LMFDB - Embedded newform 845.2.k.b.577.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(268,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("845.268");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.k (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.619810816.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{5} + 14x^{4} - 8x^{3} + 2x^{2} + 2x + 1 $ x^8 - 2x^5 + 14x^4 - 8x^3 + 2x^2 + 2*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			577.2
Root			$-1.49094 + 1.49094i$ of defining polynomial
Character	$\chi$	$=$	845.577
Dual form			845.2.k.b.268.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.134632 q^{2} +(-2.15558 + 2.15558i) q^{3} -1.98187 q^{4} +(-1.82630 - 1.29021i) q^{5} +(-0.290209 + 0.290209i) q^{6} -1.90970i q^{7} -0.536087 q^{8} -6.29303i q^{9} +O(q^{10})$	\(q+0.134632 q^{2} +(-2.15558 + 2.15558i) q^{3} -1.98187 q^{4} +(-1.82630 - 1.29021i) q^{5} +(-0.290209 + 0.290209i) q^{6} -1.90970i q^{7} -0.536087 q^{8} -6.29303i q^{9} +(-0.245878 - 0.173703i) q^{10} +(0.290209 + 0.290209i) q^{11} +(4.27208 - 4.27208i) q^{12} -0.257106i q^{14} +(6.71787 - 1.15558i) q^{15} +3.89157 q^{16} +(-2.53609 + 2.53609i) q^{17} -0.847242i q^{18} +(-3.15558 - 3.15558i) q^{19} +(3.61949 + 2.55703i) q^{20} +(4.11651 + 4.11651i) q^{21} +(0.0390714 + 0.0390714i) q^{22} +(-2.27208 - 2.27208i) q^{23} +(1.15558 - 1.15558i) q^{24} +(1.67072 + 4.71261i) q^{25} +(7.09838 + 7.09838i) q^{27} +3.78478i q^{28} -2.40146i q^{29} +(0.904440 - 0.155578i) q^{30} +(-2.02095 + 2.02095i) q^{31} +1.59610 q^{32} -1.25114 q^{33} +(-0.341438 + 0.341438i) q^{34} +(-2.46391 + 3.48768i) q^{35} +12.4720i q^{36} +5.32928i q^{37} +(-0.424841 - 0.424841i) q^{38} +(0.979054 + 0.691665i) q^{40} +(1.51796 - 1.51796i) q^{41} +(0.554213 + 0.554213i) q^{42} +(0.888754 + 0.888754i) q^{43} +(-0.575159 - 0.575159i) q^{44} +(-8.11933 + 11.4929i) q^{45} +(-0.305895 - 0.305895i) q^{46} +6.94562i q^{47} +(-8.38859 + 8.38859i) q^{48} +3.35305 q^{49} +(0.224932 + 0.634468i) q^{50} -10.9335i q^{51} +(-1.09030 + 1.09030i) q^{53} +(0.955668 + 0.955668i) q^{54} +(-0.155578 - 0.904440i) q^{55} +1.02377i q^{56} +13.6042 q^{57} -0.323312i q^{58} +(-8.31642 + 8.31642i) q^{59} +(-13.3140 + 2.29021i) q^{60} +7.17300 q^{61} +(-0.272084 + 0.272084i) q^{62} -12.0178 q^{63} -7.56826 q^{64} -0.168443 q^{66} +0.939983 q^{67} +(5.02621 - 5.02621i) q^{68} +9.79531 q^{69} +(-0.331721 + 0.469553i) q^{70} +(7.37643 - 7.37643i) q^{71} +3.37361i q^{72} +6.63447 q^{73} +0.717491i q^{74} +(-13.7598 - 6.55703i) q^{75} +(6.25396 + 6.25396i) q^{76} +(0.554213 - 0.554213i) q^{77} +4.39982i q^{79} +(-7.10717 - 5.02095i) q^{80} -11.7231 q^{81} +(0.204366 - 0.204366i) q^{82} +13.4842i q^{83} +(-8.15840 - 8.15840i) q^{84} +(7.90373 - 1.35956i) q^{85} +(0.119655 + 0.119655i) q^{86} +(5.17652 + 5.17652i) q^{87} +(-0.155578 - 0.155578i) q^{88} +(10.0238 - 10.0238i) q^{89} +(-1.09312 + 1.54732i) q^{90} +(4.50298 + 4.50298i) q^{92} -8.71261i q^{93} +0.935102i q^{94} +(1.69166 + 9.83438i) q^{95} +(-3.44053 + 3.44053i) q^{96} +4.39982 q^{97} +0.451427 q^{98} +(1.82630 - 1.82630i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - 6 q^{3} + 8 q^{4} - 2 q^{5} + 6 q^{6}+O(q^{10}) $ 8 * q + 4 * q^2 - 6 * q^3 + 8 * q^4 - 2 * q^5 + 6 * q^6	$ 8 q + 4 q^{2} - 6 q^{3} + 8 q^{4} - 2 q^{5} + 6 q^{6} - 6 q^{10} - 6 q^{11} + 2 q^{12} + 2 q^{15} - 8 q^{16} - 16 q^{17} - 14 q^{19} + 22 q^{20} + 12 q^{21} + 10 q^{22} + 14 q^{23} - 2 q^{24} + 12 q^{25} + 12 q^{27} + 14 q^{30} - 2 q^{31} + 4 q^{32} + 8 q^{33} - 24 q^{35} + 2 q^{38} + 22 q^{40} - 16 q^{41} + 24 q^{42} + 6 q^{43} - 10 q^{44} - 6 q^{45} - 2 q^{46} - 14 q^{48} - 24 q^{49} + 20 q^{50} - 24 q^{53} + 20 q^{54} + 10 q^{55} + 40 q^{57} - 22 q^{59} - 46 q^{60} + 20 q^{61} + 30 q^{62} - 16 q^{63} - 48 q^{64} - 36 q^{66} + 12 q^{67} + 4 q^{68} - 4 q^{69} - 20 q^{70} + 10 q^{71} + 4 q^{73} - 30 q^{75} - 6 q^{76} + 24 q^{77} - 2 q^{80} - 20 q^{81} - 20 q^{82} - 16 q^{84} + 20 q^{85} + 46 q^{86} + 16 q^{87} + 10 q^{88} + 28 q^{89} + 14 q^{90} + 50 q^{92} - 2 q^{95} - 30 q^{96} - 12 q^{97} - 92 q^{98} + 2 q^{99}+O(q^{100}) $ 8 * q + 4 * q^2 - 6 * q^3 + 8 * q^4 - 2 * q^5 + 6 * q^6 - 6 * q^10 - 6 * q^11 + 2 * q^12 + 2 * q^15 - 8 * q^16 - 16 * q^17 - 14 * q^19 + 22 * q^20 + 12 * q^21 + 10 * q^22 + 14 * q^23 - 2 * q^24 + 12 * q^25 + 12 * q^27 + 14 * q^30 - 2 * q^31 + 4 * q^32 + 8 * q^33 - 24 * q^35 + 2 * q^38 + 22 * q^40 - 16 * q^41 + 24 * q^42 + 6 * q^43 - 10 * q^44 - 6 * q^45 - 2 * q^46 - 14 * q^48 - 24 * q^49 + 20 * q^50 - 24 * q^53 + 20 * q^54 + 10 * q^55 + 40 * q^57 - 22 * q^59 - 46 * q^60 + 20 * q^61 + 30 * q^62 - 16 * q^63 - 48 * q^64 - 36 * q^66 + 12 * q^67 + 4 * q^68 - 4 * q^69 - 20 * q^70 + 10 * q^71 + 4 * q^73 - 30 * q^75 - 6 * q^76 + 24 * q^77 - 2 * q^80 - 20 * q^81 - 20 * q^82 - 16 * q^84 + 20 * q^85 + 46 * q^86 + 16 * q^87 + 10 * q^88 + 28 * q^89 + 14 * q^90 + 50 * q^92 - 2 * q^95 - 30 * q^96 - 12 * q^97 - 92 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	0.134632			0.0951991			0.0475996	−	0.998866i	$-0.484843\pi$
$2$	0.134632			0.0951991			0.0475996	+	0.998866i	$0.484843\pi$
$3$	−2.15558	+	2.15558i	−1.24452	+	1.24452i	−0.286419	+	0.958105i	$0.592465\pi$
$3$	−2.15558	+	2.15558i	−1.24452	+	1.24452i	−0.958105	+	0.286419i	$0.907535\pi$
$4$	−1.98187			−0.990937
$5$	−1.82630	−	1.29021i	−0.816745	−	0.576999i
$5$	−1.82630	−	1.29021i	−0.816745	−	0.576999i
$6$	−0.290209	+	0.290209i	−0.118478	+	0.118478i
$7$		−	1.90970i		−	0.721799i	−0.932605	−	0.360899i	$-0.882470\pi$
$7$		−	1.90970i		−	0.721799i	0.932605	−	0.360899i	$-0.117530\pi$
$8$	−0.536087			−0.189535
$9$		−	6.29303i		−	2.09768i
$10$	−0.245878	−	0.173703i	−0.0777534	−	0.0549298i
$11$	0.290209	+	0.290209i	0.0875014	+	0.0875014i	0.749503	−	0.662001i	$-0.230293\pi$
$11$	0.290209	+	0.290209i	0.0875014	+	0.0875014i	−0.662001	+	0.749503i	$0.730293\pi$
$12$	4.27208	−	4.27208i	1.23324	−	1.23324i
$13$		0			0
$13$		0			0
$14$		−	0.257106i		−	0.0687146i
$15$	6.71787	−	1.15558i	1.73455	−	0.298369i
$16$	3.89157			0.972894
$17$	−2.53609	+	2.53609i	−0.615091	+	0.615091i	−0.944268	−	0.329177i	$-0.893229\pi$
$17$	−2.53609	+	2.53609i	−0.615091	+	0.615091i	0.329177	+	0.944268i	$0.393229\pi$
$18$		−	0.847242i		−	0.199697i
$19$	−3.15558	−	3.15558i	−0.723939	−	0.723939i	0.245466	−	0.969405i	$-0.421059\pi$
$19$	−3.15558	−	3.15558i	−0.723939	−	0.723939i	−0.969405	+	0.245466i	$0.921059\pi$
$20$	3.61949	+	2.55703i	0.809343	+	0.571770i
$21$	4.11651	+	4.11651i	0.898295	+	0.898295i
$22$	0.0390714	+	0.0390714i	0.00833006	+	0.00833006i
$23$	−2.27208	−	2.27208i	−0.473762	−	0.473762i	0.429368	−	0.903130i	$-0.358736\pi$
$23$	−2.27208	−	2.27208i	−0.473762	−	0.473762i	−0.903130	+	0.429368i	$0.858736\pi$
$24$	1.15558	−	1.15558i	0.235881	−	0.235881i
$25$	1.67072	+	4.71261i	0.334144	+	0.942522i
$26$		0			0
$27$	7.09838	+	7.09838i	1.36608	+	1.36608i
$28$			3.78478i			0.715257i
$29$		−	2.40146i		−	0.445939i	−0.974825	−	0.222970i	$-0.928425\pi$
$29$		−	2.40146i		−	0.445939i	0.974825	−	0.222970i	$-0.0715750\pi$
$30$	0.904440	−	0.155578i	0.165127	−	0.0284045i
$31$	−2.02095	+	2.02095i	−0.362973	+	0.362973i	−0.864906	−	0.501934i	$-0.832622\pi$
$31$	−2.02095	+	2.02095i	−0.362973	+	0.362973i	0.501934	+	0.864906i	$0.332622\pi$
$32$	1.59610			0.282154
$33$	−1.25114			−0.217795
$34$	−0.341438	+	0.341438i	−0.0585562	+	0.0585562i
$35$	−2.46391	+	3.48768i	−0.416477	+	0.589525i
$36$			12.4720i			2.07867i
$37$			5.32928i			0.876128i	0.898944	+	0.438064i	$0.144336\pi$
$37$			5.32928i			0.876128i	−0.898944	+	0.438064i	$0.855664\pi$
$38$	−0.424841	−	0.424841i	−0.0689184	−	0.0689184i
$39$		0			0
$40$	0.979054	+	0.691665i	0.154802	+	0.109362i
$41$	1.51796	−	1.51796i	0.237066	−	0.237066i	−0.578568	−	0.815634i	$-0.696388\pi$
$41$	1.51796	−	1.51796i	0.237066	−	0.237066i	0.815634	+	0.578568i	$0.196388\pi$
$42$	0.554213	+	0.554213i	0.0855169	+	0.0855169i
$43$	0.888754	+	0.888754i	0.135534	+	0.135534i	0.771619	−	0.636085i	$-0.219447\pi$
$43$	0.888754	+	0.888754i	0.135534	+	0.135534i	−0.636085	+	0.771619i	$0.719447\pi$
$44$	−0.575159	−	0.575159i	−0.0867084	−	0.0867084i
$45$	−8.11933	+	11.4929i	−1.21036	+	1.71327i
$46$	−0.305895	−	0.305895i	−0.0451017	−	0.0451017i
$47$			6.94562i			1.01312i	0.862204	+	0.506562i	$0.169084\pi$
$47$			6.94562i			1.01312i	−0.862204	+	0.506562i	$0.830916\pi$
$48$	−8.38859	+	8.38859i	−1.21079	+	1.21079i
$49$	3.35305			0.479007
$50$	0.224932	+	0.634468i	0.0318102	+	0.0897273i
$51$		−	10.9335i		−	1.53099i
$52$		0			0
$53$	−1.09030	+	1.09030i	−0.149764	+	0.149764i	−0.778013	−	0.628248i	$-0.783772\pi$
