LMFDB - Embedded newform 845.2.d.d.844.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(844,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("845.844");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.d (of order $2$, degree $1$, 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:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$12$
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} + 22x^{10} + 147x^{8} + 390x^{6} + 413x^{4} + 128x^{2} + 4 $ x^12 + 22x^10 + 147x^8 + 390x^6 + 413x^4 + 128*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			844.3
Root			$2.18733i$ of defining polynomial
Character	$\chi$	$=$	845.844
Dual form			845.2.d.d.844.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.18733 q^{2} -0.345110i q^{3} -0.590239 q^{4} +(1.71029 + 1.44045i) q^{5} +0.409761i q^{6} +2.02956 q^{7} +3.07548 q^{8} +2.88090 q^{9} +O(q^{10})$	\(q-1.18733 q^{2} -0.345110i q^{3} -0.590239 q^{4} +(1.71029 + 1.44045i) q^{5} +0.409761i q^{6} +2.02956 q^{7} +3.07548 q^{8} +2.88090 q^{9} +(-2.03069 - 1.71029i) q^{10} -3.88090i q^{11} +0.203698i q^{12} -2.40976 q^{14} +(0.497113 - 0.590239i) q^{15} -2.47114 q^{16} +5.45014i q^{17} -3.42059 q^{18} -5.88090i q^{19} +(-1.00948 - 0.850210i) q^{20} -0.700420i q^{21} +4.60792i q^{22} -0.345110i q^{23} -1.06138i q^{24} +(0.850210 + 4.92718i) q^{25} -2.02956i q^{27} -1.19792 q^{28} -3.00000 q^{29} +(-0.590239 + 0.700811i) q^{30} +1.18048i q^{31} -3.21689 q^{32} -1.33934 q^{33} -6.47114i q^{34} +(3.47114 + 2.92347i) q^{35} -1.70042 q^{36} +5.45014 q^{37} +6.98259i q^{38} +(5.25997 + 4.43007i) q^{40} +0.180479i q^{41} +0.831632i q^{42} -1.33934i q^{43} +2.29066i q^{44} +(4.92718 + 4.14979i) q^{45} +0.409761i q^{46} +12.2807 q^{47} +0.852815i q^{48} -2.88090 q^{49} +(-1.00948 - 5.85021i) q^{50} +1.88090 q^{51} -2.42636i q^{53} +2.40976i q^{54} +(5.59024 - 6.63748i) q^{55} +6.24186 q^{56} -2.02956 q^{57} +3.56200 q^{58} -7.06138i q^{59} +(-0.293416 + 0.348383i) q^{60} +6.76180 q^{61} -1.40162i q^{62} +5.84695 q^{63} +8.76180 q^{64} +1.59024 q^{66} +4.40422 q^{67} -3.21689i q^{68} -0.119101 q^{69} +(-4.12140 - 3.47114i) q^{70} -1.88090i q^{71} +8.86014 q^{72} -8.86014 q^{73} -6.47114 q^{74} +(1.70042 - 0.293416i) q^{75} +3.47114i q^{76} -7.87651i q^{77} -11.1805 q^{79} +(-4.22637 - 3.55955i) q^{80} +7.94228 q^{81} -0.214289i q^{82} +7.83540 q^{83} +0.413416i q^{84} +(-7.85066 + 9.32135i) q^{85} +1.59024i q^{86} +1.03533i q^{87} -11.9356i q^{88} +12.2419i q^{89} +(-5.85021 - 4.92718i) q^{90} +0.203698i q^{92} +0.407395 q^{93} -14.5813 q^{94} +(8.47114 - 10.0581i) q^{95} +1.11018i q^{96} +5.80585 q^{97} +3.42059 q^{98} -11.1805i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 8 q^{4} - 12 q^{9}+O(q^{10}) $ 12 * q + 8 * q^4 - 12 * q^9	$ 12 q + 8 q^{4} - 12 q^{9} + 14 q^{10} - 44 q^{14} + 32 q^{16} + 2 q^{25} - 36 q^{29} + 8 q^{30} - 20 q^{35} - 4 q^{36} + 70 q^{40} + 12 q^{49} - 24 q^{51} + 52 q^{55} - 32 q^{56} - 12 q^{61} + 12 q^{64} + 4 q^{66} - 48 q^{69} - 16 q^{74} + 4 q^{75} - 104 q^{79} - 28 q^{81} - 62 q^{90} - 112 q^{94} + 40 q^{95}+O(q^{100}) $ 12 * q + 8 * q^4 - 12 * q^9 + 14 * q^10 - 44 * q^14 + 32 * q^16 + 2 * q^25 - 36 * q^29 + 8 * q^30 - 20 * q^35 - 4 * q^36 + 70 * q^40 + 12 * q^49 - 24 * q^51 + 52 * q^55 - 32 * q^56 - 12 * q^61 + 12 * q^64 + 4 * q^66 - 48 * q^69 - 16 * q^74 + 4 * q^75 - 104 * q^79 - 28 * q^81 - 62 * q^90 - 112 * q^94 + 40 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$171$	$677$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−1.18733			−0.839571			−0.419786	−	0.907623i	$-0.637895\pi$
$2$	−1.18733			−0.839571			−0.419786	+	0.907623i	$0.637895\pi$
$3$		−	0.345110i		−	0.199249i	−0.995025	−	0.0996247i	$-0.968236\pi$
$3$		−	0.345110i		−	0.199249i	0.995025	−	0.0996247i	$-0.0317642\pi$
$4$	−0.590239			−0.295120
$5$	1.71029	+	1.44045i	0.764867	+	0.644189i
$5$	1.71029	+	1.44045i	0.764867	+	0.644189i
$6$			0.409761i			0.167284i
$7$	2.02956			0.767100			0.383550	−	0.923520i	$-0.374701\pi$
$7$	2.02956			0.767100			0.383550	+	0.923520i	$0.374701\pi$
$8$	3.07548			1.08735
$9$	2.88090			0.960300
$10$	−2.03069	−	1.71029i	−0.642160	−	0.540842i
$11$		−	3.88090i		−	1.17014i	−0.810985	−	0.585068i	$-0.801068\pi$
$11$		−	3.88090i		−	1.17014i	0.810985	−	0.585068i	$-0.198932\pi$
$12$			0.203698i			0.0588024i
$13$		0			0
$13$		0			0
$14$	−2.40976			−0.644036
$15$	0.497113	−	0.590239i	0.128354	−	0.152399i
$16$	−2.47114			−0.617785
$17$			5.45014i			1.32185i	0.750450	+	0.660927i	$0.229837\pi$
$17$			5.45014i			1.32185i	−0.750450	+	0.660927i	$0.770163\pi$
$18$	−3.42059			−0.806240
$19$		−	5.88090i		−	1.34917i	−0.738197	−	0.674585i	$-0.764322\pi$
$19$		−	5.88090i		−	1.34917i	0.738197	−	0.674585i	$-0.235678\pi$
$20$	−1.00948	−	0.850210i	−0.225727	−	0.190113i
$21$		−	0.700420i		−	0.152844i
$22$			4.60792i			0.982412i
$23$		−	0.345110i		−	0.0719604i	−0.999353	−	0.0359802i	$-0.988545\pi$
$23$		−	0.345110i		−	0.0719604i	0.999353	−	0.0359802i	$-0.0114553\pi$
$24$		−	1.06138i		−	0.216653i
$25$	0.850210	+	4.92718i	0.170042	+	0.985437i
$26$		0			0
$27$		−	2.02956i		−	0.390588i
$28$	−1.19792			−0.226386
$29$	−3.00000			−0.557086			−0.278543	−	0.960424i	$-0.589851\pi$
$29$	−3.00000			−0.557086			−0.278543	+	0.960424i	$0.589851\pi$
$30$	−0.590239	+	0.700811i	−0.107762	+	0.127950i
$31$			1.18048i			0.212020i	0.994365	+	0.106010i	$0.0338076\pi$
$31$			1.18048i			0.212020i	−0.994365	+	0.106010i	$0.966192\pi$
$32$	−3.21689			−0.568671
$33$	−1.33934			−0.233149
$34$		−	6.47114i		−	1.10979i
$35$	3.47114	+	2.92347i	0.586730	+	0.494157i
$36$	−1.70042			−0.283403
$37$	5.45014			0.895998			0.447999	−	0.894034i	$-0.352137\pi$
$37$	5.45014			0.895998			0.447999	+	0.894034i	$0.352137\pi$
$38$			6.98259i			1.13273i
$39$		0			0
$40$	5.25997	+	4.43007i	0.831674	+	0.700456i
$41$			0.180479i			0.0281861i	0.999901	+	0.0140930i	$0.00448610\pi$
$41$			0.180479i			0.0281861i	−0.999901	+	0.0140930i	$0.995514\pi$
$42$			0.831632i			0.128324i
$43$		−	1.33934i		−	0.204247i	−0.994772	−	0.102123i	$-0.967436\pi$
$43$		−	1.33934i		−	0.204247i	0.994772	−	0.102123i	$-0.0325637\pi$
$44$			2.29066i			0.345330i
$45$	4.92718	+	4.14979i	0.734501	+	0.618614i
$46$			0.409761i			0.0604159i
$47$	12.2807			1.79133			0.895664	−	0.444731i	$-0.146701\pi$
$47$	12.2807			1.79133			0.895664	+	0.444731i	$0.146701\pi$
$48$			0.852815i			0.123093i
$49$	−2.88090			−0.411557
$50$	−1.00948	−	5.85021i	−0.142762	−	0.827345i
$51$	1.88090			0.263379
$52$		0			0
$53$		−	2.42636i		−	0.333286i	−0.986017	−	0.166643i	$-0.946707\pi$
$53$		−	2.42636i		−	0.333286i	0.986017	−	0.166643i	$-0.0532928\pi$
$54$			2.40976i			0.327927i
$55$	5.59024	−	6.63748i	0.753788	−	0.894997i
$56$	6.24186			0.834103
$57$	−2.02956			−0.268821
$58$	3.56200			0.467714
$59$		−	7.06138i		−	0.919313i	−0.888097	−	0.459657i	$-0.847973\pi$
$59$		−	7.06138i		−	0.919313i	0.888097	−	0.459657i	$-0.152027\pi$
$60$	−0.293416	+	0.348383i	−0.0378798	+	0.0449760i
$61$	6.76180			0.865760			0.432880	−	0.901452i	$-0.357497\pi$
$61$	6.76180			0.865760			0.432880	+	0.901452i	$0.357497\pi$
$62$		−	1.40162i		−	0.178006i
$63$	5.84695			0.736646
$64$	8.76180			1.09522
$65$		0			0
