LMFDB - Embedded newform 950.2.bb.d.143.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(143,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([27, 34]))

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

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

chi := DirichletCharacter("950.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.bb (of order $36$, degree $12$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$8$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			143.8
Character	$\chi$	$=$	950.143
Dual form			950.2.bb.d.857.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.573576 - 0.819152i) q^{2} +(0.282278 - 3.22645i) q^{3} +(-0.342020 - 0.939693i) q^{4} +(-2.48104 - 2.08184i) q^{6} +(0.0261014 + 0.0974119i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(-7.37587 - 1.30056i) q^{9} +O(q^{10})$	\(q+(0.573576 - 0.819152i) q^{2} +(0.282278 - 3.22645i) q^{3} +(-0.342020 - 0.939693i) q^{4} +(-2.48104 - 2.08184i) q^{6} +(0.0261014 + 0.0974119i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(-7.37587 - 1.30056i) q^{9} +(-0.855053 - 1.48099i) q^{11} +(-3.12841 + 0.838256i) q^{12} +(-1.15843 + 0.101349i) q^{13} +(0.0947663 + 0.0344921i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(2.46869 + 1.72859i) q^{17} +(-5.29598 + 5.29598i) q^{18} +(-4.25721 + 0.936022i) q^{19} +(0.321662 - 0.0567177i) q^{21} +(-1.70360 - 0.149045i) q^{22} +(1.73364 + 0.808409i) q^{23} +(-1.10773 + 3.04345i) q^{24} +(-0.581425 + 1.00706i) q^{26} +(-3.76348 + 14.0455i) q^{27} +(0.0826100 - 0.0578442i) q^{28} +(1.69050 - 9.58728i) q^{29} +(-6.88675 - 3.97606i) q^{31} +(0.0871557 + 0.996195i) q^{32} +(-5.01972 + 2.34073i) q^{33} +(2.83196 - 1.03075i) q^{34} +(1.30056 + 7.37587i) q^{36} +(7.24662 + 7.24662i) q^{37} +(-1.67509 + 4.02419i) q^{38} +3.76621i q^{39} +(2.14840 + 2.56036i) q^{41} +(0.138037 - 0.296022i) q^{42} +(-4.21487 - 9.03882i) q^{43} +(-1.09923 + 1.31002i) q^{44} +(1.65658 - 0.956430i) q^{46} +(-4.34895 - 6.21094i) q^{47} +(1.85768 + 2.65305i) q^{48} +(6.05337 - 3.49491i) q^{49} +(6.27407 - 7.47714i) q^{51} +(0.491442 + 1.05390i) q^{52} +(3.14660 - 6.74792i) q^{53} +(9.34675 + 11.1390i) q^{54} -0.100848i q^{56} +(1.81831 + 13.9999i) q^{57} +(-6.88381 - 6.88381i) q^{58} +(-0.106508 - 0.604035i) q^{59} +(-8.08886 + 2.94410i) q^{61} +(-7.20708 + 3.36072i) q^{62} +(-0.0658303 - 0.752444i) q^{63} +(0.866025 + 0.500000i) q^{64} +(-0.961775 + 5.45450i) q^{66} +(8.06137 - 5.64463i) q^{67} +(0.780005 - 2.91102i) q^{68} +(3.09766 - 5.36530i) q^{69} +(-3.69203 + 10.1438i) q^{71} +(6.78793 + 3.16526i) q^{72} +(11.8877 + 1.04004i) q^{73} +(10.0926 - 1.77959i) q^{74} +(2.33563 + 3.68033i) q^{76} +(0.121948 - 0.121948i) q^{77} +(3.08510 + 2.16021i) q^{78} +(4.84541 - 4.06578i) q^{79} +(23.1408 + 8.42256i) q^{81} +(3.32960 - 0.291302i) q^{82} +(-4.23886 + 1.13580i) q^{83} +(-0.163312 - 0.282865i) q^{84} +(-9.82172 - 1.73183i) q^{86} +(-30.4557 - 8.16057i) q^{87} +(0.442608 + 1.65183i) q^{88} +(8.17141 + 6.85663i) q^{89} +(-0.0401092 - 0.110199i) q^{91} +(0.166717 - 1.90558i) q^{92} +(-14.7725 + 21.0974i) q^{93} -7.58216 q^{94} +3.23877 q^{96} +(3.77883 - 5.39674i) q^{97} +(0.609204 - 6.96323i) q^{98} +(4.38063 + 12.0357i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 12 q^{6}+O(q^{10}) $ 96 * q - 12 * q^6	$ 96 q - 12 q^{6} + 12 q^{26} - 72 q^{31} + 12 q^{36} - 24 q^{41} + 12 q^{51} - 72 q^{61} - 36 q^{66} + 168 q^{71} - 12 q^{76} + 12 q^{81} - 48 q^{86} - 72 q^{91}+O(q^{100}) $ 96 * q - 12 * q^6 + 12 * q^26 - 72 * q^31 + 12 * q^36 - 24 * q^41 + 12 * q^51 - 72 * q^61 - 36 * q^66 + 168 * q^71 - 12 * q^76 + 12 * q^81 - 48 * q^86 - 72 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{17}{18}\right)$

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 $

$2$	0.573576	−	0.819152i	0.405580	−	0.579228i
$2$	0.573576	−	0.819152i	0.405580	−	0.579228i
$3$	0.282278	−	3.22645i	0.162973	−	1.86279i	−0.271934	−	0.962316i	$-0.587663\pi$
$3$	0.282278	−	3.22645i	0.162973	−	1.86279i	0.434907	−	0.900475i	$-0.356781\pi$
$4$	−0.342020	−	0.939693i	−0.171010	−	0.469846i
$5$		0			0
$5$		0			0
$6$	−2.48104	−	2.08184i	−1.01288	−	0.849909i
$7$	0.0261014	+	0.0974119i	0.00986541	+	0.0368182i	0.970683	−	0.240363i	$-0.0772665\pi$
$7$	0.0261014	+	0.0974119i	0.00986541	+	0.0368182i	−0.960818	+	0.277181i	$0.910600\pi$
$8$	−0.965926	−	0.258819i	−0.341506	−	0.0915064i
$9$	−7.37587	−	1.30056i	−2.45862	−	0.433521i
$10$		0			0
$11$	−0.855053	−	1.48099i	−0.257808	−	0.446537i	0.707846	−	0.706366i	$-0.249667\pi$
$11$	−0.855053	−	1.48099i	−0.257808	−	0.446537i	−0.965654	+	0.259830i	$0.916334\pi$
$12$	−3.12841	+	0.838256i	−0.903096	+	0.241984i
$13$	−1.15843	+	0.101349i	−0.321289	+	0.0281092i	−0.246660	−	0.969102i	$-0.579333\pi$
$13$	−1.15843	+	0.101349i	−0.321289	+	0.0281092i	−0.0746297	+	0.997211i	$0.523777\pi$
$14$	0.0947663	+	0.0344921i	0.0253274	+	0.00921841i
$15$		0			0
$16$	−0.766044	+	0.642788i	−0.191511	+	0.160697i
$17$	2.46869	+	1.72859i	0.598744	+	0.419245i	0.833271	−	0.552864i	$-0.186465\pi$
$17$	2.46869	+	1.72859i	0.598744	+	0.419245i	−0.234527	+	0.972110i	$0.575354\pi$
$18$	−5.29598	+	5.29598i	−1.24828	+	1.24828i
$19$	−4.25721	+	0.936022i	−0.976672	+	0.214738i
$19$	−4.25721	+	0.936022i	−0.976672	+	0.214738i
$20$		0			0
$21$	0.321662	−	0.0567177i	0.0701925	−	0.0123768i
$22$	−1.70360	−	0.149045i	−0.363208	−	0.0317766i
$23$	1.73364	+	0.808409i	0.361489	+	0.168565i	0.594873	−	0.803820i	$-0.297202\pi$
$23$	1.73364	+	0.808409i	0.361489	+	0.168565i	−0.233384	+	0.972385i	$0.574980\pi$
$24$	−1.10773	+	3.04345i	−0.226114	+	0.621242i
$25$		0			0
$26$	−0.581425	+	1.00706i	−0.114027	+	0.197500i
$27$	−3.76348	+	14.0455i	−0.724282	+	2.70306i
$28$	0.0826100	−	0.0578442i	0.0156118	−	0.0109315i
$29$	1.69050	−	9.58728i	0.313917	−	1.78031i	−0.264311	−	0.964438i	$-0.585144\pi$
$29$	1.69050	−	9.58728i	0.313917	−	1.78031i	0.578228	−	0.815875i	$-0.303744\pi$
$30$		0			0
$31$	−6.88675	−	3.97606i	−1.23690	−	0.714122i	−0.268438	−	0.963297i	$-0.586507\pi$
$31$	−6.88675	−	3.97606i	−1.23690	−	0.714122i	−0.968459	+	0.249175i	$0.919841\pi$
$32$	0.0871557	+	0.996195i	0.0154071	+	0.176104i
$33$	−5.01972	+	2.34073i	−0.873820	+	0.407469i
$34$	2.83196	−	1.03075i	0.485677	−	0.176772i
$35$		0			0
$36$	1.30056	+	7.37587i	0.216761	+	1.22931i
$37$	7.24662	+	7.24662i	1.19134	+	1.19134i	0.976692	+	0.214644i	$0.0688592\pi$
$37$	7.24662	+	7.24662i	1.19134	+	1.19134i	0.214644	+	0.976692i	$0.431141\pi$
$38$	−1.67509	+	4.02419i	−0.271736	+	0.652809i
$39$			3.76621i			0.603076i
$40$		0			0
$41$	2.14840	+	2.56036i	0.335524	+	0.399862i	0.907256	−	0.420578i	$-0.138173\pi$
$41$	2.14840	+	2.56036i	0.335524	+	0.399862i	−0.571732	+	0.820440i	$0.693728\pi$
$42$	0.138037	−	0.296022i	0.0212996	−	0.0456772i
$43$	−4.21487	−	9.03882i	−0.642762	−	1.37841i	−0.909932	−	0.414758i	$-0.863866\pi$
$43$	−4.21487	−	9.03882i	−0.642762	−	1.37841i	0.267170	−	0.963649i	$-0.413912\pi$
$44$	−1.09923	+	1.31002i	−0.165716	+	0.197492i
$45$		0			0
$46$	1.65658	−	0.956430i	0.244250	−	0.141018i
$47$	−4.34895	−	6.21094i	−0.634359	−	0.905959i	0.365330	−	0.930878i	$-0.380956\pi$
$47$	−4.34895	−	6.21094i	−0.634359	−	0.905959i	−0.999689	+	0.0249189i	$0.992067\pi$
$48$	1.85768	+	2.65305i	0.268134	+	0.382934i
$49$	6.05337	−	3.49491i	0.864767	−	0.499274i
$50$		0			0
$51$	6.27407	−	7.47714i	0.878545	−	1.04701i
$52$	0.491442	+	1.05390i	0.0681507	+	0.146150i
$53$	3.14660	−	6.74792i	0.432219	−	0.926897i	−0.562741	−	0.826633i	$-0.690253\pi$
$53$	3.14660	−	6.74792i	0.432219	−	0.926897i	0.994961	−	0.100264i	$-0.0319689\pi$
$54$	9.34675	+	11.1390i	1.27193	+	1.51583i
$55$		0			0
$56$		−	0.100848i		−	0.0134764i
$57$	1.81831	+	13.9999i	0.240841	+	1.85433i
$58$	−6.88381	−	6.88381i	−0.903888	−	0.903888i
$59$	−0.106508	−	0.604035i	−0.0138661	−	0.0786387i	0.977089	−	0.212829i	$-0.0682677\pi$
$59$	−0.106508	−	0.604035i	−0.0138661	−	0.0786387i	−0.990956	+	0.134190i	$0.957157\pi$
$60$		0			0
$61$	−8.08886	+	2.94410i	−1.03567	+	0.376954i	−0.803238	−	0.595658i	$-0.796891\pi$
$61$	−8.08886	+	2.94410i	−1.03567	+	0.376954i	−0.232434	+	0.972612i	$0.574669\pi$
$62$	−7.20708	+	3.36072i	−0.915300	+	0.426811i
$63$	−0.0658303	−	0.752444i	−0.00829384	−	0.0947990i
$64$	0.866025	+	0.500000i	0.108253	+	0.0625000i
$65$		0			0
$66$	−0.961775	+	5.45450i	−0.118386	+	0.671402i
$67$	8.06137	−	5.64463i	0.984853	−	0.689602i	0.0340573	−	0.999420i	$-0.489157\pi$
$67$	8.06137	−	5.64463i	0.984853	−	0.689602i	0.950796	+	0.309818i	$0.100268\pi$
$68$	0.780005	−	2.91102i	0.0945895	−	0.353013i
