LMFDB - Embedded newform 425.2.j.d.174.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(149,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("425.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.j (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{10} + 119x^{8} + 364x^{6} + 519x^{4} + 278x^{2} + 1 $ x^12 + 18x^10 + 119x^8 + 364x^6 + 519x^4 + 278*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			174.1
Root			$-2.08389i$ of defining polynomial
Character	$\chi$	$=$	425.174
Dual form			425.2.j.d.149.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.08389 q^{2} +(-1.31060 - 1.31060i) q^{3} +2.34261 q^{4} +(2.73116 + 2.73116i) q^{6} +(-0.971529 + 0.971529i) q^{7} -0.713960 q^{8} +0.435362i q^{9} +O(q^{10})$	\(q-2.08389 q^{2} +(-1.31060 - 1.31060i) q^{3} +2.34261 q^{4} +(2.73116 + 2.73116i) q^{6} +(-0.971529 + 0.971529i) q^{7} -0.713960 q^{8} +0.435362i q^{9} +(-0.384742 - 0.384742i) q^{11} +(-3.07023 - 3.07023i) q^{12} -5.39918i q^{13} +(2.02456 - 2.02456i) q^{14} -3.19740 q^{16} +(3.38083 + 2.36008i) q^{17} -0.907247i q^{18} -4.86186i q^{19} +2.54658 q^{21} +(0.801760 + 0.801760i) q^{22} +(-1.26379 + 1.26379i) q^{23} +(0.935718 + 0.935718i) q^{24} +11.2513i q^{26} +(-3.36122 + 3.36122i) q^{27} +(-2.27591 + 2.27591i) q^{28} +(-1.29694 + 1.29694i) q^{29} +(-5.73710 + 5.73710i) q^{31} +8.09096 q^{32} +1.00849i q^{33} +(-7.04529 - 4.91815i) q^{34} +1.01988i q^{36} +(-4.22194 - 4.22194i) q^{37} +10.1316i q^{38} +(-7.07618 + 7.07618i) q^{39} +(-2.70269 - 2.70269i) q^{41} -5.30680 q^{42} -3.66628 q^{43} +(-0.901299 - 0.901299i) q^{44} +(2.63360 - 2.63360i) q^{46} +9.07290i q^{47} +(4.19053 + 4.19053i) q^{48} +5.11226i q^{49} +(-1.33781 - 7.52406i) q^{51} -12.6482i q^{52} -10.5471 q^{53} +(7.00443 - 7.00443i) q^{54} +(0.693633 - 0.693633i) q^{56} +(-6.37197 + 6.37197i) q^{57} +(2.70269 - 2.70269i) q^{58} +6.52808i q^{59} +(-10.9360 - 10.9360i) q^{61} +(11.9555 - 11.9555i) q^{62} +(-0.422967 - 0.422967i) q^{63} -10.4659 q^{64} -2.10158i q^{66} -5.68704i q^{67} +(7.91997 + 5.52874i) q^{68} +3.31265 q^{69} +(0.749500 - 0.749500i) q^{71} -0.310831i q^{72} +(10.3821 + 10.3821i) q^{73} +(8.79807 + 8.79807i) q^{74} -11.3894i q^{76} +0.747575 q^{77} +(14.7460 - 14.7460i) q^{78} +(0.878559 + 0.878559i) q^{79} +10.1165 q^{81} +(5.63211 + 5.63211i) q^{82} -13.5038 q^{83} +5.96564 q^{84} +7.64014 q^{86} +3.39955 q^{87} +(0.274690 + 0.274690i) q^{88} +0.989860 q^{89} +(5.24546 + 5.24546i) q^{91} +(-2.96056 + 2.96056i) q^{92} +15.0381 q^{93} -18.9070i q^{94} +(-10.6040 - 10.6040i) q^{96} +(-8.05428 - 8.05428i) q^{97} -10.6534i q^{98} +(0.167502 - 0.167502i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{2} + 2 q^{3} + 12 q^{4} + 6 q^{6} + 12 q^{8}+O(q^{10}) $ 12 * q + 4 * q^2 + 2 * q^3 + 12 * q^4 + 6 * q^6 + 12 * q^8	$ 12 q + 4 q^{2} + 2 q^{3} + 12 q^{4} + 6 q^{6} + 12 q^{8} - 4 q^{11} - 4 q^{12} - 14 q^{14} + 4 q^{16} - 10 q^{17} + 8 q^{21} + 10 q^{22} + 12 q^{23} + 8 q^{24} - 22 q^{27} - 34 q^{28} + 6 q^{29} - 6 q^{31} + 48 q^{32} - 30 q^{34} + 18 q^{37} - 16 q^{39} + 6 q^{41} - 56 q^{42} + 16 q^{43} - 32 q^{44} + 30 q^{46} + 10 q^{48} - 40 q^{51} - 48 q^{53} - 16 q^{54} - 56 q^{56} + 18 q^{57} - 6 q^{58} - 8 q^{61} + 22 q^{62} + 30 q^{63} + 44 q^{64} - 18 q^{68} + 72 q^{69} - 20 q^{71} + 18 q^{73} + 26 q^{74} - 24 q^{77} + 38 q^{78} + 14 q^{79} - 8 q^{81} - 10 q^{82} - 52 q^{83} - 36 q^{84} + 84 q^{86} + 48 q^{87} - 66 q^{88} + 24 q^{89} + 12 q^{91} + 32 q^{92} + 60 q^{93} + 22 q^{96} - 52 q^{97} - 30 q^{99}+O(q^{100}) $ 12 * q + 4 * q^2 + 2 * q^3 + 12 * q^4 + 6 * q^6 + 12 * q^8 - 4 * q^11 - 4 * q^12 - 14 * q^14 + 4 * q^16 - 10 * q^17 + 8 * q^21 + 10 * q^22 + 12 * q^23 + 8 * q^24 - 22 * q^27 - 34 * q^28 + 6 * q^29 - 6 * q^31 + 48 * q^32 - 30 * q^34 + 18 * q^37 - 16 * q^39 + 6 * q^41 - 56 * q^42 + 16 * q^43 - 32 * q^44 + 30 * q^46 + 10 * q^48 - 40 * q^51 - 48 * q^53 - 16 * q^54 - 56 * q^56 + 18 * q^57 - 6 * q^58 - 8 * q^61 + 22 * q^62 + 30 * q^63 + 44 * q^64 - 18 * q^68 + 72 * q^69 - 20 * q^71 + 18 * q^73 + 26 * q^74 - 24 * q^77 + 38 * q^78 + 14 * q^79 - 8 * q^81 - 10 * q^82 - 52 * q^83 - 36 * q^84 + 84 * q^86 + 48 * q^87 - 66 * q^88 + 24 * q^89 + 12 * q^91 + 32 * q^92 + 60 * q^93 + 22 * q^96 - 52 * q^97 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−2.08389			−1.47353			−0.736767	−	0.676146i	$-0.763649\pi$
$2$	−2.08389			−1.47353			−0.736767	+	0.676146i	$0.763649\pi$
$3$	−1.31060	−	1.31060i	−0.756677	−	0.756677i	0.219039	−	0.975716i	$-0.429708\pi$
$3$	−1.31060	−	1.31060i	−0.756677	−	0.756677i	−0.975716	+	0.219039i	$0.929708\pi$
$4$	2.34261			1.17130
$5$		0			0
$5$		0			0
$6$	2.73116	+	2.73116i	1.11499	+	1.11499i
$7$	−0.971529	+	0.971529i	−0.367204	+	0.367204i	−0.866456	−	0.499253i	$-0.833608\pi$
$7$	−0.971529	+	0.971529i	−0.367204	+	0.367204i	0.499253	+	0.866456i	$0.333608\pi$
$8$	−0.713960			−0.252423
$9$			0.435362i			0.145121i
$10$		0			0
$11$	−0.384742	−	0.384742i	−0.116004	−	0.116004i	0.646722	−	0.762726i	$-0.276139\pi$
$11$	−0.384742	−	0.384742i	−0.116004	−	0.116004i	−0.762726	+	0.646722i	$0.776139\pi$
$12$	−3.07023	−	3.07023i	−0.886299	−	0.886299i
$13$		−	5.39918i		−	1.49746i	−0.662874	−	0.748731i	$-0.730663\pi$
$13$		−	5.39918i		−	1.49746i	0.662874	−	0.748731i	$-0.269337\pi$
$14$	2.02456	−	2.02456i	0.541087	−	0.541087i
$15$		0			0
$16$	−3.19740			−0.799351
$17$	3.38083	+	2.36008i	0.819973	+	0.572403i
$17$	3.38083	+	2.36008i	0.819973	+	0.572403i
$18$		−	0.907247i		−	0.213840i
$19$		−	4.86186i		−	1.11539i	−0.830047	−	0.557694i	$-0.811686\pi$
$19$		−	4.86186i		−	1.11539i	0.830047	−	0.557694i	$-0.188314\pi$
$20$		0			0
$21$	2.54658			0.555709
$22$	0.801760	+	0.801760i	0.170936	+	0.170936i
$23$	−1.26379	+	1.26379i	−0.263518	+	0.263518i	−0.826482	−	0.562963i	$-0.809661\pi$
$23$	−1.26379	+	1.26379i	−0.263518	+	0.263518i	0.562963	+	0.826482i	$0.309661\pi$
$24$	0.935718	+	0.935718i	0.191003	+	0.191003i
$25$		0			0
$26$			11.2513i			2.20656i
$27$	−3.36122	+	3.36122i	−0.646868	+	0.646868i
$28$	−2.27591	+	2.27591i	−0.430107	+	0.430107i
$29$	−1.29694	+	1.29694i	−0.240836	+	0.240836i	−0.817196	−	0.576360i	$-0.804473\pi$
$29$	−1.29694	+	1.29694i	−0.240836	+	0.240836i	0.576360	+	0.817196i	$0.304473\pi$
$30$		0			0
$31$	−5.73710	+	5.73710i	−1.03041	+	1.03041i	−0.0308916	+	0.999523i	$0.509835\pi$
$31$	−5.73710	+	5.73710i	−1.03041	+	1.03041i	−0.999523	+	0.0308916i	$0.990165\pi$
$32$	8.09096			1.43029
$33$			1.00849i			0.175555i
$34$	−7.04529	−	4.91815i	−1.20826	−	0.843455i
$35$		0			0
$36$			1.01988i			0.169980i
$37$	−4.22194	−	4.22194i	−0.694083	−	0.694083i	0.269045	−	0.963128i	$-0.413292\pi$
$37$	−4.22194	−	4.22194i	−0.694083	−	0.694083i	−0.963128	+	0.269045i	$0.913292\pi$
$38$			10.1316i			1.64356i
$39$	−7.07618	+	7.07618i	−1.13310	+	1.13310i
$40$		0			0
$41$	−2.70269	−	2.70269i	−0.422089	−	0.422089i	0.463834	−	0.885922i	$-0.346474\pi$
$41$	−2.70269	−	2.70269i	−0.422089	−	0.422089i	−0.885922	+	0.463834i	$0.846474\pi$
$42$	−5.30680			−0.818857
$43$	−3.66628			−0.559103			−0.279551	−	0.960131i	$-0.590186\pi$
$43$	−3.66628			−0.559103			−0.279551	+	0.960131i	$0.590186\pi$
$44$	−0.901299	−	0.901299i	−0.135876	−	0.135876i
$45$		0			0
$46$	2.63360	−	2.63360i	0.388303	−	0.388303i
$47$			9.07290i			1.32342i	0.749760	+	0.661709i	$0.230169\pi$
$47$			9.07290i			1.32342i	−0.749760	+	0.661709i	$0.769831\pi$
$48$	4.19053	+	4.19053i	0.604850	+	0.604850i
$49$			5.11226i			0.730323i
$50$		0			0
$51$	−1.33781	−	7.52406i	−0.187330	−	1.05358i
$52$		−	12.6482i		−	1.75398i
$53$	−10.5471			−1.44875			−0.724376	−	0.689405i	$-0.757872\pi$
$53$	−10.5471			−1.44875			−0.724376	+	0.689405i	$0.757872\pi$
$54$	7.00443	−	7.00443i	0.953182	−	0.953182i
