LMFDB - Embedded newform 930.2.bn.b.19.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(19,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 15, 4]))

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

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

chi := DirichletCharacter("930.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bn (of order $30$, degree $8$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$18$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			19.5
Character	$\chi$	$=$	930.19
Dual form			930.2.bn.b.49.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.587785 + 0.809017i) q^{2} +(-0.406737 + 0.913545i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-0.293219 - 2.21676i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(1.44492 + 1.30102i) q^{7} +(0.951057 + 0.309017i) q^{8} +(-0.669131 - 0.743145i) q^{9} +O(q^{10})$	\(q+(-0.587785 + 0.809017i) q^{2} +(-0.406737 + 0.913545i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-0.293219 - 2.21676i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(1.44492 + 1.30102i) q^{7} +(0.951057 + 0.309017i) q^{8} +(-0.669131 - 0.743145i) q^{9} +(1.96575 + 1.06576i) q^{10} +(-5.64884 - 1.20070i) q^{11} +(0.994522 + 0.104528i) q^{12} +(3.28767 - 0.345548i) q^{13} +(-1.90185 + 0.404250i) q^{14} +(2.14437 + 0.633769i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(0.0364977 + 0.171708i) q^{17} +(0.994522 - 0.104528i) q^{18} +(-0.0150665 + 0.143348i) q^{19} +(-2.01765 + 0.963884i) q^{20} +(-1.77624 + 0.790833i) q^{21} +(4.29169 - 3.86426i) q^{22} +(-3.27136 - 1.06293i) q^{23} +(-0.669131 + 0.743145i) q^{24} +(-4.82805 + 1.29999i) q^{25} +(-1.65289 + 2.86289i) q^{26} +(0.951057 - 0.309017i) q^{27} +(0.790833 - 1.77624i) q^{28} +(-3.04683 - 2.21365i) q^{29} +(-1.77316 + 1.36231i) q^{30} +(-4.47788 - 3.30887i) q^{31} -1.00000i q^{32} +(3.39448 - 4.67211i) q^{33} +(-0.160368 - 0.0714003i) q^{34} +(2.46036 - 3.58453i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-5.58998 + 3.22738i) q^{37} +(-0.107115 - 0.0964471i) q^{38} +(-1.02154 + 3.14398i) q^{39} +(0.406149 - 2.19887i) q^{40} +(10.9387 - 4.87021i) q^{41} +(0.404250 - 1.90185i) q^{42} +(-10.6580 - 1.12020i) q^{43} +(0.603656 + 5.74340i) q^{44} +(-1.45117 + 1.70121i) q^{45} +(2.78279 - 2.02181i) q^{46} +(-3.74526 - 5.15490i) q^{47} +(-0.207912 - 0.978148i) q^{48} +(-0.336535 - 3.20192i) q^{49} +(1.78614 - 4.67009i) q^{50} +(-0.171708 - 0.0364977i) q^{51} +(-1.34458 - 3.01998i) q^{52} +(-2.88281 + 2.59569i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(-1.00531 + 12.8742i) q^{55} +(0.972168 + 1.68385i) q^{56} +(-0.124827 - 0.0720689i) q^{57} +(3.58176 - 1.16378i) q^{58} +(-11.8032 - 5.25514i) q^{59} +(-0.0598980 - 2.23527i) q^{60} +12.0835 q^{61} +(5.30896 - 1.67777i) q^{62} -1.94434i q^{63} +(0.809017 + 0.587785i) q^{64} +(-1.73000 - 7.18664i) q^{65} +(1.78459 + 5.49239i) q^{66} +(2.86681 + 1.65515i) q^{67} +(0.152026 - 0.0877721i) q^{68} +(2.30162 - 2.55621i) q^{69} +(1.45378 + 4.09741i) q^{70} +(-6.46534 - 7.18049i) q^{71} +(-0.406737 - 0.913545i) q^{72} +(2.81013 - 13.2206i) q^{73} +(0.674705 - 6.41939i) q^{74} +(0.776142 - 4.93939i) q^{75} +(0.140988 - 0.0299679i) q^{76} +(-6.60002 - 9.08415i) q^{77} +(-1.94309 - 2.67443i) q^{78} +(0.852468 - 0.181198i) q^{79} +(1.54020 + 1.62105i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(-2.48950 + 11.7122i) q^{82} +(2.58718 + 5.81090i) q^{83} +(1.30102 + 1.44492i) q^{84} +(0.369934 - 0.131255i) q^{85} +(7.17087 - 7.96406i) q^{86} +(3.26152 - 1.88304i) q^{87} +(-5.00133 - 2.88752i) q^{88} +(2.52224 + 7.76265i) q^{89} +(-0.523327 - 2.17397i) q^{90} +(5.19999 + 3.77801i) q^{91} +3.43972i q^{92} +(4.84412 - 2.74490i) q^{93} +6.37181 q^{94} +(0.322186 - 0.00863357i) q^{95} +(0.913545 + 0.406737i) q^{96} +(11.8413 - 3.84748i) q^{97} +(2.78822 + 1.60978i) q^{98} +(2.88752 + 5.00133i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 36 q^{4} + 2 q^{5} - 72 q^{6} - 18 q^{9}+O(q^{10}) $ 144 * q + 36 * q^4 + 2 * q^5 - 72 * q^6 - 18 * q^9	$ 144 q + 36 q^{4} + 2 q^{5} - 72 q^{6} - 18 q^{9} - 18 q^{11} - 8 q^{14} - 36 q^{16} - 24 q^{19} - 2 q^{20} + 28 q^{21} - 18 q^{24} + 10 q^{25} - 12 q^{26} - 4 q^{30} - 4 q^{31} + 10 q^{34} - 2 q^{35} - 72 q^{36} + 16 q^{39} + 4 q^{41} - 2 q^{44} - 2 q^{45} - 2 q^{46} - 78 q^{49} + 32 q^{50} + 10 q^{51} + 36 q^{54} - 50 q^{55} - 12 q^{56} + 28 q^{59} + 88 q^{61} + 36 q^{64} - 124 q^{65} + 6 q^{66} - 46 q^{69} - 10 q^{70} + 140 q^{71} + 34 q^{74} - 32 q^{75} + 24 q^{76} + 16 q^{79} + 12 q^{80} + 18 q^{81} - 8 q^{84} + 74 q^{85} - 98 q^{86} + 148 q^{89} + 44 q^{91} - 108 q^{94} - 80 q^{95} + 18 q^{96} - 2 q^{99}+O(q^{100}) $ 144 * q + 36 * q^4 + 2 * q^5 - 72 * q^6 - 18 * q^9 - 18 * q^11 - 8 * q^14 - 36 * q^16 - 24 * q^19 - 2 * q^20 + 28 * q^21 - 18 * q^24 + 10 * q^25 - 12 * q^26 - 4 * q^30 - 4 * q^31 + 10 * q^34 - 2 * q^35 - 72 * q^36 + 16 * q^39 + 4 * q^41 - 2 * q^44 - 2 * q^45 - 2 * q^46 - 78 * q^49 + 32 * q^50 + 10 * q^51 + 36 * q^54 - 50 * q^55 - 12 * q^56 + 28 * q^59 + 88 * q^61 + 36 * q^64 - 124 * q^65 + 6 * q^66 - 46 * q^69 - 10 * q^70 + 140 * q^71 + 34 * q^74 - 32 * q^75 + 24 * q^76 + 16 * q^79 + 12 * q^80 + 18 * q^81 - 8 * q^84 + 74 * q^85 - 98 * q^86 + 148 * q^89 + 44 * q^91 - 108 * q^94 - 80 * q^95 + 18 * q^96 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{15}\right)$

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 $

$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i
$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i
$3$	−0.406737	+	0.913545i	−0.234830	+	0.527436i
$3$	−0.406737	+	0.913545i	−0.234830	+	0.527436i
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$	−0.293219	−	2.21676i	−0.131131	−	0.991365i
$5$	−0.293219	−	2.21676i	−0.131131	−	0.991365i
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	1.44492	+	1.30102i	0.546130	+	0.491738i	0.895387	−	0.445290i	$-0.146899\pi$
$7$	1.44492	+	1.30102i	0.546130	+	0.491738i	−0.349257	+	0.937027i	$0.613566\pi$
$8$	0.951057	+	0.309017i	0.336249	+	0.109254i
$9$	−0.669131	−	0.743145i	−0.223044	−	0.247715i
$10$	1.96575	+	1.06576i	0.621623	+	0.337023i
$11$	−5.64884	−	1.20070i	−1.70319	−	0.362024i	−0.749311	−	0.662218i	$-0.769615\pi$
$11$	−5.64884	−	1.20070i	−1.70319	−	0.362024i	−0.953878	+	0.300194i	$0.902949\pi$
$12$	0.994522	+	0.104528i	0.287094	+	0.0301748i
$13$	3.28767	−	0.345548i	0.911834	−	0.0958377i	0.363019	−	0.931782i	$-0.381746\pi$
$13$	3.28767	−	0.345548i	0.911834	−	0.0958377i	0.548815	+	0.835944i	$0.315079\pi$
$14$	−1.90185	+	0.404250i	−0.508290	+	0.108040i
$15$	2.14437	+	0.633769i	0.553675	+	0.163638i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	0.0364977	+	0.171708i	0.00885199	+	0.0416454i	0.982352	−	0.187042i	$-0.0598900\pi$
$17$	0.0364977	+	0.171708i	0.00885199	+	0.0416454i	−0.973500	+	0.228687i	$0.926557\pi$
$18$	0.994522	−	0.104528i	0.234411	−	0.0246376i
$19$	−0.0150665	+	0.143348i	−0.00345649	+	0.0328863i	−0.996114	−	0.0880710i	$-0.971930\pi$
$19$	−0.0150665	+	0.143348i	−0.00345649	+	0.0328863i	0.992658	+	0.120957i	$0.0385964\pi$
$20$	−2.01765	+	0.963884i	−0.451161	+	0.215531i
$21$	−1.77624	+	0.790833i	−0.387607	+	0.172574i
$22$	4.29169	−	3.86426i	0.914992	−	0.823862i
$23$	−3.27136	−	1.06293i	−0.682126	−	0.221636i	−0.0526004	−	0.998616i	$-0.516751\pi$
$23$	−3.27136	−	1.06293i	−0.682126	−	0.221636i	−0.629526	+	0.776979i	$0.716751\pi$
$24$	−0.669131	+	0.743145i	−0.136586	+	0.151694i
$25$	−4.82805	+	1.29999i	−0.965609	+	0.259998i
$26$	−1.65289	+	2.86289i	−0.324158	+	0.561458i
$27$	0.951057	−	0.309017i	0.183031	−	0.0594703i
$28$	0.790833	−	1.77624i	0.149453	−	0.335678i
$29$	−3.04683	−	2.21365i	−0.565781	−	0.411064i	0.267789	−	0.963478i	$-0.413707\pi$
$29$	−3.04683	−	2.21365i	−0.565781	−	0.411064i	−0.833570	+	0.552413i	$0.813707\pi$
$30$	−1.77316	+	1.36231i	−0.323733	+	0.248723i
$31$	−4.47788	−	3.30887i	−0.804250	−	0.594291i
$31$	−4.47788	−	3.30887i	−0.804250	−	0.594291i
$32$		−	1.00000i		−	0.176777i
$33$	3.39448	−	4.67211i	0.590904	−	0.813309i
$34$	−0.160368	−	0.0714003i	−0.0275028	−	0.0122450i
$35$	2.46036	−	3.58453i	0.415877	−	0.605896i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−5.58998	+	3.22738i	−0.918987	+	0.530577i	−0.883312	−	0.468786i	$-0.844691\pi$
$37$	−5.58998	+	3.22738i	−0.918987	+	0.530577i	−0.0356751	+	0.999363i	$0.511358\pi$
$38$	−0.107115	−	0.0964471i	−0.0173764	−	0.0156458i
$39$	−1.02154	+	3.14398i	−0.163577	+	0.503440i
$40$	0.406149	−	2.19887i	0.0642178	−	0.347672i
$41$	10.9387	−	4.87021i	1.70833	−	0.760598i	0.709919	−	0.704283i	$-0.248732\pi$
$41$	10.9387	−	4.87021i	1.70833	−	0.760598i	0.998413	−	0.0563149i	$-0.0179351\pi$
$42$	0.404250	−	1.90185i	0.0623772	−	0.293462i
$43$	−10.6580	−	1.12020i	−1.62533	−	0.170829i	−0.752410	−	0.658695i	$-0.771109\pi$
$43$	−10.6580	−	1.12020i	−1.62533	−	0.170829i	−0.872918	+	0.487866i	$0.837775\pi$
$44$	0.603656	+	5.74340i	0.0910046	+	0.865851i
$45$	−1.45117	+	1.70121i	−0.216328	+	0.253601i
$46$	2.78279	−	2.02181i	0.410300	−	0.298100i
$47$	−3.74526	−	5.15490i	−0.546302	−	0.751920i	0.443203	−	0.896421i	$-0.353842\pi$
$47$	−3.74526	−	5.15490i	−0.546302	−	0.751920i	−0.989505	+	0.144501i	$0.953842\pi$
$48$	−0.207912	−	0.978148i	−0.0300095	−	0.141183i
$49$	−0.336535	−	3.20192i	−0.0480764	−	0.457417i
$50$	1.78614	−	4.67009i	0.252598	−	0.660450i
$51$	−0.171708	−	0.0364977i	−0.0240440	−	0.00511070i
$52$	−1.34458	−	3.01998i	−0.186460	−	0.418795i
$53$	−2.88281	+	2.59569i	−0.395984	+	0.356545i	−0.842937	−	0.538012i	$-0.819176\pi$
$53$	−2.88281	+	2.59569i	−0.395984	+	0.356545i	0.446954	+	0.894557i	$0.352509\pi$
$54$	−0.309017	+	0.951057i	−0.0420519	+	0.129422i
$55$	−1.00531	+	12.8742i	−0.135556	+	1.73596i
$56$	0.972168	+	1.68385i	0.129911	+	0.225013i
$57$	−0.124827	−	0.0720689i	−0.0165337	−	0.00954576i
