LMFDB - Embedded newform 91.2.q.a.43.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,2,Mod(36,91)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("91.36");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	91.q (of order $6$, degree $2$, 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:	$0.726638658394$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.58891012706304.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} - 2x^{9} + 15x^{8} + 2x^{7} - 30x^{6} + 4x^{5} + 60x^{4} - 16x^{3} - 80x^{2} + 64 $ x^12 - 5x^10 - 2x^9 + 15x^8 + 2x^7 - 30x^6 + 4x^5 + 60x^4 - 16x^3 - 80*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			43.5
Root			$1.40744 - 0.138282i$ of defining polynomial
Character	$\chi$	$=$	91.43
Dual form			91.2.q.a.36.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.10554 + 0.638282i) q^{2} +(0.583963 - 1.01145i) q^{3} +(-0.185192 - 0.320762i) q^{4} +1.81487i q^{5} +(1.29118 - 0.745466i) q^{6} +(-0.866025 + 0.500000i) q^{7} -3.02595i q^{8} +(0.817975 + 1.41677i) q^{9} +O(q^{10})$	\(q+(1.10554 + 0.638282i) q^{2} +(0.583963 - 1.01145i) q^{3} +(-0.185192 - 0.320762i) q^{4} +1.81487i q^{5} +(1.29118 - 0.745466i) q^{6} +(-0.866025 + 0.500000i) q^{7} -3.02595i q^{8} +(0.817975 + 1.41677i) q^{9} +(-1.15840 + 2.00641i) q^{10} +(-2.40625 - 1.38925i) q^{11} -0.432581 q^{12} +(-3.58305 + 0.402155i) q^{13} -1.27656 q^{14} +(1.83566 + 1.05982i) q^{15} +(1.56102 - 2.70377i) q^{16} +(1.37198 + 2.37634i) q^{17} +2.08840i q^{18} +(-5.08351 + 2.93497i) q^{19} +(0.582143 - 0.336100i) q^{20} +1.16793i q^{21} +(-1.77346 - 3.07173i) q^{22} +(3.49955 - 6.06139i) q^{23} +(-3.06060 - 1.76704i) q^{24} +1.70623 q^{25} +(-4.21789 - 1.84240i) q^{26} +5.41444 q^{27} +(0.320762 + 0.185192i) q^{28} +(1.75806 - 3.04505i) q^{29} +(1.35293 + 2.34334i) q^{30} -2.06697i q^{31} +(-1.78956 + 1.03320i) q^{32} +(-2.81031 + 1.62254i) q^{33} +3.50284i q^{34} +(-0.907437 - 1.57173i) q^{35} +(0.302965 - 0.524751i) q^{36} +(1.50950 + 0.871512i) q^{37} -7.49334 q^{38} +(-1.68561 + 3.85893i) q^{39} +5.49171 q^{40} +(5.51406 + 3.18355i) q^{41} +(-0.745466 + 1.29118i) q^{42} +(4.55195 + 7.88422i) q^{43} +1.02911i q^{44} +(-2.57127 + 1.48452i) q^{45} +(7.73776 - 4.46740i) q^{46} -6.65932i q^{47} +(-1.82316 - 3.15780i) q^{48} +(0.500000 - 0.866025i) q^{49} +(1.88631 + 1.08906i) q^{50} +3.20474 q^{51} +(0.792549 + 1.07483i) q^{52} -10.4879 q^{53} +(5.98587 + 3.45594i) q^{54} +(2.52131 - 4.36703i) q^{55} +(1.51297 + 2.62055i) q^{56} +6.85564i q^{57} +(3.88720 - 2.24427i) q^{58} +(2.66212 - 1.53698i) q^{59} -0.785080i q^{60} +(-0.540892 - 0.936853i) q^{61} +(1.31931 - 2.28511i) q^{62} +(-1.41677 - 0.817975i) q^{63} -8.88199 q^{64} +(-0.729860 - 6.50279i) q^{65} -4.14254 q^{66} +(4.34568 + 2.50898i) q^{67} +(0.508159 - 0.880158i) q^{68} +(-4.08721 - 7.07925i) q^{69} -2.31680i q^{70} +(2.35453 - 1.35939i) q^{71} +(4.28709 - 2.47515i) q^{72} +7.67213i q^{73} +(1.11254 + 1.92698i) q^{74} +(0.996377 - 1.72578i) q^{75} +(1.88285 + 1.08706i) q^{76} +2.77849 q^{77} +(-4.32659 + 3.19030i) q^{78} -15.7399 q^{79} +(4.90700 + 2.83306i) q^{80} +(0.707906 - 1.22613i) q^{81} +(4.06400 + 7.03905i) q^{82} -7.97408i q^{83} +(0.374626 - 0.216290i) q^{84} +(-4.31275 + 2.48997i) q^{85} +11.6217i q^{86} +(-2.05328 - 3.55639i) q^{87} +(-4.20379 + 7.28117i) q^{88} +(-13.9118 - 8.03198i) q^{89} -3.79017 q^{90} +(2.90194 - 2.13980i) q^{91} -2.59235 q^{92} +(-2.09064 - 1.20703i) q^{93} +(4.25052 - 7.36212i) q^{94} +(-5.32659 - 9.22592i) q^{95} +2.41340i q^{96} +(-12.3209 + 7.11347i) q^{97} +(1.10554 - 0.638282i) q^{98} -4.54548i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{4} - 18 q^{6} - 4 q^{9}+O(q^{10}) $ 12 * q + 4 * q^4 - 18 * q^6 - 4 * q^9	$ 12 q + 4 q^{4} - 18 q^{6} - 4 q^{9} + 12 q^{10} + 6 q^{11} - 4 q^{12} + 4 q^{13} - 8 q^{14} + 6 q^{15} - 8 q^{16} - 4 q^{17} - 12 q^{20} + 6 q^{22} - 12 q^{23} + 12 q^{24} - 20 q^{25} - 42 q^{26} + 12 q^{27} + 8 q^{29} + 8 q^{30} + 36 q^{32} - 30 q^{33} + 6 q^{35} - 10 q^{36} - 42 q^{37} + 4 q^{38} - 4 q^{39} + 92 q^{40} + 30 q^{41} + 4 q^{42} + 2 q^{43} + 12 q^{46} - 2 q^{48} + 6 q^{49} - 18 q^{50} + 52 q^{51} + 2 q^{52} - 44 q^{53} + 12 q^{54} - 6 q^{55} - 12 q^{56} - 12 q^{58} + 18 q^{59} + 14 q^{61} - 4 q^{62} + 12 q^{63} - 52 q^{64} + 60 q^{65} - 52 q^{66} - 24 q^{67} - 8 q^{68} + 4 q^{69} - 24 q^{71} + 60 q^{72} + 6 q^{74} + 46 q^{75} - 18 q^{76} + 8 q^{77} - 10 q^{78} - 56 q^{79} - 72 q^{80} + 2 q^{81} + 14 q^{82} + 18 q^{84} - 48 q^{85} - 2 q^{87} - 14 q^{88} - 12 q^{89} + 24 q^{90} + 14 q^{91} + 24 q^{92} - 18 q^{93} + 4 q^{94} - 22 q^{95} + 6 q^{97}+O(q^{100}) $ 12 * q + 4 * q^4 - 18 * q^6 - 4 * q^9 + 12 * q^10 + 6 * q^11 - 4 * q^12 + 4 * q^13 - 8 * q^14 + 6 * q^15 - 8 * q^16 - 4 * q^17 - 12 * q^20 + 6 * q^22 - 12 * q^23 + 12 * q^24 - 20 * q^25 - 42 * q^26 + 12 * q^27 + 8 * q^29 + 8 * q^30 + 36 * q^32 - 30 * q^33 + 6 * q^35 - 10 * q^36 - 42 * q^37 + 4 * q^38 - 4 * q^39 + 92 * q^40 + 30 * q^41 + 4 * q^42 + 2 * q^43 + 12 * q^46 - 2 * q^48 + 6 * q^49 - 18 * q^50 + 52 * q^51 + 2 * q^52 - 44 * q^53 + 12 * q^54 - 6 * q^55 - 12 * q^56 - 12 * q^58 + 18 * q^59 + 14 * q^61 - 4 * q^62 + 12 * q^63 - 52 * q^64 + 60 * q^65 - 52 * q^66 - 24 * q^67 - 8 * q^68 + 4 * q^69 - 24 * q^71 + 60 * q^72 + 6 * q^74 + 46 * q^75 - 18 * q^76 + 8 * q^77 - 10 * q^78 - 56 * q^79 - 72 * q^80 + 2 * q^81 + 14 * q^82 + 18 * q^84 - 48 * q^85 - 2 * q^87 - 14 * q^88 - 12 * q^89 + 24 * q^90 + 14 * q^91 + 24 * q^92 - 18 * q^93 + 4 * q^94 - 22 * q^95 + 6 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	1.10554	+	0.638282i	0.781733	+	0.451334i	0.837044	−	0.547136i	$-0.184282\pi$
$2$	1.10554	+	0.638282i	0.781733	+	0.451334i	−0.0553113	+	0.998469i	$0.517615\pi$
$3$	0.583963	−	1.01145i	0.337151	−	0.583963i	−0.646745	−	0.762707i	$-0.723870\pi$
$3$	0.583963	−	1.01145i	0.337151	−	0.583963i	0.983896	+	0.178744i	$0.0572034\pi$
$4$	−0.185192	−	0.320762i	−0.0925960	−	0.160381i
$5$			1.81487i			0.811636i	0.913954	+	0.405818i	$0.133013\pi$
$5$			1.81487i			0.811636i	−0.913954	+	0.405818i	$0.866987\pi$
$6$	1.29118	−	0.745466i	0.527124	−	0.304335i
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i
$8$		−	3.02595i		−	1.06983i
$9$	0.817975	+	1.41677i	0.272658	+	0.472258i
$10$	−1.15840	+	2.00641i	−0.366319	+	0.634482i
$11$	−2.40625	−	1.38925i	−0.725510	−	0.418874i	0.0912671	−	0.995826i	$-0.470908\pi$
$11$	−2.40625	−	1.38925i	−0.725510	−	0.418874i	−0.816777	+	0.576953i	$0.804242\pi$
$12$	−0.432581			−0.124875
$13$	−3.58305	+	0.402155i	−0.993760	+	0.111538i
$13$	−3.58305	+	0.402155i	−0.993760	+	0.111538i
$14$	−1.27656			−0.341176
$15$	1.83566	+	1.05982i	0.473965	+	0.273644i
$16$	1.56102	−	2.70377i	0.390256	−	0.675943i
$17$	1.37198	+	2.37634i	0.332754	+	0.576347i	0.983051	−	0.183334i	$-0.0586888\pi$
$17$	1.37198	+	2.37634i	0.332754	+	0.576347i	−0.650297	+	0.759680i	$0.725355\pi$
$18$			2.08840i			0.492240i
$19$	−5.08351	+	2.93497i	−1.16624	+	0.673327i	−0.952791	−	0.303628i	$-0.901802\pi$
$19$	−5.08351	+	2.93497i	−1.16624	+	0.673327i	−0.213446	+	0.976955i	$0.568469\pi$
$20$	0.582143	−	0.336100i	0.130171	−	0.0751543i
$21$			1.16793i			0.254862i
$22$	−1.77346	−	3.07173i	−0.378103	−	0.654894i
$23$	3.49955	−	6.06139i	0.729706	−	1.26389i	−0.227302	−	0.973824i	$-0.572990\pi$
