q^{39} -2874.14i q^{40} -1.67967e6i q^{41} +(-138832. - 138832. i) q^{42} +(4.15489e6 + 4.15489e6i) q^{43} +12717.0 q^{44} +(7570.99 + 7570.99i) q^{45} +1.64029e6 q^{46} +7.92167e6 q^{47} +1.55062e6i q^{48} -223305. q^{49} +(863551. + 863551. i) q^{50} +(-2.16922e6 + 2.16922e6i) q^{51} +(2.63603e6 - 2.63603e6i) q^{52} -5.44162e6 q^{53} +(731910. + 731910. i) q^{54} +(66.8498 - 66.8498i) q^{55} +(2.61363e6 + 2.61363e6i) q^{56} +(741137. - 741137. i) q^{57} +368005. i q^{58} +(8.47355e6 + 8.47355e6i) q^{59} +(8502.05 + 8502.05i) q^{60} +(-1.06301e7 + 1.06301e7i) q^{61} -4.00110e6i q^{62} -1.37695e7 q^{63} -1.30551e7i q^{64} -27713.7i q^{65} +(3045.98 - 3045.98i) q^{66} +5.04917e6i q^{67} +(2.00214e7 - 2.00214e7i) q^{68} +(-9.89694e6 + 9.89694e6i) q^{69} +13471.7 q^{70} -1.56156e6 q^{71} +(-6.49435e6 - 6.49435e6i) q^{72} -3.14542e7i q^{73} +(3.61998e6 - 4.60743e6i) q^{74} -1.04208e7 q^{75} +(-6.84051e6 + 6.84051e6i) q^{76} +121581. i q^{77} -1.26276e6i q^{78} +(-3.51185e7 - 3.51185e7i) q^{79} +(-75233.1 - 75233.1i) q^{80} +2.95452e7 q^{81} +(3.71327e6 + 3.71327e6i) q^{82} -3.80958e7 q^{83} -1.54629e7 q^{84} -210494. i q^{85} -1.83705e7 q^{86} +(-2.22042e6 - 2.22042e6i) q^{87} +(-57343.3 + 57343.3i) q^{88} +(-5.24137e7 + 5.24137e7i) q^{89} -33474.6 q^{90} +(2.52017e7 + 2.52017e7i) q^{91} +(9.13463e7 - 9.13463e7i) q^{92} +(2.41413e7 + 2.41413e7i) q^{93} +(-1.75125e7 + 1.75125e7i) q^{94} +71917.3i q^{95} +(-1.10105e7 - 1.10105e7i) q^{96} +(-4.45807e7 - 4.45807e7i) q^{97} +(493664. - 493664. i) q^{98} -302105. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q + 4 q^{2} + 124 q^{5} + 510 q^{6} - 4 q^{7} - 5256 q^{8} - 93534 q^{9}+O(q^{10}) $ 50 * q + 4 * q^2 + 124 * q^5 + 510 * q^6 - 4 * q^7 - 5256 * q^8 - 93534 * q^9	\( 50 q + 4 q^{2} + 124 q^{5} + 510 q^{6} - 4 q^{7} - 5256 q^{8} - 93534 q^{9} - 10756 q^{10} - 45440 q^{12} + 63592 q^{13} - 80206 q^{14} - 124346 q^{15} - 639128 q^{16} - 178796 q^{17} - 45882 q^{18} + 264774 q^{19} + 469204 q^{20} + 714574 q^{22} - 654272 q^{23} - 1573644 q^{24} + 1841660 q^{26} - 1683686 q^{29} + 1766336 q^{31} - 4332632 q^{32} - 1438888 q^{33} - 5838452 q^{34} - 650482 q^{35} - 2870078 q^{37} - 2281528 q^{38} + 11036546 q^{39} - 7453902 q^{42} + 5097830 q^{43} - 14992464 q^{44} - 15078446 q^{45} + 28776464 q^{46} + 13992320 q^{47} + 4370314 q^{49} + 7603288 q^{50} + 19417938 q^{51} + 54318452 q^{52} + 28075952 q^{53} - 19197122 q^{54} - 6104306 q^{55} + 47803128 q^{56} + 17462426 q^{57} - 677072 q^{59} + 24953316 q^{60} + 4206386 q^{61} - 18098032 q^{63} - 56061730 q^{66} - 52579760 q^{68} + 88118984 q^{69} - 295493636 q^{70} - 37172476 q^{71} - 74582504 q^{72} - 224754524 q^{74} - 144364996 q^{75} + 189294548 q^{76} + 271163438 q^{79} - 312998084 q^{80} + 41535626 q^{81} - 177494710 q^{82} - 74250268 q^{83} - 82088924 q^{84} + 112964036 q^{86} - 142771908 q^{87} + 224951860 q^{88} + 84928780 q^{89} + 716592116 q^{90} - 40969098 q^{91} - 701292428 q^{92} - 83761576 q^{93} + 553881406 q^{94} - 7259376 q^{96} + 467792674 q^{97} + 538649310 q^{98}+O(q^{100}) \) 50 * q + 4 * q^2 + 124 * q^5 + 510 * q^6 - 4 * q^7 - 5256 * q^8 - 93534 * q^9 - 10756 * q^10 - 45440 * q^12 + 63592 * q^13 - 80206 * q^14 - 124346 * q^15 - 639128 * q^16 - 178796 * q^17 - 45882 * q^18 + 264774 * q^19 + 469204 * q^20 + 714574 * q^22 - 654272 * q^23 - 1573644 * q^24 + 1841660 * q^26 - 1683686 * q^29 + 1766336 * q^31 - 4332632 * q^32 - 1438888 * q^33 - 5838452 * q^34 - 650482 * q^35 - 2870078 * q^37 - 2281528 * q^38 + 11036546 * q^39 - 7453902 * q^42 + 5097830 * q^43 - 14992464 * q^44 - 15078446 * q^45 + 28776464 * q^46 + 13992320 * q^47 + 4370314 * q^49 + 7603288 * q^50 + 19417938 * q^51 + 54318452 * q^52 + 28075952 * q^53 - 19197122 * q^54 - 6104306 * q^55 + 47803128 * q^56 + 17462426 * q^57 - 677072 * q^59 + 24953316 * q^60 + 4206386 * q^61 - 18098032 * q^63 - 56061730 * q^66 - 52579760 * q^68 + 88118984 * q^69 - 295493636 * q^70 - 37172476 * q^71 - 74582504 * q^72 - 224754524 * q^74 - 144364996 * q^75 + 189294548 * q^76 + 271163438 * q^79 - 312998084 * q^80 + 41535626 * q^81 - 177494710 * q^82 - 74250268 * q^83 - 82088924 * q^84 + 112964036 * q^86 - 142771908 * q^87 + 224951860 * q^88 + 84928780 * q^89 + 716592116 * q^90 - 40969098 * q^91 - 701292428 * q^92 - 83761576 * q^93 + 553881406 * q^94 - 7259376 * q^96 + 467792674 * q^97 + 538649310 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/37\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−2.21071	+	2.21071i	−0.138169	+	0.138169i	−0.772809	−	0.634639i	$-0.781149\pi$
$2$	−2.21071	+	2.21071i	−0.138169	+	0.138169i	0.634639	+	0.772809i	$0.281149\pi$
$3$		−	26.6774i		−	0.329350i	−0.986348	−	0.164675i	$-0.947342\pi$
$3$		−	26.6774i		−	0.329350i	0.986348	−	0.164675i	$-0.0526576\pi$
$4$			246.226i			0.961818i
$5$	1.29434	+	1.29434i	0.00207094	+	0.00207094i	0.708141	−	0.706071i	$-0.249534\pi$
$5$	1.29434	+	1.29434i	0.00207094	+	0.00207094i	−0.706071	+	0.708141i	$0.749534\pi$
$6$	58.9759	+	58.9759i	0.0455061	+	0.0455061i
$7$	−2354.04			−0.980441			−0.490220	−	0.871599i	$-0.663084\pi$
$7$	−2354.04			−0.980441			−0.490220	+	0.871599i	$0.663084\pi$
$8$	−1110.28	−	1110.28i	−0.271063	−	0.271063i
$9$	5849.32			0.891528
$10$	−5.72281			−0.000572281
$11$		−	51.6478i		−	0.00352762i	−0.999998	−	0.00176381i	$-0.999439\pi$
$11$		−	51.6478i		−	0.00352762i	0.999998	−	0.00176381i	$-0.000561438\pi$
$12$	6568.65			0.316775
$13$	−10705.7	−	10705.7i	−0.374838	−	0.374838i	0.494398	−	0.869236i	$-0.335389\pi$
$13$	−10705.7	−	10705.7i	−0.374838	−	0.374838i	−0.869236	+	0.494398i	$0.835389\pi$
$14$	5204.10	−	5204.10i	0.135467	−	0.135467i
$15$	34.5295	−	34.5295i	0.000682065	−	0.000682065i
$16$	−58124.7			−0.886913
$17$	−81313.2	−	81313.2i	−0.973566	−	0.973566i	0.0260937	−	0.999660i	$-0.491693\pi$
$17$	−81313.2	−	81313.2i	−0.973566	−	0.973566i	−0.999660	+	0.0260937i	$0.991693\pi$
$18$	−12931.1	+	12931.1i	−0.123182	+	0.123182i
$19$	27781.5	+	27781.5i	0.213177	+	0.213177i	0.805616	−	0.592438i	$-0.201835\pi$
$19$	27781.5	+	27781.5i	0.213177	+	0.213177i	−0.592438	+	0.805616i	$0.701835\pi$
$20$	−318.699	+	318.699i	−0.00199187	+	0.00199187i
$21$			62799.5i			0.322908i
$22$	114.178	+	114.178i	0.000487409	+	0.000487409i
$23$	−370986.	−	370986.i	−1.32570	−	1.32570i	−0.909078	−	0.416625i	$-0.863213\pi$
$23$	−370986.	−	370986.i	−1.32570	−	1.32570i	−0.416625	−	0.909078i	$-0.636787\pi$
$24$	−29619.2	+	29619.2i	−0.0892748	+	0.0892748i
$25$		−	390622.i		−	0.999991i
$26$	47334.6			0.103582
$27$		−	331075.i		−	0.622975i
$28$		−	579624.i		−	0.943006i
$29$	83232.4	−	83232.4i	0.117679	−	0.117679i	−0.645815	−	0.763494i	$-0.723482\pi$
$29$	83232.4	−	83232.4i	0.117679	−	0.117679i	0.763494	+	0.645815i	$0.223482\pi$
$30$			152.670i			0.000188481i
$31$	−904935.	+	904935.i	−0.979875	+	0.979875i	−0.999801	−	0.0199264i	$-0.993657\pi$
$31$	−904935.	+	904935.i	−0.979875	+	0.979875i	0.0199264	+	0.999801i	$0.493657\pi$
$32$	412727.	−	412727.i	0.393608	−	0.393608i
$33$	−1377.83			−0.00116182
$34$	359520.			0.269034
$35$	−3046.92	−	3046.92i	−0.00203043	−	0.00203043i
$36$			1.44025e6i			0.857488i
$37$	−1.86081e6	+	223332.i	−0.992875	+	0.119164i
$37$	−1.86081e6	+	223332.i	−0.992875	+	0.119164i
$38$	−122834.			−0.0589092
$39$	−285601.	+	285601.i	−0.123453	+	0.123453i
$40$		−	2874.14i		−	0.00112271i
$41$		−	1.67967e6i		−	0.594415i	−0.954813	−	0.297208i	$-0.903945\pi$
$41$		−	1.67967e6i		−	0.594415i	0.954813	−	0.297208i	$-0.0960553\pi$
$42$	−138832.	−	138832.i	−0.0446161	−	0.0446161i
$43$	4.15489e6	+	4.15489e6i	1.21531	+	1.21531i	0.969257	+	0.246050i	$0.0791327\pi$
$43$	4.15489e6	+	4.15489e6i	1.21531	+	1.21531i	0.246050	+	0.969257i	$0.420867\pi$
$44$	12717.0			0.00339293
$45$	7570.99	+	7570.99i	0.00184630	+	0.00184630i
$46$	1.64029e6			0.366343
$47$	7.92167e6			1.62340			0.811699	−	0.584076i	$-0.198543\pi$
$47$	7.92167e6			1.62340			0.811699	+	0.584076i	$0.198543\pi$
$48$			1.55062e6i			0.292105i
$49$	−223305.			−0.0387360
$50$	863551.	+	863551.i	0.138168	+	0.138168i
$51$	−2.16922e6	+	2.16922e6i	−0.320644	+	0.320644i
$52$	2.63603e6	−	2.63603e6i	0.360526	−	0.360526i
$53$	−5.44162e6			−0.689644			−0.344822	−	0.938668i	$-0.612061\pi$
$53$	−5.44162e6			−0.689644			−0.344822	+	0.938668i	$0.612061\pi$
$54$	731910.	+	731910.i	0.0860761	+	0.0860761i
$55$	66.8498	−	66.8498i	7.30549e−6	−	7.30549e-6i
$56$	2.61363e6	+	2.61363e6i	0.265761	+	0.265761i
$57$	741137.	−	741137.i	0.0702100	−	0.0702100i
$58$			368005.i			0.0325194i
$59$	8.47355e6	+	8.47355e6i	0.699290	+	0.699290i	0.964257	−	0.264967i	$-0.0853612\pi$
$59$	8.47355e6	+	8.47355e6i	0.699290	+	0.699290i	−0.264967	+	0.964257i	$0.585361\pi$
$60$	8502.05	+	8502.05i	0.000656023	+	0.000656023i
$61$	−1.06301e7	+	1.06301e7i	−0.767745	+	0.767745i	−0.977709	−	0.209964i	$-0.932665\pi$
$61$	−1.06301e7	+	1.06301e7i	−0.767745	+	0.767745i	0.209964	+	0.977709i	$0.432665\pi$
$62$		−	4.00110e6i		−	0.270778i
$63$	−1.37695e7			−0.874091
$64$		−	1.30551e7i		−	0.778144i
$65$		−	27713.7i		−	0.00155253i
$66$	3045.98	−	3045.98i	0.000160528	−	0.000160528i
