LMFDB - Embedded newform 190.2.r.a.143.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [190,2,Mod(3,190)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(190, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([27, 26]))

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

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

chi := DirichletCharacter("190.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 190 = 2 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	190.r (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:	$1.51715763840$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$10$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			143.2
Character	$\chi$	$=$	190.143
Dual form			190.2.r.a.97.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.573576 + 0.819152i) q^{2} +(-0.0709170 + 0.810585i) q^{3} +(-0.342020 - 0.939693i) q^{4} +(2.23567 + 0.0422352i) q^{5} +(-0.623316 - 0.523024i) q^{6} +(-0.211848 - 0.790626i) q^{7} +(0.965926 + 0.258819i) q^{8} +(2.30240 + 0.405976i) q^{9} +O(q^{10})$	\(q+(-0.573576 + 0.819152i) q^{2} +(-0.0709170 + 0.810585i) q^{3} +(-0.342020 - 0.939693i) q^{4} +(2.23567 + 0.0422352i) q^{5} +(-0.623316 - 0.523024i) q^{6} +(-0.211848 - 0.790626i) q^{7} +(0.965926 + 0.258819i) q^{8} +(2.30240 + 0.405976i) q^{9} +(-1.31692 + 1.80713i) q^{10} +(2.32600 + 4.02876i) q^{11} +(0.785956 - 0.210596i) q^{12} +(-2.88003 + 0.251970i) q^{13} +(0.769154 + 0.279949i) q^{14} +(-0.192782 + 1.80921i) q^{15} +(-0.766044 + 0.642788i) q^{16} +(-5.85454 - 4.09939i) q^{17} +(-1.65316 + 1.65316i) q^{18} +(1.08540 + 4.22160i) q^{19} +(-0.724956 - 2.11529i) q^{20} +(0.655893 - 0.115652i) q^{21} +(-4.63431 - 0.405449i) q^{22} +(5.90604 + 2.75403i) q^{23} +(-0.278296 + 0.764611i) q^{24} +(4.99643 + 0.188848i) q^{25} +(1.44552 - 2.50371i) q^{26} +(-1.12415 + 4.19537i) q^{27} +(-0.670489 + 0.469482i) q^{28} +(1.50414 - 8.53038i) q^{29} +(-1.37144 - 1.19564i) q^{30} +(-6.69401 - 3.86479i) q^{31} +(-0.0871557 - 0.996195i) q^{32} +(-3.43061 + 1.59972i) q^{33} +(6.71605 - 2.44444i) q^{34} +(-0.440229 - 1.77653i) q^{35} +(-0.405976 - 2.30240i) q^{36} +(2.44013 + 2.44013i) q^{37} +(-4.08069 - 1.53230i) q^{38} -2.35238i q^{39} +(2.14856 + 0.619430i) q^{40} +(-3.03158 - 3.61289i) q^{41} +(-0.281469 + 0.603611i) q^{42} +(-1.67745 - 3.59730i) q^{43} +(2.99025 - 3.56365i) q^{44} +(5.13027 + 1.00487i) q^{45} +(-5.64354 + 3.25830i) q^{46} +(-5.50012 - 7.85498i) q^{47} +(-0.466709 - 0.666529i) q^{48} +(5.48197 - 3.16502i) q^{49} +(-3.02053 + 3.98452i) q^{50} +(3.73810 - 4.45489i) q^{51} +(1.22180 + 2.62017i) q^{52} +(2.45888 - 5.27308i) q^{53} +(-2.79186 - 3.32721i) q^{54} +(5.03002 + 9.10521i) q^{55} -0.818516i q^{56} +(-3.49894 + 0.580428i) q^{57} +(6.12494 + 6.12494i) q^{58} +(-0.124865 - 0.708143i) q^{59} +(1.76603 - 0.437629i) q^{60} +(-8.02406 + 2.92052i) q^{61} +(7.00538 - 3.26666i) q^{62} +(-0.166784 - 1.90634i) q^{63} +(0.866025 + 0.500000i) q^{64} +(-6.44944 + 0.441683i) q^{65} +(0.657303 - 3.72775i) q^{66} +(-8.69157 + 6.08591i) q^{67} +(-1.84980 + 6.90354i) q^{68} +(-2.65122 + 4.59204i) q^{69} +(1.70775 + 0.658359i) q^{70} +(1.92060 - 5.27682i) q^{71} +(2.11888 + 0.988049i) q^{72} +(1.99394 + 0.174447i) q^{73} +(-3.39844 + 0.599237i) q^{74} +(-0.507409 + 4.03664i) q^{75} +(3.59578 - 2.46382i) q^{76} +(2.69248 - 2.69248i) q^{77} +(1.92696 + 1.34927i) q^{78} +(-8.08325 + 6.78265i) q^{79} +(-1.73977 + 1.40471i) q^{80} +(3.26980 + 1.19011i) q^{81} +(4.69835 - 0.411052i) q^{82} +(-4.46595 + 1.19665i) q^{83} +(-0.333006 - 0.576783i) q^{84} +(-12.9157 - 9.41216i) q^{85} +(3.90888 + 0.689241i) q^{86} +(6.80793 + 1.82418i) q^{87} +(1.20403 + 4.49350i) q^{88} +(-1.66002 - 1.39292i) q^{89} +(-3.76574 + 3.62610i) q^{90} +(0.809342 + 2.22365i) q^{91} +(0.567959 - 6.49180i) q^{92} +(3.60746 - 5.15199i) q^{93} +9.58917 q^{94} +(2.24830 + 9.48394i) q^{95} +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^{15} + 36 q^{17} - 96 q^{21} + 24 q^{22} - 24 q^{25} - 12 q^{26} - 96 q^{33} + 36 q^{35} - 12 q^{41} - 72 q^{43} - 36 q^{45} - 24 q^{47} - 144 q^{50} + 24 q^{51} + 36 q^{53} - 72 q^{55} + 84 q^{57} - 24 q^{60} + 48 q^{61} - 24 q^{62} + 36 q^{63} - 180 q^{65} - 24 q^{66} - 96 q^{67} - 12 q^{68} - 48 q^{70} - 36 q^{73} + 12 q^{76} + 96 q^{78} + 144 q^{81} + 48 q^{82} + 24 q^{83} + 48 q^{85} + 48 q^{86} + 72 q^{87} + 168 q^{90} + 72 q^{91} + 72 q^{92} + 156 q^{93} + 24 q^{95} + 120 q^{97} + 24 q^{98}+O(q^{100}) $ 120 * q - 12 * q^7 - 36 * q^15 + 36 * q^17 - 96 * q^21 + 24 * q^22 - 24 * q^25 - 12 * q^26 - 96 * q^33 + 36 * q^35 - 12 * q^41 - 72 * q^43 - 36 * q^45 - 24 * q^47 - 144 * q^50 + 24 * q^51 + 36 * q^53 - 72 * q^55 + 84 * q^57 - 24 * q^60 + 48 * q^61 - 24 * q^62 + 36 * q^63 - 180 * q^65 - 24 * q^66 - 96 * q^67 - 12 * q^68 - 48 * q^70 - 36 * q^73 + 12 * q^76 + 96 * q^78 + 144 * q^81 + 48 * q^82 + 24 * q^83 + 48 * q^85 + 48 * q^86 + 72 * q^87 + 168 * q^90 + 72 * q^91 + 72 * q^92 + 156 * q^93 + 24 * q^95 + 120 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/190\mathbb{Z}\right)^\times$.

