LMFDB - Embedded newform 65.3.h.a.38.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [65,3,Mod(12,65)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(65, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 2]))

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

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

chi := DirichletCharacter("65.12");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 65 = 5 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	65.h (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:	$1.77112171834$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			38.1
Character	$\chi$	$=$	65.38
Dual form			65.3.h.a.12.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.66395 - 2.66395i) q^{2} +(-2.12513 - 2.12513i) q^{3} +10.1932i q^{4} +(-4.54019 - 2.09444i) q^{5} +11.3225i q^{6} +(2.95114 + 2.95114i) q^{7} +(16.4984 - 16.4984i) q^{8} +0.0323960i q^{9} +O(q^{10})$	\(q+(-2.66395 - 2.66395i) q^{2} +(-2.12513 - 2.12513i) q^{3} +10.1932i q^{4} +(-4.54019 - 2.09444i) q^{5} +11.3225i q^{6} +(2.95114 + 2.95114i) q^{7} +(16.4984 - 16.4984i) q^{8} +0.0323960i q^{9} +(6.51533 + 17.6743i) q^{10} +8.43761i q^{11} +(21.6620 - 21.6620i) q^{12} +(-9.88656 + 8.44132i) q^{13} -15.7234i q^{14} +(5.19753 + 14.0995i) q^{15} -47.1290 q^{16} +(-9.34548 + 9.34548i) q^{17} +(0.0863012 - 0.0863012i) q^{18} -12.7666 q^{19} +(21.3492 - 46.2792i) q^{20} -12.5431i q^{21} +(22.4773 - 22.4773i) q^{22} +(-28.0399 - 28.0399i) q^{23} -70.1228 q^{24} +(16.2266 + 19.0183i) q^{25} +(48.8245 + 3.85003i) q^{26} +(-19.0574 + 19.0574i) q^{27} +(-30.0816 + 30.0816i) q^{28} +32.7061i q^{29} +(23.7143 - 51.4062i) q^{30} -36.2540i q^{31} +(59.5554 + 59.5554i) q^{32} +(17.9311 - 17.9311i) q^{33} +49.7917 q^{34} +(-7.21773 - 19.5797i) q^{35} -0.330220 q^{36} +(17.1445 + 17.1445i) q^{37} +(34.0096 + 34.0096i) q^{38} +(38.9492 + 3.07132i) q^{39} +(-109.461 + 40.3509i) q^{40} -26.7772i q^{41} +(-33.4142 + 33.4142i) q^{42} +(-34.4650 - 34.4650i) q^{43} -86.0065 q^{44} +(0.0678516 - 0.147084i) q^{45} +149.393i q^{46} +(-9.09020 - 9.09020i) q^{47} +(100.156 + 100.156i) q^{48} -31.5816i q^{49} +(7.43703 - 93.8907i) q^{50} +39.7208 q^{51} +(-86.0444 - 100.776i) q^{52} +(31.0096 + 31.0096i) q^{53} +101.536 q^{54} +(17.6721 - 38.3083i) q^{55} +97.3783 q^{56} +(27.1308 + 27.1308i) q^{57} +(87.1275 - 87.1275i) q^{58} -68.4880 q^{59} +(-143.719 + 52.9797i) q^{60} -30.3455 q^{61} +(-96.5789 + 96.5789i) q^{62} +(-0.0956050 + 0.0956050i) q^{63} -128.789i q^{64} +(62.5667 - 17.6184i) q^{65} -95.5348 q^{66} +(-5.29514 - 5.29514i) q^{67} +(-95.2606 - 95.2606i) q^{68} +119.177i q^{69} +(-32.9317 + 71.3870i) q^{70} -2.71090i q^{71} +(0.534483 + 0.534483i) q^{72} +(-29.3778 + 29.3778i) q^{73} -91.3441i q^{74} +(5.93281 - 74.9003i) q^{75} -130.133i q^{76} +(-24.9005 + 24.9005i) q^{77} +(-95.5769 - 111.940i) q^{78} -12.1312i q^{79} +(213.975 + 98.7091i) q^{80} +81.2905 q^{81} +(-71.3330 + 71.3330i) q^{82} +(-3.27251 + 3.27251i) q^{83} +127.855 q^{84} +(62.0038 - 22.8566i) q^{85} +183.626i q^{86} +(69.5050 - 69.5050i) q^{87} +(139.207 + 139.207i) q^{88} -68.3722 q^{89} +(-0.572577 + 0.211071i) q^{90} +(-54.0881 - 4.26508i) q^{91} +(285.817 - 285.817i) q^{92} +(-77.0447 + 77.0447i) q^{93} +48.4316i q^{94} +(57.9628 + 26.7389i) q^{95} -253.127i q^{96} +(51.9549 + 51.9549i) q^{97} +(-84.1316 + 84.1316i) q^{98} -0.273345 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{3}+O(q^{10}) $ 24 * q - 4 * q^3	$ 24 q - 4 q^{3} + 16 q^{10} + 72 q^{12} - 36 q^{13} - 104 q^{16} - 48 q^{17} + 8 q^{22} - 104 q^{23} - 88 q^{25} + 88 q^{26} + 56 q^{27} - 24 q^{30} - 64 q^{35} + 256 q^{36} + 124 q^{38} - 368 q^{40} + 216 q^{42} + 8 q^{43} + 196 q^{48} - 296 q^{51} + 16 q^{52} + 220 q^{53} + 332 q^{55} + 584 q^{56} - 8 q^{61} - 596 q^{62} + 420 q^{65} - 360 q^{66} - 640 q^{68} - 184 q^{75} + 388 q^{77} - 636 q^{78} - 224 q^{81} - 1004 q^{82} - 52 q^{87} + 780 q^{88} + 452 q^{90} - 512 q^{91} + 812 q^{92} - 136 q^{95}+O(q^{100}) $ 24 * q - 4 * q^3 + 16 * q^10 + 72 * q^12 - 36 * q^13 - 104 * q^16 - 48 * q^17 + 8 * q^22 - 104 * q^23 - 88 * q^25 + 88 * q^26 + 56 * q^27 - 24 * q^30 - 64 * q^35 + 256 * q^36 + 124 * q^38 - 368 * q^40 + 216 * q^42 + 8 * q^43 + 196 * q^48 - 296 * q^51 + 16 * q^52 + 220 * q^53 + 332 * q^55 + 584 * q^56 - 8 * q^61 - 596 * q^62 + 420 * q^65 - 360 * q^66 - 640 * q^68 - 184 * q^75 + 388 * q^77 - 636 * q^78 - 224 * q^81 - 1004 * q^82 - 52 * q^87 + 780 * q^88 + 452 * q^90 - 512 * q^91 + 812 * q^92 - 136 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/65\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−2.66395	−	2.66395i	−1.33197	−	1.33197i	−0.903603	−	0.428370i	$-0.859088\pi$
$2$	−2.66395	−	2.66395i	−1.33197	−	1.33197i	−0.428370	−	0.903603i	$-0.640912\pi$
$3$	−2.12513	−	2.12513i	−0.708378	−	0.708378i	0.257816	−	0.966194i	$-0.416997\pi$
$3$	−2.12513	−	2.12513i	−0.708378	−	0.708378i	−0.966194	+	0.257816i	$0.916997\pi$
$4$			10.1932i			2.54831i
$5$	−4.54019	−	2.09444i	−0.908038	−	0.418889i
$5$	−4.54019	−	2.09444i	−0.908038	−	0.418889i
$6$			11.3225i			1.88708i
$7$	2.95114	+	2.95114i	0.421591	+	0.421591i	0.885751	−	0.464160i	$-0.153644\pi$
$7$	2.95114	+	2.95114i	0.421591	+	0.421591i	−0.464160	+	0.885751i	$0.653644\pi$
$8$	16.4984	−	16.4984i	2.06230	−	2.06230i
$9$			0.0323960i			0.00359955i
$10$	6.51533	+	17.6743i	0.651533	+	1.76743i
$11$			8.43761i			0.767055i	0.923529	+	0.383528i	$0.125291\pi$
$11$			8.43761i			0.767055i	−0.923529	+	0.383528i	$0.874709\pi$
$12$	21.6620	−	21.6620i	1.80517	−	1.80517i
$13$	−9.88656	+	8.44132i	−0.760504	+	0.649333i
$13$	−9.88656	+	8.44132i	−0.760504	+	0.649333i
$14$		−	15.7234i		−	1.12310i
$15$	5.19753	+	14.0995i	0.346502	+	0.939966i
$16$	−47.1290			−2.94556
$17$	−9.34548	+	9.34548i	−0.549734	+	0.549734i	−0.926364	−	0.376630i	$-0.877083\pi$
$17$	−9.34548	+	9.34548i	−0.549734	+	0.549734i	0.376630	+	0.926364i	$0.377083\pi$
$18$	0.0863012	−	0.0863012i	0.00479451	−	0.00479451i
$19$	−12.7666			−0.671927			−0.335963	−	0.941875i	$-0.609062\pi$
$19$	−12.7666			−0.671927			−0.335963	+	0.941875i	$0.609062\pi$
$20$	21.3492	−	46.2792i	1.06746	−	2.31396i
$21$		−	12.5431i		−	0.597292i
$22$	22.4773	−	22.4773i	1.02170	−	1.02170i
$23$	−28.0399	−	28.0399i	−1.21912	−	1.21912i	−0.967939	−	0.251185i	$-0.919180\pi$
$23$	−28.0399	−	28.0399i	−1.21912	−	1.21912i	−0.251185	−	0.967939i	$-0.580820\pi$
$24$	−70.1228			−2.92178
$25$	16.2266	+	19.0183i	0.649064	+	0.760734i
$26$	48.8245	+	3.85003i	1.87787	+	0.148078i
$27$	−19.0574	+	19.0574i	−0.705828	+	0.705828i
$28$	−30.0816	+	30.0816i	−1.07434	+	1.07434i
$29$			32.7061i			1.12780i	0.825844	+	0.563899i	$0.190699\pi$
$29$			32.7061i			1.12780i	−0.825844	+	0.563899i	$0.809301\pi$
$30$	23.7143	−	51.4062i	0.790478	−	1.71354i
$31$		−	36.2540i		−	1.16949i	−0.811219	−	0.584743i	$-0.801195\pi$
$31$		−	36.2540i		−	1.16949i	0.811219	−	0.584743i	$-0.198805\pi$
$32$	59.5554	+	59.5554i	1.86111	+	1.86111i
$33$	17.9311	−	17.9311i	0.543365	−	0.543365i
$34$	49.7917			1.46446
$35$	−7.21773	−	19.5797i	−0.206221	−	0.559420i
$36$	−0.330220			−0.00917277
$37$	17.1445	+	17.1445i	0.463365	+	0.463365i	0.899757	−	0.436392i	$-0.143744\pi$
$37$	17.1445	+	17.1445i	0.463365	+	0.463365i	−0.436392	+	0.899757i	$0.643744\pi$
$38$	34.0096	+	34.0096i	0.894989	+	0.894989i
$39$	38.9492	+	3.07132i	0.998698	+	0.0787517i
$40$	−109.461	+	40.3509i	−2.73653	+	1.00877i
$41$		−	26.7772i		−	0.653102i	−0.945180	−	0.326551i	$-0.894113\pi$
$41$		−	26.7772i		−	0.653102i	0.945180	−	0.326551i	$-0.105887\pi$
$42$	−33.4142	+	33.4142i	−0.795577	+	0.795577i
$43$	−34.4650	−	34.4650i	−0.801511	−	0.801511i	0.181820	−	0.983332i	$-0.441801\pi$
$43$	−34.4650	−	34.4650i	−0.801511	−	0.801511i	−0.983332	+	0.181820i	$0.941801\pi$
$44$	−86.0065			−1.95469
$45$	0.0678516	−	0.147084i	0.00150781	−	0.00326853i
$46$			149.393i			3.24768i
$47$	−9.09020	−	9.09020i	−0.193408	−	0.193408i	0.603759	−	0.797167i	$-0.293669\pi$
$47$	−9.09020	−	9.09020i	−0.193408	−	0.193408i	−0.797167	+	0.603759i	$0.793669\pi$
$48$	100.156	+	100.156i	2.08657	+	2.08657i
$49$		−	31.5816i		−	0.644522i
$50$	7.43703	−	93.8907i	0.148741	−	1.87781i
$51$	39.7208			0.778839
$52$	−86.0444	−	100.776i	−1.65470	−	1.93800i
$53$	31.0096	+	31.0096i	0.585088	+	0.585088i	0.936297	−	0.351209i	$-0.114229\pi$
$53$	31.0096	+	31.0096i	0.585088	+	0.585088i	−0.351209	+	0.936297i	$0.614229\pi$
$54$	101.536			1.88029
$55$	17.6721	−	38.3083i	0.321311	−	0.696515i
$56$	97.3783			1.73890
$57$	27.1308	+	27.1308i	0.475978	+	0.475978i
$58$	87.1275	−	87.1275i	1.50220	−	1.50220i
