LMFDB - Embedded newform 425.2.n.e.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(49,425)]

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([4, 3]))

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

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

chi := DirichletCharacter("425.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.n (of order $8$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.39364208590$
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			49.1
Character	$\chi$	$=$	425.49
Dual form			425.2.n.e.399.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.91681 + 1.91681i) q^{2} +(0.977976 - 0.405091i) q^{3} -5.34834i q^{4} +(-1.09811 + 2.65108i) q^{6} +(-0.544082 + 1.31353i) q^{7} +(6.41814 + 6.41814i) q^{8} +(-1.32898 + 1.32898i) q^{9} +O(q^{10})$	\(q+(-1.91681 + 1.91681i) q^{2} +(0.977976 - 0.405091i) q^{3} -5.34834i q^{4} +(-1.09811 + 2.65108i) q^{6} +(-0.544082 + 1.31353i) q^{7} +(6.41814 + 6.41814i) q^{8} +(-1.32898 + 1.32898i) q^{9} +(1.82748 - 4.41194i) q^{11} +(-2.16656 - 5.23055i) q^{12} -1.14504 q^{13} +(-1.47489 - 3.56069i) q^{14} -13.9080 q^{16} +(4.02881 - 0.876759i) q^{17} -5.09482i q^{18} +(5.07242 + 5.07242i) q^{19} +1.50500i q^{21} +(4.95391 + 11.9598i) q^{22} +(4.43872 + 1.83858i) q^{23} +(8.87671 + 3.67685i) q^{24} +(2.19483 - 2.19483i) q^{26} +(-1.97663 + 4.77200i) q^{27} +(7.02521 + 2.90994i) q^{28} +(7.95673 - 3.29579i) q^{29} +(1.22724 + 2.96282i) q^{31} +(13.8228 - 13.8228i) q^{32} -5.05506i q^{33} +(-6.04189 + 9.40305i) q^{34} +(7.10785 + 7.10785i) q^{36} +(-2.33702 + 0.968027i) q^{37} -19.4457 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} -5.03535 q^{47} +(-13.6017 + 5.63402i) q^{48} +(3.52041 + 3.52041i) q^{49} +(3.58491 - 2.48948i) q^{51} +6.12408i q^{52} +(3.89859 - 3.89859i) q^{53} +(-5.35820 - 12.9358i) q^{54} +(-11.9224 + 4.93842i) q^{56} +(7.01549 + 2.90591i) q^{57} +(-8.93416 + 21.5690i) q^{58} +(0.928288 - 0.928288i) q^{59} +(-6.05613 - 2.50853i) q^{61} +(-8.03155 - 3.32678i) q^{62} +(-1.02258 - 2.46873i) q^{63} +25.1755i q^{64} +(9.68961 + 9.68961i) q^{66} +1.95325i q^{67} +(-4.68921 - 21.5474i) q^{68} +5.08575 q^{69} +(0.794980 + 1.91925i) q^{71} -17.0592 q^{72} +(1.35615 + 3.27403i) q^{73} +(2.62411 - 6.33516i) q^{74} +(27.1290 - 27.1290i) q^{76} +(4.80091 + 4.80091i) q^{77} +(1.25739 - 3.03560i) q^{78} +(0.477176 - 1.15200i) q^{79} -0.170782i q^{81} +(-15.2819 + 6.32995i) q^{82} +(-2.88654 + 2.88654i) q^{83} +8.04927 q^{84} +11.7282 q^{86} +(6.44640 - 6.44640i) q^{87} +(40.0454 - 16.5874i) q^{88} +8.34827i q^{89} +(0.622997 - 1.50405i) q^{91} +(9.83334 - 23.7398i) q^{92} +(2.40042 + 2.40042i) q^{93} +(9.65181 - 9.65181i) q^{94} +(7.91890 - 19.1179i) q^{96} +(1.02623 + 2.47754i) q^{97} -13.4959 q^{98} +(3.43469 + 8.29208i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{3} - 8 q^{6} - 12 q^{9}+O(q^{10}) $ 24 * q + 4 * q^3 - 8 * q^6 - 12 * q^9	$ 24 q + 4 q^{3} - 8 q^{6} - 12 q^{9} + 4 q^{11} - 20 q^{12} + 16 q^{13} + 24 q^{14} - 24 q^{16} + 20 q^{19} + 12 q^{22} + 8 q^{23} - 16 q^{24} + 16 q^{26} + 16 q^{27} + 20 q^{28} - 4 q^{29} + 24 q^{31} + 60 q^{32} - 16 q^{34} + 60 q^{36} - 16 q^{37} - 48 q^{38} - 8 q^{39} - 20 q^{41} + 12 q^{42} - 32 q^{43} - 64 q^{44} - 40 q^{46} - 88 q^{47} + 4 q^{48} - 24 q^{49} + 16 q^{51} - 12 q^{53} + 20 q^{54} - 32 q^{56} - 56 q^{57} - 28 q^{58} + 16 q^{59} - 64 q^{61} + 16 q^{62} - 40 q^{63} - 72 q^{66} + 48 q^{68} + 48 q^{69} - 24 q^{71} + 120 q^{72} + 20 q^{73} - 32 q^{74} + 52 q^{76} + 24 q^{77} - 100 q^{78} + 48 q^{79} + 8 q^{82} + 12 q^{83} + 40 q^{84} - 16 q^{86} - 24 q^{87} + 80 q^{88} + 24 q^{91} - 56 q^{92} + 32 q^{93} + 40 q^{94} + 132 q^{96} - 24 q^{97} + 48 q^{98} + 80 q^{99}+O(q^{100}) $ 24 * q + 4 * q^3 - 8 * q^6 - 12 * q^9 + 4 * q^11 - 20 * q^12 + 16 * q^13 + 24 * q^14 - 24 * q^16 + 20 * q^19 + 12 * q^22 + 8 * q^23 - 16 * q^24 + 16 * q^26 + 16 * q^27 + 20 * q^28 - 4 * q^29 + 24 * q^31 + 60 * q^32 - 16 * q^34 + 60 * q^36 - 16 * q^37 - 48 * q^38 - 8 * q^39 - 20 * q^41 + 12 * q^42 - 32 * q^43 - 64 * q^44 - 40 * q^46 - 88 * q^47 + 4 * q^48 - 24 * q^49 + 16 * q^51 - 12 * q^53 + 20 * q^54 - 32 * q^56 - 56 * q^57 - 28 * q^58 + 16 * q^59 - 64 * q^61 + 16 * q^62 - 40 * q^63 - 72 * q^66 + 48 * q^68 + 48 * q^69 - 24 * q^71 + 120 * q^72 + 20 * q^73 - 32 * q^74 + 52 * q^76 + 24 * q^77 - 100 * q^78 + 48 * q^79 + 8 * q^82 + 12 * q^83 + 40 * q^84 - 16 * q^86 - 24 * q^87 + 80 * q^88 + 24 * q^91 - 56 * q^92 + 32 * q^93 + 40 * q^94 + 132 * q^96 - 24 * q^97 + 48 * q^98 + 80 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$52$	$326$
$\chi(n)$	$-1$	$e\left(\frac{3}{8}\right)$

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	$0.842129\pi$
$3$	0.977976	−	0.405091i	0.564635	−	0.233879i	−0.0820613	−	0.996627i	$-0.526150\pi$
$3$	0.977976	−	0.405091i	0.564635	−	0.233879i	0.646696	+	0.762748i	$0.276150\pi$
$4$		−	5.34834i		−	2.67417i
$5$		0			0
$5$		0			0
$6$	−1.09811	+	2.65108i	−0.448303	+	1.08230i
$7$	−0.544082	+	1.31353i	−0.205644	+	0.496468i	−0.992728	−	0.120377i	$-0.961590\pi$
$7$	−0.544082	+	1.31353i	−0.205644	+	0.496468i	0.787084	+	0.616845i	$0.211590\pi$
$8$	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	−0.365716	−	0.930726i	$-0.619176\pi$
$11$	1.82748	−	4.41194i	0.551007	−	1.33025i	0.916723	−	0.399523i	$-0.130824\pi$
$12$	−2.16656	−	5.23055i	−0.625433	−	1.50993i
$13$	−1.14504			−0.317578			−0.158789	−	0.987313i	$-0.550759\pi$
$13$	−1.14504			−0.317578			−0.158789	+	0.987313i	$0.550759\pi$
$14$	−1.47489	−	3.56069i	−0.394180	−	0.951636i
$15$		0			0
$16$	−13.9080			−3.47701
$17$	4.02881	−	0.876759i	0.977129	−	0.212645i
$17$	4.02881	−	0.876759i	0.977129	−	0.212645i
$18$		−	5.09482i		−	1.20086i
$19$	5.07242	+	5.07242i	1.16369	+	1.16369i	0.983661	+	0.180031i	$0.0576199\pi$
$19$	5.07242	+	5.07242i	1.16369	+	1.16369i	0.180031	+	0.983661i	$0.442380\pi$
$20$		0			0
$21$			1.50500i			0.328419i
$22$	4.95391	+	11.9598i	1.05618	+	2.54984i
$23$	4.43872	+	1.83858i	0.925538	+	0.383370i	0.793984	−	0.607939i	$-0.208003\pi$
$23$	4.43872	+	1.83858i	0.925538	+	0.383370i	0.131554	+	0.991309i	$0.458003\pi$
$24$	8.87671	+	3.67685i	1.81195	+	0.750534i
$25$		0			0
$26$	2.19483	−	2.19483i	0.430442	−	0.430442i
$27$	−1.97663	+	4.77200i	−0.380402	+	0.918372i
$28$	7.02521	+	2.90994i	1.32764	+	0.549926i
$29$	7.95673	−	3.29579i	1.47753	−	0.612012i	0.508967	−	0.860786i	$-0.330028\pi$
$29$	7.95673	−	3.29579i	1.47753	−	0.612012i	0.968562	+	0.248774i	$0.0800277\pi$
$30$		0			0
$31$	1.22724	+	2.96282i	0.220419	+	0.532138i	0.994947	−	0.100402i	$-0.0320128\pi$
$31$	1.22724	+	2.96282i	0.220419	+	0.532138i	−0.774528	+	0.632539i	$0.782013\pi$
$32$	13.8228	−	13.8228i	2.44356	−	2.44356i
$33$		−	5.05506i		−	0.879974i
$34$	−6.04189	+	9.40305i	−1.03617	+	1.61261i
$35$		0			0
$36$	7.10785	+	7.10785i	1.18464	+	1.18464i
$37$	−2.33702	+	0.968027i	−0.384204	+	0.159143i	−0.566422	−	0.824116i	$-0.691673\pi$
$37$	−2.33702	+	0.968027i	−0.384204	+	0.159143i	0.182217	+	0.983258i	$0.441673\pi$
$38$	−19.4457			−3.15452
$39$	−1.11982	+	0.463846i	−0.179315	+	0.0742749i
$40$		0			0
$41$	5.63744	+	2.33510i	0.880420	+	0.364682i	0.776660	−	0.629921i	$-0.216913\pi$
$41$	5.63744	+	2.33510i	0.880420	+	0.364682i	0.103760	+	0.994602i	$0.466913\pi$