$58$	3.58176	−	1.16378i	0.470308	−	0.152812i
$59$	−11.8032	−	5.25514i	−1.53665	−	0.684161i	−0.548290	−	0.836288i	$-0.684721\pi$
$59$	−11.8032	−	5.25514i	−1.53665	−	0.684161i	−0.988361	+	0.152127i	$0.951388\pi$
$60$	−0.0598980	−	2.23527i	−0.00773280	−	0.288572i
$61$	12.0835			1.54713			0.773567	−	0.633715i	$-0.218471\pi$
$61$	12.0835			1.54713			0.773567	+	0.633715i	$0.218471\pi$
$62$	5.30896	−	1.67777i	0.674239	−	0.213077i
$63$		−	1.94434i		−	0.244963i
$64$	0.809017	+	0.587785i	0.101127	+	0.0734732i
$65$	−1.73000	−	7.18664i	−0.214580	−	0.891393i
$66$	1.78459	+	5.49239i	0.219667	+	0.676066i
$67$	2.86681	+	1.65515i	0.350236	+	0.202209i	0.664789	−	0.747031i	$-0.268521\pi$
$67$	2.86681	+	1.65515i	0.350236	+	0.202209i	−0.314553	+	0.949240i	$0.601855\pi$
$68$	0.152026	−	0.0877721i	0.0184358	−	0.0106439i
$69$	2.30162	−	2.55621i	0.277082	−	0.307731i
$70$	1.45378	+	4.09741i	0.173760	+	0.489734i
$71$	−6.46534	−	7.18049i	−0.767295	−	0.852168i	0.225218	−	0.974308i	$-0.427691\pi$
$71$	−6.46534	−	7.18049i	−0.767295	−	0.852168i	−0.992513	+	0.122141i	$0.961024\pi$
$72$	−0.406737	−	0.913545i	−0.0479344	−	0.107662i
$73$	2.81013	−	13.2206i	0.328901	−	1.54736i	−0.434042	−	0.900893i	$-0.642913\pi$
$73$	2.81013	−	13.2206i	0.328901	−	1.54736i	0.762943	−	0.646466i	$-0.223754\pi$
$74$	0.674705	−	6.41939i	0.0784329	−	0.746239i
$75$	0.776142	−	4.93939i	0.0896212	−	0.570352i
$76$	0.140988	−	0.0299679i	0.0161724	−	0.00343756i
$77$	−6.60002	−	9.08415i	−0.752142	−	1.03523i
$78$	−1.94309	−	2.67443i	−0.220011	−	0.302819i
$79$	0.852468	−	0.181198i	0.0959102	−	0.0203863i	−0.159707	−	0.987165i	$-0.551055\pi$
$79$	0.852468	−	0.181198i	0.0959102	−	0.0203863i	0.255617	+	0.966778i	$0.417721\pi$
$80$	1.54020	+	1.62105i	0.172199	+	0.181239i
$81$	−0.104528	+	0.994522i	−0.0116143	+	0.110502i
$82$	−2.48950	+	11.7122i	−0.274920	+	1.29340i
$83$	2.58718	+	5.81090i	0.283980	+	0.637829i	0.998062	−	0.0622331i	$-0.0198222\pi$
$83$	2.58718	+	5.81090i	0.283980	+	0.637829i	−0.714082	+	0.700062i	$0.753156\pi$
$84$	1.30102	+	1.44492i	0.141952	+	0.157654i
$85$	0.369934	−	0.131255i	0.0401250	−	0.0142366i
$86$	7.17087	−	7.96406i	0.773255	−	0.858787i
$87$	3.26152	−	1.88304i	0.349672	−	0.201883i
$88$	−5.00133	−	2.88752i	−0.533144	−	0.307811i
$89$	2.52224	+	7.76265i	0.267357	+	0.822839i	0.991141	+	0.132813i	$0.0424010\pi$
$89$	2.52224	+	7.76265i	0.267357	+	0.822839i	−0.723784	+	0.690026i	$0.757599\pi$
$90$	−0.523327	−	2.17397i	−0.0551635	−	0.229156i
$91$	5.19999	+	3.77801i	0.545107	+	0.396043i
$92$			3.43972i			0.358615i
$93$	4.84412	−	2.74490i	0.502312	−	0.284633i
$94$	6.37181			0.657202
$95$	0.322186	−	0.00863357i	0.0330556	−	0.000885785i
$96$	0.913545	+	0.406737i	0.0932383	+	0.0415124i
$97$	11.8413	−	3.84748i	1.20231	−	0.390653i	0.361697	−	0.932296i	$-0.382198\pi$
$97$	11.8413	−	3.84748i	1.20231	−	0.390653i	0.840609	+	0.541643i	$0.182198\pi$
$98$	2.78822	+	1.60978i	0.281652	+	0.162612i
$99$	2.88752	+	5.00133i	0.290207	+	0.502653i
$100$	2.72831	+	4.19002i	0.272831	+	0.419002i
$101$	4.69999	−	14.4651i	0.467667	−	1.43933i	−0.387931	−	0.921689i	$-0.626810\pi$
$101$	4.69999	−	14.4651i	0.467667	−	1.43933i	0.855597	−	0.517642i	$-0.173190\pi$
$102$	0.130455	−	0.117462i	0.0129170	−	0.0116305i
$103$	−0.923234	−	2.07362i	−0.0909690	−	0.204320i	0.862331	−	0.506345i	$-0.169004\pi$
$103$	−0.923234	−	2.07362i	−0.0909690	−	0.204320i	−0.953300	+	0.302026i	$0.902337\pi$
$104$	3.23354	+	0.687309i	0.317074	+	0.0673962i
$105$	2.27391	+	3.70561i	0.221911	+	0.361630i
$106$	−0.405487	−	3.85795i	−0.0393843	−	0.374717i
$107$	−0.262963	−	1.23714i	−0.0254216	−	0.119599i	0.963607	−	0.267322i	$-0.0861389\pi$
$107$	−0.262963	−	1.23714i	−0.0254216	−	0.119599i	−0.989029	+	0.147723i	$0.952806\pi$
$108$	−0.587785	−	0.809017i	−0.0565597	−	0.0778477i
$109$	−15.1988	+	11.0426i	−1.45578	+	1.05769i	−0.471342	+	0.881951i	$0.656230\pi$
$109$	−15.1988	+	11.0426i	−1.45578	+	1.05769i	−0.984438	+	0.175735i	$0.943770\pi$
$110$	−9.82453	−	8.38057i	−0.936732	−	0.799056i
$111$	−0.674705	−	6.41939i	−0.0640402	−	0.609302i
$112$	−1.93369	−	0.203239i	−0.182716	−	0.0192042i
$113$	−2.66837	+	12.5537i	−0.251019	+	1.18095i	0.654305	+	0.756231i	$0.272961\pi$
$113$	−2.66837	+	12.5537i	−0.251019	+	1.18095i	−0.905324	+	0.424721i	$0.860372\pi$
$114$	0.131676	−	0.0586262i	0.0123326	−	0.00549084i
$115$	−1.39704	+	7.56350i	−0.130274	+	0.705300i
$116$	−1.16378	+	3.58176i	−0.108055	+	0.332558i
$117$	−2.45667	−	2.21200i	−0.227119	−	0.204499i
$118$	11.1893	−	6.46013i	1.03006	−	0.594703i
$119$	−0.170659	+	0.295589i	−0.0156442	+	0.0270966i
$120$	1.84358	+	1.26540i	0.168295	+	0.115514i
$121$	20.4187	+	9.09101i	1.85625	+	0.826455i
$122$	−7.10250	+	9.77576i	−0.643031	+	0.885056i
$123$			11.9739i			1.07965i
$124$	−1.76318	+	5.28121i	−0.158339	+	0.474267i
$125$	4.29744	+	10.3214i	0.384375	+	0.923177i
$126$	1.57300	+	1.14285i	0.140134	+	0.101813i
$127$	5.29126	−	11.8844i	0.469524	−	1.05457i	−0.511252	−	0.859431i	$-0.670818\pi$
$127$	5.29126	−	11.8844i	0.469524	−	1.05457i	0.980776	−	0.195137i	$-0.0625151\pi$
$128$	−0.951057	+	0.309017i	−0.0840623	+	0.0273135i
$129$	5.35835	−	9.28093i	0.471776	−	0.817141i
$130$	6.83099	+	2.82460i	0.599117	+	0.247734i
$131$	7.07388	−	7.85634i	0.618048	−	0.686412i	−0.350122	−	0.936704i	$-0.613860\pi$
$131$	7.07388	−	7.85634i	0.618048	−	0.686412i	0.968170	+	0.250292i	$0.0805267\pi$
$132$	−5.49239	−	1.78459i	−0.478051	−	0.155328i
$133$	−0.208268	+	0.187526i	−0.0180591	+	0.0162605i
$134$	−3.02411	+	1.34642i	−0.261244	+	0.116313i
$135$	−0.963884	−	2.01765i	−0.0829579	−	0.173652i
$136$	−0.0183494	+	0.174583i	−0.00157345	+	0.0149703i
$137$	−14.7000	+	1.54503i	−1.25590	+	0.132001i	−0.709008	−	0.705201i	$-0.750857\pi$
$137$	−14.7000	+	1.54503i	−1.25590	+	0.132001i	−0.546895	+	0.837201i	$0.684190\pi$
$138$	0.715157	+	3.36455i	0.0608782	+	0.286409i
$139$	−0.354604	+	0.257635i	−0.0300771	+	0.0218523i	−0.602722	−	0.797951i	$-0.705917\pi$
$139$	−0.354604	+	0.257635i	−0.0300771	+	0.0218523i	0.572645	+	0.819803i	$0.305917\pi$
$140$	−4.16938	−	1.23226i	−0.352377	−	0.104145i
$141$	6.23257	−	1.32477i	0.524877	−	0.111566i
$142$	9.60937	−	1.00999i	0.806401	−	0.0847561i
$143$	−18.9864	−	1.99555i	−1.58772	−	0.166876i
$144$	0.978148	+	0.207912i	0.0815123	+	0.0173260i
$145$	−4.01374	+	7.40316i	−0.333323	+	0.614799i
$146$	9.04397	+	10.0443i	0.748484	+	0.831276i
$147$	3.06198	+	0.994897i	0.252548	+	0.0820577i
$148$	4.79682	+	4.31907i	0.394296	+	0.355026i
$149$	−3.27716	−	5.67620i	−0.268475	−	0.465012i	0.699993	−	0.714149i	$-0.253186\pi$
$149$	−3.27716	−	5.67620i	−0.268475	−	0.465012i	−0.968468	+	0.249137i	$0.919853\pi$
$150$	3.53985	+	3.53121i	0.289027	+	0.288322i
$151$	2.23955	+	6.89263i	0.182252	+	0.560915i	0.999890	−	0.0148180i	$-0.00471690\pi$
$151$	2.23955	+	6.89263i	0.182252	+	0.560915i	−0.817638	+	0.575733i	$0.804717\pi$
$152$	−0.0586262	+	0.131676i	−0.00475521	+	0.0106804i
$153$	0.103182	−	0.142018i	0.00834180	−	0.0114815i
$154$	11.2286			0.904828
$155$	−6.02197	+	10.8966i	−0.483697	+	0.875236i
$156$	3.30578			0.264674
$157$	−10.0791	+	13.8726i	−0.804396	+	1.10716i	0.187768	+	0.982213i	$0.439875\pi$
$157$	−10.0791	+	13.8726i	−0.804396	+	1.10716i	−0.992164	+	0.124942i	$0.960125\pi$
$158$	−0.354476	+	0.796167i	−0.0282006	+	0.0633396i
$159$	−1.19874	−	3.68934i	−0.0950661	−	0.292583i
$160$	−2.21676	+	0.293219i	−0.175250	+	0.0231810i
$161$	−3.34398	−	5.79195i	−0.263543	−	0.456469i
$162$	−0.743145	−	0.669131i	−0.0583870	−	0.0525719i
$163$	−7.00022	−	2.27451i	−0.548300	−	0.178153i	0.0217501	−	0.999763i	$-0.493076\pi$
$163$	−7.00022	−	2.27451i	−0.548300	−	0.178153i	−0.570050	+	0.821610i	$0.693076\pi$
$164$	−8.01207	−	8.89831i	−0.625638	−	0.694841i
$165$	−11.3523	−	6.15480i	−0.883772	−	0.479151i
$166$	−6.22182	−	1.32249i	−0.482907	−	0.102645i
$167$	−0.583853	−	0.0613655i	−0.0451799	−	0.00474860i	0.0819115	−	0.996640i	$-0.473898\pi$
$167$	−0.583853	−	0.0613655i	−0.0451799	−	0.00474860i	−0.127091	+	0.991891i	$0.540564\pi$
$168$	−1.93369	+	0.203239i	−0.149187	+	0.0156802i
$169$	−2.02658	+	0.430762i	−0.155890	+	0.0331355i
$170$	−0.111254	+	0.376432i	−0.00853283	+	0.0288710i
$171$	0.116610	−	0.0847221i	0.00891739	−	0.00647886i
$172$	2.22813	+	10.4825i	0.169893	+	0.799284i
$173$	−17.5295	+	1.84242i	−1.33274	+	0.140077i	−0.743965	−	0.668219i	$-0.767057\pi$
$173$	−17.5295	+	1.84242i	−1.33274	+	0.140077i	−0.588777	+	0.808295i	$0.700390\pi$
$174$	−0.393663	+	3.74545i	−0.0298435	+	0.283942i
$175$	−8.66747	−	4.40297i	−0.655199	−	0.332833i
$176$	5.27576	−	2.34892i	0.397675	−	0.177057i
$177$	9.60162	−	8.64534i	0.721702	−	0.649823i
$178$	−7.76265	−	2.52224i	−0.581835	−	0.189050i
$179$	−7.43947	+	8.26237i	−0.556052	+	0.617559i	−0.953984	−	0.299856i	$-0.903061\pi$
$179$	−7.43947	+	8.26237i	−0.556052	+	0.617559i	0.397932	+	0.917415i	$0.369728\pi$
$180$	2.06638	+	0.854445i	0.154019	+	0.0636866i
$181$	−3.75852	+	6.50995i	−0.279369	+	0.483881i	−0.971228	−	0.238152i	$-0.923458\pi$
$181$	−3.75852	+	6.50995i	−0.279369	+	0.483881i	0.691859	+	0.722032i	$0.256792\pi$
$182$	−6.11295	+	1.98622i	−0.453122	+	0.147228i
$183$	−4.91480	+	11.0388i	−0.363313	+	0.816014i
$184$	−2.78279	−	2.02181i	−0.205150	−	0.149050i
$185$	8.79340	+	11.4453i	0.646504	+	0.841476i
$186$	−0.626628	+	5.53239i	−0.0459466	+	0.405655i
$187$		−	1.01378i		−	0.0741346i
$188$	−3.74526	+	5.15490i	−0.273151	+	0.375960i
$189$	1.77624	+	0.790833i	0.129202	+	0.0575246i
$190$	−0.182392	+	0.265729i	−0.0132321	+	0.0192780i
$191$	3.47708	−	6.02248i	0.251593	−	0.435771i	−0.712372	−	0.701802i	$-0.752379\pi$
$191$	3.47708	−	6.02248i	0.251593	−	0.435771i	0.963964	+	0.266031i	$0.0857124\pi$
$192$	−0.866025	+	0.500000i	−0.0625000	+	0.0360844i
$193$	−10.1136	−	9.10634i	−0.727994	−	0.655489i	0.219372	−	0.975641i	$-0.429599\pi$
