LMFDB - Embedded newform 637.2.x.b.19.4

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			19.4
Character	$\chi$	$=$	637.19
Dual form			637.2.x.b.570.3

$q$-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 $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$

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	−0.0406221	−	0.999175i	$-0.512934\pi$
$2$	−0.813723	−	0.218036i	−0.575389	−	0.154175i	−0.534767	+	0.845000i	$0.679601\pi$
$3$			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	$-0.687136\pi$
$5$	−1.38386	+	0.370805i	−0.618883	+	0.165829i	−0.0642629	+	0.997933i	$0.520470\pi$
$6$	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	0.999370	+	0.0355032i	$0.0113034\pi$
$11$	3.43228	+	3.43228i	1.03487	+	1.03487i	0.0355032	+	0.999370i	$0.488697\pi$
$12$	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	$-0.951152\pi$
$17$	−1.49151	+	2.58338i	−0.361745	+	0.626561i	0.626503	+	0.779419i	$0.284486\pi$
$18$	−0.769645	−	0.206226i	−0.181407	−	0.0486079i
$19$	−4.44020	−	4.44020i	−1.01865	−	1.01865i	−0.999823	−	0.0188279i	$-0.994007\pi$
$19$	−4.44020	−	4.44020i	−1.01865	−	1.01865i	−0.0188279	−	0.999823i	$-0.505993\pi$
$20$	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	−0.389603	−	0.920983i	$-0.627388\pi$
$23$	1.02242	−	0.590296i	0.213190	−	0.123085i	0.602793	+	0.797898i	$0.294055\pi$
$24$	−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	0.483758	+	0.875202i	$0.339271\pi$
$29$	−2.77911	+	4.81356i	−0.516068	+	0.893856i	−0.999826	+	0.0186541i	$0.994062\pi$
$30$			1.72982i			0.315820i
$31$	−1.75449	+	6.54786i	−0.315116	+	1.17603i	0.608765	+	0.793351i	$0.291665\pi$
$31$	−1.75449	+	6.54786i	−0.315116	+	1.17603i	−0.923881	+	0.382680i	$0.875001\pi$
$32$	−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	0.738853	+	0.673867i	$0.235368\pi$
$37$	−1.44737	+	5.40165i	−0.237946	+	0.888027i	−0.976799	+	0.214160i	$0.931299\pi$
$38$	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	$-0.707845\pi$
$41$	−4.71621	+	1.26371i	−0.736549	+	0.197358i	−0.129005	+	0.991644i	$0.541178\pi$
$42$		0			0
$43$	−2.90941	+	1.67975i	−0.443681	+	0.256159i	−0.705158	−	0.709050i	$-0.749124\pi$
$43$	−2.90941	+	1.67975i	−0.443681	+	0.256159i	0.261477	+	0.965210i	$0.415790\pi$
$44$	−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	0.984193	+	0.177100i	$0.0566716\pi$
$47$	1.51103	+	5.63925i	0.220407	+	0.822570i	−0.763786	+	0.645470i	$0.776662\pi$
$48$	−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	0.595588	−	0.803290i	$-0.296919\pi$
$53$	−2.89658	−	5.01702i	−0.397875	−	0.689141i	−0.993464	+	0.114149i	$0.963586\pi$
$54$	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	−0.852950	−	0.521992i	$-0.825189\pi$
$59$	−2.88250	−	10.7576i	−0.375270	−	1.40053i	0.477681	−	0.878534i	$-0.341478\pi$
$60$	−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	−0.786856	−	0.617137i	$-0.788292\pi$
$67$	−1.38921	+	1.38921i	−0.169719	+	0.169719i	0.617137	+	0.786856i	$0.288292\pi$
$68$	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	0.0644501	−	0.997921i	$-0.479471\pi$
$71$	−3.19094	−	0.855010i	−0.378695	−	0.101471i	−0.443145	+	0.896450i	$0.646137\pi$
$72$	1.85383	+	1.85383i	0.218476	+	0.218476i
$73$	−0.482220	−	0.129211i	−0.0564396	−	0.0151230i	0.230489	−	0.973075i	$-0.425968\pi$
$73$	−0.482220	−	0.129211i	−0.0564396	−	0.0151230i	−0.286928	+	0.957952i	$0.592634\pi$
$74$	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	−0.601403	−	0.798946i	$-0.705391\pi$
$79$	3.47711	−	6.02254i	0.391206	−	0.677588i	0.992609	+	0.121357i	$0.0387247\pi$