$67$			5.04917e6i			0.250565i	0.992121	+	0.125283i	$0.0399838\pi$
$67$			5.04917e6i			0.250565i	−0.992121	+	0.125283i	$0.960016\pi$
$68$	2.00214e7	−	2.00214e7i	0.936394	−	0.936394i
$69$	−9.89694e6	+	9.89694e6i	−0.436621	+	0.436621i
$70$	13471.7			0.000561088
$71$	−1.56156e6			−0.0614503			−0.0307252	−	0.999528i	$-0.509782\pi$
$71$	−1.56156e6			−0.0614503			−0.0307252	+	0.999528i	$0.509782\pi$
$72$	−6.49435e6	−	6.49435e6i	−0.241661	−	0.241661i
$73$		−	3.14542e7i		−	1.10761i	−0.832646	−	0.553805i	$-0.813175\pi$
$73$		−	3.14542e7i		−	1.10761i	0.832646	−	0.553805i	$-0.186825\pi$
$74$	3.61998e6	−	4.60743e6i	0.120720	−	0.153650i
$75$	−1.04208e7			−0.329347
$76$	−6.84051e6	+	6.84051e6i	−0.205038	+	0.205038i
$77$			121581.i			0.00345862i
$78$		−	1.26276e6i		−	0.0341148i
$79$	−3.51185e7	−	3.51185e7i	−0.901628	−	0.901628i	0.0939494	−	0.995577i	$-0.470051\pi$
$79$	−3.51185e7	−	3.51185e7i	−0.901628	−	0.901628i	−0.995577	+	0.0939494i	$0.970051\pi$
$80$	−75233.1	−	75233.1i	−0.00183674	−	0.00183674i
$81$	2.95452e7			0.686351
$82$	3.71327e6	+	3.71327e6i	0.0821300	+	0.0821300i
$83$	−3.80958e7			−0.802722			−0.401361	−	0.915920i	$-0.631463\pi$
$83$	−3.80958e7			−0.802722			−0.401361	+	0.915920i	$0.631463\pi$
$84$	−1.54629e7			−0.310579
$85$		−	210494.i		−	0.00403239i
$86$	−1.83705e7			−0.335837
$87$	−2.22042e6	−	2.22042e6i	−0.0387577	−	0.0387577i
$88$	−57343.3	+	57343.3i	−0.000956208	+	0.000956208i
$89$	−5.24137e7	+	5.24137e7i	−0.835381	+	0.835381i	−0.988247	−	0.152866i	$-0.951150\pi$
$89$	−5.24137e7	+	5.24137e7i	−0.835381	+	0.835381i	0.152866	+	0.988247i	$0.451150\pi$
$90$	−33474.6			−0.000510205
$91$	2.52017e7	+	2.52017e7i	0.367506	+	0.367506i
$92$	9.13463e7	−	9.13463e7i	1.27509	−	1.27509i
$93$	2.41413e7	+	2.41413e7i	0.322722	+	0.322722i
$94$	−1.75125e7	+	1.75125e7i	−0.224304	+	0.224304i
$95$			71917.3i			0.000882956i
$96$	−1.10105e7	−	1.10105e7i	−0.129635	−	0.129635i
$97$	−4.45807e7	−	4.45807e7i	−0.503570	−	0.503570i	0.408975	−	0.912545i	$-0.365886\pi$
$97$	−4.45807e7	−	4.45807e7i	−0.503570	−	0.503570i	−0.912545	+	0.408975i	$0.865886\pi$
$98$	493664.	−	493664.i	0.00535213	−	0.00535213i
$99$		−	302105.i		−	0.00314497i
$100$	9.61810e7			0.961810
$101$			1.04295e8i			1.00225i	0.865374	+	0.501126i	$0.167081\pi$
$101$			1.04295e8i			1.00225i	−0.865374	+	0.501126i	$0.832919\pi$
$102$		−	9.59104e6i		−	0.0886064i
$103$	2.04472e7	−	2.04472e7i	0.181670	−	0.181670i	−0.610413	−	0.792083i	$-0.708996\pi$
$103$	2.04472e7	−	2.04472e7i	0.181670	−	0.181670i	0.792083	+	0.610413i	$0.208996\pi$
$104$			2.37726e7i			0.203210i
$105$	−81283.8	+	81283.8i	−0.000668724	+	0.000668724i
$106$	1.20298e7	−	1.20298e7i	0.0952877	−	0.0952877i
$107$	1.70547e7			0.130110			0.0650549	−	0.997882i	$-0.479278\pi$
$107$	1.70547e7			0.130110			0.0650549	+	0.997882i	$0.479278\pi$
$108$	8.15190e7			0.599189
$109$	8.51400e7	+	8.51400e7i	0.603153	+	0.603153i	0.941148	−	0.337995i	$-0.109749\pi$
$109$	8.51400e7	+	8.51400e7i	0.603153	+	0.603153i	−0.337995	+	0.941148i	$0.609749\pi$
$110$			295.571i			2.01879e-6i
$111$	5.95792e6	+	4.96414e7i	0.0392466	+	0.327004i
$112$	1.36828e8			0.869566
$113$	−2.19380e8	+	2.19380e8i	−1.34550	+	1.34550i	−0.455020	+	0.890481i	$0.650368\pi$
$113$	−2.19380e8	+	2.19380e8i	−1.34550	+	1.34550i	−0.890481	+	0.455020i	$0.849632\pi$
$114$			3.27688e6i			0.0194018i
$115$		−	960363.i		−	0.00549091i
$116$	2.04939e7	+	2.04939e7i	0.113186	+	0.113186i
$117$	−6.26213e7	−	6.26213e7i	−0.334179	−	0.334179i
$118$	−3.74651e7			−0.193241
$119$	1.91414e8	+	1.91414e8i	0.954524	+	0.954524i
$120$	−76674.6			−0.000369765
$121$	2.14356e8			0.999988
$122$		−	4.70000e7i		−	0.212158i
$123$	−4.48093e7			−0.195771
$124$	−2.22818e8	−	2.22818e8i	−0.942462	−	0.942462i
$125$	1.01120e6	−	1.01120e6i	0.00414186	−	0.00414186i
$126$	3.04404e7	−	3.04404e7i	0.120773	−	0.120773i
$127$	−4.42394e8			−1.70057			−0.850284	−	0.526325i	$-0.823570\pi$
$127$	−4.42394e8			−1.70057			−0.850284	+	0.526325i	$0.823570\pi$
$128$	1.34519e8	+	1.34519e8i	0.501123	+	0.501123i
$129$	1.10842e8	−	1.10842e8i	0.400262	−	0.400262i
$130$	61267.0	+	61267.0i	0.000214513	+	0.000214513i
$131$	1.26925e8	−	1.26925e8i	0.430984	−	0.430984i	−0.457979	−	0.888963i	$-0.651427\pi$
$131$	1.26925e8	−	1.26925e8i	0.430984	−	0.430984i	0.888963	+	0.457979i	$0.151427\pi$
$132$		−	339257.i		−	0.00111746i
$133$	−6.53987e7	−	6.53987e7i	−0.209008	−	0.209008i
$134$	−1.11623e7	−	1.11623e7i	−0.0346205	−	0.0346205i
$135$	428523.	−	428523.i	0.00129015	−	0.00129015i
$136$			1.80560e8i			0.527796i
$137$	2.02636e7			0.0575220			0.0287610	−	0.999586i	$-0.490844\pi$
$137$	2.02636e7			0.0575220			0.0287610	+	0.999586i	$0.490844\pi$
$138$		−	4.37585e7i		−	0.120655i
$139$		−	2.87504e8i		−	0.770166i	−0.922882	−	0.385083i	$-0.874173\pi$
$139$		−	2.87504e8i		−	0.770166i	0.922882	−	0.385083i	$-0.125827\pi$
$140$	750230.	−	750230.i	0.00195291	−	0.00195291i
$141$		−	2.11329e8i		−	0.534667i
$142$	3.45215e6	−	3.45215e6i	0.00849055	−	0.00849055i
$143$	−552929.	+	552929.i	−0.00132228	+	0.00132228i
$144$	−3.39990e8			−0.790708
$145$	215462.			0.000487414
$146$	6.95361e7	+	6.95361e7i	0.153038	+	0.153038i
$147$			5.95720e6i			0.0127577i
$148$	−5.49901e7	−	4.58178e8i	−0.114614	−	0.954965i
$149$	−6.04054e8			−1.22555			−0.612775	−	0.790258i	$-0.709947\pi$
$149$	−6.04054e8			−1.22555			−0.612775	+	0.790258i	$0.709947\pi$
$150$	2.30373e7	−	2.30373e7i	0.0455057	−	0.0455057i
$151$			5.33523e7i			0.102623i	0.998683	+	0.0513115i	$0.0163401\pi$
$151$			5.33523e7i			0.102623i	−0.998683	+	0.0513115i	$0.983660\pi$
$152$		−	6.16902e7i		−	0.115569i
$153$	−4.75627e8	−	4.75627e8i	−0.867962	−	0.867962i
$154$	−268780.	−	268780.i	−0.000477875	−	0.000477875i
$155$	−2.34258e6			−0.00405853
$156$	−7.03223e7	−	7.03223e7i	−0.118739	−	0.118739i
$157$	−6.44582e8			−1.06091			−0.530456	−	0.847712i	$-0.677979\pi$
$157$	−6.44582e8			−1.06091			−0.530456	+	0.847712i	$0.677979\pi$
$158$	1.55274e8			0.249155
$159$			1.45168e8i			0.227134i
$160$	1.06842e6			0.00163028
$161$	8.73316e8	+	8.73316e8i	1.29977	+	1.29977i
$162$	−6.53158e7	+	6.53158e7i	−0.0948328	+	0.0948328i
$163$	4.00076e8	−	4.00076e8i	0.566751	−	0.566751i	−0.364466	−	0.931217i	$-0.618748\pi$
$163$	4.00076e8	−	4.00076e8i	0.566751	−	0.566751i	0.931217	+	0.364466i	$0.118748\pi$
$164$	4.13579e8			0.571719
$165$	−1783.38	−	1783.38i	−2.40606e−6	−	2.40606e-6i
$166$	8.42188e7	−	8.42188e7i	0.110912	−	0.110912i
$167$	4.39411e8	+	4.39411e8i	0.564944	+	0.564944i	0.930708	−	0.365764i	$-0.119192\pi$
$167$	4.39411e8	+	4.39411e8i	0.564944	+	0.564944i	−0.365764	+	0.930708i	$0.619192\pi$
$168$	6.97248e7	−	6.97248e7i	0.0875286	−	0.0875286i
$169$		−	5.86505e8i		−	0.718993i
$170$	465340.	+	465340.i	0.000557154	+	0.000557154i
$171$	1.62503e8	+	1.62503e8i	0.190054	+	0.190054i
$172$	−1.02304e9	+	1.02304e9i	−1.16890	+	1.16890i
$173$		−	7.34072e8i		−	0.819510i	−0.912196	−	0.409755i	$-0.865614\pi$
$173$		−	7.34072e8i		−	0.819510i	0.912196	−	0.409755i	$-0.134386\pi$
$174$	9.81742e6			0.0107103
$175$			9.19538e8i			0.980432i
$176$			3.00202e6i			0.00312869i
$177$	2.26052e8	−	2.26052e8i	0.230311	−	0.230311i
$178$		−	2.31743e8i		−	0.230848i
$179$	8.65778e8	−	8.65778e8i	0.843324	−	0.843324i	−0.145965	−	0.989290i	$-0.546629\pi$
$179$	8.65778e8	−	8.65778e8i	0.843324	−	0.843324i	0.989290	+	0.145965i	$0.0466288\pi$
$180$	−1.86417e6	+	1.86417e6i	−0.00177581	+	0.00177581i
$181$	−2.36788e8			−0.220621			−0.110310	−	0.993897i	$-0.535184\pi$
$181$	−2.36788e8			−0.220621			−0.110310	+	0.993897i	$0.535184\pi$
$182$	−1.11427e8			−0.101556
$183$	2.83583e8	+	2.83583e8i	0.252857	+	0.252857i
$184$			8.23794e8i			0.718699i
$185$	−2.69758e6	−	2.11945e6i	−0.00230297	−	0.00180940i
$186$	−1.06739e8			−0.0891806
$187$	−4.19965e6	+	4.19965e6i	−0.00343437	+	0.00343437i
$188$			1.95052e9i			1.56141i
$189$			7.79362e8i			0.610790i
$190$	−158988.	−	158988.i	−0.000121997	−	0.000121997i
$191$	6.51325e8	+	6.51325e8i	0.489401	+	0.489401i	0.908117	−	0.418716i	$-0.137520\pi$
$191$	6.51325e8	+	6.51325e8i	0.489401	+	0.489401i	−0.418716	+	0.908117i	$0.637520\pi$
$192$	−3.48276e8			−0.256282
$193$	−9.35726e7	−	9.35726e7i	−0.0674403	−	0.0674403i	0.672582	−	0.740022i	$-0.265185\pi$
$193$	−9.35726e7	−	9.35726e7i	−0.0674403	−	0.0674403i	−0.740022	+	0.672582i	$0.765185\pi$
$194$	1.97110e8			0.139156
$195$	−739329.			−0.000511327
$196$		−	5.49835e7i		−	0.0372570i
$197$	2.16913e9			1.44019			0.720096	−	0.693874i	$-0.244098\pi$
$197$	2.16913e9			1.44019			0.720096	+	0.693874i	$0.244098\pi$
$198$	667866.	+	667866.i	0.000434539	+	0.000434539i
$199$	7.83551e8	−	7.83551e8i	0.499637	−	0.499637i	−0.411688	−	0.911325i	$-0.635061\pi$
$199$	7.83551e8	−	7.83551e8i	0.499637	−	0.499637i	0.911325	+	0.411688i	$0.135061\pi$
$200$	−4.33698e8	+	4.33698e8i	−0.271061	+	0.271061i
$201$	1.34699e8			0.0825238
$202$	−2.30566e8	−	2.30566e8i	−0.138481	−	0.138481i
$203$	−1.95932e8	+	1.95932e8i	−0.115378	+	0.115378i
$204$	−5.34118e8	−	5.34118e8i	−0.308401	−	0.308401i
$205$	2.17407e6	−	2.17407e6i	0.00123100	−	0.00123100i
$206$			9.04056e7i			0.0502026i
$207$	−2.17002e9	−	2.17002e9i	−1.18190	−	1.18190i
