LMFDB - Embedded newform 950.2.bb.e.143.9

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:	$120$
Relative dimension:	$10$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			143.9
Character	$\chi$	$=$	950.143
Dual form			950.2.bb.e.857.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.573576 - 0.819152i) q^{2} +(0.0709170 - 0.810585i) q^{3} +(-0.342020 - 0.939693i) q^{4} +(-0.623316 - 0.523024i) q^{6} +(0.211848 + 0.790626i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(2.30240 + 0.405976i) q^{9} +O(q^{10})$	\(q+(0.573576 - 0.819152i) q^{2} +(0.0709170 - 0.810585i) q^{3} +(-0.342020 - 0.939693i) q^{4} +(-0.623316 - 0.523024i) q^{6} +(0.211848 + 0.790626i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(2.30240 + 0.405976i) q^{9} +(2.32600 + 4.02876i) q^{11} +(-0.785956 + 0.210596i) q^{12} +(2.88003 - 0.251970i) q^{13} +(0.769154 + 0.279949i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(5.85454 + 4.09939i) q^{17} +(1.65316 - 1.65316i) q^{18} +(1.08540 + 4.22160i) q^{19} +(0.655893 - 0.115652i) q^{21} +(4.63431 + 0.405449i) q^{22} +(-5.90604 - 2.75403i) q^{23} +(-0.278296 + 0.764611i) q^{24} +(1.44552 - 2.50371i) q^{26} +(1.12415 - 4.19537i) q^{27} +(0.670489 - 0.469482i) q^{28} +(1.50414 - 8.53038i) q^{29} +(-6.69401 - 3.86479i) q^{31} +(0.0871557 + 0.996195i) q^{32} +(3.43061 - 1.59972i) q^{33} +(6.71605 - 2.44444i) q^{34} +(-0.405976 - 2.30240i) q^{36} +(-2.44013 - 2.44013i) q^{37} +(4.08069 + 1.53230i) q^{38} -2.35238i q^{39} +(-3.03158 - 3.61289i) q^{41} +(0.281469 - 0.603611i) q^{42} +(1.67745 + 3.59730i) q^{43} +(2.99025 - 3.56365i) q^{44} +(-5.64354 + 3.25830i) q^{46} +(5.50012 + 7.85498i) q^{47} +(0.466709 + 0.666529i) q^{48} +(5.48197 - 3.16502i) q^{49} +(3.73810 - 4.45489i) q^{51} +(-1.22180 - 2.62017i) q^{52} +(-2.45888 + 5.27308i) q^{53} +(-2.79186 - 3.32721i) q^{54} -0.818516i q^{56} +(3.49894 - 0.580428i) q^{57} +(-6.12494 - 6.12494i) q^{58} +(-0.124865 - 0.708143i) q^{59} +(-8.02406 + 2.92052i) q^{61} +(-7.00538 + 3.26666i) q^{62} +(0.166784 + 1.90634i) q^{63} +(0.866025 + 0.500000i) q^{64} +(0.657303 - 3.72775i) q^{66} +(8.69157 - 6.08591i) q^{67} +(1.84980 - 6.90354i) q^{68} +(-2.65122 + 4.59204i) q^{69} +(1.92060 - 5.27682i) q^{71} +(-2.11888 - 0.988049i) q^{72} +(-1.99394 - 0.174447i) q^{73} +(-3.39844 + 0.599237i) q^{74} +(3.59578 - 2.46382i) q^{76} +(-2.69248 + 2.69248i) q^{77} +(-1.92696 - 1.34927i) q^{78} +(-8.08325 + 6.78265i) q^{79} +(3.26980 + 1.19011i) q^{81} +(-4.69835 + 0.411052i) q^{82} +(4.46595 - 1.19665i) q^{83} +(-0.333006 - 0.576783i) q^{84} +(3.90888 + 0.689241i) q^{86} +(-6.80793 - 1.82418i) q^{87} +(-1.20403 - 4.49350i) q^{88} +(-1.66002 - 1.39292i) q^{89} +(0.809342 + 2.22365i) q^{91} +(-0.567959 + 6.49180i) q^{92} +(-3.60746 + 5.15199i) q^{93} +9.58917 q^{94} +0.813682 q^{96} +(2.55970 - 3.65562i) q^{97} +(0.551699 - 6.30594i) q^{98} +(3.71982 + 10.2201i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 12 q^{7}+O(q^{10}) $ 120 * q + 12 * q^7	$ 120 q + 12 q^{7} - 36 q^{17} - 96 q^{21} - 24 q^{22} - 12 q^{26} + 96 q^{33} - 12 q^{41} + 72 q^{43} + 24 q^{47} + 24 q^{51} - 36 q^{53} - 84 q^{57} + 48 q^{61} + 24 q^{62} - 36 q^{63} - 24 q^{66} + 96 q^{67} + 12 q^{68} + 36 q^{73} + 12 q^{76} - 96 q^{78} + 144 q^{81} - 48 q^{82} - 24 q^{83} + 48 q^{86} - 72 q^{87} + 72 q^{91} - 72 q^{92} - 156 q^{93} - 120 q^{97} - 24 q^{98}+O(q^{100}) $ 120 * q + 12 * q^7 - 36 * q^17 - 96 * q^21 - 24 * q^22 - 12 * q^26 + 96 * q^33 - 12 * q^41 + 72 * q^43 + 24 * q^47 + 24 * q^51 - 36 * q^53 - 84 * q^57 + 48 * q^61 + 24 * q^62 - 36 * q^63 - 24 * q^66 + 96 * q^67 + 12 * q^68 + 36 * q^73 + 12 * q^76 - 96 * q^78 + 144 * q^81 - 48 * q^82 - 24 * q^83 + 48 * q^86 - 72 * q^87 + 72 * q^91 - 72 * q^92 - 156 * q^93 - 120 * q^97 - 24 * q^98

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
$3$	0.0709170	−	0.810585i	0.0409440	−	0.467992i	−0.947851	−	0.318713i	$-0.896749\pi$
$3$	0.0709170	−	0.810585i	0.0409440	−	0.467992i	0.988795	−	0.149279i	$-0.0476951\pi$
$4$	−0.342020	−	0.939693i	−0.171010	−	0.469846i
$5$		0			0
$5$		0			0
$6$	−0.623316	−	0.523024i	−0.254468	−	0.213524i
$7$	0.211848	+	0.790626i	0.0800708	+	0.298828i	0.994335	−	0.106290i	$-0.0338971\pi$
$7$	0.211848	+	0.790626i	0.0800708	+	0.298828i	−0.914264	+	0.405118i	$0.867230\pi$
$8$	−0.965926	−	0.258819i	−0.341506	−	0.0915064i
$9$	2.30240	+	0.405976i	0.767468	+	0.135325i
$10$		0			0
$11$	2.32600	+	4.02876i	0.701317	+	1.21472i	0.968004	+	0.250933i	$0.0807375\pi$
$11$	2.32600	+	4.02876i	0.701317	+	1.21472i	−0.266688	+	0.963783i	$0.585929\pi$
$12$	−0.785956	+	0.210596i	−0.226886	+	0.0607939i
$13$	2.88003	−	0.251970i	0.798777	−	0.0698839i	0.319544	−	0.947572i	$-0.396470\pi$
$13$	2.88003	−	0.251970i	0.798777	−	0.0698839i	0.479233	+	0.877688i	$0.340915\pi$
$14$	0.769154	+	0.279949i	0.205565	+	0.0748195i
$15$		0			0
$16$	−0.766044	+	0.642788i	−0.191511	+	0.160697i
$17$	5.85454	+	4.09939i	1.41993	+	0.994249i	0.996074	+	0.0885215i	$0.0282142\pi$
$17$	5.85454	+	4.09939i	1.41993	+	0.994249i	0.423860	+	0.905727i	$0.360675\pi$
$18$	1.65316	−	1.65316i	0.389654	−	0.389654i
$19$	1.08540	+	4.22160i	0.249008	+	0.968501i
$19$	1.08540	+	4.22160i	0.249008	+	0.968501i
$20$		0			0
$21$	0.655893	−	0.115652i	0.143128	−	0.0252373i
$22$	4.63431	+	0.405449i	0.988038	+	0.0864421i
$23$	−5.90604	−	2.75403i	−1.23149	−	0.574255i	−0.305644	−	0.952146i	$-0.598872\pi$
$23$	−5.90604	−	2.75403i	−1.23149	−	0.574255i	−0.925850	+	0.377890i	$0.876650\pi$
$24$	−0.278296	+	0.764611i	−0.0568068	+	0.156075i
$25$		0			0
$26$	1.44552	−	2.50371i	0.283489	−	0.491017i
$27$	1.12415	−	4.19537i	0.216342	−	0.807400i
$28$	0.670489	−	0.469482i	0.126711	−	0.0887237i
$29$	1.50414	−	8.53038i	0.279311	−	1.58405i	−0.445615	−	0.895225i	$-0.647015\pi$
$29$	1.50414	−	8.53038i	0.279311	−	1.58405i	0.724926	−	0.688826i	$-0.241874\pi$
$30$		0			0
$31$	−6.69401	−	3.86479i	−1.20228	−	0.694137i	−0.241219	−	0.970471i	$-0.577547\pi$
$31$	−6.69401	−	3.86479i	−1.20228	−	0.694137i	−0.961062	+	0.276334i	$0.910880\pi$
$32$	0.0871557	+	0.996195i	0.0154071	+	0.176104i
$33$	3.43061	−	1.59972i	0.597192	−	0.278475i
$34$	6.71605	−	2.44444i	1.15179	−	0.419219i
$35$		0			0
$36$	−0.405976	−	2.30240i	−0.0676627	−	0.383734i
$37$	−2.44013	−	2.44013i	−0.401155	−	0.401155i	0.477485	−	0.878640i	$-0.341549\pi$
$37$	−2.44013	−	2.44013i	−0.401155	−	0.401155i	−0.878640	+	0.477485i	$0.841549\pi$
$38$	4.08069	+	1.53230i	0.661976	+	0.248572i
$39$		−	2.35238i		−	0.376682i
$40$		0			0
$41$	−3.03158	−	3.61289i	−0.473453	−	0.564239i	0.475476	−	0.879728i	$-0.342276\pi$
$41$	−3.03158	−	3.61289i	−0.473453	−	0.564239i	−0.948929	+	0.315490i	$0.897831\pi$
$42$	0.281469	−	0.603611i	0.0434316	−	0.0931393i
$43$	1.67745	+	3.59730i	0.255809	+	0.548583i	0.991709	−	0.128507i	$-0.0410185\pi$
$43$	1.67745	+	3.59730i	0.255809	+	0.548583i	−0.735900	+	0.677090i	$0.763241\pi$
$44$	2.99025	−	3.56365i	0.450798	−	0.537240i
$45$		0			0
$46$	−5.64354	+	3.25830i	−0.832094	+	0.480410i
$47$	5.50012	+	7.85498i	0.802275	+	1.14577i	0.986641	+	0.162910i	$0.0520879\pi$
$47$	5.50012	+	7.85498i	0.802275	+	1.14577i	−0.184366	+	0.982858i	$0.559023\pi$
$48$	0.466709	+	0.666529i	0.0673636	+	0.0962052i
$49$	5.48197	−	3.16502i	0.783138	−	0.452145i
$50$		0			0
$51$	3.73810	−	4.45489i	0.523438	−	0.623809i
$52$	−1.22180	−	2.62017i	−0.169434	−	0.363352i
$53$	−2.45888	+	5.27308i	−0.337753	+	0.724313i	−0.999681	−	0.0252542i	$-0.991960\pi$
$53$	−2.45888	+	5.27308i	−0.337753	+	0.724313i	0.661928	+	0.749567i	$0.269738\pi$
$54$	−2.79186	−	3.32721i	−0.379925	−	0.452776i
$55$		0			0
$56$		−	0.818516i		−	0.109379i
$57$	3.49894	−	0.580428i	0.463446	−	0.0768796i
$58$	−6.12494	−	6.12494i	−0.804244	−	0.804244i
$59$	−0.124865	−	0.708143i	−0.0162560	−	0.0921923i	0.975600	−	0.219554i	$-0.0704602\pi$
$59$	−0.124865	−	0.708143i	−0.0162560	−	0.0921923i	−0.991856	+	0.127362i	$0.959349\pi$
$60$		0			0
$61$	−8.02406	+	2.92052i	−1.02738	+	0.373934i	−0.800081	−	0.599892i	$-0.795210\pi$
$61$	−8.02406	+	2.92052i	−1.02738	+	0.373934i	−0.227294	+	0.973826i	$0.572988\pi$
$62$	−7.00538	+	3.26666i	−0.889684	+	0.414866i
$63$	0.166784	+	1.90634i	0.0210128	+	0.240177i
$64$	0.866025	+	0.500000i	0.108253	+	0.0625000i
$65$		0			0
$66$	0.657303	−	3.72775i	0.0809084	−	0.458854i
$67$	8.69157	−	6.08591i	1.06184	−	0.743512i	0.0941302	−	0.995560i	$-0.469993\pi$
$67$	8.69157	−	6.08591i	1.06184	−	0.743512i	0.967715	+	0.252048i	$0.0811041\pi$
$68$	1.84980	−	6.90354i	0.224321	−	0.837178i
$69$	−2.65122	+	4.59204i	−0.319169	+	0.552817i
$70$		0			0
