LMFDB - Embedded newform 925.2.t.c.82.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [925,2,Mod(82,925)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("925.82"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(925, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([3, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.t (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [96] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			82.10
Character	$\chi$	$=$	925.82
Dual form			925.2.t.c.643.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.242909 - 0.420731i) q^{2} +(-2.51234 + 0.673179i) q^{3} +(0.881990 - 1.52765i) q^{4} +(0.893496 + 0.893496i) q^{6} +(1.03380 - 0.277006i) q^{7} -1.82861 q^{8} +(3.26059 - 1.88250i) q^{9} +2.08952i q^{11} +(-1.18747 + 4.43171i) q^{12} +(-1.83113 + 3.17161i) q^{13} +(-0.367665 - 0.367665i) q^{14} +(-1.31980 - 2.28595i) q^{16} +(-1.60748 + 0.928076i) q^{17} +(-1.58405 - 0.914554i) q^{18} +(-0.445873 - 1.66402i) q^{19} +(-2.41078 + 1.39187i) q^{21} +(0.879123 - 0.507562i) q^{22} +3.16775 q^{23} +(4.59408 - 1.23098i) q^{24} +1.77919 q^{26} +(-1.40697 + 1.40697i) q^{27} +(0.488634 - 1.82361i) q^{28} +(2.26804 + 2.26804i) q^{29} +(-4.45483 + 4.45483i) q^{31} +(-2.46979 + 4.27780i) q^{32} +(-1.40662 - 5.24957i) q^{33} +(0.780940 + 0.450876i) q^{34} -6.64140i q^{36} +(-5.54900 - 2.49171i) q^{37} +(-0.591798 + 0.591798i) q^{38} +(2.46536 - 9.20083i) q^{39} +(8.68470 + 5.01411i) q^{41} +(1.17120 + 0.676194i) q^{42} +5.37912 q^{43} +(3.19205 + 1.84293i) q^{44} +(-0.769476 - 1.33277i) q^{46} +(1.58980 + 1.58980i) q^{47} +(4.85462 + 4.85462i) q^{48} +(-5.07016 + 2.92726i) q^{49} +(3.41376 - 3.41376i) q^{51} +(3.23008 + 5.59466i) q^{52} +(6.77518 + 1.81540i) q^{53} +(0.933722 + 0.250190i) q^{54} +(-1.89042 + 0.506536i) q^{56} +(2.24037 + 3.88043i) q^{57} +(0.403306 - 1.50516i) q^{58} +(10.7855 + 2.88997i) q^{59} +(2.94690 + 10.9980i) q^{61} +(2.95641 + 0.792167i) q^{62} +(2.84934 - 2.84934i) q^{63} -2.87944 q^{64} +(-1.86697 + 1.86697i) q^{66} +(2.74070 + 10.2284i) q^{67} +3.27422i q^{68} +(-7.95847 + 2.13247i) q^{69} +(0.439137 - 0.760607i) q^{71} +(-5.96235 + 3.44237i) q^{72} +(4.02172 + 4.02172i) q^{73} +(0.299561 + 2.93989i) q^{74} +(-2.93530 - 0.786511i) q^{76} +(0.578809 + 2.16014i) q^{77} +(-4.46993 + 1.19771i) q^{78} +(-1.52669 - 5.69770i) q^{79} +(-3.05987 + 5.29985i) q^{81} -4.87189i q^{82} +(6.15070 + 1.64807i) q^{83} +4.91045i q^{84} +(-1.30664 - 2.26316i) q^{86} +(-7.22487 - 4.17128i) q^{87} -3.82091i q^{88} +(0.569968 - 2.12715i) q^{89} +(-1.01447 + 3.78605i) q^{91} +(2.79393 - 4.83923i) q^{92} +(8.19315 - 14.1909i) q^{93} +(0.282701 - 1.05505i) q^{94} +(3.32522 - 12.4099i) q^{96} +0.682762i q^{97} +(2.46318 + 1.42212i) q^{98} +(3.93352 + 6.81306i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 40 q^{4} + 32 q^{14} - 4 q^{16} + 24 q^{19} + 36 q^{21} - 52 q^{24} + 16 q^{26} - 12 q^{29} + 4 q^{31} + 60 q^{34} - 100 q^{39} - 48 q^{41} - 48 q^{44} + 24 q^{46} + 120 q^{49} - 84 q^{51} - 104 q^{54}+ \cdots + 24 q^{99}+O(q^{100}) $ 96 * q - 40 * q^4 + 32 * q^14 - 4 * q^16 + 24 * q^19 + 36 * q^21 - 52 * q^24 + 16 * q^26 - 12 * q^29 + 4 * q^31 + 60 * q^34 - 100 * q^39 - 48 * q^41 - 48 * q^44 + 24 * q^46 + 120 * q^49 - 84 * q^51 - 104 * q^54 - 68 * q^56 + 28 * q^59 + 68 * q^61 - 48 * q^64 + 4 * q^66 - 28 * q^69 + 48 * q^71 + 48 * q^74 - 152 * q^76 + 92 * q^79 - 16 * q^81 + 20 * q^86 + 8 * q^89 - 12 * q^91 - 56 * q^94 + 252 * q^96 + 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−0.242909	−	0.420731i	−0.171763	−	0.297502i	0.767274	−	0.641320i	$-0.221613\pi$
$2$	−0.242909	−	0.420731i	−0.171763	−	0.297502i	−0.939036	+	0.343818i	$0.888280\pi$
$3$	−2.51234	+	0.673179i	−1.45050	+	0.388660i	−0.896197	−	0.443656i	$-0.853681\pi$
$3$	−2.51234	+	0.673179i	−1.45050	+	0.388660i	−0.554301	+	0.832316i	$0.687015\pi$
$4$	0.881990	−	1.52765i	0.440995	−	0.763826i
$5$		0			0
$5$		0			0
$6$	0.893496	+	0.893496i	0.364768	+	0.364768i
$7$	1.03380	−	0.277006i	0.390740	−	0.104699i	−0.0580995	−	0.998311i	$-0.518504\pi$
$7$	1.03380	−	0.277006i	0.390740	−	0.104699i	0.448840	+	0.893612i	$0.351837\pi$
$8$	−1.82861			−0.646511
$9$	3.26059	−	1.88250i	1.08686	−	0.627501i
$10$		0			0
$11$			2.08952i			0.630013i	0.949090	+	0.315006i	$0.102007\pi$
$11$			2.08952i			0.630013i	−0.949090	+	0.315006i	$0.897993\pi$
$12$	−1.18747	+	4.43171i	−0.342794	+	1.27933i
$13$	−1.83113	+	3.17161i	−0.507864	+	0.879646i	0.492094	+	0.870542i	$0.336231\pi$
$13$	−1.83113	+	3.17161i	−0.507864	+	0.879646i	−0.999959	+	0.00910465i	$0.997102\pi$
$14$	−0.367665	−	0.367665i	−0.0982626	−	0.0982626i
$15$		0			0
$16$	−1.31980	−	2.28595i	−0.329949	−	0.571488i
$17$	−1.60748	+	0.928076i	−0.389870	+	0.225092i	−0.682104	−	0.731255i	$-0.738935\pi$
$17$	−1.60748	+	0.928076i	−0.389870	+	0.225092i	0.292234	+	0.956347i	$0.405601\pi$
$18$	−1.58405	−	0.914554i	−0.373365	−	0.215563i
$19$	−0.445873	−	1.66402i	−0.102290	−	0.381753i	0.895733	−	0.444592i	$-0.146651\pi$
$19$	−0.445873	−	1.66402i	−0.102290	−	0.381753i	−0.998024	+	0.0628391i	$0.979985\pi$
$20$		0			0
$21$	−2.41078	+	1.39187i	−0.526076	+	0.303730i
$22$	0.879123	−	0.507562i	0.187430	−	0.108213i
$23$	3.16775			0.660523			0.330261	−	0.943890i	$-0.392863\pi$
$23$	3.16775			0.660523			0.330261	+	0.943890i	$0.392863\pi$
$24$	4.59408	−	1.23098i	0.937764	−	0.251273i
$25$		0			0
$26$	1.77919			0.348928
$27$	−1.40697	+	1.40697i	−0.270772	+	0.270772i
$28$	0.488634	−	1.82361i	0.0923431	−	0.344629i
$29$	2.26804	+	2.26804i	0.421164	+	0.421164i	0.885604	−	0.464440i	$-0.153745\pi$
$29$	2.26804	+	2.26804i	0.421164	+	0.421164i	−0.464440	+	0.885604i	$0.653745\pi$
$30$		0			0
$31$	−4.45483	+	4.45483i	−0.800112	+	0.800112i	−0.983113	−	0.183001i	$-0.941419\pi$
$31$	−4.45483	+	4.45483i	−0.800112	+	0.800112i	0.183001	+	0.983113i	$0.441419\pi$
$32$	−2.46979	+	4.27780i	−0.436601	+	0.756216i
$33$	−1.40662	−	5.24957i	−0.244861	−	0.913832i
$34$	0.780940	+	0.450876i	0.133930	+	0.0773246i
$35$		0			0
$36$		−	6.64140i		−	1.10690i
$37$	−5.54900	−	2.49171i	−0.912249	−	0.409635i
$37$	−5.54900	−	2.49171i	−0.912249	−	0.409635i
$38$	−0.591798	+	0.591798i	−0.0960023	+	0.0960023i
$39$	2.46536	−	9.20083i	0.394773	−	1.47331i
$40$		0			0
$41$	8.68470	+	5.01411i	1.35632	+	0.783073i	0.989126	−	0.147071i	$-0.0469845\pi$
$41$	8.68470	+	5.01411i	1.35632	+	0.783073i	0.367196	+	0.930144i	$0.380318\pi$
$42$	1.17120	+	0.676194i	0.180720	+	0.104339i
$43$	5.37912			0.820309			0.410154	−	0.912016i	$-0.365475\pi$
$43$	5.37912			0.820309			0.410154	+	0.912016i	$0.365475\pi$
$44$	3.19205	+	1.84293i	0.481220	+	0.277832i
$45$		0			0
$46$	−0.769476	−	1.33277i	−0.113453	−	0.196506i
$47$	1.58980	+	1.58980i	0.231896	+	0.231896i	0.813484	−	0.581588i	$-0.197568\pi$
$47$	1.58980	+	1.58980i	0.231896	+	0.231896i	−0.581588	+	0.813484i	$0.697568\pi$
$48$	4.85462	+	4.85462i	0.700705	+	0.700705i
$49$	−5.07016	+	2.92726i	−0.724309	+	0.418180i
$50$		0			0
$51$	3.41376	−	3.41376i	0.478022	−	0.478022i
$52$	3.23008	+	5.59466i	0.447931	+	0.775840i
$53$	6.77518	+	1.81540i	0.930643	+	0.249365i	0.692129	−	0.721774i	$-0.256673\pi$
$53$	6.77518	+	1.81540i	0.930643	+	0.249365i	0.238514	+	0.971139i	$0.423340\pi$
$54$	0.933722	+	0.250190i	0.127063	+	0.0340466i
$55$		0			0
$56$	−1.89042	+	0.506536i	−0.252618	+	0.0676888i
$57$	2.24037	+	3.88043i	0.296744	+	0.513975i
$58$	0.403306	−	1.50516i	0.0529567	−	0.197637i
$59$	10.7855	+	2.88997i	1.40416	+	0.376242i	0.879835	−	0.475279i	$-0.157653\pi$
$59$	10.7855	+	2.88997i	1.40416	+	0.376242i	0.524320	+	0.851521i	$0.324319\pi$
$60$		0			0
$61$	2.94690	+	10.9980i	0.377311	+	1.40815i	0.849938	+	0.526882i	$0.176639\pi$
$61$	2.94690	+	10.9980i	0.377311	+	1.40815i	−0.472627	+	0.881263i	$0.656694\pi$
$62$	2.95641	+	0.792167i	0.375464	+	0.100605i
$63$	2.84934	−	2.84934i	0.358983	−	0.358983i
$64$	−2.87944			−0.359930
$65$		0			0
$66$	−1.86697	+	1.86697i	−0.229809	+	0.229809i
$67$	2.74070	+	10.2284i	0.334830	+	1.24960i	0.904053	+	0.427420i	$0.140577\pi$
$67$	2.74070	+	10.2284i	0.334830	+	1.24960i	−0.569223	+	0.822183i	$0.692756\pi$
$68$			3.27422i			0.397057i
$69$	−7.95847	+	2.13247i	−0.958087	+	0.256719i
$70$		0			0