$59$	−68.4880			−1.16081			−0.580407	−	0.814327i	$-0.697107\pi$
$59$	−68.4880			−1.16081			−0.580407	+	0.814327i	$0.697107\pi$
$60$	−143.719	+	52.9797i	−2.39532	+	0.882994i
$61$	−30.3455			−0.497467			−0.248734	−	0.968572i	$-0.580014\pi$
$61$	−30.3455			−0.497467			−0.248734	+	0.968572i	$0.580014\pi$
$62$	−96.5789	+	96.5789i	−1.55772	+	1.55772i
$63$	−0.0956050	+	0.0956050i	−0.00151754	+	0.00151754i
$64$		−	128.789i		−	2.01233i
$65$	62.5667	−	17.6184i	0.962565	−	0.271052i
$66$	−95.5348			−1.44750
$67$	−5.29514	−	5.29514i	−0.0790320	−	0.0790320i	0.666486	−	0.745518i	$-0.267798\pi$
$67$	−5.29514	−	5.29514i	−0.0790320	−	0.0790320i	−0.745518	+	0.666486i	$0.767798\pi$
$68$	−95.2606	−	95.2606i	−1.40089	−	1.40089i
$69$			119.177i			1.72720i
$70$	−32.9317	+	71.3870i	−0.470453	+	1.01981i
$71$		−	2.71090i		−	0.0381816i	−0.999818	−	0.0190908i	$-0.993923\pi$
$71$		−	2.71090i		−	0.0381816i	0.999818	−	0.0190908i	$-0.00607717\pi$
$72$	0.534483	+	0.534483i	0.00742338	+	0.00742338i
$73$	−29.3778	+	29.3778i	−0.402436	+	0.402436i	−0.879091	−	0.476655i	$-0.841849\pi$
$73$	−29.3778	+	29.3778i	−0.402436	+	0.402436i	0.476655	+	0.879091i	$0.341849\pi$
$74$		−	91.3441i		−	1.23438i
$75$	5.93281	−	74.9003i	0.0791041	−	0.998670i
$76$		−	130.133i		−	1.71228i
$77$	−24.9005	+	24.9005i	−0.323384	+	0.323384i
$78$	−95.5769	−	111.940i	−1.22534	−	1.43513i
$79$		−	12.1312i		−	0.153560i	−0.997048	−	0.0767798i	$-0.975536\pi$
$79$		−	12.1312i		−	0.153560i	0.997048	−	0.0767798i	$-0.0244638\pi$
$80$	213.975	+	98.7091i	2.67468	+	1.23386i
$81$	81.2905			1.00359
$82$	−71.3330	+	71.3330i	−0.869915	+	0.869915i
$83$	−3.27251	+	3.27251i	−0.0394278	+	0.0394278i	−0.726546	−	0.687118i	$-0.758876\pi$
$83$	−3.27251	+	3.27251i	−0.0394278	+	0.0394278i	0.687118	+	0.726546i	$0.258876\pi$
$84$	127.855			1.52208
$85$	62.0038	−	22.8566i	0.729457	−	0.268902i
$86$			183.626i			2.13518i
$87$	69.5050	−	69.5050i	0.798908	−	0.798908i
$88$	139.207	+	139.207i	1.58190	+	1.58190i
$89$	−68.3722			−0.768227			−0.384113	−	0.923286i	$-0.625493\pi$
$89$	−68.3722			−0.768227			−0.384113	+	0.923286i	$0.625493\pi$
$90$	−0.572577	+	0.211071i	−0.00636196	+	0.00234523i
$91$	−54.0881	−	4.26508i	−0.594375	−	0.0468690i
$92$	285.817	−	285.817i	3.10670	−	3.10670i
$93$	−77.0447	+	77.0447i	−0.828438	+	0.828438i
$94$			48.4316i			0.515230i
$95$	57.9628	+	26.7389i	0.610135	+	0.281463i
$96$		−	253.127i		−	2.63674i
$97$	51.9549	+	51.9549i	0.535618	+	0.535618i	0.922239	−	0.386621i	$-0.126358\pi$
$97$	51.9549	+	51.9549i	0.535618	+	0.535618i	−0.386621	+	0.922239i	$0.626358\pi$
$98$	−84.1316	+	84.1316i	−0.858486	+	0.858486i
$99$	−0.273345			−0.00276106
$100$	−193.858	+	165.402i	−1.93858	+	1.65402i
$101$	−32.1801			−0.318615			−0.159307	−	0.987229i	$-0.550926\pi$
$101$	−32.1801			−0.318615			−0.159307	+	0.987229i	$0.550926\pi$
$102$	−105.814	−	105.814i	−1.03739	−	1.03739i
$103$	56.8521	+	56.8521i	0.551962	+	0.551962i	0.927007	−	0.375045i	$-0.122373\pi$
$103$	56.8521	+	56.8521i	0.551962	+	0.551962i	−0.375045	+	0.927007i	$0.622373\pi$
$104$	−23.8441	+	302.381i	−0.229270	+	2.90751i
$105$	−26.2709	+	56.9482i	−0.250199	+	0.542364i
$106$		−	165.216i		−	1.55864i
$107$	−47.0004	+	47.0004i	−0.439256	+	0.439256i	−0.891762	−	0.452506i	$-0.850530\pi$
$107$	−47.0004	+	47.0004i	−0.439256	+	0.439256i	0.452506	+	0.891762i	$0.350530\pi$
$108$	−194.256	−	194.256i	−1.79867	−	1.79867i
$109$	18.3101			0.167982			0.0839912	−	0.996466i	$-0.473233\pi$
$109$	18.3101			0.167982			0.0839912	+	0.996466i	$0.473233\pi$
$110$	−149.129	+	54.9738i	−1.35572	+	0.499762i
$111$		−	72.8687i		−	0.656475i
$112$	−139.084	−	139.084i	−1.24182	−	1.24182i
$113$	−83.2363	−	83.2363i	−0.736605	−	0.736605i	0.235314	−	0.971919i	$-0.424388\pi$
$113$	−83.2363	−	83.2363i	−0.736605	−	0.736605i	−0.971919	+	0.235314i	$0.924388\pi$
$114$		−	144.550i		−	1.26798i
$115$	68.5783	+	186.034i	0.596333	+	1.61769i
$116$	−333.381			−2.87398
$117$	−0.273465	−	0.320285i	−0.00233731	−	0.00273748i
$118$	182.449	+	182.449i	1.54617	+	1.54617i
$119$	−55.1596			−0.463526
$120$	318.371	+	146.868i	2.65309	+	1.22390i
$121$	49.8068			0.411626
$122$	80.8388	+	80.8388i	0.662613	+	0.662613i
$123$	−56.9052	+	56.9052i	−0.462644	+	0.462644i
$124$	369.546			2.98021
$125$	−33.8390	−	120.333i	−0.270712	−	0.962660i
$126$	0.509374			0.00404265
$127$	72.7910	−	72.7910i	0.573158	−	0.573158i	−0.359852	−	0.933010i	$-0.617173\pi$
$127$	72.7910	−	72.7910i	0.573158	−	0.573158i	0.933010	+	0.359852i	$0.117173\pi$
$128$	−104.866	+	104.866i	−0.819262	+	0.819262i
$129$			146.486i			1.13555i
$130$	−213.609	−	119.740i	−1.64314	−	0.921077i
$131$	60.0791			0.458619			0.229309	−	0.973354i	$-0.426353\pi$
$131$	60.0791			0.458619			0.229309	+	0.973354i	$0.426353\pi$
$132$	182.775	+	182.775i	1.38466	+	1.38466i
$133$	−37.6760	−	37.6760i	−0.283278	−	0.283278i
$134$			28.2120i			0.210537i
$135$	126.439	−	46.6094i	0.936582	−	0.345255i
$136$			308.372i			2.26744i
$137$	−105.210	−	105.210i	−0.767958	−	0.767958i	0.209789	−	0.977747i	$-0.432722\pi$
$137$	−105.210	−	105.210i	−0.767958	−	0.767958i	−0.977747	+	0.209789i	$0.932722\pi$
$138$	317.481	−	317.481i	2.30059	−	2.30059i
$139$		−	205.154i		−	1.47592i	−0.674842	−	0.737962i	$-0.735788\pi$
$139$		−	205.154i		−	1.47592i	0.674842	−	0.737962i	$-0.264212\pi$
$140$	199.581	−	73.5719i	1.42558	−	0.525514i
$141$			38.6358i			0.274013i
$142$	−7.22169	+	7.22169i	−0.0508569	+	0.0508569i
$143$	−71.2246	−	83.4189i	−0.498074	−	0.583349i
$144$		−	1.52679i		−	0.0106027i
$145$	68.5012	−	148.492i	0.472422	−	1.02408i
$146$	156.522			1.07207
$147$	−67.1151	+	67.1151i	−0.456565	+	0.456565i
$148$	−174.758	+	174.758i	−1.18080	+	1.18080i
$149$	81.0155			0.543728			0.271864	−	0.962336i	$-0.412360\pi$
$149$	81.0155			0.543728			0.271864	+	0.962336i	$0.412360\pi$
$150$	−215.335	+	183.726i	−1.43557	+	1.22484i
$151$			21.2645i			0.140824i	0.997518	+	0.0704121i	$0.0224314\pi$
$151$			21.2645i			0.140824i	−0.997518	+	0.0704121i	$0.977569\pi$
$152$	−210.629	+	210.629i	−1.38572	+	1.38572i
$153$	−0.302756	−	0.302756i	−0.00197880	−	0.00197880i
$154$	132.667			0.861477
$155$	−75.9321	+	164.600i	−0.489884	+	1.06194i
$156$	−31.3066	+	397.018i	−0.200683	+	2.54499i
$157$	−45.6214	+	45.6214i	−0.290582	+	0.290582i	−0.837310	−	0.546728i	$-0.815873\pi$
$157$	−45.6214	+	45.6214i	−0.290582	+	0.290582i	0.546728	+	0.837310i	$0.315873\pi$
$158$	−32.3169	+	32.3169i	−0.204537	+	0.204537i
$159$		−	131.799i		−	0.828927i
$160$	−145.657	−	395.128i	−0.910358	−	2.46955i
$161$		−	165.499i		−	1.02794i
$162$	−216.554	−	216.554i	−1.33675	−	1.33675i
$163$	197.869	−	197.869i	1.21392	−	1.21392i	0.244196	−	0.969726i	$-0.421476\pi$
$163$	197.869	−	197.869i	1.21392	−	1.21392i	0.969726	−	0.244196i	$-0.0785240\pi$
$164$	272.946			1.66431
$165$	−118.966	+	43.8548i	−0.721006	+	0.265786i
$166$	17.4356			0.105034
$167$	−87.4703	−	87.4703i	−0.523774	−	0.523774i	0.394935	−	0.918709i	$-0.370767\pi$
$167$	−87.4703	−	87.4703i	−0.523774	−	0.523774i	−0.918709	+	0.394935i	$0.870767\pi$
$168$	−206.942	−	206.942i	−1.23180	−	1.23180i
$169$	26.4881	−	166.911i	0.156734	−	0.987641i
$170$	−226.064	−	104.286i	−1.32979	−	0.613447i
$171$		−	0.413587i		−	0.00241864i
$172$	351.310	−	351.310i	2.04250	−	2.04250i
$173$	225.393	+	225.393i	1.30285	+	1.30285i	0.926461	+	0.376392i	$0.122835\pi$
$173$	225.393	+	225.393i	1.30285	+	1.30285i	0.376392	+	0.926461i	$0.377165\pi$
$174$	−370.315			−2.12825
$175$	−8.23879	+	104.013i	−0.0470788	+	0.594358i
$176$		−	397.656i		−	2.25941i
$177$	145.546	+	145.546i	0.822295	+	0.822295i
$178$	182.140	+	182.140i	1.02326	+	1.02326i
$179$			74.6282i			0.416917i	0.978031	+	0.208459i	$0.0668447\pi$
$179$			74.6282i			0.416917i	−0.978031	+	0.208459i	$0.933155\pi$
$180$	1.49926	+	0.691627i	0.00832922	+	0.00384237i
$181$	−158.211			−0.874093			−0.437047	−	0.899439i	$-0.643976\pi$
$181$	−158.211			−0.874093			−0.437047	+	0.899439i	$0.643976\pi$
$182$	132.726	+	155.450i	0.729263	+	0.854120i
$183$	64.4883	+	64.4883i	0.352395	+	0.352395i
$184$	−925.228			−5.02841
$185$	−41.9310	−	113.747i	−0.226654	−	0.614851i
$186$	410.486			2.20692
$187$	−78.8535	−	78.8535i	−0.421676	−	0.421676i
$188$	92.6585	−	92.6585i	0.492864	−	0.492864i
$189$	−112.482			−0.595142
$190$	−83.1787	−	225.641i	−0.437782	−	1.18758i
$191$	−2.79736			−0.0146459			−0.00732293	−	0.999973i	$-0.502331\pi$
$191$	−2.79736			−0.0146459			−0.00732293	+	0.999973i	$0.502331\pi$
$192$	−273.694	+	273.694i	−1.42549	+	1.42549i
$193$	−186.800	+	186.800i	−0.967876	+	0.967876i	−0.999500	−	0.0316238i	$-0.989932\pi$
