LMFDB - Embedded newform 845.2.l.f.654.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(654,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("845.654");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.l (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			654.3
Character	$\chi$	$=$	845.654
Dual form			845.2.l.f.699.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.593667 + 1.02826i) q^{2} +(-0.298874 - 0.172555i) q^{3} +(0.295120 + 0.511162i) q^{4} +(-1.71029 + 1.44045i) q^{5} +(0.354863 - 0.204880i) q^{6} +(1.01478 + 1.75765i) q^{7} -3.07548 q^{8} +(-1.44045 - 2.49493i) q^{9} +O(q^{10})$	\(q+(-0.593667 + 1.02826i) q^{2} +(-0.298874 - 0.172555i) q^{3} +(0.295120 + 0.511162i) q^{4} +(-1.71029 + 1.44045i) q^{5} +(0.354863 - 0.204880i) q^{6} +(1.01478 + 1.75765i) q^{7} -3.07548 q^{8} +(-1.44045 - 2.49493i) q^{9} +(-0.465813 - 2.61378i) q^{10} +(3.36096 + 1.94045i) q^{11} -0.203698i q^{12} -2.40976 q^{14} +(0.759719 - 0.135393i) q^{15} +(1.23557 - 2.14007i) q^{16} +(-4.71996 + 2.72507i) q^{17} +3.42059 q^{18} +(-5.09301 + 2.94045i) q^{19} +(-1.24105 - 0.449133i) q^{20} -0.700420i q^{21} +(-3.99058 + 2.30396i) q^{22} +(-0.298874 - 0.172555i) q^{23} +(0.919180 + 0.530689i) q^{24} +(0.850210 - 4.92718i) q^{25} +2.02956i q^{27} +(-0.598962 + 1.03743i) q^{28} +(1.50000 - 2.59808i) q^{29} +(-0.311800 + 0.861568i) q^{30} +1.18048i q^{31} +(-1.60845 - 2.78591i) q^{32} +(-0.669668 - 1.15990i) q^{33} -6.47114i q^{34} +(-4.26737 - 1.54436i) q^{35} +(0.850210 - 1.47261i) q^{36} +(2.72507 - 4.71996i) q^{37} -6.98259i q^{38} +(5.25997 - 4.43007i) q^{40} +(-0.156299 - 0.0902394i) q^{41} +(0.720215 + 0.415816i) q^{42} +(1.15990 - 0.669668i) q^{43} +2.29066i q^{44} +(6.05742 + 2.19217i) q^{45} +(0.354863 - 0.204880i) q^{46} -12.2807 q^{47} +(-0.738559 + 0.426407i) q^{48} +(1.44045 - 2.49493i) q^{49} +(4.56169 + 3.79934i) q^{50} +1.88090 q^{51} +2.42636i q^{53} +(-2.08691 - 1.20488i) q^{54} +(-8.54334 + 1.52255i) q^{55} +(-3.12093 - 5.40561i) q^{56} +2.02956 q^{57} +(1.78100 + 3.08478i) q^{58} +(-6.11533 + 3.53069i) q^{59} +(0.293416 + 0.348383i) q^{60} +(-3.38090 - 5.85589i) q^{61} +(-1.21384 - 0.700811i) q^{62} +(2.92347 - 5.06361i) q^{63} +8.76180 q^{64} +1.59024 q^{66} +(2.20211 - 3.81417i) q^{67} +(-2.78591 - 1.60845i) q^{68} +(0.0595504 + 0.103144i) q^{69} +(4.12140 - 3.47114i) q^{70} +(-1.62891 + 0.940450i) q^{71} +(4.43007 + 7.67311i) q^{72} +8.86014 q^{73} +(3.23557 + 5.60417i) q^{74} +(-1.10432 + 1.32590i) q^{75} +(-3.00609 - 1.73557i) q^{76} +7.87651i q^{77} -11.1805 q^{79} +(0.969475 + 5.43992i) q^{80} +(-3.97114 + 6.87821i) q^{81} +(0.185579 - 0.107144i) q^{82} -7.83540 q^{83} +(0.358028 - 0.206708i) q^{84} +(4.14720 - 11.4595i) q^{85} +1.59024i q^{86} +(-0.896622 + 0.517665i) q^{87} +(-10.3365 - 5.96781i) q^{88} +(-10.6018 - 6.12093i) q^{89} +(-5.85021 + 4.92718i) q^{90} -0.203698i q^{92} +(0.203698 - 0.352814i) q^{93} +(7.29066 - 12.6278i) q^{94} +(4.47497 - 12.3653i) q^{95} +1.11018i q^{96} +(2.90292 + 5.02801i) q^{97} +(1.71029 + 2.96232i) q^{98} -11.1805i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{4} + 12 q^{9}+O(q^{10}) $ 24 * q - 8 * q^4 + 12 * q^9	$ 24 q - 8 q^{4} + 12 q^{9} - 14 q^{10} - 88 q^{14} - 32 q^{16} + 4 q^{25} + 36 q^{29} - 8 q^{30} + 20 q^{35} + 4 q^{36} + 140 q^{40} - 12 q^{49} - 48 q^{51} - 52 q^{55} + 32 q^{56} + 12 q^{61} + 24 q^{64} + 8 q^{66} + 48 q^{69} + 16 q^{74} - 4 q^{75} - 208 q^{79} + 28 q^{81} - 124 q^{90} + 112 q^{94} - 40 q^{95}+O(q^{100}) $ 24 * q - 8 * q^4 + 12 * q^9 - 14 * q^10 - 88 * q^14 - 32 * q^16 + 4 * q^25 + 36 * q^29 - 8 * q^30 + 20 * q^35 + 4 * q^36 + 140 * q^40 - 12 * q^49 - 48 * q^51 - 52 * q^55 + 32 * q^56 + 12 * q^61 + 24 * q^64 + 8 * q^66 + 48 * q^69 + 16 * q^74 - 4 * q^75 - 208 * q^79 + 28 * q^81 - 124 * q^90 + 112 * q^94 - 40 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−0.593667	+	1.02826i	−0.419786	+	0.727090i	−0.995918	−	0.0902665i	$-0.971228\pi$
$2$	−0.593667	+	1.02826i	−0.419786	+	0.727090i	0.576132	+	0.817357i	$0.304561\pi$
$3$	−0.298874	−	0.172555i	−0.172555	−	0.0996247i	0.411235	−	0.911529i	$-0.365098\pi$
$3$	−0.298874	−	0.172555i	−0.172555	−	0.0996247i	−0.583790	+	0.811905i	$0.698431\pi$
$4$	0.295120	+	0.511162i	0.147560	+	0.255581i
$5$	−1.71029	+	1.44045i	−0.764867	+	0.644189i
$5$	−1.71029	+	1.44045i	−0.764867	+	0.644189i
$6$	0.354863	−	0.204880i	0.144872	−	0.0836420i
$7$	1.01478	+	1.75765i	0.383550	+	0.664328i	0.991567	−	0.129596i	$-0.0413680\pi$
$7$	1.01478	+	1.75765i	0.383550	+	0.664328i	−0.608017	+	0.793924i	$0.708035\pi$
$8$	−3.07548			−1.08735
$9$	−1.44045	−	2.49493i	−0.480150	−	0.831644i
$10$	−0.465813	−	2.61378i	−0.147303	−	0.826548i
$11$	3.36096	+	1.94045i	1.01337	+	0.585068i	0.912176	−	0.409799i	$-0.134401\pi$
$11$	3.36096	+	1.94045i	1.01337	+	0.585068i	0.101191	+	0.994867i	$0.467735\pi$
$12$		−	0.203698i		−	0.0588024i
$13$		0			0
$13$		0			0
$14$	−2.40976			−0.644036
$15$	0.759719	−	0.135393i	0.196159	−	0.0349584i
$16$	1.23557	−	2.14007i	0.308892	−	0.535017i
$17$	−4.71996	+	2.72507i	−1.14476	+	0.660927i	−0.947605	−	0.319445i	$-0.896503\pi$
$17$	−4.71996	+	2.72507i	−1.14476	+	0.660927i	−0.197155	+	0.980372i	$0.563170\pi$
$18$	3.42059			0.806240
$19$	−5.09301	+	2.94045i	−1.16842	+	0.674585i	−0.953306	−	0.302005i	$-0.902344\pi$
$19$	−5.09301	+	2.94045i	−1.16842	+	0.674585i	−0.215110	+	0.976590i	$0.569011\pi$
$20$	−1.24105	−	0.449133i	−0.277506	−	0.100429i
$21$		−	0.700420i		−	0.152844i
$22$	−3.99058	+	2.30396i	−0.850794	+	0.491206i
$23$	−0.298874	−	0.172555i	−0.0623195	−	0.0359802i	0.468516	−	0.883455i	$-0.344789\pi$
$23$	−0.298874	−	0.172555i	−0.0623195	−	0.0359802i	−0.530836	+	0.847475i	$0.678122\pi$
$24$	0.919180	+	0.530689i	0.187627	+	0.108326i
$25$	0.850210	−	4.92718i	0.170042	−	0.985437i
$26$		0			0
$27$			2.02956i			0.390588i
$28$	−0.598962	+	1.03743i	−0.113193	+	0.196056i
$29$	1.50000	−	2.59808i	0.278543	−	0.482451i	−0.692480	−	0.721437i	$-0.743482\pi$
$29$	1.50000	−	2.59808i	0.278543	−	0.482451i	0.971023	+	0.238987i	$0.0768152\pi$
$30$	−0.311800	+	0.861568i	−0.0569267	+	0.157300i
$31$			1.18048i			0.212020i	0.994365	+	0.106010i	$0.0338076\pi$
$31$			1.18048i			0.212020i	−0.994365	+	0.106010i	$0.966192\pi$
$32$	−1.60845	−	2.78591i	−0.284336	−	0.492484i
$33$	−0.669668	−	1.15990i	−0.116574	−	0.201913i
$34$		−	6.47114i		−	1.10979i
$35$	−4.26737	−	1.54436i	−0.721318	−	0.261044i
$36$	0.850210	−	1.47261i	0.141702	−	0.245435i
$37$	2.72507	−	4.71996i	0.447999	−	0.775957i	−0.550257	−	0.834996i	$-0.685470\pi$
$37$	2.72507	−	4.71996i	0.447999	−	0.775957i	0.998256	+	0.0590384i	$0.0188034\pi$
$38$		−	6.98259i		−	1.13273i
$39$		0			0
$40$	5.25997	−	4.43007i	0.831674	−	0.700456i
$41$	−0.156299	−	0.0902394i	−0.0244098	−	0.0140930i	0.487745	−	0.872986i	$-0.337819\pi$
$41$	−0.156299	−	0.0902394i	−0.0244098	−	0.0140930i	−0.512155	+	0.858893i	$0.671153\pi$
$42$	0.720215	+	0.415816i	0.111132	+	0.0641618i
$43$	1.15990	−	0.669668i	0.176883	−	0.102123i	−0.408944	−	0.912559i	$-0.634103\pi$
$43$	1.15990	−	0.669668i	0.176883	−	0.102123i	0.585827	+	0.810436i	$0.300770\pi$
$44$			2.29066i			0.345330i
$45$	6.05742	+	2.19217i	0.902986	+	0.326790i
$46$	0.354863	−	0.204880i	0.0523217	−	0.0302079i
$47$	−12.2807			−1.79133			−0.895664	−	0.444731i	$-0.853299\pi$
$47$	−12.2807			−1.79133			−0.895664	+	0.444731i	$0.853299\pi$
$48$	−0.738559	+	0.426407i	−0.106602	+	0.0615466i
$49$	1.44045	−	2.49493i	0.205779	−	0.356419i
$50$	4.56169	+	3.79934i	0.645120	+	0.537308i
$51$	1.88090			0.263379
$52$		0			0
$53$			2.42636i			0.333286i	0.986017	+	0.166643i	$0.0532928\pi$
$53$			2.42636i			0.333286i	−0.986017	+	0.166643i	$0.946707\pi$
$54$	−2.08691	−	1.20488i	−0.283993	−	0.163963i
$55$	−8.54334	+	1.52255i	−1.15198	+	0.205301i
$56$	−3.12093	−	5.40561i	−0.417052	−	0.722355i
$57$	2.02956			0.268821
$58$	1.78100	+	3.08478i	0.233857	+	0.405052i
$59$	−6.11533	+	3.53069i	−0.796149	+	0.459657i	−0.842123	−	0.539286i	$-0.818694\pi$
$59$	−6.11533	+	3.53069i	−0.796149	+	0.459657i	0.0459741	+	0.998943i	$0.485361\pi$
$60$	0.293416	+	0.348383i	0.0378798	+	0.0449760i
$61$	−3.38090	−	5.85589i	−0.432880	−	0.749770i	0.564240	−	0.825611i	$-0.309169\pi$
$61$	−3.38090	−	5.85589i	−0.432880	−	0.749770i	−0.997120	+	0.0758409i	$0.975836\pi$
$62$	−1.21384	−	0.700811i	−0.154158	−	0.0890031i
$63$	2.92347	−	5.06361i	0.368323	−	0.637954i
$64$	8.76180			1.09522
$65$		0			0
$66$	1.59024			0.195745
$67$	2.20211	−	3.81417i	0.269031	−	0.465975i	−0.699581	−	0.714553i	$-0.746630\pi$