$71$	1.92060	−	5.27682i	0.227934	−	0.626243i	−0.772023	−	0.635595i	$-0.780755\pi$
$71$	1.92060	−	5.27682i	0.227934	−	0.626243i	0.999956	+	0.00935234i	$0.00297699\pi$
$72$	−2.11888	−	0.988049i	−0.249712	−	0.116443i
$73$	−1.99394	−	0.174447i	−0.233373	−	0.0204175i	−0.0301308	−	0.999546i	$-0.509592\pi$
$73$	−1.99394	−	0.174447i	−0.233373	−	0.0204175i	−0.203242	+	0.979128i	$0.565148\pi$
$74$	−3.39844	+	0.599237i	−0.395061	+	0.0696598i
$75$		0			0
$76$	3.59578	−	2.46382i	0.412464	−	0.282619i
$77$	−2.69248	+	2.69248i	−0.306837	+	0.306837i
$78$	−1.92696	−	1.34927i	−0.218185	−	0.152775i
$79$	−8.08325	+	6.78265i	−0.909436	+	0.763108i	−0.972012	−	0.234933i	$-0.924513\pi$
$79$	−8.08325	+	6.78265i	−0.909436	+	0.763108i	0.0625755	+	0.998040i	$0.480069\pi$
$80$		0			0
$81$	3.26980	+	1.19011i	0.363311	+	0.132234i
$82$	−4.69835	+	0.411052i	−0.518846	+	0.0453931i
$83$	4.46595	−	1.19665i	0.490202	−	0.131349i	−0.00524722	−	0.999986i	$-0.501670\pi$
$83$	4.46595	−	1.19665i	0.490202	−	0.131349i	0.495449	+	0.868637i	$0.335004\pi$
$84$	−0.333006	−	0.576783i	−0.0363339	−	0.0629322i
$85$		0			0
$86$	3.90888	+	0.689241i	0.421505	+	0.0743228i
$87$	−6.80793	−	1.82418i	−0.729887	−	0.195573i
$88$	−1.20403	−	4.49350i	−0.128350	−	0.479008i
$89$	−1.66002	−	1.39292i	−0.175962	−	0.147649i	0.550553	−	0.834800i	$-0.314417\pi$
$89$	−1.66002	−	1.39292i	−0.175962	−	0.147649i	−0.726515	+	0.687151i	$0.758861\pi$
$90$		0			0
$91$	0.809342	+	2.22365i	0.0848421	+	0.233102i
$92$	−0.567959	+	6.49180i	−0.0592138	+	0.676817i
$93$	−3.60746	+	5.15199i	−0.374076	+	0.534236i
$94$	9.58917			0.989047
$95$		0			0
$96$	0.813682			0.0830460
$97$	2.55970	−	3.65562i	0.259898	−	0.371172i	−0.667903	−	0.744248i	$-0.732808\pi$
$97$	2.55970	−	3.65562i	0.259898	−	0.371172i	0.927801	+	0.373076i	$0.121697\pi$
$98$	0.551699	−	6.30594i	0.0557300	−	0.636997i
$99$	3.71982	+	10.2201i	0.373856	+	1.02716i
$100$		0			0
$101$	6.88476	+	5.77700i	0.685059	+	0.574833i	0.917480	−	0.397783i	$-0.130220\pi$
$101$	6.88476	+	5.77700i	0.685059	+	0.574833i	−0.232421	+	0.972615i	$0.574665\pi$
$102$	−1.50515	−	5.61729i	−0.149032	−	0.556194i
$103$	−0.752308	−	0.201580i	−0.0741271	−	0.0198623i	0.221565	−	0.975146i	$-0.428884\pi$
$103$	−0.752308	−	0.201580i	−0.0741271	−	0.0198623i	−0.295692	+	0.955283i	$0.595550\pi$
$104$	−2.84711	−	0.502023i	−0.279182	−	0.0492274i
$105$		0			0
$106$	2.90910	+	5.03871i	0.282557	+	0.489402i
$107$	−10.4930	+	2.81158i	−1.01439	+	0.271806i	−0.727464	−	0.686146i	$-0.759301\pi$
$107$	−10.4930	+	2.81158i	−1.01439	+	0.271806i	−0.286929	+	0.957952i	$0.592634\pi$
$108$	−4.32684	+	0.378550i	−0.416351	+	0.0364259i
$109$	−4.50873	−	1.64104i	−0.431858	−	0.157183i	0.116939	−	0.993139i	$-0.462692\pi$
$109$	−4.50873	−	1.64104i	−0.431858	−	0.157183i	−0.548797	+	0.835956i	$0.684914\pi$
$110$		0			0
$111$	−2.15098	+	1.80489i	−0.204162	+	0.171312i
$112$	−0.670489	−	0.469482i	−0.0633553	−	0.0443618i
$113$	2.64108	−	2.64108i	0.248452	−	0.248452i	−0.571883	−	0.820335i	$-0.693787\pi$
$113$	2.64108	−	2.64108i	0.248452	−	0.248452i	0.820335	+	0.571883i	$0.193787\pi$
$114$	1.53145	−	3.19908i	0.143433	−	0.299622i
$115$		0			0
$116$	−8.53038	+	1.50414i	−0.792026	+	0.139655i
$117$	6.73329	+	0.589086i	0.622493	+	0.0544611i
$118$	−0.651696	−	0.303891i	−0.0599935	−	0.0279754i
$119$	−2.00082	+	5.49720i	−0.183415	+	0.503927i
$120$		0			0
$121$	−5.32060	+	9.21554i	−0.483691	+	0.837777i
$122$	−2.21006	+	8.24806i	−0.200090	+	0.746745i
$123$	−3.14355	+	2.20114i	−0.283444	+	0.198470i
$124$	−1.34223	+	7.61215i	−0.120536	+	0.683591i
$125$		0			0
$126$	1.65725	+	0.956813i	0.147640	+	0.0852397i
$127$	0.630802	+	7.21010i	0.0559746	+	0.639793i	0.971423	+	0.237357i	$0.0762810\pi$
$127$	0.630802	+	7.21010i	0.0559746	+	0.639793i	−0.915448	+	0.402436i	$0.868163\pi$
$128$	0.906308	−	0.422618i	0.0801070	−	0.0373545i
$129$	3.03488	−	1.10461i	0.267206	−	0.0972551i
$130$		0			0
$131$	−2.06381	−	11.7044i	−0.180316	−	1.02262i	−0.931828	−	0.362901i	$-0.881786\pi$
$131$	−2.06381	−	11.7044i	−0.180316	−	1.02262i	0.751512	−	0.659719i	$-0.229325\pi$
$132$	−2.67658	−	2.67658i	−0.232966	−	0.232966i
$133$	−3.10777	+	1.75248i	−0.269477	+	0.151960i
$134$		−	10.6105i		−	0.916604i
$135$		0			0
$136$	−4.59405	−	5.47498i	−0.393937	−	0.469475i
$137$	6.29688	−	13.5037i	0.537979	−	1.15370i	−0.430037	−	0.902811i	$-0.641500\pi$
$137$	6.29688	−	13.5037i	0.537979	−	1.15370i	0.968016	−	0.250888i	$-0.0807227\pi$
$138$	2.24091	+	4.80564i	0.190759	+	0.409083i
$139$	0.407209	−	0.485293i	0.0345390	−	0.0411620i	−0.748498	−	0.663137i	$-0.769225\pi$
$139$	0.407209	−	0.485293i	0.0345390	−	0.0411620i	0.783037	+	0.621975i	$0.213669\pi$
$140$		0			0
$141$	6.75719	−	3.90126i	0.569058	−	0.328546i
$142$	−3.22090	−	4.59992i	−0.270292	−	0.386017i
$143$	7.71409	+	11.0169i	0.645085	+	0.921277i
$144$	−2.02470	+	1.16896i	−0.168725	+	0.0974134i
$145$		0			0
$146$	−1.28658	+	1.53328i	−0.106478	+	0.126895i
$147$	−2.17675	−	4.66806i	−0.179535	−	0.385015i
$148$	−1.45840	+	3.12755i	−0.119880	+	0.257083i
$149$	−13.8389	−	16.4926i	−1.13373	−	1.35112i	−0.928029	−	0.372508i	$-0.878498\pi$
$149$	−13.8389	−	16.4926i	−1.13373	−	1.35112i	−0.205698	−	0.978615i	$-0.565947\pi$
$150$		0			0
$151$			7.12067i			0.579472i	0.957107	+	0.289736i	$0.0935674\pi$
$151$			7.12067i			0.579472i	−0.957107	+	0.289736i	$0.906433\pi$
$152$	0.0442120	−	4.35867i	0.00358606	−	0.353535i
$153$	11.8153	+	11.8153i	0.955207	+	0.955207i
$154$	0.661208	+	3.74990i	0.0532817	+	0.302175i
$155$		0			0
$156$	−2.21051	+	0.804561i	−0.176983	+	0.0644165i
$157$	−2.97175	+	1.38575i	−0.237171	+	0.110595i	−0.537571	−	0.843219i	$-0.680658\pi$
$157$	−2.97175	+	1.38575i	−0.237171	+	0.110595i	0.300399	+	0.953814i	$0.402880\pi$
$158$	0.919661	+	10.5118i	0.0731643	+	0.836272i
$159$	4.09990	+	2.36708i	0.325143	+	0.187722i
$160$		0			0
$161$	0.926229	−	5.25290i	0.0729971	−	0.413987i
$162$	2.85036	−	1.99584i	0.223945	−	0.156808i
$163$	−2.17629	+	8.12203i	−0.170460	+	0.636167i	0.826820	+	0.562466i	$0.190147\pi$
$163$	−2.17629	+	8.12203i	−0.170460	+	0.636167i	−0.997280	+	0.0737002i	$0.976519\pi$
$164$	−2.35815	+	4.08443i	−0.184140	+	0.318941i
$165$		0			0
$166$	1.58133	−	4.34466i	0.122735	−	0.337211i
$167$	−7.11132	−	3.31606i	−0.550291	−	0.256605i	0.127527	−	0.991835i	$-0.459296\pi$
$167$	−7.11132	−	3.31606i	−0.550291	−	0.256605i	−0.677817	+	0.735230i	$0.737074\pi$
$168$	−0.663477	−	0.0580467i	−0.0511884	−	0.00447840i
$169$	−4.57141	+	0.806063i	−0.351647	+	0.0620048i
$170$		0			0
$171$	0.785167	+	10.1605i	0.0600432	+	0.776991i
$172$	2.80664	−	2.80664i	0.214004	−	0.214004i
$173$	−17.1249	−	11.9910i	−1.30198	−	0.911658i	−0.302839	−	0.953042i	$-0.597934\pi$
$173$	−17.1249	−	11.9910i	−1.30198	−	0.911658i	−0.999143	+	0.0413841i	$0.986823\pi$
$174$	−5.39915	+	4.53042i	−0.409308	+	0.343450i
$175$		0			0
$176$	−4.37146	−	1.59108i	−0.329511	−	0.119932i
$177$	−0.582865	+	0.0509941i	−0.0438108	+	0.00383295i
$178$	−2.09316	+	0.560861i	−0.156889	+	0.0420383i
$179$	6.97067	+	12.0736i	0.521012	+	0.902420i	0.999701	+	0.0244352i	$0.00777876\pi$
$179$	6.97067	+	12.0736i	0.521012	+	0.902420i	−0.478689	+	0.877984i	$0.658888\pi$
$180$		0			0
$181$	21.0727	+	3.71569i	1.56632	+	0.276185i	0.888443	−	0.458986i	$-0.151787\pi$
$181$	21.0727	+	3.71569i	1.56632	+	0.276185i	0.677881	+	0.735171i	$0.262898\pi$
$182$	2.28573	+	0.612458i	0.169429	+	0.0453984i
$183$	1.79829	+	6.71130i	0.132933	+	0.496113i
$184$	4.99200	+	4.18879i	0.368015	+	0.308801i
$185$		0			0
$186$	2.15111	+	5.91012i	0.157727	+	0.433351i
$187$	−2.89778	+	33.1217i	−0.211906	+	2.42210i
$188$	5.50012	−	7.85498i	0.401137	−	0.572884i
$189$	3.55512			0.258597
$190$		0			0
$191$	8.10976			0.586801			0.293401	−	0.955990i	$-0.405213\pi$
$191$	8.10976			0.586801			0.293401	+	0.955990i	$0.405213\pi$
$192$	0.466709	−	0.666529i	0.0336818	−	0.0481026i
$193$	−0.515018	+	5.88668i	−0.0370718	+	0.423733i	0.954869	+	0.297028i	$0.0959955\pi$
$193$	−0.515018	+	5.88668i	−0.0370718	+	0.423733i	−0.991941	+	0.126704i	$0.959560\pi$
$194$	−1.52633	−	4.19356i	−0.109584	−	0.301080i
$195$		0			0
$196$	−4.84909	−	4.06887i	−0.346363	−	0.290633i
$197$	−1.29256	−	4.82391i	−0.0920912	−	0.343689i	0.904471	−	0.426535i	$-0.140266\pi$
$197$	−1.29256	−	4.82391i	−0.0920912	−	0.343689i	−0.996562	+	0.0828457i	$0.973599\pi$
$198$	10.5054	+	2.81493i	0.746589	+	0.200048i
$199$	−13.6596	−	2.40855i	−0.968300	−	0.170737i	−0.332936	−	0.942950i	$-0.608039\pi$
$199$	−13.6596	−	2.40855i	−0.968300	−	0.170737i	−0.635365	+	0.772212i	$0.719150\pi$
$200$		0			0
$201$	−4.31677	−	7.47686i	−0.304481	−	0.527377i
$202$	8.68118	−	2.32611i	0.610805	−	0.163665i
