LMFDB - Embedded newform 784.2.x.p.165.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(165,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 8]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("784.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.x (of order $12$, degree $4$, not 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:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			165.20
Character	$\chi$	$=$	784.165
Dual form			784.2.x.p.765.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22699 + 0.703197i) q^{2} +(0.269295 + 1.00502i) q^{3} +(1.01103 + 1.72564i) q^{4} +(-0.290260 + 1.08326i) q^{5} +(-0.376306 + 1.42253i) q^{6} +(0.0270652 + 2.82830i) q^{8} +(1.66052 - 0.958704i) q^{9} +O(q^{10})$	\(q+(1.22699 + 0.703197i) q^{2} +(0.269295 + 1.00502i) q^{3} +(1.01103 + 1.72564i) q^{4} +(-0.290260 + 1.08326i) q^{5} +(-0.376306 + 1.42253i) q^{6} +(0.0270652 + 2.82830i) q^{8} +(1.66052 - 0.958704i) q^{9} +(-1.11790 + 1.12505i) q^{10} +(-1.84450 + 0.494232i) q^{11} +(-1.46204 + 1.48081i) q^{12} +(-4.46503 + 4.46503i) q^{13} -1.16687 q^{15} +(-1.95564 + 3.48934i) q^{16} +(0.496035 - 0.859158i) q^{17} +(2.71161 - 0.00864930i) q^{18} +(-1.18083 - 0.316402i) q^{19} +(-2.16278 + 0.594329i) q^{20} +(-2.61073 - 0.690626i) q^{22} +(5.19466 - 2.99914i) q^{23} +(-2.83522 + 0.788848i) q^{24} +(3.24091 + 1.87114i) q^{25} +(-8.61836 + 2.33877i) q^{26} +(3.61788 + 3.61788i) q^{27} +(-1.52780 + 1.52780i) q^{29} +(-1.43175 - 0.820541i) q^{30} +(3.15591 - 5.46620i) q^{31} +(-4.85325 + 2.90620i) q^{32} +(-0.993431 - 1.72067i) q^{33} +(1.21279 - 0.705372i) q^{34} +(3.33321 + 1.89618i) q^{36} +(1.65406 - 6.17305i) q^{37} +(-1.22638 - 1.21858i) q^{38} +(-5.68988 - 3.28505i) q^{39} +(-3.07165 - 0.791623i) q^{40} +4.40594i q^{41} +(3.93520 + 3.93520i) q^{43} +(-2.71771 - 2.68325i) q^{44} +(0.556547 + 2.07706i) q^{45} +(8.48280 - 0.0270578i) q^{46} +(-1.47708 - 2.55838i) q^{47} +(-4.03351 - 1.02580i) q^{48} +(2.66080 + 4.57488i) q^{50} +(0.997054 + 0.267160i) q^{51} +(-12.2193 - 3.19074i) q^{52} +(-7.90224 + 2.11740i) q^{53} +(1.89503 + 6.98319i) q^{54} -2.14154i q^{55} -1.27197i q^{57} +(-2.94895 + 0.800259i) q^{58} +(1.15964 - 0.310723i) q^{59} +(-1.17974 - 2.01360i) q^{60} +(-7.23546 - 1.93873i) q^{61} +(7.71610 - 4.48777i) q^{62} +(-7.99853 + 0.153097i) q^{64} +(-3.54079 - 6.13283i) q^{65} +(-0.00896260 - 2.80983i) q^{66} +(-2.87850 - 10.7427i) q^{67} +(1.98410 - 0.0126576i) q^{68} +(4.41310 + 4.41310i) q^{69} +7.05303i q^{71} +(2.75644 + 4.67051i) q^{72} +(11.6774 + 6.74194i) q^{73} +(6.37040 - 6.41117i) q^{74} +(-1.00778 + 3.76109i) q^{75} +(-0.647858 - 2.35757i) q^{76} +(-4.67141 - 8.03184i) q^{78} +(6.06076 + 10.4976i) q^{79} +(-3.21223 - 3.13129i) q^{80} +(0.214336 - 0.371241i) q^{81} +(-3.09824 + 5.40606i) q^{82} +(12.3456 - 12.3456i) q^{83} +(0.786717 + 0.786717i) q^{85} +(2.06125 + 7.59568i) q^{86} +(-1.94691 - 1.12405i) q^{87} +(-1.44776 - 5.20342i) q^{88} +(12.7823 - 7.37988i) q^{89} +(-0.777702 + 2.93990i) q^{90} +(10.4274 + 5.93187i) q^{92} +(6.34354 + 1.69975i) q^{93} +(-0.0133260 - 4.17779i) q^{94} +(0.685495 - 1.18731i) q^{95} +(-4.22775 - 4.09501i) q^{96} -9.55202 q^{97} +(-2.58901 + 2.58901i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 4 q^{4}+O(q^{10}) $ 96 * q + 4 * q^4	$ 96 q + 4 q^{4} + 8 q^{11} + 64 q^{15} - 36 q^{16} - 20 q^{18} - 56 q^{22} - 32 q^{29} - 96 q^{30} - 40 q^{32} + 80 q^{36} + 16 q^{37} + 16 q^{43} - 4 q^{44} - 64 q^{46} - 56 q^{50} - 16 q^{53} + 20 q^{58} - 8 q^{60} + 88 q^{64} - 40 q^{67} + 196 q^{72} + 28 q^{74} + 112 q^{78} - 80 q^{79} + 48 q^{81} + 108 q^{86} + 100 q^{88} + 128 q^{95} - 80 q^{99}+O(q^{100}) $ 96 * q + 4 * q^4 + 8 * q^11 + 64 * q^15 - 36 * q^16 - 20 * q^18 - 56 * q^22 - 32 * q^29 - 96 * q^30 - 40 * q^32 + 80 * q^36 + 16 * q^37 + 16 * q^43 - 4 * q^44 - 64 * q^46 - 56 * q^50 - 16 * q^53 + 20 * q^58 - 8 * q^60 + 88 * q^64 - 40 * q^67 + 196 * q^72 + 28 * q^74 + 112 * q^78 - 80 * q^79 + 48 * q^81 + 108 * q^86 + 100 * q^88 + 128 * q^95 - 80 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	1.22699	+	0.703197i	0.867616	+	0.497235i
$2$	1.22699	+	0.703197i	0.867616	+	0.497235i
$3$	0.269295	+	1.00502i	0.155478	+	0.580251i	0.999064	+	0.0432570i	$0.0137734\pi$
$3$	0.269295	+	1.00502i	0.155478	+	0.580251i	−0.843586	+	0.536994i	$0.819560\pi$
$4$	1.01103	+	1.72564i	0.505515	+	0.862818i
$5$	−0.290260	+	1.08326i	−0.129808	+	0.484451i	−0.999965	−	0.00832350i	$-0.997351\pi$
$5$	−0.290260	+	1.08326i	−0.129808	+	0.484451i	0.870157	+	0.492774i	$0.164017\pi$
$6$	−0.376306	+	1.42253i	−0.153626	+	0.580744i
$7$		0			0
$7$		0			0
$8$	0.0270652	+	2.82830i	0.00956901	+	0.999954i
$9$	1.66052	−	0.958704i	0.553508	−	0.319568i
$10$	−1.11790	+	1.12505i	−0.353510	+	0.355772i
$11$	−1.84450	+	0.494232i	−0.556138	+	0.149017i	−0.525931	−	0.850527i	$-0.676283\pi$
$11$	−1.84450	+	0.494232i	−0.556138	+	0.149017i	−0.0302064	+	0.999544i	$0.509616\pi$
$12$	−1.46204	+	1.48081i	−0.422055	+	0.427474i
$13$	−4.46503	+	4.46503i	−1.23838	+	1.23838i	−0.277713	+	0.960664i	$0.589576\pi$
$13$	−4.46503	+	4.46503i	−1.23838	+	1.23838i	−0.960664	+	0.277713i	$0.910424\pi$
$14$		0			0
$15$	−1.16687			−0.301285
$16$	−1.95564	+	3.48934i	−0.488910	+	0.872334i
$17$	0.496035	−	0.859158i	0.120306	−	0.208376i	−0.799582	−	0.600557i	$-0.794946\pi$
$17$	0.496035	−	0.859158i	0.120306	−	0.208376i	0.919888	+	0.392180i	$0.128279\pi$
$18$	2.71161	−	0.00864930i	0.639133	−	0.00203866i
$19$	−1.18083	−	0.316402i	−0.270901	−	0.0725877i	0.120811	−	0.992675i	$-0.461450\pi$
$19$	−1.18083	−	0.316402i	−0.270901	−	0.0725877i	−0.391712	+	0.920088i	$0.628117\pi$
$20$	−2.16278	+	0.594329i	−0.483613	+	0.132896i
$21$		0			0
$22$	−2.61073	−	0.690626i	−0.556610	−	0.147242i
$23$	5.19466	−	2.99914i	1.08316	−	0.625363i	0.151413	−	0.988471i	$-0.451618\pi$
$23$	5.19466	−	2.99914i	1.08316	−	0.625363i	0.931747	+	0.363107i	$0.118284\pi$
$24$	−2.83522	+	0.788848i	−0.578736	+	0.161023i
$25$	3.24091	+	1.87114i	0.648183	+	0.374229i
$26$	−8.61836	+	2.33877i	−1.69020	+	0.458671i
$27$	3.61788	+	3.61788i	0.696261	+	0.696261i
$28$		0			0
$29$	−1.52780	+	1.52780i	−0.283706	+	0.283706i	−0.834585	−	0.550879i	$-0.814292\pi$
$29$	−1.52780	+	1.52780i	−0.283706	+	0.283706i	0.550879	+	0.834585i	$0.314292\pi$
$30$	−1.43175	−	0.820541i	−0.261400	−	0.149810i
$31$	3.15591	−	5.46620i	0.566819	−	0.981759i	−0.430059	−	0.902801i	$-0.641507\pi$
$31$	3.15591	−	5.46620i	0.566819	−	0.981759i	0.996878	−	0.0789584i	$-0.0251594\pi$
$32$	−4.85325	+	2.90620i	−0.857941	+	0.513748i
$33$	−0.993431	−	1.72067i	−0.172934	−	0.299531i
$34$	1.21279	−	0.705372i	0.207992	−	0.120970i
$35$		0			0
$36$	3.33321	+	1.89618i	0.555535	+	0.316030i
$37$	1.65406	−	6.17305i	0.271927	−	1.01484i	−0.685947	−	0.727652i	$-0.740612\pi$
$37$	1.65406	−	6.17305i	0.271927	−	1.01484i	0.957873	−	0.287192i	$-0.0927217\pi$
$38$	−1.22638	−	1.21858i	−0.198945	−	0.197680i
$39$	−5.68988	−	3.28505i	−0.911109	−	0.526029i
$40$	−3.07165	−	0.791623i	−0.485671	−	0.125167i
$41$			4.40594i			0.688092i	0.938953	+	0.344046i	$0.111798\pi$
$41$			4.40594i			0.688092i	−0.938953	+	0.344046i	$0.888202\pi$
$42$		0			0
$43$	3.93520	+	3.93520i	0.600112	+	0.600112i	0.940342	−	0.340230i	$-0.110505\pi$
$43$	3.93520	+	3.93520i	0.600112	+	0.600112i	−0.340230	+	0.940342i	$0.610505\pi$
$44$	−2.71771	−	2.68325i	−0.409710	−	0.404516i
$45$	0.556547	+	2.07706i	0.0829651	+	0.309630i
$46$	8.48280	−	0.0270578i	1.25072	−	0.00398946i
$47$	−1.47708	−	2.55838i	−0.215454	−	0.373178i	0.737959	−	0.674846i	$-0.235790\pi$
$47$	−1.47708	−	2.55838i	−0.215454	−	0.373178i	−0.953413	+	0.301668i	$0.902457\pi$
$48$	−4.03351	−	1.02580i	−0.582187	−	0.148062i
$49$		0			0
$50$	2.66080	+	4.57488i	0.376294	+	0.646986i
$51$	0.997054	+	0.267160i	0.139616	+	0.0374099i
$52$	−12.2193	−	3.19074i	−1.69451	−	0.442477i
$53$	−7.90224	+	2.11740i	−1.08546	+	0.290847i	−0.756829	−	0.653613i	$-0.773252\pi$
$53$	−7.90224	+	2.11740i	−1.08546	+	0.290847i	−0.328627	+	0.944460i	$0.606586\pi$
$54$	1.89503	+	6.98319i	0.257882	+	0.950292i
$55$		−	2.14154i		−	0.288765i
$56$		0			0
$57$		−	1.27197i		−	0.168476i
$58$	−2.94895	+	0.800259i	−0.387216	+	0.105079i
$59$	1.15964	−	0.310723i	0.150972	−	0.0404527i	−0.182542	−	0.983198i	$-0.558432\pi$
$59$	1.15964	−	0.310723i	0.150972	−	0.0404527i	0.333513	+	0.942745i	$0.391766\pi$
$60$	−1.17974	−	2.01360i	−0.152304	−	0.259954i
$61$	−7.23546	−	1.93873i	−0.926405	−	0.248230i	−0.236084	−	0.971733i	$-0.575864\pi$
$61$	−7.23546	−	1.93873i	−0.926405	−	0.248230i	−0.690321	+	0.723503i	$0.742531\pi$
$62$	7.71610	−	4.48777i	0.979946	−	0.569948i
$63$		0			0
$64$	−7.99853	+	0.153097i	−0.999817	+	0.0191371i
$65$	−3.54079	−	6.13283i	−0.439181	−	0.760684i
$66$	−0.00896260	−	2.80983i	−0.00110322	−	0.345866i