$53$	−1.09030	+	1.09030i	−0.149764	+	0.149764i	0.628248	+	0.778013i	$0.283772\pi$
$54$	0.955668	+	0.955668i	0.130050	+	0.130050i
$55$	−0.155578	−	0.904440i	−0.0209781	−	0.121955i
$56$			1.02377i			0.136806i
$57$	13.6042			1.80192
$58$		−	0.323312i		−	0.0424530i
$59$	−8.31642	+	8.31642i	−1.08271	+	1.08271i	−0.0864488	+	0.996256i	$0.527552\pi$
$59$	−8.31642	+	8.31642i	−1.08271	+	1.08271i	−0.996256	+	0.0864488i	$0.972448\pi$
$60$	−13.3140	+	2.29021i	−1.71883	+	0.295665i
$61$	7.17300			0.918408			0.459204	−	0.888331i	$-0.348135\pi$
$61$	7.17300			0.918408			0.459204	+	0.888331i	$0.348135\pi$
$62$	−0.272084	+	0.272084i	−0.0345547	+	0.0345547i
$63$	−12.0178			−1.51410
$64$	−7.56826			−0.946033
$65$		0			0
$66$	−0.168443			−0.0207339
$67$	0.939983			0.114837			0.0574186	−	0.998350i	$-0.481713\pi$
$67$	0.939983			0.114837			0.0574186	+	0.998350i	$0.481713\pi$
$68$	5.02621	−	5.02621i	0.609517	−	0.609517i
$69$	9.79531			1.17922
$70$	−0.331721	+	0.469553i	−0.0396483	+	0.0561223i
$71$	7.37643	−	7.37643i	0.875421	−	0.875421i	−0.117635	−	0.993057i	$-0.537531\pi$
$71$	7.37643	−	7.37643i	0.875421	−	0.875421i	0.993057	+	0.117635i	$0.0375314\pi$
$72$			3.37361i			0.397584i
$73$	6.63447			0.776506			0.388253	−	0.921553i	$-0.373079\pi$
$73$	6.63447			0.776506			0.388253	+	0.921553i	$0.373079\pi$
$74$			0.717491i			0.0834066i
$75$	−13.7598	−	6.55703i	−1.58884	−	0.757141i
$76$	6.25396	+	6.25396i	0.717378	+	0.717378i
$77$	0.554213	−	0.554213i	0.0631584	−	0.0631584i
$78$		0			0
$79$			4.39982i			0.495018i	0.968886	+	0.247509i	$0.0796120\pi$
$79$			4.39982i			0.495018i	−0.968886	+	0.247509i	$0.920388\pi$
$80$	−7.10717	−	5.02095i	−0.794606	−	0.561359i
$81$	−11.7231			−1.30257
$82$	0.204366	−	0.204366i	0.0225684	−	0.0225684i
$83$			13.4842i			1.48008i	0.672564	+	0.740039i	$0.265193\pi$
$83$			13.4842i			1.48008i	−0.672564	+	0.740039i	$0.734807\pi$
$84$	−8.15840	−	8.15840i	−0.890154	−	0.890154i
$85$	7.90373	−	1.35956i	0.857280	−	0.147465i
$86$	0.119655	+	0.119655i	0.0129027	+	0.0129027i
$87$	5.17652	+	5.17652i	0.554982	+	0.554982i
$88$	−0.155578	−	0.155578i	−0.0165846	−	0.0165846i
$89$	10.0238	−	10.0238i	1.06252	−	1.06252i	0.0646062	−	0.997911i	$-0.479421\pi$
$89$	10.0238	−	10.0238i	1.06252	−	1.06252i	0.997911	−	0.0646062i	$-0.0205791\pi$
$90$	−1.09312	+	1.54732i	−0.115225	+	0.163101i
$91$		0			0
$92$	4.50298	+	4.50298i	0.469469	+	0.469469i
$93$		−	8.71261i		−	0.903456i
$94$			0.935102i			0.0964484i
$95$	1.69166	+	9.83438i	0.173561	+	1.00899i
$96$	−3.44053	+	3.44053i	−0.351147	+	0.351147i
$97$	4.39982			0.446734			0.223367	−	0.974734i	$-0.428295\pi$
$97$	4.39982			0.446734			0.223367	+	0.974734i	$0.428295\pi$
$98$	0.451427			0.0456010
$99$	1.82630	−	1.82630i	0.183550	−	0.183550i
$100$	−3.31116	−	9.33980i	−0.331116	−	0.933980i
$101$		−	3.55014i		−	0.353252i	−0.984278	−	0.176626i	$-0.943482\pi$
$101$		−	3.55014i		−	0.353252i	0.984278	−	0.176626i	$-0.0565183\pi$
$102$		−	1.47199i		−	0.145749i
$103$	7.44861	+	7.44861i	0.733933	+	0.733933i	0.971396	−	0.237463i	$-0.0763160\pi$
$103$	7.44861	+	7.44861i	0.733933	+	0.733933i	−0.237463	+	0.971396i	$0.576316\pi$
$104$		0			0
$105$	−2.20681	−	12.8291i	−0.215362	−	1.25199i
$106$	−0.146789	+	0.146789i	−0.0142574	+	0.0142574i
$107$	9.56511	+	9.56511i	0.924694	+	0.924694i	0.997357	−	0.0726622i	$-0.0231495\pi$
$107$	9.56511	+	9.56511i	0.924694	+	0.924694i	−0.0726622	+	0.997357i	$0.523150\pi$
$108$	−14.0681	−	14.0681i	−1.35370	−	1.35370i
$109$	−8.08622	−	8.08622i	−0.774520	−	0.774520i	0.204373	−	0.978893i	$-0.434484\pi$
$109$	−8.08622	−	8.08622i	−0.774520	−	0.774520i	−0.978893	+	0.204373i	$0.934484\pi$
$110$	−0.0209457	−	0.121766i	−0.00199709	−	0.0116100i
$111$	−11.4877	−	11.4877i	−1.09036	−	1.09036i
$112$		−	7.43174i		−	0.702233i
$113$	4.97943	−	4.97943i	0.468426	−	0.468426i	−0.432979	−	0.901404i	$-0.642537\pi$
$113$	4.97943	−	4.97943i	0.468426	−	0.468426i	0.901404	+	0.432979i	$0.142537\pi$
$114$	1.83156			0.171541
$115$	1.21804	+	7.08096i	0.113582	+	0.660303i
$116$			4.75938i			0.441898i
$117$		0			0
$118$	−1.11965	+	1.11965i	−0.103073	+	0.103073i
$119$	4.84317	+	4.84317i	0.443972	+	0.443972i
$120$	−3.60136	+	0.619490i	−0.328758	+	0.0565515i
$121$		−	10.8316i		−	0.984687i
$122$	0.965714			0.0874316
$123$			6.54417i			0.590068i
$124$	4.00526	−	4.00526i	0.359683	−	0.359683i
$125$	3.02903	−	10.7622i	0.270924	−	0.962601i
$126$	−1.61798			−0.144141
$127$	7.01742	−	7.01742i	0.622695	−	0.622695i	−0.323525	−	0.946220i	$-0.604868\pi$
$127$	7.01742	−	7.01742i	0.622695	−	0.622695i	0.946220	+	0.323525i	$0.104868\pi$
$128$	−4.21114			−0.372216
$129$	−3.83156			−0.337350
$130$		0			0
$131$	−11.3052			−0.987739			−0.493869	−	0.869536i	$-0.664418\pi$
$131$	−11.3052			−0.987739			−0.493869	+	0.869536i	$0.664418\pi$
$132$	2.47960			0.215821
$133$	−6.02621	+	6.02621i	−0.522538	+	0.522538i
$134$	0.126552			0.0109324
$135$	−3.80535	−	22.1221i	−0.327512	−	1.90397i
$136$	1.35956	−	1.35956i	0.116582	−	0.116582i
$137$		−	1.92186i		−	0.164195i	−0.996624	−	0.0820977i	$-0.973838\pi$
$137$		−	1.92186i		−	0.164195i	0.996624	−	0.0820977i	$-0.0261619\pi$
$138$	1.31876			0.112260
$139$		−	15.2914i		−	1.29700i	−0.761215	−	0.648499i	$-0.775397\pi$
$139$		−	15.2914i		−	1.29700i	0.761215	−	0.648499i	$-0.224603\pi$
$140$	4.88317	−	6.91214i	0.412703	−	0.584182i
$141$	−14.9718	−	14.9718i	−1.26086	−	1.26086i
$142$	0.993103	−	0.993103i	0.0833394	−	0.0833394i
$143$		0			0
$144$		−	24.4898i		−	2.04082i
$145$	−3.09838	+	4.38577i	−0.257306	+	0.364218i
$146$	0.893211			0.0739227
$147$	−7.22775	+	7.22775i	−0.596135	+	0.596135i
$148$		−	10.5620i		−	0.868188i
$149$	13.8291	+	13.8291i	1.13293	+	1.13293i	0.989688	+	0.143237i	$0.0457511\pi$
$149$	13.8291	+	13.8291i	1.13293	+	1.13293i	0.143237	+	0.989688i	$0.454249\pi$
$150$	−1.85250	−	0.882786i	−0.151256	−	0.0720791i
$151$	8.55106	+	8.55106i	0.695876	+	0.695876i	0.963518	−	0.267643i	$-0.0862446\pi$
$151$	8.55106	+	8.55106i	0.695876	+	0.695876i	−0.267643	+	0.963518i	$0.586245\pi$
$152$	1.69166	+	1.69166i	0.137212	+	0.137212i
$153$	15.9597	+	15.9597i	1.29026	+	1.29026i
$154$	0.0746147	−	0.0746147i	0.00601263	−	0.00601263i
$155$	6.29829	−	1.08340i	0.505891	−	0.0870210i
$156$		0			0
$157$	−4.00808	−	4.00808i	−0.319880	−	0.319880i	0.528841	−	0.848721i	$-0.322627\pi$
$157$	−4.00808	−	4.00808i	−0.319880	−	0.319880i	−0.848721	+	0.528841i	$0.822627\pi$
$158$			0.592356i			0.0471253i
$159$		−	4.70045i		−	0.372770i
$160$	−2.91496	−	2.05931i	−0.230448	−	0.162803i
$161$	−4.33900	+	4.33900i	−0.341961	+	0.341961i
$162$	−1.57831			−0.124004
$163$	13.2930			1.04119			0.520595	−	0.853804i	$-0.325710\pi$
$163$	13.2930			1.04119			0.520595	+	0.853804i	$0.325710\pi$
$164$	−3.00841	+	3.00841i	−0.234917	+	0.234917i
$165$	2.28495	+	1.61423i	0.177883	+	0.125668i
$166$			1.81540i			0.140902i
$167$			12.9980i			1.00582i	0.864339	+	0.502909i	$0.167737\pi$
$167$			12.9980i			1.00582i	−0.864339	+	0.502909i	$0.832263\pi$
$168$	−2.20681	−	2.20681i	−0.170259	−	0.170259i
$169$		0			0
$170$	1.06409	−	0.183041i	0.0816123	−	0.0140386i
$171$	−19.8581	+	19.8581i	−1.51859	+	1.51859i
$172$	−1.76140	−	1.76140i	−0.134305	−	0.134305i
$173$	10.3052	+	10.3052i	0.783489	+	0.783489i	0.980418	−	0.196929i	$-0.0630968\pi$
$173$	10.3052	+	10.3052i	0.783489	+	0.783489i	−0.196929	+	0.980418i	$0.563097\pi$
$174$	0.696925	+	0.696925i	0.0528338	+	0.0528338i
$175$	8.99967	−	3.19057i	0.680311	−	0.241185i
$176$	1.12937	+	1.12937i	0.0851296	+	0.0851296i
$177$		−	35.8534i		−	2.69490i
$178$	1.34952	−	1.34952i	0.101151	−	0.101151i
$179$	−6.59094			−0.492630			−0.246315	−	0.969190i	$-0.579220\pi$
$179$	−6.59094			−0.492630			−0.246315	+	0.969190i	$0.579220\pi$
$180$	16.0915	−	22.7776i	1.19939	−	1.69774i
$181$			15.7953i			1.17406i	0.809567	+	0.587028i	$0.199702\pi$
$181$			15.7953i			1.17406i	−0.809567	+	0.587028i	$0.800298\pi$
$182$		0			0
$183$	−15.4619	+	15.4619i	−1.14298	+	1.14298i
$184$	1.21804	+	1.21804i	0.0897947	+	0.0897947i
$185$	6.87589	−	9.73285i	0.505525	−	0.715573i
$186$		−	1.17300i		−	0.0860082i
$187$	−1.47199			−0.107643
$188$		−	13.7654i		−	1.00394i
$189$	13.5558	−	13.5558i	0.986038	−	0.986038i
$190$	0.227752	+	1.32402i	0.0165229	+	0.0960546i
$191$	−13.0116			−0.941487			−0.470743	−	0.882270i	$-0.656014\pi$
$191$	−13.0116			−0.941487			−0.470743	+	0.882270i	$0.656014\pi$
$192$	16.3140	−	16.3140i	1.17736	−	1.17736i
$193$	17.4833			1.25847			0.629237	−	0.777214i	$-0.283368\pi$
$193$	17.4833			1.25847			0.629237	+	0.777214i	$0.283368\pi$
$194$	0.592356			0.0425287
$195$		0			0
$196$	−6.64532			−0.474665
$197$	−14.2749			−1.01704			−0.508522	−	0.861049i	$-0.669808\pi$
$197$	−14.2749			−1.01704			−0.508522	+	0.861049i	$0.669808\pi$