$203$	7.06298	−	0.617931i	0.495724	−	0.0433702i
$204$	−5.46473	−	1.98900i	−0.382608	−	0.139258i
$205$		0			0
$206$	−0.596631	+	0.500633i	−0.0415692	+	0.0348807i
$207$	−12.4800	−	8.73861i	−0.867422	−	0.607375i
$208$	−2.04427	+	2.04427i	−0.141745	+	0.141745i
$209$	−14.4832	+	14.1923i	−1.00182	+	0.981701i
$210$		0			0
$211$	−13.1023	+	2.31030i	−0.902002	+	0.159047i	−0.605370	−	0.795944i	$-0.706975\pi$
$211$	−13.1023	+	2.31030i	−0.902002	+	0.159047i	−0.296633	+	0.954992i	$0.595864\pi$
$212$	5.79606	+	0.507089i	0.398075	+	0.0348270i
$213$	−4.14111	−	1.93103i	−0.283744	−	0.132312i
$214$	−3.71540	+	10.2080i	−0.253980	+	0.697804i
$215$		0			0
$216$	−2.17168	+	3.76147i	−0.147764	+	0.255935i
$217$	1.63749	−	6.11121i	0.111160	−	0.414856i
$218$	−3.93037	+	2.75207i	−0.266198	+	0.186394i
$219$	−0.282809	+	1.60389i	−0.0191104	+	0.108381i
$220$		0			0
$221$	17.8942	+	10.3312i	1.20369	+	0.694953i
$222$	0.244725	+	2.79722i	0.0164249	+	0.187737i
$223$	−2.22450	+	1.03730i	−0.148963	+	0.0694627i	−0.495670	−	0.868511i	$-0.665078\pi$
$223$	−2.22450	+	1.03730i	−0.148963	+	0.0694627i	0.346707	+	0.937973i	$0.387300\pi$
$224$	−0.769154	+	0.279949i	−0.0513912	+	0.0187049i
$225$		0			0
$226$	−0.648584	−	3.67830i	−0.0431432	−	0.244677i
$227$	−18.1855	−	18.1855i	−1.20702	−	1.20702i	−0.971989	−	0.235027i	$-0.924482\pi$
$227$	−18.1855	−	18.1855i	−1.20702	−	1.20702i	−0.235027	−	0.971989i	$-0.575518\pi$
$228$	−1.74213	−	3.08941i	−0.115376	−	0.204601i
$229$			2.17867i			0.143971i	0.997406	+	0.0719853i	$0.0229335\pi$
$229$			2.17867i			0.143971i	−0.997406	+	0.0719853i	$0.977067\pi$
$230$		0			0
$231$	1.99154	+	2.37343i	0.131034	+	0.156160i
$232$	−3.66071	+	7.85041i	−0.240337	+	0.515405i
$233$	0.902376	+	1.93515i	0.0591166	+	0.126776i	0.933647	−	0.358195i	$-0.116608\pi$
$233$	0.902376	+	1.93515i	0.0591166	+	0.126776i	−0.874530	+	0.484971i	$0.838830\pi$
$234$	4.34461	−	5.17770i	0.284016	−	0.338477i
$235$		0			0
$236$	−0.622730	+	0.359534i	−0.0405363	+	0.0234036i
$237$	4.92468	+	7.03317i	0.319892	+	0.456853i
$238$	3.35542	+	4.79204i	0.217500	+	0.310622i
$239$	−0.171779	+	0.0991766i	−0.0111115	+	0.00641520i	−0.505545	−	0.862800i	$-0.668709\pi$
$239$	−0.171779	+	0.0991766i	−0.0111115	+	0.00641520i	0.494434	+	0.869215i	$0.335375\pi$
$240$		0			0
$241$	−11.2959	+	13.4619i	−0.727630	+	0.867156i	−0.995348	−	0.0963413i	$-0.969286\pi$
$241$	−11.2959	+	13.4619i	−0.727630	+	0.867156i	0.267718	+	0.963497i	$0.413730\pi$
$242$	4.49716	+	9.64420i	0.289089	+	0.619952i
$243$	6.70333	−	14.3753i	0.430019	−	0.922178i
$244$	5.48878	+	6.54127i	0.351383	+	0.418762i
$245$		0			0
$246$			3.83756i			0.244674i
$247$	4.18971	+	11.8848i	0.266585	+	0.756215i
$248$	5.46564	+	5.46564i	0.347068	+	0.347068i
$249$	−0.653273	−	3.70490i	−0.0413995	−	0.234788i
$250$		0			0
$251$	−12.6226	+	4.59426i	−0.796733	+	0.289987i	−0.708132	−	0.706080i	$-0.750462\pi$
$251$	−12.6226	+	4.59426i	−0.796733	+	0.289987i	−0.0886009	+	0.996067i	$0.528240\pi$
$252$	1.73433	−	0.808734i	0.109253	−	0.0509454i
$253$	−2.64215	−	30.1999i	−0.166111	−	1.89865i
$254$	6.26798	+	3.61882i	0.393288	+	0.227065i
$255$		0			0
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	12.6675	−	8.86986i	0.790176	−	0.553287i	−0.107364	−	0.994220i	$-0.534241\pi$
$257$	12.6675	−	8.86986i	0.790176	−	0.553287i	0.897540	+	0.440933i	$0.145352\pi$
$258$	0.835895	−	3.11960i	0.0520406	−	0.194218i
$259$	1.41229	−	2.44617i	0.0877557	−	0.151997i
$260$		0			0
$261$	6.92625	−	19.0297i	0.428724	−	1.17791i
$262$	−10.7715	−	5.02281i	−0.665463	−	0.310310i
$263$	1.85637	+	0.162411i	0.114468	+	0.0100147i	0.144246	−	0.989542i	$-0.453924\pi$
$263$	1.85637	+	0.162411i	0.114468	+	0.0100147i	−0.0297775	+	0.999557i	$0.509480\pi$
$264$	−3.72775	+	0.657303i	−0.229427	+	0.0404542i
$265$		0			0
$266$	−0.346991	+	3.55092i	−0.0212754	+	0.217721i
$267$	−1.24680	+	1.24680i	−0.0763032	+	0.0763032i
$268$	−8.69157	−	6.08591i	−0.530922	−	0.371756i
$269$	10.9981	−	9.22848i	0.670564	−	0.562670i	−0.242668	−	0.970109i	$-0.578023\pi$
$269$	10.9981	−	9.22848i	0.670564	−	0.562670i	0.913232	+	0.407439i	$0.133578\pi$
$270$		0			0
$271$	8.01704	+	2.91797i	0.487001	+	0.177254i	0.573838	−	0.818969i	$-0.305454\pi$
$271$	8.01704	+	2.91797i	0.487001	+	0.177254i	−0.0868374	+	0.996222i	$0.527676\pi$
$272$	−7.11988	+	0.622909i	−0.431706	+	0.0377694i
$273$	1.85985	−	0.498346i	0.112563	−	0.0301613i
$274$	−7.44984	−	12.9035i	−0.450062	−	0.779530i
$275$		0			0
$276$	5.22188	+	0.920758i	0.314320	+	0.0554231i
$277$	−16.4751	−	4.41450i	−0.989894	−	0.265241i	−0.272688	−	0.962102i	$-0.587913\pi$
$277$	−16.4751	−	4.41450i	−0.989894	−	0.265241i	−0.717206	+	0.696861i	$0.754579\pi$
$278$	−0.163963	−	0.611919i	−0.00983386	−	0.0367005i
$279$	−13.8433	−	11.6159i	−0.828777	−	0.695427i
$280$		0			0
$281$	7.72570	+	21.2262i	0.460877	+	1.26625i	0.924827	+	0.380387i	$0.124209\pi$
$281$	7.72570	+	21.2262i	0.460877	+	1.26625i	−0.463951	+	0.885861i	$0.653568\pi$
$282$	0.680035	−	7.77284i	0.0404955	−	0.462866i
$283$	−0.991073	+	1.41540i	−0.0589132	+	0.0841367i	−0.847528	−	0.530751i	$-0.821910\pi$
$283$	−0.991073	+	1.41540i	−0.0589132	+	0.0841367i	0.788615	+	0.614888i	$0.210799\pi$
$284$	−5.61547			−0.333217
$285$		0			0
$286$	13.4491			0.795263
$287$	2.21421	−	3.16222i	0.130701	−	0.186660i
$288$	−0.203763	+	2.32903i	−0.0120069	+	0.137239i
$289$	11.6563	+	32.0254i	0.685663	+	1.88384i
$290$		0			0
$291$	−2.78167	−	2.33410i	−0.163064	−	0.136827i
$292$	0.518041	+	1.93336i	0.0303161	+	0.113141i
$293$	−25.7643	−	6.90352i	−1.50517	−	0.403308i	−0.590339	−	0.807155i	$-0.701006\pi$
$293$	−25.7643	−	6.90352i	−1.50517	−	0.403308i	−0.914826	+	0.403848i	$0.867673\pi$
$294$	−5.07238	−	0.894398i	−0.295827	−	0.0521623i
$295$		0			0
$296$	1.72543	+	2.98854i	0.100289	+	0.173705i
$297$	19.5169	−	5.22954i	1.13249	−	0.303449i
$298$	−21.4476	+	1.87642i	−1.24243	+	0.108698i
$299$	−17.7035	−	6.44355i	−1.02382	−	0.372640i
$300$		0			0
$301$	−2.48876	+	2.08831i	−0.143449	+	0.120368i
$302$	5.83291	+	4.08425i	0.335646	+	0.235022i
$303$	5.17100	−	5.17100i	0.297066	−	0.297066i
$304$	−3.54506	−	2.53625i	−0.203323	−	0.145464i
$305$		0			0
$306$	16.4555	−	2.90154i	0.940696	−	0.165870i
$307$	−15.3079	−	1.33927i	−0.873668	−	0.0764361i	−0.358505	−	0.933528i	$-0.616713\pi$
$307$	−15.3079	−	1.33927i	−0.873668	−	0.0764361i	−0.515164	+	0.857092i	$0.672269\pi$
$308$	3.45099	+	1.60922i	0.196638	+	0.0916940i
$309$	−0.216749	+	0.595514i	−0.0123304	+	0.0338776i
$310$		0			0
$311$	0.909453	−	1.57522i	0.0515704	−	0.0893225i	−0.839088	−	0.543996i	$-0.816911\pi$
$311$	0.909453	−	1.57522i	0.0515704	−	0.0893225i	0.890658	+	0.454673i	$0.150244\pi$
$312$	−0.608841	+	2.27222i	−0.0344688	+	0.128639i
$313$	23.7399	−	16.6228i	1.34186	−	0.939579i	0.341857	−	0.939752i	$-0.388944\pi$
$313$	23.7399	−	16.6228i	1.34186	−	0.939579i	1.00000		0.000173367i	$5.51843e-5\pi$
$314$	−0.569386	+	3.22915i	−0.0321323	+	0.182231i
$315$		0			0
$316$	9.13824	+	5.27596i	0.514066	+	0.296796i
$317$	2.77871	+	31.7608i	0.156068	+	1.78386i	0.521725	+	0.853114i	$0.325289\pi$
$317$	2.77871	+	31.7608i	0.156068	+	1.78386i	−0.365657	+	0.930750i	$0.619156\pi$
$318$	4.29061	−	2.00074i	0.240605	−	0.112196i
$319$	37.8654	−	13.7819i	2.12006	−	0.771638i
$320$		0			0
$321$	1.53490	+	8.70483i	0.0856696	+	0.485856i
$322$	−3.77166	−	3.77166i	−0.210187	−	0.210187i
$323$	−10.9515	+	29.1650i	−0.609356	+	1.62279i
$324$		−	3.47965i		−	0.193314i
$325$		0			0
$326$	5.40491	+	6.44132i	0.299350	+	0.356752i
$327$	−1.64995	+	3.53833i	−0.0912425	+	0.195670i
$328$	1.99319	+	4.27442i	0.110056	+	0.236015i
$329$	−5.04517	+	6.01260i	−0.278149	+	0.331485i
$330$		0			0
$331$	−15.4104	+	8.89719i	−0.847031	+	0.489034i	−0.859648	−	0.510887i	$-0.829317\pi$
$331$	−15.4104	+	8.89719i	−0.847031	+	0.489034i	0.0126167	+	0.999920i	$0.495984\pi$
$332$	−2.65193	−	3.78734i	−0.145543	−	0.207857i
$333$	−4.62753	−	6.60880i	−0.253587	−	0.362160i
$334$	−6.79525	+	3.92324i	−0.371819	+	0.214670i
$335$		0			0
$336$	−0.428104	+	0.510194i	−0.0233550	+	0.0278334i
$337$	3.02769	+	6.49291i	0.164929	+	0.353691i	0.971351	−	0.237649i	$-0.0763768\pi$
$337$	3.02769	+	6.49291i	0.164929	+	0.353691i	−0.806422	+	0.591340i	$0.798599\pi$
$338$	−1.96176	+	4.20702i	−0.106706	+	0.228832i
$339$	−1.95352	−	2.32812i	−0.106101	−	0.126446i
$340$		0			0
$341$		−	35.9581i		−	1.94724i
$342$	8.77333	+	5.18464i	0.474407	+	0.280353i
$343$	7.71513	+	7.71513i	0.416578	+	0.416578i
$344$	−0.689241	−	3.90888i	−0.0371614	−	0.210753i
$345$		0			0
$346$	−19.6449	+	7.15015i	−1.05612	+	0.384395i
$347$	−13.8248	+	6.44663i	−0.742157	+	0.346073i	−0.756649	−	0.653822i	$-0.773165\pi$
