LMFDB - Embedded newform 380.2.bb.a.59.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(59,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 1]))

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

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

chi := DirichletCharacter("380.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.bb (of order $18$, degree $6$, 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:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$56$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			59.16
Character	$\chi$	$=$	380.59
Dual form			380.2.bb.a.219.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.906917 + 1.08513i) q^{2} +(1.82738 - 2.17779i) q^{3} +(-0.355003 - 1.96824i) q^{4} +(1.74742 - 1.39518i) q^{5} +(0.705894 + 3.95801i) q^{6} +(1.71831 + 2.97619i) q^{7} +(2.45775 + 1.39981i) q^{8} +(-0.882491 - 5.00485i) q^{9} +O(q^{10})$	\(q+(-0.906917 + 1.08513i) q^{2} +(1.82738 - 2.17779i) q^{3} +(-0.355003 - 1.96824i) q^{4} +(1.74742 - 1.39518i) q^{5} +(0.705894 + 3.95801i) q^{6} +(1.71831 + 2.97619i) q^{7} +(2.45775 + 1.39981i) q^{8} +(-0.882491 - 5.00485i) q^{9} +(-0.0708181 + 3.16148i) q^{10} +(4.04311 + 2.33429i) q^{11} +(-4.93513 - 2.82360i) q^{12} +(-3.55608 + 2.98391i) q^{13} +(-4.78791 - 0.834579i) q^{14} +(0.154799 - 6.35503i) q^{15} +(-3.74795 + 1.39746i) q^{16} +(-0.850042 - 0.149885i) q^{17} +(6.23125 + 3.58137i) q^{18} +(3.58397 - 2.48096i) q^{19} +(-3.36639 - 2.94405i) q^{20} +(9.62150 + 1.69653i) q^{21} +(-6.19976 + 2.27028i) q^{22} +(-4.09159 - 1.48922i) q^{23} +(7.53972 - 2.79448i) q^{24} +(1.10695 - 4.87593i) q^{25} +(-0.0128485 - 6.56496i) q^{26} +(-5.12608 - 2.95954i) q^{27} +(5.24786 - 4.43860i) q^{28} +(-6.10835 + 1.07707i) q^{29} +(6.75562 + 5.93146i) q^{30} +(-4.32882 - 7.49774i) q^{31} +(1.88265 - 5.33438i) q^{32} +(12.4719 - 4.53939i) q^{33} +(0.933562 - 0.786471i) q^{34} +(7.15492 + 2.80332i) q^{35} +(-9.53747 + 3.51369i) q^{36} -3.71390 q^{37} +(-0.558206 + 6.13909i) q^{38} +13.1971i q^{39} +(6.24770 - 0.982950i) q^{40} +(-6.52905 + 7.78102i) q^{41} +(-10.5669 + 8.90195i) q^{42} +(0.131946 - 0.0480244i) q^{43} +(3.15913 - 8.78649i) q^{44} +(-8.52475 - 7.51435i) q^{45} +(5.32672 - 3.08930i) q^{46} +(0.640662 + 3.63338i) q^{47} +(-3.80554 + 10.7159i) q^{48} +(-2.40515 + 4.16584i) q^{49} +(4.28709 + 5.62325i) q^{50} +(-1.87977 + 1.57731i) q^{51} +(7.13547 + 5.93993i) q^{52} +(-0.917952 - 0.334107i) q^{53} +(7.86041 - 2.87839i) q^{54} +(10.3218 - 1.56187i) q^{55} +(0.0570708 + 9.72004i) q^{56} +(1.14627 - 12.3388i) q^{57} +(4.37101 - 7.60514i) q^{58} +(-1.50948 + 8.56070i) q^{59} +(-12.5632 + 1.95137i) q^{60} +(-4.15281 - 1.51150i) q^{61} +(12.0619 + 2.10250i) q^{62} +(13.3790 - 11.2263i) q^{63} +(4.08108 + 6.88076i) q^{64} +(-2.05089 + 10.1755i) q^{65} +(-6.38513 + 17.6504i) q^{66} +(2.42352 - 0.427332i) q^{67} +(0.00675722 + 1.72630i) q^{68} +(-10.7201 + 6.18924i) q^{69} +(-9.53087 + 5.22163i) q^{70} +(-2.04891 + 0.745741i) q^{71} +(4.83689 - 13.5360i) q^{72} +(2.57634 - 3.07036i) q^{73} +(3.36819 - 4.03005i) q^{74} +(-8.59590 - 11.3209i) q^{75} +(-6.15545 - 6.17337i) q^{76} +16.0441i q^{77} +(-14.3206 - 11.9687i) q^{78} +(3.64005 + 3.05437i) q^{79} +(-4.59952 + 7.67101i) q^{80} +(-1.48581 + 0.540791i) q^{81} +(-2.52209 - 14.1416i) q^{82} +(-3.22919 - 5.59312i) q^{83} +(-0.0764839 - 19.5397i) q^{84} +(-1.69450 + 0.924048i) q^{85} +(-0.0675514 + 0.186732i) q^{86} +(-8.81664 + 15.2709i) q^{87} +(6.66939 + 11.3967i) q^{88} +(5.30431 + 6.32142i) q^{89} +(15.8853 - 2.43555i) q^{90} +(-14.9911 - 5.45632i) q^{91} +(-1.47861 + 8.58191i) q^{92} +(-24.2389 - 4.27397i) q^{93} +(-4.52370 - 2.59997i) q^{94} +(2.80132 - 9.33556i) q^{95} +(-8.17683 - 13.8479i) q^{96} +(3.18610 - 18.0692i) q^{97} +(-2.33920 - 6.38796i) q^{98} +(8.11477 - 22.2951i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9}+O(q^{10}) $ 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9	$ 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9} - 15 q^{10} + 18 q^{14} - 6 q^{16} - 42 q^{20} + 12 q^{21} + 12 q^{24} - 12 q^{25} + 18 q^{26} - 24 q^{29} - 24 q^{30} + 12 q^{34} - 6 q^{36} - 48 q^{40} - 12 q^{41} - 36 q^{44} - 6 q^{45} - 18 q^{46} - 108 q^{49} - 36 q^{50} + 36 q^{54} - 30 q^{60} - 24 q^{61} + 18 q^{64} - 18 q^{65} - 48 q^{66} - 180 q^{69} - 21 q^{70} - 30 q^{74} - 48 q^{76} + 3 q^{80} - 60 q^{81} + 90 q^{84} - 36 q^{85} + 102 q^{86} - 48 q^{89} - 78 q^{90} + 24 q^{96}+O(q^{100}) $ 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9 - 15 * q^10 + 18 * q^14 - 6 * q^16 - 42 * q^20 + 12 * q^21 + 12 * q^24 - 12 * q^25 + 18 * q^26 - 24 * q^29 - 24 * q^30 + 12 * q^34 - 6 * q^36 - 48 * q^40 - 12 * q^41 - 36 * q^44 - 6 * q^45 - 18 * q^46 - 108 * q^49 - 36 * q^50 + 36 * q^54 - 30 * q^60 - 24 * q^61 + 18 * q^64 - 18 * q^65 - 48 * q^66 - 180 * q^69 - 21 * q^70 - 30 * q^74 - 48 * q^76 + 3 * q^80 - 60 * q^81 + 90 * q^84 - 36 * q^85 + 102 * q^86 - 48 * q^89 - 78 * q^90 + 24 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{1}{18}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−0.906917	+	1.08513i	−0.641287	+	0.767301i
$2$	−0.906917	+	1.08513i	−0.641287	+	0.767301i
$3$	1.82738	−	2.17779i	1.05504	−	1.25734i	0.0898031	−	0.995960i	$-0.471376\pi$
$3$	1.82738	−	2.17779i	1.05504	−	1.25734i	0.965235	−	0.261385i	$-0.0841793\pi$
$4$	−0.355003	−	1.96824i	−0.177502	−	0.984121i
$5$	1.74742	−	1.39518i	0.781470	−	0.623943i
$5$	1.74742	−	1.39518i	0.781470	−	0.623943i
$6$	0.705894	+	3.95801i	0.288180	+	1.61585i
$7$	1.71831	+	2.97619i	0.649458	+	1.12490i	0.983252	+	0.182249i	$0.0583377\pi$
$7$	1.71831	+	2.97619i	0.649458	+	1.12490i	−0.333794	+	0.942646i	$0.608329\pi$
$8$	2.45775	+	1.39981i	0.868946	+	0.494907i
$9$	−0.882491	−	5.00485i	−0.294164	−	1.66828i
$10$	−0.0708181	+	3.16148i	−0.0223947	+	0.999749i
$11$	4.04311	+	2.33429i	1.21904	+	0.703814i	0.964713	−	0.263303i	$-0.0848120\pi$
$11$	4.04311	+	2.33429i	1.21904	+	0.703814i	0.254329	+	0.967118i	$0.418145\pi$
$12$	−4.93513	−	2.82360i	−1.42465	−	0.815103i
$13$	−3.55608	+	2.98391i	−0.986280	+	0.827588i	−0.985025	−	0.172412i	$-0.944844\pi$
$13$	−3.55608	+	2.98391i	−0.986280	+	0.827588i	−0.00125547	+	0.999999i	$0.500400\pi$
$14$	−4.78791	−	0.834579i	−1.27962	−	0.223051i
$15$	0.154799	−	6.35503i	0.0399689	−	1.64086i
$16$	−3.74795	+	1.39746i	−0.936986	+	0.349366i
$17$	−0.850042	−	0.149885i	−0.206166	−	0.0363525i	0.0696115	−	0.997574i	$-0.477824\pi$
$17$	−0.850042	−	0.149885i	−0.206166	−	0.0363525i	−0.275777	+	0.961222i	$0.588935\pi$
$18$	6.23125	+	3.58137i	1.46872	+	0.844137i
$19$	3.58397	−	2.48096i	0.822219	−	0.569171i
$19$	3.58397	−	2.48096i	0.822219	−	0.569171i
$20$	−3.36639	−	2.94405i	−0.752747	−	0.658310i
$21$	9.62150	+	1.69653i	2.09958	+	0.370213i
$22$	−6.19976	+	2.27028i	−1.32179	+	0.484025i
$23$	−4.09159	−	1.48922i	−0.853155	−	0.310523i	−0.121829	−	0.992551i	$-0.538876\pi$
$23$	−4.09159	−	1.48922i	−0.853155	−	0.310523i	−0.731326	+	0.682028i	$0.761098\pi$
$24$	7.53972	−	2.79448i	1.53904	−	0.570420i
$25$	1.10695	−	4.87593i	0.221391	−	0.975185i
$26$	−0.0128485	−	6.56496i	−0.00251980	−	1.28750i
$27$	−5.12608	−	2.95954i	−0.986514	−	0.569564i
$28$	5.24786	−	4.43860i	0.991752	−	0.838816i
$29$	−6.10835	+	1.07707i	−1.13429	+	0.200006i	−0.709107	−	0.705101i	$-0.750902\pi$
$29$	−6.10835	+	1.07707i	−1.13429	+	0.200006i	−0.425184	+	0.905107i	$0.639791\pi$
$30$	6.75562	+	5.93146i	1.23340	+	1.08293i
$31$	−4.32882	−	7.49774i	−0.777479	−	1.34663i	−0.933390	−	0.358863i	$-0.883165\pi$
$31$	−4.32882	−	7.49774i	−0.777479	−	1.34663i	0.155911	−	0.987771i	$-0.450169\pi$
$32$	1.88265	−	5.33438i	0.332808	−	0.942994i
$33$	12.4719	−	4.53939i	2.17107	−	0.790206i
$34$	0.933562	−	0.786471i	0.160105	−	0.134879i
$35$	7.15492	+	2.80332i	1.20940	+	0.473847i
$36$	−9.53747	+	3.51369i	−1.58958	+	0.585616i
$37$	−3.71390			−0.610561			−0.305280	−	0.952263i	$-0.598750\pi$
$37$	−3.71390			−0.610561			−0.305280	+	0.952263i	$0.598750\pi$
$38$	−0.558206	+	6.13909i	−0.0905529	+	0.995892i
$39$			13.1971i			2.11323i
$40$	6.24770	−	0.982950i	0.987849	−	0.155418i
$41$	−6.52905	+	7.78102i	−1.01967	+	1.21519i	−0.0433013	+	0.999062i	$0.513788\pi$
$41$	−6.52905	+	7.78102i	−1.01967	+	1.21519i	−0.976365	+	0.216129i	$0.930657\pi$
$42$	−10.5669	+	8.90195i	−1.63050	+	1.37360i
$43$	0.131946	−	0.0480244i	0.0201216	−	0.00732365i	−0.331940	−	0.943301i	$-0.607703\pi$
