LMFDB - Embedded newform 25.3.f.a.8.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,3,Mod(2,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("25.2");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	25.f (of order $20$, degree $8$, 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:	$0.681200660901$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			8.3
Character	$\chi$	$=$	25.8
Dual form			25.3.f.a.22.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.972743 + 0.495637i) q^{2} +(0.872241 + 0.138149i) q^{3} +(-1.65057 - 2.27181i) q^{4} +(-2.66494 + 4.23062i) q^{5} +(0.779995 + 0.566699i) q^{6} +(1.62783 - 1.62783i) q^{7} +(-1.16272 - 7.34115i) q^{8} +(-7.81779 - 2.54015i) q^{9} +O(q^{10})$	\(q+(0.972743 + 0.495637i) q^{2} +(0.872241 + 0.138149i) q^{3} +(-1.65057 - 2.27181i) q^{4} +(-2.66494 + 4.23062i) q^{5} +(0.779995 + 0.566699i) q^{6} +(1.62783 - 1.62783i) q^{7} +(-1.16272 - 7.34115i) q^{8} +(-7.81779 - 2.54015i) q^{9} +(-4.68915 + 2.79446i) q^{10} +(3.53016 + 10.8647i) q^{11} +(-1.12584 - 2.20959i) q^{12} +(7.63976 - 3.89265i) q^{13} +(2.39027 - 0.776647i) q^{14} +(-2.90893 + 3.32196i) q^{15} +(-0.963505 + 2.96536i) q^{16} +(25.1372 - 3.98134i) q^{17} +(-6.34570 - 6.34570i) q^{18} +(-5.60535 + 7.71510i) q^{19} +(14.0098 - 0.928682i) q^{20} +(1.64474 - 1.19498i) q^{21} +(-1.95102 + 12.3182i) q^{22} +(-5.39644 + 10.5911i) q^{23} -6.56388i q^{24} +(-10.7962 - 22.5487i) q^{25} +9.36086 q^{26} +(-13.5498 - 6.90398i) q^{27} +(-6.38497 - 1.01128i) q^{28} +(5.56383 + 7.65796i) q^{29} +(-4.47612 + 1.78964i) q^{30} +(-42.2846 - 30.7215i) q^{31} +(-23.4297 + 23.4297i) q^{32} +(1.57820 + 9.96433i) q^{33} +(26.4253 + 8.58610i) q^{34} +(2.54866 + 11.2248i) q^{35} +(7.13304 + 21.9532i) q^{36} +(-21.6541 - 42.4985i) q^{37} +(-9.27645 + 4.72659i) q^{38} +(7.20148 - 2.33990i) q^{39} +(34.1562 + 14.6447i) q^{40} +(16.6504 - 51.2445i) q^{41} +(2.19219 - 0.347209i) q^{42} +(46.5461 + 46.5461i) q^{43} +(18.8558 - 25.9528i) q^{44} +(31.5803 - 26.3047i) q^{45} +(-10.4987 + 7.62775i) q^{46} +(-8.92142 + 56.3277i) q^{47} +(-1.25007 + 2.45341i) q^{48} +43.7003i q^{49} +(0.674010 - 27.2851i) q^{50} +22.4757 q^{51} +(-21.4533 - 10.9310i) q^{52} +(-17.7814 - 2.81630i) q^{53} +(-9.75862 - 13.4316i) q^{54} +(-55.3720 - 14.0190i) q^{55} +(-13.8429 - 10.0574i) q^{56} +(-5.95505 + 5.95505i) q^{57} +(1.61661 + 10.2069i) q^{58} +(-13.2502 - 4.30525i) q^{59} +(12.3482 + 1.12542i) q^{60} +(0.671981 + 2.06814i) q^{61} +(-25.9053 - 50.8420i) q^{62} +(-16.8610 + 8.59109i) q^{63} +(-22.5423 + 7.32443i) q^{64} +(-3.89117 + 42.6945i) q^{65} +(-3.40352 + 10.4749i) q^{66} +(116.666 - 18.4780i) q^{67} +(-50.5355 - 50.5355i) q^{68} +(-6.17015 + 8.49249i) q^{69} +(-3.08423 + 12.1820i) q^{70} +(-57.1398 + 41.5145i) q^{71} +(-9.55772 + 60.3450i) q^{72} +(28.5805 - 56.0923i) q^{73} -52.0727i q^{74} +(-6.30182 - 21.1594i) q^{75} +26.7793 q^{76} +(23.4324 + 11.9394i) q^{77} +(8.16493 + 1.29320i) q^{78} +(19.9697 + 27.4860i) q^{79} +(-9.97763 - 11.9787i) q^{80} +(48.9869 + 35.5911i) q^{81} +(41.5952 - 41.5952i) q^{82} +(-7.27847 - 45.9545i) q^{83} +(-5.42953 - 1.76416i) q^{84} +(-50.1455 + 116.956i) q^{85} +(22.2074 + 68.3474i) q^{86} +(3.79506 + 7.44823i) q^{87} +(75.6548 - 38.5480i) q^{88} +(-30.3143 + 9.84970i) q^{89} +(43.7571 - 9.93533i) q^{90} +(6.09965 - 18.7728i) q^{91} +(32.9682 - 5.22165i) q^{92} +(-32.6382 - 32.6382i) q^{93} +(-36.5963 + 50.3705i) q^{94} +(-17.7017 - 44.2743i) q^{95} +(-23.6732 + 17.1996i) q^{96} +(10.7597 - 67.9342i) q^{97} +(-21.6595 + 42.5092i) q^{98} -93.9051i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 10 q^{2} - 10 q^{3} - 10 q^{4} - 10 q^{5} - 6 q^{6} - 10 q^{7} - 10 q^{8} - 10 q^{9}+O(q^{10}) $ 32 * q - 10 * q^2 - 10 * q^3 - 10 * q^4 - 10 * q^5 - 6 * q^6 - 10 * q^7 - 10 * q^8 - 10 * q^9	\( 32 q - 10 q^{2} - 10 q^{3} - 10 q^{4} - 10 q^{5} - 6 q^{6} - 10 q^{7} - 10 q^{8} - 10 q^{9} - 10 q^{10} - 6 q^{11} - 10 q^{12} - 10 q^{13} - 10 q^{14} - 10 q^{15} + 2 q^{16} + 60 q^{17} + 140 q^{18} + 90 q^{19} + 130 q^{20} - 6 q^{21} + 70 q^{22} + 10 q^{23} - 40 q^{25} + 4 q^{26} - 100 q^{27} - 250 q^{28} - 110 q^{29} - 250 q^{30} - 6 q^{31} - 290 q^{32} - 190 q^{33} - 260 q^{34} - 120 q^{35} - 58 q^{36} + 50 q^{37} + 320 q^{38} + 390 q^{39} + 440 q^{40} - 86 q^{41} + 690 q^{42} + 230 q^{43} + 340 q^{44} + 310 q^{45} - 6 q^{46} + 70 q^{47} + 160 q^{48} - 100 q^{50} - 16 q^{51} - 320 q^{52} - 190 q^{53} - 660 q^{54} - 250 q^{55} - 70 q^{56} - 650 q^{57} - 640 q^{58} - 260 q^{59} - 550 q^{60} + 114 q^{61} + 60 q^{62} - 20 q^{63} + 340 q^{64} + 360 q^{65} + 138 q^{66} + 270 q^{67} + 710 q^{68} + 340 q^{69} + 310 q^{70} - 66 q^{71} + 360 q^{72} + 30 q^{73} - 90 q^{75} - 80 q^{76} - 250 q^{77} - 500 q^{78} - 210 q^{79} - 850 q^{80} + 62 q^{81} + 30 q^{82} - 10 q^{84} + 600 q^{85} - 6 q^{86} + 300 q^{87} + 190 q^{88} - 10 q^{89} + 380 q^{90} - 6 q^{91} - 30 q^{92} + 520 q^{93} + 790 q^{94} + 310 q^{95} + 174 q^{96} + 270 q^{97} + 170 q^{98}+O(q^{100}) \) 32 * q - 10 * q^2 - 10 * q^3 - 10 * q^4 - 10 * q^5 - 6 * q^6 - 10 * q^7 - 10 * q^8 - 10 * q^9 - 10 * q^10 - 6 * q^11 - 10 * q^12 - 10 * q^13 - 10 * q^14 - 10 * q^15 + 2 * q^16 + 60 * q^17 + 140 * q^18 + 90 * q^19 + 130 * q^20 - 6 * q^21 + 70 * q^22 + 10 * q^23 - 40 * q^25 + 4 * q^26 - 100 * q^27 - 250 * q^28 - 110 * q^29 - 250 * q^30 - 6 * q^31 - 290 * q^32 - 190 * q^33 - 260 * q^34 - 120 * q^35 - 58 * q^36 + 50 * q^37 + 320 * q^38 + 390 * q^39 + 440 * q^40 - 86 * q^41 + 690 * q^42 + 230 * q^43 + 340 * q^44 + 310 * q^45 - 6 * q^46 + 70 * q^47 + 160 * q^48 - 100 * q^50 - 16 * q^51 - 320 * q^52 - 190 * q^53 - 660 * q^54 - 250 * q^55 - 70 * q^56 - 650 * q^57 - 640 * q^58 - 260 * q^59 - 550 * q^60 + 114 * q^61 + 60 * q^62 - 20 * q^63 + 340 * q^64 + 360 * q^65 + 138 * q^66 + 270 * q^67 + 710 * q^68 + 340 * q^69 + 310 * q^70 - 66 * q^71 + 360 * q^72 + 30 * q^73 - 90 * q^75 - 80 * q^76 - 250 * q^77 - 500 * q^78 - 210 * q^79 - 850 * q^80 + 62 * q^81 + 30 * q^82 - 10 * q^84 + 600 * q^85 - 6 * q^86 + 300 * q^87 + 190 * q^88 - 10 * q^89 + 380 * q^90 - 6 * q^91 - 30 * q^92 + 520 * q^93 + 790 * q^94 + 310 * q^95 + 174 * q^96 + 270 * q^97 + 170 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{20}\right)$

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 $

$2$	0.972743	+	0.495637i	0.486371	+	0.247819i	0.679940	−	0.733268i	$-0.262006\pi$
$2$	0.972743	+	0.495637i	0.486371	+	0.247819i	−0.193568	+	0.981087i	$0.562006\pi$
$3$	0.872241	+	0.138149i	0.290747	+	0.0460498i	0.300104	−	0.953906i	$-0.402979\pi$
$3$	0.872241	+	0.138149i	0.290747	+	0.0460498i	−0.00935716	+	0.999956i	$0.502979\pi$
$4$	−1.65057	−	2.27181i	−0.412642	−	0.567953i
$5$	−2.66494	+	4.23062i	−0.532988	+	0.846123i
$5$	−2.66494	+	4.23062i	−0.532988	+	0.846123i
$6$	0.779995	+	0.566699i	0.129999	+	0.0944499i
$7$	1.62783	−	1.62783i	0.232547	−	0.232547i	−0.581208	−	0.813755i	$-0.697420\pi$
$7$	1.62783	−	1.62783i	0.232547	−	0.232547i	0.813755	+	0.581208i	$0.197420\pi$
$8$	−1.16272	−	7.34115i	−0.145340	−	0.917644i
$9$	−7.81779	−	2.54015i	−0.868643	−	0.282239i
$10$	−4.68915	+	2.79446i	−0.468915	+	0.279446i
$11$	3.53016	+	10.8647i	0.320923	+	0.987700i	0.973247	+	0.229760i	$0.0737941\pi$
$11$	3.53016	+	10.8647i	0.320923	+	0.987700i	−0.652324	+	0.757940i	$0.726206\pi$
$12$	−1.12584	−	2.20959i	−0.0938204	−	0.184133i
$13$	7.63976	−	3.89265i	0.587674	−	0.299435i	−0.134756	−	0.990879i	$-0.543025\pi$
$13$	7.63976	−	3.89265i	0.587674	−	0.299435i	0.722430	+	0.691444i	$0.243025\pi$
$14$	2.39027	−	0.776647i	0.170734	−	0.0554748i
$15$	−2.90893	+	3.32196i	−0.193928	+	0.221464i
$16$	−0.963505	+	2.96536i	−0.0602191	+	0.185335i
$17$	25.1372	−	3.98134i	1.47866	−	0.234196i	0.635599	−	0.772019i	$-0.280753\pi$
$17$	25.1372	−	3.98134i	1.47866	−	0.234196i	0.843058	+	0.537823i	$0.180753\pi$
$18$	−6.34570	−	6.34570i	−0.352539	−	0.352539i
$19$	−5.60535	+	7.71510i	−0.295018	+	0.406058i	−0.930636	−	0.365946i	$-0.880745\pi$
$19$	−5.60535	+	7.71510i	−0.295018	+	0.406058i	0.635618	+	0.772004i	$0.280745\pi$
$20$	14.0098	−	0.928682i	0.700491	−	0.0464341i
$21$	1.64474	−	1.19498i	0.0783212	−	0.0569037i
$22$	−1.95102	+	12.3182i	−0.0886826	+	0.559920i
$23$	−5.39644	+	10.5911i	−0.234628	+	0.460483i	−0.978059	−	0.208330i	$-0.933197\pi$
$23$	−5.39644	+	10.5911i	−0.234628	+	0.460483i	0.743431	+	0.668813i	$0.233197\pi$
$24$		−	6.56388i		−	0.273495i
$25$	−10.7962	−	22.5487i	−0.431849	−	0.901946i
$26$	9.36086			0.360033
$27$	−13.5498	−	6.90398i	−0.501845	−	0.255703i
$28$	−6.38497	−	1.01128i	−0.228035	−	0.0361171i
$29$	5.56383	+	7.65796i	0.191856	+	0.264068i	0.894098	−	0.447871i	$-0.147818\pi$
$29$	5.56383	+	7.65796i	0.191856	+	0.264068i	−0.702242	+	0.711938i	$0.747818\pi$
$30$	−4.47612	+	1.78964i	−0.149204	+	0.0596546i
$31$	−42.2846	−	30.7215i	−1.36402	−	0.991017i	−0.998178	−	0.0603394i	$-0.980782\pi$
$31$	−42.2846	−	30.7215i	−1.36402	−	0.991017i	−0.365840	−	0.930678i	$-0.619218\pi$
$32$	−23.4297	+	23.4297i	−0.732179	+	0.732179i
$33$	1.57820	+	9.96433i	0.0478241	+	0.301949i
$34$	26.4253	+	8.58610i	0.777215	+	0.252532i
$35$	2.54866	+	11.2248i	0.0728188	+	0.320708i
$36$	7.13304	+	21.9532i	0.198140	+	0.609812i
$37$	−21.6541	−	42.4985i	−0.585245	−	1.14861i	−0.973847	−	0.227203i	$-0.927042\pi$
$37$	−21.6541	−	42.4985i	−0.585245	−	1.14861i	0.388602	−	0.921406i	$-0.372958\pi$
$38$	−9.27645	+	4.72659i	−0.244117	+	0.124384i
$39$	7.20148	−	2.33990i	0.184653	−	0.0599975i
$40$	34.1562	+	14.6447i	0.853904	+	0.366117i
$41$	16.6504	−	51.2445i	0.406106	−	1.24987i	−0.513862	−	0.857873i	$-0.671786\pi$
$41$	16.6504	−	51.2445i	0.406106	−	1.24987i	0.919968	−	0.391994i	$-0.128214\pi$
$42$	2.19219	−	0.347209i	0.0521950	−	0.00826687i
$43$	46.5461	+	46.5461i	1.08247	+	1.08247i	0.996279	+	0.0861893i	$0.0274690\pi$
$43$	46.5461	+	46.5461i	1.08247	+	1.08247i	0.0861893	+	0.996279i	$0.472531\pi$
$44$	18.8558	−	25.9528i	0.428541	−	0.589836i
$45$	31.5803	−	26.3047i	0.701785	−	0.584549i
