LMFDB - Embedded newform 525.2.bc.e.157.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(82,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 10]))

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

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

chi := DirichletCharacter("525.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bc (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			157.4
Character	$\chi$	$=$	525.157
Dual form			525.2.bc.e.418.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.105703 + 0.394487i) q^{2} +(0.965926 - 0.258819i) q^{3} +(1.58760 + 0.916603i) q^{4} +0.408404i q^{6} +(-2.57548 + 0.605712i) q^{7} +(-1.10697 + 1.10697i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.105703 + 0.394487i) q^{2} +(0.965926 - 0.258819i) q^{3} +(1.58760 + 0.916603i) q^{4} +0.408404i q^{6} +(-2.57548 + 0.605712i) q^{7} +(-1.10697 + 1.10697i) q^{8} +(0.866025 - 0.500000i) q^{9} +(-0.463738 + 0.803218i) q^{11} +(1.77074 + 0.474469i) q^{12} +(4.08169 + 4.08169i) q^{13} +(0.0332893 - 1.08002i) q^{14} +(1.51353 + 2.62151i) q^{16} +(0.192844 + 0.719705i) q^{17} +(0.105703 + 0.394487i) q^{18} +(1.21966 + 2.11252i) q^{19} +(-2.33096 + 1.25166i) q^{21} +(-0.267841 - 0.267841i) q^{22} +(5.00751 + 1.34176i) q^{23} +(-0.782747 + 1.35576i) q^{24} +(-2.04162 + 1.17873i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-4.64404 - 1.39907i) q^{28} -8.08080i q^{29} +(-1.05279 - 0.607827i) q^{31} +(-4.21844 + 1.13033i) q^{32} +(-0.240048 + 0.895873i) q^{33} -0.304299 q^{34} +1.83321 q^{36} +(0.472316 - 1.76271i) q^{37} +(-0.962282 + 0.257843i) q^{38} +(4.99903 + 2.88619i) q^{39} -6.97323i q^{41} +(-0.247375 - 1.05184i) q^{42} +(0.781574 - 0.781574i) q^{43} +(-1.47246 + 0.850128i) q^{44} +(-1.05861 + 1.83357i) q^{46} +(-10.0896 - 2.70351i) q^{47} +(2.14045 + 2.14045i) q^{48} +(6.26622 - 3.12000i) q^{49} +(0.372547 + 0.645270i) q^{51} +(2.73882 + 10.2214i) q^{52} +(-1.72055 - 6.42117i) q^{53} +(0.204202 + 0.353688i) q^{54} +(2.18048 - 3.52149i) q^{56} +(1.72486 + 1.72486i) q^{57} +(3.18778 + 0.854162i) q^{58} +(-5.91173 + 10.2394i) q^{59} +(-3.72841 + 2.15260i) q^{61} +(0.351062 - 0.351062i) q^{62} +(-1.92758 + 1.81230i) q^{63} +4.27052i q^{64} +(-0.328037 - 0.189392i) q^{66} +(10.4844 - 2.80929i) q^{67} +(-0.353523 + 1.31937i) q^{68} +5.18415 q^{69} +9.89994 q^{71} +(-0.405180 + 1.51215i) q^{72} +(-4.02609 + 1.07879i) q^{73} +(0.645441 + 0.372646i) q^{74} +4.47178i q^{76} +(0.707830 - 2.34957i) q^{77} +(-1.66698 + 1.66698i) q^{78} +(-7.02976 + 4.05863i) q^{79} +(0.500000 - 0.866025i) q^{81} +(2.75085 + 0.737088i) q^{82} +(-5.91429 - 5.91429i) q^{83} +(-4.84791 - 0.149426i) q^{84} +(0.225707 + 0.390935i) q^{86} +(-2.09147 - 7.80546i) q^{87} +(-0.375795 - 1.40248i) q^{88} +(-7.78809 - 13.4894i) q^{89} +(-12.9847 - 8.04000i) q^{91} +(6.72008 + 6.72008i) q^{92} +(-1.17423 - 0.314634i) q^{93} +(2.13300 - 3.69446i) q^{94} +(-3.78215 + 2.18363i) q^{96} +(4.89426 - 4.89426i) q^{97} +(0.568446 + 2.80174i) q^{98} +0.927476i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 8 q^{7} + 24 q^{8}+O(q^{10}) $ 32 * q - 8 * q^7 + 24 * q^8	$ 32 q - 8 q^{7} + 24 q^{8} - 8 q^{11} - 8 q^{21} + 8 q^{22} + 8 q^{23} + 24 q^{26} + 24 q^{28} + 24 q^{31} - 24 q^{32} + 36 q^{33} - 32 q^{36} - 4 q^{37} - 12 q^{38} - 16 q^{42} - 40 q^{43} - 40 q^{46} + 60 q^{47} - 8 q^{51} + 108 q^{52} + 24 q^{53} - 48 q^{56} - 16 q^{57} - 4 q^{58} - 24 q^{61} - 4 q^{63} + 72 q^{66} - 8 q^{67} - 132 q^{68} - 16 q^{71} - 12 q^{72} - 36 q^{73} - 60 q^{77} - 80 q^{78} + 16 q^{81} - 12 q^{82} - 16 q^{86} + 24 q^{87} + 32 q^{88} - 24 q^{91} + 56 q^{92} + 24 q^{93} + 72 q^{98}+O(q^{100}) $ 32 * q - 8 * q^7 + 24 * q^8 - 8 * q^11 - 8 * q^21 + 8 * q^22 + 8 * q^23 + 24 * q^26 + 24 * q^28 + 24 * q^31 - 24 * q^32 + 36 * q^33 - 32 * q^36 - 4 * q^37 - 12 * q^38 - 16 * q^42 - 40 * q^43 - 40 * q^46 + 60 * q^47 - 8 * q^51 + 108 * q^52 + 24 * q^53 - 48 * q^56 - 16 * q^57 - 4 * q^58 - 24 * q^61 - 4 * q^63 + 72 * q^66 - 8 * q^67 - 132 * q^68 - 16 * q^71 - 12 * q^72 - 36 * q^73 - 60 * q^77 - 80 * q^78 + 16 * q^81 - 12 * q^82 - 16 * q^86 + 24 * q^87 + 32 * q^88 - 24 * q^91 + 56 * q^92 + 24 * q^93 + 72 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.105703	+	0.394487i	−0.0747430	+	0.278945i	−0.993175	−	0.116634i	$-0.962789\pi$
$2$	−0.105703	+	0.394487i	−0.0747430	+	0.278945i	0.918432	+	0.395579i	$0.129456\pi$
$3$	0.965926	−	0.258819i	0.557678	−	0.149429i
$3$	0.965926	−	0.258819i	0.557678	−	0.149429i
$4$	1.58760	+	0.916603i	0.793802	+	0.458302i
$5$		0			0
$5$		0			0
$6$			0.408404i			0.166730i
$7$	−2.57548	+	0.605712i	−0.973441	+	0.228938i
$7$	−2.57548	+	0.605712i	−0.973441	+	0.228938i
$8$	−1.10697	+	1.10697i	−0.391374	+	0.391374i
$9$	0.866025	−	0.500000i	0.288675	−	0.166667i
$10$		0			0
$11$	−0.463738	+	0.803218i	−0.139822	+	0.242179i	−0.927429	−	0.373999i	$-0.877986\pi$
$11$	−0.463738	+	0.803218i	−0.139822	+	0.242179i	0.787607	+	0.616178i	$0.211320\pi$
$12$	1.77074	+	0.474469i	0.511169	+	0.136967i
$13$	4.08169	+	4.08169i	1.13206	+	1.13206i	0.989835	+	0.142224i	$0.0454252\pi$
$13$	4.08169	+	4.08169i	1.13206	+	1.13206i	0.142224	+	0.989835i	$0.454575\pi$
$14$	0.0332893	−	1.08002i	0.00889694	−	0.288648i
$15$		0			0
$16$	1.51353	+	2.62151i	0.378382	+	0.655378i
$17$	0.192844	+	0.719705i	0.0467716	+	0.174554i	0.985361	−	0.170483i	$-0.0545329\pi$
$17$	0.192844	+	0.719705i	0.0467716	+	0.174554i	−0.938589	+	0.345037i	$0.887866\pi$
$18$	0.105703	+	0.394487i	0.0249143	+	0.0929816i
$19$	1.21966	+	2.11252i	0.279810	+	0.484644i	0.971337	−	0.237706i	$-0.0763953\pi$
$19$	1.21966	+	2.11252i	0.279810	+	0.484644i	−0.691528	+	0.722350i	$0.743062\pi$
$20$		0			0
$21$	−2.33096	+	1.25166i	−0.508656	+	0.273134i
$22$	−0.267841	−	0.267841i	−0.0571039	−	0.0571039i
$23$	5.00751	+	1.34176i	1.04414	+	0.279776i	0.739827	−	0.672797i	$-0.234907\pi$
$23$	5.00751	+	1.34176i	1.04414	+	0.279776i	0.304311	+	0.952573i	$0.401574\pi$
$24$	−0.782747	+	1.35576i	−0.159778	+	0.276743i
$25$		0			0
$26$	−2.04162	+	1.17873i	−0.400395	+	0.231168i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	−4.64404	−	1.39907i	−0.877642	−	0.264398i
$29$		−	8.08080i		−	1.50057i	−0.661116	−	0.750284i	$-0.729917\pi$
$29$		−	8.08080i		−	1.50057i	0.661116	−	0.750284i	$-0.270083\pi$
$30$		0			0
$31$	−1.05279	−	0.607827i	−0.189086	−	0.109169i	0.402469	−	0.915434i	$-0.368152\pi$
$31$	−1.05279	−	0.607827i	−0.189086	−	0.109169i	−0.591555	+	0.806265i	$0.701486\pi$
$32$	−4.21844	+	1.13033i	−0.745722	+	0.199816i
$33$	−0.240048	+	0.895873i	−0.0417871	+	0.155951i
$34$	−0.304299			−0.0521868
$35$		0			0
$36$	1.83321			0.305534
$37$	0.472316	−	1.76271i	0.0776483	−	0.289787i	−0.916172	−	0.400784i	$-0.868738\pi$
$37$	0.472316	−	1.76271i	0.0776483	−	0.289787i	0.993821	+	0.110997i	$0.0354044\pi$
$38$	−0.962282	+	0.257843i	−0.156103	+	0.0418276i
$39$	4.99903	+	2.88619i	0.800486	+	0.462161i
$40$		0			0
$41$		−	6.97323i		−	1.08903i	−0.838749	−	0.544517i	$-0.816713\pi$
$41$		−	6.97323i		−	1.08903i	0.838749	−	0.544517i	$-0.183287\pi$
$42$	−0.247375	−	1.05184i	−0.0381708	−	0.162302i
$43$	0.781574	−	0.781574i	0.119189	−	0.119189i	−0.644997	−	0.764185i	$-0.723141\pi$
$43$	0.781574	−	0.781574i	0.119189	−	0.119189i	0.764185	+	0.644997i	$0.223141\pi$
$44$	−1.47246	+	0.850128i	−0.221982	+	0.128162i
$45$		0			0
$46$	−1.05861	+	1.83357i	−0.156084	+	0.270345i
$47$	−10.0896	−	2.70351i	−1.47172	−	0.394347i	−0.568202	−	0.822889i	$-0.692361\pi$
$47$	−10.0896	−	2.70351i	−1.47172	−	0.394347i	−0.903522	+	0.428542i	$0.859027\pi$
$48$	2.14045	+	2.14045i	0.308948	+	0.308948i
$49$	6.26622	−	3.12000i	0.895175	−	0.445715i
$50$		0			0
$51$	0.372547	+	0.645270i	0.0521670	+	0.0903558i
$52$	2.73882	+	10.2214i	0.379806	+	1.41745i
$53$	−1.72055	−	6.42117i	−0.236335	−	0.882016i	−0.977542	−	0.210739i	$-0.932413\pi$
$53$	−1.72055	−	6.42117i	−0.236335	−	0.882016i	0.741207	−	0.671277i	$-0.234254\pi$
$54$	0.204202	+	0.353688i	0.0277883	+	0.0481308i
$55$		0			0
$56$	2.18048	−	3.52149i	0.291379	−	0.470580i
$57$	1.72486	+	1.72486i	0.228464	+	0.228464i
$58$	3.18778	+	0.854162i	0.418575	+	0.112157i
$59$	−5.91173	+	10.2394i	−0.769642	+	1.33306i	0.168115	+	0.985767i	$0.446232\pi$
$59$	−5.91173	+	10.2394i	−0.769642	+	1.33306i	−0.937757	+	0.347292i	$0.887101\pi$
$60$		0			0
$61$	−3.72841	+	2.15260i	−0.477374	+	0.275612i	−0.719322	−	0.694677i	$-0.755547\pi$
$61$	−3.72841	+	2.15260i	−0.477374	+	0.275612i	0.241947	+	0.970289i	$0.422214\pi$
$62$	0.351062	−	0.351062i	0.0445849	−	0.0445849i
$63$	−1.92758	+	1.81230i	−0.242852	+	0.228329i