$55$		0			0
$56$	0.693633	−	0.693633i	0.0926906	−	0.0926906i
$57$	−6.37197	+	6.37197i	−0.843988	+	0.843988i
$58$	2.70269	−	2.70269i	0.354880	−	0.354880i
$59$			6.52808i			0.849884i	0.905221	+	0.424942i	$0.139705\pi$
$59$			6.52808i			0.849884i	−0.905221	+	0.424942i	$0.860295\pi$
$60$		0			0
$61$	−10.9360	−	10.9360i	−1.40021	−	1.40021i	−0.799355	−	0.600859i	$-0.794825\pi$
$61$	−10.9360	−	10.9360i	−1.40021	−	1.40021i	−0.600859	−	0.799355i	$-0.705175\pi$
$62$	11.9555	−	11.9555i	1.51835	−	1.51835i
$63$	−0.422967	−	0.422967i	−0.0532888	−	0.0532888i
$64$	−10.4659			−1.30824
$65$		0			0
$66$		−	2.10158i		−	0.258686i
$67$		−	5.68704i		−	0.694782i	−0.937720	−	0.347391i	$-0.887068\pi$
$67$		−	5.68704i		−	0.694782i	0.937720	−	0.347391i	$-0.112932\pi$
$68$	7.91997	+	5.52874i	0.960437	+	0.670458i
$69$	3.31265			0.398797
$70$		0			0
$71$	0.749500	−	0.749500i	0.0889492	−	0.0889492i	−0.661232	−	0.750181i	$-0.729966\pi$
$71$	0.749500	−	0.749500i	0.0889492	−	0.0889492i	0.750181	+	0.661232i	$0.229966\pi$
$72$		−	0.310831i		−	0.0366317i
$73$	10.3821	+	10.3821i	1.21513	+	1.21513i	0.969316	+	0.245819i	$0.0790567\pi$
$73$	10.3821	+	10.3821i	1.21513	+	1.21513i	0.245819	+	0.969316i	$0.420943\pi$
$74$	8.79807	+	8.79807i	1.02275	+	1.02275i
$75$		0			0
$76$		−	11.3894i		−	1.30646i
$77$	0.747575			0.0851941
$78$	14.7460	−	14.7460i	1.66966	−	1.66966i
$79$	0.878559	+	0.878559i	0.0988456	+	0.0988456i	0.754800	−	0.655955i	$-0.227734\pi$
$79$	0.878559	+	0.878559i	0.0988456	+	0.0988456i	−0.655955	+	0.754800i	$0.727734\pi$
$80$		0			0
$81$	10.1165			1.12406
$82$	5.63211	+	5.63211i	0.621962	+	0.621962i
$83$	−13.5038			−1.48224			−0.741119	−	0.671374i	$-0.765704\pi$
$83$	−13.5038			−1.48224			−0.741119	+	0.671374i	$0.765704\pi$
$84$	5.96564			0.650904
$85$		0			0
$86$	7.64014			0.823858
$87$	3.39955			0.364470
$88$	0.274690	+	0.274690i	0.0292820	+	0.0292820i
$89$	0.989860			0.104925			0.0524625	−	0.998623i	$-0.483293\pi$
$89$	0.989860			0.104925			0.0524625	+	0.998623i	$0.483293\pi$
$90$		0			0
$91$	5.24546	+	5.24546i	0.549873	+	0.549873i
$92$	−2.96056	+	2.96056i	−0.308660	+	0.308660i
$93$	15.0381			1.55938
$94$		−	18.9070i		−	1.95010i
$95$		0			0
$96$	−10.6040	−	10.6040i	−1.08227	−	1.08227i
$97$	−8.05428	−	8.05428i	−0.817788	−	0.817788i	0.167999	−	0.985787i	$-0.446269\pi$
$97$	−8.05428	−	8.05428i	−0.817788	−	0.817788i	−0.985787	+	0.167999i	$0.946269\pi$
$98$		−	10.6534i		−	1.07616i
$99$	0.167502	−	0.167502i	0.0168346	−	0.0168346i
$100$		0			0
$101$	6.02268			0.599279			0.299639	−	0.954053i	$-0.403134\pi$
$101$	6.02268			0.599279			0.299639	+	0.954053i	$0.403134\pi$
$102$	2.78785	+	15.6793i	0.276038	+	1.55248i
$103$		−	18.1789i		−	1.79122i	−0.444836	−	0.895612i	$-0.646738\pi$
$103$		−	18.1789i		−	1.79122i	0.444836	−	0.895612i	$-0.353262\pi$
$104$			3.85479i			0.377994i
$105$		0			0
$106$	21.9790			2.13479
$107$	6.77836	+	6.77836i	0.655289	+	0.655289i	0.954262	−	0.298973i	$-0.0966439\pi$
$107$	6.77836	+	6.77836i	0.655289	+	0.655289i	−0.298973	+	0.954262i	$0.596644\pi$
$108$	−7.87403	+	7.87403i	−0.757679	+	0.757679i
$109$	2.81350	+	2.81350i	0.269484	+	0.269484i	0.828892	−	0.559408i	$-0.188972\pi$
$109$	2.81350	+	2.81350i	0.269484	+	0.269484i	−0.559408	+	0.828892i	$0.688972\pi$
$110$		0			0
$111$			11.0666i			1.05039i
$112$	3.10637	−	3.10637i	0.293524	−	0.293524i
$113$	2.51696	−	2.51696i	0.236776	−	0.236776i	−0.578738	−	0.815514i	$-0.696455\pi$
$113$	2.51696	−	2.51696i	0.236776	−	0.236776i	0.815514	+	0.578738i	$0.196455\pi$
$114$	13.2785	−	13.2785i	1.24365	−	1.24365i
$115$		0			0
$116$	−3.03823	+	3.03823i	−0.282092	+	0.282092i
$117$	2.35059			0.217313
$118$		−	13.6038i		−	1.25233i
$119$	−5.57746	+	0.991695i	−0.511285	+	0.0909085i
$120$		0			0
$121$		−	10.7039i		−	0.973086i
$122$	22.7895	+	22.7895i	2.06326	+	2.06326i
$123$			7.08430i			0.638770i
$124$	−13.4398	+	13.4398i	−1.20693	+	1.20693i
$125$		0			0
$126$	0.881417	+	0.881417i	0.0785229	+	0.0785229i
$127$	−7.76925			−0.689409			−0.344705	−	0.938711i	$-0.612021\pi$
$127$	−7.76925			−0.689409			−0.344705	+	0.938711i	$0.612021\pi$
$128$	5.62787			0.497438
$129$	4.80504	+	4.80504i	0.423060	+	0.423060i
$130$		0			0
$131$	−14.2801	+	14.2801i	−1.24765	+	1.24765i	−0.290902	+	0.956753i	$0.593955\pi$
$131$	−14.2801	+	14.2801i	−1.24765	+	1.24765i	−0.956753	+	0.290902i	$0.906045\pi$
$132$			2.36249i			0.205628i
$133$	4.72344	+	4.72344i	0.409574	+	0.409574i
$134$			11.8512i			1.02379i
$135$		0			0
$136$	−2.41378	−	1.68500i	−0.206980	−	0.144488i
$137$		−	16.6892i		−	1.42585i	−0.701239	−	0.712926i	$-0.747370\pi$
$137$		−	16.6892i		−	1.42585i	0.701239	−	0.712926i	$-0.252630\pi$
$138$	−6.90321			−0.587641
$139$	−4.38272	+	4.38272i	−0.371738	+	0.371738i	−0.868110	−	0.496372i	$-0.834665\pi$
$139$	−4.38272	+	4.38272i	−0.371738	+	0.371738i	0.496372	+	0.868110i	$0.334665\pi$
$140$		0			0
$141$	11.8910	−	11.8910i	1.00140	−	1.00140i
$142$	−1.56188	+	1.56188i	−0.131070	+	0.131070i
$143$	−2.07729	+	2.07729i	−0.173712	+	0.173712i
$144$		−	1.39203i		−	0.116002i
$145$		0			0
$146$	−21.6352	−	21.6352i	−1.79054	−	1.79054i
$147$	6.70015	−	6.70015i	0.552619	−	0.552619i
$148$	−9.89035	−	9.89035i	−0.812982	−	0.812982i
$149$	4.48964			0.367805			0.183903	−	0.982944i	$-0.441127\pi$
$149$	4.48964			0.367805			0.183903	+	0.982944i	$0.441127\pi$
$150$		0			0
$151$			6.35198i			0.516917i	0.966022	+	0.258458i	$0.0832145\pi$
$151$			6.35198i			0.516917i	−0.966022	+	0.258458i	$0.916786\pi$
$152$			3.47117i			0.281549i
$153$	−1.02749	+	1.47189i	−0.0830674	+	0.118995i
$154$	−1.55787			−0.125536
$155$		0			0
$156$	−16.5767	+	16.5767i	−1.32720	+	1.32720i
$157$			6.37303i			0.508624i	0.967122	+	0.254312i	$0.0818489\pi$
$157$			6.37303i			0.508624i	−0.967122	+	0.254312i	$0.918151\pi$
$158$	−1.83082	−	1.83082i	−0.145652	−	0.145652i
$159$	13.8230	+	13.8230i	1.09624	+	1.09624i
$160$		0			0
$161$		−	2.45562i		−	0.193530i
$162$	−21.0818			−1.65634
$163$	2.96192	−	2.96192i	0.231996	−	0.231996i	−0.581530	−	0.813525i	$-0.697546\pi$
$163$	2.96192	−	2.96192i	0.231996	−	0.231996i	0.813525	+	0.581530i	$0.197546\pi$
$164$	−6.33133	−	6.33133i	−0.494394	−	0.494394i
$165$		0			0
$166$	28.1405			2.18413
$167$	−9.35974	−	9.35974i	−0.724278	−	0.724278i	0.245195	−	0.969474i	$-0.421148\pi$
$167$	−9.35974	−	9.35974i	−0.724278	−	0.724278i	−0.969474	+	0.245195i	$0.921148\pi$
$168$	−1.81815			−0.140274
$169$	−16.1511			−1.24239
$170$		0			0
$171$	2.11667			0.161866
$172$	−8.58867			−0.654880
$173$	−6.24926	−	6.24926i	−0.475123	−	0.475123i	0.428445	−	0.903568i	$-0.359062\pi$
$173$	−6.24926	−	6.24926i	−0.475123	−	0.475123i	−0.903568	+	0.428445i	$0.859062\pi$
$174$	−7.08430			−0.537059
$175$		0			0
$176$	1.23017	+	1.23017i	0.0927278	+	0.0927278i
$177$	8.55572	−	8.55572i	0.643088	−	0.643088i
$178$	−2.06276			−0.154611
$179$		−	19.2951i		−	1.44218i	−0.692841	−	0.721091i	$-0.743641\pi$
$179$		−	19.2951i		−	1.44218i	0.692841	−	0.721091i	$-0.256359\pi$
$180$		0			0
$181$	−3.47399	−	3.47399i	−0.258220	−	0.258220i	0.566110	−	0.824330i	$-0.308448\pi$
$181$	−3.47399	−	3.47399i	−0.258220	−	0.258220i	−0.824330	+	0.566110i	$0.808448\pi$
$182$	−10.9310	−	10.9310i	−0.810258	−	0.810258i
$183$			28.6656i			2.11902i
$184$	0.902294	−	0.902294i	0.0665180	−	0.0665180i
$185$		0			0
$186$	−31.3379			−2.29780
$187$	−0.392727	−	2.20877i	−0.0287191	−	0.161521i
$188$			21.2543i			1.55013i
$189$		−	6.53105i		−	0.475064i
$190$		0			0
$191$	5.60780			0.405766			0.202883	−	0.979203i	$-0.434969\pi$
$191$	5.60780			0.405766			0.202883	+	0.979203i	$0.434969\pi$
$192$	13.7166	+	13.7166i	0.989913	+	0.989913i
$193$	−5.90046	+	5.90046i	−0.424724	+	0.424724i	−0.886827	−	0.462102i	$-0.847095\pi$