$46$	−10.4987	+	7.62775i	−0.228232	+	0.165821i
$47$	−8.92142	+	56.3277i	−0.189818	+	1.19846i	0.690235	+	0.723585i	$0.257507\pi$
$47$	−8.92142	+	56.3277i	−0.189818	+	1.19846i	−0.880053	+	0.474876i	$0.842493\pi$
$48$	−1.25007	+	2.45341i	−0.0260432	+	0.0511126i
$49$			43.7003i			0.891844i
$50$	0.674010	−	27.2851i	0.0134802	−	0.545701i
$51$	22.4757			0.440700
$52$	−21.4533	−	10.9310i	−0.412564	−	0.210212i
$53$	−17.7814	−	2.81630i	−0.335499	−	0.0531378i	−0.0135877	−	0.999908i	$-0.504325\pi$
$53$	−17.7814	−	2.81630i	−0.335499	−	0.0531378i	−0.321911	+	0.946770i	$0.604325\pi$
$54$	−9.75862	−	13.4316i	−0.180715	−	0.248733i
$55$	−55.3720	−	14.0190i	−1.00676	−	0.254891i
$56$	−13.8429	−	10.0574i	−0.247194	−	0.179597i
$57$	−5.95505	+	5.95505i	−0.104475	+	0.104475i
$58$	1.61661	+	10.2069i	0.0278726	+	0.175980i
$59$	−13.2502	−	4.30525i	−0.224579	−	0.0729703i	0.194566	−	0.980889i	$-0.437670\pi$
$59$	−13.2502	−	4.30525i	−0.224579	−	0.0729703i	−0.419145	+	0.907919i	$0.637670\pi$
$60$	12.3482	+	1.12542i	0.205804	+	0.0187569i
$61$	0.671981	+	2.06814i	0.0110161	+	0.0339040i	0.956413	−	0.292016i	$-0.0943260\pi$
$61$	0.671981	+	2.06814i	0.0110161	+	0.0339040i	−0.945397	+	0.325920i	$0.894326\pi$
$62$	−25.9053	−	50.8420i	−0.417827	−	0.820032i
$63$	−16.8610	+	8.59109i	−0.267634	+	0.136367i
$64$	−22.5423	+	7.32443i	−0.352223	+	0.114444i
$65$	−3.89117	+	42.6945i	−0.0598641	+	0.656839i
$66$	−3.40352	+	10.4749i	−0.0515684	+	0.158711i
$67$	116.666	−	18.4780i	1.74128	−	0.275791i	0.796771	−	0.604282i	$-0.206540\pi$
$67$	116.666	−	18.4780i	1.74128	−	0.275791i	0.944507	+	0.328490i	$0.106540\pi$
$68$	−50.5355	−	50.5355i	−0.743168	−	0.743168i
$69$	−6.17015	+	8.49249i	−0.0894225	+	0.123079i
$70$	−3.08423	+	12.1820i	−0.0440605	+	0.174029i
$71$	−57.1398	+	41.5145i	−0.804786	+	0.584712i	−0.912314	−	0.409491i	$-0.865706\pi$
$71$	−57.1398	+	41.5145i	−0.804786	+	0.584712i	0.107528	+	0.994202i	$0.465706\pi$
$72$	−9.55772	+	60.3450i	−0.132746	+	0.838126i
$73$	28.5805	−	56.0923i	0.391513	−	0.768388i	−0.608163	−	0.793812i	$-0.708093\pi$
$73$	28.5805	−	56.0923i	0.391513	−	0.768388i	0.999677	+	0.0254236i	$0.00809346\pi$
$74$		−	52.0727i		−	0.703685i
$75$	−6.30182	−	21.1594i	−0.0840243	−	0.282125i
$76$	26.7793			0.352359
$77$	23.4324	+	11.9394i	0.304317	+	0.155057i
$78$	8.16493	+	1.29320i	0.104679	+	0.0165795i
$79$	19.9697	+	27.4860i	0.252781	+	0.347924i	0.916483	−	0.400074i	$-0.131015\pi$
$79$	19.9697	+	27.4860i	0.252781	+	0.347924i	−0.663702	+	0.747998i	$0.731015\pi$
$80$	−9.97763	−	11.9787i	−0.124720	−	0.149734i
$81$	48.9869	+	35.5911i	0.604777	+	0.439396i
$82$	41.5952	−	41.5952i	0.507259	−	0.507259i
$83$	−7.27847	−	45.9545i	−0.0876924	−	0.553668i	−0.991945	−	0.126670i	$-0.959571\pi$
$83$	−7.27847	−	45.9545i	−0.0876924	−	0.553668i	0.904252	−	0.426998i	$-0.140429\pi$
$84$	−5.42953	−	1.76416i	−0.0646372	−	0.0210019i
$85$	−50.1455	+	116.956i	−0.589947	+	1.37595i
$86$	22.2074	+	68.3474i	0.258226	+	0.794737i
$87$	3.79506	+	7.44823i	0.0436214	+	0.0856118i
$88$	75.6548	−	38.5480i	0.859714	−	0.438046i
$89$	−30.3143	+	9.84970i	−0.340610	+	0.110671i	−0.474327	−	0.880349i	$-0.657309\pi$
$89$	−30.3143	+	9.84970i	−0.340610	+	0.110671i	0.133717	+	0.991020i	$0.457309\pi$
$90$	43.7571	−	9.93533i	0.486190	−	0.110393i
$91$	6.09965	−	18.7728i	0.0670291	−	0.206294i
$92$	32.9682	−	5.22165i	0.358350	−	0.0567571i
$93$	−32.6382	−	32.6382i	−0.350948	−	0.350948i
$94$	−36.5963	+	50.3705i	−0.389323	+	0.535857i
$95$	−17.7017	−	44.2743i	−0.186334	−	0.466045i
$96$	−23.6732	+	17.1996i	−0.246596	+	0.179162i
$97$	10.7597	−	67.9342i	0.110925	−	0.700353i	−0.868066	−	0.496449i	$-0.834637\pi$
$97$	10.7597	−	67.9342i	0.110925	−	0.700353i	0.978991	−	0.203904i	$-0.0653630\pi$
$98$	−21.6595	+	42.5092i	−0.221015	+	0.433767i
$99$		−	93.9051i		−	0.948536i
$100$	−33.4064	+	61.7451i	−0.334064	+	0.617451i
$101$	69.5184			0.688301			0.344151	−	0.938914i	$-0.388167\pi$
$101$	69.5184			0.688301			0.344151	+	0.938914i	$0.388167\pi$
$102$	21.8631	+	11.1398i	0.214344	+	0.109214i
$103$	65.2238	+	10.3304i	0.633240	+	0.100295i	0.464799	−	0.885416i	$-0.346127\pi$
$103$	65.2238	+	10.3304i	0.633240	+	0.100295i	0.168441	+	0.985712i	$0.446127\pi$
$104$	−37.4595	−	51.5585i	−0.360187	−	0.495755i
$105$	0.672346	+	10.1428i	0.00640330	+	0.0965983i
$106$	−15.9009	−	11.5527i	−0.150008	−	0.108988i
$107$	−64.9353	+	64.9353i	−0.606872	+	0.606872i	−0.942127	−	0.335255i	$-0.891177\pi$
$107$	−64.9353	+	64.9353i	−0.606872	+	0.606872i	0.335255	+	0.942127i	$0.391177\pi$
$108$	6.68036	+	42.1781i	0.0618552	+	0.390538i
$109$	−84.4770	−	27.4482i	−0.775018	−	0.251819i	−0.105307	−	0.994440i	$-0.533582\pi$
$109$	−84.4770	−	27.4482i	−0.775018	−	0.251819i	−0.669712	+	0.742621i	$0.733582\pi$
$110$	−46.9144	−	41.0813i	−0.426495	−	0.373467i
$111$	−13.0164	−	40.0605i	−0.117265	−	0.360905i
$112$	3.25869	+	6.39553i	0.0290954	+	0.0571029i
$113$	−105.145	+	53.5740i	−0.930485	+	0.474106i	−0.852429	−	0.522843i	$-0.824871\pi$
$113$	−105.145	+	53.5740i	−0.930485	+	0.474106i	−0.0780563	+	0.996949i	$0.524871\pi$
$114$	−8.74428	+	2.84119i	−0.0767042	+	0.0249227i
$115$	−30.4257	−	51.0549i	−0.264572	−	0.443956i
$116$	8.21396	−	25.2800i	0.0708100	−	0.217931i
$117$	−69.6139	+	11.0258i	−0.594991	+	0.0942373i
$118$	−10.7552	−	10.7552i	−0.0911456	−	0.0911456i
$119$	34.4381	−	47.4000i	0.289396	−	0.398319i
$120$	27.7693	+	17.4923i	0.231411	+	0.145769i
$121$	−7.68870	+	5.58617i	−0.0635430	+	0.0461667i
$122$	−0.371385	+	2.34483i	−0.00304414	+	0.0192199i
$123$	21.6025	−	42.3974i	0.175630	−	0.344694i
$124$			146.771i			1.18363i
$125$	124.166	+	14.4161i	0.993327	+	0.115329i
$126$	−20.6595			−0.163964
$127$	−86.0489	−	43.8441i	−0.677550	−	0.345229i	0.0811197	−	0.996704i	$-0.474150\pi$
$127$	−86.0489	−	43.8441i	−0.677550	−	0.345229i	−0.758670	+	0.651475i	$0.774150\pi$
$128$	105.349	+	16.6856i	0.823036	+	0.130356i
$129$	34.1691	+	47.0298i	0.264877	+	0.364572i
$130$	−24.9461	+	39.6022i	−0.191893	+	0.304632i
$131$	33.1579	+	24.0906i	0.253114	+	0.183898i	0.707106	−	0.707108i	$-0.250000\pi$
$131$	33.1579	+	24.0906i	0.253114	+	0.183898i	−0.453992	+	0.891006i	$0.650000\pi$
$132$	20.0322	−	20.0322i	0.151759	−	0.151759i
$133$	3.43432	+	21.6834i	0.0258219	+	0.163033i
$134$	122.644	+	39.8495i	0.915254	+	0.297384i
$135$	65.3175	−	38.9254i	0.483833	−	0.288336i
$136$	−58.4551	−	179.906i	−0.429817	−	1.32284i
$137$	8.37765	+	16.4421i	0.0611507	+	0.120015i	0.919559	−	0.392952i	$-0.128546\pi$
$137$	8.37765	+	16.4421i	0.0611507	+	0.120015i	−0.858408	+	0.512967i	$0.828546\pi$
$138$	−10.2112	+	5.20285i	−0.0739939	+	0.0377018i
$139$	234.953	−	76.3408i	1.69031	−	0.549214i	0.703441	−	0.710753i	$-0.251646\pi$
$139$	234.953	−	76.3408i	1.69031	−	0.549214i	0.986866	+	0.161539i	$0.0516458\pi$
$140$	21.2939	−	24.3174i	0.152099	−	0.173695i
$141$	−15.5633	+	47.8988i	−0.110378	+	0.339708i
$142$	−76.1585	+	12.0623i	−0.536328	+	0.0849459i
$143$	69.2620	+	69.2620i	0.484350	+	0.484350i
$144$	15.0650	−	20.7351i	0.104618	−	0.143994i
$145$	−47.2251	+	3.13045i	−0.325691	+	0.0215893i
$146$	55.6029	−	40.3979i	0.380842	−	0.276698i
$147$	−6.03718	+	38.1172i	−0.0410692	+	0.259301i
$148$	−60.8071	+	119.341i	−0.410859	+	0.806356i
$149$			57.3361i			0.384806i	0.981316	+	0.192403i	$0.0616281\pi$
$149$			57.3361i			0.384806i	−0.981316	+	0.192403i	$0.938372\pi$
$150$	4.35731	−	23.7060i	0.0290488	−	0.158040i
$151$	−217.048			−1.43740			−0.718702	−	0.695318i	$-0.755264\pi$
$151$	−217.048			−1.43740			−0.718702	+	0.695318i	$0.755264\pi$
$152$	63.1551	+	32.1792i	0.415494	+	0.211705i
$153$	−206.630	−	32.7270i	−1.35052	−	0.213902i
$154$	16.8761	+	23.2279i	0.109585	+	0.150831i
$155$	242.657	−	97.0187i	1.56553	−	0.625927i
$156$	−17.2024	−	12.4982i	−0.110272	−	0.0801169i
$157$	16.5724	−	16.5724i	0.105557	−	0.105557i	−0.652356	−	0.757913i	$-0.726219\pi$
$157$	16.5724	−	16.5724i	0.105557	−	0.105557i	0.757913	+	0.652356i	$0.226219\pi$
$158$	5.80234	+	36.6345i	0.0367237	+	0.231864i
$159$	−15.1206	−	4.91299i	−0.0950983	−	0.0308993i
$160$	−36.6834	−	161.561i	−0.229271	−	1.00976i
$161$	8.45604	+	26.0250i	0.0525220	+	0.161646i
$162$	30.0114	+	58.9007i	0.185256	+	0.363585i
$163$	−6.41890	+	3.27059i	−0.0393798	+	0.0200650i	−0.473570	−	0.880756i	$-0.657035\pi$
$163$	−6.41890	+	3.27059i	−0.0393798	+	0.0200650i	0.434190	+	0.900821i	$0.357035\pi$
$164$	−143.901	+	46.7561i	−0.877442	+	0.285098i
$165$	−46.3610	−	19.8776i	−0.280976	−	0.120470i
$166$	15.6967	−	48.3094i	0.0945582	−	0.291020i
$167$	−226.862	+	35.9314i	−1.35845	+	0.215158i	−0.792798	−	0.609484i	$-0.791377\pi$
$167$	−226.862	+	35.9314i	−1.35845	+	0.215158i	−0.565655	+	0.824642i	$0.691377\pi$
$168$	−10.6849	−	10.6849i	−0.0636005	−	0.0636005i
$169$	−56.1225	+	77.2461i	−0.332086	+	0.457077i
$170$	−106.746	+	88.9139i	−0.627919	+	0.523023i
$171$	63.4189	−	46.0766i	0.370871	−	0.269454i
$172$	28.9165	−	182.572i	0.168119	−	1.06146i
$173$	9.37245	−	18.3945i	0.0541760	−	0.106326i	−0.862331	−	0.506345i	$-0.830996\pi$
$173$	9.37245	−	18.3945i	0.0541760	−	0.106326i	0.916507	+	0.400018i	$0.130996\pi$
$174$			9.12619i			0.0524493i
$175$	−54.2798	−	19.1310i	−0.310170	−	0.109320i
$176$	−35.6191			−0.202381
$177$	−10.9626	−	5.58572i	−0.0619356	−	0.0315577i
$178$	−34.3699	−	5.44365i	−0.193089	−	0.0305823i
$179$	−18.2382	−	25.1027i	−0.101889	−	0.140238i	0.755028	−	0.655693i	$-0.227623\pi$
$179$	−18.2382	−	25.1027i	−0.101889	−	0.140238i	−0.856917	+	0.515454i	$0.827623\pi$
$180$	−111.885	−	28.3269i	−0.621583	−	0.157372i
$181$	43.2316	+	31.4096i	0.238849	+	0.173534i	0.700770	−	0.713387i	$-0.252840\pi$
$181$	43.2316	+	31.4096i	0.238849	+	0.173534i	−0.461921	+	0.886921i	$0.652840\pi$
$182$	15.2379	−	15.2379i	0.0837247	−	0.0837247i
$183$	0.300416	+	1.89675i	0.00164162	+	0.0103648i
$184$	84.0254	+	27.3015i	0.456660	+	0.148378i
$185$	237.502	+	21.6458i	1.28379	+	0.117004i
$186$	−15.5719	−	47.9253i	−0.0837197	−	0.257663i
$187$	131.994	+	259.053i	0.705851	+	1.38531i
$188$	142.691	−	72.7048i	0.758996	−	0.386728i
$189$	−33.2953	+	10.8183i	−0.176166	+	0.0572397i
