LMFDB - Embedded newform 418.2.v.a.13.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(13,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(90))

chi = DirichletCharacter(H, H._module([9, 25]))

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

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

chi := DirichletCharacter("418.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.v (of order $90$, degree $24$, 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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$10$ over $\Q(\zeta_{90})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{90}]$

Embedding invariants

Embedding label			13.3
Character	$\chi$	$=$	418.13
Dual form			418.2.v.a.193.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.374607 + 0.927184i) q^{2} +(-0.301053 - 1.04990i) q^{3} +(-0.719340 + 0.694658i) q^{4} +(-0.793784 + 0.422062i) q^{5} +(0.860670 - 0.672429i) q^{6} +(-0.868426 - 1.95052i) q^{7} +(-0.913545 - 0.406737i) q^{8} +(1.53250 - 0.957610i) q^{9} +O(q^{10})$	\(q+(0.374607 + 0.927184i) q^{2} +(-0.301053 - 1.04990i) q^{3} +(-0.719340 + 0.694658i) q^{4} +(-0.793784 + 0.422062i) q^{5} +(0.860670 - 0.672429i) q^{6} +(-0.868426 - 1.95052i) q^{7} +(-0.913545 - 0.406737i) q^{8} +(1.53250 - 0.957610i) q^{9} +(-0.688686 - 0.577876i) q^{10} +(3.30400 - 0.289054i) q^{11} +(0.945878 + 0.546103i) q^{12} +(-0.0445023 - 1.27438i) q^{13} +(1.48317 - 1.53587i) q^{14} +(0.682093 + 0.706328i) q^{15} +(0.0348995 - 0.999391i) q^{16} +(2.84124 - 4.54694i) q^{17} +(1.46196 + 1.06218i) q^{18} +(4.07928 + 1.53605i) q^{19} +(0.277811 - 0.855015i) q^{20} +(-1.78640 + 1.49897i) q^{21} +(1.50571 + 2.95514i) q^{22} +(0.891361 - 5.05516i) q^{23} +(-0.152006 + 1.08158i) q^{24} +(-2.34401 + 3.47514i) q^{25} +(1.16491 - 0.518653i) q^{26} +(-3.90175 - 3.51316i) q^{27} +(1.97964 + 0.799825i) q^{28} +(0.497986 + 1.99731i) q^{29} +(-0.399379 + 0.897020i) q^{30} +(1.23199 - 1.10929i) q^{31} +(0.939693 - 0.342020i) q^{32} +(-1.29816 - 3.38184i) q^{33} +(5.28020 + 0.931041i) q^{34} +(1.51258 + 1.18176i) q^{35} +(-0.437174 + 1.75341i) q^{36} +(0.971351 - 1.33695i) q^{37} +(0.103924 + 4.35766i) q^{38} +(-1.32457 + 0.430378i) q^{39} +(0.896826 - 0.0627122i) q^{40} +(-11.0076 + 3.15639i) q^{41} +(-2.05901 - 1.09480i) q^{42} +(9.89845 - 1.74536i) q^{43} +(-2.17591 + 2.50308i) q^{44} +(-0.812299 + 1.40694i) q^{45} +(5.02097 - 1.06724i) q^{46} +(-5.44569 - 0.380800i) q^{47} +(-1.05976 + 0.264229i) q^{48} +(1.63356 - 1.81426i) q^{49} +(-4.10017 - 0.871518i) q^{50} +(-5.62918 - 1.61414i) q^{51} +(0.917270 + 0.885798i) q^{52} +(-3.63374 + 6.83408i) q^{53} +(1.79572 - 4.93370i) q^{54} +(-2.50067 + 1.62394i) q^{55} +2.13511i q^{56} +(0.384614 - 4.74525i) q^{57} +(-1.66533 + 1.20993i) q^{58} +(-0.409467 - 5.85565i) q^{59} +(-0.981313 - 0.0342682i) q^{60} +(1.00653 + 7.16187i) q^{61} +(1.49003 + 0.726735i) q^{62} +(-3.19869 - 2.15754i) q^{63} +(0.669131 + 0.743145i) q^{64} +(0.573193 + 0.992799i) q^{65} +(2.64929 - 2.47049i) q^{66} +(6.54439 - 7.79931i) q^{67} +(1.11475 + 5.24449i) q^{68} +(-5.57574 + 0.586034i) q^{69} +(-0.529084 + 1.84514i) q^{70} +(5.56936 + 10.4744i) q^{71} +(-1.78950 + 0.251498i) q^{72} +(-11.1069 + 7.49168i) q^{73} +(1.60347 + 0.399791i) q^{74} +(4.35420 + 1.41477i) q^{75} +(-4.00142 + 1.72877i) q^{76} +(-3.43309 - 6.19349i) q^{77} +(-0.895232 - 1.06690i) q^{78} +(-9.36358 + 11.9848i) q^{79} +(0.394103 + 0.808030i) q^{80} +(-0.137291 + 0.281488i) q^{81} +(-7.05009 - 9.02370i) q^{82} +(0.631908 - 2.97289i) q^{83} +(0.243758 - 2.31920i) q^{84} +(-0.336241 + 4.80847i) q^{85} +(5.32630 + 8.52386i) q^{86} +(1.94705 - 1.12413i) q^{87} +(-3.13593 - 1.07980i) q^{88} +(3.20996 + 8.81928i) q^{89} +(-1.60879 - 0.226100i) q^{90} +(-2.44705 + 1.19351i) q^{91} +(2.87042 + 4.25557i) q^{92} +(-1.53553 - 0.959508i) q^{93} +(-1.68692 - 5.19181i) q^{94} +(-3.88638 + 0.502419i) q^{95} +(-0.641983 - 0.883613i) q^{96} +(6.79653 - 2.74598i) q^{97} +(2.29409 + 0.834982i) q^{98} +(4.78657 - 3.60692i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 3 q^{3} - 12 q^{6} + 33 q^{7} - 30 q^{8} + 3 q^{9}+O(q^{10}) $ 240 * q + 3 * q^3 - 12 * q^6 + 33 * q^7 - 30 * q^8 + 3 * q^9	$ 240 q + 3 q^{3} - 12 q^{6} + 33 q^{7} - 30 q^{8} + 3 q^{9} - 3 q^{11} - 6 q^{13} - 18 q^{14} + 21 q^{15} + 21 q^{17} - 60 q^{18} + 45 q^{19} + 12 q^{20} + 48 q^{21} - 12 q^{22} + 12 q^{24} - 18 q^{25} - 96 q^{26} - 9 q^{27} - 6 q^{28} + 18 q^{29} + 9 q^{31} + 87 q^{33} - 24 q^{34} - 36 q^{35} - 12 q^{36} - 36 q^{38} + 60 q^{41} - 6 q^{42} - 12 q^{43} + 18 q^{44} + 48 q^{45} + 12 q^{46} - 54 q^{47} + 6 q^{48} - 81 q^{49} - 21 q^{50} - 75 q^{51} + 3 q^{52} - 39 q^{53} + 27 q^{54} - 126 q^{55} - 90 q^{57} - 24 q^{58} + 69 q^{59} - 42 q^{60} + 66 q^{61} - 45 q^{62} - 9 q^{63} + 30 q^{64} - 12 q^{66} - 9 q^{67} + 12 q^{68} - 54 q^{69} + 9 q^{70} + 48 q^{71} + 6 q^{72} - 12 q^{74} + 72 q^{77} - 36 q^{79} - 27 q^{81} + 45 q^{82} + 36 q^{83} + 36 q^{84} - 210 q^{85} + 3 q^{86} + 216 q^{87} + 3 q^{88} + 18 q^{89} - 96 q^{90} - 108 q^{91} - 30 q^{92} + 147 q^{93} - 18 q^{94} + 66 q^{95} - 9 q^{97} - 12 q^{98} - 42 q^{99}+O(q^{100}) $ 240 * q + 3 * q^3 - 12 * q^6 + 33 * q^7 - 30 * q^8 + 3 * q^9 - 3 * q^11 - 6 * q^13 - 18 * q^14 + 21 * q^15 + 21 * q^17 - 60 * q^18 + 45 * q^19 + 12 * q^20 + 48 * q^21 - 12 * q^22 + 12 * q^24 - 18 * q^25 - 96 * q^26 - 9 * q^27 - 6 * q^28 + 18 * q^29 + 9 * q^31 + 87 * q^33 - 24 * q^34 - 36 * q^35 - 12 * q^36 - 36 * q^38 + 60 * q^41 - 6 * q^42 - 12 * q^43 + 18 * q^44 + 48 * q^45 + 12 * q^46 - 54 * q^47 + 6 * q^48 - 81 * q^49 - 21 * q^50 - 75 * q^51 + 3 * q^52 - 39 * q^53 + 27 * q^54 - 126 * q^55 - 90 * q^57 - 24 * q^58 + 69 * q^59 - 42 * q^60 + 66 * q^61 - 45 * q^62 - 9 * q^63 + 30 * q^64 - 12 * q^66 - 9 * q^67 + 12 * q^68 - 54 * q^69 + 9 * q^70 + 48 * q^71 + 6 * q^72 - 12 * q^74 + 72 * q^77 - 36 * q^79 - 27 * q^81 + 45 * q^82 + 36 * q^83 + 36 * q^84 - 210 * q^85 + 3 * q^86 + 216 * q^87 + 3 * q^88 + 18 * q^89 - 96 * q^90 - 108 * q^91 - 30 * q^92 + 147 * q^93 - 18 * q^94 + 66 * q^95 - 9 * q^97 - 12 * q^98 - 42 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{10}\right)$

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 $

$2$	0.374607	+	0.927184i	0.264887	+	0.655618i
$2$	0.374607	+	0.927184i	0.264887	+	0.655618i
$3$	−0.301053	−	1.04990i	−0.173813	−	0.606158i	−0.999138	−	0.0415005i	$-0.986786\pi$
$3$	−0.301053	−	1.04990i	−0.173813	−	0.606158i	0.825326	−	0.564657i	$-0.190992\pi$
$4$	−0.719340	+	0.694658i	−0.359670	+	0.347329i
$5$	−0.793784	+	0.422062i	−0.354991	+	0.188752i	−0.637383	−	0.770547i	$-0.719983\pi$
$5$	−0.793784	+	0.422062i	−0.354991	+	0.188752i	0.282392	+	0.959299i	$0.408872\pi$
$6$	0.860670	−	0.672429i	0.351367	−	0.274518i
$7$	−0.868426	−	1.95052i	−0.328234	−	0.737226i	0.671760	−	0.740769i	$-0.265539\pi$
$7$	−0.868426	−	1.95052i	−0.328234	−	0.737226i	−0.999994	+	0.00354334i	$0.998872\pi$
$8$	−0.913545	−	0.406737i	−0.322987	−	0.143803i
$9$	1.53250	−	0.957610i	0.510832	−	0.319203i
$10$	−0.688686	−	0.577876i	−0.217782	−	0.182741i
$11$	3.30400	−	0.289054i	0.996195	−	0.0871531i
$11$	3.30400	−	0.289054i	0.996195	−	0.0871531i
$12$	0.945878	+	0.546103i	0.273052	+	0.157646i
$13$	−0.0445023	−	1.27438i	−0.0123427	−	0.353449i	−0.989813	−	0.142375i	$-0.954526\pi$
$13$	−0.0445023	−	1.27438i	−0.0123427	−	0.353449i	0.977470	−	0.211074i	$-0.0676961\pi$
$14$	1.48317	−	1.53587i	0.396394	−	0.410478i
$15$	0.682093	+	0.706328i	0.176116	+	0.182373i
$16$	0.0348995	−	0.999391i	0.00872487	−	0.249848i
$17$	2.84124	−	4.54694i	0.689103	−	1.10279i	−0.299767	−	0.954012i	$-0.596909\pi$
$17$	2.84124	−	4.54694i	0.689103	−	1.10279i	0.988870	−	0.148782i	$-0.0475354\pi$
$18$	1.46196	+	1.06218i	0.344588	+	0.250358i
$19$	4.07928	+	1.53605i	0.935852	+	0.352394i
$19$	4.07928	+	1.53605i	0.935852	+	0.352394i
$20$	0.277811	−	0.855015i	0.0621205	−	0.191187i
$21$	−1.78640	+	1.49897i	−0.389824	+	0.327101i
$22$	1.50571	+	2.95514i	0.321018	+	0.630038i
$23$	0.891361	−	5.05516i	0.185862	−	1.05407i	−0.738982	−	0.673725i	$-0.764693\pi$
$23$	0.891361	−	5.05516i	0.185862	−	1.05407i	0.924843	−	0.380348i	$-0.124196\pi$
$24$	−0.152006	+	1.08158i	−0.0310280	+	0.220776i
$25$	−2.34401	+	3.47514i	−0.468802	+	0.695027i
$26$	1.16491	−	0.518653i	0.228458	−	0.101716i
$27$	−3.90175	−	3.51316i	−0.750893	−	0.676107i
$28$	1.97964	+	0.799825i	0.374116	+	0.151153i
$29$	0.497986	+	1.99731i	0.0924737	+	0.370892i	0.998646	−	0.0520164i	$-0.0165648\pi$
$29$	0.497986	+	1.99731i	0.0924737	+	0.370892i	−0.906172	+	0.422908i	$0.861009\pi$
$30$	−0.399379	+	0.897020i	−0.0729163	+	0.163773i
$31$	1.23199	−	1.10929i	0.221272	−	0.199234i	−0.551038	−	0.834480i	$-0.685768\pi$
$31$	1.23199	−	1.10929i	0.221272	−	0.199234i	0.772310	+	0.635246i	$0.219101\pi$
$32$	0.939693	−	0.342020i	0.166116	−	0.0604612i
$33$	−1.29816	−	3.38184i	−0.225980	−	0.588703i
$34$	5.28020	+	0.931041i	0.905546	+	0.159672i
$35$	1.51258	+	1.18176i	0.255673	+	0.199754i
$36$	−0.437174	+	1.75341i	−0.0728623	+	0.292235i
$37$	0.971351	−	1.33695i	0.159689	−	0.219793i	−0.721674	−	0.692234i	$-0.756627\pi$
$37$	0.971351	−	1.33695i	0.159689	−	0.219793i	0.881363	+	0.472440i	$0.156627\pi$
$38$	0.103924	+	4.35766i	0.0168587	+	0.706906i
$39$	−1.32457	+	0.430378i	−0.212101	+	0.0689157i
$40$	0.896826	−	0.0627122i	0.141801	−	0.00991567i
$41$	−11.0076	+	3.15639i	−1.71910	+	0.492945i	−0.982951	−	0.183870i	$-0.941138\pi$
$41$	−11.0076	+	3.15639i	−1.71910	+	0.492945i	−0.736153	+	0.676815i	$0.763360\pi$
$42$	−2.05901	−	1.09480i	−0.317713	−	0.168931i
$43$	9.89845	−	1.74536i	1.50950	−	0.266165i	0.643203	−	0.765696i	$-0.277605\pi$
$43$	9.89845	−	1.74536i	1.50950	−	0.266165i	0.866296	+	0.499530i	$0.166494\pi$
$44$	−2.17591	+	2.50308i	−0.328031	+	0.377354i
$45$	−0.812299	+	1.40694i	−0.121090	+	0.209735i
$46$	5.02097	−	1.06724i	0.740302	−	0.157356i
$47$	−5.44569	−	0.380800i	−0.794335	−	0.0555453i	−0.333178	−	0.942864i	$-0.608121\pi$
$47$	−5.44569	−	0.380800i	−0.794335	−	0.0555453i	−0.461157	+	0.887319i	$0.652566\pi$
$48$	−1.05976	+	0.264229i	−0.152964	+	0.0381381i
