LMFDB - Embedded newform 845.2.e.d.191.2

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			191.2
Root			$-0.651388 + 1.12824i$ of defining polynomial
Character	$\chi$	$=$	845.191
Dual form			845.2.e.d.146.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.651388 - 1.12824i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.151388 + 0.262211i) q^{4} +1.00000 q^{5} +(0.651388 + 1.12824i) q^{6} +(-0.500000 - 0.866025i) q^{7} +3.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +(0.651388 - 1.12824i) q^{10} +(-2.80278 + 4.85455i) q^{11} -0.302776 q^{12} -1.30278 q^{14} +(-0.500000 + 0.866025i) q^{15} +(1.65139 - 2.86029i) q^{16} +(-0.197224 - 0.341603i) q^{17} +2.60555 q^{18} +(0.802776 + 1.39045i) q^{19} +(0.151388 + 0.262211i) q^{20} +1.00000 q^{21} +(3.65139 + 6.32439i) q^{22} +(1.50000 - 2.59808i) q^{23} +(-1.50000 + 2.59808i) q^{24} +1.00000 q^{25} -5.00000 q^{27} +(0.151388 - 0.262211i) q^{28} +(-4.10555 + 7.11102i) q^{29} +(0.651388 + 1.12824i) q^{30} +4.00000 q^{31} +(0.848612 + 1.46984i) q^{32} +(-2.80278 - 4.85455i) q^{33} -0.513878 q^{34} +(-0.500000 - 0.866025i) q^{35} +(-0.302776 + 0.524423i) q^{36} +(-1.80278 + 3.12250i) q^{37} +2.09167 q^{38} +3.00000 q^{40} +(1.50000 - 2.59808i) q^{41} +(0.651388 - 1.12824i) q^{42} +(-2.10555 - 3.64692i) q^{43} -1.69722 q^{44} +(1.00000 + 1.73205i) q^{45} +(-1.95416 - 3.38471i) q^{46} +5.21110 q^{47} +(1.65139 + 2.86029i) q^{48} +(3.00000 - 5.19615i) q^{49} +(0.651388 - 1.12824i) q^{50} +0.394449 q^{51} +11.2111 q^{53} +(-3.25694 + 5.64118i) q^{54} +(-2.80278 + 4.85455i) q^{55} +(-1.50000 - 2.59808i) q^{56} -1.60555 q^{57} +(5.34861 + 9.26407i) q^{58} +(5.40833 + 9.36750i) q^{59} -0.302776 q^{60} +(0.500000 + 0.866025i) q^{61} +(2.60555 - 4.51295i) q^{62} +(1.00000 - 1.73205i) q^{63} +8.81665 q^{64} -7.30278 q^{66} +(-3.50000 + 6.06218i) q^{67} +(0.0597147 - 0.103429i) q^{68} +(1.50000 + 2.59808i) q^{69} -1.30278 q^{70} +(-8.40833 - 14.5636i) q^{71} +(3.00000 + 5.19615i) q^{72} +15.2111 q^{73} +(2.34861 + 4.06792i) q^{74} +(-0.500000 + 0.866025i) q^{75} +(-0.243061 + 0.420994i) q^{76} +5.60555 q^{77} -9.21110 q^{79} +(1.65139 - 2.86029i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.95416 - 3.38471i) q^{82} -5.21110 q^{83} +(0.151388 + 0.262211i) q^{84} +(-0.197224 - 0.341603i) q^{85} -5.48612 q^{86} +(-4.10555 - 7.11102i) q^{87} +(-8.40833 + 14.5636i) q^{88} +(4.10555 - 7.11102i) q^{89} +2.60555 q^{90} +0.908327 q^{92} +(-2.00000 + 3.46410i) q^{93} +(3.39445 - 5.87936i) q^{94} +(0.802776 + 1.39045i) q^{95} -1.69722 q^{96} +(-7.80278 - 13.5148i) q^{97} +(-3.90833 - 6.76942i) q^{98} -11.2111 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 $

$2$	0.651388	−	1.12824i	0.460601	−	0.797784i	−0.538390	−	0.842696i	$-0.680967\pi$
$2$	0.651388	−	1.12824i	0.460601	−	0.797784i	0.998991	+	0.0449118i	$0.0143007\pi$
$3$	−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	$0.259881\pi$
$4$	0.151388	+	0.262211i	0.0756939	+	0.131106i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	0.651388	+	1.12824i	0.265928	+	0.460601i
$7$	−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
$10$	0.651388	−	1.12824i	0.205987	−	0.356780i
$11$	−2.80278	+	4.85455i	−0.845069	+	1.46370i	0.0404929	+	0.999180i	$0.487107\pi$
$11$	−2.80278	+	4.85455i	−0.845069	+	1.46370i	−0.885562	+	0.464522i	$0.846226\pi$
$12$	−0.302776			−0.0874038
$13$		0			0
$13$		0			0
$14$	−1.30278			−0.348181
$15$	−0.500000	+	0.866025i	−0.129099	+	0.223607i
$16$	1.65139	−	2.86029i	0.412847	−	0.715072i
$17$	−0.197224	−	0.341603i	−0.0478339	−	0.0828508i	0.841117	−	0.540853i	$-0.181898\pi$
$17$	−0.197224	−	0.341603i	−0.0478339	−	0.0828508i	−0.888951	+	0.458002i	$0.848565\pi$
$18$	2.60555			0.614134
$19$	0.802776	+	1.39045i	0.184169	+	0.318991i	0.943296	−	0.331952i	$-0.107707\pi$
$19$	0.802776	+	1.39045i	0.184169	+	0.318991i	−0.759127	+	0.650943i	$0.774374\pi$
$20$	0.151388	+	0.262211i	0.0338513	+	0.0586323i
$21$	1.00000			0.218218
$22$	3.65139	+	6.32439i	0.778478	+	1.34836i
$23$	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
$28$	0.151388	−	0.262211i	0.0286096	−	0.0495533i
$29$	−4.10555	+	7.11102i	−0.762382	+	1.32048i	0.179238	+	0.983806i	$0.442637\pi$
$29$	−4.10555	+	7.11102i	−0.762382	+	1.32048i	−0.941620	+	0.336678i	$0.890697\pi$
$30$	0.651388	+	1.12824i	0.118927	+	0.205987i
$31$	4.00000			0.718421			0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000			0.718421			0.359211	+	0.933257i	$0.383046\pi$
$32$	0.848612	+	1.46984i	0.150015	+	0.259833i
$33$	−2.80278	−	4.85455i	−0.487901	−	0.845069i
$34$	−0.513878			−0.0881294
$35$	−0.500000	−	0.866025i	−0.0845154	−	0.146385i
$36$	−0.302776	+	0.524423i	−0.0504626	+	0.0874038i
$37$	−1.80278	+	3.12250i	−0.296374	+	0.513336i	−0.975304	−	0.220868i	$-0.929111\pi$
$37$	−1.80278	+	3.12250i	−0.296374	+	0.513336i	0.678929	+	0.734204i	$0.262444\pi$
$38$	2.09167			0.339314
$39$		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	$0.0913998\pi$
$42$	0.651388	−	1.12824i	0.100511	−	0.174091i
$43$	−2.10555	−	3.64692i	−0.321094	−	0.556150i	0.659620	−	0.751599i	$-0.270717\pi$
$43$	−2.10555	−	3.64692i	−0.321094	−	0.556150i	−0.980714	+	0.195449i	$0.937384\pi$
$44$	−1.69722			−0.255866
$45$	1.00000	+	1.73205i	0.149071	+	0.258199i
$46$	−1.95416	−	3.38471i	−0.288126	−	0.499048i
$47$	5.21110			0.760117			0.380059	−	0.924962i	$-0.375904\pi$
$47$	5.21110			0.760117			0.380059	+	0.924962i	$0.375904\pi$
$48$	1.65139	+	2.86029i	0.238357	+	0.412847i
$49$	3.00000	−	5.19615i	0.428571	−	0.742307i
$50$	0.651388	−	1.12824i	0.0921201	−	0.159557i
$51$	0.394449			0.0552339
$52$		0			0
$53$	11.2111			1.53996			0.769982	−	0.638066i	$-0.220265\pi$
$53$	11.2111			1.53996			0.769982	+	0.638066i	$0.220265\pi$
$54$	−3.25694	+	5.64118i	−0.443213	+	0.767668i
$55$	−2.80278	+	4.85455i	−0.377926	+	0.654587i
$56$	−1.50000	−	2.59808i	−0.200446	−	0.347183i
$57$	−1.60555			−0.212660
$58$	5.34861	+	9.26407i	0.702307	+	1.21643i
$59$	5.40833	+	9.36750i	0.704104	+	1.21954i	0.967014	+	0.254724i	$0.0819845\pi$
$59$	5.40833	+	9.36750i	0.704104	+	1.21954i	−0.262910	+	0.964820i	$0.584682\pi$
$60$	−0.302776			−0.0390882
$61$	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	$0.812942\pi$
$62$	2.60555	−	4.51295i	0.330905	−	0.573145i
$63$	1.00000	−	1.73205i	0.125988	−	0.218218i
$64$	8.81665			1.10208
$65$		0			0
$66$	−7.30278			−0.898910
$67$	−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	$0.307305\pi$
$68$	0.0597147	−	0.103429i	0.00724147	−	0.0125426i
$69$	1.50000	+	2.59808i	0.180579	+	0.312772i
$70$	−1.30278			−0.155711
$71$	−8.40833	−	14.5636i	−0.997885	−	1.72839i	−0.555240	−	0.831690i	$-0.687374\pi$
$71$	−8.40833	−	14.5636i	−0.997885	−	1.72839i	−0.442645	−	0.896697i	$-0.645960\pi$
$72$	3.00000	+	5.19615i	0.353553	+	0.612372i
$73$	15.2111			1.78032			0.890162	−	0.455643i	$-0.150591\pi$
$73$	15.2111			1.78032			0.890162	+	0.455643i	$0.150591\pi$
$74$	2.34861	+	4.06792i	0.273021	+	0.472886i
$75$	−0.500000	+	0.866025i	−0.0577350	+	0.100000i
$76$	−0.243061	+	0.420994i	−0.0278810	+	0.0482913i
$77$	5.60555			0.638812
$78$		0			0
$79$	−9.21110			−1.03633			−0.518165	−	0.855281i	$-0.673385\pi$
$79$	−9.21110			−1.03633			−0.518165	+	0.855281i	$0.673385\pi$
$80$	1.65139	−	2.86029i	0.184631	−	0.319790i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−1.95416	−	3.38471i	−0.215801	−	0.373779i
$83$	−5.21110			−0.571993			−0.285996	−	0.958231i	$-0.592325\pi$
$83$	−5.21110			−0.571993			−0.285996	+	0.958231i	$0.592325\pi$
$84$	0.151388	+	0.262211i	0.0165178	+	0.0286096i
$85$	−0.197224	−	0.341603i	−0.0213920	−	0.0370520i
$86$	−5.48612			−0.591584
$87$	−4.10555	−	7.11102i	−0.440161	−	0.762382i
$88$	−8.40833	+	14.5636i	−0.896331	+	1.55249i
$89$	4.10555	−	7.11102i	0.435188	−	0.753767i	−0.562123	−	0.827053i	$-0.690015\pi$
