LMFDB - Embedded newform 845.2.e.d.191.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(146,845)]

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([0, 2]))

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

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

chi := DirichletCharacter("845.146");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.e (of order $3$, 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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{13})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 4x^{2} + 3x + 9 $ x^4 - x^3 + 4x^2 + 3x + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			191.1
Root			$1.15139 - 1.99426i$ of defining polynomial
Character	$\chi$	$=$	845.191
Dual form			845.2.e.d.146.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.15139 + 1.99426i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-1.65139 - 2.86029i) q^{4} +1.00000 q^{5} +(-1.15139 - 1.99426i) q^{6} +(-0.500000 - 0.866025i) q^{7} +3.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +(-1.15139 + 1.99426i) q^{10} +(0.802776 - 1.39045i) q^{11} +3.30278 q^{12} +2.30278 q^{14} +(-0.500000 + 0.866025i) q^{15} +(-0.151388 + 0.262211i) q^{16} +(-3.80278 - 6.58660i) q^{17} -4.60555 q^{18} +(-2.80278 - 4.85455i) q^{19} +(-1.65139 - 2.86029i) q^{20} +1.00000 q^{21} +(1.84861 + 3.20189i) q^{22} +(1.50000 - 2.59808i) q^{23} +(-1.50000 + 2.59808i) q^{24} +1.00000 q^{25} -5.00000 q^{27} +(-1.65139 + 2.86029i) q^{28} +(3.10555 - 5.37897i) q^{29} +(-1.15139 - 1.99426i) q^{30} +4.00000 q^{31} +(2.65139 + 4.59234i) q^{32} +(0.802776 + 1.39045i) q^{33} +17.5139 q^{34} +(-0.500000 - 0.866025i) q^{35} +(3.30278 - 5.72058i) q^{36} +(1.80278 - 3.12250i) q^{37} +12.9083 q^{38} +3.00000 q^{40} +(1.50000 - 2.59808i) q^{41} +(-1.15139 + 1.99426i) q^{42} +(5.10555 + 8.84307i) q^{43} -5.30278 q^{44} +(1.00000 + 1.73205i) q^{45} +(3.45416 + 5.98279i) q^{46} -9.21110 q^{47} +(-0.151388 - 0.262211i) q^{48} +(3.00000 - 5.19615i) q^{49} +(-1.15139 + 1.99426i) q^{50} +7.60555 q^{51} -3.21110 q^{53} +(5.75694 - 9.97131i) q^{54} +(0.802776 - 1.39045i) q^{55} +(-1.50000 - 2.59808i) q^{56} +5.60555 q^{57} +(7.15139 + 12.3866i) q^{58} +(-5.40833 - 9.36750i) q^{59} +3.30278 q^{60} +(0.500000 + 0.866025i) q^{61} +(-4.60555 + 7.97705i) q^{62} +(1.00000 - 1.73205i) q^{63} -12.8167 q^{64} -3.69722 q^{66} +(-3.50000 + 6.06218i) q^{67} +(-12.5597 + 21.7541i) q^{68} +(1.50000 + 2.59808i) q^{69} +2.30278 q^{70} +(2.40833 + 4.17134i) q^{71} +(3.00000 + 5.19615i) q^{72} +0.788897 q^{73} +(4.15139 + 7.19041i) q^{74} +(-0.500000 + 0.866025i) q^{75} +(-9.25694 + 16.0335i) q^{76} -1.60555 q^{77} +5.21110 q^{79} +(-0.151388 + 0.262211i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(3.45416 + 5.98279i) q^{82} +9.21110 q^{83} +(-1.65139 - 2.86029i) q^{84} +(-3.80278 - 6.58660i) q^{85} -23.5139 q^{86} +(3.10555 + 5.37897i) q^{87} +(2.40833 - 4.17134i) q^{88} +(-3.10555 + 5.37897i) q^{89} -4.60555 q^{90} -9.90833 q^{92} +(-2.00000 + 3.46410i) q^{93} +(10.6056 - 18.3694i) q^{94} +(-2.80278 - 4.85455i) q^{95} -5.30278 q^{96} +(-4.19722 - 7.26981i) q^{97} +(6.90833 + 11.9656i) q^{98} +3.21110 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} - 2 q^{3} - 3 q^{4} + 4 q^{5} - q^{6} - 2 q^{7} + 12 q^{8} + 4 q^{9} - q^{10} - 4 q^{11} + 6 q^{12} + 2 q^{14} - 2 q^{15} + 3 q^{16} - 8 q^{17} - 4 q^{18} - 4 q^{19} - 3 q^{20} + 4 q^{21}+ \cdots - 16 q^{99}+O(q^{100}) $ 4 * q - q^2 - 2 * q^3 - 3 * q^4 + 4 * q^5 - q^6 - 2 * q^7 + 12 * q^8 + 4 * q^9 - q^10 - 4 * q^11 + 6 * q^12 + 2 * q^14 - 2 * q^15 + 3 * q^16 - 8 * q^17 - 4 * q^18 - 4 * q^19 - 3 * q^20 + 4 * q^21 + 11 * q^22 + 6 * q^23 - 6 * q^24 + 4 * q^25 - 20 * q^27 - 3 * q^28 - 2 * q^29 - q^30 + 16 * q^31 + 7 * q^32 - 4 * q^33 + 34 * q^34 - 2 * q^35 + 6 * q^36 + 30 * q^38 + 12 * q^40 + 6 * q^41 - q^42 + 6 * q^43 - 14 * q^44 + 4 * q^45 + 3 * q^46 - 8 * q^47 + 3 * q^48 + 12 * q^49 - q^50 + 16 * q^51 + 16 * q^53 + 5 * q^54 - 4 * q^55 - 6 * q^56 + 8 * q^57 + 25 * q^58 + 6 * q^60 + 2 * q^61 - 4 * q^62 + 4 * q^63 - 8 * q^64 - 22 * q^66 - 14 * q^67 - 25 * q^68 + 6 * q^69 + 2 * q^70 - 12 * q^71 + 12 * q^72 + 32 * q^73 + 13 * q^74 - 2 * q^75 - 19 * q^76 + 8 * q^77 - 8 * q^79 + 3 * q^80 - 2 * q^81 + 3 * q^82 + 8 * q^83 - 3 * q^84 - 8 * q^85 - 58 * q^86 - 2 * q^87 - 12 * q^88 + 2 * q^89 - 4 * q^90 - 18 * q^92 - 8 * q^93 + 28 * q^94 - 4 * q^95 - 14 * q^96 - 24 * q^97 + 6 * q^98 - 16 * q^99

Character values

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

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−1.15139	+	1.99426i	−0.814154	+	1.41016i	0.0957796	+	0.995403i	$0.469466\pi$
$2$	−1.15139	+	1.99426i	−0.814154	+	1.41016i	−0.909934	+	0.414754i	$0.863868\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i	−0.973494	−	0.228714i	$-0.926548\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i	0.684819	+	0.728714i	$0.259881\pi$
$4$	−1.65139	−	2.86029i	−0.825694	−	1.43014i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−1.15139	−	1.99426i	−0.470052	−	0.814154i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i	0.755929	−	0.654654i	$-0.227186\pi$
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i	−0.944911	+	0.327327i	$0.893852\pi$
$8$	3.00000			1.06066
$9$	1.00000	+	1.73205i	0.333333	+	0.577350i
$10$	−1.15139	+	1.99426i	−0.364101	+	0.630641i
$11$	0.802776	−	1.39045i	0.242046	−	0.419236i	−0.719251	−	0.694750i	$-0.755515\pi$
$11$	0.802776	−	1.39045i	0.242046	−	0.419236i	0.961297	+	0.275514i	$0.0888482\pi$
$12$	3.30278			0.953429
$13$		0			0
$13$		0			0
$14$	2.30278			0.615443
$15$	−0.500000	+	0.866025i	−0.129099	+	0.223607i
$16$	−0.151388	+	0.262211i	−0.0378470	+	0.0655528i
$17$	−3.80278	−	6.58660i	−0.922309	−	1.59749i	−0.795834	−	0.605516i	$-0.792967\pi$
$17$	−3.80278	−	6.58660i	−0.922309	−	1.59749i	−0.126475	−	0.991970i	$-0.540366\pi$
$18$	−4.60555			−1.08554
$19$	−2.80278	−	4.85455i	−0.643001	−	1.11371i	−0.984759	−	0.173922i	$-0.944356\pi$
$19$	−2.80278	−	4.85455i	−0.643001	−	1.11371i	0.341759	−	0.939788i	$-0.388977\pi$
$20$	−1.65139	−	2.86029i	−0.369262	−	0.639580i
$21$	1.00000			0.218218
$22$	1.84861	+	3.20189i	0.394125	+	0.682645i
$23$	1.50000	−	2.59808i	0.312772	−	0.541736i	−0.666190	−	0.745782i	$-0.732076\pi$
$23$	1.50000	−	2.59808i	0.312772	−	0.541736i	0.978961	+	0.204046i	$0.0654092\pi$
$24$	−1.50000	+	2.59808i	−0.306186	+	0.530330i
$25$	1.00000			0.200000
$26$		0			0
$27$	−5.00000			−0.962250
$28$	−1.65139	+	2.86029i	−0.312083	+	0.540544i
$29$	3.10555	−	5.37897i	0.576686	−	0.998850i	−0.419170	−	0.907908i	$-0.637679\pi$
$29$	3.10555	−	5.37897i	0.576686	−	0.998850i	0.995856	−	0.0909423i	$-0.0289879\pi$
$30$	−1.15139	−	1.99426i	−0.210214	−	0.364101i
$31$	4.00000			0.718421			0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000			0.718421			0.359211	+	0.933257i	$0.383046\pi$
$32$	2.65139	+	4.59234i	0.468704	+	0.811818i
$33$	0.802776	+	1.39045i	0.139745	+	0.242046i
$34$	17.5139			3.00361
$35$	−0.500000	−	0.866025i	−0.0845154	−	0.146385i
$36$	3.30278	−	5.72058i	0.550463	−	0.953429i
$37$	1.80278	−	3.12250i	0.296374	−	0.513336i	−0.678929	−	0.734204i	$-0.737556\pi$
$37$	1.80278	−	3.12250i	0.296374	−	0.513336i	0.975304	+	0.220868i	$0.0708890\pi$
$38$	12.9083			2.09401
$39$		0			0
$40$	3.00000			0.474342
$41$	1.50000	−	2.59808i	0.234261	−	0.405751i	−0.724797	−	0.688963i	$-0.758066\pi$
$41$	1.50000	−	2.59808i	0.234261	−	0.405751i	0.959058	+	0.283211i	$0.0913998\pi$
$42$	−1.15139	+	1.99426i	−0.177663	+	0.307721i
$43$	5.10555	+	8.84307i	0.778589	+	1.34856i	0.932755	+	0.360511i	$0.117398\pi$
$43$	5.10555	+	8.84307i	0.778589	+	1.34856i	−0.154166	+	0.988045i	$0.549269\pi$
$44$	−5.30278			−0.799424
$45$	1.00000	+	1.73205i	0.149071	+	0.258199i
$46$	3.45416	+	5.98279i	0.509289	+	0.882114i
$47$	−9.21110			−1.34358			−0.671789	−	0.740743i	$-0.734474\pi$
$47$	−9.21110			−1.34358			−0.671789	+	0.740743i	$0.734474\pi$
$48$	−0.151388	−	0.262211i	−0.0218509	−	0.0378470i
$49$	3.00000	−	5.19615i	0.428571	−	0.742307i
$50$	−1.15139	+	1.99426i	−0.162831	+	0.282031i
$51$	7.60555			1.06499
$52$		0			0
$53$	−3.21110			−0.441079			−0.220539	−	0.975378i	$-0.570782\pi$
$53$	−3.21110			−0.441079			−0.220539	+	0.975378i	$0.570782\pi$
$54$	5.75694	−	9.97131i	0.783420	−	1.35692i
$55$	0.802776	−	1.39045i	0.108246	−	0.187488i
$56$	−1.50000	−	2.59808i	−0.200446	−	0.347183i
$57$	5.60555			0.742473
$58$	7.15139	+	12.3866i	0.939023	+	1.62644i
