LMFDB - Embedded newform 845.2.m.d.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(316,845)]

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, 1]))

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

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

chi := DirichletCharacter("845.316");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.m (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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.592240896.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 7x^{6} + 40x^{4} - 63x^{2} + 81 $ x^8 - 7x^6 + 40x^4 - 63*x^2 + 81
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			361.1
Root			$-1.99426 + 1.15139i$ of defining polynomial
Character	$\chi$	$=$	845.361
Dual form			845.2.m.d.316.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.99426 + 1.15139i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(1.65139 - 2.86029i) q^{4} -1.00000i q^{5} +(1.99426 + 1.15139i) q^{6} +(-0.866025 - 0.500000i) q^{7} +3.00000i q^{8} +(1.00000 - 1.73205i) q^{9} +(1.15139 + 1.99426i) q^{10} +(-1.39045 + 0.802776i) q^{11} -3.30278 q^{12} +2.30278 q^{14} +(-0.866025 + 0.500000i) q^{15} +(-0.151388 - 0.262211i) q^{16} +(3.80278 - 6.58660i) q^{17} +4.60555i q^{18} +(4.85455 + 2.80278i) q^{19} +(-2.86029 - 1.65139i) q^{20} +1.00000i q^{21} +(1.84861 - 3.20189i) q^{22} +(-1.50000 - 2.59808i) q^{23} +(2.59808 - 1.50000i) q^{24} -1.00000 q^{25} -5.00000 q^{27} +(-2.86029 + 1.65139i) q^{28} +(3.10555 + 5.37897i) q^{29} +(1.15139 - 1.99426i) q^{30} -4.00000i q^{31} +(-4.59234 - 2.65139i) q^{32} +(1.39045 + 0.802776i) q^{33} +17.5139i q^{34} +(-0.500000 + 0.866025i) q^{35} +(-3.30278 - 5.72058i) q^{36} +(-3.12250 + 1.80278i) q^{37} -12.9083 q^{38} +3.00000 q^{40} +(2.59808 - 1.50000i) q^{41} +(-1.15139 - 1.99426i) q^{42} +(-5.10555 + 8.84307i) q^{43} +5.30278i q^{44} +(-1.73205 - 1.00000i) q^{45} +(5.98279 + 3.45416i) q^{46} -9.21110i q^{47} +(-0.151388 + 0.262211i) q^{48} +(-3.00000 - 5.19615i) q^{49} +(1.99426 - 1.15139i) q^{50} -7.60555 q^{51} -3.21110 q^{53} +(9.97131 - 5.75694i) q^{54} +(0.802776 + 1.39045i) q^{55} +(1.50000 - 2.59808i) q^{56} -5.60555i q^{57} +(-12.3866 - 7.15139i) q^{58} +(-9.36750 - 5.40833i) q^{59} +3.30278i q^{60} +(0.500000 - 0.866025i) q^{61} +(4.60555 + 7.97705i) q^{62} +(-1.73205 + 1.00000i) q^{63} +12.8167 q^{64} -3.69722 q^{66} +(-6.06218 + 3.50000i) q^{67} +(-12.5597 - 21.7541i) q^{68} +(-1.50000 + 2.59808i) q^{69} -2.30278i q^{70} +(-4.17134 - 2.40833i) q^{71} +(5.19615 + 3.00000i) q^{72} +0.788897i q^{73} +(4.15139 - 7.19041i) q^{74} +(0.500000 + 0.866025i) q^{75} +(16.0335 - 9.25694i) q^{76} +1.60555 q^{77} +5.21110 q^{79} +(-0.262211 + 0.151388i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-3.45416 + 5.98279i) q^{82} -9.21110i q^{83} +(2.86029 + 1.65139i) q^{84} +(-6.58660 - 3.80278i) q^{85} -23.5139i q^{86} +(3.10555 - 5.37897i) q^{87} +(-2.40833 - 4.17134i) q^{88} +(5.37897 - 3.10555i) q^{89} +4.60555 q^{90} -9.90833 q^{92} +(-3.46410 + 2.00000i) q^{93} +(10.6056 + 18.3694i) q^{94} +(2.80278 - 4.85455i) q^{95} +5.30278i q^{96} +(7.26981 + 4.19722i) q^{97} +(11.9656 + 6.90833i) q^{98} +3.21110i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} + 6 q^{4} + 8 q^{9} + 2 q^{10} - 12 q^{12} + 4 q^{14} + 6 q^{16} + 16 q^{17} + 22 q^{22} - 12 q^{23} - 8 q^{25} - 40 q^{27} - 4 q^{29} + 2 q^{30} - 4 q^{35} - 12 q^{36} - 60 q^{38} + 24 q^{40}+ \cdots + 8 q^{95}+O(q^{100}) $ 8 * q - 4 * q^3 + 6 * q^4 + 8 * q^9 + 2 * q^10 - 12 * q^12 + 4 * q^14 + 6 * q^16 + 16 * q^17 + 22 * q^22 - 12 * q^23 - 8 * q^25 - 40 * q^27 - 4 * q^29 + 2 * q^30 - 4 * q^35 - 12 * q^36 - 60 * q^38 + 24 * q^40 - 2 * q^42 - 12 * q^43 + 6 * q^48 - 24 * q^49 - 32 * q^51 + 32 * q^53 - 8 * q^55 + 12 * q^56 + 4 * q^61 + 8 * q^62 + 16 * q^64 - 44 * q^66 - 50 * q^68 - 12 * q^69 + 26 * q^74 + 4 * q^75 - 16 * q^77 - 16 * q^79 - 4 * q^81 - 6 * q^82 - 4 * q^87 + 24 * q^88 + 8 * q^90 - 36 * q^92 + 56 * q^94 + 8 * q^95

Character values

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

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.99426	+	1.15139i	−1.41016	+	0.814154i	−0.995403	−	0.0957796i	$-0.969466\pi$
$2$	−1.99426	+	1.15139i	−1.41016	+	0.814154i	−0.414754	+	0.909934i	$0.636132\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i	0.684819	−	0.728714i	$-0.259881\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i	−0.973494	+	0.228714i	$0.926548\pi$
$4$	1.65139	−	2.86029i	0.825694	−	1.43014i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	1.99426	+	1.15139i	0.814154	+	0.470052i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i	0.327327	−	0.944911i	$-0.393852\pi$
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i	−0.654654	+	0.755929i	$0.727186\pi$
$8$			3.00000i			1.06066i
$9$	1.00000	−	1.73205i	0.333333	−	0.577350i
$10$	1.15139	+	1.99426i	0.364101	+	0.630641i
$11$	−1.39045	+	0.802776i	−0.419236	+	0.242046i	−0.694750	−	0.719251i	$-0.744485\pi$
$11$	−1.39045	+	0.802776i	−0.419236	+	0.242046i	0.275514	+	0.961297i	$0.411152\pi$
$12$	−3.30278			−0.953429
$13$		0			0
$13$		0			0
$14$	2.30278			0.615443
$15$	−0.866025	+	0.500000i	−0.223607	+	0.129099i
$16$	−0.151388	−	0.262211i	−0.0378470	−	0.0655528i
$17$	3.80278	−	6.58660i	0.922309	−	1.59749i	0.126475	−	0.991970i	$-0.459634\pi$
$17$	3.80278	−	6.58660i	0.922309	−	1.59749i	0.795834	−	0.605516i	$-0.207033\pi$
$18$			4.60555i			1.08554i
$19$	4.85455	+	2.80278i	1.11371	+	0.643001i	0.939788	−	0.341759i	$-0.111023\pi$
$19$	4.85455	+	2.80278i	1.11371	+	0.643001i	0.173922	+	0.984759i	$0.444356\pi$
$20$	−2.86029	−	1.65139i	−0.639580	−	0.369262i
$21$			1.00000i			0.218218i
$22$	1.84861	−	3.20189i	0.394125	−	0.682645i
$23$	−1.50000	−	2.59808i	−0.312772	−	0.541736i	0.666190	−	0.745782i	$-0.267924\pi$
$23$	−1.50000	−	2.59808i	−0.312772	−	0.541736i	−0.978961	+	0.204046i	$0.934591\pi$
$24$	2.59808	−	1.50000i	0.530330	−	0.306186i
$25$	−1.00000			−0.200000
$26$		0			0
$27$	−5.00000			−0.962250
$28$	−2.86029	+	1.65139i	−0.540544	+	0.312083i
$29$	3.10555	+	5.37897i	0.576686	+	0.998850i	0.995856	+	0.0909423i	$0.0289879\pi$
$29$	3.10555	+	5.37897i	0.576686	+	0.998850i	−0.419170	+	0.907908i	$0.637679\pi$
$30$	1.15139	−	1.99426i	0.210214	−	0.364101i
$31$		−	4.00000i		−	0.718421i	−0.933257	−	0.359211i	$-0.883046\pi$
$31$		−	4.00000i		−	0.718421i	0.933257	−	0.359211i	$-0.116954\pi$
$32$	−4.59234	−	2.65139i	−0.811818	−	0.468704i
$33$	1.39045	+	0.802776i	0.242046	+	0.139745i
$34$			17.5139i			3.00361i
$35$	−0.500000	+	0.866025i	−0.0845154	+	0.146385i
$36$	−3.30278	−	5.72058i	−0.550463	−	0.953429i
$37$	−3.12250	+	1.80278i	−0.513336	+	0.296374i	−0.734204	−	0.678929i	$-0.762444\pi$
$37$	−3.12250	+	1.80278i	−0.513336	+	0.296374i	0.220868	+	0.975304i	$0.429111\pi$
$38$	−12.9083			−2.09401
$39$		0			0
$40$	3.00000			0.474342
$41$	2.59808	−	1.50000i	0.405751	−	0.234261i	−0.283211	−	0.959058i	$-0.591400\pi$
$41$	2.59808	−	1.50000i	0.405751	−	0.234261i	0.688963	+	0.724797i	$0.258066\pi$
$42$	−1.15139	−	1.99426i	−0.177663	−	0.307721i
$43$	−5.10555	+	8.84307i	−0.778589	+	1.34856i	0.154166	+	0.988045i	$0.450731\pi$
$43$	−5.10555	+	8.84307i	−0.778589	+	1.34856i	−0.932755	+	0.360511i	$0.882602\pi$
$44$			5.30278i			0.799424i
$45$	−1.73205	−	1.00000i	−0.258199	−	0.149071i
$46$	5.98279	+	3.45416i	0.882114	+	0.509289i
$47$		−	9.21110i		−	1.34358i	−0.740743	−	0.671789i	$-0.765526\pi$
$47$		−	9.21110i		−	1.34358i	0.740743	−	0.671789i	$-0.234474\pi$
$48$	−0.151388	+	0.262211i	−0.0218509	+	0.0378470i
$49$	−3.00000	−	5.19615i	−0.428571	−	0.742307i
$50$	1.99426	−	1.15139i	0.282031	−	0.162831i
$51$	−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	$0.570782\pi$
$54$	9.97131	−	5.75694i	1.35692	−	0.783420i
$55$	0.802776	+	1.39045i	0.108246	+	0.187488i
$56$	1.50000	−	2.59808i	0.200446	−	0.347183i
$57$		−	5.60555i		−	0.742473i
$58$	−12.3866	−	7.15139i	−1.62644	−	0.939023i
$59$	−9.36750	−	5.40833i	−1.21954	−	0.704104i	−0.254724	−	0.967014i	$-0.581985\pi$
$59$	−9.36750	−	5.40833i	−1.21954	−	0.704104i	−0.964820	+	0.262910i	$0.915318\pi$
$60$			3.30278i			0.426387i
$61$	0.500000	−	0.866025i	0.0640184	−	0.110883i	−0.832240	−	0.554416i	$-0.812942\pi$
$61$	0.500000	−	0.866025i	0.0640184	−	0.110883i	0.896258	+	0.443533i	$0.146275\pi$
