LMFDB - Embedded newform 1134.2.e.r.919.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1134,2,Mod(865,1134)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1134, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 4]))

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

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

chi := DirichletCharacter("1134.865");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.e (of order $3$, degree $2$, not 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:	$9.05503558921$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			919.2
Root			$0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1134.919
Dual form			1134.2.e.r.865.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{4} +(1.62132 + 2.09077i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{4} +(1.62132 + 2.09077i) q^{7} -1.00000 q^{8} +(2.12132 - 3.67423i) q^{11} +(-3.12132 + 5.40629i) q^{13} +(-1.62132 - 2.09077i) q^{14} +1.00000 q^{16} +(-3.12132 + 5.40629i) q^{19} +(-2.12132 + 3.67423i) q^{22} +(3.62132 + 6.27231i) q^{23} +(2.50000 - 4.33013i) q^{25} +(3.12132 - 5.40629i) q^{26} +(1.62132 + 2.09077i) q^{28} +(-2.12132 - 3.67423i) q^{29} +0.757359 q^{31} -1.00000 q^{32} +(2.00000 - 3.46410i) q^{37} +(3.12132 - 5.40629i) q^{38} +(-2.74264 + 4.75039i) q^{41} +(3.24264 + 5.61642i) q^{43} +(2.12132 - 3.67423i) q^{44} +(-3.62132 - 6.27231i) q^{46} -13.2426 q^{47} +(-1.74264 + 6.77962i) q^{49} +(-2.50000 + 4.33013i) q^{50} +(-3.12132 + 5.40629i) q^{52} +(2.12132 + 3.67423i) q^{53} +(-1.62132 - 2.09077i) q^{56} +(2.12132 + 3.67423i) q^{58} +6.24264 q^{61} -0.757359 q^{62} +1.00000 q^{64} -8.24264 q^{67} +7.24264 q^{71} +(3.50000 + 6.06218i) q^{73} +(-2.00000 + 3.46410i) q^{74} +(-3.12132 + 5.40629i) q^{76} +(11.1213 - 1.52192i) q^{77} +9.24264 q^{79} +(2.74264 - 4.75039i) q^{82} +(3.87868 + 6.71807i) q^{83} +(-3.24264 - 5.61642i) q^{86} +(-2.12132 + 3.67423i) q^{88} +(-2.74264 + 4.75039i) q^{89} +(-16.3640 + 2.23936i) q^{91} +(3.62132 + 6.27231i) q^{92} +13.2426 q^{94} +(6.24264 + 10.8126i) q^{97} +(1.74264 - 6.77962i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 4 q^{4} - 2 q^{7} - 4 q^{8}+O(q^{10}) $ 4 * q - 4 * q^2 + 4 * q^4 - 2 * q^7 - 4 * q^8	$ 4 q - 4 q^{2} + 4 q^{4} - 2 q^{7} - 4 q^{8} - 4 q^{13} + 2 q^{14} + 4 q^{16} - 4 q^{19} + 6 q^{23} + 10 q^{25} + 4 q^{26} - 2 q^{28} + 20 q^{31} - 4 q^{32} + 8 q^{37} + 4 q^{38} + 6 q^{41} - 4 q^{43} - 6 q^{46} - 36 q^{47} + 10 q^{49} - 10 q^{50} - 4 q^{52} + 2 q^{56} + 8 q^{61} - 20 q^{62} + 4 q^{64} - 16 q^{67} + 12 q^{71} + 14 q^{73} - 8 q^{74} - 4 q^{76} + 36 q^{77} + 20 q^{79} - 6 q^{82} + 24 q^{83} + 4 q^{86} + 6 q^{89} - 40 q^{91} + 6 q^{92} + 36 q^{94} + 8 q^{97} - 10 q^{98}+O(q^{100}) $ 4 * q - 4 * q^2 + 4 * q^4 - 2 * q^7 - 4 * q^8 - 4 * q^13 + 2 * q^14 + 4 * q^16 - 4 * q^19 + 6 * q^23 + 10 * q^25 + 4 * q^26 - 2 * q^28 + 20 * q^31 - 4 * q^32 + 8 * q^37 + 4 * q^38 + 6 * q^41 - 4 * q^43 - 6 * q^46 - 36 * q^47 + 10 * q^49 - 10 * q^50 - 4 * q^52 + 2 * q^56 + 8 * q^61 - 20 * q^62 + 4 * q^64 - 16 * q^67 + 12 * q^71 + 14 * q^73 - 8 * q^74 - 4 * q^76 + 36 * q^77 + 20 * q^79 - 6 * q^82 + 24 * q^83 + 4 * q^86 + 6 * q^89 - 40 * q^91 + 6 * q^92 + 36 * q^94 + 8 * q^97 - 10 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$5$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$6$		0			0
$7$	1.62132	+	2.09077i	0.612801	+	0.790237i
$7$	1.62132	+	2.09077i	0.612801	+	0.790237i
$8$	−1.00000			−0.353553
$9$		0			0
$10$		0			0
$11$	2.12132	−	3.67423i	0.639602	−	1.10782i	−0.345918	−	0.938265i	$-0.612432\pi$
$11$	2.12132	−	3.67423i	0.639602	−	1.10782i	0.985520	−	0.169559i	$-0.0542342\pi$
$12$		0			0
$13$	−3.12132	+	5.40629i	−0.865699	+	1.49943i	0.000653431		1.00000i	$0.499792\pi$
$13$	−3.12132	+	5.40629i	−0.865699	+	1.49943i	−0.866352	+	0.499434i	$0.833541\pi$
$14$	−1.62132	−	2.09077i	−0.433316	−	0.558782i
$15$		0			0
$16$	1.00000			0.250000
$17$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$17$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$18$		0			0
$19$	−3.12132	+	5.40629i	−0.716080	+	1.24029i	0.246462	+	0.969153i	$0.420732\pi$
$19$	−3.12132	+	5.40629i	−0.716080	+	1.24029i	−0.962542	+	0.271134i	$0.912601\pi$
$20$		0			0
$21$		0			0
$22$	−2.12132	+	3.67423i	−0.452267	+	0.783349i
$23$	3.62132	+	6.27231i	0.755097	+	1.30787i	0.945326	+	0.326127i	$0.105744\pi$
$23$	3.62132	+	6.27231i	0.755097	+	1.30787i	−0.190228	+	0.981740i	$0.560923\pi$
$24$		0			0
$25$	2.50000	−	4.33013i	0.500000	−	0.866025i
$26$	3.12132	−	5.40629i	0.612141	−	1.06026i
$27$		0			0
$28$	1.62132	+	2.09077i	0.306401	+	0.395118i
$29$	−2.12132	−	3.67423i	−0.393919	−	0.682288i	0.599043	−	0.800717i	$-0.295548\pi$
$29$	−2.12132	−	3.67423i	−0.393919	−	0.682288i	−0.992963	+	0.118428i	$0.962214\pi$
$30$		0			0
$31$	0.757359			0.136026			0.0680129	−	0.997684i	$-0.478334\pi$
$31$	0.757359			0.136026			0.0680129	+	0.997684i	$0.478334\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$		0			0
$35$		0			0
$36$		0			0
$37$	2.00000	−	3.46410i	0.328798	−	0.569495i	−0.653476	−	0.756948i	$-0.726690\pi$
$37$	2.00000	−	3.46410i	0.328798	−	0.569495i	0.982274	+	0.187453i	$0.0600231\pi$
$38$	3.12132	−	5.40629i	0.506345	−	0.877015i
$39$		0			0
$40$		0			0
$41$	−2.74264	+	4.75039i	−0.428329	+	0.741887i	−0.996725	−	0.0808682i	$-0.974231\pi$
$41$	−2.74264	+	4.75039i	−0.428329	+	0.741887i	0.568396	+	0.822755i	$0.307564\pi$
$42$		0			0
$43$	3.24264	+	5.61642i	0.494498	+	0.856496i	0.999980	−	0.00634147i	$-0.00201857\pi$
$43$	3.24264	+	5.61642i	0.494498	+	0.856496i	−0.505482	+	0.862837i	$0.668685\pi$
$44$	2.12132	−	3.67423i	0.319801	−	0.553912i
$45$		0			0
$46$	−3.62132	−	6.27231i	−0.533935	−	0.924802i
$47$	−13.2426			−1.93164			−0.965819	−	0.259218i	$-0.916535\pi$
$47$	−13.2426			−1.93164			−0.965819	+	0.259218i	$0.916535\pi$
$48$		0			0
$49$	−1.74264	+	6.77962i	−0.248949	+	0.968517i
$50$	−2.50000	+	4.33013i	−0.353553	+	0.612372i
$51$		0			0
$52$	−3.12132	+	5.40629i	−0.432849	+	0.749717i
$53$	2.12132	+	3.67423i	0.291386	+	0.504695i	0.974138	−	0.225955i	$-0.0725503\pi$
$53$	2.12132	+	3.67423i	0.291386	+	0.504695i	−0.682752	+	0.730650i	$0.739217\pi$
$54$		0			0
$55$		0			0
$56$	−1.62132	−	2.09077i	−0.216658	−	0.279391i
$57$		0			0
$58$	2.12132	+	3.67423i	0.278543	+	0.482451i
$59$		0			0			−	1.00000i	$-0.5\pi$
$59$		0			0				1.00000i	$0.5\pi$
$60$		0			0
$61$	6.24264			0.799288			0.399644	−	0.916670i	$-0.369134\pi$
$61$	6.24264			0.799288			0.399644	+	0.916670i	$0.369134\pi$
$62$	−0.757359			−0.0961847
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	−8.24264			−1.00700			−0.503499	−	0.863996i	$-0.667954\pi$