$193$	−10.1136	−	9.10634i	−0.727994	−	0.655489i	−0.947366	+	0.320153i	$0.896266\pi$
$194$	−3.84748	+	11.8413i	−0.276233	+	0.850158i
$195$	7.26898	+	1.34264i	0.520542	+	0.0961482i
$196$	−2.94121	+	1.30951i	−0.210086	+	0.0935365i
$197$	1.66806	−	7.84760i	0.118844	−	0.559118i	−0.877925	−	0.478798i	$-0.841072\pi$
$197$	1.66806	−	7.84760i	0.118844	−	0.559118i	0.996769	−	0.0803199i	$-0.0255942\pi$
$198$	−5.74340	−	0.603656i	−0.408166	−	0.0429000i
$199$	−1.70844	−	16.2547i	−0.121108	−	1.15227i	−0.871198	−	0.490931i	$-0.836657\pi$
$199$	−1.70844	−	16.2547i	−0.121108	−	1.15227i	0.750090	−	0.661335i	$-0.230010\pi$
$200$	−4.99346	−	0.255583i	−0.353091	−	0.0180725i
$201$	−2.67809	+	1.94575i	−0.188898	+	0.137243i
$202$	8.93992	+	12.3047i	0.629010	+	0.865759i
$203$	−1.52244	−	7.16252i	−0.106854	−	0.502710i
$204$	0.0183494	+	0.174583i	0.00128471	+	0.0122232i
$205$	−14.0035	−	22.8203i	−0.978047	−	1.59384i
$206$	2.22026	+	0.471930i	0.154693	+	0.0328809i
$207$	1.39906	+	3.14234i	0.0972413	+	0.218407i
$208$	−2.45667	+	2.21200i	−0.170339	+	0.153374i
$209$	0.257226	−	0.791661i	0.0177927	−	0.0547604i
$210$	−4.33447	−	0.338468i	−0.299107	−	0.0233565i
$211$	10.8717	+	18.8304i	0.748441	+	1.29634i	0.948570	+	0.316568i	$0.102530\pi$
$211$	10.8717	+	18.8304i	0.748441	+	1.29634i	−0.200129	+	0.979769i	$0.564136\pi$
$212$	3.35948	+	1.93960i	0.230730	+	0.133212i
$213$	9.18940	−	2.98582i	0.629647	−	0.204585i
$214$	1.15544	+	0.514433i	0.0789840	+	0.0351659i
$215$	0.641909	+	23.9547i	0.0437778	+	1.63369i
$216$	1.00000			0.0680414
$217$	−2.16530	−	10.6069i	−0.146990	−	0.720040i
$218$		−	18.7867i		−	1.27240i
$219$	10.9347	+	7.94450i	0.738896	+	0.536840i
$220$	12.5547	−	3.02223i	0.846440	−	0.203759i
$221$	0.179326	+	0.551907i	0.0120627	+	0.0371253i
$222$	5.58998	+	3.22738i	0.375175	+	0.216607i
$223$	−11.9041	+	6.87282i	−0.797156	+	0.460238i	−0.842476	−	0.538734i	$-0.818903\pi$
$223$	−11.9041	+	6.87282i	−0.797156	+	0.460238i	0.0453199	+	0.998973i	$0.485569\pi$
$224$	1.30102	−	1.44492i	0.0869277	−	0.0965430i
$225$	4.19667	+	2.71807i	0.279778	+	0.181205i
$226$	−8.58772	−	9.53763i	−0.571247	−	0.634434i
$227$	9.96585	+	22.3837i	0.661457	+	1.48566i	0.862491	+	0.506072i	$0.168903\pi$
$227$	9.96585	+	22.3837i	0.661457	+	1.48566i	−0.201035	+	0.979584i	$0.564430\pi$
$228$	−0.0299679	+	0.140988i	−0.00198468	+	0.00933717i
$229$	−2.13774	+	20.3392i	−0.141266	+	1.34405i	0.662479	+	0.749080i	$0.269504\pi$
$229$	−2.13774	+	20.3392i	−0.141266	+	1.34405i	−0.803745	+	0.594974i	$0.797162\pi$
$230$	−5.29784	−	5.57594i	−0.349329	−	0.367666i
$231$	10.9832	−	2.33456i	0.722645	−	0.153603i
$232$	−2.21365	−	3.04683i	−0.145333	−	0.200034i
$233$	8.28790	+	11.4073i	0.542958	+	0.747318i	0.989036	−	0.147676i	$-0.0471794\pi$
$233$	8.28790	+	11.4073i	0.542958	+	0.747318i	−0.446078	+	0.894994i	$0.647179\pi$
$234$	3.23354	−	0.687309i	0.211383	−	0.0449308i
$235$	−10.3290	+	9.81385i	−0.673790	+	0.640185i
$236$	−1.35053	+	12.8495i	−0.0879123	+	0.836430i
$237$	−0.181198	+	0.852468i	−0.0117701	+	0.0553738i
$238$	−0.138826	−	0.311809i	−0.00899877	−	0.0202116i
$239$	4.89385	+	5.43517i	0.316557	+	0.351572i	0.880334	−	0.474355i	$-0.157319\pi$
$239$	4.89385	+	5.43517i	0.316557	+	0.351572i	−0.563777	+	0.825927i	$0.690652\pi$
$240$	−2.10735	+	0.747701i	−0.136029	+	0.0482639i
$241$	10.0555	−	11.1677i	0.647729	−	0.719376i	−0.326434	−	0.945220i	$-0.605847\pi$
$241$	10.0555	−	11.1677i	0.647729	−	0.719376i	0.974164	+	0.225844i	$0.0725138\pi$
$242$	−19.3566	+	11.1755i	−1.24429	+	0.718391i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	−3.73401	−	11.4921i	−0.239045	−	0.735706i
$245$	−6.99920	+	1.68488i	−0.447163	+	0.107643i
$246$	−9.68705	−	7.03806i	−0.617624	−	0.448730i
$247$			0.476487i			0.0303182i
$248$	−3.23622	−	4.53066i	−0.205500	−	0.287697i
$249$	−6.36082			−0.403101
$250$	−10.8762	−	2.59008i	−0.687871	−	0.163811i
$251$	1.67504	+	0.745774i	0.105727	+	0.0470728i	0.458919	−	0.888478i	$-0.348237\pi$
$251$	1.67504	+	0.745774i	0.105727	+	0.0470728i	−0.353191	+	0.935551i	$0.614904\pi$
$252$	−1.84917	+	0.600833i	−0.116487	+	0.0378489i
$253$	17.2032	+	9.93225i	1.08155	+	0.624435i
$254$	6.50453	+	11.2662i	0.408131	+	0.706903i
$255$	−0.0305586	+	0.391338i	−0.00191365	+	0.0245065i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	18.0562	−	16.2579i	1.12632	−	1.01414i	0.126564	−	0.991958i	$-0.459605\pi$
$257$	18.0562	−	16.2579i	1.12632	−	1.01414i	0.999754	−	0.0221825i	$-0.00706148\pi$
$258$	4.35887	+	9.79019i	0.271372	+	0.609511i
$259$	−12.2760	−	2.60934i	−0.762791	−	0.162136i
$260$	−6.30030	+	3.86612i	−0.390728	+	0.239767i
$261$	0.393663	+	3.74545i	0.0243671	+	0.231838i
$262$	2.19799	+	10.3407i	0.135792	+	0.638853i
$263$	12.5395	+	17.2592i	0.773220	+	1.06425i	0.995998	+	0.0893765i	$0.0284874\pi$
$263$	12.5395	+	17.2592i	0.773220	+	1.06425i	−0.222778	+	0.974869i	$0.571513\pi$
$264$	4.67211	−	3.39448i	0.287548	−	0.208916i
$265$	6.59931	+	5.62938i	0.405393	+	0.345810i
$266$	−0.0292944	−	0.278717i	−0.00179615	−	0.0170893i
$267$	−8.11742	−	0.853175i	−0.496778	−	0.0522135i
$268$	0.688251	−	3.23797i	0.0420416	−	0.197790i
$269$	−6.39326	+	2.84646i	−0.389804	+	0.173552i	−0.592274	−	0.805736i	$-0.701770\pi$
$269$	−6.39326	+	2.84646i	−0.389804	+	0.173552i	0.202470	+	0.979288i	$0.435103\pi$
$270$	2.19887	+	0.406149i	0.133819	+	0.0247174i
$271$	−3.68868	+	11.3526i	−0.224071	+	0.689620i	0.774313	+	0.632802i	$0.218095\pi$
$271$	−3.68868	+	11.3526i	−0.224071	+	0.689620i	−0.998385	+	0.0568180i	$0.981905\pi$
$272$	−0.130455	−	0.117462i	−0.00790998	−	0.00712218i
$273$	−5.56641	+	3.21377i	−0.336895	+	0.194506i
$274$	7.39047	−	12.8007i	0.446475	−	0.773317i
$275$	28.8338	−	1.54642i	1.73874	−	0.0932524i
$276$	−3.14234	−	1.39906i	−0.189146	−	0.0842134i
$277$	1.76407	−	2.42803i	0.105993	−	0.145886i	−0.752726	−	0.658334i	$-0.771261\pi$
$277$	1.76407	−	2.42803i	0.105993	−	0.145886i	0.858718	+	0.512448i	$0.171261\pi$
$278$		−	0.438315i		−	0.0262884i
$279$	0.537314	+	5.54178i	0.0321681	+	0.331778i
$280$	3.44762	−	2.64880i	0.206035	−	0.158296i
$281$	10.1153	+	7.34920i	0.603428	+	0.438416i	0.847094	−	0.531443i	$-0.178350\pi$
$281$	10.1153	+	7.34920i	0.603428	+	0.438416i	−0.243666	+	0.969859i	$0.578350\pi$
$282$	−2.59165	+	5.82094i	−0.154330	+	0.346632i
$283$	14.7004	−	4.77644i	0.873847	−	0.283930i	0.162447	−	0.986717i	$-0.448061\pi$
$283$	14.7004	−	4.77644i	0.873847	−	0.283930i	0.711400	+	0.702787i	$0.248061\pi$
$284$	−4.83115	+	8.36780i	−0.286676	+	0.496538i
$285$	−0.123158	+	0.297844i	−0.00729524	+	0.0176427i
$286$	12.7744	−	14.1874i	0.755364	−	0.838916i
$287$	22.1417	+	7.19429i	1.30699	+	0.424665i
$288$	−0.743145	+	0.669131i	−0.0437902	+	0.0394289i
$289$	15.5021	−	6.90199i	0.911889	−	0.405999i
$290$	−3.63007	−	7.59865i	−0.213165	−	0.446208i
$291$	−1.30145	+	12.3825i	−0.0762926	+	0.725876i
$292$	−13.4420	+	1.41281i	−0.786631	+	0.0826782i
$293$	−2.61389	−	12.2974i	−0.152705	−	0.718422i	−0.986155	−	0.165826i	$-0.946971\pi$
$293$	−2.61389	−	12.2974i	−0.152705	−	0.718422i	0.833450	−	0.552595i	$-0.186362\pi$
$294$	−2.60467	+	1.89241i	−0.151908	+	0.110367i
$295$	−8.18845	+	27.7058i	−0.476750	+	1.61310i
$296$	−6.31370	+	1.34202i	−0.366976	+	0.0780032i
$297$	−5.74340	+	0.603656i	−0.333266	+	0.0350277i
$298$	6.51840	+	0.685112i	0.377601	+	0.0396875i
$299$	−11.1224	−	2.36415i	−0.643228	−	0.136722i
$300$	−4.93748	+	0.788201i	−0.285066	+	0.0455068i
$301$	−13.9426	−	15.4848i	−0.803637	−	0.892530i
$302$	−6.89263	−	2.23955i	−0.396627	−	0.128872i
$303$	11.3029	+	10.1771i	0.649332	+	0.584661i
$304$	−0.0720689	−	0.124827i	−0.00413344	−	0.00715932i
$305$	−3.54311	−	26.7862i	−0.202878	−	1.53377i
$306$	0.0542462	+	0.166953i	0.00310105	+	0.00954404i
$307$	−0.263545	+	0.591932i	−0.0150413	+	0.0337834i	−0.920910	−	0.389775i	$-0.872553\pi$
$307$	−0.263545	+	0.591932i	−0.0150413	+	0.0337834i	0.905869	+	0.423559i	$0.139219\pi$
$308$	−6.60002	+	9.08415i	−0.376071	+	0.517617i
$309$	2.26986			0.129128
$310$	−5.27591	−	11.2767i	−0.299651	−	0.640476i
$311$	18.5407			1.05135			0.525674	−	0.850686i	$-0.323813\pi$
$311$	18.5407			1.05135			0.525674	+	0.850686i	$0.323813\pi$
$312$	−1.94309	+	2.67443i	−0.110006	+	0.151410i
$313$	7.78626	−	17.4882i	0.440106	−	0.988494i	−0.548248	−	0.836316i	$-0.684705\pi$
$313$	7.78626	−	17.4882i	0.440106	−	0.988494i	0.988353	−	0.152177i	$-0.0486285\pi$
$314$	−5.29887	−	16.3082i	−0.299033	−	0.920328i
$315$	−4.31013	+	0.570116i	−0.242848	+	0.0321224i
$316$	−0.435756	−	0.754752i	−0.0245132	−	0.0424581i
$317$	3.76044	+	3.38591i	0.211207	+	0.190172i	0.767944	−	0.640517i	$-0.221280\pi$
$317$	3.76044	+	3.38591i	0.211207	+	0.190172i	−0.556737	+	0.830689i	$0.687947\pi$
$318$	3.68934	+	1.19874i	0.206888	+	0.0672219i
$319$	14.5531	+	16.1629i	0.814818	+	0.904947i
$320$	1.06576	−	1.96575i	0.0595778	−	0.109889i
$321$	1.23714	+	0.262963i	0.0690506	+	0.0146772i
$322$	6.65133	+	0.699083i	0.370664	+	0.0389584i
$323$	−0.0251640	+	0.00264484i	−0.00140016	+	0.000147163i
$324$	0.978148	−	0.207912i	0.0543415	−	0.0115506i
$325$	−15.4238	+	5.94225i	−0.855558	+	0.329617i
$326$	5.95475	−	4.32638i	0.329803	−	0.239616i
$327$	−3.90598	−	18.3762i	−0.216001	−	1.01621i
$328$	11.9083	−	1.25161i	0.657524	−	0.0691085i
$329$	1.29500	−	12.3211i	0.0713955	−	0.679283i
$330$	11.6520	−	5.56647i	0.641423	−	0.306424i
$331$	−1.98110	+	0.882040i	−0.108891	+	0.0484813i	−0.460459	−	0.887681i	$-0.652315\pi$
$331$	−1.98110	+	0.882040i	−0.108891	+	0.0484813i	0.351568	+	0.936162i	$0.385649\pi$
$332$	4.72701	−	4.25622i	0.259429	−	0.233590i
$333$	6.13883	+	1.99463i	0.336406	+	0.109305i
$334$	0.392826	−	0.436278i	0.0214945	−	0.0238721i
$335$	2.82847	−	6.84035i	0.154536	−	0.373728i
$336$	0.972168	−	1.68385i	0.0530361	−	0.0918613i
$337$	−15.0591	+	4.89301i	−0.820323	+	0.266539i	−0.688964	−	0.724796i	$-0.741934\pi$
$337$	−15.0591	+	4.89301i	−0.820323	+	0.266539i	−0.131359	+	0.991335i	$0.541934\pi$