$69$	3.09766	−	5.36530i	0.372914	−	0.645907i
$70$		0			0
$71$	−3.69203	+	10.1438i	−0.438164	+	1.20384i	0.502522	+	0.864565i	$0.332406\pi$
$71$	−3.69203	+	10.1438i	−0.438164	+	1.20384i	−0.940685	+	0.339280i	$0.889817\pi$
$72$	6.78793	+	3.16526i	0.799965	+	0.373030i
$73$	11.8877	+	1.04004i	1.39135	+	0.121727i	0.758057	−	0.652189i	$-0.226149\pi$
$73$	11.8877	+	1.04004i	1.39135	+	0.121727i	0.633289	+	0.773916i	$0.281705\pi$
$74$	10.0926	−	1.77959i	1.17324	−	0.206873i
$75$		0			0
$76$	2.33563	+	3.68033i	0.267915	+	0.422163i
$77$	0.121948	−	0.121948i	0.0138973	−	0.0138973i
$78$	3.08510	+	2.16021i	0.349319	+	0.244595i
$79$	4.84541	−	4.06578i	0.545151	−	0.457436i	−0.328144	−	0.944628i	$-0.606423\pi$
$79$	4.84541	−	4.06578i	0.545151	−	0.457436i	0.873295	+	0.487192i	$0.161979\pi$
$80$		0			0
$81$	23.1408	+	8.42256i	2.57120	+	0.935840i
$82$	3.32960	−	0.291302i	0.367693	−	0.0321690i
$83$	−4.23886	+	1.13580i	−0.465275	+	0.124670i	−0.483838	−	0.875158i	$-0.660758\pi$
$83$	−4.23886	+	1.13580i	−0.465275	+	0.124670i	0.0185628	+	0.999828i	$0.494091\pi$
$84$	−0.163312	−	0.282865i	−0.0178188	−	0.0308631i
$85$		0			0
$86$	−9.82172	−	1.73183i	−1.05910	−	0.186748i
$87$	−30.4557	−	8.16057i	−3.26519	−	0.874905i
$88$	0.442608	+	1.65183i	0.0471822	+	0.176086i
$89$	8.17141	+	6.85663i	0.866168	+	0.726801i	0.963288	−	0.268472i	$-0.0865186\pi$
$89$	8.17141	+	6.85663i	0.866168	+	0.726801i	−0.0971200	+	0.995273i	$0.530963\pi$
$90$		0			0
$91$	−0.0401092	−	0.110199i	−0.00420458	−	0.0115520i
$92$	0.166717	−	1.90558i	0.0173814	−	0.198671i
$93$	−14.7725	+	21.0974i	−1.53184	+	2.18770i
$94$	−7.58216			−0.782040
$95$		0			0
$96$	3.23877			0.330556
$97$	3.77883	−	5.39674i	0.383683	−	0.547955i	−0.580134	−	0.814521i	$-0.697000\pi$
$97$	3.77883	−	5.39674i	0.383683	−	0.547955i	0.963817	+	0.266565i	$0.0858888\pi$
$98$	0.609204	−	6.96323i	0.0615389	−	0.703393i
$99$	4.38063	+	12.0357i	0.440269	+	1.20963i
$100$		0			0
$101$	−4.05468	−	3.40228i	−0.403456	−	0.338540i	0.418372	−	0.908276i	$-0.362601\pi$
$101$	−4.05468	−	3.40228i	−0.403456	−	0.338540i	−0.821828	+	0.569736i	$0.807045\pi$
$102$	−2.52626	−	9.42813i	−0.250137	−	0.933524i
$103$	1.22440	+	0.328078i	0.120644	+	0.0323264i	0.318636	−	0.947877i	$-0.396775\pi$
$103$	1.22440	+	0.328078i	0.120644	+	0.0323264i	−0.197992	+	0.980204i	$0.563442\pi$
$104$	1.14518	+	0.201927i	0.112295	+	0.0198006i
$105$		0			0
$106$	−3.72275	−	6.44799i	−0.361585	−	0.626284i
$107$	−2.96645	+	0.794857i	−0.286777	+	0.0768417i	−0.399340	−	0.916803i	$-0.630761\pi$
$107$	−2.96645	+	0.794857i	−0.286777	+	0.0768417i	0.112563	+	0.993645i	$0.464094\pi$
$108$	14.4856	−	1.26733i	1.39388	−	0.121949i
$109$	−13.6928	−	4.98377i	−1.31153	−	0.477359i	−0.410797	−	0.911727i	$-0.634749\pi$
$109$	−13.6928	−	4.98377i	−1.31153	−	0.477359i	−0.900735	+	0.434369i	$0.856972\pi$
$110$		0			0
$111$	25.4264	−	21.3353i	2.41337	−	2.02506i
$112$	−0.0826100	−	0.0578442i	−0.00780591	−	0.00546576i
$113$	−12.2667	+	12.2667i	−1.15395	+	1.15395i	−0.168198	+	0.985753i	$0.553795\pi$
$113$	−12.2667	+	12.2667i	−1.15395	+	1.15395i	−0.985753	+	0.168198i	$0.946205\pi$
$114$	12.5110	+	6.54054i	1.17176	+	0.612577i
$115$		0			0
$116$	−9.58728	+	1.69050i	−0.890156	+	0.156959i
$117$	8.67620	+	0.759069i	0.802115	+	0.0701760i
$118$	−0.555887	−	0.259214i	−0.0511735	−	0.0238626i
$119$	−0.103949	+	0.285598i	−0.00952901	+	0.0261807i
$120$		0			0
$121$	4.03777	−	6.99362i	0.367070	−	0.635784i
$122$	−2.22791	+	8.31467i	−0.201706	+	0.752775i
$123$	8.86733	−	6.20897i	0.799540	−	0.559844i
$124$	−1.38087	+	7.83132i	−0.124006	+	0.703273i
$125$		0			0
$126$	−0.654124	−	0.377659i	−0.0582740	−	0.0336445i
$127$	0.764002	+	8.73259i	0.0677942	+	0.774892i	0.951660	+	0.307152i	$0.0993760\pi$
$127$	0.764002	+	8.73259i	0.0677942	+	0.774892i	−0.883866	+	0.467740i	$0.845068\pi$
$128$	0.906308	−	0.422618i	0.0801070	−	0.0373545i
$129$	−30.3531	+	11.0476i	−2.67244	+	0.972688i
$130$		0			0
$131$	0.586971	+	3.32888i	0.0512839	+	0.290845i	0.999654	−	0.0263218i	$-0.00837946\pi$
$131$	0.586971	+	3.32888i	0.0512839	+	0.290845i	−0.948370	+	0.317167i	$0.897268\pi$
$132$	3.91641	+	3.91641i	0.340880	+	0.340880i
$133$	−0.202299	−	0.390272i	−0.0175416	−	0.0338408i
$134$		−	9.84112i		−	0.850143i
$135$		0			0
$136$	−1.93717	−	2.30863i	−0.166111	−	0.197964i
$137$	7.99829	−	17.1524i	0.683340	−	1.46543i	−0.191739	−	0.981446i	$-0.561413\pi$
$137$	7.99829	−	17.1524i	0.683340	−	1.46543i	0.875079	−	0.483981i	$-0.160810\pi$
$138$	−2.61825	−	5.61487i	−0.222881	−	0.477969i
$139$	8.45515	−	10.0765i	0.717156	−	0.854674i	−0.277195	−	0.960814i	$-0.589405\pi$
$139$	8.45515	−	10.0765i	0.717156	−	0.854674i	0.994351	+	0.106140i	$0.0338492\pi$
$140$		0			0
$141$	−21.2669	+	12.2785i	−1.79100	+	1.03403i
$142$	6.19163	+	8.84257i	0.519590	+	0.742052i
$143$	1.14061	+	1.62896i	0.0953828	+	0.136221i
$144$	6.48623	−	3.74483i	0.540519	−	0.312069i
$145$		0			0
$146$	7.67043	−	9.14126i	0.634809	−	0.756536i
$147$	−9.56743	−	20.5174i	−0.789108	−	1.69225i
$148$	4.33110	−	9.28808i	0.356015	−	0.763476i
$149$	−3.33221	−	3.97117i	−0.272985	−	0.325331i	0.612082	−	0.790794i	$-0.290332\pi$
$149$	−3.33221	−	3.97117i	−0.272985	−	0.325331i	−0.885067	+	0.465463i	$0.845888\pi$
$150$		0			0
$151$		−	16.4211i		−	1.33633i	−0.744012	−	0.668167i	$-0.767079\pi$
$151$		−	16.4211i		−	1.33633i	0.744012	−	0.668167i	$-0.232921\pi$
$152$	4.35441	+	0.197720i	0.353189	+	0.0160372i
$153$	−15.9606	−	15.9606i	−1.29033	−	1.29033i
$154$	−0.0299475	−	0.169841i	−0.00241324	−	0.0136862i
$155$		0			0
$156$	3.53908	−	1.28812i	0.283353	−	0.103132i
$157$	9.03059	−	4.21103i	0.720719	−	0.336077i	−0.0274150	−	0.999624i	$-0.508728\pi$
$157$	9.03059	−	4.21103i	0.720719	−	0.336077i	0.748134	+	0.663547i	$0.230950\pi$
$158$	−0.551280	−	6.30116i	−0.0438575	−	0.501293i
$159$	−20.8836	−	12.0571i	−1.65618	−	0.956194i
$160$		0			0
$161$	−0.0334982	+	0.189978i	−0.00264003	+	0.0149723i
$162$	20.1724	−	14.1249i	1.58489	−	1.10975i
$163$	2.35083	−	8.77341i	0.184131	−	0.687187i	−0.810684	−	0.585484i	$-0.800904\pi$
$163$	2.35083	−	8.77341i	0.184131	−	0.687187i	0.994815	−	0.101702i	$-0.0324290\pi$
$164$	1.67116	−	2.89453i	0.130496	−	0.226025i
$165$		0			0
$166$	−1.50092	+	4.12374i	−0.116494	+	0.320064i
$167$	9.85025	+	4.59325i	0.762236	+	0.355436i	0.764553	−	0.644561i	$-0.222960\pi$
$167$	9.85025	+	4.59325i	0.762236	+	0.355436i	−0.00231733	+	0.999997i	$0.500738\pi$
$168$	−0.325382	−	0.0284672i	−0.0251037	−	0.00219629i
$169$	−11.4708	+	2.02262i	−0.882371	+	0.155586i
$170$		0			0
$171$	32.6180	−	1.36720i	2.49436	−	0.104552i
$172$	−7.05214	+	7.05214i	−0.537721	+	0.537721i
$173$	8.52234	+	5.96741i	0.647941	+	0.453693i	0.850782	−	0.525518i	$-0.176129\pi$
$173$	8.52234	+	5.96741i	0.647941	+	0.453693i	−0.202841	+	0.979212i	$0.565017\pi$
$174$	−24.1534	+	20.2671i	−1.83106	+	1.53645i
$175$		0			0
$176$	1.60697	+	0.584890i	0.121130	+	0.0440878i
$177$	−1.97895	+	0.173136i	−0.148747	+	0.0130137i
$178$	10.3035	−	2.76083i	0.772283	−	0.206933i
$179$	−0.399726	−	0.692345i	−0.0298769	−	0.0517483i	0.850700	−	0.525651i	$-0.176178\pi$
$179$	−0.399726	−	0.692345i	−0.0298769	−	0.0517483i	−0.880577	+	0.473903i	$0.842845\pi$
$180$		0			0
$181$	−12.4000	−	2.18645i	−0.921683	−	0.162518i	−0.307379	−	0.951587i	$-0.599452\pi$
$181$	−12.4000	−	2.18645i	−0.921683	−	0.162518i	−0.614304	+	0.789069i	$0.710563\pi$
$182$	−0.113275	−	0.0303521i	−0.00839654	−	0.00224984i
$183$	7.21570	+	26.9293i	0.533400	+	1.99067i
$184$	−1.46534	−	1.22956i	−0.108026	−	0.0906445i
$185$		0			0
$186$	8.80878	+	24.2019i	0.645891	+	1.77457i
$187$	0.449180	−	5.13415i	0.0328473	−	0.375446i
$188$	−4.34895	+	6.21094i	−0.317180	+	0.452980i
$189$	−1.46643			−0.106667
$190$		0			0
$191$	−14.9995			−1.08533			−0.542664	−	0.839950i	$-0.682584\pi$
$191$	−14.9995			−1.08533			−0.542664	+	0.839950i	$0.682584\pi$
$192$	1.85768	−	2.65305i	0.134067	−	0.191467i
$193$	0.280010	−	3.20053i	0.0201556	−	0.230379i	−0.979435	−	0.201761i	$-0.935334\pi$
$193$	0.280010	−	3.20053i	0.0201556	−	0.230379i	0.999590	−	0.0286184i	$-0.00911076\pi$
$194$	−2.25330	−	6.19088i	−0.161777	−	0.444479i
$195$		0			0
$196$	−5.35452	−	4.49298i	−0.382466	−	0.320927i
$197$	−0.508165	−	1.89650i	−0.0362052	−	0.135120i	0.945458	−	0.325745i	$-0.105615\pi$
$197$	−0.508165	−	1.89650i	−0.0362052	−	0.135120i	−0.981663	+	0.190625i	$0.938948\pi$
$198$	12.3717	+	3.31498i	0.879216	+	0.235585i
$199$	4.73530	+	0.834962i	0.335677	+	0.0591889i	0.338946	−	0.940806i	$-0.389930\pi$
$199$	4.73530	+	0.834962i	0.335677	+	0.0591889i	−0.00326934	+	0.999995i	$0.501041\pi$