$49$	1.63356	−	1.81426i	0.233366	−	0.259179i
$50$	−4.10017	−	0.871518i	−0.579852	−	0.123251i
$51$	−5.62918	−	1.61414i	−0.788243	−	0.226025i
$52$	0.917270	+	0.885798i	0.127203	+	0.122838i
$53$	−3.63374	+	6.83408i	−0.499133	+	0.938733i	0.498292	+	0.867009i	$0.333961\pi$
$53$	−3.63374	+	6.83408i	−0.499133	+	0.938733i	−0.997425	+	0.0717231i	$0.977150\pi$
$54$	1.79572	−	4.93370i	0.244366	−	0.671391i
$55$	−2.50067	+	1.62394i	−0.337190	+	0.218972i
$56$			2.13511i			0.285316i
$57$	0.384614	−	4.74525i	0.0509434	−	0.628524i
$58$	−1.66533	+	1.20993i	−0.218668	+	0.158872i
$59$	−0.409467	−	5.85565i	−0.0533080	−	0.762341i	−0.948523	−	0.316707i	$-0.897423\pi$
$59$	−0.409467	−	5.85565i	−0.0533080	−	0.762341i	0.895215	−	0.445634i	$-0.147022\pi$
$60$	−0.981313	−	0.0342682i	−0.126687	−	0.00442400i
$61$	1.00653	+	7.16187i	0.128874	+	0.916983i	0.942170	+	0.335134i	$0.108782\pi$
$61$	1.00653	+	7.16187i	0.128874	+	0.916983i	−0.813297	+	0.581849i	$0.802329\pi$
$62$	1.49003	+	0.726735i	0.189234	+	0.0922954i
$63$	−3.19869	−	2.15754i	−0.402997	−	0.271825i
$64$	0.669131	+	0.743145i	0.0836413	+	0.0928931i
$65$	0.573193	+	0.992799i	0.0710958	+	0.123142i
$66$	2.64929	−	2.47049i	0.326105	−	0.304096i
$67$	6.54439	−	7.79931i	0.799525	−	0.952837i	−0.200112	−	0.979773i	$-0.564131\pi$
$67$	6.54439	−	7.79931i	0.799525	−	0.952837i	0.999637	+	0.0269362i	$0.00857509\pi$
$68$	1.11475	+	5.24449i	0.135183	+	0.635988i
$69$	−5.57574	+	0.586034i	−0.671240	+	0.0705502i
$70$	−0.529084	+	1.84514i	−0.0632377	+	0.220536i
$71$	5.56936	+	10.4744i	0.660962	+	1.24309i	0.957601	+	0.288099i	$0.0930231\pi$
$71$	5.56936	+	10.4744i	0.660962	+	1.24309i	−0.296639	+	0.954990i	$0.595866\pi$
$72$	−1.78950	+	0.251498i	−0.210895	+	0.0296393i
$73$	−11.1069	+	7.49168i	−1.29996	+	0.876835i	−0.997093	−	0.0761979i	$-0.975722\pi$
$73$	−11.1069	+	7.49168i	−1.29996	+	0.876835i	−0.302868	+	0.953032i	$0.597944\pi$
$74$	1.60347	+	0.399791i	0.186400	+	0.0464747i
$75$	4.35420	+	1.41477i	0.502780	+	0.163363i
$76$	−4.00142	+	1.72877i	−0.458994	+	0.198303i
$77$	−3.43309	−	6.19349i	−0.391237	−	0.705814i
$78$	−0.895232	−	1.06690i	−0.101365	−	0.120802i
$79$	−9.36358	+	11.9848i	−1.05349	+	1.34840i	−0.118802	+	0.992918i	$0.537905\pi$
$79$	−9.36358	+	11.9848i	−1.05349	+	1.34840i	−0.934683	+	0.355481i	$0.884317\pi$
$80$	0.394103	+	0.808030i	0.0440620	+	0.0903405i
$81$	−0.137291	+	0.281488i	−0.0152545	+	0.0312765i
$82$	−7.05009	−	9.02370i	−0.778552	−	0.996501i
$83$	0.631908	−	2.97289i	0.0693609	−	0.326317i	−0.929763	−	0.368158i	$-0.879989\pi$
$83$	0.631908	−	2.97289i	0.0693609	−	0.326317i	0.999124	+	0.0418402i	$0.0133220\pi$
$84$	0.243758	−	2.31920i	0.0265962	−	0.253046i
$85$	−0.336241	+	4.80847i	−0.0364705	+	0.521552i
$86$	5.32630	+	8.52386i	0.574349	+	0.919151i
$87$	1.94705	−	1.12413i	0.208746	−	0.120519i
$88$	−3.13593	−	1.07980i	−0.334291	−	0.115107i
$89$	3.20996	+	8.81928i	0.340255	+	0.934842i	0.985320	+	0.170715i	$0.0546077\pi$
$89$	3.20996	+	8.81928i	0.340255	+	0.934842i	−0.645066	+	0.764127i	$0.723170\pi$
$90$	−1.60879	−	0.226100i	−0.169581	−	0.0238331i
$91$	−2.44705	+	1.19351i	−0.256521	+	0.125113i
$92$	2.87042	+	4.25557i	0.299262	+	0.443674i
$93$	−1.53553	−	0.959508i	−0.159227	−	0.0994963i
$94$	−1.68692	−	5.19181i	−0.173992	−	0.535494i
$95$	−3.88638	+	0.502419i	−0.398734	+	0.0515471i
$96$	−0.641983	−	0.883613i	−0.0655221	−	0.0901834i
$97$	6.79653	−	2.74598i	0.690083	−	0.278812i	−0.00265963	−	0.999996i	$-0.500847\pi$
$97$	6.79653	−	2.74598i	0.690083	−	0.278812i	0.692743	+	0.721185i	$0.256402\pi$
$98$	2.29409	+	0.834982i	0.231738	+	0.0843459i
$99$	4.78657	−	3.60692i	0.481069	−	0.362509i
$100$	−0.727893	−	4.12809i	−0.0727893	−	0.412809i
$101$	−17.1402	+	0.598547i	−1.70551	+	0.0595577i	−0.870953	−	0.491366i	$-0.836498\pi$
$101$	−17.1402	+	0.598547i	−1.70551	+	0.0595577i	−0.834556	+	0.550923i	$0.814276\pi$
$102$	−0.612122	−	5.82395i	−0.0606091	−	0.576657i
$103$	10.9277	+	1.14855i	1.07674	+	0.113170i	0.626258	−	0.779616i	$-0.284586\pi$
$103$	10.9277	+	1.14855i	1.07674	+	0.113170i	0.450482	+	0.892786i	$0.351252\pi$
$104$	−0.477682	+	1.18230i	−0.0468406	+	0.115934i
$105$	0.785357	−	1.94383i	0.0766430	−	0.189698i
$106$	−7.69767	−	0.809058i	−0.747664	−	0.0785826i
$107$	0.652990	+	6.21279i	0.0631269	+	0.600613i	0.979662	+	0.200657i	$0.0643077\pi$
$107$	0.652990	+	6.21279i	0.0631269	+	0.600613i	−0.916535	+	0.399955i	$0.869026\pi$
$108$	5.24713	−	0.183234i	0.504905	−	0.0176317i
$109$	−3.16523	−	17.9509i	−0.303174	−	1.71938i	−0.631978	−	0.774986i	$-0.717757\pi$
$109$	−3.16523	−	17.9509i	−0.303174	−	1.71938i	0.328804	−	0.944398i	$-0.393354\pi$
$110$	−2.44246	−	1.71024i	−0.232879	−	0.163065i
$111$	−1.69609	−	0.617325i	−0.160985	−	0.0585939i
$112$	−1.97964	+	0.799825i	−0.187058	+	0.0755763i
$113$	0.393385	+	0.541448i	0.0370065	+	0.0509351i	0.827119	−	0.562026i	$-0.189978\pi$
$113$	0.393385	+	0.541448i	0.0370065	+	0.0509351i	−0.790113	+	0.612961i	$0.789978\pi$
$114$	4.54380	−	1.42100i	0.425566	−	0.133088i
$115$	1.42604	+	4.38891i	0.132979	+	0.409268i
$116$	−1.74567	−	1.09082i	−0.162082	−	0.101280i
$117$	−1.28856	−	1.91036i	−0.119127	−	0.176613i
$118$	5.27587	−	2.57322i	0.485684	−	0.236884i
$119$	−11.3363	−	1.59321i	−1.03920	−	0.146049i
$120$	−0.335833	−	0.922694i	−0.0306572	−	0.0842301i
$121$	10.8329	−	1.91007i	0.984809	−	0.173643i
$122$	−6.26331	+	3.61613i	−0.567054	+	0.327389i
$123$	6.62776	+	10.6066i	0.597605	+	0.956368i
$124$	−0.115643	+	1.65377i	−0.0103850	+	0.148513i
$125$	0.863776	−	8.21828i	0.0772585	−	0.735065i
$126$	0.802190	−	3.77401i	0.0714647	−	0.336215i
$127$	−4.66286	−	5.96819i	−0.413762	−	0.529591i	0.535308	−	0.844657i	$-0.320196\pi$
$127$	−4.66286	−	5.96819i	−0.413762	−	0.529591i	−0.949070	+	0.315066i	$0.897973\pi$
$128$	−0.438371	+	0.898794i	−0.0387469	+	0.0794429i
$129$	−4.81241	−	9.86689i	−0.423709	−	0.868732i
$130$	−0.705785	+	0.903364i	−0.0619015	+	0.0792303i
$131$	0.0478119	+	0.0569801i	0.00417735	+	0.00497837i	0.768129	−	0.640295i	$-0.221188\pi$
$131$	0.0478119	+	0.0569801i	0.00417735	+	0.00497837i	−0.763952	+	0.645273i	$0.776743\pi$
$132$	3.28304	+	1.53092i	0.285752	+	0.133249i
$133$	−0.546461	−	9.29065i	−0.0473842	−	0.805602i
$134$	9.68296	+	3.14619i	0.836481	+	0.271789i
$135$	4.57992	+	1.14190i	0.394177	+	0.0982793i
$136$	−4.44501	+	2.99820i	−0.381157	+	0.257093i
$137$	−5.78591	+	0.813156i	−0.494323	+	0.0694726i	−0.381930	−	0.924191i	$-0.624741\pi$
$137$	−5.78591	+	0.813156i	−0.494323	+	0.0694726i	−0.112393	+	0.993664i	$0.535852\pi$
$138$	−2.63207	−	4.95020i	−0.224057	−	0.421389i
$139$	−1.46877	+	5.12220i	−0.124579	+	0.434459i	−0.998684	−	0.0512774i	$-0.983671\pi$
$139$	−1.46877	+	5.12220i	−0.124579	+	0.434459i	0.874105	+	0.485736i	$0.161449\pi$
$140$	−1.90898	+	0.200642i	−0.161338	+	0.0169573i
$141$	1.23964	+	5.83205i	0.104397	+	0.491147i
$142$	−7.62542	+	9.08762i	−0.639911	+	0.762616i
$143$	−0.515400	−	4.19769i	−0.0430999	−	0.351029i
$144$	−0.903543	−	1.56498i	−0.0752952	−	0.130415i
$145$	−1.23828	−	1.37525i	−0.102834	−	0.114209i
$146$	−11.1069	−	7.49168i	−0.919211	−	0.620016i
$147$	−2.39657	−	1.16889i	−0.197666	−	0.0964080i
$148$	0.229992	+	1.63648i	0.0189052	+	0.134518i
$149$	4.01686	+	0.140272i	0.329074	+	0.0114915i	0.198960	−	0.980008i	$-0.436244\pi$
$149$	4.01686	+	0.140272i	0.329074	+	0.0114915i	0.130114	+	0.991499i	$0.458466\pi$
$150$	0.319364	+	4.56712i	0.0260760	+	0.372904i
$151$	−6.56375	+	4.76884i	−0.534150	+	0.388083i	−0.821908	−	0.569620i	$-0.807090\pi$
$151$	−6.56375	+	4.76884i	−0.534150	+	0.388083i	0.287758	+	0.957703i	$0.407090\pi$
$152$	−3.10184	−	3.06245i	−0.251593	−	0.248397i
$153$		−	9.68897i		−	0.783306i
$154$	4.45645	−	5.50323i	0.359111	−	0.443463i
$155$	−0.509745	+	1.40051i	−0.0409437	+	0.112492i
$156$	0.653849	−	1.22971i	0.0523498	−	0.0984556i
$157$	2.99502	+	2.89226i	0.239029	+	0.230828i	0.804518	−	0.593928i	$-0.202424\pi$
$157$	2.99502	+	2.89226i	0.239029	+	0.230828i	−0.565489	+	0.824756i	$0.691313\pi$
$158$	−14.6198	−	4.19216i	−1.16309	−	0.333510i
$159$	8.26902	+	1.75763i	0.655776	+	0.139389i
$160$	−0.601559	+	0.668099i	−0.0475574	+	0.0528179i
$161$	−10.6343	+	2.65142i	−0.838096	+	0.208961i
$162$	−0.312421	−	0.0218466i	−0.0245461	−	0.00171643i
$163$	11.6623	−	2.47889i	0.913460	−	0.194162i	0.272875	−	0.962049i	$-0.412025\pi$
$163$	11.6623	−	2.47889i	0.913460	−	0.194162i	0.640585	+	0.767887i	$0.278692\pi$
$164$	5.72562	−	9.91706i	0.447096	−	0.774392i
$165$	2.45780	+	2.13655i	0.191340	+	0.166330i
$166$	2.99313	−	0.527770i	0.232312	−	0.0409629i
$167$	16.9551	+	9.01518i	1.31202	+	0.697616i	0.970236	−	0.242161i	$-0.0778562\pi$
$167$	16.9551	+	9.01518i	1.31202	+	0.697616i	0.341789	+	0.939777i	$0.388967\pi$
$168$	2.24164	−	0.642780i	0.172946	−	0.0495915i
$169$	11.3463	−	0.793409i	0.872790	−	0.0610314i
$170$	−4.58429	+	1.48953i	−0.351599	+	0.114242i
$171$	7.72242	−	1.55237i	0.590548	−	0.118713i
$172$	−5.90792	+	8.13155i	−0.450474	+	0.620025i
$173$	−4.72607	+	18.9552i	−0.359316	+	1.44114i	0.470152	+	0.882585i	$0.344199\pi$
$173$	−4.72607	+	18.9552i	−0.359316	+	1.44114i	−0.829469	+	0.558553i	$0.811357\pi$
$174$	1.77165	+	1.38417i	0.134309	+	0.104934i
$175$	8.81390	+	1.55413i	0.666269	+	0.117481i
$176$	−0.173570	−	3.31208i	−0.0130833	−	0.249657i
$177$	−6.02455	+	2.19276i	−0.452833	+	0.164818i
$178$	−6.97462	+	6.27998i	−0.522770	+	0.470704i
$179$	3.41082	−	7.66082i	0.254936	−	0.572596i	−0.740056	−	0.672545i	$-0.765201\pi$
$179$	3.41082	−	7.66082i	0.254936	−	0.572596i	0.994993	+	0.0999486i	$0.0318678\pi$
$180$	−0.393026	−	1.57634i	−0.0292944	−	0.117494i
$181$	4.79264	+	1.93635i	0.356234	+	0.143928i	0.545746	−	0.837950i	$-0.316246\pi$
$181$	4.79264	+	1.93635i	0.356234	+	0.143928i	−0.189512	+	0.981878i	$0.560691\pi$
$182$	−2.02328	−	1.82177i	−0.149976	−	0.135039i
$183$	7.21619	−	3.21286i	0.533436	−	0.237501i
$184$	−2.87042	+	4.25557i	−0.211610	+	0.313725i
$185$	−0.206766	+	1.47122i	−0.0152018	+	0.108166i
$186$	0.314419	−	1.78316i	0.0230543	−	0.130748i
$187$	8.07317	−	15.8444i	0.590369	−	1.15866i
$188$	4.18183	−	3.50897i	0.304991	−	0.255918i
$189$	−3.46408	+	10.6614i	−0.251975	+	0.775499i