$23$	3.49955	−	6.06139i	0.729706	−	1.26389i	0.957007	−	0.290063i	$-0.0936763\pi$
$24$	−3.06060	−	1.76704i	−0.624743	−	0.360696i
$25$	1.70623			0.341247
$26$	−4.21789	−	1.84240i	−0.827195	−	0.361325i
$27$	5.41444			1.04201
$28$	0.320762	+	0.185192i	0.0606183	+	0.0349980i
$29$	1.75806	−	3.04505i	0.326463	−	0.565451i	−0.655344	−	0.755330i	$-0.727476\pi$
$29$	1.75806	−	3.04505i	0.326463	−	0.565451i	0.981807	+	0.189879i	$0.0608097\pi$
$30$	1.35293	+	2.34334i	0.247009	+	0.427833i
$31$		−	2.06697i		−	0.371238i	−0.982622	−	0.185619i	$-0.940571\pi$
$31$		−	2.06697i		−	0.371238i	0.982622	−	0.185619i	$-0.0594290\pi$
$32$	−1.78956	+	1.03320i	−0.316352	+	0.182646i
$33$	−2.81031	+	1.62254i	−0.489213	+	0.282447i
$34$			3.50284i			0.600732i
$35$	−0.907437	−	1.57173i	−0.153385	−	0.265670i
$36$	0.302965	−	0.524751i	0.0504942	−	0.0874585i
$37$	1.50950	+	0.871512i	0.248161	+	0.143276i	0.618922	−	0.785453i	$-0.287570\pi$
$37$	1.50950	+	0.871512i	0.248161	+	0.143276i	−0.370761	+	0.928728i	$0.620903\pi$
$38$	−7.49334			−1.21558
$39$	−1.68561	+	3.85893i	−0.269913	+	0.617924i
$40$	5.49171			0.868316
$41$	5.51406	+	3.18355i	0.861152	+	0.497186i	0.864398	−	0.502808i	$-0.167700\pi$
$41$	5.51406	+	3.18355i	0.861152	+	0.497186i	−0.00324599	+	0.999995i	$0.501033\pi$
$42$	−0.745466	+	1.29118i	−0.115028	+	0.199234i
$43$	4.55195	+	7.88422i	0.694167	+	1.20233i	0.970461	+	0.241259i	$0.0775603\pi$
$43$	4.55195	+	7.88422i	0.694167	+	1.20233i	−0.276294	+	0.961073i	$0.589106\pi$
$44$			1.02911i			0.155144i
$45$	−2.57127	+	1.48452i	−0.383302	+	0.221299i
$46$	7.73776	−	4.46740i	1.14087	−	0.658681i
$47$		−	6.65932i		−	0.971361i	−0.874136	−	0.485681i	$-0.838572\pi$
$47$		−	6.65932i		−	0.971361i	0.874136	−	0.485681i	$-0.161428\pi$
$48$	−1.82316	−	3.15780i	−0.263150	−	0.455790i
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$	1.88631	+	1.08906i	0.266764	+	0.154016i
$51$	3.20474			0.448753
$52$	0.792549	+	1.07483i	0.109907	+	0.149052i
$53$	−10.4879			−1.44063			−0.720313	−	0.693649i	$-0.756002\pi$
$53$	−10.4879			−1.44063			−0.720313	+	0.693649i	$0.756002\pi$
$54$	5.98587	+	3.45594i	0.814573	+	0.470294i
$55$	2.52131	−	4.36703i	0.339973	−	0.588850i
$56$	1.51297	+	2.62055i	0.202180	+	0.350185i
$57$			6.85564i			0.908052i
$58$	3.88720	−	2.24427i	0.510414	−	0.294688i
$59$	2.66212	−	1.53698i	0.346579	−	0.200097i	−0.316598	−	0.948560i	$-0.602541\pi$
$59$	2.66212	−	1.53698i	0.346579	−	0.200097i	0.663177	+	0.748462i	$0.269207\pi$
$60$		−	0.785080i		−	0.101353i
$61$	−0.540892	−	0.936853i	−0.0692541	−	0.119952i	0.829319	−	0.558775i	$-0.188729\pi$
$61$	−0.540892	−	0.936853i	−0.0692541	−	0.119952i	−0.898573	+	0.438824i	$0.855395\pi$
$62$	1.31931	−	2.28511i	0.167552	−	0.290209i
$63$	−1.41677	−	0.817975i	−0.178497	−	0.103055i
$64$	−8.88199			−1.11025
$65$	−0.729860	−	6.50279i	−0.0905280	−	0.806572i
$66$	−4.14254			−0.509912
$67$	4.34568	+	2.50898i	0.530910	+	0.306521i	0.741387	−	0.671078i	$-0.234168\pi$
$67$	4.34568	+	2.50898i	0.530910	+	0.306521i	−0.210477	+	0.977599i	$0.567502\pi$
$68$	0.508159	−	0.880158i	0.0616234	−	0.106735i
$69$	−4.08721	−	7.07925i	−0.492042	−	0.852242i
$70$		−	2.31680i		−	0.276911i
$71$	2.35453	−	1.35939i	0.279431	−	0.161330i	−0.353735	−	0.935346i	$-0.615088\pi$
$71$	2.35453	−	1.35939i	0.279431	−	0.161330i	0.633166	+	0.774016i	$0.281755\pi$
$72$	4.28709	−	2.47515i	0.505238	−	0.291699i
$73$			7.67213i			0.897955i	0.893543	+	0.448978i	$0.148212\pi$
$73$			7.67213i			0.897955i	−0.893543	+	0.448978i	$0.851788\pi$
$74$	1.11254	+	1.92698i	0.129330	+	0.224006i
$75$	0.996377	−	1.72578i	0.115052	−	0.199275i
$76$	1.88285	+	1.08706i	0.215978	+	0.124695i
$77$	2.77849			0.316639
$78$	−4.32659	+	3.19030i	−0.489890	+	0.361230i
$79$	−15.7399			−1.77087			−0.885436	−	0.464761i	$-0.846140\pi$
$79$	−15.7399			−1.77087			−0.885436	+	0.464761i	$0.846140\pi$
$80$	4.90700	+	2.83306i	0.548620	+	0.316746i
$81$	0.707906	−	1.22613i	0.0786563	−	0.136237i
$82$	4.06400	+	7.03905i	0.448794	+	0.777333i
$83$		−	7.97408i		−	0.875269i	−0.899153	−	0.437635i	$-0.855816\pi$
$83$		−	7.97408i		−	0.875269i	0.899153	−	0.437635i	$-0.144184\pi$
$84$	0.374626	−	0.216290i	0.0408751	−	0.0235992i
$85$	−4.31275	+	2.48997i	−0.467784	+	0.270075i
$86$			11.6217i			1.25320i
$87$	−2.05328	−	3.55639i	−0.220135	−	0.381285i
$88$	−4.20379	+	7.28117i	−0.448125	+	0.776176i
$89$	−13.9118	−	8.03198i	−1.47465	−	0.851388i	−0.475055	−	0.879956i	$-0.657572\pi$
$89$	−13.9118	−	8.03198i	−1.47465	−	0.851388i	−0.999592	+	0.0285683i	$0.990905\pi$
$90$	−3.79017			−0.399519
$91$	2.90194	−	2.13980i	0.304206	−	0.224312i
$92$	−2.59235			−0.270271
$93$	−2.09064	−	1.20703i	−0.216789	−	0.125163i
$94$	4.25052	−	7.36212i	0.438408	−	0.759345i
$95$	−5.32659	−	9.22592i	−0.546497	−	0.946560i
$96$			2.41340i			0.246317i
$97$	−12.3209	+	7.11347i	−1.25100	+	0.722263i	−0.971307	−	0.237827i	$-0.923565\pi$
$97$	−12.3209	+	7.11347i	−1.25100	+	0.722263i	−0.279689	+	0.960091i	$0.590231\pi$
$98$	1.10554	−	0.638282i	0.111676	−	0.0644762i
$99$		−	4.54548i		−	0.456838i
$100$	−0.315981	−	0.547295i	−0.0315981	−	0.0547295i
$101$	−0.0365612	+	0.0633259i	−0.00363798	+	0.00630117i	−0.867839	−	0.496846i	$-0.834491\pi$
$101$	−0.0365612	+	0.0633259i	−0.00363798	+	0.00630117i	0.864201	+	0.503147i	$0.167825\pi$
$102$	3.54296	+	2.04553i	0.350805	+	0.202537i
$103$	12.9196			1.27301			0.636503	−	0.771275i	$-0.280380\pi$
$103$	12.9196			1.27301			0.636503	+	0.771275i	$0.280380\pi$
$104$	1.21690	+	10.8421i	0.119327	+	1.06316i
$105$	−2.11964			−0.206855
$106$	−11.5948	−	6.69425i	−1.12618	−	0.650203i
$107$	−2.00427	+	3.47150i	−0.193761	+	0.335603i	−0.946493	−	0.322723i	$-0.895402\pi$
$107$	−2.00427	+	3.47150i	−0.193761	+	0.335603i	0.752733	+	0.658326i	$0.228735\pi$
$108$	−1.00271	−	1.73675i	−0.0964860	−	0.167119i
$109$			1.98589i			0.190214i	0.995467	+	0.0951071i	$0.0303194\pi$
$109$			1.98589i			0.190214i	−0.995467	+	0.0951071i	$0.969681\pi$
$110$	5.57479	−	3.21861i	0.531536	−	0.306882i
$111$	1.76299	−	1.01786i	0.167335	−	0.0966110i
$112$			3.12205i			0.295006i
$113$	5.28711	+	9.15754i	0.497369	+	0.861469i	0.999995	−	0.00303506i	$-0.000966090\pi$
$113$	5.28711	+	9.15754i	0.497369	+	0.861469i	−0.502626	+	0.864504i	$0.667633\pi$
$114$	−4.37583	+	7.57916i	−0.409834	+	0.709854i
$115$	11.0007	+	6.35123i	1.02582	+	0.592256i
$116$	−1.30231			−0.120917
$117$	−3.50061	−	4.74743i	−0.323632	−	0.438900i
$118$	3.92410			0.361243
$119$	−2.37634	−	1.37198i	−0.217839	−	0.125769i
$120$	3.20695	−	5.55461i	0.292753	−	0.507064i
$121$	−1.63999	−	2.84054i	−0.149090	−	0.258231i
$122$		−	1.38097i		−	0.125027i
$123$	6.44001	−	3.71814i	0.580676	−	0.335254i
$124$	−0.663004	+	0.382786i	−0.0595395	+	0.0343752i
$125$			12.1710i			1.08860i
$126$	−1.04420	−	1.80860i	−0.0930246	−	0.161123i
$127$	5.63478	−	9.75972i	0.500006	−	0.866035i	−0.499994	−	0.866029i	$-0.666665\pi$
$127$	5.63478	−	9.75972i	0.500006	−	0.866035i	1.00000		6.53271e-6i	$-2.07943e-6\pi$
$128$	−6.24025	−	3.60281i	−0.551566	−	0.318447i
$129$	10.6327			0.936156
$130$	3.34373	−	7.65493i	0.293264	−	0.671382i
$131$	3.06481			0.267774			0.133887	−	0.990997i	$-0.457254\pi$
$131$	3.06481			0.267774			0.133887	+	0.990997i	$0.457254\pi$
$132$	1.04090	+	0.600962i	0.0905984	+	0.0523070i
$133$	2.93497	−	5.08351i	0.254494	−	0.440796i
$134$	3.20288	+	5.54754i	0.276686	+	0.479235i
$135$			9.82653i			0.845733i
