LMFDB - Embedded newform 357.2.bh.a.100.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [357,2,Mod(25,357)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(357, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([0, 16, 15]))

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

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

chi := DirichletCharacter("357.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 357 = 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	357.bh (of order $24$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.85065935216$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$24$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			100.10
Character	$\chi$	$=$	357.100
Dual form			357.2.bh.a.25.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.749407 + 0.200803i) q^{2} +(-0.608761 + 0.793353i) q^{3} +(-1.21076 + 0.699034i) q^{4} +(-0.559525 + 4.25001i) q^{5} +(0.296902 - 0.716785i) q^{6} +(-1.97366 + 1.76200i) q^{7} +(1.86419 - 1.86419i) q^{8} +(-0.258819 - 0.965926i) q^{9} +(-0.434103 - 3.29734i) q^{10} +(-1.17616 + 0.154845i) q^{11} +(0.182484 - 1.38611i) q^{12} -1.32321i q^{13} +(1.12526 - 1.71677i) q^{14} +(-3.03114 - 3.03114i) q^{15} +(0.375365 - 0.650151i) q^{16} +(4.09626 - 0.469777i) q^{17} +(0.387921 + 0.671900i) q^{18} +(1.23530 - 0.330997i) q^{19} +(-2.29345 - 5.53688i) q^{20} +(-0.196403 - 2.63845i) q^{21} +(0.850330 - 0.352218i) q^{22} +(0.475433 + 0.619596i) q^{23} +(0.344115 + 2.61381i) q^{24} +(-12.9199 - 3.46188i) q^{25} +(0.265705 + 0.991626i) q^{26} +(0.923880 + 0.382683i) q^{27} +(1.15793 - 3.51302i) q^{28} +(4.66396 - 1.93188i) q^{29} +(2.88022 + 1.66290i) q^{30} +(-4.56332 + 5.94703i) q^{31} +(-1.51543 + 5.65567i) q^{32} +(0.593155 - 1.02737i) q^{33} +(-2.97543 + 1.17459i) q^{34} +(-6.38423 - 9.37397i) q^{35} +(0.988583 + 0.988583i) q^{36} +(-8.18938 - 1.07815i) q^{37} +(-0.859274 + 0.496102i) q^{38} +(1.04978 + 0.805522i) q^{39} +(6.87978 + 8.96590i) q^{40} +(3.55444 + 1.47230i) q^{41} +(0.676995 + 1.93783i) q^{42} +(-7.00164 + 7.00164i) q^{43} +(1.31581 - 1.00966i) q^{44} +(4.25001 - 0.559525i) q^{45} +(-0.480709 - 0.368861i) q^{46} +(4.97122 + 2.87014i) q^{47} +(0.287292 + 0.693583i) q^{48} +(0.790680 - 6.95520i) q^{49} +10.3774 q^{50} +(-2.12094 + 3.53576i) q^{51} +(0.924972 + 1.60210i) q^{52} +(1.42201 - 5.30700i) q^{53} +(-0.769205 - 0.101268i) q^{54} -5.08534i q^{55} +(-0.394570 + 6.96400i) q^{56} +(-0.489403 + 1.18152i) q^{57} +(-3.10728 + 2.38430i) q^{58} +(-14.0866 - 3.77450i) q^{59} +(5.78887 + 1.55112i) q^{60} +(5.92432 - 4.54589i) q^{61} +(2.22560 - 5.37307i) q^{62} +(2.21279 + 1.45037i) q^{63} -3.04124i q^{64} +(5.62368 + 0.740371i) q^{65} +(-0.238214 + 0.889029i) q^{66} +(0.874010 + 1.51383i) q^{67} +(-4.63120 + 3.43221i) q^{68} -0.780984 q^{69} +(6.66670 + 5.74294i) q^{70} +(2.55867 + 6.17717i) q^{71} +(-2.28316 - 1.31818i) q^{72} +(6.73256 + 5.16608i) q^{73} +(6.35367 - 0.836477i) q^{74} +(10.6116 - 8.14259i) q^{75} +(-1.26427 + 1.26427i) q^{76} +(2.04851 - 2.37801i) q^{77} +(-0.948461 - 0.392865i) q^{78} +(-2.06054 - 2.68534i) q^{79} +(2.55312 + 1.95908i) q^{80} +(-0.866025 + 0.500000i) q^{81} +(-2.95936 - 0.389608i) q^{82} +(1.79946 + 1.79946i) q^{83} +(2.08216 + 3.05724i) q^{84} +(-0.295398 + 17.6720i) q^{85} +(3.84113 - 6.65303i) q^{86} +(-1.30658 + 4.87622i) q^{87} +(-1.90393 + 2.48125i) q^{88} +(-8.86973 - 5.12094i) q^{89} +(-3.07263 + 1.27273i) q^{90} +(2.33151 + 2.61158i) q^{91} +(-1.00875 - 0.417840i) q^{92} +(-1.94012 - 7.24064i) q^{93} +(-4.30180 - 1.15266i) q^{94} +(0.715561 + 5.43522i) q^{95} +(-3.56441 - 4.64523i) q^{96} +(-9.30496 + 3.85424i) q^{97} +(0.804084 + 5.37105i) q^{98} +(0.453981 + 1.09601i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 8 q^{5} + 8 q^{11} - 80 q^{14} + 96 q^{16} - 16 q^{17} + 16 q^{22} + 8 q^{25} - 64 q^{26} - 88 q^{28} - 40 q^{32} - 32 q^{33} - 32 q^{35} + 32 q^{37} - 64 q^{40} - 64 q^{41} - 56 q^{42} - 32 q^{43}+ \cdots - 16 q^{99}+O(q^{100}) $ 192 * q - 8 * q^5 + 8 * q^11 - 80 * q^14 + 96 * q^16 - 16 * q^17 + 16 * q^22 + 8 * q^25 - 64 * q^26 - 88 * q^28 - 40 * q^32 - 32 * q^33 - 32 * q^35 + 32 * q^37 - 64 * q^40 - 64 * q^41 - 56 * q^42 - 32 * q^43 + 32 * q^44 + 56 * q^49 + 64 * q^50 + 96 * q^52 + 64 * q^53 - 152 * q^56 - 32 * q^58 - 16 * q^59 + 40 * q^61 - 112 * q^62 + 32 * q^65 - 16 * q^67 + 48 * q^68 - 128 * q^69 - 120 * q^70 + 96 * q^71 + 8 * q^73 - 64 * q^74 - 112 * q^76 + 32 * q^77 - 16 * q^78 + 16 * q^79 + 192 * q^80 - 8 * q^82 - 16 * q^83 + 48 * q^84 - 64 * q^86 + 24 * q^87 - 136 * q^88 - 160 * q^92 + 48 * q^93 - 64 * q^94 - 104 * q^95 - 48 * q^96 - 96 * q^97 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/357\mathbb{Z}\right)^\times$.

$n$	$52$	$190$	$239$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{8}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.749407	+	0.200803i	−0.529911	+	0.141989i	−0.513847	−	0.857882i	$-0.671780\pi$
$2$	−0.749407	+	0.200803i	−0.529911	+	0.141989i	−0.0160636	+	0.999871i	$0.505113\pi$
$3$	−0.608761	+	0.793353i	−0.351469	+	0.458043i
$3$	−0.608761	+	0.793353i	−0.351469	+	0.458043i
$4$	−1.21076	+	0.699034i	−0.605381	+	0.349517i
$5$	−0.559525	+	4.25001i	−0.250227	+	1.90066i	0.157434	+	0.987530i	$0.449678\pi$
$5$	−0.559525	+	4.25001i	−0.250227	+	1.90066i	−0.407661	+	0.913133i	$0.633655\pi$
$6$	0.296902	−	0.716785i	0.121210	−	0.292626i
$7$	−1.97366	+	1.76200i	−0.745974	+	0.665975i
$7$	−1.97366	+	1.76200i	−0.745974	+	0.665975i
$8$	1.86419	−	1.86419i	0.659092	−	0.659092i
$9$	−0.258819	−	0.965926i	−0.0862730	−	0.321975i
$10$	−0.434103	−	3.29734i	−0.137275	−	1.04271i
$11$	−1.17616	+	0.154845i	−0.354626	+	0.0466874i	−0.305735	−	0.952117i	$-0.598902\pi$
$11$	−1.17616	+	0.154845i	−0.354626	+	0.0466874i	−0.0488911	+	0.998804i	$0.515569\pi$
$12$	0.182484	−	1.38611i	0.0526787	−	0.400135i
$13$		−	1.32321i		−	0.366994i	−0.983020	−	0.183497i	$-0.941258\pi$
$13$		−	1.32321i		−	0.366994i	0.983020	−	0.183497i	$-0.0587417\pi$
$14$	1.12526	−	1.71677i	0.300738	−	0.458827i
$15$	−3.03114	−	3.03114i	−0.782638	−	0.782638i
$16$	0.375365	−	0.650151i	0.0938411	−	0.162538i
$17$	4.09626	−	0.469777i	0.993488	−	0.113938i
$17$	4.09626	−	0.469777i	0.993488	−	0.113938i
$18$	0.387921	+	0.671900i	0.0914340	+	0.158368i
$19$	1.23530	−	0.330997i	0.283396	−	0.0759358i	−0.114321	−	0.993444i	$-0.536469\pi$
$19$	1.23530	−	0.330997i	0.283396	−	0.0759358i	0.397717	+	0.917508i	$0.369803\pi$
$20$	−2.29345	−	5.53688i	−0.512831	−	1.23808i
$21$	−0.196403	−	2.63845i	−0.0428587	−	0.575757i
$22$	0.850330	−	0.352218i	0.181291	−	0.0750931i
$23$	0.475433	+	0.619596i	0.0991346	+	0.129195i	0.840286	−	0.542143i	$-0.182387\pi$
$23$	0.475433	+	0.619596i	0.0991346	+	0.129195i	−0.741152	+	0.671337i	$0.765720\pi$
$24$	0.344115	+	2.61381i	0.0702422	+	0.533542i
$25$	−12.9199	−	3.46188i	−2.58398	−	0.692375i
$26$	0.265705	+	0.991626i	0.0521091	+	0.194474i
$27$	0.923880	+	0.382683i	0.177801	+	0.0736475i
$28$	1.15793	−	3.51302i	0.218829	−	0.663899i
$29$	4.66396	−	1.93188i	0.866076	−	0.358741i	0.0949954	−	0.995478i	$-0.469716\pi$
$29$	4.66396	−	1.93188i	0.866076	−	0.358741i	0.771081	+	0.636737i	$0.219716\pi$
$30$	2.88022	+	1.66290i	0.525854	+	0.303602i
$31$	−4.56332	+	5.94703i	−0.819596	+	1.06812i	0.176880	+	0.984232i	$0.443400\pi$
$31$	−4.56332	+	5.94703i	−0.819596	+	1.06812i	−0.996475	+	0.0838853i	$0.973267\pi$
$32$	−1.51543	+	5.65567i	−0.267893	+	0.999791i
$33$	0.593155	−	1.02737i	0.103255	−	0.178843i
$34$	−2.97543	+	1.17459i	−0.510282	+	0.201441i
$35$	−6.38423	−	9.37397i	−1.07913	−	1.58449i
$36$	0.988583	+	0.988583i	0.164764	+	0.164764i
$37$	−8.18938	−	1.07815i	−1.34633	−	0.177247i	−0.577336	−	0.816507i	$-0.695908\pi$
$37$	−8.18938	−	1.07815i	−1.34633	−	0.177247i	−0.768991	+	0.639260i	$0.779241\pi$
$38$	−0.859274	+	0.496102i	−0.139393	+	0.0804784i
$39$	1.04978	+	0.805522i	0.168099	+	0.128987i
$40$	6.87978	+	8.96590i	1.08779	+	1.41763i
$41$	3.55444	+	1.47230i	0.555110	+	0.229934i	0.642561	−	0.766235i	$-0.277872\pi$
$41$	3.55444	+	1.47230i	0.555110	+	0.229934i	−0.0874505	+	0.996169i	$0.527872\pi$
$42$	0.676995	+	1.93783i	0.104463	+	0.299014i
$43$	−7.00164	+	7.00164i	−1.06774	+	1.06774i	−0.0702083	+	0.997532i	$0.522366\pi$
$43$	−7.00164	+	7.00164i	−1.06774	+	1.06774i	−0.997532	+	0.0702083i	$0.977634\pi$
$44$	1.31581	−	1.00966i	0.198366	−	0.152211i
$45$	4.25001	−	0.559525i	0.633554	−	0.0834090i
$46$	−0.480709	−	0.368861i	−0.0708767	−	0.0543856i
$47$	4.97122	+	2.87014i	0.725128	+	0.418653i	0.816637	−	0.577152i	$-0.195836\pi$
$47$	4.97122	+	2.87014i	0.725128	+	0.418653i	−0.0915094	+	0.995804i	$0.529169\pi$
$48$	0.287292	+	0.693583i	0.0414670	+	0.100110i
$49$	0.790680	−	6.95520i	0.112954	−	0.993600i
$50$	10.3774			1.46759
$51$	−2.12094	+	3.53576i	−0.296991	+	0.495105i
$52$	0.924972	+	1.60210i	0.128271	+	0.222171i
$53$	1.42201	−	5.30700i	0.195327	−	0.728972i	−0.796854	−	0.604171i	$-0.793504\pi$
$53$	1.42201	−	5.30700i	0.195327	−	0.728972i	0.992182	−	0.124801i	$-0.0398291\pi$
$54$	−0.769205	−	0.101268i	−0.104676	−	0.0137808i
$55$		−	5.08534i		−	0.685707i
$56$	−0.394570	+	6.96400i	−0.0527266	+	0.930604i
$57$	−0.489403	+	1.18152i	−0.0648231	+	0.156497i
$58$	−3.10728	+	2.38430i	−0.408006	+	0.313074i
$59$	−14.0866	−	3.77450i	−1.83392	−	0.491398i	−0.835603	−	0.549334i	$-0.814882\pi$
$59$	−14.0866	−	3.77450i	−1.83392	−	0.491398i	−0.998320	+	0.0579356i	$0.981548\pi$
$60$	5.78887	+	1.55112i	0.747339	+	0.200249i
$61$	5.92432	−	4.54589i	0.758532	−	0.582042i	−0.155428	−	0.987847i	$-0.549676\pi$
