LMFDB - Embedded newform 637.2.x.b.570.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(19,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 5]))

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

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

chi := DirichletCharacter("637.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.x (of order $12$, degree $4$, 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			570.4
Character	$\chi$	$=$	637.570
Dual form			637.2.x.b.19.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.813723 + 0.218036i) q^{2} +1.43324i q^{3} +(-1.11745 + 0.645157i) q^{4} +(1.38386 + 0.370805i) q^{5} +(-0.312498 - 1.16626i) q^{6} +(1.96000 - 1.96000i) q^{8} +0.945832 q^{9} +O(q^{10})$	\(q+(-0.813723 + 0.218036i) q^{2} +1.43324i q^{3} +(-1.11745 + 0.645157i) q^{4} +(1.38386 + 0.370805i) q^{5} +(-0.312498 - 1.16626i) q^{6} +(1.96000 - 1.96000i) q^{8} +0.945832 q^{9} -1.20693 q^{10} +(3.43228 - 3.43228i) q^{11} +(-0.924663 - 1.60156i) q^{12} +(1.04975 - 3.44935i) q^{13} +(-0.531452 + 1.98341i) q^{15} +(0.122771 - 0.212645i) q^{16} +(1.49151 + 2.58338i) q^{17} +(-0.769645 + 0.206226i) q^{18} +(4.44020 - 4.44020i) q^{19} +(-1.78562 + 0.478455i) q^{20} +(-2.04457 + 3.54129i) q^{22} +(1.02242 + 0.590296i) q^{23} +(2.80914 + 2.80914i) q^{24} +(-2.55254 - 1.47371i) q^{25} +(-0.102119 + 3.03570i) q^{26} +5.65531i q^{27} +(-2.77911 - 4.81356i) q^{29} -1.72982i q^{30} +(1.75449 + 6.54786i) q^{31} +(-1.48835 + 5.55461i) q^{32} +(4.91928 + 4.91928i) q^{33} +(-1.77695 - 1.77695i) q^{34} +(-1.05692 + 0.610210i) q^{36} +(-1.44737 - 5.40165i) q^{37} +(-2.64497 + 4.58121i) q^{38} +(4.94374 + 1.50454i) q^{39} +(3.43915 - 1.98559i) q^{40} +(4.71621 + 1.26371i) q^{41} +(-2.90941 - 1.67975i) q^{43} +(-1.62103 + 6.04975i) q^{44} +(1.30890 + 0.350719i) q^{45} +(-0.960674 - 0.257412i) q^{46} +(-1.51103 + 5.63925i) q^{47} +(0.304771 + 0.175960i) q^{48} +(2.39839 + 0.642646i) q^{50} +(-3.70259 + 2.13769i) q^{51} +(1.05234 + 4.53171i) q^{52} +(-2.89658 + 5.01702i) q^{53} +(-1.23306 - 4.60186i) q^{54} +(6.02252 - 3.47711i) q^{55} +(6.36385 + 6.36385i) q^{57} +(3.31096 + 3.31096i) q^{58} +(2.88250 - 10.7576i) q^{59} +(-0.685740 - 2.55922i) q^{60} +9.18124i q^{61} +(-2.85534 - 4.94560i) q^{62} -4.35335i q^{64} +(2.73174 - 4.38418i) q^{65} +(-5.07551 - 2.93035i) q^{66} +(-1.38921 - 1.38921i) q^{67} +(-3.33337 - 1.92452i) q^{68} +(-0.846033 + 1.46537i) q^{69} +(-3.19094 + 0.855010i) q^{71} +(1.85383 - 1.85383i) q^{72} +(0.482220 - 0.129211i) q^{73} +(2.35552 + 4.07987i) q^{74} +(2.11218 - 3.65840i) q^{75} +(-2.09705 + 7.82630i) q^{76} +(-4.35088 - 0.146360i) q^{78} +(3.47711 + 6.02254i) q^{79} +(0.248748 - 0.248748i) q^{80} -5.26791 q^{81} -4.11322 q^{82} +(3.22886 - 3.22886i) q^{83} +(1.10612 + 4.12811i) q^{85} +(2.73370 + 0.732493i) q^{86} +(6.89897 - 3.98312i) q^{87} -13.4545i q^{88} +(0.237487 - 0.0636346i) q^{89} -1.14155 q^{90} -1.52333 q^{92} +(-9.38464 + 2.51461i) q^{93} -4.91825i q^{94} +(7.79107 - 4.49818i) q^{95} +(-7.96108 - 2.13316i) q^{96} +(2.43374 + 9.08284i) q^{97} +(3.24636 - 3.24636i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{2} + 12 q^{4} - 16 q^{8} - 16 q^{9}+O(q^{10}) $ 32 * q + 4 * q^2 + 12 * q^4 - 16 * q^8 - 16 * q^9	$ 32 q + 4 q^{2} + 12 q^{4} - 16 q^{8} - 16 q^{9} + 20 q^{11} - 8 q^{15} + 12 q^{16} - 64 q^{18} + 4 q^{22} + 12 q^{23} + 4 q^{29} + 64 q^{32} + 4 q^{37} + 36 q^{39} - 48 q^{43} - 84 q^{44} - 108 q^{46} - 44 q^{50} + 12 q^{51} - 36 q^{53} - 92 q^{57} + 44 q^{58} + 28 q^{60} + 28 q^{65} + 64 q^{67} + 84 q^{71} + 4 q^{72} - 24 q^{74} + 148 q^{78} + 40 q^{79} - 56 q^{81} + 36 q^{85} + 108 q^{86} + 24 q^{92} - 24 q^{93} + 84 q^{95} - 60 q^{99}+O(q^{100}) $ 32 * q + 4 * q^2 + 12 * q^4 - 16 * q^8 - 16 * q^9 + 20 * q^11 - 8 * q^15 + 12 * q^16 - 64 * q^18 + 4 * q^22 + 12 * q^23 + 4 * q^29 + 64 * q^32 + 4 * q^37 + 36 * q^39 - 48 * q^43 - 84 * q^44 - 108 * q^46 - 44 * q^50 + 12 * q^51 - 36 * q^53 - 92 * q^57 + 44 * q^58 + 28 * q^60 + 28 * q^65 + 64 * q^67 + 84 * q^71 + 4 * q^72 - 24 * q^74 + 148 * q^78 + 40 * q^79 - 56 * q^81 + 36 * q^85 + 108 * q^86 + 24 * q^92 - 24 * q^93 + 84 * q^95 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.813723	+	0.218036i	−0.575389	+	0.154175i	−0.534767	−	0.845000i	$-0.679601\pi$
$2$	−0.813723	+	0.218036i	−0.575389	+	0.154175i	−0.0406221	+	0.999175i	$0.512934\pi$
$3$			1.43324i			0.827480i	0.910395	+	0.413740i	$0.135778\pi$
$3$			1.43324i			0.827480i	−0.910395	+	0.413740i	$0.864222\pi$
$4$	−1.11745	+	0.645157i	−0.558723	+	0.322579i
$5$	1.38386	+	0.370805i	0.618883	+	0.165829i	0.554620	−	0.832104i	$-0.312864\pi$
$5$	1.38386	+	0.370805i	0.618883	+	0.165829i	0.0642629	+	0.997933i	$0.479530\pi$
$6$	−0.312498	−	1.16626i	−0.127577	−	0.476123i
$7$		0			0
$7$		0			0
$8$	1.96000	−	1.96000i	0.692963	−	0.692963i
$9$	0.945832			0.315277
$10$	−1.20693			−0.381665
$11$	3.43228	−	3.43228i	1.03487	−	1.03487i	0.0355032	−	0.999370i	$-0.488697\pi$
$11$	3.43228	−	3.43228i	1.03487	−	1.03487i	0.999370	−	0.0355032i	$-0.0113034\pi$
$12$	−0.924663	−	1.60156i	−0.266927	−	0.462332i
$13$	1.04975	−	3.44935i	0.291147	−	0.956678i
$13$	1.04975	−	3.44935i	0.291147	−	0.956678i
$14$		0			0
$15$	−0.531452	+	1.98341i	−0.137220	+	0.512113i
$16$	0.122771	−	0.212645i	0.0306927	−	0.0531613i
$17$	1.49151	+	2.58338i	0.361745	+	0.626561i	0.988248	−	0.152858i	$-0.0488477\pi$
$17$	1.49151	+	2.58338i	0.361745	+	0.626561i	−0.626503	+	0.779419i	$0.715514\pi$
$18$	−0.769645	+	0.206226i	−0.181407	+	0.0486079i
$19$	4.44020	−	4.44020i	1.01865	−	1.01865i	0.0188279	−	0.999823i	$-0.494007\pi$
$19$	4.44020	−	4.44020i	1.01865	−	1.01865i	0.999823	−	0.0188279i	$-0.00599346\pi$
$20$	−1.78562	+	0.478455i	−0.399277	+	0.106986i
$21$		0			0
$22$	−2.04457	+	3.54129i	−0.435903	+	0.755006i
$23$	1.02242	+	0.590296i	0.213190	+	0.123085i	0.602793	−	0.797898i	$-0.294055\pi$
$23$	1.02242	+	0.590296i	0.213190	+	0.123085i	−0.389603	+	0.920983i	$0.627388\pi$
$24$	2.80914	+	2.80914i	0.573413	+	0.573413i
$25$	−2.55254	−	1.47371i	−0.510509	−	0.294742i
$26$	−0.102119	+	3.03570i	−0.0200271	+	0.595350i
$27$			5.65531i			1.08837i
$28$		0			0
$29$	−2.77911	−	4.81356i	−0.516068	−	0.893856i	−0.999826	−	0.0186541i	$-0.994062\pi$
$29$	−2.77911	−	4.81356i	−0.516068	−	0.893856i	0.483758	−	0.875202i	$-0.339271\pi$
$30$		−	1.72982i		−	0.315820i
$31$	1.75449	+	6.54786i	0.315116	+	1.17603i	0.923881	+	0.382680i	$0.124999\pi$
$31$	1.75449	+	6.54786i	0.315116	+	1.17603i	−0.608765	+	0.793351i	$0.708335\pi$
$32$	−1.48835	+	5.55461i	−0.263106	+	0.981926i
$33$	4.91928	+	4.91928i	0.856336	+	0.856336i
$34$	−1.77695	−	1.77695i	−0.304744	−	0.304744i
$35$		0			0
$36$	−1.05692	+	0.610210i	−0.176153	+	0.101702i
$37$	−1.44737	−	5.40165i	−0.237946	−	0.888027i	−0.976799	−	0.214160i	$-0.931299\pi$
$37$	−1.44737	−	5.40165i	−0.237946	−	0.888027i	0.738853	−	0.673867i	$-0.235368\pi$
$38$	−2.64497	+	4.58121i	−0.429070	+	0.743171i
$39$	4.94374	+	1.50454i	0.791632	+	0.240919i
$40$	3.43915	−	1.98559i	0.543777	−	0.313950i
$41$	4.71621	+	1.26371i	0.736549	+	0.197358i	0.607544	−	0.794286i	$-0.292155\pi$
$41$	4.71621	+	1.26371i	0.736549	+	0.197358i	0.129005	+	0.991644i	$0.458822\pi$
$42$		0			0
$43$	−2.90941	−	1.67975i	−0.443681	−	0.256159i	0.261477	−	0.965210i	$-0.415790\pi$
$43$	−2.90941	−	1.67975i	−0.443681	−	0.256159i	−0.705158	+	0.709050i	$0.749124\pi$
$44$	−1.62103	+	6.04975i	−0.244379	+	0.912035i
$45$	1.30890	+	0.350719i	0.195120	+	0.0522822i
$46$	−0.960674	−	0.257412i	−0.141644	−	0.0379533i
$47$	−1.51103	+	5.63925i	−0.220407	+	0.822570i	0.763786	+	0.645470i	$0.223338\pi$
$47$	−1.51103	+	5.63925i	−0.220407	+	0.822570i	−0.984193	+	0.177100i	$0.943328\pi$
$48$	0.304771	+	0.175960i	0.0439899	+	0.0253976i
$49$		0			0
$50$	2.39839	+	0.642646i	0.339183	+	0.0908839i
$51$	−3.70259	+	2.13769i	−0.518467	+	0.299337i
$52$	1.05234	+	4.53171i	0.145933	+	0.628436i
$53$	−2.89658	+	5.01702i	−0.397875	+	0.689141i	−0.993464	−	0.114149i	$-0.963586\pi$
$53$	−2.89658	+	5.01702i	−0.397875	+	0.689141i	0.595588	+	0.803290i	$0.296919\pi$
$54$	−1.23306	−	4.60186i	−0.167799	−	0.626234i
$55$	6.02252	−	3.47711i	0.812077	−	0.468853i
$56$		0			0
$57$	6.36385	+	6.36385i	0.842913	+	0.842913i
$58$	3.31096	+	3.31096i	0.434750	+	0.434750i
$59$	2.88250	−	10.7576i	0.375270	−	1.40053i	−0.477681	−	0.878534i	$-0.658522\pi$
$59$	2.88250	−	10.7576i	0.375270	−	1.40053i	0.852950	−	0.521992i	$-0.174811\pi$
$60$	−0.685740	−	2.55922i	−0.0885287	−	0.330393i
$61$			9.18124i			1.17554i	0.809029	+	0.587768i	$0.199993\pi$
$61$			9.18124i			1.17554i	−0.809029	+	0.587768i	$0.800007\pi$
$62$	−2.85534	−	4.94560i	−0.362629	−	0.628092i
$63$		0			0
$64$		−	4.35335i		−	0.544169i