$71$	0.439137	−	0.760607i	0.0521159	−	0.0902674i	−0.838791	−	0.544454i	$-0.816737\pi$
$71$	0.439137	−	0.760607i	0.0521159	−	0.0902674i	0.890906	+	0.454187i	$0.150070\pi$
$72$	−5.96235	+	3.44237i	−0.702670	+	0.405687i
$73$	4.02172	+	4.02172i	0.470707	+	0.470707i	0.902143	−	0.431437i	$-0.141993\pi$
$73$	4.02172	+	4.02172i	0.470707	+	0.470707i	−0.431437	+	0.902143i	$0.641993\pi$
$74$	0.299561	+	2.93989i	0.0348233	+	0.341756i
$75$		0			0
$76$	−2.93530	−	0.786511i	−0.336702	−	0.0902190i
$77$	0.578809	+	2.16014i	0.0659614	+	0.246171i
$78$	−4.46993	+	1.19771i	−0.506120	+	0.135614i
$79$	−1.52669	−	5.69770i	−0.171766	−	0.641041i	−0.997080	−	0.0763662i	$-0.975668\pi$
$79$	−1.52669	−	5.69770i	−0.171766	−	0.641041i	0.825313	−	0.564675i	$-0.190998\pi$
$80$		0			0
$81$	−3.05987	+	5.29985i	−0.339985	+	0.588872i
$82$		−	4.87189i		−	0.538011i
$83$	6.15070	+	1.64807i	0.675127	+	0.180900i	0.580063	−	0.814571i	$-0.303028\pi$
$83$	6.15070	+	1.64807i	0.675127	+	0.180900i	0.0950638	+	0.995471i	$0.469695\pi$
$84$			4.91045i			0.535774i
$85$		0			0
$86$	−1.30664	−	2.26316i	−0.140898	−	0.244043i
$87$	−7.22487	−	4.17128i	−0.774587	−	0.447208i
$88$		−	3.82091i		−	0.407310i
$89$	0.569968	−	2.12715i	0.0604164	−	0.225477i	−0.929116	−	0.369789i	$-0.879430\pi$
$89$	0.569968	−	2.12715i	0.0604164	−	0.225477i	0.989532	+	0.144311i	$0.0460967\pi$
$90$		0			0
$91$	−1.01447	+	3.78605i	−0.106345	+	0.396886i
$92$	2.79393	−	4.83923i	0.291287	−	0.504524i
$93$	8.19315	−	14.1909i	0.849590	−	1.47153i
$94$	0.282701	−	1.05505i	0.0291583	−	0.108820i
$95$		0			0
$96$	3.32522	−	12.4099i	0.339379	−	1.26658i
$97$			0.682762i			0.0693240i	0.999399	+	0.0346620i	$0.0110355\pi$
$97$			0.682762i			0.0693240i	−0.999399	+	0.0346620i	$0.988965\pi$
$98$	2.46318	+	1.42212i	0.248818	+	0.143655i
$99$	3.93352	+	6.81306i	0.395334	+	0.684738i
$100$		0			0
$101$			13.2653i			1.31994i	0.751291	+	0.659972i	$0.229432\pi$
$101$			13.2653i			1.31994i	−0.751291	+	0.659972i	$0.770568\pi$
$102$	−2.26551	−	0.607041i	−0.224319	−	0.0601060i
$103$		−	2.82512i		−	0.278368i	−0.990267	−	0.139184i	$-0.955552\pi$
$103$		−	2.82512i		−	0.278368i	0.990267	−	0.139184i	$-0.0444479\pi$
$104$	3.34842	−	5.79964i	0.328340	−	0.568701i
$105$		0			0
$106$	−0.881956	−	3.29151i	−0.0856632	−	0.319699i
$107$	9.59031	−	2.56972i	0.927131	−	0.248424i	0.236500	−	0.971632i	$-0.424000\pi$
$107$	9.59031	−	2.56972i	0.927131	−	0.248424i	0.690631	+	0.723208i	$0.257333\pi$
$108$	0.908428	+	3.39030i	0.0874135	+	0.326232i
$109$	−4.78161	−	1.28123i	−0.457995	−	0.122719i	0.0224428	−	0.999748i	$-0.492856\pi$
$109$	−4.78161	−	1.28123i	−0.457995	−	0.122719i	−0.480438	+	0.877029i	$0.659522\pi$
$110$		0			0
$111$	15.6183	+	2.52456i	1.48243	+	0.239620i
$112$	−1.99763	−	1.99763i	−0.188758	−	0.188758i
$113$	−6.98088	+	4.03041i	−0.656706	+	0.379149i	−0.791021	−	0.611789i	$-0.790450\pi$
$113$	−6.98088	+	4.03041i	−0.656706	+	0.379149i	0.134315	+	0.990939i	$0.457117\pi$
$114$	1.08841	−	1.88518i	0.101939	−	0.176563i
$115$		0			0
$116$	5.46516	−	1.46439i	0.507427	−	0.135965i
$117$			13.7884i			1.27474i
$118$	−1.40400	−	5.23980i	−0.129249	−	0.482363i
$119$	−1.40473	+	1.40473i	−0.128771	+	0.128771i
$120$		0			0
$121$	6.63393			0.603084
$122$	3.91135	−	3.91135i	0.354117	−	0.354117i
$123$	−25.1943	−	6.75079i	−2.27169	−	0.608698i
$124$	2.87632	+	10.7346i	0.258301	+	0.963992i
$125$		0			0
$126$	−1.89094	−	0.506675i	−0.168458	−	0.0451382i
$127$	5.29873	−	19.7751i	0.470187	−	1.75476i	−0.168907	−	0.985632i	$-0.554024\pi$
$127$	5.29873	−	19.7751i	0.470187	−	1.75476i	0.639094	−	0.769129i	$-0.279309\pi$
$128$	5.63902	+	9.76707i	0.498424	+	0.863296i
$129$	−13.5142	+	3.62111i	−1.18986	+	0.318821i
$130$		0			0
$131$	−9.44396	−	2.53050i	−0.825123	−	0.221091i	−0.178538	−	0.983933i	$-0.557137\pi$
$131$	−9.44396	−	2.53050i	−0.825123	−	0.221091i	−0.646585	+	0.762842i	$0.723803\pi$
$132$	−9.26013	−	2.48125i	−0.805991	−	0.215965i
$133$	−0.921888	−	1.59676i	−0.0799379	−	0.138456i
$134$	3.63768	−	3.63768i	0.314248	−	0.314248i
$135$		0			0
$136$	2.93944	−	1.69709i	0.252055	−	0.145524i
$137$	−11.1133	−	11.1133i	−0.949474	−	0.949474i	0.0493096	−	0.998784i	$-0.484298\pi$
$137$	−11.1133	−	11.1133i	−0.949474	−	0.949474i	−0.998784	+	0.0493096i	$0.984298\pi$
$138$	2.83038	+	2.83038i	0.240938	+	0.240938i
$139$	−4.61807	−	7.99874i	−0.391700	−	0.678444i	0.600974	−	0.799269i	$-0.294780\pi$
$139$	−4.61807	−	7.99874i	−0.391700	−	0.678444i	−0.992674	+	0.120824i	$0.961446\pi$
$140$		0			0
$141$	−5.06433	−	2.92389i	−0.426493	−	0.246236i
$142$	−0.426681			−0.0358063
$143$	−6.62713	−	3.82617i	−0.554188	−	0.319961i
$144$	−8.60663	−	4.96904i	−0.717219	−	0.414087i
$145$		0			0
$146$	0.715149	−	2.66897i	0.0591862	−	0.220886i
$147$	10.7674	−	10.7674i	0.888080	−	0.888080i
$148$	−8.70063	+	6.27927i	−0.715188	+	0.516153i
$149$			6.04883i			0.495539i	0.968819	+	0.247770i	$0.0796976\pi$
$149$			6.04883i			0.495539i	−0.968819	+	0.247770i	$0.920302\pi$
$150$		0			0
$151$	5.70690	+	3.29488i	0.464421	+	0.268134i	0.713901	−	0.700246i	$-0.246926\pi$
$151$	5.70690	+	3.29488i	0.464421	+	0.268134i	−0.249480	+	0.968380i	$0.580260\pi$
$152$	0.815328	+	3.04284i	0.0661318	+	0.246807i
$153$	−3.49421	+	6.05216i	−0.282491	+	0.489288i
$154$	0.768241	−	0.768241i	0.0619066	−	0.0619066i
$155$		0			0
$156$	−11.8813	−	11.8813i	−0.951262	−	0.951262i
$157$	1.78303	−	6.65438i	0.142302	−	0.531077i	−0.857559	−	0.514386i	$-0.828020\pi$
$157$	1.78303	−	6.65438i	0.142302	−	0.531077i	0.999861	−	0.0166914i	$-0.00531329\pi$
$158$	−2.02635	+	2.02635i	−0.161208	+	0.161208i
$159$	−18.2436			−1.44681
$160$		0			0
$161$	3.27483	−	0.877488i	0.258093	−	0.0691557i
$162$	2.97308			0.233587
$163$	−21.6148	+	12.4793i	−1.69300	+	0.977455i	−0.740928	+	0.671585i	$0.765614\pi$
$163$	−21.6148	+	12.4793i	−1.69300	+	0.977455i	−0.952073	+	0.305870i	$0.901053\pi$
$164$	15.3196	−	8.84480i	1.19626	−	0.690663i
$165$		0			0
$166$	−0.800665	−	2.98812i	−0.0621436	−	0.231923i
$167$	4.48968	+	2.59212i	0.347422	+	0.200584i	0.663549	−	0.748133i	$-0.269049\pi$
$167$	4.48968	+	2.59212i	0.347422	+	0.200584i	−0.316127	+	0.948717i	$0.602383\pi$
$168$	4.40838	−	2.54518i	0.340114	−	0.196365i
$169$	−0.206075	−	0.356933i	−0.0158520	−	0.0274564i
$170$		0			0
$171$	−4.58634	−	4.58634i	−0.350726	−	0.350726i
$172$	4.74434	−	8.21743i	0.361752	−	0.626573i
$173$	−5.45131	+	20.3446i	−0.414455	+	1.54677i	0.371469	+	0.928445i	$0.378854\pi$
$173$	−5.45131	+	20.3446i	−0.414455	+	1.54677i	−0.785924	+	0.618323i	$0.787812\pi$
$174$			4.05297i			0.307255i
$175$		0			0
$176$	4.77653	−	2.75773i	0.360045	−	0.207872i
$177$	−29.0423			−2.18296
$178$	−1.03341	+	0.276901i	−0.0774571	+	0.0207546i
$179$	14.6472	+	14.6472i	1.09478	+	1.09478i	0.995010	+	0.0997713i	$0.0318111\pi$
$179$	14.6472	+	14.6472i	1.09478	+	1.09478i	0.0997713	+	0.995010i	$0.468189\pi$
$180$		0			0
$181$	−10.9090	+	18.8950i	−0.810862	+	1.40445i	0.101400	+	0.994846i	$0.467668\pi$
$181$	−10.9090	+	18.8950i	−0.810862	+	1.40445i	−0.912262	+	0.409608i	$0.865666\pi$
$182$	1.83933	−	0.492847i	0.136340	−	0.0365323i
$183$	−14.8072	−	25.6468i	−1.09458	−	1.89587i
$184$	−5.79259			−0.427035
$185$		0			0
$186$	−7.96076			−0.583711
$187$	−1.93923	−	3.35884i	−0.141810	−	0.245623i
$188$	3.83084	−	1.02647i	0.279393	−	0.0748631i
$189$	−1.06479	+	1.84427i	−0.0774520	+	0.134151i
$190$		0			0
$191$	−17.9295	−	17.9295i	−1.29733	−	1.29733i	−0.930149	−	0.367183i	$-0.880322\pi$
$191$	−17.9295	−	17.9295i	−1.29733	−	1.29733i	−0.367183	−	0.930149i	$-0.619678\pi$
$192$	7.23413	−	1.93838i	0.522078	−	0.139891i
$193$	2.76514			0.199039			0.0995196	−	0.995036i	$-0.468269\pi$
$193$	2.76514			0.199039			0.0995196	+	0.995036i	$0.468269\pi$
$194$	0.287259	−	0.165849i	0.0206240	−	0.0119073i
$195$		0			0
$196$			10.3273i			0.737662i
$197$	3.53967	−	13.2102i	0.252191	−	0.941189i	−0.717441	−	0.696619i	$-0.754687\pi$
$197$	3.53967	−	13.2102i	0.252191	−	0.941189i	0.969632	−	0.244570i	$-0.0786467\pi$
$198$	1.91098	−	3.30991i	0.135807	−	0.235225i
$199$	−2.86901	−	2.86901i	−0.203378	−	0.203378i	0.598067	−	0.801446i	$-0.295935\pi$
$199$	−2.86901	−	2.86901i	−0.203378	−	0.203378i	−0.801446	+	0.598067i	$0.795935\pi$
$200$		0			0
$201$	−13.7711	−	23.8523i	−0.971341	−	1.68241i
$202$	5.58111	−	3.22225i	0.392685	−	0.226717i