$136$	7.19067	−	4.15154i	0.616595	−	0.355991i
$137$	18.9512	−	10.9415i	1.61911	−	0.934796i	0.631965	−	0.774997i	$-0.282249\pi$
$137$	18.9512	−	10.9415i	1.61911	−	0.934796i	0.987150	−	0.159799i	$-0.0510845\pi$
$138$		−	10.4352i		−	0.888300i
$139$	−5.53535	−	9.58750i	−0.469502	−	0.813201i	0.529890	−	0.848066i	$-0.322233\pi$
$139$	−5.53535	−	9.58750i	−0.469502	−	0.813201i	−0.999392	+	0.0348652i	$0.988900\pi$
$140$	−0.336100	+	0.582143i	−0.0284056	+	0.0492000i
$141$	−6.73559	−	3.88879i	−0.567239	−	0.327495i
$142$	3.47069			0.291254
$143$	9.18040	+	4.01006i	0.767703	+	0.335338i
$144$	5.10752			0.425626
$145$	5.52637	+	3.19065i	0.458940	+	0.264969i
$146$	−4.89699	+	8.48183i	−0.405277	+	0.701961i
$147$	−0.583963	−	1.01145i	−0.0481644	−	0.0834232i
$148$		−	0.645588i		−	0.0530670i
$149$	−1.99824	+	1.15369i	−0.163702	+	0.0945136i	−0.579613	−	0.814892i	$-0.696796\pi$
$149$	−1.99824	+	1.15369i	−0.163702	+	0.0945136i	0.415911	+	0.909406i	$0.363463\pi$
$150$	2.20306	−	1.27194i	0.179879	−	0.103853i
$151$			20.6158i			1.67769i	0.544371	+	0.838845i	$0.316768\pi$
$151$			20.6158i			1.67769i	−0.544371	+	0.838845i	$0.683232\pi$
$152$	8.88105	+	15.3824i	0.720348	+	1.24768i
$153$	−2.24449	+	3.88757i	−0.181456	+	0.314292i
$154$	3.07173	+	1.77346i	0.247527	+	0.142910i
$155$	3.75128			0.301310
$156$	1.54996	−	0.173964i	0.124096	−	0.0139283i
$157$	2.89649			0.231165			0.115582	−	0.993298i	$-0.463127\pi$
$157$	2.89649			0.231165			0.115582	+	0.993298i	$0.463127\pi$
$158$	−17.4010	−	10.0465i	−1.38435	−	0.799254i
$159$	−6.12455	+	10.6080i	−0.485709	+	0.841272i
$160$	−1.87513	−	3.24782i	−0.148242	−	0.256763i
$161$			6.99909i			0.551606i
$162$	1.56523	−	0.903688i	0.122976	−	0.0710004i
$163$	−20.2944	+	11.7170i	−1.58958	+	0.917743i	−0.596201	+	0.802835i	$0.703324\pi$
$163$	−20.2944	+	11.7170i	−1.58958	+	0.917743i	−0.993376	+	0.114907i	$0.963343\pi$
$164$		−	2.35827i		−	0.184150i
$165$	−2.94470	−	5.10037i	−0.229244	−	0.397063i
$166$	5.08971	−	8.81564i	0.395038	−	0.684226i
$167$	6.58349	+	3.80098i	0.509446	+	0.294129i	0.732606	−	0.680653i	$-0.238304\pi$
$167$	6.58349	+	3.80098i	0.509446	+	0.294129i	−0.223160	+	0.974782i	$0.571637\pi$
$168$	3.53408			0.272660
$169$	12.6765	−	2.88188i	0.975119	−	0.221683i
$170$	−6.35721			−0.487576
$171$	−8.31637	−	4.80146i	−0.635969	−	0.367177i
$172$	1.68597	−	2.92019i	0.128554	−	0.222662i
$173$	2.69861	+	4.67412i	0.205171	+	0.355367i	0.950187	−	0.311679i	$-0.100892\pi$
$173$	2.69861	+	4.67412i	0.205171	+	0.355367i	−0.745016	+	0.667047i	$0.767558\pi$
$174$		−	5.24229i		−	0.397417i
$175$	−1.47764	+	0.853117i	−0.111699	+	0.0644896i
$176$	−7.51241	+	4.33729i	−0.566269	+	0.326936i
$177$		−	3.59015i		−	0.269852i
$178$	−10.2533	−	17.7593i	−0.768520	−	1.33112i
$179$	−6.14571	+	10.6447i	−0.459352	+	0.795621i	−0.998927	−	0.0463168i	$-0.985252\pi$
$179$	−6.14571	+	10.6447i	−0.459352	+	0.795621i	0.539575	+	0.841938i	$0.318585\pi$
$180$	0.952357	+	0.549843i	0.0709845	+	0.0409829i
$181$	−21.8525			−1.62428			−0.812140	−	0.583463i	$-0.801697\pi$
$181$	−21.8525			−1.62428			−0.812140	+	0.583463i	$0.801697\pi$
$182$	4.57400	−	0.513376i	0.339047	−	0.0380540i
$183$	−1.26344			−0.0933964
$184$	−18.3415	−	10.5894i	−1.35215	−	0.780664i
$185$	−1.58168	+	2.73956i	−0.116288	+	0.201416i
$186$	−1.54085	−	2.66883i	−0.112981	−	0.195688i
$187$		−	7.62407i		−	0.557527i
$188$	−2.13606	+	1.23325i	−0.155788	+	0.0899442i
$189$	−4.68905	+	2.70722i	−0.341078	+	0.196921i
$190$		−	13.5995i		−	0.986609i
$191$	−1.37858	−	2.38777i	−0.0997507	−	0.172773i	0.811831	−	0.583893i	$-0.198471\pi$
$191$	−1.37858	−	2.38777i	−0.0997507	−	0.172773i	−0.911581	+	0.411120i	$0.865138\pi$
$192$	−5.18675	+	8.98371i	−0.374321	+	0.648344i
$193$	11.2491	+	6.49467i	0.809728	+	0.467497i	0.846861	−	0.531814i	$-0.178489\pi$
$193$	11.2491	+	6.49467i	0.809728	+	0.467497i	−0.0371334	+	0.999310i	$0.511823\pi$
$194$	−18.1616			−1.30393
$195$	−7.00347	−	3.05917i	−0.501529	−	0.219071i
$196$	−0.370384			−0.0264560
$197$	16.4772	+	9.51312i	1.17395	+	0.677781i	0.954608	−	0.297866i	$-0.0962749\pi$
$197$	16.4772	+	9.51312i	1.17395	+	0.677781i	0.219344	+	0.975648i	$0.429608\pi$
$198$	2.90130	−	5.02519i	0.206186	−	0.357125i
$199$	−10.0159	−	17.3480i	−0.710006	−	1.22977i	−0.964854	−	0.262786i	$-0.915359\pi$
$199$	−10.0159	−	17.3480i	−0.710006	−	1.22977i	0.254848	−	0.966981i	$-0.417975\pi$
$200$		−	5.16298i		−	0.365078i
$201$	5.07543	−	2.93030i	0.357993	−	0.206688i
$202$	−0.0808396	+	0.0466728i	−0.00568785	+	0.00328388i
$203$			3.51612i			0.246783i
$204$	−0.593492	−	1.02796i	−0.0415528	−	0.0719715i
$205$	−5.77773	+	10.0073i	−0.403534	+	0.698942i
$206$	14.2831	+	8.24634i	0.995150	+	0.574550i
$207$	11.4502			0.795842
$208$	−4.50590	+	10.3155i	−0.312428	+	0.715254i
$209$	16.3096			1.12816
$210$	−2.34334	−	1.35293i	−0.161706	−	0.0933608i
$211$	−5.00015	+	8.66052i	−0.344225	+	0.596215i	−0.985213	−	0.171336i	$-0.945192\pi$
$211$	−5.00015	+	8.66052i	−0.344225	+	0.596215i	0.640988	+	0.767551i	$0.278525\pi$
$212$	1.94228	+	3.36413i	0.133396	+	0.231049i
$213$		−	3.17532i		−	0.217570i
$214$	−4.43160	+	2.55858i	−0.302938	+	0.174901i
$215$	−14.3089	+	8.26122i	−0.975856	+	0.563411i
$216$		−	16.3838i		−	1.11478i
$217$	1.03348	+	1.79004i	0.0701574	+	0.121516i
$218$	−1.26756	+	2.19548i	−0.0858501	+	0.148697i
$219$	7.76000	+	4.48024i	0.524372	+	0.302747i
$220$	−1.86770			−0.125921
$221$	−5.87153	−	7.96280i	−0.394962	−	0.535636i
$222$	2.59873			0.174415
$223$	7.25954	+	4.19130i	0.486135	+	0.280670i	0.722970	−	0.690880i	$-0.242777\pi$
$223$	7.25954	+	4.19130i	0.486135	+	0.280670i	−0.236835	+	0.971550i	$0.576110\pi$
$224$	1.03320	−	1.78956i	0.0690336	−	0.119570i
$225$	1.39566	+	2.41735i	0.0930439	+	0.161157i
$226$			13.4987i			0.897918i
$227$	−0.796500	+	0.459860i	−0.0528656	+	0.0305220i	−0.526200	−	0.850361i	$-0.676384\pi$
$227$	−0.796500	+	0.459860i	−0.0528656	+	0.0305220i	0.473334	+	0.880883i	$0.343050\pi$
$228$	2.19903	−	1.26961i	0.145634	−	0.0840820i
$229$		−	24.6208i		−	1.62699i	−0.581574	−	0.813494i	$-0.697563\pi$
$229$		−	24.6208i		−	1.62699i	0.581574	−	0.813494i	$-0.302437\pi$
$230$	8.10776	+	14.0430i	0.534610	+	0.925971i
$231$	1.62254	−	2.81031i	0.106755	−	0.184905i
$232$	−9.21415	−	5.31979i	−0.604939	−	0.349261i
$233$	17.2769			1.13185			0.565925	−	0.824457i	$-0.308519\pi$
$233$	17.2769			1.13185			0.565925	+	0.824457i	$0.308519\pi$
$234$	−0.839858	−	7.48283i	−0.0549032	−	0.489168i
$235$	12.0858			0.788392
$236$	−0.986008	−	0.569272i	−0.0641837	−	0.0370565i
$237$	−9.19149	+	15.9201i	−0.597051	+	1.03412i
$238$	−1.75142	−	3.03355i	−0.113528	−	0.196636i
$239$		−	14.4828i		−	0.936816i	−0.883512	−	0.468408i	$-0.844828\pi$
$239$		−	14.4828i		−	0.936816i	0.883512	−	0.468408i	$-0.155172\pi$
$240$	5.73101	−	3.30880i	0.369935	−	0.213582i
$241$	−7.30441	+	4.21720i	−0.470518	+	0.271654i	−0.716457	−	0.697632i	$-0.754237\pi$
$241$	−7.30441	+	4.21720i	−0.470518	+	0.271654i	0.245938	+	0.969285i	$0.420904\pi$
$242$		−	4.18710i		−	0.269157i
$243$	7.29488	+	12.6351i	0.467967	+	0.810543i
$244$	−0.200338	+	0.346995i	−0.0128253	+	0.0222141i
$245$	1.57173	+	0.907437i	0.100414	+	0.0579740i
$246$	9.49290			0.605245
$247$	17.0342	−	12.5605i	1.08386	−	0.799205i
$248$	−6.25453			−0.397163
$249$	−8.06541	−	4.65657i	−0.511124	−	0.295098i
$250$	−7.76851	+	13.4555i	−0.491324	+	0.850998i
