LMFDB - Embedded newform 756.2.be.c.107.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(107,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 2]))

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

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

chi := DirichletCharacter("756.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.be (of order $6$, degree $2$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			107.1
Character	$\chi$	$=$	756.107
Dual form			756.2.be.c.431.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39533 + 0.230338i) q^{2} +(1.89389 - 0.642794i) q^{4} +(-0.936239 - 0.540538i) q^{5} +(-0.749282 - 2.53743i) q^{7} +(-2.49454 + 1.33314i) q^{8} +O(q^{10})$	\(q+(-1.39533 + 0.230338i) q^{2} +(1.89389 - 0.642794i) q^{4} +(-0.936239 - 0.540538i) q^{5} +(-0.749282 - 2.53743i) q^{7} +(-2.49454 + 1.33314i) q^{8} +(1.43087 + 0.538577i) q^{10} +(2.43972 + 4.22571i) q^{11} +0.815997 q^{13} +(1.62996 + 3.36797i) q^{14} +(3.17363 - 2.43476i) q^{16} +(-1.47016 + 0.848796i) q^{17} +(3.58740 + 2.07119i) q^{19} +(-2.12059 - 0.421910i) q^{20} +(-4.37755 - 5.33430i) q^{22} +(1.75645 - 3.04226i) q^{23} +(-1.91564 - 3.31798i) q^{25} +(-1.13858 + 0.187955i) q^{26} +(-3.05011 - 4.32399i) q^{28} -9.61003i q^{29} +(7.73929 - 4.46828i) q^{31} +(-3.86745 + 4.12830i) q^{32} +(1.85585 - 1.52298i) q^{34} +(-0.670072 + 2.78066i) q^{35} +(-3.37978 + 5.85395i) q^{37} +(-5.48267 - 2.06367i) q^{38} +(3.05610 + 0.100252i) q^{40} -6.96667i q^{41} -0.510241i q^{43} +(7.33682 + 6.43480i) q^{44} +(-1.75008 + 4.64953i) q^{46} +(3.40777 - 5.90243i) q^{47} +(-5.87715 + 3.80251i) q^{49} +(3.43720 + 4.18843i) q^{50} +(1.54541 - 0.524518i) q^{52} +(-2.99884 + 1.73138i) q^{53} -5.27504i q^{55} +(5.25188 + 5.33083i) q^{56} +(2.21355 + 13.4092i) q^{58} +(-2.50722 - 4.34263i) q^{59} +(6.85713 - 11.8769i) q^{61} +(-9.76964 + 8.01737i) q^{62} +(4.44546 - 6.65116i) q^{64} +(-0.763968 - 0.441077i) q^{65} +(-3.66826 + 2.11787i) q^{67} +(-2.23872 + 2.55253i) q^{68} +(0.294480 - 4.03428i) q^{70} +11.8557 q^{71} +(-1.49777 - 2.59421i) q^{73} +(3.36752 - 8.94668i) q^{74} +(8.12548 + 1.61664i) q^{76} +(8.89444 - 9.35688i) q^{77} +(3.41517 + 1.97175i) q^{79} +(-4.28736 + 0.564050i) q^{80} +(1.60469 + 9.72080i) q^{82} +11.3326 q^{83} +1.83523 q^{85} +(0.117528 + 0.711954i) q^{86} +(-11.7195 - 7.28872i) q^{88} +(0.313438 + 0.180963i) q^{89} +(-0.611412 - 2.07054i) q^{91} +(1.37097 - 6.89073i) q^{92} +(-3.39541 + 9.02077i) q^{94} +(-2.23911 - 3.87825i) q^{95} +8.12677 q^{97} +(7.32470 - 6.65949i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 4 q^{4} - 2 q^{7}+O(q^{10}) $ 28 * q - 4 * q^4 - 2 * q^7	$ 28 q - 4 q^{4} - 2 q^{7} - 20 q^{10} + 8 q^{13} + 12 q^{16} + 42 q^{19} + 4 q^{22} + 6 q^{25} - 28 q^{28} - 30 q^{31} + 24 q^{34} + 12 q^{37} + 36 q^{40} - 12 q^{46} - 14 q^{49} + 84 q^{52} + 28 q^{58} + 6 q^{61} + 8 q^{64} - 24 q^{67} + 128 q^{70} - 22 q^{73} - 48 q^{79} - 36 q^{82} - 24 q^{85} - 16 q^{88} - 16 q^{91} - 12 q^{94} - 4 q^{97}+O(q^{100}) $ 28 * q - 4 * q^4 - 2 * q^7 - 20 * q^10 + 8 * q^13 + 12 * q^16 + 42 * q^19 + 4 * q^22 + 6 * q^25 - 28 * q^28 - 30 * q^31 + 24 * q^34 + 12 * q^37 + 36 * q^40 - 12 * q^46 - 14 * q^49 + 84 * q^52 + 28 * q^58 + 6 * q^61 + 8 * q^64 - 24 * q^67 + 128 * q^70 - 22 * q^73 - 48 * q^79 - 36 * q^82 - 24 * q^85 - 16 * q^88 - 16 * q^91 - 12 * q^94 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	−1.39533	+	0.230338i	−0.986647	+	0.162873i
$2$	−1.39533	+	0.230338i	−0.986647	+	0.162873i
$3$		0			0
$3$		0			0
$4$	1.89389	−	0.642794i	0.946945	−	0.321397i
$5$	−0.936239	−	0.540538i	−0.418699	−	0.241736i	0.275822	−	0.961209i	$-0.411050\pi$
$5$	−0.936239	−	0.540538i	−0.418699	−	0.241736i	−0.694520	+	0.719473i	$0.744383\pi$
$6$		0			0
$7$	−0.749282	−	2.53743i	−0.283202	−	0.959060i
$7$	−0.749282	−	2.53743i	−0.283202	−	0.959060i
$8$	−2.49454	+	1.33314i	−0.881953	+	0.471337i
$9$		0			0
$10$	1.43087	+	0.538577i	0.452480	+	0.170313i
$11$	2.43972	+	4.22571i	0.735602	+	1.27410i	0.954459	+	0.298343i	$0.0964341\pi$
$11$	2.43972	+	4.22571i	0.735602	+	1.27410i	−0.218856	+	0.975757i	$0.570233\pi$
$12$		0			0
$13$	0.815997			0.226317			0.113158	−	0.993577i	$-0.463903\pi$
$13$	0.815997			0.226317			0.113158	+	0.993577i	$0.463903\pi$
$14$	1.62996	+	3.36797i	0.435626	+	0.900128i
$15$		0			0
$16$	3.17363	−	2.43476i	0.793408	−	0.608690i
$17$	−1.47016	+	0.848796i	−0.356566	+	0.205863i	−0.667573	−	0.744544i	$-0.732667\pi$
$17$	−1.47016	+	0.848796i	−0.356566	+	0.205863i	0.311007	+	0.950407i	$0.399334\pi$
$18$		0			0
$19$	3.58740	+	2.07119i	0.823006	+	0.475163i	0.851452	−	0.524433i	$-0.175723\pi$
$19$	3.58740	+	2.07119i	0.823006	+	0.475163i	−0.0284462	+	0.999595i	$0.509056\pi$
$20$	−2.12059	−	0.421910i	−0.474178	−	0.0943419i
$21$		0			0
$22$	−4.37755	−	5.33430i	−0.933297	−	1.13728i
$23$	1.75645	−	3.04226i	0.366245	−	0.634354i	−0.622730	−	0.782436i	$-0.713977\pi$
$23$	1.75645	−	3.04226i	0.366245	−	0.634354i	0.988975	+	0.148082i	$0.0473100\pi$
$24$		0			0
$25$	−1.91564	−	3.31798i	−0.383128	−	0.663596i
$26$	−1.13858	+	0.187955i	−0.223295	+	0.0368610i
$27$		0			0
$28$	−3.05011	−	4.32399i	−0.576416	−	0.817157i
$29$		−	9.61003i		−	1.78454i	−0.451504	−	0.892269i	$-0.649112\pi$
$29$		−	9.61003i		−	1.78454i	0.451504	−	0.892269i	$-0.350888\pi$
$30$		0			0
$31$	7.73929	−	4.46828i	1.39002	−	0.802527i	0.396700	−	0.917948i	$-0.370155\pi$
$31$	7.73929	−	4.46828i	1.39002	−	0.802527i	0.993317	+	0.115422i	$0.0368219\pi$
$32$	−3.86745	+	4.12830i	−0.683674	+	0.729787i
$33$		0			0
$34$	1.85585	−	1.52298i	0.318275	−	0.261190i
$35$	−0.670072	+	2.78066i	−0.113263	+	0.470017i
$36$		0			0
$37$	−3.37978	+	5.85395i	−0.555632	+	0.962383i	0.442222	+	0.896906i	$0.354190\pi$
$37$	−3.37978	+	5.85395i	−0.555632	+	0.962383i	−0.997854	+	0.0654777i	$0.979143\pi$
$38$	−5.48267	−	2.06367i	−0.889407	−	0.334772i
$39$		0			0
$40$	3.05610	+	0.100252i	0.483212	+	0.0158513i
$41$		−	6.96667i		−	1.08801i	−0.839082	−	0.544005i	$-0.816907\pi$
$41$		−	6.96667i		−	1.08801i	0.839082	−	0.544005i	$-0.183093\pi$
$42$		0			0
$43$		−	0.510241i		−	0.0778110i	−0.999243	−	0.0389055i	$-0.987613\pi$
$43$		−	0.510241i		−	0.0778110i	0.999243	−	0.0389055i	$-0.0123871\pi$
$44$	7.33682	+	6.43480i	1.10607	+	0.970082i
$45$		0			0
$46$	−1.75008	+	4.64953i	−0.258035	+	0.685535i
$47$	3.40777	−	5.90243i	0.497074	−	0.860958i	−0.502920	−	0.864333i	$-0.667741\pi$
$47$	3.40777	−	5.90243i	0.497074	−	0.860958i	0.999994	+	0.00337527i	$0.00107438\pi$
$48$		0			0
$49$	−5.87715	+	3.80251i	−0.839593	+	0.543216i
$50$	3.43720	+	4.18843i	0.486094	+	0.592334i
$51$		0			0
$52$	1.54541	−	0.524518i	0.214310	−	0.0727376i
$53$	−2.99884	+	1.73138i	−0.411922	+	0.237824i	−0.691615	−	0.722266i	$-0.743101\pi$
$53$	−2.99884	+	1.73138i	−0.411922	+	0.237824i	0.279693	+	0.960090i	$0.409767\pi$
$54$		0			0
$55$		−	5.27504i		−	0.711286i
$56$	5.25188	+	5.33083i	0.701812	+	0.712362i
$57$		0			0
$58$	2.21355	+	13.4092i	0.290654	+	1.76071i
$59$	−2.50722	−	4.34263i	−0.326412	−	0.565362i	0.655385	−	0.755295i	$-0.272506\pi$
$59$	−2.50722	−	4.34263i	−0.326412	−	0.565362i	−0.981797	+	0.189933i	$0.939173\pi$
$60$		0			0
$61$	6.85713	−	11.8769i	0.877966	−	1.52068i	0.0243965	−	0.999702i	$-0.492234\pi$
$61$	6.85713	−	11.8769i	0.877966	−	1.52068i	0.853569	−	0.520979i	$-0.174433\pi$
$62$	−9.76964	+	8.01737i	−1.24075	+	1.01821i
$63$		0			0
$64$	4.44546	−	6.65116i	0.555682	−	0.831395i
$65$	−0.763968	−	0.441077i	−0.0947586	−	0.0547089i
$66$		0			0
$67$	−3.66826	+	2.11787i	−0.448150	+	0.258739i	−0.707048	−	0.707165i	$-0.749974\pi$
