LMFDB - Embedded newform 770.2.bd.a.527.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(263,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 8, 6]))

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

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

chi := DirichletCharacter("770.263");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.bd (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			527.17
Character	$\chi$	$=$	770.527
Dual form			770.2.bd.a.263.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 - 0.965926i) q^{2} +(1.01597 + 0.272228i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(0.755631 + 2.10452i) q^{5} -1.05181i q^{6} +(-1.57788 + 2.12375i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.63999 - 0.946852i) q^{9} +O(q^{10})$	\(q+(-0.258819 - 0.965926i) q^{2} +(1.01597 + 0.272228i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(0.755631 + 2.10452i) q^{5} -1.05181i q^{6} +(-1.57788 + 2.12375i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.63999 - 0.946852i) q^{9} +(1.83724 - 1.27457i) q^{10} +(1.27594 + 3.06137i) q^{11} +(-1.01597 + 0.272228i) q^{12} +(-3.80412 - 3.80412i) q^{13} +(2.45977 + 0.974444i) q^{14} +(0.194787 + 2.34383i) q^{15} +(0.500000 - 0.866025i) q^{16} +(2.13709 + 0.572632i) q^{17} +(-0.490126 + 1.82918i) q^{18} +(-1.10162 + 1.90806i) q^{19} +(-1.70666 - 1.44476i) q^{20} +(-2.18121 + 1.72812i) q^{21} +(2.62682 - 2.02480i) q^{22} +(1.76287 + 6.57913i) q^{23} +(0.525903 + 0.910891i) q^{24} +(-3.85804 + 3.18049i) q^{25} +(-2.68992 + 4.65907i) q^{26} +(-3.63964 - 3.63964i) q^{27} +(0.304606 - 2.62816i) q^{28} -3.51700 q^{29} +(2.21355 - 0.794778i) q^{30} +(2.30011 + 3.98390i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(0.462926 + 3.45760i) q^{33} -2.21248i q^{34} +(-5.66177 - 1.71591i) q^{35} +1.89370 q^{36} +(-6.65632 + 1.78356i) q^{37} +(2.12817 + 0.570241i) q^{38} +(-2.82927 - 4.90044i) q^{39} +(-0.953811 + 2.02244i) q^{40} +6.44737i q^{41} +(2.23377 + 1.65962i) q^{42} +(3.27026 + 3.27026i) q^{43} +(-2.63568 - 2.01325i) q^{44} +(0.753440 - 4.16688i) q^{45} +(5.89869 - 3.40561i) q^{46} +(0.121120 - 0.0324540i) q^{47} +(0.743740 - 0.743740i) q^{48} +(-2.02062 - 6.70202i) q^{49} +(4.07065 + 2.90341i) q^{50} +(2.01533 + 1.16355i) q^{51} +(5.19652 + 1.39240i) q^{52} +(1.88773 + 0.505816i) q^{53} +(-2.57361 + 4.45763i) q^{54} +(-5.47858 + 4.99851i) q^{55} +(-2.61744 + 0.385991i) q^{56} +(-1.63864 + 1.63864i) q^{57} +(0.910267 + 3.39716i) q^{58} +(-1.86866 + 1.07887i) q^{59} +(-1.34061 - 1.93242i) q^{60} +(3.54246 + 2.04524i) q^{61} +(3.25284 - 3.25284i) q^{62} +(4.59858 - 1.98892i) q^{63} +1.00000i q^{64} +(5.13135 - 10.8804i) q^{65} +(3.21997 - 1.34204i) q^{66} +(3.78627 - 14.1306i) q^{67} +(-2.13709 + 0.572632i) q^{68} +7.16408i q^{69} +(-0.192063 + 5.91296i) q^{70} +7.05264 q^{71} +(-0.490126 - 1.82918i) q^{72} +(-2.44097 + 9.10983i) q^{73} +(3.44556 + 5.96789i) q^{74} +(-4.78546 + 2.18101i) q^{75} -2.20324i q^{76} +(-8.51485 - 2.12068i) q^{77} +(-4.00120 + 4.00120i) q^{78} +(4.14156 - 7.17339i) q^{79} +(2.20039 + 0.397866i) q^{80} +(0.133610 + 0.231420i) q^{81} +(6.22769 - 1.66870i) q^{82} +(-1.34396 - 1.34396i) q^{83} +(1.02493 - 2.58720i) q^{84} +(0.409736 + 4.93026i) q^{85} +(2.31242 - 4.00524i) q^{86} +(-3.57316 - 0.957425i) q^{87} +(-1.26249 + 3.06694i) q^{88} +(3.00167 + 1.73302i) q^{89} +(-4.21990 + 0.350700i) q^{90} +(14.0814 - 2.07657i) q^{91} +(-4.81626 - 4.81626i) q^{92} +(1.25231 + 4.67367i) q^{93} +(-0.0626964 - 0.108593i) q^{94} +(-4.84798 - 0.876595i) q^{95} +(-0.910891 - 0.525903i) q^{96} +(10.8433 + 10.8433i) q^{97} +(-5.95068 + 3.68638i) q^{98} +(0.806124 - 6.22876i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 8 q^{5}+O(q^{10}) $ 192 * q + 8 * q^5	$ 192 q + 8 q^{5} + 4 q^{11} + 16 q^{15} + 96 q^{16} + 24 q^{22} - 8 q^{23} + 24 q^{25} - 8 q^{26} - 16 q^{33} - 160 q^{36} - 40 q^{37} - 40 q^{42} + 32 q^{45} - 40 q^{47} + 40 q^{53} + 8 q^{55} + 16 q^{56} + 32 q^{58} - 48 q^{67} - 72 q^{70} + 32 q^{71} - 48 q^{75} - 72 q^{77} - 8 q^{80} + 64 q^{81} + 16 q^{82} - 12 q^{88} - 112 q^{91} - 16 q^{92} + 80 q^{93} - 64 q^{97}+O(q^{100}) $ 192 * q + 8 * q^5 + 4 * q^11 + 16 * q^15 + 96 * q^16 + 24 * q^22 - 8 * q^23 + 24 * q^25 - 8 * q^26 - 16 * q^33 - 160 * q^36 - 40 * q^37 - 40 * q^42 + 32 * q^45 - 40 * q^47 + 40 * q^53 + 8 * q^55 + 16 * q^56 + 32 * q^58 - 48 * q^67 - 72 * q^70 + 32 * q^71 - 48 * q^75 - 72 * q^77 - 8 * q^80 + 64 * q^81 + 16 * q^82 - 12 * q^88 - 112 * q^91 - 16 * q^92 + 80 * q^93 - 64 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$3$	1.01597	+	0.272228i	0.586569	+	0.157171i	0.539885	−	0.841739i	$-0.318468\pi$
$3$	1.01597	+	0.272228i	0.586569	+	0.157171i	0.0466843	+	0.998910i	$0.485135\pi$
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	0.755631	+	2.10452i	0.337929	+	0.941172i
$5$	0.755631	+	2.10452i	0.337929	+	0.941172i
$6$		−	1.05181i		−	0.429398i
$7$	−1.57788	+	2.12375i	−0.596381	+	0.802702i
$7$	−1.57788	+	2.12375i	−0.596381	+	0.802702i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−1.63999	−	0.946852i	−0.546665	−	0.315617i
$10$	1.83724	−	1.27457i	0.580987	−	0.403056i
$11$	1.27594	+	3.06137i	0.384711	+	0.923037i
$11$	1.27594	+	3.06137i	0.384711	+	0.923037i
$12$	−1.01597	+	0.272228i	−0.293284	+	0.0785853i
$13$	−3.80412	−	3.80412i	−1.05507	−	1.05507i	−0.998392	−	0.0566802i	$-0.981948\pi$
$13$	−3.80412	−	3.80412i	−1.05507	−	1.05507i	−0.0566802	−	0.998392i	$-0.518052\pi$
$14$	2.45977	+	0.974444i	0.657401	+	0.260431i
$15$	0.194787	+	2.34383i	0.0502938	+	0.605174i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	2.13709	+	0.572632i	0.518321	+	0.138884i	0.508490	−	0.861068i	$-0.330204\pi$
$17$	2.13709	+	0.572632i	0.518321	+	0.138884i	0.00983118	+	0.999952i	$0.496871\pi$
$18$	−0.490126	+	1.82918i	−0.115524	+	0.431141i
$19$	−1.10162	+	1.90806i	−0.252729	+	0.437740i	−0.964276	−	0.264899i	$-0.914661\pi$
$19$	−1.10162	+	1.90806i	−0.252729	+	0.437740i	0.711547	+	0.702638i	$0.247995\pi$
$20$	−1.70666	−	1.44476i	−0.381620	−	0.323057i
$21$	−2.18121	+	1.72812i	−0.475980	+	0.377106i
$22$	2.62682	−	2.02480i	0.560039	−	0.431690i
$23$	1.76287	+	6.57913i	0.367584	+	1.37184i	0.863883	+	0.503692i	$0.168025\pi$
$23$	1.76287	+	6.57913i	0.367584	+	1.37184i	−0.496299	+	0.868152i	$0.665308\pi$
$24$	0.525903	+	0.910891i	0.107350	+	0.185935i
$25$	−3.85804	+	3.18049i	−0.771609	+	0.636098i
$26$	−2.68992	+	4.65907i	−0.527536	+	0.913720i
$27$	−3.63964	−	3.63964i	−0.700449	−	0.700449i
$28$	0.304606	−	2.62816i	0.0575651	−	0.496675i
$29$	−3.51700			−0.653091			−0.326545	−	0.945182i	$-0.605885\pi$
$29$	−3.51700			−0.653091			−0.326545	+	0.945182i	$0.605885\pi$
$30$	2.21355	−	0.794778i	0.404137	−	0.145106i
$31$	2.30011	+	3.98390i	0.413112	+	0.715530i	0.995228	−	0.0975750i	$-0.0311086\pi$
$31$	2.30011	+	3.98390i	0.413112	+	0.715530i	−0.582117	+	0.813105i	$0.697775\pi$
$32$	−0.965926	−	0.258819i	−0.170753	−	0.0457532i
$33$	0.462926	+	3.45760i	0.0805850	+	0.601890i
$34$		−	2.21248i		−	0.379437i
$35$	−5.66177	−	1.71591i	−0.957014	−	0.290041i
$36$	1.89370			0.315617
$37$	−6.65632	+	1.78356i	−1.09429	+	0.293215i	−0.760438	−	0.649410i	$-0.775016\pi$
$37$	−6.65632	+	1.78356i	−1.09429	+	0.293215i	−0.333854	+	0.942625i	$0.608349\pi$
$38$	2.12817	+	0.570241i	0.345234	+	0.0925053i
$39$	−2.82927	−	4.90044i	−0.453046	−	0.784699i
$40$	−0.953811	+	2.02244i	−0.150811	+	0.319775i
$41$			6.44737i			1.00691i	0.864021	+	0.503455i	$0.167938\pi$
$41$			6.44737i			1.00691i	−0.864021	+	0.503455i	$0.832062\pi$
$42$	2.23377	+	1.65962i	0.344679	+	0.256085i
$43$	3.27026	+	3.27026i	0.498710	+	0.498710i	0.911036	−	0.412326i	$-0.135284\pi$
$43$	3.27026	+	3.27026i	0.498710	+	0.498710i	−0.412326	+	0.911036i	$0.635284\pi$
$44$	−2.63568	−	2.01325i	−0.397344	−	0.303509i
$45$	0.753440	−	4.16688i	0.112316	−	0.621162i
$46$	5.89869	−	3.40561i	0.869714	−	0.502130i
$47$	0.121120	−	0.0324540i	0.0176672	−	0.00473391i	−0.249975	−	0.968252i	$-0.580422\pi$
$47$	0.121120	−	0.0324540i	0.0176672	−	0.00473391i	0.267642	+	0.963518i	$0.413756\pi$
$48$	0.743740	−	0.743740i	0.107350	−	0.107350i
$49$	−2.02062	−	6.70202i	−0.288660	−	0.957432i
$50$	4.07065	+	2.90341i	0.575677	+	0.410604i
$51$	2.01533	+	1.16355i	0.282203	+	0.162930i
$52$	5.19652	+	1.39240i	0.720628	+	0.193092i
$53$	1.88773	+	0.505816i	0.259300	+	0.0694792i	0.386127	−	0.922446i	$-0.373813\pi$
$53$	1.88773	+	0.505816i	0.259300	+	0.0694792i	−0.126827	+	0.991925i	$0.540479\pi$
$54$	−2.57361	+	4.45763i	−0.350225	+	0.606607i
$55$	−5.47858	+	4.99851i	−0.738732	+	0.674000i
$56$	−2.61744	+	0.385991i	−0.349771	+	0.0515802i
$57$	−1.63864	+	1.63864i	−0.217043	+	0.217043i
$58$	0.910267	+	3.39716i	0.119524	+	0.446069i
$59$	−1.86866	+	1.07887i	−0.243278	+	0.140457i	−0.616683	−	0.787212i	$-0.711524\pi$
$59$	−1.86866	+	1.07887i	−0.243278	+	0.140457i	0.373404	+	0.927669i	$0.378190\pi$
$60$	−1.34061	−	1.93242i	−0.173071	−	0.249475i
$61$	3.54246	+	2.04524i	0.453566	+	0.261866i	0.709335	−	0.704871i	$-0.248995\pi$
$61$	3.54246	+	2.04524i	0.453566	+	0.261866i	−0.255769	+	0.966738i	$0.582329\pi$
$62$	3.25284	−	3.25284i	0.413112	−	0.413112i
$63$	4.59858	−	1.98892i	0.579367	−	0.250581i
$64$			1.00000i			0.125000i
$65$	5.13135	−	10.8804i	0.636465	−	1.34954i
$66$	3.21997	−	1.34204i	0.396351	−	0.165194i
$67$	3.78627	−	14.1306i	0.462567	−	1.72632i	−0.202267	−	0.979330i	$-0.564831\pi$