$80$	−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	$-0.330631\pi$
$83$	−3.22886	−	3.22886i	−0.354413	−	0.354413i	−0.861749	+	0.507335i	$0.830631\pi$
$84$		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	$-0.420815\pi$
$89$	−0.237487	−	0.0636346i	−0.0251736	−	0.00674525i	−0.271384	+	0.962471i	$0.587481\pi$
$90$	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	0.725203	+	0.688535i	$0.241746\pi$
$97$	−2.43374	+	9.08284i	−0.247109	+	0.922223i	−0.972312	+	0.233688i	$0.924921\pi$
$98$		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	$-0.248334\pi$
$101$	14.2869			1.42160			0.710799	+	0.703396i	$0.248334\pi$
$102$	2.54679	+	2.54679i	0.252170	+	0.252170i
$103$	−3.72565	+	6.45301i	−0.367099	+	0.635834i	−0.989111	−	0.147174i	$-0.952982\pi$
$103$	−3.72565	+	6.45301i	−0.367099	+	0.635834i	0.622012	+	0.783008i	$0.286316\pi$
$104$	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	0.956722	−	0.291004i	$-0.0939894\pi$
$107$	2.34132	+	4.05528i	0.226344	+	0.392039i	−0.730378	+	0.683043i	$0.760656\pi$
$108$	3.64857	−	6.31950i	0.351083	−	0.608094i
$109$	4.15534	+	1.11342i	0.398009	+	0.106646i	0.452271	−	0.891880i	$-0.350614\pi$
$109$	4.15534	+	1.11342i	0.398009	+	0.106646i	−0.0542619	+	0.998527i	$0.517281\pi$
$110$	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	0.945375	−	0.325986i	$-0.105696\pi$
$113$	2.02372	+	3.50518i	0.190375	+	0.329740i	−0.754999	+	0.655725i	$0.772363\pi$
$114$	−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	0.892561	−	0.450926i	$-0.148906\pi$
$127$	10.6871	+	6.17021i	0.948328	+	0.547518i	0.0557671	+	0.998444i	$0.482240\pi$
$128$	−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	$-0.238585\pi$
$131$	5.81415	+	3.35680i	0.507985	+	0.293285i	−0.224020	+	0.974584i	$0.571918\pi$
$132$	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	−0.995002	−	0.0998520i	$-0.968163\pi$
$137$	−21.1477	+	5.66652i	−1.80677	+	0.484124i	−0.811771	+	0.583976i	$0.801496\pi$
$138$	−0.368932	−	1.37687i	−0.0314056	−	0.117207i
$139$	−3.49682	+	2.01889i	−0.296597	+	0.171240i	−0.640913	−	0.767614i	$-0.721444\pi$
$139$	−3.49682	+	2.01889i	−0.296597	+	0.171240i	0.344316	+	0.938854i	$0.388111\pi$
$140$		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	−0.620154	−	0.784480i	$-0.712930\pi$
$149$	2.00586	−	2.00586i	0.164327	−	0.164327i	0.784480	+	0.620154i	$0.212930\pi$
$150$	0.921064	+	3.43746i	0.0752045	+	0.280667i
$151$	4.33327	−	16.1720i	0.352636	−	1.31606i	−0.530796	−	0.847499i	$-0.678107\pi$
$151$	4.33327	−	16.1720i	0.352636	−	1.31606i	0.883433	−	0.468558i	$-0.155226\pi$
$152$		−	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	$-0.703184\pi$
$157$	−2.48434	+	1.43433i	−0.198272	+	0.114472i	0.397577	+	0.917569i	$0.369851\pi$
$158$	−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	−0.901076	−	0.433660i	$-0.857222\pi$
$163$	−17.0408	−	17.0408i	−1.33474	−	1.33474i	−0.433660	−	0.901076i	$-0.642778\pi$
$164$	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	0.991860	+	0.127330i	$0.0406408\pi$
$167$	2.53997	+	9.47931i	0.196549	+	0.733531i	−0.795311	+	0.606201i	$0.792693\pi$
$168$		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	$-0.436196\pi$
$173$	5.23766			0.398212			0.199106	+	0.979978i	$0.436196\pi$
$174$	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	$0.319571\pi$
$179$			22.5733i			1.68721i	−0.536965	+	0.843605i	$0.680429\pi$
$180$	1.68890	+	0.452538i	0.125883	+	0.0337302i
$181$	22.4803			1.67095			0.835474	−	0.549530i	$-0.185193\pi$
$181$	22.4803			1.67095			0.835474	+	0.549530i	$0.185193\pi$
$182$		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	0.614146	−	0.789193i	$-0.289501\pi$