$193$	−5.90046	+	5.90046i	−0.424724	+	0.424724i	0.462102	+	0.886827i	$0.347095\pi$
$194$	16.7842	+	16.7842i	1.20504	+	1.20504i
$195$		0			0
$196$			11.9760i			0.855431i
$197$	4.29543	−	4.29543i	0.306037	−	0.306037i	−0.537333	−	0.843370i	$-0.680568\pi$
$197$	4.29543	−	4.29543i	0.306037	−	0.306037i	0.843370	+	0.537333i	$0.180568\pi$
$198$	−0.349056	+	0.349056i	−0.0248063	+	0.0248063i
$199$	−6.71471	+	6.71471i	−0.475993	+	0.475993i	−0.903848	−	0.427855i	$-0.859270\pi$
$199$	−6.71471	+	6.71471i	−0.475993	+	0.475993i	0.427855	+	0.903848i	$0.359270\pi$
$200$		0			0
$201$	−7.45345	+	7.45345i	−0.525726	+	0.525726i
$202$	−12.5506			−0.883058
$203$		−	2.52003i		−	0.176872i
$204$	−3.13396	−	17.6259i	−0.219421	−	1.23406i
$205$		0			0
$206$			37.8829i			2.63943i
$207$	−0.550205	−	0.550205i	−0.0382419	−	0.0382419i
$208$			17.2633i			1.19700i
$209$	−1.87056	+	1.87056i	−0.129389	+	0.129389i
$210$		0			0
$211$	14.5004	+	14.5004i	0.998251	+	0.998251i	0.999998	−	0.00174728i	$-0.000556176\pi$
$211$	14.5004	+	14.5004i	0.998251	+	0.998251i	−0.00174728	+	0.999998i	$0.500556\pi$
$212$	−24.7077			−1.69693
$213$	−1.96459			−0.134612
$214$	−14.1254	−	14.1254i	−0.965591	−	0.965591i
$215$		0			0
$216$	2.39978	−	2.39978i	0.163284	−	0.163284i
$217$		−	11.1475i		−	0.756744i
$218$	−5.86303	−	5.86303i	−0.397094	−	0.397094i
$219$		−	27.2137i		−	1.83893i
$220$		0			0
$221$	12.7425	−	18.2537i	0.857152	−	1.22788i
$222$		−	23.0616i		−	1.54779i
$223$	−6.64902			−0.445252			−0.222626	−	0.974904i	$-0.571463\pi$
$223$	−6.64902			−0.445252			−0.222626	+	0.974904i	$0.571463\pi$
$224$	−7.86061	+	7.86061i	−0.525209	+	0.525209i
$225$		0			0
$226$	−5.24508	+	5.24508i	−0.348897	+	0.348897i
$227$	−7.43313	+	7.43313i	−0.493354	+	0.493354i	−0.909361	−	0.416007i	$-0.863429\pi$
$227$	−7.43313	+	7.43313i	−0.493354	+	0.493354i	0.416007	+	0.909361i	$0.363429\pi$
$228$	−14.9270	+	14.9270i	−0.988567	+	0.988567i
$229$		−	15.3731i		−	1.01589i	−0.861391	−	0.507943i	$-0.830406\pi$
$229$		−	15.3731i		−	1.01589i	0.861391	−	0.507943i	$-0.169594\pi$
$230$		0			0
$231$	−0.979775	−	0.979775i	−0.0644644	−	0.0644644i
$232$	0.925963	−	0.925963i	0.0607925	−	0.0607925i
$233$	14.8719	+	14.8719i	0.974290	+	0.974290i	0.999678	−	0.0253878i	$-0.00808207\pi$
$233$	14.8719	+	14.8719i	0.974290	+	0.974290i	−0.0253878	+	0.999678i	$0.508082\pi$
$234$	−4.89839			−0.320218
$235$		0			0
$236$			15.2927i			0.995472i
$237$		−	2.30288i		−	0.149588i
$238$	11.6228	−	2.06659i	0.753396	−	0.133957i
$239$	9.10195			0.588756			0.294378	−	0.955689i	$-0.404887\pi$
$239$	9.10195			0.588756			0.294378	+	0.955689i	$0.404887\pi$
$240$		0			0
$241$	−9.00000	+	9.00000i	−0.579741	+	0.579741i	−0.934832	−	0.355091i	$-0.884450\pi$
$241$	−9.00000	+	9.00000i	−0.579741	+	0.579741i	0.355091	+	0.934832i	$0.384450\pi$
$242$			22.3059i			1.43388i
$243$	−3.17511	−	3.17511i	−0.203683	−	0.203683i
$244$	−25.6188	−	25.6188i	−1.64008	−	1.64008i
$245$		0			0
$246$		−	14.7629i		−	0.941249i
$247$	−26.2501			−1.67025
$248$	4.09606	−	4.09606i	0.260100	−	0.260100i
$249$	17.6982	+	17.6982i	1.12158	+	1.12158i
$250$		0			0
$251$	−10.1470			−0.640475			−0.320238	−	0.947337i	$-0.603763\pi$
$251$	−10.1470			−0.640475			−0.320238	+	0.947337i	$0.603763\pi$
$252$	−0.990845	−	0.990845i	−0.0624174	−	0.0624174i
$253$	0.972465			0.0611383
$254$	16.1903			1.01587
$255$		0			0
$256$	9.20390			0.575244
$257$	19.0187			1.18635			0.593176	−	0.805073i	$-0.297874\pi$
$257$	19.0187			1.18635			0.593176	+	0.805073i	$0.297874\pi$
$258$	−10.0132	−	10.0132i	−0.623394	−	0.623394i
$259$	8.20348			0.509739
$260$		0			0
$261$	−0.564638	−	0.564638i	−0.0349502	−	0.0349502i
$262$	29.7581	−	29.7581i	1.83846	−	1.83846i
$263$	−12.6346			−0.779086			−0.389543	−	0.921008i	$-0.627367\pi$
$263$	−12.6346			−0.779086			−0.389543	+	0.921008i	$0.627367\pi$
$264$		−	0.720019i		−	0.0443141i
$265$		0			0
$266$	−9.84315	−	9.84315i	−0.603522	−	0.603522i
$267$	−1.29731	−	1.29731i	−0.0793943	−	0.0793943i
$268$		−	13.3225i		−	0.813802i
$269$	19.7441	−	19.7441i	1.20382	−	1.20382i	0.230824	−	0.972996i	$-0.425858\pi$
$269$	19.7441	−	19.7441i	1.20382	−	1.20382i	0.972996	−	0.230824i	$-0.0741422\pi$
$270$		0			0
$271$	−7.78171			−0.472705			−0.236353	−	0.971667i	$-0.575952\pi$
$271$	−7.78171			−0.472705			−0.236353	+	0.971667i	$0.575952\pi$
$272$	−10.8099	−	7.54612i	−0.655446	−	0.457550i
$273$		−	13.7494i		−	0.832153i
$274$			34.7784i			2.10104i
$275$		0			0
$276$	7.76025			0.467112
$277$	21.9022	+	21.9022i	1.31598	+	1.31598i	0.916930	+	0.399049i	$0.130660\pi$
$277$	21.9022	+	21.9022i	1.31598	+	1.31598i	0.399049	+	0.916930i	$0.369340\pi$
$278$	9.13312	−	9.13312i	0.547768	−	0.547768i
$279$	−2.49772	−	2.49772i	−0.149534	−	0.149534i
$280$		0			0
$281$			2.25506i			0.134525i	0.997735	+	0.0672627i	$0.0214266\pi$
$281$			2.25506i			0.134525i	−0.997735	+	0.0672627i	$0.978573\pi$
$282$	−24.7795	+	24.7795i	−1.47560	+	1.47560i
$283$	18.5973	−	18.5973i	1.10550	−	1.10550i	0.111761	−	0.993735i	$-0.464351\pi$
$283$	18.5973	−	18.5973i	1.10550	−	1.10550i	0.993735	−	0.111761i	$-0.0356492\pi$
$284$	1.75578	−	1.75578i	0.104187	−	0.104187i
$285$		0			0
$286$	4.32884	−	4.32884i	0.255970	−	0.255970i
$287$	5.25148			0.309985
$288$			3.52249i			0.207565i
$289$	5.86007	+	15.9581i	0.344710	+	0.938709i
$290$		0			0
$291$			21.1119i			1.23760i
$292$	24.3212	+	24.3212i	1.42329	+	1.42329i
$293$		−	8.22869i		−	0.480725i	−0.970683	−	0.240363i	$-0.922734\pi$
$293$		−	8.22869i		−	0.480725i	0.970683	−	0.240363i	$-0.0772664\pi$
$294$	−13.9624	+	13.9624i	−0.814303	+	0.814303i
$295$		0			0
$296$	3.01429	+	3.01429i	0.175202	+	0.175202i
$297$	2.58640			0.150078
$298$	−9.35592			−0.541974
$299$	6.82342	+	6.82342i	0.394609	+	0.394609i
$300$		0			0
$301$	3.56190	−	3.56190i	0.205305	−	0.205305i
$302$		−	13.2368i		−	0.761695i
$303$	−7.89334	−	7.89334i	−0.453460	−	0.453460i
$304$			15.5453i			0.891586i
$305$		0			0
$306$	2.14117	−	3.06725i	0.122403	−	0.175343i
$307$		−	0.620204i		−	0.0353969i	−0.999843	−	0.0176985i	$-0.994366\pi$
$307$		−	0.620204i		−	0.0353969i	0.999843	−	0.0176985i	$-0.00563389\pi$
$308$	1.75128			0.0997882
$309$	−23.8254	+	23.8254i	−1.35538	+	1.35538i
$310$		0			0
$311$	16.3224	−	16.3224i	0.925559	−	0.925559i	−0.0718561	−	0.997415i	$-0.522892\pi$
$311$	16.3224	−	16.3224i	0.925559	−	0.925559i	0.997415	+	0.0718561i	$0.0228922\pi$
$312$	5.05210	−	5.05210i	0.286019	−	0.286019i
$313$	−5.19586	+	5.19586i	−0.293688	+	0.293688i	−0.838535	−	0.544848i	$-0.816588\pi$
$313$	−5.19586	+	5.19586i	−0.293688	+	0.293688i	0.544848	+	0.838535i	$0.316588\pi$
$314$		−	13.2807i		−	0.749474i
$315$		0			0
$316$	2.05812	+	2.05812i	0.115778	+	0.115778i
$317$	−18.4299	+	18.4299i	−1.03513	+	1.03513i	−0.0357671	+	0.999360i	$0.511387\pi$
$317$	−18.4299	+	18.4299i	−1.03513	+	1.03513i	−0.999360	+	0.0357671i	$0.988613\pi$
$318$	−28.8057	−	28.8057i	−1.61534	−	1.61534i
$319$	0.997974			0.0558758
$320$		0			0
$321$		−	17.7675i		−	0.991685i
$322$			5.11724i			0.285173i
$323$	11.4744	−	16.4371i	0.638451	−	0.914587i
$324$	23.6991			1.31662
$325$		0			0
$326$	−6.17233	+	6.17233i	−0.341853	+	0.341853i
$327$		−	7.37476i		−	0.407825i
$328$	1.92961	+	1.92961i	0.106545	+	0.106545i
$329$	−8.81459	−	8.81459i	−0.485964	−	0.485964i
$330$		0			0
$331$			0.0195086i			0.00107229i	1.00000		0.000536145i	$0.000170660\pi$
$331$			0.0195086i			0.00107229i	−1.00000		0.000536145i	$0.999829\pi$
$332$	−31.6342			−1.73615
$333$	1.83807	−	1.83807i	0.100726	−	0.100726i
$334$	19.5047	+	19.5047i	1.06725	+	1.06725i
$335$		0			0
$336$	−8.14244			−0.444206
$337$	18.6470	+	18.6470i	1.01577	+	1.01577i	0.999874	+	0.0158922i	$0.00505886\pi$
$337$	18.6470	+	18.6470i	1.01577	+	1.01577i	0.0158922	+	0.999874i	$0.494941\pi$