$64$			4.27052i			0.533815i
$65$		0			0
$66$	−0.328037	−	0.189392i	−0.0403786	−	0.0233126i
$67$	10.4844	−	2.80929i	1.28088	−	0.343210i	0.446688	−	0.894690i	$-0.352603\pi$
$67$	10.4844	−	2.80929i	1.28088	−	0.343210i	0.834188	+	0.551480i	$0.185937\pi$
$68$	−0.353523	+	1.31937i	−0.0428710	+	0.159997i
$69$	5.18415			0.624099
$70$		0			0
$71$	9.89994			1.17491			0.587454	−	0.809258i	$-0.300130\pi$
$71$	9.89994			1.17491			0.587454	+	0.809258i	$0.300130\pi$
$72$	−0.405180	+	1.51215i	−0.0477509	+	0.178209i
$73$	−4.02609	+	1.07879i	−0.471218	+	0.126262i	−0.486610	−	0.873619i	$-0.661767\pi$
$73$	−4.02609	+	1.07879i	−0.471218	+	0.126262i	0.0153927	+	0.999882i	$0.495100\pi$
$74$	0.645441	+	0.372646i	0.0750310	+	0.0433192i
$75$		0			0
$76$			4.47178i			0.512949i
$77$	0.707830	−	2.34957i	0.0806648	−	0.267758i
$78$	−1.66698	+	1.66698i	−0.188748	+	0.188748i
$79$	−7.02976	+	4.05863i	−0.790910	+	0.456632i	−0.840283	−	0.542148i	$-0.817611\pi$
$79$	−7.02976	+	4.05863i	−0.790910	+	0.456632i	0.0493729	+	0.998780i	$0.484278\pi$
$80$		0			0
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	2.75085	+	0.737088i	0.303781	+	0.0813978i
$83$	−5.91429	−	5.91429i	−0.649177	−	0.649177i	0.303617	−	0.952794i	$-0.401806\pi$
$83$	−5.91429	−	5.91429i	−0.649177	−	0.649177i	−0.952794	+	0.303617i	$0.901806\pi$
$84$	−4.84791	−	0.149426i	−0.528950	−	0.0163037i
$85$		0			0
$86$	0.225707	+	0.390935i	0.0243386	+	0.0421557i
$87$	−2.09147	−	7.80546i	−0.224229	−	0.836833i
$88$	−0.375795	−	1.40248i	−0.0400598	−	0.149505i
$89$	−7.78809	−	13.4894i	−0.825536	−	1.42987i	−0.901509	−	0.432761i	$-0.857540\pi$
$89$	−7.78809	−	13.4894i	−0.825536	−	1.42987i	0.0759727	−	0.997110i	$-0.475794\pi$
$90$		0			0
$91$	−12.9847	−	8.04000i	−1.36116	−	0.842821i
$92$	6.72008	+	6.72008i	0.700617	+	0.700617i
$93$	−1.17423	−	0.314634i	−0.121762	−	0.0326260i
$94$	2.13300	−	3.69446i	0.220002	−	0.381055i
$95$		0			0
$96$	−3.78215	+	2.18363i	−0.386014	+	0.222865i
$97$	4.89426	−	4.89426i	0.496936	−	0.496936i	−0.413547	−	0.910483i	$-0.635710\pi$
$97$	4.89426	−	4.89426i	0.496936	−	0.496936i	0.910483	+	0.413547i	$0.135710\pi$
$98$	0.568446	+	2.80174i	0.0574217	+	0.283018i
$99$			0.927476i			0.0932149i
$100$		0			0
$101$	7.19322	+	4.15301i	0.715753	+	0.413240i	0.813187	−	0.582002i	$-0.197730\pi$
$101$	7.19322	+	4.15301i	0.715753	+	0.413240i	−0.0974348	+	0.995242i	$0.531064\pi$
$102$	−0.293930	+	0.0787583i	−0.0291034	+	0.00779823i
$103$	−0.679662	+	2.53653i	−0.0669691	+	0.249932i	−0.991293	−	0.131678i	$-0.957964\pi$
$103$	−0.679662	+	2.53653i	−0.0669691	+	0.249932i	0.924323	+	0.381610i	$0.124630\pi$
$104$	−9.03664			−0.886116
$105$		0			0
$106$	2.71494			0.263698
$107$	−0.228263	+	0.851889i	−0.0220670	+	0.0823553i	−0.976081	−	0.217406i	$-0.930240\pi$
$107$	−0.228263	+	0.851889i	−0.0220670	+	0.0823553i	0.954014	+	0.299761i	$0.0969071\pi$
$108$	1.77074	−	0.474469i	0.170390	−	0.0456558i
$109$	−10.7021	−	6.17883i	−1.02507	−	0.591825i	−0.109502	−	0.993987i	$-0.534926\pi$
$109$	−10.7021	−	6.17883i	−1.02507	−	0.591825i	−0.915569	+	0.402162i	$0.868259\pi$
$110$		0			0
$111$		−	1.82489i		−	0.173211i
$112$	−5.48595	−	5.83489i	−0.518374	−	0.551345i
$113$	13.7439	−	13.7439i	1.29291	−	1.29291i	0.359938	−	0.932976i	$-0.382798\pi$
$113$	13.7439	−	13.7439i	1.29291	−	1.29291i	0.932976	−	0.359938i	$-0.117202\pi$
$114$	−0.862759	+	0.498114i	−0.0808048	+	0.0466527i
$115$		0			0
$116$	7.40689	−	12.8291i	0.687713	−	1.19115i
$117$	5.57570	+	1.49400i	0.515473	+	0.138121i
$118$	−3.41444	−	3.41444i	−0.314324	−	0.314324i
$119$	−0.932601	−	1.73678i	−0.0854914	−	0.159210i
$120$		0			0
$121$	5.06989	+	8.78131i	0.460899	+	0.798301i
$122$	−0.455071	−	1.69835i	−0.0412002	−	0.153761i
$123$	−1.80480	−	6.73562i	−0.162734	−	0.607330i
$124$	−1.11427	−	1.92998i	−0.100065	−	0.173317i
$125$		0			0
$126$	−0.511181	−	0.951970i	−0.0455396	−	0.0848083i
$127$	−9.30227	−	9.30227i	−0.825443	−	0.825443i	0.161440	−	0.986883i	$-0.448386\pi$
$127$	−9.30227	−	9.30227i	−0.825443	−	0.825443i	−0.986883	+	0.161440i	$0.948386\pi$
$128$	−10.1215	−	2.71206i	−0.894627	−	0.239715i
$129$	0.552656	−	0.957229i	0.0486587	−	0.0842793i
$130$		0			0
$131$	−8.95081	+	5.16775i	−0.782036	+	0.451509i	−0.837151	−	0.546971i	$-0.815781\pi$
$131$	−8.95081	+	5.16775i	−0.782036	+	0.451509i	0.0551154	+	0.998480i	$0.482447\pi$
$132$	−1.20226	+	1.20226i	−0.104643	+	0.104643i
$133$	−4.42079	−	4.70198i	−0.383332	−	0.407714i
$134$			4.43292i			0.382946i
$135$		0			0
$136$	−1.01017	−	0.583220i	−0.0866211	−	0.0500107i
$137$	0.853123	−	0.228594i	0.0728872	−	0.0195301i	−0.222191	−	0.975003i	$-0.571321\pi$
$137$	0.853123	−	0.228594i	0.0728872	−	0.0195301i	0.295078	+	0.955473i	$0.404654\pi$
$138$	−0.547979	+	2.04508i	−0.0466470	+	0.174089i
$139$	18.6742			1.58392			0.791961	−	0.610572i	$-0.209060\pi$
$139$	18.6742			1.58392			0.791961	+	0.610572i	$0.209060\pi$
$140$		0			0
$141$	−10.4456			−0.879674
$142$	−1.04645	+	3.90540i	−0.0878161	+	0.327734i
$143$	−5.17133	+	1.38565i	−0.432448	+	0.115874i
$144$	2.62151	+	1.51353i	0.218459	+	0.126127i
$145$		0			0
$146$		−	1.70227i		−	0.140881i
$147$	5.24519	−	4.63551i	0.432616	−	0.382330i
$148$	2.36555	−	2.36555i	0.194447	−	0.194447i
$149$	−4.96877	+	2.86872i	−0.407057	+	0.235015i	−0.689524	−	0.724262i	$-0.742180\pi$
$149$	−4.96877	+	2.86872i	−0.407057	+	0.235015i	0.282467	+	0.959277i	$0.408847\pi$
$150$		0			0
$151$	9.44257	−	16.3550i	0.768425	−	1.33095i	−0.169991	−	0.985446i	$-0.554374\pi$
$151$	9.44257	−	16.3550i	0.768425	−	1.33095i	0.938417	−	0.345506i	$-0.112293\pi$
$152$	−3.68863	−	0.988365i	−0.299187	−	0.0801670i
$153$	0.526861	+	0.526861i	0.0425941	+	0.0425941i
$154$	0.852055	+	0.527585i	0.0686605	+	0.0425140i
$155$		0			0
$156$	5.29099	+	9.16426i	0.423618	+	0.733728i
$157$	−1.15493	−	4.31024i	−0.0921731	−	0.343995i	0.904403	−	0.426680i	$-0.140317\pi$
$157$	−1.15493	−	4.31024i	−0.0921731	−	0.343995i	−0.996576	+	0.0826855i	$0.973650\pi$
$158$	−0.858016	−	3.20216i	−0.0682601	−	0.254750i
$159$	−3.32384	−	5.75707i	−0.263598	−	0.456565i
$160$		0			0
$161$	−13.7095	−	0.422564i	−1.08046	−	0.0333027i
$162$	0.288785	+	0.288785i	0.0226891	+	0.0226891i
$163$	3.14897	+	0.843763i	0.246646	+	0.0660886i	0.380024	−	0.924977i	$-0.375916\pi$
$163$	3.14897	+	0.843763i	0.246646	+	0.0660886i	−0.133378	+	0.991065i	$0.542582\pi$
$164$	6.39168	−	11.0707i	0.499107	−	0.864478i
$165$		0			0
$166$	2.95827	−	1.70796i	0.229606	−	0.132563i
$167$	−2.23479	+	2.23479i	−0.172933	+	0.172933i	−0.788267	−	0.615334i	$-0.789021\pi$
$167$	−2.23479	+	2.23479i	−0.172933	+	0.172933i	0.615334	+	0.788267i	$0.289021\pi$
$168$	1.19475	−	3.96585i	0.0921772	−	0.305972i
$169$			20.3205i			1.56311i
$170$		0			0
$171$	2.11252	+	1.21966i	0.161548	+	0.0932699i
$172$	1.95722	−	0.524436i	0.149237	−	0.0399879i
$173$	−4.15104	+	15.4919i	−0.315598	+	1.17783i	0.607834	+	0.794064i	$0.292039\pi$
$173$	−4.15104	+	15.4919i	−0.315598	+	1.17783i	−0.923432	+	0.383763i	$0.874628\pi$
$174$	3.30023			0.250190
$175$		0			0
$176$	−2.80753			−0.211625
$177$	−3.06014	+	11.4206i	−0.230014	+	0.858424i
$178$	6.14461	−	1.64644i	0.460558	−	0.123406i
$179$	7.94393	+	4.58643i	0.593758	+	0.342806i	0.766582	−	0.642147i	$-0.221956\pi$
$179$	7.94393	+	4.58643i	0.593758	+	0.342806i	−0.172824	+	0.984953i	$0.555289\pi$
$180$		0			0
$181$		−	5.57424i		−	0.414330i	−0.978306	−	0.207165i	$-0.933576\pi$
$181$		−	5.57424i		−	0.414330i	0.978306	−	0.207165i	$-0.0664237\pi$
$182$	4.54419	−	4.27244i	0.336838	−	0.316694i
$183$	−3.04424	+	3.04424i	−0.225036	+	0.225036i
$184$	−7.02846	+	4.05788i	−0.518145	+	0.299151i
$185$		0			0
$186$	0.248238	−	0.429962i	0.0182017	−	0.0315263i
$187$	−0.667509	−	0.178859i	−0.0488131	−	0.0130794i
$188$	−13.5403	−	13.5403i	−0.987527	−	0.987527i
$189$	−1.39284	+	2.24944i	−0.101314	+	0.163623i
$190$		0			0
$191$	−0.290017	−	0.502325i	−0.0209849	−	0.0363469i	0.855342	−	0.518063i	$-0.173347\pi$
$191$	−0.290017	−	0.502325i	−0.0209849	−	0.0363469i	−0.876327	+	0.481716i	$0.840014\pi$
$192$	1.10529	+	4.12500i	0.0797675	+	0.297697i
$193$	−1.56618	−	5.84505i	−0.112736	−	0.420736i	0.886372	−	0.462974i	$-0.153218\pi$
$193$	−1.56618	−	5.84505i	−0.112736	−	0.420736i	−0.999108	+	0.0422384i	$0.986551\pi$
$194$	1.41339	+	2.44806i	0.101475	+	0.175760i
$195$		0			0
$196$	12.8081	+	0.790313i	0.914863	+	0.0564509i
$197$	6.05651	+	6.05651i	0.431508	+	0.431508i	0.889141	−	0.457633i	$-0.151303\pi$
$197$	6.05651	+	6.05651i	0.431508	+	0.431508i	−0.457633	+	0.889141i	$0.651303\pi$
$198$	−0.365878	−	0.0980366i	−0.0260018	−	0.00696716i