$62$	4.60555	+	7.97705i	0.584906	+	1.01309i
$63$	−1.73205	+	1.00000i	−0.218218	+	0.125988i
$64$	12.8167			1.60208
$65$		0			0
$66$	−3.69722			−0.455097
$67$	−6.06218	+	3.50000i	−0.740613	+	0.427593i	−0.822292	−	0.569066i	$-0.807305\pi$
$67$	−6.06218	+	3.50000i	−0.740613	+	0.427593i	0.0816792	+	0.996659i	$0.473972\pi$
$68$	−12.5597	−	21.7541i	−1.52309	−	2.63807i
$69$	−1.50000	+	2.59808i	−0.180579	+	0.312772i
$70$		−	2.30278i		−	0.275234i
$71$	−4.17134	−	2.40833i	−0.495048	−	0.285816i	0.231619	−	0.972807i	$-0.425598\pi$
$71$	−4.17134	−	2.40833i	−0.495048	−	0.285816i	−0.726666	+	0.686991i	$0.758931\pi$
$72$	5.19615	+	3.00000i	0.612372	+	0.353553i
$73$			0.788897i			0.0923335i	0.998934	+	0.0461667i	$0.0147006\pi$
$73$			0.788897i			0.0923335i	−0.998934	+	0.0461667i	$0.985299\pi$
$74$	4.15139	−	7.19041i	0.482589	−	0.835869i
$75$	0.500000	+	0.866025i	0.0577350	+	0.100000i
$76$	16.0335	−	9.25694i	1.83917	−	1.06184i
$77$	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	$0.405297\pi$
$80$	−0.262211	+	0.151388i	−0.0293161	+	0.0169257i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−3.45416	+	5.98279i	−0.381449	+	0.660688i
$83$		−	9.21110i		−	1.01105i	−0.862812	−	0.505525i	$-0.831299\pi$
$83$		−	9.21110i		−	1.01105i	0.862812	−	0.505525i	$-0.168701\pi$
$84$	2.86029	+	1.65139i	0.312083	+	0.180181i
$85$	−6.58660	−	3.80278i	−0.714417	−	0.412469i
$86$		−	23.5139i		−	2.53557i
$87$	3.10555	−	5.37897i	0.332950	−	0.576686i
$88$	−2.40833	−	4.17134i	−0.256729	−	0.444667i
$89$	5.37897	−	3.10555i	0.570170	−	0.329188i	−0.187047	−	0.982351i	$-0.559892\pi$
$89$	5.37897	−	3.10555i	0.570170	−	0.329188i	0.757217	+	0.653163i	$0.226558\pi$
$90$	4.60555			0.485468
$91$		0			0
$92$	−9.90833			−1.03301
$93$	−3.46410	+	2.00000i	−0.359211	+	0.207390i
$94$	10.6056	+	18.3694i	1.09388	+	1.89465i
$95$	2.80278	−	4.85455i	0.287559	−	0.498066i
$96$			5.30278i			0.541212i
$97$	7.26981	+	4.19722i	0.738137	+	0.426164i	0.821392	−	0.570365i	$-0.193198\pi$
$97$	7.26981	+	4.19722i	0.738137	+	0.426164i	−0.0832546	+	0.996528i	$0.526531\pi$
$98$	11.9656	+	6.90833i	1.20871	+	0.697846i
$99$			3.21110i			0.322728i
$100$	−1.65139	+	2.86029i	−0.165139	+	0.286029i
$101$	−4.50000	−	7.79423i	−0.447767	−	0.775555i	0.550474	−	0.834853i	$-0.314447\pi$
$101$	−4.50000	−	7.79423i	−0.447767	−	0.775555i	−0.998240	+	0.0592978i	$0.981114\pi$
$102$	15.1675	−	8.75694i	1.50180	−	0.867066i
$103$	4.00000			0.394132			0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000			0.394132			0.197066	+	0.980390i	$0.436859\pi$
$104$		0			0
$105$	1.00000			0.0975900
$106$	6.40378	−	3.69722i	0.621990	−	0.359106i
$107$	−3.10555	−	5.37897i	−0.300225	−	0.520005i	0.675962	−	0.736937i	$-0.263728\pi$
$107$	−3.10555	−	5.37897i	−0.300225	−	0.520005i	−0.976187	+	0.216932i	$0.930395\pi$
$108$	−8.25694	+	14.3014i	−0.794524	+	1.37616i
$109$		−	19.2111i		−	1.84009i	−0.391813	−	0.920045i	$-0.628152\pi$
$109$		−	19.2111i		−	1.84009i	0.391813	−	0.920045i	$-0.371848\pi$
$110$	−3.20189	−	1.84861i	−0.305288	−	0.176258i
$111$	3.12250	+	1.80278i	0.296374	+	0.171112i
$112$			0.302776i			0.0286096i
$113$	0.802776	−	1.39045i	0.0755188	−	0.130802i	−0.825793	−	0.563973i	$-0.809272\pi$
$113$	0.802776	−	1.39045i	0.0755188	−	0.130802i	0.901312	+	0.433171i	$0.142605\pi$
$114$	6.45416	+	11.1789i	0.604488	+	1.04700i
$115$	−2.59808	+	1.50000i	−0.242272	+	0.139876i
$116$	20.5139			1.90467
$117$		0			0
$118$	24.9083			2.29300
$119$	−6.58660	+	3.80278i	−0.603793	+	0.348600i
$120$	−1.50000	−	2.59808i	−0.136931	−	0.237171i
$121$	−4.21110	+	7.29384i	−0.382828	+	0.663077i
$122$			2.30278i			0.208484i
$123$	−2.59808	−	1.50000i	−0.234261	−	0.135250i
$124$	−11.4412	−	6.60555i	−1.02745	−	0.593196i
$125$			1.00000i			0.0894427i
$126$	2.30278	−	3.98852i	0.205148	−	0.355326i
$127$	−2.10555	−	3.64692i	−0.186837	−	0.323612i	0.757357	−	0.653001i	$-0.226490\pi$
$127$	−2.10555	−	3.64692i	−0.186837	−	0.323612i	−0.944194	+	0.329389i	$0.893157\pi$
$128$	−16.3751	+	9.45416i	−1.44737	+	0.835638i
$129$	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	$0.877292\pi$
$132$	4.59234	−	2.65139i	0.399712	−	0.230774i
$133$	−2.80278	−	4.85455i	−0.243031	−	0.420943i
$134$	8.05971	−	13.9598i	0.696253	−	1.20595i
$135$			5.00000i			0.430331i
$136$	19.7598	+	11.4083i	1.69439	+	0.978256i
$137$	−1.39045	−	0.802776i	−0.118794	−	0.0685858i	0.439426	−	0.898279i	$-0.355182\pi$
$137$	−1.39045	−	0.802776i	−0.118794	−	0.0685858i	−0.558220	+	0.829693i	$0.688515\pi$
$138$		−	6.90833i		−	0.588076i
$139$	−3.19722	+	5.53776i	−0.271185	+	0.469706i	−0.969166	−	0.246410i	$-0.920749\pi$
$139$	−3.19722	+	5.53776i	−0.271185	+	0.469706i	0.697981	+	0.716117i	$0.254082\pi$
$140$	1.65139	+	2.86029i	0.139568	+	0.241738i
$141$	−7.97705	+	4.60555i	−0.671789	+	0.387857i
$142$	11.0917			0.930793
$143$		0			0
$144$	−0.605551			−0.0504626
$145$	5.37897	−	3.10555i	0.446699	−	0.257902i
$146$	−0.908327	−	1.57327i	−0.0751737	−	0.130205i
$147$	−3.00000	+	5.19615i	−0.247436	+	0.428571i
$148$			11.9083i			0.978858i
$149$	−2.59808	−	1.50000i	−0.212843	−	0.122885i	0.389789	−	0.920904i	$-0.372548\pi$
$149$	−2.59808	−	1.50000i	−0.212843	−	0.122885i	−0.602632	+	0.798019i	$0.705881\pi$
$150$	−1.99426	−	1.15139i	−0.162831	−	0.0940104i
$151$			1.21110i			0.0985581i	0.998785	+	0.0492791i	$0.0156924\pi$
$151$			1.21110i			0.0985581i	−0.998785	+	0.0492791i	$0.984308\pi$
$152$	−8.40833	+	14.5636i	−0.682005	+	1.18127i
$153$	−7.60555	−	13.1732i	−0.614872	−	1.06499i
$154$	−3.20189	+	1.84861i	−0.258016	+	0.148965i
$155$	−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	$0.352360\pi$
$158$	−10.3923	+	6.00000i	−0.826767	+	0.477334i
$159$	1.60555	+	2.78090i	0.127328	+	0.220539i
$160$	−2.65139	+	4.59234i	−0.209611	+	0.363056i
$161$			3.00000i			0.236433i
$162$	1.99426	+	1.15139i	0.156684	+	0.0904616i
$163$	−3.28128	−	1.89445i	−0.257010	−	0.148385i	0.365960	−	0.930631i	$-0.380741\pi$
$163$	−3.28128	−	1.89445i	−0.257010	−	0.148385i	−0.622970	+	0.782246i	$0.714074\pi$
$164$		−	9.90833i		−	0.773710i
$165$	0.802776	−	1.39045i	0.0624960	−	0.108246i
$166$	10.6056	+	18.3694i	0.823150	+	1.42574i
$167$	−7.79423	+	4.50000i	−0.603136	+	0.348220i	−0.770274	−	0.637713i	$-0.779881\pi$
$167$	−7.79423	+	4.50000i	−0.603136	+	0.348220i	0.167139	+	0.985933i	$0.446547\pi$
$168$	−3.00000			−0.231455
$169$		0			0
$170$	17.5139			1.34325
$171$	9.70910	−	5.60555i	0.742473	−	0.428667i
$172$	16.8625	+	29.2067i	1.28575	+	2.22699i
$173$	2.40833	−	4.17134i	0.183102	−	0.317141i	−0.759834	−	0.650118i	$-0.774720\pi$
$173$	2.40833	−	4.17134i	0.183102	−	0.317141i	0.942935	+	0.332976i	$0.108053\pi$
$174$			14.3028i			1.08429i
$175$	0.866025	+	0.500000i	0.0654654	+	0.0377964i
$176$	0.420994	+	0.243061i	0.0317336	+	0.0183214i
$177$			10.8167i			0.813029i
$178$	−7.15139	+	12.3866i	−0.536019	+	0.928412i
$179$	11.4083	+	19.7598i	0.852698	+	1.47692i	0.878764	+	0.477257i	$0.158369\pi$
$179$	11.4083	+	19.7598i	0.852698	+	1.47692i	−0.0260655	+	0.999660i	$0.508298\pi$
$180$	−5.72058	+	3.30278i	−0.426387	+	0.246174i
$181$	−17.6333			−1.31067			−0.655337	−	0.755337i	$-0.727473\pi$
$181$	−17.6333			−1.31067			−0.655337	+	0.755337i	$0.727473\pi$
$182$		0			0
$183$	−1.00000			−0.0739221
$184$	7.79423	−	4.50000i	0.574598	−	0.331744i
$185$	1.80278	+	3.12250i	0.132543	+	0.229571i
$186$	4.60555	−	7.97705i	0.337695	−	0.584906i
$187$			12.2111i			0.892964i
$188$	−26.3464	−	15.2111i	−1.92151	−	1.10938i
$189$	4.33013	+	2.50000i	0.314970	+	0.181848i
$190$			12.9083i			0.936468i
$191$	−8.40833	+	14.5636i	−0.608405	+	1.05379i	0.383098	+	0.923708i	$0.374857\pi$
$191$	−8.40833	+	14.5636i	−0.608405	+	1.05379i	−0.991503	+	0.130081i	$0.958476\pi$
$192$	−6.40833	−	11.0995i	−0.462481	−	0.801041i
$193$	−13.5148	+	7.80278i	−0.972817	+	0.561656i	−0.900094	−	0.435696i	$-0.856502\pi$
$193$	−13.5148	+	7.80278i	−0.972817	+	0.561656i	−0.0727230	+	0.997352i	$0.523169\pi$
$194$	−19.3305			−1.38785
$195$		0			0
$196$	−19.8167			−1.41548
$197$	1.02481	−	0.591673i	0.0730145	−	0.0421550i	−0.463048	−	0.886333i	$-0.653244\pi$
$197$	1.02481	−	0.591673i	0.0730145	−	0.0421550i	0.536063	+	0.844178i	$0.319911\pi$
$198$	−3.69722	−	6.40378i	−0.262750	−	0.455097i
$199$	6.40833	−	11.0995i	0.454274	−	0.786826i	−0.544372	−	0.838844i	$-0.683232\pi$
$199$	6.40833	−	11.0995i	0.454274	−	0.786826i	0.998646	+	0.0520179i	$0.0165653\pi$