$59$	−5.40833	−	9.36750i	−0.704104	−	1.21954i	−0.967014	−	0.254724i	$-0.918015\pi$
$59$	−5.40833	−	9.36750i	−0.704104	−	1.21954i	0.262910	−	0.964820i	$-0.415318\pi$
$60$	3.30278			0.426387
$61$	0.500000	+	0.866025i	0.0640184	+	0.110883i	0.896258	−	0.443533i	$-0.146275\pi$
$61$	0.500000	+	0.866025i	0.0640184	+	0.110883i	−0.832240	+	0.554416i	$0.812942\pi$
$62$	−4.60555	+	7.97705i	−0.584906	+	1.01309i
$63$	1.00000	−	1.73205i	0.125988	−	0.218218i
$64$	−12.8167			−1.60208
$65$		0			0
$66$	−3.69722			−0.455097
$67$	−3.50000	+	6.06218i	−0.427593	+	0.740613i	−0.996659	−	0.0816792i	$-0.973972\pi$
$67$	−3.50000	+	6.06218i	−0.427593	+	0.740613i	0.569066	+	0.822292i	$0.307305\pi$
$68$	−12.5597	+	21.7541i	−1.52309	+	2.63807i
$69$	1.50000	+	2.59808i	0.180579	+	0.312772i
$70$	2.30278			0.275234
$71$	2.40833	+	4.17134i	0.285816	+	0.495048i	0.972807	−	0.231619i	$-0.0744021\pi$
$71$	2.40833	+	4.17134i	0.285816	+	0.495048i	−0.686991	+	0.726666i	$0.741069\pi$
$72$	3.00000	+	5.19615i	0.353553	+	0.612372i
$73$	0.788897			0.0923335			0.0461667	−	0.998934i	$-0.485299\pi$
$73$	0.788897			0.0923335			0.0461667	+	0.998934i	$0.485299\pi$
$74$	4.15139	+	7.19041i	0.482589	+	0.835869i
$75$	−0.500000	+	0.866025i	−0.0577350	+	0.100000i
$76$	−9.25694	+	16.0335i	−1.06184	+	1.83917i
$77$	−1.60555			−0.182970
$78$		0			0
$79$	5.21110			0.586295			0.293147	−	0.956067i	$-0.405297\pi$
$79$	5.21110			0.586295			0.293147	+	0.956067i	$0.405297\pi$
$80$	−0.151388	+	0.262211i	−0.0169257	+	0.0293161i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	3.45416	+	5.98279i	0.381449	+	0.660688i
$83$	9.21110			1.01105			0.505525	−	0.862812i	$-0.331299\pi$
$83$	9.21110			1.01105			0.505525	+	0.862812i	$0.331299\pi$
$84$	−1.65139	−	2.86029i	−0.180181	−	0.312083i
$85$	−3.80278	−	6.58660i	−0.412469	−	0.714417i
$86$	−23.5139			−2.53557
$87$	3.10555	+	5.37897i	0.332950	+	0.576686i
$88$	2.40833	−	4.17134i	0.256729	−	0.444667i
$89$	−3.10555	+	5.37897i	−0.329188	+	0.570170i	−0.982351	−	0.187047i	$-0.940108\pi$
$89$	−3.10555	+	5.37897i	−0.329188	+	0.570170i	0.653163	+	0.757217i	$0.273442\pi$
$90$	−4.60555			−0.485468
$91$		0			0
$92$	−9.90833			−1.03301
$93$	−2.00000	+	3.46410i	−0.207390	+	0.359211i
$94$	10.6056	−	18.3694i	1.09388	−	1.89465i
$95$	−2.80278	−	4.85455i	−0.287559	−	0.498066i
$96$	−5.30278			−0.541212
$97$	−4.19722	−	7.26981i	−0.426164	−	0.738137i	0.570365	−	0.821392i	$-0.306802\pi$
$97$	−4.19722	−	7.26981i	−0.426164	−	0.738137i	−0.996528	+	0.0832546i	$0.973469\pi$
$98$	6.90833	+	11.9656i	0.697846	+	1.20871i
$99$	3.21110			0.322728
$100$	−1.65139	−	2.86029i	−0.165139	−	0.286029i
$101$	4.50000	−	7.79423i	0.447767	−	0.775555i	−0.550474	−	0.834853i	$-0.685553\pi$
$101$	4.50000	−	7.79423i	0.447767	−	0.775555i	0.998240	+	0.0592978i	$0.0188862\pi$
$102$	−8.75694	+	15.1675i	−0.867066	+	1.50180i
$103$	−4.00000			−0.394132			−0.197066	−	0.980390i	$-0.563141\pi$
$103$	−4.00000			−0.394132			−0.197066	+	0.980390i	$0.563141\pi$
$104$		0			0
$105$	1.00000			0.0975900
$106$	3.69722	−	6.40378i	0.359106	−	0.621990i
$107$	−3.10555	+	5.37897i	−0.300225	+	0.520005i	−0.976187	−	0.216932i	$-0.930395\pi$
$107$	−3.10555	+	5.37897i	−0.300225	+	0.520005i	0.675962	+	0.736937i	$0.263728\pi$
$108$	8.25694	+	14.3014i	0.794524	+	1.37616i
$109$	19.2111			1.84009			0.920045	−	0.391813i	$-0.128152\pi$
$109$	19.2111			1.84009			0.920045	+	0.391813i	$0.128152\pi$
$110$	1.84861	+	3.20189i	0.176258	+	0.305288i
$111$	1.80278	+	3.12250i	0.171112	+	0.296374i
$112$	0.302776			0.0286096
$113$	0.802776	+	1.39045i	0.0755188	+	0.130802i	0.901312	−	0.433171i	$-0.142605\pi$
$113$	0.802776	+	1.39045i	0.0755188	+	0.130802i	−0.825793	+	0.563973i	$0.809272\pi$
$114$	−6.45416	+	11.1789i	−0.604488	+	1.04700i
$115$	1.50000	−	2.59808i	0.139876	−	0.242272i
$116$	−20.5139			−1.90467
$117$		0			0
$118$	24.9083			2.29300
$119$	−3.80278	+	6.58660i	−0.348600	+	0.603793i
$120$	−1.50000	+	2.59808i	−0.136931	+	0.237171i
$121$	4.21110	+	7.29384i	0.382828	+	0.663077i
$122$	−2.30278			−0.208484
$123$	1.50000	+	2.59808i	0.135250	+	0.234261i
$124$	−6.60555	−	11.4412i	−0.593196	−	1.02745i
$125$	1.00000			0.0894427
$126$	2.30278	+	3.98852i	0.205148	+	0.355326i
$127$	2.10555	−	3.64692i	0.186837	−	0.323612i	−0.757357	−	0.653001i	$-0.773510\pi$
$127$	2.10555	−	3.64692i	0.186837	−	0.323612i	0.944194	+	0.329389i	$0.106843\pi$
$128$	9.45416	−	16.3751i	0.835638	−	1.44737i
$129$	−10.2111			−0.899037
$130$		0			0
$131$	−21.2111			−1.85322			−0.926611	−	0.376021i	$-0.877292\pi$
$131$	−21.2111			−1.85322			−0.926611	+	0.376021i	$0.877292\pi$
$132$	2.65139	−	4.59234i	0.230774	−	0.399712i
$133$	−2.80278	+	4.85455i	−0.243031	+	0.420943i
$134$	−8.05971	−	13.9598i	−0.696253	−	1.20595i
$135$	−5.00000			−0.430331
$136$	−11.4083	−	19.7598i	−0.978256	−	1.69439i
$137$	−0.802776	−	1.39045i	−0.0685858	−	0.118794i	0.829693	−	0.558220i	$-0.188515\pi$
$137$	−0.802776	−	1.39045i	−0.0685858	−	0.118794i	−0.898279	+	0.439426i	$0.855182\pi$
$138$	−6.90833			−0.588076
$139$	−3.19722	−	5.53776i	−0.271185	−	0.469706i	0.697981	−	0.716117i	$-0.254082\pi$
$139$	−3.19722	−	5.53776i	−0.271185	−	0.469706i	−0.969166	+	0.246410i	$0.920749\pi$
$140$	−1.65139	+	2.86029i	−0.139568	+	0.241738i
$141$	4.60555	−	7.97705i	0.387857	−	0.671789i
$142$	−11.0917			−0.930793
$143$		0			0
$144$	−0.605551			−0.0504626
$145$	3.10555	−	5.37897i	0.257902	−	0.446699i
$146$	−0.908327	+	1.57327i	−0.0751737	+	0.130205i
$147$	3.00000	+	5.19615i	0.247436	+	0.428571i
$148$	−11.9083			−0.978858
$149$	1.50000	+	2.59808i	0.122885	+	0.212843i	0.920904	−	0.389789i	$-0.127452\pi$
$149$	1.50000	+	2.59808i	0.122885	+	0.212843i	−0.798019	+	0.602632i	$0.794119\pi$
$150$	−1.15139	−	1.99426i	−0.0940104	−	0.162831i
$151$	1.21110			0.0985581			0.0492791	−	0.998785i	$-0.484308\pi$
$151$	1.21110			0.0985581			0.0492791	+	0.998785i	$0.484308\pi$
$152$	−8.40833	−	14.5636i	−0.682005	−	1.18127i
$153$	7.60555	−	13.1732i	0.614872	−	1.06499i
$154$	1.84861	−	3.20189i	0.148965	−	0.258016i
$155$	4.00000			0.321288
$156$		0			0
$157$	11.2111			0.894743			0.447372	−	0.894348i	$-0.352360\pi$
$157$	11.2111			0.894743			0.447372	+	0.894348i	$0.352360\pi$
$158$	−6.00000	+	10.3923i	−0.477334	+	0.826767i
$159$	1.60555	−	2.78090i	0.127328	−	0.220539i
$160$	2.65139	+	4.59234i	0.209611	+	0.363056i
$161$	−3.00000			−0.236433
$162$	−1.15139	−	1.99426i	−0.0904616	−	0.156684i
$163$	−1.89445	−	3.28128i	−0.148385	−	0.257010i	0.782246	−	0.622970i	$-0.214074\pi$
$163$	−1.89445	−	3.28128i	−0.148385	−	0.257010i	−0.930631	+	0.365960i	$0.880741\pi$
$164$	−9.90833			−0.773710
$165$	0.802776	+	1.39045i	0.0624960	+	0.108246i
$166$	−10.6056	+	18.3694i	−0.823150	+	1.42574i
$167$	4.50000	−	7.79423i	0.348220	−	0.603136i	−0.637713	−	0.770274i	$-0.720119\pi$
$167$	4.50000	−	7.79423i	0.348220	−	0.603136i	0.985933	+	0.167139i	$0.0534527\pi$
$168$	3.00000			0.231455
$169$		0			0
$170$	17.5139			1.34325
$171$	5.60555	−	9.70910i	0.428667	−	0.742473i
$172$	16.8625	−	29.2067i	1.28575	−	2.22699i
$173$	−2.40833	−	4.17134i	−0.183102	−	0.317141i	0.759834	−	0.650118i	$-0.225280\pi$
$173$	−2.40833	−	4.17134i	−0.183102	−	0.317141i	−0.942935	+	0.332976i	$0.891947\pi$
$174$	−14.3028			−1.08429
$175$	−0.500000	−	0.866025i	−0.0377964	−	0.0654654i
$176$	0.243061	+	0.420994i	0.0183214	+	0.0317336i
$177$	10.8167			0.813029
$178$	−7.15139	−	12.3866i	−0.536019	−	0.928412i
$179$	−11.4083	+	19.7598i	−0.852698	+	1.47692i	0.0260655	+	0.999660i	$0.491702\pi$
$179$	−11.4083	+	19.7598i	−0.852698	+	1.47692i	−0.878764	+	0.477257i	$0.841631\pi$
$180$	3.30278	−	5.72058i	0.246174	−	0.426387i
$181$	17.6333			1.31067			0.655337	−	0.755337i	$-0.272527\pi$
$181$	17.6333			1.31067			0.655337	+	0.755337i	$0.272527\pi$
$182$		0			0
$183$	−1.00000			−0.0739221
$184$	4.50000	−	7.79423i	0.331744	−	0.574598i
$185$	1.80278	−	3.12250i	0.132543	−	0.229571i
$186$	−4.60555	−	7.97705i	−0.337695	−	0.584906i
$187$	−12.2111			−0.892964
$188$	15.2111	+	26.3464i	1.10938	+	1.92151i
$189$	2.50000	+	4.33013i	0.181848	+	0.314970i
$190$	12.9083			0.936468
$191$	−8.40833	−	14.5636i	−0.608405	−	1.05379i	−0.991503	−	0.130081i	$-0.958476\pi$
$191$	−8.40833	−	14.5636i	−0.608405	−	1.05379i	0.383098	−	0.923708i	$-0.374857\pi$
$192$	6.40833	−	11.0995i	0.462481	−	0.801041i
$193$	7.80278	−	13.5148i	0.561656	−	0.972817i	−0.435696	−	0.900094i	$-0.643498\pi$
$193$	7.80278	−	13.5148i	0.561656	−	0.972817i	0.997352	−	0.0727230i	$-0.0231689\pi$
$194$	19.3305			1.38785
$195$		0			0
$196$	−19.8167			−1.41548