$193$	−2.43183	−	2.43183i	−0.175047	−	0.175047i	−0.789193	+	0.614146i	$0.789501\pi$
$194$	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	0.919293	−	0.393575i	$-0.128762\pi$
$197$	−1.03338	−	3.85664i	−0.0736255	−	0.274774i	−0.992918	+	0.118801i	$0.962095\pi$
$198$	−1.93382	−	3.34947i	−0.137430	−	0.238036i
$199$	0.511550	−	0.886031i	0.0362628	−	0.0628091i	−0.847324	−	0.531076i	$-0.821788\pi$
$199$	0.511550	−	0.886031i	0.0362628	−	0.0628091i	0.883587	+	0.468267i	$0.155121\pi$
$200$	−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	−0.757968	−	0.652292i	$-0.773808\pi$
$211$	2.70061	−	4.67759i	0.185918	−	0.322019i	0.943885	+	0.330273i	$0.107141\pi$
$212$			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	$-0.778679\pi$
$223$	−16.6138	+	4.45165i	−1.11254	+	0.298105i	−0.344680	+	0.938720i	$0.612013\pi$
$224$		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	$-0.476076\pi$
$227$	9.62310	−	2.57850i	0.638707	−	0.171141i	0.563618	+	0.826036i	$0.309409\pi$
$228$	−11.2169	+	3.00557i	−0.742860	+	0.199049i
$229$	−1.07935	−	4.02820i	−0.0713257	−	0.266191i	0.921049	−	0.389446i	$-0.127333\pi$
$229$	−1.07935	−	4.02820i	−0.0713257	−	0.266191i	−0.992375	+	0.123255i	$0.960667\pi$
$230$	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	0.309690	−	0.950838i	$-0.399775\pi$
$233$	−5.47860	−	3.16307i	−0.358915	−	0.207220i	−0.668605	+	0.743618i	$0.733108\pi$
$234$	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	−0.406438	−	0.913679i	$-0.633229\pi$
$239$	7.84175	−	7.84175i	0.507241	−	0.507241i	0.913679	+	0.406438i	$0.133229\pi$
$240$	0.356515	−	0.356515i	0.0230129	−	0.0230129i
$241$	3.61892	+	13.5060i	0.233115	+	0.869996i	0.978990	+	0.203910i	$0.0653650\pi$
$241$	3.61892	+	13.5060i	0.233115	+	0.869996i	−0.745875	+	0.666086i	$0.767968\pi$
$242$	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	−0.896599	−	0.442843i	$-0.853970\pi$
$251$	−13.1784	−	22.8256i	−0.831813	−	1.44074i	0.0647865	−	0.997899i	$-0.479363\pi$
$252$		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	$-0.0575133\pi$
$257$	5.39025	+	9.33618i	0.336234	+	0.582375i	−0.647487	+	0.762077i	$0.724180\pi$
$258$	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	$-0.0399122\pi$
$269$	22.6324	+	13.0668i	1.37992	+	0.796697i	0.387770	+	0.921756i	$0.373246\pi$
$270$			6.82557i			0.415391i
$271$	−6.35804	−	1.70363i	−0.386223	−	0.103488i	0.0604821	−	0.998169i	$-0.480736\pi$
$271$	−6.35804	−	1.70363i	−0.386223	−	0.103488i	−0.446706	+	0.894681i	$0.647403\pi$
$272$	−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	0.999770	+	0.0214270i	$0.00682096\pi$
$277$	25.2681	+	14.5885i	1.51821	+	0.876540i	0.518442	+	0.855113i	$0.326512\pi$
$278$	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	0.920025	−	0.391859i	$-0.128168\pi$
$281$	8.85369	+	8.85369i	0.528167	+	0.528167i	−0.391859	+	0.920025i	$0.628168\pi$
$282$	7.04902			0.419763
$283$	−31.9411			−1.89870			−0.949351	−	0.314217i	$-0.898258\pi$
$283$	−31.9411			−1.89870			−0.949351	+	0.314217i	$0.898258\pi$
$284$	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	$-0.293460\pi$
$293$	12.4822	+	3.34459i	0.729218	+	0.195393i	0.124937	+	0.992165i	$0.460127\pi$
$294$		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	$-0.820261\pi$
$307$	−5.42520	+	5.42520i	−0.309632	+	0.309632i	0.535135	+	0.844767i	$0.320261\pi$
$308$		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	$-0.162304\pi$
$311$	0.241688	+	0.418616i	0.0137049	+	0.0237375i	−0.859092	+	0.511822i	$0.828971\pi$
$312$	12.6386	+	6.74083i	0.715520	+	0.381624i