$67$	2.20211	−	3.81417i	0.269031	−	0.465975i	0.968612	+	0.248578i	$0.0799633\pi$
$68$	−2.78591	−	1.60845i	−0.337841	−	0.195053i
$69$	0.0595504	+	0.103144i	0.00716903	+	0.0124171i
$70$	4.12140	−	3.47114i	0.492601	−	0.414880i
$71$	−1.62891	+	0.940450i	−0.193316	+	0.111611i	−0.593534	−	0.804809i	$-0.702268\pi$
$71$	−1.62891	+	0.940450i	−0.193316	+	0.111611i	0.400218	+	0.916420i	$0.368934\pi$
$72$	4.43007	+	7.67311i	0.522089	+	0.904284i
$73$	8.86014			1.03700			0.518501	−	0.855077i	$-0.326490\pi$
$73$	8.86014			1.03700			0.518501	+	0.855077i	$0.326490\pi$
$74$	3.23557	+	5.60417i	0.376127	+	0.651472i
$75$	−1.10432	+	1.32590i	−0.127515	+	0.153102i
$76$	−3.00609	−	1.73557i	−0.344823	−	0.199083i
$77$			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	$0.716515\pi$
$80$	0.969475	+	5.43992i	0.108391	+	0.608202i
$81$	−3.97114	+	6.87821i	−0.441238	+	0.764246i
$82$	0.185579	−	0.107144i	0.0204938	−	0.0118321i
$83$	−7.83540			−0.860047			−0.430024	−	0.902818i	$-0.641495\pi$
$83$	−7.83540			−0.860047			−0.430024	+	0.902818i	$0.641495\pi$
$84$	0.358028	−	0.206708i	0.0390641	−	0.0225537i
$85$	4.14720	−	11.4595i	0.449827	−	1.24296i
$86$			1.59024i			0.171480i
$87$	−0.896622	+	0.517665i	−0.0961280	+	0.0554995i
$88$	−10.3365	−	5.96781i	−1.10188	−	0.636171i
$89$	−10.6018	−	6.12093i	−1.12378	−	0.648817i	−0.181420	−	0.983406i	$-0.558069\pi$
$89$	−10.6018	−	6.12093i	−1.12378	−	0.648817i	−0.942364	+	0.334589i	$0.891403\pi$
$90$	−5.85021	+	4.92718i	−0.616666	+	0.519371i
$91$		0			0
$92$		−	0.203698i		−	0.0212369i
$93$	0.203698	−	0.352814i	0.0211224	−	0.0365852i
$94$	7.29066	−	12.6278i	0.751974	−	1.30246i
$95$	4.47497	−	12.3653i	0.459122	−	1.26865i
$96$			1.11018i			0.113307i
$97$	2.90292	+	5.02801i	0.294747	+	0.510517i	0.974926	−	0.222529i	$-0.0714312\pi$
$97$	2.90292	+	5.02801i	0.294747	+	0.510517i	−0.680179	+	0.733046i	$0.738098\pi$
$98$	1.71029	+	2.96232i	0.172766	+	0.299239i
$99$		−	11.1805i		−	1.12368i
$100$	2.76950	−	1.01951i	0.276950	−	0.101951i
$101$	−2.97114	+	5.14616i	−0.295639	+	0.512062i	−0.975133	−	0.221619i	$-0.928866\pi$
$101$	−2.97114	+	5.14616i	−0.295639	+	0.512062i	0.679494	+	0.733681i	$0.262199\pi$
$102$	−1.11663	+	1.93405i	−0.110563	+	0.191500i
$103$			6.43378i			0.633939i	0.948436	+	0.316970i	$0.102665\pi$
$103$			6.43378i			0.633939i	−0.948436	+	0.316970i	$0.897335\pi$
$104$		0			0
$105$	1.00892	+	1.19792i	0.0984605	+	0.116905i
$106$	−2.49493	−	1.44045i	−0.242329	−	0.139909i
$107$	15.3106	+	8.83959i	1.48013	+	0.854555i	0.999747	−	0.0225015i	$-0.00716305\pi$
$107$	15.3106	+	8.83959i	1.48013	+	0.854555i	0.480387	+	0.877057i	$0.340496\pi$
$108$	−1.03743	+	0.598962i	−0.0998270	+	0.0576352i
$109$		−	5.76180i		−	0.551880i	−0.961175	−	0.275940i	$-0.911011\pi$
$109$		−	5.76180i		−	0.551880i	0.961175	−	0.275940i	$-0.0889891\pi$
$110$	3.50632	−	9.68867i	0.334314	−	0.923779i
$111$	−1.62891	+	0.940450i	−0.154609	+	0.0892635i
$112$	5.01532			0.473903
$113$	−4.12222	+	2.37996i	−0.387785	+	0.223888i	−0.681200	−	0.732097i	$-0.738542\pi$
$113$	−4.12222	+	2.37996i	−0.387785	+	0.223888i	0.293415	+	0.955985i	$0.405208\pi$
$114$	−1.20488	+	2.08691i	−0.112847	+	0.195457i
$115$	0.759719	−	0.135393i	0.0708442	−	0.0126255i
$116$	1.77072			0.164407
$117$		0			0
$118$		−	8.38421i		−	0.771829i
$119$	−9.57943	−	5.53069i	−0.878145	−	0.506997i
$120$	−2.33650	+	0.416399i	−0.213292	+	0.0380118i
$121$	2.03069	+	3.51726i	0.184608	+	0.319751i
$122$	8.02851			0.726867
$123$	0.0311425	+	0.0539404i	0.00280803	+	0.00486365i
$124$	−0.603416	+	0.348383i	−0.0541884	+	0.0312857i
$125$	5.64325	+	9.65162i	0.504748	+	0.863267i
$126$	3.47114	+	6.01219i	0.309234	+	0.535608i
$127$	14.4679	+	8.35307i	1.28382	+	0.741215i	0.977545	−	0.210728i	$-0.0675833\pi$
$127$	14.4679	+	8.35307i	1.28382	+	0.741215i	0.306277	+	0.951942i	$0.400917\pi$
$128$	−1.98470	+	3.43760i	−0.175424	+	0.303844i
$129$	−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	$0.356093\pi$
$132$	0.395265	−	0.684619i	0.0344034	−	0.0595884i
$133$	−10.3365	−	5.96781i	−0.896292	−	0.517475i
$134$	2.61464	+	4.52869i	0.225871	+	0.391219i
$135$	−2.92347	−	3.47114i	−0.251613	−	0.298748i
$136$	14.5161	−	8.38090i	1.24475	−	0.718656i
$137$	0.988931	+	1.71288i	0.0844901	+	0.146341i	0.905174	−	0.425042i	$-0.139741\pi$
$137$	0.988931	+	1.71288i	0.0844901	+	0.146341i	−0.820684	+	0.571383i	$0.806407\pi$
$138$	−0.141412			−0.0120378
$139$	4.35021	+	7.53478i	0.368980	+	0.639092i	0.989406	−	0.145173i	$-0.0463737\pi$
$139$	4.35021	+	7.53478i	0.368980	+	0.639092i	−0.620426	+	0.784265i	$0.713040\pi$
$140$	−0.469969	−	2.63709i	−0.0397196	−	0.222875i
$141$	3.67039	+	2.11910i	0.309103	+	0.178460i
$142$		−	2.23325i		−	0.187411i
$143$		0			0
$144$	−7.11910			−0.593258
$145$	1.17696	+	6.60415i	0.0977410	+	0.548445i
$146$	−5.25997	+	9.11054i	−0.435318	+	0.753993i
$147$	−0.861026	+	0.497113i	−0.0710162	+	0.0410012i
$148$	3.21689			0.264427
$149$	−19.3152	+	11.1516i	−1.58236	+	0.913576i	−0.587846	+	0.808973i	$0.700024\pi$
$149$	−19.3152	+	11.1516i	−1.58236	+	0.913576i	−0.994514	+	0.104603i	$0.966643\pi$
$150$	−0.707775	−	1.92267i	−0.0577896	−	0.156985i
$151$			19.1626i			1.55943i	0.626132	+	0.779717i	$0.284637\pi$
$151$			19.1626i			1.55943i	−0.626132	+	0.779717i	$0.715363\pi$
$152$	15.6634	−	9.04329i	1.27047	−	0.733507i
$153$	13.5977	+	7.85066i	1.09931	+	0.634688i
$154$	−8.09910	−	4.67602i	−0.652644	−	0.376804i
$155$	−1.70042	−	2.01897i	−0.136581	−	0.162167i
$156$		0			0
$157$			6.20265i			0.495025i	0.968885	+	0.247513i	$0.0796132\pi$
$157$			6.20265i			0.495025i	−0.968885	+	0.247513i	$0.920387\pi$
$158$	6.63748	−	11.4964i	0.528049	−	0.914608i
$159$	0.418681	−	0.725176i	0.0332035	−	0.0575102i
$160$	6.76387	+	2.44784i	0.534731	+	0.193519i
$161$		−	0.700420i		−	0.0552008i
$162$	−4.71507	−	8.16673i	−0.370451	−	0.641639i
$163$	−5.96781	−	10.3365i	−0.467435	−	0.809621i	0.531873	−	0.846824i	$-0.321488\pi$
$163$	−5.96781	−	10.3365i	−0.467435	−	0.809621i	−0.999308	+	0.0372032i	$0.988155\pi$
$164$		−	0.106526i		−	0.00831826i
$165$	2.81611	+	1.01915i	0.219234	+	0.0793404i
$166$	4.65162	−	8.05684i	0.361036	−	0.625332i
$167$	−1.01478	+	1.75765i	−0.0785259	+	0.136011i	−0.902614	−	0.430451i	$-0.858355\pi$
$167$	−1.01478	+	1.75765i	−0.0785259	+	0.136011i	0.824088	+	0.566461i	$0.191688\pi$
$168$			2.15413i			0.166195i
$169$		0			0
$170$	9.32135	+	11.0675i	0.714915	+	0.848842i
$171$	14.6724	+	8.47114i	1.12203	+	0.647804i
$172$	0.684619	+	0.395265i	0.0522017	+	0.0301387i
$173$	−1.15990	+	0.669668i	−0.0881855	+	0.0509139i	−0.543444	−	0.839445i	$-0.682880\pi$
$173$	−1.15990	+	0.669668i	−0.0881855	+	0.0509139i	0.455259	+	0.890359i	$0.349547\pi$
$174$		−	1.22928i		−	0.0931916i
$175$	9.52303	−	3.50563i	0.719873	−	0.265001i
$176$	8.30539	−	4.79512i	0.626042	−	0.361446i
$177$	2.43695			0.183173
$178$	12.5878	−	7.26758i	0.943497	−	0.544728i
$179$	−10.1120	+	17.5145i	−0.755807	+	1.30910i	0.189165	+	0.981945i	$0.439422\pi$
$179$	−10.1120	+	17.5145i	−0.755807	+	1.30910i	−0.944972	+	0.327151i	$0.893911\pi$
$180$	0.667107	+	3.74328i	0.0497232	+	0.279007i
$181$	−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
$184$	0.919180	+	0.530689i	0.0677629	+	0.0391229i
$185$	2.13820	+	11.9979i	0.157203	+	0.882100i
$186$	0.241857	+	0.418908i	0.0177338	+	0.0307159i
$187$	−21.1515			−1.54675
$188$	−3.62429	−	6.27745i	−0.264328	−	0.457830i
$189$	−3.56725	+	2.05955i	−0.259479	+	0.149810i
$190$	10.0581	+	11.9423i	0.729689	+	0.866384i
$191$	−0.768891	−	1.33176i	−0.0556350	−	0.0963626i	0.836867	−	0.547407i	$-0.184385\pi$
$191$	−0.768891	−	1.33176i	−0.0556350	−	0.0963626i	−0.892502	+	0.451044i	$0.851052\pi$
$192$	−2.61867	−	1.51189i	−0.188986	−	0.109111i
$193$	−10.6016	+	18.3625i	−0.763118	+	1.32176i	0.178117	+	0.984009i	$0.442999\pi$
$193$	−10.6016	+	18.3625i	−0.763118	+	1.32176i	−0.941236	+	0.337750i	$0.890334\pi$
$194$	−6.89347			−0.494923
$195$		0			0
$196$	1.70042			0.121459
$197$	4.62847	−	8.01675i	0.329765	−	0.571170i	−0.652700	−	0.757616i	$-0.726364\pi$
$197$	4.62847	−	8.01675i	0.329765	−	0.571170i	0.982465	+	0.186447i	$0.0596971\pi$
$198$	11.4964	+	6.63748i	0.817017	+	0.471705i
$199$	8.70225	+	15.0727i	0.616886	+	1.06848i	0.990050	+	0.140713i	$0.0449394\pi$
$199$	8.70225	+	15.0727i	0.616886	+	1.06848i	−0.373164	+	0.927765i	$0.621727\pi$
$200$	−2.61480	+	15.1534i	−0.184894	+	1.07151i
$201$	−1.31631	+	0.759971i	−0.0928452	+	0.0536042i
$202$	−3.52773	−	6.11021i	−0.248210	−	0.429913i
$203$	6.08867			0.427341
$204$	0.555090	+	0.961445i	0.0388641	+	0.0673146i