$190$	4.72479	−	51.8412i	0.0248673	−	0.272848i
$191$	−76.7471	+	236.203i	−0.401817	+	1.23667i	0.521707	+	0.853125i	$0.325296\pi$
$191$	−76.7471	+	236.203i	−0.401817	+	1.23667i	−0.923524	+	0.383541i	$0.874704\pi$
$192$	−20.6742	+	3.27447i	−0.107678	+	0.0170545i
$193$	71.7654	+	71.7654i	0.371841	+	0.371841i	0.868148	−	0.496306i	$-0.165311\pi$
$193$	71.7654	+	71.7654i	0.371841	+	0.371841i	−0.496306	+	0.868148i	$0.665311\pi$
$194$	44.1372	−	60.7496i	0.227511	−	0.313142i
$195$	−9.29227	+	36.7024i	−0.0476526	+	0.188217i
$196$	99.2790	−	72.1304i	0.506525	−	0.368012i
$197$	40.8820	−	258.119i	0.207523	−	1.31025i	−0.635387	−	0.772194i	$-0.719159\pi$
$197$	40.8820	−	258.119i	0.207523	−	1.31025i	0.842910	−	0.538055i	$-0.180841\pi$
$198$	46.5429	−	91.3455i	0.235065	−	0.461341i
$199$		−	199.974i		−	1.00490i	−0.864607	−	0.502448i	$-0.832433\pi$
$199$		−	199.974i		−	1.00490i	0.864607	−	0.502448i	$-0.167567\pi$
$200$	−152.980	+	105.474i	−0.764900	+	0.527372i
$201$	104.313			0.518972
$202$	67.6235	+	34.4559i	0.334770	+	0.170574i
$203$	21.5228	+	3.40888i	0.106024	+	0.0167925i
$204$	−37.0977	−	51.0606i	−0.181851	−	0.250297i
$205$	172.424	+	207.005i	0.841091	+	1.00978i
$206$	58.3258	+	42.3762i	0.283135	+	0.205710i
$207$	69.0912	−	69.0912i	0.333774	−	0.333774i
$208$	4.18218	+	26.4052i	0.0201066	+	0.126948i
$209$	−103.610	−	33.6649i	−0.495742	−	0.161076i
$210$	−4.37314	+	10.1996i	−0.0208245	+	0.0485695i
$211$	35.5483	+	109.407i	0.168475	+	0.518514i	0.999276	−	0.0380567i	$-0.0121167\pi$
$211$	35.5483	+	109.407i	0.168475	+	0.518514i	−0.830800	+	0.556571i	$0.812117\pi$
$212$	22.9514	+	45.0446i	0.108261	+	0.212474i
$213$	−55.5749	+	28.3168i	−0.260915	+	0.132943i
$214$	−95.3497	+	30.9810i	−0.445559	+	0.144771i
$215$	−320.961	+	72.8762i	−1.49284	+	0.338959i
$216$	−34.9284	+	107.499i	−0.161706	+	0.497679i
$217$	−118.841	+	18.8226i	−0.547657	+	0.0867403i
$218$	−68.5700	−	68.5700i	−0.314542	−	0.314542i
$219$	32.6782	−	44.9777i	0.149216	−	0.205378i
$220$	59.5467	+	148.934i	0.270667	+	0.676974i
$221$	176.544	−	128.267i	0.798841	−	0.580392i
$222$	7.19382	−	45.4200i	0.0324046	−	0.204594i
$223$	115.036	−	225.771i	0.515857	−	1.01243i	−0.475311	−	0.879818i	$-0.657665\pi$
$223$	115.036	−	225.771i	0.515857	−	1.01243i	0.991168	−	0.132609i	$-0.0423354\pi$
$224$			76.2792i			0.340532i
$225$	27.1255	+	203.705i	0.120558	+	0.905354i
$226$	−128.832			−0.570054
$227$	117.757	+	60.0004i	0.518755	+	0.264319i	0.693706	−	0.720258i	$-0.255977\pi$
$227$	117.757	+	60.0004i	0.518755	+	0.264319i	−0.174951	+	0.984577i	$0.555977\pi$
$228$	23.3580	+	3.69954i	0.102447	+	0.0162261i
$229$	−41.4686	−	57.0767i	−0.181086	−	0.249243i	0.708818	−	0.705391i	$-0.249229\pi$
$229$	−41.4686	−	57.0767i	−0.181086	−	0.249243i	−0.889904	+	0.456148i	$0.849229\pi$
$230$	−4.29170	−	64.7434i	−0.0186596	−	0.281493i
$231$	18.7893	+	13.6512i	0.0813388	+	0.0590961i
$232$	49.7490	−	49.7490i	0.214435	−	0.214435i
$233$	−67.0897	−	423.588i	−0.287939	−	1.81797i	−0.530327	−	0.847793i	$-0.677931\pi$
$233$	−67.0897	−	423.588i	−0.287939	−	1.81797i	0.242388	−	0.970179i	$-0.422069\pi$
$234$	−73.1813	−	23.7780i	−0.312740	−	0.101616i
$235$	−214.526	−	187.853i	−0.912875	−	0.799374i
$236$	12.0896	+	37.2080i	0.0512272	+	0.157661i
$237$	13.6213	+	26.7332i	0.0574737	+	0.112798i
$238$	56.9926	−	29.0392i	0.239465	−	0.122013i
$239$	−132.260	+	42.9740i	−0.553391	+	0.179808i	−0.572345	−	0.820013i	$-0.693966\pi$
$239$	−132.260	+	42.9740i	−0.553391	+	0.179808i	0.0189544	+	0.999820i	$0.493966\pi$
$240$	−7.04805	−	11.8267i	−0.0293669	−	0.0492781i
$241$	−25.8767	+	79.6401i	−0.107372	+	0.330457i	−0.990280	−	0.139089i	$-0.955582\pi$
$241$	−25.8767	+	79.6401i	−0.107372	+	0.330457i	0.882908	+	0.469546i	$0.155582\pi$
$242$	−10.2478	+	1.62310i	−0.0423464	+	0.00670702i
$243$	134.590	+	134.590i	0.553870	+	0.553870i
$244$	3.58929	−	4.94023i	0.0147102	−	0.0202468i
$245$	−184.879	−	116.459i	−0.754610	−	0.475342i
$246$	42.0274	−	30.5347i	0.170843	−	0.124125i
$247$	−12.7913	+	80.7611i	−0.0517867	+	0.326968i
$248$	−176.366	+	346.138i	−0.711153	+	1.39572i
$249$		−	41.0889i		−	0.165016i
$250$	113.636	+	75.5644i	0.454545	+	0.302258i
$251$	−174.255			−0.694242			−0.347121	−	0.937820i	$-0.612841\pi$
$251$	−174.255			−0.694242			−0.347121	+	0.937820i	$0.612841\pi$
$252$	47.3475	+	24.1248i	0.187887	+	0.0957332i
$253$	−134.119	−	21.2424i	−0.530116	−	0.0839622i
$254$	−61.9727	−	85.2980i	−0.243987	−	0.335819i
$255$	−59.8963	+	95.0860i	−0.234888	+	0.372886i
$256$	170.910	+	124.173i	0.667615	+	0.485051i
$257$	178.989	−	178.989i	0.696455	−	0.696455i	−0.267189	−	0.963644i	$-0.586095\pi$
$257$	178.989	−	178.989i	0.696455	−	0.696455i	0.963644	+	0.267189i	$0.0860949\pi$
$258$	9.92807	+	62.6834i	0.0384809	+	0.242959i
$259$	−104.430	−	33.9312i	−0.403203	−	0.131009i
$260$	103.417	−	61.6303i	0.397756	−	0.237039i
$261$	−24.0445	−	74.0013i	−0.0921244	−	0.283530i
$262$	20.3139	+	39.8683i	0.0775340	+	0.152169i
$263$	−86.2059	+	43.9241i	−0.327779	+	0.167012i	−0.610134	−	0.792298i	$-0.708884\pi$
$263$	−86.2059	+	43.9241i	−0.327779	+	0.167012i	0.282355	+	0.959310i	$0.408884\pi$
$264$	71.3146	−	23.1715i	0.270131	−	0.0877709i
$265$	59.3011	−	67.7211i	0.223778	−	0.255551i
$266$	−7.40640	+	22.7946i	−0.0278436	+	0.0856939i
$267$	−27.8021	+	4.40342i	−0.104128	+	0.0164922i
$268$	−234.543	−	234.543i	−0.875161	−	0.875161i
$269$	−72.8230	+	100.232i	−0.270718	+	0.372611i	−0.922632	−	0.385682i	$-0.873966\pi$
$269$	−72.8230	+	100.232i	−0.270718	+	0.372611i	0.651914	+	0.758293i	$0.273966\pi$
$270$	82.8300	−	5.49063i	0.306778	−	0.0203357i
$271$	59.1893	−	43.0035i	0.218411	−	0.158685i	−0.473200	−	0.880955i	$-0.656901\pi$
$271$	59.1893	−	43.0035i	0.218411	−	0.158685i	0.691611	+	0.722270i	$0.256901\pi$
$272$	−12.4137	+	78.3769i	−0.0456385	+	0.288150i
$273$	7.91382	−	15.5317i	0.0289884	−	0.0568928i
$274$			20.1462i			0.0735262i
$275$	206.872	−	196.898i	0.752262	−	0.715992i
$276$	29.4776			0.106803
$277$	104.428	+	53.2086i	0.376995	+	0.192089i	0.632212	−	0.774795i	$-0.282147\pi$
$277$	104.428	+	53.2086i	0.376995	+	0.192089i	−0.255217	+	0.966884i	$0.582147\pi$
$278$	266.386	+	42.1914i	0.958223	+	0.151768i
$279$	252.534	+	347.584i	0.905141	+	1.24582i
$280$	79.4394	−	31.7614i	0.283712	−	0.113434i
$281$	−163.568	−	118.839i	−0.582092	−	0.422914i	0.257386	−	0.966309i	$-0.417139\pi$
$281$	−163.568	−	118.839i	−0.582092	−	0.422914i	−0.839478	+	0.543394i	$0.817139\pi$
$282$	−38.8795	+	38.8795i	−0.137871	+	0.137871i
$283$	41.9632	+	264.945i	0.148280	+	0.936201i	0.943858	+	0.330351i	$0.107167\pi$
$283$	41.9632	+	264.945i	0.148280	+	0.936201i	−0.795579	+	0.605850i	$0.792833\pi$
$284$	188.626	+	61.2884i	0.664178	+	0.215804i
$285$	−9.32369	−	41.0634i	−0.0327147	−	0.144082i
$286$	33.0453	+	101.703i	0.115543	+	0.355605i
$287$	−56.3134	−	110.521i	−0.196214	−	0.385092i
$288$	242.684	−	123.653i	0.842652	−	0.429352i
$289$	341.171	−	110.853i	1.18052	−	0.383575i
$290$	−47.4895	−	20.3614i	−0.163757	−	0.0702118i
$291$	18.7702	−	57.7686i	0.0645022	−	0.198517i
$292$	−174.605	+	27.6548i	−0.597963	+	0.0947081i
$293$	29.7605	+	29.7605i	0.101572	+	0.101572i	0.756067	−	0.654495i	$-0.227119\pi$
$293$	29.7605	+	29.7605i	0.101572	+	0.101572i	−0.654495	+	0.756067i	$0.727119\pi$
$294$	−24.7650	+	34.0860i	−0.0842345	+	0.115939i
$295$	53.5248	−	44.5832i	0.181440	−	0.151130i
$296$	−286.810	+	208.380i	−0.968953	+	0.703986i
$297$	27.1767	−	171.587i	0.0915040	−	0.577734i
$298$	−28.4179	+	55.7733i	−0.0953621	+	0.187159i
$299$			101.920i			0.340869i
$300$	−37.6685	+	49.2415i	−0.125562	+	0.164138i
$301$	151.538			0.503450
$302$	−211.132	−	107.577i	−0.699112	−	0.356216i
$303$	60.6368	+	9.60393i	0.200122	+	0.0316961i
$304$	−17.4773	−	24.0554i	−0.0574911	−	0.0791297i
$305$	−10.5403	−	2.66858i	−0.0345584	−	0.00874945i
$306$	−184.777	−	134.249i	−0.603848	−	0.438721i
$307$	−285.812	+	285.812i	−0.930984	+	0.930984i	−0.997767	−	0.0667835i	$-0.978726\pi$
$307$	−285.812	+	285.812i	−0.930984	+	0.930984i	0.0667835	+	0.997767i	$0.478726\pi$
$308$	−11.5527	−	72.9408i	−0.0375087	−	0.236821i
$309$	55.4637	+	18.0213i	0.179494	+	0.0583212i
$310$	284.129	+	25.8954i	0.916544	+	0.0835335i
$311$	−149.454	−	459.971i	−0.480559	−	1.47901i	−0.838312	−	0.545191i	$-0.816457\pi$
$311$	−149.454	−	459.971i	−0.480559	−	1.47901i	0.357753	−	0.933816i	$-0.383543\pi$
$312$	−25.5509	−	50.1465i	−0.0818939	−	0.160726i
$313$	−218.081	+	111.118i	−0.696746	+	0.355010i	−0.766224	−	0.642574i	$-0.777867\pi$
$313$	−218.081	+	111.118i	−0.696746	+	0.355010i	0.0694779	+	0.997583i	$0.477867\pi$
$314$	24.3346	−	7.90679i	0.0774987	−	0.0251809i
$315$	8.58782	−	94.2270i	0.0272629	−	0.299133i
$316$	29.4816	−	90.7350i	0.0932962	−	0.287136i
$317$	−72.9033	+	11.5468i	−0.229979	+	0.0364251i	−0.270360	−	0.962759i	$-0.587143\pi$
$317$	−72.9033	+	11.5468i	−0.229979	+	0.0364251i	0.0403812	+	0.999184i	$0.487143\pi$
$318$	−12.2734	−	12.2734i	−0.0385957	−	0.0385957i
$319$	−63.5602	+	87.4832i	−0.199248	+	0.274242i
$320$	29.0869	−	114.887i	0.0908966	−	0.359021i
$321$	−65.6100	+	47.6685i	−0.204393	+	0.148500i
$322$	−4.67341	+	29.5068i	−0.0145137	+	0.0916359i
$323$	−110.186	+	216.252i	−0.341133	+	0.669512i
$324$		−	170.035i		−	0.524798i
$325$	−170.254	−	130.240i	−0.523860	−	0.400739i
$326$	−7.86497			−0.0241257
$327$	−69.8924	−	35.6119i	−0.213738	−	0.108905i
$328$	−395.554	−	62.6495i	−1.20596	−	0.191005i
$329$	77.1693	+	106.214i	0.234557	+	0.322840i
$330$	−35.2453	−	42.3140i	−0.106804	−	0.128224i
$331$	99.7298	+	72.4579i	0.301298	+	0.218906i	0.728154	−	0.685414i	$-0.240379\pi$
$331$	99.7298	+	72.4579i	0.301298	+	0.218906i	−0.426855	+	0.904320i	$0.640379\pi$
$332$	−92.3863	+	92.3863i	−0.278272	+	0.278272i
$333$	61.3342	+	387.249i	0.184187	+	1.16291i
$334$	−238.487	−	77.4891i	−0.714033	−	0.232003i
$335$	−232.733	+	542.810i	−0.694726	+	1.62033i
$336$	1.95882	+	6.02863i	0.00582982	+	0.0179424i
$337$	−5.34607	−	10.4923i	−0.0158637	−	0.0311343i	0.882939	−	0.469488i	$-0.155562\pi$
