LMFDB - Embedded newform 1690.2.e.m.991.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1690,2,Mod(191,1690)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1690, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1690.191"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1690 = 2 \cdot 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1690.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,2,0,-2,4,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$13.4947179416$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 10x^{2} + 100 $ x^4 + 10*x^2 + 100
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			991.1
Root			$-1.58114 - 2.73861i$ of defining polynomial
Character	$\chi$	$=$	1690.991
Dual form			1690.2.e.m.191.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(-1.58114 - 2.73861i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(1.58114 - 2.73861i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +(-3.50000 + 6.06218i) q^{9} +(0.500000 + 0.866025i) q^{10} +(1.08114 + 1.87259i) q^{11} +3.16228 q^{12} -1.00000 q^{14} +(-1.58114 - 2.73861i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.58114 - 4.47066i) q^{17} -7.00000 q^{18} +(-0.918861 + 1.59151i) q^{19} +(-0.500000 + 0.866025i) q^{20} +3.16228 q^{21} +(-1.08114 + 1.87259i) q^{22} +(-3.00000 - 5.19615i) q^{23} +(1.58114 + 2.73861i) q^{24} +1.00000 q^{25} +12.6491 q^{27} +(-0.500000 - 0.866025i) q^{28} +(-5.16228 - 8.94133i) q^{29} +(1.58114 - 2.73861i) q^{30} -7.16228 q^{31} +(0.500000 - 0.866025i) q^{32} +(3.41886 - 5.92164i) q^{33} +5.16228 q^{34} +(-0.500000 + 0.866025i) q^{35} +(-3.50000 - 6.06218i) q^{36} +(-0.0811388 - 0.140537i) q^{37} -1.83772 q^{38} -1.00000 q^{40} +(-5.16228 - 8.94133i) q^{41} +(1.58114 + 2.73861i) q^{42} +(-1.00000 + 1.73205i) q^{43} -2.16228 q^{44} +(-3.50000 + 6.06218i) q^{45} +(3.00000 - 5.19615i) q^{46} +3.00000 q^{47} +(-1.58114 + 2.73861i) q^{48} +(3.00000 + 5.19615i) q^{49} +(0.500000 + 0.866025i) q^{50} -16.3246 q^{51} -2.16228 q^{53} +(6.32456 + 10.9545i) q^{54} +(1.08114 + 1.87259i) q^{55} +(0.500000 - 0.866025i) q^{56} +5.81139 q^{57} +(5.16228 - 8.94133i) q^{58} +(-5.16228 + 8.94133i) q^{59} +3.16228 q^{60} +(3.74342 - 6.48379i) q^{61} +(-3.58114 - 6.20271i) q^{62} +(-3.50000 - 6.06218i) q^{63} +1.00000 q^{64} +6.83772 q^{66} +(-1.16228 - 2.01312i) q^{67} +(2.58114 + 4.47066i) q^{68} +(-9.48683 + 16.4317i) q^{69} -1.00000 q^{70} +(-2.16228 + 3.74517i) q^{71} +(3.50000 - 6.06218i) q^{72} -2.83772 q^{73} +(0.0811388 - 0.140537i) q^{74} +(-1.58114 - 2.73861i) q^{75} +(-0.918861 - 1.59151i) q^{76} -2.16228 q^{77} -13.4868 q^{79} +(-0.500000 - 0.866025i) q^{80} +(-9.50000 - 16.4545i) q^{81} +(5.16228 - 8.94133i) q^{82} -9.48683 q^{83} +(-1.58114 + 2.73861i) q^{84} +(2.58114 - 4.47066i) q^{85} -2.00000 q^{86} +(-16.3246 + 28.2750i) q^{87} +(-1.08114 - 1.87259i) q^{88} +(-3.66228 - 6.34325i) q^{89} -7.00000 q^{90} +6.00000 q^{92} +(11.3246 + 19.6147i) q^{93} +(1.50000 + 2.59808i) q^{94} +(-0.918861 + 1.59151i) q^{95} -3.16228 q^{96} +(-3.74342 + 6.48379i) q^{97} +(-3.00000 + 5.19615i) q^{98} -15.1359 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} + 4 q^{5} - 2 q^{7} - 4 q^{8} - 14 q^{9} + 2 q^{10} - 2 q^{11} - 4 q^{14} - 2 q^{16} + 4 q^{17} - 28 q^{18} - 10 q^{19} - 2 q^{20} + 2 q^{22} - 12 q^{23} + 4 q^{25} - 2 q^{28} - 8 q^{29}+ \cdots + 28 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 + 4 * q^5 - 2 * q^7 - 4 * q^8 - 14 * q^9 + 2 * q^10 - 2 * q^11 - 4 * q^14 - 2 * q^16 + 4 * q^17 - 28 * q^18 - 10 * q^19 - 2 * q^20 + 2 * q^22 - 12 * q^23 + 4 * q^25 - 2 * q^28 - 8 * q^29 - 16 * q^31 + 2 * q^32 + 20 * q^33 + 8 * q^34 - 2 * q^35 - 14 * q^36 + 6 * q^37 - 20 * q^38 - 4 * q^40 - 8 * q^41 - 4 * q^43 + 4 * q^44 - 14 * q^45 + 12 * q^46 + 12 * q^47 + 12 * q^49 + 2 * q^50 - 40 * q^51 + 4 * q^53 - 2 * q^55 + 2 * q^56 - 40 * q^57 + 8 * q^58 - 8 * q^59 - 4 * q^61 - 8 * q^62 - 14 * q^63 + 4 * q^64 + 40 * q^66 + 8 * q^67 + 4 * q^68 - 4 * q^70 + 4 * q^71 + 14 * q^72 - 24 * q^73 - 6 * q^74 - 10 * q^76 + 4 * q^77 - 16 * q^79 - 2 * q^80 - 38 * q^81 + 8 * q^82 + 4 * q^85 - 8 * q^86 - 40 * q^87 + 2 * q^88 - 2 * q^89 - 28 * q^90 + 24 * q^92 + 20 * q^93 + 6 * q^94 - 10 * q^95 + 4 * q^97 - 12 * q^98 + 28 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1690\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−1.58114	−	2.73861i	−0.912871	−	1.58114i	−0.809989	−	0.586445i	$-0.800527\pi$
$3$	−1.58114	−	2.73861i	−0.912871	−	1.58114i	−0.102882	−	0.994694i	$-0.532806\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	1.58114	−	2.73861i	0.645497	−	1.11803i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i	−0.944911	−	0.327327i	$-0.893852\pi$
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i	0.755929	+	0.654654i	$0.227186\pi$
$8$	−1.00000			−0.353553
$9$	−3.50000	+	6.06218i	−1.16667	+	2.02073i
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	1.08114	+	1.87259i	0.325976	+	0.564606i	0.981709	−	0.190386i	$-0.0609739\pi$
$11$	1.08114	+	1.87259i	0.325976	+	0.564606i	−0.655734	+	0.754992i	$0.727641\pi$
$12$	3.16228			0.912871
$13$		0			0
$13$		0			0
$14$	−1.00000			−0.267261
$15$	−1.58114	−	2.73861i	−0.408248	−	0.707107i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.58114	−	4.47066i	0.626018	−	1.08430i	−0.362325	−	0.932052i	$-0.618017\pi$
$17$	2.58114	−	4.47066i	0.626018	−	1.08430i	0.988343	−	0.152243i	$-0.0486497\pi$
$18$	−7.00000			−1.64992
$19$	−0.918861	+	1.59151i	−0.210801	+	0.365118i	−0.951966	−	0.306205i	$-0.900941\pi$
$19$	−0.918861	+	1.59151i	−0.210801	+	0.365118i	0.741164	+	0.671324i	$0.234274\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$	3.16228			0.690066
$22$	−1.08114	+	1.87259i	−0.230500	+	0.399237i
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	−0.988436	−	0.151642i	$-0.951544\pi$
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	0.362892	−	0.931831i	$-0.381789\pi$
$24$	1.58114	+	2.73861i	0.322749	+	0.559017i
$25$	1.00000			0.200000
$26$		0			0
$27$	12.6491			2.43432
$28$	−0.500000	−	0.866025i	−0.0944911	−	0.163663i
$29$	−5.16228	−	8.94133i	−0.958611	−	1.66036i	−0.725880	−	0.687822i	$-0.758567\pi$
$29$	−5.16228	−	8.94133i	−0.958611	−	1.66036i	−0.232731	−	0.972541i	$-0.574766\pi$
$30$	1.58114	−	2.73861i	0.288675	−	0.500000i
$31$	−7.16228			−1.28638			−0.643192	−	0.765705i	$-0.722390\pi$
$31$	−7.16228			−1.28638			−0.643192	+	0.765705i	$0.722390\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	3.41886	−	5.92164i	0.595147	−	1.03083i
$34$	5.16228			0.885323
$35$	−0.500000	+	0.866025i	−0.0845154	+	0.146385i
$36$	−3.50000	−	6.06218i	−0.583333	−	1.01036i
$37$	−0.0811388	−	0.140537i	−0.0133391	−	0.0231041i	0.859279	−	0.511508i	$-0.170913\pi$
$37$	−0.0811388	−	0.140537i	−0.0133391	−	0.0231041i	−0.872618	+	0.488403i	$0.837579\pi$
$38$	−1.83772			−0.298118
$39$		0			0
$40$	−1.00000			−0.158114
$41$	−5.16228	−	8.94133i	−0.806212	−	1.39640i	−0.915470	−	0.402387i	$-0.868181\pi$
$41$	−5.16228	−	8.94133i	−0.806212	−	1.39640i	0.109257	−	0.994014i	$-0.465153\pi$
$42$	1.58114	+	2.73861i	0.243975	+	0.422577i
$43$	−1.00000	+	1.73205i	−0.152499	+	0.264135i	−0.932145	−	0.362084i	$-0.882065\pi$
$43$	−1.00000	+	1.73205i	−0.152499	+	0.264135i	0.779647	+	0.626219i	$0.215399\pi$
$44$	−2.16228			−0.325976
$45$	−3.50000	+	6.06218i	−0.521749	+	0.903696i
$46$	3.00000	−	5.19615i	0.442326	−	0.766131i
$47$	3.00000			0.437595			0.218797	−	0.975770i	$-0.429787\pi$
$47$	3.00000			0.437595			0.218797	+	0.975770i	$0.429787\pi$
$48$	−1.58114	+	2.73861i	−0.228218	+	0.395285i
$49$	3.00000	+	5.19615i	0.428571	+	0.742307i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	−16.3246			−2.28589
$52$		0			0
$53$	−2.16228			−0.297012			−0.148506	−	0.988912i	$-0.547446\pi$
$53$	−2.16228			−0.297012			−0.148506	+	0.988912i	$0.547446\pi$
$54$	6.32456	+	10.9545i	0.860663	+	1.49071i
$55$	1.08114	+	1.87259i	0.145781	+	0.252500i
$56$	0.500000	−	0.866025i	0.0668153	−	0.115728i
$57$	5.81139			0.769737
$58$	5.16228	−	8.94133i	0.677840	−	1.17405i
$59$	−5.16228	+	8.94133i	−0.672071	+	1.16406i	0.305244	+	0.952274i	$0.401262\pi$
$59$	−5.16228	+	8.94133i	−0.672071	+	1.16406i	−0.977316	+	0.211788i	$0.932071\pi$
$60$	3.16228			0.408248
$61$	3.74342	−	6.48379i	0.479295	−	0.830164i	−0.520423	−	0.853909i	$-0.674226\pi$
$61$	3.74342	−	6.48379i	0.479295	−	0.830164i	0.999718	+	0.0237449i	$0.00755894\pi$