$251$	−7.33631	−	12.7069i	−0.463064	−	0.802050i	0.536048	−	0.844188i	$-0.319917\pi$
$251$	−7.33631	−	12.7069i	−0.463064	−	0.802050i	−0.999112	+	0.0421373i	$0.986583\pi$
$252$			0.605930i			0.0381700i
$253$	−16.8415	+	9.72346i	−1.05882	+	0.611309i
$254$	12.4589	−	7.19315i	0.781742	−	0.451339i
$255$			5.81620i			0.364224i
$256$	4.28277	+	7.41797i	0.267673	+	0.463623i
$257$	14.6643	−	25.3993i	0.914733	−	1.58436i	0.107441	−	0.994211i	$-0.465734\pi$
$257$	14.6643	−	25.3993i	0.914733	−	1.58436i	0.807292	−	0.590152i	$-0.200932\pi$
$258$	11.7548	+	6.78665i	0.731824	+	0.422519i
$259$	−1.74302			−0.108306
$260$	−1.95068	+	1.43838i	−0.120976	+	0.0892043i
$261$	5.75219			0.356052
$262$	3.38826	+	1.95622i	0.209328	+	0.120855i
$263$	−9.95747	+	17.2468i	−0.614004	+	1.06349i	0.376555	+	0.926394i	$0.377109\pi$
$263$	−9.95747	+	17.2468i	−0.614004	+	1.06349i	−0.990558	+	0.137091i	$0.956225\pi$
$264$	4.90971	+	8.50386i	0.302172	+	0.523377i
$265$		−	19.0342i		−	1.16926i
$266$	6.48942	−	3.74667i	0.397892	−	0.229723i
$267$	−16.2479	+	9.38075i	−0.994357	+	0.574092i
$268$		−	1.85857i		−	0.113530i
$269$	11.1625	+	19.3340i	0.680589	+	1.17881i	0.974801	+	0.223074i	$0.0716093\pi$
$269$	11.1625	+	19.3340i	0.680589	+	1.17881i	−0.294213	+	0.955740i	$0.595057\pi$
$270$	−6.27210	+	10.8636i	−0.381708	+	0.661137i
$271$	−8.14054	−	4.69994i	−0.494502	−	0.285501i	0.231938	−	0.972731i	$-0.425493\pi$
$271$	−8.14054	−	4.69994i	−0.494502	−	0.285501i	−0.726440	+	0.687230i	$0.758827\pi$
$272$	8.56677			0.519437
$273$	−0.469686	−	4.18474i	−0.0284267	−	0.253272i
$274$	27.9351			1.68762
$275$	−4.10562	−	2.37038i	−0.247578	−	0.142939i
$276$	−1.51384	+	2.62204i	−0.0911223	+	0.157828i
$277$	−7.17133	−	12.4211i	−0.430883	−	0.746312i	0.566066	−	0.824360i	$-0.308465\pi$
$277$	−7.17133	−	12.4211i	−0.430883	−	0.746312i	−0.996950	+	0.0780478i	$0.975131\pi$
$278$		−	14.1324i		−	0.847608i
$279$	2.92842	−	1.69073i	0.175320	−	0.101221i
$280$	−4.75596	+	2.74586i	−0.284223	+	0.164096i
$281$		−	0.0988416i		−	0.00589640i	−0.999996	−	0.00294820i	$-0.999062\pi$
$281$		−	0.0988416i		−	0.00589640i	0.999996	−	0.00294820i	$-0.000938442\pi$
$282$	−4.96429	−	8.59841i	−0.295619	−	0.512028i
$283$	−0.310336	+	0.537518i	−0.0184476	+	0.0319521i	−0.875102	−	0.483939i	$-0.839206\pi$
$283$	−0.310336	+	0.537518i	−0.0184476	+	0.0319521i	0.856654	+	0.515891i	$0.172539\pi$
$284$	−0.872079	−	0.503495i	−0.0517484	−	0.0298769i
$285$	−12.4421			−0.737007
$286$	7.58972	+	10.2930i	0.448789	+	0.608635i
$287$	−6.36709			−0.375837
$288$	−2.92763	−	1.69027i	−0.172512	−	0.0995998i
$289$	4.73534	−	8.20186i	0.278550	−	0.482462i
$290$	4.07307	+	7.05477i	0.239179	+	0.414270i
$291$			16.6160i			0.974047i
$292$	2.46093	−	1.42082i	0.144015	−	0.0831471i
$293$	21.5586	−	12.4469i	1.25947	−	0.727153i	0.286496	−	0.958082i	$-0.407510\pi$
$293$	21.5586	−	12.4469i	1.25947	−	0.727153i	0.972971	+	0.230928i	$0.0741762\pi$
$294$		−	1.49093i		−	0.0869529i
$295$	2.78942	+	4.83142i	0.162406	+	0.281296i
$296$	2.63715	−	4.56767i	0.153281	−	0.265491i
$297$	−13.0285	−	7.52200i	−0.755989	−	0.436471i
$298$	−2.94551			−0.170629
$299$	−10.1014	+	23.1256i	−0.584182	+	1.33739i
$300$	−0.738085			−0.0426133
$301$	−7.88422	−	4.55195i	−0.454439	−	0.262370i
$302$	−13.1587	+	22.7915i	−0.757197	+	1.31150i
$303$	0.0427008	+	0.0739599i	0.00245310	+	0.00424889i
$304$			18.3262i			1.05108i
$305$	1.70027	−	0.981651i	0.0973571	−	0.0562091i
$306$	−4.96274	+	2.86524i	−0.283701	+	0.163795i
$307$		−	9.89767i		−	0.564890i	−0.959284	−	0.282445i	$-0.908855\pi$
$307$		−	9.89767i		−	0.564890i	0.959284	−	0.282445i	$-0.0911455\pi$
$308$	−0.514555	−	0.891235i	−0.0293195	−	0.0507828i
$309$	7.54456	−	13.0676i	0.429195	−	0.743387i
$310$	4.14718	+	2.39437i	0.235544	+	0.135991i
$311$	−7.23790			−0.410423			−0.205212	−	0.978718i	$-0.565788\pi$
$311$	−7.23790			−0.410423			−0.205212	+	0.978718i	$0.565788\pi$
$312$	11.6769	+	5.10056i	0.661076	+	0.288763i
$313$	32.6606			1.84609			0.923043	−	0.384696i	$-0.125694\pi$
$313$	32.6606			1.84609			0.923043	+	0.384696i	$0.125694\pi$
$314$	3.20217	+	1.84877i	0.180709	+	0.104332i
$315$	1.48452	−	2.57127i	0.0836433	−	0.144874i
$316$	2.91490	+	5.04875i	0.163976	+	0.284014i
$317$		−	17.1744i		−	0.964608i	−0.876004	−	0.482304i	$-0.839800\pi$
$317$		−	17.1744i		−	0.964608i	0.876004	−	0.482304i	$-0.160200\pi$
$318$	−13.5418	+	7.81838i	−0.759388	+	0.438433i
$319$	−8.46064	+	4.88475i	−0.473705	+	0.273494i
$320$		−	16.1197i		−	0.901118i
$321$	2.34084	+	4.05446i	0.130653	+	0.226298i
$322$	−4.46740	+	7.73776i	−0.248958	+	0.431208i
$323$	−13.9489	−	8.05342i	−0.776140	−	0.448105i
$324$	−0.524395			−0.0291330
$325$	−6.11353	+	0.686170i	−0.339118	+	0.0380619i
$326$	−29.9149			−1.65683
$327$	2.00864	+	1.15969i	0.111078	+	0.0641309i
$328$	9.63324	−	16.6853i	0.531907	−	0.921289i
$329$	3.32966	+	5.76714i	0.183570	+	0.317953i
$330$		−	7.51819i		−	0.413863i
$331$	17.2633	−	9.96698i	0.948877	−	0.547835i	0.0561454	−	0.998423i	$-0.482119\pi$
$331$	17.2633	−	9.96698i	0.948877	−	0.547835i	0.892732	+	0.450588i	$0.148786\pi$
$332$	−2.55778	+	1.47674i	−0.140377	+	0.0810465i
$333$			2.85150i			0.156261i
$334$	4.85219	+	8.40424i	0.265500	+	0.459860i
$335$	−4.55348	+	7.88687i	−0.248783	+	0.430905i
$336$	3.15780	+	1.82316i	0.172272	+	0.0994615i
$337$	1.27189			0.0692842			0.0346421	−	0.999400i	$-0.488971\pi$
$337$	1.27189			0.0692842			0.0346421	+	0.999400i	$0.488971\pi$
$338$	15.8538	+	4.90518i	0.862335	+	0.266807i
$339$	12.3499			0.670754
$340$	1.59738	+	0.922245i	0.0866298	+	0.0500158i
$341$	−2.87152	+	4.97363i	−0.155502	+	0.269337i
$342$	−6.12937	−	10.6164i	−0.331438	−	0.574068i
$343$			1.00000i			0.0539949i
$344$	23.8572	−	13.7740i	1.28630	−	0.742643i
$345$	12.8479	−	7.41777i	0.691710	−	0.399359i
$346$			6.88989i			0.370403i
$347$	−12.9417	−	22.4156i	−0.694744	−	1.20333i	−0.970267	−	0.242038i	$-0.922184\pi$
$347$	−12.9417	−	22.4156i	−0.694744	−	1.20333i	0.275522	−	0.961295i	$-0.411149\pi$
$348$	−0.760503	+	1.31723i	−0.0407672	+	0.0706109i
$349$	−14.9967	−	8.65837i	−0.802757	−	0.463472i	0.0416774	−	0.999131i	$-0.486730\pi$
$349$	−14.9967	−	8.65837i	−0.802757	−	0.463472i	−0.844434	+	0.535659i	$0.820063\pi$
$350$	−2.17812			−0.116425
$351$	−19.4002	+	2.17744i	−1.03551	+	0.116223i
$352$	5.74148			0.306022
$353$	−21.9533	−	12.6747i	−1.16846	−	0.674608i	−0.215140	−	0.976583i	$-0.569021\pi$
$353$	−21.9533	−	12.6747i	−1.16846	−	0.674608i	−0.953316	+	0.301975i	$0.902354\pi$
$354$	2.29153	−	3.96904i	0.121793	−	0.210952i
$355$	2.46711	+	4.27317i	0.130941	+	0.226796i
$356$			5.94983i			0.315341i
$357$	−2.77539	+	1.60237i	−0.146889	+	0.0848064i
$358$	−13.5886	+	7.84539i	−0.718181	+	0.414642i
$359$			5.27044i			0.278163i	0.990281	+	0.139082i	$0.0444151\pi$
$359$			5.27044i			0.278163i	−0.990281	+	0.139082i	$0.955585\pi$
$360$	4.49208	+	7.78052i	0.236754	+	0.410069i
$361$	7.72804	−	13.3854i	0.406739	−	0.704493i
$362$	−24.1587	−	13.9480i	−1.26975	−	0.733092i
$363$	−3.83077			−0.201063
$364$	−1.22378	−	0.534557i	−0.0641437	−	0.0280184i
$365$	−13.9240			−0.728813
$366$	−1.39678	−	0.806433i	−0.0730110	−	0.0421529i
$367$	−12.6588	+	21.9257i	−0.660783	+	1.14451i	0.319627	+	0.947544i	$0.396443\pi$
$367$	−12.6588	+	21.9257i	−0.660783	+	1.14451i	−0.980410	+	0.196967i	$0.936891\pi$
$368$	−10.9257	−	18.9240i	−0.569544	−	0.986479i