$n$	$21$	$77$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.573576	+	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	$0.103251\pi$
$3$	−0.0709170	+	0.810585i	−0.0409440	+	0.467992i	−0.988795	+	0.149279i	$0.952305\pi$
$4$	−0.342020	−	0.939693i	−0.171010	−	0.469846i
$5$	2.23567	+	0.0422352i	0.999822	+	0.0188881i
$5$	2.23567	+	0.0422352i	0.999822	+	0.0188881i
$6$	−0.623316	−	0.523024i	−0.254468	−	0.213524i
$7$	−0.211848	−	0.790626i	−0.0800708	−	0.298828i	0.914264	−	0.405118i	$-0.132770\pi$
$7$	−0.211848	−	0.790626i	−0.0800708	−	0.298828i	−0.994335	+	0.106290i	$0.966103\pi$
$8$	0.965926	+	0.258819i	0.341506	+	0.0915064i
$9$	2.30240	+	0.405976i	0.767468	+	0.135325i
$10$	−1.31692	+	1.80713i	−0.416448	+	0.571464i
$11$	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	−0.479233	−	0.877688i	$-0.659085\pi$
$13$	−2.88003	+	0.251970i	−0.798777	+	0.0698839i	−0.319544	+	0.947572i	$0.603530\pi$
$14$	0.769154	+	0.279949i	0.205565	+	0.0748195i
$15$	−0.192782	+	1.80921i	−0.0497762	+	0.467135i
$16$	−0.766044	+	0.642788i	−0.191511	+	0.160697i
$17$	−5.85454	−	4.09939i	−1.41993	−	0.994249i	−0.996074	−	0.0885215i	$-0.971786\pi$
$17$	−5.85454	−	4.09939i	−1.41993	−	0.994249i	−0.423860	−	0.905727i	$-0.639325\pi$
$18$	−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
$20$	−0.724956	−	2.11529i	−0.162105	−	0.472993i
$21$	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	0.925850	−	0.377890i	$-0.123350\pi$
$23$	5.90604	+	2.75403i	1.23149	+	0.574255i	0.305644	+	0.952146i	$0.401128\pi$
$24$	−0.278296	+	0.764611i	−0.0568068	+	0.156075i
$25$	4.99643	+	0.188848i	0.999286	+	0.0377695i
$26$	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	$-0.241874\pi$
$30$	−1.37144	−	1.19564i	−0.250389	−	0.218292i
$31$	−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
$35$	−0.440229	−	1.77653i	−0.0744122	−	0.300288i
$36$	−0.405976	−	2.30240i	−0.0676627	−	0.383734i
$37$	2.44013	+	2.44013i	0.401155	+	0.401155i	0.878640	−	0.477485i	$-0.158451\pi$
$37$	2.44013	+	2.44013i	0.401155	+	0.401155i	−0.477485	+	0.878640i	$0.658451\pi$
$38$	−4.08069	−	1.53230i	−0.661976	−	0.248572i
$39$		−	2.35238i		−	0.376682i
$40$	2.14856	+	0.619430i	0.339717	+	0.0979404i
$41$	−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	0.735900	−	0.677090i	$-0.236759\pi$
$43$	−1.67745	−	3.59730i	−0.255809	−	0.548583i	−0.991709	+	0.128507i	$0.958982\pi$
$44$	2.99025	−	3.56365i	0.450798	−	0.537240i
$45$	5.13027	+	1.00487i	0.764775	+	0.149797i
$46$	−5.64354	+	3.25830i	−0.832094	+	0.480410i
$47$	−5.50012	−	7.85498i	−0.802275	−	1.14577i	−0.986641	−	0.162910i	$-0.947912\pi$
$47$	−5.50012	−	7.85498i	−0.802275	−	1.14577i	0.184366	−	0.982858i	$-0.440977\pi$
$48$	−0.466709	−	0.666529i	−0.0673636	−	0.0962052i
$49$	5.48197	−	3.16502i	0.783138	−	0.452145i
$50$	−3.02053	+	3.98452i	−0.427168	+	0.563496i
$51$	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	−0.661928	−	0.749567i	$-0.730262\pi$
$53$	2.45888	−	5.27308i	0.337753	−	0.724313i	0.999681	+	0.0252542i	$0.00803951\pi$
$54$	−2.79186	−	3.32721i	−0.379925	−	0.452776i
$55$	5.03002	+	9.10521i	0.678248	+	1.22775i
$56$		−	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	$0.959349\pi$
$60$	1.76603	−	0.437629i	0.227994	−	0.0564976i
$61$	−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
$65$	−6.44944	+	0.441683i	−0.799954	+	0.0547840i
$66$	0.657303	−	3.72775i	0.0809084	−	0.458854i
$67$	−8.69157	+	6.08591i	−1.06184	+	0.743512i	−0.967715	−	0.252048i	$-0.918896\pi$
$67$	−8.69157	+	6.08591i	−1.06184	+	0.743512i	−0.0941302	+	0.995560i	$0.530007\pi$
$68$	−1.84980	+	6.90354i	−0.224321	+	0.837178i
$69$	−2.65122	+	4.59204i	−0.319169	+	0.552817i
$70$	1.70775	+	0.658359i	0.204115	+	0.0786889i
$71$	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	0.203242	−	0.979128i	$-0.434852\pi$
$73$	1.99394	+	0.174447i	0.233373	+	0.0204175i	0.0301308	+	0.999546i	$0.490408\pi$
$74$	−3.39844	+	0.599237i	−0.395061	+	0.0696598i
$75$	−0.507409	+	4.03664i	−0.0585906	+	0.466111i
$76$	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	$0.480069\pi$
$80$	−1.73977	+	1.40471i	−0.194512	+	0.157051i
$81$	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	−0.495449	−	0.868637i	$-0.664996\pi$
$83$	−4.46595	+	1.19665i	−0.490202	+	0.131349i	0.00524722	+	0.999986i	$0.498330\pi$
$84$	−0.333006	−	0.576783i	−0.0363339	−	0.0629322i
$85$	−12.9157	−	9.41216i	−1.40090	−	1.02089i
$86$	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	$0.758861\pi$
$90$	−3.76574	+	3.62610i	−0.396944	+	0.382224i
$91$	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
$95$	2.24830	+	9.48394i	0.230671	+	0.973032i
$96$	0.813682			0.0830460
$97$	−2.55970	+	3.65562i	−0.259898	+	0.371172i	−0.927801	−	0.373076i	$-0.878303\pi$
$97$	−2.55970	+	3.65562i	−0.259898	+	0.371172i	0.667903	+	0.744248i	$0.267192\pi$
$98$	−0.551699	+	6.30594i	−0.0557300	+	0.636997i
$99$	3.71982	+	10.2201i	0.373856	+	1.02716i
$100$	−1.53142	−	4.75970i	−0.153142	−	0.475970i
$101$	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	0.295692	−	0.955283i	$-0.404450\pi$
$103$	0.752308	+	0.201580i	0.0741271	+	0.0198623i	−0.221565	+	0.975146i	$0.571116\pi$
$104$	−2.84711	−	0.502023i	−0.279182	−	0.0492274i
$105$	1.47124	−	0.230857i	0.143579	−	0.0225293i
$106$	2.90910	+	5.03871i	0.282557	+	0.489402i
$107$	10.4930	−	2.81158i	1.01439	−	0.271806i	0.286929	−	0.957952i	$-0.407366\pi$
$107$	10.4930	−	2.81158i	1.01439	−	0.271806i	0.727464	+	0.686146i	$0.240699\pi$
$108$	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	$0.684914\pi$
$110$	−10.3437	−	1.10218i	−0.986229	−	0.105089i
$111$	−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	−0.820335	−	0.571883i	$-0.806213\pi$
$113$	−2.64108	+	2.64108i	−0.248452	+	0.248452i	0.571883	+	0.820335i	$0.306213\pi$
$114$	1.53145	−	3.19908i	0.143433	−	0.299622i
$115$	13.0876	+	6.40655i	1.22043	+	0.597414i
$116$	−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
$120$	−0.654470	+	1.69766i	−0.0597447	+	0.154975i
$121$	−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
$125$	11.1624	+	0.633226i	0.998395	+	0.0566375i
$126$	1.65725	+	0.956813i	0.147640	+	0.0852397i
$127$	−0.630802	−	7.21010i	−0.0559746	−	0.639793i	−0.971423	−	0.237357i	$-0.923719\pi$
$127$	−0.630802	−	7.21010i	−0.0559746	−	0.639793i	0.915448	−	0.402436i	$-0.131837\pi$
$128$	−0.906308	+	0.422618i	−0.0801070	+	0.0373545i
$129$	3.03488	−	1.10461i	0.267206	−	0.0972551i
$130$	3.33744	−	5.53641i	0.292713	−	0.485575i
$131$	−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