$67$	−2.87850	−	10.7427i	−0.351665	−	1.31243i	−0.884629	−	0.466295i	$-0.845589\pi$
$67$	−2.87850	−	10.7427i	−0.351665	−	1.31243i	0.532964	−	0.846138i	$-0.321078\pi$
$68$	1.98410	−	0.0126576i	0.240608	−	0.00153496i
$69$	4.41310	+	4.41310i	0.531275	+	0.531275i
$70$		0			0
$71$			7.05303i			0.837041i	0.908207	+	0.418521i	$0.137451\pi$
$71$			7.05303i			0.837041i	−0.908207	+	0.418521i	$0.862549\pi$
$72$	2.75644	+	4.67051i	0.324850	+	0.550425i
$73$	11.6774	+	6.74194i	1.36673	+	0.789084i	0.990509	−	0.137445i	$-0.0438890\pi$
$73$	11.6774	+	6.74194i	1.36673	+	0.789084i	0.376224	+	0.926529i	$0.377222\pi$
$74$	6.37040	−	6.41117i	0.740544	−	0.745283i
$75$	−1.00778	+	3.76109i	−0.116368	+	0.434293i
$76$	−0.647858	−	2.35757i	−0.0743144	−	0.270432i
$77$		0			0
$78$	−4.67141	−	8.03184i	−0.528933	−	0.909427i
$79$	6.06076	+	10.4976i	0.681889	+	1.18107i	0.974404	+	0.224806i	$0.0721748\pi$
$79$	6.06076	+	10.4976i	0.681889	+	1.18107i	−0.292514	+	0.956261i	$0.594492\pi$
$80$	−3.21223	−	3.13129i	−0.359138	−	0.350089i
$81$	0.214336	−	0.371241i	0.0238151	−	0.0412490i
$82$	−3.09824	+	5.40606i	−0.342143	+	0.596999i
$83$	12.3456	−	12.3456i	1.35511	−	1.35511i	0.475260	−	0.879845i	$-0.342354\pi$
$83$	12.3456	−	12.3456i	1.35511	−	1.35511i	0.879845	−	0.475260i	$-0.157646\pi$
$84$		0			0
$85$	0.786717	+	0.786717i	0.0853314	+	0.0853314i
$86$	2.06125	+	7.59568i	0.222270	+	0.819063i
$87$	−1.94691	−	1.12405i	−0.208730	−	0.120511i
$88$	−1.44776	−	5.20342i	−0.154332	−	0.554686i
$89$	12.7823	−	7.37988i	1.35492	−	0.782265i	0.365989	−	0.930619i	$-0.380731\pi$
$89$	12.7823	−	7.37988i	1.35492	−	0.782265i	0.988934	+	0.148354i	$0.0473975\pi$
$90$	−0.777702	+	2.93990i	−0.0819770	+	0.309893i
$91$		0			0
$92$	10.4274	+	5.93187i	1.08713	+	0.618441i
$93$	6.34354	+	1.69975i	0.657794	+	0.176255i
$94$	−0.0133260	−	4.17779i	−0.00137447	−	0.430906i
$95$	0.685495	−	1.18731i	0.0703303	−	0.121816i
$96$	−4.22775	−	4.09501i	−0.431493	−	0.417945i
$97$	−9.55202			−0.969860			−0.484930	−	0.874553i	$-0.661155\pi$
$97$	−9.55202			−0.969860			−0.484930	+	0.874553i	$0.661155\pi$
$98$		0			0
$99$	−2.58901	+	2.58901i	−0.260206	+	0.260206i
$100$	0.0477470	+	7.48442i	0.00477470	+	0.748442i
$101$	7.64571	−	2.04866i	0.760776	−	0.203849i	0.142483	−	0.989797i	$-0.454491\pi$
$101$	7.64571	−	2.04866i	0.760776	−	0.203849i	0.618293	+	0.785948i	$0.287825\pi$
$102$	1.03551	+	1.02893i	0.102531	+	0.101879i
$103$	15.0619	−	8.69598i	1.48409	−	0.856841i	0.484255	−	0.874927i	$-0.339091\pi$
$103$	15.0619	−	8.69598i	1.48409	−	0.856841i	0.999836	+	0.0180858i	$0.00575720\pi$
$104$	−12.7493	−	12.5076i	−1.25017	−	1.22647i
$105$		0			0
$106$	−11.1849	−	2.95879i	−1.08638	−	0.287383i
$107$	4.97478	−	18.5661i	0.480931	−	1.79486i	−0.116795	−	0.993156i	$-0.537262\pi$
$107$	4.97478	−	18.5661i	0.480931	−	1.79486i	0.597725	−	0.801701i	$-0.296071\pi$
$108$	−2.58536	+	9.90092i	−0.248776	+	0.952716i
$109$	1.95440	+	7.29392i	0.187197	+	0.698630i	0.994149	+	0.108013i	$0.0344489\pi$
$109$	1.95440	+	7.29392i	0.187197	+	0.698630i	−0.806952	+	0.590617i	$0.798884\pi$
$110$	1.50592	−	2.62765i	0.143584	−	0.250537i
$111$	6.64950			0.631142
$112$		0			0
$113$	6.74986			0.634973			0.317487	−	0.948263i	$-0.397161\pi$
$113$	6.74986			0.634973			0.317487	+	0.948263i	$0.397161\pi$
$114$	0.894443	−	1.56070i	0.0837723	−	0.146173i
$115$	1.74106	+	6.49772i	0.162355	+	0.605915i
$116$	−4.18108	−	1.09178i	−0.388204	−	0.101369i
$117$	−3.13365	+	11.6949i	−0.289706	+	1.08120i
$118$	1.64136	+	0.434196i	0.151100	+	0.0399710i
$119$		0			0
$120$	−0.0315817	−	3.30026i	−0.00288300	−	0.301271i
$121$	−6.36836	+	3.67678i	−0.578942	+	0.334252i
$122$	−7.51455	−	7.46677i	−0.680336	−	0.676009i
$123$	−4.42807	+	1.18650i	−0.399266	+	0.106983i
$124$	12.6234	−	0.0805313i	1.13361	−	0.00723192i
$125$	−6.93268	+	6.93268i	−0.620077	+	0.620077i
$126$		0			0
$127$	−19.9530			−1.77055			−0.885273	−	0.465072i	$-0.846028\pi$
$127$	−19.9530			−1.77055			−0.885273	+	0.465072i	$0.846028\pi$
$128$	−9.92181	−	5.43669i	−0.876973	−	0.480540i
$129$	−2.89524	+	5.01470i	−0.254911	+	0.441519i
$130$	−0.0319446	−	10.0148i	−0.00280172	−	0.878358i
$131$	16.7180	+	4.47958i	1.46066	+	0.391383i	0.899718	−	0.436472i	$-0.143772\pi$
$131$	16.7180	+	4.47958i	1.46066	+	0.391383i	0.560942	+	0.827855i	$0.310439\pi$
$132$	1.96487	−	3.45395i	0.171020	−	0.300628i
$133$		0			0
$134$	4.02234	−	15.2054i	0.347477	−	1.31355i
$135$	−4.96924	+	2.86899i	−0.427684	+	0.246924i
$136$	2.44338	+	1.37968i	0.209518	+	0.118307i
$137$	7.24930	+	4.18538i	0.619349	+	0.357581i	0.776616	−	0.629975i	$-0.216935\pi$
$137$	7.24930	+	4.18538i	0.619349	+	0.357581i	−0.157266	+	0.987556i	$0.550268\pi$
$138$	2.31157	+	8.51812i	0.196774	+	0.725111i
$139$	−3.36051	−	3.36051i	−0.285035	−	0.285035i	0.550078	−	0.835113i	$-0.314598\pi$
$139$	−3.36051	−	3.36051i	−0.285035	−	0.285035i	−0.835113	+	0.550078i	$0.814598\pi$
$140$		0			0
$141$	2.17346	−	2.17346i	0.183038	−	0.183038i
$142$	−4.95967	+	8.65403i	−0.416206	+	0.726230i
$143$	6.02899	−	10.4425i	0.504169	−	0.873247i
$144$	0.0978531	+	7.66900i	0.00815443	+	0.639084i
$145$	−1.21155	−	2.09847i	−0.100614	−	0.174269i
$146$	9.58716	+	16.4838i	0.793439	+	1.36421i
$147$		0			0
$148$	12.3248	−	3.38682i	1.01309	−	0.278395i
$149$	−0.852573	+	3.18185i	−0.0698455	+	0.260667i	−0.992015	−	0.126119i	$-0.959748\pi$
$149$	−0.852573	+	3.18185i	−0.0698455	+	0.260667i	0.922170	+	0.386786i	$0.126415\pi$
$150$	−3.88132	+	3.90616i	−0.316909	+	0.318937i
$151$	3.29450	+	1.90208i	0.268103	+	0.154789i	0.628025	−	0.778193i	$-0.283863\pi$
$151$	3.29450	+	1.90208i	0.268103	+	0.154789i	−0.359922	+	0.932982i	$0.617197\pi$
$152$	0.862920	−	3.34830i	0.0699921	−	0.271583i
$153$		−	1.90220i		−	0.153784i
$154$		0			0
$155$	5.00531	+	5.00531i	0.402036	+	0.402036i
$156$	−0.0838265	−	13.1399i	−0.00671149	−	1.05204i
$157$	1.25781	+	4.69422i	0.100384	+	0.374639i	0.997781	−	0.0665859i	$-0.0212106\pi$
$157$	1.25781	+	4.69422i	0.100384	+	0.374639i	−0.897396	+	0.441225i	$0.854544\pi$
$158$	0.0546794	+	17.1423i	0.00435006	+	1.36377i
$159$	−4.25607	−	7.37173i	−0.337528	−	0.584616i
$160$	−1.73948	−	6.10091i	−0.137518	−	0.482319i
$161$		0			0
$162$	0.524045	−	0.304790i	0.0411729	−	0.0239466i
$163$	−10.6510	−	2.85392i	−0.834248	−	0.223536i	−0.183682	−	0.982986i	$-0.558802\pi$
$163$	−10.6510	−	2.85392i	−0.834248	−	0.223536i	−0.650566	+	0.759450i	$0.725468\pi$
$164$	−7.60304	+	4.45453i	−0.593698	+	0.347840i
$165$	2.15230	−	0.576706i	0.167556	−	0.0448965i
$166$	23.8294	−	6.46659i	1.84952	−	0.501905i
$167$		−	9.05247i		−	0.700502i	−0.936656	−	0.350251i	$-0.886096\pi$
$167$		−	9.05247i		−	0.700502i	0.936656	−	0.350251i	$-0.113904\pi$
$168$		0			0
$169$		−	26.8730i		−	2.06716i
$170$	0.412080	+	1.51851i	0.0316051	+	0.116465i
$171$	−2.26413	+	0.606672i	−0.173142	+	0.0463934i
$172$	−2.81212	+	10.7693i	−0.214422	+	0.821152i
$173$	−19.1688	−	5.13627i	−1.45738	−	0.390503i	−0.558794	−	0.829306i	$-0.688736\pi$
$173$	−19.1688	−	5.13627i	−1.45738	−	0.390503i	−0.898583	+	0.438803i	$0.855402\pi$
$174$	−1.59842	−	2.74826i	−0.121176	−	0.208345i
$175$		0			0
$176$	1.88264	−	7.40262i	0.141909	−	0.557994i
$177$	0.624569	+	1.08178i	0.0469454	+	0.0813119i
$178$	20.8733	−	0.0665803i	1.56452	−	0.00499040i
$179$	−1.16742	−	4.35687i	−0.0872570	−	0.325648i	0.908475	−	0.417939i	$-0.137248\pi$
$179$	−1.16742	−	4.35687i	−0.0872570	−	0.325648i	−0.995732	+	0.0922915i	$0.970581\pi$
$180$	−3.02157	+	3.06037i	−0.225214	+	0.228106i
$181$	3.20937	+	3.20937i	0.238550	+	0.238550i	0.816250	−	0.577699i	$-0.196049\pi$
$181$	3.20937	+	3.20937i	0.238550	+	0.238550i	−0.577699	+	0.816250i	$0.696049\pi$
$182$		0			0
$183$		−	7.79390i		−	0.576142i
$184$	8.62304	+	14.6109i	0.635699	+	1.07713i
$185$	6.20694	+	3.58358i	0.456344	+	0.263470i
$186$	6.58823	+	6.54633i	0.483072	+	0.480000i
$187$	−0.490313	+	1.82987i	−0.0358553	+	0.133814i
$188$	2.92146	−	5.13550i	0.213069	−	0.374545i
$189$		0			0
$190$	1.67601	−	0.974787i	0.121591	−	0.0707185i
$191$	−1.89632	−	3.28453i	−0.137213	−	0.237660i	0.789228	−	0.614101i	$-0.210481\pi$
$191$	−1.89632	−	3.28453i	−0.137213	−	0.237660i	−0.926441	+	0.376441i	$0.877148\pi$
$192$	−2.30783	−	7.99749i	−0.166554	−	0.577169i
$193$	−8.73269	+	15.1255i	−0.628593	+	1.08875i	0.359242	+	0.933245i	$0.383035\pi$
$193$	−8.73269	+	15.1255i	−0.628593	+	1.08875i	−0.987834	+	0.155510i	$0.950298\pi$
$194$	−11.7203	−	6.71695i	−0.841466	−	0.482249i
$195$	5.21012	−	5.21012i	0.373105	−	0.373105i
$196$		0			0
$197$	3.79497	+	3.79497i	0.270380	+	0.270380i	0.829253	−	0.558873i	$-0.188766\pi$
$197$	3.79497	+	3.79497i	0.270380	+	0.270380i	−0.558873	+	0.829253i	$0.688766\pi$
$198$	−4.99729	+	1.35612i	−0.355142	+	0.0963752i
$199$	2.32214	+	1.34069i	0.164612	+	0.0950387i	0.580043	−	0.814586i	$-0.303036\pi$
$199$	2.32214	+	1.34069i	0.164612	+	0.0950387i	−0.415431	+	0.909625i	$0.636369\pi$