$338$	0.842698	−	1.89273i	0.0458367	−	0.102951i
$339$	−10.3830	−	7.54372i	−0.563930	−	0.409719i
$340$	−0.239147	−	0.311268i	−0.0129695	−	0.0168809i
$341$	21.3219	+	24.0679i	1.15464	+	1.30335i
$342$			0.144138i			0.00779408i
$343$	11.6794	−	16.0754i	0.630631	−	0.867989i
$344$	−9.79019	−	4.35887i	−0.527852	−	0.235015i
$345$	−6.34137	−	4.35261i	−0.341408	−	0.234337i
$346$	8.81302	−	15.2646i	0.473791	−	0.820630i
$347$	−13.4728	+	7.77852i	−0.723257	+	0.417573i	−0.815950	−	0.578122i	$-0.803786\pi$
$347$	−13.4728	+	7.77852i	−0.723257	+	0.417573i	0.0926931	+	0.995695i	$0.470452\pi$
$348$	−2.79875	−	2.52000i	−0.150028	−	0.135086i
$349$	9.34704	−	28.7672i	0.500335	−	1.53987i	−0.308138	−	0.951342i	$-0.599706\pi$
$349$	9.34704	−	28.7672i	0.500335	−	1.53987i	0.808474	−	0.588533i	$-0.200294\pi$
$350$	8.65669	−	4.42412i	0.462719	−	0.236479i
$351$	3.01998	−	1.34458i	0.161194	−	0.0717684i
$352$	−1.20070	+	5.64884i	−0.0639974	+	0.301084i
$353$	2.24328	+	0.235778i	0.119398	+	0.0125492i	0.164039	−	0.986454i	$-0.447548\pi$
$353$	2.24328	+	0.235778i	0.119398	+	0.0125492i	−0.0446412	+	0.999003i	$0.514214\pi$
$354$	1.35053	+	12.8495i	0.0717801	+	0.682942i
$355$	−14.0217	+	16.4376i	−0.744193	+	0.872415i
$356$	6.60330	−	4.79758i	0.349974	−	0.254271i
$357$	−0.200621	−	0.276131i	−0.0106180	−	0.0146144i
$358$	−2.31159	−	10.8752i	−0.122171	−	0.574770i
$359$	1.04923	+	9.98273i	0.0553761	+	0.526868i	0.986686	+	0.162639i	$0.0520007\pi$
$359$	1.04923	+	9.98273i	0.0553761	+	0.526868i	−0.931309	+	0.364229i	$0.881333\pi$
$360$	−1.90585	+	1.16951i	−0.100447	+	0.0616384i
$361$	18.5645	+	3.94600i	0.977078	+	0.207684i
$362$	−3.05746	−	6.86716i	−0.160696	−	0.360930i
$363$	−16.6101	+	14.9558i	−0.871804	+	0.784976i
$364$	1.98622	−	6.11295i	0.104106	−	0.320406i
$365$	−30.1310	−	2.35285i	−1.57713	−	0.123154i
$366$	−6.04175	−	10.4646i	−0.315807	−	0.546994i
$367$	−6.33470	−	3.65734i	−0.330669	−	0.190912i	0.325469	−	0.945553i	$-0.394478\pi$
$367$	−6.33470	−	3.65734i	−0.330669	−	0.190912i	−0.656138	+	0.754641i	$0.727811\pi$
$368$	3.27136	−	1.06293i	0.170532	−	0.0554091i
$369$	−10.9387	−	4.87021i	−0.569444	−	0.253533i
$370$	−14.4281	+	0.386627i	−0.750080	+	0.0200998i
$371$	−7.54247			−0.391585
$372$	−4.10747	−	3.75881i	−0.212963	−	0.194885i
$373$		−	24.7965i		−	1.28391i	−0.766741	−	0.641956i	$-0.778123\pi$
$373$		−	24.7965i		−	1.28391i	0.766741	−	0.641956i	$-0.221877\pi$
$374$	0.820161	+	0.595882i	0.0424095	+	0.0308123i
$375$	−11.1770	−	0.272198i	−0.577179	−	0.0140563i
$376$	−1.96900	−	6.05995i	−0.101543	−	0.312518i
$377$	−10.7819	−	6.22491i	−0.555294	−	0.320599i
$378$	−1.68385	+	0.972168i	−0.0866076	+	0.0500029i
$379$	−6.76918	+	7.51794i	−0.347709	+	0.386171i	−0.891477	−	0.453065i	$-0.850331\pi$
$379$	−6.76918	+	7.51794i	−0.347709	+	0.386171i	0.543768	+	0.839236i	$0.316997\pi$
$380$	−0.107772	−	0.303750i	−0.00552859	−	0.0155820i
$381$	8.70476	+	9.66762i	0.445959	+	0.495287i
$382$	2.82851	+	6.35294i	0.144719	+	0.325045i
$383$	0.359268	−	1.69022i	0.0183577	−	0.0863664i	−0.968015	−	0.250892i	$-0.919276\pi$
$383$	0.359268	−	1.69022i	0.0183577	−	0.0863664i	0.986373	+	0.164526i	$0.0526094\pi$
$384$	0.104528	−	0.994522i	0.00533420	−	0.0507515i
$385$	−18.2021	+	17.2943i	−0.927666	+	0.881399i
$386$	13.3118	−	2.82951i	0.677554	−	0.144018i
$387$	6.29912	+	8.66999i	0.320202	+	0.440720i
$388$	−7.31835	−	10.0728i	−0.371533	−	0.511371i
$389$	−22.5482	+	4.79277i	−1.14324	+	0.243003i	−0.740334	−	0.672239i	$-0.765333\pi$
$389$	−22.5482	+	4.79277i	−1.14324	+	0.243003i	−0.402905	+	0.915242i	$0.631999\pi$
$390$	−5.35882	+	5.09155i	−0.271354	+	0.257820i
$391$	0.0631166	−	0.600514i	0.00319194	−	0.0303693i
$392$	0.669383	−	3.14920i	0.0338089	−	0.159059i
$393$	4.29992	+	9.65778i	0.216902	+	0.487170i
$394$	5.36838	+	5.96219i	0.270455	+	0.300371i
$395$	−0.651631	−	1.83659i	−0.0327871	−	0.0924087i
$396$	3.86426	−	4.29169i	0.194186	−	0.215666i
$397$	29.1497	−	16.8296i	1.46298	−	0.844653i	0.463834	−	0.885922i	$-0.346473\pi$
$397$	29.1497	−	16.8296i	1.46298	−	0.844653i	0.999148	+	0.0412688i	$0.0131400\pi$
$398$	14.1545	+	8.17213i	0.709503	+	0.409632i
$399$	−0.0866028	−	0.266536i	−0.00433556	−	0.0133435i
$400$	3.14186	−	3.88957i	0.157093	−	0.194478i
$401$	−22.2440	−	16.1612i	−1.11081	−	0.807054i	−0.128023	−	0.991771i	$-0.540863\pi$
$401$	−22.2440	−	16.1612i	−1.11081	−	0.807054i	−0.982792	+	0.184717i	$0.940863\pi$
$402$		−	3.31031i		−	0.165103i
$403$	−15.8651	−	9.33114i	−0.790299	−	0.464817i
$404$	−15.2095			−0.756701
$405$	2.23527	−	0.0598980i	0.111071	−	0.00297636i
$406$	6.68947	+	2.97834i	0.331993	+	0.147813i
$407$	35.4520	−	11.5191i	1.75729	−	0.570978i
$408$	−0.152026	−	0.0877721i	−0.00752640	−	0.00434537i
$409$	10.0610	+	17.4262i	0.497485	+	0.861669i	0.999996	−	0.00290176i	$-0.000923660\pi$
$409$	10.0610	+	17.4262i	0.497485	+	0.861669i	−0.502511	+	0.864571i	$0.667590\pi$
$410$	26.6931	+	2.08440i	1.31828	+	0.102941i
$411$	4.56756	−	14.0575i	0.225301	−	0.693406i
$412$	−1.68683	+	1.51883i	−0.0831043	+	0.0748275i
$413$	−10.2178	−	22.9495i	−0.502783	−	1.12927i
$414$	−3.36455	−	0.715157i	−0.165359	−	0.0351481i
$415$	12.1228	−	7.43902i	0.595083	−	0.365167i
$416$	−0.345548	−	3.28767i	−0.0169419	−	0.161191i
$417$	−0.0911308	−	0.428737i	−0.00446270	−	0.0209953i
$418$	0.489274	+	0.673427i	0.0239312	+	0.0329384i
$419$	16.5918	−	12.0546i	0.810562	−	0.588908i	−0.103431	−	0.994637i	$-0.532982\pi$
$419$	16.5918	−	12.0546i	0.810562	−	0.588908i	0.913994	+	0.405729i	$0.132982\pi$
$420$	2.82157	−	3.30772i	0.137678	−	0.161400i
$421$	−2.20130	−	20.9439i	−0.107285	−	1.02075i	−0.907219	−	0.420658i	$-0.861799\pi$
$421$	−2.20130	−	20.9439i	−0.107285	−	1.02075i	0.799935	−	0.600087i	$-0.204867\pi$
$422$	−21.6243	−	2.27281i	−1.05266	−	0.110639i
$423$	−1.32477	+	6.23257i	−0.0644127	+	0.303038i
$424$	−3.54382	+	1.57781i	−0.172103	+	0.0766253i
$425$	−0.399432	−	0.781568i	−0.0193753	−	0.0379116i
$426$	−2.98582	+	9.18940i	−0.144663	+	0.445228i
$427$	17.4597	+	15.7208i	0.844936	+	0.760784i
$428$	−1.09533	+	0.632391i	−0.0529449	+	0.0305678i
$429$	9.54549	−	16.5333i	0.460861	−	0.798234i
$430$	−19.7570	−	13.5609i	−0.952769	−	0.653964i
$431$	21.5123	+	9.57788i	1.03621	+	0.461350i	0.853103	−	0.521743i	$-0.174718\pi$
$431$	21.5123	+	9.57788i	1.03621	+	0.461350i	0.183107	+	0.983093i	$0.441385\pi$
$432$	−0.587785	+	0.809017i	−0.0282798	+	0.0389238i
$433$			23.7804i			1.14281i	0.820668	+	0.571406i	$0.193602\pi$
$433$			23.7804i			1.14281i	−0.820668	+	0.571406i	$0.806398\pi$
$434$	9.85385	+	4.48279i	0.473000	+	0.215181i
$435$	−5.13059	−	6.67787i	−0.245993	−	0.320179i
$436$	15.1988	+	11.0426i	0.727890	+	0.528843i
$437$	0.201657	−	0.452930i	0.00964658	−	0.0216666i
$438$	−12.8545	+	4.17667i	−0.614211	+	0.199569i
$439$	−0.984088	+	1.70449i	−0.0469680	+	0.0813509i	−0.888554	−	0.458773i	$-0.848289\pi$
$439$	−0.984088	+	1.70449i	−0.0469680	+	0.0813509i	0.841586	+	0.540124i	$0.181623\pi$
$440$	−4.93445	+	11.9334i	−0.235241	+	0.568904i
$441$	−2.15430	+	2.39260i	−0.102586	+	0.113933i
$442$	−0.551907	−	0.179326i	−0.0262516	−	0.00852965i
$443$	−11.1308	+	10.0222i	−0.528839	+	0.476169i	−0.889761	−	0.456427i	$-0.849129\pi$
$443$	−11.1308	+	10.0222i	−0.528839	+	0.476169i	0.360922	+	0.932596i	$0.382462\pi$
$444$	−5.89671	+	2.62538i	−0.279845	+	0.124595i
$445$	16.4684	−	7.86735i	0.780675	−	0.372948i
$446$	1.43681	−	13.6703i	0.0680350	−	0.647309i
$447$	6.51840	−	0.685112i	0.308310	−	0.0324047i
$448$	0.404250	+	1.90185i	0.0190990	+	0.0898539i
$449$	−15.1555	+	11.0111i	−0.715231	+	0.519646i	−0.884857	−	0.465863i	$-0.845744\pi$
$449$	−15.1555	+	11.0111i	−0.715231	+	0.519646i	0.169626	+	0.985509i	$0.445744\pi$
$450$	−4.66571	+	1.79754i	−0.219944	+	0.0847367i
$451$	−67.6384	+	14.3770i	−3.18497	+	0.676986i
$452$	12.7638	−	1.34153i	0.600361	−	0.0631005i
$453$	−7.20764	−	0.757554i	−0.338645	−	0.0355930i
$454$	−23.9665	−	5.09425i	−1.12481	−	0.239085i
$455$	6.85021	−	12.6349i	0.321143	−	0.592334i
$456$	−0.0964471	−	0.107115i	−0.00451655	−	0.00501613i
$457$	−21.7190	−	7.05695i	−1.01597	−	0.330110i	−0.246743	−	0.969081i	$-0.579360\pi$
$457$	−21.7190	−	7.05695i	−1.01597	−	0.330110i	−0.769231	+	0.638971i	$0.779360\pi$
$458$	−15.1983	−	13.6846i	−0.710168	−	0.639438i
$459$	0.0877721	+	0.152026i	0.00409685	+	0.00709596i
$460$	7.62502	−	1.00859i	0.355518	−	0.0470257i
$461$	7.32911	+	22.5567i	0.341351	+	1.05057i	0.963508	+	0.267678i	$0.0862563\pi$
$461$	7.32911	+	22.5567i	0.341351	+	1.05057i	−0.622158	+	0.782892i	$0.713744\pi$
$462$	−4.56709	+	10.2579i	−0.212480	+	0.477239i
$463$	10.4931	−	14.4424i	0.487653	−	0.671197i	−0.492300	−	0.870426i	$-0.663844\pi$
$463$	10.4931	−	14.4424i	0.487653	−	0.671197i	0.979953	+	0.199228i	$0.0638436\pi$
$464$	3.76608			0.174836
$465$	−7.50518	−	9.93339i	−0.348044	−	0.460650i
$466$	−14.1002			−0.653180
$467$	−0.342044	+	0.470783i	−0.0158279	+	0.0217852i	−0.816858	−	0.576839i	$-0.804286\pi$
$467$	−0.342044	+	0.470783i	−0.0158279	+	0.0217852i	0.801030	+	0.598625i	$0.204286\pi$
$468$	−1.34458	+	3.01998i	−0.0621532	+	0.139598i
$469$	1.98894	+	6.12133i	0.0918408	+	0.282657i
$470$	−1.86833	−	14.1248i	−0.0861799	−	0.651527i
$471$	−8.57375	−	14.8502i	−0.395058	−	0.684260i
$472$	−9.60162	−	8.64534i	−0.441950	−	0.397934i
$473$	58.8603	+	19.1249i	2.70640	+	0.879362i
$474$	−0.583156	−	0.647660i	−0.0267852	−	0.0297480i
$475$	−0.113610	−	0.711678i	−0.00521277	−	0.0326540i
$476$	0.333859	+	0.0709638i	0.0153024	+	0.00325262i
$477$	3.85795	+	0.405487i	0.176643	+	0.0185660i
$478$	−7.27368	+	0.764495i	−0.332690	+	0.0349672i
$479$	13.6379	−	2.89882i	0.623130	−	0.132450i	0.114482	−	0.993425i	$-0.463479\pi$
$479$	13.6379	−	2.89882i	0.623130	−	0.132450i	0.508647	+	0.860975i	$0.330146\pi$
$480$	0.633769	−	2.14437i	0.0289275	−	0.0978768i
$481$	−17.2628	+	12.5421i	−0.787115	+	0.571872i