$42$	−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
$47$	−5.03535			−0.734481			−0.367240	−	0.930126i	$-0.619697\pi$
$47$	−5.03535			−0.734481			−0.367240	+	0.930126i	$0.619697\pi$
$48$	−13.6017	+	5.63402i	−1.96324	+	0.813201i
$49$	3.52041	+	3.52041i	0.502916	+	0.502916i
$50$		0			0
$51$	3.58491	−	2.48948i	0.501988	−	0.348597i
$52$			6.12408i			0.849257i
$53$	3.89859	−	3.89859i	0.535512	−	0.535512i	−0.386695	−	0.922208i	$-0.626383\pi$
$53$	3.89859	−	3.89859i	0.535512	−	0.535512i	0.922208	+	0.386695i	$0.126383\pi$
$54$	−5.35820	−	12.9358i	−0.729159	−	1.76035i
$55$		0			0
$56$	−11.9224	+	4.93842i	−1.59320	+	0.659925i
$57$	7.01549	+	2.90591i	0.929224	+	0.384897i
$58$	−8.93416	+	21.5690i	−1.17311	+	2.83214i
$59$	0.928288	−	0.928288i	0.120853	−	0.120853i	−0.644094	−	0.764947i	$-0.722765\pi$
$59$	0.928288	−	0.928288i	0.120853	−	0.120853i	0.764947	+	0.644094i	$0.222765\pi$
$60$		0			0
$61$	−6.05613	−	2.50853i	−0.775408	−	0.321185i	−0.0403474	−	0.999186i	$-0.512846\pi$
$61$	−6.05613	−	2.50853i	−0.775408	−	0.321185i	−0.735061	+	0.678001i	$0.762846\pi$
$62$	−8.03155	−	3.32678i	−1.02001	−	0.422501i
$63$	−1.02258	−	2.46873i	−0.128833	−	0.311031i
$64$			25.1755i			3.14694i
$65$		0			0
$66$	9.68961	+	9.68961i	1.19271	+	1.19271i
$67$			1.95325i			0.238628i	0.992857	+	0.119314i	$0.0380695\pi$
$67$			1.95325i			0.238628i	−0.992857	+	0.119314i	$0.961931\pi$
$68$	−4.68921	−	21.5474i	−0.568650	−	2.61301i
$69$	5.08575			0.612253
$70$		0			0
$71$	0.794980	+	1.91925i	0.0943468	+	0.227773i	0.964007	−	0.265878i	$-0.0856619\pi$
$71$	0.794980	+	1.91925i	0.0943468	+	0.227773i	−0.869660	+	0.493651i	$0.835662\pi$
$72$	−17.0592			−2.01044
$73$	1.35615	+	3.27403i	0.158725	+	0.383196i	0.983157	−	0.182766i	$-0.0585049\pi$
$73$	1.35615	+	3.27403i	0.158725	+	0.383196i	−0.824431	+	0.565962i	$0.808505\pi$
$74$	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
$78$	1.25739	−	3.03560i	0.142371	−	0.343714i
$79$	0.477176	−	1.15200i	0.0536865	−	0.129611i	−0.894761	−	0.446546i	$-0.852654\pi$
$79$	0.477176	−	1.15200i	0.0536865	−	0.129611i	0.948447	+	0.316936i	$0.102654\pi$
$80$		0			0
$81$		−	0.170782i		−	0.0189758i
$82$	−15.2819	+	6.32995i	−1.68760	+	0.699026i
$83$	−2.88654	+	2.88654i	−0.316839	+	0.316839i	−0.847552	−	0.530713i	$-0.821924\pi$
$83$	−2.88654	+	2.88654i	−0.316839	+	0.316839i	0.530713	+	0.847552i	$0.321924\pi$
$84$	8.04927			0.878247
$85$		0			0
$86$	11.7282			1.26469
$87$	6.44640	−	6.44640i	0.691126	−	0.691126i
$88$	40.0454	−	16.5874i	4.26886	−	1.76822i
$89$			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
$92$	9.83334	−	23.7398i	1.02520	−	2.47504i
$93$	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
$97$	1.02623	+	2.47754i	0.104198	+	0.251556i	0.967377	−	0.253342i	$-0.0815299\pi$
$97$	1.02623	+	2.47754i	0.104198	+	0.251556i	−0.863179	+	0.504899i	$0.831530\pi$
$98$	−13.4959			−1.36329
$99$	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	$0.829435\pi$
$102$	−2.09973	+	11.6435i	−0.207904	+	1.15288i
$103$		−	13.6466i		−	1.34464i	−0.740259	−	0.672322i	$-0.765297\pi$
$103$		−	13.6466i		−	1.34464i	0.740259	−	0.672322i	$-0.234703\pi$
$104$	−7.34904	−	7.34904i	−0.720633	−	0.720633i
$105$		0			0
$106$			14.9457i			1.45166i
$107$	−5.18598	−	12.5201i	−0.501348	−	1.21036i	−0.948750	−	0.316028i	$-0.897651\pi$
$107$	−5.18598	−	12.5201i	−0.501348	−	1.21036i	0.447402	−	0.894333i	$-0.352349\pi$
$108$	25.5223	+	10.5717i	2.45588	+	1.01726i
$109$	−6.80733	−	2.81969i	−0.652024	−	0.270077i	0.0320540	−	0.999486i	$-0.489795\pi$
$109$	−6.80733	−	2.81969i	−0.652024	−	0.270077i	−0.684078	+	0.729409i	$0.739795\pi$
$110$		0			0
$111$	−1.89341	+	1.89341i	−0.179715	+	0.179715i
$112$	7.56712	−	18.2686i	0.715025	−	1.72622i
$113$	14.8410	+	6.14736i	1.39613	+	0.578295i	0.948744	−	0.316047i	$-0.102356\pi$
$113$	14.8410	+	6.14736i	1.39613	+	0.578295i	0.447384	+	0.894342i	$0.352356\pi$
$114$	−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
$118$			3.55871i			0.327606i
$119$	−1.04035	+	5.76899i	−0.0953689	+	0.528843i
$120$		0			0
$121$	−8.34731	−	8.34731i	−0.758847	−	0.758847i
$122$	16.4169	−	6.80008i	1.48631	−	0.615651i
$123$	6.45920			0.582407
$124$	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	0.388803	−	0.921321i	$-0.372889\pi$
$127$	−6.00118	−	6.00118i	−0.532518	−	0.532518i	−0.921321	+	0.388803i	$0.872889\pi$
$128$	−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	0.254888	−	0.966971i	$-0.417961\pi$
$131$	12.8061	−	5.30445i	1.11887	−	0.463452i	0.863985	+	0.503518i	$0.167961\pi$
$132$	−27.0362			−2.35320
$133$	−9.42258	+	3.90296i	−0.817042	+	0.338430i
$134$	−3.74402	−	3.74402i	−0.323434	−	0.323434i
$135$		0			0
$136$	31.4846	+	20.2303i	2.69978	+	1.73473i
$137$		−	0.471082i		−	0.0402473i	−0.999797	−	0.0201236i	$-0.993594\pi$
$137$		−	0.471082i		−	0.0402473i	0.999797	−	0.0201236i	$-0.00640599\pi$
$138$	−9.74844	+	9.74844i	−0.829842	+	0.829842i
$139$	−1.54005	−	3.71802i	−0.130626	−	0.315358i	0.845012	−	0.534748i	$-0.179593\pi$
$139$	−1.54005	−	3.71802i	−0.130626	−	0.315358i	−0.975637	+	0.219390i	$0.929593\pi$
$140$		0			0
$141$	−4.92445	+	2.03977i	−0.414713	+	0.171780i
$142$	−5.20267	−	2.15502i	−0.436599	−	0.180845i
$143$	−2.09255	+	5.05186i	−0.174988	+	0.422457i
$144$	18.4835	−	18.4835i	1.54030	−	1.54030i
$145$		0			0
$146$	−8.87519	−	3.67622i	−0.734516	−	0.304246i
$147$	4.86896	+	2.01679i	0.401585	+	0.166342i
$148$	5.17734	+	12.4992i	0.425574	+	1.02743i
$149$		−	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	0.913687	−	0.406419i	$-0.133223\pi$
$151$	6.23341	+	6.23341i	0.507268	+	0.507268i	−0.406419	+	0.913687i	$0.633223\pi$
$152$			65.1109i			5.28119i
$153$	−4.18902	+	6.51941i	−0.338662	+	0.527063i
$154$	−18.4049			−1.48311
$155$		0			0
$156$	2.48081	+	5.98920i	0.198624	+	0.479520i
$157$	7.63116			0.609033			0.304517	−	0.952507i	$-0.401505\pi$
$157$	7.63116			0.609033			0.304517	+	0.952507i	$0.401505\pi$
$158$	1.29352	+	3.12283i	0.102907	+	0.248439i
$159$	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
$163$	9.16827	−	22.1342i	0.718115	−	1.73368i	0.0394639	−	0.999221i	$-0.487435\pi$
$163$	9.16827	−	22.1342i	0.718115	−	1.73368i	0.678651	−	0.734461i	$-0.262565\pi$
$164$	12.4889	−	30.1509i	0.975221	−	2.35439i
$165$		0			0
$166$		−	11.0659i		−	0.858880i
$167$	4.32172	−	1.79012i	0.334425	−	0.138523i	−0.209151	−	0.977883i	$-0.567070\pi$
$167$	4.32172	−	1.79012i	0.334425	−	0.138523i	0.543576	+	0.839360i	$0.317070\pi$
$168$	−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
$173$	−13.4145	+	5.55646i	−1.01988	+	0.422450i	−0.829051	−	0.559172i	$-0.811119\pi$
$173$	−13.4145	+	5.55646i	−1.01988	+	0.422450i	−0.190833	+	0.981622i	$0.561119\pi$
$174$			24.7131i			1.87349i
$175$		0			0
$176$	−25.4167	+	61.3614i	−1.91586	+	4.62529i
$177$	0.531802	−	1.28388i	0.0399727	−	0.0965026i
$178$	−16.0021	−	16.0021i	−1.19941	−	1.19941i
$179$	−13.5266	+	13.5266i	−1.01103	+	1.01103i	−0.0110900	+	0.999939i	$0.503530\pi$
$179$	−13.5266	+	13.5266i	−1.01103	+	1.01103i	−0.999939	+	0.0110900i	$0.996470\pi$
$180$		0			0
$181$	−2.49861	+	6.03218i	−0.185720	+	0.448368i	−0.989127	−	0.147062i	$-0.953018\pi$
$181$	−2.49861	+	6.03218i	−0.185720	+	0.448368i	0.803407	+	0.595430i	$0.203018\pi$