$200$		−	3.00000i		−	0.212132i
$201$	6.06218	+	3.50000i	0.427593	+	0.246871i
$202$	17.9484	+	10.3625i	1.26284	+	0.729102i
$203$		−	6.21110i		−	0.435934i
$204$	−12.5597	+	21.7541i	−0.879356	+	1.52309i
$205$	−1.50000	−	2.59808i	−0.104765	−	0.181458i
$206$	−7.97705	+	4.60555i	−0.555787	+	0.320884i
$207$	−6.00000			−0.417029
$208$		0			0
$209$	−9.00000			−0.622543
$210$	−1.99426	+	1.15139i	−0.137617	+	0.0794533i
$211$	11.8028	+	20.4430i	0.812537	+	1.40735i	0.911083	+	0.412222i	$0.135247\pi$
$211$	11.8028	+	20.4430i	0.812537	+	1.40735i	−0.0985467	+	0.995132i	$0.531419\pi$
$212$	−5.30278	+	9.18468i	−0.364196	+	0.630806i
$213$			4.81665i			0.330032i
$214$	12.3866	+	7.15139i	0.846728	+	0.488859i
$215$	8.84307	+	5.10555i	0.603093	+	0.348196i
$216$		−	15.0000i		−	1.02062i
$217$	−2.00000	+	3.46410i	−0.135769	+	0.235159i
$218$	22.1194	+	38.3120i	1.49812	+	2.59481i
$219$	0.683205	−	0.394449i	0.0461667	−	0.0266544i
$220$	5.30278			0.357513
$221$		0			0
$222$	−8.30278			−0.557246
$223$	−3.64692	+	2.10555i	−0.244216	+	0.140998i	−0.617113	−	0.786875i	$-0.711698\pi$
$223$	−3.64692	+	2.10555i	−0.244216	+	0.140998i	0.372897	+	0.927873i	$0.378364\pi$
$224$	2.65139	+	4.59234i	0.177153	+	0.306839i
$225$	−1.00000	+	1.73205i	−0.0666667	+	0.115470i
$226$			3.69722i			0.245936i
$227$	23.7483	+	13.7111i	1.57623	+	0.910038i	0.995378	+	0.0960296i	$0.0306143\pi$
$227$	23.7483	+	13.7111i	1.57623	+	0.910038i	0.580853	+	0.814008i	$0.302719\pi$
$228$	−16.0335	−	9.25694i	−1.06184	−	0.613056i
$229$		−	14.0000i		−	0.925146i	−0.886581	−	0.462573i	$-0.846926\pi$
$229$		−	14.0000i		−	0.925146i	0.886581	−	0.462573i	$-0.153074\pi$
$230$	3.45416	−	5.98279i	0.227761	−	0.394493i
$231$	−0.802776	−	1.39045i	−0.0528188	−	0.0914848i
$232$	−16.1369	+	9.31665i	−1.05944	+	0.611668i
$233$	−15.2111			−0.996512			−0.498256	−	0.867030i	$-0.666026\pi$
$233$	−15.2111			−0.996512			−0.498256	+	0.867030i	$0.666026\pi$
$234$		0			0
$235$	−9.21110			−0.600866
$236$	−30.9387	+	17.8625i	−2.01394	+	1.16275i
$237$	−2.60555	−	4.51295i	−0.169249	−	0.293147i
$238$	8.75694	−	15.1675i	0.567628	−	0.983161i
$239$		0			0		1.00000			$0$
$239$		0			0		−1.00000			$\pi$
$240$	0.262211	+	0.151388i	0.0169257	+	0.00977204i
$241$	1.54923	+	0.894449i	0.0997947	+	0.0576165i	0.549067	−	0.835778i	$-0.314983\pi$
$241$	1.54923	+	0.894449i	0.0997947	+	0.0576165i	−0.449272	+	0.893395i	$0.648317\pi$
$242$		−	19.3944i		−	1.24672i
$243$	−8.00000	+	13.8564i	−0.513200	+	0.888889i
$244$	−1.65139	−	2.86029i	−0.105719	−	0.183111i
$245$	−5.19615	+	3.00000i	−0.331970	+	0.191663i
$246$	6.90833			0.440459
$247$		0			0
$248$	12.0000			0.762001
$249$	−7.97705	+	4.60555i	−0.505525	+	0.291865i
$250$	−1.15139	−	1.99426i	−0.0728202	−	0.126128i
$251$	−3.59167	+	6.22096i	−0.226704	+	0.392664i	−0.956829	−	0.290650i	$-0.906128\pi$
$251$	−3.59167	+	6.22096i	−0.226704	+	0.392664i	0.730125	+	0.683314i	$0.239462\pi$
$252$			6.60555i			0.416111i
$253$	4.17134	+	2.40833i	0.262250	+	0.151410i
$254$	8.39804	+	4.84861i	0.526940	+	0.304229i
$255$			7.60555i			0.476278i
$256$	8.95416	−	15.5091i	0.559635	−	0.969317i
$257$	−8.19722	−	14.1980i	−0.511329	−	0.885647i	−0.999914	−	0.0131312i	$-0.995820\pi$
$257$	−8.19722	−	14.1980i	−0.511329	−	0.885647i	0.488585	−	0.872516i	$-0.337513\pi$
$258$	−20.3636	+	11.7569i	−1.26778	+	0.731955i
$259$	3.60555			0.224038
$260$		0			0
$261$	12.4222			0.768915
$262$	42.3005	−	24.4222i	2.61333	−	1.50881i
$263$	−5.89445	−	10.2095i	−0.363467	−	0.629544i	0.625062	−	0.780575i	$-0.285074\pi$
$263$	−5.89445	−	10.2095i	−0.363467	−	0.629544i	−0.988529	+	0.151032i	$0.951740\pi$
$264$	−2.40833	+	4.17134i	−0.148222	+	0.256729i
$265$			3.21110i			0.197256i
$266$	11.1789	+	6.45416i	0.685425	+	0.395730i
$267$	−5.37897	−	3.10555i	−0.329188	−	0.190057i
$268$			23.1194i			1.41224i
$269$	4.50000	−	7.79423i	0.274370	−	0.475223i	−0.695606	−	0.718423i	$-0.744864\pi$
$269$	4.50000	−	7.79423i	0.274370	−	0.475223i	0.969976	+	0.243201i	$0.0781974\pi$
$270$	−5.75694	−	9.97131i	−0.350356	−	0.606835i
$271$	18.0278	−	10.4083i	1.09511	−	0.632261i	0.160176	−	0.987088i	$-0.448794\pi$
$271$	18.0278	−	10.4083i	1.09511	−	0.632261i	0.934932	+	0.354828i	$0.115460\pi$
$272$	−2.30278			−0.139626
$273$		0			0
$274$	3.69722			0.223357
$275$	1.39045	−	0.802776i	0.0838472	−	0.0484092i
$276$	4.95416	+	8.58086i	0.298206	+	0.516507i
$277$	13.8028	−	23.9071i	0.829328	−	1.43644i	−0.0692374	−	0.997600i	$-0.522057\pi$
$277$	13.8028	−	23.9071i	0.829328	−	1.43644i	0.898566	−	0.438839i	$-0.144610\pi$
$278$		−	14.7250i		−	0.883146i
$279$	−6.92820	−	4.00000i	−0.414781	−	0.239474i
$280$	−2.59808	−	1.50000i	−0.155265	−	0.0896421i
$281$			6.00000i			0.357930i	0.983855	+	0.178965i	$0.0572749\pi$
$281$			6.00000i			0.357930i	−0.983855	+	0.178965i	$0.942725\pi$
$282$	10.6056	−	18.3694i	0.631551	−	1.09388i
$283$	2.50000	+	4.33013i	0.148610	+	0.257399i	0.930714	−	0.365748i	$-0.119187\pi$
$283$	2.50000	+	4.33013i	0.148610	+	0.257399i	−0.782104	+	0.623148i	$0.785854\pi$
$284$	−13.7770	+	7.95416i	−0.817515	+	0.471993i
$285$	−5.60555			−0.332044
$286$		0			0
$287$	−3.00000			−0.177084
$288$	−9.18468	+	5.30278i	−0.541212	+	0.312469i
$289$	−20.4222	−	35.3723i	−1.20131	−	2.08072i
$290$	−7.15139	+	12.3866i	−0.419944	+	0.727364i
$291$		−	8.39445i		−	0.492091i
$292$	2.25647	+	1.30278i	0.132050	+	0.0762392i
$293$	9.00186	+	5.19722i	0.525894	+	0.303625i	0.739343	−	0.673329i	$-0.235136\pi$
$293$	9.00186	+	5.19722i	0.525894	+	0.303625i	−0.213449	+	0.976954i	$0.568470\pi$
$294$		−	13.8167i		−	0.805804i
$295$	−5.40833	+	9.36750i	−0.314885	+	0.545397i
$296$	−5.40833	−	9.36750i	−0.314353	−	0.544475i
$297$	6.95224	−	4.01388i	0.403410	−	0.232909i
$298$	6.90833			0.400189
$299$		0			0
$300$	3.30278			0.190686
$301$	8.84307	−	5.10555i	0.509706	−	0.294279i
$302$	−1.39445	−	2.41526i	−0.0802415	−	0.138982i
$303$	−4.50000	+	7.79423i	−0.258518	+	0.447767i
$304$		−	1.69722i		−	0.0973425i
$305$	−0.866025	−	0.500000i	−0.0495885	−	0.0286299i
$306$	30.3349	+	17.5139i	1.73413	+	1.00120i
$307$			16.0000i			0.913168i	0.889680	+	0.456584i	$0.150927\pi$
$307$			16.0000i			0.913168i	−0.889680	+	0.456584i	$0.849073\pi$
$308$	2.65139	−	4.59234i	0.151077	−	0.261673i
$309$	−2.00000	−	3.46410i	−0.113776	−	0.197066i
$310$	7.97705	−	4.60555i	0.453066	−	0.261578i
$311$	9.21110			0.522314			0.261157	−	0.965296i	$-0.415896\pi$
$311$	9.21110			0.522314			0.261157	+	0.965296i	$0.415896\pi$
$312$		0			0
$313$	14.0000			0.791327			0.395663	−	0.918396i	$-0.370515\pi$
$313$	14.0000			0.791327			0.395663	+	0.918396i	$0.370515\pi$
$314$	−22.3579	+	12.9083i	−1.26173	+	0.728459i
$315$	1.00000	+	1.73205i	0.0563436	+	0.0975900i
$316$	8.60555	−	14.9053i	0.484100	−	0.838486i
$317$			6.00000i			0.336994i	0.985702	+	0.168497i	$0.0538913\pi$
$317$			6.00000i			0.336994i	−0.985702	+	0.168497i	$0.946109\pi$
$318$	−6.40378	−	3.69722i	−0.359106	−	0.207330i
$319$	−8.63622	−	4.98612i	−0.483535	−	0.279169i
$320$		−	12.8167i		−	0.716473i
$321$	−3.10555	+	5.37897i	−0.173335	+	0.300225i
$322$	−3.45416	−	5.98279i	−0.192493	−	0.333408i
$323$	36.9215	−	21.3167i	2.05437	−	1.18609i
$324$	−3.30278			−0.183488
$325$		0			0
$326$	8.72498			0.483232
$327$	−16.6373	+	9.60555i	−0.920045	+	0.531188i
$328$	4.50000	+	7.79423i	0.248471	+	0.430364i
$329$	−4.60555	+	7.97705i	−0.253912	+	0.439789i
$330$			3.69722i			0.203526i
$331$	−8.68429	−	5.01388i	−0.477332	−	0.275588i	0.241972	−	0.970283i	$-0.422206\pi$
$331$	−8.68429	−	5.01388i	−0.477332	−	0.275588i	−0.719304	+	0.694696i	$0.755539\pi$
$332$	−26.3464	−	15.2111i	−1.44595	−	0.834818i
$333$			7.21110i			0.395166i
$334$	10.3625	−	17.9484i	0.567010	−	0.982091i
$335$	3.50000	+	6.06218i	0.191225	+	0.331212i
$336$	0.262211	−	0.151388i	0.0143048	−	0.00825888i
$337$	25.6333			1.39634			0.698168	−	0.715934i	$-0.253999\pi$
$337$	25.6333			1.39634			0.698168	+	0.715934i	$0.253999\pi$
$338$		0			0
$339$	−1.60555			−0.0872016
$340$	−21.7541	+	12.5597i	−1.17978	+	0.681146i
$341$	3.21110	+	5.56179i	0.173891	+	0.301188i
$342$	−12.9083	+	22.3579i	−0.698002	+	1.20898i
$343$			13.0000i			0.701934i
$344$	−26.5292	−	15.3167i	−1.43036	−	0.825819i
$345$	2.59808	+	1.50000i	0.139876	+	0.0807573i
$346$			11.0917i			0.596292i
$347$	−2.89445	+	5.01333i	−0.155382	+	0.269130i	−0.933198	−	0.359362i	$-0.882994\pi$