$200$		0			0
$201$	−15.9366	−	27.6029i	−1.12408	−	1.94696i
$202$	−5.11266	+	1.36993i	−0.359725	+	0.0963881i
$203$	0.978039	−	0.0855673i	0.0686449	−	0.00600565i
$204$	−9.17208	−	3.33836i	−0.642174	−	0.233732i
$205$		0			0
$206$	0.971034	−	0.814794i	0.0676551	−	0.0567694i
$207$	−11.7357	−	8.21743i	−0.815688	−	0.571151i
$208$	0.822260	−	0.822260i	0.0570134	−	0.0570134i
$209$	5.02639	+	5.50456i	0.347682	+	0.380758i
$210$		0			0
$211$	−24.3774	+	4.29839i	−1.67821	+	0.295914i	−0.930003	−	0.367553i	$-0.880196\pi$
$211$	−24.3774	+	4.29839i	−1.67821	+	0.295914i	−0.748206	+	0.663466i	$0.769085\pi$
$212$	−7.41717	−	0.648918i	−0.509413	−	0.0445679i
$213$	31.6862	+	14.7755i	2.17110	+	1.01240i
$214$	−1.05037	+	2.88588i	−0.0718021	+	0.197275i
$215$		0			0
$216$	7.27048	−	12.5928i	0.494694	−	0.856834i
$217$	0.207562	−	0.774632i	0.0140902	−	0.0525854i
$218$	−11.9363	+	8.35791i	−0.808430	+	0.566069i
$219$	6.71124	−	38.0613i	0.453504	−	2.57195i
$220$		0			0
$221$	−3.03498	−	1.75225i	−0.204155	−	0.117869i
$222$	−2.89286	−	33.0655i	−0.194156	−	2.21921i
$223$	−8.57482	+	3.99850i	−0.574213	+	0.267760i	−0.687958	−	0.725750i	$-0.741493\pi$
$223$	−8.57482	+	3.99850i	−0.574213	+	0.267760i	0.113746	+	0.993510i	$0.463715\pi$
$224$	−0.0947663	+	0.0344921i	−0.00633184	+	0.00230460i
$225$		0			0
$226$	3.01239	+	17.0841i	0.200382	+	1.13642i
$227$	−13.1535	−	13.1535i	−0.873028	−	0.873028i	0.119773	−	0.992801i	$-0.461783\pi$
$227$	−13.1535	−	13.1535i	−0.873028	−	0.873028i	−0.992801	+	0.119773i	$0.961783\pi$
$228$	12.5337	−	6.49690i	0.830065	−	0.430268i
$229$			13.8433i			0.914794i	0.889263	+	0.457397i	$0.151218\pi$
$229$			13.8433i			0.914794i	−0.889263	+	0.457397i	$0.848782\pi$
$230$		0			0
$231$	−0.359037	−	0.427883i	−0.0236229	−	0.0281527i
$232$	−4.11426	+	8.82307i	−0.270115	+	0.579263i
$233$	8.61218	+	18.4689i	0.564202	+	1.20994i	0.956940	+	0.290285i	$0.0937502\pi$
$233$	8.61218	+	18.4689i	0.564202	+	1.20994i	−0.392738	+	0.919651i	$0.628472\pi$
$234$	5.59826	−	6.67175i	0.365970	−	0.436146i
$235$		0			0
$236$	−0.531180	+	0.306677i	−0.0345769	+	0.0199630i
$237$	−11.7503	−	16.7811i	−0.763262	−	1.09005i
$238$	0.174325	+	0.248962i	0.0112998	+	0.0161378i
$239$	6.24131	−	3.60342i	0.403717	−	0.233086i	−0.284370	−	0.958715i	$-0.591784\pi$
$239$	6.24131	−	3.60342i	0.403717	−	0.233086i	0.688087	+	0.725629i	$0.258451\pi$
$240$		0			0
$241$	−1.78969	+	2.13287i	−0.115284	+	0.137390i	−0.820600	−	0.571503i	$-0.806361\pi$
$241$	−1.78969	+	2.13287i	−0.115284	+	0.137390i	0.705316	+	0.708893i	$0.250805\pi$
$242$	−3.41287	−	7.31892i	−0.219388	−	0.470478i
$243$	15.2713	−	32.7493i	0.979652	−	2.10087i
$244$	5.53311	+	6.59410i	0.354221	+	0.422144i
$245$		0			0
$246$		−	10.8250i		−	0.690178i
$247$	4.83680	−	1.51578i	0.307758	−	0.0964466i
$248$	5.62300	+	5.62300i	0.357061	+	0.357061i
$249$	2.46806	+	13.9971i	0.156407	+	0.887028i
$250$		0			0
$251$	20.5427	−	7.47694i	1.29665	−	0.471940i	0.400743	−	0.916191i	$-0.368752\pi$
$251$	20.5427	−	7.47694i	1.29665	−	0.471940i	0.895903	+	0.444250i	$0.146530\pi$
$252$	−0.684550	+	0.319211i	−0.0431226	+	0.0201084i
$253$	−0.285103	−	3.25874i	−0.0179243	−	0.204875i
$254$	7.59153	+	4.38297i	0.476335	+	0.275012i
$255$		0			0
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−17.9598	+	12.5756i	−1.12030	+	0.784443i	−0.978662	−	0.205476i	$-0.934126\pi$
$257$	−17.9598	+	12.5756i	−1.12030	+	0.784443i	−0.141638	+	0.989918i	$0.545237\pi$
$258$	−8.36013	+	31.2004i	−0.520479	+	1.94245i
$259$	−0.516760	+	0.895054i	−0.0321099	+	0.0556159i
$260$		0			0
$261$	−24.9377	+	68.5159i	−1.54361	+	4.24103i
$262$	3.06353	+	1.42855i	0.189265	+	0.0882560i
$263$	1.02710	+	0.0898598i	0.0633339	+	0.00554099i	0.118779	−	0.992921i	$-0.462102\pi$
$263$	1.02710	+	0.0898598i	0.0633339	+	0.00554099i	−0.0554448	+	0.998462i	$0.517658\pi$
$264$	5.45450	−	0.961775i	0.335701	−	0.0591932i
$265$		0			0
$266$	−0.435726	−	0.0581369i	−0.0267161	−	0.00356460i
$267$	24.4292	−	24.4292i	1.49504	−	1.49504i
$268$	−8.06137	−	5.64463i	−0.492427	−	0.344801i
$269$	17.9554	−	15.0664i	1.09476	−	0.918614i	0.0976996	−	0.995216i	$-0.468852\pi$
$269$	17.9554	−	15.0664i	1.09476	−	0.918614i	0.997062	+	0.0766021i	$0.0244071\pi$
$270$		0			0
$271$	18.6707	+	6.79557i	1.13416	+	0.412802i	0.839802	−	0.542893i	$-0.182671\pi$
$271$	18.6707	+	6.79557i	1.13416	+	0.412802i	0.294361	+	0.955694i	$0.404893\pi$
$272$	−3.00224	+	0.262662i	−0.182038	+	0.0159262i
$273$	−0.366874	+	0.0983035i	−0.0222042	+	0.00594960i
$274$	−9.46278	−	16.3900i	−0.571667	−	0.990157i
$275$		0			0
$276$	−6.10120	−	1.07581i	−0.367249	−	0.0647559i
$277$	12.4206	+	3.32808i	0.746279	+	0.199965i	0.611867	−	0.790961i	$-0.290419\pi$
$277$	12.4206	+	3.32808i	0.746279	+	0.199965i	0.134412	+	0.990926i	$0.457085\pi$
$278$	−3.40447	−	12.7057i	−0.204187	−	0.762036i
$279$	45.6246	+	38.2836i	2.73147	+	2.29198i
$280$		0			0
$281$	9.32049	+	25.6078i	0.556014	+	1.52764i	0.825368	+	0.564595i	$0.190967\pi$
$281$	9.32049	+	25.6078i	0.556014	+	1.52764i	−0.269355	+	0.963041i	$0.586810\pi$
$282$	−2.14028	+	24.4635i	−0.127452	+	1.45678i
$283$	14.1552	−	20.2157i	0.841438	−	1.20170i	−0.136049	−	0.990702i	$-0.543440\pi$
$283$	14.1552	−	20.2157i	0.841438	−	1.20170i	0.977487	−	0.210996i	$-0.0676706\pi$
$284$	10.7948			0.640552
$285$		0			0
$286$	1.98860			0.117588
$287$	−0.193334	+	0.276109i	−0.0114121	+	0.0162982i
$288$	0.652766	−	7.46115i	0.0384646	−	0.439653i
$289$	−2.70797	−	7.44007i	−0.159292	−	0.437651i
$290$		0			0
$291$	−16.3456	−	13.7156i	−0.958197	−	0.804022i
$292$	−3.08851	−	11.5265i	−0.180741	−	0.674535i
$293$	16.8628	+	4.51838i	0.985137	+	0.263967i	0.715207	−	0.698913i	$-0.246333\pi$
$293$	16.8628	+	4.51838i	0.985137	+	0.263967i	0.269931	+	0.962880i	$0.412999\pi$
$294$	−22.2945	−	3.93113i	−1.30024	−	0.229268i
$295$		0			0
$296$	−5.12413	−	8.87526i	−0.297834	−	0.515864i
$297$	24.0193	−	6.43594i	1.39374	−	0.373451i
$298$	−5.16427	+	0.451815i	−0.299158	+	0.0261730i
$299$	−2.09022	−	0.760779i	−0.120881	−	0.0439970i
$300$		0			0
$301$	0.770474	−	0.646505i	0.0444094	−	0.0372639i
$302$	−13.4514	−	9.41878i	−0.774041	−	0.541990i
$303$	−12.1218	+	12.1218i	−0.696381	+	0.696381i
$304$	2.65955	−	3.45352i	0.152536	−	0.198073i
$305$		0			0
$306$	−22.2287	+	3.91952i	−1.27073	+	0.224064i
$307$	26.4520	+	2.31425i	1.50969	+	0.132081i	0.811722	−	0.584043i	$-0.198530\pi$
$307$	26.4520	+	2.31425i	1.50969	+	0.132081i	0.697973	+	0.716125i	$0.254086\pi$
$308$	−0.156303	−	0.0728852i	−0.00890618	−	0.00415302i
$309$	1.40415	−	3.85786i	0.0798791	−	0.219466i
$310$		0			0
$311$	−10.4366	+	18.0767i	−0.591805	+	1.02504i	0.402184	+	0.915559i	$0.368251\pi$
$311$	−10.4366	+	18.0767i	−0.591805	+	1.02504i	−0.993989	+	0.109478i	$0.965082\pi$
$312$	0.974767	−	3.63788i	0.0551853	−	0.205954i
$313$	26.3321	−	18.4379i	1.48838	−	1.04217i	0.504484	−	0.863421i	$-0.331683\pi$
$313$	26.3321	−	18.4379i	1.48838	−	1.04217i	0.983894	−	0.178752i	$-0.0572061\pi$
$314$	1.73026	−	9.81277i	0.0976440	−	0.553767i
$315$		0			0
$316$	−5.47781	−	3.16261i	−0.308151	−	0.177911i
$317$	1.19739	+	13.6862i	0.0672518	+	0.768692i	0.952692	+	0.303938i	$0.0983016\pi$
$317$	1.19739	+	13.6862i	0.0672518	+	0.768692i	−0.885440	+	0.464754i	$0.846143\pi$
$318$	−21.8550	+	10.1911i	−1.22557	+	0.571491i
$319$	−15.6442	+	5.69401i	−0.875905	+	0.318803i
$320$		0			0
$321$	1.72720	+	9.79545i	0.0964031	+	0.546729i
$322$	0.136407	+	0.136407i	0.00760166	+	0.00760166i
$323$	−12.1277	−	5.04824i	−0.674804	−	0.280892i
$324$		−	24.6259i		−	1.36811i
$325$		0			0
$326$	−5.83838	−	6.95791i	−0.323358	−	0.385363i
$327$	−19.9450	+	42.7723i	−1.10296	+	2.36531i
$328$	−1.41252	−	3.02917i	−0.0779936	−	0.167258i
$329$	0.491506	−	0.585754i	0.0270976	−	0.0322937i
$330$		0			0
$331$	1.56908	−	0.905912i	0.0862447	−	0.0497934i	−0.456257	−	0.889848i	$-0.650810\pi$
$331$	1.56908	−	0.905912i	0.0862447	−	0.0497934i	0.542502	+	0.840054i	$0.317477\pi$
$332$	2.51708	+	3.59476i	0.138143	+	0.197288i
$333$	−44.0254	−	62.8748i	−2.41258	−	3.44552i
$334$	9.41244	−	5.43428i	0.515026	−	0.297350i
$335$		0			0
$336$	−0.209950	+	0.250209i	−0.0114537	+	0.0136500i
$337$	4.96457	+	10.6466i	0.270437	+	0.579955i	0.993884	−	0.110425i	$-0.0352212\pi$
$337$	4.96457	+	10.6466i	0.270437	+	0.579955i	−0.723447	+	0.690380i	$0.757443\pi$
$338$	−4.92256	+	10.5565i	−0.267752	+	0.574196i
$339$	36.1152	+	43.0404i	1.96151	+	2.33763i
$340$		0			0
$341$			13.5990i			0.736426i
$342$	17.5890	−	27.5033i	0.951103	−	1.48721i
$343$	0.997621	+	0.997621i	0.0538665	+	0.0538665i
$344$	1.73183	+	9.82172i	0.0933742	+	0.529552i