$67$	3.78627	−	14.1306i	0.462567	−	1.72632i	0.664833	−	0.746992i	$-0.268503\pi$
$68$	−2.13709	+	0.572632i	−0.259161	+	0.0694419i
$69$			7.16408i			0.862454i
$70$	−0.192063	+	5.91296i	−0.0229559	+	0.706734i
$71$	7.05264			0.836995			0.418497	−	0.908218i	$-0.362557\pi$
$71$	7.05264			0.836995			0.418497	+	0.908218i	$0.362557\pi$
$72$	−0.490126	−	1.82918i	−0.0577620	−	0.215571i
$73$	−2.44097	+	9.10983i	−0.285694	+	1.06623i	0.662636	+	0.748941i	$0.269438\pi$
$73$	−2.44097	+	9.10983i	−0.285694	+	1.06623i	−0.948331	+	0.317284i	$0.897229\pi$
$74$	3.44556	+	5.96789i	0.400539	+	0.693753i
$75$	−4.78546	+	2.18101i	−0.552577	+	0.251841i
$76$		−	2.20324i		−	0.252729i
$77$	−8.51485	−	2.12068i	−0.970358	−	0.241674i
$78$	−4.00120	+	4.00120i	−0.453046	+	0.453046i
$79$	4.14156	−	7.17339i	0.465962	−	0.807069i	−0.533283	−	0.845937i	$-0.679042\pi$
$79$	4.14156	−	7.17339i	0.465962	−	0.807069i	0.999244	+	0.0388680i	$0.0123752\pi$
$80$	2.20039	+	0.397866i	0.246011	+	0.0444828i
$81$	0.133610	+	0.231420i	0.0148456	+	0.0257133i
$82$	6.22769	−	1.66870i	0.687733	−	0.184277i
$83$	−1.34396	−	1.34396i	−0.147519	−	0.147519i	0.629490	−	0.777009i	$-0.283264\pi$
$83$	−1.34396	−	1.34396i	−0.147519	−	0.147519i	−0.777009	+	0.629490i	$0.783264\pi$
$84$	1.02493	−	2.58720i	0.111829	−	0.282287i
$85$	0.409736	+	4.93026i	0.0444421	+	0.534762i
$86$	2.31242	−	4.00524i	0.249355	−	0.431896i
$87$	−3.57316	−	0.957425i	−0.383083	−	0.102647i
$88$	−1.26249	+	3.06694i	−0.134582	+	0.326937i
$89$	3.00167	+	1.73302i	0.318177	+	0.183699i	0.650580	−	0.759438i	$-0.274526\pi$
$89$	3.00167	+	1.73302i	0.318177	+	0.183699i	−0.332403	+	0.943138i	$0.607859\pi$
$90$	−4.21990	+	0.350700i	−0.444817	+	0.0369671i
$91$	14.0814	−	2.07657i	1.47613	−	0.217683i
$92$	−4.81626	−	4.81626i	−0.502130	−	0.502130i
$93$	1.25231	+	4.67367i	0.129858	+	0.484637i
$94$	−0.0626964	−	0.108593i	−0.00646663	−	0.0112005i
$95$	−4.84798	−	0.876595i	−0.497393	−	0.0899367i
$96$	−0.910891	−	0.525903i	−0.0929674	−	0.0536748i
$97$	10.8433	+	10.8433i	1.10097	+	1.10097i	0.994293	+	0.106679i	$0.0340218\pi$
$97$	10.8433	+	10.8433i	1.10097	+	1.10097i	0.106679	+	0.994293i	$0.465978\pi$
$98$	−5.95068	+	3.68638i	−0.601110	+	0.372380i
$99$	0.806124	−	6.22876i	0.0810185	−	0.626013i
$100$	1.75092	−	4.68341i	0.175092	−	0.468341i
$101$	8.90529	−	5.14147i	0.886109	−	0.511595i	0.0134413	−	0.999910i	$-0.495721\pi$
$101$	8.90529	−	5.14147i	0.886109	−	0.511595i	0.872668	+	0.488314i	$0.162388\pi$
$102$	0.602298	−	2.24781i	0.0596364	−	0.222566i
$103$	−1.64420	−	6.13622i	−0.162007	−	0.604620i	−0.998403	−	0.0564936i	$-0.982008\pi$
$103$	−1.64420	−	6.13622i	−0.162007	−	0.604620i	0.836396	−	0.548126i	$-0.184659\pi$
$104$		−	5.37984i		−	0.527536i
$105$	−5.28506	−	3.28459i	−0.515769	−	0.320544i
$106$		−	1.95432i		−	0.189821i
$107$	−5.11253	−	19.0802i	−0.494246	−	1.84455i	−0.534210	−	0.845352i	$-0.679391\pi$
$107$	−5.11253	−	19.0802i	−0.494246	−	1.84455i	0.0399635	−	0.999201i	$-0.487276\pi$
$108$	4.97184	+	1.33220i	0.478416	+	0.128191i
$109$	9.52774	+	16.5025i	0.912592	+	1.58065i	0.810390	+	0.585891i	$0.199255\pi$
$109$	9.52774	+	16.5025i	0.912592	+	1.58065i	0.102202	+	0.994764i	$0.467411\pi$
$110$	6.24616	+	3.99819i	0.595548	+	0.381213i
$111$	−7.24813			−0.687962
$112$	1.05028	+	2.42835i	0.0992424	+	0.229458i
$113$	12.0989	−	12.0989i	1.13817	−	1.13817i	0.149394	−	0.988778i	$-0.452268\pi$
$113$	12.0989	−	12.0989i	1.13817	−	1.13817i	0.988778	−	0.149394i	$-0.0477324\pi$
$114$	2.00691	+	1.15869i	0.187965	+	0.108521i
$115$	−12.5139	+	8.68141i	−1.16692	+	0.809545i
$116$	3.04581	−	1.75850i	0.282797	−	0.163273i
$117$	2.63680	+	9.84067i	0.243772	+	0.909770i
$118$	1.52575	+	1.52575i	0.140457	+	0.140457i
$119$	−4.58819	+	3.63511i	−0.420599	+	0.333230i
$120$	−1.51960	+	1.79507i	−0.138720	+	0.163867i
$121$	−7.74395	+	7.81225i	−0.703995	+	0.710205i
$122$	1.05870	−	3.95110i	0.0958498	−	0.357716i
$123$	−1.75515	+	6.55032i	−0.158257	+	0.590622i
$124$	−3.98390	−	2.30011i	−0.357765	−	0.206556i
$125$	−9.60867	−	5.71607i	−0.859426	−	0.511261i
$126$	−3.11135	−	3.92712i	−0.277181	−	0.349856i
$127$	−12.4570	+	12.4570i	−1.10538	+	1.10538i	−0.111632	+	0.993750i	$0.535608\pi$
$127$	−12.4570	+	12.4570i	−1.10538	+	1.10538i	−0.993750	+	0.111632i	$0.964392\pi$
$128$	0.965926	−	0.258819i	0.0853766	−	0.0228766i
$129$	2.43222	+	4.21273i	0.214145	+	0.370910i
$130$	−11.8377	−	2.14045i	−1.03824	−	0.187730i
$131$	10.9336	+	6.31251i	0.955271	+	0.551526i	0.894714	−	0.446639i	$-0.147379\pi$
$131$	10.9336	+	6.31251i	0.955271	+	0.551526i	0.0605569	+	0.998165i	$0.480712\pi$
$132$	−2.12970	−	2.76290i	−0.185367	−	0.240480i
$133$	−2.31403	−	5.35025i	−0.200651	−	0.463926i
$134$	−14.6290			−1.26376
$135$	4.90948	−	10.4099i	0.422541	−	0.895945i
$136$	1.10624	+	1.91606i	0.0948593	+	0.164301i
$137$	3.71127	−	13.8507i	0.317075	−	1.18334i	−0.604966	−	0.796251i	$-0.706813\pi$
$137$	3.71127	−	13.8507i	0.317075	−	1.18334i	0.922042	−	0.387091i	$-0.126520\pi$
$138$	6.91997	−	1.85420i	0.589067	−	0.157840i
$139$	17.2812			1.46577			0.732884	−	0.680354i	$-0.238174\pi$
$139$	17.2812			1.46577			0.732884	+	0.680354i	$0.238174\pi$
$140$	5.76119	−	1.34487i	0.486910	−	0.113662i
$141$	0.131889			0.0111070
$142$	−1.82536	−	6.81233i	−0.153181	−	0.571678i
$143$	6.79197	−	16.4996i	0.567973	−	1.37977i
$144$	−1.63999	+	0.946852i	−0.136666	+	0.0789043i
$145$	−2.65756	−	7.40161i	−0.220698	−	0.614670i
$146$	9.43119			0.780531
$147$	−0.228406	−	7.35910i	−0.0188386	−	0.606968i
$148$	4.87276	−	4.87276i	0.400539	−	0.400539i
$149$	−6.84503	+	11.8559i	−0.560766	+	0.971276i	0.436663	+	0.899625i	$0.356160\pi$
$149$	−6.84503	+	11.8559i	−0.560766	+	0.971276i	−0.997430	+	0.0716509i	$0.977173\pi$
$150$	3.34526	+	4.05791i	0.273139	+	0.331327i
$151$	−0.309026	+	0.178416i	−0.0251482	+	0.0145193i	−0.512521	−	0.858674i	$-0.671288\pi$
$151$	−0.309026	+	0.178416i	−0.0251482	+	0.0145193i	0.487373	+	0.873194i	$0.337955\pi$
$152$	−2.12817	+	0.570241i	−0.172617	+	0.0462526i
$153$	−2.96262	−	2.96262i	−0.239514	−	0.239514i
$154$	0.155388	+	8.77359i	0.0125215	+	0.706996i
$155$	−6.64619	+	7.85100i	−0.533835	+	0.630607i
$156$	4.90044	+	2.82927i	0.392350	+	0.226523i
$157$	1.99685	−	7.45236i	0.159366	−	0.594763i	−0.839326	−	0.543629i	$-0.817050\pi$
$157$	1.99685	−	7.45236i	0.159366	−	0.594763i	0.998692	−	0.0511337i	$-0.0162835\pi$
$158$	−8.00087	−	2.14383i	−0.636515	−	0.170554i
$159$	1.78018	+	1.02779i	0.141177	+	0.0815087i
$160$	−0.185193	−	2.22839i	−0.0146408	−	0.176169i
$161$	−16.7540	−	6.63715i	−1.32040	−	0.523081i
$162$	0.188954	−	0.188954i	0.0148456	−	0.0148456i
$163$	−4.22375	−	15.7632i	−0.330829	−	1.23467i	−0.908320	−	0.418275i	$-0.862635\pi$
$163$	−4.22375	−	15.7632i	−0.330829	−	1.23467i	0.577491	−	0.816397i	$-0.304032\pi$
$164$	−3.22369	−	5.58359i	−0.251728	−	0.436005i
$165$	−6.92679	+	3.58691i	−0.539250	+	0.279240i
$166$	−0.950324	+	1.64601i	−0.0737594	+	0.127755i
$167$	−1.11990	+	1.11990i	−0.0866605	+	0.0866605i	−0.749108	−	0.662448i	$-0.769518\pi$
$167$	−1.11990	+	1.11990i	−0.0866605	+	0.0866605i	0.662448	+	0.749108i	$0.269518\pi$
$168$	−2.76431	−	0.320386i	−0.213271	−	0.0247183i
$169$			15.9426i			1.22636i
$170$	4.65622	−	1.67182i	0.357116	−	0.128223i
$171$	3.61330	−	2.08614i	0.276316	−	0.159531i
$172$	−4.46726	−	1.19700i	−0.340625	−	0.0912703i
$173$	−22.3149	+	5.97925i	−1.69657	+	0.454594i	−0.972071	−	0.234685i	$-0.924594\pi$
$173$	−22.3149	+	5.97925i	−1.69657	+	0.454594i	−0.724496	+	0.689279i	$0.757927\pi$
$174$			3.69920i			0.280436i
$175$	−0.667048	−	13.2119i	−0.0504241	−	0.998728i
$176$	3.28919	+	0.425686i	0.247932	+	0.0320873i
$177$	−2.19219	+	0.587396i	−0.164775	+	0.0441514i
$178$	0.897076	−	3.34793i	0.0672387	−	0.250938i
$179$	5.14664	−	2.97142i	0.384678	−	0.222094i	−0.295174	−	0.955444i	$-0.595377\pi$
$179$	5.14664	−	2.97142i	0.384678	−	0.222094i	0.679852	+	0.733350i	$0.262044\pi$
$180$	1.43094	+	3.98534i	0.106656	+	0.297050i
$181$	11.7076			0.870222			0.435111	−	0.900377i	$-0.356709\pi$
$181$	11.7076			0.870222			0.435111	+	0.900377i	$0.356709\pi$
$182$	−5.65035	−	13.0641i	−0.418832	−	0.968379i
$183$	3.04226	+	3.04226i	0.224890	+	0.224890i
$184$	−3.40561	+	5.89869i	−0.251065	+	0.434857i
$185$	−8.78326	−	12.6607i	−0.645758	−	0.930831i
$186$	4.19030	−	2.41927i	0.307247	−	0.177389i
$187$	0.973767	+	7.27307i	0.0712089	+	0.531860i
$188$	−0.0886660	+	0.0886660i	−0.00646663	+	0.00646663i
$189$	13.4726	−	1.98678i	0.979986	−	0.144517i
$190$	0.408025	+	4.90967i	0.0296012	+	0.356185i
$191$	0.755768	−	1.30903i	0.0546855	−	0.0947180i	−0.837387	−	0.546611i	$-0.815918\pi$
$191$	0.755768	−	1.30903i	0.0546855	−	0.0947180i	0.892072	+	0.451893i	$0.149251\pi$
$192$	−0.272228	+	1.01597i	−0.0196463	+	0.0733211i
$193$	3.33303	−	12.4390i	0.239916	−	0.895380i	−0.735954	−	0.677031i	$-0.763266\pi$
$193$	3.33303	−	12.4390i	0.239916	−	0.895380i	0.975871	−	0.218349i	$-0.0700671\pi$
$194$	7.66739	−	13.2803i	0.550486	−	0.953470i
$195$	8.17522	−	9.65720i	0.585439	−	0.691567i
$196$	5.10092	+	4.79381i	0.364351	+	0.342415i
$197$	−3.78139	+	3.78139i	−0.269413	+	0.269413i	−0.828864	−	0.559451i	$-0.811012\pi$
$197$	−3.78139	+	3.78139i	−0.269413	+	0.269413i	0.559451	+	0.828864i	$0.311012\pi$
$198$	−6.22516	+	0.833465i	−0.442403	+	0.0592318i
$199$	−16.2668	+	9.39164i	−1.15312	+	0.665755i	−0.949646	−	0.313324i	$-0.898557\pi$
$199$	−16.2668	+	9.39164i	−1.15312	+	0.665755i	−0.203476	+	0.979080i	$0.565224\pi$