$89$	4.10555	−	7.11102i	0.435188	−	0.753767i	0.997311	+	0.0732864i	$0.0233487\pi$
$90$	2.60555			0.274649
$91$		0			0
$92$	0.908327			0.0946996
$93$	−2.00000	+	3.46410i	−0.207390	+	0.359211i
$94$	3.39445	−	5.87936i	0.350111	−	0.606409i
$95$	0.802776	+	1.39045i	0.0823630	+	0.142657i
$96$	−1.69722			−0.173222
$97$	−7.80278	−	13.5148i	−0.792252	−	1.37222i	−0.924570	−	0.381013i	$-0.875575\pi$
$97$	−7.80278	−	13.5148i	−0.792252	−	1.37222i	0.132318	−	0.991207i	$-0.457758\pi$
$98$	−3.90833	−	6.76942i	−0.394801	−	0.683815i
$99$	−11.2111			−1.12676
$100$	0.151388	+	0.262211i	0.0151388	+	0.0262211i
$101$	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	$0.0188862\pi$
$102$	0.256939	−	0.445032i	0.0254408	−	0.0440647i
$103$	−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
$106$	7.30278	−	12.6488i	0.709308	−	1.22856i
$107$	4.10555	−	7.11102i	0.396899	−	0.687449i	−0.596443	−	0.802656i	$-0.703420\pi$
$107$	4.10555	−	7.11102i	0.396899	−	0.687449i	0.993342	+	0.115207i	$0.0367531\pi$
$108$	−0.756939	−	1.31106i	−0.0728365	−	0.126157i
$109$	4.78890			0.458693			0.229347	−	0.973345i	$-0.426341\pi$
$109$	4.78890			0.458693			0.229347	+	0.973345i	$0.426341\pi$
$110$	3.65139	+	6.32439i	0.348146	+	0.603007i
$111$	−1.80278	−	3.12250i	−0.171112	−	0.296374i
$112$	−3.30278			−0.312083
$113$	−2.80278	−	4.85455i	−0.263663	−	0.456678i	0.703550	−	0.710646i	$-0.251597\pi$
$113$	−2.80278	−	4.85455i	−0.263663	−	0.456678i	−0.967212	+	0.253969i	$0.918264\pi$
$114$	−1.04584	+	1.81144i	−0.0979516	+	0.169657i
$115$	1.50000	−	2.59808i	0.139876	−	0.242272i
$116$	−2.48612			−0.230831
$117$		0			0
$118$	14.0917			1.29724
$119$	−0.197224	+	0.341603i	−0.0180795	+	0.0313147i
$120$	−1.50000	+	2.59808i	−0.136931	+	0.237171i
$121$	−10.2111	−	17.6861i	−0.928282	−	1.60783i
$122$	1.30278			0.117948
$123$	1.50000	+	2.59808i	0.135250	+	0.234261i
$124$	0.605551	+	1.04885i	0.0543801	+	0.0941891i
$125$	1.00000			0.0894427
$126$	−1.30278	−	2.25647i	−0.116060	−	0.201023i
$127$	−5.10555	+	8.84307i	−0.453044	+	0.784696i	−0.998573	−	0.0533960i	$-0.982995\pi$
$127$	−5.10555	+	8.84307i	−0.453044	+	0.784696i	0.545529	+	0.838092i	$0.316329\pi$
$128$	4.04584	−	7.00759i	0.357605	−	0.619390i
$129$	4.21110			0.370767
$130$		0			0
$131$	−6.78890			−0.593149			−0.296574	−	0.955010i	$-0.595844\pi$
$131$	−6.78890			−0.593149			−0.296574	+	0.955010i	$0.595844\pi$
$132$	0.848612	−	1.46984i	0.0738622	−	0.127933i
$133$	0.802776	−	1.39045i	0.0696095	−	0.120567i
$134$	4.55971	+	7.89766i	0.393899	+	0.682254i
$135$	−5.00000			−0.430331
$136$	−0.591673	−	1.02481i	−0.0507355	−	0.0878765i
$137$	2.80278	+	4.85455i	0.239457	+	0.414752i	0.960559	−	0.278077i	$-0.0896972\pi$
$137$	2.80278	+	4.85455i	0.239457	+	0.414752i	−0.721101	+	0.692830i	$0.756364\pi$
$138$	3.90833			0.332699
$139$	−6.80278	−	11.7828i	−0.577004	−	0.999400i	−0.995821	−	0.0913293i	$-0.970888\pi$
$139$	−6.80278	−	11.7828i	−0.577004	−	0.999400i	0.418817	−	0.908071i	$-0.362445\pi$
$140$	0.151388	−	0.262211i	0.0127946	−	0.0221609i
$141$	−2.60555	+	4.51295i	−0.219427	+	0.380059i
$142$	−21.9083			−1.83851
$143$		0			0
$144$	6.60555			0.550463
$145$	−4.10555	+	7.11102i	−0.340947	+	0.590538i
$146$	9.90833	−	17.1617i	0.820019	−	1.42031i
$147$	3.00000	+	5.19615i	0.247436	+	0.428571i
$148$	−1.09167			−0.0897350
$149$	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	$0.794119\pi$
$150$	0.651388	+	1.12824i	0.0531856	+	0.0921201i
$151$	−13.2111			−1.07510			−0.537552	−	0.843231i	$-0.680651\pi$
$151$	−13.2111			−1.07510			−0.537552	+	0.843231i	$0.680651\pi$
$152$	2.40833	+	4.17134i	0.195341	+	0.338341i
$153$	0.394449	−	0.683205i	0.0318893	−	0.0552339i
$154$	3.65139	−	6.32439i	0.294237	−	0.509634i
$155$	4.00000			0.321288
$156$		0			0
$157$	−3.21110			−0.256274			−0.128137	−	0.991756i	$-0.540900\pi$
$157$	−3.21110			−0.256274			−0.128137	+	0.991756i	$0.540900\pi$
$158$	−6.00000	+	10.3923i	−0.477334	+	0.826767i
$159$	−5.60555	+	9.70910i	−0.444549	+	0.769982i
$160$	0.848612	+	1.46984i	0.0670887	+	0.116201i
$161$	−3.00000			−0.236433
$162$	0.651388	+	1.12824i	0.0511779	+	0.0886427i
$163$	−9.10555	−	15.7713i	−0.713202	−	1.23530i	−0.963649	−	0.267172i	$-0.913911\pi$
$163$	−9.10555	−	15.7713i	−0.713202	−	1.23530i	0.250447	−	0.968130i	$-0.419422\pi$
$164$	0.908327			0.0709284
$165$	−2.80278	−	4.85455i	−0.218196	−	0.377926i
$166$	−3.39445	+	5.87936i	−0.263460	+	0.456327i
$167$	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
$170$	−0.513878			−0.0394127
$171$	−1.60555	+	2.78090i	−0.122780	+	0.212660i
$172$	0.637510	−	1.10420i	0.0486097	−	0.0841944i
$173$	8.40833	+	14.5636i	0.639273	+	1.10725i	0.985593	+	0.169137i	$0.0540981\pi$
$173$	8.40833	+	14.5636i	0.639273	+	1.10725i	−0.346319	+	0.938117i	$0.612569\pi$
$174$	−10.6972			−0.810954
$175$	−0.500000	−	0.866025i	−0.0377964	−	0.0654654i
$176$	9.25694	+	16.0335i	0.697768	+	1.20857i
$177$	−10.8167			−0.813029
$178$	−5.34861	−	9.26407i	−0.400895	−	0.694371i
$179$	−0.591673	+	1.02481i	−0.0442237	+	0.0765977i	−0.887290	−	0.461212i	$-0.847415\pi$
$179$	−0.591673	+	1.02481i	−0.0442237	+	0.0765977i	0.843066	+	0.537810i	$0.180748\pi$
$180$	−0.302776	+	0.524423i	−0.0225676	+	0.0390882i
$181$	−25.6333			−1.90531			−0.952654	−	0.304055i	$-0.901659\pi$
$181$	−25.6333			−1.90531			−0.952654	+	0.304055i	$0.901659\pi$
$182$		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
$186$	2.60555	+	4.51295i	0.191048	+	0.330905i
$187$	2.21110			0.161692
$188$	0.788897	+	1.36641i	0.0575363	+	0.0996557i
$189$	2.50000	+	4.33013i	0.181848	+	0.314970i
$190$	2.09167			0.151746
$191$	2.40833	+	4.17134i	0.174260	+	0.301828i	0.939905	−	0.341436i	$-0.110913\pi$
$191$	2.40833	+	4.17134i	0.174260	+	0.301828i	−0.765645	+	0.643264i	$0.777580\pi$
$192$	−4.40833	+	7.63545i	−0.318144	+	0.551041i
$193$	4.19722	−	7.26981i	0.302123	−	0.523292i	−0.674494	−	0.738281i	$-0.735638\pi$
$193$	4.19722	−	7.26981i	0.302123	−	0.523292i	0.976617	+	0.214988i	$0.0689714\pi$
$194$	−20.3305			−1.45965
$195$		0			0
$196$	1.81665			0.129761
$197$	11.4083	−	19.7598i	0.812810	−	1.40783i	−0.0980804	−	0.995178i	$-0.531270\pi$
$197$	11.4083	−	19.7598i	0.812810	−	1.40783i	0.910890	−	0.412649i	$-0.135396\pi$
$198$	−7.30278	+	12.6488i	−0.518986	+	0.898910i
$199$	4.40833	+	7.63545i	0.312498	+	0.541262i	0.978902	−	0.204328i	$-0.0655009\pi$
$199$	4.40833	+	7.63545i	0.312498	+	0.541262i	−0.666404	+	0.745590i	$0.732168\pi$
$200$	3.00000			0.212132
$201$	−3.50000	−	6.06218i	−0.246871	−	0.427593i
$202$	−5.86249	−	10.1541i	−0.412483	−	0.714442i
$203$	8.21110			0.576306
$204$	0.0597147	+	0.103429i	0.00418087	+	0.00724147i
$205$	1.50000	−	2.59808i	0.104765	−	0.181458i
$206$	−2.60555	+	4.51295i	−0.181537	+	0.314432i
$207$	6.00000			0.417029
$208$		0			0
$209$	−9.00000			−0.622543
$210$	0.651388	−	1.12824i	0.0449500	−	0.0778557i
$211$	8.19722	−	14.1980i	0.564320	−	0.977431i	−0.432792	−	0.901494i	$-0.642472\pi$
$211$	8.19722	−	14.1980i	0.564320	−	0.977431i	0.997113	−	0.0759376i	$-0.0241950\pi$
$212$	1.69722	+	2.93968i	0.116566	+	0.201898i
$213$	16.8167			1.15226
$214$	−5.34861	−	9.26407i	−0.365624	−	0.633279i
$215$	−2.10555	−	3.64692i	−0.143597	−	0.248718i
$216$	−15.0000			−1.02062
$217$	−2.00000	−	3.46410i	−0.135769	−	0.235159i
$218$	3.11943	−	5.40301i	0.211274	−	0.365938i
$219$	−7.60555	+	13.1732i	−0.513936	+	0.890162i
$220$	−1.69722			−0.114427
$221$		0			0
$222$	−4.69722			−0.315257
$223$	5.10555	−	8.84307i	0.341893	−	0.592176i	−0.642891	−	0.765957i	$-0.722265\pi$
$223$	5.10555	−	8.84307i	0.341893	−	0.592176i	0.984784	+	0.173781i	$0.0555986\pi$
$224$	0.848612	−	1.46984i	0.0567003	−	0.0982078i
$225$	1.00000	+	1.73205i	0.0666667	+	0.115470i
$226$	−7.30278			−0.485773
$227$	0.711103	+	1.23167i	0.0471975	+	0.0817485i	0.888659	−	0.458569i	$-0.151638\pi$
$227$	0.711103	+	1.23167i	0.0471975	+	0.0817485i	−0.841462	+	0.540317i	$0.818304\pi$