$61$	5.92432	−	4.54589i	0.758532	−	0.582042i	0.913960	+	0.405805i	$0.133009\pi$
$62$	2.22560	−	5.37307i	0.282651	−	0.682381i
$63$	2.21279	+	1.45037i	0.278785	+	0.182729i
$64$		−	3.04124i		−	0.380155i
$65$	5.62368	+	0.740371i	0.697531	+	0.0918318i
$66$	−0.238214	+	0.889029i	−0.0293222	+	0.109432i
$67$	0.874010	+	1.51383i	0.106777	+	0.184944i	0.914463	−	0.404670i	$-0.132613\pi$
$67$	0.874010	+	1.51383i	0.106777	+	0.184944i	−0.807686	+	0.589613i	$0.799280\pi$
$68$	−4.63120	+	3.43221i	−0.561616	+	0.416217i
$69$	−0.780984			−0.0940194
$70$	6.66670	+	5.74294i	0.796823	+	0.686413i
$71$	2.55867	+	6.17717i	0.303658	+	0.733095i	0.999883	+	0.0152721i	$0.00486146\pi$
$71$	2.55867	+	6.17717i	0.303658	+	0.733095i	−0.696225	+	0.717823i	$0.745139\pi$
$72$	−2.28316	−	1.31818i	−0.269073	−	0.155349i
$73$	6.73256	+	5.16608i	0.787987	+	0.604644i	0.922380	−	0.386285i	$-0.126242\pi$
$73$	6.73256	+	5.16608i	0.787987	+	0.604644i	−0.134393	+	0.990928i	$0.542908\pi$
$74$	6.35367	−	0.836477i	0.738600	−	0.0972385i
$75$	10.6116	−	8.14259i	1.22533	−	0.940225i
$76$	−1.26427	+	1.26427i	−0.145022	+	0.145022i
$77$	2.04851	−	2.37801i	0.233449	−	0.271000i
$78$	−0.948461	−	0.392865i	−0.107392	−	0.0444833i
$79$	−2.06054	−	2.68534i	−0.231828	−	0.302125i	0.662925	−	0.748686i	$-0.269315\pi$
$79$	−2.06054	−	2.68534i	−0.231828	−	0.302125i	−0.894753	+	0.446562i	$0.852648\pi$
$80$	2.55312	+	1.95908i	0.285448	+	0.219032i
$81$	−0.866025	+	0.500000i	−0.0962250	+	0.0555556i
$82$	−2.95936	−	0.389608i	−0.326807	−	0.0430250i
$83$	1.79946	+	1.79946i	0.197516	+	0.197516i	0.798934	−	0.601418i	$-0.205397\pi$
$83$	1.79946	+	1.79946i	0.197516	+	0.197516i	−0.601418	+	0.798934i	$0.705397\pi$
$84$	2.08216	+	3.05724i	0.227183	+	0.333573i
$85$	−0.295398	+	17.6720i	−0.0320404	+	1.91680i
$86$	3.84113	−	6.65303i	0.414200	−	0.717415i
$87$	−1.30658	+	4.87622i	−0.140080	+	0.522786i
$88$	−1.90393	+	2.48125i	−0.202960	+	0.264502i
$89$	−8.86973	−	5.12094i	−0.940190	−	0.542819i	−0.0501701	−	0.998741i	$-0.515976\pi$
$89$	−8.86973	−	5.12094i	−0.940190	−	0.542819i	−0.890020	+	0.455922i	$0.849310\pi$
$90$	−3.07263	+	1.27273i	−0.323884	+	0.134157i
$91$	2.33151	+	2.61158i	0.244409	+	0.273768i
$92$	−1.00875	−	0.417840i	−0.105170	−	0.0435628i
$93$	−1.94012	−	7.24064i	−0.201182	−	0.750820i
$94$	−4.30180	−	1.15266i	−0.443697	−	0.118888i
$95$	0.715561	+	5.43522i	0.0734150	+	0.557642i
$96$	−3.56441	−	4.64523i	−0.363791	−	0.474102i
$97$	−9.30496	+	3.85424i	−0.944776	+	0.391339i	−0.801265	−	0.598310i	$-0.795839\pi$
$97$	−9.30496	+	3.85424i	−0.944776	+	0.391339i	−0.143511	+	0.989649i	$0.545839\pi$
$98$	0.804084	+	5.37105i	0.0812247	+	0.542558i
$99$	0.453981	+	1.09601i	0.0456268	+	0.110153i
$100$	18.0629	−	4.83994i	1.80629	−	0.483994i
$101$	3.59173	+	6.22106i	0.357391	+	0.619019i	0.987524	−	0.157468i	$-0.0503331\pi$
$101$	3.59173	+	6.22106i	0.357391	+	0.619019i	−0.630133	+	0.776487i	$0.717000\pi$
$102$	0.879458	−	3.07561i	0.0870793	−	0.304531i
$103$	3.37528	−	5.84615i	0.332576	−	0.576039i	−0.650440	−	0.759558i	$-0.725416\pi$
$103$	3.37528	−	5.84615i	0.332576	−	0.576039i	0.983016	+	0.183519i	$0.0587489\pi$
$104$	−2.46673	−	2.46673i	−0.241883	−	0.241883i
$105$	11.3233	+	0.641563i	1.10504	+	0.0626101i
$106$			4.26264i			0.414024i
$107$	−1.57083	+	11.9317i	−0.151858	+	1.15348i	0.730504	+	0.682908i	$0.239285\pi$
$107$	−1.57083	+	11.9317i	−0.151858	+	1.15348i	−0.882363	+	0.470570i	$0.844048\pi$
$108$	−1.38611	+	0.182484i	−0.133378	+	0.0175596i
$109$	−1.16554	−	8.85313i	−0.111638	−	0.847976i	−0.952032	−	0.306000i	$-0.901009\pi$
$109$	−1.16554	−	8.85313i	−0.111638	−	0.847976i	0.840393	−	0.541977i	$-0.182324\pi$
$110$	1.02115	+	3.81098i	0.0973629	+	0.363363i
$111$	5.84074	−	5.84074i	0.554378	−	0.554378i
$112$	0.404726	+	1.94457i	0.0382430	+	0.183745i
$113$	−7.39748	+	17.8591i	−0.695896	+	1.68004i	0.0366528	+	0.999328i	$0.488330\pi$
$113$	−7.39748	+	17.8591i	−0.695896	+	1.68004i	−0.732549	+	0.680714i	$0.761670\pi$
$114$	0.129509	−	0.983716i	0.0121296	−	0.0921334i
$115$	−2.89931	+	1.67392i	−0.270362	+	0.156093i
$116$	−4.29650	+	5.59931i	−0.398920	+	0.519883i
$117$	−1.27813	+	0.342473i	−0.118163	+	0.0316617i
$118$	11.3145			1.04159
$119$	−7.25687	+	8.14480i	−0.665236	+	0.746633i
$120$	−11.3013			−1.03166
$121$	−9.26581	+	2.48277i	−0.842346	+	0.225706i
$122$	−3.52690	+	4.59634i	−0.319310	+	0.416133i
$123$	−3.33186	+	1.92365i	−0.300424	+	0.173450i
$124$	1.36792	−	10.3903i	0.122842	−	0.933081i
$125$	13.7398	−	33.1708i	1.22893	−	2.96689i
$126$	−1.94952	−	0.642583i	−0.173677	−	0.0572459i
$127$	7.45558	−	7.45558i	0.661575	−	0.661575i	−0.294176	−	0.955751i	$-0.595045\pi$
$127$	7.45558	−	7.45558i	0.661575	−	0.661575i	0.955751	+	0.294176i	$0.0950452\pi$
$128$	−2.42017	−	9.03221i	−0.213915	−	0.798343i
$129$	−1.29245	−	9.81711i	−0.113794	−	0.864348i
$130$	−4.36309	+	0.574412i	−0.382668	+	0.0503792i
$131$	−0.328265	+	2.49342i	−0.0286806	+	0.217851i	−0.999783	−	0.0208106i	$-0.993375\pi$
$131$	−0.328265	+	2.49342i	−0.0286806	+	0.217851i	0.971103	+	0.238661i	$0.0767086\pi$
$132$			1.65854i			0.144358i
$133$	−1.85484	+	2.82987i	−0.160835	+	0.245381i
$134$	−0.958970	−	0.958970i	−0.0828424	−	0.0828424i
$135$	−2.14334	+	3.71238i	−0.184470	+	0.319511i
$136$	6.76046	−	8.51197i	0.579704	−	0.729895i
$137$	7.99908	+	13.8548i	0.683408	+	1.18370i	0.973934	+	0.226830i	$0.0728361\pi$
$137$	7.99908	+	13.8548i	0.683408	+	1.18370i	−0.290527	+	0.956867i	$0.593831\pi$
$138$	0.585274	−	0.156824i	0.0498219	−	0.0133497i
$139$	−7.87499	−	19.0119i	−0.667948	−	1.61257i	−0.785038	−	0.619448i	$-0.787356\pi$
$139$	−7.87499	−	19.0119i	−0.667948	−	1.61257i	0.117089	−	0.993121i	$-0.462644\pi$
$140$	14.2825	+	6.88686i	1.20709	+	0.582046i
$141$	−5.30332	+	2.19671i	−0.446620	+	0.184996i
$142$	−3.15788	−	4.11543i	−0.265003	−	0.345359i
$143$	0.204893	+	1.55631i	0.0171340	+	0.130145i
$144$	−0.725149	−	0.194303i	−0.0604291	−	0.0161919i
$145$	5.60090	+	20.9028i	0.465129	+	1.73589i
$146$	−6.08279	−	2.51957i	−0.503415	−	0.208521i
$147$	5.03660	+	4.86135i	0.415411	+	0.400957i
$148$	10.6691	−	4.41927i	0.876991	−	0.363262i
$149$	0.128364	+	0.0741108i	0.0105160	+	0.00607139i	0.505249	−	0.862974i	$-0.331401\pi$
$149$	0.128364	+	0.0741108i	0.0105160	+	0.00607139i	−0.494733	+	0.869045i	$0.664734\pi$
$150$	−6.31737	+	8.23296i	−0.515811	+	0.672218i
$151$	−0.456805	+	1.70482i	−0.0371742	+	0.138736i	−0.982019	−	0.188783i	$-0.939546\pi$
$151$	−0.456805	+	1.70482i	−0.0371742	+	0.138736i	0.944845	+	0.327519i	$0.106212\pi$
$152$	1.68579	−	2.91987i	0.136736	−	0.236833i
$153$	−1.51396	−	3.83509i	−0.122396	−	0.310049i
$154$	−1.05765	+	2.19344i	−0.0852281	+	0.176753i
$155$	−22.7216	−	22.7216i	−1.82505	−	1.82505i
$156$	−1.83412	−	0.241466i	−0.146847	−	0.0193328i
$157$	−3.07327	+	1.77435i	−0.245273	+	0.141609i	−0.617598	−	0.786494i	$-0.711894\pi$
$157$	−3.07327	+	1.77435i	−0.245273	+	0.141609i	0.372325	+	0.928103i	$0.378561\pi$
$158$	2.08340	+	1.59865i	0.165747	+	0.127182i
$159$	3.34466	+	4.35885i	0.265249	+	0.345679i
$160$	−23.1887	−	9.60509i	−1.83323	−	0.759349i
$161$	−2.03007	−	0.385158i	−0.159992	−	0.0303547i
$162$	0.548604	−	0.548604i	0.0431024	−	0.0431024i
$163$	−15.0230	+	11.5276i	−1.17669	+	0.902910i	−0.996733	−	0.0807639i	$-0.974264\pi$
$163$	−15.0230	+	11.5276i	−1.17669	+	0.902910i	−0.179962	+	0.983674i	$0.557597\pi$
$164$	−5.33277	+	0.702072i	−0.416419	+	0.0548226i
$165$	4.03447	+	3.09576i	0.314083	+	0.241004i
$166$	−1.70986	−	0.987190i	−0.132711	−	0.0766208i
$167$	3.00830	+	7.26269i	0.232790	+	0.562004i	0.996503	−	0.0835511i	$-0.0266262\pi$
$167$	3.00830	+	7.26269i	0.232790	+	0.562004i	−0.763714	+	0.645555i	$0.776626\pi$
$168$	−5.28472	−	4.55245i	−0.407725	−	0.351229i
$169$	11.2491			0.865316
$170$	−3.32721	−	13.3028i	−0.255186	−	1.02028i
$171$	−0.639436	−	1.10754i	−0.0488989	−	0.0846954i
$172$	3.58294	−	13.3717i	0.273197	−	1.01958i
$173$	7.22775	+	0.951552i	0.549516	+	0.0723451i	0.400172	−	0.916440i	$-0.368950\pi$
$173$	7.22775	+	0.951552i	0.549516	+	0.0723451i	0.149344	+	0.988785i	$0.452284\pi$
$174$		−	3.91664i		−	0.296920i
$175$	31.5994	−	15.9323i	2.38869	−	1.20437i
$176$	−0.340817	+	0.822805i	−0.0256900	+	0.0620212i
$177$	11.5699	−	8.87791i	0.869648	−	0.667304i
$178$	7.67534	+	2.05660i	0.575291	+	0.154149i
$179$	−21.7376	−	5.82458i	−1.62475	−	0.435349i	−0.672355	−	0.740229i	$-0.734717\pi$
$179$	−21.7376	−	5.82458i	−1.62475	−	0.435349i	−0.952391	+	0.304880i	$0.901384\pi$
$180$	−4.75463	+	3.64835i	−0.354389	+	0.271932i
$181$	−1.78187	+	4.30181i	−0.132445	+	0.319751i	−0.976164	−	0.217035i	$-0.930362\pi$
$181$	−1.78187	+	4.30181i	−0.132445	+	0.319751i	0.843719	+	0.536785i	$0.180362\pi$
$182$	−2.27166	−	1.48896i	−0.168387	−	0.110369i
$183$			7.46744i			0.552009i
$184$	2.04135	+	0.268748i	0.150490	+	0.0198124i
$185$	9.16432	−	34.2017i	0.673774	−	2.51456i
$186$	2.90788	+	5.03660i	0.213216	+	0.369302i
$187$	−4.74511	+	1.18682i	−0.346997	+	0.0867886i
$188$	−8.02529			−0.585305
$189$	−2.49772	+	0.872592i	−0.181682	+	0.0634718i
$190$	−1.62765	−	3.92951i	−0.118082	−	0.285076i
$191$	−5.51588	−	3.18460i	−0.399115	−	0.230429i	0.286987	−	0.957935i	$-0.407346\pi$
$191$	−5.51588	−	3.18460i	−0.399115	−	0.230429i	−0.686102	+	0.727505i	$0.740680\pi$
$192$	2.41278	+	1.85139i	0.174127	+	0.133613i
$193$	−0.671367	+	0.0883872i	−0.0483261	+	0.00636225i	−0.154650	−	0.987969i	$-0.549425\pi$
$193$	−0.671367	+	0.0883872i	−0.0483261	+	0.00636225i	0.106324	+	0.994331i	$0.466092\pi$
$194$	6.19926	−	4.75686i	0.445081	−	0.341523i
$195$	−4.01085	+	4.01085i	−0.287223	+	0.287223i
$196$	3.90460	+	8.97381i	0.278900	+	0.640986i