$62$	−3.58114	−	6.20271i	−0.454805	−	0.787746i
$63$	−3.50000	−	6.06218i	−0.440959	−	0.763763i
$64$	1.00000			0.125000
$65$		0			0
$66$	6.83772			0.841665
$67$	−1.16228	−	2.01312i	−0.141995	−	0.245942i	0.786253	−	0.617905i	$-0.212018\pi$
$67$	−1.16228	−	2.01312i	−0.141995	−	0.245942i	−0.928248	+	0.371963i	$0.878685\pi$
$68$	2.58114	+	4.47066i	0.313009	+	0.542148i
$69$	−9.48683	+	16.4317i	−1.14208	+	1.97814i
$70$	−1.00000			−0.119523
$71$	−2.16228	+	3.74517i	−0.256615	+	0.444470i	−0.965333	−	0.261022i	$-0.915941\pi$
$71$	−2.16228	+	3.74517i	−0.256615	+	0.444470i	0.708718	+	0.705492i	$0.249274\pi$
$72$	3.50000	−	6.06218i	0.412479	−	0.714435i
$73$	−2.83772			−0.332130			−0.166065	−	0.986115i	$-0.553106\pi$
$73$	−2.83772			−0.332130			−0.166065	+	0.986115i	$0.553106\pi$
$74$	0.0811388	−	0.140537i	0.00943220	−	0.0163370i
$75$	−1.58114	−	2.73861i	−0.182574	−	0.316228i
$76$	−0.918861	−	1.59151i	−0.105401	−	0.182559i
$77$	−2.16228			−0.246414
$78$		0			0
$79$	−13.4868			−1.51739			−0.758694	−	0.651448i	$-0.774162\pi$
$79$	−13.4868			−1.51739			−0.758694	+	0.651448i	$0.774162\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	−9.50000	−	16.4545i	−1.05556	−	1.82828i
$82$	5.16228	−	8.94133i	0.570078	−	0.987404i
$83$	−9.48683			−1.04132			−0.520658	−	0.853766i	$-0.674313\pi$
$83$	−9.48683			−1.04132			−0.520658	+	0.853766i	$0.674313\pi$
$84$	−1.58114	+	2.73861i	−0.172516	+	0.298807i
$85$	2.58114	−	4.47066i	0.279964	−	0.484912i
$86$	−2.00000			−0.215666
$87$	−16.3246	+	28.2750i	−1.75018	+	3.03139i
$88$	−1.08114	−	1.87259i	−0.115250	−	0.199618i
$89$	−3.66228	−	6.34325i	−0.388201	−	0.672383i	0.604007	−	0.796979i	$-0.293570\pi$
$89$	−3.66228	−	6.34325i	−0.388201	−	0.672383i	−0.992208	+	0.124596i	$0.960237\pi$
$90$	−7.00000			−0.737865
$91$		0			0
$92$	6.00000			0.625543
$93$	11.3246	+	19.6147i	1.17430	+	2.03395i
$94$	1.50000	+	2.59808i	0.154713	+	0.267971i
$95$	−0.918861	+	1.59151i	−0.0942732	+	0.163286i
$96$	−3.16228			−0.322749
$97$	−3.74342	+	6.48379i	−0.380086	+	0.658329i	−0.991074	−	0.133311i	$-0.957439\pi$
$97$	−3.74342	+	6.48379i	−0.380086	+	0.658329i	0.610988	+	0.791640i	$0.290772\pi$
$98$	−3.00000	+	5.19615i	−0.303046	+	0.524891i
$99$	−15.1359			−1.52122
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	5.58114	+	9.66682i	0.555344	+	0.961884i	0.997877	+	0.0651317i	$0.0207468\pi$
$101$	5.58114	+	9.66682i	0.555344	+	0.961884i	−0.442533	+	0.896752i	$0.645920\pi$
$102$	−8.16228	−	14.1375i	−0.808186	−	1.39982i
$103$	0.675445			0.0665535			0.0332768	−	0.999446i	$-0.489406\pi$
$103$	0.675445			0.0665535			0.0332768	+	0.999446i	$0.489406\pi$
$104$		0			0
$105$	3.16228			0.308607
$106$	−1.08114	−	1.87259i	−0.105009	−	0.181882i
$107$	1.74342	+	3.01969i	0.168542	+	0.291924i	0.937908	−	0.346885i	$-0.112761\pi$
$107$	1.74342	+	3.01969i	0.168542	+	0.291924i	−0.769365	+	0.638809i	$0.779427\pi$
$108$	−6.32456	+	10.9545i	−0.608581	+	1.05409i
$109$	−10.6491			−1.02000			−0.510000	−	0.860174i	$-0.670355\pi$
$109$	−10.6491			−1.02000			−0.510000	+	0.860174i	$0.670355\pi$
$110$	−1.08114	+	1.87259i	−0.103083	+	0.178544i
$111$	−0.256584	+	0.444416i	−0.0243538	+	0.0421821i
$112$	1.00000			0.0944911
$113$	4.32456	−	7.49035i	0.406820	−	0.704633i	−0.587711	−	0.809071i	$-0.699971\pi$
$113$	4.32456	−	7.49035i	0.406820	−	0.704633i	0.994531	+	0.104438i	$0.0333043\pi$
$114$	2.90569	+	5.03281i	0.272143	+	0.471366i
$115$	−3.00000	−	5.19615i	−0.279751	−	0.484544i
$116$	10.3246			0.958611
$117$		0			0
$118$	−10.3246			−0.950452
$119$	2.58114	+	4.47066i	0.236613	+	0.409825i
$120$	1.58114	+	2.73861i	0.144338	+	0.250000i
$121$	3.16228	−	5.47723i	0.287480	−	0.497930i
$122$	7.48683			0.677826
$123$	−16.3246	+	28.2750i	−1.47194	+	2.54947i
$124$	3.58114	−	6.20271i	0.321596	−	0.557020i
$125$	1.00000			0.0894427
$126$	3.50000	−	6.06218i	0.311805	−	0.540062i
$127$	−1.66228	−	2.87915i	−0.147503	−	0.255483i	0.782801	−	0.622272i	$-0.213790\pi$
$127$	−1.66228	−	2.87915i	−0.147503	−	0.255483i	−0.930304	+	0.366789i	$0.880457\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	6.32456			0.556846
$130$		0			0
$131$	−10.8114			−0.944595			−0.472298	−	0.881439i	$-0.656575\pi$
$131$	−10.8114			−0.944595			−0.472298	+	0.881439i	$0.656575\pi$
$132$	3.41886	+	5.92164i	0.297574	+	0.515413i
$133$	−0.918861	−	1.59151i	−0.0796754	−	0.138002i
$134$	1.16228	−	2.01312i	0.100405	−	0.173907i
$135$	12.6491			1.08866
$136$	−2.58114	+	4.47066i	−0.221331	+	0.383356i
$137$	7.74342	−	13.4120i	0.661565	−	1.14586i	−0.318640	−	0.947876i	$-0.603226\pi$
$137$	7.74342	−	13.4120i	0.661565	−	1.14586i	0.980204	−	0.197988i	$-0.0634406\pi$
$138$	−18.9737			−1.61515
$139$	6.08114	−	10.5328i	0.515795	−	0.893384i	−0.484036	−	0.875048i	$-0.660830\pi$
$139$	6.08114	−	10.5328i	0.515795	−	0.893384i	0.999832	−	0.0183361i	$-0.00583689\pi$
$140$	−0.500000	−	0.866025i	−0.0422577	−	0.0731925i
$141$	−4.74342	−	8.21584i	−0.399468	−	0.691898i
$142$	−4.32456			−0.362909
$143$		0			0
$144$	7.00000			0.583333
$145$	−5.16228	−	8.94133i	−0.428704	−	0.742537i
$146$	−1.41886	−	2.45754i	−0.117426	−	0.203387i
$147$	9.48683	−	16.4317i	0.782461	−	1.35526i
$148$	0.162278			0.0133391
$149$	8.16228	−	14.1375i	0.668680	−	1.15819i	−0.309594	−	0.950869i	$-0.600193\pi$
$149$	8.16228	−	14.1375i	0.668680	−	1.15819i	0.978273	−	0.207319i	$-0.0664736\pi$
$150$	1.58114	−	2.73861i	0.129099	−	0.223607i
$151$	4.83772			0.393688			0.196844	−	0.980435i	$-0.436931\pi$
$151$	4.83772			0.393688			0.196844	+	0.980435i	$0.436931\pi$
$152$	0.918861	−	1.59151i	0.0745295	−	0.129089i
$153$	18.0680	+	31.2946i	1.46071	+	2.53002i
$154$	−1.08114	−	1.87259i	−0.0871206	−	0.150897i
$155$	−7.16228			−0.575288
$156$		0			0
$157$	−12.1623			−0.970655			−0.485328	−	0.874332i	$-0.661300\pi$
$157$	−12.1623			−0.970655			−0.485328	+	0.874332i	$0.661300\pi$
$158$	−6.74342	−	11.6799i	−0.536477	−	0.929206i
$159$	3.41886	+	5.92164i	0.271133	+	0.469617i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	6.00000			0.472866
$162$	9.50000	−	16.4545i	0.746390	−	1.29279i
$163$	8.74342	−	15.1440i	0.684837	−	1.18617i	−0.288651	−	0.957434i	$-0.593207\pi$
$163$	8.74342	−	15.1440i	0.684837	−	1.18617i	0.973488	−	0.228738i	$-0.0734600\pi$
$164$	10.3246			0.806212
$165$	3.41886	−	5.92164i	0.266158	−	0.460999i
$166$	−4.74342	−	8.21584i	−0.368161	−	0.637673i
$167$	6.66228	+	11.5394i	0.515543	+	0.892946i	0.999837	+	0.0180409i	$0.00574292\pi$
$167$	6.66228	+	11.5394i	0.515543	+	0.892946i	−0.484295	+	0.874905i	$0.660924\pi$
$168$	−3.16228			−0.243975
$169$		0			0
$170$	5.16228			0.395929
$171$	−6.43203	−	11.1406i	−0.491869	−	0.851943i
$172$	−1.00000	−	1.73205i	−0.0762493	−	0.132068i
$173$	−1.08114	+	1.87259i	−0.0821975	+	0.142370i	−0.904194	−	0.427123i	$-0.859527\pi$
$173$	−1.08114	+	1.87259i	−0.0821975	+	0.142370i	0.821996	+	0.569493i	$0.192860\pi$
$174$	−32.6491			−2.47512
$175$	−0.500000	+	0.866025i	−0.0377964	+	0.0654654i
$176$	1.08114	−	1.87259i	0.0814939	−	0.141152i
$177$	32.6491			2.45406
$178$	3.66228	−	6.34325i	0.274499	−	0.475447i
$179$	−11.1623	−	19.3336i	−0.834308	−	1.44506i	−0.894593	−	0.446882i	$-0.852534\pi$
$179$	−11.1623	−	19.3336i	−0.834308	−	1.44506i	0.0602850	−	0.998181i	$-0.480799\pi$
$180$	−3.50000	−	6.06218i	−0.260875	−	0.451848i
$181$	9.81139			0.729275			0.364637	−	0.931150i	$-0.381193\pi$
$181$	9.81139			0.729275			0.364637	+	0.931150i	$0.381193\pi$
$182$		0			0
$183$	−23.6754			−1.75014
$184$	3.00000	+	5.19615i	0.221163	+	0.383065i
$185$	−0.0811388	−	0.140537i	−0.00596545	−	0.0103325i
$186$	−11.3246	+	19.6147i	−0.830357	+	1.43822i
$187$	11.1623			0.816267
$188$	−1.50000	+	2.59808i	−0.109399	+	0.189484i
$189$	−6.32456	+	10.9545i	−0.460044	+	0.796819i
$190$	−1.83772			−0.133322
$191$	−4.74342	+	8.21584i	−0.343222	+	0.594477i	−0.985029	−	0.172389i	$-0.944852\pi$
$191$	−4.74342	+	8.21584i	−0.343222	+	0.594477i	0.641807	+	0.766866i	$0.278185\pi$
$192$	−1.58114	−	2.73861i	−0.114109	−	0.197642i
$193$	−2.00000	−	3.46410i	−0.143963	−	0.249351i	0.785022	−	0.619467i	$-0.212651\pi$
$193$	−2.00000	−	3.46410i	−0.143963	−	0.249351i	−0.928986	+	0.370116i	$0.879318\pi$
$194$	−7.48683			−0.537523
$195$		0			0
$196$	−6.00000			−0.428571
$197$	−9.24342	−	16.0101i	−0.658566	−	1.14067i	−0.980987	−	0.194074i	$-0.937830\pi$
$197$	−9.24342	−	16.0101i	−0.658566	−	1.14067i	0.322421	−	0.946596i	$-0.395503\pi$
$198$	−7.56797	−	13.1081i	−0.537832	−	0.931553i