$347$	−2.89445	+	5.01333i	−0.155382	+	0.269130i	0.777816	+	0.628492i	$0.216328\pi$
$348$	−10.2569	−	17.7655i	−0.549830	−	0.952333i
$349$	3.28128	−	1.89445i	0.175643	−	0.101408i	−0.409601	−	0.912265i	$-0.634332\pi$
$349$	3.28128	−	1.89445i	0.175643	−	0.101408i	0.585244	+	0.810857i	$0.300999\pi$
$350$	−2.30278			−0.123089
$351$		0			0
$352$	8.51388			0.453791
$353$	14.5636	−	8.40833i	0.775145	−	0.447530i	−0.0595620	−	0.998225i	$-0.518970\pi$
$353$	14.5636	−	8.40833i	0.775145	−	0.447530i	0.834707	+	0.550695i	$0.185637\pi$
$354$	−12.4542	−	21.5712i	−0.661931	−	1.14650i
$355$	−2.40833	+	4.17134i	−0.127821	+	0.221392i
$356$		−	20.5139i		−	1.08723i
$357$	6.58660	+	3.80278i	0.348600	+	0.201264i
$358$	−45.5024	−	26.2708i	−2.40488	−	1.38846i
$359$		−	18.4222i		−	0.972287i	−0.873879	−	0.486143i	$-0.838403\pi$
$359$		−	18.4222i		−	0.972287i	0.873879	−	0.486143i	$-0.161597\pi$
$360$	3.00000	−	5.19615i	0.158114	−	0.273861i
$361$	6.21110	+	10.7579i	0.326900	+	0.566208i
$362$	35.1654	−	20.3028i	1.84825	−	1.06709i
$363$	8.42221			0.442051
$364$		0			0
$365$	0.788897			0.0412928
$366$	1.99426	−	1.15139i	0.104242	−	0.0601840i
$367$	−5.71110	−	9.89192i	−0.298117	−	0.516354i	0.677588	−	0.735442i	$-0.263025\pi$
$367$	−5.71110	−	9.89192i	−0.298117	−	0.516354i	−0.975705	+	0.219088i	$0.929692\pi$
$368$	−0.454163	+	0.786634i	−0.0236749	+	0.0410061i
$369$		−	6.00000i		−	0.312348i
$370$	−7.19041	−	4.15139i	−0.373812	−	0.215820i
$371$	2.78090	+	1.60555i	0.144377	+	0.0833561i
$372$			13.2111i			0.684964i
$373$	10.1972	−	17.6621i	0.527992	−	0.914509i	−0.471475	−	0.881879i	$-0.656278\pi$
$373$	10.1972	−	17.6621i	0.527992	−	0.914509i	0.999467	−	0.0326301i	$-0.0103883\pi$
$374$	−14.0597	−	24.3521i	−0.727011	−	1.25922i
$375$	0.866025	−	0.500000i	0.0447214	−	0.0258199i
$376$	27.6333			1.42508
$377$		0			0
$378$	−11.5139			−0.592210
$379$	8.31865	−	4.80278i	0.427300	−	0.246702i	−0.270895	−	0.962609i	$-0.587320\pi$
$379$	8.31865	−	4.80278i	0.427300	−	0.246702i	0.698196	+	0.715907i	$0.253986\pi$
$380$	−9.25694	−	16.0335i	−0.474871	−	0.822501i
$381$	−2.10555	+	3.64692i	−0.107871	+	0.186837i
$382$		−	38.7250i		−	1.98134i
$383$	21.3331	+	12.3167i	1.09007	+	0.629352i	0.933595	−	0.358330i	$-0.116654\pi$
$383$	21.3331	+	12.3167i	1.09007	+	0.629352i	0.156474	+	0.987682i	$0.449987\pi$
$384$	16.3751	+	9.45416i	0.835638	+	0.482456i
$385$		−	1.60555i		−	0.0818265i
$386$	17.9680	−	31.1216i	0.914549	−	1.58405i
$387$	10.2111	+	17.6861i	0.519060	+	0.899037i
$388$	24.0105	−	13.8625i	1.21895	−	0.703761i
$389$	15.2111			0.771234			0.385617	−	0.922659i	$-0.373989\pi$
$389$	15.2111			0.771234			0.385617	+	0.922659i	$0.373989\pi$
$390$		0			0
$391$	−22.8167			−1.15389
$392$	15.5885	−	9.00000i	0.787336	−	0.454569i
$393$	10.6056	+	18.3694i	0.534979	+	0.926611i
$394$	−1.36249	+	2.35990i	−0.0686413	+	0.118890i
$395$		−	5.21110i		−	0.262199i
$396$	9.18468	+	5.30278i	0.461547	+	0.266475i
$397$	19.0766	+	11.0139i	0.957427	+	0.552771i	0.895380	−	0.445303i	$-0.146904\pi$
$397$	19.0766	+	11.0139i	0.957427	+	0.552771i	0.0620468	+	0.998073i	$0.480237\pi$
$398$			29.5139i			1.47940i
$399$	−2.80278	+	4.85455i	−0.140314	+	0.243031i
$400$	0.151388	+	0.262211i	0.00756939	+	0.0131106i
$401$	−10.5751	+	6.10555i	−0.528097	+	0.304897i	−0.740241	−	0.672342i	$-0.765289\pi$
$401$	−10.5751	+	6.10555i	−0.528097	+	0.304897i	0.212144	+	0.977238i	$0.431955\pi$
$402$	−16.1194			−0.803964
$403$		0			0
$404$	−29.7250			−1.47887
$405$	−0.866025	+	0.500000i	−0.0430331	+	0.0248452i
$406$	7.15139	+	12.3866i	0.354917	+	0.614735i
$407$	2.89445	−	5.01333i	0.143472	−	0.248502i
$408$		−	22.8167i		−	1.12959i
$409$	−7.11102	−	4.10555i	−0.351617	−	0.203006i	0.313780	−	0.949496i	$-0.398405\pi$
$409$	−7.11102	−	4.10555i	−0.351617	−	0.203006i	−0.665397	+	0.746489i	$0.731738\pi$
$410$	5.98279	+	3.45416i	0.295469	+	0.170589i
$411$			1.60555i			0.0791960i
$412$	6.60555	−	11.4412i	0.325432	−	0.563665i
$413$	5.40833	+	9.36750i	0.266126	+	0.460944i
$414$	11.9656	−	6.90833i	0.588076	−	0.339526i
$415$	−9.21110			−0.452155
$416$		0			0
$417$	6.39445			0.313138
$418$	17.9484	−	10.3625i	0.877883	−	0.506846i
$419$	−8.61943	−	14.9293i	−0.421087	−	0.729344i	0.574959	−	0.818182i	$-0.305018\pi$
$419$	−8.61943	−	14.9293i	−0.421087	−	0.729344i	−0.996046	+	0.0888384i	$0.971685\pi$
$420$	1.65139	−	2.86029i	0.0805795	−	0.139568i
$421$			32.4222i			1.58016i	0.613003	+	0.790081i	$0.289961\pi$
$421$			32.4222i			1.58016i	−0.613003	+	0.790081i	$0.710039\pi$
$422$	−47.0757	−	27.1791i	−2.29161	−	1.32306i
$423$	−15.9541	−	9.21110i	−0.775715	−	0.447859i
$424$		−	9.63331i		−	0.467835i
$425$	−3.80278	+	6.58660i	−0.184462	+	0.319497i
$426$	−5.54584	−	9.60567i	−0.268697	−	0.465396i
$427$	−0.866025	+	0.500000i	−0.0419099	+	0.0241967i
$428$	−20.5139			−0.991576
$429$		0			0
$430$	−23.5139			−1.13394
$431$	25.3216	−	14.6194i	1.21970	−	0.704193i	0.254845	−	0.966982i	$-0.417976\pi$
$431$	25.3216	−	14.6194i	1.21970	−	0.704193i	0.964853	+	0.262789i	$0.0846422\pi$
$432$	0.756939	+	1.31106i	0.0364182	+	0.0630783i
$433$	1.80278	−	3.12250i	0.0866359	−	0.150058i	−0.819451	−	0.573149i	$-0.805722\pi$
$433$	1.80278	−	3.12250i	0.0866359	−	0.150058i	0.906087	+	0.423091i	$0.139055\pi$
$434$		−	9.21110i		−	0.442147i
$435$	−5.37897	−	3.10555i	−0.257902	−	0.148900i
$436$	−54.9493	−	31.7250i	−2.63159	−	1.51935i
$437$		−	16.8167i		−	0.804450i
$438$	−0.908327	+	1.57327i	−0.0434015	+	0.0751737i
$439$	−13.6194	−	23.5895i	−0.650020	−	1.12587i	−0.983118	−	0.182975i	$-0.941427\pi$
$439$	−13.6194	−	23.5895i	−0.650020	−	1.12587i	0.333098	−	0.942892i	$-0.391906\pi$
$440$	−4.17134	+	2.40833i	−0.198861	+	0.114812i
$441$	−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	$0.451247\pi$
$444$	10.3129	−	5.95416i	0.489429	−	0.282572i
$445$	−3.10555	−	5.37897i	−0.147217	−	0.254988i
$446$	4.84861	−	8.39804i	0.229588	−	0.397659i
$447$			3.00000i			0.141895i
$448$	−11.0995	−	6.40833i	−0.524404	−	0.302765i
$449$	26.5292	+	15.3167i	1.25199	+	0.722838i	0.971505	−	0.237020i	$-0.0761708\pi$
$449$	26.5292	+	15.3167i	1.25199	+	0.722838i	0.280487	+	0.959858i	$0.409504\pi$
$450$		−	4.60555i		−	0.217108i
$451$	−2.40833	+	4.17134i	−0.113404	+	0.196421i
$452$	−2.65139	−	4.59234i	−0.124711	−	0.216005i
$453$	1.04885	−	0.605551i	0.0492791	−	0.0284513i
$454$	−63.1472			−2.96364
$455$		0			0
$456$	16.8167			0.787512
$457$	−23.2239	+	13.4083i	−1.08637	+	0.627215i	−0.932607	−	0.360893i	$-0.882472\pi$
$457$	−23.2239	+	13.4083i	−1.08637	+	0.627215i	−0.153761	+	0.988108i	$0.549139\pi$
$458$	16.1194	+	27.9197i	0.753211	+	1.30460i
$459$	−19.0139	+	32.9330i	−0.887492	+	1.53718i
$460$			9.90833i			0.461978i
$461$	−31.3597	−	18.1056i	−1.46057	−	0.843260i	−0.461531	−	0.887124i	$-0.652700\pi$
$461$	−31.3597	−	18.1056i	−1.46057	−	0.843260i	−0.999037	+	0.0438645i	$0.986033\pi$
$462$	3.20189	+	1.84861i	0.148965	+	0.0860052i
$463$			34.4222i			1.59974i	0.600176	+	0.799868i	$0.295097\pi$
$463$			34.4222i			1.59974i	−0.600176	+	0.799868i	$0.704903\pi$
$464$	0.940285	−	1.62862i	0.0436516	−	0.0756069i
$465$	2.00000	+	3.46410i	0.0927478	+	0.160644i
$466$	30.3349	−	17.5139i	1.40524	−	0.811315i
$467$	−2.78890			−0.129055			−0.0645274	−	0.997916i	$-0.520554\pi$
$467$	−2.78890			−0.129055			−0.0645274	+	0.997916i	$0.520554\pi$
$468$		0			0
$469$	7.00000			0.323230
$470$	18.3694	−	10.6056i	0.847315	−	0.489198i
$471$	−5.60555	−	9.70910i	−0.258290	−	0.447372i
$472$	16.2250	−	28.1025i	0.746815	−	1.29352i
$473$		−	16.3944i		−	0.753818i
$474$	10.3923	+	6.00000i	0.477334	+	0.275589i
$475$	−4.85455	−	2.80278i	−0.222742	−	0.128600i
$476$			25.1194i			1.15135i
$477$	−3.21110	+	5.56179i	−0.147026	+	0.254657i
$478$		0			0
$479$	24.9560	−	14.4083i	1.14027	−	0.658333i	0.193770	−	0.981047i	$-0.437928\pi$
$479$	24.9560	−	14.4083i	1.14027	−	0.658333i	0.946497	+	0.322714i	$0.104595\pi$
$480$	5.30278			0.242037
$481$		0			0
$482$	−4.11943			−0.187635
$483$	2.59808	−	1.50000i	0.118217	−	0.0682524i
$484$	13.9083	+	24.0899i	0.632197	+	1.09500i
$485$	4.19722	−	7.26981i	0.190586	−	0.330105i
$486$		−	36.8444i		−	1.67130i
$487$	0.866025	+	0.500000i	0.0392434	+	0.0226572i	0.519493	−	0.854475i	$-0.326121\pi$
$487$	0.866025	+	0.500000i	0.0392434	+	0.0226572i	−0.480250	+	0.877132i	$0.659454\pi$
$488$	2.59808	+	1.50000i	0.117609	+	0.0679018i
