LMFDB - Embedded newform 845.2.n.e.484.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(484,845)]

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, 2]))

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

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

chi := DirichletCharacter("845.484");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.n (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:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
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} - 8x^{10} + 54x^{8} - 78x^{6} + 92x^{4} - 10x^{2} + 1 $ x^12 - 8x^10 + 54x^8 - 78x^6 + 92x^4 - 10*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			484.5
Root			$1.02826 + 0.593667i$ of defining polynomial
Character	$\chi$	$=$	845.484
Dual form			845.2.n.e.529.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.02826 - 0.593667i) q^{2} +(0.298874 - 0.172555i) q^{3} +(-0.295120 + 0.511162i) q^{4} +(-1.44045 - 1.71029i) q^{5} +(0.204880 - 0.354863i) q^{6} +(-1.75765 - 1.01478i) q^{7} +3.07548i q^{8} +(-1.44045 + 2.49493i) q^{9} +O(q^{10})$	\(q+(1.02826 - 0.593667i) q^{2} +(0.298874 - 0.172555i) q^{3} +(-0.295120 + 0.511162i) q^{4} +(-1.44045 - 1.71029i) q^{5} +(0.204880 - 0.354863i) q^{6} +(-1.75765 - 1.01478i) q^{7} +3.07548i q^{8} +(-1.44045 + 2.49493i) q^{9} +(-2.49650 - 0.903481i) q^{10} +(1.94045 + 3.36096i) q^{11} +0.203698i q^{12} -2.40976 q^{14} +(-0.725633 - 0.262606i) q^{15} +(1.23557 + 2.14007i) q^{16} +(-4.71996 - 2.72507i) q^{17} +3.42059i q^{18} +(-2.94045 + 5.09301i) q^{19} +(1.29934 - 0.231562i) q^{20} -0.700420 q^{21} +(3.99058 + 2.30396i) q^{22} +(-0.298874 + 0.172555i) q^{23} +(0.530689 + 0.919180i) q^{24} +(-0.850210 + 4.92718i) q^{25} +2.02956i q^{27} +(1.03743 - 0.598962i) q^{28} +(1.50000 + 2.59808i) q^{29} +(-0.902040 + 0.160757i) q^{30} -1.18048 q^{31} +(-2.78591 - 1.60845i) q^{32} +(1.15990 + 0.669668i) q^{33} -6.47114 q^{34} +(0.796234 + 4.46783i) q^{35} +(-0.850210 - 1.47261i) q^{36} +(4.71996 - 2.72507i) q^{37} +6.98259i q^{38} +(5.25997 - 4.43007i) q^{40} +(0.0902394 + 0.156299i) q^{41} +(-0.720215 + 0.415816i) q^{42} +(1.15990 + 0.669668i) q^{43} -2.29066 q^{44} +(6.34196 - 1.13023i) q^{45} +(-0.204880 + 0.354863i) q^{46} +12.2807i q^{47} +(0.738559 + 0.426407i) q^{48} +(-1.44045 - 2.49493i) q^{49} +(2.05087 + 5.57117i) q^{50} -1.88090 q^{51} +2.42636i q^{53} +(1.20488 + 2.08691i) q^{54} +(2.95310 - 8.16003i) q^{55} +(3.12093 - 5.40561i) q^{56} +2.02956i q^{57} +(3.08478 + 1.78100i) q^{58} +(3.53069 - 6.11533i) q^{59} +(0.348383 - 0.293416i) q^{60} +(-3.38090 + 5.85589i) q^{61} +(-1.21384 + 0.700811i) q^{62} +(5.06361 - 2.92347i) q^{63} -8.76180 q^{64} +1.59024 q^{66} +(-3.81417 + 2.20211i) q^{67} +(2.78591 - 1.60845i) q^{68} +(-0.0595504 + 0.103144i) q^{69} +(3.47114 + 4.12140i) q^{70} +(-0.940450 + 1.62891i) q^{71} +(-7.67311 - 4.43007i) q^{72} -8.86014i q^{73} +(3.23557 - 5.60417i) q^{74} +(0.596104 + 1.61932i) q^{75} +(-1.73557 - 3.00609i) q^{76} -7.87651i q^{77} -11.1805 q^{79} +(1.88037 - 5.19585i) q^{80} +(-3.97114 - 6.87821i) q^{81} +(0.185579 + 0.107144i) q^{82} -7.83540i q^{83} +(0.206708 - 0.358028i) q^{84} +(2.13820 + 11.9979i) q^{85} +1.59024 q^{86} +(0.896622 + 0.517665i) q^{87} +(-10.3365 + 5.96781i) q^{88} +(-6.12093 - 10.6018i) q^{89} +(5.85021 - 4.92718i) q^{90} -0.203698i q^{92} +(-0.352814 + 0.203698i) q^{93} +(7.29066 + 12.6278i) q^{94} +(12.9461 - 2.30719i) q^{95} -1.11018 q^{96} +(5.02801 + 2.90292i) q^{97} +(-2.96232 - 1.71029i) q^{98} -11.1805 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{4} + 6 q^{5} + 10 q^{6} + 6 q^{9}+O(q^{10}) $ 12 * q + 4 * q^4 + 6 * q^5 + 10 * q^6 + 6 * q^9	$ 12 q + 4 q^{4} + 6 q^{5} + 10 q^{6} + 6 q^{9} + 7 q^{10} - 44 q^{14} + 4 q^{15} - 16 q^{16} - 12 q^{19} + q^{20} + 8 q^{21} - 32 q^{24} - 2 q^{25} + 18 q^{29} + 4 q^{30} + 16 q^{31} - 16 q^{34} + 10 q^{35} - 2 q^{36} + 70 q^{40} - 14 q^{41} + 4 q^{44} + 29 q^{45} - 10 q^{46} + 6 q^{49} + 31 q^{50} + 24 q^{51} + 22 q^{54} - 26 q^{55} - 16 q^{56} + 4 q^{59} + 96 q^{60} + 6 q^{61} - 12 q^{64} + 4 q^{66} - 24 q^{69} - 20 q^{70} + 12 q^{71} + 8 q^{74} + 2 q^{75} + 10 q^{76} - 104 q^{79} - 33 q^{80} + 14 q^{81} - 90 q^{84} - 21 q^{85} + 4 q^{86} - 20 q^{89} + 62 q^{90} + 56 q^{94} + 20 q^{95} - 12 q^{96} - 104 q^{99}+O(q^{100}) $ 12 * q + 4 * q^4 + 6 * q^5 + 10 * q^6 + 6 * q^9 + 7 * q^10 - 44 * q^14 + 4 * q^15 - 16 * q^16 - 12 * q^19 + q^20 + 8 * q^21 - 32 * q^24 - 2 * q^25 + 18 * q^29 + 4 * q^30 + 16 * q^31 - 16 * q^34 + 10 * q^35 - 2 * q^36 + 70 * q^40 - 14 * q^41 + 4 * q^44 + 29 * q^45 - 10 * q^46 + 6 * q^49 + 31 * q^50 + 24 * q^51 + 22 * q^54 - 26 * q^55 - 16 * q^56 + 4 * q^59 + 96 * q^60 + 6 * q^61 - 12 * q^64 + 4 * q^66 - 24 * q^69 - 20 * q^70 + 12 * q^71 + 8 * q^74 + 2 * q^75 + 10 * q^76 - 104 * q^79 - 33 * q^80 + 14 * q^81 - 90 * q^84 - 21 * q^85 + 4 * q^86 - 20 * q^89 + 62 * q^90 + 56 * q^94 + 20 * q^95 - 12 * q^96 - 104 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	1.02826	−	0.593667i	0.727090	−	0.419786i	−0.0902665	−	0.995918i	$-0.528772\pi$
$2$	1.02826	−	0.593667i	0.727090	−	0.419786i	0.817357	+	0.576132i	$0.195439\pi$
$3$	0.298874	−	0.172555i	0.172555	−	0.0996247i	−0.411235	−	0.911529i	$-0.634902\pi$
$3$	0.298874	−	0.172555i	0.172555	−	0.0996247i	0.583790	+	0.811905i	$0.301569\pi$
$4$	−0.295120	+	0.511162i	−0.147560	+	0.255581i
$5$	−1.44045	−	1.71029i	−0.644189	−	0.764867i
$5$	−1.44045	−	1.71029i	−0.644189	−	0.764867i
$6$	0.204880	−	0.354863i	0.0836420	−	0.144872i
$7$	−1.75765	−	1.01478i	−0.664328	−	0.383550i	0.129596	−	0.991567i	$-0.458632\pi$
$7$	−1.75765	−	1.01478i	−0.664328	−	0.383550i	−0.793924	+	0.608017i	$0.791965\pi$
$8$			3.07548i			1.08735i
$9$	−1.44045	+	2.49493i	−0.480150	+	0.831644i
$10$	−2.49650	−	0.903481i	−0.789463	−	0.285706i
$11$	1.94045	+	3.36096i	0.585068	+	1.01337i	0.994867	+	0.101191i	$0.0322653\pi$
$11$	1.94045	+	3.36096i	0.585068	+	1.01337i	−0.409799	+	0.912176i	$0.634401\pi$
$12$			0.203698i			0.0588024i
$13$		0			0
$13$		0			0
$14$	−2.40976			−0.644036
$15$	−0.725633	−	0.262606i	−0.187358	−	0.0678045i
$16$	1.23557	+	2.14007i	0.308892	+	0.535017i
$17$	−4.71996	−	2.72507i	−1.14476	−	0.660927i	−0.197155	−	0.980372i	$-0.563170\pi$
$17$	−4.71996	−	2.72507i	−1.14476	−	0.660927i	−0.947605	+	0.319445i	$0.896503\pi$
$18$			3.42059i			0.806240i
$19$	−2.94045	+	5.09301i	−0.674585	+	1.16842i	0.302005	+	0.953306i	$0.402344\pi$
$19$	−2.94045	+	5.09301i	−0.674585	+	1.16842i	−0.976590	+	0.215110i	$0.930989\pi$
$20$	1.29934	−	0.231562i	0.290542	−	0.0517789i
$21$	−0.700420			−0.152844
$22$	3.99058	+	2.30396i	0.850794	+	0.491206i
$23$	−0.298874	+	0.172555i	−0.0623195	+	0.0359802i	−0.530836	−	0.847475i	$-0.678122\pi$
$23$	−0.298874	+	0.172555i	−0.0623195	+	0.0359802i	0.468516	+	0.883455i	$0.344789\pi$
$24$	0.530689	+	0.919180i	0.108326	+	0.187627i
$25$	−0.850210	+	4.92718i	−0.170042	+	0.985437i
$26$		0			0
$27$			2.02956i			0.390588i
$28$	1.03743	−	0.598962i	0.196056	−	0.113193i
$29$	1.50000	+	2.59808i	0.278543	+	0.482451i	0.971023	−	0.238987i	$-0.0768152\pi$
$29$	1.50000	+	2.59808i	0.278543	+	0.482451i	−0.692480	+	0.721437i	$0.743482\pi$
$30$	−0.902040	+	0.160757i	−0.164689	+	0.0293501i
$31$	−1.18048			−0.212020			−0.106010	−	0.994365i	$-0.533808\pi$
$31$	−1.18048			−0.212020			−0.106010	+	0.994365i	$0.533808\pi$
$32$	−2.78591	−	1.60845i	−0.492484	−	0.284336i
$33$	1.15990	+	0.669668i	0.201913	+	0.116574i
$34$	−6.47114			−1.10979
$35$	0.796234	+	4.46783i	0.134588	+	0.755201i
$36$	−0.850210	−	1.47261i	−0.141702	−	0.245435i
$37$	4.71996	−	2.72507i	0.775957	−	0.447999i	−0.0590384	−	0.998256i	$-0.518803\pi$
$37$	4.71996	−	2.72507i	0.775957	−	0.447999i	0.834996	+	0.550257i	$0.185470\pi$
$38$			6.98259i			1.13273i
$39$		0			0
$40$	5.25997	−	4.43007i	0.831674	−	0.700456i
$41$	0.0902394	+	0.156299i	0.0140930	+	0.0244098i	0.872986	−	0.487745i	$-0.162181\pi$
$41$	0.0902394	+	0.156299i	0.0140930	+	0.0244098i	−0.858893	+	0.512155i	$0.828847\pi$
$42$	−0.720215	+	0.415816i	−0.111132	+	0.0641618i
$43$	1.15990	+	0.669668i	0.176883	+	0.102123i	0.585827	−	0.810436i	$-0.300770\pi$
$43$	1.15990	+	0.669668i	0.176883	+	0.102123i	−0.408944	+	0.912559i	$0.634103\pi$
$44$	−2.29066			−0.345330
$45$	6.34196	−	1.13023i	0.945404	−	0.168485i
$46$	−0.204880	+	0.354863i	−0.0302079	+	0.0523217i
$47$			12.2807i			1.79133i	0.444731	+	0.895664i	$0.353299\pi$
$47$			12.2807i			1.79133i	−0.444731	+	0.895664i	$0.646701\pi$
$48$	0.738559	+	0.426407i	0.106602	+	0.0615466i
$49$	−1.44045	−	2.49493i	−0.205779	−	0.356419i
$50$	2.05087	+	5.57117i	0.290036	+	0.787883i
$51$	−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	$0.946707\pi$
$54$	1.20488	+	2.08691i	0.163963	+	0.283993i
$55$	2.95310	−	8.16003i	0.398197	−	1.10030i