$135$	−2.69041	+	9.33199i	−0.231554	+	0.803169i
$136$	−4.59405	−	5.47498i	−0.393937	−	0.469475i
$137$	−6.29688	+	13.5037i	−0.537979	+	1.15370i	0.430037	+	0.902811i	$0.358500\pi$
$137$	−6.29688	+	13.5037i	−0.537979	+	1.15370i	−0.968016	+	0.250888i	$0.919277\pi$
$138$	−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	$0.213669\pi$
$140$	−1.51882	+	1.02129i	−0.128364	+	0.0863145i
$141$	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
$145$	3.72303	−	19.0076i	0.309181	−	1.57849i
$146$	−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	$-0.565947\pi$
$150$	−3.01559	−	2.73097i	−0.246222	−	0.222983i
$151$			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
$155$	−14.8024	−	8.92311i	−1.18895	−	0.716722i
$156$	−2.21051	+	0.804561i	−0.176983	+	0.0644165i
$157$	2.97175	−	1.38575i	0.237171	−	0.110595i	−0.300399	−	0.953814i	$-0.597120\pi$
$157$	2.97175	−	1.38575i	0.237171	−	0.110595i	0.537571	+	0.843219i	$0.319342\pi$
$158$	−0.919661	−	10.5118i	−0.0731643	−	0.836272i
$159$	4.09990	+	2.36708i	0.325143	+	0.187722i
$160$	−0.152777	−	2.23084i	−0.0120781	−	0.176364i
$161$	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	$-0.809853\pi$
$163$	2.17629	−	8.12203i	0.170460	−	0.636167i	0.997280	−	0.0737002i	$-0.0234808\pi$
$164$	−2.35815	+	4.08443i	−0.184140	+	0.318941i
$165$	−7.73726	+	3.43155i	−0.602345	+	0.267146i
$166$	1.58133	−	4.34466i	0.122735	−	0.337211i
$167$	7.11132	+	3.31606i	0.550291	+	0.256605i	0.677817	−	0.735230i	$-0.262926\pi$
$167$	7.11132	+	3.31606i	0.550291	+	0.256605i	−0.127527	+	0.991835i	$0.540704\pi$
$168$	0.663477	+	0.0580467i	0.0511884	+	0.00447840i
$169$	−4.57141	+	0.806063i	−0.351647	+	0.0620048i
$170$	15.1181	−	5.18131i	1.15951	−	0.397389i
$171$	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	0.999143	−	0.0413841i	$-0.0131767\pi$
$173$	17.1249	+	11.9910i	1.30198	+	0.911658i	0.302839	+	0.953042i	$0.402066\pi$
$174$	−5.39915	+	4.53042i	−0.409308	+	0.343450i
$175$	−0.909174	−	3.99032i	−0.0687271	−	0.301639i
$176$	−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	$0.658888\pi$
$180$	−0.810385	−	5.16456i	−0.0604026	−	0.384944i
$181$	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
$185$	5.35227	+	5.55838i	0.393506	+	0.408661i
$186$	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
$190$	−9.05836	−	3.59806i	−0.657163	−	0.261031i
$191$	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	$-0.904004\pi$
$193$	0.515018	−	5.88668i	0.0370718	−	0.423733i	0.991941	−	0.126704i	$-0.0404400\pi$
$194$	−1.52633	−	4.19356i	−0.109584	−	0.301080i
$195$	0.0993532	−	5.25914i	0.00711483	−	0.376615i
$196$	−4.84909	−	4.06887i	−0.346363	−	0.290633i
$197$	1.29256	+	4.82391i	0.0920912	+	0.343689i	0.996562	−	0.0828457i	$-0.0264009\pi$
$197$	1.29256	+	4.82391i	0.0920912	+	0.343689i	−0.904471	+	0.426535i	$0.859734\pi$
$198$	−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	$0.719150\pi$
$200$	4.77731	+	1.47558i	0.337807	+	0.104340i
$201$	−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
$205$	−6.62501	−	8.20527i	−0.462711	−	0.573081i
$206$	−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
$210$	−0.654764	+	1.33759i	−0.0451830	+	0.0923023i
$211$	−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
$215$	−3.59829	−	8.11322i	−0.245401	−	0.553317i
$216$	−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
$220$	6.83573	−	7.84084i	0.460865	−	0.528629i
$221$	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	−0.346707	−	0.937973i	$-0.612700\pi$
$223$	2.22450	−	1.03730i	0.148963	−	0.0694627i	0.495670	+	0.868511i	$0.334922\pi$
$224$	−0.769154	+	0.279949i	−0.0513912	+	0.0187049i
$225$	11.4271	+	2.46324i	0.761809	+	0.164216i
$226$	−0.648584	−	3.67830i	−0.0431432	−	0.244677i
$227$	18.1855	+	18.1855i	1.20702	+	1.20702i	0.971989	+	0.235027i	$0.0755177\pi$
$227$	18.1855	+	18.1855i	1.20702	+	1.20702i	0.235027	+	0.971989i	$0.424482\pi$
$228$	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	$0.977067\pi$
$230$	−12.7547	+	7.04612i	−0.841020	+	0.464607i
$231$	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	0.874530	−	0.484971i	$-0.161170\pi$
$233$	−0.902376	−	1.93515i	−0.0591166	−	0.126776i	−0.933647	+	0.358195i	$0.883392\pi$
$234$	4.34461	−	5.17770i	0.284016	−	0.338477i
$235$	−11.9647	−	17.7934i	−0.780490	−	1.16072i
$236$	−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	$0.335375\pi$
$240$	−1.01526	−	1.50985i	−0.0655344	−	0.0974604i
$241$	−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
$245$	12.3895	−	6.84440i	0.791539	−	0.437272i
$246$			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
$250$	−6.92119	+	8.78049i	−0.437735	+	0.555327i
$251$	−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
$255$	8.54530	−	9.80178i	0.535127	−	0.613811i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−12.6675	+	8.86986i	−0.790176	+	0.553287i	−0.897540	−	0.440933i	$-0.854648\pi$
$257$	−12.6675	+	8.86986i	−0.790176	+	0.553287i	0.107364	+	0.994220i	$0.465759\pi$
$258$	−0.835895	+	3.11960i	−0.0520406	+	0.194218i
$259$	1.41229	−	2.44617i	0.0877557	−	0.151997i
$260$	2.62088	+	5.90943i	0.162540	+	0.366487i
$261$	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	0.0297775	−	0.999557i	$-0.490520\pi$
$263$	−1.85637	−	0.162411i	−0.114468	−	0.0100147i	−0.144246	+	0.989542i	$0.546076\pi$
$264$	−3.72775	+	0.657303i	−0.229427	+	0.0404542i
$265$	5.71994	−	11.6850i	0.351373	−	0.717804i
$266$	−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	$0.133578\pi$
$270$	−6.10116	−	7.55646i	−0.371305	−	0.459872i
$271$	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
$275$	10.8609	+	20.5687i	0.654937	+	1.24034i
$276$	5.22188	+	0.920758i	0.314320	+	0.0554231i
$277$	16.4751	+	4.41450i	0.989894	+	0.265241i	0.717206	−	0.696861i	$-0.245421\pi$
$277$	16.4751	+	4.41450i	0.989894	+	0.265241i	0.272688	+	0.962102i	$0.412087\pi$
$278$	0.163963	+	0.611919i	0.00983386	+	0.0367005i
$279$	−13.8433	−	11.6159i	−0.828777	−	0.695427i
$280$	0.0345702	−	1.82993i	0.00206596	−	0.109359i
$281$	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	−0.788615	−	0.614888i	$-0.789201\pi$
$283$	0.991073	−	1.41540i	0.0589132	−	0.0841367i	0.847528	+	0.530751i	$0.178090\pi$
$284$	−5.61547			−0.333217
$285$	−7.84699	+	1.14987i	−0.464815	+	0.0681122i
$286$	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
$290$	13.4346	+	13.9520i	0.788910	+	0.819291i
$291$	−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	0.914826	−	0.403848i	$-0.132327\pi$
