LMFDB - Embedded newform 425.2.m.d.76.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(26,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("425.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$425 = 5^{2} \cdot 17$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	425.m (of order $8$ , 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:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			76.1
Character	$\chi$	$=$	425.76
Dual form			425.2.m.d.151.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.91681 + 1.91681i) q^{2} +(-0.405091 + 0.977976i) q^{3} -5.34834i q^{4} +(-1.09811 - 2.65108i) q^{6} +(-1.31353 + 0.544082i) q^{7} +(6.41814 + 6.41814i) q^{8} +(1.32898 + 1.32898i) q^{9} +(1.82748 + 4.41194i) q^{11} +(5.23055 + 2.16656i) q^{12} -1.14504i q^{13} +(1.47489 - 3.56069i) q^{14} -13.9080 q^{16} +(0.876759 - 4.02881i) q^{17} -5.09482 q^{18} +(-5.07242 + 5.07242i) q^{19} -1.50500i q^{21} +(-11.9598 - 4.95391i) q^{22} +(1.83858 + 4.43872i) q^{23} +(-8.87671 + 3.67685i) q^{24} +(2.19483 + 2.19483i) q^{26} +(-4.77200 + 1.97663i) q^{27} +(2.90994 + 7.02521i) q^{28} +(-7.95673 - 3.29579i) q^{29} +(1.22724 - 2.96282i) q^{31} +(13.8228 - 13.8228i) q^{32} -5.05506 q^{33} +(6.04189 + 9.40305i) q^{34} +(7.10785 - 7.10785i) q^{36} +(-0.968027 + 2.33702i) q^{37} -19.4457i q^{38} +(1.11982 + 0.463846i) q^{39} +(5.63744 - 2.33510i) q^{41} +(2.88481 + 2.88481i) q^{42} +(-3.05931 - 3.05931i) q^{43} +(23.5965 - 9.77400i) q^{44} +(-12.0324 - 4.98399i) q^{46} +5.03535i q^{47} +(5.63402 - 13.6017i) q^{48} +(-3.52041 + 3.52041i) q^{49} +(3.58491 + 2.48948i) q^{51} -6.12408 q^{52} +(-3.89859 + 3.89859i) q^{53} +(5.35820 - 12.9358i) q^{54} +(-11.9224 - 4.93842i) q^{56} +(-2.90591 - 7.01549i) q^{57} +(21.5690 - 8.93416i) q^{58} +(-0.928288 - 0.928288i) q^{59} +(-6.05613 + 2.50853i) q^{61} +(3.32678 + 8.03155i) q^{62} +(-2.46873 - 1.02258i) q^{63} +25.1755i q^{64} +(9.68961 - 9.68961i) q^{66} -1.95325 q^{67} +(-21.5474 - 4.68921i) q^{68} -5.08575 q^{69} +(0.794980 - 1.91925i) q^{71} +17.0592i q^{72} +(3.27403 + 1.35615i) q^{73} +(-2.62411 - 6.33516i) q^{74} +(27.1290 + 27.1290i) q^{76} +(-4.80091 - 4.80091i) q^{77} +(-3.03560 + 1.25739i) q^{78} +(-0.477176 - 1.15200i) q^{79} +0.170782i q^{81} +(-6.32995 + 15.2819i) q^{82} +(2.88654 - 2.88654i) q^{83} -8.04927 q^{84} +11.7282 q^{86} +(6.44640 - 6.44640i) q^{87} +(-16.5874 + 40.0454i) q^{88} +8.34827i q^{89} +(0.622997 + 1.50405i) q^{91} +(23.7398 - 9.83334i) q^{92} +(2.40042 + 2.40042i) q^{93} +(-9.65181 - 9.65181i) q^{94} +(7.91890 + 19.1179i) q^{96} +(-2.47754 - 1.02623i) q^{97} -13.4959i q^{98} +(-3.43469 + 8.29208i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$24 q - 8 q^{6} + 12 q^{9} + 4 q^{11} + 12 q^{12} - 24 q^{14} - 24 q^{16} - 4 q^{17} + 40 q^{18} - 20 q^{19} - 16 q^{22} - 8 q^{23} + 16 q^{24} + 16 q^{26} + 12 q^{27} - 48 q^{28} + 4 q^{29} + 24 q^{31}+ \cdots - 80 q^{99}+O(q^{100})$ 24 * q - 8 * q^6 + 12 * q^9 + 4 * q^11 + 12 * q^12 - 24 * q^14 - 24 * q^16 - 4 * q^17 + 40 * q^18 - 20 * q^19 - 16 * q^22 - 8 * q^23 + 16 * q^24 + 16 * q^26 + 12 * q^27 - 48 * q^28 + 4 * q^29 + 24 * q^31 + 60 * q^32 - 48 * q^33 + 16 * q^34 + 60 * q^36 + 12 * q^37 + 8 * q^39 - 20 * q^41 - 12 * q^42 - 32 * q^43 + 64 * q^44 - 40 * q^46 + 40 * q^48 + 24 * q^49 + 16 * q^51 + 48 * q^52 + 12 * q^53 - 20 * q^54 - 32 * q^56 - 68 * q^57 + 16 * q^58 - 16 * q^59 - 64 * q^61 - 100 * q^62 + 44 * q^63 - 72 * q^66 - 40 * q^67 - 20 * q^68 - 48 * q^69 - 24 * q^71 + 32 * q^74 + 52 * q^76 - 24 * q^77 + 16 * q^78 - 48 * q^79 - 100 * q^82 - 12 * q^83 - 40 * q^84 - 16 * q^86 - 24 * q^87 - 4 * q^88 + 24 * q^91 + 88 * q^92 + 32 * q^93 - 40 * q^94 + 132 * q^96 + 88 * q^97 - 80 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$ .

$n$	$52$	$326$
$\chi(n)$	$1$	$e\left(\frac{5}{8}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	−1.91681	+	1.91681i	−1.35539	+	1.35539i	−0.475882	+	0.879509i	$0.657871\pi$
$2$	−1.91681	+	1.91681i	−1.35539	+	1.35539i	−0.879509	+	0.475882i	$0.842129\pi$
$3$	−0.405091	+	0.977976i	−0.233879	+	0.564635i	−0.996627	−	0.0820613i	$-0.973850\pi$
$3$	−0.405091	+	0.977976i	−0.233879	+	0.564635i	0.762748	+	0.646696i	$0.223850\pi$
$4$		−	5.34834i		−	2.67417i
$5$		0			0
$5$		0			0
$6$	−1.09811	−	2.65108i	−0.448303	−	1.08230i
$7$	−1.31353	+	0.544082i	−0.496468	+	0.205644i	−0.616845	−	0.787084i	$-0.711590\pi$
$7$	−1.31353	+	0.544082i	−0.496468	+	0.205644i	0.120377	+	0.992728i	$0.461590\pi$
$8$	6.41814	+	6.41814i	2.26915	+	2.26915i
$9$	1.32898	+	1.32898i	0.442994	+	0.442994i
$10$		0			0
$11$	1.82748	+	4.41194i	0.551007	+	1.33025i	0.916723	+	0.399523i	$0.130824\pi$
$11$	1.82748	+	4.41194i	0.551007	+	1.33025i	−0.365716	+	0.930726i	$0.619176\pi$
$12$	5.23055	+	2.16656i	1.50993	+	0.625433i
$13$		−	1.14504i		−	0.317578i	−0.987313	−	0.158789i	$-0.949241\pi$
$13$		−	1.14504i		−	0.317578i	0.987313	−	0.158789i	$-0.0507589\pi$
$14$	1.47489	−	3.56069i	0.394180	−	0.951636i
$15$		0			0
$16$	−13.9080			−3.47701
$17$	0.876759	−	4.02881i	0.212645	−	0.977129i
$17$	0.876759	−	4.02881i	0.212645	−	0.977129i
$18$	−5.09482			−1.20086
$19$	−5.07242	+	5.07242i	−1.16369	+	1.16369i	−0.180031	+	0.983661i	$0.557620\pi$
$19$	−5.07242	+	5.07242i	−1.16369	+	1.16369i	−0.983661	+	0.180031i	$0.942380\pi$
$20$		0			0
$21$		−	1.50500i		−	0.328419i
$22$	−11.9598	−	4.95391i	−2.54984	−	1.05618i
$23$	1.83858	+	4.43872i	0.383370	+	0.925538i	0.991309	+	0.131554i	$0.0419966\pi$
$23$	1.83858	+	4.43872i	0.383370	+	0.925538i	−0.607939	+	0.793984i	$0.708003\pi$
$24$	−8.87671	+	3.67685i	−1.81195	+	0.750534i
$25$		0			0
$26$	2.19483	+	2.19483i	0.430442	+	0.430442i
$27$	−4.77200	+	1.97663i	−0.918372	+	0.380402i
$28$	2.90994	+	7.02521i	0.549926	+	1.32764i
$29$	−7.95673	−	3.29579i	−1.47753	−	0.612012i	−0.508967	−	0.860786i	$-0.669972\pi$
$29$	−7.95673	−	3.29579i	−1.47753	−	0.612012i	−0.968562	+	0.248774i	$0.919972\pi$
$30$		0			0
$31$	1.22724	−	2.96282i	0.220419	−	0.532138i	−0.774528	−	0.632539i	$-0.782013\pi$
$31$	1.22724	−	2.96282i	0.220419	−	0.532138i	0.994947	+	0.100402i	$0.0320128\pi$
$32$	13.8228	−	13.8228i	2.44356	−	2.44356i
$33$	−5.05506			−0.879974
$34$	6.04189	+	9.40305i	1.03617	+	1.61261i
$35$		0			0
$36$	7.10785	−	7.10785i	1.18464	−	1.18464i
$37$	−0.968027	+	2.33702i	−0.159143	+	0.384204i	−0.983258	−	0.182217i	$-0.941673\pi$
$37$	−0.968027	+	2.33702i	−0.159143	+	0.384204i	0.824116	+	0.566422i	$0.191673\pi$
$38$		−	19.4457i		−	3.15452i
$39$	1.11982	+	0.463846i	0.179315	+	0.0742749i
$40$		0			0
$41$	5.63744	−	2.33510i	0.880420	−	0.364682i	0.103760	−	0.994602i	$-0.466913\pi$
$41$	5.63744	−	2.33510i	0.880420	−	0.364682i	0.776660	+	0.629921i	$0.216913\pi$
$42$	2.88481	+	2.88481i	0.445136	+	0.445136i
$43$	−3.05931	−	3.05931i	−0.466541	−	0.466541i	0.434251	−	0.900792i	$-0.357013\pi$
$43$	−3.05931	−	3.05931i	−0.466541	−	0.466541i	−0.900792	+	0.434251i	$0.857013\pi$
$44$	23.5965	−	9.77400i	3.55731	−	1.47349i
$45$		0			0
$46$	−12.0324	−	4.98399i	−1.77408	−	0.734849i
$47$			5.03535i			0.734481i	0.930126	+	0.367240i	$0.119697\pi$
$47$			5.03535i			0.734481i	−0.930126	+	0.367240i	$0.880303\pi$
$48$	5.63402	−	13.6017i	0.813201	−	1.96324i
$49$	−3.52041	+	3.52041i	−0.502916	+	0.502916i
$50$		0			0
$51$	3.58491	+	2.48948i	0.501988	+	0.348597i
$52$	−6.12408			−0.849257
$53$	−3.89859	+	3.89859i	−0.535512	+	0.535512i	−0.922208	−	0.386695i	$-0.873617\pi$
$53$	−3.89859	+	3.89859i	−0.535512	+	0.535512i	0.386695	+	0.922208i	$0.373617\pi$
$54$	5.35820	−	12.9358i	0.729159	−	1.76035i
$55$		0			0
$56$	−11.9224	−	4.93842i	−1.59320	−	0.659925i
$57$	−2.90591	−	7.01549i	−0.384897	−	0.929224i
$58$	21.5690	−	8.93416i	2.83214	−	1.17311i