$199$	0.675445	−	1.16990i	0.0478810	−	0.0829323i	−0.841092	−	0.540893i	$-0.818087\pi$
$199$	0.675445	−	1.16990i	0.0478810	−	0.0829323i	0.888973	+	0.457960i	$0.151420\pi$
$200$	−1.00000			−0.0707107
$201$	−3.67544	+	6.36606i	−0.259246	+	0.449027i
$202$	−5.58114	+	9.66682i	−0.392688	+	0.680155i
$203$	10.3246			0.724642
$204$	8.16228	−	14.1375i	0.571474	−	0.989822i
$205$	−5.16228	−	8.94133i	−0.360549	−	0.624489i
$206$	0.337722	+	0.584952i	0.0235302	+	0.0407556i
$207$	42.0000			2.91920
$208$		0			0
$209$	−3.97367			−0.274864
$210$	1.58114	+	2.73861i	0.109109	+	0.188982i
$211$	−5.91886	−	10.2518i	−0.407471	−	0.705761i	0.587134	−	0.809489i	$-0.300256\pi$
$211$	−5.91886	−	10.2518i	−0.407471	−	0.705761i	−0.994606	+	0.103729i	$0.966923\pi$
$212$	1.08114	−	1.87259i	0.0742529	−	0.128610i
$213$	13.6754			0.937026
$214$	−1.74342	+	3.01969i	−0.119177	+	0.206421i
$215$	−1.00000	+	1.73205i	−0.0681994	+	0.118125i
$216$	−12.6491			−0.860663
$217$	3.58114	−	6.20271i	0.243104	−	0.421068i
$218$	−5.32456	−	9.22240i	−0.360624	−	0.624620i
$219$	4.48683	+	7.77142i	0.303192	+	0.525144i
$220$	−2.16228			−0.145781
$221$		0			0
$222$	−0.513167			−0.0344415
$223$	1.66228	+	2.87915i	0.111314	+	0.192802i	0.916300	−	0.400492i	$-0.131161\pi$
$223$	1.66228	+	2.87915i	0.111314	+	0.192802i	−0.804986	+	0.593294i	$0.797827\pi$
$224$	0.500000	+	0.866025i	0.0334077	+	0.0578638i
$225$	−3.50000	+	6.06218i	−0.233333	+	0.404145i
$226$	8.64911			0.575330
$227$	5.16228	−	8.94133i	0.342632	−	0.593457i	−0.642288	−	0.766463i	$-0.722015\pi$
$227$	5.16228	−	8.94133i	0.342632	−	0.593457i	0.984921	+	0.173006i	$0.0553481\pi$
$228$	−2.90569	+	5.03281i	−0.192434	+	0.333306i
$229$	−2.83772			−0.187522			−0.0937610	−	0.995595i	$-0.529889\pi$
$229$	−2.83772			−0.187522			−0.0937610	+	0.995595i	$0.529889\pi$
$230$	3.00000	−	5.19615i	0.197814	−	0.342624i
$231$	3.41886	+	5.92164i	0.224945	+	0.389615i
$232$	5.16228	+	8.94133i	0.338920	+	0.587027i
$233$	9.48683			0.621503			0.310752	−	0.950491i	$-0.399419\pi$
$233$	9.48683			0.621503			0.310752	+	0.950491i	$0.399419\pi$
$234$		0			0
$235$	3.00000			0.195698
$236$	−5.16228	−	8.94133i	−0.336036	−	0.582031i
$237$	21.3246	+	36.9352i	1.38518	+	2.39920i
$238$	−2.58114	+	4.47066i	−0.167310	+	0.289790i
$239$	−11.1623			−0.722028			−0.361014	−	0.932560i	$-0.617569\pi$
$239$	−11.1623			−0.722028			−0.361014	+	0.932560i	$0.617569\pi$
$240$	−1.58114	+	2.73861i	−0.102062	+	0.176777i
$241$	−12.9868	+	22.4939i	−0.836555	+	1.44896i	0.0562022	+	0.998419i	$0.482101\pi$
$241$	−12.9868	+	22.4939i	−0.836555	+	1.44896i	−0.892758	+	0.450537i	$0.851232\pi$
$242$	6.32456			0.406558
$243$	−11.0680	+	19.1703i	−0.710011	+	1.22977i
$244$	3.74342	+	6.48379i	0.239648	+	0.415082i
$245$	3.00000	+	5.19615i	0.191663	+	0.331970i
$246$	−32.6491			−2.08163
$247$		0			0
$248$	7.16228			0.454805
$249$	15.0000	+	25.9808i	0.950586	+	1.64646i
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$	−6.24342	+	10.8139i	−0.394081	+	0.682568i	−0.992983	−	0.118254i	$-0.962270\pi$
$251$	−6.24342	+	10.8139i	−0.394081	+	0.682568i	0.598902	+	0.800822i	$0.295604\pi$
$252$	7.00000			0.440959
$253$	6.48683	−	11.2355i	0.407824	−	0.706371i
$254$	1.66228	−	2.87915i	0.104301	−	0.180654i
$255$	−16.3246			−1.02228
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$257$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$258$	3.16228	+	5.47723i	0.196875	+	0.340997i
$259$	0.162278			0.0100834
$260$		0			0
$261$	72.2719			4.47352
$262$	−5.40569	−	9.36294i	−0.333965	−	0.578444i
$263$	5.82456	+	10.0884i	0.359157	+	0.622079i	0.987820	−	0.155599i	$-0.0497308\pi$
$263$	5.82456	+	10.0884i	0.359157	+	0.622079i	−0.628663	+	0.777678i	$0.716397\pi$
$264$	−3.41886	+	5.92164i	−0.210416	+	0.364452i
$265$	−2.16228			−0.132828
$266$	0.918861	−	1.59151i	0.0563390	−	0.0975820i
$267$	−11.5811	+	20.0591i	−0.708754	+	1.22760i
$268$	2.32456			0.141995
$269$	−1.25658	+	2.17647i	−0.0766152	+	0.132702i	−0.901788	−	0.432180i	$-0.857745\pi$
$269$	−1.25658	+	2.17647i	−0.0766152	+	0.132702i	0.825172	+	0.564881i	$0.191078\pi$
$270$	6.32456	+	10.9545i	0.384900	+	0.666667i
$271$	3.16228	+	5.47723i	0.192095	+	0.332718i	0.945944	−	0.324329i	$-0.105139\pi$
$271$	3.16228	+	5.47723i	0.192095	+	0.332718i	−0.753850	+	0.657047i	$0.771805\pi$
$272$	−5.16228			−0.313009
$273$		0			0
$274$	15.4868			0.935594
$275$	1.08114	+	1.87259i	0.0651951	+	0.112921i
$276$	−9.48683	−	16.4317i	−0.571040	−	0.989071i
$277$	−0.756584	+	1.31044i	−0.0454587	+	0.0787368i	−0.887859	−	0.460115i	$-0.847808\pi$
$277$	−0.756584	+	1.31044i	−0.0454587	+	0.0787368i	0.842401	+	0.538851i	$0.181142\pi$
$278$	12.1623			0.729445
$279$	25.0680	−	43.4190i	1.50078	−	2.59943i
$280$	0.500000	−	0.866025i	0.0298807	−	0.0517549i
$281$	18.9737			1.13187			0.565937	−	0.824448i	$-0.308515\pi$
$281$	18.9737			1.13187			0.565937	+	0.824448i	$0.308515\pi$
$282$	4.74342	−	8.21584i	0.282466	−	0.489246i
$283$	11.0000	+	19.0526i	0.653882	+	1.13256i	0.982173	+	0.187980i	$0.0601941\pi$
$283$	11.0000	+	19.0526i	0.653882	+	1.13256i	−0.328291	+	0.944577i	$0.606473\pi$
$284$	−2.16228	−	3.74517i	−0.128308	−	0.222235i
$285$	5.81139			0.344237
$286$		0			0
$287$	10.3246			0.609439
$288$	3.50000	+	6.06218i	0.206239	+	0.357217i
$289$	−4.82456	−	8.35637i	−0.283797	−	0.491551i
$290$	5.16228	−	8.94133i	0.303139	−	0.525053i
$291$	23.6754			1.38788
$292$	1.41886	−	2.45754i	0.0830326	−	0.143817i
$293$	−10.9189	+	18.9120i	−0.637887	+	1.10485i	0.348009	+	0.937491i	$0.386858\pi$
$293$	−10.9189	+	18.9120i	−0.637887	+	1.10485i	−0.985896	+	0.167361i	$0.946475\pi$
$294$	18.9737			1.10657
$295$	−5.16228	+	8.94133i	−0.300559	+	0.520584i
$296$	0.0811388	+	0.140537i	0.00471610	+	0.00816852i
$297$	13.6754	+	23.6866i	0.793530	+	1.37443i
$298$	16.3246			0.945656
$299$		0			0
$300$	3.16228			0.182574
$301$	−1.00000	−	1.73205i	−0.0576390	−	0.0998337i
$302$	2.41886	+	4.18959i	0.139190	+	0.241084i
$303$	17.6491	−	30.5692i	1.01391	−	1.75615i
$304$	1.83772			0.105401
$305$	3.74342	−	6.48379i	0.214347	−	0.371261i
$306$	−18.0680	+	31.2946i	−1.03288	+	1.78900i
$307$	−15.6754			−0.894645			−0.447322	−	0.894373i	$-0.647622\pi$
$307$	−15.6754			−0.894645			−0.447322	+	0.894373i	$0.647622\pi$
$308$	1.08114	−	1.87259i	0.0616036	−	0.106701i
$309$	−1.06797	−	1.84978i	−0.0607548	−	0.105230i
$310$	−3.58114	−	6.20271i	−0.203395	−	0.352291i
$311$	−3.48683			−0.197720			−0.0988601	−	0.995101i	$-0.531520\pi$
$311$	−3.48683			−0.197720			−0.0988601	+	0.995101i	$0.531520\pi$
$312$		0			0
$313$	−8.32456			−0.470532			−0.235266	−	0.971931i	$-0.575596\pi$
$313$	−8.32456			−0.470532			−0.235266	+	0.971931i	$0.575596\pi$
$314$	−6.08114	−	10.5328i	−0.343179	−	0.594403i
$315$	−3.50000	−	6.06218i	−0.197203	−	0.341565i
$316$	6.74342	−	11.6799i	0.379347	−	0.657048i
$317$	−12.4868			−0.701330			−0.350665	−	0.936501i	$-0.614044\pi$
$317$	−12.4868			−0.701330			−0.350665	+	0.936501i	$0.614044\pi$
$318$	−3.41886	+	5.92164i	−0.191720	+	0.332069i
$319$	11.1623	−	19.3336i	0.624968	−	1.08248i
$320$	1.00000			0.0559017
$321$	5.51317	−	9.54909i	0.307715	−	0.532978i
$322$	3.00000	+	5.19615i	0.167183	+	0.289570i
$323$	4.74342	+	8.21584i	0.263931	+	0.457141i
$324$	19.0000			1.05556
$325$		0			0
$326$	17.4868			0.968506
$327$	16.8377	+	29.1638i	0.931128	+	1.61276i
$328$	5.16228	+	8.94133i	0.285039	+	0.493702i
$329$	−1.50000	+	2.59808i	−0.0826977	+	0.143237i
$330$	6.83772			0.376404
$331$	−12.3246	+	21.3468i	−0.677419	+	1.17332i	0.298337	+	0.954461i	$0.403568\pi$
$331$	−12.3246	+	21.3468i	−0.677419	+	1.17332i	−0.975756	+	0.218863i	$0.929765\pi$
$332$	4.74342	−	8.21584i	0.260329	−	0.450903i
$333$	1.13594			0.0622493
$334$	−6.66228	+	11.5394i	−0.364544	+	0.631408i
$335$	−1.16228	−	2.01312i	−0.0635020	−	0.109989i
$336$	−1.58114	−	2.73861i	−0.0862582	−	0.149404i
$337$	17.4868			0.952568			0.476284	−	0.879291i	$-0.341983\pi$
$337$	17.4868			0.952568			0.476284	+	0.879291i	$0.341983\pi$
$338$		0			0
$339$	−27.3509			−1.48550
$340$	2.58114	+	4.47066i	0.139982	+	0.242456i
$341$	−7.74342	−	13.4120i	−0.419330	−	0.726300i
$342$	6.43203	−	11.1406i	0.347804	−	0.602415i
$343$	−13.0000			−0.701934
$344$	1.00000	−	1.73205i	0.0539164	−	0.0933859i
$345$	−9.48683	+	16.4317i	−0.510754	+	0.884652i
$346$	−2.16228			−0.116245
$347$	−1.25658	+	2.17647i	−0.0674569	+	0.116839i	−0.897781	−	0.440442i	$-0.854822\pi$
$347$	−1.25658	+	2.17647i	−0.0674569	+	0.116839i	0.830324	+	0.557281i	$0.188155\pi$