$337$	−5.34607	−	10.4923i	−0.0158637	−	0.0311343i	−0.898802	+	0.438354i	$0.855562\pi$
$338$	−92.8788	+	47.3241i	−0.274789	+	0.140012i
$339$	−99.1129	+	32.2037i	−0.292368	+	0.0949963i
$340$	348.470	−	79.1223i	1.02491	−	0.232713i
$341$	184.509	−	567.861i	0.541083	−	1.66528i
$342$	84.5276	−	13.3879i	0.247157	−	0.0391458i
$343$	150.900	+	150.900i	0.439943	+	0.439943i
$344$	287.582	−	395.822i	0.835993	−	1.15065i
$345$	−19.4854	−	48.7355i	−0.0564793	−	0.141262i
$346$	18.2340	−	13.2478i	0.0526993	−	0.0382883i
$347$	−47.2216	+	298.146i	−0.136085	+	0.859209i	0.821321	+	0.570466i	$0.193237\pi$
$347$	−47.2216	+	298.146i	−0.136085	+	0.859209i	−0.957407	+	0.288743i	$0.906763\pi$
$348$	10.6570	−	20.9155i	0.0306235	−	0.0601020i
$349$		−	82.2048i		−	0.235544i	−0.993041	−	0.117772i	$-0.962425\pi$
$349$		−	82.2048i		−	0.235544i	0.993041	−	0.117772i	$-0.0375752\pi$
$350$	−43.3182	−	45.5126i	−0.123766	−	0.130036i
$351$	−130.392			−0.371488
$352$	−337.267	−	171.846i	−0.958146	−	0.488200i
$353$	544.436	+	86.2301i	1.54231	+	0.244278i	0.868899	−	0.494990i	$-0.164828\pi$
$353$	544.436	+	86.2301i	1.54231	+	0.244278i	0.673412	+	0.739268i	$0.264828\pi$
$354$	−7.89529	−	10.8669i	−0.0223031	−	0.0306976i
$355$	−23.3579	−	352.370i	−0.0657968	−	0.992592i
$356$	72.4124	+	52.6107i	0.203406	+	0.147783i
$357$	36.5866	−	36.5866i	0.102483	−	0.102483i
$358$	−5.29922	−	33.4579i	−0.0148023	−	0.0934579i
$359$	474.921	+	154.311i	1.32290	+	0.429836i	0.883490	−	0.468450i	$-0.155187\pi$
$359$	474.921	+	154.311i	1.32290	+	0.429836i	0.439411	+	0.898286i	$0.355187\pi$
$360$	−229.826	−	201.251i	−0.638405	−	0.559030i
$361$	83.4523	+	256.840i	0.231170	+	0.711468i
$362$	26.4855	+	51.9807i	0.0731643	+	0.143593i
$363$	−7.47813	+	3.81030i	−0.0206009	+	0.0104967i
$364$	−52.7162	+	17.1285i	−0.144825	+	0.0470564i
$365$	161.140	+	270.396i	0.441479	+	0.740810i
$366$	−0.647874	+	1.99395i	−0.00177015	+	0.00544796i
$367$	656.071	−	103.911i	1.78766	−	0.283137i	0.827271	−	0.561803i	$-0.189892\pi$
$367$	656.071	−	103.911i	1.78766	−	0.283137i	0.960388	+	0.278666i	$0.0898921\pi$
$368$	−26.2070	−	26.2070i	−0.0712146	−	0.0712146i
$369$	−260.338	+	358.324i	−0.705523	+	0.971069i
$370$	220.300	+	138.770i	0.595404	+	0.375055i
$371$	−33.5296	+	24.3607i	−0.0903763	+	0.0656622i
$372$	−20.2763	+	128.019i	−0.0545061	+	0.344138i
$373$	223.689	−	439.014i	0.599702	−	1.17698i	−0.369156	−	0.929367i	$-0.620353\pi$
$373$	223.689	−	439.014i	0.599702	−	1.17698i	0.968859	−	0.247615i	$-0.0796468\pi$
$374$			317.413i			0.848699i
$375$	106.311	+	29.7278i	0.283496	+	0.0792741i
$376$	423.883			1.12735
$377$	72.3161	+	36.8469i	0.191820	+	0.0977371i
$378$	−37.7497	−	5.97897i	−0.0998670	−	0.0158174i
$379$	−313.360	−	431.303i	−0.826808	−	1.13800i	−0.988509	−	0.151163i	$-0.951698\pi$
$379$	−313.360	−	431.303i	−0.826808	−	1.13800i	0.161701	−	0.986840i	$-0.448302\pi$
$380$	−71.3651	+	113.293i	−0.187803	+	0.298139i
$381$	−68.9983	−	50.1302i	−0.181098	−	0.131575i
$382$	−191.726	+	191.726i	−0.501901	+	0.501901i
$383$	−24.1368	−	152.394i	−0.0630204	−	0.397895i	−0.998954	−	0.0457195i	$-0.985442\pi$
$383$	−24.1368	−	152.394i	−0.0630204	−	0.397895i	0.935934	−	0.352176i	$-0.114558\pi$
$384$	89.5843	+	29.1077i	0.233292	+	0.0758013i
$385$	−112.957	+	67.3157i	−0.293394	+	0.174846i
$386$	34.2397	+	105.379i	0.0887038	+	0.273002i
$387$	−245.653	−	482.122i	−0.634764	−	1.24579i
$388$	−172.093	+	87.6860i	−0.443540	+	0.225995i
$389$	−229.157	+	74.4578i	−0.589094	+	0.191408i	−0.588370	−	0.808592i	$-0.700230\pi$
$389$	−229.157	+	74.4578i	−0.589094	+	0.191408i	−0.000723401		1.00000i	$0.500230\pi$
$390$	−27.2301	+	31.0964i	−0.0698207	+	0.0797343i
$391$	−93.4844	+	287.715i	−0.239091	+	0.735845i
$392$	320.811	−	50.8114i	0.818395	−	0.129621i
$393$	25.5936	+	25.5936i	0.0651237	+	0.0651237i
$394$	167.701	−	230.821i	0.425637	−	0.585839i
$395$	−169.501	+	11.2358i	−0.429116	+	0.0284452i
$396$	−213.335	+	154.997i	−0.538724	+	0.391406i
$397$	−40.3718	+	254.898i	−0.101692	+	0.642059i	0.883214	+	0.468970i	$0.155375\pi$
$397$	−40.3718	+	254.898i	−0.101692	+	0.642059i	−0.984906	+	0.173089i	$0.944625\pi$
$398$	99.1148	−	194.524i	0.249032	−	0.488753i
$399$			19.3876i			0.0485905i
$400$	77.2672	−	10.2890i	0.193168	−	0.0257224i
$401$	213.307			0.531939			0.265969	−	0.963981i	$-0.414308\pi$
$401$	213.307			0.531939			0.265969	+	0.963981i	$0.414308\pi$
$402$	101.470	+	51.7016i	0.252413	+	0.128611i
$403$	−442.632	−	70.1060i	−1.09834	−	0.173960i
$404$	−114.745	−	157.933i	−0.284022	−	0.390923i
$405$	−281.119	+	112.397i	−0.694122	+	0.277523i
$406$	19.2466	+	13.9835i	0.0474054	+	0.0344421i
$407$	385.291	−	385.291i	0.946662	−	0.946662i
$408$	−26.1330	−	164.997i	−0.0640515	−	0.404405i
$409$	−439.961	−	142.952i	−1.07570	−	0.349516i	−0.282995	−	0.959121i	$-0.591328\pi$
$409$	−439.961	−	142.952i	−1.07570	−	0.349516i	−0.792705	+	0.609605i	$0.791328\pi$
$410$	65.1247	+	286.822i	0.158841	+	0.699566i
$411$	5.03587	+	15.4988i	0.0122527	+	0.0377100i
$412$	−84.1875	−	165.227i	−0.204339	−	0.401037i
$413$	−28.5773	+	14.5608i	−0.0691943	+	0.0352563i
$414$	101.452	−	32.9638i	0.245054	−	0.0796228i
$415$	213.812	+	91.6734i	0.515211	+	0.220900i
$416$	−87.7936	+	270.201i	−0.211042	+	0.649522i
$417$	215.482	−	34.1290i	0.516743	−	0.0818441i
$418$	−84.1003	−	84.1003i	−0.201197	−	0.201197i
$419$	−73.2462	+	100.815i	−0.174812	+	0.240608i	−0.887428	−	0.460946i	$-0.847510\pi$
$419$	−73.2462	+	100.815i	−0.174812	+	0.240608i	0.712616	+	0.701554i	$0.247510\pi$
$420$	21.9328	−	18.2689i	0.0522210	−	0.0434973i
$421$	−610.547	+	443.589i	−1.45023	+	1.05365i	−0.464454	+	0.885597i	$0.653749\pi$
$421$	−610.547	+	443.589i	−1.45023	+	1.05365i	−0.985777	+	0.168057i	$0.946251\pi$
$422$	−19.6466	+	124.043i	−0.0465558	+	0.293942i
$423$	212.827	−	417.696i	0.503136	−	0.987461i
$424$			133.811i			0.315591i
$425$	−361.160	−	523.826i	−0.849788	−	1.23253i
$426$	−68.0950			−0.159847
$427$	4.46046	+	2.27272i	0.0104460	+	0.00532252i
$428$	254.701	+	40.3407i	0.595096	+	0.0942539i
$429$	50.8447	+	69.9817i	0.118519	+	0.163128i
$430$	−348.333	−	88.1905i	−0.810077	−	0.205094i
$431$	−67.5456	−	49.0748i	−0.156718	−	0.113863i	0.506662	−	0.862144i	$-0.330879\pi$
$431$	−67.5456	−	49.0748i	−0.156718	−	0.113863i	−0.663381	+	0.748282i	$0.730879\pi$
$432$	33.5281	−	33.5281i	0.0776114	−	0.0776114i
$433$	4.60134	+	29.0517i	0.0106267	+	0.0670940i	0.992432	−	0.122797i	$-0.0391865\pi$
$433$	4.60134	+	29.0517i	0.0106267	+	0.0670940i	−0.981805	+	0.189891i	$0.939186\pi$
$434$	−124.931	−	40.5927i	−0.287860	−	0.0935315i
$435$	−41.6242	−	3.79362i	−0.0956878	−	0.00872096i
$436$	77.0778	+	237.221i	0.176784	+	0.544085i
$437$	−51.4625	−	101.001i	−0.117763	−	0.231123i
$438$	54.0801	−	27.5552i	0.123471	−	0.0629114i
$439$	37.3878	−	12.1480i	0.0851657	−	0.0276720i	−0.266124	−	0.963939i	$-0.585743\pi$
$439$	37.3878	−	12.1480i	0.0851657	−	0.0276720i	0.351290	+	0.936267i	$0.385743\pi$
$440$	−38.5334	+	422.794i	−0.0875758	+	0.960897i
$441$	111.006	−	341.640i	0.251713	−	0.774694i
$442$	235.306	−	37.2687i	0.532365	−	0.0843184i
$443$	−300.808	−	300.808i	−0.679026	−	0.679026i	0.280754	−	0.959780i	$-0.409416\pi$
$443$	−300.808	−	300.808i	−0.679026	−	0.679026i	−0.959780	+	0.280754i	$0.909416\pi$
$444$	−69.5254	+	95.6934i	−0.156589	+	0.215526i
$445$	39.1153	−	154.497i	0.0878996	−	0.347184i
$446$	223.801	−	162.601i	0.501796	−	0.364576i
$447$	−7.92095	+	50.0109i	−0.0177203	+	0.111881i
$448$	−24.7721	+	48.6179i	−0.0552948	+	0.108522i
$449$		−	48.8102i		−	0.108709i	−0.998522	−	0.0543544i	$-0.982690\pi$
$449$		−	48.8102i		−	0.108709i	0.998522	−	0.0543544i	$-0.0173101\pi$
$450$	−74.5775	+	211.597i	−0.165728	+	0.470215i
$451$	615.535			1.36482
$452$	295.259	+	150.442i	0.653227	+	0.332836i
$453$	−189.318	−	29.9851i	−0.417921	−	0.0661922i
$454$	84.8093	+	116.730i	0.186805	+	0.257115i
$455$	63.1653	+	75.8336i	0.138825	+	0.166667i
$456$	50.6410	+	36.7928i	0.111055	+	0.0806861i
$457$	−313.342	+	313.342i	−0.685649	+	0.685649i	−0.961267	−	0.275618i	$-0.911117\pi$
$457$	−313.342	+	313.342i	−0.685649	+	0.685649i	0.275618	+	0.961267i	$0.411117\pi$
$458$	−12.0490	−	76.0743i	−0.0263078	−	0.166101i
$459$	−368.091	−	119.600i	−0.801941	−	0.260567i
$460$	−65.7674	+	153.391i	−0.142973	+	0.333459i
$461$	168.963	+	520.016i	0.366515	+	1.12802i	0.949027	+	0.315195i	$0.102070\pi$
$461$	168.963	+	520.016i	0.366515	+	1.12802i	−0.582512	+	0.812822i	$0.697930\pi$
$462$	11.5111	+	22.5918i	0.0249158	+	0.0488999i
$463$	419.884	−	213.942i	0.906878	−	0.462077i	0.0626338	−	0.998037i	$-0.480050\pi$
$463$	419.884	−	213.942i	0.906878	−	0.462077i	0.844244	+	0.535959i	$0.180050\pi$
$464$	−28.0694	+	9.12030i	−0.0604944	+	0.0196558i
$465$	225.058	−	51.1009i	0.483996	−	0.109894i
$466$	144.685	−	445.294i	0.310482	−	0.955567i
$467$	533.967	−	84.5721i	1.14340	−	0.181097i	0.444135	−	0.895960i	$-0.353511\pi$
$467$	533.967	−	84.5721i	1.14340	−	0.181097i	0.699264	+	0.714863i	$0.253511\pi$
$468$	139.951	+	139.951i	0.299041	+	0.299041i
$469$	159.833	−	219.991i	0.340795	−	0.469064i
$470$	−115.571	−	289.059i	−0.245897	−	0.615020i
$471$	16.7446	−	12.1657i	0.0355512	−	0.0258295i
$472$	−16.1991	+	102.277i	−0.0343202	+	0.216689i
$473$	−341.395	+	670.025i	−0.721765	+	1.41654i
$474$			32.7558i			0.0691050i
$475$	234.482	+	43.0992i	0.493645	+	0.0907351i
$476$	−164.526			−0.345643
$477$	131.858	+	67.1848i	0.276431	+	0.140849i
$478$	−149.955	−	23.7505i	−0.313713	−	0.0496873i
$479$	−9.71483	−	13.3713i	−0.0202815	−	0.0279151i	0.798756	−	0.601655i	$-0.205492\pi$
$479$	−9.71483	−	13.3713i	−0.0202815	−	0.0279151i	−0.819037	+	0.573740i	$0.805492\pi$
$480$	−9.67723	−	145.988i	−0.0201609	−	0.304141i
$481$	−330.864	−	240.387i	−0.687866	−	0.499764i
$482$	−64.6440	+	64.6440i	−0.134116	+	0.134116i
$483$	3.78036	+	23.8683i	0.00782684	+	0.0494167i
$484$	25.3814	+	8.24693i	0.0524410	+	0.0170391i
$485$	258.730	+	226.561i	0.533463	+	0.467135i
$486$	64.2138	+	197.630i	0.132127	+	0.406646i
$487$	−116.964	−	229.555i	−0.240172	−	0.471365i	0.739185	−	0.673503i	$-0.235211\pi$