$43$	0.131946	−	0.0480244i	0.0201216	−	0.00732365i	0.352061	+	0.935977i	$0.385481\pi$
$44$	3.15913	−	8.78649i	0.476256	−	1.32461i
$45$	−8.52475	−	7.51435i	−1.27079	−	1.12017i
$46$	5.32672	−	3.08930i	0.785382	−	0.455492i
$47$	0.640662	+	3.63338i	0.0934502	+	0.529982i	0.995211	+	0.0977475i	$0.0311637\pi$
$47$	0.640662	+	3.63338i	0.0934502	+	0.529982i	−0.901761	+	0.432235i	$0.857725\pi$
$48$	−3.80554	+	10.7159i	−0.549282	+	1.54671i
$49$	−2.40515	+	4.16584i	−0.343593	+	0.595120i
$50$	4.28709	+	5.62325i	0.606286	+	0.795247i
$51$	−1.87977	+	1.57731i	−0.263220	+	0.220868i
$52$	7.13547	+	5.93993i	0.989512	+	0.823721i
$53$	−0.917952	−	0.334107i	−0.126090	−	0.0458931i	0.278204	−	0.960522i	$-0.410261\pi$
$53$	−0.917952	−	0.334107i	−0.126090	−	0.0458931i	−0.404295	+	0.914629i	$0.632483\pi$
$54$	7.86041	−	2.87839i	1.06967	−	0.391699i
$55$	10.3218	−	1.56187i	1.39178	−	0.210603i
$56$	0.0570708	+	9.72004i	0.00762641	+	1.29889i
$57$	1.14627	−	12.3388i	0.151828	−	1.63431i
$58$	4.37101	−	7.60514i	0.573941	−	0.998604i
$59$	−1.50948	+	8.56070i	−0.196518	+	1.11451i	0.713723	+	0.700429i	$0.247008\pi$
$59$	−1.50948	+	8.56070i	−0.196518	+	1.11451i	−0.910240	+	0.414080i	$0.864103\pi$
$60$	−12.5632	+	1.95137i	−1.62190	+	0.251921i
$61$	−4.15281	−	1.51150i	−0.531713	−	0.193528i	0.0621903	−	0.998064i	$-0.480191\pi$
$61$	−4.15281	−	1.51150i	−0.531713	−	0.193528i	−0.593903	+	0.804537i	$0.702414\pi$
$62$	12.0619	+	2.10250i	1.53186	+	0.267018i
$63$	13.3790	−	11.2263i	1.68560	−	1.41438i
$64$	4.08108	+	6.88076i	0.510135	+	0.860094i
$65$	−2.05089	+	10.1755i	−0.254381	+	1.26212i
$66$	−6.38513	+	17.6504i	−0.785955	+	2.17262i
$67$	2.42352	−	0.427332i	0.296080	−	0.0522069i	−0.0236350	−	0.999721i	$-0.507524\pi$
$67$	2.42352	−	0.427332i	0.296080	−	0.0522069i	0.319715	+	0.947514i	$0.396413\pi$
$68$	0.00675722	+	1.72630i	0.000819433	+	0.209344i
$69$	−10.7201	+	6.18924i	−1.29055	+	0.745097i
$70$	−9.53087	+	5.22163i	−1.13916	+	0.624104i
$71$	−2.04891	+	0.745741i	−0.243161	+	0.0885032i	−0.460726	−	0.887543i	$-0.652411\pi$
$71$	−2.04891	+	0.745741i	−0.243161	+	0.0885032i	0.217565	+	0.976046i	$0.430189\pi$
$72$	4.83689	−	13.5360i	0.570033	−	1.59523i
$73$	2.57634	−	3.07036i	0.301538	−	0.359359i	−0.593905	−	0.804535i	$-0.702415\pi$
$73$	2.57634	−	3.07036i	0.301538	−	0.359359i	0.895443	+	0.445176i	$0.146859\pi$
$74$	3.36819	−	4.03005i	0.391545	−	0.468484i
$75$	−8.59590	−	11.3209i	−0.992569	−	1.30722i
$76$	−6.15545	−	6.17337i	−0.706078	−	0.708134i
$77$			16.0441i			1.82839i
$78$	−14.3206	−	11.9687i	−1.62148	−	1.35519i
$79$	3.64005	+	3.05437i	0.409538	+	0.343643i	0.824166	−	0.566348i	$-0.191644\pi$
$79$	3.64005	+	3.05437i	0.409538	+	0.343643i	−0.414629	+	0.909991i	$0.636088\pi$
$80$	−4.59952	+	7.67101i	−0.514242	+	0.857645i
$81$	−1.48581	+	0.540791i	−0.165090	+	0.0600879i
$82$	−2.52209	−	14.1416i	−0.278518	−	1.56168i
$83$	−3.22919	−	5.59312i	−0.354449	−	0.613924i	0.632574	−	0.774500i	$-0.281998\pi$
$83$	−3.22919	−	5.59312i	−0.354449	−	0.613924i	−0.987024	+	0.160575i	$0.948665\pi$
$84$	−0.0764839	−	19.5397i	−0.00834508	−	2.13196i
$85$	−1.69450	+	0.924048i	−0.183794	+	0.100227i
$86$	−0.0675514	+	0.186732i	−0.00728426	+	0.0201359i
$87$	−8.81664	+	15.2709i	−0.945243	+	1.63721i
$88$	6.66939	+	11.3967i	0.710960	+	1.21489i
$89$	5.30431	+	6.32142i	0.562255	+	0.670070i	0.970022	−	0.243016i	$-0.0781369\pi$
$89$	5.30431	+	6.32142i	0.562255	+	0.670070i	−0.407767	+	0.913086i	$0.633692\pi$
$90$	15.8853	−	2.43555i	1.67445	−	0.256729i
$91$	−14.9911	−	5.45632i	−1.57150	−	0.571978i
$92$	−1.47861	+	8.58191i	−0.154156	+	0.894726i
$93$	−24.2389	−	4.27397i	−2.51345	−	0.443190i
$94$	−4.52370	−	2.59997i	−0.466584	−	0.268166i
$95$	2.80132	−	9.33556i	0.287409	−	0.957808i
$96$	−8.17683	−	13.8479i	−0.834544	−	1.41335i
$97$	3.18610	−	18.0692i	0.323499	−	1.83465i	−0.196521	−	0.980500i	$-0.562964\pi$
$97$	3.18610	−	18.0692i	0.323499	−	1.83465i	0.520020	−	0.854154i	$-0.325925\pi$
$98$	−2.33920	−	6.38796i	−0.236295	−	0.645282i
$99$	8.11477	−	22.2951i	0.815565	−	2.24075i
$100$	−9.98997	−	0.447781i	−0.998997	−	0.0447781i
$101$	−0.621433	+	0.521445i	−0.0618349	+	0.0518857i	−0.673181	−	0.739477i	$-0.735073\pi$
$101$	−0.621433	+	0.521445i	−0.0618349	+	0.0518857i	0.611346	+	0.791363i	$0.290628\pi$
$102$	−0.00679180	−	3.47028i	−0.000672488	−	0.343609i
$103$	4.11262	+	2.37442i	0.405228	+	0.233959i	0.688737	−	0.725011i	$-0.258165\pi$
$103$	4.11262	+	2.37442i	0.405228	+	0.233959i	−0.283509	+	0.958969i	$0.591499\pi$
$104$	−12.9169	+	2.35587i	−1.26660	+	0.231012i
$105$	19.1798	−	10.4592i	1.87175	−	1.02071i
$106$	1.19505	−	0.693087i	0.116074	−	0.0673186i
$107$	−1.07436	+	0.620284i	−0.103863	+	0.0599652i	−0.551032	−	0.834484i	$-0.685766\pi$
$107$	−1.07436	+	0.620284i	−0.103863	+	0.0599652i	0.447169	+	0.894450i	$0.352432\pi$
$108$	−4.00532	+	11.1400i	−0.385412	+	1.07195i
$109$	−2.29956	−	6.31798i	−0.220257	−	0.605152i	0.779517	−	0.626381i	$-0.215464\pi$
$109$	−2.29956	−	6.31798i	−0.220257	−	0.605152i	−0.999775	+	0.0212285i	$0.993242\pi$
$110$	−7.66614	+	12.6169i	−0.730938	+	1.20297i
$111$	−6.78669	+	8.08807i	−0.644164	+	0.767685i
$112$	−10.5992	−	8.75334i	−1.00153	−	0.827113i
$113$	2.90665			0.273434			0.136717	−	0.990610i	$-0.456345\pi$
$113$	2.90665			0.273434			0.136717	+	0.990610i	$0.456345\pi$
$114$	12.3496	+	12.4341i	1.15664	+	1.16456i
$115$	−9.22745	+	3.10621i	−0.860464	+	0.289656i
$116$	4.28841	+	11.6403i	0.398169	+	1.08078i
$117$	18.0722	+	15.1644i	1.67078	+	1.40195i
$118$	−7.92048	−	9.40183i	−0.729139	−	0.865508i
$119$	−1.01454	−	2.78744i	−0.0930031	−	0.255524i
$120$	9.27627	−	15.4024i	0.846804	−	1.40604i
$121$	5.39780	+	9.34927i	0.490709	+	0.849933i
$122$	5.40642	−	3.13552i	0.489474	−	0.283877i
$123$	5.01434	+	28.4377i	0.452128	+	2.56414i
$124$	−13.2206	+	11.1819i	−1.18725	+	1.00416i
$125$	−4.86848	−	10.0647i	−0.435450	−	0.900213i
$126$	0.0483398	+	24.6993i	0.00430645	+	2.20039i
$127$	4.50820	+	5.37267i	0.400038	+	0.476747i	0.928032	−	0.372501i	$-0.121500\pi$
$127$	4.50820	+	5.37267i	0.400038	+	0.476747i	−0.527993	+	0.849249i	$0.677055\pi$
$128$	−11.1677	−	1.81178i	−0.987094	−	0.160141i
$129$	0.136528	−	0.375109i	0.0120207	−	0.0330265i
$130$	−9.18175	−	11.4538i	−0.805293	−	1.00457i
$131$	−0.872822	−	0.153902i	−0.0762588	−	0.0134465i	0.135389	−	0.990793i	$-0.456772\pi$
$131$	−0.872822	−	0.153902i	−0.0762588	−	0.0134465i	−0.211647	+	0.977346i	$0.567883\pi$
$132$	−13.3622	−	22.9361i	−1.16303	−	1.99633i
$133$	13.5422	+	6.40354i	1.17425	+	0.555257i
$134$	−1.73422	+	3.01738i	−0.149814	+	0.260662i
$135$	−13.0865	+	1.98023i	−1.12631	+	0.170431i
$136$	−1.87938	−	1.55828i	−0.161156	−	0.133621i
$137$	−3.47747	+	9.55428i	−0.297101	+	0.816277i	0.697881	+	0.716214i	$0.254127\pi$
$137$	−3.47747	+	9.55428i	−0.297101	+	0.816277i	−0.994981	+	0.100063i	$0.968096\pi$
$138$	3.00611	−	17.2458i	0.255897	−	1.46806i
$139$	−0.774938	−	0.923535i	−0.0657294	−	0.0783332i	0.732178	−	0.681114i	$-0.238504\pi$
$139$	−0.774938	−	0.923535i	−0.0657294	−	0.0783332i	−0.797907	+	0.602780i	$0.794060\pi$
$140$	2.97758	−	15.0778i	0.251651	−	1.27431i
$141$	9.08344	+	5.24433i	0.764964	+	0.441652i
$142$	1.04896	−	2.89965i	0.0880271	−	0.243333i
$143$	−21.3429	+	3.76333i	−1.78479	+	0.314706i
$144$	10.3016	+	17.5247i	0.858469	+	1.46039i
$145$	−9.17114	+	10.4043i	−0.761622	+	0.864032i
$146$	0.995208	+	5.58022i	0.0823640	+	0.461822i
$147$	4.67719	+	12.8505i	0.385768	+	1.05989i
$148$	1.31844	+	7.30984i	0.108376	+	0.600865i
$149$	11.9994	+	10.0687i	0.983030	+	0.824860i	0.984544	−	0.175138i	$-0.0560373\pi$
$149$	11.9994	+	10.0687i	0.983030	+	0.824860i	−0.00151347	+	0.999999i	$0.500482\pi$
$150$	20.0804	+	0.939445i	1.63955	+	0.0767053i
$151$	21.0575			1.71364			0.856818	−	0.515619i	$-0.172438\pi$
$151$	21.0575			1.71364			0.856818	+	0.515619i	$0.172438\pi$
$152$	12.2814	−	1.08071i	0.996151	−	0.0876574i
$153$			4.38661i			0.354636i
$154$	−17.4099	−	14.5506i	−1.40293	−	1.17252i
$155$	−18.0250	−	7.06222i	−1.44780	−	0.567251i
$156$	25.9751	−	4.68502i	2.07967	−	0.375102i
$157$	4.76506	+	13.0919i	0.380293	+	1.04485i	0.971233	+	0.238132i	$0.0765349\pi$
$157$	4.76506	+	13.0919i	0.380293	+	1.04485i	−0.590940	+	0.806716i	$0.701243\pi$
$158$	−6.61560	+	1.17986i	−0.526309	+	0.0938649i
$159$	−2.40506	+	1.38856i	−0.190734	+	0.110120i
$160$	−4.15264	−	11.9480i	−0.328295	−	0.944575i
$161$	−2.59840	−	14.7363i	−0.204783	−	1.16138i
$162$	0.760680	−	2.10275i	0.0597647	−	0.165207i