$348$	−16.3246	−	28.2750i	−0.875088	−	1.51570i
$349$	8.74342	+	15.1440i	0.468024	+	0.810642i	0.999332	−	0.0365368i	$-0.0116326\pi$
$349$	8.74342	+	15.1440i	0.468024	+	0.810642i	−0.531308	+	0.847179i	$0.678299\pi$
$350$	−1.00000			−0.0534522
$351$		0			0
$352$	2.16228			0.115250
$353$	2.58114	+	4.47066i	0.137380	+	0.237949i	0.926504	−	0.376284i	$-0.122798\pi$
$353$	2.58114	+	4.47066i	0.137380	+	0.237949i	−0.789124	+	0.614234i	$0.789465\pi$
$354$	16.3246	+	28.2750i	0.867640	+	1.50280i
$355$	−2.16228	+	3.74517i	−0.114762	+	0.198773i
$356$	7.32456			0.388201
$357$	8.16228	−	14.1375i	0.431994	−	0.748235i
$358$	11.1623	−	19.3336i	0.589945	−	1.02181i
$359$	6.00000			0.316668			0.158334	−	0.987386i	$-0.449388\pi$
$359$	6.00000			0.316668			0.158334	+	0.987386i	$0.449388\pi$
$360$	3.50000	−	6.06218i	0.184466	−	0.319505i
$361$	7.81139	+	13.5297i	0.411126	+	0.712091i
$362$	4.90569	+	8.49691i	0.257838	+	0.446588i
$363$	−20.0000			−1.04973
$364$		0			0
$365$	−2.83772			−0.148533
$366$	−11.8377	−	20.5035i	−0.618768	−	1.07174i
$367$	−2.32456	−	4.02625i	−0.121341	−	0.210168i	0.798956	−	0.601390i	$-0.205386\pi$
$367$	−2.32456	−	4.02625i	−0.121341	−	0.210168i	−0.920297	+	0.391221i	$0.872053\pi$
$368$	−3.00000	+	5.19615i	−0.156386	+	0.270868i
$369$	72.2719			3.76232
$370$	0.0811388	−	0.140537i	0.00421821	−	0.00730615i
$371$	1.08114	−	1.87259i	0.0561299	−	0.0972199i
$372$	−22.6491			−1.17430
$373$	15.3246	−	26.5429i	0.793475	−	1.37434i	−0.130327	−	0.991471i	$-0.541603\pi$
$373$	15.3246	−	26.5429i	0.793475	−	1.37434i	0.923803	−	0.382869i	$-0.125064\pi$
$374$	5.58114	+	9.66682i	0.288594	+	0.499859i
$375$	−1.58114	−	2.73861i	−0.0816497	−	0.141421i
$376$	−3.00000			−0.154713
$377$		0			0
$378$	−12.6491			−0.650600
$379$	−19.4057	−	33.6116i	−0.996804	−	1.72651i	−0.567590	−	0.823311i	$-0.692124\pi$
$379$	−19.4057	−	33.6116i	−0.996804	−	1.72651i	−0.429214	−	0.903203i	$-0.641209\pi$
$380$	−0.918861	−	1.59151i	−0.0471366	−	0.0816430i
$381$	−5.25658	+	9.10467i	−0.269303	+	0.466446i
$382$	−9.48683			−0.485389
$383$	15.0000	−	25.9808i	0.766464	−	1.32755i	−0.173005	−	0.984921i	$-0.555348\pi$
$383$	15.0000	−	25.9808i	0.766464	−	1.32755i	0.939469	−	0.342634i	$-0.111319\pi$
$384$	1.58114	−	2.73861i	0.0806872	−	0.139754i
$385$	−2.16228			−0.110200
$386$	2.00000	−	3.46410i	0.101797	−	0.176318i
$387$	−7.00000	−	12.1244i	−0.355830	−	0.616316i
$388$	−3.74342	−	6.48379i	−0.190043	−	0.329164i
$389$	12.8377			0.650898			0.325449	−	0.945560i	$-0.394484\pi$
$389$	12.8377			0.650898			0.325449	+	0.945560i	$0.394484\pi$
$390$		0			0
$391$	−30.9737			−1.56641
$392$	−3.00000	−	5.19615i	−0.151523	−	0.262445i
$393$	17.0943	+	29.6082i	0.862294	+	1.49354i
$394$	9.24342	−	16.0101i	0.465677	−	0.806576i
$395$	−13.4868			−0.678596
$396$	7.56797	−	13.1081i	0.380305	−	0.658707i
$397$	19.2434	−	33.3306i	0.965799	−	1.67281i	0.258348	−	0.966052i	$-0.416822\pi$
$397$	19.2434	−	33.3306i	0.965799	−	1.67281i	0.707452	−	0.706762i	$-0.249845\pi$
$398$	1.35089			0.0677140
$399$	−2.90569	+	5.03281i	−0.145467	+	0.251956i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	10.9868	+	19.0298i	0.548656	+	0.950301i	0.998367	+	0.0571262i	$0.0181938\pi$
$401$	10.9868	+	19.0298i	0.548656	+	0.950301i	−0.449711	+	0.893174i	$0.648473\pi$
$402$	−7.35089			−0.366629
$403$		0			0
$404$	−11.1623			−0.555344
$405$	−9.50000	−	16.4545i	−0.472059	−	0.817630i
$406$	5.16228	+	8.94133i	0.256200	+	0.443751i
$407$	0.175445	−	0.303879i	0.00869647	−	0.0150627i
$408$	16.3246			0.808186
$409$	−10.8246	+	18.7487i	−0.535240	+	0.927063i	0.463912	+	0.885881i	$0.346445\pi$
$409$	−10.8246	+	18.7487i	−0.535240	+	0.927063i	−0.999152	+	0.0411812i	$0.986888\pi$
$410$	5.16228	−	8.94133i	0.254947	−	0.441581i
$411$	−48.9737			−2.41569
$412$	−0.337722	+	0.584952i	−0.0166384	+	0.0288185i
$413$	−5.16228	−	8.94133i	−0.254019	−	0.439974i
$414$	21.0000	+	36.3731i	1.03209	+	1.78764i
$415$	−9.48683			−0.465690
$416$		0			0
$417$	−38.4605			−1.88342
$418$	−1.98683	−	3.44130i	−0.0971792	−	0.168319i
$419$	−7.32456	−	12.6865i	−0.357828	−	0.619776i	0.629770	−	0.776782i	$-0.283149\pi$
$419$	−7.32456	−	12.6865i	−0.357828	−	0.619776i	−0.987598	+	0.157006i	$0.949816\pi$
$420$	−1.58114	+	2.73861i	−0.0771517	+	0.133631i
$421$	3.16228			0.154120			0.0770600	−	0.997026i	$-0.475447\pi$
$421$	3.16228			0.154120			0.0770600	+	0.997026i	$0.475447\pi$
$422$	5.91886	−	10.2518i	0.288126	−	0.499048i
$423$	−10.5000	+	18.1865i	−0.510527	+	0.884260i
$424$	2.16228			0.105009
$425$	2.58114	−	4.47066i	0.125204	−	0.216859i
$426$	6.83772	+	11.8433i	0.331289	+	0.573809i
$427$	3.74342	+	6.48379i	0.181157	+	0.313772i
$428$	−3.48683			−0.168542
$429$		0			0
$430$	−2.00000			−0.0964486
$431$	7.74342	+	13.4120i	0.372987	+	0.646033i	0.990024	−	0.140902i	$-0.0450002\pi$
$431$	7.74342	+	13.4120i	0.372987	+	0.646033i	−0.617036	+	0.786935i	$0.711667\pi$
$432$	−6.32456	−	10.9545i	−0.304290	−	0.527046i
$433$	−3.16228	+	5.47723i	−0.151969	+	0.263219i	−0.931951	−	0.362583i	$-0.881895\pi$
$433$	−3.16228	+	5.47723i	−0.151969	+	0.263219i	0.779982	+	0.625802i	$0.215228\pi$
$434$	7.16228			0.343800
$435$	−16.3246	+	28.2750i	−0.782703	+	1.35568i
$436$	5.32456	−	9.22240i	0.255000	−	0.441673i
$437$	11.0263			0.527461
$438$	−4.48683	+	7.77142i	−0.214389	+	0.371333i
$439$	−1.90569	−	3.30076i	−0.0909538	−	0.157537i	0.816959	−	0.576696i	$-0.195658\pi$
$439$	−1.90569	−	3.30076i	−0.0909538	−	0.157537i	−0.907913	+	0.419159i	$0.862325\pi$
$440$	−1.08114	−	1.87259i	−0.0515413	−	0.0892721i
$441$	−42.0000			−2.00000
$442$		0			0
$443$	26.6491			1.26614			0.633069	−	0.774096i	$-0.281795\pi$
$443$	26.6491			1.26614			0.633069	+	0.774096i	$0.281795\pi$
$444$	−0.256584	−	0.444416i	−0.0121769	−	0.0210910i
$445$	−3.66228	−	6.34325i	−0.173609	−	0.300699i
$446$	−1.66228	+	2.87915i	−0.0787111	+	0.136332i
$447$	−51.6228			−2.44167
$448$	−0.500000	+	0.866025i	−0.0236228	+	0.0409159i
$449$	−1.01317	+	1.75486i	−0.0478143	+	0.0828168i	−0.888942	−	0.458020i	$-0.848559\pi$
$449$	−1.01317	+	1.75486i	−0.0478143	+	0.0828168i	0.841128	+	0.540837i	$0.181892\pi$
$450$	−7.00000			−0.329983
$451$	11.1623	−	19.3336i	0.525611	−	0.910385i
$452$	4.32456	+	7.49035i	0.203410	+	0.352316i
$453$	−7.64911	−	13.2486i	−0.359387	−	0.622476i
$454$	10.3246			0.484555
$455$		0			0
$456$	−5.81139			−0.272143
$457$	12.2302	+	21.1834i	0.572107	+	0.990918i	0.996349	+	0.0853696i	$0.0272071\pi$
$457$	12.2302	+	21.1834i	0.572107	+	0.990918i	−0.424242	+	0.905549i	$0.639460\pi$
$458$	−1.41886	−	2.45754i	−0.0662990	−	0.114833i
$459$	32.6491	−	56.5499i	1.52393	−	2.63952i
$460$	6.00000			0.279751
$461$	10.7434	−	18.6081i	0.500371	−	0.866668i	−0.499629	−	0.866239i	$-0.666530\pi$
$461$	10.7434	−	18.6081i	0.500371	−	0.866668i	1.00000		0.000428205i	$-0.000136302\pi$
$462$	−3.41886	+	5.92164i	−0.159060	+	0.275500i
$463$	−12.3246			−0.572771			−0.286385	−	0.958115i	$-0.592454\pi$
$463$	−12.3246			−0.572771			−0.286385	+	0.958115i	$0.592454\pi$
$464$	−5.16228	+	8.94133i	−0.239653	+	0.415091i
$465$	11.3246	+	19.6147i	0.525164	+	0.909610i
$466$	4.74342	+	8.21584i	0.219735	+	0.380591i
$467$	32.6491			1.51082			0.755410	−	0.655252i	$-0.227438\pi$
$467$	32.6491			1.51082			0.755410	+	0.655252i	$0.227438\pi$
$468$		0			0
$469$	2.32456			0.107338
$470$	1.50000	+	2.59808i	0.0691898	+	0.119840i
$471$	19.2302	+	33.3078i	0.886083	+	1.53474i
$472$	5.16228	−	8.94133i	0.237613	−	0.411558i
$473$	−4.32456			−0.198843
$474$	−21.3246	+	36.9352i	−0.979469	+	1.69649i
$475$	−0.918861	+	1.59151i	−0.0421602	+	0.0730237i
$476$	−5.16228			−0.236613
$477$	7.56797	−	13.1081i	0.346514	−	0.600179i
$478$	−5.58114	−	9.66682i	−0.255275	−	0.442150i
$479$	−6.06797	−	10.5100i	−0.277253	−	0.480216i	0.693448	−	0.720506i	$-0.256091\pi$
$479$	−6.06797	−	10.5100i	−0.277253	−	0.480216i	−0.970701	+	0.240291i	$0.922757\pi$
$480$	−3.16228			−0.144338
$481$		0			0
$482$	−25.9737			−1.18307
$483$	−9.48683	−	16.4317i	−0.431666	−	0.747667i
$484$	3.16228	+	5.47723i	0.143740	+	0.248965i
$485$	−3.74342	+	6.48379i	−0.169980	+	0.294414i
$486$	−22.1359			−1.00411
$487$	−0.500000	+	0.866025i	−0.0226572	+	0.0392434i	−0.877132	−	0.480250i	$-0.840546\pi$
$487$	−0.500000	+	0.866025i	−0.0226572	+	0.0392434i	0.854475	+	0.519493i	$0.173879\pi$
$488$	−3.74342	+	6.48379i	−0.169457	+	0.293507i
$489$	−55.2982			−2.50067
$490$	−3.00000	+	5.19615i	−0.135526	+	0.234738i
$491$	−8.75658	−	15.1668i	−0.395179	−	0.684470i	0.597945	−	0.801537i	$-0.295984\pi$