$208$	6.22269e8	+	6.22269e8i	0.332449	+	0.332449i
$209$	1.43485e6	−	1.43485e6i	0.000752008	−	0.000752008i
$210$		−	359390.i		−	0.000184794i
$211$	1.17028e9			0.590418			0.295209	−	0.955433i	$-0.404611\pi$
$211$	1.17028e9			0.590418			0.295209	+	0.955433i	$0.404611\pi$
$212$		−	1.33987e9i		−	0.663312i
$213$			4.16582e7i			0.0202387i
$214$	−3.77031e7	+	3.77031e7i	−0.0179772	+	0.0179772i
$215$			1.07557e7i			0.00503366i
$216$	−3.67584e8	+	3.67584e8i	−0.168866	+	0.168866i
$217$	2.13025e9	−	2.13025e9i	0.960709	−	0.960709i
$218$	−3.76440e8			−0.166675
$219$	−8.39115e8			−0.364792
$220$	16460.1	+	16460.1i	7.02655e−6	+	7.02655e-6i
$221$			1.74104e9i			0.729859i
$222$	−1.22914e8	−	9.65716e7i	−0.0506046	−	0.0397592i
$223$	−2.70757e9			−1.09487			−0.547433	−	0.836849i	$-0.684395\pi$
$223$	−2.70757e9			−1.09487			−0.547433	+	0.836849i	$0.684395\pi$
$224$	−9.71576e8	+	9.71576e8i	−0.385909	+	0.385909i
$225$		−	2.28487e9i		−	0.891521i
$226$		−	9.69973e8i		−	0.371814i
$227$	2.24377e9	+	2.24377e9i	0.845036	+	0.845036i	0.989509	−	0.144473i	$-0.0461487\pi$
$227$	2.24377e9	+	2.24377e9i	0.845036	+	0.845036i	−0.144473	+	0.989509i	$0.546149\pi$
$228$	1.82487e8	+	1.82487e8i	0.0675293	+	0.0675293i
$229$	−3.78443e9			−1.37613			−0.688064	−	0.725650i	$-0.741539\pi$
$229$	−3.78443e9			−1.37613			−0.688064	+	0.725650i	$0.741539\pi$
$230$	2.12308e6	+	2.12308e6i	0.000758675	+	0.000758675i
$231$	3.24346e6			0.00113910
$232$	−1.84822e8			−0.0637971
$233$		−	3.24889e9i		−	1.10233i	−0.834396	−	0.551165i	$-0.814184\pi$
$233$		−	3.24889e9i		−	1.10233i	0.834396	−	0.551165i	$-0.185816\pi$
$234$	2.76875e8			0.0923465
$235$	1.02533e7	+	1.02533e7i	0.00336196	+	0.00336196i
$236$	−2.08640e9	+	2.08640e9i	−0.672590	+	0.672590i
$237$	−9.36868e8	+	9.36868e8i	−0.296951	+	0.296951i
$238$	−8.46323e8			−0.263772
$239$	2.96877e9	+	2.96877e9i	0.909883	+	0.909883i	0.996262	−	0.0863798i	$-0.0275298\pi$
$239$	2.96877e9	+	2.96877e9i	0.909883	+	0.909883i	−0.0863798	+	0.996262i	$0.527530\pi$
$240$	−2.00702e6	+	2.00702e6i	−0.000604932	+	0.000604932i
$241$	−3.64313e9	−	3.64313e9i	−1.07996	−	1.07996i	−0.996512	−	0.0834461i	$-0.973407\pi$
$241$	−3.64313e9	−	3.64313e9i	−1.07996	−	1.07996i	−0.0834461	−	0.996512i	$-0.526593\pi$
$242$	−4.73880e8	+	4.73880e8i	−0.138168	+	0.138168i
$243$		−	2.96037e9i		−	0.849025i
$244$	−2.61740e9	−	2.61740e9i	−0.738431	−	0.738431i
$245$	−289033.	−	289033.i	−8.02200e−5	−	8.02200e-5i
$246$	9.90604e7	−	9.90604e7i	0.0270495	−	0.0270495i
$247$		−	5.94843e8i		−	0.159814i
$248$	2.00945e9			0.531216
$249$			1.01630e9i			0.264377i
$250$			4.47093e6i			0.00114456i
$251$	−2.44536e9	+	2.44536e9i	−0.616096	+	0.616096i	−0.944528	−	0.328432i	$-0.893480\pi$
$251$	−2.44536e9	+	2.44536e9i	−0.616096	+	0.616096i	0.328432	+	0.944528i	$0.393480\pi$
$252$		−	3.39041e9i		−	0.840717i
$253$	−1.91606e7	+	1.91606e7i	−0.00467658	+	0.00467658i
$254$	9.78004e8	−	9.78004e8i	0.234966	−	0.234966i
$255$	−5.61541e6			−0.00132807
$256$	2.74734e9			0.639664
$257$	2.84972e9	+	2.84972e9i	0.653236	+	0.653236i	0.953771	−	0.300535i	$-0.0971651\pi$
$257$	2.84972e9	+	2.84972e9i	0.653236	+	0.653236i	−0.300535	+	0.953771i	$0.597165\pi$
$258$			4.90077e8i			0.110608i
$259$	4.38041e9	−	5.25733e8i	0.973455	−	0.116833i
$260$	6.82382e6			0.00149326
$261$	4.86853e8	−	4.86853e8i	0.104915	−	0.104915i
$262$			5.61188e8i			0.119098i
$263$		−	3.01458e9i		−	0.630091i	−0.949077	−	0.315045i	$-0.897980\pi$
$263$		−	3.01458e9i		−	0.630091i	0.949077	−	0.315045i	$-0.102020\pi$
$264$	1.52977e6	+	1.52977e6i	0.000314927	+	0.000314927i
$265$	−7.04330e6	−	7.04330e6i	−0.00142821	−	0.00142821i
$266$	2.89155e8			0.0577570
$267$	1.39826e9	+	1.39826e9i	0.275133	+	0.275133i
$268$	−1.24324e9			−0.240998
$269$	−3.74624e9			−0.715461			−0.357731	−	0.933825i	$-0.616449\pi$
$269$	−3.74624e9			−0.715461			−0.357731	+	0.933825i	$0.616449\pi$
$270$			1.89468e6i			0.000356517i
$271$	6.57275e9			1.21862			0.609312	−	0.792930i	$-0.291446\pi$
$271$	6.57275e9			1.21862			0.609312	+	0.792930i	$0.291446\pi$
$272$	4.72631e9	+	4.72631e9i	0.863468	+	0.863468i
$273$	6.72316e8	−	6.72316e8i	0.121038	−	0.121038i
$274$	−4.47969e7	+	4.47969e7i	−0.00794778	+	0.00794778i
$275$	−2.01748e7			−0.00352759
$276$	−2.43688e9	−	2.43688e9i	−0.419950	−	0.419950i
$277$	−7.19407e8	+	7.19407e8i	−0.122196	+	0.122196i	−0.765560	−	0.643364i	$-0.777538\pi$
$277$	−7.19407e8	+	7.19407e8i	−0.122196	+	0.122196i	0.643364	+	0.765560i	$0.277538\pi$
$278$	6.35588e8	+	6.35588e8i	0.106413	+	0.106413i
$279$	−5.29325e9	+	5.29325e9i	−0.873586	+	0.873586i
$280$			6.76584e6i			0.00110075i
$281$	3.17604e8	+	3.17604e8i	0.0509402	+	0.0509402i	0.732118	−	0.681178i	$-0.238532\pi$
$281$	3.17604e8	+	3.17604e8i	0.0509402	+	0.0509402i	−0.681178	+	0.732118i	$0.738532\pi$
$282$	4.67188e8	+	4.67188e8i	0.0738746	+	0.0738746i
$283$	−5.66547e9	+	5.66547e9i	−0.883264	+	0.883264i	−0.993865	−	0.110601i	$-0.964722\pi$
$283$	−5.66547e9	+	5.66547e9i	−0.883264	+	0.883264i	0.110601	+	0.993865i	$0.464722\pi$
$284$		−	3.84495e8i		−	0.0591041i
$285$	1.91856e6			0.000290802
$286$		−	2.44473e6i		−	0.000365399i
$287$			3.95402e9i			0.582789i
$288$	2.41417e9	−	2.41417e9i	0.350912	−	0.350912i
$289$			6.24791e9i			0.895661i
$290$	−476323.	+	476323.i	−6.73457e−5	+	6.73457e-5i
$291$	−1.18930e9	+	1.18930e9i	−0.165851	+	0.165851i
$292$	7.74482e9			1.06532
$293$	6.16654e9			0.836702			0.418351	−	0.908285i	$-0.362608\pi$
$293$	6.16654e9			0.836702			0.418351	+	0.908285i	$0.362608\pi$
$294$	−1.31696e7	−	1.31696e7i	−0.00176273	−	0.00176273i
$295$			2.19353e7i			0.00289638i
$296$	2.31397e9	+	1.81805e9i	0.301433	+	0.236831i
$297$	−1.70993e7			−0.00219762
$298$	1.33539e9	−	1.33539e9i	0.169333	−	0.169333i
$299$			7.94337e9i			0.993848i
$300$		−	2.56586e9i		−	0.316772i
$301$	−9.78078e9	−	9.78078e9i	−1.19154	−	1.19154i
$302$	−1.17946e8	−	1.17946e8i	−0.0141794	−	0.0141794i
$303$	2.78231e9			0.330092
$304$	−1.61479e9	−	1.61479e9i	−0.189070	−	0.189070i
$305$	−2.75178e7			−0.00317991
$306$	2.10295e9			0.239851
$307$			1.18991e10i			1.33955i	0.742563	+	0.669776i	$0.233610\pi$
$307$			1.18991e10i			1.33955i	−0.742563	+	0.669776i	$0.766390\pi$
$308$	−2.99363e7			−0.00332656
$309$	−5.45477e8	−	5.45477e8i	−0.0598332	−	0.0598332i
$310$	5.17878e6	−	5.17878e6i	0.000560764	−	0.000560764i
$311$	2.39811e9	−	2.39811e9i	0.256346	−	0.256346i	−0.567220	−	0.823566i	$-0.691981\pi$
$311$	2.39811e9	−	2.39811e9i	0.256346	−	0.256346i	0.823566	+	0.567220i	$0.191981\pi$
$312$	6.34192e8			0.0669271
$313$	1.16472e9	+	1.16472e9i	0.121351	+	0.121351i	0.765174	−	0.643823i	$-0.222653\pi$
$313$	1.16472e9	+	1.16472e9i	0.121351	+	0.121351i	−0.643823	+	0.765174i	$0.722653\pi$
$314$	1.42498e9	−	1.42498e9i	0.146586	−	0.146586i
$315$	−1.78224e7	−	1.78224e7i	−0.00181019	−	0.00181019i
$316$	8.64706e9	−	8.64706e9i	0.867202	−	0.867202i
$317$		−	1.72605e10i		−	1.70930i	−0.519208	−	0.854648i	$-0.673773\pi$
$317$		−	1.72605e10i		−	1.70930i	0.519208	−	0.854648i	$-0.326227\pi$
$318$	−3.20925e8	−	3.20925e8i	−0.0313830	−	0.0313830i
$319$	−4.29877e6	−	4.29877e6i	−0.000415128	−	0.000415128i
$320$	1.68977e7	−	1.68977e7i	0.00161149	−	0.00161149i
$321$		−	4.54976e8i		−	0.0428517i
$322$	−3.86130e9			−0.359178
$323$		−	4.51800e9i		−	0.415085i
$324$			7.27478e9i			0.660145i
$325$	−4.18190e9	+	4.18190e9i	−0.374835	+	0.374835i
$326$			1.76891e9i			0.156615i
$327$	2.27131e9	−	2.27131e9i	0.198649	−	0.198649i
$328$	−1.86490e9	+	1.86490e9i	−0.161124	+	0.161124i
$329$	−1.86479e10			−1.59165
$330$	7885.06			6.64889e−7
$331$	−9.77314e9	−	9.77314e9i	−0.814184	−	0.814184i	0.171075	−	0.985258i	$-0.445276\pi$
$331$	−9.77314e9	−	9.77314e9i	−0.814184	−	0.814184i	−0.985258	+	0.171075i	$0.945276\pi$
$332$		−	9.38016e9i		−	0.772072i
$333$	−1.08845e10	+	1.30634e9i	−0.885176	+	0.106238i
$334$	−1.94282e9			−0.156116
$335$	−6.53534e6	+	6.53534e6i	−0.000518906	+	0.000518906i
$336$		−	3.65021e9i		−	0.286392i
$337$		−	9.99212e8i		−	0.0774708i	−0.999250	−	0.0387354i	$-0.987667\pi$
$337$		−	9.99212e8i		−	0.0774708i	0.999250	−	0.0387354i	$-0.0123329\pi$
$338$	1.29659e9	+	1.29659e9i	0.0993429	+	0.0993429i
$339$	5.85249e9	+	5.85249e9i	0.443141	+	0.443141i
$340$	5.18289e7			0.00387843
$341$	4.67380e7	+	4.67380e7i	0.00345662	+	0.00345662i
$342$	−7.18493e8			−0.0525192
$343$	1.40962e10			1.01842
$344$		−	9.22615e9i		−	0.658850i
$345$	−2.56200e7			−0.00180843
$346$	1.62282e9	+	1.62282e9i	0.113231	+	0.113231i
$347$	−9.65293e9	+	9.65293e9i	−0.665796	+	0.665796i	−0.956740	−	0.290944i	$-0.906031\pi$
$347$	−9.65293e9	+	9.65293e9i	−0.665796	+	0.665796i	0.290944	+	0.956740i	$0.406031\pi$
$348$	5.46724e8	−	5.46724e8i	0.0372779	−	0.0372779i
$349$	−1.58340e10			−1.06731			−0.533653	−	0.845703i	$-0.679181\pi$
$349$	−1.58340e10			−1.06731			−0.533653	+	0.845703i	$0.679181\pi$
$350$	−2.03283e9	−	2.03283e9i	−0.135466	−	0.135466i
$351$	−3.54440e9	+	3.54440e9i	−0.233515	+	0.233515i
$352$	−2.13165e7	−	2.13165e7i	−0.00138850	−	0.00138850i
$353$	−2.53024e9	+	2.53024e9i	−0.162954	+	0.162954i	−0.783874	−	0.620920i	$-0.786759\pi$
$353$	−2.53024e9	+	2.53024e9i	−0.162954	+	0.162954i	0.620920	+	0.783874i	$0.286759\pi$