$163$	7.40579	−	12.8272i	0.580066	−	1.00470i	−0.415405	−	0.909637i	$-0.636360\pi$
$163$	7.40579	−	12.8272i	0.580066	−	1.00470i	0.995471	−	0.0950672i	$-0.0303066\pi$
$164$	17.6328	+	10.0885i	1.37689	+	0.787776i
$165$	15.4603	−	25.3327i	1.20358	−	1.97215i
$166$	8.99785	+	1.56841i	0.698369	+	0.121732i
$167$	4.90918	−	13.4879i	0.379884	−	1.04372i	−0.591520	−	0.806290i	$-0.701472\pi$
$167$	4.90918	−	13.4879i	0.379884	−	1.04372i	0.971404	−	0.237432i	$-0.0763057\pi$
$168$	21.2724	+	17.6379i	1.64120	+	1.36079i
$169$	1.48460	−	8.41957i	0.114200	−	0.647659i
$170$	0.534059	−	2.67678i	0.0409604	−	0.205300i
$171$	−15.5797	−	15.7478i	−1.19141	−	1.20427i
$172$	−0.141365	−	0.242653i	−0.0107790	−	0.0185021i
$173$	−1.52104	+	8.62625i	−0.115643	+	0.655842i	0.870787	+	0.491660i	$0.163610\pi$
$173$	−1.52104	+	8.62625i	−0.115643	+	0.655842i	−0.986430	+	0.164182i	$0.947502\pi$
$174$	−8.57488	−	23.4166i	−0.650060	−	1.77521i
$175$	16.4138	−	5.08383i	1.24077	−	0.384301i
$176$	−18.4154	−	3.09869i	−1.38811	−	0.233573i
$177$	15.8850	+	18.9310i	1.19399	+	1.42294i
$178$	−11.6701	+	0.0228400i	−0.874712	+	0.00171193i
$179$	−1.23910	+	2.14619i	−0.0926148	+	0.160414i	−0.908611	−	0.417644i	$-0.862856\pi$
$179$	−1.23910	+	2.14619i	−0.0926148	+	0.160414i	0.815996	+	0.578058i	$0.196189\pi$
$180$	−11.7637	+	19.4464i	−0.876817	+	1.44945i
$181$	−22.8937	+	4.03678i	−1.70168	+	0.300052i	−0.938280	−	0.345877i	$-0.887582\pi$
$181$	−22.8937	+	4.03678i	−1.70168	+	0.300052i	−0.763398	+	0.645928i	$0.776470\pi$
$182$	19.5165	−	11.3189i	1.44666	−	0.839009i
$183$	−10.8805	+	6.28184i	−0.804308	+	0.464367i
$184$	−7.97149	−	9.38756i	−0.587666	−	0.692060i
$185$	−6.48973	+	5.18155i	−0.477135	+	0.380955i
$186$	26.6204	−	22.4261i	1.95191	−	1.64436i
$187$	−3.08693	−	2.59025i	−0.225739	−	0.189418i
$188$	6.92392	−	2.55084i	0.504979	−	0.186039i
$189$		−	20.3416i		−	1.47963i
$190$	7.58971	+	11.5064i	0.550615	+	0.834759i
$191$			9.80543i			0.709496i	0.934962	+	0.354748i	$0.115433\pi$
$191$			9.80543i			0.709496i	−0.934962	+	0.354748i	$0.884567\pi$
$192$	22.4425	+	3.68603i	1.61965	+	0.266017i
$193$	−13.8351	−	11.6090i	−0.995870	−	0.835634i	−0.00946292	−	0.999955i	$-0.503012\pi$
$193$	−13.8351	−	11.6090i	−0.995870	−	0.835634i	−0.986407	+	0.164321i	$0.947457\pi$
$194$	16.7179	+	19.8446i	1.20028	+	1.42476i
$195$	18.4123	+	23.0609i	1.31854	+	1.65143i
$196$	9.05321	+	3.25502i	0.646658	+	0.232502i
$197$	7.66980	−	4.42816i	0.546451	−	0.315494i	−0.201238	−	0.979542i	$-0.564497\pi$
$197$	7.66980	−	4.42816i	0.546451	−	0.315494i	0.747689	+	0.664049i	$0.231163\pi$
$198$	16.8336	+	29.0254i	1.19632	+	2.06275i
$199$	−4.42663	+	0.780533i	−0.313795	+	0.0553306i	−0.328328	−	0.944564i	$-0.606485\pi$
$199$	−4.42663	+	0.780533i	−0.313795	+	0.0553306i	0.0145327	+	0.999894i	$0.495374\pi$
$200$	9.54597	−	10.4343i	0.675002	−	0.737816i
$201$	3.49805	−	6.05880i	0.246733	−	0.427355i
$202$	−0.00224530	−	1.14724i	−0.000157979	−	0.0807196i
$203$	−13.7016	−	16.3289i	−0.961661	−	1.14606i
$204$	3.77185	+	3.13988i	0.264083	+	0.219836i
$205$	−0.553081	+	22.7059i	−0.0386289	+	1.58585i
$206$	−6.30635	+	2.30931i	−0.439384	+	0.160897i
$207$	−3.84252	+	21.7920i	−0.267074	+	1.51465i
$208$	9.15811	−	16.1530i	0.635000	−	1.12001i
$209$	20.2816	−	1.66476i	1.40291	−	0.115154i
$210$	−6.04493	+	30.2981i	−0.417140	+	2.09077i
$211$	−2.29936	+	13.0403i	−0.158295	+	0.897734i	0.797417	+	0.603429i	$0.206199\pi$
$211$	−2.29936	+	13.0403i	−0.158295	+	0.897734i	−0.955712	+	0.294305i	$0.904912\pi$
$212$	−0.331727	+	1.92536i	−0.0227831	+	0.132234i
$213$	−2.12007	+	5.82483i	−0.145264	+	0.399111i
$214$	0.301271	−	1.72837i	0.0205945	−	0.118149i
$215$	0.163562	−	0.268007i	0.0111549	−	0.0182779i
$216$	−8.45584	−	14.4493i	−0.575347	−	0.983153i
$217$	14.8765	−	25.7668i	1.00988	−	1.74917i
$218$	8.94131	+	3.23457i	0.605582	+	0.219073i
$219$	−1.97864	−	11.2214i	−0.133704	−	0.758274i
$220$	−6.73840	−	19.7612i	−0.454303	−	1.33230i
$221$	3.47007	−	2.00344i	0.233422	−	0.134766i
$222$	−2.62162	−	14.6996i	−0.175951	−	0.986575i
$223$	1.95899	+	5.38228i	0.131184	+	0.360424i	0.987842	−	0.155460i	$-0.0496858\pi$
$223$	1.95899	+	5.38228i	0.131184	+	0.360424i	−0.856659	+	0.515884i	$0.827464\pi$
$224$	19.1111	−	3.56297i	1.27692	−	0.238061i
$225$	−25.3802	−	1.23718i	−1.69201	−	0.0824786i
$226$	−2.63609	+	3.15408i	−0.175350	+	0.209806i
$227$			12.6209i			0.837678i	0.908061	+	0.418839i	$0.137563\pi$
$227$			12.6209i			0.837678i	−0.908061	+	0.418839i	$0.862437\pi$
$228$	−24.6926	+	2.12416i	−1.63531	+	0.140676i
$229$	8.13430			0.537530			0.268765	−	0.963206i	$-0.413385\pi$
$229$	8.13430			0.537530			0.268765	+	0.963206i	$0.413385\pi$
$230$	4.99789	−	12.8300i	0.329551	−	0.845987i
$231$	34.9406	+	29.3186i	2.29892	+	1.92902i
$232$	−16.5205	−	5.90335i	−1.08462	−	0.387574i
$233$	1.12043	+	3.07837i	0.0734021	+	0.201670i	0.970968	−	0.239210i	$-0.0768885\pi$
$233$	1.12043	+	3.07837i	0.0734021	+	0.201670i	−0.897566	+	0.440881i	$0.854666\pi$
$234$	−32.8453	+	5.85782i	−2.14717	+	0.382938i
$235$	6.18871	+	5.45520i	0.403707	+	0.355858i
$236$	17.3854	−	0.0680513i	1.13169	−	0.00442977i
$237$	13.3035	−	2.34577i	0.864156	−	0.152374i
$238$	3.94483	+	1.42706i	0.255706	+	0.0925029i
$239$	6.39890	+	3.69441i	0.413910	+	0.238971i	0.692468	−	0.721448i	$-0.256523\pi$
$239$	6.39890	+	3.69441i	0.413910	+	0.238971i	−0.278558	+	0.960419i	$0.589857\pi$
$240$	8.30074	+	24.0346i	0.535811	+	1.55143i
$241$	−8.67239	−	10.3353i	−0.558637	−	0.665758i	0.410620	−	0.911807i	$-0.365312\pi$
$241$	−8.67239	−	10.3353i	−0.558637	−	0.665758i	−0.969258	+	0.246048i	$0.920868\pi$
$242$	−15.0405	−	2.62171i	−0.966840	−	0.168530i
$243$	4.53593	−	12.4624i	0.290980	−	0.799461i
$244$	−1.50073	+	8.71031i	−0.0960746	+	0.557621i
$245$	1.60929	+	10.6351i	0.102813	+	0.679450i
$246$	−35.4062	−	20.3495i	−2.25741	−	1.29743i
$247$	−5.34194	+	19.5167i	−0.339900	+	1.24182i
$248$	−0.143775	−	24.4871i	−0.00912972	−	1.55493i
$249$	−18.0816	−	3.18827i	−1.14587	−	0.202048i
$250$	15.3368	+	3.84492i	0.969983	+	0.243174i
$251$	7.74655	−	21.2835i	0.488958	−	1.34340i	−0.412667	−	0.910882i	$-0.635403\pi$
$251$	7.74655	−	21.2835i	0.488958	−	1.34340i	0.901625	−	0.432519i	$-0.142375\pi$
$252$	−26.8457	−	22.3478i	−1.69112	−	1.40778i
$253$	−13.0665	−	15.5720i	−0.821481	−	0.979003i
$254$	−9.91860	+	0.0194120i	−0.622348	+	0.00121802i
$255$	−1.08411	+	5.37884i	−0.0678897	+	0.336836i
$256$	12.0942	−	10.4752i	0.755887	−	0.654702i
$257$	0.620867	+	3.52111i	0.0387286	+	0.219641i	0.998030	−	0.0627446i	$-0.0199853\pi$
$257$	0.620867	+	3.52111i	0.0387286	+	0.219641i	−0.959301	+	0.282386i	$0.908874\pi$
$258$	0.283221	+	0.488343i	0.0176326	+	0.0304029i
$259$	−6.38161	−	11.0533i	−0.396534	−	0.686817i
$260$	20.7559	+	0.424298i	1.28723	+	0.0263138i
$261$	10.7811	+	29.6209i	0.667334	+	1.83349i
$262$	0.958580	−	0.807547i	0.0592213	−	0.0498904i
$263$	−5.61188	−	4.70893i	−0.346043	−	0.290365i	0.453156	−	0.891431i	$-0.350298\pi$
$263$	−5.61188	−	4.70893i	−0.346043	−	0.290365i	−0.799199	+	0.601067i	$0.794743\pi$
$264$	37.0070	+	6.30152i	2.27762	+	0.387832i
$265$	−2.07019	+	0.696881i	−0.127171	+	0.0428091i
$266$	−19.2303	+	8.88750i	−1.17908	+	0.544928i
$267$	23.4597			1.43571
$268$	−1.70145	−	4.61837i	−0.103933	−	0.282112i
$269$	12.7358	−	15.1779i	0.776515	−	0.925415i	−0.222255	−	0.974989i	$-0.571342\pi$
$269$	12.7358	−	15.1779i	0.776515	−	0.925415i	0.998770	+	0.0495737i	$0.0157863\pi$
$270$	9.71957	−	15.9964i	0.591514	−	0.973512i
$271$	5.37147	+	14.7580i	0.326293	+	0.896484i	0.989041	+	0.147641i	$0.0471680\pi$
$271$	5.37147	+	14.7580i	0.326293	+	0.896484i	−0.662748	+	0.748843i	$0.730610\pi$
$272$	3.39537	−	0.626141i	0.205875	−	0.0379654i
$273$	−39.2772	+	22.6767i	−2.37716	+	1.37246i
$274$	−7.21383	−	12.4384i	−0.435803	−	0.751434i
$275$	15.8573	−	17.1299i	0.956234	−	1.03297i
$276$	15.9876	+	18.9025i	0.962339	+	1.13780i
$277$	−13.2484	−	7.64898i	−0.796021	−	0.459583i	0.0460571	−	0.998939i	$-0.485334\pi$
$277$	−13.2484	−	7.64898i	−0.796021	−	0.459583i	−0.842078	+	0.539356i	$0.818668\pi$
$278$	1.70496	−	0.00333683i	0.102257	−	0.000200130i
$279$	−33.7050	+	28.2818i	−2.01786	+	1.69319i
$280$	13.6609	+	16.9054i	0.816396	+	1.01029i
$281$	−6.33825	+	17.4142i	−0.378108	+	1.03884i	0.594032	+	0.804442i	$0.297535\pi$
$281$	−6.33825	+	17.4142i	−0.378108	+	1.03884i	−0.972140	+	0.234402i	$0.924687\pi$
$282$	−13.9287	+	5.10052i	−0.829442	+	0.303732i
$283$	1.99634	−	11.3218i	0.118670	−	0.673013i	−0.866197	−	0.499703i	$-0.833443\pi$