$369$			10.4162i			0.542248i
$370$	−3.49722	+	2.01912i	−0.181812	+	0.104969i
$371$	9.08280	−	5.24396i	0.471556	−	0.272253i
$372$			0.894130i			0.0463585i
$373$	3.39391	+	5.87842i	0.175730	+	0.304373i	0.940414	−	0.340033i	$-0.110438\pi$
$373$	3.39391	+	5.87842i	0.175730	+	0.304373i	−0.764684	+	0.644406i	$0.777105\pi$
$374$	4.86631	−	8.42869i	0.251631	−	0.435837i
$375$	12.3104	+	7.10739i	0.635704	+	0.367024i
$376$	−20.1507			−1.03920
$377$	−5.07464	+	11.6176i	−0.261357	+	0.598336i
$378$	−6.91188			−0.355509
$379$	10.6717	+	6.16130i	0.548168	+	0.316485i	0.748383	−	0.663267i	$-0.230831\pi$
$379$	10.6717	+	6.16130i	0.548168	+	0.316485i	−0.200215	+	0.979752i	$0.564164\pi$
$380$	−1.97288	+	3.41714i	−0.101207	+	0.175295i
$381$	−6.58100	−	11.3986i	−0.337155	−	0.583969i
$382$		−	3.51970i		−	0.180083i
$383$	−6.28662	+	3.62958i	−0.321232	+	0.185463i	−0.651941	−	0.758269i	$-0.726045\pi$
$383$	−6.28662	+	3.62958i	−0.321232	+	0.185463i	0.330710	+	0.943732i	$0.392712\pi$
$384$	−7.28815	+	4.20782i	−0.371922	+	0.214729i
$385$			5.04261i			0.256995i
$386$	8.29086	+	14.3602i	0.421994	+	0.730915i
$387$	−7.44677	+	12.8982i	−0.378541	+	0.655652i
$388$	4.56346	+	2.63472i	0.231675	+	0.133757i
$389$	7.14811			0.362424			0.181212	−	0.983444i	$-0.441998\pi$
$389$	7.14811			0.362424			0.181212	+	0.983444i	$0.441998\pi$
$390$	−5.78999	−	7.85221i	−0.293187	−	0.397612i
$391$	19.2052			0.971250
$392$	−2.62055	−	1.51297i	−0.132358	−	0.0764167i
$393$	1.78974	−	3.09991i	0.0902802	−	0.156370i
$394$	12.1441	+	21.0342i	0.611811	+	1.05969i
$395$		−	28.5659i		−	1.43730i
$396$	−1.45802	+	0.841786i	−0.0732681	+	0.0423014i
$397$	−19.4520	+	11.2306i	−0.976266	+	0.563647i	−0.901141	−	0.433527i	$-0.857269\pi$
$397$	−19.4520	+	11.2306i	−0.976266	+	0.563647i	−0.0751252	+	0.997174i	$0.523936\pi$
$398$		−	25.5718i		−	1.28180i
$399$	−3.42782	−	5.93716i	−0.171606	−	0.297230i
$400$	2.66347	−	4.61327i	0.133174	−	0.230663i
$401$	−2.64547	−	1.52736i	−0.132108	−	0.0762729i	0.432489	−	0.901639i	$-0.357635\pi$
$401$	−2.64547	−	1.52736i	−0.132108	−	0.0762729i	−0.564598	+	0.825366i	$0.690969\pi$
$402$	7.48144			0.373140
$403$	0.831240	+	7.40605i	0.0414070	+	0.368921i
$404$	0.0270834			0.00134745
$405$	2.22527	+	1.28476i	0.110575	+	0.0638403i
$406$	−2.24427	+	3.88720i	−0.111381	+	0.192918i
$407$	−2.42149	−	4.19414i	−0.120029	−	0.207896i
$408$		−	9.69737i		−	0.480091i
$409$	4.85482	−	2.80293i	0.240055	−	0.138596i	−0.375147	−	0.926965i	$-0.622408\pi$
$409$	4.85482	−	2.80293i	0.240055	−	0.138596i	0.615202	+	0.788369i	$0.289074\pi$
$410$	−12.7750	+	7.37564i	−0.630912	+	0.364257i
$411$		−	25.5577i		−	1.26067i
$412$	−2.39261	−	4.14412i	−0.117875	−	0.204166i
$413$	−1.53698	+	2.66212i	−0.0756297	+	0.130995i
$414$	12.6586	+	7.30844i	0.622136	+	0.359190i
$415$	14.4719			0.710400
$416$	5.99657	−	4.42169i	0.294006	−	0.216791i
$417$	−12.9297			−0.633172
$418$	18.0308	+	10.4101i	0.881916	+	0.509175i
$419$	−3.06969	+	5.31687i	−0.149964	+	0.259746i	−0.931214	−	0.364473i	$-0.881249\pi$
$419$	−3.06969	+	5.31687i	−0.149964	+	0.259746i	0.781250	+	0.624219i	$0.214583\pi$
$420$	0.392540	+	0.679899i	0.0191540	+	0.0331757i
$421$			1.92589i			0.0938622i	0.998898	+	0.0469311i	$0.0149441\pi$
$421$			1.92589i			0.0938622i	−0.998898	+	0.0469311i	$0.985056\pi$
$422$	−11.0557	+	6.38302i	−0.538184	+	0.310720i
$423$	9.43475	−	5.44716i	0.458733	−	0.264850i
$424$			31.7359i			1.54123i
$425$	2.34092	+	4.05459i	0.113551	+	0.196677i
$426$	2.02675	−	3.51044i	0.0981965	−	0.170081i
$427$	0.936853	+	0.540892i	0.0453375	+	0.0261756i
$428$	1.48470			0.0717658
$429$	9.41700	−	6.94381i	0.454657	−	0.335250i
$430$	−21.0920			−1.01714
$431$	9.30923	+	5.37469i	0.448410	+	0.258890i	0.707158	−	0.707055i	$-0.249977\pi$
$431$	9.30923	+	5.37469i	0.448410	+	0.258890i	−0.258749	+	0.965945i	$0.583310\pi$
$432$	8.45207	−	14.6394i	0.406651	−	0.704340i
$433$	20.1328	+	34.8710i	0.967520	+	1.67579i	0.702685	+	0.711501i	$0.251984\pi$
$433$	20.1328	+	34.8710i	0.967520	+	1.67579i	0.264835	+	0.964294i	$0.414682\pi$
$434$			2.63861i			0.126658i
$435$	6.45439	−	3.72644i	0.309464	−	0.178669i
$436$	0.637000	−	0.367772i	0.0305068	−	0.0176131i
$437$			41.0842i			1.96532i
$438$	5.71931	+	9.90614i	0.273279	+	0.473334i
$439$	−10.9754	+	19.0099i	−0.523826	+	0.907294i	0.475789	+	0.879560i	$0.342163\pi$
$439$	−10.9754	+	19.0099i	−0.523826	+	0.907294i	−0.999615	+	0.0277345i	$0.991171\pi$
$440$	−13.2144	−	7.62934i	−0.629972	−	0.363715i
$441$	1.63595			0.0779024
$442$	−1.40868	−	12.5509i	−0.0670042	−	0.596984i
$443$	−27.8963			−1.32539			−0.662697	−	0.748887i	$-0.730588\pi$
$443$	−27.8963			−1.32539			−0.662697	+	0.748887i	$0.730588\pi$
$444$	−0.652982	−	0.376999i	−0.0309892	−	0.0178916i
$445$	14.5770	−	25.2481i	0.691017	−	1.19688i
$446$	5.35046	+	9.26727i	0.253352	+	0.438818i
$447$			2.69484i			0.127461i
$448$	7.69203	−	4.44099i	0.363414	−	0.209817i
$449$	19.1056	−	11.0306i	0.901648	−	0.520567i	0.0239134	−	0.999714i	$-0.492387\pi$
$449$	19.1056	−	11.0306i	0.901648	−	0.520567i	0.877734	+	0.479147i	$0.159054\pi$
$450$			3.56329i			0.167975i
$451$	−8.84546	−	15.3208i	−0.416516	−	0.721427i
$452$	1.95826	−	3.39181i	0.0921088	−	0.159537i
$453$	20.8519	+	12.0389i	0.979708	+	0.565635i
$454$	−1.17408			−0.0551023
$455$	3.88347	+	5.26665i	0.182060	+	0.246904i
$456$	20.7448			0.971464
$457$	4.77724	+	2.75814i	0.223470	+	0.129020i	0.607556	−	0.794277i	$-0.292150\pi$
$457$	4.77724	+	2.75814i	0.223470	+	0.129020i	−0.384086	+	0.923297i	$0.625483\pi$
$458$	15.7150	−	27.2192i	0.734314	−	1.27187i
$459$	7.42851	+	12.8665i	0.346733	+	0.600559i
$460$		−	4.70479i		−	0.219362i
$461$	25.0092	−	14.4391i	1.16479	−	0.672494i	0.212346	−	0.977195i	$-0.431890\pi$
$461$	25.0092	−	14.4391i	1.16479	−	0.672494i	0.952448	+	0.304700i	$0.0985562\pi$
$462$	3.58755	−	2.07127i	0.166908	−	0.0963643i
$463$		−	14.2284i		−	0.661251i	−0.943762	−	0.330625i	$-0.892740\pi$
$463$		−	14.2284i		−	0.661251i	0.943762	−	0.330625i	$-0.107260\pi$
$464$	−5.48874	−	9.50678i	−0.254808	−	0.441341i
$465$	2.19061	−	3.79424i	0.101587	−	0.175954i
$466$	19.1003	+	11.0276i	0.884804	+	0.510842i
$467$	4.54326			0.210237			0.105118	−	0.994460i	$-0.466478\pi$
$467$	4.54326			0.210237			0.105118	+	0.994460i	$0.466478\pi$
$468$	−0.874509	+	2.00205i	−0.0404242	+	0.0925448i
$469$	−5.01796			−0.231708
$470$	13.3613	+	7.71416i	0.616312	+	0.355828i
$471$	1.69144	−	2.92966i	0.0779374	−	0.134992i
$472$	−4.65081	−	8.05545i	−0.214071	−	0.370782i
$473$		−	25.2951i		−	1.16307i
$474$	−20.3231	+	11.7335i	−0.933469	+	0.538939i
$475$	−8.67366	+	5.00774i	−0.397975	+	0.229771i
$476$			1.01632i			0.0465829i
$477$	−8.57886	−	14.8590i	−0.392799	−	0.680348i
$478$	9.24413	−	16.0113i	0.422817	−	0.732340i
$479$	−1.44239	−	0.832764i	−0.0659044	−	0.0380499i	0.466686	−	0.884423i	$-0.345448\pi$
$479$	−1.44239	−	0.832764i	−0.0659044	−	0.0380499i	−0.532590	+	0.846373i	$0.678781\pi$
$480$	−4.38002			−0.199920
$481$	−5.75911	−	2.51562i	−0.262593	−	0.114702i
$482$	−10.7671			−0.490426
$483$	7.07925	+	4.08721i	0.322117	+	0.185974i
$484$	−0.607426	+	1.05209i	−0.0276103	+	0.0478224i
$485$	−12.9100	−	22.3608i	−0.586215	−	1.01535i
$486$			18.6248i			0.844837i
$487$	−1.28598	+	0.742463i	−0.0582735	+	0.0336442i	−0.528854	−	0.848713i	$-0.677378\pi$