$67$	−8.24264			−1.00700			−0.503499	+	0.863996i	$0.667954\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	7.24264			0.859543			0.429772	−	0.902938i	$-0.358594\pi$
$71$	7.24264			0.859543			0.429772	+	0.902938i	$0.358594\pi$
$72$		0			0
$73$	3.50000	+	6.06218i	0.409644	+	0.709524i	0.994850	−	0.101361i	$-0.0323196\pi$
$73$	3.50000	+	6.06218i	0.409644	+	0.709524i	−0.585206	+	0.810885i	$0.698986\pi$
$74$	−2.00000	+	3.46410i	−0.232495	+	0.402694i
$75$		0			0
$76$	−3.12132	+	5.40629i	−0.358040	+	0.620143i
$77$	11.1213	−	1.52192i	1.26739	−	0.173439i
$78$		0			0
$79$	9.24264			1.03988			0.519939	−	0.854203i	$-0.325955\pi$
$79$	9.24264			1.03988			0.519939	+	0.854203i	$0.325955\pi$
$80$		0			0
$81$		0			0
$82$	2.74264	−	4.75039i	0.302874	−	0.524593i
$83$	3.87868	+	6.71807i	0.425740	+	0.737404i	0.996489	−	0.0837207i	$-0.0266803\pi$
$83$	3.87868	+	6.71807i	0.425740	+	0.737404i	−0.570749	+	0.821125i	$0.693347\pi$
$84$		0			0
$85$		0			0
$86$	−3.24264	−	5.61642i	−0.349663	−	0.605634i
$87$		0			0
$88$	−2.12132	+	3.67423i	−0.226134	+	0.391675i
$89$	−2.74264	+	4.75039i	−0.290719	+	0.503541i	−0.973980	−	0.226634i	$-0.927228\pi$
$89$	−2.74264	+	4.75039i	−0.290719	+	0.503541i	0.683261	+	0.730175i	$0.260561\pi$
$90$		0			0
$91$	−16.3640	+	2.23936i	−1.71541	+	0.234748i
$92$	3.62132	+	6.27231i	0.377549	+	0.653934i
$93$		0			0
$94$	13.2426			1.36587
$95$		0			0
$96$		0			0
$97$	6.24264	+	10.8126i	0.633844	+	1.09785i	0.986759	+	0.162195i	$0.0518573\pi$
$97$	6.24264	+	10.8126i	0.633844	+	1.09785i	−0.352915	+	0.935656i	$0.614809\pi$
$98$	1.74264	−	6.77962i	0.176033	−	0.684845i
$99$		0			0
$100$	2.50000	−	4.33013i	0.250000	−	0.433013i
$101$	3.87868	−	6.71807i	0.385943	−	0.668473i	−0.605956	−	0.795498i	$-0.707209\pi$
$101$	3.87868	−	6.71807i	0.385943	−	0.668473i	0.991900	+	0.127025i	$0.0405428\pi$
$102$		0			0
$103$	−0.378680	−	0.655892i	−0.0373124	−	0.0646270i	0.846766	−	0.531965i	$-0.178546\pi$
$103$	−0.378680	−	0.655892i	−0.0373124	−	0.0646270i	−0.884079	+	0.467338i	$0.845213\pi$
$104$	3.12132	−	5.40629i	0.306071	−	0.530130i
$105$		0			0
$106$	−2.12132	−	3.67423i	−0.206041	−	0.356873i
$107$	−1.24264	+	2.15232i	−0.120131	+	0.208072i	−0.919819	−	0.392343i	$-0.871665\pi$
$107$	−1.24264	+	2.15232i	−0.120131	+	0.208072i	0.799688	+	0.600415i	$0.204998\pi$
$108$		0			0
$109$	1.12132	+	1.94218i	0.107403	+	0.186027i	0.914717	−	0.404094i	$-0.132413\pi$
$109$	1.12132	+	1.94218i	0.107403	+	0.186027i	−0.807314	+	0.590122i	$0.799080\pi$
$110$		0			0
$111$		0			0
$112$	1.62132	+	2.09077i	0.153200	+	0.197559i
$113$	−10.2426	+	17.7408i	−0.963547	+	1.66891i	−0.250076	+	0.968226i	$0.580456\pi$
$113$	−10.2426	+	17.7408i	−0.963547	+	1.66891i	−0.713470	+	0.700686i	$0.752878\pi$
$114$		0			0
$115$		0			0
$116$	−2.12132	−	3.67423i	−0.196960	−	0.341144i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−3.50000	−	6.06218i	−0.318182	−	0.551107i
$122$	−6.24264			−0.565182
$123$		0			0
$124$	0.757359			0.0680129
$125$		0			0
$126$		0			0
$127$	6.75736			0.599619			0.299809	−	0.953999i	$-0.403077\pi$
$127$	6.75736			0.599619			0.299809	+	0.953999i	$0.403077\pi$
$128$	−1.00000			−0.0883883
$129$		0			0
$130$		0			0
$131$	−3.87868	−	6.71807i	−0.338882	−	0.586961i	0.645341	−	0.763895i	$-0.276715\pi$
$131$	−3.87868	−	6.71807i	−0.338882	−	0.586961i	−0.984223	+	0.176934i	$0.943382\pi$
$132$		0			0
$133$	−16.3640	+	2.23936i	−1.41894	+	0.194177i
$134$	8.24264			0.712056
$135$		0			0
$136$		0			0
$137$	−9.98528	+	17.2950i	−0.853100	+	1.47761i	0.0252962	+	0.999680i	$0.491947\pi$
$137$	−9.98528	+	17.2950i	−0.853100	+	1.47761i	−0.878396	+	0.477933i	$0.841386\pi$
$138$		0			0
$139$	2.36396	−	4.09450i	0.200509	−	0.347291i	−0.748184	−	0.663491i	$-0.769074\pi$
$139$	2.36396	−	4.09450i	0.200509	−	0.347291i	0.948692	+	0.316200i	$0.102407\pi$
$140$		0			0
$141$		0			0
$142$	−7.24264			−0.607789
$143$	13.2426	+	22.9369i	1.10741	+	1.91808i
$144$		0			0
$145$		0			0
$146$	−3.50000	−	6.06218i	−0.289662	−	0.501709i
$147$		0			0
$148$	2.00000	−	3.46410i	0.164399	−	0.284747i
$149$	8.12132	+	14.0665i	0.665324	+	1.15238i	0.979197	+	0.202911i	$0.0650401\pi$
$149$	8.12132	+	14.0665i	0.665324	+	1.15238i	−0.313873	+	0.949465i	$0.601627\pi$
$150$		0			0
$151$	1.37868	−	2.38794i	0.112195	−	0.194328i	−0.804460	−	0.594007i	$-0.797545\pi$
$151$	1.37868	−	2.38794i	0.112195	−	0.194328i	0.916655	+	0.399679i	$0.130878\pi$
$152$	3.12132	−	5.40629i	0.253173	−	0.438508i
$153$		0			0
$154$	−11.1213	+	1.52192i	−0.896182	+	0.122640i
$155$		0			0
$156$		0			0
$157$	14.0000			1.11732			0.558661	−	0.829396i	$-0.311315\pi$
$157$	14.0000			1.11732			0.558661	+	0.829396i	$0.311315\pi$
$158$	−9.24264			−0.735305
$159$		0			0
$160$		0			0
$161$	−7.24264	+	17.7408i	−0.570800	+	1.39817i
$162$		0			0
$163$	5.87868	−	10.1822i	0.460454	−	0.797529i	−0.538530	−	0.842606i	$-0.681020\pi$
$163$	5.87868	−	10.1822i	0.460454	−	0.797529i	0.998984	+	0.0450772i	$0.0143534\pi$
$164$	−2.74264	+	4.75039i	−0.214164	+	0.370943i
$165$		0			0
$166$	−3.87868	−	6.71807i	−0.301044	−	0.521423i
$167$	12.1066	−	20.9692i	0.936837	−	1.62265i	0.165512	−	0.986208i	$-0.447072\pi$
$167$	12.1066	−	20.9692i	0.936837	−	1.62265i	0.771325	−	0.636441i	$-0.219594\pi$
$168$		0			0
$169$	−12.9853	−	22.4912i	−0.998868	−	1.73009i
$170$		0			0
$171$		0			0
$172$	3.24264	+	5.61642i	0.247249	+	0.428248i
$173$	10.9706			0.834076			0.417038	−	0.908889i	$-0.363068\pi$
$173$	10.9706			0.834076			0.417038	+	0.908889i	$0.363068\pi$
$174$		0			0
$175$	13.1066	−	1.79360i	0.990766	−	0.135583i
$176$	2.12132	−	3.67423i	0.159901	−	0.276956i
$177$		0			0
$178$	2.74264	−	4.75039i	0.205570	−	0.356057i
$179$	−8.12132	−	14.0665i	−0.607016	−	1.05138i	−0.991729	−	0.128346i	$-0.959033\pi$
$179$	−8.12132	−	14.0665i	−0.607016	−	1.05138i	0.384713	−	0.923036i	$-0.374300\pi$
$180$		0			0
$181$	−20.2426			−1.50462			−0.752312	−	0.658807i	$-0.771061\pi$
$181$	−20.2426			−1.50462			−0.752312	+	0.658807i	$0.771061\pi$
$182$	16.3640	−	2.23936i	1.21298	−	0.165992i
$183$		0			0
$184$	−3.62132	−	6.27231i	−0.266967	−	0.462401i
$185$		0			0
$186$		0			0
$187$		0			0
$188$	−13.2426			−0.965819
$189$		0			0
$190$		0			0
$191$	−8.48528			−0.613973			−0.306987	−	0.951714i	$-0.599321\pi$
$191$	−8.48528			−0.613973			−0.306987	+	0.951714i	$0.599321\pi$
$192$		0			0
$193$	−4.51472			−0.324977			−0.162488	−	0.986710i	$-0.551952\pi$
$193$	−4.51472			−0.324977			−0.162488	+	0.986710i	$0.551952\pi$
$194$	−6.24264	−	10.8126i	−0.448195	−	0.776297i
$195$		0			0
$196$	−1.74264	+	6.77962i	−0.124474	+	0.484258i
$197$	−16.9706			−1.20910			−0.604551	−	0.796566i	$-0.706648\pi$
$197$	−16.9706			−1.20910			−0.604551	+	0.796566i	$0.706648\pi$
$198$		0			0
$199$	7.37868	+	12.7802i	0.523061	+	0.905968i	0.999640	+	0.0268362i	$0.00854325\pi$