$56$	3.12093	−	5.40561i	0.417052	−	0.722355i
$57$			2.02956i			0.268821i
$58$	3.08478	+	1.78100i	0.405052	+	0.233857i
$59$	3.53069	−	6.11533i	0.459657	−	0.796149i	−0.539286	−	0.842123i	$-0.681306\pi$
$59$	3.53069	−	6.11533i	0.459657	−	0.796149i	0.998943	+	0.0459741i	$0.0146392\pi$
$60$	0.348383	−	0.293416i	0.0449760	−	0.0378798i
$61$	−3.38090	+	5.85589i	−0.432880	+	0.749770i	−0.997120	−	0.0758409i	$-0.975836\pi$
$61$	−3.38090	+	5.85589i	−0.432880	+	0.749770i	0.564240	+	0.825611i	$0.309169\pi$
$62$	−1.21384	+	0.700811i	−0.154158	+	0.0890031i
$63$	5.06361	−	2.92347i	0.637954	−	0.368323i
$64$	−8.76180			−1.09522
$65$		0			0
$66$	1.59024			0.195745
$67$	−3.81417	+	2.20211i	−0.465975	+	0.269031i	−0.714553	−	0.699581i	$-0.753370\pi$
$67$	−3.81417	+	2.20211i	−0.465975	+	0.269031i	0.248578	+	0.968612i	$0.420037\pi$
$68$	2.78591	−	1.60845i	0.337841	−	0.195053i
$69$	−0.0595504	+	0.103144i	−0.00716903	+	0.0124171i
$70$	3.47114	+	4.12140i	0.414880	+	0.492601i
$71$	−0.940450	+	1.62891i	−0.111611	+	0.193316i	−0.916420	−	0.400218i	$-0.868934\pi$
$71$	−0.940450	+	1.62891i	−0.111611	+	0.193316i	0.804809	+	0.593534i	$0.202268\pi$
$72$	−7.67311	−	4.43007i	−0.904284	−	0.522089i
$73$		−	8.86014i		−	1.03700i	−0.855077	−	0.518501i	$-0.826490\pi$
$73$		−	8.86014i		−	1.03700i	0.855077	−	0.518501i	$-0.173510\pi$
$74$	3.23557	−	5.60417i	0.376127	−	0.651472i
$75$	0.596104	+	1.61932i	0.0688322	+	0.186982i
$76$	−1.73557	−	3.00609i	−0.199083	−	0.344823i
$77$		−	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	$0.716515\pi$
$80$	1.88037	−	5.19585i	0.210232	−	0.580913i
$81$	−3.97114	−	6.87821i	−0.441238	−	0.764246i
$82$	0.185579	+	0.107144i	0.0204938	+	0.0118321i
$83$		−	7.83540i		−	0.860047i	−0.902818	−	0.430024i	$-0.858505\pi$
$83$		−	7.83540i		−	0.860047i	0.902818	−	0.430024i	$-0.141495\pi$
$84$	0.206708	−	0.358028i	0.0225537	−	0.0390641i
$85$	2.13820	+	11.9979i	0.231920	+	1.30135i
$86$	1.59024			0.171480
$87$	0.896622	+	0.517665i	0.0961280	+	0.0554995i
$88$	−10.3365	+	5.96781i	−1.10188	+	0.636171i
$89$	−6.12093	−	10.6018i	−0.648817	−	1.12378i	−0.983406	−	0.181420i	$-0.941931\pi$
$89$	−6.12093	−	10.6018i	−0.648817	−	1.12378i	0.334589	−	0.942364i	$-0.391403\pi$
$90$	5.85021	−	4.92718i	0.616666	−	0.519371i
$91$		0			0
$92$		−	0.203698i		−	0.0212369i
$93$	−0.352814	+	0.203698i	−0.0365852	+	0.0211224i
$94$	7.29066	+	12.6278i	0.751974	+	1.30246i
$95$	12.9461	−	2.30719i	1.32824	−	0.236713i
$96$	−1.11018			−0.113307
$97$	5.02801	+	2.90292i	0.510517	+	0.294747i	0.733046	−	0.680179i	$-0.238098\pi$
$97$	5.02801	+	2.90292i	0.510517	+	0.294747i	−0.222529	+	0.974926i	$0.571431\pi$
$98$	−2.96232	−	1.71029i	−0.299239	−	0.172766i
$99$	−11.1805			−1.12368
$100$	−2.26768	−	1.88870i	−0.226768	−	0.188870i
$101$	2.97114	+	5.14616i	0.295639	+	0.512062i	0.975133	−	0.221619i	$-0.0711340\pi$
$101$	2.97114	+	5.14616i	0.295639	+	0.512062i	−0.679494	+	0.733681i	$0.737801\pi$
$102$	−1.93405	+	1.11663i	−0.191500	+	0.110563i
$103$		−	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
$106$	1.44045	+	2.49493i	0.139909	+	0.242329i
$107$	−15.3106	+	8.83959i	−1.48013	+	0.854555i	−0.999747	−	0.0225015i	$-0.992837\pi$
$107$	−15.3106	+	8.83959i	−1.48013	+	0.854555i	−0.480387	+	0.877057i	$0.659504\pi$
$108$	−1.03743	−	0.598962i	−0.0998270	−	0.0576352i
$109$	5.76180			0.551880			0.275940	−	0.961175i	$-0.411011\pi$
$109$	5.76180			0.551880			0.275940	+	0.961175i	$0.411011\pi$
$110$	−1.80777	−	10.1438i	−0.172365	−	0.967173i
$111$	0.940450	−	1.62891i	0.0892635	−	0.154609i
$112$		−	5.01532i		−	0.473903i
$113$	4.12222	+	2.37996i	0.387785	+	0.223888i	0.681200	−	0.732097i	$-0.261458\pi$
$113$	4.12222	+	2.37996i	0.387785	+	0.223888i	−0.293415	+	0.955985i	$0.594792\pi$
$114$	1.20488	+	2.08691i	0.112847	+	0.195457i
$115$	0.725633	+	0.262606i	0.0676656	+	0.0244881i
$116$	−1.77072			−0.164407
$117$		0			0
$118$		−	8.38421i		−	0.771829i
$119$	5.53069	+	9.57943i	0.506997	+	0.878145i
$120$	0.807638	−	2.23167i	0.0737269	−	0.203722i
$121$	−2.03069	+	3.51726i	−0.184608	+	0.319751i
$122$			8.02851i			0.726867i
$123$	0.0539404	+	0.0311425i	0.00486365	+	0.00280803i
$124$	0.348383	−	0.603416i	0.0312857	−	0.0541884i
$125$	9.65162	−	5.64325i	0.863267	−	0.504748i
$126$	3.47114	−	6.01219i	0.309234	−	0.535608i
$127$	14.4679	−	8.35307i	1.28382	−	0.741215i	0.306277	−	0.951942i	$-0.400917\pi$
$127$	14.4679	−	8.35307i	1.28382	−	0.741215i	0.977545	+	0.210728i	$0.0675833\pi$
$128$	−3.43760	+	1.98470i	−0.303844	+	0.175424i
$129$	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	$0.356093\pi$
$132$	−0.684619	+	0.395265i	−0.0595884	+	0.0344034i
$133$	10.3365	−	5.96781i	0.896292	−	0.517475i
$134$	−2.61464	+	4.52869i	−0.225871	+	0.391219i
$135$	3.47114	−	2.92347i	0.298748	−	0.251613i
$136$	8.38090	−	14.5161i	0.718656	−	1.24475i
$137$	−1.71288	−	0.988931i	−0.146341	−	0.0844901i	0.425042	−	0.905174i	$-0.360259\pi$
$137$	−1.71288	−	0.988931i	−0.146341	−	0.0844901i	−0.571383	+	0.820684i	$0.693593\pi$
$138$			0.141412i			0.0120378i
$139$	4.35021	−	7.53478i	0.368980	−	0.639092i	−0.620426	−	0.784265i	$-0.713040\pi$
$139$	4.35021	−	7.53478i	0.368980	−	0.639092i	0.989406	+	0.145173i	$0.0463737\pi$
$140$	−2.51877	−	0.911540i	−0.212875	−	0.0770392i
$141$	2.11910	+	3.67039i	0.178460	+	0.309103i
$142$			2.23325i			0.187411i
$143$		0			0
$144$	−7.11910			−0.593258
$145$	2.28280	−	6.30784i	0.189576	−	0.523837i
$146$	−5.25997	−	9.11054i	−0.435318	−	0.753993i
$147$	−0.861026	−	0.497113i	−0.0710162	−	0.0410012i
$148$			3.21689i			0.264427i
$149$	−11.1516	+	19.3152i	−0.913576	+	1.58236i	−0.104603	+	0.994514i	$0.533357\pi$
$149$	−11.1516	+	19.3152i	−0.913576	+	1.58236i	−0.808973	+	0.587846i	$0.799976\pi$
$150$	1.57428	+	1.31119i	0.128540	+	0.107058i
$151$	19.1626			1.55943			0.779717	−	0.626132i	$-0.215363\pi$
$151$	19.1626			1.55943			0.779717	+	0.626132i	$0.215363\pi$
$152$	−15.6634	−	9.04329i	−1.27047	−	0.733507i
$153$	13.5977	−	7.85066i	1.09931	−	0.634688i
$154$	−4.67602	−	8.09910i	−0.376804	−	0.652644i
$155$	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	$0.920387\pi$
$158$	−11.4964	+	6.63748i	−0.914608	+	0.528049i
$159$	0.418681	+	0.725176i	0.0332035	+	0.0575102i
$160$	1.26205	+	7.08161i	0.0997736	+	0.559850i
$161$	0.700420			0.0552008
$162$	−8.16673	−	4.71507i	−0.641639	−	0.370451i
$163$	10.3365	+	5.96781i	0.809621	+	0.467435i	0.846824	−	0.531873i	$-0.178512\pi$
$163$	10.3365	+	5.96781i	0.809621	+	0.467435i	−0.0372032	+	0.999308i	$0.511845\pi$
$164$	−0.106526			−0.00831826
$165$	−0.525447	−	2.94839i	−0.0409060	−	0.229532i
$166$	−4.65162	−	8.05684i	−0.361036	−	0.625332i
$167$	−1.75765	+	1.01478i	−0.136011	+	0.0785259i	−0.566461	−	0.824088i	$-0.691688\pi$
$167$	−1.75765	+	1.01478i	−0.136011	+	0.0785259i	0.430451	+	0.902614i	$0.358355\pi$
$168$		−	2.15413i		−	0.166195i
$169$		0			0
$170$	9.32135	+	11.0675i	0.714915	+	0.848842i
$171$	−8.47114	−	14.6724i	−0.647804	−	1.12203i
$172$	−0.684619	+	0.395265i	−0.0522017	+	0.0301387i
$173$	−1.15990	−	0.669668i	−0.0881855	−	0.0509139i	0.455259	−	0.890359i	$-0.349547\pi$
$173$	−1.15990	−	0.669668i	−0.0881855	−	0.0509139i	−0.543444	+	0.839445i	$0.682880\pi$
$174$	1.22928			0.0931916
$175$	6.49437	−	7.79748i	0.490928	−	0.589434i
$176$	−4.79512	+	8.30539i	−0.361446	+	0.626042i
$177$		−	2.43695i		−	0.183173i
$178$	−12.5878	−	7.26758i	−0.943497	−	0.544728i
$179$	10.1120	+	17.5145i	0.755807	+	1.30910i	0.944972	+	0.327151i	$0.106089\pi$
$179$	10.1120	+	17.5145i	0.755807	+	1.30910i	−0.189165	+	0.981945i	$0.560578\pi$
$180$	−1.29391	+	3.57533i	−0.0964421	+	0.266489i
$181$	19.8232			1.47345			0.736723	−	0.676195i	$-0.236372\pi$
$181$	19.8232			1.47345			0.736723	+	0.676195i	$0.236372\pi$
$182$		0			0
$183$			2.33356i			0.172502i
$184$	−0.530689	−	0.919180i	−0.0391229	−	0.0677629i
$185$	−11.4595	−	4.14720i	−0.842522	−	0.304908i
$186$	−0.241857	+	0.418908i	−0.0177338	+	0.0307159i
$187$		−	21.1515i		−	1.54675i
$188$	−6.27745	−	3.62429i	−0.457830	−	0.264328i
$189$	2.05955	−	3.56725i	0.149810	−	0.259479i
$190$	11.9423	−	10.0581i	0.866384	−	0.729689i
$191$	−0.768891	+	1.33176i	−0.0556350	+	0.0963626i	−0.892502	−	0.451044i	$-0.851052\pi$
$191$	−0.768891	+	1.33176i	−0.0556350	+	0.0963626i	0.836867	+	0.547407i	$0.184385\pi$
$192$	−2.61867	+	1.51189i	−0.188986	+	0.109111i
$193$	−18.3625	+	10.6016i	−1.32176	+	0.763118i	−0.984009	−	0.178117i	$-0.942999\pi$
$193$	−18.3625	+	10.6016i	−1.32176	+	0.763118i	−0.337750	+	0.941236i	$0.609666\pi$
$194$	6.89347			0.494923
$195$		0			0
$196$	1.70042			0.121459
$197$	−8.01675	+	4.62847i	−0.571170	+	0.329765i	−0.757616	−	0.652700i	$-0.773636\pi$
$197$	−8.01675	+	4.62847i	−0.571170	+	0.329765i	0.186447	+	0.982465i	$0.440303\pi$
$198$	−11.4964	+	6.63748i	−0.817017	+	0.471705i