$66$	1.59024			0.195745
$67$	4.40422			0.538062			0.269031	−	0.963132i	$-0.413297\pi$
$67$	4.40422			0.538062			0.269031	+	0.963132i	$0.413297\pi$
$68$		−	3.21689i		−	0.390105i
$69$	−0.119101			−0.0143381
$70$	−4.12140	−	3.47114i	−0.492601	−	0.414880i
$71$		−	1.88090i		−	0.223222i	−0.993752	−	0.111611i	$-0.964399\pi$
$71$		−	1.88090i		−	0.223222i	0.993752	−	0.111611i	$-0.0356010\pi$
$72$	8.86014			1.04418
$73$	−8.86014			−1.03700			−0.518501	−	0.855077i	$-0.673510\pi$
$73$	−8.86014			−1.03700			−0.518501	+	0.855077i	$0.673510\pi$
$74$	−6.47114			−0.752255
$75$	1.70042	−	0.293416i	0.196348	−	0.0338808i
$76$			3.47114i			0.398167i
$77$		−	7.87651i		−	0.897611i
$78$		0			0
$79$	−11.1805			−1.25790			−0.628951	−	0.777445i	$-0.716515\pi$
$79$	−11.1805			−1.25790			−0.628951	+	0.777445i	$0.716515\pi$
$80$	−4.22637	−	3.55955i	−0.472523	−	0.397970i
$81$	7.94228			0.882475
$82$		−	0.214289i		−	0.0236642i
$83$	7.83540			0.860047			0.430024	−	0.902818i	$-0.358505\pi$
$83$	7.83540			0.860047			0.430024	+	0.902818i	$0.358505\pi$
$84$			0.413416i			0.0451073i
$85$	−7.85066	+	9.32135i	−0.851523	+	1.01104i
$86$			1.59024i			0.171480i
$87$			1.03533i			0.110999i
$88$		−	11.9356i		−	1.27234i
$89$			12.2419i			1.29763i	0.760944	+	0.648817i	$0.224736\pi$
$89$			12.2419i			1.29763i	−0.760944	+	0.648817i	$0.775264\pi$
$90$	−5.85021	−	4.92718i	−0.616666	−	0.519371i
$91$		0			0
$92$			0.203698i			0.0212369i
$93$	0.407395			0.0422449
$94$	−14.5813			−1.50395
$95$	8.47114	−	10.0581i	0.869120	−	1.03194i
$96$			1.11018i			0.113307i
$97$	5.80585			0.589494			0.294747	−	0.955575i	$-0.404765\pi$
$97$	5.80585			0.589494			0.294747	+	0.955575i	$0.404765\pi$
$98$	3.42059			0.345532
$99$		−	11.1805i		−	1.12368i
$100$	−0.501828	−	2.90822i	−0.0501828	−	0.290822i
$101$	5.94228			0.591279			0.295639	−	0.955300i	$-0.404467\pi$
$101$	5.94228			0.591279			0.295639	+	0.955300i	$0.404467\pi$
$102$	−2.23325			−0.221125
$103$		−	6.43378i		−	0.633939i	−0.948436	−	0.316970i	$-0.897335\pi$
$103$		−	6.43378i		−	0.633939i	0.948436	−	0.316970i	$-0.102665\pi$
$104$		0			0
$105$	1.00892	−	1.19792i	0.0984605	−	0.116905i
$106$			2.88090i			0.279818i
$107$			17.6792i			1.70911i	0.519360	+	0.854555i	$0.326170\pi$
$107$			17.6792i			1.70911i	−0.519360	+	0.854555i	$0.673830\pi$
$108$			1.19792i			0.115270i
$109$		−	5.76180i		−	0.551880i	−0.961175	−	0.275940i	$-0.911011\pi$
$109$		−	5.76180i		−	0.551880i	0.961175	−	0.275940i	$-0.0889891\pi$
$110$	−6.63748	+	7.88090i	−0.632859	+	0.751414i
$111$		−	1.88090i		−	0.178527i
$112$	−5.01532			−0.473903
$113$			4.75992i			0.447776i	0.974615	+	0.223888i	$0.0718750\pi$
$113$			4.75992i			0.447776i	−0.974615	+	0.223888i	$0.928125\pi$
$114$	2.40976			0.225695
$115$	0.497113	−	0.590239i	0.0463561	−	0.0550401i
$116$	1.77072			0.164407
$117$		0			0
$118$			8.38421i			0.771829i
$119$			11.0614i			1.01399i
$120$	1.52886	−	1.81527i	0.139565	−	0.165711i
$121$	−4.06138			−0.369216
$122$	−8.02851			−0.726867
$123$	0.0622851			0.00561605
$124$		−	0.696765i		−	0.0625714i
$125$	−5.64325	+	9.65162i	−0.504748	+	0.863267i
$126$	−6.94228			−0.618467
$127$			16.7061i			1.48243i	0.671268	+	0.741215i	$0.265750\pi$
$127$			16.7061i			1.48243i	−0.671268	+	0.741215i	$0.734250\pi$
$128$	−3.96940			−0.350848
$129$	−0.462218			−0.0406961
$130$		0			0
$131$	10.0000			0.873704			0.436852	−	0.899533i	$-0.356093\pi$
$131$	10.0000			0.873704			0.436852	+	0.899533i	$0.356093\pi$
$132$	0.790529			0.0688068
$133$		−	11.9356i		−	1.03495i
$134$	−5.22928			−0.451741
$135$	2.92347	−	3.47114i	0.251613	−	0.298748i
$136$			16.7618i			1.43731i
$137$	1.97786			0.168980			0.0844901	−	0.996424i	$-0.473074\pi$
$137$	1.97786			0.168980			0.0844901	+	0.996424i	$0.473074\pi$
$138$	0.141412			0.0120378
$139$	−8.70042			−0.737960			−0.368980	−	0.929437i	$-0.620293\pi$
$139$	−8.70042			−0.737960			−0.368980	+	0.929437i	$0.620293\pi$
$140$	−2.04880	−	1.72555i	−0.173155	−	0.145836i
$141$		−	4.23820i		−	0.356921i
$142$			2.23325i			0.187411i
$143$		0			0
$144$	−7.11910			−0.593258
$145$	−5.13088	−	4.32135i	−0.426097	−	0.358868i
$146$	10.5199			0.870637
$147$			0.994227i			0.0820025i
$148$	−3.21689			−0.264427
$149$		−	22.3032i		−	1.82715i	−0.406668	−	0.913576i	$-0.633309\pi$
$149$		−	22.3032i		−	1.82715i	0.406668	−	0.913576i	$-0.366691\pi$
$150$	−2.01897	+	0.348383i	−0.164848	+	0.0284453i
$151$			19.1626i			1.55943i	0.626132	+	0.779717i	$0.284637\pi$
$151$			19.1626i			1.55943i	−0.626132	+	0.779717i	$0.715363\pi$
$152$		−	18.0866i		−	1.46701i
$153$			15.7013i			1.26938i
$154$			9.35204i			0.753609i
$155$	−1.70042	+	2.01897i	−0.136581	+	0.162167i
$156$		0			0
$157$		−	6.20265i		−	0.495025i	−0.968885	−	0.247513i	$-0.920387\pi$
$157$		−	6.20265i		−	0.495025i	0.968885	−	0.247513i	$-0.0796132\pi$
$158$	13.2750			1.05610
$159$	−0.837361			−0.0664071
$160$	−5.50183	−	4.63377i	−0.434958	−	0.366332i
$161$		−	0.700420i		−	0.0552008i
$162$	−9.43013			−0.740901
$163$	−11.9356			−0.934870			−0.467435	−	0.884027i	$-0.654822\pi$
$163$	−11.9356			−0.934870			−0.467435	+	0.884027i	$0.654822\pi$
$164$		−	0.106526i		−	0.00831826i
$165$	−2.29066	−	1.92925i	−0.178328	−	0.150192i
$166$	−9.30323			−0.722071
$167$	−2.02956			−0.157052			−0.0785259	−	0.996912i	$-0.525021\pi$
$167$	−2.02956			−0.157052			−0.0785259	+	0.996912i	$0.525021\pi$
$168$		−	2.15413i		−	0.166195i
$169$		0			0
$170$	9.32135	−	11.0675i	0.714915	−	0.848842i
$171$		−	16.9423i		−	1.29561i
$172$			0.790529i			0.0602773i
$173$			1.33934i			0.101828i	0.998703	+	0.0509139i	$0.0162134\pi$
$173$			1.33934i			0.101828i	−0.998703	+	0.0509139i	$0.983787\pi$
$174$		−	1.22928i		−	0.0931916i
$175$	1.72555	+	10.0000i	0.130439	+	0.755929i
$176$			9.59024i			0.722891i
$177$	−2.43695			−0.183173
$178$		−	14.5352i		−	1.08946i
$179$	20.2240			1.51161			0.755807	−	0.654794i	$-0.227245\pi$
$179$	20.2240			1.51161			0.755807	+	0.654794i	$0.227245\pi$
$180$	−2.90822	−	2.44937i	−0.216766	−	0.182565i
$181$	−19.8232			−1.47345			−0.736723	−	0.676195i	$-0.763628\pi$
$181$	−19.8232			−1.47345			−0.736723	+	0.676195i	$0.763628\pi$
$182$		0			0
$183$		−	2.33356i		−	0.172502i
$184$		−	1.06138i		−	0.0782458i
$185$	9.32135	+	7.85066i	0.685319	+	0.577192i
$186$	−0.483714			−0.0354676
$187$	21.1515			1.54675
$188$	−7.24857			−0.528656
$189$		−	4.11910i		−	0.299621i
$190$	−10.0581	+	11.9423i	−0.729689	+	0.866384i
$191$	1.53778			0.111270			0.0556350	−	0.998451i	$-0.482282\pi$
$191$	1.53778			0.111270			0.0556350	+	0.998451i	$0.482282\pi$
$192$		−	3.02378i		−	0.218223i
$193$	−21.2032			−1.52624			−0.763118	−	0.646259i	$-0.776333\pi$
$193$	−21.2032			−1.52624			−0.763118	+	0.646259i	$0.776333\pi$
$194$	−6.89347			−0.494923
$195$		0			0
$196$	1.70042			0.121459
$197$	9.25695			0.659530			0.329765	−	0.944063i	$-0.393030\pi$
$197$	9.25695			0.659530			0.329765	+	0.944063i	$0.393030\pi$
$198$			13.2750i			0.943410i
$199$	−17.4045			−1.23377			−0.616886	−	0.787053i	$-0.711606\pi$
$199$	−17.4045			−1.23377			−0.616886	+	0.787053i	$0.711606\pi$
$200$	2.61480	+	15.1534i	0.184894	+	1.07151i
$201$		−	1.51994i		−	0.107208i
$202$	−7.05546			−0.496421
$203$	−6.08867			−0.427341
$204$	−1.11018			−0.0777282