$65$	2.73174	−	4.38418i	0.338831	−	0.543791i
$66$	−5.07551	−	2.93035i	−0.624752	−	0.360701i
$67$	−1.38921	−	1.38921i	−0.169719	−	0.169719i	0.617137	−	0.786856i	$-0.288292\pi$
$67$	−1.38921	−	1.38921i	−0.169719	−	0.169719i	−0.786856	+	0.617137i	$0.788292\pi$
$68$	−3.33337	−	1.92452i	−0.404231	−	0.233383i
$69$	−0.846033	+	1.46537i	−0.101850	+	0.176410i
$70$		0			0
$71$	−3.19094	+	0.855010i	−0.378695	+	0.101471i	−0.443145	−	0.896450i	$-0.646137\pi$
$71$	−3.19094	+	0.855010i	−0.378695	+	0.101471i	0.0644501	+	0.997921i	$0.479471\pi$
$72$	1.85383	−	1.85383i	0.218476	−	0.218476i
$73$	0.482220	−	0.129211i	0.0564396	−	0.0151230i	−0.230489	−	0.973075i	$-0.574032\pi$
$73$	0.482220	−	0.129211i	0.0564396	−	0.0151230i	0.286928	+	0.957952i	$0.407366\pi$
$74$	2.35552	+	4.07987i	0.273823	+	0.474275i
$75$	2.11218	−	3.65840i	0.243893	−	0.422436i
$76$	−2.09705	+	7.82630i	−0.240548	+	0.897738i
$77$		0			0
$78$	−4.35088	−	0.146360i	−0.492640	−	0.0165720i
$79$	3.47711	+	6.02254i	0.391206	+	0.677588i	0.992609	−	0.121357i	$-0.0387247\pi$
$79$	3.47711	+	6.02254i	0.391206	+	0.677588i	−0.601403	+	0.798946i	$0.705391\pi$
$80$	0.248748	−	0.248748i	0.0278109	−	0.0278109i
$81$	−5.26791			−0.585323
$82$	−4.11322			−0.454230
$83$	3.22886	−	3.22886i	0.354413	−	0.354413i	−0.507335	−	0.861749i	$-0.669369\pi$
$83$	3.22886	−	3.22886i	0.354413	−	0.354413i	0.861749	+	0.507335i	$0.169369\pi$
$84$		0			0
$85$	1.10612	+	4.12811i	0.119976	+	0.447756i
$86$	2.73370	+	0.732493i	0.294783	+	0.0789867i
$87$	6.89897	−	3.98312i	0.739648	−	0.427036i
$88$		−	13.4545i		−	1.43426i
$89$	0.237487	−	0.0636346i	0.0251736	−	0.00674525i	−0.246210	−	0.969216i	$-0.579185\pi$
$89$	0.237487	−	0.0636346i	0.0251736	−	0.00674525i	0.271384	+	0.962471i	$0.412519\pi$
$90$	−1.14155			−0.120330
$91$		0			0
$92$	−1.52333			−0.158819
$93$	−9.38464	+	2.51461i	−0.973141	+	0.260752i
$94$		−	4.91825i		−	0.507279i
$95$	7.79107	−	4.49818i	0.799347	−	0.461503i
$96$	−7.96108	−	2.13316i	−0.812524	−	0.217715i
$97$	2.43374	+	9.08284i	0.247109	+	0.922223i	0.972312	+	0.233688i	$0.0750793\pi$
$97$	2.43374	+	9.08284i	0.247109	+	0.922223i	−0.725203	+	0.688535i	$0.758254\pi$
$98$		0			0
$99$	3.24636	−	3.24636i	0.326272	−	0.326272i
$100$	3.80310			0.380310
$101$	−14.2869			−1.42160			−0.710799	−	0.703396i	$-0.751666\pi$
$101$	−14.2869			−1.42160			−0.710799	+	0.703396i	$0.751666\pi$
$102$	2.54679	−	2.54679i	0.252170	−	0.252170i
$103$	3.72565	+	6.45301i	0.367099	+	0.635834i	0.989111	−	0.147174i	$-0.0470177\pi$
$103$	3.72565	+	6.45301i	0.367099	+	0.635834i	−0.622012	+	0.783008i	$0.713684\pi$
$104$	−4.70322	−	8.81822i	−0.461189	−	0.864698i
$105$		0			0
$106$	1.26312	−	4.71402i	0.122685	−	0.457866i
$107$	2.34132	−	4.05528i	0.226344	−	0.392039i	−0.730378	−	0.683043i	$-0.760656\pi$
$107$	2.34132	−	4.05528i	0.226344	−	0.392039i	0.956722	+	0.291004i	$0.0939894\pi$
$108$	−3.64857	−	6.31950i	−0.351083	−	0.608094i
$109$	4.15534	−	1.11342i	0.398009	−	0.106646i	−0.0542619	−	0.998527i	$-0.517281\pi$
$109$	4.15534	−	1.11342i	0.398009	−	0.106646i	0.452271	+	0.891880i	$0.350614\pi$
$110$	−4.14253	+	4.14253i	−0.394975	+	0.394975i
$111$	7.74185	−	2.07442i	0.734824	−	0.196895i
$112$		0			0
$113$	2.02372	−	3.50518i	0.190375	−	0.329740i	−0.754999	−	0.655725i	$-0.772363\pi$
$113$	2.02372	−	3.50518i	0.190375	−	0.329740i	0.945375	+	0.325986i	$0.105696\pi$
$114$	−6.56597	−	3.79086i	−0.614959	−	0.355047i
$115$	1.19601	+	1.19601i	0.111528	+	0.111528i
$116$	6.21101	+	3.58593i	0.576678	+	0.332945i
$117$	0.992884	−	3.26251i	0.0917921	−	0.301619i
$118$			9.38223i			0.863705i
$119$		0			0
$120$	2.84582	+	4.92911i	0.259787	+	0.449964i
$121$		−	12.5612i		−	1.14192i
$122$	−2.00184	−	7.47099i	−0.181238	−	0.676391i
$123$	−1.81119	+	6.75945i	−0.163309	+	0.609479i
$124$	−6.18495	−	6.18495i	−0.555425	−	0.555425i
$125$	−8.05121	−	8.05121i	−0.720122	−	0.720122i
$126$		0			0
$127$	10.6871	−	6.17021i	0.948328	−	0.547518i	0.0557671	−	0.998444i	$-0.482240\pi$
$127$	10.6871	−	6.17021i	0.948328	−	0.547518i	0.892561	+	0.450926i	$0.148906\pi$
$128$	−2.02752	−	7.56681i	−0.179209	−	0.668817i
$129$	2.40748	−	4.16987i	0.211967	−	0.367137i
$130$	−1.26697	+	4.16313i	−0.111121	+	0.365131i
$131$	−5.81415	+	3.35680i	−0.507985	+	0.293285i	−0.732005	−	0.681299i	$-0.761415\pi$
$131$	−5.81415	+	3.35680i	−0.507985	+	0.293285i	0.224020	+	0.974584i	$0.428082\pi$
$132$	−8.67073	−	2.32332i	−0.754690	−	0.202219i
$133$		0			0
$134$	1.43333	+	0.827533i	0.123821	+	0.0714879i
$135$	−2.09702	+	7.82618i	−0.180483	+	0.673571i
$136$	7.98678	+	2.14005i	0.684860	+	0.183508i
$137$	−21.1477	−	5.66652i	−1.80677	−	0.484124i	−0.811771	−	0.583976i	$-0.801496\pi$
$137$	−21.1477	−	5.66652i	−1.80677	−	0.484124i	−0.995002	+	0.0998520i	$0.968163\pi$
$138$	0.368932	−	1.37687i	0.0314056	−	0.117207i
$139$	3.49682	+	2.01889i	0.296597	+	0.171240i	0.640913	−	0.767614i	$-0.278556\pi$
$139$	3.49682	+	2.01889i	0.296597	+	0.171240i	−0.344316	+	0.938854i	$0.611889\pi$
$140$		0			0
$141$	−8.08239	−	2.16567i	−0.680660	−	0.182382i
$142$	2.41012	−	1.39148i	0.202253	−	0.116771i
$143$	−8.23613	−	15.4422i	−0.688740	−	1.29134i
$144$	0.116121	−	0.201127i	0.00967671	−	0.0167606i
$145$	−2.06102	−	7.69182i	−0.171158	−	0.638771i
$146$	−0.364221	+	0.210283i	−0.0301432	+	0.0174032i
$147$		0			0
$148$	5.10227	+	5.10227i	0.419404	+	0.419404i
$149$	2.00586	+	2.00586i	0.164327	+	0.164327i	0.784480	−	0.620154i	$-0.212930\pi$
$149$	2.00586	+	2.00586i	0.164327	+	0.164327i	−0.620154	+	0.784480i	$0.712930\pi$
$150$	−0.921064	+	3.43746i	−0.0752045	+	0.280667i
$151$	4.33327	+	16.1720i	0.352636	+	1.31606i	0.883433	+	0.468558i	$0.155226\pi$
$151$	4.33327	+	16.1720i	0.352636	+	1.31606i	−0.530796	+	0.847499i	$0.678107\pi$
$152$		−	17.4055i		−	1.41178i
$153$	1.41072	+	2.44344i	0.114050	+	0.197541i
$154$		0			0
$155$			9.71192i			0.780080i
$156$	−6.49502	+	1.50825i	−0.520018	+	0.120757i
$157$	2.48434	+	1.43433i	0.198272	+	0.114472i	0.595849	−	0.803096i	$-0.296816\pi$
$157$	2.48434	+	1.43433i	0.198272	+	0.114472i	−0.397577	+	0.917569i	$0.630149\pi$
$158$	−4.14254	−	4.14254i	−0.329563	−	0.329563i
$159$	−7.19058	−	4.15148i	−0.570250	−	0.329234i
$160$	−4.11936	+	7.13494i	−0.325664	+	0.564067i
$161$		0			0
$162$	4.28662	−	1.14860i	0.336789	−	0.0902422i
$163$	−17.0408	+	17.0408i	−1.33474	+	1.33474i	−0.433660	+	0.901076i	$0.642778\pi$
$163$	−17.0408	+	17.0408i	−1.33474	+	1.33474i	−0.901076	+	0.433660i	$0.857222\pi$
$164$	−6.08540	+	1.63058i	−0.475190	+	0.127327i
$165$	4.98352	+	8.63170i	0.387966	+	0.671977i
$166$	−1.92339	+	3.33141i	−0.149284	+	0.258567i
$167$	−2.53997	+	9.47931i	−0.196549	+	0.733531i	0.795311	+	0.606201i	$0.207307\pi$
$167$	−2.53997	+	9.47931i	−0.196549	+	0.733531i	−0.991860	+	0.127330i	$0.959359\pi$
$168$		0			0
$169$	−10.7961	−	7.24189i	−0.830466	−	0.557069i
$170$	−1.80016	−	3.11796i	−0.138066	−	0.239137i
$171$	4.19968	−	4.19968i	0.321157	−	0.321157i
$172$	4.33481			0.330526
$173$	−5.23766			−0.398212			−0.199106	−	0.979978i	$-0.563804\pi$
$173$	−5.23766			−0.398212			−0.199106	+	0.979978i	$0.563804\pi$
$174$	−4.74539	+	4.74539i	−0.359747	+	0.359747i
$175$		0			0
$176$	−0.308475	−	1.15124i	−0.0232522	−	0.0867783i
$177$	15.4183	+	4.13131i	1.15891	+	0.310528i
$178$	−0.179374	+	0.103562i	−0.0134447	+	0.00776229i
$179$		−	22.5733i		−	1.68721i	−0.536965	−	0.843605i	$-0.680429\pi$
$179$		−	22.5733i		−	1.68721i	0.536965	−	0.843605i	$-0.319571\pi$
$180$	−1.68890	+	0.452538i	−0.125883	+	0.0337302i
$181$	−22.4803			−1.67095			−0.835474	−	0.549530i	$-0.814807\pi$
$181$	−22.4803			−1.67095			−0.835474	+	0.549530i	$0.814807\pi$
$182$		0			0
$183$	−13.1589			−0.972733
$184$	3.16092	−	0.846966i	0.233026	−	0.0624392i
$185$		−	8.01185i		−	0.589043i
$186$	7.08822	−	4.09239i	0.519733	−	0.300068i
$187$	13.9862	+	3.74759i	1.02277	+	0.274051i
$188$	−1.94971	−	7.27641i	−0.142197	−	0.530687i
$189$		0			0
$190$	−5.35901	+	5.35901i	−0.388783	+	0.388783i
$191$	24.6708			1.78511			0.892557	−	0.450935i	$-0.148909\pi$
$191$	24.6708			1.78511			0.892557	+	0.450935i	$0.148909\pi$
$192$	6.23938			0.450289
$193$	−2.43183	+	2.43183i	−0.175047	+	0.175047i	−0.789193	−	0.614146i	$-0.789501\pi$
$193$	−2.43183	+	2.43183i	−0.175047	+	0.175047i	0.614146	+	0.789193i	$0.289501\pi$
$194$	−3.96078	−	6.86027i	−0.284367	−	0.492539i
$195$	6.28357	+	3.91524i	0.449976	+	0.280376i
$196$		0			0
$197$	−1.03338	+	3.85664i	−0.0736255	+	0.274774i	−0.992918	−	0.118801i	$-0.962095\pi$
$197$	−1.03338	+	3.85664i	−0.0736255	+	0.274774i	0.919293	+	0.393575i	$0.128762\pi$
$198$	−1.93382	+	3.34947i	−0.137430	+	0.238036i
$199$	−0.511550	−	0.886031i	−0.0362628	−	0.0628091i	0.847324	−	0.531076i	$-0.178212\pi$
$199$	−0.511550	−	0.886031i	−0.0362628	−	0.0628091i	−0.883587	+	0.468267i	$0.844879\pi$