$293$	25.7643	+	6.90352i	1.50517	+	0.403308i	0.590339	+	0.807155i	$0.298994\pi$
$294$	−5.07238	−	0.894398i	−0.295827	−	0.0521623i
$295$	−0.249248	−	1.58845i	−0.0145118	−	0.0924829i
$296$	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
$300$	3.96675	−	0.903804i	0.229020	−	0.0521812i
$301$	−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
$305$	−18.0625	+	6.19042i	−1.03426	+	0.354462i
$306$	16.4555	−	2.90154i	0.940696	−	0.165870i
$307$	15.3079	+	1.33927i	0.873668	+	0.0764361i	0.515164	−	0.857092i	$-0.327731\pi$
$307$	15.3079	+	1.33927i	0.873668	+	0.0764361i	0.358505	+	0.933528i	$0.383287\pi$
$308$	−3.45099	−	1.60922i	−0.196638	−	0.0916940i
$309$	−0.216749	+	0.595514i	−0.0123304	+	0.0338776i
$310$	15.7997	−	7.00730i	0.897361	−	0.397988i
$311$	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	−1.00000		0.000173367i	$-0.999945\pi$
$313$	−23.7399	+	16.6228i	−1.34186	+	0.939579i	−0.341857	+	0.939752i	$0.611056\pi$
$314$	−0.569386	+	3.22915i	−0.0321323	+	0.182231i
$315$	−0.292358	−	4.26900i	−0.0164725	−	0.240531i
$316$	9.13824	+	5.27596i	0.514066	+	0.296796i
$317$	−2.77871	−	31.7608i	−0.156068	−	1.78386i	−0.521725	−	0.853114i	$-0.674711\pi$
$317$	−2.77871	−	31.7608i	−0.156068	−	1.78386i	0.365657	−	0.930750i	$-0.380844\pi$
$318$	−4.29061	+	2.00074i	−0.240605	+	0.112196i
$319$	37.8654	−	13.7819i	2.12006	−	0.771638i
$320$	1.91503	+	1.15441i	0.107053	+	0.0645336i
$321$	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
$325$	−14.4375	+	0.715064i	−0.800847	+	0.0396646i
$326$	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
$330$	1.62695	−	8.30625i	0.0895608	−	0.457244i
$331$	−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
$335$	−19.6885	+	13.2390i	−1.07570	+	0.723323i
$336$	−0.428104	+	0.510194i	−0.0233550	+	0.0278334i
$337$	−3.02769	−	6.49291i	−0.164929	−	0.353691i	0.806422	−	0.591340i	$-0.201401\pi$
$337$	−3.02769	−	6.49291i	−0.164929	−	0.353691i	−0.971351	+	0.237649i	$0.923623\pi$
$338$	1.96176	−	4.20702i	0.106706	−	0.228832i
$339$	−1.95352	−	2.32812i	−0.106101	−	0.126446i
$340$	−4.42711	+	15.3559i	−0.240094	+	0.832791i
$341$		−	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
$345$	−6.12119	+	10.1543i	−0.329554	+	0.546690i
$346$	−19.6449	+	7.15015i	−1.05612	+	0.384395i
$347$	13.8248	−	6.44663i	0.742157	−	0.346073i	−0.0144919	−	0.999895i	$-0.504613\pi$
$347$	13.8248	−	6.44663i	0.742157	−	0.346073i	0.756649	+	0.653822i	$0.226835\pi$
$348$	−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	$0.622889\pi$
$350$	3.79016	+	1.54400i	0.202592	+	0.0825302i
$351$	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	$0.254419\pi$
$353$	−4.97923	+	18.5827i	−0.265018	+	0.989060i	−0.962239	+	0.272204i	$0.912247\pi$
$354$	−0.292546	+	0.506704i	−0.0155486	+	0.0269310i
$355$	4.51670	−	11.7161i	0.239722	−	0.621826i
$356$	−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	$0.392696\pi$
$360$	4.69538	+	2.29844i	0.247468	+	0.121138i
$361$	−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
$365$	4.45042	+	0.474221i	0.232946	+	0.0248218i
$366$	6.52903	+	2.37637i	0.341278	+	0.124215i
$367$	−6.43348	+	0.562857i	−0.335825	+	0.0293809i	−0.253821	−	0.967251i	$-0.581687\pi$
$367$	−6.43348	+	0.562857i	−0.335825	+	0.0293809i	−0.0820037	+	0.996632i	$0.526132\pi$
$368$	−6.29455	+	1.68662i	−0.328126	+	0.0879211i
$369$	−5.51317	−	9.54908i	−0.287004	−	0.497105i
$370$	−7.62310	+	1.19616i	−0.396306	+	0.0621855i
$371$	−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	0.989677	−	0.143315i	$-0.0457761\pi$
$373$	1.17684	+	4.39201i	0.0609342	+	0.227410i	−0.928743	+	0.370724i	$0.879109\pi$
$374$	25.4696	+	21.3716i	1.31700	+	1.10510i
$375$	−1.30489	+	9.00317i	−0.0673841	+	0.464921i
$376$	−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	$0.703170\pi$
$380$	8.14303	−	5.35641i	0.417728	−	0.274778i
$381$	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	$0.103327\pi$
$383$	−0.802086	+	9.16789i	−0.0409847	+	0.468457i	−0.988759	+	0.149516i	$0.952228\pi$
$384$	−0.278296	−	0.764611i	−0.0142017	−	0.0390189i
$385$	6.13322	−	5.90578i	0.312578	−	0.300986i
$386$	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	$0.264481\pi$
$390$	4.25105	+	3.09791i	0.215260	+	0.156869i
$391$	−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
$395$	−18.3579	+	14.8224i	−0.923688	+	0.745794i
$396$	8.33153	−	6.99098i	0.418675	−	0.351310i
$397$	−6.54164	−	4.58050i	−0.328315	−	0.229889i	0.397783	−	0.917479i	$-0.369780\pi$
$397$	−6.54164	−	4.58050i	−0.328315	−	0.229889i	−0.726099	+	0.687590i	$0.758668\pi$
$398$	9.80777	−	9.80777i	0.491619	−	0.491619i
$399$	1.20014	+	2.64339i	0.0600823	+	0.132335i
$400$	−3.94888	+	3.06698i	−0.197444	+	0.153349i
$401$	−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
$405$	7.25992	+	2.79879i	0.360748	+	0.139073i
$406$	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	$0.00299163\pi$
$410$	10.5213	−	0.720541i	0.519611	−	0.0355850i
$411$	−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
$415$	−10.0349	+	2.48669i	−0.492595	+	0.122067i
$416$	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	$-0.196346\pi$
$420$	−0.720130	−	1.30356i	−0.0351388	−	0.0636072i
$421$	−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
$425$	−28.4777	−	21.5880i	−1.38137	−	1.04717i
$426$	−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
$430$	8.70985	+	1.70601i	0.420026	+	0.0822710i
$431$	−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	$-0.634073\pi$
$433$	11.5080	−	24.6791i	0.553041	−	1.18600i	0.961900	−	0.273402i	$-0.0881490\pi$
$434$	−4.06678	−	4.84660i	−0.195212	−	0.232644i
$435$	15.1432	+	4.36579i	0.726062	+	0.209324i
$436$			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	$0.941023\pi$
$440$	2.50203	+	10.0968i	0.119279	+	0.481347i
$441$	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	$0.00808741\pi$
$443$	0.412507	+	4.71498i	0.0195988	+	0.224015i	−0.980078	+	0.198611i	$0.936357\pi$
$444$	2.43172	+	1.40395i	0.115404	+	0.0666287i
$445$	−3.65242	−	3.18422i	−0.173141	−	0.150947i
$446$	−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	$-0.120989\pi$
$450$	−8.57210	+	7.94771i	−0.404093	+	0.374659i
$451$	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
$455$	1.71550	+	5.00552i	0.0804241	+	0.234663i
$456$	−3.52994	−	0.344942i	−0.165305	−	0.0161534i
$457$	−8.45415	+	8.45415i	−0.395468	+	0.395468i	−0.876631	−	0.481163i	$-0.840215\pi$
$457$	−8.45415	+	8.45415i	−0.395468	+	0.395468i	0.481163	+	0.876631i	$0.340215\pi$
$458$	−1.78466	−	1.24963i	−0.0833918	−	0.0583916i