$203$	2.97296	+	1.71644i	0.208661	+	0.120470i
$204$	−2.20413	−	8.22594i	−0.154320	−	0.575931i
$205$		0			0
$206$	−1.18862	+	0.686248i	−0.0828148	+	0.0478132i
$207$	10.3288	−	5.96331i	0.717898	−	0.414479i
$208$	9.66687			0.670277
$209$	3.47700	−	0.931658i	0.240509	−	0.0644442i
$210$		0			0
$211$	6.57006			0.452301			0.226151	−	0.974092i	$-0.427386\pi$
$211$	6.57006			0.452301			0.226151	+	0.974092i	$0.427386\pi$
$212$	8.74895	−	8.74895i	0.600880	−	0.600880i
$213$	−0.591235	+	2.20652i	−0.0405107	+	0.151188i
$214$	−3.41073	−	3.41073i	−0.233153	−	0.233153i
$215$		0			0
$216$	2.57280	−	2.57280i	0.175057	−	0.175057i
$217$	−3.37140	+	5.83943i	−0.228865	+	0.396407i
$218$	0.622444	+	2.32299i	0.0421572	+	0.157333i
$219$	−12.8113	−	7.39658i	−0.865704	−	0.499815i
$220$		0			0
$221$		−	6.79771i		−	0.457264i
$222$	−2.73167	−	7.18435i	−0.183338	−	0.482182i
$223$	18.9226	−	18.9226i	1.26715	−	1.26715i	0.319593	−	0.947555i	$-0.396454\pi$
$223$	18.9226	−	18.9226i	1.26715	−	1.26715i	0.947555	−	0.319593i	$-0.103546\pi$
$224$	−1.36829	+	5.10655i	−0.0914230	+	0.341195i
$225$		0			0
$226$	3.39144	+	1.95805i	0.225595	+	0.130247i
$227$	10.0933	+	5.82737i	0.669916	+	0.386776i	0.796045	−	0.605238i	$-0.206922\pi$
$227$	10.0933	+	5.82737i	0.669916	+	0.386776i	−0.126129	+	0.992014i	$0.540255\pi$
$228$	7.90393			0.523450
$229$	−14.4306	−	8.33150i	−0.953600	−	0.550561i	−0.0594025	−	0.998234i	$-0.518920\pi$
$229$	−14.4306	−	8.33150i	−0.953600	−	0.550561i	−0.894197	+	0.447673i	$0.852253\pi$
$230$		0			0
$231$	−2.90833	−	5.03737i	−0.191354	−	0.331435i
$232$	−4.14736	−	4.14736i	−0.272287	−	0.272287i
$233$	−2.60164	−	2.60164i	−0.170439	−	0.170439i	0.616733	−	0.787172i	$-0.288456\pi$
$233$	−2.60164	−	2.60164i	−0.170439	−	0.170439i	−0.787172	+	0.616733i	$0.788456\pi$
$234$	5.80122	−	3.34934i	0.379238	−	0.218953i
$235$		0			0
$236$	13.9276	−	13.9276i	0.906610	−	0.906610i
$237$	7.67114	+	13.2868i	0.498294	+	0.863071i
$238$	0.932233	+	0.249791i	0.0604277	+	0.0161916i
$239$	−7.01240	−	1.87897i	−0.453594	−	0.121540i	0.0247864	−	0.999693i	$-0.492109\pi$
$239$	−7.01240	−	1.87897i	−0.453594	−	0.121540i	−0.478381	+	0.878153i	$0.658776\pi$
$240$		0			0
$241$	−24.1435	+	6.46922i	−1.55522	+	0.416719i	−0.931145	−	0.364649i	$-0.881189\pi$
$241$	−24.1435	+	6.46922i	−1.55522	+	0.416719i	−0.624071	+	0.781368i	$0.714522\pi$
$242$	−1.61144	−	2.79110i	−0.103587	−	0.179419i
$243$	5.66464	−	21.1407i	0.363387	−	1.35618i
$244$	19.4002	+	5.19827i	1.24197	+	0.332785i
$245$		0			0
$246$	3.27965	+	12.2398i	0.209103	+	0.780384i
$247$	6.09408	+	1.63290i	0.387757	+	0.103899i
$248$	8.14615	−	8.14615i	0.517281	−	0.517281i
$249$	−16.5621			−1.04958
$250$		0			0
$251$	3.06212	−	3.06212i	0.193279	−	0.193279i	−0.603832	−	0.797111i	$-0.706360\pi$
$251$	3.06212	−	3.06212i	0.193279	−	0.193279i	0.797111	+	0.603832i	$0.206360\pi$
$252$	−1.83971	−	6.86589i	−0.115891	−	0.432511i
$253$			6.61907i			0.416137i
$254$	−9.60712	+	2.57422i	−0.602804	+	0.161521i
$255$		0			0
$256$	−0.139904	+	0.242321i	−0.00874400	+	0.0151450i
$257$	−26.8141	+	15.4811i	−1.67262	+	0.965687i	−0.706456	+	0.707757i	$0.749707\pi$
$257$	−26.8141	+	15.4811i	−1.67262	+	0.965687i	−0.966163	+	0.257931i	$0.916959\pi$
$258$	4.80623	+	4.80623i	0.299223	+	0.299223i
$259$	−6.42678	−	1.03883i	−0.399341	−	0.0645497i
$260$		0			0
$261$	11.6647	+	3.12556i	0.722029	+	0.193467i
$262$	1.22936	+	4.58805i	0.0759503	+	0.283451i
$263$	−12.2595	+	3.28492i	−0.755953	+	0.202557i	−0.616157	−	0.787623i	$-0.711311\pi$
$263$	−12.2595	+	3.28492i	−0.755953	+	0.202557i	−0.139796	+	0.990180i	$0.544645\pi$
$264$	2.57215	+	9.59941i	0.158305	+	0.590803i
$265$		0			0
$266$	−0.447870	+	0.775734i	−0.0274607	+	0.0475633i
$267$			5.72780i			0.350536i
$268$	18.0428	+	4.83455i	1.10214	+	0.295317i
$269$			16.7531i			1.02145i	0.859744	+	0.510726i	$0.170623\pi$
$269$			16.7531i			1.02145i	−0.859744	+	0.510726i	$0.829377\pi$
$270$		0			0
$271$	−9.55233	−	16.5451i	−0.580263	−	1.00504i	−0.995448	−	0.0953075i	$-0.969617\pi$
$271$	−9.55233	−	16.5451i	−0.580263	−	1.00504i	0.415185	−	0.909737i	$-0.363717\pi$
$272$	4.24308	+	2.44974i	0.257274	+	0.148537i
$273$		−	10.1948i		−	0.617015i
$274$	−1.97619	+	7.37523i	−0.119386	+	0.445554i
$275$		0			0
$276$	−3.76163	+	14.0386i	−0.226423	+	0.845024i
$277$	−8.41266	+	14.5711i	−0.505468	+	0.875495i	0.494512	+	0.869171i	$0.335347\pi$
$277$	−8.41266	+	14.5711i	−0.505468	+	0.875495i	−0.999980	+	0.00632489i	$0.997987\pi$
$278$	−2.24354	+	3.88593i	−0.134559	+	0.233063i
$279$	−6.13916	+	22.9116i	−0.367542	+	1.37168i
$280$		0			0
$281$	5.84495	−	21.8136i	0.348680	−	1.30129i	−0.539573	−	0.841939i	$-0.681414\pi$
$281$	5.84495	−	21.8136i	0.348680	−	1.30129i	0.888253	−	0.459354i	$-0.151919\pi$
$282$			2.84096i			0.169177i
$283$	3.78721	+	2.18654i	0.225126	+	0.129977i	0.608322	−	0.793691i	$-0.291843\pi$
$283$	3.78721	+	2.18654i	0.225126	+	0.129977i	−0.383196	+	0.923667i	$0.625176\pi$
$284$	−0.774628	−	1.34170i	−0.0459657	−	0.0796150i
$285$		0			0
$286$			3.71765i			0.219829i
$287$	10.3672	+	2.77788i	0.611956	+	0.163973i
$288$			18.5976i			1.09587i
$289$	−6.77735	+	11.7387i	−0.398668	+	0.690513i
$290$		0			0
$291$	−0.459621	−	1.71533i	−0.0269435	−	0.100554i
$292$	9.69091	−	2.59667i	0.567117	−	0.151959i
$293$	7.39929	+	27.6145i	0.432271	+	1.61326i	0.747513	+	0.664247i	$0.231248\pi$
$293$	7.39929	+	27.6145i	0.432271	+	1.61326i	−0.315242	+	0.949011i	$0.602086\pi$
$294$	−7.14567	−	1.91468i	−0.416744	−	0.111666i
$295$		0			0
$296$	10.1470	+	4.55637i	0.589780	+	0.264834i
$297$	−2.93989	−	2.93989i	−0.170590	−	0.170590i
$298$	2.54493	−	1.46931i	0.147424	−	0.0851151i
$299$	−5.80057	+	10.0469i	−0.335456	+	0.581026i
$300$		0			0
$301$	5.56095	−	1.49005i	0.320528	−	0.0858851i
$302$		−	3.20142i		−	0.184221i
$303$	−8.92989	−	33.3268i	−0.513009	−	1.91458i
$304$	−3.21541	+	3.21541i	−0.184416	+	0.184416i
$305$		0			0
$306$	3.39510			0.194085
$307$	−0.859218	+	0.859218i	−0.0490382	+	0.0490382i	−0.731201	−	0.682162i	$-0.761040\pi$
$307$	−0.859218	+	0.859218i	−0.0490382	+	0.0490382i	0.682162	+	0.731201i	$0.261040\pi$
$308$	3.81045	+	1.02101i	0.217121	+	0.0581773i
$309$	1.90181	+	7.09766i	0.108190	+	0.403772i
$310$		0			0
$311$	27.8607	+	7.46525i	1.57983	+	0.423315i	0.938875	−	0.344259i	$-0.111870\pi$
$311$	27.8607	+	7.46525i	1.57983	+	0.423315i	0.640959	+	0.767575i	$0.278537\pi$
$312$	−4.50817	+	16.8247i	−0.255225	+	0.952513i
$313$	0.671228	+	1.16260i	0.0379400	+	0.0657141i	0.884372	−	0.466783i	$-0.154587\pi$
$313$	0.671228	+	1.16260i	0.0379400	+	0.0657141i	−0.846432	+	0.532497i	$0.821254\pi$
$314$	−3.23282	+	0.866230i	−0.182438	+	0.0488842i
$315$		0			0
$316$	−10.0506	−	2.69306i	−0.565392	−	0.151496i
$317$	14.2632	+	3.82182i	0.801102	+	0.214655i	0.636068	−	0.771633i	$-0.280560\pi$
$317$	14.2632	+	3.82182i	0.801102	+	0.214655i	0.165034	+	0.986288i	$0.447227\pi$
$318$	4.43154	+	7.67566i	0.248509	+	0.430429i
$319$	−4.73910	+	4.73910i	−0.265339	+	0.265339i
$320$		0			0
$321$	−22.3642	+	12.9120i	−1.24825	+	0.720677i
$322$	−1.16467	−	1.16467i	−0.0649046	−	0.0649046i
$323$	2.26107	+	2.26107i	0.125809	+	0.125809i
$324$	5.39755	+	9.34883i	0.299864	+	0.519380i
$325$		0			0
$326$	10.5009	+	6.06267i	0.581589	+	0.335780i
$327$	12.8755			0.712017
$328$	−15.8809	−	9.16886i	−0.876877	−	0.506265i
$329$	2.08392	+	1.20315i	0.114890	+	0.0663319i
$330$		0			0
$331$	−4.83434	+	18.0420i	−0.265719	+	0.991678i	0.696089	+	0.717955i	$0.254922\pi$
$331$	−4.83434	+	18.0420i	−0.265719	+	0.991678i	−0.961809	+	0.273723i	$0.911745\pi$
$332$	7.94254	−	7.94254i	0.435904	−	0.435904i
$333$	−22.7837	+	2.32155i	−1.24854	+	0.127220i
$334$		−	2.51860i		−	0.137811i
$335$		0			0
$336$	6.36348	+	3.67396i	0.347156	+	0.200431i
$337$	1.58050	+	5.89849i	0.0860951	+	0.321311i	0.995519	−	0.0945584i	$-0.0301439\pi$
$337$	1.58050	+	5.89849i	0.0860951	+	0.321311i	−0.909424	+	0.415870i	$0.863477\pi$
$338$	−0.100115	+	0.173405i	−0.00544555	+	0.00943197i
$339$	14.8251	−	14.8251i	0.805191	−	0.805191i
$340$		0			0
$341$	−9.30844	−	9.30844i	−0.504081	−	0.504081i
$342$	−0.815550	+	3.04367i	−0.0440999	+	0.164583i
$343$	−9.72824	+	9.72824i	−0.525276	+	0.525276i
$344$	−9.83632			−0.530339
$345$		0			0
$346$	9.88376	−	2.64834i	0.531354	−	0.142376i