$59$	−0.928288	−	0.928288i	−0.120853	−	0.120853i	0.644094	−	0.764947i	$-0.277235\pi$
$59$	−0.928288	−	0.928288i	−0.120853	−	0.120853i	−0.764947	+	0.644094i	$0.777235\pi$
$60$		0			0
$61$	−6.05613	+	2.50853i	−0.775408	+	0.321185i	−0.735061	−	0.678001i	$-0.762846\pi$
$61$	−6.05613	+	2.50853i	−0.775408	+	0.321185i	−0.0403474	+	0.999186i	$0.512846\pi$
$62$	3.32678	+	8.03155i	0.422501	+	1.02001i
$63$	−2.46873	−	1.02258i	−0.311031	−	0.128833i
$64$			25.1755i			3.14694i
$65$		0			0
$66$	9.68961	−	9.68961i	1.19271	−	1.19271i
$67$	−1.95325			−0.238628			−0.119314	−	0.992857i	$-0.538069\pi$
$67$	−1.95325			−0.238628			−0.119314	+	0.992857i	$0.538069\pi$
$68$	−21.5474	−	4.68921i	−2.61301	−	0.568650i
$69$	−5.08575			−0.612253
$70$		0			0
$71$	0.794980	−	1.91925i	0.0943468	−	0.227773i	−0.869660	−	0.493651i	$-0.835662\pi$
$71$	0.794980	−	1.91925i	0.0943468	−	0.227773i	0.964007	+	0.265878i	$0.0856619\pi$
$72$			17.0592i			2.01044i
$73$	3.27403	+	1.35615i	0.383196	+	0.158725i	0.565962	−	0.824431i	$-0.308505\pi$
$73$	3.27403	+	1.35615i	0.383196	+	0.158725i	−0.182766	+	0.983157i	$0.558505\pi$
$74$	−2.62411	−	6.33516i	−0.305047	−	0.736448i
$75$		0			0
$76$	27.1290	+	27.1290i	3.11191	+	3.11191i
$77$	−4.80091	−	4.80091i	−0.547115	−	0.547115i
$78$	−3.03560	+	1.25739i	−0.343714	+	0.142371i
$79$	−0.477176	−	1.15200i	−0.0536865	−	0.129611i	0.894761	−	0.446546i	$-0.147346\pi$
$79$	−0.477176	−	1.15200i	−0.0536865	−	0.129611i	−0.948447	+	0.316936i	$0.897346\pi$
$80$		0			0
$81$			0.170782i			0.0189758i
$82$	−6.32995	+	15.2819i	−0.699026	+	1.68760i
$83$	2.88654	−	2.88654i	0.316839	−	0.316839i	−0.530713	−	0.847552i	$-0.678076\pi$
$83$	2.88654	−	2.88654i	0.316839	−	0.316839i	0.847552	+	0.530713i	$0.178076\pi$
$84$	−8.04927			−0.878247
$85$		0			0
$86$	11.7282			1.26469
$87$	6.44640	−	6.44640i	0.691126	−	0.691126i
$88$	−16.5874	+	40.0454i	−1.76822	+	4.26886i
$89$			8.34827i			0.884914i	0.896790	+	0.442457i	$0.145893\pi$
$89$			8.34827i			0.884914i	−0.896790	+	0.442457i	$0.854107\pi$
$90$		0			0
$91$	0.622997	+	1.50405i	0.0653079	+	0.157667i
$92$	23.7398	−	9.83334i	2.47504	−	1.02520i
$93$	2.40042	+	2.40042i	0.248912	+	0.248912i
$94$	−9.65181	−	9.65181i	−0.995509	−	0.995509i
$95$		0			0
$96$	7.91890	+	19.1179i	0.808219	+	1.95121i
$97$	−2.47754	−	1.02623i	−0.251556	−	0.104198i	0.253342	−	0.967377i	$-0.418470\pi$
$97$	−2.47754	−	1.02623i	−0.251556	−	0.104198i	−0.504899	+	0.863179i	$0.668470\pi$
$98$		−	13.4959i		−	1.36329i
$99$	−3.43469	+	8.29208i	−0.345200	+	0.833385i
$100$		0			0
$101$	−17.2825			−1.71967			−0.859836	−	0.510569i	$-0.829435\pi$
$101$	−17.2825			−1.71967			−0.859836	+	0.510569i	$0.829435\pi$
$102$	−11.6435	+	2.09973i	−1.15288	+	0.207904i
$103$	−13.6466			−1.34464			−0.672322	−	0.740259i	$-0.734703\pi$
$103$	−13.6466			−1.34464			−0.672322	+	0.740259i	$0.734703\pi$
$104$	7.34904	−	7.34904i	0.720633	−	0.720633i
$105$		0			0
$106$		−	14.9457i		−	1.45166i
$107$	12.5201	+	5.18598i	1.21036	+	0.501348i	0.894333	−	0.447402i	$-0.147651\pi$
$107$	12.5201	+	5.18598i	1.21036	+	0.501348i	0.316028	+	0.948750i	$0.397651\pi$
$108$	10.5717	+	25.5223i	1.01726	+	2.45588i
$109$	6.80733	−	2.81969i	0.652024	−	0.270077i	−0.0320540	−	0.999486i	$-0.510205\pi$
$109$	6.80733	−	2.81969i	0.652024	−	0.270077i	0.684078	+	0.729409i	$0.260205\pi$
$110$		0			0
$111$	−1.89341	−	1.89341i	−0.179715	−	0.179715i
$112$	18.2686	−	7.56712i	1.72622	−	0.715025i
$113$	6.14736	+	14.8410i	0.578295	+	1.39613i	0.894342	+	0.447384i	$0.147644\pi$
$113$	6.14736	+	14.8410i	0.578295	+	1.39613i	−0.316047	+	0.948744i	$0.602356\pi$
$114$	19.0175	+	7.87729i	1.78115	+	0.737776i
$115$		0			0
$116$	−17.6270	+	42.5553i	−1.63662	+	3.95116i
$117$	1.52174	−	1.52174i	0.140685	−	0.140685i
$118$	3.55871			0.327606
$119$	1.04035	+	5.76899i	0.0953689	+	0.528843i
$120$		0			0
$121$	−8.34731	+	8.34731i	−0.758847	+	0.758847i
$122$	6.80008	−	16.4169i	0.615651	−	1.48631i
$123$			6.45920i			0.582407i
$124$	−15.8461	−	6.56369i	−1.42303	−	0.589437i
$125$		0			0
$126$	6.69220	−	2.77200i	0.596189	−	0.246949i
$127$	6.00118	+	6.00118i	0.532518	+	0.532518i	0.921321	−	0.388803i	$-0.127111\pi$
$127$	6.00118	+	6.00118i	0.532518	+	0.532518i	−0.388803	+	0.921321i	$0.627111\pi$
$128$	−20.6110	−	20.6110i	−1.82177	−	1.82177i
$129$	4.23123	−	1.75263i	0.372539	−	0.154311i
$130$		0			0
$131$	12.8061	+	5.30445i	1.11887	+	0.463452i	0.863985	−	0.503518i	$-0.167961\pi$
$131$	12.8061	+	5.30445i	1.11887	+	0.463452i	0.254888	+	0.966971i	$0.417961\pi$
$132$			27.0362i			2.35320i
$133$	3.90296	−	9.42258i	0.338430	−	0.817042i
$134$	3.74402	−	3.74402i	0.323434	−	0.323434i
$135$		0			0
$136$	31.4846	−	20.2303i	2.69978	−	1.73473i
$137$	0.471082			0.0402473			0.0201236	−	0.999797i	$-0.493594\pi$
$137$	0.471082			0.0402473			0.0201236	+	0.999797i	$0.493594\pi$
$138$	9.74844	−	9.74844i	0.829842	−	0.829842i
$139$	1.54005	−	3.71802i	0.130626	−	0.315358i	−0.845012	−	0.534748i	$-0.820407\pi$
$139$	1.54005	−	3.71802i	0.130626	−	0.315358i	0.975637	+	0.219390i	$0.0704066\pi$
$140$		0			0
$141$	−4.92445	−	2.03977i	−0.414713	−	0.171780i
$142$	2.15502	+	5.20267i	0.180845	+	0.436599i
$143$	5.05186	−	2.09255i	0.422457	−	0.174988i
$144$	−18.4835	−	18.4835i	−1.54030	−	1.54030i
$145$		0			0
$146$	−8.87519	+	3.67622i	−0.734516	+	0.304246i
$147$	−2.01679	−	4.86896i	−0.166342	−	0.401585i
$148$	12.4992	+	5.17734i	1.02743	+	0.425574i
$149$		−	7.65894i		−	0.627445i	−0.949515	−	0.313722i	$-0.898424\pi$
$149$		−	7.65894i		−	0.627445i	0.949515	−	0.313722i	$-0.101576\pi$
$150$		0			0
$151$	6.23341	−	6.23341i	0.507268	−	0.507268i	−0.406419	−	0.913687i	$-0.633223\pi$
$151$	6.23341	−	6.23341i	0.507268	−	0.507268i	0.913687	+	0.406419i	$0.133223\pi$
$152$	−65.1109			−5.28119
$153$	6.51941	−	4.18902i	0.527063	−	0.338662i
$154$	18.4049			1.48311
$155$		0			0
$156$	2.48081	−	5.98920i	0.198624	−	0.479520i
$157$		−	7.63116i		−	0.609033i	−0.952507	−	0.304517i	$-0.901505\pi$
$157$		−	7.63116i		−	0.609033i	0.952507	−	0.304517i	$-0.0984949\pi$
$158$	3.12283	+	1.29352i	0.248439	+	0.102907i
$159$	−2.23344	−	5.39201i	−0.177124	−	0.427614i
$160$		0			0
$161$	−4.83006	−	4.83006i	−0.380662	−	0.380662i
$162$	−0.327357	−	0.327357i	−0.0257196	−	0.0257196i
$163$	−22.1342	+	9.16827i	−1.73368	+	0.718115i	−0.734461	+	0.678651i	$0.762565\pi$
$163$	−22.1342	+	9.16827i	−1.73368	+	0.718115i	−0.999221	+	0.0394639i	$0.987435\pi$
$164$	−12.4889	−	30.1509i	−0.975221	−	2.35439i
$165$		0			0
$166$			11.0659i			0.858880i
$167$	1.79012	−	4.32172i	0.138523	−	0.334425i	−0.839360	−	0.543576i	$-0.817070\pi$
$167$	1.79012	−	4.32172i	0.138523	−	0.334425i	0.977883	+	0.209151i	$0.0670700\pi$
$168$	9.65932	−	9.65932i	0.745233	−	0.745233i
$169$	11.6889			0.899144
$170$		0			0
$171$	−13.4823			−1.03102
$172$	−16.3622	+	16.3622i	−1.24761	+	1.24761i
$173$	5.55646	−	13.4145i	0.422450	−	1.01988i	−0.559172	−	0.829051i	$-0.688881\pi$
$173$	5.55646	−	13.4145i	0.422450	−	1.01988i	0.981622	−	0.190833i	$-0.0611190\pi$
$174$			24.7131i			1.87349i
$175$		0			0
$176$	−25.4167	−	61.3614i	−1.91586	−	4.62529i
$177$	1.28388	−	0.531802i	0.0965026	−	0.0399727i
$178$	−16.0021	−	16.0021i	−1.19941	−	1.19941i
$179$	13.5266	+	13.5266i	1.01103	+	1.01103i	0.999939	+	0.0110900i	$0.00353012\pi$
$179$	13.5266	+	13.5266i	1.01103	+	1.01103i	0.0110900	+	0.999939i	$0.496470\pi$
$180$		0			0
$181$	−2.49861	−	6.03218i	−0.185720	−	0.448368i	0.803407	−	0.595430i	$-0.203018\pi$
$181$	−2.49861	−	6.03218i	−0.185720	−	0.448368i	−0.989127	+	0.147062i	$0.953018\pi$
$182$	−4.07715	−	1.68881i	−0.302218	−	0.125183i
$183$		−	6.93893i		−	0.512941i
$184$	−16.6881	+	40.2886i	−1.23026	+	2.97011i
$185$		0			0
$186$	−9.20231			−0.674746
$187$	19.3771	−	3.49438i	1.41699	−	0.255534i