$197$	0.591673	−	1.02481i	0.0421550	−	0.0730145i	−0.844178	−	0.536063i	$-0.819911\pi$
$197$	0.591673	−	1.02481i	0.0421550	−	0.0730145i	0.886333	+	0.463048i	$0.153244\pi$
$198$	−3.69722	+	6.40378i	−0.262750	+	0.455097i
$199$	−6.40833	−	11.0995i	−0.454274	−	0.786826i	0.544372	−	0.838844i	$-0.316768\pi$
$199$	−6.40833	−	11.0995i	−0.454274	−	0.786826i	−0.998646	+	0.0520179i	$0.983435\pi$
$200$	3.00000			0.212132
$201$	−3.50000	−	6.06218i	−0.246871	−	0.427593i
$202$	10.3625	+	17.9484i	0.729102	+	1.26284i
$203$	−6.21110			−0.435934
$204$	−12.5597	−	21.7541i	−0.879356	−	1.52309i
$205$	1.50000	−	2.59808i	0.104765	−	0.181458i
$206$	4.60555	−	7.97705i	0.320884	−	0.555787i
$207$	6.00000			0.417029
$208$		0			0
$209$	−9.00000			−0.622543
$210$	−1.15139	+	1.99426i	−0.0794533	+	0.137617i
$211$	11.8028	−	20.4430i	0.812537	−	1.40735i	−0.0985467	−	0.995132i	$-0.531419\pi$
$211$	11.8028	−	20.4430i	0.812537	−	1.40735i	0.911083	−	0.412222i	$-0.135247\pi$
$212$	5.30278	+	9.18468i	0.364196	+	0.630806i
$213$	−4.81665			−0.330032
$214$	−7.15139	−	12.3866i	−0.488859	−	0.846728i
$215$	5.10555	+	8.84307i	0.348196	+	0.603093i
$216$	−15.0000			−1.02062
$217$	−2.00000	−	3.46410i	−0.135769	−	0.235159i
$218$	−22.1194	+	38.3120i	−1.49812	+	2.59481i
$219$	−0.394449	+	0.683205i	−0.0266544	+	0.0461667i
$220$	−5.30278			−0.357513
$221$		0			0
$222$	−8.30278			−0.557246
$223$	−2.10555	+	3.64692i	−0.140998	+	0.244216i	−0.927873	−	0.372897i	$-0.878364\pi$
$223$	−2.10555	+	3.64692i	−0.140998	+	0.244216i	0.786875	+	0.617113i	$0.211698\pi$
$224$	2.65139	−	4.59234i	0.177153	−	0.306839i
$225$	1.00000	+	1.73205i	0.0666667	+	0.115470i
$226$	−3.69722			−0.245936
$227$	−13.7111	−	23.7483i	−0.910038	−	1.57623i	−0.814008	−	0.580853i	$-0.802719\pi$
$227$	−13.7111	−	23.7483i	−0.910038	−	1.57623i	−0.0960296	−	0.995378i	$-0.530614\pi$
$228$	−9.25694	−	16.0335i	−0.613056	−	1.06184i
$229$	−14.0000			−0.925146			−0.462573	−	0.886581i	$-0.653074\pi$
$229$	−14.0000			−0.925146			−0.462573	+	0.886581i	$0.653074\pi$
$230$	3.45416	+	5.98279i	0.227761	+	0.394493i
$231$	0.802776	−	1.39045i	0.0528188	−	0.0914848i
$232$	9.31665	−	16.1369i	0.611668	−	1.05944i
$233$	15.2111			0.996512			0.498256	−	0.867030i	$-0.333974\pi$
$233$	15.2111			0.996512			0.498256	+	0.867030i	$0.333974\pi$
$234$		0			0
$235$	−9.21110			−0.600866
$236$	−17.8625	+	30.9387i	−1.16275	+	2.01394i
$237$	−2.60555	+	4.51295i	−0.169249	+	0.293147i
$238$	−8.75694	−	15.1675i	−0.567628	−	0.983161i
$239$		0			0			−	1.00000i	$-0.5\pi$
$239$		0			0				1.00000i	$0.5\pi$
$240$	−0.151388	−	0.262211i	−0.00977204	−	0.0169257i
$241$	0.894449	+	1.54923i	0.0576165	+	0.0997947i	0.893395	−	0.449272i	$-0.148317\pi$
$241$	0.894449	+	1.54923i	0.0576165	+	0.0997947i	−0.835778	+	0.549067i	$0.814983\pi$
$242$	−19.3944			−1.24672
$243$	−8.00000	−	13.8564i	−0.513200	−	0.888889i
$244$	1.65139	−	2.86029i	0.105719	−	0.183111i
$245$	3.00000	−	5.19615i	0.191663	−	0.331970i
$246$	−6.90833			−0.440459
$247$		0			0
$248$	12.0000			0.762001
$249$	−4.60555	+	7.97705i	−0.291865	+	0.505525i
$250$	−1.15139	+	1.99426i	−0.0728202	+	0.126128i
$251$	3.59167	+	6.22096i	0.226704	+	0.392664i	0.956829	−	0.290650i	$-0.0938715\pi$
$251$	3.59167	+	6.22096i	0.226704	+	0.392664i	−0.730125	+	0.683314i	$0.760538\pi$
$252$	−6.60555			−0.416111
$253$	−2.40833	−	4.17134i	−0.151410	−	0.262250i
$254$	4.84861	+	8.39804i	0.304229	+	0.526940i
$255$	7.60555			0.476278
$256$	8.95416	+	15.5091i	0.559635	+	0.969317i
$257$	8.19722	−	14.1980i	0.511329	−	0.885647i	−0.488585	−	0.872516i	$-0.662487\pi$
$257$	8.19722	−	14.1980i	0.511329	−	0.885647i	0.999914	−	0.0131312i	$-0.00417990\pi$
$258$	11.7569	−	20.3636i	0.731955	−	1.26778i
$259$	−3.60555			−0.224038
$260$		0			0
$261$	12.4222			0.768915
$262$	24.4222	−	42.3005i	1.50881	−	2.61333i
$263$	−5.89445	+	10.2095i	−0.363467	+	0.629544i	−0.988529	−	0.151032i	$-0.951740\pi$
$263$	−5.89445	+	10.2095i	−0.363467	+	0.629544i	0.625062	+	0.780575i	$0.285074\pi$
$264$	2.40833	+	4.17134i	0.148222	+	0.256729i
$265$	−3.21110			−0.197256
$266$	−6.45416	−	11.1789i	−0.395730	−	0.685425i
$267$	−3.10555	−	5.37897i	−0.190057	−	0.329188i
$268$	23.1194			1.41224
$269$	4.50000	+	7.79423i	0.274370	+	0.475223i	0.969976	−	0.243201i	$-0.0781974\pi$
$269$	4.50000	+	7.79423i	0.274370	+	0.475223i	−0.695606	+	0.718423i	$0.744864\pi$
$270$	5.75694	−	9.97131i	0.350356	−	0.606835i
$271$	−10.4083	+	18.0278i	−0.632261	+	1.09511i	0.354828	+	0.934932i	$0.384540\pi$
$271$	−10.4083	+	18.0278i	−0.632261	+	1.09511i	−0.987088	+	0.160176i	$0.948794\pi$
$272$	2.30278			0.139626
$273$		0			0
$274$	3.69722			0.223357
$275$	0.802776	−	1.39045i	0.0484092	−	0.0838472i
$276$	4.95416	−	8.58086i	0.298206	−	0.516507i
$277$	−13.8028	−	23.9071i	−0.829328	−	1.43644i	−0.898566	−	0.438839i	$-0.855390\pi$
$277$	−13.8028	−	23.9071i	−0.829328	−	1.43644i	0.0692374	−	0.997600i	$-0.477943\pi$
$278$	14.7250			0.883146
$279$	4.00000	+	6.92820i	0.239474	+	0.414781i
$280$	−1.50000	−	2.59808i	−0.0896421	−	0.155265i
$281$	6.00000			0.357930			0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000			0.357930			0.178965	+	0.983855i	$0.442725\pi$
$282$	10.6056	+	18.3694i	0.631551	+	1.09388i
$283$	−2.50000	+	4.33013i	−0.148610	+	0.257399i	−0.930714	−	0.365748i	$-0.880813\pi$
$283$	−2.50000	+	4.33013i	−0.148610	+	0.257399i	0.782104	+	0.623148i	$0.214146\pi$
$284$	7.95416	−	13.7770i	0.471993	−	0.817515i
$285$	5.60555			0.332044
$286$		0			0
$287$	−3.00000			−0.177084
$288$	−5.30278	+	9.18468i	−0.312469	+	0.541212i
$289$	−20.4222	+	35.3723i	−1.20131	+	2.08072i
$290$	7.15139	+	12.3866i	0.419944	+	0.727364i
$291$	8.39445			0.492091
$292$	−1.30278	−	2.25647i	−0.0762392	−	0.132050i
$293$	5.19722	+	9.00186i	0.303625	+	0.525894i	0.976954	−	0.213449i	$-0.0684696\pi$
$293$	5.19722	+	9.00186i	0.303625	+	0.525894i	−0.673329	+	0.739343i	$0.735136\pi$
$294$	−13.8167			−0.805804
$295$	−5.40833	−	9.36750i	−0.314885	−	0.545397i
$296$	5.40833	−	9.36750i	0.314353	−	0.544475i
$297$	−4.01388	+	6.95224i	−0.232909	+	0.403410i
$298$	−6.90833			−0.400189
$299$		0			0
$300$	3.30278			0.190686
$301$	5.10555	−	8.84307i	0.294279	−	0.509706i
$302$	−1.39445	+	2.41526i	−0.0802415	+	0.138982i
$303$	4.50000	+	7.79423i	0.258518	+	0.447767i
$304$	1.69722			0.0973425
$305$	0.500000	+	0.866025i	0.0286299	+	0.0495885i
$306$	17.5139	+	30.3349i	1.00120	+	1.73413i
$307$	16.0000			0.913168			0.456584	−	0.889680i	$-0.349073\pi$
$307$	16.0000			0.913168			0.456584	+	0.889680i	$0.349073\pi$
$308$	2.65139	+	4.59234i	0.151077	+	0.261673i
$309$	2.00000	−	3.46410i	0.113776	−	0.197066i
$310$	−4.60555	+	7.97705i	−0.261578	+	0.453066i
$311$	−9.21110			−0.522314			−0.261157	−	0.965296i	$-0.584104\pi$
$311$	−9.21110			−0.522314			−0.261157	+	0.965296i	$0.584104\pi$
$312$		0			0
$313$	14.0000			0.791327			0.395663	−	0.918396i	$-0.370515\pi$
$313$	14.0000			0.791327			0.395663	+	0.918396i	$0.370515\pi$
$314$	−12.9083	+	22.3579i	−0.728459	+	1.26173i
$315$	1.00000	−	1.73205i	0.0563436	−	0.0975900i
$316$	−8.60555	−	14.9053i	−0.484100	−	0.838486i
$317$	−6.00000			−0.336994			−0.168497	−	0.985702i	$-0.553891\pi$
$317$	−6.00000			−0.336994			−0.168497	+	0.985702i	$0.553891\pi$
$318$	3.69722	+	6.40378i	0.207330	+	0.359106i
$319$	−4.98612	−	8.63622i	−0.279169	−	0.483535i
$320$	−12.8167			−0.716473
$321$	−3.10555	−	5.37897i	−0.173335	−	0.300225i
$322$	3.45416	−	5.98279i	0.192493	−	0.333408i
$323$	−21.3167	+	36.9215i	−1.18609	+	2.05437i
$324$	3.30278			0.183488
$325$		0			0
$326$	8.72498			0.483232
$327$	−9.60555	+	16.6373i	−0.531188	+	0.920045i
$328$	4.50000	−	7.79423i	0.248471	−	0.430364i
$329$	4.60555	+	7.97705i	0.253912	+	0.439789i
$330$	−3.69722			−0.203526
$331$	5.01388	+	8.68429i	0.275588	+	0.477332i	0.970283	−	0.241972i	$-0.0777942\pi$
$331$	5.01388	+	8.68429i	0.275588	+	0.477332i	−0.694696	+	0.719304i	$0.744461\pi$
$332$	−15.2111	−	26.3464i	−0.834818	−	1.44595i
$333$	7.21110			0.395166
$334$	10.3625	+	17.9484i	0.567010	+	0.982091i
$335$	−3.50000	+	6.06218i	−0.191225	+	0.331212i
$336$	−0.151388	+	0.262211i	−0.00825888	+	0.0143048i
$337$	−25.6333			−1.39634			−0.698168	−	0.715934i	$-0.746001\pi$
$337$	−25.6333			−1.39634			−0.698168	+	0.715934i	$0.746001\pi$
$338$		0			0
$339$	−1.60555			−0.0872016
$340$	−12.5597	+	21.7541i	−0.681146	+	1.17978i
$341$	3.21110	−	5.56179i	0.173891	−	0.301188i
$342$	12.9083	+	22.3579i	0.698002	+	1.20898i
$343$	−13.0000			−0.701934
$344$	15.3167	+	26.5292i	0.825819	+	1.43036i