$199$	7.37868	+	12.7802i	0.523061	+	0.905968i	−0.476579	+	0.879132i	$0.658123\pi$
$200$	−2.50000	+	4.33013i	−0.176777	+	0.306186i
$201$		0			0
$202$	−3.87868	+	6.71807i	−0.272903	+	0.472682i
$203$	4.24264	−	10.3923i	0.297775	−	0.729397i
$204$		0			0
$205$		0			0
$206$	0.378680	+	0.655892i	0.0263839	+	0.0456982i
$207$		0			0
$208$	−3.12132	+	5.40629i	−0.216425	+	0.374858i
$209$	13.2426	+	22.9369i	0.916013	+	1.58658i
$210$		0			0
$211$	3.24264	−	5.61642i	0.223233	−	0.386650i	−0.732555	−	0.680708i	$-0.761672\pi$
$211$	3.24264	−	5.61642i	0.223233	−	0.386650i	0.955788	+	0.294058i	$0.0950057\pi$
$212$	2.12132	+	3.67423i	0.145693	+	0.252347i
$213$		0			0
$214$	1.24264	−	2.15232i	0.0849452	−	0.147129i
$215$		0			0
$216$		0			0
$217$	1.22792	+	1.58346i	0.0833568	+	0.107493i
$218$	−1.12132	−	1.94218i	−0.0759454	−	0.131541i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−5.86396	−	10.1567i	−0.392680	−	0.680141i	0.600122	−	0.799908i	$-0.295119\pi$
$223$	−5.86396	−	10.1567i	−0.392680	−	0.680141i	−0.992802	+	0.119767i	$0.961785\pi$
$224$	−1.62132	−	2.09077i	−0.108329	−	0.139695i
$225$		0			0
$226$	10.2426	−	17.7408i	0.681330	−	1.18010i
$227$	13.2426	−	22.9369i	0.878945	−	1.52238i	0.0264448	−	0.999650i	$-0.491581\pi$
$227$	13.2426	−	22.9369i	0.878945	−	1.52238i	0.852500	−	0.522727i	$-0.175085\pi$
$228$		0			0
$229$	−12.4853	−	21.6251i	−0.825051	−	1.42903i	−0.901881	−	0.431985i	$-0.857813\pi$
$229$	−12.4853	−	21.6251i	−0.825051	−	1.42903i	0.0768300	−	0.997044i	$-0.475520\pi$
$230$		0			0
$231$		0			0
$232$	2.12132	+	3.67423i	0.139272	+	0.241225i
$233$	10.2426	−	17.7408i	0.671018	−	1.16224i	−0.306598	−	0.951839i	$-0.599191\pi$
$233$	10.2426	−	17.7408i	0.671018	−	1.16224i	0.977616	−	0.210398i	$-0.0674759\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	1.86396	−	3.22848i	0.120570	−	0.208833i	−0.799423	−	0.600769i	$-0.794861\pi$
$239$	1.86396	−	3.22848i	0.120570	−	0.208833i	0.919992	+	0.391936i	$0.128195\pi$
$240$		0			0
$241$	−4.25736	+	7.37396i	−0.274241	+	0.474999i	−0.969943	−	0.243331i	$-0.921760\pi$
$241$	−4.25736	+	7.37396i	−0.274241	+	0.474999i	0.695703	+	0.718330i	$0.255093\pi$
$242$	3.50000	+	6.06218i	0.224989	+	0.389692i
$243$		0			0
$244$	6.24264			0.399644
$245$		0			0
$246$		0			0
$247$	−19.4853	−	33.7495i	−1.23982	−	2.14743i
$248$	−0.757359			−0.0480924
$249$		0			0
$250$		0			0
$251$	−18.7279			−1.18210			−0.591048	−	0.806636i	$-0.701286\pi$
$251$	−18.7279			−1.18210			−0.591048	+	0.806636i	$0.701286\pi$
$252$		0			0
$253$	30.7279			1.93185
$254$	−6.75736			−0.423994
$255$		0			0
$256$	1.00000			0.0625000
$257$	2.74264	+	4.75039i	0.171081	+	0.296321i	0.938798	−	0.344468i	$-0.111941\pi$
$257$	2.74264	+	4.75039i	0.171081	+	0.296321i	−0.767717	+	0.640789i	$0.778607\pi$
$258$		0			0
$259$	10.4853	−	1.43488i	0.651524	−	0.0891590i
$260$		0			0
$261$		0			0
$262$	3.87868	+	6.71807i	0.239626	+	0.415044i
$263$	11.4853	−	19.8931i	0.708213	−	1.22666i	−0.257307	−	0.966330i	$-0.582835\pi$
$263$	11.4853	−	19.8931i	0.708213	−	1.22666i	0.965519	−	0.260331i	$-0.0838316\pi$
$264$		0			0
$265$		0			0
$266$	16.3640	−	2.23936i	1.00334	−	0.137304i
$267$		0			0
$268$	−8.24264			−0.503499
$269$	−5.48528	−	9.50079i	−0.334444	−	0.579273i	0.648934	−	0.760844i	$-0.275215\pi$
$269$	−5.48528	−	9.50079i	−0.334444	−	0.579273i	−0.983378	+	0.181571i	$0.941882\pi$
$270$		0			0
$271$	6.24264	−	10.8126i	0.379213	−	0.656817i	−0.611735	−	0.791063i	$-0.709528\pi$
$271$	6.24264	−	10.8126i	0.379213	−	0.656817i	0.990948	+	0.134246i	$0.0428613\pi$
$272$		0			0
$273$		0			0
$274$	9.98528	−	17.2950i	0.603233	−	1.04483i
$275$	−10.6066	−	18.3712i	−0.639602	−	1.10782i
$276$		0			0
$277$	9.60660	−	16.6391i	0.577205	−	0.999748i	−0.418593	−	0.908174i	$-0.637477\pi$
$277$	9.60660	−	16.6391i	0.577205	−	0.999748i	0.995798	−	0.0915743i	$-0.0291899\pi$
$278$	−2.36396	+	4.09450i	−0.141781	+	0.245572i
$279$		0			0
$280$		0			0
$281$	11.2279	+	19.4473i	0.669802	+	1.16013i	0.977959	+	0.208795i	$0.0669542\pi$
$281$	11.2279	+	19.4473i	0.669802	+	1.16013i	−0.308158	+	0.951335i	$0.599712\pi$
$282$		0			0
$283$	24.9706			1.48435			0.742173	−	0.670208i	$-0.233795\pi$
$283$	24.9706			1.48435			0.742173	+	0.670208i	$0.233795\pi$
$284$	7.24264			0.429772
$285$		0			0
$286$	−13.2426	−	22.9369i	−0.783054	−	1.35629i
$287$	−14.3787	+	1.96768i	−0.848747	+	0.116148i
$288$		0			0
$289$	8.50000	−	14.7224i	0.500000	−	0.866025i
$290$		0			0
$291$		0			0
$292$	3.50000	+	6.06218i	0.204822	+	0.354762i
$293$	−5.48528	+	9.50079i	−0.320454	+	0.555042i	−0.980582	−	0.196111i	$-0.937169\pi$
$293$	−5.48528	+	9.50079i	−0.320454	+	0.555042i	0.660128	+	0.751153i	$0.270502\pi$
$294$		0			0
$295$		0			0
$296$	−2.00000	+	3.46410i	−0.116248	+	0.201347i
$297$		0			0
$298$	−8.12132	−	14.0665i	−0.470455	−	0.814853i
$299$	−45.2132			−2.61475
$300$		0			0
$301$	−6.48528	+	15.8856i	−0.373805	+	0.915633i
$302$	−1.37868	+	2.38794i	−0.0793341	+	0.137411i
$303$		0			0
$304$	−3.12132	+	5.40629i	−0.179020	+	0.310072i
$305$		0			0
$306$		0			0
$307$	−28.0000			−1.59804			−0.799022	−	0.601302i	$-0.794649\pi$
$307$	−28.0000			−1.59804			−0.799022	+	0.601302i	$0.794649\pi$
$308$	11.1213	−	1.52192i	0.633696	−	0.0867193i
$309$		0			0
$310$		0			0
$311$	10.9706			0.622084			0.311042	−	0.950396i	$-0.399322\pi$
$311$	10.9706			0.622084			0.311042	+	0.950396i	$0.399322\pi$
$312$		0			0
$313$	−17.9706			−1.01576			−0.507878	−	0.861429i	$-0.669570\pi$
$313$	−17.9706			−1.01576			−0.507878	+	0.861429i	$0.669570\pi$
$314$	−14.0000			−0.790066
$315$		0			0
$316$	9.24264			0.519939
$317$	16.9706			0.953162			0.476581	−	0.879131i	$-0.341876\pi$
$317$	16.9706			0.953162			0.476581	+	0.879131i	$0.341876\pi$
$318$		0			0
$319$	−18.0000			−1.00781
$320$		0			0
$321$		0			0
$322$	7.24264	−	17.7408i	0.403617	−	0.988655i
$323$		0			0
$324$		0			0
$325$	15.6066	+	27.0314i	0.865699	+	1.49943i
$326$	−5.87868	+	10.1822i	−0.325590	+	0.563938i
$327$		0			0
$328$	2.74264	−	4.75039i	0.151437	−	0.262297i
$329$	−21.4706	−	27.6873i	−1.18371	−	1.52645i
$330$		0			0
$331$	−18.4853			−1.01604			−0.508021	−	0.861344i	$-0.669623\pi$
$331$	−18.4853			−1.01604			−0.508021	+	0.861344i	$0.669623\pi$
$332$	3.87868	+	6.71807i	0.212870	+	0.368702i
$333$		0			0
$334$	−12.1066	+	20.9692i	−0.662444	+	1.14739i
$335$		0			0
$336$		0			0
$337$	−2.24264	+	3.88437i	−0.122164	+	0.211595i	−0.920621	−	0.390457i	$-0.872317\pi$
$337$	−2.24264	+	3.88437i	−0.122164	+	0.211595i	0.798457	+	0.602052i	$0.205650\pi$
$338$	12.9853	+	22.4912i	0.706306	+	1.22336i
$339$		0			0
$340$		0			0
$341$	1.60660	−	2.78272i	0.0870024	−	0.150693i
$342$		0			0
$343$	−17.0000	+	7.34847i	−0.917914	+	0.396780i
$344$	−3.24264	−	5.61642i	−0.174831	−	0.302817i