$67$	−3.66826	+	2.11787i	−0.448150	+	0.258739i	0.258899	+	0.965904i	$0.416640\pi$
$68$	−2.23872	+	2.55253i	−0.271484	+	0.309540i
$69$		0			0
$70$	0.294480	−	4.03428i	0.0351971	−	0.482189i
$71$	11.8557			1.40701			0.703503	−	0.710692i	$-0.251618\pi$
$71$	11.8557			1.40701			0.703503	+	0.710692i	$0.251618\pi$
$72$		0			0
$73$	−1.49777	−	2.59421i	−0.175301	−	0.303630i	0.764965	−	0.644072i	$-0.222756\pi$
$73$	−1.49777	−	2.59421i	−0.175301	−	0.303630i	−0.940265	+	0.340443i	$0.889423\pi$
$74$	3.36752	−	8.94668i	0.391466	−	1.04003i
$75$		0			0
$76$	8.12548	+	1.61664i	0.932056	+	0.185441i
$77$	8.89444	−	9.35688i	1.01362	−	1.06631i
$78$		0			0
$79$	3.41517	+	1.97175i	0.384237	+	0.221839i	0.679660	−	0.733527i	$-0.262127\pi$
$79$	3.41517	+	1.97175i	0.384237	+	0.221839i	−0.295423	+	0.955366i	$0.595461\pi$
$80$	−4.28736	+	0.564050i	−0.479341	+	0.0630627i
$81$		0			0
$82$	1.60469	+	9.72080i	0.177208	+	1.07348i
$83$	11.3326			1.24392			0.621960	−	0.783049i	$-0.286337\pi$
$83$	11.3326			1.24392			0.621960	+	0.783049i	$0.286337\pi$
$84$		0			0
$85$	1.83523			0.199058
$86$	0.117528	+	0.711954i	0.0126733	+	0.0767720i
$87$		0			0
$88$	−11.7195	−	7.28872i	−1.24930	−	0.776980i
$89$	0.313438	+	0.180963i	0.0332243	+	0.0191821i	0.516520	−	0.856275i	$-0.327227\pi$
$89$	0.313438	+	0.180963i	0.0332243	+	0.0191821i	−0.483296	+	0.875457i	$0.660560\pi$
$90$		0			0
$91$	−0.611412	−	2.07054i	−0.0640934	−	0.217052i
$92$	1.37097	−	6.89073i	0.142934	−	0.718408i
$93$		0			0
$94$	−3.39541	+	9.02077i	−0.350210	+	0.930421i
$95$	−2.23911	−	3.87825i	−0.229728	−	0.397900i
$96$		0			0
$97$	8.12677			0.825148			0.412574	−	0.910924i	$-0.364630\pi$
$97$	8.12677			0.825148			0.412574	+	0.910924i	$0.364630\pi$
$98$	7.32470	−	6.65949i	0.739907	−	0.672710i
$99$		0			0
$100$	−5.76078	−	5.05253i	−0.576078	−	0.505253i
$101$	−1.32037	+	0.762317i	−0.131382	+	0.0758534i	−0.564250	−	0.825604i	$-0.690835\pi$
$101$	−1.32037	+	0.762317i	−0.131382	+	0.0758534i	0.432869	+	0.901457i	$0.357501\pi$
$102$		0			0
$103$	−6.69999	−	3.86824i	−0.660170	−	0.381149i	0.132172	−	0.991227i	$-0.457805\pi$
$103$	−6.69999	−	3.86824i	−0.660170	−	0.381149i	−0.792342	+	0.610078i	$0.791138\pi$
$104$	−2.03554	+	1.08784i	−0.199601	+	0.106672i
$105$		0			0
$106$	3.78557	−	3.10659i	0.367687	−	0.301739i
$107$	−0.602928	+	1.04430i	−0.0582873	+	0.100957i	−0.893697	−	0.448672i	$-0.851897\pi$
$107$	−0.602928	+	1.04430i	−0.0582873	+	0.100957i	0.835409	+	0.549628i	$0.185231\pi$
$108$		0			0
$109$	0.314166	+	0.544151i	0.0300916	+	0.0521202i	0.880679	−	0.473713i	$-0.157087\pi$
$109$	0.314166	+	0.544151i	0.0300916	+	0.0521202i	−0.850587	+	0.525834i	$0.823753\pi$
$110$	1.21504	+	7.36041i	0.115849	+	0.701788i
$111$		0			0
$112$	−8.55599	−	6.22856i	−0.808465	−	0.588544i
$113$		−	11.7870i		−	1.10882i	−0.832242	−	0.554412i	$-0.812943\pi$
$113$		−	11.7870i		−	1.10882i	0.832242	−	0.554412i	$-0.187057\pi$
$114$		0			0
$115$	−3.28891	+	1.89885i	−0.306692	+	0.177069i
$116$	−6.17727	−	18.2003i	−0.573545	−	1.68986i
$117$		0			0
$118$	4.49867	+	5.48189i	0.414136	+	0.504649i
$119$	3.25533	+	3.09444i	0.298416	+	0.283667i
$120$		0			0
$121$	−6.40444	+	11.0928i	−0.582222	+	1.00844i
$122$	−6.83226	+	18.1516i	−0.618564	+	1.64337i
$123$		0			0
$124$	11.7852	−	13.4372i	1.05834	−	1.20670i
$125$			9.54728i			0.853934i
$126$		0			0
$127$			5.46528i			0.484966i	0.970156	+	0.242483i	$0.0779618\pi$
$127$			5.46528i			0.484966i	−0.970156	+	0.242483i	$0.922038\pi$
$128$	−4.67087	+	10.3045i	−0.412850	+	0.910799i
$129$		0			0
$130$	1.16758	+	0.439478i	0.102404	+	0.0385447i
$131$	7.94069	−	13.7537i	0.693782	−	1.20167i	−0.276808	−	0.960925i	$-0.589277\pi$
$131$	7.94069	−	13.7537i	0.693782	−	1.20167i	0.970590	−	0.240740i	$-0.0773901\pi$
$132$		0			0
$133$	2.56752	−	10.6547i	0.222633	−	0.923879i
$134$	4.63061	−	3.80007i	0.400024	−	0.328276i
$135$		0			0
$136$	2.53580	−	4.07729i	0.217443	−	0.349625i
$137$	−10.7072	+	6.18180i	−0.914777	+	0.528147i	−0.881965	−	0.471315i	$-0.843780\pi$
$137$	−10.7072	+	6.18180i	−0.914777	+	0.528147i	−0.0328121	+	0.999462i	$0.510446\pi$
$138$		0			0
$139$			17.2243i			1.46095i	0.682941	+	0.730473i	$0.260701\pi$
$139$			17.2243i			1.46095i	−0.682941	+	0.730473i	$0.739299\pi$
$140$	0.518350	+	5.69698i	0.0438085	+	0.481483i
$141$		0			0
$142$	−16.5425	+	2.73080i	−1.38822	+	0.229164i
$143$	1.99080	+	3.44817i	0.166479	+	0.288350i
$144$		0			0
$145$	−5.19459	+	8.99729i	−0.431387	+	0.747184i
$146$	2.68743	+	3.27479i	0.222413	+	0.271024i
$147$		0			0
$148$	−2.63804	+	13.2592i	−0.216846	+	1.08990i
$149$	9.97002	+	5.75619i	0.816776	+	0.471566i	0.849303	−	0.527905i	$-0.177022\pi$
$149$	9.97002	+	5.75619i	0.816776	+	0.471566i	−0.0325274	+	0.999471i	$0.510356\pi$
$150$		0			0
$151$	−9.30760	+	5.37375i	−0.757442	+	0.437309i	−0.828377	−	0.560172i	$-0.810735\pi$
$151$	−9.30760	+	5.37375i	−0.757442	+	0.437309i	0.0709346	+	0.997481i	$0.477402\pi$
$152$	−11.7101	−	0.384138i	−0.949814	−	0.0311577i
$153$		0			0
$154$	−10.2554	+	15.1046i	−0.826406	+	1.21717i
$155$	−9.66109			−0.775998
$156$		0			0
$157$	11.7042	+	20.2723i	0.934099	+	1.61791i	0.776233	+	0.630446i	$0.217128\pi$
$157$	11.7042	+	20.2723i	0.934099	+	1.61791i	0.157865	+	0.987461i	$0.449539\pi$
$158$	−5.21946	−	1.96460i	−0.415238	−	0.156295i
$159$		0			0
$160$	5.85236	−	1.77458i	0.462669	−	0.140292i
$161$	−9.03560	−	2.17736i	−0.712105	−	0.171600i
$162$		0			0
$163$	2.35163	+	1.35771i	0.184193	+	0.106344i	0.589261	−	0.807942i	$-0.299419\pi$
$163$	2.35163	+	1.35771i	0.184193	+	0.106344i	−0.405068	+	0.914287i	$0.632752\pi$
$164$	−4.47813	−	13.1941i	−0.349683	−	1.03029i
$165$		0			0
$166$	−15.8128	+	2.61034i	−1.22731	+	0.202601i
$167$	−6.84595			−0.529756			−0.264878	−	0.964282i	$-0.585332\pi$
$167$	−6.84595			−0.529756			−0.264878	+	0.964282i	$0.585332\pi$
$168$		0			0
$169$	−12.3341			−0.948781
$170$	−2.56074	+	0.422722i	−0.196400	+	0.0324213i
$171$		0			0
$172$	−0.327980	−	0.966340i	−0.0250082	−	0.0736827i
$173$	−7.19348	−	4.15316i	−0.546910	−	0.315759i	0.200965	−	0.979599i	$-0.435592\pi$
$173$	−7.19348	−	4.15316i	−0.546910	−	0.315759i	−0.747875	+	0.663840i	$0.768926\pi$
$174$		0			0
$175$	−6.98381	+	7.34691i	−0.527926	+	0.555374i
$176$	18.0314	+	7.47073i	1.35917	+	0.563128i
$177$		0			0
$178$	−0.479032	−	0.180307i	−0.0359050	−	0.0135146i
$179$	10.4832	+	18.1575i	0.783554	+	1.35716i	0.929859	+	0.367917i	$0.119929\pi$
$179$	10.4832	+	18.1575i	0.783554	+	1.35716i	−0.146304	+	0.989240i	$0.546738\pi$
$180$		0			0
$181$	17.8558			1.32721			0.663605	−	0.748083i	$-0.269026\pi$
$181$	17.8558			1.32721			0.663605	+	0.748083i	$0.269026\pi$
$182$	1.33004	+	2.74825i	0.0985895	+	0.203714i
$183$		0			0
$184$	−0.325764	+	9.93063i	−0.0240157	+	0.732095i
$185$	6.32856	−	3.65380i	0.465285	−	0.268633i
$186$		0			0
$187$	−7.17354	−	4.14165i	−0.524581	−	0.302867i
$188$	2.65989	−	13.3690i	0.193992	−	0.975037i
$189$		0			0
$190$	4.01760	+	4.89568i	0.291467	+	0.355170i
$191$	−9.10942	+	15.7780i	−0.659135	+	1.14165i	0.321705	+	0.946840i	$0.395744\pi$
$191$	−9.10942	+	15.7780i	−0.659135	+	1.14165i	−0.980840	+	0.194815i	$0.937589\pi$
$192$		0			0
$193$	−9.35386	−	16.2014i	−0.673306	−	1.16620i	−0.976961	−	0.213418i	$-0.931540\pi$
$193$	−9.35386	−	16.2014i	−0.673306	−	1.16620i	0.303655	−	0.952782i	$-0.401793\pi$
$194$	−11.3395	+	1.87190i	−0.814130	+	0.134395i
$195$		0			0
$196$	−8.68644	+	10.9793i	−0.620460	+	0.784238i
$197$		−	22.2223i		−	1.58327i	−0.610994	−	0.791635i	$-0.709230\pi$
$197$		−	22.2223i		−	1.58327i	0.610994	−	0.791635i	$-0.290770\pi$
$198$		0			0
$199$	−13.8519	+	7.99738i	−0.981934	+	0.566920i	−0.902853	−	0.429949i	$-0.858532\pi$