$345$	1.50000	+	2.59808i	0.0807573	+	0.139876i
$346$	11.0917			0.596292
$347$	−2.89445	−	5.01333i	−0.155382	−	0.269130i	0.777816	−	0.628492i	$-0.216328\pi$
$347$	−2.89445	−	5.01333i	−0.155382	−	0.269130i	−0.933198	+	0.359362i	$0.882994\pi$
$348$	10.2569	−	17.7655i	0.549830	−	0.952333i
$349$	−1.89445	+	3.28128i	−0.101408	+	0.175643i	−0.912265	−	0.409601i	$-0.865668\pi$
$349$	−1.89445	+	3.28128i	−0.101408	+	0.175643i	0.810857	+	0.585244i	$0.199001\pi$
$350$	2.30278			0.123089
$351$		0			0
$352$	8.51388			0.453791
$353$	8.40833	−	14.5636i	0.447530	−	0.775145i	−0.550695	−	0.834707i	$-0.685637\pi$
$353$	8.40833	−	14.5636i	0.447530	−	0.775145i	0.998225	+	0.0595620i	$0.0189704\pi$
$354$	−12.4542	+	21.5712i	−0.661931	+	1.14650i
$355$	2.40833	+	4.17134i	0.127821	+	0.221392i
$356$	20.5139			1.08723
$357$	−3.80278	−	6.58660i	−0.201264	−	0.348600i
$358$	−26.2708	−	45.5024i	−1.38846	−	2.40488i
$359$	−18.4222			−0.972287			−0.486143	−	0.873879i	$-0.661597\pi$
$359$	−18.4222			−0.972287			−0.486143	+	0.873879i	$0.661597\pi$
$360$	3.00000	+	5.19615i	0.158114	+	0.273861i
$361$	−6.21110	+	10.7579i	−0.326900	+	0.566208i
$362$	−20.3028	+	35.1654i	−1.06709	+	1.84825i
$363$	−8.42221			−0.442051
$364$		0			0
$365$	0.788897			0.0412928
$366$	1.15139	−	1.99426i	0.0601840	−	0.104242i
$367$	−5.71110	+	9.89192i	−0.298117	+	0.516354i	−0.975705	−	0.219088i	$-0.929692\pi$
$367$	−5.71110	+	9.89192i	−0.298117	+	0.516354i	0.677588	+	0.735442i	$0.263025\pi$
$368$	0.454163	+	0.786634i	0.0236749	+	0.0410061i
$369$	6.00000			0.312348
$370$	4.15139	+	7.19041i	0.215820	+	0.373812i
$371$	1.60555	+	2.78090i	0.0833561	+	0.144377i
$372$	13.2111			0.684964
$373$	10.1972	+	17.6621i	0.527992	+	0.914509i	0.999467	+	0.0326301i	$0.0103883\pi$
$373$	10.1972	+	17.6621i	0.527992	+	0.914509i	−0.471475	+	0.881879i	$0.656278\pi$
$374$	14.0597	−	24.3521i	0.727011	−	1.25922i
$375$	−0.500000	+	0.866025i	−0.0258199	+	0.0447214i
$376$	−27.6333			−1.42508
$377$		0			0
$378$	−11.5139			−0.592210
$379$	4.80278	−	8.31865i	0.246702	−	0.427300i	−0.715907	−	0.698196i	$-0.753986\pi$
$379$	4.80278	−	8.31865i	0.246702	−	0.427300i	0.962609	+	0.270895i	$0.0873198\pi$
$380$	−9.25694	+	16.0335i	−0.474871	+	0.822501i
$381$	2.10555	+	3.64692i	0.107871	+	0.186837i
$382$	38.7250			1.98134
$383$	−12.3167	−	21.3331i	−0.629352	−	1.09007i	−0.987682	−	0.156474i	$-0.949987\pi$
$383$	−12.3167	−	21.3331i	−0.629352	−	1.09007i	0.358330	−	0.933595i	$-0.383346\pi$
$384$	9.45416	+	16.3751i	0.482456	+	0.835638i
$385$	−1.60555			−0.0818265
$386$	17.9680	+	31.1216i	0.914549	+	1.58405i
$387$	−10.2111	+	17.6861i	−0.519060	+	0.899037i
$388$	−13.8625	+	24.0105i	−0.703761	+	1.21895i
$389$	−15.2111			−0.771234			−0.385617	−	0.922659i	$-0.626011\pi$
$389$	−15.2111			−0.771234			−0.385617	+	0.922659i	$0.626011\pi$
$390$		0			0
$391$	−22.8167			−1.15389
$392$	9.00000	−	15.5885i	0.454569	−	0.787336i
$393$	10.6056	−	18.3694i	0.534979	−	0.926611i
$394$	1.36249	+	2.35990i	0.0686413	+	0.118890i
$395$	5.21110			0.262199
$396$	−5.30278	−	9.18468i	−0.266475	−	0.461547i
$397$	11.0139	+	19.0766i	0.552771	+	0.957427i	0.998073	+	0.0620468i	$0.0197628\pi$
$397$	11.0139	+	19.0766i	0.552771	+	0.957427i	−0.445303	+	0.895380i	$0.646904\pi$
$398$	29.5139			1.47940
$399$	−2.80278	−	4.85455i	−0.140314	−	0.243031i
$400$	−0.151388	+	0.262211i	−0.00756939	+	0.0131106i
$401$	6.10555	−	10.5751i	0.304897	−	0.528097i	−0.672342	−	0.740241i	$-0.734711\pi$
$401$	6.10555	−	10.5751i	0.304897	−	0.528097i	0.977238	+	0.212144i	$0.0680447\pi$
$402$	16.1194			0.803964
$403$		0			0
$404$	−29.7250			−1.47887
$405$	−0.500000	+	0.866025i	−0.0248452	+	0.0430331i
$406$	7.15139	−	12.3866i	0.354917	−	0.614735i
$407$	−2.89445	−	5.01333i	−0.143472	−	0.248502i
$408$	22.8167			1.12959
$409$	4.10555	+	7.11102i	0.203006	+	0.351617i	0.949496	−	0.313780i	$-0.101595\pi$
$409$	4.10555	+	7.11102i	0.203006	+	0.351617i	−0.746489	+	0.665397i	$0.768262\pi$
$410$	3.45416	+	5.98279i	0.170589	+	0.295469i
$411$	1.60555			0.0791960
$412$	6.60555	+	11.4412i	0.325432	+	0.563665i
$413$	−5.40833	+	9.36750i	−0.266126	+	0.460944i
$414$	−6.90833	+	11.9656i	−0.339526	+	0.588076i
$415$	9.21110			0.452155
$416$		0			0
$417$	6.39445			0.313138
$418$	10.3625	−	17.9484i	0.506846	−	0.877883i
$419$	−8.61943	+	14.9293i	−0.421087	+	0.729344i	−0.996046	−	0.0888384i	$-0.971685\pi$
$419$	−8.61943	+	14.9293i	−0.421087	+	0.729344i	0.574959	+	0.818182i	$0.305018\pi$
$420$	−1.65139	−	2.86029i	−0.0805795	−	0.139568i
$421$	−32.4222			−1.58016			−0.790081	−	0.613003i	$-0.789961\pi$
$421$	−32.4222			−1.58016			−0.790081	+	0.613003i	$0.789961\pi$
$422$	27.1791	+	47.0757i	1.32306	+	2.29161i
$423$	−9.21110	−	15.9541i	−0.447859	−	0.775715i
$424$	−9.63331			−0.467835
$425$	−3.80278	−	6.58660i	−0.184462	−	0.319497i
$426$	5.54584	−	9.60567i	0.268697	−	0.465396i
$427$	0.500000	−	0.866025i	0.0241967	−	0.0419099i
$428$	20.5139			0.991576
$429$		0			0
$430$	−23.5139			−1.13394
$431$	14.6194	−	25.3216i	0.704193	−	1.21970i	−0.262789	−	0.964853i	$-0.584642\pi$
$431$	14.6194	−	25.3216i	0.704193	−	1.21970i	0.966982	−	0.254845i	$-0.0820244\pi$
$432$	0.756939	−	1.31106i	0.0364182	−	0.0630783i
$433$	−1.80278	−	3.12250i	−0.0866359	−	0.150058i	0.819451	−	0.573149i	$-0.194278\pi$
$433$	−1.80278	−	3.12250i	−0.0866359	−	0.150058i	−0.906087	+	0.423091i	$0.860945\pi$
$434$	9.21110			0.442147
$435$	3.10555	+	5.37897i	0.148900	+	0.257902i
$436$	−31.7250	−	54.9493i	−1.51935	−	2.63159i
$437$	−16.8167			−0.804450
$438$	−0.908327	−	1.57327i	−0.0434015	−	0.0751737i
$439$	13.6194	−	23.5895i	0.650020	−	1.12587i	−0.333098	−	0.942892i	$-0.608094\pi$
$439$	13.6194	−	23.5895i	0.650020	−	1.12587i	0.983118	−	0.182975i	$-0.0585728\pi$
$440$	2.40833	−	4.17134i	0.114812	−	0.198861i
$441$	12.0000			0.571429
$442$		0			0
$443$	6.42221			0.305128			0.152564	−	0.988294i	$-0.451247\pi$
$443$	6.42221			0.305128			0.152564	+	0.988294i	$0.451247\pi$
$444$	5.95416	−	10.3129i	0.282572	−	0.489429i
$445$	−3.10555	+	5.37897i	−0.147217	+	0.254988i
$446$	−4.84861	−	8.39804i	−0.229588	−	0.397659i
$447$	−3.00000			−0.141895
$448$	6.40833	+	11.0995i	0.302765	+	0.524404i
$449$	15.3167	+	26.5292i	0.722838	+	1.25199i	0.959858	+	0.280487i	$0.0904959\pi$
$449$	15.3167	+	26.5292i	0.722838	+	1.25199i	−0.237020	+	0.971505i	$0.576171\pi$
$450$	−4.60555			−0.217108
$451$	−2.40833	−	4.17134i	−0.113404	−	0.196421i
$452$	2.65139	−	4.59234i	0.124711	−	0.216005i
$453$	−0.605551	+	1.04885i	−0.0284513	+	0.0492791i
$454$	63.1472			2.96364
$455$		0			0
$456$	16.8167			0.787512
$457$	−13.4083	+	23.2239i	−0.627215	+	1.08637i	0.360893	+	0.932607i	$0.382472\pi$
$457$	−13.4083	+	23.2239i	−0.627215	+	1.08637i	−0.988108	+	0.153761i	$0.950861\pi$
$458$	16.1194	−	27.9197i	0.753211	−	1.30460i
$459$	19.0139	+	32.9330i	0.887492	+	1.53718i
$460$	−9.90833			−0.461978
$461$	18.1056	+	31.3597i	0.843260	+	1.46057i	0.887124	+	0.461531i	$0.152700\pi$
$461$	18.1056	+	31.3597i	0.843260	+	1.46057i	−0.0438645	+	0.999037i	$0.513967\pi$
$462$	1.84861	+	3.20189i	0.0860052	+	0.148965i
$463$	34.4222			1.59974			0.799868	−	0.600176i	$-0.204903\pi$
$463$	34.4222			1.59974			0.799868	+	0.600176i	$0.204903\pi$
$464$	0.940285	+	1.62862i	0.0436516	+	0.0756069i
$465$	−2.00000	+	3.46410i	−0.0927478	+	0.160644i
$466$	−17.5139	+	30.3349i	−0.811315	+	1.40524i
$467$	2.78890			0.129055			0.0645274	−	0.997916i	$-0.479446\pi$
$467$	2.78890			0.129055			0.0645274	+	0.997916i	$0.479446\pi$
$468$		0			0
$469$	7.00000			0.323230
$470$	10.6056	−	18.3694i	0.489198	−	0.847315i
$471$	−5.60555	+	9.70910i	−0.258290	+	0.447372i
$472$	−16.2250	−	28.1025i	−0.746815	−	1.29352i
$473$	16.3944			0.753818
$474$	−6.00000	−	10.3923i	−0.275589	−	0.477334i
$475$	−2.80278	−	4.85455i	−0.128600	−	0.222742i
$476$	25.1194			1.15135
$477$	−3.21110	−	5.56179i	−0.147026	−	0.254657i
$478$		0			0
$479$	−14.4083	+	24.9560i	−0.658333	+	1.14027i	0.322714	+	0.946497i	$0.395405\pi$
$479$	−14.4083	+	24.9560i	−0.658333	+	1.14027i	−0.981047	+	0.193770i	$0.937928\pi$
$480$	−5.30278			−0.242037
$481$		0			0
$482$	−4.11943			−0.187635
$483$	1.50000	−	2.59808i	0.0682524	−	0.118217i
$484$	13.9083	−	24.0899i	0.632197	−	1.09500i
$485$	−4.19722	−	7.26981i	−0.190586	−	0.330105i
$486$	36.8444			1.67130
$487$	−0.500000	−	0.866025i	−0.0226572	−	0.0392434i	0.854475	−	0.519493i	$-0.173879\pi$
$487$	−0.500000	−	0.866025i	−0.0226572	−	0.0392434i	−0.877132	+	0.480250i	$0.840546\pi$
$488$	1.50000	+	2.59808i	0.0679018	+	0.117609i
$489$	3.78890			0.171340