$345$		0			0
$346$	9.77642	−	3.55833i	0.525584	−	0.191297i
$347$	20.2219	−	9.42965i	1.08557	−	0.506210i	0.204342	−	0.978900i	$-0.434495\pi$
$347$	20.2219	−	9.42965i	1.08557	−	0.506210i	0.881229	+	0.472689i	$0.156717\pi$
$348$	2.74802	+	31.4100i	0.147310	+	1.68376i
$349$	11.3588	+	6.55800i	0.608022	+	0.351042i	0.772191	−	0.635391i	$-0.219161\pi$
$349$	11.3588	+	6.55800i	0.608022	+	0.351042i	−0.164169	+	0.986432i	$0.552494\pi$
$350$		0			0
$351$	2.93621	−	16.6521i	0.156723	−	0.888822i
$352$	1.40084	−	0.980876i	0.0746648	−	0.0522809i
$353$	−5.05689	+	18.8726i	−0.269151	+	1.00449i	0.690509	+	0.723323i	$0.257386\pi$
$353$	−5.05689	+	18.8726i	−0.269151	+	1.00449i	−0.959660	+	0.281162i	$0.909280\pi$
$354$	−0.993256	+	1.72037i	−0.0527910	+	0.0914367i
$355$		0			0
$356$	3.64833	−	10.0237i	0.193361	−	0.531256i
$357$	0.892125	+	0.416005i	0.0472163	+	0.0220173i
$358$	−0.796409	−	0.0696767i	−0.0420915	−	0.00368253i
$359$	−5.52860	+	0.974840i	−0.291788	+	0.0514501i	−0.317626	−	0.948216i	$-0.602886\pi$
$359$	−5.52860	+	0.974840i	−0.291788	+	0.0514501i	0.0258380	+	0.999666i	$0.491775\pi$
$360$		0			0
$361$	17.2477	−	7.96969i	0.907775	−	0.419457i
$362$	−8.90337	+	8.90337i	−0.467951	+	0.467951i
$363$	−21.4248	−	15.0018i	−1.12451	−	0.787390i
$364$	−0.0898351	+	0.0753806i	−0.00470864	+	0.00395102i
$365$		0			0
$366$	26.1980	+	9.53529i	1.36939	+	0.498417i
$367$	−11.0588	+	0.967518i	−0.577263	+	0.0505040i	−0.372049	−	0.928213i	$-0.621345\pi$
$367$	−11.0588	+	0.967518i	−0.577263	+	0.0505040i	−0.205214	+	0.978717i	$0.565789\pi$
$368$	−1.84768	+	0.495084i	−0.0963170	+	0.0258081i
$369$	−12.5164	−	21.6790i	−0.651578	−	1.12857i
$370$		0			0
$371$	0.739458	+	0.130386i	0.0383907	+	0.00676932i
$372$	24.8776	+	6.66592i	1.28984	+	0.345612i
$373$	0.846597	+	3.15954i	0.0438351	+	0.163595i	0.984374	−	0.176092i	$-0.0563456\pi$
$373$	0.846597	+	3.15954i	0.0438351	+	0.163595i	−0.940539	+	0.339687i	$0.889679\pi$
$374$	−3.94801	−	3.31277i	−0.204147	−	0.171299i
$375$		0			0
$376$	2.59325	+	7.12490i	0.133737	+	0.367439i
$377$	−0.986651	+	11.2775i	−0.0508151	+	0.580820i
$378$	−0.841110	+	1.20123i	−0.0432620	+	0.0617846i
$379$	13.3933			0.687965			0.343983	−	0.938976i	$-0.388224\pi$
$379$	13.3933			0.687965			0.343983	+	0.938976i	$0.388224\pi$
$380$		0			0
$381$	28.3909			1.45451
$382$	−8.60338	+	12.2869i	−0.440187	+	0.628653i
$383$	−1.95120	+	22.3023i	−0.0997017	+	1.13960i	0.767299	+	0.641289i	$0.221600\pi$
$383$	−1.95120	+	22.3023i	−0.0997017	+	1.13960i	−0.867001	+	0.498306i	$0.833955\pi$
$384$	−1.10773	−	3.04345i	−0.0565284	−	0.155310i
$385$		0			0
$386$	−2.46111	−	2.06512i	−0.125267	−	0.105112i
$387$	19.3328	+	72.1509i	0.982740	+	3.66763i
$388$	−6.36371	−	1.70515i	−0.323068	−	0.0865659i
$389$	−8.81257	−	1.55389i	−0.446815	−	0.0787856i	−0.0542867	−	0.998525i	$-0.517288\pi$
$389$	−8.81257	−	1.55389i	−0.446815	−	0.0787856i	−0.392529	+	0.919740i	$0.628400\pi$
$390$		0			0
$391$	2.88240	+	4.99246i	0.145769	+	0.252480i
$392$	−6.75166	+	1.80910i	−0.341010	+	0.0913734i
$393$	10.9061	−	0.954164i	0.550142	−	0.0481312i
$394$	−1.84499	−	0.671521i	−0.0929493	−	0.0338308i
$395$		0			0
$396$	9.81157	−	8.23288i	0.493050	−	0.413718i
$397$	−26.7522	−	18.7321i	−1.34266	−	0.940138i	−1.00000		0.000676484i	$-0.999785\pi$
$397$	−26.7522	−	18.7321i	−1.34266	−	0.940138i	−0.342656	−	0.939461i	$-0.611326\pi$
$398$	3.40002	−	3.40002i	0.170428	−	0.170428i
$399$	−1.31630	+	0.542543i	−0.0658972	+	0.0271611i
$400$		0			0
$401$	7.45948	−	1.31531i	0.372509	−	0.0656834i	0.0157402	−	0.999876i	$-0.494990\pi$
$401$	7.45948	−	1.31531i	0.372509	−	0.0656834i	0.356769	+	0.934193i	$0.383878\pi$
$402$	−31.7519	−	2.77793i	−1.58364	−	0.138550i
$403$	8.38075	+	3.90801i	0.417475	+	0.194672i
$404$	−1.81032	+	4.97380i	−0.0900666	+	0.247456i
$405$		0			0
$406$	0.490888	−	0.850242i	0.0243623	−	0.0421968i
$407$	4.53596	−	16.9284i	0.224839	−	0.839112i
$408$	−7.99551	+	5.59852i	−0.395837	+	0.277168i
$409$	3.49787	−	19.8374i	0.172958	−	0.980896i	−0.767516	−	0.641030i	$-0.778507\pi$
$409$	3.49787	−	19.8374i	0.172958	−	0.980896i	0.940474	−	0.339866i	$-0.110382\pi$
$410$		0			0
$411$	−53.0835	−	30.6478i	−2.61842	−	1.51174i
$412$	−0.110478	−	1.26277i	−0.00544287	−	0.0622123i
$413$	0.0560602	−	0.0261413i	0.00275854	−	0.00128633i
$414$	−13.4626	+	4.90000i	−0.661653	+	0.240822i
$415$		0			0
$416$	−0.201927	−	1.14518i	−0.00990028	−	0.0561473i
$417$	−30.1245	−	30.1245i	−1.47520	−	1.47520i
$418$	7.39209	−	0.960087i	0.361559	−	0.0469594i
$419$			17.7197i			0.865666i	0.901474	+	0.432833i	$0.142486\pi$
$419$			17.7197i			0.865666i	−0.901474	+	0.432833i	$0.857514\pi$
$420$		0			0
$421$	−8.44908	−	10.0692i	−0.411783	−	0.490744i	0.519792	−	0.854293i	$-0.326009\pi$
$421$	−8.44908	−	10.0692i	−0.411783	−	0.490744i	−0.931575	+	0.363549i	$0.881565\pi$
$422$	−10.4613	+	22.4342i	−0.509246	+	1.09208i
$423$	23.9995	+	51.4672i	1.16690	+	2.50242i
$424$	−4.78588	+	5.70358i	−0.232423	+	0.276991i
$425$		0			0
$426$	30.2779	−	17.4809i	1.46697	−	0.846954i
$427$	−0.497922	−	0.711106i	−0.0240961	−	0.0344128i
$428$	1.76150	+	2.51569i	0.0851456	+	0.121600i
$429$	5.57774	−	3.22031i	0.269296	−	0.155478i
$430$		0			0
$431$	17.9802	−	21.4279i	0.866075	−	1.03215i	−0.133083	−	0.991105i	$-0.542488\pi$
$431$	17.9802	−	21.4279i	0.866075	−	1.03215i	0.999157	−	0.0410427i	$-0.0130680\pi$
$432$	−6.14528	−	13.1786i	−0.295665	−	0.634055i
$433$	3.40195	−	7.29551i	0.163487	−	0.350600i	−0.807449	−	0.589937i	$-0.799152\pi$
$433$	3.40195	−	7.29551i	0.163487	−	0.350600i	0.970936	+	0.239338i	$0.0769302\pi$
$434$	−0.515489	−	0.614335i	−0.0247442	−	0.0294890i
$435$		0			0
$436$			14.5716i			0.697851i
$437$	−8.13716	−	1.81885i	−0.389253	−	0.0870072i
$438$	−27.3286	−	27.3286i	−1.30581	−	1.30581i
$439$	2.39988	+	13.6104i	0.114540	+	0.649588i	0.986977	+	0.160861i	$0.0514272\pi$
$439$	2.39988	+	13.6104i	0.114540	+	0.649588i	−0.872437	+	0.488726i	$0.837462\pi$
$440$		0			0
$441$	−49.1942	+	17.9052i	−2.34258	+	0.852630i
$442$	−3.17615	+	1.48106i	−0.151074	+	0.0704470i
$443$	−0.207315	−	2.36963i	−0.00984985	−	0.112584i	0.989678	−	0.143309i	$-0.0457742\pi$
$443$	−0.207315	−	2.36963i	−0.00984985	−	0.112584i	−0.999528	+	0.0307243i	$0.990219\pi$
$444$	−28.7449	−	16.5959i	−1.36417	−	0.787607i
$445$		0			0
$446$	−1.64293	+	9.31753i	−0.0777951	+	0.441198i
$447$	−13.7534	+	9.63023i	−0.650513	+	0.455494i
$448$	−0.0261014	+	0.0974119i	−0.00123318	+	0.00460228i
$449$	−9.37315	+	16.2348i	−0.442346	+	0.766166i	−0.997863	−	0.0653390i	$-0.979187\pi$
$449$	−9.37315	+	16.2348i	−0.442346	+	0.766166i	0.555517	+	0.831505i	$0.312520\pi$
$450$		0			0
$451$	1.95489	−	5.37102i	0.0920522	−	0.252911i
$452$	15.7223	+	7.33145i	0.739517	+	0.344842i
$453$	−52.9820	−	4.63532i	−2.48931	−	0.217786i
$454$	−18.3193	+	3.23018i	−0.859765	+	0.151600i
$455$		0			0
$456$	1.86709	−	13.9935i	0.0874343	−	0.655305i
$457$	10.2542	−	10.2542i	0.479669	−	0.479669i	−0.425357	−	0.905026i	$-0.639851\pi$
$457$	10.2542	−	10.2542i	0.479669	−	0.479669i	0.905026	+	0.425357i	$0.139851\pi$
$458$	11.3398	+	7.94022i	0.529874	+	0.371022i
$459$	−33.5698	+	28.1684i	−1.56690	+	1.31479i
$460$		0			0
$461$	38.8075	+	14.1248i	1.80745	+	0.657857i	0.997446	+	0.0714282i	$0.0227557\pi$
$461$	38.8075	+	14.1248i	1.80745	+	0.657857i	0.810001	+	0.586429i	$0.199467\pi$
$462$	−0.556437	+	0.0486819i	−0.0258878	+	0.00226489i
$463$	7.41732	−	1.98747i	0.344712	−	0.0923653i	−0.0823093	−	0.996607i	$-0.526230\pi$
$463$	7.41732	−	1.98747i	0.344712	−	0.0923653i	0.427021	+	0.904241i	$0.359563\pi$
$464$	4.86759	+	8.43091i	0.225972	+	0.391395i
$465$		0			0
$466$	20.0686	+	3.53863i	0.929658	+	0.163924i
$467$	10.9347	+	2.92993i	0.505995	+	0.135581i	0.502781	−	0.864414i	$-0.332310\pi$
$467$	10.9347	+	2.92993i	0.505995	+	0.135581i	0.00321433	+	0.999995i	$0.498977\pi$
$468$	−2.25414	−	8.41258i	−0.104198	−	0.388872i
$469$	0.760268	+	0.637940i	0.0351059	+	0.0294573i
$470$		0			0
$471$	−11.0375	−	30.3254i	−0.508583	−	1.39732i
$472$	−0.0534573	+	0.611019i	−0.00246057	+	0.0281245i
$473$	−9.78251	+	13.9709i	−0.449800	+	0.642381i
$474$	−20.4860			−0.940952
$475$		0			0
$476$	0.303927			0.0139305
$477$	−31.9850	+	45.6794i	−1.46449	+	2.09151i
$478$	0.628118	−	7.17942i	0.0287295	−	0.328379i
$479$	1.89214	+	5.19861i	0.0864541	+	0.237531i	0.975384	−	0.220512i	$-0.0707729\pi$
$479$	1.89214	+	5.19861i	0.0864541	+	0.237531i	−0.888930	+	0.458043i	$0.848551\pi$
$480$		0			0
$481$	−9.12911	−	7.66023i	−0.416251	−	0.349276i
$482$	0.720621	+	2.68939i	0.0328234	+	0.122498i
$483$	0.603498	+	0.161707i	0.0274601	+	0.00735791i