$313$	−0.385666	−	0.222664i	−0.0217991	−	0.0125857i	0.489061	−	0.872250i	$-0.337340\pi$
$313$	−0.385666	−	0.222664i	−0.0217991	−	0.0125857i	−0.510860	+	0.859664i	$0.670673\pi$
$314$	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	−0.872797	−	0.488084i	$-0.837696\pi$
$317$	−6.42697	−	23.9858i	−0.360975	−	1.34718i	0.511822	−	0.859091i	$-0.328971\pi$
$318$	−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	−0.355846	−	0.934545i	$-0.615807\pi$
$331$	10.5285	−	10.5285i	0.578699	−	0.578699i	0.934545	+	0.355846i	$0.115807\pi$
$332$	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	$-0.936849\pi$
$337$		−	7.23643i		−	0.394194i	0.980384	−	0.197097i	$-0.0631513\pi$
$338$	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	−0.646587	−	0.762840i	$-0.723804\pi$
$347$	6.28405	−	10.8843i	0.337345	−	0.584299i	0.983933	+	0.178541i	$0.0571376\pi$
$348$	5.13948	+	8.90185i	0.275505	+	0.477189i
$349$	−4.81774	−	17.9800i	−0.257888	−	0.962450i	−0.966461	−	0.256813i	$-0.917328\pi$
$349$	−4.81774	−	17.9800i	−0.257888	−	0.962450i	0.708574	−	0.705637i	$-0.249339\pi$
$350$		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	$-0.196732\pi$
$353$	4.42576	+	4.42576i	0.235559	+	0.235559i	−0.579449	+	0.815008i	$0.696732\pi$
$354$	−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	−0.198265	−	0.980148i	$-0.563531\pi$
$359$	2.27568	−	0.609768i	0.120106	−	0.0321823i	0.318371	+	0.947966i	$0.396864\pi$
$360$	−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	−0.967084	−	0.254457i	$-0.918103\pi$
$379$	−4.99923	−	18.6574i	−0.256793	−	0.958365i	0.710291	−	0.703908i	$-0.248563\pi$
$380$	−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	$-0.0446911\pi$
$383$	16.6391	+	16.6391i	0.850219	+	0.850219i	−0.139941	+	0.990160i	$0.544691\pi$
$384$	−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	0.261100	−	0.965312i	$-0.415915\pi$
$389$	24.2127	−	13.9792i	1.22763	−	0.708775i	0.966535	+	0.256536i	$0.0825813\pi$
$390$	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	$-0.652668\pi$
$397$	8.48258	−	8.48258i	0.425729	−	0.425729i	0.887170	+	0.461442i	$0.152668\pi$
$398$	−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	0.711686	+	0.702497i	$0.247932\pi$
$401$	−5.12441	+	19.1246i	−0.255901	+	0.955035i	−0.967587	+	0.252537i	$0.918735\pi$
$402$	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	$-0.438269\pi$
$409$	17.1952	−	4.60743i	0.850247	−	0.227823i	0.657527	+	0.753431i	$0.271602\pi$
$410$	−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	$-0.260565\pi$
$419$	8.03474	+	4.63886i	0.392523	+	0.226623i	−0.290730	+	0.956805i	$0.593898\pi$
$420$		0			0
$421$	−13.2205	+	13.2205i	−0.644329	+	0.644329i	−0.951617	−	0.307288i	$-0.900579\pi$
$421$	−13.2205	+	13.2205i	−0.644329	+	0.644329i	0.307288	+	0.951617i	$0.400579\pi$
$422$	−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	−0.598901	−	0.800823i	$-0.704396\pi$
$431$	4.19200	−	4.19200i	0.201921	−	0.201921i	0.800823	+	0.598901i	$0.204396\pi$
$432$	−1.20258	+	0.694307i	−0.0578589	+	0.0334049i
$433$	6.32385	+	10.9532i	0.303905	+	0.526379i	0.977017	−	0.213162i	$-0.0683762\pi$
$433$	6.32385	+	10.9532i	0.303905	+	0.526379i	−0.673112	+	0.739541i	$0.735043\pi$
$434$		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	−0.990442	−	0.137928i	$-0.955956\pi$
$439$	−12.8788	−	22.3067i	−0.614670	−	1.06464i	0.375772	−	0.926712i	$-0.377378\pi$
$440$	−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	−0.994850	−	0.101358i	$-0.967681\pi$
$443$	−8.62206	+	14.9338i	−0.409647	+	0.709529i	0.585203	+	0.810886i	$0.301015\pi$