$459$	23.7798	−	19.9537i	1.10995	−	0.931357i
$460$	1.54395	−	14.4895i	0.0719870	−	0.675578i
$461$	−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	0.340967	−	0.940075i	$-0.389245\pi$
$463$	23.8046	−	6.37841i	1.10629	−	0.296430i	0.765324	+	0.643645i	$0.222579\pi$
$464$	4.33099	+	7.50149i	0.201061	+	0.348248i
$465$	8.28269	−	11.3658i	0.384100	−	0.527075i
$466$	2.10276	+	0.370774i	0.0974087	+	0.0171758i
$467$	−21.8306	−	5.84948i	−1.01020	−	0.270682i	−0.284486	−	0.958680i	$-0.591823\pi$
$467$	−21.8306	−	5.84948i	−1.01020	−	0.270682i	−0.725712	+	0.687999i	$0.758489\pi$
$468$	1.74936	+	6.52870i	0.0808642	+	0.301789i
$469$	6.65296	+	5.58250i	0.307205	+	0.257776i
$470$	21.4382	+	0.405000i	0.988871	+	0.0186813i
$471$	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
$475$	4.62590	+	21.2979i	0.212251	+	0.977215i
$476$	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	$0.976341\pi$
$480$	1.81912	+	0.0343660i	0.0830312	+	0.00156859i
$481$	−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
$485$	−5.87703	+	8.06466i	−0.266862	+	0.366197i
$486$	−7.93072	−	13.7364i	−0.359745	−	0.623096i
$487$	16.8345	−	4.51078i	0.762842	−	0.204403i	0.143635	−	0.989631i	$-0.454121\pi$
$487$	16.8345	−	4.51078i	0.762842	−	0.204403i	0.619207	+	0.785228i	$0.287454\pi$
$488$	−8.50653	+	0.744225i	−0.385073	+	0.0336895i
$489$	6.42926	+	2.34006i	0.290741	+	0.105821i
$490$	−1.49975	+	14.0747i	−0.0677517	+	0.635830i
$491$	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
$495$	7.88465	+	23.0059i	0.354388	+	1.03404i
$496$	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	$0.895498\pi$
$500$	−3.22273	−	10.7058i	−0.144125	−	0.478778i
$501$	−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	$0.675824\pi$
$503$	−33.7336	+	23.6205i	−1.50411	+	1.05319i	−0.979406	+	0.201903i	$0.935288\pi$
$504$	0.332298	−	1.88455i	0.0148017	−	0.0839447i
$505$	15.1481	+	13.2062i	0.674079	+	0.587670i
$506$	−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	$0.473090\pi$
$510$	3.12776	+	12.6220i	0.138500	+	0.558910i
$511$	−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
$515$	1.67340	+	0.482441i	0.0737387	+	0.0212589i
$516$	−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
$520$	−6.34400	−	1.24260i	−0.278203	−	0.0544918i
$521$	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	0.470539	−	0.882379i	$-0.344059\pi$
$523$	−11.8819	−	16.9691i	−0.519560	−	0.742008i	−0.990099	+	0.140371i	$0.955171\pi$
$524$	−10.2927	+	5.94249i	−0.449639	+	0.259599i
$525$	3.29897	−	0.453982i	0.143979	−	0.0198134i
$526$	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
$530$	6.29097	+	11.3877i	0.273262	+	0.494652i
$531$		−	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
$535$	23.5775	−	5.84259i	1.01935	−	0.252597i
$536$	−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
$540$	9.68937	−	0.663567i	0.416964	−	0.0285554i
$541$	−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
$545$	−10.0107	−	3.85926i	−0.428812	−	0.165312i
$546$	0.658546	−	1.80934i	0.0281832	−	0.0774327i
$547$	−7.62478	−	3.55549i	−0.326012	−	0.152022i	0.252721	−	0.967539i	$-0.418675\pi$
$547$	−7.62478	−	3.55549i	−0.326012	−	0.152022i	−0.578732	+	0.815517i	$0.696452\pi$
$548$	14.8430	+	1.29859i	0.634061	+	0.0554732i
$549$	−19.6603	+	3.46664i	−0.839080	+	0.147953i
$550$	−23.0784	−	2.90098i	−0.984068	−	0.123698i
$551$	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
$555$	−4.88511	+	3.94428i	−0.207361	+	0.167426i
$556$	−0.595300	−	0.216671i	−0.0252463	−	0.00918892i
$557$	−5.36840	+	0.469674i	−0.227466	+	0.0199007i	−0.200319	−	0.979731i	$-0.564198\pi$
$557$	−5.36840	+	0.469674i	−0.227466	+	0.0199007i	−0.0271472	+	0.999631i	$0.508642\pi$
$558$	17.4554	−	4.67716i	0.738946	−	0.198000i
$559$	5.73752	+	9.93767i	0.242671	+	0.420319i
$560$	1.47916	+	1.07792i	0.0625061	+	0.0455506i
$561$	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	$0.100542\pi$
$563$	6.70696	+	25.0307i	0.282665	+	1.05492i	−0.667864	+	0.744283i	$0.732791\pi$
$564$	−5.97708	−	5.01537i	−0.251681	−	0.211185i
$565$	−6.01612	+	5.79303i	−0.253100	+	0.243714i
$566$	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	$0.563663\pi$
$570$	3.55893	−	7.08741i	0.149067	−	0.296859i
$571$	−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
$575$	28.9890	+	14.8757i	1.20893	+	0.620359i
$576$	1.79095	+	1.50279i	0.0746230	+	0.0626161i
$577$	3.32677	+	12.4157i	0.138495	+	0.516872i	0.999959	+	0.00905266i	$0.00288159\pi$
$577$	3.32677	+	12.4157i	0.138495	+	0.516872i	−0.861464	+	0.507819i	$0.830452\pi$
$578$	−32.9194	−	8.82073i	−1.36927	−	0.366894i
$579$	4.73513	+	0.834932i	0.196785	+	0.0346986i
$580$	−19.1346	+	3.00247i	−0.794522	+	0.124671i
$581$	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
$585$	−15.0285	−	1.60138i	−0.621353	−	0.0662091i
$586$	−20.4328	+	17.1452i	−0.844072	+	0.708260i
$587$	−1.29145	−	0.904282i	−0.0533038	−	0.0373237i	0.546621	−	0.837380i	$-0.315914\pi$
$587$	−1.29145	−	0.904282i	−0.0533038	−	0.0373237i	−0.599925	+	0.800056i	$0.704803\pi$
$588$	3.64205	−	3.64205i	0.150195	−	0.150195i
$589$	9.04990	−	32.4543i	0.372894	−	1.33726i
$590$	1.44414	+	0.706924i	0.0594544	+	0.0291036i
$591$	−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	0.629645	−	0.776883i	$-0.283201\pi$
$593$	10.6963	+	4.98777i	0.439245	+	0.204823i	−0.190399	+	0.981707i	$0.560978\pi$
$594$	6.91065	−	18.9869i	0.283547	−	0.779040i
$595$	−4.70534	+	12.2054i	−0.192900	+	0.500373i
$596$	−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	$-0.135167\pi$
$600$	−1.53488	+	3.76777i	−0.0626612	+	0.153819i
$601$	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
$605$	−12.2843	+	20.3782i	−0.499428	+	0.828491i
$606$	−1.26987	−	7.20179i	−0.0515850	−	0.292553i
$607$	−23.0572	−	23.0572i	−0.935861	−	0.935861i	0.0622023	−	0.998064i	$-0.480188\pi$
$607$	−23.0572	−	23.0572i	−0.935861	−	0.935861i	−0.998064	+	0.0622023i	$0.980188\pi$
$608$	4.11094	−	1.44921i	0.166720	−	0.0587732i
$609$		−	5.76897i		−	0.233771i
$610$	5.28933	−	18.3466i	0.214159	−	0.742832i
$611$	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	0.999985	−	0.00556187i	$-0.00177041\pi$
$613$	8.73854	+	18.7399i	0.352946	+	0.756896i	−0.647038	+	0.762457i	$0.723993\pi$
$614$	−9.87732	+	11.7713i	−0.398616	+	0.475052i
$615$	7.12090	−	4.78824i	0.287142	−	0.193081i
$616$	3.29760	−	1.90387i	0.132864	−	0.0767092i
$617$	1.06559	+	1.52182i	0.0428991	+	0.0612663i	0.840029	−	0.542542i	$-0.182538\pi$
$617$	1.06559	+	1.52182i	0.0428991	+	0.0612663i	−0.797130	+	0.603808i	$0.793649\pi$