$347$	−36.4201			−1.95513			−0.977565	−	0.210632i	$-0.932448\pi$
$347$	−36.4201			−1.95513			−0.977565	+	0.210632i	$0.932448\pi$
$348$	−12.7445	+	7.35806i	−0.683179	+	0.394433i
$349$	5.28579	−	3.05175i	0.282942	−	0.163357i	−0.351813	−	0.936070i	$-0.614435\pi$
$349$	5.28579	−	3.05175i	0.282942	−	0.163357i	0.634754	+	0.772714i	$0.281101\pi$
$350$		0			0
$351$	−1.88602	−	7.03871i	−0.100668	−	0.375699i
$352$	−8.93853	−	5.16066i	−0.476425	−	0.275064i
$353$	20.2094	−	11.6679i	1.07564	−	0.621021i	0.145923	−	0.989296i	$-0.453385\pi$
$353$	20.2094	−	11.6679i	1.07564	−	0.621021i	0.929717	+	0.368275i	$0.120052\pi$
$354$	7.05465	+	12.2190i	0.374950	+	0.649433i
$355$		0			0
$356$	−2.74684	−	2.74684i	−0.145582	−	0.145582i
$357$	2.58352	−	4.47478i	0.136734	−	0.236831i
$358$	2.60459	−	9.72045i	0.137657	−	0.513742i
$359$		−	13.7535i		−	0.725881i	−0.931812	−	0.362941i	$-0.881773\pi$
$359$		−	13.7535i		−	0.725881i	0.931812	−	0.362941i	$-0.118227\pi$
$360$		0			0
$361$	13.8843	−	8.01612i	0.730754	−	0.421901i
$362$	10.5996			0.557103
$363$	−16.6667	+	4.46582i	−0.874773	+	0.234395i
$364$	4.88902	+	4.88902i	0.256254	+	0.256254i
$365$		0			0
$366$	−7.19360	+	12.4597i	−0.376016	+	0.651278i
$367$	−5.65412	+	1.51502i	−0.295143	+	0.0790832i	−0.403352	−	0.915045i	$-0.632155\pi$
$367$	−5.65412	+	1.51502i	−0.295143	+	0.0790832i	0.108209	+	0.994128i	$0.465488\pi$
$368$	−4.18079	−	7.24134i	−0.217939	−	0.377481i
$369$	37.7563			1.96552
$370$		0			0
$371$	7.50707			0.389748
$372$	−14.4526	−	25.0326i	−0.749330	−	1.29788i
$373$	26.4467	−	7.08637i	1.36936	−	0.366918i	0.502114	−	0.864802i	$-0.332556\pi$
$373$	26.4467	−	7.08637i	1.36936	−	0.366918i	0.867244	+	0.497883i	$0.165889\pi$
$374$	−0.942113	+	1.63179i	−0.0487155	+	0.0843777i
$375$		0			0
$376$	−2.90712	−	2.90712i	−0.149923	−	0.149923i
$377$	−11.3464	+	3.04026i	−0.584369	+	0.156581i
$378$	1.03459			0.0532134
$379$	14.5045	−	8.37420i	0.745048	−	0.430154i	−0.0788540	−	0.996886i	$-0.525126\pi$
$379$	14.5045	−	8.37420i	0.745048	−	0.430154i	0.823902	+	0.566733i	$0.191793\pi$
$380$		0			0
$381$			53.2488i			2.72802i
$382$	−3.18825	+	11.8987i	−0.163125	+	0.608791i
$383$	−15.8124	+	27.3880i	−0.807978	+	1.39946i	0.106284	+	0.994336i	$0.466105\pi$
$383$	−15.8124	+	27.3880i	−0.807978	+	1.39946i	−0.914262	+	0.405123i	$0.867229\pi$
$384$	−20.7421	−	20.7421i	−1.05849	−	1.05849i
$385$		0			0
$386$	−0.671677	−	1.16338i	−0.0341875	−	0.0592144i
$387$	17.5391	−	10.1262i	0.891564	−	0.514745i
$388$	1.04302	+	0.602190i	0.0529515	+	0.0305716i
$389$	−9.26758	−	34.5871i	−0.469885	−	1.75364i	−0.640163	−	0.768239i	$-0.721133\pi$
$389$	−9.26758	−	34.5871i	−0.469885	−	1.75364i	0.170278	−	0.985396i	$-0.445533\pi$
$390$		0			0
$391$	−5.09209	+	2.93992i	−0.257518	+	0.148678i
$392$	9.27135	−	5.35282i	0.468274	−	0.270358i
$393$	25.4299			1.28277
$394$	−6.41776	+	1.71963i	−0.323322	+	0.0866339i
$395$		0			0
$396$	13.8773			0.697361
$397$	−15.6873	+	15.6873i	−0.787325	+	0.787325i	−0.981055	−	0.193730i	$-0.937941\pi$
$397$	−15.6873	+	15.6873i	−0.787325	+	0.787325i	0.193730	+	0.981055i	$0.437941\pi$
$398$	−0.510172	+	1.90399i	−0.0255726	+	0.0954382i
$399$	3.39100	+	3.39100i	0.169762	+	0.169762i
$400$		0			0
$401$	14.8433	−	14.8433i	0.741241	−	0.741241i	−0.231576	−	0.972817i	$-0.574388\pi$
$401$	14.8433	−	14.8433i	0.741241	−	0.741241i	0.972817	+	0.231576i	$0.0743882\pi$
$402$	−6.69027	+	11.5879i	−0.333680	+	0.577951i
$403$	−5.97162	−	22.2864i	−0.297468	−	1.11016i
$404$	20.2647	+	11.6998i	1.00821	+	0.582089i
$405$		0			0
$406$		−	1.66776i		−	0.0827693i
$407$	5.20647	−	11.5947i	0.258075	−	0.574729i
$408$	−6.24243	+	6.24243i	−0.309046	+	0.309046i
$409$	9.15489	−	34.1665i	0.452680	−	1.68943i	−0.242139	−	0.970242i	$-0.577849\pi$
$409$	9.15489	−	34.1665i	0.452680	−	1.68943i	0.694819	−	0.719185i	$-0.255484\pi$
$410$		0			0
$411$	35.4016	+	20.4391i	1.74623	+	1.00819i
$412$	−4.31581	−	2.49173i	−0.212625	−	0.122759i
$413$	11.9506			0.588052
$414$	−5.01790	−	2.89708i	−0.246616	−	0.142384i
$415$		0			0
$416$	−9.04501	−	15.6664i	−0.443468	−	0.768110i
$417$	16.9867	+	16.9867i	0.831844	+	0.831844i
$418$	−1.23657	−	1.23657i	−0.0604827	−	0.0604827i
$419$	12.8247	−	7.40437i	0.626530	−	0.361727i	−0.152877	−	0.988245i	$-0.548854\pi$
$419$	12.8247	−	7.40437i	0.626530	−	0.361727i	0.779407	+	0.626518i	$0.215521\pi$
$420$		0			0
$421$	−13.0213	+	13.0213i	−0.634620	+	0.634620i	−0.949223	−	0.314603i	$-0.898129\pi$
$421$	−13.0213	+	13.0213i	−0.634620	+	0.634620i	0.314603	+	0.949223i	$0.398129\pi$
$422$	−1.59593	−	2.76423i	−0.0776885	−	0.134560i
$423$	8.17648	+	2.19088i	0.397554	+	0.106524i
$424$	−12.3892	−	3.31967i	−0.601671	−	0.161217i
$425$		0			0
$426$	1.07197	−	0.287233i	0.0519369	−	0.0139165i
$427$	6.09301	+	10.5534i	0.294861	+	0.510715i
$428$	4.53293	−	16.9171i	0.219107	−	0.817720i
$429$	19.2253	+	5.15140i	0.928205	+	0.248712i
$430$		0			0
$431$	−9.92884	−	37.0549i	−0.478255	−	1.78487i	−0.608681	−	0.793415i	$-0.708301\pi$
$431$	−9.92884	−	37.0549i	−0.478255	−	1.78487i	0.130425	−	0.991458i	$-0.458366\pi$
$432$	5.07318	+	1.35936i	0.244084	+	0.0654020i
$433$	−10.7074	+	10.7074i	−0.514566	+	0.514566i	−0.915922	−	0.401356i	$-0.868539\pi$
$433$	−10.7074	+	10.7074i	−0.514566	+	0.514566i	0.401356	+	0.915922i	$0.368539\pi$
$434$	3.27577			0.157242
$435$		0			0
$436$	−6.17461	+	6.17461i	−0.295710	+	0.295710i
$437$	−1.41242	−	5.27121i	−0.0675650	−	0.252156i
$438$			7.18678i			0.343398i
$439$	−5.94424	+	1.59276i	−0.283703	+	0.0760181i	−0.397865	−	0.917444i	$-0.630249\pi$
$439$	−5.94424	+	1.59276i	−0.283703	+	0.0760181i	0.114161	+	0.993462i	$0.463582\pi$
$440$		0			0
$441$	−11.0212	+	19.0892i	−0.524817	+	0.909010i
$442$	−2.86001	+	1.65123i	−0.136037	+	0.0785408i
$443$	2.15090	+	2.15090i	0.102192	+	0.102192i	0.756354	−	0.654162i	$-0.226979\pi$
$443$	2.15090	+	2.15090i	0.102192	+	0.102192i	−0.654162	+	0.756354i	$0.726979\pi$
$444$	17.6319	−	21.6327i	0.836771	−	1.02664i
$445$		0			0
$446$	−12.5578	−	3.36484i	−0.594627	−	0.159330i
$447$	−4.07194	−	15.1967i	−0.192596	−	0.718779i
$448$	−2.97677	+	0.797624i	−0.140639	+	0.0376842i
$449$	5.83410	+	21.7731i	0.275328	+	1.02754i	0.955621	+	0.294598i	$0.0951858\pi$
$449$	5.83410	+	21.7731i	0.275328	+	1.02754i	−0.680293	+	0.732940i	$0.738148\pi$
$450$		0			0
$451$	−10.4771	+	18.1468i	−0.493346	+	0.854500i
$452$			14.2191i			0.668812i
$453$	−16.5557	−	4.43609i	−0.777855	−	0.208426i
$454$		−	5.66208i		−	0.265735i
$455$		0			0
$456$	−4.09676	−	7.09579i	−0.191848	−	0.332291i
$457$	−5.06014	−	2.92148i	−0.236704	−	0.136661i	0.376957	−	0.926231i	$-0.376970\pi$
$457$	−5.06014	−	2.92148i	−0.236704	−	0.136661i	−0.613661	+	0.789570i	$0.710304\pi$
$458$			8.09519i			0.378263i
$459$	0.955895	−	3.56745i	0.0446173	−	0.166514i
$460$		0			0
$461$	2.21024	−	8.24872i	0.102941	−	0.384181i	−0.895162	−	0.445740i	$-0.852941\pi$
$461$	2.21024	−	8.24872i	0.102941	−	0.384181i	0.998103	+	0.0615588i	$0.0196072\pi$
$462$	−1.41292	+	2.44724i	−0.0657349	+	0.113856i
$463$	2.56935	−	4.45024i	0.119408	−	0.206820i	−0.800125	−	0.599833i	$-0.795234\pi$
$463$	2.56935	−	4.45024i	0.119408	−	0.206820i	0.919533	+	0.393012i	$0.128567\pi$
$464$	2.19128	−	8.17797i	0.101728	−	0.379653i
$465$		0			0
$466$	−0.462628	+	1.72655i	−0.0214308	+	0.0799810i
$467$			10.8145i			0.500436i	0.968189	+	0.250218i	$0.0805023\pi$
$467$			10.8145i			0.500436i	−0.968189	+	0.250218i	$0.919498\pi$
$468$	21.0639	+	12.1613i	0.973681	+	0.562155i
$469$	5.66669	+	9.81499i	0.261663	+	0.453214i
$470$		0			0
$471$			17.9183i			0.825633i
$472$	−19.7225	−	5.28463i	−0.907802	−	0.243245i
$473$			11.2398i			0.516805i
$474$	3.72678	−	6.45497i	0.171177	−	0.296487i
$475$		0			0
$476$	0.906979	+	3.38489i	0.0415713	+	0.155146i
$477$	25.5086	−	6.83501i	1.16796	−	0.312954i
$478$	0.912836	+	3.40675i	0.0417521	+	0.155821i
$479$	−3.94037	−	1.05582i	−0.180040	−	0.0482416i	0.167673	−	0.985843i	$-0.446375\pi$
$479$	−3.94037	−	1.05582i	−0.180040	−	0.0482416i	−0.347713	+	0.937601i	$0.613042\pi$
$480$		0			0
$481$	18.0637	−	13.0366i	0.823633	−	0.594418i
$482$	8.58646	+	8.58646i	0.391103	+	0.391103i
$483$	−7.63677	+	4.40909i	−0.347485	+	0.200621i
$484$	5.85106	−	10.1343i	0.265957	−	0.460651i
$485$		0			0
$486$	−10.2705	+	2.75198i	−0.465881	+	0.124833i