$228$	−0.243061	−	0.420994i	−0.0160971	−	0.0278810i
$229$	−14.0000			−0.925146			−0.462573	−	0.886581i	$-0.653074\pi$
$229$	−14.0000			−0.925146			−0.462573	+	0.886581i	$0.653074\pi$
$230$	−1.95416	−	3.38471i	−0.128854	−	0.223181i
$231$	−2.80278	+	4.85455i	−0.184409	+	0.319406i
$232$	−12.3167	+	21.3331i	−0.808628	+	1.40058i
$233$	0.788897			0.0516824			0.0258412	−	0.999666i	$-0.491774\pi$
$233$	0.788897			0.0516824			0.0258412	+	0.999666i	$0.491774\pi$
$234$		0			0
$235$	5.21110			0.339935
$236$	−1.63751	+	2.83625i	−0.106593	+	0.184624i
$237$	4.60555	−	7.97705i	0.299163	−	0.518165i
$238$	0.256939	+	0.445032i	0.0166549	+	0.0288471i
$239$		0			0			−	1.00000i	$-0.5\pi$
$239$		0			0				1.00000i	$0.5\pi$
$240$	1.65139	+	2.86029i	0.106597	+	0.184631i
$241$	8.10555	+	14.0392i	0.522124	+	0.904346i	0.999669	+	0.0257384i	$0.00819369\pi$
$241$	8.10555	+	14.0392i	0.522124	+	0.904346i	−0.477544	+	0.878608i	$0.658473\pi$
$242$	−26.6056			−1.71027
$243$	−8.00000	−	13.8564i	−0.513200	−	0.888889i
$244$	−0.151388	+	0.262211i	−0.00969161	+	0.0167864i
$245$	3.00000	−	5.19615i	0.191663	−	0.331970i
$246$	3.90833			0.249186
$247$		0			0
$248$	12.0000			0.762001
$249$	2.60555	−	4.51295i	0.165120	−	0.285996i
$250$	0.651388	−	1.12824i	0.0411974	−	0.0713560i
$251$	14.4083	+	24.9560i	0.909446	+	1.57521i	0.814836	+	0.579691i	$0.196827\pi$
$251$	14.4083	+	24.9560i	0.909446	+	1.57521i	0.0946094	+	0.995514i	$0.469840\pi$
$252$	0.605551			0.0381461
$253$	8.40833	+	14.5636i	0.528627	+	0.915609i
$254$	6.65139	+	11.5205i	0.417345	+	0.722863i
$255$	0.394449			0.0247013
$256$	3.54584	+	6.14157i	0.221615	+	0.383848i
$257$	11.8028	−	20.4430i	0.736237	−	1.27520i	−0.217942	−	0.975962i	$-0.569934\pi$
$257$	11.8028	−	20.4430i	0.736237	−	1.27520i	0.954179	−	0.299238i	$-0.0967324\pi$
$258$	2.74306	−	4.75112i	0.170776	−	0.295792i
$259$	3.60555			0.224038
$260$		0			0
$261$	−16.4222			−1.01651
$262$	−4.42221	+	7.65948i	−0.273205	+	0.473204i
$263$	−13.1056	+	22.6995i	−0.808123	+	1.39971i	0.106040	+	0.994362i	$0.466183\pi$
$263$	−13.1056	+	22.6995i	−0.808123	+	1.39971i	−0.914162	+	0.405348i	$0.867150\pi$
$264$	−8.40833	−	14.5636i	−0.517497	−	0.896331i
$265$	11.2111			0.688693
$266$	−1.04584	−	1.81144i	−0.0641244	−	0.111067i
$267$	4.10555	+	7.11102i	0.251256	+	0.435188i
$268$	−2.11943			−0.129465
$269$	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	$0.744864\pi$
$270$	−3.25694	+	5.64118i	−0.198211	+	0.343312i
$271$	0.408327	−	0.707243i	0.0248041	−	0.0429620i	−0.853357	−	0.521327i	$-0.825437\pi$
$271$	0.408327	−	0.707243i	0.0248041	−	0.0429620i	0.878161	+	0.478365i	$0.158770\pi$
$272$	−1.30278			−0.0789924
$273$		0			0
$274$	7.30278			0.441177
$275$	−2.80278	+	4.85455i	−0.169014	+	0.292740i
$276$	−0.454163	+	0.786634i	−0.0273374	+	0.0473498i
$277$	−10.1972	−	17.6621i	−0.612692	−	1.06121i	−0.990785	−	0.135446i	$-0.956753\pi$
$277$	−10.1972	−	17.6621i	−0.612692	−	1.06121i	0.378093	−	0.925768i	$-0.376580\pi$
$278$	−17.7250			−1.06307
$279$	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	$0.442725\pi$
$282$	3.39445	+	5.87936i	0.202136	+	0.350111i
$283$	−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	$0.214146\pi$
$284$	2.54584	−	4.40952i	0.151068	−	0.261657i
$285$	−1.60555			−0.0951046
$286$		0			0
$287$	−3.00000			−0.177084
$288$	−1.69722	+	2.93968i	−0.100010	+	0.173222i
$289$	8.42221	−	14.5877i	0.495424	−	0.858099i
$290$	5.34861	+	9.26407i	0.314081	+	0.544005i
$291$	15.6056			0.914814
$292$	2.30278	+	3.98852i	0.134760	+	0.233411i
$293$	8.80278	+	15.2469i	0.514264	+	0.890731i	0.999863	+	0.0165493i	$0.00526805\pi$
$293$	8.80278	+	15.2469i	0.514264	+	0.890731i	−0.485599	+	0.874181i	$0.661399\pi$
$294$	7.81665			0.455877
$295$	5.40833	+	9.36750i	0.314885	+	0.545397i
$296$	−5.40833	+	9.36750i	−0.314353	+	0.544475i
$297$	14.0139	−	24.2727i	0.813168	−	1.40845i
$298$	3.90833			0.226403
$299$		0			0
$300$	−0.302776			−0.0174808
$301$	−2.10555	+	3.64692i	−0.121362	+	0.210205i
$302$	−8.60555	+	14.9053i	−0.495194	+	0.857701i
$303$	4.50000	+	7.79423i	0.258518	+	0.447767i
$304$	5.30278			0.304135
$305$	0.500000	+	0.866025i	0.0286299	+	0.0495885i
$306$	−0.513878	−	0.890063i	−0.0293765	−	0.0508815i
$307$	16.0000			0.913168			0.456584	−	0.889680i	$-0.349073\pi$
$307$	16.0000			0.913168			0.456584	+	0.889680i	$0.349073\pi$
$308$	0.848612	+	1.46984i	0.0483542	+	0.0837519i
$309$	2.00000	−	3.46410i	0.113776	−	0.197066i
$310$	2.60555	−	4.51295i	0.147985	−	0.256318i
$311$	5.21110			0.295495			0.147747	−	0.989025i	$-0.452798\pi$
$311$	5.21110			0.295495			0.147747	+	0.989025i	$0.452798\pi$
$312$		0			0
$313$	14.0000			0.791327			0.395663	−	0.918396i	$-0.370515\pi$
$313$	14.0000			0.791327			0.395663	+	0.918396i	$0.370515\pi$
$314$	−2.09167	+	3.62288i	−0.118040	+	0.204451i
$315$	1.00000	−	1.73205i	0.0563436	−	0.0975900i
$316$	−1.39445	−	2.41526i	−0.0784439	−	0.135869i
$317$	−6.00000			−0.336994			−0.168497	−	0.985702i	$-0.553891\pi$
$317$	−6.00000			−0.336994			−0.168497	+	0.985702i	$0.553891\pi$
$318$	7.30278	+	12.6488i	0.409519	+	0.709308i
$319$	−23.0139	−	39.8612i	−1.28853	−	2.23180i
$320$	8.81665			0.492866
$321$	4.10555	+	7.11102i	0.229150	+	0.396899i
$322$	−1.95416	+	3.38471i	−0.108901	+	0.188623i
$323$	0.316654	−	0.548461i	0.0176191	−	0.0305172i
$324$	−0.302776			−0.0168209
$325$		0			0
$326$	−23.7250			−1.31401
$327$	−2.39445	+	4.14731i	−0.132413	+	0.229347i
$328$	4.50000	−	7.79423i	0.248471	−	0.430364i
$329$	−2.60555	−	4.51295i	−0.143649	−	0.248807i
$330$	−7.30278			−0.402005
$331$	−13.0139	−	22.5407i	−0.715307	−	1.23895i	−0.962841	−	0.270069i	$-0.912953\pi$
$331$	−13.0139	−	22.5407i	−0.715307	−	1.23895i	0.247533	−	0.968879i	$-0.420380\pi$
$332$	−0.788897	−	1.36641i	−0.0432964	−	0.0749915i
$333$	−7.21110			−0.395166
$334$	−5.86249	−	10.1541i	−0.320781	−	0.555609i
$335$	−3.50000	+	6.06218i	−0.191225	+	0.331212i
$336$	1.65139	−	2.86029i	0.0900906	−	0.156041i
$337$	17.6333			0.960547			0.480274	−	0.877119i	$-0.340537\pi$
$337$	17.6333			0.960547			0.480274	+	0.877119i	$0.340537\pi$
$338$		0			0
$339$	5.60555			0.304452
$340$	0.0597147	−	0.103429i	0.00323849	−	0.00560922i
$341$	−11.2111	+	19.4182i	−0.607115	+	1.05155i
$342$	2.09167	+	3.62288i	0.113105	+	0.195903i
$343$	−13.0000			−0.701934
$344$	−6.31665	−	10.9408i	−0.340571	−	0.589887i
$345$	1.50000	+	2.59808i	0.0807573	+	0.139876i
$346$	21.9083			1.17780
$347$	−10.1056	−	17.5033i	−0.542494	−	0.939628i	−0.998760	−	0.0497842i	$-0.984147\pi$
$347$	−10.1056	−	17.5033i	−0.542494	−	0.939628i	0.456266	−	0.889844i	$-0.349187\pi$
$348$	1.24306	−	2.15304i	0.0666351	−	0.115415i
$349$	−9.10555	+	15.7713i	−0.487409	+	0.844217i	−0.999895	−	0.0144783i	$-0.995391\pi$
$349$	−9.10555	+	15.7713i	−0.487409	+	0.844217i	0.512486	+	0.858695i	$0.328725\pi$
$350$	−1.30278			−0.0696363
$351$		0			0
$352$	−9.51388			−0.507091
$353$	−2.40833	+	4.17134i	−0.128182	+	0.222018i	−0.922972	−	0.384866i	$-0.874248\pi$
$353$	−2.40833	+	4.17134i	−0.128182	+	0.222018i	0.794790	+	0.606884i	$0.207581\pi$
$354$	−7.04584	+	12.2037i	−0.374482	+	0.648622i
$355$	−8.40833	−	14.5636i	−0.446268	−	0.772958i
$356$	2.48612			0.131764
$357$	−0.197224	−	0.341603i	−0.0104382	−	0.0180795i
$358$	0.770817	+	1.33509i	0.0407390	+	0.0705619i
$359$	10.4222			0.550063			0.275031	−	0.961435i	$-0.411312\pi$
$359$	10.4222			0.550063			0.275031	+	0.961435i	$0.411312\pi$
$360$	3.00000	+	5.19615i	0.158114	+	0.273861i
$361$	8.21110	−	14.2220i	0.432163	−	0.748529i
$362$	−16.6972	+	28.9204i	−0.877587	+	1.52002i
$363$	20.4222			1.07189
$364$		0			0
$365$	15.2111			0.796185
$366$	−0.651388	+	1.12824i	−0.0340486	+	0.0589739i
$367$	8.71110	−	15.0881i	0.454716	−	0.787591i	−0.543956	−	0.839114i	$-0.683074\pi$
$367$	8.71110	−	15.0881i	0.454716	−	0.787591i	0.998672	+	0.0515228i	$0.0164075\pi$
$368$	−4.95416	−	8.58086i	−0.258254	−	0.447308i