$200$	−7.89145	+	2.11451i	−0.558010	+	0.149518i
$201$	1.99106	−	1.99106i	0.140439	−	0.140439i
$202$	11.6256	−	3.11506i	0.817972	−	0.219175i
$203$		0			0
$204$	2.75830	−	4.77751i	0.193119	−	0.334493i
$205$	6.05801	+	3.49759i	0.423110	+	0.244282i
$206$	−4.43864	−	4.43864i	−0.309255	−	0.309255i
$207$	0.967039	+	0.558320i	0.0672139	+	0.0388059i
$208$	−0.604610	−	0.646704i	−0.0419222	−	0.0448408i
$209$		−	30.4800i		−	2.10835i
$210$		0			0
$211$	2.70061	+	4.67759i	0.185918	+	0.322019i	0.943885	−	0.330273i	$-0.107141\pi$
$211$	2.70061	+	4.67759i	0.185918	+	0.322019i	−0.757968	+	0.652292i	$0.773808\pi$
$212$		−	7.47499i		−	0.513385i
$213$	−1.22543	−	4.57337i	−0.0839652	−	0.313362i
$214$	−1.02099	+	3.81037i	−0.0697932	+	0.260472i
$215$	−3.40337	−	3.40337i	−0.232108	−	0.232108i
$216$	11.0844	+	11.0844i	0.754197	+	0.754197i
$217$		0			0
$218$	−3.13853	+	1.81203i	−0.212568	+	0.122726i
$219$	0.185189	+	0.691136i	0.0125139	+	0.0467026i
$220$	−4.48656	+	7.77095i	−0.302484	+	0.523917i
$221$	10.4767	−	2.43287i	0.704739	−	0.163652i
$222$	−5.84742	+	3.37601i	−0.392453	+	0.226583i
$223$	16.6138	+	4.45165i	1.11254	+	0.298105i	0.767862	−	0.640616i	$-0.221321\pi$
$223$	16.6138	+	4.45165i	1.11254	+	0.298105i	0.344680	+	0.938720i	$0.387987\pi$
$224$		0			0
$225$	−2.41428	−	1.39388i	−0.160952	−	0.0929256i
$226$	−0.882488	+	3.29349i	−0.0587022	+	0.219080i
$227$	−9.62310	−	2.57850i	−0.638707	−	0.171141i	−0.0750896	−	0.997177i	$-0.523924\pi$
$227$	−9.62310	−	2.57850i	−0.638707	−	0.171141i	−0.563618	+	0.826036i	$0.690591\pi$
$228$	−11.2169	−	3.00557i	−0.742860	−	0.199049i
$229$	1.07935	−	4.02820i	0.0713257	−	0.266191i	−0.921049	−	0.389446i	$-0.872667\pi$
$229$	1.07935	−	4.02820i	0.0713257	−	0.266191i	0.992375	+	0.123255i	$0.0393332\pi$
$230$	−1.23399	−	0.712446i	−0.0813671	−	0.0469773i
$231$		0			0
$232$	−14.8816	−	3.98752i	−0.977026	−	0.261793i
$233$	−5.47860	+	3.16307i	−0.358915	+	0.207220i	−0.668605	−	0.743618i	$-0.733108\pi$
$233$	−5.47860	+	3.16307i	−0.358915	+	0.207220i	0.309690	+	0.950838i	$0.399775\pi$
$234$	−0.0965870	+	2.87126i	−0.00631409	+	0.187700i
$235$	−4.18213	+	7.24366i	−0.272812	+	0.472524i
$236$	3.71933	+	13.8807i	0.242108	+	0.903560i
$237$	−8.63172	+	4.98353i	−0.560691	+	0.323715i
$238$		0			0
$239$	7.84175	+	7.84175i	0.507241	+	0.507241i	0.913679	−	0.406438i	$-0.133229\pi$
$239$	7.84175	+	7.84175i	0.507241	+	0.507241i	−0.406438	+	0.913679i	$0.633229\pi$
$240$	0.356515	+	0.356515i	0.0230129	+	0.0230129i
$241$	−3.61892	+	13.5060i	−0.233115	+	0.869996i	0.745875	+	0.666086i	$0.232032\pi$
$241$	−3.61892	+	13.5060i	−0.233115	+	0.869996i	−0.978990	+	0.203910i	$0.934635\pi$
$242$	2.73879	+	10.2213i	0.176056	+	0.657050i
$243$			9.41578i			0.604022i
$244$	−5.92334	−	10.2595i	−0.379203	−	0.656799i
$245$		0			0
$246$		−	5.89523i		−	0.375866i
$247$	−10.6547	−	19.9769i	−0.677943	−	1.27110i
$248$	16.2726	+	9.39498i	1.03331	+	0.596582i
$249$	4.62772	+	4.62772i	0.293270	+	0.293270i
$250$	8.30691	+	4.79600i	0.525375	+	0.303325i
$251$	13.1784	−	22.8256i	0.831813	−	1.44074i	−0.0647865	−	0.997899i	$-0.520637\pi$
$251$	13.1784	−	22.8256i	0.831813	−	1.44074i	0.896599	−	0.442843i	$-0.146030\pi$
$252$		0			0
$253$	5.53531	−	1.48318i	0.348002	−	0.0932468i
$254$	−7.35102	+	7.35102i	−0.461244	+	0.461244i
$255$	−5.91655	+	1.58534i	−0.370509	+	0.0992776i
$256$	7.65303	+	13.2554i	0.478314	+	0.828465i
$257$	−5.39025	+	9.33618i	−0.336234	+	0.582375i	−0.983721	−	0.179702i	$-0.942487\pi$
$257$	−5.39025	+	9.33618i	−0.336234	+	0.582375i	0.647487	+	0.762077i	$0.275820\pi$
$258$	−1.04984	+	3.91804i	−0.0653599	+	0.243927i
$259$		0			0
$260$	−0.224087	+	6.66149i	−0.0138973	+	0.413128i
$261$	−2.62857	−	4.55282i	−0.162704	−	0.281812i
$262$	3.99920	−	3.99920i	0.247072	−	0.247072i
$263$	−15.4912			−0.955231			−0.477616	−	0.878569i	$-0.658499\pi$
$263$	−15.4912			−0.955231			−0.477616	+	0.878569i	$0.658499\pi$
$264$	19.2835			1.18682
$265$	−5.86881	+	5.86881i	−0.360518	+	0.360518i
$266$		0			0
$267$	0.0912034	+	0.340376i	0.00558156	+	0.0208307i
$268$	2.44862	+	0.656106i	0.149573	+	0.0400781i
$269$	−22.6324	+	13.0668i	−1.37992	+	0.796697i	−0.992149	−	0.125060i	$-0.960088\pi$
$269$	−22.6324	+	13.0668i	−1.37992	+	0.796697i	−0.387770	+	0.921756i	$0.626754\pi$
$270$		−	6.82557i		−	0.415391i
$271$	6.35804	−	1.70363i	0.386223	−	0.103488i	−0.0604821	−	0.998169i	$-0.519264\pi$
$271$	6.35804	−	1.70363i	0.386223	−	0.103488i	0.446706	+	0.894681i	$0.352597\pi$
$272$	0.732458			0.0444118
$273$		0			0
$274$	18.4439			1.11424
$275$	−13.8193	+	3.70286i	−0.833333	+	0.223291i
$276$		−	2.18330i		−	0.131419i
$277$	25.2681	−	14.5885i	1.51821	−	0.876540i	0.518442	−	0.855113i	$-0.326512\pi$
$277$	25.2681	−	14.5885i	1.51821	−	0.876540i	0.999770	−	0.0214270i	$-0.00682096\pi$
$278$	−3.28564	−	0.880384i	−0.197059	−	0.0528019i
$279$	1.65946	+	6.19317i	0.0993490	+	0.370776i
$280$		0			0
$281$	8.85369	−	8.85369i	0.528167	−	0.528167i	−0.391859	−	0.920025i	$-0.628168\pi$
$281$	8.85369	−	8.85369i	0.528167	−	0.528167i	0.920025	+	0.391859i	$0.128168\pi$
$282$	7.04902			0.419763
$283$	31.9411			1.89870			0.949351	−	0.314217i	$-0.101742\pi$
$283$	31.9411			1.89870			0.949351	+	0.314217i	$0.101742\pi$
$284$	3.01408	−	3.01408i	0.178853	−	0.178853i
$285$	6.44696	+	11.1665i	0.381885	+	0.661444i
$286$	10.0689	+	10.7699i	0.595386	+	0.636837i
$287$		0			0
$288$	−1.40773	+	5.25373i	−0.0829514	+	0.309579i
$289$	4.05077	−	7.01614i	0.238281	−	0.412714i
$290$	3.35420	+	5.80964i	0.196965	+	0.341154i
$291$	−13.0179	+	3.48813i	−0.763121	+	0.204478i
$292$	−0.455494	+	0.455494i	−0.0266558	+	0.0266558i
$293$	−12.4822	+	3.34459i	−0.729218	+	0.195393i	−0.604281	−	0.796771i	$-0.706540\pi$
$293$	−12.4822	+	3.34459i	−0.729218	+	0.195393i	−0.124937	+	0.992165i	$0.539873\pi$
$294$		0			0
$295$	7.97798	−	13.8183i	0.464496	−	0.804531i
$296$	−13.4241	−	7.75039i	−0.780258	−	0.450482i
$297$	19.4106	+	19.4106i	1.12632	+	1.12632i
$298$	−2.06957	−	1.19486i	−0.119887	−	0.0692167i
$299$	3.10942	−	2.90703i	0.179822	−	0.168118i
$300$			5.45075i			0.314699i
$301$		0			0
$302$	−7.05216	−	12.2147i	−0.405806	−	0.702877i
$303$		−	20.4765i		−	1.17634i
$304$	−0.399060	−	1.48931i	−0.0228877	−	0.0854180i
$305$	−3.40445	+	12.7056i	−0.194938	+	0.727520i
$306$	−1.68070	−	1.68070i	−0.0960790	−	0.0960790i
$307$	5.42520	+	5.42520i	0.309632	+	0.309632i	0.844767	−	0.535135i	$-0.179739\pi$
$307$	5.42520	+	5.42520i	0.309632	+	0.309632i	−0.535135	+	0.844767i	$0.679739\pi$
$308$		0			0
$309$	−9.24869	+	5.33974i	−0.526140	+	0.303767i
$310$	−2.11755	−	7.90282i	−0.120269	−	0.448850i
$311$	−0.241688	+	0.418616i	−0.0137049	+	0.0237375i	−0.872797	−	0.488084i	$-0.837696\pi$
$311$	−0.241688	+	0.418616i	−0.0137049	+	0.0237375i	0.859092	+	0.511822i	$0.171029\pi$
$312$	12.6386	−	6.74083i	0.715520	−	0.381624i
$313$	0.385666	−	0.222664i	0.0217991	−	0.0125857i	−0.489061	−	0.872250i	$-0.662660\pi$
$313$	0.385666	−	0.222664i	0.0217991	−	0.0125857i	0.510860	+	0.859664i	$0.329327\pi$
$314$	−2.33430	−	0.625474i	−0.131732	−	0.0352976i
$315$		0			0
$316$	−7.77097	−	4.48657i	−0.437151	−	0.252389i
$317$	−6.42697	+	23.9858i	−0.360975	+	1.34718i	0.511822	+	0.859091i	$0.328971\pi$
$317$	−6.42697	+	23.9858i	−0.360975	+	1.34718i	−0.872797	+	0.488084i	$0.837696\pi$
$318$	6.75631	+	1.81035i	0.378875	+	0.101519i
$319$	−26.0602	−	6.98281i	−1.45909	−	0.390962i
$320$	1.61424	−	6.02444i	0.0902390	−	0.336777i
$321$	5.81218	+	3.35567i	0.324404	+	0.187295i
$322$		0			0
$323$	18.0933	+	4.84809i	1.00674	+	0.269755i
$324$	5.88660	−	3.39863i	0.327033	−	0.188813i
$325$	−7.76288	+	7.25760i	−0.430607	+	0.402579i
$326$	10.1510	−	17.5820i	0.562210	−	0.973776i
$327$	1.59579	+	5.95559i	0.0882476	+	0.329345i
$328$	11.7206	−	6.76690i	0.647163	−	0.373640i
$329$		0			0
$330$	−5.93723	−	5.93723i	−0.326834	−	0.326834i
$331$	10.5285	+	10.5285i	0.578699	+	0.578699i	0.934545	−	0.355846i	$-0.115807\pi$
$331$	10.5285	+	10.5285i	0.578699	+	0.578699i	−0.355846	+	0.934545i	$0.615807\pi$
$332$	−1.52495	+	5.69120i	−0.0836926	+	0.312345i
$333$	−1.36897	−	5.10906i	−0.0750190	−	0.279975i
$334$		−	8.26734i		−	0.452369i
$335$	−1.40735	−	2.43760i	−0.0768917	−	0.133180i
$336$		0			0
$337$			7.23643i			0.394194i	0.980384	+	0.197097i	$0.0631513\pi$
$337$			7.23643i			0.394194i	−0.980384	+	0.197097i	$0.936849\pi$
$338$	10.3640	+	3.53896i	0.563727	+	0.192494i
$339$	5.02375	+	2.90046i	0.272853	+	0.157532i
$340$	−3.89931	−	3.89931i	−0.211470	−	0.211470i
$341$	28.4960	+	16.4522i	1.54315	+	0.890936i
$342$	−2.50169	+	4.33306i	−0.135276	+	0.234305i
$343$		0			0
$344$	−8.99474	+	2.41013i	−0.484964	+	0.129946i
$345$	−1.71416	+	1.71416i	−0.0922874	+	0.0922874i