$354$			9.99471e8i			0.0636440i
$355$	−2.02118e6	−	2.02118e6i	−0.000127260	−	0.000127260i
$356$	−1.29056e10	−	1.29056e10i	−0.803485	−	0.803485i
$357$	5.10643e9	−	5.10643e9i	0.314373	−	0.314373i
$358$			3.82797e9i			0.233043i
$359$	1.30190e10			0.783789			0.391894	−	0.920010i	$-0.371820\pi$
$359$	1.30190e10			0.783789			0.391894	+	0.920010i	$0.371820\pi$
$360$		−	1.68118e7i		−	0.00100093i
$361$		−	1.54399e10i		−	0.909111i
$362$	5.23471e8	−	5.23471e8i	0.0304830	−	0.0304830i
$363$		−	5.71846e9i		−	0.329346i
$364$	−6.20531e9	+	6.20531e9i	−0.353474	+	0.353474i
$365$	4.07123e7	−	4.07123e7i	0.00229380	−	0.00229380i
$366$	−1.25384e9			−0.0698742
$367$	1.40633e9			0.0775218			0.0387609	−	0.999249i	$-0.487659\pi$
$367$	1.40633e9			0.0775218			0.0387609	+	0.999249i	$0.487659\pi$
$368$	2.15635e10	+	2.15635e10i	1.17578	+	1.17578i
$369$		−	9.82495e9i		−	0.529938i
$370$	1.06490e7	−	1.27809e6i	0.000568204	−	6.81952e-5i
$371$	1.28098e10			0.676155
$372$	−5.94420e9	+	5.94420e9i	−0.310400	+	0.310400i
$373$		−	7.75139e9i		−	0.400446i	−0.979750	−	0.200223i	$-0.935833\pi$
$373$		−	7.75139e9i		−	0.400446i	0.979750	−	0.200223i	$-0.0641667\pi$
$374$		−	1.85684e7i		−	0.000949049i
$375$	−2.69761e7	−	2.69761e7i	−0.00136412	−	0.00136412i
$376$	−8.79523e9	−	8.79523e9i	−0.440044	−	0.440044i
$377$	−1.78213e9			−0.0882214
$378$	−1.72294e9	−	1.72294e9i	−0.0843925	−	0.0843925i
$379$	2.44045e10			1.18281			0.591404	−	0.806376i	$-0.298574\pi$
$379$	2.44045e10			1.18281			0.591404	+	0.806376i	$0.298574\pi$
$380$	−1.77079e7			−0.000849243
$381$			1.18019e10i			0.560082i
$382$	−2.87978e9			−0.135240
$383$	−1.34137e10	−	1.34137e10i	−0.623381	−	0.623381i	0.323013	−	0.946394i	$-0.395304\pi$
$383$	−1.34137e10	−	1.34137e10i	−0.623381	−	0.623381i	−0.946394	+	0.323013i	$0.895304\pi$
$384$	3.58862e9	−	3.58862e9i	0.165045	−	0.165045i
$385$	−157367.	+	157367.i	−7.16260e−6	+	7.16260e-6i
$386$	4.13724e8			0.0186364
$387$	2.43033e10	+	2.43033e10i	1.08348	+	1.08348i
$388$	1.09769e10	−	1.09769e10i	0.484343	−	0.484343i
$389$	1.38955e10	+	1.38955e10i	0.606841	+	0.606841i	0.942119	−	0.335278i	$-0.108830\pi$
$389$	1.38955e10	+	1.38955e10i	0.606841	+	0.606841i	−0.335278	+	0.942119i	$0.608830\pi$
$390$	1.63444e6	−	1.63444e6i	7.06498e−5	−	7.06498e-5i
$391$			6.03321e10i			2.58132i
$392$	2.47930e8	+	2.47930e8i	0.0104999	+	0.0104999i
$393$	−3.38602e9	−	3.38602e9i	−0.141945	−	0.141945i
$394$	−4.79532e9	+	4.79532e9i	−0.198991	+	0.198991i
$395$		−	9.09103e7i		−	0.00373443i
$396$	7.43859e7			0.00302489
$397$		−	4.25934e8i		−	0.0171467i	−0.999963	−	0.00857335i	$-0.997271\pi$
$397$		−	4.25934e8i		−	0.0171467i	0.999963	−	0.00857335i	$-0.00272901\pi$
$398$			3.46441e9i			0.138069i
$399$	−1.74467e9	+	1.74467e9i	−0.0688368	+	0.0688368i
$400$			2.27048e10i			0.886906i
$401$	4.15789e9	−	4.15789e9i	0.160804	−	0.160804i	−0.622119	−	0.782923i	$-0.713728\pi$
$401$	4.15789e9	−	4.15789e9i	0.160804	−	0.160804i	0.782923	+	0.622119i	$0.213728\pi$
$402$	−2.97780e8	+	2.97780e8i	−0.0114023	+	0.0114023i
$403$	1.93760e10			0.734589
$404$	−2.56800e10			−0.963985
$405$	3.82414e7	+	3.82414e7i	0.00142139	+	0.00142139i
$406$		−	8.66299e8i		−	0.0318833i
$407$	1.15346e7	+	9.61067e7i	0.000420364	+	0.00350248i
$408$	4.81687e9			0.173830
$409$	−2.32885e9	+	2.32885e9i	−0.0832238	+	0.0832238i	−0.747493	−	0.664269i	$-0.768743\pi$
$409$	−2.32885e9	+	2.32885e9i	−0.0832238	+	0.0832238i	0.664269	+	0.747493i	$0.268743\pi$
$410$			9.61246e6i			0.000340173i
$411$		−	5.40579e8i		−	0.0189449i
$412$	5.03462e9	+	5.03462e9i	0.174734	+	0.174734i
$413$	−1.99471e10	−	1.99471e10i	−0.685612	−	0.685612i
$414$	9.59456e9			0.326606
$415$	−4.93089e7	−	4.93089e7i	−0.00166239	−	0.00166239i
$416$	−8.83711e9			−0.295078
$417$	−7.66985e9			−0.253654
$418$			6.34409e6i			0.000207809i
$419$	−4.12254e10			−1.33755			−0.668773	−	0.743466i	$-0.733180\pi$
$419$	−4.12254e10			−1.33755			−0.668773	+	0.743466i	$0.733180\pi$
$420$	−2.00142e7	−	2.00142e7i	−0.000643191	−	0.000643191i
$421$	3.92886e10	−	3.92886e10i	1.25066	−	1.25066i	0.295232	−	0.955426i	$-0.404603\pi$
$421$	3.92886e10	−	3.92886e10i	1.25066	−	1.25066i	0.955426	−	0.295232i	$-0.0953969\pi$
$422$	−2.58715e9	+	2.58715e9i	−0.0815776	+	0.0815776i
$423$	4.63363e10			1.44731
$424$	6.04170e9	+	6.04170e9i	0.186937	+	0.186937i
$425$	−3.17627e10	+	3.17627e10i	−0.973557	+	0.973557i
$426$	−9.20942e7	−	9.20942e7i	−0.00279637	−	0.00279637i
$427$	2.50236e10	−	2.50236e10i	0.752729	−	0.752729i
$428$			4.19931e9i			0.125142i
$429$	1.47507e7	+	1.47507e7i	0.000435495	+	0.000435495i
$430$	−2.37777e7	−	2.37777e7i	−0.000695498	−	0.000695498i
$431$	2.05850e10	−	2.05850e10i	0.596542	−	0.596542i	−0.342849	−	0.939391i	$-0.611392\pi$
$431$	2.05850e10	−	2.05850e10i	0.596542	−	0.596542i	0.939391	+	0.342849i	$0.111392\pi$
$432$			1.92436e10i			0.552525i
$433$	2.45139e10			0.697367			0.348683	−	0.937241i	$-0.386629\pi$
$433$	2.45139e10			0.697367			0.348683	+	0.937241i	$0.386629\pi$
$434$			9.41874e9i			0.265481i
$435$		−	5.74795e6i		−	0.000160530i
$436$	−2.09636e10	+	2.09636e10i	−0.580124	+	0.580124i
$437$		−	2.06131e10i		−	0.565220i
$438$	1.85504e9	−	1.85504e9i	0.0504031	−	0.0504031i
$439$	−6.38960e9	+	6.38960e9i	−0.172034	+	0.172034i	−0.787873	−	0.615838i	$-0.788818\pi$
$439$	−6.38960e9	+	6.38960e9i	−0.172034	+	0.172034i	0.615838	+	0.787873i	$0.288818\pi$
$440$	−148443.			−3.96050e−6
$441$	−1.30618e9			−0.0345343
$442$	−3.84893e9	−	3.84893e9i	−0.100844	−	0.100844i
$443$		−	5.93791e10i		−	1.54177i	−0.636977	−	0.770883i	$-0.719815\pi$
$443$		−	5.93791e10i		−	1.54177i	0.636977	−	0.770883i	$-0.280185\pi$
$444$	−1.22230e10	+	1.46699e9i	−0.314518	+	0.0377481i
$445$	−1.35682e8			−0.00346005
$446$	5.98566e9	−	5.98566e9i	0.151277	−	0.151277i
$447$			1.61146e10i			0.403635i
$448$			3.07322e10i			0.762924i
$449$	−2.77048e10	−	2.77048e10i	−0.681664	−	0.681664i	0.278711	−	0.960375i	$-0.410093\pi$
$449$	−2.77048e10	−	2.77048e10i	−0.681664	−	0.681664i	−0.960375	+	0.278711i	$0.910093\pi$
$450$	5.05119e9	+	5.05119e9i	0.123181	+	0.123181i
$451$	−8.67516e7			−0.00209687
$452$	−5.40171e10	−	5.40171e10i	−1.29413	−	1.29413i
$453$	1.42330e9			0.0337989
$454$	−9.92065e9			−0.233516
$455$			6.52391e7i			0.00152217i
$456$	−1.64573e9			−0.0380627
$457$	−1.64164e10	−	1.64164e10i	−0.376368	−	0.376368i	0.493422	−	0.869790i	$-0.335746\pi$
$457$	−1.64164e10	−	1.64164e10i	−0.376368	−	0.376368i	−0.869790	+	0.493422i	$0.835746\pi$
$458$	8.36628e9	−	8.36628e9i	0.190139	−	0.190139i
$459$	−2.69207e10	+	2.69207e10i	−0.606508	+	0.606508i
$460$	2.36466e8			0.00528126
$461$	−2.28720e10	−	2.28720e10i	−0.506408	−	0.506408i	0.407014	−	0.913422i	$-0.366570\pi$
$461$	−2.28720e10	−	2.28720e10i	−0.506408	−	0.506408i	−0.913422	+	0.407014i	$0.866570\pi$
$462$	−7.17035e6	+	7.17035e6i	−0.000157388	+	0.000157388i
$463$	−2.66944e9	−	2.66944e9i	−0.0580893	−	0.0580893i	0.677465	−	0.735555i	$-0.263078\pi$
$463$	−2.66944e9	−	2.66944e9i	−0.0580893	−	0.0580893i	−0.735555	+	0.677465i	$0.763078\pi$
$464$	−4.83786e9	+	4.83786e9i	−0.104371	+	0.104371i
$465$			6.24940e7i			0.00133668i
$466$	7.18236e9	+	7.18236e9i	0.152308	+	0.152308i
$467$	−8.05161e8	−	8.05161e8i	−0.0169284	−	0.0169284i	0.698592	−	0.715520i	$-0.253810\pi$
$467$	−8.05161e8	−	8.05161e8i	−0.0169284	−	0.0169284i	−0.715520	+	0.698592i	$0.753810\pi$
$468$	1.54190e10	−	1.54190e10i	0.321419	−	0.321419i
$469$		−	1.18859e10i		−	0.245664i
$470$	−4.53342e7			−0.000929040
$471$			1.71958e10i			0.349412i
$472$		−	1.88159e10i		−	0.379104i
$473$	2.14591e8	−	2.14591e8i	0.00428714	−	0.00428714i
$474$		−	4.14229e9i		−	0.0820592i
$475$	1.08521e10	−	1.08521e10i	0.213176	−	0.213176i
$476$	−4.71311e10	+	4.71311e10i	−0.918078	+	0.918078i
$477$	−3.18298e10			−0.614837
$478$	−1.31262e10			−0.251436
$479$	−2.33155e10	−	2.33155e10i	−0.442898	−	0.442898i	0.450087	−	0.892985i	$-0.351393\pi$
$479$	−2.33155e10	−	2.33155e10i	−0.442898	−	0.442898i	−0.892985	+	0.450087i	$0.851393\pi$
$480$		−	2.85026e7i		−	0.000536932i
$481$	2.23123e10	+	1.75304e10i	0.416834	+	0.327500i
$482$	1.61078e10			0.298434
$483$	2.32978e10	−	2.32978e10i	0.428081	−	0.428081i
$484$			5.27800e10i			0.961806i
$485$		−	1.15405e8i		−	0.00208573i
$486$	6.54452e9	+	6.54452e9i	0.117309	+	0.117309i
$487$	−1.10358e10	−	1.10358e10i	−0.196194	−	0.196194i	0.602172	−	0.798366i	$-0.294302\pi$
$487$	−1.10358e10	−	1.10358e10i	−0.196194	−	0.196194i	−0.798366	+	0.602172i	$0.794302\pi$
$488$	2.36046e10			0.416215
$489$	−1.06730e10	−	1.06730e10i	−0.186660	−	0.186660i
$490$	1.27794e6			2.21679e−5
$491$	9.11478e10			1.56827			0.784134	−	0.620592i	$-0.213108\pi$
$491$	9.11478e10			1.56827			0.784134	+	0.620592i	$0.213108\pi$
$492$		−	1.10332e10i		−	0.188296i
$493$	−1.35358e10			−0.229137
$494$	1.31503e9	+	1.31503e9i	0.0220814	+	0.0220814i
$495$	391026.	−	391026.i	6.51305e−6	−	6.51305e-6i
$496$	5.25991e10	−	5.25991e10i	0.869064	−	0.869064i
$497$	3.67596e9			0.0602484
$498$	−2.24674e9	−	2.24674e9i	−0.0365288	−	0.0365288i
$499$	−8.38475e10	+	8.38475e10i	−1.35235	+	1.35235i	−0.469315	+	0.883031i	$0.655499\pi$