$190$	−1.92170	−	3.41518i	−0.139415	−	0.247763i
$191$	9.06780	+	6.58814i	0.656123	+	0.476701i	0.865351	−	0.501166i	$-0.167095\pi$
$191$	9.06780	+	6.58814i	0.656123	+	0.476701i	−0.209229	+	0.977867i	$0.567095\pi$
$192$	0.578781	−	0.926243i	0.0417699	−	0.0668459i
$193$	−0.931928	+	26.6869i	−0.0670816	+	1.92097i	0.242599	+	0.970127i	$0.422000\pi$
$193$	−0.931928	+	26.6869i	−0.0670816	+	1.92097i	−0.309681	+	0.950841i	$0.600222\pi$
$194$	5.09205	+	5.27297i	0.365588	+	0.378577i
$195$	0.869774	−	0.900678i	0.0622858	−	0.0644989i
$196$	0.0852009	+	2.43984i	0.00608578	+	0.174274i
$197$	−2.05966	−	1.18915i	−0.146745	−	0.0847232i	0.424830	−	0.905273i	$-0.360334\pi$
$197$	−2.05966	−	1.18915i	−0.146745	−	0.0847232i	−0.571575	+	0.820550i	$0.693667\pi$
$198$	5.13736	+	3.08686i	0.365096	+	0.219373i
$199$	14.4834	+	12.1530i	1.02670	+	0.861502i	0.990454	−	0.137841i	$-0.0440162\pi$
$199$	14.4834	+	12.1530i	1.02670	+	0.861502i	0.0362439	+	0.999343i	$0.488461\pi$
$200$	3.55482	−	2.22130i	0.251364	−	0.157070i
$201$	−10.1587	−	4.52293i	−0.716537	−	0.319023i
$202$	−6.97578	−	15.6679i	−0.490814	−	1.10239i
$203$	3.46333	−	2.70585i	0.243078	−	0.189913i
$204$	5.17057	−	2.74924i	0.362012	−	0.192485i
$205$	7.40549	−	7.15140i	0.517222	−	0.499475i
$206$	3.02868	+	10.5623i	0.211018	+	0.735907i
$207$	−3.47486	−	8.60059i	−0.241520	−	0.597782i
$208$	−1.27516			−0.0884162
$209$	13.9220	+	3.89599i	0.963003	+	0.269491i
$210$	2.09648			0.144671
$211$	4.73333	+	11.7154i	0.325856	+	0.806522i	0.997823	+	0.0659414i	$0.0210051\pi$
$211$	4.73333	+	11.7154i	0.325856	+	0.806522i	−0.671967	+	0.740581i	$0.734551\pi$
$212$	−2.13345	−	7.44023i	−0.146526	−	0.510997i
$213$	9.32041	−	9.00061i	0.638624	−	0.616712i
$214$	−5.51578	+	2.93279i	−0.377051	+	0.200482i
$215$	−7.12058	+	5.56320i	−0.485619	+	0.379407i
$216$	2.13550	+	4.79641i	0.145302	+	0.326355i
$217$	−3.23358	−	1.43968i	−0.219510	−	0.0977320i
$218$	15.4581	−	9.65927i	1.04695	−	0.654209i
$219$	11.2092	+	9.40567i	0.757450	+	0.635576i
$220$	0.670744	−	2.90528i	0.0452216	−	0.195874i
$221$	−5.92097	−	3.41847i	−0.398287	−	0.229951i
$222$	−0.0629914	−	1.80384i	−0.00422770	−	0.121066i
$223$	−4.88097	+	5.05439i	−0.326854	+	0.338467i	−0.862576	−	0.505927i	$-0.831151\pi$
$223$	−4.88097	+	5.05439i	−0.326854	+	0.338467i	0.535722	+	0.844394i	$0.320039\pi$
$224$	−1.48317	−	1.53587i	−0.0990984	−	0.102619i
$225$	−0.264360	+	7.57027i	−0.0176240	+	0.504685i
$226$	−0.354657	+	0.567570i	−0.0235914	+	0.0377542i
$227$	−13.9905	−	10.1647i	−0.928585	−	0.674656i	0.0170610	−	0.999854i	$-0.494569\pi$
$227$	−13.9905	−	10.1647i	−0.928585	−	0.674656i	−0.945646	+	0.325198i	$0.894569\pi$
$228$	3.01966	+	3.68063i	0.199982	+	0.243755i
$229$	6.02154	−	18.5324i	0.397914	−	1.22465i	−0.528754	−	0.848775i	$-0.677341\pi$
$229$	6.02154	−	18.5324i	0.397914	−	1.22465i	0.926668	−	0.375880i	$-0.122659\pi$
$230$	−3.53513	+	2.96632i	−0.233099	+	0.195593i
$231$	−5.46898	+	5.46895i	−0.359833	+	0.359831i
$232$	0.357448	−	2.02719i	0.0234676	−	0.133091i
$233$	−3.99592	+	28.4324i	−0.261781	+	1.86267i	0.205628	+	0.978630i	$0.434076\pi$
$233$	−3.99592	+	28.4324i	−0.261781	+	1.86267i	−0.467409	+	0.884041i	$0.654813\pi$
$234$	1.28856	−	1.91036i	0.0842356	−	0.124884i
$235$	4.48342	−	1.99615i	0.292466	−	0.130214i
$236$	4.36222	+	3.92776i	0.283956	+	0.255676i
$237$	15.4018	+	6.22272i	1.00045	+	0.404209i
$238$	−2.76945	−	11.1077i	−0.179517	−	0.720002i
$239$	3.84898	−	8.64496i	0.248970	−	0.559196i	−0.745222	−	0.666816i	$-0.767657\pi$
$239$	3.84898	−	8.64496i	0.248970	−	0.559196i	0.994192	+	0.107621i	$0.0343232\pi$
$240$	0.729702	−	0.657027i	0.0471021	−	0.0424109i
$241$	19.4873	−	7.09280i	1.25529	−	0.456887i	0.373103	−	0.927790i	$-0.378294\pi$
$241$	19.4873	−	7.09280i	1.25529	−	0.456887i	0.882185	+	0.470903i	$0.156072\pi$
$242$	5.82906	+	9.32856i	0.374706	+	0.599663i
$243$	−15.1748	−	2.67573i	−0.973466	−	0.171648i
$244$	−5.69909	−	4.45262i	−0.364847	−	0.285050i
$245$	−0.530967	+	2.12959i	−0.0339223	+	0.136055i
$246$	−7.35150	+	10.1185i	−0.468714	+	0.645130i
$247$	1.77597	−	5.26691i	0.113003	−	0.335125i
$248$	−1.57667	+	0.512291i	−0.100119	+	0.0325305i
$249$	−3.31147	+	0.231560i	−0.209856	+	0.0146745i
$250$	7.94343	−	2.27774i	0.502387	−	0.144057i
$251$	0.549650	+	0.292254i	0.0346936	+	0.0184469i	0.486728	−	0.873554i	$-0.338190\pi$
$251$	0.549650	+	0.292254i	0.0346936	+	0.0184469i	−0.452034	+	0.892001i	$0.649301\pi$
$252$	3.79970	−	0.669990i	0.239359	−	0.0422054i
$253$	1.48385	−	16.9599i	0.0932886	−	1.06626i
$254$	3.78687	−	6.55905i	0.237609	−	0.411551i
$255$	5.14962	−	1.09459i	0.322482	−	0.0685456i
$256$	−0.997564	−	0.0697565i	−0.0623478	−	0.00435978i
$257$	−2.06073	+	0.513797i	−0.128545	+	0.0320498i	−0.305663	−	0.952140i	$-0.598878\pi$
$257$	−2.06073	+	0.513797i	−0.128545	+	0.0320498i	0.177118	+	0.984190i	$0.443323\pi$
$258$	7.34567	−	8.15819i	0.457321	−	0.507907i
$259$	−3.45129	−	0.733594i	−0.214453	−	0.0455833i
$260$	−1.10198	−	0.315987i	−0.0683417	−	0.0195967i
$261$	2.67581	+	2.58400i	0.165628	+	0.159945i
$262$	−0.0349203	+	0.0656756i	−0.00215738	+	0.00405745i
$263$	−0.692692	+	1.90316i	−0.0427132	+	0.117354i	−0.959215	−	0.282676i	$-0.908778\pi$
$263$	−0.692692	+	1.90316i	−0.0427132	+	0.117354i	0.916502	+	0.400030i	$0.131000\pi$
$264$	−0.189593	+	3.61747i	−0.0116687	+	0.222640i
$265$		−	6.95845i		−	0.427454i
$266$	8.40944	−	3.98701i	0.515616	−	0.244459i
$267$	8.29296	−	6.02519i	0.507521	−	0.368735i
$268$	0.710209	+	10.1565i	0.0433829	+	0.620405i
$269$	−21.8621	−	0.763443i	−1.33296	−	0.0465479i	−0.640474	−	0.767980i	$-0.721262\pi$
$269$	−21.8621	−	0.763443i	−1.33296	−	0.0465479i	−0.692485	+	0.721432i	$0.743484\pi$
$270$	0.656915	+	4.67419i	0.0399786	+	0.284462i
$271$	−21.3265	−	10.4016i	−1.29549	−	0.631853i	−0.343838	−	0.939029i	$-0.611727\pi$
$271$	−21.3265	−	10.4016i	−1.29549	−	0.631853i	−0.951653	+	0.307176i	$0.900616\pi$
$272$	−4.44501	−	2.99820i	−0.269518	−	0.181792i
$273$	1.98975	+	2.20984i	0.120425	+	0.133746i
$274$	−2.92138	−	5.05999i	−0.176487	−	0.305685i
$275$	−6.74011	+	12.1594i	−0.406444	+	0.733240i
$276$	3.60376	−	4.29479i	0.216921	−	0.258516i
$277$	−0.127061	−	0.597775i	−0.00763435	−	0.0359168i	0.974166	−	0.225835i	$-0.0725110\pi$
$277$	−0.127061	−	0.597775i	−0.00763435	−	0.0359168i	−0.981800	+	0.189918i	$0.939178\pi$
$278$	−5.29943	+	0.556992i	−0.317838	+	0.0334062i
$279$	0.825755	−	2.87975i	0.0494366	−	0.172406i
$280$	−0.901148	−	1.69481i	−0.0538539	−	0.101284i
$281$	−20.9317	+	2.94176i	−1.24868	+	0.175491i	−0.732369	−	0.680908i	$-0.761585\pi$
$281$	−20.9317	+	2.94176i	−1.24868	+	0.175491i	−0.516314	+	0.856399i	$0.672696\pi$
$282$	−4.94300	+	3.33410i	−0.294352	+	0.198543i
$283$	24.9876	+	6.23011i	1.48536	+	0.370342i	0.898365	−	0.439249i	$-0.144755\pi$
$283$	24.9876	+	6.23011i	1.48536	+	0.370342i	0.586995	+	0.809591i	$0.300311\pi$
$284$	−11.2824	−	3.66588i	−0.669489	−	0.217530i
$285$	1.69749	+	3.92904i	0.100551	+	0.232736i
$286$	3.69896	−	2.05035i	0.218724	−	0.121240i
$287$	15.7159	+	18.7295i	0.927680	+	1.10557i
$288$	1.11255	−	1.42400i	0.0655578	−	0.0839102i
$289$	−5.14969	−	10.5584i	−0.302923	−	0.621084i
$290$	0.811244	−	1.66330i	0.0476379	−	0.0976722i
$291$	−4.92910	−	6.30897i	−0.288949	−	0.369838i
$292$	2.78546	−	13.1045i	0.163007	−	0.766885i
$293$	1.06492	−	10.1320i	0.0622132	−	0.591919i	−0.918357	−	0.395752i	$-0.870484\pi$
$293$	1.06492	−	10.1320i	0.0622132	−	0.591919i	0.980571	−	0.196167i	$-0.0628495\pi$
$294$	0.186001	−	2.65993i	0.0108478	−	0.155130i
$295$	2.79648	+	4.47530i	0.162817	+	0.260562i
$296$	−1.43116	+	0.826280i	−0.0831844	+	0.0480266i
$297$	−13.9069	−	10.4797i	−0.806961	−	0.608092i
$298$	1.37468	+	3.77691i	0.0796333	+	0.218791i
$299$	−6.48186	−	0.910966i	−0.374855	−	0.0526825i
$300$	−4.11493	+	2.00698i	−0.237575	+	0.115873i
$301$	−12.0004	−	17.7914i	−0.691693	−	1.02548i
$302$	−6.88042	−	4.29936i	−0.395924	−	0.247400i
$303$	5.78850	+	17.8152i	0.332541	+	1.02346i
$304$	1.67748	−	4.02319i	0.0962101	−	0.230746i
$305$	−3.82173	−	5.26015i	−0.218831	−	0.301196i
$306$	8.98345	−	3.62955i	0.513550	−	0.207488i
$307$	−1.26921	−	0.461953i	−0.0724374	−	0.0263650i	0.305547	−	0.952177i	$-0.401161\pi$
$307$	−1.26921	−	0.461953i	−0.0724374	−	0.0263650i	−0.377985	+	0.925812i	$0.623383\pi$
$308$	6.77192	+	2.07040i	0.385866	+	0.117972i
$309$	−2.08396	−	11.8187i	−0.118552	−	0.672345i
$310$	−1.48949	+	0.0520141i	−0.0845972	+	0.00295420i
$311$	−1.87659	−	17.8545i	−0.106411	−	1.01244i	−0.909253	−	0.416244i	$-0.863346\pi$
$311$	−1.87659	−	17.8545i	−0.106411	−	1.01244i	0.802841	−	0.596193i	$-0.203321\pi$
$312$	1.38510	+	0.145580i	0.0784160	+	0.00824186i
$313$	−3.39791	+	8.41012i	−0.192061	+	0.475368i	−0.992232	−	0.124405i	$-0.960298\pi$
$313$	−3.39791	+	8.41012i	−0.192061	+	0.475368i	0.800170	+	0.599773i	$0.204742\pi$
$314$	−1.55970	+	3.86040i	−0.0880191	+	0.217855i
$315$	3.44969	+	0.362577i	0.194368	+	0.0204289i
$316$	−1.58977	−	15.1257i	−0.0894316	−	0.850885i
$317$	−4.61005	+	0.160987i	−0.258926	+	0.00904190i	−0.164069	−	0.986449i	$-0.552462\pi$
$317$	−4.61005	+	0.160987i	−0.258926	+	0.00904190i	−0.0948577	+	0.995491i	$0.530240\pi$
$318$	1.46798	+	8.32532i	0.0823202	+	0.466861i
$319$	2.22268	+	6.45519i	0.124446	+	0.361421i
$320$	−0.844799	−	0.307482i	−0.0472257	−	0.0171887i
$321$	6.32619	−	2.55595i	0.353094	−	0.142659i
$322$	−6.44201	−	8.86667i	−0.358999	−	0.494120i
$323$	18.5746	−	14.1840i	1.03352	−	0.789216i
$324$	−0.0967792	−	0.297856i	−0.00537662	−	0.0165475i
$325$	4.53295	+	2.83250i	0.251443	+	0.157119i
$326$	6.66716	+	9.88447i	0.369260	+	0.547450i
$327$	−17.8937	+	8.72733i	−0.989522	+	0.482622i
$328$	11.3398	+	1.59370i	0.626135	+	0.0879976i
$329$	3.98642	+	10.9526i	0.219779	+	0.603836i
$330$	−1.06026	+	3.07920i	−0.0583656	+	0.169504i
$331$	−4.27481	+	2.46806i	−0.234965	+	0.135657i	−0.612860	−	0.790191i	$-0.709981\pi$
$331$	−4.27481	+	2.46806i	−0.234965	+	0.135657i	0.377895	+	0.925848i	$0.376648\pi$
$332$	1.61059	+	2.57748i	0.0883925	+	0.141458i
$333$	0.208315	−	2.97904i	0.0114156	−	0.163251i
$334$	−2.00724	+	19.0976i	−0.109831	+	1.04498i