$200$	−5.20443	+	9.21691i	−0.368009	+	0.651734i
$201$	10.0215	−	5.78593i	0.706864	−	0.408108i
$202$	10.8218	+	2.86274i	0.761423	+	0.201422i
$203$		0			0
$204$	0.547030	+	1.99066i	0.0382998	+	0.139374i
$205$	−4.77280	−	1.27887i	−0.333346	−	0.0893199i
$206$	24.5958	−	0.0784540i	1.71367	−	0.00546615i
$207$	5.75057	−	9.96027i	0.399692	−	0.692287i
$208$	−6.84800	−	24.3120i	−0.474824	−	1.68573i
$209$	2.33442			0.161475
$210$		0			0
$211$	13.8800	−	13.8800i	0.955539	−	0.955539i	−0.0435139	−	0.999053i	$-0.513855\pi$
$211$	13.8800	−	13.8800i	0.955539	−	0.955539i	0.999053	+	0.0435139i	$0.0138553\pi$
$212$	−11.6432	−	11.4956i	−0.799662	−	0.789523i
$213$	−7.08847	+	1.89935i	−0.485694	+	0.130141i
$214$	19.1597	−	19.2823i	1.30973	−	1.31811i
$215$	−5.40509	+	3.12063i	−0.368624	+	0.212825i
$216$	−10.1345	+	10.3304i	−0.689566	+	0.702891i
$217$		0			0
$218$	−2.73102	+	10.3239i	−0.184968	+	0.699224i
$219$	−3.63114	+	13.5516i	−0.245370	+	0.915733i
$220$	3.69552	−	2.16516i	0.249152	−	0.145975i
$221$	1.62136	+	6.05098i	0.109064	+	0.407033i
$222$	8.15889	+	4.67590i	0.547589	+	0.313826i
$223$	−27.4961			−1.84128			−0.920638	−	0.390417i	$-0.872331\pi$
$223$	−27.4961			−1.84128			−0.920638	+	0.390417i	$0.872331\pi$
$224$		0			0
$225$	7.17549			0.478366
$226$	8.28203	+	4.74648i	0.550913	+	0.315731i
$227$	−4.51157	−	16.8374i	−0.299443	−	1.11754i	−0.937624	−	0.347651i	$-0.886980\pi$
$227$	−4.51157	−	16.8374i	−0.299443	−	1.11754i	0.638181	−	0.769886i	$-0.279687\pi$
$228$	2.19495	−	1.28600i	0.145364	−	0.0851672i
$229$	−0.986767	+	3.68266i	−0.0652074	+	0.243357i	−0.990835	−	0.135079i	$-0.956871\pi$
$229$	−0.986767	+	3.68266i	−0.0652074	+	0.243357i	0.925628	+	0.378436i	$0.123538\pi$
$230$	−2.43291	+	9.19697i	−0.160421	+	0.606430i
$231$		0			0
$232$	−4.36243	−	4.27973i	−0.286408	−	0.280978i
$233$	−12.3245	+	7.11557i	−0.807407	+	0.466157i	−0.846055	−	0.533096i	$-0.821028\pi$
$233$	−12.3245	+	7.11557i	−0.807407	+	0.466157i	0.0386475	+	0.999253i	$0.487695\pi$
$234$	−12.0688	+	12.1460i	−0.788962	+	0.794012i
$235$	3.20014	−	0.857474i	0.208754	−	0.0559355i
$236$	1.70862	+	1.68696i	0.111222	+	0.109812i
$237$	−8.91815	+	8.91815i	−0.579296	+	0.579296i
$238$		0			0
$239$	−10.3101			−0.666903			−0.333451	−	0.942767i	$-0.608213\pi$
$239$	−10.3101			−0.666903			−0.333451	+	0.942767i	$0.608213\pi$
$240$	2.28198	−	4.07161i	0.147301	−	0.262821i
$241$	−9.82271	+	17.0134i	−0.632736	+	1.09593i	0.354253	+	0.935149i	$0.384735\pi$
$241$	−9.82271	+	17.0134i	−0.632736	+	1.09593i	−0.986990	+	0.160782i	$0.948598\pi$
$242$	−10.3994	+	0.0331714i	−0.668501	+	0.00213234i
$243$	15.2572	+	4.08814i	0.978747	+	0.262255i
$244$	−3.96971	−	14.4459i	−0.254134	−	0.924803i
$245$		0			0
$246$	−6.26756	−	1.65798i	−0.399605	−	0.105709i
$247$	6.68519	−	3.85970i	0.425368	−	0.245587i
$248$	15.5455	+	8.77792i	0.987138	+	0.557399i
$249$	15.7322	+	9.08301i	0.996990	+	0.575612i
$250$	−13.3814	+	3.63132i	−0.846313	+	0.229665i
$251$	11.9870	+	11.9870i	0.756610	+	0.756610i	0.975704	−	0.219093i	$-0.0703099\pi$
$251$	11.9870	+	11.9870i	0.756610	+	0.756610i	−0.219093	+	0.975704i	$0.570310\pi$
$252$		0			0
$253$	−8.09928	+	8.09928i	−0.509197	+	0.509197i
$254$	−24.4823	−	14.0309i	−1.53615	−	0.880377i
$255$	−0.578810	+	1.00253i	−0.0362465	+	0.0627808i
$256$	−8.35094	−	13.6478i	−0.521934	−	0.852986i
$257$	−2.01973	−	3.49828i	−0.125987	−	0.218216i	0.796131	−	0.605124i	$-0.206877\pi$
$257$	−2.01973	−	3.49828i	−0.125987	−	0.218216i	−0.922118	+	0.386908i	$0.873543\pi$
$258$	−7.07875	+	4.11708i	−0.440704	+	0.256318i
$259$		0			0
$260$	7.00319	−	12.3106i	0.434320	−	0.763471i
$261$	−1.07224	+	4.00166i	−0.0663701	+	0.247697i
$262$	17.3629	+	17.2525i	1.07268	+	1.06586i
$263$	−2.53844	−	1.46557i	−0.156527	−	0.0903708i	0.419691	−	0.907667i	$-0.362139\pi$
$263$	−2.53844	−	1.46557i	−0.156527	−	0.0903708i	−0.576217	+	0.817296i	$0.695472\pi$
$264$	4.83969	−	2.85629i	0.297862	−	0.175792i
$265$		−	9.17481i		−	0.563604i
$266$		0			0
$267$	10.8592	+	10.8592i	0.664570	+	0.664570i
$268$	15.6278	−	15.8285i	0.954619	−	0.966877i
$269$	−2.45103	−	9.14738i	−0.149442	−	0.557726i	−0.999517	−	0.0310645i	$-0.990110\pi$
$269$	−2.45103	−	9.14738i	−0.149442	−	0.557726i	0.850075	−	0.526661i	$-0.176556\pi$
$270$	−8.11470	+	0.0258837i	−0.493845	+	0.00157523i
$271$	−4.71964	−	8.17466i	−0.286698	−	0.496575i	0.686322	−	0.727298i	$-0.259224\pi$
$271$	−4.71964	−	8.17466i	−0.286698	−	0.496575i	−0.973019	+	0.230723i	$0.925891\pi$
$272$	2.02783	+	3.41104i	0.122955	+	0.206825i
$273$		0			0
$274$	5.95170	+	10.2331i	0.359555	+	0.618206i
$275$	−6.90265	−	1.84956i	−0.416245	−	0.111533i
$276$	−3.15363	+	12.0772i	−0.189826	+	0.726961i
$277$	5.98348	−	1.60327i	0.359512	−	0.0963310i	−0.0745417	−	0.997218i	$-0.523749\pi$
$277$	5.98348	−	1.60327i	0.359512	−	0.0963310i	0.434054	+	0.900887i	$0.357083\pi$
$278$	−1.76023	−	6.48642i	−0.105571	−	0.389030i
$279$		−	12.1023i		−	0.724548i
$280$		0			0
$281$		−	27.8512i		−	1.66146i	−0.556673	−	0.830732i	$-0.687922\pi$
$281$		−	27.8512i		−	1.66146i	0.556673	−	0.830732i	$-0.312078\pi$
$282$	4.19519	−	1.13845i	0.249820	−	0.0677939i
$283$	−23.2155	+	6.22059i	−1.38002	+	0.369775i	−0.871129	−	0.491055i	$-0.836611\pi$
$283$	−23.2155	+	6.22059i	−1.38002	+	0.369775i	−0.508892	+	0.860830i	$0.669945\pi$
$284$	−12.1710	+	7.13082i	−0.722214	+	0.423136i
$285$	1.37788	+	0.369201i	0.0816184	+	0.0218696i
$286$	14.7407	−	8.57334i	0.871635	−	0.506952i
$287$		0			0
$288$	−5.27275	+	9.47863i	−0.310700	+	0.558534i
$289$	8.00790	+	13.8701i	0.471053	+	0.815887i
$290$	−0.0109305	−	3.42678i	−0.000641860	−	0.201227i
$291$	−2.57231	−	9.60000i	−0.150792	−	0.562762i
$292$	0.172038	+	26.9672i	0.0100678	+	1.57814i
$293$	−1.30078	−	1.30078i	−0.0759921	−	0.0759921i	0.668089	−	0.744081i	$-0.267112\pi$
$293$	−1.30078	−	1.30078i	−0.0759921	−	0.0759921i	−0.744081	+	0.668089i	$0.767112\pi$
$294$		0			0
$295$			1.34638i			0.0783894i
$296$	17.5040	+	4.51111i	1.01740	+	0.262203i
$297$	−8.46125	−	4.88510i	−0.490971	−	0.283462i
$298$	−3.28356	+	3.30458i	−0.190212	+	0.191429i
$299$	−9.80307	+	36.5856i	−0.566926	+	2.11580i
$300$	−7.50916	+	2.06351i	−0.433542	+	0.119137i
$301$		0			0
$302$	2.70480	+	4.65053i	0.155644	+	0.267608i
$303$	4.11791	+	7.13242i	0.236567	+	0.409747i
$304$	3.41331	−	3.50154i	0.195767	−	0.200827i
$305$	4.20033	−	7.27518i	0.240510	−	0.416576i
$306$	1.33762	−	2.33399i	0.0764668	−	0.133425i
$307$	−1.33097	+	1.33097i	−0.0759626	+	0.0759626i	−0.744067	−	0.668105i	$-0.767106\pi$
$307$	−1.33097	+	1.33097i	−0.0759626	+	0.0759626i	0.668105	+	0.744067i	$0.267106\pi$
$308$		0			0
$309$	12.7958	+	12.7958i	0.727926	+	0.727926i
$310$	2.62177	+	9.66121i	0.148907	+	0.548720i
$311$	−11.9362	−	6.89135i	−0.676838	−	0.390772i	0.121825	−	0.992552i	$-0.461125\pi$
$311$	−11.9362	−	6.89135i	−0.676838	−	0.390772i	−0.798663	+	0.601779i	$0.794459\pi$
$312$	9.13711	−	16.1816i	0.517287	−	0.916101i
$313$	−0.733620	+	0.423556i	−0.0414666	+	0.0239408i	−0.520590	−	0.853807i	$-0.674288\pi$
$313$	−0.733620	+	0.423556i	−0.0414666	+	0.0239408i	0.479123	+	0.877748i	$0.340955\pi$
$314$	−1.75763	+	6.64427i	−0.0991888	+	0.374958i
$315$		0			0
$316$	−11.9873	+	21.0720i	−0.674341	+	1.18539i
$317$	15.7173	+	4.21144i	0.882772	+	0.236538i	0.671603	−	0.740911i	$-0.265606\pi$
$317$	15.7173	+	4.21144i	0.882772	+	0.236538i	0.211169	+	0.977449i	$0.432273\pi$
$318$	−0.0383977	−	12.0379i	−0.00215324	−	0.675053i
$319$	2.06294	−	3.57312i	0.115503	−	0.200056i
$320$	2.15581	−	8.70897i	0.120513	−	0.486846i
$321$	19.9991			1.11624
$322$		0			0
$323$	−0.857573	+	0.857573i	−0.0477166	+	0.0477166i
$324$	0.857327	−	0.00546934i	0.0476293	−	0.000303852i
$325$	−22.8255	+	6.11608i	−1.26613	+	0.339259i
$326$	−11.0618	−	10.9915i	−0.612657	−	0.608761i
$327$	−6.80425	+	3.92843i	−0.376276	+	0.217243i
$328$	−12.4613	+	0.119248i	−0.688060	+	0.00658435i
$329$		0			0
$330$	3.04639	+	0.805873i	0.167698	+	0.0443618i
$331$	−1.16154	+	4.33493i	−0.0638441	+	0.238269i	−0.990473	−	0.137708i	$-0.956026\pi$
$331$	−1.16154	+	4.33493i	−0.0638441	+	0.238269i	0.926629	+	0.375978i	$0.122693\pi$
$332$	33.7858	+	8.82225i	1.85424	+	0.484184i
$333$	−3.17152	−	11.8363i	−0.173798	−	0.648623i
$334$	6.36567	−	11.1073i	0.348314	−	0.607766i
$335$	12.4727			0.681458
$336$		0			0
$337$	0.529441			0.0288405			0.0144202	−	0.999896i	$-0.495410\pi$
$337$	0.529441			0.0288405			0.0144202	+	0.999896i	$0.495410\pi$
$338$	18.8970	−	32.9730i	1.02786	−	1.79350i
$339$	1.81770	+	6.78377i	0.0987242	+	0.368444i
$340$	−0.562193	+	2.15298i	−0.0304892	+	0.116762i
$341$	−3.11951	+	11.6422i	−0.168931	+	0.630459i
$342$	−3.20469	−	0.847746i	−0.173290	−	0.0458409i
$343$		0			0
$344$	−11.0234	+	11.2364i	−0.594342	+	0.605827i
$345$	−6.06150	+	3.49961i	−0.326340	+	0.188413i
$346$	−19.9082	−	19.7816i	−1.07027	−	1.06347i