$338$	33.6572			1.83071
$339$	−6.59748			−0.358326
$340$		0			0
$341$	4.41461			0.239064
$342$	−4.41091			−0.238515
$343$	−11.7674	−	11.7674i	−0.635381	−	0.635381i
$344$	2.61758			0.141130
$345$		0			0
$346$	13.0228	+	13.0228i	0.700110	+	0.700110i
$347$	−6.67838	+	6.67838i	−0.358514	+	0.358514i	−0.863265	−	0.504751i	$-0.831584\pi$
$347$	−6.67838	+	6.67838i	−0.358514	+	0.358514i	0.504751	+	0.863265i	$0.331584\pi$
$348$	7.96382			0.426905
$349$		−	13.9171i		−	0.744964i	−0.928039	−	0.372482i	$-0.878507\pi$
$349$		−	13.9171i		−	0.744964i	0.928039	−	0.372482i	$-0.121493\pi$
$350$		0			0
$351$	18.1478	+	18.1478i	0.968660	+	0.968660i
$352$	−3.11293	−	3.11293i	−0.165920	−	0.165920i
$353$			13.3125i			0.708554i	0.935140	+	0.354277i	$0.115273\pi$
$353$			13.3125i			0.708554i	−0.935140	+	0.354277i	$0.884727\pi$
$354$	−17.8292	+	17.8292i	−0.947612	+	0.947612i
$355$		0			0
$356$	2.31886			0.122899
$357$	8.60956	+	6.01012i	0.455666	+	0.318089i
$358$			40.2088i			2.12510i
$359$		−	34.6894i		−	1.83084i	−0.402502	−	0.915419i	$-0.631859\pi$
$359$		−	34.6894i		−	1.83084i	0.402502	−	0.915419i	$-0.368141\pi$
$360$		0			0
$361$	−4.63771			−0.244090
$362$	7.23942	+	7.23942i	0.380496	+	0.380496i
$363$	−14.0286	+	14.0286i	−0.736312	+	0.736312i
$364$	12.2881	+	12.2881i	0.644069	+	0.644069i
$365$		0			0
$366$		−	59.7360i		−	3.12245i
$367$	1.15604	−	1.15604i	0.0603449	−	0.0603449i	−0.676290	−	0.736635i	$-0.736413\pi$
$367$	1.15604	−	1.15604i	0.0603449	−	0.0603449i	0.736635	+	0.676290i	$0.236413\pi$
$368$	4.04084	−	4.04084i	0.210644	−	0.210644i
$369$	1.17665	−	1.17665i	0.0612537	−	0.0612537i
$370$		0			0
$371$	10.2468	−	10.2468i	0.531987	−	0.531987i
$372$	35.2285			1.82651
$373$		−	26.2859i		−	1.36103i	−0.732734	−	0.680515i	$-0.761756\pi$
$373$		−	26.2859i		−	1.36103i	0.732734	−	0.680515i	$-0.238244\pi$
$374$	0.818402	+	4.60283i	0.0423186	+	0.238007i
$375$		0			0
$376$		−	6.47769i		−	0.334061i
$377$	7.00241	+	7.00241i	0.360643	+	0.360643i
$378$			13.6100i			0.700024i
$379$	20.6456	−	20.6456i	1.06049	−	1.06049i	0.0624440	−	0.998048i	$-0.480111\pi$
$379$	20.6456	−	20.6456i	1.06049	−	1.06049i	0.998048	−	0.0624440i	$-0.0198895\pi$
$380$		0			0
$381$	10.1824	+	10.1824i	0.521660	+	0.521660i
$382$	−11.6860			−0.597910
$383$	−7.23455			−0.369668			−0.184834	−	0.982770i	$-0.559175\pi$
$383$	−7.23455			−0.369668			−0.184834	+	0.982770i	$0.559175\pi$
$384$	−7.37591	−	7.37591i	−0.376400	−	0.376400i
$385$		0			0
$386$	12.2959	−	12.2959i	0.625846	−	0.625846i
$387$		−	1.59616i		−	0.0811373i
$388$	−18.8680	−	18.8680i	−0.957878	−	0.957878i
$389$			16.1985i			0.821295i	0.911794	+	0.410648i	$0.134697\pi$
$389$			16.1985i			0.821295i	−0.911794	+	0.410648i	$0.865303\pi$
$390$		0			0
$391$	−7.25530	+	1.29002i	−0.366916	+	0.0652392i
$392$		−	3.64995i		−	0.184350i
$393$	37.4310			1.88814
$394$	−8.95122	+	8.95122i	−0.450956	+	0.450956i
$395$		0			0
$396$	0.392391	−	0.392391i	0.0197184	−	0.0197184i
$397$	20.6884	−	20.6884i	1.03832	−	1.03832i	0.0390863	−	0.999236i	$-0.487555\pi$
$397$	20.6884	−	20.6884i	1.03832	−	1.03832i	0.999236	−	0.0390863i	$-0.0124447\pi$
$398$	13.9927	−	13.9927i	0.701392	−	0.701392i
$399$		−	12.3811i		−	0.619831i
$400$		0			0
$401$	−14.8573	−	14.8573i	−0.741936	−	0.741936i	0.231014	−	0.972950i	$-0.425796\pi$
$401$	−14.8573	−	14.8573i	−0.741936	−	0.741936i	−0.972950	+	0.231014i	$0.925796\pi$
$402$	15.5322	−	15.5322i	0.774675	−	0.774675i
$403$	30.9756	+	30.9756i	1.54301	+	1.54301i
$404$	14.1088			0.701938
$405$		0			0
$406$			5.25148i			0.260626i
$407$			3.24871i			0.161033i
$408$	0.955140	+	5.37187i	0.0472865	+	0.265947i
$409$	−17.5170			−0.866161			−0.433080	−	0.901355i	$-0.642573\pi$
$409$	−17.5170			−0.866161			−0.433080	+	0.901355i	$0.642573\pi$
$410$		0			0
$411$	−21.8729	+	21.8729i	−1.07891	+	1.07891i
$412$		−	42.5861i		−	2.09807i
$413$	−6.34222	−	6.34222i	−0.312080	−	0.312080i
$414$	1.14657	+	1.14657i	0.0563508	+	0.0563508i
$415$		0			0
$416$		−	43.6845i		−	2.14181i
$417$	11.4880			0.562571
$418$	3.89805	−	3.89805i	0.190660	−	0.190660i
$419$	−20.3872	−	20.3872i	−0.995980	−	0.995980i	0.00401203	−	0.999992i	$-0.498723\pi$
$419$	−20.3872	−	20.3872i	−0.995980	−	0.995980i	−0.999992	+	0.00401203i	$0.998723\pi$
$420$		0			0
$421$	−25.5578			−1.24561			−0.622806	−	0.782376i	$-0.714008\pi$
$421$	−25.5578			−1.24561			−0.622806	+	0.782376i	$0.714008\pi$
$422$	−30.2174	−	30.2174i	−1.47096	−	1.47096i
$423$	−3.94999			−0.192055
$424$	7.53019			0.365698
$425$		0			0
$426$	4.09400			0.198355
$427$	21.2493			1.02833
$428$	15.8791	+	15.8791i	0.767543	+	0.767543i
$429$	5.44500			0.262887
$430$		0			0
$431$	−16.1083	−	16.1083i	−0.775910	−	0.775910i	0.203222	−	0.979133i	$-0.434859\pi$
$431$	−16.1083	−	16.1083i	−0.775910	−	0.775910i	−0.979133	+	0.203222i	$0.934859\pi$
$432$	10.7472	−	10.7472i	0.517074	−	0.517074i
$433$	33.5441			1.61203			0.806014	−	0.591896i	$-0.201621\pi$
$433$	33.5441			1.61203			0.806014	+	0.591896i	$0.201621\pi$
$434$			23.2303i			1.11509i
$435$		0			0
$436$	6.59093	+	6.59093i	0.315648	+	0.315648i
$437$	6.14437	+	6.14437i	0.293925	+	0.293925i
$438$			56.7103i			2.70973i
$439$	2.75867	−	2.75867i	0.131664	−	0.131664i	−0.638204	−	0.769868i	$-0.720322\pi$
$439$	2.75867	−	2.75867i	0.131664	−	0.131664i	0.769868	+	0.638204i	$0.220322\pi$
$440$		0			0
$441$	−2.22568			−0.105985
$442$	−26.5539	+	38.0388i	−1.26304	+	1.80932i
$443$			21.1747i			1.00604i	0.864275	+	0.503020i	$0.167778\pi$
$443$			21.1747i			1.00604i	−0.864275	+	0.503020i	$0.832222\pi$
$444$			25.9247i			1.23033i
$445$		0			0
$446$	13.8559			0.656094
$447$	−5.88413	−	5.88413i	−0.278310	−	0.278310i
$448$	10.1679	−	10.1679i	0.480389	−	0.480389i
$449$	−27.3305	−	27.3305i	−1.28980	−	1.28980i	−0.934904	−	0.354900i	$-0.884515\pi$
$449$	−27.3305	−	27.3305i	−1.28980	−	1.28980i	−0.354900	−	0.934904i	$-0.615485\pi$
$450$		0			0
$451$			2.07967i			0.0979279i
$452$	5.89626	−	5.89626i	0.277337	−	0.277337i
$453$	8.32492	−	8.32492i	0.391139	−	0.391139i
$454$	15.4898	−	15.4898i	0.726974	−	0.726974i
$455$		0			0
$456$	4.54933	−	4.54933i	0.213042	−	0.213042i
$457$	−17.9273			−0.838605			−0.419303	−	0.907847i	$-0.637725\pi$
$457$	−17.9273			−0.838605			−0.419303	+	0.907847i	$0.637725\pi$
$458$			32.0360i			1.49694i
$459$	−19.2965	+	3.43099i	−0.900683	+	0.160145i
$460$		0			0
$461$		−	33.2184i		−	1.54713i	−0.633715	−	0.773567i	$-0.718471\pi$
$461$		−	33.2184i		−	1.54713i	0.633715	−	0.773567i	$-0.281529\pi$
$462$	2.04175	+	2.04175i	0.0949906	+	0.0949906i
$463$		−	25.4598i		−	1.18322i	−0.806225	−	0.591609i	$-0.798493\pi$
$463$		−	25.4598i		−	1.18322i	0.806225	−	0.591609i	$-0.201507\pi$
$464$	4.14684	−	4.14684i	0.192512	−	0.192512i
$465$		0			0
$466$	−30.9914	−	30.9914i	−1.43565	−	1.43565i
$467$	−6.31549			−0.292246			−0.146123	−	0.989266i	$-0.546680\pi$
$467$	−6.31549			−0.292246			−0.146123	+	0.989266i	$0.546680\pi$
$468$	5.50652			0.254539
$469$	5.52513	+	5.52513i	0.255127	+	0.255127i
$470$		0			0
$471$	8.35252	−	8.35252i	0.384864	−	0.384864i
$472$		−	4.66078i		−	0.214530i
$473$	1.41057	+	1.41057i	0.0648581	+	0.0648581i
$474$			4.79896i			0.220424i
$475$		0			0
$476$	−13.0658	+	2.32315i	−0.598871	+	0.106482i
$477$		−	4.59179i		−	0.210244i
$478$	−18.9675			−0.867553
$479$	−20.2237	+	20.2237i	−0.924046	+	0.924046i	−0.997312	−	0.0732661i	$-0.976658\pi$
$479$	−20.2237	+	20.2237i	−0.924046	+	0.924046i	0.0732661	+	0.997312i	$0.476658\pi$
$480$		0			0
$481$	−22.7950	+	22.7950i	−1.03936	+	1.03936i
$482$	18.7550	−	18.7550i	0.854268	−	0.854268i
$483$	−3.21834	+	3.21834i	−0.146440	+	0.146440i
$484$		−	25.0752i		−	1.13978i
$485$		0			0
$486$	6.61658	+	6.61658i	0.300134	+	0.300134i