$369$	6.00000			0.312348
$370$	2.34861	+	4.06792i	0.122099	+	0.211481i
$371$	−5.60555	−	9.70910i	−0.291026	−	0.504071i
$372$	−1.21110			−0.0627927
$373$	13.8028	+	23.9071i	0.714681	+	1.23786i	0.963083	+	0.269206i	$0.0867613\pi$
$373$	13.8028	+	23.9071i	0.714681	+	1.23786i	−0.248402	+	0.968657i	$0.579905\pi$
$374$	1.44029	−	2.49465i	0.0744754	−	0.128995i
$375$	−0.500000	+	0.866025i	−0.0258199	+	0.0447214i
$376$	15.6333			0.806226
$377$		0			0
$378$	6.51388			0.335038
$379$	1.19722	−	2.07365i	0.0614973	−	0.106516i	−0.833638	−	0.552312i	$-0.813746\pi$
$379$	1.19722	−	2.07365i	0.0614973	−	0.106516i	0.895135	+	0.445795i	$0.147079\pi$
$380$	−0.243061	+	0.420994i	−0.0124688	+	0.0215965i
$381$	−5.10555	−	8.84307i	−0.261565	−	0.453044i
$382$	6.27502			0.321058
$383$	9.31665	+	16.1369i	0.476059	+	0.824558i	0.999624	−	0.0274277i	$-0.00873162\pi$
$383$	9.31665	+	16.1369i	0.476059	+	0.824558i	−0.523565	+	0.851986i	$0.675398\pi$
$384$	4.04584	+	7.00759i	0.206463	+	0.357605i
$385$	5.60555			0.285685
$386$	−5.46804	−	9.47093i	−0.278316	−	0.482057i
$387$	4.21110	−	7.29384i	0.214062	−	0.370767i
$388$	2.36249	−	4.09195i	0.119937	−	0.207737i
$389$	−0.788897			−0.0399987			−0.0199993	−	0.999800i	$-0.506366\pi$
$389$	−0.788897			−0.0399987			−0.0199993	+	0.999800i	$0.506366\pi$
$390$		0			0
$391$	−1.18335			−0.0598444
$392$	9.00000	−	15.5885i	0.454569	−	0.787336i
$393$	3.39445	−	5.87936i	0.171227	−	0.296574i
$394$	−14.8625	−	25.7426i	−0.748761	−	1.29689i
$395$	−9.21110			−0.463461
$396$	−1.69722	−	2.93968i	−0.0852887	−	0.147724i
$397$	−7.01388	−	12.1484i	−0.352016	−	0.609710i	0.634586	−	0.772852i	$-0.281171\pi$
$397$	−7.01388	−	12.1484i	−0.352016	−	0.609710i	−0.986603	+	0.163142i	$0.947837\pi$
$398$	11.4861			0.575747
$399$	0.802776	+	1.39045i	0.0401890	+	0.0696095i
$400$	1.65139	−	2.86029i	0.0825694	−	0.143014i
$401$	−1.10555	+	1.91487i	−0.0552086	+	0.0956241i	−0.892309	−	0.451425i	$-0.850916\pi$
$401$	−1.10555	+	1.91487i	−0.0552086	+	0.0956241i	0.837100	+	0.547049i	$0.184249\pi$
$402$	−9.11943			−0.454836
$403$		0			0
$404$	2.72498			0.135573
$405$	−0.500000	+	0.866025i	−0.0248452	+	0.0430331i
$406$	5.34861	−	9.26407i	0.265447	−	0.459768i
$407$	−10.1056	−	17.5033i	−0.500914	−	0.867608i
$408$	1.18335			0.0585844
$409$	−3.10555	−	5.37897i	−0.153560	−	0.265973i	0.778974	−	0.627056i	$-0.215740\pi$
$409$	−3.10555	−	5.37897i	−0.153560	−	0.265973i	−0.932534	+	0.361083i	$0.882407\pi$
$410$	−1.95416	−	3.38471i	−0.0965093	−	0.167159i
$411$	−5.60555			−0.276501
$412$	−0.605551	−	1.04885i	−0.0298334	−	0.0516729i
$413$	5.40833	−	9.36750i	0.266126	−	0.460944i
$414$	3.90833	−	6.76942i	0.192084	−	0.332699i
$415$	−5.21110			−0.255803
$416$		0			0
$417$	13.6056			0.666267
$418$	−5.86249	+	10.1541i	−0.286744	+	0.496655i
$419$	16.6194	−	28.7857i	0.811912	−	1.40627i	−0.0996117	−	0.995026i	$-0.531760\pi$
$419$	16.6194	−	28.7857i	0.811912	−	1.40627i	0.911524	−	0.411247i	$-0.134907\pi$
$420$	0.151388	+	0.262211i	0.00738697	+	0.0127946i
$421$	−3.57779			−0.174371			−0.0871855	−	0.996192i	$-0.527787\pi$
$421$	−3.57779			−0.174371			−0.0871855	+	0.996192i	$0.527787\pi$
$422$	−10.6791	−	18.4968i	−0.519853	−	0.900411i
$423$	5.21110	+	9.02589i	0.253372	+	0.438854i
$424$	33.6333			1.63338
$425$	−0.197224	−	0.341603i	−0.00956679	−	0.0165702i
$426$	10.9542	−	18.9732i	0.530731	−	0.919253i
$427$	0.500000	−	0.866025i	0.0241967	−	0.0419099i
$428$	2.48612			0.120171
$429$		0			0
$430$	−5.48612			−0.264564
$431$	−10.6194	+	18.3934i	−0.511520	+	0.885978i	0.488391	+	0.872625i	$0.337584\pi$
$431$	−10.6194	+	18.3934i	−0.511520	+	0.885978i	−0.999911	+	0.0133535i	$0.995749\pi$
$432$	−8.25694	+	14.3014i	−0.397262	+	0.688078i
$433$	1.80278	+	3.12250i	0.0866359	+	0.150058i	0.906087	−	0.423091i	$-0.139055\pi$
$433$	1.80278	+	3.12250i	0.0866359	+	0.150058i	−0.819451	+	0.573149i	$0.805722\pi$
$434$	−5.21110			−0.250141
$435$	−4.10555	−	7.11102i	−0.196846	−	0.340947i
$436$	0.724981	+	1.25570i	0.0347203	+	0.0601373i
$437$	4.81665			0.230412
$438$	9.90833	+	17.1617i	0.473438	+	0.820019i
$439$	−11.6194	+	20.1254i	−0.554565	+	0.960535i	0.443372	+	0.896338i	$0.353782\pi$
$439$	−11.6194	+	20.1254i	−0.554565	+	0.960535i	−0.997937	+	0.0641973i	$0.979551\pi$
$440$	−8.40833	+	14.5636i	−0.400851	+	0.694295i
$441$	12.0000			0.571429
$442$		0			0
$443$	−22.4222			−1.06531			−0.532656	−	0.846332i	$-0.678806\pi$
$443$	−22.4222			−1.06531			−0.532656	+	0.846332i	$0.678806\pi$
$444$	0.545837	−	0.945417i	0.0259043	−	0.0448675i
$445$	4.10555	−	7.11102i	0.194622	−	0.337095i
$446$	−6.65139	−	11.5205i	−0.314952	−	0.545513i
$447$	−3.00000			−0.141895
$448$	−4.40833	−	7.63545i	−0.208274	−	0.360741i
$449$	−6.31665	−	10.9408i	−0.298101	−	0.516327i	0.677600	−	0.735430i	$-0.263020\pi$
$449$	−6.31665	−	10.9408i	−0.298101	−	0.516327i	−0.975702	+	0.219104i	$0.929687\pi$
$450$	2.60555			0.122827
$451$	8.40833	+	14.5636i	0.395933	+	0.685775i
$452$	0.848612	−	1.46984i	0.0399154	−	0.0691354i
$453$	6.60555	−	11.4412i	0.310356	−	0.537552i
$454$	1.85281			0.0869569
$455$		0			0
$456$	−4.81665			−0.225560
$457$	−2.59167	+	4.48891i	−0.121233	+	0.209982i	−0.920254	−	0.391321i	$-0.872018\pi$
$457$	−2.59167	+	4.48891i	−0.121233	+	0.209982i	0.799021	+	0.601303i	$0.205352\pi$
$458$	−9.11943	+	15.7953i	−0.426123	+	0.738067i
$459$	0.986122	+	1.70801i	0.0460282	+	0.0797232i
$460$	0.908327			0.0423510
$461$	10.8944	+	18.8697i	0.507405	+	0.878851i	0.999963	+	0.00857184i	$0.00272854\pi$
$461$	10.8944	+	18.8697i	0.507405	+	0.878851i	−0.492558	+	0.870280i	$0.663938\pi$
$462$	3.65139	+	6.32439i	0.169878	+	0.294237i
$463$	5.57779			0.259222			0.129611	−	0.991565i	$-0.458627\pi$
$463$	5.57779			0.259222			0.129611	+	0.991565i	$0.458627\pi$
$464$	13.5597	+	23.4861i	0.629494	+	1.09032i
$465$	−2.00000	+	3.46410i	−0.0927478	+	0.160644i
$466$	0.513878	−	0.890063i	0.0238049	−	0.0412314i
$467$	17.2111			0.796435			0.398217	−	0.917291i	$-0.369629\pi$
$467$	17.2111			0.796435			0.398217	+	0.917291i	$0.369629\pi$
$468$		0			0
$469$	7.00000			0.323230
$470$	3.39445	−	5.87936i	0.156574	−	0.271195i
$471$	1.60555	−	2.78090i	0.0739799	−	0.128137i
$472$	16.2250	+	28.1025i	0.746815	+	1.29352i
$473$	23.6056			1.08538
$474$	−6.00000	−	10.3923i	−0.275589	−	0.477334i
$475$	0.802776	+	1.39045i	0.0368339	+	0.0637981i
$476$	−0.119429			−0.00547404
$477$	11.2111	+	19.4182i	0.513321	+	0.889098i
$478$		0			0
$479$	−3.59167	+	6.22096i	−0.164108	+	0.284243i	−0.936338	−	0.351100i	$-0.885808\pi$
$479$	−3.59167	+	6.22096i	−0.164108	+	0.284243i	0.772230	+	0.635343i	$0.219141\pi$
$480$	−1.69722			−0.0774673
$481$		0			0
$482$	21.1194			0.961964
$483$	1.50000	−	2.59808i	0.0682524	−	0.118217i
$484$	3.09167	−	5.35493i	0.140531	−	0.243406i
$485$	−7.80278	−	13.5148i	−0.354306	−	0.613676i
$486$	−20.8444			−0.945522
$487$	−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
$489$	18.2111			0.823535
$490$	−3.90833	−	6.76942i	−0.176560	−	0.305811i
$491$	−2.40833	+	4.17134i	−0.108686	+	0.188250i	−0.915238	−	0.402913i	$-0.867998\pi$
$491$	−2.40833	+	4.17134i	−0.108686	+	0.188250i	0.806552	+	0.591163i	$0.201331\pi$
$492$	−0.454163	+	0.786634i	−0.0204753	+	0.0354642i
$493$	3.23886			0.145871
$494$		0			0
$495$	−11.2111			−0.503902
$496$	6.60555	−	11.4412i	0.296598	−	0.513723i
$497$	−8.40833	+	14.5636i	−0.377165	+	0.653269i
$498$	−3.39445	−	5.87936i	−0.152109	−	0.263460i
$499$	26.4222			1.18282			0.591410	−	0.806371i	$-0.298571\pi$
$499$	26.4222			1.18282			0.591410	+	0.806371i	$0.298571\pi$
$500$	0.151388	+	0.262211i	0.00677027	+	0.0117265i
$501$	4.50000	+	7.79423i	0.201045	+	0.348220i
$502$	37.5416			1.67557
$503$	−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
$506$	21.9083			0.973944
$507$		0			0
$508$	−3.09167			−0.137171
$509$	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	$0.145488\pi$