$491$	−8.75658	−	15.1668i	−0.395179	−	0.684470i	−0.993124	+	0.117067i	$0.962651\pi$
$492$	−16.3246	−	28.2750i	−0.735968	−	1.27473i
$493$	−53.2982			−2.40043
$494$		0			0
$495$	−15.1359			−0.680310
$496$	3.58114	+	6.20271i	0.160798	+	0.278510i
$497$	−2.16228	−	3.74517i	−0.0969914	−	0.167994i
$498$	−15.0000	+	25.9808i	−0.672166	+	1.16423i
$499$	22.0000			0.984855			0.492428	−	0.870353i	$-0.336110\pi$
$499$	22.0000			0.984855			0.492428	+	0.870353i	$0.336110\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$	21.0680	−	36.4908i	0.941248	−	1.63029i
$502$	−12.4868			−0.557315
$503$	7.14911	−	12.3826i	0.318763	−	0.552114i	−0.661467	−	0.749974i	$-0.730066\pi$
$503$	7.14911	−	12.3826i	0.318763	−	0.552114i	0.980230	+	0.197860i	$0.0633992\pi$
$504$	3.50000	+	6.06218i	0.155902	+	0.270031i
$505$	5.58114	+	9.66682i	0.248357	+	0.430168i
$506$	12.9737			0.576750
$507$		0			0
$508$	3.32456			0.147503
$509$	−0.486833	−	0.843219i	−0.0215785	−	0.0373750i	0.855035	−	0.518571i	$-0.173536\pi$
$509$	−0.486833	−	0.843219i	−0.0215785	−	0.0373750i	−0.876613	+	0.481196i	$0.840203\pi$
$510$	−8.16228	−	14.1375i	−0.361432	−	0.626018i
$511$	1.41886	−	2.45754i	0.0627667	−	0.108715i
$512$	−1.00000			−0.0441942
$513$	−11.6228	+	20.1312i	−0.513158	+	0.888816i
$514$		0			0
$515$	0.675445			0.0297636
$516$	−3.16228	+	5.47723i	−0.139212	+	0.241121i
$517$	3.24342	+	5.61776i	0.142645	+	0.247069i
$518$	0.0811388	+	0.140537i	0.00356504	+	0.00617482i
$519$	6.83772			0.300143
$520$		0			0
$521$	22.6754			0.993429			0.496715	−	0.867914i	$-0.334540\pi$
$521$	22.6754			0.993429			0.496715	+	0.867914i	$0.334540\pi$
$522$	36.1359	+	62.5893i	1.58163	+	2.73946i
$523$	19.6491	+	34.0333i	0.859196	+	1.48817i	0.872697	+	0.488262i	$0.162369\pi$
$523$	19.6491	+	34.0333i	0.859196	+	1.48817i	−0.0135017	+	0.999909i	$0.504298\pi$
$524$	5.40569	−	9.36294i	0.236149	−	0.409022i
$525$	3.16228			0.138013
$526$	−5.82456	+	10.0884i	−0.253963	+	0.439876i
$527$	−18.4868	+	32.0201i	−0.805299	+	1.39482i
$528$	−6.83772			−0.297574
$529$	−6.50000	+	11.2583i	−0.282609	+	0.489493i
$530$	−1.08114	−	1.87259i	−0.0469617	−	0.0813400i
$531$	−36.1359	−	62.5893i	−1.56817	−	2.71614i
$532$	1.83772			0.0796754
$533$		0			0
$534$	−23.1623			−1.00233
$535$	1.74342	+	3.01969i	0.0753745	+	0.130552i
$536$	1.16228	+	2.01312i	0.0502027	+	0.0869537i
$537$	−35.2982	+	61.1383i	−1.52323	+	2.63831i
$538$	−2.51317			−0.108350
$539$	−6.48683	+	11.2355i	−0.279408	+	0.483948i
$540$	−6.32456	+	10.9545i	−0.272166	+	0.471405i
$541$	−26.8377			−1.15384			−0.576922	−	0.816799i	$-0.695746\pi$
$541$	−26.8377			−1.15384			−0.576922	+	0.816799i	$0.695746\pi$
$542$	−3.16228	+	5.47723i	−0.135831	+	0.235267i
$543$	−15.5132	−	26.8696i	−0.665734	−	1.15308i
$544$	−2.58114	−	4.47066i	−0.110665	−	0.191678i
$545$	−10.6491			−0.456158
$546$		0			0
$547$	−6.64911			−0.284295			−0.142148	−	0.989845i	$-0.545401\pi$
$547$	−6.64911			−0.284295			−0.142148	+	0.989845i	$0.545401\pi$
$548$	7.74342	+	13.4120i	0.330782	+	0.572932i
$549$	26.2039	+	45.3865i	1.11836	+	1.93705i
$550$	−1.08114	+	1.87259i	−0.0460999	+	0.0798474i
$551$	18.9737			0.808305
$552$	9.48683	−	16.4317i	0.403786	−	0.699379i
$553$	6.74342	−	11.6799i	0.286759	−	0.496682i
$554$	−1.51317			−0.0642883
$555$	−0.256584	+	0.444416i	−0.0108914	+	0.0188644i
$556$	6.08114	+	10.5328i	0.257898	+	0.446692i
$557$	7.91886	+	13.7159i	0.335533	+	0.581160i	0.983587	−	0.180434i	$-0.0577503\pi$
$557$	7.91886	+	13.7159i	0.335533	+	0.581160i	−0.648054	+	0.761594i	$0.724417\pi$
$558$	50.1359			2.12242
$559$		0			0
$560$	1.00000			0.0422577
$561$	−17.6491	−	30.5692i	−0.745146	−	1.29063i
$562$	9.48683	+	16.4317i	0.400178	+	0.693128i
$563$	12.0000	−	20.7846i	0.505740	−	0.875967i	−0.494238	−	0.869326i	$-0.664553\pi$
$563$	12.0000	−	20.7846i	0.505740	−	0.875967i	0.999978	−	0.00664037i	$-0.00211371\pi$
$564$	9.48683			0.399468
$565$	4.32456	−	7.49035i	0.181935	−	0.315121i
$566$	−11.0000	+	19.0526i	−0.462364	+	0.800839i
$567$	19.0000			0.797925
$568$	2.16228	−	3.74517i	0.0907272	−	0.157144i
$569$	16.9868	+	29.4221i	0.712125	+	1.23344i	0.964058	+	0.265692i	$0.0856005\pi$
$569$	16.9868	+	29.4221i	0.712125	+	1.23344i	−0.251933	+	0.967745i	$0.581066\pi$
$570$	2.90569	+	5.03281i	0.121706	+	0.210801i
$571$	−25.1359			−1.05191			−0.525953	−	0.850513i	$-0.676291\pi$
$571$	−25.1359			−1.05191			−0.525953	+	0.850513i	$0.676291\pi$
$572$		0			0
$573$	30.0000			1.25327
$574$	5.16228	+	8.94133i	0.215469	+	0.373204i
$575$	−3.00000	−	5.19615i	−0.125109	−	0.216695i
$576$	−3.50000	+	6.06218i	−0.145833	+	0.252591i
$577$	−7.16228			−0.298170			−0.149085	−	0.988824i	$-0.547633\pi$
$577$	−7.16228			−0.298170			−0.149085	+	0.988824i	$0.547633\pi$
$578$	4.82456	−	8.35637i	0.200675	−	0.347579i
$579$	−6.32456	+	10.9545i	−0.262840	+	0.455251i
$580$	10.3246			0.428704
$581$	4.74342	−	8.21584i	0.196790	−	0.340850i
$582$	11.8377	+	20.5035i	0.490689	+	0.849899i
$583$	−2.33772	−	4.04905i	−0.0968186	−	0.167695i
$584$	2.83772			0.117426
$585$		0			0
$586$	−21.8377			−0.902108
$587$	6.48683	+	11.2355i	0.267740	+	0.463740i	0.968278	−	0.249876i	$-0.0803898\pi$
$587$	6.48683	+	11.2355i	0.267740	+	0.463740i	−0.700538	+	0.713615i	$0.747056\pi$
$588$	9.48683	+	16.4317i	0.391230	+	0.677631i
$589$	6.58114	−	11.3989i	0.271171	−	0.469682i
$590$	−10.3246			−0.425055
$591$	−29.2302	+	50.6283i	−1.20237	+	2.08257i
$592$	−0.0811388	+	0.140537i	−0.00333479	+	0.00577602i
$593$	3.35089			0.137605			0.0688023	−	0.997630i	$-0.478082\pi$
$593$	3.35089			0.137605			0.0688023	+	0.997630i	$0.478082\pi$
$594$	−13.6754	+	23.6866i	−0.561110	+	0.971872i
$595$	2.58114	+	4.47066i	0.105816	+	0.183279i
$596$	8.16228	+	14.1375i	0.334340	+	0.579094i
$597$	−4.27189			−0.174837
$598$		0			0
$599$	43.9473			1.79564			0.897820	−	0.440363i	$-0.145150\pi$
$599$	43.9473			1.79564			0.897820	+	0.440363i	$0.145150\pi$
$600$	1.58114	+	2.73861i	0.0645497	+	0.111803i
$601$	−17.1491	−	29.7031i	−0.699527	−	1.21162i	−0.968631	−	0.248505i	$-0.920061\pi$
$601$	−17.1491	−	29.7031i	−0.699527	−	1.21162i	0.269104	−	0.963111i	$-0.413273\pi$
$602$	1.00000	−	1.73205i	0.0407570	−	0.0705931i
$603$	16.2719			0.662642
$604$	−2.41886	+	4.18959i	−0.0984221	+	0.170472i
$605$	3.16228	−	5.47723i	0.128565	−	0.222681i
$606$	35.2982			1.43389
$607$	−2.50000	+	4.33013i	−0.101472	+	0.175754i	−0.912291	−	0.409542i	$-0.865689\pi$
$607$	−2.50000	+	4.33013i	−0.101472	+	0.175754i	0.810819	+	0.585296i	$0.199022\pi$
$608$	0.918861	+	1.59151i	0.0372647	+	0.0645444i
$609$	−16.3246	−	28.2750i	−0.661504	−	1.14576i
$610$	7.48683			0.303133
$611$		0			0
$612$	−36.1359			−1.46071
$613$	10.2434	+	17.7421i	0.413728	+	0.716597i	0.995294	−	0.0969016i	$-0.0308932\pi$
$613$	10.2434	+	17.7421i	0.413728	+	0.716597i	−0.581566	+	0.813499i	$0.697560\pi$
$614$	−7.83772	−	13.5753i	−0.316305	−	0.547856i
$615$	−16.3246	+	28.2750i	−0.658270	+	1.14016i
$616$	2.16228			0.0871206
$617$	−15.9737	+	27.6672i	−0.643076	+	1.11384i	0.341667	+	0.939821i	$0.389009\pi$
$617$	−15.9737	+	27.6672i	−0.643076	+	1.11384i	−0.984742	+	0.174018i	$0.944325\pi$
$618$	1.06797	−	1.84978i	0.0429601	−	0.0744091i
$619$	29.4605			1.18412			0.592059	−	0.805895i	$-0.298315\pi$
$619$	29.4605			1.18412			0.592059	+	0.805895i	$0.298315\pi$
$620$	3.58114	−	6.20271i	0.143822	−	0.249107i
$621$	−37.9473	−	65.7267i	−1.52277	−	2.63752i
$622$	−1.74342	−	3.01969i	−0.0699046	−	0.121078i
$623$	7.32456			0.293452
$624$		0			0
$625$	1.00000			0.0400000
$626$	−4.16228	−	7.20928i	−0.166358	−	0.288141i
$627$	6.28292	+	10.8823i	0.250916	+	0.434598i
$628$	6.08114	−	10.5328i	0.242664	−	0.420306i
$629$	−0.837722			−0.0334022
$630$	3.50000	−	6.06218i	0.139443	−	0.241523i
$631$	−7.16228	+	12.4054i	−0.285126	+	0.493852i	−0.972640	−	0.232319i	$-0.925369\pi$
$631$	−7.16228	+	12.4054i	−0.285126	+	0.493852i	0.687514	+	0.726171i	$0.258702\pi$
$632$	13.4868			0.536477
$633$	−18.7171	+	32.4189i	−0.743937	+	1.28854i
$634$	−6.24342	−	10.8139i	−0.247958	−	0.429475i
$635$	−1.66228	−	2.87915i	−0.0659655	−	0.114256i
$636$	−6.83772			−0.271133
$637$		0			0
$638$	22.3246			0.883838
$639$	−15.1359	−	26.2162i	−0.598769	−	1.03710i
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	4.98683	−	8.63745i	0.196968	−	0.341159i	−0.750576	−	0.660784i	$-0.770224\pi$
$641$	4.98683	−	8.63745i	0.196968	−	0.341159i	0.947544	+	0.319626i	$0.103557\pi$
$642$	11.0263			0.435175