$487$	3.62691	−	3.62691i	0.164351	−	0.164351i	−0.620140	−	0.784491i	$-0.712924\pi$
$487$	3.62691	−	3.62691i	0.164351	−	0.164351i	0.784491	+	0.620140i	$0.212924\pi$
$488$	7.80788	+	7.80788i	0.353446	+	0.353446i
$489$	−7.76381			−0.351091
$490$		0			0
$491$			29.5051i			1.33155i	0.746155	+	0.665773i	$0.231898\pi$
$491$			29.5051i			1.33155i	−0.746155	+	0.665773i	$0.768102\pi$
$492$			16.5957i			0.748194i
$493$	−7.44562	+	1.32386i	−0.335334	+	0.0596237i
$494$	54.7023			2.46117
$495$		0			0
$496$	18.3438	−	18.3438i	0.823662	−	0.823662i
$497$			1.45632i			0.0653249i
$498$	−36.8811	−	36.8811i	−1.65268	−	1.65268i
$499$	2.71072	+	2.71072i	0.121349	+	0.121349i	0.765173	−	0.643825i	$-0.222653\pi$
$499$	2.71072	+	2.71072i	0.121349	+	0.121349i	−0.643825	+	0.765173i	$0.722653\pi$
$500$		0			0
$501$			24.5338i			1.09609i
$502$	21.1453			0.943762
$503$	−20.2499	+	20.2499i	−0.902897	+	0.902897i	−0.995686	−	0.0927885i	$-0.970422\pi$
$503$	−20.2499	+	20.2499i	−0.902897	+	0.902897i	0.0927885	+	0.995686i	$0.470422\pi$
$504$	0.301981	+	0.301981i	0.0134513	+	0.0134513i
$505$		0			0
$506$	−2.02651			−0.0900894
$507$	21.1677	+	21.1677i	0.940090	+	0.940090i
$508$	−18.2003			−0.807508
$509$	−23.6043			−1.04624			−0.523122	−	0.852258i	$-0.675233\pi$
$509$	−23.6043			−1.04624			−0.523122	+	0.852258i	$0.675233\pi$
$510$		0			0
$511$	−20.1731			−0.892403
$512$	−30.4357			−1.34508
$513$	16.3418	+	16.3418i	0.721508	+	0.721508i
$514$	−39.6329			−1.74813
$515$		0			0
$516$	11.2563	+	11.2563i	0.495532	+	0.495532i
$517$	3.49072	−	3.49072i	0.153522	−	0.153522i
$518$	−17.0952			−0.751118
$519$			16.3806i			0.719029i
$520$		0			0
$521$	12.3497	+	12.3497i	0.541051	+	0.541051i	0.923837	−	0.382786i	$-0.125035\pi$
$521$	12.3497	+	12.3497i	0.541051	+	0.541051i	−0.382786	+	0.923837i	$0.625035\pi$
$522$	1.17665	+	1.17665i	0.0515004	+	0.0515004i
$523$		−	16.1755i		−	0.707304i	−0.935377	−	0.353652i	$-0.884940\pi$
$523$		−	16.1755i		−	0.707304i	0.935377	−	0.353652i	$-0.115060\pi$
$524$	−33.4526	+	33.4526i	−1.46138	+	1.46138i
$525$		0			0
$526$	26.3293			1.14801
$527$	−32.9362	+	5.85619i	−1.43472	+	0.255099i
$528$		−	3.22454i		−	0.140330i
$529$			19.8057i			0.861116i
$530$		0			0
$531$	−2.84208			−0.123336
$532$	11.0652	+	11.0652i	0.479736	+	0.479736i
$533$	−14.5923	+	14.5923i	−0.632062	+	0.632062i
$534$	2.70346	+	2.70346i	0.116990	+	0.116990i
$535$		0			0
$536$			4.06032i			0.175379i
$537$	−25.2882	+	25.2882i	−1.09127	+	1.09127i
$538$	−41.1446	+	41.1446i	−1.77387	+	1.77387i
$539$	1.96690	−	1.96690i	0.0847204	−	0.0847204i
$540$		0			0
$541$	6.34556	−	6.34556i	0.272817	−	0.272817i	−0.557416	−	0.830233i	$-0.688207\pi$
$541$	6.34556	−	6.34556i	0.272817	−	0.272817i	0.830233	+	0.557416i	$0.188207\pi$
$542$	16.2163			0.696548
$543$			9.10605i			0.390778i
$544$	27.3542	+	19.0953i	1.17280	+	0.818704i
$545$		0			0
$546$			28.6523i			1.22621i
$547$	−31.1141	−	31.1141i	−1.33034	−	1.33034i	−0.905061	−	0.425281i	$-0.860175\pi$
$547$	−31.1141	−	31.1141i	−1.33034	−	1.33034i	−0.425281	−	0.905061i	$-0.639825\pi$
$548$		−	39.0962i		−	1.67011i
$549$	4.76112	−	4.76112i	0.203200	−	0.203200i
$550$		0			0
$551$	6.30555	+	6.30555i	0.268625	+	0.268625i
$552$	−2.36510			−0.100665
$553$	−1.70709			−0.0725929
$554$	−45.6419	−	45.6419i	−1.93914	−	1.93914i
$555$		0			0
$556$	−10.2670	+	10.2670i	−0.435418	+	0.435418i
$557$			37.7611i			1.59999i	0.600007	+	0.799995i	$0.295165\pi$
$557$			37.7611i			1.59999i	−0.600007	+	0.799995i	$0.704835\pi$
$558$	5.20497	+	5.20497i	0.220344	+	0.220344i
$559$			19.7949i			0.837236i
$560$		0			0
$561$	−2.38011	+	3.40953i	−0.100488	+	0.143950i
$562$		−	4.69929i		−	0.198228i
$563$	32.4625			1.36813			0.684065	−	0.729421i	$-0.260211\pi$
$563$	32.4625			1.36813			0.684065	+	0.729421i	$0.260211\pi$
$564$	27.8559	−	27.8559i	1.17295	−	1.17295i
$565$		0			0
$566$	−38.7548	+	38.7548i	−1.62899	+	1.62899i
$567$	−9.82852	+	9.82852i	−0.412759	+	0.412759i
$568$	−0.535112	+	0.535112i	−0.0224528	+	0.0224528i
$569$		−	11.3302i		−	0.474986i	−0.971389	−	0.237493i	$-0.923674\pi$
$569$		−	11.3302i		−	0.474986i	0.971389	−	0.237493i	$-0.0763257\pi$
$570$		0			0
$571$	−8.12281	−	8.12281i	−0.339929	−	0.339929i	0.516412	−	0.856340i	$-0.327267\pi$
$571$	−8.12281	−	8.12281i	−0.339929	−	0.339929i	−0.856340	+	0.516412i	$0.827267\pi$
$572$	−4.86627	+	4.86627i	−0.203469	+	0.203469i
$573$	−7.34960	−	7.34960i	−0.307034	−	0.307034i
$574$	−10.9435			−0.456773
$575$		0			0
$576$		−	4.55645i		−	0.189852i
$577$			0.378762i			0.0157681i	0.999969	+	0.00788404i	$0.00250959\pi$
$577$			0.378762i			0.0157681i	−0.999969	+	0.00788404i	$0.997490\pi$
$578$	−12.2118	−	33.2549i	−0.507942	−	1.38322i
$579$	15.4663			0.642759
$580$		0			0
$581$	13.1194	−	13.1194i	0.544283	−	0.544283i
$582$		−	43.9950i		−	1.82365i
$583$	4.05790	+	4.05790i	0.168061	+	0.168061i
$584$	−7.41241	−	7.41241i	−0.306728	−	0.306728i
$585$		0			0
$586$			17.1477i			0.708366i
$587$	11.6262			0.479863			0.239931	−	0.970790i	$-0.422875\pi$
$587$	11.6262			0.479863			0.239931	+	0.970790i	$0.422875\pi$
$588$	15.6958	−	15.6958i	0.647285	−	0.647285i
$589$	27.8930	+	27.8930i	1.14931	+	1.14931i
$590$		0			0
$591$	−11.2592			−0.463142
$592$	13.4992	+	13.4992i	0.554815	+	0.554815i
$593$	−24.0394			−0.987181			−0.493590	−	0.869695i	$-0.664316\pi$
$593$	−24.0394			−0.987181			−0.493590	+	0.869695i	$0.664316\pi$
$594$	−5.38979			−0.221146
$595$		0			0
$596$	10.5175			0.430812
$597$	17.6006			0.720346
$598$	−14.2193	−	14.2193i	−0.581470	−	0.581470i
$599$	41.0811			1.67853			0.839263	−	0.543725i	$-0.182987\pi$
$599$	41.0811			1.67853			0.839263	+	0.543725i	$0.182987\pi$
$600$		0			0
$601$	−17.3030	−	17.3030i	−0.705804	−	0.705804i	0.259846	−	0.965650i	$-0.416328\pi$
$601$	−17.3030	−	17.3030i	−0.705804	−	0.705804i	−0.965650	+	0.259846i	$0.916328\pi$
$602$	−7.42262	+	7.42262i	−0.302523	+	0.302523i
$603$	2.47592			0.100827
$604$			14.8802i			0.605467i
$605$		0			0
$606$	16.4489	+	16.4489i	0.668190	+	0.668190i
$607$	−0.971227	−	0.971227i	−0.0394209	−	0.0394209i	0.687122	−	0.726542i	$-0.258874\pi$
$607$	−0.971227	−	0.971227i	−0.0394209	−	0.0394209i	−0.726542	+	0.687122i	$0.758874\pi$
$608$		−	39.3371i		−	1.59533i
$609$	−3.30276	+	3.30276i	−0.133835	+	0.133835i
$610$		0			0
$611$	48.9862			1.98177
$612$	−2.40700	+	3.44805i	−0.0972972	+	0.139379i
$613$			1.94295i			0.0784750i	0.999230	+	0.0392375i	$0.0124929\pi$
$613$			1.94295i			0.0784750i	−0.999230	+	0.0392375i	$0.987507\pi$
$614$			1.29244i			0.0521586i
$615$		0			0
$616$	−0.533739			−0.0215049
$617$	−1.63022	−	1.63022i	−0.0656302	−	0.0656302i	0.673530	−	0.739160i	$-0.264777\pi$
$617$	−1.63022	−	1.63022i	−0.0656302	−	0.0656302i	−0.739160	+	0.673530i	$0.764777\pi$
$618$	49.6495	−	49.6495i	1.99720	−	1.99720i
$619$	−19.5217	−	19.5217i	−0.784643	−	0.784643i	0.195967	−	0.980610i	$-0.437215\pi$
$619$	−19.5217	−	19.5217i	−0.784643	−	0.784643i	−0.980610	+	0.195967i	$0.937215\pi$
$620$		0			0
$621$		−	8.49576i		−	0.340923i
$622$	−34.0141	+	34.0141i	−1.36384	+	1.36384i
$623$	−0.961678	+	0.961678i	−0.0385288	+	0.0385288i
$624$	22.6254	−	22.6254i	0.905740	−	0.905740i
$625$		0			0
$626$	10.8276	−	10.8276i	0.432759	−	0.432759i
$627$	4.90313			0.195812
$628$			14.9295i			0.595753i
$629$	−4.30957	−	24.2378i	−0.171834	−	0.966424i
$630$		0			0
$631$		−	10.0851i		−	0.401480i	−0.979645	−	0.200740i	$-0.935665\pi$
$631$		−	10.0851i		−	0.401480i	0.979645	−	0.200740i	$-0.0643346\pi$
$632$	−0.627255	−	0.627255i	−0.0249509	−	0.0249509i
$633$		−	38.0086i		−	1.51071i
$634$	38.4060	−	38.4060i	1.52530	−	1.52530i
$635$		0			0
$636$	32.3820	+	32.3820i	1.28403	+	1.28403i
$637$	27.6020			1.09363
$638$	−2.07967			−0.0823350
$639$	0.326303	+	0.326303i	0.0129084	+	0.0129084i
$640$		0			0