$484$	−7.95285	−	1.40230i	−0.361493	−	0.0637410i
$485$		0			0
$486$	−18.0674	−	31.2937i	−0.819556	−	1.41951i
$487$	29.3564	−	7.86602i	1.33026	−	0.356443i	0.477451	−	0.878658i	$-0.341561\pi$
$487$	29.3564	−	7.86602i	1.33026	−	0.356443i	0.852814	+	0.522215i	$0.174894\pi$
$488$	8.57523	−	0.750235i	0.388182	−	0.0339616i
$489$	−27.6434	−	10.0614i	−1.25008	−	0.454991i
$490$		0			0
$491$	12.8344	−	10.7694i	0.579210	−	0.486015i	−0.305478	−	0.952199i	$-0.598816\pi$
$491$	12.8344	−	10.7694i	0.579210	−	0.486015i	0.884688	+	0.466184i	$0.154372\pi$
$492$	−8.86733	−	6.20897i	−0.399770	−	0.279922i
$493$	20.7458	−	20.7458i	0.934344	−	0.934344i
$494$	1.53262	−	4.83149i	0.0689559	−	0.217379i
$495$		0			0
$496$	7.83132	−	1.38087i	0.351637	−	0.0620030i
$497$	−1.08449	−	0.0948807i	−0.0486461	−	0.00425598i
$498$	12.8813	+	6.00667i	0.577227	+	0.269165i
$499$	−2.97640	+	8.17759i	−0.133242	+	0.366079i	−0.988314	−	0.152429i	$-0.951290\pi$
$499$	−2.97640	+	8.17759i	−0.133242	+	0.366079i	0.855072	+	0.518509i	$0.173513\pi$
$500$		0			0
$501$	17.6004	−	30.4848i	0.786327	−	1.36196i
$502$	5.65807	−	21.1162i	0.252532	−	0.942463i
$503$	−14.8525	+	10.3998i	−0.662241	+	0.463706i	−0.855748	−	0.517393i	$-0.826903\pi$
$503$	−14.8525	+	10.3998i	−0.662241	+	0.463706i	0.193507	+	0.981099i	$0.438014\pi$
$504$	−0.131160	+	0.743843i	−0.00584231	+	0.0331334i
$505$		0			0
$506$	−2.83293	−	1.63560i	−0.125939	−	0.0727111i
$507$	3.28791	+	37.5810i	0.146021	+	1.66903i
$508$	7.94464	−	3.70465i	0.352487	−	0.164367i
$509$	−5.01252	+	1.82441i	−0.222176	+	0.0808655i	−0.450710	−	0.892670i	$-0.648829\pi$
$509$	−5.01252	+	1.82441i	−0.222176	+	0.0808655i	0.228534	+	0.973536i	$0.426607\pi$
$510$		0			0
$511$	0.208973	+	1.18515i	0.00924443	+	0.0524278i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	2.87504	−	63.3173i	0.126936	−	2.79553i
$514$			21.9248i			0.967064i
$515$		0			0
$516$	20.7627	+	24.7440i	0.914028	+	1.08930i
$517$	−5.47979	+	11.7515i	−0.241001	+	0.516828i
$518$	0.436784	+	0.936686i	0.0191912	+	0.0411556i
$519$	21.6592	−	25.8124i	0.950733	−	1.13304i
$520$		0			0
$521$	−8.69468	+	5.01988i	−0.380921	+	0.219925i	−0.678219	−	0.734860i	$-0.737248\pi$
$521$	−8.69468	+	5.01988i	−0.380921	+	0.219925i	0.297298	+	0.954785i	$0.403915\pi$
$522$	41.8212	+	59.7269i	1.83047	+	2.61418i
$523$	−20.9810	−	29.9640i	−0.917436	−	1.31023i	−0.950482	−	0.310780i	$-0.899410\pi$
$523$	−20.9810	−	29.9640i	−0.917436	−	1.31023i	0.0330460	−	0.999454i	$-0.489479\pi$
$524$	2.92737	−	1.69012i	0.127883	−	0.0738330i
$525$		0			0
$526$	0.662731	−	0.789812i	0.0288964	−	0.0344374i
$527$	−10.1282	−	21.7200i	−0.441192	−	0.946139i
$528$	2.34073	−	5.01972i	0.101867	−	0.218455i
$529$	−12.4321	−	14.8160i	−0.540528	−	0.644176i
$530$		0			0
$531$			4.59380i			0.199354i
$532$	−0.297545	+	0.323580i	−0.0129002	+	0.0140290i
$533$	−2.74825	−	2.74825i	−0.119040	−	0.119040i
$534$	−5.99920	−	34.0232i	−0.259611	−	1.47233i
$535$		0			0
$536$	−9.24762	+	3.36586i	−0.399436	+	0.145383i
$537$	−2.34665	+	1.09426i	−0.101265	+	0.0472208i
$538$	−2.04286	−	23.3499i	−0.0880738	−	1.00669i
$539$	−10.3519	−	5.97667i	−0.445888	−	0.257434i
$540$		0			0
$541$	−2.15494	+	12.2213i	−0.0926482	+	0.525434i	0.902794	+	0.430072i	$0.141512\pi$
$541$	−2.15494	+	12.2213i	−0.0926482	+	0.525434i	−0.995443	+	0.0953618i	$0.969599\pi$
$542$	16.2757	−	11.3963i	0.699100	−	0.489515i
$543$	−10.5547	+	39.3907i	−0.452946	+	1.69042i
$544$	−1.50685	+	2.60995i	−0.0646058	+	0.111901i
$545$		0			0
$546$	−0.129905	+	0.356910i	−0.00555940	+	0.0152743i
$547$	7.62684	+	3.55645i	0.326100	+	0.152063i	0.578773	−	0.815489i	$-0.303532\pi$
$547$	7.62684	+	3.55645i	0.326100	+	0.152063i	−0.252673	+	0.967552i	$0.581310\pi$
$548$	−18.8535	−	1.64947i	−0.805383	−	0.0704619i
$549$	63.4914	−	11.1952i	2.70974	−	0.477801i
$550$		0			0
$551$	1.77710	+	42.3974i	0.0757072	+	1.80619i
$552$	−4.38075	+	4.38075i	−0.186457	+	0.186457i
$553$	0.522527	+	0.365877i	0.0222201	+	0.0155587i
$554$	9.85034	−	8.26542i	0.418501	−	0.351164i
$555$		0			0
$556$	−12.3606	−	4.49889i	−0.524206	−	0.190796i
$557$	−34.1839	+	2.99071i	−1.44842	+	0.126720i	−0.784057	−	0.620689i	$-0.786853\pi$
$557$	−34.1839	+	2.99071i	−1.44842	+	0.126720i	−0.664363	+	0.747410i	$0.731297\pi$
$558$	57.5293	−	15.4149i	2.43541	−	0.652566i
$559$	5.79869	+	10.0436i	0.245259	+	0.424800i
$560$		0			0
$561$	−16.4383	−	2.89851i	−0.694024	−	0.122375i
$562$	26.3227	+	7.05315i	1.11036	+	0.297519i
$563$	−0.758482	−	2.83069i	−0.0319662	−	0.119299i	0.948099	−	0.317975i	$-0.103003\pi$
$563$	−0.758482	−	2.83069i	−0.0319662	−	0.119299i	−0.980065	+	0.198675i	$0.936336\pi$
$564$	18.8117	+	15.7849i	0.792115	+	0.664663i
$565$		0			0
$566$	−8.44065	−	23.1905i	−0.354787	−	0.974769i
$567$	−0.216450	+	2.47403i	−0.00909003	+	0.103899i
$568$	6.19163	−	8.84257i	0.259795	−	0.371026i
$569$	−41.7384			−1.74976			−0.874882	−	0.484336i	$-0.839061\pi$
$569$	−41.7384			−1.74976			−0.874882	+	0.484336i	$0.839061\pi$
$570$		0			0
$571$	19.2326			0.804858			0.402429	−	0.915451i	$-0.368166\pi$
$571$	19.2326			0.804858			0.402429	+	0.915451i	$0.368166\pi$
$572$	1.14061	−	1.62896i	0.0476914	−	0.0681104i
$573$	−4.23404	+	48.3952i	−0.176879	+	2.02174i
$574$	0.115284	+	0.316739i	0.00481185	+	0.0132204i
$575$		0			0
$576$	−5.73741	−	4.81426i	−0.239059	−	0.200594i
$577$	8.60748	+	32.1235i	0.358334	+	1.33732i	0.876237	+	0.481881i	$0.160046\pi$
$577$	8.60748	+	32.1235i	0.358334	+	1.33732i	−0.517903	+	0.855440i	$0.673287\pi$
$578$	−7.64778	−	2.04922i	−0.318106	−	0.0852361i
$579$	−10.2473	−	1.80688i	−0.425863	−	0.0750912i
$580$		0			0
$581$	−0.221281	−	0.383269i	−0.00918026	−	0.0159007i
$582$	−20.6106	+	5.52260i	−0.854337	+	0.228919i
$583$	−12.6841	+	1.10972i	−0.525323	+	0.0459598i
$584$	−11.2134	−	4.08135i	−0.464014	−	0.168887i
$585$		0			0
$586$	13.3734	−	11.2216i	0.552449	−	0.463560i
$587$	16.2414	+	11.3723i	0.670352	+	0.469386i	0.858540	−	0.512747i	$-0.171372\pi$
$587$	16.2414	+	11.3723i	0.670352	+	0.469386i	−0.188187	+	0.982133i	$0.560261\pi$
$588$	−16.0078	+	16.0078i	−0.660151	+	0.660151i
$589$	33.0400	+	10.4808i	1.36139	+	0.431854i
$590$		0			0
$591$	−6.26239	+	1.10423i	−0.257600	+	0.0454219i
$592$	−10.2093	−	0.893195i	−0.419598	−	0.0367101i
$593$	−13.3909	−	6.24426i	−0.549896	−	0.256421i	0.127753	−	0.991806i	$-0.459224\pi$
$593$	−13.3909	−	6.24426i	−0.549896	−	0.256421i	−0.677649	+	0.735385i	$0.737001\pi$
$594$	8.50487	−	23.3669i	0.348959	−	0.958757i
$595$		0			0
$596$	−2.59200	+	4.48947i	−0.106172	+	0.183896i
$597$	4.03063	−	15.0425i	0.164963	−	0.615650i
$598$	−1.82210	+	1.27585i	−0.0745111	+	0.0521732i
$599$	−8.16880	+	46.3275i	−0.333768	+	1.89289i	0.105304	+	0.994440i	$0.466419\pi$
$599$	−8.16880	+	46.3275i	−0.333768	+	1.89289i	−0.439072	+	0.898452i	$0.644693\pi$
$600$		0			0
$601$	10.0904	+	5.82571i	0.411597	+	0.237636i	0.691476	−	0.722400i	$-0.256961\pi$
$601$	10.0904	+	5.82571i	0.411597	+	0.237636i	−0.279879	+	0.960035i	$0.590294\pi$
$602$	−0.0876598	−	1.00196i	−0.00357274	−	0.0408367i
$603$	−66.8008	+	31.1497i	−2.72034	+	1.26851i
$604$	−15.4308	+	5.61636i	−0.627871	+	0.228526i
$605$		0			0
$606$	2.97683	+	16.8824i	0.120925	+	0.685802i
$607$	−6.91417	−	6.91417i	−0.280638	−	0.280638i	0.552726	−	0.833363i	$-0.313588\pi$
$607$	−6.91417	−	6.91417i	−0.280638	−	0.280638i	−0.833363	+	0.552726i	$0.813588\pi$
$608$	−1.30350	−	4.15943i	−0.0528639	−	0.168687i
$609$		−	3.17975i		−	0.128850i
$610$		0			0
$611$	5.66741	+	6.75415i	0.229279	+	0.273244i
$612$	−9.53918	+	20.4568i	−0.385599	+	0.826919i
$613$	3.03318	+	6.50467i	0.122509	+	0.262721i	0.957992	−	0.286795i	$-0.0925899\pi$
$613$	3.03318	+	6.50467i	0.122509	+	0.262721i	−0.835483	+	0.549516i	$0.814812\pi$
$614$	17.0680	−	20.3408i	0.688807	−	0.820888i
$615$		0			0
$616$	−0.149356	+	0.0862305i	−0.00601771	+	0.00347433i
$617$	−2.84065	−	4.05687i	−0.114360	−	0.163324i	0.757891	−	0.652381i	$-0.226230\pi$
$617$	−2.84065	−	4.05687i	−0.114360	−	0.163324i	−0.872252	+	0.489057i	$0.837341\pi$
$618$	−2.35479	−	3.36299i	−0.0947235	−	0.135279i
$619$	−11.0809	+	6.39754i	−0.445378	+	0.257139i	−0.705876	−	0.708335i	$-0.749446\pi$
$619$	−11.0809	+	6.39754i	−0.445378	+	0.257139i	0.260498	+	0.965474i	$0.416113\pi$
$620$		0			0
$621$	−17.8790	+	21.3074i	−0.717460	+	0.855036i
$622$	8.82140	+	18.9175i	0.353706	+	0.758524i
$623$	−0.454631	+	0.974960i	−0.0182144	+	0.0390609i
$624$	−2.42087	−	2.88508i	−0.0969125	−	0.115496i
$625$		0			0
$626$		−	32.1456i		−	1.28479i
$627$	19.1790	−	14.6636i	0.765936	−	0.585606i
$628$	−7.04572	−	7.04572i	−0.281155	−	0.281155i