$643$	6.23025	−	10.7911i	0.245697	−	0.425560i	−0.716630	−	0.697453i	$-0.754316\pi$
$643$	6.23025	−	10.7911i	0.245697	−	0.425560i	0.962327	+	0.271893i	$0.0876498\pi$
$644$	−3.00000	+	5.19615i	−0.118217	+	0.204757i
$645$	6.32456			0.249029
$646$	−4.74342	+	8.21584i	−0.186627	+	0.323248i
$647$	7.98683	+	13.8336i	0.313995	+	0.543855i	0.979223	−	0.202785i	$-0.0649992\pi$
$647$	7.98683	+	13.8336i	0.313995	+	0.543855i	−0.665229	+	0.746640i	$0.731666\pi$
$648$	9.50000	+	16.4545i	0.373195	+	0.646393i
$649$	−22.3246			−0.876315
$650$		0			0
$651$	−22.6491			−0.887689
$652$	8.74342	+	15.1440i	0.342419	+	0.593086i
$653$	−8.75658	−	15.1668i	−0.342672	−	0.593525i	0.642256	−	0.766490i	$-0.277998\pi$
$653$	−8.75658	−	15.1668i	−0.342672	−	0.593525i	−0.984928	+	0.172965i	$0.944665\pi$
$654$	−16.8377	+	29.1638i	−0.658407	+	1.14039i
$655$	−10.8114			−0.422436
$656$	−5.16228	+	8.94133i	−0.201553	+	0.349100i
$657$	9.93203	−	17.2028i	0.387485	−	0.671144i
$658$	−3.00000			−0.116952
$659$	−11.6491	+	20.1769i	−0.453785	+	0.785979i	−0.998617	−	0.0525663i	$-0.983260\pi$
$659$	−11.6491	+	20.1769i	−0.453785	+	0.785979i	0.544833	+	0.838545i	$0.316593\pi$
$660$	3.41886	+	5.92164i	0.133079	+	0.230500i
$661$	−5.41886	−	9.38574i	−0.210769	−	0.365063i	0.741186	−	0.671299i	$-0.234264\pi$
$661$	−5.41886	−	9.38574i	−0.210769	−	0.365063i	−0.951956	+	0.306236i	$0.900930\pi$
$662$	−24.6491			−0.958015
$663$		0			0
$664$	9.48683			0.368161
$665$	−0.918861	−	1.59151i	−0.0356319	−	0.0617163i
$666$	0.567972	+	0.983756i	0.0220085	+	0.0381198i
$667$	−30.9737	+	53.6480i	−1.19931	+	2.07726i
$668$	−13.3246			−0.515543
$669$	5.25658	−	9.10467i	0.203231	−	0.352007i
$670$	1.16228	−	2.01312i	0.0449027	−	0.0777738i
$671$	16.1886			0.624954
$672$	1.58114	−	2.73861i	0.0609938	−	0.105644i
$673$	−7.48683	−	12.9676i	−0.288596	−	0.499863i	0.684879	−	0.728657i	$-0.259855\pi$
$673$	−7.48683	−	12.9676i	−0.288596	−	0.499863i	−0.973475	+	0.228794i	$0.926522\pi$
$674$	8.74342	+	15.1440i	0.336784	+	0.583327i
$675$	12.6491			0.486864
$676$		0			0
$677$	−12.9737			−0.498618			−0.249309	−	0.968424i	$-0.580204\pi$
$677$	−12.9737			−0.498618			−0.249309	+	0.968424i	$0.580204\pi$
$678$	−13.6754	−	23.6866i	−0.525202	−	0.909677i
$679$	−3.74342	−	6.48379i	−0.143659	−	0.248825i
$680$	−2.58114	+	4.47066i	−0.0989822	+	0.171442i
$681$	−32.6491			−1.25112
$682$	7.74342	−	13.4120i	0.296511	−	0.513572i
$683$	9.83772	−	17.0394i	0.376430	−	0.651996i	−0.614110	−	0.789220i	$-0.710485\pi$
$683$	9.83772	−	17.0394i	0.376430	−	0.651996i	0.990540	+	0.137225i	$0.0438182\pi$
$684$	12.8641			0.491869
$685$	7.74342	−	13.4120i	0.295861	−	0.512446i
$686$	−6.50000	−	11.2583i	−0.248171	−	0.429845i
$687$	4.48683	+	7.77142i	0.171183	+	0.296498i
$688$	2.00000			0.0762493
$689$		0			0
$690$	−18.9737			−0.722315
$691$	−18.5680	−	32.1607i	−0.706359	−	1.22345i	−0.966199	−	0.257798i	$-0.917003\pi$
$691$	−18.5680	−	32.1607i	−0.706359	−	1.22345i	0.259840	−	0.965652i	$-0.416330\pi$
$692$	−1.08114	−	1.87259i	−0.0410987	−	0.0711851i
$693$	7.56797	−	13.1081i	0.287483	−	0.497936i
$694$	−2.51317			−0.0953985
$695$	6.08114	−	10.5328i	0.230671	−	0.399533i
$696$	16.3246	−	28.2750i	0.618781	−	1.07176i
$697$	−53.2982			−2.01881
$698$	−8.74342	+	15.1440i	−0.330943	+	0.573210i
$699$	−15.0000	−	25.9808i	−0.567352	−	0.982683i
$700$	−0.500000	−	0.866025i	−0.0188982	−	0.0327327i
$701$	−23.1623			−0.874827			−0.437414	−	0.899260i	$-0.644105\pi$
$701$	−23.1623			−0.874827			−0.437414	+	0.899260i	$0.644105\pi$
$702$		0			0
$703$	0.298221			0.0112476
$704$	1.08114	+	1.87259i	0.0407470	+	0.0705758i
$705$	−4.74342	−	8.21584i	−0.178647	−	0.309426i
$706$	−2.58114	+	4.47066i	−0.0971424	+	0.168256i
$707$	−11.1623			−0.419801
$708$	−16.3246	+	28.2750i	−0.613514	+	1.06264i
$709$	20.7434	−	35.9287i	0.779035	−	1.34933i	−0.153463	−	0.988154i	$-0.549043\pi$
$709$	20.7434	−	35.9287i	0.779035	−	1.34933i	0.932498	−	0.361174i	$-0.117624\pi$
$710$	−4.32456			−0.162298
$711$	47.2039	−	81.7596i	1.77029	−	3.06622i
$712$	3.66228	+	6.34325i	0.137250	+	0.237723i
$713$	21.4868	+	37.2163i	0.804688	+	1.39376i
$714$	16.3246			0.610931
$715$		0			0
$716$	22.3246			0.834308
$717$	17.6491	+	30.5692i	0.659118	+	1.14163i
$718$	3.00000	+	5.19615i	0.111959	+	0.193919i
$719$	−6.00000	+	10.3923i	−0.223762	+	0.387568i	−0.955947	−	0.293538i	$-0.905167\pi$
$719$	−6.00000	+	10.3923i	−0.223762	+	0.387568i	0.732185	+	0.681106i	$0.238501\pi$
$720$	7.00000			0.260875
$721$	−0.337722	+	0.584952i	−0.0125774	+	0.0217848i
$722$	−7.81139	+	13.5297i	−0.290710	+	0.503524i
$723$	82.1359			3.05467
$724$	−4.90569	+	8.49691i	−0.182319	+	0.315785i
$725$	−5.16228	−	8.94133i	−0.191722	−	0.332073i
$726$	−10.0000	−	17.3205i	−0.371135	−	0.642824i
$727$	−20.6754			−0.766810			−0.383405	−	0.923580i	$-0.625249\pi$
$727$	−20.6754			−0.766810			−0.383405	+	0.923580i	$0.625249\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$	−1.41886	−	2.45754i	−0.0525144	−	0.0909576i
$731$	5.16228	+	8.94133i	0.190934	+	0.330707i
$732$	11.8377	−	20.5035i	0.437535	−	0.757833i
$733$	−8.48683			−0.313468			−0.156734	−	0.987641i	$-0.550097\pi$
$733$	−8.48683			−0.313468			−0.156734	+	0.987641i	$0.550097\pi$
$734$	2.32456	−	4.02625i	0.0858009	−	0.148612i
$735$	9.48683	−	16.4317i	0.349927	−	0.606092i
$736$	−6.00000			−0.221163
$737$	2.51317	−	4.35293i	0.0925737	−	0.160342i
$738$	36.1359	+	62.5893i	1.33018	+	2.30394i
$739$	−22.4057	−	38.8078i	−0.824207	−	1.42757i	−0.902524	−	0.430640i	$-0.858288\pi$
$739$	−22.4057	−	38.8078i	−0.824207	−	1.42757i	0.0783172	−	0.996928i	$-0.475045\pi$
$740$	0.162278			0.00596545
$741$		0			0
$742$	2.16228			0.0793797
$743$	−9.00000	−	15.5885i	−0.330178	−	0.571885i	0.652369	−	0.757902i	$-0.273775\pi$
$743$	−9.00000	−	15.5885i	−0.330178	−	0.571885i	−0.982547	+	0.186017i	$0.940442\pi$
$744$	−11.3246	−	19.6147i	−0.415178	−	0.719110i
$745$	8.16228	−	14.1375i	0.299043	−	0.517957i
$746$	30.6491			1.12214
$747$	33.2039	−	57.5109i	1.21487	−	2.10421i
$748$	−5.58114	+	9.66682i	−0.204067	+	0.353454i
$749$	−3.48683			−0.127406
$750$	1.58114	−	2.73861i	0.0577350	−	0.100000i
$751$	17.4868	+	30.2881i	0.638104	+	1.10523i	0.985849	+	0.167639i	$0.0536142\pi$
$751$	17.4868	+	30.2881i	0.638104	+	1.10523i	−0.347745	+	0.937589i	$0.613052\pi$
$752$	−1.50000	−	2.59808i	−0.0546994	−	0.0947421i
$753$	39.4868			1.43898
$754$		0			0
$755$	4.83772			0.176063
$756$	−6.32456	−	10.9545i	−0.230022	−	0.398410i
$757$	−17.0811	−	29.5854i	−0.620825	−	1.07530i	−0.989332	−	0.145675i	$-0.953465\pi$
$757$	−17.0811	−	29.5854i	−0.620825	−	1.07530i	0.368508	−	0.929625i	$-0.379869\pi$
$758$	19.4057	−	33.6116i	0.704847	−	1.22083i
$759$	−41.0263			−1.48916
$760$	0.918861	−	1.59151i	0.0333306	−	0.0577303i
$761$	−4.14911	+	7.18647i	−0.150405	+	0.260509i	−0.931376	−	0.364058i	$-0.881391\pi$
$761$	−4.14911	+	7.18647i	−0.150405	+	0.260509i	0.780971	+	0.624567i	$0.214724\pi$
$762$	−10.5132			−0.380852
$763$	5.32456	−	9.22240i	0.192762	−	0.333873i
$764$	−4.74342	−	8.21584i	−0.171611	−	0.297239i
$765$	18.0680	+	31.2946i	0.653249	+	1.13146i
$766$	30.0000			1.08394
$767$		0			0
$768$	3.16228			0.114109
$769$	3.16228	+	5.47723i	0.114035	+	0.197514i	0.917393	−	0.397981i	$-0.130289\pi$
$769$	3.16228	+	5.47723i	0.114035	+	0.197514i	−0.803359	+	0.595495i	$0.796956\pi$
$770$	−1.08114	−	1.87259i	−0.0389615	−	0.0674834i
$771$		0			0
$772$	4.00000			0.143963
$773$	23.8925	−	41.3831i	0.859354	−	1.48845i	−0.0131912	−	0.999913i	$-0.504199\pi$
$773$	23.8925	−	41.3831i	0.859354	−	1.48845i	0.872546	−	0.488533i	$-0.162468\pi$
$774$	7.00000	−	12.1244i	0.251610	−	0.435801i
$775$	−7.16228			−0.257277
$776$	3.74342	−	6.48379i	0.134381	−	0.232754i
$777$	−0.256584	−	0.444416i	−0.00920488	−	0.0159433i
$778$	6.41886	+	11.1178i	0.230127	+	0.398592i
$779$	18.9737			0.679802
$780$		0			0
$781$	−9.35089			−0.334601
$782$	−15.4868	−	26.8240i	−0.553808	−	0.959224i
$783$	−65.2982	−	113.100i	−2.33357	−	4.04186i
$784$	3.00000	−	5.19615i	0.107143	−	0.185577i
$785$	−12.1623			−0.434090
$786$	−17.0943	+	29.6082i	−0.609734	+	1.05609i
$787$	−23.0680	+	39.9549i	−0.822284	+	1.42424i	0.0816928	+	0.996658i	$0.473967\pi$
$787$	−23.0680	+	39.9549i	−0.822284	+	1.42424i	−0.903977	+	0.427581i	$0.859366\pi$
$788$	18.4868			0.658566
$789$	18.4189	−	31.9024i	0.655729	−	1.13576i
$790$	−6.74342	−	11.6799i	−0.239920	−	0.415554i
$791$	4.32456	+	7.49035i	0.153763	+	0.266326i
$792$	15.1359			0.537832
$793$		0			0
$794$	38.4868			1.36585
