LMFDB - Embedded newform 85.2.e.a.21.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [85,2,Mod(21,85)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(85, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("85.21");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 85 = 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	85.e (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:	$0.678728417181$
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} + 83x^{8} + 152x^{6} + 111x^{4} + 22x^{2} + 1 $ x^12 + 18x^10 + 83x^8 + 152x^6 + 111x^4 + 22*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			21.2
Root			$-0.455023i$ of defining polynomial
Character	$\chi$	$=$	85.21
Dual form			85.2.e.a.81.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.783476i q^{2} +(0.385357 - 0.385357i) q^{3} +1.38617 q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.301918 - 0.301918i) q^{6} +(-0.840380 - 0.840380i) q^{7} -2.65298i q^{8} +2.70300i q^{9} +(0.554001 + 0.554001i) q^{10} +(-1.80608 - 1.80608i) q^{11} +(0.534168 - 0.534168i) q^{12} -0.368117 q^{13} +(-0.658417 + 0.658417i) q^{14} +0.544977i q^{15} +0.693788 q^{16} +(-2.46531 + 3.30488i) q^{17} +2.11773 q^{18} +6.61138i q^{19} +(-0.980167 + 0.980167i) q^{20} -0.647692 q^{21} +(-1.41502 + 1.41502i) q^{22} +(-2.73186 - 2.73186i) q^{23} +(-1.02234 - 1.02234i) q^{24} -1.00000i q^{25} +0.288411i q^{26} +(2.19769 + 2.19769i) q^{27} +(-1.16491 - 1.16491i) q^{28} +(-1.63466 + 1.63466i) q^{29} +0.426976 q^{30} +(4.68480 - 4.68480i) q^{31} -5.84952i q^{32} -1.39197 q^{33} +(2.58929 + 1.93151i) q^{34} +1.18848 q^{35} +3.74681i q^{36} +(2.24619 - 2.24619i) q^{37} +5.17986 q^{38} +(-0.141856 + 0.141856i) q^{39} +(1.87594 + 1.87594i) q^{40} +(-5.16572 - 5.16572i) q^{41} +0.507451i q^{42} -6.82350i q^{43} +(-2.50353 - 2.50353i) q^{44} +(-1.91131 - 1.91131i) q^{45} +(-2.14034 + 2.14034i) q^{46} +7.80793 q^{47} +(0.267356 - 0.267356i) q^{48} -5.58752i q^{49} -0.783476 q^{50} +(0.323534 + 2.22358i) q^{51} -0.510272 q^{52} +8.01219i q^{53} +(1.72184 - 1.72184i) q^{54} +2.55419 q^{55} +(-2.22951 + 2.22951i) q^{56} +(2.54774 + 2.54774i) q^{57} +(1.28072 + 1.28072i) q^{58} -5.22381i q^{59} +0.755428i q^{60} +(5.74267 + 5.74267i) q^{61} +(-3.67043 - 3.67043i) q^{62} +(2.27155 - 2.27155i) q^{63} -3.19538 q^{64} +(0.260298 - 0.260298i) q^{65} +1.09058i q^{66} -7.94564 q^{67} +(-3.41733 + 4.58111i) q^{68} -2.10548 q^{69} -0.931143i q^{70} +(8.40610 - 8.40610i) q^{71} +7.17100 q^{72} +(-10.4176 + 10.4176i) q^{73} +(-1.75984 - 1.75984i) q^{74} +(-0.385357 - 0.385357i) q^{75} +9.16447i q^{76} +3.03559i q^{77} +(0.111141 + 0.111141i) q^{78} +(0.575011 + 0.575011i) q^{79} +(-0.490582 + 0.490582i) q^{80} -6.41521 q^{81} +(-4.04721 + 4.04721i) q^{82} +3.99116i q^{83} -0.897809 q^{84} +(-0.593666 - 4.08014i) q^{85} -5.34604 q^{86} +1.25986i q^{87} +(-4.79150 + 4.79150i) q^{88} +9.14311 q^{89} +(-1.49746 + 1.49746i) q^{90} +(0.309359 + 0.309359i) q^{91} +(-3.78681 - 3.78681i) q^{92} -3.61064i q^{93} -6.11732i q^{94} +(-4.67495 - 4.67495i) q^{95} +(-2.25415 - 2.25415i) q^{96} +(-4.99529 + 4.99529i) q^{97} -4.37769 q^{98} +(4.88185 - 4.88185i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{3} - 12 q^{4} - 4 q^{10} - 4 q^{11} - 8 q^{12} - 4 q^{14} + 4 q^{16} + 12 q^{17} + 28 q^{18} - 8 q^{20} - 16 q^{21} + 20 q^{22} + 12 q^{23} + 4 q^{24} - 4 q^{27} + 4 q^{28} - 12 q^{29} - 8 q^{30}+ \cdots + 44 q^{98}+O(q^{100}) $ 12 * q - 4 * q^3 - 12 * q^4 - 4 * q^10 - 4 * q^11 - 8 * q^12 - 4 * q^14 + 4 * q^16 + 12 * q^17 + 28 * q^18 - 8 * q^20 - 16 * q^21 + 20 * q^22 + 12 * q^23 + 4 * q^24 - 4 * q^27 + 4 * q^28 - 12 * q^29 - 8 * q^30 - 16 * q^33 - 12 * q^34 + 16 * q^35 + 12 * q^37 + 24 * q^38 - 20 * q^39 - 8 * q^40 - 24 * q^41 + 8 * q^44 + 8 * q^45 - 24 * q^46 - 48 * q^47 - 20 * q^48 + 4 * q^50 + 32 * q^51 - 56 * q^52 + 28 * q^54 + 40 * q^56 + 36 * q^58 + 40 * q^61 + 40 * q^62 + 12 * q^63 + 28 * q^64 + 4 * q^65 - 8 * q^67 - 40 * q^68 + 28 * q^71 + 20 * q^72 - 48 * q^73 + 28 * q^74 + 4 * q^75 - 92 * q^78 - 8 * q^79 + 16 * q^80 + 28 * q^81 + 40 * q^82 - 4 * q^85 - 96 * q^86 - 72 * q^88 + 24 * q^89 - 16 * q^90 - 36 * q^91 - 16 * q^92 - 8 * q^95 - 32 * q^96 + 4 * q^97 + 44 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/85\mathbb{Z}\right)^\times$.

$n$	$52$	$71$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$		−	0.783476i		−	0.554001i	−0.960870	−	0.277000i	$-0.910660\pi$
$2$		−	0.783476i		−	0.554001i	0.960870	−	0.277000i	$-0.0893404\pi$
$3$	0.385357	−	0.385357i	0.222486	−	0.222486i	−0.587059	−	0.809544i	$-0.699714\pi$
$3$	0.385357	−	0.385357i	0.222486	−	0.222486i	0.809544	+	0.587059i	$0.199714\pi$
$4$	1.38617			0.693083
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$	−0.301918	−	0.301918i	−0.123257	−	0.123257i
$7$	−0.840380	−	0.840380i	−0.317634	−	0.317634i	0.530224	−	0.847858i	$-0.322108\pi$
$7$	−0.840380	−	0.840380i	−0.317634	−	0.317634i	−0.847858	+	0.530224i	$0.822108\pi$
$8$		−	2.65298i		−	0.937970i
$9$			2.70300i			0.901000i
$10$	0.554001	+	0.554001i	0.175190	+	0.175190i
$11$	−1.80608	−	1.80608i	−0.544555	−	0.544555i	0.380306	−	0.924861i	$-0.375819\pi$
$11$	−1.80608	−	1.80608i	−0.544555	−	0.544555i	−0.924861	+	0.380306i	$0.875819\pi$
$12$	0.534168	−	0.534168i	0.154201	−	0.154201i
$13$	−0.368117			−0.102097			−0.0510487	−	0.998696i	$-0.516256\pi$
$13$	−0.368117			−0.102097			−0.0510487	+	0.998696i	$0.516256\pi$
$14$	−0.658417	+	0.658417i	−0.175969	+	0.175969i
$15$			0.544977i			0.140712i
$16$	0.693788			0.173447
$17$	−2.46531	+	3.30488i	−0.597926	+	0.801552i
$17$	−2.46531	+	3.30488i	−0.597926	+	0.801552i
$18$	2.11773			0.499155
$19$			6.61138i			1.51676i	0.651816	+	0.758378i	$0.274008\pi$
$19$			6.61138i			1.51676i	−0.651816	+	0.758378i	$0.725992\pi$
$20$	−0.980167	+	0.980167i	−0.219172	+	0.219172i
$21$	−0.647692			−0.141338
$22$	−1.41502	+	1.41502i	−0.301684	+	0.301684i
$23$	−2.73186	−	2.73186i	−0.569632	−	0.569632i	0.362394	−	0.932025i	$-0.381960\pi$
$23$	−2.73186	−	2.73186i	−0.569632	−	0.569632i	−0.932025	+	0.362394i	$0.881960\pi$
$24$	−1.02234	−	1.02234i	−0.208685	−	0.208685i
$25$		−	1.00000i		−	0.200000i
$26$			0.288411i			0.0565621i
$27$	2.19769	+	2.19769i	0.422945	+	0.422945i
$28$	−1.16491	−	1.16491i	−0.220147	−	0.220147i
$29$	−1.63466	+	1.63466i	−0.303549	+	0.303549i	−0.842401	−	0.538851i	$-0.818858\pi$
$29$	−1.63466	+	1.63466i	−0.303549	+	0.303549i	0.538851	+	0.842401i	$0.318858\pi$
$30$	0.426976			0.0779548
$31$	4.68480	−	4.68480i	0.841415	−	0.841415i	−0.147628	−	0.989043i	$-0.547164\pi$
$31$	4.68480	−	4.68480i	0.841415	−	0.841415i	0.989043	+	0.147628i	$0.0471639\pi$
$32$		−	5.84952i		−	1.03406i
$33$	−1.39197			−0.242311
$34$	2.58929	+	1.93151i	0.444060	+	0.331251i
$35$	1.18848			0.200889
$36$			3.74681i			0.624468i
$37$	2.24619	−	2.24619i	0.369271	−	0.369271i	−0.497940	−	0.867211i	$-0.665910\pi$
$37$	2.24619	−	2.24619i	0.369271	−	0.369271i	0.867211	+	0.497940i	$0.165910\pi$
$38$	5.17986			0.840284
$39$	−0.141856	+	0.141856i	−0.0227152	+	0.0227152i
$40$	1.87594	+	1.87594i	0.296612	+	0.296612i
$41$	−5.16572	−	5.16572i	−0.806749	−	0.806749i	0.177391	−	0.984140i	$-0.443234\pi$
$41$	−5.16572	−	5.16572i	−0.806749	−	0.806749i	−0.984140	+	0.177391i	$0.943234\pi$
$42$			0.507451i			0.0783014i
$43$		−	6.82350i		−	1.04057i	−0.853992	−	0.520287i	$-0.825825\pi$
$43$		−	6.82350i		−	1.04057i	0.853992	−	0.520287i	$-0.174175\pi$
$44$	−2.50353	−	2.50353i	−0.377422	−	0.377422i
$45$	−1.91131	−	1.91131i	−0.284921	−	0.284921i
$46$	−2.14034	+	2.14034i	−0.315576	+	0.315576i
$47$	7.80793			1.13890			0.569452	−	0.822025i	$-0.307156\pi$
$47$	7.80793			1.13890			0.569452	+	0.822025i	$0.307156\pi$
$48$	0.267356	−	0.267356i	0.0385895	−	0.0385895i
$49$		−	5.58752i		−	0.798218i
$50$	−0.783476			−0.110800
$51$	0.323534	+	2.22358i	0.0453038	+	0.311364i
$52$	−0.510272			−0.0707620
$53$			8.01219i			1.10056i	0.834980	+	0.550280i	$0.185479\pi$
$53$			8.01219i			1.10056i	−0.834980	+	0.550280i	$0.814521\pi$
$54$	1.72184	−	1.72184i	0.234312	−	0.234312i
$55$	2.55419			0.344407
$56$	−2.22951	+	2.22951i	−0.297931	+	0.297931i
$57$	2.54774	+	2.54774i	0.337456	+	0.337456i
$58$	1.28072	+	1.28072i	0.168167	+	0.168167i
$59$		−	5.22381i		−	0.680082i	−0.940411	−	0.340041i	$-0.889559\pi$
$59$		−	5.22381i		−	0.680082i	0.940411	−	0.340041i	$-0.110441\pi$
$60$			0.755428i			0.0975253i