$487$	−1.28598	+	0.742463i	−0.0582735	+	0.0336442i	0.470580	+	0.882357i	$0.344045\pi$
$488$	−2.83487	+	1.63671i	−0.128328	+	0.0740904i
$489$			27.3691i			1.23767i
$490$	1.15840	+	2.00641i	0.0523312	+	0.0906403i
$491$	7.99791	−	13.8528i	0.360941	−	0.625167i	−0.627175	−	0.778878i	$-0.715789\pi$
$491$	7.99791	−	13.8528i	0.360941	−	0.625167i	0.988116	+	0.153711i	$0.0491224\pi$
$492$	−2.38528	−	1.37714i	−0.107537	−	0.0620863i
$493$	9.64808			0.434528
$494$	26.8490	−	3.01348i	1.20800	−	0.135583i
$495$	8.24947			0.370786
$496$	−5.58860	−	3.22658i	−0.250936	−	0.144878i
$497$	−1.35939	+	2.35453i	−0.0609768	+	0.105615i
$498$	−5.94440	−	10.2960i	−0.266375	−	0.461375i
$499$			17.7199i			0.793253i	0.917980	+	0.396627i	$0.129819\pi$
$499$			17.7199i			0.793253i	−0.917980	+	0.396627i	$0.870181\pi$
$500$	3.90398	−	2.25397i	0.174591	−	0.100800i
$501$	7.68902	−	4.43926i	0.343520	−	0.198331i
$502$		−	18.7305i		−	0.835985i
$503$	0.598451	+	1.03655i	0.0266836	+	0.0462174i	0.879059	−	0.476713i	$-0.158172\pi$
$503$	0.598451	+	1.03655i	0.0266836	+	0.0462174i	−0.852375	+	0.522931i	$0.824839\pi$
$504$	−2.47515	+	4.28709i	−0.110252	+	0.190962i
$505$	−0.114929	−	0.0663540i	−0.00511425	−	0.00295272i
$506$	−24.8253			−1.10362
$507$	4.48774	−	14.5046i	0.199307	−	0.644174i
$508$	−4.17406			−0.185194
$509$	5.44396	+	3.14307i	0.241299	+	0.139314i	0.615774	−	0.787923i	$-0.288844\pi$
$509$	5.44396	+	3.14307i	0.241299	+	0.139314i	−0.374474	+	0.927237i	$0.622177\pi$
$510$	−3.71237	+	6.43002i	−0.164387	+	0.284726i
$511$	−3.83607	−	6.64426i	−0.169698	−	0.293925i
$512$			25.3457i			1.12013i
$513$	−27.5244	+	15.8912i	−1.21523	+	0.701614i
$514$	32.4238	−	18.7199i	1.43015	−	0.825699i
$515$			23.4474i			1.03322i
$516$	−1.96909	−	3.41056i	−0.0866843	−	0.150142i
$517$	−9.25143	+	16.0240i	−0.406878	+	0.704733i
$518$	−1.92698	−	1.11254i	−0.0846665	−	0.0488822i
$519$	6.30354			0.276695
$520$	−19.6771	+	2.20852i	−0.862898	+	0.0968499i
$521$	−10.8473			−0.475230			−0.237615	−	0.971359i	$-0.576366\pi$
$521$	−10.8473			−0.475230			−0.237615	+	0.971359i	$0.576366\pi$
$522$	6.35926	+	3.67152i	0.278337	+	0.160698i
$523$	−0.673629	+	1.16676i	−0.0294557	+	0.0510188i	−0.880377	−	0.474274i	$-0.842711\pi$
$523$	−0.673629	+	1.16676i	−0.0294557	+	0.0510188i	0.850922	+	0.525292i	$0.176044\pi$
$524$	−0.567579	−	0.983076i	−0.0247948	−	0.0429459i
$525$			1.99275i			0.0869709i
$526$	−22.0167	+	12.7113i	−0.959974	+	0.554241i
$527$	4.91181	−	2.83583i	0.213962	−	0.123531i
$528$			10.1313i			0.440907i
$529$	−12.9936	−	22.5057i	−0.564941	−	0.978507i
$530$	12.1492	−	21.0431i	0.527728	−	0.914052i
$531$	4.35510	+	2.51442i	0.188995	+	0.109117i
$532$	−2.17413			−0.0942605
$533$	−21.0375	−	9.18931i	−0.911233	−	0.398033i
$534$	−23.9502			−1.03643
$535$	−6.30034	−	3.63750i	−0.272388	−	0.157263i
$536$	7.59205	−	13.1498i	0.327926	−	0.567985i
$537$	7.17773	+	12.4322i	0.309742	+	0.536489i
$538$			28.4993i			1.22869i
$539$	−2.40625	+	1.38925i	−0.103644	+	0.0598391i
$540$	3.15198	−	1.81980i	0.135640	−	0.0783115i
$541$			20.1571i			0.866621i	0.901245	+	0.433310i	$0.142655\pi$
$541$			20.1571i			0.866621i	−0.901245	+	0.433310i	$0.857345\pi$
$542$	−5.99978	−	10.3919i	−0.257712	−	0.446371i
$543$	−12.7610	+	22.1027i	−0.547628	+	0.948519i
$544$	−4.91047	−	2.83506i	−0.210535	−	0.121552i
$545$	−3.60415			−0.154385
$546$	2.15179	−	4.92618i	0.0920880	−	0.210821i
$547$	−3.42286			−0.146351			−0.0731755	−	0.997319i	$-0.523313\pi$
$547$	−3.42286			−0.146351			−0.0731755	+	0.997319i	$0.523313\pi$
$548$	−7.01924	−	4.05256i	−0.299847	−	0.173117i
$549$	0.884873	−	1.53264i	0.0377654	−	0.0654117i
$550$	−3.02594	−	5.24109i	−0.129027	−	0.223481i
$551$			20.6394i			0.879266i
$552$	−21.4214	+	12.3677i	−0.911757	+	0.526403i
$553$	13.6311	−	7.86993i	0.579654	−	0.334663i
$554$		−	18.3093i		−	0.777889i
$555$	1.84729	+	3.19960i	0.0784130	+	0.135815i
$556$	−2.05020	+	3.55106i	−0.0869480	+	0.150598i
$557$	−20.4948	−	11.8327i	−0.868394	−	0.501367i	−0.00157977	−	0.999999i	$-0.500503\pi$
$557$	−20.4948	−	11.8327i	−0.868394	−	0.501367i	−0.866814	+	0.498631i	$0.833836\pi$
$558$	4.31664			0.182738
$559$	−19.4806	−	26.4190i	−0.823940	−	1.11740i
$560$	−5.66612			−0.239437
$561$	−7.71139	−	4.45217i	−0.325575	−	0.187971i
$562$	0.0630888	−	0.109273i	0.00266124	−	0.00460941i
$563$	14.4037	+	24.9480i	0.607045	+	1.05143i	0.991725	+	0.128382i	$0.0409784\pi$
$563$	14.4037	+	24.9480i	0.607045	+	1.05143i	−0.384680	+	0.923050i	$0.625688\pi$
$564$			2.88069i			0.121299i
$565$	−16.6198	+	9.59543i	−0.699199	+	0.403683i
$566$	−0.686177	+	0.396164i	−0.0288422	+	0.0166520i
$567$			1.41581i			0.0594585i
$568$	−4.11343	−	7.12467i	−0.172596	−	0.298945i
$569$	−13.8361	+	23.9648i	−0.580040	+	1.00466i	0.415434	+	0.909623i	$0.363630\pi$
$569$	−13.8361	+	23.9648i	−0.580040	+	1.00466i	−0.995474	+	0.0950353i	$0.969704\pi$
$570$	−13.7552	−	7.94158i	−0.576143	−	0.332636i
$571$	−12.9655			−0.542588			−0.271294	−	0.962497i	$-0.587452\pi$
$571$	−12.9655			−0.542588			−0.271294	+	0.962497i	$0.587452\pi$
$572$	−0.413861	−	3.68736i	−0.0173044	−	0.154176i
$573$	−3.22016			−0.134524
$574$	−7.03905	−	4.06400i	−0.293804	−	0.169628i
$575$	5.97105	−	10.3422i	0.249010	−	0.431298i
$576$	−7.26525	−	12.5838i	−0.302719	−	0.524324i
$577$			9.46047i			0.393844i	0.980419	+	0.196922i	$0.0630947\pi$
$577$			9.46047i			0.393844i	−0.980419	+	0.196922i	$0.936905\pi$
$578$	10.4702	−	6.04497i	0.435503	−	0.251438i
$579$	13.1381	−	7.58529i	0.546001	−	0.315234i
$580$		−	2.36354i		−	0.0981405i
$581$	3.98704	+	6.90576i	0.165410	+	0.286499i
$582$	−10.6057	+	18.3696i	−0.439620	+	0.761444i
$583$	25.2365	+	14.5703i	1.04519	+	0.603440i
$584$	23.2155			0.960663
$585$	8.61598	−	6.35317i	0.356227	−	0.262671i
$586$	31.7784			1.31275
$587$	−18.6673	−	10.7776i	−0.770481	−	0.444837i	0.0625654	−	0.998041i	$-0.480072\pi$
$587$	−18.6673	−	10.7776i	−0.770481	−	0.444837i	−0.833046	+	0.553204i	$0.813405\pi$
$588$	−0.216290	+	0.374626i	−0.00891967	+	0.0154493i
$589$	6.06647	+	10.5074i	0.249965	+	0.432951i
$590$			7.12175i			0.293198i
$591$	19.2441	−	11.1106i	0.791598	−	0.457029i
$592$	4.71274	−	2.72090i	0.193692	−	0.111828i
$593$			3.97234i			0.163124i	0.996668	+	0.0815622i	$0.0259909\pi$
$593$			3.97234i			0.163124i	−0.996668	+	0.0815622i	$0.974009\pi$
$594$	−9.60231	−	16.6317i	−0.393988	−	0.682407i
$595$	2.48997	−	4.31275i	0.102079	−	0.176806i
$596$	0.740117	+	0.427307i	0.0303164	+	0.0175032i
$597$	−23.3956			−0.957517
$598$	−25.9282	+	19.1187i	−1.06028	+	0.781821i
$599$	−19.5049			−0.796950			−0.398475	−	0.917179i	$-0.630460\pi$
$599$	−19.5049			−0.796950			−0.398475	+	0.917179i	$0.630460\pi$
$600$	−5.22211	−	3.01498i	−0.213192	−	0.123086i
$601$	13.4368	−	23.2733i	0.548100	−	0.949336i	−0.450305	−	0.892875i	$-0.648685\pi$
$601$	13.4368	−	23.2733i	0.548100	−	0.949336i	0.998405	−	0.0564616i	$-0.0179818\pi$
$602$	−5.81086	−	10.0647i	−0.236833	−	0.410207i
$603$			8.20914i			0.334302i
$604$	6.61276	−	3.81788i	0.269070	−	0.155347i
$605$	5.15523	−	2.97637i	0.209590	−	0.121007i
$606$			0.109021i			0.00442866i
$607$	−12.5102	−	21.6682i	−0.507772	−	0.879487i	−0.999960	−	0.00899773i	$-0.997136\pi$
$607$	−12.5102	−	21.6682i	−0.507772	−	0.879487i	0.492187	−	0.870489i	$-0.336197\pi$
$608$	6.06482	−	10.5046i	0.245961	−	0.426016i
$609$	3.55639	+	2.05328i	0.144112	+	0.0832031i
$610$	2.50628			0.101476