$193$	−186.800	+	186.800i	−0.967876	+	0.967876i	0.0316238	+	0.999500i	$0.489932\pi$
$194$		−	276.810i		−	1.42686i
$195$	−170.404	−	95.5213i	−0.873867	−	0.489853i
$196$	321.918			1.64244
$197$	221.266	+	221.266i	1.12318	+	1.12318i	0.991261	+	0.131915i	$0.0421125\pi$
$197$	221.266	+	221.266i	1.12318	+	1.12318i	0.131915	+	0.991261i	$0.457888\pi$
$198$	0.728176	+	0.728176i	0.00367766	+	0.00367766i
$199$			90.1204i			0.452866i	0.974027	+	0.226433i	$0.0727065\pi$
$199$			90.1204i			0.452866i	−0.974027	+	0.226433i	$0.927293\pi$
$200$	581.487	+	46.0592i	2.90743	+	0.230296i
$201$			22.5058i			0.111969i
$202$	85.7261	+	85.7261i	0.424387	+	0.424387i
$203$	−96.5204	+	96.5204i	−0.475470	+	0.475470i
$204$			404.883i			1.98472i
$205$	−56.0833	+	121.573i	−0.273577	+	0.593041i
$206$		−	302.902i		−	1.47040i
$207$	0.908379	−	0.908379i	0.00438830	−	0.00438830i
$208$	465.944	−	397.831i	2.24011	−	1.91265i
$209$		−	107.720i		−	0.515405i
$210$	221.691	−	81.7227i	1.05567	−	0.389156i
$211$	−291.643			−1.38220			−0.691098	−	0.722761i	$-0.742873\pi$
$211$	−291.643			−1.38220			−0.691098	+	0.722761i	$0.742873\pi$
$212$	−316.088	+	316.088i	−1.49098	+	1.49098i
$213$	−5.76102	+	5.76102i	−0.0270471	+	0.0270471i
$214$	250.413			1.17015
$215$	84.2925	+	228.663i	0.392058	+	1.06355i
$216$			628.834i			2.91127i
$217$	106.991	−	106.991i	0.493045	−	0.493045i
$218$	−48.7771	−	48.7771i	−0.223748	−	0.223748i
$219$	124.864			0.570154
$220$	390.486	+	180.136i	1.77493	+	0.818799i
$221$	13.5064	−	171.283i	0.0611149	−	0.775035i
$222$	−194.118	+	194.118i	−0.874407	+	0.874407i
$223$	−154.775	+	154.775i	−0.694059	+	0.694059i	−0.963123	−	0.269063i	$-0.913286\pi$
$223$	−154.775	+	154.775i	−0.694059	+	0.694059i	0.269063	+	0.963123i	$0.413286\pi$
$224$			351.513i			1.56925i
$225$	−0.616118	+	0.525677i	−0.00273830	+	0.00233634i
$226$			443.474i			1.96228i
$227$	−256.834	−	256.834i	−1.13143	−	1.13143i	−0.989940	−	0.141490i	$-0.954811\pi$
$227$	−256.834	−	256.834i	−1.13143	−	1.13143i	−0.141490	−	0.989940i	$-0.545189\pi$
$228$	−276.550	+	276.550i	−1.21294	+	1.21294i
$229$	−262.035			−1.14426			−0.572130	−	0.820163i	$-0.693883\pi$
$229$	−262.035			−1.14426			−0.572130	+	0.820163i	$0.693883\pi$
$230$	312.896	−	678.274i	1.36042	−	2.94902i
$231$	105.834			0.458156
$232$	539.600	+	539.600i	2.32586	+	2.32586i
$233$	184.996	+	184.996i	0.793976	+	0.793976i	0.982138	−	0.188162i	$-0.0602530\pi$
$233$	184.996	+	184.996i	0.793976	+	0.793976i	−0.188162	+	0.982138i	$0.560253\pi$
$234$	−0.124725	+	1.58172i	−0.000533014	+	0.00675948i
$235$	22.2323	+	60.3101i	0.0946055	+	0.256639i
$236$		−	698.114i		−	2.95811i
$237$	−25.7804	+	25.7804i	−0.108778	+	0.108778i
$238$	146.942	+	146.942i	0.617404	+	0.617404i
$239$	67.3472			0.281788			0.140894	−	0.990025i	$-0.455002\pi$
$239$	67.3472			0.281788			0.140894	+	0.990025i	$0.455002\pi$
$240$	−244.955	−	664.495i	−1.02064	−	2.76873i
$241$			262.060i			1.08738i	0.839285	+	0.543692i	$0.182974\pi$
$241$			262.060i			1.08738i	−0.839285	+	0.543692i	$0.817026\pi$
$242$	−132.683	−	132.683i	−0.548275	−	0.548275i
$243$	−1.23699	−	1.23699i	−0.00509051	−	0.00509051i
$244$		−	309.319i		−	1.26770i
$245$	−66.1458	+	143.386i	−0.269983	+	0.585250i
$246$	303.185			1.23246
$247$	126.218	−	107.767i	0.511003	−	0.436304i
$248$	−598.135	−	598.135i	−2.41184	−	2.41184i
$249$	13.9090			0.0558596
$250$	−230.414	+	410.705i	−0.921657	+	1.64282i
$251$	−331.448			−1.32051			−0.660255	−	0.751042i	$-0.729552\pi$
$251$	−331.448			−1.32051			−0.660255	+	0.751042i	$0.729552\pi$
$252$	−0.974524	−	0.974524i	−0.00386716	−	0.00386716i
$253$	236.589	−	236.589i	0.935136	−	0.935136i
$254$	−387.823			−1.52686
$255$	−180.340	−	83.1930i	−0.707215	−	0.326247i
$256$	43.5563			0.170142
$257$	−11.4821	+	11.4821i	−0.0446774	+	0.0446774i	−0.729093	−	0.684415i	$-0.760058\pi$
$257$	−11.4821	+	11.4821i	−0.0446774	+	0.0446774i	0.684415	+	0.729093i	$0.260058\pi$
$258$	390.230	−	390.230i	1.51252	−	1.51252i
$259$			101.192i			0.390701i
$260$	179.588	+	637.757i	0.690723	+	2.45291i
$261$	−1.05955			−0.00405957
$262$	−160.047	−	160.047i	−0.610868	−	0.610868i
$263$	191.600	+	191.600i	0.728518	+	0.728518i	0.970324	−	0.241807i	$-0.0777400\pi$
$263$	191.600	+	191.600i	0.728518	+	0.728518i	−0.241807	+	0.970324i	$0.577740\pi$
$264$		−	591.669i		−	2.24117i
$265$	−75.8416	−	205.738i	−0.286195	−	0.776368i
$266$			200.734i			0.754639i
$267$	145.300	+	145.300i	0.544195	+	0.544195i
$268$	53.9746	−	53.9746i	0.201398	−	0.201398i
$269$		−	190.819i		−	0.709364i	−0.934987	−	0.354682i	$-0.884589\pi$
$269$		−	190.819i		−	0.709364i	0.934987	−	0.354682i	$-0.115411\pi$
$270$	−460.991	−	212.661i	−1.70737	−	0.787632i
$271$		−	25.3299i		−	0.0934681i	−0.998907	−	0.0467341i	$-0.985119\pi$
$271$		−	25.3299i		−	0.0934681i	0.998907	−	0.0467341i	$-0.0148813\pi$
$272$	440.443	−	440.443i	1.61928	−	1.61928i
$273$	105.881	+	124.008i	0.387841	+	0.454243i
$274$			560.549i			2.04580i
$275$	−160.469	+	136.914i	−0.583525	+	0.497868i
$276$	−1214.80			−4.40144
$277$	338.472	−	338.472i	1.22192	−	1.22192i	0.254971	−	0.966949i	$-0.417934\pi$
$277$	338.472	−	338.472i	1.22192	−	1.22192i	0.966949	−	0.254971i	$-0.0820658\pi$
$278$	−546.518	+	546.518i	−1.96589	+	1.96589i
$279$	1.17449			0.00420963
$280$	−442.116	−	203.953i	−1.57899	−	0.728405i
$281$			454.600i			1.61780i	0.587949	+	0.808898i	$0.299935\pi$
$281$			454.600i			1.61780i	−0.587949	+	0.808898i	$0.700065\pi$
$282$	102.924	−	102.924i	0.364978	−	0.364978i
$283$	−60.2612	−	60.2612i	−0.212937	−	0.212937i	0.592577	−	0.805514i	$-0.298111\pi$
$283$	−60.2612	−	60.2612i	−0.212937	−	0.212937i	−0.805514	+	0.592577i	$0.798111\pi$
$284$	27.6328			0.0972986
$285$	−66.3549	−	180.003i	−0.232824	−	0.631588i
$286$	−32.4850	+	411.962i	−0.113584	+	1.44043i
$287$	79.0232	−	79.0232i	0.275342	−	0.275342i
$288$	−1.92936	+	1.92936i	−0.00669916	+	0.00669916i
$289$			114.324i			0.395585i
$290$	−578.059	+	213.091i	−1.99331	+	0.734798i
$291$		−	220.823i		−	0.758840i
$292$	−299.455	−	299.455i	−1.02553	−	1.02553i
$293$	281.011	−	281.011i	0.959080	−	0.959080i	−0.0401147	−	0.999195i	$-0.512772\pi$
$293$	281.011	−	281.011i	0.959080	−	0.959080i	0.999195	+	0.0401147i	$0.0127723\pi$
$294$	357.582			1.21627
$295$	310.949	+	143.444i	1.05406	+	0.486252i
$296$	565.715			1.91120
$297$	−160.799	−	160.799i	−0.541409	−	0.541409i
$298$	−215.821	−	215.821i	−0.724231	−	0.724231i
$299$	513.911	+	40.5241i	1.71877	+	0.135532i
$300$	763.476	+	60.4745i	2.54492	+	0.201582i
$301$		−	203.422i		−	0.675820i
$302$	56.6474	−	56.6474i	0.187574	−	0.187574i
$303$	68.3871	+	68.3871i	0.225700	+	0.225700i
$304$	601.678			1.97920
$305$	137.774	+	63.5570i	0.451719	+	0.208384i
$306$			1.61305i			0.00527141i
$307$	57.2744	+	57.2744i	0.186561	+	0.186561i	0.794208	−	0.607646i	$-0.207886\pi$
$307$	57.2744	+	57.2744i	0.186561	+	0.186561i	−0.607646	+	0.794208i	$0.707886\pi$
$308$	−253.817	−	253.817i	−0.824081	−	0.824081i
$309$		−	241.637i		−	0.781996i
$310$	640.765	−	236.207i	2.06698	−	0.761958i
$311$	440.156			1.41529			0.707646	−	0.706567i	$-0.249757\pi$
$311$	440.156			1.41529			0.707646	+	0.706567i	$0.249757\pi$
$312$	693.273	−	591.929i	2.22203	−	1.89721i
$313$	−393.408	−	393.408i	−1.25690	−	1.25690i	−0.952567	−	0.304328i	$-0.901568\pi$
$313$	−393.408	−	393.408i	−1.25690	−	1.25690i	−0.304328	−	0.952567i	$-0.598432\pi$
$314$	243.066			0.774096
$315$	0.634304	−	0.233825i	0.00201366	−	0.000742303i
$316$	123.656			0.391317
$317$	232.951	+	232.951i	0.734860	+	0.734860i	0.971578	−	0.236718i	$-0.0760718\pi$
$317$	232.951	+	232.951i	0.734860	+	0.734860i	−0.236718	+	0.971578i	$0.576072\pi$
$318$	−351.106	+	351.106i	−1.10411	+	1.10411i
$319$	−275.962			−0.865084
$320$	−269.742	+	584.727i	−0.842943	+	1.82727i
$321$	199.764			0.622319
$322$	−440.881	+	440.881i	−1.36919	+	1.36919i
$323$	119.310	−	119.310i	0.369381	−	0.369381i
$324$			828.613i			2.55745i
$325$	−320.965	−	51.0519i	−0.987585	−	0.157083i
$326$	−1054.23			−3.23382
$327$	−38.9114	−	38.9114i	−0.118995	−	0.118995i
$328$	−441.782	−	441.782i	−1.34690	−	1.34690i
$329$		−	53.6529i		−	0.163079i
$330$	433.746	+	200.092i	1.31438	+	0.606340i
$331$		−	129.916i		−	0.392496i	−0.980554	−	0.196248i	$-0.937124\pi$
$331$		−	129.916i		−	0.392496i	0.980554	−	0.196248i	$-0.0628758\pi$
$332$	−33.3574	−	33.3574i	−0.100474	−	0.100474i
$333$	−0.555413	+	0.555413i	−0.00166791	+	0.00166791i
$334$			466.032i			1.39531i
$335$	12.9506	+	35.1313i	0.0386584	+	0.104870i
$336$			591.145i			1.75936i
$337$	−112.533	+	112.533i	−0.333926	+	0.333926i	−0.854075	−	0.520149i	$-0.825876\pi$
$337$	−112.533	+	112.533i	−0.333926	+	0.333926i	0.520149	+	0.854075i	$0.325876\pi$