$188$	26.9307			1.96413
$189$	5.19272	−	5.19272i	0.377715	−	0.377715i
$190$		0			0
$191$			19.3014i			1.39660i	0.715806	+	0.698299i	$0.246059\pi$
$191$			19.3014i			1.39660i	−0.715806	+	0.698299i	$0.753941\pi$
$192$	−24.6210	−	10.1984i	−1.77687	−	0.736003i
$193$	0.802917	+	1.93841i	0.0577952	+	0.139530i	0.950139	−	0.311826i	$-0.100941\pi$
$193$	0.802917	+	1.93841i	0.0577952	+	0.139530i	−0.892344	+	0.451356i	$0.850941\pi$
$194$	6.71608	−	2.78189i	0.482186	−	0.199728i
$195$		0			0
$196$	18.8283	+	18.8283i	1.34488	+	1.34488i
$197$	14.4140	−	5.97048i	1.02696	−	0.425379i	0.195343	−	0.980735i	$-0.437418\pi$
$197$	14.4140	−	5.97048i	1.02696	−	0.425379i	0.831613	+	0.555356i	$0.187418\pi$
$198$	−9.31070	−	22.4780i	−0.661683	−	1.59744i
$199$	23.4064	+	9.69526i	1.65924	+	0.687278i	0.998019	−	0.0629154i	$-0.0200398\pi$
$199$	23.4064	+	9.69526i	1.65924	+	0.687278i	0.661218	+	0.750194i	$0.270040\pi$
$200$		0			0
$201$	0.791244	−	1.91023i	0.0558101	−	0.134737i
$202$	33.1273	−	33.1273i	2.33083	−	2.33083i
$203$	12.2446			0.859402
$204$	13.3146	−	19.1733i	0.932208	−	1.34240i
$205$		0			0
$206$	26.1581	−	26.1581i	1.82252	−	1.82252i
$207$	−3.45554	+	8.34242i	−0.240177	+	0.579838i
$208$			15.9253i			1.10422i
$209$	−31.6489	−	13.1094i	−2.18920	−	0.906798i
$210$		0			0
$211$	3.14022	−	1.30072i	0.216182	−	0.0895453i	−0.271964	−	0.962307i	$-0.587673\pi$
$211$	3.14022	−	1.30072i	0.216182	−	0.0895453i	0.488146	+	0.872762i	$0.337673\pi$
$212$	20.8510	+	20.8510i	1.43205	+	1.43205i
$213$	1.55494	+	1.55494i	0.106543	+	0.106543i
$214$	−33.9392	+	14.0581i	−2.32003	+	0.960990i
$215$		0			0
$216$	−43.3136	−	17.9411i	−2.94712	−	1.22074i
$217$			4.55947i			0.309517i
$218$	−7.64356	+	18.4532i	−0.517687	+	1.24981i
$219$	−2.65256	+	2.65256i	−0.179243	+	0.179243i
$220$		0			0
$221$	−4.61316	−	1.00393i	−0.310315	−	0.0675314i
$222$	7.25864			0.487168
$223$	7.58368	−	7.58368i	0.507841	−	0.507841i	−0.406022	−	0.913863i	$-0.633085\pi$
$223$	7.58368	−	7.58368i	0.507841	−	0.507841i	0.913863	+	0.406022i	$0.133085\pi$
$224$	−10.6360	+	25.6775i	−0.710645	+	1.71565i
$225$		0			0
$226$	−40.2308	−	16.6642i	−2.67611	−	1.10848i
$227$	4.04015	+	9.75380i	0.268154	+	0.647382i	0.999397	−	0.0347359i	$-0.0110590\pi$
$227$	4.04015	+	9.75380i	0.268154	+	0.647382i	−0.731242	+	0.682118i	$0.761059\pi$
$228$	−37.5212	+	15.5418i	−2.48490	+	1.02928i
$229$	9.07841	+	9.07841i	0.599918	+	0.599918i	0.940291	−	0.340372i	$-0.110553\pi$
$229$	9.07841	+	9.07841i	0.599918	+	0.599918i	−0.340372	+	0.940291i	$0.610553\pi$
$230$		0			0
$231$	6.63998	−	2.75037i	0.436879	−	0.180961i
$232$	−29.9146	−	72.2202i	−1.96399	−	4.74149i
$233$	24.8035	+	10.2740i	1.62493	+	0.673070i	0.994651	−	0.103295i	$-0.0329387\pi$
$233$	24.8035	+	10.2740i	1.62493	+	0.673070i	0.630283	+	0.776365i	$0.282939\pi$
$234$			5.83379i			0.381367i
$235$		0			0
$236$	−4.96480	+	4.96480i	−0.323181	+	0.323181i
$237$	1.31993			0.0857388
$238$	−13.0522	−	9.06391i	−0.846051	−	0.587526i
$239$	−4.40382			−0.284860			−0.142430	−	0.989805i	$-0.545491\pi$
$239$	−4.40382			−0.284860			−0.142430	+	0.989805i	$0.545491\pi$
$240$		0			0
$241$	2.68549	−	6.48334i	0.172987	−	0.417629i	−0.813478	−	0.581595i	$-0.802429\pi$
$241$	2.68549	−	6.48334i	0.172987	−	0.417629i	0.986466	+	0.163966i	$0.0524288\pi$
$242$		−	32.0005i		−	2.05707i
$243$	−14.4830	−	5.99906i	−0.929086	−	0.384840i
$244$	13.4165	+	32.3902i	0.858902	+	2.07357i
$245$		0			0
$246$	−12.3811	−	12.3811i	−0.789389	−	0.789389i
$247$	5.80813	+	5.80813i	0.369563	+	0.369563i
$248$	26.8923	−	11.1392i	1.70767	−	0.707338i
$249$	1.65365	+	3.99227i	0.104796	+	0.253000i
$250$		0			0
$251$			15.3498i			0.968873i	0.874826	+	0.484437i	$0.160975\pi$
$251$			15.3498i			0.968873i	−0.874826	+	0.484437i	$0.839025\pi$
$252$	−5.46912	+	13.2036i	−0.344522	+	0.831750i
$253$	−16.2234	+	16.2234i	−1.01996	+	1.01996i
$254$	−23.0063			−1.44354
$255$		0			0
$256$	28.6638			1.79149
$257$	−7.20084	+	7.20084i	−0.449176	+	0.449176i	−0.895080	−	0.445905i	$-0.852882\pi$
$257$	−7.20084	+	7.20084i	−0.449176	+	0.449176i	0.445905	+	0.895080i	$0.352882\pi$
$258$	−4.75101	+	11.4699i	−0.295785	+	0.714088i
$259$		−	3.59644i		−	0.223472i
$260$		0			0
$261$	−6.19431	−	14.9544i	−0.383418	−	0.925654i
$262$	−34.7145	+	14.3792i	−2.14467	+	0.888351i
$263$	0.108060	+	0.108060i	0.00666326	+	0.00666326i	0.710431	−	0.703767i	$-0.248500\pi$
$263$	0.108060	+	0.108060i	0.00666326	+	0.00666326i	−0.703767	+	0.710431i	$0.748500\pi$
$264$	−32.4441	−	32.4441i	−1.99680	−	1.99680i
$265$		0			0
$266$	10.5801	+	25.5426i	0.648706	+	1.56612i
$267$	−8.16440	−	3.38181i	−0.499653	−	0.206963i
$268$			10.4467i			0.638131i
$269$	6.28235	−	15.1669i	0.383042	−	0.924745i	−0.608332	−	0.793682i	$-0.708161\pi$
$269$	6.28235	−	15.1669i	0.383042	−	0.924745i	0.991374	−	0.131062i	$-0.0418388\pi$
$270$		0			0
$271$	11.0378			0.670499			0.335249	−	0.942129i	$-0.391179\pi$
$271$	11.0378			0.670499			0.335249	+	0.942129i	$0.391179\pi$
$272$	−12.1940	+	56.0328i	−0.739370	+	3.39749i
$273$	−1.72329			−0.104298
$274$	−0.902976	+	0.902976i	−0.0545508	+	0.0545508i
$275$		0			0
$276$			27.2003i			1.63727i
$277$	−2.60167	−	1.07765i	−0.156319	−	0.0647496i	0.303152	−	0.952942i	$-0.401961\pi$
$277$	−2.60167	−	1.07765i	−0.156319	−	0.0647496i	−0.459471	+	0.888193i	$0.651961\pi$
$278$	4.17475	+	10.0787i	0.250385	+	0.604482i
$279$	5.56851	−	2.30655i	0.333378	−	0.138090i
$280$		0			0
$281$	2.64770	+	2.64770i	0.157949	+	0.157949i	0.781657	−	0.623708i	$-0.214375\pi$
$281$	2.64770	+	2.64770i	0.157949	+	0.157949i	−0.623708	+	0.781657i	$0.714375\pi$
$282$	13.3491	−	5.52938i	0.794927	−	0.329270i
$283$	−9.46151	−	22.8421i	−0.562428	−	1.35782i	−0.907819	−	0.419363i	$-0.862253\pi$
$283$	−9.46151	−	22.8421i	−0.562428	−	1.35782i	0.345390	−	0.938459i	$-0.387747\pi$
$284$	−10.2648	−	4.25182i	−0.609104	−	0.252299i
$285$		0			0
$286$	−5.67244	+	13.6945i	−0.335418	+	0.809772i
$287$	−6.13446	+	6.13446i	−0.362106	+	0.362106i
$288$	36.7406			2.16496
$289$	−15.4626	−	7.06459i	−0.909564	−	0.415564i
$290$		0			0
$291$	2.00726	−	2.00726i	0.117668	−	0.117668i
$292$	7.25314	−	17.5106i	0.424458	−	1.02473i
$293$		−	5.52823i		−	0.322963i	−0.986876	−	0.161481i	$-0.948373\pi$
$293$		−	5.52823i		−	0.322963i	0.986876	−	0.161481i	$-0.0516272\pi$
$294$	13.1987	+	5.46708i	0.769763	+	0.318846i
$295$		0			0
$296$	−21.2123	+	8.78641i	−1.23294	+	0.510700i
$297$	−17.4415	−	17.4415i	−1.01206	−	1.01206i
$298$	14.6807	+	14.6807i	0.850433	+	0.850433i
$299$	5.08253	−	2.10525i	0.293930	−	0.121750i
$300$		0			0
$301$	5.68302	+	2.35398i	0.327564	+	0.135681i
$302$			23.8966i			1.37509i
$303$	7.00098	−	16.9019i	0.402196	−	0.970987i
$304$	70.5474	−	70.5474i	4.04617	−	4.04617i
$305$		0			0
$306$	−4.46693	+	20.5260i	−0.255357	+	1.17340i
$307$	24.0823			1.37445			0.687224	−	0.726446i	$-0.258829\pi$
$307$	24.0823			1.37445			0.687224	+	0.726446i	$0.258829\pi$
$308$	−25.6769	+	25.6769i	−1.46308	+	1.46308i
$309$	5.52813	−	13.3461i	0.314484	−	0.759232i
$310$		0			0
$311$	−1.44060	−	0.596714i	−0.0816887	−	0.0338366i	0.341465	−	0.939895i	$-0.389077\pi$
$311$	−1.44060	−	0.596714i	−0.0816887	−	0.0338366i	−0.423154	+	0.906058i	$0.639077\pi$
$312$	4.21015	+	10.1642i	0.238353	+	0.575435i
$313$	18.9492	−	7.84901i	1.07107	−	0.443652i	0.223703	−	0.974657i	$-0.428185\pi$
$313$	18.9492	−	7.84901i	1.07107	−	0.443652i	0.847369	+	0.531005i	$0.178185\pi$
$314$	14.6275	+	14.6275i	0.825478	+	0.825478i
$315$		0			0
$316$	−6.16131	+	2.55210i	−0.346601	+	0.143567i
$317$	8.01624	+	19.3529i	0.450237	+	1.08697i	0.972232	+	0.234019i	$0.0751878\pi$
$317$	8.01624	+	19.3529i	0.450237	+	1.08697i	−0.521995	+	0.852948i	$0.674812\pi$
$318$	14.6166	+	6.05438i	0.819656	+	0.339513i