$200$	−4.97699	−	0.479103i	−0.351927	−	0.0338777i
$201$	7.69345	−	13.3255i	0.542654	−	0.939905i
$202$	−7.27114	−	7.27114i	−0.511595	−	0.511595i
$203$	5.54939	−	7.46923i	0.389491	−	0.524237i
$204$	−2.32710			−0.162930
$205$	−13.5687	+	4.87184i	−0.947676	+	0.340264i
$206$	−5.50159	+	3.17634i	−0.383314	+	0.221306i
$207$	3.33836	−	12.4589i	0.232032	−	0.865955i
$208$	−5.19652	+	1.39240i	−0.360314	+	0.0965458i
$209$	−7.24688	−	0.937890i	−0.501277	−	0.0648752i
$210$	−1.80480	+	5.95509i	−0.124543	+	0.410940i
$211$			15.9855i			1.10049i	0.835004	+	0.550244i	$0.185465\pi$
$211$			15.9855i			1.10049i	−0.835004	+	0.550244i	$0.814535\pi$
$212$	−1.88773	+	0.505816i	−0.129650	+	0.0347396i
$213$	7.16525	+	1.91992i	0.490955	+	0.131551i
$214$	−17.1068	+	9.87664i	−1.16940	+	0.675153i
$215$	−4.41123	+	9.35345i	−0.300843	+	0.637900i
$216$		−	5.14723i		−	0.350225i
$217$	−12.0901	−	1.40125i	−0.820729	−	0.0951232i
$218$	13.4743	−	13.4743i	0.912592	−	0.912592i
$219$	−4.95990	+	8.59079i	−0.335159	+	0.580512i
$220$	2.24533	−	7.06813i	0.151380	−	0.476533i
$221$	−5.95139	−	10.3081i	−0.400334	−	0.693399i
$222$	1.87596	+	7.00116i	0.125906	+	0.469887i
$223$	2.20492	−	2.20492i	0.147652	−	0.147652i	−0.629416	−	0.777068i	$-0.716706\pi$
$223$	2.20492	−	2.20492i	0.147652	−	0.147652i	0.777068	+	0.629416i	$0.216706\pi$
$224$	2.07378	−	1.64300i	0.138560	−	0.109778i
$225$	9.33862	−	1.56299i	0.622575	−	0.104199i
$226$	−14.8181	−	8.55524i	−0.985686	−	0.569086i
$227$	22.4146	+	6.00597i	1.48771	+	0.398631i	0.908963	−	0.416877i	$-0.136875\pi$
$227$	22.4146	+	6.00597i	1.48771	+	0.398631i	0.578747	+	0.815507i	$0.303542\pi$
$228$	0.599783	−	2.23842i	0.0397216	−	0.148243i
$229$	7.11179	+	4.10599i	0.469960	+	0.271332i	0.716223	−	0.697871i	$-0.245869\pi$
$229$	7.11179	+	4.10599i	0.469960	+	0.271332i	−0.246263	+	0.969203i	$0.579203\pi$
$230$	11.6244	+	9.84055i	0.766492	+	0.648866i
$231$	−8.07350	−	4.47252i	−0.531198	−	0.294270i
$232$	−2.48690	−	2.48690i	−0.163273	−	0.163273i
$233$	−9.48552	+	2.54164i	−0.621417	+	0.166508i	−0.555772	−	0.831335i	$-0.687577\pi$
$233$	−9.48552	+	2.54164i	−0.621417	+	0.166508i	−0.0656452	+	0.997843i	$0.520911\pi$
$234$	8.82290	−	5.09391i	0.576771	−	0.332999i
$235$	0.159822	+	0.230377i	0.0104257	+	0.0150281i
$236$	1.07887	−	1.86866i	0.0702284	−	0.121639i
$237$	6.16048	−	6.16048i	0.400166	−	0.400166i
$238$	4.69875	+	3.49102i	0.304575	+	0.226289i
$239$	−14.3996			−0.931432			−0.465716	−	0.884934i	$-0.654203\pi$
$239$	−14.3996			−0.931432			−0.465716	+	0.884934i	$0.654203\pi$
$240$	2.12721	+	1.00322i	0.137311	+	0.0647579i
$241$	3.23895	−	1.87001i	0.208639	−	0.120458i	−0.392040	−	0.919948i	$-0.628230\pi$
$241$	3.23895	−	1.87001i	0.208639	−	0.120458i	0.600679	+	0.799490i	$0.294897\pi$
$242$	9.55034	+	5.45812i	0.613919	+	0.350861i
$243$	4.06935	+	15.1870i	0.261049	+	0.974247i
$244$	−4.09048			−0.261866
$245$	12.5777	−	9.31670i	0.803561	−	0.595222i
$246$	6.78139			0.432366
$247$	11.4492	−	3.06780i	0.728495	−	0.195200i
$248$	−1.19062	+	4.44347i	−0.0756047	+	0.282161i
$249$	−0.999557	−	1.73128i	−0.0633443	−	0.109716i
$250$	−3.03439	+	10.7607i	−0.191912	+	0.680566i
$251$	−10.3685			−0.654456			−0.327228	−	0.944945i	$-0.606115\pi$
$251$	−10.3685			−0.654456			−0.327228	+	0.944945i	$0.606115\pi$
$252$	−2.98803	+	4.02175i	−0.188228	+	0.253346i
$253$	−17.8918	+	13.7914i	−1.12485	+	0.867057i
$254$	15.2567	+	8.80844i	0.957289	+	0.552691i
$255$	−0.925875	+	5.12052i	−0.0579805	+	0.320660i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−9.78329	+	2.62142i	−0.610265	+	0.163520i	−0.550698	−	0.834704i	$-0.685639\pi$
$257$	−9.78329	+	2.62142i	−0.610265	+	0.163520i	−0.0595665	+	0.998224i	$0.518972\pi$
$258$	3.43968	−	3.43968i	0.214145	−	0.214145i
$259$	6.71502	−	16.9506i	0.417251	−	1.05326i
$260$	0.996308	+	11.9884i	0.0617884	+	0.743486i
$261$	5.76786	+	3.33008i	0.357022	+	0.206127i
$262$	3.26759	−	12.1948i	0.201873	−	0.753399i
$263$	2.78755	−	10.4033i	0.171888	−	0.641493i	−0.825173	−	0.564880i	$-0.808923\pi$
$263$	2.78755	−	10.4033i	0.171888	−	0.641493i	0.997061	−	0.0766135i	$-0.0244108\pi$
$264$	−2.11755	+	2.77223i	−0.130326	+	0.170619i
$265$	0.361927	+	4.35499i	0.0222330	+	0.267525i
$266$	−4.56903	+	3.61992i	−0.280145	+	0.221952i
$267$	2.57783	+	2.57783i	0.157760	+	0.157760i
$268$	3.78627	+	14.1306i	0.231283	+	0.863161i
$269$	−11.2048	+	6.46911i	−0.683170	+	0.394428i	−0.801048	−	0.598600i	$-0.795724\pi$
$269$	−11.2048	+	6.46911i	−0.683170	+	0.394428i	0.117878	+	0.993028i	$0.462391\pi$
$270$	−11.3259	−	2.04791i	−0.689272	−	0.124632i
$271$	13.2594	+	7.65532i	0.805451	+	0.465027i	0.845374	−	0.534175i	$-0.179378\pi$
$271$	13.2594	+	7.65532i	0.805451	+	0.465027i	−0.0399226	+	0.999203i	$0.512711\pi$
$272$	1.56446	−	1.56446i	0.0948593	−	0.0948593i
$273$	14.8716	+	1.72363i	0.900067	+	0.104319i
$274$	−14.3393			−0.866266
$275$	−14.6593	−	7.75277i	−0.883988	−	0.467510i
$276$	−3.58204	−	6.20428i	−0.215614	−	0.373454i
$277$	5.08020	+	1.36124i	0.305240	+	0.0817888i	0.408188	−	0.912898i	$-0.366161\pi$
$277$	5.08020	+	1.36124i	0.305240	+	0.0817888i	−0.102948	+	0.994687i	$0.532828\pi$
$278$	−4.47269	−	16.6923i	−0.268254	−	1.00114i
$279$		−	8.71144i		−	0.521541i
$280$	−2.79015	−	5.21681i	−0.166743	−	0.311764i
$281$		−	16.2299i		−	0.968192i	−0.875015	−	0.484096i	$-0.839148\pi$
$281$		−	16.2299i		−	0.968192i	0.875015	−	0.484096i	$-0.160852\pi$
$282$	−0.0341353	−	0.127395i	−0.00203273	−	0.00758625i
$283$	2.03970	−	7.61225i	0.121247	−	0.452501i	−0.878431	−	0.477870i	$-0.841409\pi$
$283$	2.03970	−	7.61225i	0.121247	−	0.452501i	0.999678	+	0.0253681i	$0.00807580\pi$
$284$	−6.10777	+	3.52632i	−0.362429	+	0.209249i
$285$	−4.68676	−	2.21035i	−0.277620	−	0.130930i
$286$	−17.6953	−	2.29012i	−1.04635	−	0.135418i
$287$	−13.6926	−	10.1732i	−0.808249	−	0.600502i
$288$	1.33905	+	1.33905i	0.0789043	+	0.0789043i
$289$	−10.4832	−	6.05246i	−0.616657	−	0.356027i
$290$	−6.46158	+	4.48268i	−0.379437	+	0.263232i
$291$	8.06461	+	13.9683i	0.472756	+	0.818837i
$292$	−2.44097	−	9.10983i	−0.142847	−	0.533113i
$293$	12.5119	+	12.5119i	0.730956	+	0.730956i	0.970809	−	0.239853i	$-0.0770994\pi$
$293$	12.5119	+	12.5119i	0.730956	+	0.730956i	−0.239853	+	0.970809i	$0.577099\pi$
$294$	−7.04923	+	2.12530i	−0.411119	+	0.123950i
$295$	−3.68252	−	3.11741i	−0.214405	−	0.181502i
$296$	−5.96789	−	3.44556i	−0.346877	−	0.200269i
$297$	6.49831	−	15.7862i	0.377070	−	0.916011i
$298$	13.2236	+	3.54325i	0.766021	+	0.205255i
$299$	18.3216	−	31.7340i	1.05957	−	1.83522i
$300$	3.05383	−	4.28154i	0.176313	−	0.247195i
$301$	−12.1053	+	1.78515i	−0.697737	+	0.102894i
$302$	0.252319	+	0.252319i	0.0145193	+	0.0145193i
$303$	10.4471	−	2.79930i	0.600172	−	0.160816i
$304$	1.10162	+	1.90806i	0.0631823	+	0.109435i
$305$	−1.62747	+	9.00065i	−0.0931884	+	0.515376i
$306$	−2.09489	+	3.62846i	−0.119757	+	0.207425i
$307$	9.46479	−	9.46479i	0.540184	−	0.540184i	−0.383399	−	0.923583i	$-0.625247\pi$
$307$	9.46479	−	9.46479i	0.540184	−	0.540184i	0.923583	+	0.383399i	$0.125247\pi$
$308$	8.43442	−	2.42086i	0.480596	−	0.137942i
$309$		−	6.68180i		−	0.380114i
$310$	9.30364	+	4.38774i	0.528411	+	0.249207i
$311$	4.95916	+	8.58951i	0.281208	+	0.487066i	0.971683	−	0.236290i	$-0.0759316\pi$
$311$	4.95916	+	8.58951i	0.281208	+	0.487066i	−0.690475	+	0.723357i	$0.742598\pi$
$312$	1.46454	−	5.46574i	0.0829132	−	0.309436i
$313$	−1.78384	−	6.65737i	−0.100828	−	0.376297i	0.897010	−	0.442010i	$-0.145734\pi$
$313$	−1.78384	−	6.65737i	−0.100828	−	0.376297i	−0.997839	+	0.0657131i	$0.979068\pi$
$314$	−7.71525			−0.435397
$315$	7.66057	+	8.17493i	0.431624	+	0.460605i
$316$			8.28311i			0.465962i
$317$	5.33404	−	1.42925i	0.299589	−	0.0802747i	−0.105893	−	0.994378i	$-0.533770\pi$
$317$	5.33404	−	1.42925i	0.299589	−	0.0802747i	0.405483	+	0.914103i	$0.367103\pi$
$318$	0.532021	−	1.98553i	0.0298343	−	0.111343i
$319$	−4.48749	−	10.7668i	−0.251251	−	0.602827i
$320$	−2.10452	+	0.755631i	−0.117646	+	0.0422411i
$321$		−	20.7766i		−	1.15964i
$322$	−2.07474	+	17.9010i	−0.115621	+	0.997581i
$323$	−3.44688	+	3.44688i	−0.191790	+	0.191790i
$324$	−0.231420	−	0.133610i	−0.0128567	−	0.00742280i
$325$	26.7754	+	2.57750i	1.48523	+	0.142974i
$326$	−14.1329	+	8.15965i	−0.782751	+	0.451921i
$327$	5.18742	+	19.3597i	0.286865	+	1.07060i
$328$	−4.55898	+	4.55898i	−0.251728	+	0.251728i
$329$	−0.122188	+	0.308437i	−0.00673645	+	0.0170047i
$330$	5.25747	+	5.76241i	0.289414	+	0.317210i
$331$	−12.2007	+	21.1323i	−0.670612	+	1.16153i	0.307118	+	0.951671i	$0.400635\pi$
$331$	−12.2007	+	21.1323i	−0.670612	+	1.16153i	−0.977731	+	0.209863i	$0.932698\pi$
$332$	1.83588	+	0.491924i	0.100757	+	0.0269978i
$333$	12.6051	+	3.37752i	0.690755	+	0.185087i
$334$	1.37159	+	0.791890i	0.0750502	+	0.0433303i
$335$	32.5991	−	2.70919i	1.78108	−	0.148019i
$336$	0.405988	+	2.75304i	0.0221484	+	0.150191i
$337$	−12.0473	+	12.0473i	−0.656257	+	0.656257i	−0.954492	−	0.298236i	$-0.903602\pi$
$337$	−12.0473	+	12.0473i	−0.656257	+	0.656257i	0.298236	+	0.954492i	$0.403602\pi$
$338$	15.3994	−	4.12626i	0.837617	−	0.224439i
$339$	15.5858	−	8.99846i	0.846504	−	0.488729i
$340$	−2.81997	−	4.06486i	−0.152934	−	0.220448i
$341$	−9.26139	+	12.1247i	−0.501533	+	0.656590i
$342$	−2.95025	−	2.95025i	−0.159531	−	0.159531i
$343$	17.4217	+	6.28367i	0.940683	+	0.339286i
$344$			4.62485i			0.249355i
$345$	−15.0770	+	5.41341i	−0.811718	+	0.291448i
$346$	11.5510	+	20.0070i	0.620987	+	1.07558i