$335$	−1.90304	+	8.95311i	−0.103974	+	0.489160i
$336$	1.43571	+	1.83762i	0.0783243	+	0.100250i
$337$	4.60918	−	9.45022i	0.251078	−	0.514786i	−0.735611	−	0.677404i	$-0.763105\pi$
$337$	4.60918	−	9.45022i	0.251078	−	0.514786i	0.986689	+	0.162618i	$0.0519938\pi$
$338$	4.98602	+	10.2229i	0.271204	+	0.556050i
$339$	0.450034	−	0.576017i	0.0244425	−	0.0312850i
$340$	−3.09837	−	3.69250i	−0.168033	−	0.200254i
$341$	3.74986	−	4.02121i	0.203066	−	0.217761i
$342$	4.33220	+	6.57858i	0.234259	+	0.355729i
$343$	−19.1716	−	6.22923i	−1.03517	−	0.336347i
$344$	−9.75258	−	2.43159i	−0.525824	−	0.131103i
$345$	4.17859	−	2.81849i	0.224968	−	0.151743i
$346$	−19.3454	+	2.71882i	−1.04001	+	0.146165i
$347$	0.854011	+	1.60616i	0.0458457	+	0.0862232i	0.904817	−	0.425800i	$-0.140007\pi$
$347$	0.854011	+	1.60616i	0.0458457	+	0.0862232i	−0.858972	+	0.512023i	$0.828896\pi$
$348$	−0.619705	+	2.16117i	−0.0332197	+	0.115851i
$349$	0.766085	−	0.0805187i	0.0410076	−	0.00431007i	−0.0840025	−	0.996466i	$-0.526770\pi$
$349$	0.766085	−	0.0805187i	0.0410076	−	0.00431007i	0.125010	+	0.992155i	$0.460104\pi$
$350$	1.86078	+	8.75430i	0.0994631	+	0.467937i
$351$	−4.30346	+	5.12866i	−0.229701	+	0.273748i
$352$	3.00589	−	1.40166i	0.160214	−	0.0747086i
$353$	−12.7741	−	22.1254i	−0.679898	−	1.17762i	−0.975011	−	0.222155i	$-0.928691\pi$
$353$	−12.7741	−	22.1254i	−0.679898	−	1.17762i	0.295114	−	0.955462i	$-0.404642\pi$
$354$	−4.28993	−	4.76444i	−0.228007	−	0.253227i
$355$	−8.84174	−	5.96383i	−0.469271	−	0.316527i
$356$	−8.43543	−	4.11424i	−0.447077	−	0.218054i
$357$	1.74012	+	12.3816i	0.0920967	+	0.655302i
$358$	8.38070	+	0.292660i	0.442934	+	0.0154676i
$359$	−0.390256	−	5.58092i	−0.0205969	−	0.294550i	−0.996931	−	0.0782828i	$-0.975056\pi$
$359$	−0.390256	−	5.58092i	−0.0205969	−	0.294550i	0.976334	−	0.216267i	$-0.0693881\pi$
$360$	1.31433	−	0.954915i	0.0692712	−	0.0503285i
$361$	14.2811	+	12.5320i	0.751636	+	0.659578i
$362$			5.16903i			0.271678i
$363$	−5.26665	−	10.7984i	−0.276427	−	0.566768i
$364$	0.931182	−	2.55840i	0.0488072	−	0.134097i
$365$	5.65450	−	10.6346i	0.295970	−	0.556639i
$366$	5.68214	+	5.48718i	0.297010	+	0.286820i
$367$	−30.3436	−	8.70090i	−1.58392	−	0.454183i	−0.635740	−	0.771903i	$-0.719305\pi$
$367$	−30.3436	−	8.70090i	−1.58392	−	0.454183i	−0.948185	+	0.317720i	$0.897083\pi$
$368$	−5.02097	−	1.06724i	−0.261736	−	0.0556338i
$369$	−13.8466	+	15.3782i	−0.720823	+	0.800555i
$370$	−1.44155	+	0.359418i	−0.0749425	+	0.0186853i
$371$	16.4856	+	1.15279i	0.855890	+	0.0598497i
$372$	1.77110	−	0.376459i	0.0918273	−	0.0195185i
$373$	0.478801	−	0.829308i	0.0247914	−	0.0429399i	−0.853364	−	0.521316i	$-0.825441\pi$
$373$	0.478801	−	0.829308i	0.0247914	−	0.0429399i	0.878155	+	0.478376i	$0.158775\pi$
$374$	17.7149	+	1.54990i	0.916017	+	0.0801435i
$375$	−8.88838	+	1.56726i	−0.458994	+	0.0809330i
$376$	4.82000	+	2.56284i	0.248572	+	0.132168i
$377$	2.52317	−	0.723508i	0.129950	−	0.0372626i
$378$	−11.1827	+	0.781971i	−0.575176	+	0.0402202i
$379$	17.6097	−	5.72174i	0.904549	−	0.293906i	0.180436	−	0.983587i	$-0.442249\pi$
$379$	17.6097	−	5.72174i	0.904549	−	0.293906i	0.724114	+	0.689681i	$0.242249\pi$
$380$	2.44662	−	3.06112i	0.125509	−	0.157032i
$381$	−4.86221	+	6.69226i	−0.249098	+	0.342855i
$382$	−2.71156	+	10.8755i	−0.138736	+	0.556438i
$383$	−9.72814	−	7.60045i	−0.497085	−	0.388365i	0.335694	−	0.941971i	$-0.391029\pi$
$383$	−9.72814	−	7.60045i	−0.497085	−	0.388365i	−0.832779	+	0.553606i	$0.813251\pi$
$384$	1.07561	+	0.189660i	0.0548897	+	0.00967853i
$385$	5.33917	+	3.46732i	0.272109	+	0.176711i
$386$	−25.0928	+	9.13303i	−1.27719	+	0.464859i
$387$	13.4980	−	12.1536i	0.686139	−	0.617803i
$388$	−2.98150	+	6.69656i	−0.151363	+	0.339966i
$389$	1.20312	+	4.82545i	0.0610006	+	0.244660i	0.993054	−	0.117661i	$-0.0375398\pi$
$389$	1.20312	+	4.82545i	0.0610006	+	0.244660i	−0.932053	+	0.362322i	$0.881984\pi$
$390$	1.16092	+	0.469041i	0.0587853	+	0.0237508i
$391$	−20.4529	−	18.4159i	−1.03435	−	0.931332i
$392$	−2.23026	+	0.992975i	−0.112645	+	0.0501528i
$393$	0.0454292	−	0.0673516i	0.00229160	−	0.00339744i
$394$	0.330994	−	2.35515i	0.0166753	−	0.118651i
$395$	2.37431	−	13.4654i	0.119465	−	0.677517i
$396$	−0.937594	+	5.91963i	−0.0471159	+	0.297473i
$397$	−6.92998	+	5.81494i	−0.347806	+	0.291844i	−0.799908	−	0.600122i	$-0.795119\pi$
$397$	−6.92998	+	5.81494i	−0.347806	+	0.291844i	0.452103	+	0.891966i	$0.350674\pi$
$398$	−5.84249	+	17.9813i	−0.292857	+	0.901322i
$399$	−9.58971	+	3.37071i	−0.480086	+	0.168746i
$400$	3.39121	+	2.46386i	0.169561	+	0.123193i
$401$	−12.4102	+	19.8604i	−0.619734	+	0.991782i	0.378085	+	0.925771i	$0.376583\pi$
$401$	−12.4102	+	19.8604i	−0.619734	+	0.991782i	−0.997819	+	0.0660110i	$0.978973\pi$
$402$	0.388084	−	11.1133i	0.0193559	−	0.554280i
$403$	−1.46848	−	1.52066i	−0.0731503	−	0.0757494i
$404$	11.9138	−	12.3371i	0.592734	−	0.613794i
$405$	−0.00982622	−	0.281386i	−0.000488269	−	0.0139822i
$406$	3.80621	+	2.19751i	0.188899	+	0.109061i
$407$	2.82290	−	4.69806i	0.139926	−	0.232874i
$408$	4.48598	+	3.76418i	0.222089	+	0.186355i
$409$	3.38502	−	2.11520i	0.167379	−	0.104590i	−0.443643	−	0.896203i	$-0.646314\pi$
$409$	3.38502	−	2.11520i	0.167379	−	0.104590i	0.611022	+	0.791614i	$0.290759\pi$
$410$	9.40481	+	4.18729i	0.464470	+	0.206796i
$411$	2.59559	+	5.82980i	0.128031	+	0.287563i
$412$	−8.65859	+	6.76483i	−0.426578	+	0.333279i
$413$	−11.0659	+	5.88387i	−0.544520	+	0.289526i
$414$	6.67262	−	6.44367i	0.327941	−	0.316689i
$415$	0.753148	+	2.62654i	0.0369706	+	0.128932i
$416$	−0.477682	−	1.18230i	−0.0234203	−	0.0579672i
$417$	5.81995			0.285004
$418$	1.60297	+	14.3677i	0.0784036	+	0.702747i
$419$	−31.8315			−1.55507			−0.777535	−	0.628839i	$-0.783530\pi$
$419$	−31.8315			−1.55507			−0.777535	+	0.628839i	$0.783530\pi$
$420$	0.785357	+	1.94383i	0.0383215	+	0.0948490i
$421$	8.74507	+	30.4977i	0.426209	+	1.48637i	0.822779	+	0.568362i	$0.192423\pi$
$421$	8.74507	+	30.4977i	0.426209	+	1.48637i	−0.396570	+	0.918004i	$0.629800\pi$
$422$	−9.08920	+	8.77734i	−0.442455	+	0.427274i
$423$	−8.71015	+	4.63127i	−0.423502	+	0.225180i
$424$	6.09926	−	4.76526i	0.296206	−	0.231422i
$425$	9.14133	+	20.5318i	0.443420	+	0.995937i
$426$	11.8367	+	5.27004i	0.573490	+	0.255334i
$427$	13.0952	−	8.18281i	0.633723	−	0.395994i
$428$	−4.78549	−	4.01550i	−0.231315	−	0.194096i
$429$	−4.25198	+	1.80484i	−0.205287	+	0.0871387i
$430$	−7.82553	−	4.51807i	−0.377380	−	0.217881i
$431$	1.37472	+	39.3668i	0.0662178	+	1.89623i	0.349115	+	0.937080i	$0.386482\pi$
$431$	1.37472	+	39.3668i	0.0662178	+	1.89623i	−0.282897	+	0.959150i	$0.591295\pi$
$432$	−3.64718	+	3.77677i	−0.175475	+	0.181710i
$433$	−1.44187	−	1.49310i	−0.0692919	−	0.0717539i	0.683799	−	0.729671i	$-0.260327\pi$
$433$	−1.44187	−	1.49310i	−0.0692919	−	0.0717539i	−0.753091	+	0.657917i	$0.771438\pi$
$434$	0.123530	−	3.53744i	0.00592963	−	0.169802i
$435$	−1.07109	+	1.71409i	−0.0513546	+	0.0821845i
$436$	14.7466	+	10.7140i	0.706235	+	0.513110i
$437$	11.4011	−	19.2522i	0.545388	−	0.920960i
$438$	−4.52173	+	13.9164i	−0.216057	+	0.664954i
$439$	−27.6898	+	23.2345i	−1.32156	+	1.10892i	−0.335589	+	0.942008i	$0.608935\pi$
$439$	−27.6898	+	23.2345i	−1.32156	+	1.10892i	−0.985972	+	0.166913i	$0.946620\pi$
$440$	2.94499	−	0.466433i	0.140397	−	0.0222363i
$441$	0.766080	−	4.34466i	0.0364800	−	0.206888i
$442$	0.951519	−	6.77041i	0.0452591	−	0.322035i
$443$	−16.4226	+	24.3474i	−0.780259	+	1.15678i	0.203813	+	0.979010i	$0.434667\pi$
$443$	−16.4226	+	24.3474i	−0.780259	+	1.15678i	−0.984072	+	0.177772i	$0.943111\pi$
$444$	1.64889	−	0.734134i	0.0782529	−	0.0348405i
$445$	−6.27030	−	5.64580i	−0.297241	−	0.267637i
$446$	−6.51480	−	2.63215i	−0.308485	−	0.124636i
$447$	−1.06202	−	4.25951i	−0.0502316	−	0.201468i
$448$	0.868426	−	1.95052i	0.0410293	−	0.0921532i
$449$	−7.40870	+	6.67082i	−0.349638	+	0.314815i	−0.825172	−	0.564882i	$-0.808922\pi$
$449$	−7.40870	+	6.67082i	−0.349638	+	0.314815i	0.475534	+	0.879698i	$0.342255\pi$
$450$	−7.11807	+	2.59076i	−0.335549	+	0.122130i
$451$	−35.4569	+	13.6105i	−1.66960	+	0.640895i
$452$	−0.659099	−	0.116217i	−0.0310014	−	0.00546638i
$453$	6.98282	+	5.45558i	0.328082	+	0.256325i
$454$	4.18362	−	16.7796i	0.196347	−	0.787505i
$455$	1.43870	−	1.98019i	0.0674471	−	0.0928329i
$456$	−2.28143	+	4.17857i	−0.106838	+	0.195679i
$457$	15.1224	−	4.91356i	0.707395	−	0.229846i	0.0668451	−	0.997763i	$-0.478707\pi$
$457$	15.1224	−	4.91356i	0.707395	−	0.229846i	0.640549	+	0.767917i	$0.278707\pi$
$458$	19.4386	−	1.35928i	0.908308	−	0.0635151i
$459$	−27.0599	+	7.75931i	−1.26305	+	0.362174i
$460$	−4.07461	−	2.16651i	−0.189980	−	0.101014i
$461$	−1.57725	+	0.278112i	−0.0734599	+	0.0129530i	−0.210257	−	0.977646i	$-0.567430\pi$
$461$	−1.57725	+	0.278112i	−0.0734599	+	0.0129530i	0.136797	+	0.990599i	$0.456319\pi$
$462$	−7.11944	−	3.02205i	−0.331226	−	0.140598i
$463$	6.97611	−	12.0830i	0.324207	−	0.561543i	−0.657144	−	0.753765i	$-0.728236\pi$
$463$	6.97611	−	12.0830i	0.324207	−	0.561543i	0.981352	+	0.192221i	$0.0615692\pi$
$464$	2.01348	−	0.427978i	0.0934733	−	0.0198684i
$465$	1.62385	+	0.113551i	0.0753044	+	0.00526580i
$466$	−27.8590	+	6.94603i	−1.29054	+	0.321769i
$467$	23.7680	−	26.3970i	1.09985	−	1.22151i	0.126554	−	0.991960i	$-0.459608\pi$
$467$	23.7680	−	26.3970i	1.09985	−	1.22151i	0.973297	−	0.229549i	$-0.0737250\pi$
$468$	2.25396	+	0.479094i	0.104189	+	0.0221461i
$469$	−20.8960	−	5.99183i	−0.964887	−	0.276677i
$470$	3.53032	+	3.40919i	0.162841	+	0.157254i
$471$	2.13491	−	4.01519i	0.0983716	−	0.185010i
$472$	−2.00764	+	5.51595i	−0.0924091	+	0.253892i
$473$	32.2000	−	8.62788i	1.48056	−	0.396710i
$474$			16.6113i			0.762984i
$475$	−14.8999	+	10.5755i	−0.683652	+	0.485239i
$476$	9.26138	−	6.72879i	0.424495	−	0.308413i
$477$	0.975682	+	13.9529i	0.0446734	+	0.638859i
$478$	9.45732	+	0.330257i	0.432568	+	0.0151056i
$479$	−0.142486	−	1.01384i	−0.00651033	−	0.0463234i	0.986742	−	0.162297i	$-0.0518902\pi$
$479$	−0.142486	−	1.01384i	−0.00651033	−	0.0463234i	−0.993252	+	0.115973i	$0.963001\pi$
$480$	0.882536	+	0.430441i	0.0402821	+	0.0196469i
$481$	−1.74701	−	1.17837i	−0.0796567	−	0.0537291i