$487$			10.4321i			0.472725i	0.971665	+	0.236363i	$0.0759553\pi$
$487$			10.4321i			0.472725i	−0.971665	+	0.236363i	$0.924045\pi$
$488$	−5.38872	−	20.1110i	−0.243936	−	0.910382i
$489$	45.9028	−	45.9028i	2.07580	−	2.07580i
$490$		0			0
$491$	−7.43200			−0.335401			−0.167701	−	0.985838i	$-0.553634\pi$
$491$	−7.43200			−0.335401			−0.167701	+	0.985838i	$0.553634\pi$
$492$	−32.5340	+	32.5340i	−1.46674	+	1.46674i
$493$	−5.75073	−	1.54090i	−0.259000	−	0.0693987i
$494$	−0.793294	−	2.96061i	−0.0356920	−	0.133204i
$495$		0			0
$496$	16.0630	+	4.30407i	0.721250	+	0.193258i
$497$	0.243287	−	0.907960i	0.0109129	−	0.0407276i
$498$	4.02308	+	6.96818i	0.180278	+	0.312251i
$499$	24.1425	−	6.46895i	1.08077	−	0.289590i	0.325856	−	0.945419i	$-0.394348\pi$
$499$	24.1425	−	6.46895i	1.08077	−	0.289590i	0.754909	+	0.655829i	$0.227681\pi$
$500$		0			0
$501$	−13.0246	−	3.48992i	−0.581894	−	0.155918i
$502$	−2.03214	−	0.544511i	−0.0906990	−	0.0243027i
$503$	10.4163	+	18.0415i	0.464438	+	0.804431i	0.999176	−	0.0405874i	$-0.0129229\pi$
$503$	10.4163	+	18.0415i	0.464438	+	0.804431i	−0.534738	+	0.845018i	$0.679590\pi$
$504$	−5.21033	+	5.21033i	−0.232087	+	0.232087i
$505$		0			0
$506$	2.78485	−	1.60783i	0.123802	−	0.0714769i
$507$	0.758011	+	0.758011i	0.0336645	+	0.0336645i
$508$	−25.5361	−	25.5361i	−1.13298	−	1.13298i
$509$	8.54631	+	14.8026i	0.378808	+	0.656115i	0.990889	−	0.134680i	$-0.0430006\pi$
$509$	8.54631	+	14.8026i	0.378808	+	0.656115i	−0.612081	+	0.790795i	$0.709667\pi$
$510$		0			0
$511$	5.27170	+	3.04362i	0.233206	+	0.134642i
$512$	22.6920			1.00286
$513$	2.96856	+	1.71390i	0.131065	+	0.0756705i
$514$	13.0268	+	7.52102i	0.574587	+	0.331738i
$515$		0			0
$516$	−6.38757	+	23.8387i	−0.281197	+	1.04944i
$517$	−3.32191	+	3.32191i	−0.146097	+	0.146097i
$518$	1.12406	+	2.95629i	0.0493882	+	0.129892i
$519$		−	54.7821i		−	2.40467i
$520$		0			0
$521$	29.6690	+	17.1294i	1.29982	+	0.750453i	0.980373	−	0.197150i	$-0.0631686\pi$
$521$	29.6690	+	17.1294i	1.29982	+	0.750453i	0.319450	+	0.947603i	$0.396502\pi$
$522$	−1.51845	−	5.66694i	−0.0664608	−	0.248035i
$523$	−6.79166	+	11.7635i	−0.296979	+	0.514382i	−0.975443	−	0.220251i	$-0.929312\pi$
$523$	−6.79166	+	11.7635i	−0.296979	+	0.514382i	0.678465	+	0.734633i	$0.262646\pi$
$524$	−12.1952	+	12.1952i	−0.532750	+	0.532750i
$525$		0			0
$526$	4.36001	+	4.36001i	0.190105	+	0.190105i
$527$	3.02661	−	11.2955i	0.131841	−	0.492038i
$528$	−10.1438	+	10.1438i	−0.441453	+	0.441453i
$529$	−12.9653			−0.563710
$530$		0			0
$531$	40.6076	−	10.8808i	1.76222	−	0.472185i
$532$	−3.25239			−0.141009
$533$	−31.8056	+	18.3630i	−1.37765	+	0.795389i
$534$	2.40986	−	1.39134i	0.104285	−	0.0602090i
$535$		0			0
$536$	−5.01168	−	18.7038i	−0.216471	−	0.807882i
$537$	−46.6588	−	26.9385i	−2.01348	−	1.16248i
$538$	7.04853	−	4.06947i	0.303883	−	0.175447i
$539$	−6.11656	−	10.5942i	−0.263459	−	0.456324i
$540$		0			0
$541$	−14.8341	−	14.8341i	−0.637767	−	0.637767i	0.312237	−	0.950004i	$-0.398922\pi$
$541$	−14.8341	−	14.8341i	−0.637767	−	0.637767i	−0.950004	+	0.312237i	$0.898922\pi$
$542$	−4.64069	+	8.03792i	−0.199335	+	0.345258i
$543$	14.6874	−	54.8143i	0.630299	−	2.35231i
$544$		−	9.16861i		−	0.393101i
$545$		0			0
$546$	−4.28925	+	2.47640i	−0.183563	+	0.105980i
$547$	23.4215			1.00143			0.500715	−	0.865612i	$-0.333070\pi$
$547$	23.4215			1.00143			0.500715	+	0.865612i	$0.333070\pi$
$548$	−26.7791	+	7.17544i	−1.14395	+	0.306520i
$549$	30.3123	+	30.3123i	1.29370	+	1.29370i
$550$		0			0
$551$	2.76280	−	4.78532i	0.117699	−	0.203861i
$552$	14.5529	−	3.89945i	0.619414	−	0.165971i
$553$	−3.15660	−	5.46739i	−0.134232	−	0.232497i
$554$	8.17404			0.347282
$555$		0			0
$556$	−16.2924			−0.690951
$557$	−6.13483	−	10.6258i	−0.259941	−	0.450231i	0.706285	−	0.707928i	$-0.250370\pi$
$557$	−6.13483	−	10.6258i	−0.259941	−	0.450231i	−0.966226	+	0.257697i	$0.917036\pi$
$558$	11.1309	−	2.98251i	0.471208	−	0.126260i
$559$	−9.84988	+	17.0605i	−0.416605	+	0.721582i
$560$		0			0
$561$	7.13310	+	7.13310i	0.301160	+	0.301160i
$562$	−10.5975	+	2.83958i	−0.447027	+	0.119780i
$563$	2.53059			0.106652			0.0533258	−	0.998577i	$-0.483018\pi$
$563$	2.53059			0.106652			0.0533258	+	0.998577i	$0.483018\pi$
$564$	−8.93337	+	5.15769i	−0.376163	+	0.217178i
$565$		0			0
$566$		−	2.12453i		−	0.0893005i
$567$	−1.69521	+	6.32660i	−0.0711920	+	0.265692i
$568$	−0.803009	+	1.39085i	−0.0336935	+	0.0583589i
$569$	24.7731	+	24.7731i	1.03854	+	1.03854i	0.999227	+	0.0393138i	$0.0125172\pi$
$569$	24.7731	+	24.7731i	1.03854	+	1.03854i	0.0393138	+	0.999227i	$0.487483\pi$
$570$		0			0
$571$	−20.6850	−	35.8275i	−0.865642	−	1.49934i	−0.866408	−	0.499336i	$-0.833577\pi$
$571$	−20.6850	−	35.8275i	−0.865642	−	1.49934i	0.000766004	−	1.00000i	$-0.499756\pi$
$572$	−11.6901	+	6.74930i	−0.488789	+	0.282202i
$573$	57.1146	+	32.9752i	2.38600	+	1.37756i
$574$	−1.34954	−	5.03657i	−0.0563289	−	0.210222i
$575$		0			0
$576$	−9.38869	+	5.42056i	−0.391195	+	0.225857i
$577$	−28.4613	+	16.4321i	−1.18486	+	0.684078i	−0.957134	−	0.289647i	$-0.906462\pi$
$577$	−28.4613	+	16.4321i	−1.18486	+	0.684078i	−0.227725	+	0.973725i	$0.573129\pi$
$578$	6.58512			0.273905
$579$	−6.94696	+	1.86143i	−0.288706	+	0.0773585i
$580$		0			0
$581$	6.81513			0.282739
$582$	−0.610046	+	0.610046i	−0.0252872	+	0.0252872i
$583$	−3.79331	+	14.1568i	−0.157103	+	0.586317i
$584$	−7.35416	−	7.35416i	−0.304317	−	0.304317i
$585$		0			0
$586$	9.82093	−	9.82093i	0.405699	−	0.405699i
$587$	10.2866	−	17.8170i	0.424574	−	0.735385i	−0.571806	−	0.820389i	$-0.693757\pi$
$587$	10.2866	−	17.8170i	0.424574	−	0.735385i	0.996381	+	0.0850042i	$0.0270904\pi$
$588$	−6.95209	−	25.9456i	−0.286700	−	1.06998i
$589$	9.39923	+	5.42665i	0.387288	+	0.223601i
$590$		0			0
$591$			35.5714i			1.46321i
$592$	1.62760	+	15.9733i	0.0668941	+	0.656498i
$593$	14.5325	−	14.5325i	0.596779	−	0.596779i	−0.342675	−	0.939454i	$-0.611333\pi$
$593$	14.5325	−	14.5325i	0.596779	−	0.596779i	0.939454	+	0.342675i	$0.111333\pi$
$594$	−0.522776	+	1.95103i	−0.0214498	+	0.0800516i
$595$		0			0
$596$	9.24050	+	5.33501i	0.378506	+	0.218530i
$597$	9.13926	+	5.27656i	0.374045	+	0.215955i
$598$	5.63604			0.230475
$599$	−18.6453	−	10.7649i	−0.761827	−	0.439841i	0.0681245	−	0.997677i	$-0.478299\pi$
$599$	−18.6453	−	10.7649i	−0.761827	−	0.439841i	−0.829951	+	0.557836i	$0.811632\pi$
$600$		0			0
$601$	−6.57451	−	11.3874i	−0.268180	−	0.464501i	0.700212	−	0.713935i	$-0.253089\pi$
$601$	−6.57451	−	11.3874i	−0.268180	−	0.464501i	−0.968392	+	0.249434i	$0.919755\pi$
$602$	−1.97771	−	1.97771i	−0.0806056	−	0.0806056i
$603$	28.1914	+	28.1914i	1.14804	+	1.14804i
$604$	10.0669	−	5.81211i	0.409615	−	0.236491i
$605$		0			0
$606$	−11.8525	+	11.8525i	−0.481474	+	0.481474i
$607$	0.817317	+	1.41563i	0.0331739	+	0.0574588i	0.882136	−	0.470995i	$-0.156105\pi$
$607$	0.817317	+	1.41563i	0.0331739	+	0.0574588i	−0.848962	+	0.528454i	$0.822772\pi$
$608$	8.21956	+	2.20243i	0.333347	+	0.0893201i
$609$	−8.62455	−	2.31094i	−0.349484	−	0.0936441i
$610$		0			0
$611$	−7.95335	+	2.13109i	−0.321758	+	0.0862148i
$612$	6.16373	+	10.6759i	0.249154	+	0.431547i
$613$	8.64586	−	32.2668i	0.349203	−	1.30324i	−0.538422	−	0.842676i	$-0.680979\pi$
$613$	8.64586	−	32.2668i	0.349203	−	1.30324i	0.887625	−	0.460568i	$-0.152354\pi$
$614$	0.570211	+	0.152788i	0.0230119	+	0.00616601i
$615$		0			0
$616$	−1.05842	−	3.95006i	−0.0426448	−	0.159152i
$617$	8.00465	+	2.14484i	0.322255	+	0.0863480i	0.416320	−	0.909218i	$-0.363320\pi$
$617$	8.00465	+	2.14484i	0.322255	+	0.0863480i	−0.0940651	+	0.995566i	$0.529986\pi$
$618$	2.52424	−	2.52424i	0.101540	−	0.101540i
$619$	−35.3283			−1.41997			−0.709983	−	0.704219i	$-0.751297\pi$
$619$	−35.3283			−1.41997			−0.709983	+	0.704219i	$0.751297\pi$
$620$		0			0
$621$	−4.45694	+	4.45694i	−0.178851	+	0.178851i
$622$	−3.62675	−	13.5352i	−0.145419	−	0.542713i
$623$		−	2.35693i		−	0.0944286i
$624$	−24.2864	+	6.50753i	−0.972235	+	0.260510i
$625$		0			0
$626$	0.326095	−	0.564812i	0.0130334	−	0.0225744i
$627$	−8.10821	+	4.68128i	−0.323811	+	0.186952i
$628$	−8.59295	−	8.59295i	−0.342896	−	0.342896i
$629$	11.2324	−	1.14453i	0.447864	−	0.0456352i
$630$		0			0
$631$	16.9880	+	4.55192i	0.676281	+	0.181209i	0.580583	−	0.814201i	$-0.302825\pi$