$61$	5.74267	+	5.74267i	0.735273	+	0.735273i	0.971659	−	0.236386i	$-0.0759630\pi$
$61$	5.74267	+	5.74267i	0.735273	+	0.735273i	−0.236386	+	0.971659i	$0.575963\pi$
$62$	−3.67043	−	3.67043i	−0.466145	−	0.466145i
$63$	2.27155	−	2.27155i	0.286188	−	0.286188i
$64$	−3.19538			−0.399423
$65$	0.260298	−	0.260298i	0.0322860	−	0.0322860i
$66$			1.09058i			0.134241i
$67$	−7.94564			−0.970715			−0.485357	−	0.874316i	$-0.661310\pi$
$67$	−7.94564			−0.970715			−0.485357	+	0.874316i	$0.661310\pi$
$68$	−3.41733	+	4.58111i	−0.414412	+	0.555542i
$69$	−2.10548			−0.253470
$70$		−	0.931143i		−	0.111293i
$71$	8.40610	−	8.40610i	0.997621	−	0.997621i	−0.00237624	−	0.999997i	$-0.500756\pi$
$71$	8.40610	−	8.40610i	0.997621	−	0.997621i	0.999997	+	0.00237624i	$0.000756380\pi$
$72$	7.17100			0.845111
$73$	−10.4176	+	10.4176i	−1.21929	+	1.21929i	−0.251409	+	0.967881i	$0.580894\pi$
$73$	−10.4176	+	10.4176i	−1.21929	+	1.21929i	−0.967881	+	0.251409i	$0.919106\pi$
$74$	−1.75984	−	1.75984i	−0.204577	−	0.204577i
$75$	−0.385357	−	0.385357i	−0.0444972	−	0.0444972i
$76$			9.16447i			1.05124i
$77$			3.03559i			0.345938i
$78$	0.111141	+	0.111141i	0.0125843	+	0.0125843i
$79$	0.575011	+	0.575011i	0.0646938	+	0.0646938i	0.738713	−	0.674020i	$-0.235434\pi$
$79$	0.575011	+	0.575011i	0.0646938	+	0.0646938i	−0.674020	+	0.738713i	$0.735434\pi$
$80$	−0.490582	+	0.490582i	−0.0548488	+	0.0548488i
$81$	−6.41521			−0.712801
$82$	−4.04721	+	4.04721i	−0.446940	+	0.446940i
$83$			3.99116i			0.438087i	0.975715	+	0.219044i	$0.0702937\pi$
$83$			3.99116i			0.438087i	−0.975715	+	0.219044i	$0.929706\pi$
$84$	−0.897809			−0.0979590
$85$	−0.593666	−	4.08014i	−0.0643921	−	0.442554i
$86$	−5.34604			−0.576479
$87$			1.25986i			0.135071i
$88$	−4.79150	+	4.79150i	−0.510776	+	0.510776i
$89$	9.14311			0.969168			0.484584	−	0.874745i	$-0.338971\pi$
$89$	9.14311			0.969168			0.484584	+	0.874745i	$0.338971\pi$
$90$	−1.49746	+	1.49746i	−0.157847	+	0.157847i
$91$	0.309359	+	0.309359i	0.0324296	+	0.0324296i
$92$	−3.78681	−	3.78681i	−0.394802	−	0.394802i
$93$		−	3.61064i		−	0.374406i
$94$		−	6.11732i		−	0.630953i
$95$	−4.67495	−	4.67495i	−0.479640	−	0.479640i
$96$	−2.25415	−	2.25415i	−0.230063	−	0.230063i
$97$	−4.99529	+	4.99529i	−0.507195	+	0.507195i	−0.913664	−	0.406470i	$-0.866760\pi$
$97$	−4.99529	+	4.99529i	−0.507195	+	0.507195i	0.406470	+	0.913664i	$0.366760\pi$
$98$	−4.37769			−0.442213
$99$	4.88185	−	4.88185i	0.490644	−	0.490644i
$100$		−	1.38617i		−	0.138617i
$101$	0.296263			0.0294793			0.0147396	−	0.999891i	$-0.495308\pi$
$101$	0.296263			0.0294793			0.0147396	+	0.999891i	$0.495308\pi$
$102$	1.74212	−	0.253481i	0.172496	−	0.0250984i
$103$	17.0372			1.67873			0.839363	−	0.543571i	$-0.182928\pi$
$103$	17.0372			1.67873			0.839363	+	0.543571i	$0.182928\pi$
$104$			0.976608i			0.0957642i
$105$	0.457987	−	0.457987i	0.0446950	−	0.0446950i
$106$	6.27736			0.609711
$107$	−2.69319	+	2.69319i	−0.260360	+	0.260360i	−0.825200	−	0.564840i	$-0.808938\pi$
$107$	−2.69319	+	2.69319i	−0.260360	+	0.260360i	0.564840	+	0.825200i	$0.308938\pi$
$108$	3.04636	+	3.04636i	0.293136	+	0.293136i
$109$	−8.51171	−	8.51171i	−0.815274	−	0.815274i	0.170145	−	0.985419i	$-0.445576\pi$
$109$	−8.51171	−	8.51171i	−0.815274	−	0.815274i	−0.985419	+	0.170145i	$0.945576\pi$
$110$		−	2.00114i		−	0.190802i
$111$		−	1.73117i		−	0.164315i
$112$	−0.583046	−	0.583046i	−0.0550926	−	0.0550926i
$113$	11.6545	+	11.6545i	1.09636	+	1.09636i	0.994833	+	0.101526i	$0.0323724\pi$
$113$	11.6545	+	11.6545i	1.09636	+	1.09636i	0.101526	+	0.994833i	$0.467628\pi$
$114$	1.99609	−	1.99609i	0.186951	−	0.186951i
$115$	3.86343			0.360267
$116$	−2.26592	+	2.26592i	−0.210385	+	0.210385i
$117$		−	0.995022i		−	0.0919898i
$118$	−4.09272			−0.376766
$119$	4.84915	−	0.705558i	0.444521	−	0.0646784i
$120$	1.44581			0.131984
$121$		−	4.47612i		−	0.406920i
$122$	4.49924	−	4.49924i	0.407342	−	0.407342i
$123$	−3.98129			−0.358980
$124$	6.49391	−	6.49391i	0.583170	−	0.583170i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	−1.77970	−	1.77970i	−0.158548	−	0.158548i
$127$			4.48798i			0.398244i	0.979975	+	0.199122i	$0.0638090\pi$
$127$			4.48798i			0.398244i	−0.979975	+	0.199122i	$0.936191\pi$
$128$		−	9.19554i		−	0.812779i
$129$	−2.62948	−	2.62948i	−0.231513	−	0.231513i
$130$	−0.203937	−	0.203937i	−0.0178865	−	0.0178865i
$131$	−6.60646	+	6.60646i	−0.577209	+	0.577209i	−0.934133	−	0.356924i	$-0.883826\pi$
$131$	−6.60646	+	6.60646i	−0.577209	+	0.577209i	0.356924	+	0.934133i	$0.383826\pi$
$132$	−1.92951			−0.167942
$133$	5.55607	−	5.55607i	0.481773	−	0.481773i
$134$			6.22522i			0.537777i
$135$	−3.10800			−0.267494
$136$	8.76778	+	6.54042i	0.751831	+	0.560836i
$137$	8.47822			0.724344			0.362172	−	0.932111i	$-0.382035\pi$
$137$	8.47822			0.724344			0.362172	+	0.932111i	$0.382035\pi$
$138$			1.64959i			0.140423i
$139$	−4.24761	+	4.24761i	−0.360277	+	0.360277i	−0.863915	−	0.503638i	$-0.831995\pi$
$139$	−4.24761	+	4.24761i	−0.360277	+	0.360277i	0.503638	+	0.863915i	$0.331995\pi$
$140$	1.64743			0.139233
$141$	3.00884	−	3.00884i	0.253390	−	0.253390i
$142$	−6.58598	−	6.58598i	−0.552683	−	0.552683i
$143$	0.664851	+	0.664851i	0.0555976	+	0.0555976i
$144$			1.87531i			0.156276i
$145$		−	2.31176i		−	0.191982i
$146$	8.16195	+	8.16195i	0.675488	+	0.675488i
$147$	−2.15319	−	2.15319i	−0.177592	−	0.177592i
$148$	3.11359	−	3.11359i	0.255936	−	0.255936i
$149$	9.11821			0.746993			0.373497	−	0.927632i	$-0.378159\pi$
$149$	9.11821			0.746993			0.373497	+	0.927632i	$0.378159\pi$
$150$	−0.301918	+	0.301918i	−0.0246515	+	0.0246515i
$151$		−	13.1144i		−	1.06724i	−0.845725	−	0.533619i	$-0.820832\pi$
$151$		−	13.1144i		−	1.06724i	0.845725	−	0.533619i	$-0.179168\pi$
$152$	17.5399			1.42267
$153$	−8.93310	−	6.66374i	−0.722198	−	0.538731i
$154$	2.37831			0.191650
$155$			6.62531i			0.532157i
$156$	−0.196637	+	0.196637i	−0.0157435	+	0.0157435i
$157$	−20.0496			−1.60013			−0.800065	−	0.599913i	$-0.795202\pi$
$157$	−20.0496			−1.60013			−0.800065	+	0.599913i	$0.795202\pi$
$158$	0.450507	−	0.450507i	0.0358404	−	0.0358404i
$159$	3.08755	+	3.08755i	0.244859	+	0.244859i
$160$	4.13624	+	4.13624i	0.326998	+	0.326998i
$161$			4.59160i			0.361869i
$162$			5.02616i			0.394893i
$163$	−10.0910	−	10.0910i	−0.790386	−	0.790386i	0.191170	−	0.981557i	$-0.438772\pi$
$163$	−10.0910	−	10.0910i	−0.790386	−	0.790386i	−0.981557	+	0.191170i	$0.938772\pi$
$164$	−7.16054	−	7.16054i	−0.559144	−	0.559144i
$165$	0.984274	−	0.984274i	0.0766256	−	0.0766256i
$166$	3.12698			0.242701
$167$	−0.157215	+	0.157215i	−0.0121656	+	0.0121656i	−0.713163	−	0.700998i	$-0.752738\pi$
$167$	−0.157215	+	0.157215i	−0.0121656	+	0.0121656i	0.700998	+	0.713163i	$0.252738\pi$
$168$			1.71831i			0.132571i
$169$	−12.8645			−0.989576
$170$	−3.19669	+	0.465123i	−0.245175	+	0.0356733i
$171$	−17.8706			−1.36660
$172$		−	9.45850i		−	0.721204i
$173$	−14.1383	+	14.1383i	−1.07492	+	1.07492i	−0.0779592	+	0.996957i	$0.524840\pi$
$173$	−14.1383	+	14.1383i	−1.07492	+	1.07492i	−0.996957	+	0.0779592i	$0.975160\pi$
$174$	0.987067			0.0748294
$175$	−0.840380	+	0.840380i	−0.0635268	+	0.0635268i
$176$	−1.25304	−	1.25304i	−0.0944514	−	0.0944514i
$177$	−2.01303	−	2.01303i	−0.151308	−	0.151308i
$178$		−	7.16341i		−	0.536920i
$179$			24.3120i			1.81716i	0.417708	+	0.908581i	$0.362834\pi$
$179$			24.3120i			1.81716i	−0.417708	+	0.908581i	$0.637166\pi$
$180$	−2.64939	−	2.64939i	−0.197474	−	0.197474i
$181$	8.40507	+	8.40507i	0.624744	+	0.624744i	0.946741	−	0.321997i	$-0.104354\pi$
$181$	8.40507	+	8.40507i	0.624744	+	0.624744i	−0.321997	+	0.946741i	$0.604354\pi$
$182$	0.242375	−	0.242375i	0.0179660	−	0.0179660i
$183$	4.42595			0.327176
$184$	−7.24756	+	7.24756i	−0.534297	+	0.534297i
$185$			3.17659i			0.233548i
$186$	−2.82885			−0.207421
$187$	10.4215	−	1.51634i	0.762092	−	0.110885i
$188$	10.8231			0.789354
$189$		−	3.69379i		−	0.268684i
$190$	−3.66271	+	3.66271i	−0.265721	+	0.265721i
$191$	−17.2930			−1.25128			−0.625638	−	0.780114i	$-0.715161\pi$
$191$	−17.2930			−1.25128			−0.625638	+	0.780114i	$0.715161\pi$
$192$	−1.23136	+	1.23136i	−0.0888659	+	0.0888659i
$193$	1.27952	+	1.27952i	0.0921022	+	0.0921022i	0.751657	−	0.659555i	$-0.229255\pi$
$193$	1.27952	+	1.27952i	0.0921022	+	0.0921022i	−0.659555	+	0.751657i	$0.729255\pi$
$194$	3.91369	+	3.91369i	0.280986	+	0.280986i
$195$		−	0.200615i		−	0.0143664i
$196$		−	7.74523i		−	0.553231i
$197$	11.7227	+	11.7227i	0.835207	+	0.835207i	0.988224	−	0.153017i	$-0.0488989\pi$