$205$	0.397303	−	0.0708053i	0.0277488	−	0.00494526i
$206$	−6.61560	−	3.81952i	−0.460931	−	0.266119i
$207$			0.994227i			0.0691036i
$208$		0			0
$209$	−22.8232			−1.57871
$210$	−1.83074	+	0.326265i	−0.126333	+	0.0225144i
$211$	3.64087	−	6.30617i	0.250648	−	0.434135i	−0.713057	−	0.701107i	$-0.752690\pi$
$211$	3.64087	−	6.30617i	0.250648	−	0.434135i	0.963704	+	0.266972i	$0.0860231\pi$
$212$	−1.24026	+	0.716067i	−0.0851817	+	0.0491797i
$213$	0.649117			0.0444768
$214$	−18.1788	+	10.4955i	−1.24268	+	0.717460i
$215$	−1.01915	+	2.81611i	−0.0695052	+	0.192057i
$216$		−	6.24186i		−	0.424705i
$217$	−2.07487	+	1.19792i	−0.140851	+	0.0813204i
$218$	5.92463	+	3.42059i	0.401267	+	0.231671i
$219$	−2.64807	−	1.52886i	−0.178940	−	0.103311i
$220$	−3.29958	−	3.91770i	−0.222458	−	0.264131i
$221$		0			0
$222$		−	2.23325i		−	0.149886i
$223$	−9.73351	+	16.8589i	−0.651804	+	1.12896i	0.330881	+	0.943672i	$0.392654\pi$
$223$	−9.73351	+	16.8589i	−0.651804	+	1.12896i	−0.982685	+	0.185285i	$0.940679\pi$
$224$	3.26443	−	5.65416i	0.218114	−	0.377784i
$225$	−13.5177	+	4.97614i	−0.901178	+	0.331743i
$226$		−	5.65162i		−	0.375940i
$227$	−2.40581	−	4.16698i	−0.159679	−	0.276572i	0.775074	−	0.631871i	$-0.217713\pi$
$227$	−2.40581	−	4.16698i	−0.159679	−	0.276572i	−0.934753	+	0.355298i	$0.884379\pi$
$228$	0.598962	+	1.03743i	0.0396672	+	0.0687057i
$229$			1.52360i			0.100682i	0.998732	+	0.0503410i	$0.0160308\pi$
$229$			1.52360i			0.100682i	−0.998732	+	0.0503410i	$0.983969\pi$
$230$	−0.311800	+	0.861568i	−0.0205595	+	0.0568101i
$231$	1.35913	−	2.35408i	0.0894242	−	0.154887i
$232$	−4.61322	+	7.99033i	−0.302873	+	0.524591i
$233$			13.9652i			0.914889i	0.889238	+	0.457445i	$0.151235\pi$
$233$			13.9652i			0.914889i	−0.889238	+	0.457445i	$0.848765\pi$
$234$		0			0
$235$	21.0037	−	17.6898i	1.37013	−	1.15395i
$236$	−3.60951	−	2.08395i	−0.234959	−	0.135654i
$237$	3.34155	+	1.92925i	0.217057	+	0.125318i
$238$	11.3740	−	6.56677i	0.737266	−	0.425661i
$239$		−	4.00000i		−	0.258738i	−0.991596	−	0.129369i	$-0.958705\pi$
$239$		−	4.00000i		−	0.258738i	0.991596	−	0.129369i	$-0.0412952\pi$
$240$	0.648935	−	1.79314i	0.0418886	−	0.115747i
$241$	15.1259	−	8.73294i	0.974344	−	0.562538i	0.0737864	−	0.997274i	$-0.476492\pi$
$241$	15.1259	−	8.73294i	0.974344	−	0.562538i	0.900558	+	0.434736i	$0.143158\pi$
$242$	−4.82221			−0.309983
$243$	7.64668	−	4.41481i	0.490535	−	0.283210i
$244$	1.99554	−	3.45638i	0.127751	−	0.221272i
$245$	1.13023	+	6.34196i	0.0722078	+	0.405173i
$246$	−0.0739531			−0.00471508
$247$		0			0
$248$		−	3.63054i		−	0.230539i
$249$	2.34180	+	1.35204i	0.148405	+	0.0856819i
$250$	−13.2746	+	0.0728904i	−0.839559	+	0.00460999i
$251$	4.64979	+	8.05367i	0.293492	+	0.508343i	0.974633	−	0.223809i	$-0.0718492\pi$
$251$	4.64979	+	8.05367i	0.293492	+	0.508343i	−0.681141	+	0.732152i	$0.738516\pi$
$252$	3.45110			0.217399
$253$	−0.669668	−	1.15990i	−0.0421017	−	0.0729223i
$254$	−17.1783	+	9.91788i	−1.07786	+	0.622303i
$255$	−3.21689	+	2.70934i	−0.201449	+	0.169665i
$256$	6.40530	+	11.0943i	0.400331	+	0.693394i
$257$	−9.43076	−	5.44485i	−0.588274	−	0.339640i	0.176141	−	0.984365i	$-0.443639\pi$
$257$	−9.43076	−	5.44485i	−0.588274	−	0.339640i	−0.764415	+	0.644725i	$0.776972\pi$
$258$	0.274404	−	0.475281i	0.0170836	−	0.0295897i
$259$	11.0614			0.687321
$260$		0			0
$261$	−8.64270			−0.534970
$262$	−5.93667	+	10.2826i	−0.366769	+	0.635262i
$263$	11.6399	+	6.72031i	0.717749	+	0.414392i	0.813923	−	0.580972i	$-0.197327\pi$
$263$	11.6399	+	6.72031i	0.717749	+	0.414392i	−0.0961749	+	0.995364i	$0.530661\pi$
$264$	2.05955	+	3.56725i	0.126757	+	0.219549i
$265$	−3.49505	−	4.14979i	−0.214699	−	0.254920i
$266$	12.2729	−	7.08578i	0.752502	−	0.434457i
$267$	2.11239	+	3.65877i	0.129276	+	0.223913i
$268$	2.59955			0.158793
$269$	1.83027	+	3.17012i	0.111593	+	0.193286i	0.916413	−	0.400234i	$-0.131071\pi$
$269$	1.83027	+	3.17012i	0.111593	+	0.193286i	−0.804819	+	0.593520i	$0.797738\pi$
$270$	5.30481	−	0.945395i	0.322840	−	0.0575349i
$271$	19.0557	+	11.0018i	1.15755	+	0.668313i	0.950716	−	0.310062i	$-0.100350\pi$
$271$	19.0557	+	11.0018i	1.15755	+	0.668313i	0.206837	+	0.978376i	$0.433683\pi$
$272$			13.4681i			0.816621i
$273$		0			0
$274$	−2.34838			−0.141871
$275$	12.4185	−	14.9103i	0.748862	−	0.899123i
$276$	−0.0351490	+	0.0608799i	−0.00211572	+	0.00366454i
$277$	8.56973	−	4.94774i	0.514905	−	0.297281i	−0.219943	−	0.975513i	$-0.570587\pi$
$277$	8.56973	−	4.94774i	0.514905	−	0.297281i	0.734848	+	0.678232i	$0.237254\pi$
$278$	−10.3303			−0.619570
$279$	2.94521	−	1.70042i	0.176325	−	0.101801i
$280$	13.1242	+	4.74964i	0.784321	+	0.283845i
$281$		−	4.06138i		−	0.242281i	−0.992635	−	0.121141i	$-0.961345\pi$
$281$		−	4.06138i		−	0.242281i	0.992635	−	0.121141i	$-0.0386552\pi$
$282$	−4.35798	+	2.51608i	−0.259514	+	0.149830i
$283$	−5.27294	−	3.04434i	−0.313444	−	0.180967i	0.335023	−	0.942210i	$-0.391256\pi$
$283$	−5.27294	−	3.04434i	−0.313444	−	0.180967i	−0.648467	+	0.761243i	$0.724589\pi$
$284$	−0.961445	−	0.555090i	−0.0570513	−	0.0329386i
$285$	−3.47114	+	2.92347i	−0.205613	+	0.173172i
$286$		0			0
$287$		−	0.366292i		−	0.0216215i
$288$	−4.63377	+	8.02592i	−0.273047	+	0.472932i
$289$	6.35204	−	11.0021i	0.373649	−	0.647180i
$290$	−7.48951	−	2.71044i	−0.439799	−	0.159163i
$291$		−	2.00366i		−	0.117456i
$292$	2.61480	+	4.52897i	0.153020	+	0.265038i
$293$	4.89604	+	8.48019i	0.286030	+	0.495418i	0.972858	−	0.231401i	$-0.0743310\pi$
$293$	4.89604	+	8.48019i	0.286030	+	0.495418i	−0.686829	+	0.726819i	$0.740998\pi$
$294$		−	1.18048i		−	0.0688469i
$295$	5.37324	−	14.8473i	0.312842	−	0.864446i
$296$	−8.38090	+	14.5161i	−0.487130	+	0.843734i
$297$	−3.93825	+	6.82125i	−0.228521	+	0.395809i
$298$		−	26.4814i		−	1.53402i
$299$		0			0
$300$	−1.00366	−	0.173186i	−0.0579461	−	0.00999888i
$301$	2.35408	+	1.35913i	0.135687	+	0.0783390i
$302$	−19.7042	−	11.3762i	−1.13385	−	0.654628i
$303$	1.77599	−	1.02537i	0.102028	−	0.0589059i
$304$			14.5325i			0.833497i
$305$	14.2174	+	5.14528i	0.814088	+	0.294618i
$306$	−16.1450	+	9.32135i	−0.922951	+	0.532866i
$307$	22.1046			1.26158			0.630788	−	0.775955i	$-0.282732\pi$
$307$	22.1046			1.26158			0.630788	+	0.775955i	$0.282732\pi$
$308$	−4.02617	+	2.32451i	−0.229412	+	0.132451i
$309$	1.11018	−	1.92289i	0.0631560	−	0.109389i
$310$	3.08551	−	0.549883i	0.175245	−	0.0312313i
$311$	−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	$0.264622\pi$
$313$			26.1425i			1.47766i	−0.673891	+	0.738831i	$0.735378\pi$
$314$	−6.37794	−	3.68231i	−0.359928	−	0.207805i
$315$	2.29387	+	12.8714i	0.129245	+	0.725220i
$316$	−3.29958	−	5.71504i	−0.185616	−	0.321496i
$317$	11.8428			0.665159			0.332580	−	0.943075i	$-0.392081\pi$
$317$	11.8428			0.665159			0.332580	+	0.943075i	$0.392081\pi$
$318$	0.497113	+	0.861026i	0.0278767	+	0.0482839i
$319$	10.0829	−	5.82135i	0.564532	−	0.325933i
$320$	−14.9852	+	12.6209i	−0.837701	+	0.705531i
$321$	−3.05063	−	5.28385i	−0.170270	−	0.294916i
$322$	0.720215	+	0.415816i	0.0401360	+	0.0231725i
$323$	16.0259	−	27.7576i	0.891704	−	1.54448i
$324$	−4.68785			−0.260436
$325$		0			0
$326$	14.1716			0.784890
$327$	−0.994227	+	1.72205i	−0.0549809	+	0.0952297i
$328$	0.480695	+	0.277529i	0.0265419	+	0.0153240i
$329$	−12.4622	−	21.5852i	−0.687064	−	1.19003i
$330$	−2.71978	+	2.29066i	−0.149719	+	0.126097i
$331$	−10.9989	+	6.35021i	−0.604553	+	0.349039i	−0.770831	−	0.637040i	$-0.780159\pi$
$331$	−10.9989	+	6.35021i	−0.604553	+	0.349039i	0.166277	+	0.986079i	$0.446825\pi$
$332$	−2.31238	−	4.00516i	−0.126908	−	0.219812i
$333$	−15.7013			−0.860427
$334$	−1.20488	−	2.08691i	−0.0659281	−	0.114191i
$335$	1.72786	+	9.69538i	0.0944031	+	0.529715i
$336$	−1.49895	−	0.865418i	−0.0817743	−	0.0472124i
$337$		−	15.2939i		−	0.833113i	−0.909110	−	0.416556i	$-0.863237\pi$
$337$		−	15.2939i		−	0.833113i	0.909110	−	0.416556i	$-0.136763\pi$
$338$		0			0
$339$	1.64270			0.0892191
$340$	7.08161	−	1.26205i	0.384054	−	0.0684441i
$341$	−2.29066	+	3.96754i	−0.124046	+	0.214854i
$342$	−17.4211	+	10.0581i	−0.942024	+	0.543878i
$343$	20.0538			1.08281
$344$	−3.56725	+	2.05955i	−0.192333	+	0.111044i
$345$	−0.250423	−	0.0906278i	−0.0134823	−	0.00487924i
$346$		−	1.59024i		−	0.0854918i
$347$	−10.5998	+	6.11981i	−0.569029	+	0.328529i	−0.756761	−	0.653691i	$-0.773219\pi$
$347$	−10.5998	+	6.11981i	−0.569029	+	0.328529i	0.187733	+	0.982220i	$0.439886\pi$
$348$	−0.529222	−	0.305546i	−0.0283693	−	0.0163790i
$349$	−16.1950	−	9.35021i	−0.866901	−	0.500505i	−0.000583538	−	1.00000i	$-0.500186\pi$