$618$	−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	$0.410537\pi$
$620$	−3.32228	+	16.9616i	−0.133426	+	0.681193i
$621$	−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
$625$	24.9287	+	1.88713i	0.997147	+	0.0754852i
$626$		−	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
$630$	3.66465	+	2.20911i	0.146003	+	0.0880131i
$631$	−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
$635$	−1.10574	−	16.1460i	−0.0438801	−	0.640736i
$636$	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
$640$	−2.04405	+	0.906557i	−0.0807983	+	0.0358348i
$641$	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	0.645213	−	0.764003i	$-0.276769\pi$
$643$	29.1092	+	2.54673i	1.14796	+	0.100433i	0.502743	+	0.864436i	$0.332324\pi$
$644$	−5.25290	+	0.926229i	−0.206993	+	0.0364985i
$645$	6.83164	−	2.34135i	0.268995	−	0.0921907i
$646$	17.6091	+	25.6993i	0.692820	+	1.01112i
$647$	−3.93374	+	3.93374i	−0.154651	+	0.154651i	−0.780192	−	0.625540i	$-0.784879\pi$
$647$	−3.93374	+	3.93374i	−0.154651	+	0.154651i	0.625540	+	0.780192i	$0.284879\pi$
$648$	2.85036	+	1.99584i	0.111973	+	0.0784041i
$649$	2.56250	−	2.15019i	0.100587	−	0.0844025i
$650$	7.69524	−	12.2366i	0.301832	−	0.479960i
$651$	−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	−0.0655502	−	0.997849i	$-0.520880\pi$
$653$	9.62375	−	2.57868i	0.376606	−	0.100911i	0.442157	+	0.896938i	$0.354214\pi$
$654$	1.95206	+	3.38107i	0.0763316	+	0.132210i
$655$	−4.11965	−	26.2544i	−0.160968	−	1.02584i
$656$	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	$0.836664\pi$
$660$	5.87090	+	6.09699i	0.228524	+	0.237325i
$661$	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
$665$	7.02195	−	3.78671i	0.272300	−	0.146842i
$666$	−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
$670$	0.448134	−	23.7215i	0.0173129	−	0.916440i
$671$	−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	0.388101	−	0.921617i	$-0.373131\pi$
$673$	6.83314	+	1.83093i	0.263398	+	0.0705773i	−0.124703	+	0.992194i	$0.539798\pi$
$674$	7.05529	+	1.24404i	0.271760	+	0.0479186i
$675$	−6.40901	+	20.7496i	−0.246683	+	0.798653i
$676$	2.32097	+	4.02003i	0.0892679	+	0.154617i
$677$	7.17150	−	1.92160i	0.275623	−	0.0738530i	−0.118360	−	0.992971i	$-0.537764\pi$
$677$	7.17150	−	1.92160i	0.275623	−	0.0738530i	0.393983	+	0.919118i	$0.371097\pi$
$678$	3.02757	−	0.264878i	0.116273	−	0.0101726i
$679$	3.43250	+	1.24933i	0.131727	+	0.0479448i
$680$	−10.0395	−	12.4343i	−0.384999	−	0.476832i
$681$	−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	−0.239457	−	0.970907i	$-0.576969\pi$
$683$	19.1159	−	19.1159i	0.731451	−	0.731451i	0.970907	+	0.239457i	$0.0769693\pi$
$684$	9.27918	−	4.21290i	0.354798	−	0.161084i
$685$	−14.6481	+	29.9239i	−0.559674	+	1.14333i
$686$	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
$690$	−4.80696	−	10.8385i	−0.182998	−	0.412613i
$691$	−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
$695$	0.930881	−	1.06776i	0.0353103	−	0.0405023i
$696$	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
$700$	−3.43871	+	2.21911i	−0.129971	+	0.0838746i
$701$	−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
$705$	15.2716	−	8.43654i	0.575162	−	0.317739i
$706$	−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	$0.0789783\pi$
$710$	7.00659	+	10.4199i	0.262953	+	0.391053i
$711$	−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
$715$	−16.7809	−	24.9559i	−0.627569	−	0.933297i
$716$	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	$0.637521\pi$
$720$	−4.57593	+	2.52790i	−0.170535	+	0.0942091i
$721$		−	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
$725$	9.12625	−	42.3374i	0.338941	−	1.57237i
$726$	8.13637	−	2.96140i	0.301969	−	0.109908i
$727$	−7.67045	+	3.57679i	−0.284481	+	0.132656i	−0.559622	−	0.828748i	$-0.689053\pi$
$727$	−7.67045	+	3.57679i	−0.284481	+	0.132656i	0.275140	+	0.961404i	$0.411276\pi$
$728$	0.206242	+	2.35735i	0.00764382	+	0.0873693i
$729$	−2.13667	−	1.23361i	−0.0791360	−	0.0456892i
$730$	−2.94112	+	3.37357i	−0.108856	+	0.124862i
$731$	−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	$-0.587818\pi$
$733$	12.0370	−	44.9227i	0.444597	−	1.65926i	0.716999	−	0.697074i	$-0.245515\pi$
$734$	3.22903	−	5.59284i	0.119186	−	0.206436i
$735$	4.66934	+	10.5282i	0.172231	+	0.388337i
$736$	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	$0.370500\pi$
$740$	3.39259	−	6.93056i	0.124714	−	0.254773i
$741$	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	$-0.902698\pi$
$743$	−42.5934	−	29.8242i	−1.56260	−	1.09415i	−0.608960	−	0.793201i	$-0.708413\pi$
$744$	4.81797	−	4.04276i	0.176635	−	0.148215i
$745$	−30.2426	−	37.4564i	−1.10800	−	1.37230i
$746$	−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
$750$	−6.62651	−	6.23291i	−0.241966	−	0.227594i
$751$	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
$755$	−0.300743	+	15.9195i	−0.0109451	+	0.579368i
$756$	−1.21592	−	3.34072i	−0.0442226	−	0.121501i
$757$	−3.13261	+	35.8059i	−0.113857	+	1.30139i	0.697394	+	0.716688i	$0.254343\pi$
$757$	−3.13261	+	35.8059i	−0.113857	+	1.30139i	−0.811251	+	0.584698i	$0.801213\pi$
$758$	13.3061	−	19.0031i	0.483299	−	0.690222i
$759$	−24.6670			−0.895355
$760$	−0.282933	+	9.74269i	−0.0102630	+	0.353404i
$761$	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
$765$	−25.9160	−	26.9140i	−0.936995	−	0.973079i
$766$	−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	$0.435887\pi$
$770$	1.31986	+	8.41145i	0.0475646	+	0.303128i
$771$	−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	−0.110281	−	0.993900i	$-0.535175\pi$
$773$	−1.28721	+	0.112617i	−0.0462978	+	0.00405054i	0.0639833	+	0.997951i	$0.479620\pi$
$774$	8.72001	+	3.17382i	0.313434	+	0.114081i
$775$	−32.7163	−	20.5743i	−1.17521	−	0.739051i
$776$	−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
$780$	−4.97596	+	1.70537i	−0.178168	+	0.0610621i
$781$	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
$785$	6.70237	−	2.97256i	0.239218	−	0.106095i
$786$	−4.83530	+	8.37498i	−0.172469	+	0.298726i
$787$	−7.86788	+	29.3633i	−0.280460	+	1.04669i	0.671634	+	0.740883i	$0.265593\pi$
$787$	−7.86788	+	29.3633i	−0.280460	+	1.04669i	−0.952094	+	0.305806i	$0.901074\pi$
$788$	4.09091	−	2.86448i	0.145733	−	0.102043i
$789$	0.263296	−	1.49323i	0.00937359	−	0.0531603i
$790$	−1.61209	−	23.5397i	−0.0573556	−	0.837505i
$791$	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
$795$	9.06605	+	5.46517i	0.321540	+	0.193830i
$796$	2.40855	+	13.6596i	0.0853687	+	0.484150i