$197$	−8.52845	−	3.53260i	−0.607627	−	0.251687i	0.0575865	−	0.998341i	$-0.481660\pi$
$197$	−8.52845	−	3.53260i	−0.607627	−	0.251687i	−0.665214	+	0.746653i	$0.731660\pi$
$198$	−0.560298	−	0.730195i	−0.0398186	−	0.0518927i
$199$	5.81183	+	4.45957i	0.411989	+	0.316131i	0.793877	−	0.608078i	$-0.208059\pi$
$199$	5.81183	+	4.45957i	0.411989	+	0.316131i	−0.381888	+	0.924209i	$0.624726\pi$
$200$	−30.5388	+	17.6316i	−2.15942	+	1.24674i
$201$	−1.73307	−	0.228162i	−0.122241	−	0.0160933i
$202$	−3.94088	−	3.94088i	−0.277279	−	0.277279i
$203$	−5.80111	+	12.0308i	−0.407158	+	0.844396i
$204$	0.0963418	−	5.76358i	0.00674527	−	0.403531i
$205$	−8.24608	+	14.2826i	−0.575931	+	0.997542i
$206$	−1.35553	+	5.05891i	−0.0944443	+	0.352471i
$207$	0.475433	−	0.619596i	0.0330449	−	0.0430649i
$208$	−0.860289	−	0.496688i	−0.0596503	−	0.0344391i
$209$	−1.40165	+	0.580584i	−0.0969544	+	0.0401598i
$210$	−8.61461	+	1.79297i	−0.594465	+	0.123727i
$211$	−0.0104845	−	0.00434281i	−0.000721781	−	0.000298972i	0.382323	−	0.924029i	$-0.375124\pi$
$211$	−0.0104845	−	0.00434281i	−0.000721781	−	0.000298972i	−0.383044	+	0.923730i	$0.625124\pi$
$212$	1.98806	+	7.41954i	0.136541	+	0.509576i
$213$	−6.45830	−	1.73050i	−0.442515	−	0.118572i
$214$	−1.21872	−	9.25710i	−0.0833100	−	0.632802i
$215$	−25.8395	−	33.6747i	−1.76224	−	2.29659i
$216$	2.43569	−	1.00889i	0.165727	−	0.0686465i
$217$	−1.47225	−	19.7780i	−0.0999429	−	1.34262i
$218$	2.65120	+	6.40055i	0.179562	+	0.433500i
$219$	−8.19705	+	2.19639i	−0.553905	+	0.148418i
$220$	3.55482	+	6.15713i	0.239666	+	0.415114i
$221$	−0.621616	−	5.42023i	−0.0418144	−	0.364604i
$222$	−3.20425	+	5.54992i	−0.215055	+	0.372487i
$223$	12.8999	+	12.8999i	0.863843	+	0.863843i	0.991782	−	0.127939i	$-0.0408363\pi$
$223$	12.8999	+	12.8999i	0.863843	+	0.863843i	−0.127939	+	0.991782i	$0.540836\pi$
$224$	−6.97437	−	13.8326i	−0.465994	−	0.924228i
$225$			13.3757i			0.891711i
$226$	1.95756	−	14.8692i	0.130215	−	0.989082i
$227$	−11.1569	+	1.46884i	−0.740512	+	0.0974902i	−0.491339	−	0.870969i	$-0.663492\pi$
$227$	−11.1569	+	1.46884i	−0.740512	+	0.0974902i	−0.249173	+	0.968459i	$0.580159\pi$
$228$	−0.233374	−	1.77265i	−0.0154556	−	0.117397i
$229$	7.17501	+	26.7775i	0.474138	+	1.76951i	0.624657	+	0.780899i	$0.285239\pi$
$229$	7.17501	+	26.7775i	0.474138	+	1.76951i	−0.150519	+	0.988607i	$0.548095\pi$
$230$	1.83663	−	1.83663i	0.121104	−	0.121104i
$231$	0.639551	+	3.07283i	0.0420794	+	0.202177i
$232$	5.09314	−	12.2959i	0.334381	−	0.807267i
$233$	−0.418479	+	3.17866i	−0.0274155	+	0.208241i	−0.999670	−	0.0256839i	$-0.991824\pi$
$233$	−0.418479	+	3.17866i	−0.0274155	+	0.208241i	0.972255	+	0.233925i	$0.0751570\pi$
$234$	0.889068	−	0.513303i	0.0581202	−	0.0335557i
$235$	−14.9796	+	19.5218i	−0.977164	+	1.27346i
$236$	19.6941	−	5.27701i	1.28197	−	0.343504i
$237$	3.38480			0.219866
$238$	3.80285	−	7.56097i	0.246502	−	0.490105i
$239$	−4.85520			−0.314057			−0.157028	−	0.987594i	$-0.550191\pi$
$239$	−4.85520			−0.314057			−0.157028	+	0.987594i	$0.550191\pi$
$240$	−3.10848	+	0.832916i	−0.200652	+	0.0537645i
$241$	12.7654	−	16.6362i	0.822294	−	1.07163i	−0.173926	−	0.984759i	$-0.555645\pi$
$241$	12.7654	−	16.6362i	0.822294	−	1.07163i	0.996219	−	0.0868750i	$-0.0276881\pi$
$242$	6.44531	−	3.72120i	0.414320	−	0.239208i
$243$	0.130526	−	0.991445i	0.00837326	−	0.0636012i
$244$	−3.99521	+	9.64530i	−0.255767	+	0.617477i
$245$	29.1173	+	7.25201i	1.86023	+	0.463314i
$246$	2.11064	−	2.11064i	0.134570	−	0.134570i
$247$	−0.437980	−	1.63456i	−0.0278680	−	0.104005i
$248$	2.57951	+	19.5933i	0.163799	+	1.24418i
$249$	−2.52305	+	0.332166i	−0.159892	+	0.0210501i
$250$	−3.63590	+	27.6174i	−0.229955	+	1.74668i
$251$			10.6261i			0.670713i	0.942091	+	0.335356i	$0.108857\pi$
$251$			10.6261i			0.670713i	−0.942091	+	0.335356i	$0.891143\pi$
$252$	−3.69302	−	0.209241i	−0.232638	−	0.0131809i
$253$	−0.655126	−	0.655126i	−0.0411875	−	0.0411875i
$254$	−4.09016	+	7.08436i	−0.256639	+	0.444512i
$255$	−13.8403	−	10.9924i	−0.866713	−	0.688369i
$256$	6.66863	+	11.5504i	0.416790	+	0.721901i
$257$	21.9560	−	5.88309i	1.36958	−	0.366977i	0.502253	−	0.864721i	$-0.332505\pi$
$257$	21.9560	−	5.88309i	1.36958	−	0.366977i	0.867324	+	0.497744i	$0.165838\pi$
$258$	2.93987	+	7.09748i	0.183028	+	0.441870i
$259$	18.0628	−	12.3018i	1.12237	−	0.764398i
$260$	−7.32648	+	3.03473i	−0.454369	+	0.188206i
$261$	−3.07317	−	4.00504i	−0.190225	−	0.247906i
$262$	−0.254682	−	1.93450i	−0.0157343	−	0.119514i
$263$	19.6448	+	5.26380i	1.21135	+	0.324580i	0.807291	−	0.590154i	$-0.200933\pi$
$263$	19.6448	+	5.26380i	1.21135	+	0.324580i	0.404057	+	0.914734i	$0.367600\pi$
$264$	−0.809469	−	3.02098i	−0.0498194	−	0.185928i
$265$	21.7591	+	9.01293i	1.33665	+	0.553660i
$266$	0.821782	−	2.49318i	0.0503867	−	0.152867i
$267$	9.46227	−	3.91940i	0.579082	−	0.239863i
$268$	−2.11644	−	1.22193i	−0.129282	−	0.0746410i
$269$	12.5785	−	16.3926i	0.766922	−	0.999472i	−0.232716	−	0.972545i	$-0.574761\pi$
$269$	12.5785	−	16.3926i	0.766922	−	0.999472i	0.999637	−	0.0269270i	$-0.00857217\pi$
$270$	0.860779	−	3.21247i	0.0523853	−	0.195505i
$271$	−10.9450	+	18.9573i	−0.664862	+	1.15157i	0.314461	+	0.949270i	$0.398176\pi$
$271$	−10.9450	+	18.9573i	−0.664862	+	1.15157i	−0.979323	+	0.202304i	$0.935157\pi$
$272$	1.23216	−	2.83952i	0.0747109	−	0.172171i
$273$	−3.49124	+	0.259884i	−0.211299	+	0.0157289i
$274$	−8.77665	−	8.77665i	−0.530217	−	0.530217i
$275$	15.7319	+	2.07115i	0.948671	+	0.124895i
$276$	0.945586	−	0.545934i	0.0569176	−	0.0328614i
$277$	−7.09677	−	5.44554i	−0.426403	−	0.327191i	0.373166	−	0.927765i	$-0.378272\pi$
$277$	−7.09677	−	5.44554i	−0.426403	−	0.327191i	−0.799569	+	0.600574i	$0.794939\pi$
$278$	9.71922	+	12.6663i	0.582920	+	0.759676i
$279$	6.92546	+	2.86862i	0.414616	+	0.171740i
$280$	−29.3763	−	5.57346i	−1.75557	−	0.333078i
$281$	5.34624	−	5.34624i	0.318930	−	0.318930i	−0.529426	−	0.848356i	$-0.677593\pi$
$281$	5.34624	−	5.34624i	0.318930	−	0.318930i	0.848356	+	0.529426i	$0.177593\pi$
$282$	3.53324	−	2.71115i	0.210401	−	0.161447i
$283$	−2.46587	+	0.324639i	−0.146581	+	0.0192978i	−0.203460	−	0.979083i	$-0.565219\pi$
$283$	−2.46587	+	0.324639i	−0.146581	+	0.0192978i	0.0568785	+	0.998381i	$0.481885\pi$
$284$	−7.41599	−	5.69049i	−0.440058	−	0.337669i
$285$	−4.74766	−	2.74106i	−0.281227	−	0.162366i
$286$	−0.466060	−	1.12517i	−0.0275587	−	0.0665326i
$287$	−9.60946	+	3.35712i	−0.567228	+	0.198165i
$288$	5.85518			0.345020
$289$	16.5586	−	3.84865i	0.974036	−	0.226391i
$290$	−8.39470	−	14.5400i	−0.492954	−	0.853821i
$291$	2.60673	−	9.72844i	0.152809	−	0.570291i
$292$	−11.7628	−	1.54860i	−0.688365	−	0.0906250i
$293$			21.4483i			1.25302i	0.779412	+	0.626511i	$0.215518\pi$
$293$			21.4483i			1.25302i	−0.779412	+	0.626511i	$0.784482\pi$
$294$	−4.75063	−	2.63176i	−0.277062	−	0.153488i
$295$	23.9235	−	57.7564i	1.39288	−	3.36271i
$296$	−17.2765	+	13.2567i	−1.00417	+	0.770530i
$297$	−1.14589	−	0.307040i	−0.0664911	−	0.0178162i
$298$	−0.111078	−	0.0297633i	−0.00643459	−	0.00172414i
$299$	0.819859	−	0.629100i	0.0474137	−	0.0363818i
$300$	−7.15621	+	17.2766i	−0.413164	+	0.997466i
$301$	1.48195	−	26.1558i	0.0854180	−	1.50760i
$302$		−	1.36933i		−	0.0787961i
$303$	−7.12201	−	0.937630i	−0.409149	−	0.0538655i
$304$	0.248489	−	0.927373i	0.0142518	−	0.0531885i
$305$	16.0053	+	27.7220i	0.916460	+	1.58736i
$306$	1.90467	+	2.57004i	0.108883	+	0.146919i
$307$	−4.61821			−0.263575			−0.131787	−	0.991278i	$-0.542072\pi$
$307$	−4.61821			−0.263575			−0.131787	+	0.991278i	$0.542072\pi$
$308$	−0.817944	+	4.31118i	−0.0466067	+	0.245652i
$309$	2.58333	+	6.23670i	0.146960	+	0.354793i
$310$	21.5903	+	12.4652i	1.22625	+	0.707975i
$311$	24.5259	+	18.8194i	1.39074	+	1.06715i	0.988436	+	0.151642i	$0.0484560\pi$
$311$	24.5259	+	18.8194i	1.39074	+	1.06715i	0.402300	+	0.915508i	$0.368211\pi$
$312$	3.45864	−	0.455338i	0.195807	−	0.0257784i
$313$	3.75073	−	2.87803i	0.212004	−	0.162676i	−0.497301	−	0.867578i	$-0.665676\pi$
$313$	3.75073	−	2.87803i	0.212004	−	0.162676i	0.709305	+	0.704902i	$0.249009\pi$
$314$	1.94683	−	1.94683i	0.109866	−	0.109866i
$315$	−7.40220	+	8.59285i	−0.417067	+	0.484152i
$316$	4.37196	+	1.81093i	0.245942	+	0.101873i
$317$	20.2231	+	26.3553i	1.13584	+	1.48026i	0.853608	+	0.520916i	$0.174410\pi$
$317$	20.2231	+	26.3553i	1.13584	+	1.48026i	0.282237	+	0.959345i	$0.408924\pi$
$318$	−3.38178	−	2.59493i	−0.189641	−	0.145517i
$319$	−5.18643	+	2.99439i	−0.290384	+	0.167654i
$320$	12.9253	+	1.70165i	0.722547	+	0.0951251i
$321$	−8.50977	−	8.50977i	−0.474969	−	0.474969i
$322$	1.59869	−	0.119005i	0.0890916	−	0.00663187i
$323$	4.90459	−	1.93616i	0.272899	−	0.107731i
$324$	0.699034	−	1.21076i	0.0388352	−	0.0672646i
$325$	−4.58081	+	17.0958i	−0.254097	+	0.948305i
$326$	8.94359	−	11.6555i	0.495340	−	0.645539i
$327$	7.73320	+	4.46476i	0.427647	+	0.246902i
$328$	9.37081	−	3.88152i	0.517416	−	0.214321i
$329$	−14.8687	+	3.09464i	−0.819739	+	0.170613i
$330$	−3.64509	−	1.50985i	−0.200656	−	0.0831144i
$331$	−5.99925	−	22.3895i	−0.329748	−	1.23064i	−0.909451	−	0.415810i	$-0.863498\pi$
$331$	−5.99925	−	22.3895i	−0.329748	−	1.23064i	0.579703	−	0.814828i	$-0.303169\pi$
$332$	−3.43660	−	0.920834i	−0.188608	−	0.0505374i
$333$	1.07815	+	8.18938i	0.0590824	+	0.448775i
$334$	−3.71281	−	4.83863i	−0.203156	−	0.264758i
$335$	−6.92282	+	2.86753i	−0.378234	+	0.156670i
$336$	−1.78911	−	0.862690i	−0.0976041	−	0.0470636i
$337$	12.5264	+	30.2415i	0.682358	+	1.64736i	0.759636	+	0.650349i	$0.225377\pi$
$337$	12.5264	+	30.2415i	0.682358	+	1.64736i	−0.0772772	+	0.997010i	$0.524623\pi$