$347$	−13.8248	+	6.44663i	−0.742157	+	0.346073i	0.0144919	+	0.999895i	$0.495387\pi$
$348$	0.614281	+	7.02127i	0.0329289	+	0.376379i
$349$	4.43618	+	2.56123i	0.237463	+	0.137099i	0.614010	−	0.789298i	$-0.289555\pi$
$349$	4.43618	+	2.56123i	0.237463	+	0.137099i	−0.376547	+	0.926398i	$0.622889\pi$
$350$		0			0
$351$	2.18047	−	12.3661i	0.116385	−	0.660051i
$352$	−3.81070	+	2.66828i	−0.203111	+	0.142220i
$353$	4.97923	−	18.5827i	0.265018	−	0.989060i	−0.697222	−	0.716856i	$-0.745581\pi$
$353$	4.97923	−	18.5827i	0.265018	−	0.989060i	0.962239	−	0.272204i	$-0.0877526\pi$
$354$	−0.292546	+	0.506704i	−0.0155486	+	0.0269310i
$355$		0			0
$356$	−0.741158	+	2.03631i	−0.0392813	+	0.107924i
$357$	4.31406	+	2.01168i	0.228324	+	0.106469i
$358$	13.8883	+	1.21507i	0.734019	+	0.0642183i
$359$	6.04030	−	1.06507i	0.318795	−	0.0562122i	−0.0119610	−	0.999928i	$-0.503807\pi$
$359$	6.04030	−	1.06507i	0.318795	−	0.0562122i	0.330756	+	0.943716i	$0.392696\pi$
$360$		0			0
$361$	−16.6438	+	9.16427i	−0.875990	+	0.482330i
$362$	15.1305	−	15.1305i	0.795244	−	0.795244i
$363$	7.09266	+	4.96634i	0.372268	+	0.260665i
$364$	1.81273	−	1.52106i	0.0950131	−	0.0797255i
$365$		0			0
$366$	6.52903	+	2.37637i	0.341278	+	0.124215i
$367$	6.43348	−	0.562857i	0.335825	−	0.0293809i	0.0820037	−	0.996632i	$-0.473868\pi$
$367$	6.43348	−	0.562857i	0.335825	−	0.0293809i	0.253821	+	0.967251i	$0.418313\pi$
$368$	6.29455	−	1.68662i	0.328126	−	0.0879211i
$369$	−5.51317	−	9.54908i	−0.287004	−	0.497105i
$370$		0			0
$371$	−4.68994	−	0.826963i	−0.243489	−	0.0429338i
$372$	6.07511	+	1.62782i	0.314980	+	0.0843986i
$373$	−1.17684	−	4.39201i	−0.0609342	−	0.227410i	0.928743	−	0.370724i	$-0.120891\pi$
$373$	−1.17684	−	4.39201i	−0.0609342	−	0.227410i	−0.989677	+	0.143315i	$0.954224\pi$
$374$	25.4696	+	21.3716i	1.31700	+	1.10510i
$375$		0			0
$376$	−3.27969	−	9.01087i	−0.169137	−	0.464700i
$377$	2.18256	−	24.9467i	0.112407	−	1.28482i
$378$	2.03913	−	2.91218i	0.104882	−	0.149786i
$379$	−23.1984			−1.19162			−0.595812	−	0.803124i	$-0.703170\pi$
$379$	−23.1984			−1.19162			−0.595812	+	0.803124i	$0.703170\pi$
$380$		0			0
$381$	5.88914			0.301710
$382$	4.65157	−	6.64312i	0.237995	−	0.339892i
$383$	0.802086	−	9.16789i	0.0409847	−	0.468457i	−0.947775	−	0.318941i	$-0.896673\pi$
$383$	0.802086	−	9.16789i	0.0409847	−	0.468457i	0.988759	−	0.149516i	$-0.0477716\pi$
$384$	−0.278296	−	0.764611i	−0.0142017	−	0.0390189i
$385$		0			0
$386$	4.52669	+	3.79834i	0.230402	+	0.193330i
$387$	2.40175	+	8.96344i	0.122088	+	0.455637i
$388$	−4.31063	−	1.15503i	−0.218839	−	0.0586378i
$389$	30.7752	+	5.42651i	1.56037	+	0.275135i	0.886150	−	0.463398i	$-0.153370\pi$
$389$	30.7752	+	5.42651i	1.56037	+	0.275135i	0.674217	+	0.738533i	$0.264481\pi$
$390$		0			0
$391$	−23.2873	−	40.3348i	−1.17769	−	2.03982i
$392$	−6.11434	+	1.63833i	−0.308821	+	0.0827483i
$393$	−9.63379	+	0.842848i	−0.485961	+	0.0425160i
$394$	−4.69290	−	1.70807i	−0.236425	−	0.0860515i
$395$		0			0
$396$	8.33153	−	6.99098i	0.418675	−	0.351310i
$397$	6.54164	+	4.58050i	0.328315	+	0.229889i	0.726099	−	0.687590i	$-0.241332\pi$
$397$	6.54164	+	4.58050i	0.328315	+	0.229889i	−0.397783	+	0.917479i	$0.630220\pi$
$398$	−9.80777	+	9.80777i	−0.491619	+	0.491619i
$399$	1.20014	+	2.64339i	0.0600823	+	0.132335i
$400$		0			0
$401$	−18.9142	+	3.33509i	−0.944532	+	0.166547i	−0.624645	−	0.780909i	$-0.714756\pi$
$401$	−18.9142	+	3.33509i	−0.944532	+	0.166547i	−0.319888	+	0.947456i	$0.603645\pi$
$402$	−8.60068	−	0.752462i	−0.428963	−	0.0375294i
$403$	−20.2528	−	9.44403i	−1.00886	−	0.470440i
$404$	3.07388	−	8.44541i	0.152931	−	0.420175i
$405$		0			0
$406$	3.54498	−	6.14009i	0.175934	−	0.304727i
$407$	4.15494	−	15.5065i	0.205953	−	0.768626i
$408$	−4.76373	+	3.33560i	−0.235840	+	0.165137i
$409$	1.15458	−	6.54795i	0.0570903	−	0.323775i	−0.942866	−	0.333173i	$-0.891881\pi$
$409$	1.15458	−	6.54795i	0.0570903	−	0.323775i	0.999956	+	0.00939834i	$0.00299163\pi$
$410$		0			0
$411$	−10.4993	−	6.06180i	−0.517895	−	0.299007i
$412$	0.0678809	+	0.775882i	0.00334425	+	0.0382250i
$413$	0.533424	−	0.248740i	0.0262481	−	0.0122397i
$414$	−14.3165	+	5.21078i	−0.703617	+	0.256096i
$415$		0			0
$416$	0.502023	+	2.84711i	0.0246137	+	0.139591i
$417$	−0.364493	−	0.364493i	−0.0178493	−	0.0178493i
$418$	3.31844	+	20.0043i	0.162310	+	0.978441i
$419$		−	23.6815i		−	1.15692i	−0.815711	−	0.578459i	$-0.803654\pi$
$419$		−	23.6815i		−	1.15692i	0.815711	−	0.578459i	$-0.196346\pi$
$420$		0			0
$421$	−0.651402	−	0.776311i	−0.0317474	−	0.0378351i	0.749937	−	0.661509i	$-0.230084\pi$
$421$	−0.651402	−	0.776311i	−0.0317474	−	0.0378351i	−0.781685	+	0.623674i	$0.785639\pi$
$422$	−5.62271	+	12.0579i	−0.273709	+	0.586971i
$423$	9.47456	+	20.3183i	0.460669	+	0.987908i
$424$	3.73986	−	4.45700i	0.181624	−	0.216451i
$425$		0			0
$426$	−3.95705	+	2.28460i	−0.191720	+	0.110689i
$427$	−4.00891	−	5.72532i	−0.194005	−	0.277068i
$428$	6.23083	+	8.89854i	0.301178	+	0.430127i
$429$	9.47717	−	5.47165i	0.457562	−	0.264174i
$430$		0			0
$431$	−17.1580	+	20.4481i	−0.826471	+	0.984950i	0.173529	+	0.984829i	$0.444483\pi$
$431$	−17.1580	+	20.4481i	−0.826471	+	0.984950i	−1.00000		0.000121177i	$0.999961\pi$
$432$	1.83559	+	3.93643i	0.0883147	+	0.189392i
$433$	−11.5080	+	24.6791i	−0.553041	+	1.18600i	0.408859	+	0.912598i	$0.365927\pi$
$433$	−11.5080	+	24.6791i	−0.553041	+	1.18600i	−0.961900	+	0.273402i	$0.911851\pi$
$434$	−4.06678	−	4.84660i	−0.195212	−	0.232644i
$435$		0			0
$436$			4.79809i			0.229787i
$437$	5.21599	−	27.9222i	0.249515	−	1.33570i
$438$	1.15162	+	1.15162i	0.0550263	+	0.0550263i
$439$	0.0782193	+	0.443604i	0.00373320	+	0.0211721i	0.986617	−	0.163052i	$-0.0521339\pi$
$439$	0.0782193	+	0.443604i	0.00373320	+	0.0211721i	−0.982884	+	0.184224i	$0.941023\pi$
$440$		0			0
$441$	13.9066	−	5.06160i	0.662220	−	0.241028i
$442$	18.7265	−	8.73232i	0.890730	−	0.415354i
$443$	−0.412507	−	4.71498i	−0.0195988	−	0.224015i	−0.999677	−	0.0254046i	$-0.991913\pi$
$443$	−0.412507	−	4.71498i	−0.0195988	−	0.224015i	0.980078	−	0.198611i	$-0.0636430\pi$
$444$	2.43172	+	1.40395i	0.115404	+	0.0666287i
$445$		0			0
$446$	−0.426212	+	2.41717i	−0.0201817	+	0.114456i
$447$	−14.3500	+	10.0480i	−0.678734	+	0.475255i
$448$	−0.211848	+	0.790626i	−0.0100089	+	0.0373536i
$449$	16.6470	−	28.8334i	0.785619	−	1.36073i	−0.143010	−	0.989721i	$-0.545678\pi$
$449$	16.6470	−	28.8334i	0.785619	−	1.36073i	0.928629	−	0.371011i	$-0.120989\pi$
$450$		0			0
$451$	7.50401	−	20.6171i	0.353350	−	0.970821i
$452$	−3.38510	−	1.57850i	−0.159222	−	0.0742463i
$453$	5.77191	+	0.504976i	0.271188	+	0.0237259i
$454$	−25.3275	+	4.46592i	−1.18868	+	0.209596i
$455$		0			0
$456$	−3.52994	−	0.344942i	−0.165305	−	0.0161534i
$457$	8.45415	−	8.45415i	0.395468	−	0.395468i	−0.481163	−	0.876631i	$-0.659785\pi$
$457$	8.45415	−	8.45415i	0.395468	−	0.395468i	0.876631	+	0.481163i	$0.159785\pi$
$458$	1.78466	+	1.24963i	0.0833918	+	0.0583916i
$459$	23.7798	−	19.9537i	1.10995	−	0.931357i
$460$		0			0
$461$	−21.1237	−	7.68838i	−0.983827	−	0.358084i	−0.200500	−	0.979694i	$-0.564257\pi$
$461$	−21.1237	−	7.68838i	−0.983827	−	0.358084i	−0.783327	+	0.621610i	$0.786479\pi$
$462$	3.08650	−	0.270034i	0.143597	−	0.0125631i
$463$	−23.8046	+	6.37841i	−1.10629	+	0.296430i	−0.765324	−	0.643645i	$-0.777421\pi$
$463$	−23.8046	+	6.37841i	−1.10629	+	0.296430i	−0.340967	+	0.940075i	$0.610755\pi$
$464$	4.33099	+	7.50149i	0.201061	+	0.348248i
$465$		0			0
$466$	2.10276	+	0.370774i	0.0974087	+	0.0171758i
$467$	21.8306	+	5.84948i	1.01020	+	0.270682i	0.725712	−	0.687999i	$-0.241511\pi$
$467$	21.8306	+	5.84948i	1.01020	+	0.270682i	0.284486	+	0.958680i	$0.408177\pi$
$468$	−1.74936	−	6.52870i	−0.0808642	−	0.301789i
$469$	6.65296	+	5.58250i	0.307205	+	0.257776i
$470$		0			0
$471$	0.912520	+	2.50713i	0.0420467	+	0.115522i
$472$	−0.0626708	+	0.716331i	−0.00288466	+	0.0329718i
$473$	−10.5909	+	15.1254i	−0.486970	+	0.695465i
$474$	8.58591			0.394364
$475$		0			0
$476$	5.85000			0.268134
$477$	−7.80207	+	11.1425i	−0.357232	+	0.510180i
$478$	−0.0172876	+	0.197598i	−0.000790718	+	0.00903794i
$479$	−4.06156	−	11.1590i	−0.185577	−	0.509870i	0.811662	−	0.584128i	$-0.198563\pi$
$479$	−4.06156	−	11.1590i	−0.185577	−	0.509870i	−0.997239	+	0.0742580i	$0.976341\pi$
$480$		0			0
$481$	−7.64249	−	6.41281i	−0.348468	−	0.292399i
$482$	4.54829	+	16.9744i	0.207169	+	0.773165i
$483$	−4.19224	−	1.12331i	−0.190754	−	0.0511123i
$484$	10.4795	+	1.84782i	0.476342	+	0.0839920i
$485$		0			0
$486$	−7.93072	−	13.7364i	−0.359745	−	0.623096i
$487$	−16.8345	+	4.51078i	−0.762842	+	0.204403i	−0.619207	−	0.785228i	$-0.712546\pi$