$349$	−16.1950	−	9.35021i	−0.866901	−	0.500505i	−0.866317	+	0.499495i	$0.833519\pi$
$350$	−2.04880	+	11.8733i	−0.109513	+	0.634656i
$351$		0			0
$352$		−	12.4844i		−	0.665422i
$353$	0.654413	−	1.13348i	0.0348309	−	0.0603288i	−0.848084	−	0.529861i	$-0.822244\pi$
$353$	0.654413	−	1.13348i	0.0348309	−	0.0603288i	0.882915	+	0.469532i	$0.155577\pi$
$354$	−1.44674	+	2.50582i	−0.0768932	+	0.133183i
$355$	1.43124	−	3.95480i	0.0759623	−	0.209899i
$356$		−	7.22563i		−	0.382957i
$357$	1.90870	+	3.30596i	0.101019	+	0.174970i
$358$	−12.0063	−	20.7956i	−0.634554	−	1.09908i
$359$		−	29.4082i		−	1.55210i	−0.630670	−	0.776051i	$-0.717220\pi$
$359$		−	29.4082i		−	1.55210i	0.630670	−	0.776051i	$-0.282780\pi$
$360$	−18.6294	−	6.74198i	−0.981858	−	0.355333i
$361$	7.79249	−	13.4970i	0.410131	−	0.710368i
$362$	11.7684	−	20.3834i	0.618531	−	1.07133i
$363$		−	1.40162i		−	0.0735661i
$364$		0			0
$365$	−15.1534	+	12.7626i	−0.793168	+	0.668024i
$366$	−2.39951	−	1.38536i	−0.125425	−	0.0724139i
$367$	−28.9531	−	16.7161i	−1.51134	−	0.872573i	−0.999912	−	0.0132473i	$-0.995783\pi$
$367$	−28.9531	−	16.7161i	−1.51134	−	0.872573i	−0.511429	−	0.859326i	$-0.670884\pi$
$368$	−0.738559	+	0.426407i	−0.0385001	+	0.0222280i
$369$			0.519941i			0.0270671i
$370$	−13.6063	−	4.92410i	−0.707358	−	0.255992i
$371$	−4.26469	+	2.46222i	−0.221412	+	0.127832i
$372$	0.240461			0.0124673
$373$	−29.8589	+	17.2391i	−1.54604	+	0.892604i	−0.547598	+	0.836742i	$0.684458\pi$
$373$	−29.8589	+	17.2391i	−1.54604	+	0.892604i	−0.998438	+	0.0558628i	$0.982209\pi$
$374$	12.5569	−	21.7492i	0.649303	−	1.12463i
$375$	−0.0211863	−	3.85839i	−0.00109406	−	0.199246i
$376$	37.7691			1.94779
$377$		0			0
$378$		−	4.89075i		−	0.251553i
$379$	−15.0727	−	8.70225i	−0.774234	−	0.447004i	0.0601487	−	0.998189i	$-0.480843\pi$
$379$	−15.0727	−	8.70225i	−0.774234	−	0.447004i	−0.834383	+	0.551185i	$0.814176\pi$
$380$	7.64130	−	1.36179i	0.391991	−	0.0698585i
$381$	−2.88273	−	4.99303i	−0.147687	−	0.255801i
$382$	1.82586			0.0934191
$383$	0.873366	+	1.51271i	0.0446269	+	0.0772961i	0.887476	−	0.460854i	$-0.152457\pi$
$383$	0.873366	+	1.51271i	0.0446269	+	0.0772961i	−0.842849	+	0.538150i	$0.819123\pi$
$384$	1.18635	−	0.684939i	0.0605406	−	0.0349531i
$385$	−11.3457	−	13.4711i	−0.578231	−	0.686553i
$386$	−12.5876	−	21.8024i	−0.640692	−	1.10971i
$387$	−3.34155	−	1.92925i	−0.169861	−	0.0980692i
$388$	−1.71342	+	2.96773i	−0.0869857	+	0.150664i
$389$	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
$392$	−4.43007	+	7.67311i	−0.223752	+	0.387550i
$393$	−2.98874	−	1.72555i	−0.150762	−	0.0870425i
$394$	5.49554	+	9.51855i	0.276861	+	0.479538i
$395$	19.1219	−	16.1049i	0.962127	−	0.810326i
$396$	5.71504	−	3.29958i	0.287192	−	0.165810i
$397$	−11.2660	−	19.5132i	−0.565422	−	0.979339i	−0.997010	−	0.0772687i	$-0.975380\pi$
$397$	−11.2660	−	19.5132i	−0.565422	−	0.979339i	0.431588	−	0.902071i	$-0.357953\pi$
$398$	−20.6649			−1.03584
$399$	2.05955	+	3.56725i	0.103106	+	0.178586i
$400$	−9.49402	−	7.90739i	−0.474701	−	0.395369i
$401$	−3.20782	−	1.85204i	−0.160191	−	0.0924863i	0.417761	−	0.908557i	$-0.362815\pi$
$401$	−3.20782	−	1.85204i	−0.160191	−	0.0924863i	−0.577953	+	0.816070i	$0.696148\pi$
$402$		−	1.80468i		−	0.0900091i
$403$		0			0
$404$	−3.50737			−0.174498
$405$	−3.11591	−	17.4840i	−0.154831	−	0.868787i
$406$	−3.61464	+	6.26074i	−0.179392	+	0.310715i
$407$	18.3177	−	10.5757i	0.907975	−	0.524220i
$408$	−5.78466			−0.286384
$409$	11.6772	−	6.74186i	0.577402	−	0.333363i	−0.182698	−	0.983169i	$-0.558483\pi$
$409$	11.6772	−	6.74186i	0.577402	−	0.333363i	0.760100	+	0.649806i	$0.225150\pi$
$410$	−0.163059	+	0.450566i	−0.00805292	+	0.0222519i
$411$		−	0.682580i		−	0.0336692i
$412$	−3.28871	+	1.89874i	−0.162023	+	0.0935440i
$413$	−12.4114	−	7.16573i	−0.610726	−	0.352603i
$414$	−1.02232	−	0.590239i	−0.0502445	−	0.0290087i
$415$	13.4008	−	11.2865i	0.657821	−	0.554033i
$416$		0			0
$417$		−	3.00260i		−	0.147038i
$418$	13.5494	−	23.4682i	0.662721	−	1.14787i
$419$	8.41159	−	14.5693i	0.410933	−	0.711757i	−0.584059	−	0.811711i	$-0.698536\pi$
$419$	8.41159	−	14.5693i	0.410933	−	0.711757i	0.994992	+	0.0999544i	$0.0318697\pi$
$420$	−0.314582	+	0.869253i	−0.0153500	+	0.0424152i
$421$			17.1013i			0.833464i	0.909029	+	0.416732i	$0.136825\pi$
$421$			17.1013i			0.833464i	−0.909029	+	0.416732i	$0.863175\pi$
$422$	4.32293	+	7.48753i	0.210437	+	0.364487i
$423$	17.6898	+	30.6396i	0.860106	+	1.48975i
$424$		−	7.46222i		−	0.362397i
$425$	9.41397	+	25.5730i	0.456645	+	1.24047i
$426$	−0.385359	+	0.667462i	−0.0186707	+	0.0323386i
$427$	6.86173	−	11.8849i	0.332062	−	0.575149i
$428$			10.4349i			0.504392i
$429$		0			0
$430$	−2.29066	−	2.71978i	−0.110465	−	0.131159i
$431$	−8.36627	−	4.83027i	−0.402989	−	0.232666i	0.284784	−	0.958592i	$-0.408078\pi$
$431$	−8.36627	−	4.83027i	−0.402989	−	0.232666i	−0.687773	+	0.725926i	$0.741412\pi$
$432$	4.34339	+	2.50766i	0.208972	+	0.120650i
$433$	−21.4538	+	12.3863i	−1.03100	+	0.595249i	−0.917272	−	0.398262i	$-0.869613\pi$
$433$	−21.4538	+	12.3863i	−1.03100	+	0.595249i	−0.113730	+	0.993512i	$0.536280\pi$
$434$		−	2.84467i		−	0.136549i
$435$	0.787817	−	2.17690i	0.0377729	−	0.104374i
$436$	2.94521	−	1.70042i	0.141050	−	0.0814354i
$437$	2.02956			0.0970869
$438$	3.14414	−	1.81527i	0.150233	−	0.0867369i
$439$	−3.53069	+	6.11533i	−0.168511	+	0.291869i	−0.937896	−	0.346915i	$-0.887229\pi$
$439$	−3.53069	+	6.11533i	−0.168511	+	0.291869i	0.769386	+	0.638784i	$0.220562\pi$
$440$	26.2749	−	4.68257i	1.25261	−	0.223233i
$441$	−8.29958			−0.395218
$442$		0			0
$443$		−	38.2438i		−	1.81702i	−0.417865	−	0.908509i	$-0.637222\pi$
$443$		−	38.2438i		−	1.81702i	0.417865	−	0.908509i	$-0.362778\pi$
$444$	−0.961445	−	0.555090i	−0.0456282	−	0.0263434i
$445$	26.9490	−	4.80271i	1.27751	−	0.227670i
$446$	−11.5569	−	20.0172i	−0.547236	−	0.947840i
$447$	7.69707			0.364059
$448$	8.89128	+	15.4002i	0.420074	+	0.727589i
$449$	−10.8080	+	6.24003i	−0.510063	+	0.294485i	−0.732860	−	0.680380i	$-0.761815\pi$
$449$	−10.8080	+	6.24003i	−0.510063	+	0.294485i	0.222796	+	0.974865i	$0.428481\pi$
$450$	2.90822	−	16.8539i	0.137095	−	0.794499i
$451$	−0.350210	−	0.606582i	−0.0164908	−	0.0285628i
$452$	−2.43309	−	1.40475i	−0.114443	−	0.0660738i
$453$	3.30661	−	5.72721i	0.155358	−	0.269088i
$454$	5.71300			0.268124
$455$		0			0
$456$	−6.24186			−0.292302
$457$	−4.11610	+	7.12930i	−0.192543	+	0.333495i	−0.946092	−	0.323897i	$-0.895007\pi$
$457$	−4.11610	+	7.12930i	−0.192543	+	0.333495i	0.753549	+	0.657392i	$0.228340\pi$
$458$	−1.56665	−	0.904508i	−0.0732050	−	0.0422649i
$459$	−5.53069	−	9.57943i	−0.258150	−	0.447130i
$460$	0.293416	+	0.348383i	0.0136806	+	0.0162434i
$461$	−3.93300	+	2.27072i	−0.183178	+	0.105758i	−0.588785	−	0.808290i	$-0.700394\pi$
$461$	−3.93300	+	2.27072i	−0.183178	+	0.105758i	0.405607	+	0.914048i	$0.367060\pi$
$462$	1.61374	+	2.79508i	0.0750780	+	0.130039i
$463$	−1.98845			−0.0924113			−0.0462056	−	0.998932i	$-0.514713\pi$
$463$	−1.98845			−0.0924113			−0.0462056	+	0.998932i	$0.514713\pi$
$464$	−3.70671	−	6.42021i	−0.172080	−	0.298051i
$465$	0.159829	+	0.896832i	0.00741188	+	0.0415896i
$466$	−14.3598	−	8.29066i	−0.665207	−	0.384057i
$467$		−	32.8043i		−	1.51800i	−0.651091	−	0.759000i	$-0.725688\pi$
$467$		−	32.8043i		−	1.51800i	0.651091	−	0.759000i	$-0.274312\pi$
$468$		0			0
$469$	8.93862			0.412747
$470$	5.72053	+	32.0991i	0.263868	+	1.48062i
$471$	1.07030	−	1.85381i	0.0493167	−	0.0854191i
$472$	18.8076	−	10.8586i	0.865689	−	0.499806i
$473$	5.19783			0.238997
$474$	−3.96754	+	2.29066i	−0.182235	+	0.105213i
$475$	10.1580	+	27.5942i	0.466081	+	1.26611i
$476$		−	6.52886i		−	0.299250i
$477$	6.05360	−	3.49505i	0.277176	−	0.160027i
$478$	4.11304	+	2.37467i	0.188126	+	0.108615i
$479$	26.6782	+	15.4027i	1.21896	+	0.703766i	0.964695	−	0.263369i	$-0.0848337\pi$
$479$	26.6782	+	15.4027i	1.21896	+	0.703766i	0.254263	+	0.967135i	$0.418167\pi$
$480$	−1.59916	−	1.89874i	−0.0729913	−	0.0866650i
$481$		0			0
$482$			20.7378i			0.944582i
$483$	−0.120861	+	0.209337i	−0.00549937	+	0.00952518i
$484$	−1.19859	+	2.07602i	−0.0544815	+	0.0943647i
$485$	−12.2074	−	4.41786i	−0.554312	−	0.200605i
$486$			10.4837i			0.475551i
$487$	11.1626	+	19.3341i	0.505824	+	0.876113i	0.999977	+	0.00673807i	$0.00214481\pi$
$487$	11.1626	+	19.3341i	0.505824	+	0.876113i	−0.494153	+	0.869375i	$0.664522\pi$
$488$	10.3979	+	18.0097i	0.470690	+	0.815259i
$489$			4.11910i			0.186272i
$490$	−7.19217	−	2.60284i	−0.324909	−	0.117584i