$510$	0.256939	−	0.445032i	0.0113775	−	0.0197063i
$511$	−7.60555	−	13.1732i	−0.336450	−	0.582748i
$512$	25.4222			1.12351
$513$	−4.01388	−	6.95224i	−0.177217	−	0.306949i
$514$	−15.3764	−	26.6327i	−0.678223	−	1.17472i
$515$	−4.00000			−0.176261
$516$	0.637510	+	1.10420i	0.0280648	+	0.0486097i
$517$	−14.6056	+	25.2976i	−0.642351	+	1.11259i
$518$	2.34861	−	4.06792i	0.103192	−	0.178734i
$519$	−16.8167			−0.738169
$520$		0			0
$521$	18.0000			0.788594			0.394297	−	0.918983i	$-0.370988\pi$
$521$	18.0000			0.788594			0.394297	+	0.918983i	$0.370988\pi$
$522$	−10.6972	+	18.5281i	−0.468205	+	0.810954i
$523$	−13.7111	+	23.7483i	−0.599545	+	1.03844i	0.393344	+	0.919392i	$0.371318\pi$
$523$	−13.7111	+	23.7483i	−0.599545	+	1.03844i	−0.992888	+	0.119050i	$0.962015\pi$
$524$	−1.02776	−	1.78013i	−0.0448977	−	0.0777652i
$525$	1.00000			0.0436436
$526$	17.0736	+	29.5723i	0.744444	+	1.28941i
$527$	−0.788897	−	1.36641i	−0.0343649	−	0.0595218i
$528$	−18.5139			−0.805713
$529$	7.00000	+	12.1244i	0.304348	+	0.527146i
$530$	7.30278	−	12.6488i	0.317212	−	0.549428i
$531$	−10.8167	+	18.7350i	−0.469403	+	0.813029i
$532$	0.486122			0.0210761
$533$		0			0
$534$	10.6972			0.462914
$535$	4.10555	−	7.11102i	0.177498	−	0.307436i
$536$	−10.5000	+	18.1865i	−0.453531	+	0.785539i
$537$	−0.591673	−	1.02481i	−0.0255326	−	0.0442237i
$538$	11.7250			0.505500
$539$	16.8167	+	29.1273i	0.724345	+	1.25460i
$540$	−0.756939	−	1.31106i	−0.0325735	−	0.0564189i
$541$	−17.6333			−0.758115			−0.379058	−	0.925373i	$-0.623752\pi$
$541$	−17.6333			−0.758115			−0.379058	+	0.925373i	$0.623752\pi$
$542$	−0.531958	−	0.921379i	−0.0228496	−	0.0395766i
$543$	12.8167	−	22.1991i	0.550015	−	0.952654i
$544$	0.334734	−	0.579776i	0.0143516	−	0.0248577i
$545$	4.78890			0.205134
$546$		0			0
$547$	−24.8444			−1.06227			−0.531135	−	0.847287i	$-0.678234\pi$
$547$	−24.8444			−1.06227			−0.531135	+	0.847287i	$0.678234\pi$
$548$	−0.848612	+	1.46984i	−0.0362509	+	0.0627884i
$549$	−1.00000	+	1.73205i	−0.0426790	+	0.0739221i
$550$	3.65139	+	6.32439i	0.155696	+	0.269673i
$551$	−13.1833			−0.561629
$552$	4.50000	+	7.79423i	0.191533	+	0.331744i
$553$	4.60555	+	7.97705i	0.195848	+	0.339219i
$554$	−26.5694			−1.12883
$555$	−1.80278	−	3.12250i	−0.0765236	−	0.132543i
$556$	2.05971	−	3.56753i	0.0873514	−	0.151297i
$557$	2.80278	−	4.85455i	0.118757	−	0.205694i	−0.800518	−	0.599309i	$-0.795442\pi$
$557$	2.80278	−	4.85455i	0.118757	−	0.205694i	0.919276	+	0.393615i	$0.128776\pi$
$558$	10.4222			0.441207
$559$		0			0
$560$	−3.30278			−0.139568
$561$	−1.10555	+	1.91487i	−0.0466764	+	0.0808459i
$562$	3.90833	−	6.76942i	0.164863	−	0.285551i
$563$	9.71110	+	16.8201i	0.409274	+	0.708884i	0.994809	−	0.101764i	$-0.0324486\pi$
$563$	9.71110	+	16.8201i	0.409274	+	0.708884i	−0.585534	+	0.810648i	$0.699115\pi$
$564$	−1.57779			−0.0664372
$565$	−2.80278	−	4.85455i	−0.117914	−	0.204232i
$566$	3.25694	+	5.64118i	0.136899	+	0.237117i
$567$	1.00000			0.0419961
$568$	−25.2250	−	43.6909i	−1.05842	−	1.83323i
$569$	−0.711103	+	1.23167i	−0.0298110	+	0.0516341i	−0.880546	−	0.473961i	$-0.842824\pi$
$569$	−0.711103	+	1.23167i	−0.0298110	+	0.0516341i	0.850735	+	0.525595i	$0.176157\pi$
$570$	−1.04584	+	1.81144i	−0.0438053	+	0.0758730i
$571$	−36.8444			−1.54189			−0.770945	−	0.636901i	$-0.780216\pi$
$571$	−36.8444			−1.54189			−0.770945	+	0.636901i	$0.780216\pi$
$572$		0			0
$573$	−4.81665			−0.201219
$574$	−1.95416	+	3.38471i	−0.0815652	+	0.141275i
$575$	1.50000	−	2.59808i	0.0625543	−	0.108347i
$576$	8.81665	+	15.2709i	0.367361	+	0.636287i
$577$	−29.6333			−1.23365			−0.616825	−	0.787100i	$-0.711582\pi$
$577$	−29.6333			−1.23365			−0.616825	+	0.787100i	$0.711582\pi$
$578$	−10.9722	−	19.0045i	−0.456385	−	0.790482i
$579$	4.19722	+	7.26981i	0.174431	+	0.302123i
$580$	−2.48612			−0.103231
$581$	2.60555	+	4.51295i	0.108096	+	0.187229i
$582$	10.1653	−	17.6068i	0.421364	−	0.729824i
$583$	−31.4222	+	54.4249i	−1.30137	+	2.25405i
$584$	45.6333			1.88832
$585$		0			0
$586$	22.9361			0.947481
$587$	−2.28890	+	3.96449i	−0.0944729	+	0.163632i	−0.909389	−	0.415948i	$-0.863450\pi$
$587$	−2.28890	+	3.96449i	−0.0944729	+	0.163632i	0.814916	+	0.579580i	$0.196783\pi$
$588$	−0.908327	+	1.57327i	−0.0374588	+	0.0648805i
$589$	3.21110	+	5.56179i	0.132311	+	0.229170i
$590$	14.0917			0.580145
$591$	11.4083	+	19.7598i	0.469276	+	0.812810i
$592$	5.95416	+	10.3129i	0.244715	+	0.423858i
$593$	−35.2111			−1.44595			−0.722973	−	0.690876i	$-0.757225\pi$
$593$	−35.2111			−1.44595			−0.722973	+	0.690876i	$0.757225\pi$
$594$	−18.2569	−	31.6219i	−0.749091	−	1.29746i
$595$	−0.197224	+	0.341603i	−0.00808541	+	0.0140043i
$596$	−0.454163	+	0.786634i	−0.0186033	+	0.0322218i
$597$	−8.81665			−0.360842
$598$		0			0
$599$	−6.78890			−0.277387			−0.138693	−	0.990335i	$-0.544290\pi$
$599$	−6.78890			−0.277387			−0.138693	+	0.990335i	$0.544290\pi$
$600$	−1.50000	+	2.59808i	−0.0612372	+	0.106066i
$601$	−14.1056	+	24.4315i	−0.575377	+	0.996583i	0.420623	+	0.907235i	$0.361811\pi$
$601$	−14.1056	+	24.4315i	−0.575377	+	0.996583i	−0.996001	+	0.0893475i	$0.971522\pi$
$602$	2.74306	+	4.75112i	0.111799	+	0.193641i
$603$	−14.0000			−0.570124
$604$	−2.00000	−	3.46410i	−0.0813788	−	0.140952i
$605$	−10.2111	−	17.6861i	−0.415140	−	0.719044i
$606$	11.7250			0.476295
$607$	9.89445	+	17.1377i	0.401603	+	0.695597i	0.993920	−	0.110108i	$-0.0351197\pi$
$607$	9.89445	+	17.1377i	0.401603	+	0.695597i	−0.592316	+	0.805706i	$0.701786\pi$
$608$	−1.36249	+	2.35990i	−0.0552563	+	0.0957067i
$609$	−4.10555	+	7.11102i	−0.166365	+	0.288153i
$610$	1.30278			0.0527478
$611$		0			0
$612$	0.238859			0.00965530
$613$	0.802776	−	1.39045i	0.0324238	−	0.0561597i	−0.849358	−	0.527817i	$-0.823011\pi$
$613$	0.802776	−	1.39045i	0.0324238	−	0.0561597i	0.881782	+	0.471657i	$0.156344\pi$
$614$	10.4222	−	18.0518i	0.420606	−	0.728511i
$615$	1.50000	+	2.59808i	0.0604858	+	0.104765i
$616$	16.8167			0.677562
$617$	13.2250	+	22.9063i	0.532418	+	0.922174i	0.999284	+	0.0378463i	$0.0120497\pi$
$617$	13.2250	+	22.9063i	0.532418	+	0.922174i	−0.466866	+	0.884328i	$0.654617\pi$
$618$	−2.60555	−	4.51295i	−0.104811	−	0.181537i
$619$	14.4222			0.579677			0.289839	−	0.957076i	$-0.406398\pi$
$619$	14.4222			0.579677			0.289839	+	0.957076i	$0.406398\pi$
$620$	0.605551	+	1.04885i	0.0243195	+	0.0421227i
$621$	−7.50000	+	12.9904i	−0.300965	+	0.521286i
$622$	3.39445	−	5.87936i	0.136105	−	0.235741i
$623$	−8.21110			−0.328971
$624$		0			0
$625$	1.00000			0.0400000
$626$	9.11943	−	15.7953i	0.364486	−	0.631308i
$627$	4.50000	−	7.79423i	0.179713	−	0.311272i
$628$	−0.486122	−	0.841988i	−0.0193984	−	0.0335990i
$629$	1.42221			0.0567070
$630$	−1.30278	−	2.25647i	−0.0519038	−	0.0899001i
$631$	0.0138782	+	0.0240377i	0.000552482	+	0.000956927i	0.866302	−	0.499521i	$-0.166491\pi$
$631$	0.0138782	+	0.0240377i	0.000552482	+	0.000956927i	−0.865749	+	0.500478i	$0.833157\pi$
$632$	−27.6333			−1.09919
$633$	8.19722	+	14.1980i	0.325810	+	0.564320i
$634$	−3.90833	+	6.76942i	−0.155219	+	0.268848i
$635$	−5.10555	+	8.84307i	−0.202608	+	0.350927i
$636$	−3.39445			−0.134599
$637$		0			0
$638$	−59.9638			−2.37399
$639$	16.8167	−	29.1273i	0.665257	−	1.15226i
$640$	4.04584	−	7.00759i	0.159926	−	0.276999i
$641$	9.71110	+	16.8201i	0.383565	+	0.664355i	0.991569	−	0.129579i	$-0.0413627\pi$
$641$	9.71110	+	16.8201i	0.383565	+	0.664355i	−0.608004	+	0.793934i	$0.708029\pi$
$642$	10.6972			0.422186
$643$	−20.3167	−	35.1895i	−0.801211	−	1.38774i	−0.918820	−	0.394678i	$-0.870856\pi$
$643$	−20.3167	−	35.1895i	−0.801211	−	1.38774i	0.117609	−	0.993060i	$-0.462477\pi$
$644$	−0.454163	−	0.786634i	−0.0178965	−	0.0309977i
$645$	4.21110			0.165812
$646$	−0.412529	−	0.714521i	−0.0162307	−	0.0281125i
$647$	−5.28890	+	9.16064i	−0.207928	+	0.360142i	−0.951062	−	0.309001i	$-0.900005\pi$
$647$	−5.28890	+	9.16064i	−0.207928	+	0.360142i	0.743134	+	0.669143i	$0.233339\pi$