$199$	−8.70225	+	15.0727i	−0.616886	+	1.06848i	0.373164	+	0.927765i	$0.378273\pi$
$199$	−8.70225	+	15.0727i	−0.616886	+	1.06848i	−0.990050	+	0.140713i	$0.955061\pi$
$200$	−15.1534	−	2.61480i	−1.07151	−	0.184894i
$201$	−0.759971	+	1.31631i	−0.0536042	+	0.0928452i
$202$	6.11021	+	3.52773i	0.429913	+	0.248210i
$203$		−	6.08867i		−	0.427341i
$204$	0.555090	−	0.961445i	0.0388641	−	0.0673146i
$205$	0.137332	−	0.379477i	0.00959171	−	0.0265038i
$206$	−3.81952	−	6.61560i	−0.266119	−	0.460931i
$207$		−	0.994227i		−	0.0691036i
$208$		0			0
$209$	−22.8232			−1.57871
$210$	1.74860	+	0.632817i	0.120665	+	0.0436685i
$211$	3.64087	+	6.30617i	0.250648	+	0.434135i	0.963704	−	0.266972i	$-0.0860231\pi$
$211$	3.64087	+	6.30617i	0.250648	+	0.434135i	−0.713057	+	0.701107i	$0.752690\pi$
$212$	−1.24026	−	0.716067i	−0.0851817	−	0.0491797i
$213$			0.649117i			0.0444768i
$214$	−10.4955	+	18.1788i	−0.717460	+	1.24268i
$215$	−0.525447	−	2.94839i	−0.0358352	−	0.201079i
$216$	−6.24186			−0.424705
$217$	2.07487	+	1.19792i	0.140851	+	0.0813204i
$218$	5.92463	−	3.42059i	0.401267	−	0.231671i
$219$	−1.52886	−	2.64807i	−0.103311	−	0.178940i
$220$	3.29958	+	3.91770i	0.222458	+	0.264131i
$221$		0			0
$222$		−	2.23325i		−	0.149886i
$223$	16.8589	−	9.73351i	1.12896	−	0.651804i	0.185285	−	0.982685i	$-0.440679\pi$
$223$	16.8589	−	9.73351i	1.12896	−	0.651804i	0.943672	+	0.330881i	$0.107346\pi$
$224$	3.26443	+	5.65416i	0.218114	+	0.377784i
$225$	−11.0683	−	9.21858i	−0.737887	−	0.614572i
$226$	5.65162			0.375940
$227$	−4.16698	−	2.40581i	−0.276572	−	0.159679i	0.355298	−	0.934753i	$-0.384379\pi$
$227$	−4.16698	−	2.40581i	−0.276572	−	0.159679i	−0.631871	+	0.775074i	$0.717713\pi$
$228$	−1.03743	−	0.598962i	−0.0687057	−	0.0396672i
$229$	1.52360			0.100682			0.0503410	−	0.998732i	$-0.483969\pi$
$229$	1.52360			0.100682			0.0503410	+	0.998732i	$0.483969\pi$
$230$	0.902040	−	0.160757i	0.0594787	−	0.0106000i
$231$	−1.35913	−	2.35408i	−0.0894242	−	0.154887i
$232$	−7.99033	+	4.61322i	−0.524591	+	0.302873i
$233$		−	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
$236$	2.08395	+	3.60951i	0.135654	+	0.234959i
$237$	−3.34155	+	1.92925i	−0.217057	+	0.125318i
$238$	11.3740	+	6.56677i	0.737266	+	0.425661i
$239$	4.00000			0.258738			0.129369	−	0.991596i	$-0.458705\pi$
$239$	4.00000			0.258738			0.129369	+	0.991596i	$0.458705\pi$
$240$	−0.334575	−	1.87737i	−0.0215967	−	0.121184i
$241$	−8.73294	+	15.1259i	−0.562538	+	0.974344i	0.434736	+	0.900558i	$0.356842\pi$
$241$	−8.73294	+	15.1259i	−0.562538	+	0.974344i	−0.997274	+	0.0737864i	$0.976492\pi$
$242$			4.82221i			0.309983i
$243$	−7.64668	−	4.41481i	−0.490535	−	0.283210i
$244$	−1.99554	−	3.45638i	−0.127751	−	0.221272i
$245$	−2.19217	+	6.05742i	−0.140053	+	0.386994i
$246$	0.0739531			0.00471508
$247$		0			0
$248$		−	3.63054i		−	0.230539i
$249$	−1.35204	−	2.34180i	−0.0856819	−	0.148405i
$250$	6.57417	−	11.5326i	0.415787	−	0.729384i
$251$	−4.64979	+	8.05367i	−0.293492	+	0.508343i	−0.974633	−	0.223809i	$-0.928151\pi$
$251$	−4.64979	+	8.05367i	−0.293492	+	0.508343i	0.681141	+	0.732152i	$0.261484\pi$
$252$			3.45110i			0.217399i
$253$	−1.15990	−	0.669668i	−0.0729223	−	0.0421017i
$254$	9.91788	−	17.1783i	0.622303	−	1.07786i
$255$	2.70934	+	3.21689i	0.169665	+	0.201449i
$256$	6.40530	−	11.0943i	0.400331	−	0.693394i
$257$	−9.43076	+	5.44485i	−0.588274	+	0.339640i	−0.764415	−	0.644725i	$-0.776972\pi$
$257$	−9.43076	+	5.44485i	−0.588274	+	0.339640i	0.176141	+	0.984365i	$0.443639\pi$
$258$	0.475281	−	0.274404i	0.0295897	−	0.0170836i
$259$	−11.0614			−0.687321
$260$		0			0
$261$	−8.64270			−0.534970
$262$	10.2826	−	5.93667i	0.635262	−	0.366769i
$263$	−11.6399	+	6.72031i	−0.717749	+	0.414392i	−0.813923	−	0.580972i	$-0.802673\pi$
$263$	−11.6399	+	6.72031i	−0.717749	+	0.414392i	0.0961749	+	0.995364i	$0.469339\pi$
$264$	−2.05955	+	3.56725i	−0.126757	+	0.219549i
$265$	4.14979	−	3.49505i	0.254920	−	0.214699i
$266$	7.08578	−	12.2729i	0.434457	−	0.752502i
$267$	−3.65877	−	2.11239i	−0.223913	−	0.129276i
$268$		−	2.59955i		−	0.158793i
$269$	1.83027	−	3.17012i	0.111593	−	0.193286i	−0.804819	−	0.593520i	$-0.797738\pi$
$269$	1.83027	−	3.17012i	0.111593	−	0.193286i	0.916413	+	0.400234i	$0.131071\pi$
$270$	1.83367	−	5.06679i	0.111593	−	0.308355i
$271$	11.0018	+	19.0557i	0.668313	+	1.15755i	0.978376	+	0.206837i	$0.0663168\pi$
$271$	11.0018	+	19.0557i	0.668313	+	1.15755i	−0.310062	+	0.950716i	$0.600350\pi$
$272$		−	13.4681i		−	0.816621i
$273$		0			0
$274$	−2.34838			−0.141871
$275$	−18.2098	+	6.70343i	−1.09809	+	0.404232i
$276$	−0.0351490	−	0.0608799i	−0.00211572	−	0.00366454i
$277$	8.56973	+	4.94774i	0.514905	+	0.297281i	0.734848	−	0.678232i	$-0.237254\pi$
$277$	8.56973	+	4.94774i	0.514905	+	0.297281i	−0.219943	+	0.975513i	$0.570587\pi$
$278$		−	10.3303i		−	0.619570i
$279$	1.70042	−	2.94521i	0.101801	−	0.176325i
$280$	−13.7407	+	2.44880i	−0.821165	+	0.146344i
$281$	−4.06138			−0.242281			−0.121141	−	0.992635i	$-0.538655\pi$
$281$	−4.06138			−0.242281			−0.121141	+	0.992635i	$0.538655\pi$
$282$	4.35798	+	2.51608i	0.259514	+	0.149830i
$283$	−5.27294	+	3.04434i	−0.313444	+	0.180967i	−0.648467	−	0.761243i	$-0.724589\pi$
$283$	−5.27294	+	3.04434i	−0.313444	+	0.180967i	0.335023	+	0.942210i	$0.391256\pi$
$284$	−0.555090	−	0.961445i	−0.0329386	−	0.0570513i
$285$	3.47114	−	2.92347i	0.205613	−	0.173172i
$286$		0			0
$287$		−	0.366292i		−	0.0216215i
$288$	8.02592	−	4.63377i	0.472932	−	0.273047i
$289$	6.35204	+	11.0021i	0.373649	+	0.647180i
$290$	−1.39744	−	7.84133i	−0.0820605	−	0.460458i
$291$	2.00366			0.117456
$292$	4.52897	+	2.61480i	0.265038	+	0.153020i
$293$	−8.48019	−	4.89604i	−0.495418	−	0.286030i	0.231401	−	0.972858i	$-0.425669\pi$
$293$	−8.48019	−	4.89604i	−0.495418	−	0.286030i	−0.726819	+	0.686829i	$0.759002\pi$
$294$	−1.18048			−0.0688469
$295$	−15.5448	+	2.77031i	−0.905053	+	0.161294i
$296$	8.38090	+	14.5161i	0.487130	+	0.843734i
$297$	−6.82125	+	3.93825i	−0.395809	+	0.228521i
$298$			26.4814i			1.53402i
$299$		0			0
$300$	−1.00366	−	0.173186i	−0.0579461	−	0.00999888i
$301$	−1.35913	−	2.35408i	−0.0783390	−	0.135687i
$302$	19.7042	−	11.3762i	1.13385	−	0.654628i
$303$	1.77599	+	1.02537i	0.102028	+	0.0589059i
$304$	−14.5325			−0.833497
$305$	14.8853	−	2.65278i	0.852330	−	0.151898i
$306$	9.32135	−	16.1450i	0.532866	−	0.922951i
$307$		−	22.1046i		−	1.26158i	−0.775955	−	0.630788i	$-0.782732\pi$
$307$		−	22.1046i		−	1.26158i	0.775955	−	0.630788i	$-0.217268\pi$
$308$	4.02617	+	2.32451i	0.229412	+	0.132451i
$309$	−1.11018	−	1.92289i	−0.0631560	−	0.109389i
$310$	2.94707	+	1.06654i	0.167382	+	0.0605754i
$311$	7.63904			0.433170			0.216585	−	0.976264i	$-0.430508\pi$
$311$	7.63904			0.433170			0.216585	+	0.976264i	$0.430508\pi$
$312$		0			0
$313$			26.1425i			1.47766i	0.673891	+	0.738831i	$0.264622\pi$
$313$			26.1425i			1.47766i	−0.673891	+	0.738831i	$0.735378\pi$
$314$	3.68231	+	6.37794i	0.207805	+	0.359928i
$315$	−12.2939	−	4.44914i	−0.692681	−	0.250680i
$316$	3.29958	−	5.71504i	0.185616	−	0.321496i
$317$			11.8428i			0.665159i	0.943075	+	0.332580i	$0.107919\pi$
$317$			11.8428i			0.665159i	−0.943075	+	0.332580i	$0.892081\pi$
$318$	0.861026	+	0.497113i	0.0482839	+	0.0278767i
$319$	−5.82135	+	10.0829i	−0.325933	+	0.564532i
$320$	12.6209	+	14.9852i	0.705531	+	0.837701i
$321$	−3.05063	+	5.28385i	−0.170270	+	0.294916i
$322$	0.720215	−	0.415816i	0.0401360	−	0.0231725i
$323$	27.7576	−	16.0259i	1.54448	−	0.891704i
$324$	4.68785			0.260436
$325$		0			0
$326$	14.1716			0.784890
$327$	1.72205	−	0.994227i	0.0952297	−	0.0549809i
$328$	−0.480695	+	0.277529i	−0.0265419	+	0.0153240i
$329$	12.4622	−	21.5852i	0.687064	−	1.19003i
$330$	−2.29066	−	2.71978i	−0.126097	−	0.149719i
$331$	−6.35021	+	10.9989i	−0.349039	+	0.604553i	−0.986079	−	0.166277i	$-0.946825\pi$
$331$	−6.35021	+	10.9989i	−0.349039	+	0.604553i	0.637040	+	0.770831i	$0.280159\pi$
$332$	4.00516	+	2.31238i	0.219812	+	0.126908i
$333$			15.7013i			0.860427i
$334$	−1.20488	+	2.08691i	−0.0659281	+	0.114191i
$335$	9.26038	+	3.35132i	0.505948	+	0.183102i
$336$	−0.865418	−	1.49895i	−0.0472124	−	0.0817743i
$337$			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
$340$	−6.76387	−	2.44784i	−0.366823	−	0.132753i
$341$	−2.29066	−	3.96754i	−0.124046	−	0.214854i
$342$	−17.4211	−	10.0581i	−0.942024	−	0.543878i
$343$			20.0538i			1.08281i
$344$	−2.05955	+	3.56725i	−0.111044	+	0.192333i
$345$	0.262187	−	0.0467255i	0.0141157	−	0.00251562i
$346$	−1.59024			−0.0854918
$347$	10.5998	+	6.11981i	0.569029	+	0.328529i	0.756761	−	0.653691i	$-0.226781\pi$
$347$	10.5998	+	6.11981i	0.569029	+	0.328529i	−0.187733	+	0.982220i	$0.560114\pi$
$348$	−0.529222	+	0.305546i	−0.0283693	+	0.0163790i
$349$	−9.35021	−	16.1950i	−0.500505	−	0.866901i	−1.00000		0.000583538i	$-0.999814\pi$
$349$	−9.35021	−	16.1950i	−0.500505	−	0.866901i	0.499495	−	0.866317i	$-0.333519\pi$