$487$	−116.964	−	229.555i	−0.240172	−	0.471365i	−0.979357	+	0.202138i	$0.935211\pi$
$488$	14.4012	−	7.33779i	0.0295107	−	0.0150365i
$489$	−6.05066	+	1.96598i	−0.0123735	+	0.00402041i
$490$	−122.119	−	204.917i	−0.249222	−	0.418199i
$491$	59.3544	−	182.674i	0.120885	−	0.372045i	−0.872244	−	0.489071i	$-0.837336\pi$
$491$	59.3544	−	182.674i	0.120885	−	0.372045i	0.993129	+	0.117026i	$0.0373360\pi$
$492$	−131.975	+	20.9028i	−0.268243	+	0.0424854i
$493$	170.348	+	170.348i	0.345533	+	0.345533i
$494$	−52.4709	+	72.2200i	−0.106216	+	0.146194i
$495$	397.276	+	250.251i	0.802578	+	0.505558i
$496$	131.842	−	95.7887i	0.265810	−	0.193122i
$497$	−25.4354	+	160.593i	−0.0511778	+	0.323124i
$498$	20.3652	−	39.9689i	0.0408940	−	0.0802589i
$499$		−	575.735i		−	1.15378i	−0.816823	−	0.576889i	$-0.804267\pi$
$499$		−	575.735i		−	1.15378i	0.816823	−	0.576889i	$-0.195733\pi$
$500$	−172.194	−	305.876i	−0.344387	−	0.611753i
$501$	−202.842			−0.404874
$502$	−169.505	−	86.3671i	−0.337660	−	0.172046i
$503$	421.054	+	66.6884i	0.837086	+	0.132581i	0.560237	−	0.828332i	$-0.310710\pi$
$503$	421.054	+	66.6884i	0.837086	+	0.132581i	0.276849	+	0.960914i	$0.410710\pi$
$504$	82.6731	+	113.790i	0.164034	+	0.225773i
$505$	−185.262	+	294.106i	−0.366856	+	0.582387i
$506$	−119.935	−	87.1380i	−0.237026	−	0.172210i
$507$	−59.6239	+	59.6239i	−0.117601	+	0.117601i
$508$	42.4240	+	267.855i	0.0835118	+	0.527273i
$509$	688.456	+	223.693i	1.35257	+	0.439475i	0.893554	−	0.448955i	$-0.148204\pi$
$509$	688.456	+	223.693i	1.35257	+	0.439475i	0.459012	+	0.888430i	$0.348204\pi$
$510$	−105.392	+	62.8074i	−0.206651	+	0.123152i
$511$	−44.7846	−	137.833i	−0.0876412	−	0.269732i
$512$	−88.9875	−	174.648i	−0.173804	−	0.341109i
$513$	129.216	−	65.8390i	0.251884	−	0.128341i
$514$	262.824	−	85.3966i	0.511330	−	0.166141i
$515$	−217.521	+	248.407i	−0.422371	+	0.482343i
$516$	50.4443	−	155.252i	0.0977604	−	0.300875i
$517$	−643.477	+	101.917i	−1.24464	+	0.197131i
$518$	−84.7655	−	84.7655i	−0.163640	−	0.163640i
$519$	10.7162	−	14.7496i	0.0206478	−	0.0284193i
$520$	317.951	−	21.0763i	0.611445	−	0.0405314i
$521$	−65.4656	+	47.5636i	−0.125654	+	0.0912928i	−0.648837	−	0.760927i	$-0.724744\pi$
$521$	−65.4656	+	47.5636i	−0.125654	+	0.0912928i	0.523183	+	0.852220i	$0.324744\pi$
$522$	13.2887	−	83.9016i	0.0254573	−	0.160731i
$523$	−241.973	+	474.898i	−0.462663	+	0.908026i	0.535327	+	0.844645i	$0.320188\pi$
$523$	−241.973	+	474.898i	−0.462663	+	0.908026i	−0.997989	+	0.0633814i	$0.979812\pi$
$524$		−	115.092i		−	0.219641i
$525$	−44.7021	−	24.1855i	−0.0851469	−	0.0460677i
$526$	−105.627			−0.200811
$527$	−1185.23	−	603.903i	−2.24901	−	1.14593i
$528$	−31.0685	−	4.92076i	−0.0588418	−	0.00931962i
$529$	227.888	+	313.662i	0.430791	+	0.592933i
$530$	91.2499	−	36.4834i	0.172170	−	0.0688366i
$531$	92.6512	+	67.3150i	0.174484	+	0.126770i
$532$	43.5921	−	43.5921i	0.0819400	−	0.0819400i
$533$	−72.2724	−	456.310i	−0.135595	−	0.856116i
$534$	−29.2268	−	9.49636i	−0.0547318	−	0.0177834i
$535$	−101.668	−	447.765i	−0.190033	−	0.836943i
$536$	−271.300	−	834.975i	−0.506156	−	1.55779i
$537$	−12.4402	−	24.4152i	−0.0231660	−	0.0454659i
$538$	−120.517	+	61.4065i	−0.224009	+	0.114138i
$539$	−474.791	+	154.269i	−0.880874	+	0.286213i
$540$	−196.242	−	84.1401i	−0.363412	−	0.155815i
$541$	−159.367	+	490.480i	−0.294578	+	0.906618i	0.688785	+	0.724966i	$0.258145\pi$
$541$	−159.367	+	490.480i	−0.294578	+	0.906618i	−0.983363	+	0.181652i	$0.941855\pi$
$542$	78.8901	−	12.4950i	0.145554	−	0.0230535i
$543$	33.3692	+	33.3692i	0.0614534	+	0.0614534i
$544$	−495.675	+	682.238i	−0.911167	+	1.25411i
$545$	341.249	−	284.242i	0.626145	−	0.521545i
$546$	15.3962	−	11.1860i	0.0281982	−	0.0204872i
$547$	−109.562	+	691.746i	−0.200296	+	1.26462i	0.658610	+	0.752485i	$0.271145\pi$
$547$	−109.562	+	691.746i	−0.200296	+	1.26462i	−0.858906	+	0.512134i	$0.828855\pi$
$548$	23.5254	−	46.1712i	0.0429296	−	0.0842540i
$549$		−	17.8752i		−	0.0325597i
$550$	298.823	−	88.9976i	0.543315	−	0.161814i
$551$	−90.2691			−0.163828
$552$	69.5188	+	35.4216i	0.125940	+	0.0641695i
$553$	77.2498	+	12.2352i	0.139692	+	0.0221251i
$554$	75.2092	+	103.517i	0.135757	+	0.186853i
$555$	204.168	+	51.6911i	0.367871	+	0.0931371i
$556$	−561.238	−	407.763i	−1.00942	−	0.733387i
$557$	−311.242	+	311.242i	−0.558783	+	0.558783i	−0.928961	−	0.370178i	$-0.879297\pi$
$557$	−311.242	+	311.242i	−0.558783	+	0.558783i	0.370178	+	0.928961i	$0.379297\pi$
$558$	73.3756	+	463.275i	0.131497	+	0.830242i
$559$	536.789	+	174.413i	0.960266	+	0.312009i
$560$	−35.7412	−	3.25744i	−0.0638236	−	0.00581686i
$561$	79.3427	+	244.192i	0.141431	+	0.435279i
$562$	−100.208	−	196.670i	−0.178307	−	0.349947i
$563$	−662.831	+	337.729i	−1.17732	+	0.599874i	−0.929460	−	0.368922i	$-0.879727\pi$
$563$	−662.831	+	337.729i	−1.17732	+	0.599874i	−0.247859	+	0.968796i	$0.579727\pi$
$564$	134.505	−	43.7034i	0.238485	−	0.0774884i
$565$	53.5536	−	587.599i	0.0947851	−	1.04000i
$566$	−90.4972	+	278.522i	−0.159889	+	0.492088i
$567$	137.679	−	21.8062i	0.242820	−	0.0384588i
$568$	371.202	+	371.202i	0.653525	+	0.653525i
$569$	551.281	−	758.773i	0.968859	−	1.33352i	0.0262386	−	0.999656i	$-0.491647\pi$
$569$	551.281	−	758.773i	0.968859	−	1.33352i	0.942621	−	0.333865i	$-0.108353\pi$
$570$	11.2830	−	44.5653i	0.0197947	−	0.0781847i
$571$	574.791	−	417.610i	1.00664	−	0.731366i	0.0431378	−	0.999069i	$-0.486265\pi$
$571$	574.791	−	417.610i	1.00664	−	0.731366i	0.963502	+	0.267703i	$0.0862646\pi$
$572$	43.0286	−	271.672i	0.0752249	−	0.474951i
$573$	−99.5733	+	195.424i	−0.173775	+	0.341054i
$574$		−	135.420i		−	0.235923i
$575$	297.076	+	7.33854i	0.516654	+	0.0127627i
$576$	194.836			0.338257
$577$	791.204	+	403.139i	1.37124	+	0.698680i	0.975565	−	0.219711i	$-0.0705115\pi$
$577$	791.204	+	403.139i	1.37124	+	0.698680i	0.395672	+	0.918392i	$0.370512\pi$
$578$	386.814	+	61.2653i	0.669229	+	0.105995i
$579$	52.6824	+	72.5111i	0.0909885	+	0.125235i
$580$	85.0601	+	102.120i	0.146655	+	0.176068i
$581$	−86.6542	−	62.9579i	−0.149147	−	0.108361i
$582$	46.8908	−	46.8908i	0.0805684	−	0.0805684i
$583$	−32.1729	−	203.132i	−0.0551852	−	0.348425i
$584$	−445.013	−	144.594i	−0.762009	−	0.247592i
$585$	138.871	−	323.893i	0.237386	−	0.553663i
$586$	14.1989	+	43.6998i	0.0242302	+	0.0745730i
$587$	125.740	+	246.778i	0.214207	+	0.420405i	0.972960	−	0.230973i	$-0.0741910\pi$
$587$	125.740	+	246.778i	0.214207	+	0.420405i	−0.758753	+	0.651378i	$0.774191\pi$
$588$	96.5600	−	49.1998i	0.164218	−	0.0836731i
$589$	474.039	−	154.025i	0.804820	−	0.261502i
$590$	74.1630	−	16.8392i	0.125700	−	0.0285409i
$591$	71.3180	−	219.494i	0.120673	−	0.371395i
$592$	146.887	−	23.2647i	0.248121	−	0.0392984i
$593$	−3.78295	−	3.78295i	−0.00637934	−	0.00637934i	0.703910	−	0.710289i	$-0.251436\pi$
$593$	−3.78295	−	3.78295i	−0.00637934	−	0.00637934i	−0.710289	+	0.703910i	$0.751436\pi$
$594$	111.481	−	153.440i	0.187678	−	0.258317i
$595$	108.756	+	272.012i	0.182783	+	0.457163i
$596$	130.257	−	94.6372i	0.218552	−	0.158787i
$597$	27.6264	−	174.426i	0.0462753	−	0.292171i
$598$	−50.5153	+	99.1419i	−0.0844738	+	0.165789i
$599$			985.621i			1.64544i	0.568444	+	0.822722i	$0.307546\pi$
$599$			985.621i			1.64544i	−0.568444	+	0.822722i	$0.692454\pi$
$600$	−148.007	+	70.8651i	−0.246678	+	0.118108i
$601$	−541.104			−0.900339			−0.450170	−	0.892943i	$-0.648636\pi$
$601$	−541.104			−0.900339			−0.450170	+	0.892943i	$0.648636\pi$
$602$	147.408	+	75.1081i	0.244864	+	0.124764i
$603$	−959.004	−	151.891i	−1.59039	−	0.251893i
$604$	358.253	+	493.092i	0.593134	+	0.816378i
$605$	−3.14302	−	47.4147i	−0.00519508	−	0.0783714i
$606$	54.2240	+	39.3960i	0.0894785	+	0.0650100i
$607$	503.664	−	503.664i	0.829760	−	0.829760i	−0.157724	−	0.987483i	$-0.550416\pi$
$607$	503.664	−	503.664i	0.829760	−	0.829760i	0.987483	+	0.157724i	$0.0504155\pi$
$608$	−49.4309	−	312.094i	−0.0813008	−	0.513313i
$609$	18.3022	+	5.94673i	0.0300528	+	0.00976475i
$610$	−8.93036	−	7.82002i	−0.0146399	−	0.0128197i
$611$	151.106	+	465.058i	0.247310	+	0.761142i
$612$	266.708	+	523.443i	0.435797	+	0.855300i
$613$	615.498	−	313.612i	1.00407	−	0.511601i	0.126973	−	0.991906i	$-0.459474\pi$
$613$	615.498	−	313.612i	1.00407	−	0.511601i	0.877102	+	0.480305i	$0.159474\pi$
$614$	−419.681	+	136.363i	−0.683519	+	0.222089i
$615$	121.798	+	204.378i	0.198045	+	0.332323i
$616$	60.4035	−	185.903i	0.0980576	−	0.301790i
$617$	−1062.82	+	168.334i	−1.72256	+	0.272827i	−0.937851	−	0.347037i	$-0.887188\pi$
$617$	−1062.82	+	168.334i	−1.72256	+	0.272827i	−0.784709	+	0.619864i	$0.787188\pi$
$618$	45.0199	+	45.0199i	0.0728478	+	0.0728478i
$619$	−268.616	+	369.718i	−0.433951	+	0.597283i	−0.968855	−	0.247631i	$-0.920348\pi$
$619$	−268.616	+	369.718i	−0.433951	+	0.597283i	0.534903	+	0.844913i	$0.320348\pi$
$620$	−620.930	−	391.134i	−1.00150	−	0.630862i
$621$	146.242	−	106.251i	0.235494	−	0.171096i
$622$	82.5989	−	521.509i	0.132796	−	0.838438i
$623$	−33.3128	+	65.3801i	−0.0534716	+	0.104944i
$624$			23.6095i			0.0378358i
$625$	−391.883	+	486.880i	−0.627014	+	0.779008i
$626$	−267.211			−0.426855
$627$	−85.7221	−	43.6776i	−0.136718	−	0.0696612i
$628$	−65.0033	−	10.2955i	−0.103508	−	0.0163941i
$629$	−713.523	−	982.080i	−1.13438	−	1.56134i
$630$	55.0562	−	87.4022i	0.0873907	−	0.138734i
$631$	405.653	+	294.724i	0.642873	+	0.467074i	0.860836	−	0.508883i	$-0.169941\pi$
$631$	405.653	+	294.724i	0.642873	+	0.467074i	−0.217963	+	0.975957i	$0.569941\pi$
$632$	178.559	−	178.559i	0.282531	−	0.282531i
$633$	15.8923	+	100.340i	0.0251063	+	0.158515i
$634$	−76.6392	−	24.9016i	−0.120882	−	0.0392769i
$635$	414.802	−	247.198i	0.653232	−	0.389288i
$636$	13.7962	+	42.4605i	0.0216922	+	0.0667617i
$637$	170.110	+	333.860i	0.267049	+	0.524113i
$638$	−105.188	+	53.5958i	−0.164871	+	0.0840060i
$639$	552.160	−	179.408i	0.864101	−	0.280763i
$640$	−351.338	+	401.223i	−0.548965	+	0.626912i
$641$	−165.623	+	509.734i	−0.258382	+	0.795217i	0.734763	+	0.678324i	$0.237293\pi$
$641$	−165.623	+	509.734i	−0.258382	+	0.795217i	−0.993145	+	0.116893i	$0.962707\pi$