$199$	−13.8519	+	7.99738i	−0.981934	+	0.566920i	−0.0790802	+	0.996868i	$0.525198\pi$
$200$	9.20198	+	5.72302i	0.650678	+	0.404679i
$201$		0			0
$202$	1.66676	−	1.36781i	0.117273	−	0.0962391i
$203$	−24.3848	+	7.20063i	−1.71148	+	0.505385i
$204$		0			0
$205$	−3.76575	+	6.52247i	−0.263011	+	0.455549i
$206$	10.2397	+	3.85421i	0.713434	+	0.268536i
$207$		0			0
$208$	2.58967	−	1.98676i	0.179562	−	0.137757i
$209$			20.2124i			1.39812i
$210$		0			0
$211$		−	8.32079i		−	0.572827i	−0.958106	−	0.286414i	$-0.907537\pi$
$211$		−	8.32079i		−	0.572827i	0.958106	−	0.286414i	$-0.0924631\pi$
$212$	−4.56655	+	5.20668i	−0.313632	+	0.357596i
$213$		0			0
$214$	0.600742	−	1.59602i	0.0410659	−	0.109102i
$215$	−0.275804	+	0.477707i	−0.0188097	+	0.0325794i
$216$		0			0
$217$	−17.1369	−	16.2899i	−1.16333	−	1.10583i
$218$	−0.563704	−	0.686906i	−0.0381788	−	0.0465232i
$219$		0			0
$220$	−3.39076	−	9.99033i	−0.228605	−	0.673548i
$221$	−1.19965	+	0.692615i	−0.0806969	+	0.0465904i
$222$		0			0
$223$		−	8.91285i		−	0.596848i	−0.954433	−	0.298424i	$-0.903539\pi$
$223$		−	8.91285i		−	0.596848i	0.954433	−	0.298424i	$-0.0964610\pi$
$224$	13.3731	+	6.72013i	0.893528	+	0.449007i
$225$		0			0
$226$	2.71498	+	16.4467i	0.180598	+	1.09402i
$227$	−10.2145	−	17.6920i	−0.677957	−	1.17426i	−0.975595	−	0.219578i	$-0.929532\pi$
$227$	−10.2145	−	17.6920i	−0.677957	−	1.17426i	0.297638	−	0.954679i	$-0.403801\pi$
$228$		0			0
$229$	6.21367	−	10.7624i	0.410611	−	0.711199i	−0.584346	−	0.811505i	$-0.698649\pi$
$229$	6.21367	−	10.7624i	0.410611	−	0.711199i	0.994957	+	0.100306i	$0.0319821\pi$
$230$	4.15173	−	3.40708i	0.273757	−	0.224657i
$231$		0			0
$232$	12.8116	+	23.9726i	0.841120	+	1.57388i
$233$	2.18246	+	1.26005i	0.142978	+	0.0825484i	0.569783	−	0.821796i	$-0.307027\pi$
$233$	2.18246	+	1.26005i	0.142978	+	0.0825484i	−0.426805	+	0.904344i	$0.640361\pi$
$234$		0			0
$235$	−6.38097	+	3.68405i	−0.416249	+	0.240321i
$236$	−7.53981	−	6.61284i	−0.490800	−	0.430459i
$237$		0			0
$238$	−5.25502	−	3.56794i	−0.340633	−	0.231275i
$239$	−25.2624			−1.63409			−0.817045	−	0.576574i	$-0.804389\pi$
$239$	−25.2624			−1.63409			−0.817045	+	0.576574i	$0.804389\pi$
$240$		0			0
$241$	7.31705	+	12.6735i	0.471333	+	0.816372i	0.999462	−	0.0327917i	$-0.0104398\pi$
$241$	7.31705	+	12.6735i	0.471333	+	0.816372i	−0.528130	+	0.849164i	$0.677106\pi$
$242$	6.38121	−	16.9533i	0.410200	−	1.08980i
$243$		0			0
$244$	5.35225	−	26.9013i	0.342643	−	1.72218i
$245$	7.55782	−	0.383236i	0.482851	−	0.0244841i
$246$		0			0
$247$	2.92731	+	1.69008i	0.186260	+	0.107537i
$248$	−13.3491	+	21.4639i	−0.847669	+	1.36296i
$249$		0			0
$250$	−2.19910	−	13.3216i	−0.139083	−	0.842532i
$251$	11.3947			0.719227			0.359613	−	0.933101i	$-0.382909\pi$
$251$	11.3947			0.719227			0.359613	+	0.933101i	$0.382909\pi$
$252$		0			0
$253$	17.1409			1.07764
$254$	−1.25886	−	7.62587i	−0.0789879	−	0.478490i
$255$		0			0
$256$	4.14388	−	15.4541i	0.258992	−	0.965879i
$257$	19.8884	+	11.4826i	1.24060	+	0.716263i	0.969217	−	0.246208i	$-0.0791846\pi$
$257$	19.8884	+	11.4826i	1.24060	+	0.716263i	0.271386	+	0.962471i	$0.412518\pi$
$258$		0			0
$259$	17.3864	+	4.18971i	1.08034	+	0.260336i
$260$	−1.73039	−	0.344277i	−0.107314	−	0.0213512i
$261$		0			0
$262$	−7.91189	+	21.0200i	−0.488798	+	1.29862i
$263$	11.6566	+	20.1898i	0.718775	+	1.24495i	0.961485	+	0.274856i	$0.0886301\pi$
$263$	11.6566	+	20.1898i	0.718775	+	1.24495i	−0.242711	+	0.970099i	$0.578037\pi$
$264$		0			0
$265$	3.74351			0.229962
$266$	−1.12836	+	15.4582i	−0.0691845	+	0.947803i
$267$		0			0
$268$	−5.58593	+	6.36895i	−0.341215	+	0.389046i
$269$	−25.3140	+	14.6150i	−1.54342	+	0.891094i	−0.544801	+	0.838565i	$0.683395\pi$
$269$	−25.3140	+	14.6150i	−1.54342	+	0.891094i	−0.998619	+	0.0525290i	$0.983272\pi$
$270$		0			0
$271$	0.829286	+	0.478788i	0.0503755	+	0.0290843i	0.524976	−	0.851117i	$-0.324074\pi$
$271$	0.829286	+	0.478788i	0.0503755	+	0.0290843i	−0.474601	+	0.880201i	$0.657408\pi$
$272$	−2.59913	+	6.27325i	−0.157595	+	0.380372i
$273$		0			0
$274$	13.5162	−	11.0919i	0.816541	−	0.670087i
$275$	9.34723	−	16.1899i	0.563659	−	0.976286i
$276$		0			0
$277$	−6.06856	−	10.5111i	−0.364624	−	0.631548i	0.624091	−	0.781351i	$-0.285469\pi$
$277$	−6.06856	−	10.5111i	−0.364624	−	0.631548i	−0.988716	+	0.149803i	$0.952136\pi$
$278$	−3.96741	−	24.0336i	−0.237949	−	1.44144i
$279$		0			0
$280$	−2.03550	−	7.82977i	−0.121644	−	0.467918i
$281$			23.7714i			1.41808i	0.705168	+	0.709041i	$0.250872\pi$
$281$			23.7714i			1.41808i	−0.705168	+	0.709041i	$0.749128\pi$
$282$		0			0
$283$	2.93570	−	1.69493i	0.174509	−	0.100753i	−0.410201	−	0.911995i	$-0.634542\pi$
$283$	2.93570	−	1.69493i	0.174509	−	0.100753i	0.584710	+	0.811242i	$0.301208\pi$
$284$	22.4533	−	7.62074i	1.33236	−	0.452208i
$285$		0			0
$286$	−3.57207	−	4.35278i	−0.211221	−	0.257385i
$287$	−17.6775	+	5.22000i	−1.04347	+	0.308127i
$288$		0			0
$289$	−7.05909	+	12.2267i	−0.415241	+	0.719218i
$290$	5.17575	−	13.7507i	0.303930	−	0.807468i
$291$		0			0
$292$	−4.50416	−	3.95040i	−0.263586	−	0.231179i
$293$			14.2017i			0.829673i	0.909896	+	0.414837i	$0.136161\pi$
$293$			14.2017i			0.829673i	−0.909896	+	0.414837i	$0.863839\pi$
$294$		0			0
$295$			5.42099i			0.315622i
$296$	0.626840	−	19.1086i	0.0364344	−	1.11067i
$297$		0			0
$298$	−15.2373	−	5.73532i	−0.882675	−	0.332238i
$299$	1.43326	−	2.48247i	0.0828873	−	0.143565i
$300$		0			0
$301$	−1.29470	+	0.382315i	−0.0746254	+	0.0220362i
$302$	11.7494	−	9.64204i	0.676102	−	0.554837i
$303$		0			0
$304$	16.4279	−	2.16128i	0.942206	−	0.123958i
$305$	−12.8398	+	7.41308i	−0.735206	+	0.424472i
$306$		0			0
$307$		−	25.7078i		−	1.46722i	−0.679571	−	0.733610i	$-0.737834\pi$
$307$		−	25.7078i		−	1.46722i	0.679571	−	0.733610i	$-0.262166\pi$
$308$	10.8305	−	23.4382i	0.617127	−	1.33551i
$309$		0			0
$310$	13.4804	−	2.22531i	0.765636	−	0.126389i
$311$	−4.39864	−	7.61867i	−0.249424	−	0.432015i	0.713942	−	0.700205i	$-0.246908\pi$
$311$	−4.39864	−	7.61867i	−0.249424	−	0.432015i	−0.963366	+	0.268190i	$0.913575\pi$
$312$		0			0
$313$	−6.87877	+	11.9144i	−0.388811	+	0.673440i	−0.992290	−	0.123939i	$-0.960447\pi$
$313$	−6.87877	+	11.9144i	−0.388811	+	0.673440i	0.603479	+	0.797379i	$0.293781\pi$
$314$	−21.0007	−	25.5906i	−1.18514	−	1.44416i
$315$		0			0
$316$	7.73539	+	1.53902i	0.435149	+	0.0865769i
$317$	9.53960	+	5.50769i	0.535797	+	0.309343i	0.743374	−	0.668876i	$-0.233224\pi$
$317$	9.53960	+	5.50769i	0.535797	+	0.309343i	−0.207577	+	0.978219i	$0.566558\pi$
$318$		0			0
$319$	40.6092	−	23.4458i	2.27368	−	1.31271i
$320$	−7.75721	+	3.82414i	−0.433641	+	0.213776i
$321$		0			0
$322$	13.1092	+	0.956898i	0.730546	+	0.0533258i
$323$	−7.03206			−0.391274
$324$		0			0
$325$	−1.56316	−	2.70746i	−0.0867082	−	0.150183i
$326$	−3.59402	−	1.35279i	−0.199055	−	0.0749239i
$327$		0			0
$328$	9.28757	+	17.3786i	0.512820	+	0.959574i
$329$	−17.5304	−	4.22440i	−0.966483	−	0.232899i
$330$		0			0
$331$	2.42290	+	1.39886i	0.133175	+	0.0768884i	0.565107	−	0.825017i	$-0.308835\pi$
$331$	2.42290	+	1.39886i	0.133175	+	0.0768884i	−0.431933	+	0.901906i	$0.642168\pi$
$332$	21.4628	−	7.28456i	1.17792	−	0.399792i
$333$		0			0
$334$	9.55236	−	1.57688i	0.522682	−	0.0862831i
$335$	4.57916			0.250186
$336$		0			0
$337$	−3.38341			−0.184306			−0.0921530	−	0.995745i	$-0.529375\pi$
$337$	−3.38341			−0.184306			−0.0921530	+	0.995745i	$0.529375\pi$
$338$	17.2102	−	2.84102i	0.936112	−	0.154531i
$339$		0			0
$340$	3.47571	−	1.17967i	0.188497	−	0.0639767i
$341$	37.7633	+	21.8027i	2.04500	+	1.18068i
$342$		0			0