$347$	1.29357	−	0.346611i	0.0694425	−	0.0186071i	−0.223931	−	0.974605i	$-0.571889\pi$
$347$	1.29357	−	0.346611i	0.0694425	−	0.0186071i	0.293373	+	0.955998i	$0.405222\pi$
$348$	−0.0286830	−	4.49610i	−0.00153757	−	0.241016i
$349$	−10.5875	+	10.5875i	−0.566737	+	0.566737i	−0.931213	−	0.364476i	$-0.881248\pi$
$349$	−10.5875	+	10.5875i	−0.566737	+	0.566737i	0.364476	+	0.931213i	$0.381248\pi$
$350$		0			0
$351$	−32.3079			−1.72447
$352$	7.51548	−	7.75911i	0.400577	−	0.413562i
$353$	15.4522	−	26.7641i	0.822440	−	1.42451i	−0.0814202	−	0.996680i	$-0.525946\pi$
$353$	15.4522	−	26.7641i	0.822440	−	1.42451i	0.903860	−	0.427828i	$-0.140721\pi$
$354$	0.00563477	+	1.76654i	0.000299485	+	0.0938904i
$355$	−7.64030	−	2.04721i	−0.405505	−	0.108655i
$356$	25.6583	+	14.5964i	1.35989	+	0.773606i
$357$		0			0
$358$	1.63132	−	6.16678i	0.0862179	−	0.325924i
$359$	−24.6970	+	14.2588i	−1.30346	+	0.752552i	−0.980995	−	0.194031i	$-0.937844\pi$
$359$	−24.6970	+	14.2588i	−1.30346	+	0.752552i	−0.322462	+	0.946582i	$0.604511\pi$
$360$	−5.85948	+	1.63030i	−0.308822	+	0.0859241i
$361$	−15.1602	−	8.75277i	−0.797907	−	0.460672i
$362$	1.68106	+	6.19469i	0.0883545	+	0.325586i
$363$	−5.41022	−	5.41022i	−0.283963	−	0.283963i
$364$		0			0
$365$	−10.6928	+	10.6928i	−0.559686	+	0.559686i
$366$	5.48064	−	9.56307i	0.286478	−	0.499870i
$367$	−0.668312	+	1.15755i	−0.0348856	+	0.0604236i	−0.882941	−	0.469484i	$-0.844440\pi$
$367$	−0.668312	+	1.15755i	−0.0348856	+	0.0604236i	0.848055	+	0.529907i	$0.177773\pi$
$368$	0.306116	+	23.9911i	0.0159574	+	1.25062i
$369$	4.22399	+	7.31616i	0.219892	+	0.380864i
$370$	5.09592	+	8.76173i	0.264924	+	0.455501i
$371$		0			0
$372$	3.48036	+	12.6651i	0.180448	+	0.656656i
$373$	2.49002	−	9.29287i	0.128928	−	0.481166i	−0.871021	−	0.491246i	$-0.836542\pi$
$373$	2.49002	−	9.29287i	0.128928	−	0.481166i	0.999949	+	0.0100792i	$0.00320838\pi$
$374$	−1.88837	+	1.90046i	−0.0976454	+	0.0982704i
$375$	−8.83444	−	5.10057i	−0.456209	−	0.263392i
$376$	7.19588	−	4.24687i	0.371099	−	0.219015i
$377$		−	13.6434i		−	0.702670i
$378$		0			0
$379$	−5.95022	−	5.95022i	−0.305642	−	0.305642i	0.537574	−	0.843217i	$-0.319341\pi$
$379$	−5.95022	−	5.95022i	−0.305642	−	0.305642i	−0.843217	+	0.537574i	$0.819341\pi$
$380$	2.74192	−	0.0174922i	0.140658	−	0.000897329i
$381$	−5.37326	−	20.0533i	−0.275280	−	1.02736i
$382$	−0.0171084	−	5.36358i	−0.000875341	−	0.274425i
$383$	−13.3692	−	23.1561i	−0.683134	−	1.18322i	−0.974019	−	0.226465i	$-0.927283\pi$
$383$	−13.3692	−	23.1561i	−0.683134	−	1.18322i	0.290885	−	0.956758i	$-0.406050\pi$
$384$	2.79211	−	11.4357i	0.142484	−	0.583577i
$385$		0			0
$386$	−21.3511	+	12.4181i	−1.08674	+	0.632062i
$387$	10.3072	+	2.76180i	0.523943	+	0.140390i
$388$	−9.65737	−	16.4833i	−0.490279	−	0.836813i
$389$	11.0157	−	2.95165i	0.558518	−	0.149654i	0.0314927	−	0.999504i	$-0.489974\pi$
$389$	11.0157	−	2.95165i	0.558518	−	0.149654i	0.527025	+	0.849849i	$0.323307\pi$
$390$	10.0565	−	2.72905i	0.509232	−	0.138191i
$391$		−	5.95071i		−	0.300940i
$392$		0			0
$393$			18.0083i			0.908400i
$394$	1.98780	+	7.32502i	0.100144	+	0.369029i
$395$	−13.1308	+	3.51839i	−0.660684	+	0.177030i
$396$	−7.08526	−	1.85013i	−0.356048	−	0.0929724i
$397$	−26.8811	−	7.20277i	−1.34912	−	0.361497i	−0.489312	−	0.872109i	$-0.662752\pi$
$397$	−26.8811	−	7.20277i	−1.34912	−	0.361497i	−0.859811	+	0.510612i	$0.829419\pi$
$398$	1.90648	+	3.27793i	0.0955633	+	0.164308i
$399$		0			0
$400$	−12.8671	+	7.64936i	−0.643356	+	0.382468i
$401$	−6.45526	−	11.1808i	−0.322360	−	0.558344i	0.658614	−	0.752481i	$-0.271143\pi$
$401$	−6.45526	−	11.1808i	−0.322360	−	0.558344i	−0.980975	+	0.194137i	$0.937810\pi$
$402$	16.3650	−	0.0521999i	0.816212	−	0.00260350i
$403$	10.3155	+	38.4980i	0.513853	+	1.91772i
$404$	11.2653	+	11.1225i	0.560468	+	0.553363i
$405$	0.339939	+	0.339939i	0.0168917	+	0.0168917i
$406$		0			0
$407$			12.2037i			0.604915i
$408$	−0.728622	+	2.82720i	−0.0360722	+	0.139967i
$409$	−13.0138	−	7.51352i	−0.643491	−	0.371520i	0.142467	−	0.989800i	$-0.454496\pi$
$409$	−13.0138	−	7.51352i	−0.643491	−	0.371520i	−0.785958	+	0.618280i	$0.787830\pi$
$410$	−4.95690	−	4.92538i	−0.244804	−	0.243247i
$411$	−2.25421	+	8.41282i	−0.111192	+	0.414974i
$412$	30.2341	+	17.1994i	1.48953	+	0.847356i
$413$		0			0
$414$	14.0599	−	8.17742i	0.691008	−	0.401898i
$415$	9.79012	+	16.9570i	0.480578	+	0.832386i
$416$	8.69366	−	34.6462i	0.426242	−	1.69867i
$417$	2.47242	−	4.28236i	0.121075	−	0.209708i
$418$	2.86432	+	1.64155i	0.140098	+	0.0802910i
$419$	−6.32749	+	6.32749i	−0.309118	+	0.309118i	−0.844567	−	0.535449i	$-0.820142\pi$
$419$	−6.32749	+	6.32749i	−0.309118	+	0.309118i	0.535449	+	0.844567i	$0.320142\pi$
$420$		0			0
$421$	18.5385	+	18.5385i	0.903511	+	0.903511i	0.995738	−	0.0922266i	$-0.0293984\pi$
$421$	18.5385	+	18.5385i	0.903511	+	0.903511i	−0.0922266	+	0.995738i	$0.529398\pi$
$422$	26.7911	−	7.27031i	1.30417	−	0.353913i
$423$	−4.90545	−	2.83216i	−0.238511	−	0.137705i
$424$	−6.20251	−	22.2926i	−0.301220	−	1.08262i
$425$	3.21522	−	1.85631i	0.155961	−	0.0900441i
$426$	−10.0331	−	2.65410i	−0.486106	−	0.128591i
$427$		0			0
$428$	37.0681	−	10.1862i	1.79175	−	0.492371i
$429$	12.1186	+	3.24716i	0.585089	+	0.156774i
$430$	−8.82643	+	0.0281539i	−0.425648	+	0.00135770i
$431$	2.22036	−	3.84578i	0.106951	−	0.185245i	−0.807583	−	0.589754i	$-0.799225\pi$
$431$	2.22036	−	3.84578i	0.106951	−	0.185245i	0.914534	+	0.404510i	$0.132558\pi$
$432$	−19.6993	+	5.54872i	−0.947781	+	0.266963i
$433$	−19.9611			−0.959270			−0.479635	−	0.877468i	$-0.659231\pi$
$433$	−19.9611			−0.959270			−0.479635	+	0.877468i	$0.659231\pi$
$434$		0			0
$435$	1.78275	−	1.78275i	0.0854764	−	0.0854764i
$436$	−10.6107	+	10.7469i	−0.508160	+	0.514685i
$437$	−7.08294	+	1.89787i	−0.338823	+	0.0907873i
$438$	−13.9848	+	14.0743i	−0.668221	+	0.672498i
$439$	−13.9312	+	8.04316i	−0.664898	+	0.383879i	−0.794141	−	0.607734i	$-0.792079\pi$
$439$	−13.9312	+	8.04316i	−0.664898	+	0.383879i	0.129243	+	0.991613i	$0.458745\pi$
$440$	6.05691	−	0.0579612i	0.288752	−	0.00276319i
$441$		0			0
$442$	−2.26564	+	8.56465i	−0.107765	+	0.407379i
$443$	6.98583	−	26.0715i	0.331907	−	1.23869i	−0.575277	−	0.817959i	$-0.695106\pi$
$443$	6.98583	−	26.0715i	0.331907	−	1.23869i	0.907184	−	0.420734i	$-0.138228\pi$
$444$	6.72284	+	11.4746i	0.319052	+	0.544561i
$445$	4.28417	+	15.9887i	0.203089	+	0.757938i
$446$	−33.7376	−	19.3352i	−1.59752	−	0.915547i
$447$	−3.42742			−0.162112
$448$		0			0
$449$	−34.9486			−1.64933			−0.824663	−	0.565624i	$-0.808635\pi$
$449$	−34.9486			−1.64933			−0.824663	+	0.565624i	$0.808635\pi$
$450$	8.80428	+	5.04578i	0.415038	+	0.237860i
$451$	−2.17756	−	8.12675i	−0.102537	−	0.382674i
$452$	6.82430	+	11.6478i	0.320988	+	0.547866i
$453$	−1.02444	+	3.82328i	−0.0481326	+	0.179633i
$454$	6.30433	−	23.8319i	0.295877	−	1.11849i
$455$		0			0
$456$	3.59750	−	0.0344261i	0.168468	−	0.00161215i
$457$	−16.7124	+	9.64891i	−0.781773	+	0.451357i	−0.837058	−	0.547113i	$-0.815727\pi$
$457$	−16.7124	+	9.64891i	−0.781773	+	0.451357i	0.0552850	+	0.998471i	$0.482393\pi$
$458$	−3.80039	+	3.82471i	−0.177581	+	0.178717i
$459$	4.90292	−	1.31373i	0.228849	−	0.0613199i
$460$	−9.45244	+	9.57382i	−0.440722	+	0.446381i
$461$	25.9786	−	25.9786i	1.20994	−	1.20994i	0.238899	−	0.971044i	$-0.423213\pi$
$461$	25.9786	−	25.9786i	1.20994	−	1.20994i	0.971044	−	0.238899i	$-0.0767866\pi$
$462$		0			0
$463$	27.5321			1.27953			0.639764	−	0.768572i	$-0.279032\pi$
$463$	27.5321			1.27953			0.639764	+	0.768572i	$0.279032\pi$
$464$	−2.34318	−	8.31885i	−0.108780	−	0.386193i
$465$	−3.68255	+	6.37836i	−0.170774	+	0.295790i
$466$	−20.1258	+	0.0641958i	−0.932309	+	0.00297381i
$467$	9.98249	+	2.67480i	0.461934	+	0.123775i	0.482278	−	0.876018i	$-0.339809\pi$
$467$	9.98249	+	2.67480i	0.461934	+	0.123775i	−0.0203439	+	0.999793i	$0.506476\pi$
$468$	−23.3494	+	6.41638i	−1.07933	+	0.296597i
$469$		0			0
$470$	4.52952	+	1.19821i	0.208931	+	0.0552693i
$471$	−4.37908	+	2.52826i	−0.201777	+	0.116496i
$472$	0.910204	+	3.27138i	0.0418955	+	0.150578i
$473$	−9.20337	−	5.31357i	−0.423171	−	0.244318i
$474$	−17.2137	+	4.67131i	−0.790653	+	0.214560i
$475$	−3.23493	−	3.23493i	−0.148429	−	0.148429i
$476$		0			0
$477$	−11.0919	+	11.0919i	−0.507863	+	0.507863i
$478$	−12.6504	−	7.25001i	−0.578616	−	0.331608i
$479$	−2.69651	+	4.67049i	−0.123207	+	0.213400i	−0.921030	−	0.389491i	$-0.872651\pi$
$479$	−2.69651	+	4.67049i	−0.123207	+	0.213400i	0.797824	+	0.602890i	$0.205984\pi$
$480$	5.66312	−	3.39116i	0.258485	−	0.154785i
$481$	20.1774	+	34.9483i	0.920012	+	1.59351i
$482$	−24.0162	+	13.9681i	−1.09391	+	0.636229i
$483$		0			0
$484$	−12.7834	−	7.27215i	−0.581063	−	0.330552i
$485$	2.77257	−	10.3474i	0.125896	−	0.469850i
$486$	15.8457	+	15.7449i	0.718774	+	0.714204i