$489$			3.78890i			0.171340i
$490$	6.90833	−	11.9656i	0.312086	−	0.540549i
$491$	−8.40833	−	14.5636i	−0.379462	−	0.657248i	0.611522	−	0.791228i	$-0.290558\pi$
$491$	−8.40833	−	14.5636i	−0.379462	−	0.657248i	−0.990984	+	0.133979i	$0.957224\pi$
$492$	−8.58086	+	4.95416i	−0.386855	+	0.223351i
$493$	47.2389			2.12753
$494$		0			0
$495$	3.21110			0.144328
$496$	−1.04885	+	0.605551i	−0.0470946	+	0.0271901i
$497$	2.40833	+	4.17134i	0.108028	+	0.187110i
$498$	10.6056	−	18.3694i	0.475246	−	0.823150i
$499$			2.42221i			0.108433i	0.998529	+	0.0542164i	$0.0172661\pi$
$499$			2.42221i			0.108433i	−0.998529	+	0.0542164i	$0.982734\pi$
$500$	2.86029	+	1.65139i	0.127916	+	0.0738523i
$501$	7.79423	+	4.50000i	0.348220	+	0.201045i
$502$		−	16.5416i		−	0.738289i
$503$	−1.50000	+	2.59808i	−0.0668817	+	0.115842i	−0.897527	−	0.440959i	$-0.854638\pi$
$503$	−1.50000	+	2.59808i	−0.0668817	+	0.115842i	0.830645	+	0.556802i	$0.187972\pi$
$504$	−3.00000	−	5.19615i	−0.133631	−	0.231455i
$505$	−7.79423	+	4.50000i	−0.346839	+	0.200247i
$506$	−11.0917			−0.493085
$507$		0			0
$508$	−13.9083			−0.617082
$509$	2.59808	−	1.50000i	0.115158	−	0.0664863i	−0.441315	−	0.897352i	$-0.645488\pi$
$509$	2.59808	−	1.50000i	0.115158	−	0.0664863i	0.556473	+	0.830866i	$0.312154\pi$
$510$	−8.75694	−	15.1675i	−0.387764	−	0.671627i
$511$	0.394449	−	0.683205i	0.0174494	−	0.0302232i
$512$			3.42221i			0.151242i
$513$	−24.2727	−	14.0139i	−1.07167	−	0.618728i
$514$	32.6948	+	18.8764i	1.44211	+	0.832601i
$515$		−	4.00000i		−	0.176261i
$516$	16.8625	−	29.2067i	0.742330	−	1.28575i
$517$	7.39445	+	12.8076i	0.325207	+	0.563276i
$518$	−7.19041	+	4.15139i	−0.315929	+	0.182402i
$519$	−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	$0.370988\pi$
$522$	−24.7731	+	14.3028i	−1.08429	+	0.626015i
$523$	0.711103	+	1.23167i	0.0310943	+	0.0538570i	0.881154	−	0.472830i	$-0.156767\pi$
$523$	0.711103	+	1.23167i	0.0310943	+	0.0538570i	−0.850059	+	0.526687i	$0.823434\pi$
$524$	−35.0278	+	60.6699i	−1.53019	+	2.65037i
$525$		−	1.00000i		−	0.0436436i
$526$	23.5102	+	13.5736i	1.02509	+	0.591837i
$527$	−26.3464	−	15.2111i	−1.14767	−	0.662606i
$528$		−	0.486122i		−	0.0211557i
$529$	7.00000	−	12.1244i	0.304348	−	0.527146i
$530$	−3.69722	−	6.40378i	−0.160597	−	0.278162i
$531$	−18.7350	+	10.8167i	−0.813029	+	0.469403i
$532$	−18.5139			−0.802678
$533$		0			0
$534$	14.3028			0.618942
$535$	−5.37897	+	3.10555i	−0.232553	+	0.134265i
$536$	−10.5000	−	18.1865i	−0.453531	−	0.785539i
$537$	11.4083	−	19.7598i	0.492306	−	0.852698i
$538$			20.7250i			0.893517i
$539$	8.34269	+	4.81665i	0.359345	+	0.207468i
$540$	14.3014	+	8.25694i	0.615436	+	0.355322i
$541$			25.6333i			1.10206i	0.834485	+	0.551031i	$0.185765\pi$
$541$			25.6333i			1.10206i	−0.834485	+	0.551031i	$0.814235\pi$
$542$	−23.9680	+	41.5139i	−1.02952	+	1.78317i
$543$	8.81665	+	15.2709i	0.378359	+	0.655337i
$544$	−34.9273	+	20.1653i	−1.49749	+	0.864579i
$545$	−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	$0.252218\pi$
$548$	−4.59234	+	2.65139i	−0.196175	+	0.113262i
$549$	−1.00000	−	1.73205i	−0.0426790	−	0.0739221i
$550$	−1.84861	+	3.20189i	−0.0788251	+	0.136529i
$551$			34.8167i			1.48324i
$552$	−7.79423	−	4.50000i	−0.331744	−	0.191533i
$553$	−4.51295	−	2.60555i	−0.191910	−	0.110799i
$554$			63.5694i			2.70080i
$555$	1.80278	−	3.12250i	0.0765236	−	0.132543i
$556$	10.5597	+	18.2900i	0.447832	+	0.775667i
$557$	1.39045	−	0.802776i	0.0589152	−	0.0340147i	−0.470253	−	0.882532i	$-0.655837\pi$
$557$	1.39045	−	0.802776i	0.0589152	−	0.0340147i	0.529168	+	0.848517i	$0.322504\pi$
$558$	18.4222			0.779874
$559$		0			0
$560$	0.302776			0.0127946
$561$	10.5751	−	6.10555i	0.446482	−	0.257777i
$562$	−6.90833	−	11.9656i	−0.291410	−	0.504737i
$563$	4.71110	−	8.15987i	0.198549	−	0.343897i	−0.749509	−	0.661994i	$-0.769710\pi$
$563$	4.71110	−	8.15987i	0.198549	−	0.343897i	0.948058	+	0.318097i	$0.103044\pi$
$564$			30.4222i			1.28101i
$565$	−1.39045	−	0.802776i	−0.0584966	−	0.0337730i
$566$	−9.97131	−	5.75694i	−0.419125	−	0.241982i
$567$			1.00000i			0.0419961i
$568$	7.22498	−	12.5140i	0.303153	−	0.525077i
$569$	−13.7111	−	23.7483i	−0.574799	−	0.995582i	−0.996063	−	0.0886436i	$-0.971747\pi$
$569$	−13.7111	−	23.7483i	−0.574799	−	0.995582i	0.421264	−	0.906938i	$-0.361587\pi$
$570$	11.1789	−	6.45416i	0.468234	−	0.270335i
$571$	−20.8444			−0.872311			−0.436156	−	0.899871i	$-0.643660\pi$
$571$	−20.8444			−0.872311			−0.436156	+	0.899871i	$0.643660\pi$
$572$		0			0
$573$	16.8167			0.702526
$574$	5.98279	−	3.45416i	0.249717	−	0.144174i
$575$	1.50000	+	2.59808i	0.0625543	+	0.108347i
$576$	12.8167	−	22.1991i	0.534027	−	0.924962i
$577$		−	13.6333i		−	0.567562i	−0.958889	−	0.283781i	$-0.908411\pi$
$577$		−	13.6333i		−	0.567562i	0.958889	−	0.283781i	$-0.0915889\pi$
$578$	81.4545	+	47.0278i	3.38806	+	1.95610i
$579$	13.5148	+	7.80278i	0.561656	+	0.324272i
$580$		−	20.5139i		−	0.851792i
$581$	−4.60555	+	7.97705i	−0.191070	+	0.330944i
$582$	9.66527	+	16.7407i	0.400638	+	0.693926i
$583$	4.46487	−	2.57779i	0.184916	−	0.106761i
$584$	−2.36669			−0.0979344
$585$		0			0
$586$	−23.9361			−0.988790
$587$	−28.9445	+	16.7111i	−1.19467	+	0.689741i	−0.959361	−	0.282181i	$-0.908942\pi$
$587$	−28.9445	+	16.7111i	−1.19467	+	0.689741i	−0.235305	+	0.971922i	$0.575609\pi$
$588$	9.90833	+	17.1617i	0.408613	+	0.707738i
$589$	11.2111	−	19.4182i	0.461945	−	0.800113i
$590$		−	24.9083i		−	1.02546i
$591$	−1.02481	−	0.591673i	−0.0421550	−	0.0243382i
$592$	0.945417	+	0.545837i	0.0388564	+	0.0224337i
$593$		−	20.7889i		−	0.853698i	−0.904323	−	0.426849i	$-0.859624\pi$
$593$		−	20.7889i		−	0.853698i	0.904323	−	0.426849i	$-0.140376\pi$
$594$	−9.24306	+	16.0095i	−0.379247	+	0.656876i
$595$	3.80278	+	6.58660i	0.155899	+	0.270024i
$596$	−8.58086	+	4.95416i	−0.351486	+	0.202930i
$597$	−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	$0.642662\pi$
$600$	−2.59808	+	1.50000i	−0.106066	+	0.0612372i
$601$	−6.89445	−	11.9415i	−0.281230	−	0.487105i	0.690458	−	0.723373i	$-0.257409\pi$
$601$	−6.89445	−	11.9415i	−0.281230	−	0.487105i	−0.971688	+	0.236267i	$0.924076\pi$
$602$	−11.7569	+	20.3636i	−0.479177	+	0.829959i
$603$			14.0000i			0.570124i
$604$	3.46410	+	2.00000i	0.140952	+	0.0813788i
$605$	7.29384	+	4.21110i	0.296537	+	0.171206i
$606$		−	20.7250i		−	0.841895i
$607$	17.1056	−	29.6277i	0.694293	−	1.20255i	−0.276126	−	0.961122i	$-0.589051\pi$
$607$	17.1056	−	29.6277i	0.694293	−	1.20255i	0.970418	−	0.241429i	$-0.0776161\pi$
$608$	−14.8625	−	25.7426i	−0.602754	−	1.04400i
$609$	−5.37897	+	3.10555i	−0.217967	+	0.125843i
$610$	2.30278			0.0932367
$611$		0			0
$612$	−50.2389			−2.03079
$613$	−4.85455	+	2.80278i	−0.196073	+	0.113203i	−0.594823	−	0.803857i	$-0.702778\pi$
$613$	−4.85455	+	2.80278i	−0.196073	+	0.113203i	0.398749	+	0.917060i	$0.369444\pi$
$614$	−18.4222	−	31.9082i	−0.743460	−	1.28771i
$615$	−1.50000	+	2.59808i	−0.0604858	+	0.104765i
$616$			4.81665i			0.194069i
$617$	33.2986	+	19.2250i	1.34055	+	0.773969i	0.986888	−	0.161404i	$-0.0516021\pi$
$617$	33.2986	+	19.2250i	1.34055	+	0.773969i	0.353664	+	0.935372i	$0.384935\pi$
$618$	7.97705	+	4.60555i	0.320884	+	0.185262i
$619$		−	14.4222i		−	0.579677i	−0.957076	−	0.289839i	$-0.906398\pi$
$619$		−	14.4222i		−	0.579677i	0.957076	−	0.289839i	$-0.0936017\pi$
$620$	−6.60555	+	11.4412i	−0.265285	+	0.459488i
$621$	7.50000	+	12.9904i	0.300965	+	0.521286i
$622$	−18.3694	+	10.6056i	−0.736544	+	0.425244i
$623$	−6.21110			−0.248843
$624$		0			0
$625$	1.00000			0.0400000
$626$	−27.9197	+	16.1194i	−1.11589	+	0.644262i
$627$	4.50000	+	7.79423i	0.179713	+	0.311272i
$628$	18.5139	−	32.0670i	0.738784	−	1.27961i
$629$			27.4222i			1.09339i
$630$	−3.98852	−	2.30278i	−0.158907	−	0.0917448i
$631$	−31.2010	−	18.0139i	−1.24209	−	0.717121i	−0.272571	−	0.962136i	$-0.587874\pi$
$631$	−31.2010	−	18.0139i	−1.24209	−	0.717121i	−0.969519	+	0.245015i	$0.921207\pi$
$632$			15.6333i			0.621860i
$633$	11.8028	−	20.4430i	0.469118	−	0.812537i
$634$	−6.90833	−	11.9656i	−0.274365	−	0.475214i
$635$	−3.64692	+	2.10555i	−0.144724	+	0.0835563i
$636$	10.6056			0.420537
$637$		0			0
$638$	22.9638			0.909147
$639$	−8.34269	+	4.81665i	−0.330032	+	0.190544i
$640$	9.45416	+	16.3751i	0.373709	+	0.647282i
$641$	4.71110	−	8.15987i	0.186077	−	0.322295i	−0.757862	−	0.652415i	$-0.773756\pi$