$343$	14.0523	+	12.0637i	0.758751	+	0.651380i
$344$	0.680224	+	1.27282i	0.0366752	+	0.0686257i
$345$		0			0
$346$	10.9939	+	4.13810i	0.591036	+	0.222465i
$347$	−1.96566	−	3.40462i	−0.105522	−	0.182770i	0.808429	−	0.588593i	$-0.200318\pi$
$347$	−1.96566	−	3.40462i	−0.105522	−	0.182770i	−0.913951	+	0.405824i	$0.866985\pi$
$348$		0			0
$349$	16.1233			0.863058			0.431529	−	0.902099i	$-0.357974\pi$
$349$	16.1233			0.863058			0.431529	+	0.902099i	$0.357974\pi$
$350$	8.05245	−	11.8600i	0.430421	−	0.633944i
$351$		0			0
$352$	−26.8805	−	6.27083i	−1.43273	−	0.334236i
$353$	32.2263	−	18.6059i	1.71523	−	0.990290i	0.788106	−	0.615539i	$-0.211062\pi$
$353$	32.2263	−	18.6059i	1.71523	−	0.990290i	0.927126	−	0.374750i	$-0.122272\pi$
$354$		0			0
$355$	−11.0997	−	6.40843i	−0.589112	−	0.340124i
$356$	0.709939	+	0.141249i	0.0376267	+	0.00748617i
$357$		0			0
$358$	−18.8099	−	22.9210i	−0.994136	−	1.21141i
$359$	10.7770	−	18.6664i	0.568790	−	0.985173i	−0.427896	−	0.903828i	$-0.640745\pi$
$359$	10.7770	−	18.6664i	0.568790	−	0.985173i	0.996686	−	0.0813452i	$-0.0259216\pi$
$360$		0			0
$361$	−0.920383	−	1.59415i	−0.0484412	−	0.0839026i
$362$	−24.9147	+	4.11286i	−1.30949	+	0.216167i
$363$		0			0
$364$	−2.48888	−	3.52836i	−0.130453	−	0.184936i
$365$			3.23841i			0.169506i
$366$		0			0
$367$	−1.45961	+	0.842704i	−0.0761908	+	0.0439888i	−0.537611	−	0.843193i	$-0.680673\pi$
$367$	−1.45961	+	0.842704i	−0.0761908	+	0.0439888i	0.461421	+	0.887182i	$0.347340\pi$
$368$	−1.83285	−	13.9315i	−0.0955438	−	0.726231i
$369$		0			0
$370$	−7.98882	+	6.55596i	−0.415319	+	0.340828i
$371$	6.64025	+	6.31207i	0.344744	+	0.327706i
$372$		0			0
$373$	2.14560	−	3.71630i	0.111095	−	0.192422i	−0.805117	−	0.593116i	$-0.797897\pi$
$373$	2.14560	−	3.71630i	0.111095	−	0.192422i	0.916212	+	0.400694i	$0.131231\pi$
$374$	10.9634	+	4.12662i	0.566905	+	0.213383i
$375$		0			0
$376$	−0.632031	+	19.2669i	−0.0325945	+	0.993614i
$377$		−	7.84176i		−	0.403871i
$378$		0			0
$379$		−	3.00059i		−	0.154130i	−0.997026	−	0.0770650i	$-0.975445\pi$
$379$		−	3.00059i		−	0.154130i	0.997026	−	0.0770650i	$-0.0245549\pi$
$380$	−6.73354	−	5.90569i	−0.345423	−	0.302955i
$381$		0			0
$382$	9.07638	−	24.1137i	0.464388	−	1.23377i
$383$	10.5636	−	18.2967i	0.539774	−	0.934916i	−0.459142	−	0.888363i	$-0.651843\pi$
$383$	10.5636	−	18.2967i	0.539774	−	0.934916i	0.998916	−	0.0465530i	$-0.0148236\pi$
$384$		0			0
$385$	−13.3851	+	3.95249i	−0.682166	+	0.201438i
$386$	16.7835	+	20.4517i	0.854258	+	1.04096i
$387$		0			0
$388$	15.3912	−	5.22384i	0.781370	−	0.265200i
$389$	−29.5830	+	17.0798i	−1.49992	+	0.865979i	−1.00000		9.28896e-5i	$-0.999970\pi$
$389$	−29.5830	+	17.0798i	−1.49992	+	0.865979i	−0.499920	+	0.866072i	$0.666637\pi$
$390$		0			0
$391$			5.96347i			0.301585i
$392$	9.59150	−	17.3206i	0.484444	−	0.874822i
$393$		0			0
$394$	5.11862	+	31.0074i	0.257872	+	1.56213i
$395$	−2.13161	−	3.69206i	−0.107253	−	0.185768i
$396$		0			0
$397$	8.42503	−	14.5926i	0.422840	−	0.732380i	−0.573376	−	0.819292i	$-0.694367\pi$
$397$	8.42503	−	14.5926i	0.422840	−	0.732380i	0.996216	+	0.0869120i	$0.0276999\pi$
$398$	17.4858	−	14.3496i	0.876486	−	0.719280i
$399$		0			0
$400$	−14.1580	−	5.86593i	−0.707901	−	0.293297i
$401$	8.58950	+	4.95915i	0.428939	+	0.247648i	0.698894	−	0.715225i	$-0.253676\pi$
$401$	8.58950	+	4.95915i	0.428939	+	0.247648i	−0.269956	+	0.962873i	$0.587009\pi$
$402$		0			0
$403$	6.31524	−	3.64610i	0.314584	−	0.181625i
$404$	−2.01062	+	2.29247i	−0.100032	+	0.114055i
$405$		0			0
$406$	32.3663	−	15.6640i	1.60631	−	0.777391i
$407$	−32.9828			−1.63490
$408$		0			0
$409$	−18.0859	−	31.3257i	−0.894291	−	1.54896i	−0.834680	−	0.550736i	$-0.814347\pi$
$409$	−18.0859	−	31.3257i	−0.894291	−	1.54896i	−0.0596111	−	0.998222i	$-0.518986\pi$
$410$	3.75209	−	9.96838i	0.185302	−	0.492303i
$411$		0			0
$412$	−15.1755	−	3.01931i	−0.747645	−	0.148751i
$413$	−9.14053	+	9.61576i	−0.449776	+	0.473161i
$414$		0			0
$415$	−10.6101	−	6.12572i	−0.520828	−	0.300700i
$416$	−3.15582	+	3.36868i	−0.154727	+	0.165163i
$417$		0			0
$418$	−4.65568	−	28.2030i	−0.227717	−	1.37945i
$419$	−30.7098			−1.50027			−0.750137	−	0.661283i	$-0.770012\pi$
$419$	−30.7098			−1.50027			−0.750137	+	0.661283i	$0.770012\pi$
$420$		0			0
$421$	10.9036			0.531411			0.265706	−	0.964054i	$-0.414395\pi$
$421$	10.9036			0.531411			0.265706	+	0.964054i	$0.414395\pi$
$422$	1.91659	+	11.6102i	0.0932982	+	0.565178i
$423$		0			0
$424$	5.17255	−	8.31689i	0.251201	−	0.403904i
$425$	5.63258	+	3.25197i	0.273220	+	0.157744i
$426$		0			0
$427$	−35.2748	−	8.50037i	−1.70707	−	0.411362i
$428$	−0.470608	+	2.36535i	−0.0227477	+	0.114334i
$429$		0			0
$430$	0.274804	−	0.730087i	0.0132522	−	0.0352079i
$431$	7.83169	+	13.5649i	0.377239	+	0.653398i	0.990659	−	0.136359i	$-0.0435401\pi$
$431$	7.83169	+	13.5649i	0.377239	+	0.653398i	−0.613420	+	0.789757i	$0.710207\pi$
$432$		0			0
$433$	−22.8956			−1.10029			−0.550145	−	0.835069i	$-0.685428\pi$
$433$	−22.8956			−1.10029			−0.550145	+	0.835069i	$0.685428\pi$
$434$	27.6638	+	18.7826i	1.32790	+	0.901591i
$435$		0			0
$436$	0.944773	+	0.828618i	0.0452464	+	0.0396836i
$437$	12.6022	−	7.27586i	0.602843	−	0.348051i
$438$		0			0
$439$	14.9901	+	8.65454i	0.715438	+	0.413059i	0.813071	−	0.582164i	$-0.197794\pi$
$439$	14.9901	+	8.65454i	0.715438	+	0.413059i	−0.0976331	+	0.995222i	$0.531127\pi$
$440$	7.03238	+	13.1588i	0.335256	+	0.627321i
$441$		0			0
$442$	1.51436	−	1.24275i	0.0720310	−	0.0591116i
$443$	−5.69268	+	9.86000i	−0.270467	+	0.468463i	−0.968982	−	0.247133i	$-0.920512\pi$
$443$	−5.69268	+	9.86000i	−0.270467	+	0.468463i	0.698514	+	0.715596i	$0.253845\pi$
$444$		0			0
$445$	−0.195635	−	0.338850i	−0.00927400	−	0.0160630i
$446$	2.05296	+	12.4364i	0.0972107	+	0.588879i
$447$		0			0
$448$	−20.2078	−	6.29646i	−0.954728	−	0.297480i
$449$			11.1088i			0.524258i	0.965033	+	0.262129i	$0.0844245\pi$
$449$			11.1088i			0.524258i	−0.965033	+	0.262129i	$0.915575\pi$
$450$		0			0
$451$	29.4391	−	16.9967i	1.38624	−	0.800343i
$452$	−7.57658	−	22.3232i	−0.356373	−	1.04999i
$453$		0			0
$454$	18.3277	+	22.3333i	0.860160	+	1.04816i
$455$	−0.546777	+	2.26901i	−0.0256333	+	0.106373i
$456$		0			0
$457$	−13.5658	+	23.4967i	−0.634582	+	1.09913i	0.352022	+	0.935992i	$0.385494\pi$
$457$	−13.5658	+	23.4967i	−0.634582	+	1.09913i	−0.986604	+	0.163136i	$0.947839\pi$
$458$	−6.19113	+	16.4483i	−0.289293	+	0.768580i
$459$		0			0
$460$	−5.00826	+	5.71031i	−0.233511	+	0.266244i
$461$			13.2528i			0.617246i	0.951184	+	0.308623i	$0.0998682\pi$
$461$			13.2528i			0.617246i	−0.951184	+	0.308623i	$0.900132\pi$
$462$		0			0
$463$			4.07186i			0.189235i	0.995514	+	0.0946176i	$0.0301629\pi$
$463$			4.07186i			0.189235i	−0.995514	+	0.0946176i	$0.969837\pi$
$464$	−23.3981	−	30.4987i	−1.08623	−	1.41587i
$465$		0			0
$466$	−3.33549	−	1.25548i	−0.154514	−	0.0581588i
$467$	−11.7529	+	20.3565i	−0.543857	+	0.941988i	0.454821	+	0.890583i	$0.349703\pi$
$467$	−11.7529	+	20.3565i	−0.543857	+	0.941988i	−0.998678	+	0.0514053i	$0.983630\pi$
$468$		0			0
$469$	8.12253	+	7.72109i	0.375064	+	0.356527i
$470$	8.05498	−	6.61025i	0.371549	−	0.304908i
$471$		0			0
$472$	12.0437	+	7.49038i	0.554356	+	0.344773i
$473$	2.15613	−	1.24484i	0.0991390	−	0.0572380i
$474$		0			0
$475$		−	15.8706i		−	0.728191i
$476$	8.15432	+	3.76803i	0.373753	+	0.172707i
$477$		0			0
$478$	35.2494	−	5.81889i	1.61227	−	0.266150i
$479$	−1.86090	−	3.22317i	−0.0850266	−	0.147270i	0.820376	−	0.571825i	$-0.193764\pi$
$479$	−1.86090	−	3.22317i	−0.0850266	−	0.147270i	−0.905403	+	0.424554i	$0.860431\pi$
$480$		0			0
$481$	−2.75789	+	4.77681i	−0.125749	+	0.217804i