$490$	6.90833	+	11.9656i	0.312086	+	0.540549i
$491$	8.40833	−	14.5636i	0.379462	−	0.657248i	−0.611522	−	0.791228i	$-0.709442\pi$
$491$	8.40833	−	14.5636i	0.379462	−	0.657248i	0.990984	+	0.133979i	$0.0427756\pi$
$492$	4.95416	−	8.58086i	0.223351	−	0.386855i
$493$	−47.2389			−2.12753
$494$		0			0
$495$	3.21110			0.144328
$496$	−0.605551	+	1.04885i	−0.0271901	+	0.0470946i
$497$	2.40833	−	4.17134i	0.108028	−	0.187110i
$498$	−10.6056	−	18.3694i	−0.475246	−	0.823150i
$499$	−2.42221			−0.108433			−0.0542164	−	0.998529i	$-0.517266\pi$
$499$	−2.42221			−0.108433			−0.0542164	+	0.998529i	$0.517266\pi$
$500$	−1.65139	−	2.86029i	−0.0738523	−	0.127916i
$501$	4.50000	+	7.79423i	0.201045	+	0.348220i
$502$	−16.5416			−0.738289
$503$	−1.50000	−	2.59808i	−0.0668817	−	0.115842i	0.830645	−	0.556802i	$-0.187972\pi$
$503$	−1.50000	−	2.59808i	−0.0668817	−	0.115842i	−0.897527	+	0.440959i	$0.854638\pi$
$504$	3.00000	−	5.19615i	0.133631	−	0.231455i
$505$	4.50000	−	7.79423i	0.200247	−	0.346839i
$506$	11.0917			0.493085
$507$		0			0
$508$	−13.9083			−0.617082
$509$	1.50000	−	2.59808i	0.0664863	−	0.115158i	−0.830866	−	0.556473i	$-0.812154\pi$
$509$	1.50000	−	2.59808i	0.0664863	−	0.115158i	0.897352	+	0.441315i	$0.145488\pi$
$510$	−8.75694	+	15.1675i	−0.387764	+	0.671627i
$511$	−0.394449	−	0.683205i	−0.0174494	−	0.0302232i
$512$	−3.42221			−0.151242
$513$	14.0139	+	24.2727i	0.618728	+	1.07167i
$514$	18.8764	+	32.6948i	0.832601	+	1.44211i
$515$	−4.00000			−0.176261
$516$	16.8625	+	29.2067i	0.742330	+	1.28575i
$517$	−7.39445	+	12.8076i	−0.325207	+	0.563276i
$518$	4.15139	−	7.19041i	0.182402	−	0.315929i
$519$	4.81665			0.211428
$520$		0			0
$521$	18.0000			0.788594			0.394297	−	0.918983i	$-0.370988\pi$
$521$	18.0000			0.788594			0.394297	+	0.918983i	$0.370988\pi$
$522$	−14.3028	+	24.7731i	−0.626015	+	1.08429i
$523$	0.711103	−	1.23167i	0.0310943	−	0.0538570i	−0.850059	−	0.526687i	$-0.823434\pi$
$523$	0.711103	−	1.23167i	0.0310943	−	0.0538570i	0.881154	+	0.472830i	$0.156767\pi$
$524$	35.0278	+	60.6699i	1.53019	+	2.65037i
$525$	1.00000			0.0436436
$526$	−13.5736	−	23.5102i	−0.591837	−	1.02509i
$527$	−15.2111	−	26.3464i	−0.662606	−	1.14767i
$528$	−0.486122			−0.0211557
$529$	7.00000	+	12.1244i	0.304348	+	0.527146i
$530$	3.69722	−	6.40378i	0.160597	−	0.278162i
$531$	10.8167	−	18.7350i	0.469403	−	0.813029i
$532$	18.5139			0.802678
$533$		0			0
$534$	14.3028			0.618942
$535$	−3.10555	+	5.37897i	−0.134265	+	0.232553i
$536$	−10.5000	+	18.1865i	−0.453531	+	0.785539i
$537$	−11.4083	−	19.7598i	−0.492306	−	0.852698i
$538$	−20.7250			−0.893517
$539$	−4.81665	−	8.34269i	−0.207468	−	0.359345i
$540$	8.25694	+	14.3014i	0.355322	+	0.615436i
$541$	25.6333			1.10206			0.551031	−	0.834485i	$-0.314235\pi$
$541$	25.6333			1.10206			0.551031	+	0.834485i	$0.314235\pi$
$542$	−23.9680	−	41.5139i	−1.02952	−	1.78317i
$543$	−8.81665	+	15.2709i	−0.378359	+	0.655337i
$544$	20.1653	−	34.9273i	0.864579	−	1.49749i
$545$	19.2111			0.822913
$546$		0			0
$547$	32.8444			1.40433			0.702163	−	0.712016i	$-0.252218\pi$
$547$	32.8444			1.40433			0.702163	+	0.712016i	$0.252218\pi$
$548$	−2.65139	+	4.59234i	−0.113262	+	0.196175i
$549$	−1.00000	+	1.73205i	−0.0426790	+	0.0739221i
$550$	1.84861	+	3.20189i	0.0788251	+	0.136529i
$551$	−34.8167			−1.48324
$552$	4.50000	+	7.79423i	0.191533	+	0.331744i
$553$	−2.60555	−	4.51295i	−0.110799	−	0.191910i
$554$	63.5694			2.70080
$555$	1.80278	+	3.12250i	0.0765236	+	0.132543i
$556$	−10.5597	+	18.2900i	−0.447832	+	0.775667i
$557$	−0.802776	+	1.39045i	−0.0340147	+	0.0589152i	−0.882532	−	0.470253i	$-0.844163\pi$
$557$	−0.802776	+	1.39045i	−0.0340147	+	0.0589152i	0.848517	+	0.529168i	$0.177496\pi$
$558$	−18.4222			−0.779874
$559$		0			0
$560$	0.302776			0.0127946
$561$	6.10555	−	10.5751i	0.257777	−	0.446482i
$562$	−6.90833	+	11.9656i	−0.291410	+	0.504737i
$563$	−4.71110	−	8.15987i	−0.198549	−	0.343897i	0.749509	−	0.661994i	$-0.230290\pi$
$563$	−4.71110	−	8.15987i	−0.198549	−	0.343897i	−0.948058	+	0.318097i	$0.896956\pi$
$564$	−30.4222			−1.28101
$565$	0.802776	+	1.39045i	0.0337730	+	0.0584966i
$566$	−5.75694	−	9.97131i	−0.241982	−	0.419125i
$567$	1.00000			0.0419961
$568$	7.22498	+	12.5140i	0.303153	+	0.525077i
$569$	13.7111	−	23.7483i	0.574799	−	0.995582i	−0.421264	−	0.906938i	$-0.638413\pi$
$569$	13.7111	−	23.7483i	0.574799	−	0.995582i	0.996063	−	0.0886436i	$-0.0282532\pi$
$570$	−6.45416	+	11.1789i	−0.270335	+	0.468234i
$571$	20.8444			0.872311			0.436156	−	0.899871i	$-0.356340\pi$
$571$	20.8444			0.872311			0.436156	+	0.899871i	$0.356340\pi$
$572$		0			0
$573$	16.8167			0.702526
$574$	3.45416	−	5.98279i	0.144174	−	0.249717i
$575$	1.50000	−	2.59808i	0.0625543	−	0.108347i
$576$	−12.8167	−	22.1991i	−0.534027	−	0.924962i
$577$	13.6333			0.567562			0.283781	−	0.958889i	$-0.408411\pi$
$577$	13.6333			0.567562			0.283781	+	0.958889i	$0.408411\pi$
$578$	−47.0278	−	81.4545i	−1.95610	−	3.38806i
$579$	7.80278	+	13.5148i	0.324272	+	0.561656i
$580$	−20.5139			−0.851792
$581$	−4.60555	−	7.97705i	−0.191070	−	0.330944i
$582$	−9.66527	+	16.7407i	−0.400638	+	0.693926i
$583$	−2.57779	+	4.46487i	−0.106761	+	0.184916i
$584$	2.36669			0.0979344
$585$		0			0
$586$	−23.9361			−0.988790
$587$	−16.7111	+	28.9445i	−0.689741	+	1.19467i	0.282181	+	0.959361i	$0.408942\pi$
$587$	−16.7111	+	28.9445i	−0.689741	+	1.19467i	−0.971922	+	0.235305i	$0.924391\pi$
$588$	9.90833	−	17.1617i	0.408613	−	0.707738i
$589$	−11.2111	−	19.4182i	−0.461945	−	0.800113i
$590$	24.9083			1.02546
$591$	0.591673	+	1.02481i	0.0243382	+	0.0421550i
$592$	0.545837	+	0.945417i	0.0224337	+	0.0388564i
$593$	−20.7889			−0.853698			−0.426849	−	0.904323i	$-0.640376\pi$
$593$	−20.7889			−0.853698			−0.426849	+	0.904323i	$0.640376\pi$
$594$	−9.24306	−	16.0095i	−0.379247	−	0.656876i
$595$	−3.80278	+	6.58660i	−0.155899	+	0.270024i
$596$	4.95416	−	8.58086i	0.202930	−	0.351486i
$597$	12.8167			0.524551
$598$		0			0
$599$	−21.2111			−0.866662			−0.433331	−	0.901235i	$-0.642662\pi$
$599$	−21.2111			−0.866662			−0.433331	+	0.901235i	$0.642662\pi$
$600$	−1.50000	+	2.59808i	−0.0612372	+	0.106066i
$601$	−6.89445	+	11.9415i	−0.281230	+	0.487105i	−0.971688	−	0.236267i	$-0.924076\pi$
$601$	−6.89445	+	11.9415i	−0.281230	+	0.487105i	0.690458	+	0.723373i	$0.257409\pi$
$602$	11.7569	+	20.3636i	0.479177	+	0.829959i
$603$	−14.0000			−0.570124
$604$	−2.00000	−	3.46410i	−0.0813788	−	0.140952i
$605$	4.21110	+	7.29384i	0.171206	+	0.296537i
$606$	−20.7250			−0.841895
$607$	17.1056	+	29.6277i	0.694293	+	1.20255i	0.970418	+	0.241429i	$0.0776161\pi$
$607$	17.1056	+	29.6277i	0.694293	+	1.20255i	−0.276126	+	0.961122i	$0.589051\pi$
$608$	14.8625	−	25.7426i	0.602754	−	1.04400i
$609$	3.10555	−	5.37897i	0.125843	−	0.217967i
$610$	−2.30278			−0.0932367
$611$		0			0
$612$	−50.2389			−2.03079
$613$	−2.80278	+	4.85455i	−0.113203	+	0.196073i	−0.917060	−	0.398749i	$-0.869444\pi$
$613$	−2.80278	+	4.85455i	−0.113203	+	0.196073i	0.803857	+	0.594823i	$0.202778\pi$
$614$	−18.4222	+	31.9082i	−0.743460	+	1.28771i
$615$	1.50000	+	2.59808i	0.0604858	+	0.104765i
$616$	−4.81665			−0.194069
$617$	−19.2250	−	33.2986i	−0.773969	−	1.34055i	−0.935372	−	0.353664i	$-0.884935\pi$
$617$	−19.2250	−	33.2986i	−0.773969	−	1.34055i	0.161404	−	0.986888i	$-0.448398\pi$
$618$	4.60555	+	7.97705i	0.185262	+	0.320884i
$619$	−14.4222			−0.579677			−0.289839	−	0.957076i	$-0.593602\pi$
$619$	−14.4222			−0.579677			−0.289839	+	0.957076i	$0.593602\pi$
$620$	−6.60555	−	11.4412i	−0.265285	−	0.459488i
$621$	−7.50000	+	12.9904i	−0.300965	+	0.521286i
$622$	10.6056	−	18.3694i	0.425244	−	0.736544i
$623$	6.21110			0.248843
$624$		0			0
$625$	1.00000			0.0400000
$626$	−16.1194	+	27.9197i	−0.644262	+	1.11589i
$627$	4.50000	−	7.79423i	0.179713	−	0.311272i
$628$	−18.5139	−	32.0670i	−0.738784	−	1.27961i
$629$	−27.4222			−1.09339
$630$	2.30278	+	3.98852i	0.0917448	+	0.158907i
$631$	−18.0139	−	31.2010i	−0.717121	−	1.24209i	−0.962136	−	0.272571i	$-0.912126\pi$
$631$	−18.0139	−	31.2010i	−0.717121	−	1.24209i	0.245015	−	0.969519i	$-0.421207\pi$
$632$	15.6333			0.621860
$633$	11.8028	+	20.4430i	0.469118	+	0.812537i
$634$	6.90833	−	11.9656i	0.274365	−	0.475214i
$635$	2.10555	−	3.64692i	0.0835563	−	0.144724i
$636$	−10.6056			−0.420537
$637$		0			0
$638$	22.9638			0.909147
$639$	−4.81665	+	8.34269i	−0.190544	+	0.330032i
$640$	9.45416	−	16.3751i	0.373709	−	0.647282i
$641$	−4.71110	−	8.15987i	−0.186077	−	0.322295i	0.757862	−	0.652415i	$-0.226244\pi$
$641$	−4.71110	−	8.15987i	−0.186077	−	0.322295i	−0.943939	+	0.330120i	$0.892911\pi$