$197$	11.7227	+	11.7227i	0.835207	+	0.835207i	−0.153017	+	0.988224i	$0.548899\pi$
$198$	−3.82481	−	3.82481i	−0.271817	−	0.271817i
$199$	−17.7915	+	17.7915i	−1.26121	+	1.26121i	−0.310698	+	0.950509i	$0.600563\pi$
$199$	−17.7915	+	17.7915i	−1.26121	+	1.26121i	−0.950509	+	0.310698i	$0.899437\pi$
$200$	−2.65298			−0.187594
$201$	−3.06191	+	3.06191i	−0.215970	+	0.215970i
$202$		−	0.232115i		−	0.0163315i
$203$	2.74748			0.192835
$204$	0.448472	+	3.08225i	0.0313993	+	0.215801i
$205$	7.30543			0.510233
$206$		−	13.3482i		−	0.930016i
$207$	7.38421	−	7.38421i	0.513238	−	0.513238i
$208$	−0.255396			−0.0177085
$209$	11.9407	−	11.9407i	0.825956	−	0.825956i
$210$	−0.358822	−	0.358822i	−0.0247611	−	0.0247611i
$211$	5.94554	+	5.94554i	0.409308	+	0.409308i	0.881497	−	0.472189i	$-0.156536\pi$
$211$	5.94554	+	5.94554i	0.409308	+	0.409308i	−0.472189	+	0.881497i	$0.656536\pi$
$212$			11.1062i			0.762779i
$213$		−	6.47870i		−	0.443913i
$214$	2.11005	+	2.11005i	0.144240	+	0.144240i
$215$	4.82494	+	4.82494i	0.329058	+	0.329058i
$216$	5.83042	−	5.83042i	0.396710	−	0.396710i
$217$	−7.87402			−0.534524
$218$	−6.66872	+	6.66872i	−0.451663	+	0.451663i
$219$			8.02900i			0.542549i
$220$	3.54053			0.238702
$221$	0.907524	−	1.21658i	0.0610467	−	0.0818363i
$222$	−1.35633			−0.0910308
$223$		−	16.5499i		−	1.10826i	−0.832429	−	0.554132i	$-0.813050\pi$
$223$		−	16.5499i		−	1.10826i	0.832429	−	0.554132i	$-0.186950\pi$
$224$	−4.91582	+	4.91582i	−0.328452	+	0.328452i
$225$	2.70300			0.180200
$226$	9.13098	−	9.13098i	0.607384	−	0.607384i
$227$	−5.03248	−	5.03248i	−0.334017	−	0.334017i	0.520093	−	0.854110i	$-0.325897\pi$
$227$	−5.03248	−	5.03248i	−0.334017	−	0.334017i	−0.854110	+	0.520093i	$0.825897\pi$
$228$	3.53159	+	3.53159i	0.233885	+	0.233885i
$229$			1.46774i			0.0969907i	0.998823	+	0.0484953i	$0.0154426\pi$
$229$			1.46774i			0.0969907i	−0.998823	+	0.0484953i	$0.984557\pi$
$230$		−	3.02690i		−	0.199588i
$231$	1.16979	+	1.16979i	0.0769663	+	0.0769663i
$232$	4.33673	+	4.33673i	0.284720	+	0.284720i
$233$	16.3810	−	16.3810i	1.07316	−	1.07316i	0.0760541	−	0.997104i	$-0.475768\pi$
$233$	16.3810	−	16.3810i	1.07316	−	1.07316i	0.997104	−	0.0760541i	$-0.0242322\pi$
$234$	−0.779575			−0.0509624
$235$	−5.52104	+	5.52104i	−0.360153	+	0.360153i
$236$		−	7.24106i		−	0.471353i
$237$	0.443169			0.0287869
$238$	−0.552788	−	3.79919i	−0.0358319	−	0.246265i
$239$	−6.43252			−0.416085			−0.208042	−	0.978120i	$-0.566709\pi$
$239$	−6.43252			−0.416085			−0.208042	+	0.978120i	$0.566709\pi$
$240$			0.378098i			0.0244061i
$241$	19.3719	−	19.3719i	1.24785	−	1.24785i	0.291183	−	0.956667i	$-0.405951\pi$
$241$	19.3719	−	19.3719i	1.24785	−	1.24785i	0.956667	−	0.291183i	$-0.0940490\pi$
$242$	−3.50693			−0.225434
$243$	−9.06521	+	9.06521i	−0.581534	+	0.581534i
$244$	7.96029	+	7.96029i	0.509605	+	0.509605i
$245$	3.95098	+	3.95098i	0.252419	+	0.252419i
$246$			3.11924i			0.198875i
$247$		−	2.43376i		−	0.154857i
$248$	−12.4287	−	12.4287i	−0.789221	−	0.789221i
$249$	1.53802	+	1.53802i	0.0974681	+	0.0974681i
$250$	0.554001	−	0.554001i	0.0350381	−	0.0350381i
$251$	0.234413			0.0147960			0.00739800	−	0.999973i	$-0.497645\pi$
$251$	0.234413			0.0147960			0.00739800	+	0.999973i	$0.497645\pi$
$252$	3.14874	−	3.14874i	0.198352	−	0.198352i
$253$			9.86793i			0.620391i
$254$	3.51623			0.220628
$255$	−1.80108	−	1.34354i	−0.112788	−	0.0841355i
$256$	−13.5952			−0.849703
$257$		−	3.56040i		−	0.222092i	−0.993815	−	0.111046i	$-0.964580\pi$
$257$		−	3.56040i		−	0.222092i	0.993815	−	0.111046i	$-0.0354201\pi$
$258$	−2.06013	+	2.06013i	−0.128258	+	0.128258i
$259$	−3.77531			−0.234586
$260$	0.360817	−	0.360817i	0.0223769	−	0.0223769i
$261$	−4.41850	−	4.41850i	−0.273498	−	0.273498i
$262$	5.17600	+	5.17600i	0.319775	+	0.319775i
$263$		−	30.0000i		−	1.84988i	−0.380112	−	0.924940i	$-0.624115\pi$
$263$		−	30.0000i		−	1.84988i	0.380112	−	0.924940i	$-0.375885\pi$
$264$			3.69287i			0.227281i
$265$	−5.66547	−	5.66547i	−0.348027	−	0.348027i
$266$	−4.35305	−	4.35305i	−0.266902	−	0.266902i
$267$	3.52336	−	3.52336i	0.215626	−	0.215626i
$268$	−11.0140			−0.672786
$269$	−0.268165	+	0.268165i	−0.0163503	+	0.0163503i	−0.715235	−	0.698884i	$-0.753680\pi$
$269$	−0.268165	+	0.268165i	−0.0163503	+	0.0163503i	0.698884	+	0.715235i	$0.253680\pi$
$270$			2.43504i			0.148192i
$271$	10.6144			0.644780			0.322390	−	0.946607i	$-0.395514\pi$
$271$	10.6144			0.644780			0.322390	+	0.946607i	$0.395514\pi$
$272$	−1.71040	+	2.29289i	−0.103708	+	0.139027i
$273$	0.238427			0.0144302
$274$		−	6.64248i		−	0.401287i
$275$	−1.80608	+	1.80608i	−0.108911	+	0.108911i
$276$	−2.91854			−0.175676
$277$	21.5614	−	21.5614i	1.29550	−	1.29550i	0.364167	−	0.931334i	$-0.381354\pi$
$277$	21.5614	−	21.5614i	1.29550	−	1.29550i	0.931334	−	0.364167i	$-0.118646\pi$
$278$	3.32790	+	3.32790i	0.199594	+	0.199594i
$279$	12.6630	+	12.6630i	0.758115	+	0.758115i
$280$		−	3.15300i		−	0.188428i
$281$			26.4402i			1.57729i	0.614849	+	0.788645i	$0.289217\pi$
$281$			26.4402i			1.57729i	−0.614849	+	0.788645i	$0.710783\pi$
$282$	−2.35735	−	2.35735i	−0.140378	−	0.140378i
$283$	13.1353	+	13.1353i	0.780813	+	0.780813i	0.979968	−	0.199155i	$-0.0638198\pi$
$283$	13.1353	+	13.1353i	0.780813	+	0.780813i	−0.199155	+	0.979968i	$0.563820\pi$
$284$	11.6523	−	11.6523i	0.691434	−	0.691434i
$285$	−3.60305			−0.213426
$286$	0.520895	−	0.520895i	0.0308011	−	0.0308011i
$287$			8.68233i			0.512502i
$288$	15.8113			0.931688
$289$	−4.84448	−	16.2951i	−0.284970	−	0.958537i
$290$	−1.81121			−0.106358
$291$			3.84993i			0.225687i
$292$	−14.4405	+	14.4405i	−0.845069	+	0.845069i
$293$	3.59958			0.210289			0.105145	−	0.994457i	$-0.466469\pi$
$293$	3.59958			0.210289			0.105145	+	0.994457i	$0.466469\pi$
$294$	−1.68697	+	1.68697i	−0.0983861	+	0.0983861i
$295$	3.69379	+	3.69379i	0.215061	+	0.215061i
$296$	−5.95910	−	5.95910i	−0.346365	−	0.346365i
$297$		−	7.93842i		−	0.460634i
$298$		−	7.14390i		−	0.413835i
$299$	1.00564	+	1.00564i	0.0581579	+	0.0581579i
$300$	−0.534168	−	0.534168i	−0.0308402	−	0.0308402i
$301$	−5.73433	+	5.73433i	−0.330521	+	0.330521i
$302$	−10.2748			−0.591251
$303$	0.114167	−	0.114167i	0.00655872	−	0.00655872i
$304$			4.58690i			0.263077i
$305$	−8.12136			−0.465027
$306$	−5.22087	+	6.99886i	−0.298458	+	0.400098i
$307$	−33.4128			−1.90697			−0.953486	−	0.301438i	$-0.902533\pi$
$307$	−33.4128			−1.90697			−0.953486	+	0.301438i	$0.902533\pi$
$308$			4.20784i			0.239764i
$309$	6.56540	−	6.56540i	0.373493	−	0.373493i
$310$	5.19077			0.294816
$311$	9.75529	−	9.75529i	0.553172	−	0.553172i	−0.374183	−	0.927355i	$-0.622077\pi$
$311$	9.75529	−	9.75529i	0.553172	−	0.553172i	0.927355	+	0.374183i	$0.122077\pi$
$312$	0.376342	+	0.376342i	0.0213062	+	0.0213062i
$313$	21.6164	+	21.6164i	1.22183	+	1.22183i	0.966980	+	0.254853i	$0.0820271\pi$
$313$	21.6164	+	21.6164i	1.22183	+	1.22183i	0.254853	+	0.966980i	$0.417973\pi$
$314$			15.7084i			0.886473i
$315$			3.21245i			0.181001i
$316$	0.797061	+	0.797061i	0.0448382	+	0.0448382i
$317$	−2.27476	−	2.27476i	−0.127763	−	0.127763i	0.640334	−	0.768097i	$-0.278796\pi$
$317$	−2.27476	−	2.27476i	−0.127763	−	0.127763i	−0.768097	+	0.640334i	$0.778796\pi$
$318$	2.41902	−	2.41902i	0.135652	−	0.135652i
$319$	5.90468			0.330599
$320$	2.25948	−	2.25948i	0.126309	−	0.126309i
$321$			2.07568i			0.115853i
$322$	3.59740			0.200475
$323$	−21.8498	−	16.2991i	−1.21576	−	0.906907i
$324$	−8.89255			−0.494031
$325$			0.368117i			0.0204195i
$326$	−7.90604	+	7.90604i	−0.437875	+	0.437875i
$327$	−6.56009			−0.362774
$328$	−13.7045	+	13.7045i	−0.756706	+	0.756706i
$329$	−6.56163	−	6.56163i	−0.361754	−	0.361754i
$330$	−0.771154	−	0.771154i	−0.0424507	−	0.0424507i
$331$			29.7637i			1.63596i	0.575246	+	0.817981i	$0.304906\pi$
$331$			29.7637i			1.63596i	−0.575246	+	0.817981i	$0.695094\pi$
$332$			5.53242i			0.303631i
$333$	6.07145	+	6.07145i	0.332714	+	0.332714i
$334$	0.123174	+	0.123174i	0.00673977	+	0.00673977i
$335$	5.61842	−	5.61842i	0.306967	−	0.306967i
$336$	−0.449361			−0.0245147
$337$	7.58826	−	7.58826i	0.413359	−	0.413359i	−0.469548	−	0.882907i	$-0.655583\pi$
$337$	7.58826	−	7.58826i	0.413359	−	0.413359i	0.882907	+	0.469548i	$0.155583\pi$
$338$			10.0790i			0.548226i
$339$	8.98224			0.487848
$340$	−0.822920	−	5.65575i	−0.0446291	−	0.306726i
$341$	−16.9223			−0.916393
$342$			14.0012i			0.757096i
$343$	−10.5783	+	10.5783i	−0.571175	+	0.571175i