$629$	5.36317	+	30.4161i	0.213844	+	1.21277i
$630$		0			0
$631$	37.4387	−	13.6266i	1.49041	−	0.542466i	0.536854	−	0.843675i	$-0.319612\pi$
$631$	37.4387	−	13.6266i	1.49041	−	0.542466i	0.953558	+	0.301209i	$0.0973902\pi$
$632$	−5.73260	+	2.67316i	−0.228031	+	0.106332i
$633$	6.98735	+	79.8657i	0.277722	+	3.17438i
$634$	11.8978	+	6.86923i	0.472524	+	0.272812i
$635$		0			0
$636$	−4.18740	+	23.7479i	−0.166041	+	0.941667i
$637$	−6.65817	+	4.66210i	−0.263806	+	0.184719i
$638$	−4.30887	+	16.0809i	−0.170590	+	0.636649i
$639$	40.4246	−	70.0174i	1.59917	−	2.76985i
$640$		0			0
$641$	1.19154	−	3.27373i	0.0470630	−	0.129305i	−0.913934	−	0.405862i	$-0.866971\pi$
$641$	1.19154	−	3.27373i	0.0470630	−	0.129305i	0.960997	+	0.276557i	$0.0891936\pi$
$642$	9.01465	+	4.20360i	0.355780	+	0.165903i
$643$	12.0007	+	1.04992i	0.473260	+	0.0414049i	0.321291	−	0.946980i	$-0.395883\pi$
$643$	12.0007	+	1.04992i	0.473260	+	0.0414049i	0.151969	+	0.988385i	$0.451439\pi$
$644$	0.189978	−	0.0334982i	0.00748617	−	0.00132001i
$645$		0			0
$646$	−11.0915	+	7.03890i	−0.436387	+	0.276942i
$647$	−15.5902	+	15.5902i	−0.612914	+	0.612914i	−0.943704	−	0.330790i	$-0.892685\pi$
$647$	−15.5902	+	15.5902i	−0.612914	+	0.612914i	0.330790	+	0.943704i	$0.392685\pi$
$648$	−20.1724	−	14.1249i	−0.792446	−	0.554877i
$649$	−0.803503	+	0.674219i	−0.0315403	+	0.0264654i
$650$		0			0
$651$	−2.44072	−	0.888349i	−0.0956594	−	0.0348172i
$652$	−9.04834	+	0.791627i	−0.354360	+	0.0310025i
$653$	35.6955	−	9.56459i	1.39687	−	0.374291i	0.519653	−	0.854377i	$-0.326061\pi$
$653$	35.6955	−	9.56459i	1.39687	−	0.374291i	0.877222	+	0.480086i	$0.159394\pi$
$654$	23.5970	+	40.8712i	0.922716	+	1.59819i
$655$		0			0
$656$	−3.29154	−	0.580388i	−0.128513	−	0.0226603i
$657$	−86.3292	−	23.1318i	−3.36802	−	0.902459i
$658$	−0.197905	−	0.738593i	−0.00771515	−	0.0287933i
$659$	−6.08841	−	5.10878i	−0.237171	−	0.199010i	0.516454	−	0.856315i	$-0.327252\pi$
$659$	−6.08841	−	5.10878i	−0.237171	−	0.199010i	−0.753625	+	0.657305i	$0.771696\pi$
$660$		0			0
$661$	1.10701	+	3.04149i	0.0430577	+	0.118300i	0.959358	−	0.282192i	$-0.0910615\pi$
$661$	1.10701	+	3.04149i	0.0430577	+	0.118300i	−0.916300	+	0.400492i	$0.868839\pi$
$662$	0.157911	−	1.80493i	0.00613738	−	0.0701505i
$663$	−6.51024	+	9.29759i	−0.252837	+	0.361088i
$664$	4.38839			0.170303
$665$		0			0
$666$	−76.7559			−2.97423
$667$	10.6812	−	15.2543i	0.413576	−	0.590648i
$668$	0.947257	−	10.8272i	0.0366505	−	0.418917i
$669$	10.4805	+	28.7949i	0.405199	+	1.11328i
$670$		0			0
$671$	11.2766	+	9.46219i	0.435328	+	0.365284i
$672$	0.0845366	+	0.315495i	0.00326107	+	0.0121705i
$673$	6.98129	+	1.87063i	0.269109	+	0.0721075i	0.390850	−	0.920454i	$-0.372181\pi$
$673$	6.98129	+	1.87063i	0.269109	+	0.0721075i	−0.121741	+	0.992562i	$0.538848\pi$
$674$	11.5687	+	2.03988i	0.445610	+	0.0785731i
$675$		0			0
$676$	5.82389	+	10.0873i	0.223996	+	0.387972i
$677$	28.1102	−	7.53211i	1.08036	−	0.289483i	0.325619	−	0.945501i	$-0.394427\pi$
$677$	28.1102	−	7.53211i	1.08036	−	0.289483i	0.754745	+	0.656019i	$0.227761\pi$
$678$	55.9714	−	4.89687i	2.14957	−	0.188063i
$679$	0.624339	+	0.227241i	0.0239599	+	0.00872070i
$680$		0			0
$681$	−46.1520	+	38.7261i	−1.76855	+	1.48399i
$682$	11.1396	+	7.80005i	0.426559	+	0.298679i
$683$	3.58657	−	3.58657i	0.137236	−	0.137236i	−0.635151	−	0.772388i	$-0.719062\pi$
$683$	3.58657	−	3.58657i	0.137236	−	0.137236i	0.772388	+	0.635151i	$0.219062\pi$
$684$	−12.4408	−	30.1833i	−0.475684	−	1.15409i
$685$		0			0
$686$	1.38942	−	0.244991i	0.0530481	−	0.00935381i
$687$	44.6649	+	3.90767i	1.70407	+	0.149087i
$688$	9.03882	+	4.21487i	0.344602	+	0.160690i
$689$	−2.96121	+	8.13586i	−0.112813	+	0.309952i
$690$		0			0
$691$	−12.3983	+	21.4745i	−0.471653	+	0.816927i	−0.999474	−	0.0324285i	$-0.989676\pi$
$691$	−12.3983	+	21.4745i	−0.471653	+	0.816927i	0.527821	+	0.849356i	$0.323009\pi$
$692$	2.69272	−	10.0494i	0.102362	−	0.382019i
$693$	−1.05808	+	0.740873i	−0.0401930	+	0.0281434i
$694$	3.87452	−	21.9735i	0.147075	−	0.834102i
$695$		0			0
$696$	27.3058	+	15.7650i	1.03502	+	0.597571i
$697$	0.877900	+	10.0344i	0.0332528	+	0.380082i
$698$	11.8871	−	5.54306i	0.449935	−	0.209808i
$699$	62.0199	−	22.5734i	2.34581	−	0.853804i
$700$		0			0
$701$	4.50385	+	25.5426i	0.170108	+	0.964731i	0.943640	+	0.330974i	$0.107377\pi$
$701$	4.50385	+	25.5426i	0.170108	+	0.964731i	−0.773532	+	0.633757i	$0.781512\pi$
$702$	−11.9564	−	11.9564i	−0.451267	−	0.451267i
$703$	−37.6334	−	24.0674i	−1.41937	−	0.907719i
$704$		−	1.71011i		−	0.0644520i
$705$		0			0
$706$	12.5590	+	14.9672i	0.472664	+	0.563299i
$707$	0.225590	−	0.483779i	0.00848417	−	0.0181944i
$708$	0.839537	+	1.80039i	0.0315517	+	0.0676629i
$709$	−4.75410	+	5.66571i	−0.178544	+	0.212780i	−0.847893	−	0.530168i	$-0.822129\pi$
$709$	−4.75410	+	5.66571i	−0.178544	+	0.212780i	0.669349	+	0.742948i	$0.266573\pi$
$710$		0			0
$711$	−41.0269	+	23.6869i	−1.53863	+	0.888327i
$712$	−6.11835	−	8.73791i	−0.229295	−	0.327467i
$713$	−8.72485	−	12.4604i	−0.326748	−	0.466645i
$714$	0.852473	−	0.492175i	0.0319030	−	0.0184192i
$715$		0			0
$716$	−0.513877	+	0.612415i	−0.0192045	+	0.0228870i
$717$	−9.86448	−	21.1544i	−0.368396	−	0.790027i
$718$	−2.37253	+	5.08791i	−0.0885420	+	0.189879i
$719$	−17.1888	−	20.4848i	−0.641035	−	0.763955i	0.343499	−	0.939153i	$-0.388388\pi$
$719$	−17.1888	−	20.4848i	−0.641035	−	0.763955i	−0.984533	+	0.175198i	$0.943944\pi$
$720$		0			0
$721$			0.127835i			0.00476081i
$722$	3.36450	−	18.6997i	0.125214	−	0.695932i
$723$	6.37641	+	6.37641i	0.237141	+	0.237141i
$724$	2.18645	+	12.4000i	0.0812588	+	0.460842i
$725$		0			0
$726$	−24.5775	+	8.94548i	−0.912157	+	0.331998i
$727$	−15.1685	+	7.07321i	−0.562570	+	0.262331i	−0.683033	−	0.730387i	$-0.739340\pi$
$727$	−15.1685	+	7.07321i	−0.562570	+	0.262331i	0.120463	+	0.992718i	$0.461562\pi$
$728$	0.0102209	+	0.116825i	0.000378811	+	0.00432983i
$729$	−37.3733	−	21.5775i	−1.38420	−	0.799166i
$730$		0			0
$731$	5.21924	−	29.5998i	0.193041	−	1.09479i
$732$	22.8374	−	15.9909i	0.844094	−	0.591041i
$733$	4.06846	−	15.1837i	0.150272	−	0.560823i	−0.849192	−	0.528084i	$-0.822910\pi$
$733$	4.06846	−	15.1837i	0.150272	−	0.560823i	0.999464	−	0.0327386i	$-0.0104229\pi$
$734$	−5.55051	+	9.61377i	−0.204873	+	0.354851i
$735$		0			0
$736$	−0.654236	+	1.79750i	−0.0241155	+	0.0662567i
$737$	−15.2526	−	7.11239i	−0.561835	−	0.261988i
$738$	−24.9375	−	2.18175i	−0.917964	−	0.0803114i
$739$	31.3848	−	5.53399i	1.15451	−	0.203571i	0.436566	−	0.899672i	$-0.356195\pi$
$739$	31.3848	−	5.53399i	1.15451	−	0.203571i	0.717944	+	0.696101i	$0.245083\pi$
$740$		0			0
$741$	−3.52526	−	16.0336i	−0.129504	−	0.589007i
$742$	0.530942	−	0.530942i	0.0194915	−	0.0194915i
$743$	−5.79579	−	4.05826i	−0.212627	−	0.148883i	0.462412	−	0.886665i	$-0.346984\pi$
$743$	−5.79579	−	4.05826i	−0.212627	−	0.148883i	−0.675039	+	0.737782i	$0.735873\pi$
$744$	19.7296	−	16.5551i	0.723322	−	0.606939i
$745$		0			0
$746$	3.07373	+	1.11875i	0.112537	+	0.0409603i
$747$	32.7424	−	2.86459i	1.19798	−	0.104810i
$748$	−4.97815	+	1.33389i	−0.182019	+	0.0487719i
$749$	−0.154857	−	0.268220i	−0.00565835	−	0.00980055i
$750$		0			0
$751$	−20.8511	−	3.67662i	−0.760869	−	0.134162i	−0.220266	−	0.975440i	$-0.570693\pi$
$751$	−20.8511	−	3.67662i	−0.760869	−	0.134162i	−0.540603	+	0.841278i	$0.681804\pi$
$752$	7.32381	+	1.96241i	0.267072	+	0.0715617i
$753$	−18.3252	−	68.3906i	−0.667808	−	2.49229i
$754$	8.67205	+	7.27671i	0.315817	+	0.265002i
$755$		0			0
$756$	0.501549	+	1.37799i	0.0182411	+	0.0501171i
$757$	3.55272	−	40.6078i	0.129126	−	1.47592i	−0.604632	−	0.796505i	$-0.706680\pi$
$757$	3.55272	−	40.6078i	0.129126	−	1.47592i	0.733758	−	0.679411i	$-0.237764\pi$
$758$	7.68206	−	10.9711i	0.279025	−	0.398489i
$759$	−10.5946			−0.384561
$760$		0			0
$761$	21.5592			0.781520			0.390760	−	0.920493i	$-0.372212\pi$
$761$	21.5592			0.781520			0.390760	+	0.920493i	$0.372212\pi$
$762$	16.2844	−	23.2565i	0.589920	−	0.842493i
$763$	0.128077	−	1.46392i	0.00463669	−	0.0529976i
$764$	5.13014	+	14.0950i	0.185602	+	0.509938i
$765$		0			0
$766$	17.1498	+	14.3904i	0.619649	+	0.519947i
$767$	0.184600	+	0.688935i	0.00666551	+	0.0248760i
$768$	−3.12841	−	0.838256i	−0.112887	−	0.0302480i
$769$	14.1042	+	2.48695i	0.508611	+	0.0896819i	0.422064	−	0.906566i	$-0.361306\pi$
$769$	14.1042	+	2.48695i	0.508611	+	0.0896819i	0.0865468	+	0.996248i	$0.472417\pi$
$770$		0			0
$771$	35.5048	+	61.4961i	1.27867	+	2.21473i
$772$	−3.10328	+	0.831522i	−0.111690	+	0.0299271i
$773$	−25.2113	+	2.20570i	−0.906787	+	0.0793336i	−0.530999	−	0.847372i	$-0.678183\pi$