$648$	−1.50000	+	2.59808i	−0.0589256	+	0.102062i
$649$	−60.6333			−2.38007
$650$		0			0
$651$	4.00000			0.156772
$652$	2.75694	−	4.77516i	0.107970	−	0.187010i
$653$	14.4083	−	24.9560i	0.563841	−	0.976602i	−0.433315	−	0.901243i	$-0.642656\pi$
$653$	14.4083	−	24.9560i	0.563841	−	0.976602i	0.997156	−	0.0753594i	$-0.0240104\pi$
$654$	3.11943	+	5.40301i	0.121979	+	0.211274i
$655$	−6.78890			−0.265264
$656$	−4.95416	−	8.58086i	−0.193428	−	0.335026i
$657$	15.2111	+	26.3464i	0.593442	+	1.02787i
$658$	−6.78890			−0.264659
$659$	6.59167	+	11.4171i	0.256775	+	0.444748i	0.965376	−	0.260862i	$-0.0840067\pi$
$659$	6.59167	+	11.4171i	0.256775	+	0.444748i	−0.708601	+	0.705609i	$0.750673\pi$
$660$	0.848612	−	1.46984i	0.0330322	−	0.0572134i
$661$	19.3167	−	33.4574i	0.751331	−	1.30134i	−0.195847	−	0.980634i	$-0.562746\pi$
$661$	19.3167	−	33.4574i	0.751331	−	1.30134i	0.947178	−	0.320709i	$-0.103921\pi$
$662$	−33.9083			−1.31788
$663$		0			0
$664$	−15.6333			−0.606690
$665$	0.802776	−	1.39045i	0.0311303	−	0.0539193i
$666$	−4.69722	+	8.13583i	−0.182014	+	0.315257i
$667$	12.3167	+	21.3331i	0.476903	+	0.826020i
$668$	2.72498			0.105433
$669$	5.10555	+	8.84307i	0.197392	+	0.341893i
$670$	4.55971	+	7.89766i	0.176157	+	0.305113i
$671$	−5.60555			−0.216400
$672$	0.848612	+	1.46984i	0.0327359	+	0.0567003i
$673$	5.19722	−	9.00186i	0.200338	−	0.346996i	−0.748299	−	0.663361i	$-0.769129\pi$
$673$	5.19722	−	9.00186i	0.200338	−	0.346996i	0.948637	+	0.316365i	$0.102463\pi$
$674$	11.4861	−	19.8945i	0.442429	−	0.766309i
$675$	−5.00000			−0.192450
$676$		0			0
$677$	33.6333			1.29263			0.646317	−	0.763069i	$-0.276309\pi$
$677$	33.6333			1.29263			0.646317	+	0.763069i	$0.276309\pi$
$678$	3.65139	−	6.32439i	0.140231	−	0.242887i
$679$	−7.80278	+	13.5148i	−0.299443	+	0.518651i
$680$	−0.591673	−	1.02481i	−0.0226896	−	0.0392996i
$681$	−1.42221			−0.0544990
$682$	14.6056	+	25.2976i	0.559275	+	0.968694i
$683$	10.8944	+	18.8697i	0.416864	+	0.722030i	0.995622	−	0.0934691i	$-0.0297956\pi$
$683$	10.8944	+	18.8697i	0.416864	+	0.722030i	−0.578758	+	0.815500i	$0.696462\pi$
$684$	−0.972244			−0.0371747
$685$	2.80278	+	4.85455i	0.107089	+	0.185483i
$686$	−8.46804	+	14.6671i	−0.323311	+	0.559992i
$687$	7.00000	−	12.1244i	0.267067	−	0.462573i
$688$	−13.9083			−0.530250
$689$		0			0
$690$	3.90833			0.148787
$691$	3.01388	−	5.22019i	0.114653	−	0.198585i	−0.802988	−	0.595995i	$-0.796758\pi$
$691$	3.01388	−	5.22019i	0.114653	−	0.198585i	0.917641	+	0.397410i	$0.130091\pi$
$692$	−2.54584	+	4.40952i	−0.0967782	+	0.167625i
$693$	5.60555	+	9.70910i	0.212937	+	0.368818i
$694$	−26.3305			−0.999493
$695$	−6.80278	−	11.7828i	−0.258044	−	0.446945i
$696$	−12.3167	−	21.3331i	−0.466862	−	0.808628i
$697$	−1.18335			−0.0448224
$698$	11.8625	+	20.5464i	0.449002	+	0.777694i
$699$	−0.394449	+	0.683205i	−0.0149194	+	0.0258412i
$700$	0.151388	−	0.262211i	0.00572192	−	0.00991066i
$701$	−7.57779			−0.286209			−0.143105	−	0.989708i	$-0.545709\pi$
$701$	−7.57779			−0.286209			−0.143105	+	0.989708i	$0.545709\pi$
$702$		0			0
$703$	−5.78890			−0.218332
$704$	−24.7111	+	42.8009i	−0.931335	+	1.61312i
$705$	−2.60555	+	4.51295i	−0.0981307	+	0.169967i
$706$	3.13751	+	5.43433i	0.118082	+	0.204524i
$707$	−9.00000			−0.338480
$708$	−1.63751	−	2.83625i	−0.0615414	−	0.106593i
$709$	21.9222	+	37.9704i	0.823306	+	1.42601i	0.903207	+	0.429205i	$0.141206\pi$
$709$	21.9222	+	37.9704i	0.823306	+	1.42601i	−0.0799016	+	0.996803i	$0.525461\pi$
$710$	−21.9083			−0.822205
$711$	−9.21110	−	15.9541i	−0.345443	−	0.598325i
$712$	12.3167	−	21.3331i	0.461586	−	0.799491i
$713$	6.00000	−	10.3923i	0.224702	−	0.389195i
$714$	−0.513878			−0.0192314
$715$		0			0
$716$	−0.358288			−0.0133899
$717$		0			0
$718$	6.78890	−	11.7587i	0.253359	−	0.438831i
$719$	9.19722	+	15.9301i	0.342999	+	0.594091i	0.984988	−	0.172622i	$-0.0552241\pi$
$719$	9.19722	+	15.9301i	0.342999	+	0.594091i	−0.641989	+	0.766713i	$0.721891\pi$
$720$	6.60555			0.246174
$721$	2.00000	+	3.46410i	0.0744839	+	0.129010i
$722$	−10.6972	−	18.5281i	−0.398109	−	0.689546i
$723$	−16.2111			−0.602897
$724$	−3.88057	−	6.72135i	−0.144220	−	0.249797i
$725$	−4.10555	+	7.11102i	−0.152476	+	0.264097i
$726$	13.3028	−	23.0411i	0.493712	−	0.855135i
$727$	42.4222			1.57335			0.786676	−	0.617366i	$-0.211800\pi$
$727$	42.4222			1.57335			0.786676	+	0.617366i	$0.211800\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$	9.90833	−	17.1617i	0.366724	−	0.635184i
$731$	−0.830532	+	1.43852i	−0.0307183	+	0.0532057i
$732$	−0.151388	−	0.262211i	−0.00559545	−	0.00969161i
$733$	−10.8444			−0.400547			−0.200274	−	0.979740i	$-0.564183\pi$
$733$	−10.8444			−0.400547			−0.200274	+	0.979740i	$0.564183\pi$
$734$	−11.3486	−	19.6564i	−0.418885	−	0.725530i
$735$	3.00000	+	5.19615i	0.110657	+	0.191663i
$736$	5.09167			0.187682
$737$	−19.6194	−	33.9818i	−0.722691	−	1.25174i
$738$	3.90833	−	6.76942i	0.143868	−	0.249186i
$739$	−14.1972	+	24.5903i	−0.522253	+	0.904569i	0.477411	+	0.878680i	$0.341575\pi$
$739$	−14.1972	+	24.5903i	−0.522253	+	0.904569i	−0.999665	+	0.0258895i	$0.991758\pi$
$740$	−1.09167			−0.0401307
$741$		0			0
$742$	−14.6056			−0.536187
$743$	−3.31665	+	5.74461i	−0.121676	+	0.210749i	−0.920429	−	0.390910i	$-0.872160\pi$
$743$	−3.31665	+	5.74461i	−0.121676	+	0.210749i	0.798753	+	0.601660i	$0.205494\pi$
$744$	−6.00000	+	10.3923i	−0.219971	+	0.381000i
$745$	1.50000	+	2.59808i	0.0549557	+	0.0951861i
$746$	35.9638			1.31673
$747$	−5.21110	−	9.02589i	−0.190664	−	0.330240i
$748$	0.334734	+	0.579776i	0.0122391	+	0.0211987i
$749$	−8.21110			−0.300027
$750$	0.651388	+	1.12824i	0.0237853	+	0.0411974i
$751$	9.22498	−	15.9781i	0.336624	−	0.583050i	−0.647171	−	0.762345i	$-0.724048\pi$
$751$	9.22498	−	15.9781i	0.336624	−	0.583050i	0.983795	+	0.179294i	$0.0573814\pi$
$752$	8.60555	−	14.9053i	0.313812	−	0.543539i
$753$	−28.8167			−1.05014
$754$		0			0
$755$	−13.2111			−0.480801
$756$	−0.756939	+	1.31106i	−0.0275296	+	0.0476827i
$757$	10.4083	−	18.0278i	0.378297	−	0.655230i	−0.612518	−	0.790457i	$-0.709843\pi$
$757$	10.4083	−	18.0278i	0.378297	−	0.655230i	0.990815	+	0.135227i	$0.0431764\pi$
$758$	−1.55971	−	2.70151i	−0.0566514	−	0.0981231i
$759$	−16.8167			−0.610406
$760$	2.40833	+	4.17134i	0.0873592	+	0.151311i
$761$	−12.3167	−	21.3331i	−0.446478	−	0.773323i	0.551676	−	0.834059i	$-0.313989\pi$
$761$	−12.3167	−	21.3331i	−0.446478	−	0.773323i	−0.998154	+	0.0607356i	$0.980655\pi$
$762$	−13.3028			−0.481909
$763$	−2.39445	−	4.14731i	−0.0866849	−	0.150143i
$764$	−0.729183	+	1.26298i	−0.0263809	+	0.0456931i
$765$	0.394449	−	0.683205i	0.0142613	−	0.0247013i
$766$	24.2750			0.877092
$767$		0			0
$768$	−7.09167			−0.255899
$769$	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	$0.103113\pi$
$770$	3.65139	−	6.32439i	0.131587	−	0.227915i
$771$	11.8028	+	20.4430i	0.425067	+	0.736237i
$772$	2.54163			0.0914754
$773$	14.8028	+	25.6392i	0.532419	+	0.922176i	0.999284	+	0.0378477i	$0.0120502\pi$
$773$	14.8028	+	25.6392i	0.532419	+	0.922176i	−0.466865	+	0.884329i	$0.654616\pi$
$774$	−5.48612	−	9.50224i	−0.197195	−	0.341551i
$775$	4.00000			0.143684
$776$	−23.4083	−	40.5444i	−0.840310	−	1.45546i
$777$	−1.80278	+	3.12250i	−0.0646742	+	0.112019i
$778$	−0.513878	+	0.890063i	−0.0184234	+	0.0319103i
$779$	4.81665			0.172575
$780$		0			0
$781$	94.2666			3.37312
$782$	−0.770817	+	1.33509i	−0.0275644	+	0.0477429i
$783$	20.5278	−	35.5551i	0.733602	−	1.27064i
$784$	−9.90833	−	17.1617i	−0.353869	−	0.612919i
$785$	−3.21110			−0.114609
$786$	−4.42221	−	7.65948i	−0.157735	−	0.273205i
$787$	−14.3167	−	24.7972i	−0.510334	−	0.883924i	−0.999928	−	0.0119736i	$-0.996189\pi$
$787$	−14.3167	−	24.7972i	−0.510334	−	0.883924i	0.489595	−	0.871950i	$-0.337145\pi$
$788$	6.90833			0.246099
$789$	−13.1056	−	22.6995i	−0.466570	−	0.808123i