$346$	4.26201	−	1.14200i	0.229127	−	0.0613944i
$347$	6.28405	+	10.8843i	0.337345	+	0.584299i	0.983933	−	0.178541i	$-0.0571376\pi$
$347$	6.28405	+	10.8843i	0.337345	+	0.584299i	−0.646587	+	0.762840i	$0.723804\pi$
$348$	−5.13948	+	8.90185i	−0.275505	+	0.477189i
$349$	4.81774	−	17.9800i	0.257888	−	0.962450i	−0.708574	−	0.705637i	$-0.750661\pi$
$349$	4.81774	−	17.9800i	0.257888	−	0.962450i	0.966461	−	0.256813i	$-0.0826723\pi$
$350$		0			0
$351$	19.5072	+	5.93665i	1.04122	+	0.316875i
$352$	13.9566	+	24.1735i	0.743887	+	1.28845i
$353$	−4.42576	+	4.42576i	−0.235559	+	0.235559i	−0.815008	−	0.579449i	$-0.803268\pi$
$353$	−4.42576	+	4.42576i	−0.235559	+	0.235559i	0.579449	+	0.815008i	$0.303268\pi$
$354$	−13.4470			−0.714698
$355$	−4.73287			−0.251195
$356$	−0.224325	+	0.224325i	−0.0118892	+	0.0118892i
$357$		0			0
$358$	4.92181	+	18.3684i	0.260126	+	0.970802i
$359$	2.27568	+	0.609768i	0.120106	+	0.0321823i	0.318371	−	0.947966i	$-0.396864\pi$
$359$	2.27568	+	0.609768i	0.120106	+	0.0321823i	−0.198265	+	0.980148i	$0.563531\pi$
$360$	3.25285	−	1.87804i	0.171440	−	0.0989812i
$361$		−	20.4307i		−	1.07530i
$362$	18.2928	−	4.90153i	0.961446	−	0.257619i
$363$	18.0031			0.944918
$364$		0			0
$365$	0.715239			0.0374373
$366$	10.7077	−	2.86912i	0.559700	−	0.149971i
$367$			19.3296i			1.00900i	0.863412	+	0.504499i	$0.168323\pi$
$367$			19.3296i			1.00900i	−0.863412	+	0.504499i	$0.831677\pi$
$368$	0.251047	−	0.144942i	0.0130867	−	0.00755563i
$369$	4.46074	+	1.19525i	0.232217	+	0.0622224i
$370$	1.74687	+	6.51943i	0.0908157	+	0.338929i
$371$		0			0
$372$	8.86450	−	8.86450i	0.459603	−	0.459603i
$373$	−8.34749			−0.432217			−0.216108	−	0.976369i	$-0.569336\pi$
$373$	−8.34749			−0.432217			−0.216108	+	0.976369i	$0.569336\pi$
$374$	−12.1980			−0.630743
$375$	11.5393	−	11.5393i	0.595886	−	0.595886i
$376$	8.09130	+	14.0145i	0.417277	+	0.722745i
$377$	−19.5210	+	4.53311i	−1.00538	+	0.233467i
$378$		0			0
$379$	−4.99923	+	18.6574i	−0.256793	+	0.958365i	0.710291	+	0.703908i	$0.248563\pi$
$379$	−4.99923	+	18.6574i	−0.256793	+	0.958365i	−0.967084	+	0.254457i	$0.918103\pi$
$380$	−5.80407	+	10.0529i	−0.297742	+	0.515705i
$381$	8.84337	+	15.3172i	0.453060	+	0.784723i
$382$	−20.0752	+	5.37912i	−1.02713	+	0.275220i
$383$	−16.6391	+	16.6391i	−0.850219	+	0.850219i	−0.990160	−	0.139941i	$-0.955309\pi$
$383$	−16.6391	+	16.6391i	−0.850219	+	0.850219i	0.139941	+	0.990160i	$0.455309\pi$
$384$	10.8450	−	2.90592i	0.553433	−	0.148292i
$385$		0			0
$386$	1.44861	−	2.50906i	0.0737323	−	0.127708i
$387$	−2.75181	−	1.58876i	−0.139882	−	0.0807612i
$388$	−8.57943	−	8.57943i	−0.435555	−	0.435555i
$389$	24.2127	+	13.9792i	1.22763	+	0.708775i	0.966535	−	0.256536i	$-0.0825813\pi$
$389$	24.2127	+	13.9792i	1.22763	+	0.708775i	0.261100	+	0.965312i	$0.415915\pi$
$390$	−5.96675	−	1.81587i	−0.302138	−	0.0919502i
$391$			3.52174i			0.178102i
$392$		0			0
$393$	−4.81109	−	8.33305i	−0.242687	−	0.420347i
$394$		−	3.36355i		−	0.169453i
$395$	2.57866	+	9.62371i	0.129747	+	0.484221i
$396$	−1.53322	+	5.72205i	−0.0770471	+	0.287544i
$397$	−8.48258	−	8.48258i	−0.425729	−	0.425729i	0.461442	−	0.887170i	$-0.347332\pi$
$397$	−8.48258	−	8.48258i	−0.425729	−	0.425729i	−0.887170	+	0.461442i	$0.847332\pi$
$398$	0.609447	+	0.609447i	0.0305488	+	0.0305488i
$399$		0			0
$400$	−0.626756	+	0.361858i	−0.0313378	+	0.0180929i
$401$	−5.12441	−	19.1246i	−0.255901	−	0.955035i	−0.967587	−	0.252537i	$-0.918735\pi$
$401$	−5.12441	−	19.1246i	−0.255901	−	0.955035i	0.711686	−	0.702497i	$-0.247932\pi$
$402$	−1.18605	+	2.05430i	−0.0591548	+	0.102459i
$403$	24.4277	+	0.821727i	1.21683	+	0.0409332i
$404$	15.9648	−	9.21728i	0.794279	−	0.458577i
$405$	−7.29007	−	1.95337i	−0.362246	−	0.0970636i
$406$		0			0
$407$	−23.5078	−	13.5722i	−1.16524	−	0.672751i
$408$	−3.06720	+	11.4469i	−0.151849	+	0.566708i
$409$	−17.1952	−	4.60743i	−0.850247	−	0.227823i	−0.192720	−	0.981254i	$-0.561731\pi$
$409$	−17.1952	−	4.60743i	−0.850247	−	0.227823i	−0.657527	+	0.753431i	$0.728398\pi$
$410$	−5.69214	−	1.52521i	−0.281115	−	0.0753245i
$411$	8.12147	−	30.3097i	0.400602	−	1.49507i
$412$	−8.32642	−	4.80726i	−0.410213	−	0.236837i
$413$		0			0
$414$	−0.908636	−	0.243468i	−0.0446570	−	0.0119658i
$415$	5.66558	−	3.27102i	0.278112	−	0.160568i
$416$	17.5974	+	10.9648i	0.862785	+	0.537593i
$417$	−2.89355	+	5.01178i	−0.141698	+	0.245428i
$418$	6.64576	+	24.8023i	0.325055	+	1.21312i
$419$	−8.03474	+	4.63886i	−0.392523	+	0.226623i	−0.683253	−	0.730182i	$-0.739435\pi$
$419$	−8.03474	+	4.63886i	−0.392523	+	0.226623i	0.290730	+	0.956805i	$0.406102\pi$
$420$		0			0
$421$	−13.2205	−	13.2205i	−0.644329	−	0.644329i	0.307288	−	0.951617i	$-0.400579\pi$
$421$	−13.2205	−	13.2205i	−0.644329	−	0.644329i	−0.951617	+	0.307288i	$0.900579\pi$
$422$	−3.21743	−	3.21743i	−0.156622	−	0.156622i
$423$	−1.42918	+	5.33379i	−0.0694893	+	0.259338i
$424$	4.15606	+	15.5106i	0.201836	+	0.753262i
$425$		−	8.79225i		−	0.426487i
$426$	1.99432	+	3.45427i	0.0966253	+	0.167360i
$427$		0			0
$428$			6.04208i			0.292055i
$429$	22.1323	−	11.8043i	1.06856	−	0.569918i
$430$	3.51146	+	2.02734i	0.169338	+	0.0977671i
$431$	4.19200	+	4.19200i	0.201921	+	0.201921i	0.800823	−	0.598901i	$-0.204396\pi$
$431$	4.19200	+	4.19200i	0.201921	+	0.201921i	−0.598901	+	0.800823i	$0.704396\pi$
$432$	1.20258	+	0.694307i	0.0578589	+	0.0334049i
$433$	−6.32385	+	10.9532i	−0.303905	+	0.526379i	−0.977017	−	0.213162i	$-0.931624\pi$
$433$	−6.32385	+	10.9532i	−0.303905	+	0.526379i	0.673112	+	0.739541i	$0.264957\pi$
$434$		0			0
$435$	11.0242	−	2.95393i	0.528570	−	0.141630i
$436$	−3.92503	+	3.92503i	−0.187975	+	0.187975i
$437$	7.16078	−	1.91873i	0.342547	−	0.0917851i
$438$	−0.301386	−	0.522015i	−0.0144008	−	0.0249429i
$439$	12.8788	−	22.3067i	0.614670	−	1.06464i	−0.375772	−	0.926712i	$-0.622622\pi$
$439$	12.8788	−	22.3067i	0.614670	−	1.06464i	0.990442	−	0.137928i	$-0.0440442\pi$
$440$	4.98901	−	18.6192i	0.237842	−	0.887638i
$441$		0			0
$442$	−7.99468	+	4.26398i	−0.380268	+	0.202817i
$443$	−8.62206	−	14.9338i	−0.409647	−	0.709529i	0.585203	−	0.810886i	$-0.301015\pi$
$443$	−8.62206	−	14.9338i	−0.409647	−	0.709529i	−0.994850	+	0.101358i	$0.967681\pi$
$444$	−7.31277	+	7.31277i	−0.347049	+	0.347049i
$445$	0.352246			0.0166981
$446$	−14.4896			−0.686105
$447$	−2.87487	+	2.87487i	−0.135977	+	0.135977i
$448$		0			0
$449$	−1.50842	−	5.62952i	−0.0711870	−	0.265673i	0.921155	−	0.389197i	$-0.127247\pi$
$449$	−1.50842	−	5.62952i	−0.0711870	−	0.265673i	−0.992342	+	0.123523i	$0.960581\pi$
$450$	2.26847	+	0.607835i	0.106937	+	0.0286536i
$451$	20.5248	−	11.8500i	0.966474	−	0.557994i
$452$			5.22246i			0.245644i
$453$	−23.1783	+	6.21060i	−1.08901	+	0.291800i
$454$	8.39274			0.393891
$455$		0			0
$456$	24.9463			1.16822
$457$	−21.4480	+	5.74697i	−1.00329	+	0.268832i	−0.722825	−	0.691031i	$-0.757157\pi$
$457$	−21.4480	+	5.74697i	−1.00329	+	0.268832i	−0.280469	+	0.959863i	$0.590490\pi$
$458$			3.51318i			0.164160i
$459$	−14.6098	+	8.43498i	−0.681928	+	0.393711i
$460$	−2.10809	−	0.564860i	−0.0982901	−	0.0263367i
$461$	−5.52093	−	20.6044i	−0.257135	−	0.959642i	−0.966890	−	0.255193i	$-0.917861\pi$
$461$	−5.52093	−	20.6044i	−0.257135	−	0.959642i	0.709755	−	0.704449i	$-0.248806\pi$
$462$		0			0
$463$	−5.14657	+	5.14657i	−0.239181	+	0.239181i	−0.816511	−	0.577330i	$-0.804095\pi$
$463$	−5.14657	+	5.14657i	−0.239181	+	0.239181i	0.577330	+	0.816511i	$0.304095\pi$
$464$	−1.36477			−0.0633581
$465$	−13.9195			−0.645501
$466$	3.76840	−	3.76840i	0.174568	−	0.174568i
$467$	−14.2554	−	24.6911i	−0.659661	−	1.14257i	−0.980703	−	0.195502i	$-0.937366\pi$
$467$	−14.2554	−	24.6911i	−0.659661	−	1.14257i	0.321042	−	0.947065i	$-0.395967\pi$
$468$	0.995337	+	4.28624i	0.0460095	+	0.198131i
$469$		0			0
$470$	1.82371	−	6.80619i	0.0841216	−	0.313946i
$471$	−2.05574	+	3.56065i	−0.0947235	+	0.164066i
$472$	−15.4352	−	26.7346i	−0.710465	−	1.23056i
$473$	−15.7513	+	4.22055i	−0.724245	+	0.194061i
$474$	5.93724	−	5.93724i	0.272707	−	0.272707i
$475$	−17.8774	+	4.79022i	−0.820270	+	0.219791i
$476$		0			0
$477$	−2.73967	+	4.74526i	−0.125441	+	0.217270i
$478$	−8.09080	−	4.67123i	−0.370065	−	0.213657i
$479$	−23.2801	−	23.2801i	−1.06369	−	1.06369i	−0.997829	−	0.0658656i	$-0.979019\pi$
$479$	−23.2801	−	23.2801i	−1.06369	−	1.06369i	−0.0658656	−	0.997829i	$-0.520981\pi$
$480$	−10.2261	−	5.90402i	−0.466754	−	0.269480i
$481$	−20.1516	−	0.677884i	−0.918833	−	0.0309088i
$482$		−	11.7792i		−	0.536527i
$483$		0			0
$484$	8.10392	+	14.0364i	0.368360	+	0.638018i
$485$			13.4719i			0.611726i
$486$	−2.05298	−	7.66184i	−0.0931252	−	0.347548i
$487$	−3.66858	+	13.6913i	−0.166239	+	0.620414i	0.831640	+	0.555316i	$0.187403\pi$
$487$	−3.66858	+	13.6913i	−0.166239	+	0.620414i	−0.997879	+	0.0650979i	$0.979264\pi$