$642$	14.3028			0.564486
$643$	1.31665	+	2.28051i	0.0519238	+	0.0899346i	0.890819	−	0.454358i	$-0.150131\pi$
$643$	1.31665	+	2.28051i	0.0519238	+	0.0899346i	−0.838895	+	0.544293i	$0.816798\pi$
$644$	4.95416	+	8.58086i	0.195221	+	0.338133i
$645$	−10.2111			−0.402062
$646$	−49.0875	−	85.0220i	−1.93132	−	3.34515i
$647$	−19.7111	+	34.1406i	−0.774923	+	1.34221i	0.159914	+	0.987131i	$0.448878\pi$
$647$	−19.7111	+	34.1406i	−0.774923	+	1.34221i	−0.934838	+	0.355076i	$0.884455\pi$
$648$	−1.50000	+	2.59808i	−0.0589256	+	0.102062i
$649$	−17.3667			−0.681702
$650$		0			0
$651$	4.00000			0.156772
$652$	−6.25694	+	10.8373i	−0.245041	+	0.424423i
$653$	3.59167	−	6.22096i	0.140553	−	0.243445i	−0.787152	−	0.616759i	$-0.788445\pi$
$653$	3.59167	−	6.22096i	0.140553	−	0.243445i	0.927705	+	0.373314i	$0.121779\pi$
$654$	−22.1194	−	38.3120i	−0.864938	−	1.49812i
$655$	−21.2111			−0.828786
$656$	0.454163	+	0.786634i	0.0177321	+	0.0307129i
$657$	0.788897	+	1.36641i	0.0307778	+	0.0533087i
$658$	−21.2111			−0.826895
$659$	17.4083	+	30.1521i	0.678132	+	1.17456i	0.975543	+	0.219810i	$0.0705436\pi$
$659$	17.4083	+	30.1521i	0.678132	+	1.17456i	−0.297411	+	0.954750i	$0.596123\pi$
$660$	2.65139	−	4.59234i	0.103205	−	0.178757i
$661$	−2.31665	+	4.01256i	−0.0901074	+	0.156071i	−0.907556	−	0.419931i	$-0.862054\pi$
$661$	−2.31665	+	4.01256i	−0.0901074	+	0.156071i	0.817449	+	0.576001i	$0.195388\pi$
$662$	−23.0917			−0.897483
$663$		0			0
$664$	27.6333			1.07238
$665$	−2.80278	+	4.85455i	−0.108687	+	0.188251i
$666$	−8.30278	+	14.3808i	−0.321726	+	0.557246i
$667$	−9.31665	−	16.1369i	−0.360742	−	0.624824i
$668$	−29.7250			−1.15009
$669$	−2.10555	−	3.64692i	−0.0814053	−	0.140998i
$670$	−8.05971	−	13.9598i	−0.311374	−	0.539315i
$671$	1.60555			0.0619816
$672$	2.65139	+	4.59234i	0.102280	+	0.177153i
$673$	8.80278	−	15.2469i	0.339322	−	0.587723i	−0.644983	−	0.764197i	$-0.723136\pi$
$673$	8.80278	−	15.2469i	0.339322	−	0.587723i	0.984305	+	0.176474i	$0.0564690\pi$
$674$	29.5139	−	51.1195i	1.13683	−	1.96905i
$675$	−5.00000			−0.192450
$676$		0			0
$677$	−9.63331			−0.370238			−0.185119	−	0.982716i	$-0.559267\pi$
$677$	−9.63331			−0.370238			−0.185119	+	0.982716i	$0.559267\pi$
$678$	1.84861	−	3.20189i	0.0709955	−	0.122968i
$679$	−4.19722	+	7.26981i	−0.161075	+	0.278990i
$680$	−11.4083	−	19.7598i	−0.437489	−	0.757754i
$681$	27.4222			1.05082
$682$	7.39445	+	12.8076i	0.283148	+	0.490427i
$683$	18.1056	+	31.3597i	0.692790	+	1.19995i	0.970920	+	0.239404i	$0.0769519\pi$
$683$	18.1056	+	31.3597i	0.692790	+	1.19995i	−0.278130	+	0.960543i	$0.589715\pi$
$684$	−37.0278			−1.41579
$685$	−0.802776	−	1.39045i	−0.0306725	−	0.0531263i
$686$	14.9680	−	25.9254i	0.571482	−	0.989837i
$687$	7.00000	−	12.1244i	0.267067	−	0.462573i
$688$	−3.09167			−0.117869
$689$		0			0
$690$	−6.90833			−0.262996
$691$	−15.0139	+	26.0048i	−0.571155	+	0.989269i	0.425293	+	0.905056i	$0.360171\pi$
$691$	−15.0139	+	26.0048i	−0.571155	+	0.989269i	−0.996448	+	0.0842134i	$0.973162\pi$
$692$	−7.95416	+	13.7770i	−0.302372	+	0.523724i
$693$	−1.60555	−	2.78090i	−0.0609898	−	0.105638i
$694$	13.3305			0.506020
$695$	−3.19722	−	5.53776i	−0.121278	−	0.210059i
$696$	9.31665	+	16.1369i	0.353147	+	0.611668i
$697$	−22.8167			−0.864242
$698$	−4.36249	−	7.55605i	−0.165123	−	0.286001i
$699$	−7.60555	+	13.1732i	−0.287668	+	0.498256i
$700$	−1.65139	+	2.86029i	−0.0624166	+	0.108109i
$701$	−36.4222			−1.37565			−0.687824	−	0.725878i	$-0.741434\pi$
$701$	−36.4222			−1.37565			−0.687824	+	0.725878i	$0.741434\pi$
$702$		0			0
$703$	−20.2111			−0.762276
$704$	−10.2889	+	17.8209i	−0.387777	+	0.671650i
$705$	4.60555	−	7.97705i	0.173455	−	0.300433i
$706$	19.3625	+	33.5368i	0.728717	+	1.26217i
$707$	−9.00000			−0.338480
$708$	−17.8625	−	30.9387i	−0.671313	−	1.16275i
$709$	−6.92221	−	11.9896i	−0.259969	−	0.450279i	0.706264	−	0.707948i	$-0.250379\pi$
$709$	−6.92221	−	11.9896i	−0.259969	−	0.450279i	−0.966233	+	0.257669i	$0.917046\pi$
$710$	−11.0917			−0.416263
$711$	5.21110	+	9.02589i	0.195432	+	0.338497i
$712$	−9.31665	+	16.1369i	−0.349156	+	0.604757i
$713$	6.00000	−	10.3923i	0.224702	−	0.389195i
$714$	17.5139			0.655440
$715$		0			0
$716$	75.3583			2.81627
$717$		0			0
$718$	21.2111	−	36.7387i	0.791591	−	1.37108i
$719$	12.8028	+	22.1751i	0.477463	+	0.826990i	0.999666	−	0.0258309i	$-0.00822314\pi$
$719$	12.8028	+	22.1751i	0.477463	+	0.826990i	−0.522203	+	0.852821i	$0.674890\pi$
$720$	−0.605551			−0.0225676
$721$	2.00000	+	3.46410i	0.0744839	+	0.129010i
$722$	−14.3028	−	24.7731i	−0.532294	−	0.921961i
$723$	−1.78890			−0.0665298
$724$	−29.1194	−	50.4363i	−1.08222	−	1.87445i
$725$	3.10555	−	5.37897i	0.115337	−	0.199770i
$726$	9.69722	−	16.7961i	0.359898	−	0.623361i
$727$	13.5778			0.503573			0.251786	−	0.967783i	$-0.418982\pi$
$727$	13.5778			0.503573			0.251786	+	0.967783i	$0.418982\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$	−0.908327	+	1.57327i	−0.0336187	+	0.0582293i
$731$	38.8305	−	67.2565i	1.43620	−	2.48757i
$732$	1.65139	+	2.86029i	0.0610371	+	0.105719i
$733$	46.8444			1.73024			0.865119	−	0.501567i	$-0.167243\pi$
$733$	46.8444			1.73024			0.865119	+	0.501567i	$0.167243\pi$
$734$	−13.1514	−	22.7789i	−0.485427	−	0.840784i
$735$	3.00000	+	5.19615i	0.110657	+	0.191663i
$736$	15.9083			0.586389
$737$	5.61943	+	9.73314i	0.206994	+	0.358525i
$738$	−6.90833	+	11.9656i	−0.254299	+	0.440459i
$739$	−17.8028	+	30.8353i	−0.654886	+	1.13430i	0.327037	+	0.945012i	$0.393950\pi$
$739$	−17.8028	+	30.8353i	−0.654886	+	1.13430i	−0.981922	+	0.189284i	$0.939383\pi$
$740$	−11.9083			−0.437759
$741$		0			0
$742$	−7.39445			−0.271459
$743$	18.3167	−	31.7254i	0.671973	−	1.16389i	−0.305371	−	0.952233i	$-0.598780\pi$
$743$	18.3167	−	31.7254i	0.671973	−	1.16389i	0.977344	−	0.211658i	$-0.0678862\pi$
$744$	−6.00000	+	10.3923i	−0.219971	+	0.381000i
$745$	1.50000	+	2.59808i	0.0549557	+	0.0951861i
$746$	−46.9638			−1.71947
$747$	9.21110	+	15.9541i	0.337017	+	0.583730i
$748$	20.1653	+	34.9273i	0.737315	+	1.27707i
$749$	6.21110			0.226949
$750$	−1.15139	−	1.99426i	−0.0420427	−	0.0728202i
$751$	−23.2250	+	40.2268i	−0.847492	+	1.46790i	0.0359481	+	0.999354i	$0.488555\pi$
$751$	−23.2250	+	40.2268i	−0.847492	+	1.46790i	−0.883440	+	0.468545i	$0.844778\pi$
$752$	1.39445	−	2.41526i	0.0508503	−	0.0880753i
$753$	−7.18335			−0.261776
$754$		0			0
$755$	1.21110			0.0440765
$756$	8.25694	−	14.3014i	0.300302	−	0.520138i
$757$	−0.408327	+	0.707243i	−0.0148409	+	0.0257052i	−0.873350	−	0.487092i	$-0.838058\pi$
$757$	−0.408327	+	0.707243i	−0.0148409	+	0.0257052i	0.858510	+	0.512798i	$0.171391\pi$
$758$	11.0597	+	19.1560i	0.401707	+	0.695777i
$759$	4.81665			0.174833
$760$	−8.40833	−	14.5636i	−0.305002	−	0.528279i
$761$	9.31665	+	16.1369i	0.337728	+	0.584963i	0.984005	−	0.178140i	$-0.0570081\pi$
$761$	9.31665	+	16.1369i	0.337728	+	0.584963i	−0.646277	+	0.763103i	$0.723675\pi$
$762$	−9.69722			−0.351293
$763$	−9.60555	−	16.6373i	−0.347744	−	0.602311i
$764$	−27.7708	+	48.1005i	−1.00471	+	1.74021i
$765$	7.60555	−	13.1732i	0.274979	−	0.476278i
$766$	56.7250			2.04956
$767$		0			0
$768$	−17.9083			−0.646211
$769$	5.50000	−	9.52628i	0.198335	−	0.343526i	−0.749654	−	0.661830i	$-0.769780\pi$
$769$	5.50000	−	9.52628i	0.198335	−	0.343526i	0.947989	+	0.318304i	$0.103113\pi$
$770$	1.84861	−	3.20189i	0.0666194	−	0.115388i
$771$	8.19722	+	14.1980i	0.295216	+	0.511329i
$772$	−51.5416			−1.85502
$773$	11.1972	+	19.3942i	0.402736	+	0.697560i	0.994055	−	0.108878i	$-0.0347259\pi$
$773$	11.1972	+	19.3942i	0.402736	+	0.697560i	−0.591319	+	0.806438i	$0.701393\pi$
$774$	−23.5139	−	40.7272i	−0.845189	−	1.46391i
$775$	4.00000			0.143684
$776$	−12.5917	−	21.8094i	−0.452015	−	0.782912i
$777$	1.80278	−	3.12250i	0.0646742	−	0.112019i
$778$	17.5139	−	30.3349i	0.627903	−	1.08756i
$779$	−16.8167			−0.602519
$780$		0			0
$781$	7.73338			0.276722
$782$	26.2708	−	45.5024i	0.939443	−	1.62716i
$783$	−15.5278	+	26.8949i	−0.554917	+	0.961144i
$784$	0.908327	+	1.57327i	0.0324402	+	0.0561882i
$785$	11.2111			0.400141
$786$	24.4222	+	42.3005i	0.871111	+	1.50881i
$787$	7.31665	+	12.6728i	0.260811	+	0.451737i	0.966458	−	0.256826i	$-0.0826769\pi$
$787$	7.31665	+	12.6728i	0.260811	+	0.451737i	−0.705647	+	0.708564i	$0.749344\pi$
$788$	−3.90833			−0.139228
$789$	−5.89445	−	10.2095i	−0.209848	−	0.363467i
$790$	−6.00000	+	10.3923i	−0.213470	+	0.369742i
$791$	0.802776	−	1.39045i	0.0285434	−	0.0494386i
$792$	9.63331			0.342305
$793$		0			0