$199$	5.61335	−	9.72261i	0.397920	−	0.689218i	−0.595549	−	0.803319i	$-0.703065\pi$
$199$	5.61335	−	9.72261i	0.397920	−	0.689218i	0.993469	+	0.114101i	$0.0363988\pi$
$200$		0			0
$201$	9.40008	−	5.42714i	0.663030	−	0.382801i
$202$	−2.39865	+	2.39865i	−0.168769	+	0.168769i
$203$	4.89464	+	20.8120i	0.343537	+	1.46071i
$204$			1.36591i			0.0956328i
$205$		0			0
$206$	−0.928789	−	0.536237i	−0.0647118	−	0.0373614i
$207$	5.00751	−	1.34176i	0.348046	−	0.0932586i
$208$	−4.52244	+	16.8780i	−0.313575	+	1.17028i
$209$	−2.26241			−0.156494
$210$		0			0
$211$	−4.46617			−0.307464			−0.153732	−	0.988113i	$-0.549129\pi$
$211$	−4.46617			−0.307464			−0.153732	+	0.988113i	$0.549129\pi$
$212$	3.15412	−	11.7713i	0.216626	−	0.808459i
$213$	9.56261	−	2.56229i	0.655219	−	0.175565i
$214$	−0.311932	−	0.180094i	−0.0213232	−	0.0123110i
$215$		0			0
$216$			1.56549i			0.106518i
$217$	3.07960	+	0.927761i	0.209057	+	0.0629805i
$218$	3.56871	−	3.56871i	0.241703	−	0.241703i
$219$	−3.60969	+	2.08406i	−0.243920	+	0.140827i
$220$		0			0
$221$	−2.15048	+	3.72475i	−0.144657	+	0.250554i
$222$	0.719896	+	0.192896i	0.0483163	+	0.0129463i
$223$	3.05982	+	3.05982i	0.204900	+	0.204900i	0.802096	−	0.597195i	$-0.203718\pi$
$223$	3.05982	+	3.05982i	0.204900	+	0.204900i	−0.597195	+	0.802096i	$0.703718\pi$
$224$	10.1799	−	5.46630i	0.680171	−	0.365233i
$225$		0			0
$226$	3.96902	+	6.87455i	0.264015	+	0.457288i
$227$	−0.377892	−	1.41031i	−0.0250816	−	0.0936057i	0.952250	−	0.305318i	$-0.0987627\pi$
$227$	−0.377892	−	1.41031i	−0.0250816	−	0.0936057i	−0.977332	+	0.211712i	$0.932096\pi$
$228$	1.15738	+	4.31941i	0.0766495	+	0.286060i
$229$	−7.79011	−	13.4929i	−0.514785	−	0.891633i	−0.999853	−	0.0171570i	$-0.994538\pi$
$229$	−7.79011	−	13.4929i	−0.514785	−	0.891633i	0.485068	−	0.874476i	$-0.338795\pi$
$230$		0			0
$231$	0.0755993	−	2.45271i	0.00497407	−	0.161376i
$232$	8.94522	+	8.94522i	0.587283	+	0.587283i
$233$	22.4723	+	6.02142i	1.47221	+	0.394476i	0.903687	−	0.428194i	$-0.140850\pi$
$233$	22.4723	+	6.02142i	1.47221	+	0.394476i	0.568519	+	0.822670i	$0.307517\pi$
$234$	−1.17873	+	2.04162i	−0.0770561	+	0.133465i
$235$		0			0
$236$	−18.7710	+	10.8374i	−1.22189	+	0.705456i
$237$	−5.73978	+	5.73978i	−0.372838	+	0.372838i
$238$	0.783716	−	0.184318i	0.0508008	−	0.0119475i
$239$		−	1.48712i		−	0.0961937i	−0.998843	−	0.0480968i	$-0.984684\pi$
$239$		−	1.48712i		−	0.0961937i	0.998843	−	0.0480968i	$-0.0153156\pi$
$240$		0			0
$241$	1.28163	+	0.739950i	0.0825571	+	0.0476643i	0.540710	−	0.841209i	$-0.318156\pi$
$241$	1.28163	+	0.739950i	0.0825571	+	0.0476643i	−0.458153	+	0.888873i	$0.651489\pi$
$242$	−4.00002	+	1.07180i	−0.257131	+	0.0688980i
$243$	0.258819	−	0.965926i	0.0166032	−	0.0619642i
$244$	−7.89232			−0.505254
$245$		0			0
$246$	2.84789			0.181575
$247$	−3.64436	+	13.6009i	−0.231885	+	0.865406i
$248$	1.83825	−	0.492558i	0.116729	−	0.0312775i
$249$	−7.24349	−	4.18203i	−0.459038	−	0.265026i
$250$		0			0
$251$			18.3956i			1.16112i	0.814218	+	0.580559i	$0.197166\pi$
$251$			18.3956i			1.16112i	−0.814218	+	0.580559i	$0.802834\pi$
$252$	−4.72139	+	1.11040i	−0.297420	+	0.0699484i
$253$	−3.39990	+	3.39990i	−0.213750	+	0.213750i
$254$	4.65290	−	2.68635i	0.291949	−	0.168557i
$255$		0			0
$256$	−2.13077	+	3.69060i	−0.133173	+	0.230663i
$257$	−9.44356	−	2.53039i	−0.589073	−	0.157842i	−0.0480436	−	0.998845i	$-0.515299\pi$
$257$	−9.44356	−	2.53039i	−0.589073	−	0.157842i	−0.541030	+	0.841004i	$0.681965\pi$
$258$	0.319197	+	0.319197i	0.0198724	+	0.0198724i
$259$	−0.148748	+	4.82591i	−0.00924276	+	0.299868i
$260$		0			0
$261$	−4.04040	−	6.99818i	−0.250095	−	0.433177i
$262$	−1.09249	−	4.07723i	−0.0674943	−	0.251892i
$263$	2.87639	+	10.7348i	0.177366	+	0.661939i	0.996137	+	0.0878181i	$0.0279894\pi$
$263$	2.87639	+	10.7348i	0.177366	+	0.661939i	−0.818771	+	0.574121i	$0.805344\pi$
$264$	−0.725980	−	1.25743i	−0.0446810	−	0.0773897i
$265$		0			0
$266$	2.32216	−	1.24694i	0.142381	−	0.0764546i
$267$	−11.0140	−	11.0140i	−0.674047	−	0.674047i
$268$	19.2201	+	5.15001i	1.17406	+	0.314587i
$269$	−4.23477	+	7.33484i	−0.258199	+	0.447213i	−0.965759	−	0.259439i	$-0.916462\pi$
$269$	−4.23477	+	7.33484i	−0.258199	+	0.447213i	0.707561	+	0.706652i	$0.249796\pi$
$270$		0			0
$271$	−20.3136	+	11.7281i	−1.23396	+	0.712429i	−0.967854	−	0.251514i	$-0.919072\pi$
$271$	−20.3136	+	11.7281i	−1.23396	+	0.712429i	−0.266110	+	0.963943i	$0.585738\pi$
$272$	−1.59484	+	1.59484i	−0.0967013	+	0.0967013i
$273$	−14.6231	−	4.40537i	−0.885032	−	0.266625i
$274$			0.360709i			0.0217912i
$275$		0			0
$276$	8.23038	+	4.75181i	0.495411	+	0.286026i
$277$	−7.07963	+	1.89698i	−0.425374	+	0.113979i	−0.465154	−	0.885230i	$-0.654001\pi$
$277$	−7.07963	+	1.89698i	−0.425374	+	0.113979i	0.0397799	+	0.999208i	$0.487334\pi$
$278$	−1.97391	+	7.36672i	−0.118387	+	0.441827i
$279$	−1.21565			−0.0727792
$280$		0			0
$281$	16.9863			1.01332			0.506658	−	0.862147i	$-0.330881\pi$
$281$	16.9863			1.01332			0.506658	+	0.862147i	$0.330881\pi$
$282$	1.10412	−	4.12064i	0.0657495	−	0.245380i
$283$	1.27688	−	0.342140i	0.0759029	−	0.0203381i	−0.220668	−	0.975349i	$-0.570824\pi$
$283$	1.27688	−	0.342140i	0.0759029	−	0.0203381i	0.296571	+	0.955011i	$0.404157\pi$
$284$	15.7172	+	9.07432i	0.932643	+	0.538462i
$285$		0			0
$286$		−	2.18649i		−	0.129290i
$287$	4.22377	+	17.9594i	0.249321	+	1.06011i
$288$	−3.08811	+	3.08811i	−0.181969	+	0.181969i
$289$	14.2416	−	8.22242i	0.837744	−	0.483672i
$290$		0			0
$291$	3.46076	−	5.99421i	0.202873	−	0.351387i
$292$	−7.38065	−	1.97764i	−0.431920	−	0.115733i
$293$	2.80762	+	2.80762i	0.164023	+	0.164023i	0.784346	−	0.620323i	$-0.212999\pi$
$293$	2.80762	+	2.80762i	0.164023	+	0.164023i	−0.620323	+	0.784346i	$0.712999\pi$
$294$	1.27422	+	2.55915i	0.0743141	+	0.149253i
$295$		0			0
$296$	1.42843	+	2.47411i	0.0830257	+	0.143805i
$297$	0.240048	+	0.895873i	0.0139290	+	0.0519838i
$298$	−0.606462	−	2.26335i	−0.0351314	−	0.131112i
$299$	14.9625	+	25.9158i	0.865302	+	1.49875i
$300$		0			0
$301$	−1.53952	+	2.48634i	−0.0887365	+	0.143310i
$302$	5.45374	+	5.45374i	0.313828	+	0.313828i
$303$	8.02300	+	2.14976i	0.460909	+	0.123500i
$304$	−3.69199	+	6.39471i	−0.211750	+	0.366762i
$305$		0			0
$306$	−0.263530	+	0.152149i	−0.0150650	+	0.00869780i
$307$	−9.39163	+	9.39163i	−0.536009	+	0.536009i	−0.922354	−	0.386345i	$-0.873737\pi$
$307$	−9.39163	+	9.39163i	−0.536009	+	0.536009i	0.386345	+	0.922354i	$0.373737\pi$
$308$	3.27737	−	3.08138i	0.186746	−	0.175578i
$309$			2.62601i			0.149389i
$310$		0			0
$311$	1.04801	+	0.605067i	0.0594270	+	0.0343102i	0.529419	−	0.848360i	$-0.322410\pi$
$311$	1.04801	+	0.605067i	0.0594270	+	0.0343102i	−0.469992	+	0.882671i	$0.655743\pi$
$312$	−8.72873	+	2.33886i	−0.494167	+	0.132412i
$313$	7.08623	−	26.4462i	0.400538	−	1.49483i	−0.411602	−	0.911364i	$-0.635031\pi$
$313$	7.08623	−	26.4462i	0.400538	−	1.49483i	0.812140	−	0.583463i	$-0.198303\pi$
$314$	1.82241			0.102845
$315$		0			0
$316$	−14.8806			−0.837101
$317$	−3.73676	+	13.9458i	−0.209877	+	0.783273i	0.778030	+	0.628227i	$0.216219\pi$
$317$	−3.73676	+	13.9458i	−0.209877	+	0.783273i	−0.987907	+	0.155046i	$0.950448\pi$
$318$	2.62243	−	0.702678i	0.147059	−	0.0394042i
$319$	6.49065	+	3.74738i	0.363406	+	0.209813i
$320$		0			0
$321$			0.881941i			0.0492251i
$322$	1.61582	−	5.36355i	0.0900463	−	0.298899i
$323$	−1.28518	+	1.28518i	−0.0715095	+	0.0715095i
$324$	1.58760	−	0.916603i	0.0882002	−	0.0509224i
$325$		0			0
$326$	−0.665708	+	1.15304i	−0.0368702	+	0.0638610i
$327$	−11.9366	−	3.19840i	−0.660095	−	0.176872i
$328$	7.71917	+	7.71917i	0.426220	+	0.426220i
$329$	27.6232	+	0.851425i	1.52292	+	0.0469406i
$330$		0			0
$331$	3.39956	+	5.88820i	0.186856	+	0.323645i	0.944201	−	0.329371i	$-0.106837\pi$
$331$	3.39956	+	5.88820i	0.186856	+	0.323645i	−0.757344	+	0.653016i	$0.773503\pi$
$332$	−3.96849	−	14.8106i	−0.217799	−	0.812837i
$333$	−0.472316	−	1.76271i	−0.0258828	−	0.0965958i
$334$	−0.645374	−	1.11782i	−0.0353133	−	0.0611644i
$335$		0			0
$336$	−6.80920	−	4.21620i	−0.371472	−	0.230013i
$337$	−3.49179	−	3.49179i	−0.190210	−	0.190210i	0.605577	−	0.795787i	$-0.292942\pi$
$337$	−3.49179	−	3.49179i	−0.190210	−	0.190210i	−0.795787	+	0.605577i	$0.792942\pi$
$338$	−8.01616	−	2.14792i	−0.436022	−	0.116832i
$339$	9.71838	−	16.8327i	0.527830	−	0.914229i
$340$		0			0
$341$	0.976434	−	0.563745i	0.0528769	−	0.0305285i
$342$	−0.704440	+	0.704440i	−0.0380917	+	0.0380917i
$343$	−14.2487	+	11.8310i	−0.769359	+	0.638817i
$344$			1.73036i			0.0932948i
$345$		0			0
$346$	−5.67258	−	3.27507i	−0.304960	−	0.176069i
$347$	12.0095	−	3.21794i	0.644704	−	0.172748i	0.0783710	−	0.996924i	$-0.475028\pi$