$488$	17.9952	+	17.9952i	0.814604	+	0.814604i
$489$	−24.4235	−	24.4235i	−1.10447	−	1.10447i
$490$		0			0
$491$	−25.7788	+	14.8834i	−1.16338	+	0.671678i	−0.952112	−	0.305750i	$-0.901093\pi$
$491$	−25.7788	+	14.8834i	−1.16338	+	0.671678i	−0.211269	+	0.977428i	$0.567759\pi$
$492$	−2.33700	−	8.72182i	−0.105360	−	0.393210i
$493$	8.29017	−	14.3590i	0.373370	−	0.646696i
$494$	13.0257	+	13.9325i	0.586053	+	0.626854i
$495$	5.69629	−	3.28876i	0.256029	−	0.147819i
$496$	1.60777	+	0.430801i	0.0721911	+	0.0193435i
$497$		0			0
$498$	−4.77470	−	2.75667i	−0.213959	−	0.123529i
$499$	4.78371	−	17.8531i	0.214148	−	0.799213i	−0.772316	−	0.635238i	$-0.780902\pi$
$499$	4.78371	−	17.8531i	0.214148	−	0.799213i	0.986465	−	0.163974i	$-0.0524314\pi$
$500$	14.1911	+	3.80249i	0.634644	+	0.170052i
$501$	−13.5861	−	3.64039i	−0.606982	−	0.162640i
$502$	−5.74674	+	21.4471i	−0.256490	+	0.957232i
$503$	5.05931	+	2.92099i	0.225583	+	0.130241i	0.608533	−	0.793529i	$-0.291758\pi$
$503$	5.05931	+	2.92099i	0.225583	+	0.130241i	−0.382949	+	0.923769i	$0.625092\pi$
$504$		0			0
$505$	−19.7711	−	5.29765i	−0.879802	−	0.235742i
$506$	−4.18082	+	2.41380i	−0.185860	+	0.107306i
$507$	10.3793	−	15.4733i	0.460963	−	0.687194i
$508$	−7.96151	+	13.7897i	−0.353235	+	0.611821i
$509$	−7.59031	−	28.3274i	−0.336435	−	1.25559i	−0.902306	−	0.431097i	$-0.858127\pi$
$509$	−7.59031	−	28.3274i	−0.336435	−	1.25559i	0.565871	−	0.824494i	$-0.308540\pi$
$510$	4.46878	−	2.58005i	0.197881	−	0.114246i
$511$		0			0
$512$	1.96096	+	1.96096i	0.0866629	+	0.0866629i
$513$	25.1107	+	25.1107i	1.10866	+	1.10866i
$514$	2.35054	−	8.77234i	0.103678	−	0.386931i
$515$	2.76298	+	10.3116i	0.121751	+	0.454382i
$516$			6.21281i			0.273504i
$517$	14.1692	+	24.5418i	0.623162	+	1.07935i
$518$		0			0
$519$		−	7.50681i		−	0.329513i
$520$	−3.23877	−	13.9472i	−0.142030	−	0.611625i
$521$	−35.5182	−	20.5064i	−1.55608	−	0.898402i	−0.997626	−	0.0688659i	$-0.978062\pi$
$521$	−35.5182	−	20.5064i	−1.55608	−	0.898402i	−0.558453	−	0.829536i	$-0.688605\pi$
$522$	3.13161	+	3.13161i	0.137067	+	0.137067i
$523$	−38.4309	−	22.1881i	−1.68047	−	0.970217i	−0.961351	−	0.275325i	$-0.911215\pi$
$523$	−38.4309	−	22.1881i	−1.68047	−	0.970217i	−0.719114	−	0.694892i	$-0.755452\pi$
$524$	4.33133	−	7.50208i	0.189215	−	0.327730i
$525$		0			0
$526$	12.6056	−	3.37766i	0.549630	−	0.147273i
$527$	−14.2987	+	14.2987i	−0.622863	+	0.622863i
$528$	1.65000	−	0.442118i	0.0718072	−	0.0192407i
$529$	−10.8031	−	18.7115i	−0.469700	−	0.813544i
$530$	3.49597	−	6.05520i	0.151855	−	0.263021i
$531$	2.72636	−	10.1749i	0.118314	−	0.441554i
$532$		0			0
$533$	9.30979	−	14.9413i	0.403252	−	0.647180i
$534$	−0.148429	−	0.257086i	−0.00642314	−	0.0111252i
$535$	4.74379	−	4.74379i	0.205092	−	0.205092i
$536$	−5.44569			−0.235218
$537$	32.3529			1.39613
$538$	15.5674	−	15.5674i	0.671160	−	0.671160i
$539$		0			0
$540$	−2.70581	−	10.0982i	−0.116440	−	0.434559i
$541$	6.62524	+	1.77523i	0.284841	+	0.0763230i	0.398411	−	0.917207i	$-0.369562\pi$
$541$	6.62524	+	1.77523i	0.284841	+	0.0763230i	−0.113570	+	0.993530i	$0.536228\pi$
$542$	−4.80223	+	2.77257i	−0.206273	+	0.119092i
$543$		−	32.2196i		−	1.38268i
$544$	−16.5696	+	4.43980i	−0.710414	+	0.190355i
$545$	6.16329			0.264006
$546$		0			0
$547$	−16.7670			−0.716904			−0.358452	−	0.933548i	$-0.616695\pi$
$547$	−16.7670			−0.716904			−0.358452	+	0.933548i	$0.616695\pi$
$548$	27.2872	−	7.31159i	1.16565	−	0.312336i
$549$			8.68391i			0.370620i
$550$	10.4377	−	6.02620i	0.445065	−	0.256958i
$551$	−33.7129	−	9.03336i	−1.43622	−	0.384834i
$552$	1.21390	+	4.53035i	0.0516672	+	0.192824i
$553$		0			0
$554$	−17.3804	+	17.3804i	−0.738422	+	0.738422i
$555$	11.4829			0.487421
$556$	−5.21001			−0.220954
$557$	27.8578	−	27.8578i	1.18037	−	1.18037i	0.200725	−	0.979648i	$-0.435670\pi$
$557$	27.8578	−	27.8578i	1.18037	−	1.18037i	0.979648	−	0.200725i	$-0.0643298\pi$
$558$	−2.70068	−	4.67771i	−0.114329	−	0.198023i
$559$	−8.84819	+	8.27227i	−0.374238	+	0.349880i
$560$		0			0
$561$	−5.37118	+	20.0455i	−0.226772	+	0.846323i
$562$	−5.27402	+	9.13488i	−0.222471	+	0.385332i
$563$	−1.05586	−	1.82880i	−0.0444991	−	0.0770748i	0.842918	−	0.538042i	$-0.180836\pi$
$563$	−1.05586	−	1.82880i	−0.0444991	−	0.0770748i	−0.887417	+	0.460967i	$0.847503\pi$
$564$	10.4288	−	2.79440i	0.439133	−	0.117665i
$565$	4.10029	−	4.10029i	0.172500	−	0.172500i
$566$	−25.9912	+	6.96433i	−1.09249	+	0.292733i
$567$		0			0
$568$	−4.57841	+	7.93005i	−0.192106	+	0.332737i
$569$	−31.5451	−	18.2126i	−1.32244	−	0.763512i	−0.338323	−	0.941030i	$-0.609860\pi$
$569$	−31.5451	−	18.2126i	−1.32244	−	0.763512i	−0.984117	+	0.177518i	$0.943193\pi$
$570$	−7.68073	−	7.68073i	−0.321710	−	0.321710i
$571$	−13.1672	−	7.60209i	−0.551030	−	0.318138i	0.198507	−	0.980099i	$-0.436391\pi$
$571$	−13.1672	−	7.60209i	−0.551030	−	0.318138i	−0.749537	+	0.661962i	$0.769724\pi$
$572$	19.1661	+	11.9422i	0.801374	+	0.499329i
$573$			35.3590i			1.47715i
$574$		0			0
$575$	−1.73985	−	3.01351i	−0.0725568	−	0.125672i
$576$		−	4.11754i		−	0.171564i
$577$	2.93081	+	10.9379i	0.122011	+	0.455352i	0.999716	−	0.0238508i	$-0.00759266\pi$
$577$	2.93081	+	10.9379i	0.122011	+	0.455352i	−0.877704	+	0.479202i	$0.840926\pi$
$578$	−1.76643	+	6.59241i	−0.0734739	+	0.274208i
$579$	−3.48539	−	3.48539i	−0.144848	−	0.144848i
$580$	7.26551	+	7.26551i	0.301684	+	0.301684i
$581$		0			0
$582$	9.83240	−	5.67674i	0.407566	−	0.235308i
$583$	7.27796	+	27.1617i	0.301422	+	1.12492i
$584$	0.691898	−	1.19840i	0.0286309	−	0.0495902i
$585$	2.58377	−	4.14670i	0.106826	−	0.171445i
$586$	9.42781	−	5.44315i	0.389459	−	0.224854i
$587$	−3.32195	−	0.890113i	−0.137111	−	0.0367389i	0.189611	−	0.981859i	$-0.439277\pi$
$587$	−3.32195	−	0.890113i	−0.137111	−	0.0367389i	−0.326722	+	0.945120i	$0.605944\pi$
$588$		0			0
$589$	36.8641	+	21.2835i	1.51896	+	0.876971i
$590$	−3.47898	+	12.9837i	−0.143227	+	0.534532i
$591$	−5.52747	−	1.48108i	−0.227370	−	0.0609236i
$592$	−1.32633	−	0.355389i	−0.0545119	−	0.0146064i
$593$	−12.0428	+	44.9445i	−0.494540	+	1.84565i	0.0380481	+	0.999276i	$0.487886\pi$
$593$	−12.0428	+	44.9445i	−0.494540	+	1.84565i	−0.532589	+	0.846374i	$0.678781\pi$
$594$	−20.0271	−	11.5627i	−0.821722	−	0.474422i
$595$		0			0
$596$	−3.53554	−	0.947344i	−0.144821	−	0.0388047i
$597$	1.26989	−	0.733173i	0.0519732	−	0.0300068i
$598$	−1.89637	+	3.04349i	−0.0775483	+	0.124457i
$599$	−3.80885	+	6.59712i	−0.155625	+	0.269551i	−0.933287	−	0.359133i	$-0.883073\pi$
$599$	−3.80885	+	6.59712i	−0.155625	+	0.269551i	0.777661	+	0.628684i	$0.216406\pi$
$600$	−3.03059	−	11.3103i	−0.123723	−	0.461742i
$601$	−32.3774	+	18.6931i	−1.32070	+	0.762508i	−0.983841	−	0.179045i	$-0.942699\pi$
$601$	−32.3774	+	18.6931i	−1.32070	+	0.762508i	−0.336863	+	0.941554i	$0.609366\pi$
$602$		0			0
$603$	−1.31396	−	1.31396i	−0.0535085	−	0.0535085i
$604$	−15.2757	−	15.2757i	−0.621558	−	0.621558i
$605$	4.65774	−	17.3829i	0.189364	−	0.706717i
$606$	4.46462	+	16.6622i	0.181363	+	0.676855i
$607$			18.9804i			0.770390i	0.922835	+	0.385195i	$0.125866\pi$
$607$			18.9804i			0.770390i	−0.922835	+	0.385195i	$0.874134\pi$
$608$	18.0550	+	31.2722i	0.732226	+	1.26825i
$609$		0			0
$610$		−	11.0811i		−	0.448661i
$611$	17.8656	+	11.1319i	0.722764	+	0.450348i
$612$	−3.15281	−	1.82027i	−0.127445	−	0.0735802i
$613$	−3.10787	−	3.10787i	−0.125526	−	0.125526i	0.641553	−	0.767079i	$-0.278290\pi$
$613$	−3.10787	−	3.10787i	−0.125526	−	0.125526i	−0.767079	+	0.641553i	$0.778290\pi$
$614$	−5.59750	−	3.23172i	−0.225897	−	0.130421i
$615$	−5.01288	+	8.68256i	−0.202139	+	0.350115i
$616$		0			0
$617$	23.9468	−	6.41652i	0.964061	−	0.258319i	0.257743	−	0.966214i	$-0.417021\pi$
$617$	23.9468	−	6.41652i	0.964061	−	0.258319i	0.706318	+	0.707894i	$0.250355\pi$
$618$	6.36162	−	6.36162i	0.255902	−	0.255902i
$619$	23.5480	−	6.30966i	0.946473	−	0.253607i	0.247608	−	0.968860i	$-0.420355\pi$
$619$	23.5480	−	6.30966i	0.946473	−	0.253607i	0.698865	+	0.715254i	$0.253689\pi$
$620$	−6.26572	−	10.8525i	−0.251637	−	0.435849i
$621$	−3.33831	+	5.78211i	−0.133962	+	0.232028i
$622$	0.105394	−	0.393334i	0.00422590	−	0.0157713i
$623$		0			0
$624$	0.926879	−	0.866550i	0.0371049	−	0.0346898i
$625$	−0.787786	−	1.36449i	−0.0315115	−	0.0545794i
$626$	−0.265276	+	0.265276i	−0.0106026	+	0.0106026i
$627$	43.6851			1.74461
$628$	−3.70149			−0.147705
$629$	11.7957	−	11.7957i	0.470327	−	0.470327i
$630$		0			0
$631$	0.701056	+	2.61638i	0.0279086	+	0.104156i	0.978475	−	0.206364i	$-0.0661633\pi$
$631$	0.701056	+	2.61638i	0.0279086	+	0.104156i	−0.950567	+	0.310521i	$0.899497\pi$
$632$	18.6193	+	4.98902i	0.740635	+	0.198453i
$633$	−6.70410	+	3.87061i	−0.266464	+	0.153843i
$634$		−	20.9191i		−	0.830803i