$611$	2.67808	+	23.8607i	0.108343	+	0.965300i
$612$	1.66265			0.0672086
$613$	−18.4970	−	10.6793i	−0.747088	−	0.431332i	0.0775527	−	0.996988i	$-0.475289\pi$
$613$	−18.4970	−	10.6793i	−0.747088	−	0.431332i	−0.824641	+	0.565657i	$0.808623\pi$
$614$	6.31751	−	10.9422i	0.254954	−	0.441593i
$615$	6.74796	+	11.6878i	0.272104	+	0.471298i
$616$		−	8.40757i		−	0.338751i
$617$	−28.5425	+	16.4790i	−1.14908	+	0.663420i	−0.948662	−	0.316291i	$-0.897562\pi$
$617$	−28.5425	+	16.4790i	−1.14908	+	0.663420i	−0.200415	+	0.979711i	$0.564229\pi$
$618$	16.6816	−	9.63111i	0.671031	−	0.387420i
$619$		−	48.9117i		−	1.96593i	−0.183795	−	0.982965i	$-0.558838\pi$
$619$		−	48.9117i		−	1.96593i	0.183795	−	0.982965i	$-0.441162\pi$
$620$	−0.694707	−	1.20327i	−0.0279001	−	0.0483244i
$621$	18.9481	−	32.8191i	0.760361	−	1.31698i
$622$	−8.00176	−	4.61982i	−0.320841	−	0.185238i
$623$	16.0640			0.643589
$624$	7.80240	+	10.5814i	0.312346	+	0.423595i
$625$	−13.5576			−0.542304
$626$	36.1075	+	20.8467i	1.44315	+	0.833201i
$627$	9.52417	−	16.4964i	0.380359	−	0.658801i
$628$	−0.536406	−	0.929083i	−0.0214049	−	0.0370744i
$629$			4.78278i			0.190702i
$630$	3.28239	−	1.89509i	0.130773	−	0.0755021i
$631$	4.65076	−	2.68512i	0.185144	−	0.106893i	−0.404563	−	0.914510i	$-0.632576\pi$
$631$	4.65076	−	2.68512i	0.185144	−	0.106893i	0.589707	+	0.807617i	$0.299243\pi$
$632$			47.6280i			1.89454i
$633$	5.83981	+	10.1148i	0.232111	+	0.402029i
$634$	10.9621	−	18.9869i	0.435360	−	0.754066i
$635$	17.7127	+	10.2264i	0.702905	+	0.405823i
$636$	4.53687			0.179899
$637$	−1.44325	+	3.30409i	−0.0571837	+	0.130913i
$638$	−12.4714			−0.493747
$639$	3.85189	+	2.22389i	0.152378	+	0.0879757i
$640$	6.53865	−	11.3253i	0.258463	−	0.447671i
$641$	19.8510	+	34.3829i	0.784066	+	1.35804i	0.929555	+	0.368683i	$0.120191\pi$
$641$	19.8510	+	34.3829i	0.784066	+	1.35804i	−0.145489	+	0.989360i	$0.546475\pi$
$642$			5.97647i			0.235872i
$643$	27.8388	−	16.0727i	1.09785	−	0.633847i	0.162198	−	0.986758i	$-0.448142\pi$
$643$	27.8388	−	16.0727i	1.09785	−	0.633847i	0.935657	+	0.352911i	$0.114808\pi$
$644$	2.24504	−	1.29618i	0.0884671	−	0.0510765i
$645$			19.2970i			0.759818i
$646$	−10.2807	−	17.8067i	−0.404489	−	0.700596i
$647$	−9.92502	+	17.1906i	−0.390193	+	0.675833i	−0.992475	−	0.122450i	$-0.960925\pi$
$647$	−9.92502	+	17.1906i	−0.390193	+	0.675833i	0.602282	+	0.798283i	$0.294258\pi$
$648$	−3.71020	−	2.14209i	−0.145751	−	0.0841491i
$649$	−8.54096			−0.335262
$650$	−7.19670	−	3.14357i	−0.282278	−	0.123301i
$651$	2.41406			0.0946145
$652$	7.51671	+	4.33977i	0.294377	+	0.169959i
$653$	9.50024	−	16.4549i	0.371773	−	0.643930i	−0.618065	−	0.786127i	$-0.712083\pi$
$653$	9.50024	−	16.4549i	0.371773	−	0.643930i	0.989838	+	0.142197i	$0.0454165\pi$
$654$	1.48042	+	2.56416i	0.0578889	+	0.100266i
$655$			5.56225i			0.217335i
$656$	17.2152	−	9.93918i	0.672139	−	0.388060i
$657$	−10.8697	+	6.27562i	−0.424067	+	0.244835i
$658$			8.50105i			0.331405i
$659$	3.60729	+	6.24801i	0.140520	+	0.243388i	0.927693	−	0.373345i	$-0.121789\pi$
$659$	3.60729	+	6.24801i	0.140520	+	0.243388i	−0.787173	+	0.616733i	$0.788456\pi$
$660$	−1.09067	+	1.88909i	−0.0424542	+	0.0735329i
$661$	14.5068	+	8.37548i	0.564248	+	0.325769i	0.754849	−	0.655899i	$-0.227710\pi$
$661$	14.5068	+	8.37548i	0.564248	+	0.325769i	−0.190601	+	0.981668i	$0.561044\pi$
$662$	25.4470			0.989025
$663$	−11.4828	+	1.28880i	−0.445953	+	0.0500529i
$664$	−24.1291			−0.936393
$665$	9.22592	+	5.32659i	0.357766	+	0.206556i
$666$	−1.82006	+	3.15244i	−0.0705259	+	0.122155i
$667$	−12.3048	−	21.3126i	−0.476444	−	0.825226i
$668$		−	2.81564i		−	0.108941i
$669$	8.47860	−	4.89512i	0.327802	−	0.189256i
$670$	−10.0681	+	5.81281i	−0.388964	+	0.224569i
$671$			3.00573i			0.116035i
$672$	−1.20670	−	2.09007i	−0.0465495	−	0.0806261i
$673$	−18.6684	+	32.3346i	−0.719614	+	1.24641i	0.241539	+	0.970391i	$0.422348\pi$
$673$	−18.6684	+	32.3346i	−0.719614	+	1.24641i	−0.961153	+	0.276016i	$0.910986\pi$
$674$	1.40612	+	0.811824i	0.0541618	+	0.0312703i
$675$	9.23831			0.355583
$676$	−3.27199	−	3.53245i	−0.125846	−	0.135864i
$677$	28.1341			1.08128			0.540641	−	0.841253i	$-0.318182\pi$
$677$	28.1341			1.08128			0.540641	+	0.841253i	$0.318182\pi$
$678$	13.6533	+	7.88271i	0.524350	+	0.302734i
$679$	7.11347	−	12.3209i	0.272990	−	0.472832i
$680$	7.53452	+	13.0502i	0.288935	+	0.500451i
$681$			1.07416i			0.0411620i
$682$	−6.34915	+	3.66568i	−0.243122	+	0.140366i
$683$	−1.79295	+	1.03516i	−0.0686053	+	0.0396093i	−0.533910	−	0.845541i	$-0.679278\pi$
$683$	−1.79295	+	1.03516i	−0.0686053	+	0.0396093i	0.465305	+	0.885150i	$0.345945\pi$
$684$			3.55677i			0.135996i
$685$	19.8574	+	34.3941i	0.758714	+	1.31413i
$686$	−0.638282	+	1.10554i	−0.0243697	+	0.0422096i
$687$	−24.9028	−	14.3776i	−0.950100	−	0.548540i
$688$	28.4228			1.08361
$689$	37.5788	−	4.21776i	1.43164	−	0.160684i
$690$	18.9385			0.720977
$691$	31.0542	+	17.9291i	1.18136	+	0.682057i	0.956328	−	0.292295i	$-0.0944190\pi$
$691$	31.0542	+	17.9291i	1.18136	+	0.682057i	0.225029	+	0.974352i	$0.427752\pi$
$692$	0.999521	−	1.73122i	0.0379961	−	0.0658112i
$693$	2.27274	+	3.93650i	0.0863342	+	0.149535i
$694$		−	33.0417i		−	1.25425i
$695$	17.4001	−	10.0460i	0.660023	−	0.381065i
$696$	−10.7614	+	6.21312i	−0.407911	+	0.235508i
$697$			17.4710i			0.661763i
$698$	−11.0530	−	19.1443i	−0.418361	−	0.724622i
$699$	10.0891	−	17.4748i	0.381604	−	0.660958i
$700$	0.547295	+	0.315981i	0.0206858	+	0.0119430i
$701$	−44.8940			−1.69562			−0.847812	−	0.530297i	$-0.822081\pi$
$701$	−44.8940			−1.69562			−0.847812	+	0.530297i	$0.822081\pi$
$702$	−22.8375	−	9.97558i	−0.861946	−	0.376504i
$703$	−10.2314			−0.385885
$704$	21.3722	+	12.3393i	0.805497	+	0.465054i
$705$	7.05767	−	12.2242i	0.265807	−	0.460391i
$706$	−16.1801	−	28.0248i	−0.608947	−	1.05473i
$707$		−	0.0731225i		−	0.00275005i
$708$	−1.15158	+	0.664867i	−0.0432792	+	0.0249872i
$709$	−14.0864	+	8.13279i	−0.529026	+	0.305433i	−0.740620	−	0.671924i	$-0.765468\pi$
$709$	−14.0864	+	8.13279i	−0.529026	+	0.305433i	0.211594	+	0.977358i	$0.432135\pi$
$710$			6.29886i			0.236392i
$711$	−12.8748	−	22.2998i	−0.482843	−	0.836309i
$712$	−24.3043	+	42.0963i	−0.910843	+	1.57763i
$713$	−12.5287	−	7.23344i	−0.469203	−	0.270894i
$714$	−4.09105			−0.153104
$715$	−7.27775	+	16.6613i	−0.272173	+	0.623096i
$716$	4.55255			0.170137
$717$	−14.6487	−	8.45743i	−0.547066	−	0.315849i
$718$	−3.36403	+	5.82667i	−0.125544	+	0.217449i
$719$	−5.00744	−	8.67314i	−0.186746	−	0.323454i	0.757417	−	0.652931i	$-0.226461\pi$
$719$	−5.00744	−	8.67314i	−0.186746	−	0.323454i	−0.944164	+	0.329477i	$0.893127\pi$
$720$			9.26949i			0.345454i
$721$	−11.1887	+	6.45980i	−0.416689	+	0.240575i
$722$	17.0873	−	9.86534i	0.635922	−	0.367150i
$723$			9.85076i			0.366354i
$724$	4.04690	+	7.00944i	0.150402	+	0.260504i
$725$	2.99966	−	5.19556i	0.111405	−	0.192958i
$726$	−4.23506	−	2.44511i	−0.157178	−	0.0907466i
$727$	34.5299			1.28064			0.640322	−	0.768106i	$-0.278801\pi$
$727$	34.5299			1.28064			0.640322	+	0.768106i	$0.278801\pi$
$728$	−6.47493	−	8.78111i	−0.239977	−	0.325450i
$729$	21.2872			0.788415
$730$	−15.3934	−	8.88741i	−0.569737	−	0.328938i
$731$	−12.4904	+	21.6340i	−0.461973	+	0.800161i
$732$	0.233980	+	0.405265i	0.00864814	+	0.0149790i
$733$		−	33.1360i		−	1.22391i	−0.790894	−	0.611953i	$-0.790384\pi$