$347$	12.0095	−	3.21794i	0.644704	−	0.172748i	0.566333	+	0.824176i	$0.308361\pi$
$348$	3.83409	−	14.3090i	0.205529	−	0.767044i
$349$	−0.973873			−0.0521302			−0.0260651	−	0.999660i	$-0.508298\pi$
$349$	−0.973873			−0.0521302			−0.0260651	+	0.999660i	$0.508298\pi$
$350$		0			0
$351$	5.77239			0.308107
$352$	1.04835	−	3.91250i	0.0558774	−	0.208537i
$353$	−2.09762	+	0.562056i	−0.111645	+	0.0299152i	−0.314209	−	0.949354i	$-0.601739\pi$
$353$	−2.09762	+	0.562056i	−0.111645	+	0.0299152i	0.202564	+	0.979269i	$0.435073\pi$
$354$	−4.18181	−	2.41437i	−0.222261	−	0.128322i
$355$		0			0
$356$		−	28.5544i		−	1.51338i
$357$	−1.35034	−	1.43623i	−0.0714673	−	0.0760131i
$358$	−2.64899	+	2.64899i	−0.140003	+	0.140003i
$359$	−17.9132	+	10.3422i	−0.945422	+	0.545840i	−0.891656	−	0.452714i	$-0.850456\pi$
$359$	−17.9132	+	10.3422i	−0.945422	+	0.545840i	−0.0537661	+	0.998554i	$0.517123\pi$
$360$		0			0
$361$	6.52485	−	11.3014i	0.343413	−	0.594809i
$362$	2.19897	+	0.589212i	0.115575	+	0.0309683i
$363$	7.16991	+	7.16991i	0.376323	+	0.376323i
$364$	−13.2450	−	24.6661i	−0.694227	−	1.29286i
$365$		0			0
$366$	−0.879130	−	1.52270i	−0.0459528	−	0.0795927i
$367$	1.77714	+	6.63239i	0.0927662	+	0.346208i	0.996671	−	0.0815249i	$-0.0259790\pi$
$367$	1.77714	+	6.63239i	0.0927662	+	0.346208i	−0.903905	+	0.427733i	$0.859312\pi$
$368$	4.06158	+	15.1580i	0.211725	+	0.790167i
$369$	−3.48661	−	6.03899i	−0.181506	−	0.314377i
$370$		0			0
$371$	8.32063	+	15.4955i	0.431985	+	0.804484i
$372$	−1.57582	−	1.57582i	−0.0817024	−	0.0817024i
$373$	−24.6845	−	6.61420i	−1.27812	−	0.342470i	−0.444981	−	0.895540i	$-0.646790\pi$
$373$	−24.6845	−	6.61420i	−1.27812	−	0.342470i	−0.833135	+	0.553070i	$0.813456\pi$
$374$	0.141115	−	0.244418i	0.00729688	−	0.0126386i
$375$		0			0
$376$	14.1616	−	8.17623i	0.730331	−	0.421657i
$377$	32.9834	−	32.9834i	1.69873	−	1.69873i
$378$	−0.740151	−	0.787229i	−0.0380693	−	0.0404907i
$379$		−	36.6543i		−	1.88281i	−0.337284	−	0.941403i	$-0.609508\pi$
$379$		−	36.6543i		−	1.88281i	0.337284	−	0.941403i	$-0.390492\pi$
$380$		0			0
$381$	−11.3929	−	6.57770i	−0.583676	−	0.336986i
$382$	0.228816	−	0.0613112i	0.0117073	−	0.00313695i
$383$	−3.74645	+	13.9820i	−0.191435	+	0.714445i	0.801726	+	0.597692i	$0.203915\pi$
$383$	−3.74645	+	13.9820i	−0.191435	+	0.714445i	−0.993161	+	0.116753i	$0.962751\pi$
$384$	−10.4786			−0.534734
$385$		0			0
$386$	2.47135			0.125788
$387$	0.286076	−	1.06765i	0.0145421	−	0.0542717i
$388$	12.2562	−	3.28405i	0.622216	−	0.166722i
$389$	2.22749	+	1.28604i	0.112938	+	0.0652050i	0.555405	−	0.831580i	$-0.312563\pi$
$389$	2.22749	+	1.28604i	0.112938	+	0.0652050i	−0.442467	+	0.896785i	$0.645897\pi$
$390$		0			0
$391$			3.86268i			0.195344i
$392$	−3.48278	+	10.3903i	−0.175907	+	0.524789i
$393$	−7.30831	+	7.30831i	−0.368655	+	0.368655i
$394$	−3.02941	+	1.74903i	−0.152619	+	0.0881148i
$395$		0			0
$396$	−0.850128	+	1.47246i	−0.0427205	+	0.0739941i
$397$	8.59074	+	2.30188i	0.431157	+	0.115528i	0.467869	−	0.883798i	$-0.345022\pi$
$397$	8.59074	+	2.30188i	0.431157	+	0.115528i	−0.0367123	+	0.999326i	$0.511689\pi$
$398$	3.24210	+	3.24210i	0.162512	+	0.162512i
$399$	−5.48712	−	3.39758i	−0.274700	−	0.170092i
$400$		0			0
$401$	15.9532	+	27.6318i	0.796665	+	1.37986i	0.921776	+	0.387722i	$0.126738\pi$
$401$	15.9532	+	27.6318i	0.796665	+	1.37986i	−0.125111	+	0.992143i	$0.539929\pi$
$402$	1.14733	+	4.28188i	0.0572234	+	0.213561i
$403$	−1.81619	−	6.77811i	−0.0904709	−	0.337642i
$404$	7.61333	+	13.1867i	0.378777	+	0.656061i
$405$		0			0
$406$	−8.72744	−	0.269004i	−0.433136	−	0.0133505i
$407$	1.19681	+	1.19681i	0.0593235	+	0.0593235i
$408$	−1.12669	−	0.301897i	−0.0557797	−	0.0149461i
$409$	−16.4328	+	28.4625i	−0.812550	+	1.40738i	0.0985239	+	0.995135i	$0.468588\pi$
$409$	−16.4328	+	28.4625i	−0.812550	+	1.40738i	−0.911074	+	0.412243i	$0.864745\pi$
$410$		0			0
$411$	0.764889	−	0.441609i	0.0377292	−	0.0217830i
$412$	−3.40403	+	3.40403i	−0.167705	+	0.167705i
$413$	9.02342	−	29.9523i	0.444013	−	1.47385i
$414$			2.11723i			0.104056i
$415$		0			0
$416$	−21.8320	−	12.6047i	−1.07040	−	0.617998i
$417$	18.0379	−	4.83323i	0.883317	−	0.236684i
$418$	0.239143	−	0.892494i	0.0116969	−	0.0436533i
$419$	−12.2544			−0.598669			−0.299334	−	0.954148i	$-0.596765\pi$
$419$	−12.2544			−0.598669			−0.299334	+	0.954148i	$0.596765\pi$
$420$		0			0
$421$	34.4993			1.68140			0.840698	−	0.541505i	$-0.182145\pi$
$421$	34.4993			1.68140			0.840698	+	0.541505i	$0.182145\pi$
$422$	0.472085	−	1.76185i	0.0229808	−	0.0857654i
$423$	−10.0896	+	2.70351i	−0.490574	+	0.131449i
$424$	9.01266	+	5.20346i	0.437693	+	0.252702i
$425$		0			0
$426$			4.04317i			0.195892i
$427$	8.29861	−	7.80233i	0.401598	−	0.377581i
$428$	−1.14324	+	1.14324i	−0.0552604	+	0.0552604i
$429$	−4.63648	+	2.67688i	−0.223852	+	0.129241i
$430$		0			0
$431$	−8.92167	+	15.4528i	−0.429742	+	0.744334i	−0.996850	−	0.0793088i	$-0.974729\pi$
$431$	−8.92167	+	15.4528i	−0.429742	+	0.744334i	0.567109	+	0.823643i	$0.308062\pi$
$432$	2.92391	+	0.783461i	0.140677	+	0.0376943i
$433$	−2.49490	−	2.49490i	−0.119897	−	0.119897i	0.644612	−	0.764510i	$-0.277019\pi$
$433$	−2.49490	−	2.49490i	−0.119897	−	0.119897i	−0.764510	+	0.644612i	$0.777019\pi$
$434$	−0.691512	+	1.11680i	−0.0331936	+	0.0536080i
$435$		0			0
$436$	−11.3271	−	19.6191i	−0.542469	−	0.939583i
$437$	3.27298	+	12.2149i	0.156568	+	0.584319i
$438$	−0.440580	−	1.64427i	−0.0210517	−	0.0785661i
$439$	−1.77922	−	3.08171i	−0.0849177	−	0.147082i	0.820438	−	0.571735i	$-0.193729\pi$
$439$	−1.77922	−	3.08171i	−0.0849177	−	0.147082i	−0.905356	+	0.424653i	$0.860396\pi$
$440$		0			0
$441$	3.86671	−	5.83512i	0.184129	−	0.277863i
$442$	−1.24205	−	1.24205i	−0.0590785	−	0.0590785i
$443$	−4.54905	−	1.21891i	−0.216132	−	0.0579124i	0.149128	−	0.988818i	$-0.452353\pi$
$443$	−4.54905	−	1.21891i	−0.216132	−	0.0579124i	−0.365260	+	0.930905i	$0.619020\pi$
$444$	1.67270	−	2.89720i	0.0793828	−	0.137495i
$445$		0			0
$446$	−1.53049	+	0.883629i	−0.0724708	+	0.0418410i
$447$	−4.05698	+	4.05698i	−0.191889	+	0.191889i
$448$	−2.58671	−	10.9986i	−0.122210	−	0.519637i
$449$		−	34.4214i		−	1.62444i	−0.583348	−	0.812222i	$-0.698258\pi$
$449$		−	34.4214i		−	1.62444i	0.583348	−	0.812222i	$-0.301742\pi$
$450$		0			0
$451$	5.60102	+	3.23375i	0.263742	+	0.152271i
$452$	34.4175	−	9.22214i	1.61886	−	0.433773i
$453$	4.88783	−	18.2416i	0.229650	−	0.857067i
$454$	0.596294			0.0279855
$455$		0			0
$456$	−3.81875			−0.178829
$457$	0.316680	−	1.18187i	0.0148137	−	0.0552853i	−0.958123	−	0.286356i	$-0.907556\pi$
$457$	0.316680	−	1.18187i	0.0148137	−	0.0552853i	0.972937	+	0.231070i	$0.0742228\pi$
$458$	6.14620	−	1.64687i	0.287193	−	0.0769532i
$459$	0.645270	+	0.372547i	0.0301186	+	0.0173890i
$460$		0			0
$461$		−	15.0355i		−	0.700272i	−0.936699	−	0.350136i	$-0.886135\pi$
$461$		−	15.0355i		−	0.700272i	0.936699	−	0.350136i	$-0.113865\pi$
$462$	0.959571	+	0.289080i	0.0446433	+	0.0134492i
$463$	−25.5793	+	25.5793i	−1.18877	+	1.18877i	−0.211366	+	0.977407i	$0.567791\pi$
$463$	−25.5793	+	25.5793i	−1.18877	+	1.18877i	−0.977407	+	0.211366i	$0.932209\pi$
$464$	21.1839	−	12.2305i	0.983438	−	0.567788i
$465$		0			0
$466$	−4.75075	+	8.22854i	−0.220074	+	0.381180i
$467$	10.9162	+	2.92500i	0.505144	+	0.135353i	0.502386	−	0.864643i	$-0.332456\pi$
$467$	10.9162	+	2.92500i	0.505144	+	0.135353i	0.00275754	+	0.999996i	$0.499122\pi$
$468$	7.48259	+	7.48259i	0.345883	+	0.345883i
$469$	−25.3008	+	13.5858i	−1.16828	+	0.627335i
$470$		0			0
$471$	−2.23114	−	3.86445i	−0.102806	−	0.178065i
$472$	−4.79063	−	17.8789i	−0.220507	−	0.822942i
$473$	0.265329	+	0.990220i	0.0121998	+	0.0455303i
$474$	−1.65756	−	2.87098i	−0.0761343	−	0.131868i
$475$		0			0
$476$	0.111336	−	3.61214i	0.00510309	−	0.165562i
$477$	−4.70062	−	4.70062i	−0.215227	−	0.215227i
$478$	0.586649	+	0.157192i	0.0268327	+	0.00718981i
$479$	−7.26651	+	12.5860i	−0.332015	+	0.575067i	−0.982907	−	0.184104i	$-0.941062\pi$
$479$	−7.26651	+	12.5860i	−0.332015	+	0.575067i	0.650892	+	0.759171i	$0.274395\pi$
$480$		0			0
$481$	9.12268	−	5.26698i	0.415959	−	0.240154i
$482$	−0.427372	+	0.427372i	−0.0194663	+	0.0194663i
$483$	−13.3517	+	3.14011i	−0.607523	+	0.142880i
$484$			18.5883i			0.844924i
$485$		0			0
$486$	0.353688	+	0.204202i	0.0160436	+	0.00926278i
$487$	−37.3116	+	9.99761i	−1.69075	+	0.453035i	−0.970583	−	0.240767i	$-0.922601\pi$
$487$	−37.3116	+	9.99761i	−1.69075	+	0.453035i	−0.720166	+	0.693802i	$0.755934\pi$
$488$	1.74438	−	6.51012i	0.0789644	−	0.294699i
$489$	3.26005			0.147425
$490$		0			0
$491$	−25.2637			−1.14014			−0.570068	−	0.821598i	$-0.693083\pi$