$795$	3.41886	+	5.92164i	0.121255	+	0.210019i
$796$	0.675445	+	1.16990i	0.0239405	+	0.0414662i
$797$	6.83772	−	11.8433i	0.242205	−	0.419511i	−0.719137	−	0.694868i	$-0.755463\pi$
$797$	6.83772	−	11.8433i	0.242205	−	0.419511i	0.961342	+	0.275357i	$0.0887962\pi$
$798$	−5.81139			−0.205721
$799$	7.74342	−	13.4120i	0.273942	−	0.474482i
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	51.2719			1.81160
$802$	−10.9868	+	19.0298i	−0.387959	+	0.671964i
$803$	−3.06797	−	5.31388i	−0.108266	−	0.187523i
$804$	−3.67544	−	6.36606i	−0.129623	−	0.224514i
$805$	6.00000			0.211472
$806$		0			0
$807$	7.94733			0.279759
$808$	−5.58114	−	9.66682i	−0.196344	−	0.340077i
$809$	−5.16228	−	8.94133i	−0.181496	−	0.314360i	0.760894	−	0.648876i	$-0.224761\pi$
$809$	−5.16228	−	8.94133i	−0.181496	−	0.314360i	−0.942390	+	0.334516i	$0.891427\pi$
$810$	9.50000	−	16.4545i	0.333796	−	0.578152i
$811$	6.16228			0.216387			0.108193	−	0.994130i	$-0.465493\pi$
$811$	6.16228			0.216387			0.108193	+	0.994130i	$0.465493\pi$
$812$	−5.16228	+	8.94133i	−0.181160	+	0.313779i
$813$	10.0000	−	17.3205i	0.350715	−	0.607457i
$814$	0.350889			0.0122987
$815$	8.74342	−	15.1440i	0.306269	−	0.530473i
$816$	8.16228	+	14.1375i	0.285737	+	0.494911i
$817$	−1.83772	−	3.18303i	−0.0642938	−	0.111360i
$818$	−21.6491			−0.756943
$819$		0			0
$820$	10.3246			0.360549
$821$	−2.58114	−	4.47066i	−0.0900824	−	0.156027i	0.817463	−	0.575981i	$-0.195380\pi$
$821$	−2.58114	−	4.47066i	−0.0900824	−	0.156027i	−0.907546	+	0.419954i	$0.862046\pi$
$822$	−24.4868	−	42.4124i	−0.854076	−	1.47930i
$823$	−23.5000	+	40.7032i	−0.819159	+	1.41882i	0.0871445	+	0.996196i	$0.472226\pi$
$823$	−23.5000	+	40.7032i	−0.819159	+	1.41882i	−0.906303	+	0.422628i	$0.861108\pi$
$824$	−0.675445			−0.0235302
$825$	3.41886	−	5.92164i	0.119029	−	0.206165i
$826$	5.16228	−	8.94133i	0.179619	−	0.311109i
$827$	51.4868			1.79037			0.895186	−	0.445692i	$-0.147042\pi$
$827$	51.4868			1.79037			0.895186	+	0.445692i	$0.147042\pi$
$828$	−21.0000	+	36.3731i	−0.729800	+	1.26405i
$829$	−16.0000	−	27.7128i	−0.555703	−	0.962506i	−0.997848	−	0.0655624i	$-0.979116\pi$
$829$	−16.0000	−	27.7128i	−0.555703	−	0.962506i	0.442145	−	0.896943i	$-0.354217\pi$
$830$	−4.74342	−	8.21584i	−0.164646	−	0.285176i
$831$	4.78505			0.165992
$832$		0			0
$833$	30.9737			1.07317
$834$	−19.2302	−	33.3078i	−0.665889	−	1.15335i
$835$	6.66228	+	11.5394i	0.230558	+	0.399338i
$836$	1.98683	−	3.44130i	0.0687161	−	0.119020i
$837$	−90.5964			−3.13147
$838$	7.32456	−	12.6865i	0.253023	−	0.438248i
$839$	−11.5811	+	20.0591i	−0.399825	+	0.692518i	−0.993704	−	0.112037i	$-0.964263\pi$
$839$	−11.5811	+	20.0591i	−0.399825	+	0.692518i	0.593879	+	0.804555i	$0.297596\pi$
$840$	−3.16228			−0.109109
$841$	−38.7982	+	67.2005i	−1.33787	+	2.31726i
$842$	1.58114	+	2.73861i	0.0544896	+	0.0943788i
$843$	−30.0000	−	51.9615i	−1.03325	−	1.78965i
$844$	11.8377			0.407471
$845$		0			0
$846$	−21.0000			−0.721995
$847$	3.16228	+	5.47723i	0.108657	+	0.188200i
$848$	1.08114	+	1.87259i	0.0371265	+	0.0643049i
$849$	34.7851	−	60.2495i	1.19382	−	2.06776i
$850$	5.16228			0.177065
$851$	−0.486833	+	0.843219i	−0.0166884	+	0.0289052i
$852$	−6.83772	+	11.8433i	−0.234257	+	0.405744i
$853$	−56.2719			−1.92671			−0.963356	−	0.268225i	$-0.913563\pi$
$853$	−56.2719			−1.92671			−0.963356	+	0.268225i	$0.913563\pi$
$854$	−3.74342	+	6.48379i	−0.128097	+	0.221871i
$855$	−6.43203	−	11.1406i	−0.219971	−	0.381000i
$856$	−1.74342	−	3.01969i	−0.0595887	−	0.103211i
$857$	30.1359			1.02942			0.514712	−	0.857363i	$-0.327899\pi$
$857$	30.1359			1.02942			0.514712	+	0.857363i	$0.327899\pi$
$858$		0			0
$859$	47.1359			1.60826			0.804129	−	0.594455i	$-0.202632\pi$
$859$	47.1359			1.60826			0.804129	+	0.594455i	$0.202632\pi$
$860$	−1.00000	−	1.73205i	−0.0340997	−	0.0590624i
$861$	−16.3246	−	28.2750i	−0.556339	−	0.963608i
$862$	−7.74342	+	13.4120i	−0.263742	+	0.456814i
$863$	18.0000			0.612727			0.306364	−	0.951915i	$-0.400888\pi$
$863$	18.0000			0.612727			0.306364	+	0.951915i	$0.400888\pi$
$864$	6.32456	−	10.9545i	0.215166	−	0.372678i
$865$	−1.08114	+	1.87259i	−0.0367598	+	0.0636699i
$866$	−6.32456			−0.214917
$867$	−15.2566	+	26.4252i	−0.518141	+	0.897446i
$868$	3.58114	+	6.20271i	0.121552	+	0.210534i
$869$	−14.5811	−	25.2553i	−0.494631	−	0.856726i
$870$	−32.6491			−1.10691
$871$		0			0
$872$	10.6491			0.360624
$873$	−26.2039	−	45.3865i	−0.886868	−	1.53610i
$874$	5.51317	+	9.54909i	0.186486	+	0.323003i
$875$	−0.500000	+	0.866025i	−0.0169031	+	0.0292770i
$876$	−8.97367			−0.303192
$877$	−11.8377	+	20.5035i	−0.399731	+	0.692355i	−0.993693	−	0.112139i	$-0.964230\pi$
$877$	−11.8377	+	20.5035i	−0.399731	+	0.692355i	0.593961	+	0.804494i	$0.297563\pi$
$878$	1.90569	−	3.30076i	0.0643141	−	0.111395i
$879$	69.0569			2.32923
$880$	1.08114	−	1.87259i	0.0364452	−	0.0631249i
$881$	28.9868	+	50.2067i	0.976591	+	1.69151i	0.674581	+	0.738201i	$0.264324\pi$
$881$	28.9868	+	50.2067i	0.976591	+	1.69151i	0.302010	+	0.953305i	$0.402342\pi$
$882$	−21.0000	−	36.3731i	−0.707107	−	1.22474i
$883$	35.4868			1.19423			0.597114	−	0.802157i	$-0.296314\pi$
$883$	35.4868			1.19423			0.597114	+	0.802157i	$0.296314\pi$
$884$		0			0
$885$	32.6491			1.09749
$886$	13.3246	+	23.0788i	0.447647	+	0.775348i
$887$	−18.3114	−	31.7163i	−0.614836	−	1.06493i	−0.990413	−	0.138136i	$-0.955889\pi$
$887$	−18.3114	−	31.7163i	−0.614836	−	1.06493i	0.375577	−	0.926791i	$-0.377445\pi$
$888$	0.256584	−	0.444416i	0.00861038	−	0.0149136i
$889$	3.32456			0.111502
$890$	3.66228	−	6.34325i	0.122760	−	0.212626i
$891$	20.5416	−	35.5792i	0.688171	−	1.19195i
$892$	−3.32456			−0.111314
$893$	−2.75658	+	4.77454i	−0.0922455	+	0.159774i
$894$	−25.8114	−	44.7066i	−0.863262	−	1.49521i
$895$	−11.1623	−	19.3336i	−0.373114	−	0.646252i
$896$	−1.00000			−0.0334077
$897$		0			0
$898$	−2.02633			−0.0676196
$899$	36.9737	+	64.0403i	1.23314	+	2.13586i
$900$	−3.50000	−	6.06218i	−0.116667	−	0.202073i
$901$	−5.58114	+	9.66682i	−0.185935	+	0.322048i
$902$	22.3246			0.743326
$903$	−3.16228	+	5.47723i	−0.105234	+	0.182271i
$904$	−4.32456	+	7.49035i	−0.143833	+	0.249125i
$905$	9.81139			0.326142
$906$	7.64911	−	13.2486i	0.254125	−	0.440157i
$907$	8.06797	+	13.9741i	0.267893	+	0.464004i	0.968317	−	0.249723i	$-0.0803394\pi$
$907$	8.06797	+	13.9741i	0.267893	+	0.464004i	−0.700425	+	0.713726i	$0.747006\pi$
$908$	5.16228	+	8.94133i	0.171316	+	0.296728i
$909$	−78.1359			−2.59161
$910$		0			0
$911$	−17.2982			−0.573116			−0.286558	−	0.958063i	$-0.592511\pi$
$911$	−17.2982			−0.573116			−0.286558	+	0.958063i	$0.592511\pi$
$912$	−2.90569	−	5.03281i	−0.0962171	−	0.166653i
$913$	−10.2566	−	17.7649i	−0.339443	−	0.587933i
$914$	−12.2302	+	21.1834i	−0.404541	+	0.700685i
$915$	−23.6754			−0.782686
$916$	1.41886	−	2.45754i	0.0468805	−	0.0811994i
$917$	5.40569	−	9.36294i	0.178512	−	0.309191i
$918$	65.2982			2.15516
$919$	5.83772	−	10.1112i	0.192569	−	0.333539i	−0.753532	−	0.657411i	$-0.771652\pi$
$919$	5.83772	−	10.1112i	0.192569	−	0.333539i	0.946101	+	0.323872i	$0.104985\pi$
$920$	3.00000	+	5.19615i	0.0989071	+	0.171312i
$921$	24.7851	+	42.9290i	0.816695	+	1.41456i
$922$	21.4868			0.707631
$923$		0			0
$924$	−6.83772			−0.224945
$925$	−0.0811388	−	0.140537i	−0.00266783	−	0.00462081i
$926$	−6.16228	−	10.6734i	−0.202505	−	0.350749i
$927$	−2.36406	+	4.09467i	−0.0776458	+	0.134486i
$928$	−10.3246			−0.338920
$929$	27.0000	−	46.7654i	0.885841	−	1.53432i	0.0410949	−	0.999155i	$-0.486915\pi$
$929$	27.0000	−	46.7654i	0.885841	−	1.53432i	0.844746	−	0.535167i	$-0.179751\pi$
$930$	−11.3246	+	19.6147i	−0.371347	+	0.643192i
$931$	−11.0263			−0.361374
$932$	−4.74342	+	8.21584i	−0.155376	+	0.269119i
$933$	5.51317	+	9.54909i	0.180493	+	0.312623i
$934$	16.3246	+	28.2750i	0.534156	+	0.925185i
$935$	11.1623			0.365046
$936$		0			0
$937$	27.6754			0.904117			0.452059	−	0.891988i	$-0.350690\pi$
$937$	27.6754			0.904117			0.452059	+	0.891988i	$0.350690\pi$
$938$	1.16228	+	2.01312i	0.0379497	+	0.0657308i
$939$	13.1623	+	22.7977i	0.429535	+	0.743976i
$940$	−1.50000	+	2.59808i	−0.0489246	+	0.0847399i
$941$	−22.3246			−0.727760			−0.363880	−	0.931446i	$-0.618548\pi$
$941$	−22.3246			−0.727760			−0.363880	+	0.931446i	$0.618548\pi$
$942$	−19.2302	+	33.3078i	−0.626555	+	1.08523i
$943$	−30.9737	+	53.6480i	−1.00864	+	1.74702i
$944$	10.3246			0.336036
$945$	−6.32456	+	10.9545i	−0.205738	+	0.356348i
$946$	−2.16228	−	3.74517i	−0.0703017	−	0.121766i