$499$	−8.38475e10	+	8.38475e10i	−1.35235	+	1.35235i	−0.883031	+	0.469315i	$0.844501\pi$
$500$	2.48983e8	+	2.48983e8i	0.00398372	+	0.00398372i
$501$	1.17223e10	−	1.17223e10i	0.186064	−	0.186064i
$502$		−	1.08120e10i		−	0.170251i
$503$	−9.18266e9	−	9.18266e9i	−0.143449	−	0.143449i	0.631735	−	0.775184i	$-0.282343\pi$
$503$	−9.18266e9	−	9.18266e9i	−0.143449	−	0.143449i	−0.775184	+	0.631735i	$0.782343\pi$
$504$	1.52880e10	+	1.52880e10i	0.236934	+	0.236934i
$505$	−1.34993e8	+	1.34993e8i	−0.00207561	+	0.00207561i
$506$		−	8.47173e7i		−	0.00129232i
$507$	−1.56464e10			−0.236801
$508$		−	1.08929e11i		−	1.63564i
$509$		−	3.19098e10i		−	0.475393i	−0.971339	−	0.237696i	$-0.923608\pi$
$509$		−	3.19098e10i		−	0.475393i	0.971339	−	0.237696i	$-0.0763923\pi$
$510$	1.24141e7	−	1.24141e7i	0.000183499	−	0.000183499i
$511$			7.40444e10i			1.08595i
$512$	−4.05105e10	+	4.05105e10i	−0.589505	+	0.589505i
$513$	9.19775e9	−	9.19775e9i	0.132804	−	0.132804i
$514$	−1.25998e10			−0.180515
$515$	5.29311e7			0.000752458
$516$	2.72920e10	+	2.72920e10i	0.384979	+	0.384979i
$517$		−	4.09137e8i		−	0.00572673i
$518$	−8.52158e9	+	1.08461e10i	−0.118359	+	0.150644i
$519$	−1.95831e10			−0.269906
$520$	−3.07698e7	+	3.07698e7i	−0.000420835	+	0.000420835i
$521$		−	7.92441e10i		−	1.07551i	−0.843100	−	0.537757i	$-0.819272\pi$
$521$		−	7.92441e10i		−	1.07551i	0.843100	−	0.537757i	$-0.180728\pi$
$522$			2.15258e9i			0.0289920i
$523$	5.37861e10	+	5.37861e10i	0.718892	+	0.718892i	0.968378	−	0.249487i	$-0.0802619\pi$
$523$	5.37861e10	+	5.37861e10i	0.718892	+	0.718892i	−0.249487	+	0.968378i	$0.580262\pi$
$524$	3.12521e10	+	3.12521e10i	0.414528	+	0.414528i
$525$	2.45309e10			0.322906
$526$	6.66435e9	+	6.66435e9i	0.0870593	+	0.0870593i
$527$	1.47166e11			1.90795
$528$	8.00859e7			0.00103043
$529$			1.96951e11i			2.51498i
$530$	3.11414e7			0.000394670
$531$	4.95645e10	+	4.95645e10i	0.623437	+	0.623437i
$532$	1.61028e10	−	1.61028e10i	0.201028	−	0.201028i
$533$	−1.79822e10	+	1.79822e10i	−0.222809	+	0.222809i
$534$	−6.18229e9			−0.0760299
$535$	2.20746e7	+	2.20746e7i	0.000269450	+	0.000269450i
$536$	5.60597e9	−	5.60597e9i	0.0679191	−	0.0679191i
$537$	−2.30967e10	−	2.30967e10i	−0.277749	−	0.277749i
$538$	8.28184e9	−	8.28184e9i	0.0988548	−	0.0988548i
$539$			1.15332e7i			0.000136646i
$540$	1.05513e8	+	1.05513e8i	0.00124089	+	0.00124089i
$541$	−6.67602e10	−	6.67602e10i	−0.779343	−	0.779343i	0.200376	−	0.979719i	$-0.435784\pi$
$541$	−6.67602e10	−	6.67602e10i	−0.779343	−	0.779343i	−0.979719	+	0.200376i	$0.935784\pi$
$542$	−1.45305e10	+	1.45305e10i	−0.168377	+	0.168377i
$543$			6.31689e9i			0.0726615i
$544$	−6.71204e10			−0.766406
$545$			2.20400e8i			0.00249819i
$546$			2.97259e9i			0.0334476i
$547$	5.63667e9	−	5.63667e9i	0.0629612	−	0.0629612i	−0.674925	−	0.737886i	$-0.735824\pi$
$547$	5.63667e9	−	5.63667e9i	0.0629612	−	0.0629612i	0.737886	+	0.674925i	$0.235824\pi$
$548$			4.98941e9i			0.0553257i
$549$	−6.21787e10	+	6.21787e10i	−0.684467	+	0.684467i
$550$	4.46006e7	−	4.46006e7i	0.000487405	−	0.000487405i
$551$	4.62464e9			0.0501732
$552$	2.19766e10			0.236704
$553$	8.26702e10	+	8.26702e10i	0.883992	+	0.883992i
$554$		−	3.18080e9i		−	0.0337674i
$555$	−5.65412e7	+	7.19644e7i	−0.000595927	+	0.000758482i
$556$	7.07908e10			0.740760
$557$	6.25430e10	−	6.25430e10i	0.649767	−	0.649767i	−0.303169	−	0.952937i	$-0.598045\pi$
$557$	6.25430e10	−	6.25430e10i	0.649767	−	0.649767i	0.952937	+	0.303169i	$0.0980448\pi$
$558$		−	2.34037e10i		−	0.241406i
$559$		−	8.89624e10i		−	0.911086i
$560$	1.77101e8	+	1.77101e8i	0.00180082	+	0.00180082i
$561$	1.12036e8	+	1.12036e8i	0.00113111	+	0.00113111i
$562$	−1.40426e9			−0.0140767
$563$	−1.42513e10	−	1.42513e10i	−0.141847	−	0.141847i	0.632618	−	0.774464i	$-0.281981\pi$
$563$	−1.42513e10	−	1.42513e10i	−0.141847	−	0.141847i	−0.774464	+	0.632618i	$0.781981\pi$
$564$	5.20346e10			0.514252
$565$	−5.67905e8			−0.00557291
$566$		−	2.50494e10i		−	0.244080i
$567$	−6.95505e10			−0.672927
$568$	1.73376e9	+	1.73376e9i	0.0166569	+	0.0166569i
$569$	−1.82386e10	+	1.82386e10i	−0.173998	+	0.173998i	−0.788733	−	0.614736i	$-0.789263\pi$
$569$	−1.82386e10	+	1.82386e10i	−0.173998	+	0.173998i	0.614736	+	0.788733i	$0.289263\pi$
$570$	−4.24139e6	+	4.24139e6i	−4.01799e−5	+	4.01799e-5i
$571$	7.04088e10			0.662343			0.331171	−	0.943571i	$-0.392556\pi$
$571$	7.04088e10			0.662343			0.331171	+	0.943571i	$0.392556\pi$
$572$	−1.36145e8	−	1.36145e8i	−0.00127180	−	0.00127180i
$573$	1.73756e10	−	1.73756e10i	0.161184	−	0.161184i
$574$	−8.74119e9	−	8.74119e9i	−0.0805236	−	0.0805236i
$575$	−1.44915e11	+	1.44915e11i	−1.32569	+	1.32569i
$576$		−	7.63634e10i		−	0.693738i
$577$	−7.33906e10	−	7.33906e10i	−0.662120	−	0.662120i	0.293759	−	0.955879i	$-0.405094\pi$
$577$	−7.33906e10	−	7.33906e10i	−0.662120	−	0.662120i	−0.955879	+	0.293759i	$0.905094\pi$
$578$	−1.38123e10	−	1.38123e10i	−0.123753	−	0.123753i
$579$	−2.49627e9	+	2.49627e9i	−0.0222115	+	0.0222115i
$580$			5.30522e7i			0.000468804i
$581$	8.96790e10			0.787021
$582$		−	5.25838e9i		−	0.0458310i
$583$			2.81048e8i			0.00243280i
$584$	−3.49228e10	+	3.49228e10i	−0.300232	+	0.300232i
$585$		−	1.62106e8i		−	0.00138413i
$586$	−1.36324e10	+	1.36324e10i	−0.115607	+	0.115607i
$587$	−9.09393e10	+	9.09393e10i	−0.765948	+	0.765948i	−0.977390	−	0.211443i	$-0.932184\pi$
$587$	−9.09393e10	+	9.09393e10i	−0.765948	+	0.765948i	0.211443	+	0.977390i	$0.432184\pi$
$588$	−1.46682e9			−0.0122706
$589$	−5.02809e10			−0.417774
$590$	−4.84925e7	−	4.84925e7i	−0.000400191	−	0.000400191i
$591$		−	5.78667e10i		−	0.474328i
$592$	1.08159e11	−	1.29811e10i	0.880594	−	0.105688i
$593$	8.79369e10			0.711135			0.355568	−	0.934651i	$-0.384288\pi$
$593$	8.79369e10			0.711135			0.355568	+	0.934651i	$0.384288\pi$
$594$	3.78016e7	−	3.78016e7i	0.000303644	−	0.000303644i
$595$			4.95510e8i			0.00395352i
$596$		−	1.48734e11i		−	1.17876i
$597$	−2.09031e10	−	2.09031e10i	−0.164556	−	0.164556i
$598$	−1.75605e10	−	1.75605e10i	−0.137319	−	0.137319i
$599$	−1.95791e11			−1.52084			−0.760421	−	0.649430i	$-0.775008\pi$
$599$	−1.95791e11			−1.52084			−0.760421	+	0.649430i	$0.775008\pi$
$600$	1.15699e10	+	1.15699e10i	0.0892740	+	0.0892740i
$601$	−1.08080e11			−0.828416			−0.414208	−	0.910182i	$-0.635941\pi$
$601$	−1.08080e11			−0.828416			−0.414208	+	0.910182i	$0.635941\pi$
$602$	4.32449e10			0.329268
$603$			2.95342e10i			0.223386i
$604$	−1.31367e10			−0.0987048
$605$	2.77449e8	+	2.77449e8i	0.00207091	+	0.00207091i
$606$	−6.15088e9	+	6.15088e9i	−0.0456086	+	0.0456086i
$607$	−1.56506e11	+	1.56506e11i	−1.15286	+	1.15286i	−0.166885	+	0.985976i	$0.553371\pi$
$607$	−1.56506e11	+	1.56506e11i	−1.15286	+	1.15286i	−0.985976	+	0.166885i	$0.946629\pi$
$608$	2.29324e10			0.167816
$609$	5.22696e9	+	5.22696e9i	0.0379997	+	0.0379997i
$610$	6.08339e7	−	6.08339e7i	0.000439366	−	0.000439366i
$611$	−8.48073e10	−	8.48073e10i	−0.608511	−	0.608511i
$612$	1.17111e11	−	1.17111e11i	0.834821	−	0.834821i
$613$		−	2.33044e11i		−	1.65042i	−0.564824	−	0.825212i	$-0.691056\pi$
$613$		−	2.33044e11i		−	1.65042i	0.564824	−	0.825212i	$-0.308944\pi$
$614$	−2.63054e10	−	2.63054e10i	−0.185085	−	0.185085i
$615$	−5.79984e7	−	5.79984e7i	−0.000405430	−	0.000405430i
$616$	1.34988e8	−	1.34988e8i	0.000937505	−	0.000937505i
$617$			3.07290e10i			0.212035i	0.994364	+	0.106017i	$0.0338099\pi$
$617$			3.07290e10i			0.212035i	−0.994364	+	0.106017i	$0.966190\pi$
$618$	2.41178e9			0.0165342
$619$		−	9.88334e10i		−	0.673196i	−0.941648	−	0.336598i	$-0.890724\pi$
$619$		−	9.88334e10i		−	0.673196i	0.941648	−	0.336598i	$-0.109276\pi$
$620$		−	5.76804e8i		−	0.00390357i
$621$	−1.22824e11	+	1.22824e11i	−0.825881	+	0.825881i
$622$			1.06030e10i			0.0708384i
$623$	1.23384e11	−	1.23384e11i	0.819042	−	0.819042i
$624$	1.66005e10	−	1.66005e10i	0.109492	−	0.109492i
$625$	−1.52584e11			−0.999974
$626$	−5.14970e9			−0.0335340
$627$	−3.82781e7	−	3.82781e7i	−0.000247674	−	0.000247674i
$628$		−	1.58713e11i		−	1.02041i
$629$	1.69468e11	+	1.33148e11i	1.08264	+	0.850615i
$630$	7.88004e7			0.000500226
$631$	1.67883e9	−	1.67883e9i	0.0105898	−	0.0105898i	−0.701792	−	0.712382i	$-0.747616\pi$
$631$	1.67883e9	−	1.67883e9i	0.0105898	−	0.0105898i	0.712382	+	0.701792i	$0.247616\pi$
$632$			7.79823e10i			0.488796i
$633$		−	3.12199e10i		−	0.194454i
$634$	3.81580e10	+	3.81580e10i	0.236172	+	0.236172i
$635$	−5.72607e8	−	5.72607e8i	−0.00352177	−	0.00352177i
$636$	−3.57441e10			−0.218462
$637$	2.39065e9	+	2.39065e9i	0.0145197	+	0.0145197i
$638$	1.90067e7			0.000114716
$639$	−9.13404e9			−0.0547847
$640$			3.48227e8i			0.00207559i
$641$	1.95340e11			1.15707			0.578535	−	0.815657i	$-0.303624\pi$
$641$	1.95340e11			1.15707			0.578535	+	0.815657i	$0.303624\pi$
$642$	1.00582e9	+	1.00582e9i	0.00592079	+	0.00592079i
$643$	2.08113e11	−	2.08113e11i	1.21746	−	1.21746i	0.248941	−	0.968519i	$-0.419917\pi$
$643$	2.08113e11	−	2.08113e11i	1.21746	−	1.21746i	0.968519	−	0.248941i	$-0.0800825\pi$
$644$	−2.15033e11	+	2.15033e11i	−1.25015	+	1.25015i
$645$	2.86933e8			0.00165784
$646$	9.98800e9	+	9.98800e9i	0.0573520	+	0.0573520i
$647$	9.79040e10	−	9.79040e10i	0.558706	−	0.558706i	−0.370233	−	0.928939i	$-0.620722\pi$