$487$	14.4250	+	8.32830i	0.653661	+	0.377391i	0.789857	−	0.613291i	$-0.210155\pi$
$487$	14.4250	+	8.32830i	0.653661	+	0.377391i	−0.136197	+	0.990682i	$0.543488\pi$
$488$	5.28749	−	20.5165i	0.239353	−	0.928738i
$489$		−	11.4730i		−	0.518828i
$490$		0			0
$491$	19.7533	+	19.7533i	0.891454	+	0.891454i	0.994660	−	0.103206i	$-0.0329100\pi$
$491$	19.7533	+	19.7533i	0.891454	+	0.891454i	−0.103206	+	0.994660i	$0.532910\pi$
$492$	−6.52437	−	6.44165i	−0.294141	−	0.290412i
$493$	0.554780	+	2.07047i	0.0249860	+	0.0932492i
$494$	10.9168	−	0.0348217i	0.491171	−	0.00156670i
$495$	−2.05310	−	3.55607i	−0.0922800	−	0.159834i
$496$	12.9016	+	21.7020i	0.579299	+	0.974447i
$497$		0			0
$498$	12.9162	+	22.2077i	0.578789	+	0.995149i
$499$	−10.5108	−	2.81637i	−0.470530	−	0.126078i	0.0157598	−	0.999876i	$-0.494983\pi$
$499$	−10.5108	−	2.81637i	−0.470530	−	0.126078i	−0.486290	+	0.873798i	$0.661650\pi$
$500$	−18.9724	−	4.95414i	−0.848472	−	0.221556i
$501$	9.09795	−	2.43779i	0.406467	−	0.108912i
$502$	6.27874	+	23.1371i	0.280234	+	1.03266i
$503$			40.5320i			1.80723i	0.428341	+	0.903617i	$0.359098\pi$
$503$			40.5320i			1.80723i	−0.428341	+	0.903617i	$0.640902\pi$
$504$		0			0
$505$			8.87697i			0.395020i
$506$	−15.6331	+	4.24238i	−0.694978	+	0.188597i
$507$	27.0080	−	7.23678i	1.19947	−	0.321397i
$508$	−20.1731	−	34.4317i	−0.895036	−	1.52766i
$509$	−4.21708	−	1.12996i	−0.186919	−	0.0500848i	0.164145	−	0.986436i	$-0.447513\pi$
$509$	−4.21708	−	1.12996i	−0.186919	−	0.0500848i	−0.351064	+	0.936351i	$0.614180\pi$
$510$	−1.41517	+	0.823079i	−0.0626648	+	0.0364466i
$511$		0			0
$512$	−0.649486	−	22.6181i	−0.0287035	−	0.999588i
$513$	−3.12739	−	5.41680i	−0.138078	−	0.239158i
$514$	−0.0182217	−	5.71263i	−0.000803727	−	0.251973i
$515$	5.04819	+	18.8401i	0.222450	+	0.830194i
$516$	−11.5807	+	0.0738794i	−0.509812	+	0.00325236i
$517$	3.98891	+	3.98891i	0.175432	+	0.175432i
$518$		0			0
$519$		−	20.6483i		−	0.906359i
$520$	17.2496	−	10.1804i	0.756447	−	0.446440i
$521$	17.7952	+	10.2741i	0.779624	+	0.450116i	0.836297	−	0.548277i	$-0.184716\pi$
$521$	17.7952	+	10.2741i	0.779624	+	0.450116i	−0.0566732	+	0.998393i	$0.518049\pi$
$522$	−4.12959	+	4.15602i	−0.180747	+	0.181904i
$523$	−1.43726	+	5.36392i	−0.0628469	+	0.234548i	−0.990204	−	0.139630i	$-0.955409\pi$
$523$	−1.43726	+	5.36392i	−0.0628469	+	0.234548i	0.927357	+	0.374178i	$0.122075\pi$
$524$	9.17228	+	33.3782i	0.400693	+	1.45813i
$525$		0			0
$526$	−2.08407	−	3.58326i	−0.0908696	−	0.156238i
$527$	−3.13089	−	5.42286i	−0.136384	−	0.236223i
$528$	7.94680	−	0.101398i	0.345840	−	0.00441277i
$529$	6.48964	−	11.2404i	0.282158	−	0.488712i
$530$	6.45170	−	11.2574i	0.280244	−	0.488992i
$531$	1.62771	−	1.62771i	0.0706366	−	0.0706366i
$532$		0			0
$533$	−19.6726	−	19.6726i	−0.852117	−	0.852117i
$534$	5.68801	+	20.9603i	0.246144	+	0.907039i
$535$	18.6681	+	10.7780i	0.807091	+	0.465974i
$536$	30.3057	−	8.43202i	1.30901	−	0.364208i
$537$	4.06438	−	2.34657i	0.175391	−	0.101262i
$538$	3.42500	−	12.9473i	0.147662	−	0.558200i
$539$		0			0
$540$	−9.97489	−	5.67447i	−0.429251	−	0.244190i
$541$	−12.9485	−	3.46954i	−0.556700	−	0.149167i	−0.0305103	−	0.999534i	$-0.509713\pi$
$541$	−12.9485	−	3.46954i	−0.556700	−	0.149167i	−0.526190	+	0.850367i	$0.676380\pi$
$542$	−0.0425800	−	13.3491i	−0.00182897	−	0.573393i
$543$	−2.36122	+	4.08976i	−0.101330	+	0.175508i
$544$	0.0894996	+	5.61128i	0.00383727	+	0.240582i
$545$	−8.46853			−0.362752
$546$		0			0
$547$	5.59249	−	5.59249i	0.239118	−	0.239118i	−0.577367	−	0.816485i	$-0.695920\pi$
$547$	5.59249	−	5.59249i	0.239118	−	0.239118i	0.816485	+	0.577367i	$0.195920\pi$
$548$	0.106801	+	16.7412i	0.00456230	+	0.715148i
$549$	−13.8733	+	3.71734i	−0.592099	+	0.158652i
$550$	−7.16890	−	7.12332i	−0.305683	−	0.303739i
$551$	2.28747	−	1.32067i	0.0974497	−	0.0562626i
$552$	−12.3621	+	12.6010i	−0.526167	+	0.536334i
$553$		0			0
$554$	8.46910	+	2.24036i	0.359818	+	0.0951838i
$555$	−1.93008	+	7.20317i	−0.0819275	+	0.305757i
$556$	2.40144	−	9.19658i	0.101844	−	0.390022i
$557$	−8.36782	−	31.2291i	−0.354556	−	1.32322i	−0.881042	−	0.473038i	$-0.843157\pi$
$557$	−8.36782	−	31.2291i	−0.354556	−	1.32322i	0.526486	−	0.850184i	$-0.323509\pi$
$558$	8.51033	−	14.8495i	0.360271	−	0.628630i
$559$	−35.1416			−1.48633
$560$		0			0
$561$	−1.97111			−0.0832202
$562$	19.5849	−	34.1733i	0.826138	−	1.44151i
$563$	7.50293	+	28.0013i	0.316211	+	1.18012i	0.922857	+	0.385143i	$0.125848\pi$
$563$	7.50293	+	28.0013i	0.316211	+	1.18012i	−0.606646	+	0.794972i	$0.707485\pi$
$564$	5.94803	+	1.55317i	0.250457	+	0.0654002i
$565$	−1.95921	+	7.31188i	−0.0824247	+	0.307613i
$566$	−32.8596	−	8.69247i	−1.38119	−	0.365372i
$567$		0			0
$568$	−19.9481	+	0.190892i	−0.837003	+	0.00800965i
$569$	−4.19339	+	2.42105i	−0.175796	+	0.101496i	−0.585316	−	0.810805i	$-0.699030\pi$
$569$	−4.19339	+	2.42105i	−0.175796	+	0.101496i	0.409520	+	0.912301i	$0.365696\pi$
$570$	1.43103	+	1.42193i	0.0599391	+	0.0595579i
$571$	−0.276160	+	0.0739969i	−0.0115570	+	0.00309668i	−0.264593	−	0.964360i	$-0.585238\pi$
$571$	−0.276160	+	0.0739969i	−0.0115570	+	0.00309668i	0.253036	+	0.967457i	$0.418571\pi$
$572$	24.1155	−	0.153845i	1.00832	−	0.00643259i
$573$	2.79036	−	2.79036i	0.116569	−	0.116569i
$574$		0			0
$575$	22.4473			0.936115
$576$	−13.1350	+	7.92245i	−0.547291	+	0.330102i
$577$	−12.8069	+	22.1821i	−0.533157	+	0.923455i	0.466093	+	0.884736i	$0.345661\pi$
$577$	−12.8069	+	22.1821i	−0.533157	+	0.923455i	−0.999250	+	0.0387193i	$0.987672\pi$
$578$	0.0722462	+	22.6496i	0.00300505	+	0.942101i
$579$	−17.5531	−	4.70334i	−0.729483	−	0.195464i
$580$	2.39629	−	4.21232i	0.0995004	−	0.174907i
$581$		0			0
$582$	3.59448	−	13.5880i	0.148996	−	0.563240i
$583$	13.5292	−	7.81108i	0.560322	−	0.323502i
$584$	−18.7522	+	33.2096i	−0.775970	+	1.37422i
$585$	−11.7591	−	6.78914i	−0.486181	−	0.280696i
$586$	−0.681343	−	2.51074i	−0.0281460	−	0.103718i
$587$	24.5903	+	24.5903i	1.01495	+	1.01495i	0.999887	+	0.0150628i	$0.00479482\pi$
$587$	24.5903	+	24.5903i	1.01495	+	1.01495i	0.0150628	+	0.999887i	$0.495205\pi$
$588$		0			0
$589$	−5.45612	+	5.45612i	−0.224815	+	0.224815i
$590$	−0.946772	+	1.65200i	−0.0389780	+	0.0680119i
$591$	−2.79207	+	4.83600i	−0.114850	+	0.198927i
$592$	18.3051	+	17.8439i	0.752335	+	0.733378i
$593$	−12.0148	−	20.8103i	−0.493390	−	0.854576i	0.506581	−	0.862192i	$-0.330909\pi$
$593$	−12.0148	−	20.8103i	−0.493390	−	0.854576i	−0.999971	+	0.00761620i	$0.997576\pi$
$594$	−6.94671	−	11.9439i	−0.285027	−	0.490065i
$595$		0			0
$596$	−6.35268	+	1.74571i	−0.260216	+	0.0715070i
$597$	−0.722081	+	2.69484i	−0.0295528	+	0.110293i
$598$	−37.7551	+	37.9968i	−1.54392	+	1.55380i
$599$	12.0280	+	6.94436i	0.491450	+	0.283739i	0.725176	−	0.688564i	$-0.241758\pi$
$599$	12.0280	+	6.94436i	0.491450	+	0.283739i	−0.233726	+	0.972303i	$0.575092\pi$
$600$	−10.6647	−	2.74851i	−0.435387	−	0.112207i
$601$			2.22402i			0.0907196i	0.998971	+	0.0453598i	$0.0144434\pi$
$601$			2.22402i			0.0907196i	−0.998971	+	0.0453598i	$0.985557\pi$
$602$		0			0
$603$	−15.0789	−	15.0789i	−0.614061	−	0.614061i
$604$	0.0485365	+	7.60818i	0.00197492	+	0.309572i
$605$	−2.13444	−	7.96585i	−0.0867774	−	0.323858i
$606$	0.0371512	+	11.6471i	0.00150916	+	0.473133i
$607$	−21.0831	−	36.5170i	−0.855737	−	1.48218i	−0.875959	−	0.482385i	$-0.839771\pi$
$607$	−21.0831	−	36.5170i	−0.855737	−	1.48218i	0.0202222	−	0.999796i	$-0.493563\pi$
$608$	6.65039	−	1.89614i	0.269709	−	0.0768987i
$609$		0			0
$610$	10.2697	−	5.97295i	0.415806	−	0.241838i
$611$	18.0185	+	4.82803i	0.728949	+	0.195321i
$612$	3.28251	−	1.92318i	0.132688	−	0.0777401i
$613$	−22.5125	+	6.03221i	−0.909272	+	0.243639i	−0.682994	−	0.730424i	$-0.739322\pi$
$613$	−22.5125	+	6.03221i	−0.909272	+	0.243639i	−0.226278	+	0.974063i	$0.572656\pi$
$614$	−2.56903	+	0.697160i	−0.103678	+	0.0281351i
$615$		−	5.14117i		−	0.207312i
$616$		0			0
$617$		−	18.1135i		−	0.729221i	−0.931160	−	0.364611i	$-0.881202\pi$
$617$		−	18.1135i		−	0.729221i	0.931160	−	0.364611i	$-0.118798\pi$
$618$	6.70239	+	24.6983i	0.269610	+	0.993510i
$619$	−10.1988	+	2.73275i	−0.409923	+	0.109839i	−0.457887	−	0.889010i	$-0.651394\pi$
$619$	−10.1988	+	2.73275i	−0.409923	+	0.109839i	0.0479636	+	0.998849i	$0.484727\pi$
$620$	−3.57683	+	13.6979i	−0.143649	+	0.550119i
$621$	29.6441	+	7.94312i	1.18958	+	0.318746i
$622$	−9.79963	−	16.8491i	−0.392929	−	0.675588i
$623$		0			0
$624$	22.5900	−	13.4295i	0.904324	−	0.537611i
$625$	3.85807	+	6.68237i	0.154323	+	0.267295i
$626$	−1.19799	+	0.00382126i	−0.0478813	+	0.000152728i
$627$	0.628647	+	2.34614i	0.0251058	+	0.0936960i
$628$	−6.82883	+	6.91652i	−0.272500	+	0.275999i
$629$	−4.48316	−	4.48316i	−0.178755	−	0.178755i
$630$		0			0
$631$		−	12.0528i		−	0.479815i	−0.970796	−	0.239908i	$-0.922883\pi$
$631$		−	12.0528i		−	0.479815i	0.970796	−	0.239908i	$-0.0771172\pi$