$182$	1.68881	+	4.07715i	0.125183	+	0.302218i
$183$	−6.93893			−0.512941
$184$	16.6881	+	40.2886i	1.23026	+	2.97011i
$185$		0			0
$186$	−9.20231			−0.674746
$187$	3.49438	−	19.3771i	0.255534	−	1.41699i
$188$			26.9307i			1.96413i
$189$	−5.19272	−	5.19272i	−0.377715	−	0.377715i
$190$		0			0
$191$		−	19.3014i		−	1.39660i	−0.715806	−	0.698299i	$-0.753941\pi$
$191$		−	19.3014i		−	1.39660i	0.715806	−	0.698299i	$-0.246059\pi$
$192$	10.1984	+	24.6210i	0.736003	+	1.77687i
$193$	1.93841	+	0.802917i	0.139530	+	0.0577952i	0.451356	−	0.892344i	$-0.350941\pi$
$193$	1.93841	+	0.802917i	0.139530	+	0.0577952i	−0.311826	+	0.950139i	$0.600941\pi$
$194$	−6.71608	−	2.78189i	−0.482186	−	0.199728i
$195$		0			0
$196$	18.8283	−	18.8283i	1.34488	−	1.34488i
$197$	5.97048	−	14.4140i	0.425379	−	1.02696i	−0.555356	−	0.831613i	$-0.687418\pi$
$197$	5.97048	−	14.4140i	0.425379	−	1.02696i	0.980735	−	0.195343i	$-0.0625820\pi$
$198$	−22.4780	−	9.31070i	−1.59744	−	0.661683i
$199$	−23.4064	+	9.69526i	−1.65924	+	0.687278i	−0.998019	−	0.0629154i	$-0.979960\pi$
$199$	−23.4064	+	9.69526i	−1.65924	+	0.687278i	−0.661218	+	0.750194i	$0.729960\pi$
$200$		0			0
$201$	0.791244	+	1.91023i	0.0558101	+	0.134737i
$202$	33.1273	−	33.1273i	2.33083	−	2.33083i
$203$			12.2446i			0.859402i
$204$	−13.3146	−	19.1733i	−0.932208	−	1.34240i
$205$		0			0
$206$	26.1581	+	26.1581i	1.82252	+	1.82252i
$207$	−8.34242	+	3.45554i	−0.579838	+	0.240177i
$208$	15.9253			1.10422
$209$	31.6489	−	13.1094i	2.18920	−	0.906798i
$210$		0			0
$211$	3.14022	+	1.30072i	0.216182	+	0.0895453i	0.488146	−	0.872762i	$-0.337673\pi$
$211$	3.14022	+	1.30072i	0.216182	+	0.0895453i	−0.271964	+	0.962307i	$0.587673\pi$
$212$	−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
$217$	−4.55947			−0.309517
$218$	18.4532	−	7.64356i	1.24981	−	0.517687i
$219$	2.65256	+	2.65256i	0.179243	+	0.179243i
$220$		0			0
$221$	−4.61316	+	1.00393i	−0.310315	+	0.0675314i
$222$		−	7.25864i		−	0.487168i
$223$	−7.58368	+	7.58368i	−0.507841	+	0.507841i	−0.913863	−	0.406022i	$-0.866915\pi$
$223$	−7.58368	+	7.58368i	−0.507841	+	0.507841i	0.406022	+	0.913863i	$0.366915\pi$
$224$	10.6360	+	25.6775i	0.710645	+	1.71565i
$225$		0			0
$226$	−40.2308	+	16.6642i	−2.67611	+	1.10848i
$227$	−9.75380	−	4.04015i	−0.647382	−	0.268154i	0.0347359	−	0.999397i	$-0.488941\pi$
$227$	−9.75380	−	4.04015i	−0.647382	−	0.268154i	−0.682118	+	0.731242i	$0.738941\pi$
$228$	15.5418	−	37.5212i	1.02928	−	2.48490i
$229$	−9.07841	+	9.07841i	−0.599918	+	0.599918i	−0.940291	−	0.340372i	$-0.889447\pi$
$229$	−9.07841	+	9.07841i	−0.599918	+	0.599918i	0.340372	+	0.940291i	$0.389447\pi$
$230$		0			0
$231$	6.63998	+	2.75037i	0.436879	+	0.180961i
$232$	72.2202	+	29.9146i	4.74149	+	1.96399i
$233$	10.2740	+	24.8035i	0.673070	+	1.62493i	0.776365	+	0.630283i	$0.217061\pi$
$233$	10.2740	+	24.8035i	0.673070	+	1.62493i	−0.103295	+	0.994651i	$0.532939\pi$
$234$			5.83379i			0.381367i
$235$		0			0
$236$	−4.96480	−	4.96480i	−0.323181	−	0.323181i
$237$		−	1.31993i		−	0.0857388i
$238$	−9.06391	−	13.0522i	−0.587526	−	0.846051i
$239$	4.40382			0.284860			0.142430	−	0.989805i	$-0.454509\pi$
$239$	4.40382			0.284860			0.142430	+	0.989805i	$0.454509\pi$
$240$		0			0
$241$	2.68549	+	6.48334i	0.172987	+	0.417629i	0.986466	−	0.163966i	$-0.0524288\pi$
$241$	2.68549	+	6.48334i	0.172987	+	0.417629i	−0.813478	+	0.581595i	$0.802429\pi$
$242$	32.0005			2.05707
$243$	−5.99906	−	14.4830i	−0.384840	−	0.929086i
$244$	−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
$248$	−11.1392	+	26.8923i	−0.707338	+	1.70767i
$249$	−1.65365	+	3.99227i	−0.104796	+	0.253000i
$250$		0			0
$251$		−	15.3498i		−	0.968873i	−0.874826	−	0.484437i	$-0.839025\pi$
$251$		−	15.3498i		−	0.968873i	0.874826	−	0.484437i	$-0.160975\pi$
$252$	−13.2036	+	5.46912i	−0.831750	+	0.344522i
$253$	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	$0.352882\pi$
$258$	11.4699	−	4.75101i	0.714088	−	0.295785i
$259$		−	3.59644i		−	0.223472i
$260$		0			0
$261$	−6.19431	+	14.9544i	−0.383418	+	0.925654i
$262$	−14.3792	+	34.7145i	−0.888351	+	2.14467i
$263$	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
$267$	3.38181	+	8.16440i	0.206963	+	0.499653i
$268$	10.4467			0.638131
$269$	−6.28235	−	15.1669i	−0.383042	−	0.924745i	−0.991374	−	0.131062i	$-0.958161\pi$
$269$	−6.28235	−	15.1669i	−0.383042	−	0.924745i	0.608332	−	0.793682i	$-0.291839\pi$
$270$		0			0
$271$	11.0378			0.670499			0.335249	−	0.942129i	$-0.391179\pi$
$271$	11.0378			0.670499			0.335249	+	0.942129i	$0.391179\pi$
$272$	−56.0328	+	12.1940i	−3.39749	+	0.739370i
$273$		−	1.72329i		−	0.104298i
$274$	0.902976	+	0.902976i	0.0545508	+	0.0545508i
$275$		0			0
$276$		−	27.2003i		−	1.63727i
$277$	1.07765	+	2.60167i	0.0647496	+	0.156319i	0.952942	−	0.303152i	$-0.0980389\pi$
$277$	1.07765	+	2.60167i	0.0647496	+	0.156319i	−0.888193	+	0.459471i	$0.848039\pi$
$278$	10.0787	+	4.17475i	0.604482	+	0.250385i
$279$	−5.56851	−	2.30655i	−0.333378	−	0.138090i
$280$		0			0
$281$	2.64770	−	2.64770i	0.157949	−	0.157949i	−0.623708	−	0.781657i	$-0.714375\pi$
$281$	2.64770	−	2.64770i	0.157949	−	0.157949i	0.781657	+	0.623708i	$0.214375\pi$
$282$	5.52938	−	13.3491i	0.329270	−	0.794927i
$283$	−22.8421	−	9.46151i	−1.35782	−	0.562428i	−0.419363	−	0.907819i	$-0.637747\pi$
$283$	−22.8421	−	9.46151i	−1.35782	−	0.562428i	−0.938459	+	0.345390i	$0.887747\pi$
$284$	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
$288$			36.7406i			2.16496i
$289$	15.4626	−	7.06459i	0.909564	−	0.415564i
$290$		0			0
$291$	2.00726	+	2.00726i	0.117668	+	0.117668i
$292$	17.5106	−	7.25314i	1.02473	−	0.424458i
$293$	−5.52823			−0.322963			−0.161481	−	0.986876i	$-0.551627\pi$
$293$	−5.52823			−0.322963			−0.161481	+	0.986876i	$0.551627\pi$
$294$	−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
$302$	−23.8966			−1.37509
$303$	−16.9019	+	7.00098i	−0.970987	+	0.402196i
$304$	−70.5474	−	70.5474i	−4.04617	−	4.04617i
$305$		0			0
$306$	−4.46693	−	20.5260i	−0.255357	−	1.17340i
$307$		−	24.0823i		−	1.37445i	−0.726446	−	0.687224i	$-0.758829\pi$
$307$		−	24.0823i		−	1.37445i	0.726446	−	0.687224i	$-0.241171\pi$
$308$	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	−0.423154	−	0.906058i	$-0.639077\pi$
$311$	−1.44060	+	0.596714i	−0.0816887	+	0.0338366i	0.341465	+	0.939895i	$0.389077\pi$
$312$	−10.1642	−	4.21015i	−0.575435	−	0.238353i
$313$	−7.84901	+	18.9492i	−0.443652	+	1.07107i	0.531005	+	0.847369i	$0.321815\pi$
$313$	−7.84901	+	18.9492i	−0.443652	+	1.07107i	−0.974657	+	0.223703i	$0.928185\pi$
$314$	−14.6275	+	14.6275i	−0.825478	+	0.825478i
$315$		0			0
$316$	−6.16131	−	2.55210i	−0.346601	−	0.143567i
$317$	−19.3529	−	8.01624i	−1.08697	−	0.450237i	−0.234019	−	0.972232i	$-0.575188\pi$
$317$	−19.3529	−	8.01624i	−1.08697	−	0.450237i	−0.852948	+	0.521995i	$0.825188\pi$
$318$	6.05438	+	14.6166i	0.339513	+	0.819656i
$319$		−	41.1276i		−	2.30270i
$320$		0			0
$321$	−10.1435	−	10.1435i	−0.566157	−	0.566157i
$322$		−	18.5166i		−	1.03189i
$323$	24.8831	+	15.9885i	1.38453	+	0.889624i
$324$	−0.913401			−0.0507445
$325$		0			0
$326$	24.8532	+	60.0009i	1.37649	+	3.32314i
$327$	−7.79963			−0.431321
$328$	21.1948	+	51.1688i	1.17029	+	2.82533i
$329$	2.73964	−	6.61408i	0.151041	−	0.364646i
$330$		0			0