$283$	1.99634	−	11.3218i	0.118670	−	0.673013i	0.984867	−	0.173310i	$-0.0554463\pi$
$284$	2.19517	+	3.76800i	0.130259	+	0.223590i
$285$	−15.2118	−	23.1603i	−0.901067	−	1.37190i
$286$	15.2726	−	26.5728i	0.903086	−	1.57128i
$287$	−34.3767	−	6.06154i	−2.02919	−	0.357801i
$288$	−28.3592	−	4.71484i	−1.67108	−	0.277825i
$289$	−15.2747	−	5.55952i	−0.898510	−	0.327031i
$290$	−2.97255	−	19.3877i	−0.174554	−	1.13849i
$291$	−33.5287	−	39.9580i	−1.96549	−	2.34238i
$292$	−6.95782	−	3.98087i	−0.407176	−	0.232963i
$293$	10.9159	−	18.9069i	0.637715	−	1.10455i	−0.348219	−	0.937413i	$-0.613213\pi$
$293$	10.9159	−	18.9069i	0.637715	−	1.10455i	0.985933	−	0.167141i	$-0.0534534\pi$
$294$	−18.1862	−	6.57896i	−1.06064	−	0.383693i
$295$	9.30601	+	17.0651i	0.541817	+	0.993571i
$296$	−9.12783	−	5.19874i	−0.530544	−	0.302170i
$297$	−13.8169	−	23.9315i	−0.801735	−	1.38865i
$298$	−21.8083	+	3.88942i	−1.26332	+	0.225308i
$299$	18.9937	−	6.91315i	1.09844	−	0.399798i
$300$	−19.2306	+	20.9377i	−1.11028	+	1.20884i
$301$	0.369653	+	0.310176i	0.0213065	+	0.0178782i
$302$	−19.0974	+	22.8501i	−1.09893	+	1.31488i
$303$			2.30623i			0.132489i
$304$	−9.96547	+	14.3070i	−0.571559	+	0.820561i
$305$	−9.36551	+	3.15269i	−0.536268	+	0.180522i
$306$	−4.76003	−	3.97829i	−0.272113	−	0.227424i
$307$	−17.7548	+	21.1593i	−1.01332	+	1.20763i	−0.0352433	+	0.999379i	$0.511221\pi$
$307$	−17.7548	+	21.1593i	−1.01332	+	1.20763i	−0.978076	+	0.208248i	$0.933224\pi$
$308$	31.5786	−	5.69570i	1.79936	−	0.324543i
$309$	12.6863	−	4.61743i	0.721697	−	0.262676i
$310$	24.0106	−	13.1545i	1.36371	−	0.747127i
$311$	−6.34142	+	3.66122i	−0.359589	+	0.207609i	−0.668900	−	0.743352i	$-0.733235\pi$
$311$	−6.34142	+	3.66122i	−0.359589	+	0.207609i	0.309312	+	0.950961i	$0.399901\pi$
$312$	−18.4734	+	32.4352i	−1.04585	+	1.83628i
$313$	26.2011	−	4.61996i	1.48097	−	0.261135i	0.626006	−	0.779819i	$-0.284689\pi$
$313$	26.2011	−	4.61996i	1.48097	−	0.261135i	0.854966	+	0.518683i	$0.173578\pi$
$314$	−18.5279	−	6.70257i	−1.04559	−	0.378248i
$315$	7.71603	−	38.2832i	0.434749	−	2.15702i
$316$	4.71950	−	8.24881i	0.265493	−	0.464032i
$317$	−12.9765	+	10.8886i	−0.728831	+	0.611562i	−0.929813	−	0.368033i	$-0.880031\pi$
$317$	−12.9765	+	10.8886i	−0.728831	+	0.611562i	0.200981	+	0.979595i	$0.435587\pi$
$318$	0.674423	−	3.86911i	0.0378197	−	0.216969i
$319$	−27.2109	−	9.90395i	−1.52352	−	0.554514i
$320$	16.7312	+	6.32974i	0.935305	+	0.353843i
$321$	−0.612424	+	3.47323i	−0.0341822	+	0.193857i
$322$	18.3473	+	10.5450i	1.02245	+	0.587649i
$323$	−3.41839	+	1.57174i	−0.190204	+	0.0874537i
$324$	1.59187	+	2.73245i	0.0884375	+	0.151803i
$325$	10.6129	+	20.6423i	0.588698	+	1.14503i
$326$	7.20271	+	19.6694i	0.398921	+	1.08939i
$327$	−17.9614	−	6.53740i	−0.993265	−	0.361519i
$328$	−26.9387	+	9.98439i	−1.48744	+	0.551296i
$329$	−9.71277	+	8.14998i	−0.535482	+	0.449323i
$330$	13.4680	+	39.7511i	0.741387	+	2.18822i
$331$	9.76891	−	16.9202i	0.536948	−	0.930021i	−0.462119	−	0.886818i	$-0.652911\pi$
$331$	9.76891	−	16.9202i	0.536948	−	0.930021i	0.999066	−	0.0432025i	$-0.0137561\pi$
$332$	−9.86223	+	8.34139i	−0.541260	+	0.457794i
$333$	3.27748	+	18.5875i	0.179605	+	1.01859i
$334$	10.1838	+	17.5595i	0.557234	+	0.960811i
$335$	3.63870	−	4.12797i	0.198804	−	0.225535i
$336$	−38.4317	+	7.08720i	−2.09662	+	0.386638i
$337$	−28.4901	+	10.3696i	−1.55196	+	0.564866i	−0.968875	−	0.247549i	$-0.920375\pi$
$337$	−28.4901	+	10.3696i	−1.55196	+	0.564866i	−0.583080	+	0.812415i	$0.698153\pi$
$338$	7.78990	+	9.24683i	0.423715	+	0.502961i
$339$	5.31154	−	6.33005i	0.288483	−	0.343801i
$340$	2.42030	+	3.00714i	0.131259	+	0.163085i
$341$		−	40.4189i		−	2.18880i
$342$	31.2179	−	2.62395i	1.68807	−	0.141887i
$343$	7.52516			0.406321
$344$	0.391515	+	0.0666669i	0.0211091	+	0.00359444i
$345$	−10.0974	+	25.7716i	−0.543625	+	1.38750i
$346$	−7.98113	−	9.47382i	−0.429068	−	0.509316i
$347$	4.54198	−	1.65315i	0.243826	−	0.0887455i	−0.217216	−	0.976123i	$-0.569698\pi$
$347$	4.54198	−	1.65315i	0.243826	−	0.0887455i	0.461043	+	0.887378i	$0.347476\pi$
$348$	33.1867	+	11.9321i	1.77899	+	0.639626i
$349$	2.55060	+	4.41777i	0.136531	+	0.236478i	0.926181	−	0.377079i	$-0.123071\pi$
$349$	2.55060	+	4.41777i	0.136531	+	0.236478i	−0.789651	+	0.613557i	$0.789738\pi$
$350$	−9.36934	+	22.4216i	−0.500812	+	1.19849i
$351$	27.0598	−	4.77137i	1.44434	−	0.254677i
$352$	20.0637	−	17.1728i	1.06940	−	0.915315i
$353$	19.8591	+	11.4657i	1.05700	+	0.610257i	0.924600	−	0.380940i	$-0.124400\pi$
$353$	19.8591	+	11.4657i	1.05700	+	0.610257i	0.132396	+	0.991197i	$0.457733\pi$
$354$	−34.9489	+	0.0683996i	−1.85751	+	0.00363540i
$355$	−2.53986	+	4.16171i	−0.134802	+	0.220881i
$356$	10.5590	−	12.6843i	0.559628	−	0.672265i
$357$	−7.92440	−	2.88425i	−0.419404	−	0.152650i
$358$	−1.20512	−	3.29100i	−0.0636928	−	0.173935i
$359$	0.881437	+	0.155421i	0.0465205	+	0.00820281i	0.196860	−	0.980432i	$-0.436926\pi$
$359$	0.881437	+	0.155421i	0.0465205	+	0.00820281i	−0.150340	+	0.988634i	$0.548037\pi$
$360$	−10.4331	−	30.4014i	−0.549871	−	1.60229i
$361$	6.68968	−	17.7834i	0.352088	−	0.935967i
$362$	16.3823	−	28.5036i	0.861034	−	1.49812i
$363$	30.2245	+	5.32940i	1.58638	+	0.279721i
$364$	−5.41746	+	31.4432i	−0.283952	+	1.64807i
$365$	0.218244	−	8.95966i	0.0114234	−	0.468970i
$366$	3.05108	−	17.5038i	0.159483	−	0.914939i
$367$	22.9620	−	19.2674i	1.19861	−	1.00575i	0.198937	−	0.980012i	$-0.436251\pi$
$367$	22.9620	−	19.2674i	1.19861	−	1.00575i	0.999669	−	0.0257372i	$-0.00819333\pi$
$368$	17.4162	−	0.136346i	0.907881	−	0.00710751i
$369$	44.7047	+	25.8103i	2.32723	+	1.34363i
$370$	0.263011	−	11.7414i	0.0136733	−	0.610407i
$371$	−0.582954	−	3.30610i	−0.0302655	−	0.171644i
$372$	0.192681	+	49.2252i	0.00999006	+	2.55221i
$373$	−12.2669	−	21.2470i	−0.635158	−	1.10013i	−0.986482	−	0.163872i	$-0.947602\pi$
$373$	−12.2669	−	21.2470i	−0.635158	−	1.10013i	0.351324	−	0.936254i	$-0.385732\pi$
$374$	5.61034	−	1.00058i	0.290104	−	0.0517388i
$375$	−30.8153	−	7.78950i	−1.59129	−	0.402248i
$376$	−3.51144	+	9.82674i	−0.181089	+	0.506775i
$377$	18.5079	−	22.0569i	0.953207	−	1.13599i
$378$	22.0732	+	18.4481i	1.13532	+	0.948870i
$379$	−8.65227			−0.444437			−0.222219	−	0.974997i	$-0.571330\pi$
$379$	−8.65227			−0.444437			−0.222219	+	0.974997i	$0.571330\pi$
$380$	−19.3691	−	2.19952i	−0.993614	−	0.112833i
$381$	19.9387			1.02149
$382$	−10.6401	−	8.89271i	−0.544397	−	0.454990i
$383$	19.1029	−	22.7660i	0.976114	−	1.16329i	−0.0104555	−	0.999945i	$-0.503328\pi$
$383$	19.1029	−	22.7660i	0.976114	−	1.16329i	0.986570	−	0.163342i	$-0.0522274\pi$
$384$	−24.3533	+	21.0100i	−1.24277	+	1.07216i
$385$	22.3844	+	28.0357i	1.14081	+	1.42883i
$386$	25.1445	−	4.48441i	1.27982	−	0.228251i
$387$	−0.356796	−	0.617989i	−0.0181370	−	0.0314141i
$388$	−36.6957	+	0.143637i	−1.86294	+	0.00729208i
$389$	−1.11628	−	6.33074i	−0.0565976	−	0.320981i	0.943344	−	0.331817i	$-0.107662\pi$
$389$	−1.11628	−	6.33074i	−0.0565976	−	0.320981i	−0.999941	+	0.0108363i	$0.996551\pi$
$390$	−41.7225	−	0.934595i	−2.11270	−	0.0473251i
$391$	3.25481	+	1.87917i	0.164603	+	0.0950335i
$392$	−11.7426	+	6.87185i	−0.593092	+	0.347081i
$393$	−1.93014	+	1.61958i	−0.0973628	+	0.0816971i
$394$	−2.15075	+	12.3387i	−0.108353	+	0.621614i
$395$	10.6221	+	0.258738i	0.534455	+	0.0130185i
$396$	−46.7630	−	8.05697i	−2.34993	−	0.404878i
$397$	7.38246	+	1.30173i	0.370515	+	0.0653318i	0.355805	−	0.934560i	$-0.384207\pi$
$397$	7.38246	+	1.30173i	0.370515	+	0.0653318i	0.0147094	+	0.999892i	$0.495318\pi$
$398$	3.16760	−	5.51133i	0.158778	−	0.276258i
$399$	38.6922	−	17.7902i	1.93703	−	0.890626i
$400$	2.66513	+	19.8216i	0.133257	+	0.991082i
$401$	−15.6217	−	2.75453i	−0.780112	−	0.137555i	−0.230609	−	0.973047i	$-0.574072\pi$
$401$	−15.6217	−	2.75453i	−0.780112	−	0.137555i	−0.549503	+	0.835492i	$0.685183\pi$
$402$	3.40213	+	9.29066i	0.169683	+	0.463376i
$403$	37.7662	+	13.7458i	1.88127	+	0.684726i
$404$	1.24694	+	1.03802i	0.0620376	+	0.0516432i
$405$	−1.84184	+	3.01796i	−0.0915216	+	0.149964i
$406$	30.1451	−	0.0589980i	1.49608	−	0.00292802i
$407$	−15.0157	−	8.66930i	−0.744299	−	0.429721i
$408$	−6.82793	+	1.24533i	−0.338033	+	0.0616529i
$409$	16.8767	−	2.97582i	0.834501	−	0.147145i	0.259958	−	0.965620i	$-0.416291\pi$
$409$	16.8767	−	2.97582i	0.834501	−	0.147145i	0.574542	+	0.818475i	$0.305180\pi$
$410$	−24.1372	−	21.1925i	−1.19205	−	1.04662i
$411$	14.4525	+	25.0325i	0.712890	+	1.23476i