$632$	−29.5262	+	17.4258i	−1.17449	+	0.693160i
$633$	17.6876	+	10.2119i	0.703017	+	0.405887i
$634$	16.3236	+	16.2198i	0.648292	+	0.644170i
$635$	5.79157	−	21.6144i	0.229831	−	0.857742i
$636$	8.41791	−	14.7975i	0.333792	−	0.586758i
$637$		0			0
$638$	5.04382	−	2.93354i	0.199687	−	0.116140i
$639$	6.76177	+	11.7117i	0.267491	+	0.463309i
$640$	8.76928	−	9.16990i	0.346636	−	0.362472i
$641$	−0.807178	+	1.39807i	−0.0318816	+	0.0552206i	−0.881526	−	0.472136i	$-0.843483\pi$
$641$	−0.807178	+	1.39807i	−0.0318816	+	0.0552206i	0.849644	+	0.527356i	$0.176817\pi$
$642$	24.5388	+	14.0633i	0.968469	+	0.555034i
$643$	−14.5001	+	14.5001i	−0.571830	+	0.571830i	−0.932640	−	0.360809i	$-0.882500\pi$
$643$	−14.5001	+	14.5001i	−0.571830	+	0.571830i	0.360809	+	0.932640i	$0.382500\pi$
$644$		0			0
$645$	−4.59187	−	4.59187i	−0.180805	−	0.180805i
$646$	−1.65528	+	0.449194i	−0.0651261	+	0.0176733i
$647$	16.4069	+	9.47252i	0.645021	+	0.372403i	0.786546	−	0.617531i	$-0.211867\pi$
$647$	16.4069	+	9.47252i	0.645021	+	0.372403i	−0.141525	+	0.989935i	$0.545200\pi$
$648$	1.05578	+	0.596159i	0.0414750	+	0.0234193i
$649$	−1.98538	+	1.14626i	−0.0779329	+	0.0449946i
$650$	−32.3076	−	8.54643i	−1.26721	−	0.335219i
$651$		0			0
$652$	−5.84361	−	21.2651i	−0.228854	−	0.832805i
$653$	−8.04648	−	2.15605i	−0.314883	−	0.0843727i	0.0979163	−	0.995195i	$-0.468782\pi$
$653$	−8.04648	−	2.15605i	−0.314883	−	0.0843727i	−0.412799	+	0.910822i	$0.635449\pi$
$654$	−11.1112	+	0.0354418i	−0.434484	+	0.00138588i
$655$	−9.70514	+	16.8098i	−0.379211	+	0.656813i
$656$	−15.3738	−	8.61643i	−0.600246	−	0.336415i
$657$	25.8541			1.00866
$658$		0			0
$659$	2.66978	−	2.66978i	0.104000	−	0.104000i	−0.653192	−	0.757192i	$-0.726571\pi$
$659$	2.66978	−	2.66978i	0.104000	−	0.104000i	0.757192	+	0.653192i	$0.226571\pi$
$660$	3.17122	+	3.13101i	0.123440	+	0.121875i
$661$	33.9050	−	9.08481i	1.31875	−	0.353358i	0.470241	−	0.882538i	$-0.344167\pi$
$661$	33.9050	−	9.08481i	1.31875	−	0.353358i	0.848510	+	0.529180i	$0.177500\pi$
$662$	−4.47351	+	4.50214i	−0.173868	+	0.174981i
$663$	−5.64476	+	3.25900i	−0.219224	+	0.126569i
$664$	35.2512	+	34.5829i	1.36801	+	1.34208i
$665$		0			0
$666$	4.43179	−	16.7532i	0.171728	−	0.649174i
$667$	−3.35432	+	12.5185i	−0.129880	+	0.484718i
$668$	15.6213	−	9.15232i	0.604405	−	0.354114i
$669$	−7.40458	−	27.6343i	−0.286277	−	1.06840i
$670$	15.3040	+	8.77078i	0.591244	+	0.338845i
$671$	14.3040			0.552199
$672$		0			0
$673$	43.8358			1.68975			0.844873	−	0.534968i	$-0.179676\pi$
$673$	43.8358			1.68975			0.844873	+	0.534968i	$0.179676\pi$
$674$	0.649621	+	0.372301i	0.0250225	+	0.0143405i
$675$	4.95567	+	18.4948i	0.190744	+	0.711865i
$676$	46.3731	−	27.1694i	1.78358	−	1.04498i
$677$	10.6918	−	39.9022i	0.410918	−	1.53357i	−0.381956	−	0.924180i	$-0.624750\pi$
$677$	10.6918	−	39.9022i	0.410918	−	1.53357i	0.792874	−	0.609385i	$-0.208584\pi$
$678$	−2.54001	+	9.60184i	−0.0975484	+	0.368757i
$679$		0			0
$680$	−2.20378	+	2.24636i	−0.0845110	+	0.0861441i
$681$	15.7070	−	9.06846i	0.601895	−	0.347504i
$682$	−12.0144	+	12.0912i	−0.460053	+	0.462998i
$683$	−24.9420	+	6.68319i	−0.954380	+	0.255725i	−0.702220	−	0.711960i	$-0.747808\pi$
$683$	−24.9420	+	6.68319i	−0.954380	+	0.255725i	−0.252160	+	0.967686i	$0.581141\pi$
$684$	−3.33600	−	3.29370i	−0.127555	−	0.125938i
$685$	−6.63806	+	6.63806i	−0.253627	+	0.253627i
$686$		0			0
$687$	−3.96690			−0.151346
$688$	−21.4271	+	6.03540i	−0.816899	+	0.230097i
$689$	25.8295	−	44.7380i	0.984025	−	1.70438i
$690$	−9.89834	+	0.0315730i	−0.376823	+	0.00120196i
$691$	24.9058	+	6.67349i	0.947461	+	0.253871i	0.699285	−	0.714843i	$-0.253502\pi$
$691$	24.9058	+	6.67349i	0.947461	+	0.253871i	0.248177	+	0.968715i	$0.420169\pi$
$692$	−10.5169	−	38.2713i	−0.399792	−	1.45486i
$693$		0			0
$694$	1.83094	+	0.484345i	0.0695015	+	0.0183855i
$695$	4.61574	−	2.66490i	0.175085	−	0.101085i
$696$	3.12645	−	5.53686i	0.118508	−	0.209874i
$697$	3.78540	+	2.18550i	0.143382	+	0.0827817i
$698$	−20.4359	+	5.54572i	−0.773512	+	0.209909i
$699$	−10.4703	−	10.4703i	−0.396022	−	0.396022i
$700$		0			0
$701$	−1.56163	+	1.56163i	−0.0589821	+	0.0589821i	−0.735983	−	0.677000i	$-0.763279\pi$
$701$	−1.56163	+	1.56163i	−0.0589821	+	0.0589821i	0.677000	+	0.735983i	$0.263279\pi$
$702$	−39.6416	−	22.7188i	−1.49617	−	0.857465i
$703$	−3.90634	+	6.76597i	−0.147330	+	0.255184i
$704$	14.6776	−	4.23552i	0.553184	−	0.159632i
$705$	1.72356	+	2.98530i	0.0649132	+	0.112433i
$706$	37.7802	−	21.9734i	1.42188	−	0.826980i
$707$		0			0
$708$	−1.23531	+	2.17149i	−0.0464258	+	0.0816097i
$709$	6.81045	−	25.4170i	0.255772	−	0.954554i	−0.711887	−	0.702294i	$-0.752159\pi$
$709$	6.81045	−	25.4170i	0.255772	−	0.954554i	0.967659	−	0.252260i	$-0.0811739\pi$
$710$	−7.93501	−	7.88455i	−0.297796	−	0.295902i
$711$	20.1281	+	11.6210i	0.754862	+	0.435820i
$712$	21.2184	+	35.9525i	0.795195	+	1.34738i
$713$		−	37.8601i		−	1.41787i
$714$		0			0
$715$	9.56204	+	9.56204i	0.357600	+	0.357600i
$716$	6.33808	−	6.41946i	0.236865	−	0.239907i
$717$	−2.77645	−	10.3619i	−0.103689	−	0.386971i
$718$	−40.3298	+	0.128641i	−1.50510	+	0.00480085i
$719$	24.7148	+	42.8073i	0.921708	+	1.59644i	0.796772	+	0.604280i	$0.206539\pi$
$719$	24.7148	+	42.8073i	0.921708	+	1.59644i	0.124936	+	0.992165i	$0.460128\pi$
$720$	−8.33597	−	2.12000i	−0.310663	−	0.0790079i
$721$		0			0
$722$	−12.4466	−	21.4002i	−0.463215	−	0.796434i
$723$	−19.7441	−	5.29042i	−0.734292	−	0.196753i
$724$	−2.29344	+	8.78297i	−0.0852349	+	0.326416i
$725$	−7.81021	+	2.09274i	−0.290064	+	0.0777224i
$726$	−2.83386	−	10.4428i	−0.105174	−	0.387567i
$727$			37.5639i			1.39317i	0.717475	+	0.696585i	$0.245298\pi$
$727$			37.5639i			1.39317i	−0.717475	+	0.696585i	$0.754702\pi$
$728$		0			0
$729$			15.1487i			0.561063i
$730$	−20.6391	+	5.60085i	−0.763887	+	0.207297i
$731$	5.33295	−	1.42896i	0.197246	−	0.0528520i
$732$	13.4494	−	7.87986i	0.497105	−	0.291248i
$733$	31.4186	+	8.41858i	1.16047	+	0.310947i	0.787154	−	0.616756i	$-0.211554\pi$
$733$	31.4186	+	8.41858i	1.16047	+	0.310947i	0.373317	+	0.927704i	$0.378220\pi$
$734$	−1.63400	+	0.950352i	−0.0603120	+	0.0350781i
$735$		0			0
$736$	−16.4949	+	29.6522i	−0.608009	+	1.09300i
$737$	10.6188	+	18.3923i	0.391149	+	0.677489i
$738$	0.0381082	+	11.9472i	0.00140278	+	0.439782i
$739$	8.91922	+	33.2870i	0.328099	+	1.22448i	0.911160	+	0.412053i	$0.135188\pi$
$739$	8.91922	+	33.2870i	0.328099	+	1.22448i	−0.583061	+	0.812428i	$0.698145\pi$
$740$	0.0914443	+	14.3340i	0.00336156	+	0.526929i
$741$	5.67938	+	5.67938i	0.208637	+	0.208637i
$742$		0			0
$743$		−	28.1040i		−	1.03104i	−0.856879	−	0.515518i	$-0.827600\pi$
$743$		−	28.1040i		−	1.03104i	0.856879	−	0.515518i	$-0.172400\pi$
$744$	−4.63570	+	17.9874i	−0.169953	+	0.659451i
$745$	−3.19931	−	1.84712i	−0.117214	−	0.0676734i
$746$	9.58995	−	9.65132i	0.351113	−	0.353360i
$747$	8.66439	−	32.3359i	0.317013	−	1.18311i
$748$	−3.65342	+	1.00395i	−0.133582	+	0.0367082i
$749$		0			0
$750$	−7.25311	−	12.4707i	−0.264846	−	0.455366i
$751$	−24.5979	−	42.6048i	−0.897590	−	1.55467i	−0.830566	−	0.556920i	$-0.811983\pi$
$751$	−24.5979	−	42.6048i	−0.897590	−	1.55467i	−0.0670240	−	0.997751i	$-0.521350\pi$
$752$	11.8157	−	0.150763i	0.430873	−	0.00549776i
$753$	−8.81915	+	15.2752i	−0.321388	+	0.556660i
$754$	9.59397	−	16.7403i	0.349392	−	0.609647i
$755$	−3.01672	+	3.01672i	−0.109790	+	0.109790i
$756$		0			0
$757$	−1.54043	−	1.54043i	−0.0559880	−	0.0559880i	0.678558	−	0.734546i	$-0.262605\pi$
$757$	−1.54043	−	1.54043i	−0.0559880	−	0.0559880i	−0.734546	+	0.678558i	$0.762605\pi$
$758$	−3.11671	−	11.4851i	−0.113204	−	0.417156i
$759$	−10.3211	−	5.95887i	−0.374631	−	0.216293i
$760$	3.37663	+	1.90665i	0.122483	+	0.0691614i
$761$	35.3669	−	20.4191i	1.28205	−	0.740191i	0.304826	−	0.952408i	$-0.401402\pi$
$761$	35.3669	−	20.4191i	1.28205	−	0.740191i	0.977223	+	0.212217i	$0.0680684\pi$
$762$	7.50844	−	28.3837i	0.272002	−	1.02823i
$763$		0			0
$764$	3.75066	−	6.59312i	0.135694	−	0.238531i
$765$	2.06059	+	0.552133i	0.0745008	+	0.0199624i
$766$	−0.120615	−	37.8136i	−0.00435800	−	1.36626i
$767$	−3.79042	+	6.56520i	−0.136864	+	0.237056i
$768$	11.4675	−	12.0682i	0.413797	−	0.435473i
$769$	13.4109			0.483609			0.241804	−	0.970325i	$-0.422261\pi$
$769$	13.4109			0.483609			0.241804	+	0.970325i	$0.422261\pi$
$770$		0			0
$771$	2.97195	−	2.97195i	0.107032	−	0.107032i
$772$	−34.9300	+	0.222837i	−1.25716	+	0.00802008i
$773$	10.0298	−	2.68746i	0.360745	−	0.0966613i	−0.0738939	−	0.997266i	$-0.523543\pi$
$773$	10.0298	−	2.68746i	0.360745	−	0.0966613i	0.434639	+	0.900605i	$0.356876\pi$
$774$	10.7048	+	10.6367i	0.384774	+	0.382327i
$775$	20.4561	−	11.8103i	0.734805	−	0.424240i
$776$	−0.258528	−	27.0159i	−0.00928060	−	0.969816i
$777$		0			0
$778$	15.5918	+	4.12455i	0.558993	+	0.147872i
$779$	1.39405	−	5.20266i	0.0499470	−	0.186405i