$319$		−	41.1276i		−	2.30270i
$320$		0			0
$321$	−10.1435	+	10.1435i	−0.566157	+	0.566157i
$322$	18.5166			1.03189
$323$	15.9885	+	24.8831i	0.889624	+	1.38453i
$324$	0.913401			0.0507445
$325$		0			0
$326$	24.8532	−	60.0009i	1.37649	−	3.32314i
$327$			7.79963i			0.431321i
$328$	51.1688	+	21.1948i	2.82533	+	1.17029i
$329$	−2.73964	−	6.61408i	−0.151041	−	0.364646i
$330$		0			0
$331$	1.14575	+	1.14575i	0.0629760	+	0.0629760i	0.737893	−	0.674917i	$-0.235821\pi$
$331$	1.14575	+	1.14575i	0.0629760	+	0.0629760i	−0.674917	+	0.737893i	$0.735821\pi$
$332$	−15.4382	−	15.4382i	−0.847280	−	0.847280i
$333$	−4.39235	+	1.81937i	−0.240700	+	0.0997010i
$334$	4.85261	+	11.7152i	0.265523	+	0.641030i
$335$		0			0
$336$			20.9317i			1.14192i
$337$	−3.83641	+	9.26190i	−0.208982	+	0.504528i	−0.993264	−	0.115878i	$-0.963032\pi$
$337$	−3.83641	+	9.26190i	−0.208982	+	0.504528i	0.784281	+	0.620406i	$0.213032\pi$
$338$	−22.4054	+	22.4054i	−1.21869	+	1.21869i
$339$	−17.0044			−0.923553
$340$		0			0
$341$	15.3145			0.829328
$342$	25.8430	−	25.8430i	1.39743	−	1.39743i
$343$	6.51735	−	15.7343i	0.351904	−	0.849571i
$344$		−	39.2701i		−	2.11730i
$345$		0			0
$346$	15.0624	+	36.3637i	0.809757	+	1.95493i
$347$	−11.2116	+	4.64398i	−0.601869	+	0.249302i	−0.662747	−	0.748843i	$-0.730610\pi$
$347$	−11.2116	+	4.64398i	−0.601869	+	0.249302i	0.0608788	+	0.998145i	$0.480610\pi$
$348$	−34.4775	−	34.4775i	−1.84819	−	1.84819i
$349$	19.1558	+	19.1558i	1.02539	+	1.02539i	0.999669	+	0.0257160i	$0.00818655\pi$
$349$	19.1558	+	19.1558i	1.02539	+	1.02539i	0.0257160	+	0.999669i	$0.491813\pi$
$350$		0			0
$351$	2.26332	+	5.46414i	0.120807	+	0.291654i
$352$	86.2465	+	35.7245i	4.59695	+	1.90412i
$353$			18.6941i			0.994986i	0.867468	+	0.497493i	$0.165746\pi$
$353$			18.6941i			0.994986i	−0.867468	+	0.497493i	$0.834254\pi$
$354$	−1.44160	+	3.48033i	−0.0766202	+	0.184977i
$355$		0			0
$356$	44.6494			2.36641
$357$	−6.06337	−	1.31953i	−0.320908	−	0.0698367i
$358$	−51.8561			−2.74068
$359$	−0.959920	+	0.959920i	−0.0506626	+	0.0506626i	−0.731984	−	0.681322i	$-0.761406\pi$
$359$	−0.959920	+	0.959920i	−0.0506626	+	0.0506626i	0.681322	+	0.731984i	$0.261406\pi$
$360$		0			0
$361$		−	32.4588i		−	1.70836i
$362$	16.3519	+	6.77318i	0.859437	+	0.355991i
$363$	−4.78205	−	11.5449i	−0.250993	−	0.605950i
$364$	8.04416	−	3.33200i	0.421629	−	0.174644i
$365$		0			0
$366$	13.3006	+	13.3006i	0.695235	+	0.695235i
$367$	−31.4726	+	13.0364i	−1.64285	+	0.680493i	−0.996582	−	0.0826132i	$-0.973673\pi$
$367$	−31.4726	+	13.0364i	−1.64285	+	0.680493i	−0.646273	+	0.763106i	$0.723673\pi$
$368$	−25.5710	−	61.7339i	−1.33298	−	3.21810i
$369$	10.5954	+	4.38874i	0.551573	+	0.228469i
$370$		0			0
$371$	2.99976	−	7.24207i	0.155740	−	0.375989i
$372$	12.8383	−	12.8383i	0.665632	−	0.665632i
$373$	0.465809			0.0241187			0.0120593	−	0.999927i	$-0.496161\pi$
$373$	0.465809			0.0241187			0.0120593	+	0.999927i	$0.496161\pi$
$374$	−30.4442	+	43.8403i	−1.57423	+	2.26693i
$375$		0			0
$376$	−32.3175	+	32.3175i	−1.66665	+	1.66665i
$377$	−3.77382	+	9.11080i	−0.194361	+	0.469230i
$378$			19.9069i			1.02390i
$379$	−12.1522	−	5.03360i	−0.624216	−	0.258559i	0.0480776	−	0.998844i	$-0.484691\pi$
$379$	−12.1522	−	5.03360i	−0.624216	−	0.258559i	−0.672293	+	0.740285i	$0.734691\pi$
$380$		0			0
$381$	−8.30003	+	3.43798i	−0.425223	+	0.176133i
$382$	−36.9971	−	36.9971i	−1.89294	−	1.89294i
$383$	−0.650971	−	0.650971i	−0.0332631	−	0.0332631i	0.690280	−	0.723543i	$-0.257488\pi$
$383$	−0.650971	−	0.650971i	−0.0332631	−	0.0332631i	−0.723543	+	0.690280i	$0.757488\pi$
$384$	28.5064	−	11.8077i	1.45471	−	0.602561i
$385$		0			0
$386$	−5.25462	−	2.17653i	−0.267453	−	0.110783i
$387$		−	8.13154i		−	0.413349i
$388$	−5.48864	+	13.2507i	−0.278643	+	0.672704i
$389$	−14.5372	+	14.5372i	−0.737064	+	0.737064i	−0.972009	−	0.234945i	$-0.924509\pi$
$389$	−14.5372	+	14.5372i	−0.737064	+	0.737064i	0.234945	+	0.972009i	$0.424509\pi$
$390$		0			0
$391$	19.4948	−	3.51559i	0.985892	−	0.177791i
$392$	−45.1889			−2.28239
$393$	−10.3753	+	10.3753i	−0.523362	+	0.523362i
$394$	−16.1847	+	39.0732i	−0.815372	+	1.96848i
$395$		0			0
$396$	44.3488	+	18.3699i	2.22861	+	0.923122i
$397$	−11.4107	−	27.5479i	−0.572687	−	1.38259i	−0.899259	−	0.437416i	$-0.855894\pi$
$397$	−11.4107	−	27.5479i	−0.572687	−	1.38259i	0.326572	−	0.945172i	$-0.394106\pi$
$398$	−63.4497	+	26.2817i	−3.18045	+	1.31738i
$399$	7.63401	+	7.63401i	0.382178	+	0.382178i
$400$		0			0
$401$	4.40094	−	1.82293i	0.219773	−	0.0910328i	−0.270081	−	0.962838i	$-0.587050\pi$
$401$	4.40094	−	1.82293i	0.219773	−	0.0910328i	0.489853	+	0.871805i	$0.337050\pi$
$402$	2.14489	+	5.17823i	0.106977	+	0.258266i
$403$	−3.39255	−	1.40524i	−0.168995	−	0.0700000i
$404$			92.4327i			4.59870i
$405$		0			0
$406$	−23.4706	+	23.4706i	−1.16483	+	1.16483i
$407$	−12.0799			−0.598776
$408$	7.03060	+	38.9863i	0.348066	+	1.93011i
$409$	−32.0852			−1.58651			−0.793256	−	0.608888i	$-0.791616\pi$
$409$	−32.0852			−1.58651			−0.793256	+	0.608888i	$0.791616\pi$
$410$		0			0
$411$	−0.190831	+	0.460707i	−0.00941301	+	0.0227250i
$412$			72.9869i			3.59581i
$413$	1.72440	+	0.714270i	0.0848522	+	0.0351469i
$414$	−9.36723	−	22.6145i	−0.460374	−	1.11144i
$415$		0			0
$416$	−15.8277	−	15.8277i	−0.776019	−	0.776019i
$417$	3.01227	+	3.01227i	0.147511	+	0.147511i
$418$	85.7934	−	35.5368i	4.19629	−	1.73816i
$419$	6.70745	+	16.1932i	0.327680	+	0.791090i	0.998764	+	0.0497086i	$0.0158292\pi$
$419$	6.70745	+	16.1932i	0.327680	+	0.791090i	−0.671083	+	0.741382i	$0.734171\pi$
$420$		0			0
$421$		−	27.4320i		−	1.33695i	−0.743733	−	0.668477i	$-0.766946\pi$
$421$		−	27.4320i		−	1.33695i	0.743733	−	0.668477i	$-0.233054\pi$
$422$	−3.52597	+	8.51245i	−0.171642	+	0.414379i
$423$	−6.69189	+	6.69189i	−0.325371	+	0.325371i
$424$	−50.0433			−2.43032
$425$		0			0
$426$	−5.96107			−0.288815
$427$	6.59007	−	6.59007i	0.318916	−	0.318916i
$428$	27.7364	−	66.9616i	1.34069	−	3.23671i
$429$			5.78827i			0.279460i
$430$		0			0
$431$	3.33847	+	8.05979i	0.160809	+	0.388226i	0.983661	−	0.180028i	$-0.0576189\pi$
$431$	3.33847	+	8.05979i	0.160809	+	0.388226i	−0.822853	+	0.568255i	$0.807619\pi$
$432$	66.3692	−	27.4910i	3.19319	−	1.32266i
$433$	−6.86854	−	6.86854i	−0.330081	−	0.330081i	0.522536	−	0.852617i	$-0.324986\pi$
$433$	−6.86854	−	6.86854i	−0.330081	−	0.330081i	−0.852617	+	0.522536i	$0.824986\pi$
$434$	−8.73964	−	8.73964i	−0.419516	−	0.419516i
$435$		0			0
$436$	−15.0806	−	36.4079i	−0.722232	−	1.74362i
$437$	−31.8411	−	13.1890i	−1.52317	−	0.630916i
$438$		−	10.1689i		−	0.485890i
$439$	8.84357	−	21.3503i	0.422080	−	1.01899i	−0.559652	−	0.828727i	$-0.689065\pi$
$439$	8.84357	−	21.3503i	0.422080	−	1.01899i	0.981733	−	0.190265i	$-0.0609347\pi$
$440$		0			0
$441$	−9.35713			−0.445577
$442$	10.7669	−	6.91822i	0.512129	−	0.329066i
$443$	−0.787522			−0.0374163			−0.0187081	−	0.999825i	$-0.505955\pi$
$443$	−0.787522			−0.0374163			−0.0187081	+	0.999825i	$0.505955\pi$
$444$	−10.1266	+	10.1266i	−0.480588	+	0.480588i
$445$		0			0
$446$			29.0730i			1.37665i
$447$	7.49025	+	3.10257i	0.354277	+	0.146746i
$448$	−13.6975	−	33.0688i	−0.647147	−	1.56235i
$449$	18.6440	−	7.72258i	0.879863	−	0.364451i	0.103419	−	0.994638i	$-0.467022\pi$
$449$	18.6440	−	7.72258i	0.879863	−	0.364451i	0.776444	+	0.630187i	$0.217022\pi$
$450$		0			0
$451$	20.6046	+	20.6046i	0.970235	+	0.970235i
$452$	79.3749	−	32.8782i	3.73348	−	1.54646i
$453$	3.57103	+	8.62123i	0.167782	+	0.405061i
$454$	−26.4404	−	10.9520i	−1.24091	−	0.514002i
$455$		0			0
$456$	26.3758	−	63.6769i	1.23516	−	2.98194i
$457$	−4.91406	+	4.91406i	−0.229870	+	0.229870i	−0.812638	−	0.582768i	$-0.801970\pi$