$635$	17.0775	−	4.57589i	0.677698	−	0.181589i
$636$	10.7134			0.424815
$637$		0			0
$638$	22.7283			0.899822
$639$	−3.01809	+	0.808695i	−0.119394	+	0.0319915i
$640$		−	11.2232i		−	0.443638i
$641$	−2.71103	+	1.56522i	−0.107079	+	0.0618223i	−0.552583	−	0.833458i	$-0.686358\pi$
$641$	−2.71103	+	1.56522i	−0.107079	+	0.0618223i	0.445504	+	0.895280i	$0.353025\pi$
$642$	−5.46117	−	1.46331i	−0.215535	−	0.0577524i
$643$	0.747638	+	2.79022i	0.0294840	+	0.110036i	0.979100	−	0.203381i	$-0.0651930\pi$
$643$	0.747638	+	2.79022i	0.0294840	+	0.110036i	−0.949616	+	0.313417i	$0.898526\pi$
$644$		0			0
$645$	4.87783	−	4.87783i	0.192064	−	0.192064i
$646$	−15.7800			−0.620856
$647$	17.7360			0.697275			0.348637	−	0.937258i	$-0.386645\pi$
$647$	17.7360			0.697275			0.348637	+	0.937258i	$0.386645\pi$
$648$	−10.3251	+	10.3251i	−0.405607	+	0.405607i
$649$	−27.0297	−	46.8169i	−1.06101	−	1.83772i
$650$	4.73441	−	7.59827i	0.185699	−	0.298029i
$651$		0			0
$652$	8.04815	−	30.0361i	0.315190	−	1.17631i
$653$	11.0978	−	19.2219i	0.434289	−	0.752211i	−0.562948	−	0.826492i	$-0.690333\pi$
$653$	11.0978	−	19.2219i	0.434289	−	0.752211i	0.997237	+	0.0742811i	$0.0236662\pi$
$654$	−2.59707	−	4.49826i	−0.101553	−	0.175896i
$655$	−9.29071	+	2.48944i	−0.363018	+	0.0972704i
$656$	0.847734	−	0.847734i	0.0330985	−	0.0330985i
$657$	0.456099	−	0.122211i	0.0177941	−	0.00476792i
$658$		0			0
$659$	14.4500	−	25.0282i	0.562893	−	0.974960i	−0.434349	−	0.900745i	$-0.643021\pi$
$659$	14.4500	−	25.0282i	0.562893	−	0.974960i	0.997242	−	0.0742153i	$-0.0236452\pi$
$660$	−11.1376	−	6.43031i	−0.433531	−	0.250299i
$661$	−2.74283	−	2.74283i	−0.106684	−	0.106684i	0.651750	−	0.758434i	$-0.274035\pi$
$661$	−2.74283	−	2.74283i	−0.106684	−	0.106684i	−0.758434	+	0.651750i	$0.774035\pi$
$662$	−10.8629	−	6.27169i	−0.422198	−	0.243756i
$663$	3.48687	+	15.0156i	0.135419	+	0.583157i
$664$		−	12.6571i		−	0.491191i
$665$		0			0
$666$	2.22792	+	3.85887i	0.0863302	+	0.149528i
$667$		−	6.56199i		−	0.254081i
$668$	−3.27737	−	12.2313i	−0.126805	−	0.473243i
$669$	−6.38027	+	23.8115i	−0.246676	+	0.920606i
$670$	1.67668	+	1.67668i	0.0647757	+	0.0647757i
$671$	31.5126	+	31.5126i	1.21653	+	1.21653i
$672$		0			0
$673$	14.8015	−	8.54566i	0.570557	−	0.329411i	−0.186815	−	0.982395i	$-0.559816\pi$
$673$	14.8015	−	8.54566i	0.570557	−	0.329411i	0.757372	+	0.652984i	$0.226483\pi$
$674$	−1.57781	−	5.88845i	−0.0607748	−	0.226815i
$675$	8.33430	−	14.4354i	0.320787	−	0.555620i
$676$	16.7362	+	1.12726i	0.643699	+	0.0433561i
$677$	−26.4773	+	15.2867i	−1.01760	+	0.587514i	−0.913409	−	0.407043i	$-0.866560\pi$
$677$	−26.4773	+	15.2867i	−1.01760	+	0.587514i	−0.104195	+	0.994557i	$0.533227\pi$
$678$	−4.72035	−	1.26481i	−0.181284	−	0.0485749i
$679$		0			0
$680$	10.2591	+	5.92308i	0.393417	+	0.227140i
$681$	3.69560	−	13.7922i	0.141616	−	0.528517i
$682$	−26.7751	−	7.17436i	−1.02527	−	0.274720i
$683$	−6.12129	−	1.64019i	−0.234224	−	0.0627603i	0.139797	−	0.990180i	$-0.455355\pi$
$683$	−6.12129	−	1.64019i	−0.234224	−	0.0627603i	−0.374022	+	0.927420i	$0.622022\pi$
$684$	−1.98346	+	7.40236i	−0.0758394	+	0.283036i
$685$	−27.1644	−	15.6834i	−1.03790	−	0.599231i
$686$		0			0
$687$	5.77337	+	1.54697i	0.220268	+	0.0590206i
$688$	−0.714381	+	0.412448i	−0.0272355	+	0.0157244i
$689$	14.2648	+	15.2579i	0.543445	+	0.581280i
$690$	1.02110	−	1.76860i	0.0388728	−	0.0673296i
$691$	1.23455	+	4.60739i	0.0469643	+	0.175273i	0.985424	−	0.170115i	$-0.0544139\pi$
$691$	1.23455	+	4.60739i	0.0469643	+	0.175273i	−0.938460	+	0.345388i	$0.887747\pi$
$692$	5.85280	−	3.37912i	0.222490	−	0.128455i
$693$		0			0
$694$	−7.48665	−	7.48665i	−0.284189	−	0.284189i
$695$	4.09051	+	4.09051i	0.155162	+	0.155162i
$696$	5.71506	−	21.3289i	0.216629	−	0.808469i
$697$	3.76967	+	14.0686i	0.142786	+	0.532886i
$698$			15.6812i			0.593543i
$699$	−4.53343	−	7.85213i	−0.171470	−	0.296995i
$700$		0			0
$701$			29.4647i			1.11287i	0.830892	+	0.556433i	$0.187831\pi$
$701$			29.4647i			1.11287i	−0.830892	+	0.556433i	$0.812169\pi$
$702$	−17.1678	−	0.577513i	−0.647958	−	0.0217968i
$703$	−30.4110	−	17.5578i	−1.14697	−	0.662205i
$704$	−14.9419	−	14.9419i	−0.563145	−	0.563145i
$705$	−10.3819	−	5.99398i	−0.391004	−	0.225746i
$706$	2.63637	−	4.56632i	0.0992209	−	0.171856i
$707$		0			0
$708$	−19.8944	+	5.33069i	−0.747677	+	0.200340i
$709$	−11.8528	+	11.8528i	−0.445140	+	0.445140i	−0.893735	−	0.448595i	$-0.851925\pi$
$709$	−11.8528	+	11.8528i	−0.445140	+	0.445140i	0.448595	+	0.893735i	$0.351925\pi$
$710$	3.85124	−	1.03194i	0.144535	−	0.0387279i
$711$	3.28876	+	5.69631i	0.123338	+	0.213628i
$712$	0.340751	−	0.590198i	0.0127702	−	0.0221186i
$713$	−2.07134	+	7.73035i	−0.0775723	+	0.289504i
$714$		0			0
$715$	−5.67164	−	24.4239i	−0.212107	−	0.913402i
$716$	14.5633	+	25.2245i	0.544258	+	0.942682i
$717$	−11.2391	+	11.2391i	−0.419732	+	0.419732i
$718$	−1.98473			−0.0740694
$719$	−17.9279			−0.668598			−0.334299	−	0.942467i	$-0.608500\pi$
$719$	−17.9279			−0.668598			−0.334299	+	0.942467i	$0.608500\pi$
$720$	0.235274	−	0.235274i	0.00876814	−	0.00876814i
$721$		0			0
$722$	4.45463	+	16.6249i	0.165784	+	0.618715i
$723$	−19.3573	−	5.18676i	−0.719904	−	0.192898i
$724$	25.1205	−	14.5033i	0.933597	−	0.539012i
$725$			16.3824i			0.608428i
$726$	−14.6496	+	3.92534i	−0.543696	+	0.145683i
$727$	32.6548			1.21110			0.605549	−	0.795808i	$-0.292954\pi$
$727$	32.6548			1.21110			0.605549	+	0.795808i	$0.292954\pi$
$728$		0			0
$729$	−29.2988			−1.08514
$730$	−0.582007	+	0.155948i	−0.0215410	+	0.00577190i
$731$		−	10.0215i		−	0.370658i
$732$	14.7043	−	8.48955i	0.543488	−	0.313783i
$733$	34.2658	+	9.18149i	1.26564	+	0.339126i	0.828358	−	0.560200i	$-0.189276\pi$
$733$	34.2658	+	9.18149i	1.26564	+	0.339126i	0.437279	+	0.899326i	$0.355942\pi$
$734$	−4.21456	−	15.7290i	−0.155562	−	0.580567i
$735$		0			0
$736$	−4.80059	+	4.80059i	−0.176952	+	0.176952i
$737$	−9.53631			−0.351275
$738$	−3.89042			−0.143208
$739$	−10.1559	+	10.1559i	−0.373590	+	0.373590i	−0.868783	−	0.495193i	$-0.835097\pi$
$739$	−10.1559	+	10.1559i	−0.373590	+	0.373590i	0.495193	+	0.868783i	$0.335097\pi$
$740$	5.16890	+	8.95280i	0.190013	+	0.329112i
$741$	28.6316	−	15.2707i	1.05181	−	0.560984i
$742$		0			0
$743$	6.76509	−	25.2477i	0.248187	−	0.926247i	−0.723568	−	0.690254i	$-0.757499\pi$
$743$	6.76509	−	25.2477i	0.248187	−	0.926247i	0.971755	−	0.235993i	$-0.0758344\pi$
$744$	−13.4652	+	23.3225i	−0.493659	+	0.855043i
$745$	2.03206	+	3.51962i	0.0744487	+	0.128949i
$746$	6.79255	−	1.82006i	0.248693	−	0.0666370i
$747$	3.05396	−	3.05396i	0.111738	−	0.111738i
$748$	−18.0466	+	4.83557i	−0.659849	+	0.176806i
$749$		0			0
$750$	−6.87380	+	11.9058i	−0.250996	+	0.434737i
$751$	−10.2898	−	5.94079i	−0.375479	−	0.216783i	0.300371	−	0.953823i	$-0.402890\pi$
$751$	−10.2898	−	5.94079i	−0.375479	−	0.216783i	−0.675849	+	0.737040i	$0.736223\pi$
$752$	1.01365	+	1.01365i	0.0369640	+	0.0369640i
$753$	32.7146	+	18.8878i	1.19218	+	0.688308i
$754$	14.8963	−	7.94500i	0.542492	−	0.289340i
$755$			23.9866i			0.872963i
$756$		0			0
$757$	21.1088	+	36.5615i	0.767212	+	1.32885i	0.939069	+	0.343729i	$0.111690\pi$
$757$	21.1088	+	36.5615i	0.767212	+	1.32885i	−0.171857	+	0.985122i	$0.554977\pi$
$758$		−	16.2720i		−	0.591024i
$759$	2.12575	+	7.93340i	0.0771598	+	0.287964i
$760$	6.45406	−	24.0869i	0.234114	−	0.873723i
$761$	20.3544	+	20.3544i	0.737845	+	0.737845i	0.972161	−	0.234316i	$-0.0752849\pi$
$761$	20.3544	+	20.3544i	0.737845	+	0.737845i	−0.234316	+	0.972161i	$0.575285\pi$
$762$	−10.5358	−	10.5358i	−0.381670	−	0.381670i
$763$		0			0
$764$	−27.5682	+	15.9165i	−0.997383	+	0.575840i
$765$	1.04621	+	3.90449i	0.0378257	+	0.141167i
$766$	9.91170	−	17.1676i	0.358124	−	0.620290i
$767$	−34.0810	−	21.2356i	−1.23059	−	0.766772i
$768$	−18.9982	+	10.9686i	−0.685538	+	0.395795i
$769$	−33.9039	−	9.08451i	−1.22260	−	0.327596i	−0.410909	−	0.911676i	$-0.634789\pi$
$769$	−33.9039	−	9.08451i	−1.22260	−	0.327596i	−0.811696	+	0.584081i	$0.801455\pi$
$770$		0			0
$771$	−13.3810	−	7.72550i	−0.481903	−	0.278227i
$772$	1.14852	−	4.28635i	0.0413363	−	0.154269i
$773$	29.3542	+	7.86544i	1.05580	+	0.282900i	0.744646	−	0.667460i	$-0.232619\pi$
$773$	29.3542	+	7.86544i	1.05580	+	0.282900i	0.311152	+	0.950360i	$0.399285\pi$
$774$	2.58562	+	0.692815i	0.0929382	+	0.0249027i
$775$	5.17124	−	19.2993i	0.185756	−	0.693252i
$776$	22.5725	+	13.0322i	0.810304	+	0.467829i
$777$		0			0
$778$	−22.7505	−	6.09597i	−0.815643	−	0.218551i
$779$	26.5520	−	15.3298i	0.951324	−	0.549247i
$780$	−9.54749	−	0.321170i	−0.341855	−	0.0114997i
$781$	−8.01758	+	13.8868i	−0.286891	+	0.496911i
$782$	−0.767867	−	2.86572i	−0.0274589	−	0.102478i
$783$	27.2222	−	15.7167i	0.972842	−	0.561670i
$784$		0			0
$785$	2.90613	+	2.90613i	0.103724	+	0.103724i