$198$	0.245878	−	0.245878i	0.0174738	−	0.0174738i
$199$	−4.76666			−0.337900			−0.168950	−	0.985625i	$-0.554038\pi$
$199$	−4.76666			−0.337900			−0.168950	+	0.985625i	$0.554038\pi$
$200$	−0.895651	−	2.52637i	−0.0633321	−	0.178641i
$201$	−2.02621	+	2.02621i	−0.142918	+	0.142918i
$202$		−	0.477961i		−	0.0336293i
$203$	−4.58606			−0.321878
$204$			21.6688i			1.51712i
$205$	−4.73074	+	0.813760i	−0.330409	+	0.0568354i
$206$	1.00282	+	1.00282i	0.0698698	+	0.0698698i
$207$	−14.2983	+	14.2983i	−0.993800	+	0.993800i
$208$		0			0
$209$		−	1.83156i		−	0.126691i
$210$	−0.297106	−	1.72721i	−0.0205023	−	0.119189i
$211$	11.6025			0.798752			0.399376	−	0.916787i	$-0.369227\pi$
$211$	11.6025			0.798752			0.399376	+	0.916787i	$0.369227\pi$
$212$	2.16084	−	2.16084i	0.148407	−	0.148407i
$213$			31.8009i			2.17896i
$214$	1.28777	+	1.28777i	0.0880301	+	0.0880301i
$215$	−0.476450	−	2.76981i	−0.0324936	−	0.188899i
$216$	−3.80535	−	3.80535i	−0.258921	−	0.258921i
$217$	3.85940	+	3.85940i	0.261993	+	0.261993i
$218$	−1.08866	−	1.08866i	−0.0737336	−	0.0737336i
$219$	−14.3011	+	14.3011i	−0.966379	+	0.966379i
$220$	0.308335	+	1.79249i	0.0207880	+	0.120849i
$221$		0			0
$222$	−1.54661	−	1.54661i	−0.103802	−	0.103802i
$223$			15.2511i			1.02129i	0.859791	+	0.510646i	$0.170594\pi$
$223$			15.2511i			1.02129i	−0.859791	+	0.510646i	$0.829406\pi$
$224$		−	3.04808i		−	0.203658i
$225$	29.6566	−	10.5139i	1.97711	−	0.700926i
$226$	0.670391	−	0.670391i	0.0445937	−	0.0445937i
$227$	−15.4292			−1.02407			−0.512037	−	0.858964i	$-0.671109\pi$
$227$	−15.4292			−1.02407			−0.512037	+	0.858964i	$0.671109\pi$
$228$	−26.9618			−1.78559
$229$	−4.10191	+	4.10191i	−0.271062	+	0.271062i	−0.829528	−	0.558466i	$-0.811390\pi$
$229$	−4.10191	+	4.10191i	−0.271062	+	0.271062i	0.558466	+	0.829528i	$0.311390\pi$
$230$	0.163986	+	0.953323i	0.0108129	+	0.0628603i
$231$			2.38930i			0.157204i
$232$			1.28739i			0.0845213i
$233$	−18.4776	−	18.4776i	−1.21051	−	1.21051i	−0.970859	−	0.239651i	$-0.922967\pi$
$233$	−18.4776	−	18.4776i	−1.21051	−	1.21051i	−0.239651	−	0.970859i	$-0.577033\pi$
$234$		0			0
$235$	8.96131	−	12.6848i	0.584571	−	0.827463i
$236$	16.4821	−	16.4821i	1.07289	−	1.07289i
$237$	−9.48415	−	9.48415i	−0.616062	−	0.616062i
$238$	0.652044	+	0.652044i	0.0422658	+	0.0422658i
$239$	7.82819	+	7.82819i	0.506363	+	0.506363i	0.913408	−	0.407045i	$-0.133441\pi$
$239$	7.82819	+	7.82819i	0.506363	+	0.506363i	−0.407045	+	0.913408i	$0.633441\pi$
$240$	26.1431	−	4.49702i	1.68753	−	0.290281i
$241$	9.29059	+	9.29059i	0.598459	+	0.598459i	0.939902	−	0.341443i	$-0.110916\pi$
$241$	9.29059	+	9.29059i	0.598459	+	0.598459i	−0.341443	+	0.939902i	$0.610916\pi$
$242$		−	1.45827i		−	0.0937413i
$243$	3.97498	−	3.97498i	0.254995	−	0.254995i
$244$	−14.2160			−0.910085
$245$	−6.12366	−	4.32613i	−0.391226	−	0.276386i
$246$			0.881054i			0.0561739i
$247$		0			0
$248$	1.08340	−	1.08340i	0.0687962	−	0.0687962i
$249$	−29.0661	−	29.0661i	−1.84199	−	1.84199i
$250$	0.407803	−	1.44894i	0.0257918	−	0.0916387i
$251$		−	13.4477i		−	0.848810i	−0.905472	−	0.424405i	$-0.860483\pi$
$251$		−	13.4477i		−	0.848810i	0.905472	−	0.424405i	$-0.139517\pi$
$252$	23.8178			1.50038
$253$		−	1.31876i		−	0.0829098i
$254$	0.944768	−	0.944768i	0.0592800	−	0.0592800i
$255$	−14.1065	+	19.9678i	−0.883381	+	1.25043i
$256$	14.5696			0.910598
$257$	2.36553	−	2.36553i	0.147558	−	0.147558i	−0.629468	−	0.777026i	$-0.716727\pi$
$257$	2.36553	−	2.36553i	0.147558	−	0.147558i	0.777026	+	0.629468i	$0.216727\pi$
$258$	−0.515850			−0.0321154
$259$	10.1773			0.632388
$260$		0			0
$261$	−15.1124			−0.935436
$262$	−1.52204			−0.0940319
$263$	−10.3418	+	10.3418i	−0.637704	+	0.637704i	−0.949989	−	0.312285i	$-0.898906\pi$
$263$	−10.3418	+	10.3418i	−0.637704	+	0.637704i	0.312285	+	0.949989i	$0.398906\pi$
$264$	0.670719			0.0412799
$265$	3.39793	−	0.584496i	0.208733	−	0.0359053i
$266$	−0.811319	+	0.811319i	−0.0497452	+	0.0497452i
$267$			43.2140i			2.64465i
$268$	−1.86293			−0.113796
$269$			31.6138i			1.92753i	0.266754	+	0.963765i	$0.414049\pi$
$269$			31.6138i			1.92753i	−0.266754	+	0.963765i	$0.585951\pi$
$270$	−0.512322	−	2.97835i	−0.0311789	−	0.181256i
$271$	−20.1850	−	20.1850i	−1.22615	−	1.22615i	−0.965409	−	0.260742i	$-0.916033\pi$
$271$	−20.1850	−	20.1850i	−1.22615	−	1.22615i	−0.260742	−	0.965409i	$-0.583967\pi$
$272$	−9.86937	+	9.86937i	−0.598419	+	0.598419i
$273$		0			0
$274$		−	0.258743i		−	0.0156313i
$275$	−0.882786	+	1.85250i	−0.0532340	+	0.111710i
$276$	−19.4131			−1.16853
$277$	−9.04189	+	9.04189i	−0.543275	+	0.543275i	−0.924487	−	0.381213i	$-0.875507\pi$
$277$	−9.04189	+	9.04189i	−0.543275	+	0.543275i	0.381213	+	0.924487i	$0.375507\pi$
$278$		−	2.05871i		−	0.123473i
$279$	12.7179	+	12.7179i	0.761399	+	0.761399i
$280$	1.32087	−	1.86970i	0.0789372	−	0.111736i
$281$	−6.06213	−	6.06213i	−0.361636	−	0.361636i	0.502779	−	0.864415i	$-0.332311\pi$
$281$	−6.06213	−	6.06213i	−0.361636	−	0.361636i	−0.864415	+	0.502779i	$0.832311\pi$
$282$	−2.01569	−	2.01569i	−0.120032	−	0.120032i
$283$	10.6076	+	10.6076i	0.630554	+	0.630554i	0.948207	−	0.317653i	$-0.102895\pi$
$283$	10.6076	+	10.6076i	0.630554	+	0.630554i	−0.317653	+	0.948207i	$0.602895\pi$
$284$	−14.6192	+	14.6192i	−0.867488	+	0.867488i
$285$	−24.8453	−	17.5522i	−1.47171	−	1.03971i
$286$		0			0
$287$	−2.89885	−	2.89885i	−0.171114	−	0.171114i
$288$		−	10.0443i		−	0.591868i
$289$			4.13652i			0.243325i
$290$	−0.417141	+	0.590464i	−0.0244953	+	0.0346733i
$291$	−9.48415	+	9.48415i	−0.555971	+	0.555971i
$292$	−13.1487			−0.769468
$293$	−21.9991			−1.28520			−0.642601	−	0.766201i	$-0.722145\pi$
$293$	−21.9991			−1.28520			−0.642601	+	0.766201i	$0.722145\pi$
$294$	−0.973086	+	0.973086i	−0.0567515	+	0.0567515i
$295$	25.9182	−	4.45832i	1.50901	−	0.259574i
$296$		−	2.85696i		−	0.166057i
$297$			4.12003i			0.239069i
$298$	1.86184	+	1.86184i	0.107853	+	0.107853i
$299$		0			0
$300$	27.2701	+	12.9952i	1.57444	+	0.750279i
$301$	1.69725	−	1.69725i	0.0978281	−	0.0978281i
$302$	1.15125	+	1.15125i	0.0662468	+	0.0662468i
$303$	7.65259	+	7.65259i	0.439630	+	0.439630i
$304$	−12.2802	−	12.2802i	−0.704316	−	0.704316i
$305$	−13.1000	−	9.25467i	−0.750105	−	0.529921i
$306$	2.14868	+	2.14868i	0.122832	+	0.122832i
$307$		−	9.59930i		−	0.547861i	−0.961749	−	0.273931i	$-0.911676\pi$
$307$		−	9.59930i		−	0.547861i	0.961749	−	0.273931i	$-0.0883239\pi$
$308$	−1.09838	+	1.09838i	−0.0625860	+	0.0625860i
$309$	−32.1121			−1.82679
$310$	0.847951	−	0.145861i	0.0481604	−	0.00828433i
$311$			4.28684i			0.243084i	0.992586	+	0.121542i	$0.0387840\pi$
$311$			4.28684i			0.243084i	−0.992586	+	0.121542i	$0.961216\pi$
$312$		0			0
$313$	5.55258	−	5.55258i	0.313850	−	0.313850i	−0.532549	−	0.846399i	$-0.678766\pi$
$313$	5.55258	−	5.55258i	0.313850	−	0.313850i	0.846399	+	0.532549i	$0.178766\pi$
$314$	−0.539615	−	0.539615i	−0.0304523	−	0.0304523i
$315$	21.9481	+	15.5055i	1.23663	+	0.873635i
$316$		−	8.71989i		−	0.490532i
$317$	18.5306			1.04078			0.520391	−	0.853928i	$-0.325786\pi$
$317$	18.5306			1.04078			0.520391	+	0.853928i	$0.325786\pi$
$318$		−	0.632831i		−	0.0354874i
$319$	0.696925	−	0.696925i	0.0390203	−	0.0390203i
$320$	13.8219	+	9.76464i	0.772667	+	0.545860i
$321$	−41.2367			−2.30161
$322$	−0.584167	+	0.584167i	−0.0325544	+	0.0325544i
$323$	16.0056			0.890578
$324$	23.2338			1.29077
$325$		0			0
$326$	1.78967			0.0991204
$327$	34.8610			1.92782
$328$	−0.813760	+	0.813760i	−0.0449324	+	0.0449324i
$329$	13.2641			0.731271
$330$	0.307627	+	0.217327i	0.0169343	+	0.0119634i
$331$	−1.66302	+	1.66302i	−0.0914078	+	0.0914078i	−0.751332	−	0.659924i	$-0.770588\pi$
$331$	−1.66302	+	1.66302i	−0.0914078	+	0.0914078i	0.659924	+	0.751332i	$0.270588\pi$
$332$		−	26.7239i		−	1.46666i
$333$	33.5373			1.83783
$334$			1.74995i			0.0957530i
$335$	−1.71669	−	1.21277i	−0.0937927	−	0.0662610i
$336$	16.0197	+	16.0197i	0.873946	+	0.873946i
$337$	7.30111	−	7.30111i	0.397717	−	0.397717i	−0.479710	−	0.877427i	$-0.659258\pi$
$337$	7.30111	−	7.30111i	0.397717	−	0.397717i	0.877427	+	0.479710i	$0.159258\pi$
$338$		0			0
$339$			21.4671i			1.16593i
$340$	−15.6642	+	2.69448i	−0.849511	+	0.146129i
$341$	−1.17300			−0.0635212
$342$	−2.67354	+	2.67354i	−0.144568	+	0.144568i
$343$		−	19.7712i		−	1.06755i
$344$	−0.476450	−	0.476450i	−0.0256884	−	0.0256884i
$345$	−17.8891	−	12.6380i	−0.963119	−	0.680407i
$346$	1.38741	+	1.38741i	0.0745874	+	0.0745874i
$347$	−9.54455	−	9.54455i	−0.512378	−	0.512378i	0.402876	−	0.915254i	$-0.368010\pi$
$347$	−9.54455	−	9.54455i	−0.512378	−	0.512378i	−0.915254	+	0.402876i	$0.868010\pi$
$348$	−10.2592	−	10.2592i	−0.549952	−	0.549952i