$482$	−13.1289	−	15.9983i	−0.598004	−	0.728704i
$483$		0			0
$484$	−4.99890	+	25.1253i	−0.227223	+	1.14206i
$485$	−7.60860	−	4.39283i	−0.345489	−	0.199468i
$486$		0			0
$487$	−14.5697	+	8.41182i	−0.660216	+	0.381176i	−0.792359	−	0.610055i	$-0.791147\pi$
$487$	−14.5697	+	8.41182i	−0.660216	+	0.381176i	0.132143	+	0.991231i	$0.457814\pi$
$488$	−1.27178	+	38.7689i	−0.0575707	+	1.75499i
$489$		0			0
$490$	−10.4574	+	2.27559i	−0.472416	+	0.102801i
$491$	6.75735			0.304955			0.152477	−	0.988307i	$-0.451275\pi$
$491$	6.75735			0.304955			0.152477	+	0.988307i	$0.451275\pi$
$492$		0			0
$493$	8.15696	+	14.1283i	0.367371	+	0.636305i
$494$	−4.47385	−	1.68395i	−0.201288	−	0.0757646i
$495$		0			0
$496$	13.6825	−	33.0240i	0.614360	−	1.48282i
$497$	−8.88323	−	30.0829i	−0.398467	−	1.34940i
$498$		0			0
$499$	14.9780	+	8.64752i	0.670505	+	0.387116i	0.796268	−	0.604944i	$-0.206805\pi$
$499$	14.9780	+	8.64752i	0.670505	+	0.387116i	−0.125763	+	0.992060i	$0.540138\pi$
$500$	6.13693	+	18.0815i	0.274452	+	0.808628i
$501$		0			0
$502$	−15.8994	+	2.62463i	−0.709623	+	0.117143i
$503$	6.05186			0.269839			0.134920	−	0.990857i	$-0.456922\pi$
$503$	6.05186			0.269839			0.134920	+	0.990857i	$0.456922\pi$
$504$		0			0
$505$	1.64824			0.0733459
$506$	−23.9173	+	3.94820i	−1.06325	+	0.175519i
$507$		0			0
$508$	3.51305	+	10.3506i	0.155866	+	0.459235i
$509$	−15.4989	−	8.94831i	−0.686978	−	0.396627i	0.115501	−	0.993307i	$-0.463153\pi$
$509$	−15.4989	−	8.94831i	−0.686978	−	0.396627i	−0.802479	+	0.596681i	$0.796486\pi$
$510$		0			0
$511$	−5.46040	+	5.74429i	−0.241554	+	0.254113i
$512$	−2.22242	+	22.5180i	−0.0982182	+	0.995165i
$513$		0			0
$514$	−30.3957	−	11.4409i	−1.34070	−	0.504637i
$515$	4.18186	+	7.24320i	0.184275	+	0.319173i
$516$		0			0
$517$	33.2560			1.46260
$518$	−25.2248	−	1.84128i	−1.10832	−	0.0809010i
$519$		0			0
$520$	2.49377	+	0.0818056i	0.109359	+	0.00358741i
$521$	6.17964	−	3.56782i	0.270735	−	0.156309i	−0.358487	−	0.933535i	$-0.616707\pi$
$521$	6.17964	−	3.56782i	0.270735	−	0.156309i	0.629222	+	0.777226i	$0.283374\pi$
$522$		0			0
$523$	37.1480	+	21.4474i	1.62437	+	0.937830i	0.985732	+	0.168323i	$0.0538352\pi$
$523$	37.1480	+	21.4474i	1.62437	+	0.937830i	0.638638	+	0.769507i	$0.279498\pi$
$524$	6.19801	−	31.1522i	0.270761	−	1.36089i
$525$		0			0
$526$	−20.9152	−	25.4864i	−0.911947	−	1.11126i
$527$	−7.58532	+	13.1382i	−0.330422	+	0.572307i
$528$		0			0
$529$	5.32978	+	9.23146i	0.231730	+	0.401368i
$530$	−5.22343	+	0.862271i	−0.226891	+	0.0374547i
$531$		0			0
$532$	−1.98617	−	21.8292i	−0.0861112	−	0.946416i
$533$		−	5.68478i		−	0.246235i
$534$		0			0
$535$	1.12897	−	0.651811i	0.0488096	−	0.0281803i
$536$	6.32720	−	10.1734i	0.273293	−	0.439426i
$537$		0			0
$538$	31.9550	−	26.2235i	1.37768	−	1.13058i
$539$	−30.4069	−	15.5581i	−1.30972	−	0.670135i
$540$		0			0
$541$	6.68983	−	11.5871i	0.287618	−	0.498170i	−0.685622	−	0.727957i	$-0.740470\pi$
$541$	6.68983	−	11.5871i	0.287618	−	0.498170i	0.973241	+	0.229788i	$0.0738032\pi$
$542$	−1.26741	−	0.477052i	−0.0544399	−	0.0204911i
$543$		0			0
$544$	2.18167	−	9.35193i	0.0935384	−	0.400961i
$545$		−	0.679274i		−	0.0290969i
$546$		0			0
$547$		−	16.1576i		−	0.690849i	−0.938447	−	0.345424i	$-0.887735\pi$
$547$		−	16.1576i		−	0.690849i	0.938447	−	0.345424i	$-0.112265\pi$
$548$	−16.3046	+	18.5902i	−0.696498	+	0.794132i
$549$		0			0
$550$	−9.31333	+	24.7432i	−0.397122	+	1.05505i
$551$	19.9042	−	34.4750i	0.847946	−	1.46869i
$552$		0			0
$553$	2.44426	−	10.1432i	0.103940	−	0.431332i
$554$	10.8887	+	13.2686i	0.462618	+	0.563727i
$555$		0			0
$556$	11.0717	+	32.6209i	0.469544	+	1.38344i
$557$	−4.80203	+	2.77245i	−0.203469	+	0.117473i	−0.598272	−	0.801293i	$-0.704146\pi$
$557$	−4.80203	+	2.77245i	−0.203469	+	0.117473i	0.394804	+	0.918765i	$0.370813\pi$
$558$		0			0
$559$		−	0.416355i		−	0.0176099i
$560$	4.64368	+	10.4563i	0.196231	+	0.441858i
$561$		0			0
$562$	−5.47544	−	33.1689i	−0.230968	−	1.39915i
$563$	21.7530	+	37.6772i	0.916778	+	1.58791i	0.804277	+	0.594255i	$0.202553\pi$
$563$	21.7530	+	37.6772i	0.916778	+	1.58791i	0.112501	+	0.993652i	$0.464114\pi$
$564$		0			0
$565$	−6.37130	+	11.0354i	−0.268042	+	0.464263i
$566$	−3.70586	+	3.04118i	−0.155769	+	0.127830i
$567$		0			0
$568$	−29.5744	+	15.8053i	−1.24091	+	0.663175i
$569$	−31.6927	−	18.2978i	−1.32863	−	0.767083i	−0.343539	−	0.939138i	$-0.611626\pi$
$569$	−31.6927	−	18.2978i	−1.32863	−	0.767083i	−0.985087	+	0.172056i	$0.944959\pi$
$570$		0			0
$571$	−17.5668	+	10.1422i	−0.735148	+	0.424438i	−0.820303	−	0.571930i	$-0.806195\pi$
$571$	−17.5668	+	10.1422i	−0.735148	+	0.424438i	0.0851545	+	0.996368i	$0.472862\pi$
$572$	5.98682	+	5.25078i	0.250322	+	0.219546i
$573$		0			0
$574$	23.4635	−	11.3554i	0.979349	−	0.473966i
$575$	−13.4589			−0.561274
$576$		0			0
$577$	4.86675	+	8.42945i	0.202605	+	0.350923i	0.949367	−	0.314169i	$-0.101726\pi$
$577$	4.86675	+	8.42945i	0.202605	+	0.350923i	−0.746762	+	0.665092i	$0.768392\pi$
$578$	7.03349	−	18.6863i	0.292554	−	0.777246i
$579$		0			0
$580$	−4.05457	+	20.3789i	−0.168357	+	0.846188i
$581$	−8.49135	−	28.7559i	−0.352281	−	1.19299i
$582$		0			0
$583$	−14.6326	−	8.44816i	−0.606022	−	0.349887i
$584$	7.19471	+	4.47463i	0.297719	+	0.185161i
$585$		0			0
$586$	−3.27119	−	19.8161i	−0.135132	−	0.818595i
$587$	32.9781			1.36115			0.680576	−	0.732678i	$-0.261730\pi$
$587$	32.9781			1.36115			0.680576	+	0.732678i	$0.261730\pi$
$588$		0			0
$589$	37.0185			1.52532
$590$	−1.24866	−	7.56406i	−0.0514064	−	0.311407i
$591$		0			0
$592$	3.52679	+	26.8072i	0.144950	+	1.10177i
$593$	30.7424	+	17.7491i	1.26244	+	0.728869i	0.973546	−	0.228493i	$-0.0733798\pi$
$593$	30.7424	+	17.7491i	1.26244	+	0.728869i	0.288892	+	0.957362i	$0.406713\pi$
$594$		0			0
$595$	−1.37510	−	4.65677i	−0.0563737	−	0.190909i
$596$	22.5822	+	4.49293i	0.925001	+	0.184037i
$597$		0			0
$598$	−1.42806	+	3.79400i	−0.0583976	+	0.155148i
$599$	14.8924	+	25.7944i	0.608488	+	1.05393i	0.991490	+	0.130185i	$0.0415570\pi$
$599$	14.8924	+	25.7944i	0.608488	+	1.05393i	−0.383002	+	0.923748i	$0.625110\pi$
$600$		0			0
$601$	−46.8743			−1.91204			−0.956021	−	0.293298i	$-0.905247\pi$
$601$	−46.8743			−1.91204			−0.956021	+	0.293298i	$0.905247\pi$
$602$	1.71848	−	0.831674i	0.0700399	−	0.0338965i
$603$		0			0
$604$	−14.1734	+	16.1601i	−0.576706	+	0.657547i
$605$	11.9922	−	6.92368i	0.487551	−	0.281488i
$606$		0			0
$607$	−19.2150	−	11.0938i	−0.779912	−	0.450283i	0.0564869	−	0.998403i	$-0.482010\pi$
$607$	−19.2150	−	11.0938i	−0.779912	−	0.450283i	−0.836399	+	0.548121i	$0.815343\pi$
$608$	−22.4245	+	6.79966i	−0.909435	+	0.275763i
$609$		0			0
$610$	16.2083	−	13.3012i	0.656254	−	0.538549i
$611$	2.78073	−	4.81636i	0.112496	−	0.194849i
$612$		0			0
$613$	−6.05599	−	10.4893i	−0.244599	−	0.423658i	0.717420	−	0.696641i	$-0.245323\pi$
$613$	−6.05599	−	10.4893i	−0.244599	−	0.423658i	−0.962019	+	0.272983i	$0.911990\pi$
$614$	5.92147	+	35.8708i	0.238971	+	1.44763i
$615$		0			0
$616$	−9.71347	+	35.1987i	−0.391367	+	1.41819i
$617$			19.5363i			0.786501i	0.919431	+	0.393250i	$0.128649\pi$
$617$			19.5363i			0.786501i	−0.919431	+	0.393250i	$0.871351\pi$
$618$		0			0
$619$	−0.819203	+	0.472967i	−0.0329265	+	0.0190102i	−0.516373	−	0.856364i	$-0.672718\pi$
$619$	−0.819203	+	0.472967i	−0.0329265	+	0.0190102i	0.483446	+	0.875374i	$0.339385\pi$
$620$	−18.2970	+	6.21009i	−0.734827	+	0.249403i
$621$		0			0
$622$	7.89242	+	9.61738i	0.316457	+	0.385622i
$623$	0.224329	−	0.930921i	0.00898757	−	0.0372966i
$624$		0			0
$625$	−4.41753	+	7.65138i	−0.176701	+	0.306055i
$626$	6.85382	−	18.2089i	0.273934	−	0.727775i