$331$	1.14575	−	1.14575i	0.0629760	−	0.0629760i	−0.674917	−	0.737893i	$-0.735821\pi$
$331$	1.14575	−	1.14575i	0.0629760	−	0.0629760i	0.737893	+	0.674917i	$0.235821\pi$
$332$	15.4382	+	15.4382i	0.847280	+	0.847280i
$333$	1.81937	−	4.39235i	0.0997010	−	0.240700i
$334$	−4.85261	+	11.7152i	−0.265523	+	0.641030i
$335$		0			0
$336$		−	20.9317i		−	1.14192i
$337$	−9.26190	+	3.83641i	−0.504528	+	0.208982i	−0.620406	−	0.784281i	$-0.713032\pi$
$337$	−9.26190	+	3.83641i	−0.504528	+	0.208982i	0.115878	+	0.993264i	$0.463032\pi$
$338$	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
$343$	−15.7343	+	6.51735i	−0.849571	+	0.351904i
$344$		−	39.2701i		−	2.11730i
$345$		0			0
$346$	15.0624	−	36.3637i	0.809757	−	1.95493i
$347$	−4.64398	+	11.2116i	−0.249302	+	0.601869i	−0.998145	−	0.0608788i	$-0.980610\pi$
$347$	−4.64398	+	11.2116i	−0.249302	+	0.601869i	0.748843	+	0.662747i	$0.230610\pi$
$348$	−34.4775	−	34.4775i	−1.84819	−	1.84819i
$349$	−19.1558	+	19.1558i	−1.02539	+	1.02539i	−0.0257160	+	0.999669i	$0.508187\pi$
$349$	−19.1558	+	19.1558i	−1.02539	+	1.02539i	−0.999669	+	0.0257160i	$0.991813\pi$
$350$		0			0
$351$	2.26332	−	5.46414i	0.120807	−	0.291654i
$352$	−35.7245	−	86.2465i	−1.90412	−	4.59695i
$353$	18.6941			0.994986			0.497493	−	0.867468i	$-0.334254\pi$
$353$	18.6941			0.994986			0.497493	+	0.867468i	$0.334254\pi$
$354$	1.44160	+	3.48033i	0.0766202	+	0.184977i
$355$		0			0
$356$	44.6494			2.36641
$357$	1.31953	+	6.06337i	0.0698367	+	0.320908i
$358$		−	51.8561i		−	2.74068i
$359$	0.959920	+	0.959920i	0.0506626	+	0.0506626i	0.731984	−	0.681322i	$-0.238594\pi$
$359$	0.959920	+	0.959920i	0.0506626	+	0.0506626i	−0.681322	+	0.731984i	$0.738594\pi$
$360$		0			0
$361$			32.4588i			1.70836i
$362$	−6.77318	−	16.3519i	−0.355991	−	0.859437i
$363$	−11.5449	−	4.78205i	−0.605950	−	0.250993i
$364$	−8.04416	−	3.33200i	−0.421629	−	0.174644i
$365$		0			0
$366$	13.3006	−	13.3006i	0.695235	−	0.695235i
$367$	−13.0364	+	31.4726i	−0.680493	+	1.64285i	0.0826132	+	0.996582i	$0.473673\pi$
$367$	−13.0364	+	31.4726i	−0.680493	+	1.64285i	−0.763106	+	0.646273i	$0.776327\pi$
$368$	−61.7339	−	25.5710i	−3.21810	−	1.33298i
$369$	−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
$373$			0.465809i			0.0241187i	0.999927	+	0.0120593i	$0.00383870\pi$
$373$			0.465809i			0.0241187i	−0.999927	+	0.0120593i	$0.996161\pi$
$374$	30.4442	+	43.8403i	1.57423	+	2.26693i
$375$		0			0
$376$	−32.3175	−	32.3175i	−1.66665	−	1.66665i
$377$	−9.11080	+	3.77382i	−0.469230	+	0.194361i
$378$	19.9069			1.02390
$379$	12.1522	−	5.03360i	0.624216	−	0.258559i	−0.0480776	−	0.998844i	$-0.515309\pi$
$379$	12.1522	−	5.03360i	0.624216	−	0.258559i	0.672293	+	0.740285i	$0.265309\pi$
$380$		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
$387$	8.13154			0.413349
$388$	13.2507	−	5.48864i	0.672704	−	0.278643i
$389$	14.5372	+	14.5372i	0.737064	+	0.737064i	0.972009	−	0.234945i	$-0.0754910\pi$
$389$	14.5372	+	14.5372i	0.737064	+	0.737064i	−0.234945	+	0.972009i	$0.575491\pi$
$390$		0			0
$391$	19.4948	+	3.51559i	0.985892	+	0.177791i
$392$			45.1889i			2.28239i
$393$	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
$397$	27.5479	+	11.4107i	1.38259	+	0.572687i	0.945172	−	0.326572i	$-0.105894\pi$
$397$	27.5479	+	11.4107i	1.38259	+	0.572687i	0.437416	+	0.899259i	$0.355894\pi$
$398$	26.2817	−	63.4497i	1.31738	−	3.18045i
$399$	−7.63401	+	7.63401i	−0.382178	+	0.382178i
$400$		0			0
$401$	4.40094	+	1.82293i	0.219773	+	0.0910328i	0.489853	−	0.871805i	$-0.337050\pi$
$401$	4.40094	+	1.82293i	0.219773	+	0.0910328i	−0.270081	+	0.962838i	$0.587050\pi$
$402$	−5.17823	−	2.14489i	−0.258266	−	0.106977i
$403$	−1.40524	−	3.39255i	−0.0700000	−	0.168995i
$404$			92.4327i			4.59870i
$405$		0			0
$406$	−23.4706	−	23.4706i	−1.16483	−	1.16483i
$407$			12.0799i			0.598776i
$408$	38.9863	+	7.03060i	1.93011	+	0.348066i
$409$	32.0852			1.58651			0.793256	−	0.608888i	$-0.208384\pi$
$409$	32.0852			1.58651			0.793256	+	0.608888i	$0.208384\pi$
$410$		0			0
$411$	−0.190831	−	0.460707i	−0.00941301	−	0.0227250i
$412$	−72.9869			−3.59581
$413$	0.714270	+	1.72440i	0.0351469	+	0.0848522i
$414$	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
$418$	−35.5368	+	85.7934i	−1.73816	+	4.19629i
$419$	−6.70745	+	16.1932i	−0.327680	+	0.791090i	0.671083	+	0.741382i	$0.265829\pi$
$419$	−6.70745	+	16.1932i	−0.327680	+	0.791090i	−0.998764	+	0.0497086i	$0.984171\pi$
$420$		0			0
$421$			27.4320i			1.33695i	0.743733	+	0.668477i	$0.233054\pi$
$421$			27.4320i			1.33695i	−0.743733	+	0.668477i	$0.766946\pi$
$422$	−8.51245	+	3.52597i	−0.414379	+	0.171642i
$423$	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
$428$	−66.9616	+	27.7364i	−3.23671	+	1.34069i
$429$			5.78827i			0.279460i
$430$		0			0
$431$	3.33847	−	8.05979i	0.160809	−	0.388226i	−0.822853	−	0.568255i	$-0.807619\pi$
$431$	3.33847	−	8.05979i	0.160809	−	0.388226i	0.983661	+	0.180028i	$0.0576189\pi$
$432$	27.4910	−	66.3692i	1.32266	−	3.19319i
$433$	−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
$437$	13.1890	+	31.8411i	0.630916	+	1.52317i
$438$	−10.1689			−0.485890
$439$	−8.84357	−	21.3503i	−0.422080	−	1.01899i	−0.981733	−	0.190265i	$-0.939065\pi$
$439$	−8.84357	−	21.3503i	−0.422080	−	1.01899i	0.559652	−	0.828727i	$-0.310935\pi$
$440$		0			0
$441$	−9.35713			−0.445577
$442$	6.91822	−	10.7669i	0.329066	−	0.512129i
$443$		−	0.787522i		−	0.0374163i	−0.999825	−	0.0187081i	$-0.994045\pi$
$443$		−	0.787522i		−	0.0374163i	0.999825	−	0.0187081i	$-0.00595533\pi$
$444$	10.1266	+	10.1266i	0.480588	+	0.480588i
$445$		0			0
$446$		−	29.0730i		−	1.37665i
$447$	−3.10257	−	7.49025i	−0.146746	−	0.354277i
$448$	−33.0688	−	13.6975i	−1.56235	−	0.647147i
$449$	−18.6440	−	7.72258i	−0.879863	−	0.364451i	−0.103419	−	0.994638i	$-0.532978\pi$
$449$	−18.6440	−	7.72258i	−0.879863	−	0.364451i	−0.776444	+	0.630187i	$0.782978\pi$
$450$		0			0
$451$	20.6046	−	20.6046i	0.970235	−	0.970235i
$452$	32.8782	−	79.3749i	1.54646	−	3.73348i
$453$	8.62123	+	3.57103i	0.405061	+	0.167782i
$454$	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	$0.301970\pi$
$458$		−	34.8032i		−	1.62625i
$459$	−3.77955	+	20.9585i	−0.176414	+	0.978259i
$460$		0			0
$461$	−4.93835	−	4.93835i	−0.230002	−	0.230002i	0.582692	−	0.812693i	$-0.302000\pi$
$461$	−4.93835	−	4.93835i	−0.230002	−	0.230002i	−0.812693	+	0.582692i	$0.802000\pi$
$462$	−17.9995	+	7.45565i	−0.837414	+	0.346868i
$463$	8.07063			0.375074			0.187537	−	0.982258i	$-0.439950\pi$
$463$	8.07063			0.375074			0.187537	+	0.982258i	$0.439950\pi$
$464$	−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	0.786710	−	0.617322i	$-0.211783\pi$
$467$	3.66051	+	3.66051i	0.169388	+	0.169388i	−0.617322	+	0.786710i	$0.711783\pi$
$468$	−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
$472$	11.9158			0.548467
$473$	−19.0883	+	7.90665i	−0.877682	+	0.363548i
$474$	2.53006	+	2.53006i	0.116210	+	0.116210i
$475$		0			0
$476$	30.8545	+	5.56416i	1.41421	+	0.255033i
$477$			10.3623i			0.474458i
$478$	−8.44130	+	8.44130i	−0.386096	+	0.386096i
$479$	−10.8407	−	26.1717i	−0.495323	−	1.19581i	−0.951977	−	0.306171i	$-0.900952\pi$
$479$	−10.8407	−	26.1717i	−0.495323	−	1.19581i	0.456654	−	0.889644i	$-0.349048\pi$
$480$		0			0
$481$	2.67599	−	1.10843i	0.122015	−	0.0505402i