$733$		−	33.1360i		−	1.22391i	0.790894	−	0.611953i	$-0.209616\pi$
$734$	−27.9895	+	16.1598i	−1.03311	+	0.596468i
$735$	1.83566	−	1.05982i	0.0677093	−	0.0390920i
$736$			14.4629i			0.533111i
$737$	−6.97119	−	12.0745i	−0.256787	−	0.444768i
$738$	−6.64850	+	11.5155i	−0.244735	+	0.423893i
$739$	−3.47767	−	2.00784i	−0.127928	−	0.0738594i	0.434670	−	0.900590i	$-0.356865\pi$
$739$	−3.47767	−	2.00784i	−0.127928	−	0.0738594i	−0.562598	+	0.826730i	$0.690198\pi$
$740$	1.17166			0.0430711
$741$	−2.75703	−	24.5641i	−0.101282	−	0.902386i
$742$	13.3885			0.491507
$743$	10.8361	+	6.25622i	0.397538	+	0.229519i	0.685421	−	0.728147i	$-0.259618\pi$
$743$	10.8361	+	6.25622i	0.397538	+	0.229519i	−0.287883	+	0.957666i	$0.592952\pi$
$744$	−3.65241	+	6.32616i	−0.133904	+	0.231928i
$745$	−2.09379	−	3.62656i	−0.0767107	−	0.132867i
$746$			8.66508i			0.317251i
$747$	11.2975	−	6.52260i	0.413353	−	0.238650i
$748$	−2.44551	+	1.41192i	−0.0894168	+	0.0516248i
$749$		−	4.00855i		−	0.146469i
$750$	9.07304	+	15.7150i	0.331300	+	0.573829i
$751$	18.7579	−	32.4896i	0.684486	−	1.18556i	−0.289112	−	0.957295i	$-0.593360\pi$
$751$	18.7579	−	32.4896i	0.684486	−	1.18556i	0.973598	−	0.228269i	$-0.0733065\pi$
$752$	−18.0053	−	10.3954i	−0.656585	−	0.379080i
$753$	−17.1365			−0.624490
$754$	−13.0255	+	9.60461i	−0.474360	+	0.349779i
$755$	−37.4150			−1.36167
$756$	1.73675	+	1.00271i	0.0631649	+	0.0364683i
$757$	17.5223	−	30.3496i	0.636860	−	1.10307i	−0.349258	−	0.937027i	$-0.613566\pi$
$757$	17.5223	−	30.3496i	0.636860	−	1.10307i	0.986118	−	0.166047i	$-0.0531004\pi$
$758$	7.86530	+	13.6231i	0.285680	+	0.494813i
$759$			22.7126i			0.824414i
$760$	−27.9172	+	16.1180i	−1.01266	+	0.584661i
$761$	−3.72586	+	2.15113i	−0.135062	+	0.0779782i	−0.566009	−	0.824399i	$-0.691513\pi$
$761$	−3.72586	+	2.15113i	−0.135062	+	0.0779782i	0.430946	+	0.902378i	$0.358180\pi$
$762$		−	16.8021i		−	0.608677i
$763$	−0.992947	−	1.71984i	−0.0359471	−	0.0622622i
$764$	−0.510605	+	0.884394i	−0.0184730	+	0.0319962i
$765$	−7.05545	−	4.07347i	−0.255090	−	0.147277i
$766$	−9.26679			−0.334823
$767$	−8.92043	+	6.57766i	−0.322098	+	0.237506i
$768$	10.0039			0.360985
$769$	10.6146	+	6.12834i	0.382772	+	0.220994i	0.679024	−	0.734116i	$-0.262403\pi$
$769$	10.6146	+	6.12834i	0.382772	+	0.220994i	−0.296251	+	0.955110i	$0.595737\pi$
$770$	−3.21861	+	5.57479i	−0.115991	+	0.200902i

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:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	91.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.10554 + 0.638282i) q^{2} +(0.583963 - 1.01145i) q^{3} +(-0.185192 - 0.320762i) q^{4} +1.81487i q^{5} +(1.29118 - 0.745466i) q^{6} +(-0.866025 + 0.500000i) q^{7} -3.02595i q^{8} +(0.817975 + 1.41677i) q^{9} +O(q^{10})\)	\(q+(1.10554 + 0.638282i) q^{2} +(0.583963 - 1.01145i) q^{3} +(-0.185192 - 0.320762i) q^{4} +1.81487i q^{5} +(1.29118 - 0.745466i) q^{6} +(-0.866025 + 0.500000i) q^{7} -3.02595i q^{8} +(0.817975 + 1.41677i) q^{9} +(-1.15840 + 2.00641i) q^{10} +(-2.40625 - 1.38925i) q^{11} -0.432581 q^{12} +(-3.58305 + 0.402155i) q^{13} -1.27656 q^{14} +(1.83566 + 1.05982i) q^{15} +(1.56102 - 2.70377i) q^{16} +(1.37198 + 2.37634i) q^{17} +2.08840i q^{18} +(-5.08351 + 2.93497i) q^{19} +(0.582143 - 0.336100i) q^{20} +1.16793i q^{21} +(-1.77346 - 3.07173i) q^{22} +(3.49955 - 6.06139i) q^{23} +(-3.06060 - 1.76704i) q^{24} +1.70623 q^{25} +(-4.21789 - 1.84240i) q^{26} +5.41444 q^{27} +(0.320762 + 0.185192i) q^{28} +(1.75806 - 3.04505i) q^{29} +(1.35293 + 2.34334i) q^{30} -2.06697i q^{31} +(-1.78956 + 1.03320i) q^{32} +(-2.81031 + 1.62254i) q^{33} +3.50284i q^{34} +(-0.907437 - 1.57173i) q^{35} +(0.302965 - 0.524751i) q^{36} +(1.50950 + 0.871512i) q^{37} -7.49334 q^{38} +(-1.68561 + 3.85893i) q^{39} +5.49171 q^{40} +(5.51406 + 3.18355i) q^{41} +(-0.745466 + 1.29118i) q^{42} +(4.55195 + 7.88422i) q^{43} +1.02911i q^{44} +(-2.57127 + 1.48452i) q^{45} +(7.73776 - 4.46740i) q^{46} -6.65932i q^{47} +(-1.82316 - 3.15780i) q^{48} +(0.500000 - 0.866025i) q^{49} +(1.88631 + 1.08906i) q^{50} +3.20474 q^{51} +(0.792549 + 1.07483i) q^{52} -10.4879 q^{53} +(5.98587 + 3.45594i) q^{54} +(2.52131 - 4.36703i) q^{55} +(1.51297 + 2.62055i) q^{56} +6.85564i q^{57} +(3.88720 - 2.24427i) q^{58} +(2.66212 - 1.53698i) q^{59} -0.785080i q^{60} +(-0.540892 - 0.936853i) q^{61} +(1.31931 - 2.28511i) q^{62} +(-1.41677 - 0.817975i) q^{63} -8.88199 q^{64} +(-0.729860 - 6.50279i) q^{65} -4.14254 q^{66} +(4.34568 + 2.50898i) q^{67} +(0.508159 - 0.880158i) q^{68} +(-4.08721 - 7.07925i) q^{69} -2.31680i q^{70} +(2.35453 - 1.35939i) q^{71} +(4.28709 - 2.47515i) q^{72} +7.67213i q^{73} +(1.11254 + 1.92698i) q^{74} +(0.996377 - 1.72578i) q^{75} +(1.88285 + 1.08706i) q^{76} +2.77849 q^{77} +(-4.32659 + 3.19030i) q^{78} -15.7399 q^{79} +(4.90700 + 2.83306i) q^{80} +(0.707906 - 1.22613i) q^{81} +(4.06400 + 7.03905i) q^{82} -7.97408i q^{83} +(0.374626 - 0.216290i) q^{84} +(-4.31275 + 2.48997i) q^{85} +11.6217i q^{86} +(-2.05328 - 3.55639i) q^{87} +(-4.20379 + 7.28117i) q^{88} +(-13.9118 - 8.03198i) q^{89} -3.79017 q^{90} +(2.90194 - 2.13980i) q^{91} -2.59235 q^{92} +(-2.09064 - 1.20703i) q^{93} +(4.25052 - 7.36212i) q^{94} +(-5.32659 - 9.22592i) q^{95} +2.41340i q^{96} +(-12.3209 + 7.11347i) q^{97} +(1.10554 - 0.638282i) q^{98} -4.54548i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{4} - 18 q^{6} - 4 q^{9}+O(q^{10}) \) 12 * q + 4 * q^4 - 18 * q^6 - 4 * q^9	\( 12 q + 4 q^{4} - 18 q^{6} - 4 q^{9} + 12 q^{10} + 6 q^{11} - 4 q^{12} + 4 q^{13} - 8 q^{14} + 6 q^{15} - 8 q^{16} - 4 q^{17} - 12 q^{20} + 6 q^{22} - 12 q^{23} + 12 q^{24} - 20 q^{25} - 42 q^{26} + 12 q^{27} + 8 q^{29} + 8 q^{30} + 36 q^{32} - 30 q^{33} + 6 q^{35} - 10 q^{36} - 42 q^{37} + 4 q^{38} - 4 q^{39} + 92 q^{40} + 30 q^{41} + 4 q^{42} + 2 q^{43} + 12 q^{46} - 2 q^{48} + 6 q^{49} - 18 q^{50} + 52 q^{51} + 2 q^{52} - 44 q^{53} + 12 q^{54} - 6 q^{55} - 12 q^{56} - 12 q^{58} + 18 q^{59} + 14 q^{61} - 4 q^{62} + 12 q^{63} - 52 q^{64} + 60 q^{65} - 52 q^{66} - 24 q^{67} - 8 q^{68} + 4 q^{69} - 24 q^{71} + 60 q^{72} + 6 q^{74} + 46 q^{75} - 18 q^{76} + 8 q^{77} - 10 q^{78} - 56 q^{79} - 72 q^{80} + 2 q^{81} + 14 q^{82} + 18 q^{84} - 48 q^{85} - 2 q^{87} - 14 q^{88} - 12 q^{89} + 24 q^{90} + 14 q^{91} + 24 q^{92} - 18 q^{93} + 4 q^{94} - 22 q^{95} + 6 q^{97}+O(q^{100}) \) 12 * q + 4 * q^4 - 18 * q^6 - 4 * q^9 + 12 * q^10 + 6 * q^11 - 4 * q^12 + 4 * q^13 - 8 * q^14 + 6 * q^15 - 8 * q^16 - 4 * q^17 - 12 * q^20 + 6 * q^22 - 12 * q^23 + 12 * q^24 - 20 * q^25 - 42 * q^26 + 12 * q^27 + 8 * q^29 + 8 * q^30 + 36 * q^32 - 30 * q^33 + 6 * q^35 - 10 * q^36 - 42 * q^37 + 4 * q^38 - 4 * q^39 + 92 * q^40 + 30 * q^41 + 4 * q^42 + 2 * q^43 + 12 * q^46 - 2 * q^48 + 6 * q^49 - 18 * q^50 + 52 * q^51 + 2 * q^52 - 44 * q^53 + 12 * q^54 - 6 * q^55 - 12 * q^56 - 12 * q^58 + 18 * q^59 + 14 * q^61 - 4 * q^62 + 12 * q^63 - 52 * q^64 + 60 * q^65 - 52 * q^66 - 24 * q^67 - 8 * q^68 + 4 * q^69 - 24 * q^71 + 60 * q^72 + 6 * q^74 + 46 * q^75 - 18 * q^76 + 8 * q^77 - 10 * q^78 - 56 * q^79 - 72 * q^80 + 2 * q^81 + 14 * q^82 + 18 * q^84 - 48 * q^85 - 2 * q^87 - 14 * q^88 - 12 * q^89 + 24 * q^90 + 14 * q^91 + 24 * q^92 - 18 * q^93 + 4 * q^94 - 22 * q^95 + 6 * q^97

Introduction

L-functions

Modular forms

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