$790$	−6.00000	+	10.3923i	−0.213470	+	0.369742i
$791$	−2.80278	+	4.85455i	−0.0996552	+	0.172608i
$792$	−33.6333			−1.19511
$793$		0			0
$794$	−18.2750			−0.648556
$795$	−5.60555	+	9.70910i	−0.198808	+	0.344346i
$796$	−1.33473	+	2.31183i	−0.0473084	+	0.0819405i
$797$	−25.2250	−	43.6909i	−0.893515	−	1.54761i	−0.835632	−	0.549289i	$-0.814898\pi$
$797$	−25.2250	−	43.6909i	−0.893515	−	1.54761i	−0.0578825	−	0.998323i	$-0.518435\pi$
$798$	2.09167			0.0740444
$799$	−1.02776	−	1.78013i	−0.0363594	−	0.0629763i
$800$	0.848612	+	1.46984i	0.0300030	+	0.0519667i
$801$	16.4222			0.580250
$802$	1.44029	+	2.49465i	0.0508582	+	0.0880891i
$803$	−42.6333	+	73.8431i	−1.50450	+	2.60586i
$804$	1.05971	−	1.83548i	0.0373733	−	0.0647324i
$805$	−3.00000			−0.105736
$806$		0			0
$807$	−9.00000			−0.316815
$808$	13.5000	−	23.3827i	0.474928	−	0.822600i
$809$	−8.52776	+	14.7705i	−0.299820	+	0.519303i	−0.976095	−	0.217346i	$-0.930260\pi$
$809$	−8.52776	+	14.7705i	−0.299820	+	0.519303i	0.676275	+	0.736650i	$0.263593\pi$
$810$	0.651388	+	1.12824i	0.0228874	+	0.0396422i
$811$	17.5778			0.617240			0.308620	−	0.951185i	$-0.400133\pi$
$811$	17.5778			0.617240			0.308620	+	0.951185i	$0.400133\pi$
$812$	1.24306	+	2.15304i	0.0436229	+	0.0755571i
$813$	0.408327	+	0.707243i	0.0143207	+	0.0248041i
$814$	−26.3305			−0.922885
$815$	−9.10555	−	15.7713i	−0.318954	−	0.552444i
$816$	0.651388	−	1.12824i	0.0228031	−	0.0394962i
$817$	3.38057	−	5.85532i	0.118271	−	0.204852i
$818$	−8.09167			−0.282919
$819$		0			0
$820$	0.908327			0.0317202
$821$	−3.71110	+	6.42782i	−0.129518	+	0.224332i	−0.923490	−	0.383622i	$-0.874676\pi$
$821$	−3.71110	+	6.42782i	−0.129518	+	0.224332i	0.793972	+	0.607955i	$0.208010\pi$
$822$	−3.65139	+	6.32439i	−0.127357	+	0.220588i
$823$	−13.3167	−	23.0651i	−0.464189	−	0.804000i	0.534975	−	0.844868i	$-0.320321\pi$
$823$	−13.3167	−	23.0651i	−0.464189	−	0.804000i	−0.999165	+	0.0408682i	$0.986988\pi$
$824$	−12.0000			−0.418040
$825$	−2.80278	−	4.85455i	−0.0975801	−	0.169014i
$826$	−7.04584	−	12.2037i	−0.245156	−	0.424623i
$827$	13.5778			0.472146			0.236073	−	0.971735i	$-0.424140\pi$
$827$	13.5778			0.472146			0.236073	+	0.971735i	$0.424140\pi$
$828$	0.908327	+	1.57327i	0.0315665	+	0.0546749i
$829$	−0.288897	+	0.500385i	−0.0100338	+	0.0173791i	−0.870999	−	0.491285i	$-0.836527\pi$
$829$	−0.288897	+	0.500385i	−0.0100338	+	0.0173791i	0.860965	+	0.508664i	$0.169861\pi$
$830$	−3.39445	+	5.87936i	−0.117823	+	0.204075i
$831$	20.3944			0.707476
$832$		0			0
$833$	−2.36669			−0.0820010
$834$	8.86249	−	15.3503i	0.306883	−	0.531537i
$835$	4.50000	−	7.79423i	0.155729	−	0.269730i
$836$	−1.36249	−	2.35990i	−0.0471227	−	0.0816189i
$837$	−20.0000			−0.691301
$838$	−21.6514	−	37.5013i	−0.747935	−	1.29546i
$839$	8.01388	+	13.8804i	0.276670	+	0.479206i	0.970555	−	0.240879i	$-0.0774358\pi$
$839$	8.01388	+	13.8804i	0.276670	+	0.479206i	−0.693885	+	0.720086i	$0.744103\pi$
$840$	3.00000			0.103510
$841$	−19.2111	−	33.2746i	−0.662452	−	1.14740i
$842$	−2.33053	+	4.03660i	−0.0803154	+	0.139110i
$843$	−3.00000	+	5.19615i	−0.103325	+	0.178965i
$844$	4.96384			0.170862
$845$		0			0
$846$	13.5778			0.466814
$847$	−10.2111	+	17.6861i	−0.350858	+	0.607703i
$848$	18.5139	−	32.0670i	0.635769	−	1.10118i
$849$	−2.50000	−	4.33013i	−0.0857998	−	0.148610i
$850$	−0.513878			−0.0176259
$851$	5.40833	+	9.36750i	0.185395	+	0.321114i
$852$	2.54584	+	4.40952i	0.0872189	+	0.151068i
$853$	−32.7889			−1.12267			−0.561335	−	0.827589i	$-0.689712\pi$
$853$	−32.7889			−1.12267			−0.561335	+	0.827589i	$0.689712\pi$
$854$	−0.651388	−	1.12824i	−0.0222900	−	0.0386075i
$855$	−1.60555	+	2.78090i	−0.0549087	+	0.0951046i
$856$	12.3167	−	21.3331i	0.420975	−	0.729149i
$857$	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
$859$	25.2111			0.860192			0.430096	−	0.902783i	$-0.358480\pi$
$859$	25.2111			0.860192			0.430096	+	0.902783i	$0.358480\pi$
$860$	0.637510	−	1.10420i	0.0217389	−	0.0376529i
$861$	1.50000	−	2.59808i	0.0511199	−	0.0885422i
$862$	13.8347	+	23.9625i	0.471213	+	0.816165i
$863$	−36.0000			−1.22545			−0.612727	−	0.790295i	$-0.709928\pi$
$863$	−36.0000			−1.22545			−0.612727	+	0.790295i	$0.709928\pi$
$864$	−4.24306	−	7.34920i	−0.144352	−	0.250025i
$865$	8.40833	+	14.5636i	0.285892	+	0.495179i
$866$	4.69722			0.159618
$867$	8.42221	+	14.5877i	0.286033	+	0.495424i
$868$	0.605551	−	1.04885i	0.0205537	−	0.0356001i
$869$	25.8167	−	44.7158i	0.875770	−	1.51688i
$870$	−10.6972			−0.362670
$871$		0			0
$872$	14.3667			0.486518
$873$	15.6056	−	27.0296i	0.528168	−	0.914814i
$874$	3.13751	−	5.43433i	0.106128	−	0.183819i
$875$	−0.500000	−	0.866025i	−0.0169031	−	0.0292770i
$876$	−4.60555			−0.155607
$877$	−19.0139	−	32.9330i	−0.642053	−	1.11207i	−0.984974	−	0.172704i	$-0.944750\pi$
$877$	−19.0139	−	32.9330i	−0.642053	−	1.11207i	0.342921	−	0.939364i	$-0.388584\pi$
$878$	15.1375	+	26.2189i	0.510866	+	0.884846i
$879$	−17.6056			−0.593821
$880$	9.25694	+	16.0335i	0.312051	+	0.540489i
$881$	−17.9222	+	31.0422i	−0.603814	+	1.04584i	0.388423	+	0.921481i	$0.373020\pi$
$881$	−17.9222	+	31.0422i	−0.603814	+	1.04584i	−0.992238	+	0.124356i	$0.960313\pi$
$882$	7.81665	−	13.5388i	0.263200	−	0.455877i
$883$	−31.6333			−1.06455			−0.532273	−	0.846573i	$-0.678662\pi$
$883$	−31.6333			−1.06455			−0.532273	+	0.846573i	$0.678662\pi$
$884$		0			0
$885$	−10.8167			−0.363598
$886$	−14.6056	+	25.2976i	−0.490683	+	0.849888i
$887$	−17.5278	+	30.3590i	−0.588524	+	1.01935i	0.405901	+	0.913917i	$0.366958\pi$
$887$	−17.5278	+	30.3590i	−0.588524	+	1.01935i	−0.994426	+	0.105437i	$0.966376\pi$
$888$	−5.40833	−	9.36750i	−0.181492	−	0.314353i
$889$	10.2111			0.342469
$890$	−5.34861	−	9.26407i	−0.179286	−	0.310532i
$891$	−2.80278	−	4.85455i	−0.0938965	−	0.162634i
$892$	3.09167			0.103517
$893$	4.18335	+	7.24577i	0.139990	+	0.242470i
$894$	−1.95416	+	3.38471i	−0.0653570	+	0.113202i
$895$	−0.591673	+	1.02481i	−0.0197775	+	0.0342555i
$896$	−8.09167			−0.270324
$897$		0			0
$898$	−16.4584			−0.549223
$899$	−16.4222	+	28.4441i	−0.547711	+	0.948664i
$900$	−0.302776	+	0.524423i	−0.0100925	+	0.0174808i
$901$	−2.21110	−	3.82974i	−0.0736625	−	0.127587i
$902$	21.9083			0.729467
$903$	−2.10555	−	3.64692i	−0.0700684	−	0.121362i
$904$	−8.40833	−	14.5636i	−0.279657	−	0.484380i
$905$	−25.6333			−0.852080
$906$	−8.60555	−	14.9053i	−0.285900	−	0.495194i
$907$	−24.1333	+	41.8001i	−0.801333	+	1.38795i	0.117405	+	0.993084i	$0.462542\pi$
$907$	−24.1333	+	41.8001i	−0.801333	+	1.38795i	−0.918739	+	0.394866i	$0.870791\pi$
$908$	−0.215305	+	0.372918i	−0.00714513	+	0.0123757i
$909$	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	$0.703390\pi$
$912$	−2.65139	+	4.59234i	−0.0877962	+	0.152068i
$913$	14.6056	−	25.2976i	0.483373	−	0.837227i
$914$	3.37637	+	5.84804i	0.111680	+	0.193436i
$915$	−1.00000			−0.0330590
$916$	−2.11943	−	3.67096i	−0.0700279	−	0.121292i
$917$	3.39445	+	5.87936i	0.112095	+	0.194153i
$918$	2.56939			0.0848025
$919$	8.59167	+	14.8812i	0.283413	+	0.490886i	0.972223	−	0.234056i	$-0.0751999\pi$
$919$	8.59167	+	14.8812i	0.283413	+	0.490886i	−0.688810	+	0.724942i	$0.741867\pi$
$920$	4.50000	−	7.79423i	0.148361	−	0.256968i
$921$	−8.00000	+	13.8564i	−0.263609	+	0.456584i
$922$	28.3860			0.934845
$923$		0			0
$924$	−1.69722			−0.0558346
$925$	−1.80278	+	3.12250i	−0.0592749	+	0.102667i
$926$	3.63331	−	6.29307i	0.119398	−	0.206803i
$927$	−4.00000	−	6.92820i	−0.131377	−	0.227552i
$928$	−13.9361			−0.457474
$929$	6.71110	+	11.6240i	0.220184	+	0.381370i	0.954864	−	0.297044i	$-0.0960008\pi$
$929$	6.71110	+	11.6240i	0.220184	+	0.381370i	−0.734680	+	0.678414i	$0.762668\pi$
$930$	2.60555	+	4.51295i	0.0854394	+	0.147985i
$931$	9.63331			0.315719
$932$	0.119429	+	0.206858i	0.00391204	+	0.00677586i
$933$	−2.60555	+	4.51295i	−0.0853019	+	0.147747i
$934$	11.2111	−	19.4182i	0.366838	−	0.635383i
$935$	2.21110			0.0723108
$936$		0			0