$487$	−16.8345	+	4.51078i	−0.762842	+	0.204403i	−0.143635	+	0.989631i	$0.545879\pi$
$488$	8.50653	−	0.744225i	0.385073	−	0.0336895i
$489$	6.42926	+	2.34006i	0.290741	+	0.105821i
$490$		0			0
$491$	20.6185	−	17.3009i	0.930498	−	0.780780i	−0.0454089	−	0.998968i	$-0.514459\pi$
$491$	20.6185	−	17.3009i	0.930498	−	0.780780i	0.975907	+	0.218188i	$0.0700146\pi$
$492$	3.14355	+	2.20114i	0.141722	+	0.0992349i
$493$	43.7754	−	43.7754i	1.97154	−	1.97154i
$494$	12.1386	+	3.38486i	0.546142	+	0.152292i
$495$		0			0
$496$	7.61215	−	1.34223i	0.341796	−	0.0602678i
$497$	4.57886	+	0.400599i	0.205390	+	0.0179693i
$498$	−3.40958	−	1.58991i	−0.152787	−	0.0712456i
$499$	−9.57685	+	26.3122i	−0.428719	+	1.17789i	0.517872	+	0.855458i	$0.326724\pi$
$499$	−9.57685	+	26.3122i	−0.428719	+	1.17789i	−0.946591	+	0.322437i	$0.895498\pi$
$500$		0			0
$501$	−3.19227	+	5.52917i	−0.142620	+	0.247025i
$502$	−3.47664	+	12.9750i	−0.155170	+	0.579103i
$503$	33.7336	−	23.6205i	1.50411	−	1.05319i	0.524703	−	0.851285i	$-0.324176\pi$
$503$	33.7336	−	23.6205i	1.50411	−	1.05319i	0.979406	−	0.201903i	$-0.0647124\pi$
$504$	0.332298	−	1.88455i	0.0148017	−	0.0839447i
$505$		0			0
$506$	−26.2538	−	15.1576i	−1.16712	−	0.673839i
$507$	0.329192	+	3.76268i	0.0146199	+	0.167107i
$508$	6.55953	−	3.05876i	0.291032	−	0.135710i
$509$	−11.0858	+	4.03490i	−0.491369	+	0.178844i	−0.575808	−	0.817585i	$-0.695312\pi$
$509$	−11.0858	+	4.03490i	−0.491369	+	0.178844i	0.0844391	+	0.996429i	$0.473090\pi$
$510$		0			0
$511$	−0.284489	−	1.61342i	−0.0125851	−	0.0713734i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	18.9313	+	0.192029i	0.835839	+	0.00847828i
$514$		−	15.4641i		−	0.682094i
$515$		0			0
$516$	−2.07598	−	2.47406i	−0.0913899	−	0.108914i
$517$	−18.8525	+	40.4294i	−0.829133	+	1.77808i
$518$	−1.19372	−	2.55995i	−0.0524492	−	0.112478i
$519$	−10.9342	+	13.0308i	−0.479957	+	0.571990i
$520$		0			0
$521$	37.0114	−	21.3685i	1.62150	−	0.936173i	0.634980	−	0.772529i	$-0.281008\pi$
$521$	37.0114	−	21.3685i	1.62150	−	0.936173i	0.986519	−	0.163644i	$-0.0523249\pi$
$522$	−11.6155	−	16.5887i	−0.508397	−	0.726066i
$523$	11.8819	+	16.9691i	0.519560	+	0.742008i	0.990099	−	0.140371i	$-0.0448294\pi$
$523$	11.8819	+	16.9691i	0.519560	+	0.742008i	−0.470539	+	0.882379i	$0.655941\pi$
$524$	−10.2927	+	5.94249i	−0.449639	+	0.259599i
$525$		0			0
$526$	1.19781	−	1.42749i	0.0522269	−	0.0622416i
$527$	−23.3471	−	50.0680i	−1.01701	−	2.18099i
$528$	−1.59972	+	3.43061i	−0.0696188	+	0.149298i
$529$	12.5125	+	14.9118i	0.544023	+	0.648341i
$530$		0			0
$531$		−	1.68112i		−	0.0729545i
$532$	2.70971	+	2.32096i	0.117481	+	0.100626i
$533$	−9.64138	−	9.64138i	−0.417614	−	0.417614i
$534$	0.306185	+	1.73646i	0.0132499	+	0.0751440i
$535$		0			0
$536$	−9.97057	+	3.62899i	−0.430663	+	0.156748i
$537$	10.2810	−	4.79410i	0.443657	−	0.206881i
$538$	−1.25129	−	14.3023i	−0.0539470	−	0.616617i
$539$	25.5022	+	14.7237i	1.09846	+	0.634194i
$540$		0			0
$541$	−2.96663	+	16.8246i	−0.127545	+	0.723345i	0.852218	+	0.523186i	$0.175257\pi$
$541$	−2.96663	+	16.8246i	−0.127545	+	0.723345i	−0.979764	+	0.200159i	$0.935854\pi$
$542$	6.98865	−	4.89350i	0.300188	−	0.210194i
$543$	4.50630	−	16.8178i	0.193384	−	0.721719i
$544$	−3.57354	+	6.18955i	−0.153214	+	0.265375i
$545$		0			0
$546$	0.658546	−	1.80934i	0.0281832	−	0.0774327i
$547$	7.62478	+	3.55549i	0.326012	+	0.152022i	0.578732	−	0.815517i	$-0.303548\pi$
$547$	7.62478	+	3.55549i	0.326012	+	0.152022i	−0.252721	+	0.967539i	$0.581325\pi$
$548$	−14.8430	−	1.29859i	−0.634061	−	0.0554732i
$549$	−19.6603	+	3.46664i	−0.839080	+	0.147953i
$550$		0			0
$551$	37.6444	−	2.90903i	1.60371	−	0.123929i
$552$	3.74939	−	3.74939i	0.159585	−	0.159585i
$553$	−7.07495	−	4.95394i	−0.300858	−	0.210663i
$554$	−13.0659	+	10.9636i	−0.555116	+	0.465798i
$555$		0			0
$556$	−0.595300	−	0.216671i	−0.0252463	−	0.00918892i
$557$	5.36840	−	0.469674i	0.227466	−	0.0199007i	0.0271472	−	0.999631i	$-0.491358\pi$
$557$	5.36840	−	0.469674i	0.227466	−	0.0199007i	0.200319	+	0.979731i	$0.435802\pi$
$558$	−17.4554	+	4.67716i	−0.738946	+	0.198000i
$559$	5.73752	+	9.93767i	0.242671	+	0.420319i
$560$		0			0
$561$	26.6425	+	4.69779i	1.12485	+	0.198341i
$562$	21.8188	+	5.84632i	0.920369	+	0.246612i
$563$	−6.70696	−	25.0307i	−0.282665	−	1.05492i	−0.950529	−	0.310636i	$-0.899458\pi$
$563$	−6.70696	−	25.0307i	−0.282665	−	1.05492i	0.667864	−	0.744283i	$-0.267209\pi$
$564$	−5.97708	−	5.01537i	−0.251681	−	0.211185i
$565$		0			0
$566$	0.590971	+	1.62368i	0.0248404	+	0.0682483i
$567$	−0.248232	+	2.83731i	−0.0104248	+	0.119156i
$568$	−3.22090	+	4.59992i	−0.135146	+	0.193009i
$569$	−9.47820			−0.397347			−0.198673	−	0.980066i	$-0.563663\pi$
$569$	−9.47820			−0.397347			−0.198673	+	0.980066i	$0.563663\pi$
$570$		0			0
$571$	−26.2053			−1.09666			−0.548328	−	0.836263i	$-0.684735\pi$
$571$	−26.2053			−1.09666			−0.548328	+	0.836263i	$0.684735\pi$
$572$	7.71409	−	11.0169i	0.322542	−	0.460638i
$573$	0.575120	−	6.57365i	0.0240260	−	0.274618i
$574$	−1.32032	−	3.62756i	−0.0551092	−	0.151411i
$575$		0			0
$576$	1.79095	+	1.50279i	0.0746230	+	0.0626161i
$577$	−3.32677	−	12.4157i	−0.138495	−	0.516872i	−0.999959	−	0.00905266i	$-0.997118\pi$
$577$	−3.32677	−	12.4157i	−0.138495	−	0.516872i	0.861464	−	0.507819i	$-0.169548\pi$
$578$	32.9194	+	8.82073i	1.36927	+	0.366894i
$579$	4.73513	+	0.834932i	0.196785	+	0.0346986i
$580$		0			0
$581$	1.89220	+	3.27739i	0.0785017	+	0.135969i
$582$	−3.50748	+	0.939827i	−0.145390	+	0.0389571i
$583$	−26.9633	+	2.35898i	−1.11671	+	0.0976991i
$584$	1.88085	+	0.684573i	0.0778301	+	0.0283278i
$585$		0			0
$586$	−20.4328	+	17.1452i	−0.844072	+	0.708260i
$587$	1.29145	+	0.904282i	0.0533038	+	0.0373237i	0.599925	−	0.800056i	$-0.295197\pi$
$587$	1.29145	+	0.904282i	0.0533038	+	0.0373237i	−0.546621	+	0.837380i	$0.684086\pi$
$588$	−3.64205	+	3.64205i	−0.150195	+	0.150195i
$589$	9.04990	−	32.4543i	0.372894	−	1.33726i
$590$		0			0
$591$	−4.00185	+	0.705634i	−0.164614	+	0.0290259i
$592$	3.43773	+	0.300763i	0.141290	+	0.0123613i
$593$	−10.6963	−	4.98777i	−0.439245	−	0.204823i	0.190399	−	0.981707i	$-0.439022\pi$
$593$	−10.6963	−	4.98777i	−0.439245	−	0.204823i	−0.629645	+	0.776883i	$0.716799\pi$
$594$	6.91065	−	18.9869i	0.283547	−	0.779040i
$595$		0			0
$596$	−10.7648	+	18.6451i	−0.440942	+	0.763733i
$597$	−2.92103	+	10.9014i	−0.119550	+	0.446166i
$598$	−15.4326	+	10.8060i	−0.631085	+	0.441890i
$599$	4.79359	−	27.1858i	0.195861	−	1.11078i	−0.715327	−	0.698790i	$-0.753722\pi$
$599$	4.79359	−	27.1858i	0.195861	−	1.11078i	0.911188	−	0.411992i	$-0.135167\pi$
$600$		0			0
$601$	18.7469	+	10.8235i	0.764701	+	0.441500i	0.830981	−	0.556301i	$-0.187780\pi$
$601$	18.7469	+	10.8235i	0.764701	+	0.441500i	−0.0662799	+	0.997801i	$0.521113\pi$
$602$	0.283155	+	3.23648i	0.0115405	+	0.131909i
$603$	22.4822	−	10.4836i	0.915548	−	0.426927i
$604$	6.69124	−	2.43541i	0.272263	−	0.0990955i
$605$		0			0
$606$	−1.26987	−	7.20179i	−0.0515850	−	0.292553i
$607$	23.0572	+	23.0572i	0.935861	+	0.935861i	0.998064	−	0.0622023i	$-0.0198124\pi$
$607$	23.0572	+	23.0572i	0.935861	+	0.935861i	−0.0622023	+	0.998064i	$0.519812\pi$
$608$	−4.11094	+	1.44921i	−0.166720	+	0.0587732i
$609$		−	5.76897i		−	0.233771i
$610$		0			0
$611$	17.8197	+	21.2367i	0.720909	+	0.859146i
$612$	7.06166	−	15.1438i	0.285451	−	0.612151i
$613$	−8.73854	−	18.7399i	−0.352946	−	0.756896i	0.647038	−	0.762457i	$-0.276007\pi$
$613$	−8.73854	−	18.7399i	−0.352946	−	0.756896i	−0.999985	+	0.00556187i	$0.998230\pi$
$614$	−9.87732	+	11.7713i	−0.398616	+	0.475052i
$615$		0			0
$616$	3.29760	−	1.90387i	0.132864	−	0.0767092i
$617$	−1.06559	−	1.52182i	−0.0428991	−	0.0612663i	0.797130	−	0.603808i	$-0.206351\pi$
$617$	−1.06559	−	1.52182i	−0.0428991	−	0.0612663i	−0.840029	+	0.542542i	$0.817462\pi$
$618$	0.363494	+	0.519124i	0.0146219	+	0.0208822i
$619$	−10.3497	+	5.97542i	−0.415991	+	0.240173i	−0.693361	−	0.720591i	$-0.743871\pi$
$619$	−10.3497	+	5.97542i	−0.415991	+	0.240173i	0.277370	+	0.960763i	$0.410537\pi$
$620$		0			0
$621$	−18.1934	+	21.6821i	−0.730078	+	0.870073i
$622$	−0.768703	−	1.64849i	−0.0308222	−	0.0660984i
$623$	0.749608	−	1.60754i	0.0300324	−	0.0644047i
$624$	1.51208	+	1.80203i	0.0605317	+	0.0721388i
$625$		0			0
$626$		−	28.9810i		−	1.15832i
$627$	10.4770	+	12.7463i	0.418409	+	0.509038i
$628$	2.31858	+	2.31858i	0.0925212	+	0.0925212i
$629$	−4.28279	−	24.2889i	−0.170766	−	0.968462i
$630$		0			0
$631$	−23.5108	+	8.55725i	−0.935952	+	0.340659i	−0.764566	−	0.644545i	$-0.777047\pi$
$631$	−23.5108	+	8.55725i	−0.935952	+	0.340659i	−0.171386	+	0.985204i	$0.554825\pi$