$794$	−50.7250			−1.80016
$795$	1.60555	−	2.78090i	0.0569430	−	0.0986282i
$796$	−21.1653	+	36.6593i	−0.750183	+	1.29936i
$797$	7.22498	+	12.5140i	0.255922	+	0.443270i	0.965146	−	0.261714i	$-0.0842877\pi$
$797$	7.22498	+	12.5140i	0.255922	+	0.443270i	−0.709224	+	0.704984i	$0.750954\pi$
$798$	12.9083			0.456950
$799$	35.0278	+	60.6699i	1.23919	+	2.14635i
$800$	2.65139	+	4.59234i	0.0937407	+	0.162364i
$801$	−12.4222			−0.438917
$802$	14.0597	+	24.3521i	0.496466	+	0.859904i
$803$	0.633308	−	1.09692i	0.0223489	−	0.0387095i
$804$	−11.5597	+	20.0220i	−0.407680	+	0.706122i
$805$	−3.00000			−0.105736
$806$		0			0
$807$	−9.00000			−0.316815
$808$	13.5000	−	23.3827i	0.474928	−	0.822600i
$809$	27.5278	−	47.6795i	0.967824	−	1.67632i	0.265997	−	0.963974i	$-0.414299\pi$
$809$	27.5278	−	47.6795i	0.967824	−	1.67632i	0.701827	−	0.712347i	$-0.252368\pi$
$810$	−1.15139	−	1.99426i	−0.0404556	−	0.0700712i
$811$	46.4222			1.63010			0.815052	−	0.579388i	$-0.196708\pi$
$811$	46.4222			1.63010			0.815052	+	0.579388i	$0.196708\pi$
$812$	10.2569	+	17.7655i	0.359948	+	0.623448i
$813$	−10.4083	−	18.0278i	−0.365036	−	0.632261i
$814$	13.3305			0.467235
$815$	−1.89445	−	3.28128i	−0.0663596	−	0.114938i
$816$	−1.15139	+	1.99426i	−0.0403066	+	0.0698131i
$817$	28.6194	−	49.5703i	1.00127	−	1.73425i
$818$	−18.9083			−0.661114
$819$		0			0
$820$	−9.90833			−0.346014
$821$	10.7111	−	18.5522i	0.373820	−	0.647475i	−0.616330	−	0.787488i	$-0.711381\pi$
$821$	10.7111	−	18.5522i	0.373820	−	0.647475i	0.990150	+	0.140013i	$0.0447144\pi$
$822$	−1.84861	+	3.20189i	−0.0644778	+	0.111679i
$823$	8.31665	+	14.4049i	0.289900	+	0.502122i	0.973786	−	0.227467i	$-0.0730445\pi$
$823$	8.31665	+	14.4049i	0.289900	+	0.502122i	−0.683885	+	0.729589i	$0.739711\pi$
$824$	−12.0000			−0.418040
$825$	0.802776	+	1.39045i	0.0279491	+	0.0484092i
$826$	−12.4542	−	21.5712i	−0.433336	−	0.750560i
$827$	42.4222			1.47516			0.737582	−	0.675257i	$-0.235967\pi$
$827$	42.4222			1.47516			0.737582	+	0.675257i	$0.235967\pi$
$828$	−9.90833	−	17.1617i	−0.344338	−	0.596411i
$829$	−14.7111	+	25.4804i	−0.510938	+	0.884970i	0.488982	+	0.872294i	$0.337368\pi$
$829$	−14.7111	+	25.4804i	−0.510938	+	0.884970i	−0.999920	+	0.0126762i	$0.995965\pi$
$830$	−10.6056	+	18.3694i	−0.368124	+	0.637610i
$831$	27.6056			0.957626
$832$		0			0
$833$	−45.6333			−1.58110
$834$	−7.36249	+	12.7522i	−0.254942	+	0.441573i
$835$	4.50000	−	7.79423i	0.155729	−	0.269730i
$836$	14.8625	+	25.7426i	0.514030	+	0.890326i
$837$	−20.0000			−0.691301
$838$	−19.8486	−	34.3788i	−0.685659	−	1.18760i
$839$	−10.0139	−	17.3445i	−0.345717	−	0.598800i	0.639766	−	0.768569i	$-0.279031\pi$
$839$	−10.0139	−	17.3445i	−0.345717	−	0.598800i	−0.985484	+	0.169769i	$0.945698\pi$
$840$	3.00000			0.103510
$841$	−4.78890	−	8.29461i	−0.165134	−	0.286021i
$842$	37.3305	−	64.6584i	1.28650	−	2.22827i
$843$	−3.00000	+	5.19615i	−0.103325	+	0.178965i
$844$	−77.9638			−2.68363
$845$		0			0
$846$	42.4222			1.45851
$847$	4.21110	−	7.29384i	0.144695	−	0.250619i
$848$	0.486122	−	0.841988i	0.0166935	−	0.0289140i
$849$	−2.50000	−	4.33013i	−0.0857998	−	0.148610i
$850$	17.5139			0.600721
$851$	−5.40833	−	9.36750i	−0.185395	−	0.321114i
$852$	7.95416	+	13.7770i	0.272505	+	0.471993i
$853$	−47.2111			−1.61648			−0.808239	−	0.588855i	$-0.799579\pi$
$853$	−47.2111			−1.61648			−0.808239	+	0.588855i	$0.799579\pi$
$854$	1.15139	+	1.99426i	0.0393997	+	0.0682422i
$855$	5.60555	−	9.70910i	0.191706	−	0.332044i
$856$	−9.31665	+	16.1369i	−0.318437	+	0.551548i
$857$	6.00000			0.204956			0.102478	−	0.994735i	$-0.467323\pi$
$857$	6.00000			0.204956			0.102478	+	0.994735i	$0.467323\pi$
$858$		0			0
$859$	10.7889			0.368112			0.184056	−	0.982916i	$-0.441077\pi$
$859$	10.7889			0.368112			0.184056	+	0.982916i	$0.441077\pi$
$860$	16.8625	−	29.2067i	0.575006	−	0.995940i
$861$	1.50000	−	2.59808i	0.0511199	−	0.0885422i
$862$	33.6653	+	58.3100i	1.14664	+	1.98604i
$863$	−36.0000			−1.22545			−0.612727	−	0.790295i	$-0.709928\pi$
$863$	−36.0000			−1.22545			−0.612727	+	0.790295i	$0.709928\pi$
$864$	−13.2569	−	22.9617i	−0.451010	−	0.781173i
$865$	−2.40833	−	4.17134i	−0.0818856	−	0.141830i
$866$	8.30278			0.282140
$867$	−20.4222	−	35.3723i	−0.693574	−	1.20131i
$868$	−6.60555	+	11.4412i	−0.224207	+	0.388338i
$869$	4.18335	−	7.24577i	0.141910	−	0.245796i
$870$	−14.3028			−0.484910
$871$		0			0
$872$	57.6333			1.95171
$873$	8.39445	−	14.5396i	0.284109	−	0.492091i
$874$	19.3625	−	33.5368i	0.654946	−	1.13440i
$875$	−0.500000	−	0.866025i	−0.0169031	−	0.0292770i
$876$	2.60555			0.0880334
$877$	−0.986122	−	1.70801i	−0.0332990	−	0.0576755i	0.848896	−	0.528560i	$-0.177268\pi$
$877$	−0.986122	−	1.70801i	−0.0332990	−	0.0576755i	−0.882195	+	0.470885i	$0.843935\pi$
$878$	31.3625	+	54.3214i	1.05843	+	1.83326i
$879$	−10.3944			−0.350596
$880$	0.243061	+	0.420994i	0.00819358	+	0.0141917i
$881$	10.9222	−	18.9178i	0.367978	−	0.637357i	−0.621271	−	0.783596i	$-0.713383\pi$
$881$	10.9222	−	18.9178i	0.367978	−	0.637357i	0.989249	+	0.146238i	$0.0467167\pi$
$882$	−13.8167	+	23.9311i	−0.465231	+	0.805804i
$883$	11.6333			0.391492			0.195746	−	0.980655i	$-0.437287\pi$
$883$	11.6333			0.391492			0.195746	+	0.980655i	$0.437287\pi$
$884$		0			0
$885$	10.8167			0.363598
$886$	−7.39445	+	12.8076i	−0.248421	+	0.430278i
$887$	18.5278	−	32.0910i	0.622101	−	1.07751i	−0.366993	−	0.930224i	$-0.619613\pi$
$887$	18.5278	−	32.0910i	0.622101	−	1.07751i	0.989094	−	0.147287i	$-0.0470541\pi$
$888$	5.40833	+	9.36750i	0.181492	+	0.314353i
$889$	−4.21110			−0.141236
$890$	−7.15139	−	12.3866i	−0.239715	−	0.415199i
$891$	0.802776	+	1.39045i	0.0268940	+	0.0465818i
$892$	13.9083			0.465685
$893$	25.8167	+	44.7158i	0.863921	+	1.49636i
$894$	3.45416	−	5.98279i	0.115525	−	0.200094i
$895$	−11.4083	+	19.7598i	−0.381338	+	0.660497i
$896$	−18.9083			−0.631683
$897$		0			0
$898$	−70.5416			−2.35400
$899$	12.4222	−	21.5159i	0.414304	−	0.717595i
$900$	3.30278	−	5.72058i	0.110093	−	0.190686i
$901$	12.2111	+	21.1503i	0.406811	+	0.704617i
$902$	11.0917			0.369312
$903$	5.10555	+	8.84307i	0.169902	+	0.294279i
$904$	2.40833	+	4.17134i	0.0800998	+	0.138737i
$905$	17.6333			0.586151
$906$	−1.39445	−	2.41526i	−0.0463275	−	0.0802415i
$907$	19.1333	−	33.1399i	0.635311	−	1.10039i	−0.351138	−	0.936324i	$-0.614205\pi$
$907$	19.1333	−	33.1399i	0.635311	−	1.10039i	0.986449	−	0.164067i	$-0.0524614\pi$
$908$	−45.2847	+	78.4354i	−1.50283	+	2.60297i
$909$	18.0000			0.597022
$910$		0			0
$911$	−36.0000			−1.19273			−0.596367	−	0.802712i	$-0.703390\pi$
$911$	−36.0000			−1.19273			−0.596367	+	0.802712i	$0.703390\pi$
$912$	−0.848612	+	1.46984i	−0.0281004	+	0.0486712i
$913$	7.39445	−	12.8076i	0.244721	−	0.423868i
$914$	−30.8764	−	53.4794i	−1.02130	−	1.76894i
$915$	−1.00000			−0.0330590
$916$	23.1194	+	40.0440i	0.763887	+	1.32309i
$917$	10.6056	+	18.3694i	0.350226	+	0.606610i
$918$	−87.5694			−2.89022
$919$	19.4083	+	33.6162i	0.640222	+	1.10890i	0.985383	+	0.170353i	$0.0544908\pi$
$919$	19.4083	+	33.6162i	0.640222	+	1.10890i	−0.345161	+	0.938543i	$0.612176\pi$
$920$	4.50000	−	7.79423i	0.148361	−	0.256968i
$921$	−8.00000	+	13.8564i	−0.263609	+	0.456584i
$922$	−83.3860			−2.74617
$923$		0			0
$924$	−5.30278			−0.174449
$925$	1.80278	−	3.12250i	0.0592749	−	0.102667i
$926$	−39.6333	+	68.6469i	−1.30243	+	2.25588i
$927$	−4.00000	−	6.92820i	−0.131377	−	0.227552i
$928$	32.9361			1.08118
$929$	−7.71110	−	13.3560i	−0.252993	−	0.438197i	0.711355	−	0.702832i	$-0.248082\pi$
$929$	−7.71110	−	13.3560i	−0.252993	−	0.438197i	−0.964348	+	0.264636i	$0.914748\pi$
$930$	−4.60555	−	7.97705i	−0.151022	−	0.261578i
$931$	−33.6333			−1.10229
$932$	−25.1194	−	43.5081i	−0.822814	−	1.42516i
$933$	4.60555	−	7.97705i	0.150779	−	0.261157i
$934$	−3.21110	+	5.56179i	−0.105070	+	0.181987i
$935$	−12.2111			−0.399346
$936$		0			0
$937$	54.4777			1.77971			0.889855	−	0.456244i	$-0.150806\pi$
$937$	54.4777			1.77971			0.889855	+	0.456244i	$0.150806\pi$
$938$	−8.05971	+	13.9598i	−0.263159	+	0.455805i
$939$	−7.00000	+	12.1244i	−0.228436	+	0.395663i
$940$	15.2111	+	26.3464i	0.496131	+	0.859325i
$941$	9.63331			0.314037			0.157018	−	0.987596i	$-0.449812\pi$
$941$	9.63331			0.314037			0.157018	+	0.987596i	$0.449812\pi$
$942$	−12.9083	−	22.3579i	−0.420576	−	0.728459i
$943$	−4.50000	−	7.79423i	−0.146540	−	0.253815i
$944$	3.27502			0.106593
$945$	2.50000	+	4.33013i	0.0813250	+	0.140859i
$946$	−18.8764	+	32.6948i	−0.613724	+	1.06300i
$947$	−9.31665	+	16.1369i	−0.302751	+	0.524379i	−0.976758	−	0.214345i	$-0.931238\pi$