$338$	−8.43015	+	2.25885i	−0.458540	+	0.122865i
$339$	−9.66527	−	16.7407i	−0.524946	−	0.909232i
$340$	−11.9957	−	21.6031i	−0.650556	−	1.17159i
$341$	4.44633	−	7.70127i	0.240782	−	0.417047i
$342$	0.701594	+	0.701594i	0.0379379	+	0.0379379i
$343$	10.6946	+	15.1204i	0.577452	+	0.816425i
$344$			26.1048i			1.40748i
$345$	0.436980	−	3.31919i	0.0235262	−	0.178699i
$346$	−5.60760	+	0.738255i	−0.301466	+	0.0396888i
$347$	−1.61974	−	12.3032i	−0.0869522	−	0.660468i	−0.978307	−	0.207161i	$-0.933578\pi$
$347$	−1.61974	−	12.3032i	−0.0869522	−	0.660468i	0.891355	−	0.453307i	$-0.149756\pi$
$348$	−1.82669	−	6.81729i	−0.0979207	−	0.365445i
$349$	−6.87040	+	6.87040i	−0.367764	+	0.367764i	−0.866661	−	0.498897i	$-0.833738\pi$
$349$	−6.87040	+	6.87040i	−0.367764	+	0.367764i	0.498897	+	0.866661i	$0.333738\pi$
$350$	−20.4815	+	18.2851i	−1.09478	+	0.977377i
$351$	0.506372	−	1.22249i	0.0270282	−	0.0652517i
$352$	0.906643	−	6.88663i	0.0483242	−	0.367059i
$353$	−10.8138	+	6.24333i	−0.575558	+	0.332299i	−0.759366	−	0.650663i	$-0.774491\pi$
$353$	−10.8138	+	6.24333i	−0.575558	+	0.332299i	0.183808	+	0.982962i	$0.441158\pi$
$354$	−6.88786	+	8.97643i	−0.366086	+	0.477092i
$355$	−27.6847	+	7.41809i	−1.46935	+	0.393711i
$356$	14.3189			0.758898
$357$	−2.04400	−	10.7155i	−0.108180	−	0.567125i
$358$	17.4599			0.922785
$359$	4.98932	−	1.33688i	0.263326	−	0.0705580i	−0.124740	−	0.992189i	$-0.539810\pi$
$359$	4.98932	−	1.33688i	0.263326	−	0.0705580i	0.388066	+	0.921631i	$0.373143\pi$
$360$	6.87978	−	8.96590i	0.362596	−	0.472545i
$361$	−15.0381	+	8.68224i	−0.791478	+	0.456960i
$362$	0.471527	−	3.58161i	0.0247829	−	0.188245i
$363$	3.67096	−	8.86247i	0.192675	−	0.465159i
$364$	−4.64849	−	1.53220i	−0.243647	−	0.0803089i
$365$	−25.7229	+	25.7229i	−1.34640	+	1.34640i
$366$	−1.49948	−	5.59615i	−0.0783793	−	0.292516i
$367$	0.144334	+	1.09633i	0.00753419	+	0.0572278i	0.994799	−	0.101858i	$-0.0324787\pi$
$367$	0.144334	+	1.09633i	0.00753419	+	0.0572278i	−0.987265	+	0.159086i	$0.949145\pi$
$368$	0.581291	−	0.0765285i	0.0303019	−	0.00398932i
$369$	0.502173	−	3.81438i	0.0261421	−	0.198569i
$370$			27.4712i			1.42816i
$371$	6.54439	+	12.9798i	0.339768	+	0.673877i
$372$	7.41048	+	7.41048i	0.384216	+	0.384216i
$373$	−9.44236	+	16.3547i	−0.488907	+	0.846812i	−0.999919	−	0.0127620i	$-0.995938\pi$
$373$	−9.44236	+	16.3547i	−0.488907	+	0.846812i	0.511012	+	0.859574i	$0.329271\pi$
$374$	3.31770	−	1.84224i	0.171554	−	0.0952600i
$375$	17.9519	+	31.0936i	0.927033	+	1.60567i
$376$	14.6178	−	3.91683i	0.753856	−	0.201995i
$377$	−2.55629	−	6.17143i	−0.131656	−	0.317845i
$378$	1.69659	−	1.15548i	0.0872629	−	0.0594312i
$379$	−11.9069	+	4.93198i	−0.611614	+	0.253339i	−0.666918	−	0.745131i	$-0.732387\pi$
$379$	−11.9069	+	4.93198i	−0.611614	+	0.253339i	0.0553045	+	0.998470i	$0.482387\pi$
$380$	−4.66578	−	6.08056i	−0.239349	−	0.311926i
$381$	1.37624	+	10.4536i	0.0705069	+	0.535553i
$382$	4.77312	+	1.27895i	0.244214	+	0.0654369i
$383$	−4.58441	−	17.1093i	−0.234252	−	0.874242i	−0.978484	−	0.206321i	$-0.933851\pi$
$383$	−4.58441	−	17.1093i	−0.234252	−	0.874242i	0.744232	−	0.667921i	$-0.232816\pi$
$384$	8.63905	+	3.57841i	0.440859	+	0.182610i
$385$	8.96038	+	10.0367i	0.456664	+	0.511519i
$386$	0.485379	−	0.201050i	0.0247051	−	0.0102332i
$387$	8.57523	+	4.95091i	0.435903	+	0.251669i
$388$	8.57185	−	11.1711i	0.435170	−	0.567124i
$389$	5.01979	−	18.7341i	0.254513	−	0.949857i	−0.713847	−	0.700302i	$-0.753049\pi$
$389$	5.01979	−	18.7341i	0.254513	−	0.949857i	0.968360	−	0.249556i	$-0.0802845\pi$
$390$	2.20037	−	3.81115i	0.111420	−	0.192985i
$391$	2.23857	+	2.31468i	0.113209	+	0.117058i
$392$	−11.4919	−	14.4398i	−0.580426	−	0.729321i
$393$	−1.77833	−	1.77833i	−0.0897047	−	0.0897047i
$394$	7.10064	+	0.934816i	0.357725	+	0.0470954i
$395$	12.5657	−	7.25478i	0.632247	−	0.365028i
$396$	−1.31581	−	1.00966i	−0.0661219	−	0.0507371i
$397$	10.4011	+	13.5549i	0.522014	+	0.680302i	0.977740	−	0.209818i	$-0.0672872\pi$
$397$	10.4011	+	13.5549i	0.522014	+	0.680302i	−0.455727	+	0.890120i	$0.650620\pi$
$398$	−5.25092	−	2.17500i	−0.263205	−	0.109023i
$399$	−1.11593	−	3.19426i	−0.0558666	−	0.159913i
$400$	−7.10041	+	7.10041i	−0.355021	+	0.355021i
$401$	3.46856	−	2.66152i	0.173212	−	0.132910i	−0.518518	−	0.855067i	$-0.673516\pi$
$401$	3.46856	−	2.66152i	0.173212	−	0.132910i	0.691729	+	0.722157i	$0.256849\pi$
$402$	1.34459	−	0.177018i	0.0670619	−	0.00882886i
$403$	7.86920	+	6.03825i	0.391993	+	0.300786i
$404$	−8.69747	−	5.02149i	−0.432715	−	0.249828i
$405$	−1.64044	−	3.96038i	−0.0815143	−	0.196793i
$406$	1.93157	−	10.1808i	0.0958623	−	0.505267i
$407$	9.79898			0.485717
$408$	2.63749	+	10.5452i	0.130575	+	0.522064i
$409$	−16.5337	−	28.6372i	−0.817537	−	1.41602i	−0.907492	−	0.420070i	$-0.862005\pi$
$409$	−16.5337	−	28.6372i	−0.817537	−	1.41602i	0.0899541	−	0.995946i	$-0.471328\pi$
$410$	3.31167	−	12.3593i	0.163552	−	0.610384i
$411$	−15.8613	−	2.08818i	−0.782380	−	0.103002i
$412$			9.43773i			0.464964i
$413$	34.4529	−	17.3711i	1.69532	−	0.854777i
$414$	−0.231876	+	0.559798i	−0.0113961	+	0.0275126i
$415$	−8.65457	+	6.64088i	−0.424836	+	0.325988i
$416$	7.48367	+	2.00524i	0.366917	+	0.0983151i
$417$	19.8772	+	5.32607i	0.973389	+	0.260819i
$418$	0.933826	−	0.716550i	0.0456749	−	0.0350476i
$419$	0.882085	−	2.12954i	0.0430927	−	0.104035i	−0.900868	−	0.434094i	$-0.857069\pi$
$419$	0.882085	−	2.12954i	0.0430927	−	0.104035i	0.943960	+	0.330059i	$0.107069\pi$
$420$	−14.1583	+	7.13862i	−0.690857	+	0.348329i
$421$		−	4.68883i		−	0.228519i	−0.993451	−	0.114260i	$-0.963550\pi$
$421$		−	4.68883i		−	0.228519i	0.993451	−	0.114260i	$-0.0364496\pi$
$422$	0.00872919	+	0.00114922i	0.000424930	+	5.59431e-5i
$423$	1.48569	−	5.54468i	0.0722369	−	0.269592i
$424$	−7.24237	−	12.5442i	−0.351721	−	0.609198i
$425$	−54.5495	−	8.11126i	−2.64604	−	0.393454i
$426$	5.18738			0.251329
$427$	−3.68272	+	19.4107i	−0.178220	+	0.939351i
$428$	−6.43873	−	15.5445i	−0.311228	−	0.751371i
$429$	−1.35944	−	0.784871i	−0.0656342	−	0.0378939i
$430$	26.1262	+	20.0474i	1.25992	+	0.966770i
$431$	8.46302	−	1.11418i	0.407649	−	0.0536681i	0.0760866	−	0.997101i	$-0.475757\pi$
$431$	8.46302	−	1.11418i	0.407649	−	0.0536681i	0.331563	+	0.943433i	$0.392424\pi$
$432$	0.595594	−	0.457015i	0.0286555	−	0.0219881i
$433$	11.8775	−	11.8775i	0.570794	−	0.570794i	−0.361556	−	0.932350i	$-0.617754\pi$
$433$	11.8775	−	11.8775i	0.570794	−	0.570794i	0.932350	+	0.361556i	$0.117754\pi$
$434$	5.07480	+	14.5261i	0.243598	+	0.697277i
$435$	−19.9929	−	8.28135i	−0.958588	−	0.397060i
$436$	7.59983	+	9.90429i	0.363966	+	0.474329i
$437$	0.792384	+	0.608018i	0.0379049	+	0.0290854i
$438$	5.70188	−	3.29198i	0.272446	−	0.157297i
$439$	4.65513	+	0.612860i	0.222177	+	0.0292502i	0.240793	−	0.970577i	$-0.422593\pi$
$439$	4.65513	+	0.612860i	0.222177	+	0.0292502i	−0.0186156	+	0.999827i	$0.505926\pi$
$440$	−9.48005	−	9.48005i	−0.451943	−	0.451943i
$441$	−6.92285	+	1.03640i	−0.329660	+	0.0493524i
$442$	1.55424	+	3.93713i	0.0739277	+	0.187270i
$443$	5.49805	−	9.52290i	0.261220	−	0.452446i	−0.705346	−	0.708863i	$-0.749209\pi$
$443$	5.49805	−	9.52290i	0.261220	−	0.452446i	0.966566	+	0.256416i	$0.0825418\pi$
$444$	−2.98887	+	11.1546i	−0.141846	+	0.529375i
$445$	26.7269	−	34.8312i	1.26698	−	1.65116i
$446$	−12.2576	−	7.07694i	−0.580415	−	0.335103i
$447$	−0.136939	+	0.0567219i	−0.00647698	+	0.00268285i
$448$	5.35868	+	6.00238i	0.253174	+	0.283586i
$449$	−24.5208	−	10.1569i	−1.15721	−	0.479332i	−0.280264	−	0.959923i	$-0.590422\pi$
$449$	−24.5208	−	10.1569i	−1.15721	−	0.479332i	−0.876945	+	0.480591i	$0.840422\pi$
$450$	−2.68587	−	10.0238i	−0.126613	−	0.472527i
$451$	−4.40857	−	1.18127i	−0.207591	−	0.0556240i
$452$	−3.52752	−	26.7942i	−0.165921	−	1.26029i
$453$	−1.07444	−	1.40023i	−0.0504815	−	0.0657888i
$454$	8.06613	−	3.34110i	0.378562	−	0.156806i
$455$	−12.4038	+	8.44770i	−0.581498	+	0.396034i
$456$	1.29025	+	3.11493i	0.0604213	+	0.145870i
$457$	−5.46610	+	1.46464i	−0.255693	+	0.0685128i	−0.384389	−	0.923171i	$-0.625588\pi$
$457$	−5.46610	+	1.46464i	−0.255693	+	0.0685128i	0.128695	+	0.991684i	$0.458921\pi$
$458$	−10.7540	−	18.6265i	−0.502501	−	0.870358i
$459$	3.96422	+	1.13355i	0.185034	+	0.0529097i
$460$	2.34025	−	4.05343i	0.109115	−	0.188992i
$461$	19.0285	+	19.0285i	0.886246	+	0.886246i	0.994160	−	0.107914i	$-0.0344171\pi$
$461$	19.0285	+	19.0285i	0.886246	+	0.886246i	−0.107914	+	0.994160i	$0.534417\pi$
$462$	−1.09632	−	2.17438i	−0.0510053	−	0.101161i
$463$		−	18.0406i		−	0.838416i	−0.907890	−	0.419208i	$-0.862308\pi$
$463$		−	18.0406i		−	0.838416i	0.907890	−	0.419208i	$-0.137692\pi$
$464$	0.494676	−	3.75744i	0.0229648	−	0.174435i
$465$	31.8584	−	4.19423i	1.47740	−	0.194503i
$466$	−0.324674	−	2.46614i	−0.0150402	−	0.114242i
$467$	1.99720	+	7.45364i	0.0924193	+	0.344914i	0.996616	−	0.0822037i	$-0.0261958\pi$
$467$	1.99720	+	7.45364i	0.0924193	+	0.344914i	−0.904196	+	0.427117i	$0.859529\pi$
$468$	1.30811	−	1.30811i	0.0604673	−	0.0604673i
$469$	−4.39238	−	1.44778i	−0.202821	−	0.0668522i
$470$	7.30580	−	17.6378i	0.336991	−	0.813569i
$471$	0.463199	−	3.51834i	0.0213431	−	0.162117i
$472$	−33.2966	+	19.2238i	−1.53260	+	0.884847i
$473$	7.15089	−	9.31922i	0.328798	−	0.428498i
$474$	−2.53659	+	0.679678i	−0.116510	+	0.0312186i
$475$	−17.1058			−0.784867
$476$	3.09286	−	14.9342i	0.141761	−	0.684509i
$477$	−5.49421			−0.251562
$478$	3.63852	−	0.974938i	0.166422	−	0.0445926i
$479$	−14.3414	+	18.6901i	−0.655277	+	0.853973i	−0.996288	−	0.0860860i	$-0.972564\pi$
$479$	−14.3414	+	18.6901i	−0.655277	+	0.853973i	0.341011	+	0.940059i	$0.389231\pi$