$457$	−4.91406	+	4.91406i	−0.229870	+	0.229870i	0.582768	+	0.812638i	$0.301970\pi$
$458$	−34.8032			−1.62625
$459$	3.77955	+	20.9585i	0.176414	+	0.978259i
$460$		0			0
$461$	−4.93835	+	4.93835i	−0.230002	+	0.230002i	−0.812693	−	0.582692i	$-0.802000\pi$
$461$	−4.93835	+	4.93835i	−0.230002	+	0.230002i	0.582692	+	0.812693i	$0.302000\pi$
$462$	−7.45565	+	17.9995i	−0.346868	+	0.837414i
$463$			8.07063i			0.375074i	0.982258	+	0.187537i	$0.0600505\pi$
$463$			8.07063i			0.375074i	−0.982258	+	0.187537i	$0.939950\pi$
$464$	110.663	+	45.8379i	5.13738	+	2.12797i
$465$		0			0
$466$	−67.2370	+	27.8505i	−3.11469	+	1.29015i
$467$	−3.66051	−	3.66051i	−0.169388	−	0.169388i	0.617322	−	0.786710i	$-0.288217\pi$
$467$	−3.66051	−	3.66051i	−0.169388	−	0.169388i	−0.786710	+	0.617322i	$0.788217\pi$
$468$	−8.13879	−	8.13879i	−0.376216	−	0.376216i
$469$	2.56566	−	1.06273i	0.118471	−	0.0490723i
$470$		0			0
$471$	7.46309	+	3.09131i	0.343881	+	0.142440i
$472$		−	11.9158i		−	0.548467i
$473$	7.90665	−	19.0883i	0.363548	−	0.877682i
$474$	−2.53006	+	2.53006i	−0.116210	+	0.116210i
$475$		0			0
$476$	30.8545	−	5.56416i	1.41421	−	0.255033i
$477$	−10.3623			−0.474458
$478$	8.44130	−	8.44130i	0.386096	−	0.386096i
$479$	10.8407	−	26.1717i	0.495323	−	1.19581i	−0.456654	−	0.889644i	$-0.650952\pi$
$479$	10.8407	−	26.1717i	0.495323	−	1.19581i	0.951977	−	0.306171i	$-0.0990478\pi$
$480$		0			0
$481$	2.67599	+	1.10843i	0.122015	+	0.0505402i
$482$	7.27977	+	17.5749i	0.331585	+	0.800516i
$483$	6.68029	−	2.76707i	0.303964	−	0.125906i
$484$	44.6443	+	44.6443i	2.02928	+	2.02928i
$485$		0			0
$486$	39.2603	−	16.2621i	1.78088	−	0.737666i
$487$	−7.07109	−	17.0711i	−0.320422	−	0.773567i	−0.999229	−	0.0392506i	$-0.987503\pi$
$487$	−7.07109	−	17.0711i	−0.320422	−	0.773567i	0.678808	−	0.734316i	$-0.262497\pi$
$488$	−54.9692	−	22.7690i	−2.48834	−	1.03070i
$489$		−	25.3607i		−	1.14685i
$490$		0			0
$491$	−10.1423	+	10.1423i	−0.457714	+	0.457714i	−0.897905	−	0.440190i	$-0.854911\pi$
$491$	−10.1423	+	10.1423i	−0.457714	+	0.457714i	0.440190	+	0.897905i	$0.354911\pi$
$492$	34.5460			1.55745
$493$	−20.2542	+	29.1665i	−0.912205	+	1.31359i
$494$	−22.2662			−1.00180
$495$		0			0
$496$	−17.0685	+	41.2070i	−0.766398	+	1.85025i
$497$			2.95353i			0.132484i
$498$	−10.8222	−	4.48269i	−0.484953	−	0.200874i
$499$	12.7071	+	30.6775i	0.568846	+	1.37332i	0.902529	+	0.430630i	$0.141709\pi$
$499$	12.7071	+	30.6775i	0.568846	+	1.37332i	−0.333683	+	0.942685i	$0.608291\pi$
$500$		0			0
$501$	3.50138	+	3.50138i	0.156430	+	0.156430i
$502$	−29.4228	−	29.4228i	−1.31320	−	1.31320i
$503$	−4.11079	+	1.70275i	−0.183291	+	0.0759217i	−0.472442	−	0.881362i	$-0.656627\pi$
$503$	−4.11079	+	1.70275i	−0.183291	+	0.0759217i	0.289150	+	0.957284i	$0.406627\pi$
$504$	−9.28159	−	22.4077i	−0.413435	−	0.998120i
$505$		0			0
$506$		−	62.1944i		−	2.76488i
$507$	−4.73506	+	11.4314i	−0.210291	+	0.507688i
$508$	32.0963	−	32.0963i	1.42404	−	1.42404i
$509$	−31.7678			−1.40808			−0.704041	−	0.710159i	$-0.748623\pi$
$509$	−31.7678			−1.40808			−0.704041	+	0.710159i	$0.748623\pi$
$510$		0			0
$511$	−5.03840			−0.222886
$512$	−13.7212	+	13.7212i	−0.606398	+	0.606398i
$513$	14.1793	−	34.2318i	0.626031	−	1.51137i
$514$		−	27.6053i		−	1.21762i
$515$		0			0
$516$	−9.37368	−	22.6301i	−0.412653	−	0.996233i
$517$	−22.2156	+	9.20202i	−0.977042	+	0.404704i
$518$	6.89370	+	6.89370i	0.302892	+	0.302892i
$519$	10.8682	+	10.8682i	0.477060	+	0.477060i
$520$		0			0
$521$	−14.7255	−	35.5506i	−0.645137	−	1.55750i	−0.819663	−	0.572846i	$-0.805839\pi$
$521$	−14.7255	−	35.5506i	−0.645137	−	1.55750i	0.174526	−	0.984653i	$-0.444161\pi$
$522$	40.5381	+	16.7914i	1.77430	+	0.734941i
$523$		−	13.6513i		−	0.596930i	−0.954421	−	0.298465i	$-0.903525\pi$
$523$		−	13.6513i		−	0.596930i	0.954421	−	0.298465i	$-0.0964746\pi$
$524$	28.3700	−	68.4913i	1.23935	−	2.99206i
$525$		0			0
$526$	−0.414261			−0.0180627
$527$	−10.8606	−	7.54199i	−0.473096	−	0.328534i
$528$	70.3061			3.05968
$529$	−0.0584274	+	0.0584274i	−0.00254032	+	0.00254032i
$530$		0			0
$531$		−	2.46736i		−	0.107074i
$532$	−50.3952	−	20.8744i	−2.18491	−	0.905018i
$533$	−2.67379	−	6.45511i	−0.115815	−	0.279602i
$534$	22.1319	−	9.16734i	0.957742	−	0.396710i
$535$		0			0
$536$	−12.5362	−	12.5362i	−0.541483	−	0.541483i
$537$	−18.7082	+	7.74921i	−0.807320	+	0.334403i
$538$	17.0301	+	41.1143i	0.734219	+	1.77256i
$539$	−21.9653	−	9.09833i	−0.946113	−	0.391893i
$540$		0			0
$541$	2.59149	−	6.25641i	0.111417	−	0.268984i	−0.858329	−	0.513099i	$-0.828497\pi$
$541$	2.59149	−	6.25641i	0.111417	−	0.268984i	0.969746	+	0.244115i	$0.0784974\pi$
$542$	−21.1574	+	21.1574i	−0.908788	+	0.908788i
$543$	6.91149			0.296600
$544$	−43.5703	−	67.8089i	−1.86806	−	2.90728i
$545$		0			0
$546$	3.30323	−	3.30323i	0.141365	−	0.141365i
$547$	−5.21748	+	12.5961i	−0.223084	+	0.538571i	−0.995306	−	0.0967813i	$-0.969145\pi$
$547$	−5.21748	+	12.5961i	−0.223084	+	0.538571i	0.772222	+	0.635353i	$0.219145\pi$
$548$		−	2.51951i		−	0.107628i
$549$	−11.3823	−	4.71470i	−0.485784	−	0.201218i
$550$		0			0
$551$	57.0775	−	23.6423i	2.43158	−	1.00719i
$552$	−32.6411	−	32.6411i	−1.38930	−	1.38930i
$553$	1.25357	+	1.25357i	0.0533072	+	0.0533072i
$554$	7.05257	−	2.92127i	0.299635	−	0.124113i
$555$		0			0
$556$	−19.8852	−	8.23672i	−0.843321	−	0.349315i
$557$			37.3500i			1.58257i	0.611448	+	0.791285i	$0.290587\pi$
$557$			37.3500i			1.58257i	−0.611448	+	0.791285i	$0.709413\pi$
$558$	−6.25256	+	15.0950i	−0.264692	+	0.639023i
$559$	−3.50304	+	3.50304i	−0.148163	+	0.148163i
$560$		0			0
$561$	−4.43208	+	20.3659i	−0.187122	+	0.859848i
$562$	−10.1503			−0.428165
$563$	−21.1992	+	21.1992i	−0.893440	+	0.893440i	−0.994845	−	0.101405i	$-0.967666\pi$
$563$	−21.1992	+	21.1992i	−0.893440	+	0.893440i	0.101405	+	0.994845i	$0.467666\pi$
$564$	−10.9094	+	26.3376i	−0.459368	+	1.10901i
$565$		0			0
$566$	61.9200	+	25.6481i	2.60269	+	1.07807i
$567$	−0.0929195	−	0.224328i	−0.00390225	−	0.00942087i
$568$	17.4203	−	7.21573i	0.730940	−	0.302765i
$569$	−9.38514	−	9.38514i	−0.393446	−	0.393446i	0.482468	−	0.875914i	$-0.339740\pi$
$569$	−9.38514	−	9.38514i	−0.393446	−	0.393446i	−0.875914	+	0.482468i	$0.839740\pi$
$570$		0			0
$571$	−10.1419	+	4.20092i	−0.424426	+	0.175803i	−0.584664	−	0.811275i	$-0.698774\pi$
$571$	−10.1419	+	4.20092i	−0.424426	+	0.175803i	0.160238	+	0.987078i	$0.448774\pi$
$572$	−11.1917	−	27.0190i	−0.467946	−	1.12972i
$573$	−18.8763	−	7.81881i	−0.788568	−	0.326635i
$574$		−	23.5172i		−	0.981589i
$575$		0			0
$576$	−33.4578	+	33.4578i	−1.39407	+	1.39407i
$577$	35.5804			1.48123			0.740615	−	0.671930i	$-0.234534\pi$
$577$	35.5804			1.48123			0.740615	+	0.671930i	$0.234534\pi$
$578$	43.1804	−	16.0974i	1.79607	−	0.669563i
$579$	−2.22098			−0.0923006
$580$		0			0
$581$	−2.22104	+	5.36207i	−0.0921443	+	0.222456i
$582$			7.69508i			0.318971i
$583$	−24.3249	−	10.0757i	−1.00744	−	0.417294i
$584$	12.3092	+	29.7171i	0.509360	+	1.22970i
$585$		0			0
$586$	10.5966	+	10.5966i	0.437741	+	0.437741i
$587$	−5.84325	−	5.84325i	−0.241177	−	0.241177i	0.576160	−	0.817337i	$-0.304551\pi$
$587$	−5.84325	−	5.84325i	−0.241177	−	0.241177i	−0.817337	+	0.576160i	$0.804551\pi$
$588$	−26.0409	+	10.7865i	−1.07391	+	0.444827i
$589$	8.80357	+	21.2537i	0.362745	+	0.875744i
$590$		0			0
$591$			16.5151i			0.679342i
$592$	13.4634	−	32.5034i	0.553341	−	1.33588i
$593$	2.13713	−	2.13713i	0.0877612	−	0.0877612i	−0.661863	−	0.749625i	$-0.730234\pi$
$593$	2.13713	−	2.13713i	0.0877612	−	0.0877612i	0.749625	+	0.661863i	$0.230234\pi$
$594$	66.8642			2.74347
$595$		0			0
$596$	−40.9626			−1.67789
$597$	−18.9634	+	18.9634i	−0.776122	+	0.776122i
$598$	−5.70688	+	13.7776i	−0.233372	+	0.563409i
$599$		−	18.9682i		−	0.775020i	−0.921865	−	0.387510i	$-0.873335\pi$