$797$	−13.5806	−	13.5806i	−0.481049	−	0.481049i	0.424418	−	0.905467i	$-0.360479\pi$
$797$	−13.5806	−	13.5806i	−0.481049	−	0.481049i	−0.905467	+	0.424418i	$0.860479\pi$
$798$	−2.85371	−	0.533086i	−0.101020	−	0.0188711i
$799$			68.5345i			2.42458i
$800$	−0.247339	−	4.99388i	−0.00874474	−	0.176560i
$801$	−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
$805$	2.29260	−	11.7046i	0.0808035	−	0.412534i
$806$	−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	$0.975772\pi$
$810$	−6.45676	+	4.34166i	−0.226867	+	0.152550i
$811$	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
$815$	5.20850	−	18.0663i	0.182446	−	0.632834i
$816$			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
$820$	−5.44454	+	9.03184i	−0.190132	+	0.315406i
$821$	−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	$-0.978480\pi$
$823$	−0.771373	−	8.81683i	−0.0268884	−	0.307336i	0.970827	−	0.239780i	$-0.0770754\pi$
$824$	0.674501	+	0.389423i	0.0234973	+	0.0135662i
$825$	−17.4429	+	7.34502i	−0.607284	+	0.255721i
$826$	0.102204	−	0.579626i	0.00355612	−	0.0201678i
$827$	−26.9905	+	18.8989i	−0.938551	+	0.657180i	−0.939401	−	0.342819i	$-0.888618\pi$
$827$	−26.9905	+	18.8989i	−0.938551	+	0.657180i	0.000850677		1.00000i	$0.499729\pi$
$828$	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	$0.275552\pi$
$830$	3.71882	−	9.64644i	0.129082	−	0.334833i
$831$	−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
$835$	15.7585	+	7.71397i	0.545346	+	0.266953i
$836$	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	$0.448834\pi$
$840$	1.48086	+	0.157795i	0.0510947	+	0.00544446i
$841$	−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
$845$	−10.2542	+	1.60902i	−0.352755	+	0.0553518i
$846$	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
$850$	34.0179	−	10.9452i	1.16681	−	0.375417i
$851$	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	−0.965807	−	0.259262i	$-0.916521\pi$
$853$	−11.4446	+	16.3446i	−0.391855	+	0.559627i	0.573952	+	0.818889i	$0.305410\pi$
$854$	−6.98933			−0.239170
$855$	1.32624	+	22.7486i	0.0453566	+	0.777986i
$856$	10.8631			0.371294
$857$	32.1099	−	45.8577i	1.09685	−	1.56647i	0.308521	−	0.951218i	$-0.400166\pi$
$857$	32.1099	−	45.8577i	1.09685	−	1.56647i	0.788332	−	0.615250i	$-0.210945\pi$
$858$	−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	$0.864082\pi$
$860$	−6.39325	+	6.15617i	−0.218008	+	0.209924i
$861$	−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	0.201616	−	0.979465i	$-0.435381\pi$
$863$	−3.33461	−	0.893507i	−0.113512	−	0.0304153i	−0.315128	+	0.949049i	$0.602047\pi$
$864$	4.27738	+	0.754218i	0.145520	+	0.0256590i
$865$	37.7792	+	27.5311i	1.28453	+	0.936087i
$866$	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
$870$	−12.2621	+	9.90049i	−0.415722	+	0.335658i
$871$	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
$875$	−1.86408	−	8.95942i	−0.0630174	−	0.302884i
$876$	1.60389	−	0.282809i	0.0541904	−	0.00955522i
$877$	3.57559	+	0.312824i	0.120739	+	0.0105633i	0.147365	−	0.989082i	$-0.452921\pi$
$877$	3.57559	+	0.312824i	0.120739	+	0.0105633i	−0.0266259	+	0.999645i	$0.508476\pi$
$878$	−0.408244	−	0.190367i	−0.0137776	−	0.00642458i
$879$	−7.42302	+	20.3946i	−0.250372	+	0.687892i
$880$	−9.70594	−	3.74176i	−0.327187	−	0.126135i
$881$	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	$-0.318039\pi$
$883$	45.0588	−	31.5505i	1.51635	−	1.06176i	0.975331	−	0.220747i	$-0.0708496\pi$
$884$	3.58799	−	20.3485i	0.120677	−	0.684395i
$885$	1.30525	−	0.0893885i	0.0438754	−	0.00300476i
$886$	−4.09889	−	2.36649i	−0.137705	−	0.0795039i
$887$	−0.520732	−	5.95199i	−0.0174845	−	0.199848i	−0.999913	−	0.0132079i	$-0.995796\pi$
$887$	−0.520732	−	5.95199i	−0.0174845	−	0.199848i	0.982428	−	0.186640i	$-0.0597599\pi$
$888$	−2.54483	+	1.18667i	−0.0853988	+	0.0398221i
$889$	−5.56686	+	2.02617i	−0.186706	+	0.0679556i
$890$	4.70330	−	1.16549i	0.157655	−	0.0390675i
$891$	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
$895$	15.0742	+	27.2869i	0.503874	+	0.912100i
$896$	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
$900$	−1.59363	−	11.5805i	−0.0531209	−	0.386016i
$901$	−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
$905$	46.9547	+	9.19707i	1.56083	+	0.305721i
$906$	3.72428	−	4.43843i	0.123731	−	0.147457i
$907$	22.0096	+	47.1998i	0.730818	+	1.56724i	0.820744	+	0.571296i	$0.193559\pi$
$907$	22.0096	+	47.1998i	0.730818	+	1.56724i	−0.0899257	+	0.995948i	$0.528663\pi$
$908$	10.8690	−	23.3086i	0.360700	−	0.773524i
$909$	13.5062	+	16.0960i	0.447971	+	0.533872i
$910$	−5.08426	−	1.46579i	−0.168541	−	0.0485905i
$911$		−	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
$915$	−3.73692	−	15.0802i	−0.123539	−	0.498536i
$916$	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	$0.865986\pi$
$920$	10.9836	+	9.57558i	0.362117	+	0.315698i
$921$	−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
$925$	11.7311	+	12.6528i	0.385717	+	0.416020i
$926$	−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	$0.480089\pi$
$930$	4.55955	+	13.3039i	0.149514	+	0.436253i
$931$	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
$935$	7.87737	−	73.9269i	0.257618	−	2.41767i
$936$	−6.35139	−	2.31172i	−0.207602	−	0.0755608i
$937$	24.1919	−	2.11652i	0.790316	−	0.0691437i	0.315152	−	0.949041i	$-0.397944\pi$
$937$	24.1919	−	2.11652i	0.790316	−	0.0691437i	0.475164	+	0.879897i	$0.342389\pi$
$938$	−8.38890	+	2.24780i	−0.273907	+	0.0733932i
$939$	−11.7907	−	20.4220i	−0.384774	−	0.666448i
$940$	−12.6282	+	17.3288i	−0.411887	+	0.565205i
$941$	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
$945$	7.94807	+	0.150151i	0.258551	+	0.00488441i
$946$	6.31529	+	17.3511i	0.205328	+	0.564133i
$947$	−4.80850	+	54.9614i	−0.156255	+	1.78601i	0.363403	+	0.931632i	$0.381615\pi$
$947$	−4.80850	+	54.9614i	−0.156255	+	1.78601i	−0.519658	+	0.854374i	$0.673941\pi$
$948$	−4.92468	+	7.03317i	−0.159946	+	0.228427i
$949$	−5.78657			−0.187840
$950$	−20.0995	−	8.42666i	−0.652115	−	0.273397i
$951$	25.9419			0.841223
$952$	−3.35542	+	4.79204i	−0.108750	+	0.155311i
$953$	0.440341	−	5.03312i	0.0142640	−	0.163039i	−0.985722	−	0.168383i	$-0.946146\pi$
$953$	0.440341	−	5.03312i	0.0142640	−	0.163039i	0.999986	+	0.00534415i	$0.00170110\pi$
$954$	4.65233	+	12.7822i	0.150625	+	0.413838i
$955$	18.1307	+	0.342517i	0.586697	+	0.0110836i
$956$	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
$960$	−1.07156	+	1.47043i	−0.0345844	+	0.0474578i
$961$	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
$965$	1.40003	−	13.1389i	0.0450687	−	0.422957i