$205$	−0.259971	+	0.308672i	−0.0181571	+	0.0215586i
$206$			7.63904i			0.532237i
$207$		−	0.994227i		−	0.0691036i
$208$		0			0
$209$	−22.8232			−1.57871
$210$	−1.19792	+	1.42234i	−0.0826646	+	0.0981505i
$211$	−7.28174			−0.501296			−0.250648	−	0.968078i	$-0.580644\pi$
$211$	−7.28174			−0.501296			−0.250648	+	0.968078i	$0.580644\pi$
$212$			1.43213i			0.0983594i
$213$	−0.649117			−0.0444768
$214$		−	20.9911i		−	1.43492i
$215$	1.92925	−	2.29066i	0.131574	−	0.156222i
$216$		−	6.24186i		−	0.424705i
$217$			2.39585i			0.162641i
$218$			6.84118i			0.463343i
$219$			3.05772i			0.206622i
$220$	−3.29958	+	3.91770i	−0.222458	+	0.264131i
$221$		0			0
$222$			2.23325i			0.149886i
$223$	−19.4670			−1.30361			−0.651804	−	0.758388i	$-0.725987\pi$
$223$	−19.4670			−1.30361			−0.651804	+	0.758388i	$0.725987\pi$
$224$	−6.52886			−0.436228
$225$	2.44937	+	14.1947i	0.163291	+	0.946315i
$226$		−	5.65162i		−	0.375940i
$227$	−4.81162			−0.319358			−0.159679	−	0.987169i	$-0.551046\pi$
$227$	−4.81162			−0.319358			−0.159679	+	0.987169i	$0.551046\pi$
$228$	1.19792			0.0793345
$229$			1.52360i			0.100682i	0.998732	+	0.0503410i	$0.0160308\pi$
$229$			1.52360i			0.100682i	−0.998732	+	0.0503410i	$0.983969\pi$
$230$	−0.590239	+	0.700811i	−0.0389192	+	0.0462101i
$231$	−2.71826			−0.178848
$232$	−9.22643			−0.605745
$233$		−	13.9652i		−	0.914889i	−0.889238	−	0.457445i	$-0.848765\pi$
$233$		−	13.9652i		−	0.914889i	0.889238	−	0.457445i	$-0.151235\pi$
$234$		0			0
$235$	21.0037	+	17.6898i	1.37013	+	1.15395i
$236$			4.16790i			0.271307i
$237$			3.85849i			0.250636i
$238$		−	13.1335i		−	0.851321i
$239$		−	4.00000i		−	0.258738i	−0.991596	−	0.129369i	$-0.958705\pi$
$239$		−	4.00000i		−	0.258738i	0.991596	−	0.129369i	$-0.0412952\pi$
$240$	−1.22844	+	1.45856i	−0.0792952	+	0.0941499i
$241$			17.4659i			1.12508i	0.826771	+	0.562538i	$0.190175\pi$
$241$			17.4659i			1.12508i	−0.826771	+	0.562538i	$0.809825\pi$
$242$	4.82221			0.309983
$243$		−	8.82963i		−	0.566421i
$244$	−3.99108			−0.255503
$245$	−4.92718	−	4.14979i	−0.314786	−	0.265120i
$246$	−0.0739531			−0.00471508
$247$		0			0
$248$			3.63054i			0.230539i
$249$		−	2.70408i		−	0.171364i
$250$	6.70042	−	11.4597i	0.423772	−	0.724774i
$251$	−9.29958			−0.586984			−0.293492	−	0.955961i	$-0.594817\pi$
$251$	−9.29958			−0.586984			−0.293492	+	0.955961i	$0.594817\pi$
$252$	−3.45110			−0.217399
$253$	−1.33934			−0.0842034
$254$		−	19.8358i		−	1.24461i
$255$	3.21689	+	2.70934i	0.201449	+	0.169665i
$256$	−12.8106			−0.800663
$257$		−	10.8897i		−	0.679281i	−0.940555	−	0.339640i	$-0.889695\pi$
$257$		−	10.8897i		−	0.679281i	0.940555	−	0.339640i	$-0.110305\pi$
$258$	0.548807			0.0341673
$259$	11.0614			0.687321
$260$		0			0
$261$	−8.64270			−0.534970
$262$	−11.8733			−0.733537
$263$			13.4406i			0.828785i	0.910098	+	0.414392i	$0.136006\pi$
$263$			13.4406i			0.828785i	−0.910098	+	0.414392i	$0.863994\pi$
$264$	−4.11910			−0.253513
$265$	3.49505	−	4.14979i	0.214699	−	0.254920i
$266$			14.1716i			0.868914i
$267$	4.22479			0.258553
$268$	−2.59955			−0.158793
$269$	−3.66054			−0.223187			−0.111593	−	0.993754i	$-0.535595\pi$
$269$	−3.66054			−0.223187			−0.111593	+	0.993754i	$0.535595\pi$
$270$	−3.47114	+	4.12140i	−0.211247	+	0.250820i
$271$		−	22.0037i		−	1.33663i	−0.743880	−	0.668313i	$-0.767017\pi$
$271$		−	22.0037i		−	1.33663i	0.743880	−	0.668313i	$-0.232983\pi$
$272$		−	13.4681i		−	0.816621i
$273$		0			0
$274$	−2.34838			−0.141871
$275$	19.1219	−	3.29958i	1.15309	−	0.198972i
$276$	0.0702980			0.00423144
$277$		−	9.89547i		−	0.594561i	−0.954790	−	0.297281i	$-0.903920\pi$
$277$		−	9.89547i		−	0.594561i	0.954790	−	0.297281i	$-0.0960797\pi$
$278$	10.3303			0.619570
$279$			3.40084i			0.203603i
$280$	10.6754	+	8.99108i	0.637978	+	0.537320i
$281$		−	4.06138i		−	0.242281i	−0.992635	−	0.121141i	$-0.961345\pi$
$281$		−	4.06138i		−	0.242281i	0.992635	−	0.121141i	$-0.0386552\pi$
$282$			5.03216i			0.299661i
$283$		−	6.08867i		−	0.361934i	−0.983489	−	0.180967i	$-0.942077\pi$
$283$		−	6.08867i		−	0.361934i	0.983489	−	0.180967i	$-0.0579227\pi$
$284$			1.11018i			0.0658771i
$285$	−3.47114	−	2.92347i	−0.205613	−	0.173172i
$286$		0			0
$287$			0.366292i			0.0216215i
$288$	−9.26754			−0.546095
$289$	−12.7041			−0.747299
$290$	6.09207	+	5.13088i	0.357738	+	0.301296i
$291$		−	2.00366i		−	0.117456i
$292$	5.22960			0.306039
$293$	9.79208			0.572060			0.286030	−	0.958221i	$-0.407664\pi$
$293$	9.79208			0.572060			0.286030	+	0.958221i	$0.407664\pi$
$294$		−	1.18048i		−	0.0688469i
$295$	10.1716	−	12.0770i	0.592211	−	0.703152i
$296$	16.7618			0.974260
$297$	−7.87651			−0.457041
$298$			26.4814i			1.53402i
$299$		0			0
$300$	−1.00366	+	0.173186i	−0.0579461	+	0.00999888i
$301$		−	2.71826i		−	0.156678i
$302$		−	22.7524i		−	1.30926i
$303$		−	2.05074i		−	0.117812i
$304$			14.5325i			0.833497i
$305$	11.5647	+	9.74003i	0.662191	+	0.557712i
$306$		−	18.6427i		−	1.06573i
$307$	−22.1046			−1.26158			−0.630788	−	0.775955i	$-0.717268\pi$
$307$	−22.1046			−1.26158			−0.630788	+	0.775955i	$0.717268\pi$
$308$			4.64902i			0.264903i
$309$	−2.22036			−0.126312
$310$	2.01897	−	2.39719i	0.114670	−	0.136151i
$311$	−7.63904			−0.433170			−0.216585	−	0.976264i	$-0.569492\pi$
$311$	−7.63904			−0.433170			−0.216585	+	0.976264i	$0.569492\pi$
$312$		0			0
$313$		−	26.1425i		−	1.47766i	−0.673891	−	0.738831i	$-0.735378\pi$
$313$		−	26.1425i		−	1.47766i	0.673891	−	0.738831i	$-0.264622\pi$
$314$			7.36461i			0.415609i
$315$	10.0000	+	8.42223i	0.563436	+	0.474539i
$316$	6.59916			0.371232
$317$	−11.8428			−0.665159			−0.332580	−	0.943075i	$-0.607919\pi$
$317$	−11.8428			−0.665159			−0.332580	+	0.943075i	$0.607919\pi$
$318$	0.994227			0.0557535
$319$			11.6427i			0.651866i
$320$	14.9852	+	12.6209i	0.837701	+	0.705531i
$321$	6.10126			0.340539
$322$			0.831632i			0.0463451i
$323$	32.0518			1.78341
$324$	−4.68785			−0.260436
$325$		0			0
$326$	14.1716			0.784890
$327$	−1.98845			−0.109962
$328$			0.555059i			0.0306480i
$329$	24.9244			1.37413
$330$	2.71978	+	2.29066i	0.149719	+	0.126097i
$331$		−	12.7004i		−	0.698078i	−0.937108	−	0.349039i	$-0.886508\pi$
$331$		−	12.7004i		−	0.698078i	0.937108	−	0.349039i	$-0.113492\pi$
$332$	−4.62476			−0.253817
$333$	15.7013			0.860427
$334$	2.40976			0.131856
$335$	7.53252	+	6.34406i	0.411545	+	0.346613i
$336$			1.73084i			0.0944248i
$337$			15.2939i			0.833113i	0.909110	+	0.416556i	$0.136763\pi$
$337$			15.2939i			0.833113i	−0.909110	+	0.416556i	$0.863237\pi$
$338$		0			0
$339$	1.64270			0.0892191
$340$	4.63377	−	5.50183i	0.251301	−	0.298378i
$341$	4.58132			0.248092
$342$			20.1161i			1.08776i
$343$	−20.0538			−1.08281
$344$		−	4.11910i		−	0.222087i
$345$	−0.203698	−	0.171559i	−0.0109667	−	0.00923642i
$346$		−	1.59024i		−	0.0854918i
$347$			12.2396i			0.657058i	0.944494	+	0.328529i	$0.106553\pi$
$347$			12.2396i			0.657058i	−0.944494	+	0.328529i	$0.893447\pi$
$348$		−	0.611093i		−	0.0327580i
$349$			18.7004i			1.00101i	0.865733	+	0.500505i	$0.166852\pi$
$349$			18.7004i			1.00101i	−0.865733	+	0.500505i	$0.833148\pi$
$350$	−2.04880	−	11.8733i	−0.109513	−	0.634656i
$351$		0			0
$352$			12.4844i			0.665422i
$353$	1.30883			0.0696617			0.0348309	−	0.999393i	$-0.488911\pi$