$345$		0			0
$346$	−10.9706			−0.589781
$347$	6.72792			0.361174			0.180587	−	0.983559i	$-0.442200\pi$
$347$	6.72792			0.361174			0.180587	+	0.983559i	$0.442200\pi$
$348$		0			0
$349$	−12.4853	−	21.6251i	−0.668322	−	1.15757i	−0.978373	−	0.206848i	$-0.933680\pi$
$349$	−12.4853	−	21.6251i	−0.668322	−	1.15757i	0.310051	−	0.950720i	$-0.399654\pi$
$350$	−13.1066	+	1.79360i	−0.700577	+	0.0958718i
$351$		0			0
$352$	−2.12132	+	3.67423i	−0.113067	+	0.195837i
$353$	10.5000	−	18.1865i	0.558859	−	0.967972i	−0.438733	−	0.898617i	$-0.644573\pi$
$353$	10.5000	−	18.1865i	0.558859	−	0.967972i	0.997592	−	0.0693543i	$-0.0220939\pi$
$354$		0			0
$355$		0			0
$356$	−2.74264	+	4.75039i	−0.145360	+	0.251770i
$357$		0			0
$358$	8.12132	+	14.0665i	0.429225	+	0.743440i
$359$	5.37868	−	9.31615i	0.283876	−	0.491687i	−0.688460	−	0.725274i	$-0.741713\pi$
$359$	5.37868	−	9.31615i	0.283876	−	0.491687i	0.972336	+	0.233587i	$0.0750463\pi$
$360$		0			0
$361$	−9.98528	−	17.2950i	−0.525541	−	0.910264i
$362$	20.2426			1.06393
$363$		0			0
$364$	−16.3640	+	2.23936i	−0.857705	+	0.117374i
$365$		0			0
$366$		0			0
$367$	−5.86396	+	10.1567i	−0.306096	+	0.530174i	−0.977505	−	0.210913i	$-0.932356\pi$
$367$	−5.86396	+	10.1567i	−0.306096	+	0.530174i	0.671409	+	0.741087i	$0.265690\pi$
$368$	3.62132	+	6.27231i	0.188774	+	0.326967i
$369$		0			0
$370$		0			0
$371$	−4.24264	+	10.3923i	−0.220267	+	0.539542i
$372$		0			0
$373$	3.60660	+	6.24682i	0.186743	+	0.323448i	0.944162	−	0.329480i	$-0.106874\pi$
$373$	3.60660	+	6.24682i	0.186743	+	0.323448i	−0.757420	+	0.652928i	$0.773540\pi$
$374$		0			0
$375$		0			0
$376$	13.2426			0.682937
$377$	26.4853			1.36406
$378$		0			0
$379$	1.27208			0.0653423			0.0326711	−	0.999466i	$-0.489599\pi$
$379$	1.27208			0.0653423			0.0326711	+	0.999466i	$0.489599\pi$
$380$		0			0
$381$		0			0
$382$	8.48528			0.434145
$383$	−12.1066	−	20.9692i	−0.618618	−	1.07148i	−0.989738	−	0.142894i	$-0.954359\pi$
$383$	−12.1066	−	20.9692i	−0.618618	−	1.07148i	0.371120	−	0.928585i	$-0.378974\pi$
$384$		0			0
$385$		0			0
$386$	4.51472			0.229793
$387$		0			0
$388$	6.24264	+	10.8126i	0.316922	+	0.548925i
$389$	5.12132	−	8.87039i	0.259661	−	0.449746i	−0.706490	−	0.707723i	$-0.749722\pi$
$389$	5.12132	−	8.87039i	0.259661	−	0.449746i	0.966151	+	0.257977i	$0.0830558\pi$
$390$		0			0
$391$		0			0
$392$	1.74264	−	6.77962i	0.0880166	−	0.342422i
$393$		0			0
$394$	16.9706			0.854965
$395$		0			0
$396$		0			0
$397$	10.1213	−	17.5306i	0.507975	−	0.879838i	−0.491983	−	0.870605i	$-0.663728\pi$
$397$	10.1213	−	17.5306i	0.507975	−	0.879838i	0.999957	−	0.00923278i	$-0.00293893\pi$
$398$	−7.37868	−	12.7802i	−0.369860	−	0.640616i
$399$		0			0
$400$	2.50000	−	4.33013i	0.125000	−	0.216506i
$401$	14.7426	+	25.5350i	0.736212	+	1.27516i	0.954189	+	0.299203i	$0.0967209\pi$
$401$	14.7426	+	25.5350i	0.736212	+	1.27516i	−0.217977	+	0.975954i	$0.569946\pi$
$402$		0			0
$403$	−2.36396	+	4.09450i	−0.117757	+	0.203962i
$404$	3.87868	−	6.71807i	0.192972	−	0.334236i
$405$		0			0
$406$	−4.24264	+	10.3923i	−0.210559	+	0.515761i
$407$	−8.48528	−	14.6969i	−0.420600	−	0.728500i
$408$		0			0
$409$	35.0000			1.73064			0.865319	−	0.501221i	$-0.167116\pi$
$409$	35.0000			1.73064			0.865319	+	0.501221i	$0.167116\pi$
$410$		0			0
$411$		0			0
$412$	−0.378680	−	0.655892i	−0.0186562	−	0.0323135i
$413$		0			0
$414$		0			0
$415$		0			0
$416$	3.12132	−	5.40629i	0.153035	−	0.265065i
$417$		0			0
$418$	−13.2426	−	22.9369i	−0.647719	−	1.12188i
$419$	−3.87868	+	6.71807i	−0.189486	+	0.328199i	−0.945079	−	0.326842i	$-0.894015\pi$
$419$	−3.87868	+	6.71807i	−0.189486	+	0.328199i	0.755593	+	0.655041i	$0.227349\pi$
$420$		0			0
$421$	7.12132	+	12.3345i	0.347072	+	0.601146i	0.985728	−	0.168346i	$-0.0538426\pi$
$421$	7.12132	+	12.3345i	0.347072	+	0.601146i	−0.638656	+	0.769492i	$0.720509\pi$
$422$	−3.24264	+	5.61642i	−0.157849	+	0.273403i
$423$		0			0
$424$	−2.12132	−	3.67423i	−0.103020	−	0.178437i
$425$		0			0
$426$		0			0
$427$	10.1213	+	13.0519i	0.489805	+	0.631627i
$428$	−1.24264	+	2.15232i	−0.0600653	+	0.104036i
$429$		0			0
$430$		0			0
$431$	−18.6213	−	32.2531i	−0.896957	−	1.55358i	−0.831363	−	0.555729i	$-0.812439\pi$
$431$	−18.6213	−	32.2531i	−0.896957	−	1.55358i	−0.0655943	−	0.997846i	$-0.520894\pi$
$432$		0			0
$433$	3.97056			0.190813			0.0954065	−	0.995438i	$-0.469585\pi$
$433$	3.97056			0.190813			0.0954065	+	0.995438i	$0.469585\pi$
$434$	−1.22792	−	1.58346i	−0.0589421	−	0.0760087i
$435$		0			0
$436$	1.12132	+	1.94218i	0.0537015	+	0.0930137i
$437$	−45.2132			−2.16284
$438$		0			0
$439$	11.7279			0.559743			0.279872	−	0.960037i	$-0.409708\pi$
$439$	11.7279			0.559743			0.279872	+	0.960037i	$0.409708\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−9.51472			−0.452058			−0.226029	−	0.974121i	$-0.572574\pi$
$443$	−9.51472			−0.452058			−0.226029	+	0.974121i	$0.572574\pi$
$444$		0			0
$445$		0			0
$446$	5.86396	+	10.1567i	0.277667	+	0.480933i
$447$		0			0
$448$	1.62132	+	2.09077i	0.0766002	+	0.0987796i
$449$	4.97056			0.234575			0.117288	−	0.993098i	$-0.462580\pi$
$449$	4.97056			0.234575			0.117288	+	0.993098i	$0.462580\pi$
$450$		0			0
$451$	11.6360	+	20.1542i	0.547920	+	0.949025i
$452$	−10.2426	+	17.7408i	−0.481773	+	0.834456i
$453$		0			0
$454$	−13.2426	+	22.9369i	−0.621508	+	1.07648i
$455$		0			0
$456$		0			0
$457$	11.5147			0.538636			0.269318	−	0.963051i	$-0.413202\pi$
$457$	11.5147			0.538636			0.269318	+	0.963051i	$0.413202\pi$
$458$	12.4853	+	21.6251i	0.583399	+	1.01048i
$459$		0			0
$460$		0			0
$461$	17.1213	+	29.6550i	0.797419	+	1.38117i	0.921291	+	0.388873i	$0.127135\pi$
$461$	17.1213	+	29.6550i	0.797419	+	1.38117i	−0.123872	+	0.992298i	$0.539531\pi$
$462$		0			0
$463$	4.37868	−	7.58410i	0.203495	−	0.352463i	−0.746158	−	0.665769i	$-0.768103\pi$
$463$	4.37868	−	7.58410i	0.203495	−	0.352463i	0.949652	+	0.313307i	$0.101437\pi$
$464$	−2.12132	−	3.67423i	−0.0984798	−	0.170572i
$465$		0			0
$466$	−10.2426	+	17.7408i	−0.474481	+	0.821825i
$467$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$467$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$468$		0			0
$469$	−13.3640	−	17.2335i	−0.617090	−	0.795768i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	27.5147			1.26513
$474$		0			0
$475$	15.6066	+	27.0314i	0.716080	+	1.24029i
$476$		0			0
$477$		0			0
$478$	−1.86396	+	3.22848i	−0.0852556	+	0.147667i
$479$	−6.62132	+	11.4685i	−0.302536	+	0.524007i	−0.976710	−	0.214565i	$-0.931167\pi$
$479$	−6.62132	+	11.4685i	−0.302536	+	0.524007i	0.674174	+	0.738573i	$0.264500\pi$
$480$		0			0
$481$	12.4853	+	21.6251i	0.569280	+	0.986022i
$482$	4.25736	−	7.37396i	0.193917	−	0.335875i
$483$		0			0
$484$	−3.50000	−	6.06218i	−0.159091	−	0.275554i
$485$		0			0