$482$	3.12442	+	14.6993i	0.142314	+	0.669533i
$483$	6.65133	−	0.699083i	0.302646	−	0.0318094i
$484$	2.33632	−	22.2286i	0.106197	−	1.01039i
$485$	−12.0010	−	25.1212i	−0.544939	−	1.14070i
$486$	0.913545	−	0.406737i	0.0414393	−	0.0184499i
$487$	19.6211	−	17.6669i	0.889115	−	0.800563i	−0.0916428	−	0.995792i	$-0.529212\pi$
$487$	19.6211	−	17.6669i	0.889115	−	0.800563i	0.980758	+	0.195229i	$0.0625451\pi$
$488$	11.4921	+	3.73401i	0.520223	+	0.169031i
$489$	4.92512	−	5.46990i	0.222721	−	0.247357i
$490$	2.75093	−	6.65282i	0.124274	−	0.300544i
$491$	9.08073	−	15.7283i	0.409808	−	0.709808i	−0.585060	−	0.810990i	$-0.698929\pi$
$491$	9.08073	−	15.7283i	0.409808	−	0.709808i	0.994868	+	0.101182i	$0.0322624\pi$
$492$	11.3878	−	3.70012i	0.513402	−	0.166815i
$493$	0.268899	−	0.603958i	0.0121106	−	0.0272009i
$494$	−0.385486	−	0.280072i	−0.0173439	−	0.0126010i
$495$	10.2401	−	7.86742i	0.460257	−	0.353614i
$496$	5.56758	+	0.0449032i	0.249992	+	0.00201621i
$497$		−	18.7868i		−	0.842702i
$498$	3.73880	−	5.14601i	0.167540	−	0.230598i
$499$	−14.4273	−	6.42344i	−0.645853	−	0.287552i	0.0575507	−	0.998343i	$-0.481671\pi$
$499$	−14.4273	−	6.42344i	−0.645853	−	0.287552i	−0.703404	+	0.710790i	$0.748338\pi$
$500$	8.48829	−	7.27661i	0.379608	−	0.325420i
$501$	0.293535	−	0.508417i	0.0131142	−	0.0227144i
$502$	−1.58790	+	0.916777i	−0.0708716	+	0.0409178i
$503$	12.1269	+	10.9191i	0.540713	+	0.486861i	0.893636	−	0.448792i	$-0.148146\pi$
$503$	12.1269	+	10.9191i	0.540713	+	0.486861i	−0.352923	+	0.935652i	$0.614812\pi$
$504$	0.600833	−	1.84917i	0.0267632	−	0.0823688i
$505$	−33.4438	−	6.17732i	−1.48823	−	0.274887i
$506$	−18.1471	+	8.07962i	−0.806738	+	0.359183i
$507$	0.430762	−	2.02658i	0.0191308	−	0.0900034i
$508$	−12.9378	−	1.35982i	−0.574022	−	0.0603321i
$509$	0.739161	+	7.03265i	0.0327627	+	0.311717i	0.998615	+	0.0526215i	$0.0167577\pi$
$509$	0.739161	+	7.03265i	0.0327627	+	0.311717i	−0.965852	+	0.259095i	$0.916576\pi$
$510$	−0.298637	−	0.254745i	−0.0132239	−	0.0112803i
$511$	21.2607	−	15.4468i	0.940517	−	0.683326i
$512$	0.587785	+	0.809017i	0.0259767	+	0.0357538i
$513$	0.0299679	+	0.140988i	0.00132312	+	0.00622478i
$514$	2.53974	+	24.1640i	0.112023	+	1.06583i
$515$	−4.32600	+	2.65461i	−0.190627	+	0.116976i
$516$	−10.4825	−	2.22813i	−0.461467	−	0.0980878i
$517$	14.9669	+	33.6162i	0.658243	+	1.47844i
$518$	9.32662	−	8.39773i	0.409788	−	0.368975i
$519$	5.44675	−	16.7634i	0.239086	−	0.735830i
$520$	0.575466	−	7.36950i	0.0252359	−	0.323174i
$521$	−12.0303	−	20.8371i	−0.527056	−	0.912888i	−0.999503	−	0.0315289i	$-0.989962\pi$
$521$	−12.0303	−	20.8371i	−0.527056	−	0.912888i	0.472447	−	0.881359i	$-0.343371\pi$
$522$	−3.26152	−	1.88304i	−0.142753	−	0.0824185i
$523$	0.709332	−	0.230476i	0.0310169	−	0.0100780i	−0.293467	−	0.955969i	$-0.594809\pi$
$523$	0.709332	−	0.230476i	0.0310169	−	0.0100780i	0.324484	+	0.945891i	$0.394809\pi$
$524$	−9.65778	−	4.29992i	−0.421902	−	0.187843i
$525$	7.54769	−	6.12727i	0.329408	−	0.267416i
$526$	−21.3335			−0.930185
$527$	0.404728	−	0.889654i	0.0176302	−	0.0387539i
$528$			5.77504i			0.251326i
$529$	−9.03539	−	6.56460i	−0.392843	−	0.285417i
$530$	−8.43324	+	2.03009i	−0.366317	+	0.0881814i
$531$	3.99258	+	12.2879i	0.173263	+	0.533249i
$532$	0.242706	+	0.140126i	0.0105226	+	0.00607524i
$533$	34.2798	−	19.7914i	1.48482	−	0.857262i
$534$	5.46153	−	6.06565i	0.236344	−	0.262486i
$535$	−2.66534	+	0.945679i	−0.115233	+	0.0408853i
$536$	2.21503	+	2.46004i	0.0956746	+	0.106257i
$537$	−4.52215	−	10.1569i	−0.195145	−	0.438303i
$538$	1.45503	−	6.84537i	0.0627307	−	0.295125i
$539$	−1.94350	+	18.4912i	−0.0837126	+	0.796472i
$540$	−1.62105	+	1.54020i	−0.0697587	+	0.0662795i
$541$	30.7246	−	6.53071i	1.32095	−	0.280777i	0.507119	−	0.861876i	$-0.330710\pi$
$541$	30.7246	−	6.53071i	1.32095	−	0.280777i	0.813833	+	0.581099i	$0.197377\pi$
$542$	−7.01628	−	9.65709i	−0.301375	−	0.414807i
$543$	−4.41841	−	6.08141i	−0.189612	−	0.260978i
$544$	0.171708	−	0.0364977i	0.00736193	−	0.00156483i
$545$	28.9353	+	30.4542i	1.23945	+	1.30451i
$546$	0.671861	−	6.39233i	0.0287530	−	0.273566i
$547$	−0.858769	+	4.04019i	−0.0367183	+	0.172746i	−0.992686	−	0.120726i	$-0.961478\pi$
$547$	−0.858769	+	4.04019i	−0.0367183	+	0.172746i	0.955967	+	0.293473i	$0.0948109\pi$
$548$	6.01195	+	13.5031i	0.256818	+	0.576822i
$549$	−8.08544	−	8.97979i	−0.345078	−	0.383248i
$550$	−15.6970	+	24.2360i	−0.669322	+	1.03342i
$551$	0.363228	−	0.403405i	0.0154740	−	0.0171856i
$552$	2.97888	−	1.71986i	0.126790	−	0.0732020i
$553$	1.46749	+	0.847257i	0.0624041	+	0.0360290i
$554$	0.927427	+	2.85433i	0.0394026	+	0.121269i
$555$	−14.0324	+	3.37795i	−0.595643	+	0.143386i
$556$	0.354604	+	0.257635i	0.0150386	+	0.0109262i
$557$		−	40.2089i		−	1.70370i	−0.523782	−	0.851852i	$-0.675479\pi$
$557$		−	40.2089i		−	1.70370i	0.523782	−	0.851852i	$-0.324521\pi$
$558$	−4.79922	−	2.82268i	−0.203167	−	0.119494i
$559$	−35.4270			−1.49840
$560$	0.116462	+	4.34611i	0.00492141	+	0.183657i
$561$	0.926130	+	0.412339i	0.0391012	+	0.0174090i
$562$	−11.8913	+	3.86370i	−0.501602	+	0.162980i
$563$	27.8312	+	16.0683i	1.17294	+	0.677200i	0.954372	−	0.298621i	$-0.0965267\pi$
$563$	27.8312	+	16.0683i	1.17294	+	0.677200i	0.218572	+	0.975821i	$0.429860\pi$
$564$	−3.18591	−	5.51815i	−0.134151	−	0.232356i
$565$	28.6109	+	2.23416i	1.20367	+	0.0939917i
$566$	−4.77644	+	14.7004i	−0.200769	+	0.617903i
$567$	−1.44492	+	1.30102i	−0.0606811	+	0.0546375i
$568$	−3.93001	−	8.82695i	−0.164900	−	0.370371i
$569$	12.2656	+	2.60714i	0.514201	+	0.109297i	0.457702	−	0.889106i	$-0.348673\pi$
$569$	12.2656	+	2.60714i	0.514201	+	0.109297i	0.0564995	+	0.998403i	$0.482006\pi$
$570$	−0.168570	−	0.274705i	−0.00706062	−	0.0115061i
$571$	−3.85647	−	36.6919i	−0.161388	−	1.53551i	−0.712856	−	0.701310i	$-0.752599\pi$
$571$	−3.85647	−	36.6919i	−0.161388	−	1.53551i	0.551468	−	0.834196i	$-0.314068\pi$
$572$	3.96924	+	18.6738i	0.165962	+	0.780791i
$573$	4.08755	+	5.62603i	0.170760	+	0.235031i
$574$	−18.8349	+	13.6844i	−0.786153	+	0.571174i
$575$	17.1761	+	0.879134i	0.716293	+	0.0366624i
$576$	−0.104528	−	0.994522i	−0.00435535	−	0.0414384i
$577$	−38.6529	−	4.06259i	−1.60914	−	0.169128i	−0.743129	−	0.669148i	$-0.766659\pi$
$577$	−38.6529	−	4.06259i	−1.60914	−	0.169128i	−0.866014	+	0.500020i	$0.833326\pi$
$578$	−3.52809	+	16.5984i	−0.146749	+	0.690401i
$579$	12.4326	−	5.53536i	0.516683	−	0.230042i
$580$	8.28114	+	1.52959i	0.343856	+	0.0635128i
$581$	−3.82179	+	11.7623i	−0.158555	+	0.487981i
$582$	−9.25268	−	8.33115i	−0.383536	−	0.345337i
$583$	19.4012	−	11.2013i	0.803514	−	0.463909i
$584$	6.75800	−	11.7052i	0.279648	−	0.484364i
$585$	−4.18312	+	6.09444i	−0.172951	+	0.251974i
$586$	11.4852	+	5.11355i	0.474450	+	0.211239i
$587$	13.0913	−	18.0187i	0.540337	−	0.743711i	−0.448324	−	0.893871i	$-0.647979\pi$
$587$	13.0913	−	18.0187i	0.540337	−	0.743711i	0.988662	+	0.150160i	$0.0479790\pi$
$588$		−	3.21955i		−	0.132772i
$589$	0.541787	−	0.592043i	0.0223239	−	0.0243947i
$590$	−17.6015	−	22.9097i	−0.724640	−	0.943177i
$591$	6.49068	+	4.71575i	0.266991	+	0.193980i
$592$	2.62538	−	5.89671i	0.107903	−	0.242353i
$593$	−19.1266	+	6.21462i	−0.785437	+	0.255204i	−0.674160	−	0.738586i	$-0.735494\pi$
$593$	−19.1266	+	6.21462i	−0.785437	+	0.255204i	−0.111277	+	0.993789i	$0.535494\pi$
$594$	2.88752	−	5.00133i	0.118476	−	0.205207i
$595$	0.705291	+	0.291637i	0.0289141	+	0.0119559i
$596$	−4.38569	+	4.87080i	−0.179645	+	0.199516i
$597$	15.5443	+	5.05065i	0.636186	+	0.206709i
$598$	8.45024	−	7.60863i	0.345556	−	0.311140i
$599$	−14.6733	+	6.53295i	−0.599533	+	0.266929i	−0.683982	−	0.729499i	$-0.739753\pi$
$599$	−14.6733	+	6.53295i	−0.599533	+	0.266929i	0.0844496	+	0.996428i	$0.473087\pi$
$600$	2.26451	−	4.45780i	0.0924483	−	0.181989i
$601$	−1.80468	+	17.1704i	−0.0736145	+	0.700395i	0.894018	+	0.448031i	$0.147875\pi$
$601$	−1.80468	+	17.1704i	−0.0736145	+	0.700395i	−0.967632	+	0.252364i	$0.918792\pi$
$602$	20.7227	−	2.17805i	0.844595	−	0.0887705i
$603$	−0.688251	−	3.23797i	−0.0280278	−	0.131860i
$604$	5.86323	−	4.25988i	0.238571	−	0.173332i
$605$	14.1654	−	47.9291i	0.575906	−	1.94859i
$606$	−14.8771	+	3.16223i	−0.604342	+	0.128457i
$607$	−25.1110	+	2.63927i	−1.01923	+	0.107125i	−0.599375	−	0.800469i	$-0.704584\pi$
$607$	−25.1110	+	2.63927i	−1.01923	+	0.107125i	−0.419850	+	0.907593i	$0.637917\pi$
$608$	0.143348	+	0.0150665i	0.00581354	+	0.000611028i
$609$	7.16252	+	1.52244i	0.290240	+	0.0616924i
$610$	23.7531	+	12.8781i	0.961735	+	0.521419i
$611$	−14.0944	−	15.6534i	−0.570199	−	0.633270i
$612$	−0.166953	−	0.0542462i	−0.00674866	−	0.00219277i
$613$	10.8172	+	9.73983i	0.436902	+	0.393388i	0.858019	−	0.513618i	$-0.171695\pi$
$613$	10.8172	+	9.73983i	0.436902	+	0.393388i	−0.421117	+	0.907006i	$0.638362\pi$
$614$	−0.323975	−	0.561142i	−0.0130746	−	0.0226458i
$615$	26.5432	−	3.51096i	1.07032	−	0.141576i
$616$	−3.46984	−	10.6791i	−0.139804	−	0.430271i
$617$	0.247973	−	0.556956i	0.00998300	−	0.0224222i	−0.908485	−	0.417917i	$-0.862760\pi$
$617$	0.247973	−	0.556956i	0.00998300	−	0.0224222i	0.918468	+	0.395495i	$0.129427\pi$
$618$	−1.33419	+	1.83635i	−0.0536690	+	0.0738690i
$619$	7.41722			0.298123			0.149062	−	0.988828i	$-0.452375\pi$
$619$	7.41722			0.298123			0.149062	+	0.988828i	$0.452375\pi$
$620$	12.2242	+	2.36000i	0.490935	+	0.0947800i
$621$	−3.43972			−0.138031
$622$	−10.8980	+	14.9998i	−0.436969	+	0.601436i
$623$	−6.45488	+	14.4979i	−0.258609	+	0.580846i
$624$	−1.02154	−	3.14398i	−0.0408944	−	0.125860i
$625$	21.6200	−	12.5528i	0.864802	−	0.502113i
$626$	9.57163	+	16.5785i	0.382559	+	0.662612i
$627$	0.618595	+	0.556986i	0.0247043	+	0.0222439i
$628$	16.3082	+	5.29887i	0.650770	+	0.211448i
$629$	−0.758188	−	0.842053i	−0.0302309	−	0.0335749i
$630$	2.07220	−	3.82207i	0.0825582	−	0.152275i
$631$	−10.5370	−	2.23971i	−0.419472	−	0.0891615i	−0.00666013	−	0.999978i	$-0.502120\pi$