$631$	16.9880	+	4.55192i	0.676281	+	0.181209i	0.0956987	+	0.995410i	$0.469491\pi$
$632$	2.79173	+	10.4189i	0.111049	+	0.414440i
$633$	−16.5062	+	4.42282i	−0.656062	+	0.175791i
$634$	−1.85671	−	6.92933i	−0.0737393	−	0.275199i
$635$		0			0
$636$	−16.0907	+	27.8699i	−0.638038	+	1.10511i
$637$		−	21.4408i		−	0.849515i
$638$	3.14505	+	0.842715i	0.124514	+	0.0333634i
$639$		−	3.30671i		−	0.130811i
$640$		0			0
$641$	−1.89712	−	3.28591i	−0.0749317	−	0.129785i	0.826125	−	0.563487i	$-0.190541\pi$
$641$	−1.89712	−	3.28591i	−0.0749317	−	0.129785i	−0.901057	+	0.433702i	$0.857207\pi$
$642$	10.8649	+	6.27288i	0.428805	+	0.247571i
$643$			12.8924i			0.508428i	0.967148	+	0.254214i	$0.0818168\pi$
$643$			12.8924i			0.508428i	−0.967148	+	0.254214i	$0.918183\pi$
$644$	1.54787	−	5.77674i	0.0609947	−	0.227635i
$645$		0			0
$646$	0.402067	−	1.50053i	0.0158191	−	0.0590377i
$647$	−2.15099	+	3.72562i	−0.0845640	+	0.146469i	−0.905205	−	0.424974i	$-0.860283\pi$
$647$	−2.15099	+	3.72562i	−0.0845640	+	0.146469i	0.820641	+	0.571444i	$0.193616\pi$
$648$	5.59531	−	9.69136i	0.219804	−	0.380712i
$649$	−6.03864	+	22.5365i	−0.237037	+	0.884636i
$650$		0			0
$651$	4.53911	−	16.9402i	0.177902	−	0.663938i
$652$			44.0265i			1.72421i
$653$	1.73760	+	1.00320i	0.0679976	+	0.0392584i	0.533613	−	0.845729i	$-0.320834\pi$
$653$	1.73760	+	1.00320i	0.0679976	+	0.0392584i	−0.465616	+	0.884987i	$0.654167\pi$
$654$	−3.12758	−	5.41712i	−0.122298	−	0.211826i
$655$		0			0
$656$		−	26.4704i		−	1.03350i
$657$	20.6841	+	5.54229i	0.806963	+	0.216225i
$658$		−	1.16903i		−	0.0455733i
$659$	−20.0335	+	34.6990i	−0.780394	+	1.35168i	0.151319	+	0.988485i	$0.451648\pi$
$659$	−20.0335	+	34.6990i	−0.780394	+	1.35168i	−0.931713	+	0.363197i	$0.881685\pi$
$660$		0			0
$661$	8.62310	+	32.1818i	0.335400	+	1.25173i	0.903435	+	0.428725i	$0.141037\pi$
$661$	8.62310	+	32.1818i	0.335400	+	1.25173i	−0.568036	+	0.823004i	$0.692296\pi$
$662$	8.76513	−	2.34861i	0.340666	−	0.0912813i
$663$	4.57608	+	17.0781i	0.177720	+	0.663260i
$664$	−11.2472	−	3.01369i	−0.436477	−	0.116954i
$665$		0			0
$666$	6.51111	+	9.02187i	0.252300	+	0.349590i
$667$	7.18459	+	7.18459i	0.278188	+	0.278188i
$668$	7.91971	−	4.57245i	0.306423	−	0.176913i
$669$	−34.8016	+	60.2781i	−1.34551	+	2.33049i
$670$		0			0
$671$	−22.9804	+	6.15758i	−0.887149	+	0.237711i
$672$		−	13.7505i		−	0.530436i
$673$	−10.5436	−	39.3491i	−0.406424	−	1.51680i	−0.801414	−	0.598111i	$-0.795918\pi$
$673$	−10.5436	−	39.3491i	−0.406424	−	1.51680i	0.394989	−	0.918686i	$-0.370748\pi$
$674$	2.09776	−	2.09776i	0.0808027	−	0.0808027i
$675$		0			0
$676$	−0.727026			−0.0279626
$677$	−11.1292	+	11.1292i	−0.427732	+	0.427732i	−0.887855	−	0.460123i	$-0.847805\pi$
$677$	−11.1292	+	11.1292i	−0.427732	+	0.427732i	0.460123	+	0.887855i	$0.347805\pi$
$678$	−9.83855	−	2.63623i	−0.377847	−	0.101244i
$679$	0.189129	+	0.705841i	0.00725812	+	0.0270877i
$680$		0			0
$681$	−29.2806	−	7.84572i	−1.12204	−	0.300649i
$682$	−1.65524	+	6.17745i	−0.0633826	+	0.236547i
$683$	11.7592	+	20.3675i	0.449952	+	0.779340i	0.998382	−	0.0568564i	$-0.0181077\pi$
$683$	11.7592	+	20.3675i	0.449952	+	0.779340i	−0.548430	+	0.836196i	$0.684774\pi$
$684$	−11.0514	+	2.96122i	−0.422562	+	0.113225i
$685$		0			0
$686$	6.45605	+	1.72989i	0.246493	+	0.0660476i
$687$	41.8631	+	11.2172i	1.59718	+	0.427962i
$688$	−7.09934	−	12.2964i	−0.270660	−	0.468797i
$689$	−18.1640	+	18.1640i	−0.691993	+	0.691993i
$690$		0			0
$691$	34.9969	−	20.2055i	1.33135	−	0.768653i	0.345840	−	0.938294i	$-0.387594\pi$
$691$	34.9969	−	20.2055i	1.33135	−	0.768653i	0.985506	+	0.169641i	$0.0542607\pi$
$692$	26.2714	+	26.2714i	0.998689	+	0.998689i
$693$	5.95374	+	5.95374i	0.226164	+	0.226164i
$694$	8.84676	+	15.3230i	0.335818	+	0.581655i
$695$		0			0
$696$	13.2115	+	7.62764i	0.500779	+	0.289125i
$697$	−18.6139			−0.705052
$698$	−2.56793	−	1.48260i	−0.0971977	−	0.0561171i
$699$	8.28757	+	4.78483i	0.313465	+	0.180979i
$700$		0			0
$701$	−1.40325	+	5.23699i	−0.0529999	+	0.197798i	−0.987349	−	0.158560i	$-0.949315\pi$
$701$	−1.40325	+	5.23699i	−0.0529999	+	0.197798i	0.934350	+	0.356358i	$0.115982\pi$
$702$	−2.50327	+	2.50327i	−0.0944799	+	0.0944799i
$703$	−1.67211	+	10.3446i	−0.0630649	+	0.390155i
$704$		−	6.01664i		−	0.226761i
$705$		0			0
$706$	−9.81811	−	5.66849i	−0.369509	−	0.213336i
$707$	3.67456	+	13.7137i	0.138196	+	0.515755i
$708$	−25.6151	+	44.3666i	−0.962673	+	1.66740i
$709$	27.6470	−	27.6470i	1.03830	−	1.03830i	0.0390675	−	0.999237i	$-0.487561\pi$
$709$	27.6470	−	27.6470i	1.03830	−	1.03830i	0.999237	−	0.0390675i	$-0.0124387\pi$
$710$		0			0
$711$	−15.7039	−	15.7039i	−0.588941	−	0.588941i
$712$	−1.04225	+	3.88972i	−0.0390599	+	0.145774i
$713$	−14.1118	+	14.1118i	−0.528492	+	0.528492i
$714$	−2.51024			−0.0939433
$715$		0			0
$716$	35.2945	−	9.45712i	1.31902	−	0.353429i
$717$	18.8824			0.705176
$718$	−5.78652	+	3.34085i	−0.215951	+	0.124679i
$719$	17.5989	−	10.1607i	0.656328	−	0.378931i	−0.134548	−	0.990907i	$-0.542958\pi$
$719$	17.5989	−	10.1607i	0.656328	−	0.378931i	0.790877	+	0.611976i	$0.209625\pi$
$720$		0			0
$721$	−0.782577	−	2.92062i	−0.0291447	−	0.108769i
$722$	−6.74525	−	3.89437i	−0.251032	−	0.144934i
$723$	56.3016	−	32.5057i	2.09388	−	1.20890i
$724$	19.2433	+	33.3304i	0.715172	+	1.23871i
$725$		0			0
$726$	5.92739	+	5.92739i	0.219986	+	0.219986i
$727$	17.0686	−	29.5637i	0.633039	−	1.09646i	−0.353888	−	0.935288i	$-0.615140\pi$
$727$	17.0686	−	29.5637i	0.633039	−	1.09646i	0.986927	−	0.161168i	$-0.0515262\pi$
$728$	1.85507	−	6.92321i	0.0687534	−	0.256591i
$729$			38.5667i			1.42840i
$730$		0			0
$731$	−8.64681	+	4.99224i	−0.319814	+	0.184645i
$732$	−52.2392			−1.93082
$733$	−19.7857	+	5.30156i	−0.730802	+	0.195818i	−0.604986	−	0.796236i	$-0.706821\pi$
$733$	−19.7857	+	5.30156i	−0.730802	+	0.195818i	−0.125815	+	0.992054i	$0.540155\pi$
$734$	2.01085	+	2.01085i	0.0742218	+	0.0742218i
$735$		0			0
$736$	−7.82369	+	13.5510i	−0.288385	+	0.499497i
$737$	−21.3725	+	5.72674i	−0.787266	+	0.210947i
$738$	−9.17136	−	15.8853i	−0.337602	−	0.584744i
$739$	−36.2323			−1.33283			−0.666414	−	0.745582i	$-0.732172\pi$
$739$	−36.2323			−1.33283			−0.666414	+	0.745582i	$0.732172\pi$
$740$		0			0
$741$	−16.4096			−0.602822
$742$	−1.82354	−	3.15846i	−0.0669441	−	0.115951i
$743$	32.4293	−	8.68941i	1.18972	−	0.318784i	0.390943	−	0.920415i	$-0.372149\pi$
$743$	32.4293	−	8.68941i	1.18972	−	0.318784i	0.798774	+	0.601631i	$0.205482\pi$
$744$	−14.9821	+	25.9497i	−0.549269	+	0.951362i
$745$		0			0
$746$	−9.40559	−	9.40559i	−0.344363	−	0.344363i
$747$	23.1574	−	6.20502i	0.847286	−	0.227030i
$748$	−6.84153			−0.250151
$749$	9.20265	−	5.31315i	0.336258	−	0.194138i
$750$		0			0
$751$			33.4106i			1.21917i	0.792721	+	0.609585i	$0.208664\pi$
$751$			33.4106i			1.21917i	−0.792721	+	0.609585i	$0.791336\pi$
$752$	1.53599	−	5.73241i	0.0560119	−	0.209039i
$753$	−5.63172	+	9.75443i	−0.205231	+	0.355471i
$754$	4.03527	+	4.03527i	0.146956	+	0.146956i
$755$		0			0
$756$	1.87827	+	3.25325i	0.0683119	+	0.118320i
$757$	12.5431	−	7.24176i	0.455886	−	0.263206i	−0.254427	−	0.967092i	$-0.581887\pi$
$757$	12.5431	−	7.24176i	0.455886	−	0.263206i	0.710313	+	0.703886i	$0.248553\pi$
$758$	−7.04656	−	4.06834i	−0.255943	−	0.147769i
$759$	−4.45582	−	16.6293i	−0.161736	−	0.603607i
$760$		0			0
$761$	18.3530	−	10.5961i	0.665296	−	0.384109i	−0.128996	−	0.991645i	$-0.541175\pi$
$761$	18.3530	−	10.5961i	0.665296	−	0.384109i	0.794292	+	0.607536i	$0.207842\pi$
$762$	22.4034	−	12.9346i	0.811590	−	0.468572i
$763$	−5.29814			−0.191806
$764$	−43.2036	+	11.5764i	−1.56305	+	0.418819i
$765$		0			0
$766$	15.3639			0.555122
$767$	−28.9156	+	28.9156i	−1.04408	+	1.04408i
$768$	0.188361	−	0.702972i	0.00679688	−	0.0253663i
$769$	−27.0019	−	27.0019i	−0.973712	−	0.973712i	0.0259516	−	0.999663i	$-0.491738\pi$
$769$	−27.0019	−	27.0019i	−0.973712	−	0.973712i	−0.999663	+	0.0259516i	$0.991738\pi$
$770$		0			0
$771$	56.9446	−	56.9446i	2.05081	−	2.05081i
$772$	2.43883	−	4.22417i	0.0877753	−	0.152031i
$773$	−2.37183	−	8.85179i	−0.0853088	−	0.318377i	0.910064	−	0.414468i	$-0.136032\pi$
$773$	−2.37183	−	8.85179i	−0.0853088	−	0.318377i	−0.995372	+	0.0960916i	$0.969366\pi$
$774$	−8.52083	−	4.91950i	−0.306275	−	0.176828i