$480$	21.7366	−	12.5497i	0.992138	−	0.572811i
$481$	−1.42663	+	10.8363i	−0.0650486	+	0.494093i
$482$	−6.22589	+	15.0306i	−0.283582	+	0.684627i
$483$	1.54140	−	1.37610i	0.0701360	−	0.0626146i
$484$	9.48315	−	9.48315i	0.431052	−	0.431052i
$485$	−11.1742	−	41.7027i	−0.507395	−	1.89362i
$486$	0.101268	+	0.769205i	0.00459360	+	0.0348919i
$487$	−10.6214	+	1.39834i	−0.481302	+	0.0633647i	−0.367274	−	0.930113i	$-0.619709\pi$
$487$	−10.6214	+	1.39834i	−0.481302	+	0.0633647i	−0.114028	+	0.993477i	$0.536376\pi$
$488$	2.56966	−	19.5185i	0.116323	−	0.883561i
$489$		−	18.9361i		−	0.856321i
$490$	−23.2769	+	0.412133i	−1.05154	+	0.0186183i
$491$	8.52592	+	8.52592i	0.384770	+	0.384770i	0.872817	−	0.488048i	$-0.162291\pi$
$491$	8.52592	+	8.52592i	0.384770	+	0.384770i	−0.488048	+	0.872817i	$0.662291\pi$
$492$	2.68939	−	4.65816i	0.121247	−	0.210006i
$493$	18.1972	−	10.1045i	0.819562	−	0.455083i
$494$	0.656450	+	1.13700i	0.0295351	+	0.0511562i
$495$	−4.91206	+	1.31618i	−0.220781	+	0.0591580i
$496$	2.15356	+	5.19915i	0.0966975	+	0.233449i
$497$	−15.9342	−	7.68326i	−0.714744	−	0.344641i
$498$	1.82409	−	0.755563i	0.0817394	−	0.0338576i
$499$	2.29482	+	2.99067i	0.102730	+	0.133881i	0.841889	−	0.539650i	$-0.181443\pi$
$499$	2.29482	+	2.99067i	0.102730	+	0.133881i	−0.739159	+	0.673531i	$0.764777\pi$
$500$	6.55189	+	49.7666i	0.293009	+	2.22563i
$501$	−7.59322	−	2.03460i	−0.339240	−	0.0908991i
$502$	−2.13375	−	7.96326i	−0.0952339	−	0.355418i
$503$	8.45588	+	3.50254i	0.377029	+	0.156171i	0.563147	−	0.826357i	$-0.309591\pi$
$503$	8.45588	+	3.50254i	0.377029	+	0.156171i	−0.186118	+	0.982527i	$0.559591\pi$
$504$	6.82883	−	1.42129i	0.304180	−	0.0633094i
$505$	−28.4493	+	11.7841i	−1.26598	+	0.524384i
$506$	0.622507	+	0.359405i	0.0276738	+	0.0159775i
$507$	−6.84802	+	8.92451i	−0.304131	+	0.396352i
$508$	−3.81523	+	14.2386i	−0.169273	+	0.631737i
$509$	5.84590	−	10.1254i	0.259115	−	0.448800i	−0.706890	−	0.707323i	$-0.749903\pi$
$509$	5.84590	−	10.1254i	0.259115	−	0.448800i	0.966005	+	0.258523i	$0.0832359\pi$
$510$	12.5793	+	5.45859i	0.557021	+	0.241710i
$511$	−22.3904	+	1.66672i	−0.990495	+	0.0737313i
$512$	5.90721	+	5.90721i	0.261064	+	0.261064i
$513$	1.26793	+	0.166926i	0.0559805	+	0.00736998i
$514$	−15.2726	+	8.81765i	−0.673646	+	0.388930i
$515$	22.9577	+	17.6160i	1.01164	+	0.776255i
$516$	8.42734	+	10.9827i	0.370993	+	0.483487i
$517$	−6.29138	−	2.60598i	−0.276695	−	0.114611i
$518$	−11.0661	+	12.8461i	−0.486218	+	0.564426i
$519$	−5.15489	+	5.15489i	−0.226275	+	0.226275i
$520$	11.8638	−	9.10343i	0.520263	−	0.399212i
$521$	−7.72239	+	1.01667i	−0.338324	+	0.0445412i	−0.297774	−	0.954636i	$-0.596244\pi$
$521$	−7.72239	+	1.01667i	−0.338324	+	0.0445412i	−0.0405498	+	0.999178i	$0.512911\pi$
$522$	3.10728	+	2.38430i	0.136002	+	0.104358i
$523$	3.42295	+	1.97624i	0.149675	+	0.0864151i	0.572967	−	0.819578i	$-0.305792\pi$
$523$	3.42295	+	1.97624i	0.149675	+	0.0864151i	−0.423292	+	0.905993i	$0.639126\pi$
$524$	−1.34553	−	3.24840i	−0.0587799	−	0.141907i
$525$	−6.59648	+	34.7684i	−0.287894	+	1.51742i
$526$	−15.7789			−0.687993
$527$	−15.8987	+	26.5043i	−0.692559	+	1.15454i
$528$	−0.445299	−	0.771280i	−0.0193791	−	0.0335657i
$529$	5.79498	−	21.6271i	0.251955	−	0.940310i
$530$	−18.1163	−	2.38505i	−0.786921	−	0.103600i
$531$			14.5836i			0.632872i
$532$	0.267592	−	4.72290i	0.0116016	−	0.204764i
$533$	1.94817	−	4.70329i	0.0843844	−	0.203722i
$534$	−6.30406	+	4.83728i	−0.272803	+	0.209329i
$535$	−49.8308	−	13.3521i	−2.15437	−	0.577263i
$536$	4.45139	+	1.19275i	0.192271	+	0.0515188i
$537$	17.8540	−	13.6998i	0.770456	−	0.591191i
$538$	−6.13470	+	14.8105i	−0.264486	+	0.638525i
$539$	0.147008	+	8.30287i	0.00633208	+	0.357630i
$540$		−	5.99308i		−	0.257901i
$541$	−27.2917	−	3.59303i	−1.17336	−	0.154476i	−0.481461	−	0.876467i	$-0.659894\pi$
$541$	−27.2917	−	3.59303i	−1.17336	−	0.154476i	−0.691902	+	0.721991i	$0.743227\pi$
$542$	4.39558	−	16.4045i	0.188806	−	0.704634i
$543$	−2.32812	−	4.03242i	−0.0999092	−	0.173048i
$544$	−3.55069	+	23.8790i	−0.152235	+	1.02380i
$545$	38.2781			1.63965
$546$	2.56417	−	0.895809i	0.109736	−	0.0383371i
$547$	10.2144	+	24.6596i	0.436734	+	1.05437i	0.977070	+	0.212920i	$0.0682975\pi$
$547$	10.2144	+	24.6596i	0.436734	+	1.05437i	−0.540335	+	0.841450i	$0.681703\pi$
$548$	−19.3700	−	11.1833i	−0.827444	−	0.477725i
$549$	−5.92432	−	4.54589i	−0.252844	−	0.194014i
$550$	−12.2055	+	1.60689i	−0.520445	+	0.0685178i
$551$	5.12193	−	3.93020i	0.218202	−	0.167432i
$552$	−1.45590	+	1.45590i	−0.0619674	+	0.0619674i
$553$	8.79838	+	1.66928i	0.374145	+	0.0709852i
$554$	6.41185	+	2.65587i	0.272413	+	0.112837i
$555$	21.5552	+	28.0912i	0.914966	+	1.19241i
$556$	22.8247	+	17.5140i	0.967984	+	0.742760i
$557$	27.9679	−	16.1473i	1.18504	−	0.684183i	0.227865	−	0.973693i	$-0.426826\pi$
$557$	27.9679	−	16.1473i	1.18504	−	0.684183i	0.957175	+	0.289510i	$0.0934923\pi$
$558$	−5.76601	−	0.759110i	−0.244095	−	0.0321357i
$559$	9.26468	+	9.26468i	0.391854	+	0.391854i
$560$	−8.49090	+	0.632053i	−0.358806	+	0.0267091i
$561$	1.94708	−	4.48704i	0.0822057	−	0.189443i
$562$	−2.93296	+	5.08004i	−0.123720	+	0.214289i
$563$	−1.98992	+	7.42647i	−0.0838650	+	0.312988i	−0.995097	−	0.0989055i	$-0.968466\pi$
$563$	−1.98992	+	7.42647i	−0.0838650	+	0.312988i	0.911232	+	0.411894i	$0.135133\pi$
$564$	4.88549	−	6.36689i	0.205716	−	0.268095i
$565$	−71.7623	−	41.4320i	−3.01906	−	1.74306i
$566$	1.78275	−	0.738441i	0.0749348	−	0.0310390i
$567$	0.828239	−	2.51277i	0.0347828	−	0.105526i
$568$	16.2853	+	6.74559i	0.683316	+	0.283039i
$569$	−0.525405	−	1.96084i	−0.0220261	−	0.0822026i	0.954038	−	0.299686i	$-0.0968819\pi$
$569$	−0.525405	−	1.96084i	−0.0220261	−	0.0822026i	−0.976064	+	0.217483i	$0.930215\pi$
$570$	4.10834	+	1.10083i	0.172079	+	0.0461085i
$571$	−2.36095	−	17.9332i	−0.0988028	−	0.750481i	−0.967093	−	0.254424i	$-0.918114\pi$
$571$	−2.36095	−	17.9332i	−0.0988028	−	0.750481i	0.868290	−	0.496057i	$-0.165219\pi$
$572$	−1.33599	−	1.74110i	−0.0558606	−	0.0727990i
$573$	5.88437	−	2.43739i	0.245823	−	0.101823i
$574$	6.52727	−	4.44546i	0.272443	−	0.185550i
$575$	−3.99758	−	9.65101i	−0.166711	−	0.402475i
$576$	−2.93761	+	0.787131i	−0.122401	+	0.0327971i
$577$	16.6347	+	28.8121i	0.692511	+	1.19946i	0.971013	+	0.239028i	$0.0768288\pi$
$577$	16.6347	+	28.8121i	0.692511	+	1.19946i	−0.278502	+	0.960436i	$0.589838\pi$
$578$	−11.6363	+	6.20923i	−0.484007	+	0.258270i
$579$	0.338580	−	0.586438i	0.0140709	−	0.0243715i
$580$	−21.3931	−	21.3931i	−0.888302	−	0.888302i
$581$	−6.72218	−	0.380868i	−0.278883	−	0.0158011i
$582$			7.81399i			0.323900i
$583$	−0.850748	+	6.46207i	−0.0352344	+	0.267632i
$584$	22.1814	−	2.92023i	0.917871	−	0.120840i
$585$	−0.740371	−	5.62368i	−0.0306106	−	0.232510i
$586$	−4.30688	−	16.0735i	−0.177916	−	0.663990i
$587$	−14.2535	+	14.2535i	−0.588303	+	0.588303i	−0.937172	−	0.348869i	$-0.886566\pi$
$587$	−14.2535	+	14.2535i	−0.588303	+	0.588303i	0.348869	+	0.937172i	$0.386566\pi$
$588$	−9.49637	−	2.36518i	−0.391624	−	0.0975385i
$589$	−3.66860	+	8.85678i	−0.151162	+	0.364937i
$590$	−6.33077	+	48.0870i	−0.260634	+	1.97971i
$591$	7.99439	−	4.61557i	0.328845	−	0.189859i
$592$	−3.77497	+	4.91963i	−0.155150	+	0.202196i
$593$	−22.2735	+	5.96817i	−0.914664	+	0.245083i	−0.685303	−	0.728258i	$-0.740330\pi$
$593$	−22.2735	+	5.96817i	−0.914664	+	0.245083i	−0.229361	+	0.973341i	$0.573664\pi$
$594$	0.920390			0.0377641
$595$	−30.5551	−	35.3990i	−1.25264	−	1.45122i
$596$	−0.207224			−0.00848821
$597$	−7.07603	+	1.89602i	−0.289603	+	0.0775988i
$598$	−0.488083	+	0.636082i	−0.0199592	+	0.0260113i
$599$	20.6267	−	11.9088i	0.842784	−	0.486582i	−0.0154255	−	0.999881i	$-0.504910\pi$
$599$	20.6267	−	11.9088i	0.842784	−	0.486582i	0.858210	+	0.513299i	$0.171577\pi$
$600$	4.60277	−	34.9615i	0.187907	−	1.42730i
$601$	−2.33160	+	5.62898i	−0.0951079	+	0.229611i	−0.964273	−	0.264912i	$-0.914657\pi$
$601$	−2.33160	+	5.62898i	−0.0951079	+	0.229611i	0.869165	+	0.494523i	$0.164657\pi$
$602$	4.14158	+	19.8989i	0.168798	+	0.811019i
$603$	1.23604	−	1.23604i	0.0503353	−	0.0503353i
$604$	−0.638644	−	2.38345i	−0.0259860	−	0.0969813i
$605$	−5.36733	−	40.7690i	−0.218213	−	1.65749i
$606$	5.52556	−	0.727454i	0.224461	−	0.0295508i
$607$	5.08478	−	38.6228i	0.206385	−	1.56765i	−0.503917	−	0.863752i	$-0.668108\pi$
$607$	5.08478	−	38.6228i	0.206385	−	1.56765i	0.710302	−	0.703897i	$-0.248558\pi$
$608$			7.48803i			0.303680i
$609$	−6.01318	−	11.9262i	−0.243666	−	0.483275i
$610$	−17.5611	−	17.5611i	−0.711029	−	0.711029i
$611$	3.79781	−	6.57800i	0.153643	−	0.266117i
$612$	4.51390	+	3.58508i	0.182464	+	0.144918i
$613$	−6.81062	−	11.7963i	−0.275078	−	0.476450i	0.695076	−	0.718936i	$-0.255371\pi$
$613$	−6.81062	−	11.7963i	−0.275078	−	0.476450i	−0.970155	+	0.242486i	$0.922037\pi$
$614$	3.46091	−	0.927349i	0.139671	−	0.0374248i
$615$	−6.31127	−	15.2368i	−0.254495	−	0.614406i
$616$	−0.614260	−	8.25188i	−0.0247492	−	0.332478i
$617$	0.265133	−	0.109822i	0.0106739	−	0.00442126i	−0.377340	−	0.926075i	$-0.623161\pi$
$617$	0.265133	−	0.109822i	0.0106739	−	0.00442126i	0.388014	+	0.921653i	$0.373161\pi$
$618$	−3.18831	−	4.15509i	−0.128253	−	0.167142i
$619$	−2.27439	−	17.2757i	−0.0914154	−	0.694369i	−0.974377	−	0.224923i	$-0.927787\pi$
$619$	−2.27439	−	17.2757i	−0.0914154	−	0.694369i	0.882961	−	0.469446i	$-0.155546\pi$
$620$	43.3937	+	11.6273i	1.74273	+	0.466964i
$621$	0.202133	+	0.754372i	0.00811134	+	0.0302719i
$622$	−22.1589	−	9.17850i	−0.888489	−	0.368024i
$623$	26.5290	−	5.52150i	1.06286	−	0.221214i
$624$	0.917760	−	0.380149i	0.0367398	−	0.0152181i