$482$	13.8764	+	15.4113i	0.632053	+	0.701966i
$483$	5.98518	+	10.3666i	0.272335	+	0.471699i
$484$	−6.46569	+	8.89915i	−0.293895	+	0.404507i
$485$	−4.23600	+	5.04827i	−0.192347	+	0.229230i
$486$	−3.20370	−	15.0722i	−0.145323	−	0.683689i
$487$	−4.76375	+	0.500690i	−0.215866	+	0.0226884i	−0.211844	−	0.977303i	$-0.567947\pi$
$487$	−4.76375	+	0.500690i	−0.215866	+	0.0226884i	−0.00402196	+	0.999992i	$0.501280\pi$
$488$	1.99348	−	6.95209i	0.0902405	−	0.314706i
$489$	−6.11354	−	11.4979i	−0.276464	−	0.519953i
$490$	−2.17343	+	0.305455i	−0.0981855	+	0.0137991i
$491$	18.4153	−	12.4213i	0.831073	−	0.560566i	−0.0683420	−	0.997662i	$-0.521771\pi$
$491$	18.4153	−	12.4213i	0.831073	−	0.560566i	0.899415	+	0.437096i	$0.143993\pi$
$492$	−12.1356	−	3.02574i	−0.547115	−	0.136411i
$493$	10.4966	+	3.41054i	0.472742	+	0.153603i
$494$	5.54869	−	0.326365i	0.249647	−	0.0146838i
$495$	−2.27716	+	4.88335i	−0.102351	+	0.219490i
$496$	−1.06562	−	1.26995i	−0.0478477	−	0.0570226i
$497$	15.5940	−	19.9594i	0.699487	−	0.895302i
$498$	−1.45520	−	2.98359i	−0.0652089	−	0.133698i
$499$	6.77607	−	13.8930i	0.303339	−	0.621937i	−0.691616	−	0.722266i	$-0.743101\pi$
$499$	6.77607	−	13.8930i	0.303339	−	0.621937i	0.994954	+	0.100329i	$0.0319896\pi$
$500$	5.08755	+	6.51177i	0.227522	+	0.291215i
$501$	4.36063	−	20.5151i	0.194818	−	0.916548i
$502$	−0.0650708	+	0.619107i	−0.00290425	+	0.0276321i
$503$	0.684607	−	9.79033i	0.0305251	−	0.436529i	−0.958131	−	0.286331i	$-0.907564\pi$
$503$	0.684607	−	9.79033i	0.0305251	−	0.436529i	0.988656	−	0.150198i	$-0.0479912\pi$
$504$	2.04460	+	3.27204i	0.0910736	+	0.145748i
$505$	13.3530	−	7.70933i	0.594199	−	0.343061i
$506$	16.2808	−	4.97750i	0.723771	−	0.221277i
$507$	−4.24882	−	11.6735i	−0.188697	−	0.518440i
$508$	7.50003	+	1.05406i	0.332760	+	0.0467664i
$509$	−16.4105	+	8.00393i	−0.727382	+	0.354768i	−0.764570	−	0.644540i	$-0.777049\pi$
$509$	−16.4105	+	8.00393i	−0.727382	+	0.354768i	0.0371883	+	0.999308i	$0.488160\pi$
$510$	2.94396	+	4.36460i	0.130361	+	0.193268i
$511$	24.2581	+	15.1582i	1.07312	+	0.670558i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$	−10.5200	−	20.3244i	−0.464468	−	0.897346i
$514$	−1.24835	−	1.71820i	−0.0550622	−	0.0757867i
$515$	−9.15901	+	3.70048i	−0.403594	+	0.163063i
$516$	10.3159	+	3.75467i	0.454131	+	0.165290i
$517$	−18.1027	+	0.315935i	−0.796154	+	0.0138948i
$518$	−0.612699	−	3.47479i	−0.0269204	−	0.152673i
$519$	21.3238	−	0.744644i	0.936011	−	0.0326862i
$520$	−0.119830	−	1.14011i	−0.00525489	−	0.0499969i
$521$	10.2258	+	1.07477i	0.447999	+	0.0470866i	0.325842	−	0.945424i	$-0.394352\pi$
$521$	10.2258	+	1.07477i	0.447999	+	0.0470866i	0.122157	+	0.992511i	$0.461019\pi$
$522$	−1.39347	+	3.44895i	−0.0609904	+	0.150956i
$523$	−1.95563	+	4.84035i	−0.0855137	+	0.211654i	−0.963881	−	0.266332i	$-0.914188\pi$
$523$	−1.95563	+	4.84035i	−0.0855137	+	0.211654i	0.878368	+	0.477985i	$0.158633\pi$
$524$	−0.0739747	−	0.00777505i	−0.00323160	−	0.000339655i
$525$	−1.02178	−	9.72156i	−0.0445940	−	0.424284i
$526$	−2.02406	+	0.0706818i	−0.0882533	+	0.00308187i
$527$	−1.54349	−	8.75355i	−0.0672354	−	0.381311i
$528$	−3.42509	+	1.17934i	−0.149058	+	0.0513242i
$529$	−3.14718	−	1.14548i	−0.136834	−	0.0498035i
$530$	6.45176	−	2.60668i	0.280247	−	0.113227i
$531$	−6.23493	−	8.58165i	−0.270573	−	0.372412i
$532$	6.84692	+	6.30353i	0.296852	+	0.273293i
$533$	4.51230	+	13.8874i	0.195449	+	0.601532i
$534$	8.69305	+	5.43202i	0.376185	+	0.235067i
$535$	−3.14052	−	4.65601i	−0.135776	−	0.201297i
$536$	−9.15086	+	4.46318i	−0.395257	+	0.192780i
$537$	−9.06990	−	1.27469i	−0.391395	−	0.0550070i
$538$	−7.48185	−	20.5562i	−0.322566	−	0.886242i
$539$	4.87288	−	6.46650i	0.209890	−	0.278532i
$540$	−4.08775	+	2.36006i	−0.175909	+	0.101561i
$541$	−4.09639	−	6.55559i	−0.176117	−	0.281847i	0.748199	−	0.663475i	$-0.230919\pi$
$541$	−4.09639	−	6.55559i	−0.176117	−	0.281847i	−0.924316	+	0.381628i	$0.875363\pi$
$542$	1.65517	−	23.6701i	0.0710957	−	1.01672i
$543$	0.590131	−	5.61472i	0.0253249	−	0.240951i
$544$	1.11475	−	5.24449i	0.0477945	−	0.224856i
$545$	10.0889	+	12.9132i	0.432161	+	0.553141i
$546$	−1.30355	+	2.67268i	−0.0557870	+	0.114380i
$547$	−8.48576	−	17.3984i	−0.362825	−	0.743901i	0.636807	−	0.771023i	$-0.280255\pi$
$547$	−8.48576	−	17.3984i	−0.362825	−	0.743901i	−0.999632	+	0.0271217i	$0.991366\pi$
$548$	3.59717	−	4.60416i	0.153663	−	0.196680i
$549$	8.40078	+	10.0117i	0.358537	+	0.427287i
$550$	−13.7989	−	1.69433i	−0.588387	−	0.0722464i
$551$	−1.03655	+	8.91254i	−0.0441585	+	0.379687i
$552$	5.33205	+	1.73249i	0.226947	+	0.0737396i
$553$	31.5082	+	7.85587i	1.33986	+	0.334066i
$554$	0.506649	−	0.341739i	0.0215255	−	0.0145191i
$555$	1.60688	−	0.225832i	0.0682081	−	0.00958602i
$556$	−2.50163	−	4.70489i	−0.106093	−	0.199532i
$557$	7.99231	−	27.8725i	0.338645	−	1.18100i	−0.589187	−	0.807997i	$-0.700552\pi$
$557$	7.99231	−	27.8725i	0.338645	−	1.18100i	0.927832	−	0.372998i	$-0.121670\pi$
$558$	2.97939	−	0.313146i	0.126128	−	0.0132565i
$559$	−2.66476	−	12.5367i	−0.112707	−	0.530246i
$560$	1.23383	−	1.47042i	0.0521387	−	0.0621365i
$561$	−19.0654	−	3.70599i	−0.804942	−	0.156467i
$562$	−10.5687	−	18.3056i	−0.445815	−	0.772174i
$563$	−19.6277	−	21.7988i	−0.827208	−	0.918708i	0.170569	−	0.985346i	$-0.445439\pi$
$563$	−19.6277	−	21.7988i	−0.827208	−	0.918708i	−0.997777	+	0.0666378i	$0.978773\pi$
$564$	−4.94300	−	3.33410i	−0.208138	−	0.140391i
$565$	−0.540787	−	0.263760i	−0.0227511	−	0.0110964i
$566$	3.58407	+	25.5020i	0.150650	+	1.07193i
$567$	0.668274	+	0.0233366i	0.0280649	+	0.000980047i
$568$	−0.827524	−	11.8341i	−0.0347221	−	0.496550i
$569$	−14.3300	+	10.4114i	−0.600745	+	0.436467i	−0.846143	−	0.532956i	$-0.821081\pi$
$569$	−14.3300	+	10.4114i	−0.600745	+	0.436467i	0.245398	+	0.969422i	$0.421081\pi$
$570$	−3.00705	+	3.04573i	−0.125951	+	0.127572i
$571$			40.0331i			1.67533i	0.546181	+	0.837667i	$0.316081\pi$
$571$			40.0331i			1.67533i	−0.546181	+	0.837667i	$0.683919\pi$
$572$	3.28671	+	2.66154i	0.137424	+	0.111285i
$573$	4.18698	−	11.5036i	0.174913	−	0.480571i
$574$	−11.4784	+	21.5877i	−0.479099	+	0.901054i
$575$	15.4780	+	14.9469i	0.645477	+	0.623330i
$576$	1.73708	+	0.498100i	0.0723784	+	0.0207542i
$577$	27.8246	+	5.91430i	1.15835	+	0.246216i	0.746723	−	0.665135i	$-0.231626\pi$
$577$	27.8246	+	5.91430i	1.15835	+	0.246216i	0.411630	+	0.911351i	$0.364959\pi$
$578$	7.86049	−	8.72996i	0.326953	−	0.363118i
$579$	28.2991	−	7.05575i	1.17607	−	0.293227i
$580$	1.84608	+	0.129090i	0.0766543	+	0.00536019i
$581$	−6.34744	+	1.34919i	−0.263336	+	0.0559738i
$582$	4.00310	−	6.93357i	0.165934	−	0.287406i
$583$	−10.0305	+	23.6302i	−0.415420	+	0.978662i
$584$	13.1938	−	2.32642i	0.545962	−	0.0962678i
$585$	1.82913	+	0.972565i	0.0756252	+	0.0402106i
$586$	9.79318	−	2.80815i	0.404552	−	0.116004i
$587$	−0.822857	+	0.0575398i	−0.0339630	+	0.00237492i	−0.0867278	−	0.996232i	$-0.527641\pi$
$587$	−0.822857	+	0.0575398i	−0.0339630	+	0.00237492i	0.0527649	+	0.998607i	$0.483197\pi$
$588$	2.53592	−	0.823972i	0.104580	−	0.0339800i
$589$	6.72957	−	2.63271i	0.277287	−	0.108479i
$590$	−3.10185	+	4.26933i	−0.127701	+	0.175765i
$591$	−0.628413	+	2.52043i	−0.0258495	+	0.103677i
$592$	−1.30224	−	1.01742i	−0.0535215	−	0.0418156i
$593$	−6.97997	−	1.23076i	−0.286633	−	0.0505412i	0.0284830	−	0.999594i	$-0.490932\pi$
$593$	−6.97997	−	1.23076i	−0.286633	−	0.0505412i	−0.315116	+	0.949053i	$0.602043\pi$
$594$	4.50696	−	16.8200i	0.184923	−	0.690133i
$595$	9.67100	−	3.51996i	0.396472	−	0.144304i
$596$	−2.98693	+	2.68944i	−0.122349	+	0.110164i
$597$	8.39911	−	18.8647i	0.343753	−	0.772081i
$598$	−1.58351	−	6.35113i	−0.0647547	−	0.259717i
$599$	−29.3574	−	11.8611i	−1.19951	−	0.484633i	−0.314075	−	0.949398i	$-0.601694\pi$
$599$	−29.3574	−	11.8611i	−1.19951	−	0.484633i	−0.885434	+	0.464765i	$0.846139\pi$
$600$	−3.40232	−	3.06347i	−0.138899	−	0.125065i
$601$	−4.22228	+	1.87988i	−0.172230	+	0.0766819i	−0.491041	−	0.871137i	$-0.663383\pi$
$601$	−4.22228	+	1.87988i	−0.172230	+	0.0766819i	0.318810	+	0.947819i	$0.396717\pi$
$602$	12.0004	−	17.7914i	0.489101	−	0.725122i
$603$	2.56057	−	18.2194i	0.104274	−	0.741950i
$604$	1.40885	−	7.98998i	0.0573253	−	0.325108i
$605$	−7.79281	+	6.08834i	−0.316823	+	0.247526i
$606$	−14.3495	+	12.0407i	−0.582910	+	0.489120i
$607$	−8.84852	+	27.2330i	−0.359150	+	1.10535i	0.594413	+	0.804160i	$0.297384\pi$
$607$	−8.84852	+	27.2330i	−0.359150	+	1.10535i	−0.953564	+	0.301192i	$0.902616\pi$
$608$	4.35863	+	0.0482192i	0.176766	+	0.00195554i
$609$	−3.88351	−	2.82153i	−0.157368	−	0.114334i
$610$	3.44549	−	5.51393i	0.139504	−	0.223253i
$611$	−0.242937	+	6.95682i	−0.00982820	+	0.281443i
$612$	6.73052	+	6.96966i	0.272065	+	0.281732i
$613$	−11.0075	+	11.3986i	−0.444590	+	0.460386i	−0.903809	−	0.427937i	$-0.859241\pi$
$613$	−11.0075	+	11.3986i	−0.444590	+	0.460386i	0.459219	+	0.888323i	$0.348129\pi$
$614$	−0.0471374	−	1.34984i	−0.00190231	−	0.0544750i
$615$	−9.73767	−	5.62205i	−0.392661	−	0.226703i
$616$	0.617161	+	7.05440i	0.0248661	+	0.284230i
$617$	3.78457	+	3.17563i	0.152361	+	0.127846i	0.715782	−	0.698324i	$-0.246071\pi$
$617$	3.78457	+	3.17563i	0.152361	+	0.127846i	−0.563421	+	0.826170i	$0.690515\pi$
$618$	10.1775	−	6.35959i	0.409398	−	0.255820i
$619$	6.89775	+	3.07108i	0.277244	+	0.123437i	0.540649	−	0.841248i	$-0.318179\pi$
$619$	6.89775	+	3.07108i	0.277244	+	0.123437i	−0.263405	+	0.964685i	$0.584845\pi$
$620$	−0.606199	−	1.36154i	−0.0243455	−	0.0546809i
$621$	−21.2374	+	16.5925i	−0.852229	+	0.665834i
$622$	15.8514	−	8.42836i	0.635585	−	0.337946i
$623$	14.4145	−	13.9200i	0.577506	−	0.557691i
$624$	0.383889	+	1.33878i	0.0153679	+	0.0535941i
$625$	−5.06835	−	12.5446i	−0.202734	−	0.501784i
$626$	−9.07060			−0.362534
$627$	−0.100867	−	15.7895i	−0.00402826	−	0.630573i
$628$	−4.16357			−0.166145
$629$	−3.31919	−	8.21527i	−0.132345	−	0.327564i
$630$	0.956101	+	3.33432i	0.0380920	+	0.132842i
$631$	21.0709	−	20.3479i	0.838818	−	0.810037i	−0.144958	−	0.989438i	$-0.546305\pi$
$631$	21.0709	−	20.3479i	0.838818	−	0.810037i	0.983776	+	0.179401i	$0.0574159\pi$
$632$	13.4287	−	7.14018i	0.534166	−	0.284021i