$350$	2.04880	−	11.8733i	0.109513	−	0.634656i
$351$		0			0
$352$		−	12.4844i		−	0.665422i
$353$	−1.13348	+	0.654413i	−0.0603288	+	0.0348309i	−0.529861	−	0.848084i	$-0.677756\pi$
$353$	−1.13348	+	0.654413i	−0.0603288	+	0.0348309i	0.469532	+	0.882915i	$0.344423\pi$
$354$	−1.44674	−	2.50582i	−0.0768932	−	0.133183i
$355$	4.14058	−	0.737912i	0.219759	−	0.0391643i
$356$	7.22563			0.382957
$357$	3.30596	+	1.90870i	0.174970	+	0.101019i
$358$	20.7956	+	12.0063i	1.09908	+	0.634554i
$359$	−29.4082			−1.55210			−0.776051	−	0.630670i	$-0.782780\pi$
$359$	−29.4082			−1.55210			−0.776051	+	0.630670i	$0.782780\pi$
$360$	3.47600	+	19.5046i	0.183201	+	1.02798i
$361$	−7.79249	−	13.4970i	−0.410131	−	0.710368i
$362$	20.3834	−	11.7684i	1.07133	−	0.618531i
$363$			1.40162i			0.0735661i
$364$		0			0
$365$	−15.1534	+	12.7626i	−0.793168	+	0.668024i
$366$	1.38536	+	2.39951i	0.0724139	+	0.125425i
$367$	28.9531	−	16.7161i	1.51134	−	0.872573i	0.511429	−	0.859326i	$-0.329116\pi$
$367$	28.9531	−	16.7161i	1.51134	−	0.872573i	0.999912	−	0.0132473i	$-0.00421687\pi$
$368$	−0.738559	−	0.426407i	−0.0385001	−	0.0222280i
$369$	−0.519941			−0.0270671
$370$	−14.2455	+	2.53875i	−0.740586	+	0.131983i
$371$	2.46222	−	4.26469i	0.127832	−	0.221412i
$372$		−	0.240461i		−	0.0124673i
$373$	29.8589	+	17.2391i	1.54604	+	0.892604i	0.998438	+	0.0558628i	$0.0177909\pi$
$373$	29.8589	+	17.2391i	1.54604	+	0.892604i	0.547598	+	0.836742i	$0.315542\pi$
$374$	−12.5569	−	21.7492i	−0.649303	−	1.12463i
$375$	1.91085	−	3.35206i	0.0986757	−	0.173099i
$376$	−37.7691			−1.94779
$377$		0			0
$378$		−	4.89075i		−	0.251553i
$379$	8.70225	+	15.0727i	0.447004	+	0.774234i	0.998189	−	0.0601487i	$-0.0191575\pi$
$379$	8.70225	+	15.0727i	0.447004	+	0.774234i	−0.551185	+	0.834383i	$0.685824\pi$
$380$	−2.64130	+	7.29846i	−0.135496	+	0.374403i
$381$	2.88273	−	4.99303i	0.147687	−	0.255801i
$382$			1.82586i			0.0934191i
$383$	1.51271	+	0.873366i	0.0772961	+	0.0446269i	0.538150	−	0.842849i	$-0.319123\pi$
$383$	1.51271	+	0.873366i	0.0772961	+	0.0446269i	−0.460854	+	0.887476i	$0.652457\pi$
$384$	−0.684939	+	1.18635i	−0.0349531	+	0.0605406i
$385$	−13.4711	+	11.3457i	−0.686553	+	0.578231i
$386$	−12.5876	+	21.8024i	−0.640692	+	1.10971i
$387$	−3.34155	+	1.92925i	−0.169861	+	0.0980692i
$388$	−2.96773	+	1.71342i	−0.150664	+	0.0869857i
$389$	−22.0435			−1.11765			−0.558826	−	0.829285i	$-0.688748\pi$
$389$	−22.0435			−1.11765			−0.558826	+	0.829285i	$0.688748\pi$
$390$		0			0
$391$	1.88090			0.0951212
$392$	7.67311	−	4.43007i	0.387550	−	0.223752i
$393$	2.98874	−	1.72555i	0.150762	−	0.0870425i
$394$	−5.49554	+	9.51855i	−0.276861	+	0.479538i
$395$	16.1049	+	19.1219i	0.810326	+	0.962127i
$396$	3.29958	−	5.71504i	0.165810	−	0.287192i
$397$	19.5132	+	11.2660i	0.979339	+	0.565422i	0.902071	−	0.431588i	$-0.142047\pi$
$397$	19.5132	+	11.2660i	0.979339	+	0.565422i	0.0772687	+	0.997010i	$0.475380\pi$
$398$			20.6649i			1.03584i
$399$	2.05955	−	3.56725i	0.103106	−	0.178586i
$400$	−11.5950	+	4.26837i	−0.579750	+	0.213418i
$401$	−1.85204	−	3.20782i	−0.0924863	−	0.160191i	0.816070	−	0.577953i	$-0.196148\pi$
$401$	−1.85204	−	3.20782i	−0.0924863	−	0.160191i	−0.908557	+	0.417761i	$0.862815\pi$
$402$			1.80468i			0.0900091i
$403$		0			0
$404$	−3.50737			−0.174498
$405$	−6.04354	+	16.6995i	−0.300306	+	0.829807i
$406$	−3.61464	−	6.26074i	−0.179392	−	0.310715i
$407$	18.3177	+	10.5757i	0.907975	+	0.524220i
$408$		−	5.78466i		−	0.286384i
$409$	6.74186	−	11.6772i	0.333363	−	0.577402i	−0.649806	−	0.760100i	$-0.725150\pi$
$409$	6.74186	−	11.6772i	0.333363	−	0.577402i	0.983169	+	0.182698i	$0.0584831\pi$
$410$	−0.0840695	−	0.471731i	−0.00415190	−	0.0232971i
$411$	−0.682580			−0.0336692
$412$	3.28871	+	1.89874i	0.162023	+	0.0935440i
$413$	−12.4114	+	7.16573i	−0.610726	+	0.352603i
$414$	−0.590239	−	1.02232i	−0.0290087	−	0.0502445i
$415$	−13.4008	+	11.2865i	−0.657821	+	0.554033i
$416$		0			0
$417$		−	3.00260i		−	0.147038i
$418$	−23.4682	+	13.5494i	−1.14787	+	0.662721i
$419$	8.41159	+	14.5693i	0.410933	+	0.711757i	0.994992	−	0.0999544i	$-0.0318697\pi$
$419$	8.41159	+	14.5693i	0.410933	+	0.711757i	−0.584059	+	0.811711i	$0.698536\pi$
$420$	−0.910086	+	0.162191i	−0.0444077	+	0.00791410i
$421$	−17.1013			−0.833464			−0.416732	−	0.909029i	$-0.636825\pi$
$421$	−17.1013			−0.833464			−0.416732	+	0.909029i	$0.636825\pi$
$422$	7.48753	+	4.32293i	0.364487	+	0.210437i
$423$	−30.6396	−	17.6898i	−1.48975	−	0.860106i
$424$	−7.46222			−0.362397
$425$	17.4399	−	20.9392i	0.845959	−	1.01570i
$426$	0.385359	+	0.667462i	0.0186707	+	0.0323386i
$427$	11.8849	−	6.86173i	0.575149	−	0.332062i
$428$		−	10.4349i		−	0.504392i
$429$		0			0
$430$	−2.29066	−	2.71978i	−0.110465	−	0.131159i
$431$	4.83027	+	8.36627i	0.232666	+	0.402989i	0.958592	−	0.284784i	$-0.0919218\pi$
$431$	4.83027	+	8.36627i	0.232666	+	0.402989i	−0.725926	+	0.687773i	$0.758588\pi$
$432$	−4.34339	+	2.50766i	−0.208972	+	0.120650i
$433$	−21.4538	−	12.3863i	−1.03100	−	0.595249i	−0.113730	−	0.993512i	$-0.536280\pi$
$433$	−21.4538	−	12.3863i	−1.03100	−	0.595249i	−0.917272	+	0.398262i	$0.869613\pi$
$434$	2.84467			0.136549
$435$	−0.406180	−	2.27916i	−0.0194748	−	0.109277i
$436$	−1.70042	+	2.94521i	−0.0814354	+	0.141050i
$437$		−	2.02956i		−	0.0970869i
$438$	−3.14414	−	1.81527i	−0.150233	−	0.0867369i
$439$	3.53069	+	6.11533i	0.168511	+	0.291869i	0.937896	−	0.346915i	$-0.112771\pi$
$439$	3.53069	+	6.11533i	0.168511	+	0.291869i	−0.769386	+	0.638784i	$0.779438\pi$
$440$	25.0960	+	9.08221i	1.19640	+	0.432977i
$441$	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	$-0.362778\pi$
$444$	0.555090	+	0.961445i	0.0263434	+	0.0456282i
$445$	−9.31523	+	25.7399i	−0.441584	+	1.22019i
$446$	11.5569	−	20.0172i	0.547236	−	0.947840i
$447$			7.69707i			0.364059i
$448$	15.4002	+	8.89128i	0.727589	+	0.420074i
$449$	6.24003	−	10.8080i	0.294485	−	0.510063i	−0.680380	−	0.732860i	$-0.738185\pi$
$449$	6.24003	−	10.8080i	0.294485	−	0.510063i	0.974865	+	0.222796i	$0.0715185\pi$
$450$	−16.8539	−	2.90822i	−0.794499	−	0.137095i
$451$	−0.350210	+	0.606582i	−0.0164908	+	0.0285628i
$452$	−2.43309	+	1.40475i	−0.114443	+	0.0660738i
$453$	5.72721	−	3.30661i	0.269088	−	0.155358i
$454$	−5.71300			−0.268124
$455$		0			0
$456$	−6.24186			−0.292302
$457$	7.12930	−	4.11610i	0.333495	−	0.192543i	−0.323897	−	0.946092i	$-0.604993\pi$
$457$	7.12930	−	4.11610i	0.333495	−	0.192543i	0.657392	+	0.753549i	$0.271660\pi$
$458$	1.56665	−	0.904508i	0.0732050	−	0.0422649i
$459$	5.53069	−	9.57943i	0.258150	−	0.447130i
$460$	−0.348383	+	0.293416i	−0.0162434	+	0.0136806i
$461$	−2.27072	+	3.93300i	−0.105758	+	0.183178i	−0.914048	−	0.405607i	$-0.867060\pi$
$461$	−2.27072	+	3.93300i	−0.105758	+	0.183178i	0.808290	+	0.588785i	$0.200394\pi$
$462$	−2.79508	−	1.61374i	−0.130039	−	0.0750780i
$463$			1.98845i			0.0924113i	0.998932	+	0.0462056i	$0.0147130\pi$
$463$			1.98845i			0.0924113i	−0.998932	+	0.0462056i	$0.985287\pi$
$464$	−3.70671	+	6.42021i	−0.172080	+	0.298051i
$465$	0.856594	+	0.310000i	0.0397236	+	0.0143759i
$466$	−8.29066	−	14.3598i	−0.384057	−	0.665207i
$467$			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
$470$	11.0954	−	30.6589i	0.511793	−	1.41419i
$471$	1.07030	+	1.85381i	0.0493167	+	0.0854191i
$472$	18.8076	+	10.8586i	0.865689	+	0.499806i
$473$			5.19783i			0.238997i
$474$	−2.29066	+	3.96754i	−0.105213	+	0.182235i
$475$	−22.5942	−	18.8183i	−1.03669	−	0.863441i
$476$	−6.52886			−0.299250
$477$	−6.05360	−	3.49505i	−0.277176	−	0.160027i
$478$	4.11304	−	2.37467i	0.188126	−	0.108615i
$479$	15.4027	+	26.6782i	0.703766	+	1.21896i	0.967135	+	0.254263i	$0.0818329\pi$
$479$	15.4027	+	26.6782i	0.703766	+	1.21896i	−0.263369	+	0.964695i	$0.584834\pi$
$480$	1.59916	+	1.89874i	0.0729913	+	0.0866650i
$481$		0			0
$482$			20.7378i			0.944582i
$483$	0.209337	−	0.120861i	0.00952518	−	0.00549937i
$484$	−1.19859	−	2.07602i	−0.0544815	−	0.0943647i
$485$	−2.27774	−	12.7809i	−0.103427	−	0.580350i
$486$	−10.4837			−0.475551
$487$	19.3341	+	11.1626i	0.876113	+	0.505824i	0.869375	−	0.494153i	$-0.164522\pi$
$487$	19.3341	+	11.1626i	0.876113	+	0.505824i	0.00673807	+	0.999977i	$0.497855\pi$
$488$	−18.0097	−	10.3979i	−0.815259	−	0.470690i
$489$	4.11910			0.186272
$490$	1.34196	+	7.53002i	0.0606236	+	0.340172i
$491$	−5.34129	−	9.25139i	−0.241049	−	0.417509i	0.719964	−	0.694011i	$-0.244158\pi$
$491$	−5.34129	−	9.25139i	−0.241049	−	0.417509i	−0.961013	+	0.276502i	$0.910825\pi$
$492$	−0.0318378	+	0.0183815i	−0.00143536	+	0.000828704i
$493$		−	16.3504i		−	0.736386i
$494$		0			0
$495$	16.1049	+	19.1219i	0.723862	+	0.859466i
$496$	−1.45856	−	2.52631i	−0.0654914	−	0.113434i
$497$	3.30596	−	1.90870i	0.148292	−	0.0856167i
$498$	−2.78049	−	1.60532i	−0.124597	−	0.0719361i