$338$	−515.206	+	374.080i	−1.52428	+	1.10675i
$339$			353.777i			1.04359i
$340$	232.983	+	632.019i	0.685244	+	1.85888i
$341$	305.897			0.897060
$342$	−1.10177	+	1.10177i	−0.00322156	+	0.00322156i
$343$	237.807	−	237.807i	0.693316	−	0.693316i
$344$	−1137.24			−3.30592
$345$	249.610	−	541.086i	0.723506	−	1.56836i
$346$		−	1200.87i		−	3.47073i
$347$	−434.905	+	434.905i	−1.25333	+	1.25333i	−0.299109	+	0.954219i	$0.596690\pi$
$347$	−434.905	+	434.905i	−1.25333	+	1.25333i	−0.954219	+	0.299109i	$0.903310\pi$
$348$	708.480	+	708.480i	2.03586	+	2.03586i
$349$	−569.873			−1.63287			−0.816436	−	0.577435i	$-0.804054\pi$
$349$	−569.873			−1.63287			−0.816436	+	0.577435i	$0.804054\pi$
$350$	299.032	−	255.137i	0.854377	−	0.728962i
$351$	27.5423	−	349.281i	0.0784682	−	0.995103i
$352$	−502.506	+	502.506i	−1.42757	+	1.42757i
$353$	−28.3941	+	28.3941i	−0.0804364	+	0.0804364i	−0.746180	−	0.665744i	$-0.768114\pi$
$353$	−28.3941	+	28.3941i	−0.0804364	+	0.0804364i	0.665744	+	0.746180i	$0.268114\pi$
$354$		−	775.455i		−	2.19055i
$355$	−5.67782	+	12.3080i	−0.0159939	+	0.0346704i
$356$		−	696.933i		−	1.95768i
$357$	117.222	+	117.222i	0.328352	+	0.328352i
$358$	198.806	−	198.806i	0.555323	−	0.555323i
$359$	159.330			0.443817			0.221908	−	0.975068i	$-0.428771\pi$
$359$	159.330			0.443817			0.221908	+	0.975068i	$0.428771\pi$
$360$	−1.30721	−	3.54610i	−0.00363114	−	0.00985028i
$361$	−198.014			−0.548515
$362$	421.465	+	421.465i	1.16427	+	1.16427i
$363$	−105.846	−	105.846i	−0.291587	−	0.291587i
$364$	43.4750	−	551.333i	0.119437	−	1.51465i
$365$	194.911	−	71.8506i	0.534003	−	0.196851i
$366$		−	343.587i		−	0.938762i
$367$	88.1476	−	88.1476i	0.240184	−	0.240184i	−0.576742	−	0.816926i	$-0.695676\pi$
$367$	88.1476	−	88.1476i	0.240184	−	0.240184i	0.816926	+	0.576742i	$0.195676\pi$
$368$	1321.49	+	1321.49i	3.59101	+	3.59101i
$369$	0.867474			0.00235088
$370$	−191.315	+	414.719i	−0.517068	+	1.12086i
$371$			183.027i			0.493335i
$372$	−785.335	−	785.335i	−2.11111	−	2.11111i
$373$	−183.429	−	183.429i	−0.491766	−	0.491766i	0.417097	−	0.908862i	$-0.363048\pi$
$373$	−183.429	−	183.429i	−0.491766	−	0.491766i	−0.908862	+	0.417097i	$0.863048\pi$
$374$			420.123i			1.12332i
$375$	−183.810	+	327.635i	−0.490161	+	0.873694i
$376$	−299.948			−0.797734
$377$	−276.083	−	323.351i	−0.732316	−	0.857696i
$378$	299.646	+	299.646i	0.792713	+	0.792713i
$379$	425.507			1.12271			0.561355	−	0.827575i	$-0.310280\pi$
$379$	425.507			1.12271			0.561355	+	0.827575i	$0.310280\pi$
$380$	−272.556	+	590.828i	−0.717253	+	1.55481i
$381$	−309.382			−0.812025
$382$	7.45201	+	7.45201i	0.0195079	+	0.0195079i
$383$	−201.277	+	201.277i	−0.525526	+	0.525526i	−0.919235	−	0.393709i	$-0.871192\pi$
$383$	−201.277	+	201.277i	−0.525526	+	0.525526i	0.393709	+	0.919235i	$0.371192\pi$
$384$	445.707			1.16070
$385$	165.206	−	60.9003i	0.429106	−	0.158183i
$386$	995.251			2.57837
$387$	1.11653	−	1.11653i	0.00288508	−	0.00288508i
$388$	−529.589	+	529.589i	−1.36492	+	1.36492i
$389$		−	492.525i		−	1.26613i	−0.774098	−	0.633066i	$-0.781796\pi$
$389$		−	492.525i		−	1.26613i	0.774098	−	0.633066i	$-0.218204\pi$
$390$	199.484	+	708.411i	0.511497	+	1.81644i
$391$	524.092			1.34039
$392$	−521.046	−	521.046i	−1.32920	−	1.32920i
$393$	−127.676	−	127.676i	−0.324876	−	0.324876i
$394$		−	1178.88i		−	2.99208i
$395$	−25.4081	+	55.0779i	−0.0643244	+	0.139438i
$396$		−	2.78626i		−	0.00703602i
$397$	−18.1558	−	18.1558i	−0.0457325	−	0.0457325i	0.683871	−	0.729603i	$-0.260295\pi$
$397$	−18.1558	−	18.1558i	−0.0457325	−	0.0457325i	−0.729603	+	0.683871i	$0.760295\pi$
$398$	240.076	−	240.076i	0.603206	−	0.603206i
$399$			160.133i			0.401336i
$400$	−764.744	−	896.316i	−1.91186	−	2.24079i
$401$			398.038i			0.992612i	0.868148	+	0.496306i	$0.165311\pi$
$401$			398.038i			0.992612i	−0.868148	+	0.496306i	$0.834689\pi$
$402$	59.9542	−	59.9542i	0.149140	−	0.149140i
$403$	306.032	+	358.428i	0.759385	+	0.889399i
$404$		−	328.019i		−	0.811929i
$405$	−369.074	−	170.258i	−0.911294	−	0.420391i
$406$	514.250			1.26663
$407$	−144.659	+	144.659i	−0.355426	+	0.355426i
$408$	655.331	−	655.331i	1.60620	−	1.60620i
$409$	478.886			1.17087			0.585436	−	0.810719i	$-0.300923\pi$
$409$	478.886			1.17087			0.585436	+	0.810719i	$0.300923\pi$
$410$	473.268	−	174.462i	1.15431	−	0.425518i
$411$			447.172i			1.08801i
$412$	−579.507	+	579.507i	−1.40657	+	1.40657i
$413$	−202.118	−	202.118i	−0.489389	−	0.489389i
$414$	−4.83975			−0.0116902
$415$	21.7119	−	8.00371i	0.0523178	−	0.0192861i
$416$	−1091.53	−	86.0715i	−2.62386	−	0.206903i
$417$	−435.979	+	435.979i	−1.04551	+	1.04551i
$418$	−286.959	+	286.959i	−0.686506	+	0.686506i
$419$			502.124i			1.19839i	0.800604	+	0.599194i	$0.204512\pi$
$419$			502.124i			1.19839i	−0.800604	+	0.599194i	$0.795488\pi$
$420$	−580.486	−	267.785i	−1.38211	−	0.637584i
$421$			610.454i			1.45001i	0.688744	+	0.725005i	$0.258162\pi$
$421$			610.454i			1.45001i	−0.688744	+	0.725005i	$0.741838\pi$
$422$	776.922	+	776.922i	1.84105	+	1.84105i
$423$	0.294486	−	0.294486i	0.000696184	−	0.000696184i
$424$	1023.22			2.41326
$425$	−329.381	−	26.0901i	−0.775014	−	0.0613884i
$426$	30.6941			0.0720519
$427$	−89.5538	−	89.5538i	−0.209728	−	0.209728i
$428$	−479.086	−	479.086i	−1.11936	−	1.11936i
$429$	−25.9146	+	328.638i	−0.0604069	+	0.766057i
$430$	384.594	−	833.696i	0.894405	−	1.93883i
$431$			108.921i			0.252717i	0.991985	+	0.126359i	$0.0403290\pi$
$431$			108.921i			0.252717i	−0.991985	+	0.126359i	$0.959671\pi$
$432$	898.155	−	898.155i	2.07906	−	2.07906i
$433$	−308.581	−	308.581i	−0.712657	−	0.712657i	0.254433	−	0.967090i	$-0.418111\pi$
$433$	−308.581	−	308.581i	−0.712657	−	0.712657i	−0.967090	+	0.254433i	$0.918111\pi$
$434$	−570.035			−1.31345
$435$	−461.140	+	169.991i	−1.06009	+	0.390785i
$436$			186.639i			0.428071i
$437$	357.974	+	357.974i	0.819162	+	0.819162i
$438$	−332.630	−	332.630i	−0.759430	−	0.759430i
$439$			357.475i			0.814294i	0.913363	+	0.407147i	$0.133476\pi$
$439$			357.475i			0.814294i	−0.913363	+	0.407147i	$0.866524\pi$
$440$	−340.465	−	923.589i	−0.773785	−	2.09907i
$441$	1.02312			0.00231999
$442$	−492.269	+	420.308i	−1.11373	+	0.950923i
$443$	−364.767	−	364.767i	−0.823402	−	0.823402i	0.163192	−	0.986594i	$-0.447821\pi$
$443$	−364.767	−	364.767i	−0.823402	−	0.823402i	−0.986594	+	0.163192i	$0.947821\pi$
$444$	742.768			1.67290
$445$	310.422	+	143.202i	0.697579	+	0.321802i
$446$	824.626			1.84894
$447$	−172.169	−	172.169i	−0.385165	−	0.385165i
$448$	380.074	−	380.074i	0.848380	−	0.848380i
$449$	−361.939			−0.806101			−0.403050	−	0.915178i	$-0.632050\pi$
$449$	−361.939			−0.806101			−0.403050	+	0.915178i	$0.632050\pi$
$450$	3.04168	+	0.240930i	0.00675929	+	0.000535400i
$451$	225.935			0.500966
$452$	848.447	−	848.447i	1.87710	−	1.87710i
$453$	45.1898	−	45.1898i	0.0997568	−	0.0997568i
$454$			1368.39i			3.01407i
$455$	236.637	+	132.649i	0.520082	+	0.291536i
$456$	895.230			1.96322
$457$	12.2731	+	12.2731i	0.0268557	+	0.0268557i	0.720407	−	0.693551i	$-0.243955\pi$
$457$	12.2731	+	12.2731i	0.0268557	+	0.0268557i	−0.693551	+	0.720407i	$0.743955\pi$
$458$	698.049	+	698.049i	1.52412	+	1.52412i
$459$		−	356.200i		−	0.776036i
$460$	−1896.29	+	699.034i	−4.12237	+	1.51964i
$461$		−	108.768i		−	0.235940i	−0.993017	−	0.117970i	$-0.962361\pi$
$461$		−	108.768i		−	0.235940i	0.993017	−	0.117970i	$-0.0376386\pi$
$462$	−281.936	−	281.936i	−0.610252	−	0.610252i
$463$	−159.026	+	159.026i	−0.343468	+	0.343468i	−0.857669	−	0.514201i	$-0.828088\pi$
$463$	−159.026	+	159.026i	−0.343468	+	0.343468i	0.514201	+	0.857669i	$0.328088\pi$
$464$		−	1541.41i		−	3.32200i
$465$	511.163	−	188.432i	1.09928	−	0.405229i
$466$		−	985.641i		−	2.11511i
$467$	15.6061	−	15.6061i	0.0334179	−	0.0334179i	−0.690200	−	0.723618i	$-0.742478\pi$
$467$	15.6061	−	15.6061i	0.0334179	−	0.0334179i	0.723618	+	0.690200i	$0.242478\pi$
$468$	3.26474	−	2.78749i	0.00697593	−	0.00595618i
$469$		−	31.2534i		−	0.0666384i
$470$	101.437	−	219.889i	0.215824	−	0.467848i
$471$	193.903			0.411684
$472$	−1129.95	+	1129.95i	−2.39395	+	2.39395i
$473$	290.802	−	290.802i	0.614804	−	0.614804i
$474$	137.355			0.289779
$475$	−207.159	−	242.800i	−0.436124	−	0.511157i
$476$		−	562.254i		−	1.18121i
$477$	−1.00459	+	1.00459i	−0.00210605	+	0.00210605i
$478$	−179.409	−	179.409i	−0.375334	−	0.375334i
$479$	841.881			1.75758			0.878790	−	0.477209i	$-0.158352\pi$
$479$	841.881			1.75758			0.878790	+	0.477209i	$0.158352\pi$
$480$	−530.160	+	1149.24i	−1.10450	+	2.39426i
$481$	−314.222	−	24.7778i	−0.653269	−	0.0515131i