$491$	5.34129	−	9.25139i	0.241049	−	0.417509i	−0.719964	−	0.694011i	$-0.755842\pi$
$491$	5.34129	−	9.25139i	0.241049	−	0.417509i	0.961013	+	0.276502i	$0.0891752\pi$
$492$	−0.0183815	+	0.0318378i	−0.000828704	+	0.00143536i
$493$			16.3504i			0.736386i
$494$		0			0
$495$	16.1049	+	19.1219i	0.723862	+	0.859466i
$496$	2.52631	+	1.45856i	0.113434	+	0.0654914i
$497$	−3.30596	−	1.90870i	−0.148292	−	0.0856167i
$498$	−2.78049	+	1.60532i	−0.124597	+	0.0719361i
$499$		−	18.8195i		−	0.842477i	−0.906950	−	0.421239i	$-0.861595\pi$
$499$		−	18.8195i		−	0.842477i	0.906950	−	0.421239i	$-0.138405\pi$
$500$	−3.26811	+	5.73300i	−0.146154	+	0.256388i
$501$	0.606582	−	0.350210i	0.0271001	−	0.0156462i
$502$	−11.0417			−0.492815
$503$	−4.92013	+	2.84064i	−0.219378	+	0.126658i	−0.605662	−	0.795722i	$-0.707092\pi$
$503$	−4.92013	+	2.84064i	−0.219378	+	0.126658i	0.386284	+	0.922380i	$0.373758\pi$
$504$	−8.99108	+	15.5730i	−0.400495	+	0.693677i
$505$	−2.33127	−	13.0812i	−0.103740	−	0.582107i
$506$	1.59024			0.0706948
$507$		0			0
$508$			9.86062i			0.437494i
$509$	24.1833	+	13.9622i	1.07190	+	0.618864i	0.928701	−	0.370829i	$-0.120926\pi$
$509$	24.1833	+	13.9622i	1.07190	+	0.618864i	0.143203	+	0.989693i	$0.454260\pi$
$510$	−0.876148	−	4.91625i	−0.0387965	−	0.217695i
$511$	8.99108	+	15.5730i	0.397742	+	0.688909i
$512$	−23.1492			−1.02306
$513$	−5.96781	−	10.3365i	−0.263485	−	0.456370i
$514$	11.1975	−	6.46485i	0.493898	−	0.285152i
$515$	−9.26754	−	11.0037i	−0.408376	−	0.484879i
$516$	−0.136410	−	0.236269i	−0.00600511	−	0.0104011i
$517$	−41.2750	−	23.8301i	−1.81527	−	1.04805i
$518$	−6.56677	+	11.3740i	−0.288527	+	0.499744i
$519$	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	$0.455934\pi$
$522$	5.13088	−	8.88695i	0.224573	−	0.388971i
$523$	−19.7948	−	11.4285i	−0.865567	−	0.499735i	0.000305526	−	1.00000i	$-0.499903\pi$
$523$	−19.7948	−	11.4285i	−0.865567	−	0.499735i	−0.865873	+	0.500265i	$0.833236\pi$
$524$	2.95120	+	5.11162i	0.128924	+	0.223302i
$525$	−3.45110	−	0.595504i	−0.150618	−	0.0259899i
$526$	−13.8205	+	7.97925i	−0.602601	+	0.347912i
$527$	−3.21689	−	5.57182i	−0.140130	−	0.242712i
$528$	−3.30969			−0.144036
$529$	−11.4404	−	19.8154i	−0.497411	−	0.861541i
$530$	6.34196	−	1.13023i	0.275477	−	0.0490941i
$531$	17.6177	+	10.1716i	0.764541	+	0.441408i
$532$		−	7.04487i		−	0.305434i
$533$		0			0
$534$	−5.01623			−0.217074
$535$	−38.9186	+	6.93588i	−1.68260	+	0.299864i
$536$	−6.77255	+	11.7304i	−0.292529	+	0.506676i
$537$	6.04443	−	3.48975i	0.260837	−	0.150594i
$538$	−4.34628			−0.187381
$539$	9.68258	−	5.59024i	0.417058	−	0.240789i
$540$	0.911540	−	2.51877i	0.0392265	−	0.108391i
$541$			9.48006i			0.407580i	0.979015	+	0.203790i	$0.0653259\pi$
$541$			9.48006i			0.407580i	−0.979015	+	0.203790i	$0.934674\pi$
$542$	−22.6255	+	13.0628i	−0.971848	+	0.561097i
$543$	5.92463	+	3.42059i	0.254250	+	0.146791i
$544$	15.1836	+	8.76626i	0.650992	+	0.375850i
$545$	8.29958	+	9.85437i	0.355515	+	0.422115i
$546$		0			0
$547$		−	33.3911i		−	1.42770i	−0.700299	−	0.713850i	$-0.746950\pi$
$547$		−	33.3911i		−	1.42770i	0.700299	−	0.713850i	$-0.253050\pi$
$548$	−0.583706	+	1.01101i	−0.0249347	+	0.0431882i
$549$	−9.74003	+	16.8702i	−0.415694	+	0.720004i
$550$	7.95921	+	21.6212i	0.339382	+	0.921929i
$551$			17.6427i			0.751604i
$552$	−0.183146	−	0.317218i	−0.00779521	−	0.0135017i
$553$	−11.3457	−	19.6513i	−0.482469	−	0.835660i
$554$			11.7492i			0.499177i
$555$	1.43124	−	3.95480i	0.0607527	−	0.167872i
$556$	−2.56767	+	4.44733i	−0.108893	+	0.188609i
$557$	−18.8824	+	32.7053i	−0.800073	+	1.38577i	0.119495	+	0.992835i	$0.461873\pi$
$557$	−18.8824	+	32.7053i	−0.800073	+	1.38577i	−0.919567	+	0.392932i	$0.871461\pi$
$558$			4.03793i			0.170939i
$559$		0			0
$560$	−8.57766	+	7.22431i	−0.362472	+	0.305283i
$561$	6.32162	+	3.64979i	0.266899	+	0.154094i
$562$	4.17616	+	2.41110i	0.176161	+	0.101706i
$563$	−22.4307	+	12.9504i	−0.945343	+	0.545794i	−0.891631	−	0.452762i	$-0.850439\pi$
$563$	−22.4307	+	12.9504i	−0.945343	+	0.545794i	−0.0537120	+	0.998556i	$0.517105\pi$
$564$			2.50155i			0.105334i
$565$	3.62198	−	10.0083i	0.152378	−	0.421051i
$566$	6.26074	−	3.61464i	0.263159	−	0.151935i
$567$	−16.1193			−0.676947
$568$	5.00967	−	2.89233i	0.210201	−	0.121360i
$569$	10.7725	−	18.6586i	0.451609	−	0.782209i	−0.546878	−	0.837213i	$-0.684184\pi$
$569$	10.7725	−	18.6586i	0.451609	−	0.782209i	0.998486	+	0.0550035i	$0.0175170\pi$
$570$	−0.945395	−	5.30481i	−0.0395982	−	0.222194i
$571$	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
$574$	0.376644	+	0.217455i	0.0157208	+	0.00907641i
$575$	−1.10432	+	1.32590i	−0.0460532	+	0.0552938i
$576$	−12.6209	−	21.8601i	−0.525872	−	0.910837i
$577$	6.20265			0.258220			0.129110	−	0.991630i	$-0.458788\pi$
$577$	6.20265			0.258220			0.129110	+	0.991630i	$0.458788\pi$
$578$	7.54199	+	13.0631i	0.313705	+	0.543353i
$579$	6.33707	−	3.65871i	0.263360	−	0.152051i
$580$	−3.02845	+	2.55063i	−0.125749	+	0.105909i
$581$	−7.95120	−	13.7719i	−0.329871	−	0.571354i
$582$	2.06028	+	1.18950i	0.0854014	+	0.0493065i
$583$	−4.70823	+	8.15489i	−0.194995	+	0.337741i
$584$	−27.2492			−1.12758
$585$		0			0
$586$	−11.6265			−0.480285
$587$	−0.914469	+	1.58391i	−0.0377442	+	0.0653748i	−0.884280	−	0.466956i	$-0.845351\pi$
$587$	−0.914469	+	1.58391i	−0.0377442	+	0.0653748i	0.846536	+	0.532331i	$0.178684\pi$
$588$	−0.508211	−	0.293416i	−0.0209583	−	0.0121003i
$589$	−3.47114	−	6.01219i	−0.143026	−	0.247728i
$590$	12.0770	+	14.3395i	0.497204	+	0.590346i
$591$	−2.76666	+	1.59733i	−0.113805	+	0.0657055i
$592$	−6.73403	−	11.6637i	−0.276767	−	0.479374i
$593$	0.0728761			0.00299266			0.00149633	−	0.999999i	$-0.499524\pi$
$593$	0.0728761			0.00299266			0.00149633	+	0.999999i	$0.499524\pi$
$594$	−4.67602	−	8.09910i	−0.191859	−	0.332310i
$595$	24.3503	−	4.33959i	0.998266	−	0.177906i
$596$	−11.4006	−	6.58212i	−0.466986	−	0.269614i
$597$		−	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	$0.403718\pi$
$600$	3.39630	−	4.07777i	0.138653	−	0.166474i
$601$	22.2041	−	38.4586i	0.905723	−	1.56876i	0.0857795	−	0.996314i	$-0.472662\pi$
$601$	22.2041	−	38.4586i	0.905723	−	1.56876i	0.819944	−	0.572444i	$-0.194005\pi$
$602$	−2.79508	+	1.61374i	−0.113919	+	0.0657712i
$603$	−12.6881			−0.516700
$604$	−9.79522	+	5.65527i	−0.398562	+	0.230110i
$605$	−8.53951	−	3.09044i	−0.347180	−	0.125644i
$606$			2.43491i			0.0989115i
$607$	31.3808	−	18.1177i	1.27371	−	0.735375i	0.298024	−	0.954558i	$-0.403672\pi$
$607$	31.3808	−	18.1177i	1.27371	−	0.735375i	0.975684	+	0.219183i	$0.0703392\pi$
$608$	16.3836	+	9.45910i	0.664445	+	0.383617i
$609$	−1.81975	−	1.05063i	−0.0737398	−	0.0425737i
$610$	−13.7311	+	11.5647i	−0.555956	+	0.468239i
$611$		0			0
$612$			9.26754i			0.374618i
$613$	−1.67915	+	2.90838i	−0.0678203	+	0.117468i	−0.897942	−	0.440115i	$-0.854938\pi$
$613$	−1.67915	+	2.90838i	−0.0678203	+	0.117468i	0.830121	+	0.557583i	$0.188271\pi$
$614$	−13.1228	+	22.7293i	−0.529591	+	0.917279i
$615$	−0.130961	−	0.0473948i	−0.00528087	−	0.00191114i
$616$		−	24.2240i		−	0.976013i
$617$	−10.5910	−	18.3441i	−0.426377	−	0.738507i	0.570171	−	0.821526i	$-0.306877\pi$
$617$	−10.5910	−	18.3441i	−0.426377	−	0.738507i	−0.996548	+	0.0830194i	$0.973544\pi$
$618$	1.31815	+	2.28311i	0.0530240	+	0.0918402i
$619$			25.4082i			1.02124i	0.859807	+	0.510620i	$0.170584\pi$
$619$			25.4082i			1.02124i	−0.859807	+	0.510620i	$0.829416\pi$
$620$	0.530192	−	1.46503i	0.0212930	−	0.0588369i
$621$	0.350210	−	0.606582i	0.0140534	−	0.0243413i
$622$	4.53504	−	7.85493i	0.181839	−	0.314954i
$623$		−	24.8455i		−	0.995416i
$624$		0			0
$625$	−23.5543	−	8.37828i	−0.942171	−	0.335131i
$626$	−26.8813	−	15.5199i	−1.07439	−	0.620302i
$627$	6.82125	+	3.93825i	0.272415	+	0.157279i
$628$	−3.17056	+	1.83052i	−0.126519	+	0.0730459i
$629$			29.7041i			1.18438i
$630$	−14.5969	−	5.28261i	−0.581555	−	0.210464i
$631$	−37.7112	+	21.7725i	−1.50126	+	0.866751i	−0.501258	+	0.865298i	$0.667129\pi$
$631$	−37.7112	+	21.7725i	−1.50126	+	0.866751i	−0.999999	+	0.00145375i	$0.999537\pi$
$632$	34.3853			1.36777
$633$	−2.17632	+	1.25650i	−0.0865011	+	0.0499414i
$634$	−7.03069	+	12.1775i	−0.279224	+	0.483631i
$635$	−36.7766	+	6.55413i	−1.45943	+	0.260093i
$636$	0.494244			0.0195980
$637$		0			0
$638$			13.8238i			0.547288i
$639$	4.69272	+	2.70934i	0.185641	+	0.107180i
$640$	−1.55727	−	8.73816i	−0.0615565	−	0.345406i
$641$	24.1427	+	41.8164i	0.953579	+	1.65165i	0.737586	+	0.675253i	$0.235965\pi$
$641$	24.1427	+	41.8164i	0.953579	+	1.65165i	0.215993	+	0.976395i	$0.430701\pi$