$642$	−87.4480	+	13.8504i	−0.136212	+	0.0215738i
$643$	−737.073	−	737.073i	−1.14630	−	1.14630i	−0.987274	−	0.159030i	$-0.949163\pi$
$643$	−737.073	−	737.073i	−1.14630	−	1.14630i	−0.159030	−	0.987274i	$-0.550837\pi$
$644$	45.1667	−	62.1666i	0.0701346	−	0.0965319i
$645$	−290.024	+	19.2250i	−0.449649	+	0.0298063i
$646$	−214.366	+	155.746i	−0.331835	+	0.241092i
$647$	63.9040	−	403.474i	0.0987697	−	0.623608i	−0.887795	−	0.460239i	$-0.847764\pi$
$647$	63.9040	−	403.474i	0.0987697	−	0.623608i	0.986565	−	0.163369i	$-0.0522361\pi$
$648$	204.321	−	401.003i	0.315311	−	0.618832i
$649$		−	159.158i		−	0.245235i
$650$	−101.062	−	211.075i	−0.155480	−	0.324731i
$651$	−106.259			−0.163224
$652$	18.0250	+	9.18420i	0.0276457	+	0.0140862i
$653$	108.376	+	17.1651i	0.165967	+	0.0262866i	0.238865	−	0.971053i	$-0.423225\pi$
$653$	108.376	+	17.1651i	0.165967	+	0.0262866i	−0.0728978	+	0.997339i	$0.523225\pi$
$654$	−50.3367	−	69.2825i	−0.0769675	−	0.105937i
$655$	−190.282	+	76.0784i	−0.290507	+	0.116150i
$656$	135.916	+	98.7487i	0.207189	+	0.150532i
$657$	−365.919	+	365.919i	−0.556955	+	0.556955i
$658$	22.4221	+	141.567i	0.0340761	+	0.215148i
$659$	−562.545	−	182.782i	−0.853634	−	0.277363i	−0.150667	−	0.988585i	$-0.548142\pi$
$659$	−562.545	−	182.782i	−0.853634	−	0.277363i	−0.702968	+	0.711222i	$0.748142\pi$
$660$	31.3639	+	138.133i	0.0475211	+	0.209292i
$661$	−176.026	−	541.751i	−0.266302	−	0.819593i	−0.991391	−	0.130938i	$-0.958201\pi$
$661$	−176.026	−	541.751i	−0.266302	−	0.819593i	0.725089	−	0.688656i	$-0.241799\pi$
$662$	61.0986	+	119.913i	0.0922939	+	0.181137i
$663$	171.709	−	87.4900i	0.258988	−	0.131961i
$664$	−328.896	+	106.865i	−0.495325	+	0.160941i
$665$	−100.886	−	43.2557i	−0.151709	−	0.0650461i
$666$	−132.273	+	407.093i	−0.198608	+	0.611251i
$667$	−111.131	+	17.6014i	−0.166613	+	0.0263890i
$668$	456.080	+	456.080i	0.682755	+	0.682755i
$669$	131.529	−	181.035i	0.196606	−	0.270605i
$670$	−495.427	+	412.664i	−0.739443	+	0.615916i
$671$	−20.0976	+	14.6017i	−0.0299517	+	0.0217612i
$672$	−10.5379	+	66.5339i	−0.0156814	+	0.0990087i
$673$	424.837	−	833.790i	0.631259	−	1.23892i	−0.324811	−	0.945779i	$-0.605301\pi$
$673$	424.837	−	833.790i	0.631259	−	1.23892i	0.956070	−	0.293137i	$-0.0946992\pi$
$674$		−	12.8560i		−	0.0190742i
$675$	−9.38863	+	380.067i	−0.0139091	+	0.563062i
$676$	268.123			0.396631
$677$	761.590	+	388.049i	1.12495	+	0.573190i	0.914569	−	0.404430i	$-0.132530\pi$
$677$	761.590	+	388.049i	1.12495	+	0.573190i	0.210379	+	0.977620i	$0.432530\pi$
$678$	−112.373	−	17.7981i	−0.165742	−	0.0262509i
$679$	−93.0704	−	128.100i	−0.137070	−	0.188660i
$680$	916.894	+	232.138i	1.34837	+	0.341380i
$681$	94.4239	+	68.6030i	0.138655	+	0.100739i
$682$	460.933	−	460.933i	0.675855	−	0.675855i
$683$	−46.2450	−	291.979i	−0.0677086	−	0.427495i	−0.998137	−	0.0610204i	$-0.980565\pi$
$683$	−46.2450	−	291.979i	−0.0677086	−	0.427495i	0.930428	−	0.366475i	$-0.119435\pi$
$684$	−209.355	−	68.0234i	−0.306074	−	0.0994495i
$685$	−91.8860	−	8.37446i	−0.134140	−	0.0122255i
$686$	71.9954	+	221.579i	0.104950	+	0.323002i
$687$	−28.2855	−	55.5135i	−0.0411725	−	0.0808057i
$688$	−182.874	+	93.1788i	−0.265805	+	0.135434i
$689$	−146.809	+	47.7010i	−0.213075	+	0.0692323i
$690$	5.20087	−	57.0648i	0.00753749	−	0.0827026i
$691$	−86.3193	+	265.664i	−0.124919	+	0.384462i	−0.993886	−	0.110408i	$-0.964784\pi$
$691$	−86.3193	+	265.664i	−0.124919	+	0.384462i	0.868967	+	0.494870i	$0.164784\pi$
$692$	−57.2587	+	9.06888i	−0.0827437	+	0.0131053i
$693$	−152.862	−	152.862i	−0.220579	−	0.220579i
$694$	−193.707	+	266.614i	−0.279116	+	0.384170i
$695$	−303.166	+	1197.44i	−0.436210	+	1.72293i
$696$	50.2659	−	36.5203i	0.0722212	−	0.0524718i
$697$	214.521	−	1354.43i	0.307778	−	1.94323i
$698$	40.7438	−	79.9641i	0.0583722	−	0.114562i
$699$		−	378.739i		−	0.541830i
$700$	46.1305	+	154.890i	0.0659007	+	0.221272i
$701$	624.470			0.890827			0.445414	−	0.895325i	$-0.353057\pi$
$701$	624.470			0.890827			0.445414	+	0.895325i	$0.353057\pi$
$702$	−126.838	−	64.6272i	−0.180681	−	0.0920615i
$703$	449.259	+	71.1556i	0.639059	+	0.101217i
$704$	−159.156	−	219.059i	−0.226073	−	0.311163i
$705$	−161.166	−	193.490i	−0.228605	−	0.274453i
$706$	486.857	+	353.722i	0.689599	+	0.501023i
$707$	113.164	−	113.164i	0.160062	−	0.160062i
$708$	5.40480	+	34.1246i	0.00763390	+	0.0481986i
$709$	−45.8262	−	14.8898i	−0.0646350	−	0.0210012i	0.276521	−	0.961008i	$-0.410818\pi$
$709$	−45.8262	−	14.8898i	−0.0646350	−	0.0210012i	−0.341156	+	0.940007i	$0.610818\pi$
$710$	151.927	−	354.343i	0.213981	−	0.499074i
$711$	−86.3006	−	265.606i	−0.121379	−	0.373567i
$712$	107.555	+	211.089i	0.151061	+	0.296473i
$713$	553.561	−	282.053i	0.776383	−	0.395587i
$714$	53.7230	−	17.4557i	0.0752424	−	0.0244477i
$715$	−477.600	+	108.442i	−0.667972	+	0.151667i
$716$	−26.9252	+	82.8673i	−0.0376051	+	0.115736i
$717$	−121.300	+	19.2120i	−0.169177	+	0.0267950i
$718$	385.494	+	385.494i	0.536900	+	0.536900i
$719$	62.9033	−	86.5790i	0.0874873	−	0.120416i	−0.763030	−	0.646363i	$-0.776289\pi$
$719$	62.9033	−	86.5790i	0.0874873	−	0.120416i	0.850517	+	0.525947i	$0.176289\pi$
$720$	47.5752	+	118.992i	0.0660767	+	0.165267i
$721$	122.989	−	89.3570i	0.170582	−	0.123935i
$722$	−46.1217	+	291.201i	−0.0638805	+	0.403326i
$723$	−33.5729	+	65.8906i	−0.0464356	+	0.0911350i
$724$		−	150.058i		−	0.207262i
$725$	112.608	−	208.134i	0.155322	−	0.287081i
$726$	−9.16282			−0.0126210
$727$	−119.147	−	60.7083i	−0.163888	−	0.0835052i	0.370122	−	0.928983i	$-0.379316\pi$
$727$	−119.147	−	60.7083i	−0.163888	−	0.0835052i	−0.534011	+	0.845478i	$0.679316\pi$
$728$	−144.906	−	22.9509i	−0.199047	−	0.0315259i
$729$	−221.518	−	304.894i	−0.303866	−	0.418235i
$730$	22.7296	+	342.892i	0.0311365	+	0.469716i
$731$	1355.35	+	984.722i	1.85411	+	1.34709i
$732$	3.81321	−	3.81321i	0.00520931	−	0.00520931i
$733$	120.963	+	763.727i	0.165024	+	1.04192i	0.921636	+	0.388056i	$0.126853\pi$
$733$	120.963	+	763.727i	0.165024	+	1.04192i	−0.756612	+	0.653864i	$0.773147\pi$
$734$	689.691	+	224.094i	0.939633	+	0.305305i
$735$	−145.171	−	127.121i	−0.197511	−	0.172954i
$736$	−121.710	−	374.584i	−0.165366	−	0.508945i
$737$	612.606	+	1202.31i	0.831216	+	1.63135i
$738$	−430.841	+	219.524i	−0.583795	+	0.297459i
$739$	−1135.97	+	369.099i	−1.53717	+	0.499457i	−0.950594	−	0.310436i	$-0.899525\pi$
$739$	−1135.97	+	369.099i	−1.53717	+	0.499457i	−0.586577	+	0.809894i	$0.699525\pi$
$740$	−342.837	−	575.287i	−0.463294	−	0.777415i
$741$	−22.3142	+	68.6761i	−0.0301136	+	0.0926803i
$742$	−44.6898	+	7.07816i	−0.0602288	+	0.00953930i
$743$	−298.510	−	298.510i	−0.401763	−	0.401763i	0.477091	−	0.878854i	$-0.341691\pi$
$743$	−298.510	−	298.510i	−0.401763	−	0.401763i	−0.878854	+	0.477091i	$0.841691\pi$
$744$	−201.653	+	277.551i	−0.271038	+	0.373052i
$745$	−242.567	−	152.797i	−0.325593	−	0.205097i
$746$	435.184	−	316.180i	0.583356	−	0.423833i
$747$	−59.8298	+	377.751i	−0.0800935	+	0.505690i
$748$	370.655	−	727.451i	0.495528	−	0.972528i
$749$			211.407i			0.282253i
$750$	88.6792	+	81.6092i	0.118239	+	0.108812i
$751$	−1343.94			−1.78954			−0.894770	−	0.446527i	$-0.852661\pi$
$751$	−1343.94			−1.78954			−0.894770	+	0.446527i	$0.852661\pi$
$752$	−158.436	−	80.7272i	−0.210686	−	0.107350i
$753$	−151.992	−	24.0732i	−0.201849	−	0.0319697i
$754$	52.0823	+	71.6851i	0.0690746	+	0.0950731i
$755$	578.419	−	918.247i	0.766119	−	1.21622i
$756$	79.5333	+	57.7843i	0.105203	+	0.0764343i
$757$	191.645	−	191.645i	0.253164	−	0.253164i	−0.569103	−	0.822267i	$-0.692709\pi$
$757$	191.645	−	191.645i	0.253164	−	0.253164i	0.822267	+	0.569103i	$0.192709\pi$
$758$	−91.0489	−	574.860i	−0.120117	−	0.758391i
$759$	−114.050	−	37.0571i	−0.150263	−	0.0488235i
$760$	−304.442	+	181.430i	−0.400582	+	0.238723i
$761$	−178.298	−	548.746i	−0.234295	−	0.721085i	−0.997214	−	0.0745914i	$-0.976235\pi$
$761$	−178.298	−	548.746i	−0.234295	−	0.721085i	0.762920	−	0.646493i	$-0.223765\pi$
$762$	−42.2712	−	82.9620i	−0.0554741	−	0.108874i
$763$	−182.195	+	92.8331i	−0.238788	+	0.121669i
$764$	663.286	−	215.515i	0.868175	−	0.282087i
$765$	689.112	−	786.958i	0.900800	−	1.02870i
$766$	52.0532	−	160.203i	0.0679545	−	0.209142i
$767$	−117.987	+	18.6873i	−0.153829	+	0.0243642i
$768$	131.920	+	131.920i	0.171771	+	0.171771i
$769$	411.778	−	566.764i	0.535472	−	0.737014i	−0.452480	−	0.891775i	$-0.649461\pi$
$769$	411.778	−	566.764i	0.535472	−	0.737014i	0.987952	+	0.154761i	$0.0494606\pi$
$770$	−143.242	+	9.49522i	−0.186029	+	0.0123314i
$771$	180.849	−	131.394i	0.234564	−	0.170421i
$772$	44.5838	−	281.491i	0.0577510	−	0.364626i
$773$	−515.270	+	1011.27i	−0.666585	+	1.30825i	0.271699	+	0.962382i	$0.412414\pi$
$773$	−515.270	+	1011.27i	−0.666585	+	1.30825i	−0.938284	+	0.345865i	$0.887586\pi$
$774$		−	590.736i		−	0.763225i
$775$	−236.216	+	1285.14i	−0.304795	+	1.65824i
$776$	−511.226			−0.658796
$777$	−86.4002	−	44.0231i	−0.111197	−	0.0566578i
$778$	−259.815	−	41.1507i	−0.333953	−	0.0528929i
$779$	302.026	+	415.703i	0.387709	+	0.533636i
$780$	98.7185	−	39.4695i	0.126562	−	0.0506019i
$781$	−652.755	−	474.255i	−0.835794	−	0.607240i
$782$	−233.539	+	233.539i	−0.298643	+	0.298643i
$783$	−22.5185	−	142.177i	−0.0287593	−	0.181579i
$784$	−129.587	−	42.1055i	−0.165290	−	0.0537060i
$785$	25.9471	+	114.276i	0.0330536	+	0.145574i
$786$	12.2109	+	37.5811i	0.0155354	+	0.0478131i
$787$	−9.08349	−	17.8274i	−0.0115419	−	0.0226523i	0.885164	−	0.465280i	$-0.154046\pi$
$787$	−9.08349	−	17.8274i	−0.0115419	−	0.0226523i	−0.896705	+	0.442628i	$0.854046\pi$
$788$	−653.876	+	333.167i	−0.829792	+	0.422800i
$789$	−81.2604	+	26.4031i	−0.102992	+	0.0334640i
$790$	−170.450	−	73.0813i	−0.215759	−	0.0925080i
$791$	−83.9486	+	258.367i	−0.106130	+	0.326634i
$792$	−689.371	+	109.186i	−0.870418	+	0.137861i
$793$	13.1843	+	13.1843i	0.0166259	+	0.0166259i
$794$	−165.608	+	227.940i	−0.208575	+	0.287078i
$795$	61.0805	−	50.8768i	0.0768308	−	0.0639959i
$796$	−454.304	+	330.071i	−0.570734	+	0.414663i
$797$	184.169	−	1162.80i	0.231078	−	1.45897i	−0.550331	−	0.834947i	$-0.685498\pi$