$627$		0			0
$628$	35.1974	+	30.8701i	1.40453	+	1.23185i
$629$		−	11.4750i		−	0.457537i
$630$		0			0
$631$			6.23847i			0.248350i	0.992260	+	0.124175i	$0.0396284\pi$
$631$			6.23847i			0.248350i	−0.992260	+	0.124175i	$0.960372\pi$
$632$	−11.1479	−	0.365696i	−0.443440	−	0.0145466i
$633$		0			0
$634$	−14.5795	−	5.48771i	−0.579026	−	0.217945i
$635$	2.95419	−	5.11681i	0.117234	−	0.203054i
$636$		0			0
$637$	−4.79574	+	3.10284i	−0.190014	+	0.122939i
$638$	−51.2628	+	42.0684i	−2.02952	+	1.66550i
$639$		0			0
$640$	9.94303	−	7.12271i	0.393033	−	0.281550i
$641$	−6.36278	+	3.67355i	−0.251315	+	0.145097i	−0.620366	−	0.784312i	$-0.713016\pi$
$641$	−6.36278	+	3.67355i	−0.251315	+	0.145097i	0.369051	+	0.929409i	$0.379683\pi$
$642$		0			0
$643$			44.8033i			1.76687i	0.468553	+	0.883436i	$0.344776\pi$
$643$			44.8033i			1.76687i	−0.468553	+	0.883436i	$0.655224\pi$
$644$	−18.5120	+	1.68435i	−0.729476	+	0.0663726i
$645$		0			0
$646$	9.81204	−	1.61975i	0.386049	−	0.0637281i
$647$	−4.89449	−	8.47750i	−0.192422	−	0.333285i	0.753630	−	0.657299i	$-0.228301\pi$
$647$	−4.89449	−	8.47750i	−0.192422	−	0.333285i	−0.946052	+	0.324014i	$0.894968\pi$
$648$		0			0
$649$	12.2338	−	21.1896i	0.480219	−	0.831764i
$650$	2.80475	+	3.41775i	0.110011	+	0.134055i
$651$		0			0
$652$	5.32645	+	1.05974i	0.208600	+	0.0415028i
$653$	−0.378115	−	0.218305i	−0.0147968	−	0.00854292i	0.492583	−	0.870265i	$-0.336053\pi$
$653$	−0.378115	−	0.218305i	−0.0147968	−	0.00854292i	−0.507380	+	0.861722i	$0.669386\pi$
$654$		0			0
$655$	−14.8688	+	8.58449i	−0.580971	+	0.335424i
$656$	−16.9622	−	22.1096i	−0.662261	−	0.863236i
$657$		0			0
$658$	25.4337	+	1.85652i	0.991510	+	0.0723748i
$659$	−26.0531			−1.01489			−0.507443	−	0.861685i	$-0.669409\pi$
$659$	−26.0531			−1.01489			−0.507443	+	0.861685i	$0.669409\pi$
$660$		0			0
$661$	−19.9044	−	34.4754i	−0.774191	−	1.34094i	−0.935248	−	0.353993i	$-0.884824\pi$
$661$	−19.9044	−	34.4754i	−0.774191	−	1.34094i	0.161057	−	0.986945i	$-0.448510\pi$
$662$	−3.70296	−	1.39379i	−0.143919	−	0.0541711i
$663$		0			0
$664$	−28.2697	+	15.1080i	−1.09708	+	0.586306i
$665$	−8.16308	+	8.58749i	−0.316551	+	0.333009i
$666$		0			0
$667$	−29.2362	−	16.8795i	−1.13203	−	0.653578i
$668$	−12.9655	+	4.40054i	−0.501649	+	0.170262i
$669$		0			0
$670$	−6.38944	+	1.05475i	−0.246846	+	0.0407487i
$671$	66.9179			2.58333
$672$		0			0
$673$	−8.26652			−0.318651			−0.159326	−	0.987226i	$-0.550932\pi$
$673$	−8.26652			−0.318651			−0.159326	+	0.987226i	$0.550932\pi$
$674$	4.72097	−	0.779326i	0.181845	−	0.0300185i
$675$		0			0
$676$	−23.3595	+	7.92832i	−0.898443	+	0.304935i
$677$	3.77905	+	2.18184i	0.145241	+	0.0838548i	0.570859	−	0.821048i	$-0.306610\pi$
$677$	3.77905	+	2.18184i	0.145241	+	0.0838548i	−0.425619	+	0.904903i	$0.639943\pi$
$678$		0			0
$679$	−6.08924	−	20.6211i	−0.233684	−	0.791367i
$680$	−4.57804	+	2.44662i	−0.175560	+	0.0938236i
$681$		0			0
$682$	−57.7143	−	21.7236i	−2.20999	−	0.831839i
$683$	11.8552	+	20.5339i	0.453628	+	0.785706i	0.998608	−	0.0527426i	$-0.0167963\pi$
$683$	11.8552	+	20.5339i	0.453628	+	0.785706i	−0.544981	+	0.838449i	$0.683463\pi$
$684$		0			0
$685$	13.3660			0.510688
$686$	−22.3863	−	13.5961i	−0.854712	−	0.519102i
$687$		0			0
$688$	−1.24231	−	1.61932i	−0.0473628	−	0.0617359i
$689$	−2.44705	+	1.41280i	−0.0932250	+	0.0538235i
$690$		0			0
$691$	19.8985	+	11.4884i	0.756974	+	0.437039i	0.828208	−	0.560421i	$-0.189361\pi$
$691$	19.8985	+	11.4884i	0.756974	+	0.437039i	−0.0712345	+	0.997460i	$0.522694\pi$
$692$	−16.2933	−	3.24170i	−0.619378	−	0.123231i
$693$		0			0
$694$	3.52695	+	4.29780i	0.133881	+	0.163142i
$695$	9.31039	−	16.1261i	0.353163	−	0.611697i
$696$		0			0
$697$	5.91328	+	10.2421i	0.223982	+	0.387947i
$698$	−22.4973	+	3.71379i	−0.851534	+	0.140569i
$699$		0			0
$700$	−8.50401	+	18.4034i	−0.321421	+	0.695583i
$701$		−	37.9118i		−	1.43191i	−0.698146	−	0.715955i	$-0.745991\pi$
$701$		−	37.9118i		−	1.43191i	0.698146	−	0.715955i	$-0.254009\pi$
$702$		0			0
$703$	−24.2492	+	14.0003i	−0.914577	+	0.528031i
$704$	38.9515	+	2.55829i	1.46804	+	0.0964191i
$705$		0			0
$706$	−40.6807	+	33.3842i	−1.53104	+	1.25643i
$707$	2.92366	+	2.77917i	0.109956	+	0.104521i
$708$		0			0
$709$	14.4546	−	25.0361i	0.542855	−	0.940252i	−0.455884	−	0.890039i	$-0.650677\pi$
$709$	14.4546	−	25.0361i	0.542855	−	0.940252i	0.998739	−	0.0502127i	$-0.0159899\pi$
$710$	16.9639	+	6.38518i	0.636643	+	0.239632i
$711$		0			0
$712$	−1.02313	−	0.0335629i	−0.0383435	−	0.00125782i
$713$		−	31.3932i		−	1.17568i
$714$		0			0
$715$		−	4.30441i		−	0.160976i
$716$	31.5256	+	27.6497i	1.17817	+	1.03332i
$717$		0			0
$718$	−10.7379	+	28.5281i	−0.400737	+	1.06466i
$719$	15.2533	−	26.4195i	0.568852	−	0.985280i	−0.427828	−	0.903860i	$-0.640721\pi$
$719$	15.2533	−	26.4195i	0.568852	−	0.985280i	0.996680	−	0.0814198i	$-0.0259454\pi$
$720$		0			0
$721$	−4.79523	+	19.8992i	−0.178584	+	0.741085i
$722$	1.65143	+	2.01237i	0.0614599	+	0.0748925i
$723$		0			0
$724$	33.8169	−	11.4776i	1.25679	−	0.426561i
$725$	−31.8859	+	18.4093i	−1.18421	+	0.683706i
$726$		0			0
$727$			19.4515i			0.721415i	0.932679	+	0.360708i	$0.117465\pi$
$727$			19.4515i			0.721415i	−0.932679	+	0.360708i	$0.882535\pi$
$728$	4.28552	+	4.34994i	0.158832	+	0.161220i
$729$		0			0
$730$	−0.745927	−	4.51864i	−0.0276080	−	0.167242i
$731$	0.433091	+	0.750135i	0.0160184	+	0.0277447i
$732$		0			0
$733$	−9.52314	+	16.4946i	−0.351745	+	0.609241i	−0.986555	−	0.163428i	$-0.947745\pi$
$733$	−9.52314	+	16.4946i	−0.351745	+	0.609241i	0.634810	+	0.772668i	$0.281078\pi$
$734$	1.84253	−	1.51205i	0.0680089	−	0.0558109i
$735$		0			0
$736$	5.76638	+	19.0169i	0.212552	+	0.700972i
$737$	−17.8990	−	10.3340i	−0.659320	−	0.380658i
$738$		0			0
$739$	−26.3030	+	15.1860i	−0.967571	+	0.558628i	−0.898495	−	0.438984i	$-0.855339\pi$
$739$	−26.3030	+	15.1860i	−0.967571	+	0.558628i	−0.0690765	+	0.997611i	$0.522005\pi$
$740$	9.63696	−	10.9878i	0.354262	−	0.403921i
$741$		0			0
$742$	−10.7192	−	7.27792i	−0.393516	−	0.267181i
$743$	−13.1841			−0.483676			−0.241838	−	0.970317i	$-0.577750\pi$
$743$	−13.1841			−0.483676			−0.241838	+	0.970317i	$0.577750\pi$
$744$		0			0
$745$	−6.22288	−	10.7783i	−0.227989	−	0.394888i
$746$	−2.13782	+	5.67967i	−0.0782712	+	0.207947i
$747$		0			0
$748$	−16.2481	−	3.23271i	−0.594090	−	0.118200i
$749$	3.10161	+	0.747414i	0.113331	+	0.0273099i
$750$		0			0
$751$	28.5934	+	16.5084i	1.04339	+	0.602400i	0.920791	−	0.390057i	$-0.127545\pi$
$751$	28.5934	+	16.5084i	1.04339	+	0.602400i	0.122596	+	0.992457i	$0.460878\pi$
$752$	−3.55600	−	27.0292i	−0.129674	−	0.985655i
$753$		0			0
$754$	1.80625	+	10.9418i	0.0657798	+	0.398478i
$755$	11.6189			0.422853
$756$		0			0
$757$	−31.2886			−1.13720			−0.568601	−	0.822613i	$-0.692515\pi$
$757$	−31.2886			−1.13720			−0.568601	+	0.822613i	$0.692515\pi$
$758$	0.691149	+	4.18682i	0.0251037	+	0.152072i
$759$		0			0
$760$	10.7558	+	6.68939i	0.390154	+	0.242650i
$761$	−4.37627	−	2.52664i	−0.158640	−	0.0915906i	0.418579	−	0.908181i	$-0.362528\pi$
$761$	−4.37627	−	2.52664i	−0.158640	−	0.0915906i	−0.577218	+	0.816590i	$0.695862\pi$
$762$		0			0
$763$	1.14535	−	1.20490i	0.0414644	−	0.0436203i
$764$	−7.11024	+	35.7372i	−0.257240	+	1.29293i
$765$		0			0
$766$	−10.5253	+	27.9631i	−0.380293	+	1.01035i
$767$	−2.04588	−	3.54357i	−0.0738726	−	0.127951i
$768$		0			0
$769$	−5.29930			−0.191098			−0.0955489	−	0.995425i	$-0.530461\pi$
$769$	−5.29930			−0.191098			−0.0955489	+	0.995425i	$0.530461\pi$
$770$	17.7662	−	8.59811i	0.640248	−	0.309854i
$771$		0			0
$772$	−28.1293	−	24.6710i	−1.01240	−	0.887928i