$347$	22.3855	+	5.99818i	1.20172	+	0.321999i	0.803507	−	0.595295i	$-0.202965\pi$
$347$	22.3855	+	5.99818i	1.20172	+	0.321999i	0.398210	+	0.917294i	$0.369631\pi$
$348$	3.57316	−	0.957425i	0.191541	−	0.0513233i
$349$	17.8952			0.957906			0.478953	−	0.877841i	$-0.341016\pi$
$349$	17.8952			0.957906			0.478953	+	0.877841i	$0.341016\pi$
$350$	−12.5891	+	4.06382i	−0.672916	+	0.217220i
$351$			27.6912i			1.47805i
$352$	−0.440124	−	3.28729i	−0.0234587	−	0.175213i
$353$	16.7608	+	4.49103i	0.892086	+	0.239034i	0.675614	−	0.737255i	$-0.263878\pi$
$353$	16.7608	+	4.49103i	0.892086	+	0.239034i	0.216471	+	0.976289i	$0.430545\pi$
$354$	1.13476	+	1.96547i	0.0603119	+	0.104463i
$355$	5.32920	+	14.8425i	0.282844	+	0.787756i
$356$	−3.46604			−0.183699
$357$	−5.65103	+	2.44411i	−0.299084	+	0.129356i
$358$	−4.20222	−	4.20222i	−0.222094	−	0.222094i
$359$	2.58275	−	4.47346i	0.136313	−	0.236100i	−0.789786	−	0.613383i	$-0.789808\pi$
$359$	2.58275	−	4.47346i	0.136313	−	0.236100i	0.926098	+	0.377283i	$0.123142\pi$
$360$	3.47919	−	2.41367i	0.183369	−	0.127211i
$361$	7.07286	+	12.2506i	0.372256	+	0.644766i
$362$	−3.03016	−	11.3087i	−0.159262	−	0.594373i
$363$	−9.99431	+	5.82887i	−0.524565	+	0.305937i
$364$	−11.1566	+	8.83907i	−0.584764	+	0.463293i
$365$	−21.0163	+	1.74659i	−1.10005	+	0.0914207i
$366$	2.15120	−	3.72599i	0.112445	−	0.194760i
$367$	−6.19199	+	23.1088i	−0.323219	+	1.20627i	0.592871	+	0.805297i	$0.297994\pi$
$367$	−6.19199	+	23.1088i	−0.323219	+	1.20627i	−0.916090	+	0.400972i	$0.868672\pi$
$368$	6.57913	+	1.76287i	0.342961	+	0.0918961i
$369$	6.10471	−	10.5737i	0.317798	−	0.550443i
$370$	−9.95600	+	11.7608i	−0.517588	+	0.611415i
$371$	−4.05283	+	3.21095i	−0.210413	+	0.166704i
$372$	−3.42136	−	3.42136i	−0.177389	−	0.177389i
$373$	−32.4724	+	8.70096i	−1.68136	+	0.450519i	−0.968137	−	0.250420i	$-0.919431\pi$
$373$	−32.4724	+	8.70096i	−1.68136	+	0.450519i	−0.713221	+	0.700939i	$0.752765\pi$
$374$	6.77322	−	2.82300i	0.350235	−	0.145974i
$375$	−8.20602	−	8.42308i	−0.423757	−	0.434966i
$376$	0.108593	+	0.0626964i	0.00560027	+	0.00323332i
$377$	13.3791	+	13.3791i	0.689058	+	0.689058i
$378$	−5.40605	−	12.4993i	−0.278057	−	0.642894i
$379$			25.4917i			1.30942i	0.755881	+	0.654710i	$0.227209\pi$
$379$			25.4917i			1.30942i	−0.755881	+	0.654710i	$0.772791\pi$
$380$	4.63677	−	1.66484i	0.237861	−	0.0854044i
$381$	−16.0471	+	9.26478i	−0.822116	+	0.474649i
$382$	−1.46003	−	0.391214i	−0.0747017	−	0.0200163i
$383$	1.10109	+	4.10933i	0.0562632	+	0.209977i	0.988335	−	0.152297i	$-0.0486671\pi$
$383$	1.10109	+	4.10933i	0.0562632	+	0.209977i	−0.932072	+	0.362274i	$0.882000\pi$
$384$	1.05181			0.0536748
$385$	−1.97107	−	19.5222i	−0.100455	−	0.994942i
$386$	−12.8778			−0.655464
$387$	−2.26676	−	8.45966i	−0.115226	−	0.430029i
$388$	−14.8123	−	3.96893i	−0.751978	−	0.201492i
$389$	10.8765	−	6.27953i	0.551459	−	0.318385i	−0.198252	−	0.980151i	$-0.563526\pi$
$389$	10.8765	−	6.27953i	0.551459	−	0.318385i	0.749710	+	0.661766i	$0.230193\pi$
$390$	−11.4440	−	5.39718i	−0.579492	−	0.273297i
$391$			15.0697i			0.762107i
$392$	3.31025	−	6.16784i	0.167193	−	0.311523i
$393$	9.38972	+	9.38972i	0.473649	+	0.473649i
$394$	4.63124	+	2.67385i	0.233319	+	0.134707i
$395$	18.2261	+	3.29557i	0.917052	+	0.165818i
$396$	2.41625	+	5.79732i	0.121421	+	0.291326i
$397$	−26.4559	+	7.08885i	−1.32779	+	0.355779i	−0.851889	−	0.523722i	$-0.824543\pi$
$397$	−26.4559	+	7.08885i	−1.32779	+	0.355779i	−0.475896	+	0.879501i	$0.657876\pi$
$398$	13.2818	+	13.2818i	0.665755	+	0.665755i
$399$	−0.894488	−	6.06562i	−0.0447804	−	0.303661i
$400$	0.825363	+	4.93141i	0.0412681	+	0.246570i
$401$	−9.68586	+	16.7764i	−0.483689	+	0.837773i	−0.999825	−	0.0187334i	$-0.994037\pi$
$401$	−9.68586	+	16.7764i	−0.483689	+	0.837773i	0.516136	+	0.856507i	$0.327370\pi$
$402$	−14.8626	−	3.98242i	−0.741280	−	0.198625i
$403$	6.40536	−	23.9051i	0.319074	−	1.19080i
$404$	−5.14147	+	8.90529i	−0.255798	+	0.443055i
$405$	−0.386069	+	0.456054i	−0.0191839	+	0.0226615i
$406$	−8.65101	−	3.42712i	−0.429342	−	0.170085i
$407$	−13.9532	−	18.1017i	−0.691634	−	0.897270i
$408$	0.602298	+	2.24781i	0.0298182	+	0.111283i
$409$	16.2255	+	28.1034i	0.802299	+	1.38962i	0.918100	+	0.396350i	$0.129723\pi$
$409$	16.2255	+	28.1034i	0.802299	+	1.38962i	−0.115801	+	0.993272i	$0.536943\pi$
$410$	8.21766	+	11.8454i	0.405841	+	0.585002i
$411$	7.54106	−	13.0615i	0.371973	−	0.644276i
$412$	4.49203	+	4.49203i	0.221306	+	0.221306i
$413$	0.657260	−	5.67088i	0.0323416	−	0.279046i
$414$	−12.8984			−0.633923
$415$	1.81286	−	3.84394i	0.0889897	−	0.188691i
$416$	2.68992	+	4.65907i	0.131884	+	0.228430i
$417$	17.5571	+	4.70441i	0.859774	+	0.230376i
$418$	0.969700	+	7.24270i	0.0474296	+	0.354252i
$419$			17.0307i			0.832005i	0.909363	+	0.416003i	$0.136569\pi$
$419$			17.0307i			0.832005i	−0.909363	+	0.416003i	$0.863431\pi$
$420$	6.21929	+	0.202013i	0.303470	+	0.00985723i
$421$	28.7332			1.40037			0.700184	−	0.713962i	$-0.253101\pi$
$421$	28.7332			1.40037			0.700184	+	0.713962i	$0.253101\pi$
$422$	15.4408	−	4.13735i	0.751647	−	0.201403i
$423$	−0.229365	−	0.0614583i	−0.0111521	−	0.00298820i
$424$	0.977162	+	1.69249i	0.0474552	+	0.0821948i
$425$	−10.0662	+	4.58776i	−0.488285	+	0.222539i
$426$		−	7.41802i		−	0.359404i
$427$	−9.93315	+	4.29617i	−0.480699	+	0.207906i
$428$	13.9677	+	13.9677i	0.675153	+	0.675153i
$429$	11.3921	−	14.9141i	0.550015	−	0.720061i
$430$	10.1765	+	1.84007i	0.490752	+	0.0887360i
$431$	8.78767	−	5.07356i	0.423287	−	0.244385i	−0.273196	−	0.961959i	$-0.588081\pi$
$431$	8.78767	−	5.07356i	0.423287	−	0.244385i	0.696483	+	0.717574i	$0.254747\pi$
$432$	−4.97184	+	1.33220i	−0.239208	+	0.0640955i
$433$	−21.1975	+	21.1975i	−1.01869	+	1.01869i	−0.0188656	+	0.999822i	$0.506005\pi$
$433$	−21.1975	+	21.1975i	−1.01869	+	1.01869i	−0.999822	+	0.0188656i	$0.993995\pi$
$434$	1.77564	+	12.0408i	0.0852335	+	0.577977i
$435$	−0.685066	−	8.24325i	−0.0328464	−	0.395234i
$436$	−16.5025	−	9.52774i	−0.790327	−	0.456296i
$437$	−14.4954	−	3.88403i	−0.693410	−	0.185799i
$438$	9.58178	+	2.56743i	0.457835	+	0.122677i
$439$	9.55325	−	16.5467i	0.455952	−	0.789732i	−0.542790	−	0.839868i	$-0.682632\pi$
$439$	9.55325	−	16.5467i	0.455952	−	0.789732i	0.998742	+	0.0501363i	$0.0159656\pi$
$440$	−7.40843	−	0.339458i	−0.353183	−	0.0161830i
$441$	−3.03202	+	12.9045i	−0.144382	+	0.614500i
$442$	−8.41654	+	8.41654i	−0.400334	+	0.400334i
$443$	−9.73893	−	36.3462i	−0.462711	−	1.72686i	−0.664370	−	0.747404i	$-0.731300\pi$
$443$	−9.73893	−	36.3462i	−0.462711	−	1.72686i	0.201660	−	0.979456i	$-0.435367\pi$
$444$	6.27707	−	3.62407i	0.297896	−	0.171991i
$445$	−1.37902	+	7.62662i	−0.0653717	+	0.361536i
$446$	−2.70046	−	1.55911i	−0.127871	−	0.0738261i
$447$	−10.1818	+	10.1818i	−0.481584	+	0.481584i
$448$	−2.12375	−	1.57788i	−0.100338	−	0.0745476i
$449$			0.0874576i			0.00412738i	0.999998	+	0.00206369i	$0.000656893\pi$
$449$			0.0874576i			0.00412738i	−0.999998	+	0.00206369i	$0.999343\pi$
$450$	−3.92675	−	8.61588i	−0.185109	−	0.406157i
$451$	−19.7378	+	8.22647i	−0.929416	+	0.387369i
$452$	−4.42852	+	16.5275i	−0.208300	+	0.777386i
$453$	−0.362530	+	0.0971396i	−0.0170331	+	0.00456402i
$454$		−	23.2053i		−	1.08908i
$455$	15.0105	+	28.0656i	0.703705	+	1.31573i
$456$	−2.31738			−0.108521
$457$	3.52768	+	13.1655i	0.165018	+	0.615855i	0.998038	+	0.0626122i	$0.0199431\pi$
$457$	3.52768	+	13.1655i	0.165018	+	0.615855i	−0.833020	+	0.553243i	$0.813390\pi$
$458$	2.12542	−	7.93217i	0.0993143	−	0.370646i
$459$	−5.69407	−	9.86242i	−0.265777	−	0.460339i
$460$	6.49662	−	13.7752i	0.302906	−	0.642274i
$461$		−	9.63849i		−	0.448909i	−0.974485	−	0.224455i	$-0.927940\pi$
$461$		−	9.63849i		−	0.448909i	0.974485	−	0.224455i	$-0.0720601\pi$
$462$	−2.23054	+	8.95598i	−0.103774	+	0.416670i
$463$	−10.4172	+	10.4172i	−0.484130	+	0.484130i	−0.906448	−	0.422318i	$-0.861217\pi$
$463$	−10.4172	+	10.4172i	−0.484130	+	0.484130i	0.422318	+	0.906448i	$0.361217\pi$
$464$	−1.75850	+	3.04581i	−0.0816363	+	0.141398i
$465$	−8.88957	+	6.16708i	−0.412244	+	0.285991i
$466$	4.91007	+	8.50448i	0.227454	+	0.393963i
$467$	36.9835	−	9.90971i	1.71139	−	0.458567i	0.735628	−	0.677385i	$-0.236887\pi$
$467$	36.9835	−	9.90971i	1.71139	−	0.458567i	0.975765	+	0.218819i	$0.0702204\pi$
$468$	−7.20387	−	7.20387i	−0.332999	−	0.332999i
$469$	24.0355	+	30.3373i	1.10986	+	1.40085i
$470$	0.181162	−	0.214002i	0.00835637	−	0.00987120i
$471$	4.05747	−	7.02775i	0.186958	−	0.323822i
$472$	−2.08422	−	0.558464i	−0.0959338	−	0.0257054i
$473$	−5.83881	+	14.1841i	−0.268469	+	0.652187i
$474$	−7.54501	−	4.35612i	−0.346554	−	0.200083i
$475$	−1.81847	−	10.8651i	−0.0834372	−	0.498524i
$476$	2.15594	−	5.44219i	0.0988173	−	0.249442i
$477$	−2.61694	−	2.61694i	−0.119821	−	0.119821i
$478$	3.72689	+	13.9089i	0.170464	+	0.636180i
$479$	16.3890	+	28.3866i	0.748833	+	1.29702i	0.948383	+	0.317129i	$0.102719\pi$
$479$	16.3890	+	28.3866i	0.748833	+	1.29702i	−0.199550	+	0.979888i	$0.563948\pi$
$480$	0.418478	−	2.31438i	0.0191008	−	0.105637i
$481$	32.1063	+	18.5366i	1.46392	+	0.845195i
$482$	−2.64459	−	2.64459i	−0.120458	−	0.120458i
$483$	−15.2147	−	11.3040i	−0.692293	−	0.514351i
$484$	2.80033	−	10.6376i	0.127288	−	0.483526i
$485$	−14.6265	+	31.0136i	−0.664154	+	1.40825i
$486$	13.6163	−	7.86138i	0.617648	−	0.356599i
$487$	−3.18311	+	11.8795i	−0.144240	+	0.538312i	0.855548	+	0.517724i	$0.173221\pi$
$487$	−3.18311	+	11.8795i	−0.144240	+	0.538312i	−0.999788	+	0.0205882i	$0.993446\pi$