$412$	3.21344	−	8.93754i	0.158315	−	0.440321i
$413$	−28.0721	+	10.2174i	−1.38134	+	0.502765i
$414$	−20.1623	−	23.9332i	−0.990922	−	1.17625i
$415$	−13.4461	−	5.26823i	−0.660045	−	0.258607i
$416$	9.22246	+	24.5872i	0.452168	+	1.20549i
$417$	−3.42737			−0.167839
$418$	−16.5873	+	23.5180i	−0.811311	+	1.15030i
$419$		−	6.05663i		−	0.295886i	−0.988996	−	0.147943i	$-0.952735\pi$
$419$		−	6.05663i		−	0.295886i	0.988996	−	0.147943i	$-0.0472652\pi$
$420$	−27.3950	−	34.0374i	−1.33674	−	1.66085i
$421$	6.50178	−	7.74852i	0.316877	−	0.377640i	−0.583970	−	0.811775i	$-0.698502\pi$
$421$	6.50178	−	7.74852i	0.316877	−	0.377640i	0.900848	+	0.434135i	$0.142946\pi$
$422$	−12.0651	−	14.3216i	−0.587320	−	0.697165i
$423$	17.6191	−	6.41284i	0.856672	−	0.311803i
$424$	−1.78841	−	2.10611i	−0.0868529	−	0.102282i
$425$	−1.67179	+	3.97883i	−0.0810936	+	0.193001i
$426$	−4.39796	−	7.58318i	−0.213082	−	0.367406i
$427$	−2.63728	−	14.9568i	−0.127627	−	0.723809i
$428$	1.60227	+	1.89440i	0.0774487	+	0.0915695i
$429$	−30.8059	+	53.3574i	−1.48732	+	2.57612i
$430$	0.142484	+	0.420546i	0.00687120	+	0.0202805i
$431$	−20.1606	+	16.9168i	−0.971103	+	0.814852i	−0.982723	−	0.185080i	$-0.940745\pi$
$431$	−20.1606	+	16.9168i	−0.971103	+	0.814852i	0.0116205	+	0.999932i	$0.496301\pi$
$432$	23.3481	+	3.92870i	1.12334	+	0.189019i
$433$	29.3923	+	10.6979i	1.41251	+	0.514110i	0.931864	−	0.362807i	$-0.118182\pi$
$433$	29.3923	+	10.6979i	1.41251	+	0.514110i	0.480641	+	0.876917i	$0.340404\pi$
$434$	14.4686	+	39.5112i	0.694513	+	1.89660i
$435$	5.89922	+	38.9854i	0.282846	+	1.86921i
$436$	−11.6189	+	6.76898i	−0.556447	+	0.324175i
$437$	−18.3588	+	4.81376i	−0.878221	+	0.230273i
$438$	13.9711	+	8.02982i	0.667567	+	0.383680i
$439$	2.60807	−	14.7911i	0.124476	−	0.705940i	−0.857141	−	0.515081i	$-0.827762\pi$
$439$	2.60807	−	14.7911i	0.124476	−	0.705940i	0.981618	−	0.190859i	$-0.0611272\pi$
$440$	27.5546	+	10.6098i	1.31361	+	0.505801i
$441$	22.9719	+	8.36110i	1.09390	+	0.398148i
$442$	−0.973070	+	5.58242i	−0.0462842	+	0.265529i
$443$	−10.5270	+	8.83324i	−0.500155	+	0.419680i	−0.857649	−	0.514236i	$-0.828076\pi$
$443$	−10.5270	+	8.83324i	−0.500155	+	0.419680i	0.357494	+	0.933915i	$0.383631\pi$
$444$	18.3286	+	10.4866i	0.869835	+	0.497670i
$445$	18.0884	+	3.64573i	0.857471	+	0.172824i
$446$	−7.61710	−	2.75553i	−0.360680	−	0.130478i
$447$	43.8550	−	7.73281i	2.07427	−	0.365749i
$448$	−13.4659	+	23.9693i	−0.636205	+	1.13244i
$449$	1.96533	−	1.13468i	0.0927497	−	0.0535491i	−0.452908	−	0.891557i	$-0.649613\pi$
$449$	1.96533	−	1.13468i	0.0927497	−	0.0535491i	0.545657	+	0.838008i	$0.316280\pi$
$450$	24.3602	−	26.4187i	1.14835	−	1.24539i
$451$	−44.5608	+	16.2188i	−2.09828	+	0.763713i
$452$	−1.03187	−	5.72098i	−0.0485350	−	0.269092i
$453$	38.4801	−	45.8588i	1.80795	−	2.15463i
$454$	−13.6953	−	11.4461i	−0.642751	−	0.537192i
$455$	−33.8083	+	11.3808i	−1.58496	+	0.533541i
$456$	20.0892	−	28.7211i	0.940761	−	1.34499i
$457$			0.929220i			0.0434671i	0.999764	+	0.0217335i	$0.00691854\pi$
$457$			0.929220i			0.0434671i	−0.999764	+	0.0217335i	$0.993081\pi$
$458$	−7.37713	+	8.82675i	−0.344711	+	0.412447i
$459$	3.91379	+	3.28406i	0.182680	+	0.153287i
$460$	9.38954	+	17.0591i	0.437790	+	0.795386i
$461$	−31.5614	+	11.4874i	−1.46996	+	0.535022i	−0.948090	−	0.318003i	$-0.896988\pi$
$461$	−31.5614	+	11.4874i	−1.46996	+	0.535022i	−0.521871	+	0.853025i	$0.674766\pi$
$462$	−63.5026	+	11.3254i	−2.95441	+	0.526906i
$463$	5.32246	+	9.21877i	0.247356	+	0.428433i	0.962791	−	0.270246i	$-0.0871051\pi$
$463$	5.32246	+	9.21877i	0.247356	+	0.428433i	−0.715436	+	0.698679i	$0.753772\pi$
$464$	21.3886	−	12.5730i	0.992940	−	0.583686i
$465$	−48.3184	+	26.3491i	−2.24071	+	1.22191i
$466$	−4.35656	−	1.57601i	−0.201814	−	0.0730072i
$467$	3.02908	−	5.24652i	0.140169	−	0.242780i	−0.787391	−	0.616454i	$-0.788569\pi$
$467$	3.02908	−	5.24652i	0.140169	−	0.242780i	0.927560	+	0.373674i	$0.121902\pi$
$468$	23.4315	−	40.9539i	1.08312	−	1.89310i
$469$	5.43617	+	6.47857i	0.251019	+	0.299153i
$470$	−11.5322	+	1.76813i	−0.531942	+	0.0815580i
$471$	37.2189	+	13.5466i	1.71496	+	0.624193i
$472$	−15.6933	+	18.9271i	−0.722341	+	0.871190i
$473$	0.645574	+	0.113832i	0.0296835	+	0.00523401i
$474$	−9.51972	+	16.5634i	−0.437255	+	0.760783i
$475$	−8.12969	−	20.2215i	−0.373016	−	0.927825i
$476$	−5.12618	+	2.98642i	−0.234958	+	0.136882i
$477$	−0.862073	+	4.88906i	−0.0394716	+	0.223855i
$478$	−9.81217	+	3.59310i	−0.448798	+	0.164345i
$479$	2.52323	−	6.93251i	0.115289	−	0.316754i	−0.868605	−	0.495505i	$-0.834983\pi$
$479$	2.52323	−	6.93251i	0.115289	−	0.316754i	0.983894	+	0.178750i	$0.0572054\pi$
$480$	−33.6087	−	12.7900i	−1.53402	−	0.583783i
$481$	13.2069	−	11.0819i	0.602184	−	0.505292i
$482$	19.0803	−	0.0373427i	0.869084	−	0.00170091i
$483$	−36.8407	−	21.2700i	−1.67631	−	0.967819i
$484$	16.4854	−	13.9432i	0.749335	−	0.633782i
$485$	−19.6424	−	36.0197i	−0.891914	−	1.63557i
$486$	9.40954	+	16.2244i	0.426825	+	0.735953i
$487$	7.61067	−	4.39402i	0.344873	−	0.199112i	−0.317552	−	0.948241i	$-0.602861\pi$
$487$	7.61067	−	4.39402i	0.344873	−	0.199112i	0.662425	+	0.749129i	$0.269527\pi$
$488$	−8.09076	−	9.52802i	−0.366252	−	0.431313i
$489$	−14.4017	−	39.5684i	−0.651268	−	1.78934i
$490$	−12.9999	−	7.89885i	−0.587276	−	0.356834i
$491$	14.0462	−	16.7396i	0.633896	−	0.755448i	−0.349497	−	0.936938i	$-0.613647\pi$
$491$	14.0462	−	16.7396i	0.633896	−	0.755448i	0.983393	+	0.181490i	$0.0580919\pi$
$492$	54.1922	−	19.9649i	2.44317	−	0.900088i
$493$	5.35379			0.241122
$494$	−16.3335	−	23.4968i	−0.734877	−	1.05717i
$495$	−16.9258	−	50.2805i	−0.760758	−	2.25994i
$496$	26.7020	+	22.0517i	1.19896	+	0.990153i
$497$	−5.74012	−	4.81653i	−0.257479	−	0.216051i
$498$	19.8581	−	16.7293i	0.889865	−	0.749658i
$499$	10.2528	+	28.1692i	0.458976	+	1.26103i	0.926248	+	0.376914i	$0.123015\pi$
$499$	10.2528	+	28.1692i	0.458976	+	1.26103i	−0.467272	+	0.884114i	$0.654763\pi$
$500$	−18.0814	+	13.1553i	−0.808625	+	0.588324i
$501$	−20.4027	−	35.3386i	−0.911527	−	1.57881i
$502$	16.0698	+	27.7083i	0.717230	+	1.23668i
$503$	−4.97150	−	28.1948i	−0.221668	−	1.25714i	−0.868953	−	0.494895i	$-0.835207\pi$
$503$	−4.97150	−	28.1948i	−0.221668	−	1.25714i	0.647284	−	0.762249i	$-0.275905\pi$
$504$	48.5970	−	8.86347i	2.16468	−	0.394810i
$505$	−0.358397	+	1.77819i	−0.0159485	+	0.0791286i
$506$	28.7478	−	0.0562633i	1.27800	−	0.00250121i
$507$	−15.6231	−	18.6189i	−0.693846	−	0.826893i
$508$	8.97428	−	10.7805i	0.398169	−	0.478309i
$509$	6.83422	−	18.7769i	0.302922	−	0.832270i	−0.691067	−	0.722790i	$-0.742859\pi$
$509$	6.83422	−	18.7769i	0.302922	−	0.832270i	0.993989	−	0.109480i	$-0.0349185\pi$
$510$	−4.85353	−	6.05456i	−0.214918	−	0.268100i
$511$	13.5649	+	2.39186i	0.600077	+	0.105810i
$512$	0.398543	+	22.6239i	0.0176133	+	0.999845i
$513$	−25.7142	+	2.11068i	−1.13531	+	0.0931889i
$514$	−4.38393	−	2.51964i	−0.193367	−	0.111136i
$515$	10.4992	−	1.58872i	0.462650	−	0.0700076i
$516$	−0.786772	−	0.135556i	−0.0346357	−	0.00596752i
$517$	−5.89108	+	16.1856i	−0.259089	+	0.711842i
$518$	17.7818	+	3.09954i	0.781287	+	0.136186i
$519$	16.0066	+	19.0759i	0.702612	+	0.837341i
$520$	−19.2843	+	22.1380i	−0.845674	+	0.970817i
$521$	−31.5755	−	18.2301i	−1.38335	−	0.798676i	−0.390793	−	0.920479i	$-0.627799\pi$
$521$	−31.5755	−	18.2301i	−1.38335	−	0.798676i	−0.992554	+	0.121803i	$0.961133\pi$
$522$	−41.9200	−	15.1648i	−1.83479	−	0.663745i
$523$	−15.1193	+	2.66594i	−0.661120	+	0.116573i	−0.494134	−	0.869386i	$-0.664515\pi$
$523$	−15.1193	+	2.66594i	−0.661120	+	0.116573i	−0.166986	+	0.985959i	$0.553404\pi$
$524$	0.00693830	+	1.77256i	0.000303101	+	0.0774346i
$525$	18.9227	−	45.0358i	0.825855	−	1.96552i
$526$	10.1993	−	1.81900i	0.444710	−	0.0793122i
$527$	2.55588	+	7.02222i	0.111336	+	0.305893i
$528$	−40.4002	+	34.4424i	−1.75819	+	1.49891i
$529$	−3.09569	−	2.59760i	−0.134595	−	0.112939i
$530$	1.12128	−	2.87843i	0.0487054	−	0.125031i
$531$	44.1772			1.91713
$532$	7.79619	−	28.9275i	0.338008	−	1.25417i
$533$		−	47.1520i		−	2.04238i
$534$	−21.2760	+	25.4567i	−0.920702	+	1.10162i
$535$	−1.01196	+	2.58283i	−0.0437507	+	0.111665i
$536$	6.55459	+	2.34218i	0.283115	+	0.101167i
$537$	2.40963	+	6.62039i	0.103983	+	0.285691i
$538$	4.91968	+	27.5851i	0.212102	+	1.18928i
$539$	−19.4485	+	11.2286i	−0.837708	+	0.483651i
$540$	8.54333	+	25.0544i	0.367646	+	1.07817i
$541$	−4.74621	−	26.9171i	−0.204055	−	1.15726i	−0.898919	−	0.438114i	$-0.855647\pi$