$486$		0			0
$487$	1.37868	+	2.38794i	0.0624739	+	0.108208i	0.895571	−	0.444919i	$-0.146768\pi$
$487$	1.37868	+	2.38794i	0.0624739	+	0.108208i	−0.833097	+	0.553127i	$0.813434\pi$
$488$	−6.24264			−0.282591
$489$		0			0
$490$		0			0
$491$	3.36396	−	5.82655i	0.151813	−	0.262949i	−0.780081	−	0.625679i	$-0.784822\pi$
$491$	3.36396	−	5.82655i	0.151813	−	0.262949i	0.931894	+	0.362730i	$0.118155\pi$
$492$		0			0
$493$		0			0
$494$	19.4853	+	33.7495i	0.876684	+	1.51846i
$495$		0			0
$496$	0.757359			0.0340064
$497$	11.7426	+	15.1427i	0.526729	+	0.679243i
$498$		0			0
$499$	5.36396	+	9.29065i	0.240124	+	0.415907i	0.960749	−	0.277418i	$-0.0894786\pi$
$499$	5.36396	+	9.29065i	0.240124	+	0.415907i	−0.720626	+	0.693325i	$0.756145\pi$
$500$		0			0
$501$		0			0
$502$	18.7279			0.835868
$503$	24.2132			1.07961			0.539807	−	0.841789i	$-0.318497\pi$
$503$	24.2132			1.07961			0.539807	+	0.841789i	$0.318497\pi$
$504$		0			0
$505$		0			0
$506$	−30.7279			−1.36602
$507$		0			0
$508$	6.75736			0.299809
$509$	3.87868	+	6.71807i	0.171919	+	0.297773i	0.939091	−	0.343669i	$-0.111670\pi$
$509$	3.87868	+	6.71807i	0.171919	+	0.297773i	−0.767171	+	0.641442i	$0.778336\pi$
$510$		0			0
$511$	−7.00000	+	17.1464i	−0.309662	+	0.758513i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−2.74264	−	4.75039i	−0.120973	−	0.209531i
$515$		0			0
$516$		0			0
$517$	−28.0919	+	48.6566i	−1.23548	+	2.13991i
$518$	−10.4853	+	1.43488i	−0.460697	+	0.0630449i
$519$		0			0
$520$		0			0
$521$	8.22792	+	14.2512i	0.360472	+	0.624355i	0.988039	−	0.154207i	$-0.0492824\pi$
$521$	8.22792	+	14.2512i	0.360472	+	0.624355i	−0.627567	+	0.778563i	$0.715949\pi$
$522$		0			0
$523$	10.1213	−	17.5306i	0.442574	−	0.766561i	−0.555305	−	0.831647i	$-0.687399\pi$
$523$	10.1213	−	17.5306i	0.442574	−	0.766561i	0.997880	+	0.0650852i	$0.0207319\pi$
$524$	−3.87868	−	6.71807i	−0.169441	−	0.293480i
$525$		0			0
$526$	−11.4853	+	19.8931i	−0.500782	+	0.867380i
$527$		0			0
$528$		0			0
$529$	−14.7279	+	25.5095i	−0.640344	+	1.10911i
$530$		0			0
$531$		0			0
$532$	−16.3640	+	2.23936i	−0.709468	+	0.0970884i
$533$	−17.1213	−	29.6550i	−0.741607	−	1.28450i
$534$		0			0
$535$		0			0
$536$	8.24264			0.356028
$537$		0			0
$538$	5.48528	+	9.50079i	0.236487	+	0.409608i
$539$	21.2132	+	20.7846i	0.913717	+	0.895257i
$540$		0			0
$541$	7.48528	−	12.9649i	0.321817	−	0.557404i	−0.659046	−	0.752103i	$-0.729040\pi$
$541$	7.48528	−	12.9649i	0.321817	−	0.557404i	0.980863	+	0.194699i	$0.0623730\pi$
$542$	−6.24264	+	10.8126i	−0.268144	+	0.464440i
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	3.24264	+	5.61642i	0.138645	+	0.240141i	0.926984	−	0.375101i	$-0.122392\pi$
$547$	3.24264	+	5.61642i	0.138645	+	0.240141i	−0.788339	+	0.615241i	$0.789059\pi$
$548$	−9.98528	+	17.2950i	−0.426550	+	0.738806i
$549$		0			0
$550$	10.6066	+	18.3712i	0.452267	+	0.783349i
$551$	26.4853			1.12831
$552$		0			0
$553$	14.9853	+	19.3242i	0.637239	+	0.821750i
$554$	−9.60660	+	16.6391i	−0.408145	+	0.706929i
$555$		0			0
$556$	2.36396	−	4.09450i	0.100254	−	0.173646i
$557$	−20.4853	−	35.4815i	−0.867989	−	1.50340i	−0.864048	−	0.503409i	$-0.832079\pi$
$557$	−20.4853	−	35.4815i	−0.867989	−	1.50340i	−0.00394110	−	0.999992i	$-0.501254\pi$
$558$		0			0
$559$	−40.4853			−1.71234
$560$		0			0
$561$		0			0
$562$	−11.2279	−	19.4473i	−0.473621	−	0.820336i
$563$	−18.7279			−0.789288			−0.394644	−	0.918834i	$-0.629132\pi$
$563$	−18.7279			−0.789288			−0.394644	+	0.918834i	$0.629132\pi$
$564$		0			0
$565$		0			0
$566$	−24.9706			−1.04959
$567$		0			0
$568$	−7.24264			−0.303894
$569$	−24.9411			−1.04559			−0.522793	−	0.852460i	$-0.675110\pi$
$569$	−24.9411			−1.04559			−0.522793	+	0.852460i	$0.675110\pi$
$570$		0			0
$571$	−20.9706			−0.877591			−0.438795	−	0.898587i	$-0.644595\pi$
$571$	−20.9706			−0.877591			−0.438795	+	0.898587i	$0.644595\pi$
$572$	13.2426	+	22.9369i	0.553703	+	0.959041i
$573$		0			0
$574$	14.3787	−	1.96768i	0.600154	−	0.0821293i
$575$	36.2132			1.51019
$576$		0			0
$577$	−17.9706	−	31.1259i	−0.748124	−	1.29579i	−0.948721	−	0.316115i	$-0.897621\pi$
$577$	−17.9706	−	31.1259i	−0.748124	−	1.29579i	0.200596	−	0.979674i	$-0.435712\pi$
$578$	−8.50000	+	14.7224i	−0.353553	+	0.612372i
$579$		0			0
$580$		0			0
$581$	−7.75736	+	19.0016i	−0.321829	+	0.788318i
$582$		0			0
$583$	18.0000			0.745484
$584$	−3.50000	−	6.06218i	−0.144831	−	0.250855i
$585$		0			0
$586$	5.48528	−	9.50079i	0.226595	−	0.392474i
$587$	−1.60660	−	2.78272i	−0.0663115	−	0.114855i	0.830963	−	0.556327i	$-0.187790\pi$
$587$	−1.60660	−	2.78272i	−0.0663115	−	0.114855i	−0.897275	+	0.441472i	$0.854456\pi$
$588$		0			0
$589$	−2.36396	+	4.09450i	−0.0974053	+	0.168711i
$590$		0			0
$591$		0			0
$592$	2.00000	−	3.46410i	0.0821995	−	0.142374i
$593$	−2.74264	+	4.75039i	−0.112627	+	0.195075i	−0.916829	−	0.399281i	$-0.869260\pi$
$593$	−2.74264	+	4.75039i	−0.112627	+	0.195075i	0.804202	+	0.594356i	$0.202593\pi$
$594$		0			0
$595$		0			0
$596$	8.12132	+	14.0665i	0.332662	+	0.576188i
$597$		0			0
$598$	45.2132			1.84891
$599$	−22.9706			−0.938552			−0.469276	−	0.883052i	$-0.655485\pi$
$599$	−22.9706			−0.938552			−0.469276	+	0.883052i	$0.655485\pi$
$600$		0			0
$601$	8.98528	+	15.5630i	0.366517	+	0.634827i	0.989018	−	0.147792i	$-0.0472167\pi$
$601$	8.98528	+	15.5630i	0.366517	+	0.634827i	−0.622501	+	0.782619i	$0.713883\pi$
$602$	6.48528	−	15.8856i	0.264320	−	0.647450i
$603$		0			0
$604$	1.37868	−	2.38794i	0.0560977	−	0.0971640i
$605$		0			0
$606$		0			0
$607$	19.4853	+	33.7495i	0.790883	+	1.36985i	0.925421	+	0.378941i	$0.123712\pi$
$607$	19.4853	+	33.7495i	0.790883	+	1.36985i	−0.134538	+	0.990909i	$0.542955\pi$
$608$	3.12132	−	5.40629i	0.126586	−	0.219254i
$609$		0			0
$610$		0			0
$611$	41.3345	−	71.5935i	1.67222	−	2.89636i
$612$		0			0
$613$	18.9706	+	32.8580i	0.766214	+	1.32712i	0.939602	+	0.342268i	$0.111195\pi$
$613$	18.9706	+	32.8580i	0.766214	+	1.32712i	−0.173389	+	0.984853i	$0.555472\pi$
$614$	28.0000			1.12999
$615$		0			0
$616$	−11.1213	+	1.52192i	−0.448091	+	0.0613198i
$617$	−14.2279	+	24.6435i	−0.572795	+	0.992109i	0.423483	+	0.905904i	$0.360807\pi$
$617$	−14.2279	+	24.6435i	−0.572795	+	0.992109i	−0.996277	+	0.0862052i	$0.972526\pi$
$618$		0			0
$619$	0.757359	−	1.31178i	0.0304408	−	0.0527251i	−0.850404	−	0.526131i	$-0.823642\pi$
$619$	0.757359	−	1.31178i	0.0304408	−	0.0527251i	0.880844	+	0.473406i	$0.156976\pi$
$620$		0			0
$621$		0			0
$622$	−10.9706			−0.439879
$623$	−14.3787	+	1.96768i	−0.576070	+	0.0788333i
$624$		0			0
$625$	−12.5000	−	21.6506i	−0.500000	−	0.866025i
$626$	17.9706			0.718248
$627$		0			0
$628$	14.0000			0.558661
$629$		0			0
$630$		0			0
$631$	−24.4853			−0.974744			−0.487372	−	0.873195i	$-0.662044\pi$