$349$	18.1608	−	18.1608i	0.972127	−	0.972127i	−0.0274946	−	0.999622i	$-0.508753\pi$
$349$	18.1608	−	18.1608i	0.972127	−	0.972127i	0.999622	+	0.0274946i	$0.00875290\pi$
$350$	1.21164	−	0.429553i	0.0647650	−	0.0229606i
$351$		0			0
$352$	0.463205	+	0.463205i	0.0246889	+	0.0246889i
$353$			4.19276i			0.223158i	0.993756	+	0.111579i	$0.0355908\pi$
$353$			4.19276i			0.223158i	−0.993756	+	0.111579i	$0.964409\pi$
$354$		−	4.82700i		−	0.256552i
$355$	−22.9887	+	3.95441i	−1.22011	+	0.209878i
$356$	−19.8658	+	19.8658i	−1.05289	+	1.05289i
$357$	−20.8796			−1.10507
$358$	−0.887351			−0.0468979
$359$	−6.13909	+	6.13909i	−0.324009	+	0.324009i	−0.850303	−	0.526294i	$-0.823581\pi$
$359$	−6.13909	+	6.13909i	−0.324009	+	0.324009i	0.526294	+	0.850303i	$0.323581\pi$
$360$	4.35267	−	6.16122i	0.229406	−	0.324725i
$361$			0.915340i			0.0481758i
$362$			2.12655i			0.111769i
$363$	23.3483	+	23.3483i	1.22547	+	1.22547i
$364$		0			0
$365$	−12.1165	−	8.55985i	−0.634207	−	0.448043i
$366$	−2.08167	+	2.08167i	−0.108811	+	0.108811i
$367$	−4.59729	−	4.59729i	−0.239976	−	0.239976i	0.576864	−	0.816840i	$-0.304276\pi$
$367$	−4.59729	−	4.59729i	−0.239976	−	0.239976i	−0.816840	+	0.576864i	$0.804276\pi$
$368$	−8.84198	−	8.84198i	−0.460920	−	0.460920i
$369$	−9.55258	−	9.55258i	−0.497287	−	0.497287i
$370$	0.925714	−	1.31035i	0.0481256	−	0.0681219i
$371$	2.08215	+	2.08215i	0.108100	+	0.108100i
$372$			17.2673i			0.895268i
$373$	13.6188	−	13.6188i	0.705154	−	0.705154i	−0.260358	−	0.965512i	$-0.583841\pi$
$373$	13.6188	−	13.6188i	0.705154	−	0.705154i	0.965512	+	0.260358i	$0.0838407\pi$
$374$	−0.198177			−0.0102475
$375$	16.6695	+	29.7281i	0.860807	+	1.53515i
$376$		−	3.72346i		−	0.192023i
$377$		0			0
$378$	1.82504	−	1.82504i	0.0938699	−	0.0938699i
$379$	19.3439	+	19.3439i	0.993631	+	0.993631i	0.999980	−	0.00634892i	$-0.00202094\pi$
$379$	19.3439	+	19.3439i	0.993631	+	0.993631i	−0.00634892	+	0.999980i	$0.502021\pi$
$380$	−3.35267	−	19.4905i	−0.171988	−	0.999841i
$381$			30.2532i			1.54992i
$382$	−1.75178			−0.0896287
$383$		−	7.13110i		−	0.364382i	−0.983263	−	0.182191i	$-0.941681\pi$
$383$		−	7.13110i		−	0.364382i	0.983263	−	0.182191i	$-0.0583190\pi$
$384$	9.07743	−	9.07743i	0.463231	−	0.463231i
$385$	−1.72721	+	0.297106i	−0.0880267	+	0.0151419i
$386$	2.35381			0.119806
$387$	5.59296	−	5.59296i	0.284306	−	0.284306i
$388$	−8.71989			−0.442685
$389$	25.6987			1.30298			0.651488	−	0.758659i	$-0.274145\pi$
$389$	25.6987			1.30298			0.651488	+	0.758659i	$0.274145\pi$
$390$		0			0
$391$	11.5244			0.582814
$392$	−1.79753			−0.0907887
$393$	24.3692	−	24.3692i	1.22926	−	1.22926i
$394$	−1.92186			−0.0968218
$395$	5.67669	−	8.03537i	0.285625	−	0.404304i
$396$	−3.61949	+	3.61949i	−0.181886	+	0.181886i
$397$			14.8794i			0.746777i	0.927675	+	0.373388i	$0.121804\pi$
$397$			14.8794i			0.746777i	−0.927675	+	0.373388i	$0.878196\pi$
$398$	−0.641744			−0.0321677
$399$		−	25.9799i		−	1.30062i
$400$	6.50173	+	18.3395i	0.325086	+	0.916974i
$401$	−9.52637	−	9.52637i	−0.475724	−	0.475724i	0.428037	−	0.903761i	$-0.359205\pi$
$401$	−9.52637	−	9.52637i	−0.475724	−	0.475724i	−0.903761	+	0.428037i	$0.859205\pi$
$402$	−0.272792	+	0.272792i	−0.0136056	+	0.0136056i
$403$		0			0
$404$			7.03592i			0.350050i
$405$	21.4099	+	15.1253i	1.06387	+	0.751582i
$406$	−0.617430			−0.0306425
$407$	−1.54661	+	1.54661i	−0.0766625	+	0.0766625i
$408$			5.86129i			0.290177i
$409$	8.19410	+	8.19410i	0.405172	+	0.405172i	0.880051	−	0.474879i	$-0.157508\pi$
$409$	8.19410	+	8.19410i	0.405172	+	0.405172i	−0.474879	+	0.880051i	$0.657508\pi$
$410$	−0.636908	+	0.109558i	−0.0314546	+	0.00541068i
$411$	4.14271	+	4.14271i	0.204345	+	0.204345i
$412$	−14.7622	−	14.7622i	−0.727282	−	0.727282i
$413$	15.8819	+	15.8819i	0.781495	+	0.781495i
$414$	−1.92501	+	1.92501i	−0.0946089	+	0.0946089i
$415$	17.3974	−	24.6261i	0.854004	−	1.20885i
$416$		0			0
$417$	32.9618	+	32.9618i	1.61415	+	1.61415i
$418$		−	0.246586i		−	0.0120609i
$419$			26.7652i			1.30757i	0.756681	+	0.653784i	$0.226819\pi$
$419$			26.7652i			1.30757i	−0.756681	+	0.653784i	$0.773181\pi$
$420$	4.37361	+	25.4257i	0.213410	+	1.24065i
$421$	25.6977	−	25.6977i	1.25243	−	1.25243i	0.297800	−	0.954628i	$-0.403747\pi$
$421$	25.6977	−	25.6977i	1.25243	−	1.25243i	0.954628	−	0.297800i	$-0.0962530\pi$
$422$	1.56207			0.0760405
$423$	43.7090			2.12520
$424$	0.584496	−	0.584496i	0.0283856	−	0.0283856i
$425$	−16.1887	−	7.71450i	−0.785266	−	0.374208i
$426$			4.28142i			0.207436i
$427$		−	13.6983i		−	0.662906i
$428$	−18.9569	−	18.9569i	−0.916314	−	0.916314i
$429$		0			0
$430$	−0.0641453	−	0.372904i	−0.00309336	−	0.0179830i
$431$	13.6422	−	13.6422i	0.657120	−	0.657120i	−0.297578	−	0.954698i	$-0.596179\pi$
$431$	13.6422	−	13.6422i	0.657120	−	0.657120i	0.954698	+	0.297578i	$0.0961787\pi$
$432$	27.6239	+	27.6239i	1.32905	+	1.32905i
$433$	−25.0267	−	25.0267i	−1.20271	−	1.20271i	−0.973340	−	0.229365i	$-0.926335\pi$
$433$	−25.0267	−	25.0267i	−1.20271	−	1.20271i	−0.229365	−	0.973340i	$-0.573665\pi$
$434$	0.519598	+	0.519598i	0.0249415	+	0.0249415i
$435$	−2.77507	−	16.1327i	−0.133054	−	0.773502i
$436$	16.0259	+	16.0259i	0.767500	+	0.767500i
$437$			14.3395i			0.685950i
$438$	−1.92539	+	1.92539i	−0.0919985	+	0.0919985i
$439$	32.0588			1.53008			0.765042	−	0.643981i	$-0.222718\pi$
$439$	32.0588			1.53008			0.765042	+	0.643981i	$0.222718\pi$
$440$	0.0834032	+	0.484858i	0.00397609	+	0.0231147i
$441$		−	21.1008i		−	1.00480i
$442$		0			0
$443$	3.91063	−	3.91063i	0.185800	−	0.185800i	−0.608078	−	0.793877i	$-0.708059\pi$
$443$	3.91063	−	3.91063i	0.185800	−	0.185800i	0.793877	+	0.608078i	$0.208059\pi$
$444$	22.7671	+	22.7671i	1.08048	+	1.08048i
$445$	−31.2391	+	5.37361i	−1.48088	+	0.254734i
$446$			2.05329i			0.0972261i
$447$	−59.6195			−2.81990
$448$			14.4531i			0.682845i
$449$	2.54173	−	2.54173i	0.119952	−	0.119952i	−0.644583	−	0.764534i	$-0.722969\pi$
$449$	2.54173	−	2.54173i	0.119952	−	0.119952i	0.764534	+	0.644583i	$0.222969\pi$
$450$	3.99272	−	1.41550i	0.188219	−	0.0667275i
$451$	0.881054			0.0414872
$452$	−9.86861	+	9.86861i	−0.464180	+	0.464180i
$453$	−36.8650			−1.73207
$454$	−2.07727			−0.0974909
$455$		0			0
$456$	−7.29303			−0.341527
$457$	23.2189			1.08613			0.543067	−	0.839689i	$-0.317263\pi$
$457$	23.2189			1.08613			0.543067	+	0.839689i	$0.317263\pi$
$458$	−0.552248	+	0.552248i	−0.0258048	+	0.0258048i
$459$	−36.0042			−1.68053
$460$	−2.41399	−	14.0336i	−0.112553	−	0.654319i
$461$	−28.8356	+	28.8356i	−1.34301	+	1.34301i	−0.449954	+	0.893052i	$0.648560\pi$
$461$	−28.8356	+	28.8356i	−1.34301	+	1.34301i	−0.893052	+	0.449954i	$0.851440\pi$
$462$			0.321676i			0.0149657i
$463$	−5.03192			−0.233853			−0.116927	−	0.993141i	$-0.537304\pi$
$463$	−5.03192			−0.233853			−0.116927	+	0.993141i	$0.537304\pi$
$464$		−	9.34544i		−	0.433851i
$465$	−11.2411	+	15.9118i	−0.521293	+	0.737893i
$466$	−2.48768	−	2.48768i	−0.115239	−	0.115239i
$467$	4.64570	−	4.64570i	0.214977	−	0.214977i	−0.591401	−	0.806378i	$-0.701425\pi$
$467$	4.64570	−	4.64570i	0.214977	−	0.214977i	0.806378	+	0.591401i	$0.201425\pi$
$468$		0			0
$469$		−	1.79509i		−	0.0828893i
$470$	1.20648	−	1.70777i	0.0556507	−	0.0787737i
$471$	17.2795			0.796195
$472$	4.45832	−	4.45832i	0.205211	−	0.205211i
$473$			0.515850i			0.0237188i
$474$	−1.27687	−	1.27687i	−0.0586485	−	0.0586485i
$475$	9.59892	−	20.1431i	0.440429	−	0.924228i
$476$	−9.59854	−	9.59854i	−0.439949	−	0.439949i
$477$	6.86129	+	6.86129i	0.314157	+	0.314157i
$478$	1.05392	+	1.05392i	0.0482053	+	0.0482053i
$479$	6.05279	−	6.05279i	0.276559	−	0.276559i	−0.555175	−	0.831734i	$-0.687349\pi$
$479$	6.05279	−	6.05279i	0.276559	−	0.276559i	0.831734	+	0.555175i	$0.187349\pi$
$480$	10.7224	−	1.84442i	0.489409	−	0.0841860i
$481$		0			0
$482$	1.25081	+	1.25081i	0.0569728	+	0.0569728i
$483$		−	18.7061i		−	0.851157i
$484$			21.4668i			0.975763i
$485$	−8.03537	−	5.67669i	−0.364868	−	0.257765i
$486$	0.535159	−	0.535159i	0.0242753	−	0.0242753i
$487$	8.30574			0.376369			0.188184	−	0.982134i	$-0.439740\pi$
$487$	8.30574			0.376369			0.188184	+	0.982134i	$0.439740\pi$
$488$	−3.84535			−0.174071
$489$	−28.6542	+	28.6542i	−1.29579	+	1.29579i
$490$	−0.824440	−	0.582435i	−0.0372444	−	0.0263117i
$491$		−	4.54905i		−	0.205296i	−0.994718	−	0.102648i	$-0.967269\pi$
$491$		−	4.54905i		−	0.205296i	0.994718	−	0.102648i	$-0.0327315\pi$
$492$		−	12.9697i		−	0.584720i
$493$	6.09030	+	6.09030i	0.274293	+	0.274293i
$494$		0			0
$495$	−5.69166	+	0.979054i	−0.255821	+	0.0440052i
$496$	−7.86466	+	7.86466i	−0.353134	+	0.353134i
$497$	−14.0868	−	14.0868i	−0.631878	−	0.631878i
$498$	−3.91323	−	3.91323i	−0.175356	−	0.175356i