$482$	698.113	−	698.113i	1.44837	−	1.44837i
$483$	−351.708	+	351.708i	−0.728173	+	0.728173i
$484$			507.692i			1.04895i
$485$	−127.068	−	344.702i	−0.261997	−	0.710726i
$486$			6.59058i			0.0135609i
$487$	−629.552	−	629.552i	−1.29272	−	1.29272i	−0.933101	−	0.359614i	$-0.882908\pi$
$487$	−629.552	−	629.552i	−1.29272	−	1.29272i	−0.359614	−	0.933101i	$-0.617092\pi$
$488$	−500.653	+	500.653i	−1.02593	+	1.02593i
$489$	−840.998			−1.71983
$490$	558.182	−	205.764i	1.13915	−	0.419927i
$491$	−640.405			−1.30429			−0.652144	−	0.758095i	$-0.726130\pi$
$491$	−640.405			−1.30429			−0.652144	+	0.758095i	$0.726130\pi$
$492$	−580.047	−	580.047i	−1.17896	−	1.17896i
$493$	−305.655	−	305.655i	−0.619989	−	0.619989i
$494$	−623.323	−	49.1518i	−1.26179	−	0.0994975i
$495$	1.24104	+	0.572505i	0.00250714	+	0.00115658i
$496$			1708.62i			3.44479i
$497$	8.00023	−	8.00023i	0.0160970	−	0.0160970i
$498$	−37.0529	−	37.0529i	−0.0744035	−	0.0744035i
$499$	8.68516			0.0174051			0.00870257	−	0.999962i	$-0.497230\pi$
$499$	8.68516			0.0174051			0.00870257	+	0.999962i	$0.497230\pi$
$500$	1226.58	−	344.929i	2.45315	−	0.689857i
$501$			371.772i			0.742061i
$502$	882.960	+	882.960i	1.75888	+	1.75888i
$503$	263.128	+	263.128i	0.523118	+	0.523118i	0.918512	−	0.395394i	$-0.129392\pi$
$503$	263.128	+	263.128i	0.523118	+	0.523118i	−0.395394	+	0.918512i	$0.629392\pi$
$504$			3.15467i			0.00625926i
$505$	146.104	+	67.3995i	0.289314	+	0.133464i
$506$	−1260.52			−2.49115
$507$	−411.000	+	298.418i	−0.810650	+	0.588596i
$508$	741.976	+	741.976i	1.46058	+	1.46058i
$509$	−79.2120			−0.155623			−0.0778114	−	0.996968i	$-0.524793\pi$
$509$	−79.2120			−0.155623			−0.0778114	+	0.996968i	$0.524793\pi$
$510$	258.794	+	702.038i	0.507440	+	1.37654i
$511$	−173.396			−0.339327
$512$	303.431	+	303.431i	0.592638	+	0.592638i
$513$	243.298	−	243.298i	0.474265	−	0.474265i
$514$	61.1754			0.119018
$515$	−139.046	−	377.193i	−0.269992	−	0.732413i
$516$	−1493.16			−2.89372
$517$	76.6995	−	76.6995i	0.148355	−	0.148355i
$518$	269.569	−	269.569i	0.520403	−	0.520403i
$519$		−	957.983i		−	1.84582i
$520$	741.578	−	1322.93i	1.42611	−	2.54409i
$521$	464.159			0.890899			0.445450	−	0.895307i	$-0.353044\pi$
$521$	464.159			0.890899			0.445450	+	0.895307i	$0.353044\pi$
$522$	2.82258	+	2.82258i	0.00540724	+	0.00540724i
$523$	−309.407	−	309.407i	−0.591601	−	0.591601i	0.346463	−	0.938064i	$-0.387383\pi$
$523$	−309.407	−	309.407i	−0.591601	−	0.591601i	−0.938064	+	0.346463i	$0.887383\pi$
$524$			612.400i			1.16870i
$525$	238.550	−	203.532i	0.454380	−	0.387681i
$526$		−	1020.83i		−	1.94073i
$527$	338.811	+	338.811i	0.642906	+	0.642906i
$528$	−845.073	+	845.073i	−1.60052	+	1.60052i
$529$			1043.47i			1.97253i
$530$	−346.036	+	750.112i	−0.652898	+	1.41531i
$531$		−	2.21874i		−	0.00417841i
$532$	384.040	−	384.040i	0.721880	−	0.721880i
$533$	226.035	+	264.734i	0.424081	+	0.496687i
$534$		−	774.143i		−	1.44971i
$535$	311.830	−	114.951i	0.582860	−	0.214861i
$536$	−174.723			−0.325976
$537$	158.595	−	158.595i	0.295335	−	0.295335i
$538$	−508.331	+	508.331i	−0.944854	+	0.944854i
$539$	266.473			0.494384
$540$	475.101	+	1288.82i	0.879816	+	2.38670i
$541$			200.396i			0.370418i	0.982699	+	0.185209i	$0.0592962\pi$
$541$			200.396i			0.370418i	−0.982699	+	0.185209i	$0.940704\pi$
$542$	−67.4774	+	67.4774i	−0.124497	+	0.124497i
$543$	336.219	+	336.219i	0.619189	+	0.619189i
$544$	−1113.15			−2.04623
$545$	−83.1312	−	38.3495i	−0.152534	−	0.0703660i
$546$	48.2914	−	612.412i	0.0884457	−	1.12163i
$547$	40.5405	−	40.5405i	0.0741142	−	0.0741142i	−0.669078	−	0.743192i	$-0.733311\pi$
$547$	40.5405	−	40.5405i	0.0741142	−	0.0741142i	0.743192	+	0.669078i	$0.233311\pi$
$548$	1072.43	−	1072.43i	1.95699	−	1.95699i
$549$		−	0.983073i		−	0.00179066i
$550$	792.213	+	62.7508i	1.44039	+	0.114092i
$551$		−	417.547i		−	0.757798i
$552$	1966.23	+	1966.23i	3.56202	+	3.56202i
$553$	35.8009	−	35.8009i	0.0647393	−	0.0647393i
$554$	−1803.34			−3.25513
$555$	−152.619	+	330.838i	−0.274990	+	0.596104i
$556$	2091.18			3.76111
$557$	−366.623	−	366.623i	−0.658210	−	0.658210i	0.296746	−	0.954956i	$-0.404098\pi$
$557$	−366.623	−	366.623i	−0.658210	−	0.658210i	−0.954956	+	0.296746i	$0.904098\pi$
$558$	−3.12877	−	3.12877i	−0.00560711	−	0.00560711i
$559$	631.670	+	49.8100i	1.13000	+	0.0891055i
$560$	340.164	+	922.773i	0.607436	+	1.64781i
$561$			335.149i			0.597413i
$562$	1211.03	−	1211.03i	2.15486	−	2.15486i
$563$	−191.657	−	191.657i	−0.340421	−	0.340421i	0.516104	−	0.856526i	$-0.327382\pi$
$563$	−191.657	−	191.657i	−0.340421	−	0.340421i	−0.856526	+	0.516104i	$0.827382\pi$
$564$	−393.823			−0.698269
$565$	203.575	+	552.243i	0.360309	+	0.977420i
$566$			321.065i			0.567253i
$567$	239.900	+	239.900i	0.423103	+	0.423103i
$568$	−44.7256	−	44.7256i	−0.0787422	−	0.0787422i
$569$			740.469i			1.30135i	0.759355	+	0.650676i	$0.225514\pi$
$569$			740.469i			1.30135i	−0.759355	+	0.650676i	$0.774486\pi$
$570$	−302.752	+	656.283i	−0.531143	+	1.15137i
$571$	−454.593			−0.796135			−0.398068	−	0.917356i	$-0.630319\pi$
$571$	−454.593			−0.796135			−0.398068	+	0.917356i	$0.630319\pi$
$572$	850.308	−	726.009i	1.48655	−	1.26925i
$573$	5.94476	+	5.94476i	0.0103748	+	0.0103748i
$574$	−421.027			−0.733497
$575$	78.2798	−	988.263i	0.136139	−	1.71872i
$576$	4.17225			0.00724349
$577$	36.0387	+	36.0387i	0.0624588	+	0.0624588i	0.737646	−	0.675187i	$-0.235937\pi$
$577$	36.0387	+	36.0387i	0.0624588	+	0.0624588i	−0.675187	+	0.737646i	$0.735937\pi$
$578$	304.553	−	304.553i	0.526909	−	0.526909i
$579$	793.951			1.37124
$580$	1513.61	+	698.249i	2.60968	+	1.20388i
$581$	−19.3152			−0.0332448
$582$	−588.260	+	588.260i	−1.01076	+	1.01076i
$583$	−261.647	+	261.647i	−0.448794	+	0.448794i
$584$			969.377i			1.65989i
$585$	0.570764	+	2.02691i	0.000975665	+	0.00346480i
$586$	−1497.19			−2.55494
$587$	−462.764	−	462.764i	−0.788354	−	0.788354i	0.192870	−	0.981224i	$-0.438220\pi$
$587$	−462.764	−	462.764i	−0.788354	−	0.788354i	−0.981224	+	0.192870i	$0.938220\pi$
$588$	−684.120	−	684.120i	−1.16347	−	1.16347i
$589$			462.841i			0.785808i
$590$	−446.222	−	1210.48i	−0.756309	−	2.05166i
$591$		−	940.438i		−	1.59127i
$592$	−808.003	−	808.003i	−1.36487	−	1.36487i
$593$	375.711	−	375.711i	0.633578	−	0.633578i	−0.315386	−	0.948963i	$-0.602134\pi$
$593$	375.711	−	375.711i	0.633578	−	0.633578i	0.948963	+	0.315386i	$0.102134\pi$
$594$			856.718i			1.44229i
$595$	250.435	+	115.529i	0.420899	+	0.194166i
$596$			825.809i			1.38559i
$597$	191.518	−	191.518i	0.320801	−	0.320801i
$598$	−1261.08	−	1476.99i	−2.10883	−	2.46988i
$599$		−	431.642i		−	0.720605i	−0.932836	−	0.360302i	$-0.882674\pi$
$599$		−	431.642i		−	0.720605i	0.932836	−	0.360302i	$-0.117326\pi$
$600$	−1137.86	−	1333.62i	−1.89643	−	2.22270i
$601$	−751.240			−1.24998			−0.624992	−	0.780632i	$-0.714898\pi$
$601$	−751.240			−1.24998			−0.624992	+	0.780632i	$0.714898\pi$
$602$	−541.905	+	541.905i	−0.900175	+	0.900175i
$603$	0.171541	−	0.171541i	0.000284480	−	0.000284480i
$604$	−216.753			−0.358863
$605$	−226.132	−	104.318i	−0.373772	−	0.172426i
$606$		−	364.359i		−	0.601253i
$607$	320.904	−	320.904i	0.528672	−	0.528672i	−0.391504	−	0.920176i	$-0.628045\pi$
$607$	320.904	−	320.904i	0.528672	−	0.528672i	0.920176	+	0.391504i	$0.128045\pi$
$608$	−760.321	−	760.321i	−1.25053	−	1.25053i
$609$	410.238			0.673625
$610$	−197.711	−	536.336i	−0.324116	−	0.879239i
$611$	166.604	+	13.1375i	0.272674	+	0.0215016i
$612$	3.08606	−	3.08606i	0.00504258	−	0.00504258i
$613$	648.018	−	648.018i	1.05713	−	1.05713i	0.0588595	−	0.998266i	$-0.481254\pi$
$613$	648.018	−	648.018i	1.05713	−	1.05713i	0.998266	−	0.0588595i	$-0.0187464\pi$
$614$		−	305.152i		−	0.496990i
$615$	377.545	−	139.175i	0.613894	−	0.226301i
$616$			821.640i			1.33383i
$617$	−202.856	−	202.856i	−0.328778	−	0.328778i	0.523344	−	0.852122i	$-0.324684\pi$
$617$	−202.856	−	202.856i	−0.328778	−	0.328778i	−0.852122	+	0.523344i	$0.824684\pi$
$618$	−643.708	+	643.708i	−1.04160	+	1.04160i
$619$	−800.383			−1.29303			−0.646513	−	0.762903i	$-0.723773\pi$
$619$	−800.383			−1.29303			−0.646513	+	0.762903i	$0.723773\pi$
$620$	−1677.81	−	773.993i	−2.70614	−	1.24838i
$621$	1068.73			1.72099
$622$	−1172.55	−	1172.55i	−1.88513	−	1.88513i
$623$	−201.776	−	201.776i	−0.323878	−	0.323878i
$624$	−1835.64	−	144.748i	−2.94173	−	0.231968i
$625$	−98.3945	+	617.206i	−0.157431	+	0.987530i
$626$			2096.04i			3.34830i
$627$	−228.919	+	228.919i	−0.365102	+	0.365102i
$628$	−465.030	−	465.030i	−0.740493	−	0.740493i
$629$	−320.447			−0.509455
$630$	−2.31265	−	1.06685i	−0.00367088	−	0.00169342i