$773$	−25.2113	+	2.20570i	−0.906787	+	0.0793336i	−0.375788	+	0.926706i	$0.622628\pi$
$774$	70.1913	+	25.5476i	2.52298	+	0.918288i
$775$		0			0
$776$	−5.04685	+	4.23481i	−0.181171	+	0.152021i
$777$	2.74198	+	1.91995i	0.0983678	+	0.0688779i
$778$	−6.32756	+	6.32756i	−0.226854	+	0.226854i
$779$	−11.5428	−	8.88907i	−0.413562	−	0.318484i
$780$		0			0
$781$	18.1798	−	3.20558i	0.650523	−	0.114705i
$782$	5.74286	+	0.502436i	0.205364	+	0.0179671i
$783$	128.296	+	59.8254i	4.58492	+	2.13798i
$784$	−2.39066	+	6.56829i	−0.0853808	+	0.234582i
$785$		0			0
$786$	5.47390	−	9.48107i	0.195248	−	0.338179i
$787$	2.22567	−	8.30633i	0.0793367	−	0.296089i	−0.914845	−	0.403805i	$-0.867687\pi$
$787$	2.22567	−	8.30633i	0.0793367	−	0.296089i	0.994182	+	0.107717i	$0.0343540\pi$
$788$	−1.60832	+	1.12616i	−0.0572941	+	0.0401177i
$789$	0.579856	−	3.28853i	0.0206434	−	0.117075i
$790$		0			0
$791$	−1.51510	−	0.874742i	−0.0538706	−	0.0311022i
$792$	−1.11630	−	12.7594i	−0.0396660	−	0.453384i
$793$	9.07196	−	4.23032i	0.322155	−	0.150223i
$794$	−30.6889	+	11.1698i	−1.08911	+	0.396403i
$795$		0			0
$796$	−0.834962	−	4.73530i	−0.0295944	−	0.167838i
$797$	7.93919	+	7.93919i	0.281220	+	0.281220i	0.833596	−	0.552375i	$-0.186278\pi$
$797$	7.93919	+	7.93919i	0.281220	+	0.281220i	−0.552375	+	0.833596i	$0.686278\pi$
$798$	−0.310571	+	1.38944i	−0.0109941	+	0.0491855i
$799$		−	22.8504i		−	0.808390i
$800$		0			0
$801$	−51.3537	−	61.2010i	−1.81450	−	2.16243i
$802$	3.20115	−	6.86488i	0.113036	−	0.242407i
$803$	−8.62429	−	18.4948i	−0.304345	−	0.652669i
$804$	−20.4877	+	24.4162i	−0.722544	+	0.861094i
$805$		0			0
$806$	8.00826	−	4.62357i	0.282079	−	0.162858i
$807$	−43.5425	−	62.1852i	−1.53277	−	2.18902i
$808$	3.03595	+	4.33578i	0.106804	+	0.152532i
$809$	24.9739	−	14.4187i	0.878035	−	0.506934i	0.00802513	−	0.999968i	$-0.497445\pi$
$809$	24.9739	−	14.4187i	0.878035	−	0.506934i	0.870010	+	0.493034i	$0.164112\pi$
$810$		0			0
$811$	18.4541	−	21.9928i	0.648013	−	0.772271i	−0.337600	−	0.941290i	$-0.609615\pi$
$811$	18.4541	−	21.9928i	0.648013	−	0.772271i	0.985613	+	0.169018i	$0.0540597\pi$
$812$	−0.414916	−	0.889790i	−0.0145607	−	0.0312255i
$813$	27.1959	−	58.3217i	0.953801	−	2.04543i
$814$	−11.2652	−	13.4254i	−0.394847	−	0.470560i
$815$		0			0
$816$			9.76072i			0.341693i
$817$	26.4041	+	34.5350i	0.923764	+	1.20823i
$818$	−14.2435	−	14.2435i	−0.498014	−	0.498014i
$819$	0.152519	+	0.864978i	0.00532944	+	0.0302248i
$820$		0			0
$821$	−1.50284	+	0.546989i	−0.0524495	+	0.0190900i	−0.368112	−	0.929782i	$-0.619996\pi$
$821$	−1.50284	+	0.546989i	−0.0524495	+	0.0190900i	0.315662	+	0.948872i	$0.397773\pi$
$822$	−55.5527	+	25.9046i	−1.93762	+	0.903528i
$823$	−1.91830	−	21.9263i	−0.0668677	−	0.764302i	−0.953415	−	0.301663i	$-0.902458\pi$
$823$	−1.91830	−	21.9263i	−0.0668677	−	0.764302i	0.886547	−	0.462639i	$-0.153097\pi$
$824$	−1.09777	−	0.633797i	−0.0382426	−	0.0220794i
$825$		0			0
$826$	0.0107411	−	0.0609159i	0.000373731	−	0.00211953i
$827$	−0.175107	+	0.122611i	−0.00608905	+	0.00426360i	−0.576617	−	0.817015i	$-0.695628\pi$
$827$	−0.175107	+	0.122611i	−0.00608905	+	0.00426360i	0.570528	+	0.821278i	$0.306739\pi$
$828$	−3.70801	+	13.8385i	−0.128862	+	0.480921i
$829$	−25.9932	+	45.0215i	−0.902780	+	1.56366i	−0.0789101	+	0.996882i	$0.525144\pi$
$829$	−25.9932	+	45.0215i	−0.902780	+	1.56366i	−0.823870	+	0.566779i	$0.808189\pi$
$830$		0			0
$831$	14.2439	−	39.1348i	0.494116	−	1.35757i
$832$	−1.05390	−	0.491442i	−0.0365374	−	0.0170377i
$833$	20.9851	+	1.83596i	0.727092	+	0.0636123i
$834$	−41.9552	+	7.39783i	−1.45279	+	0.256166i
$835$		0			0
$836$	3.45347	−	6.60593i	0.119441	−	0.228471i
$837$	81.7639	−	81.7639i	2.82617	−	2.82617i
$838$	14.5152	+	10.1636i	0.501418	+	0.351097i
$839$	−12.2272	+	10.2598i	−0.422129	+	0.354208i	−0.828972	−	0.559290i	$-0.811074\pi$
$839$	−12.2272	+	10.2598i	−0.422129	+	0.354208i	0.406843	+	0.913498i	$0.366630\pi$
$840$		0			0
$841$	−61.8070	−	22.4959i	−2.13128	−	0.775721i
$842$	−13.0944	+	1.14561i	−0.451264	+	0.0394804i
$843$	85.2533	−	22.8436i	2.93628	−	0.786774i
$844$	12.3767	+	21.4371i	0.426025	+	0.737896i
$845$		0			0
$846$	55.9250	+	9.86109i	1.92274	+	0.339031i
$847$	0.786654	+	0.210783i	0.0270297	+	0.00724260i
$848$	1.92704	+	7.19180i	0.0661747	+	0.246967i
$849$	−61.2292	−	51.3774i	−2.10138	−	1.76327i
$850$		0			0
$851$	6.70479	+	18.4213i	0.229837	+	0.631473i
$852$	3.04713	−	34.8288i	0.104393	−	1.19322i
$853$	−12.0480	+	17.2064i	−0.412517	+	0.589135i	−0.970614	−	0.240641i	$-0.922643\pi$
$853$	−12.0480	+	17.2064i	−0.412517	+	0.589135i	0.558098	+	0.829775i	$0.311531\pi$
$854$	−0.868100			−0.0297058
$855$		0			0
$856$	3.07109			0.104968
$857$	27.0133	−	38.5790i	0.922756	−	1.31783i	−0.0252835	−	0.999680i	$-0.508049\pi$
$857$	27.0133	−	38.5790i	0.922756	−	1.31783i	0.948040	−	0.318152i	$-0.103062\pi$
$858$	0.561337	−	6.41611i	0.0191637	−	0.219042i
$859$	−11.5174	−	31.6437i	−0.392968	−	1.07967i	−0.965640	−	0.259885i	$-0.916315\pi$
$859$	−11.5174	−	31.6437i	−0.392968	−	1.07967i	0.572672	−	0.819785i	$-0.305907\pi$
$860$		0			0
$861$	0.836278	+	0.701720i	0.0285003	+	0.0239146i
$862$	−7.23974	−	27.0191i	−0.246586	−	0.920273i
$863$	−26.3657	−	7.06466i	−0.897498	−	0.240484i	−0.219556	−	0.975600i	$-0.570461\pi$
$863$	−26.3657	−	7.06466i	−0.897498	−	0.240484i	−0.677941	+	0.735116i	$0.737128\pi$
$864$	−14.3201	−	2.52501i	−0.487178	−	0.0859026i
$865$		0			0
$866$	−4.02485	−	6.97125i	−0.136770	−	0.236893i
$867$	−24.7694	+	6.63694i	−0.841213	+	0.225402i
$868$	−0.798906	+	0.0698952i	−0.0271166	+	0.00237240i
$869$	−10.1645	−	3.69957i	−0.344806	−	0.125499i
$870$		0			0
$871$	−8.76642	+	7.35590i	−0.297039	+	0.249245i
$872$	11.9363	+	8.35791i	0.404215	+	0.283034i
$873$	−34.8910	+	34.8910i	−1.18088	+	1.18088i
$874$	−6.15720	+	5.62233i	−0.208270	+	0.190178i
$875$		0			0
$876$	−38.0613	+	6.71124i	−1.28597	+	0.226752i
$877$	−36.2717	−	3.17336i	−1.22481	−	0.107157i	−0.543662	−	0.839304i	$-0.682963\pi$
$877$	−36.2717	−	3.17336i	−1.22481	−	0.107157i	−0.681146	+	0.732147i	$0.738518\pi$
$878$	12.5255	+	5.84073i	0.422714	+	0.197115i
$879$	19.3383	−	53.1316i	0.652266	−	1.79209i
$880$		0			0
$881$	1.24432	−	2.15522i	0.0419221	−	0.0726112i	−0.844303	−	0.535866i	$-0.819985\pi$
$881$	1.24432	−	2.15522i	0.0419221	−	0.0726112i	0.886225	+	0.463255i	$0.153319\pi$
$882$	−13.5495	+	50.5676i	−0.456237	+	1.70270i
$883$	0.152531	−	0.106803i	0.00513308	−	0.00359422i	−0.571007	−	0.820945i	$-0.693447\pi$
$883$	0.152531	−	0.106803i	0.00513308	−	0.00359422i	0.576140	+	0.817351i	$0.304558\pi$
$884$	−0.608549	+	3.45125i	−0.0204677	+	0.116078i
$885$		0			0
$886$	−2.05999	−	1.18934i	−0.0692069	−	0.0399566i
$887$	3.01116	+	34.4177i	0.101105	+	1.15563i	0.862052	+	0.506819i	$0.169179\pi$
$887$	3.01116	+	34.4177i	0.101105	+	1.15563i	−0.760947	+	0.648814i	$0.775266\pi$
$888$	−30.0820	+	14.0275i	−1.00949	+	0.470731i
$889$	−0.830716	+	0.302356i	−0.0278613	+	0.0101407i
$890$		0			0
$891$	−7.31283	−	41.4731i	−0.244989	−	1.38940i
$892$	6.69013	+	6.69013i	0.224002	+	0.224002i
$893$	24.3280	+	22.3706i	0.814105	+	0.748603i
$894$			16.7898i			0.561535i
$895$		0			0
$896$	0.0648240	+	0.0772542i	0.00216562	+	0.00258088i
$897$	−3.04464	+	6.52925i	−0.101658	+	0.218005i
$898$	7.92253	+	16.9899i	0.264378	+	0.566961i
$899$	−49.7617	+	59.3036i	−1.65964	+	1.97789i
$900$		0			0
$901$	19.4324	−	11.2193i	0.647386	−	0.373769i
$902$	−3.27840	−	4.68204i	−0.109159	−	0.155895i
$903$	−1.86843	−	2.66839i	−0.0621774	−	0.0887985i
$904$	15.0235	−	8.67385i	0.499676	−	0.288488i
$905$		0			0
$906$	−34.1862	+	40.7416i	−1.13576	+	1.35355i
$907$	3.26481	+	7.00140i	0.108406	+	0.232478i	0.953026	−	0.302889i	$-0.0979512\pi$
$907$	3.26481	+	7.00140i	0.108406	+	0.232478i	−0.844620	+	0.535367i	$0.820173\pi$
$908$	−7.86148	+	16.8590i	−0.260892	+	0.559486i
$909$	25.4819	+	30.3682i	0.845182	+	1.00725i
$910$		0			0
$911$		−	48.4654i		−	1.60573i	−0.596161	−	0.802865i	$-0.703308\pi$
$911$		−	48.4654i		−	1.60573i	0.596161	−	0.802865i	$-0.296692\pi$
$912$	−10.3919	−	9.55576i	−0.344109	−	0.316423i
$913$	5.30656	+	5.30656i	0.175621	+	0.175621i
$914$	−2.51817	−	14.2813i	−0.0832937	−	0.472382i
$915$		0			0
$916$	13.0085	−	4.73470i	0.429813	−	0.156439i
$917$	−0.308951	+	0.144066i	−0.0102025	+	0.00475749i
$918$	3.81936	+	43.6555i	0.126058	+	1.44085i
$919$	9.11898	+	5.26485i	0.300807	+	0.173671i	0.642806	−	0.766029i	$-0.277770\pi$
$919$	9.11898	+	5.26485i	0.300807	+	0.173671i	−0.341998	+	0.939701i	$0.611104\pi$
$920$		0			0
$921$	14.9336	−	84.6927i	0.492079	−	2.79072i