$647$	9.79040e10	−	9.79040e10i	0.558706	−	0.558706i	0.928939	+	0.370233i	$0.120722\pi$
$648$	−3.28033e10	−	3.28033e10i	−0.186045	−	0.186045i
$649$	4.37641e8	−	4.37641e8i	0.00246683	−	0.00246683i
$650$		−	1.84899e10i		−	0.103581i
$651$	−5.68295e10	−	5.68295e10i	−0.316410	−	0.316410i
$652$	9.85090e10	+	9.85090e10i	0.545112	+	0.545112i
$653$	−1.02730e11	+	1.02730e11i	−0.564993	+	0.564993i	−0.930722	−	0.365728i	$-0.880820\pi$
$653$	−1.02730e11	+	1.02730e11i	−0.564993	+	0.564993i	0.365728	+	0.930722i	$0.380820\pi$
$654$			1.00424e10i			0.0548943i
$655$	3.28567e8			0.00178508
$656$			9.76307e10i			0.527194i
$657$		−	1.83986e11i		−	0.987466i
$658$	4.12251e10	−	4.12251e10i	0.219917	−	0.219917i
$659$			1.48433e11i			0.787026i	0.919319	+	0.393513i	$0.128740\pi$
$659$			1.48433e11i			0.787026i	−0.919319	+	0.393513i	$0.871260\pi$
$660$	439113.	−	439113.i	2.31420e−6	−	2.31420e-6i
$661$	−1.53911e11	+	1.53911e11i	−0.806239	+	0.806239i	−0.984062	−	0.177824i	$-0.943094\pi$
$661$	−1.53911e11	+	1.53911e11i	−0.806239	+	0.806239i	0.177824	+	0.984062i	$0.443094\pi$
$662$	4.32112e10			0.224990
$663$	4.64463e10			0.240379
$664$	4.22968e10	+	4.22968e10i	0.217588	+	0.217588i
$665$		−	1.69296e8i		−	0.000865686i
$666$	2.11744e10	−	2.69503e10i	0.107625	−	0.136983i
$667$	−6.17561e10			−0.312016
$668$	−1.08194e11	+	1.08194e11i	−0.543373	+	0.543373i
$669$			7.22310e10i			0.360594i
$670$		−	2.88955e7i		−	0.000143394i
$671$	5.49021e8	+	5.49021e8i	0.00270831	+	0.00270831i
$672$	2.59191e10	+	2.59191e10i	0.127099	+	0.127099i
$673$	2.57351e11			1.25449			0.627243	−	0.778824i	$-0.284183\pi$
$673$	2.57351e11			1.25449			0.627243	+	0.778824i	$0.284183\pi$
$674$	2.20897e9	+	2.20897e9i	0.0107041	+	0.0107041i
$675$	−1.29325e11			−0.622970
$676$	1.44412e11			0.691541
$677$			3.59297e11i			1.71041i	0.518293	+	0.855203i	$0.326568\pi$
$677$			3.59297e11i			1.71041i	−0.518293	+	0.855203i	$0.673432\pi$
$678$	−2.58763e10			−0.122457
$679$	1.04945e11	+	1.04945e11i	0.493720	+	0.493720i
$680$	−2.33706e8	+	2.33706e8i	−0.00109303	+	0.00109303i
$681$	5.98579e10	−	5.98579e10i	0.278313	−	0.278313i
$682$	−2.06648e8			−0.000955199
$683$	1.28828e11	+	1.28828e11i	0.592007	+	0.592007i	0.938173	−	0.346166i	$-0.112517\pi$
$683$	1.28828e11	+	1.28828e11i	0.592007	+	0.592007i	−0.346166	+	0.938173i	$0.612517\pi$
$684$	−4.00123e10	+	4.00123e10i	−0.182797	+	0.182797i
$685$	2.62279e7	+	2.62279e7i	0.000119125	+	0.000119125i
$686$	−3.11627e10	+	3.11627e10i	−0.140714	+	0.140714i
$687$			1.00959e11i			0.453228i
$688$	−2.41502e11	−	2.41502e11i	−1.07787	−	1.07787i
$689$	5.82566e10	+	5.82566e10i	0.258505	+	0.258505i
$690$	5.66383e7	−	5.66383e7i	0.000249870	−	0.000249870i
$691$		−	1.54730e11i		−	0.678676i	−0.940664	−	0.339338i	$-0.889797\pi$
$691$		−	1.54730e11i		−	0.678676i	0.940664	−	0.339338i	$-0.110203\pi$
$692$	1.80747e11			0.788220
$693$			7.11166e8i			0.00308346i
$694$		−	4.26797e10i		−	0.183985i
$695$	3.72127e8	−	3.72127e8i	0.00159497	−	0.00159497i
$696$			4.93056e9i			0.0210116i
$697$	−1.36580e11	+	1.36580e11i	−0.578702	+	0.578702i
$698$	3.50044e10	−	3.50044e10i	0.147469	−	0.147469i
$699$	−8.66719e10			−0.363053
$700$	−2.26414e11			−0.942998
$701$	3.01511e11	+	3.01511e11i	1.24862	+	1.24862i	0.956328	+	0.292296i	$0.0944192\pi$
$701$	3.01511e11	+	3.01511e11i	1.24862	+	1.24862i	0.292296	+	0.956328i	$0.405581\pi$
$702$		−	1.56713e10i		−	0.0645292i
$703$	−5.79005e10	−	4.54915e10i	−0.237061	−	0.186255i
$704$	−6.74267e8			−0.00274499
$705$	2.73531e8	−	2.73531e8i	0.00110726	−	0.00110726i
$706$		−	1.11873e10i		−	0.0450304i
$707$		−	2.45514e11i		−	0.982649i
$708$	5.56598e10	+	5.56598e10i	0.221518	+	0.221518i
$709$	−1.14500e10	−	1.14500e10i	−0.0453130	−	0.0453130i	0.684087	−	0.729400i	$-0.260201\pi$
$709$	−1.14500e10	−	1.14500e10i	−0.0453130	−	0.0453130i	−0.729400	+	0.684087i	$0.760201\pi$
$710$	8.93649e6			3.51669e−5
$711$	−2.05419e11	−	2.05419e11i	−0.803827	−	0.803827i
$712$	1.16387e11			0.452882
$713$	6.71437e11			2.59805
$714$			2.25777e10i			0.0868733i
$715$	−1.43135e6			−5.47675e−6
$716$	2.13177e11	+	2.13177e11i	0.811125	+	0.811125i
$717$	7.91990e10	−	7.91990e10i	0.299670	−	0.299670i
$718$	−2.87812e10	+	2.87812e10i	−0.108296	+	0.108296i
$719$	−1.00337e10			−0.0375444			−0.0187722	−	0.999824i	$-0.505976\pi$
$719$	−1.00337e10			−0.0375444			−0.0187722	+	0.999824i	$0.505976\pi$
$720$	−4.40062e8	−	4.40062e8i	−0.00163751	−	0.00163751i
$721$	−4.81334e10	+	4.81334e10i	−0.178117	+	0.178117i
$722$	3.41332e10	+	3.41332e10i	0.125611	+	0.125611i
$723$	−9.71892e10	+	9.71892e10i	−0.355685	+	0.355685i
$724$		−	5.83033e10i		−	0.212197i
$725$	−3.25124e10	−	3.25124e10i	−0.117678	−	0.117678i
$726$	1.26419e10	+	1.26419e10i	0.0455056	+	0.0455056i
$727$	−2.11856e11	+	2.11856e11i	−0.758410	+	0.758410i	−0.976033	−	0.217623i	$-0.930170\pi$
$727$	−2.11856e11	+	2.11856e11i	−0.758410	+	0.758410i	0.217623	+	0.976033i	$0.430170\pi$
$728$		−	5.59617e10i		−	0.199235i
$729$	1.14871e11			0.406725
$730$			1.80006e8i			0.000633865i
$731$		−	6.75695e11i		−	2.36636i
$732$	−6.98253e10	+	6.98253e10i	−0.243203	+	0.243203i
$733$		−	4.77588e11i		−	1.65439i	−0.561915	−	0.827195i	$-0.689935\pi$
$733$		−	4.77588e11i		−	1.65439i	0.561915	−	0.827195i	$-0.310065\pi$
$734$	−3.10899e9	+	3.10899e9i	−0.0107111	+	0.0107111i
$735$	−7.71063e6	+	7.71063e6i	−2.64205e−5	+	2.64205e-5i
$736$	−3.06232e11			−1.04361
$737$	2.60779e8			0.000883899
$738$	2.17201e10	+	2.17201e10i	0.0732212	+	0.0732212i
$739$			2.11589e10i			0.0709441i	0.999371	+	0.0354720i	$0.0112935\pi$
$739$			2.11589e10i			0.0709441i	−0.999371	+	0.0354720i	$0.988707\pi$
$740$	5.21862e8	−	6.64213e8i	0.00174032	−	0.00221503i
$741$	−1.58689e10			−0.0526348
$742$	−2.83187e10	+	2.83187e10i	−0.0934239	+	0.0934239i
$743$			2.24627e11i			0.737067i	0.929614	+	0.368534i	$0.120140\pi$
$743$			2.24627e11i			0.737067i	−0.929614	+	0.368534i	$0.879860\pi$
$744$		−	5.36070e10i		−	0.174956i
$745$	−7.81850e8	−	7.81850e8i	−0.00253804	−	0.00253804i
$746$	1.71361e10	+	1.71361e10i	0.0553294	+	0.0553294i
$747$	−2.22835e11			−0.715649
$748$	−1.03406e9	−	1.03406e9i	−0.00330324	−	0.00330324i
$749$	−4.01475e10			−0.127565
$750$	1.19273e8			0.000376960
$751$		−	2.22791e11i		−	0.700386i	−0.936678	−	0.350193i	$-0.886116\pi$
$751$		−	2.22791e11i		−	0.700386i	0.936678	−	0.350193i	$-0.113884\pi$
$752$	−4.60445e11			−1.43981
$753$	6.52359e10	+	6.52359e10i	0.202911	+	0.202911i
$754$	3.93977e9	−	3.93977e9i	0.0121895	−	0.0121895i
$755$	−6.90558e7	+	6.90558e7i	−0.000212526	+	0.000212526i
$756$	−1.91899e11			−0.587469
$757$	1.65681e11	+	1.65681e11i	0.504532	+	0.504532i	0.912843	−	0.408311i	$-0.133882\pi$
$757$	1.65681e11	+	1.65681e11i	0.504532	+	0.504532i	−0.408311	+	0.912843i	$0.633882\pi$
$758$	−5.39514e10	+	5.39514e10i	−0.163428	+	0.163428i
$759$	5.11155e8	+	5.11155e8i	0.00154023	+	0.00154023i
$760$	7.98480e7	−	7.98480e7i	0.000239337	−	0.000239337i
$761$		−	3.56595e11i		−	1.06325i	−0.846979	−	0.531626i	$-0.821581\pi$
$761$		−	3.56595e11i		−	1.06325i	0.846979	−	0.531626i	$-0.178419\pi$
$762$	−2.60906e10	−	2.60906e10i	−0.0773862	−	0.0773862i
$763$	−2.00423e11	−	2.00423e11i	−0.591356	−	0.591356i
$764$	−1.60373e11	+	1.60373e11i	−0.470715	+	0.470715i
$765$		−	1.23124e9i		−	0.00359499i
$766$	5.93077e10			0.172264
$767$		−	1.81431e11i		−	0.524241i
$768$		−	7.32917e10i		−	0.210674i
$769$	−2.27854e11	+	2.27854e11i	−0.651555	+	0.651555i	−0.953367	−	0.301812i	$-0.902408\pi$
$769$	−2.27854e11	+	2.27854e11i	−0.651555	+	0.651555i	0.301812	+	0.953367i	$0.402408\pi$
$770$		−	695785.i		−	1.97930e-6i
$771$	7.60231e10	−	7.60231e10i	0.215144	−	0.215144i
$772$	2.30400e10	−	2.30400e10i	0.0648653	−	0.0648653i
$773$	−6.17259e11			−1.72882			−0.864409	−	0.502789i	$-0.832307\pi$
$773$	−6.17259e11			−1.72882			−0.864409	+	0.502789i	$0.832307\pi$
$774$	−1.07455e11			−0.299408
$775$	3.53487e11	+	3.53487e11i	0.979867	+	0.979867i
$776$			9.89936e10i			0.272999i
$777$	−1.40252e10	−	1.16858e11i	−0.0384790	−	0.320608i
$778$	−6.14377e10			−0.167694
$779$	4.66639e10	−	4.66639e10i	0.126716	−	0.126716i
$780$		−	1.82042e8i		−	0.000491804i
$781$			8.06510e7i			0.000216773i
$782$	−1.33377e11	−	1.33377e11i	−0.356659	−	0.356659i
$783$	−2.75561e10	−	2.75561e10i	−0.0733114	−	0.0733114i
$784$	1.29796e10			0.0343555
$785$	−8.34307e8	−	8.34307e8i	−0.00219709	−	0.00219709i
$786$	1.49710e10			0.0392248
$787$	6.41776e11			1.67296			0.836478	−	0.548001i	$-0.184611\pi$
$787$	6.41776e11			1.67296			0.836478	+	0.548001i	$0.184611\pi$
$788$			5.34095e11i			1.38520i
$789$	−8.04209e10			−0.207521
$790$	2.00976e8	+	2.00976e8i	0.000515985	+	0.000515985i
$791$	5.16430e11	−	5.16430e11i	1.31918	−	1.31918i
$792$	−3.35419e8	+	3.35419e8i	−0.000852486	+	0.000852486i
$793$	2.27606e11			0.575560
$794$	9.41617e8	+	9.41617e8i	0.00236915	+	0.00236915i
$795$	−1.87897e8	+	1.87897e8i	−0.000470382	+	0.000470382i
$796$	1.92930e11	+	1.92930e11i	0.480560	+	0.480560i
$797$	4.65545e11	−	4.65545e11i	1.15379	−	1.15379i	0.168008	−	0.985786i	$-0.446266\pi$
$797$	4.65545e11	−	4.65545e11i	1.15379	−	1.15379i	0.985786	−	0.168008i	$-0.0537336\pi$