$499$	18.8195			0.842477			0.421239	−	0.906950i	$-0.361595\pi$
$499$	18.8195			0.842477			0.421239	+	0.906950i	$0.361595\pi$
$500$	0.0362348	+	6.59898i	0.00162047	+	0.295115i
$501$	−0.350210	+	0.606582i	−0.0156462	+	0.0271001i
$502$			11.0417i			0.492815i
$503$	4.92013	+	2.84064i	0.219378	+	0.126658i	0.605662	−	0.795722i	$-0.292908\pi$
$503$	4.92013	+	2.84064i	0.219378	+	0.126658i	−0.386284	+	0.922380i	$0.626242\pi$
$504$	8.99108	+	15.5730i	0.400495	+	0.693677i
$505$	4.52168	−	12.4943i	0.201212	−	0.555989i
$506$	−1.59024			−0.0706948
$507$		0			0
$508$			9.86062i			0.437494i
$509$	−13.9622	−	24.1833i	−0.618864	−	1.07190i	−0.989693	−	0.143203i	$-0.954260\pi$
$509$	−13.9622	−	24.1833i	−0.618864	−	1.07190i	0.370829	−	0.928701i	$-0.379074\pi$
$510$	4.69567	+	1.69936i	0.207928	+	0.0752488i
$511$	−8.99108	+	15.5730i	−0.397742	+	0.688909i
$512$		−	23.1492i		−	1.02306i
$513$	−10.3365	−	5.96781i	−0.456370	−	0.263485i
$514$	−6.46485	+	11.1975i	−0.285152	+	0.493898i
$515$	−11.0037	+	9.26754i	−0.484879	+	0.408376i
$516$	−0.136410	+	0.236269i	−0.00600511	+	0.0104011i
$517$	−41.2750	+	23.8301i	−1.81527	+	1.04805i
$518$	−11.3740	+	6.56677i	−0.499744	+	0.288527i
$519$	−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	$0.455934\pi$
$522$	−8.88695	+	5.13088i	−0.388971	+	0.224573i
$523$	19.7948	−	11.4285i	0.865567	−	0.499735i	−0.000305526	−	1.00000i	$-0.500097\pi$
$523$	19.7948	−	11.4285i	0.865567	−	0.499735i	0.865873	+	0.500265i	$0.166764\pi$
$524$	−2.95120	+	5.11162i	−0.128924	+	0.223302i
$525$	0.595504	−	3.45110i	0.0259899	−	0.150618i
$526$	−7.97925	+	13.8205i	−0.347912	+	0.602601i
$527$	5.57182	+	3.21689i	0.242712	+	0.140130i
$528$			3.30969i			0.144036i
$529$	−11.4404	+	19.8154i	−0.497411	+	0.861541i
$530$	2.19217	−	6.05742i	0.0952219	−	0.263117i
$531$	10.1716	+	17.6177i	0.441408	+	0.764541i
$532$			7.04487i			0.305434i
$533$		0			0
$534$	−5.01623			−0.217074
$535$	37.1725	+	13.4527i	1.60711	+	0.581610i
$536$	−6.77255	−	11.7304i	−0.292529	−	0.506676i
$537$	6.04443	+	3.48975i	0.260837	+	0.150594i
$538$		−	4.34628i		−	0.187381i
$539$	5.59024	−	9.68258i	0.240789	−	0.417058i
$540$	0.469969	+	2.63709i	0.0202242	+	0.113482i
$541$	9.48006			0.407580			0.203790	−	0.979015i	$-0.434674\pi$
$541$	9.48006			0.407580			0.203790	+	0.979015i	$0.434674\pi$
$542$	22.6255	+	13.0628i	0.971848	+	0.561097i
$543$	5.92463	−	3.42059i	0.254250	−	0.146791i
$544$	8.76626	+	15.1836i	0.375850	+	0.650992i
$545$	−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	$-0.253050\pi$
$548$	1.01101	−	0.583706i	0.0431882	−	0.0249347i
$549$	−9.74003	−	16.8702i	−0.415694	−	0.720004i
$550$	−14.7449	+	17.7035i	−0.628723	+	0.754878i
$551$	−17.6427			−0.751604
$552$	−0.317218	−	0.183146i	−0.0135017	−	0.00779521i
$553$	19.6513	+	11.3457i	0.835660	+	0.482469i
$554$	11.7492			0.499177
$555$	−4.14058	+	0.737912i	−0.175758	+	0.0313226i
$556$	2.56767	+	4.44733i	0.108893	+	0.188609i
$557$	−32.7053	+	18.8824i	−1.38577	+	0.800073i	−0.992835	−	0.119495i	$-0.961873\pi$
$557$	−32.7053	+	18.8824i	−1.38577	+	0.800073i	−0.392932	+	0.919567i	$0.628539\pi$
$558$		−	4.03793i		−	0.170939i
$559$		0			0
$560$	−8.57766	+	7.22431i	−0.362472	+	0.305283i
$561$	−3.64979	−	6.32162i	−0.154094	−	0.266899i
$562$	−4.17616	+	2.41110i	−0.176161	+	0.101706i
$563$	−22.4307	−	12.9504i	−0.945343	−	0.545794i	−0.0537120	−	0.998556i	$-0.517105\pi$
$563$	−22.4307	−	12.9504i	−0.945343	−	0.545794i	−0.891631	+	0.452762i	$0.850439\pi$
$564$	−2.50155			−0.105334
$565$	−1.86741	−	10.4784i	−0.0785625	−	0.440830i
$566$	−3.61464	+	6.26074i	−0.151935	+	0.263159i
$567$			16.1193i			0.676947i
$568$	−5.00967	−	2.89233i	−0.210201	−	0.121360i
$569$	−10.7725	−	18.6586i	−0.451609	−	0.782209i	0.546878	−	0.837213i	$-0.315816\pi$
$569$	−10.7725	−	18.6586i	−0.451609	−	0.782209i	−0.998486	+	0.0550035i	$0.982483\pi$
$570$	1.83367	−	5.06679i	0.0768038	−	0.212225i
$571$	−2.22036			−0.0929192			−0.0464596	−	0.998920i	$-0.514794\pi$
$571$	−2.22036			−0.0929192			−0.0464596	+	0.998920i	$0.514794\pi$
$572$		0			0
$573$			0.530704i			0.0221705i
$574$	−0.217455	−	0.376644i	−0.00907641	−	0.0157208i
$575$	−0.596104	−	1.61932i	−0.0248593	−	0.0675301i
$576$	12.6209	−	21.8601i	0.525872	−	0.910837i
$577$			6.20265i			0.258220i	0.991630	+	0.129110i	$0.0412120\pi$
$577$			6.20265i			0.258220i	−0.991630	+	0.129110i	$0.958788\pi$
$578$	13.0631	+	7.54199i	0.543353	+	0.313705i
$579$	−3.65871	+	6.33707i	−0.152051	+	0.263360i
$580$	2.55063	+	3.02845i	0.105909	+	0.125749i
$581$	−7.95120	+	13.7719i	−0.329871	+	0.571354i
$582$	2.06028	−	1.18950i	0.0854014	−	0.0493065i
$583$	−8.15489	+	4.70823i	−0.337741	+	0.194995i
$584$	27.2492			1.12758
$585$		0			0
$586$	−11.6265			−0.480285
$587$	1.58391	−	0.914469i	0.0653748	−	0.0377442i	−0.466956	−	0.884280i	$-0.654649\pi$
$587$	1.58391	−	0.914469i	0.0653748	−	0.0377442i	0.532331	+	0.846536i	$0.321316\pi$
$588$	0.508211	−	0.293416i	0.0209583	−	0.0121003i
$589$	3.47114	−	6.01219i	0.143026	−	0.247728i
$590$	−14.3395	+	12.0770i	−0.590346	+	0.497204i
$591$	−1.59733	+	2.76666i	−0.0657055	+	0.113805i
$592$	11.6637	+	6.73403i	0.479374	+	0.276767i
$593$		−	0.0728761i		−	0.00299266i	−0.999999	−	0.00149633i	$-0.999524\pi$
$593$		−	0.0728761i		−	0.00299266i	0.999999	−	0.00149633i	$-0.000476297\pi$
$594$	−4.67602	+	8.09910i	−0.191859	+	0.332310i
$595$	8.41697	−	23.2578i	0.345062	−	0.953477i
$596$	−6.58212	−	11.4006i	−0.269614	−	0.466986i
$597$			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	$0.403718\pi$
$600$	−4.98017	+	1.83331i	−0.203314	+	0.0748444i
$601$	22.2041	+	38.4586i	0.905723	+	1.56876i	0.819944	+	0.572444i	$0.194005\pi$
$601$	22.2041	+	38.4586i	0.905723	+	1.56876i	0.0857795	+	0.996314i	$0.472662\pi$
$602$	−2.79508	−	1.61374i	−0.113919	−	0.0657712i
$603$		−	12.6881i		−	0.516700i
$604$	−5.65527	+	9.79522i	−0.230110	+	0.398562i
$605$	8.94065	−	1.59336i	0.363489	−	0.0647791i
$606$	2.43491			0.0989115
$607$	−31.3808	−	18.1177i	−1.27371	−	0.735375i	−0.298024	−	0.954558i	$-0.596328\pi$
$607$	−31.3808	−	18.1177i	−1.27371	−	0.735375i	−0.975684	+	0.219183i	$0.929661\pi$
$608$	16.3836	−	9.45910i	0.664445	−	0.383617i
$609$	−1.05063	−	1.81975i	−0.0425737	−	0.0737398i
$610$	13.7311	−	11.5647i	0.555956	−	0.468239i
$611$		0			0
$612$			9.26754i			0.374618i
$613$	2.90838	−	1.67915i	0.117468	−	0.0678203i	−0.440115	−	0.897942i	$-0.645062\pi$
$613$	2.90838	−	1.67915i	0.117468	−	0.0678203i	0.557583	+	0.830121i	$0.311729\pi$
$614$	−13.1228	−	22.7293i	−0.529591	−	0.917279i
$615$	−0.0244356	−	0.137113i	−0.000985339	−	0.00552894i
$616$	24.2240			0.976013
$617$	−18.3441	−	10.5910i	−0.738507	−	0.426377i	0.0830194	−	0.996548i	$-0.473544\pi$
$617$	−18.3441	−	10.5910i	−0.738507	−	0.426377i	−0.821526	+	0.570171i	$0.806877\pi$
$618$	−2.28311	−	1.31815i	−0.0918402	−	0.0530240i
$619$	25.4082			1.02124			0.510620	−	0.859807i	$-0.329416\pi$
$619$	25.4082			1.02124			0.510620	+	0.859807i	$0.329416\pi$
$620$	−1.53385	+	0.273354i	−0.0616008	+	0.0109782i
$621$	−0.350210	−	0.606582i	−0.0140534	−	0.0243413i
$622$	7.85493	−	4.53504i	0.314954	−	0.181839i
$623$			24.8455i			0.995416i
$624$		0			0
$625$	−23.5543	−	8.37828i	−0.942171	−	0.335131i
$626$	15.5199	+	26.8813i	0.620302	+	1.07439i
$627$	−6.82125	+	3.93825i	−0.272415	+	0.157279i
$628$	−3.17056	−	1.83052i	−0.126519	−	0.0730459i
$629$	−29.7041			−1.18438
$630$	−15.2826	+	2.72359i	−0.608874	+	0.108510i
$631$	21.7725	−	37.7112i	0.866751	−	1.50126i	0.00145375	−	0.999999i	$-0.499537\pi$
$631$	21.7725	−	37.7112i	0.866751	−	1.50126i	0.865298	−	0.501258i	$-0.167129\pi$
$632$		−	34.3853i		−	1.36777i
$633$	2.17632	+	1.25650i	0.0865011	+	0.0499414i
$634$	7.03069	+	12.1775i	0.279224	+	0.483631i
$635$	−35.1265	−	12.7123i	−1.39395	−	0.504470i
$636$	−0.494244			−0.0195980
$637$		0			0
$638$			13.8238i			0.547288i
$639$	−2.70934	−	4.69272i	−0.107180	−	0.185641i
$640$	8.34610	+	3.02044i	0.329909	+	0.119394i
$641$	−24.1427	+	41.8164i	−0.953579	+	1.65165i	−0.215993	+	0.976395i	$0.569299\pi$
$641$	−24.1427	+	41.8164i	−0.953579	+	1.65165i	−0.737586	+	0.675253i	$0.764035\pi$
$642$			7.24423i			0.285907i
$643$	−36.6710	−	21.1720i	−1.44616	−	0.834943i	−0.447913	−	0.894077i	$-0.647833\pi$
$643$	−36.6710	−	21.1720i	−1.44616	−	0.834943i	−0.998250	+	0.0591344i	$0.981166\pi$
$644$	−0.206708	+	0.358028i	−0.00814543	+	0.0141083i
$645$	−0.665802	−	0.790529i	−0.0262159	−	0.0311271i
$646$	19.0281	−	32.9576i	0.748649	−	1.29670i
$647$	29.7958	−	17.2026i	1.17139	−	0.676305i	0.217386	−	0.976086i	$-0.430247\pi$
$647$	29.7958	−	17.2026i	1.17139	−	0.676305i	0.954008	+	0.299781i	$0.0969136\pi$
$648$	21.1538	−	12.2131i	0.830999	−	0.479778i
$649$	27.4045			1.07572
$650$		0			0
$651$	0.826831			0.0324061
$652$	−6.10104	+	3.52244i	−0.238935	+	0.137949i
$653$	−12.4114	+	7.16573i	−0.485696	+	0.280417i	−0.722787	−	0.691071i	$-0.757139\pi$