$641$	4.71110	−	8.15987i	0.186077	−	0.322295i	0.943939	+	0.330120i	$0.107089\pi$
$642$		−	14.3028i		−	0.564486i
$643$	−2.28051	−	1.31665i	−0.0899346	−	0.0519238i	0.454358	−	0.890819i	$-0.349869\pi$
$643$	−2.28051	−	1.31665i	−0.0899346	−	0.0519238i	−0.544293	+	0.838895i	$0.683202\pi$
$644$	8.58086	+	4.95416i	0.338133	+	0.195221i
$645$		−	10.2111i		−	0.402062i
$646$	−49.0875	+	85.0220i	−1.93132	+	3.34515i
$647$	19.7111	+	34.1406i	0.774923	+	1.34221i	0.934838	+	0.355076i	$0.115545\pi$
$647$	19.7111	+	34.1406i	0.774923	+	1.34221i	−0.159914	+	0.987131i	$0.551122\pi$
$648$	2.59808	−	1.50000i	0.102062	−	0.0589256i
$649$	17.3667			0.681702
$650$		0			0
$651$	4.00000			0.156772
$652$	−10.8373	+	6.25694i	−0.424423	+	0.245041i
$653$	3.59167	+	6.22096i	0.140553	+	0.243445i	0.927705	−	0.373314i	$-0.121779\pi$
$653$	3.59167	+	6.22096i	0.140553	+	0.243445i	−0.787152	+	0.616759i	$0.788445\pi$
$654$	22.1194	−	38.3120i	0.864938	−	1.49812i
$655$			21.2111i			0.828786i
$656$	−0.786634	−	0.454163i	−0.0307129	−	0.0177321i
$657$	1.36641	+	0.788897i	0.0533087	+	0.0307778i
$658$		−	21.2111i		−	0.826895i
$659$	17.4083	−	30.1521i	0.678132	−	1.17456i	−0.297411	−	0.954750i	$-0.596123\pi$
$659$	17.4083	−	30.1521i	0.678132	−	1.17456i	0.975543	−	0.219810i	$-0.0705436\pi$
$660$	−2.65139	−	4.59234i	−0.103205	−	0.178757i
$661$	4.01256	−	2.31665i	0.156071	−	0.0901074i	−0.419931	−	0.907556i	$-0.637946\pi$
$661$	4.01256	−	2.31665i	0.156071	−	0.0901074i	0.576001	+	0.817449i	$0.304612\pi$
$662$	23.0917			0.897483
$663$		0			0
$664$	27.6333			1.07238
$665$	−4.85455	+	2.80278i	−0.188251	+	0.108687i
$666$	−8.30278	−	14.3808i	−0.321726	−	0.557246i
$667$	9.31665	−	16.1369i	0.360742	−	0.624824i
$668$			29.7250i			1.15009i
$669$	3.64692	+	2.10555i	0.140998	+	0.0814053i
$670$	−13.9598	−	8.05971i	−0.539315	−	0.311374i
$671$			1.60555i			0.0619816i
$672$	2.65139	−	4.59234i	0.102280	−	0.177153i
$673$	−8.80278	−	15.2469i	−0.339322	−	0.587723i	0.644983	−	0.764197i	$-0.276864\pi$
$673$	−8.80278	−	15.2469i	−0.339322	−	0.587723i	−0.984305	+	0.176474i	$0.943531\pi$
$674$	−51.1195	+	29.5139i	−1.96905	+	1.13683i
$675$	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	$0.559267\pi$
$678$	3.20189	−	1.84861i	0.122968	−	0.0709955i
$679$	−4.19722	−	7.26981i	−0.161075	−	0.278990i
$680$	11.4083	−	19.7598i	0.437489	−	0.757754i
$681$		−	27.4222i		−	1.05082i
$682$	−12.8076	−	7.39445i	−0.490427	−	0.283148i
$683$	31.3597	+	18.1056i	1.19995	+	0.692790i	0.960543	−	0.278130i	$-0.0897148\pi$
$683$	31.3597	+	18.1056i	1.19995	+	0.692790i	0.239404	+	0.970920i	$0.423048\pi$
$684$		−	37.0278i		−	1.41579i
$685$	−0.802776	+	1.39045i	−0.0306725	+	0.0531263i
$686$	−14.9680	−	25.9254i	−0.571482	−	0.989837i
$687$	−12.1244	+	7.00000i	−0.462573	+	0.267067i
$688$	3.09167			0.117869
$689$		0			0
$690$	−6.90833			−0.262996
$691$	−26.0048	+	15.0139i	−0.989269	+	0.571155i	−0.905056	−	0.425293i	$-0.860171\pi$
$691$	−26.0048	+	15.0139i	−0.989269	+	0.571155i	−0.0842134	+	0.996448i	$0.526838\pi$
$692$	−7.95416	−	13.7770i	−0.302372	−	0.523724i
$693$	1.60555	−	2.78090i	0.0609898	−	0.105638i
$694$		−	13.3305i		−	0.506020i
$695$	5.53776	+	3.19722i	0.210059	+	0.121278i
$696$	16.1369	+	9.31665i	0.611668	+	0.353147i
$697$		−	22.8167i		−	0.864242i
$698$	−4.36249	+	7.55605i	−0.165123	+	0.286001i
$699$	7.60555	+	13.1732i	0.287668	+	0.498256i
$700$	2.86029	−	1.65139i	0.108109	−	0.0624166i
$701$	36.4222			1.37565			0.687824	−	0.725878i	$-0.258566\pi$
$701$	36.4222			1.37565			0.687824	+	0.725878i	$0.258566\pi$
$702$		0			0
$703$	−20.2111			−0.762276
$704$	−17.8209	+	10.2889i	−0.671650	+	0.387777i
$705$	4.60555	+	7.97705i	0.173455	+	0.300433i
$706$	−19.3625	+	33.5368i	−0.728717	+	1.26217i
$707$			9.00000i			0.338480i
$708$	30.9387	+	17.8625i	1.16275	+	0.671313i
$709$	−11.9896	−	6.92221i	−0.450279	−	0.259969i	0.257669	−	0.966233i	$-0.417046\pi$
$709$	−11.9896	−	6.92221i	−0.450279	−	0.259969i	−0.707948	+	0.706264i	$0.750379\pi$
$710$		−	11.0917i		−	0.416263i
$711$	5.21110	−	9.02589i	0.195432	−	0.338497i
$712$	9.31665	+	16.1369i	0.349156	+	0.604757i
$713$	−10.3923	+	6.00000i	−0.389195	+	0.224702i
$714$	−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	$-0.991777\pi$
$719$	−12.8028	+	22.1751i	−0.477463	+	0.826990i	0.522203	+	0.852821i	$0.325110\pi$
$720$			0.605551i			0.0225676i
$721$	−3.46410	−	2.00000i	−0.129010	−	0.0744839i
$722$	−24.7731	−	14.3028i	−0.921961	−	0.532294i
$723$		−	1.78890i		−	0.0665298i
$724$	−29.1194	+	50.4363i	−1.08222	+	1.87445i
$725$	−3.10555	−	5.37897i	−0.115337	−	0.199770i
$726$	−16.7961	+	9.69722i	−0.623361	+	0.359898i
$727$	−13.5778			−0.503573			−0.251786	−	0.967783i	$-0.581018\pi$
$727$	−13.5778			−0.503573			−0.251786	+	0.967783i	$0.581018\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$	−1.57327	+	0.908327i	−0.0582293	+	0.0336187i
$731$	38.8305	+	67.2565i	1.43620	+	2.48757i
$732$	−1.65139	+	2.86029i	−0.0610371	+	0.105719i
$733$		−	46.8444i		−	1.73024i	−0.501567	−	0.865119i	$-0.667243\pi$
$733$		−	46.8444i		−	1.73024i	0.501567	−	0.865119i	$-0.332757\pi$
$734$	22.7789	+	13.1514i	0.840784	+	0.485427i
$735$	5.19615	+	3.00000i	0.191663	+	0.110657i
$736$			15.9083i			0.586389i
$737$	5.61943	−	9.73314i	0.206994	−	0.358525i
$738$	6.90833	+	11.9656i	0.254299	+	0.440459i
$739$	30.8353	−	17.8028i	1.13430	−	0.654886i	0.189284	−	0.981922i	$-0.439383\pi$
$739$	30.8353	−	17.8028i	1.13430	−	0.654886i	0.945012	+	0.327037i	$0.106050\pi$
$740$	11.9083			0.437759
$741$		0			0
$742$	−7.39445			−0.271459
$743$	31.7254	−	18.3167i	1.16389	−	0.671973i	0.211658	−	0.977344i	$-0.432114\pi$
$743$	31.7254	−	18.3167i	1.16389	−	0.671973i	0.952233	+	0.305371i	$0.0987805\pi$
$744$	−6.00000	−	10.3923i	−0.219971	−	0.381000i
$745$	−1.50000	+	2.59808i	−0.0549557	+	0.0951861i
$746$			46.9638i			1.71947i
$747$	−15.9541	−	9.21110i	−0.583730	−	0.337017i
$748$	34.9273	+	20.1653i	1.27707	+	0.737315i
$749$			6.21110i			0.226949i
$750$	−1.15139	+	1.99426i	−0.0420427	+	0.0728202i
$751$	23.2250	+	40.2268i	0.847492	+	1.46790i	0.883440	+	0.468545i	$0.155222\pi$
$751$	23.2250	+	40.2268i	0.847492	+	1.46790i	−0.0359481	+	0.999354i	$0.511445\pi$
$752$	−2.41526	+	1.39445i	−0.0880753	+	0.0508503i
$753$	7.18335			0.261776
$754$		0			0
$755$	1.21110			0.0440765
$756$	14.3014	−	8.25694i	0.520138	−	0.300302i
$757$	−0.408327	−	0.707243i	−0.0148409	−	0.0257052i	0.858510	−	0.512798i	$-0.171391\pi$
$757$	−0.408327	−	0.707243i	−0.0148409	−	0.0257052i	−0.873350	+	0.487092i	$0.838058\pi$
$758$	−11.0597	+	19.1560i	−0.401707	+	0.695777i
$759$		−	4.81665i		−	0.174833i
$760$	14.5636	+	8.40833i	0.528279	+	0.305002i
$761$	16.1369	+	9.31665i	0.584963	+	0.337728i	0.763103	−	0.646277i	$-0.223675\pi$
$761$	16.1369	+	9.31665i	0.584963	+	0.337728i	−0.178140	+	0.984005i	$0.557008\pi$
$762$		−	9.69722i		−	0.351293i
$763$	−9.60555	+	16.6373i	−0.347744	+	0.602311i
$764$	27.7708	+	48.1005i	1.00471	+	1.74021i
$765$	−13.1732	+	7.60555i	−0.476278	+	0.274979i
$766$	−56.7250			−2.04956
$767$		0			0
$768$	−17.9083			−0.646211
$769$	9.52628	−	5.50000i	0.343526	−	0.198335i	−0.318304	−	0.947989i	$-0.603113\pi$
$769$	9.52628	−	5.50000i	0.343526	−	0.198335i	0.661830	+	0.749654i	$0.269780\pi$
$770$	1.84861	+	3.20189i	0.0666194	+	0.115388i
$771$	−8.19722	+	14.1980i	−0.295216	+	0.511329i
$772$			51.5416i			1.85502i
$773$	−19.3942	−	11.1972i	−0.697560	−	0.402736i	0.108878	−	0.994055i	$-0.465274\pi$
$773$	−19.3942	−	11.1972i	−0.697560	−	0.402736i	−0.806438	+	0.591319i	$0.798607\pi$
$774$	−40.7272	−	23.5139i	−1.46391	−	0.845189i
$775$			4.00000i			0.143684i
$776$	−12.5917	+	21.8094i	−0.452015	+	0.782912i
$777$	−1.80278	−	3.12250i	−0.0646742	−	0.112019i
$778$	−30.3349	+	17.5139i	−1.08756	+	0.627903i
$779$	16.8167			0.602519
$780$		0			0
$781$	7.73338			0.276722
$782$	45.5024	−	26.2708i	1.62716	−	0.939443i
$783$	−15.5278	−	26.8949i	−0.554917	−	0.961144i
$784$	−0.908327	+	1.57327i	−0.0324402	+	0.0561882i
$785$		−	11.2111i		−	0.400141i
$786$	−42.3005	−	24.4222i	−1.50881	−	0.871111i
$787$	12.6728	+	7.31665i	0.451737	+	0.260811i	0.708564	−	0.705647i	$-0.249344\pi$
$787$	12.6728	+	7.31665i	0.451737	+	0.260811i	−0.256826	+	0.966458i	$0.582677\pi$
$788$		−	3.90833i		−	0.139228i
$789$	−5.89445	+	10.2095i	−0.209848	+	0.363467i
$790$	6.00000	+	10.3923i	0.213470	+	0.369742i