$798$		−	7.71390e9i		−	0.0190223i
$799$	−6.44136e11	−	6.44136e11i	−1.58048	−	1.58048i
$800$	−1.61220e11	−	1.61220e11i	−0.393604	−	0.393604i
$801$	−3.06584e11	+	3.06584e11i	−0.744766	+	0.744766i
$802$			1.83838e10i			0.0444363i
$803$	−1.62454e9			−0.00390723
$804$			3.31662e10i			0.0793729i
$805$			2.26073e9i			0.00538351i
$806$	−4.28347e10	+	4.28347e10i	−0.101498	+	0.101498i
$807$			9.99397e10i			0.235637i
$808$	1.15796e11	−	1.15796e11i	0.271674	−	0.271674i
$809$	−1.35082e11	+	1.35082e11i	−0.315358	+	0.315358i	−0.846981	−	0.531623i	$-0.821582\pi$
$809$	−1.35082e11	+	1.35082e11i	−0.315358	+	0.315358i	0.531623	+	0.846981i	$0.321582\pi$
$810$	−1.69082e8			−0.000392786
$811$	−4.63841e11			−1.07222			−0.536112	−	0.844147i	$-0.680107\pi$
$811$	−4.63841e11			−1.07222			−0.536112	+	0.844147i	$0.680107\pi$
$812$	−4.82435e10	−	4.82435e10i	−0.110972	−	0.110972i
$813$		−	1.75344e11i		−	0.401354i
$814$	−2.37964e8	−	1.86964e8i	−0.000542017	−	0.000425854i
$815$	1.03567e9			0.00234742
$816$	1.26085e11	−	1.26085e11i	0.284384	−	0.284384i
$817$			2.30858e11i			0.518152i
$818$		−	1.02968e10i		−	0.0229980i
$819$	1.47413e11	+	1.47413e11i	0.327642	+	0.327642i
$820$	5.35311e8	+	5.35311e8i	0.00118400	+	0.00118400i
$821$	2.53705e11			0.558414			0.279207	−	0.960231i	$-0.409928\pi$
$821$	2.53705e11			0.558414			0.279207	+	0.960231i	$0.409928\pi$
$822$	1.19506e9	+	1.19506e9i	0.00261760	+	0.00261760i
$823$	3.14622e11			0.685789			0.342894	−	0.939374i	$-0.388593\pi$
$823$	3.14622e11			0.685789			0.342894	+	0.939374i	$0.388593\pi$
$824$	−4.54040e10			−0.0984884
$825$			5.38210e8i			0.00116181i
$826$	8.81943e10			0.189461
$827$	1.57299e11	+	1.57299e11i	0.336283	+	0.336283i	0.854966	−	0.518683i	$-0.173578\pi$
$827$	1.57299e11	+	1.57299e11i	0.336283	+	0.336283i	−0.518683	+	0.854966i	$0.673578\pi$
$828$	5.34313e11	−	5.34313e11i	1.13678	−	1.13678i
$829$	−3.79541e11	+	3.79541e11i	−0.803602	+	0.803602i	−0.983657	−	0.180055i	$-0.942373\pi$
$829$	−3.79541e11	+	3.79541e11i	−0.803602	+	0.803602i	0.180055	+	0.983657i	$0.442373\pi$
$830$	2.18015e8			0.000459383
$831$	1.91919e10	+	1.91919e10i	0.0402451	+	0.0402451i
$832$	−1.39764e11	+	1.39764e11i	−0.291678	+	0.291678i
$833$	1.81577e10	+	1.81577e10i	0.0377121	+	0.0377121i
$834$	1.69558e10	−	1.69558e10i	0.0350473	−	0.0350473i
$835$			1.13749e9i			0.00233993i
$836$	3.53298e8	+	3.53298e8i	0.000723295	+	0.000723295i
$837$	2.99601e11	+	2.99601e11i	0.610438	+	0.610438i
$838$	9.11375e10	−	9.11375e10i	0.184808	−	0.184808i
$839$			8.67138e11i			1.75001i	0.484114	+	0.875005i	$0.339142\pi$
$839$			8.67138e11i			1.75001i	−0.484114	+	0.875005i	$0.660858\pi$
$840$	1.80495e8			0.000362533
$841$			4.86391e11i			0.972303i
$842$			1.73712e11i			0.345605i
$843$	8.47283e9	−	8.47283e9i	0.0167772	−	0.0167772i
$844$			2.88152e11i			0.567875i
$845$	7.59135e8	−	7.59135e8i	0.00148899	−	0.00148899i
$846$	−1.02436e11	+	1.02436e11i	−0.199973	+	0.199973i
$847$	−5.04603e11			−0.980429
$848$	3.16293e11			0.611654
$849$	1.51140e11	+	1.51140e11i	0.290903	+	0.290903i
$850$		−	1.40436e11i		−	0.269032i
$851$	7.73187e11	+	6.07481e11i	1.47423	+	1.15828i
$852$	−1.02573e10			−0.0194659
$853$	1.67855e11	−	1.67855e11i	0.317058	−	0.317058i	−0.530578	−	0.847636i	$-0.678025\pi$
$853$	1.67855e11	−	1.67855e11i	0.317058	−	0.317058i	0.847636	+	0.530578i	$0.178025\pi$
$854$			1.10640e11i			0.208008i
$855$			4.20667e8i			0.000787180i
$856$	−1.89355e10	−	1.89355e10i	−0.0352680	−	0.0352680i
$857$	−4.22699e11	−	4.22699e11i	−0.783625	−	0.783625i	0.196816	−	0.980440i	$-0.436940\pi$
$857$	−4.22699e11	−	4.22699e11i	−0.783625	−	0.783625i	−0.980440	+	0.196816i	$0.936940\pi$
$858$	−6.52190e7			−0.000120344
$859$	−5.56622e11	−	5.56622e11i	−1.02232	−	1.02232i	−0.999745	−	0.0225763i	$-0.992813\pi$
$859$	−5.56622e11	−	5.56622e11i	−1.02232	−	1.02232i	−0.0225763	−	0.999745i	$-0.507187\pi$
$860$	−2.64832e9			−0.00484147
$861$	1.05483e11			0.191942
$862$			9.10148e10i			0.164848i
$863$	−4.11649e11			−0.742137			−0.371068	−	0.928606i	$-0.621008\pi$
$863$	−4.11649e11			−0.742137			−0.371068	+	0.928606i	$0.621008\pi$
$864$	−1.36644e11	−	1.36644e11i	−0.245208	−	0.245208i
$865$	9.50137e8	−	9.50137e8i	0.00169716	−	0.00169716i
$866$	−5.41932e10	+	5.41932e10i	−0.0963548	+	0.0963548i
$867$	1.66678e11			0.294986
$868$	5.24522e11	+	5.24522e11i	0.924028	+	0.924028i
$869$	−1.81379e9	+	1.81379e9i	−0.00318060	+	0.00318060i
$870$	1.27071e7	+	1.27071e7i	2.21803e−5	+	2.21803e-5i
$871$	5.40551e10	−	5.40551e10i	0.0939214	−	0.0939214i
$872$		−	1.89058e11i		−	0.326985i
$873$	−2.60767e11	−	2.60767e11i	−0.448947	−	0.448947i
$874$	4.55696e10	+	4.55696e10i	0.0780961	+	0.0780961i
$875$	−2.38040e9	+	2.38040e9i	−0.00406085	+	0.00406085i
$876$		−	2.06612e11i		−	0.350863i
$877$	7.45866e11			1.26085			0.630424	−	0.776251i	$-0.282881\pi$
$877$	7.45866e11			1.26085			0.630424	+	0.776251i	$0.282881\pi$
$878$		−	2.82511e10i		−	0.0475398i
$879$		−	1.64507e11i		−	0.275568i
$880$	−3.88563e6	+	3.88563e6i	−6.47933e−6	+	6.47933e-6i
$881$			8.28880e11i			1.37590i	0.725756	+	0.687952i	$0.241490\pi$
$881$			8.28880e11i			1.37590i	−0.725756	+	0.687952i	$0.758510\pi$
$882$	2.88760e9	−	2.88760e9i	0.00477158	−	0.00477158i
$883$	−5.30668e11	+	5.30668e11i	−0.872931	+	0.872931i	−0.992791	−	0.119860i	$-0.961756\pi$
$883$	−5.30668e11	+	5.30668e11i	−0.872931	+	0.872931i	0.119860	+	0.992791i	$0.461756\pi$
$884$	−4.28688e11			−0.701991
$885$	5.85175e8			0.000953922
$886$	1.31270e11	+	1.31270e11i	0.213025	+	0.213025i
$887$		−	1.12010e12i		−	1.80952i	−0.425925	−	0.904758i	$-0.640051\pi$
$887$		−	1.12010e12i		−	1.80952i	0.425925	−	0.904758i	$-0.359949\pi$
$888$	4.85007e10	−	6.17306e10i	0.0780003	−	0.0992770i
$889$	1.04141e12			1.66731
$890$	2.99954e8	−	2.99954e8i	0.000478073	−	0.000478073i
$891$		−	1.52594e9i		−	0.00242118i
$892$		−	6.66674e11i		−	1.05306i
$893$	2.20076e11	+	2.20076e11i	0.346072	+	0.346072i
$894$	−3.56247e10	−	3.56247e10i	−0.0557700	−	0.0557700i
$895$	2.24122e9			0.00349295
$896$	−3.16663e11	−	3.16663e11i	−0.491322	−	0.491322i
$897$	2.11908e11			0.327324
$898$	1.22495e11			0.188370
$899$			1.50640e11i			0.230622i
$900$	5.62593e11			0.857481
$901$	4.42476e11	+	4.42476e11i	0.671414	+	0.671414i
$902$	1.91783e8	−	1.91783e8i	0.000289723	−	0.000289723i
$903$	−2.60925e11	+	2.60925e11i	−0.392433	+	0.392433i
$904$	4.87145e11			0.729432
$905$	−3.06484e8	−	3.06484e8i	−0.000456892	−	0.000456892i
$906$	−3.14650e9	+	3.14650e9i	−0.00466998	+	0.00466998i
$907$	−5.72843e11	−	5.72843e11i	−0.846461	−	0.846461i	0.143229	−	0.989690i	$-0.454251\pi$
$907$	−5.72843e11	−	5.72843e11i	−0.846461	−	0.846461i	−0.989690	+	0.143229i	$0.954251\pi$
$908$	−5.52474e11	+	5.52474e11i	−0.812771	+	0.812771i
$909$			6.10053e11i			0.893536i
$910$	−1.44225e8	−	1.44225e8i	−0.000210317	−	0.000210317i
$911$	−7.86032e11	−	7.86032e11i	−1.14121	−	1.14121i	−0.988229	−	0.152985i	$-0.951111\pi$
$911$	−7.86032e11	−	7.86032e11i	−1.14121	−	1.14121i	−0.152985	−	0.988229i	$-0.548889\pi$
$912$	−4.30784e10	+	4.30784e10i	−0.0622702	+	0.0622702i
$913$			1.96757e9i			0.00283169i
$914$	7.25837e10			0.104005
$915$			7.34103e8i			0.00104730i
$916$		−	9.31823e11i		−	1.32358i
$917$	−2.98786e11	+	2.98786e11i	−0.422554	+	0.422554i
$918$		−	1.19028e11i		−	0.167602i
$919$	−2.24900e11	+	2.24900e11i	−0.315303	+	0.315303i	−0.846960	−	0.531657i	$-0.821570\pi$
$919$	−2.24900e11	+	2.24900e11i	−0.315303	+	0.315303i	0.531657	+	0.846960i	$0.321570\pi$
$920$	−1.06627e9	+	1.06627e9i	−0.00148838	+	0.00148838i
$921$	3.17436e11			0.441182
$922$	1.01127e11			0.139940
$923$	1.67176e10	+	1.67176e10i	0.0230339	+	0.0230339i
$924$			7.98623e8i			0.00109560i
$925$	8.72384e10	+	7.26871e11i	0.119163	+	0.992866i
$926$	1.18027e10			0.0160523
$927$	1.19602e11	−	1.19602e11i	0.161964	−	0.161964i
$928$		−	6.87046e10i		−	0.0926390i
$929$		−	1.33944e12i		−	1.79829i	−0.437654	−	0.899143i	$-0.644191\pi$
$929$		−	1.33944e12i		−	1.79829i	0.437654	−	0.899143i	$-0.355809\pi$
$930$	−1.38156e8	−	1.38156e8i	−0.000184688	−	0.000184688i
$931$	−6.20376e9	−	6.20376e9i	−0.00825764	−	0.00825764i
$932$	7.99960e11			1.06024
$933$	−6.39752e10	−	6.39752e10i	−0.0844277	−	0.0844277i
$934$	3.55996e9			0.00467797
$935$	−1.08715e7			−1.42247e−5
$936$			1.39054e11i			0.181167i
$937$	−1.03597e12			−1.34397			−0.671985	−	0.740565i	$-0.734558\pi$
$937$	−1.03597e12			−1.34397			−0.671985	+	0.740565i	$0.734558\pi$
$938$	2.62764e10	+	2.62764e10i	0.0339433	+	0.0339433i
$939$	3.10716e10	−	3.10716e10i	0.0399669	−	0.0399669i
$940$	−2.52463e9	+	2.52463e9i	−0.00323360	+	0.00323360i
$941$	−1.27971e12			−1.63213			−0.816064	−	0.577962i	$-0.803848\pi$
$941$	−1.27971e12			−1.63213			−0.816064	+	0.577962i	$0.803848\pi$
$942$	−3.80148e10	−	3.80148e10i	−0.0482780	−	0.0482780i
$943$	−6.23136e11	+	6.23136e11i	−0.788018	+	0.788018i
$944$	−4.92523e11	−	4.92523e11i	−0.620209	−	0.620209i
$945$	−1.00876e9	+	1.00876e9i	−0.00126491	+	0.00126491i
$946$			9.48798e8i			0.00118470i
$947$	−7.82828e11	−	7.82828e11i	−0.973344	−	0.973344i	0.0263097	−	0.999654i	$-0.491624\pi$