$632$	9.56329	−	4.45944i	0.380407	−	0.177387i
$633$	0.943513	+	10.7844i	0.0375013	+	0.428642i
$634$	27.6107	+	15.9411i	1.09656	+	0.633100i
$635$		0			0
$636$	0.822078	−	4.66224i	0.0325975	−	0.184870i
$637$	14.9908	−	10.4966i	0.593955	−	0.415892i
$638$	10.4293	−	38.9225i	0.412898	−	1.54096i
$639$	6.56427	−	11.3696i	0.259678	−	0.449776i
$640$		0			0
$641$	11.1871	−	30.7363i	0.441864	−	1.21401i	−0.496400	−	0.868094i	$-0.665345\pi$
$641$	11.1871	−	30.7363i	0.441864	−	1.21401i	0.938265	−	0.345919i	$-0.112433\pi$
$642$	8.01096	+	3.73557i	0.316167	+	0.147431i
$643$	−29.1092	−	2.54673i	−1.14796	−	0.100433i	−0.502743	−	0.864436i	$-0.667676\pi$
$643$	−29.1092	−	2.54673i	−1.14796	−	0.100433i	−0.645213	+	0.764003i	$0.723231\pi$
$644$	−5.25290	+	0.926229i	−0.206993	+	0.0364985i
$645$		0			0
$646$	17.6091	+	25.6993i	0.692820	+	1.01112i
$647$	3.93374	−	3.93374i	0.154651	−	0.154651i	−0.625540	−	0.780192i	$-0.715121\pi$
$647$	3.93374	−	3.93374i	0.154651	−	0.154651i	0.780192	+	0.625540i	$0.215121\pi$
$648$	−2.85036	−	1.99584i	−0.111973	−	0.0784041i
$649$	2.56250	−	2.15019i	0.100587	−	0.0844025i
$650$		0			0
$651$	−4.83753	−	1.76072i	−0.189598	−	0.0690079i
$652$	8.37655	−	0.732853i	0.328051	−	0.0287007i
$653$	−9.62375	+	2.57868i	−0.376606	+	0.100911i	−0.442157	−	0.896938i	$-0.645786\pi$
$653$	−9.62375	+	2.57868i	−0.376606	+	0.100911i	0.0655502	+	0.997849i	$0.479120\pi$
$654$	1.95206	+	3.38107i	0.0763316	+	0.132210i
$655$		0			0
$656$	4.64464	+	0.818976i	0.181343	+	0.0319756i
$657$	−4.52004	−	1.21114i	−0.176343	−	0.0472511i
$658$	2.03144	+	7.58144i	0.0791938	+	0.295555i
$659$	−13.8377	−	11.6112i	−0.539041	−	0.452309i	0.332169	−	0.943220i	$-0.392220\pi$
$659$	−13.8377	−	11.6112i	−0.539041	−	0.452309i	−0.871210	+	0.490911i	$0.836664\pi$
$660$		0			0
$661$	0.318689	+	0.875591i	0.0123956	+	0.0340566i	0.945736	−	0.324936i	$-0.105343\pi$
$661$	0.318689	+	0.875591i	0.0123956	+	0.0340566i	−0.933341	+	0.358992i	$0.883120\pi$
$662$	−1.55088	+	17.7267i	−0.0602768	+	0.688966i
$663$	9.64333	−	13.7721i	0.374516	−	0.534864i
$664$	−4.62349			−0.179426
$665$		0			0
$666$	−8.06786			−0.312623
$667$	−32.3764	+	46.2383i	−1.25362	+	1.79035i
$668$	−0.683866	+	7.81662i	−0.0264596	+	0.302434i
$669$	0.683065	+	1.87671i	0.0264088	+	0.0725576i
$670$		0			0
$671$	−30.4301	−	25.5339i	−1.17474	−	0.985723i
$672$	0.172376	+	0.643318i	0.00664957	+	0.0248165i
$673$	−6.83314	−	1.83093i	−0.263398	−	0.0705773i	0.124703	−	0.992194i	$-0.460202\pi$
$673$	−6.83314	−	1.83093i	−0.263398	−	0.0705773i	−0.388101	+	0.921617i	$0.626869\pi$
$674$	7.05529	+	1.24404i	0.271760	+	0.0479186i
$675$		0			0
$676$	2.32097	+	4.02003i	0.0892679	+	0.154617i
$677$	−7.17150	+	1.92160i	−0.275623	+	0.0738530i	−0.393983	−	0.919118i	$-0.628903\pi$
$677$	−7.17150	+	1.92160i	−0.275623	+	0.0738530i	0.118360	+	0.992971i	$0.462236\pi$
$678$	−3.02757	+	0.264878i	−0.116273	+	0.0101726i
$679$	3.43250	+	1.24933i	0.131727	+	0.0479448i
$680$		0			0
$681$	−16.0306	+	13.4513i	−0.614293	+	0.515453i
$682$	−29.4551	−	20.6247i	−1.12790	−	0.789761i
$683$	−19.1159	+	19.1159i	−0.731451	+	0.731451i	−0.970907	−	0.239457i	$-0.923031\pi$
$683$	−19.1159	+	19.1159i	−0.731451	+	0.731451i	0.239457	+	0.970907i	$0.423031\pi$
$684$	9.27918	−	4.21290i	0.354798	−	0.161084i
$685$		0			0
$686$	10.7451	−	1.89465i	0.410249	−	0.0723380i
$687$	1.76600	+	0.154505i	0.0673770	+	0.00589473i
$688$	−3.59730	−	1.67745i	−0.137146	−	0.0639521i
$689$	−5.75298	+	15.8062i	−0.219171	+	0.602168i
$690$		0			0
$691$	−16.1506	+	27.9737i	−0.614398	+	1.06417i	0.376091	+	0.926583i	$0.377268\pi$
$691$	−16.1506	+	27.9737i	−0.614398	+	1.06417i	−0.990490	+	0.137587i	$0.956065\pi$
$692$	−5.41078	+	20.1933i	−0.205687	+	0.767634i
$693$	−7.29226	+	5.10610i	−0.277010	+	0.193965i
$694$	−2.64884	+	15.0223i	−0.100548	+	0.570238i
$695$		0			0
$696$	6.10382	+	3.52404i	0.231365	+	0.133579i
$697$	−2.93782	−	33.5794i	−0.111278	−	1.27191i
$698$	4.64252	−	2.16484i	0.175722	−	0.0819406i
$699$	1.63260	−	0.594218i	0.0617506	−	0.0224754i
$700$		0			0
$701$	−1.28835	−	7.30660i	−0.0486604	−	0.275967i	0.950763	−	0.309919i	$-0.100302\pi$
$701$	−1.28835	−	7.30660i	−0.0486604	−	0.275967i	−0.999423	+	0.0339519i	$0.989191\pi$
$702$	−8.87901	−	8.87901i	−0.335117	−	0.335117i
$703$	7.65273	−	12.9498i	0.288628	−	0.488410i
$704$			4.65201i			0.175329i
$705$		0			0
$706$	−12.3661	−	14.7374i	−0.465405	−	0.554648i
$707$	−3.10893	+	6.66711i	−0.116923	+	0.250743i
$708$	0.247270	+	0.530273i	0.00929299	+	0.0199289i
$709$	14.8898	−	17.7449i	0.559197	−	0.666425i	−0.410179	−	0.912005i	$-0.634534\pi$
$709$	14.8898	−	17.7449i	0.559197	−	0.666425i	0.969376	+	0.245580i	$0.0789783\pi$
$710$		0			0
$711$	−21.3645	+	12.3348i	−0.801231	+	0.462591i
$712$	1.24294	+	1.77510i	0.0465812	+	0.0665248i
$713$	28.8914	+	41.2611i	1.08199	+	1.54524i
$714$	4.12231	−	2.38002i	0.154274	−	0.0890699i
$715$		0			0
$716$	8.96132	−	10.6797i	0.334900	−	0.399119i
$717$	0.0682091	+	0.146275i	0.00254731	+	0.00546273i
$718$	2.59212	−	5.55882i	0.0967372	−	0.207453i
$719$	14.7025	+	17.5217i	0.548309	+	0.653449i	0.967029	−	0.254666i	$-0.0819656\pi$
$719$	14.7025	+	17.5217i	0.548309	+	0.653449i	−0.418720	+	0.908115i	$0.637521\pi$
$720$		0			0
$721$		−	0.637498i		−	0.0237417i
$722$	−2.03956	+	18.8902i	−0.0759047	+	0.703021i
$723$	10.1109	+	10.1109i	0.376030	+	0.376030i
$724$	−3.71569	−	21.0727i	−0.138093	−	0.783162i
$725$		0			0
$726$	8.13637	−	2.96140i	0.301969	−	0.109908i
$727$	7.67045	−	3.57679i	0.284481	−	0.132656i	−0.275140	−	0.961404i	$-0.588724\pi$
$727$	7.67045	−	3.57679i	0.284481	−	0.132656i	0.559622	+	0.828748i	$0.310947\pi$
$728$	−0.206242	−	2.35735i	−0.00764382	−	0.0873693i
$729$	−2.13667	−	1.23361i	−0.0791360	−	0.0456892i
$730$		0			0
$731$	−4.92606	+	27.9371i	−0.182197	+	1.03329i
$732$	5.69151	−	3.98524i	0.210364	−	0.147299i
$733$	−12.0370	+	44.9227i	−0.444597	+	1.65926i	0.272402	+	0.962184i	$0.412182\pi$
$733$	−12.0370	+	44.9227i	−0.444597	+	1.65926i	−0.716999	+	0.697074i	$0.754485\pi$
$734$	3.22903	−	5.59284i	0.119186	−	0.206436i
$735$		0			0
$736$	2.22881	−	6.12360i	0.0821549	−	0.225719i
$737$	44.7353	+	20.8604i	1.64785	+	0.768403i
$738$	−10.9844	−	0.961008i	−0.404340	−	0.0353752i
$739$	12.3267	−	2.17354i	0.453446	−	0.0799548i	0.0577394	−	0.998332i	$-0.481611\pi$
$739$	12.3267	−	2.17354i	0.453446	−	0.0799548i	0.395707	+	0.918377i	$0.370500\pi$
$740$		0			0
$741$	9.93081	−	2.55328i	0.364817	−	0.0937971i
$742$	−3.36745	+	3.36745i	−0.123623	+	0.123623i
$743$	42.5934	+	29.8242i	1.56260	+	1.09415i	0.953642	+	0.300945i	$0.0973020\pi$
$743$	42.5934	+	29.8242i	1.56260	+	1.09415i	0.608960	+	0.793201i	$0.291587\pi$
$744$	4.81797	−	4.04276i	0.176635	−	0.148215i
$745$		0			0
$746$	−4.27273	−	1.55515i	−0.156436	−	0.0569379i
$747$	10.7682	−	0.942098i	0.393989	−	0.0344696i
$748$	32.1154	−	8.60528i	1.17425	−	0.314640i
$749$	−4.44582	−	7.70038i	−0.162447	−	0.281366i
$750$		0			0
$751$	38.0116	+	6.70246i	1.38706	+	0.244576i	0.816816	−	0.576898i	$-0.195737\pi$
$751$	38.0116	+	6.70246i	1.38706	+	0.244576i	0.570245	+	0.821474i	$0.306848\pi$
$752$	−9.26242	−	2.48186i	−0.337766	−	0.0905041i
$753$	2.82888	+	10.5575i	0.103090	+	0.384737i
$754$	−19.1833	−	16.0967i	−0.698615	−	0.586208i
$755$		0			0
$756$	−1.21592	−	3.34072i	−0.0442226	−	0.121501i
$757$	3.13261	−	35.8059i	0.113857	−	1.30139i	−0.697394	−	0.716688i	$-0.745657\pi$
$757$	3.13261	−	35.8059i	0.113857	−	1.30139i	0.811251	−	0.584698i	$-0.198787\pi$
$758$	−13.3061	+	19.0031i	−0.483299	+	0.690222i
$759$	−24.6670			−0.895355
$760$		0			0
$761$	51.3426			1.86117			0.930584	−	0.366079i	$-0.119300\pi$
$761$	51.3426			1.86117			0.930584	+	0.366079i	$0.119300\pi$
$762$	3.37787	−	4.82410i	0.122367	−	0.174759i
$763$	0.342288	−	3.91237i	0.0123917	−	0.141637i
$764$	−2.77370	−	7.62068i	−0.100349	−	0.275706i
$765$		0			0
$766$	−7.04984	−	5.91551i	−0.254721	−	0.213736i
$767$	−0.538045	−	2.00801i	−0.0194277	−	0.0725051i
$768$	−0.785956	−	0.210596i	−0.0283607	−	0.00759924i
$769$	20.0537	+	3.53600i	0.723154	+	0.127512i	0.523098	−	0.852273i	$-0.324776\pi$
$769$	20.0537	+	3.53600i	0.723154	+	0.127512i	0.200056	+	0.979784i	$0.435887\pi$
$770$		0			0
$771$	−6.29144	−	10.8971i	−0.226581	−	0.392449i
$772$	5.70782	−	1.52941i	0.205429	−	0.0550445i
$773$	1.28721	−	0.112617i	0.0462978	−	0.00405054i	−0.0639833	−	0.997951i	$-0.520380\pi$
$773$	1.28721	−	0.112617i	0.0462978	−	0.00405054i	0.110281	+	0.993900i	$0.464825\pi$
$774$	8.72001	+	3.17382i	0.313434	+	0.114081i
$775$		0			0
$776$	−3.41862	+	2.86856i	−0.122721	+	0.102975i
$777$	−1.88267	−	1.31826i	−0.0675404	−	0.0472923i