$631$	−24.4853			−0.974744			−0.487372	+	0.873195i	$0.662044\pi$
$632$	−9.24264			−0.367653
$633$		0			0
$634$	−16.9706			−0.673987
$635$		0			0
$636$		0			0
$637$	−31.2132	−	30.5826i	−1.23671	−	1.21173i
$638$	18.0000			0.712627
$639$		0			0
$640$		0			0
$641$	−2.22792	+	3.85887i	−0.0879976	+	0.152416i	−0.906665	−	0.421852i	$-0.861380\pi$
$641$	−2.22792	+	3.85887i	−0.0879976	+	0.152416i	0.818667	+	0.574269i	$0.194713\pi$
$642$		0			0
$643$	23.3640	−	40.4676i	0.921385	−	1.59589i	0.124110	−	0.992268i	$-0.460392\pi$
$643$	23.3640	−	40.4676i	0.921385	−	1.59589i	0.797275	−	0.603617i	$-0.206274\pi$
$644$	−7.24264	+	17.7408i	−0.285400	+	0.699084i
$645$		0			0
$646$		0			0
$647$	1.13604	+	1.96768i	0.0446623	+	0.0773574i	0.887492	−	0.460822i	$-0.152445\pi$
$647$	1.13604	+	1.96768i	0.0446623	+	0.0773574i	−0.842830	+	0.538180i	$0.819112\pi$
$648$		0			0
$649$		0			0
$650$	−15.6066	−	27.0314i	−0.612141	−	1.06026i
$651$		0			0
$652$	5.87868	−	10.1822i	0.230227	−	0.398765i
$653$	12.0000	+	20.7846i	0.469596	+	0.813365i	0.999396	−	0.0347583i	$-0.0110661\pi$
$653$	12.0000	+	20.7846i	0.469596	+	0.813365i	−0.529799	+	0.848123i	$0.677733\pi$
$654$		0			0
$655$		0			0
$656$	−2.74264	+	4.75039i	−0.107082	+	0.185472i
$657$		0			0
$658$	21.4706	+	27.6873i	0.837010	+	1.07936i
$659$	−19.6066	−	33.9596i	−0.763765	−	1.32288i	−0.940897	−	0.338692i	$-0.890015\pi$
$659$	−19.6066	−	33.9596i	−0.763765	−	1.32288i	0.177132	−	0.984187i	$-0.443318\pi$
$660$		0			0
$661$	−42.1838			−1.64076			−0.820379	−	0.571820i	$-0.806238\pi$
$661$	−42.1838			−1.64076			−0.820379	+	0.571820i	$0.806238\pi$
$662$	18.4853			0.718451
$663$		0			0
$664$	−3.87868	−	6.71807i	−0.150522	−	0.260712i
$665$		0			0
$666$		0			0
$667$	15.3640	−	26.6112i	0.594895	−	1.03039i
$668$	12.1066	−	20.9692i	0.468418	−	0.811325i
$669$		0			0
$670$		0			0
$671$	13.2426	−	22.9369i	0.511226	−	0.885470i
$672$		0			0
$673$	13.7426	+	23.8030i	0.529740	+	0.917536i	0.999398	+	0.0346881i	$0.0110438\pi$
$673$	13.7426	+	23.8030i	0.529740	+	0.917536i	−0.469658	+	0.882848i	$0.655623\pi$
$674$	2.24264	−	3.88437i	0.0863833	−	0.149620i
$675$		0			0
$676$	−12.9853	−	22.4912i	−0.499434	−	0.865045i
$677$	−34.2426			−1.31605			−0.658026	−	0.752995i	$-0.728608\pi$
$677$	−34.2426			−1.31605			−0.658026	+	0.752995i	$0.728608\pi$
$678$		0			0
$679$	−12.4853	+	30.5826i	−0.479141	+	1.17365i
$680$		0			0
$681$		0			0
$682$	−1.60660	+	2.78272i	−0.0615200	+	0.106556i
$683$	20.8492	+	36.1119i	0.797774	+	1.38179i	0.921063	+	0.389414i	$0.127323\pi$
$683$	20.8492	+	36.1119i	0.797774	+	1.38179i	−0.123289	+	0.992371i	$0.539344\pi$
$684$		0			0
$685$		0			0
$686$	17.0000	−	7.34847i	0.649063	−	0.280566i
$687$		0			0
$688$	3.24264	+	5.61642i	0.123625	+	0.214124i
$689$	−26.4853			−1.00901
$690$		0			0
$691$	6.24264			0.237481			0.118741	−	0.992925i	$-0.462114\pi$
$691$	6.24264			0.237481			0.118741	+	0.992925i	$0.462114\pi$
$692$	10.9706			0.417038
$693$		0			0
$694$	−6.72792			−0.255388
$695$		0			0
$696$		0			0
$697$		0			0
$698$	12.4853	+	21.6251i	0.472575	+	0.818524i
$699$		0			0
$700$	13.1066	−	1.79360i	0.495383	−	0.0677916i
$701$	−13.7574			−0.519608			−0.259804	−	0.965661i	$-0.583658\pi$
$701$	−13.7574			−0.519608			−0.259804	+	0.965661i	$0.583658\pi$
$702$		0			0
$703$	12.4853	+	21.6251i	0.470891	+	0.815608i
$704$	2.12132	−	3.67423i	0.0799503	−	0.138478i
$705$		0			0
$706$	−10.5000	+	18.1865i	−0.395173	+	0.684459i
$707$	20.3345	−	2.78272i	0.764758	−	0.104655i
$708$		0			0
$709$	25.6985			0.965127			0.482563	−	0.875861i	$-0.339706\pi$
$709$	25.6985			0.965127			0.482563	+	0.875861i	$0.339706\pi$
$710$		0			0
$711$		0			0
$712$	2.74264	−	4.75039i	0.102785	−	0.178029i
$713$	2.74264	+	4.75039i	0.102713	+	0.177904i
$714$		0			0
$715$		0			0
$716$	−8.12132	−	14.0665i	−0.303508	−	0.525691i
$717$		0			0
$718$	−5.37868	+	9.31615i	−0.200731	+	0.347675i
$719$	−1.13604	+	1.96768i	−0.0423671	+	0.0733820i	−0.886431	−	0.462860i	$-0.846823\pi$
$719$	−1.13604	+	1.96768i	−0.0423671	+	0.0733820i	0.844064	+	0.536242i	$0.180157\pi$
$720$		0			0
$721$	0.757359	−	1.85514i	0.0282055	−	0.0690892i
$722$	9.98528	+	17.2950i	0.371614	+	0.643654i
$723$		0			0
$724$	−20.2426			−0.752312
$725$	−21.2132			−0.787839
$726$		0			0
$727$	12.8640	+	22.2810i	0.477098	+	0.826358i	0.999656	−	0.0262462i	$-0.00835537\pi$
$727$	12.8640	+	22.2810i	0.477098	+	0.826358i	−0.522558	+	0.852604i	$0.675022\pi$
$728$	16.3640	−	2.23936i	0.606489	−	0.0829961i
$729$		0			0
$730$		0			0
$731$		0			0
$732$		0			0
$733$	19.4853	+	33.7495i	0.719705	+	1.24657i	0.961116	+	0.276143i	$0.0890564\pi$
$733$	19.4853	+	33.7495i	0.719705	+	1.24657i	−0.241411	+	0.970423i	$0.577610\pi$
$734$	5.86396	−	10.1567i	0.216443	−	0.374890i
$735$		0			0
$736$	−3.62132	−	6.27231i	−0.133484	−	0.231200i
$737$	−17.4853	+	30.2854i	−0.644079	+	1.11558i
$738$		0			0
$739$	−5.24264	−	9.08052i	−0.192854	−	0.334032i	0.753341	−	0.657630i	$-0.228441\pi$
$739$	−5.24264	−	9.08052i	−0.192854	−	0.334032i	−0.946195	+	0.323598i	$0.895108\pi$
$740$		0			0
$741$		0			0
$742$	4.24264	−	10.3923i	0.155752	−	0.381514i
$743$	17.3787	−	30.1008i	0.637562	−	1.10429i	−0.348404	−	0.937344i	$-0.613276\pi$
$743$	17.3787	−	30.1008i	0.637562	−	1.10429i	0.985966	−	0.166945i	$-0.0533903\pi$
$744$		0			0
$745$		0			0
$746$	−3.60660	−	6.24682i	−0.132047	−	0.228712i
$747$		0			0
$748$		0			0
$749$	−6.51472	+	0.891519i	−0.238043	+	0.0325754i
$750$		0			0
$751$	8.62132	+	14.9326i	0.314596	+	0.544897i	0.979352	−	0.202164i	$-0.0647975\pi$
$751$	8.62132	+	14.9326i	0.314596	+	0.544897i	−0.664755	+	0.747061i	$0.731464\pi$
$752$	−13.2426			−0.482909
$753$		0			0
$754$	−26.4853			−0.964537
$755$		0			0
$756$		0			0
$757$	12.9706			0.471423			0.235712	−	0.971823i	$-0.424258\pi$
$757$	12.9706			0.471423			0.235712	+	0.971823i	$0.424258\pi$
$758$	−1.27208			−0.0462040
$759$		0			0
$760$		0			0
$761$	10.5000	+	18.1865i	0.380625	+	0.659261i	0.991152	−	0.132734i	$-0.0423756\pi$
$761$	10.5000	+	18.1865i	0.380625	+	0.659261i	−0.610527	+	0.791995i	$0.709042\pi$
$762$		0			0
$763$	−2.24264	+	5.49333i	−0.0811890	+	0.198872i
$764$	−8.48528			−0.306987
$765$		0			0
$766$	12.1066	+	20.9692i	0.437429	+	0.757650i
$767$		0			0
$768$		0			0
$769$	6.24264	−	10.8126i	0.225115	−	0.389911i	−0.731239	−	0.682122i	$-0.761057\pi$
$769$	6.24264	−	10.8126i	0.225115	−	0.389911i	0.956354	+	0.292210i	$0.0943908\pi$
$770$		0			0
$771$		0			0
$772$	−4.51472			−0.162488
$773$	−22.6066	−	39.1558i	−0.813103	−	1.40834i	−0.910682	−	0.413108i	$-0.864443\pi$
$773$	−22.6066	−	39.1558i	−0.813103	−	1.40834i	0.0975792	−	0.995228i	$-0.468890\pi$
$774$		0			0
$775$	1.89340	−	3.27946i	0.0680129	−	0.117802i
$776$	−6.24264	−	10.8126i	−0.224098	−	0.388149i
$777$		0			0