$482$	−17.5749	−	7.27977i	−0.800516	−	0.331585i
$483$	−2.76707	+	6.68029i	−0.125906	+	0.303964i
$484$	−44.6443	+	44.6443i	−2.02928	+	2.02928i
$485$		0			0
$486$	39.2603	+	16.2621i	1.78088	+	0.737666i
$487$	17.0711	+	7.07109i	0.773567	+	0.320422i	0.734316	−	0.678808i	$-0.237503\pi$
$487$	17.0711	+	7.07109i	0.773567	+	0.320422i	0.0392506	+	0.999229i	$0.487503\pi$
$488$	−22.7690	−	54.9692i	−1.03070	−	2.48834i
$489$		−	25.3607i		−	1.14685i
$490$		0			0
$491$	−10.1423	−	10.1423i	−0.457714	−	0.457714i	0.440190	−	0.897905i	$-0.354911\pi$
$491$	−10.1423	−	10.1423i	−0.457714	−	0.457714i	−0.897905	+	0.440190i	$0.854911\pi$
$492$		−	34.5460i		−	1.55745i
$493$	29.1665	−	20.2542i	1.31359	−	0.912205i
$494$	22.2662			1.00180
$495$		0			0
$496$	−17.0685	−	41.2070i	−0.766398	−	1.85025i
$497$	−2.95353			−0.132484
$498$	−4.48269	−	10.8222i	−0.200874	−	0.484953i
$499$	−12.7071	+	30.6775i	−0.568846	+	1.37332i	0.333683	+	0.942685i	$0.391709\pi$
$499$	−12.7071	+	30.6775i	−0.568846	+	1.37332i	−0.902529	+	0.430630i	$0.858291\pi$
$500$		0			0
$501$	3.50138	−	3.50138i	0.156430	−	0.156430i
$502$	29.4228	+	29.4228i	1.31320	+	1.31320i
$503$	1.70275	−	4.11079i	0.0759217	−	0.183291i	−0.881362	−	0.472442i	$-0.843373\pi$
$503$	1.70275	−	4.11079i	0.0759217	−	0.183291i	0.957284	+	0.289150i	$0.0933728\pi$
$504$	9.28159	−	22.4077i	0.413435	−	0.998120i
$505$		0			0
$506$			62.1944i			2.76488i
$507$	−11.4314	+	4.73506i	−0.507688	+	0.210291i
$508$	−32.0963	+	32.0963i	−1.42404	+	1.42404i
$509$	31.7678			1.40808			0.704041	−	0.710159i	$-0.251377\pi$
$509$	31.7678			1.40808			0.704041	+	0.710159i	$0.251377\pi$
$510$		0			0
$511$	−5.03840			−0.222886
$512$	−13.7212	+	13.7212i	−0.606398	+	0.606398i
$513$	−34.2318	+	14.1793i	−1.51137	+	0.626031i
$514$		−	27.6053i		−	1.21762i
$515$		0			0
$516$	−9.37368	+	22.6301i	−0.412653	+	0.996233i
$517$	−9.20202	+	22.2156i	−0.404704	+	0.977042i
$518$	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	0.174526	+	0.984653i	$0.444161\pi$
$521$	−14.7255	+	35.5506i	−0.645137	+	1.55750i	−0.819663	+	0.572846i	$0.805839\pi$
$522$	−16.7914	−	40.5381i	−0.734941	−	1.77430i
$523$	−13.6513			−0.596930			−0.298465	−	0.954421i	$-0.596475\pi$
$523$	−13.6513			−0.596930			−0.298465	+	0.954421i	$0.596475\pi$
$524$	−28.3700	−	68.4913i	−1.23935	−	2.99206i
$525$		0			0
$526$	−0.414261			−0.0180627
$527$	7.54199	+	10.8606i	0.328534	+	0.473096i
$528$			70.3061i			3.05968i
$529$	0.0584274	+	0.0584274i	0.00254032	+	0.00254032i
$530$		0			0
$531$			2.46736i			0.107074i
$532$	20.8744	+	50.3952i	0.905018	+	2.18491i
$533$	−6.45511	−	2.67379i	−0.279602	−	0.115815i
$534$	−22.1319	−	9.16734i	−0.957742	−	0.396710i
$535$		0			0
$536$	−12.5362	+	12.5362i	−0.541483	+	0.541483i
$537$	−7.74921	+	18.7082i	−0.334403	+	0.807320i
$538$	41.1143	+	17.0301i	1.77256	+	0.734219i
$539$	21.9653	−	9.09833i	0.946113	−	0.391893i
$540$		0			0
$541$	2.59149	+	6.25641i	0.111417	+	0.268984i	0.969746	−	0.244115i	$-0.0784974\pi$
$541$	2.59149	+	6.25641i	0.111417	+	0.268984i	−0.858329	+	0.513099i	$0.828497\pi$
$542$	−21.1574	+	21.1574i	−0.908788	+	0.908788i
$543$			6.91149i			0.296600i
$544$	43.5703	−	67.8089i	1.86806	−	2.90728i
$545$		0			0
$546$	3.30323	+	3.30323i	0.141365	+	0.141365i
$547$	−12.5961	+	5.21748i	−0.538571	+	0.223084i	−0.635353	−	0.772222i	$-0.719145\pi$
$547$	−12.5961	+	5.21748i	−0.538571	+	0.223084i	0.0967813	+	0.995306i	$0.469145\pi$
$548$	−2.51951			−0.107628
$549$	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
$557$	−37.3500			−1.58257			−0.791285	−	0.611448i	$-0.790587\pi$
$557$	−37.3500			−1.58257			−0.791285	+	0.611448i	$0.790587\pi$
$558$	15.0950	−	6.25256i	0.639023	−	0.264692i
$559$	3.50304	+	3.50304i	0.148163	+	0.148163i
$560$		0			0
$561$	−4.43208	−	20.3659i	−0.187122	−	0.859848i
$562$			10.1503i			0.428165i
$563$	21.1992	−	21.1992i	0.893440	−	0.893440i	−0.101405	−	0.994845i	$-0.532334\pi$
$563$	21.1992	−	21.1992i	0.893440	−	0.893440i	0.994845	+	0.101405i	$0.0323338\pi$
$564$	10.9094	+	26.3376i	0.459368	+	1.10901i
$565$		0			0
$566$	61.9200	−	25.6481i	2.60269	−	1.07807i
$567$	0.224328	+	0.0929195i	0.00942087	+	0.00390225i
$568$	−7.21573	+	17.4203i	−0.302765	+	0.730940i
$569$	9.38514	−	9.38514i	0.393446	−	0.393446i	−0.482468	−	0.875914i	$-0.660260\pi$
$569$	9.38514	−	9.38514i	0.393446	−	0.393446i	0.875914	+	0.482468i	$0.160260\pi$
$570$		0			0
$571$	−10.1419	−	4.20092i	−0.424426	−	0.175803i	0.160238	−	0.987078i	$-0.448774\pi$
$571$	−10.1419	−	4.20092i	−0.424426	−	0.175803i	−0.584664	+	0.811275i	$0.698774\pi$
$572$	27.0190	+	11.1917i	1.12972	+	0.467946i
$573$	−7.81881	−	18.8763i	−0.326635	−	0.788568i
$574$		−	23.5172i		−	0.981589i
$575$		0			0
$576$	−33.4578	−	33.4578i	−1.39407	−	1.39407i
$577$		−	35.5804i		−	1.48123i	−0.671930	−	0.740615i	$-0.734534\pi$
$577$		−	35.5804i		−	1.48123i	0.671930	−	0.740615i	$-0.265466\pi$
$578$	−16.0974	+	43.1804i	−0.669563	+	1.79607i
$579$	2.22098			0.0923006
$580$		0			0
$581$	−2.22104	−	5.36207i	−0.0921443	−	0.222456i
$582$	−7.69508			−0.318971
$583$	−10.0757	−	24.3249i	−0.417294	−	1.00744i
$584$	−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	0.817337	−	0.576160i	$-0.195449\pi$
$587$	5.84325	+	5.84325i	0.241177	+	0.241177i	−0.576160	+	0.817337i	$0.695449\pi$
$588$	10.7865	−	26.0409i	0.444827	−	1.07391i
$589$	−8.80357	+	21.2537i	−0.362745	+	0.875744i
$590$		0			0
$591$		−	16.5151i		−	0.679342i
$592$	32.5034	−	13.4634i	1.33588	−	0.553341i
$593$	−2.13713	+	2.13713i	−0.0877612	+	0.0877612i	−0.749625	−	0.661863i	$-0.769766\pi$
$593$	−2.13713	+	2.13713i	−0.0877612	+	0.0877612i	0.661863	+	0.749625i	$0.269766\pi$
$594$	−66.8642			−2.74347
$595$		0			0
$596$	−40.9626			−1.67789
$597$	−18.9634	+	18.9634i	−0.776122	+	0.776122i
$598$	13.7776	−	5.70688i	0.563409	−	0.233372i
$599$		−	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	−0.935469	−	0.353408i	$-0.885023\pi$
$601$	−0.590707	+	1.42609i	−0.0240954	+	0.0581716i	0.911374	+	0.411580i	$0.135023\pi$
$602$	−6.38113	+	15.4054i	−0.260076	+	0.627878i
$603$	−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
$607$	−14.1190	−	34.0864i	−0.573074	−	1.38352i	−0.898925	−	0.438102i	$-0.855651\pi$
$607$	−14.1190	−	34.0864i	−0.573074	−	1.38352i	0.325851	−	0.945421i	$-0.394349\pi$
$608$	140.230			5.68709
$609$	4.96017	+	11.9749i	0.200996	+	0.485248i
$610$		0			0
$611$	5.76569			0.233255
$612$	34.8680	+	22.4043i	1.40946	+	0.905639i
$613$			20.1267i			0.812911i	0.913671	+	0.406455i	$0.133235\pi$
$613$			20.1267i			0.812911i	−0.913671	+	0.406455i	$0.866765\pi$
$614$	46.1612	+	46.1612i	1.86291	+	1.86291i
$615$		0			0
$616$			61.6258i			2.48297i
$617$	−10.9026	−	26.3211i	−0.438921	−	1.05965i	−0.976322	−	0.216322i	$-0.930594\pi$
$617$	−10.9026	−	26.3211i	−0.438921	−	1.05965i	0.537401	−	0.843327i	$-0.319406\pi$
$618$	36.1783	+	14.9856i	1.45531	+	0.602807i
$619$	−10.0301	−	4.15459i	−0.403142	−	0.166987i	0.171893	−	0.985116i	$-0.445012\pi$
$619$	−10.0301	−	4.15459i	−0.403142	−	0.166987i	−0.575035	+	0.818129i	$0.695012\pi$
$620$		0			0
$621$	−17.5474	+	17.5474i	−0.704153	+	0.704153i
$622$	1.61756	−	3.90514i	0.0648583	−	0.156582i
$623$	−10.9657	−	4.54214i	−0.439332	−	0.181977i
$624$	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
$628$		−	40.8140i		−	1.62866i