$786$	5.73181	+	5.73181i	0.204447	+	0.204447i
$787$	−2.62934	+	9.81284i	−0.0937260	+	0.349790i	−0.996823	−	0.0796460i	$-0.974621\pi$
$787$	−2.62934	+	9.81284i	−0.0937260	+	0.349790i	0.903097	+	0.429436i	$0.141288\pi$
$788$	−1.33339	−	4.97628i	−0.0475000	−	0.177272i
$789$		−	22.2026i		−	0.790434i
$790$	−4.19664	−	7.26879i	−0.149310	−	0.258612i
$791$		0			0
$792$		−	12.7257i		−	0.452189i
$793$	31.6693	+	9.63797i	1.12461	+	0.342254i
$794$	8.75199	+	5.05296i	0.310596	+	0.179323i
$795$	−8.41139	−	8.41139i	−0.298321	−	0.298321i
$796$	1.14326	+	0.660061i	0.0405217	+	0.0233952i
$797$	−18.3972	+	31.8649i	−0.651662	+	1.12871i	0.331057	+	0.943611i	$0.392595\pi$
$797$	−18.3972	+	31.8649i	−0.651662	+	1.12871i	−0.982719	+	0.185101i	$0.940739\pi$
$798$		0			0
$799$	−16.8221	+	4.50746i	−0.595122	+	0.159462i
$800$	11.9850	−	11.9850i	0.423733	−	0.423733i
$801$	0.224623	−	0.0601876i	0.00793667	−	0.00212662i
$802$	8.33970	+	14.4448i	0.294485	+	0.510063i
$803$	1.21163	−	2.09860i	0.0427575	−	0.0740582i
$804$	−0.940356	+	3.50946i	−0.0331638	+	0.123769i
$805$		0			0
$806$	−20.0565	+	4.65746i	−0.706460	+	0.164052i
$807$	−18.7278	−	32.4375i	−0.659250	−	1.14186i
$808$	−28.0022	+	28.0022i	−0.985115	+	0.985115i
$809$	−18.7612			−0.659607			−0.329804	−	0.944050i	$-0.606983\pi$
$809$	−18.7612			−0.659607			−0.329804	+	0.944050i	$0.606983\pi$
$810$	6.35800			0.223397
$811$	3.85841	−	3.85841i	0.135487	−	0.135487i	−0.636111	−	0.771598i	$-0.719458\pi$
$811$	3.85841	−	3.85841i	0.135487	−	0.135487i	0.771598	+	0.636111i	$0.219458\pi$
$812$		0			0
$813$	2.44171	+	9.11258i	0.0856344	+	0.319592i
$814$	22.0881	+	5.91848i	0.774187	+	0.207443i
$815$	−29.9009	+	17.2633i	−1.04738	+	0.604707i
$816$			1.04979i			0.0367498i
$817$	−20.3768	+	5.45994i	−0.712893	+	0.191019i
$818$	14.9967			0.524347
$819$		0			0
$820$	−9.02599			−0.315201
$821$	1.99738	−	0.535196i	0.0697089	−	0.0186785i	−0.223796	−	0.974636i	$-0.571845\pi$
$821$	1.99738	−	0.535196i	0.0697089	−	0.0186785i	0.293505	+	0.955958i	$0.405178\pi$
$822$			26.4345i			0.922009i
$823$	23.4776	−	13.5548i	0.818379	−	0.472491i	−0.0314782	−	0.999504i	$-0.510021\pi$
$823$	23.4776	−	13.5548i	0.818379	−	0.472491i	0.849857	+	0.527013i	$0.176688\pi$
$824$	19.9501	+	5.34562i	0.694996	+	0.186224i
$825$	−5.30707	−	19.8063i	−0.184769	−	0.689566i
$826$		0			0
$827$	−18.8233	+	18.8233i	−0.654550	+	0.654550i	−0.954085	−	0.299535i	$-0.903168\pi$
$827$	−18.8233	+	18.8233i	−0.654550	+	0.654550i	0.299535	+	0.954085i	$0.403168\pi$
$828$	−1.44082			−0.0500719
$829$	−5.01498			−0.174177			−0.0870887	−	0.996201i	$-0.527756\pi$
$829$	−5.01498			−0.174177			−0.0870887	+	0.996201i	$0.527756\pi$
$830$	−3.89701	+	3.89701i	−0.135267	+	0.135267i
$831$	20.9088	+	36.2152i	0.725319	+	1.25629i
$832$	−15.0162	−	4.56991i	−0.520594	−	0.158433i
$833$		0			0
$834$	1.26180	−	4.70910i	0.0436925	−	0.163063i
$835$	−7.02996	+	12.1762i	−0.243282	+	0.421376i
$836$	19.6644	+	34.0598i	0.680108	+	1.17798i
$837$	−37.0302	+	9.92221i	−1.27995	+	0.342962i
$838$	5.52661	−	5.52661i	0.190914	−	0.190914i
$839$	1.91166	−	0.512227i	0.0659978	−	0.0176840i	−0.225669	−	0.974204i	$-0.572457\pi$
$839$	1.91166	−	0.512227i	0.0659978	−	0.0176840i	0.291667	+	0.956520i	$0.405790\pi$
$840$		0			0
$841$	−0.946916	+	1.64011i	−0.0326523	+	0.0565554i
$842$	13.6404	+	7.87529i	0.470079	+	0.271400i
$843$	12.6894	+	12.6894i	0.437047	+	0.437047i
$844$	−6.03557	−	3.48464i	−0.207753	−	0.119946i
$845$	−12.2550	−	14.0250i	−0.421583	−	0.482476i
$846$		−	4.65184i		−	0.159934i
$847$		0			0
$848$	0.711230	+	1.23189i	0.0244238	+	0.0423032i
$849$			45.7792i			1.57114i
$850$	1.91703	+	7.15446i	0.0657536	+	0.245396i
$851$	1.70875	−	6.37714i	0.0585752	−	0.218606i
$852$	4.31990	+	4.31990i	0.147997	+	0.147997i
$853$	−0.494551	−	0.494551i	−0.0169331	−	0.0169331i	0.698590	−	0.715523i	$-0.253811\pi$
$853$	−0.494551	−	0.494551i	−0.0169331	−	0.0169331i	−0.715523	+	0.698590i	$0.753811\pi$
$854$		0			0
$855$	7.36904	−	4.25452i	0.252016	−	0.145502i
$856$	−3.35937	−	12.5373i	−0.114821	−	0.428517i
$857$	−7.68803	+	13.3161i	−0.262618	+	0.454868i	−0.966937	−	0.255016i	$-0.917919\pi$
$857$	−7.68803	+	13.3161i	−0.262618	+	0.454868i	0.704319	+	0.709884i	$0.251253\pi$
$858$	−15.4358	+	14.4311i	−0.526970	+	0.492670i
$859$	28.7090	−	16.5752i	0.979540	−	0.565538i	0.0774086	−	0.996999i	$-0.475335\pi$
$859$	28.7090	−	16.5752i	0.979540	−	0.565538i	0.902131	+	0.431462i	$0.142002\pi$
$860$	5.99879	+	1.60737i	0.204557	+	0.0548109i
$861$		0			0
$862$	−4.32513	−	2.49712i	−0.147315	−	0.0850521i
$863$	6.83800	−	25.5198i	0.232768	−	0.868703i	−0.746374	−	0.665527i	$-0.768207\pi$
$863$	6.83800	−	25.5198i	0.232768	−	0.868703i	0.979142	−	0.203176i	$-0.0651264\pi$
$864$	−31.4131	−	8.41711i	−1.06869	−	0.286356i
$865$	−7.24822	−	1.94215i	−0.246447	−	0.0660352i
$866$	2.75766	−	10.2917i	0.0937091	−	0.349727i
$867$	10.0558	+	5.80571i	0.341513	+	0.197172i
$868$		0			0
$869$	32.6055	+	8.73662i	1.10607	+	0.296370i
$870$	−8.32659	+	4.80736i	−0.282298	+	0.162985i
$871$	−6.25018	+	3.33355i	−0.211779	+	0.112953i
$872$	5.96215	−	10.3268i	0.201904	−	0.349708i
$873$	2.30191	+	8.59084i	0.0779078	+	0.290756i
$874$	−5.40854	+	3.12262i	−0.182947	+	0.105624i
$875$		0			0
$876$	−0.652830	−	0.652830i	−0.0220571	−	0.0220571i
$877$	10.2068	+	10.2068i	0.344659	+	0.344659i	0.858116	−	0.513456i	$-0.171635\pi$
$877$	10.2068	+	10.2068i	0.344659	+	0.344659i	−0.513456	+	0.858116i	$0.671635\pi$
$878$	−5.61608	+	20.9595i	−0.189534	+	0.707349i
$879$	−4.79360	−	17.8899i	−0.161684	−	0.603413i
$880$		−	1.70755i		−	0.0575615i
$881$	−2.13690	−	3.70122i	−0.0719941	−	0.124697i	0.827781	−	0.561051i	$-0.189603\pi$
$881$	−2.13690	−	3.70122i	−0.0719941	−	0.124697i	−0.899775	+	0.436354i	$0.856270\pi$
$882$		0			0
$883$		−	32.6002i		−	1.09708i	−0.836123	−	0.548542i	$-0.815183\pi$
$883$		−	32.6002i		−	1.09708i	0.836123	−	0.548542i	$-0.184817\pi$
$884$	−10.1376	+	9.47771i	−0.340963	+	0.318770i
$885$	19.8049	+	11.4343i	0.665733	+	0.384361i
$886$	10.2721	+	10.2721i	0.345098	+	0.345098i
$887$	15.4078	+	8.89570i	0.517343	+	0.298688i	0.735847	−	0.677148i	$-0.236784\pi$
$887$	15.4078	+	8.89570i	0.517343	+	0.298688i	−0.218504	+	0.975836i	$0.570118\pi$
$888$	11.1081	−	19.2399i	0.372765	−	0.645648i
$889$		0			0
$890$	−0.286631	+	0.0768025i	−0.00960789	+	0.00257443i
$891$	−18.0810	+	18.0810i	−0.605735	+	0.605735i
$892$	−21.4370	+	5.74403i	−0.717764	+	0.192324i
$893$	18.3301	+	31.7487i	0.613394	+	1.06243i
$894$	1.71252	−	2.96618i	0.0572754	−	0.0992039i
$895$	8.37031	−	31.2384i	0.279789	−	1.04418i
$896$		0			0
$897$	4.16647	+	4.45654i	0.139114	+	0.148799i
$898$	2.45488	+	4.25198i	0.0819204	+	0.141890i
$899$	26.6426	−	26.6426i	0.888580	−	0.888580i
$900$	3.59710			0.119903
$901$	−17.2811			−0.575718
$902$	−14.1178	+	14.1178i	−0.470070	+	0.470070i
$903$		0			0
$904$	−2.90366	−	10.8366i	−0.0965744	−	0.360421i
$905$	−31.1097	−	8.33582i	−1.03412	−	0.277092i
$906$	17.5066	−	10.1074i	0.581617	−	0.335797i
$907$			32.4152i			1.07633i	0.842839	+	0.538165i	$0.180882\pi$
$907$			32.4152i			1.07633i	−0.842839	+	0.538165i	$0.819118\pi$
$908$	12.4168	−	3.32708i	0.412067	−	0.110413i
$909$	−13.5130			−0.448197
$910$		0			0
$911$	−15.2599			−0.505585			−0.252792	−	0.967521i	$-0.581349\pi$
$911$	−15.2599			−0.505585			−0.252792	+	0.967521i	$0.581349\pi$
$912$	2.13454	−	0.571948i	0.0706816	−	0.0189391i
$913$		−	22.1647i		−	0.733545i
$914$	16.1997	−	9.35288i	0.535838	−	0.309366i
$915$	−18.2101	−	4.87938i	−0.602008	−	0.161307i
$916$	1.39271	+	5.19765i	0.0460163	+	0.171735i
$917$		0			0
$918$	10.0492	−	10.0492i	0.331673	−	0.331673i
$919$	12.2111			0.402807			0.201404	−	0.979508i	$-0.435450\pi$
$919$	12.2111			0.402807			0.201404	+	0.979508i	$0.435450\pi$
$920$	4.68834			0.154570
$921$	−7.77559	+	7.77559i	−0.256214	+	0.256214i
$922$	8.98501	+	15.5625i	0.295906	+	0.512523i
$923$	−0.400449	+	11.9042i	−0.0131809	+	0.391832i
$924$		0			0
$925$	−4.26601	+	15.9210i	−0.140266	+	0.523478i
$926$	3.06574	−	5.31002i	0.100747	−	0.174498i
$927$	3.52384	+	6.10346i	0.115738	+	0.200464i
$928$	30.8738	−	8.27260i	1.01348	−	0.271561i
$929$	25.7604	−	25.7604i	0.845172	−	0.845172i	−0.144354	−	0.989526i	$-0.546110\pi$
$929$	25.7604	−	25.7604i	0.845172	−	0.845172i	0.989526	+	0.144354i	$0.0461105\pi$
$930$	11.3266	−	3.03496i	0.371414	−	0.0995201i
$931$		0			0
$932$	4.08135	−	7.06911i	0.133689	−	0.231556i
$933$	−0.599976	−	0.346396i	−0.0196423	−	0.0113405i
$934$	16.9835	+	16.9835i	0.555717	+	0.555717i
$935$	17.9654	+	10.3723i	0.587530	+	0.339211i
$936$	−4.44845	−	8.34055i	−0.145402	−	0.272619i
$937$		−	37.8200i		−	1.23553i	−0.786365	−	0.617763i	$-0.788039\pi$
$937$		−	37.8200i		−	1.23553i	0.786365	−	0.617763i	$-0.211961\pi$