$353$	1.30883			0.0696617			0.0348309	+	0.999393i	$0.488911\pi$
$354$	2.89347			0.153786
$355$	2.70934	−	3.21689i	0.143797	−	0.170735i
$356$		−	7.22563i		−	0.382957i
$357$	3.81739			0.202038
$358$	−24.0127			−1.26911
$359$		−	29.4082i		−	1.55210i	−0.630670	−	0.776051i	$-0.717220\pi$
$359$		−	29.4082i		−	1.55210i	0.630670	−	0.776051i	$-0.282780\pi$
$360$	15.1534	+	12.7626i	0.798657	+	0.672647i
$361$	−15.5850			−0.820262
$362$	23.5367			1.23706
$363$			1.40162i			0.0735661i
$364$		0			0
$365$	−15.1534	−	12.7626i	−0.793168	−	0.668024i
$366$			2.77072i			0.144828i
$367$		−	33.4322i		−	1.74515i	−0.488484	−	0.872573i	$-0.662450\pi$
$367$		−	33.4322i		−	1.74515i	0.488484	−	0.872573i	$-0.337550\pi$
$368$			0.852815i			0.0444560i
$369$			0.519941i			0.0270671i
$370$	−11.0675	−	9.32135i	−0.575374	−	0.484594i
$371$		−	4.92444i		−	0.255664i
$372$	−0.240461			−0.0124673
$373$			34.4781i			1.78521i	0.450841	+	0.892604i	$0.351124\pi$
$373$			34.4781i			1.78521i	−0.450841	+	0.892604i	$0.648876\pi$
$374$	−25.1138			−1.29861
$375$	3.33087	+	1.94754i	0.172005	+	0.100571i
$376$	37.7691			1.94779
$377$		0			0
$378$			4.89075i			0.251553i
$379$			17.4045i			0.894009i	0.894532	+	0.447004i	$0.147509\pi$
$379$			17.4045i			0.894009i	−0.894532	+	0.447004i	$0.852491\pi$
$380$	−5.00000	+	5.93667i	−0.256495	+	0.304545i
$381$	5.76545			0.295373
$382$	−1.82586			−0.0934191
$383$	1.74673			0.0892538			0.0446269	−	0.999004i	$-0.485790\pi$
$383$	1.74673			0.0892538			0.0446269	+	0.999004i	$0.485790\pi$
$384$			1.36988i			0.0699063i
$385$	11.3457	−	13.4711i	0.578231	−	0.686553i
$386$	25.1752			1.28138
$387$		−	3.85849i		−	0.196138i
$388$	−3.42684			−0.173971
$389$	22.0435			1.11765			0.558826	−	0.829285i	$-0.311252\pi$
$389$	22.0435			1.11765			0.558826	+	0.829285i	$0.311252\pi$
$390$		0			0
$391$	1.88090			0.0951212
$392$	−8.86014			−0.447505
$393$		−	3.45110i		−	0.174085i
$394$	−10.9911			−0.553723
$395$	−19.1219	−	16.1049i	−0.962127	−	0.810326i
$396$			6.59916i			0.331620i
$397$	−22.5319			−1.13084			−0.565422	−	0.824802i	$-0.691287\pi$
$397$	−22.5319			−1.13084			−0.565422	+	0.824802i	$0.691287\pi$
$398$	20.6649			1.03584
$399$	−4.11910			−0.206213
$400$	−2.10099	−	12.1758i	−0.105049	−	0.608788i
$401$			3.70408i			0.184973i	0.995714	+	0.0924863i	$0.0294815\pi$
$401$			3.70408i			0.184973i	−0.995714	+	0.0924863i	$0.970519\pi$
$402$			1.80468i			0.0900091i
$403$		0			0
$404$	−3.50737			−0.174498
$405$	13.5836	+	11.4404i	0.674976	+	0.568481i
$406$	7.22928			0.358783
$407$		−	21.1515i		−	1.04844i
$408$	5.78466			0.286384
$409$			13.4837i			0.666727i	0.942798	+	0.333363i	$0.108184\pi$
$409$			13.4837i			0.666727i	−0.942798	+	0.333363i	$0.891816\pi$
$410$	0.308672	−	0.366496i	0.0152442	−	0.0181000i
$411$		−	0.682580i		−	0.0336692i
$412$			3.79747i			0.187088i
$413$		−	14.3315i		−	0.705205i
$414$			1.18048i			0.0580174i
$415$	13.4008	+	11.2865i	0.657821	+	0.554033i
$416$		0			0
$417$			3.00260i			0.147038i
$418$	27.0987			1.32544
$419$	−16.8232			−0.821866			−0.410933	−	0.911666i	$-0.634797\pi$
$419$	−16.8232			−0.821866			−0.410933	+	0.911666i	$0.634797\pi$
$420$	−0.595504	+	0.707062i	−0.0290576	+	0.0345011i
$421$			17.1013i			0.833464i	0.909029	+	0.416732i	$0.136825\pi$
$421$			17.1013i			0.833464i	−0.909029	+	0.416732i	$0.863175\pi$
$422$	8.64585			0.420874
$423$	35.3795			1.72021
$424$		−	7.46222i		−	0.362397i
$425$	−26.8539	+	4.63377i	−1.30260	+	0.224771i
$426$	0.770718			0.0373414
$427$	13.7235			0.664124
$428$		−	10.4349i		−	0.504392i
$429$		0			0
$430$	−2.29066	+	2.71978i	−0.110465	+	0.131159i
$431$			9.66054i			0.465332i	0.972557	+	0.232666i	$0.0747448\pi$
$431$			9.66054i			0.465332i	−0.972557	+	0.232666i	$0.925255\pi$
$432$			5.01532i			0.241300i
$433$			24.7727i			1.19050i	0.803541	+	0.595249i	$0.202947\pi$
$433$			24.7727i			1.19050i	−0.803541	+	0.595249i	$0.797053\pi$
$434$		−	2.84467i		−	0.136549i
$435$	−1.49134	+	1.77072i	−0.0715043	+	0.0848994i
$436$			3.40084i			0.162871i
$437$	−2.02956			−0.0970869
$438$		−	3.63054i		−	0.173474i
$439$	7.06138			0.337021			0.168511	−	0.985700i	$-0.446104\pi$
$439$	7.06138			0.337021			0.168511	+	0.985700i	$0.446104\pi$
$440$	17.1927	−	20.4134i	0.819628	−	0.973171i
$441$	−8.29958			−0.395218
$442$		0			0
$443$			38.2438i			1.81702i	0.417865	+	0.908509i	$0.362778\pi$
$443$			38.2438i			1.81702i	−0.417865	+	0.908509i	$0.637222\pi$
$444$			1.11018i			0.0526869i
$445$	−17.6338	+	20.9372i	−0.835921	+	0.992517i
$446$	23.1138			1.09447
$447$	−7.69707			−0.364059
$448$	17.7826			0.840147
$449$		−	12.4801i		−	0.588970i	−0.955656	−	0.294485i	$-0.904852\pi$
$449$		−	12.4801i		−	0.588970i	0.955656	−	0.294485i	$-0.0951482\pi$
$450$	−2.90822	−	16.8539i	−0.137095	−	0.794499i
$451$	0.700420			0.0329815
$452$		−	2.80950i		−	0.132148i
$453$	6.61322			0.310716
$454$	5.71300			0.268124
$455$		0			0
$456$	−6.24186			−0.292302
$457$	−8.23221			−0.385086			−0.192543	−	0.981289i	$-0.561674\pi$
$457$	−8.23221			−0.385086			−0.192543	+	0.981289i	$0.561674\pi$
$458$		−	1.80902i		−	0.0845298i
$459$	11.0614			0.516301
$460$	−0.293416	+	0.348383i	−0.0136806	+	0.0162434i
$461$		−	4.54144i		−	0.211516i	−0.994392	−	0.105758i	$-0.966273\pi$
$461$		−	4.54144i		−	0.211516i	0.994392	−	0.105758i	$-0.0337269\pi$
$462$	3.22748			0.150156
$463$	1.98845			0.0924113			0.0462056	−	0.998932i	$-0.485287\pi$
$463$	1.98845			0.0924113			0.0462056	+	0.998932i	$0.485287\pi$
$464$	7.41342			0.344159
$465$	0.696765	+	0.586832i	0.0323117	+	0.0272137i
$466$			16.5813i			0.768115i
$467$			32.8043i			1.51800i	0.651091	+	0.759000i	$0.274312\pi$
$467$			32.8043i			1.51800i	−0.651091	+	0.759000i	$0.725688\pi$
$468$		0			0
$469$	8.93862			0.412747
$470$	−24.9383	−	21.0037i	−1.15032	−	0.968826i
$471$	−2.14060			−0.0986335
$472$		−	21.7171i		−	0.999611i
$473$	−5.19783			−0.238997
$474$		−	4.58132i		−	0.210427i
$475$	28.9763	−	5.00000i	1.32952	−	0.229416i
$476$		−	6.52886i		−	0.299250i
$477$		−	6.99010i		−	0.320055i
$478$			4.74933i			0.217229i
$479$		−	30.8053i		−	1.40753i	−0.710432	−	0.703766i	$-0.751500\pi$
$479$		−	30.8053i		−	1.40753i	0.710432	−	0.703766i	$-0.248500\pi$
$480$	−1.59916	+	1.89874i	−0.0729913	+	0.0866650i
$481$		0			0
$482$		−	20.7378i		−	0.944582i
$483$	−0.241722			−0.0109987
$484$	2.39719			0.108963
$485$	9.92970	+	8.36303i	0.450885	+	0.379746i
$486$			10.4837i			0.475551i
$487$	22.3251			1.01165			0.505824	−	0.862637i	$-0.331189\pi$
$487$	22.3251			1.01165			0.505824	+	0.862637i	$0.331189\pi$
$488$	20.7958			0.941380
$489$			4.11910i			0.186272i
$490$	5.85021	+	4.92718i	0.264286	+	0.222587i
$491$	−10.6826			−0.482098			−0.241049	−	0.970513i	$-0.577491\pi$
$491$	−10.6826			−0.482098			−0.241049	+	0.970513i	$0.577491\pi$
$492$	−0.0367631			−0.00165741
$493$		−	16.3504i		−	0.736386i
$494$		0			0
$495$	16.1049	−	19.1219i	0.723862	−	0.859466i
$496$		−	2.91713i		−	0.130983i
$497$		−	3.81739i		−	0.171233i
$498$			3.21064i			0.143872i
$499$		−	18.8195i		−	0.842477i	−0.906950	−	0.421239i	$-0.861595\pi$
$499$		−	18.8195i		−	0.842477i	0.906950	−	0.421239i	$-0.138405\pi$
$500$	3.33087	−	5.69677i	0.148961	−	0.254767i
$501$			0.700420i			0.0312925i