$775$		0			0
$776$		−	1.24851i		−	0.0448187i
$777$	16.8456	−	1.71648i	0.604331	−	0.0615785i
$778$	−12.3007	+	12.3007i	−0.441001	+	0.441001i
$779$	4.47131	−	16.6872i	0.160201	−	0.597880i
$780$		0			0
$781$	1.58930	+	0.917582i	0.0568696	+	0.0328337i
$782$	2.47383	+	1.42827i	0.0884639	+	0.0510747i
$783$	−6.38213			−0.228079
$784$	13.3832	+	7.72677i	0.477970	+	0.275956i
$785$		0			0
$786$	−6.17715	−	10.6991i	−0.220332	−	0.381626i
$787$	−2.37899	−	2.37899i	−0.0848017	−	0.0848017i	0.663434	−	0.748235i	$-0.269099\pi$
$787$	−2.37899	−	2.37899i	−0.0848017	−	0.0848017i	−0.748235	+	0.663434i	$0.769099\pi$
$788$	−17.0587	−	17.0587i	−0.607690	−	0.607690i
$789$	28.5886	−	16.5057i	1.01778	−	0.587617i
$790$		0			0
$791$	−6.10040	+	6.10040i	−0.216905	+	0.216905i
$792$	−7.19287	−	12.4584i	−0.255588	−	0.442691i
$793$	−40.2774	−	10.7923i	−1.43029	−	0.383246i
$794$	10.4107	+	2.78955i	0.369463	+	0.0989974i
$795$		0			0
$796$	−6.91328	+	1.85241i	−0.245035	+	0.0656568i
$797$	−27.4458	−	47.5375i	−0.972179	−	1.68386i	−0.688947	−	0.724811i	$-0.741927\pi$
$797$	−27.4458	−	47.5375i	−0.972179	−	1.68386i	−0.283231	−	0.959052i	$-0.591406\pi$
$798$	0.602993	−	2.25040i	0.0213457	−	0.0796633i
$799$	−4.03101	−	1.08011i	−0.142607	−	0.0382114i
$800$		0			0
$801$	−2.14593	−	8.00873i	−0.0758228	−	0.282975i
$802$	−9.85063	−	2.63947i	−0.347838	−	0.0932028i
$803$	−8.40344	+	8.40344i	−0.296551	+	0.296551i
$804$	−48.5841			−1.71343
$805$		0			0
$806$	−7.92601	+	7.92601i	−0.279182	+	0.279182i
$807$	−11.2778	−	42.0893i	−0.396997	−	1.48161i
$808$		−	24.2570i		−	0.853358i
$809$	1.18348	−	0.317113i	0.0416090	−	0.0111491i	−0.237955	−	0.971276i	$-0.576477\pi$
$809$	1.18348	−	0.317113i	0.0416090	−	0.0111491i	0.279563	+	0.960127i	$0.409810\pi$
$810$		0			0
$811$	16.2208	−	28.0952i	0.569588	−	0.986556i	−0.427018	−	0.904243i	$-0.640436\pi$
$811$	16.2208	−	28.0952i	0.569588	−	0.986556i	0.996607	−	0.0823128i	$-0.0262307\pi$
$812$	5.24425	−	3.02777i	0.184037	−	0.106254i
$813$	35.1365	+	35.1365i	1.23229	+	1.23229i
$814$	−6.14295	+	0.625938i	−0.215310	+	0.0219391i
$815$		0			0
$816$	−12.3091	−	3.29823i	−0.430906	−	0.115461i
$817$	−2.39841	−	8.95097i	−0.0839096	−	0.313155i
$818$	−16.5987	+	4.44761i	−0.580361	+	0.155507i
$819$	3.81948	+	14.2545i	0.133464	+	0.498093i
$820$		0			0
$821$	−15.4623	+	26.7814i	−0.539637	+	0.934678i	0.459287	+	0.888288i	$0.348105\pi$
$821$	−15.4623	+	26.7814i	−0.539637	+	0.934678i	−0.998923	+	0.0463901i	$0.985228\pi$
$822$		−	19.8594i		−	0.692676i
$823$	20.3920	+	5.46402i	0.710820	+	0.190464i	0.596072	−	0.802931i	$-0.296727\pi$
$823$	20.3920	+	5.46402i	0.710820	+	0.190464i	0.114748	+	0.993395i	$0.463394\pi$
$824$			5.16605i			0.179968i
$825$		0			0
$826$	−2.90292	−	5.02800i	−0.101005	−	0.174946i
$827$	−8.36201	−	4.82781i	−0.290776	−	0.167879i	0.347516	−	0.937674i	$-0.387025\pi$
$827$	−8.36201	−	4.82781i	−0.290776	−	0.167879i	−0.638292	+	0.769795i	$0.720359\pi$
$828$		−	21.0383i		−	0.731133i
$829$	−3.28514	+	12.2603i	−0.114097	+	0.425818i	−0.999218	−	0.0395446i	$-0.987409\pi$
$829$	−3.28514	+	12.2603i	−0.114097	+	0.425818i	0.885120	+	0.465362i	$0.154076\pi$
$830$		0			0
$831$	11.3264	−	42.2709i	0.392910	−	1.46636i
$832$	5.27263	−	9.13247i	0.182796	−	0.316611i
$833$	5.43344	−	9.41100i	0.188258	−	0.326072i
$834$	3.02061	−	11.2731i	0.104595	−	0.390355i
$835$		0			0
$836$	1.64343	−	6.13335i	0.0568391	−	0.212127i
$837$		−	12.5356i		−	0.433295i
$838$	−6.23049	−	3.59718i	−0.215229	−	0.124262i
$839$	9.34812	+	16.1914i	0.322733	+	0.558990i	0.981051	−	0.193750i	$-0.0620651\pi$
$839$	9.34812	+	16.1914i	0.322733	+	0.558990i	−0.658318	+	0.752740i	$0.728732\pi$
$840$		0			0
$841$		−	18.7120i		−	0.645242i
$842$	8.64147	+	2.31547i	0.297805	+	0.0797965i
$843$			58.7379i			2.02304i
$844$	5.79473	−	10.0368i	0.199463	−	0.345480i
$845$		0			0
$846$	−1.06437	−	3.97228i	−0.0365938	−	0.136570i
$847$	6.85816	−	1.83764i	0.235649	−	0.0631420i
$848$	−4.79192	−	17.8837i	−0.164555	−	0.614129i
$849$	−10.9867	−	2.94387i	−0.377062	−	0.101033i
$850$		0			0
$851$	−17.5779	−	7.89313i	−0.602561	−	0.270573i
$852$	2.84933	+	2.84933i	0.0976164	+	0.0976164i
$853$	7.07448	−	4.08446i	0.242226	−	0.139849i	−0.373974	−	0.927439i	$-0.622005\pi$
$853$	7.07448	−	4.08446i	0.242226	−	0.139849i	0.616199	+	0.787590i	$0.288672\pi$
$854$	2.96009	−	5.12703i	0.101292	−	0.175444i
$855$		0			0
$856$	−17.5369	+	4.69901i	−0.599400	+	0.160609i
$857$			1.03295i			0.0352847i	0.999844	+	0.0176424i	$0.00561603\pi$
$857$			1.03295i			0.0352847i	−0.999844	+	0.0176424i	$0.994384\pi$
$858$	−2.50264	−	9.33999i	−0.0854388	−	0.318862i
$859$	20.1427	−	20.1427i	0.687259	−	0.687259i	−0.274367	−	0.961625i	$-0.588468\pi$
$859$	20.1427	−	20.1427i	0.687259	−	0.687259i	0.961625	+	0.274367i	$0.0884682\pi$
$860$		0			0
$861$	−27.9159			−0.951371
$862$	−13.1783	+	13.1783i	−0.448856	+	0.448856i
$863$	−25.4613	−	6.82233i	−0.866712	−	0.232235i	−0.202046	−	0.979376i	$-0.564759\pi$
$863$	−25.4613	−	6.82233i	−0.866712	−	0.232235i	−0.664665	+	0.747141i	$0.731426\pi$
$864$	−2.54382	−	9.49367i	−0.0865425	−	0.322981i
$865$		0			0
$866$	7.10587	+	1.90401i	0.241467	+	0.0647010i
$867$	9.12473	−	34.0540i	0.309892	−	1.15653i
$868$	5.94708	+	10.3006i	0.201857	+	0.349627i
$869$	11.9054	−	3.19005i	0.403864	−	0.108215i
$870$		0			0
$871$	−37.4592	−	10.0372i	−1.26926	−	0.340096i
$872$	8.74370	+	2.34287i	0.296099	+	0.0793395i
$873$	1.28530	+	2.22621i	0.0435009	+	0.0753458i
$874$	−1.87467	+	1.87467i	−0.0634117	+	0.0634117i
$875$		0			0
$876$	−22.5988	+	13.0474i	−0.763543	+	0.440832i
$877$	34.9927	+	34.9927i	1.18162	+	1.18162i	0.979325	+	0.202294i	$0.0648395\pi$
$877$	34.9927	+	34.9927i	1.18162	+	1.18162i	0.202294	+	0.979325i	$0.435160\pi$
$878$	2.11403	+	2.11403i	0.0713451	+	0.0713451i
$879$	−37.1790	−	64.3960i	−1.25402	−	2.17202i
$880$		0			0
$881$	17.4478	+	10.0735i	0.587831	+	0.339384i	0.764239	−	0.644933i	$-0.223115\pi$
$881$	17.4478	+	10.0735i	0.587831	+	0.339384i	−0.176408	+	0.984317i	$0.556448\pi$
$882$	10.7086			0.360576
$883$	19.6558	+	11.3483i	0.661471	+	0.381901i	0.792837	−	0.609433i	$-0.208603\pi$
$883$	19.6558	+	11.3483i	0.661471	+	0.381901i	−0.131366	+	0.991334i	$0.541936\pi$
$884$	−10.3845	−	5.99552i	−0.349270	−	0.201651i
$885$		0			0
$886$	0.382476	−	1.42742i	0.0128495	−	0.0479552i
$887$	−11.4898	+	11.4898i	−0.385791	+	0.385791i	−0.873183	−	0.487392i	$-0.837948\pi$
$887$	−11.4898	+	11.4898i	−0.385791	+	0.385791i	0.487392	+	0.873183i	$0.337948\pi$
$888$	−28.5598	−	4.61643i	−0.958405	−	0.154917i
$889$		−	21.9114i		−	0.734883i
$890$		0			0
$891$	−11.0741	−	6.39364i	−0.370997	−	0.214195i
$892$	−12.2176	−	45.5966i	−0.409074	−	1.52669i
$893$	1.93661	−	3.35430i	0.0648061	−	0.112247i
$894$	−5.40460	+	5.40460i	−0.180757	+	0.180757i
$895$		0			0
$896$	8.53517	+	8.53517i	0.285140	+	0.285140i
$897$	7.80964	−	29.1460i	0.260756	−	0.973156i
$898$	7.74348	−	7.74348i	0.258403	−	0.258403i
$899$	−20.2075			−0.673957
$900$		0			0
$901$	−12.5758	+	3.36967i	−0.418960	+	0.112260i
$902$	10.1799			0.338953
$903$	−12.9679	+	7.48702i	−0.431545	+	0.249153i
$904$	12.7653	−	7.37005i	0.424568	−	0.245124i
$905$		0			0
$906$	2.15513	+	8.04306i	0.0715994	+	0.267213i
$907$	−16.8581	−	9.73301i	−0.559763	−	0.323179i	0.193287	−	0.981142i	$-0.438085\pi$
$907$	−16.8581	−	9.73301i	−0.559763	−	0.323179i	−0.753050	+	0.657963i	$0.771418\pi$
$908$	17.8044	−	10.2794i	0.590859	−	0.341133i
$909$	24.9719	+	43.2526i	0.828266	+	1.43460i
$910$		0			0
$911$	−10.7957	−	10.7957i	−0.357678	−	0.357678i	0.505279	−	0.862956i	$-0.331390\pi$
$911$	−10.7957	−	10.7957i	−0.357678	−	0.357678i	−0.862956	+	0.505279i	$0.831390\pi$
$912$	5.91365	−	10.2427i	0.195820	−	0.339171i
$913$	−3.44368	+	12.8520i	−0.113969	+	0.425338i
$914$			2.83861i			0.0938929i
$915$		0			0
$916$	−25.4553	+	14.6966i	−0.841066	+	0.485590i
$917$	−10.4642			−0.345557
$918$	−1.73313	+	0.464391i	−0.0572018	+	0.0153272i
$919$	−0.633274	−	0.633274i	−0.0208898	−	0.0208898i	0.696585	−	0.717475i	$-0.254702\pi$
$919$	−0.633274	−	0.633274i	−0.0208898	−	0.0208898i	−0.717475	+	0.696585i	$0.754702\pi$
$920$		0			0
$921$	1.58024	−	2.73705i	0.0520706	−	0.0901890i
$922$	−4.00738	+	1.07377i	−0.131976	+	0.0353629i
$923$	1.60823	+	2.78554i	0.0529356	+	0.0916872i