$599$		−	18.9682i		−	0.775020i	0.921865	−	0.387510i	$-0.126665\pi$
$600$		0			0
$601$	−0.590707	−	1.42609i	−0.0240954	−	0.0581716i	0.911374	−	0.411580i	$-0.135023\pi$
$601$	−0.590707	−	1.42609i	−0.0240954	−	0.0581716i	−0.935469	+	0.353408i	$0.885023\pi$
$602$	−15.4054	+	6.38113i	−0.627878	+	0.260076i
$603$	−2.59584	−	2.59584i	−0.105711	−	0.105711i
$604$	−33.3384	−	33.3384i	−1.35652	−	1.35652i
$605$		0			0
$606$	18.9781	+	45.8173i	0.770934	+	1.86120i
$607$	34.0864	+	14.1190i	1.38352	+	0.573074i	0.945421	−	0.325851i	$-0.105651\pi$
$607$	34.0864	+	14.1190i	1.38352	+	0.573074i	0.438102	+	0.898925i	$0.355651\pi$
$608$			140.230i			5.68709i
$609$	−4.96017	+	11.9749i	−0.200996	+	0.485248i
$610$		0			0
$611$	5.76569			0.233255
$612$	−22.4043	−	34.8680i	−0.905639	−	1.40946i
$613$	20.1267			0.812911			0.406455	−	0.913671i	$-0.366765\pi$
$613$	20.1267			0.812911			0.406455	+	0.913671i	$0.366765\pi$
$614$	−46.1612	+	46.1612i	−1.86291	+	1.86291i
$615$		0			0
$616$		−	61.6258i		−	2.48297i
$617$	26.3211	+	10.9026i	1.05965	+	0.438921i	0.843327	−	0.537401i	$-0.180594\pi$
$617$	26.3211	+	10.9026i	1.05965	+	0.438921i	0.216322	+	0.976322i	$0.430594\pi$
$618$	14.9856	+	36.1783i	0.602807	+	1.45531i
$619$	10.0301	−	4.15459i	0.403142	−	0.166987i	−0.171893	−	0.985116i	$-0.554988\pi$
$619$	10.0301	−	4.15459i	0.403142	−	0.166987i	0.575035	+	0.818129i	$0.304988\pi$
$620$		0			0
$621$	−17.5474	−	17.5474i	−0.704153	−	0.704153i
$622$	3.90514	−	1.61756i	0.156582	−	0.0648583i
$623$	−4.54214	−	10.9657i	−0.181977	−	0.439332i
$624$	−15.5746	−	6.45120i	−0.623482	−	0.258255i
$625$		0			0
$626$	−21.2770	+	51.3671i	−0.850398	+	2.05304i
$627$	25.6414	−	25.6414i	1.02402	−	1.02402i
$628$	−40.8140			−1.62866
$629$	8.56669	+	5.94900i	0.341576	+	0.237202i
$630$		0			0
$631$	−23.8783	+	23.8783i	−0.950579	+	0.950579i	−0.998835	−	0.0482559i	$-0.984634\pi$
$631$	−23.8783	+	23.8783i	−0.950579	+	0.950579i	0.0482559	+	0.998835i	$0.484634\pi$
$632$	4.33114	−	10.4563i	0.172283	−	0.415929i
$633$			3.59797i			0.143006i
$634$	−52.4615	−	21.7303i	−2.08351	−	0.863019i
$635$		0			0
$636$	−28.8383	+	11.9452i	−1.14351	+	0.473658i
$637$	4.03102	+	4.03102i	0.159715	+	0.159715i
$638$	78.8339	+	78.8339i	3.12106	+	3.12106i
$639$	3.60717	−	1.49414i	0.142697	−	0.0591072i
$640$		0			0
$641$	13.5542	+	5.61433i	0.535359	+	0.221753i	0.633948	−	0.773375i	$-0.281433\pi$
$641$	13.5542	+	5.61433i	0.535359	+	0.221753i	−0.0985897	+	0.995128i	$0.531433\pi$
$642$		−	38.8865i		−	1.53473i
$643$	−9.71032	+	23.4428i	−0.382938	+	0.924493i	0.608457	+	0.793587i	$0.291789\pi$
$643$	−9.71032	+	23.4428i	−0.382938	+	0.924493i	−0.991395	+	0.130906i	$0.958211\pi$
$644$	−25.8328	+	25.8328i	−1.01795	+	1.01795i
$645$		0			0
$646$	−78.3431	−	17.0492i	−3.08237	−	0.670793i
$647$	37.8459			1.48788			0.743939	−	0.668248i	$-0.232955\pi$
$647$	37.8459			1.48788			0.743939	+	0.668248i	$0.232955\pi$
$648$	−1.09610	+	1.09610i	−0.0430590	+	0.0430590i
$649$	2.39912	−	5.79198i	0.0941736	−	0.227355i
$650$		0			0
$651$	−4.45905	−	1.84700i	−0.174764	−	0.0723896i
$652$	49.0350	+	118.381i	1.92036	+	4.63616i
$653$	30.3372	−	12.5661i	1.18718	−	0.491748i	0.300348	−	0.953830i	$-0.402897\pi$
$653$	30.3372	−	12.5661i	1.18718	−	0.491748i	0.886837	+	0.462082i	$0.152897\pi$
$654$	−14.9504	−	14.9504i	−0.584608	−	0.584608i
$655$		0			0
$656$	−78.4057	+	32.4767i	−3.06123	+	1.26800i
$657$	2.54883	+	6.15343i	0.0994394	+	0.240068i
$658$	17.9293	+	7.42657i	0.698958	+	0.289518i
$659$		−	35.5896i		−	1.38638i	−0.720757	−	0.693188i	$-0.756206\pi$
$659$		−	35.5896i		−	1.38638i	0.720757	−	0.693188i	$-0.243794\pi$
$660$		0			0
$661$	−2.10600	+	2.10600i	−0.0819139	+	0.0819139i	−0.746877	−	0.664963i	$-0.768447\pi$
$661$	−2.10600	+	2.10600i	−0.0819139	+	0.0819139i	0.664963	+	0.746877i	$0.268447\pi$
$662$	−4.39236			−0.170714
$663$	2.85056	−	4.10487i	0.110707	−	0.159420i
$664$	37.0524			1.43791
$665$		0			0
$666$	4.93192	−	11.9067i	0.191108	−	0.461376i
$667$		−	41.3773i		−	1.60213i
$668$	−23.1140	−	9.57415i	−0.894309	−	0.370435i
$669$	4.34457	+	10.4887i	0.167971	+	0.405518i
$670$		0			0
$671$	−22.1350	−	22.1350i	−0.854511	−	0.854511i
$672$	−20.8034	−	20.8034i	−0.802509	−	0.802509i
$673$	−29.9359	+	12.3999i	−1.15394	+	0.477979i	−0.875854	−	0.482576i	$-0.839701\pi$
$673$	−29.9359	+	12.3999i	−1.15394	+	0.477979i	−0.278090	+	0.960555i	$0.589701\pi$
$674$	−10.3997	−	25.1070i	−0.400580	−	0.967086i
$675$		0			0
$676$		−	62.5161i		−	2.40446i
$677$	15.5710	−	37.5918i	0.598443	−	1.44477i	−0.276725	−	0.960949i	$-0.589249\pi$
$677$	15.5710	−	37.5918i	0.598443	−	1.44477i	0.875168	−	0.483820i	$-0.160751\pi$
$678$	32.5943	−	32.5943i	1.25178	−	1.25178i
$679$	3.81268			0.146317
$680$		0			0
$681$	−11.1756			−0.428250
$682$	−29.3551	+	29.3551i	−1.12406	+	1.12406i
$683$	−8.46078	+	20.4261i	−0.323743	+	0.781584i	0.675288	+	0.737554i	$0.264020\pi$
$683$	−8.46078	+	20.4261i	−0.323743	+	0.781584i	−0.999030	+	0.0440293i	$0.985980\pi$
$684$			72.1079i			2.75711i
$685$		0			0
$686$	17.6671	+	42.6522i	0.674533	+	1.62847i
$687$	−12.5560	+	5.20088i	−0.479043	+	0.198426i
$688$	42.5490	+	42.5490i	1.62217	+	1.62217i
$689$	4.46405	+	4.46405i	0.170067	+	0.170067i
$690$		0			0
$691$	2.80528	+	6.77255i	0.106718	+	0.257640i	0.968214	−	0.250125i	$-0.0804718\pi$
$691$	2.80528	+	6.77255i	0.106718	+	0.257640i	−0.861496	+	0.507765i	$0.830472\pi$
$692$	−71.7452	−	29.7178i	−2.72734	−	1.12970i
$693$		−	12.7607i		−	0.484737i
$694$	12.5888	−	30.3921i	0.477865	−	1.15367i
$695$		0			0
$696$	82.7477			3.13654
$697$	−4.46500	−	24.7595i	−0.169124	−	0.937832i
$698$	−73.4361			−2.77960
$699$	−20.0954	+	20.0954i	−0.760077	+	0.760077i
$700$		0			0
$701$			45.6656i			1.72477i	0.506255	+	0.862384i	$0.331029\pi$
$701$			45.6656i			1.72477i	−0.506255	+	0.862384i	$0.668971\pi$
$702$	−14.8121	−	6.13537i	−0.559047	−	0.231565i
$703$	−6.94412	−	16.7646i	−0.261903	−	0.632289i
$704$	−111.073	+	46.0078i	−4.18621	+	1.73398i
$705$		0			0
$706$	−35.8331	−	35.8331i	−1.34859	−	1.34859i
$707$	22.7011	−	9.40310i	0.853762	−	0.353640i
$708$	−2.84426	−	6.86665i	−0.106894	−	0.258064i
$709$	42.2410	+	17.4968i	1.58639	+	0.657105i	0.989410	−	0.145149i	$-0.0463661\pi$
$709$	42.2410	+	17.4968i	1.58639	+	0.657105i	0.596983	+	0.802254i	$0.296366\pi$
$710$		0			0
$711$	0.896835	−	2.16515i	0.0336339	−	0.0811995i
$712$	−53.5803	+	53.5803i	−2.00801	+	2.00801i
$713$	15.4075			0.577015
$714$	14.1516	−	9.09306i	0.529611	−	0.340299i
$715$		0			0
$716$	72.3450	−	72.3450i	2.70366	−	2.70366i
$717$	1.78395	−	4.30683i	0.0666227	−	0.160842i
$718$		−	3.67997i		−	0.137335i
$719$	0.497733	+	0.206168i	0.0185623	+	0.00768877i	0.391945	−	0.919989i	$-0.371802\pi$
$719$	0.497733	+	0.206168i	0.0185623	+	0.00768877i	−0.373383	+	0.927677i	$0.621802\pi$
$720$		0			0
$721$	17.9253	−	7.42490i	0.667572	−	0.276518i
$722$	62.2174	+	62.2174i	2.31549	+	2.31549i
$723$	5.25268	+	5.25268i	0.195349	+	0.195349i
$724$	−32.2621	+	13.3634i	−1.19901	+	0.496647i
$725$		0			0
$726$	31.2957	+	12.9631i	1.16149	+	0.481106i
$727$			42.2238i			1.56600i	0.622025	+	0.782998i	$0.286310\pi$
$727$			42.2238i			1.56600i	−0.622025	+	0.782998i	$0.713690\pi$
$728$	−5.65471	+	13.6517i	−0.209577	+	0.505965i
$729$	11.3716	−	11.3716i	0.421170	−	0.421170i
$730$		0			0
$731$	−15.0077	+	9.64310i	−0.555078	+	0.356663i
$732$	−37.1118			−1.37169
$733$	−2.67745	+	2.67745i	−0.0988939	+	0.0988939i	−0.754823	−	0.655929i	$-0.772277\pi$
$733$	−2.67745	+	2.67745i	−0.0988939	+	0.0988939i	0.655929	+	0.754823i	$0.272277\pi$
$734$	35.3387	−	85.3153i	1.30438	−	3.14904i
$735$		0			0
$736$	86.7701	+	35.9414i	3.19839	+	1.32482i
$737$	−3.56954	−	8.61762i	−0.131486	−	0.317434i
$738$	−28.7217	+	11.8969i	−1.05726	+	0.437932i