$797$	184.169	−	1162.80i	0.231078	−	1.45897i	0.781408	−	0.624020i	$-0.214502\pi$
$798$	−9.60923	+	18.8592i	−0.0120416	+	0.0236330i
$799$			1451.44i			1.81657i
$800$	781.261	+	275.356i	0.976576	+	0.344195i
$801$	262.010			0.327104
$802$	207.493	+	105.723i	0.258720	+	0.131824i
$803$	710.320	+	112.504i	0.884583	+	0.140104i
$804$	−172.176	−	236.980i	−0.214150	−	0.294752i
$805$	−132.637	−	33.5808i	−0.164766	−	0.0417152i
$806$	−395.820	−	287.580i	−0.491092	−	0.356799i
$807$	−77.3663	+	77.3663i	−0.0958690	+	0.0958690i
$808$	−80.8307	−	510.345i	−0.100038	−	0.631615i
$809$	796.194	+	258.699i	0.984170	+	0.319776i	0.756523	−	0.653967i	$-0.226897\pi$
$809$	796.194	+	258.699i	0.984170	+	0.319776i	0.227647	+	0.973744i	$0.426897\pi$
$810$	−329.165	−	30.0000i	−0.406377	−	0.0370370i
$811$	−343.826	−	1058.19i	−0.423954	−	1.30479i	−0.903993	−	0.427548i	$-0.859378\pi$
$811$	−343.826	−	1058.19i	−0.423954	−	1.30479i	0.480039	−	0.877247i	$-0.340622\pi$
$812$	−27.7806	−	54.5224i	−0.0342125	−	0.0671458i
$813$	57.5683	−	29.3325i	0.0708097	−	0.0360793i
$814$	565.754	−	183.825i	0.695030	−	0.225829i
$815$	3.26935	−	35.8718i	0.00401147	−	0.0440145i
$816$	−21.6554	+	66.6486i	−0.0265385	+	0.0816772i
$817$	−620.015	+	98.2007i	−0.758892	+	0.120197i
$818$	−357.117	−	357.117i	−0.436573	−	0.436573i
$819$	−95.3716	+	131.268i	−0.116449	+	0.160278i
$820$	185.679	−	733.390i	0.226438	−	0.894378i
$821$	−1060.41	+	770.433i	−1.29161	+	0.938408i	−0.999837	−	0.0180796i	$-0.994245\pi$
$821$	−1060.41	+	770.433i	−1.29161	+	0.938408i	−0.291772	+	0.956488i	$0.594245\pi$
$822$	−2.78318	+	17.5723i	−0.00338587	+	0.0213775i
$823$	−109.559	+	215.021i	−0.133121	+	0.261265i	−0.947939	−	0.318452i	$-0.896837\pi$
$823$	−109.559	+	215.021i	−0.133121	+	0.261265i	0.814818	+	0.579717i	$0.196837\pi$
$824$		−	490.829i		−	0.595666i
$825$	207.644	−	143.163i	0.251689	−	0.173531i
$826$	−35.0152			−0.0423913
$827$	−145.615	−	74.1944i	−0.176076	−	0.0897151i	0.363731	−	0.931504i	$-0.381503\pi$
$827$	−145.615	−	74.1944i	−0.176076	−	0.0897151i	−0.539807	+	0.841789i	$0.681503\pi$
$828$	−271.002	−	42.9225i	−0.327297	−	0.0518388i
$829$	816.399	+	1123.68i	0.984799	+	1.35546i	0.934203	+	0.356741i	$0.116112\pi$
$829$	816.399	+	1123.68i	0.984799	+	1.35546i	0.0505961	+	0.998719i	$0.483888\pi$
$830$	162.548	+	195.148i	0.195841	+	0.235118i
$831$	83.7354	+	60.8373i	0.100765	+	0.0732098i
$832$	−143.706	+	143.706i	−0.172724	+	0.172724i
$833$	173.986	+	1098.50i	0.208866	+	1.31873i
$834$	226.524	+	73.6022i	0.271612	+	0.0882520i
$835$	452.560	−	1055.52i	0.541989	−	1.26410i
$836$	94.5350	+	290.949i	0.113080	+	0.348025i
$837$	360.847	+	708.203i	0.431120	+	0.846121i
$838$	−121.217	+	61.7633i	−0.144651	+	0.0737032i
$839$	570.281	−	185.295i	0.679715	−	0.220853i	0.0512443	−	0.998686i	$-0.483681\pi$
$839$	570.281	−	185.295i	0.679715	−	0.220853i	0.628471	+	0.777833i	$0.283681\pi$
$840$	73.6782	−	16.7291i	0.0877121	−	0.0199156i
$841$	232.195	−	714.623i	0.276094	−	0.849731i
$842$	−813.765	+	128.888i	−0.966466	+	0.153073i
$843$	−126.253	−	126.253i	−0.149766	−	0.149766i
$844$	189.876	−	261.342i	0.224972	−	0.309647i
$845$	−177.235	−	443.289i	−0.209746	−	0.524602i
$846$	414.051	−	300.826i	0.489422	−	0.355586i
$847$	−3.42256	+	21.6092i	−0.00404081	+	0.0255127i
$848$	25.4839	−	50.0149i	0.0300517	−	0.0589798i
$849$			236.893i			0.279026i
$850$	−91.6882	−	688.552i	−0.107869	−	0.810061i
$851$	566.961			0.666229
$852$	156.061	+	79.5170i	0.183170	+	0.0933298i
$853$	1079.77	+	171.019i	1.26585	+	0.200491i	0.753018	−	0.658000i	$-0.228597\pi$
$853$	1079.77	+	171.019i	1.26585	+	0.200491i	0.512830	+	0.858490i	$0.328597\pi$
$854$	3.21244	+	4.42154i	0.00376163	+	0.00517744i
$855$	25.9247	+	391.092i	0.0303213	+	0.457418i
$856$	552.201	+	401.198i	0.645095	+	0.468689i
$857$	−30.8079	+	30.8079i	−0.0359485	+	0.0359485i	−0.724853	−	0.688904i	$-0.758092\pi$
$857$	−30.8079	+	30.8079i	−0.0359485	+	0.0359485i	0.688904	+	0.724853i	$0.258092\pi$
$858$	14.7733	+	93.2747i	0.0172183	+	0.108712i
$859$	−383.090	−	124.473i	−0.445972	−	0.144905i	0.0774174	−	0.996999i	$-0.475333\pi$
$859$	−383.090	−	124.473i	−0.445972	−	0.144905i	−0.523389	+	0.852094i	$0.675333\pi$
$860$	695.330	+	608.877i	0.808523	+	0.707996i
$861$	−33.8504	−	104.181i	−0.0393153	−	0.121000i
$862$	−41.3812	−	81.2152i	−0.0480061	−	0.0942172i
$863$	102.607	−	52.2808i	0.118895	−	0.0605803i	−0.393531	−	0.919311i	$-0.628747\pi$
$863$	102.607	−	52.2808i	0.118895	−	0.0605803i	0.512427	+	0.858731i	$0.328747\pi$
$864$	479.227	−	155.710i	0.554661	−	0.180220i
$865$	52.8429	+	88.6713i	0.0610901	+	0.102510i
$866$	−9.92320	+	30.5405i	−0.0114587	+	0.0352661i
$867$	312.897	−	49.5581i	0.360897	−	0.0571604i
$868$	238.918	+	238.918i	0.275251	+	0.275251i
$869$	−228.131	+	313.995i	−0.262521	+	0.361329i
$870$	−38.6094	−	24.3207i	−0.0443786	−	0.0279548i
$871$	819.369	−	595.306i	0.940722	−	0.683474i
$872$	−103.278	+	652.073i	−0.118438	+	0.747790i
$873$	−256.681	+	503.764i	−0.294021	+	0.577049i
$874$		−	123.755i		−	0.141596i
$875$	225.588	−	178.654i	0.257815	−	0.204176i
$876$	−156.118			−0.178217
$877$	−166.528	−	84.8503i	−0.189884	−	0.0967506i	0.356464	−	0.934309i	$-0.383982\pi$
$877$	−166.528	−	84.8503i	−0.189884	−	0.0967506i	−0.546348	+	0.837558i	$0.683982\pi$
$878$	42.3897	+	6.71387i	0.0482798	+	0.00764677i
$879$	21.8470	+	30.0698i	0.0248543	+	0.0342091i
$880$	94.9227	−	150.691i	0.107867	−	0.171240i
$881$	−473.929	−	344.330i	−0.537944	−	0.390839i	0.285377	−	0.958415i	$-0.407881\pi$
$881$	−473.929	−	344.330i	−0.537944	−	0.390839i	−0.823321	+	0.567576i	$0.807881\pi$
$882$	277.309	−	277.309i	0.314410	−	0.314410i
$883$	205.794	+	1299.33i	0.233062	+	1.47150i	0.775472	+	0.631382i	$0.217512\pi$
$883$	205.794	+	1299.33i	0.233062	+	1.47150i	−0.542410	+	0.840114i	$0.682488\pi$
$884$	−582.795	−	189.362i	−0.659271	−	0.214210i
$885$	52.8457	−	31.4929i	0.0597126	−	0.0355852i
$886$	−143.517	−	441.701i	−0.161984	−	0.498534i
$887$	−448.302	−	879.842i	−0.505414	−	0.991930i	−0.992917	−	0.118809i	$-0.962092\pi$
$887$	−448.302	−	879.842i	−0.505414	−	0.991930i	0.487503	−	0.873121i	$-0.337908\pi$
$888$	−278.955	+	142.135i	−0.314139	+	0.160062i
$889$	−211.444	+	68.7022i	−0.237844	+	0.0772803i
$890$	114.624	−	130.899i	0.128790	−	0.147077i
$891$	−213.755	+	657.871i	−0.239905	+	0.738351i
$892$	−702.785	+	111.310i	−0.787875	+	0.124787i
$893$	−384.566	−	384.566i	−0.430645	−	0.430645i
$894$	−32.4923	+	44.7219i	−0.0363449	+	0.0500244i
$895$	154.803	−	10.2616i	0.172965	−	0.0114655i
$896$	198.651	−	144.328i	0.221709	−	0.161081i
$897$	−14.0802	+	88.8988i	−0.0156970	+	0.0991068i
$898$	24.1922	−	47.4798i	0.0269401	−	0.0528728i
$899$		−	494.743i		−	0.550326i
$900$	418.006	−	397.853i	0.464451	−	0.442058i
$901$	−458.187			−0.508532
$902$	598.757	+	305.082i	0.663811	+	0.338228i
$903$	132.178	+	20.9349i	0.146377	+	0.0231838i
$904$	515.549	+	709.592i	0.570297	+	0.784947i
$905$	−248.092	+	99.1917i	−0.274134	+	0.109604i
$906$	−169.296	−	123.001i	−0.186861	−	0.135763i
$907$	624.820	−	624.820i	0.688886	−	0.688886i	−0.273099	−	0.961986i	$-0.588049\pi$
$907$	624.820	−	624.820i	0.688886	−	0.688886i	0.961986	+	0.273099i	$0.0880488\pi$
$908$	−58.0570	−	366.558i	−0.0639395	−	0.403698i
$909$	−543.480	−	176.587i	−0.597888	−	0.194266i
$910$	23.8576	+	105.074i	0.0262172	+	0.115466i
$911$	−129.402	−	398.260i	−0.142044	−	0.437167i	0.854575	−	0.519328i	$-0.173818\pi$
$911$	−129.402	−	398.260i	−0.142044	−	0.437167i	−0.996619	+	0.0821609i	$0.973818\pi$
$912$	−11.9212	−	23.3966i	−0.0130715	−	0.0256542i
$913$	473.587	−	241.305i	0.518716	−	0.264299i
$914$	−460.105	+	149.497i	−0.503397	+	0.163563i
$915$	−8.82503	−	3.78379i	−0.00964484	−	0.00413529i
$916$	−61.2207	+	188.418i	−0.0668348	+	0.205696i
$917$	93.1909	−	14.7600i	0.101626	−	0.0160960i
$918$	−298.780	−	298.780i	−0.325468	−	0.325468i
$919$	28.4241	−	39.1225i	0.0309294	−	0.0425707i	−0.793272	−	0.608867i	$-0.791624\pi$
$919$	28.4241	−	39.1225i	0.0309294	−	0.0425707i	0.824202	+	0.566296i	$0.191624\pi$
$920$	−339.425	+	282.722i	−0.368940	+	0.307307i
$921$	−288.782	+	209.812i	−0.313553	+	0.227809i
$922$	−93.3812	+	589.586i	−0.101281	+	0.639464i
$923$	−274.933	+	539.586i	−0.297869	+	0.584601i
$924$		−	65.2179i		−	0.0705822i
$925$	−724.502	+	947.093i	−0.783246	+	1.02388i
$926$	514.477			0.555591
$927$	−483.665	−	246.439i	−0.521753	−	0.265846i
$928$	−309.783	−	49.0648i	−0.333818	−	0.0528715i
$929$	−933.297	−	1284.57i	−1.00463	−	1.38275i	−0.922444	−	0.386132i	$-0.873811\pi$
$929$	−933.297	−	1284.57i	−1.00463	−	1.38275i	−0.0821823	−	0.996617i	$-0.526189\pi$
$930$	244.251	+	61.8393i	0.262636	+	0.0664938i
$931$	−337.152	−	244.956i	−0.362140	−	0.263110i
$932$	−851.576	+	851.576i	−0.913708	+	0.913708i
$933$	−66.8149	−	421.853i	−0.0716130	−	0.452147i
$934$	561.330	+	182.387i	0.600996	+	0.195275i
$935$	−1447.71	−	131.944i	−1.54835	−	0.141116i
$936$	161.884	+	498.226i	0.172953	+	0.532293i
$937$	−292.250	−	573.574i	−0.311900	−	0.612139i	0.680838	−	0.732434i	$-0.261616\pi$
$937$	−292.250	−	573.574i	−0.311900	−	0.612139i	−0.992738	+	0.120296i	$0.961616\pi$
$938$	264.512	−	134.776i	0.281996	−	0.143684i
$939$	−205.571	+	66.7939i	−0.218925	+	0.0711331i
$940$	−72.6771	+	797.426i	−0.0773161	+	0.848325i
$941$	442.874	−	1363.03i	0.470642	−	1.44849i	−0.381104	−	0.924532i	$-0.624456\pi$
$941$	442.874	−	1363.03i	0.470642	−	1.44849i	0.851746	−	0.523955i	$-0.175544\pi$
$942$	22.3180	−	3.53482i	0.0236921	−	0.00375246i
$943$	452.884	+	452.884i	0.480258	+	0.480258i
$944$	25.5332	−	35.1435i	0.0270479	−	0.0372283i
$945$	42.9618	−	169.690i	0.0454623	−	0.179566i
$946$	−664.179	+	482.554i	−0.702092	+	0.510099i
$947$	−116.733	+	737.026i	−0.123267	+	0.778275i	0.846166	+	0.532919i	$0.178905\pi$
$947$	−116.733	+	737.026i	−0.123267	+	0.778275i	−0.969433	+	0.245356i	$0.921095\pi$
$948$	38.2500	−	75.0699i	0.0403482	−	0.0791877i
$949$		−	539.786i		−	0.568794i
$950$	206.729	+	158.142i	0.217609	+	0.166465i
$951$	−65.1845			−0.0685431