$444$	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	−0.992342	−	0.123523i	$-0.960581\pi$
$449$	−1.50842	+	5.62952i	−0.0711870	+	0.265673i	0.921155	+	0.389197i	$0.127247\pi$
$450$	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	−0.280469	−	0.959863i	$-0.590490\pi$
$457$	−21.4480	−	5.74697i	−1.00329	−	0.268832i	−0.722825	+	0.691031i	$0.757157\pi$
$458$			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	−0.709755	−	0.704449i	$-0.751194\pi$
$461$	5.52093	−	20.6044i	0.257135	−	0.959642i	0.966890	−	0.255193i	$-0.0821390\pi$
$462$		0			0
$463$	−5.14657	−	5.14657i	−0.239181	−	0.239181i	0.577330	−	0.816511i	$-0.304095\pi$
$463$	−5.14657	−	5.14657i	−0.239181	−	0.239181i	−0.816511	+	0.577330i	$0.804095\pi$
$464$	−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	−0.321042	−	0.947065i	$-0.604033\pi$
$467$	14.2554	−	24.6911i	0.659661	−	1.14257i	0.980703	−	0.195502i	$-0.0626336\pi$
$468$	−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	0.0658656	−	0.997829i	$-0.479019\pi$
$479$	23.2801	−	23.2801i	1.06369	−	1.06369i	0.997829	−	0.0658656i	$-0.0209808\pi$
$480$	−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	−0.997879	−	0.0650979i	$-0.979264\pi$
$487$	−3.66858	−	13.6913i	−0.166239	−	0.620414i	0.831640	−	0.555316i	$-0.187403\pi$
$488$	−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	−0.211269	−	0.977428i	$-0.567759\pi$
$491$	−25.7788	−	14.8834i	−1.16338	−	0.671678i	−0.952112	+	0.305750i	$0.901093\pi$
$492$	−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	0.986465	+	0.163974i	$0.0524314\pi$
$499$	4.78371	+	17.8531i	0.214148	+	0.799213i	−0.772316	+	0.635238i	$0.780902\pi$
$500$	−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	$-0.708242\pi$
$503$	−5.05931	+	2.92099i	−0.225583	+	0.130241i	0.382949	+	0.923769i	$0.374908\pi$
$504$		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	−0.565871	−	0.824494i	$-0.691460\pi$
$509$	7.59031	−	28.3274i	0.336435	−	1.25559i	0.902306	−	0.431097i	$-0.141873\pi$
$510$	−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	0.558453	−	0.829536i	$-0.311395\pi$
$521$	35.5182	−	20.5064i	1.55608	−	0.898402i	0.997626	−	0.0688659i	$-0.0219381\pi$
$522$	3.13161	−	3.13161i	0.137067	−	0.137067i
$523$	38.4309	−	22.1881i	1.68047	−	0.970217i	0.719114	−	0.694892i	$-0.244548\pi$
$523$	38.4309	−	22.1881i	1.68047	−	0.970217i	0.961351	−	0.275325i	$-0.0887854\pi$
$524$	−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	−0.113570	−	0.993530i	$-0.536228\pi$
$541$	6.62524	−	1.77523i	0.284841	−	0.0763230i	0.398411	+	0.917207i	$0.369562\pi$
$542$	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	0.979648	+	0.200725i	$0.0643298\pi$
$557$	27.8578	+	27.8578i	1.18037	+	1.18037i	0.200725	+	0.979648i	$0.435670\pi$
$558$	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	$-0.819164\pi$
$563$	1.05586	−	1.82880i	0.0444991	−	0.0770748i	0.887417	+	0.460967i	$0.152497\pi$
$564$	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	−0.984117	−	0.177518i	$-0.943193\pi$
$569$	−31.5451	+	18.2126i	−1.32244	+	0.763512i	−0.338323	+	0.941030i	$0.609860\pi$
$570$	7.68073	−	7.68073i	0.321710	−	0.321710i
$571$	−13.1672	+	7.60209i	−0.551030	+	0.318138i	−0.749537	−	0.661962i	$-0.769724\pi$
$571$	−13.1672	+	7.60209i	−0.551030	+	0.318138i	0.198507	+	0.980099i	$0.436391\pi$
$572$	−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	$-0.992407\pi$
$577$	−2.93081	+	10.9379i	−0.122011	+	0.455352i	0.877704	+	0.479202i	$0.159074\pi$
$578$	−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	$-0.560723\pi$
$587$	3.32195	−	0.890113i	0.137111	−	0.0367389i	0.326722	+	0.945120i	$0.394056\pi$