$499$	10.9444	+	10.9444i	0.489937	+	0.489937i	0.908286	−	0.418349i	$-0.137391\pi$
$499$	10.9444	+	10.9444i	0.489937	+	0.489937i	−0.418349	+	0.908286i	$0.637391\pi$
$500$	−6.00315	+	21.3293i	−0.268469	+	0.953877i
$501$	−28.0183	−	28.0183i	−1.25176	−	1.25176i
$502$		−	1.81049i		−	0.0808060i
$503$	−9.60700	+	9.60700i	−0.428355	+	0.428355i	−0.888068	−	0.459713i	$-0.847952\pi$
$503$	−9.60700	+	9.60700i	−0.428355	+	0.428355i	0.459713	+	0.888068i	$0.347952\pi$
$504$	6.44259			0.286976
$505$	−4.58042	+	6.48360i	−0.203826	+	0.288516i
$506$		−	0.177547i		−	0.00789294i
$507$		0			0
$508$	−13.9076	+	13.9076i	−0.617052	+	0.617052i
$509$	−1.01052	−	1.01052i	−0.0447905	−	0.0447905i	0.684357	−	0.729147i	$-0.260083\pi$
$509$	−1.01052	−	1.01052i	−0.0447905	−	0.0447905i	−0.729147	+	0.684357i	$0.760083\pi$
$510$	−1.89918	+	2.68830i	−0.0840971	+	0.119040i
$511$		−	12.6698i		−	0.560481i
$512$	10.3838			0.458904
$513$		−	44.7990i		−	1.97792i
$514$	0.318476	−	0.318476i	0.0140474	−	0.0140474i
$515$	−3.99310	−	23.2136i	−0.175957	−	1.02291i
$516$	7.59366			0.334292
$517$	−2.01569	+	2.01569i	−0.0886497	+	0.0886497i
$518$	1.37019			0.0602028
$519$	−44.4273			−1.95014
$520$		0			0
$521$	39.4816			1.72972			0.864861	−	0.502012i	$-0.167406\pi$
$521$	39.4816			1.72972			0.864861	+	0.502012i	$0.167406\pi$
$522$	−2.03461			−0.0890527
$523$	−15.7663	+	15.7663i	−0.689411	+	0.689411i	−0.962102	−	0.272691i	$-0.912086\pi$
$523$	−15.7663	+	15.7663i	−0.689411	+	0.689411i	0.272691	+	0.962102i	$0.412086\pi$
$524$	22.4055			0.978787
$525$	−12.5220	+	26.2770i	−0.546503	+	1.14682i
$526$	−1.39234	+	1.39234i	−0.0607088	+	0.0607088i
$527$		−	10.2506i		−	0.446523i
$528$	−4.86890			−0.211892
$529$		−	12.6753i		−	0.551099i
$530$	0.457469	−	0.0786918i	0.0198712	−	0.00341815i
$531$	52.3354	+	52.3354i	2.27116	+	2.27116i
$532$	11.9432	−	11.9432i	0.517803	−	0.517803i
$533$		0			0
$534$			5.81798i			0.251769i
$535$	−5.12773	−	29.8097i	−0.221691	−	1.28879i
$536$	−0.503913			−0.0217657
$537$	14.2073	−	14.2073i	0.613089	−	0.613089i
$538$			4.25623i			0.183499i
$539$	0.973086	+	0.973086i	0.0419138	+	0.0419138i
$540$	7.54173	+	43.8433i	0.324544	+	1.88672i
$541$	22.2954	+	22.2954i	0.958554	+	0.958554i	0.999175	−	0.0406207i	$-0.0129335\pi$
$541$	22.2954	+	22.2954i	0.958554	+	0.958554i	−0.0406207	+	0.999175i	$0.512934\pi$
$542$	−2.71754	−	2.71754i	−0.116728	−	0.116728i
$543$	−34.0480	−	34.0480i	−1.46114	−	1.46114i
$544$	−4.04786	+	4.04786i	−0.173551	+	0.173551i
$545$	4.33492	+	25.2008i	0.185688	+	1.07948i
$546$		0			0
$547$	3.38779	+	3.38779i	0.144851	+	0.144851i	0.775814	−	0.630962i	$-0.217340\pi$
$547$	3.38779	+	3.38779i	0.144851	+	0.144851i	−0.630962	+	0.775814i	$0.717340\pi$
$548$			3.80888i			0.162707i
$549$		−	45.1399i		−	1.92652i
$550$	−0.118851	+	0.249406i	−0.00506783	+	0.0106347i
$551$	−7.57798	+	7.57798i	−0.322833	+	0.322833i
$552$	−5.25114			−0.223503
$553$	8.40233			0.357304
$554$	−1.21733	+	1.21733i	−0.0517193	+	0.0517193i
$555$	6.15840	+	35.8014i	0.261409	+	1.51969i
$556$			30.3056i			1.28524i
$557$			5.28065i			0.223748i	0.993722	+	0.111874i	$0.0356854\pi$
$557$			5.28065i			0.223748i	−0.993722	+	0.111874i	$0.964315\pi$
$558$	1.71223	+	1.71223i	0.0724845	+	0.0724845i
$559$		0			0
$560$	−9.58850	+	13.5726i	−0.405188	+	0.573545i
$561$	3.17300	−	3.17300i	0.133964	−	0.133964i
$562$	−0.816156	−	0.816156i	−0.0344275	−	0.0344275i
$563$	29.6592	+	29.6592i	1.24999	+	1.24999i	0.955725	+	0.294261i	$0.0950735\pi$
$563$	29.6592	+	29.6592i	1.24999	+	1.24999i	0.294261	+	0.955725i	$0.404927\pi$
$564$	29.6723	+	29.6723i	1.24943	+	1.24943i
$565$	−15.5184	+	2.66941i	−0.652866	+	0.112303i
$566$	1.42811	+	1.42811i	0.0600281	+	0.0600281i
$567$			22.3877i			0.940193i
$568$	−3.95441	+	3.95441i	−0.165923	+	0.165923i
$569$	−22.3322			−0.936216			−0.468108	−	0.883671i	$-0.655064\pi$
$569$	−22.3322			−0.936216			−0.468108	+	0.883671i	$0.655064\pi$
$570$	−3.34497	−	2.36309i	−0.140105	−	0.0989790i
$571$			11.9099i			0.498415i	0.968450	+	0.249207i	$0.0801701\pi$
$571$			11.9099i			0.498415i	−0.968450	+	0.249207i	$0.919830\pi$
$572$		0			0
$573$	28.0475	−	28.0475i	1.17170	−	1.17170i
$574$	−0.390278	−	0.390278i	−0.0162899	−	0.0162899i
$575$	6.91143	−	14.5035i	0.288227	−	0.604836i
$576$			47.6273i			1.98447i
$577$	31.5179			1.31211			0.656053	−	0.754714i	$-0.272225\pi$
$577$	31.5179			1.31211			0.656053	+	0.754714i	$0.272225\pi$
$578$			0.556908i			0.0231643i
$579$	−37.6866	+	37.6866i	−1.56620	+	1.56620i
$580$	6.14060	−	8.69204i	0.254975	−	0.360918i
$581$	25.7507			1.06832
$582$	−1.27687	+	1.27687i	−0.0529279	+	0.0529279i
$583$	−0.632831			−0.0262092
$584$	−3.55665			−0.147175
$585$		0			0
$586$	−2.96178			−0.122350
$587$	−33.0231			−1.36301			−0.681505	−	0.731814i	$-0.738674\pi$
$587$	−33.0231			−1.36301			−0.681505	+	0.731814i	$0.738674\pi$
$588$	14.3245	−	14.3245i	0.590732	−	0.590732i
$589$	12.7545			0.525540
$590$	3.48941	−	0.600233i	0.143657	−	0.0247112i
$591$	30.7707	−	30.7707i	1.26574	−	1.26574i
$592$			20.7393i			0.852380i
$593$	−20.1991			−0.829479			−0.414739	−	0.909940i	$-0.636127\pi$
$593$	−20.1991			−0.829479			−0.414739	+	0.909940i	$0.636127\pi$
$594$			0.554688i			0.0227591i
$595$	−2.59636	−	15.0938i	−0.106440	−	0.618784i
$596$	−27.4076	−	27.4076i	−1.12266	−	1.12266i
$597$	10.2749	−	10.2749i	0.420524	−	0.420524i
$598$		0			0
$599$			10.8205i			0.442113i	0.975261	+	0.221057i	$0.0709505\pi$
$599$			10.8205i			0.442113i	−0.975261	+	0.221057i	$0.929049\pi$
$600$	7.37643	+	3.51514i	0.301142	+	0.143505i
$601$	−5.12131			−0.208903			−0.104451	−	0.994530i	$-0.533309\pi$
$601$	−5.12131			−0.208903			−0.104451	+	0.994530i	$0.533309\pi$
$602$	0.228504	−	0.228504i	0.00931315	−	0.00931315i
$603$		−	5.91534i		−	0.240891i
$604$	−16.9471	−	16.9471i	−0.689569	−	0.689569i
$605$	−13.9750	+	19.7816i	−0.568164	+	0.804238i
$606$	1.03028	+	1.03028i	0.0418524	+	0.0418524i
$607$	11.3669	+	11.3669i	0.461370	+	0.461370i	0.899104	−	0.437735i	$-0.144219\pi$
$607$	11.3669	+	11.3669i	0.461370	+	0.461370i	−0.437735	+	0.899104i	$0.644219\pi$
$608$	−5.03663	−	5.03663i	−0.204262	−	0.204262i
$609$	9.88561	−	9.88561i	0.400585	−	0.400585i
$610$	−1.76368	−	1.24597i	−0.0714093	−	0.0504480i
$611$		0			0
$612$	−31.6301	−	31.6301i	−1.27857	−	1.27857i
$613$			31.0334i			1.25343i	0.779250	+	0.626714i	$0.215600\pi$
$613$			31.0334i			1.25343i	−0.779250	+	0.626714i	$0.784400\pi$
$614$		−	1.29237i		−	0.0521559i
$615$	8.44335	−	11.9516i	0.340469	−	0.481935i
$616$	−0.297106	+	0.297106i	−0.0119708	+	0.0119708i
$617$	39.2697			1.58094			0.790469	−	0.612502i	$-0.209837\pi$
$617$	39.2697			1.58094			0.790469	+	0.612502i	$0.209837\pi$
$618$	−4.32331			−0.173909
$619$	20.7839	−	20.7839i	0.835374	−	0.835374i	−0.152872	−	0.988246i	$-0.548852\pi$
$619$	20.7839	−	20.7839i	0.835374	−	0.835374i	0.988246	+	0.152872i	$0.0488523\pi$
$620$	−12.4824	+	2.14717i	−0.501306	+	0.0862324i
$621$		−	32.2562i		−	1.29440i
$622$			0.577145i			0.0231414i
$623$	−19.1424	−	19.1424i	−0.766923	−	0.766923i
$624$		0			0
$625$	−19.4174	+	15.7469i	−0.776696	+	0.629876i
$626$	0.747554	−	0.747554i	0.0298783	−	0.0298783i
$627$	3.94806	+	3.94806i	0.157670	+	0.157670i
$628$	7.94351	+	7.94351i	0.316981	+	0.316981i
$629$	−13.5155	−	13.5155i	−0.538899	−	0.538899i
$630$	2.95491	+	2.08753i	0.117726	+	0.0831692i
$631$	−13.0898	−	13.0898i	−0.521099	−	0.521099i	0.396805	−	0.917903i	$-0.370119\pi$
$631$	−13.0898	−	13.0898i	−0.521099	−	0.521099i	−0.917903	+	0.396805i	$0.870119\pi$
$632$		−	2.35869i		−	0.0938235i
$633$	−25.0102	+	25.0102i	−0.994066	+	0.994066i
$634$	2.49481			0.0990815
$635$	−21.8698	+	3.76195i	−0.867878	+	0.149288i
$636$			9.31571i			0.369392i
$637$		0			0
$638$	0.0938283	−	0.0938283i	0.00371470	−	0.00371470i
$639$	−46.4201	−	46.4201i	−1.83635	−	1.83635i
$640$	7.69079	+	5.43325i	0.304005	+	0.214768i
$641$		−	41.7149i		−	1.64764i	−0.566853	−	0.823819i	$-0.691839\pi$
$641$		−	41.7149i		−	1.64764i	0.566853	−	0.823819i	$-0.308161\pi$
$642$	−5.55177			−0.219111
$643$			38.6757i			1.52522i	0.646858	+	0.762610i	$0.276083\pi$
$643$			38.6757i			1.52522i	−0.646858	+	0.762610i	$0.723917\pi$
$644$	8.59935	−	8.59935i	0.338862	−	0.338862i
$645$	6.99756	+	4.94351i	0.275529	+	0.194651i
$646$	2.15487			0.0847822
$647$	−21.8936	+	21.8936i	−0.860726	+	0.860726i	−0.991422	−	0.130697i	$-0.958279\pi$
$647$	−21.8936	+	21.8936i	−0.860726	+	0.860726i	0.130697	+	0.991422i	$0.458279\pi$
$648$	6.28462			0.246883
$649$	−4.82700			−0.189477
$650$		0			0
$651$	−16.6385			−0.652113
$652$	−26.3451			−1.03175
$653$	−21.0962	+	21.0962i	−0.825558	+	0.825558i	−0.986899	−	0.161341i	$-0.948418\pi$
$653$	−21.0962	+	21.0962i	−0.825558	+	0.825558i	0.161341	+	0.986899i	$0.448418\pi$