$541$	−4.74621	−	26.9171i	−0.204055	−	1.15726i	0.694864	−	0.719141i	$-0.255465\pi$
$542$	−20.8858	−	7.55554i	−0.897120	−	0.324538i
$543$	−33.0443	+	57.2344i	−1.41807	+	2.45616i
$544$	−2.39988	+	4.25227i	−0.102894	+	0.182315i
$545$	−12.8330	−	7.83187i	−0.549705	−	0.335480i
$546$	11.0140	−	63.1866i	0.471357	−	2.70414i
$547$	6.21084	−	17.0641i	0.265556	−	0.729610i	−0.733212	−	0.680000i	$-0.761980\pi$
$547$	6.21084	−	17.0641i	0.265556	−	0.729610i	0.998769	−	0.0496104i	$-0.0157980\pi$
$548$	20.0396	+	3.45271i	0.856051	+	0.147492i
$549$	−3.90001	+	22.1181i	−0.166449	+	0.943977i
$550$	4.20687	+	32.7427i	0.179382	+	1.39615i
$551$	−19.2200	+	19.0147i	−0.818798	+	0.810055i
$552$	−35.0110	+	0.205566i	−1.49017	+	0.00874946i
$553$	−2.83566	+	16.0818i	−0.120585	+	0.683869i
$554$	20.3153	−	7.43924i	0.863116	−	0.316063i
$555$	−0.574906	+	23.6019i	−0.0244034	+	1.00184i
$556$	−1.54263	+	1.85312i	−0.0654223	+	0.0785899i
$557$	30.0001	+	35.7528i	1.27115	+	1.51489i	0.750020	+	0.661415i	$0.230044\pi$
$557$	30.0001	+	35.7528i	1.27115	+	1.51489i	0.521127	+	0.853479i	$0.325512\pi$
$558$	−0.121780	−	62.2234i	−0.00515534	−	2.63413i
$559$	−0.325910	+	0.564493i	−0.0137845	+	0.0238755i
$560$	−30.7338	−	0.507926i	−1.29874	−	0.0214638i
$561$	−11.2820	+	1.98932i	−0.476326	+	0.0839892i
$562$	−13.1484	−	22.6710i	−0.554630	−	0.956320i
$563$	−19.0270	+	10.9853i	−0.801893	+	0.462973i	−0.844133	−	0.536134i	$-0.819884\pi$
$563$	−19.0270	+	10.9853i	−0.801893	+	0.462973i	0.0422394	+	0.999108i	$0.486551\pi$
$564$	7.09745	−	19.7402i	0.298857	−	0.831211i
$565$	5.07913	−	4.05529i	0.213681	−	0.170607i
$566$	10.4751	+	12.4343i	0.440302	+	0.522651i
$567$	−4.16258	−	3.49282i	−0.174812	−	0.146684i
$568$	−6.07960	−	1.03523i	−0.255094	−	0.0434373i
$569$			37.1428i			1.55711i	0.627579	+	0.778553i	$0.284046\pi$
$569$			37.1428i			1.55711i	−0.627579	+	0.778553i	$0.715954\pi$
$570$	38.9277	+	4.49773i	1.63050	+	0.188389i
$571$			26.5171i			1.10971i	0.831948	+	0.554854i	$0.187226\pi$
$571$			26.5171i			1.10971i	−0.831948	+	0.554854i	$0.812774\pi$
$572$	14.9840	+	40.6720i	0.626511	+	1.70058i
$573$	21.3541	+	17.9182i	0.892081	+	0.748545i
$574$	37.7544	−	31.8058i	1.57584	−	1.32755i
$575$	−11.7905	+	18.3018i	−0.491698	+	0.763237i
$576$	30.8357	−	26.4974i	1.28482	−	1.10406i
$577$	19.8642	−	11.4686i	0.826956	−	0.477443i	−0.0258536	−	0.999666i	$-0.508230\pi$
$577$	19.8642	−	11.4686i	0.826956	−	0.477443i	0.852809	+	0.522223i	$0.174897\pi$
$578$	19.8856	−	11.5329i	0.827134	−	0.479707i
$579$	−50.5638	+	8.91576i	−2.10136	+	0.370527i
$580$	23.7340	+	14.3575i	0.985500	+	0.596161i
$581$	11.0975	−	19.2214i	0.460400	−	0.797437i
$582$	73.7673	−	0.144372i	3.05775	−	0.00598443i
$583$	−2.93147	−	3.49359i	−0.121409	−	0.144690i
$584$	10.6299	−	3.93980i	0.439869	−	0.163030i
$585$	52.7369	+	1.28459i	2.18040	+	0.0531112i
$586$	10.6166	+	28.9922i	0.438567	+	1.19766i
$587$	−6.60964	+	37.4852i	−0.272809	+	1.54718i	0.473027	+	0.881048i	$0.343161\pi$
$587$	−6.60964	+	37.4852i	−0.272809	+	1.54718i	−0.745836	+	0.666130i	$0.767950\pi$
$588$	23.6324	−	13.7678i	0.974583	−	0.567774i
$589$	−34.1160	−	16.1320i	−1.40572	−	0.664709i
$590$	−26.9576	−	5.37846i	−1.10983	−	0.221428i
$591$	4.37205	−	24.7951i	0.179842	−	1.01993i
$592$	13.9195	−	5.19003i	0.572087	−	0.213309i
$593$	−2.34352	+	6.43876i	−0.0962367	+	0.264408i	−0.978465	−	0.206414i	$-0.933821\pi$
$593$	−2.34352	+	6.43876i	−0.0962367	+	0.264408i	0.882228	+	0.470822i	$0.156043\pi$
$594$	38.4995	+	6.71083i	1.57965	+	0.275349i
$595$	−5.66181	−	3.45535i	−0.232112	−	0.141656i
$596$	15.5578	−	27.1922i	0.637273	−	1.11383i
$597$	−6.38929	+	11.0666i	−0.261496	+	0.452925i
$598$	−9.72408	+	26.8803i	−0.397647	+	1.09922i
$599$	4.92120	+	27.9095i	0.201075	+	1.14035i	0.903498	+	0.428593i	$0.140990\pi$
$599$	4.92120	+	27.9095i	0.201075	+	1.14035i	−0.702423	+	0.711760i	$0.747898\pi$
$600$	−5.27954	−	39.8565i	−0.215536	−	1.62713i
$601$	24.7723	−	14.3023i	1.01048	−	0.583403i	0.0991509	−	0.995072i	$-0.468387\pi$
$601$	24.7723	−	14.3023i	1.01048	−	0.583403i	0.911333	+	0.411669i	$0.135054\pi$
$602$	−0.671825	+	0.119817i	−0.0273815	+	0.00488338i
$603$	−4.27747	−	11.7522i	−0.174192	−	0.478588i
$604$	−7.47549	−	41.4463i	−0.304173	−	1.68642i
$605$	22.4761	+	8.80620i	0.913784	+	0.358023i
$606$	−2.50255	−	2.09155i	−0.101659	−	0.0849636i
$607$		−	10.8352i		−	0.439787i	−0.975524	−	0.219893i	$-0.929429\pi$
$607$		−	10.8352i		−	0.439787i	0.975524	−	0.219893i	$-0.0705709\pi$
$608$	−6.48703	−	23.7890i	−0.263084	−	0.964773i
$609$	−60.5987			−2.45558
$610$	5.07267	−	13.0220i	0.205387	−	0.527245i
$611$	−13.1199	−	11.0089i	−0.530775	−	0.445373i
$612$	8.63391	−	1.55726i	0.349005	−	0.0629485i
$613$	−1.27385	−	3.49987i	−0.0514503	−	0.141359i	0.911306	−	0.411731i	$-0.135076\pi$
$613$	−1.27385	−	3.49987i	−0.0514503	−	0.141359i	−0.962756	+	0.270372i	$0.912853\pi$
$614$	−6.85846	−	38.4560i	−0.276785	−	1.55196i
$615$	48.4379	+	42.6968i	1.95320	+	1.72170i
$616$	−22.4586	+	39.4324i	−0.904884	+	1.58877i
$617$	−31.4246	+	5.54100i	−1.26511	+	0.223072i	−0.765644	−	0.643264i	$-0.777580\pi$
$617$	−31.4246	+	5.54100i	−1.26511	+	0.223072i	−0.499461	+	0.866336i	$0.666469\pi$
$618$	−6.49490	+	17.9539i	−0.261263	+	0.722210i
$619$	6.35552	+	3.66936i	0.255450	+	0.147484i	0.622257	−	0.782813i	$-0.286216\pi$
$619$	6.35552	+	3.66936i	0.255450	+	0.147484i	−0.366807	+	0.930297i	$0.619549\pi$
$620$	−7.50123	+	37.9846i	−0.301257	+	1.52550i
$621$	16.5664	+	19.7431i	0.664787	+	0.792262i
$622$	1.77825	−	10.2017i	0.0713013	−	0.409050i
$623$	−9.69936	+	26.6488i	−0.388597	+	1.06766i
$624$	−18.4425	−	49.4621i	−0.738291	−	1.98007i
$625$	−22.5493	−	10.7948i	−0.901972	−	0.431794i
$626$	−18.7490	+	32.6214i	−0.749359	+	1.30381i
$627$	33.4367	−	47.2112i	1.33533	−	1.88543i
$628$	24.0764	−	14.0265i	0.960753	−	0.559717i
$629$	3.15697	+	0.556659i	0.125877	+	0.0221954i
$630$	34.5444	+	43.0926i	1.37628	+	1.71685i
$631$	−6.73065	+	18.4923i	−0.267943	+	0.736168i	0.730630	+	0.682773i	$0.239226\pi$
$631$	−6.73065	+	18.4923i	−0.267943	+	0.736168i	−0.998573	+	0.0533944i	$0.982996\pi$
$632$	4.67082	+	12.6022i	0.185795	+	0.501290i
$633$	24.1973	+	28.8372i	0.961754	+	1.14617i
$634$	−0.0468854	−	23.9561i	−0.00186206	−	0.951420i
$635$	15.3736	+	3.09856i	0.610081	+	0.122963i
$636$	3.58683	+	4.24079i	0.142227	+	0.168158i
$637$	−3.87757	−	21.9908i	−0.153635	−	0.871308i
$638$	35.4250	−	20.5452i	1.40249	−	0.813392i
$639$	5.54047	+	9.59637i	0.219178	+	0.379627i
$640$	−22.0424	+	12.4150i	−0.871303	+	0.490745i
$641$	2.71749	+	7.46623i	0.107334	+	0.294898i	0.981719	−	0.190334i	$-0.0609572\pi$
$641$	2.71749	+	7.46623i	0.107334	+	0.294898i	−0.874385	+	0.485233i	$0.838735\pi$
$642$	−3.21348	−	3.81449i	−0.126826	−	0.150546i
$643$	7.22956	+	6.06632i	0.285106	+	0.239232i	0.774113	−	0.633047i	$-0.218196\pi$
$643$	7.22956	+	6.06632i	0.285106	+	0.239232i	−0.489007	+	0.872280i	$0.662641\pi$
$644$	−28.0821	+	10.3457i	−1.10659	+	0.407678i
$645$	−0.284771	−	0.845954i	−0.0112129	−	0.0333094i
$646$	1.39466	−	5.13482i	0.0548721	−	0.202027i
$647$	36.5463			1.43678			0.718391	−	0.695640i	$-0.244879\pi$
$647$	36.5463			1.43678			0.718391	+	0.695640i	$0.244879\pi$
$648$	−4.40876	−	0.750720i	−0.173192	−	0.0294911i
$649$	−26.0861	+	31.0883i	−1.02397	+	1.22032i
$650$	−32.0245	−	7.20446i	−1.25610	−	0.282582i
$651$	−28.9296	−	79.4835i	−1.13384	−	3.11520i
$652$	−27.8761	−	10.0227i	−1.09171	−	0.392518i
$653$	−37.8679	+	21.8631i	−1.48189	+	0.855567i	−0.999789	−	0.0205502i	$-0.993458\pi$
$653$	−37.8679	+	21.8631i	−1.48189	+	0.855567i	−0.482097	+	0.876118i	$0.660125\pi$
$654$	23.3834	−	13.5615i	0.914362	−	0.530296i
$655$	−1.73991	+	0.948811i	−0.0679838	+	0.0370731i
$656$	13.5968	−	38.2869i	0.530867	−	1.49485i
$657$	−17.6403	−	10.1846i	−0.688214	−	0.397340i
$658$	−0.0350933	−	17.9310i	−0.00136808	−	0.699021i
$659$	7.93151	−	6.65533i	0.308968	−	0.259255i	−0.475097	−	0.879933i	$-0.657587\pi$
$659$	7.93151	−	6.65533i	0.308968	−	0.259255i	0.784065	+	0.620678i	$0.213143\pi$
$660$	−55.3493	−	21.4365i	−2.15447	−	0.834413i
$661$	−2.38897	+	6.56364i	−0.0929201	+	0.255296i	−0.977442	−	0.211202i	$-0.932262\pi$
$661$	−2.38897	+	6.56364i	−0.0929201	+	0.255296i	0.884522	+	0.466498i	$0.154484\pi$
$662$	9.50103	+	25.9458i	0.369268	+	1.00841i
$663$	1.97806	−	11.2181i	0.0768213	−	0.435675i
$664$	−0.107252	−	18.2667i	−0.00416220	−	0.708887i
$665$	32.5979	−	7.70408i	1.26409	−	0.298751i
$666$	−23.1422	−	13.3008i	−0.896742	−	0.515397i