$491$	−25.2637			−1.14014			−0.570068	+	0.821598i	$0.693083\pi$
$492$	3.30858	−	12.3478i	0.149162	−	0.556681i
$493$	5.81579	−	1.55834i	0.261930	−	0.0701840i
$494$	−4.98018	−	2.87531i	−0.224069	−	0.129366i
$495$		0			0
$496$		−	3.67985i		−	0.165230i
$497$	−25.4971	+	5.99652i	−1.14370	+	0.268981i
$498$	2.41542	−	2.41542i	0.108237	−	0.108237i
$499$	−2.71355	+	1.56667i	−0.121475	+	0.0701339i	−0.559506	−	0.828826i	$-0.689009\pi$
$499$	−2.71355	+	1.56667i	−0.121475	+	0.0701339i	0.438031	+	0.898960i	$0.355676\pi$
$500$		0			0
$501$	−1.58024	+	2.73705i	−0.0705997	+	0.122282i
$502$	−7.25682	−	1.94446i	−0.323888	−	0.0867854i
$503$	−23.8589	−	23.8589i	−1.06382	−	1.06382i	−0.997820	−	0.0659958i	$-0.978978\pi$
$503$	−23.8589	−	23.8589i	−1.06382	−	1.06382i	−0.0659958	−	0.997820i	$-0.521022\pi$
$504$	0.127605	−	4.13994i	0.00568397	−	0.184408i
$505$		0			0
$506$	−0.981839	−	1.70059i	−0.0436480	−	0.0756006i
$507$	5.25932	+	19.6280i	0.233575	+	0.871712i
$508$	−6.24182	−	23.2948i	−0.276936	−	1.03354i
$509$	0.244582	+	0.423629i	0.0108409	+	0.0187770i	0.871395	−	0.490582i	$-0.163216\pi$
$509$	0.244582	+	0.423629i	0.0108409	+	0.0187770i	−0.860554	+	0.509359i	$0.829882\pi$
$510$		0			0
$511$	9.71568	−	5.21705i	0.429796	−	0.230789i
$512$	−16.0496	−	16.0496i	−0.709301	−	0.709301i
$513$	2.35621	+	0.631343i	0.104029	+	0.0278745i
$514$	1.99642	−	3.45790i	0.0880582	−	0.152521i
$515$		0			0
$516$	1.75480	−	1.01313i	0.0772507	−	0.0446007i
$517$	6.85045	−	6.85045i	0.301282	−	0.301282i
$518$	−1.88804	−	0.568791i	−0.0829557	−	0.0249912i
$519$			16.0384i			0.704007i
$520$		0			0
$521$	−7.19061	−	4.15150i	−0.315026	−	0.181881i	0.334147	−	0.942521i	$-0.391552\pi$
$521$	−7.19061	−	4.15150i	−0.315026	−	0.181881i	−0.649173	+	0.760640i	$0.724885\pi$
$522$	3.18778	−	0.854162i	0.139525	−	0.0373857i
$523$	4.24121	−	15.8284i	0.185455	−	0.692128i	−0.809078	−	0.587702i	$-0.800033\pi$
$523$	4.24121	−	15.8284i	0.185455	−	0.692128i	0.994533	−	0.104426i	$-0.0333005\pi$
$524$	−18.9471			−0.827709
$525$		0			0
$526$	−4.53880			−0.197901
$527$	0.234432	−	0.874911i	0.0102120	−	0.0381117i
$528$	−2.71186	+	0.726641i	−0.118019	+	0.0316230i
$529$	3.35624	+	1.93773i	0.145924	+	0.0842490i
$530$		0			0
$531$			11.8235i			0.513095i
$532$	−2.70861	−	11.5170i	−0.117433	−	0.499325i
$533$	28.4626	−	28.4626i	1.23285	−	1.23285i
$534$	5.50911	−	3.18068i	0.238402	−	0.137642i
$535$		0			0
$536$	−8.49616	+	14.7158i	−0.366978	+	0.635625i
$537$	8.86031	+	2.37411i	0.382351	+	0.102451i
$538$	−2.44588	−	2.44588i	−0.105449	−	0.105449i
$539$	−0.399844	+	6.48001i	−0.0172225	+	0.279114i
$540$		0			0
$541$	−10.9266	−	18.9255i	−0.469772	−	0.813670i	0.529630	−	0.848229i	$-0.322331\pi$
$541$	−10.9266	−	18.9255i	−0.469772	−	0.813670i	−0.999403	+	0.0345590i	$0.988997\pi$
$542$	−2.47937	−	9.25315i	−0.106498	−	0.397457i
$543$	−1.44272	−	5.38430i	−0.0619130	−	0.231062i
$544$	−1.62700	−	2.81806i	−0.0697573	−	0.120823i
$545$		0			0
$546$	3.28356	−	5.30298i	0.140524	−	0.226947i
$547$	5.48357	+	5.48357i	0.234460	+	0.234460i	0.814552	−	0.580091i	$-0.196983\pi$
$547$	5.48357	+	5.48357i	0.234460	+	0.234460i	−0.580091	+	0.814552i	$0.696983\pi$
$548$	1.56395	+	0.419059i	0.0668087	+	0.0179013i
$549$	−2.15260	+	3.72841i	−0.0918708	+	0.159125i
$550$		0			0
$551$	17.0708	−	9.85585i	0.727242	−	0.419873i
$552$	−5.73871	+	5.73871i	−0.244256	+	0.244256i
$553$	15.6467	−	14.7110i	0.665364	−	0.625573i
$554$		−	2.99334i		−	0.127175i
$555$		0			0
$556$	29.6472	+	17.1168i	1.25732	+	0.725914i
$557$	−25.5490	+	6.84583i	−1.08254	+	0.290067i	−0.755638	−	0.654990i	$-0.772673\pi$
$557$	−25.5490	+	6.84583i	−1.08254	+	0.290067i	−0.326907	+	0.945057i	$0.606006\pi$
$558$	0.128498	−	0.479560i	0.00543974	−	0.0203014i
$559$	6.38029			0.269858
$560$		0			0
$561$	−0.691056			−0.0291764
$562$	−1.79549	+	6.70087i	−0.0757383	+	0.282659i
$563$	−41.0771	+	11.0066i	−1.73119	+	0.463872i	−0.980458	−	0.196730i	$-0.936968\pi$
$563$	−41.0771	+	11.0066i	−1.73119	+	0.463872i	−0.750736	+	0.660602i	$0.770301\pi$
$564$	−16.5834	−	9.57443i	−0.698287	−	0.403156i
$565$		0			0
$566$			0.539880i			0.0226929i
$567$	−0.763179	+	2.53329i	−0.0320505	+	0.106388i
$568$	−10.9590	+	10.9590i	−0.459828	+	0.459828i
$569$	−17.6275	+	10.1772i	−0.738982	+	0.426651i	−0.821699	−	0.569922i	$-0.806974\pi$
$569$	−17.6275	+	10.1772i	−0.738982	+	0.426651i	0.0827171	+	0.996573i	$0.473640\pi$
$570$		0			0
$571$	5.57836	−	9.66200i	0.233447	−	0.404342i	−0.725373	−	0.688356i	$-0.758333\pi$
$571$	5.57836	−	9.66200i	0.233447	−	0.404342i	0.958820	+	0.284014i	$0.0916661\pi$
$572$	−9.48011	−	2.54019i	−0.396383	−	0.106211i
$573$	−0.410146	−	0.410146i	−0.0171341	−	0.0171341i
$574$	−7.53123	−	0.232134i	−0.314348	−	0.00968907i
$575$		0			0
$576$	2.13526	+	3.69838i	0.0889691	+	0.154099i
$577$	4.60090	+	17.1708i	0.191538	+	0.714830i	0.993136	+	0.116966i	$0.0373169\pi$
$577$	4.60090	+	17.1708i	0.191538	+	0.714830i	−0.801598	+	0.597864i	$0.796016\pi$
$578$	1.73826	+	6.48728i	0.0723022	+	0.269835i
$579$	−3.02562	−	5.24053i	−0.125740	−	0.217789i
$580$		0			0
$581$	18.8145	+	11.6498i	0.780557	+	0.483315i
$582$	1.99883	+	1.99883i	0.0828542	+	0.0828542i
$583$	5.95548	+	1.59577i	0.246651	+	0.0660899i
$584$	3.26258	−	5.65095i	0.135006	−	0.233838i
$585$		0			0
$586$	−1.40434	+	0.810798i	−0.0580129	+	0.0334938i
$587$	19.9795	−	19.9795i	0.824644	−	0.824644i	−0.162126	−	0.986770i	$-0.551835\pi$
$587$	19.9795	−	19.9795i	0.824644	−	0.824644i	0.986770	+	0.162126i	$0.0518351\pi$
$588$	12.5762	−	2.55159i	0.518634	−	0.105226i
$589$		−	2.96537i		−	0.122186i
$590$		0			0
$591$	7.41768	+	4.28260i	0.305123	+	0.176163i
$592$	5.33582	−	1.42973i	0.219301	−	0.0587615i
$593$	−6.04327	+	22.5538i	−0.248167	+	0.926172i	0.723598	+	0.690222i	$0.242487\pi$
$593$	−6.04327	+	22.5538i	−0.248167	+	0.926172i	−0.971765	+	0.235951i	$0.924180\pi$
$594$	−0.378784			−0.0155417
$595$		0			0
$596$	−10.5179			−0.430830
$597$	2.90569	−	10.8442i	0.118922	−	0.443822i
$598$	−11.8050	+	3.16314i	−0.482743	+	0.129351i
$599$	−12.7696	−	7.37252i	−0.521751	−	0.301233i	0.215900	−	0.976416i	$-0.430732\pi$
$599$	−12.7696	−	7.37252i	−0.521751	−	0.301233i	−0.737651	+	0.675182i	$0.764065\pi$
$600$		0			0
$601$			31.4686i			1.28363i	0.766859	+	0.641815i	$0.221818\pi$
$601$			31.4686i			1.28363i	−0.766859	+	0.641815i	$0.778182\pi$
$602$	−0.818098	−	0.870134i	−0.0333432	−	0.0354640i
$603$	7.67513	−	7.67513i	0.312556	−	0.312556i
$604$	29.9821	−	17.3102i	1.21995	−	0.704341i
$605$		0			0
$606$	−1.69610	+	2.93774i	−0.0688995	+	0.119337i
$607$	20.8371	+	5.58329i	0.845753	+	0.226619i	0.655574	−	0.755131i	$-0.272427\pi$
$607$	20.8371	+	5.58329i	0.845753	+	0.226619i	0.190178	+	0.981750i	$0.439093\pi$
$608$	−7.53291	−	7.53291i	−0.305500	−	0.305500i
$609$	10.1144	+	18.8360i	0.409856	+	0.763273i
$610$		0			0
$611$	−30.1479	−	52.2177i	−1.21965	−	2.11250i
$612$	0.353523	+	1.31937i	0.0142903	+	0.0533323i
$613$	7.70959	+	28.7726i	0.311388	+	1.16211i	0.927306	+	0.374304i	$0.122118\pi$
$613$	7.70959	+	28.7726i	0.311388	+	1.16211i	−0.615918	+	0.787810i	$0.711215\pi$
$614$	−2.71216	−	4.69760i	−0.109454	−	0.189580i
$615$		0			0
$616$	1.81736	+	3.38445i	0.0732233	+	0.136363i
$617$	12.6484	+	12.6484i	0.509204	+	0.509204i	0.914282	−	0.405078i	$-0.132756\pi$
$617$	12.6484	+	12.6484i	0.509204	+	0.509204i	−0.405078	+	0.914282i	$0.632756\pi$
$618$	−1.03593	−	0.277576i	−0.0416712	−	0.0111658i
$619$	−9.98720	+	17.2983i	−0.401419	+	0.695279i	−0.993897	−	0.110308i	$-0.964816\pi$
$619$	−9.98720	+	17.2983i	−0.401419	+	0.695279i	0.592478	+	0.805587i	$0.298150\pi$
$620$		0			0
$621$	4.48961	−	2.59208i	0.180162	−	0.104016i
$622$	−0.349468	+	0.349468i	−0.0140124	+	0.0140124i
$623$	28.2288	+	30.0243i	1.13096	+	1.20290i
$624$			17.4734i			0.699494i
$625$		0			0
$626$	9.68366	+	5.59086i	0.387037	+	0.223456i
$627$	−2.18532	+	0.585556i	−0.0872734	+	0.0233848i
$628$	2.11722	−	7.90156i	0.0844861	−	0.315307i
$629$	1.35971			0.0542153
$630$		0			0
$631$	−33.1850			−1.32107			−0.660536	−	0.750794i	$-0.729671\pi$
$631$	−33.1850			−1.32107			−0.660536	+	0.750794i	$0.729671\pi$
$632$	3.28895	−	12.2745i	0.130828	−	0.488255i
$633$	−4.31399	+	1.15593i	−0.171466	+	0.0459440i
$634$	−5.10645	−	2.94821i	−0.202803	−	0.117088i
$635$		0			0
$636$		−	12.1866i		−	0.483229i
$637$	38.3117	+	12.8419i	1.51797	+	0.508815i
$638$	−2.16437	+	2.16437i	−0.0856883	+	0.0856883i
$639$	8.57360	−	4.94997i	0.339166	−	0.195818i
$640$		0			0
$641$	−5.49850	+	9.52368i	−0.217178	+	0.376163i	−0.953944	−	0.299985i	$-0.903018\pi$