$654$	4.69340			0.183526
$655$	20.6466	+	14.5861i	0.806730	+	0.569924i
$656$	5.90726	−	5.90726i	0.230640	−	0.230640i
$657$		−	41.7509i		−	1.62886i
$658$	1.78576			0.0696164
$659$			26.6328i			1.03747i	0.854936	+	0.518734i	$0.173596\pi$
$659$			26.6328i			1.03747i	−0.854936	+	0.518734i	$0.826404\pi$
$660$	−4.52848	−	3.19920i	−0.176271	−	0.124529i
$661$	6.53609	+	6.53609i	0.254224	+	0.254224i	0.822700	−	0.568476i	$-0.192467\pi$
$661$	6.53609	+	6.53609i	0.254224	+	0.254224i	−0.568476	+	0.822700i	$0.692467\pi$
$662$	−0.223895	+	0.223895i	−0.00870194	+	0.00870194i
$663$		0			0
$664$		−	7.22868i		−	0.280527i
$665$	18.7807	−	3.23057i	0.728285	−	0.125276i
$666$	4.51519			0.174960
$667$	−5.45631	+	5.45631i	−0.211269	+	0.211269i
$668$		−	25.7605i		−	0.996703i
$669$	−32.8750	−	32.8750i	−1.27102	−	1.27102i
$670$	−0.231121	−	0.163278i	−0.00892898	−	0.00630799i
$671$	2.08167	+	2.08167i	0.0803620	+	0.0803620i
$672$	6.57037	+	6.57037i	0.253458	+	0.253458i
$673$	−5.50580	−	5.50580i	−0.212233	−	0.212233i	0.592982	−	0.805215i	$-0.297950\pi$
$673$	−5.50580	−	5.50580i	−0.212233	−	0.212233i	−0.805215	+	0.592982i	$0.797950\pi$
$674$	0.982962	−	0.982962i	0.0378623	−	0.0378623i
$675$	−21.5925	+	45.3113i	−0.831096	+	1.74403i
$676$		0			0
$677$	1.67072	+	1.67072i	0.0642110	+	0.0642110i	0.738483	−	0.674272i	$-0.235542\pi$
$677$	1.67072	+	1.67072i	0.0642110	+	0.0642110i	−0.674272	+	0.738483i	$0.735542\pi$
$678$			2.89016i			0.110996i
$679$		−	8.40233i		−	0.322452i
$680$	−4.23709	+	0.728845i	−0.162485	+	0.0279499i
$681$	33.2589	−	33.2589i	1.27448	−	1.27448i
$682$	−0.157923			−0.00604717
$683$	−42.2726			−1.61752			−0.808758	−	0.588141i	$-0.799860\pi$
$683$	−42.2726			−1.61752			−0.808758	+	0.588141i	$0.799860\pi$
$684$	39.3563	−	39.3563i	1.50483	−	1.50483i
$685$	−2.47960	+	3.50988i	−0.0947406	+	0.134106i
$686$		−	2.66184i		−	0.101629i
$687$		−	17.6840i		−	0.674685i
$688$	3.45865	+	3.45865i	0.131860	+	0.131860i
$689$		0			0
$690$	−2.40845	−	1.70148i	−0.0916880	−	0.0647741i
$691$	19.9284	−	19.9284i	0.758110	−	0.758110i	−0.217868	−	0.975978i	$-0.569910\pi$
$691$	19.9284	−	19.9284i	0.758110	−	0.758110i	0.975978	+	0.217868i	$0.0699102\pi$
$692$	−20.4236	−	20.4236i	−0.776388	−	0.776388i
$693$	−3.48768	−	3.48768i	−0.132486	−	0.132486i
$694$	−1.28500	−	1.28500i	−0.0487779	−	0.0487779i
$695$	−19.7291	+	27.9266i	−0.748367	+	1.05932i
$696$	−2.77507	−	2.77507i	−0.105189	−	0.105189i
$697$			7.69937i			0.291634i
$698$	2.44503	−	2.44503i	0.0925457	−	0.0925457i
$699$	79.6599			3.01302
$700$	−17.8362	+	6.32331i	−0.674146	+	0.238999i
$701$		−	13.2327i		−	0.499792i	−0.968273	−	0.249896i	$-0.919604\pi$
$701$		−	13.2327i		−	0.499792i	0.968273	−	0.249896i	$-0.0803964\pi$
$702$		0			0
$703$	16.8170	−	16.8170i	0.634264	−	0.634264i
$704$	−2.19638	−	2.19638i	−0.0827792	−	0.0827792i
$705$	8.02621	+	46.6598i	0.302284	+	1.75731i
$706$			0.564479i			0.0212444i
$707$	−6.77969			−0.254977
$708$			71.0568i			2.67048i
$709$	−5.07651	+	5.07651i	−0.190652	+	0.190652i	−0.795978	−	0.605326i	$-0.793043\pi$
$709$	−5.07651	+	5.07651i	−0.190652	+	0.190652i	0.605326	+	0.795978i	$0.293043\pi$
$710$	−3.09501	+	0.532390i	−0.116154	+	0.0199802i
$711$	27.6882			1.03839
$712$	−5.37361	+	5.37361i	−0.201385	+	0.201385i
$713$	9.18352			0.343925
$714$	−2.81106			−0.105201
$715$		0			0
$716$	13.0624			0.488165
$717$	−33.7485			−1.26036
$718$	−0.826517	+	0.826517i	−0.0308453	+	0.0308453i
$719$	−21.0560			−0.785257			−0.392628	−	0.919697i	$-0.628434\pi$
$719$	−21.0560			−0.785257			−0.392628	+	0.919697i	$0.628434\pi$
$720$	−31.5970	+	44.7256i	−1.17755	+	1.66683i
$721$	14.2246	−	14.2246i	0.529752	−	0.529752i
$722$			0.123234i			0.00458629i
$723$	−40.0532			−1.48959
$724$		−	31.3043i		−	1.16342i
$725$	11.3171	−	4.01216i	0.420307	−	0.149008i
$726$	3.14342	+	3.14342i	0.116663	+	0.116663i
$727$	−12.7325	+	12.7325i	−0.472221	+	0.472221i	−0.902633	−	0.430412i	$-0.858368\pi$
$727$	−12.7325	+	12.7325i	−0.472221	+	0.472221i	0.430412	+	0.902633i	$0.358368\pi$
$728$		0			0
$729$		−	18.0326i		−	0.667876i
$730$	−1.63127	−	1.15243i	−0.0603759	−	0.0426533i
$731$	−4.50792			−0.166731
$732$	30.6436	−	30.6436i	1.13262	−	1.13262i
$733$		−	21.9710i		−	0.811517i	−0.913980	−	0.405759i	$-0.867007\pi$
$733$		−	21.9710i		−	0.811517i	0.913980	−	0.405759i	$-0.132993\pi$
$734$	−0.618941	−	0.618941i	−0.0228455	−	0.0228455i
$735$	22.5253	−	3.87471i	0.830859	−	0.142921i
$736$	−3.62648	−	3.62648i	−0.133674	−	0.133674i
$737$	0.272792	+	0.272792i	0.0100484	+	0.0100484i
$738$	−1.28608	−	1.28608i	−0.0473413	−	0.0473413i
$739$	2.55220	−	2.55220i	0.0938841	−	0.0938841i	−0.658605	−	0.752489i	$-0.728853\pi$
$739$	2.55220	−	2.55220i	0.0938841	−	0.0938841i	0.752489	+	0.658605i	$0.228853\pi$
$740$	−13.6271	+	19.2893i	−0.500944	+	0.709088i
$741$		0			0
$742$	0.280323	+	0.280323i	0.0102910	+	0.0102910i
$743$			9.53234i			0.349708i	0.984594	+	0.174854i	$0.0559453\pi$
$743$			9.53234i			0.349708i	−0.984594	+	0.174854i	$0.944055\pi$
$744$			4.67072i			0.171237i
$745$	−7.41361	−	43.0985i	−0.271614	−	1.57901i
$746$	1.83352	−	1.83352i	0.0671300	−	0.0671300i
$747$	84.8562			3.10472
$748$	2.91731			0.106667
$749$	18.2665	−	18.2665i	0.667443	−	0.667443i
$750$	2.24424	+	4.00234i	0.0819481	+	0.146145i
$751$		−	3.05948i		−	0.111642i	−0.998441	−	0.0558210i	$-0.982222\pi$
$751$		−	3.05948i		−	0.111642i	0.998441	−	0.0558210i	$-0.0177776\pi$
$752$			27.0294i			0.985661i
$753$	28.9875	+	28.9875i	1.05636	+	1.05636i
$754$		0			0
$755$	−4.58412	−	26.6494i	−0.166833	−	0.969873i
$756$	−26.8658	+	26.8658i	−0.977101	+	0.977101i
$757$	−12.1746	−	12.1746i	−0.442495	−	0.442495i	0.450355	−	0.892850i	$-0.351297\pi$
$757$	−12.1746	−	12.1746i	−0.442495	−	0.442495i	−0.892850	+	0.450355i	$0.851297\pi$
$758$	2.60431	+	2.60431i	0.0945928	+	0.0945928i
$759$	2.84269	+	2.84269i	0.103183	+	0.103183i
$760$	−0.906880	−	5.27208i	−0.0328960	−	0.191239i
$761$	32.0020	+	32.0020i	1.16007	+	1.16007i	0.984459	+	0.175614i	$0.0561910\pi$
$761$	32.0020	+	32.0020i	1.16007	+	1.16007i	0.175614	+	0.984459i	$0.443809\pi$
$762$			4.07304i			0.147551i
$763$	−15.4423	+	15.4423i	−0.559047	+	0.559047i
$764$	25.7874			0.932954
$765$	−8.55578	−	49.7384i	−0.309335	−	1.79830i
$766$		−	0.960074i		−	0.0346889i
$767$		0			0
$768$	−31.4058	+	31.4058i	−1.13326	+	1.13326i
$769$	32.4213	+	32.4213i	1.16914	+	1.16914i	0.982411	+	0.186730i	$0.0597891\pi$
$769$	32.4213	+	32.4213i	1.16914	+	1.16914i	0.186730	+	0.982411i	$0.440211\pi$
$770$	−0.232537	+	0.0400000i	−0.00838006	+	0.00144150i
$771$			10.1982i			0.367278i
$772$	−34.6496			−1.24707
$773$		−	41.2156i		−	1.48242i	−0.671271	−	0.741212i	$-0.734251\pi$
$773$		−	41.2156i		−	1.48242i	0.671271	−	0.741212i	$-0.265749\pi$
$774$	0.752990	−	0.752990i	0.0270657	−	0.0270657i
$775$	−12.9004	−	6.14750i	−0.463395	−	0.220825i
$776$	−2.35869			−0.0846719
$777$	−21.9380	+	21.9380i	−0.787022	+	0.787022i
$778$	3.45987			0.124042
$779$	−9.58009			−0.343242
$780$		0			0
$781$	4.28142			0.153201
$782$	1.55155			0.0554834
$783$	17.0464	−	17.0464i	0.609190	−	0.609190i
$784$	13.0486			0.466022
$785$	2.14868	+	12.4912i	0.0766897	+	0.445830i
$786$	3.28087	−	3.28087i	0.117025	−	0.117025i
$787$		−	46.0209i		−	1.64047i	−0.572028	−	0.820234i	$-0.693843\pi$
$787$		−	46.0209i		−	1.64047i	0.572028	−	0.820234i	$-0.306157\pi$
$788$	28.2911			1.00783
$789$		−	44.5852i		−	1.58727i
$790$	0.764263	−	1.08182i	0.0271913	−	0.0384893i
$791$	−9.50922	−	9.50922i	−0.338109	−	0.338109i
$792$	−0.979054	+	0.979054i	−0.0347892	+	0.0347892i
$793$		0			0
$794$			2.00324i			0.0710925i
$795$	−6.06457	+	8.58442i	−0.215088	+	0.304458i
$796$	9.44692			0.334837
$797$	−31.8556	+	31.8556i	−1.12838	+	1.12838i	−0.137942	+	0.990440i	$0.544049\pi$
$797$	−31.8556	+	31.8556i	−1.12838	+	1.12838i	−0.990440	+	0.137942i	$0.955951\pi$
$798$		−	3.49772i		−	0.123818i
$799$	−17.6147	−	17.6147i	−0.623163	−	0.623163i
$800$	2.66664	+	7.52182i	0.0942800	+	0.265936i
$801$	−63.0799	−	63.0799i	−2.22882	−	2.22882i
$802$	−1.28255	−	1.28255i	−0.0452885	−	0.0452885i
$803$	1.92539	+	1.92539i	0.0679454	+	0.0679454i
$804$	4.01569	−	4.01569i	0.141622	−	0.141622i
$805$	13.5225	−	2.32608i	0.476606	−	0.0819836i
$806$		0			0
$807$	−68.1461	−	68.1461i	−2.39885	−	2.39885i
$808$			1.90318i			0.0669537i
$809$		−	16.8940i		−	0.593960i	−0.954884	−	0.296980i	$-0.904020\pi$
$809$		−	16.8940i		−	0.593960i	0.954884	−	0.296980i	$-0.0959795\pi$
$810$	2.88246	+	2.03635i	0.101279	+	0.0715499i
$811$	−13.2761	+	13.2761i	−0.466186	+	0.466186i	−0.900677	−	0.434490i	$-0.856929\pi$
$811$	−13.2761	+	13.2761i	−0.466186	+	0.466186i	0.434490	+	0.900677i	$0.356929\pi$