$966$	−3.32473	+	2.78978i	−0.106971	+	0.0897597i
$967$	−25.4812	−	17.8421i	−0.819419	−	0.573763i	0.0869682	−	0.996211i	$-0.472282\pi$
$967$	−25.4812	−	17.8421i	−0.819419	−	0.573763i	−0.906387	+	0.422448i	$0.861171\pi$
$968$	−7.52446	+	7.52446i	−0.241845	+	0.241845i
$969$	22.8641	+	10.9454i	0.734500	+	0.351617i
$970$	−3.23526	−	9.43988i	−0.103878	−	0.303096i
$971$	−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
$975$	0.444242	−	11.7535i	0.0142271	−	0.376414i
$976$	4.26951	−	7.39501i	0.136664	−	0.236709i
$977$	4.04465	−	15.0949i	0.129400	−	0.482927i	−0.870558	−	0.492065i	$-0.836242\pi$
$977$	4.04465	−	15.0949i	0.129400	−	0.482927i	0.999958	+	0.00913806i	$0.00290877\pi$
$978$	−5.60454	+	3.92434i	−0.179213	+	0.125487i
$979$	1.75053	−	9.92775i	0.0559472	−	0.317292i
$980$	−10.6691	−	9.30144i	−0.340812	−	0.297124i
$981$	−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	−0.585580	−	0.810614i	$-0.699133\pi$
$983$	−10.6919	+	4.98570i	−0.341018	+	0.159019i	0.244563	+	0.969633i	$0.421356\pi$
$984$	3.60613	−	1.31252i	0.114959	−	0.0418417i
$985$	2.68600	+	10.8392i	0.0855831	+	0.345367i
$986$	−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
$990$	−23.3678	−	6.73694i	−0.742678	−	0.214114i
$991$	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
$995$	−30.4365	−	5.96163i	−0.964903	−	0.188996i
$996$	−3.25803	+	1.88103i	−0.103235	+	0.0596026i
$997$	−6.31453	−	9.01808i	−0.199983	−	0.285605i	0.706617	−	0.707596i	$-0.250220\pi$
$997$	−6.31453	−	9.01808i	−0.199983	−	0.285605i	−0.906600	+	0.421991i	$0.861331\pi$
$998$	−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	190.2.r.a.143.2	yes	120
5.2	odd	4	inner	190.2.r.a.67.4	✓	120
5.3	odd	4		950.2.bb.e.257.7		120
5.4	even	2		950.2.bb.e.143.9		120
19.2	odd	18	inner	190.2.r.a.173.4	yes	120
95.2	even	36	inner	190.2.r.a.97.2	yes	120
95.59	odd	18		950.2.bb.e.743.7		120
95.78	even	36		950.2.bb.e.857.9		120

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

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:	\( N \)	\(=\)	\( 190 = 2 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	190.r (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.573576 + 0.819152i) q^{2} +(-0.0709170 + 0.810585i) q^{3} +(-0.342020 - 0.939693i) q^{4} +(2.23567 + 0.0422352i) q^{5} +(-0.623316 - 0.523024i) q^{6} +(-0.211848 - 0.790626i) q^{7} +(0.965926 + 0.258819i) q^{8} +(2.30240 + 0.405976i) q^{9} +O(q^{10})\)	\(q+(-0.573576 + 0.819152i) q^{2} +(-0.0709170 + 0.810585i) q^{3} +(-0.342020 - 0.939693i) q^{4} +(2.23567 + 0.0422352i) q^{5} +(-0.623316 - 0.523024i) q^{6} +(-0.211848 - 0.790626i) q^{7} +(0.965926 + 0.258819i) q^{8} +(2.30240 + 0.405976i) q^{9} +(-1.31692 + 1.80713i) q^{10} +(2.32600 + 4.02876i) q^{11} +(0.785956 - 0.210596i) q^{12} +(-2.88003 + 0.251970i) q^{13} +(0.769154 + 0.279949i) q^{14} +(-0.192782 + 1.80921i) q^{15} +(-0.766044 + 0.642788i) q^{16} +(-5.85454 - 4.09939i) q^{17} +(-1.65316 + 1.65316i) q^{18} +(1.08540 + 4.22160i) q^{19} +(-0.724956 - 2.11529i) q^{20} +(0.655893 - 0.115652i) q^{21} +(-4.63431 - 0.405449i) q^{22} +(5.90604 + 2.75403i) q^{23} +(-0.278296 + 0.764611i) q^{24} +(4.99643 + 0.188848i) q^{25} +(1.44552 - 2.50371i) q^{26} +(-1.12415 + 4.19537i) q^{27} +(-0.670489 + 0.469482i) q^{28} +(1.50414 - 8.53038i) q^{29} +(-1.37144 - 1.19564i) q^{30} +(-6.69401 - 3.86479i) q^{31} +(-0.0871557 - 0.996195i) q^{32} +(-3.43061 + 1.59972i) q^{33} +(6.71605 - 2.44444i) q^{34} +(-0.440229 - 1.77653i) q^{35} +(-0.405976 - 2.30240i) q^{36} +(2.44013 + 2.44013i) q^{37} +(-4.08069 - 1.53230i) q^{38} -2.35238i q^{39} +(2.14856 + 0.619430i) q^{40} +(-3.03158 - 3.61289i) q^{41} +(-0.281469 + 0.603611i) q^{42} +(-1.67745 - 3.59730i) q^{43} +(2.99025 - 3.56365i) q^{44} +(5.13027 + 1.00487i) q^{45} +(-5.64354 + 3.25830i) q^{46} +(-5.50012 - 7.85498i) q^{47} +(-0.466709 - 0.666529i) q^{48} +(5.48197 - 3.16502i) q^{49} +(-3.02053 + 3.98452i) q^{50} +(3.73810 - 4.45489i) q^{51} +(1.22180 + 2.62017i) q^{52} +(2.45888 - 5.27308i) q^{53} +(-2.79186 - 3.32721i) q^{54} +(5.03002 + 9.10521i) q^{55} -0.818516i q^{56} +(-3.49894 + 0.580428i) q^{57} +(6.12494 + 6.12494i) q^{58} +(-0.124865 - 0.708143i) q^{59} +(1.76603 - 0.437629i) q^{60} +(-8.02406 + 2.92052i) q^{61} +(7.00538 - 3.26666i) q^{62} +(-0.166784 - 1.90634i) q^{63} +(0.866025 + 0.500000i) q^{64} +(-6.44944 + 0.441683i) q^{65} +(0.657303 - 3.72775i) q^{66} +(-8.69157 + 6.08591i) q^{67} +(-1.84980 + 6.90354i) q^{68} +(-2.65122 + 4.59204i) q^{69} +(1.70775 + 0.658359i) q^{70} +(1.92060 - 5.27682i) q^{71} +(2.11888 + 0.988049i) q^{72} +(1.99394 + 0.174447i) q^{73} +(-3.39844 + 0.599237i) q^{74} +(-0.507409 + 4.03664i) q^{75} +(3.59578 - 2.46382i) q^{76} +(2.69248 - 2.69248i) q^{77} +(1.92696 + 1.34927i) q^{78} +(-8.08325 + 6.78265i) q^{79} +(-1.73977 + 1.40471i) q^{80} +(3.26980 + 1.19011i) q^{81} +(4.69835 - 0.411052i) q^{82} +(-4.46595 + 1.19665i) q^{83} +(-0.333006 - 0.576783i) q^{84} +(-12.9157 - 9.41216i) q^{85} +(3.90888 + 0.689241i) q^{86} +(6.80793 + 1.82418i) q^{87} +(1.20403 + 4.49350i) q^{88} +(-1.66002 - 1.39292i) q^{89} +(-3.76574 + 3.62610i) q^{90} +(0.809342 + 2.22365i) q^{91} +(0.567959 - 6.49180i) q^{92} +(3.60746 - 5.15199i) q^{93} +9.58917 q^{94} +(2.24830 + 9.48394i) q^{95} +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	\( 120 q - 12 q^{7} - 36 q^{15} + 36 q^{17} - 96 q^{21} + 24 q^{22} - 24 q^{25} - 12 q^{26} - 96 q^{33} + 36 q^{35} - 12 q^{41} - 72 q^{43} - 36 q^{45} - 24 q^{47} - 144 q^{50} + 24 q^{51} + 36 q^{53} - 72 q^{55} + 84 q^{57} - 24 q^{60} + 48 q^{61} - 24 q^{62} + 36 q^{63} - 180 q^{65} - 24 q^{66} - 96 q^{67} - 12 q^{68} - 48 q^{70} - 36 q^{73} + 12 q^{76} + 96 q^{78} + 144 q^{81} + 48 q^{82} + 24 q^{83} + 48 q^{85} + 48 q^{86} + 72 q^{87} + 168 q^{90} + 72 q^{91} + 72 q^{92} + 156 q^{93} + 24 q^{95} + 120 q^{97} + 24 q^{98}+O(q^{100}) \) 120 * q - 12 * q^7 - 36 * q^15 + 36 * q^17 - 96 * q^21 + 24 * q^22 - 24 * q^25 - 12 * q^26 - 96 * q^33 + 36 * q^35 - 12 * q^41 - 72 * q^43 - 36 * q^45 - 24 * q^47 - 144 * q^50 + 24 * q^51 + 36 * q^53 - 72 * q^55 + 84 * q^57 - 24 * q^60 + 48 * q^61 - 24 * q^62 + 36 * q^63 - 180 * q^65 - 24 * q^66 - 96 * q^67 - 12 * q^68 - 48 * q^70 - 36 * q^73 + 12 * q^76 + 96 * q^78 + 144 * q^81 + 48 * q^82 + 24 * q^83 + 48 * q^85 + 48 * q^86 + 72 * q^87 + 168 * q^90 + 72 * q^91 + 72 * q^92 + 156 * q^93 + 24 * q^95 + 120 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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