$653$	−12.4114	+	7.16573i	−0.485696	+	0.280417i	0.237091	+	0.971487i	$0.423806\pi$
$654$	1.18048	−	2.04465i	0.0461604	−	0.0799521i
$655$	−14.4045	−	17.1029i	−0.562830	−	0.668267i
$656$	−0.222994	+	0.386237i	−0.00870646	+	0.0150800i
$657$	22.1054	+	12.7626i	0.862416	+	0.497916i
$658$		−	29.5936i		−	1.15368i
$659$	11.4116	−	19.7655i	0.444532	−	0.769953i	−0.553487	−	0.832858i	$-0.686703\pi$
$659$	11.4116	−	19.7655i	0.444532	−	0.769953i	0.998020	+	0.0629051i	$0.0200365\pi$
$660$	1.66218	+	0.601540i	0.0647002	+	0.0234149i
$661$	7.20934	+	12.4869i	0.280411	+	0.485686i	0.971486	−	0.237097i	$-0.0761960\pi$
$661$	7.20934	+	12.4869i	0.280411	+	0.485686i	−0.691075	+	0.722783i	$0.742863\pi$
$662$			15.0796i			0.586087i
$663$		0			0
$664$	24.0976			0.935168
$665$	−25.0960	−	9.08221i	−0.973181	−	0.352193i
$666$	9.32135	+	16.1450i	0.361195	+	0.625608i
$667$	−0.896622	−	0.517665i	−0.0347173	−	0.0200441i
$668$		−	1.19792i		−	0.0463491i
$669$	3.35913	−	5.81818i	0.129871	−	0.224944i
$670$	11.5117	−	2.05155i	0.444734	−	0.0792582i
$671$	−26.2419			−1.01306
$672$	1.95131	+	1.12659i	0.0752733	+	0.0434591i
$673$	−29.5956	+	17.0871i	−1.14083	+	0.658657i	−0.946636	−	0.322306i	$-0.895542\pi$
$673$	−29.5956	+	17.0871i	−1.14083	+	0.658657i	−0.194193	+	0.980963i	$0.562209\pi$
$674$	9.07949	+	15.7261i	0.349729	+	0.605748i
$675$	−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	$-0.0358404\pi$
$678$	1.68912	−	0.975215i	0.0648703	−	0.0374529i
$679$	−5.89165	−	10.2046i	−0.226101	−	0.391618i
$680$	−36.8991	+	6.57597i	−1.41502	+	0.252177i
$681$	−1.66054			−0.0636319
$682$	−4.71079	−	2.71978i	−0.180386	−	0.104146i
$683$	−9.82834	−	5.67439i	−0.376071	−	0.217125i	0.300036	−	0.953928i	$-0.403001\pi$
$683$	−9.82834	−	5.67439i	−0.376071	−	0.217125i	−0.676107	+	0.736803i	$0.736334\pi$
$684$	10.0000			0.382360
$685$	0.775953	+	4.35403i	0.0296476	+	0.166359i
$686$	11.9053	+	20.6206i	0.454546	+	0.787298i
$687$	0.455363	−	0.262904i	0.0173732	−	0.0100304i
$688$			3.30969i			0.126181i
$689$		0			0
$690$	0.241857	−	0.203698i	0.00920733	−	0.00775463i
$691$	−9.41159	−	16.3013i	−0.358034	−	0.620133i	0.629599	−	0.776921i	$-0.283219\pi$
$691$	−9.41159	−	16.3013i	−0.358034	−	0.620133i	−0.987632	+	0.156788i	$0.949886\pi$
$692$	0.684619	−	0.395265i	0.0260253	−	0.0150257i
$693$	19.6513	+	11.3457i	0.746493	+	0.430988i
$694$	14.5325			0.551647
$695$	−19.1530	+	3.41334i	−0.726513	+	0.129475i
$696$	−1.59207	+	2.75754i	−0.0603471	+	0.104524i
$697$		−	0.983636i		−	0.0372579i
$698$	−19.2289	−	11.1018i	−0.727825	−	0.420210i
$699$	−2.40976	−	4.17383i	−0.0911455	−	0.157869i
$700$	2.06916	+	5.62087i	0.0782069	+	0.212449i
$701$	19.1626			0.723763			0.361881	−	0.932224i	$-0.382135\pi$
$701$	19.1626			0.723763			0.361881	+	0.932224i	$0.382135\pi$
$702$		0			0
$703$			32.0518i			1.20885i
$704$	−17.0018	−	29.4480i	−0.640780	−	1.10986i
$705$	3.22499	−	8.91130i	0.121460	−	0.335619i
$706$	−0.777006	+	1.34581i	−0.0292430	+	0.0506504i
$707$		−	12.0602i		−	0.453570i
$708$	1.24568	+	0.719193i	0.0468154	+	0.0270289i
$709$	−11.7419	+	20.3375i	−0.440975	+	0.763791i	−0.997762	−	0.0668645i	$-0.978700\pi$
$709$	−11.7419	+	20.3375i	−0.440975	+	0.763791i	0.556787	+	0.830655i	$0.312034\pi$
$710$	3.81952	−	3.21689i	0.143344	−	0.120728i
$711$	16.1049	−	27.8945i	0.603982	−	1.04613i
$712$	32.6055	−	18.8248i	1.22194	−	0.705488i
$713$	0.352814	−	0.203698i	0.0132130	−	0.00762853i
$714$	4.53252			0.169625
$715$		0			0
$716$	−11.9370			−0.446107
$717$	1.19550	−	0.690220i	0.0446466	−	0.0257767i
$718$	−30.2393	+	17.4586i	−1.12852	+	0.651551i
$719$	−7.05429	+	12.2184i	−0.263080	+	0.455669i	−0.967059	−	0.254553i	$-0.918072\pi$
$719$	−7.05429	+	12.2184i	−0.263080	+	0.455669i	0.703978	+	0.710221i	$0.251405\pi$
$720$	10.2547	+	12.1758i	0.382170	+	0.453764i
$721$	−6.52886	+	11.3083i	−0.243148	+	0.421144i
$722$	−16.0254	−	9.25228i	−0.596404	−	0.344334i
$723$			6.02765i			0.224171i
$724$	−5.85021	+	10.1329i	−0.217421	+	0.376585i
$725$	−14.0765	+	5.18187i	−0.522789	+	0.192450i
$726$	0.832096	+	1.44123i	0.0308820	+	0.0534892i
$727$		−	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
$730$	−8.00497	+	22.1194i	−0.296277	+	0.818674i
$731$	−3.64979	−	6.32162i	−0.134992	−	0.233814i
$732$	−1.19283	−	0.688681i	−0.0440883	−	0.0254544i
$733$			10.6692i			0.394074i	0.980396	+	0.197037i	$0.0631320\pi$
$733$			10.6692i			0.394074i	−0.980396	+	0.197037i	$0.936868\pi$
$734$	19.8476	−	34.3770i	0.732587	−	1.26888i
$735$	0.390054	+	2.18867i	0.0143874	+	0.0807305i
$736$	1.11018			0.0409218
$737$	−14.8024	−	8.54617i	−0.545254	−	0.314802i
$738$	−0.534635	+	0.308672i	−0.0196802	+	0.0113624i
$739$	0.707513	+	1.22545i	0.0260263	+	0.0450788i	0.878745	−	0.477291i	$-0.158381\pi$
$739$	0.707513	+	1.22545i	0.0260263	+	0.0450788i	−0.852719	+	0.522370i	$0.825048\pi$
$740$	5.50183	−	4.63377i	0.202251	−	0.170341i
$741$		0			0
$742$		−	5.84695i		−	0.214648i
$743$	25.8748	−	14.9389i	0.949256	−	0.548053i	0.0564064	−	0.998408i	$-0.482036\pi$
$743$	25.8748	−	14.9389i	0.949256	−	0.548053i	0.892850	+	0.450355i	$0.148702\pi$
$744$	−0.626467	−	1.08507i	−0.0229674	−	0.0397807i
$745$	49.0980	−	8.74998i	1.79881	−	0.320575i
$746$	40.9370			1.49881
$747$	19.5488	+	11.2865i	0.715253	+	0.412952i
$748$	10.8118	+	6.24221i	0.395320	+	0.228238i
$749$	35.8809			1.31106
$750$	−0.0251552	−	4.58119i	−0.000918538	−	0.167282i
$751$	9.99291	+	17.3082i	0.364646	+	0.631586i	0.988719	−	0.149780i	$-0.0478565\pi$
$751$	9.99291	+	17.3082i	0.364646	+	0.631586i	−0.624073	+	0.781366i	$0.714523\pi$
$752$	−26.2816	+	15.1737i	−0.958391	+	0.553328i
$753$			3.20938i			0.116956i
$754$		0			0
$755$	−27.6028	−	32.7737i	−1.00457	−	1.19276i
$756$	1.21563	+	2.10553i	0.0442120	+	0.0765774i
$757$	14.8024	−	8.54617i	0.538003	−	0.310616i	−0.206266	−	0.978496i	$-0.566131\pi$
$757$	14.8024	−	8.54617i	0.538003	−	0.310616i	0.744269	+	0.667880i	$0.232798\pi$
$758$	17.8964	+	10.3325i	0.650025	+	0.375292i
$759$	−0.462218			−0.0167775
$760$	7.09571	+	39.8155i	0.257388	+	1.44426i
$761$	−21.1120	+	36.5671i	−0.765310	+	1.32556i	0.174773	+	0.984609i	$0.444081\pi$
$761$	−21.1120	+	36.5671i	−0.765310	+	1.32556i	−0.940083	+	0.340947i	$0.889252\pi$
$762$		−	6.84552i		−	0.247987i
$763$	−10.1272	−	5.84695i	−0.366630	−	0.211674i
$764$	−0.453830	−	0.786056i	−0.0164190	−	0.0284385i
$765$	−33.0138	−	11.9477i	−1.19362	−	0.431968i
$766$	2.07395			0.0749350
$767$		0			0
$768$		−	4.42107i		−	0.159531i
$769$	11.8827	+	20.5815i	0.428502	+	0.742187i	0.996740	−	0.0806767i	$-0.0257081\pi$
$769$	11.8827	+	20.5815i	0.428502	+	0.742187i	−0.568238	+	0.822864i	$0.692375\pi$
$770$	−7.11628	+	19.6637i	−0.256453	+	0.708631i
$771$	−1.87907	+	3.25465i	−0.0676731	+	0.117213i
$772$		−	12.5149i		−	0.450422i
$773$	−0.246026	−	0.142043i	−0.00884894	−	0.00510894i	0.495569	−	0.868569i	$-0.334960\pi$
$773$	−0.246026	−	0.142043i	−0.00884894	−	0.00510894i	−0.504418	+	0.863460i	$0.668293\pi$
$774$	−2.29066	+	3.96754i	−0.0823361	+	0.142610i
$775$	1.00366	−	5.81644i	0.0360524	−	0.208933i
$776$	−8.92787	+	15.4635i	−0.320492	+	0.555108i
$777$	−3.30596	+	1.90870i	−0.118601	+	0.0684741i
$778$	−22.6665	+	13.0865i	−0.812634	+	0.469174i
$779$	−1.06138			−0.0380278
$780$		0			0
$781$	−7.29958			−0.261199
$782$	1.93405	−	1.11663i	0.0691617	−	0.0399305i
$783$	−5.27294	+	3.04434i	−0.188440	+	0.108796i
$784$	3.55955	−	6.16532i	0.127127	−	0.220190i
$785$	10.6084	−	8.93460i	0.378628	−	0.318890i
$786$	2.04880	−	3.54863i	0.0730784	−	0.126575i
$787$	−20.9008	−	12.0671i	−0.745032	−	0.430145i	0.0788638	−	0.996885i	$-0.474871\pi$
$787$	−20.9008	−	12.0671i	−0.745032	−	0.430145i	−0.823896	+	0.566741i	$0.808204\pi$
$788$		−	5.46381i		−	0.194640i
$789$	−2.31925	+	4.01705i	−0.0825674	+	0.143011i
$790$	27.9121	+	10.1014i	0.993068	+	0.359390i
$791$	−4.83027	−	8.36627i	−0.171745	−	0.297470i
$792$		−	34.3853i		−	1.22183i
$793$		0			0
$794$	26.7529			0.949424
$795$	0.637176	−	1.76065i	0.0225983	−	0.0624437i
$796$	−5.13641	−	8.89652i	−0.182055	−	0.315329i
$797$	−29.7430	−	17.1721i	−1.05355	−	0.608267i	−0.129909	−	0.991526i	$-0.541468\pi$
$797$	−29.7430	−	17.1721i	−1.05355	−	0.608267i	−0.923641	+	0.383259i	$0.874802\pi$
$798$		−	4.89075i		−	0.173131i
$799$	33.4659	−	57.9646i	1.18394	−	2.05064i
$800$	10.2937	−	12.3592i	0.363938	−	0.436963i
$801$	35.2676			1.24612
$802$	−3.80876	−	2.19899i	−0.134492	−	0.0776489i
$803$	29.7786	−	17.1927i	1.05086	−	0.606716i
$804$	−0.448565	−	0.776937i	−0.0158197	−	0.0274004i
$805$	−1.00892	−	1.19792i	−0.0355598	−	0.0422213i
$806$		0			0
$807$		−	1.26329i		−	0.0444698i
$808$	−15.8269	+	9.13767i	−0.556789	+	0.321462i
$809$	−23.8431	−	41.2975i	−0.838279	−	1.45194i	−0.891332	−	0.453351i	$-0.850229\pi$
$809$	−23.8431	−	41.2975i	−0.838279	−	1.45194i	0.0530528	−	0.998592i	$-0.483105\pi$