$502$	11.0417			0.492815
$503$			5.68128i			0.253316i	0.991946	+	0.126658i	$0.0404250\pi$
$503$			5.68128i			0.253316i	−0.991946	+	0.126658i	$0.959575\pi$
$504$	17.9822			0.800989
$505$	10.1630	+	8.55955i	0.452249	+	0.380895i
$506$	1.59024			0.0706948
$507$		0			0
$508$		−	9.86062i		−	0.437494i
$509$		−	27.9244i		−	1.23773i	−0.785498	−	0.618864i	$-0.787593\pi$
$509$		−	27.9244i		−	1.23773i	0.785498	−	0.618864i	$-0.212407\pi$
$510$	−3.81952	−	3.21689i	−0.169131	−	0.142446i
$511$	−17.9822			−0.795484
$512$	23.1492			1.02306
$513$	−11.9356			−0.526970
$514$			12.9297i			0.570305i
$515$	9.26754	−	11.0037i	0.408376	−	0.484879i
$516$	0.272820			0.0120102
$517$		−	47.6603i		−	2.09610i
$518$	−13.1335			−0.577055
$519$	0.462218			0.0202891
$520$		0			0
$521$	6.29958			0.275990			0.137995	−	0.990433i	$-0.455934\pi$
$521$	6.29958			0.275990			0.137995	+	0.990433i	$0.455934\pi$
$522$	10.2618			0.449145
$523$		−	22.8571i		−	0.999471i	−0.866178	−	0.499735i	$-0.833431\pi$
$523$		−	22.8571i		−	0.999471i	0.866178	−	0.499735i	$-0.166569\pi$
$524$	−5.90239			−0.257847
$525$	3.45110	−	0.595504i	0.150618	−	0.0259899i
$526$		−	15.9585i		−	0.695824i
$527$	−6.43378			−0.280260
$528$	3.30969			0.144036
$529$	22.8809			0.994822
$530$	−4.14979	+	4.92718i	−0.180255	+	0.214023i
$531$		−	20.3431i		−	0.882816i
$532$			7.04487i			0.305434i
$533$		0			0
$534$	−5.01623			−0.217074
$535$	−25.4660	+	30.2366i	−1.10099	+	1.30724i
$536$	13.5451			0.585059
$537$		−	6.97951i		−	0.301188i
$538$	4.34628			0.187381
$539$			11.1805i			0.481577i
$540$	−1.72555	+	2.04880i	−0.0742558	+	0.0881664i
$541$			9.48006i			0.407580i	0.979015	+	0.203790i	$0.0653259\pi$
$541$			9.48006i			0.407580i	−0.979015	+	0.203790i	$0.934674\pi$
$542$			26.1257i			1.12219i
$543$			6.84118i			0.293583i
$544$		−	17.5325i		−	0.751700i
$545$	8.29958	−	9.85437i	0.355515	−	0.422115i
$546$		0			0
$547$			33.3911i			1.42770i	0.700299	+	0.713850i	$0.253050\pi$
$547$			33.3911i			1.42770i	−0.700299	+	0.713850i	$0.746950\pi$
$548$	−1.16741			−0.0498694
$549$	19.4801			0.831389
$550$	−22.7041	+	3.91770i	−0.968105	+	0.167051i
$551$			17.6427i			0.751604i
$552$	−0.366292			−0.0155904
$553$	−22.6914			−0.964937
$554$			11.7492i			0.499177i
$555$	2.70934	−	3.21689i	0.115005	−	0.136549i
$556$	5.13533			0.217787
$557$	−37.7648			−1.60015			−0.800073	−	0.599903i	$-0.795206\pi$
$557$	−37.7648			−1.60015			−0.800073	+	0.599903i	$0.795206\pi$
$558$		−	4.03793i		−	0.170939i
$559$		0			0
$560$	−8.57766	−	7.22431i	−0.362472	−	0.305283i
$561$		−	7.29958i		−	0.308188i
$562$			4.82221i			0.203413i
$563$			25.9008i			1.09159i	0.837919	+	0.545794i	$0.183772\pi$
$563$			25.9008i			1.09159i	−0.837919	+	0.545794i	$0.816228\pi$
$564$			2.50155i			0.105334i
$565$	−6.85643	+	8.14087i	−0.288452	+	0.342489i
$566$			7.22928i			0.303869i
$567$	16.1193			0.676947
$568$		−	5.78466i		−	0.242719i
$569$	−21.5451			−0.903217			−0.451609	−	0.892216i	$-0.649150\pi$
$569$	−21.5451			−0.903217			−0.451609	+	0.892216i	$0.649150\pi$
$570$	4.12140	+	3.47114i	0.172626	+	0.145390i
$571$	2.22036			0.0929192			0.0464596	−	0.998920i	$-0.485206\pi$
$571$	2.22036			0.0929192			0.0464596	+	0.998920i	$0.485206\pi$
$572$		0			0
$573$		−	0.530704i		−	0.0221705i
$574$		−	0.434911i		−	0.0181528i
$575$	1.70042	−	0.293416i	0.0709124	−	0.0122363i
$576$	25.2419			1.05174
$577$	−6.20265			−0.258220			−0.129110	−	0.991630i	$-0.541212\pi$
$577$	−6.20265			−0.258220			−0.129110	+	0.991630i	$0.541212\pi$
$578$	15.0840			0.627411
$579$			7.31742i			0.304102i
$580$	3.02845	+	2.55063i	0.125749	+	0.105909i
$581$	15.9024			0.659742
$582$			2.37901i			0.0986130i
$583$	−9.41646			−0.389990
$584$	−27.2492			−1.12758
$585$		0			0
$586$	−11.6265			−0.480285
$587$	−1.82894			−0.0754883			−0.0377442	−	0.999287i	$-0.512017\pi$
$587$	−1.82894			−0.0754883			−0.0377442	+	0.999287i	$0.512017\pi$
$588$		−	0.586832i		−	0.0242005i
$589$	6.94228			0.286052
$590$	−12.0770	+	14.3395i	−0.497204	+	0.590346i
$591$		−	3.19466i		−	0.131411i
$592$	−13.4681			−0.553534
$593$	−0.0728761			−0.00299266			−0.00149633	−	0.999999i	$-0.500476\pi$
$593$	−0.0728761			−0.00299266			−0.00149633	+	0.999999i	$0.500476\pi$
$594$	9.35204			0.383719
$595$	−15.9334	+	18.9182i	−0.653204	+	0.775571i
$596$			13.1642i			0.539229i
$597$			6.00646i			0.245828i
$598$		0			0
$599$	14.5813			0.595777			0.297888	−	0.954601i	$-0.403718\pi$
$599$	14.5813			0.595777			0.297888	+	0.954601i	$0.403718\pi$
$600$	5.22960	−	0.902394i	0.213498	−	0.0368401i
$601$	−44.4082			−1.81145			−0.905723	−	0.423870i	$-0.860671\pi$
$601$	−44.4082			−1.81145			−0.905723	+	0.423870i	$0.860671\pi$
$602$			3.22748i			0.131542i
$603$	12.6881			0.516700
$604$		−	11.3105i		−	0.460220i
$605$	−6.94615	−	5.85021i	−0.282401	−	0.237845i
$606$			2.43491i			0.0989115i
$607$		−	36.2354i		−	1.47075i	−0.677660	−	0.735375i	$-0.737006\pi$
$607$		−	36.2354i		−	1.47075i	0.677660	−	0.735375i	$-0.262994\pi$
$608$			18.9182i			0.767235i
$609$			2.10126i			0.0851474i
$610$	−13.7311	−	11.5647i	−0.555956	−	0.468239i
$611$		0			0
$612$		−	9.26754i		−	0.374618i
$613$	−3.35830			−0.135641			−0.0678203	−	0.997698i	$-0.521604\pi$
$613$	−3.35830			−0.135641			−0.0678203	+	0.997698i	$0.521604\pi$
$614$	26.2455			1.05918
$615$	0.106526	+	0.0897185i	0.00429553	+	0.00361780i
$616$		−	24.2240i		−	0.976013i
$617$	−21.1820			−0.852754			−0.426377	−	0.904546i	$-0.640210\pi$
$617$	−21.1820			−0.852754			−0.426377	+	0.904546i	$0.640210\pi$
$618$	2.63631			0.106048
$619$			25.4082i			1.02124i	0.859807	+	0.510620i	$0.170584\pi$
$619$			25.4082i			1.02124i	−0.859807	+	0.510620i	$0.829416\pi$
$620$	1.00366	−	1.19167i	0.0403078	−	0.0478587i
$621$	−0.700420			−0.0281069
$622$	9.07009			0.363677
$623$			24.8455i			0.995416i
$624$		0			0
$625$	−23.5543	+	8.37828i	−0.942171	+	0.335131i
$626$			31.0399i			1.24060i
$627$			7.87651i			0.314557i
$628$			3.66105i			0.146092i
$629$			29.7041i			1.18438i
$630$	−11.8733	−	10.0000i	−0.473045	−	0.398410i
$631$		−	43.5451i		−	1.73350i	−0.498740	−	0.866751i	$-0.666204\pi$
$631$		−	43.5451i		−	1.73350i	0.498740	−	0.866751i	$-0.333796\pi$
$632$	−34.3853			−1.36777
$633$			2.51300i			0.0998828i
$634$	14.0614			0.558449
$635$	−24.0643	+	28.5724i	−0.954964	+	1.13386i
$636$	0.494244			0.0195980
$637$		0			0
$638$		−	13.8238i		−	0.547288i
$639$		−	5.41868i		−	0.214360i
$640$	−6.78883	−	5.71771i	−0.268352	−	0.226012i
$641$	−48.2854			−1.90716			−0.953579	−	0.301142i	$-0.902632\pi$
$641$	−48.2854			−1.90716			−0.953579	+	0.301142i	$0.902632\pi$
$642$	−7.24423			−0.285907
$643$	−42.3440			−1.66989			−0.834943	−	0.550337i	$-0.814499\pi$
$643$	−42.3440			−1.66989			−0.834943	+	0.550337i	$0.814499\pi$
$644$			0.413416i			0.0162909i
$645$	−0.790529	−	0.665802i	−0.0311271	−	0.0262159i
$646$	−38.0561			−1.49730
$647$			34.4052i			1.35261i	0.736622	+	0.676305i	$0.236420\pi$
$647$			34.4052i			1.35261i	−0.736622	+	0.676305i	$0.763580\pi$
$648$	24.4263			0.959556
$649$	−27.4045			−1.07572
$650$		0			0
$651$	0.826831			0.0324061
$652$	7.04487			0.275899
$653$			14.3315i			0.560834i	0.959878	+	0.280417i	$0.0904727\pi$
$653$			14.3315i			0.560834i	−0.959878	+	0.280417i	$0.909527\pi$