$631$	−10.5370	−	2.23971i	−0.419472	−	0.0891615i	−0.412812	+	0.910816i	$0.635453\pi$
$632$	0.866739	+	0.0910979i	0.0344770	+	0.00362368i
$633$	−21.6243	+	2.27281i	−0.859490	+	0.0903361i
$634$	−4.94959	+	1.05207i	−0.196573	+	0.0417830i
$635$	−27.8963	−	8.24474i	−1.10703	−	0.327182i
$636$	−3.13834	+	2.28014i	−0.124443	+	0.0904132i
$637$	−2.21283	−	10.4105i	−0.0876755	−	0.412481i
$638$	−21.6301	+	2.27342i	−0.856345	+	0.0900055i
$639$	−1.00999	+	9.60937i	−0.0399544	+	0.380141i
$640$	0.963884	+	2.01765i	0.0381009	+	0.0797548i
$641$	−28.8667	+	12.8523i	−1.14016	+	0.507634i	−0.887906	−	0.460026i	$-0.847840\pi$
$641$	−28.8667	+	12.8523i	−1.14016	+	0.507634i	−0.252259	+	0.967660i	$0.581174\pi$
$642$	−0.939916	+	0.846304i	−0.0370955	+	0.0334010i
$643$	−7.83620	−	2.54614i	−0.309030	−	0.100410i	0.150397	−	0.988626i	$-0.451945\pi$
$643$	−7.83620	−	2.54614i	−0.309030	−	0.100410i	−0.459426	+	0.888216i	$0.651945\pi$
$644$	−4.47512	+	4.97013i	−0.176345	+	0.195850i
$645$	−22.1448	−	9.15683i	−0.871949	−	0.360550i
$646$	0.0126513	−	0.0219127i	0.000497758	−	0.000862143i
$647$	7.68834	−	2.49809i	0.302260	−	0.0982102i	−0.153961	−	0.988077i	$-0.549203\pi$
$647$	7.68834	−	2.49809i	0.302260	−	0.0982102i	0.456220	+	0.889867i	$0.349203\pi$
$648$	−0.406737	+	0.913545i	−0.0159781	+	0.0358875i
$649$	60.3648	+	43.8576i	2.36953	+	1.72156i
$650$	4.25849	−	15.9709i	0.167032	−	0.626429i
$651$	10.5705	+	2.33610i	0.414292	+	0.0915588i
$652$			7.36047i			0.288258i
$653$	−18.2913	+	25.1758i	−0.715793	+	0.985204i	0.283860	+	0.958866i	$0.408385\pi$
$653$	−18.2913	+	25.1758i	−0.715793	+	0.985204i	−0.999653	+	0.0263386i	$0.991615\pi$
$654$	17.1625	+	7.64125i	0.671108	+	0.298797i
$655$	−19.4898	−	13.3775i	−0.761530	−	0.522701i
$656$	−5.98693	+	10.3697i	−0.233750	+	0.404867i
$657$	−11.7052	+	6.75800i	−0.456663	+	0.263655i
$658$	9.20678	+	8.28983i	0.358918	+	0.323171i
$659$	8.87429	−	27.3122i	0.345693	−	1.06393i	−0.615519	−	0.788122i	$-0.711053\pi$
$659$	8.87429	−	27.3122i	0.345693	−	1.06393i	0.961212	−	0.275812i	$-0.0889466\pi$
$660$	−2.34553	+	12.6986i	−0.0912994	+	0.494292i
$661$	−16.6539	+	7.41481i	−0.647763	+	0.288403i	−0.704198	−	0.710004i	$-0.748693\pi$
$661$	−16.6539	+	7.41481i	−0.647763	+	0.288403i	0.0564350	+	0.998406i	$0.482027\pi$
$662$	0.450873	−	2.12119i	0.0175237	−	0.0824424i
$663$	−0.577131	−	0.0606589i	−0.0224139	−	0.00235580i
$664$	0.664887	+	6.32598i	0.0258026	+	0.245496i
$665$	0.476767	+	0.406695i	0.0184882	+	0.0157709i
$666$	−5.22200	+	3.79401i	−0.202349	+	0.147015i
$667$	7.61432	+	10.4802i	0.294828	+	0.405795i
$668$	0.122059	+	0.574241i	0.00472259	+	0.0222180i
$669$	−1.43681	−	13.6703i	−0.0555503	−	0.528526i
$670$	3.87142	+	6.30894i	0.149566	+	0.243736i
$671$	−68.2578	−	14.5086i	−2.63506	−	0.560100i
$672$	0.790833	+	1.77624i	0.0305070	+	0.0685199i
$673$	−31.3346	+	28.2138i	−1.20786	+	1.08756i	−0.214008	+	0.976832i	$0.568652\pi$
$673$	−31.3346	+	28.2138i	−1.20786	+	1.08756i	−0.993851	+	0.110729i	$0.964681\pi$
$674$	4.89301	−	15.0591i	0.188472	−	0.580056i
$675$	−4.19002	+	2.72831i	−0.161274	+	0.105013i
$676$	1.03593	+	1.79428i	0.0398433	+	0.0690106i
$677$	13.9210	+	8.03730i	0.535028	+	0.308898i	0.743061	−	0.669223i	$-0.233373\pi$
$677$	13.9210	+	8.03730i	0.535028	+	0.308898i	−0.208034	+	0.978122i	$0.566706\pi$
$678$	12.2060	−	3.96597i	0.468769	−	0.152312i
$679$	22.1155	+	9.84644i	0.848713	+	0.377872i
$680$	0.392388	−	0.0105147i	0.0150474	−	0.000403222i
$681$	−24.5020			−0.938917
$682$	−32.0040	+	3.10301i	−1.22550	+	0.118820i
$683$			9.32698i			0.356887i	0.983950	+	0.178444i	$0.0571062\pi$
$683$			9.32698i			0.356887i	−0.983950	+	0.178444i	$0.942894\pi$
$684$	−0.116610	−	0.0847221i	−0.00445869	−	0.00323943i
$685$	7.73526	+	32.1333i	0.295549	+	1.22775i
$686$	6.14025	+	18.8977i	0.234436	+	0.721519i
$687$	−17.7113	−	10.2256i	−0.675729	−	0.390132i
$688$	9.28093	−	5.35835i	0.353832	−	0.204285i
$689$	−8.58077	+	9.52991i	−0.326901	+	0.363061i
$690$	7.24870	−	2.57188i	0.275953	−	0.0979098i
$691$	−20.7882	−	23.0876i	−0.790820	−	0.878295i	0.204101	−	0.978950i	$-0.434573\pi$
$691$	−20.7882	−	23.0876i	−0.790820	−	0.878295i	−0.994921	+	0.100655i	$0.967906\pi$
$692$	7.16916	+	16.1022i	0.272530	+	0.612113i
$693$	−2.33456	+	10.9832i	−0.0886827	+	0.417219i
$694$	1.62615	−	15.4718i	0.0617279	−	0.587302i
$695$	0.675092	+	0.710529i	0.0256077	+	0.0269519i
$696$	3.68379	−	0.783013i	0.139634	−	0.0296800i
$697$	1.23549	+	1.70051i	0.0467975	+	0.0644113i
$698$	17.7791	+	24.4709i	0.672950	+	0.926236i
$699$	−13.7921	+	2.93160i	−0.521665	+	0.110883i
$700$	−1.50908	+	9.60384i	−0.0570379	+	0.362991i
$701$	0.468628	−	4.45870i	0.0176998	−	0.168403i	−0.982101	−	0.188354i	$-0.939685\pi$
$701$	0.468628	−	4.45870i	0.0176998	−	0.168403i	0.999801	+	0.0199518i	$0.00635128\pi$
$702$	−0.687309	+	3.23354i	−0.0259408	+	0.122042i
$703$	−0.378417	−	0.849939i	−0.0142723	−	0.0320561i
$704$	−3.86426	−	4.29169i	−0.145640	−	0.161749i
$705$	−4.76421	−	13.4277i	−0.179431	−	0.505715i
$706$	−1.50931	+	1.67626i	−0.0568038	+	0.0630870i
$707$	25.6104	−	14.7862i	0.963180	−	0.556092i
$708$	−11.1893	−	6.46013i	−0.420518	−	0.242786i
$709$	1.45667	+	4.48316i	0.0547063	+	0.168369i	0.974676	−	0.223620i	$-0.0717874\pi$
$709$	1.45667	+	4.48316i	0.0547063	+	0.168369i	−0.919970	+	0.391988i	$0.871787\pi$
$710$	−5.05654	−	21.0055i	−0.189769	−	0.788323i
$711$	−0.705069	−	0.512262i	−0.0264421	−	0.0192113i
$712$			8.16213i			0.305889i
$713$	11.1317	+	15.5842i	0.416884	+	0.583633i
$714$	0.341317			0.0127735
$715$	1.14351	+	42.6734i	0.0427649	+	1.59590i
$716$	10.1569	+	4.52215i	0.379581	+	0.169001i
$717$	−6.95579	+	2.26007i	−0.259769	+	0.0844039i
$718$	−8.69292	−	5.01886i	−0.324417	−	0.187302i
$719$	23.7687	+	41.1687i	0.886425	+	1.53533i	0.844072	+	0.536230i	$0.180152\pi$
$719$	23.7687	+	41.1687i	0.886425	+	1.53533i	0.0423528	+	0.999103i	$0.486515\pi$
$720$	0.174079	−	2.22928i	0.00648754	−	0.0830804i
$721$	1.36381	−	4.19736i	0.0507908	−	0.156318i
$722$	−14.1043	+	12.6996i	−0.524908	+	0.472629i
$723$	6.11230	+	13.7284i	0.227319	+	0.510566i
$724$	7.35278	+	1.56288i	0.273264	+	0.0580840i
$725$	17.5879	+	6.72675i	0.653199	+	0.249825i
$726$	−2.33632	−	22.2286i	−0.0867091	−	0.824982i
$727$	−7.81567	−	36.7699i	−0.289867	−	1.36372i	−0.846247	−	0.532790i	$-0.821143\pi$
$727$	−7.81567	−	36.7699i	−0.289867	−	1.36372i	0.556380	−	0.830928i	$-0.312190\pi$
$728$	3.77801	+	5.19999i	0.140022	+	0.192724i
$729$	0.809017	−	0.587785i	0.0299636	−	0.0217698i
$730$	19.6140	−	22.9935i	0.725948	−	0.851027i
$731$	−0.196645	−	1.87095i	−0.00727317	−	0.0691996i
$732$	12.0173	+	1.26307i	0.444172	+	0.0466844i
$733$	8.58415	−	40.3853i	0.317063	−	1.49166i	−0.474325	−	0.880350i	$-0.657308\pi$
$733$	8.58415	−	40.3853i	0.317063	−	1.49166i	0.791388	−	0.611314i	$-0.209359\pi$
$734$	6.68230	−	2.97515i	0.246648	−	0.109815i
$735$	1.30762	−	7.07939i	0.0482322	−	0.261127i
$736$	−1.06293	+	3.27136i	−0.0391801	+	0.120584i
$737$	−14.2068	−	12.7919i	−0.523314	−	0.471194i
$738$	10.3697	−	5.98693i	0.381713	−	0.220382i
$739$	18.4191	−	31.9027i	0.677556	−	1.17356i	−0.298159	−	0.954516i	$-0.596373\pi$
$739$	18.4191	−	31.9027i	0.677556	−	1.17356i	0.975715	−	0.219045i	$-0.0702941\pi$
$740$	8.16783	−	11.8998i	0.300255	−	0.437446i
$741$	−0.435293	−	0.193805i	−0.0159909	−	0.00711960i
$742$	4.43335	−	6.10198i	0.162753	−	0.224011i
$743$		−	33.6073i		−	1.23293i	−0.787381	−	0.616466i	$-0.788564\pi$
$743$		−	33.6073i		−	1.23293i	0.787381	−	0.616466i	$-0.211436\pi$
$744$	5.45525	−	1.11364i	0.199999	−	0.0408282i
$745$	−11.6218	+	8.92903i	−0.425791	+	0.327134i
$746$	20.0608	+	14.5750i	0.734477	+	0.533628i
$747$	2.58718	−	5.81090i	0.0946599	−	0.212610i
$748$	−0.964157	+	0.313274i	−0.0352531	+	0.0114544i
$749$	1.22958	−	2.12970i	0.0449279	−	0.0778174i
$750$	6.78990	−	8.88241i	0.247932	−	0.324340i
$751$	9.92756	−	11.0257i	0.362262	−	0.402332i	−0.534269	−	0.845315i	$-0.679413\pi$
$751$	9.92756	−	11.0257i	0.362262	−	0.402332i	0.896530	+	0.442982i	$0.146080\pi$
$752$	6.05995	+	1.96900i	0.220984	+	0.0718020i
$753$	−1.36260	+	1.22689i	−0.0496558	+	0.0447103i
$754$	11.3735	−	5.06380i	0.414198	−	0.184413i
$755$	14.6226	−	6.98560i	0.532172	−	0.254232i
$756$	0.203239	−	1.93369i	0.00739171	−	0.0703275i
$757$	10.4354	−	1.09681i	0.379283	−	0.0398642i	0.0870309	−	0.996206i	$-0.472262\pi$
$757$	10.4354	−	1.09681i	0.379283	−	0.0398642i	0.292252	+	0.956341i	$0.405595\pi$
$758$	−2.10331	−	9.89532i	−0.0763958	−	0.359414i
$759$	−16.0707	+	11.6761i	−0.583330	+	0.423814i
$760$	0.309085	+	0.0913501i	0.0112117	+	0.00331362i
$761$	−16.6468	+	3.53839i	−0.603446	+	0.128267i	−0.499496	−	0.866316i	$-0.666482\pi$
$761$	−16.6468	+	3.53839i	−0.603446	+	0.128267i	−0.103950	+	0.994583i	$0.533148\pi$
$762$	−12.9378	+	1.35982i	−0.468687	+	0.0492610i
$763$	−36.3276	−	3.81819i	−1.31515	−	0.138228i
$764$	−6.80219	−	1.44585i	−0.246095	−	0.0523090i
$765$	−0.345075	−	0.187088i	−0.0124762	−	0.00676418i
$766$	1.15625	+	1.28414i	0.0417769	+	0.0463979i
$767$	−40.6210	−	13.1986i	−1.46674	−	0.476573i
$768$	0.743145	+	0.669131i	0.0268159	+	0.0241452i
$769$	−5.78942	−	10.0276i	−0.208772	−	0.361604i	0.742556	−	0.669784i	$-0.233613\pi$
$769$	−5.78942	−	10.0276i	−0.208772	−	0.361604i	−0.951328	+	0.308180i	$0.900280\pi$
$770$	−3.29244	−	24.8912i	−0.118651	−	0.897015i
$771$	7.50821	+	23.1079i	0.270402	+	0.832210i
$772$	−5.53536	+	12.4326i	−0.199222	+	0.447460i
$773$	−11.9608	+	16.4627i	−0.430201	+	0.592121i	−0.967999	−	0.250953i	$-0.919256\pi$
$773$	−11.9608	+	16.4627i	−0.430201	+	0.592121i	0.537798	+	0.843073i	$0.319256\pi$
$774$	−10.7167			−0.385204
$775$	25.9209	+	10.1542i	0.931106	+	0.364749i
$776$	12.4507			0.446955
$777$	7.37683	−	10.1533i	0.264642	−	0.364249i
$778$	9.37607	−	21.0590i	0.336148	−	0.755001i
$779$	0.533328	+	1.64142i	0.0191085	+	0.0588098i