$810$	3.69962	+	20.7593i	0.129991	+	0.729408i
$811$	−24.5992			−0.863793			−0.431897	−	0.901923i	$-0.642155\pi$
$811$	−24.5992			−0.863793			−0.431897	+	0.901923i	$0.642155\pi$
$812$	3.11230	+	1.79689i	0.109220	+	0.0630584i
$813$	6.57632	+	3.79684i	0.230642	+	0.133161i
$814$	25.1138			0.880239
$815$	−4.68257	−	26.2749i	−0.164023	−	0.920368i
$816$	−2.32398	−	4.02525i	−0.0813556	−	0.140912i
$817$	−6.82125	+	3.93825i	−0.238645	+	0.137782i
$818$		−	16.0097i		−	0.559765i
$819$		0			0
$820$	0.153445	+	0.182190i	0.00535853	+	0.00636236i
$821$	8.64979	+	14.9819i	0.301880	+	0.522871i	0.976562	−	0.215237i	$-0.0690526\pi$
$821$	8.64979	+	14.9819i	0.301880	+	0.522871i	−0.674682	+	0.738109i	$0.735719\pi$
$822$	−0.701870	+	0.405225i	−0.0244805	+	0.0141338i
$823$	28.2000	+	16.2813i	0.982990	+	0.567529i	0.903171	−	0.429280i	$-0.141233\pi$
$823$	28.2000	+	16.2813i	0.982990	+	0.567529i	0.0798182	+	0.996809i	$0.474566\pi$
$824$	19.7869			0.689311
$825$	−4.28574	+	5.14568i	−0.149210	+	0.179150i
$826$	−8.50812	+	14.7365i	−0.296035	+	0.512748i
$827$		−	15.4702i		−	0.537951i	−0.963147	−	0.268976i	$-0.913315\pi$
$827$		−	15.4702i		−	0.537951i	0.963147	−	0.268976i	$-0.0866851\pi$
$828$	0.508211	+	0.293416i	0.0176616	+	0.0101969i
$829$	−7.26180	−	12.5778i	−0.252213	−	0.436845i	0.711922	−	0.702258i	$-0.247825\pi$
$829$	−7.26180	−	12.5778i	−0.252213	−	0.436845i	−0.964135	+	0.265413i	$0.914492\pi$
$830$	−7.07914	+	19.5611i	−0.245721	+	0.678976i
$831$	3.41503			0.118466
$832$		0			0
$833$			15.7013i			0.544018i
$834$	−1.78254	−	3.08746i	−0.0617245	−	0.106910i
$835$	4.26737	+	1.54436i	0.147679	+	0.0534447i
$836$	6.73557	−	11.6663i	0.232955	−	0.403489i
$837$		−	2.39585i		−	0.0828127i
$838$	17.2986	+	9.98736i	0.597571	+	0.345008i
$839$	−0.407933	+	0.706561i	−0.0140834	+	0.0243932i	−0.872981	−	0.487754i	$-0.837816\pi$
$839$	−0.407933	+	0.706561i	−0.0140834	+	0.0243932i	0.858898	+	0.512147i	$0.171150\pi$
$840$	−3.68419	+	3.10291i	−0.127117	+	0.107061i
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$	−17.5846	+	10.1524i	−0.606004	+	0.349876i
$843$	−1.21384	+	0.700811i	−0.0418069	+	0.0241372i
$844$	−4.29797			−0.147942
$845$		0			0
$846$	−42.0073			−1.44424
$847$	7.13847	−	4.12140i	0.245281	−	0.141613i
$848$	−5.19258	+	2.99794i	−0.178314	+	0.102950i
$849$	−1.05063	+	1.81975i	−0.0360575	+	0.0624535i
$850$	5.50183	−	31.8845i	0.188711	−	1.09363i
$851$	−0.940450	+	1.62891i	−0.0322382	+	0.0558382i
$852$	−0.331804	−	0.191567i	−0.0113674	−	0.00656299i
$853$		−	20.0856i		−	0.687719i	−0.939021	−	0.343859i	$-0.888266\pi$
$853$		−	20.0856i		−	0.687719i	0.939021	−	0.343859i	$-0.111734\pi$
$854$	8.14716	−	14.1113i	0.278790	−	0.482878i
$855$	−12.8919	+	35.6230i	−0.440895	+	1.21828i
$856$	−27.1860	−	47.0875i	−0.929197	−	1.60942i
$857$		−	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	$0.259972\pi$
$860$	1.66218	+	0.601540i	0.0566798	+	0.0205123i
$861$	−0.0632055	−	0.109475i	−0.00215404	−	0.00373090i
$862$	9.93355	+	5.73514i	0.338338	+	0.195340i
$863$			20.8275i			0.708977i	0.935060	+	0.354489i	$0.115345\pi$
$863$			20.8275i			0.708977i	−0.935060	+	0.354489i	$0.884655\pi$
$864$	3.26443	−	5.65416i	0.111058	−	0.192358i
$865$	0.525447	+	2.94839i	0.0178657	+	0.100248i
$866$	−29.4134			−0.999509
$867$	3.79692	+	2.19215i	0.128950	+	0.0744494i
$868$	−1.22467	+	0.707062i	−0.0415679	+	0.0239993i
$869$	−21.6952	−	37.5771i	−0.735958	−	1.27472i
$870$	−1.77072	−	2.10243i	−0.0600330	−	0.0712792i
$871$		0			0
$872$			17.7203i			0.600084i
$873$	−14.4852	+	8.36303i	−0.490249	+	0.283046i
$874$	−1.20488	−	2.08691i	−0.0407557	−	0.0705909i
$875$	−22.6908	+	0.124594i	−0.767089	+	0.00421206i
$876$	1.80479			0.0609782
$877$	−40.3520	−	23.2972i	−1.36259	−	0.786691i	−0.372621	−	0.927984i	$-0.621541\pi$
$877$	−40.3520	−	23.2972i	−1.36259	−	0.786691i	−0.989968	+	0.141293i	$0.954874\pi$
$878$	7.26094	+	4.19210i	0.245045	+	0.141477i
$879$	−3.37935			−0.113982
$880$	21.1118	−	3.76243i	0.711678	−	0.126832i
$881$	−11.9223	−	20.6501i	−0.401674	−	0.695719i	0.592254	−	0.805751i	$-0.298238\pi$
$881$	−11.9223	−	20.6501i	−0.401674	−	0.695719i	−0.993928	+	0.110032i	$0.964905\pi$
$882$	8.53413	−	4.92718i	0.287359	−	0.165907i
$883$		−	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
$886$	−22.7041	−	39.3246i	−0.762758	−	1.32114i
$887$	−24.7505	+	14.2897i	−0.831042	+	0.479802i	−0.854209	−	0.519929i	$-0.825958\pi$
$887$	−24.7505	+	14.2897i	−0.831042	+	0.479802i	0.0231673	+	0.999732i	$0.492625\pi$
$888$	5.00967	+	2.89233i	0.168113	+	0.0970603i
$889$	−33.9060			−1.13717
$890$	5.70242	+	31.9975i	0.191146	+	1.07256i
$891$	15.4116	−	26.6937i	0.516308	−	0.894271i
$892$			11.4902i			0.384720i
$893$	−62.5459	−	36.1109i	−2.09302	−	1.20840i
$894$	4.56949	+	7.91459i	0.152827	+	0.264704i
$895$	15.3891	−	42.5233i	0.514402	−	1.42140i
$896$	8.05611			0.269136
$897$		0			0
$898$		−	14.8180i		−	0.494483i
$899$	−1.77072	−	3.06697i	−0.0590568	−	0.102289i
$900$	7.97866	−	2.93712i	0.265955	−	0.0979039i
$901$	6.61201	−	11.4523i	0.220278	−	0.381533i
$902$			0.831632i			0.0276903i
$903$	−0.812417	−	0.469049i	−0.0270356	−	0.0156090i
$904$	−7.31952	+	12.6778i	−0.243444	+	0.421657i
$905$	−28.5543	−	33.9035i	−0.949177	−	1.12699i
$906$	3.92605	−	6.80011i	0.130434	−	0.225919i
$907$	−5.55457	+	3.20693i	−0.184436	+	0.106484i	−0.589375	−	0.807859i	$-0.700626\pi$
$907$	−5.55457	+	3.20693i	−0.184436	+	0.106484i	0.404939	+	0.914344i	$0.367293\pi$
$908$	2.45952	−	1.42000i	0.0816220	−	0.0471245i
$909$	−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	$0.380010\pi$
$912$	−4.34339	+	2.50766i	−0.143824	+	0.0830369i
$913$	26.3345	−	15.2042i	0.871543	−	0.503186i
$914$	4.88719	−	8.46486i	0.161654	−	0.279993i
$915$	3.99108	−	3.36138i	0.131941	−	0.111124i
$916$	−0.449643	+	0.778805i	−0.0148566	+	0.0257324i
$917$	−17.5765	−	10.1478i	−0.580426	−	0.335109i
$918$		−	13.1335i		−	0.433472i
$919$	13.0632	−	22.6261i	0.430915	−	0.746367i	−0.566037	−	0.824380i	$-0.691524\pi$
$919$	13.0632	−	22.6261i	0.430915	−	0.746367i	0.996952	+	0.0780125i	$0.0248574\pi$
$920$	−0.807638	+	2.23167i	−0.0266270	+	0.0735759i
$921$	−3.81426	−	6.60649i	−0.125684	−	0.217691i
$922$			5.39220i			0.177583i
$923$		0			0
$924$	1.60442			0.0527817
$925$	9.41397	+	25.5730i	0.309529	+	0.840836i
$926$	1.18048	+	2.04465i	0.0387929	+	0.0671913i
$927$	16.0518	+	9.26754i	0.527212	+	0.304386i
$928$		−	9.65067i		−	0.316799i
$929$	11.9711	−	20.7346i	0.392760	−	0.680281i	−0.600052	−	0.799961i	$-0.704854\pi$
$929$	11.9711	−	20.7346i	0.392760	−	0.680281i	0.992813	+	0.119680i	$0.0381869\pi$
$930$	1.06484	−	0.189770i	0.0349174	−	0.00622281i
$931$	16.9423			0.555261
$932$	7.13847	+	4.12140i	0.233828	+	0.135001i
$933$	2.28311	−	1.31815i	0.0747457	−	0.0431544i
$934$	19.4748	+	33.7313i	0.637235	+	1.10372i
$935$	−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	$0.902259\pi$
$938$	9.19124	−	5.30656i	0.300104	−	0.173265i
$939$	4.51102	+	7.81332i	0.147212	+	0.254978i
$940$	2.84375	+	15.9569i	0.0927530	+	0.520456i
$941$	14.3788			0.468735			0.234368	−	0.972148i	$-0.424698\pi$
$941$	14.3788			0.468735			0.234368	+	0.972148i	$0.424698\pi$
$942$	2.20109	+	1.27080i	0.0717154	+	0.0414049i
$943$	−0.0539404	−	0.0311425i	−0.00175654	−	0.00101414i
$944$	17.4496			0.567938
$945$	−9.06772	+	1.61600i	−0.294973	+	0.0525685i
$946$	3.08578	+	5.34473i	0.100327	+	0.173772i
$947$	50.5056	−	29.1594i	1.64121	−	0.947554i	0.660807	−	0.750555i	$-0.270214\pi$
$947$	50.5056	−	29.1594i	1.64121	−	0.947554i	0.980404	−	0.196998i	$-0.0631194\pi$
$948$		−	2.27744i		−	0.0739677i
$949$		0			0
$950$	−34.4045	−	5.93667i	−1.11623	−	0.192611i
$951$	2.04354	+	3.53951i	0.0662663	+	0.114777i
$952$	−29.4613	+	17.0095i	−0.954847	+	0.551281i
$953$	11.9507	+	6.89975i	0.387122	+	0.223505i	0.680912	−	0.732365i	$-0.261583\pi$
$953$	11.9507	+	6.89975i	0.387122	+	0.223505i	−0.293791	+	0.955870i	$0.594917\pi$
$954$	−8.29958			−0.268709
$955$	3.38525	−	0.603301i	0.109544	−	0.0195224i
$956$	−1.18048	+	2.04465i	−0.0381794	+	0.0661287i
$957$			4.01801i			0.129884i
$958$	31.6759	+	18.2881i	1.02340	+	0.590862i
$959$	2.00709	+	3.47639i	0.0648124	+	0.112258i
$960$	6.35785	+	2.30090i	0.205199	+	0.0742611i
$961$	−29.6065			−0.955047
$962$		0			0
$963$		−	50.9319i		−	1.64126i
$964$	−5.15452	−	8.92790i	−0.166016	−	0.287548i
$965$	44.5820	+	16.1342i	1.43515	+	0.519378i
$966$	0.143502	−	0.248553i	0.00461711	−	0.00799707i
$967$			30.3474i			0.975906i	0.872870	+	0.487953i	$0.162256\pi$
$967$			30.3474i			0.975906i	−0.872870	+	0.487953i	$0.837744\pi$
$968$	−10.8172	−	6.24534i	−0.347679	−	0.200733i
$969$	5.53069	−	9.57943i	0.177671	−	0.307736i
$970$	−9.92970	−	11.7899i	−0.318824	−	0.378550i
$971$	−22.0506	+	38.1928i	−0.707638	+	1.22567i	0.258092	+	0.966120i	$0.416906\pi$