$488$	1.05870	+	3.95110i	0.0479249	+	0.178858i
$489$		−	17.1647i		−	0.776217i
$490$	−12.2546	−	9.73781i	−0.553606	−	0.439909i
$491$		−	29.0698i		−	1.31190i	−0.754803	−	0.655951i	$-0.772268\pi$
$491$		−	29.0698i		−	1.31190i	0.754803	−	0.655951i	$-0.227732\pi$
$492$	−1.75515	−	6.55032i	−0.0791284	−	0.295311i
$493$	−7.51616	−	2.01395i	−0.338511	−	0.0907037i
$494$	−5.92654	−	10.2651i	−0.266648	−	0.461847i
$495$	13.7177	−	3.01014i	0.616565	−	0.135296i
$496$	4.60022			0.206556
$497$	−11.1282	+	14.9780i	−0.499168	+	0.671857i
$498$	−1.41359	+	1.41359i	−0.0633443	+	0.0633443i
$499$	4.16265	+	2.40331i	0.186346	+	0.107587i	0.590271	−	0.807205i	$-0.299021\pi$
$499$	4.16265	+	2.40331i	0.186346	+	0.107587i	−0.403925	+	0.914792i	$0.632354\pi$
$500$	11.1794	+	0.145922i	0.499957	+	0.00652585i
$501$	−1.44265	+	0.832915i	−0.0644529	+	0.0372119i
$502$	2.68358	+	10.0152i	0.119774	+	0.447002i
$503$	−13.0863	−	13.0863i	−0.583488	−	0.583488i	0.352372	−	0.935860i	$-0.385375\pi$
$503$	−13.0863	−	13.0863i	−0.583488	−	0.583488i	−0.935860	+	0.352372i	$0.885375\pi$
$504$	4.65807	+	1.84531i	0.207487	+	0.0821965i
$505$	17.5495	+	14.8563i	0.780941	+	0.661098i
$506$	17.9522	+	13.7127i	0.798073	+	0.609604i
$507$	−4.34002	+	16.1972i	−0.192747	+	0.719342i
$508$	4.55959	−	17.0166i	0.202299	−	0.754990i
$509$	−9.95354	−	5.74668i	−0.441183	−	0.254717i	0.262916	−	0.964819i	$-0.415316\pi$
$509$	−9.95354	−	5.74668i	−0.441183	−	0.254717i	−0.704099	+	0.710102i	$0.748649\pi$
$510$	5.18568	−	0.430963i	0.229626	−	0.0190834i
$511$	−15.4954	−	19.5582i	−0.685478	−	0.865204i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	10.9542	−	2.93516i	0.483638	−	0.129590i
$514$	5.06420	+	8.77146i	0.223372	+	0.386892i
$515$	11.6714	−	8.09697i	0.514304	−	0.356795i
$516$	−4.21273	−	2.43222i	−0.185455	−	0.107073i
$517$	0.253896	+	0.329384i	0.0111663	+	0.0144863i
$518$	−18.1110	−	2.09908i	−0.795751	−	0.0922282i
$519$	−24.2989			−1.06660
$520$	11.3220	−	4.06517i	0.496502	−	0.178270i
$521$	−11.4675	−	19.8623i	−0.502400	−	0.870182i	−0.999996	−	0.00277317i	$-0.999117\pi$
$521$	−11.4675	−	19.8623i	−0.502400	−	0.870182i	0.497596	−	0.867409i	$-0.334216\pi$
$522$	1.72378	−	6.43322i	0.0754476	−	0.281574i
$523$	6.22196	−	1.66717i	0.272067	−	0.0729002i	−0.120206	−	0.992749i	$-0.538355\pi$
$523$	6.22196	−	1.66717i	0.272067	−	0.0729002i	0.392273	+	0.919849i	$0.371689\pi$
$524$	−12.6250			−0.551526
$525$	2.91895	−	13.6045i	0.127394	−	0.593748i
$526$	−10.7703			−0.469606
$527$	2.63423	+	9.83109i	0.114749	+	0.428249i
$528$	3.22583	+	1.32789i	0.140386	+	0.0577891i
$529$	−20.2587	+	11.6963i	−0.880812	+	0.508537i
$530$	4.11292	−	1.47675i	0.178654	−	0.0641459i
$531$	4.08612			0.177322
$532$	4.67913	+	3.47644i	0.202866	+	0.150723i
$533$	24.5266	−	24.5266i	1.06236	−	1.06236i
$534$	1.82280	−	3.15718i	0.0788802	−	0.136625i
$535$	36.2916	−	25.1770i	1.56902	−	1.08850i
$536$	12.6691	−	7.31451i	0.547222	−	0.315939i
$537$	6.03772	−	1.61780i	0.260547	−	0.0698133i
$538$	9.14870	+	9.14870i	0.394428	+	0.394428i
$539$	17.9392	−	14.7372i	0.772695	−	0.634778i
$540$	0.953230	+	11.4700i	0.0410205	+	0.493591i
$541$	−25.1344	−	14.5114i	−1.08061	−	0.623893i	−0.149552	−	0.988754i	$-0.547783\pi$
$541$	−25.1344	−	14.5114i	−1.08061	−	0.623893i	−0.931062	+	0.364861i	$0.881116\pi$
$542$	3.96268	−	14.7889i	0.170212	−	0.635239i
$543$	11.8946	+	3.18714i	0.510445	+	0.136773i
$544$	−1.91606	−	1.10624i	−0.0821506	−	0.0474297i
$545$	−27.5305	+	32.5212i	−1.17928	+	1.39305i
$546$	−2.18415	−	14.8109i	−0.0934728	−	0.633849i
$547$	20.4524	−	20.4524i	0.874483	−	0.874483i	−0.118474	−	0.992957i	$-0.537800\pi$
$547$	20.4524	−	20.4524i	0.874483	−	0.874483i	0.992957	+	0.118474i	$0.0378003\pi$
$548$	3.71127	+	13.8507i	0.158538	+	0.591671i
$549$	−3.87308	−	6.70837i	−0.165299	−	0.286306i
$550$	−3.69450	+	16.1663i	−0.157534	+	0.689335i
$551$	3.87440	−	6.71066i	0.165055	−	0.285884i
$552$	−5.06577	+	5.06577i	−0.215614	+	0.215614i
$553$	8.69961	+	20.1143i	0.369945	+	0.855349i
$554$		−	5.25941i		−	0.223451i
$555$	−5.47692	−	15.2539i	−0.232482	−	0.647491i
$556$	−14.9659	+	8.64058i	−0.634696	+	0.366442i
$557$	−35.3772	−	9.47930i	−1.49898	−	0.401651i	−0.586223	−	0.810150i	$-0.699386\pi$
$557$	−35.3772	−	9.47930i	−1.49898	−	0.401651i	−0.912759	+	0.408499i	$0.866052\pi$
$558$	−8.41461	+	2.25469i	−0.356219	+	0.0954485i
$559$		−	24.8809i		−	1.05235i
$560$	−4.31690	+	4.04529i	−0.182422	+	0.170945i
$561$	−0.990616	+	7.65429i	−0.0418238	+	0.323164i
$562$	−15.6768	+	4.20060i	−0.661288	+	0.177191i
$563$	1.48295	−	5.53445i	0.0624990	−	0.233249i	−0.927610	−	0.373550i	$-0.878140\pi$
$563$	1.48295	−	5.53445i	0.0624990	−	0.233249i	0.990109	+	0.140301i	$0.0448070\pi$
$564$	−0.114219	+	0.0659444i	−0.00480949	+	0.00277676i
$565$	34.6048	+	16.3202i	1.45584	+	0.686595i
$566$	−7.88078			−0.331254
$567$	−0.702298	−	0.0813970i	−0.0294938	−	0.00341835i
$568$	4.98697	+	4.98697i	0.209249	+	0.209249i
$569$	16.2500	−	28.1458i	0.681235	−	1.17993i	−0.293369	−	0.955999i	$-0.594777\pi$
$569$	16.2500	−	28.1458i	0.681235	−	1.17993i	0.974604	−	0.223934i	$-0.0718901\pi$
$570$	−0.922008	+	5.09914i	−0.0386187	+	0.213579i
$571$	9.33476	−	5.38943i	0.390648	−	0.225541i	−0.291793	−	0.956481i	$-0.594252\pi$
$571$	9.33476	−	5.38943i	0.390648	−	0.225541i	0.682441	+	0.730941i	$0.260919\pi$
$572$	2.36780	+	17.6851i	0.0990025	+	0.739451i
$573$	1.12419	−	1.12419i	0.0469637	−	0.0469637i
$574$	−6.28261	+	15.8590i	−0.262231	+	0.661944i
$575$	−27.7261	−	19.7758i	−1.15626	−	0.824707i
$576$	0.946852	−	1.63999i	0.0394521	−	0.0683331i
$577$	6.37192	−	23.7803i	0.265267	−	0.989989i	−0.696820	−	0.717246i	$-0.745403\pi$
$577$	6.37192	−	23.7803i	0.265267	−	0.989989i	0.962087	−	0.272743i	$-0.0879308\pi$
$578$	−3.13299	+	11.6925i	−0.130315	+	0.486342i
$579$	6.77249	−	11.7303i	0.281455	−	0.487494i
$580$	6.00232	+	5.08121i	0.249233	+	0.210986i
$581$	4.97484	−	0.733632i	0.206391	−	0.0304362i
$582$	11.4051	−	11.4051i	0.472756	−	0.472756i
$583$	0.860146	+	6.42444i	0.0356236	+	0.266073i
$584$	−8.16765	+	4.71560i	−0.337980	+	0.195133i
$585$	−18.7175	+	12.9851i	−0.773872	+	0.536869i
$586$	8.84728	−	15.3239i	0.365478	−	0.633026i
$587$	0.627651	+	0.627651i	0.0259059	+	0.0259059i	0.719941	−	0.694035i	$-0.244169\pi$
$587$	0.627651	+	0.627651i	0.0259059	+	0.0259059i	−0.694035	+	0.719941i	$0.744169\pi$
$588$	3.87736	+	6.25897i	0.159899	+	0.258115i
$589$	−10.1354			−0.417621
$590$	−2.05808	+	4.36389i	−0.0847296	+	0.179658i
$591$	−4.87117	+	2.81237i	−0.200373	+	0.115686i
$592$	−1.78356	+	6.65632i	−0.0733037	+	0.273573i
$593$	−12.5926	+	3.37419i	−0.517118	+	0.138561i	−0.507933	−	0.861396i	$-0.669590\pi$
$593$	−12.5926	+	3.37419i	−0.517118	+	0.138561i	−0.00918475	+	0.999958i	$0.502924\pi$
$594$	−16.9302	−	2.19111i	−0.694656	−	0.0899021i
$595$	−11.1171	−	6.90916i	−0.455759	−	0.283248i
$596$		−	13.6901i		−	0.560766i
$597$	−19.0832	+	5.11332i	−0.781023	+	0.209274i
$598$	−35.3946	−	9.48397i	−1.44739	−	0.387828i
$599$	0.462332	−	0.266927i	0.0188904	−	0.0109064i	−0.490525	−	0.871427i	$-0.663195\pi$
$599$	0.462332	−	0.266927i	0.0188904	−	0.0109064i	0.509415	+	0.860521i	$0.329862\pi$
$600$	−4.92604	−	1.84163i	−0.201105	−	0.0751841i
$601$		−	22.8160i		−	0.930685i	−0.885131	−	0.465342i	$-0.845931\pi$
$601$		−	22.8160i		−	0.930685i	0.885131	−	0.465342i	$-0.154069\pi$
$602$	4.85740	+	11.2308i	0.197973	+	0.457732i
$603$	−19.5890	+	19.5890i	−0.797726	+	0.797726i
$604$	0.178416	−	0.309026i	0.00725965	−	0.0125741i
$605$	−22.2926	−	10.3941i	−0.906325	−	0.422582i
$606$	−5.40783	−	9.36664i	−0.219678	−	0.380494i
$607$	−12.1914	−	45.4990i	−0.494835	−	1.84675i	−0.530953	−	0.847401i	$-0.678166\pi$
$607$	−12.1914	−	45.4990i	−0.494835	−	1.84675i	0.0361184	−	0.999348i	$-0.488501\pi$
$608$	1.55793	−	1.55793i	0.0631823	−	0.0631823i
$609$	7.67133	−	6.07779i	0.310858	−	0.246285i
$610$	9.11518	−	0.757529i	0.369063	−	0.0306714i
$611$	−0.584214	−	0.337296i	−0.0236348	−	0.0136455i
$612$	4.04702	+	1.08440i	0.163591	+	0.0438341i
$613$	−3.54457	+	13.2285i	−0.143164	+	0.534295i	0.856666	+	0.515871i	$0.172531\pi$
$613$	−3.54457	+	13.2285i	−0.143164	+	0.534295i	−0.999830	+	0.0184239i	$0.994135\pi$
$614$	−11.5919	−	6.69261i	−0.467813	−	0.270092i
$615$	−15.1116	+	1.25587i	−0.609357	+	0.0506414i
$616$	−4.52136	−	7.52046i	−0.182171	−	0.303008i
$617$	−9.94405	−	9.94405i	−0.400332	−	0.400332i	0.478018	−	0.878350i	$-0.341355\pi$
$617$	−9.94405	−	9.94405i	−0.400332	−	0.400332i	−0.878350	+	0.478018i	$0.841355\pi$
$618$	−6.45412	+	1.72938i	−0.259623	+	0.0695657i
$619$	10.2510	−	5.91841i	0.412022	−	0.237881i	−0.279636	−	0.960106i	$-0.590214\pi$
$619$	10.2510	−	5.91841i	0.412022	−	0.237881i	0.691658	+	0.722225i	$0.256881\pi$
$620$	1.83027	−	10.1223i	0.0735054	−	0.406520i
$621$	17.5294	−	30.3619i	0.703433	−	1.21838i
$622$	7.01330	−	7.01330i	0.281208	−	0.281208i
$623$	−8.41676	+	3.64032i	−0.337210	+	0.145846i
$624$	−5.65855			−0.226523
$625$	4.76898	−	24.5409i	0.190759	−	0.981637i
$626$	−5.96884	+	3.44611i	−0.238563	+	0.137734i
$627$	−7.10728	−	2.92567i	−0.283837	−	0.116840i
$628$	1.99685	+	7.45236i	0.0796831	+	0.297381i
$629$	−15.2465			−0.607917
$630$	5.91368	−	9.51537i	0.235607	−	0.379101i
$631$	−19.2594			−0.766705			−0.383352	−	0.923602i	$-0.625230\pi$
$631$	−19.2594			−0.766705			−0.383352	+	0.923602i	$0.625230\pi$
$632$	8.00087	−	2.14383i	0.318258	−	0.0852769i
$633$	−4.35170	+	16.2407i	−0.172964	+	0.645512i
$634$	−2.76110	−	4.78237i	−0.109657	−	0.189932i