$937$	−46.4777			−1.51836			−0.759180	−	0.650880i	$-0.774400\pi$
$937$	−46.4777			−1.51836			−0.759180	+	0.650880i	$0.774400\pi$
$938$	4.55971	−	7.89766i	0.148880	−	0.257868i
$939$	−7.00000	+	12.1244i	−0.228436	+	0.395663i
$940$	0.788897	+	1.36641i	0.0257310	+	0.0445674i
$941$	−33.6333			−1.09641			−0.548207	−	0.836343i	$-0.684689\pi$
$941$	−33.6333			−1.09641			−0.548207	+	0.836343i	$0.684689\pi$
$942$	−2.09167	−	3.62288i	−0.0681504	−	0.118040i
$943$	−4.50000	−	7.79423i	−0.146540	−	0.253815i
$944$	35.7250			1.16275
$945$	2.50000	+	4.33013i	0.0813250	+	0.140859i
$946$	15.3764	−	26.6327i	0.499929	−	0.865902i
$947$	12.3167	−	21.3331i	0.400237	−	0.693232i	−0.593517	−	0.804822i	$-0.702261\pi$
$947$	12.3167	−	21.3331i	0.400237	−	0.693232i	0.993754	+	0.111590i	$0.0355943\pi$
$948$	2.78890			0.0905792
$949$		0			0
$950$	2.09167			0.0678628
$951$	3.00000	−	5.19615i	0.0972817	−	0.168497i
$952$	−0.591673	+	1.02481i	−0.0191762	+	0.0332142i
$953$	−25.2250	−	43.6909i	−0.817117	−	1.41529i	−0.907798	−	0.419409i	$-0.862237\pi$
$953$	−25.2250	−	43.6909i	−0.817117	−	1.41529i	0.0906803	−	0.995880i	$-0.471096\pi$
$954$	29.2111			0.945744
$955$	2.40833	+	4.17134i	0.0779316	+	0.134982i
$956$		0			0
$957$	46.0278			1.48787
$958$	4.67914	+	8.10452i	0.151176	+	0.261845i
$959$	2.80278	−	4.85455i	0.0905063	−	0.156762i
$960$	−4.40833	+	7.63545i	−0.142278	+	0.246433i
$961$	−15.0000			−0.483871
$962$		0			0
$963$	16.4222			0.529198
$964$	−2.45416	+	4.25074i	−0.0790433	+	0.136907i
$965$	4.19722	−	7.26981i	0.135113	−	0.234023i
$966$	−1.95416	−	3.38471i	−0.0628742	−	0.108901i
$967$	−56.4777			−1.81620			−0.908100	−	0.418752i	$-0.862468\pi$
$967$	−56.4777			−1.81620			−0.908100	+	0.418752i	$0.862468\pi$
$968$	−30.6333	−	53.0584i	−0.984592	−	1.70536i
$969$	0.316654	+	0.548461i	0.0101724	+	0.0176191i
$970$	−20.3305			−0.652774
$971$	3.98612	+	6.90417i	0.127921	+	0.221565i	0.922871	−	0.385110i	$-0.125836\pi$
$971$	3.98612	+	6.90417i	0.127921	+	0.221565i	−0.794950	+	0.606675i	$0.792503\pi$
$972$	2.42221	−	4.19538i	0.0776923	−	0.134567i
$973$	−6.80278	+	11.7828i	−0.218087	+	0.377738i
$974$	−1.30278			−0.0417436
$975$		0			0
$976$	3.30278			0.105719
$977$	3.59167	−	6.22096i	0.114908	−	0.199026i	−0.802835	−	0.596201i	$-0.796676\pi$
$977$	3.59167	−	6.22096i	0.114908	−	0.199026i	0.917743	+	0.397175i	$0.130009\pi$
$978$	11.8625	−	20.5464i	0.379321	−	0.657003i
$979$	23.0139	+	39.8612i	0.735527	+	1.27397i
$980$	1.81665			0.0580309
$981$	4.78890	+	8.29461i	0.152898	+	0.264827i
$982$	3.13751	+	5.43433i	0.100122	+	0.173416i
$983$	10.4222			0.332417			0.166208	−	0.986091i	$-0.446848\pi$
$983$	10.4222			0.332417			0.166208	+	0.986091i	$0.446848\pi$
$984$	4.50000	+	7.79423i	0.143455	+	0.248471i
$985$	11.4083	−	19.7598i	0.363500	−	0.629600i
$986$	2.10975	−	3.65420i	0.0671882	−	0.116373i
$987$	5.21110			0.165871
$988$		0			0
$989$	−12.6333			−0.401716
$990$	−7.30278	+	12.6488i	−0.232097	+	0.402005i
$991$	−1.98612	+	3.44006i	−0.0630912	+	0.109277i	−0.895846	−	0.444365i	$-0.853429\pi$
$991$	−1.98612	+	3.44006i	−0.0630912	+	0.109277i	0.832754	+	0.553642i	$0.186763\pi$
$992$	3.39445	+	5.87936i	0.107774	+	0.186670i
$993$	26.0278			0.825966
$994$	10.9542	+	18.9732i	0.347445	+	0.601792i
$995$	4.40833	+	7.63545i	0.139753	+	0.242060i
$996$	1.57779			0.0499943
$997$	−23.2250	−	40.2268i	−0.735543	−	1.27400i	−0.954485	−	0.298259i	$-0.903594\pi$
$997$	−23.2250	−	40.2268i	−0.735543	−	1.27400i	0.218942	−	0.975738i	$-0.429739\pi$
$998$	17.2111	−	29.8105i	0.544808	−	0.943635i
$999$	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.191.2		4
13.2	odd	12		845.2.m.d.361.3		8
13.3	even	3	inner	845.2.e.d.146.2		4
13.4	even	6		845.2.a.c.1.2		2
13.5	odd	4		845.2.m.d.316.2		8
13.6	odd	12		845.2.c.d.506.3		4
13.7	odd	12		845.2.c.d.506.2		4
13.8	odd	4		845.2.m.d.316.3		8
13.9	even	3		845.2.a.f.1.1		2
13.10	even	6		65.2.e.b.16.1	✓	4
13.11	odd	12		845.2.m.d.361.2		8
13.12	even	2		65.2.e.b.61.1	yes	4
39.17	odd	6		7605.2.a.bg.1.1		2
39.23	odd	6		585.2.j.d.406.2		4
39.35	odd	6		7605.2.a.bb.1.2		2
39.38	odd	2		585.2.j.d.451.2		4
52.23	odd	6		1040.2.q.o.81.1		4
52.51	odd	2		1040.2.q.o.321.1		4
65.4	even	6		4225.2.a.x.1.1		2
65.9	even	6		4225.2.a.t.1.2		2
65.12	odd	4		325.2.o.b.74.2		8
65.23	odd	12		325.2.o.b.224.2		8
65.38	odd	4		325.2.o.b.74.3		8
65.49	even	6		325.2.e.a.276.2		4
65.62	odd	12		325.2.o.b.224.3		8
65.64	even	2		325.2.e.a.126.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.e.b.16.1	✓	4	13.10	even	6
65.2.e.b.61.1	yes	4	13.12	even	2
325.2.e.a.126.2		4	65.64	even	2
325.2.e.a.276.2		4	65.49	even	6
325.2.o.b.74.2		8	65.12	odd	4
325.2.o.b.74.3		8	65.38	odd	4
325.2.o.b.224.2		8	65.23	odd	12
325.2.o.b.224.3		8	65.62	odd	12
585.2.j.d.406.2		4	39.23	odd	6
585.2.j.d.451.2		4	39.38	odd	2
845.2.a.c.1.2		2	13.4	even	6
845.2.a.f.1.1		2	13.9	even	3
845.2.c.d.506.2		4	13.7	odd	12
845.2.c.d.506.3		4	13.6	odd	12
845.2.e.d.146.2		4	13.3	even	3	inner
845.2.e.d.191.2		4	1.1	even	1	trivial
845.2.m.d.316.2		8	13.5	odd	4
845.2.m.d.316.3		8	13.8	odd	4
845.2.m.d.361.2		8	13.11	odd	12
845.2.m.d.361.3		8	13.2	odd	12
1040.2.q.o.81.1		4	52.23	odd	6
1040.2.q.o.321.1		4	52.51	odd	2
4225.2.a.t.1.2		2	65.9	even	6
4225.2.a.x.1.1		2	65.4	even	6
7605.2.a.bb.1.2		2	39.35	odd	6
7605.2.a.bg.1.1		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+(0.651388 - 1.12824i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.151388 + 0.262211i) q^{4} +1.00000 q^{5} +(0.651388 + 1.12824i) q^{6} +(-0.500000 - 0.866025i) q^{7} +3.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +(0.651388 - 1.12824i) q^{10} +(-2.80278 + 4.85455i) q^{11} -0.302776 q^{12} -1.30278 q^{14} +(-0.500000 + 0.866025i) q^{15} +(1.65139 - 2.86029i) q^{16} +(-0.197224 - 0.341603i) q^{17} +2.60555 q^{18} +(0.802776 + 1.39045i) q^{19} +(0.151388 + 0.262211i) q^{20} +1.00000 q^{21} +(3.65139 + 6.32439i) q^{22} +(1.50000 - 2.59808i) q^{23} +(-1.50000 + 2.59808i) q^{24} +1.00000 q^{25} -5.00000 q^{27} +(0.151388 - 0.262211i) q^{28} +(-4.10555 + 7.11102i) q^{29} +(0.651388 + 1.12824i) q^{30} +4.00000 q^{31} +(0.848612 + 1.46984i) q^{32} +(-2.80278 - 4.85455i) q^{33} -0.513878 q^{34} +(-0.500000 - 0.866025i) q^{35} +(-0.302776 + 0.524423i) q^{36} +(-1.80278 + 3.12250i) q^{37} +2.09167 q^{38} +3.00000 q^{40} +(1.50000 - 2.59808i) q^{41} +(0.651388 - 1.12824i) q^{42} +(-2.10555 - 3.64692i) q^{43} -1.69722 q^{44} +(1.00000 + 1.73205i) q^{45} +(-1.95416 - 3.38471i) q^{46} +5.21110 q^{47} +(1.65139 + 2.86029i) q^{48} +(3.00000 - 5.19615i) q^{49} +(0.651388 - 1.12824i) q^{50} +0.394449 q^{51} +11.2111 q^{53} +(-3.25694 + 5.64118i) q^{54} +(-2.80278 + 4.85455i) q^{55} +(-1.50000 - 2.59808i) q^{56} -1.60555 q^{57} +(5.34861 + 9.26407i) q^{58} +(5.40833 + 9.36750i) q^{59} -0.302776 q^{60} +(0.500000 + 0.866025i) q^{61} +(2.60555 - 4.51295i) q^{62} +(1.00000 - 1.73205i) q^{63} +8.81665 q^{64} -7.30278 q^{66} +(-3.50000 + 6.06218i) q^{67} +(0.0597147 - 0.103429i) q^{68} +(1.50000 + 2.59808i) q^{69} -1.30278 q^{70} +(-8.40833 - 14.5636i) q^{71} +(3.00000 + 5.19615i) q^{72} +15.2111 q^{73} +(2.34861 + 4.06792i) q^{74} +(-0.500000 + 0.866025i) q^{75} +(-0.243061 + 0.420994i) q^{76} +5.60555 q^{77} -9.21110 q^{79} +(1.65139 - 2.86029i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.95416 - 3.38471i) q^{82} -5.21110 q^{83} +(0.151388 + 0.262211i) q^{84} +(-0.197224 - 0.341603i) q^{85} -5.48612 q^{86} +(-4.10555 - 7.11102i) q^{87} +(-8.40833 + 14.5636i) q^{88} +(4.10555 - 7.11102i) q^{89} +2.60555 q^{90} +0.908327 q^{92} +(-2.00000 + 3.46410i) q^{93} +(3.39445 - 5.87936i) q^{94} +(0.802776 + 1.39045i) q^{95} -1.69722 q^{96} +(-7.80278 - 13.5148i) q^{97} +(-3.90833 - 6.76942i) q^{98} -11.2111 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

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