$780$	14.2584	+	3.72319i	0.510531	+	0.133312i
$781$	−3.48584	−	13.0093i	−0.124733	−	0.465510i
$782$	4.18452	−	7.30149i	0.149638	−	0.261101i
$783$	−11.0548			−0.395066
$784$		0			0
$785$	−5.45017			−0.194525
$786$	−12.6634	+	22.0961i	−0.451688	+	0.788142i
$787$	−1.54314	−	5.75907i	−0.0550069	−	0.205289i	0.932953	−	0.359998i	$-0.117223\pi$
$787$	−1.54314	−	5.75907i	−0.0550069	−	0.205289i	−0.987960	+	0.154709i	$0.950556\pi$
$788$	−2.71191	+	10.3856i	−0.0966079	+	0.369970i
$789$	0.789341	−	2.94586i	0.0281013	−	0.104875i
$790$	−18.5856	−	4.91650i	−0.661245	−	0.174921i
$791$		0			0
$792$	−7.39257	−	7.25243i	−0.262684	−	0.257704i
$793$	40.9631	−	23.6500i	1.45464	−	0.839837i
$794$	−27.9180	−	27.7405i	−0.990772	−	0.984472i
$795$	9.22090	−	2.47073i	0.327032	−	0.0876279i
$796$	0.0342111	+	5.36264i	0.00121258	+	0.190074i
$797$	20.9386	−	20.9386i	0.741682	−	0.741682i	−0.231220	−	0.972902i	$-0.574272\pi$
$797$	20.9386	−	20.9386i	0.741682	−	0.741682i	0.972902	+	0.231220i	$0.0742717\pi$
$798$		0			0
$799$	−2.93074			−0.103682
$800$	−21.1669	+	0.337610i	−0.748362	+	0.0119363i
$801$	14.1502	−	24.5089i	0.499974	−	0.865980i
$802$	−0.0582385	−	18.2581i	−0.00205647	−	0.644717i
$803$	−24.8710	−	6.66417i	−0.877679	−	0.235173i
$804$	20.1165	+	11.4438i	0.709453	+	0.403590i
$805$		0			0
$806$	−14.4146	+	54.4907i	−0.507733	+	1.91935i
$807$	8.53328	−	4.92669i	0.300386	−	0.173428i
$808$	6.00116	+	21.5689i	0.211120	+	0.758791i
$809$	−39.6081	−	22.8677i	−1.39255	−	0.803987i	−0.398950	−	0.916973i	$-0.630625\pi$
$809$	−39.6081	−	22.8677i	−1.39255	−	0.803987i	−0.993597	+	0.112985i	$0.963959\pi$
$810$	0.178059	+	0.656148i	0.00625637	+	0.0230547i
$811$	11.4330	+	11.4330i	0.401466	+	0.401466i	0.878749	−	0.477284i	$-0.158379\pi$
$811$	11.4330	+	11.4330i	0.401466	+	0.401466i	−0.477284	+	0.878749i	$0.658379\pi$
$812$		0			0
$813$	6.94475	−	6.94475i	0.243563	−	0.243563i
$814$	−8.58159	+	14.9739i	−0.300785	+	0.524833i
$815$	6.18310	−	10.7094i	0.216584	−	0.375135i
$816$	−2.88209	+	2.95659i	−0.100893	+	0.103501i
$817$	−3.40169	−	5.89190i	−0.119010	−	0.206131i
$818$	−10.6844	−	18.3703i	−0.373570	−	0.642302i
$819$		0			0
$820$	−2.61858	−	9.52908i	−0.0914447	−	0.332770i
$821$	−6.06389	+	22.6307i	−0.211631	+	0.789818i	0.775694	+	0.631109i	$0.217400\pi$
$821$	−6.06389	+	22.6307i	−0.211631	+	0.789818i	−0.987325	+	0.158709i	$0.949267\pi$
$822$	−8.68177	+	8.73733i	−0.302811	+	0.304749i
$823$	−22.7332	−	13.1250i	−0.792429	−	0.457509i	0.0483881	−	0.998829i	$-0.484592\pi$
$823$	−22.7332	−	13.1250i	−0.792429	−	0.457509i	−0.840817	+	0.541320i	$0.817925\pi$
$824$	25.0025	+	42.3641i	0.871003	+	1.47582i
$825$		−	7.43540i		−	0.258867i
$826$		0			0
$827$	−19.3742	−	19.3742i	−0.673706	−	0.673706i	0.284862	−	0.958568i	$-0.408052\pi$
$827$	−19.3742	−	19.3742i	−0.673706	−	0.673706i	−0.958568	+	0.284862i	$0.908052\pi$
$828$	23.0018	−	0.146740i	0.799368	−	0.00509958i
$829$	−0.911026	−	3.39999i	−0.0316412	−	0.118087i	0.948299	−	0.317378i	$-0.102803\pi$
$829$	−0.911026	−	3.39999i	−0.0316412	−	0.118087i	−0.979940	+	0.199292i	$0.936136\pi$
$830$	0.0883252	+	27.6905i	0.00306581	+	0.961151i
$831$	3.22264	+	5.58178i	0.111792	+	0.193630i
$832$	35.0301	−	36.3973i	1.21445	−	1.26185i
$833$		0			0
$834$	6.04499	−	3.51583i	0.209321	−	0.121743i
$835$	9.80623	+	2.62757i	0.339359	+	0.0909308i
$836$	2.36016	+	4.02835i	0.0816279	+	0.139324i
$837$	31.1938	−	8.35834i	1.07821	−	0.288907i
$838$	−12.2133	+	3.31432i	−0.421900	+	0.114491i
$839$		−	27.1787i		−	0.938311i	−0.883115	−	0.469156i	$-0.844558\pi$
$839$		−	27.1787i		−	0.938311i	0.883115	−	0.469156i	$-0.155442\pi$
$840$		0			0
$841$			24.3316i			0.839022i
$842$	9.71042	+	35.7829i	0.334643	+	1.23316i
$843$	27.9911	−	7.50020i	0.964065	−	0.258321i
$844$	37.9849	+	9.91875i	1.30750	+	0.341417i
$845$	29.1106	+	7.80016i	1.00144	+	0.268334i
$846$	−4.02739	−	6.92455i	−0.138465	−	0.238071i
$847$		0			0
$848$	8.06562	−	31.7144i	0.276974	−	1.08908i
$849$	−12.5037	−	21.6570i	−0.429125	−	0.743266i
$850$	5.25040	−	0.0167473i	0.180087	−	0.000574429i
$851$	−9.92153	−	37.0277i	−0.340106	−	1.26929i
$852$	−10.4442	−	10.3118i	−0.357813	−	0.353277i
$853$	10.1868	+	10.1868i	0.348789	+	0.348789i	0.859658	−	0.510869i	$-0.170676\pi$
$853$	10.1868	+	10.1868i	0.348789	+	0.348789i	−0.510869	+	0.859658i	$0.670676\pi$
$854$		0			0
$855$		−	2.62875i		−	0.0899012i
$856$	52.6452	+	13.5677i	1.79938	+	0.463734i
$857$	−26.0838	−	15.0595i	−0.891007	−	0.514423i	−0.0167350	−	0.999860i	$-0.505327\pi$
$857$	−26.0838	−	15.0595i	−0.891007	−	0.514423i	−0.874272	+	0.485437i	$0.838660\pi$
$858$	12.5860	+	12.5060i	0.429679	+	0.426947i
$859$	6.57954	−	24.5552i	0.224491	−	0.837812i	−0.758117	−	0.652119i	$-0.773880\pi$
$859$	6.57954	−	24.5552i	0.224491	−	0.837812i	0.982608	−	0.185693i	$-0.0594530\pi$
$860$	−10.8498	−	6.17217i	−0.369974	−	0.210469i
$861$		0			0
$862$	5.42871	−	3.15740i	0.184903	−	0.107541i
$863$	4.63983	+	8.03642i	0.157942	+	0.273563i	0.934126	−	0.356943i	$-0.116181\pi$
$863$	4.63983	+	8.03642i	0.157942	+	0.273563i	−0.776185	+	0.630506i	$0.782848\pi$
$864$	−28.0727	−	7.04420i	−0.955053	−	0.239648i
$865$	11.1279	−	19.2740i	0.378359	−	0.655337i
$866$	−24.4922	−	14.0366i	−0.832278	−	0.476983i
$867$	−11.7833	+	11.7833i	−0.400181	+	0.400181i
$868$		0			0
$869$	−16.3673	−	16.3673i	−0.555223	−	0.555223i
$870$	3.44105	−	0.933800i	0.116662	−	0.0316588i
$871$	60.8192	+	35.1140i	2.06078	+	1.18979i
$872$	−20.5765	+	5.72503i	−0.696807	+	0.193874i
$873$	−15.8613	+	9.15755i	−0.536825	+	0.309936i
$874$	−10.0253	−	2.65203i	−0.339111	−	0.0897061i
$875$		0			0
$876$	−27.0563	+	7.43504i	−0.914149	+	0.251207i
$877$	3.46440	+	0.928283i	0.116985	+	0.0313459i	0.316836	−	0.948480i	$-0.397379\pi$
$877$	3.46440	+	0.928283i	0.116985	+	0.0313459i	−0.199852	+	0.979826i	$0.564046\pi$
$878$	−22.7494	+	0.0725643i	−0.767754	+	0.00244893i
$879$	0.957017	−	1.65760i	0.0322794	−	0.0559095i
$880$	7.47255	+	4.18808i	0.251900	+	0.141180i
$881$	22.7848			0.767641			0.383820	−	0.923408i	$-0.374608\pi$
$881$	22.7848			0.767641			0.383820	+	0.923408i	$0.374608\pi$
$882$		0			0
$883$	3.62031	−	3.62031i	0.121833	−	0.121833i	−0.643561	−	0.765394i	$-0.722544\pi$
$883$	3.62031	−	3.62031i	0.121833	−	0.121833i	0.765394	+	0.643561i	$0.222544\pi$
$884$	−8.80256	+	8.91559i	−0.296062	+	0.299864i
$885$	−1.35315	+	0.362574i	−0.0454855	+	0.0121878i
$886$	26.9049	−	27.0771i	0.903889	−	0.909674i
$887$	−5.54877	+	3.20358i	−0.186309	+	0.107566i	−0.590254	−	0.807218i	$-0.700972\pi$
$887$	−5.54877	+	3.20358i	−0.186309	+	0.107566i	0.403944	+	0.914784i	$0.367639\pi$
$888$	0.179970	+	18.8068i	0.00603941	+	0.631113i
$889$		0			0
$890$	−5.98657	+	22.6307i	−0.200670	+	0.758582i
$891$	−0.211864	+	0.790686i	−0.00709770	+	0.0264890i
$892$	−27.7994	−	47.4483i	−0.930792	−	1.58869i
$893$	0.934703	+	3.48836i	0.0312786	+	0.116733i
$894$	−4.20543	−	2.41015i	−0.140651	−	0.0806076i
$895$	5.05850			0.169087
$896$		0			0
$897$	−39.4093			−1.31584
$898$	−42.8817	−	24.5757i	−1.43098	−	0.820103i
$899$	3.52967	+	13.1729i	0.117721	+	0.439341i
$900$	7.25463	+	12.3823i	0.241821	+	0.412743i
$901$	−2.10061	+	7.83957i	−0.0699814	+	0.261174i
$902$	3.04285	−	11.5027i	0.101316	−	0.382999i
$903$		0			0
$904$	0.182686	+	19.0906i	0.00607606	+	0.634944i
$905$	−4.40815	+	2.54504i	−0.146532	+	0.0846001i
$906$	−3.94550	+	3.97075i	−0.131081	+	0.131919i
$907$	−5.65230	+	1.51453i	−0.187682	+	0.0502891i	−0.351436	−	0.936212i	$-0.614306\pi$
$907$	−5.65230	+	1.51453i	−0.187682	+	0.0502891i	0.163754	+	0.986501i	$0.447640\pi$
$908$	24.4939	−	24.8084i	0.812858	−	0.823296i
$909$	10.7318	−	10.7318i	0.355952	−	0.355952i
$910$		0			0
$911$	44.6737			1.48011			0.740054	−	0.672548i	$-0.234800\pi$
$911$	44.6737			1.48011			0.740054	+	0.672548i	$0.234800\pi$
$912$	4.43832	+	2.48751i	0.146968	+	0.0823697i
$913$	−16.6699	+	28.8731i	−0.551692	+	0.955559i
$914$	−27.2911	+	0.0870512i	−0.902710	+	0.00287940i
$915$	8.44286	+	2.26226i	0.279112	+	0.0747879i
$916$	−7.35259	+	2.02048i	−0.242936	+	0.0667585i
$917$		0			0
$918$	6.93967	+	1.83577i	0.229043	+	0.0605896i
$919$	13.1031	−	7.56505i	0.432230	−	0.249548i	−0.268066	−	0.963400i	$-0.586385\pi$
$919$	13.1031	−	7.56505i	0.432230	−	0.249548i	0.700296	+	0.713852i	$0.253051\pi$
$920$	−18.3304	+	5.10009i	−0.604334	+	0.168145i
$921$	−1.69608	−	0.979234i	−0.0558878	−	0.0322668i
$922$	50.1436	−	13.6075i	1.65139	−	0.448140i
$923$	−31.4920	−	31.4920i	−1.03657	−	1.03657i
$924$		0			0
$925$	16.9113	−	16.9113i	0.556042	−	0.556042i
$926$	33.7818	+	19.3605i	1.11014	+	0.636226i
$927$	16.6737	−	28.8798i	0.547638	−	0.948536i
$928$	2.97471	−	11.8549i	0.0976497	−	0.389156i
$929$	−7.46329	−	12.9268i	−0.244862	−	0.424114i	0.717230	−	0.696836i	$-0.245409\pi$
$929$	−7.46329	−	12.9268i	−0.244862	−	0.424114i	−0.962093	+	0.272722i	$0.912076\pi$