$344$	−18.1026			−0.976026
$345$	1.48880	−	1.48880i	0.0801542	−	0.0801542i
$346$	11.0770	+	11.0770i	0.595504	+	0.595504i
$347$	0.809045	+	0.809045i	0.0434318	+	0.0434318i	0.728489	−	0.685057i	$-0.240223\pi$
$347$	0.809045	+	0.809045i	0.0434318	+	0.0434318i	−0.685057	+	0.728489i	$0.740223\pi$
$348$			1.74637i			0.0936153i
$349$		−	18.6531i		−	0.998476i	−0.866465	−	0.499238i	$-0.833613\pi$
$349$		−	18.6531i		−	0.998476i	0.866465	−	0.499238i	$-0.166387\pi$
$350$	0.658417	+	0.658417i	0.0351939	+	0.0351939i
$351$	−0.809008	−	0.809008i	−0.0431816	−	0.0431816i
$352$	−10.5647	+	10.5647i	−0.563102	+	0.563102i
$353$	4.34305			0.231157			0.115579	−	0.993298i	$-0.463128\pi$
$353$	4.34305			0.231157			0.115579	+	0.993298i	$0.463128\pi$
$354$	−1.57716	+	1.57716i	−0.0838250	+	0.0838250i
$355$			11.8880i			0.630951i
$356$	12.6739			0.671714
$357$	1.59676	−	2.14055i	0.0845096	−	0.113290i
$358$	19.0478			1.00671
$359$		−	6.35821i		−	0.335573i	−0.985823	−	0.167787i	$-0.946338\pi$
$359$		−	6.35821i		−	0.335573i	0.985823	−	0.167787i	$-0.0536620\pi$
$360$	−5.07066	+	5.07066i	−0.267247	+	0.267247i
$361$	−24.7104			−1.30055
$362$	6.58517	−	6.58517i	0.346109	−	0.346109i
$363$	−1.72490	−	1.72490i	−0.0905339	−	0.0905339i
$364$	0.428822	+	0.428822i	0.0224764	+	0.0224764i
$365$		−	14.7327i		−	0.771147i
$366$		−	3.46762i		−	0.181256i
$367$	−11.4655	−	11.4655i	−0.598496	−	0.598496i	0.341416	−	0.939912i	$-0.389093\pi$
$367$	−11.4655	−	11.4655i	−0.598496	−	0.598496i	−0.939912	+	0.341416i	$0.889093\pi$
$368$	−1.89533	−	1.89533i	−0.0988009	−	0.0988009i
$369$	13.9629	−	13.9629i	0.726881	−	0.726881i
$370$	2.48878			0.129386
$371$	6.73329	−	6.73329i	0.349575	−	0.349575i
$372$		−	5.00494i		−	0.259494i
$373$	−18.5947			−0.962797			−0.481398	−	0.876502i	$-0.659871\pi$
$373$	−18.5947			−0.962797			−0.481398	+	0.876502i	$0.659871\pi$
$374$	−1.18801	−	8.16495i	−0.0614306	−	0.422200i
$375$	0.544977			0.0281425
$376$		−	20.7143i		−	1.06826i
$377$	0.601748	−	0.601748i	0.0309916	−	0.0309916i
$378$	−2.89399			−0.148851
$379$	−6.40722	+	6.40722i	−0.329117	+	0.329117i	−0.852251	−	0.523134i	$-0.824763\pi$
$379$	−6.40722	+	6.40722i	−0.329117	+	0.329117i	0.523134	+	0.852251i	$0.324763\pi$
$380$	−6.48026	−	6.48026i	−0.332430	−	0.332430i
$381$	1.72947	+	1.72947i	0.0886037	+	0.0886037i
$382$			13.5486i			0.693208i
$383$			2.75136i			0.140588i	0.997526	+	0.0702941i	$0.0223938\pi$
$383$			2.75136i			0.140588i	−0.997526	+	0.0702941i	$0.977606\pi$
$384$	−3.54356	−	3.54356i	−0.180832	−	0.180832i
$385$	−2.14649	−	2.14649i	−0.109395	−	0.109395i
$386$	1.00248	−	1.00248i	0.0510247	−	0.0510247i
$387$	18.4439			0.937557
$388$	−6.92430	+	6.92430i	−0.351528	+	0.351528i
$389$		−	27.3962i		−	1.38904i	−0.719472	−	0.694521i	$-0.755616\pi$
$389$		−	27.3962i		−	1.38904i	0.719472	−	0.694521i	$-0.244384\pi$
$390$	−0.157177			−0.00795898
$391$	15.7633	−	2.29359i	0.797187	−	0.115992i
$392$	−14.8236			−0.748704
$393$			5.09169i			0.256842i
$394$	9.18444	−	9.18444i	0.462705	−	0.462705i
$395$	−0.813189			−0.0409160
$396$	6.76705	−	6.76705i	0.340057	−	0.340057i
$397$	17.6654	+	17.6654i	0.886603	+	0.886603i	0.994195	−	0.107592i	$-0.0343139\pi$
$397$	17.6654	+	17.6654i	0.886603	+	0.886603i	−0.107592	+	0.994195i	$0.534314\pi$
$398$	13.9392	+	13.9392i	0.698710	+	0.698710i
$399$		−	4.28214i		−	0.214375i
$400$		−	0.693788i		−	0.0346894i
$401$	22.4405	+	22.4405i	1.12063	+	1.12063i	0.991648	+	0.128978i	$0.0411695\pi$
$401$	22.4405	+	22.4405i	1.12063	+	1.12063i	0.128978	+	0.991648i	$0.458830\pi$
$402$	2.39893	+	2.39893i	0.119648	+	0.119648i
$403$	−1.72456	+	1.72456i	−0.0859063	+	0.0859063i
$404$	0.410670			0.0204316
$405$	4.53624	−	4.53624i	0.225408	−	0.225408i
$406$		−	2.15258i		−	0.106831i
$407$	−8.11362			−0.402177
$408$	5.89912	−	0.858329i	0.292050	−	0.0424936i
$409$	0.721793			0.0356904			0.0178452	−	0.999841i	$-0.494319\pi$
$409$	0.721793			0.0356904			0.0178452	+	0.999841i	$0.494319\pi$
$410$		−	5.72362i		−	0.282670i
$411$	3.26714	−	3.26714i	0.161156	−	0.161156i
$412$	23.6164			1.16350
$413$	−4.38998	+	4.38998i	−0.216017	+	0.216017i
$414$	−5.78535	−	5.78535i	−0.284334	−	0.284334i
$415$	−2.82218	−	2.82218i	−0.138535	−	0.138535i
$416$			2.15331i			0.105575i
$417$			3.27369i			0.160313i
$418$	−9.35526	−	9.35526i	−0.457581	−	0.457581i
$419$	−10.1371	−	10.1371i	−0.495230	−	0.495230i	0.414719	−	0.909949i	$-0.363880\pi$
$419$	−10.1371	−	10.1371i	−0.495230	−	0.495230i	−0.909949	+	0.414719i	$0.863880\pi$
$420$	0.634847	−	0.634847i	0.0309773	−	0.0309773i
$421$	2.94304			0.143435			0.0717175	−	0.997425i	$-0.477152\pi$
$421$	2.94304			0.143435			0.0717175	+	0.997425i	$0.477152\pi$
$422$	4.65818	−	4.65818i	0.226757	−	0.226757i
$423$			21.1048i			1.02615i
$424$	21.2562			1.03229
$425$	3.30488	+	2.46531i	0.160310	+	0.119585i
$426$	−5.07590			−0.245928
$427$		−	9.65204i		−	0.467095i
$428$	−3.73320	+	3.73320i	−0.180451	+	0.180451i
$429$	0.512410			0.0247394
$430$	3.78022	−	3.78022i	0.182299	−	0.182299i
$431$	−22.7514	−	22.7514i	−1.09590	−	1.09590i	−0.994885	−	0.101013i	$-0.967792\pi$
$431$	−22.7514	−	22.7514i	−1.09590	−	1.09590i	−0.101013	−	0.994885i	$-0.532208\pi$
$432$	1.52473	+	1.52473i	0.0733586	+	0.0733586i
$433$			1.76074i			0.0846158i	0.999105	+	0.0423079i	$0.0134710\pi$
$433$			1.76074i			0.0846158i	−0.999105	+	0.0423079i	$0.986529\pi$
$434$			6.16911i			0.296127i
$435$	−0.890854	−	0.890854i	−0.0427132	−	0.0427132i
$436$	−11.7986	−	11.7986i	−0.565053	−	0.565053i
$437$	18.0614	−	18.0614i	0.863992	−	0.863992i
$438$	6.29052			0.300573
$439$	0.390096	−	0.390096i	0.0186183	−	0.0186183i	−0.697736	−	0.716355i	$-0.745809\pi$
$439$	0.390096	−	0.390096i	0.0186183	−	0.0186183i	0.716355	+	0.697736i	$0.245809\pi$
$440$		−	6.77621i		−	0.323043i
$441$	15.1031			0.719194
$442$	−0.953164	−	0.711023i	−0.0453374	−	0.0338199i
$443$	2.19117			0.104106			0.0520528	−	0.998644i	$-0.483424\pi$
$443$	2.19117			0.104106			0.0520528	+	0.998644i	$0.483424\pi$
$444$		−	2.39969i		−	0.113884i
$445$	−6.46516	+	6.46516i	−0.306478	+	0.306478i
$446$	−12.9665			−0.613980
$447$	3.51376	−	3.51376i	0.166195	−	0.166195i
$448$	2.68534	+	2.68534i	0.126870	+	0.126870i
$449$	1.52719	+	1.52719i	0.0720727	+	0.0720727i	0.742224	−	0.670152i	$-0.233771\pi$
$449$	1.52719	+	1.52719i	0.0720727	+	0.0720727i	−0.670152	+	0.742224i	$0.733771\pi$
$450$		−	2.11773i		−	0.0998310i
$451$			18.6594i			0.878639i
$452$	16.1550	+	16.1550i	0.759868	+	0.759868i
$453$	−5.05374	−	5.05374i	−0.237445	−	0.237445i
$454$	−3.94282	+	3.94282i	−0.185046	+	0.185046i
$455$	−0.437499			−0.0205103
$456$	6.75910	−	6.75910i	0.316524	−	0.316524i
$457$			9.46893i			0.442938i	0.975167	+	0.221469i	$0.0710851\pi$
$457$			9.46893i			0.442938i	−0.975167	+	0.221469i	$0.928915\pi$
$458$	1.14993			0.0537329
$459$	−12.6811	+	1.84512i	−0.591903	+	0.0861226i
$460$	5.35536			0.249695
$461$			16.6646i			0.776149i	0.921628	+	0.388075i	$0.126860\pi$
$461$			16.6646i			0.776149i	−0.921628	+	0.388075i	$0.873140\pi$
$462$	0.916499	−	0.916499i	0.0426394	−	0.0426394i
$463$	14.3738			0.668009			0.334005	−	0.942571i	$-0.391600\pi$
$463$	14.3738			0.668009			0.334005	+	0.942571i	$0.391600\pi$
$464$	−1.13411	+	1.13411i	−0.0526498	+	0.0526498i
$465$	2.55311	+	2.55311i	0.118397	+	0.118397i
$466$	−12.8341	−	12.8341i	−0.594530	−	0.594530i
$467$		−	12.9129i		−	0.597537i	−0.954326	−	0.298769i	$-0.903424\pi$
$467$		−	12.9129i		−	0.597537i	0.954326	−	0.298769i	$-0.0965759\pi$
$468$		−	1.37927i		−	0.0637565i
$469$	6.67736	+	6.67736i	0.308332	+	0.308332i
$470$	4.32560	+	4.32560i	0.199525	+	0.199525i
$471$	−7.72624	+	7.72624i	−0.356006	+	0.356006i
$472$	−13.8586			−0.637896
$473$	−12.3238	+	12.3238i	−0.566650	+	0.566650i
$474$		−	0.347212i		−	0.0159480i
$475$	6.61138			0.303351
$476$	6.72173	−	0.978021i	0.308090	−	0.0448275i
$477$	−21.6570			−0.991604
$478$			5.03972i			0.230511i
$479$	4.25108	−	4.25108i	0.194237	−	0.194237i	−0.603287	−	0.797524i	$-0.706143\pi$
$479$	4.25108	−	4.25108i	0.194237	−	0.194237i	0.797524	+	0.603287i	$0.206143\pi$
$480$	3.18785			0.145505
$481$	−0.826862	+	0.826862i	−0.0377017	+	0.0377017i
$482$	−15.1774	−	15.1774i	−0.691310	−	0.691310i
$483$	1.76940	+	1.76940i	0.0805106	+	0.0805106i
$484$		−	6.20464i		−	0.282029i
$485$		−	7.06440i		−	0.320778i
$486$	7.10237	+	7.10237i	0.322170	+	0.322170i
$487$	23.4059	+	23.4059i	1.06062	+	1.06062i	0.998040	+	0.0625852i	$0.0199345\pi$