$938$		0			0
$939$	0.319131	+	0.552750i	0.0104144	+	0.0180383i
$940$		−	10.7925i		−	0.352013i
$941$	6.42761	+	23.9882i	0.209534	+	0.781992i	0.988019	+	0.154329i	$0.0493217\pi$
$941$	6.42761	+	23.9882i	0.209534	+	0.781992i	−0.778485	+	0.627663i	$0.784012\pi$
$942$	0.896453	−	3.34561i	0.0292080	−	0.109006i
$943$	4.07600	+	4.07600i	0.132733	+	0.132733i
$944$	−1.93368	−	1.93368i	−0.0629358	−	0.0629358i
$945$		0			0
$946$	11.8970	−	6.86871i	0.386804	−	0.223321i
$947$	6.51827	+	24.3265i	0.211815	+	0.790505i	0.987263	+	0.159094i	$0.0508573\pi$
$947$	6.51827	+	24.3265i	0.211815	+	0.790505i	−0.775448	+	0.631411i	$0.782476\pi$
$948$	6.43032	−	11.1376i	0.208847	−	0.361734i
$949$	0.0605165	−	1.79899i	0.00196445	−	0.0583976i
$950$	13.5028	−	7.79583i	0.438088	−	0.252930i
$951$	−34.3773	−	9.21137i	−1.11476	−	0.298699i
$952$		0			0
$953$	15.6650	+	9.04419i	0.507439	+	0.292970i	0.731780	−	0.681541i	$-0.238690\pi$
$953$	15.6650	+	9.04419i	0.507439	+	0.292970i	−0.224341	+	0.974511i	$0.572023\pi$
$954$	1.19470	−	4.45867i	0.0386798	−	0.144355i
$955$	34.1410	+	9.14805i	1.10478	+	0.296024i
$956$	−13.8219	−	3.70357i	−0.447032	−	0.119782i
$957$	10.0080	−	37.3505i	0.323514	−	1.20737i
$958$	24.0194	+	13.8676i	0.776033	+	0.448043i
$959$		0			0
$960$	8.63446	+	2.31360i	0.278676	+	0.0746710i
$961$	−12.9494	+	7.47636i	−0.417724	+	0.241173i
$962$	16.5456	−	3.84217i	0.533452	−	0.123877i
$963$	2.21449	−	3.83562i	0.0713611	−	0.123601i
$964$	−4.66954	−	17.4270i	−0.150396	−	0.561285i
$965$	−4.26706	+	2.46359i	−0.137361	+	0.0793057i
$966$		0			0
$967$	−2.32489	−	2.32489i	−0.0747635	−	0.0747635i	0.668736	−	0.743500i	$-0.266836\pi$
$967$	−2.32489	−	2.32489i	−0.0747635	−	0.0747635i	−0.743500	+	0.668736i	$0.766836\pi$
$968$	−24.6198	−	24.6198i	−0.791311	−	0.791311i
$969$	−6.94846	+	25.9320i	−0.223217	+	0.833056i
$970$	−2.93736	−	10.9624i	−0.0943128	−	0.351980i
$971$			14.8168i			0.475494i	0.971327	+	0.237747i	$0.0764090\pi$
$971$			14.8168i			0.475494i	−0.971327	+	0.237747i	$0.923591\pi$
$972$	−6.07466	−	10.5216i	−0.194845	−	0.337481i
$973$		0			0
$974$		−	11.9408i		−	0.382609i
$975$	−10.4019	−	11.1260i	−0.333126	−	0.356319i
$976$	1.95235	+	1.12719i	0.0624931	+	0.0360804i
$977$	−13.3280	−	13.3280i	−0.426400	−	0.426400i	0.461000	−	0.887400i	$-0.347491\pi$
$977$	−13.3280	−	13.3280i	−0.426400	−	0.426400i	−0.887400	+	0.461000i	$0.847491\pi$
$978$	25.1992	+	14.5487i	0.805780	+	0.465217i
$979$	0.596712	−	1.03354i	0.0190710	−	0.0330320i
$980$		0			0
$981$	3.93025	−	1.05311i	0.125483	−	0.0336231i
$982$	17.7317	−	17.7317i	0.565840	−	0.565840i
$983$	−4.69722	+	1.25862i	−0.149818	+	0.0401436i	−0.332949	−	0.942945i	$-0.608044\pi$
$983$	−4.69722	+	1.25862i	−0.149818	+	0.0401436i	0.183131	+	0.983089i	$0.441377\pi$
$984$	9.69857	+	16.7984i	0.309179	+	0.535514i
$985$	−2.86012	+	4.95388i	−0.0911311	+	0.157844i
$986$	−3.61512	+	13.4918i	−0.115129	+	0.429666i
$987$		0			0
$988$	24.7943	+	15.4491i	0.788812	+	0.491501i
$989$	−1.98310	−	3.43482i	−0.0630588	−	0.109221i
$990$	−3.91814	+	3.91814i	−0.124527	+	0.124527i
$991$	−16.0923			−0.511190			−0.255595	−	0.966784i	$-0.582271\pi$
$991$	−16.0923			−0.511190			−0.255595	+	0.966784i	$0.582271\pi$
$992$	−38.9821			−1.23768
$993$	−15.0898	+	15.0898i	−0.478862	+	0.478862i
$994$		0			0
$995$	−0.379371	−	1.41583i	−0.0120269	−	0.0448849i
$996$	−8.15683	−	2.18562i	−0.258459	−	0.0692539i
$997$	−22.1768	+	12.8038i	−0.702346	+	0.405500i	−0.808221	−	0.588880i	$-0.799569\pi$
$997$	−22.1768	+	12.8038i	−0.702346	+	0.405500i	0.105875	+	0.994379i	$0.466236\pi$
$998$			15.5705i			0.492875i
$999$	30.5480	−	8.18532i	0.966497	−	0.258972i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.x.b.570.4		32
7.2	even	3		637.2.bb.b.362.5		32
7.3	odd	6		91.2.bc.a.76.5	yes	32
7.4	even	3		91.2.bc.a.76.6	yes	32
7.5	odd	6		637.2.bb.b.362.6		32
7.6	odd	2	inner	637.2.x.b.570.3		32
13.6	odd	12		637.2.bb.b.227.6		32
21.11	odd	6		819.2.fm.g.622.4		32
21.17	even	6		819.2.fm.g.622.3		32
91.6	even	12		637.2.bb.b.227.5		32
91.19	even	12	inner	637.2.x.b.19.3		32
91.32	odd	12		91.2.bc.a.6.5	✓	32
91.45	even	12		91.2.bc.a.6.6	yes	32
91.58	odd	12	inner	637.2.x.b.19.4		32
273.32	even	12		819.2.fm.g.370.3		32
273.227	odd	12		819.2.fm.g.370.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.bc.a.6.5	✓	32	91.32	odd	12
91.2.bc.a.6.6	yes	32	91.45	even	12
91.2.bc.a.76.5	yes	32	7.3	odd	6
91.2.bc.a.76.6	yes	32	7.4	even	3
637.2.x.b.19.3		32	91.19	even	12	inner
637.2.x.b.19.4		32	91.58	odd	12	inner
637.2.x.b.570.3		32	7.6	odd	2	inner
637.2.x.b.570.4		32	1.1	even	1	trivial
637.2.bb.b.227.5		32	91.6	even	12
637.2.bb.b.227.6		32	13.6	odd	12
637.2.bb.b.362.5		32	7.2	even	3
637.2.bb.b.362.6		32	7.5	odd	6
819.2.fm.g.370.3		32	273.32	even	12
819.2.fm.g.370.4		32	273.227	odd	12
819.2.fm.g.622.3		32	21.17	even	6
819.2.fm.g.622.4		32	21.11	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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.813723 + 0.218036i) q^{2} +1.43324i q^{3} +(-1.11745 + 0.645157i) q^{4} +(1.38386 + 0.370805i) q^{5} +(-0.312498 - 1.16626i) q^{6} +(1.96000 - 1.96000i) q^{8} +0.945832 q^{9} +O(q^{10})\)	\(q+(-0.813723 + 0.218036i) q^{2} +1.43324i q^{3} +(-1.11745 + 0.645157i) q^{4} +(1.38386 + 0.370805i) q^{5} +(-0.312498 - 1.16626i) q^{6} +(1.96000 - 1.96000i) q^{8} +0.945832 q^{9} -1.20693 q^{10} +(3.43228 - 3.43228i) q^{11} +(-0.924663 - 1.60156i) q^{12} +(1.04975 - 3.44935i) q^{13} +(-0.531452 + 1.98341i) q^{15} +(0.122771 - 0.212645i) q^{16} +(1.49151 + 2.58338i) q^{17} +(-0.769645 + 0.206226i) q^{18} +(4.44020 - 4.44020i) q^{19} +(-1.78562 + 0.478455i) q^{20} +(-2.04457 + 3.54129i) q^{22} +(1.02242 + 0.590296i) q^{23} +(2.80914 + 2.80914i) q^{24} +(-2.55254 - 1.47371i) q^{25} +(-0.102119 + 3.03570i) q^{26} +5.65531i q^{27} +(-2.77911 - 4.81356i) q^{29} -1.72982i q^{30} +(1.75449 + 6.54786i) q^{31} +(-1.48835 + 5.55461i) q^{32} +(4.91928 + 4.91928i) q^{33} +(-1.77695 - 1.77695i) q^{34} +(-1.05692 + 0.610210i) q^{36} +(-1.44737 - 5.40165i) q^{37} +(-2.64497 + 4.58121i) q^{38} +(4.94374 + 1.50454i) q^{39} +(3.43915 - 1.98559i) q^{40} +(4.71621 + 1.26371i) q^{41} +(-2.90941 - 1.67975i) q^{43} +(-1.62103 + 6.04975i) q^{44} +(1.30890 + 0.350719i) q^{45} +(-0.960674 - 0.257412i) q^{46} +(-1.51103 + 5.63925i) q^{47} +(0.304771 + 0.175960i) q^{48} +(2.39839 + 0.642646i) q^{50} +(-3.70259 + 2.13769i) q^{51} +(1.05234 + 4.53171i) q^{52} +(-2.89658 + 5.01702i) q^{53} +(-1.23306 - 4.60186i) q^{54} +(6.02252 - 3.47711i) q^{55} +(6.36385 + 6.36385i) q^{57} +(3.31096 + 3.31096i) q^{58} +(2.88250 - 10.7576i) q^{59} +(-0.685740 - 2.55922i) q^{60} +9.18124i q^{61} +(-2.85534 - 4.94560i) q^{62} -4.35335i q^{64} +(2.73174 - 4.38418i) q^{65} +(-5.07551 - 2.93035i) q^{66} +(-1.38921 - 1.38921i) q^{67} +(-3.33337 - 1.92452i) q^{68} +(-0.846033 + 1.46537i) q^{69} +(-3.19094 + 0.855010i) q^{71} +(1.85383 - 1.85383i) q^{72} +(0.482220 - 0.129211i) q^{73} +(2.35552 + 4.07987i) q^{74} +(2.11218 - 3.65840i) q^{75} +(-2.09705 + 7.82630i) q^{76} +(-4.35088 - 0.146360i) q^{78} +(3.47711 + 6.02254i) q^{79} +(0.248748 - 0.248748i) q^{80} -5.26791 q^{81} -4.11322 q^{82} +(3.22886 - 3.22886i) q^{83} +(1.10612 + 4.12811i) q^{85} +(2.73370 + 0.732493i) q^{86} +(6.89897 - 3.98312i) q^{87} -13.4545i q^{88} +(0.237487 - 0.0636346i) q^{89} -1.14155 q^{90} -1.52333 q^{92} +(-9.38464 + 2.51461i) q^{93} -4.91825i q^{94} +(7.79107 - 4.49818i) q^{95} +(-7.96108 - 2.13316i) q^{96} +(2.43374 + 9.08284i) q^{97} +(3.24636 - 3.24636i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{2} + 12 q^{4} - 16 q^{8} - 16 q^{9}+O(q^{10}) \) 32 * q + 4 * q^2 + 12 * q^4 - 16 * q^8 - 16 * q^9	\( 32 q + 4 q^{2} + 12 q^{4} - 16 q^{8} - 16 q^{9} + 20 q^{11} - 8 q^{15} + 12 q^{16} - 64 q^{18} + 4 q^{22} + 12 q^{23} + 4 q^{29} + 64 q^{32} + 4 q^{37} + 36 q^{39} - 48 q^{43} - 84 q^{44} - 108 q^{46} - 44 q^{50} + 12 q^{51} - 36 q^{53} - 92 q^{57} + 44 q^{58} + 28 q^{60} + 28 q^{65} + 64 q^{67} + 84 q^{71} + 4 q^{72} - 24 q^{74} + 148 q^{78} + 40 q^{79} - 56 q^{81} + 36 q^{85} + 108 q^{86} + 24 q^{92} - 24 q^{93} + 84 q^{95} - 60 q^{99}+O(q^{100}) \) 32 * q + 4 * q^2 + 12 * q^4 - 16 * q^8 - 16 * q^9 + 20 * q^11 - 8 * q^15 + 12 * q^16 - 64 * q^18 + 4 * q^22 + 12 * q^23 + 4 * q^29 + 64 * q^32 + 4 * q^37 + 36 * q^39 - 48 * q^43 - 84 * q^44 - 108 * q^46 - 44 * q^50 + 12 * q^51 - 36 * q^53 - 92 * q^57 + 44 * q^58 + 28 * q^60 + 28 * q^65 + 64 * q^67 + 84 * q^71 + 4 * q^72 - 24 * q^74 + 148 * q^78 + 40 * q^79 - 56 * q^81 + 36 * q^85 + 108 * q^86 + 24 * q^92 - 24 * q^93 + 84 * q^95 - 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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