$631$		−	215.017i		−	0.340755i	−0.985379	−	0.170378i	$-0.945501\pi$
$631$		−	215.017i		−	0.340755i	0.985379	−	0.170378i	$-0.0544988\pi$
$632$	−200.146	−	200.146i	−0.316687	−	0.316687i
$633$	619.781	+	619.781i	0.979117	+	0.979117i
$634$		−	1241.14i		−	1.95763i
$635$	−482.942	+	178.028i	−0.760538	+	0.280359i
$636$	1343.46			2.11236
$637$	266.590	+	312.233i	0.418509	+	0.490162i
$638$	735.147	+	735.147i	1.15227	+	1.15227i
$639$	0.0878222			0.000137437
$640$	695.745	−	256.474i	1.08710	−	0.400741i
$641$	384.514			0.599866			0.299933	−	0.953960i	$-0.403036\pi$
$641$	384.514			0.599866			0.299933	+	0.953960i	$0.403036\pi$
$642$	−532.161	−	532.161i	−0.828912	−	0.828912i
$643$	−588.562	+	588.562i	−0.915337	+	0.915337i	−0.996686	−	0.0813489i	$-0.974077\pi$
$643$	−588.562	+	588.562i	−0.915337	+	0.915337i	0.0813489	+	0.996686i	$0.474077\pi$
$644$	1686.97			2.61952
$645$	306.806	−	665.072i	0.475668	−	1.03112i
$646$	−635.671			−0.984011
$647$	−572.797	+	572.797i	−0.885312	+	0.885312i	−0.994068	−	0.108757i	$-0.965313\pi$
$647$	−572.797	+	572.797i	−0.885312	+	0.885312i	0.108757	+	0.994068i	$0.465313\pi$
$648$	1341.17	−	1341.17i	2.06970	−	2.06970i
$649$		−	577.875i		−	0.890409i
$650$	719.035	+	991.034i	1.10621	+	1.52467i
$651$	−454.739			−0.698524
$652$	2016.93	+	2016.93i	3.09345	+	3.09345i
$653$	347.181	+	347.181i	0.531671	+	0.531671i	0.921069	−	0.389398i	$-0.127317\pi$
$653$	347.181	+	347.181i	0.531671	+	0.531671i	−0.389398	+	0.921069i	$0.627317\pi$
$654$			207.316i			0.316997i
$655$	−272.770	−	125.832i	−0.416443	−	0.192110i
$656$			1261.98i			1.92375i
$657$	−0.951724	−	0.951724i	−0.00144859	−	0.00144859i
$658$	−142.928	+	142.928i	−0.217216	+	0.217216i
$659$		−	720.838i		−	1.09384i	−0.837186	−	0.546918i	$-0.815801\pi$
$659$		−	720.838i		−	1.09384i	0.837186	−	0.546918i	$-0.184199\pi$
$660$	−447.022	−	1212.65i	−0.677305	−	1.83734i
$661$		−	829.018i		−	1.25419i	−0.778944	−	0.627093i	$-0.784244\pi$
$661$		−	829.018i		−	1.25419i	0.778944	−	0.627093i	$-0.215756\pi$
$662$	−346.090	+	346.090i	−0.522795	+	0.522795i
$663$	−392.702	+	335.296i	−0.592311	+	0.505726i
$664$			107.982i			0.162624i
$665$	92.1459	+	249.967i	0.138565	+	0.375889i
$666$	2.95918			0.00444321
$667$	917.076	−	917.076i	1.37493	−	1.37493i
$668$	891.605	−	891.605i	1.33474	−	1.33474i
$669$	657.836			0.983313
$670$	59.0884	−	128.088i	0.0881916	−	0.191176i
$671$		−	256.044i		−	0.381585i
$672$	747.012	−	747.012i	1.11162	−	1.11162i
$673$	404.875	+	404.875i	0.601597	+	0.601597i	0.940736	−	0.339139i	$-0.110136\pi$
$673$	404.875	+	404.875i	0.601597	+	0.601597i	−0.339139	+	0.940736i	$0.610136\pi$
$674$	599.564			0.889561
$675$	−671.676	−	53.2031i	−0.995075	−	0.0788194i
$676$	1701.37	+	269.999i	2.51681	+	0.399407i
$677$	433.153	−	433.153i	0.639812	−	0.639812i	−0.310697	−	0.950509i	$-0.600563\pi$
$677$	433.153	−	433.153i	0.639812	−	0.639812i	0.950509	+	0.310697i	$0.100563\pi$
$678$	942.443	−	942.443i	1.39003	−	1.39003i
$679$			306.652i			0.451624i
$680$	645.867	−	1400.06i	0.949804	−	2.05892i
$681$			1091.62i			1.60296i
$682$	−814.895	−	814.895i	−1.19486	−	1.19486i
$683$	−62.7373	+	62.7373i	−0.0918555	+	0.0918555i	−0.751541	−	0.659686i	$-0.770689\pi$
$683$	−62.7373	+	62.7373i	−0.0918555	+	0.0918555i	0.659686	+	0.751541i	$0.270689\pi$
$684$	4.21579			0.00616343
$685$	257.317	+	698.031i	0.375645	+	1.01902i
$686$	−1267.01			−1.84696
$687$	556.861	+	556.861i	0.810569	+	0.810569i
$688$	1624.30	+	1624.30i	2.36090	+	2.36090i
$689$	−568.341	−	44.8162i	−0.824878	−	0.0650452i
$690$	−2106.37	+	776.477i	−3.05271	+	1.12533i
$691$			899.306i			1.30146i	0.759311	+	0.650728i	$0.225536\pi$
$691$			899.306i			1.30146i	−0.759311	+	0.650728i	$0.774464\pi$
$692$	−2297.49	+	2297.49i	−3.32007	+	3.32007i
$693$	−0.806678	−	0.806678i	−0.00116404	−	0.00116404i
$694$	2317.13			3.33880
$695$	−429.683	+	931.436i	−0.618248	+	1.34020i
$696$		−	2293.45i		−	3.29518i
$697$	250.246	+	250.246i	0.359033	+	0.359033i
$698$	1518.11	+	1518.11i	2.17494	+	2.17494i
$699$		−	786.285i		−	1.12487i
$700$	−1060.23	−	83.9799i	−1.51461	−	0.119971i
$701$	439.927			0.627570			0.313785	−	0.949494i	$-0.398403\pi$
$701$	439.927			0.627570			0.313785	+	0.949494i	$0.398403\pi$
$702$	−1003.84	+	857.095i	−1.42997	+	1.22093i
$703$	−218.877	−	218.877i	−0.311347	−	0.311347i
$704$	1086.67			1.54357
$705$	80.9205	−	175.414i	0.114781	−	0.248814i
$706$	151.281			0.214278
$707$	−94.9680	−	94.9680i	−0.134325	−	0.134325i
$708$	−1483.59	+	1483.59i	−2.09546	+	2.09546i
$709$	−1362.23			−1.92134			−0.960668	−	0.277699i	$-0.910428\pi$
$709$	−1362.23			−1.92134			−0.960668	+	0.277699i	$0.910428\pi$
$710$	47.9132	−	17.6624i	0.0674834	−	0.0248766i
$711$	0.393002			0.000552746
$712$	−1128.03	+	1128.03i	−1.58432	+	1.58432i
$713$	−1016.56	+	1016.56i	−1.42575	+	1.42575i
$714$		−	624.544i		−	0.874712i
$715$	148.657	+	527.913i	0.207912	+	0.738340i
$716$	−760.702			−1.06243
$717$	−143.122	−	143.122i	−0.199612	−	0.199612i
$718$	−424.447	−	424.447i	−0.591152	−	0.591152i
$719$		−	13.9212i		−	0.0193619i	−0.999953	−	0.00968095i	$-0.996918\pi$
$719$		−	13.9212i		−	0.0193619i	0.999953	−	0.00968095i	$-0.00308159\pi$
$720$	−3.19778	+	6.93192i	−0.00444136	+	0.00962766i
$721$			335.557i			0.465405i
$722$	527.498	+	527.498i	0.730607	+	0.730607i
$723$	556.912	−	556.912i	0.770279	−	0.770279i
$724$		−	1612.68i		−	2.22746i
$725$	−622.017	+	530.710i	−0.857954	+	0.732014i
$726$			563.937i			0.776773i
$727$	532.730	−	532.730i	0.732778	−	0.732778i	−0.238391	−	0.971169i	$-0.576620\pi$
$727$	532.730	−	532.730i	0.732778	−	0.732778i	0.971169	+	0.238391i	$0.0766200\pi$
$728$	−962.737	+	822.002i	−1.32244	+	1.12912i
$729$		−	726.357i		−	0.996375i
$730$	−710.639	−	327.827i	−0.973478	−	0.449078i
$731$	644.184			0.881236
$732$	−657.344	+	657.344i	−0.898011	+	0.898011i
$733$	429.158	−	429.158i	0.585482	−	0.585482i	−0.350922	−	0.936405i	$-0.614132\pi$
$733$	429.158	−	429.158i	0.585482	−	0.585482i	0.936405	+	0.350922i	$0.114132\pi$
$734$	−469.641			−0.639838
$735$	445.284	−	164.146i	0.605828	−	0.223328i
$736$		−	3339.85i		−	4.53784i
$737$	44.6784	−	44.6784i	0.0606219	−	0.0606219i
$738$	−2.31090	−	2.31090i	−0.00313131	−	0.00313131i
$739$	726.063			0.982494			0.491247	−	0.871020i	$-0.336541\pi$
$739$	726.063			0.982494			0.491247	+	0.871020i	$0.336541\pi$
$740$	1159.45	−	427.413i	1.56683	−	0.577585i
$741$	−497.249	−	39.2103i	−0.671052	−	0.0529154i
$742$	487.575	−	487.575i	0.657110	−	0.657110i
$743$	166.294	−	166.294i	0.223814	−	0.223814i	−0.586288	−	0.810102i	$-0.699411\pi$
$743$	166.294	−	166.294i	0.223814	−	0.223814i	0.810102	+	0.586288i	$0.199411\pi$
$744$			2542.24i			3.41698i
$745$	−367.825	−	169.682i	−0.493725	−	0.227762i
$746$			977.288i			1.31004i
$747$	−0.106016	−	0.106016i	−0.000141922	−	0.000141922i
$748$	803.772	−	803.772i	1.07456	−	1.07456i
$749$	−277.409			−0.370373
$750$	1362.46	−	383.142i	1.81662	−	0.510856i
$751$	407.736			0.542924			0.271462	−	0.962449i	$-0.412493\pi$
$751$	407.736			0.542924			0.271462	+	0.962449i	$0.412493\pi$
$752$	428.412	+	428.412i	0.569697	+	0.569697i
$753$	704.371	+	704.371i	0.935420	+	0.935420i
$754$	−125.919	+	1596.86i	−0.167002	+	2.11785i
$755$	44.5372	−	96.5446i	0.0589897	−	0.127874i
$756$		−	1146.55i		−	1.51660i
$757$	−853.705	+	853.705i	−1.12775	+	1.12775i	−0.137205	+	0.990543i	$0.543812\pi$
$757$	−853.705	+	853.705i	−1.12775	+	1.12775i	−0.990543	+	0.137205i	$0.956188\pi$
$758$	−1133.53	−	1133.53i	−1.49542	−	1.49542i
$759$	−1005.57			−1.32486
$760$	1397.45	−	515.145i	1.83874	−	0.677822i
$761$		−	801.677i		−	1.05345i	−0.850035	−	0.526726i	$-0.823419\pi$
$761$		−	801.677i		−	1.05345i	0.850035	−	0.526726i	$-0.176581\pi$
$762$	824.176	+	824.176i	1.08160	+	1.08160i
$763$	54.0356	+	54.0356i	0.0708199	+	0.0708199i
$764$		−	28.5141i		−	0.0373221i
$765$	0.740463	+	2.00867i	0.000967926	+	0.00262572i
$766$	1072.38			1.39997
$767$	677.111	−	578.130i	0.882804	−	0.753755i
$768$	−92.5631	−	92.5631i	−0.120525	−	0.120525i
$769$	−580.457			−0.754820			−0.377410	−	0.926046i	$-0.623185\pi$
$769$	−580.457			−0.754820			−0.377410	+	0.926046i	$0.623185\pi$
$770$	−602.335	−	277.865i	−0.782254	−	0.360863i
$771$	48.8020			0.0632970
$772$	−1904.10	−	1904.10i	−2.46645	−	2.46645i
$773$	−486.345	+	486.345i	−0.629165	+	0.629165i	−0.947858	−	0.318693i	$-0.896756\pi$
$773$	−486.345	+	486.345i	−0.629165	+	0.629165i	0.318693	+	0.947858i	$0.396756\pi$
$774$	−5.94874			−0.00768571
$775$	689.492	−	588.280i	0.889667	−	0.759071i
$776$	1714.35			2.20921
$777$	215.046	−	215.046i	0.276764	−	0.276764i
$778$	−1312.06	+	1312.06i	−1.68645	+	1.68645i
$779$			341.854i			0.438837i