$588$		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	0.532589	+	0.846374i	$0.321219\pi$
$593$	12.0428	+	44.9445i	0.494540	+	1.84565i	−0.0380481	+	0.999276i	$0.512114\pi$
$594$	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	0.777661	−	0.628684i	$-0.216406\pi$
$599$	−3.80885	−	6.59712i	−0.155625	−	0.269551i	−0.933287	+	0.359133i	$0.883073\pi$
$600$	3.03059	−	11.3103i	0.123723	−	0.461742i
$601$	32.3774	+	18.6931i	1.32070	+	0.762508i	0.983841	−	0.179045i	$-0.0573009\pi$
$601$	32.3774	+	18.6931i	1.32070	+	0.762508i	0.336863	+	0.941554i	$0.390634\pi$
$602$		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	−0.767079	−	0.641553i	$-0.778290\pi$
$613$	−3.10787	+	3.10787i	−0.125526	+	0.125526i	0.641553	+	0.767079i	$0.278290\pi$
$614$	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	0.706318	−	0.707894i	$-0.250355\pi$
$617$	23.9468	+	6.41652i	0.964061	+	0.258319i	0.257743	+	0.966214i	$0.417021\pi$
$618$	6.36162	+	6.36162i	0.255902	+	0.255902i
$619$	−23.5480	−	6.30966i	−0.946473	−	0.253607i	−0.247608	−	0.968860i	$-0.579645\pi$
$619$	−23.5480	−	6.30966i	−0.946473	−	0.253607i	−0.698865	+	0.715254i	$0.746311\pi$
$620$	−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	−0.950567	−	0.310521i	$-0.899497\pi$
$631$	0.701056	−	2.61638i	0.0279086	−	0.104156i	0.978475	+	0.206364i	$0.0661633\pi$
$632$	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	0.445504	−	0.895280i	$-0.353025\pi$
$641$	−2.71103	−	1.56522i	−0.107079	−	0.0618223i	−0.552583	+	0.833458i	$0.686358\pi$
$642$	5.46117	−	1.46331i	0.215535	−	0.0577524i
$643$	−0.747638	+	2.79022i	−0.0294840	+	0.110036i	−0.979100	−	0.203381i	$-0.934807\pi$
$643$	−0.747638	+	2.79022i	−0.0294840	+	0.110036i	0.949616	+	0.313417i	$0.101474\pi$
$644$		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	$-0.613355\pi$
$647$	−17.7360			−0.697275			−0.348637	+	0.937258i	$0.613355\pi$
$648$	−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	0.997237	−	0.0742811i	$-0.0236662\pi$
$653$	11.0978	+	19.2219i	0.434289	+	0.752211i	−0.562948	+	0.826492i	$0.690333\pi$
$654$	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	0.997242	+	0.0742153i	$0.0236452\pi$
$659$	14.4500	+	25.0282i	0.562893	+	0.974960i	−0.434349	+	0.900745i	$0.643021\pi$
$660$	−11.1376	+	6.43031i	−0.433531	+	0.250299i
$661$	2.74283	−	2.74283i	0.106684	−	0.106684i	−0.651750	−	0.758434i	$-0.725965\pi$
$661$	2.74283	−	2.74283i	0.106684	−	0.106684i	0.758434	+	0.651750i	$0.225965\pi$
$662$	−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	0.757372	−	0.652984i	$-0.226483\pi$
$673$	14.8015	+	8.54566i	0.570557	+	0.329411i	−0.186815	+	0.982395i	$0.559816\pi$
$674$	−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	$-0.133440\pi$
$677$	26.4773	+	15.2867i	1.01760	+	0.587514i	0.104195	+	0.994557i	$0.466773\pi$
$678$	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	−0.374022	−	0.927420i	$-0.622022\pi$
$683$	−6.12129	+	1.64019i	−0.234224	+	0.0627603i	0.139797	+	0.990180i	$0.455355\pi$
$684$	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	$-0.945586\pi$
$691$	−1.23455	+	4.60739i	−0.0469643	+	0.175273i	0.938460	+	0.345388i	$0.112253\pi$
$692$	−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	$-0.812169\pi$
$701$		−	29.4647i		−	1.11287i	0.830892	−	0.556433i	$-0.187831\pi$
$702$	−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	0.448595	−	0.893735i	$-0.351925\pi$
$709$	−11.8528	−	11.8528i	−0.445140	−	0.445140i	−0.893735	+	0.448595i	$0.851925\pi$
$710$	−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	$-0.391500\pi$