$773$	20.1963	−	11.6604i	0.726411	−	0.419394i	−0.0906965	−	0.995879i	$-0.528909\pi$
$773$	20.1963	−	11.6604i	0.726411	−	0.419394i	0.817108	+	0.576485i	$0.195576\pi$
$774$		0			0
$775$	−29.6513	−	17.1192i	−1.06511	−	0.614940i
$776$	−20.2725	+	10.8341i	−0.727742	+	0.388923i
$777$		0			0
$778$	37.3440	−	30.6460i	1.33885	−	1.09871i
$779$	14.4293	−	24.9922i	0.516982	−	0.895439i
$780$		0			0
$781$	28.9244	+	50.0986i	1.03500	+	1.79267i
$782$	−1.37361	−	8.32100i	−0.0491202	−	0.297558i
$783$		0			0
$784$	−9.39371	+	26.3772i	−0.335490	+	0.942044i
$785$		−	25.3063i		−	0.903220i
$786$		0			0
$787$	−36.4126	+	21.0228i	−1.29797	+	0.749383i	−0.980053	−	0.198735i	$-0.936317\pi$
$787$	−36.4126	+	21.0228i	−1.29797	+	0.749383i	−0.317917	+	0.948119i	$0.602983\pi$
$788$	−14.2843	−	42.0865i	−0.508858	−	1.49927i
$789$		0			0
$790$	3.82472	+	4.66065i	0.136077	+	0.165818i
$791$	−29.9086	+	8.83176i	−1.06343	+	0.314021i
$792$		0			0
$793$	5.59540	−	9.69152i	0.198699	−	0.344156i
$794$	−8.39447	+	22.3021i	−0.297909	+	0.791470i
$795$		0			0
$796$	−21.0932	+	24.0501i	−0.747630	+	0.852432i
$797$		−	21.9503i		−	0.777519i	−0.921339	−	0.388760i	$-0.872904\pi$
$797$		−	21.9503i		−	0.777519i	0.921339	−	0.388760i	$-0.127096\pi$
$798$		0			0
$799$			11.5700i			0.409317i
$800$	21.1063	+	4.92379i	0.746219	+	0.174082i
$801$		0			0
$802$	−13.1275	−	4.94116i	−0.463547	−	0.174478i
$803$	7.30827	−	12.6583i	0.257903	−	0.446702i
$804$		0			0
$805$	7.28254	+	6.92262i	0.256676	+	0.243990i
$806$	−7.97200	+	6.54215i	−0.280802	+	0.230437i
$807$		0			0
$808$	2.27744	−	3.66187i	0.0801201	−	0.128824i
$809$	42.1387	−	24.3288i	1.48152	−	0.855355i	0.481739	−	0.876315i	$-0.340005\pi$
$809$	42.1387	−	24.3288i	1.48152	−	0.855355i	0.999780	+	0.0209595i	$0.00667210\pi$
$810$		0			0
$811$			2.14916i			0.0754672i	0.999288	+	0.0377336i	$0.0120138\pi$
$811$			2.14916i			0.0754672i	−0.999288	+	0.0377336i	$0.987986\pi$
$812$	−41.5537	+	29.3116i	−1.45825	+	1.02864i
$813$		0			0
$814$	46.0219	−	7.59719i	1.61307	−	0.266281i
$815$	−1.46779	−	2.54228i	−0.0514144	−	0.0890523i
$816$		0			0
$817$	1.05680	−	1.83044i	0.0369729	−	0.0640389i
$818$	32.4513	+	39.5438i	1.13463	+	1.38262i
$819$		0			0
$820$	−2.93931	+	14.7734i	−0.102645	+	0.515910i
$821$	11.4656	+	6.61966i	0.400152	+	0.231028i	0.686549	−	0.727083i	$-0.259125\pi$
$821$	11.4656	+	6.61966i	0.400152	+	0.231028i	−0.286398	+	0.958111i	$0.592458\pi$
$822$		0			0
$823$	48.8020	−	28.1759i	1.70113	−	0.982149i	0.756514	−	0.653977i	$-0.226901\pi$
$823$	48.8020	−	28.1759i	1.70113	−	0.982149i	0.944618	−	0.328172i	$-0.106432\pi$
$824$	21.8703	+	0.717435i	0.761889	+	0.0249930i
$825$		0			0
$826$	10.5392	−	15.5226i	0.366705	−	0.540099i
$827$	44.4024			1.54402			0.772011	−	0.635609i	$-0.219251\pi$
$827$	44.4024			1.54402			0.772011	+	0.635609i	$0.219251\pi$
$828$		0			0
$829$	16.2282	+	28.1080i	0.563627	+	0.976231i	0.997176	+	0.0751011i	$0.0239279\pi$
$829$	16.2282	+	28.1080i	0.563627	+	0.976231i	−0.433549	+	0.901130i	$0.642739\pi$
$830$	16.2155	+	6.10351i	0.562849	+	0.211856i
$831$		0			0
$832$	3.62748	−	5.42733i	0.125760	−	0.188159i
$833$	5.41279	−	10.5788i	0.187542	−	0.366534i
$834$		0			0
$835$	6.40945	+	3.70050i	0.221808	+	0.128061i
$836$	12.9924	+	38.2801i	0.449352	+	1.32394i
$837$		0			0
$838$	42.8503	−	7.07363i	1.48024	−	0.244354i
$839$	−25.8761			−0.893342			−0.446671	−	0.894698i	$-0.647391\pi$
$839$	−25.8761			−0.893342			−0.446671	+	0.894698i	$0.647391\pi$
$840$		0			0
$841$	−63.3527			−2.18458
$842$	−15.2142	+	2.51152i	−0.524315	+	0.0865527i
$843$		0			0
$844$	−5.34856	−	15.7587i	−0.184105	−	0.542435i
$845$	11.5477	+	6.66707i	0.397253	+	0.229354i
$846$		0			0
$847$	32.9460	+	7.93919i	1.13204	+	0.272794i
$848$	−5.30172	+	12.7962i	−0.182062	+	0.439424i
$849$		0			0
$850$	−8.60836	−	3.24018i	−0.295264	−	0.111137i
$851$	11.8728	+	20.5643i	0.406995	+	0.704936i
$852$		0			0
$853$	14.9017			0.510225			0.255113	−	0.966911i	$-0.417887\pi$
$853$	14.9017			0.510225			0.255113	+	0.966911i	$0.417887\pi$
$854$	51.1779	+	3.73571i	1.75127	+	0.127833i
$855$		0			0
$856$	0.111824	−	3.40884i	0.00382206	−	0.116512i
$857$	17.4299	−	10.0632i	0.595395	−	0.343751i	−0.171833	−	0.985126i	$-0.554969\pi$
$857$	17.4299	−	10.0632i	0.595395	−	0.343751i	0.767228	+	0.641375i	$0.221636\pi$
$858$		0			0
$859$	9.71584	+	5.60944i	0.331500	+	0.191392i	0.656507	−	0.754320i	$-0.272033\pi$
$859$	9.71584	+	5.60944i	0.331500	+	0.191392i	−0.325007	+	0.945712i	$0.605367\pi$
$860$	−0.215276	+	1.08201i	−0.00734084	+	0.0368962i
$861$		0			0
$862$	−14.0523	−	17.1236i	−0.478623	−	0.583231i
$863$	16.4955	−	28.5711i	0.561514	−	0.972571i	−0.435850	−	0.900019i	$-0.643552\pi$
$863$	16.4955	−	28.5711i	0.561514	−	0.972571i	0.997365	−	0.0725520i	$-0.0231143\pi$
$864$		0			0
$865$	4.48988	+	7.77670i	0.152660	+	0.264416i
$866$	31.9468	−	5.27371i	1.08560	−	0.179208i
$867$		0			0
$868$	−42.9264	−	19.8358i	−1.45702	−	0.673272i
$869$			19.2420i			0.652742i
$870$		0			0
$871$	−2.99329	+	1.72818i	−0.101424	+	0.0585571i
$872$	−1.50913	−	0.938579i	−0.0511056	−	0.0317843i
$873$		0			0
$874$	−15.9083	+	13.0550i	−0.538105	+	0.441591i
$875$	24.2256	−	7.15361i	0.818974	−	0.241836i
$876$		0			0
$877$	17.8909	−	30.9880i	0.604134	−	1.04639i	−0.388054	−	0.921637i	$-0.626852\pi$
$877$	17.8909	−	30.9880i	0.604134	−	1.04639i	0.992188	−	0.124754i	$-0.0398142\pi$
$878$	−22.9096	−	8.62315i	−0.773161	−	0.291017i
$879$		0			0
$880$	−12.8435	−	16.7410i	−0.432953	−	0.564340i
$881$			3.68853i			0.124270i	0.998068	+	0.0621348i	$0.0197909\pi$
$881$			3.68853i			0.124270i	−0.998068	+	0.0621348i	$0.980209\pi$
$882$		0			0
$883$			12.4938i			0.420449i	0.977653	+	0.210224i	$0.0674195\pi$
$883$			12.4938i			0.420449i	−0.977653	+	0.210224i	$0.932581\pi$
$884$	−1.82679	+	2.08286i	−0.0614415	+	0.0700542i
$885$		0			0
$886$	5.67203	−	15.0692i	0.190556	−	0.506259i
$887$	−0.427511	+	0.740471i	−0.0143544	+	0.0248626i	−0.873113	−	0.487517i	$-0.837903\pi$
$887$	−0.427511	+	0.740471i	−0.0143544	+	0.0248626i	0.858759	+	0.512380i	$0.171236\pi$
$888$		0			0
$889$	13.8678	−	4.09504i	0.465111	−	0.137343i
$890$	0.351025	+	0.427745i	0.0117664	+	0.0143381i
$891$		0			0
$892$	−5.72912	−	16.8799i	−0.191825	−	0.565182i
$893$	24.4500	−	14.1162i	0.818190	−	0.472382i
$894$		0			0
$895$		−	22.6664i		−	0.757653i
$896$	29.6468	+	4.13103i	0.990431	+	0.138008i
$897$		0			0
$898$	−2.55878	−	15.5005i	−0.0853876	−	0.517257i
$899$	−42.9403	−	74.3748i	−1.43214	−	2.48054i
$900$		0			0
$901$	2.93918	−	5.09081i	0.0979183	−	0.169599i
$902$	−37.1623	+	30.4969i	−1.23737	+	1.01544i
$903$		0			0
$904$	15.7137	+	29.4030i	0.522630	+	0.977930i
$905$	−16.7173	−	9.65172i	−0.555701	−	0.320834i
$906$		0			0
$907$	−25.5068	+	14.7264i	−0.846939	+	0.488981i	−0.859617	−	0.510939i	$-0.829298\pi$
$907$	−25.5068	+	14.7264i	−0.846939	+	0.488981i	0.0126776	+	0.999920i	$0.495964\pi$
$908$	−30.7173	−	26.9408i	−1.01939	−	0.894062i
$909$		0			0
$910$	0.240295	−	3.29196i	0.00796571	−	0.109127i
$911$	9.62988			0.319052			0.159526	−	0.987194i	$-0.449003\pi$
$911$	9.62988			0.319052			0.159526	+	0.987194i	$0.449003\pi$
$912$		0			0
$913$	27.6484	+	47.8885i	0.915030	+	1.58488i
$914$	13.5166	−	35.9103i	0.447089	−	1.18781i
$915$		0			0
$916$	4.85000	−	24.3769i	0.160249	−	0.805435i
$917$	−40.8489	−	9.84360i	−1.34895	−	0.325064i
$918$		0			0
$919$	5.68583	+	3.28272i	0.187558	+	0.108287i	0.590839	−	0.806790i	$-0.298797\pi$
$919$	5.68583	+	3.28272i	0.187558	+	0.108287i	−0.403281	+	0.915076i	$0.632130\pi$
$920$	5.67287	−	9.12135i	0.187029	−	0.300722i
$921$		0			0
$922$	−3.05263	−	18.4921i	−0.100533	−	0.609004i