$633$	10.8750	−	8.49647i	0.432242	−	0.337704i
$634$	−1.87622	−	4.21406i	−0.0745142	−	0.167362i
$635$	6.22025	+	2.76943i	0.246843	+	0.109902i
$636$	−7.16919	+	4.47981i	−0.284277	+	0.177636i
$637$	−2.38475	−	2.00104i	−0.0944871	−	0.0792841i
$638$	−5.15252	+	4.47899i	−0.203990	+	0.177325i
$639$	18.5655	+	10.7188i	0.734438	+	0.424028i
$640$	−0.0313752	−	0.898468i	−0.00124021	−	0.0355151i
$641$	3.21450	−	3.32871i	0.126965	−	0.131476i	−0.652847	−	0.757490i	$-0.726426\pi$
$641$	3.21450	−	3.32871i	0.126965	−	0.131476i	0.779812	+	0.626014i	$0.215315\pi$
$642$	4.73967	+	4.90807i	0.187060	+	0.193706i
$643$	1.56445	−	44.7998i	0.0616957	−	1.76673i	−0.436534	−	0.899688i	$-0.643794\pi$
$643$	1.56445	−	44.7998i	0.0616957	−	1.76673i	0.498229	−	0.867045i	$-0.333984\pi$
$644$	5.80781	−	9.29444i	0.228860	−	0.366252i
$645$	7.98446	+	5.80105i	0.314388	+	0.228416i
$646$	20.1093	+	11.9086i	0.791189	+	0.468539i
$647$	9.57917	−	29.4816i	0.376596	−	1.15904i	−0.565800	−	0.824543i	$-0.691432\pi$
$647$	9.57917	−	29.4816i	0.376596	−	1.15904i	0.942396	−	0.334500i	$-0.108568\pi$
$648$	0.239913	−	0.201311i	0.00942467	−	0.00790824i
$649$	−3.04548	−	19.2287i	−0.119546	−	0.754794i
$650$	−0.928177	+	5.26396i	−0.0364061	+	0.206469i
$651$	−0.538039	+	3.82834i	−0.0210874	+	0.150045i
$652$	−6.66716	+	9.88447i	−0.261106	+	0.387106i
$653$	41.6306	−	18.5351i	1.62913	−	0.725336i	0.630428	−	0.776248i	$-0.282879\pi$
$653$	41.6306	−	18.5351i	1.62913	−	0.725336i	0.998703	+	0.0509117i	$0.0162127\pi$
$654$	−14.7949	−	13.3214i	−0.578527	−	0.520908i
$655$	−0.0620015	−	0.0250502i	−0.00242260	−	0.000978794i
$656$	2.77031	+	11.1111i	0.108162	+	0.433815i
$657$	−9.84713	+	22.1170i	−0.384173	+	0.862867i
$658$	−8.66174	+	7.79906i	−0.337670	+	0.304039i
$659$	10.4985	−	3.82113i	0.408962	−	0.148850i	−0.129343	−	0.991600i	$-0.541287\pi$
$659$	10.4985	−	3.82113i	0.408962	−	0.148850i	0.538305	+	0.842750i	$0.319065\pi$
$660$	−3.25217	+	0.170430i	−0.126590	+	0.00663398i
$661$	18.8523	+	3.32417i	0.733270	+	0.129295i	0.527801	−	0.849368i	$-0.323017\pi$
$661$	18.8523	+	3.32417i	0.733270	+	0.129295i	0.205470	+	0.978664i	$0.434128\pi$
$662$	−3.88972	−	3.03898i	−0.151178	−	0.118113i
$663$	−1.80652	+	7.24554i	−0.0701593	+	0.281393i
$664$	−1.78646	+	2.45885i	−0.0693281	+	0.0954220i
$665$	4.35501	+	7.14413i	0.168880	+	0.277038i
$666$	2.84016	−	0.922823i	0.110054	−	0.0357587i
$667$	10.5406	−	0.737072i	0.408135	−	0.0285396i
$668$	−18.4589	+	5.29302i	−0.714198	+	0.204793i
$669$	6.77602	+	3.60287i	0.261976	+	0.139295i
$670$	−9.01407	+	1.58942i	−0.348244	+	0.0614048i
$671$	5.39576	+	23.3719i	0.208301	+	0.902262i
$672$	−1.16599	+	2.01955i	−0.0449790	+	0.0779058i
$673$	9.62895	−	2.04670i	0.371169	−	0.0788943i	−0.0185509	−	0.999828i	$-0.505905\pi$
$673$	9.62895	−	2.04670i	0.371169	−	0.0788943i	0.389720	+	0.920934i	$0.372572\pi$
$674$	10.4887	+	0.733442i	0.404010	+	0.0282511i
$675$	21.3544	−	5.32426i	0.821933	−	0.204931i
$676$	−7.61068	+	8.45251i	−0.292718	+	0.325097i
$677$	37.6369	+	7.99997i	1.44650	+	0.307464i	0.863229	−	0.504812i	$-0.168438\pi$
$677$	37.6369	+	7.99997i	1.44650	+	0.307464i	0.583274	+	0.812276i	$0.301772\pi$
$678$	0.702660	+	0.201484i	0.0269855	+	0.00773796i
$679$	−11.2584	−	10.8721i	−0.432056	−	0.417232i
$680$	2.26295	−	4.25599i	0.0867803	−	0.163210i
$681$	−6.46001	+	17.7487i	−0.247548	+	0.680133i
$682$	5.13312	+	1.97044i	0.196557	+	0.0754520i
$683$			32.5587i			1.24583i	0.782291	+	0.622913i	$0.214051\pi$
$683$			32.5587i			1.24583i	−0.782291	+	0.622913i	$0.785949\pi$
$684$	−4.47668	+	6.48112i	−0.171170	+	0.247812i
$685$	4.24956	−	3.08748i	0.162367	−	0.117967i
$686$	−1.40617	−	20.1091i	−0.0536877	−	0.767770i
$687$	−21.2699	−	0.742761i	−0.811497	−	0.0283381i
$688$	−1.39885	−	9.95333i	−0.0533306	−	0.379467i
$689$	8.87091	+	4.32663i	0.337955	+	0.164832i
$690$	4.17859	+	2.81849i	0.159076	+	0.107298i
$691$	5.89418	+	6.54615i	0.224225	+	0.249027i	0.844752	−	0.535158i	$-0.179748\pi$
$691$	5.89418	+	6.54615i	0.224225	+	0.249027i	−0.620527	+	0.784185i	$0.713081\pi$
$692$	−9.76775	−	16.9182i	−0.371314	−	0.643135i
$693$	−11.1921	−	6.20394i	−0.425154	−	0.235668i
$694$	−1.16929	+	1.39350i	−0.0443856	+	0.0528967i
$695$	−0.996004	−	4.68583i	−0.0377806	−	0.177744i
$696$	−2.23595	+	0.235007i	−0.0847533	+	0.00890793i
$697$	−16.9235	+	59.0191i	−0.641022	+	2.23551i
$698$	0.361636	+	0.680138i	0.0136881	+	0.0257436i
$699$	31.0541	−	4.36437i	1.17457	−	0.165076i
$700$	−7.41978	+	5.00471i	−0.280441	+	0.189160i
$701$	11.5599	+	2.88221i	0.436612	+	0.108860i	0.454026	−	0.890989i	$-0.349987\pi$
$701$	11.5599	+	2.88221i	0.436612	+	0.108860i	−0.0174131	+	0.999848i	$0.505543\pi$
$702$	−6.36731	−	2.06886i	−0.240319	−	0.0780843i
$703$	6.01604	−	3.96175i	0.226899	−	0.149420i
$704$	2.42562	+	2.26194i	0.0914190	+	0.0852500i
$705$	−3.44549	−	4.10618i	−0.129765	−	0.154648i
$706$	15.7291	−	20.1323i	0.591971	−	0.757688i
$707$	16.0524	+	32.9124i	0.603714	+	1.23780i
$708$	2.81048	−	5.76234i	0.105624	−	0.216562i
$709$	24.7796	+	31.7165i	0.930618	+	1.19114i	0.981312	+	0.192423i	$0.0616345\pi$
$709$	24.7796	+	31.7165i	0.930618	+	1.19114i	−0.0506939	+	0.998714i	$0.516143\pi$
$710$	2.21739	−	10.4320i	0.0832172	−	0.391506i
$711$	−2.87285	+	27.3334i	−0.107740	+	1.02508i
$712$	0.654684	−	9.36242i	0.0245353	−	0.350871i
$713$	−4.50949	−	7.21669i	−0.168882	−	0.270267i
$714$	−10.8281	+	6.25162i	−0.405232	+	0.233961i
$715$	2.18080	+	3.11453i	0.0815575	+	0.116477i
$716$	2.86812	+	7.88008i	0.107187	+	0.294492i
$717$	−10.2351	−	1.43844i	−0.382235	−	0.0537196i
$718$	5.02835	−	2.45249i	0.187656	−	0.0915261i
$719$	−16.2884	−	24.1486i	−0.607456	−	0.900591i	0.392359	−	0.919812i	$-0.371659\pi$
$719$	−16.2884	−	24.1486i	−0.607456	−	0.900591i	−0.999815	+	0.0192213i	$0.993881\pi$
$720$	1.37774	+	0.860906i	0.0513453	+	0.0320841i
$721$	−7.24965	−	22.3121i	−0.269991	−	0.830947i
$722$	−6.26965	+	17.9358i	−0.233332	+	0.667500i
$723$	−13.3134	−	18.3243i	−0.495131	−	0.681490i
$724$	−4.79264	+	1.93635i	−0.178117	+	0.0719640i
$725$	−8.10822	−	2.95115i	−0.301132	−	0.109603i
$726$	8.03916	−	8.92830i	0.298361	−	0.331360i
$727$	4.45518	+	25.2666i	0.165234	+	0.937086i	0.948823	+	0.315808i	$0.102275\pi$
$727$	4.45518	+	25.2666i	0.165234	+	0.937086i	−0.783590	+	0.621279i	$0.786614\pi$
$728$	2.72093	−	0.0950171i	0.100845	−	0.00352157i
$729$	1.85739	+	17.6719i	0.0687924	+	0.654516i
$730$	11.9784	+	1.25898i	0.443341	+	0.0465970i
$731$	20.1878	−	49.9666i	0.746674	−	1.84808i
$732$	−2.95906	+	7.32393i	−0.109370	+	0.270700i
$733$	−23.3310	−	2.45219i	−0.861750	−	0.0905736i	−0.336666	−	0.941624i	$-0.609299\pi$
$733$	−23.3310	−	2.45219i	−0.861750	−	0.0905736i	−0.525084	+	0.851050i	$0.675966\pi$
$734$	−3.29959	−	31.3935i	−0.121790	−	1.15876i
$735$	2.39570	−	0.0836597i	0.0883668	−	0.00308584i
$736$	−0.891361	−	5.05516i	−0.0328560	−	0.186336i
$737$	19.3683	−	27.6606i	0.713440	−	1.01889i
$738$	−19.4454	−	7.07755i	−0.715795	−	0.260528i
$739$	10.4984	−	4.24163i	0.386190	−	0.156031i	−0.173298	−	0.984869i	$-0.555442\pi$
$739$	10.4984	−	4.24163i	0.386190	−	0.156031i	0.559488	+	0.828839i	$0.310998\pi$
$740$	−0.873260	−	1.20194i	−0.0321017	−	0.0441842i
$741$	−6.06437	−	0.278970i	−0.222780	−	0.0102482i
$742$	5.10677	+	15.7170i	0.187476	+	0.576991i
$743$	−34.8922	−	21.8031i	−1.28007	−	0.799878i	−0.292382	−	0.956302i	$-0.594448\pi$
$743$	−34.8922	−	21.8031i	−1.28007	−	0.799878i	−0.987690	+	0.156424i	$0.950004\pi$
$744$	1.01251	+	1.50111i	0.0371205	+	0.0550334i
$745$	−3.24772	+	1.58402i	−0.118987	+	0.0580340i
$746$	0.948283	+	0.133272i	0.0347191	+	0.00487945i
$747$	−1.87847	−	5.16107i	−0.0687298	−	0.188834i
$748$	5.19908	+	17.0056i	0.190097	+	0.621786i
$749$	11.5511	−	6.66901i	0.422067	−	0.243680i
$750$	−4.78279	−	7.65406i	−0.174643	−	0.279487i
$751$	−1.02803	+	14.7015i	−0.0375133	+	0.536465i	0.942069	+	0.335420i	$0.108878\pi$
$751$	−1.02803	+	14.7015i	−0.0375133	+	0.536465i	−0.979582	+	0.201045i	$0.935566\pi$
$752$	−0.570620	+	5.42908i	−0.0208084	+	0.197978i
$753$	0.141363	−	0.665060i	0.00515155	−	0.0242361i
$754$	1.61602	+	2.06841i	0.0588521	+	0.0753272i
$755$	3.19745	−	6.55574i	0.116367	−	0.238588i
$756$	−4.91414	−	10.0755i	−0.178726	−	0.366442i
$757$	−9.51254	+	12.1755i	−0.345739	+	0.442526i	−0.929179	−	0.369630i	$-0.879484\pi$
$757$	−9.51254	+	12.1755i	−0.345739	+	0.442526i	0.583440	+	0.812157i	$0.301707\pi$
$758$	11.9018	+	14.1840i	0.432293	+	0.515187i
$759$	−18.2529	+	3.54795i	−0.662537	+	0.128782i
$760$	3.75474	+	1.12175i	0.136199	+	0.0406901i
$761$	−25.8630	−	8.40341i	−0.937534	−	0.304623i	−0.199894	−	0.979817i	$-0.564060\pi$
$761$	−25.8630	−	8.40341i	−0.937534	−	0.304623i	−0.737640	+	0.675194i	$0.764060\pi$
$762$	−8.02637	−	2.00120i	−0.290765	−	0.0724958i
$763$	−32.2648	+	21.7629i	−1.16806	+	0.787868i
$764$	−11.0993	+	1.55991i	−0.401560	+	0.0564355i
$765$	4.08935	+	7.69095i	0.147851	+	0.278067i
$766$	3.40279	−	11.8669i	0.122948	−	0.428770i
$767$	−7.44409	+	0.782406i	−0.268791	+	0.0282510i
$768$	0.227082	+	1.06834i	0.00819413	+	0.0385504i
$769$	−19.7958	+	23.5918i	−0.713856	+	0.850740i	−0.994018	−	0.109212i	$-0.965167\pi$
$769$	−19.7958	+	23.5918i	−0.713856	+	0.850740i	0.280163	+	0.959953i	$0.409612\pi$
$770$	−1.21475	+	6.24927i	−0.0437767	+	0.225208i
$771$	1.15982	+	2.00887i	0.0417700	+	0.0723477i
$772$	−17.8679	−	19.8443i	−0.643081	−	0.714213i
$773$	−2.24471	−	1.51407i	−0.0807365	−	0.0544575i	0.518161	−	0.855283i	$-0.326617\pi$
$773$	−2.24471	−	1.51407i	−0.0807365	−	0.0544575i	−0.598898	+	0.800825i	$0.704394\pi$
$774$	16.3251	+	7.96226i	0.586792	+	0.286198i
$775$	0.967135	+	6.88152i	0.0347405	+	0.247191i
$776$	−7.32583	−	0.255824i	−0.262982	−	0.00918353i
$777$	0.268823	+	3.84434i	0.00964396	+	0.137915i
$778$	−4.02339	+	2.92316i	−0.144245	+	0.104800i
$779$	−49.7516	−	4.03249i	−1.78254	−	0.144479i
$780$			1.25209i			0.0448320i
$781$	21.4289	+	32.9978i	0.766786	+	1.18075i
$782$	9.41312	−	25.8623i	0.336613	−	0.924836i
$783$	5.07385	−	9.54253i	0.181325	−	0.341022i
$784$	−1.75614	−	1.69589i	−0.0627193	−	0.0605673i
$785$	−3.59812	−	1.03174i	−0.128422	−	0.0368245i