$922$	33.8294	−	23.6876i	1.11411	−	0.780110i
$923$	3.24888	−	12.1250i	0.106938	−	0.399099i
$924$	−0.279281	+	0.483729i	−0.00918767	+	0.0159135i
$925$		0			0
$926$	2.62636	−	7.21588i	0.0863077	−	0.237128i
$927$	−8.60434	−	4.01227i	−0.282604	−	0.131780i
$928$	9.69813	+	0.848477i	0.318357	+	0.0278526i
$929$	9.89762	−	1.74522i	0.324730	−	0.0572587i	−0.00890664	−	0.999960i	$-0.502835\pi$
$929$	9.89762	−	1.74522i	0.324730	−	0.0572587i	0.333637	+	0.942702i	$0.391724\pi$
$930$		0			0
$931$	−22.4992	+	20.5447i	−0.737380	+	0.673325i
$932$	14.4095	−	14.4095i	0.472000	−	0.472000i
$933$	55.3776	+	38.7758i	1.81298	+	1.26946i
$934$	8.67192	−	7.27660i	0.283754	−	0.238098i
$935$		0			0
$936$	−8.18411	−	2.97877i	−0.267506	−	0.0973642i
$937$	−45.4167	+	3.97345i	−1.48370	+	0.129807i	−0.800019	−	0.599974i	$-0.795177\pi$
$937$	−45.4167	+	3.97345i	−1.48370	+	0.129807i	−0.683681	+	0.729781i	$0.739622\pi$
$938$	0.958642	−	0.256867i	0.0313008	−	0.00838701i
$939$	−52.0561	−	90.1638i	−1.69879	−	2.94238i
$940$		0			0
$941$	45.2460	+	7.97810i	1.47498	+	0.260078i	0.852570	−	0.522614i	$-0.175043\pi$
$941$	45.2460	+	7.97810i	1.47498	+	0.260078i	0.622409	+	0.782692i	$0.286154\pi$
$942$	−31.1720	−	8.35251i	−1.01564	−	0.272140i
$943$	1.65473	+	6.17554i	0.0538854	+	0.201103i
$944$	0.469856	+	0.394256i	0.0152925	+	0.0128319i
$945$		0			0
$946$	5.83325	+	16.0267i	0.189655	+	0.521074i
$947$	4.57561	−	52.2994i	0.148687	−	1.69950i	−0.445586	−	0.895239i	$-0.647005\pi$
$947$	4.57561	−	52.2994i	0.148687	−	1.69950i	0.594273	−	0.804263i	$-0.297440\pi$
$948$	−11.7503	+	16.7811i	−0.381631	+	0.545026i
$949$	−13.8764			−0.450446
$950$		0			0
$951$	44.4957			1.44287
$952$	0.174325	−	0.248962i	0.00564992	−	0.00806892i
$953$	2.50472	−	28.6291i	0.0811360	−	0.927388i	−0.841130	−	0.540833i	$-0.818109\pi$
$953$	2.50472	−	28.6291i	0.0811360	−	0.927388i	0.922266	−	0.386555i	$-0.126335\pi$
$954$	19.0725	+	52.4012i	0.617494	+	1.69655i
$955$		0			0
$956$	−5.52077	−	4.63247i	−0.178554	−	0.149825i
$957$	13.9554	+	52.0824i	0.451115	+	1.68358i
$958$	5.34374	+	1.43185i	0.172648	+	0.0462610i
$959$	1.87961	+	0.331426i	0.0606958	+	0.0107023i
$960$		0			0
$961$	16.1182	+	27.9175i	0.519941	+	0.900565i
$962$	−11.5111	+	3.08440i	−0.371134	+	0.0994450i
$963$	22.9139	−	2.00470i	0.738389	−	0.0646007i
$964$	2.61635	+	0.952275i	0.0842670	+	0.0306707i
$965$		0			0
$966$	0.478614	−	0.401605i	0.0153992	−	0.0129214i
$967$	24.7780	+	17.3497i	0.796807	+	0.557930i	0.899570	−	0.436776i	$-0.143880\pi$
$967$	24.7780	+	17.3497i	0.796807	+	0.557930i	−0.102764	+	0.994706i	$0.532769\pi$
$968$	−5.71027	+	5.71027i	−0.183535	+	0.183535i
$969$	−19.7113	+	37.7045i	−0.633217	+	1.21124i
$970$		0			0
$971$	−16.4605	+	2.90243i	−0.528243	+	0.0931435i	−0.431408	−	0.902157i	$-0.641983\pi$
$971$	−16.4605	+	2.90243i	−0.528243	+	0.0931435i	−0.0968351	+	0.995300i	$0.530872\pi$
$972$	−35.9974	−	3.14936i	−1.15462	−	0.101016i
$973$	1.20226	+	0.560622i	0.0385426	+	0.0179727i
$974$	10.3947	−	28.5591i	0.333067	−	0.915093i
$975$		0			0
$976$	4.30399	−	7.45473i	0.137767	−	0.238620i
$977$	−14.8017	+	55.2408i	−0.473549	+	1.76731i	0.153311	+	0.988178i	$0.451006\pi$
$977$	−14.8017	+	55.2408i	−0.473549	+	1.76731i	−0.626860	+	0.779132i	$0.715660\pi$
$978$	−24.0974	+	16.8732i	−0.770549	+	0.539544i
$979$	3.16764	−	17.9646i	0.101238	−	0.574151i
$980$		0			0
$981$	94.5145	+	54.5680i	3.01762	+	1.74222i
$982$	−1.46022	−	16.6904i	−0.0465976	−	0.532613i
$983$	−30.2795	+	14.1196i	−0.965767	+	0.450345i	−0.840520	−	0.541781i	$-0.817750\pi$
$983$	−30.2795	+	14.1196i	−0.965767	+	0.450345i	−0.125247	+	0.992126i	$0.539972\pi$
$984$	−10.1722	+	3.70237i	−0.324277	+	0.118027i
$985$		0			0
$986$	−5.09466	−	28.8933i	−0.162247	−	0.920149i
$987$	−1.75116	−	1.75116i	−0.0557402	−	0.0557402i
$988$	−3.07865	−	4.02668i	−0.0979448	−	0.128106i
$989$		−	19.0774i		−	0.606626i
$990$		0			0
$991$	19.7734	+	23.5650i	0.628121	+	0.748566i	0.982444	−	0.186557i	$-0.0597330\pi$
$991$	19.7734	+	23.5650i	0.628121	+	0.748566i	−0.354323	+	0.935123i	$0.615289\pi$
$992$	3.36072	−	7.20708i	0.106703	−	0.228825i
$993$	−2.47996	−	5.31829i	−0.0786991	−	0.168771i
$994$	−0.699761	+	0.833942i	−0.0221951	+	0.0264510i
$995$		0			0
$996$	12.3088	−	7.10650i	0.390020	−	0.225178i
$997$	19.7907	+	28.2641i	0.626779	+	0.895133i	0.999461	−	0.0328263i	$-0.0104508\pi$
$997$	19.7907	+	28.2641i	0.626779	+	0.895133i	−0.372682	+	0.927959i	$0.621562\pi$
$998$	4.99150	+	7.12860i	0.158003	+	0.225652i
$999$	−129.055	+	74.5098i	−4.08311	+	2.35739i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.bb.d.143.8	yes	96
5.2	odd	4	inner	950.2.bb.d.257.5	yes	96
5.3	odd	4	inner	950.2.bb.d.257.4	yes	96
5.4	even	2	inner	950.2.bb.d.143.1	✓	96
19.2	odd	18	inner	950.2.bb.d.743.5	yes	96
95.2	even	36	inner	950.2.bb.d.857.8	yes	96
95.59	odd	18	inner	950.2.bb.d.743.4	yes	96
95.78	even	36	inner	950.2.bb.d.857.1	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.bb.d.143.1	✓	96	5.4	even	2	inner
950.2.bb.d.143.8	yes	96	1.1	even	1	trivial
950.2.bb.d.257.4	yes	96	5.3	odd	4	inner
950.2.bb.d.257.5	yes	96	5.2	odd	4	inner
950.2.bb.d.743.4	yes	96	95.59	odd	18	inner
950.2.bb.d.743.5	yes	96	19.2	odd	18	inner
950.2.bb.d.857.1	yes	96	95.78	even	36	inner
950.2.bb.d.857.8	yes	96	95.2	even	36	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.bb (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.573576 - 0.819152i) q^{2} +(0.282278 - 3.22645i) q^{3} +(-0.342020 - 0.939693i) q^{4} +(-2.48104 - 2.08184i) q^{6} +(0.0261014 + 0.0974119i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(-7.37587 - 1.30056i) q^{9} +O(q^{10})\)	\(q+(0.573576 - 0.819152i) q^{2} +(0.282278 - 3.22645i) q^{3} +(-0.342020 - 0.939693i) q^{4} +(-2.48104 - 2.08184i) q^{6} +(0.0261014 + 0.0974119i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(-7.37587 - 1.30056i) q^{9} +(-0.855053 - 1.48099i) q^{11} +(-3.12841 + 0.838256i) q^{12} +(-1.15843 + 0.101349i) q^{13} +(0.0947663 + 0.0344921i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(2.46869 + 1.72859i) q^{17} +(-5.29598 + 5.29598i) q^{18} +(-4.25721 + 0.936022i) q^{19} +(0.321662 - 0.0567177i) q^{21} +(-1.70360 - 0.149045i) q^{22} +(1.73364 + 0.808409i) q^{23} +(-1.10773 + 3.04345i) q^{24} +(-0.581425 + 1.00706i) q^{26} +(-3.76348 + 14.0455i) q^{27} +(0.0826100 - 0.0578442i) q^{28} +(1.69050 - 9.58728i) q^{29} +(-6.88675 - 3.97606i) q^{31} +(0.0871557 + 0.996195i) q^{32} +(-5.01972 + 2.34073i) q^{33} +(2.83196 - 1.03075i) q^{34} +(1.30056 + 7.37587i) q^{36} +(7.24662 + 7.24662i) q^{37} +(-1.67509 + 4.02419i) q^{38} +3.76621i q^{39} +(2.14840 + 2.56036i) q^{41} +(0.138037 - 0.296022i) q^{42} +(-4.21487 - 9.03882i) q^{43} +(-1.09923 + 1.31002i) q^{44} +(1.65658 - 0.956430i) q^{46} +(-4.34895 - 6.21094i) q^{47} +(1.85768 + 2.65305i) q^{48} +(6.05337 - 3.49491i) q^{49} +(6.27407 - 7.47714i) q^{51} +(0.491442 + 1.05390i) q^{52} +(3.14660 - 6.74792i) q^{53} +(9.34675 + 11.1390i) q^{54} -0.100848i q^{56} +(1.81831 + 13.9999i) q^{57} +(-6.88381 - 6.88381i) q^{58} +(-0.106508 - 0.604035i) q^{59} +(-8.08886 + 2.94410i) q^{61} +(-7.20708 + 3.36072i) q^{62} +(-0.0658303 - 0.752444i) q^{63} +(0.866025 + 0.500000i) q^{64} +(-0.961775 + 5.45450i) q^{66} +(8.06137 - 5.64463i) q^{67} +(0.780005 - 2.91102i) q^{68} +(3.09766 - 5.36530i) q^{69} +(-3.69203 + 10.1438i) q^{71} +(6.78793 + 3.16526i) q^{72} +(11.8877 + 1.04004i) q^{73} +(10.0926 - 1.77959i) q^{74} +(2.33563 + 3.68033i) q^{76} +(0.121948 - 0.121948i) q^{77} +(3.08510 + 2.16021i) q^{78} +(4.84541 - 4.06578i) q^{79} +(23.1408 + 8.42256i) q^{81} +(3.32960 - 0.291302i) q^{82} +(-4.23886 + 1.13580i) q^{83} +(-0.163312 - 0.282865i) q^{84} +(-9.82172 - 1.73183i) q^{86} +(-30.4557 - 8.16057i) q^{87} +(0.442608 + 1.65183i) q^{88} +(8.17141 + 6.85663i) q^{89} +(-0.0401092 - 0.110199i) q^{91} +(0.166717 - 1.90558i) q^{92} +(-14.7725 + 21.0974i) q^{93} -7.58216 q^{94} +3.23877 q^{96} +(3.77883 - 5.39674i) q^{97} +(0.609204 - 6.96323i) q^{98} +(4.38063 + 12.0357i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 12 q^{6}+O(q^{10}) \) 96 * q - 12 * q^6	\( 96 q - 12 q^{6} + 12 q^{26} - 72 q^{31} + 12 q^{36} - 24 q^{41} + 12 q^{51} - 72 q^{61} - 36 q^{66} + 168 q^{71} - 12 q^{76} + 12 q^{81} - 48 q^{86} - 72 q^{91}+O(q^{100}) \) 96 * q - 12 * q^6 + 12 * q^26 - 72 * q^31 + 12 * q^36 - 24 * q^41 + 12 * q^51 - 72 * q^61 - 36 * q^66 + 168 * q^71 - 12 * q^76 + 12 * q^81 - 48 * q^86 - 72 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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