$667$	26.5968	+	4.68974i	1.02983	+	0.181587i
$668$	−28.2901	−	4.87421i	−1.09458	−	0.188589i
$669$	15.3013	+	5.56921i	0.591581	+	0.215318i
$670$	1.17937	+	7.69218i	0.0455632	+	0.297175i
$671$	−13.2620	−	15.8050i	−0.511973	−	0.610145i
$672$	27.1639	−	48.1308i	1.04787	−	1.85669i
$673$	−7.96086	+	13.7886i	−0.306869	+	0.531512i	−0.977676	−	0.210120i	$-0.932615\pi$
$673$	−7.96086	+	13.7886i	−0.306869	+	0.531512i	0.670807	+	0.741632i	$0.265948\pi$
$674$	14.5859	−	40.3197i	0.561827	−	1.55306i
$675$	−20.1048	+	21.7183i	−0.773836	+	0.835938i
$676$	−17.0988	+	0.0669294i	−0.657645	+	0.00257421i
$677$	−6.37809	−	11.0472i	−0.245130	−	0.424578i	0.717038	−	0.697034i	$-0.245497\pi$
$677$	−6.37809	−	11.0472i	−0.245130	−	0.424578i	−0.962168	+	0.272456i	$0.912164\pi$
$678$	2.05178	+	11.5045i	0.0787982	+	0.441829i
$679$	59.2522	−	21.5661i	2.27389	−	0.827629i
$680$	−5.45814	−	0.100890i	−0.209310	−	0.00386897i
$681$	27.4856	+	23.0631i	1.05325	+	0.883782i
$682$	43.8596	+	36.6566i	1.67947	+	1.40365i
$683$			21.5440i			0.824358i	0.911103	+	0.412179i	$0.135232\pi$
$683$			21.5440i			0.824358i	−0.911103	+	0.412179i	$0.864768\pi$
$684$	−25.4647	+	36.2551i	−0.973666	+	1.38625i
$685$	7.25332	+	21.5470i	0.277135	+	0.823270i
$686$	−6.82470	+	8.16576i	−0.260568	+	0.311770i
$687$	14.8644	−	17.7148i	0.567114	−	0.675860i
$688$	−0.427414	+	0.364382i	−0.0162950	+	0.0138920i
$689$	4.26126	−	1.55097i	0.162341	−	0.0590873i
$690$	−18.8080	−	34.3297i	−0.716009	−	1.30691i
$691$	−44.4006	+	25.6347i	−1.68908	+	0.975190i	−0.733854	+	0.679307i	$0.762281\pi$
$691$	−44.4006	+	25.6347i	−1.68908	+	0.975190i	−0.955224	+	0.295883i	$0.904386\pi$
$692$	17.5185	−	0.0685724i	0.665954	−	0.00260673i
$693$	80.2983	−	14.1588i	3.05028	−	0.537847i
$694$	−2.32533	+	6.42789i	−0.0882681	+	0.243999i
$695$	−2.64264	−	0.532627i	−0.100241	−	0.0202037i
$696$	−43.0454	+	25.1904i	−1.63163	+	0.954840i
$697$	6.71623	−	5.63558i	0.254395	−	0.213463i
$698$	−7.10703	−	1.23882i	−0.269005	−	0.0468902i
$699$	8.75148	+	3.18528i	0.331011	+	0.120478i
$700$	−15.8331	−	30.5015i	−0.598436	−	1.15285i
$701$	−1.41289	+	8.01288i	−0.0533640	+	0.302642i	−0.999795	−	0.0202649i	$-0.993549\pi$
$701$	−1.41289	+	8.01288i	−0.0533640	+	0.302642i	0.946431	+	0.322907i	$0.104660\pi$
$702$	−19.3634	+	33.6905i	−0.730826	+	1.27157i
$703$	−13.3105	+	9.21402i	−0.502015	+	0.347513i
$704$	0.438567	+	37.3460i	0.0165291	+	1.40753i
$705$	23.1894	−	3.50898i	0.873362	−	0.132156i
$706$	−30.4523	+	11.1513i	−1.14609	+	0.419684i
$707$	−2.61973	−	0.953504i	−0.0985252	−	0.0358602i
$708$	31.6215	−	37.9860i	1.18841	−	1.42760i
$709$	24.1744	−	20.2847i	0.907888	−	0.761808i	−0.0638282	−	0.997961i	$-0.520331\pi$
$709$	24.1744	−	20.2847i	0.907888	−	0.761808i	0.971716	+	0.236153i	$0.0758865\pi$
$710$	−2.21255	−	6.53040i	−0.0830355	−	0.245082i
$711$	12.0743	−	20.9134i	0.452823	−	0.784313i
$712$	4.18788	+	22.9615i	0.156948	+	0.860518i
$713$	6.54600	+	37.1242i	0.245150	+	1.39031i
$714$	10.3165	−	5.98321i	0.386087	−	0.223916i
$715$	−32.0445	+	36.3533i	−1.19840	+	1.35954i
$716$	4.66410	+	1.67695i	0.174306	+	0.0626705i
$717$	19.7388	−	7.18435i	0.737160	−	0.268304i
$718$	−0.968042	+	0.815517i	−0.0361270	+	0.0304348i
$719$	23.9085	−	28.4930i	0.891637	−	1.06261i	−0.106032	−	0.994363i	$-0.533815\pi$
$719$	23.9085	−	28.4930i	0.891637	−	1.06261i	0.997668	−	0.0682484i	$-0.0217411\pi$
$720$	42.4513	+	16.2503i	1.58207	+	0.605615i
$721$			16.3199i			0.607785i
$722$	13.2302	+	23.3872i	0.492378	+	0.870381i
$723$	−38.3559			−1.42647
$724$	16.0727	+	43.6273i	0.597338	+	1.62140i
$725$	−1.50996	+	30.9761i	−0.0560784	+	1.15042i
$726$	−33.1942	+	27.9641i	−1.23195	+	1.03785i
$727$	−45.1521	+	16.4340i	−1.67460	+	0.609505i	−0.992554	−	0.121804i	$-0.961132\pi$
$727$	−45.1521	+	16.4340i	−1.67460	+	0.609505i	−0.682046	+	0.731309i	$0.738910\pi$
$728$	−29.2067	−	34.3950i	−1.08247	−	1.27476i
$729$	−21.2232	−	36.7597i	−0.786046	−	1.36147i
$730$	9.52445	+	8.36249i	0.352516	+	0.309510i
$731$	−0.119358	+	0.0210460i	−0.00441461	+	0.000778414i
$732$	16.2268	+	19.1853i	0.599759	+	0.709110i
$733$	−9.72122	−	5.61255i	−0.359062	−	0.207304i	0.309608	−	0.950864i	$-0.399802\pi$
$733$	−9.72122	−	5.61255i	−0.359062	−	0.207304i	−0.668669	+	0.743560i	$0.733136\pi$
$734$	0.0829641	+	42.3906i	0.00306226	+	1.56467i
$735$	26.1017	+	15.9296i	0.962775	+	0.587574i
$736$	−15.6471	+	19.0224i	−0.576759	+	0.701176i
$737$	10.7961	+	3.92944i	0.397678	+	0.144743i
$738$	−68.5509	+	25.1025i	−2.52339	+	0.924036i
$739$	−29.3362	−	5.17276i	−1.07915	−	0.190283i	−0.394310	−	0.918977i	$-0.629016\pi$
$739$	−29.3362	−	5.17276i	−1.07915	−	0.190283i	−0.684839	+	0.728694i	$0.740127\pi$
$740$	12.5024	+	10.9339i	0.459598	+	0.401938i
$741$	32.7415	+	47.2981i	1.20279	+	1.73754i
$742$	4.11623	+	2.36578i	0.151112	+	0.0868504i
$743$	−25.3989	−	4.47851i	−0.931794	−	0.164300i	−0.312910	−	0.949783i	$-0.601304\pi$
$743$	−25.3989	−	4.47851i	−0.931794	−	0.164300i	−0.618884	+	0.785482i	$0.712415\pi$
$744$	−53.5904	−	44.4341i	−1.96472	−	1.62903i
$745$	35.0157	+	0.852928i	1.28287	+	0.0312489i
$746$	34.1807	+	5.95804i	1.25145	+	0.218139i
$747$	−25.1430	+	21.0975i	−0.919935	+	0.771917i
$748$	−4.00236	+	6.99538i	−0.146341	+	0.255776i
$749$	−3.69217	−	2.13168i	−0.134909	−	0.0778898i
$750$	36.3995	−	26.3741i	1.32912	−	0.963045i
$751$	−5.71418	−	32.4067i	−0.208513	−	1.18254i	−0.891814	−	0.452402i	$-0.850567\pi$
$751$	−5.71418	−	32.4067i	−0.208513	−	1.18254i	0.683301	−	0.730137i	$-0.260544\pi$
$752$	−7.47868	−	12.7224i	−0.272719	−	0.463938i
$753$	−32.1949	−	55.7633i	−1.17325	−	2.03213i
$754$	7.14938	+	40.0872i	0.260365	+	1.45989i
$755$	36.7963	−	29.3790i	1.33916	−	1.06921i
$756$	−40.0372	+	7.22133i	−1.45614	+	0.262637i
$757$	−7.90278	+	9.41817i	−0.287231	+	0.342309i	−0.890295	−	0.455384i	$-0.849502\pi$
$757$	−7.90278	+	9.41817i	−0.287231	+	0.342309i	0.603064	+	0.797693i	$0.293946\pi$
$758$	7.84689	−	9.38881i	0.285012	−	0.341017i
$759$	−57.7899			−2.09764
$760$	19.9529	−	19.0232i	0.723769	−	0.690043i
$761$	11.3331			0.410825			0.205413	−	0.978675i	$-0.434146\pi$
$761$	11.3331			0.410825			0.205413	+	0.978675i	$0.434146\pi$
$762$	−18.0828	+	21.6360i	−0.655069	+	0.783791i
$763$	14.8522	−	17.7001i	0.537685	−	0.640788i
$764$	19.2994	−	3.48096i	0.698229	−	0.125937i
$765$	6.12010	+	7.66525i	0.221273	+	0.277138i
$766$	7.37922	+	41.3760i	0.266622	+	1.49497i
$767$	−20.1765	−	34.9467i	−0.728532	−	1.26185i
$768$	−0.712153	−	45.4808i	−0.0256976	−	1.64115i
$769$	8.63211	+	48.9551i	0.311282	+	1.76537i	0.592351	+	0.805680i	$0.298200\pi$
$769$	8.63211	+	48.9551i	0.311282	+	1.76537i	−0.281069	+	0.959687i	$0.590689\pi$
$770$	−50.7231	−	1.13621i	−1.82793	−	0.0409462i
$771$	8.80279	+	5.08229i	0.317025	+	0.183034i
$772$	−17.9378	+	31.3520i	−0.645596	+	1.12838i
$773$	−28.8224	+	24.1849i	−1.03667	+	0.869870i	−0.991630	−	0.129115i	$-0.958786\pi$
$773$	−28.8224	+	24.1849i	−1.03667	+	0.869870i	−0.0450410	+	0.998985i	$0.514342\pi$
$774$	0.994181	+	0.173295i	0.0357351	+	0.00622898i
$775$	−41.3502	+	12.8074i	−1.48534	+	0.460054i
$776$	33.1241	−	39.9498i	1.18909	−	1.43411i
$777$	−35.7333	−	6.30074i	−1.28192	−	0.226038i
$778$	7.88203	+	4.53015i	0.282584	+	0.162414i
$779$	−4.09552	+	44.0852i	−0.146737	+	1.57952i
$780$	38.8530	−	44.4266i	1.39116	−	1.59073i
$781$	−10.0247	−	1.76763i	−0.358713	−	0.0632507i
$782$	−4.99098	+	1.82764i	−0.178477	+	0.0653562i
$783$	34.4995	+	12.5568i	1.23291	+	0.448743i
$784$	3.19275	−	18.9744i	0.114027	−	0.677659i
$785$	26.5921	+	16.2289i	0.949113	+	0.579236i
$786$	−0.00697381	−	3.56328i	−0.000248747	−	0.127098i
$787$	−4.36151	−	2.51812i	−0.155471	−	0.0897612i	0.420246	−	0.907410i	$-0.361944\pi$
$787$	−4.36151	−	2.51812i	−0.155471	−	0.0897612i	−0.575717	+	0.817649i	$0.695277\pi$
$788$	−11.4385	−	13.5240i	−0.407480	−	0.481773i
$789$	−20.5101	+	3.61648i	−0.730178	+	0.128750i
$790$	−9.91411	+	11.2917i	−0.352728	+	0.401739i
$791$	4.99450	+	8.65074i	0.177584	+	0.307585i
$792$	51.1530	−	43.4368i	1.81764	−	1.54346i
$793$	19.2779	−	7.01659i	0.684579	−	0.249166i
$794$	−8.10781	+	6.83035i	−0.287736	+	0.242400i
$795$	−2.26536	+	5.78189i	−0.0803439	+	0.205062i
$796$	3.10774	+	8.43557i	0.110151	+	0.298991i
$797$	7.59518			0.269035			0.134517	−	0.990911i	$-0.457052\pi$
$797$	7.59518			0.269035			0.134517	+	0.990911i	$0.457052\pi$
$798$	−15.7859	+	58.1202i	−0.558816	+	2.05743i
$799$		−	3.18455i		−	0.112661i
$800$	−23.9260	−	15.0846i	−0.845914	−	0.533320i