$786$	0.0794654	+	0.0168909i	0.00283444	+	0.000602478i
$787$	−9.89304	+	10.9873i	−0.352649	+	0.391656i	−0.893203	−	0.449653i	$-0.851548\pi$
$787$	−9.89304	+	10.9873i	−0.352649	+	0.391656i	0.540555	+	0.841309i	$0.318214\pi$
$788$	2.30765	−	0.575361i	0.0822066	−	0.0204964i
$789$	2.20665	+	0.154304i	0.0785589	+	0.00549337i
$790$	13.3743	−	2.84280i	0.475837	−	0.101142i
$791$	0.714477	−	1.23751i	0.0254039	−	0.0440008i
$792$	−5.83982	+	1.34821i	−0.207509	+	0.0479066i
$793$	9.08214	−	1.60143i	0.322516	−	0.0568683i
$794$	−7.98754	−	4.24705i	−0.283467	−	0.150722i
$795$	−7.30564	+	2.09486i	−0.259105	+	0.0742970i
$796$	−18.8606	+	1.31886i	−0.668497	+	0.0467459i
$797$	46.0434	−	14.9604i	1.63094	−	0.529925i	0.656455	−	0.754366i	$-0.272055\pi$
$797$	46.0434	−	14.9604i	1.63094	−	0.529925i	0.974488	+	0.224440i	$0.0720554\pi$
$798$	−6.71763	−	7.62873i	−0.237802	−	0.270054i
$799$	−17.2040	+	23.6793i	−0.608634	+	0.837712i
$800$	−1.01408	+	4.06726i	−0.0358532	+	0.143799i
$801$	13.3647	+	10.4416i	0.472217	+	0.368937i
$802$	−23.0632	−	4.06666i	−0.814390	−	0.143599i
$803$	−34.5317	+	27.9630i	−1.21860	+	0.986794i
$804$	10.4494	−	3.80328i	0.368523	−	0.134131i
$805$	7.32224	−	6.59297i	0.258075	−	0.232372i
$806$	0.859826	−	1.93120i	0.0302861	−	0.0680237i
$807$	5.78012	+	23.1828i	0.203470	+	0.816074i
$808$	15.9018	+	6.42473i	0.559422	+	0.226021i
$809$	1.97578	+	1.77900i	0.0694648	+	0.0625464i	0.703132	−	0.711060i	$-0.251784\pi$
$809$	1.97578	+	1.77900i	0.0694648	+	0.0625464i	−0.633667	+	0.773606i	$0.718451\pi$
$810$	0.257216	−	0.114520i	0.00903764	−	0.00402382i
$811$	19.8494	−	29.4279i	0.697006	−	1.03335i	−0.299840	−	0.953989i	$-0.596933\pi$
$811$	19.8494	−	29.4279i	0.697006	−	1.03335i	0.996846	−	0.0793638i	$-0.0252889\pi$
$812$	−0.611670	+	4.35226i	−0.0214654	+	0.152734i
$813$	−4.50022	+	25.5220i	−0.157830	+	0.895096i
$814$	5.41344	+	0.857420i	0.189741	+	0.0300525i
$815$	−8.21108	+	6.88992i	−0.287622	+	0.241343i
$816$	−1.80961	+	5.56942i	−0.0633491	+	0.194969i
$817$	43.0595	+	8.08469i	1.50646	+	0.282848i
$818$	3.22923	+	2.34617i	0.112907	+	0.0820320i
$819$	−2.60718	+	4.17236i	−0.0911023	+	0.145794i
$820$	−0.359285	+	10.2886i	−0.0125468	+	0.359293i
$821$	36.5785	+	37.8782i	1.27660	+	1.32196i	0.922125	+	0.386892i	$0.126451\pi$
$821$	36.5785	+	37.8782i	1.27660	+	1.32196i	0.354474	+	0.935066i	$0.384660\pi$
$822$	−4.43297	+	4.59047i	−0.154617	+	0.160111i
$823$	0.783321	+	22.4314i	0.0273049	+	0.781909i	0.933401	+	0.358836i	$0.116826\pi$
$823$	0.783321	+	22.4314i	0.0273049	+	0.781909i	−0.906096	+	0.423073i	$0.860951\pi$
$824$	−9.51581	−	5.49395i	−0.331499	−	0.191391i
$825$	14.7952	+	3.41579i	0.515104	+	0.118923i
$826$	−9.60080	−	8.05603i	−0.334055	−	0.280305i
$827$	30.7155	−	19.1932i	1.06808	−	0.667411i	0.122392	−	0.992482i	$-0.460944\pi$
$827$	30.7155	−	19.1932i	1.06808	−	0.667411i	0.945690	+	0.325070i	$0.105388\pi$
$828$	8.47408	+	3.77290i	0.294494	+	0.131117i
$829$	0.846896	+	1.90216i	0.0294139	+	0.0660647i	0.927655	−	0.373438i	$-0.121821\pi$
$829$	0.846896	+	1.90216i	0.0294139	+	0.0660647i	−0.898241	+	0.439503i	$0.855155\pi$
$830$	−2.15315	+	1.68223i	−0.0747369	+	0.0583909i
$831$	−0.589349	+	0.313362i	−0.0204443	+	0.0108704i
$832$	0.917270	−	0.885798i	0.0318006	−	0.0307095i
$833$	−3.60796	−	12.5825i	−0.125008	−	0.435956i
$834$	2.18019	+	5.39616i	0.0754938	+	0.186854i
$835$	−17.2637			−0.597433
$836$	−12.7210	+	6.86848i	−0.439965	+	0.237551i
$837$	−8.70403			−0.300855
$838$	−11.9243	−	29.5137i	−0.411918	−	1.01953i
$839$	−0.0823407	−	0.287156i	−0.00284272	−	0.00991373i	0.959828	−	0.280591i	$-0.0905303\pi$
$839$	−0.0823407	−	0.287156i	−0.00284272	−	0.00991373i	−0.962670	+	0.270677i	$0.912753\pi$
$840$	−1.50808	+	1.45634i	−0.0520338	+	0.0502485i
$841$	21.8642	−	11.6254i	0.753938	−	0.400876i
$842$	−25.0010	+	19.5329i	−0.861591	+	0.673149i
$843$	9.39010	+	21.0905i	0.323412	+	0.726396i
$844$	−11.5431	−	5.13931i	−0.397329	−	0.176902i
$845$	−8.67162	+	5.41863i	−0.298313	+	0.186407i
$846$	−7.55692	−	6.34101i	−0.259812	−	0.218008i
$847$	−13.1332	−	19.4710i	−0.451262	−	0.669031i
$848$	6.70310	+	3.87003i	0.230185	+	0.132898i
$849$	−0.981623	−	28.1100i	−0.0336892	−	0.964733i
$850$	−15.6123	+	16.1670i	−0.535498	+	0.554525i
$851$	−5.89267	−	6.10204i	−0.201998	−	0.209175i
$852$	−0.452189	+	12.9490i	−0.0154917	+	0.443625i
$853$	−1.21210	+	1.93976i	−0.0415015	+	0.0664163i	−0.868148	−	0.496305i	$-0.834690\pi$
$853$	−1.21210	+	1.93976i	−0.0415015	+	0.0664163i	0.826647	+	0.562721i	$0.190245\pi$
$854$	12.4925	+	9.07636i	0.427486	+	0.310587i
$855$	−5.47474	+	4.49159i	−0.187232	+	0.153609i
$856$	1.93043	−	5.94126i	0.0659808	−	0.203068i
$857$	19.6006	−	16.4468i	0.669543	−	0.561813i	−0.243387	−	0.969929i	$-0.578259\pi$
$857$	19.6006	−	16.4468i	0.669543	−	0.561813i	0.912930	+	0.408116i	$0.133814\pi$
$858$	−3.26624	−	3.26626i	−0.111508	−	0.111508i
$859$	3.04477	−	17.2677i	0.103886	−	0.589168i	−0.887773	−	0.460281i	$-0.847749\pi$
$859$	3.04477	−	17.2677i	0.103886	−	0.589168i	0.991659	−	0.128886i	$-0.0411403\pi$
$860$	1.25759	−	8.94820i	0.0428834	−	0.305131i
$861$	14.9327	−	22.1386i	0.508905	−	0.754482i
$862$	−35.9852	+	16.0217i	−1.22566	+	0.545700i
$863$	−15.3060	−	13.7816i	−0.521021	−	0.469129i	0.366159	−	0.930552i	$-0.380673\pi$
$863$	−15.3060	−	13.7816i	−0.521021	−	0.469129i	−0.887180	+	0.461423i	$0.847339\pi$
$864$	−4.86802	−	1.96681i	−0.165613	−	0.0669122i
$865$	−4.24881	−	17.0410i	−0.144464	−	0.579413i
$866$	0.844245	−	1.89621i	0.0286886	−	0.0644357i
$867$	−9.53492	+	8.58528i	−0.323823	+	0.291571i
$868$	3.32613	−	1.21061i	0.112896	−	0.0410909i
$869$	−27.4730	+	42.3045i	−0.931959	+	1.43508i
$870$	−1.99052	−	0.350982i	−0.0674848	−	0.0118994i
$871$	−10.2305	−	7.99295i	−0.346648	−	0.270831i
$872$	−4.40971	+	17.6864i	−0.149332	+	0.598936i
$873$	7.78608	−	10.7166i	0.263519	−	0.362703i
$874$	22.1213	+	3.35889i	0.748264	+	0.113616i
$875$	−16.7800	+	5.45216i	−0.567268	+	0.184317i
$876$	−14.5970	+	1.02072i	−0.493186	+	0.0344869i
$877$	23.9804	−	6.87626i	0.809759	−	0.232195i	0.154885	−	0.987933i	$-0.450499\pi$
$877$	23.9804	−	6.87626i	0.809759	−	0.232195i	0.654874	+	0.755738i	$0.272722\pi$
$878$	−31.9154	−	16.9697i	−1.07709	−	0.572700i
$879$	−10.9582	+	1.93222i	−0.369610	+	0.0651722i
$880$	1.53568	+	2.55582i	0.0517678	+	0.0861566i
$881$	6.67268	−	11.5574i	0.224808	−	0.389379i	−0.731454	−	0.681891i	$-0.761158\pi$
$881$	6.67268	−	11.5574i	0.224808	−	0.389379i	0.956262	+	0.292512i	$0.0944911\pi$
$882$	4.31527	−	0.917240i	0.145303	−	0.0308851i
$883$	−56.3208	−	3.93833i	−1.89534	−	0.132535i	−0.925888	−	0.377798i	$-0.876681\pi$
$883$	−56.3208	−	3.93833i	−1.89534	−	0.132535i	−0.969457	+	0.245263i	$0.921126\pi$
$884$	6.63386	−	1.65401i	0.223121	−	0.0556302i
$885$	3.85671	−	4.28331i	0.129642	−	0.143982i
$886$	−28.7265	−	6.10602i	−0.965087	−	0.205136i
$887$	39.8458	+	11.4256i	1.33789	+	0.383634i	0.866891	−	0.498498i	$-0.166115\pi$
$887$	39.8458	+	11.4256i	1.33789	+	0.383634i	0.471001	+	0.882133i	$0.343893\pi$
$888$	1.29836	+	1.25381i	0.0435702	+	0.0420753i
$889$	−7.59170	+	14.2779i	−0.254617	+	0.478866i
$890$	2.88580	−	7.92867i	0.0967323	−	0.265770i
$891$	−0.372245	+	0.969723i	−0.0124707	+	0.0324869i
$892$		−	7.02644i		−	0.235262i
$893$	−21.6296	−	9.91825i	−0.723806	−	0.331901i
$894$	3.55151	−	2.58032i	0.118780	−	0.0862990i
$895$	0.525892	+	7.52061i	0.0175786	+	0.251386i
$896$	2.13381	+	0.0745141i	0.0712854	+	0.00248934i
$897$	0.994962	+	7.07952i	0.0332208	+	0.236378i
$898$	−8.96042	−	4.37029i	−0.299013	−	0.145838i
$899$	2.82911	+	1.90826i	0.0943563	+	0.0636441i
$900$	−5.06859	−	5.62924i	−0.168953	−	0.187641i
$901$	20.7498	+	35.9397i	0.691275	+	1.19732i
$902$	−25.9019	−	27.7765i	−0.862437	−	0.924856i
$903$	−15.0663	+	17.9553i	−0.501376	+	0.597516i
$904$	−0.139148	−	0.654641i	−0.00462800	−	0.0217730i
$905$	−4.62159	+	0.485748i	−0.153627	+	0.0161468i
$906$	−2.44251	+	8.51806i	−0.0811471	+	0.282993i
$907$	−9.82637	−	18.4807i	−0.326279	−	0.613642i	0.664784	−	0.747036i	$-0.268524\pi$
$907$	−9.82637	−	18.4807i	−0.326279	−	0.613642i	−0.991063	+	0.133394i	$0.957413\pi$
$908$	17.1250	−	2.40676i	0.568312	−	0.0798710i
$909$	−25.6940	+	17.3308i	−0.852217	+	0.574828i
$910$	2.37495	+	0.592141i	0.0787288	+	0.0196293i
$911$	−18.1074	−	5.88344i	−0.599924	−	0.194927i	−0.00671742	−	0.999977i	$-0.502138\pi$
$911$	−18.1074	−	5.88344i	−0.599924	−	0.194927i	−0.593207	+	0.805050i	$0.702138\pi$
$912$	−4.72894	−	0.549987i	−0.156591	−	0.0182119i
$913$	1.22850	−	10.0051i	0.0406574	−	0.331121i
$914$	10.2207	+	12.1806i	0.338071	+	0.402897i
$915$	−4.37207	+	5.59600i	−0.144536	+	0.184998i
$916$	8.54215	+	17.5140i	0.282240	+	0.578679i
$917$	0.0696194	−	0.142741i	0.00229904	−	0.00471372i
$918$	−17.3311	−	22.1828i	−0.572013	−	0.732143i
$919$	−2.01338	+	9.47221i	−0.0664153	+	0.312459i	−0.998798	−	0.0490130i	$-0.984392\pi$
$919$	−2.01338	+	9.47221i	−0.0664153	+	0.312459i	0.932383	+	0.361472i	$0.117726\pi$
$920$	0.482376	−	4.58950i	0.0159035	−	0.151311i
$921$	−0.102905	+	1.47161i	−0.00339083	+	0.0484911i
$922$	−0.848709	−	1.35822i	−0.0279507	−	0.0447305i
$923$	13.1006	−	7.56362i	0.431210	−	0.248959i
$924$	0.135003	−	7.73311i	0.00444126	−	0.254401i
$925$	2.36923	+	6.50940i	0.0778997	+	0.214028i
$926$	13.8164	+	1.94177i	0.454036	+	0.0638106i
$927$	17.8465	−	8.70434i	0.586157	−	0.285888i
$928$	1.15108	+	1.70654i	0.0377859	+	0.0560199i
$929$	−43.6799	−	27.2942i	−1.43309	−	0.895495i	−0.433109	−	0.901342i	$-0.642583\pi$
$929$	−43.6799	−	27.2942i	−1.43309	−	0.895495i	−0.999983	+	0.00584680i	$0.998139\pi$
$930$	0.503024	+	1.54815i	0.0164948	+	0.0507658i
$931$	9.45056	−	4.89163i	0.309730	−	0.160317i
$932$	−16.8764	−	23.2284i	−0.552805	−	0.760871i
$933$	−18.1804	+	7.34537i	−0.595201	+	0.240477i
$934$	33.3785	+	12.1488i	1.09218	+	0.397521i
$935$	0.278966	+	15.9844i	0.00912316	+	0.522746i
$936$	0.400140	+	2.26931i	0.0130790	+	0.0741747i
$937$	8.85066	−	0.309072i	0.289139	−	0.0100969i	0.110037	−	0.993928i	$-0.464903\pi$
$937$	8.85066	−	0.309072i	0.289139	−	0.0100969i	0.179102	+	0.983831i	$0.442681\pi$
$938$	−2.27225	−	21.6190i	−0.0741916	−	0.705886i