$635$	−35.6290	−	16.8032i	−1.41389	−	0.666814i
$636$	−2.05557			−0.0815087
$637$	−17.8086	+	33.1820i	−0.705603	+	1.31472i
$638$	−9.23852	+	7.12124i	−0.365756	+	0.281933i
$639$	−11.5663	−	6.67781i	−0.457556	−	0.264170i
$640$	1.27457	+	1.83724i	0.0503820	+	0.0726234i
$641$	0.193431	+	0.335033i	0.00764007	+	0.0132330i	0.869820	−	0.493369i	$-0.164235\pi$
$641$	0.193431	+	0.335033i	0.00764007	+	0.0132330i	−0.862180	+	0.506602i	$0.830901\pi$
$642$	−20.0687	+	5.37739i	−0.792048	+	0.212229i
$643$	−3.03951	+	3.03951i	−0.119867	+	0.119867i	−0.764496	−	0.644629i	$-0.777012\pi$
$643$	−3.03951	+	3.03951i	−0.119867	+	0.119867i	0.644629	+	0.764496i	$0.277012\pi$
$644$	17.8280	−	2.62907i	0.702521	−	0.103600i
$645$	−7.02793	+	8.30194i	−0.276725	+	0.326889i
$646$	4.22155	+	2.43731i	0.166095	+	0.0958948i
$647$	−11.6188	+	43.3621i	−0.456784	+	1.70474i	0.226008	+	0.974126i	$0.427433\pi$
$647$	−11.6188	+	43.3621i	−0.456784	+	1.70474i	−0.682791	+	0.730614i	$0.739234\pi$
$648$	−0.0691618	+	0.258115i	−0.00271693	+	0.0101397i
$649$	−5.68711	−	4.34407i	−0.223239	−	0.170520i
$650$	−4.44032	−	26.5302i	−0.174163	−	1.04060i
$651$	−11.9017	−	4.71488i	−0.466464	−	0.184791i
$652$	11.5395	+	11.5395i	0.451921	+	0.451921i
$653$	−9.52690	−	35.5549i	−0.372816	−	1.39137i	−0.856509	−	0.516132i	$-0.827371\pi$
$653$	−9.52690	−	35.5549i	−0.372816	−	1.39137i	0.483693	−	0.875238i	$-0.339295\pi$
$654$	17.3575	−	10.0213i	0.678730	−	0.391865i
$655$	−5.02306	+	27.7799i	−0.196267	+	1.08545i
$656$	5.58359	+	3.22369i	0.218003	+	0.125864i
$657$	12.6288	−	12.6288i	0.492698	−	0.492698i
$658$	0.329552	+	0.0381953i	0.0128473	+	0.00148901i
$659$	−19.7901			−0.770913			−0.385457	−	0.922726i	$-0.625956\pi$
$659$	−19.7901			−0.770913			−0.385457	+	0.922726i	$0.625956\pi$
$660$	4.20532	−	6.56975i	0.163692	−	0.255727i
$661$	−13.7584	−	23.8302i	−0.535138	−	0.926886i	−0.999157	−	0.0410607i	$-0.986926\pi$
$661$	−13.7584	−	23.8302i	−0.535138	−	0.926886i	0.464019	−	0.885825i	$-0.346407\pi$
$662$	23.5700	+	6.31556i	0.916073	+	0.245461i
$663$	−3.24027	−	12.0928i	−0.125841	−	0.469647i
$664$		−	1.90065i		−	0.0737594i
$665$	9.51118	−	8.91274i	0.368828	−	0.345621i
$666$		−	13.0498i		−	0.505668i
$667$	−6.20003	−	23.1388i	−0.240066	−	0.895938i
$668$	0.409912	−	1.52981i	0.0158600	−	0.0591902i
$669$	2.84036	−	1.63988i	0.109815	−	0.0634016i
$670$	−11.0542	−	30.7871i	−0.427059	−	1.18941i
$671$	−1.74126	+	13.4544i	−0.0672207	+	0.519401i
$672$	2.55416	−	1.10469i	0.0985288	−	0.0426145i
$673$	−3.14585	−	3.14585i	−0.121263	−	0.121263i	0.643871	−	0.765134i	$-0.277327\pi$
$673$	−3.14585	−	3.14585i	−0.121263	−	0.121263i	−0.765134	+	0.643871i	$0.777327\pi$
$674$	14.7548	+	8.51871i	0.568335	+	0.328128i
$675$	25.6177	+	2.46605i	0.986027	+	0.0949184i
$676$	−7.97132	−	13.8067i	−0.306589	−	0.531028i
$677$	11.2976	+	42.1634i	0.434204	+	1.62047i	0.742964	+	0.669331i	$0.233419\pi$
$677$	11.2976	+	42.1634i	0.434204	+	1.62047i	−0.308760	+	0.951140i	$0.599914\pi$
$678$	−12.7257	−	12.7257i	−0.488729	−	0.488729i
$679$	−40.1379	+	5.91908i	−1.54035	+	0.227154i
$680$	−3.19649	+	3.77595i	−0.122580	+	0.144801i
$681$	21.1375	+	12.2037i	0.809991	+	0.467649i
$682$	14.1086	+	5.80772i	0.540246	+	0.222389i
$683$	7.67944	+	2.05770i	0.293846	+	0.0787357i	0.402730	−	0.915319i	$-0.368061\pi$
$683$	7.67944	+	2.05770i	0.293846	+	0.0787357i	−0.108885	+	0.994054i	$0.534728\pi$
$684$	−2.08614	+	3.61330i	−0.0797656	+	0.138158i
$685$	31.9534	−	2.65553i	1.22088	−	0.101463i
$686$	1.56049	−	18.4544i	0.0595799	−	0.704592i
$687$	6.10758	+	6.10758i	0.233019	+	0.233019i
$688$	4.46726	−	1.19700i	0.170313	−	0.0456351i
$689$	−5.25697	−	9.10534i	−0.200275	−	0.346886i
$690$	9.13116	+	13.1622i	0.347617	+	0.501075i
$691$	4.11804	−	7.13265i	0.156658	−	0.271339i	−0.777004	−	0.629496i	$-0.783261\pi$
$691$	4.11804	−	7.13265i	0.156658	−	0.271339i	0.933661	+	0.358157i	$0.116595\pi$
$692$	16.3356	−	16.3356i	0.620987	−	0.620987i
$693$	11.9563	+	11.5402i	0.454184	+	0.438376i
$694$		−	23.1752i		−	0.879719i
$695$	13.0582	+	36.3686i	0.495325	+	1.37954i
$696$	−1.84960	−	3.20360i	−0.0701090	−	0.121432i
$697$	−3.69197	+	13.7786i	−0.139843	+	0.521903i
$698$	−4.63161	−	17.2854i	−0.175309	−	0.654262i
$699$	−10.3289			−0.390674
$700$	7.18364	+	11.1083i	0.271516	+	0.419856i
$701$		−	12.8320i		−	0.484659i	−0.970194	−	0.242330i	$-0.922088\pi$
$701$		−	12.8320i		−	0.484659i	0.970194	−	0.242330i	$-0.0779115\pi$
$702$	26.7477	−	7.16702i	1.00953	−	0.270502i
$703$	3.92960	−	14.6655i	0.148208	−	0.553119i
$704$	−3.06137	+	1.27594i	−0.115380	+	0.0480888i
$705$	0.0996594	+	0.277563i	0.00375339	+	0.0104536i
$706$		−	17.3520i		−	0.653052i
$707$	−3.13224	+	27.0252i	−0.117800	+	1.01639i
$708$	1.60480	−	1.60480i	0.0603119	−	0.0603119i
$709$	−25.5471	−	14.7496i	−0.959440	−	0.553933i	−0.0634392	−	0.997986i	$-0.520207\pi$
$709$	−25.5471	−	14.7496i	−0.959440	−	0.553933i	−0.896001	+	0.444053i	$0.853540\pi$
$710$	12.9574	−	8.98912i	0.486283	−	0.337356i
$711$	−13.5843	+	7.84288i	−0.509450	+	0.294131i
$712$	0.897076	+	3.34793i	0.0336193	+	0.125469i
$713$	−22.1558	+	22.1558i	−0.829742	+	0.829742i
$714$	3.82343	+	4.82589i	0.143088	+	0.180604i
$715$	39.8561	+	1.82623i	1.49053	+	0.0682971i
$716$	−2.97142	+	5.14664i	−0.111047	+	0.192339i
$717$	−14.6295	−	3.91996i	−0.546349	−	0.146394i
$718$	−4.98950	−	1.33693i	−0.186206	−	0.0498939i
$719$	11.0626	+	6.38697i	0.412564	+	0.238194i	0.691891	−	0.722002i	$-0.256778\pi$
$719$	11.0626	+	6.38697i	0.412564	+	0.238194i	−0.279327	+	0.960196i	$0.590111\pi$
$720$	−3.23190	−	2.73594i	−0.120446	−	0.101962i
$721$	15.6261	+	6.19034i	0.581948	+	0.230540i
$722$	10.0025	−	10.0025i	0.372256	−	0.372256i
$723$	3.79973	−	1.01814i	0.141314	−	0.0378649i
$724$	−10.1391	+	5.85382i	−0.376817	+	0.217555i
$725$	13.5687	−	11.1858i	0.503930	−	0.415429i
$726$	8.21698	+	8.14513i	0.304961	+	0.302294i
$727$	25.0778	+	25.0778i	0.930084	+	0.930084i	0.997711	−	0.0676266i	$-0.0215427\pi$
$727$	25.0778	+	25.0778i	0.930084	+	0.930084i	−0.0676266	+	0.997711i	$0.521543\pi$
$728$	11.4254	+	8.48871i	0.423454	+	0.314613i
$729$			15.7356i			0.582801i
$730$	7.12651	+	19.8482i	0.263764	+	0.734614i
$731$	5.11619	+	8.86151i	0.189229	+	0.327755i
$732$	−4.15580	−	1.11354i	−0.153603	−	0.0411577i
$733$	−11.6733	+	3.12785i	−0.431163	+	0.115530i	−0.467872	−	0.883796i	$-0.654979\pi$
$733$	−11.6733	+	3.12785i	−0.431163	+	0.115530i	0.0367090	+	0.999326i	$0.488313\pi$
$734$	23.9240			0.883051
$735$	15.3148	−	6.04145i	0.564895	−	0.222842i
$736$		−	6.81122i		−	0.251065i
$737$	48.0899	−	6.43859i	1.77141	−	0.237169i
$738$	−11.7934	−	3.16003i	−0.434121	−	0.116322i
$739$	−1.51839	−	2.62994i	−0.0558551	−	0.0967438i	0.836746	−	0.547591i	$-0.184455\pi$
$739$	−1.51839	−	2.62994i	−0.0558551	−	0.0967438i	−0.892601	+	0.450848i	$0.851122\pi$
$740$	13.9369	+	6.57284i	0.512329	+	0.241622i
$741$	12.4671			0.457992
$742$	4.15049	+	3.08368i	0.152369	+	0.113205i
$743$	12.1445	+	12.1445i	0.445538	+	0.445538i	0.893868	−	0.448330i	$-0.147981\pi$
$743$	12.1445	+	12.1445i	0.445538	+	0.445538i	−0.448330	+	0.893868i	$0.647981\pi$
$744$	−2.41927	+	4.19030i	−0.0886947	+	0.153624i
$745$	−30.1234	−	5.44681i	−1.10364	−	0.199556i
$746$	16.8090	+	29.1140i	0.615420	+	1.06594i
$747$	0.931557	+	3.47662i	0.0340839	+	0.127203i
$748$	−4.47984	−	5.81178i	−0.163799	−	0.212500i
$749$	48.5885	+	19.2485i	1.77538	+	0.703324i
$750$	−6.01220	+	10.1065i	−0.219534	+	0.369036i
$751$	22.6922	−	39.3040i	0.828050	−	1.43422i	−0.0715157	−	0.997439i	$-0.522784\pi$
$751$	22.6922	−	39.3040i	0.828050	−	1.43422i	0.899566	−	0.436785i	$-0.143883\pi$
$752$	0.0324540	−	0.121120i	0.00118348	−	0.00441679i
$753$	−10.5341	−	2.82260i	−0.383884	−	0.102861i
$754$	9.46044	−	16.3860i	0.344529	−	0.596742i
$755$	−0.608991	−	0.515536i	−0.0221635	−	0.0187623i
$756$	−10.6742	+	8.45689i	−0.388217	+	0.307574i
$757$	31.2328	+	31.2328i	1.13518	+	1.13518i	0.989303	+	0.145874i	$0.0465993\pi$
$757$	31.2328	+	31.2328i	1.13518	+	1.13518i	0.145874	+	0.989303i	$0.453401\pi$
$758$	24.6231	−	6.59773i	0.894350	−	0.239640i
$759$	−21.9319	+	9.14095i	−0.796077	+	0.331795i
$760$	−2.80820	−	4.04789i	−0.101864	−	0.146832i
$761$	−27.5191	−	15.8882i	−0.997566	−	0.575945i	−0.0900391	−	0.995938i	$-0.528699\pi$
$761$	−27.5191	−	15.8882i	−0.997566	−	0.575945i	−0.907527	+	0.419993i	$0.862033\pi$
$762$	13.1024	+	13.1024i	0.474649	+	0.474649i
$763$	−50.0808	−	5.80441i	−1.81305	−	0.210134i
$764$			1.51154i			0.0546855i
$765$	3.99626	−	8.47356i	0.144485	−	0.306362i
$766$	3.68433	−	2.12715i	0.133120	−	0.0768569i
$767$	11.2127	+	3.00444i	0.404869	+	0.108484i
$768$	−0.272228	−	1.01597i	−0.00982317	−	0.0366606i
$769$	28.5878			1.03090			0.515452	−	0.856919i	$-0.327624\pi$
$769$	28.5878			1.03090			0.515452	+	0.856919i	$0.327624\pi$
$770$	−18.3468	+	6.95662i	−0.661173	+	0.250699i
$771$	−10.6531			−0.383663
$772$	3.33303	+	12.4390i	0.119958	+	0.447690i
$773$	−30.9780	−	8.30053i	−1.11420	−	0.298549i	−0.345667	−	0.938357i	$-0.612347\pi$
$773$	−30.9780	−	8.30053i	−1.11420	−	0.298549i	−0.768535	+	0.639808i	$0.779014\pi$
$774$	−7.58473	+	4.37904i	−0.272627	+	0.157401i
$775$	−21.5447	−	8.05460i	−0.773908	−	0.289330i
$776$			15.3348i			0.550486i
$777$	11.4367	−	15.3932i	0.410288	−	0.552229i
$778$	−8.88059	−	8.88059i	−0.318385	−	0.318385i
$779$	−12.3020	−	7.10256i	−0.440765	−	0.254476i
$780$	−2.25134	+	12.4510i	−0.0806110	+	0.445817i
$781$	8.99876	+	21.5907i	0.322001	+	0.772577i