$739$	−12.9186	−	12.9186i	−0.475219	−	0.475219i	0.428380	−	0.903599i	$-0.359084\pi$
$739$	−12.9186	−	12.9186i	−0.475219	−	0.475219i	−0.903599	+	0.428380i	$0.859084\pi$
$740$		0			0
$741$	−8.03304	+	3.32739i	−0.295101	+	0.122235i
$742$	8.13170	+	19.6317i	0.298524	+	0.720701i
$743$	12.2614	+	5.07884i	0.449827	+	0.186325i	0.596084	−	0.802922i	$-0.296723\pi$
$743$	12.2614	+	5.07884i	0.449827	+	0.186325i	−0.146257	+	0.989247i	$0.546723\pi$
$744$			30.8124i			1.12964i
$745$		0			0
$746$	−0.892868	+	0.892868i	−0.0326902	+	0.0326902i
$747$	7.67231			0.280715
$748$	−18.6891	−	103.635i	−0.683341	−	3.78928i
$749$	−19.2671			−0.704004
$750$		0			0
$751$	−1.13681	+	2.74450i	−0.0414828	+	0.100148i	−0.943263	−	0.332047i	$-0.892261\pi$
$751$	−1.13681	+	2.74450i	−0.0414828	+	0.100148i	0.901780	+	0.432195i	$0.142261\pi$
$752$		−	70.0318i		−	2.55380i
$753$	−15.0118	−	6.21808i	−0.547059	−	0.226599i
$754$	−10.2300	−	24.6974i	−0.372554	−	0.899426i
$755$		0			0
$756$	−27.7724	−	27.7724i	−1.01007	−	1.01007i
$757$	−23.3928	−	23.3928i	−0.850226	−	0.850226i	0.139934	−	0.990161i	$-0.455311\pi$
$757$	−23.3928	−	23.3928i	−0.850226	−	0.850226i	−0.990161	+	0.139934i	$0.955311\pi$
$758$	32.9419	−	13.6450i	1.19650	−	0.495608i
$759$	−9.29414	−	22.4380i	−0.337356	−	0.814449i
$760$		0			0
$761$			2.82578i			0.102434i	0.998688	+	0.0512172i	$0.0163101\pi$
$761$			2.82578i			0.102434i	−0.998688	+	0.0512172i	$0.983690\pi$
$762$	9.31962	−	22.4996i	0.337614	−	0.815073i
$763$	−7.40749	+	7.40749i	−0.268169	+	0.268169i
$764$	103.230			3.73474
$765$		0			0
$766$	2.49558			0.0901690
$767$	−1.06293	+	1.06293i	−0.0383802	+	0.0383802i
$768$	−11.6115	+	28.0325i	−0.418992	+	1.01154i
$769$			35.5112i			1.28057i	0.768139	+	0.640283i	$0.221183\pi$
$769$			35.5112i			1.28057i	−0.768139	+	0.640283i	$0.778817\pi$
$770$		0			0
$771$	−4.12525	−	9.95923i	−0.148567	−	0.358673i
$772$	10.3673	−	4.29427i	0.373127	−	0.154554i
$773$	37.8124	+	37.8124i	1.36002	+	1.36002i	0.873886	+	0.486132i	$0.161592\pi$
$773$	37.8124	+	37.8124i	1.36002	+	1.36002i	0.486132	+	0.873886i	$0.338408\pi$
$774$	15.5866	+	15.5866i	0.560250	+	0.560250i
$775$		0			0
$776$	−9.31471	−	22.4877i	−0.334379	−	0.807262i
$777$	3.51723	+	1.45688i	0.126180	+	0.0522654i
$778$		−	55.7301i		−	1.99802i
$779$	−16.7508	+	40.4400i	−0.600160	+	1.44891i
$780$		0			0
$781$	9.92043			0.354981
$782$	−30.6291	+	44.1065i	−1.09529	+	1.57725i
$783$	44.4841			1.58973
$784$	48.9620	−	48.9620i	1.74864	−	1.74864i
$785$		0			0
$786$		−	39.7748i		−	1.41872i
$787$	9.29791	+	3.85132i	0.331435	+	0.137285i	0.542194	−	0.840253i	$-0.317594\pi$
$787$	9.29791	+	3.85132i	0.331435	+	0.137285i	−0.210760	+	0.977538i	$0.567594\pi$
$788$	−31.9321	−	77.0910i	−1.13754	−	2.74625i
$789$	−0.149454	+	0.0619059i	−0.00532071	+	0.00220391i
$790$		0			0
$791$	−16.1495	−	16.1495i	−0.574210	−	0.574210i
$792$	−75.2640	+	31.1754i	−2.67439	+	1.10777i
$793$	2.87238	+	6.93453i	0.102001	+	0.246252i
$794$	74.6763	+	30.9319i	2.65016	+	1.09773i
$795$		0			0
$796$	51.8535	−	125.185i	1.83790	−	4.43708i
$797$	6.45088	−	6.45088i	0.228502	−	0.228502i	−0.583565	−	0.812067i	$-0.698343\pi$
$797$	6.45088	−	6.45088i	0.228502	−	0.228502i	0.812067	+	0.583565i	$0.198343\pi$
$798$	−29.2659			−1.03600
$799$	20.2864	+	4.41479i	0.717683	+	0.156184i
$800$		0			0
$801$	−11.0947	+	11.0947i	−0.392012	+	0.392012i
$802$	−4.94157	+	11.9300i	−0.174493	+	0.421263i
$803$			16.9232i			0.597205i
$804$	−10.2166	−	4.23184i	−0.360311	−	0.149246i
$805$		0			0
$806$	9.19647	−	3.80930i	0.323932	−	0.134177i
$807$	12.2880	+	12.2880i	0.432557	+	0.432557i
$808$	−110.921	−	110.921i	−3.90220	−	3.90220i
$809$	5.24543	−	2.17273i	0.184419	−	0.0763890i	−0.288563	−	0.957461i	$-0.593177\pi$
$809$	5.24543	−	2.17273i	0.184419	−	0.0763890i	0.472982	+	0.881072i	$0.343177\pi$
$810$		0			0
$811$	−4.12057	−	1.70680i	−0.144693	−	0.0599338i	0.309162	−	0.951009i	$-0.399952\pi$
$811$	−4.12057	−	1.70680i	−0.144693	−	0.0599338i	−0.453855	+	0.891076i	$0.649952\pi$
$812$		−	65.4882i		−	2.29819i
$813$	−4.47131	+	10.7947i	−0.156816	+	0.378587i
$814$	23.1548	−	23.1548i	0.811576	−	0.811576i
$815$		0			0
$816$	−49.8591	−	34.6238i	−1.74542	−	1.21208i
$817$	31.0362			1.08582
$818$	61.5013	−	61.5013i	2.15034	−	2.15034i
$819$	−1.17090	+	2.82681i	−0.0409146	+	0.0987766i
$820$		0			0
$821$	−45.1566	−	18.7045i	−1.57598	−	0.652791i	−0.588207	−	0.808710i	$-0.700166\pi$
$821$	−45.1566	−	18.7045i	−1.57598	−	0.652791i	−0.987770	+	0.155919i	$0.950166\pi$
$822$	−0.517302	−	1.24888i	−0.0180430	−	0.0435596i
$823$	44.1829	−	18.3012i	1.54012	−	0.637939i	0.558625	−	0.829421i	$-0.311329\pi$
$823$	44.1829	−	18.3012i	1.54012	−	0.637939i	0.981496	+	0.191482i	$0.0613293\pi$
$824$	−87.5860	−	87.5860i	−3.05120	−	3.05120i
$825$		0			0
$826$	−4.67447	+	1.93623i	−0.162646	+	0.0673700i
$827$	−7.47877	−	18.0554i	−0.260062	−	0.627846i	0.738879	−	0.673838i	$-0.235355\pi$
$827$	−7.47877	−	18.0554i	−0.260062	−	0.627846i	−0.998942	+	0.0459914i	$0.985355\pi$
$828$	44.6181	+	18.4814i	1.55059	+	0.642274i
$829$		−	0.116023i		−	0.00402965i	−0.999998	−	0.00201483i	$-0.999359\pi$
$829$		−	0.116023i		−	0.00402965i	0.999998	−	0.00201483i	$-0.000641340\pi$
$830$		0			0
$831$	2.10783	−	2.10783i	0.0731197	−	0.0731197i
$832$	28.8270			0.999397
$833$	11.0965	+	17.2696i	0.384471	+	0.598357i
$834$	−11.5479			−0.399871
$835$		0			0
$836$	−70.1136	+	169.269i	−2.42493	+	5.85430i
$837$			16.5643i			0.572548i
$838$	−43.8963	−	18.1824i	−1.51637	−	0.628102i
$839$	14.9656	+	36.1301i	0.516670	+	1.24735i	0.939938	+	0.341346i	$0.110883\pi$
$839$	14.9656	+	36.1301i	0.516670	+	1.24735i	−0.423268	+	0.906005i	$0.639117\pi$
$840$		0			0
$841$	31.9413	+	31.9413i	1.10142	+	1.10142i
$842$	52.5820	+	52.5820i	1.81210	+	1.81210i
$843$	−3.66195	+	1.51683i	−0.126124	+	0.0522424i
$844$	−6.95670	−	16.7950i	−0.239459	−	0.578106i
$845$		0			0
$846$		−	25.6542i		−	0.882009i
$847$	6.42283	−	15.5061i	0.220691	−	0.532795i
$848$	54.2217	−	54.2217i	1.86198	−	1.86198i
$849$	26.1718			0.898214
$850$		0			0
$851$	−12.1532			−0.416606
$852$	8.31636	−	8.31636i	0.284914	−	0.284914i
$853$	−9.57677	+	23.1204i	−0.327902	+	0.791626i	0.670845	+	0.741597i	$0.265931\pi$
$853$	−9.57677	+	23.1204i	−0.327902	+	0.791626i	−0.998748	+	0.0500291i	$0.984069\pi$
$854$			25.2638i			0.864511i
$855$		0			0
$856$	47.0712	+	113.640i	1.60886	+	3.88413i
$857$	34.9820	−	14.4900i	1.19496	−	0.494970i	0.305596	−	0.952161i	$-0.401144\pi$
$857$	34.9820	−	14.4900i	1.19496	−	0.494970i	0.889368	+	0.457191i	$0.151144\pi$
$858$	−11.0950	−	11.0950i	−0.378778	−	0.378778i
$859$	12.1975	+	12.1975i	0.416172	+	0.416172i	0.883882	−	0.467710i	$-0.154921\pi$
$859$	12.1975	+	12.1975i	0.416172	+	0.416172i	−0.467710	+	0.883882i	$0.654921\pi$
$860$		0			0
$861$	−3.51434	−	8.48436i	−0.119768	−	0.289146i
$862$	−21.8483	−	9.04988i	−0.744157	−	0.308240i
$863$		−	49.4684i		−	1.68392i	−0.539537	−	0.841962i	$-0.681401\pi$
$863$		−	49.4684i		−	1.68392i	0.539537	−	0.841962i	$-0.318599\pi$
$864$	−38.6400	+	93.2851i	−1.31456	+	3.17363i
$865$		0			0
$866$	26.3314			0.894778
$867$	13.1728	−	12.2602i	0.447370	−	0.416379i
$868$	24.3856			0.827700
$869$	4.21054	−	4.21054i	0.142833	−	0.142833i
$870$		0			0
$871$			2.23656i			0.0757829i
$872$	61.7875	+	25.5932i	2.09239	+	0.866696i
$873$	−1.92877	−	4.65646i	−0.0652789	−	0.157597i
$874$	86.3142	−	35.7525i	2.91962	−	1.20935i
$875$		0			0
$876$	14.1868	+	14.1868i	0.479327	+	0.479327i
$877$	51.3470	−	21.2686i	1.73387	−	0.718191i	0.734657	−	0.678439i	$-0.237343\pi$
$877$	51.3470	−	21.2686i	1.73387	−	0.718191i	0.999210	−	0.0397521i	$-0.0126568\pi$
$878$	23.9730	+	57.8759i	0.809049	+	1.95322i
$879$	5.40648	+	2.23944i	0.182356	+	0.0755343i