$971$	−22.0506	+	38.1928i	−0.707638	+	1.22567i	−0.965731	+	0.259545i	$0.916427\pi$
$972$	4.51337	−	2.60580i	0.144767	−	0.0835810i
$973$	−15.2923	+	8.82900i	−0.490248	+	0.283045i
$974$	26.5074			0.849351
$975$		0			0
$976$	−16.7093			−0.534853
$977$	−19.3314	+	11.1610i	−0.618466	+	0.357071i	−0.776271	−	0.630399i	$-0.782891\pi$
$977$	−19.3314	+	11.1610i	−0.618466	+	0.357071i	0.157806	+	0.987470i	$0.449558\pi$
$978$	4.23551	−	2.44537i	0.135437	−	0.0781944i
$979$	23.7547	−	41.1444i	0.759204	−	1.31498i
$980$	−2.44937	−	2.90822i	−0.0782422	−	0.0928996i
$981$	−8.29958	+	14.3753i	−0.264985	+	0.458968i
$982$	−10.9845	−	6.34189i	−0.350529	−	0.202378i
$983$		−	4.03793i		−	0.128790i	−0.997924	−	0.0643950i	$-0.979488\pi$
$983$		−	4.03793i		−	0.128790i	0.997924	−	0.0643950i	$-0.0205118\pi$
$984$	−0.0957781	+	0.165893i	−0.00305330	+	0.00528846i
$985$	19.4638	+	7.04392i	0.620167	+	0.224438i
$986$	−9.70671	−	16.8125i	−0.309125	−	0.535419i
$987$		−	8.60167i		−	0.273794i
$988$		0			0
$989$	−0.462218			−0.0146977
$990$	27.9121	+	10.1014i	0.887105	+	0.321042i
$991$	−14.8250	−	25.6777i	−0.470932	−	0.815678i	0.528515	−	0.848924i	$-0.322749\pi$
$991$	−14.8250	−	25.6777i	−0.470932	−	0.815678i	−0.999447	+	0.0332459i	$0.989416\pi$
$992$	3.28871	+	1.89874i	0.104417	+	0.0602849i
$993$			4.38304i			0.139092i
$994$	2.26626	−	3.92527i	0.0718813	−	0.124502i
$995$	38.3140	−	6.82811i	1.21463	−	0.216466i
$996$	1.59605			0.0505728
$997$	19.2052	+	11.0881i	0.608233	+	0.351164i	0.772274	−	0.635290i	$-0.219119\pi$
$997$	19.2052	+	11.0881i	0.608233	+	0.351164i	−0.164040	+	0.986454i	$0.552453\pi$
$998$	19.3514	−	11.1725i	0.612557	−	0.353660i
$999$	5.53069	+	9.57943i	0.174983	+	0.303080i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.n.e.484.5		12
5.4	even	2	inner	845.2.n.e.484.2		12
13.2	odd	12		845.2.d.d.844.10		12
13.3	even	3		845.2.b.e.339.5		6
13.4	even	6		65.2.n.a.9.5	yes	12
13.5	odd	4		845.2.l.f.699.4		24
13.6	odd	12		845.2.l.f.654.3		24
13.7	odd	12		845.2.l.f.654.9		24
13.8	odd	4		845.2.l.f.699.10		24
13.9	even	3	inner	845.2.n.e.529.2		12
13.10	even	6		845.2.b.d.339.2		6
13.11	odd	12		845.2.d.d.844.4		12
13.12	even	2		65.2.n.a.29.2	yes	12
39.17	odd	6		585.2.bs.a.334.2		12
39.38	odd	2		585.2.bs.a.289.5		12
52.43	odd	6		1040.2.dh.a.529.4		12
52.51	odd	2		1040.2.dh.a.289.3		12
65.3	odd	12		4225.2.a.bq.1.5		6
65.4	even	6		65.2.n.a.9.2	✓	12
65.9	even	6	inner	845.2.n.e.529.5		12
65.12	odd	4		325.2.e.e.276.2		12
65.17	odd	12		325.2.e.e.126.2		12
65.19	odd	12		845.2.l.f.654.10		24
65.23	odd	12		4225.2.a.br.1.2		6
65.24	odd	12		845.2.d.d.844.9		12
65.29	even	6		845.2.b.e.339.2		6
65.34	odd	4		845.2.l.f.699.3		24
65.38	odd	4		325.2.e.e.276.5		12
65.42	odd	12		4225.2.a.bq.1.2		6
65.43	odd	12		325.2.e.e.126.5		12
65.44	odd	4		845.2.l.f.699.9		24
65.49	even	6		845.2.b.d.339.5		6
65.54	odd	12		845.2.d.d.844.3		12
65.59	odd	12		845.2.l.f.654.4		24
65.62	odd	12		4225.2.a.br.1.5		6
65.64	even	2		65.2.n.a.29.5	yes	12
195.134	odd	6		585.2.bs.a.334.5		12
195.194	odd	2		585.2.bs.a.289.2		12
260.199	odd	6		1040.2.dh.a.529.3		12
260.259	odd	2		1040.2.dh.a.289.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.n.a.9.2	✓	12	65.4	even	6
65.2.n.a.9.5	yes	12	13.4	even	6
65.2.n.a.29.2	yes	12	13.12	even	2
65.2.n.a.29.5	yes	12	65.64	even	2
325.2.e.e.126.2		12	65.17	odd	12
325.2.e.e.126.5		12	65.43	odd	12
325.2.e.e.276.2		12	65.12	odd	4
325.2.e.e.276.5		12	65.38	odd	4
585.2.bs.a.289.2		12	195.194	odd	2
585.2.bs.a.289.5		12	39.38	odd	2
585.2.bs.a.334.2		12	39.17	odd	6
585.2.bs.a.334.5		12	195.134	odd	6
845.2.b.d.339.2		6	13.10	even	6
845.2.b.d.339.5		6	65.49	even	6
845.2.b.e.339.2		6	65.29	even	6
845.2.b.e.339.5		6	13.3	even	3
845.2.d.d.844.3		12	65.54	odd	12
845.2.d.d.844.4		12	13.11	odd	12
845.2.d.d.844.9		12	65.24	odd	12
845.2.d.d.844.10		12	13.2	odd	12
845.2.l.f.654.3		24	13.6	odd	12
845.2.l.f.654.4		24	65.59	odd	12
845.2.l.f.654.9		24	13.7	odd	12
845.2.l.f.654.10		24	65.19	odd	12
845.2.l.f.699.3		24	65.34	odd	4
845.2.l.f.699.4		24	13.5	odd	4
845.2.l.f.699.9		24	65.44	odd	4
845.2.l.f.699.10		24	13.8	odd	4
845.2.n.e.484.2		12	5.4	even	2	inner
845.2.n.e.484.5		12	1.1	even	1	trivial
845.2.n.e.529.2		12	13.9	even	3	inner
845.2.n.e.529.5		12	65.9	even	6	inner
1040.2.dh.a.289.3		12	52.51	odd	2
1040.2.dh.a.289.4		12	260.259	odd	2
1040.2.dh.a.529.3		12	260.199	odd	6
1040.2.dh.a.529.4		12	52.43	odd	6
4225.2.a.bq.1.2		6	65.42	odd	12
4225.2.a.bq.1.5		6	65.3	odd	12
4225.2.a.br.1.2		6	65.23	odd	12
4225.2.a.br.1.5		6	65.62	odd	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.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.02826 - 0.593667i) q^{2} +(0.298874 - 0.172555i) q^{3} +(-0.295120 + 0.511162i) q^{4} +(-1.44045 - 1.71029i) q^{5} +(0.204880 - 0.354863i) q^{6} +(-1.75765 - 1.01478i) q^{7} +3.07548i q^{8} +(-1.44045 + 2.49493i) q^{9} +O(q^{10})\)	\(q+(1.02826 - 0.593667i) q^{2} +(0.298874 - 0.172555i) q^{3} +(-0.295120 + 0.511162i) q^{4} +(-1.44045 - 1.71029i) q^{5} +(0.204880 - 0.354863i) q^{6} +(-1.75765 - 1.01478i) q^{7} +3.07548i q^{8} +(-1.44045 + 2.49493i) q^{9} +(-2.49650 - 0.903481i) q^{10} +(1.94045 + 3.36096i) q^{11} +0.203698i q^{12} -2.40976 q^{14} +(-0.725633 - 0.262606i) q^{15} +(1.23557 + 2.14007i) q^{16} +(-4.71996 - 2.72507i) q^{17} +3.42059i q^{18} +(-2.94045 + 5.09301i) q^{19} +(1.29934 - 0.231562i) q^{20} -0.700420 q^{21} +(3.99058 + 2.30396i) q^{22} +(-0.298874 + 0.172555i) q^{23} +(0.530689 + 0.919180i) q^{24} +(-0.850210 + 4.92718i) q^{25} +2.02956i q^{27} +(1.03743 - 0.598962i) q^{28} +(1.50000 + 2.59808i) q^{29} +(-0.902040 + 0.160757i) q^{30} -1.18048 q^{31} +(-2.78591 - 1.60845i) q^{32} +(1.15990 + 0.669668i) q^{33} -6.47114 q^{34} +(0.796234 + 4.46783i) q^{35} +(-0.850210 - 1.47261i) q^{36} +(4.71996 - 2.72507i) q^{37} +6.98259i q^{38} +(5.25997 - 4.43007i) q^{40} +(0.0902394 + 0.156299i) q^{41} +(-0.720215 + 0.415816i) q^{42} +(1.15990 + 0.669668i) q^{43} -2.29066 q^{44} +(6.34196 - 1.13023i) q^{45} +(-0.204880 + 0.354863i) q^{46} +12.2807i q^{47} +(0.738559 + 0.426407i) q^{48} +(-1.44045 - 2.49493i) q^{49} +(2.05087 + 5.57117i) q^{50} -1.88090 q^{51} +2.42636i q^{53} +(1.20488 + 2.08691i) q^{54} +(2.95310 - 8.16003i) q^{55} +(3.12093 - 5.40561i) q^{56} +2.02956i q^{57} +(3.08478 + 1.78100i) q^{58} +(3.53069 - 6.11533i) q^{59} +(0.348383 - 0.293416i) q^{60} +(-3.38090 + 5.85589i) q^{61} +(-1.21384 + 0.700811i) q^{62} +(5.06361 - 2.92347i) q^{63} -8.76180 q^{64} +1.59024 q^{66} +(-3.81417 + 2.20211i) q^{67} +(2.78591 - 1.60845i) q^{68} +(-0.0595504 + 0.103144i) q^{69} +(3.47114 + 4.12140i) q^{70} +(-0.940450 + 1.62891i) q^{71} +(-7.67311 - 4.43007i) q^{72} -8.86014i q^{73} +(3.23557 - 5.60417i) q^{74} +(0.596104 + 1.61932i) q^{75} +(-1.73557 - 3.00609i) q^{76} -7.87651i q^{77} -11.1805 q^{79} +(1.88037 - 5.19585i) q^{80} +(-3.97114 - 6.87821i) q^{81} +(0.185579 + 0.107144i) q^{82} -7.83540i q^{83} +(0.206708 - 0.358028i) q^{84} +(2.13820 + 11.9979i) q^{85} +1.59024 q^{86} +(0.896622 + 0.517665i) q^{87} +(-10.3365 + 5.96781i) q^{88} +(-6.12093 - 10.6018i) q^{89} +(5.85021 - 4.92718i) q^{90} -0.203698i q^{92} +(-0.352814 + 0.203698i) q^{93} +(7.29066 + 12.6278i) q^{94} +(12.9461 - 2.30719i) q^{95} -1.11018 q^{96} +(5.02801 + 2.90292i) q^{97} +(-2.96232 - 1.71029i) q^{98} -11.1805 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{4} + 6 q^{5} + 10 q^{6} + 6 q^{9}+O(q^{10}) \) 12 * q + 4 * q^4 + 6 * q^5 + 10 * q^6 + 6 * q^9	\( 12 q + 4 q^{4} + 6 q^{5} + 10 q^{6} + 6 q^{9} + 7 q^{10} - 44 q^{14} + 4 q^{15} - 16 q^{16} - 12 q^{19} + q^{20} + 8 q^{21} - 32 q^{24} - 2 q^{25} + 18 q^{29} + 4 q^{30} + 16 q^{31} - 16 q^{34} + 10 q^{35} - 2 q^{36} + 70 q^{40} - 14 q^{41} + 4 q^{44} + 29 q^{45} - 10 q^{46} + 6 q^{49} + 31 q^{50} + 24 q^{51} + 22 q^{54} - 26 q^{55} - 16 q^{56} + 4 q^{59} + 96 q^{60} + 6 q^{61} - 12 q^{64} + 4 q^{66} - 24 q^{69} - 20 q^{70} + 12 q^{71} + 8 q^{74} + 2 q^{75} + 10 q^{76} - 104 q^{79} - 33 q^{80} + 14 q^{81} - 90 q^{84} - 21 q^{85} + 4 q^{86} - 20 q^{89} + 62 q^{90} + 56 q^{94} + 20 q^{95} - 12 q^{96} - 104 q^{99}+O(q^{100}) \) 12 * q + 4 * q^4 + 6 * q^5 + 10 * q^6 + 6 * q^9 + 7 * q^10 - 44 * q^14 + 4 * q^15 - 16 * q^16 - 12 * q^19 + q^20 + 8 * q^21 - 32 * q^24 - 2 * q^25 + 18 * q^29 + 4 * q^30 + 16 * q^31 - 16 * q^34 + 10 * q^35 - 2 * q^36 + 70 * q^40 - 14 * q^41 + 4 * q^44 + 29 * q^45 - 10 * q^46 + 6 * q^49 + 31 * q^50 + 24 * q^51 + 22 * q^54 - 26 * q^55 - 16 * q^56 + 4 * q^59 + 96 * q^60 + 6 * q^61 - 12 * q^64 + 4 * q^66 - 24 * q^69 - 20 * q^70 + 12 * q^71 + 8 * q^74 + 2 * q^75 + 10 * q^76 - 104 * q^79 - 33 * q^80 + 14 * q^81 - 90 * q^84 - 21 * q^85 + 4 * q^86 - 20 * q^89 + 62 * q^90 + 56 * q^94 + 20 * q^95 - 12 * q^96 - 104 * q^99

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