$487$	23.4059	+	23.4059i	1.06062	+	1.06062i	0.0625852	+	0.998040i	$0.480065\pi$
$488$	15.2352	−	15.2352i	0.689664	−	0.689664i
$489$	−7.77725			−0.351699
$490$	3.09549	−	3.09549i	0.139840	−	0.139840i
$491$			18.7705i			0.847099i	0.905873	+	0.423549i	$0.139216\pi$
$491$			18.7705i			0.847099i	−0.905873	+	0.423549i	$0.860784\pi$
$492$	−5.51872			−0.248803
$493$	−1.37242	−	9.43233i	−0.0618105	−	0.424811i
$494$	−1.90680			−0.0857908
$495$			6.90397i			0.310311i
$496$	3.25026	−	3.25026i	0.145941	−	0.145941i
$497$	−14.1286			−0.633756
$498$	1.20500	−	1.20500i	0.0539974	−	0.0539974i
$499$	−5.05185	−	5.05185i	−0.226152	−	0.226152i	0.584931	−	0.811083i	$-0.301122\pi$
$499$	−5.05185	−	5.05185i	−0.226152	−	0.226152i	−0.811083	+	0.584931i	$0.801122\pi$
$500$	0.980167	+	0.980167i	0.0438344	+	0.0438344i
$501$			0.121167i			0.00541336i
$502$		−	0.183657i		−	0.00819700i
$503$	−20.7561	−	20.7561i	−0.925467	−	0.925467i	0.0719417	−	0.997409i	$-0.477080\pi$
$503$	−20.7561	−	20.7561i	−0.925467	−	0.925467i	−0.997409	+	0.0719417i	$0.977080\pi$
$504$	−6.02637	−	6.02637i	−0.268436	−	0.268436i
$505$	−0.209490	+	0.209490i	−0.00932216	+	0.00932216i
$506$	7.73128			0.343697
$507$	−4.95742	+	4.95742i	−0.220167	+	0.220167i
$508$			6.22109i			0.276016i
$509$	−9.83824			−0.436072			−0.218036	−	0.975941i	$-0.569965\pi$
$509$	−9.83824			−0.436072			−0.218036	+	0.975941i	$0.569965\pi$
$510$	−1.05263	+	1.41110i	−0.0466112	+	0.0624848i
$511$	17.5095			0.774575
$512$		−	7.73954i		−	0.342043i
$513$	−14.5298	+	14.5298i	−0.641505	+	0.641505i
$514$	−2.78949			−0.123039
$515$	−12.0471	+	12.0471i	−0.530860	+	0.530860i
$516$	−3.64490	−	3.64490i	−0.160458	−	0.160458i
$517$	−14.1018	−	14.1018i	−0.620195	−	0.620195i
$518$			2.95786i			0.129961i
$519$			10.8966i			0.478307i
$520$	−0.690566	−	0.690566i	−0.0302833	−	0.0302833i
$521$	−4.82486	−	4.82486i	−0.211381	−	0.211381i	0.593473	−	0.804854i	$-0.297756\pi$
$521$	−4.82486	−	4.82486i	−0.211381	−	0.211381i	−0.804854	+	0.593473i	$0.797756\pi$
$522$	−3.46178	+	3.46178i	−0.151518	+	0.151518i
$523$	−7.90422			−0.345628			−0.172814	−	0.984955i	$-0.555286\pi$
$523$	−7.90422			−0.345628			−0.172814	+	0.984955i	$0.555286\pi$
$524$	−9.15766	+	9.15766i	−0.400054	+	0.400054i
$525$			0.647692i			0.0282676i
$526$	−23.5043			−1.02484
$527$	3.93322	+	27.0322i	0.171334	+	1.17754i
$528$	−0.965735			−0.0420282
$529$		−	8.07391i		−	0.351040i
$530$	−4.43876	+	4.43876i	−0.192807	+	0.192807i
$531$	14.1199			0.612754
$532$	7.70164	−	7.70164i	0.333908	−	0.333908i
$533$	1.90159	+	1.90159i	0.0823670	+	0.0823670i
$534$	−2.76047	−	2.76047i	−0.119457	−	0.119457i
$535$		−	3.80874i		−	0.164666i
$536$			21.0796i			0.910501i
$537$	9.36878	+	9.36878i	0.404293	+	0.404293i
$538$	0.210101	+	0.210101i	0.00905809	+	0.00905809i
$539$	−10.0915	+	10.0915i	−0.434673	+	0.434673i
$540$	−4.30821			−0.185396
$541$	−25.6567	+	25.6567i	−1.10307	+	1.10307i	−0.109027	+	0.994039i	$0.534774\pi$
$541$	−25.6567	+	25.6567i	−1.10307	+	1.10307i	−0.994039	+	0.109027i	$0.965226\pi$
$542$		−	8.31614i		−	0.357209i
$543$	6.47790			0.277993
$544$	19.3320	+	14.4209i	0.828852	+	0.618291i
$545$	12.0374			0.515625
$546$		−	0.186802i		−	0.00799437i
$547$	19.9968	−	19.9968i	0.855002	−	0.855002i	−0.135742	−	0.990744i	$-0.543342\pi$
$547$	19.9968	−	19.9968i	0.855002	−	0.855002i	0.990744	+	0.135742i	$0.0433420\pi$
$548$	11.7522			0.502030
$549$	−15.5224	+	15.5224i	−0.662481	+	0.662481i
$550$	1.41502	+	1.41502i	0.0603368	+	0.0603368i
$551$	−10.8074	−	10.8074i	−0.460410	−	0.460410i
$552$			5.58579i			0.237747i
$553$		−	0.966456i		−	0.0410979i
$554$	−16.8928	−	16.8928i	−0.717708	−	0.717708i
$555$	1.22412	+	1.22412i	0.0519611	+	0.0519611i
$556$	−5.88789	+	5.88789i	−0.249702	+	0.249702i
$557$	−15.4059			−0.652768			−0.326384	−	0.945237i	$-0.605830\pi$
$557$	−15.4059			−0.652768			−0.326384	+	0.945237i	$0.605830\pi$
$558$	9.92116	−	9.92116i	0.419996	−	0.419996i
$559$			2.51185i			0.106240i
$560$	0.824551			0.0348437
$561$	3.43165	−	4.60031i	0.144884	−	0.194225i
$562$	20.7153			0.873820
$563$			8.51617i			0.358914i	0.983766	+	0.179457i	$0.0574340\pi$
$563$			8.51617i			0.358914i	−0.983766	+	0.179457i	$0.942566\pi$
$564$	4.17075	−	4.17075i	0.175620	−	0.175620i
$565$	−16.4819			−0.693398
$566$	10.2912	−	10.2912i	0.432571	−	0.432571i
$567$	5.39122	+	5.39122i	0.226410	+	0.226410i
$568$	−22.3012	−	22.3012i	−0.935738	−	0.935738i
$569$			10.0268i			0.420346i	0.977664	+	0.210173i	$0.0674027\pi$
$569$			10.0268i			0.420346i	−0.977664	+	0.210173i	$0.932597\pi$
$570$			2.82290i			0.118238i
$571$	−9.77041	−	9.77041i	−0.408879	−	0.408879i	0.472469	−	0.881347i	$-0.343363\pi$
$571$	−9.77041	−	9.77041i	−0.408879	−	0.408879i	−0.881347	+	0.472469i	$0.843363\pi$
$572$	0.921594	+	0.921594i	0.0385338	+	0.0385338i
$573$	−6.66396	+	6.66396i	−0.278391	+	0.278391i
$574$	6.80239			0.283926
$575$	−2.73186	+	2.73186i	−0.113926	+	0.113926i
$576$		−	8.63712i		−	0.359880i
$577$	−13.6068			−0.566457			−0.283229	−	0.959052i	$-0.591406\pi$
$577$	−13.6068			−0.566457			−0.283229	+	0.959052i	$0.591406\pi$
$578$	−12.7668	+	3.79554i	−0.531030	+	0.157873i
$579$	0.986147			0.0409829
$580$		−	3.20449i		−	0.133059i
$581$	3.35409	−	3.35409i	0.139151	−	0.139151i
$582$	3.01633			0.125031
$583$	14.4707	−	14.4707i	0.599315	−	0.599315i
$584$	27.6377	+	27.6377i	1.14366	+	1.14366i
$585$	0.703586	+	0.703586i	0.0290897	+	0.0290897i
$586$		−	2.82018i		−	0.116501i
$587$		−	27.9191i		−	1.15234i	−0.817329	−	0.576172i	$-0.804546\pi$
$587$		−	27.9191i		−	1.15234i	0.817329	−	0.576172i	$-0.195454\pi$
$588$	−2.98468	−	2.98468i	−0.123086	−	0.123086i
$589$	30.9730	+	30.9730i	1.27622	+	1.27622i
$590$	2.89399	−	2.89399i	0.119144	−	0.119144i
$591$	9.03483			0.371643
$592$	1.55838	−	1.55838i	0.0640491	−	0.0640491i
$593$		−	40.0318i		−	1.64391i	−0.569554	−	0.821954i	$-0.692884\pi$
$593$		−	40.0318i		−	1.64391i	0.569554	−	0.821954i	$-0.307116\pi$
$594$	−6.21956			−0.255192
$595$	−2.92996	+	3.92778i	−0.120117	+	0.161023i
$596$	12.6394			0.517728
$597$			13.7122i			0.561201i
$598$	0.787898	−	0.787898i	0.0322195	−	0.0322195i
$599$	25.5481			1.04387			0.521934	−	0.852986i	$-0.325211\pi$
$599$	25.5481			1.04387			0.521934	+	0.852986i	$0.325211\pi$
$600$	−1.02234	+	1.02234i	−0.0417370	+	0.0417370i
$601$	2.75133	+	2.75133i	0.112229	+	0.112229i	0.760991	−	0.648762i	$-0.224713\pi$
$601$	2.75133	+	2.75133i	0.112229	+	0.112229i	−0.648762	+	0.760991i	$0.724713\pi$
$602$	4.49271	+	4.49271i	0.183109	+	0.183109i
$603$		−	21.4771i		−	0.874614i
$604$		−	18.1788i		−	0.739684i
$605$	3.16509	+	3.16509i	0.128679	+	0.128679i
$606$	−0.0894470	−	0.0894470i	−0.00363353	−	0.00363353i
$607$	−6.94385	+	6.94385i	−0.281842	+	0.281842i	−0.833843	−	0.552001i	$-0.813864\pi$
$607$	−6.94385	+	6.94385i	−0.281842	+	0.281842i	0.552001	+	0.833843i	$0.313864\pi$
$608$	38.6734			1.56841
$609$	1.05876	−	1.05876i	0.0429031	−	0.0429031i
$610$			6.36288i			0.257626i
$611$	−2.87423			−0.116279
$612$	−12.3828	−	9.23705i	−0.500543	−	0.373385i
$613$	44.6175			1.80208			0.901042	−	0.433733i	$-0.142804\pi$
$613$	44.6175			1.80208			0.901042	+	0.433733i	$0.142804\pi$
$614$			26.1781i			1.05646i
$615$	2.81519	−	2.81519i	0.113520	−	0.113520i
$616$	8.05337			0.324479
$617$	−25.2341	+	25.2341i	−1.01589	+	1.01589i	−0.0160159	+	0.999872i	$0.505098\pi$
$617$	−25.2341	+	25.2341i	−1.01589	+	1.01589i	−0.999872	+	0.0160159i	$0.994902\pi$
$618$	−5.14383	−	5.14383i	−0.206915	−	0.206915i
$619$	−11.7276	−	11.7276i	−0.471371	−	0.471371i	0.430987	−	0.902358i	$-0.358166\pi$
$619$	−11.7276	−	11.7276i	−0.471371	−	0.471371i	−0.902358	+	0.430987i	$0.858166\pi$
$620$			9.18378i			0.368829i
$621$		−	12.0075i		−	0.481846i
$622$	−7.64303	−	7.64303i	−0.306458	−	0.306458i
$623$	−7.68369	−	7.68369i	−0.307841	−	0.307841i
$624$	−0.0984184	+	0.0984184i	−0.00393989	+	0.00393989i
$625$	−1.00000			−0.0400000
$626$	16.9359	−	16.9359i	0.676897	−	0.676897i
$627$		−	9.20287i		−	0.367527i
$628$	−27.7920			−1.10902
$629$	1.88584	+	12.9610i	0.0751932	+	0.516787i
$630$	2.51688			0.100275
$631$		−	38.0364i		−	1.51421i	−0.653295	−	0.757103i	$-0.726614\pi$
$631$		−	38.0364i		−	1.51421i	0.653295	−	0.757103i	$-0.273386\pi$
$632$	1.52549	−	1.52549i	0.0606808	−	0.0606808i
$633$	4.58231			0.182130
$634$	−1.78222	+	1.78222i	−0.0707811	+	0.0707811i
$635$	−3.17348	−	3.17348i	−0.125936	−	0.125936i
$636$	4.27986	+	4.27986i	0.169707	+	0.169707i
$637$			2.05686i			0.0814959i
$638$		−	4.62617i		−	0.183152i