$625$	75.3702	+	43.5150i	3.01481	+	1.74060i
$626$	−2.23290	+	2.90997i	−0.0892447	+	0.116306i
$627$	0.392664	−	1.46544i	0.0156815	−	0.0585242i
$628$	2.48066	−	4.29664i	0.0989893	−	0.171454i
$629$	−34.0523	−	0.569205i	−1.35775	−	0.0226957i
$630$	3.82179	−	7.92592i	0.152264	−	0.315776i
$631$	−14.7533	−	14.7533i	−0.587321	−	0.587321i	0.349584	−	0.936905i	$-0.386323\pi$
$631$	−14.7533	−	14.7533i	−0.587321	−	0.587321i	−0.936905	+	0.349584i	$0.886323\pi$
$632$	−8.84723	−	1.16476i	−0.351924	−	0.0463317i
$633$	0.00982793	−	0.00567416i	0.000390625	−	0.000225528i
$634$	−20.4476	−	15.6900i	−0.812077	−	0.623129i
$635$	27.5147	+	35.8579i	1.09189	+	1.42298i
$636$	−7.09657	−	2.93950i	−0.281397	−	0.116559i
$637$	−9.20323	−	1.04624i	−0.364645	−	0.0414535i
$638$	3.28546	−	3.28546i	0.130073	−	0.130073i
$639$	5.30446	−	4.07025i	0.209841	−	0.161017i
$640$	39.7412	−	5.23202i	1.57091	−	0.206814i
$641$	−3.83279	−	2.94101i	−0.151386	−	0.116163i	0.530291	−	0.847816i	$-0.322083\pi$
$641$	−3.83279	−	2.94101i	−0.151386	−	0.116163i	−0.681677	+	0.731653i	$0.738749\pi$
$642$	8.08606	+	4.66849i	0.319131	+	0.184251i
$643$	11.3284	+	27.3491i	0.446747	+	1.07854i	0.973533	+	0.228544i	$0.0733966\pi$
$643$	11.3284	+	27.3491i	0.446747	+	1.07854i	−0.526787	+	0.849997i	$0.676603\pi$
$644$	2.72718	−	0.952756i	0.107466	−	0.0375438i
$645$	42.4460			1.67131
$646$	−3.28675	+	2.43583i	−0.129315	+	0.0958364i
$647$	3.04283	+	5.27033i	0.119626	+	0.207198i	0.919619	−	0.392810i	$-0.128497\pi$
$647$	3.04283	+	5.27033i	0.119626	+	0.207198i	−0.799994	+	0.600009i	$0.795164\pi$
$648$	−0.682342	+	2.54653i	−0.0268049	+	0.100037i
$649$	17.1526	+	2.25818i	0.673299	+	0.0886414i
$650$		−	13.7315i		−	0.538596i
$651$	16.5872	+	10.8721i	0.650103	+	0.426110i
$652$	10.1312	−	24.4588i	0.396767	−	0.957879i
$653$	−15.3256	+	11.7597i	−0.599737	+	0.460194i	−0.863469	−	0.504401i	$-0.831713\pi$
$653$	−15.3256	+	11.7597i	−0.599737	+	0.460194i	0.263732	+	0.964596i	$0.415047\pi$
$654$	−6.69185	−	1.79308i	−0.261672	−	0.0701148i
$655$	−10.4134	−	2.79026i	−0.406884	−	0.109024i
$656$	2.29143	−	1.75827i	0.0894652	−	0.0686490i
$657$	3.24753	−	7.84023i	0.126698	−	0.305877i
$658$	10.5213	−	5.30482i	0.410163	−	0.206804i
$659$		−	41.8725i		−	1.63112i	−0.578673	−	0.815560i	$-0.696429\pi$
$659$		−	41.8725i		−	1.63112i	0.578673	−	0.815560i	$-0.303571\pi$
$660$	−7.04882	−	0.927995i	−0.274375	−	0.0361221i
$661$	−6.93888	+	25.8963i	−0.269891	+	1.00725i	0.689297	+	0.724479i	$0.257920\pi$
$661$	−6.93888	+	25.8963i	−0.269891	+	1.00725i	−0.959188	+	0.282769i	$0.908747\pi$
$662$	8.99175	+	15.5742i	0.349474	+	0.605307i
$663$	4.67857	+	2.80646i	0.181701	+	0.108994i
$664$	6.70908			0.260363
$665$	−10.9892	−	9.46647i	−0.426141	−	0.367094i
$666$	−2.45243	−	5.92068i	−0.0950296	−	0.229422i
$667$	3.41439	+	1.97130i	0.132206	+	0.0763289i
$668$	−8.71921	−	6.69048i	−0.337356	−	0.258863i
$669$	−18.0872	+	2.38122i	−0.699290	+	0.0920633i
$670$	4.61220	−	3.53907i	0.178185	−	0.136726i
$671$	−6.26405	+	6.26405i	−0.241821	+	0.241821i
$672$	15.2198	+	2.88760i	0.587118	+	0.111392i
$673$	−20.6316	−	8.54588i	−0.795289	−	0.329420i	−0.0522212	−	0.998636i	$-0.516630\pi$
$673$	−20.6316	−	8.54588i	−0.795289	−	0.329420i	−0.743068	+	0.669216i	$0.766630\pi$
$674$	−15.4600	−	20.1478i	−0.595496	−	0.776065i
$675$	−10.6116	−	8.14259i	−0.408442	−	0.313408i
$676$	−13.6200	+	7.86350i	−0.523846	+	0.302442i
$677$	7.20868	+	0.949041i	0.277052	+	0.0364746i	0.267772	−	0.963482i	$-0.413713\pi$
$677$	7.20868	+	0.949041i	0.277052	+	0.0364746i	0.00928019	+	0.999957i	$0.497046\pi$
$678$	10.6048	+	10.6048i	0.407275	+	0.407275i
$679$	11.5737	−	24.0024i	0.444156	−	0.921126i
$680$	32.3933	+	33.4947i	1.24223	+	1.28446i
$681$	5.62660	−	9.74556i	0.215612	−	0.373451i
$682$	−1.78567	+	6.66422i	−0.0683769	+	0.255186i
$683$	−13.5672	+	17.6811i	−0.519133	+	0.676547i	−0.977188	−	0.212377i	$-0.931880\pi$
$683$	−13.5672	+	17.6811i	−0.519133	+	0.676547i	0.458055	+	0.888924i	$0.348546\pi$
$684$	1.54841	+	0.893975i	0.0592050	+	0.0341820i
$685$	−63.3588	+	26.2441i	−2.42082	+	1.00273i
$686$	−11.0508	−	9.18383i	−0.421921	−	0.350640i
$687$	−25.6119	−	10.6088i	−0.977154	−	0.404750i
$688$	1.92395	+	7.18029i	0.0733500	+	0.273746i
$689$	−7.02230	−	1.88162i	−0.267528	−	0.0716840i
$690$	0.339028	+	2.57517i	0.0129066	+	0.0980350i
$691$	29.6403	+	38.6279i	1.12757	+	1.46948i	0.863066	+	0.505090i	$0.168541\pi$
$691$	29.6403	+	38.6279i	1.12757	+	1.46948i	0.264502	+	0.964385i	$0.414792\pi$
$692$	−9.41626	+	3.90034i	−0.357952	+	0.148269i
$693$	−2.82718	−	1.36323i	−0.107395	−	0.0517849i
$694$	3.68435	+	8.89481i	0.139856	+	0.337643i
$695$	85.2071	−	22.8312i	3.23209	−	0.866036i
$696$	6.65450	+	11.5259i	0.252238	+	0.436890i
$697$	15.2515	+	4.36111i	0.577694	+	0.165189i
$698$	3.76912	−	6.52832i	0.142663	−	0.247100i
$699$	−2.26705	−	2.26705i	−0.0857477	−	0.0857477i
$700$	−27.1220	+	41.3793i	−1.02512	+	1.56399i
$701$			29.5994i			1.11795i	0.829183	+	0.558977i	$0.188806\pi$
$701$			29.5994i			1.11795i	−0.829183	+	0.558977i	$0.811194\pi$
$702$	−0.133999	+	1.01782i	−0.00505747	+	0.0384153i
$703$	−10.4732	+	1.37882i	−0.395003	+	0.0520032i
$704$	0.470920	+	3.57699i	0.0177485	+	0.134813i
$705$	−6.36870	−	23.7683i	−0.239859	−	0.895166i
$706$	6.85023	−	6.85023i	0.257812	−	0.257812i
$707$	−18.0504	−	5.94963i	−0.678855	−	0.223759i
$708$	−7.80246	+	18.8368i	−0.293234	+	0.707930i
$709$	4.11738	−	31.2746i	0.154631	−	1.17454i	−0.721481	−	0.692434i	$-0.756538\pi$
$709$	4.11738	−	31.2746i	0.154631	−	1.17454i	0.876112	−	0.482107i	$-0.160128\pi$
$710$	19.2575	−	11.1183i	0.722722	−	0.417264i
$711$	−2.06054	+	2.68534i	−0.0772761	+	0.100708i
$712$	−26.0813	+	6.98847i	−0.977439	+	0.261904i
$713$	−5.85431			−0.219245
$714$	3.68349	+	7.61983i	0.137851	+	0.285165i
$715$	−6.72899			−0.251650
$716$	30.3907	−	8.14315i	1.13575	−	0.304324i
$717$	2.95566	−	3.85189i	0.110381	−	0.143851i
$718$	−3.47058	+	2.00374i	−0.129521	+	0.0747789i
$719$	−5.78918	+	43.9732i	−0.215900	+	1.63992i	0.449388	+	0.893337i	$0.351642\pi$
$719$	−5.78918	+	43.9732i	−0.215900	+	1.63992i	−0.665288	+	0.746587i	$0.731691\pi$
$720$	1.23153	−	2.97317i	0.0458964	−	0.110804i
$721$	3.63929	+	17.4856i	0.135534	+	0.651197i
$722$	9.52622	−	9.52622i	0.354529	−	0.354529i
$723$	5.42731	+	20.2550i	0.201844	+	0.753291i
$724$	−0.849692	−	6.45405i	−0.0315785	−	0.239863i
$725$	−66.9459	+	8.81359i	−2.48631	+	0.327329i
$726$	−0.971429	+	7.37873i	−0.0360531	+	0.273850i
$727$			51.0202i			1.89224i	0.323823	+	0.946118i	$0.395032\pi$
$727$			51.0202i			1.89224i	−0.323823	+	0.946118i	$0.604968\pi$
$728$	9.21487	+	0.522100i	0.341526	+	0.0193503i
$729$	0.707107	+	0.707107i	0.0261891	+	0.0261891i
$730$	14.1117	−	24.4422i	0.522297	−	0.904645i
$731$	−25.3913	+	31.9697i	−0.939132	+	1.18244i
$732$	−5.22000	−	9.04130i	−0.192937	−	0.334176i
$733$	−16.8348	+	4.51086i	−0.621806	+	0.166613i	−0.555949	−	0.831216i	$-0.687645\pi$
$733$	−16.8348	+	4.51086i	−0.621806	+	0.166613i	−0.0658576	+	0.997829i	$0.520978\pi$
$734$	−0.328311	−	0.792613i	−0.0121182	−	0.0292559i
$735$	−23.4789	+	18.6855i	−0.866032	+	0.689227i
$736$	−4.22472	+	1.74994i	−0.155725	+	0.0645035i
$737$	−1.26238	−	1.64517i	−0.0465005	−	0.0606007i
$738$	0.389608	+	2.95936i	0.0143417	+	0.108936i
$739$	45.5599	+	12.2077i	1.67595	+	0.449069i	0.966704	−	0.255896i	$-0.0823705\pi$
$739$	45.5599	+	12.2077i	1.67595	+	0.449069i	0.709242	+	0.704965i	$0.249037\pi$
$740$	12.8123	+	47.8163i	0.470991	+	1.75776i
$741$	1.56341	+	0.647586i	0.0574333	+	0.0237897i
$742$	−7.51079	−	8.41301i	−0.275730	−	0.308851i
$743$	32.0223	−	13.2641i	1.17479	−	0.486612i	0.292014	−	0.956414i	$-0.405675\pi$
$743$	32.0223	−	13.2641i	1.17479	−	0.486612i	0.882772	+	0.469802i	$0.155675\pi$
$744$	−17.1147	−	9.88119i	−0.627456	−	0.362262i
$745$	−0.386794	+	0.504080i	−0.0141710	+	0.0184681i
$746$	3.79211	−	14.1523i	0.138839	−	0.518154i
$747$	1.27241	−	2.20388i	0.0465550	−	0.0806357i
$748$	4.91558	−	4.75395i	0.179731	−	0.173822i
$749$	−17.9234	−	26.3169i	−0.654905	−	0.961598i
$750$	−19.6970	−	19.6970i	−0.719232	−	0.719232i
$751$	14.0650	+	1.85169i	0.513239	+	0.0675691i	0.382697	−	0.923874i	$-0.374995\pi$
$751$	14.0650	+	1.85169i	0.513239	+	0.0675691i	0.130541	+	0.991443i	$0.458329\pi$
$752$	3.73204	−	2.15470i	0.136094	−	0.0785737i
$753$	−8.43024	−	6.46875i	−0.307215	−	0.235734i
$754$	3.15494	+	4.11160i	0.114896	+	0.149736i
$755$	−6.98990	−	2.89531i	−0.254389	−	0.105371i
$756$	2.41417	−	2.80249i	0.0878024	−	0.101926i
$757$	20.1749	−	20.1749i	0.733271	−	0.733271i	−0.237996	−	0.971266i	$-0.576490\pi$
$757$	20.1749	−	20.1749i	0.733271	−	0.733271i	0.971266	+	0.237996i	$0.0764904\pi$
$758$	7.93272	−	6.08699i	0.288129	−	0.221089i
$759$	0.918563	−	0.120931i	0.0333417	−	0.00438952i
$760$	11.4662	+	8.79836i	0.415924	+	0.319150i
$761$	4.04237	+	2.33386i	0.146536	+	0.0846025i	0.571475	−	0.820619i	$-0.306371\pi$
$761$	4.04237	+	2.33386i	0.146536	+	0.0846025i	−0.424940	+	0.905222i	$0.639705\pi$
$762$	−3.13047	−	7.55762i	−0.113405	−	0.273784i
$763$	17.8996	+	15.4194i	0.648010	+	0.558220i
$764$	8.90457			0.322156
$765$	17.1463	−	4.28851i	0.619925	−	0.155052i
$766$	6.87117	+	11.9012i	0.248266	+	0.430009i
$767$	−4.99448	+	18.6396i	−0.180340	+	0.673038i
$768$	−13.2232	−	1.74086i	−0.477150	−	0.0628180i
$769$			37.5728i			1.35491i	0.735565	+	0.677455i	$0.236917\pi$
$769$			37.5728i			1.35491i	−0.735565	+	0.677455i	$0.763083\pi$
$770$	−8.73038	−	5.72232i	−0.314621	−	0.206218i
$771$	−8.69859	+	21.0002i	−0.313272	+	0.756306i
$772$	0.751080	−	0.576324i	0.0270320	−	0.0207424i