$791$	−1.39045	+	0.802776i	−0.0494386	+	0.0285434i
$792$	−9.63331			−0.342305
$793$		0			0
$794$	−50.7250			−1.80016
$795$	2.78090	−	1.60555i	0.0986282	−	0.0569430i
$796$	−21.1653	−	36.6593i	−0.750183	−	1.29936i
$797$	−7.22498	+	12.5140i	−0.255922	+	0.443270i	−0.965146	−	0.261714i	$-0.915712\pi$
$797$	−7.22498	+	12.5140i	−0.255922	+	0.443270i	0.709224	+	0.704984i	$0.249046\pi$
$798$		−	12.9083i		−	0.456950i
$799$	−60.6699	−	35.0278i	−2.14635	−	1.23919i
$800$	4.59234	+	2.65139i	0.162364	+	0.0937407i
$801$		−	12.4222i		−	0.438917i
$802$	14.0597	−	24.3521i	0.496466	−	0.859904i
$803$	−0.633308	−	1.09692i	−0.0223489	−	0.0387095i
$804$	20.0220	−	11.5597i	0.706122	−	0.407680i
$805$	3.00000			0.105736
$806$		0			0
$807$	−9.00000			−0.316815
$808$	23.3827	−	13.5000i	0.822600	−	0.474928i
$809$	27.5278	+	47.6795i	0.967824	+	1.67632i	0.701827	+	0.712347i	$0.252368\pi$
$809$	27.5278	+	47.6795i	0.967824	+	1.67632i	0.265997	+	0.963974i	$0.414299\pi$
$810$	1.15139	−	1.99426i	0.0404556	−	0.0700712i
$811$		−	46.4222i		−	1.63010i	−0.579388	−	0.815052i	$-0.696708\pi$
$811$		−	46.4222i		−	1.63010i	0.579388	−	0.815052i	$-0.303292\pi$
$812$	−17.7655	−	10.2569i	−0.623448	−	0.359948i
$813$	−18.0278	−	10.4083i	−0.632261	−	0.365036i
$814$			13.3305i			0.467235i
$815$	−1.89445	+	3.28128i	−0.0663596	+	0.114938i
$816$	1.15139	+	1.99426i	0.0403066	+	0.0698131i
$817$	−49.5703	+	28.6194i	−1.73425	+	1.00127i
$818$	18.9083			0.661114
$819$		0			0
$820$	−9.90833			−0.346014
$821$	18.5522	−	10.7111i	0.647475	−	0.373820i	−0.140013	−	0.990150i	$-0.544714\pi$
$821$	18.5522	−	10.7111i	0.647475	−	0.373820i	0.787488	+	0.616330i	$0.211381\pi$
$822$	−1.84861	−	3.20189i	−0.0644778	−	0.111679i
$823$	−8.31665	+	14.4049i	−0.289900	+	0.502122i	−0.973786	−	0.227467i	$-0.926955\pi$
$823$	−8.31665	+	14.4049i	−0.289900	+	0.502122i	0.683885	+	0.729589i	$0.260289\pi$
$824$			12.0000i			0.418040i
$825$	−1.39045	−	0.802776i	−0.0484092	−	0.0279491i
$826$	−21.5712	−	12.4542i	−0.750560	−	0.433336i
$827$			42.4222i			1.47516i	0.675257	+	0.737582i	$0.264033\pi$
$827$			42.4222i			1.47516i	−0.675257	+	0.737582i	$0.735967\pi$
$828$	−9.90833	+	17.1617i	−0.344338	+	0.596411i
$829$	14.7111	+	25.4804i	0.510938	+	0.884970i	0.999920	+	0.0126762i	$0.00403506\pi$
$829$	14.7111	+	25.4804i	0.510938	+	0.884970i	−0.488982	+	0.872294i	$0.662632\pi$
$830$	18.3694	−	10.6056i	0.637610	−	0.368124i
$831$	−27.6056			−0.957626
$832$		0			0
$833$	−45.6333			−1.58110
$834$	−12.7522	+	7.36249i	−0.441573	+	0.254942i
$835$	4.50000	+	7.79423i	0.155729	+	0.269730i
$836$	−14.8625	+	25.7426i	−0.514030	+	0.890326i
$837$			20.0000i			0.691301i
$838$	34.3788	+	19.8486i	1.18760	+	0.685659i
$839$	−17.3445	−	10.0139i	−0.598800	−	0.345717i	0.169769	−	0.985484i	$-0.445698\pi$
$839$	−17.3445	−	10.0139i	−0.598800	−	0.345717i	−0.768569	+	0.639766i	$0.779031\pi$
$840$			3.00000i			0.103510i
$841$	−4.78890	+	8.29461i	−0.165134	+	0.286021i
$842$	−37.3305	−	64.6584i	−1.28650	−	2.22827i
$843$	5.19615	−	3.00000i	0.178965	−	0.103325i
$844$	77.9638			2.68363
$845$		0			0
$846$	42.4222			1.45851
$847$	7.29384	−	4.21110i	0.250619	−	0.144695i
$848$	0.486122	+	0.841988i	0.0166935	+	0.0289140i
$849$	2.50000	−	4.33013i	0.0857998	−	0.148610i
$850$		−	17.5139i		−	0.600721i
$851$	9.36750	+	5.40833i	0.321114	+	0.185395i
$852$	13.7770	+	7.95416i	0.471993	+	0.272505i
$853$		−	47.2111i		−	1.61648i	−0.588855	−	0.808239i	$-0.700421\pi$
$853$		−	47.2111i		−	1.61648i	0.588855	−	0.808239i	$-0.299579\pi$
$854$	1.15139	−	1.99426i	0.0393997	−	0.0682422i
$855$	−5.60555	−	9.70910i	−0.191706	−	0.332044i
$856$	16.1369	−	9.31665i	0.551548	−	0.318437i
$857$	−6.00000			−0.204956			−0.102478	−	0.994735i	$-0.532677\pi$
$857$	−6.00000			−0.204956			−0.102478	+	0.994735i	$0.532677\pi$
$858$		0			0
$859$	10.7889			0.368112			0.184056	−	0.982916i	$-0.441077\pi$
$859$	10.7889			0.368112			0.184056	+	0.982916i	$0.441077\pi$
$860$	29.2067	−	16.8625i	0.995940	−	0.575006i
$861$	1.50000	+	2.59808i	0.0511199	+	0.0885422i
$862$	−33.6653	+	58.3100i	−1.14664	+	1.98604i
$863$			36.0000i			1.22545i	0.790295	+	0.612727i	$0.209928\pi$
$863$			36.0000i			1.22545i	−0.790295	+	0.612727i	$0.790072\pi$
$864$	22.9617	+	13.2569i	0.781173	+	0.451010i
$865$	−4.17134	−	2.40833i	−0.141830	−	0.0818856i
$866$			8.30278i			0.282140i
$867$	−20.4222	+	35.3723i	−0.693574	+	1.20131i
$868$	6.60555	+	11.4412i	0.224207	+	0.388338i
$869$	−7.24577	+	4.18335i	−0.245796	+	0.141910i
$870$	14.3028			0.484910
$871$		0			0
$872$	57.6333			1.95171
$873$	14.5396	−	8.39445i	0.492091	−	0.284109i
$874$	19.3625	+	33.5368i	0.654946	+	1.13440i
$875$	0.500000	−	0.866025i	0.0169031	−	0.0292770i
$876$		−	2.60555i		−	0.0880334i
$877$	1.70801	+	0.986122i	0.0576755	+	0.0332990i	0.528560	−	0.848896i	$-0.322732\pi$
$877$	1.70801	+	0.986122i	0.0576755	+	0.0332990i	−0.470885	+	0.882195i	$0.656065\pi$
$878$	54.3214	+	31.3625i	1.83326	+	1.05843i
$879$		−	10.3944i		−	0.350596i
$880$	0.243061	−	0.420994i	0.00819358	−	0.0141917i
$881$	−10.9222	−	18.9178i	−0.367978	−	0.637357i	0.621271	−	0.783596i	$-0.286617\pi$
$881$	−10.9222	−	18.9178i	−0.367978	−	0.637357i	−0.989249	+	0.146238i	$0.953283\pi$
$882$	23.9311	−	13.8167i	0.805804	−	0.465231i
$883$	−11.6333			−0.391492			−0.195746	−	0.980655i	$-0.562713\pi$
$883$	−11.6333			−0.391492			−0.195746	+	0.980655i	$0.562713\pi$
$884$		0			0
$885$	10.8167			0.363598
$886$	−12.8076	+	7.39445i	−0.430278	+	0.248421i
$887$	18.5278	+	32.0910i	0.622101	+	1.07751i	0.989094	+	0.147287i	$0.0470541\pi$
$887$	18.5278	+	32.0910i	0.622101	+	1.07751i	−0.366993	+	0.930224i	$0.619613\pi$
$888$	−5.40833	+	9.36750i	−0.181492	+	0.314353i
$889$			4.21110i			0.141236i
$890$	12.3866	+	7.15139i	0.415199	+	0.239715i
$891$	1.39045	+	0.802776i	0.0465818	+	0.0268940i
$892$			13.9083i			0.465685i
$893$	25.8167	−	44.7158i	0.863921	−	1.49636i
$894$	−3.45416	−	5.98279i	−0.115525	−	0.200094i
$895$	19.7598	−	11.4083i	0.660497	−	0.381338i
$896$	18.9083			0.631683
$897$		0			0
$898$	−70.5416			−2.35400
$899$	21.5159	−	12.4222i	0.717595	−	0.414304i
$900$	3.30278	+	5.72058i	0.110093	+	0.190686i
$901$	−12.2111	+	21.1503i	−0.406811	+	0.704617i
$902$		−	11.0917i		−	0.369312i
$903$	−8.84307	−	5.10555i	−0.294279	−	0.169902i
$904$	4.17134	+	2.40833i	0.138737	+	0.0800998i
$905$			17.6333i			0.586151i
$906$	−1.39445	+	2.41526i	−0.0463275	+	0.0802415i
$907$	−19.1333	−	33.1399i	−0.635311	−	1.10039i	−0.986449	−	0.164067i	$-0.947539\pi$
$907$	−19.1333	−	33.1399i	−0.635311	−	1.10039i	0.351138	−	0.936324i	$-0.385795\pi$
$908$	78.4354	−	45.2847i	2.60297	−	1.50283i
$909$	−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	$0.703390\pi$
$912$	−1.46984	+	0.848612i	−0.0486712	+	0.0281004i
$913$	7.39445	+	12.8076i	0.244721	+	0.423868i
$914$	30.8764	−	53.4794i	1.02130	−	1.76894i
$915$			1.00000i			0.0330590i
$916$	−40.0440	−	23.1194i	−1.32309	−	0.763887i
$917$	18.3694	+	10.6056i	0.606610	+	0.350226i
$918$		−	87.5694i		−	2.89022i
$919$	19.4083	−	33.6162i	0.640222	−	1.10890i	−0.345161	−	0.938543i	$-0.612176\pi$
$919$	19.4083	−	33.6162i	0.640222	−	1.10890i	0.985383	−	0.170353i	$-0.0544908\pi$
$920$	−4.50000	−	7.79423i	−0.148361	−	0.256968i
$921$	13.8564	−	8.00000i	0.456584	−	0.263609i
$922$	83.3860			2.74617
$923$		0			0
$924$	−5.30278			−0.174449
$925$	3.12250	−	1.80278i	0.102667	−	0.0592749i
$926$	−39.6333	−	68.6469i	−1.30243	−	2.25588i
$927$	4.00000	−	6.92820i	0.131377	−	0.227552i
$928$		−	32.9361i		−	1.08118i
$929$	13.3560	+	7.71110i	0.438197	+	0.252993i	0.702832	−	0.711355i	$-0.251918\pi$
$929$	13.3560	+	7.71110i	0.438197	+	0.252993i	−0.264636	+	0.964348i	$0.585252\pi$
$930$	−7.97705	−	4.60555i	−0.261578	−	0.151022i
$931$		−	33.6333i		−	1.10229i
$932$	−25.1194	+	43.5081i	−0.822814	+	1.42516i
$933$	−4.60555	−	7.97705i	−0.150779	−	0.261157i
$934$	5.56179	−	3.21110i	0.181987	−	0.105070i
$935$	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	$0.150806\pi$
$938$	−13.9598	+	8.05971i	−0.455805	+	0.263159i
$939$	−7.00000	−	12.1244i	−0.228436	−	0.395663i
$940$	−15.2111	+	26.3464i	−0.496131	+	0.859325i
$941$		−	9.63331i		−	0.314037i	−0.987596	−	0.157018i	$-0.949812\pi$
$941$		−	9.63331i		−	0.314037i	0.987596	−	0.157018i	$-0.0501882\pi$
$942$	22.3579	+	12.9083i	0.728459	+	0.420576i
$943$	−7.79423	−	4.50000i	−0.253815	−	0.146540i