$930$	−9.00371	+	5.23666i	−0.295243	+	0.171717i
$931$		0			0
$932$	−24.7394	−	14.0736i	−0.810364	−	0.460996i
$933$	3.71162	−	13.8519i	0.121513	−	0.453492i
$934$	10.3675	+	10.3016i	0.339236	+	0.337079i
$935$	−1.83992	−	1.06228i	−0.0601718	−	0.0347402i
$936$	−33.1616	−	8.54636i	−1.08392	−	0.279347i
$937$			36.0336i			1.17717i	0.808436	+	0.588584i	$0.200314\pi$
$937$			36.0336i			1.17717i	−0.808436	+	0.588584i	$0.799686\pi$
$938$		0			0
$939$	−0.623244	−	0.623244i	−0.0203388	−	0.0203388i
$940$	4.71512	+	4.65534i	0.153790	+	0.151841i
$941$	13.2170	+	49.3267i	0.430863	+	1.60800i	0.750776	+	0.660557i	$0.229680\pi$
$941$	13.2170	+	49.3267i	0.430863	+	1.60800i	−0.319913	+	0.947447i	$0.603654\pi$
$942$	−7.15097	+	0.0228096i	−0.232991	+	0.000743178i
$943$	13.2140	+	22.8873i	0.430307	+	0.745314i
$944$	−1.18361	+	4.65402i	−0.0385233	+	0.151475i
$945$		0			0
$946$	−7.55600	−	12.9915i	−0.245667	−	0.422390i
$947$	−17.7335	−	4.75167i	−0.576260	−	0.154409i	−0.0410942	−	0.999155i	$-0.513084\pi$
$947$	−17.7335	−	4.75167i	−0.576260	−	0.154409i	−0.535166	+	0.844747i	$0.679751\pi$
$948$	−24.4060	−	6.37298i	−0.792670	−	0.206985i
$949$	−82.2428	+	22.0369i	−2.66972	+	0.715348i
$950$	−1.69445	−	6.24404i	−0.0549752	−	0.202583i
$951$			16.9304i			0.549006i
$952$		0			0
$953$			42.2356i			1.36815i	0.729414	+	0.684073i	$0.239793\pi$
$953$			42.2356i			1.36815i	−0.729414	+	0.684073i	$0.760207\pi$
$954$	−21.4095	+	5.80990i	−0.693157	+	0.188103i
$955$	4.10844	−	1.10085i	0.132946	−	0.0356228i
$956$	−10.4238	−	17.7914i	−0.337129	−	0.575416i
$957$	4.14661	+	1.11108i	0.134041	+	0.0359162i
$958$	−6.59287	+	3.83448i	−0.213006	+	0.123887i
$959$		0			0
$960$	9.33327	−	0.178645i	0.301230	−	0.00576574i
$961$	−4.41959	−	7.65495i	−0.142567	−	0.246934i
$962$	0.182038	+	57.0701i	0.00586915	+	1.84001i
$963$	−9.53869	−	35.5989i	−0.307380	−	1.14716i
$964$	−39.2900	+	0.250652i	−1.26545	+	0.00807295i
$965$	−13.8501	−	13.8501i	−0.445852	−	0.445852i
$966$		0			0
$967$		−	1.49725i		−	0.0481484i	−0.999710	−	0.0240742i	$-0.992336\pi$
$967$		−	1.49725i		−	0.0481484i	0.999710	−	0.0240742i	$-0.00766379\pi$
$968$	−10.5714	−	17.9121i	−0.339777	−	0.575717i
$969$	−1.09282	−	0.630941i	−0.0351065	−	0.0202687i
$970$	10.6782	−	10.7465i	0.342855	−	0.345049i
$971$	−12.0083	+	44.8156i	−0.385365	+	1.43820i	0.452226	+	0.891904i	$0.350630\pi$
$971$	−12.0083	+	44.8156i	−0.385365	+	1.43820i	−0.837591	+	0.546298i	$0.816036\pi$
$972$	8.37078	+	30.4615i	0.268493	+	0.977054i
$973$		0			0
$974$	11.8430	+	20.3624i	0.379474	+	0.652454i
$975$	−12.2936	−	21.2931i	−0.393710	−	0.681926i
$976$	20.9149	−	21.4555i	0.669468	−	0.686773i
$977$	15.8609	−	27.4718i	0.507434	−	0.878902i	−0.492529	−	0.870296i	$-0.663927\pi$
$977$	15.8609	−	27.4718i	0.507434	−	0.878902i	0.999963	−	0.00860588i	$-0.00273937\pi$
$978$	8.06779	−	14.0773i	0.257979	−	0.450143i
$979$	−19.9296	+	19.9296i	−0.636953	+	0.636953i
$980$		0			0
$981$	10.2380	+	10.2380i	0.326875	+	0.326875i
$982$	10.3467	+	38.1277i	0.330178	+	1.21670i
$983$	−38.5618	−	22.2636i	−1.22993	−	0.710100i	−0.262914	−	0.964819i	$-0.584684\pi$
$983$	−38.5618	−	22.2636i	−1.22993	−	0.710100i	−0.967015	+	0.254720i	$0.918017\pi$
$984$	−3.47562	−	12.4918i	−0.110799	−	0.398224i
$985$	−5.21249	+	3.00943i	−0.166084	+	0.0958884i
$986$	−0.775234	+	2.93057i	−0.0246885	+	0.0933284i
$987$		0			0
$988$	13.4193	+	7.63394i	0.426926	+	0.242868i
$989$	32.2442	+	8.63980i	1.02531	+	0.274730i
$990$	−0.0185228	−	5.80702i	−0.000588693	−	0.184559i
$991$	−6.52308	+	11.2983i	−0.207212	+	0.358902i	−0.950835	−	0.309697i	$-0.899772\pi$
$991$	−6.52308	+	11.2983i	−0.207212	+	0.358902i	0.743623	+	0.668599i	$0.233106\pi$
$992$	0.569422	+	35.7006i	0.0180792	+	1.13349i
$993$	−4.66951			−0.148182
$994$		0			0
$995$	−2.12634	+	2.12634i	−0.0674096	+	0.0674096i
$996$	0.231776	+	36.3313i	0.00734411	+	1.15120i
$997$	19.6749	−	5.27187i	0.623110	−	0.166962i	0.0665689	−	0.997782i	$-0.478795\pi$
$997$	19.6749	−	5.27187i	0.623110	−	0.166962i	0.556541	+	0.830820i	$0.312128\pi$
$998$	−10.9163	−	10.8469i	−0.345549	−	0.343351i
$999$	28.3175	−	16.3491i	0.895928	−	0.517264i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.x.p.165.20		96
7.2	even	3	inner	784.2.x.p.373.13		96
7.3	odd	6		784.2.m.l.197.5	✓	48
7.4	even	3		784.2.m.l.197.6	yes	48
7.5	odd	6	inner	784.2.x.p.373.14		96
7.6	odd	2	inner	784.2.x.p.165.19		96
16.13	even	4	inner	784.2.x.p.557.13		96
112.13	odd	4	inner	784.2.x.p.557.14		96
112.45	odd	12		784.2.m.l.589.5	yes	48
112.61	odd	12	inner	784.2.x.p.765.19		96
112.93	even	12	inner	784.2.x.p.765.20		96
112.109	even	12		784.2.m.l.589.6	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
784.2.m.l.197.5	✓	48	7.3	odd	6
784.2.m.l.197.6	yes	48	7.4	even	3
784.2.m.l.589.5	yes	48	112.45	odd	12
784.2.m.l.589.6	yes	48	112.109	even	12
784.2.x.p.165.19		96	7.6	odd	2	inner
784.2.x.p.165.20		96	1.1	even	1	trivial
784.2.x.p.373.13		96	7.2	even	3	inner
784.2.x.p.373.14		96	7.5	odd	6	inner
784.2.x.p.557.13		96	16.13	even	4	inner
784.2.x.p.557.14		96	112.13	odd	4	inner
784.2.x.p.765.19		96	112.61	odd	12	inner
784.2.x.p.765.20		96	112.93	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.22699 + 0.703197i) q^{2} +(0.269295 + 1.00502i) q^{3} +(1.01103 + 1.72564i) q^{4} +(-0.290260 + 1.08326i) q^{5} +(-0.376306 + 1.42253i) q^{6} +(0.0270652 + 2.82830i) q^{8} +(1.66052 - 0.958704i) q^{9} +O(q^{10})\)	\(q+(1.22699 + 0.703197i) q^{2} +(0.269295 + 1.00502i) q^{3} +(1.01103 + 1.72564i) q^{4} +(-0.290260 + 1.08326i) q^{5} +(-0.376306 + 1.42253i) q^{6} +(0.0270652 + 2.82830i) q^{8} +(1.66052 - 0.958704i) q^{9} +(-1.11790 + 1.12505i) q^{10} +(-1.84450 + 0.494232i) q^{11} +(-1.46204 + 1.48081i) q^{12} +(-4.46503 + 4.46503i) q^{13} -1.16687 q^{15} +(-1.95564 + 3.48934i) q^{16} +(0.496035 - 0.859158i) q^{17} +(2.71161 - 0.00864930i) q^{18} +(-1.18083 - 0.316402i) q^{19} +(-2.16278 + 0.594329i) q^{20} +(-2.61073 - 0.690626i) q^{22} +(5.19466 - 2.99914i) q^{23} +(-2.83522 + 0.788848i) q^{24} +(3.24091 + 1.87114i) q^{25} +(-8.61836 + 2.33877i) q^{26} +(3.61788 + 3.61788i) q^{27} +(-1.52780 + 1.52780i) q^{29} +(-1.43175 - 0.820541i) q^{30} +(3.15591 - 5.46620i) q^{31} +(-4.85325 + 2.90620i) q^{32} +(-0.993431 - 1.72067i) q^{33} +(1.21279 - 0.705372i) q^{34} +(3.33321 + 1.89618i) q^{36} +(1.65406 - 6.17305i) q^{37} +(-1.22638 - 1.21858i) q^{38} +(-5.68988 - 3.28505i) q^{39} +(-3.07165 - 0.791623i) q^{40} +4.40594i q^{41} +(3.93520 + 3.93520i) q^{43} +(-2.71771 - 2.68325i) q^{44} +(0.556547 + 2.07706i) q^{45} +(8.48280 - 0.0270578i) q^{46} +(-1.47708 - 2.55838i) q^{47} +(-4.03351 - 1.02580i) q^{48} +(2.66080 + 4.57488i) q^{50} +(0.997054 + 0.267160i) q^{51} +(-12.2193 - 3.19074i) q^{52} +(-7.90224 + 2.11740i) q^{53} +(1.89503 + 6.98319i) q^{54} -2.14154i q^{55} -1.27197i q^{57} +(-2.94895 + 0.800259i) q^{58} +(1.15964 - 0.310723i) q^{59} +(-1.17974 - 2.01360i) q^{60} +(-7.23546 - 1.93873i) q^{61} +(7.71610 - 4.48777i) q^{62} +(-7.99853 + 0.153097i) q^{64} +(-3.54079 - 6.13283i) q^{65} +(-0.00896260 - 2.80983i) q^{66} +(-2.87850 - 10.7427i) q^{67} +(1.98410 - 0.0126576i) q^{68} +(4.41310 + 4.41310i) q^{69} +7.05303i q^{71} +(2.75644 + 4.67051i) q^{72} +(11.6774 + 6.74194i) q^{73} +(6.37040 - 6.41117i) q^{74} +(-1.00778 + 3.76109i) q^{75} +(-0.647858 - 2.35757i) q^{76} +(-4.67141 - 8.03184i) q^{78} +(6.06076 + 10.4976i) q^{79} +(-3.21223 - 3.13129i) q^{80} +(0.214336 - 0.371241i) q^{81} +(-3.09824 + 5.40606i) q^{82} +(12.3456 - 12.3456i) q^{83} +(0.786717 + 0.786717i) q^{85} +(2.06125 + 7.59568i) q^{86} +(-1.94691 - 1.12405i) q^{87} +(-1.44776 - 5.20342i) q^{88} +(12.7823 - 7.37988i) q^{89} +(-0.777702 + 2.93990i) q^{90} +(10.4274 + 5.93187i) q^{92} +(6.34354 + 1.69975i) q^{93} +(-0.0133260 - 4.17779i) q^{94} +(0.685495 - 1.18731i) q^{95} +(-4.22775 - 4.09501i) q^{96} -9.55202 q^{97} +(-2.58901 + 2.58901i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 4 q^{4}+O(q^{10}) \) 96 * q + 4 * q^4	\( 96 q + 4 q^{4} + 8 q^{11} + 64 q^{15} - 36 q^{16} - 20 q^{18} - 56 q^{22} - 32 q^{29} - 96 q^{30} - 40 q^{32} + 80 q^{36} + 16 q^{37} + 16 q^{43} - 4 q^{44} - 64 q^{46} - 56 q^{50} - 16 q^{53} + 20 q^{58} - 8 q^{60} + 88 q^{64} - 40 q^{67} + 196 q^{72} + 28 q^{74} + 112 q^{78} - 80 q^{79} + 48 q^{81} + 108 q^{86} + 100 q^{88} + 128 q^{95} - 80 q^{99}+O(q^{100}) \) 96 * q + 4 * q^4 + 8 * q^11 + 64 * q^15 - 36 * q^16 - 20 * q^18 - 56 * q^22 - 32 * q^29 - 96 * q^30 - 40 * q^32 + 80 * q^36 + 16 * q^37 + 16 * q^43 - 4 * q^44 - 64 * q^46 - 56 * q^50 - 16 * q^53 + 20 * q^58 - 8 * q^60 + 88 * q^64 - 40 * q^67 + 196 * q^72 + 28 * q^74 + 112 * q^78 - 80 * q^79 + 48 * q^81 + 108 * q^86 + 100 * q^88 + 128 * q^95 - 80 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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