$642$	7.24423			0.285907
$643$	−21.1720	−	36.6710i	−0.834943	−	1.44616i	−0.894077	−	0.447913i	$-0.852167\pi$
$643$	−21.1720	−	36.6710i	−0.834943	−	1.44616i	0.0591344	−	0.998250i	$-0.481166\pi$
$644$	0.358028	−	0.206708i	0.0141083	−	0.00814543i
$645$	0.790529	−	0.665802i	0.0311271	−	0.0262159i
$646$	19.0281	+	32.9576i	0.748649	+	1.29670i
$647$	29.7958	+	17.2026i	1.17139	+	0.676305i	0.954008	−	0.299781i	$-0.0969136\pi$
$647$	29.7958	+	17.2026i	1.17139	+	0.676305i	0.217386	+	0.976086i	$0.430247\pi$
$648$	12.2131	−	21.1538i	0.479778	−	0.830999i
$649$	−27.4045			−1.07572
$650$		0			0
$651$	0.826831			0.0324061
$652$	3.52244	−	6.10104i	0.137949	−	0.238935i
$653$	12.4114	+	7.16573i	0.485696	+	0.280417i	0.722787	−	0.691071i	$-0.242861\pi$
$653$	12.4114	+	7.16573i	0.485696	+	0.280417i	−0.237091	+	0.971487i	$0.576194\pi$
$654$	−1.18048	−	2.04465i	−0.0461604	−	0.0799521i
$655$	−17.1029	+	14.4045i	−0.668267	+	0.562830i
$656$	−0.386237	+	0.222994i	−0.0150800	+	0.00870646i
$657$	−12.7626	−	22.1054i	−0.497916	−	0.862416i
$658$	29.5936			1.15368
$659$	11.4116	+	19.7655i	0.444532	+	0.769953i	0.998020	−	0.0629051i	$-0.0200365\pi$
$659$	11.4116	+	19.7655i	0.444532	+	0.769953i	−0.553487	+	0.832858i	$0.686703\pi$
$660$	0.310140	+	1.74026i	0.0120722	+	0.0677394i
$661$	12.4869	+	7.20934i	0.485686	+	0.280411i	0.722783	−	0.691075i	$-0.242863\pi$
$661$	12.4869	+	7.20934i	0.485686	+	0.280411i	−0.237097	+	0.971486i	$0.576196\pi$
$662$		−	15.0796i		−	0.586087i
$663$		0			0
$664$	24.0976			0.935168
$665$	26.2749	−	4.68257i	1.01890	−	0.181582i
$666$	9.32135	−	16.1450i	0.361195	−	0.625608i
$667$	−0.896622	+	0.517665i	−0.0347173	+	0.0200441i
$668$	−1.19792			−0.0463491
$669$	5.81818	−	3.35913i	0.224944	−	0.129871i
$670$	−10.9952	−	3.97913i	−0.424780	−	0.153727i
$671$		−	26.2419i		−	1.01306i
$672$	−1.95131	+	1.12659i	−0.0752733	+	0.0434591i
$673$	−29.5956	−	17.0871i	−1.14083	−	0.658657i	−0.194193	−	0.980963i	$-0.562209\pi$
$673$	−29.5956	−	17.0871i	−1.14083	−	0.658657i	−0.946636	+	0.322306i	$0.895542\pi$
$674$	15.7261	+	9.07949i	0.605748	+	0.349729i
$675$	10.0000	+	1.72555i	0.384900	+	0.0664164i
$676$		0			0
$677$		−	5.84695i		−	0.224716i	−0.993668	−	0.112358i	$-0.964160\pi$
$677$		−	5.84695i		−	0.224716i	0.993668	−	0.112358i	$-0.0358404\pi$
$678$	−0.975215	+	1.68912i	−0.0374529	+	0.0648703i
$679$	−5.89165	+	10.2046i	−0.226101	+	0.391618i
$680$	−12.7546	+	35.2436i	−0.489117	+	1.35153i
$681$			1.66054i			0.0636319i
$682$	−2.71978	−	4.71079i	−0.104146	−	0.180386i
$683$	5.67439	+	9.82834i	0.217125	+	0.376071i	0.953928	−	0.300036i	$-0.0969989\pi$
$683$	5.67439	+	9.82834i	0.217125	+	0.376071i	−0.736803	+	0.676107i	$0.763666\pi$
$684$			10.0000i			0.382360i
$685$	−4.15868	−	1.50502i	−0.158895	−	0.0575039i
$686$	−11.9053	+	20.6206i	−0.454546	+	0.787298i
$687$	0.262904	−	0.455363i	0.0100304	−	0.0173732i
$688$		−	3.30969i		−	0.126181i
$689$		0			0
$690$	0.241857	−	0.203698i	0.00920733	−	0.00775463i
$691$	16.3013	+	9.41159i	0.620133	+	0.358034i	0.776921	−	0.629599i	$-0.216781\pi$
$691$	16.3013	+	9.41159i	0.620133	+	0.358034i	−0.156788	+	0.987632i	$0.550114\pi$
$692$	−0.684619	−	0.395265i	−0.0260253	−	0.0150257i
$693$	19.6513	−	11.3457i	0.746493	−	0.430988i
$694$		−	14.5325i		−	0.551647i
$695$	−18.2936	−	6.62044i	−0.693916	−	0.251128i
$696$	2.75754	−	1.59207i	0.104524	−	0.0603471i
$697$	0.983636			0.0372579
$698$	19.2289	−	11.1018i	0.727825	−	0.420210i
$699$	2.40976	−	4.17383i	0.0911455	−	0.157869i
$700$	4.60238	+	3.83323i	0.173954	+	0.144883i
$701$	−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
$704$	29.4480	+	17.0018i	1.10986	+	0.640780i
$705$	−9.32990	+	1.66273i	−0.351385	+	0.0626219i
$706$	0.777006	+	1.34581i	0.0292430	+	0.0506504i
$707$	−12.0602			−0.453570
$708$	0.719193	+	1.24568i	0.0270289	+	0.0468154i
$709$	20.3375	−	11.7419i	0.763791	−	0.440975i	−0.0668645	−	0.997762i	$-0.521300\pi$
$709$	20.3375	−	11.7419i	0.763791	−	0.440975i	0.830655	+	0.556787i	$0.187966\pi$
$710$	3.21689	+	3.81952i	0.120728	+	0.143344i
$711$	16.1049	+	27.8945i	0.603982	+	1.04613i
$712$	32.6055	+	18.8248i	1.22194	+	0.705488i
$713$	0.203698	−	0.352814i	0.00762853	−	0.0132130i
$714$	−4.53252			−0.169625
$715$		0			0
$716$	−11.9370			−0.446107
$717$	−0.690220	+	1.19550i	−0.0257767	+	0.0446466i
$718$	30.2393	+	17.4586i	1.12852	+	0.651551i
$719$	7.05429	+	12.2184i	0.263080	+	0.455669i	0.967059	−	0.254553i	$-0.0819282\pi$
$719$	7.05429	+	12.2184i	0.263080	+	0.455669i	−0.703978	+	0.710221i	$0.748595\pi$
$720$	12.1758	−	10.2547i	0.453764	−	0.382170i
$721$	−11.3083	+	6.52886i	−0.421144	+	0.243148i
$722$	9.25228	+	16.0254i	0.344334	+	0.596404i
$723$	−6.02765			−0.224171
$724$	−5.85021	−	10.1329i	−0.217421	−	0.376585i
$725$	−11.5259	−	9.59969i	−0.428061	−	0.356523i
$726$	1.44123	+	0.832096i	0.0534892	+	0.0308820i
$727$			25.3762i			0.941153i	0.882359	+	0.470576i	$0.155954\pi$
$727$			25.3762i			0.941153i	−0.882359	+	0.470576i	$0.844046\pi$
$728$		0			0
$729$	20.7796			0.769616
$730$	−4.12717	−	23.1584i	−0.152754	−	0.857131i
$731$	−3.64979	+	6.32162i	−0.134992	+	0.233814i
$732$	−1.19283	+	0.688681i	−0.0440883	+	0.0254544i
$733$	10.6692			0.394074			0.197037	−	0.980396i	$-0.436868\pi$
$733$	10.6692			0.394074			0.197037	+	0.980396i	$0.436868\pi$
$734$	34.3770	−	19.8476i	1.26888	−	0.732587i
$735$	0.756540	−	2.09047i	0.0279054	−	0.0771083i
$736$			1.11018i			0.0409218i
$737$	14.8024	−	8.54617i	0.545254	−	0.314802i
$738$	−0.534635	−	0.308672i	−0.0196802	−	0.0113624i
$739$	1.22545	+	0.707513i	0.0450788	+	0.0260263i	0.522370	−	0.852719i	$-0.325048\pi$
$739$	1.22545	+	0.707513i	0.0450788	+	0.0260263i	−0.477291	+	0.878745i	$0.658381\pi$
$740$	−5.50183	+	4.63377i	−0.202251	+	0.170341i
$741$		0			0
$742$		−	5.84695i		−	0.214648i
$743$	−14.9389	+	25.8748i	−0.548053	+	0.949256i	0.450355	+	0.892850i	$0.351298\pi$
$743$	−14.9389	+	25.8748i	−0.548053	+	0.949256i	−0.998408	+	0.0564064i	$0.982036\pi$
$744$	−0.626467	+	1.08507i	−0.0229674	+	0.0397807i
$745$	16.9713	−	46.8951i	0.621779	−	1.71810i
$746$		−	40.9370i		−	1.49881i
$747$	11.2865	+	19.5488i	0.412952	+	0.715253i
$748$	−6.24221	−	10.8118i	−0.228238	−	0.395320i
$749$			35.8809i			1.31106i
$750$	3.98001	+	2.26881i	0.145329	+	0.0828453i
$751$	−9.99291	+	17.3082i	−0.364646	+	0.631586i	−0.988719	−	0.149780i	$-0.952143\pi$
$751$	−9.99291	+	17.3082i	−0.364646	+	0.631586i	0.624073	+	0.781366i	$0.285477\pi$
$752$	−15.1737	+	26.2816i	−0.553328	+	0.958391i
$753$		−	3.20938i		−	0.116956i
$754$		0			0
$755$	−27.6028	−	32.7737i	−1.00457	−	1.19276i
$756$	−2.10553	−	1.21563i	−0.0765774	−	0.0442120i
$757$	−14.8024	−	8.54617i	−0.538003	−	0.310616i	0.206266	−	0.978496i	$-0.433869\pi$
$757$	−14.8024	−	8.54617i	−0.538003	−	0.310616i	−0.744269	+	0.667880i	$0.767202\pi$
$758$	17.8964	−	10.3325i	0.650025	−	0.375292i
$759$			0.462218i			0.0167775i
$760$	−13.7627	+	38.0291i	−0.499225	+	1.37946i
$761$	36.5671	−	21.1120i	1.32556	−	0.765310i	0.340947	−	0.940083i	$-0.389252\pi$
$761$	36.5671	−	21.1120i	1.32556	−	0.765310i	0.984609	+	0.174773i	$0.0559192\pi$
$762$	6.84552			0.247987
$763$	10.1272	−	5.84695i	0.366630	−	0.211674i
$764$	0.453830	−	0.786056i	0.0164190	−	0.0284385i
$765$	−34.5646	+	6.15992i	−1.24969	+	0.222713i
$766$	−2.07395			−0.0749350
$767$		0			0
$768$		−	4.42107i		−	0.159531i
$769$	−20.5815	−	11.8827i	−0.742187	−	0.428502i	0.0806767	−	0.996740i	$-0.474292\pi$
$769$	−20.5815	−	11.8827i	−0.742187	−	0.428502i	−0.822864	+	0.568238i	$0.807625\pi$
$770$	20.5874	−	3.66898i	0.741919	−	0.132221i
$771$	1.87907	+	3.25465i	0.0676731	+	0.117213i
$772$	−12.5149			−0.450422
$773$	−0.142043	−	0.246026i	−0.00510894	−	0.00884894i	0.863460	−	0.504418i	$-0.168293\pi$
$773$	−0.142043	−	0.246026i	−0.00510894	−	0.00884894i	−0.868569	+	0.495569i	$0.834960\pi$
$774$	3.96754	−	2.29066i	0.142610	−	0.0823361i
$775$	5.81644	+	1.00366i	0.208933	+	0.0360524i
$776$	−8.92787	−	15.4635i	−0.320492	−	0.555108i
$777$	−3.30596	−	1.90870i	−0.118601	−	0.0684741i
$778$	−13.0865	+	22.6665i	−0.469174	+	0.812634i
$779$	1.06138			0.0380278
$780$		0			0
$781$	−7.29958			−0.261199
$782$	−1.11663	+	1.93405i	−0.0399305	+	0.0691617i
$783$	5.27294	+	3.04434i	0.188440	+	0.108796i
$784$	−3.55955	−	6.16532i	−0.127127	−	0.220190i
$785$	−8.93460	−	10.6084i	−0.318890	−	0.378628i
$786$	3.54863	−	2.04880i	0.126575	−	0.0730784i
$787$	12.0671	+	20.9008i	0.430145	+	0.745032i	0.996885	−	0.0788638i	$-0.0251292\pi$
$787$	12.0671	+	20.9008i	0.430145	+	0.745032i	−0.566741	+	0.823896i	$0.691796\pi$
$788$	5.46381			0.194640