$812$	9.08899			0.318961
$813$	87.0206			3.05195
$814$	−0.208223	+	0.208223i	−0.00729820	+	0.00729820i
$815$	−24.2770	−	17.1508i	−0.850387	−	0.600766i
$816$		−	42.5484i		−	1.48949i
$817$		−	5.60907i		−	0.196236i
$818$	1.10319	+	1.10319i	0.0385720	+	0.0385720i
$819$		0			0
$820$	9.37572	−	1.61277i	0.327414	−	0.0563204i
$821$	−3.78395	+	3.78395i	−0.132061	+	0.132061i	−0.770047	−	0.637987i	$-0.779767\pi$
$821$	−3.78395	+	3.78395i	−0.132061	+	0.132061i	0.637987	+	0.770047i	$0.279767\pi$
$822$	0.557741	+	0.557741i	0.0194535	+	0.0194535i
$823$	17.1423	+	17.1423i	0.597544	+	0.597544i	0.939658	−	0.342114i	$-0.111143\pi$
$823$	17.1423	+	17.1423i	0.597544	+	0.597544i	−0.342114	+	0.939658i	$0.611143\pi$
$824$	−3.99310	−	3.99310i	−0.139106	−	0.139106i
$825$	−2.09030	−	5.89613i	−0.0727749	−	0.205277i
$826$	2.13820	+	2.13820i	0.0743976	+	0.0743976i
$827$			43.2856i			1.50519i	0.658484	+	0.752594i	$0.271198\pi$
$827$			43.2856i			1.50519i	−0.658484	+	0.752594i	$0.728802\pi$
$828$	28.3374	−	28.3374i	0.984793	−	0.984793i
$829$	1.24389			0.0432021			0.0216011	−	0.999767i	$-0.493124\pi$
$829$	1.24389			0.0432021			0.0216011	+	0.999767i	$0.493124\pi$
$830$	2.34224	−	3.31545i	0.0813004	−	0.115081i
$831$		−	38.9810i		−	1.35224i
$832$		0			0
$833$	−8.50362	+	8.50362i	−0.294633	+	0.294633i
$834$	4.43771	+	4.43771i	0.153665	+	0.153665i
$835$	16.7702	−	23.7383i	0.580356	−	0.821497i
$836$			3.62992i			0.125543i
$837$	−28.6909			−0.991702
$838$			3.60345i			0.124479i
$839$	0.836014	−	0.836014i	0.0288624	−	0.0288624i	−0.692528	−	0.721391i	$-0.743503\pi$
$839$	0.836014	−	0.836014i	0.0288624	−	0.0288624i	0.721391	+	0.692528i	$0.243503\pi$
$840$	1.18304	+	6.87753i	0.0408188	+	0.237297i
$841$	23.2330			0.801138
$842$	3.45973	−	3.45973i	0.119230	−	0.119230i
$843$	26.1348			0.900130
$844$	−22.9948			−0.791513
$845$		0			0
$846$	5.88463			0.202318
$847$	−20.6850			−0.710746
$848$	−4.24298	+	4.24298i	−0.145705	+	0.145705i
$849$	−45.7308			−1.56948
$850$	−2.17951	−	1.03862i	−0.0747567	−	0.0356243i
$851$	12.1086	−	12.1086i	0.415077	−	0.415077i
$852$		−	63.0255i		−	2.15922i
$853$	−29.9196			−1.02443			−0.512213	−	0.858858i	$-0.671174\pi$
$853$	−29.9196			−1.02443			−0.512213	+	0.858858i	$0.671174\pi$
$854$		−	1.84422i		−	0.0631080i
$855$	61.8880	−	10.6457i	2.11653	−	0.364075i
$856$	−5.12773	−	5.12773i	−0.175262	−	0.175262i
$857$	25.1427	−	25.1427i	0.858859	−	0.858859i	−0.132345	−	0.991204i	$-0.542251\pi$
$857$	25.1427	−	25.1427i	0.858859	−	0.858859i	0.991204	+	0.132345i	$0.0422507\pi$
$858$		0			0
$859$		−	27.3069i		−	0.931699i	−0.884864	−	0.465850i	$-0.845749\pi$
$859$		−	27.3069i		−	0.931699i	0.884864	−	0.465850i	$-0.154251\pi$
$860$	0.944263	+	5.48941i	0.0321991	+	0.187187i
$861$	12.4974			0.425910
$862$	1.83667	−	1.83667i	0.0625573	−	0.0625573i
$863$			1.25980i			0.0428841i	0.999770	+	0.0214421i	$0.00682575\pi$
$863$			1.25980i			0.0428841i	−0.999770	+	0.0214421i	$0.993174\pi$
$864$	11.3298	+	11.3298i	0.385446	+	0.385446i
$865$	−5.52448	−	32.1162i	−0.187838	−	1.09198i
$866$	−3.36939	−	3.36939i	−0.114497	−	0.114497i
$867$	−8.91660	−	8.91660i	−0.302824	−	0.302824i
$868$	−7.64884	−	7.64884i	−0.259619	−	0.259619i
$869$	−1.27687	+	1.27687i	−0.0433148	+	0.0433148i
$870$	−0.373613	−	2.17197i	−0.0126667	−	0.0736367i
$871$		0			0
$872$	4.33492	+	4.33492i	0.146799	+	0.146799i
$873$		−	27.6882i		−	0.937103i
$874$			1.93055i			0.0653018i
$875$	−20.5526	−	5.78453i	−0.694804	−	0.195553i
$876$	28.3430	−	28.3430i	0.957621	−	0.957621i
$877$	−30.9560			−1.04531			−0.522655	−	0.852544i	$-0.675059\pi$
$877$	−30.9560			−1.04531			−0.522655	+	0.852544i	$0.675059\pi$
$878$	4.31614			0.145663
$879$	47.4208	−	47.4208i	1.59946	−	1.59946i
$880$	−0.605442	−	3.51969i	−0.0204094	−	0.118649i
$881$			20.3144i			0.684409i	0.939625	+	0.342205i	$0.111174\pi$
$881$			20.3144i			0.684409i	−0.939625	+	0.342205i	$0.888826\pi$
$882$		−	2.84084i		−	0.0956562i
$883$	−3.19427	−	3.19427i	−0.107496	−	0.107496i	0.651313	−	0.758809i	$-0.274218\pi$
$883$	−3.19427	−	3.19427i	−0.107496	−	0.107496i	−0.758809	+	0.651313i	$0.774218\pi$
$884$		0			0
$885$	−46.2583	+	65.4789i	−1.55496	+	2.20105i
$886$	0.526495	−	0.526495i	0.0176880	−	0.0176880i
$887$	36.4242	+	36.4242i	1.22300	+	1.22300i	0.966559	+	0.256446i	$0.0825515\pi$
$887$	36.4242	+	36.4242i	1.22300	+	1.22300i	0.256446	+	0.966559i	$0.417448\pi$
$888$	6.15840	+	6.15840i	0.206662	+	0.206662i
$889$	−13.4012	−	13.4012i	−0.449461	−	0.449461i
$890$	−4.20578	+	0.723460i	−0.140978	+	0.0242504i
$891$	−3.40216	−	3.40216i	−0.113977	−	0.113977i
$892$		−	30.2258i		−	1.01204i
$893$	21.9175	−	21.9175i	0.733440	−	0.733440i
$894$	−8.02668			−0.268452
$895$	12.0370	+	8.50369i	0.402353	+	0.284247i
$896$			8.04201i			0.268665i
$897$		0			0
$898$	0.342198	−	0.342198i	0.0114193	−	0.0114193i
$899$	4.85321	+	4.85321i	0.161864	+	0.161864i
$900$	−58.7756	+	20.8372i	−1.95919	+	0.694573i
$901$		−	5.53019i		−	0.184237i
$902$	0.118618			0.00394954
$903$			7.31712i			0.243499i
$904$	−2.66941	+	2.66941i	−0.0887833	+	0.0887833i
$905$	20.3793	−	28.8469i	0.677429	−	0.958904i
$906$	−4.96320			−0.164891
$907$	9.20854	−	9.20854i	0.305764	−	0.305764i	−0.537500	−	0.843264i	$-0.680631\pi$
$907$	9.20854	−	9.20854i	0.305764	−	0.305764i	0.843264	+	0.537500i	$0.180631\pi$
$908$	30.5788			1.01479
$909$	−22.3411			−0.741008
$910$		0			0
$911$	−34.8310			−1.15400			−0.577001	−	0.816743i	$-0.695777\pi$
$911$	−34.8310			−1.15400			−0.577001	+	0.816743i	$0.695777\pi$
$912$	52.9417			1.75307
$913$	−3.91323	+	3.91323i	−0.129509	+	0.129509i
$914$	3.12600			0.103399
$915$	48.1873	−	8.28895i	1.59302	−	0.274024i
$916$	8.12947	−	8.12947i	0.268605	−	0.268605i
$917$			21.5895i			0.712949i
$918$	−4.84732			−0.159985
$919$			31.7568i			1.04756i	0.851854	+	0.523779i	$0.175478\pi$
$919$			31.7568i			1.04756i	−0.851854	+	0.523779i	$0.824522\pi$
$920$	−0.652973	−	3.79601i	−0.0215279	−	0.125151i
$921$	20.6920	+	20.6920i	0.681826	+	0.681826i
$922$	−3.88219	+	3.88219i	−0.127853	+	0.127853i
$923$		0			0
$924$		−	4.73529i		−	0.155780i
$925$	−25.1148	+	8.90373i	−0.825770	+	0.292753i
$926$	−0.677457			−0.0222626
$927$	46.8743	−	46.8743i	1.53955	−	1.53955i
$928$		−	3.83297i		−	0.125824i
$929$	7.17522	+	7.17522i	0.235411	+	0.235411i	0.814947	−	0.579536i	$-0.196766\pi$
$929$	7.17522	+	7.17522i	0.235411	+	0.235411i	−0.579536	+	0.814947i	$0.696766\pi$
$930$	−1.51341	+	2.14224i	−0.0496266	+	0.0702467i
$931$	−10.5808	−	10.5808i	−0.346772	−	0.346772i
$932$	36.6203	+	36.6203i	1.19954	+	1.19954i
$933$	−9.24062	−	9.24062i	−0.302524	−	0.302524i
$934$	0.625459	−	0.625459i	0.0204656	−	0.0204656i
$935$	2.68830	+	1.89918i	0.0879167	+	0.0621098i
$936$		0			0
$937$	7.87778	+	7.87778i	0.257356	+	0.257356i	0.823978	−	0.566622i	$-0.191750\pi$
$937$	7.87778	+	7.87778i	0.257356	+	0.257356i	−0.566622	+	0.823978i	$0.691750\pi$
$938$		−	0.241676i		−	0.00789099i
$939$			23.9380i			0.781188i
$940$	−17.7602	+	25.1396i	−0.579273	+	0.819964i
$941$	−4.01889	+	4.01889i	−0.131012	+	0.131012i	−0.769572	−	0.638560i	$-0.779530\pi$
$941$	−4.01889	+	4.01889i	−0.131012	+	0.131012i	0.638560	+	0.769572i	$0.279530\pi$
$942$	2.32637			0.0757971
$943$	−6.89787			−0.224626
$944$	−32.3639	+	32.3639i	−1.05336	+	1.05336i
$945$	−42.2467	+	7.26708i	−1.37428	+	0.236398i
$946$			0.0694498i			0.00225801i
$947$		−	46.1032i		−	1.49815i	−0.662484	−	0.749076i	$-0.730498\pi$
$947$		−	46.1032i		−	1.49815i	0.662484	−	0.749076i	$-0.269502\pi$
$948$	18.7964	+	18.7964i	0.610478	+	0.610478i
$949$		0			0
$950$	1.29232	−	2.71190i	0.0419284	−	0.0879857i
$951$	−39.9441	+	39.9441i	−1.29528	+	1.29528i
$952$	−2.59636	−	2.59636i	−0.0841485	−	0.0841485i
$953$	−24.8080	−	24.8080i	−0.803610	−	0.803610i	0.180048	−	0.983658i	$-0.442375\pi$
$953$	−24.8080	−	24.8080i	−0.803610	−	0.803610i	−0.983658	+	0.180048i	$0.942375\pi$
$954$	0.923749	+	0.923749i	0.0299075	+	0.0299075i
$955$	23.7631	+	16.7877i	0.768954	+	0.543237i
$956$	−15.5145	−	15.5145i	−0.501774	−	0.501774i
$957$			3.00455i			0.0971234i
$958$	0.814899	−	0.814899i	0.0263282	−	0.0263282i
$959$	−3.67017			−0.118516
$960$	−50.8426	+	8.74571i	−1.64094	+	0.282267i
$961$			22.8316i			0.736502i
$962$		0			0
$963$	60.1935	−	60.1935i	1.93971	−	1.93971i
$964$	−18.4128	−	18.4128i	−0.593036	−	0.593036i
$965$	−31.9296	−	22.5571i	−1.02785	−	0.726138i
$966$		−	2.51844i		−	0.0810294i
$967$	−58.4700			−1.88027			−0.940135	−	0.340803i	$-0.889301\pi$
$967$	−58.4700			−1.88027			−0.940135	+	0.340803i	$0.889301\pi$
$968$			5.80666i			0.186633i
$969$	−34.5014	+	34.5014i	−1.10834	+	1.10834i
$970$	−1.08182	−	0.764263i	−0.0347351	−	0.0245390i
$971$	−20.3886			−0.654303			−0.327151	−	0.944972i	$-0.606089\pi$