$719$	17.9279			0.668598			0.334299	+	0.942467i	$0.391500\pi$
$720$	−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	$-0.707046\pi$
$727$	−32.6548			−1.21110			−0.605549	+	0.795808i	$0.707046\pi$
$728$		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	$-0.810724\pi$
$733$	−34.2658	+	9.18149i	−1.26564	+	0.339126i	−0.437279	+	0.899326i	$0.644058\pi$
$734$	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	0.495193	−	0.868783i	$-0.335097\pi$
$739$	−10.1559	−	10.1559i	−0.373590	−	0.373590i	−0.868783	+	0.495193i	$0.835097\pi$
$740$	−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	0.971755	+	0.235993i	$0.0758344\pi$
$743$	6.76509	+	25.2477i	0.248187	+	0.926247i	−0.723568	+	0.690254i	$0.757499\pi$
$744$	−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	−0.675849	−	0.737040i	$-0.736223\pi$
$751$	−10.2898	+	5.94079i	−0.375479	+	0.216783i	0.300371	+	0.953823i	$0.402890\pi$
$752$	−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	−0.171857	−	0.985122i	$-0.554977\pi$
$757$	21.1088	−	36.5615i	0.767212	−	1.32885i	0.939069	−	0.343729i	$-0.111690\pi$
$758$			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	$-0.924715\pi$
$761$	−20.3544	+	20.3544i	−0.737845	+	0.737845i	0.234316	+	0.972161i	$0.424715\pi$
$762$	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	$-0.365211\pi$
$769$	33.9039	−	9.08451i	1.22260	−	0.327596i	0.811696	+	0.584081i	$0.198545\pi$
$770$		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	$-0.767381\pi$
$773$	−29.3542	+	7.86544i	−1.05580	+	0.282900i	−0.311152	+	0.950360i	$0.600715\pi$
$774$	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	$-0.0253790\pi$
$787$	2.62934	+	9.81284i	0.0937260	+	0.349790i	−0.903097	+	0.429436i	$0.858712\pi$
$788$	−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	0.982719	+	0.185101i	$0.0592613\pi$
$797$	18.3972	+	31.8649i	0.651662	+	1.12871i	−0.331057	+	0.943611i	$0.607405\pi$
$798$		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	$-0.280542\pi$
$811$	−3.85841	−	3.85841i	−0.135487	−	0.135487i	−0.771598	+	0.636111i	$0.780542\pi$
$812$		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	0.293505	−	0.955958i	$-0.405178\pi$
$821$	1.99738	+	0.535196i	0.0697089	+	0.0186785i	−0.223796	+	0.974636i	$0.571845\pi$
$822$			26.4345i			0.922009i
$823$	23.4776	+	13.5548i	0.818379	+	0.472491i	0.849857	−	0.527013i	$-0.176688\pi$
$823$	23.4776	+	13.5548i	0.818379	+	0.472491i	−0.0314782	+	0.999504i	$0.510021\pi$
$824$	−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	0.299535	−	0.954085i	$-0.403168\pi$
$827$	−18.8233	−	18.8233i	−0.654550	−	0.654550i	−0.954085	+	0.299535i	$0.903168\pi$
$828$	−1.44082			−0.0500719
$829$	5.01498			0.174177			0.0870887	−	0.996201i	$-0.472244\pi$
$829$	5.01498			0.174177			0.0870887	+	0.996201i	$0.472244\pi$
$830$	−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	$-0.427543\pi$
$839$	−1.91166	−	0.512227i	−0.0659978	−	0.0176840i	−0.291667	+	0.956520i	$0.594210\pi$
$840$		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	$-0.746189\pi$
$853$	0.494551	−	0.494551i	0.0169331	−	0.0169331i	0.715523	+	0.698590i	$0.246189\pi$
$854$		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	$-0.0820807\pi$
$857$	7.68803	+	13.3161i	0.262618	+	0.454868i	−0.704319	+	0.709884i	$0.748747\pi$
$858$	−15.4358	−	14.4311i	−0.526970	−	0.492670i
$859$	−28.7090	−	16.5752i	−0.979540	−	0.565538i	−0.0774086	−	0.996999i	$-0.524665\pi$
$859$	−28.7090	−	16.5752i	−0.979540	−	0.565538i	−0.902131	+	0.431462i	$0.857998\pi$
$860$	−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	0.979142	+	0.203176i	$0.0651264\pi$