$789$	−2.31925	−	4.01705i	−0.0825674	−	0.143011i
$790$	5.20802	+	29.2233i	0.185293	+	1.03972i
$791$	−8.36627	−	4.83027i	−0.297470	−	0.171745i
$792$			34.3853i			1.22183i
$793$		0			0
$794$	26.7529			0.949424
$795$	0.328513	+	1.84335i	0.0116511	+	0.0653770i
$796$	−5.13641	+	8.89652i	−0.182055	+	0.315329i
$797$	−29.7430	+	17.1721i	−1.05355	+	0.608267i	−0.923641	−	0.383259i	$-0.874802\pi$
$797$	−29.7430	+	17.1721i	−1.05355	+	0.608267i	−0.129909	+	0.991526i	$0.541468\pi$
$798$	−4.89075			−0.173131
$799$	57.9646	−	33.4659i	2.05064	−	1.18394i
$800$	−15.0942	+	5.55650i	−0.533661	+	0.196452i
$801$			35.2676i			1.24612i
$802$	3.80876	−	2.19899i	0.134492	−	0.0776489i
$803$	29.7786	+	17.1927i	1.05086	+	0.606716i
$804$	−0.776937	−	0.448565i	−0.0274004	−	0.0158197i
$805$	1.00892	+	1.19792i	0.0355598	+	0.0422213i
$806$		0			0
$807$		−	1.26329i		−	0.0444698i
$808$	9.13767	−	15.8269i	0.321462	−	0.556789i
$809$	−23.8431	+	41.2975i	−0.838279	+	1.45194i	0.0530528	+	0.998592i	$0.483105\pi$
$809$	−23.8431	+	41.2975i	−0.838279	+	1.45194i	−0.891332	+	0.453351i	$0.850229\pi$
$810$	19.8279	+	7.17570i	0.696682	+	0.252128i
$811$			24.5992i			0.863793i	0.901923	+	0.431897i	$0.142155\pi$
$811$			24.5992i			0.863793i	−0.901923	+	0.431897i	$0.857845\pi$
$812$	1.79689	+	3.11230i	0.0630584	+	0.109220i
$813$	−3.79684	−	6.57632i	−0.133161	−	0.230642i
$814$			25.1138i			0.880239i
$815$	25.0960	+	9.08221i	0.879074	+	0.318136i
$816$	2.32398	−	4.02525i	0.0813556	−	0.140912i
$817$	−3.93825	+	6.82125i	−0.137782	+	0.238645i
$818$			16.0097i			0.559765i
$819$		0			0
$820$	0.153445	+	0.182190i	0.00535853	+	0.00636236i
$821$	−14.9819	−	8.64979i	−0.522871	−	0.301880i	0.215237	−	0.976562i	$-0.430947\pi$
$821$	−14.9819	−	8.64979i	−0.522871	−	0.301880i	−0.738109	+	0.674682i	$0.764281\pi$
$822$	0.701870	+	0.405225i	0.0244805	+	0.0141338i
$823$	28.2000	−	16.2813i	0.982990	−	0.567529i	0.0798182	−	0.996809i	$-0.474566\pi$
$823$	28.2000	−	16.2813i	0.982990	−	0.567529i	0.903171	+	0.429280i	$0.141233\pi$
$824$		−	19.7869i		−	0.689311i
$825$	−6.28440	+	2.31342i	−0.218795	+	0.0805430i
$826$	14.7365	−	8.50812i	0.512748	−	0.296035i
$827$	15.4702			0.537951			0.268976	−	0.963147i	$-0.413315\pi$
$827$	15.4702			0.537951			0.268976	+	0.963147i	$0.413315\pi$
$828$	−0.508211	+	0.293416i	−0.0176616	+	0.0101969i
$829$	7.26180	−	12.5778i	0.252213	−	0.436845i	−0.711922	−	0.702258i	$-0.752175\pi$
$829$	7.26180	−	12.5778i	0.252213	−	0.436845i	0.964135	+	0.265413i	$0.0855084\pi$
$830$	3.64984	+	20.4800i	0.126688	+	0.710870i
$831$	−3.41503			−0.118466
$832$		0			0
$833$			15.7013i			0.544018i
$834$	3.08746	+	1.78254i	0.106910	+	0.0617245i
$835$	−0.796234	−	4.46783i	−0.0275548	−	0.154616i
$836$	−6.73557	−	11.6663i	−0.232955	−	0.403489i
$837$	−2.39585			−0.0828127
$838$	9.98736	+	17.2986i	0.345008	+	0.597571i
$839$	0.706561	−	0.407933i	0.0243932	−	0.0140834i	−0.487754	−	0.872981i	$-0.662184\pi$
$839$	0.706561	−	0.407933i	0.0243932	−	0.0140834i	0.512147	+	0.858898i	$0.328850\pi$
$840$	−3.10291	−	3.68419i	−0.107061	−	0.127117i
$841$	10.0000	+	17.3205i	0.344828	+	0.597259i
$842$	−17.5846	−	10.1524i	−0.606004	−	0.349876i
$843$	−0.700811	+	1.21384i	−0.0241372	+	0.0418069i
$844$	4.29797			0.147942
$845$		0			0
$846$	−42.0073			−1.44424
$847$	−4.12140	+	7.13847i	−0.141613	+	0.245281i
$848$	5.19258	+	2.99794i	0.178314	+	0.102950i
$849$	1.05063	+	1.81975i	0.0360575	+	0.0624535i
$850$	−31.8845	−	5.50183i	−1.09363	−	0.188711i
$851$	−1.62891	+	0.940450i	−0.0558382	+	0.0322382i
$852$	0.191567	+	0.331804i	0.00656299	+	0.0113674i
$853$	20.0856			0.687719			0.343859	−	0.939021i	$-0.388266\pi$
$853$	20.0856			0.687719			0.343859	+	0.939021i	$0.388266\pi$
$854$	8.14716	+	14.1113i	0.278790	+	0.482878i
$855$	−37.2964	+	6.64678i	−1.27551	+	0.227315i
$856$	−47.0875	−	27.1860i	−1.60942	−	0.929197i
$857$			40.7886i			1.39331i	0.717406	+	0.696656i	$0.245329\pi$
$857$			40.7886i			1.39331i	−0.717406	+	0.696656i	$0.754671\pi$
$858$		0			0
$859$	40.1301			1.36922			0.684610	−	0.728909i	$-0.259972\pi$
$859$	40.1301			1.36922			0.684610	+	0.728909i	$0.259972\pi$
$860$	−1.74026	+	0.310140i	−0.0593423	+	0.0105757i
$861$	−0.0632055	+	0.109475i	−0.00215404	+	0.00373090i
$862$	9.93355	−	5.73514i	0.338338	−	0.195340i
$863$	20.8275			0.708977			0.354489	−	0.935060i	$-0.384655\pi$
$863$	20.8275			0.708977			0.354489	+	0.935060i	$0.384655\pi$
$864$	5.65416	−	3.26443i	0.192358	−	0.111058i
$865$	1.01915	−	2.81611i	0.0346520	−	0.0957505i
$866$		−	29.4134i		−	0.999509i
$867$	−3.79692	+	2.19215i	−0.128950	+	0.0744494i
$868$	−1.22467	−	0.707062i	−0.0415679	−	0.0239993i
$869$	−37.5771	−	21.6952i	−1.27472	−	0.735958i
$870$	1.77072	+	2.10243i	0.0600330	+	0.0712792i
$871$		0			0
$872$			17.7203i			0.600084i
$873$	8.36303	−	14.4852i	0.283046	−	0.490249i
$874$	−1.20488	+	2.08691i	−0.0407557	+	0.0705909i
$875$	−11.2375	+	19.7131i	−0.379897	+	0.666424i
$876$		−	1.80479i		−	0.0609782i
$877$	−23.2972	−	40.3520i	−0.786691	−	1.36259i	−0.927984	−	0.372621i	$-0.878459\pi$
$877$	−23.2972	−	40.3520i	−0.786691	−	1.36259i	0.141293	−	0.989968i	$-0.454874\pi$
$878$	−4.19210	−	7.26094i	−0.141477	−	0.245045i
$879$		−	3.37935i		−	0.113982i
$880$	−7.29753	+	20.1646i	−0.246000	+	0.679747i
$881$	11.9223	−	20.6501i	0.401674	−	0.695719i	−0.592254	−	0.805751i	$-0.701762\pi$
$881$	11.9223	−	20.6501i	0.401674	−	0.695719i	0.993928	+	0.110032i	$0.0350953\pi$
$882$	4.92718	−	8.53413i	0.165907	−	0.287359i
$883$			37.2496i			1.25355i	0.779201	+	0.626774i	$0.215625\pi$
$883$			37.2496i			1.25355i	−0.779201	+	0.626774i	$0.784375\pi$
$884$		0			0
$885$	−4.16790	+	3.51031i	−0.140103	+	0.117998i
$886$	39.3246	+	22.7041i	1.32114	+	0.762758i
$887$	24.7505	+	14.2897i	0.831042	+	0.479802i	0.854209	−	0.519929i	$-0.174042\pi$
$887$	24.7505	+	14.2897i	0.831042	+	0.479802i	−0.0231673	+	0.999732i	$0.507375\pi$
$888$	5.00967	−	2.89233i	0.168113	−	0.0970603i
$889$			33.9060i			1.13717i
$890$	−11.0603	+	30.5618i	−0.370742	+	1.02443i
$891$	−26.6937	+	15.4116i	−0.894271	+	0.516308i
$892$	−11.4902			−0.384720
$893$	62.5459	−	36.1109i	2.09302	−	1.20840i
$894$	−4.56949	+	7.91459i	−0.152827	+	0.264704i
$895$	−7.93427	−	44.5208i	−0.265213	−	1.48817i
$896$	−8.05611			−0.269136
$897$		0			0
$898$		−	14.8180i		−	0.494483i
$899$	3.06697	+	1.77072i	0.102289	+	0.0590568i
$900$	−6.53295	−	5.44117i	−0.217765	−	0.181372i
$901$	−6.61201	−	11.4523i	−0.220278	−	0.381533i
$902$	0.831632			0.0276903
$903$	−0.469049	−	0.812417i	−0.0156090	−	0.0270356i
$904$	12.6778	−	7.31952i	0.421657	−	0.243444i
$905$	33.9035	−	28.5543i	1.12699	−	0.949177i
$906$	3.92605	+	6.80011i	0.130434	+	0.225919i
$907$	−5.55457	−	3.20693i	−0.184436	−	0.106484i	0.404939	−	0.914344i	$-0.367293\pi$
$907$	−5.55457	−	3.20693i	−0.184436	−	0.106484i	−0.589375	+	0.807859i	$0.700626\pi$
$908$	1.42000	−	2.45952i	0.0471245	−	0.0816220i
$909$	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	$0.380010\pi$
$912$	2.50766	−	4.34339i	0.0830369	−	0.143824i
$913$	−26.3345	−	15.2042i	−0.871543	−	0.503186i
$914$	−4.88719	−	8.46486i	−0.161654	−	0.279993i
$915$	−3.36138	−	3.99108i	−0.111124	−	0.131941i
$916$	−0.778805	+	0.449643i	−0.0257324	+	0.0148566i
$917$	10.1478	+	17.5765i	0.335109	+	0.580426i
$918$	13.1335			0.433472
$919$	13.0632	+	22.6261i	0.430915	+	0.746367i	0.996952	−	0.0780125i	$-0.0248574\pi$
$919$	13.0632	+	22.6261i	0.430915	+	0.746367i	−0.566037	+	0.824380i	$0.691524\pi$
$920$	−2.33650	+	0.416399i	−0.0770321	+	0.0137283i
$921$	−6.60649	−	3.81426i	−0.217691	−	0.125684i
$922$		−	5.39220i		−	0.177583i
$923$		0			0
$924$	1.60442			0.0527817
$925$	−20.9392	−	17.4399i	−0.688478	−	0.573420i
$926$	1.18048	−	2.04465i	0.0387929	−	0.0671913i
$927$	16.0518	−	9.26754i	0.527212	−	0.304386i
$928$	−9.65067			−0.316799
$929$	20.7346	−	11.9711i	0.680281	−	0.392760i	−0.119680	−	0.992813i	$-0.538187\pi$
$929$	20.7346	−	11.9711i	0.680281	−	0.392760i	0.799961	+	0.600052i	$0.204854\pi$
$930$	−1.01706	−	0.368074i	−0.0333508	−	0.0120696i
$931$			16.9423i			0.555261i
$932$	−7.13847	+	4.12140i	−0.233828	+	0.135001i
$933$	2.28311	+	1.31815i	0.0747457	+	0.0431544i
$934$	33.7313	+	19.4748i	1.10372	+	0.637235i
$935$	36.1752	−	30.4676i	1.18306	−	0.996397i
$936$		0			0
$937$			18.5046i			0.604518i	0.953226	+	0.302259i	$0.0977407\pi$
$937$			18.5046i			0.604518i	−0.953226	+	0.302259i	$0.902259\pi$
$938$	−5.30656	+	9.19124i	−0.173265	+	0.300104i
$939$	4.51102	−	7.81332i	0.147212	−	0.254978i
$940$	15.2409	+	5.51568i	0.497105	+	0.179902i