$654$	2.36096			0.0923208
$655$	17.1029	+	14.4045i	0.668267	+	0.562830i
$656$		−	0.445988i		−	0.0174129i
$657$	−25.5252			−0.995832
$658$	−29.5936			−1.15368
$659$	−22.8232			−0.889065			−0.444532	−	0.895763i	$-0.646630\pi$
$659$	−22.8232			−0.889065			−0.444532	+	0.895763i	$0.646630\pi$
$660$	1.35204	+	1.13872i	0.0526280	+	0.0443245i
$661$		−	14.4187i		−	0.560822i	−0.959880	−	0.280411i	$-0.909529\pi$
$661$		−	14.4187i		−	0.560822i	0.959880	−	0.280411i	$-0.0904707\pi$
$662$			15.0796i			0.586087i
$663$		0			0
$664$	24.0976			0.935168
$665$	17.1927	−	20.4134i	0.666703	−	0.791598i
$666$	−18.6427			−0.722390
$667$			1.03533i			0.0400881i
$668$	1.19792			0.0463491
$669$			6.71826i			0.259743i
$670$	−8.94361	−	7.53252i	−0.345522	−	0.291007i
$671$		−	26.2419i		−	1.01306i
$672$			2.25318i			0.0869181i
$673$		−	34.1741i		−	1.31731i	−0.752443	−	0.658657i	$-0.771125\pi$
$673$		−	34.1741i		−	1.31731i	0.752443	−	0.658657i	$-0.228875\pi$
$674$		−	18.1590i		−	0.699458i
$675$	10.0000	−	1.72555i	0.384900	−	0.0664164i
$676$		0			0
$677$			5.84695i			0.224716i	0.993668	+	0.112358i	$0.0358404\pi$
$677$			5.84695i			0.224716i	−0.993668	+	0.112358i	$0.964160\pi$
$678$	−1.95043			−0.0749058
$679$	11.7833			0.452201
$680$	−24.1445	+	28.6676i	−0.925900	+	1.09935i
$681$			1.66054i			0.0636319i
$682$	−5.43955			−0.208291
$683$	11.3488			0.434249			0.217125	−	0.976144i	$-0.430332\pi$
$683$	11.3488			0.434249			0.217125	+	0.976144i	$0.430332\pi$
$684$			10.0000i			0.382360i
$685$	3.38273	+	2.84901i	0.129247	+	0.108855i
$686$	23.8106			0.909093
$687$	0.525808			0.0200608
$688$			3.30969i			0.126181i
$689$		0			0
$690$	0.241857	+	0.203698i	0.00920733	+	0.00775463i
$691$		−	18.8232i		−	0.716067i	−0.933709	−	0.358034i	$-0.883447\pi$
$691$		−	18.8232i		−	0.716067i	0.933709	−	0.358034i	$-0.116553\pi$
$692$		−	0.790529i		−	0.0300514i
$693$		−	22.6914i		−	0.861976i
$694$		−	14.5325i		−	0.551647i
$695$	−14.8803	−	12.5325i	−0.564441	−	0.475385i
$696$			3.18413i			0.120694i
$697$	−0.983636			−0.0372579
$698$		−	22.2036i		−	0.840420i
$699$	−4.81952			−0.182291
$700$	−1.01849	−	5.90239i	−0.0384952	−	0.223090i
$701$	−19.1626			−0.723763			−0.361881	−	0.932224i	$-0.617865\pi$
$701$	−19.1626			−0.723763			−0.361881	+	0.932224i	$0.617865\pi$
$702$		0			0
$703$		−	32.0518i		−	1.20885i
$704$		−	34.0037i		−	1.28156i
$705$	6.10492	−	7.24857i	0.229924	−	0.272997i
$706$	−1.55401			−0.0584860
$707$	12.0602			0.453570
$708$	1.43839			0.0540578
$709$			23.4837i			0.881949i	0.897520	+	0.440975i	$0.145367\pi$
$709$			23.4837i			0.881949i	−0.897520	+	0.440975i	$0.854633\pi$
$710$	−3.21689	+	3.81952i	−0.120728	+	0.143344i
$711$	−32.2098			−1.20796
$712$			37.6496i			1.41098i
$713$	0.407395			0.0152571
$714$	−4.53252			−0.169625
$715$		0			0
$716$	−11.9370			−0.446107
$717$	−1.38044			−0.0515535
$718$			34.9173i			1.30310i
$719$	−14.1086			−0.526161			−0.263080	−	0.964774i	$-0.584738\pi$
$719$	−14.1086			−0.526161			−0.263080	+	0.964774i	$0.584738\pi$
$720$	−12.1758	−	10.2547i	−0.453764	−	0.382170i
$721$		−	13.0577i		−	0.486295i
$722$	18.5046			0.688668
$723$	6.02765			0.224171
$724$	11.7004			0.434843
$725$	−2.55063	−	14.7816i	−0.0947280	−	0.548973i
$726$		−	1.66419i		−	0.0617640i
$727$		−	25.3762i		−	0.941153i	−0.882359	−	0.470576i	$-0.844046\pi$
$727$		−	25.3762i		−	0.941153i	0.882359	−	0.470576i	$-0.155954\pi$
$728$		0			0
$729$	20.7796			0.769616
$730$	17.9922	+	15.1534i	0.665921	+	0.560854i
$731$	7.29958			0.269985
$732$			1.37736i			0.0509087i
$733$	−10.6692			−0.394074			−0.197037	−	0.980396i	$-0.563132\pi$
$733$	−10.6692			−0.394074			−0.197037	+	0.980396i	$0.563132\pi$
$734$			39.6952i			1.46517i
$735$	−1.43213	+	1.70042i	−0.0528251	+	0.0627209i
$736$			1.11018i			0.0409218i
$737$		−	17.0923i		−	0.629605i
$738$		−	0.617344i		−	0.0227247i
$739$		−	1.41503i		−	0.0520526i	−0.999661	−	0.0260263i	$-0.991715\pi$
$739$		−	1.41503i		−	0.0520526i	0.999661	−	0.0260263i	$-0.00828536\pi$
$740$	−5.50183	−	4.63377i	−0.202251	−	0.170341i
$741$		0			0
$742$			5.84695i			0.214648i
$743$	−29.8777			−1.09611			−0.548053	−	0.836443i	$-0.684631\pi$
$743$	−29.8777			−1.09611			−0.548053	+	0.836443i	$0.684631\pi$
$744$	1.25293			0.0459348
$745$	32.1267	−	38.1451i	1.17703	−	1.39753i
$746$		−	40.9370i		−	1.49881i
$747$	22.5730			0.825903
$748$	−12.4844			−0.456476
$749$			35.8809i			1.31106i
$750$	−3.95485	−	2.31238i	−0.144411	−	0.0844362i
$751$	19.9858			0.729293			0.364646	−	0.931146i	$-0.381190\pi$
$751$	19.9858			0.729293			0.364646	+	0.931146i	$0.381190\pi$
$752$	−30.3474			−1.10666
$753$			3.20938i			0.116956i
$754$		0			0
$755$	−27.6028	+	32.7737i	−1.00457	+	1.19276i
$756$			2.43126i			0.0884239i
$757$		−	17.0923i		−	0.621232i	−0.950535	−	0.310616i	$-0.899465\pi$
$757$		−	17.0923i		−	0.621232i	0.950535	−	0.310616i	$-0.100535\pi$
$758$		−	20.6649i		−	0.750584i
$759$			0.462218i			0.0167775i
$760$	26.0528	−	30.9334i	0.945034	−	1.12207i
$761$			42.2240i			1.53062i	0.643662	+	0.765310i	$0.277414\pi$
$761$			42.2240i			1.53062i	−0.643662	+	0.765310i	$0.722586\pi$
$762$	−6.84552			−0.247987
$763$		−	11.6939i		−	0.423347i
$764$	−0.907659			−0.0328380
$765$	−22.6170	+	26.8539i	−0.817718	+	0.970904i
$766$	−2.07395			−0.0749350
$767$		0			0
$768$			4.42107i			0.159531i
$769$			23.7655i			0.857004i	0.903541	+	0.428502i	$0.140959\pi$
$769$			23.7655i			0.857004i	−0.903541	+	0.428502i	$0.859041\pi$
$770$	−13.4711	+	15.9947i	−0.485466	+	0.576410i
$771$	−3.75814			−0.135346
$772$	12.5149			0.450422
$773$	−0.284086			−0.0102179			−0.00510894	−	0.999987i	$-0.501626\pi$
$773$	−0.284086			−0.0102179			−0.00510894	+	0.999987i	$0.501626\pi$
$774$			4.58132i			0.164672i
$775$	−5.81644	+	1.00366i	−0.208933	+	0.0360524i
$776$	17.8557			0.640984
$777$		−	3.81739i		−	0.136948i
$778$	−26.1730			−0.938349
$779$	1.06138			0.0380278
$780$		0			0
$781$	−7.29958			−0.261199
$782$	−2.23325			−0.0798610
$783$			6.08867i			0.217591i
$784$	7.11910			0.254254
$785$	8.93460	−	10.6084i	0.318890	−	0.378628i
$786$			4.09761i			0.146157i
$787$	24.1341			0.860289			0.430145	−	0.902760i	$-0.358463\pi$
$787$	24.1341			0.860289			0.430145	+	0.902760i	$0.358463\pi$
$788$	−5.46381			−0.194640
$789$	4.63849			0.165135
$790$	22.7041	+	19.1219i	0.807775	+	0.680327i
$791$			9.66054i			0.343489i
$792$		−	34.3853i		−	1.22183i
$793$		0			0
$794$	26.7529			0.949424
$795$	−1.43213	−	1.20618i	−0.0507926	−	0.0427787i
$796$	10.2728			0.364110
$797$			34.3442i			1.21653i	0.793732	+	0.608267i	$0.208135\pi$
$797$			34.3442i			1.21653i	−0.793732	+	0.608267i	$0.791865\pi$
$798$	4.89075			0.173131
$799$			66.9317i			2.36787i
$800$	−2.73503	−	15.8502i	−0.0966980	−	0.560390i
$801$			35.2676i			1.24612i
$802$		−	4.39797i		−	0.155298i
$803$			34.3853i			1.21343i
$804$			0.897129i			0.0316393i
$805$	1.00892	−	1.19792i	0.0355598	−	0.0422213i
$806$		0			0
$807$			1.26329i			0.0444698i
$808$	18.2753			0.642924
$809$	47.6862			1.67656			0.838279	−	0.545241i	$-0.183562\pi$
$809$	47.6862			1.67656			0.838279	+	0.545241i	$0.183562\pi$
$810$	−16.1283	−	13.5836i	−0.566691	−	0.477280i
$811$			24.5992i			0.863793i	0.901923	+	0.431897i	$0.142155\pi$