$863$	6.83800	+	25.5198i	0.232768	+	0.868703i	−0.746374	+	0.665527i	$0.768207\pi$
$864$	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	−0.513456	−	0.858116i	$-0.671635\pi$
$877$	10.2068	−	10.2068i	0.344659	−	0.344659i	0.858116	+	0.513456i	$0.171635\pi$
$878$	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	$-0.810397\pi$
$881$	2.13690	−	3.70122i	0.0719941	−	0.124697i	0.899775	+	0.436354i	$0.143730\pi$
$882$		0			0
$883$			32.6002i			1.09708i	0.836123	+	0.548542i	$0.184817\pi$
$883$			32.6002i			1.09708i	−0.836123	+	0.548542i	$0.815183\pi$
$884$	−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	$-0.763216\pi$
$887$	−15.4078	+	8.89570i	−0.517343	+	0.298688i	0.218504	+	0.975836i	$0.429882\pi$
$888$	−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	$-0.819118\pi$
$907$		−	32.4152i		−	1.07633i	0.842839	−	0.538165i	$-0.180882\pi$
$908$	−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	$-0.453890\pi$
$929$	−25.7604	−	25.7604i	−0.845172	−	0.845172i	−0.989526	+	0.144354i	$0.953890\pi$
$930$	−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	0.778485	+	0.627663i	$0.215988\pi$
$941$	−6.42761	+	23.9882i	−0.209534	+	0.781992i	−0.988019	+	0.154329i	$0.950678\pi$
$942$	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	−0.775448	−	0.631411i	$-0.782476\pi$
$947$	6.51827	−	24.3265i	0.211815	−	0.790505i	0.987263	−	0.159094i	$-0.0508573\pi$
$948$	−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	−0.224341	−	0.974511i	$-0.572023\pi$
$953$	15.6650	−	9.04419i	0.507439	−	0.292970i	0.731780	+	0.681541i	$0.238690\pi$
$954$	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	−0.743500	−	0.668736i	$-0.766836\pi$
$967$	−2.32489	+	2.32489i	−0.0747635	+	0.0747635i	0.668736	+	0.743500i	$0.266836\pi$
$968$	−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	−0.887400	−	0.461000i	$-0.847491\pi$
$977$	−13.3280	+	13.3280i	−0.426400	+	0.426400i	0.461000	+	0.887400i	$0.347491\pi$
$978$	−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	$-0.391956\pi$
$983$	4.69722	+	1.25862i	0.149818	+	0.0401436i	−0.183131	+	0.983089i	$0.558623\pi$
$984$	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	$-0.200431\pi$
$997$	22.1768	+	12.8038i	0.702346	+	0.405500i	−0.105875	+	0.994379i	$0.533764\pi$
$998$		−	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.19.4		32
7.2	even	3		91.2.bc.a.6.5	✓	32
7.3	odd	6		637.2.bb.b.227.5		32
7.4	even	3		637.2.bb.b.227.6		32
7.5	odd	6		91.2.bc.a.6.6	yes	32
7.6	odd	2	inner	637.2.x.b.19.3		32
13.11	odd	12		637.2.bb.b.362.5		32
21.2	odd	6		819.2.fm.g.370.3		32
21.5	even	6		819.2.fm.g.370.4		32
91.11	odd	12	inner	637.2.x.b.570.4		32
91.24	even	12	inner	637.2.x.b.570.3		32
91.37	odd	12		91.2.bc.a.76.6	yes	32
91.76	even	12		637.2.bb.b.362.6		32
91.89	even	12		91.2.bc.a.76.5	yes	32
273.89	odd	12		819.2.fm.g.622.3		32
273.128	even	12		819.2.fm.g.622.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.bc.a.6.5	✓	32	7.2	even	3
91.2.bc.a.6.6	yes	32	7.5	odd	6
91.2.bc.a.76.5	yes	32	91.89	even	12
91.2.bc.a.76.6	yes	32	91.37	odd	12
637.2.x.b.19.3		32	7.6	odd	2	inner
637.2.x.b.19.4		32	1.1	even	1	trivial
637.2.x.b.570.3		32	91.24	even	12	inner
637.2.x.b.570.4		32	91.11	odd	12	inner
637.2.bb.b.227.5		32	7.3	odd	6
637.2.bb.b.227.6		32	7.4	even	3
637.2.bb.b.362.5		32	13.11	odd	12
637.2.bb.b.362.6		32	91.76	even	12
819.2.fm.g.370.3		32	21.2	odd	6
819.2.fm.g.370.4		32	21.5	even	6
819.2.fm.g.622.3		32	273.89	odd	12
819.2.fm.g.622.4		32	273.128	even	12

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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