$629$	−8.56669	+	5.94900i	−0.341576	+	0.237202i
$630$		0			0
$631$	−23.8783	−	23.8783i	−0.950579	−	0.950579i	0.0482559	−	0.998835i	$-0.484634\pi$
$631$	−23.8783	−	23.8783i	−0.950579	−	0.950579i	−0.998835	+	0.0482559i	$0.984634\pi$
$632$	10.4563	−	4.33114i	0.415929	−	0.172283i
$633$	3.59797			0.143006
$634$	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	−0.0985897	−	0.995128i	$-0.531433\pi$
$641$	13.5542	−	5.61433i	0.535359	−	0.221753i	0.633948	+	0.773375i	$0.281433\pi$
$642$	38.8865			1.53473
$643$	23.4428	−	9.71032i	0.924493	−	0.382938i	0.130906	−	0.991395i	$-0.458211\pi$
$643$	23.4428	−	9.71032i	0.924493	−	0.382938i	0.793587	+	0.608457i	$0.208211\pi$
$644$	25.8328	+	25.8328i	1.01795	+	1.01795i
$645$		0			0
$646$	−78.3431	+	17.0492i	−3.08237	+	0.670793i
$647$		−	37.8459i		−	1.48788i	−0.668248	−	0.743939i	$-0.732955\pi$
$647$		−	37.8459i		−	1.48788i	0.668248	−	0.743939i	$-0.267045\pi$
$648$	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
$652$	−118.381	−	49.0350i	−4.63616	−	1.92036i
$653$	−12.5661	+	30.3372i	−0.491748	+	1.18718i	0.462082	+	0.886837i	$0.347103\pi$
$653$	−12.5661	+	30.3372i	−0.491748	+	1.18718i	−0.953830	+	0.300348i	$0.902897\pi$
$654$	14.9504	−	14.9504i	0.584608	−	0.584608i
$655$		0			0
$656$	−78.4057	−	32.4767i	−3.06123	−	1.26800i
$657$	−6.15343	−	2.54883i	−0.240068	−	0.0994394i
$658$	7.42657	+	17.9293i	0.289518	+	0.698958i
$659$		−	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	0.664963	−	0.746877i	$-0.268447\pi$
$661$	−2.10600	−	2.10600i	−0.0819139	−	0.0819139i	−0.746877	+	0.664963i	$0.768447\pi$
$662$			4.39236i			0.170714i
$663$	−4.10487	+	2.85056i	−0.159420	+	0.110707i
$664$	−37.0524			−1.43791
$665$		0			0
$666$	4.93192	+	11.9067i	0.191108	+	0.461376i
$667$	41.3773			1.60213
$668$	−9.57415	−	23.1140i	−0.370435	−	0.894309i
$669$	−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
$673$	12.3999	−	29.9359i	0.477979	−	1.15394i	−0.482576	−	0.875854i	$-0.660299\pi$
$673$	12.3999	−	29.9359i	0.477979	−	1.15394i	0.960555	−	0.278090i	$-0.0897013\pi$
$674$	10.3997	−	25.1070i	0.400580	−	0.967086i
$675$		0			0
$676$			62.5161i			2.40446i
$677$	37.5918	−	15.5710i	1.44477	−	0.598443i	0.483820	−	0.875168i	$-0.339249\pi$
$677$	37.5918	−	15.5710i	1.44477	−	0.598443i	0.960949	+	0.276725i	$0.0892491\pi$
$678$	−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
$683$	20.4261	−	8.46078i	0.781584	−	0.323743i	0.0440293	−	0.999030i	$-0.485980\pi$
$683$	20.4261	−	8.46078i	0.781584	−	0.323743i	0.737554	+	0.675288i	$0.235980\pi$
$684$			72.1079i			2.75711i
$685$		0			0
$686$	17.6671	−	42.6522i	0.674533	−	1.62847i
$687$	−5.20088	+	12.5560i	−0.198426	+	0.479043i
$688$	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	−0.861496	−	0.507765i	$-0.830472\pi$
$691$	2.80528	−	6.77255i	0.106718	−	0.257640i	0.968214	+	0.250125i	$0.0804718\pi$
$692$	29.7178	+	71.7452i	1.12970	+	2.72734i
$693$	−12.7607			−0.484737
$694$	−12.5888	−	30.3921i	−0.477865	−	1.15367i
$695$		0			0
$696$	82.7477			3.13654
$697$	24.7595	+	4.46500i	0.937832	+	0.169124i
$698$		−	73.4361i		−	2.77960i
$699$	20.0954	+	20.0954i	0.760077	+	0.760077i
$700$		0			0
$701$		−	45.6656i		−	1.72477i	−0.506255	−	0.862384i	$-0.668971\pi$
$701$		−	45.6656i		−	1.72477i	0.506255	−	0.862384i	$-0.331029\pi$
$702$	6.13537	+	14.8121i	0.231565	+	0.559047i
$703$	−16.7646	−	6.94412i	−0.632289	−	0.261903i
$704$	111.073	+	46.0078i	4.18621	+	1.73398i
$705$		0			0
$706$	−35.8331	+	35.8331i	−1.34859	+	1.34859i
$707$	9.40310	−	22.7011i	0.353640	−	0.853762i
$708$	−6.86665	−	2.84426i	−0.258064	−	0.106894i
$709$	−42.2410	+	17.4968i	−1.58639	+	0.657105i	−0.989410	−	0.145149i	$-0.953634\pi$
$709$	−42.2410	+	17.4968i	−1.58639	+	0.657105i	−0.596983	+	0.802254i	$0.703634\pi$
$710$		0			0
$711$	0.896835	+	2.16515i	0.0336339	+	0.0811995i
$712$	−53.5803	+	53.5803i	−2.00801	+	2.00801i
$713$			15.4075i			0.577015i
$714$	−14.1516	−	9.09306i	−0.529611	−	0.340299i
$715$		0			0
$716$	72.3450	+	72.3450i	2.70366	+	2.70366i
$717$	4.30683	−	1.78395i	0.160842	−	0.0666227i
$718$	−3.67997			−0.137335
$719$	−0.497733	+	0.206168i	−0.0185623	+	0.00768877i	−0.391945	−	0.919989i	$-0.628198\pi$
$719$	−0.497733	+	0.206168i	−0.0185623	+	0.00768877i	0.373383	+	0.927677i	$0.378198\pi$
$720$		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
$727$	−42.2238			−1.56600			−0.782998	−	0.622025i	$-0.786310\pi$
$727$	−42.2238			−1.56600			−0.782998	+	0.622025i	$0.786310\pi$
$728$	13.6517	−	5.65471i	0.505965	−	0.209577i
$729$	−11.3716	−	11.3716i	−0.421170	−	0.421170i
$730$		0			0
$731$	−15.0077	−	9.64310i	−0.555078	−	0.356663i
$732$			37.1118i			1.37169i
$733$	2.67745	−	2.67745i	0.0988939	−	0.0988939i	−0.655929	−	0.754823i	$-0.727723\pi$
$733$	2.67745	−	2.67745i	0.0988939	−	0.0988939i	0.754823	+	0.655929i	$0.227723\pi$
$734$	−35.3387	−	85.3153i	−1.30438	−	3.14904i
$735$		0			0
$736$	86.7701	−	35.9414i	3.19839	−	1.32482i
$737$	8.61762	+	3.56954i	0.317434	+	0.131486i
$738$	11.8969	−	28.7217i	0.437932	−	1.05726i
$739$	12.9186	−	12.9186i	0.475219	−	0.475219i	−0.428380	−	0.903599i	$-0.640916\pi$
$739$	12.9186	−	12.9186i	0.475219	−	0.475219i	0.903599	+	0.428380i	$0.140916\pi$
$740$		0			0
$741$	−8.03304	−	3.32739i	−0.295101	−	0.122235i
$742$	−19.6317	−	8.13170i	−0.720701	−	0.298524i
$743$	5.07884	+	12.2614i	0.186325	+	0.449827i	0.989247	−	0.146257i	$-0.0467226\pi$
$743$	5.07884	+	12.2614i	0.186325	+	0.449827i	−0.802922	+	0.596084i	$0.796723\pi$
$744$			30.8124i			1.12964i
$745$		0			0
$746$	−0.892868	−	0.892868i	−0.0326902	−	0.0326902i
$747$		−	7.67231i		−	0.280715i
$748$	−103.635	−	18.6891i	−3.78928	−	0.683341i
$749$	19.2671			0.704004
$750$		0			0
$751$	−1.13681	−	2.74450i	−0.0414828	−	0.100148i	0.901780	−	0.432195i	$-0.142261\pi$
$751$	−1.13681	−	2.74450i	−0.0414828	−	0.100148i	−0.943263	+	0.332047i	$0.892261\pi$
$752$	70.0318			2.55380
$753$	−6.21808	−	15.0118i	−0.226599	−	0.547059i
$754$	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	0.990161	−	0.139934i	$-0.0446892\pi$
$757$	23.3928	+	23.3928i	0.850226	+	0.850226i	−0.139934	+	0.990161i	$0.544689\pi$
$758$	−13.6450	+	32.9419i	−0.495608	+	1.19650i
$759$	9.29414	−	22.4380i	0.337356	−	0.814449i
$760$		0			0
$761$		−	2.82578i		−	0.102434i	−0.998688	−	0.0512172i	$-0.983690\pi$
$761$		−	2.82578i		−	0.102434i	0.998688	−	0.0512172i	$-0.0163101\pi$
$762$	22.4996	−	9.31962i	0.815073	−	0.337614i
$763$	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
$768$	28.0325	−	11.6115i	1.01154	−	0.418992i
$769$			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
$772$	4.29427	−	10.3673i	0.154554	−	0.373127i
$773$	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
$777$	−1.45688	−	3.51723i	−0.0522654	−	0.126180i
$778$	−55.7301			−1.99802
$779$	16.7508	+	40.4400i	0.600160	+	1.44891i
$780$		0			0
$781$	9.92043			0.354981
$782$	−44.1065	+	30.6291i	−1.57725	+	1.09529i
$783$			44.4841i			1.58973i
$784$	−48.9620	−	48.9620i	−1.74864	−	1.74864i
$785$		0			0
$786$			39.7748i			1.41872i
$787$	−3.85132	−	9.29791i	−0.137285	−	0.331435i	0.840253	−	0.542194i	$-0.182406\pi$
$787$	−3.85132	−	9.29791i	−0.137285	−	0.331435i	−0.977538	+	0.210760i	$0.932406\pi$
$788$	−77.0910	−	31.9321i	−2.74625	−	1.13754i
$789$	0.149454	+	0.0619059i	0.00532071	+	0.00220391i