$780$	973.671	−	1736.97i	1.24830	−	2.22688i
$781$	22.8735			0.0292874
$782$	−1396.15	−	1396.15i	−1.78536	−	1.78536i
$783$	−623.293	−	623.293i	−0.796032	−	0.796032i
$784$			1488.41i			1.89848i
$785$	302.681	−	111.578i	0.385581	−	0.142138i
$786$			680.245i			0.865452i
$787$	553.821	+	553.821i	0.703711	+	0.703711i	0.965205	−	0.261494i	$-0.0842152\pi$
$787$	553.821	+	553.821i	0.703711	+	0.703711i	−0.261494	+	0.965205i	$0.584215\pi$
$788$	−2255.41	+	2255.41i	−2.86220	+	2.86220i
$789$		−	814.352i		−	1.03213i
$790$	214.411	−	79.0388i	0.271406	−	0.100049i
$791$		−	491.284i		−	0.621092i
$792$	−4.50976	+	4.50976i	−0.00569414	+	0.00569414i
$793$	300.013	−	256.156i	0.378326	−	0.323022i
$794$			96.7321i			0.121829i
$795$	−276.046	+	598.394i	−0.347228	+	0.752696i
$796$	−918.618			−1.15404
$797$	−829.778	+	829.778i	−1.04113	+	1.04113i	−0.0420092	+	0.999117i	$0.513376\pi$
$797$	−829.778	+	829.778i	−1.04113	+	1.04113i	−0.999117	+	0.0420092i	$0.986624\pi$
$798$	426.586	−	426.586i	0.534570	−	0.534570i
$799$	169.904			0.212646
$800$	−166.263	+	2099.03i	−0.207829	+	2.62379i
$801$		−	2.21498i		−	0.00276527i
$802$	1060.35	−	1060.35i	1.32213	−	1.32213i
$803$	−247.879	−	247.879i	−0.308691	−	0.308691i
$804$	−229.407			−0.285332
$805$	−346.628	+	751.397i	−0.430594	+	0.933412i
$806$	139.579	−	1770.09i	0.173175	−	2.19614i
$807$	−405.516	+	405.516i	−0.502498	+	0.502498i
$808$	−530.922	+	530.922i	−0.657081	+	0.657081i
$809$		−	746.142i		−	0.922301i	−0.887322	−	0.461151i	$-0.847437\pi$
$809$		−	746.142i		−	0.922301i	0.887322	−	0.461151i	$-0.152563\pi$
$810$	529.635	+	1436.75i	0.653870	+	1.77377i
$811$		−	556.454i		−	0.686133i	−0.939311	−	0.343067i	$-0.888534\pi$
$811$		−	556.454i		−	0.686133i	0.939311	−	0.343067i	$-0.111466\pi$
$812$	−983.854	−	983.854i	−1.21164	−	1.21164i
$813$	−53.8294	+	53.8294i	−0.0662108	+	0.0662108i
$814$	770.725			0.946837
$815$	−1312.79	+	483.937i	−1.61078	+	0.593788i
$816$	−1872.00			−2.29412
$817$	440.001	+	440.001i	0.538557	+	0.538557i
$818$	−1275.73	−	1275.73i	−1.55957	−	1.55957i
$819$	0.138172	−	1.75224i	0.000168708	−	0.00213948i
$820$	−1239.23	−	571.670i	−1.51125	−	0.697159i
$821$		−	1330.26i		−	1.62029i	−0.586231	−	0.810144i	$-0.699389\pi$
$821$		−	1330.26i		−	1.62029i	0.586231	−	0.810144i	$-0.300611\pi$
$822$	1191.24	−	1191.24i	1.44920	−	1.44920i
$823$	872.951	+	872.951i	1.06069	+	1.06069i	0.998035	+	0.0626584i	$0.0199579\pi$
$823$	872.951	+	872.951i	1.06069	+	1.06069i	0.0626584	+	0.998035i	$0.480042\pi$
$824$	1875.94			2.27663
$825$	631.979	+	50.0587i	0.766035	+	0.0606772i
$826$			1076.86i			1.30371i
$827$	−494.383	−	494.383i	−0.597803	−	0.597803i	0.341924	−	0.939727i	$-0.388921\pi$
$827$	−494.383	−	494.383i	−0.597803	−	0.597803i	−0.939727	+	0.341924i	$0.888921\pi$
$828$	9.25932	+	9.25932i	0.0111827	+	0.0111827i
$829$			1260.53i			1.52054i	0.649608	+	0.760270i	$0.274933\pi$
$829$			1260.53i			1.52054i	−0.649608	+	0.760270i	$0.725067\pi$
$830$	−79.1608	−	36.5178i	−0.0953744	−	0.0439974i
$831$	−1438.60			−1.73116
$832$	1087.15	+	1273.28i	1.30667	+	1.53039i
$833$	295.145	+	295.145i	0.354316	+	0.354316i
$834$	2322.85			2.78519
$835$	213.930	+	580.333i	0.256203	+	0.695010i
$836$	1098.01			1.31341
$837$	690.907	+	690.907i	0.825456	+	0.825456i
$838$	1337.63	−	1337.63i	1.59622	−	1.59622i
$839$	−233.028			−0.277745			−0.138872	−	0.990310i	$-0.544348\pi$
$839$	−233.028			−0.277745			−0.138872	+	0.990310i	$0.544348\pi$
$840$	506.127	+	1372.98i	0.602532	+	1.63451i
$841$	−228.692			−0.271929
$842$	1626.22	−	1626.22i	1.93137	−	1.93137i
$843$	966.087	−	966.087i	1.14601	−	1.14601i
$844$		−	2972.79i		−	3.52226i
$845$	−469.847	+	702.331i	−0.556032	+	0.831161i
$846$	−1.56899			−0.00185460
$847$	146.987	+	146.987i	0.173538	+	0.173538i
$848$	−1461.45	−	1461.45i	−1.72341	−	1.72341i
$849$			256.126i			0.301680i
$850$	807.951	+	946.956i	0.950530	+	1.11407i
$851$		−	961.458i		−	1.12980i
$852$	−58.7234	−	58.7234i	−0.0689242	−	0.0689242i
$853$	236.180	−	236.180i	0.276881	−	0.276881i	−0.554981	−	0.831863i	$-0.687275\pi$
$853$	236.180	−	236.180i	0.276881	−	0.276881i	0.831863	+	0.554981i	$0.187275\pi$
$854$			477.133i			0.558704i
$855$	−0.866235	+	1.87776i	−0.00101314	+	0.00219621i
$856$			1550.87i			1.81176i
$857$	529.274	−	529.274i	0.617589	−	0.617589i	−0.327324	−	0.944912i	$-0.606147\pi$
$857$	529.274	−	529.274i	0.617589	−	0.617589i	0.944912	+	0.327324i	$0.106147\pi$
$858$	944.510	−	806.440i	1.10083	−	0.939907i
$859$		−	328.608i		−	0.382547i	−0.981537	−	0.191274i	$-0.938738\pi$
$859$		−	328.608i		−	0.382547i	0.981537	−	0.191274i	$-0.0612618\pi$
$860$	−2330.81	+	859.213i	−2.71024	+	0.999085i
$861$	−335.870			−0.390093
$862$	290.160	−	290.160i	0.336613	−	0.336613i
$863$	−755.204	+	755.204i	−0.875092	+	0.875092i	−0.993022	−	0.117930i	$-0.962374\pi$
$863$	−755.204	+	755.204i	−0.875092	+	0.875092i	0.117930	+	0.993022i	$0.462374\pi$
$864$	−2269.94			−2.62725
$865$	−551.254	−	1495.40i	−0.637288	−	1.72879i
$866$			1644.08i			1.89848i
$867$	242.954	−	242.954i	0.280224	−	0.280224i
$868$	1090.58	+	1090.58i	1.25643	+	1.25643i
$869$	102.358			0.117789
$870$	1681.30	+	775.605i	1.93253	+	0.891499i
$871$	97.0488	+	7.65272i	0.111422	+	0.00878613i
$872$	302.088	−	302.088i	0.346431	−	0.346431i
$873$	−1.68313	+	1.68313i	−0.00192799	+	0.00192799i
$874$		−	1907.25i		−	2.18220i
$875$	255.254	−	454.981i	0.291719	−	0.519979i
$876$			1272.76i			1.45293i
$877$	656.420	+	656.420i	0.748483	+	0.748483i	0.974194	−	0.225711i	$-0.0724706\pi$
$877$	656.420	+	656.420i	0.748483	+	0.748483i	−0.225711	+	0.974194i	$0.572471\pi$
$878$	952.295	−	952.295i	1.08462	−	1.08462i
$879$	−1194.37			−1.35878
$880$	−832.869	+	1805.43i	−0.946442	+	2.05163i
$881$	−1163.04			−1.32014			−0.660069	−	0.751205i	$-0.729473\pi$
$881$	−1163.04			−1.32014			−0.660069	+	0.751205i	$0.729473\pi$
$882$	−2.72553	−	2.72553i	−0.00309017	−	0.00309017i
$883$	511.332	+	511.332i	0.579085	+	0.579085i	0.934651	−	0.355566i	$-0.115712\pi$
$883$	511.332	+	511.332i	0.579085	+	0.579085i	−0.355566	+	0.934651i	$0.615712\pi$
$884$	1745.93	+	137.674i	1.97503	+	0.155740i
$885$	−355.969	−	965.646i	−0.402225	−	1.09113i
$886$			1943.44i			2.19350i
$887$	82.7279	−	82.7279i	0.0932671	−	0.0932671i	−0.658934	−	0.752201i	$-0.728992\pi$
$887$	82.7279	−	82.7279i	0.0932671	−	0.0932671i	0.752201	+	0.658934i	$0.228992\pi$
$888$	−1202.22	−	1202.22i	−1.35385	−	1.35385i
$889$	429.633			0.483277
$890$	−445.467	−	1208.43i	−0.500525	−	1.35779i
$891$			685.897i			0.769806i
$892$	−1577.66	−	1577.66i	−1.76868	−	1.76868i
$893$	116.051	+	116.051i	0.129956	+	0.129956i
$894$			917.297i			1.02606i
$895$	156.305	−	338.826i	0.174642	−	0.378577i
$896$	−618.946			−0.690788
$897$	−1006.01	−	1178.25i	−1.12153	−	1.31355i
$898$	964.187	+	964.187i	1.07371	+	1.07371i
$899$	1185.73			1.31894
$900$	−5.35835	−	6.28023i	−0.00595372	−	0.00697804i
$901$	−579.600			−0.643285
$902$	−601.880	−	601.880i	−0.667273	−	0.667273i
$903$	−432.299	+	432.299i	−0.478736	+	0.478736i
$904$	−2746.54			−3.03821
$905$	718.307	+	331.364i	0.793710	+	0.366148i
$906$	−240.767			−0.265747
$907$	210.562	−	210.562i	0.232152	−	0.232152i	−0.581438	−	0.813591i	$-0.697510\pi$
$907$	210.562	−	210.562i	0.232152	−	0.232152i	0.813591	+	0.581438i	$0.197510\pi$
$908$	2617.97	−	2617.97i	2.88323	−	2.88323i
$909$		−	1.04251i		−	0.00114687i
$910$	−277.020	−	983.758i	−0.304417	−	1.08105i
$911$	−293.314			−0.321969			−0.160984	−	0.986957i	$-0.551467\pi$
$911$	−293.314			−0.321969			−0.160984	+	0.986957i	$0.551467\pi$
$912$	−1278.65	−	1278.65i	−1.40202	−	1.40202i
$913$	−27.6121	−	27.6121i	−0.0302433	−	0.0302433i
$914$		−	65.3896i		−	0.0715422i
$915$	−157.722	−	427.856i	−0.172374	−	0.467602i
$916$		−	2670.99i		−	2.91593i
$917$	177.302	+	177.302i	0.193350	+	0.193350i
$918$	−948.899	+	948.899i	−1.03366	+	1.03366i
$919$		−	268.843i		−	0.292539i	−0.989245	−	0.146269i	$-0.953273\pi$
$919$		−	268.843i		−	0.292539i	0.989245	−	0.146269i	$-0.0467266\pi$
$920$	4200.71	+	1937.84i	4.56599	+	2.10635i
$921$		−	243.432i		−	0.264312i
$922$	−289.753	+	289.753i	−0.314265	+	0.314265i
$923$	22.8836	+	26.8014i	0.0247926	+	0.0290373i
$924$			1078.79i			1.16752i
$925$	−47.8629	+	604.257i	−0.0517436	+	0.653251i
$926$	847.272			0.914981
$927$	−1.84178	+	1.84178i	−0.00198682	+	0.00198682i
$928$	−1947.83	+	1947.83i	−2.09895	+	2.09895i
$929$	1505.51			1.62057			0.810284	−	0.586037i	$-0.199313\pi$
$929$	1505.51			1.62057			0.810284	+	0.586037i	$0.199313\pi$
$930$	−1863.68	−	859.741i	−2.00396	−	0.924452i
$931$			403.189i			0.433071i
$932$	−1885.71	+	1885.71i	−2.02329	+	2.02329i