$773$	15.2205	+	4.07832i	0.547443	+	0.146687i	0.521931	−	0.852988i	$-0.325212\pi$
$773$	15.2205	+	4.07832i	0.547443	+	0.146687i	0.0255120	+	0.999675i	$0.491878\pi$
$774$	−7.42049	−	1.98831i	−0.266724	−	0.0714685i
$775$	79.5454	−	61.0374i	2.85736	−	2.19253i
$776$	−10.1612	+	24.5313i	−0.364766	+	0.880622i
$777$	−1.23623	+	21.8190i	−0.0443496	+	0.782754i
$778$			15.0475i			0.539478i
$779$	4.87811	+	0.642216i	0.174776	+	0.0230098i
$780$	2.05247	−	7.65991i	0.0734901	−	0.274269i
$781$	−3.96591	−	6.86915i	−0.141911	−	0.245798i
$782$	−2.14239	−	1.28512i	−0.0766117	−	0.0459559i
$783$	5.04824			0.180409
$784$	−4.22513	−	3.12480i	−0.150898	−	0.111600i
$785$	−5.82145	−	14.0542i	−0.207776	−	0.501616i
$786$	1.68978	+	0.975596i	0.0602725	+	0.0347984i
$787$	−17.8278	−	13.6798i	−0.635494	−	0.487632i	0.240056	−	0.970759i	$-0.422834\pi$
$787$	−17.8278	−	13.6798i	−0.635494	−	0.487632i	−0.875550	+	0.483127i	$0.839501\pi$
$788$	12.7953	−	1.68454i	0.455815	−	0.0600092i
$789$	−16.1350	+	12.3808i	−0.574422	+	0.440770i
$790$	−7.96000	+	7.96000i	−0.283204	+	0.283204i
$791$	−16.8677	−	48.2822i	−0.599746	−	1.71672i
$792$	2.88948	+	1.19686i	0.102673	+	0.0425286i
$793$	−6.01519	−	7.83915i	−0.213606	−	0.278376i
$794$	−10.5165	−	8.06958i	−0.373216	−	0.286379i
$795$	−20.3966	+	11.7760i	−0.723392	+	0.417650i
$796$	−10.1541	−	1.33682i	−0.359904	−	0.0473822i
$797$	8.68173	+	8.68173i	0.307523	+	0.307523i	0.843948	−	0.536425i	$-0.180226\pi$
$797$	8.68173	+	8.68173i	0.307523	+	0.307523i	−0.536425	+	0.843948i	$0.680226\pi$
$798$	1.47771	+	2.16972i	0.0523102	+	0.0768071i
$799$	21.7117	+	9.42145i	0.768106	+	0.333307i
$800$	39.1585	−	67.8245i	1.38446	−	2.39796i
$801$	−2.65080	+	9.89290i	−0.0936613	+	0.349549i
$802$	−2.06492	+	2.69106i	−0.0729149	+	0.0950245i
$803$	−8.71851	−	5.03364i	−0.307670	−	0.177633i
$804$	2.25782	−	0.935221i	0.0796273	−	0.0329827i
$805$	2.77280	−	8.41233i	0.0977285	−	0.296496i
$806$	−7.10973	−	2.94494i	−0.250429	−	0.103731i
$807$	5.34781	+	19.9583i	0.188252	+	0.702566i
$808$	18.2929	+	4.90158i	0.643544	+	0.172437i
$809$	5.45774	+	41.4557i	0.191884	+	1.45750i	0.768165	+	0.640252i	$0.221170\pi$
$809$	5.45774	+	41.4557i	0.191884	+	1.45750i	−0.576281	+	0.817251i	$0.695497\pi$
$810$	2.02461	+	2.63853i	0.0711377	+	0.0927085i
$811$	40.6543	−	16.8396i	1.42757	−	0.591318i	0.470817	−	0.882231i	$-0.343959\pi$
$811$	40.6543	−	16.8396i	1.42757	−	0.591318i	0.956749	+	0.290913i	$0.0939591\pi$
$812$	−1.38617	−	18.6216i	−0.0486450	−	0.653490i
$813$	−8.37694	−	20.2237i	−0.293792	−	0.709277i
$814$	−7.34342	+	1.96766i	−0.257387	+	0.0689666i
$815$	−40.5866	−	70.2980i	−1.42169	−	2.46243i
$816$	1.50265	+	2.70613i	0.0526033	+	0.0947336i
$817$	−6.33158	+	10.9666i	−0.221514	+	0.383674i
$818$	18.1409	+	18.1409i	0.634281	+	0.634281i
$819$	1.91915	−	2.92799i	0.0670606	−	0.102312i
$820$		−	23.0572i		−	0.805191i
$821$	−3.05228	+	23.1844i	−0.106525	+	0.809140i	0.851882	+	0.523734i	$0.175462\pi$
$821$	−3.05228	+	23.1844i	−0.106525	+	0.809140i	−0.958407	+	0.285405i	$0.907872\pi$
$822$	12.3059	−	1.62010i	0.429217	−	0.0565074i
$823$	−4.87613	−	37.0379i	−0.169971	−	1.29106i	−0.837484	−	0.546462i	$-0.815974\pi$
$823$	−4.87613	−	37.0379i	−0.169971	−	1.29106i	0.667513	−	0.744599i	$-0.267359\pi$
$824$	−4.60619	−	17.1905i	−0.160464	−	0.598860i
$825$	−11.2201	+	11.2201i	−0.390635	+	0.390635i
$826$	−22.3311	+	19.9363i	−0.776998	+	0.693672i
$827$	3.81891	−	9.21967i	0.132797	−	0.320599i	−0.843468	−	0.537179i	$-0.819490\pi$
$827$	3.81891	−	9.21967i	0.132797	−	0.320599i	0.976265	+	0.216580i	$0.0694901\pi$
$828$	−0.142517	+	1.08253i	−0.00495282	+	0.0376204i
$829$	46.8304	−	27.0375i	1.62649	−	0.939052i	0.641355	−	0.767244i	$-0.278372\pi$
$829$	46.8304	−	27.0375i	1.62649	−	0.939052i	0.985130	−	0.171808i	$-0.0549609\pi$
$830$	5.15228	−	6.71458i	0.178838	−	0.233067i
$831$	8.64048	−	2.31521i	0.299735	−	0.0803137i
$832$	−4.02422			−0.139515
$833$	−0.0285660	−	28.8617i	−0.000989753	−	1.00000i
$834$	−15.9656			−0.552842
$835$	−32.5497	+	8.72167i	−1.12643	+	0.301826i
$836$	1.29122	−	1.68275i	0.0446578	−	0.0581992i
$837$	−6.49178	+	3.74803i	−0.224389	+	0.129551i
$838$	−0.233422	+	1.77302i	−0.00806344	+	0.0612479i
$839$	2.12687	−	5.13472i	0.0734278	−	0.177270i	−0.882904	−	0.469553i	$-0.844415\pi$
$839$	2.12687	−	5.13472i	0.0734278	−	0.177270i	0.956332	+	0.292283i	$0.0944149\pi$
$840$	22.3049	−	19.9129i	0.769592	−	0.687060i
$841$	−2.48569	+	2.48569i	−0.0857133	+	0.0857133i
$842$	0.941530	+	3.51384i	0.0324473	+	0.121095i
$843$	0.986872	+	7.49604i	0.0339897	+	0.258177i
$844$	0.0157300	−	0.00207089i	0.000541448	−	7.12830e-5i
$845$	−6.29415	+	47.8088i	−0.216525	+	1.64467i
$846$			4.45355i			0.153116i
$847$	13.9129	−	21.2265i	0.478054	−	0.729352i
$848$	−2.91658	−	2.91658i	−0.100156	−	0.100156i
$849$	1.24358	−	2.15394i	0.0426794	−	0.0739229i
$850$	42.5085	−	4.87507i	1.45803	−	0.167214i
$851$	−3.22548	−	5.58670i	−0.110568	−	0.191510i
$852$	9.02914	−	2.41935i	0.309333	−	0.0828856i
$853$	−5.11050	−	12.3378i	−0.174980	−	0.422440i	0.811921	−	0.583768i	$-0.198422\pi$
$853$	−5.11050	−	12.3378i	−0.174980	−	0.422440i	−0.986901	+	0.161328i	$0.948422\pi$
$854$	−1.13787	−	15.2860i	−0.0389373	−	0.523077i
$855$	5.06482	−	2.09792i	0.173213	−	0.0717473i
$856$	19.3146	+	25.1713i	0.660159	+	0.860336i
$857$	2.05938	+	15.6425i	0.0703471	+	0.534339i	0.989942	+	0.141472i	$0.0451835\pi$
$857$	2.05938	+	15.6425i	0.0703471	+	0.534339i	−0.919595	+	0.392867i	$0.871483\pi$
$858$	1.17638	+	0.315209i	0.0401608	+	0.0107611i
$859$	11.2777	+	42.0890i	0.384791	+	1.43606i	0.838496	+	0.544907i	$0.183435\pi$
$859$	11.2777	+	42.0890i	0.384791	+	1.43606i	−0.453706	+	0.891152i	$0.649898\pi$
$860$	54.8252	+	22.7093i	1.86952	+	0.774382i
$861$	3.18648	−	9.66738i	0.108595	−	0.329464i
$862$	−6.11851	+	2.53437i	−0.208397	+	0.0863210i
$863$	−18.3638	−	10.6023i	−0.625110	−	0.360907i	0.153746	−	0.988110i	$-0.450866\pi$
$863$	−18.3638	−	10.6023i	−0.625110	−	0.360907i	−0.778856	+	0.627203i	$0.784200\pi$
$864$	−3.56441	+	4.64523i	−0.121264	+	0.158034i
$865$	−8.08821	+	30.1856i	−0.275007	+	1.02634i
$866$	−6.51602	+	11.2861i	−0.221423	+	0.383516i
$867$	−7.02691	+	15.4797i	−0.238646	+	0.525720i
$868$	15.6080	+	22.9173i	0.529771	+	0.777864i
$869$	2.83933	+	2.83933i	0.0963177	+	0.0963177i
$870$	16.6458	+	2.19146i	0.564344	+	0.0742973i
$871$	2.00312	−	1.15650i	0.0678732	−	0.0391866i
$872$	−18.6767	−	14.3312i	−0.632474	−	0.485314i
$873$	6.13121	+	7.99035i	0.207510	+	0.270432i
$874$	−0.715910	−	0.296540i	−0.0242160	−	0.0100306i
$875$	31.3294	+	89.6775i	1.05913	+	3.03165i
$876$	8.38932	−	8.38932i	0.283449	−	0.283449i
$877$	−28.1617	+	21.6093i	−0.950955	+	0.729693i	−0.962794	−	0.270237i	$-0.912898\pi$
$877$	−28.1617	+	21.6093i	−0.950955	+	0.729693i	0.0118393	+	0.999930i	$0.496231\pi$
$878$	−3.61165	+	0.475483i	−0.121887	+	0.0160468i
$879$	−17.0161	−	13.0569i	−0.573938	−	0.440398i
$880$	−3.30623	−	1.90886i	−0.111453	−	0.0643475i
$881$	−14.1607	−	34.1869i	−0.477085	−	1.15179i	−0.960970	−	0.276654i	$-0.910774\pi$
$881$	−14.1607	−	34.1869i	−0.477085	−	1.15179i	0.483884	−	0.875132i	$-0.339226\pi$
$882$	4.97992	−	2.16681i	0.167683	−	0.0729604i
$883$	−30.0219			−1.01032			−0.505159	−	0.863026i	$-0.668566\pi$
$883$	−30.0219			−1.01032			−0.505159	+	0.863026i	$0.668566\pi$
$884$	4.54155	+	6.12807i	0.152749	+	0.206109i
$885$	31.2575	+	54.1397i	1.05071	+	1.81988i
$886$	−2.20805	+	8.24055i	−0.0741808	+	0.276847i
$887$	0.605807	+	0.0797559i	0.0203410	+	0.00267794i	0.140690	−	0.990054i	$-0.455068\pi$
$887$	0.605807	+	0.0797559i	0.0203410	+	0.00267794i	−0.120349	+	0.992732i	$0.538401\pi$
$888$		−	21.7765i		−	0.730772i
$889$	−1.57803	+	27.8515i	−0.0529253	+	0.934111i
$890$	−13.0351	+	31.4696i	−0.436938	+	1.05486i
$891$	0.941163	−	0.722180i	0.0315301	−	0.0241939i
$892$	−24.6362	−	6.60125i	−0.824882	−	0.221026i
$893$	7.09094	+	1.90001i	0.237289	+	0.0635815i
$894$	0.0912329	−	0.0700055i	0.00305129	−	0.00234133i
$895$	36.9172	−	89.1261i	1.23401	−	2.97916i
$896$	20.6914	+	13.5622i	0.691251	+	0.453081i
$897$			1.03341i			0.0345045i
$898$	20.4156	+	2.68776i	0.681277	+	0.0896918i
$899$	−9.79421	+	36.5525i	−0.326655	+	1.21909i
$900$	−9.35004	−	16.1947i	−0.311668	−	0.539825i
$901$	3.33179	−	22.4068i	0.110998	−	0.746480i
$902$	3.54102			0.117903
$903$	19.8486	+	17.0984i	0.660521	+	0.568998i
$904$	19.5025	+	47.0831i	0.648642	+	1.56596i
$905$	−17.2857	−	9.97992i	−0.574597	−	0.331744i
$906$	1.08636	+	0.833595i	0.0360920	+	0.0276943i
$907$	−44.2959	+	5.83166i	−1.47082	+	0.193637i	−0.822950	−	0.568114i	$-0.807673\pi$
$907$	−44.2959	+	5.83166i	−1.47082	+	0.193637i	−0.647870	+	0.761751i	$0.724340\pi$
$908$	12.4816	−	9.57749i	0.414217	−	0.317840i
$909$	5.07948	−	5.07948i	0.168476	−	0.168476i
$910$	7.59915	−	8.82148i	0.251909	−	0.292429i
$911$	12.0099	+	4.97465i	0.397904	+	0.164817i	0.572657	−	0.819795i	$-0.305913\pi$
$911$	12.0099	+	4.97465i	0.397904	+	0.164817i	−0.174753	+	0.984612i	$0.555913\pi$
$912$	0.584464	+	0.761688i	0.0193535	+	0.0252220i
$913$	−2.39509	−	1.83782i	−0.0792659	−	0.0608229i
$914$	3.80223	−	2.19522i	0.125767	−	0.0726114i
$915$	−31.7367	−	4.17822i	−1.04918	−	0.138128i
$916$	−27.4056	−	27.4056i	−0.905507	−	0.905507i
$917$	−3.74553	−	5.49956i	−0.123688	−	0.181612i
$918$	−3.19844	−	0.0534638i	−0.105564	−	0.00176457i
$919$	−27.6667	+	47.9201i	−0.912640	+	1.58074i	−0.102320	+	0.994752i	$0.532627\pi$
$919$	−27.6667	+	47.9201i	−0.912640	+	1.58074i	−0.810320	+	0.585988i	$0.800707\pi$
$920$	−2.28437	+	8.52537i	−0.0753133	+	0.281073i
$921$	2.81139	−	3.66387i	0.0926383	−	0.120729i
$922$	−18.0811	−	10.4391i	−0.595469	−	0.343794i