$947$	−0.905694	−	1.56871i	−0.0294311	−	0.0509762i	0.850935	−	0.525271i	$-0.176036\pi$
$947$	−0.905694	−	1.56871i	−0.0294311	−	0.0509762i	−0.880366	+	0.474295i	$0.842703\pi$
$948$	−42.6491			−1.38518
$949$		0			0
$950$	−1.83772			−0.0596236
$951$	19.7434	+	34.1966i	0.640224	+	1.10890i
$952$	−2.58114	−	4.47066i	−0.0836552	−	0.144895i
$953$	1.25658	−	2.17647i	0.0407047	−	0.0705027i	−0.844955	−	0.534837i	$-0.820373\pi$
$953$	1.25658	−	2.17647i	0.0407047	−	0.0705027i	0.885660	+	0.464334i	$0.153706\pi$
$954$	15.1359			0.490044
$955$	−4.74342	+	8.21584i	−0.153493	+	0.265858i
$956$	5.58114	−	9.66682i	0.180507	−	0.312647i
$957$	−70.5964			−2.28206
$958$	6.06797	−	10.5100i	0.196047	−	0.339564i
$959$	7.74342	+	13.4120i	0.250048	+	0.433096i
$960$	−1.58114	−	2.73861i	−0.0510310	−	0.0883883i
$961$	20.2982			0.654781
$962$		0			0
$963$	−24.4078			−0.786531
$964$	−12.9868	−	22.4939i	−0.418278	−	0.724478i
$965$	−2.00000	−	3.46410i	−0.0643823	−	0.111513i
$966$	9.48683	−	16.4317i	0.305234	−	0.528681i
$967$	16.6228			0.534552			0.267276	−	0.963620i	$-0.413876\pi$
$967$	16.6228			0.534552			0.267276	+	0.963620i	$0.413876\pi$
$968$	−3.16228	+	5.47723i	−0.101639	+	0.176045i
$969$	15.0000	−	25.9808i	0.481869	−	0.834622i
$970$	−7.48683			−0.240388
$971$	−29.8925	+	51.7754i	−0.959297	+	1.66155i	−0.235083	+	0.971975i	$0.575536\pi$
$971$	−29.8925	+	51.7754i	−0.959297	+	1.66155i	−0.724214	+	0.689576i	$0.757797\pi$
$972$	−11.0680	−	19.1703i	−0.355005	−	0.614887i
$973$	6.08114	+	10.5328i	0.194952	+	0.337667i
$974$	−1.00000			−0.0320421
$975$		0			0
$976$	−7.48683			−0.239648
$977$	9.48683	+	16.4317i	0.303511	+	0.525696i	0.976929	−	0.213566i	$-0.0685079\pi$
$977$	9.48683	+	16.4317i	0.303511	+	0.525696i	−0.673418	+	0.739262i	$0.735175\pi$
$978$	−27.6491	−	47.8897i	−0.884121	−	1.53134i
$979$	7.91886	−	13.7159i	0.253088	−	0.438361i
$980$	−6.00000			−0.191663
$981$	37.2719	−	64.5568i	1.19000	−	2.06114i
$982$	8.75658	−	15.1668i	0.279434	−	0.483994i
$983$	−30.3509			−0.968043			−0.484022	−	0.875056i	$-0.660824\pi$
$983$	−30.3509			−0.968043			−0.484022	+	0.875056i	$0.660824\pi$
$984$	16.3246	−	28.2750i	0.520408	−	0.901373i
$985$	−9.24342	−	16.0101i	−0.294520	−	0.510123i
$986$	−26.6491	−	46.1576i	−0.848681	−	1.46996i
$987$	9.48683			0.301969
$988$		0			0
$989$	12.0000			0.381578
$990$	−7.56797	−	13.1081i	−0.240526	−	0.416603i
$991$	19.6491	+	34.0333i	0.624175	+	1.08110i	0.988700	+	0.149909i	$0.0478979\pi$
$991$	19.6491	+	34.0333i	0.624175	+	1.08110i	−0.364525	+	0.931193i	$0.618769\pi$
$992$	−3.58114	+	6.20271i	−0.113701	+	0.196936i
$993$	77.9473			2.47358
$994$	2.16228	−	3.74517i	0.0685833	−	0.118790i
$995$	0.675445	−	1.16990i	0.0214130	−	0.0370885i
$996$	−30.0000			−0.950586
$997$	−5.91886	+	10.2518i	−0.187452	+	0.324677i	−0.944400	−	0.328798i	$-0.893356\pi$
$997$	−5.91886	+	10.2518i	−0.187452	+	0.324677i	0.756948	+	0.653475i	$0.226690\pi$
$998$	11.0000	+	19.0526i	0.348199	+	0.603098i
$999$	−1.02633	−	1.77766i	−0.0324718	−	0.0562428i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1690.2.e.m.991.1		4
13.2	odd	12		1690.2.d.g.1351.4		4
13.3	even	3		1690.2.a.k.1.2		2
13.4	even	6		130.2.e.c.61.1	✓	4
13.5	odd	4		1690.2.l.k.361.3		8
13.6	odd	12		1690.2.l.k.1161.1		8
13.7	odd	12		1690.2.l.k.1161.3		8
13.8	odd	4		1690.2.l.k.361.1		8
13.9	even	3	inner	1690.2.e.m.191.1		4
13.10	even	6		1690.2.a.n.1.2		2
13.11	odd	12		1690.2.d.g.1351.2		4
13.12	even	2		130.2.e.c.81.1	yes	4
39.17	odd	6		1170.2.i.q.451.2		4
39.38	odd	2		1170.2.i.q.991.2		4
52.43	odd	6		1040.2.q.m.321.2		4
52.51	odd	2		1040.2.q.m.81.2		4
65.4	even	6		650.2.e.h.451.2		4
65.12	odd	4		650.2.o.g.549.3		8
65.17	odd	12		650.2.o.g.399.2		8
65.29	even	6		8450.2.a.bj.1.1		2
65.38	odd	4		650.2.o.g.549.2		8
65.43	odd	12		650.2.o.g.399.3		8
65.49	even	6		8450.2.a.bc.1.1		2
65.64	even	2		650.2.e.h.601.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.e.c.61.1	✓	4	13.4	even	6
130.2.e.c.81.1	yes	4	13.12	even	2
650.2.e.h.451.2		4	65.4	even	6
650.2.e.h.601.2		4	65.64	even	2
650.2.o.g.399.2		8	65.17	odd	12
650.2.o.g.399.3		8	65.43	odd	12
650.2.o.g.549.2		8	65.38	odd	4
650.2.o.g.549.3		8	65.12	odd	4
1040.2.q.m.81.2		4	52.51	odd	2
1040.2.q.m.321.2		4	52.43	odd	6
1170.2.i.q.451.2		4	39.17	odd	6
1170.2.i.q.991.2		4	39.38	odd	2
1690.2.a.k.1.2		2	13.3	even	3
1690.2.a.n.1.2		2	13.10	even	6
1690.2.d.g.1351.2		4	13.11	odd	12
1690.2.d.g.1351.4		4	13.2	odd	12
1690.2.e.m.191.1		4	13.9	even	3	inner
1690.2.e.m.991.1		4	1.1	even	1	trivial
1690.2.l.k.361.1		8	13.8	odd	4
1690.2.l.k.361.3		8	13.5	odd	4
1690.2.l.k.1161.1		8	13.6	odd	12
1690.2.l.k.1161.3		8	13.7	odd	12
8450.2.a.bc.1.1		2	65.49	even	6
8450.2.a.bj.1.1		2	65.29	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1690 = 2 \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1690.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.58114 - 2.73861i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(1.58114 - 2.73861i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +(-3.50000 + 6.06218i) q^{9} +(0.500000 + 0.866025i) q^{10} +(1.08114 + 1.87259i) q^{11} +3.16228 q^{12} -1.00000 q^{14} +(-1.58114 - 2.73861i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.58114 - 4.47066i) q^{17} -7.00000 q^{18} +(-0.918861 + 1.59151i) q^{19} +(-0.500000 + 0.866025i) q^{20} +3.16228 q^{21} +(-1.08114 + 1.87259i) q^{22} +(-3.00000 - 5.19615i) q^{23} +(1.58114 + 2.73861i) q^{24} +1.00000 q^{25} +12.6491 q^{27} +(-0.500000 - 0.866025i) q^{28} +(-5.16228 - 8.94133i) q^{29} +(1.58114 - 2.73861i) q^{30} -7.16228 q^{31} +(0.500000 - 0.866025i) q^{32} +(3.41886 - 5.92164i) q^{33} +5.16228 q^{34} +(-0.500000 + 0.866025i) q^{35} +(-3.50000 - 6.06218i) q^{36} +(-0.0811388 - 0.140537i) q^{37} -1.83772 q^{38} -1.00000 q^{40} +(-5.16228 - 8.94133i) q^{41} +(1.58114 + 2.73861i) q^{42} +(-1.00000 + 1.73205i) q^{43} -2.16228 q^{44} +(-3.50000 + 6.06218i) q^{45} +(3.00000 - 5.19615i) q^{46} +3.00000 q^{47} +(-1.58114 + 2.73861i) q^{48} +(3.00000 + 5.19615i) q^{49} +(0.500000 + 0.866025i) q^{50} -16.3246 q^{51} -2.16228 q^{53} +(6.32456 + 10.9545i) q^{54} +(1.08114 + 1.87259i) q^{55} +(0.500000 - 0.866025i) q^{56} +5.81139 q^{57} +(5.16228 - 8.94133i) q^{58} +(-5.16228 + 8.94133i) q^{59} +3.16228 q^{60} +(3.74342 - 6.48379i) q^{61} +(-3.58114 - 6.20271i) q^{62} +(-3.50000 - 6.06218i) q^{63} +1.00000 q^{64} +6.83772 q^{66} +(-1.16228 - 2.01312i) q^{67} +(2.58114 + 4.47066i) q^{68} +(-9.48683 + 16.4317i) q^{69} -1.00000 q^{70} +(-2.16228 + 3.74517i) q^{71} +(3.50000 - 6.06218i) q^{72} -2.83772 q^{73} +(0.0811388 - 0.140537i) q^{74} +(-1.58114 - 2.73861i) q^{75} +(-0.918861 - 1.59151i) q^{76} -2.16228 q^{77} -13.4868 q^{79} +(-0.500000 - 0.866025i) q^{80} +(-9.50000 - 16.4545i) q^{81} +(5.16228 - 8.94133i) q^{82} -9.48683 q^{83} +(-1.58114 + 2.73861i) q^{84} +(2.58114 - 4.47066i) q^{85} -2.00000 q^{86} +(-16.3246 + 28.2750i) q^{87} +(-1.08114 - 1.87259i) q^{88} +(-3.66228 - 6.34325i) q^{89} -7.00000 q^{90} +6.00000 q^{92} +(11.3246 + 19.6147i) q^{93} +(1.50000 + 2.59808i) q^{94} +(-0.918861 + 1.59151i) q^{95} -3.16228 q^{96} +(-3.74342 + 6.48379i) q^{97} +(-3.00000 + 5.19615i) q^{98} -15.1359 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} + 4 q^{5} - 2 q^{7} - 4 q^{8} - 14 q^{9} + 2 q^{10} - 2 q^{11} - 4 q^{14} - 2 q^{16} + 4 q^{17} - 28 q^{18} - 10 q^{19} - 2 q^{20} + 2 q^{22} - 12 q^{23} + 4 q^{25} - 2 q^{28} - 8 q^{29}+ \cdots + 28 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 + 4 * q^5 - 2 * q^7 - 4 * q^8 - 14 * q^9 + 2 * q^10 - 2 * q^11 - 4 * q^14 - 2 * q^16 + 4 * q^17 - 28 * q^18 - 10 * q^19 - 2 * q^20 + 2 * q^22 - 12 * q^23 + 4 * q^25 - 2 * q^28 - 8 * q^29 - 16 * q^31 + 2 * q^32 + 20 * q^33 + 8 * q^34 - 2 * q^35 - 14 * q^36 + 6 * q^37 - 20 * q^38 - 4 * q^40 - 8 * q^41 - 4 * q^43 + 4 * q^44 - 14 * q^45 + 12 * q^46 + 12 * q^47 + 12 * q^49 + 2 * q^50 - 40 * q^51 + 4 * q^53 - 2 * q^55 + 2 * q^56 - 40 * q^57 + 8 * q^58 - 8 * q^59 - 4 * q^61 - 8 * q^62 - 14 * q^63 + 4 * q^64 + 40 * q^66 + 8 * q^67 + 4 * q^68 - 4 * q^70 + 4 * q^71 + 14 * q^72 - 24 * q^73 - 6 * q^74 - 10 * q^76 + 4 * q^77 - 16 * q^79 - 2 * q^80 - 38 * q^81 + 8 * q^82 + 4 * q^85 - 8 * q^86 - 40 * q^87 + 2 * q^88 - 2 * q^89 - 28 * q^90 + 24 * q^92 + 20 * q^93 + 6 * q^94 - 10 * q^95 + 4 * q^97 - 12 * q^98 + 28 * q^99

Introduction

L-functions

Modular forms

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