$933$	−935.391	−	935.391i	−1.00256	−	1.00256i
$934$	−83.1479			−0.0890234
$935$	192.855	+	523.164i	0.206262	+	0.559533i
$936$	−9.79595	−	0.772453i	−0.0104658	−	0.000825270i
$937$	−317.658	+	317.658i	−0.339017	+	0.339017i	−0.855997	−	0.516981i	$-0.827056\pi$
$937$	−317.658	+	317.658i	−0.339017	+	0.339017i	0.516981	+	0.855997i	$0.327056\pi$
$938$	−83.2574	+	83.2574i	−0.0887606	+	0.0887606i
$939$			1672.09i			1.78071i
$940$	−614.755	+	226.619i	−0.653994	+	0.241084i
$941$			1114.77i			1.18466i	0.805695	+	0.592330i	$0.201792\pi$
$941$			1114.77i			1.18466i	−0.805695	+	0.592330i	$0.798208\pi$
$942$	−516.548	−	516.548i	−0.548353	−	0.548353i
$943$	−750.829	+	750.829i	−0.796213	+	0.796213i
$944$	3227.77			3.41925
$945$	510.689	+	235.587i	0.540411	+	0.249298i
$946$	−1549.36			−1.63780
$947$	−835.045	−	835.045i	−0.881779	−	0.881779i	0.111936	−	0.993715i	$-0.464295\pi$
$947$	−835.045	−	835.045i	−0.881779	−	0.881779i	−0.993715	+	0.111936i	$0.964295\pi$
$948$	−262.786	−	262.786i	−0.277200	−	0.277200i
$949$	42.4578	−	538.434i	0.0447395	−	0.567369i
$950$	−94.9457	+	1198.67i	−0.0999428	+	1.26175i
$951$		−	990.103i		−	1.04112i
$952$	−910.047	+	910.047i	−0.955932	+	0.955932i
$953$	−654.299	−	654.299i	−0.686568	−	0.686568i	0.274904	−	0.961472i	$-0.411354\pi$
$953$	−654.299	−	654.299i	−0.686568	−	0.686568i	−0.961472	+	0.274904i	$0.911354\pi$
$954$	5.35234			0.00561042
$955$	12.7005	+	5.85891i	0.0132990	+	0.00613498i
$956$			686.486i			0.718081i
$957$	586.456	+	586.456i	0.612806	+	0.612806i
$958$	−2242.73	−	2242.73i	−2.34105	−	2.34105i
$959$		−	620.980i		−	0.647528i
$960$	1815.86	−	669.386i	1.89152	−	0.697277i
$961$	−353.356			−0.367696
$962$	771.065	+	903.078i	0.801523	+	0.938751i
$963$	−1.52262	−	1.52262i	−0.00158113	−	0.00158113i
$964$	−2671.23			−2.77099
$965$	1239.35	−	456.865i	1.28430	−	0.473435i
$966$	1873.86			1.93982
$967$	−24.1547	−	24.1547i	−0.0249790	−	0.0249790i	0.694507	−	0.719486i	$-0.255623\pi$
$967$	−24.1547	−	24.1547i	−0.0249790	−	0.0249790i	−0.719486	+	0.694507i	$0.755623\pi$
$968$	821.734	−	821.734i	0.848899	−	0.848899i
$969$	−507.100			−0.523323
$970$	−579.764	+	1256.77i	−0.597695	+	1.29564i
$971$	−46.1024			−0.0474792			−0.0237396	−	0.999718i	$-0.507557\pi$
$971$	−46.1024			−0.0474792			−0.0237396	+	0.999718i	$0.507557\pi$
$972$	12.6090	−	12.6090i	0.0129722	−	0.0129722i
$973$	605.436	−	605.436i	0.622237	−	0.622237i
$974$			3354.19i			3.44372i
$975$	573.602	+	790.587i	0.588310	+	0.810858i
$976$	1430.15			1.46532
$977$	−402.739	−	402.739i	−0.412220	−	0.412220i	0.470291	−	0.882511i	$-0.344149\pi$
$977$	−402.739	−	402.739i	−0.412220	−	0.412220i	−0.882511	+	0.470291i	$0.844149\pi$
$978$	2240.37	+	2240.37i	2.29077	+	2.29077i
$979$		−	576.898i		−	0.589272i
$980$	−1461.57	−	674.240i	−1.49140	−	0.688000i
$981$			0.593173i			0.000604662i
$982$	1706.01	+	1706.01i	1.73728	+	1.73728i
$983$	533.637	−	533.637i	0.542866	−	0.542866i	−0.381502	−	0.924368i	$-0.624593\pi$
$983$	533.637	−	533.637i	0.542866	−	0.542866i	0.924368	+	0.381502i	$0.124593\pi$
$984$			1877.69i			1.90822i
$985$	−541.159	−	1468.02i	−0.549400	−	1.49037i
$986$			1628.50i			1.65162i
$987$	−114.020	+	114.020i	−0.115521	+	0.115521i
$988$	1098.49	+	1286.57i	1.11184	+	1.30219i
$989$			1932.79i			1.95428i
$990$	−1.78093	−	4.83118i	−0.00179892	−	0.00487998i
$991$	871.282			0.879194			0.439597	−	0.898195i	$-0.355121\pi$
$991$	871.282			0.879194			0.439597	+	0.898195i	$0.355121\pi$
$992$	2159.13	−	2159.13i	2.17654	−	2.17654i
$993$	−276.090	+	276.090i	−0.278036	+	0.278036i
$994$	−42.6244			−0.0428817
$995$	188.752	−	409.164i	0.189701	−	0.411220i
$996$			141.778i			0.142347i
$997$	236.064	−	236.064i	0.236774	−	0.236774i	−0.578739	−	0.815513i	$-0.696455\pi$
$997$	236.064	−	236.064i	0.236774	−	0.236774i	0.815513	+	0.578739i	$0.196455\pi$
$998$	−23.1368	−	23.1368i	−0.0231832	−	0.0231832i
$999$	−653.458			−0.654112

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.3.h.a.38.1	yes	24
5.2	odd	4	inner	65.3.h.a.12.12	yes	24
5.3	odd	4		325.3.h.b.207.1		24
5.4	even	2		325.3.h.b.168.12		24
13.12	even	2	inner	65.3.h.a.38.12	yes	24
65.12	odd	4	inner	65.3.h.a.12.1	✓	24
65.38	odd	4		325.3.h.b.207.12		24
65.64	even	2		325.3.h.b.168.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.3.h.a.12.1	✓	24	65.12	odd	4	inner
65.3.h.a.12.12	yes	24	5.2	odd	4	inner
65.3.h.a.38.1	yes	24	1.1	even	1	trivial
65.3.h.a.38.12	yes	24	13.12	even	2	inner
325.3.h.b.168.1		24	65.64	even	2
325.3.h.b.168.12		24	5.4	even	2
325.3.h.b.207.1		24	5.3	odd	4
325.3.h.b.207.12		24	65.38	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	65.h (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.66395 - 2.66395i) q^{2} +(-2.12513 - 2.12513i) q^{3} +10.1932i q^{4} +(-4.54019 - 2.09444i) q^{5} +11.3225i q^{6} +(2.95114 + 2.95114i) q^{7} +(16.4984 - 16.4984i) q^{8} +0.0323960i q^{9} +O(q^{10})\)	\(q+(-2.66395 - 2.66395i) q^{2} +(-2.12513 - 2.12513i) q^{3} +10.1932i q^{4} +(-4.54019 - 2.09444i) q^{5} +11.3225i q^{6} +(2.95114 + 2.95114i) q^{7} +(16.4984 - 16.4984i) q^{8} +0.0323960i q^{9} +(6.51533 + 17.6743i) q^{10} +8.43761i q^{11} +(21.6620 - 21.6620i) q^{12} +(-9.88656 + 8.44132i) q^{13} -15.7234i q^{14} +(5.19753 + 14.0995i) q^{15} -47.1290 q^{16} +(-9.34548 + 9.34548i) q^{17} +(0.0863012 - 0.0863012i) q^{18} -12.7666 q^{19} +(21.3492 - 46.2792i) q^{20} -12.5431i q^{21} +(22.4773 - 22.4773i) q^{22} +(-28.0399 - 28.0399i) q^{23} -70.1228 q^{24} +(16.2266 + 19.0183i) q^{25} +(48.8245 + 3.85003i) q^{26} +(-19.0574 + 19.0574i) q^{27} +(-30.0816 + 30.0816i) q^{28} +32.7061i q^{29} +(23.7143 - 51.4062i) q^{30} -36.2540i q^{31} +(59.5554 + 59.5554i) q^{32} +(17.9311 - 17.9311i) q^{33} +49.7917 q^{34} +(-7.21773 - 19.5797i) q^{35} -0.330220 q^{36} +(17.1445 + 17.1445i) q^{37} +(34.0096 + 34.0096i) q^{38} +(38.9492 + 3.07132i) q^{39} +(-109.461 + 40.3509i) q^{40} -26.7772i q^{41} +(-33.4142 + 33.4142i) q^{42} +(-34.4650 - 34.4650i) q^{43} -86.0065 q^{44} +(0.0678516 - 0.147084i) q^{45} +149.393i q^{46} +(-9.09020 - 9.09020i) q^{47} +(100.156 + 100.156i) q^{48} -31.5816i q^{49} +(7.43703 - 93.8907i) q^{50} +39.7208 q^{51} +(-86.0444 - 100.776i) q^{52} +(31.0096 + 31.0096i) q^{53} +101.536 q^{54} +(17.6721 - 38.3083i) q^{55} +97.3783 q^{56} +(27.1308 + 27.1308i) q^{57} +(87.1275 - 87.1275i) q^{58} -68.4880 q^{59} +(-143.719 + 52.9797i) q^{60} -30.3455 q^{61} +(-96.5789 + 96.5789i) q^{62} +(-0.0956050 + 0.0956050i) q^{63} -128.789i q^{64} +(62.5667 - 17.6184i) q^{65} -95.5348 q^{66} +(-5.29514 - 5.29514i) q^{67} +(-95.2606 - 95.2606i) q^{68} +119.177i q^{69} +(-32.9317 + 71.3870i) q^{70} -2.71090i q^{71} +(0.534483 + 0.534483i) q^{72} +(-29.3778 + 29.3778i) q^{73} -91.3441i q^{74} +(5.93281 - 74.9003i) q^{75} -130.133i q^{76} +(-24.9005 + 24.9005i) q^{77} +(-95.5769 - 111.940i) q^{78} -12.1312i q^{79} +(213.975 + 98.7091i) q^{80} +81.2905 q^{81} +(-71.3330 + 71.3330i) q^{82} +(-3.27251 + 3.27251i) q^{83} +127.855 q^{84} +(62.0038 - 22.8566i) q^{85} +183.626i q^{86} +(69.5050 - 69.5050i) q^{87} +(139.207 + 139.207i) q^{88} -68.3722 q^{89} +(-0.572577 + 0.211071i) q^{90} +(-54.0881 - 4.26508i) q^{91} +(285.817 - 285.817i) q^{92} +(-77.0447 + 77.0447i) q^{93} +48.4316i q^{94} +(57.9628 + 26.7389i) q^{95} -253.127i q^{96} +(51.9549 + 51.9549i) q^{97} +(-84.1316 + 84.1316i) q^{98} -0.273345 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{3}+O(q^{10}) \) 24 * q - 4 * q^3	\( 24 q - 4 q^{3} + 16 q^{10} + 72 q^{12} - 36 q^{13} - 104 q^{16} - 48 q^{17} + 8 q^{22} - 104 q^{23} - 88 q^{25} + 88 q^{26} + 56 q^{27} - 24 q^{30} - 64 q^{35} + 256 q^{36} + 124 q^{38} - 368 q^{40} + 216 q^{42} + 8 q^{43} + 196 q^{48} - 296 q^{51} + 16 q^{52} + 220 q^{53} + 332 q^{55} + 584 q^{56} - 8 q^{61} - 596 q^{62} + 420 q^{65} - 360 q^{66} - 640 q^{68} - 184 q^{75} + 388 q^{77} - 636 q^{78} - 224 q^{81} - 1004 q^{82} - 52 q^{87} + 780 q^{88} + 452 q^{90} - 512 q^{91} + 812 q^{92} - 136 q^{95}+O(q^{100}) \) 24 * q - 4 * q^3 + 16 * q^10 + 72 * q^12 - 36 * q^13 - 104 * q^16 - 48 * q^17 + 8 * q^22 - 104 * q^23 - 88 * q^25 + 88 * q^26 + 56 * q^27 - 24 * q^30 - 64 * q^35 + 256 * q^36 + 124 * q^38 - 368 * q^40 + 216 * q^42 + 8 * q^43 + 196 * q^48 - 296 * q^51 + 16 * q^52 + 220 * q^53 + 332 * q^55 + 584 * q^56 - 8 * q^61 - 596 * q^62 + 420 * q^65 - 360 * q^66 - 640 * q^68 - 184 * q^75 + 388 * q^77 - 636 * q^78 - 224 * q^81 - 1004 * q^82 - 52 * q^87 + 780 * q^88 + 452 * q^90 - 512 * q^91 + 812 * q^92 - 136 * q^95

Introduction

L-functions

Modular forms

Varieties

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