$811$			24.5992i			0.863793i	−0.901923	+	0.431897i	$0.857845\pi$
$812$	3.59377			0.126117
$813$	−7.59368			−0.266322
$814$			25.1138i			0.880239i
$815$	−20.4134	−	17.1927i	−0.715051	−	0.602233i
$816$	−4.64796			−0.162711
$817$	−7.87651			−0.275564
$818$		−	16.0097i		−	0.559765i
$819$		0			0
$820$	0.153445	−	0.182190i	0.00535853	−	0.00636236i
$821$			17.2996i			0.603759i	0.953346	+	0.301880i	$0.0976141\pi$
$821$			17.2996i			0.603759i	−0.953346	+	0.301880i	$0.902386\pi$
$822$			0.810450i			0.0282677i
$823$		−	32.5625i		−	1.13506i	−0.823353	−	0.567529i	$-0.807899\pi$
$823$		−	32.5625i		−	1.13506i	0.823353	−	0.567529i	$-0.192101\pi$
$824$		−	19.7869i		−	0.689311i
$825$	−1.13872	−	6.59916i	−0.0396451	−	0.229753i
$826$			17.0162i			0.592070i
$827$	−15.4702			−0.537951			−0.268976	−	0.963147i	$-0.586685\pi$
$827$	−15.4702			−0.537951			−0.268976	+	0.963147i	$0.586685\pi$
$828$			0.586832i			0.0203938i
$829$	−14.5236			−0.504425			−0.252213	−	0.967672i	$-0.581158\pi$
$829$	−14.5236			−0.504425			−0.252213	+	0.967672i	$0.581158\pi$
$830$	−15.9113	−	13.4008i	−0.552288	−	0.465150i
$831$	−3.41503			−0.118466
$832$		0			0
$833$		−	15.7013i		−	0.544018i
$834$		−	3.56509i		−	0.123449i
$835$	−3.47114	−	2.92347i	−0.120124	−	0.101171i
$836$	13.4711			0.465909
$837$	2.39585			0.0828127
$838$	19.9747			0.690015
$839$			0.815866i			0.0281668i	0.999901	+	0.0140834i	$0.00448304\pi$
$839$			0.815866i			0.0281668i	−0.999901	+	0.0140834i	$0.995517\pi$
$840$	3.10291	−	3.68419i	0.107061	−	0.127117i
$841$	−20.0000			−0.689655
$842$		−	20.3049i		−	0.699753i
$843$	−1.40162			−0.0482744
$844$	4.29797			0.147942
$845$		0			0
$846$	−42.0073			−1.44424
$847$	−8.24280			−0.283226
$848$			5.99587i			0.205899i
$849$	−2.10126			−0.0721151
$850$	31.8845	−	5.50183i	1.09363	−	0.188711i
$851$		−	1.88090i		−	0.0644764i
$852$	0.383134			0.0131260
$853$	−20.0856			−0.687719			−0.343859	−	0.939021i	$-0.611734\pi$
$853$	−20.0856			−0.687719			−0.343859	+	0.939021i	$0.611734\pi$
$854$	−16.2943			−0.557580
$855$	24.4045	−	28.9763i	0.834616	−	0.990968i
$856$			54.3719i			1.85839i
$857$		−	40.7886i		−	1.39331i	−0.717406	−	0.696656i	$-0.754671\pi$
$857$		−	40.7886i		−	1.39331i	0.717406	−	0.696656i	$-0.245329\pi$
$858$		0			0
$859$	40.1301			1.36922			0.684610	−	0.728909i	$-0.259972\pi$
$859$	40.1301			1.36922			0.684610	+	0.728909i	$0.259972\pi$
$860$	−1.13872	+	1.35204i	−0.0388300	+	0.0461041i
$861$	0.126411			0.00430808
$862$		−	11.4703i		−	0.390679i
$863$	−20.8275			−0.708977			−0.354489	−	0.935060i	$-0.615345\pi$
$863$	−20.8275			−0.708977			−0.354489	+	0.935060i	$0.615345\pi$
$864$			6.52886i			0.222116i
$865$	−1.92925	+	2.29066i	−0.0655964	+	0.0778848i
$866$		−	29.4134i		−	0.999509i
$867$			4.38430i			0.148899i
$868$		−	1.41412i		−	0.0479985i
$869$			43.3903i			1.47192i
$870$	1.77072	−	2.10243i	0.0600330	−	0.0712792i
$871$		0			0
$872$		−	17.7203i		−	0.600084i
$873$	16.7261			0.566091
$874$	2.40976			0.0815114
$875$	−11.4533	+	19.5885i	−0.387192	+	0.662212i
$876$		−	1.80479i		−	0.0609782i
$877$	−46.5944			−1.57338			−0.786691	−	0.617347i	$-0.788207\pi$
$877$	−46.5944			−1.57338			−0.786691	+	0.617347i	$0.788207\pi$
$878$	−8.38421			−0.282953
$879$		−	3.37935i		−	0.113982i
$880$	−13.8143	+	16.4021i	−0.465678	+	0.552916i
$881$	−23.8447			−0.803347			−0.401674	−	0.915783i	$-0.631571\pi$
$881$	−23.8447			−0.803347			−0.401674	+	0.915783i	$0.631571\pi$
$882$	9.85437			0.331814
$883$		−	37.2496i		−	1.25355i	−0.779201	−	0.626774i	$-0.784375\pi$
$883$		−	37.2496i		−	1.25355i	0.779201	−	0.626774i	$-0.215625\pi$
$884$		0			0
$885$	−4.16790	−	3.51031i	−0.140103	−	0.117998i
$886$		−	45.4082i		−	1.52552i
$887$			28.5795i			0.959605i	0.877377	+	0.479802i	$0.159292\pi$
$887$			28.5795i			0.959605i	−0.877377	+	0.479802i	$0.840708\pi$
$888$		−	5.78466i		−	0.194121i
$889$			33.9060i			1.13717i
$890$	20.9372	−	24.8594i	0.701816	−	0.833289i
$891$		−	30.8232i		−	1.03262i
$892$	11.4902			0.384720
$893$		−	72.2217i		−	2.41681i
$894$	9.13899			0.305653
$895$	34.5890	+	29.1317i	1.15618	+	0.973765i
$896$	−8.05611			−0.269136
$897$		0			0
$898$			14.8180i			0.494483i
$899$		−	3.54144i		−	0.118114i
$900$	−1.44571	−	8.37828i	−0.0481905	−	0.279276i
$901$	13.2240			0.440556
$902$	−0.831632			−0.0276903
$903$	−0.938099			−0.0312180
$904$			14.6390i			0.486887i
$905$	−33.9035	−	28.5543i	−1.12699	−	0.949177i
$906$	−7.85209			−0.260868
$907$		−	6.41386i		−	0.212969i	−0.994314	−	0.106484i	$-0.966041\pi$
$907$		−	6.41386i		−	0.212969i	0.994314	−	0.106484i	$-0.0339594\pi$
$908$	2.84001			0.0942489
$909$	17.1191			0.567805
$910$		0			0
$911$	22.2204			0.736193			0.368097	−	0.929788i	$-0.380010\pi$
$911$	22.2204			0.736193			0.368097	+	0.929788i	$0.380010\pi$
$912$	5.01532			0.166074
$913$		−	30.4084i		−	1.00637i
$914$	9.77437			0.323308
$915$	3.36138	−	3.99108i	0.111124	−	0.131941i
$916$		−	0.899287i		−	0.0297133i
$917$	20.2956			0.670219
$918$	−13.1335			−0.433472
$919$	−26.1264			−0.861831			−0.430915	−	0.902392i	$-0.641809\pi$
$919$	−26.1264			−0.861831			−0.430915	+	0.902392i	$0.641809\pi$
$920$	1.52886	−	1.81527i	0.0504051	−	0.0598476i
$921$			7.62851i			0.251368i
$922$			5.39220i			0.177583i
$923$		0			0
$924$	1.60442			0.0527817
$925$	4.63377	+	26.8539i	0.152357	+	0.882950i
$926$	−2.36096			−0.0775859
$927$		−	18.5351i		−	0.608772i
$928$	9.65067			0.316799
$929$			23.9423i			0.785521i	0.919641	+	0.392760i	$0.128480\pi$
$929$			23.9423i			0.785521i	−0.919641	+	0.392760i	$0.871520\pi$
$930$	−0.827293	−	0.696765i	−0.0271280	−	0.0228478i
$931$			16.9423i			0.555261i
$932$			8.24280i			0.270002i
$933$			2.63631i			0.0863089i
$934$		−	38.9496i		−	1.27447i
$935$	36.1752	+	30.4676i	1.18306	+	0.996397i
$936$		0			0
$937$		−	18.5046i		−	0.604518i	−0.953226	−	0.302259i	$-0.902259\pi$
$937$		−	18.5046i		−	0.604518i	0.953226	−	0.302259i	$-0.0977407\pi$
$938$	−10.6131			−0.346531
$939$	−9.02204			−0.294423
$940$	−12.3972	−	10.4412i	−0.404352	−	0.340554i
$941$		−	14.3788i		−	0.468735i	−0.972148	−	0.234368i	$-0.924698\pi$
$941$		−	14.3788i		−	0.468735i	0.972148	−	0.234368i	$-0.0753020\pi$
$942$	2.54160			0.0828098
$943$	0.0622851			0.00202828
$944$			17.4496i			0.567938i
$945$	5.93336	−	7.04487i	0.193012	−	0.229170i
$946$	6.17156			0.200655
$947$	58.3188			1.89511			0.947554	−	0.319596i	$-0.103547\pi$
$947$	58.3188			1.89511			0.947554	+	0.319596i	$0.103547\pi$
$948$		−	2.27744i		−	0.0739677i
$949$		0			0
$950$	−34.4045	+	5.93667i	−1.11623	+	0.192611i
$951$			4.08708i			0.132533i
$952$			34.0190i			1.10256i
$953$		−	13.7995i		−	0.447010i	−0.974703	−	0.223505i	$-0.928250\pi$
$953$		−	13.7995i		−	0.447010i	0.974703	−	0.223505i	$-0.0717499\pi$
$954$			8.29958i			0.268709i
$955$	2.63006	+	2.21510i	0.0851067	+	0.0716788i
$956$			2.36096i			0.0763588i
$957$	4.01801			0.129884
$958$			36.5762i			1.18172i
$959$	4.01419			0.129625
$960$	4.35561	−	5.17156i	0.140577	−	0.166911i
$961$	29.6065			0.955047
$962$		0			0
$963$			50.9319i			1.64126i
$964$		−	10.3090i		−	0.332032i
$965$	−36.2636	−	30.5421i	−1.16737	−	0.983184i
$966$	0.287005			0.00923422
$967$	−30.3474			−0.975906			−0.487953	−	0.872870i	$-0.662256\pi$
$967$	−30.3474			−0.975906			−0.487953	+	0.872870i	$0.662256\pi$