$952$	−388.012	−	197.702i	−0.407576	−	0.207670i
$953$	−589.626	−	93.3875i	−0.618705	−	0.0979932i	−0.160789	−	0.986989i	$-0.551404\pi$
$953$	−589.626	−	93.3875i	−0.618705	−	0.0979932i	−0.457916	+	0.888996i	$0.651404\pi$
$954$	94.9643	+	130.707i	0.0995433	+	0.137010i
$955$	−794.759	−	954.154i	−0.832208	−	0.999115i
$956$	315.934	+	229.539i	0.330475	+	0.240104i
$957$	−67.5256	+	67.5256i	−0.0705597	+	0.0705597i
$958$	−2.82271	−	17.8219i	−0.00294646	−	0.0186032i
$959$	40.4023	+	13.1275i	0.0421296	+	0.0136887i
$960$	41.2424	−	96.1907i	0.0429608	−	0.100199i
$961$	547.206	+	1684.13i	0.569413	+	1.75247i
$962$	−202.701	−	397.823i	−0.210708	−	0.413537i
$963$	672.596	−	342.705i	0.698438	−	0.355872i
$964$	223.639	−	72.6646i	0.231990	−	0.0753782i
$965$	−494.862	+	112.361i	−0.512810	+	0.116437i
$966$	−8.15269	+	25.0914i	−0.00843963	+	0.0259745i
$967$	1563.95	−	247.705i	1.61732	−	0.256158i	0.718841	−	0.695174i	$-0.244673\pi$
$967$	1563.95	−	247.705i	1.61732	−	0.256158i	0.898479	+	0.439016i	$0.144673\pi$
$968$	49.9487	+	49.9487i	0.0515999	+	0.0515999i
$969$	−125.984	+	173.402i	−0.130014	+	0.178950i
$970$	139.385	+	348.621i	0.143696	+	0.359403i
$971$	773.570	−	562.032i	0.796674	−	0.578817i	−0.113263	−	0.993565i	$-0.536130\pi$
$971$	773.570	−	562.032i	0.796674	−	0.578817i	0.909936	+	0.414748i	$0.136130\pi$
$972$	83.6135	−	527.915i	0.0860221	−	0.543122i
$973$	258.193	−	506.733i	0.265358	−	0.520794i
$974$		−	281.269i		−	0.288777i
$975$	−130.510	−	137.122i	−0.133857	−	0.140638i
$976$	−6.78026			−0.00694698
$977$	216.701	+	110.415i	0.221802	+	0.113014i	0.561361	−	0.827571i	$-0.310278\pi$
$977$	216.701	+	110.415i	0.221802	+	0.113014i	−0.339559	+	0.940585i	$0.610278\pi$
$978$	−6.86015	−	1.08654i	−0.00701447	−	0.00111098i
$979$	−214.028	−	294.584i	−0.218619	−	0.300903i
$980$	40.5837	+	612.234i	0.0414120	+	0.624729i
$981$	590.701	+	429.169i	0.602141	+	0.437481i
$982$	148.277	−	148.277i	0.150995	−	0.150995i
$983$	−281.770	−	1779.02i	−0.286642	−	1.80979i	−0.539167	−	0.842199i	$-0.681261\pi$
$983$	−281.770	−	1779.02i	−0.286642	−	1.80979i	0.252525	−	0.967590i	$-0.418739\pi$
$984$	−336.363	−	109.291i	−0.341832	−	0.111068i
$985$	983.054	+	860.827i	0.998024	+	0.873936i
$986$	81.2739	+	250.135i	0.0824279	+	0.253687i
$987$	52.6368	+	103.305i	0.0533301	+	0.104666i
$988$	204.587	−	104.242i	0.207072	−	0.105508i
$989$	−744.158	+	241.792i	−0.752435	+	0.244481i
$990$	262.414	+	440.335i	0.265065	+	0.444783i
$991$	−111.201	+	342.241i	−0.112211	+	0.345350i	−0.991355	−	0.131206i	$-0.958115\pi$
$991$	−111.201	+	342.241i	−0.112211	+	0.345350i	0.879144	+	0.476556i	$0.158115\pi$
$992$	1710.51	−	270.918i	1.72431	−	0.273103i
$993$	76.9784	+	76.9784i	0.0775211	+	0.0775211i
$994$	−104.338	+	143.609i	−0.104968	+	0.144475i
$995$	846.015	+	532.919i	0.850266	+	0.535597i
$996$	−93.3463	+	67.8201i	−0.0937212	+	0.0680924i
$997$	−41.9523	+	264.877i	−0.0420786	+	0.265674i	−0.999754	−	0.0221764i	$-0.992940\pi$
$997$	−41.9523	+	264.877i	−0.0420786	+	0.265674i	0.957676	+	0.287850i	$0.0929404\pi$
$998$	285.356	−	560.042i	0.285928	−	0.561164i
$999$			725.347i			0.726073i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.3.f.a.8.3	✓	32
3.2	odd	2		225.3.r.a.208.2		32
4.3	odd	2		400.3.bg.c.33.2		32
5.2	odd	4		125.3.f.a.107.2		32
5.3	odd	4		125.3.f.b.107.3		32
5.4	even	2		125.3.f.c.18.2		32
25.3	odd	20		125.3.f.c.7.2		32
25.4	even	10		125.3.f.b.118.3		32
25.21	even	5		125.3.f.a.118.2		32
25.22	odd	20	inner	25.3.f.a.22.3	yes	32
75.47	even	20		225.3.r.a.172.2		32
100.47	even	20		400.3.bg.c.97.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.3.f.a.8.3	✓	32	1.1	even	1	trivial
25.3.f.a.22.3	yes	32	25.22	odd	20	inner
125.3.f.a.107.2		32	5.2	odd	4
125.3.f.a.118.2		32	25.21	even	5
125.3.f.b.107.3		32	5.3	odd	4
125.3.f.b.118.3		32	25.4	even	10
125.3.f.c.7.2		32	25.3	odd	20
125.3.f.c.18.2		32	5.4	even	2
225.3.r.a.172.2		32	75.47	even	20
225.3.r.a.208.2		32	3.2	odd	2
400.3.bg.c.33.2		32	4.3	odd	2
400.3.bg.c.97.2		32	100.47	even	20

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:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	25.f (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.972743 + 0.495637i) q^{2} +(0.872241 + 0.138149i) q^{3} +(-1.65057 - 2.27181i) q^{4} +(-2.66494 + 4.23062i) q^{5} +(0.779995 + 0.566699i) q^{6} +(1.62783 - 1.62783i) q^{7} +(-1.16272 - 7.34115i) q^{8} +(-7.81779 - 2.54015i) q^{9} +O(q^{10})\)	\(q+(0.972743 + 0.495637i) q^{2} +(0.872241 + 0.138149i) q^{3} +(-1.65057 - 2.27181i) q^{4} +(-2.66494 + 4.23062i) q^{5} +(0.779995 + 0.566699i) q^{6} +(1.62783 - 1.62783i) q^{7} +(-1.16272 - 7.34115i) q^{8} +(-7.81779 - 2.54015i) q^{9} +(-4.68915 + 2.79446i) q^{10} +(3.53016 + 10.8647i) q^{11} +(-1.12584 - 2.20959i) q^{12} +(7.63976 - 3.89265i) q^{13} +(2.39027 - 0.776647i) q^{14} +(-2.90893 + 3.32196i) q^{15} +(-0.963505 + 2.96536i) q^{16} +(25.1372 - 3.98134i) q^{17} +(-6.34570 - 6.34570i) q^{18} +(-5.60535 + 7.71510i) q^{19} +(14.0098 - 0.928682i) q^{20} +(1.64474 - 1.19498i) q^{21} +(-1.95102 + 12.3182i) q^{22} +(-5.39644 + 10.5911i) q^{23} -6.56388i q^{24} +(-10.7962 - 22.5487i) q^{25} +9.36086 q^{26} +(-13.5498 - 6.90398i) q^{27} +(-6.38497 - 1.01128i) q^{28} +(5.56383 + 7.65796i) q^{29} +(-4.47612 + 1.78964i) q^{30} +(-42.2846 - 30.7215i) q^{31} +(-23.4297 + 23.4297i) q^{32} +(1.57820 + 9.96433i) q^{33} +(26.4253 + 8.58610i) q^{34} +(2.54866 + 11.2248i) q^{35} +(7.13304 + 21.9532i) q^{36} +(-21.6541 - 42.4985i) q^{37} +(-9.27645 + 4.72659i) q^{38} +(7.20148 - 2.33990i) q^{39} +(34.1562 + 14.6447i) q^{40} +(16.6504 - 51.2445i) q^{41} +(2.19219 - 0.347209i) q^{42} +(46.5461 + 46.5461i) q^{43} +(18.8558 - 25.9528i) q^{44} +(31.5803 - 26.3047i) q^{45} +(-10.4987 + 7.62775i) q^{46} +(-8.92142 + 56.3277i) q^{47} +(-1.25007 + 2.45341i) q^{48} +43.7003i q^{49} +(0.674010 - 27.2851i) q^{50} +22.4757 q^{51} +(-21.4533 - 10.9310i) q^{52} +(-17.7814 - 2.81630i) q^{53} +(-9.75862 - 13.4316i) q^{54} +(-55.3720 - 14.0190i) q^{55} +(-13.8429 - 10.0574i) q^{56} +(-5.95505 + 5.95505i) q^{57} +(1.61661 + 10.2069i) q^{58} +(-13.2502 - 4.30525i) q^{59} +(12.3482 + 1.12542i) q^{60} +(0.671981 + 2.06814i) q^{61} +(-25.9053 - 50.8420i) q^{62} +(-16.8610 + 8.59109i) q^{63} +(-22.5423 + 7.32443i) q^{64} +(-3.89117 + 42.6945i) q^{65} +(-3.40352 + 10.4749i) q^{66} +(116.666 - 18.4780i) q^{67} +(-50.5355 - 50.5355i) q^{68} +(-6.17015 + 8.49249i) q^{69} +(-3.08423 + 12.1820i) q^{70} +(-57.1398 + 41.5145i) q^{71} +(-9.55772 + 60.3450i) q^{72} +(28.5805 - 56.0923i) q^{73} -52.0727i q^{74} +(-6.30182 - 21.1594i) q^{75} +26.7793 q^{76} +(23.4324 + 11.9394i) q^{77} +(8.16493 + 1.29320i) q^{78} +(19.9697 + 27.4860i) q^{79} +(-9.97763 - 11.9787i) q^{80} +(48.9869 + 35.5911i) q^{81} +(41.5952 - 41.5952i) q^{82} +(-7.27847 - 45.9545i) q^{83} +(-5.42953 - 1.76416i) q^{84} +(-50.1455 + 116.956i) q^{85} +(22.2074 + 68.3474i) q^{86} +(3.79506 + 7.44823i) q^{87} +(75.6548 - 38.5480i) q^{88} +(-30.3143 + 9.84970i) q^{89} +(43.7571 - 9.93533i) q^{90} +(6.09965 - 18.7728i) q^{91} +(32.9682 - 5.22165i) q^{92} +(-32.6382 - 32.6382i) q^{93} +(-36.5963 + 50.3705i) q^{94} +(-17.7017 - 44.2743i) q^{95} +(-23.6732 + 17.1996i) q^{96} +(10.7597 - 67.9342i) q^{97} +(-21.6595 + 42.5092i) q^{98} -93.9051i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 10 q^{2} - 10 q^{3} - 10 q^{4} - 10 q^{5} - 6 q^{6} - 10 q^{7} - 10 q^{8} - 10 q^{9}+O(q^{10}) \) 32 * q - 10 * q^2 - 10 * q^3 - 10 * q^4 - 10 * q^5 - 6 * q^6 - 10 * q^7 - 10 * q^8 - 10 * q^9	\( 32 q - 10 q^{2} - 10 q^{3} - 10 q^{4} - 10 q^{5} - 6 q^{6} - 10 q^{7} - 10 q^{8} - 10 q^{9} - 10 q^{10} - 6 q^{11} - 10 q^{12} - 10 q^{13} - 10 q^{14} - 10 q^{15} + 2 q^{16} + 60 q^{17} + 140 q^{18} + 90 q^{19} + 130 q^{20} - 6 q^{21} + 70 q^{22} + 10 q^{23} - 40 q^{25} + 4 q^{26} - 100 q^{27} - 250 q^{28} - 110 q^{29} - 250 q^{30} - 6 q^{31} - 290 q^{32} - 190 q^{33} - 260 q^{34} - 120 q^{35} - 58 q^{36} + 50 q^{37} + 320 q^{38} + 390 q^{39} + 440 q^{40} - 86 q^{41} + 690 q^{42} + 230 q^{43} + 340 q^{44} + 310 q^{45} - 6 q^{46} + 70 q^{47} + 160 q^{48} - 100 q^{50} - 16 q^{51} - 320 q^{52} - 190 q^{53} - 660 q^{54} - 250 q^{55} - 70 q^{56} - 650 q^{57} - 640 q^{58} - 260 q^{59} - 550 q^{60} + 114 q^{61} + 60 q^{62} - 20 q^{63} + 340 q^{64} + 360 q^{65} + 138 q^{66} + 270 q^{67} + 710 q^{68} + 340 q^{69} + 310 q^{70} - 66 q^{71} + 360 q^{72} + 30 q^{73} - 90 q^{75} - 80 q^{76} - 250 q^{77} - 500 q^{78} - 210 q^{79} - 850 q^{80} + 62 q^{81} + 30 q^{82} - 10 q^{84} + 600 q^{85} - 6 q^{86} + 300 q^{87} + 190 q^{88} - 10 q^{89} + 380 q^{90} - 6 q^{91} - 30 q^{92} + 520 q^{93} + 790 q^{94} + 310 q^{95} + 174 q^{96} + 270 q^{97} + 170 q^{98}+O(q^{100}) \) 32 * q - 10 * q^2 - 10 * q^3 - 10 * q^4 - 10 * q^5 - 6 * q^6 - 10 * q^7 - 10 * q^8 - 10 * q^9 - 10 * q^10 - 6 * q^11 - 10 * q^12 - 10 * q^13 - 10 * q^14 - 10 * q^15 + 2 * q^16 + 60 * q^17 + 140 * q^18 + 90 * q^19 + 130 * q^20 - 6 * q^21 + 70 * q^22 + 10 * q^23 - 40 * q^25 + 4 * q^26 - 100 * q^27 - 250 * q^28 - 110 * q^29 - 250 * q^30 - 6 * q^31 - 290 * q^32 - 190 * q^33 - 260 * q^34 - 120 * q^35 - 58 * q^36 + 50 * q^37 + 320 * q^38 + 390 * q^39 + 440 * q^40 - 86 * q^41 + 690 * q^42 + 230 * q^43 + 340 * q^44 + 310 * q^45 - 6 * q^46 + 70 * q^47 + 160 * q^48 - 100 * q^50 - 16 * q^51 - 320 * q^52 - 190 * q^53 - 660 * q^54 - 250 * q^55 - 70 * q^56 - 650 * q^57 - 640 * q^58 - 260 * q^59 - 550 * q^60 + 114 * q^61 + 60 * q^62 - 20 * q^63 + 340 * q^64 + 360 * q^65 + 138 * q^66 + 270 * q^67 + 710 * q^68 + 340 * q^69 + 310 * q^70 - 66 * q^71 + 360 * q^72 + 30 * q^73 - 90 * q^75 - 80 * q^76 - 250 * q^77 - 500 * q^78 - 210 * q^79 - 850 * q^80 + 62 * q^81 + 30 * q^82 - 10 * q^84 + 600 * q^85 - 6 * q^86 + 300 * q^87 + 190 * q^88 - 10 * q^89 + 380 * q^90 - 6 * q^91 - 30 * q^92 + 520 * q^93 + 790 * q^94 + 310 * q^95 + 174 * q^96 + 270 * q^97 + 170 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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