$641$	−5.49850	+	9.52368i	−0.217178	+	0.376163i	0.736766	+	0.676147i	$0.236352\pi$
$642$	−0.347915	−	0.0932234i	−0.0137311	−	0.00367924i
$643$	12.1848	+	12.1848i	0.480522	+	0.480522i	0.905298	−	0.424777i	$-0.139647\pi$
$643$	12.1848	+	12.1848i	0.480522	+	0.480522i	−0.424777	+	0.905298i	$0.639647\pi$
$644$	−21.3779	−	13.2370i	−0.842407	−	0.521611i
$645$		0			0
$646$	−0.371141	−	0.642836i	−0.0146024	−	0.0252920i
$647$	8.70340	+	32.4815i	0.342166	+	1.27698i	0.895888	+	0.444280i	$0.146540\pi$
$647$	8.70340	+	32.4815i	0.342166	+	1.27698i	−0.553722	+	0.832702i	$0.686793\pi$
$648$	0.405180	+	1.51215i	0.0159170	+	0.0594029i
$649$	−5.48299	−	9.49682i	−0.215226	−	0.372783i
$650$		0			0
$651$	3.21479	+	0.0990888i	0.125998	+	0.00388360i
$652$	4.22591	+	4.22591i	0.165500	+	0.165500i
$653$	−47.4030	−	12.7016i	−1.85502	−	0.497052i	−0.855248	−	0.518219i	$-0.826595\pi$
$653$	−47.4030	−	12.7016i	−1.85502	−	0.497052i	−0.999776	+	0.0211667i	$0.993262\pi$
$654$	2.52346	−	4.37076i	0.0986750	−	0.170910i
$655$		0			0
$656$	18.2804	−	10.5542i	0.713729	−	0.412072i
$657$	−2.94730	+	2.94730i	−0.114985	+	0.114985i
$658$	−3.25572	+	10.8070i	−0.126921	+	0.421301i
$659$			8.69642i			0.338764i	0.985550	+	0.169382i	$0.0541772\pi$
$659$			8.69642i			0.338764i	−0.985550	+	0.169382i	$0.945823\pi$
$660$		0			0
$661$	−31.2860	−	18.0630i	−1.21689	−	0.702569i	−0.252635	−	0.967562i	$-0.581297\pi$
$661$	−31.2860	−	18.0630i	−1.21689	−	0.702569i	−0.964250	+	0.264993i	$0.914630\pi$
$662$	−2.68216	+	0.718684i	−0.104245	+	0.0279324i
$663$	−1.11317	+	4.15441i	−0.0432320	+	0.161344i
$664$	13.0939			0.508142
$665$		0			0
$666$	0.745291			0.0288794
$667$	10.8425	−	40.4647i	0.419823	−	1.56680i
$668$	−5.59638	+	1.49954i	−0.216530	+	0.0580191i
$669$	3.74749	+	2.16362i	0.144886	+	0.0836502i
$670$		0			0
$671$		−	3.99297i		−	0.154147i
$672$	8.41822	−	7.91479i	0.324740	−	0.305320i
$673$	17.0769	−	17.0769i	0.658268	−	0.658268i	−0.296702	−	0.954970i	$-0.595887\pi$
$673$	17.0769	−	17.0769i	0.658268	−	0.658268i	0.954970	+	0.296702i	$0.0958869\pi$
$674$	1.74656	−	1.00838i	0.0672750	−	0.0388412i
$675$		0			0
$676$	−18.6258	+	32.2608i	−0.716377	+	1.24080i
$677$	2.24055	+	0.600353i	0.0861113	+	0.0230734i	0.301617	−	0.953429i	$-0.402473\pi$
$677$	2.24055	+	0.600353i	0.0861113	+	0.0230734i	−0.215506	+	0.976502i	$0.569140\pi$
$678$	5.61304	+	5.61304i	0.215568	+	0.215568i
$679$	−9.64056	+	15.5696i	−0.369971	+	0.597506i
$680$		0			0
$681$	−0.730031	−	1.26445i	−0.0279748	−	0.0484539i
$682$	0.119179	+	0.444780i	0.00456358	+	0.0170315i
$683$	4.07266	+	15.1994i	0.155836	+	0.581588i	0.999032	+	0.0439822i	$0.0140045\pi$
$683$	4.07266	+	15.1994i	0.155836	+	0.581588i	−0.843196	+	0.537606i	$0.819329\pi$
$684$	2.23589	+	3.87268i	0.0854915	+	0.148076i
$685$		0			0
$686$	−3.16107	−	6.87152i	−0.120690	−	0.262356i
$687$	−11.0169	−	11.0169i	−0.420320	−	0.420320i
$688$	3.23184	+	0.865969i	0.123213	+	0.0330147i
$689$	19.1865	−	33.2320i	0.730948	−	1.26604i
$690$		0			0
$691$	11.8944	−	6.86721i	0.452483	−	0.261241i	−0.256395	−	0.966572i	$-0.582535\pi$
$691$	11.8944	−	6.86721i	0.452483	−	0.261241i	0.708878	+	0.705331i	$0.249202\pi$
$692$	−20.7901	+	20.7901i	−0.790322	+	0.790322i
$693$	−0.561784	−	2.38870i	−0.0213404	−	0.0907392i
$694$			5.07775i			0.192749i
$695$		0			0
$696$	10.9556	+	6.32523i	0.415272	+	0.239757i
$697$	5.01866	−	1.34475i	0.190095	−	0.0509359i
$698$	0.102941	−	0.384181i	0.00389637	−	0.0145415i
$699$	23.2650			0.879963
$700$		0			0
$701$	50.1869			1.89553			0.947766	−	0.318966i	$-0.103336\pi$
$701$	50.1869			1.89553			0.947766	+	0.318966i	$0.103336\pi$
$702$	−0.610156	+	2.27713i	−0.0230289	+	0.0859449i
$703$	4.29981	−	1.15213i	0.162171	−	0.0434535i
$704$	−3.43016	−	1.98040i	−0.129279	−	0.0746392i
$705$		0			0
$706$		−	0.886896i		−	0.0333788i
$707$	−21.0416	−	6.33898i	−0.791349	−	0.238402i
$708$	−15.3264	+	15.3264i	−0.576003	+	0.576003i
$709$	22.2408	−	12.8408i	0.835272	−	0.482245i	−0.0203820	−	0.999792i	$-0.506488\pi$
$709$	22.2408	−	12.8408i	0.835272	−	0.482245i	0.855654	+	0.517547i	$0.173155\pi$
$710$		0			0
$711$	−4.05863	+	7.02976i	−0.152211	+	0.263637i
$712$	23.5536	+	6.31116i	0.882707	+	0.236521i
$713$	−4.45628	−	4.45628i	−0.166889	−	0.166889i
$714$	0.709307	−	0.380878i	0.0265451	−	0.0142540i
$715$		0			0
$716$	8.40788	+	14.5629i	0.314217	+	0.544240i
$717$	−0.384894	−	1.43645i	−0.0143741	−	0.0536450i
$718$	−2.18639	−	8.15972i	−0.0815954	−	0.304518i
$719$	20.2778	+	35.1222i	0.756235	+	1.30984i	0.944758	+	0.327769i	$0.106297\pi$
$719$	20.2778	+	35.1222i	0.756235	+	1.30984i	−0.188522	+	0.982069i	$0.560370\pi$
$720$		0			0
$721$	0.214048	−	6.94448i	0.00797158	−	0.258626i
$722$	3.76856	+	3.76856i	0.140251	+	0.140251i
$723$	1.42947	+	0.383026i	0.0531627	+	0.0142449i
$724$	5.10937	−	8.84968i	0.189888	−	0.328896i
$725$		0			0
$726$	−3.58632	+	2.07056i	−0.133101	+	0.0768458i
$727$	−19.3599	+	19.3599i	−0.718020	+	0.718020i	−0.968199	−	0.250180i	$-0.919510\pi$
$727$	−19.3599	+	19.3599i	−0.718020	+	0.718020i	0.250180	+	0.968199i	$0.419510\pi$
$728$	23.2737	−	5.47361i	0.862581	−	0.202865i
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	0.713225	+	0.411780i	0.0263796	+	0.0152302i
$732$	−7.62340	+	2.04268i	−0.281769	+	0.0754998i
$733$	−4.40962	+	16.4569i	−0.162873	+	0.607851i	0.835429	+	0.549599i	$0.185219\pi$
$733$	−4.40962	+	16.4569i	−0.162873	+	0.607851i	−0.998302	+	0.0582520i	$0.981447\pi$
$734$	−2.80424			−0.103507
$735$		0			0
$736$	−22.6405			−0.834540
$737$	−2.60555	+	9.72405i	−0.0959767	+	0.358190i
$738$	2.75085	−	0.737088i	0.101260	−	0.0271326i
$739$	−1.49335	−	0.862189i	−0.0549339	−	0.0317161i	0.472281	−	0.881448i	$-0.343431\pi$
$739$	−1.49335	−	0.862189i	−0.0549339	−	0.0317161i	−0.527215	+	0.849732i	$0.676764\pi$
$740$		0			0
$741$			14.0807i			0.517268i
$742$	−6.99228	+	1.64447i	−0.256695	+	0.0603705i
$743$	23.6008	−	23.6008i	0.865830	−	0.865830i	−0.126178	−	0.992008i	$-0.540271\pi$
$743$	23.6008	−	23.6008i	0.865830	−	0.865830i	0.992008	+	0.126178i	$0.0402710\pi$
$744$	1.64813	−	0.951549i	0.0604234	−	0.0348855i
$745$		0			0
$746$	5.21844	−	9.03859i	0.191060	−	0.330926i
$747$	−8.07907	−	2.16478i	−0.295598	−	0.0792051i
$748$	−0.895797	−	0.895797i	−0.0327536	−	0.0327536i
$749$	0.0718877	−	2.33229i	0.00262672	−	0.0852200i
$750$		0			0
$751$	3.70285	+	6.41353i	0.135119	+	0.234033i	0.925643	−	0.378398i	$-0.123525\pi$
$751$	3.70285	+	6.41353i	0.135119	+	0.234033i	−0.790524	+	0.612431i	$0.790192\pi$
$752$	−8.18368	−	30.5419i	−0.298428	−	1.11375i
$753$	4.76112	+	17.7687i	0.173505	+	0.647529i
$754$	9.52510	+	16.4980i	0.346884	+	0.600820i
$755$		0			0
$756$	−4.27312	+	2.29455i	−0.155412	+	0.0834518i
$757$	−13.1631	−	13.1631i	−0.478421	−	0.478421i	0.426205	−	0.904626i	$-0.359850\pi$
$757$	−13.1631	−	13.1631i	−0.478421	−	0.478421i	−0.904626	+	0.426205i	$0.859850\pi$
$758$	14.4597	+	3.87446i	0.525199	+	0.140727i
$759$	−2.40409	+	4.16401i	−0.0872629	+	0.151144i
$760$		0			0
$761$	28.4617	−	16.4324i	1.03174	−	0.595674i	0.114255	−	0.993451i	$-0.463552\pi$
$761$	28.4617	−	16.4324i	1.03174	−	0.595674i	0.917482	+	0.397778i	$0.130218\pi$
$762$	3.79908	−	3.79908i	0.137626	−	0.137626i
$763$	31.3055	+	9.43111i	1.13334	+	0.341429i
$764$		−	1.06332i		−	0.0384697i
$765$		0			0
$766$	−5.11970	−	2.95586i	−0.184982	−	0.106799i
$767$	−65.9241	+	17.6643i	−2.38038	+	0.637821i
$768$	−1.10297	+	4.11633i	−0.0397999	+	0.148535i
$769$	14.4951			0.522707			0.261353	−	0.965243i	$-0.415831\pi$
$769$	14.4951			0.522707			0.261353	+	0.965243i	$0.415831\pi$
$770$		0			0
$771$	−9.77669			−0.352099
$772$	2.87112	−	10.7152i	0.103334	−	0.385648i
$773$	27.6143	−	7.39923i	0.993218	−	0.266132i	0.274616	−	0.961554i	$-0.411449\pi$
$773$	27.6143	−	7.39923i	0.993218	−	0.266132i	0.718602	+	0.695422i	$0.244782\pi$
$774$	0.390935	+	0.225707i	0.0140519	+	0.00811286i
$775$		0			0
$776$			10.8356i			0.388976i
$777$	1.10536	+	4.69997i	0.0396545	+	0.168611i
$778$	−0.742780	+	0.742780i	−0.0266300	+	0.0266300i
$779$	14.7311	−	8.50498i	0.527795	−	0.304722i
$780$		0			0
$781$	−4.59098	+	7.95181i	−0.164278	+	0.284538i
$782$	−1.52378	−	0.408295i	−0.0544902	−	0.0146006i
$783$	−5.71399	−	5.71399i	−0.204201	−	0.204201i
$784$	17.6632	+	11.7048i	0.630830	+	0.418027i
$785$		0			0
$786$	−2.11053	−	3.65554i	−0.0752801	−	0.130389i
$787$	−2.74696	−	10.2518i	−0.0979185	−	0.365437i	0.899527	−	0.436865i	$-0.143911\pi$
$787$	−2.74696	−	10.2518i	−0.0979185	−	0.365437i	−0.997446	+	0.0714277i	$0.977244\pi$
$788$	4.06392	+	15.1668i	0.144771	+	0.540293i
$789$	5.55677	+	9.62460i	0.197826	+	0.342645i
$790$		0			0
$791$	−27.0723	+	43.7219i	−0.962579	+	1.55457i