$968$	−12.4907			−0.401466
$969$		−	11.0614i		−	0.355343i
$970$	−11.7899	−	9.92970i	−0.378550	−	0.318824i
$971$	44.1013			1.41528			0.707638	−	0.706575i	$-0.249761\pi$
$971$	44.1013			1.41528			0.707638	+	0.706575i	$0.249761\pi$
$972$			5.21160i			0.167162i
$973$	−17.6580			−0.566089
$974$	−26.5074			−0.849351
$975$		0			0
$976$	−16.7093			−0.534853
$977$	22.3220			0.714143			0.357071	−	0.934077i	$-0.383775\pi$
$977$	22.3220			0.714143			0.357071	+	0.934077i	$0.383775\pi$
$978$		−	4.89075i		−	0.156389i
$979$	47.5094			1.51841
$980$	2.90822	+	2.44937i	0.0928996	+	0.0782422i
$981$		−	16.5992i		−	0.529970i
$982$	12.6838			0.404756
$983$	−4.03793			−0.128790			−0.0643950	−	0.997924i	$-0.520512\pi$
$983$	−4.03793			−0.128790			−0.0643950	+	0.997924i	$0.520512\pi$
$984$	0.191556			0.00610659
$985$	15.8321	+	13.3342i	0.504453	+	0.424862i
$986$			19.4134i			0.618249i
$987$		−	8.60167i		−	0.273794i
$988$		0			0
$989$	−0.462218			−0.0146977
$990$	−19.1219	+	22.7041i	−0.607734	+	0.721583i
$991$	29.6500			0.941864			0.470932	−	0.882170i	$-0.343918\pi$
$991$	29.6500			0.941864			0.470932	+	0.882170i	$0.343918\pi$
$992$		−	3.79747i		−	0.120570i
$993$	−4.38304			−0.139092
$994$			4.53252i			0.143763i
$995$	−29.7668	−	25.0703i	−0.943671	−	0.794782i
$996$			1.59605i			0.0505728i
$997$			22.1762i			0.702327i	0.936314	+	0.351164i	$0.114214\pi$
$997$			22.1762i			0.702327i	−0.936314	+	0.351164i	$0.885786\pi$
$998$			22.3450i			0.707320i
$999$		−	11.0614i		−	0.349967i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.d.d.844.3		12
5.4	even	2	inner	845.2.d.d.844.10		12
13.2	odd	12		65.2.n.a.9.2	✓	12
13.3	even	3		845.2.l.f.654.10		24
13.4	even	6		845.2.l.f.699.3		24
13.5	odd	4		845.2.b.d.339.5		6
13.6	odd	12		65.2.n.a.29.5	yes	12
13.7	odd	12		845.2.n.e.484.2		12
13.8	odd	4		845.2.b.e.339.2		6
13.9	even	3		845.2.l.f.699.9		24
13.10	even	6		845.2.l.f.654.4		24
13.11	odd	12		845.2.n.e.529.5		12
13.12	even	2	inner	845.2.d.d.844.9		12
39.2	even	12		585.2.bs.a.334.5		12
39.32	even	12		585.2.bs.a.289.2		12
52.15	even	12		1040.2.dh.a.529.3		12
52.19	even	12		1040.2.dh.a.289.4		12
65.2	even	12		325.2.e.e.126.5		12
65.4	even	6		845.2.l.f.699.10		24
65.8	even	4		4225.2.a.bq.1.2		6
65.9	even	6		845.2.l.f.699.4		24
65.18	even	4		4225.2.a.br.1.5		6
65.19	odd	12		65.2.n.a.29.2	yes	12
65.24	odd	12		845.2.n.e.529.2		12
65.28	even	12		325.2.e.e.126.2		12
65.29	even	6		845.2.l.f.654.3		24
65.32	even	12		325.2.e.e.276.5		12
65.34	odd	4		845.2.b.e.339.5		6
65.44	odd	4		845.2.b.d.339.2		6
65.47	even	4		4225.2.a.bq.1.5		6
65.49	even	6		845.2.l.f.654.9		24
65.54	odd	12		65.2.n.a.9.5	yes	12
65.57	even	4		4225.2.a.br.1.2		6
65.58	even	12		325.2.e.e.276.2		12
65.59	odd	12		845.2.n.e.484.5		12
65.64	even	2	inner	845.2.d.d.844.4		12
195.119	even	12		585.2.bs.a.334.2		12
195.149	even	12		585.2.bs.a.289.5		12
260.19	even	12		1040.2.dh.a.289.3		12
260.119	even	12		1040.2.dh.a.529.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.n.a.9.2	✓	12	13.2	odd	12
65.2.n.a.9.5	yes	12	65.54	odd	12
65.2.n.a.29.2	yes	12	65.19	odd	12
65.2.n.a.29.5	yes	12	13.6	odd	12
325.2.e.e.126.2		12	65.28	even	12
325.2.e.e.126.5		12	65.2	even	12
325.2.e.e.276.2		12	65.58	even	12
325.2.e.e.276.5		12	65.32	even	12
585.2.bs.a.289.2		12	39.32	even	12
585.2.bs.a.289.5		12	195.149	even	12
585.2.bs.a.334.2		12	195.119	even	12
585.2.bs.a.334.5		12	39.2	even	12
845.2.b.d.339.2		6	65.44	odd	4
845.2.b.d.339.5		6	13.5	odd	4
845.2.b.e.339.2		6	13.8	odd	4
845.2.b.e.339.5		6	65.34	odd	4
845.2.d.d.844.3		12	1.1	even	1	trivial
845.2.d.d.844.4		12	65.64	even	2	inner
845.2.d.d.844.9		12	13.12	even	2	inner
845.2.d.d.844.10		12	5.4	even	2	inner
845.2.l.f.654.3		24	65.29	even	6
845.2.l.f.654.4		24	13.10	even	6
845.2.l.f.654.9		24	65.49	even	6
845.2.l.f.654.10		24	13.3	even	3
845.2.l.f.699.3		24	13.4	even	6
845.2.l.f.699.4		24	65.9	even	6
845.2.l.f.699.9		24	13.9	even	3
845.2.l.f.699.10		24	65.4	even	6
845.2.n.e.484.2		12	13.7	odd	12
845.2.n.e.484.5		12	65.59	odd	12
845.2.n.e.529.2		12	65.24	odd	12
845.2.n.e.529.5		12	13.11	odd	12
1040.2.dh.a.289.3		12	260.19	even	12
1040.2.dh.a.289.4		12	52.19	even	12
1040.2.dh.a.529.3		12	52.15	even	12
1040.2.dh.a.529.4		12	260.119	even	12
4225.2.a.bq.1.2		6	65.8	even	4
4225.2.a.bq.1.5		6	65.47	even	4
4225.2.a.br.1.2		6	65.57	even	4
4225.2.a.br.1.5		6	65.18	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.18733 q^{2} -0.345110i q^{3} -0.590239 q^{4} +(1.71029 + 1.44045i) q^{5} +0.409761i q^{6} +2.02956 q^{7} +3.07548 q^{8} +2.88090 q^{9} +O(q^{10})\)	\(q-1.18733 q^{2} -0.345110i q^{3} -0.590239 q^{4} +(1.71029 + 1.44045i) q^{5} +0.409761i q^{6} +2.02956 q^{7} +3.07548 q^{8} +2.88090 q^{9} +(-2.03069 - 1.71029i) q^{10} -3.88090i q^{11} +0.203698i q^{12} -2.40976 q^{14} +(0.497113 - 0.590239i) q^{15} -2.47114 q^{16} +5.45014i q^{17} -3.42059 q^{18} -5.88090i q^{19} +(-1.00948 - 0.850210i) q^{20} -0.700420i q^{21} +4.60792i q^{22} -0.345110i q^{23} -1.06138i q^{24} +(0.850210 + 4.92718i) q^{25} -2.02956i q^{27} -1.19792 q^{28} -3.00000 q^{29} +(-0.590239 + 0.700811i) q^{30} +1.18048i q^{31} -3.21689 q^{32} -1.33934 q^{33} -6.47114i q^{34} +(3.47114 + 2.92347i) q^{35} -1.70042 q^{36} +5.45014 q^{37} +6.98259i q^{38} +(5.25997 + 4.43007i) q^{40} +0.180479i q^{41} +0.831632i q^{42} -1.33934i q^{43} +2.29066i q^{44} +(4.92718 + 4.14979i) q^{45} +0.409761i q^{46} +12.2807 q^{47} +0.852815i q^{48} -2.88090 q^{49} +(-1.00948 - 5.85021i) q^{50} +1.88090 q^{51} -2.42636i q^{53} +2.40976i q^{54} +(5.59024 - 6.63748i) q^{55} +6.24186 q^{56} -2.02956 q^{57} +3.56200 q^{58} -7.06138i q^{59} +(-0.293416 + 0.348383i) q^{60} +6.76180 q^{61} -1.40162i q^{62} +5.84695 q^{63} +8.76180 q^{64} +1.59024 q^{66} +4.40422 q^{67} -3.21689i q^{68} -0.119101 q^{69} +(-4.12140 - 3.47114i) q^{70} -1.88090i q^{71} +8.86014 q^{72} -8.86014 q^{73} -6.47114 q^{74} +(1.70042 - 0.293416i) q^{75} +3.47114i q^{76} -7.87651i q^{77} -11.1805 q^{79} +(-4.22637 - 3.55955i) q^{80} +7.94228 q^{81} -0.214289i q^{82} +7.83540 q^{83} +0.413416i q^{84} +(-7.85066 + 9.32135i) q^{85} +1.59024i q^{86} +1.03533i q^{87} -11.9356i q^{88} +12.2419i q^{89} +(-5.85021 - 4.92718i) q^{90} +0.203698i q^{92} +0.407395 q^{93} -14.5813 q^{94} +(8.47114 - 10.0581i) q^{95} +1.11018i q^{96} +5.80585 q^{97} +3.42059 q^{98} -11.1805i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 8 q^{4} - 12 q^{9}+O(q^{10}) \) 12 * q + 8 * q^4 - 12 * q^9	\( 12 q + 8 q^{4} - 12 q^{9} + 14 q^{10} - 44 q^{14} + 32 q^{16} + 2 q^{25} - 36 q^{29} + 8 q^{30} - 20 q^{35} - 4 q^{36} + 70 q^{40} + 12 q^{49} - 24 q^{51} + 52 q^{55} - 32 q^{56} - 12 q^{61} + 12 q^{64} + 4 q^{66} - 48 q^{69} - 16 q^{74} + 4 q^{75} - 104 q^{79} - 28 q^{81} - 62 q^{90} - 112 q^{94} + 40 q^{95}+O(q^{100}) \) 12 * q + 8 * q^4 - 12 * q^9 + 14 * q^10 - 44 * q^14 + 32 * q^16 + 2 * q^25 - 36 * q^29 + 8 * q^30 - 20 * q^35 - 4 * q^36 + 70 * q^40 + 12 * q^49 - 24 * q^51 + 52 * q^55 - 32 * q^56 - 12 * q^61 + 12 * q^64 + 4 * q^66 - 48 * q^69 - 16 * q^74 + 4 * q^75 - 104 * q^79 - 28 * q^81 - 62 * q^90 - 112 * q^94 + 40 * q^95

Introduction

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