$639$	22.7217	+	22.7217i	0.898857	+	0.898857i
$640$	6.50223	+	6.50223i	0.257023	+	0.257023i
$641$	2.57412	−	2.57412i	0.101672	−	0.101672i	−0.654441	−	0.756113i	$-0.727096\pi$
$641$	2.57412	−	2.57412i	0.101672	−	0.101672i	0.756113	+	0.654441i	$0.227096\pi$
$642$	1.62624			0.0641826
$643$	13.0129	−	13.0129i	0.513178	−	0.513178i	−0.402321	−	0.915499i	$-0.631796\pi$
$643$	13.0129	−	13.0129i	0.513178	−	0.513178i	0.915499	+	0.402321i	$0.131796\pi$
$644$			6.36472i			0.250805i
$645$	3.71865			0.146422
$646$	−12.7700	+	17.1188i	−0.502427	+	0.673531i
$647$	3.12579			0.122888			0.0614438	−	0.998111i	$-0.480429\pi$
$647$	3.12579			0.122888			0.0614438	+	0.998111i	$0.480429\pi$
$648$			17.0194i			0.668586i
$649$	−9.43463	+	9.43463i	−0.370342	+	0.370342i
$650$	0.288411			0.0113124
$651$	−3.03431	+	3.03431i	−0.118924	+	0.118924i
$652$	−13.9878	−	13.9878i	−0.547803	−	0.547803i
$653$	9.92621	+	9.92621i	0.388443	+	0.388443i	0.874132	−	0.485689i	$-0.161431\pi$
$653$	9.92621	+	9.92621i	0.388443	+	0.388443i	−0.485689	+	0.874132i	$0.661431\pi$
$654$			5.13967i			0.200977i
$655$		−	9.34295i		−	0.365059i
$656$	−3.58391	−	3.58391i	−0.139928	−	0.139928i
$657$	−28.1588	−	28.1588i	−1.09858	−	1.09858i
$658$	−5.14087	+	5.14087i	−0.200412	+	0.200412i
$659$	4.52370			0.176218			0.0881092	−	0.996111i	$-0.471918\pi$
$659$	4.52370			0.176218			0.0881092	+	0.996111i	$0.471918\pi$
$660$	1.36437	−	1.36437i	0.0531079	−	0.0531079i
$661$		−	31.6484i		−	1.23098i	−0.788145	−	0.615490i	$-0.788958\pi$
$661$		−	31.6484i		−	1.23098i	0.788145	−	0.615490i	$-0.211042\pi$
$662$	23.3191			0.906324
$663$	−0.119099	−	0.818539i	−0.00462540	−	0.0317894i
$664$	10.5885			0.410912
$665$			7.85747i			0.304700i
$666$	4.75684	−	4.75684i	0.184324	−	0.184324i
$667$	8.93134			0.345823
$668$	−0.217925	+	0.217925i	−0.00843179	+	0.00843179i
$669$	−6.37762	−	6.37762i	−0.246573	−	0.246573i
$670$	−4.40189	−	4.40189i	−0.170060	−	0.170060i
$671$		−	20.7435i		−	0.800793i
$672$			3.78869i			0.146152i
$673$	−7.91436	−	7.91436i	−0.305076	−	0.305076i	0.537920	−	0.842996i	$-0.319210\pi$
$673$	−7.91436	−	7.91436i	−0.305076	−	0.305076i	−0.842996	+	0.537920i	$0.819210\pi$
$674$	−5.94522	−	5.94522i	−0.229001	−	0.229001i
$675$	2.19769	−	2.19769i	0.0845891	−	0.0845891i
$676$	−17.8323			−0.685858
$677$	−4.61971	+	4.61971i	−0.177550	+	0.177550i	−0.790287	−	0.612737i	$-0.790069\pi$
$677$	−4.61971	+	4.61971i	−0.177550	+	0.177550i	0.612737	+	0.790287i	$0.290069\pi$
$678$		−	7.03737i		−	0.270268i
$679$	8.39588			0.322204
$680$	−10.8245	+	1.57498i	−0.415102	+	0.0603979i
$681$	−3.87860			−0.148628
$682$			13.2582i			0.507683i
$683$	16.7322	−	16.7322i	0.640239	−	0.640239i	−0.310376	−	0.950614i	$-0.600455\pi$
$683$	16.7322	−	16.7322i	0.640239	−	0.640239i	0.950614	+	0.310376i	$0.100455\pi$
$684$	−24.7716			−0.947165
$685$	−5.99501	+	5.99501i	−0.229058	+	0.229058i
$686$	8.28784	+	8.28784i	0.316431	+	0.316431i
$687$	0.565602	+	0.565602i	0.0215790	+	0.0215790i
$688$		−	4.73406i		−	0.180484i
$689$		−	2.94943i		−	0.112364i
$690$	−1.16644	−	1.16644i	−0.0444055	−	0.0444055i
$691$	−5.73536	−	5.73536i	−0.218183	−	0.218183i	0.589549	−	0.807732i	$-0.299305\pi$
$691$	−5.73536	−	5.73536i	−0.218183	−	0.218183i	−0.807732	+	0.589549i	$0.799305\pi$
$692$	−19.5980	+	19.5980i	−0.745006	+	0.745006i
$693$	−8.20521			−0.311690
$694$	0.633867	−	0.633867i	0.0240613	−	0.0240613i
$695$		−	6.00703i		−	0.227859i
$696$	3.34237			0.126692
$697$	29.8072	−	4.33698i	1.12903	−	0.164275i
$698$	−14.6142			−0.553157
$699$		−	12.6251i		−	0.477525i
$700$	−1.16491	+	1.16491i	−0.0440293	+	0.0440293i
$701$	35.4115			1.33748			0.668738	−	0.743498i	$-0.266835\pi$
$701$	35.4115			1.33748			0.668738	+	0.743498i	$0.266835\pi$
$702$	−0.633838	+	0.633838i	−0.0239227	+	0.0239227i
$703$	14.8504	+	14.8504i	0.560094	+	0.560094i
$704$	5.77113	+	5.77113i	0.217508	+	0.217508i
$705$			4.25514i			0.160258i
$706$		−	3.40268i		−	0.128061i
$707$	−0.248973	−	0.248973i	−0.00936361	−	0.00936361i
$708$	−2.79039	−	2.79039i	−0.104869	−	0.104869i
$709$	−10.5641	+	10.5641i	−0.396745	+	0.396745i	−0.877083	−	0.480338i	$-0.840514\pi$
$709$	−10.5641	+	10.5641i	−0.396745	+	0.396745i	0.480338	+	0.877083i	$0.340514\pi$
$710$	9.31398			0.349547
$711$	−1.55426	+	1.55426i	−0.0582891	+	0.0582891i
$712$		−	24.2565i		−	0.909050i
$713$	−25.5964			−0.958593
$714$	−1.67707	−	1.25102i	−0.0627626	−	0.0468184i
$715$	−0.940241			−0.0351630
$716$			33.7004i			1.25944i
$717$	−2.47881	+	2.47881i	−0.0925730	+	0.0925730i
$718$	−4.98150			−0.185908
$719$	−16.3734	+	16.3734i	−0.610624	+	0.610624i	−0.943109	−	0.332485i	$-0.892113\pi$
$719$	−16.3734	+	16.3734i	−0.610624	+	0.610624i	0.332485	+	0.943109i	$0.392113\pi$
$720$	−1.32604	−	1.32604i	−0.0494188	−	0.0494188i
$721$	−14.3177	−	14.3177i	−0.533220	−	0.533220i
$722$			19.3600i			0.720504i
$723$		−	14.9301i		−	0.555258i
$724$	11.6508	+	11.6508i	0.433000	+	0.433000i
$725$	1.63466	+	1.63466i	0.0607099	+	0.0607099i
$726$	−1.35142	+	1.35142i	−0.0501559	+	0.0501559i
$727$	11.3367			0.420456			0.210228	−	0.977652i	$-0.432579\pi$
$727$	11.3367			0.420456			0.210228	+	0.977652i	$0.432579\pi$
$728$	0.820721	−	0.820721i	0.0304180	−	0.0304180i
$729$		−	12.2590i		−	0.454036i
$730$	−11.5427			−0.427216
$731$	22.5509	+	16.8220i	0.834074	+	0.622186i
$732$	6.13510			0.226760
$733$			3.32332i			0.122750i	0.998115	+	0.0613748i	$0.0195485\pi$
$733$			3.32332i			0.122750i	−0.998115	+	0.0613748i	$0.980452\pi$
$734$	−8.98296	+	8.98296i	−0.331567	+	0.331567i
$735$	3.04507			0.112319
$736$	−15.9801	+	15.9801i	−0.589033	+	0.589033i
$737$	14.3505	+	14.3505i	0.528607	+	0.528607i
$738$	−10.9396	−	10.9396i	−0.402693	−	0.402693i
$739$			12.5661i			0.462253i	0.972924	+	0.231127i	$0.0742412\pi$
$739$			12.5661i			0.462253i	−0.972924	+	0.231127i	$0.925759\pi$
$740$			4.40329i			0.161868i
$741$	−0.937867	−	0.937867i	−0.0344534	−	0.0344534i
$742$	−5.27537	−	5.27537i	−0.193665	−	0.193665i
$743$	−37.1805	+	37.1805i	−1.36402	+	1.36402i	−0.495297	+	0.868724i	$0.664941\pi$
$743$	−37.1805	+	37.1805i	−1.36402	+	1.36402i	−0.868724	+	0.495297i	$0.835059\pi$
$744$	−9.57894			−0.351181
$745$	−6.44755	+	6.44755i	−0.236220	+	0.236220i
$746$			14.5685i			0.533390i
$747$	−10.7881			−0.394717
$748$	14.4459	−	2.10189i	0.528193	−	0.0768528i
$749$	4.52660			0.165398
$750$		−	0.426976i		−	0.0155910i
$751$	2.78545	−	2.78545i	0.101642	−	0.101642i	−0.654457	−	0.756099i	$-0.727103\pi$
$751$	2.78545	−	2.78545i	0.101642	−	0.101642i	0.756099	+	0.654457i	$0.227103\pi$
$752$	5.41705			0.197539
$753$	0.0903325	−	0.0903325i	0.00329190	−	0.00329190i
$754$	−0.471455	−	0.471455i	−0.0171694	−	0.0171694i
$755$	9.27331	+	9.27331i	0.337490	+	0.337490i
$756$		−	5.12020i		−	0.186220i
$757$			6.38475i			0.232058i	0.993246	+	0.116029i	$0.0370165\pi$
$757$			6.38475i			0.232058i	−0.993246	+	0.116029i	$0.962984\pi$
$758$	5.01990	+	5.01990i	0.182331	+	0.182331i
$759$	3.80267	+	3.80267i	0.138028	+	0.138028i
$760$	−12.4025	+	12.4025i	−0.449888	+	0.449888i
$761$	−19.3638			−0.701938			−0.350969	−	0.936387i	$-0.614148\pi$
$761$	−19.3638			−0.701938			−0.350969	+	0.936387i	$0.614148\pi$
$762$	1.35500	−	1.35500i	0.0490865	−	0.0490865i
$763$			14.3061i			0.517917i
$764$	−23.9709			−0.867238
$765$	11.0286	−	1.60468i	0.398741	−	0.0580173i
$766$	2.15563			0.0778860
$767$			1.92297i			0.0694346i
$768$	−5.23902	+	5.23902i	−0.189047	+	0.189047i
$769$	5.10469			0.184080			0.0920398	−	0.995755i	$-0.470661\pi$
$769$	5.10469			0.184080			0.0920398	+	0.995755i	$0.470661\pi$
$770$	−1.68172	+	1.68172i	−0.0606051	+	0.0606051i
$771$	−1.37203	−	1.37203i	−0.0494123	−	0.0494123i
$772$	1.77363	+	1.77363i	0.0638345	+	0.0638345i
$773$			3.00249i			0.107992i	0.998541	+	0.0539961i	$0.0171958\pi$
$773$			3.00249i			0.107992i	−0.998541	+	0.0539961i	$0.982804\pi$
$774$		−	14.4504i		−	0.519408i
$775$	−4.68480	−	4.68480i	−0.168283	−	0.168283i
$776$	13.2524	+	13.2524i	0.475733	+	0.475733i
$777$	−1.45484	+	1.45484i	−0.0521921	+	0.0521921i
$778$	−21.4642			−0.769531
$779$	34.1525	−	34.1525i	1.22364	−	1.22364i
$780$		−	0.278086i		−	0.00995708i
$781$	−30.3643			−1.08652
$782$	−1.79697	−	12.3502i	−0.0642595	−	0.441642i
$783$	−7.18497			−0.256770
$784$		−	3.87656i		−	0.138448i
$785$	14.1772	−	14.1772i	0.506006	−	0.506006i
$786$	3.98921			0.142291
$787$	−1.86293	+	1.86293i	−0.0664063	+	0.0664063i	−0.739530	−	0.673124i	$-0.764952\pi$