$782$	14.5562	−	3.90032i	0.520529	−	0.139475i
$783$	12.8006	+	12.8006i	0.457457	+	0.457457i
$784$	−6.81443	−	1.60110i	−0.243373	−	0.0571823i
$785$	17.1925	−	1.42881i	0.613628	−	0.0509964i
$786$	6.63953	−	11.5000i	0.236824	−	0.410192i
$787$	−33.3506	−	8.93627i	−1.18882	−	0.318544i	−0.390401	−	0.920645i	$-0.627664\pi$
$787$	−33.3506	−	8.93627i	−1.18882	−	0.318544i	−0.798420	+	0.602101i	$0.794330\pi$
$788$	1.38409	−	5.16548i	0.0493060	−	0.184013i
$789$	5.66411	−	9.81053i	0.201648	−	0.349264i
$790$	−1.53397	−	18.4580i	−0.0545763	−	0.656705i
$791$	6.60449	+	44.7857i	0.234829	+	1.59240i
$792$	4.97441	−	3.83438i	0.176758	−	0.136249i
$793$	−5.69561	−	21.2563i	−0.202257	−	0.754833i
$794$	13.6946	+	23.7197i	0.486003	+	0.841782i
$795$	−0.817842	+	4.52305i	−0.0290059	+	0.160416i
$796$	9.39164	−	16.2668i	0.332878	−	0.576561i
$797$	35.2715	+	35.2715i	1.24938	+	1.24938i	0.955994	+	0.293385i	$0.0947817\pi$
$797$	35.2715	+	35.2715i	1.24938	+	1.24938i	0.293385	+	0.955994i	$0.405218\pi$
$798$	−5.62743	+	2.43391i	−0.199209	+	0.0861594i
$799$	0.277429			0.00981473
$800$	4.54975	−	2.07358i	0.160858	−	0.0733122i
$801$	−3.28182	−	5.68428i	−0.115957	−	0.200844i
$802$	18.7116	+	5.01377i	0.660731	+	0.177042i
$803$	−31.0031	+	4.15090i	−1.09408	+	0.146482i
$804$			15.3869i			0.542654i
$805$	1.30818	−	40.2745i	0.0461074	−	1.41949i
$806$	−24.7484			−0.871726
$807$	−13.1448	+	3.52214i	−0.462719	+	0.123985i
$808$	9.93256	+	2.66142i	0.349426	+	0.0936284i
$809$	−3.50388	−	6.06890i	−0.123190	−	0.213371i	0.797834	−	0.602877i	$-0.205979\pi$
$809$	−3.50388	−	6.06890i	−0.123190	−	0.213371i	−0.921024	+	0.389506i	$0.872646\pi$
$810$	0.540437	+	0.254878i	0.0189890	+	0.00895550i
$811$			27.1000i			0.951609i	0.879551	+	0.475804i	$0.157843\pi$
$811$			27.1000i			0.951609i	−0.879551	+	0.475804i	$0.842157\pi$
$812$	−1.07130	+	9.24323i	−0.0375952	+	0.324374i
$813$	11.3871	+	11.3871i	0.399364	+	0.399364i
$814$	−13.8736	+	18.1628i	−0.486269	+	0.636607i
$815$	29.9825	−	20.8002i	1.05024	−	0.728598i
$816$	2.01533	−	1.16355i	0.0705506	−	0.0407324i
$817$	−9.84245	+	2.63728i	−0.344344	+	0.0922666i
$818$	22.9463	−	22.9463i	0.802299	−	0.802299i
$819$	−25.0597	−	9.92745i	−0.875655	−	0.346893i
$820$	9.31488	−	11.0035i	0.325290	−	0.384258i
$821$	19.6996	+	11.3736i	0.687520	+	0.396940i	0.802682	−	0.596407i	$-0.203405\pi$
$821$	19.6996	+	11.3736i	0.687520	+	0.396940i	−0.115162	+	0.993347i	$0.536739\pi$
$822$	−14.5682	−	3.90354i	−0.508125	−	0.136152i
$823$	10.9245	+	2.92720i	0.380803	+	0.102036i	0.444142	−	0.895956i	$-0.353508\pi$
$823$	10.9245	+	2.92720i	0.380803	+	0.102036i	−0.0633394	+	0.997992i	$0.520175\pi$
$824$	3.17634	−	5.50159i	0.110653	−	0.191657i
$825$	−12.7828	−	11.8672i	−0.445041	−	0.413164i
$826$	−5.64776	+	0.832867i	−0.196511	+	0.0289792i
$827$	10.7907	−	10.7907i	0.375230	−	0.375230i	−0.494148	−	0.869378i	$-0.664520\pi$
$827$	10.7907	−	10.7907i	0.375230	−	0.375230i	0.869378	+	0.494148i	$0.164520\pi$
$828$	3.33836	+	12.4589i	0.116016	+	0.432977i
$829$	36.6621	−	21.1668i	1.27333	−	0.735155i	0.297713	−	0.954655i	$-0.403776\pi$
$829$	36.6621	−	21.1668i	1.27333	−	0.735155i	0.975612	+	0.219500i	$0.0704427\pi$
$830$	−4.18216	−	0.756203i	−0.145165	−	0.0262482i
$831$	4.79075	+	2.76594i	0.166189	+	0.0959495i
$832$	3.80412	−	3.80412i	0.131884	−	0.131884i
$833$	−0.480454	−	15.4799i	−0.0166467	−	0.536347i
$834$		−	18.1764i		−	0.629398i
$835$	−3.20309	−	1.51063i	−0.110848	−	0.0522774i
$836$	6.74493	−	2.81121i	0.233278	−	0.0972276i
$837$	6.12841	−	22.8715i	0.211829	−	0.790556i
$838$	16.4504	−	4.40787i	0.568270	−	0.152267i
$839$			7.02852i			0.242652i	0.992613	+	0.121326i	$0.0387146\pi$
$839$			7.02852i			0.242652i	−0.992613	+	0.121326i	$0.961285\pi$
$840$	−1.41454	−	6.05966i	−0.0488063	−	0.209078i
$841$	−16.6307			−0.573473
$842$	−7.43669	−	27.7541i	−0.256285	−	0.956470i
$843$	4.41822	−	16.4890i	0.152171	−	0.567911i
$844$	−7.99275	−	13.8439i	−0.275122	−	0.476525i
$845$	−33.5517	+	12.0468i	−1.15421	+	0.414421i
$846$			0.237457i			0.00816392i
$847$	−4.37227	−	28.7730i	−0.150233	−	0.988651i
$848$	1.38192	−	1.38192i	0.0474552	−	0.0474552i
$849$	4.14453	−	7.17854i	0.142240	−	0.246367i
$850$	7.03677	+	8.53585i	0.241359	+	0.292777i
$851$	−23.4685	−	40.6486i	−0.804490	−	1.39342i
$852$	−7.16525	+	1.91992i	−0.245478	+	0.0657755i
$853$	16.4835	+	16.4835i	0.564384	+	0.564384i	0.930550	−	0.366166i	$-0.119330\pi$
$853$	16.4835	+	16.4835i	0.564384	+	0.564384i	−0.366166	+	0.930550i	$0.619330\pi$
$854$	6.72066	+	8.48275i	0.229976	+	0.290274i
$855$	7.12066	+	6.02793i	0.243521	+	0.206151i
$856$	9.87664	−	17.1068i	0.337577	−	0.584700i
$857$	−32.4737	−	8.70130i	−1.10928	−	0.297231i	−0.342742	−	0.939430i	$-0.611356\pi$
$857$	−32.4737	−	8.70130i	−1.10928	−	0.297231i	−0.766538	+	0.642199i	$0.778022\pi$
$858$	−17.3544	−	7.14384i	−0.592470	−	0.243887i
$859$	−19.6019	−	11.3171i	−0.668807	−	0.386136i	0.126818	−	0.991926i	$-0.459524\pi$
$859$	−19.6019	−	11.3171i	−0.668807	−	0.386136i	−0.795624	+	0.605790i	$0.792857\pi$
$860$	−0.856489	−	10.3059i	−0.0292060	−	0.351430i
$861$	−11.1418	−	14.0631i	−0.379712	−	0.479269i
$862$	−7.17510	−	7.17510i	−0.244385	−	0.244385i
$863$	11.5987	+	43.2870i	0.394825	+	1.47351i	0.822078	+	0.569376i	$0.192815\pi$
$863$	11.5987	+	43.2870i	0.394825	+	1.47351i	−0.427252	+	0.904132i	$0.640518\pi$
$864$	2.57361	+	4.45763i	0.0875561	+	0.151652i
$865$	−29.4453	−	42.4441i	−1.00117	−	1.44314i
$866$	25.9615	+	14.9889i	0.882209	+	0.509344i
$867$	−9.00291	−	9.00291i	−0.305755	−	0.305755i
$868$	11.1710	−	4.83153i	0.379167	−	0.163993i
$869$	27.2448	+	3.52601i	0.924215	+	0.119612i
$870$	−7.78506	+	2.79523i	−0.263938	+	0.0947673i
$871$	−68.1577	+	39.3509i	−2.30944	+	1.33335i
$872$	−4.93192	+	18.4062i	−0.167016	+	0.623312i
$873$	−7.51598	−	28.0500i	−0.254377	−	0.949349i
$874$			15.0068i			0.507611i
$875$	27.3008	−	11.3872i	0.922935	−	0.384956i
$876$		−	9.91979i		−	0.335159i
$877$	6.21689	+	23.2017i	0.209929	+	0.783467i	0.987890	+	0.155154i	$0.0495875\pi$
$877$	6.21689	+	23.2017i	0.209929	+	0.783467i	−0.777961	+	0.628313i	$0.783746\pi$
$878$	−18.4555	−	4.94513i	−0.622842	−	0.166890i
$879$	9.30563	+	16.1178i	0.313871	+	0.543641i
$880$	1.58955	+	7.24385i	0.0535837	+	0.244190i
$881$	−55.2611			−1.86179			−0.930896	−	0.365283i	$-0.880972\pi$
$881$	−55.2611			−1.86179			−0.930896	+	0.365283i	$0.880972\pi$
$882$	13.2495	−	0.411229i	0.446135	−	0.0138468i
$883$	32.6406	−	32.6406i	1.09844	−	1.09844i	0.103851	−	0.994593i	$-0.466883\pi$
$883$	32.6406	−	32.6406i	1.09844	−	1.09844i	0.994593	−	0.103851i	$-0.0331166\pi$
$884$	10.3081	+	5.95139i	0.346699	+	0.200167i
$885$	−2.89268	−	4.16967i	−0.0972363	−	0.140162i
$886$	−32.5871	+	18.8142i	−1.09478	+	0.632074i
$887$	13.8113	+	51.5444i	0.463738	+	1.73069i	0.661041	+	0.750350i	$0.270115\pi$
$887$	13.8113	+	51.5444i	0.463738	+	1.73069i	−0.197304	+	0.980342i	$0.563219\pi$
$888$	−5.12521	−	5.12521i	−0.171991	−	0.171991i
$889$	−6.79995	−	46.1112i	−0.228063	−	1.54652i
$890$	7.72366	−	0.641885i	0.258898	−	0.0215160i
$891$	−0.537983	+	0.704309i	−0.0180231	+	0.0235952i
$892$	−0.807056	+	3.01197i	−0.0270222	+	0.100848i
$893$	−0.0715040	+	0.266857i	−0.00239279	+	0.00893002i
$894$	12.4701	+	7.19964i	0.417064	+	0.240792i
$895$	10.1424	+	8.58594i	0.339022	+	0.286996i
$896$	−0.974444	+	2.45977i	−0.0325539	+	0.0821751i
$897$	27.2530	−	27.2530i	0.909952	−	0.909952i
$898$	0.0844776	−	0.0226357i	0.00281905	−	0.000755363i
$899$	−8.08948	−	14.0114i	−0.269799	−	0.467306i
$900$	−7.30599	+	6.02290i	−0.243533	+	0.200763i
$901$	3.74461	+	2.16195i	0.124751	+	0.0720251i
$902$	13.0547	+	16.9361i	0.434673	+	0.563909i
$903$	−12.7845	−	1.48174i	−0.425442	−	0.0493092i
$904$	17.1105			0.569086
$905$	8.84666	+	24.6390i	0.294073	+	0.819028i
$906$	0.187659	+	0.325036i	0.00623457	+	0.0107986i
$907$	9.88341	−	36.8854i	0.328173	−	1.22476i	−0.582910	−	0.812537i	$-0.698086\pi$
$907$	9.88341	−	36.8854i	0.328173	−	1.22476i	0.911083	−	0.412222i	$-0.135247\pi$
$908$	−22.4146	+	6.00597i	−0.743855	+	0.199315i
$909$	−19.4728			−0.645873
$910$	23.2242	−	21.7630i	0.769876	−	0.721436i
$911$	7.56655			0.250691			0.125345	−	0.992113i	$-0.459996\pi$
$911$	7.56655			0.250691			0.125345	+	0.992113i	$0.459996\pi$
$912$	0.599783	+	2.23842i	0.0198608	+	0.0741215i
$913$	2.39954	−	5.82917i	0.0794133	−	0.192917i
$914$	11.8038	−	6.81495i	0.390436	−	0.225419i
$915$	−4.10368	+	8.70132i	−0.135663	+	0.287657i
$916$	−8.21198			−0.271332
$917$	−30.6580	+	13.2598i	−1.01242	+	0.437878i
$918$	−8.05263	+	8.05263i	−0.265777	+	0.265777i
$919$	−24.7670	+	42.8978i	−0.816989	+	1.41507i	0.0909021	+	0.995860i	$0.471025\pi$
$919$	−24.7670	+	42.8978i	−0.816989	+	1.41507i	−0.907891	+	0.419206i	$0.862308\pi$
$920$	−14.9873	−	2.70995i	−0.494117	−	0.0893445i
$921$	12.1925	−	7.03934i	0.401756	−	0.231954i
$922$	−9.31007	+	2.49463i	−0.306611	+	0.0821561i
$923$	−26.8291	−	26.8291i	−0.883090	−	0.883090i
$924$	9.22812	−	0.163438i	0.303583	−	0.00537671i
$925$	20.0078	−	28.0514i	0.657852	−	0.922324i
$926$	12.7584	+	7.36609i	0.419268	+	0.242065i
$927$	−3.11362	+	11.6202i	−0.102265	+	0.381657i
$928$	3.39716	+	0.910267i	0.111517	+	0.0298810i
$929$	15.7831	+	9.11235i	0.517825	+	0.298967i	0.736044	−	0.676933i	$-0.236691\pi$
$929$	15.7831	+	9.11235i	0.517825	+	0.298967i	−0.218219	+	0.975900i	$0.570025\pi$
$930$	8.25773	+	6.99050i	0.270782	+	0.229228i
$931$	15.0138	+	3.52762i	0.492058	+	0.115613i