$780$	−0.969315	−	7.32811i	−0.0347071	−	0.262388i
$781$	27.9001	+	48.3244i	0.998344	+	1.72918i
$782$	0.448727	+	0.404036i	0.0160465	+	0.0144483i
$783$	−3.58176	−	1.16378i	−0.128002	−	0.0415902i
$784$	2.15430	+	2.39260i	0.0769394	+	0.0854498i
$785$	33.7076	+	18.2751i	1.20308	+	0.652267i
$786$	−10.3407	−	2.19799i	−0.368842	−	0.0783997i
$787$	−44.8913	−	4.71826i	−1.60020	−	0.168188i	−0.738016	−	0.674783i	$-0.764237\pi$
$787$	−44.8913	−	4.71826i	−1.60020	−	0.168188i	−0.862184	+	0.506595i	$0.830904\pi$
$788$	−7.97897	+	0.838623i	−0.284239	+	0.0298747i
$789$	−20.8673	+	4.43548i	−0.742896	+	0.157907i
$790$	1.86885	+	0.552338i	0.0664907	+	0.0196513i
$791$	−20.1881	+	14.6675i	−0.717808	+	0.521518i
$792$	1.20070	+	5.64884i	0.0426650	+	0.200723i
$793$	39.7265	−	4.17543i	1.41073	−	0.148274i
$794$	−3.51834	+	33.4748i	−0.124861	+	1.18798i
$795$	−7.82688	+	3.73910i	−0.277591	+	0.132612i
$796$	−14.9312	+	6.64781i	−0.529223	+	0.235625i
$797$	−7.10308	+	6.39564i	−0.251604	+	0.226545i	−0.785275	−	0.619147i	$-0.787479\pi$
$797$	−7.10308	+	6.39564i	−0.251604	+	0.226545i	0.533671	+	0.845692i	$0.320812\pi$
$798$	0.266536	+	0.0866028i	0.00943527	+	0.00306571i
$799$	0.748446	−	0.831234i	0.0264781	−	0.0294069i
$800$	1.29999	+	4.82805i	0.0459616	+	0.170697i
$801$	4.08107	−	7.06861i	0.144197	−	0.249757i
$802$	26.1494	−	8.49647i	0.923369	−	0.300021i
$803$	−31.7480	+	71.3072i	−1.12036	+	2.51638i
$804$	2.67809	+	1.94575i	0.0944491	+	0.0686213i
$805$	−11.8588	+	9.11111i	−0.417969	+	0.321125i
$806$	16.8743	−	7.35045i	0.594373	−	0.258909i
$807$		−	6.99830i		−	0.246352i
$808$	8.93992	−	12.3047i	0.314505	−	0.432879i
$809$	−2.71364	−	1.20819i	−0.0954065	−	0.0424777i	0.358479	−	0.933538i	$-0.383296\pi$
$809$	−2.71364	−	1.20819i	−0.0954065	−	0.0424777i	−0.453885	+	0.891060i	$0.649962\pi$
$810$	−1.26540	+	1.84358i	−0.0444615	+	0.0647766i
$811$	−6.09689	+	10.5601i	−0.214091	+	0.370816i	−0.952991	−	0.302999i	$-0.902012\pi$
$811$	−6.09689	+	10.5601i	−0.214091	+	0.370816i	0.738900	+	0.673815i	$0.235346\pi$
$812$	−6.34150	+	3.66127i	−0.222543	+	0.128485i
$813$	−8.87078	−	7.98729i	−0.311112	−	0.280126i
$814$	−11.5191	+	35.4520i	−0.403743	+	1.24259i
$815$	−2.98945	+	16.1847i	−0.104716	+	0.566927i
$816$	0.160368	−	0.0714003i	0.00561399	−	0.00249951i
$817$	0.321157	−	1.51093i	0.0112359	−	0.0528606i
$818$	−20.0118	−	2.10332i	−0.699696	−	0.0735410i
$819$	−0.671861	−	6.39233i	−0.0234767	−	0.223366i
$820$	−17.3761	+	20.3700i	−0.606800	+	0.711351i
$821$	25.5574	−	18.5685i	0.891959	−	0.648046i	−0.0444290	−	0.999013i	$-0.514147\pi$
$821$	25.5574	−	18.5685i	0.891959	−	0.648046i	0.936388	+	0.350966i	$0.114147\pi$
$822$	8.68802	+	11.9580i	0.303029	+	0.417084i
$823$	6.02995	+	28.3687i	0.210191	+	0.988870i	0.949078	+	0.315041i	$0.102018\pi$
$823$	6.02995	+	28.3687i	0.210191	+	0.988870i	−0.738887	+	0.673829i	$0.764648\pi$
$824$	−0.237265	−	2.25742i	−0.00826551	−	0.0786411i
$825$	−10.3150	+	26.9699i	−0.359123	+	0.938973i
$826$	24.5724	+	5.22302i	0.854982	+	0.181732i
$827$	9.23323	+	20.7382i	0.321071	+	0.721137i	0.999914	−	0.0131466i	$-0.00418483\pi$
$827$	9.23323	+	20.7382i	0.321071	+	0.721137i	−0.678843	+	0.734284i	$0.737518\pi$
$828$	2.55621	−	2.30162i	0.0888343	−	0.0799868i
$829$	−0.723792	+	2.22760i	−0.0251383	+	0.0773678i	−0.962839	−	0.270077i	$-0.912951\pi$
$829$	−0.723792	+	2.22760i	−0.0251383	+	0.0773678i	0.937700	+	0.347445i	$0.112951\pi$
$830$	−1.10729	+	14.1801i	−0.0384344	+	0.492197i
$831$	1.50061	+	2.59913i	0.0520555	+	0.0901628i
$832$	2.86289	+	1.65289i	0.0992527	+	0.0573036i
$833$	0.537513	−	0.174648i	0.0186237	−	0.00605121i
$834$	0.400421	+	0.178279i	0.0138654	+	0.00617329i
$835$	0.0351643	+	1.31226i	0.00121691	+	0.0454125i
$836$	−0.832402			−0.0287892
$837$	−5.28121	−	1.76318i	−0.182545	−	0.0609445i
$838$			20.5086i			0.708458i
$839$	38.9099	+	28.2697i	1.34332	+	0.975979i	0.999315	+	0.0370107i	$0.0117836\pi$
$839$	38.9099	+	28.2697i	1.34332	+	0.975979i	0.344005	+	0.938968i	$0.388216\pi$
$840$	1.01752	+	4.22692i	0.0351079	+	0.145843i
$841$	−4.57859	−	14.0914i	−0.157882	−	0.485912i
$842$	18.2379	+	10.5297i	0.628519	+	0.362876i
$843$	−10.8281	+	6.25160i	−0.372939	+	0.215317i
$844$	14.5492	−	16.1585i	0.500804	−	0.556200i
$845$	1.54913	+	4.36612i	0.0532916	+	0.150199i
$846$	−4.26357	−	4.73518i	−0.146585	−	0.162799i
$847$	17.6760	+	39.7009i	0.607354	+	1.36414i
$848$	0.806531	−	3.79443i	0.0276964	−	0.130301i
$849$	−1.61568	+	15.3722i	−0.0554502	+	0.527573i
$850$	0.867082	+	0.136247i	0.0297407	+	0.00467324i
$851$	21.7173	−	4.61616i	0.744460	−	0.158240i
$852$	−5.67936	−	7.81697i	−0.194572	−	0.267805i
$853$	−12.0482	−	16.5829i	−0.412521	−	0.567786i	0.551310	−	0.834300i	$-0.314128\pi$
$853$	−12.0482	−	16.5829i	−0.412521	−	0.567786i	−0.963831	+	0.266514i	$0.914128\pi$
$854$	−22.9810	+	4.88476i	−0.786393	+	0.167153i
$855$	−0.222001	−	0.233654i	−0.00759227	−	0.00799080i
$856$	0.132206	−	1.25785i	0.00451870	−	0.0429925i
$857$	1.84053	−	8.65902i	0.0628714	−	0.295787i	−0.935467	−	0.353415i	$-0.885020\pi$
$857$	1.84053	−	8.65902i	0.0628714	−	0.295787i	0.998338	+	0.0576282i	$0.0183538\pi$
$858$	7.76500	+	17.4405i	0.265093	+	0.595408i
$859$	−11.4154	−	12.6780i	−0.389487	−	0.432569i	0.516231	−	0.856449i	$-0.327334\pi$
$859$	−11.4154	−	12.6780i	−0.389487	−	0.432569i	−0.905718	+	0.423880i	$0.860668\pi$
$860$	22.5839	−	8.01289i	0.770104	−	0.273237i
$861$	−15.5782	+	17.3013i	−0.530903	+	0.589627i
$862$	−20.3933	+	11.7741i	−0.694597	+	0.401026i
$863$	26.6428	+	15.3822i	0.906931	+	0.523617i	0.879442	−	0.476005i	$-0.157916\pi$
$863$	26.6428	+	15.3822i	0.906931	+	0.523617i	0.0274886	+	0.999622i	$0.491249\pi$
$864$	−0.309017	−	0.951057i	−0.0105130	−	0.0323556i
$865$	9.22418	+	38.3184i	0.313632	+	1.30287i
$866$	−19.2387	−	13.9777i	−0.653758	−	0.474983i
$867$			16.9692i			0.576304i
$868$	−9.41860	+	5.33702i	−0.319688	+	0.181150i
$869$	−5.03302			−0.170734
$870$	8.41820	−	0.225581i	0.285404	−	0.00764791i
$871$	9.99704	+	4.45097i	0.338737	+	0.150815i
$872$	−17.8672	+	5.80542i	−0.605061	+	0.196596i
$873$	−10.7826	−	6.22536i	−0.364937	−	0.210696i
$874$	0.247897	+	0.429370i	0.00838523	+	0.0145236i
$875$	−7.21887	+	20.5047i	−0.244042	+	0.693186i
$876$	4.17667	−	12.8545i	0.141117	−	0.434312i
$877$	−14.7740	+	13.3026i	−0.498883	+	0.449196i	−0.879752	−	0.475433i	$-0.842292\pi$
$877$	−14.7740	+	13.3026i	−0.498883	+	0.449196i	0.380869	+	0.924629i	$0.375625\pi$
$878$	−0.800530	−	1.79802i	−0.0270166	−	0.0606802i
$879$	12.2974	+	2.61389i	0.414781	+	0.0881644i
$880$	−6.75394	−	11.0063i	−0.227675	−	0.371024i
$881$	−0.430942	−	4.10013i	−0.0145188	−	0.138137i	0.984861	−	0.173345i	$-0.0554574\pi$
$881$	−0.430942	−	4.10013i	−0.0145188	−	0.138137i	−0.999380	+	0.0352076i	$0.988791\pi$
$882$	−0.669383	−	3.14920i	−0.0225393	−	0.106039i
$883$	−10.2341	−	14.0861i	−0.344406	−	0.474034i	0.601316	−	0.799011i	$-0.294643\pi$
$883$	−10.2341	−	14.0861i	−0.344406	−	0.474034i	−0.945722	+	0.324977i	$0.894643\pi$
$884$	0.469481	−	0.341098i	0.0157903	−	0.0114724i
$885$	−21.9800	−	18.7495i	−0.738850	−	0.630258i
$886$	−1.56562	−	14.8959i	−0.0525981	−	0.500437i
$887$	−2.84764	−	0.299299i	−0.0956144	−	0.0100495i	0.0566004	−	0.998397i	$-0.481974\pi$
$887$	−2.84764	−	0.299299i	−0.0956144	−	0.0100495i	−0.152215	+	0.988347i	$0.548641\pi$
$888$	1.34202	−	6.31370i	0.0450352	−	0.211874i
$889$	23.1072	−	10.2880i	0.774991	−	0.345048i
$890$	−3.31504	+	17.9475i	−0.111120	+	0.601601i
$891$	1.78459	−	5.49239i	0.0597859	−	0.184002i
$892$	10.2150	+	9.19763i	0.342024	+	0.307959i
$893$	0.795375	−	0.459210i	0.0266162	−	0.0153669i
$894$	−3.27716	+	5.67620i	−0.109604	+	0.189840i
$895$	20.4971	+	14.0688i	0.685142	+	0.470270i
$896$	−1.77624	−	0.790833i	−0.0593400	−	0.0264199i
$897$	6.68366	−	9.19927i	0.223161	−	0.307155i
$898$		−	18.7332i		−	0.625135i
$899$	6.31863	+	19.9940i	0.210738	+	0.666837i
$900$	1.28820	−	4.83121i	0.0429399	−	0.161040i
$901$	−0.550917	−	0.400265i	−0.0183537	−	0.0133347i
$902$	28.1256	−	63.1712i	0.936481	−	2.10337i
$903$	19.8170	−	6.43895i	0.659470	−	0.214275i
$904$	−6.41708	+	11.1147i	−0.213429	+	0.369669i
$905$	15.5331	+	6.42290i	0.516336	+	0.213504i
$906$	4.84942	−	5.38583i	0.161111	−	0.178932i
$907$	−33.8853	−	11.0100i	−1.12514	−	0.365581i	−0.313414	−	0.949617i	$-0.601473\pi$
$907$	−33.8853	−	11.0100i	−1.12514	−	0.365581i	−0.811728	+	0.584036i	$0.801473\pi$
$908$	18.2085	−	16.3950i	0.604271	−	0.544088i
$909$	−13.8946	+	6.18626i	−0.460854	+	0.205185i
$910$	6.19540	+	12.9686i	0.205376	+	0.429903i
$911$	−2.20040	+	20.9354i	−0.0729025	+	0.693621i	0.895641	+	0.444777i	$0.146717\pi$
$911$	−2.20040	+	20.9354i	−0.0729025	+	0.693621i	−0.968544	+	0.248844i	$0.919949\pi$
$912$	0.143348	−	0.0150665i	0.00474674	−	0.000498902i
$913$	−7.63743	−	35.9313i	−0.252762	−	1.18915i
$914$	18.4753	−	13.4231i	0.611109	−	0.443997i
$915$	25.9115	+	7.65815i	0.856609	+	0.253170i
$916$	20.0044	−	4.25206i	0.660963	−	0.140492i
$917$	20.4424	−	2.14859i	0.675069	−	0.0709526i
$918$	−0.174583	−	0.0183494i	−0.00576208	−	0.000605620i
$919$	−23.9122	−	5.08270i	−0.788792	−	0.167663i	−0.204134	−	0.978943i	$-0.565438\pi$
$919$	−23.9122	−	5.08270i	−0.788792	−	0.167663i	−0.584658	+	0.811280i	$0.698771\pi$
$920$	−3.66591	+	6.76161i	−0.120861	+	0.222924i
$921$	−0.433564	−	0.481521i	−0.0142864	−	0.0158667i
$922$	−22.5567	−	7.32911i	−0.742865	−	0.241371i
$923$	−23.7371	−	21.3730i	−0.781316	−	0.703500i
$924$	−5.61431	−	9.72427i	−0.184697	−	0.319905i
$925$	22.7931	−	22.8488i	0.749433	−	0.751265i
$926$	5.51652	+	16.9781i	0.181284	+	0.557935i
$927$	−0.923234	+	2.07362i	−0.0303230	+	0.0681066i
$928$	−2.21365	+	3.04683i	−0.0726666	+	0.100017i
$929$	42.6093			1.39797			0.698983	−	0.715138i	$-0.253636\pi$
$929$	42.6093			1.39797			0.698983	+	0.715138i	$0.253636\pi$
$930$	12.4477	−	0.233116i	0.408177	−	0.00764419i
$931$	0.464060			0.0152089