$944$			3.27502i			0.106593i
$945$	2.50000	−	4.33013i	0.0813250	−	0.140859i
$946$	18.8764	+	32.6948i	0.613724	+	1.06300i
$947$	16.1369	−	9.31665i	0.524379	−	0.302751i	−0.214345	−	0.976758i	$-0.568762\pi$
$947$	16.1369	−	9.31665i	0.524379	−	0.302751i	0.738725	+	0.674007i	$0.235428\pi$
$948$	−17.2111			−0.558991
$949$		0			0
$950$	12.9083			0.418801
$951$	5.19615	−	3.00000i	0.168497	−	0.0972817i
$952$	−11.4083	−	19.7598i	−0.369746	−	0.640419i
$953$	−7.22498	+	12.5140i	−0.234040	+	0.405369i	−0.958993	−	0.283429i	$-0.908528\pi$
$953$	−7.22498	+	12.5140i	−0.234040	+	0.405369i	0.724953	+	0.688798i	$0.241861\pi$
$954$		−	14.7889i		−	0.478808i
$955$	14.5636	+	8.40833i	0.471269	+	0.272087i
$956$		0			0
$957$			9.97224i			0.322357i
$958$	−33.1791	+	57.4680i	−1.07197	+	1.85671i
$959$	0.802776	+	1.39045i	0.0259230	+	0.0448999i
$960$	−11.0995	+	6.40833i	−0.358236	+	0.206828i
$961$	15.0000			0.483871
$962$		0			0
$963$	−12.4222			−0.400300
$964$	5.11676	−	2.95416i	0.164800	−	0.0951472i
$965$	7.80278	+	13.5148i	0.251180	+	0.435057i
$966$	−3.45416	+	5.98279i	−0.111136	+	0.192493i
$967$		−	44.4777i		−	1.43031i	−0.698967	−	0.715153i	$-0.746357\pi$
$967$		−	44.4777i		−	1.43031i	0.698967	−	0.715153i	$-0.253643\pi$
$968$	−21.8815	−	12.6333i	−0.703299	−	0.406050i
$969$	−36.9215	−	21.3167i	−1.18609	−	0.684790i
$970$			19.3305i			0.620666i
$971$	22.0139	−	38.1292i	0.706459	−	1.22362i	−0.259703	−	0.965688i	$-0.583625\pi$
$971$	22.0139	−	38.1292i	0.706459	−	1.22362i	0.966162	−	0.257934i	$-0.0830418\pi$
$972$	26.4222	+	45.7646i	0.847493	+	1.46790i
$973$	5.53776	−	3.19722i	0.177532	−	0.102498i
$974$	−2.30278			−0.0737857
$975$		0			0
$976$	−0.302776			−0.00969161
$977$	24.9560	−	14.4083i	0.798412	−	0.460963i	−0.0445038	−	0.999009i	$-0.514171\pi$
$977$	24.9560	−	14.4083i	0.798412	−	0.460963i	0.842915	+	0.538046i	$0.180837\pi$
$978$	−4.36249	−	7.55605i	−0.139497	−	0.241616i
$979$	−4.98612	+	8.63622i	−0.159357	+	0.276015i
$980$			19.8167i			0.633020i
$981$	−33.2746	−	19.2111i	−1.06238	−	0.613363i
$982$	33.5368	+	19.3625i	1.07020	+	0.617882i
$983$		−	18.4222i		−	0.587577i	−0.955870	−	0.293789i	$-0.905084\pi$
$983$		−	18.4222i		−	0.587577i	0.955870	−	0.293789i	$-0.0949162\pi$
$984$	4.50000	−	7.79423i	0.143455	−	0.248471i
$985$	−0.591673	−	1.02481i	−0.0188523	−	0.0326531i
$986$	−94.2067	+	54.3902i	−3.00015	+	1.73214i
$987$	9.21110			0.293193
$988$		0			0
$989$	30.6333			0.974083
$990$	−6.40378	+	3.69722i	−0.203526	+	0.117506i
$991$	−20.0139	−	34.6651i	−0.635762	−	1.10117i	−0.986353	−	0.164643i	$-0.947353\pi$
$991$	−20.0139	−	34.6651i	−0.635762	−	1.10117i	0.350591	−	0.936529i	$-0.385981\pi$
$992$	−10.6056	+	18.3694i	−0.336727	+	0.583228i
$993$			10.0278i			0.318221i
$994$	−9.60567	−	5.54584i	−0.304673	−	0.175903i
$995$	−11.0995	−	6.40833i	−0.351879	−	0.203158i
$996$			30.4222i			0.963964i
$997$	9.22498	−	15.9781i	0.292158	−	0.506033i	−0.682162	−	0.731201i	$-0.738960\pi$
$997$	9.22498	−	15.9781i	0.292158	−	0.506033i	0.974320	+	0.225169i	$0.0722933\pi$
$998$	−2.78890	−	4.83051i	−0.0882810	−	0.152907i
$999$	15.6125	−	9.01388i	0.493957	−	0.285186i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.m.d.361.1		8
13.2	odd	12		845.2.a.c.1.1		2
13.3	even	3		845.2.c.d.506.1		4
13.4	even	6	inner	845.2.m.d.316.1		8
13.5	odd	4		65.2.e.b.16.2	✓	4
13.6	odd	12		65.2.e.b.61.2	yes	4
13.7	odd	12		845.2.e.d.191.1		4
13.8	odd	4		845.2.e.d.146.1		4
13.9	even	3	inner	845.2.m.d.316.4		8
13.10	even	6		845.2.c.d.506.4		4
13.11	odd	12		845.2.a.f.1.2		2
13.12	even	2	inner	845.2.m.d.361.4		8
39.2	even	12		7605.2.a.bg.1.2		2
39.5	even	4		585.2.j.d.406.1		4
39.11	even	12		7605.2.a.bb.1.1		2
39.32	even	12		585.2.j.d.451.1		4
52.19	even	12		1040.2.q.o.321.2		4
52.31	even	4		1040.2.q.o.81.2		4
65.18	even	4		325.2.o.b.224.4		8
65.19	odd	12		325.2.e.a.126.1		4
65.24	odd	12		4225.2.a.t.1.1		2
65.32	even	12		325.2.o.b.74.4		8
65.44	odd	4		325.2.e.a.276.1		4
65.54	odd	12		4225.2.a.x.1.2		2
65.57	even	4		325.2.o.b.224.1		8
65.58	even	12		325.2.o.b.74.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.e.b.16.2	✓	4	13.5	odd	4
65.2.e.b.61.2	yes	4	13.6	odd	12
325.2.e.a.126.1		4	65.19	odd	12
325.2.e.a.276.1		4	65.44	odd	4
325.2.o.b.74.1		8	65.58	even	12
325.2.o.b.74.4		8	65.32	even	12
325.2.o.b.224.1		8	65.57	even	4
325.2.o.b.224.4		8	65.18	even	4
585.2.j.d.406.1		4	39.5	even	4
585.2.j.d.451.1		4	39.32	even	12
845.2.a.c.1.1		2	13.2	odd	12
845.2.a.f.1.2		2	13.11	odd	12
845.2.c.d.506.1		4	13.3	even	3
845.2.c.d.506.4		4	13.10	even	6
845.2.e.d.146.1		4	13.8	odd	4
845.2.e.d.191.1		4	13.7	odd	12
845.2.m.d.316.1		8	13.4	even	6	inner
845.2.m.d.316.4		8	13.9	even	3	inner
845.2.m.d.361.1		8	1.1	even	1	trivial
845.2.m.d.361.4		8	13.12	even	2	inner
1040.2.q.o.81.2		4	52.31	even	4
1040.2.q.o.321.2		4	52.19	even	12
4225.2.a.t.1.1		2	65.24	odd	12
4225.2.a.x.1.2		2	65.54	odd	12
7605.2.a.bb.1.1		2	39.11	even	12
7605.2.a.bg.1.2		2	39.2	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.99426 + 1.15139i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(1.65139 - 2.86029i) q^{4} -1.00000i q^{5} +(1.99426 + 1.15139i) q^{6} +(-0.866025 - 0.500000i) q^{7} +3.00000i q^{8} +(1.00000 - 1.73205i) q^{9} +(1.15139 + 1.99426i) q^{10} +(-1.39045 + 0.802776i) q^{11} -3.30278 q^{12} +2.30278 q^{14} +(-0.866025 + 0.500000i) q^{15} +(-0.151388 - 0.262211i) q^{16} +(3.80278 - 6.58660i) q^{17} +4.60555i q^{18} +(4.85455 + 2.80278i) q^{19} +(-2.86029 - 1.65139i) q^{20} +1.00000i q^{21} +(1.84861 - 3.20189i) q^{22} +(-1.50000 - 2.59808i) q^{23} +(2.59808 - 1.50000i) q^{24} -1.00000 q^{25} -5.00000 q^{27} +(-2.86029 + 1.65139i) q^{28} +(3.10555 + 5.37897i) q^{29} +(1.15139 - 1.99426i) q^{30} -4.00000i q^{31} +(-4.59234 - 2.65139i) q^{32} +(1.39045 + 0.802776i) q^{33} +17.5139i q^{34} +(-0.500000 + 0.866025i) q^{35} +(-3.30278 - 5.72058i) q^{36} +(-3.12250 + 1.80278i) q^{37} -12.9083 q^{38} +3.00000 q^{40} +(2.59808 - 1.50000i) q^{41} +(-1.15139 - 1.99426i) q^{42} +(-5.10555 + 8.84307i) q^{43} +5.30278i q^{44} +(-1.73205 - 1.00000i) q^{45} +(5.98279 + 3.45416i) q^{46} -9.21110i q^{47} +(-0.151388 + 0.262211i) q^{48} +(-3.00000 - 5.19615i) q^{49} +(1.99426 - 1.15139i) q^{50} -7.60555 q^{51} -3.21110 q^{53} +(9.97131 - 5.75694i) q^{54} +(0.802776 + 1.39045i) q^{55} +(1.50000 - 2.59808i) q^{56} -5.60555i q^{57} +(-12.3866 - 7.15139i) q^{58} +(-9.36750 - 5.40833i) q^{59} +3.30278i q^{60} +(0.500000 - 0.866025i) q^{61} +(4.60555 + 7.97705i) q^{62} +(-1.73205 + 1.00000i) q^{63} +12.8167 q^{64} -3.69722 q^{66} +(-6.06218 + 3.50000i) q^{67} +(-12.5597 - 21.7541i) q^{68} +(-1.50000 + 2.59808i) q^{69} -2.30278i q^{70} +(-4.17134 - 2.40833i) q^{71} +(5.19615 + 3.00000i) q^{72} +0.788897i q^{73} +(4.15139 - 7.19041i) q^{74} +(0.500000 + 0.866025i) q^{75} +(16.0335 - 9.25694i) q^{76} +1.60555 q^{77} +5.21110 q^{79} +(-0.262211 + 0.151388i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-3.45416 + 5.98279i) q^{82} -9.21110i q^{83} +(2.86029 + 1.65139i) q^{84} +(-6.58660 - 3.80278i) q^{85} -23.5139i q^{86} +(3.10555 - 5.37897i) q^{87} +(-2.40833 - 4.17134i) q^{88} +(5.37897 - 3.10555i) q^{89} +4.60555 q^{90} -9.90833 q^{92} +(-3.46410 + 2.00000i) q^{93} +(10.6056 + 18.3694i) q^{94} +(2.80278 - 4.85455i) q^{95} +5.30278i q^{96} +(7.26981 + 4.19722i) q^{97} +(11.9656 + 6.90833i) q^{98} +3.21110i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} + 6 q^{4} + 8 q^{9} + 2 q^{10} - 12 q^{12} + 4 q^{14} + 6 q^{16} + 16 q^{17} + 22 q^{22} - 12 q^{23} - 8 q^{25} - 40 q^{27} - 4 q^{29} + 2 q^{30} - 4 q^{35} - 12 q^{36} - 60 q^{38} + 24 q^{40}+ \cdots + 8 q^{95}+O(q^{100}) \) 8 * q - 4 * q^3 + 6 * q^4 + 8 * q^9 + 2 * q^10 - 12 * q^12 + 4 * q^14 + 6 * q^16 + 16 * q^17 + 22 * q^22 - 12 * q^23 - 8 * q^25 - 40 * q^27 - 4 * q^29 + 2 * q^30 - 4 * q^35 - 12 * q^36 - 60 * q^38 + 24 * q^40 - 2 * q^42 - 12 * q^43 + 6 * q^48 - 24 * q^49 - 32 * q^51 + 32 * q^53 - 8 * q^55 + 12 * q^56 + 4 * q^61 + 8 * q^62 + 16 * q^64 - 44 * q^66 - 50 * q^68 - 12 * q^69 + 26 * q^74 + 4 * q^75 - 16 * q^77 - 16 * q^79 - 4 * q^81 - 6 * q^82 - 4 * q^87 + 24 * q^88 + 8 * q^90 - 36 * q^92 + 56 * q^94 + 8 * q^95

Introduction

L-functions

Modular forms

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Database

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