$924$	−10.2605			−0.337544
$925$		0			0
$926$	−2.49647			−0.0820392
$927$	−5.31831	−	9.21158i	−0.174676	−	0.302548i
$928$	−15.3038	+	4.10064i	−0.502372	+	0.134610i
$929$	23.7899	−	41.2053i	0.780521	−	1.35190i	−0.151118	−	0.988516i	$-0.548287\pi$
$929$	23.7899	−	41.2053i	0.780521	−	1.35190i	0.931639	−	0.363386i	$-0.118379\pi$
$930$		0			0
$931$	7.13167	+	7.13167i	0.233731	+	0.233731i
$932$	−6.26903	+	1.67978i	−0.205349	+	0.0550230i
$933$	−75.0209			−2.45607
$934$	4.55000	−	2.62694i	0.148881	−	0.0859563i
$935$		0			0
$936$		−	25.2137i		−	0.824135i
$937$	12.3173	−	45.9687i	0.402388	−	1.50173i	−0.406435	−	0.913680i	$-0.633228\pi$
$937$	12.3173	−	45.9687i	0.402388	−	1.50173i	0.808823	−	0.588052i	$-0.200105\pi$
$938$	2.75298	−	4.76830i	0.0898879	−	0.155690i
$939$	−2.46899	−	2.46899i	−0.0805724	−	0.0805724i
$940$		0			0
$941$	−16.4063	−	28.4165i	−0.534829	−	0.926351i	−0.999172	−	0.0406953i	$-0.987043\pi$
$941$	−16.4063	−	28.4165i	−0.534829	−	0.926351i	0.464343	−	0.885656i	$-0.346291\pi$
$942$	7.53880	−	4.35253i	0.245627	−	0.141813i
$943$	27.5110	+	15.8835i	0.895881	+	0.517237i
$944$	−7.62834	−	28.4694i	−0.248281	−	0.926599i
$945$		0			0
$946$	4.72891	−	2.73024i	0.153750	−	0.0887677i
$947$	3.81592	−	2.20312i	0.124001	−	0.0715918i	−0.436717	−	0.899599i	$-0.643859\pi$
$947$	3.81592	−	2.20312i	0.124001	−	0.0715918i	0.560717	+	0.828007i	$0.310525\pi$
$948$	27.0635			0.878981
$949$	−20.1196	+	5.39104i	−0.653111	+	0.175000i
$950$		0			0
$951$	−38.4068			−1.24543
$952$	2.56870	−	2.56870i	0.0832520	−	0.0832520i
$953$	−4.86825	+	18.1686i	−0.157698	+	0.588538i	0.841161	+	0.540785i	$0.181873\pi$
$953$	−4.86825	+	18.1686i	−0.157698	+	0.588538i	−0.998859	+	0.0477530i	$0.984794\pi$
$954$	−9.07197	−	9.07197i	−0.293716	−	0.293716i
$955$		0			0
$956$	−9.05527	+	9.05527i	−0.292868	+	0.292868i
$957$	8.71595	−	15.0965i	0.281747	−	0.488000i
$958$	0.512936	+	1.91430i	0.0165722	+	0.0618483i
$959$	−14.5674	−	8.41050i	−0.470406	−	0.271589i
$960$		0			0
$961$		−	8.69111i		−	0.280358i
$962$	−9.87273	−	4.43324i	−0.318310	−	0.142933i
$963$	26.4326	−	26.4326i	0.851779	−	0.851779i
$964$	−11.4116	+	42.5886i	−0.367542	+	1.37169i
$965$		0			0
$966$	3.71008	+	2.14202i	0.119370	+	0.0689182i
$967$	24.0118	+	13.8632i	0.772167	+	0.445811i	0.833647	−	0.552297i	$-0.186249\pi$
$967$	24.0118	+	13.8632i	0.772167	+	0.445811i	−0.0614801	+	0.998108i	$0.519582\pi$
$968$	−12.1309			−0.389901
$969$	−7.20267	−	4.15846i	−0.231383	−	0.133589i
$970$		0			0
$971$	−17.5325	−	30.3673i	−0.562646	−	0.974532i	−0.997264	−	0.0739171i	$-0.976450\pi$
$971$	−17.5325	−	30.3673i	−0.562646	−	0.974532i	0.434618	−	0.900615i	$-0.356883\pi$
$972$	−27.2995	−	27.2995i	−0.875632	−	0.875632i
$973$	−6.98987	−	6.98987i	−0.224085	−	0.224085i
$974$	4.38912	−	2.53406i	0.140637	−	0.0811965i
$975$		0			0
$976$	21.2515	−	21.2515i	0.680245	−	0.680245i
$977$	−6.22537	−	10.7827i	−0.199167	−	0.344968i	0.749091	−	0.662467i	$-0.230490\pi$
$977$	−6.22537	−	10.7827i	−0.199167	−	0.344968i	−0.948259	+	0.317499i	$0.897157\pi$
$978$	−30.4630	−	8.16252i	−0.974098	−	0.261009i
$979$	4.44471	+	1.19096i	0.142053	+	0.0380631i
$980$		0			0
$981$	−18.0028	+	4.82384i	−0.574785	+	0.154013i
$982$	1.80530	+	3.12687i	0.0576094	+	0.0997825i
$983$	5.16785	−	19.2867i	0.164829	−	0.615150i	−0.833233	−	0.552922i	$-0.813513\pi$
$983$	5.16785	−	19.2867i	0.164829	−	0.615150i	0.998062	−	0.0622280i	$-0.0198206\pi$
$984$	46.0705	+	12.3446i	1.46867	+	0.393530i
$985$		0			0
$986$	0.748598	+	2.79381i	0.0238402	+	0.0889729i
$987$	−6.04544	−	1.61987i	−0.192429	−	0.0515611i
$988$	7.86942	−	7.86942i	0.250360	−	0.250360i
$989$	17.0397			0.541832
$990$		0			0
$991$	0.0857771	−	0.0857771i	0.00272480	−	0.00272480i	−0.705743	−	0.708468i	$-0.749387\pi$
$991$	0.0857771	−	0.0857771i	0.00272480	−	0.00272480i	0.708468	+	0.705743i	$0.249387\pi$
$992$	−8.05439	−	30.0594i	−0.255727	−	0.954387i
$993$		−	48.5820i		−	1.54170i
$994$	−0.441103	+	0.118193i	−0.0139910	+	0.00374886i
$995$		0			0
$996$	−14.6076	+	25.3011i	−0.462859	+	0.801696i
$997$	25.1030	−	14.4932i	0.795021	−	0.459006i	−0.0467059	−	0.998909i	$-0.514872\pi$
$997$	25.1030	−	14.4932i	0.795021	−	0.459006i	0.841727	+	0.539903i	$0.181539\pi$
$998$	−8.58611	−	8.58611i	−0.271789	−	0.271789i
$999$	11.3130	−	4.30151i	0.357929	−	0.136094i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.t.c.82.10	✓	96
5.2	odd	4		925.2.y.c.193.15	yes	96
5.3	odd	4		925.2.y.c.193.10	yes	96
5.4	even	2	inner	925.2.t.c.82.15	yes	96
37.14	odd	12		925.2.y.c.532.10	yes	96
185.14	odd	12		925.2.y.c.532.15	yes	96
185.88	even	12	inner	925.2.t.c.643.10	yes	96
185.162	even	12	inner	925.2.t.c.643.15	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
925.2.t.c.82.10	✓	96	1.1	even	1	trivial
925.2.t.c.82.15	yes	96	5.4	even	2	inner
925.2.t.c.643.10	yes	96	185.88	even	12	inner
925.2.t.c.643.15	yes	96	185.162	even	12	inner
925.2.y.c.193.10	yes	96	5.3	odd	4
925.2.y.c.193.15	yes	96	5.2	odd	4
925.2.y.c.532.10	yes	96	37.14	odd	12
925.2.y.c.532.15	yes	96	185.14	odd	12

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

Level:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.t (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.242909 - 0.420731i) q^{2} +(-2.51234 + 0.673179i) q^{3} +(0.881990 - 1.52765i) q^{4} +(0.893496 + 0.893496i) q^{6} +(1.03380 - 0.277006i) q^{7} -1.82861 q^{8} +(3.26059 - 1.88250i) q^{9} +2.08952i q^{11} +(-1.18747 + 4.43171i) q^{12} +(-1.83113 + 3.17161i) q^{13} +(-0.367665 - 0.367665i) q^{14} +(-1.31980 - 2.28595i) q^{16} +(-1.60748 + 0.928076i) q^{17} +(-1.58405 - 0.914554i) q^{18} +(-0.445873 - 1.66402i) q^{19} +(-2.41078 + 1.39187i) q^{21} +(0.879123 - 0.507562i) q^{22} +3.16775 q^{23} +(4.59408 - 1.23098i) q^{24} +1.77919 q^{26} +(-1.40697 + 1.40697i) q^{27} +(0.488634 - 1.82361i) q^{28} +(2.26804 + 2.26804i) q^{29} +(-4.45483 + 4.45483i) q^{31} +(-2.46979 + 4.27780i) q^{32} +(-1.40662 - 5.24957i) q^{33} +(0.780940 + 0.450876i) q^{34} -6.64140i q^{36} +(-5.54900 - 2.49171i) q^{37} +(-0.591798 + 0.591798i) q^{38} +(2.46536 - 9.20083i) q^{39} +(8.68470 + 5.01411i) q^{41} +(1.17120 + 0.676194i) q^{42} +5.37912 q^{43} +(3.19205 + 1.84293i) q^{44} +(-0.769476 - 1.33277i) q^{46} +(1.58980 + 1.58980i) q^{47} +(4.85462 + 4.85462i) q^{48} +(-5.07016 + 2.92726i) q^{49} +(3.41376 - 3.41376i) q^{51} +(3.23008 + 5.59466i) q^{52} +(6.77518 + 1.81540i) q^{53} +(0.933722 + 0.250190i) q^{54} +(-1.89042 + 0.506536i) q^{56} +(2.24037 + 3.88043i) q^{57} +(0.403306 - 1.50516i) q^{58} +(10.7855 + 2.88997i) q^{59} +(2.94690 + 10.9980i) q^{61} +(2.95641 + 0.792167i) q^{62} +(2.84934 - 2.84934i) q^{63} -2.87944 q^{64} +(-1.86697 + 1.86697i) q^{66} +(2.74070 + 10.2284i) q^{67} +3.27422i q^{68} +(-7.95847 + 2.13247i) q^{69} +(0.439137 - 0.760607i) q^{71} +(-5.96235 + 3.44237i) q^{72} +(4.02172 + 4.02172i) q^{73} +(0.299561 + 2.93989i) q^{74} +(-2.93530 - 0.786511i) q^{76} +(0.578809 + 2.16014i) q^{77} +(-4.46993 + 1.19771i) q^{78} +(-1.52669 - 5.69770i) q^{79} +(-3.05987 + 5.29985i) q^{81} -4.87189i q^{82} +(6.15070 + 1.64807i) q^{83} +4.91045i q^{84} +(-1.30664 - 2.26316i) q^{86} +(-7.22487 - 4.17128i) q^{87} -3.82091i q^{88} +(0.569968 - 2.12715i) q^{89} +(-1.01447 + 3.78605i) q^{91} +(2.79393 - 4.83923i) q^{92} +(8.19315 - 14.1909i) q^{93} +(0.282701 - 1.05505i) q^{94} +(3.32522 - 12.4099i) q^{96} +0.682762i q^{97} +(2.46318 + 1.42212i) q^{98} +(3.93352 + 6.81306i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 40 q^{4} + 32 q^{14} - 4 q^{16} + 24 q^{19} + 36 q^{21} - 52 q^{24} + 16 q^{26} - 12 q^{29} + 4 q^{31} + 60 q^{34} - 100 q^{39} - 48 q^{41} - 48 q^{44} + 24 q^{46} + 120 q^{49} - 84 q^{51} - 104 q^{54}+ \cdots + 24 q^{99}+O(q^{100}) \) 96 * q - 40 * q^4 + 32 * q^14 - 4 * q^16 + 24 * q^19 + 36 * q^21 - 52 * q^24 + 16 * q^26 - 12 * q^29 + 4 * q^31 + 60 * q^34 - 100 * q^39 - 48 * q^41 - 48 * q^44 + 24 * q^46 + 120 * q^49 - 84 * q^51 - 104 * q^54 - 68 * q^56 + 28 * q^59 + 68 * q^61 - 48 * q^64 + 4 * q^66 - 28 * q^69 + 48 * q^71 + 48 * q^74 - 152 * q^76 + 92 * q^79 - 16 * q^81 + 20 * q^86 + 8 * q^89 - 12 * q^91 - 56 * q^94 + 252 * q^96 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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