$778$	22.0971	−	22.0971i	0.792219	−	0.792219i
$779$	11.9617	−	16.7195i	0.428572	−	0.599040i
$780$		0			0
$781$	25.7264	−	4.53625i	0.920561	−	0.162320i
$782$	−46.3974	−	4.05924i	−1.65917	−	0.145158i
$783$	−34.0972	−	15.8998i	−1.21854	−	0.568213i
$784$	−2.16500	+	5.94828i	−0.0773214	+	0.212439i
$785$		0			0
$786$	−4.83530	+	8.37498i	−0.172469	+	0.298726i
$787$	7.86788	−	29.3633i	0.280460	−	1.04669i	−0.671634	−	0.740883i	$-0.734407\pi$
$787$	7.86788	−	29.3633i	0.280460	−	1.04669i	0.952094	−	0.305806i	$-0.0989260\pi$
$788$	−4.09091	+	2.86448i	−0.145733	+	0.102043i
$789$	0.263296	−	1.49323i	0.00937359	−	0.0531603i
$790$		0			0
$791$	2.64761	+	1.52860i	0.0941381	+	0.0543507i
$792$	−0.947909	−	10.8346i	−0.0336825	−	0.384993i
$793$	−22.3737	+	10.4330i	−0.794512	+	0.370487i
$794$	7.50426	−	2.73133i	0.266316	−	0.0969312i
$795$		0			0
$796$	2.40855	+	13.6596i	0.0853687	+	0.484150i
$797$	13.5806	+	13.5806i	0.481049	+	0.481049i	0.905467	−	0.424418i	$-0.139521\pi$
$797$	13.5806	+	13.5806i	0.481049	+	0.481049i	−0.424418	+	0.905467i	$0.639521\pi$
$798$	2.85371	+	0.533086i	0.101020	+	0.0188711i
$799$			68.5345i			2.42458i
$800$		0			0
$801$	−3.25654	−	3.88099i	−0.115064	−	0.137128i
$802$	−8.11682	+	17.4066i	−0.286615	+	0.614647i
$803$	−3.93511	−	8.43887i	−0.138867	−	0.297801i
$804$	−5.54953	+	6.61367i	−0.195717	+	0.233246i
$805$		0			0
$806$	−19.3526	+	11.1732i	−0.681667	+	0.393560i
$807$	−6.70052	−	9.56933i	−0.235869	−	0.336856i
$808$	−5.15497	−	7.36206i	−0.181351	−	0.258996i
$809$	−44.4139	+	25.6424i	−1.56151	+	0.901538i	−0.564406	+	0.825498i	$0.690895\pi$
$809$	−44.4139	+	25.6424i	−1.56151	+	0.901538i	−0.997105	+	0.0760408i	$0.975772\pi$
$810$		0			0
$811$	17.6265	−	21.0064i	0.618949	−	0.737635i	−0.361940	−	0.932201i	$-0.617886\pi$
$811$	17.6265	−	21.0064i	0.618949	−	0.737635i	0.980889	+	0.194566i	$0.0623300\pi$
$812$	−2.99635	−	6.42569i	−0.105151	−	0.225497i
$813$	2.93380	−	6.29157i	0.102893	−	0.220655i
$814$	−10.3190	−	12.2977i	−0.361680	−	0.431033i
$815$		0			0
$816$			5.81544i			0.203581i
$817$	−13.3657	+	10.9860i	−0.467605	+	0.384353i
$818$	−4.70152	−	4.70152i	−0.164385	−	0.164385i
$819$	0.960684	+	5.44831i	0.0335690	+	0.190379i
$820$		0			0
$821$	−43.2143	+	15.7287i	−1.50819	+	0.548936i	−0.958166	−	0.286214i	$-0.907603\pi$
$821$	−43.2143	+	15.7287i	−1.50819	+	0.548936i	−0.550023	+	0.835149i	$0.685381\pi$
$822$	−10.9877	+	5.12366i	−0.383241	+	0.178708i
$823$	0.771373	+	8.81683i	0.0268884	+	0.307336i	0.997716	+	0.0675552i	$0.0215199\pi$
$823$	0.771373	+	8.81683i	0.0268884	+	0.307336i	−0.970827	+	0.239780i	$0.922925\pi$
$824$	0.674501	+	0.389423i	0.0234973	+	0.0135662i
$825$		0			0
$826$	0.102204	−	0.579626i	0.00355612	−	0.0201678i
$827$	26.9905	−	18.8989i	0.938551	−	0.657180i	−0.000850677	−	1.00000i	$-0.500271\pi$
$827$	26.9905	−	18.8989i	0.938551	−	0.657180i	0.939401	+	0.342819i	$0.111382\pi$
$828$	−3.94318	+	14.7162i	−0.137035	+	0.511422i
$829$	−9.65812	+	16.7284i	−0.335440	+	0.581000i	−0.983569	−	0.180531i	$-0.942218\pi$
$829$	−9.65812	+	16.7284i	−0.335440	+	0.581000i	0.648129	+	0.761531i	$0.275552\pi$
$830$		0			0
$831$	−4.74669	+	13.0414i	−0.164661	+	0.452402i
$832$	2.62017	+	1.22180i	0.0908379	+	0.0423584i
$833$	45.0691	+	3.94303i	1.56155	+	0.136618i
$834$	−0.507640	+	0.0895107i	−0.0175781	+	0.00309950i
$835$		0			0
$836$	18.2899	+	8.75566i	0.632570	+	0.302821i
$837$	−23.7393	+	23.7393i	−0.820550	+	0.820550i
$838$	−19.3988	−	13.5832i	−0.670120	−	0.469223i
$839$	−22.7167	+	19.0616i	−0.784268	+	0.658079i	−0.944320	−	0.329030i	$-0.893278\pi$
$839$	−22.7167	+	19.0616i	−0.784268	+	0.658079i	0.160052	+	0.987109i	$0.448834\pi$
$840$		0			0
$841$	−43.2538	−	15.7431i	−1.49151	−	0.542865i
$842$	−1.00955	+	0.0883238i	−0.0347912	+	0.00304384i
$843$	17.7535	−	4.75704i	0.611464	−	0.163841i
$844$	6.65223	+	11.5220i	0.228979	+	0.396604i
$845$		0			0
$846$	22.0781	+	3.89297i	0.759062	+	0.133843i
$847$	−8.41320	−	2.25431i	−0.289081	−	0.0774590i
$848$	−1.50586	−	5.61995i	−0.0517114	−	0.192990i
$849$	1.07702	+	0.903725i	0.0369631	+	0.0310158i
$850$		0			0
$851$	7.69131	+	21.1317i	0.263655	+	0.724386i
$852$	−0.398232	+	4.55182i	−0.0136432	+	0.155943i
$853$	11.4446	−	16.3446i	0.391855	−	0.559627i	−0.573952	−	0.818889i	$-0.694590\pi$
$853$	11.4446	−	16.3446i	0.391855	−	0.559627i	0.965807	+	0.259262i	$0.0834792\pi$
$854$	−6.98933			−0.239170
$855$		0			0
$856$	10.8631			0.371294
$857$	−32.1099	+	45.8577i	−1.09685	+	1.56647i	−0.308521	+	0.951218i	$0.599834\pi$
$857$	−32.1099	+	45.8577i	−1.09685	+	1.56647i	−0.788332	+	0.615250i	$0.789055\pi$
$858$	0.953771	−	10.9017i	0.0325612	−	0.372176i
$859$	1.56085	+	4.28839i	0.0532554	+	0.146318i	0.963468	−	0.267823i	$-0.0863042\pi$
$859$	1.56085	+	4.28839i	0.0532554	+	0.146318i	−0.910213	+	0.414141i	$0.864082\pi$
$860$		0			0
$861$	−2.40623	−	2.01906i	−0.0820040	−	0.0688095i
$862$	6.90868	+	25.7835i	0.235311	+	0.878191i
$863$	3.33461	+	0.893507i	0.113512	+	0.0304153i	0.315128	−	0.949049i	$-0.397953\pi$
$863$	3.33461	+	0.893507i	0.113512	+	0.0304153i	−0.201616	+	0.979465i	$0.564619\pi$
$864$	4.27738	+	0.754218i	0.145520	+	0.0256590i
$865$		0			0
$866$	13.6152	+	23.5822i	0.462662	+	0.801354i
$867$	26.7859	−	7.17727i	0.909697	−	0.243753i
$868$	−6.30271	+	0.551416i	−0.213928	+	0.0187163i
$869$	−46.1273	−	16.7890i	−1.56476	−	0.569527i
$870$		0			0
$871$	23.4985	−	19.7176i	0.796218	−	0.668106i
$872$	3.93037	+	2.75207i	0.133099	+	0.0931969i
$873$	7.37755	−	7.37755i	0.249692	−	0.249692i
$874$	−19.8807	−	20.2882i	−0.672476	−	0.686258i
$875$		0			0
$876$	1.60389	−	0.282809i	0.0541904	−	0.00955522i
$877$	−3.57559	−	0.312824i	−0.120739	−	0.0105633i	0.0266259	−	0.999645i	$-0.491524\pi$
$877$	−3.57559	−	0.312824i	−0.120739	−	0.0105633i	−0.147365	+	0.989082i	$0.547079\pi$
$878$	0.408244	+	0.190367i	0.0137776	+	0.00642458i
$879$	−7.42302	+	20.3946i	−0.250372	+	0.687892i
$880$		0			0
$881$	9.00382	−	15.5951i	0.303346	−	0.525412i	−0.673545	−	0.739146i	$-0.735229\pi$
$881$	9.00382	−	15.5951i	0.303346	−	0.525412i	0.976892	+	0.213734i	$0.0685627\pi$
$882$	3.83029	−	14.2949i	0.128973	−	0.481333i
$883$	−45.0588	+	31.5505i	−1.51635	+	1.06176i	−0.541017	+	0.841011i	$0.681961\pi$
$883$	−45.0588	+	31.5505i	−1.51635	+	1.06176i	−0.975331	+	0.220747i	$0.929150\pi$
$884$	3.58799	−	20.3485i	0.120677	−	0.684395i
$885$		0			0
$886$	−4.09889	−	2.36649i	−0.137705	−	0.0795039i
$887$	0.520732	+	5.95199i	0.0174845	+	0.199848i	0.999913	+	0.0132079i	$0.00420434\pi$
$887$	0.520732	+	5.95199i	0.0174845	+	0.199848i	−0.982428	+	0.186640i	$0.940240\pi$
$888$	2.54483	−	1.18667i	0.0853988	−	0.0398221i
$889$	−5.56686	+	2.02617i	−0.186706	+	0.0679556i
$890$		0			0
$891$	2.81090	+	15.9414i	0.0941688	+	0.534058i
$892$	1.73556	+	1.73556i	0.0581110	+	0.0581110i
$893$	−27.1908	+	31.7451i	−0.909904	+	1.06231i
$894$			17.5182i			0.585895i
$895$		0			0
$896$	0.526132	+	0.627020i	0.0175768	+	0.0209473i
$897$	−6.47853	+	13.8933i	−0.216312	+	0.463882i
$898$	−14.0706	−	30.1746i	−0.469543	−	1.00694i
$899$	−43.0368	+	51.2893i	−1.43536	+	1.71059i
$900$		0			0
$901$	−36.0120	+	20.7915i	−1.19973	+	0.692667i
$902$	−12.5844	−	17.9724i	−0.419015	−	0.598416i
$903$	1.51626	+	2.16545i	0.0504580	+	0.0720615i
$904$	−3.23465	+	1.86752i	−0.107583	+	0.0621129i
$905$		0			0
$906$	3.72428	−	4.43843i	0.123731	−	0.147457i
$907$	−22.0096	−	47.1998i	−0.730818	−	1.56724i	−0.820744	−	0.571296i	$-0.806441\pi$
$907$	−22.0096	−	47.1998i	−0.730818	−	1.56724i	0.0899257	−	0.995948i	$-0.471337\pi$
$908$	−10.8690	+	23.3086i	−0.360700	+	0.773524i
$909$	13.5062	+	16.0960i	0.447971	+	0.533872i
$910$		0			0
$911$		−	35.0790i		−	1.16222i	−0.813825	−	0.581110i	$-0.802619\pi$
$911$		−	35.0790i		−	1.16222i	0.813825	−	0.581110i	$-0.197381\pi$
$912$	−2.30725	+	2.69371i	−0.0764007	+	0.0891976i
$913$	15.2088	+	15.2088i	0.503339	+	0.503339i
$914$	−2.07613	−	11.7743i	−0.0686724	−	0.389460i
$915$		0			0
$916$	2.04728	−	0.745149i	0.0676441	−	0.0246204i
$917$	8.81661	−	4.11125i	0.291150	−	0.135766i
$918$	−2.70552	−	30.9243i	−0.0892955	−	1.02065i
$919$	−30.7720	−	17.7662i	−1.01508	−	0.586054i	−0.102402	−	0.994743i	$-0.532653\pi$
$919$	−30.7720	−	17.7662i	−1.01508	−	0.586054i	−0.912674	+	0.408689i	$0.865986\pi$
$920$		0			0
$921$	−2.17118	+	12.3134i	−0.0715429	+	0.405740i
$922$	−18.4140	+	12.8936i	−0.606432	+	0.424628i
$923$	4.20180	−	15.6813i	0.138304	−	0.516157i
$924$	1.54915	−	2.68320i	0.0509632	−	0.0882708i
$925$		0			0
$926$	−8.42884	+	23.1581i	−0.276989	+	0.761021i
$927$	−1.65028	−	0.769538i	−0.0542023	−	0.0252749i
$928$	8.62901	+	0.754940i	0.283261	+	0.0247821i