$947$	−7.82828e11	−	7.82828e11i	−0.973344	−	0.973344i	−0.999654	+	0.0263097i	$0.991624\pi$
$948$	−2.30681e11	−	2.30681e11i	−0.285613	−	0.285613i
$949$	−3.36740e11	+	3.36740e11i	−0.415174	+	0.415174i
$950$			4.79815e10i			0.0589087i
$951$	−4.60466e11			−0.562957
$952$		−	4.25045e11i		−	0.517473i
$953$			2.34455e11i			0.284242i	0.989849	+	0.142121i	$0.0453922\pi$
$953$			2.34455e11i			0.284242i	−0.989849	+	0.142121i	$0.954608\pi$
$954$	7.03664e10	−	7.03664e10i	0.0849517	−	0.0849517i
$955$			1.68607e9i			0.00202704i
$956$	−7.30988e11	+	7.30988e11i	−0.875142	+	0.875142i
$957$	−1.14680e8	+	1.14680e8i	−0.000136722	+	0.000136722i
$958$	1.03088e11			0.122390
$959$	−4.77013e10			−0.0563969
$960$	−4.50786e8	−	4.50786e8i	−0.000530745	−	0.000530745i
$961$		−	7.84924e11i		−	0.920310i
$962$	−8.80805e10	+	1.05713e10i	−0.102844	+	0.0123433i
$963$	9.97586e10			0.115997
$964$	8.97033e11	−	8.97033e11i	1.03872	−	1.03872i
$965$		−	2.42229e8i		−	0.000279330i
$966$			1.03009e11i			0.118295i
$967$	5.85110e11	+	5.85110e11i	0.669163	+	0.669163i	0.957522	−	0.288360i	$-0.0931098\pi$
$967$	5.85110e11	+	5.85110e11i	0.669163	+	0.669163i	−0.288360	+	0.957522i	$0.593110\pi$
$968$	−2.37994e11	−	2.37994e11i	−0.271060	−	0.271060i
$969$	−1.20528e11			−0.136708
$970$	2.55127e8	+	2.55127e8i	0.000288184	+	0.000288184i
$971$	1.46445e12			1.64740			0.823699	−	0.567027i	$-0.191906\pi$
$971$	1.46445e12			1.64740			0.823699	+	0.567027i	$0.191906\pi$
$972$	7.28918e11			0.816608
$973$			6.76795e11i			0.755102i
$974$	4.87938e10			0.0542161
$975$	1.11562e11	+	1.11562e11i	0.123452	+	0.123452i
$976$	6.17870e11	−	6.17870e11i	0.680923	−	0.680923i
$977$	−6.53852e11	+	6.53852e11i	−0.717631	+	0.717631i	−0.968120	−	0.250489i	$-0.919409\pi$
$977$	−6.53852e11	+	6.53852e11i	−0.717631	+	0.717631i	0.250489	+	0.968120i	$0.419409\pi$
$978$	4.71897e10			0.0515813
$979$	2.70705e9	+	2.70705e9i	0.00294691	+	0.00294691i
$980$	7.11672e7	−	7.11672e7i	7.71571e−5	−	7.71571e-5i
$981$	4.98011e11	+	4.98011e11i	0.537728	+	0.537728i
$982$	−2.01501e11	+	2.01501e11i	−0.216687	+	0.216687i
$983$		−	7.42110e11i		−	0.794793i	−0.917647	−	0.397396i	$-0.869914\pi$
$983$		−	7.42110e11i		−	0.794793i	0.917647	−	0.397396i	$-0.130086\pi$
$984$	4.97507e10	+	4.97507e10i	0.0530663	+	0.0530663i
$985$	2.80759e9	+	2.80759e9i	0.00298255	+	0.00298255i
$986$	2.99237e10	−	2.99237e10i	0.0316598	−	0.0316598i
$987$			4.97477e11i			0.524209i
$988$	1.46466e11			0.153712
$989$		−	3.08282e12i		−	3.22227i
$990$			1.72889e6i			1.79981e-6i
$991$	−1.06636e12	+	1.06636e12i	−1.10563	+	1.10563i	−0.111907	+	0.993719i	$0.535696\pi$
$991$	−1.06636e12	+	1.06636e12i	−1.10563	+	1.10563i	−0.993719	+	0.111907i	$0.964304\pi$
$992$			7.46983e11i			0.771372i
$993$	−2.60722e11	+	2.60722e11i	−0.268152	+	0.268152i
$994$	−8.12649e9	+	8.12649e9i	−0.00832449	+	0.00832449i
$995$	2.02836e9			0.00206944
$996$	−2.50238e11			−0.254282
$997$	−2.27977e11	−	2.27977e11i	−0.230733	−	0.230733i	0.582266	−	0.812999i	$-0.302166\pi$
$997$	−2.27977e11	−	2.27977e11i	−0.230733	−	0.230733i	−0.812999	+	0.582266i	$0.802166\pi$
$998$		−	3.70725e11i		−	0.373706i
$999$	7.39396e10	+	6.16066e11i	0.0742361	+	0.618536i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.9.d.a.6.12	✓	50
37.31	odd	4	inner	37.9.d.a.31.12	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.9.d.a.6.12	✓	50	1.1	even	1	trivial
37.9.d.a.31.12	yes	50	37.31	odd	4	inner

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:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	37.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.21071 + 2.21071i) q^{2} -26.6774i q^{3} +246.226i q^{4} +(1.29434 + 1.29434i) q^{5} +(58.9759 + 58.9759i) q^{6} -2354.04 q^{7} +(-1110.28 - 1110.28i) q^{8} +5849.32 q^{9} +O(q^{10})\)	\(q+(-2.21071 + 2.21071i) q^{2} -26.6774i q^{3} +246.226i q^{4} +(1.29434 + 1.29434i) q^{5} +(58.9759 + 58.9759i) q^{6} -2354.04 q^{7} +(-1110.28 - 1110.28i) q^{8} +5849.32 q^{9} -5.72281 q^{10} -51.6478i q^{11} +6568.65 q^{12} +(-10705.7 - 10705.7i) q^{13} +(5204.10 - 5204.10i) q^{14} +(34.5295 - 34.5295i) q^{15} -58124.7 q^{16} +(-81313.2 - 81313.2i) q^{17} +(-12931.1 + 12931.1i) q^{18} +(27781.5 + 27781.5i) q^{19} +(-318.699 + 318.699i) q^{20} +62799.5i q^{21} +(114.178 + 114.178i) q^{22} +(-370986. - 370986. i) q^{23} +(-29619.2 + 29619.2i) q^{24} -390622. i q^{25} +47334.6 q^{26} -331075. i q^{27} -579624. i q^{28} +(83232.4 - 83232.4i) q^{29} +152.670i q^{30} +(-904935. + 904935. i) q^{31} +(412727. - 412727. i) q^{32} -1377.83 q^{33} +359520. q^{34} +(-3046.92 - 3046.92i) q^{35} +1.44025e6i q^{36} +(-1.86081e6 + 223332. i) q^{37} -122834. q^{38} +(-285601. + 285601. i) q^{39} -2874.14i q^{40} -1.67967e6i q^{41} +(-138832. - 138832. i) q^{42} +(4.15489e6 + 4.15489e6i) q^{43} +12717.0 q^{44} +(7570.99 + 7570.99i) q^{45} +1.64029e6 q^{46} +7.92167e6 q^{47} +1.55062e6i q^{48} -223305. q^{49} +(863551. + 863551. i) q^{50} +(-2.16922e6 + 2.16922e6i) q^{51} +(2.63603e6 - 2.63603e6i) q^{52} -5.44162e6 q^{53} +(731910. + 731910. i) q^{54} +(66.8498 - 66.8498i) q^{55} +(2.61363e6 + 2.61363e6i) q^{56} +(741137. - 741137. i) q^{57} +368005. i q^{58} +(8.47355e6 + 8.47355e6i) q^{59} +(8502.05 + 8502.05i) q^{60} +(-1.06301e7 + 1.06301e7i) q^{61} -4.00110e6i q^{62} -1.37695e7 q^{63} -1.30551e7i q^{64} -27713.7i q^{65} +(3045.98 - 3045.98i) q^{66} +5.04917e6i q^{67} +(2.00214e7 - 2.00214e7i) q^{68} +(-9.89694e6 + 9.89694e6i) q^{69} +13471.7 q^{70} -1.56156e6 q^{71} +(-6.49435e6 - 6.49435e6i) q^{72} -3.14542e7i q^{73} +(3.61998e6 - 4.60743e6i) q^{74} -1.04208e7 q^{75} +(-6.84051e6 + 6.84051e6i) q^{76} +121581. i q^{77} -1.26276e6i q^{78} +(-3.51185e7 - 3.51185e7i) q^{79} +(-75233.1 - 75233.1i) q^{80} +2.95452e7 q^{81} +(3.71327e6 + 3.71327e6i) q^{82} -3.80958e7 q^{83} -1.54629e7 q^{84} -210494. i q^{85} -1.83705e7 q^{86} +(-2.22042e6 - 2.22042e6i) q^{87} +(-57343.3 + 57343.3i) q^{88} +(-5.24137e7 + 5.24137e7i) q^{89} -33474.6 q^{90} +(2.52017e7 + 2.52017e7i) q^{91} +(9.13463e7 - 9.13463e7i) q^{92} +(2.41413e7 + 2.41413e7i) q^{93} +(-1.75125e7 + 1.75125e7i) q^{94} +71917.3i q^{95} +(-1.10105e7 - 1.10105e7i) q^{96} +(-4.45807e7 - 4.45807e7i) q^{97} +(493664. - 493664. i) q^{98} -302105. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 4 q^{2} + 124 q^{5} + 510 q^{6} - 4 q^{7} - 5256 q^{8} - 93534 q^{9}+O(q^{10}) \) 50 * q + 4 * q^2 + 124 * q^5 + 510 * q^6 - 4 * q^7 - 5256 * q^8 - 93534 * q^9	\( 50 q + 4 q^{2} + 124 q^{5} + 510 q^{6} - 4 q^{7} - 5256 q^{8} - 93534 q^{9} - 10756 q^{10} - 45440 q^{12} + 63592 q^{13} - 80206 q^{14} - 124346 q^{15} - 639128 q^{16} - 178796 q^{17} - 45882 q^{18} + 264774 q^{19} + 469204 q^{20} + 714574 q^{22} - 654272 q^{23} - 1573644 q^{24} + 1841660 q^{26} - 1683686 q^{29} + 1766336 q^{31} - 4332632 q^{32} - 1438888 q^{33} - 5838452 q^{34} - 650482 q^{35} - 2870078 q^{37} - 2281528 q^{38} + 11036546 q^{39} - 7453902 q^{42} + 5097830 q^{43} - 14992464 q^{44} - 15078446 q^{45} + 28776464 q^{46} + 13992320 q^{47} + 4370314 q^{49} + 7603288 q^{50} + 19417938 q^{51} + 54318452 q^{52} + 28075952 q^{53} - 19197122 q^{54} - 6104306 q^{55} + 47803128 q^{56} + 17462426 q^{57} - 677072 q^{59} + 24953316 q^{60} + 4206386 q^{61} - 18098032 q^{63} - 56061730 q^{66} - 52579760 q^{68} + 88118984 q^{69} - 295493636 q^{70} - 37172476 q^{71} - 74582504 q^{72} - 224754524 q^{74} - 144364996 q^{75} + 189294548 q^{76} + 271163438 q^{79} - 312998084 q^{80} + 41535626 q^{81} - 177494710 q^{82} - 74250268 q^{83} - 82088924 q^{84} + 112964036 q^{86} - 142771908 q^{87} + 224951860 q^{88} + 84928780 q^{89} + 716592116 q^{90} - 40969098 q^{91} - 701292428 q^{92} - 83761576 q^{93} + 553881406 q^{94} - 7259376 q^{96} + 467792674 q^{97} + 538649310 q^{98}+O(q^{100}) \) 50 * q + 4 * q^2 + 124 * q^5 + 510 * q^6 - 4 * q^7 - 5256 * q^8 - 93534 * q^9 - 10756 * q^10 - 45440 * q^12 + 63592 * q^13 - 80206 * q^14 - 124346 * q^15 - 639128 * q^16 - 178796 * q^17 - 45882 * q^18 + 264774 * q^19 + 469204 * q^20 + 714574 * q^22 - 654272 * q^23 - 1573644 * q^24 + 1841660 * q^26 - 1683686 * q^29 + 1766336 * q^31 - 4332632 * q^32 - 1438888 * q^33 - 5838452 * q^34 - 650482 * q^35 - 2870078 * q^37 - 2281528 * q^38 + 11036546 * q^39 - 7453902 * q^42 + 5097830 * q^43 - 14992464 * q^44 - 15078446 * q^45 + 28776464 * q^46 + 13992320 * q^47 + 4370314 * q^49 + 7603288 * q^50 + 19417938 * q^51 + 54318452 * q^52 + 28075952 * q^53 - 19197122 * q^54 - 6104306 * q^55 + 47803128 * q^56 + 17462426 * q^57 - 677072 * q^59 + 24953316 * q^60 + 4206386 * q^61 - 18098032 * q^63 - 56061730 * q^66 - 52579760 * q^68 + 88118984 * q^69 - 295493636 * q^70 - 37172476 * q^71 - 74582504 * q^72 - 224754524 * q^74 - 144364996 * q^75 + 189294548 * q^76 + 271163438 * q^79 - 312998084 * q^80 + 41535626 * q^81 - 177494710 * q^82 - 74250268 * q^83 - 82088924 * q^84 + 112964036 * q^86 - 142771908 * q^87 + 224951860 * q^88 + 84928780 * q^89 + 716592116 * q^90 - 40969098 * q^91 - 701292428 * q^92 - 83761576 * q^93 + 553881406 * q^94 - 7259376 * q^96 + 467792674 * q^97 + 538649310 * q^98

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