$792$	−1.02669	−	1.02669i	−0.0364818	−	0.0364818i
$793$	−24.0045	−	6.43199i	−0.852425	−	0.228407i
$794$	−1.81613	+	3.14562i	−0.0644519	+	0.111634i
$795$		0			0
$796$	17.8236	−	10.2904i	0.631739	−	0.364735i
$797$	−8.79395	+	8.79395i	−0.311498	+	0.311498i	−0.845490	−	0.533992i	$-0.820691\pi$
$797$	−8.79395	+	8.79395i	−0.311498	+	0.311498i	0.533992	+	0.845490i	$0.320691\pi$
$798$	1.92031	−	1.80547i	0.0679781	−	0.0639129i
$799$		−	7.78291i		−	0.275340i
$800$		0			0
$801$	−13.4894	−	7.78809i	−0.476624	−	0.275179i
$802$	−12.5867	+	3.37259i	−0.444451	+	0.119090i
$803$	1.00055	−	3.73410i	0.0353086	−	0.131773i
$804$	19.8981			0.701753
$805$		0			0
$806$	2.86586			0.100946
$807$	−2.19208	+	8.18095i	−0.0771648	+	0.287983i
$808$	−12.5600	+	3.36543i	−0.441858	+	0.118396i
$809$	−41.4536	−	23.9333i	−1.45743	−	0.841449i	−0.458547	−	0.888670i	$-0.651630\pi$
$809$	−41.4536	−	23.9333i	−1.45743	−	0.841449i	−0.998884	+	0.0472214i	$0.984963\pi$
$810$		0			0
$811$			20.2287i			0.710327i	0.934804	+	0.355163i	$0.115575\pi$
$811$			20.2287i			0.710327i	−0.934804	+	0.355163i	$0.884425\pi$
$812$	−11.3056	+	37.5276i	−0.396748	+	1.31696i
$813$	−16.5860	+	16.5860i	−0.581696	+	0.581696i
$814$	−0.598631	+	0.345620i	−0.0209820	+	0.0121140i
$815$		0			0
$816$	−1.12772	+	1.95327i	−0.0394781	+	0.0683781i
$817$	2.60434	+	0.697832i	0.0911144	+	0.0244140i
$818$	−9.49109	−	9.49109i	−0.331848	−	0.331848i
$819$	−15.2651	−	0.470512i	−0.533404	−	0.0164410i
$820$		0			0
$821$	−7.84950	−	13.5957i	−0.273949	−	0.474494i	0.695920	−	0.718119i	$-0.254997\pi$
$821$	−7.84950	−	13.5957i	−0.273949	−	0.474494i	−0.969870	+	0.243625i	$0.921663\pi$
$822$	0.0933584	+	0.348418i	0.00325625	+	0.0121525i
$823$	2.26862	+	8.46662i	0.0790793	+	0.295128i	0.994127	−	0.108217i	$-0.0345141\pi$
$823$	2.26862	+	8.46662i	0.0790793	+	0.295128i	−0.915048	+	0.403345i	$0.867847\pi$
$824$	−2.05551	−	3.56024i	−0.0716069	−	0.124027i
$825$		0			0
$826$	10.8620	+	6.72566i	0.377937	+	0.234016i
$827$	−12.7483	−	12.7483i	−0.443302	−	0.443302i	0.449818	−	0.893120i	$-0.351489\pi$
$827$	−12.7483	−	12.7483i	−0.443302	−	0.443302i	−0.893120	+	0.449818i	$0.851489\pi$
$828$	9.17980	+	2.45972i	0.319020	+	0.0854812i
$829$	26.2262	−	45.4252i	0.910875	−	1.57768i	0.0980444	−	0.995182i	$-0.468741\pi$
$829$	26.2262	−	45.4252i	0.910875	−	1.57768i	0.812831	−	0.582500i	$-0.197925\pi$
$830$		0			0
$831$	−6.34743	+	3.66469i	−0.220190	+	0.127127i
$832$	−17.4309	+	17.4309i	−0.604309	+	0.604309i
$833$	3.45389	+	3.90816i	0.119670	+	0.135410i
$834$			7.62659i			0.264087i
$835$		0			0
$836$	−3.59182	−	2.07374i	−0.124226	−	0.0717217i
$837$	−1.17423	+	0.314634i	−0.0405874	+	0.0108753i
$838$	1.29533	−	4.83422i	0.0447463	−	0.166995i
$839$	1.48091			0.0511267			0.0255633	−	0.999673i	$-0.491862\pi$
$839$	1.48091			0.0511267			0.0255633	+	0.999673i	$0.491862\pi$
$840$		0			0
$841$	−36.2994			−1.25170
$842$	−3.64667	+	13.6096i	−0.125673	+	0.469016i
$843$	16.4075	−	4.39637i	0.565104	−	0.151419i
$844$	−7.09050	−	4.09370i	−0.244065	−	0.140911i
$845$		0			0
$846$		−	4.26600i		−	0.146668i
$847$	−18.3764	−	19.5452i	−0.631420	−	0.671582i
$848$	14.2291	−	14.2291i	0.488628	−	0.488628i
$849$	1.14482	−	0.660964i	0.0392902	−	0.0226842i
$850$		0			0
$851$	4.73025	−	8.19304i	0.162151	−	0.280854i
$852$	17.5302	+	4.69721i	0.600576	+	0.160924i
$853$	35.7294	+	35.7294i	1.22335	+	1.22335i	0.966433	+	0.256918i	$0.0827070\pi$
$853$	35.7294	+	35.7294i	1.22335	+	1.22335i	0.256918	+	0.966433i	$0.417293\pi$
$854$	2.20074	+	4.09842i	0.0753077	+	0.140245i
$855$		0			0
$856$	−0.690337	−	1.19570i	−0.0235952	−	0.0408681i
$857$	−11.5288	−	43.0261i	−0.393816	−	1.46974i	−0.823787	−	0.566899i	$-0.808143\pi$
$857$	−11.5288	−	43.0261i	−0.393816	−	1.46974i	0.429971	−	0.902843i	$-0.358524\pi$
$858$	−0.565905	−	2.11199i	−0.0193197	−	0.0721021i
$859$	12.6056	+	21.8335i	0.430096	+	0.744948i	0.996881	−	0.0789174i	$-0.0251463\pi$
$859$	12.6056	+	21.8335i	0.430096	+	0.744948i	−0.566785	+	0.823866i	$0.691813\pi$
$860$		0			0
$861$	8.72809	+	16.2543i	0.297452	+	0.553944i
$862$	−5.15289	−	5.15289i	−0.175508	−	0.175508i
$863$	−23.0586	−	6.17854i	−0.784924	−	0.210320i	−0.155970	−	0.987762i	$-0.549850\pi$
$863$	−23.0586	−	6.17854i	−0.784924	−	0.210320i	−0.628955	+	0.777442i	$0.716517\pi$
$864$	−2.18363	+	3.78215i	−0.0742885	+	0.128671i
$865$		0			0
$866$	1.24792	−	0.720489i	0.0424062	−	0.0244832i
$867$	11.6283	−	11.6283i	0.394916	−	0.394916i
$868$	4.03880	+	4.29569i	0.137086	+	0.145805i
$869$		−	7.52857i		−	0.255389i
$870$		0			0
$871$	54.2609	+	31.3275i	1.83856	+	1.06149i
$872$	18.6867	−	5.00708i	0.632810	−	0.169561i
$873$	1.79142	−	6.68568i	0.0606304	−	0.226276i
$874$	−5.16460			−0.174695
$875$		0			0
$876$	−7.64101			−0.258166
$877$	−12.4223	+	46.3608i	−0.419472	+	1.56549i	0.356234	+	0.934397i	$0.384061\pi$
$877$	−12.4223	+	46.3608i	−0.419472	+	1.56549i	−0.775706	+	0.631095i	$0.782606\pi$
$878$	1.40376	−	0.376137i	0.0473747	−	0.0126940i
$879$	3.43862	+	1.98529i	0.115982	+	0.0669621i
$880$		0			0
$881$			17.3873i			0.585793i	0.956144	+	0.292896i	$0.0946191\pi$
$881$			17.3873i			0.585793i	−0.956144	+	0.292896i	$0.905381\pi$
$882$	1.89316	+	2.14215i	0.0637460	+	0.0721301i
$883$	−11.2463	+	11.2463i	−0.378469	+	0.378469i	−0.870550	−	0.492080i	$-0.836237\pi$
$883$	−11.2463	+	11.2463i	−0.378469	+	0.378469i	0.492080	+	0.870550i	$0.336237\pi$
$884$	−6.82823	+	3.94228i	−0.229658	+	0.132593i
$885$		0			0
$886$	0.961693	−	1.66570i	0.0323087	−	0.0559603i
$887$	18.6733	+	5.00349i	0.626987	+	0.168001i	0.558302	−	0.829638i	$-0.311453\pi$
$887$	18.6733	+	5.00349i	0.626987	+	0.168001i	0.0686850	+	0.997638i	$0.478120\pi$
$888$	2.02010	+	2.02010i	0.0677902	+	0.0677902i
$889$	29.5923	+	18.3233i	0.992495	+	0.614545i
$890$		0			0
$891$	0.463738	+	0.803218i	0.0155358	+	0.0269088i
$892$	2.05314	+	7.66241i	0.0687441	+	0.256556i
$893$	−6.59473	−	24.6119i	−0.220684	−	0.823605i
$894$	−1.17159	−	2.02926i	−0.0391840	−	0.0678687i
$895$		0			0
$896$	27.7106	+	0.854119i	0.925746	+	0.0285341i
$897$	21.1601	+	21.1601i	0.706516	+	0.706516i
$898$	13.5788	+	3.63843i	0.453130	+	0.121416i
$899$	−4.91173	+	8.50736i	−0.163815	+	0.283736i
$900$		0			0
$901$	4.28955	−	2.47657i	0.142906	−	0.0825066i
$902$	−1.86772	+	1.86772i	−0.0621882	+	0.0621882i
$903$	−0.843551	+	2.80008i	−0.0280716	+	0.0931807i
$904$			30.4282i			1.01203i
$905$		0			0
$906$	6.67944	+	3.85638i	0.221910	+	0.128120i
$907$	42.7470	−	11.4540i	1.41939	−	0.380325i	0.534123	−	0.845406i	$-0.320642\pi$
$907$	42.7470	−	11.4540i	1.41939	−	0.380325i	0.885268	+	0.465082i	$0.153975\pi$
$908$	0.692754	−	2.58539i	0.0229898	−	0.0857993i
$909$	8.30602			0.275493
$910$		0			0
$911$	−16.2351			−0.537894			−0.268947	−	0.963155i	$-0.586676\pi$
$911$	−16.2351			−0.537894			−0.268947	+	0.963155i	$0.586676\pi$
$912$	−1.91111	+	7.13237i	−0.0632833	+	0.236176i
$913$	7.49314	−	2.00778i	0.247987	−	0.0664479i
$914$	0.432757	+	0.249852i	0.0143143	+	0.00826438i
$915$		0			0
$916$		−	28.5618i		−	0.943707i
$917$	19.9225	−	18.7311i	0.657899	−	0.618555i
$918$	−0.215172	+	0.215172i	−0.00710172	+	0.00710172i
$919$	−37.3664	+	21.5735i	−1.23260	+	0.711644i	−0.967572	−	0.252596i	$-0.918716\pi$
$919$	−37.3664	+	21.5735i	−1.23260	+	0.711644i	−0.265032	+	0.964240i	$0.585382\pi$
$920$		0			0
$921$	−6.64089	+	11.5024i	−0.218825	+	0.379015i
$922$	5.93131	+	1.58929i	0.195337	+	0.0523405i
$923$	40.4085	+	40.4085i	1.33006	+	1.33006i
$924$	2.36818	−	3.82463i	0.0779074	−	0.125821i
$925$		0			0
$926$	−7.38693	−	12.7945i	−0.242750	−	0.420455i
$927$	0.679662	+	2.53653i	0.0223230	+	0.0833107i
$928$	9.13396	+	34.0884i	0.299837	+	1.11901i
$929$	−14.8286	−	25.6838i	−0.486510	−	0.842659i	0.513370	−	0.858167i	$-0.328397\pi$
$929$	−14.8286	−	25.6838i	−0.486510	−	0.842659i	−0.999880	+	0.0155078i	$0.995064\pi$
$930$		0			0
$931$	14.2337	+	9.43215i	0.466492	+	0.309126i
$932$	30.1578	+	30.1578i	0.987851	+	0.987851i
$933$	1.16890	+	0.313206i	0.0382681	+	0.0102539i
$934$	−2.30775	+	3.99714i	−0.0755119	+	0.130791i
$935$		0			0
$936$	−7.82596	+	4.51832i	−0.255800	+	0.147686i
$937$	23.5836	−	23.5836i	0.770443	−	0.770443i	−0.207741	−	0.978184i	$-0.566611\pi$
$937$	23.5836	−	23.5836i	0.770443	−	0.770443i	0.978184	+	0.207741i	$0.0666111\pi$
$938$	−2.68508	−	11.4169i	−0.0876709	−	0.372776i
$939$		−	27.3791i		−	0.893483i
$940$		0			0
$941$	−19.4488	−	11.2288i	−0.634014	−	0.366048i	0.148291	−	0.988944i	$-0.452623\pi$
$941$	−19.4488	−	11.2288i	−0.634014	−	0.366048i	−0.782305	+	0.622896i	$0.785956\pi$
$942$	1.76032	−	0.471675i	0.0573542	−	0.0153680i