$929$	−6.70840	+	1.18287i	−0.220096	+	0.0388088i	−0.282608	−	0.959235i	$-0.591200\pi$
$929$	−6.70840	+	1.18287i	−0.220096	+	0.0388088i	0.0625128	+	0.998044i	$0.480089\pi$
$930$		0			0
$931$	19.3116	+	19.7074i	0.632911	+	0.645883i
$932$	1.50982	−	1.50982i	0.0494557	−	0.0494557i
$933$	−1.21235	−	0.848899i	−0.0396907	−	0.0277917i
$934$	17.3131	−	14.5274i	0.566502	−	0.475352i
$935$		0			0
$936$	−6.35139	−	2.31172i	−0.207602	−	0.0755608i
$937$	−24.1919	+	2.11652i	−0.790316	+	0.0691437i	−0.475164	−	0.879897i	$-0.657611\pi$
$937$	−24.1919	+	2.11652i	−0.790316	+	0.0691437i	−0.315152	+	0.949041i	$0.602056\pi$
$938$	8.38890	−	2.24780i	0.273907	−	0.0733932i
$939$	−11.7907	−	20.4220i	−0.384774	−	0.666448i
$940$		0			0
$941$	11.1946	+	1.97392i	0.364935	+	0.0643479i	0.353109	−	0.935582i	$-0.385125\pi$
$941$	11.1946	+	1.97392i	0.364935	+	0.0643479i	0.0118259	+	0.999930i	$0.496236\pi$
$942$	2.57712	+	0.690537i	0.0839671	+	0.0224989i
$943$	7.95459	+	29.6870i	0.259037	+	0.966740i
$944$	0.550837	+	0.462207i	0.0179282	+	0.0150436i
$945$		0			0
$946$	6.31529	+	17.3511i	0.205328	+	0.564133i
$947$	4.80850	−	54.9614i	0.156255	−	1.78601i	−0.363403	−	0.931632i	$-0.618385\pi$
$947$	4.80850	−	54.9614i	0.156255	−	1.78601i	0.519658	−	0.854374i	$-0.326059\pi$
$948$	4.92468	−	7.03317i	0.159946	−	0.228427i
$949$	−5.78657			−0.187840
$950$		0			0
$951$	25.9419			0.841223
$952$	3.35542	−	4.79204i	0.108750	−	0.155311i
$953$	−0.440341	+	5.03312i	−0.0142640	+	0.163039i	−0.999986	−	0.00534415i	$-0.998299\pi$
$953$	−0.440341	+	5.03312i	−0.0142640	+	0.163039i	0.985722	+	0.168383i	$0.0538545\pi$
$954$	4.65233	+	12.7822i	0.150625	+	0.413838i
$955$		0			0
$956$	0.151947	+	0.127499i	0.00491433	+	0.00412361i
$957$	−8.48610	−	31.6705i	−0.274317	−	1.02376i
$958$	−11.4706	−	3.07353i	−0.370597	−	0.0993013i
$959$	12.0104	+	2.11775i	0.387835	+	0.0683857i
$960$		0			0
$961$	14.3732	+	24.8951i	0.463652	+	0.803068i
$962$	−9.63662	+	2.58213i	−0.310697	+	0.0832511i
$963$	−25.3005	+	2.21350i	−0.815296	+	0.0713292i
$964$	16.5134	+	6.01040i	0.531862	+	0.193582i
$965$		0			0
$966$	−3.32473	+	2.78978i	−0.106971	+	0.0897597i
$967$	25.4812	+	17.8421i	0.819419	+	0.573763i	0.906387	−	0.422448i	$-0.138829\pi$
$967$	25.4812	+	17.8421i	0.819419	+	0.573763i	−0.0869682	+	0.996211i	$0.527718\pi$
$968$	7.52446	−	7.52446i	0.241845	−	0.241845i
$969$	22.8641	+	10.9454i	0.734500	+	0.351617i
$970$		0			0
$971$	−2.15886	+	0.380665i	−0.0692811	+	0.0122161i	−0.208181	−	0.978090i	$-0.566754\pi$
$971$	−2.15886	+	0.380665i	−0.0692811	+	0.0122161i	0.138900	+	0.990306i	$0.455643\pi$
$972$	−15.8011	−	1.38241i	−0.506820	−	0.0443410i
$973$	0.469951	+	0.219142i	0.0150660	+	0.00702537i
$974$	−5.96083	+	16.3773i	−0.190997	+	0.524761i
$975$		0			0
$976$	4.26951	−	7.39501i	0.136664	−	0.236709i
$977$	−4.04465	+	15.0949i	−0.129400	+	0.482927i	−0.999958	−	0.00913806i	$-0.997091\pi$
$977$	−4.04465	+	15.0949i	−0.129400	+	0.482927i	0.870558	+	0.492065i	$0.163758\pi$
$978$	5.60454	−	3.92434i	0.179213	−	0.125487i
$979$	1.75053	−	9.92775i	0.0559472	−	0.317292i
$980$		0			0
$981$	−9.71469	−	5.60878i	−0.310166	−	0.179075i
$982$	−2.34584	−	26.8131i	−0.0748587	−	0.855639i
$983$	10.6919	−	4.98570i	0.341018	−	0.159019i	−0.244563	−	0.969633i	$-0.578644\pi$
$983$	10.6919	−	4.98570i	0.341018	−	0.159019i	0.585580	+	0.810614i	$0.300867\pi$
$984$	3.60613	−	1.31252i	0.114959	−	0.0418417i
$985$		0			0
$986$	−10.7502	−	60.9672i	−0.342355	−	1.94159i
$987$	4.51593	+	4.51593i	0.143744	+	0.143744i
$988$	9.73514	−	8.00190i	0.309716	−	0.254574i
$989$		−	25.8656i		−	0.822477i
$990$		0			0
$991$	1.35363	+	1.61320i	0.0429996	+	0.0512449i	0.787116	−	0.616806i	$-0.211573\pi$
$991$	1.35363	+	1.61320i	0.0429996	+	0.0512449i	−0.744116	+	0.668050i	$0.767129\pi$
$992$	3.26666	−	7.00538i	0.103717	−	0.222421i
$993$	6.11907	+	13.1224i	0.194183	+	0.416427i
$994$	2.95448	−	3.52101i	0.0937104	−	0.111680i
$995$		0			0
$996$	−3.25803	+	1.88103i	−0.103235	+	0.0596026i
$997$	6.31453	+	9.01808i	0.199983	+	0.285605i	0.906600	−	0.421991i	$-0.138669\pi$
$997$	6.31453	+	9.01808i	0.199983	+	0.285605i	−0.706617	+	0.707596i	$0.749780\pi$
$998$	16.0606	+	22.9369i	0.508390	+	0.726056i
$999$	−12.9803	+	7.49419i	−0.410679	+	0.237106i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.bb.e.143.9		120
5.2	odd	4	inner	950.2.bb.e.257.7		120
5.3	odd	4		190.2.r.a.67.4	✓	120
5.4	even	2		190.2.r.a.143.2	yes	120
19.2	odd	18	inner	950.2.bb.e.743.7		120
95.2	even	36	inner	950.2.bb.e.857.9		120
95.59	odd	18		190.2.r.a.173.4	yes	120
95.78	even	36		190.2.r.a.97.2	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.r.a.67.4	✓	120	5.3	odd	4
190.2.r.a.97.2	yes	120	95.78	even	36
190.2.r.a.143.2	yes	120	5.4	even	2
190.2.r.a.173.4	yes	120	95.59	odd	18
950.2.bb.e.143.9		120	1.1	even	1	trivial
950.2.bb.e.257.7		120	5.2	odd	4	inner
950.2.bb.e.743.7		120	19.2	odd	18	inner
950.2.bb.e.857.9		120	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)

\(f(q)\)	\(=\)	\(q+(0.573576 - 0.819152i) q^{2} +(0.0709170 - 0.810585i) q^{3} +(-0.342020 - 0.939693i) q^{4} +(-0.623316 - 0.523024i) q^{6} +(0.211848 + 0.790626i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(2.30240 + 0.405976i) q^{9} +O(q^{10})\)	\(q+(0.573576 - 0.819152i) q^{2} +(0.0709170 - 0.810585i) q^{3} +(-0.342020 - 0.939693i) q^{4} +(-0.623316 - 0.523024i) q^{6} +(0.211848 + 0.790626i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(2.30240 + 0.405976i) q^{9} +(2.32600 + 4.02876i) q^{11} +(-0.785956 + 0.210596i) q^{12} +(2.88003 - 0.251970i) q^{13} +(0.769154 + 0.279949i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(5.85454 + 4.09939i) q^{17} +(1.65316 - 1.65316i) q^{18} +(1.08540 + 4.22160i) q^{19} +(0.655893 - 0.115652i) q^{21} +(4.63431 + 0.405449i) q^{22} +(-5.90604 - 2.75403i) q^{23} +(-0.278296 + 0.764611i) q^{24} +(1.44552 - 2.50371i) q^{26} +(1.12415 - 4.19537i) q^{27} +(0.670489 - 0.469482i) q^{28} +(1.50414 - 8.53038i) q^{29} +(-6.69401 - 3.86479i) q^{31} +(0.0871557 + 0.996195i) q^{32} +(3.43061 - 1.59972i) q^{33} +(6.71605 - 2.44444i) q^{34} +(-0.405976 - 2.30240i) q^{36} +(-2.44013 - 2.44013i) q^{37} +(4.08069 + 1.53230i) q^{38} -2.35238i q^{39} +(-3.03158 - 3.61289i) q^{41} +(0.281469 - 0.603611i) q^{42} +(1.67745 + 3.59730i) q^{43} +(2.99025 - 3.56365i) q^{44} +(-5.64354 + 3.25830i) q^{46} +(5.50012 + 7.85498i) q^{47} +(0.466709 + 0.666529i) q^{48} +(5.48197 - 3.16502i) q^{49} +(3.73810 - 4.45489i) q^{51} +(-1.22180 - 2.62017i) q^{52} +(-2.45888 + 5.27308i) q^{53} +(-2.79186 - 3.32721i) q^{54} -0.818516i q^{56} +(3.49894 - 0.580428i) q^{57} +(-6.12494 - 6.12494i) q^{58} +(-0.124865 - 0.708143i) q^{59} +(-8.02406 + 2.92052i) q^{61} +(-7.00538 + 3.26666i) q^{62} +(0.166784 + 1.90634i) q^{63} +(0.866025 + 0.500000i) q^{64} +(0.657303 - 3.72775i) q^{66} +(8.69157 - 6.08591i) q^{67} +(1.84980 - 6.90354i) q^{68} +(-2.65122 + 4.59204i) q^{69} +(1.92060 - 5.27682i) q^{71} +(-2.11888 - 0.988049i) q^{72} +(-1.99394 - 0.174447i) q^{73} +(-3.39844 + 0.599237i) q^{74} +(3.59578 - 2.46382i) q^{76} +(-2.69248 + 2.69248i) q^{77} +(-1.92696 - 1.34927i) q^{78} +(-8.08325 + 6.78265i) q^{79} +(3.26980 + 1.19011i) q^{81} +(-4.69835 + 0.411052i) q^{82} +(4.46595 - 1.19665i) q^{83} +(-0.333006 - 0.576783i) q^{84} +(3.90888 + 0.689241i) q^{86} +(-6.80793 - 1.82418i) q^{87} +(-1.20403 - 4.49350i) q^{88} +(-1.66002 - 1.39292i) q^{89} +(0.809342 + 2.22365i) q^{91} +(-0.567959 + 6.49180i) q^{92} +(-3.60746 + 5.15199i) q^{93} +9.58917 q^{94} +0.813682 q^{96} +(2.55970 - 3.65562i) q^{97} +(0.551699 - 6.30594i) q^{98} +(3.71982 + 10.2201i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{7}+O(q^{10}) \) 120 * q + 12 * q^7	\( 120 q + 12 q^{7} - 36 q^{17} - 96 q^{21} - 24 q^{22} - 12 q^{26} + 96 q^{33} - 12 q^{41} + 72 q^{43} + 24 q^{47} + 24 q^{51} - 36 q^{53} - 84 q^{57} + 48 q^{61} + 24 q^{62} - 36 q^{63} - 24 q^{66} + 96 q^{67} + 12 q^{68} + 36 q^{73} + 12 q^{76} - 96 q^{78} + 144 q^{81} - 48 q^{82} - 24 q^{83} + 48 q^{86} - 72 q^{87} + 72 q^{91} - 72 q^{92} - 156 q^{93} - 120 q^{97} - 24 q^{98}+O(q^{100}) \) 120 * q + 12 * q^7 - 36 * q^17 - 96 * q^21 - 24 * q^22 - 12 * q^26 + 96 * q^33 - 12 * q^41 + 72 * q^43 + 24 * q^47 + 24 * q^51 - 36 * q^53 - 84 * q^57 + 48 * q^61 + 24 * q^62 - 36 * q^63 - 24 * q^66 + 96 * q^67 + 12 * q^68 + 36 * q^73 + 12 * q^76 - 96 * q^78 + 144 * q^81 - 48 * q^82 - 24 * q^83 + 48 * q^86 - 72 * q^87 + 72 * q^91 - 72 * q^92 - 156 * q^93 - 120 * q^97 - 24 * q^98

Introduction

L-functions

Modular forms

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