$880$		0			0
$881$	14.9186	−	36.0167i	0.502621	−	1.21343i	−0.445431	−	0.895316i	$-0.646949\pi$
$881$	14.9186	−	36.0167i	0.502621	−	1.21343i	0.948051	−	0.318117i	$-0.103051\pi$
$882$	17.9359	−	17.9359i	0.603932	−	0.603932i
$883$	−27.2502			−0.917042			−0.458521	−	0.888684i	$-0.651621\pi$
$883$	−27.2502			−0.917042			−0.458521	+	0.888684i	$0.651621\pi$
$884$	−5.36934	+	24.6727i	−0.180590	+	0.829834i
$885$		0			0
$886$	1.50953	−	1.50953i	0.0507137	−	0.0507137i
$887$	−16.0719	+	38.8009i	−0.539640	+	1.30281i	0.385334	+	0.922777i	$0.374086\pi$
$887$	−16.0719	+	38.8009i	−0.539640	+	1.30281i	−0.924974	+	0.380030i	$0.875914\pi$
$888$		−	24.3044i		−	0.815601i
$889$	−11.1479	−	4.61760i	−0.373887	−	0.154869i
$890$		0			0
$891$	−0.753480	+	0.312102i	−0.0252425	+	0.0104558i
$892$	−40.5601	−	40.5601i	−1.35805	−	1.35805i
$893$	−25.5414	−	25.5414i	−0.854709	−	0.854709i
$894$	−20.3044	+	8.41038i	−0.679082	+	0.281285i
$895$		0			0
$896$	38.2872	+	15.8591i	1.27909	+	0.529815i
$897$			5.82341i			0.194438i
$898$	−20.9342	+	50.5397i	−0.698585	+	1.68653i
$899$	−19.5296	+	19.5296i	−0.651349	+	0.651349i
$900$		0			0
$901$	12.2885	+	19.1248i	0.409391	+	0.637139i
$902$	−78.9905			−2.63010
$903$	−4.60427	+	4.60427i	−0.153221	+	0.153221i
$904$	−55.7972	+	134.706i	−1.85579	+	4.48027i
$905$		0			0
$906$	−23.3703	−	9.68028i	−0.776425	−	0.321606i
$907$	−9.89680	−	23.8930i	−0.328618	−	0.793353i	−0.998695	−	0.0510624i	$-0.983739\pi$
$907$	−9.89680	−	23.8930i	−0.328618	−	0.793353i	0.670078	−	0.742291i	$-0.266261\pi$
$908$	52.1666	−	21.6081i	1.73121	−	0.717090i
$909$	−22.9681	−	22.9681i	−0.761805	−	0.761805i
$910$		0			0
$911$	−34.0518	+	14.1047i	−1.12819	+	0.467310i	−0.867164	−	0.498023i	$-0.834059\pi$
$911$	−34.0518	+	14.1047i	−1.12819	+	0.467310i	−0.261021	+	0.965333i	$0.584059\pi$
$912$	40.4155	+	97.5717i	1.33829	+	3.23092i
$913$	18.0103	+	7.46012i	0.596054	+	0.246894i
$914$		−	18.8387i		−	0.623128i
$915$		0			0
$916$	48.5544	−	48.5544i	1.60428	−	1.60428i
$917$	−19.7072			−0.650791
$918$	−47.4182	−	32.9288i	−1.56503	−	1.08681i
$919$	−9.71950			−0.320617			−0.160308	−	0.987067i	$-0.551249\pi$
$919$	−9.71950			−0.320617			−0.160308	+	0.987067i	$0.551249\pi$
$920$		0			0
$921$	−9.75550	+	23.5519i	−0.321455	+	0.776060i
$922$		−	18.9318i		−	0.623485i
$923$	−2.19763	−	0.910286i	−0.0723357	−	0.0299624i
$924$	−14.7099	−	35.5129i	−0.483921	−	1.16829i
$925$		0			0
$926$	−15.4699	−	15.4699i	−0.508372	−	0.508372i
$927$	−18.1361	−	18.1361i	−0.595669	−	0.595669i
$928$	−155.542	+	64.4275i	−5.10591	+	2.11494i
$929$	0.943781	+	2.27849i	0.0309644	+	0.0747548i	0.938605	−	0.344993i	$-0.112119\pi$
$929$	0.943781	+	2.27849i	0.0309644	+	0.0747548i	−0.907641	+	0.419748i	$0.862119\pi$
$930$		0			0
$931$		−	35.7140i		−	1.17048i
$932$	54.9486	−	132.658i	1.79990	−	4.34535i
$933$	1.16714	−	1.16714i	0.0382106	−	0.0382106i
$934$	14.0330			0.459174
$935$		0			0
$936$	19.5335			0.638472
$937$	35.8516	−	35.8516i	1.17122	−	1.17122i	0.189302	−	0.981919i	$-0.439377\pi$
$937$	35.8516	−	35.8516i	1.17122	−	1.17122i	0.981919	−	0.189302i	$-0.0606225\pi$
$938$	−2.88083	+	6.95493i	−0.0940624	+	0.227087i
$939$			21.7114i			0.708525i
$940$		0			0
$941$	6.50204	+	15.6973i	0.211960	+	0.511718i	0.993724	−	0.111857i	$-0.0356798\pi$
$941$	6.50204	+	15.6973i	0.211960	+	0.511718i	−0.781764	+	0.623575i	$0.785680\pi$
$942$	−20.2308	+	8.37988i	−0.659156	+	0.273031i
$943$	20.7297	+	20.7297i	0.675053	+	0.675053i
$944$	12.9107	+	12.9107i	0.420207	+	0.420207i
$945$		0			0
$946$	21.4332	+	51.7443i	0.696853	+	1.68235i
$947$	−18.6520	−	7.72593i	−0.606110	−	0.251059i	0.0584545	−	0.998290i	$-0.481383\pi$
$947$	−18.6520	−	7.72593i	−0.606110	−	0.251059i	−0.664564	+	0.747231i	$0.731383\pi$
$948$		−	7.05944i		−	0.229280i
$949$	1.55285	−	3.74891i	0.0504076	−	0.121695i
$950$		0			0
$951$	−22.1740			−0.719040
$952$	−30.3490	+	43.7033i	−0.983618	+	1.41643i
$953$	−60.7088			−1.96655			−0.983275	−	0.182129i	$-0.941701\pi$
$953$	−60.7088			−1.96655			−0.983275	+	0.182129i	$0.941701\pi$
$954$	19.8626	−	19.8626i	0.643076	−	0.643076i
$955$		0			0
$956$			23.5531i			0.761762i
$957$	40.2218	+	16.6604i	1.30019	+	0.538555i
$958$	29.3867	+	70.9457i	0.949441	+	2.29215i
$959$	−0.618781	+	0.256308i	−0.0199815	+	0.00827660i
$960$		0			0
$961$	14.6481	+	14.6481i	0.472521	+	0.472521i
$962$	−7.25403	+	3.00472i	−0.233879	+	0.0968760i
$963$	9.74687	+	23.5310i	0.314089	+	0.758277i
$964$	−34.6751	−	14.3629i	−1.11681	−	0.462598i
$965$		0			0
$966$	−7.50092	+	18.1088i	−0.241338	+	0.582642i
$967$	−32.8967	+	32.8967i	−1.05789	+	1.05789i	−0.0596681	+	0.998218i	$0.519004\pi$
$967$	−32.8967	+	32.8967i	−1.05789	+	1.05789i	−0.998218	+	0.0596681i	$0.980996\pi$
$968$	−107.148			−3.44388
$969$	−30.8118	+	5.55646i	−0.989819	+	0.178499i
$970$		0			0
$971$	−13.9209	+	13.9209i	−0.446742	+	0.446742i	−0.894270	−	0.447528i	$-0.852305\pi$
$971$	−13.9209	+	13.9209i	−0.446742	+	0.446742i	0.447528	+	0.894270i	$0.352305\pi$
$972$	−32.0850	+	77.4601i	−1.02913	+	2.48453i
$973$			5.72164i			0.183427i
$974$	46.2761	+	19.1682i	1.48278	+	0.614189i
$975$		0			0
$976$	84.2289	−	34.8888i	2.69610	−	1.11676i
$977$	−6.17874	−	6.17874i	−0.197676	−	0.197676i	0.601327	−	0.799003i	$-0.294639\pi$
$977$	−6.17874	−	6.17874i	−0.197676	−	0.197676i	−0.799003	+	0.601327i	$0.794639\pi$
$978$	48.6116	+	48.6116i	1.55443	+	1.55443i
$979$	−36.8320	+	15.2563i	−1.17716	+	0.487594i
$980$		0			0
$981$	12.7941	+	5.29950i	0.408485	+	0.169200i
$982$		−	38.8817i		−	1.24076i
$983$	4.81531	−	11.6252i	0.153584	−	0.370786i	−0.828295	−	0.560292i	$-0.810689\pi$
$983$	4.81531	−	11.6252i	0.153584	−	0.370786i	0.981879	+	0.189507i	$0.0606888\pi$
$984$	−41.4560	+	41.4560i	−1.32157	+	1.32157i
$985$		0			0
$986$	−17.0832	−	94.7303i	−0.544040	−	3.01683i
$987$	7.57821			0.241217
$988$	31.0639	−	31.0639i	0.988273	−	0.988273i
$989$	7.95465	−	19.2042i	0.252943	−	0.610659i
$990$		0			0
$991$	19.7383	+	8.17588i	0.627009	+	0.259716i	0.673482	−	0.739204i	$-0.264798\pi$
$991$	19.7383	+	8.17588i	0.627009	+	0.259716i	−0.0464728	+	0.998920i	$0.514798\pi$
$992$	−23.9906	−	57.9184i	−0.761703	−	1.83891i
$993$	−1.58464	+	0.656381i	−0.0502872	+	0.0208296i
$994$	−5.66136	−	5.66136i	−0.179568	−	0.179568i
$995$		0			0
$996$	21.3520	−	8.84430i	0.676565	−	0.280242i
$997$	11.6951	+	28.2345i	0.370388	+	0.894197i	0.993684	+	0.112211i	$0.0357932\pi$
$997$	11.6951	+	28.2345i	0.370388	+	0.894197i	−0.623296	+	0.781986i	$0.714207\pi$
$998$	−83.1601	−	34.4461i	−2.63239	−	1.09037i
$999$		−	13.0657i		−	0.413381i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.m.d.76.1	yes	24
5.2	odd	4		425.2.n.e.399.1		24
5.3	odd	4		425.2.n.d.399.6		24
5.4	even	2		425.2.m.c.76.6	✓	24
17.7	odd	16		7225.2.a.cb.1.24		24
17.10	odd	16		7225.2.a.cb.1.23		24
17.15	even	8	inner	425.2.m.d.151.1	yes	24
85.24	odd	16		7225.2.a.bx.1.1		24
85.32	odd	8		425.2.n.d.49.6		24
85.44	odd	16		7225.2.a.bx.1.2		24
85.49	even	8		425.2.m.c.151.6	yes	24
85.83	odd	8		425.2.n.e.49.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.2.m.c.76.6	✓	24	5.4	even	2
425.2.m.c.151.6	yes	24	85.49	even	8
425.2.m.d.76.1	yes	24	1.1	even	1	trivial
425.2.m.d.151.1	yes	24	17.15	even	8	inner
425.2.n.d.49.6		24	85.32	odd	8
425.2.n.d.399.6		24	5.3	odd	4
425.2.n.e.49.1		24	85.83	odd	8
425.2.n.e.399.1		24	5.2	odd	4
7225.2.a.bx.1.1		24	85.24	odd	16
7225.2.a.bx.1.2		24	85.44	odd	16
7225.2.a.cb.1.23		24	17.10	odd	16
7225.2.a.cb.1.24		24	17.7	odd	16

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 $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	425.2.m.d.76.1

Level	$425$
Weight	$2$
Character	425.76
Analytic conductor	$3.394$
Analytic rank	$0$
Dimension	$24$
Inner twists	$2$