$971$	−20.3886			−0.654303			−0.327151	+	0.944972i	$0.606089\pi$
$972$	−7.87791	+	7.87791i	−0.252684	+	0.252684i
$973$	−29.2020			−0.936172
$974$	1.11822			0.0358300
$975$		0			0
$976$	27.9142			0.893513
$977$	−14.0603			−0.449830			−0.224915	−	0.974378i	$-0.572210\pi$
$977$	−14.0603			−0.449830			−0.224915	+	0.974378i	$0.572210\pi$
$978$	−3.85776	+	3.85776i	−0.123358	+	0.123358i
$979$	5.81798			0.185944
$980$	12.1363	+	8.57385i	0.387681	+	0.273882i
$981$	−50.8868	+	50.8868i	−1.62469	+	1.62469i
$982$		−	0.612447i		−	0.0195440i
$983$	1.48069			0.0472266			0.0236133	−	0.999721i	$-0.492483\pi$
$983$	1.48069			0.0472266			0.0236133	+	0.999721i	$0.492483\pi$
$984$		−	3.50824i		−	0.111839i
$985$	26.0702	+	18.4176i	0.830666	+	0.586834i
$986$	0.819949	+	0.819949i	0.0261125	+	0.0261125i
$987$	−28.5917	+	28.5917i	−0.910084	+	0.910084i
$988$		0			0
$989$		−	4.03865i		−	0.128422i
$990$	−0.766280	+	0.131812i	−0.0243540	+	0.00418926i
$991$	8.59028			0.272879			0.136440	−	0.990648i	$-0.456434\pi$
$991$	8.59028			0.272879			0.136440	+	0.990648i	$0.456434\pi$
$992$	−3.22564	+	3.22564i	−0.102414	+	0.102414i
$993$		−	7.16953i		−	0.227518i
$994$	−1.89653	−	1.89653i	−0.0601542	−	0.0601542i
$995$	8.70533	+	6.14999i	0.275978	+	0.194968i
$996$	57.6054	+	57.6054i	1.82530	+	1.82530i
$997$	−8.77426	−	8.77426i	−0.277884	−	0.277884i	0.554380	−	0.832264i	$-0.312955\pi$
$997$	−8.77426	−	8.77426i	−0.277884	−	0.277884i	−0.832264	+	0.554380i	$0.812955\pi$
$998$	1.47346	+	1.47346i	0.0466416	+	0.0466416i
$999$	−37.8293	+	37.8293i	−1.19686	+	1.19686i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.k.b.577.2		8
5.3	odd	4		845.2.f.b.408.3		8
13.2	odd	12		845.2.t.c.657.2		16
13.3	even	3		845.2.o.c.357.3		16
13.4	even	6		845.2.o.d.587.2		16
13.5	odd	4		65.2.f.b.47.3	yes	8
13.6	odd	12		845.2.t.c.427.3		16
13.7	odd	12		845.2.t.d.427.2		16
13.8	odd	4		845.2.f.b.437.2		8
13.9	even	3		845.2.o.c.587.3		16
13.10	even	6		845.2.o.d.357.2		16
13.11	odd	12		845.2.t.d.657.3		16
13.12	even	2		65.2.k.b.57.3	yes	8
39.5	even	4		585.2.n.e.307.2		8
39.38	odd	2		585.2.w.e.577.2		8
52.31	even	4		1040.2.cd.n.177.4		8
52.51	odd	2		1040.2.bg.n.577.4		8
65.3	odd	12		845.2.t.d.188.2		16
65.8	even	4	inner	845.2.k.b.268.2		8
65.12	odd	4		325.2.f.b.18.3		8
65.18	even	4		65.2.k.b.8.3	yes	8
65.23	odd	12		845.2.t.c.188.3		16
65.28	even	12		845.2.o.d.488.2		16
65.33	even	12		845.2.o.c.258.3		16
65.38	odd	4		65.2.f.b.18.2	✓	8
65.43	odd	12		845.2.t.c.418.2		16
65.44	odd	4		325.2.f.b.307.2		8
65.48	odd	12		845.2.t.d.418.3		16
65.57	even	4		325.2.k.b.268.2		8
65.58	even	12		845.2.o.d.258.2		16
65.63	even	12		845.2.o.c.488.3		16
65.64	even	2		325.2.k.b.57.2		8
195.38	even	4		585.2.n.e.343.3		8
195.83	odd	4		585.2.w.e.73.2		8
260.83	odd	4		1040.2.bg.n.593.4		8
260.103	even	4		1040.2.cd.n.993.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.f.b.18.2	✓	8	65.38	odd	4
65.2.f.b.47.3	yes	8	13.5	odd	4
65.2.k.b.8.3	yes	8	65.18	even	4
65.2.k.b.57.3	yes	8	13.12	even	2
325.2.f.b.18.3		8	65.12	odd	4
325.2.f.b.307.2		8	65.44	odd	4
325.2.k.b.57.2		8	65.64	even	2
325.2.k.b.268.2		8	65.57	even	4
585.2.n.e.307.2		8	39.5	even	4
585.2.n.e.343.3		8	195.38	even	4
585.2.w.e.73.2		8	195.83	odd	4
585.2.w.e.577.2		8	39.38	odd	2
845.2.f.b.408.3		8	5.3	odd	4
845.2.f.b.437.2		8	13.8	odd	4
845.2.k.b.268.2		8	65.8	even	4	inner
845.2.k.b.577.2		8	1.1	even	1	trivial
845.2.o.c.258.3		16	65.33	even	12
845.2.o.c.357.3		16	13.3	even	3
845.2.o.c.488.3		16	65.63	even	12
845.2.o.c.587.3		16	13.9	even	3
845.2.o.d.258.2		16	65.58	even	12
845.2.o.d.357.2		16	13.10	even	6
845.2.o.d.488.2		16	65.28	even	12
845.2.o.d.587.2		16	13.4	even	6
845.2.t.c.188.3		16	65.23	odd	12
845.2.t.c.418.2		16	65.43	odd	12
845.2.t.c.427.3		16	13.6	odd	12
845.2.t.c.657.2		16	13.2	odd	12
845.2.t.d.188.2		16	65.3	odd	12
845.2.t.d.418.3		16	65.48	odd	12
845.2.t.d.427.2		16	13.7	odd	12
845.2.t.d.657.3		16	13.11	odd	12
1040.2.bg.n.577.4		8	52.51	odd	2
1040.2.bg.n.593.4		8	260.83	odd	4
1040.2.cd.n.177.4		8	52.31	even	4
1040.2.cd.n.993.4		8	260.103	even	4

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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.134632 q^{2} +(-2.15558 + 2.15558i) q^{3} -1.98187 q^{4} +(-1.82630 - 1.29021i) q^{5} +(-0.290209 + 0.290209i) q^{6} -1.90970i q^{7} -0.536087 q^{8} -6.29303i q^{9} +O(q^{10})\)	\(q+0.134632 q^{2} +(-2.15558 + 2.15558i) q^{3} -1.98187 q^{4} +(-1.82630 - 1.29021i) q^{5} +(-0.290209 + 0.290209i) q^{6} -1.90970i q^{7} -0.536087 q^{8} -6.29303i q^{9} +(-0.245878 - 0.173703i) q^{10} +(0.290209 + 0.290209i) q^{11} +(4.27208 - 4.27208i) q^{12} -0.257106i q^{14} +(6.71787 - 1.15558i) q^{15} +3.89157 q^{16} +(-2.53609 + 2.53609i) q^{17} -0.847242i q^{18} +(-3.15558 - 3.15558i) q^{19} +(3.61949 + 2.55703i) q^{20} +(4.11651 + 4.11651i) q^{21} +(0.0390714 + 0.0390714i) q^{22} +(-2.27208 - 2.27208i) q^{23} +(1.15558 - 1.15558i) q^{24} +(1.67072 + 4.71261i) q^{25} +(7.09838 + 7.09838i) q^{27} +3.78478i q^{28} -2.40146i q^{29} +(0.904440 - 0.155578i) q^{30} +(-2.02095 + 2.02095i) q^{31} +1.59610 q^{32} -1.25114 q^{33} +(-0.341438 + 0.341438i) q^{34} +(-2.46391 + 3.48768i) q^{35} +12.4720i q^{36} +5.32928i q^{37} +(-0.424841 - 0.424841i) q^{38} +(0.979054 + 0.691665i) q^{40} +(1.51796 - 1.51796i) q^{41} +(0.554213 + 0.554213i) q^{42} +(0.888754 + 0.888754i) q^{43} +(-0.575159 - 0.575159i) q^{44} +(-8.11933 + 11.4929i) q^{45} +(-0.305895 - 0.305895i) q^{46} +6.94562i q^{47} +(-8.38859 + 8.38859i) q^{48} +3.35305 q^{49} +(0.224932 + 0.634468i) q^{50} -10.9335i q^{51} +(-1.09030 + 1.09030i) q^{53} +(0.955668 + 0.955668i) q^{54} +(-0.155578 - 0.904440i) q^{55} +1.02377i q^{56} +13.6042 q^{57} -0.323312i q^{58} +(-8.31642 + 8.31642i) q^{59} +(-13.3140 + 2.29021i) q^{60} +7.17300 q^{61} +(-0.272084 + 0.272084i) q^{62} -12.0178 q^{63} -7.56826 q^{64} -0.168443 q^{66} +0.939983 q^{67} +(5.02621 - 5.02621i) q^{68} +9.79531 q^{69} +(-0.331721 + 0.469553i) q^{70} +(7.37643 - 7.37643i) q^{71} +3.37361i q^{72} +6.63447 q^{73} +0.717491i q^{74} +(-13.7598 - 6.55703i) q^{75} +(6.25396 + 6.25396i) q^{76} +(0.554213 - 0.554213i) q^{77} +4.39982i q^{79} +(-7.10717 - 5.02095i) q^{80} -11.7231 q^{81} +(0.204366 - 0.204366i) q^{82} +13.4842i q^{83} +(-8.15840 - 8.15840i) q^{84} +(7.90373 - 1.35956i) q^{85} +(0.119655 + 0.119655i) q^{86} +(5.17652 + 5.17652i) q^{87} +(-0.155578 - 0.155578i) q^{88} +(10.0238 - 10.0238i) q^{89} +(-1.09312 + 1.54732i) q^{90} +(4.50298 + 4.50298i) q^{92} -8.71261i q^{93} +0.935102i q^{94} +(1.69166 + 9.83438i) q^{95} +(-3.44053 + 3.44053i) q^{96} +4.39982 q^{97} +0.451427 q^{98} +(1.82630 - 1.82630i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - 6 q^{3} + 8 q^{4} - 2 q^{5} + 6 q^{6}+O(q^{10}) \) 8 * q + 4 * q^2 - 6 * q^3 + 8 * q^4 - 2 * q^5 + 6 * q^6	\( 8 q + 4 q^{2} - 6 q^{3} + 8 q^{4} - 2 q^{5} + 6 q^{6} - 6 q^{10} - 6 q^{11} + 2 q^{12} + 2 q^{15} - 8 q^{16} - 16 q^{17} - 14 q^{19} + 22 q^{20} + 12 q^{21} + 10 q^{22} + 14 q^{23} - 2 q^{24} + 12 q^{25} + 12 q^{27} + 14 q^{30} - 2 q^{31} + 4 q^{32} + 8 q^{33} - 24 q^{35} + 2 q^{38} + 22 q^{40} - 16 q^{41} + 24 q^{42} + 6 q^{43} - 10 q^{44} - 6 q^{45} - 2 q^{46} - 14 q^{48} - 24 q^{49} + 20 q^{50} - 24 q^{53} + 20 q^{54} + 10 q^{55} + 40 q^{57} - 22 q^{59} - 46 q^{60} + 20 q^{61} + 30 q^{62} - 16 q^{63} - 48 q^{64} - 36 q^{66} + 12 q^{67} + 4 q^{68} - 4 q^{69} - 20 q^{70} + 10 q^{71} + 4 q^{73} - 30 q^{75} - 6 q^{76} + 24 q^{77} - 2 q^{80} - 20 q^{81} - 20 q^{82} - 16 q^{84} + 20 q^{85} + 46 q^{86} + 16 q^{87} + 10 q^{88} + 28 q^{89} + 14 q^{90} + 50 q^{92} - 2 q^{95} - 30 q^{96} - 12 q^{97} - 92 q^{98} + 2 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 - 6 * q^3 + 8 * q^4 - 2 * q^5 + 6 * q^6 - 6 * q^10 - 6 * q^11 + 2 * q^12 + 2 * q^15 - 8 * q^16 - 16 * q^17 - 14 * q^19 + 22 * q^20 + 12 * q^21 + 10 * q^22 + 14 * q^23 - 2 * q^24 + 12 * q^25 + 12 * q^27 + 14 * q^30 - 2 * q^31 + 4 * q^32 + 8 * q^33 - 24 * q^35 + 2 * q^38 + 22 * q^40 - 16 * q^41 + 24 * q^42 + 6 * q^43 - 10 * q^44 - 6 * q^45 - 2 * q^46 - 14 * q^48 - 24 * q^49 + 20 * q^50 - 24 * q^53 + 20 * q^54 + 10 * q^55 + 40 * q^57 - 22 * q^59 - 46 * q^60 + 20 * q^61 + 30 * q^62 - 16 * q^63 - 48 * q^64 - 36 * q^66 + 12 * q^67 + 4 * q^68 - 4 * q^69 - 20 * q^70 + 10 * q^71 + 4 * q^73 - 30 * q^75 - 6 * q^76 + 24 * q^77 - 2 * q^80 - 20 * q^81 - 20 * q^82 - 16 * q^84 + 20 * q^85 + 46 * q^86 + 16 * q^87 + 10 * q^88 + 28 * q^89 + 14 * q^90 + 50 * q^92 - 2 * q^95 - 30 * q^96 - 12 * q^97 - 92 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

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