$790$		0			0
$791$	−16.1495	+	16.1495i	−0.574210	+	0.574210i
$792$	−31.1754	+	75.2640i	−1.10777	+	2.67439i
$793$	6.93453	+	2.87238i	0.246252	+	0.102001i
$794$	−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	$0.198343\pi$
$798$		−	29.2659i		−	1.03600i
$799$	−20.2864	+	4.41479i	−0.717683	+	0.156184i
$800$		0			0
$801$	−11.0947	−	11.0947i	−0.392012	−	0.392012i
$802$	−11.9300	+	4.94157i	−0.421263	+	0.174493i
$803$	16.9232			0.597205
$804$	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	$-0.406823\pi$
$809$	−5.24543	−	2.17273i	−0.184419	−	0.0763890i	−0.472982	+	0.881072i	$0.656823\pi$
$810$		0			0
$811$	−4.12057	+	1.70680i	−0.144693	+	0.0599338i	−0.453855	−	0.891076i	$-0.649952\pi$
$811$	−4.12057	+	1.70680i	−0.144693	+	0.0599338i	0.309162	+	0.951009i	$0.399952\pi$
$812$	65.4882			2.29819
$813$	10.7947	−	4.47131i	0.378587	−	0.156816i
$814$	−23.1548	−	23.1548i	−0.811576	−	0.811576i
$815$		0			0
$816$	−49.8591	+	34.6238i	−1.74542	+	1.21208i
$817$		−	31.0362i		−	1.08582i
$818$	−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	−0.987770	−	0.155919i	$-0.950166\pi$
$821$	−45.1566	+	18.7045i	−1.57598	+	0.652791i	−0.588207	+	0.808710i	$0.700166\pi$
$822$	1.24888	+	0.517302i	0.0435596	+	0.0180430i
$823$	−18.3012	+	44.1829i	−0.637939	+	1.54012i	0.191482	+	0.981496i	$0.438671\pi$
$823$	−18.3012	+	44.1829i	−0.637939	+	1.54012i	−0.829421	+	0.558625i	$0.811329\pi$
$824$	87.5860	−	87.5860i	3.05120	−	3.05120i
$825$		0			0
$826$	−4.67447	−	1.93623i	−0.162646	−	0.0673700i
$827$	18.0554	+	7.47877i	0.627846	+	0.260062i	0.673838	−	0.738879i	$-0.264645\pi$
$827$	18.0554	+	7.47877i	0.627846	+	0.260062i	−0.0459914	+	0.998942i	$0.514645\pi$
$828$	18.4814	+	44.6181i	0.642274	+	1.55059i
$829$		−	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
$832$		−	28.8270i		−	0.999397i
$833$	17.2696	+	11.0965i	0.598357	+	0.384471i
$834$	11.5479			0.399871
$835$		0			0
$836$	−70.1136	−	169.269i	−2.42493	−	5.85430i
$837$	−16.5643			−0.572548
$838$	−18.1824	−	43.8963i	−0.628102	−	1.51637i
$839$	−14.9656	+	36.1301i	−0.516670	+	1.24735i	0.423268	+	0.906005i	$0.360883\pi$
$839$	−14.9656	+	36.1301i	−0.516670	+	1.24735i	−0.939938	+	0.341346i	$0.889117\pi$
$840$		0			0
$841$	31.9413	−	31.9413i	1.10142	−	1.10142i
$842$	−52.5820	−	52.5820i	−1.81210	−	1.81210i
$843$	1.51683	−	3.66195i	0.0522424	−	0.126124i
$844$	6.95670	−	16.7950i	0.239459	−	0.578106i
$845$		0			0
$846$			25.6542i			0.882009i
$847$	15.5061	−	6.42283i	0.532795	−	0.220691i
$848$	−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
$853$	23.1204	−	9.57677i	0.791626	−	0.327902i	0.0500291	−	0.998748i	$-0.484069\pi$
$853$	23.1204	−	9.57677i	0.791626	−	0.327902i	0.741597	+	0.670845i	$0.234069\pi$
$854$			25.2638i			0.864511i
$855$		0			0
$856$	47.0712	−	113.640i	1.60886	−	3.88413i
$857$	14.4900	−	34.9820i	0.494970	−	1.19496i	−0.457191	−	0.889368i	$-0.651144\pi$
$857$	14.4900	−	34.9820i	0.494970	−	1.19496i	0.952161	−	0.305596i	$-0.0988555\pi$
$858$	−11.0950	−	11.0950i	−0.378778	−	0.378778i
$859$	−12.1975	+	12.1975i	−0.416172	+	0.416172i	−0.883882	−	0.467710i	$-0.845079\pi$
$859$	−12.1975	+	12.1975i	−0.416172	+	0.416172i	0.467710	+	0.883882i	$0.345079\pi$
$860$		0			0
$861$	−3.51434	+	8.48436i	−0.119768	+	0.289146i
$862$	9.04988	+	21.8483i	0.308240	+	0.744157i
$863$	−49.4684			−1.68392			−0.841962	−	0.539537i	$-0.818599\pi$
$863$	−49.4684			−1.68392			−0.841962	+	0.539537i	$0.818599\pi$
$864$	38.6400	+	93.2851i	1.31456	+	3.17363i
$865$		0			0
$866$	26.3314			0.894778
$867$	12.2602	−	13.1728i	0.416379	−	0.447370i
$868$			24.3856i			0.827700i
$869$	−4.21054	−	4.21054i	−0.142833	−	0.142833i
$870$		0			0
$871$		−	2.23656i		−	0.0757829i
$872$	−25.5932	−	61.7875i	−0.866696	−	2.09239i
$873$	−4.65646	−	1.92877i	−0.157597	−	0.0652789i
$874$	−86.3142	−	35.7525i	−2.91962	−	1.20935i
$875$		0			0
$876$	14.1868	−	14.1868i	0.479327	−	0.479327i
$877$	21.2686	−	51.3470i	0.718191	−	1.73387i	0.0397521	−	0.999210i	$-0.487343\pi$
$877$	21.2686	−	51.3470i	0.718191	−	1.73387i	0.678439	−	0.734657i	$-0.262657\pi$
$878$	57.8759	+	23.9730i	1.95322	+	0.809049i
$879$	−5.40648	+	2.23944i	−0.182356	+	0.0755343i
$880$		0			0
$881$	14.9186	+	36.0167i	0.502621	+	1.21343i	0.948051	+	0.318117i	$0.103051\pi$
$881$	14.9186	+	36.0167i	0.502621	+	1.21343i	−0.445431	+	0.895316i	$0.646949\pi$
$882$	17.9359	−	17.9359i	0.603932	−	0.603932i
$883$		−	27.2502i		−	0.917042i	−0.888684	−	0.458521i	$-0.848379\pi$
$883$		−	27.2502i		−	0.917042i	0.888684	−	0.458521i	$-0.151621\pi$
$884$	5.36934	+	24.6727i	0.180590	+	0.829834i
$885$		0			0
$886$	1.50953	+	1.50953i	0.0507137	+	0.0507137i
$887$	−38.8009	+	16.0719i	−1.30281	+	0.539640i	−0.922777	−	0.385334i	$-0.874086\pi$
$887$	−38.8009	+	16.0719i	−1.30281	+	0.539640i	−0.380030	+	0.924974i	$0.624086\pi$
$888$	−24.3044			−0.815601
$889$	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
$897$	−5.82341			−0.194438
$898$	50.5397	−	20.9342i	1.68653	−	0.698585i
$899$	19.5296	+	19.5296i	0.651349	+	0.651349i
$900$		0			0
$901$	12.2885	−	19.1248i	0.409391	−	0.637139i
$902$			78.9905i			2.63010i
$903$	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
$907$	23.8930	+	9.89680i	0.793353	+	0.328618i	0.742291	−	0.670078i	$-0.233739\pi$
$907$	23.8930	+	9.89680i	0.793353	+	0.328618i	0.0510624	+	0.998695i	$0.483739\pi$
$908$	−21.6081	+	52.1666i	−0.717090	+	1.73121i
$909$	22.9681	−	22.9681i	0.761805	−	0.761805i
$910$		0			0
$911$	−34.0518	−	14.1047i	−1.12819	−	0.467310i	−0.261021	−	0.965333i	$-0.584059\pi$
$911$	−34.0518	−	14.1047i	−1.12819	−	0.467310i	−0.867164	+	0.498023i	$0.834059\pi$
$912$	−97.5717	−	40.4155i	−3.23092	−	1.33829i
$913$	7.46012	+	18.0103i	0.246894	+	0.596054i
$914$		−	18.8387i		−	0.623128i
$915$		0			0
$916$	48.5544	+	48.5544i	1.60428	+	1.60428i
$917$			19.7072i			0.650791i
$918$	−32.9288	−	47.4182i	−1.08681	−	1.56503i
$919$	9.71950			0.320617			0.160308	−	0.987067i	$-0.448751\pi$
$919$	9.71950			0.320617			0.160308	+	0.987067i	$0.448751\pi$
$920$		0			0
$921$	−9.75550	−	23.5519i	−0.321455	−	0.776060i
$922$	18.9318			0.623485
$923$	−0.910286	−	2.19763i	−0.0299624	−	0.0723357i
$924$	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
$928$	64.4275	−	155.542i	2.11494	−	5.10591i
$929$	−0.943781	+	2.27849i	−0.0309644	+	0.0747548i	−0.938605	−	0.344993i	$-0.887881\pi$
$929$	−0.943781	+	2.27849i	−0.0309644	+	0.0747548i	0.907641	+	0.419748i	$0.137881\pi$
$930$		0			0
$931$			35.7140i			1.17048i
$932$	132.658	−	54.9486i	4.34535	−	1.79990i
$933$	−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	$-0.0606225\pi$
$938$	6.95493	−	2.88083i	0.227087	−	0.0940624i
$939$			21.7114i			0.708525i
$940$		0			0
$941$	6.50204	−	15.6973i	0.211960	−	0.511718i	−0.781764	−	0.623575i	$-0.785680\pi$
$941$	6.50204	−	15.6973i	0.211960	−	0.511718i	0.993724	+	0.111857i	$0.0356798\pi$
$942$	−8.37988	+	20.2308i	−0.273031	+	0.659156i
$943$	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
$947$	7.72593	+	18.6520i	0.251059	+	0.606110i	0.998290	−	0.0584545i	$-0.0186172\pi$
$947$	7.72593	+	18.6520i	0.251059	+	0.606110i	−0.747231	+	0.664564i	$0.768617\pi$
$948$	−7.05944			−0.229280
$949$	−1.55285	−	3.74891i	−0.0504076	−	0.121695i
$950$		0			0
$951$	−22.1740			−0.719040