$941$		−	14.3788i		−	0.468735i	−0.972148	−	0.234368i	$-0.924698\pi$
$941$		−	14.3788i		−	0.468735i	0.972148	−	0.234368i	$-0.0753020\pi$
$942$	1.27080	+	2.20109i	0.0414049	+	0.0717154i
$943$	0.0311425	+	0.0539404i	0.00101414	+	0.00175654i
$944$			17.4496i			0.567938i
$945$	3.13436	−	8.66087i	0.101961	−	0.281738i
$946$	−3.08578	+	5.34473i	−0.100327	+	0.173772i
$947$	29.1594	−	50.5056i	0.947554	−	1.64121i	0.196998	−	0.980404i	$-0.436881\pi$
$947$	29.1594	−	50.5056i	0.947554	−	1.64121i	0.750555	−	0.660807i	$-0.229786\pi$
$948$			2.27744i			0.0739677i
$949$		0			0
$950$	−34.4045	−	5.93667i	−1.11623	−	0.192611i
$951$	−3.53951	−	2.04354i	−0.114777	−	0.0662663i
$952$	29.4613	+	17.0095i	0.954847	+	0.551281i
$953$	11.9507	−	6.89975i	0.387122	−	0.223505i	−0.293791	−	0.955870i	$-0.594917\pi$
$953$	11.9507	−	6.89975i	0.387122	−	0.223505i	0.680912	+	0.732365i	$0.261583\pi$
$954$			8.29958i			0.268709i
$955$	3.23336	+	1.17015i	0.104629	+	0.0378651i
$956$	2.04465	−	1.18048i	0.0661287	−	0.0381794i
$957$	−4.01801			−0.129884
$958$	−31.6759	+	18.2881i	−1.02340	+	0.590862i
$959$	−2.00709	+	3.47639i	−0.0648124	+	0.112258i
$960$	6.65651	−	1.18629i	0.214838	−	0.0382873i
$961$	29.6065			0.955047
$962$		0			0
$963$		−	50.9319i		−	1.64126i
$964$	8.92790	+	5.15452i	0.287548	+	0.166016i
$965$	−8.31840	−	46.6763i	−0.267779	−	1.50256i
$966$	−0.143502	−	0.248553i	−0.00461711	−	0.00799707i
$967$	30.3474			0.975906			0.487953	−	0.872870i	$-0.337744\pi$
$967$	30.3474			0.975906			0.487953	+	0.872870i	$0.337744\pi$
$968$	−6.24534	−	10.8172i	−0.200733	−	0.347679i
$969$	−9.57943	+	5.53069i	−0.307736	+	0.177671i
$970$	11.7899	−	9.92970i	0.378550	−	0.318824i
$971$	−22.0506	−	38.1928i	−0.707638	−	1.22567i	−0.965731	−	0.259545i	$-0.916427\pi$
$971$	−22.0506	−	38.1928i	−0.707638	−	1.22567i	0.258092	−	0.966120i	$-0.416906\pi$
$972$	4.51337	+	2.60580i	0.144767	+	0.0835810i
$973$	−8.82900	+	15.2923i	−0.283045	+	0.490248i
$974$	−26.5074			−0.849351
$975$		0			0
$976$	−16.7093			−0.534853
$977$	11.1610	−	19.3314i	0.357071	−	0.618466i	−0.630399	−	0.776271i	$-0.717109\pi$
$977$	11.1610	−	19.3314i	0.357071	−	0.618466i	0.987470	+	0.157806i	$0.0504420\pi$
$978$	−4.23551	−	2.44537i	−0.135437	−	0.0781944i
$979$	−23.7547	−	41.1444i	−0.759204	−	1.31498i
$980$	−2.90822	+	2.44937i	−0.0928996	+	0.0782422i
$981$	−14.3753	+	8.29958i	−0.458968	+	0.264985i
$982$	6.34189	+	10.9845i	0.202378	+	0.350529i
$983$	4.03793			0.128790			0.0643950	−	0.997924i	$-0.479488\pi$
$983$	4.03793			0.128790			0.0643950	+	0.997924i	$0.479488\pi$
$984$	−0.0957781	−	0.165893i	−0.00305330	−	0.00528846i
$985$	3.63168	+	20.3781i	0.115715	+	0.649300i
$986$	−16.8125	−	9.70671i	−0.535419	−	0.309125i
$987$			8.60167i			0.273794i
$988$		0			0
$989$	−0.462218			−0.0146977
$990$	−29.2233	+	5.20802i	−0.928776	+	0.165522i
$991$	−14.8250	+	25.6777i	−0.470932	+	0.815678i	−0.999447	−	0.0332459i	$-0.989416\pi$
$991$	−14.8250	+	25.6777i	−0.470932	+	0.815678i	0.528515	+	0.848924i	$0.322749\pi$
$992$	3.28871	−	1.89874i	0.104417	−	0.0602849i
$993$	4.38304			0.139092
$994$	3.92527	−	2.26626i	0.124502	−	0.0718813i
$995$	−36.5949	−	13.2437i	−1.16014	−	0.419852i
$996$			1.59605i			0.0505728i
$997$	−19.2052	+	11.0881i	−0.608233	+	0.351164i	−0.772274	−	0.635290i	$-0.780881\pi$
$997$	−19.2052	+	11.0881i	−0.608233	+	0.351164i	0.164040	+	0.986454i	$0.447547\pi$
$998$	19.3514	+	11.1725i	0.612557	+	0.353660i
$999$	9.57943	+	5.53069i	0.303080	+	0.174983i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.n.a.9.2	✓	12	65.44	odd	4
65.2.n.a.9.5	yes	12	13.5	odd	4
65.2.n.a.29.2	yes	12	13.2	odd	12
65.2.n.a.29.5	yes	12	65.54	odd	12
325.2.e.e.126.2		12	65.57	even	4
325.2.e.e.126.5		12	65.18	even	4
325.2.e.e.276.2		12	65.2	even	12
325.2.e.e.276.5		12	65.28	even	12
585.2.bs.a.289.2		12	195.119	even	12
585.2.bs.a.289.5		12	39.2	even	12
585.2.bs.a.334.2		12	39.5	even	4
585.2.bs.a.334.5		12	195.44	even	4
845.2.b.d.339.2		6	13.6	odd	12
845.2.b.d.339.5		6	65.19	odd	12
845.2.b.e.339.2		6	65.59	odd	12
845.2.b.e.339.5		6	13.7	odd	12
845.2.d.d.844.3		12	65.9	even	6
845.2.d.d.844.4		12	13.4	even	6
845.2.d.d.844.9		12	65.4	even	6
845.2.d.d.844.10		12	13.9	even	3
845.2.l.f.654.3		24	1.1	even	1	trivial
845.2.l.f.654.4		24	65.64	even	2	inner
845.2.l.f.654.9		24	13.12	even	2	inner
845.2.l.f.654.10		24	5.4	even	2	inner
845.2.l.f.699.3		24	65.49	even	6	inner
845.2.l.f.699.4		24	13.3	even	3	inner
845.2.l.f.699.9		24	65.29	even	6	inner
845.2.l.f.699.10		24	13.10	even	6	inner
845.2.n.e.484.2		12	65.24	odd	12
845.2.n.e.484.5		12	13.11	odd	12
845.2.n.e.529.2		12	13.8	odd	4
845.2.n.e.529.5		12	65.34	odd	4
1040.2.dh.a.289.3		12	52.15	even	12
1040.2.dh.a.289.4		12	260.119	even	12
1040.2.dh.a.529.3		12	260.239	even	4
1040.2.dh.a.529.4		12	52.31	even	4
4225.2.a.bq.1.2		6	65.7	even	12
4225.2.a.bq.1.5		6	65.33	even	12
4225.2.a.br.1.2		6	65.58	even	12
4225.2.a.br.1.5		6	65.32	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.593667 + 1.02826i) q^{2} +(-0.298874 - 0.172555i) q^{3} +(0.295120 + 0.511162i) q^{4} +(-1.71029 + 1.44045i) q^{5} +(0.354863 - 0.204880i) q^{6} +(1.01478 + 1.75765i) q^{7} -3.07548 q^{8} +(-1.44045 - 2.49493i) q^{9} +O(q^{10})\)	\(q+(-0.593667 + 1.02826i) q^{2} +(-0.298874 - 0.172555i) q^{3} +(0.295120 + 0.511162i) q^{4} +(-1.71029 + 1.44045i) q^{5} +(0.354863 - 0.204880i) q^{6} +(1.01478 + 1.75765i) q^{7} -3.07548 q^{8} +(-1.44045 - 2.49493i) q^{9} +(-0.465813 - 2.61378i) q^{10} +(3.36096 + 1.94045i) q^{11} -0.203698i q^{12} -2.40976 q^{14} +(0.759719 - 0.135393i) q^{15} +(1.23557 - 2.14007i) q^{16} +(-4.71996 + 2.72507i) q^{17} +3.42059 q^{18} +(-5.09301 + 2.94045i) q^{19} +(-1.24105 - 0.449133i) q^{20} -0.700420i q^{21} +(-3.99058 + 2.30396i) q^{22} +(-0.298874 - 0.172555i) q^{23} +(0.919180 + 0.530689i) q^{24} +(0.850210 - 4.92718i) q^{25} +2.02956i q^{27} +(-0.598962 + 1.03743i) q^{28} +(1.50000 - 2.59808i) q^{29} +(-0.311800 + 0.861568i) q^{30} +1.18048i q^{31} +(-1.60845 - 2.78591i) q^{32} +(-0.669668 - 1.15990i) q^{33} -6.47114i q^{34} +(-4.26737 - 1.54436i) q^{35} +(0.850210 - 1.47261i) q^{36} +(2.72507 - 4.71996i) q^{37} -6.98259i q^{38} +(5.25997 - 4.43007i) q^{40} +(-0.156299 - 0.0902394i) q^{41} +(0.720215 + 0.415816i) q^{42} +(1.15990 - 0.669668i) q^{43} +2.29066i q^{44} +(6.05742 + 2.19217i) q^{45} +(0.354863 - 0.204880i) q^{46} -12.2807 q^{47} +(-0.738559 + 0.426407i) q^{48} +(1.44045 - 2.49493i) q^{49} +(4.56169 + 3.79934i) q^{50} +1.88090 q^{51} +2.42636i q^{53} +(-2.08691 - 1.20488i) q^{54} +(-8.54334 + 1.52255i) q^{55} +(-3.12093 - 5.40561i) q^{56} +2.02956 q^{57} +(1.78100 + 3.08478i) q^{58} +(-6.11533 + 3.53069i) q^{59} +(0.293416 + 0.348383i) q^{60} +(-3.38090 - 5.85589i) q^{61} +(-1.21384 - 0.700811i) q^{62} +(2.92347 - 5.06361i) q^{63} +8.76180 q^{64} +1.59024 q^{66} +(2.20211 - 3.81417i) q^{67} +(-2.78591 - 1.60845i) q^{68} +(0.0595504 + 0.103144i) q^{69} +(4.12140 - 3.47114i) q^{70} +(-1.62891 + 0.940450i) q^{71} +(4.43007 + 7.67311i) q^{72} +8.86014 q^{73} +(3.23557 + 5.60417i) q^{74} +(-1.10432 + 1.32590i) q^{75} +(-3.00609 - 1.73557i) q^{76} +7.87651i q^{77} -11.1805 q^{79} +(0.969475 + 5.43992i) q^{80} +(-3.97114 + 6.87821i) q^{81} +(0.185579 - 0.107144i) q^{82} -7.83540 q^{83} +(0.358028 - 0.206708i) q^{84} +(4.14720 - 11.4595i) q^{85} +1.59024i q^{86} +(-0.896622 + 0.517665i) q^{87} +(-10.3365 - 5.96781i) q^{88} +(-10.6018 - 6.12093i) q^{89} +(-5.85021 + 4.92718i) q^{90} -0.203698i q^{92} +(0.203698 - 0.352814i) q^{93} +(7.29066 - 12.6278i) q^{94} +(4.47497 - 12.3653i) q^{95} +1.11018i q^{96} +(2.90292 + 5.02801i) q^{97} +(1.71029 + 2.96232i) q^{98} -11.1805i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{4} + 12 q^{9}+O(q^{10}) \) 24 * q - 8 * q^4 + 12 * q^9	\( 24 q - 8 q^{4} + 12 q^{9} - 14 q^{10} - 88 q^{14} - 32 q^{16} + 4 q^{25} + 36 q^{29} - 8 q^{30} + 20 q^{35} + 4 q^{36} + 140 q^{40} - 12 q^{49} - 48 q^{51} - 52 q^{55} + 32 q^{56} + 12 q^{61} + 24 q^{64} + 8 q^{66} + 48 q^{69} + 16 q^{74} - 4 q^{75} - 208 q^{79} + 28 q^{81} - 124 q^{90} + 112 q^{94} - 40 q^{95}+O(q^{100}) \) 24 * q - 8 * q^4 + 12 * q^9 - 14 * q^10 - 88 * q^14 - 32 * q^16 + 4 * q^25 + 36 * q^29 - 8 * q^30 + 20 * q^35 + 4 * q^36 + 140 * q^40 - 12 * q^49 - 48 * q^51 - 52 * q^55 + 32 * q^56 + 12 * q^61 + 24 * q^64 + 8 * q^66 + 48 * q^69 + 16 * q^74 - 4 * q^75 - 208 * q^79 + 28 * q^81 - 124 * q^90 + 112 * q^94 - 40 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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