$778$	−5.12132	+	8.87039i	−0.183608	+	0.318019i
$779$	−17.1213	−	29.6550i	−0.613435	−	1.06250i
$780$		0			0
$781$	15.3640	−	26.6112i	0.549766	−	0.952222i
$782$		0			0
$783$		0			0
$784$	−1.74264	+	6.77962i	−0.0622372	+	0.242129i
$785$		0			0
$786$		0			0
$787$	−31.2132			−1.11263			−0.556315	−	0.830971i	$-0.687785\pi$
$787$	−31.2132			−1.11263			−0.556315	+	0.830971i	$0.687785\pi$
$788$	−16.9706			−0.604551
$789$		0			0
$790$		0			0
$791$	−53.6985	+	7.34847i	−1.90930	+	0.261281i
$792$		0			0
$793$	−19.4853	+	33.7495i	−0.691943	+	1.19848i
$794$	−10.1213	+	17.5306i	−0.359192	+	0.622139i
$795$		0			0
$796$	7.37868	+	12.7802i	0.261530	+	0.452984i
$797$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$797$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$798$		0			0
$799$		0			0
$800$	−2.50000	+	4.33013i	−0.0883883	+	0.153093i
$801$		0			0
$802$	−14.7426	−	25.5350i	−0.520581	−	0.901672i
$803$	29.6985			1.04804
$804$		0			0
$805$		0			0
$806$	2.36396	−	4.09450i	0.0832670	−	0.144223i
$807$		0			0
$808$	−3.87868	+	6.71807i	−0.136451	+	0.236341i
$809$	−4.50000	−	7.79423i	−0.158212	−	0.274030i	0.776012	−	0.630718i	$-0.217239\pi$
$809$	−4.50000	−	7.79423i	−0.158212	−	0.274030i	−0.934224	+	0.356687i	$0.883906\pi$
$810$		0			0
$811$	−23.4558			−0.823646			−0.411823	−	0.911264i	$-0.635108\pi$
$811$	−23.4558			−0.823646			−0.411823	+	0.911264i	$0.635108\pi$
$812$	4.24264	−	10.3923i	0.148888	−	0.364698i
$813$		0			0
$814$	8.48528	+	14.6969i	0.297409	+	0.515127i
$815$		0			0
$816$		0			0
$817$	−40.4853			−1.41640
$818$	−35.0000			−1.22375
$819$		0			0
$820$		0			0
$821$	32.1838			1.12322			0.561611	−	0.827402i	$-0.310182\pi$
$821$	32.1838			1.12322			0.561611	+	0.827402i	$0.310182\pi$
$822$		0			0
$823$	40.6985			1.41866			0.709330	−	0.704877i	$-0.248998\pi$
$823$	40.6985			1.41866			0.709330	+	0.704877i	$0.248998\pi$
$824$	0.378680	+	0.655892i	0.0131919	+	0.0228491i
$825$		0			0
$826$		0			0
$827$	−16.9706			−0.590124			−0.295062	−	0.955478i	$-0.595340\pi$
$827$	−16.9706			−0.590124			−0.295062	+	0.955478i	$0.595340\pi$
$828$		0			0
$829$	24.9706	+	43.2503i	0.867263	+	1.50214i	0.864782	+	0.502148i	$0.167457\pi$
$829$	24.9706	+	43.2503i	0.867263	+	1.50214i	0.00248151	+	0.999997i	$0.499210\pi$
$830$		0			0
$831$		0			0
$832$	−3.12132	+	5.40629i	−0.108212	+	0.187429i
$833$		0			0
$834$		0			0
$835$		0			0
$836$	13.2426	+	22.9369i	0.458006	+	0.793290i
$837$		0			0
$838$	3.87868	−	6.71807i	0.133987	−	0.232072i
$839$	7.75736	+	13.4361i	0.267814	+	0.463867i	0.968297	−	0.249802i	$-0.0803655\pi$
$839$	7.75736	+	13.4361i	0.267814	+	0.463867i	−0.700483	+	0.713669i	$0.747032\pi$
$840$		0			0
$841$	5.50000	−	9.52628i	0.189655	−	0.328492i
$842$	−7.12132	−	12.3345i	−0.245417	−	0.425075i
$843$		0			0
$844$	3.24264	−	5.61642i	0.111616	−	0.193325i
$845$		0			0
$846$		0			0
$847$	7.00000	−	17.1464i	0.240523	−	0.589158i
$848$	2.12132	+	3.67423i	0.0728464	+	0.126174i
$849$		0			0
$850$		0			0
$851$	28.9706			0.993098
$852$		0			0
$853$	−14.0919	−	24.4079i	−0.482497	−	0.835709i	0.517301	−	0.855803i	$-0.326937\pi$
$853$	−14.0919	−	24.4079i	−0.482497	−	0.835709i	−0.999798	+	0.0200943i	$0.993603\pi$
$854$	−10.1213	−	13.0519i	−0.346344	−	0.446628i
$855$		0			0
$856$	1.24264	−	2.15232i	0.0424726	−	0.0735647i
$857$	−2.74264	+	4.75039i	−0.0936868	+	0.162270i	−0.909060	−	0.416666i	$-0.863199\pi$
$857$	−2.74264	+	4.75039i	−0.0936868	+	0.162270i	0.815373	+	0.578936i	$0.196532\pi$
$858$		0			0
$859$	−21.8492	−	37.8440i	−0.745487	−	1.29122i	−0.949967	−	0.312350i	$-0.898884\pi$
$859$	−21.8492	−	37.8440i	−0.745487	−	1.29122i	0.204481	−	0.978871i	$-0.434449\pi$
$860$		0			0
$861$		0			0
$862$	18.6213	+	32.2531i	0.634245	+	1.09854i
$863$	−0.106602	+	0.184640i	−0.00362876	+	0.00628520i	−0.867834	−	0.496854i	$-0.834488\pi$
$863$	−0.106602	+	0.184640i	−0.00362876	+	0.00628520i	0.864205	+	0.503139i	$0.167822\pi$
$864$		0			0
$865$		0			0
$866$	−3.97056			−0.134925
$867$		0			0
$868$	1.22792	+	1.58346i	0.0416784	+	0.0537463i
$869$	19.6066	−	33.9596i	0.665108	−	1.15200i
$870$		0			0
$871$	25.7279	−	44.5621i	0.871757	−	1.50993i
$872$	−1.12132	−	1.94218i	−0.0379727	−	0.0657706i
$873$		0			0
$874$	45.2132			1.52936
$875$		0			0
$876$		0			0
$877$	−12.8492	−	22.2555i	−0.433888	−	0.751516i	0.563316	−	0.826241i	$-0.309525\pi$
$877$	−12.8492	−	22.2555i	−0.433888	−	0.751516i	−0.997204	+	0.0747253i	$0.976192\pi$
$878$	−11.7279			−0.395798
$879$		0			0
$880$		0			0
$881$	36.5147			1.23021			0.615106	−	0.788444i	$-0.289113\pi$
$881$	36.5147			1.23021			0.615106	+	0.788444i	$0.289113\pi$
$882$		0			0
$883$	49.6985			1.67249			0.836244	−	0.548358i	$-0.184747\pi$
$883$	49.6985			1.67249			0.836244	+	0.548358i	$0.184747\pi$
$884$		0			0
$885$		0			0
$886$	9.51472			0.319653
$887$	19.8640	+	34.4054i	0.666967	+	1.15522i	0.978748	+	0.205066i	$0.0657409\pi$
$887$	19.8640	+	34.4054i	0.666967	+	1.15522i	−0.311782	+	0.950154i	$0.600926\pi$
$888$		0			0
$889$	10.9558	+	14.1281i	0.367447	+	0.473841i
$890$		0			0
$891$		0			0
$892$	−5.86396	−	10.1567i	−0.196340	−	0.340071i
$893$	41.3345	−	71.5935i	1.38321	−	2.39578i
$894$		0			0
$895$		0			0
$896$	−1.62132	−	2.09077i	−0.0541645	−	0.0698477i
$897$		0			0
$898$	−4.97056			−0.165870
$899$	−1.60660	−	2.78272i	−0.0535832	−	0.0928088i
$900$		0			0
$901$		0			0
$902$	−11.6360	−	20.1542i	−0.387438	−	0.671062i
$903$		0			0
$904$	10.2426	−	17.7408i	0.340665	−	0.590049i
$905$		0			0
$906$		0			0
$907$	18.9706	−	32.8580i	0.629907	−	1.09103i	−0.357663	−	0.933851i	$-0.616426\pi$
$907$	18.9706	−	32.8580i	0.629907	−	1.09103i	0.987570	−	0.157180i	$-0.0502404\pi$
$908$	13.2426	−	22.9369i	0.439472	−	0.761189i
$909$		0			0
$910$		0			0
$911$	−7.13604	−	12.3600i	−0.236428	−	0.409504i	0.723259	−	0.690577i	$-0.242643\pi$
$911$	−7.13604	−	12.3600i	−0.236428	−	0.409504i	−0.959687	+	0.281072i	$0.909310\pi$
$912$		0			0
$913$	32.9117			1.08922
$914$	−11.5147			−0.380873
$915$		0			0
$916$	−12.4853	−	21.6251i	−0.412525	−	0.714515i
$917$	7.75736	−	19.0016i	0.256171	−	0.627487i
$918$		0			0
$919$	−16.7279	+	28.9736i	−0.551803	+	0.955751i	0.446341	+	0.894863i	$0.352727\pi$
$919$	−16.7279	+	28.9736i	−0.551803	+	0.955751i	−0.998145	+	0.0608884i	$0.980607\pi$
$920$		0			0
$921$		0			0
$922$	−17.1213	−	29.6550i	−0.563861	−	0.976635i
$923$	−22.6066	+	39.1558i	−0.744105	+	1.28883i
$924$		0			0
$925$	−10.0000	−	17.3205i	−0.328798	−	0.569495i
$926$	−4.37868	+	7.58410i	−0.143892	+	0.249229i
$927$		0			0
$928$	2.12132	+	3.67423i	0.0696358	+	0.120613i
$929$	10.0294			0.329055			0.164528	−	0.986372i	$-0.447390\pi$
$929$	10.0294			0.329055			0.164528	+	0.986372i	$0.447390\pi$
$930$		0			0
$931$	−31.2132	−	30.5826i	−1.02297	−	1.00230i