$641$	2.60863	−	2.60863i	0.103035	−	0.103035i	−0.653710	−	0.756745i	$-0.726788\pi$
$641$	2.60863	−	2.60863i	0.103035	−	0.103035i	0.756745	+	0.653710i	$0.226788\pi$
$642$			37.0255i			1.46128i
$643$	−7.17437	−	7.17437i	−0.282930	−	0.282930i	0.551347	−	0.834276i	$-0.314114\pi$
$643$	−7.17437	−	7.17437i	−0.282930	−	0.282930i	−0.834276	+	0.551347i	$0.814114\pi$
$644$		−	5.75255i		−	0.226682i
$645$		0			0
$646$	−23.9114	+	34.2533i	−0.940780	+	1.34768i
$647$		−	40.6109i		−	1.59658i	−0.602273	−	0.798290i	$-0.705738\pi$
$647$		−	40.6109i		−	1.59658i	0.602273	−	0.798290i	$-0.294262\pi$
$648$	−7.22280			−0.283739
$649$	2.51162	−	2.51162i	0.0985899	−	0.0985899i
$650$		0			0
$651$	−14.6100	+	14.6100i	−0.572611	+	0.572611i
$652$	6.93862	−	6.93862i	0.271737	−	0.271737i
$653$	4.27439	−	4.27439i	0.167270	−	0.167270i	−0.618508	−	0.785778i	$-0.712263\pi$
$653$	4.27439	−	4.27439i	0.167270	−	0.167270i	0.785778	+	0.618508i	$0.212263\pi$
$654$			15.3682i			0.600944i
$655$		0			0
$656$	8.64157	+	8.64157i	0.337397	+	0.337397i
$657$	−4.51997	+	4.51997i	−0.176341	+	0.176341i
$658$	18.3687	+	18.3687i	0.716085	+	0.716085i
$659$	32.7193			1.27456			0.637281	−	0.770631i	$-0.280059\pi$
$659$	32.7193			1.27456			0.637281	+	0.770631i	$0.280059\pi$
$660$		0			0
$661$			0.0904199i			0.00351693i	0.999998	+	0.00175846i	$0.000559736\pi$
$661$			0.0904199i			0.00351693i	−0.999998	+	0.00175846i	$0.999440\pi$
$662$		−	0.0406539i		−	0.00158006i
$663$	−40.6237	+	7.22305i	−1.57769	+	0.280520i
$664$	9.64118			0.374151
$665$		0			0
$666$	−3.83034	+	3.83034i	−0.148423	+	0.148423i
$667$		−	3.27812i		−	0.126929i
$668$	−21.9262	−	21.9262i	−0.848350	−	0.848350i
$669$	8.71423	+	8.71423i	0.336912	+	0.336912i
$670$		0			0
$671$			8.41508i			0.324861i
$672$	20.6043			0.794827
$673$	8.17887	−	8.17887i	0.315272	−	0.315272i	−0.531676	−	0.846948i	$-0.678437\pi$
$673$	8.17887	−	8.17887i	0.315272	−	0.315272i	0.846948	+	0.531676i	$0.178437\pi$
$674$	−38.8583	−	38.8583i	−1.49677	−	1.49677i
$675$		0			0
$676$	−37.8357			−1.45522
$677$	−19.4874	−	19.4874i	−0.748960	−	0.748960i	0.225324	−	0.974284i	$-0.427656\pi$
$677$	−19.4874	−	19.4874i	−0.748960	−	0.748960i	−0.974284	+	0.225324i	$0.927656\pi$
$678$	13.7484			0.528005
$679$	15.6499			0.600589
$680$		0			0
$681$	19.4838			0.746619
$682$	−9.19956			−0.352269
$683$	0.144053	+	0.144053i	0.00551205	+	0.00551205i	0.709857	−	0.704345i	$-0.248759\pi$
$683$	0.144053	+	0.144053i	0.00551205	+	0.00551205i	−0.704345	+	0.709857i	$0.748759\pi$
$684$	4.95853			0.189594
$685$		0			0
$686$	24.5220	+	24.5220i	0.936256	+	0.936256i
$687$	−20.1481	+	20.1481i	−0.768697	+	0.768697i
$688$	11.7226			0.446919
$689$			56.9455i			2.16945i
$690$		0			0
$691$	18.2369	+	18.2369i	0.693764	+	0.693764i	0.963058	−	0.269294i	$-0.0867903\pi$
$691$	18.2369	+	18.2369i	0.693764	+	0.693764i	−0.269294	+	0.963058i	$0.586790\pi$
$692$	−14.6396	−	14.6396i	−0.556513	−	0.556513i
$693$			0.325466i			0.0123634i
$694$	13.9170	−	13.9170i	0.528283	−	0.528283i
$695$		0			0
$696$	−2.42714			−0.0920005
$697$	−2.75878	−	15.5159i	−0.104496	−	0.587706i
$698$			29.0017i			1.09773i
$699$		−	38.9823i		−	1.47445i
$700$		0			0
$701$	−18.4768			−0.697859			−0.348930	−	0.937149i	$-0.613455\pi$
$701$	−18.4768			−0.697859			−0.348930	+	0.937149i	$0.613455\pi$
$702$	−37.8181	−	37.8181i	−1.42735	−	1.42735i
$703$	−20.5265	+	20.5265i	−0.774171	+	0.774171i
$704$	4.02666	+	4.02666i	0.151761	+	0.151761i
$705$		0			0
$706$		−	27.7419i		−	1.04408i
$707$	−5.85121	+	5.85121i	−0.220057	+	0.220057i
$708$	20.0427	−	20.0427i	0.753251	−	0.753251i
$709$	0.483936	−	0.483936i	0.0181746	−	0.0181746i	−0.697961	−	0.716136i	$-0.745909\pi$
$709$	0.483936	−	0.483936i	0.0181746	−	0.0181746i	0.716136	+	0.697961i	$0.245909\pi$
$710$		0			0
$711$	−0.382491	+	0.382491i	−0.0143445	+	0.0143445i
$712$	−0.706720			−0.0264855
$713$		−	14.5010i		−	0.543066i
$714$	−17.9414	−	12.5245i	−0.671440	−	0.468716i
$715$		0			0
$716$		−	45.2008i		−	1.68923i
$717$	−11.9290	−	11.9290i	−0.445498	−	0.445498i
$718$			72.2890i			2.69780i
$719$	−25.6304	+	25.6304i	−0.955854	+	0.955854i	−0.999066	−	0.0432116i	$-0.986241\pi$
$719$	−25.6304	+	25.6304i	−0.955854	+	0.955854i	0.0432116	+	0.999066i	$0.486241\pi$
$720$		0			0
$721$	17.6614	+	17.6614i	0.657744	+	0.657744i
$722$	9.66449			0.359675
$723$	23.5909			0.877353
$724$	−8.13820	−	8.13820i	−0.302454	−	0.302454i
$725$		0			0
$726$	29.2342	−	29.2342i	1.08498	−	1.08498i
$727$		−	22.3302i		−	0.828182i	−0.910235	−	0.414091i	$-0.864100\pi$
$727$		−	22.3302i		−	0.828182i	0.910235	−	0.414091i	$-0.135900\pi$
$728$	−3.74504	−	3.74504i	−0.138801	−	0.138801i
$729$		−	22.0270i		−	0.815816i
$730$		0			0
$731$	−12.3951	−	8.65271i	−0.458449	−	0.320032i
$732$			67.1522i			2.48202i
$733$	−17.9985			−0.664790			−0.332395	−	0.943140i	$-0.607857\pi$
$733$	−17.9985			−0.664790			−0.332395	+	0.943140i	$0.607857\pi$
$734$	−2.40907	+	2.40907i	−0.0889203	+	0.0889203i
$735$		0			0
$736$	−10.2253	+	10.2253i	−0.376909	+	0.376909i
$737$	−2.18804	+	2.18804i	−0.0805975	+	0.0805975i
$738$	−2.45200	+	2.45200i	−0.0902595	+	0.0902595i
$739$		−	8.18227i		−	0.300990i	−0.988611	−	0.150495i	$-0.951913\pi$
$739$		−	8.18227i		−	0.300990i	0.988611	−	0.150495i	$-0.0480867\pi$
$740$		0			0
$741$	34.4034	+	34.4034i	1.26384	+	1.26384i
$742$	−21.3532	+	21.3532i	−0.783902	+	0.783902i
$743$	8.40986	+	8.40986i	0.308528	+	0.308528i	0.844338	−	0.535810i	$-0.179994\pi$
$743$	8.40986	+	8.40986i	0.308528	+	0.308528i	−0.535810	+	0.844338i	$0.679994\pi$
$744$	−10.7366			−0.393624
$745$		0			0
$746$			54.7769i			2.00553i
$747$		−	5.87905i		−	0.215103i
$748$	−0.920007	−	5.17428i	−0.0336388	−	0.189190i
$749$	−13.1708			−0.481249
$750$		0			0
$751$	29.4124	−	29.4124i	1.07327	−	1.07327i	0.0761797	−	0.997094i	$-0.475728\pi$
$751$	29.4124	−	29.4124i	1.07327	−	1.07327i	0.997094	−	0.0761797i	$-0.0242723\pi$
$752$		−	29.0097i		−	1.05788i
$753$	13.2987	+	13.2987i	0.484633	+	0.484633i
$754$	−14.5923	−	14.5923i	−0.531419	−	0.531419i
$755$		0			0
$756$		−	15.2997i		−	0.556445i
$757$	−4.10700			−0.149272			−0.0746358	−	0.997211i	$-0.523779\pi$
$757$	−4.10700			−0.149272			−0.0746358	+	0.997211i	$0.523779\pi$
$758$	−43.0232	+	43.0232i	−1.56267	+	1.56267i
$759$	−1.27452	−	1.27452i	−0.0462620	−	0.0462620i
$760$		0			0
$761$	−11.1702			−0.404920			−0.202460	−	0.979291i	$-0.564894\pi$
$761$	−11.1702			−0.404920			−0.202460	+	0.979291i	$0.564894\pi$
$762$	−21.2190	−	21.2190i	−0.768684	−	0.768684i
$763$	−5.46679			−0.197911
$764$	13.1369			0.475275
$765$		0			0
$766$	15.0760			0.544719
$767$	35.2463			1.27267
$768$	−12.0627	−	12.0627i	−0.435274	−	0.435274i
$769$	43.1786			1.55706			0.778530	−	0.627607i	$-0.215966\pi$
$769$	43.1786			1.55706			0.778530	+	0.627607i	$0.215966\pi$
$770$		0			0
$771$	−24.9259	−	24.9259i	−0.897685	−	0.897685i
$772$	−13.8225	+	13.8225i	−0.497482	+	0.497482i
$773$	−22.0379			−0.792648			−0.396324	−	0.918111i	$-0.629714\pi$
$773$	−22.0379			−0.792648			−0.396324	+	0.918111i	$0.629714\pi$
$774$			3.32622i			0.119559i
$775$		0			0
$776$	5.75043	+	5.75043i	0.206428	+	0.206428i
$777$	−10.7515	−	10.7515i	−0.385708	−	0.385708i
$778$		−	33.7559i		−	1.21021i
$779$	−13.1401	+	13.1401i	−0.470792	+	0.470792i
$780$		0			0
$781$	−0.576727			−0.0206369
$782$	15.1193	−	2.68827i	0.540664	−	0.0961322i
$783$		−	8.71862i		−	0.311578i
$784$		−	16.3460i		−	0.583784i
$785$		0			0
$786$	−78.0021			−2.78224
$787$	−14.9211	−	14.9211i	−0.531879	−	0.531879i	0.389252	−	0.921131i	$-0.372733\pi$
$787$	−14.9211	−	14.9211i	−0.531879	−	0.531879i	−0.921131	+	0.389252i	$0.872733\pi$
$788$	10.0625	−	10.0625i	0.358462	−	0.358462i
$789$	16.5590	+	16.5590i	0.589516	+	0.589516i
$790$		0			0