$947$	−9.31665	+	16.1369i	−0.302751	+	0.524379i	0.674007	+	0.738725i	$0.264572\pi$
$948$	17.2111			0.558991
$949$		0			0
$950$	12.9083			0.418801
$951$	3.00000	−	5.19615i	0.0972817	−	0.168497i
$952$	−11.4083	+	19.7598i	−0.369746	+	0.640419i
$953$	7.22498	+	12.5140i	0.234040	+	0.405369i	0.958993	−	0.283429i	$-0.0914720\pi$
$953$	7.22498	+	12.5140i	0.234040	+	0.405369i	−0.724953	+	0.688798i	$0.758139\pi$
$954$	14.7889			0.478808
$955$	−8.40833	−	14.5636i	−0.272087	−	0.471269i
$956$		0			0
$957$	9.97224			0.322357
$958$	−33.1791	−	57.4680i	−1.07197	−	1.85671i
$959$	−0.802776	+	1.39045i	−0.0259230	+	0.0448999i
$960$	6.40833	−	11.0995i	0.206828	−	0.358236i
$961$	−15.0000			−0.483871
$962$		0			0
$963$	−12.4222			−0.400300
$964$	2.95416	−	5.11676i	0.0951472	−	0.164800i
$965$	7.80278	−	13.5148i	0.251180	−	0.435057i
$966$	3.45416	+	5.98279i	0.111136	+	0.192493i
$967$	44.4777			1.43031			0.715153	−	0.698967i	$-0.246357\pi$
$967$	44.4777			1.43031			0.715153	+	0.698967i	$0.246357\pi$
$968$	12.6333	+	21.8815i	0.406050	+	0.703299i
$969$	−21.3167	−	36.9215i	−0.684790	−	1.18609i
$970$	19.3305			0.620666
$971$	22.0139	+	38.1292i	0.706459	+	1.22362i	0.966162	+	0.257934i	$0.0830418\pi$
$971$	22.0139	+	38.1292i	0.706459	+	1.22362i	−0.259703	+	0.965688i	$0.583625\pi$
$972$	−26.4222	+	45.7646i	−0.847493	+	1.46790i
$973$	−3.19722	+	5.53776i	−0.102498	+	0.177532i
$974$	2.30278			0.0737857
$975$		0			0
$976$	−0.302776			−0.00969161
$977$	14.4083	−	24.9560i	0.460963	−	0.798412i	−0.538046	−	0.842915i	$-0.680837\pi$
$977$	14.4083	−	24.9560i	0.460963	−	0.798412i	0.999009	+	0.0445038i	$0.0141707\pi$
$978$	−4.36249	+	7.55605i	−0.139497	+	0.241616i
$979$	4.98612	+	8.63622i	0.159357	+	0.276015i
$980$	−19.8167			−0.633020
$981$	19.2111	+	33.2746i	0.613363	+	1.06238i
$982$	19.3625	+	33.5368i	0.617882	+	1.07020i
$983$	−18.4222			−0.587577			−0.293789	−	0.955870i	$-0.594916\pi$
$983$	−18.4222			−0.587577			−0.293789	+	0.955870i	$0.594916\pi$
$984$	4.50000	+	7.79423i	0.143455	+	0.248471i
$985$	0.591673	−	1.02481i	0.0188523	−	0.0326531i
$986$	54.3902	−	94.2067i	1.73214	−	3.00015i
$987$	−9.21110			−0.293193
$988$		0			0
$989$	30.6333			0.974083
$990$	−3.69722	+	6.40378i	−0.117506	+	0.203526i
$991$	−20.0139	+	34.6651i	−0.635762	+	1.10117i	0.350591	+	0.936529i	$0.385981\pi$
$991$	−20.0139	+	34.6651i	−0.635762	+	1.10117i	−0.986353	+	0.164643i	$0.947353\pi$
$992$	10.6056	+	18.3694i	0.336727	+	0.583228i
$993$	−10.0278			−0.318221
$994$	5.54584	+	9.60567i	0.175903	+	0.304673i
$995$	−6.40833	−	11.0995i	−0.203158	−	0.351879i
$996$	30.4222			0.963964
$997$	9.22498	+	15.9781i	0.292158	+	0.506033i	0.974320	−	0.225169i	$-0.0722933\pi$
$997$	9.22498	+	15.9781i	0.292158	+	0.506033i	−0.682162	+	0.731201i	$0.738960\pi$
$998$	2.78890	−	4.83051i	0.0882810	−	0.152907i
$999$	−9.01388	+	15.6125i	−0.285186	+	0.493957i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.e.d.191.1		4
13.2	odd	12		845.2.m.d.361.1		8
13.3	even	3	inner	845.2.e.d.146.1		4
13.4	even	6		845.2.a.c.1.1		2
13.5	odd	4		845.2.m.d.316.4		8
13.6	odd	12		845.2.c.d.506.1		4
13.7	odd	12		845.2.c.d.506.4		4
13.8	odd	4		845.2.m.d.316.1		8
13.9	even	3		845.2.a.f.1.2		2
13.10	even	6		65.2.e.b.16.2	✓	4
13.11	odd	12		845.2.m.d.361.4		8
13.12	even	2		65.2.e.b.61.2	yes	4
39.17	odd	6		7605.2.a.bg.1.2		2
39.23	odd	6		585.2.j.d.406.1		4
39.35	odd	6		7605.2.a.bb.1.1		2
39.38	odd	2		585.2.j.d.451.1		4
52.23	odd	6		1040.2.q.o.81.2		4
52.51	odd	2		1040.2.q.o.321.2		4
65.4	even	6		4225.2.a.x.1.2		2
65.9	even	6		4225.2.a.t.1.1		2
65.12	odd	4		325.2.o.b.74.4		8
65.23	odd	12		325.2.o.b.224.4		8
65.38	odd	4		325.2.o.b.74.1		8
65.49	even	6		325.2.e.a.276.1		4
65.62	odd	12		325.2.o.b.224.1		8
65.64	even	2		325.2.e.a.126.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.e.b.16.2	✓	4	13.10	even	6
65.2.e.b.61.2	yes	4	13.12	even	2
325.2.e.a.126.1		4	65.64	even	2
325.2.e.a.276.1		4	65.49	even	6
325.2.o.b.74.1		8	65.38	odd	4
325.2.o.b.74.4		8	65.12	odd	4
325.2.o.b.224.1		8	65.62	odd	12
325.2.o.b.224.4		8	65.23	odd	12
585.2.j.d.406.1		4	39.23	odd	6
585.2.j.d.451.1		4	39.38	odd	2
845.2.a.c.1.1		2	13.4	even	6
845.2.a.f.1.2		2	13.9	even	3
845.2.c.d.506.1		4	13.6	odd	12
845.2.c.d.506.4		4	13.7	odd	12
845.2.e.d.146.1		4	13.3	even	3	inner
845.2.e.d.191.1		4	1.1	even	1	trivial
845.2.m.d.316.1		8	13.8	odd	4
845.2.m.d.316.4		8	13.5	odd	4
845.2.m.d.361.1		8	13.2	odd	12
845.2.m.d.361.4		8	13.11	odd	12
1040.2.q.o.81.2		4	52.23	odd	6
1040.2.q.o.321.2		4	52.51	odd	2
4225.2.a.t.1.1		2	65.9	even	6
4225.2.a.x.1.2		2	65.4	even	6
7605.2.a.bb.1.1		2	39.35	odd	6
7605.2.a.bg.1.2		2	39.17	odd	6

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.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.15139 + 1.99426i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-1.65139 - 2.86029i) q^{4} +1.00000 q^{5} +(-1.15139 - 1.99426i) q^{6} +(-0.500000 - 0.866025i) q^{7} +3.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +(-1.15139 + 1.99426i) q^{10} +(0.802776 - 1.39045i) q^{11} +3.30278 q^{12} +2.30278 q^{14} +(-0.500000 + 0.866025i) q^{15} +(-0.151388 + 0.262211i) q^{16} +(-3.80278 - 6.58660i) q^{17} -4.60555 q^{18} +(-2.80278 - 4.85455i) q^{19} +(-1.65139 - 2.86029i) q^{20} +1.00000 q^{21} +(1.84861 + 3.20189i) q^{22} +(1.50000 - 2.59808i) q^{23} +(-1.50000 + 2.59808i) q^{24} +1.00000 q^{25} -5.00000 q^{27} +(-1.65139 + 2.86029i) q^{28} +(3.10555 - 5.37897i) q^{29} +(-1.15139 - 1.99426i) q^{30} +4.00000 q^{31} +(2.65139 + 4.59234i) q^{32} +(0.802776 + 1.39045i) q^{33} +17.5139 q^{34} +(-0.500000 - 0.866025i) q^{35} +(3.30278 - 5.72058i) q^{36} +(1.80278 - 3.12250i) q^{37} +12.9083 q^{38} +3.00000 q^{40} +(1.50000 - 2.59808i) q^{41} +(-1.15139 + 1.99426i) q^{42} +(5.10555 + 8.84307i) q^{43} -5.30278 q^{44} +(1.00000 + 1.73205i) q^{45} +(3.45416 + 5.98279i) q^{46} -9.21110 q^{47} +(-0.151388 - 0.262211i) q^{48} +(3.00000 - 5.19615i) q^{49} +(-1.15139 + 1.99426i) q^{50} +7.60555 q^{51} -3.21110 q^{53} +(5.75694 - 9.97131i) q^{54} +(0.802776 - 1.39045i) q^{55} +(-1.50000 - 2.59808i) q^{56} +5.60555 q^{57} +(7.15139 + 12.3866i) q^{58} +(-5.40833 - 9.36750i) q^{59} +3.30278 q^{60} +(0.500000 + 0.866025i) q^{61} +(-4.60555 + 7.97705i) q^{62} +(1.00000 - 1.73205i) q^{63} -12.8167 q^{64} -3.69722 q^{66} +(-3.50000 + 6.06218i) q^{67} +(-12.5597 + 21.7541i) q^{68} +(1.50000 + 2.59808i) q^{69} +2.30278 q^{70} +(2.40833 + 4.17134i) q^{71} +(3.00000 + 5.19615i) q^{72} +0.788897 q^{73} +(4.15139 + 7.19041i) q^{74} +(-0.500000 + 0.866025i) q^{75} +(-9.25694 + 16.0335i) q^{76} -1.60555 q^{77} +5.21110 q^{79} +(-0.151388 + 0.262211i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(3.45416 + 5.98279i) q^{82} +9.21110 q^{83} +(-1.65139 - 2.86029i) q^{84} +(-3.80278 - 6.58660i) q^{85} -23.5139 q^{86} +(3.10555 + 5.37897i) q^{87} +(2.40833 - 4.17134i) q^{88} +(-3.10555 + 5.37897i) q^{89} -4.60555 q^{90} -9.90833 q^{92} +(-2.00000 + 3.46410i) q^{93} +(10.6056 - 18.3694i) q^{94} +(-2.80278 - 4.85455i) q^{95} -5.30278 q^{96} +(-4.19722 - 7.26981i) q^{97} +(6.90833 + 11.9656i) q^{98} +3.21110 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - 2 q^{3} - 3 q^{4} + 4 q^{5} - q^{6} - 2 q^{7} + 12 q^{8} + 4 q^{9} - q^{10} - 4 q^{11} + 6 q^{12} + 2 q^{14} - 2 q^{15} + 3 q^{16} - 8 q^{17} - 4 q^{18} - 4 q^{19} - 3 q^{20} + 4 q^{21}+ \cdots - 16 q^{99}+O(q^{100}) \) 4 * q - q^2 - 2 * q^3 - 3 * q^4 + 4 * q^5 - q^6 - 2 * q^7 + 12 * q^8 + 4 * q^9 - q^10 - 4 * q^11 + 6 * q^12 + 2 * q^14 - 2 * q^15 + 3 * q^16 - 8 * q^17 - 4 * q^18 - 4 * q^19 - 3 * q^20 + 4 * q^21 + 11 * q^22 + 6 * q^23 - 6 * q^24 + 4 * q^25 - 20 * q^27 - 3 * q^28 - 2 * q^29 - q^30 + 16 * q^31 + 7 * q^32 - 4 * q^33 + 34 * q^34 - 2 * q^35 + 6 * q^36 + 30 * q^38 + 12 * q^40 + 6 * q^41 - q^42 + 6 * q^43 - 14 * q^44 + 4 * q^45 + 3 * q^46 - 8 * q^47 + 3 * q^48 + 12 * q^49 - q^50 + 16 * q^51 + 16 * q^53 + 5 * q^54 - 4 * q^55 - 6 * q^56 + 8 * q^57 + 25 * q^58 + 6 * q^60 + 2 * q^61 - 4 * q^62 + 4 * q^63 - 8 * q^64 - 22 * q^66 - 14 * q^67 - 25 * q^68 + 6 * q^69 + 2 * q^70 - 12 * q^71 + 12 * q^72 + 32 * q^73 + 13 * q^74 - 2 * q^75 - 19 * q^76 + 8 * q^77 - 8 * q^79 + 3 * q^80 - 2 * q^81 + 3 * q^82 + 8 * q^83 - 3 * q^84 - 8 * q^85 - 58 * q^86 - 2 * q^87 - 12 * q^88 + 2 * q^89 - 4 * q^90 - 18 * q^92 - 8 * q^93 + 28 * q^94 - 4 * q^95 - 14 * q^96 - 24 * q^97 + 6 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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