$932$	10.2426	−	17.7408i	0.335509	−	0.581118i
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$	30.4558			0.994949			0.497475	−	0.867479i	$-0.334261\pi$
$937$	30.4558			0.994949			0.497475	+	0.867479i	$0.334261\pi$
$938$	13.3640	+	17.2335i	0.436349	+	0.562693i
$939$		0			0
$940$		0			0
$941$	40.6690			1.32577			0.662887	−	0.748720i	$-0.269331\pi$
$941$	40.6690			1.32577			0.662887	+	0.748720i	$0.269331\pi$
$942$		0			0
$943$	−39.7279			−1.29372
$944$		0			0
$945$		0			0
$946$	−27.5147			−0.894581
$947$	21.5147			0.699134			0.349567	−	0.936911i	$-0.386329\pi$
$947$	21.5147			0.699134			0.349567	+	0.936911i	$0.386329\pi$
$948$		0			0
$949$	−43.6985			−1.41851
$950$	−15.6066	−	27.0314i	−0.506345	−	0.877015i
$951$		0			0
$952$		0			0
$953$	6.51472			0.211032			0.105516	−	0.994418i	$-0.466351\pi$
$953$	6.51472			0.211032			0.105516	+	0.994418i	$0.466351\pi$
$954$		0			0
$955$		0			0
$956$	1.86396	−	3.22848i	0.0602848	−	0.104416i
$957$		0			0
$958$	6.62132	−	11.4685i	0.213925	−	0.370529i
$959$	−52.3492	+	7.16383i	−1.69045	+	0.231332i
$960$		0			0
$961$	−30.4264			−0.981497
$962$	−12.4853	−	21.6251i	−0.402542	−	0.697223i
$963$		0			0
$964$	−4.25736	+	7.37396i	−0.137120	+	0.237499i
$965$		0			0
$966$		0			0
$967$	3.34924	−	5.80106i	0.107704	−	0.186549i	−0.807136	−	0.590366i	$-0.798983\pi$
$967$	3.34924	−	5.80106i	0.107704	−	0.186549i	0.914840	+	0.403817i	$0.132317\pi$
$968$	3.50000	+	6.06218i	0.112494	+	0.194846i
$969$		0			0
$970$		0			0
$971$	−13.2426	+	22.9369i	−0.424977	+	0.736081i	−0.996418	−	0.0845617i	$-0.973051\pi$
$971$	−13.2426	+	22.9369i	−0.424977	+	0.736081i	0.571442	+	0.820643i	$0.306384\pi$
$972$		0			0
$973$	12.3934	−	1.69600i	0.397314	−	0.0543712i
$974$	−1.37868	−	2.38794i	−0.0441757	−	0.0765146i
$975$		0			0
$976$	6.24264			0.199822
$977$	13.9706			0.446958			0.223479	−	0.974709i	$-0.428259\pi$
$977$	13.9706			0.446958			0.223479	+	0.974709i	$0.428259\pi$
$978$		0			0
$979$	11.6360	+	20.1542i	0.371889	+	0.644131i
$980$		0			0
$981$		0			0
$982$	−3.36396	+	5.82655i	−0.107348	+	0.185933i
$983$	−7.75736	+	13.4361i	−0.247421	+	0.428546i	−0.962810	−	0.270181i	$-0.912917\pi$
$983$	−7.75736	+	13.4361i	−0.247421	+	0.428546i	0.715388	+	0.698727i	$0.246250\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$	−19.4853	−	33.7495i	−0.619909	−	1.07371i
$989$	−23.4853	+	40.6777i	−0.746789	+	1.29348i
$990$		0			0
$991$	−25.1066	−	43.4859i	−0.797537	−	1.38138i	−0.921215	−	0.389053i	$-0.872802\pi$
$991$	−25.1066	−	43.4859i	−0.797537	−	1.38138i	0.123678	−	0.992322i	$-0.460531\pi$
$992$	−0.757359			−0.0240462
$993$		0			0
$994$	−11.7426	−	15.1427i	−0.372454	−	0.480297i
$995$		0			0
$996$		0			0
$997$	−7.00000	+	12.1244i	−0.221692	+	0.383982i	−0.955322	−	0.295567i	$-0.904491\pi$
$997$	−7.00000	+	12.1244i	−0.221692	+	0.383982i	0.733630	+	0.679549i	$0.237825\pi$
$998$	−5.36396	−	9.29065i	−0.169793	−	0.294090i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.e.r.919.2		4
3.2	odd	2		1134.2.e.s.919.2		4
7.4	even	3		1134.2.h.s.109.2		4
9.2	odd	6		1134.2.h.r.541.1		4
9.4	even	3		1134.2.g.j.163.1	yes	4
9.5	odd	6		1134.2.g.i.163.1	✓	4
9.7	even	3		1134.2.h.s.541.1		4
21.11	odd	6		1134.2.h.r.109.2		4
63.4	even	3		1134.2.g.j.487.1	yes	4
63.5	even	6		7938.2.a.bp.1.2		2
63.11	odd	6		1134.2.e.s.865.2		4
63.23	odd	6		7938.2.a.bq.1.2		2
63.25	even	3	inner	1134.2.e.r.865.2		4
63.32	odd	6		1134.2.g.i.487.1	yes	4
63.40	odd	6		7938.2.a.bj.1.1		2
63.58	even	3		7938.2.a.bk.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1134.2.e.r.865.2		4	63.25	even	3	inner
1134.2.e.r.919.2		4	1.1	even	1	trivial
1134.2.e.s.865.2		4	63.11	odd	6
1134.2.e.s.919.2		4	3.2	odd	2
1134.2.g.i.163.1	✓	4	9.5	odd	6
1134.2.g.i.487.1	yes	4	63.32	odd	6
1134.2.g.j.163.1	yes	4	9.4	even	3
1134.2.g.j.487.1	yes	4	63.4	even	3
1134.2.h.r.109.2		4	21.11	odd	6
1134.2.h.r.541.1		4	9.2	odd	6
1134.2.h.s.109.2		4	7.4	even	3
1134.2.h.s.541.1		4	9.7	even	3
7938.2.a.bj.1.1		2	63.40	odd	6
7938.2.a.bk.1.1		2	63.58	even	3
7938.2.a.bp.1.2		2	63.5	even	6
7938.2.a.bq.1.2		2	63.23	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1134.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(1.62132 + 2.09077i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(1.62132 + 2.09077i) q^{7} -1.00000 q^{8} +(2.12132 - 3.67423i) q^{11} +(-3.12132 + 5.40629i) q^{13} +(-1.62132 - 2.09077i) q^{14} +1.00000 q^{16} +(-3.12132 + 5.40629i) q^{19} +(-2.12132 + 3.67423i) q^{22} +(3.62132 + 6.27231i) q^{23} +(2.50000 - 4.33013i) q^{25} +(3.12132 - 5.40629i) q^{26} +(1.62132 + 2.09077i) q^{28} +(-2.12132 - 3.67423i) q^{29} +0.757359 q^{31} -1.00000 q^{32} +(2.00000 - 3.46410i) q^{37} +(3.12132 - 5.40629i) q^{38} +(-2.74264 + 4.75039i) q^{41} +(3.24264 + 5.61642i) q^{43} +(2.12132 - 3.67423i) q^{44} +(-3.62132 - 6.27231i) q^{46} -13.2426 q^{47} +(-1.74264 + 6.77962i) q^{49} +(-2.50000 + 4.33013i) q^{50} +(-3.12132 + 5.40629i) q^{52} +(2.12132 + 3.67423i) q^{53} +(-1.62132 - 2.09077i) q^{56} +(2.12132 + 3.67423i) q^{58} +6.24264 q^{61} -0.757359 q^{62} +1.00000 q^{64} -8.24264 q^{67} +7.24264 q^{71} +(3.50000 + 6.06218i) q^{73} +(-2.00000 + 3.46410i) q^{74} +(-3.12132 + 5.40629i) q^{76} +(11.1213 - 1.52192i) q^{77} +9.24264 q^{79} +(2.74264 - 4.75039i) q^{82} +(3.87868 + 6.71807i) q^{83} +(-3.24264 - 5.61642i) q^{86} +(-2.12132 + 3.67423i) q^{88} +(-2.74264 + 4.75039i) q^{89} +(-16.3640 + 2.23936i) q^{91} +(3.62132 + 6.27231i) q^{92} +13.2426 q^{94} +(6.24264 + 10.8126i) q^{97} +(1.74264 - 6.77962i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 4 q^{4} - 2 q^{7} - 4 q^{8}+O(q^{10}) \) 4 * q - 4 * q^2 + 4 * q^4 - 2 * q^7 - 4 * q^8	\( 4 q - 4 q^{2} + 4 q^{4} - 2 q^{7} - 4 q^{8} - 4 q^{13} + 2 q^{14} + 4 q^{16} - 4 q^{19} + 6 q^{23} + 10 q^{25} + 4 q^{26} - 2 q^{28} + 20 q^{31} - 4 q^{32} + 8 q^{37} + 4 q^{38} + 6 q^{41} - 4 q^{43} - 6 q^{46} - 36 q^{47} + 10 q^{49} - 10 q^{50} - 4 q^{52} + 2 q^{56} + 8 q^{61} - 20 q^{62} + 4 q^{64} - 16 q^{67} + 12 q^{71} + 14 q^{73} - 8 q^{74} - 4 q^{76} + 36 q^{77} + 20 q^{79} - 6 q^{82} + 24 q^{83} + 4 q^{86} + 6 q^{89} - 40 q^{91} + 6 q^{92} + 36 q^{94} + 8 q^{97} - 10 q^{98}+O(q^{100}) \) 4 * q - 4 * q^2 + 4 * q^4 - 2 * q^7 - 4 * q^8 - 4 * q^13 + 2 * q^14 + 4 * q^16 - 4 * q^19 + 6 * q^23 + 10 * q^25 + 4 * q^26 - 2 * q^28 + 20 * q^31 - 4 * q^32 + 8 * q^37 + 4 * q^38 + 6 * q^41 - 4 * q^43 - 6 * q^46 - 36 * q^47 + 10 * q^49 - 10 * q^50 - 4 * q^52 + 2 * q^56 + 8 * q^61 - 20 * q^62 + 4 * q^64 - 16 * q^67 + 12 * q^71 + 14 * q^73 - 8 * q^74 - 4 * q^76 + 36 * q^77 + 20 * q^79 - 6 * q^82 + 24 * q^83 + 4 * q^86 + 6 * q^89 - 40 * q^91 + 6 * q^92 + 36 * q^94 + 8 * q^97 - 10 * q^98

Introduction

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