$952$	−43.7033	+	30.3490i	−1.41643	+	0.983618i
$953$		−	60.7088i		−	1.96655i	−0.182129	−	0.983275i	$-0.558299\pi$
$953$		−	60.7088i		−	1.96655i	0.182129	−	0.983275i	$-0.441701\pi$
$954$	−19.8626	−	19.8626i	−0.643076	−	0.643076i
$955$		0			0
$956$		−	23.5531i		−	0.761762i
$957$	−16.6604	−	40.2218i	−0.538555	−	1.30019i
$958$	70.9457	+	29.3867i	2.29215	+	0.949441i
$959$	0.618781	+	0.256308i	0.0199815	+	0.00827660i
$960$		0			0
$961$	14.6481	−	14.6481i	0.472521	−	0.472521i
$962$	−3.00472	+	7.25403i	−0.0968760	+	0.233879i
$963$	23.5310	+	9.74687i	0.758277	+	0.314089i
$964$	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	$0.980996\pi$
$968$		−	107.148i		−	3.44388i
$969$	30.8118	+	5.55646i	0.989819	+	0.178499i
$970$		0			0
$971$	−13.9209	−	13.9209i	−0.446742	−	0.446742i	0.447528	−	0.894270i	$-0.352305\pi$
$971$	−13.9209	−	13.9209i	−0.446742	−	0.446742i	−0.894270	+	0.447528i	$0.852305\pi$
$972$	−77.4601	+	32.0850i	−2.48453	+	1.02913i
$973$	5.72164			0.183427
$974$	−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	0.799003	−	0.601327i	$-0.205361\pi$
$977$	6.17874	+	6.17874i	0.197676	+	0.197676i	−0.601327	+	0.799003i	$0.705361\pi$
$978$	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
$982$	38.8817			1.24076
$983$	−11.6252	+	4.81531i	−0.370786	+	0.153584i	−0.560292	−	0.828295i	$-0.689311\pi$
$983$	−11.6252	+	4.81531i	−0.370786	+	0.153584i	0.189507	+	0.981879i	$0.439311\pi$
$984$	41.4560	+	41.4560i	1.32157	+	1.32157i
$985$		0			0
$986$	−17.0832	+	94.7303i	−0.544040	+	3.01683i
$987$		−	7.57821i		−	0.241217i
$988$	−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	−0.0464728	−	0.998920i	$-0.514798\pi$
$991$	19.7383	−	8.17588i	0.627009	−	0.259716i	0.673482	+	0.739204i	$0.264798\pi$
$992$	57.9184	+	23.9906i	1.83891	+	0.761703i
$993$	0.656381	−	1.58464i	0.0208296	−	0.0502872i
$994$	5.66136	−	5.66136i	0.179568	−	0.179568i
$995$		0			0
$996$	21.3520	+	8.84430i	0.676565	+	0.280242i
$997$	−28.2345	−	11.6951i	−0.894197	−	0.370388i	−0.112211	−	0.993684i	$-0.535793\pi$
$997$	−28.2345	−	11.6951i	−0.894197	−	0.370388i	−0.781986	+	0.623296i	$0.785793\pi$
$998$	−34.4461	−	83.1601i	−1.09037	−	2.63239i
$999$		−	13.0657i		−	0.413381i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.n.e.49.1		24
5.2	odd	4		425.2.m.d.151.1	yes	24
5.3	odd	4		425.2.m.c.151.6	yes	24
5.4	even	2		425.2.n.d.49.6		24
17.8	even	8		425.2.n.d.399.6		24
85.8	odd	8		425.2.m.c.76.6	✓	24
85.12	even	16		7225.2.a.cb.1.23		24
85.22	even	16		7225.2.a.cb.1.24		24
85.42	odd	8		425.2.m.d.76.1	yes	24
85.59	even	8	inner	425.2.n.e.399.1		24
85.63	even	16		7225.2.a.bx.1.2		24
85.73	even	16		7225.2.a.bx.1.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.2.m.c.76.6	✓	24	85.8	odd	8
425.2.m.c.151.6	yes	24	5.3	odd	4
425.2.m.d.76.1	yes	24	85.42	odd	8
425.2.m.d.151.1	yes	24	5.2	odd	4
425.2.n.d.49.6		24	5.4	even	2
425.2.n.d.399.6		24	17.8	even	8
425.2.n.e.49.1		24	1.1	even	1	trivial
425.2.n.e.399.1		24	85.59	even	8	inner
7225.2.a.bx.1.1		24	85.73	even	16
7225.2.a.bx.1.2		24	85.63	even	16
7225.2.a.cb.1.23		24	85.12	even	16
7225.2.a.cb.1.24		24	85.22	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.n (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.91681 + 1.91681i) q^{2} +(0.977976 - 0.405091i) q^{3} -5.34834i q^{4} +(-1.09811 + 2.65108i) q^{6} +(-0.544082 + 1.31353i) q^{7} +(6.41814 + 6.41814i) q^{8} +(-1.32898 + 1.32898i) q^{9} +O(q^{10})\)	\(q+(-1.91681 + 1.91681i) q^{2} +(0.977976 - 0.405091i) q^{3} -5.34834i q^{4} +(-1.09811 + 2.65108i) q^{6} +(-0.544082 + 1.31353i) q^{7} +(6.41814 + 6.41814i) q^{8} +(-1.32898 + 1.32898i) q^{9} +(1.82748 - 4.41194i) q^{11} +(-2.16656 - 5.23055i) q^{12} -1.14504 q^{13} +(-1.47489 - 3.56069i) q^{14} -13.9080 q^{16} +(4.02881 - 0.876759i) q^{17} -5.09482i q^{18} +(5.07242 + 5.07242i) q^{19} +1.50500i q^{21} +(4.95391 + 11.9598i) q^{22} +(4.43872 + 1.83858i) q^{23} +(8.87671 + 3.67685i) q^{24} +(2.19483 - 2.19483i) q^{26} +(-1.97663 + 4.77200i) q^{27} +(7.02521 + 2.90994i) q^{28} +(7.95673 - 3.29579i) q^{29} +(1.22724 + 2.96282i) q^{31} +(13.8228 - 13.8228i) q^{32} -5.05506i q^{33} +(-6.04189 + 9.40305i) q^{34} +(7.10785 + 7.10785i) q^{36} +(-2.33702 + 0.968027i) q^{37} -19.4457 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} -5.03535 q^{47} +(-13.6017 + 5.63402i) q^{48} +(3.52041 + 3.52041i) q^{49} +(3.58491 - 2.48948i) q^{51} +6.12408i q^{52} +(3.89859 - 3.89859i) q^{53} +(-5.35820 - 12.9358i) q^{54} +(-11.9224 + 4.93842i) q^{56} +(7.01549 + 2.90591i) q^{57} +(-8.93416 + 21.5690i) q^{58} +(0.928288 - 0.928288i) q^{59} +(-6.05613 - 2.50853i) q^{61} +(-8.03155 - 3.32678i) q^{62} +(-1.02258 - 2.46873i) q^{63} +25.1755i q^{64} +(9.68961 + 9.68961i) q^{66} +1.95325i q^{67} +(-4.68921 - 21.5474i) q^{68} +5.08575 q^{69} +(0.794980 + 1.91925i) q^{71} -17.0592 q^{72} +(1.35615 + 3.27403i) q^{73} +(2.62411 - 6.33516i) q^{74} +(27.1290 - 27.1290i) q^{76} +(4.80091 + 4.80091i) q^{77} +(1.25739 - 3.03560i) q^{78} +(0.477176 - 1.15200i) q^{79} -0.170782i q^{81} +(-15.2819 + 6.32995i) q^{82} +(-2.88654 + 2.88654i) q^{83} +8.04927 q^{84} +11.7282 q^{86} +(6.44640 - 6.44640i) q^{87} +(40.0454 - 16.5874i) q^{88} +8.34827i q^{89} +(0.622997 - 1.50405i) q^{91} +(9.83334 - 23.7398i) q^{92} +(2.40042 + 2.40042i) q^{93} +(9.65181 - 9.65181i) q^{94} +(7.91890 - 19.1179i) q^{96} +(1.02623 + 2.47754i) q^{97} -13.4959 q^{98} +(3.43469 + 8.29208i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{3} - 8 q^{6} - 12 q^{9}+O(q^{10}) \) 24 * q + 4 * q^3 - 8 * q^6 - 12 * q^9	\( 24 q + 4 q^{3} - 8 q^{6} - 12 q^{9} + 4 q^{11} - 20 q^{12} + 16 q^{13} + 24 q^{14} - 24 q^{16} + 20 q^{19} + 12 q^{22} + 8 q^{23} - 16 q^{24} + 16 q^{26} + 16 q^{27} + 20 q^{28} - 4 q^{29} + 24 q^{31} + 60 q^{32} - 16 q^{34} + 60 q^{36} - 16 q^{37} - 48 q^{38} - 8 q^{39} - 20 q^{41} + 12 q^{42} - 32 q^{43} - 64 q^{44} - 40 q^{46} - 88 q^{47} + 4 q^{48} - 24 q^{49} + 16 q^{51} - 12 q^{53} + 20 q^{54} - 32 q^{56} - 56 q^{57} - 28 q^{58} + 16 q^{59} - 64 q^{61} + 16 q^{62} - 40 q^{63} - 72 q^{66} + 48 q^{68} + 48 q^{69} - 24 q^{71} + 120 q^{72} + 20 q^{73} - 32 q^{74} + 52 q^{76} + 24 q^{77} - 100 q^{78} + 48 q^{79} + 8 q^{82} + 12 q^{83} + 40 q^{84} - 16 q^{86} - 24 q^{87} + 80 q^{88} + 24 q^{91} - 56 q^{92} + 32 q^{93} + 40 q^{94} + 132 q^{96} - 24 q^{97} + 48 q^{98} + 80 q^{99}+O(q^{100}) \) 24 * q + 4 * q^3 - 8 * q^6 - 12 * q^9 + 4 * q^11 - 20 * q^12 + 16 * q^13 + 24 * q^14 - 24 * q^16 + 20 * q^19 + 12 * q^22 + 8 * q^23 - 16 * q^24 + 16 * q^26 + 16 * q^27 + 20 * q^28 - 4 * q^29 + 24 * q^31 + 60 * q^32 - 16 * q^34 + 60 * q^36 - 16 * q^37 - 48 * q^38 - 8 * q^39 - 20 * q^41 + 12 * q^42 - 32 * q^43 - 64 * q^44 - 40 * q^46 - 88 * q^47 + 4 * q^48 - 24 * q^49 + 16 * q^51 - 12 * q^53 + 20 * q^54 - 32 * q^56 - 56 * q^57 - 28 * q^58 + 16 * q^59 - 64 * q^61 + 16 * q^62 - 40 * q^63 - 72 * q^66 + 48 * q^68 + 48 * q^69 - 24 * q^71 + 120 * q^72 + 20 * q^73 - 32 * q^74 + 52 * q^76 + 24 * q^77 - 100 * q^78 + 48 * q^79 + 8 * q^82 + 12 * q^83 + 40 * q^84 - 16 * q^86 - 24 * q^87 + 80 * q^88 + 24 * q^91 - 56 * q^92 + 32 * q^93 + 40 * q^94 + 132 * q^96 - 24 * q^97 + 48 * q^98 + 80 * q^99

Introduction

L-functions

Modular forms

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