$923$	8.17373	−	3.38567i	0.269041	−	0.111441i
$924$	−2.92236	−	3.27340i	−0.0961385	−	0.107687i
$925$	102.074	+	42.2803i	3.35616	+	1.39017i
$926$	3.62260	+	13.5197i	0.119046	+	0.444286i
$927$	−6.52054	−	1.74717i	−0.214163	−	0.0573847i
$928$	3.85814	+	29.3055i	0.126650	+	0.961999i
$929$	5.91630	+	7.71027i	0.194107	+	0.252966i	0.880260	−	0.474492i	$-0.157368\pi$
$929$	5.91630	+	7.71027i	0.194107	+	0.252966i	−0.686152	+	0.727458i	$0.740702\pi$
$930$	−23.0327	+	9.54044i	−0.755270	+	0.312843i
$931$	−1.32542	−	8.85344i	−0.0434390	−	0.290160i
$932$	−1.71531	−	4.14114i	−0.0561870	−	0.135647i
$933$	−29.8608	+	8.00119i	−0.977600	+	0.261947i
$934$	−2.99343	−	5.18477i	−0.0979479	−	0.169651i
$935$	−2.38897	−	20.8308i	−0.0781278	−	0.681241i
$936$	−1.74424	+	3.02111i	−0.0570123	+	0.0987481i
$937$	28.1203	+	28.1203i	0.918650	+	0.918650i	0.996931	−	0.0782815i	$-0.0249433\pi$
$937$	28.1203	+	28.1203i	0.918650	+	0.918650i	−0.0782815	+	0.996931i	$0.524943\pi$
$938$	3.58239	+	0.202973i	0.116969	+	0.00662730i
$939$			4.72769i			0.154282i
$940$	4.49035	−	34.1076i	0.146459	−	1.11247i
$941$	−22.8451	+	3.00761i	−0.744727	+	0.0980452i	−0.493334	−	0.869840i	$-0.664222\pi$
$941$	−22.8451	+	3.00761i	−0.744727	+	0.0980452i	−0.251393	+	0.967885i	$0.580889\pi$
$942$	0.359369	+	2.72968i	0.0117089	+	0.0889378i
$943$	0.777668	+	2.90230i	0.0253244	+	0.0945118i
$944$	−7.74162	+	7.74162i	−0.251968	+	0.251968i
$945$	−2.31099	−	11.1036i	−0.0751766	−	0.361199i
$946$	−3.48760	+	8.41981i	−0.113392	+	0.273752i
$947$	3.98748	−	30.2879i	0.129576	−	0.984225i	−0.795903	−	0.605424i	$-0.793003\pi$
$947$	3.98748	−	30.2879i	0.129576	−	0.984225i	0.925478	−	0.378800i	$-0.123663\pi$
$948$	−4.09819	+	2.36609i	−0.133103	+	0.0768470i
$949$	6.83583	−	8.90863i	0.221900	−	0.289186i
$950$	12.8192	−	3.43489i	0.415909	−	0.111442i
$951$	−33.2201			−1.07724
$952$	1.65527	+	28.7117i	0.0536476	+	0.930551i
$953$	−35.4458			−1.14820			−0.574102	−	0.818784i	$-0.694649\pi$
$953$	−35.4458			−1.14820			−0.574102	+	0.818784i	$0.694649\pi$
$954$	4.11739	−	1.10325i	0.133306	−	0.0357191i
$955$	16.6208	−	21.6607i	0.537838	−	0.700924i
$956$	5.87849	−	3.39395i	0.190124	−	0.109768i
$957$	0.781692	−	5.93754i	0.0252685	−	0.191933i
$958$	6.99454	−	16.8863i	0.225983	−	0.545572i
$959$	−40.1997	−	13.2503i	−1.29812	−	0.427874i
$960$	−9.21844	+	9.21844i	−0.297524	+	0.297524i
$961$	−6.51991	−	24.3326i	−0.210320	−	0.784923i
$962$	−1.10684	−	8.40728i	−0.0356859	−	0.271061i
$963$	11.9317	−	1.57083i	0.384493	−	0.0506194i
$964$	−3.82661	+	29.0660i	−0.123247	+	0.936152i
$965$		−	2.90277i		−	0.0934436i
$966$	−0.878809	+	1.34077i	−0.0282752	+	0.0431387i
$967$	−26.9810	−	26.9810i	−0.867649	−	0.867649i	0.124563	−	0.992212i	$-0.460247\pi$
$967$	−26.9810	−	26.9810i	−0.867649	−	0.867649i	−0.992212	+	0.124563i	$0.960247\pi$
$968$	−12.6449	+	21.9016i	−0.406422	+	0.703944i
$969$	−1.44967	+	5.06974i	−0.0465701	+	0.162863i
$970$	16.7481	+	29.0085i	0.537748	+	0.931407i
$971$	10.9786	−	2.94170i	0.352319	−	0.0944037i	−0.0783188	−	0.996928i	$-0.524955\pi$
$971$	10.9786	−	2.94170i	0.352319	−	0.0944037i	0.430638	+	0.902525i	$0.358289\pi$
$972$	0.535017	+	1.29165i	0.0171607	+	0.0414296i
$973$	49.0416	+	23.6473i	1.57220	+	0.758098i
$974$	7.67897	−	3.18073i	0.246050	−	0.101917i
$975$	−10.7744	−	14.0415i	−0.345057	−	0.449687i
$976$	−0.731734	−	5.55807i	−0.0234222	−	0.177909i
$977$	36.3525	+	9.74063i	1.16302	+	0.311630i	0.788172	−	0.615456i	$-0.211028\pi$
$977$	36.3525	+	9.74063i	1.16302	+	0.311630i	0.374849	+	0.927086i	$0.377695\pi$
$978$	3.80243	+	14.1909i	0.121588	+	0.453774i
$979$	11.2252	+	4.64962i	0.358758	+	0.148603i
$980$	−40.3235	+	11.5735i	−1.28809	+	0.369702i
$981$	−8.24981	+	3.41718i	−0.263396	+	0.109102i
$982$	−8.10141	−	4.67735i	−0.258527	−	0.149260i
$983$	1.57102	−	2.04739i	0.0501077	−	0.0653016i	−0.767627	−	0.640896i	$-0.778563\pi$
$983$	1.57102	−	2.04739i	0.0501077	−	0.0653016i	0.817735	+	0.575595i	$0.195229\pi$
$984$	−2.62517	+	9.79728i	−0.0836875	+	0.312326i
$985$	19.7855	−	34.2694i	0.630418	−	1.09192i
$986$	−11.6081	+	11.2264i	−0.369678	+	0.357522i
$987$	6.59636	−	13.6800i	0.209964	−	0.435440i
$988$	1.67290	+	1.67290i	0.0532221	+	0.0532221i
$989$	−7.66700	−	1.00938i	−0.243796	−	0.0320964i
$990$	3.41684	−	1.97271i	0.108594	−	0.0626969i
$991$	7.23162	+	5.54902i	0.229720	+	0.176270i	0.717208	−	0.696859i	$-0.245420\pi$
$991$	7.23162	+	5.54902i	0.229720	+	0.176270i	−0.487488	+	0.873130i	$0.662087\pi$
$992$	−26.7190	−	34.8209i	−0.848330	−	1.10557i
$993$	21.4149	+	8.87034i	0.679581	+	0.281492i
$994$	13.4840	+	2.55826i	0.427686	+	0.0811432i
$995$	−22.2051	+	22.2051i	−0.703949	+	0.703949i
$996$	2.82262	−	2.16587i	0.0894380	−	0.0686282i
$997$	−10.1505	+	1.33634i	−0.321469	+	0.0423222i	−0.289534	−	0.957168i	$-0.593500\pi$
$997$	−10.1505	+	1.33634i	−0.321469	+	0.0423222i	−0.0319352	+	0.999490i	$0.510167\pi$
$998$	−2.32029	−	1.78042i	−0.0734475	−	0.0563583i
$999$	−7.15341	−	4.13002i	−0.226324	−	0.130668i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.bh.a.100.10	yes	192
7.4	even	3	inner	357.2.bh.a.151.15	yes	192
17.8	even	8	inner	357.2.bh.a.331.15	yes	192
119.25	even	24	inner	357.2.bh.a.25.10	✓	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.bh.a.25.10	✓	192	119.25	even	24	inner
357.2.bh.a.100.10	yes	192	1.1	even	1	trivial
357.2.bh.a.151.15	yes	192	7.4	even	3	inner
357.2.bh.a.331.15	yes	192	17.8	even	8	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:	\( N \)	\(=\)	\( 357 = 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	357.bh (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.749407 + 0.200803i) q^{2} +(-0.608761 + 0.793353i) q^{3} +(-1.21076 + 0.699034i) q^{4} +(-0.559525 + 4.25001i) q^{5} +(0.296902 - 0.716785i) q^{6} +(-1.97366 + 1.76200i) q^{7} +(1.86419 - 1.86419i) q^{8} +(-0.258819 - 0.965926i) q^{9} +(-0.434103 - 3.29734i) q^{10} +(-1.17616 + 0.154845i) q^{11} +(0.182484 - 1.38611i) q^{12} -1.32321i q^{13} +(1.12526 - 1.71677i) q^{14} +(-3.03114 - 3.03114i) q^{15} +(0.375365 - 0.650151i) q^{16} +(4.09626 - 0.469777i) q^{17} +(0.387921 + 0.671900i) q^{18} +(1.23530 - 0.330997i) q^{19} +(-2.29345 - 5.53688i) q^{20} +(-0.196403 - 2.63845i) q^{21} +(0.850330 - 0.352218i) q^{22} +(0.475433 + 0.619596i) q^{23} +(0.344115 + 2.61381i) q^{24} +(-12.9199 - 3.46188i) q^{25} +(0.265705 + 0.991626i) q^{26} +(0.923880 + 0.382683i) q^{27} +(1.15793 - 3.51302i) q^{28} +(4.66396 - 1.93188i) q^{29} +(2.88022 + 1.66290i) q^{30} +(-4.56332 + 5.94703i) q^{31} +(-1.51543 + 5.65567i) q^{32} +(0.593155 - 1.02737i) q^{33} +(-2.97543 + 1.17459i) q^{34} +(-6.38423 - 9.37397i) q^{35} +(0.988583 + 0.988583i) q^{36} +(-8.18938 - 1.07815i) q^{37} +(-0.859274 + 0.496102i) q^{38} +(1.04978 + 0.805522i) q^{39} +(6.87978 + 8.96590i) q^{40} +(3.55444 + 1.47230i) q^{41} +(0.676995 + 1.93783i) q^{42} +(-7.00164 + 7.00164i) q^{43} +(1.31581 - 1.00966i) q^{44} +(4.25001 - 0.559525i) q^{45} +(-0.480709 - 0.368861i) q^{46} +(4.97122 + 2.87014i) q^{47} +(0.287292 + 0.693583i) q^{48} +(0.790680 - 6.95520i) q^{49} +10.3774 q^{50} +(-2.12094 + 3.53576i) q^{51} +(0.924972 + 1.60210i) q^{52} +(1.42201 - 5.30700i) q^{53} +(-0.769205 - 0.101268i) q^{54} -5.08534i q^{55} +(-0.394570 + 6.96400i) q^{56} +(-0.489403 + 1.18152i) q^{57} +(-3.10728 + 2.38430i) q^{58} +(-14.0866 - 3.77450i) q^{59} +(5.78887 + 1.55112i) q^{60} +(5.92432 - 4.54589i) q^{61} +(2.22560 - 5.37307i) q^{62} +(2.21279 + 1.45037i) q^{63} -3.04124i q^{64} +(5.62368 + 0.740371i) q^{65} +(-0.238214 + 0.889029i) q^{66} +(0.874010 + 1.51383i) q^{67} +(-4.63120 + 3.43221i) q^{68} -0.780984 q^{69} +(6.66670 + 5.74294i) q^{70} +(2.55867 + 6.17717i) q^{71} +(-2.28316 - 1.31818i) q^{72} +(6.73256 + 5.16608i) q^{73} +(6.35367 - 0.836477i) q^{74} +(10.6116 - 8.14259i) q^{75} +(-1.26427 + 1.26427i) q^{76} +(2.04851 - 2.37801i) q^{77} +(-0.948461 - 0.392865i) q^{78} +(-2.06054 - 2.68534i) q^{79} +(2.55312 + 1.95908i) q^{80} +(-0.866025 + 0.500000i) q^{81} +(-2.95936 - 0.389608i) q^{82} +(1.79946 + 1.79946i) q^{83} +(2.08216 + 3.05724i) q^{84} +(-0.295398 + 17.6720i) q^{85} +(3.84113 - 6.65303i) q^{86} +(-1.30658 + 4.87622i) q^{87} +(-1.90393 + 2.48125i) q^{88} +(-8.86973 - 5.12094i) q^{89} +(-3.07263 + 1.27273i) q^{90} +(2.33151 + 2.61158i) q^{91} +(-1.00875 - 0.417840i) q^{92} +(-1.94012 - 7.24064i) q^{93} +(-4.30180 - 1.15266i) q^{94} +(0.715561 + 5.43522i) q^{95} +(-3.56441 - 4.64523i) q^{96} +(-9.30496 + 3.85424i) q^{97} +(0.804084 + 5.37105i) q^{98} +(0.453981 + 1.09601i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 8 q^{5} + 8 q^{11} - 80 q^{14} + 96 q^{16} - 16 q^{17} + 16 q^{22} + 8 q^{25} - 64 q^{26} - 88 q^{28} - 40 q^{32} - 32 q^{33} - 32 q^{35} + 32 q^{37} - 64 q^{40} - 64 q^{41} - 56 q^{42} - 32 q^{43}+ \cdots - 16 q^{99}+O(q^{100}) \) 192 * q - 8 * q^5 + 8 * q^11 - 80 * q^14 + 96 * q^16 - 16 * q^17 + 16 * q^22 + 8 * q^25 - 64 * q^26 - 88 * q^28 - 40 * q^32 - 32 * q^33 - 32 * q^35 + 32 * q^37 - 64 * q^40 - 64 * q^41 - 56 * q^42 - 32 * q^43 + 32 * q^44 + 56 * q^49 + 64 * q^50 + 96 * q^52 + 64 * q^53 - 152 * q^56 - 32 * q^58 - 16 * q^59 + 40 * q^61 - 112 * q^62 + 32 * q^65 - 16 * q^67 + 48 * q^68 - 128 * q^69 - 120 * q^70 + 96 * q^71 + 8 * q^73 - 64 * q^74 - 112 * q^76 + 32 * q^77 - 16 * q^78 + 16 * q^79 + 192 * q^80 - 8 * q^82 - 16 * q^83 + 48 * q^84 - 64 * q^86 + 24 * q^87 - 136 * q^88 - 160 * q^92 + 48 * q^93 - 64 * q^94 - 104 * q^95 - 48 * q^96 - 96 * q^97 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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