$791$			4.89060i			0.173890i
$792$	−0.119589	+	0.119589i	−0.00424943	+	0.00424943i
$793$	−59.0455	+	59.0455i	−2.09677	+	2.09677i
$794$	−43.1125	+	43.1125i	−1.53000	+	1.53000i
$795$		0			0
$796$	−15.7299	+	15.7299i	−0.557533	+	0.557533i
$797$	36.8066			1.30376			0.651878	−	0.758324i	$-0.273981\pi$
$797$	36.8066			1.30376			0.651878	+	0.758324i	$0.273981\pi$
$798$			25.8009i			0.913343i
$799$	−21.4127	+	30.6740i	−0.757529	+	1.08517i
$800$		0			0
$801$			0.430947i			0.0152268i
$802$	30.9609	+	30.9609i	1.09327	+	1.09327i
$803$		−	7.98886i		−	0.281921i
$804$	−17.4605	+	17.4605i	−0.615785	+	0.615785i
$805$		0			0
$806$	−64.5499	−	64.5499i	−2.27367	−	2.27367i
$807$	−51.7534			−1.82181
$808$	−4.29995			−0.151272
$809$	15.3165	+	15.3165i	0.538500	+	0.538500i	0.923088	−	0.384588i	$-0.125656\pi$
$809$	15.3165	+	15.3165i	0.538500	+	0.538500i	−0.384588	+	0.923088i	$0.625656\pi$
$810$		0			0
$811$	22.6906	−	22.6906i	0.796774	−	0.796774i	−0.185811	−	0.982585i	$-0.559491\pi$
$811$	22.6906	−	22.6906i	0.796774	−	0.796774i	0.982585	+	0.185811i	$0.0594913\pi$
$812$		−	5.90345i		−	0.207170i
$813$	10.1987	+	10.1987i	0.357685	+	0.357685i
$814$		−	6.76997i		−	0.237287i
$815$		0			0
$816$	4.27751	+	24.0574i	0.149743	+	0.842179i
$817$			17.8250i			0.623617i
$818$	36.5036			1.27632
$819$	−2.28367	+	2.28367i	−0.0797979	+	0.0797979i
$820$		0			0
$821$	−3.60354	+	3.60354i	−0.125765	+	0.125765i	−0.767187	−	0.641423i	$-0.778344\pi$
$821$	−3.60354	+	3.60354i	−0.125765	+	0.125765i	0.641423	+	0.767187i	$0.278344\pi$
$822$	45.5807	−	45.5807i	1.58981	−	1.58981i
$823$	23.7004	−	23.7004i	0.826143	−	0.826143i	−0.160838	−	0.986981i	$-0.551420\pi$
$823$	23.7004	−	23.7004i	0.826143	−	0.826143i	0.986981	+	0.160838i	$0.0514197\pi$
$824$			12.9790i			0.452146i
$825$		0			0
$826$	13.2165	+	13.2165i	0.459861	+	0.459861i
$827$	2.95504	−	2.95504i	0.102757	−	0.102757i	−0.653859	−	0.756616i	$-0.726851\pi$
$827$	2.95504	−	2.95504i	0.102757	−	0.102757i	0.756616	+	0.653859i	$0.226851\pi$
$828$	−1.28892	−	1.28892i	−0.0447929	−	0.0447929i
$829$	0.834781			0.0289931			0.0144966	−	0.999895i	$-0.495385\pi$
$829$	0.834781			0.0289931			0.0144966	+	0.999895i	$0.495385\pi$
$830$		0			0
$831$		−	57.4103i		−	1.99154i
$832$			56.5072i			1.95903i
$833$	−12.0653	+	17.2837i	−0.418039	+	0.598845i
$834$	−23.9398			−0.828967
$835$		0			0
$836$	−4.38199	+	4.38199i	−0.151554	+	0.151554i
$837$		−	38.5674i		−	1.33308i
$838$	42.4847	+	42.4847i	1.46761	+	1.46761i
$839$	13.5307	+	13.5307i	0.467130	+	0.467130i	0.900984	−	0.433853i	$-0.142846\pi$
$839$	13.5307	+	13.5307i	0.467130	+	0.467130i	−0.433853	+	0.900984i	$0.642846\pi$
$840$		0			0
$841$			25.6359i			0.883996i
$842$	53.2598			1.83545
$843$	2.95548	−	2.95548i	0.101792	−	0.101792i
$844$	33.9688	+	33.9688i	1.16926	+	1.16926i
$845$		0			0
$846$	8.23136			0.283000
$847$	10.3992	+	10.3992i	0.357321	+	0.357321i
$848$	33.7233			1.15806
$849$	−48.7474			−1.67301
$850$		0			0
$851$	10.6713			0.365807
$852$	−4.60227			−0.157671
$853$	2.05052	+	2.05052i	0.0702084	+	0.0702084i	0.741339	−	0.671131i	$-0.234191\pi$
$853$	2.05052	+	2.05052i	0.0702084	+	0.0702084i	−0.671131	+	0.741339i	$0.734191\pi$
$854$	−44.2813			−1.51528
$855$		0			0
$856$	−4.83948	−	4.83948i	−0.165410	−	0.165410i
$857$	19.7142	−	19.7142i	0.673425	−	0.673425i	−0.285079	−	0.958504i	$-0.592020\pi$
$857$	19.7142	−	19.7142i	0.673425	−	0.673425i	0.958504	+	0.285079i	$0.0920200\pi$
$858$	−11.3468			−0.387373
$859$		−	2.48841i		−	0.0849034i	−0.999099	−	0.0424517i	$-0.986483\pi$
$859$		−	2.48841i		−	0.0849034i	0.999099	−	0.0424517i	$-0.0135169\pi$
$860$		0			0
$861$	−6.88260	−	6.88260i	−0.234558	−	0.234558i
$862$	33.5680	+	33.5680i	1.14333	+	1.14333i
$863$		−	26.8323i		−	0.913381i	−0.889626	−	0.456690i	$-0.849035\pi$
$863$		−	26.8323i		−	0.913381i	0.889626	−	0.456690i	$-0.150965\pi$
$864$	−27.1955	+	27.1955i	−0.925211	+	0.925211i
$865$		0			0
$866$	−69.9024			−2.37538
$867$	13.2345	−	28.5949i	0.449466	−	0.971134i
$868$		−	26.1143i		−	0.886377i
$869$		−	0.676036i		−	0.0229330i
$870$		0			0
$871$	−30.7053			−1.04041
$872$	−2.00872	−	2.00872i	−0.0680240	−	0.0680240i
$873$	3.50652	−	3.50652i	0.118678	−	0.118678i
$874$	−12.8042	−	12.8042i	−0.433109	−	0.433109i
$875$		0			0
$876$		−	63.7510i		−	2.15395i
$877$	−23.6654	+	23.6654i	−0.799125	+	0.799125i	−0.982958	−	0.183833i	$-0.941150\pi$
$877$	−23.6654	+	23.6654i	−0.799125	+	0.799125i	0.183833	+	0.982958i	$0.441150\pi$
$878$	−5.74877	+	5.74877i	−0.194012	+	0.194012i
$879$	−10.7846	+	10.7846i	−0.363754	+	0.363754i
$880$		0			0
$881$	13.3394	−	13.3394i	0.449414	−	0.449414i	−0.445746	−	0.895160i	$-0.647061\pi$
$881$	13.3394	−	13.3394i	0.449414	−	0.449414i	0.895160	+	0.445746i	$0.147061\pi$
$882$	4.63808			0.156172
$883$		−	2.82469i		−	0.0950584i	−0.998870	−	0.0475292i	$-0.984865\pi$
$883$		−	2.82469i		−	0.0950584i	0.998870	−	0.0475292i	$-0.0151347\pi$
$884$	29.8506	−	42.7613i	1.00399	−	1.43822i
$885$		0			0
$886$		−	44.1258i		−	1.48243i
$887$	0.637734	+	0.637734i	0.0214130	+	0.0214130i	0.717732	−	0.696319i	$-0.245180\pi$
$887$	0.637734	+	0.637734i	0.0214130	+	0.0214130i	−0.696319	+	0.717732i	$0.745180\pi$
$888$		−	7.90109i		−	0.265143i
$889$	7.54805	−	7.54805i	0.253154	−	0.253154i
$890$		0			0
$891$	−3.89226	−	3.89226i	−0.130395	−	0.130395i
$892$	−15.5761			−0.521525
$893$	44.1112			1.47613
$894$	12.2619	+	12.2619i	0.410099	+	0.410099i
$895$		0			0
$896$	−5.46764	+	5.46764i	−0.182661	+	0.182661i
$897$		−	17.8856i		−	0.597183i
$898$	56.9537	+	56.9537i	1.90057	+	1.90057i
$899$		−	14.8814i		−	0.496322i
$900$		0			0
$901$	−35.6579	−	24.8919i	−1.18794	−	0.829270i
$902$		−	4.33381i		−	0.144300i
$903$	−9.33648			−0.310699
$904$	−1.79701	+	1.79701i	−0.0597676	+	0.0597676i
$905$		0			0
$906$	−17.3482	+	17.3482i	−0.576357	+	0.576357i
$907$	14.7962	−	14.7962i	0.491300	−	0.491300i	−0.417416	−	0.908716i	$-0.637064\pi$
$907$	14.7962	−	14.7962i	0.491300	−	0.491300i	0.908716	+	0.417416i	$0.137064\pi$
$908$	−17.4129	+	17.4129i	−0.577868	+	0.577868i
$909$			2.62204i			0.0869676i
$910$		0			0
$911$	40.0741	+	40.0741i	1.32771	+	1.32771i	0.907360	+	0.420355i	$0.138095\pi$
$911$	40.0741	+	40.0741i	1.32771	+	1.32771i	0.420355	+	0.907360i	$0.361905\pi$
$912$	20.3738	−	20.3738i	0.674643	−	0.674643i
$913$	5.19548	+	5.19548i	0.171945	+	0.171945i
$914$	37.3586			1.23571
$915$		0			0
$916$		−	36.0132i		−	1.18991i
$917$		−	27.7470i		−	0.916286i
$918$	40.2118	−	7.14982i	1.32719	−	0.235979i
$919$	−28.1639			−0.929040			−0.464520	−	0.885563i	$-0.653773\pi$
$919$	−28.1639			−0.929040			−0.464520	+	0.885563i	$0.653773\pi$
$920$		0			0
$921$	−0.812841	+	0.812841i	−0.0267840	+	0.0267840i
$922$			69.2235i			2.27976i
$923$	−4.04668	−	4.04668i	−0.133198	−	0.133198i
$924$	−2.29523	−	2.29523i	−0.0755075	−	0.0755075i
$925$		0			0
$926$			53.0555i			1.74351i
$927$	7.91441			0.259943
$928$	−10.4935	+	10.4935i	−0.344466	+	0.344466i
$929$	−18.9732	−	18.9732i	−0.622491	−	0.622491i	0.323676	−	0.946168i	$-0.395081\pi$
$929$	−18.9732	−	18.9732i	−0.622491	−	0.622491i	−0.946168	+	0.323676i	$0.895081\pi$
$930$		0			0
$931$	24.8551			0.814594
$932$	34.8390	+	34.8390i	1.14119	+	1.14119i
$933$	−42.7844			−1.40070
$934$	13.1608			0.430635
$935$		0			0
$936$	−1.67823			−0.0548546
$937$	−19.9363			−0.651291			−0.325645	−	0.945492i	$-0.605582\pi$
$937$	−19.9363			−0.651291			−0.325645	+	0.945492i	$0.605582\pi$
$938$	−11.5138	−	11.5138i	−0.375938	−	0.375938i
$939$	13.6194			0.444453
$940$		0			0
$941$	−1.68894	−	1.68894i	−0.0550580	−	0.0550580i	0.679042	−	0.734100i	$-0.262396\pi$
$941$	−1.68894	−	1.68894i	−0.0550580	−	0.0550580i	−0.734100	+	0.679042i	$0.762396\pi$
$942$	−17.4058	+	17.4058i	−0.567110	+	0.567110i