$923$	9.67418			0.318429
$924$		0			0
$925$	25.8977			0.851512
$926$	−0.937902	−	5.68158i	−0.0308214	−	0.186708i
$927$		0			0
$928$	39.6731	+	37.1663i	1.30233	+	1.22004i
$929$	−18.6881	−	10.7896i	−0.613137	−	0.353995i	0.161055	−	0.986945i	$-0.448510\pi$
$929$	−18.6881	−	10.7896i	−0.613137	−	0.353995i	−0.774192	+	0.632951i	$0.781844\pi$
$930$		0			0
$931$	−28.9594	+	1.46845i	−0.949106	+	0.0481265i
$932$	4.94330	+	0.983513i	0.161923	+	0.0322161i
$933$		0			0
$934$	11.7102	−	31.1112i	0.383170	−	1.01799i
$935$	4.47743	+	7.75514i	0.146428	+	0.253620i
$936$		0			0
$937$	−38.5055			−1.25792			−0.628960	−	0.777437i	$-0.716519\pi$
$937$	−38.5055			−1.25792			−0.628960	+	0.777437i	$0.716519\pi$
$938$	−13.1121	−	8.90255i	−0.428124	−	0.290678i
$939$		0			0
$940$	−9.71676	+	11.0788i	−0.316926	+	0.361352i
$941$	1.30779	−	0.755052i	0.0426327	−	0.0246140i	−0.478532	−	0.878070i	$-0.658831\pi$
$941$	1.30779	−	0.755052i	0.0426327	−	0.0246140i	0.521165	+	0.853456i	$0.325498\pi$
$942$		0			0
$943$	−21.1944	−	12.2366i	−0.690184	−	0.398478i
$944$	−18.5303	−	7.67743i	−0.603108	−	0.249879i
$945$		0			0
$946$	−2.72178	+	2.23361i	−0.0884927	+	0.0726208i
$947$	−2.64972	+	4.58945i	−0.0861044	+	0.149137i	−0.905861	−	0.423574i	$-0.860775\pi$
$947$	−2.64972	+	4.58945i	−0.0861044	+	0.149137i	0.819757	+	0.572712i	$0.194109\pi$
$948$		0			0
$949$	−1.22218	−	2.11687i	−0.0396735	−	0.0687166i
$950$	3.65559	+	22.1447i	0.118603	+	0.718468i
$951$		0			0
$952$	−12.2459	−	3.37939i	−0.396891	−	0.109527i
$953$		−	60.6268i		−	1.96390i	−0.189151	−	0.981948i	$-0.560574\pi$
$953$		−	60.6268i		−	1.96390i	0.189151	−	0.981948i	$-0.439426\pi$
$954$		0			0
$955$	17.0572	−	9.84797i	0.551958	−	0.318673i
$956$	−47.8442	+	16.2385i	−1.54739	+	0.525192i
$957$		0			0
$958$	3.33899	+	4.06875i	0.107878	+	0.131455i
$959$	23.7086	+	22.5369i	0.765592	+	0.727754i
$960$		0			0
$961$	24.4310	−	42.3158i	0.788098	−	1.36503i
$962$	2.74789	−	7.30047i	0.0885955	−	0.235376i
$963$		0			0
$964$	22.0041	+	19.2989i	0.708705	+	0.621574i
$965$			20.2245i			0.651049i
$966$		0			0
$967$		−	43.5917i		−	1.40181i	−0.713253	−	0.700907i	$-0.752779\pi$
$967$		−	43.5917i		−	1.40181i	0.713253	−	0.700907i	$-0.247221\pi$
$968$	1.18782	−	36.2095i	0.0381779	−	1.16382i
$969$		0			0
$970$	11.6283	+	4.37689i	0.373363	+	0.140534i
$971$	−9.75149	+	16.8901i	−0.312940	+	0.542028i	−0.978997	−	0.203872i	$-0.934647\pi$
$971$	−9.75149	+	16.8901i	−0.312940	+	0.542028i	0.666057	+	0.745901i	$0.267981\pi$
$972$		0			0
$973$	43.7056	−	12.9059i	1.40114	−	0.413743i
$974$	18.3920	−	15.0932i	0.589317	−	0.483618i
$975$		0			0
$976$	−7.15540	−	54.3884i	−0.229039	−	1.74093i
$977$	−51.2227	+	29.5734i	−1.63876	+	0.946137i	−0.657496	+	0.753458i	$0.728384\pi$
$977$	−51.2227	+	29.5734i	−1.63876	+	0.946137i	−0.981262	+	0.192679i	$0.938282\pi$
$978$		0			0
$979$			1.76600i			0.0564416i
$980$	14.0673	−	5.58393i	0.449364	−	0.178372i
$981$		0			0
$982$	−9.42873	+	1.55647i	−0.300883	+	0.0496690i
$983$	21.1885	+	36.6996i	0.675809	+	1.17054i	0.976232	+	0.216729i	$0.0695389\pi$
$983$	21.1885	+	36.6996i	0.675809	+	1.17054i	−0.300423	+	0.953806i	$0.597128\pi$
$984$		0			0
$985$	−12.0120	+	20.8053i	−0.382733	+	0.662913i
$986$	−14.6359	−	17.8347i	−0.466103	−	0.567974i
$987$		0			0
$988$	6.63037	+	1.31917i	0.210940	+	0.0419684i
$989$	−1.55228	−	0.896211i	−0.0493597	−	0.0284979i
$990$		0			0
$991$	−17.1417	+	9.89678i	−0.544525	+	0.314381i	−0.746911	−	0.664924i	$-0.768464\pi$
$991$	−17.1417	+	9.89678i	−0.544525	+	0.314381i	0.202386	+	0.979306i	$0.435130\pi$
$992$	−11.4849	+	49.2309i	−0.364645	+	1.56308i
$993$		0			0
$994$	19.3243	+	39.9295i	0.612929	+	1.26649i
$995$	17.2916			0.548179
$996$		0			0
$997$	−20.1621	−	34.9217i	−0.638539	−	1.10598i	−0.985753	−	0.168197i	$-0.946206\pi$
$997$	−20.1621	−	34.9217i	−0.638539	−	1.10598i	0.347214	−	0.937786i	$-0.387128\pi$
$998$	−22.8910	−	8.61616i	−0.724603	−	0.272740i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.be.c.107.1	✓	28
3.2	odd	2	inner	756.2.be.c.107.14	yes	28
4.3	odd	2		756.2.be.d.107.5	yes	28
7.4	even	3		756.2.be.d.431.10	yes	28
12.11	even	2		756.2.be.d.107.10	yes	28
21.11	odd	6		756.2.be.d.431.5	yes	28
28.11	odd	6	inner	756.2.be.c.431.14	yes	28
84.11	even	6	inner	756.2.be.c.431.1	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.be.c.107.1	✓	28	1.1	even	1	trivial
756.2.be.c.107.14	yes	28	3.2	odd	2	inner
756.2.be.c.431.1	yes	28	84.11	even	6	inner
756.2.be.c.431.14	yes	28	28.11	odd	6	inner
756.2.be.d.107.5	yes	28	4.3	odd	2
756.2.be.d.107.10	yes	28	12.11	even	2
756.2.be.d.431.5	yes	28	21.11	odd	6
756.2.be.d.431.10	yes	28	7.4	even	3

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39533 + 0.230338i) q^{2} +(1.89389 - 0.642794i) q^{4} +(-0.936239 - 0.540538i) q^{5} +(-0.749282 - 2.53743i) q^{7} +(-2.49454 + 1.33314i) q^{8} +O(q^{10})\)	\(q+(-1.39533 + 0.230338i) q^{2} +(1.89389 - 0.642794i) q^{4} +(-0.936239 - 0.540538i) q^{5} +(-0.749282 - 2.53743i) q^{7} +(-2.49454 + 1.33314i) q^{8} +(1.43087 + 0.538577i) q^{10} +(2.43972 + 4.22571i) q^{11} +0.815997 q^{13} +(1.62996 + 3.36797i) q^{14} +(3.17363 - 2.43476i) q^{16} +(-1.47016 + 0.848796i) q^{17} +(3.58740 + 2.07119i) q^{19} +(-2.12059 - 0.421910i) q^{20} +(-4.37755 - 5.33430i) q^{22} +(1.75645 - 3.04226i) q^{23} +(-1.91564 - 3.31798i) q^{25} +(-1.13858 + 0.187955i) q^{26} +(-3.05011 - 4.32399i) q^{28} -9.61003i q^{29} +(7.73929 - 4.46828i) q^{31} +(-3.86745 + 4.12830i) q^{32} +(1.85585 - 1.52298i) q^{34} +(-0.670072 + 2.78066i) q^{35} +(-3.37978 + 5.85395i) q^{37} +(-5.48267 - 2.06367i) q^{38} +(3.05610 + 0.100252i) q^{40} -6.96667i q^{41} -0.510241i q^{43} +(7.33682 + 6.43480i) q^{44} +(-1.75008 + 4.64953i) q^{46} +(3.40777 - 5.90243i) q^{47} +(-5.87715 + 3.80251i) q^{49} +(3.43720 + 4.18843i) q^{50} +(1.54541 - 0.524518i) q^{52} +(-2.99884 + 1.73138i) q^{53} -5.27504i q^{55} +(5.25188 + 5.33083i) q^{56} +(2.21355 + 13.4092i) q^{58} +(-2.50722 - 4.34263i) q^{59} +(6.85713 - 11.8769i) q^{61} +(-9.76964 + 8.01737i) q^{62} +(4.44546 - 6.65116i) q^{64} +(-0.763968 - 0.441077i) q^{65} +(-3.66826 + 2.11787i) q^{67} +(-2.23872 + 2.55253i) q^{68} +(0.294480 - 4.03428i) q^{70} +11.8557 q^{71} +(-1.49777 - 2.59421i) q^{73} +(3.36752 - 8.94668i) q^{74} +(8.12548 + 1.61664i) q^{76} +(8.89444 - 9.35688i) q^{77} +(3.41517 + 1.97175i) q^{79} +(-4.28736 + 0.564050i) q^{80} +(1.60469 + 9.72080i) q^{82} +11.3326 q^{83} +1.83523 q^{85} +(0.117528 + 0.711954i) q^{86} +(-11.7195 - 7.28872i) q^{88} +(0.313438 + 0.180963i) q^{89} +(-0.611412 - 2.07054i) q^{91} +(1.37097 - 6.89073i) q^{92} +(-3.39541 + 9.02077i) q^{94} +(-2.23911 - 3.87825i) q^{95} +8.12677 q^{97} +(7.32470 - 6.65949i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 4 q^{4} - 2 q^{7}+O(q^{10}) \) 28 * q - 4 * q^4 - 2 * q^7	\( 28 q - 4 q^{4} - 2 q^{7} - 20 q^{10} + 8 q^{13} + 12 q^{16} + 42 q^{19} + 4 q^{22} + 6 q^{25} - 28 q^{28} - 30 q^{31} + 24 q^{34} + 12 q^{37} + 36 q^{40} - 12 q^{46} - 14 q^{49} + 84 q^{52} + 28 q^{58} + 6 q^{61} + 8 q^{64} - 24 q^{67} + 128 q^{70} - 22 q^{73} - 48 q^{79} - 36 q^{82} - 24 q^{85} - 16 q^{88} - 16 q^{91} - 12 q^{94} - 4 q^{97}+O(q^{100}) \) 28 * q - 4 * q^4 - 2 * q^7 - 20 * q^10 + 8 * q^13 + 12 * q^16 + 42 * q^19 + 4 * q^22 + 6 * q^25 - 28 * q^28 - 30 * q^31 + 24 * q^34 + 12 * q^37 + 36 * q^40 - 12 * q^46 - 14 * q^49 + 84 * q^52 + 28 * q^58 + 6 * q^61 + 8 * q^64 - 24 * q^67 + 128 * q^70 - 22 * q^73 - 48 * q^79 - 36 * q^82 - 24 * q^85 - 16 * q^88 - 16 * q^91 - 12 * q^94 - 4 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more