$943$	9.35638	−	34.9185i	0.304686	−	1.13710i
$944$	−35.7903			−1.16488
$945$		0			0
$946$	−0.418675			−0.0136123
$947$	0.773216	−	2.88568i	0.0251261	−	0.0937720i	−0.952224	−	0.305400i	$-0.901210\pi$
$947$	0.773216	−	2.88568i	0.0251261	−	0.0937720i	0.977350	+	0.211628i	$0.0678765\pi$
$948$	−14.3736	+	3.85139i	−0.466832	+	0.125087i
$949$	−20.8365	−	12.0300i	−0.676382	−	0.390509i
$950$		0			0
$951$			14.4377i			0.468175i
$952$	2.95493	+	0.890203i	0.0957698	+	0.0288516i
$953$	−24.1870	+	24.1870i	−0.783494	+	0.783494i	−0.980419	−	0.196924i	$-0.936905\pi$
$953$	−24.1870	+	24.1870i	−0.783494	+	0.783494i	0.196924	+	0.980419i	$0.436905\pi$
$954$	2.35121	−	1.35747i	0.0761231	−	0.0439497i
$955$		0			0
$956$	1.36310	−	2.36095i	0.0440857	−	0.0763587i
$957$	7.23937	+	1.93978i	0.234016	+	0.0627043i
$958$	−4.19691	−	4.19691i	−0.135596	−	0.135596i
$959$	−2.05874	+	1.10549i	−0.0664802	+	0.0356980i
$960$		0			0
$961$	−14.7611	−	25.5670i	−0.476164	−	0.824741i
$962$	1.11347	+	4.15552i	0.0358996	+	0.133979i
$963$	0.228263	+	0.851889i	0.00735567	+	0.0274518i
$964$	1.35648	+	2.34949i	0.0436893	+	0.0756721i
$965$		0			0
$966$	0.172577	−	5.59900i	0.00555257	−	0.180145i
$967$	−22.8071	−	22.8071i	−0.733427	−	0.733427i	0.237870	−	0.971297i	$-0.423551\pi$
$967$	−22.8071	−	22.8071i	−0.733427	−	0.733427i	−0.971297	+	0.237870i	$0.923551\pi$
$968$	−15.3329	−	4.10844i	−0.492818	−	0.132050i
$969$	−0.908762	+	1.57402i	−0.0291936	+	0.0505649i
$970$		0			0
$971$	3.42093	−	1.97508i	0.109783	−	0.0633832i	−0.444103	−	0.895976i	$-0.646478\pi$
$971$	3.42093	−	1.97508i	0.109783	−	0.0633832i	0.553886	+	0.832592i	$0.313144\pi$
$972$	1.29627	−	1.29627i	0.0415780	−	0.0415780i
$973$	−48.0950	+	11.3112i	−1.54185	+	0.362619i
$974$		−	15.7757i		−	0.505487i
$975$		0			0
$976$	−11.2861	−	6.51605i	−0.361260	−	0.208574i
$977$	−18.0188	+	4.82812i	−0.576472	+	0.154465i	−0.535263	−	0.844685i	$-0.679788\pi$
$977$	−18.0188	+	4.82812i	−0.576472	+	0.154465i	−0.0412088	+	0.999151i	$0.513121\pi$
$978$	−0.344596	+	1.28605i	−0.0110190	+	0.0411233i
$979$	14.4465			0.461713
$980$		0			0
$981$	−12.3577			−0.394550
$982$	2.67044	−	9.96622i	0.0852172	−	0.318035i
$983$	−1.11977	+	0.300042i	−0.0357152	+	0.00956985i	−0.276632	−	0.960976i	$-0.589218\pi$
$983$	−1.11977	+	0.300042i	−0.0357152	+	0.00956985i	0.240917	+	0.970546i	$0.422552\pi$
$984$	9.45401	+	5.45828i	0.301383	+	0.174003i
$985$		0			0
$986$			2.45898i			0.0783098i
$987$	26.9023	−	6.32700i	0.856311	−	0.201391i
$988$	−18.2525	+	18.2525i	−0.580688	+	0.580688i
$989$	4.96242	−	2.86505i	0.157796	−	0.0911034i
$990$		0			0
$991$	−6.38011	+	11.0507i	−0.202671	+	0.351036i	−0.949388	−	0.314105i	$-0.898295\pi$
$991$	−6.38011	+	11.0507i	−0.202671	+	0.351036i	0.746717	+	0.665142i	$0.231629\pi$
$992$	5.12816	+	1.37409i	0.162819	+	0.0436273i
$993$	4.80770	+	4.80770i	0.152568	+	0.152568i
$994$	0.329562	−	10.6921i	0.0104531	−	0.339134i
$995$		0			0
$996$	−7.66653	−	13.2788i	−0.242923	−	0.420756i
$997$	0.807643	+	3.01416i	0.0255783	+	0.0954595i	0.977535	−	0.210773i	$-0.0675981\pi$
$997$	0.807643	+	3.01416i	0.0255783	+	0.0954595i	−0.951957	+	0.306233i	$0.900931\pi$
$998$	−0.331203	−	1.23606i	−0.0104840	−	0.0391269i
$999$	−0.912445	−	1.58040i	−0.0288685	−	0.0500017i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bc.e.157.4		32
5.2	odd	4		105.2.u.a.73.4	yes	32
5.3	odd	4	inner	525.2.bc.e.493.5		32
5.4	even	2		105.2.u.a.52.5	✓	32
7.5	odd	6	inner	525.2.bc.e.82.5		32
15.2	even	4		315.2.bz.d.73.5		32
15.14	odd	2		315.2.bz.d.262.4		32
35.2	odd	12		735.2.v.b.313.5		32
35.4	even	6		735.2.m.c.97.10		32
35.9	even	6		735.2.v.b.607.4		32
35.12	even	12		105.2.u.a.103.5	yes	32
35.17	even	12		735.2.m.c.538.10		32
35.19	odd	6		105.2.u.a.82.4	yes	32
35.24	odd	6		735.2.m.c.97.9		32
35.27	even	4		735.2.v.b.178.4		32
35.32	odd	12		735.2.m.c.538.9		32
35.33	even	12	inner	525.2.bc.e.418.4		32
35.34	odd	2		735.2.v.b.472.5		32
105.47	odd	12		315.2.bz.d.208.4		32
105.89	even	6		315.2.bz.d.82.5		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.u.a.52.5	✓	32	5.4	even	2
105.2.u.a.73.4	yes	32	5.2	odd	4
105.2.u.a.82.4	yes	32	35.19	odd	6
105.2.u.a.103.5	yes	32	35.12	even	12
315.2.bz.d.73.5		32	15.2	even	4
315.2.bz.d.82.5		32	105.89	even	6
315.2.bz.d.208.4		32	105.47	odd	12
315.2.bz.d.262.4		32	15.14	odd	2
525.2.bc.e.82.5		32	7.5	odd	6	inner
525.2.bc.e.157.4		32	1.1	even	1	trivial
525.2.bc.e.418.4		32	35.33	even	12	inner
525.2.bc.e.493.5		32	5.3	odd	4	inner
735.2.m.c.97.9		32	35.24	odd	6
735.2.m.c.97.10		32	35.4	even	6
735.2.m.c.538.9		32	35.32	odd	12
735.2.m.c.538.10		32	35.17	even	12
735.2.v.b.178.4		32	35.27	even	4
735.2.v.b.313.5		32	35.2	odd	12
735.2.v.b.472.5		32	35.34	odd	2
735.2.v.b.607.4		32	35.9	even	6

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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.105703 + 0.394487i) q^{2} +(0.965926 - 0.258819i) q^{3} +(1.58760 + 0.916603i) q^{4} +0.408404i q^{6} +(-2.57548 + 0.605712i) q^{7} +(-1.10697 + 1.10697i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.105703 + 0.394487i) q^{2} +(0.965926 - 0.258819i) q^{3} +(1.58760 + 0.916603i) q^{4} +0.408404i q^{6} +(-2.57548 + 0.605712i) q^{7} +(-1.10697 + 1.10697i) q^{8} +(0.866025 - 0.500000i) q^{9} +(-0.463738 + 0.803218i) q^{11} +(1.77074 + 0.474469i) q^{12} +(4.08169 + 4.08169i) q^{13} +(0.0332893 - 1.08002i) q^{14} +(1.51353 + 2.62151i) q^{16} +(0.192844 + 0.719705i) q^{17} +(0.105703 + 0.394487i) q^{18} +(1.21966 + 2.11252i) q^{19} +(-2.33096 + 1.25166i) q^{21} +(-0.267841 - 0.267841i) q^{22} +(5.00751 + 1.34176i) q^{23} +(-0.782747 + 1.35576i) q^{24} +(-2.04162 + 1.17873i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-4.64404 - 1.39907i) q^{28} -8.08080i q^{29} +(-1.05279 - 0.607827i) q^{31} +(-4.21844 + 1.13033i) q^{32} +(-0.240048 + 0.895873i) q^{33} -0.304299 q^{34} +1.83321 q^{36} +(0.472316 - 1.76271i) q^{37} +(-0.962282 + 0.257843i) q^{38} +(4.99903 + 2.88619i) q^{39} -6.97323i q^{41} +(-0.247375 - 1.05184i) q^{42} +(0.781574 - 0.781574i) q^{43} +(-1.47246 + 0.850128i) q^{44} +(-1.05861 + 1.83357i) q^{46} +(-10.0896 - 2.70351i) q^{47} +(2.14045 + 2.14045i) q^{48} +(6.26622 - 3.12000i) q^{49} +(0.372547 + 0.645270i) q^{51} +(2.73882 + 10.2214i) q^{52} +(-1.72055 - 6.42117i) q^{53} +(0.204202 + 0.353688i) q^{54} +(2.18048 - 3.52149i) q^{56} +(1.72486 + 1.72486i) q^{57} +(3.18778 + 0.854162i) q^{58} +(-5.91173 + 10.2394i) q^{59} +(-3.72841 + 2.15260i) q^{61} +(0.351062 - 0.351062i) q^{62} +(-1.92758 + 1.81230i) q^{63} +4.27052i q^{64} +(-0.328037 - 0.189392i) q^{66} +(10.4844 - 2.80929i) q^{67} +(-0.353523 + 1.31937i) q^{68} +5.18415 q^{69} +9.89994 q^{71} +(-0.405180 + 1.51215i) q^{72} +(-4.02609 + 1.07879i) q^{73} +(0.645441 + 0.372646i) q^{74} +4.47178i q^{76} +(0.707830 - 2.34957i) q^{77} +(-1.66698 + 1.66698i) q^{78} +(-7.02976 + 4.05863i) q^{79} +(0.500000 - 0.866025i) q^{81} +(2.75085 + 0.737088i) q^{82} +(-5.91429 - 5.91429i) q^{83} +(-4.84791 - 0.149426i) q^{84} +(0.225707 + 0.390935i) q^{86} +(-2.09147 - 7.80546i) q^{87} +(-0.375795 - 1.40248i) q^{88} +(-7.78809 - 13.4894i) q^{89} +(-12.9847 - 8.04000i) q^{91} +(6.72008 + 6.72008i) q^{92} +(-1.17423 - 0.314634i) q^{93} +(2.13300 - 3.69446i) q^{94} +(-3.78215 + 2.18363i) q^{96} +(4.89426 - 4.89426i) q^{97} +(0.568446 + 2.80174i) q^{98} +0.927476i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 8 q^{7} + 24 q^{8}+O(q^{10}) \) 32 * q - 8 * q^7 + 24 * q^8	\( 32 q - 8 q^{7} + 24 q^{8} - 8 q^{11} - 8 q^{21} + 8 q^{22} + 8 q^{23} + 24 q^{26} + 24 q^{28} + 24 q^{31} - 24 q^{32} + 36 q^{33} - 32 q^{36} - 4 q^{37} - 12 q^{38} - 16 q^{42} - 40 q^{43} - 40 q^{46} + 60 q^{47} - 8 q^{51} + 108 q^{52} + 24 q^{53} - 48 q^{56} - 16 q^{57} - 4 q^{58} - 24 q^{61} - 4 q^{63} + 72 q^{66} - 8 q^{67} - 132 q^{68} - 16 q^{71} - 12 q^{72} - 36 q^{73} - 60 q^{77} - 80 q^{78} + 16 q^{81} - 12 q^{82} - 16 q^{86} + 24 q^{87} + 32 q^{88} - 24 q^{91} + 56 q^{92} + 24 q^{93} + 72 q^{98}+O(q^{100}) \) 32 * q - 8 * q^7 + 24 * q^8 - 8 * q^11 - 8 * q^21 + 8 * q^22 + 8 * q^23 + 24 * q^26 + 24 * q^28 + 24 * q^31 - 24 * q^32 + 36 * q^33 - 32 * q^36 - 4 * q^37 - 12 * q^38 - 16 * q^42 - 40 * q^43 - 40 * q^46 + 60 * q^47 - 8 * q^51 + 108 * q^52 + 24 * q^53 - 48 * q^56 - 16 * q^57 - 4 * q^58 - 24 * q^61 - 4 * q^63 + 72 * q^66 - 8 * q^67 - 132 * q^68 - 16 * q^71 - 12 * q^72 - 36 * q^73 - 60 * q^77 - 80 * q^78 + 16 * q^81 - 12 * q^82 - 16 * q^86 + 24 * q^87 + 32 * q^88 - 24 * q^91 + 56 * q^92 + 24 * q^93 + 72 * q^98

Introduction

L-functions

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