$943$	6.83125			0.222456
$944$		−	20.8729i		−	0.679355i
$945$		0			0
$946$	−2.93948	−	2.93948i	−0.0955707	−	0.0955707i
$947$	41.0290	+	41.0290i	1.33326	+	1.33326i	0.902434	+	0.430828i	$0.141778\pi$
$947$	41.0290	+	41.0290i	1.33326	+	1.33326i	0.430828	+	0.902434i	$0.358222\pi$
$948$		−	5.39475i		−	0.175213i
$949$	56.0549	−	56.0549i	1.81962	−	1.81962i
$950$		0			0
$951$	48.3086			1.56651
$952$	3.98208	−	0.708030i	0.129060	−	0.0229474i
$953$		−	10.4939i		−	0.339930i	−0.985450	−	0.169965i	$-0.945635\pi$
$953$		−	10.4939i		−	0.339930i	0.985450	−	0.169965i	$-0.0543654\pi$
$954$			9.56881i			0.309802i
$955$		0			0
$956$	21.3223			0.689613
$957$	−1.30795	−	1.30795i	−0.0422800	−	0.0422800i
$958$	42.1441	−	42.1441i	1.36161	−	1.36161i
$959$	16.2140	+	16.2140i	0.523578	+	0.523578i
$960$		0			0
$961$		−	34.8287i		−	1.12351i
$962$	47.5023	−	47.5023i	1.53154	−	1.53154i
$963$	−2.95104	+	2.95104i	−0.0950959	+	0.0950959i
$964$	−21.0835	+	21.0835i	−0.679053	+	0.679053i
$965$		0			0
$966$	6.70667	−	6.70667i	0.215784	−	0.215784i
$967$	−10.5850			−0.340391			−0.170195	−	0.985410i	$-0.554440\pi$
$967$	−10.5850			−0.340391			−0.170195	+	0.985410i	$0.554440\pi$
$968$			7.64219i			0.245629i
$969$	−36.5809	+	6.50423i	−1.17515	+	0.208946i
$970$		0			0
$971$			9.38889i			0.301304i	0.988587	+	0.150652i	$0.0481373\pi$
$971$			9.38889i			0.301304i	−0.988587	+	0.150652i	$0.951863\pi$
$972$	−7.43803	−	7.43803i	−0.238575	−	0.238575i
$973$		−	8.51588i		−	0.273007i
$974$	−7.55810	+	7.55810i	−0.242177	+	0.242177i
$975$		0			0
$976$	34.9669	+	34.9669i	1.11926	+	1.11926i
$977$	20.1085			0.643329			0.321664	−	0.946854i	$-0.395758\pi$
$977$	20.1085			0.643329			0.321664	+	0.946854i	$0.395758\pi$
$978$	16.1789			0.517345
$979$	−0.380840	−	0.380840i	−0.0121717	−	0.0121717i
$980$		0			0
$981$	−1.22489	+	1.22489i	−0.0391077	+	0.0391077i
$982$		−	61.4854i		−	1.96208i
$983$	−10.4090	−	10.4090i	−0.331994	−	0.331994i	0.521349	−	0.853343i	$-0.325429\pi$
$983$	−10.4090	−	10.4090i	−0.331994	−	0.331994i	−0.853343	+	0.521349i	$0.825429\pi$
$984$		−	5.05790i		−	0.161240i
$985$		0			0
$986$	15.5159	−	2.75878i	0.494126	−	0.0878576i
$987$			23.1049i			0.735436i
$988$	−61.4936			−1.95637
$989$	4.63341	−	4.63341i	0.147334	−	0.147334i
$990$		0			0
$991$	−21.3002	+	21.3002i	−0.676623	+	0.676623i	−0.959235	−	0.282611i	$-0.908799\pi$
$991$	−21.3002	+	21.3002i	−0.676623	+	0.676623i	0.282611	+	0.959235i	$0.408799\pi$
$992$	−46.4187	+	46.4187i	−1.47380	+	1.47380i
$993$	0.0255681	−	0.0255681i	0.000811378	−	0.000811378i
$994$		−	3.03482i		−	0.0962586i
$995$		0			0
$996$	41.4599	+	41.4599i	1.31371	+	1.31371i
$997$	−33.3429	+	33.3429i	−1.05598	+	1.05598i	−0.0576434	+	0.998337i	$0.518359\pi$
$997$	−33.3429	+	33.3429i	−1.05598	+	1.05598i	−0.998337	+	0.0576434i	$0.981641\pi$
$998$	−5.64885	−	5.64885i	−0.178811	−	0.178811i
$999$	28.3818			0.897959

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.j.d.174.1		12
5.2	odd	4		425.2.e.e.276.1	yes	12
5.3	odd	4		425.2.e.c.276.6	yes	12
5.4	even	2		425.2.j.a.174.6		12
17.13	even	4		425.2.j.a.149.6		12
85.8	odd	8		7225.2.a.bm.1.11		12
85.13	odd	4		425.2.e.c.251.1	✓	12
85.42	odd	8		7225.2.a.br.1.2		12
85.43	odd	8		7225.2.a.bm.1.12		12
85.47	odd	4		425.2.e.e.251.6	yes	12
85.64	even	4	inner	425.2.j.d.149.1		12
85.77	odd	8		7225.2.a.br.1.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.2.e.c.251.1	✓	12	85.13	odd	4
425.2.e.c.276.6	yes	12	5.3	odd	4
425.2.e.e.251.6	yes	12	85.47	odd	4
425.2.e.e.276.1	yes	12	5.2	odd	4
425.2.j.a.149.6		12	17.13	even	4
425.2.j.a.174.6		12	5.4	even	2
425.2.j.d.149.1		12	85.64	even	4	inner
425.2.j.d.174.1		12	1.1	even	1	trivial
7225.2.a.bm.1.11		12	85.8	odd	8
7225.2.a.bm.1.12		12	85.43	odd	8
7225.2.a.br.1.1		12	85.77	odd	8
7225.2.a.br.1.2		12	85.42	odd	8

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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.j (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-2.08389 q^{2} +(-1.31060 - 1.31060i) q^{3} +2.34261 q^{4} +(2.73116 + 2.73116i) q^{6} +(-0.971529 + 0.971529i) q^{7} -0.713960 q^{8} +0.435362i q^{9} +O(q^{10})\)	\(q-2.08389 q^{2} +(-1.31060 - 1.31060i) q^{3} +2.34261 q^{4} +(2.73116 + 2.73116i) q^{6} +(-0.971529 + 0.971529i) q^{7} -0.713960 q^{8} +0.435362i q^{9} +(-0.384742 - 0.384742i) q^{11} +(-3.07023 - 3.07023i) q^{12} -5.39918i q^{13} +(2.02456 - 2.02456i) q^{14} -3.19740 q^{16} +(3.38083 + 2.36008i) q^{17} -0.907247i q^{18} -4.86186i q^{19} +2.54658 q^{21} +(0.801760 + 0.801760i) q^{22} +(-1.26379 + 1.26379i) q^{23} +(0.935718 + 0.935718i) q^{24} +11.2513i q^{26} +(-3.36122 + 3.36122i) q^{27} +(-2.27591 + 2.27591i) q^{28} +(-1.29694 + 1.29694i) q^{29} +(-5.73710 + 5.73710i) q^{31} +8.09096 q^{32} +1.00849i q^{33} +(-7.04529 - 4.91815i) q^{34} +1.01988i q^{36} +(-4.22194 - 4.22194i) q^{37} +10.1316i q^{38} +(-7.07618 + 7.07618i) q^{39} +(-2.70269 - 2.70269i) q^{41} -5.30680 q^{42} -3.66628 q^{43} +(-0.901299 - 0.901299i) q^{44} +(2.63360 - 2.63360i) q^{46} +9.07290i q^{47} +(4.19053 + 4.19053i) q^{48} +5.11226i q^{49} +(-1.33781 - 7.52406i) q^{51} -12.6482i q^{52} -10.5471 q^{53} +(7.00443 - 7.00443i) q^{54} +(0.693633 - 0.693633i) q^{56} +(-6.37197 + 6.37197i) q^{57} +(2.70269 - 2.70269i) q^{58} +6.52808i q^{59} +(-10.9360 - 10.9360i) q^{61} +(11.9555 - 11.9555i) q^{62} +(-0.422967 - 0.422967i) q^{63} -10.4659 q^{64} -2.10158i q^{66} -5.68704i q^{67} +(7.91997 + 5.52874i) q^{68} +3.31265 q^{69} +(0.749500 - 0.749500i) q^{71} -0.310831i q^{72} +(10.3821 + 10.3821i) q^{73} +(8.79807 + 8.79807i) q^{74} -11.3894i q^{76} +0.747575 q^{77} +(14.7460 - 14.7460i) q^{78} +(0.878559 + 0.878559i) q^{79} +10.1165 q^{81} +(5.63211 + 5.63211i) q^{82} -13.5038 q^{83} +5.96564 q^{84} +7.64014 q^{86} +3.39955 q^{87} +(0.274690 + 0.274690i) q^{88} +0.989860 q^{89} +(5.24546 + 5.24546i) q^{91} +(-2.96056 + 2.96056i) q^{92} +15.0381 q^{93} -18.9070i q^{94} +(-10.6040 - 10.6040i) q^{96} +(-8.05428 - 8.05428i) q^{97} -10.6534i q^{98} +(0.167502 - 0.167502i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{2} + 2 q^{3} + 12 q^{4} + 6 q^{6} + 12 q^{8}+O(q^{10}) \) 12 * q + 4 * q^2 + 2 * q^3 + 12 * q^4 + 6 * q^6 + 12 * q^8	\( 12 q + 4 q^{2} + 2 q^{3} + 12 q^{4} + 6 q^{6} + 12 q^{8} - 4 q^{11} - 4 q^{12} - 14 q^{14} + 4 q^{16} - 10 q^{17} + 8 q^{21} + 10 q^{22} + 12 q^{23} + 8 q^{24} - 22 q^{27} - 34 q^{28} + 6 q^{29} - 6 q^{31} + 48 q^{32} - 30 q^{34} + 18 q^{37} - 16 q^{39} + 6 q^{41} - 56 q^{42} + 16 q^{43} - 32 q^{44} + 30 q^{46} + 10 q^{48} - 40 q^{51} - 48 q^{53} - 16 q^{54} - 56 q^{56} + 18 q^{57} - 6 q^{58} - 8 q^{61} + 22 q^{62} + 30 q^{63} + 44 q^{64} - 18 q^{68} + 72 q^{69} - 20 q^{71} + 18 q^{73} + 26 q^{74} - 24 q^{77} + 38 q^{78} + 14 q^{79} - 8 q^{81} - 10 q^{82} - 52 q^{83} - 36 q^{84} + 84 q^{86} + 48 q^{87} - 66 q^{88} + 24 q^{89} + 12 q^{91} + 32 q^{92} + 60 q^{93} + 22 q^{96} - 52 q^{97} - 30 q^{99}+O(q^{100}) \) 12 * q + 4 * q^2 + 2 * q^3 + 12 * q^4 + 6 * q^6 + 12 * q^8 - 4 * q^11 - 4 * q^12 - 14 * q^14 + 4 * q^16 - 10 * q^17 + 8 * q^21 + 10 * q^22 + 12 * q^23 + 8 * q^24 - 22 * q^27 - 34 * q^28 + 6 * q^29 - 6 * q^31 + 48 * q^32 - 30 * q^34 + 18 * q^37 - 16 * q^39 + 6 * q^41 - 56 * q^42 + 16 * q^43 - 32 * q^44 + 30 * q^46 + 10 * q^48 - 40 * q^51 - 48 * q^53 - 16 * q^54 - 56 * q^56 + 18 * q^57 - 6 * q^58 - 8 * q^61 + 22 * q^62 + 30 * q^63 + 44 * q^64 - 18 * q^68 + 72 * q^69 - 20 * q^71 + 18 * q^73 + 26 * q^74 - 24 * q^77 + 38 * q^78 + 14 * q^79 - 8 * q^81 - 10 * q^82 - 52 * q^83 - 36 * q^84 + 84 * q^86 + 48 * q^87 - 66 * q^88 + 24 * q^89 + 12 * q^91 + 32 * q^92 + 60 * q^93 + 22 * q^96 - 52 * q^97 - 30 * q^99

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