$932$	8.28790	−	11.4073i	0.271479	−	0.373659i
$933$	−7.54119	+	16.9378i	−0.246888	+	0.554519i
$934$	−0.179823	−	0.553438i	−0.00588399	−	0.0181091i
$935$	−2.24730	+	0.297258i	−0.0734944	+	0.00972137i
$936$	−1.65289	−	2.86289i	−0.0540263	−	0.0935763i
$937$	20.1050	+	18.1026i	0.656801	+	0.591387i	0.928652	−	0.370953i	$-0.120969\pi$
$937$	20.1050	+	18.1026i	0.656801	+	0.591387i	−0.271850	+	0.962340i	$0.587636\pi$
$938$	−6.12133	−	1.98894i	−0.199869	−	0.0649412i
$939$	12.8093	+	14.2262i	0.418017	+	0.464255i
$940$	12.5254	+	6.79082i	0.408532	+	0.221492i
$941$	−52.9092	−	11.2462i	−1.72479	−	0.366616i	−0.764287	−	0.644877i	$-0.776909\pi$
$941$	−52.9092	−	11.2462i	−1.72479	−	0.366616i	−0.960506	+	0.278261i	$0.910242\pi$
$942$	17.0536	+	1.79240i	0.555635	+	0.0583996i
$943$	−40.9610	+	4.30518i	−1.33387	+	0.140196i
$944$	12.6379	−	2.68627i	0.411329	−	0.0874307i
$945$	1.23226	−	4.16938i	0.0400854	−	0.135630i
$946$	−50.0695	+	36.3777i	−1.62790	+	1.18274i
$947$	5.13303	+	24.1490i	0.166801	+	0.784738i	0.979402	+	0.201918i	$0.0647174\pi$
$947$	5.13303	+	24.1490i	0.166801	+	0.784738i	−0.812601	+	0.582820i	$0.801949\pi$
$948$	0.866739	−	0.0910979i	0.0281504	−	0.00295872i
$949$	4.67042	−	44.4361i	0.151608	−	1.44246i
$950$	0.642538	+	0.326402i	0.0208467	+	0.0105899i
$951$	−4.62269	+	2.05816i	−0.149901	+	0.0667403i
$952$	−0.253648	+	0.228386i	−0.00822078	+	0.00740202i
$953$	−23.8048	−	7.73466i	−0.771114	−	0.250550i	−0.103072	−	0.994674i	$-0.532867\pi$
$953$	−23.8048	−	7.73466i	−0.771114	−	0.250550i	−0.668042	+	0.744124i	$0.732867\pi$
$954$	−2.59569	+	2.88281i	−0.0840386	+	0.0933343i
$955$	−14.3699	−	5.94195i	−0.465000	−	0.192277i
$956$	3.65687	−	6.33389i	0.118272	−	0.204853i
$957$	−20.6848	+	6.72090i	−0.668644	+	0.217256i
$958$	−5.67094	+	12.7371i	−0.183220	+	0.411518i
$959$	−23.2504	−	16.8924i	−0.750796	−	0.545485i
$960$	1.36231	+	1.77316i	0.0439685	+	0.0572285i
$961$	9.10275	+	29.6334i	0.293637	+	0.955917i
$962$		−	21.3380i		−	0.687963i
$963$	−0.743420	+	1.02323i	−0.0239564	+	0.0329731i
$964$	−13.7284	−	6.11230i	−0.442163	−	0.196864i
$965$	−17.2211	+	25.0896i	−0.554366	+	0.807663i
$966$	−3.34398	+	5.79195i	−0.107591	+	0.186353i
$967$	−10.9296	+	6.31024i	−0.351474	+	0.202923i	−0.665334	−	0.746546i	$-0.731711\pi$
$967$	−10.9296	+	6.31024i	−0.351474	+	0.202923i	0.313860	+	0.949469i	$0.398378\pi$
$968$	16.6101	+	14.9558i	0.533869	+	0.480697i
$969$	0.00781893	−	0.0240642i	0.000251180	−	0.000773053i
$970$	27.3775	+	5.05684i	0.879040	+	0.162365i
$971$	−1.98998	+	0.885995i	−0.0638614	+	0.0284329i	−0.438419	−	0.898771i	$-0.644461\pi$
$971$	−1.98998	+	0.885995i	−0.0638614	+	0.0284329i	0.374557	+	0.927204i	$0.377795\pi$
$972$	−0.207912	+	0.978148i	−0.00666877	+	0.0313741i
$973$	−0.847563	−	0.0890825i	−0.0271716	−	0.00285585i
$974$	2.75984	+	26.2581i	0.0884309	+	0.841364i
$975$	0.844901	−	16.5073i	0.0270585	−	0.528656i
$976$	−9.77576	+	7.10250i	−0.312914	+	0.227346i
$977$	−30.9891	−	42.6528i	−0.991429	−	1.36458i	−0.930439	−	0.366446i	$-0.880574\pi$
$977$	−30.9891	−	42.6528i	−0.991429	−	1.36458i	−0.0609896	−	0.998138i	$-0.519426\pi$
$978$	1.53033	+	7.19963i	0.0489345	+	0.230219i
$979$	−4.92712	−	46.8784i	−0.157471	−	1.49824i
$980$	3.76529	+	6.13598i	0.120278	+	0.196007i
$981$	18.3762	+	3.90598i	0.586707	+	0.124708i
$982$	7.38693	+	16.5913i	0.235727	+	0.529450i
$983$	33.4828	−	30.1481i	1.06794	−	0.961575i	0.0685875	−	0.997645i	$-0.478151\pi$
$983$	33.4828	−	30.1481i	1.06794	−	0.961575i	0.999349	+	0.0360706i	$0.0114841\pi$
$984$	−3.70012	+	11.3878i	−0.117956	+	0.363030i
$985$	−17.8853	−	1.39662i	−0.569875	−	0.0445001i
$986$	0.330557	+	0.572542i	0.0105271	+	0.0182334i
$987$	10.7291	+	6.19447i	0.341512	+	0.197172i
$988$	0.453166	−	0.147243i	0.0144171	−	0.00468441i
$989$	33.6755	+	14.9933i	1.07082	+	0.476759i
$990$	0.345913	+	12.9087i	0.0109938	+	0.410267i
$991$	41.0607			1.30434			0.652169	−	0.758074i	$-0.273859\pi$
$991$	41.0607			1.30434			0.652169	+	0.758074i	$0.273859\pi$
$992$	−3.30887	+	4.47788i	−0.105057	+	0.142173i
$993$		−	2.16858i		−	0.0688178i
$994$	15.1988	+	11.0426i	0.482077	+	0.350250i
$995$	−35.5319	+	8.55339i	−1.12644	+	0.271161i
$996$	1.96560	+	6.04950i	0.0622825	+	0.191686i
$997$	−9.28338	−	5.35976i	−0.294008	−	0.169745i	0.345740	−	0.938330i	$-0.387628\pi$
$997$	−9.28338	−	5.35976i	−0.294008	−	0.169745i	−0.639748	+	0.768585i	$0.720961\pi$
$998$	13.6768	−	7.89631i	0.432932	−	0.249953i
$999$	−4.31907	+	4.79682i	−0.136649	+	0.151765i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bn.b.19.5	✓	144
5.4	even	2	inner	930.2.bn.b.19.17	yes	144
31.18	even	15	inner	930.2.bn.b.49.17	yes	144
155.49	even	30	inner	930.2.bn.b.49.5	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bn.b.19.5	✓	144	1.1	even	1	trivial
930.2.bn.b.19.17	yes	144	5.4	even	2	inner
930.2.bn.b.49.5	yes	144	155.49	even	30	inner
930.2.bn.b.49.17	yes	144	31.18	even	15	inner

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bn (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.587785 + 0.809017i) q^{2} +(-0.406737 + 0.913545i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-0.293219 - 2.21676i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(1.44492 + 1.30102i) q^{7} +(0.951057 + 0.309017i) q^{8} +(-0.669131 - 0.743145i) q^{9} +O(q^{10})\)	\(q+(-0.587785 + 0.809017i) q^{2} +(-0.406737 + 0.913545i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-0.293219 - 2.21676i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(1.44492 + 1.30102i) q^{7} +(0.951057 + 0.309017i) q^{8} +(-0.669131 - 0.743145i) q^{9} +(1.96575 + 1.06576i) q^{10} +(-5.64884 - 1.20070i) q^{11} +(0.994522 + 0.104528i) q^{12} +(3.28767 - 0.345548i) q^{13} +(-1.90185 + 0.404250i) q^{14} +(2.14437 + 0.633769i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(0.0364977 + 0.171708i) q^{17} +(0.994522 - 0.104528i) q^{18} +(-0.0150665 + 0.143348i) q^{19} +(-2.01765 + 0.963884i) q^{20} +(-1.77624 + 0.790833i) q^{21} +(4.29169 - 3.86426i) q^{22} +(-3.27136 - 1.06293i) q^{23} +(-0.669131 + 0.743145i) q^{24} +(-4.82805 + 1.29999i) q^{25} +(-1.65289 + 2.86289i) q^{26} +(0.951057 - 0.309017i) q^{27} +(0.790833 - 1.77624i) q^{28} +(-3.04683 - 2.21365i) q^{29} +(-1.77316 + 1.36231i) q^{30} +(-4.47788 - 3.30887i) q^{31} -1.00000i q^{32} +(3.39448 - 4.67211i) q^{33} +(-0.160368 - 0.0714003i) q^{34} +(2.46036 - 3.58453i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-5.58998 + 3.22738i) q^{37} +(-0.107115 - 0.0964471i) q^{38} +(-1.02154 + 3.14398i) q^{39} +(0.406149 - 2.19887i) q^{40} +(10.9387 - 4.87021i) q^{41} +(0.404250 - 1.90185i) q^{42} +(-10.6580 - 1.12020i) q^{43} +(0.603656 + 5.74340i) q^{44} +(-1.45117 + 1.70121i) q^{45} +(2.78279 - 2.02181i) q^{46} +(-3.74526 - 5.15490i) q^{47} +(-0.207912 - 0.978148i) q^{48} +(-0.336535 - 3.20192i) q^{49} +(1.78614 - 4.67009i) q^{50} +(-0.171708 - 0.0364977i) q^{51} +(-1.34458 - 3.01998i) q^{52} +(-2.88281 + 2.59569i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(-1.00531 + 12.8742i) q^{55} +(0.972168 + 1.68385i) q^{56} +(-0.124827 - 0.0720689i) q^{57} +(3.58176 - 1.16378i) q^{58} +(-11.8032 - 5.25514i) q^{59} +(-0.0598980 - 2.23527i) q^{60} +12.0835 q^{61} +(5.30896 - 1.67777i) q^{62} -1.94434i q^{63} +(0.809017 + 0.587785i) q^{64} +(-1.73000 - 7.18664i) q^{65} +(1.78459 + 5.49239i) q^{66} +(2.86681 + 1.65515i) q^{67} +(0.152026 - 0.0877721i) q^{68} +(2.30162 - 2.55621i) q^{69} +(1.45378 + 4.09741i) q^{70} +(-6.46534 - 7.18049i) q^{71} +(-0.406737 - 0.913545i) q^{72} +(2.81013 - 13.2206i) q^{73} +(0.674705 - 6.41939i) q^{74} +(0.776142 - 4.93939i) q^{75} +(0.140988 - 0.0299679i) q^{76} +(-6.60002 - 9.08415i) q^{77} +(-1.94309 - 2.67443i) q^{78} +(0.852468 - 0.181198i) q^{79} +(1.54020 + 1.62105i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(-2.48950 + 11.7122i) q^{82} +(2.58718 + 5.81090i) q^{83} +(1.30102 + 1.44492i) q^{84} +(0.369934 - 0.131255i) q^{85} +(7.17087 - 7.96406i) q^{86} +(3.26152 - 1.88304i) q^{87} +(-5.00133 - 2.88752i) q^{88} +(2.52224 + 7.76265i) q^{89} +(-0.523327 - 2.17397i) q^{90} +(5.19999 + 3.77801i) q^{91} +3.43972i q^{92} +(4.84412 - 2.74490i) q^{93} +6.37181 q^{94} +(0.322186 - 0.00863357i) q^{95} +(0.913545 + 0.406737i) q^{96} +(11.8413 - 3.84748i) q^{97} +(2.78822 + 1.60978i) q^{98} +(2.88752 + 5.00133i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 36 q^{4} + 2 q^{5} - 72 q^{6} - 18 q^{9}+O(q^{10}) \) 144 * q + 36 * q^4 + 2 * q^5 - 72 * q^6 - 18 * q^9	\( 144 q + 36 q^{4} + 2 q^{5} - 72 q^{6} - 18 q^{9} - 18 q^{11} - 8 q^{14} - 36 q^{16} - 24 q^{19} - 2 q^{20} + 28 q^{21} - 18 q^{24} + 10 q^{25} - 12 q^{26} - 4 q^{30} - 4 q^{31} + 10 q^{34} - 2 q^{35} - 72 q^{36} + 16 q^{39} + 4 q^{41} - 2 q^{44} - 2 q^{45} - 2 q^{46} - 78 q^{49} + 32 q^{50} + 10 q^{51} + 36 q^{54} - 50 q^{55} - 12 q^{56} + 28 q^{59} + 88 q^{61} + 36 q^{64} - 124 q^{65} + 6 q^{66} - 46 q^{69} - 10 q^{70} + 140 q^{71} + 34 q^{74} - 32 q^{75} + 24 q^{76} + 16 q^{79} + 12 q^{80} + 18 q^{81} - 8 q^{84} + 74 q^{85} - 98 q^{86} + 148 q^{89} + 44 q^{91} - 108 q^{94} - 80 q^{95} + 18 q^{96} - 2 q^{99}+O(q^{100}) \) 144 * q + 36 * q^4 + 2 * q^5 - 72 * q^6 - 18 * q^9 - 18 * q^11 - 8 * q^14 - 36 * q^16 - 24 * q^19 - 2 * q^20 + 28 * q^21 - 18 * q^24 + 10 * q^25 - 12 * q^26 - 4 * q^30 - 4 * q^31 + 10 * q^34 - 2 * q^35 - 72 * q^36 + 16 * q^39 + 4 * q^41 - 2 * q^44 - 2 * q^45 - 2 * q^46 - 78 * q^49 + 32 * q^50 + 10 * q^51 + 36 * q^54 - 50 * q^55 - 12 * q^56 + 28 * q^59 + 88 * q^61 + 36 * q^64 - 124 * q^65 + 6 * q^66 - 46 * q^69 - 10 * q^70 + 140 * q^71 + 34 * q^74 - 32 * q^75 + 24 * q^76 + 16 * q^79 + 12 * q^80 + 18 * q^81 - 8 * q^84 + 74 * q^85 - 98 * q^86 + 148 * q^89 + 44 * q^91 - 108 * q^94 - 80 * q^95 + 18 * q^96 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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