$787$	−1.86293	+	1.86293i	−0.0664063	+	0.0664063i	0.673124	+	0.739530i	$0.264952\pi$
$788$	16.2496	+	16.2496i	0.578868	+	0.578868i
$789$	−11.5607	−	11.5607i	−0.411572	−	0.411572i
$790$			0.637113i			0.0226675i
$791$		−	19.5883i		−	0.696481i
$792$	−12.9514	−	12.9514i	−0.460209	−	0.460209i
$793$	−2.11398	−	2.11398i	−0.0750695	−	0.0750695i
$794$	13.8404	−	13.8404i	0.491179	−	0.491179i
$795$	−4.36646			−0.154862
$796$	−24.6620	+	24.6620i	−0.874121	+	0.874121i
$797$			27.2441i			0.965036i	0.875886	+	0.482518i	$0.160278\pi$
$797$			27.2441i			0.965036i	−0.875886	+	0.482518i	$0.839722\pi$
$798$	−3.35495			−0.118764
$799$	−19.2490	+	25.8043i	−0.680979	+	0.912890i
$800$	−5.84952			−0.206812
$801$			24.7138i			0.873221i
$802$	17.5816	−	17.5816i	0.620827	−	0.620827i
$803$	37.6302			1.32794
$804$	−4.24431	+	4.24431i	−0.149685	+	0.149685i
$805$	−3.24675	−	3.24675i	−0.114433	−	0.114433i
$806$	1.35115	+	1.35115i	0.0475921	+	0.0475921i
$807$			0.206679i			0.00727543i
$808$		−	0.785979i		−	0.0276506i
$809$	26.0978	+	26.0978i	0.917549	+	0.917549i	0.996851	−	0.0793013i	$-0.0252689\pi$
$809$	26.0978	+	26.0978i	0.917549	+	0.917549i	−0.0793013	+	0.996851i	$0.525269\pi$
$810$	−3.55403	−	3.55403i	−0.124876	−	0.124876i
$811$	−11.9007	+	11.9007i	−0.417891	+	0.417891i	−0.884476	−	0.466585i	$-0.845484\pi$
$811$	−11.9007	+	11.9007i	−0.417891	+	0.417891i	0.466585	+	0.884476i	$0.345484\pi$
$812$	3.80846			0.133651
$813$	4.09034	−	4.09034i	0.143454	−	0.143454i
$814$			6.35682i			0.222807i
$815$	14.2708			0.499884
$816$	0.224464	+	1.54270i	0.00785782	+	0.0540051i
$817$	45.1128			1.57830
$818$		−	0.565507i		−	0.0197725i
$819$	−0.836196	+	0.836196i	−0.0292191	+	0.0292191i
$820$	10.1265			0.353634
$821$	12.4565	−	12.4565i	0.434737	−	0.434737i	−0.455500	−	0.890236i	$-0.650539\pi$
$821$	12.4565	−	12.4565i	0.434737	−	0.434737i	0.890236	+	0.455500i	$0.150539\pi$
$822$	−2.55972	−	2.55972i	−0.0892806	−	0.0892806i
$823$	−20.8831	−	20.8831i	−0.727940	−	0.727940i	0.242269	−	0.970209i	$-0.422108\pi$
$823$	−20.8831	−	20.8831i	−0.727940	−	0.727940i	−0.970209	+	0.242269i	$0.922108\pi$
$824$		−	45.1994i		−	1.57459i
$825$			1.39197i			0.0484623i
$826$	3.43944	+	3.43944i	0.119674	+	0.119674i
$827$	−21.0943	−	21.0943i	−0.733521	−	0.733521i	0.237794	−	0.971316i	$-0.423576\pi$
$827$	−21.0943	−	21.0943i	−0.733521	−	0.733521i	−0.971316	+	0.237794i	$0.923576\pi$
$828$	10.2357	−	10.2357i	0.355717	−	0.355717i
$829$	−53.2461			−1.84931			−0.924657	−	0.380802i	$-0.875648\pi$
$829$	−53.2461			−1.84931			−0.924657	+	0.380802i	$0.875648\pi$
$830$	−2.21111	+	2.21111i	−0.0767487	+	0.0767487i
$831$		−	16.6177i		−	0.576461i
$832$	1.17628			0.0407800
$833$	18.4661	+	13.7750i	0.639812	+	0.477275i
$834$	2.56486			0.0888137
$835$		−	0.222335i		−	0.00769422i
$836$	16.5518	−	16.5518i	0.572456	−	0.572456i
$837$	20.5915			0.711745
$838$	−7.94217	+	7.94217i	−0.274358	+	0.274358i
$839$	−27.0544	−	27.0544i	−0.934022	−	0.934022i	0.0639326	−	0.997954i	$-0.479636\pi$
$839$	−27.0544	−	27.0544i	−0.934022	−	0.934022i	−0.997954	+	0.0639326i	$0.979636\pi$
$840$	−1.21503	−	1.21503i	−0.0419225	−	0.0419225i
$841$			23.6557i			0.815715i
$842$		−	2.30580i		−	0.0794632i
$843$	10.1889	+	10.1889i	0.350925	+	0.350925i
$844$	8.24150	+	8.24150i	0.283684	+	0.283684i
$845$	9.09657	−	9.09657i	0.312931	−	0.312931i
$846$	16.5351			0.568489
$847$	−3.76164	+	3.76164i	−0.129252	+	0.129252i
$848$			5.55876i			0.190889i
$849$	10.1236			0.347439
$850$	1.93151	−	2.58929i	0.0662503	−	0.0888121i
$851$	−12.2725			−0.420697
$852$		−	8.98055i		−	0.307668i
$853$	−4.75362	+	4.75362i	−0.162761	+	0.162761i	−0.783789	−	0.621028i	$-0.786715\pi$
$853$	−4.75362	+	4.75362i	−0.162761	+	0.162761i	0.621028	+	0.783789i	$0.286715\pi$
$854$	−7.56214			−0.258771
$855$	12.6364	−	12.6364i	0.432156	−	0.432156i
$856$	7.14497	+	7.14497i	0.244210	+	0.244210i
$857$	−22.7593	−	22.7593i	−0.777442	−	0.777442i	0.201953	−	0.979395i	$-0.435271\pi$
$857$	−22.7593	−	22.7593i	−0.777442	−	0.777442i	−0.979395	+	0.201953i	$0.935271\pi$
$858$		−	0.401460i		−	0.0137056i
$859$		−	46.6741i		−	1.59250i	−0.604968	−	0.796250i	$-0.706814\pi$
$859$		−	46.6741i		−	1.59250i	0.604968	−	0.796250i	$-0.293186\pi$
$860$	6.68817	+	6.68817i	0.228065	+	0.228065i
$861$	3.34579	+	3.34579i	0.114024	+	0.114024i
$862$	−17.8252	+	17.8252i	−0.607129	+	0.607129i
$863$	9.97544			0.339568			0.169784	−	0.985481i	$-0.445693\pi$
$863$	9.97544			0.339568			0.169784	+	0.985481i	$0.445693\pi$
$864$	12.8554	−	12.8554i	0.437351	−	0.437351i
$865$		−	19.9946i		−	0.679836i
$866$	1.37950			0.0468772
$867$	−8.14629	−	4.41258i	−0.276662	−	0.149859i
$868$	−10.9147			−0.370469
$869$		−	2.07704i		−	0.0704587i
$870$	−0.697962	+	0.697962i	−0.0236631	+	0.0236631i
$871$	2.92493			0.0991074
$872$	−22.5814	+	22.5814i	−0.764702	+	0.764702i
$873$	−13.5023	−	13.5023i	−0.456982	−	0.456982i
$874$	−14.1506	−	14.1506i	−0.478652	−	0.478652i
$875$		−	1.18848i		−	0.0401779i
$876$			11.1295i			0.376032i
$877$	1.09866	+	1.09866i	0.0370990	+	0.0370990i	0.725413	−	0.688314i	$-0.241649\pi$
$877$	1.09866	+	1.09866i	0.0370990	+	0.0370990i	−0.688314	+	0.725413i	$0.741649\pi$
$878$	−0.305631	−	0.305631i	−0.0103145	−	0.0103145i
$879$	1.38712	−	1.38712i	0.0467864	−	0.0467864i
$880$	1.77207			0.0597363
$881$	19.2497	−	19.2497i	0.648540	−	0.648540i	−0.304100	−	0.952640i	$-0.598356\pi$
$881$	19.2497	−	19.2497i	0.648540	−	0.648540i	0.952640	+	0.304100i	$0.0983557\pi$
$882$		−	11.8329i		−	0.398434i
$883$	41.7225			1.40407			0.702037	−	0.712140i	$-0.252274\pi$
$883$	41.7225			1.40407			0.702037	+	0.712140i	$0.252274\pi$
$884$	1.25798	−	1.68639i	0.0423104	−	0.0567194i
$885$	2.84685			0.0956959
$886$		−	1.71673i		−	0.0576746i
$887$	−5.40672	+	5.40672i	−0.181540	+	0.181540i	−0.792027	−	0.610487i	$-0.790974\pi$
$887$	−5.40672	+	5.40672i	−0.181540	+	0.181540i	0.610487	+	0.792027i	$0.290974\pi$
$888$	−4.59275			−0.154123
$889$	3.77161	−	3.77161i	0.126496	−	0.126496i
$890$	5.06529	+	5.06529i	0.169789	+	0.169789i
$891$	11.5864	+	11.5864i	0.388160	+	0.388160i
$892$		−	22.9409i		−	0.768120i
$893$			51.6212i			1.72744i
$894$	−2.75295	−	2.75295i	−0.0920724	−	0.0920724i
$895$	−17.1912	−	17.1912i	−0.574637	−	0.574637i
$896$	−7.72775	+	7.72775i	−0.258166	+	0.258166i
$897$	0.775063			0.0258786
$898$	1.19652	−	1.19652i	0.0399284	−	0.0399284i
$899$			15.3161i			0.510822i
$900$	3.74681			0.124894
$901$	−26.4793	−	19.7525i	−0.882155	−	0.658053i
$902$	14.6192			0.486767
$903$			4.41953i			0.147073i
$904$	30.9190	−	30.9190i	1.02835	−	1.02835i
$905$	−11.8866			−0.395123
$906$	−3.95948	+	3.95948i	−0.131545	+	0.131545i
$907$	30.7988	+	30.7988i	1.02266	+	1.02266i	0.999737	+	0.0229217i	$0.00729683\pi$
$907$	30.7988	+	30.7988i	1.02266	+	1.02266i	0.0229217	+	0.999737i	$0.492703\pi$
$908$	−6.97585	−	6.97585i	−0.231502	−	0.231502i
$909$			0.800799i			0.0265608i
$910$			0.342770i			0.0113627i
$911$	−23.4200	−	23.4200i	−0.775938	−	0.775938i	0.203200	−	0.979137i	$-0.434866\pi$
$911$	−23.4200	−	23.4200i	−0.775938	−	0.775938i	−0.979137	+	0.203200i	$0.934866\pi$
$912$	1.76759	+	1.76759i	0.0585308	+	0.0585308i
$913$	7.20838	−	7.20838i	0.238562	−	0.238562i
$914$	7.41867			0.245388
$915$	−3.12962	+	3.12962i	−0.103462	+	0.103462i
$916$			2.03453i			0.0672226i
$917$	11.1039			0.366682
$918$	1.44560	+	9.93532i	0.0477120	+	0.327915i
$919$	22.9512			0.757089			0.378545	−	0.925583i	$-0.376425\pi$
$919$	22.9512			0.757089			0.378545	+	0.925583i	$0.376425\pi$
$920$		−	10.2496i		−	0.337919i
$921$	−12.8759	+	12.8759i	−0.424274	+	0.424274i
$922$	13.0563			0.429987
$923$	−3.09443	+	3.09443i	−0.101855	+	0.101855i
$924$	1.62152	+	1.62152i	0.0533440	+	0.0533440i
$925$	−2.24619	−	2.24619i	−0.0738543	−	0.0738543i
$926$		−	11.2616i		−	0.370078i
$927$			46.0516i			1.51253i
$928$	9.56200	+	9.56200i	0.313888	+	0.313888i
$929$	−13.6260	−	13.6260i	−0.447055	−	0.447055i	0.447320	−	0.894374i	$-0.352379\pi$
$929$	−13.6260	−	13.6260i	−0.447055	−	0.447055i	−0.894374	+	0.447320i	$0.852379\pi$
$930$	2.00030	−	2.00030i	0.0655923	−	0.0655923i
$931$	36.9412			1.21070
$932$	22.7068	−	22.7068i	0.743787	−	0.743787i
$933$		−	7.51853i		−	0.246146i
$934$	−10.1169			−0.331036
$935$	−6.29687	+	8.44129i	−0.205930	+	0.276060i
$936$	−2.63977			−0.0862836
$937$			23.6659i			0.773132i	0.922262	+	0.386566i	$0.126339\pi$
$937$			23.6659i			0.773132i	−0.922262	+	0.386566i	$0.873661\pi$
$938$	5.23155	−	5.23155i	0.170816	−	0.170816i