$932$	6.94388	−	6.94388i	0.227454	−	0.227454i
$933$	2.70004	+	10.0767i	0.0883953	+	0.329896i
$934$	−19.1441	−	33.1585i	−0.626414	−	1.08498i
$935$	−14.5705	+	7.54508i	−0.476508	+	0.246750i
$936$	−5.09391	+	8.82290i	−0.166500	+	0.288386i
$937$	−22.4737	+	22.4737i	−0.734185	+	0.734185i	−0.971446	−	0.237261i	$-0.923750\pi$
$937$	−22.4737	+	22.4737i	−0.734185	+	0.734185i	0.237261	+	0.971446i	$0.423750\pi$
$938$	23.0828	−	31.0684i	0.753680	−	1.01442i
$939$		−	7.24928i		−	0.236571i
$940$	−0.253599	−	0.119601i	−0.00827148	−	0.00390095i
$941$	40.6311	−	23.4584i	1.32454	−	0.764721i	0.340087	−	0.940394i	$-0.389543\pi$
$941$	40.6311	−	23.4584i	1.32454	−	0.764721i	0.984449	+	0.175673i	$0.0562101\pi$
$942$	−7.83844	−	2.10030i	−0.255390	−	0.0684316i
$943$	−42.4181	+	11.3659i	−1.38132	+	0.370125i
$944$			2.15774i			0.0702284i
$945$	14.3615	+	26.8521i	0.467181	+	0.873499i
$946$	15.2120	+	1.96873i	0.494585	+	0.0640091i
$947$	8.84020	−	2.36873i	0.287268	−	0.0769732i	−0.112308	−	0.993673i	$-0.535824\pi$
$947$	8.84020	−	2.36873i	0.287268	−	0.0769732i	0.399576	+	0.916700i	$0.369158\pi$
$948$	−2.25489	+	8.41537i	−0.0732355	+	0.273319i
$949$	43.9406	−	25.3691i	1.42637	−	0.823517i
$950$	−10.0242	+	4.56860i	−0.325228	+	0.148225i
$951$	5.80829			0.188347
$952$	−5.81475	−	0.673935i	−0.188457	−	0.0218423i
$953$	4.01032	+	4.01032i	0.129907	+	0.129907i	0.769071	−	0.639164i	$-0.220719\pi$
$953$	4.01032	+	4.01032i	0.129907	+	0.129907i	−0.639164	+	0.769071i	$0.720719\pi$
$954$	−1.85046	+	3.20508i	−0.0599107	+	0.103768i
$955$	3.32596	+	0.601389i	0.107626	+	0.0194605i
$956$	12.4704	−	7.19979i	0.403322	−	0.232858i
$957$	−1.62811	−	12.1604i	−0.0526293	−	0.393089i
$958$	23.1776	−	23.1776i	0.748833	−	0.748833i
$959$	23.5594	+	29.7364i	0.760773	+	0.960239i
$960$	−2.34383	+	0.194787i	−0.0756468	+	0.00628673i
$961$	4.91900	−	8.51996i	0.158678	−	0.274838i
$962$	9.59524	−	35.8099i	0.309363	−	1.15456i
$963$	−9.68161	+	36.1322i	−0.311985	+	1.16435i
$964$	−1.87001	+	3.23895i	−0.0602289	+	0.104320i
$965$	28.6968	−	2.38488i	0.923781	−	0.0767720i
$966$	−6.98100	+	17.6220i	−0.224610	+	0.566978i
$967$	8.51244	−	8.51244i	0.273741	−	0.273741i	−0.556863	−	0.830604i	$-0.687995\pi$
$967$	8.51244	−	8.51244i	0.273741	−	0.273741i	0.830604	+	0.556863i	$0.187995\pi$
$968$	−10.9999	+	0.0482981i	−0.353550	+	0.00155236i
$969$	−4.44026	+	2.56358i	−0.142642	+	0.0823542i
$970$	33.7424	+	6.10119i	1.08340	+	0.195897i
$971$	−12.9980	+	22.5132i	−0.417126	+	0.722483i	−0.995649	−	0.0931830i	$-0.970296\pi$
$971$	−12.9980	+	22.5132i	−0.417126	+	0.722483i	0.578523	+	0.815666i	$0.303629\pi$
$972$	−11.1177	−	11.1177i	−0.356599	−	0.356599i
$973$	−27.2675	+	36.7008i	−0.874156	+	1.17657i
$974$	12.2986			0.394072
$975$	26.5013	+	9.90765i	0.848720	+	0.317299i
$976$	3.54246	−	2.04524i	0.113391	−	0.0654666i
$977$	−6.78876	+	25.3360i	−0.217192	+	0.810570i	0.768192	+	0.640220i	$0.221157\pi$
$977$	−6.78876	+	25.3360i	−0.217192	+	0.810570i	−0.985383	+	0.170351i	$0.945510\pi$
$978$	−16.5799	+	4.44256i	−0.530166	+	0.142058i
$979$	−1.47544	+	11.4005i	−0.0471554	+	0.364360i
$980$	−6.23428	+	14.3574i	−0.199147	+	0.458629i
$981$		−	36.0854i		−	1.15212i
$982$	−28.0793	+	7.52382i	−0.896046	+	0.240095i
$983$	9.21552	+	2.46929i	0.293929	+	0.0787581i	0.402770	−	0.915301i	$-0.368047\pi$
$983$	9.21552	+	2.46929i	0.293929	+	0.0787581i	−0.108841	+	0.994059i	$0.534714\pi$
$984$	−5.87286	+	3.39069i	−0.187220	+	0.108091i
$985$	−10.8154	−	5.10069i	−0.344606	−	0.162522i
$986$			7.78130i			0.247807i
$987$	−0.208104	+	0.280099i	−0.00662403	+	0.00891564i
$988$	−8.38139	+	8.38139i	−0.266648	+	0.266648i
$989$	−15.7504	+	27.2805i	−0.500834	+	0.867470i
$990$	−6.45797	−	12.4712i	−0.205248	−	0.396361i
$991$	7.27261	+	12.5965i	0.231022	+	0.400142i	0.958109	−	0.286403i	$-0.0924597\pi$
$991$	7.27261	+	12.5965i	0.231022	+	0.400142i	−0.727087	+	0.686545i	$0.759126\pi$
$992$	−1.19062	−	4.44347i	−0.0378023	−	0.141080i
$993$	−18.1483	+	18.1483i	−0.575919	+	0.575919i
$994$	17.3479	+	6.87241i	0.550241	+	0.217979i
$995$	−32.0566	−	27.1372i	−1.01626	−	0.860308i
$996$	1.73128	+	0.999557i	0.0548578	+	0.0316722i
$997$	−29.2737	−	7.84386i	−0.927107	−	0.248418i	−0.236487	−	0.971635i	$-0.575996\pi$
$997$	−29.2737	−	7.84386i	−0.927107	−	0.248418i	−0.690621	+	0.723217i	$0.742663\pi$
$998$	1.24404	−	4.64284i	0.0393795	−	0.146966i
$999$	30.7181	+	17.7351i	0.971878	+	0.561114i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.bd.a.527.17	yes	192
5.3	odd	4	inner	770.2.bd.a.373.8	yes	192
7.4	even	3	inner	770.2.bd.a.417.32	yes	192
11.10	odd	2	inner	770.2.bd.a.527.41	yes	192
35.18	odd	12	inner	770.2.bd.a.263.41	yes	192
55.43	even	4	inner	770.2.bd.a.373.32	yes	192
77.32	odd	6	inner	770.2.bd.a.417.8	yes	192
385.263	even	12	inner	770.2.bd.a.263.17	✓	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.bd.a.263.17	✓	192	385.263	even	12	inner
770.2.bd.a.263.41	yes	192	35.18	odd	12	inner
770.2.bd.a.373.8	yes	192	5.3	odd	4	inner
770.2.bd.a.373.32	yes	192	55.43	even	4	inner
770.2.bd.a.417.8	yes	192	77.32	odd	6	inner
770.2.bd.a.417.32	yes	192	7.4	even	3	inner
770.2.bd.a.527.17	yes	192	1.1	even	1	trivial
770.2.bd.a.527.41	yes	192	11.10	odd	2	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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.bd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 - 0.965926i) q^{2} +(1.01597 + 0.272228i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(0.755631 + 2.10452i) q^{5} -1.05181i q^{6} +(-1.57788 + 2.12375i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.63999 - 0.946852i) q^{9} +O(q^{10})\)	\(q+(-0.258819 - 0.965926i) q^{2} +(1.01597 + 0.272228i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(0.755631 + 2.10452i) q^{5} -1.05181i q^{6} +(-1.57788 + 2.12375i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.63999 - 0.946852i) q^{9} +(1.83724 - 1.27457i) q^{10} +(1.27594 + 3.06137i) q^{11} +(-1.01597 + 0.272228i) q^{12} +(-3.80412 - 3.80412i) q^{13} +(2.45977 + 0.974444i) q^{14} +(0.194787 + 2.34383i) q^{15} +(0.500000 - 0.866025i) q^{16} +(2.13709 + 0.572632i) q^{17} +(-0.490126 + 1.82918i) q^{18} +(-1.10162 + 1.90806i) q^{19} +(-1.70666 - 1.44476i) q^{20} +(-2.18121 + 1.72812i) q^{21} +(2.62682 - 2.02480i) q^{22} +(1.76287 + 6.57913i) q^{23} +(0.525903 + 0.910891i) q^{24} +(-3.85804 + 3.18049i) q^{25} +(-2.68992 + 4.65907i) q^{26} +(-3.63964 - 3.63964i) q^{27} +(0.304606 - 2.62816i) q^{28} -3.51700 q^{29} +(2.21355 - 0.794778i) q^{30} +(2.30011 + 3.98390i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(0.462926 + 3.45760i) q^{33} -2.21248i q^{34} +(-5.66177 - 1.71591i) q^{35} +1.89370 q^{36} +(-6.65632 + 1.78356i) q^{37} +(2.12817 + 0.570241i) q^{38} +(-2.82927 - 4.90044i) q^{39} +(-0.953811 + 2.02244i) q^{40} +6.44737i q^{41} +(2.23377 + 1.65962i) q^{42} +(3.27026 + 3.27026i) q^{43} +(-2.63568 - 2.01325i) q^{44} +(0.753440 - 4.16688i) q^{45} +(5.89869 - 3.40561i) q^{46} +(0.121120 - 0.0324540i) q^{47} +(0.743740 - 0.743740i) q^{48} +(-2.02062 - 6.70202i) q^{49} +(4.07065 + 2.90341i) q^{50} +(2.01533 + 1.16355i) q^{51} +(5.19652 + 1.39240i) q^{52} +(1.88773 + 0.505816i) q^{53} +(-2.57361 + 4.45763i) q^{54} +(-5.47858 + 4.99851i) q^{55} +(-2.61744 + 0.385991i) q^{56} +(-1.63864 + 1.63864i) q^{57} +(0.910267 + 3.39716i) q^{58} +(-1.86866 + 1.07887i) q^{59} +(-1.34061 - 1.93242i) q^{60} +(3.54246 + 2.04524i) q^{61} +(3.25284 - 3.25284i) q^{62} +(4.59858 - 1.98892i) q^{63} +1.00000i q^{64} +(5.13135 - 10.8804i) q^{65} +(3.21997 - 1.34204i) q^{66} +(3.78627 - 14.1306i) q^{67} +(-2.13709 + 0.572632i) q^{68} +7.16408i q^{69} +(-0.192063 + 5.91296i) q^{70} +7.05264 q^{71} +(-0.490126 - 1.82918i) q^{72} +(-2.44097 + 9.10983i) q^{73} +(3.44556 + 5.96789i) q^{74} +(-4.78546 + 2.18101i) q^{75} -2.20324i q^{76} +(-8.51485 - 2.12068i) q^{77} +(-4.00120 + 4.00120i) q^{78} +(4.14156 - 7.17339i) q^{79} +(2.20039 + 0.397866i) q^{80} +(0.133610 + 0.231420i) q^{81} +(6.22769 - 1.66870i) q^{82} +(-1.34396 - 1.34396i) q^{83} +(1.02493 - 2.58720i) q^{84} +(0.409736 + 4.93026i) q^{85} +(2.31242 - 4.00524i) q^{86} +(-3.57316 - 0.957425i) q^{87} +(-1.26249 + 3.06694i) q^{88} +(3.00167 + 1.73302i) q^{89} +(-4.21990 + 0.350700i) q^{90} +(14.0814 - 2.07657i) q^{91} +(-4.81626 - 4.81626i) q^{92} +(1.25231 + 4.67367i) q^{93} +(-0.0626964 - 0.108593i) q^{94} +(-4.84798 - 0.876595i) q^{95} +(-0.910891 - 0.525903i) q^{96} +(10.8433 + 10.8433i) q^{97} +(-5.95068 + 3.68638i) q^{98} +(0.806124 - 6.22876i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 8 q^{5}+O(q^{10}) \) 192 * q + 8 * q^5	\( 192 q + 8 q^{5} + 4 q^{11} + 16 q^{15} + 96 q^{16} + 24 q^{22} - 8 q^{23} + 24 q^{25} - 8 q^{26} - 16 q^{33} - 160 q^{36} - 40 q^{37} - 40 q^{42} + 32 q^{45} - 40 q^{47} + 40 q^{53} + 8 q^{55} + 16 q^{56} + 32 q^{58} - 48 q^{67} - 72 q^{70} + 32 q^{71} - 48 q^{75} - 72 q^{77} - 8 q^{80} + 64 q^{81} + 16 q^{82} - 12 q^{88} - 112 q^{91} - 16 q^{92} + 80 q^{93} - 64 q^{97}+O(q^{100}) \) 192 * q + 8 * q^5 + 4 * q^11 + 16 * q^15 + 96 * q^16 + 24 * q^22 - 8 * q^23 + 24 * q^25 - 8 * q^26 - 16 * q^33 - 160 * q^36 - 40 * q^37 - 40 * q^42 + 32 * q^45 - 40 * q^47 + 40 * q^53 + 8 * q^55 + 16 * q^56 + 32 * q^58 - 48 * q^67 - 72 * q^70 + 32 * q^71 - 48 * q^75 - 72 * q^77 - 8 * q^80 + 64 * q^81 + 16 * q^82 - 12 * q^88 - 112 * q^91 - 16 * q^92 + 80 * q^93 - 64 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more