$939$	9.85270	+	1.03556i	0.321531	+	0.0337942i
$940$	−1.83846	+	4.55036i	−0.0599641	+	0.148416i
$941$	−8.54506	+	21.1498i	−0.278561	+	0.689463i	−0.999995	−	0.00302009i	$-0.999039\pi$
$941$	−8.54506	+	21.1498i	−0.278561	+	0.689463i	0.721434	+	0.692483i	$0.243483\pi$
$942$	4.52257	+	0.475341i	0.147353	+	0.0154875i
$943$	6.14427	+	58.4588i	0.200085	+	1.90368i
$944$	−5.86637	+	0.204858i	−0.190934	+	0.00666757i
$945$	−1.75002	−	9.92487i	−0.0569282	−	0.322856i
$946$	20.0620	+	26.6233i	0.652271	+	0.865597i
$947$	28.6966	+	10.4447i	0.932515	+	0.339408i	0.763206	−	0.646155i	$-0.223624\pi$
$947$	28.6966	+	10.4447i	0.932515	+	0.339408i	0.169309	+	0.985563i	$0.445846\pi$
$948$	−15.4018	+	6.22272i	−0.500226	+	0.202104i
$949$	10.0415	+	13.8210i	0.325962	+	0.448648i
$950$	−15.3871	−	9.85324i	−0.499222	−	0.319681i
$951$	1.55689	+	4.79161i	0.0504855	+	0.155379i
$952$	9.70820	+	6.06635i	0.314644	+	0.196612i
$953$	−12.9038	−	19.1307i	−0.417995	−	0.619703i	0.559960	−	0.828520i	$-0.310817\pi$
$953$	−12.9038	−	19.1307i	−0.417995	−	0.619703i	−0.977955	+	0.208817i	$0.933039\pi$
$954$	−12.5714	+	6.13148i	−0.407014	+	0.198514i
$955$	−9.97848	−	1.40238i	−0.322896	−	0.0453801i
$956$	3.23657	+	8.89239i	0.104678	+	0.287600i
$957$	6.10813	−	4.27694i	0.197448	−	0.138254i
$958$	0.886638	−	0.511901i	0.0286460	−	0.0165388i
$959$	6.61070	+	10.5793i	0.213471	+	0.341625i
$960$	−0.0684946	+	0.979519i	−0.00221065	+	0.0316138i
$961$	−2.95310	+	28.0969i	−0.0952614	+	0.906352i
$962$	0.438127	−	2.06122i	0.0141258	−	0.0664565i
$963$	6.95013	+	8.89576i	0.223965	+	0.286662i
$964$	−9.09092	+	18.6392i	−0.292799	+	0.600327i
$965$	−10.5238	−	21.5770i	−0.338773	−	0.694588i
$966$	−7.36969	+	9.43278i	−0.237116	+	0.303495i
$967$	0.574130	+	0.684222i	0.0184628	+	0.0220031i	0.775197	−	0.631720i	$-0.217651\pi$
$967$	0.574130	+	0.684222i	0.0184628	+	0.0220031i	−0.756734	+	0.653723i	$0.773206\pi$
$968$	−10.6732	−	2.66120i	−0.343051	−	0.0855341i
$969$	−20.4836	−	15.2312i	−0.658028	−	0.489298i
$970$	−6.26751	−	2.03644i	−0.201238	−	0.0653861i
$971$	3.03855	+	0.757595i	0.0975116	+	0.0243124i	0.290372	−	0.956914i	$-0.406221\pi$
$971$	3.03855	+	0.757595i	0.0975116	+	0.0243124i	−0.192860	+	0.981226i	$0.561776\pi$
$972$	12.7746	−	8.61656i	0.409745	−	0.276376i
$973$	11.2664	−	1.58340i	0.361186	−	0.0507613i
$974$	−2.24876	−	4.22931i	−0.0720550	−	0.135516i
$975$	1.60918	−	5.61186i	0.0515349	−	0.179723i
$976$	7.19263	−	0.755976i	0.230231	−	0.0241982i
$977$	−1.15909	−	5.45310i	−0.0370826	−	0.174460i	0.955709	−	0.294313i	$-0.0950909\pi$
$977$	−1.15909	−	5.45310i	−0.0370826	−	0.174460i	−0.992792	+	0.119853i	$0.961758\pi$
$978$	8.37050	−	9.97557i	0.267659	−	0.318983i
$979$	13.1550	+	28.2111i	0.420434	+	0.901630i
$980$	−1.09739	−	1.90074i	−0.0350550	−	0.0607170i
$981$	−22.0406	−	24.4786i	−0.703704	−	0.781542i
$982$	18.4153	+	12.4213i	0.587657	+	0.396380i
$983$	−1.21931	−	0.594697i	−0.0388899	−	0.0189679i	0.418824	−	0.908068i	$-0.362443\pi$
$983$	−1.21931	−	0.594697i	−0.0388899	−	0.0189679i	−0.457714	+	0.889100i	$0.651331\pi$
$984$	−1.74065	−	12.3854i	−0.0554900	−	0.394832i
$985$	2.13682	+	0.0746195i	0.0680848	+	0.00237757i
$986$	0.769884	+	11.0099i	0.0245181	+	0.350625i
$987$	10.2990	−	7.48264i	0.327820	−	0.238175i
$988$	2.38117	+	5.02239i	0.0757553	+	0.159784i
$989$		−	51.5940i		−	1.64059i
$990$	−5.38080	−	0.282010i	−0.171013	−	0.00896287i
$991$	20.4310	−	56.1337i	0.649012	−	1.78315i	0.0276565	−	0.999617i	$-0.491196\pi$
$991$	20.4310	−	56.1337i	0.649012	−	1.78315i	0.621356	−	0.783529i	$-0.286582\pi$
$992$	0.778294	−	1.46376i	0.0247108	−	0.0464743i
$993$	3.87815	+	3.74509i	0.123070	+	0.118847i
$994$	24.3477	+	6.98158i	0.772261	+	0.221442i
$995$	−16.6260	−	3.53396i	−0.527079	−	0.112034i
$996$	2.22121	−	2.46691i	0.0703818	−	0.0781670i
$997$	0.666069	−	0.166070i	0.0210946	−	0.00525948i	−0.231360	−	0.972868i	$-0.574318\pi$
$997$	0.666069	−	0.166070i	0.0210946	−	0.00525948i	0.252455	+	0.967609i	$0.418762\pi$
$998$	15.4197	+	1.07825i	0.488103	+	0.0341315i
$999$	−8.48688	+	1.80394i	−0.268513	+	0.0570742i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.v.a.13.3	✓	240
11.6	odd	10		418.2.v.b.127.8	yes	240
19.3	odd	18		418.2.v.b.79.8	yes	240
209.193	even	90	inner	418.2.v.a.193.3	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.v.a.13.3	✓	240	1.1	even	1	trivial
418.2.v.a.193.3	yes	240	209.193	even	90	inner
418.2.v.b.79.8	yes	240	19.3	odd	18
418.2.v.b.127.8	yes	240	11.6	odd	10

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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.v (of order \(90\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(0.374607 + 0.927184i) q^{2} +(-0.301053 - 1.04990i) q^{3} +(-0.719340 + 0.694658i) q^{4} +(-0.793784 + 0.422062i) q^{5} +(0.860670 - 0.672429i) q^{6} +(-0.868426 - 1.95052i) q^{7} +(-0.913545 - 0.406737i) q^{8} +(1.53250 - 0.957610i) q^{9} +O(q^{10})\)	\(q+(0.374607 + 0.927184i) q^{2} +(-0.301053 - 1.04990i) q^{3} +(-0.719340 + 0.694658i) q^{4} +(-0.793784 + 0.422062i) q^{5} +(0.860670 - 0.672429i) q^{6} +(-0.868426 - 1.95052i) q^{7} +(-0.913545 - 0.406737i) q^{8} +(1.53250 - 0.957610i) q^{9} +(-0.688686 - 0.577876i) q^{10} +(3.30400 - 0.289054i) q^{11} +(0.945878 + 0.546103i) q^{12} +(-0.0445023 - 1.27438i) q^{13} +(1.48317 - 1.53587i) q^{14} +(0.682093 + 0.706328i) q^{15} +(0.0348995 - 0.999391i) q^{16} +(2.84124 - 4.54694i) q^{17} +(1.46196 + 1.06218i) q^{18} +(4.07928 + 1.53605i) q^{19} +(0.277811 - 0.855015i) q^{20} +(-1.78640 + 1.49897i) q^{21} +(1.50571 + 2.95514i) q^{22} +(0.891361 - 5.05516i) q^{23} +(-0.152006 + 1.08158i) q^{24} +(-2.34401 + 3.47514i) q^{25} +(1.16491 - 0.518653i) q^{26} +(-3.90175 - 3.51316i) q^{27} +(1.97964 + 0.799825i) q^{28} +(0.497986 + 1.99731i) q^{29} +(-0.399379 + 0.897020i) q^{30} +(1.23199 - 1.10929i) q^{31} +(0.939693 - 0.342020i) q^{32} +(-1.29816 - 3.38184i) q^{33} +(5.28020 + 0.931041i) q^{34} +(1.51258 + 1.18176i) q^{35} +(-0.437174 + 1.75341i) q^{36} +(0.971351 - 1.33695i) q^{37} +(0.103924 + 4.35766i) q^{38} +(-1.32457 + 0.430378i) q^{39} +(0.896826 - 0.0627122i) q^{40} +(-11.0076 + 3.15639i) q^{41} +(-2.05901 - 1.09480i) q^{42} +(9.89845 - 1.74536i) q^{43} +(-2.17591 + 2.50308i) q^{44} +(-0.812299 + 1.40694i) q^{45} +(5.02097 - 1.06724i) q^{46} +(-5.44569 - 0.380800i) q^{47} +(-1.05976 + 0.264229i) q^{48} +(1.63356 - 1.81426i) q^{49} +(-4.10017 - 0.871518i) q^{50} +(-5.62918 - 1.61414i) q^{51} +(0.917270 + 0.885798i) q^{52} +(-3.63374 + 6.83408i) q^{53} +(1.79572 - 4.93370i) q^{54} +(-2.50067 + 1.62394i) q^{55} +2.13511i q^{56} +(0.384614 - 4.74525i) q^{57} +(-1.66533 + 1.20993i) q^{58} +(-0.409467 - 5.85565i) q^{59} +(-0.981313 - 0.0342682i) q^{60} +(1.00653 + 7.16187i) q^{61} +(1.49003 + 0.726735i) q^{62} +(-3.19869 - 2.15754i) q^{63} +(0.669131 + 0.743145i) q^{64} +(0.573193 + 0.992799i) q^{65} +(2.64929 - 2.47049i) q^{66} +(6.54439 - 7.79931i) q^{67} +(1.11475 + 5.24449i) q^{68} +(-5.57574 + 0.586034i) q^{69} +(-0.529084 + 1.84514i) q^{70} +(5.56936 + 10.4744i) q^{71} +(-1.78950 + 0.251498i) q^{72} +(-11.1069 + 7.49168i) q^{73} +(1.60347 + 0.399791i) q^{74} +(4.35420 + 1.41477i) q^{75} +(-4.00142 + 1.72877i) q^{76} +(-3.43309 - 6.19349i) q^{77} +(-0.895232 - 1.06690i) q^{78} +(-9.36358 + 11.9848i) q^{79} +(0.394103 + 0.808030i) q^{80} +(-0.137291 + 0.281488i) q^{81} +(-7.05009 - 9.02370i) q^{82} +(0.631908 - 2.97289i) q^{83} +(0.243758 - 2.31920i) q^{84} +(-0.336241 + 4.80847i) q^{85} +(5.32630 + 8.52386i) q^{86} +(1.94705 - 1.12413i) q^{87} +(-3.13593 - 1.07980i) q^{88} +(3.20996 + 8.81928i) q^{89} +(-1.60879 - 0.226100i) q^{90} +(-2.44705 + 1.19351i) q^{91} +(2.87042 + 4.25557i) q^{92} +(-1.53553 - 0.959508i) q^{93} +(-1.68692 - 5.19181i) q^{94} +(-3.88638 + 0.502419i) q^{95} +(-0.641983 - 0.883613i) q^{96} +(6.79653 - 2.74598i) q^{97} +(2.29409 + 0.834982i) q^{98} +(4.78657 - 3.60692i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 3 q^{3} - 12 q^{6} + 33 q^{7} - 30 q^{8} + 3 q^{9}+O(q^{10}) \) 240 * q + 3 * q^3 - 12 * q^6 + 33 * q^7 - 30 * q^8 + 3 * q^9	\( 240 q + 3 q^{3} - 12 q^{6} + 33 q^{7} - 30 q^{8} + 3 q^{9} - 3 q^{11} - 6 q^{13} - 18 q^{14} + 21 q^{15} + 21 q^{17} - 60 q^{18} + 45 q^{19} + 12 q^{20} + 48 q^{21} - 12 q^{22} + 12 q^{24} - 18 q^{25} - 96 q^{26} - 9 q^{27} - 6 q^{28} + 18 q^{29} + 9 q^{31} + 87 q^{33} - 24 q^{34} - 36 q^{35} - 12 q^{36} - 36 q^{38} + 60 q^{41} - 6 q^{42} - 12 q^{43} + 18 q^{44} + 48 q^{45} + 12 q^{46} - 54 q^{47} + 6 q^{48} - 81 q^{49} - 21 q^{50} - 75 q^{51} + 3 q^{52} - 39 q^{53} + 27 q^{54} - 126 q^{55} - 90 q^{57} - 24 q^{58} + 69 q^{59} - 42 q^{60} + 66 q^{61} - 45 q^{62} - 9 q^{63} + 30 q^{64} - 12 q^{66} - 9 q^{67} + 12 q^{68} - 54 q^{69} + 9 q^{70} + 48 q^{71} + 6 q^{72} - 12 q^{74} + 72 q^{77} - 36 q^{79} - 27 q^{81} + 45 q^{82} + 36 q^{83} + 36 q^{84} - 210 q^{85} + 3 q^{86} + 216 q^{87} + 3 q^{88} + 18 q^{89} - 96 q^{90} - 108 q^{91} - 30 q^{92} + 147 q^{93} - 18 q^{94} + 66 q^{95} - 9 q^{97} - 12 q^{98} - 42 q^{99}+O(q^{100}) \) 240 * q + 3 * q^3 - 12 * q^6 + 33 * q^7 - 30 * q^8 + 3 * q^9 - 3 * q^11 - 6 * q^13 - 18 * q^14 + 21 * q^15 + 21 * q^17 - 60 * q^18 + 45 * q^19 + 12 * q^20 + 48 * q^21 - 12 * q^22 + 12 * q^24 - 18 * q^25 - 96 * q^26 - 9 * q^27 - 6 * q^28 + 18 * q^29 + 9 * q^31 + 87 * q^33 - 24 * q^34 - 36 * q^35 - 12 * q^36 - 36 * q^38 + 60 * q^41 - 6 * q^42 - 12 * q^43 + 18 * q^44 + 48 * q^45 + 12 * q^46 - 54 * q^47 + 6 * q^48 - 81 * q^49 - 21 * q^50 - 75 * q^51 + 3 * q^52 - 39 * q^53 + 27 * q^54 - 126 * q^55 - 90 * q^57 - 24 * q^58 + 69 * q^59 - 42 * q^60 + 66 * q^61 - 45 * q^62 - 9 * q^63 + 30 * q^64 - 12 * q^66 - 9 * q^67 + 12 * q^68 - 54 * q^69 + 9 * q^70 + 48 * q^71 + 6 * q^72 - 12 * q^74 + 72 * q^77 - 36 * q^79 - 27 * q^81 + 45 * q^82 + 36 * q^83 + 36 * q^84 - 210 * q^85 + 3 * q^86 + 216 * q^87 + 3 * q^88 + 18 * q^89 - 96 * q^90 - 108 * q^91 - 30 * q^92 + 147 * q^93 - 18 * q^94 + 66 * q^95 - 9 * q^97 - 12 * q^98 - 42 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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