$939$	16.6601			0.543681
$940$	−7.65307	+	7.65307i	−0.249616	+	0.249616i
$941$	2.22184	+	2.22184i	0.0724298	+	0.0724298i	0.742394	−	0.669964i	$-0.233690\pi$
$941$	2.22184	+	2.22184i	0.0724298	+	0.0724298i	−0.669964	+	0.742394i	$0.733690\pi$
$942$	6.05332	+	6.05332i	0.197228	+	0.197228i
$943$			28.2240i			0.919100i
$944$		−	3.62421i		−	0.117958i
$945$	2.61190	+	2.61190i	0.0849652	+	0.0849652i
$946$	9.65541	+	9.65541i	0.313924	+	0.313924i
$947$	27.0812	−	27.0812i	0.880020	−	0.880020i	−0.113516	−	0.993536i	$-0.536211\pi$
$947$	27.0812	−	27.0812i	0.880020	−	0.880020i	0.993536	+	0.113516i	$0.0362114\pi$
$948$	0.614305			0.0199517
$949$	3.83491	−	3.83491i	0.124486	−	0.124486i
$950$		−	5.17986i		−	0.168057i
$951$	−1.75319			−0.0568511
$952$	−1.87183	−	12.8647i	−0.0606664	−	0.416947i
$953$	−34.0185			−1.10197			−0.550984	−	0.834516i	$-0.685747\pi$
$953$	−34.0185			−1.10197			−0.550984	+	0.834516i	$0.685747\pi$
$954$			16.9677i			0.549349i
$955$	12.2280	−	12.2280i	0.395688	−	0.395688i
$956$	−8.91654			−0.288381
$957$	2.27541	−	2.27541i	0.0735535	−	0.0735535i
$958$	−3.33062	−	3.33062i	−0.107607	−	0.107607i
$959$	−7.12493	−	7.12493i	−0.230076	−	0.230076i
$960$		−	1.74141i		−	0.0562037i
$961$		−	12.8947i		−	0.415958i
$962$	0.647826	+	0.647826i	0.0208868	+	0.0208868i
$963$	−7.27969	−	7.27969i	−0.234585	−	0.234585i
$964$	26.8526	−	26.8526i	0.864864	−	0.864864i
$965$	−1.80952			−0.0582505
$966$	1.38628	−	1.38628i	0.0446029	−	0.0446029i
$967$			33.0762i			1.06366i	0.846852	+	0.531829i	$0.178495\pi$
$967$			33.0762i			1.06366i	−0.846852	+	0.531829i	$0.821505\pi$
$968$	−11.8750			−0.381678
$969$	−14.7009	+	2.13901i	−0.472263	+	0.0687148i
$970$	−5.53479			−0.177711
$971$			22.1601i			0.711152i	0.934647	+	0.355576i	$0.115715\pi$
$971$			22.1601i			0.711152i	−0.934647	+	0.355576i	$0.884285\pi$
$972$	−12.5659	+	12.5659i	−0.403051	+	0.403051i
$973$	7.13921			0.228873
$974$	18.3380	−	18.3380i	0.587587	−	0.587587i
$975$	0.141856	+	0.141856i	0.00454304	+	0.00454304i
$976$	3.98419	+	3.98419i	0.127531	+	0.127531i
$977$			15.7856i			0.505025i	0.967594	+	0.252513i	$0.0812570\pi$
$977$			15.7856i			0.505025i	−0.967594	+	0.252513i	$0.918743\pi$
$978$			6.09329i			0.194842i
$979$	−16.5132	−	16.5132i	−0.527765	−	0.527765i
$980$	5.47671	+	5.47671i	0.174947	+	0.174947i
$981$	23.0072	−	23.0072i	0.734562	−	0.734562i
$982$	14.7062			0.469293
$983$	−27.4094	+	27.4094i	−0.874223	+	0.874223i	−0.992929	−	0.118706i	$-0.962125\pi$
$983$	−27.4094	+	27.4094i	−0.874223	+	0.874223i	0.118706	+	0.992929i	$0.462125\pi$
$984$			10.5623i			0.336713i
$985$	−16.5784			−0.528231
$986$	−7.39000	+	1.07525i	−0.235345	+	0.0342431i
$987$	−5.05713			−0.160970
$988$		−	3.37360i		−	0.107329i
$989$	−18.6408	+	18.6408i	−0.592744	+	0.592744i
$990$	5.40909			0.171912
$991$	−22.6272	+	22.6272i	−0.718776	+	0.718776i	−0.968355	−	0.249578i	$-0.919708\pi$
$991$	−22.6272	+	22.6272i	−0.718776	+	0.718776i	0.249578	+	0.968355i	$0.419708\pi$
$992$	−27.4038	−	27.4038i	−0.870073	−	0.870073i
$993$	11.4696	+	11.4696i	0.363978	+	0.363978i
$994$			11.0694i			0.351102i
$995$		−	25.1610i		−	0.797657i
$996$	2.13195	+	2.13195i	0.0675535	+	0.0675535i
$997$	−9.85607	−	9.85607i	−0.312145	−	0.312145i	0.533595	−	0.845740i	$-0.320841\pi$
$997$	−9.85607	−	9.85607i	−0.312145	−	0.312145i	−0.845740	+	0.533595i	$0.820841\pi$
$998$	−3.95800	+	3.95800i	−0.125288	+	0.125288i
$999$	9.87286			0.312363

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	85.2.e.a.21.2	✓	12
3.2	odd	2		765.2.k.b.361.5		12
4.3	odd	2		1360.2.bt.d.1041.2		12
5.2	odd	4		425.2.j.b.174.5		12
5.3	odd	4		425.2.j.c.174.2		12
5.4	even	2		425.2.e.f.276.5		12
17.2	even	8		1445.2.d.g.866.9		12
17.8	even	8		1445.2.a.n.1.2		6
17.9	even	8		1445.2.a.o.1.2		6
17.13	even	4	inner	85.2.e.a.81.5	yes	12
17.15	even	8		1445.2.d.g.866.10		12
51.47	odd	4		765.2.k.b.676.2		12
68.47	odd	4		1360.2.bt.d.81.2		12
85.9	even	8		7225.2.a.z.1.5		6
85.13	odd	4		425.2.j.b.149.5		12
85.47	odd	4		425.2.j.c.149.2		12
85.59	even	8		7225.2.a.bb.1.5		6
85.64	even	4		425.2.e.f.251.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.e.a.21.2	✓	12	1.1	even	1	trivial
85.2.e.a.81.5	yes	12	17.13	even	4	inner
425.2.e.f.251.2		12	85.64	even	4
425.2.e.f.276.5		12	5.4	even	2
425.2.j.b.149.5		12	85.13	odd	4
425.2.j.b.174.5		12	5.2	odd	4
425.2.j.c.149.2		12	85.47	odd	4
425.2.j.c.174.2		12	5.3	odd	4
765.2.k.b.361.5		12	3.2	odd	2
765.2.k.b.676.2		12	51.47	odd	4
1360.2.bt.d.81.2		12	68.47	odd	4
1360.2.bt.d.1041.2		12	4.3	odd	2
1445.2.a.n.1.2		6	17.8	even	8
1445.2.a.o.1.2		6	17.9	even	8
1445.2.d.g.866.9		12	17.2	even	8
1445.2.d.g.866.10		12	17.15	even	8
7225.2.a.z.1.5		6	85.9	even	8
7225.2.a.bb.1.5		6	85.59	even	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:	\( N \)	\(=\)	\( 85 = 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	85.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.783476i q^{2} +(0.385357 - 0.385357i) q^{3} +1.38617 q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.301918 - 0.301918i) q^{6} +(-0.840380 - 0.840380i) q^{7} -2.65298i q^{8} +2.70300i q^{9} +(0.554001 + 0.554001i) q^{10} +(-1.80608 - 1.80608i) q^{11} +(0.534168 - 0.534168i) q^{12} -0.368117 q^{13} +(-0.658417 + 0.658417i) q^{14} +0.544977i q^{15} +0.693788 q^{16} +(-2.46531 + 3.30488i) q^{17} +2.11773 q^{18} +6.61138i q^{19} +(-0.980167 + 0.980167i) q^{20} -0.647692 q^{21} +(-1.41502 + 1.41502i) q^{22} +(-2.73186 - 2.73186i) q^{23} +(-1.02234 - 1.02234i) q^{24} -1.00000i q^{25} +0.288411i q^{26} +(2.19769 + 2.19769i) q^{27} +(-1.16491 - 1.16491i) q^{28} +(-1.63466 + 1.63466i) q^{29} +0.426976 q^{30} +(4.68480 - 4.68480i) q^{31} -5.84952i q^{32} -1.39197 q^{33} +(2.58929 + 1.93151i) q^{34} +1.18848 q^{35} +3.74681i q^{36} +(2.24619 - 2.24619i) q^{37} +5.17986 q^{38} +(-0.141856 + 0.141856i) q^{39} +(1.87594 + 1.87594i) q^{40} +(-5.16572 - 5.16572i) q^{41} +0.507451i q^{42} -6.82350i q^{43} +(-2.50353 - 2.50353i) q^{44} +(-1.91131 - 1.91131i) q^{45} +(-2.14034 + 2.14034i) q^{46} +7.80793 q^{47} +(0.267356 - 0.267356i) q^{48} -5.58752i q^{49} -0.783476 q^{50} +(0.323534 + 2.22358i) q^{51} -0.510272 q^{52} +8.01219i q^{53} +(1.72184 - 1.72184i) q^{54} +2.55419 q^{55} +(-2.22951 + 2.22951i) q^{56} +(2.54774 + 2.54774i) q^{57} +(1.28072 + 1.28072i) q^{58} -5.22381i q^{59} +0.755428i q^{60} +(5.74267 + 5.74267i) q^{61} +(-3.67043 - 3.67043i) q^{62} +(2.27155 - 2.27155i) q^{63} -3.19538 q^{64} +(0.260298 - 0.260298i) q^{65} +1.09058i q^{66} -7.94564 q^{67} +(-3.41733 + 4.58111i) q^{68} -2.10548 q^{69} -0.931143i q^{70} +(8.40610 - 8.40610i) q^{71} +7.17100 q^{72} +(-10.4176 + 10.4176i) q^{73} +(-1.75984 - 1.75984i) q^{74} +(-0.385357 - 0.385357i) q^{75} +9.16447i q^{76} +3.03559i q^{77} +(0.111141 + 0.111141i) q^{78} +(0.575011 + 0.575011i) q^{79} +(-0.490582 + 0.490582i) q^{80} -6.41521 q^{81} +(-4.04721 + 4.04721i) q^{82} +3.99116i q^{83} -0.897809 q^{84} +(-0.593666 - 4.08014i) q^{85} -5.34604 q^{86} +1.25986i q^{87} +(-4.79150 + 4.79150i) q^{88} +9.14311 q^{89} +(-1.49746 + 1.49746i) q^{90} +(0.309359 + 0.309359i) q^{91} +(-3.78681 - 3.78681i) q^{92} -3.61064i q^{93} -6.11732i q^{94} +(-4.67495 - 4.67495i) q^{95} +(-2.25415 - 2.25415i) q^{96} +(-4.99529 + 4.99529i) q^{97} -4.37769 q^{98} +(4.88185 - 4.88185i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{3} - 12 q^{4} - 4 q^{10} - 4 q^{11} - 8 q^{12} - 4 q^{14} + 4 q^{16} + 12 q^{17} + 28 q^{18} - 8 q^{20} - 16 q^{21} + 20 q^{22} + 12 q^{23} + 4 q^{24} - 4 q^{27} + 4 q^{28} - 12 q^{29} - 8 q^{30}+ \cdots + 44 q^{98}+O(q^{100}) \) 12 * q - 4 * q^3 - 12 * q^4 - 4 * q^10 - 4 * q^11 - 8 * q^12 - 4 * q^14 + 4 * q^16 + 12 * q^17 + 28 * q^18 - 8 * q^20 - 16 * q^21 + 20 * q^22 + 12 * q^23 + 4 * q^24 - 4 * q^27 + 4 * q^28 - 12 * q^29 - 8 * q^30 - 16 * q^33 - 12 * q^34 + 16 * q^35 + 12 * q^37 + 24 * q^38 - 20 * q^39 - 8 * q^40 - 24 * q^41 + 8 * q^44 + 8 * q^45 - 24 * q^46 - 48 * q^47 - 20 * q^48 + 4 * q^50 + 32 * q^51 - 56 * q^52 + 28 * q^54 + 40 * q^56 + 36 * q^58 + 40 * q^61 + 40 * q^62 + 12 * q^63 + 28 * q^64 + 4 * q^65 - 8 * q^67 - 40 * q^68 + 28 * q^71 + 20 * q^72 - 48 * q^73 + 28 * q^74 + 4 * q^75 - 92 * q^78 - 8 * q^79 + 16 * q^80 + 28 * q^81 + 40 * q^82 - 4 * q^85 - 96 * q^86 - 72 * q^88 + 24 * q^89 - 16 * q^90 - 36 * q^91 - 16 * q^92 - 8 * q^95 - 32 * q^96 + 4 * q^97 + 44 * q^98

Introduction

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