$801$	26.9568	−	32.1259i	0.952472	−	1.13511i
$802$	17.1566	−	14.4534i	0.605822	−	0.510369i
$803$	17.5835	−	6.39988i	0.620509	−	0.225847i
$804$	−13.1670	−	4.73411i	−0.464364	−	0.166959i
$805$	−25.1002	−	22.1252i	−0.884668	−	0.779812i
$806$	−49.1668	+	28.5149i	−1.73183	+	1.00439i
$807$	−9.78115	−	55.4717i	−0.344313	−	1.95269i
$808$	−2.25725	+	0.411694i	−0.0794098	+	0.0144833i
$809$	17.2282	−	29.8401i	0.605711	−	1.04912i	−0.386228	−	0.922403i	$-0.626222\pi$
$809$	17.2282	−	29.8401i	0.605711	−	1.04912i	0.991939	−	0.126718i	$-0.0404444\pi$
$810$	−1.60448	−	4.73567i	−0.0563757	−	0.166394i
$811$	37.9039	−	31.8052i	1.33099	−	1.11683i	0.347141	−	0.937813i	$-0.387152\pi$
$811$	37.9039	−	31.8052i	1.33099	−	1.11683i	0.983846	−	0.179018i	$-0.0572920\pi$
$812$	−27.2751	+	32.7648i	−0.957168	+	1.14982i
$813$	41.9554	+	15.2705i	1.47144	+	0.535561i
$814$	23.0253	−	8.43158i	0.807035	−	0.295527i
$815$	−4.95521	−	32.7469i	−0.173574	−	1.14707i
$816$	4.84103	−	8.53859i	0.169470	−	0.298910i
$817$	0.353744	−	0.499470i	0.0123759	−	0.0174743i
$818$	−12.0767	+	21.0122i	−0.422250	+	0.734676i
$819$	−14.0786	+	79.8436i	−0.491945	+	2.78996i
$820$	44.8870	−	6.97207i	1.56752	−	0.243475i
$821$	−8.44117	−	3.07233i	−0.294599	−	0.107225i	0.190493	−	0.981689i	$-0.438991\pi$
$821$	−8.44117	−	3.07233i	−0.294599	−	0.107225i	−0.485091	+	0.874463i	$0.661214\pi$
$822$	−40.2707	−	7.01957i	−1.40460	−	0.244835i
$823$	−8.79025	+	7.37589i	−0.306409	+	0.257108i	−0.783006	−	0.622014i	$-0.786315\pi$
$823$	−8.79025	+	7.37589i	−0.306409	+	0.257108i	0.476597	+	0.879122i	$0.341870\pi$
$824$	6.78405	+	11.5926i	0.236334	+	0.403847i
$825$	−8.32795	−	65.8368i	−0.289942	−	2.29214i
$826$	14.3718	−	39.7281i	0.500061	−	1.38232i
$827$	13.4169	−	2.36577i	0.466552	−	0.0822657i	0.0645699	−	0.997913i	$-0.479432\pi$
$827$	13.4169	−	2.36577i	0.466552	−	0.0822657i	0.401982	+	0.915647i	$0.368321\pi$
$828$	44.2561	−	0.173231i	1.53800	−	0.00602018i
$829$	9.34503	−	5.39535i	0.324566	−	0.187388i	−0.328860	−	0.944379i	$-0.606664\pi$
$829$	9.34503	−	5.39535i	0.324566	−	0.187388i	0.653426	+	0.756990i	$0.273331\pi$
$830$	17.9112	−	9.81293i	0.621708	−	0.340612i
$831$	−40.8677	+	14.8746i	−1.41769	+	0.515996i
$832$	−35.0442	−	12.2910i	−1.21494	−	0.426113i
$833$	2.66888	−	3.18064i	0.0924711	−	0.110203i
$834$	3.10834	−	3.71913i	0.107633	−	0.128783i
$835$	−10.2396	−	30.4181i	−0.354355	−	1.05266i
$836$	−10.4767	−	39.3282i	−0.362344	−	1.36019i
$837$			51.2454i			1.77130i
$838$	6.57222	+	5.49286i	0.227034	+	0.189748i
$839$	−30.4152	−	25.5214i	−1.05005	−	0.881097i	−0.0569512	−	0.998377i	$-0.518138\pi$
$839$	−30.4152	−	25.5214i	−1.05005	−	0.881097i	−0.993099	+	0.117280i	$0.962582\pi$
$840$	61.7799	+	1.14196i	2.13161	+	0.0394015i
$841$	8.90072	−	3.23960i	0.306921	−	0.111710i
$842$	2.51156	+	14.0825i	0.0865539	+	0.485316i
$843$	26.3420	+	45.6257i	0.907266	+	1.57143i
$844$	26.4828	−	0.103661i	0.911576	−	0.00356817i
$845$	−9.15259	−	16.7838i	−0.314859	−	0.577380i
$846$	−9.02034	+	24.9349i	−0.310126	+	0.857280i
$847$	−18.5501	+	32.1298i	−0.637390	+	1.10399i
$848$	3.90734	−	0.0305893i	0.134178	−	0.00105044i
$849$	−21.0084	−	25.0369i	−0.721008	−	0.859264i
$850$	−2.80136	−	5.42257i	−0.0960859	−	0.185993i
$851$	15.1957	+	5.53079i	0.520903	+	0.189593i
$852$	12.2173	+	2.10497i	0.418558	+	0.0721149i
$853$	−17.2293	−	3.03799i	−0.589921	−	0.104019i	−0.129284	−	0.991608i	$-0.541268\pi$
$853$	−17.2293	−	3.03799i	−0.589921	−	0.104019i	−0.460637	+	0.887589i	$0.652379\pi$
$854$	18.6218	+	10.7028i	0.637225	+	0.366241i
$855$	−49.1952	−	5.78165i	−1.68244	−	0.197728i
$856$	−3.50880	+	0.0206018i	−0.119928	+	0.000704154i
$857$	6.35083	−	36.0173i	0.216940	−	1.23033i	−0.660568	−	0.750766i	$-0.729684\pi$
$857$	6.35083	−	36.0173i	0.216940	−	1.23033i	0.877508	−	0.479562i	$-0.159204\pi$
$858$	−29.9612	−	81.8190i	−1.02286	−	2.79325i
$859$	6.49064	−	17.8329i	0.221458	−	0.608450i	−0.778355	−	0.627825i	$-0.783945\pi$
$859$	6.49064	−	17.8329i	0.221458	−	0.608450i	0.999812	+	0.0193748i	$0.00616757\pi$
$860$	−0.585567	−	0.226787i	−0.0199677	−	0.00773336i
$861$	−76.0200	+	63.7884i	−2.59075	+	2.17390i
$862$	−0.0728424	−	37.2189i	−0.00248102	−	1.26768i
$863$	48.1980	+	27.8271i	1.64068	+	0.947247i	0.980592	+	0.196057i	$0.0628139\pi$
$863$	48.1980	+	27.8271i	1.64068	+	0.947247i	0.660087	+	0.751189i	$0.270519\pi$
$864$	−25.4379	+	21.7727i	−0.865416	+	0.740722i
$865$	9.37727	+	17.1958i	0.318837	+	0.584675i
$866$	−38.2650	+	22.1923i	−1.30030	+	0.754125i
$867$	−40.0201	+	23.1056i	−1.35915	+	0.784707i
$868$	−55.9965	−	20.1332i	−1.90065	−	0.683365i
$869$	7.58734	+	20.8461i	0.257383	+	0.707154i
$870$	−47.6542	−	28.9551i	−1.61563	−	0.981671i
$871$	−7.34312	+	8.75119i	−0.248812	+	0.296523i
$872$	3.19222	−	18.7469i	0.108102	−	0.634852i
$873$	−93.2456			−3.15589
$874$	11.4264	−	24.2873i	0.386503	−	0.821531i
$875$	21.5889	−	31.7837i	0.729839	−	1.07449i
$876$	−21.3840	+	7.87808i	−0.722500	+	0.266176i
$877$	−6.45897	−	5.41972i	−0.218104	−	0.183011i	0.527189	−	0.849748i	$-0.323246\pi$
$877$	−6.45897	−	5.41972i	−0.218104	−	0.183011i	−0.745293	+	0.666737i	$0.767690\pi$
$878$	13.6849	+	16.2444i	0.461843	+	0.548221i
$879$	−21.2277	−	58.3226i	−0.715992	−	1.96717i
$880$	−36.5027	+	20.2781i	−1.23051	+	0.683574i
$881$	15.9826	+	27.6827i	0.538468	+	0.932654i	0.998987	+	0.0450041i	$0.0143301\pi$
$881$	15.9826	+	27.6827i	0.538468	+	0.932654i	−0.460519	+	0.887650i	$0.652337\pi$
$882$	−29.9065	+	17.3447i	−1.00700	+	0.584025i
$883$	−0.288800	−	1.63787i	−0.00971891	−	0.0551187i	0.979563	−	0.201140i	$-0.0644645\pi$
$883$	−0.288800	−	1.63787i	−0.00971891	−	0.0551187i	−0.989282	+	0.146021i	$0.953353\pi$
$884$	−5.17515	−	6.11870i	−0.174059	−	0.205794i
$885$	54.1698	+	10.9180i	1.82090	+	0.367004i
$886$	−0.0380353	−	19.4342i	−0.00127782	−	0.652905i
$887$	34.7629	+	41.4288i	1.16722	+	1.39104i	0.904663	+	0.426128i	$0.140123\pi$
$887$	34.7629	+	41.4288i	1.16722	+	1.39104i	0.262561	+	0.964915i	$0.415433\pi$
$888$	−28.0017	+	10.3784i	−0.939677	+	0.348276i
$889$	−8.24362	+	22.6492i	−0.276482	+	0.759629i
$890$	−20.3607	+	16.3218i	−0.682493	+	0.547108i
$891$	−7.26965	−	1.28184i	−0.243543	−	0.0429431i
$892$	9.89818	−	5.76649i	0.331416	−	0.193076i
$893$	11.3104	+	11.4325i	0.378487	+	0.382572i
$894$	−31.3817	+	54.6012i	−1.04956	+	1.82614i
$895$	0.829083	+	5.47906i	0.0277132	+	0.183145i
$896$	−13.7973	−	36.3504i	−0.460935	−	1.21438i
$897$	19.6534	−	53.9972i	0.656207	−	1.80291i
$898$	−0.551115	+	3.16170i	−0.0183909	+	0.105507i
$899$	34.5175	+	41.1364i	1.15122	+	1.37197i
$900$	6.57498	+	50.3935i	0.219166	+	1.67978i
$901$	0.730220	+	0.421593i	0.0243272	+	0.0140453i
$902$	22.8135	−	63.0632i	0.759605	−	2.09978i
$903$	1.35099	−	0.238217i	0.0449582	−	0.00792735i
$904$	7.14381	+	4.06874i	0.237600	+	0.135324i
$905$	−34.3729	+	38.9948i	−1.14260	+	1.29623i
$906$	14.8644	+	83.3459i	0.493836	+	2.76898i
$907$	−7.86501	−	21.6089i	−0.261153	−	0.717513i	−0.999090	−	0.0426434i	$-0.986422\pi$
$907$	−7.86501	−	21.6089i	−0.261153	−	0.717513i	0.737937	−	0.674870i	$-0.235800\pi$
$908$	24.8410	−	4.48046i	0.824376	−	0.148689i
$909$	3.15816	+	2.65001i	0.104750	+	0.0878954i
$910$	18.3117	−	47.0078i	0.607028	−	1.55829i
$911$	−10.5872			−0.350770			−0.175385	−	0.984500i	$-0.556117\pi$
$911$	−10.5872			−0.350770			−0.175385	+	0.984500i	$0.556117\pi$
$912$	12.9468	+	47.8469i	0.428712	+	1.58437i
$913$		−	30.1514i		−	0.997866i
$914$	−1.00832	−	0.842725i	−0.0333523	−	0.0278749i
$915$	−10.2485	+	26.1572i	−0.338804	+	0.864731i
$916$	−2.88770	−	16.0103i	−0.0954124	−	0.528994i
$917$	−1.04173	−	2.86214i	−0.0344010	−	0.0945161i
$918$	−7.11311	+	1.26859i	−0.234768	+	0.0418698i
$919$	35.0588	−	20.2412i	1.15648	−	0.667697i	0.206025	−	0.978547i	$-0.433947\pi$
$919$	35.0588	−	20.2412i	1.15648	−	0.667697i	0.950459	+	0.310850i	$0.100614\pi$
$920$	−27.0269	−	5.28236i	−0.891049	−	0.174154i
$921$	13.6358	+	77.3322i	0.449314	+	2.54818i
$922$	16.1583	−	44.6663i	0.532144	−	1.47100i
$923$	5.06086	−	8.76567i	0.166580	−	0.288526i
$924$	45.3021	−	79.1796i	1.49033	−	2.60482i
$925$	−4.11111	+	18.1087i	−0.135172	+	0.595410i
$926$	−14.8306	−	2.58511i	−0.487363	−	0.0849520i
$927$	8.25428	−	22.6784i	0.271106	−	0.744858i
$928$	−5.75439	+	34.6120i	−0.188897	+	1.13619i
$929$	10.1900	−	57.7905i	0.334324	−	1.89605i	−0.0994812	−	0.995039i	$-0.531718\pi$
$929$	10.1900	−	57.7905i	0.334324	−	1.89605i	0.433805	−	0.901007i	$-0.357171\pi$
$930$	15.2286	−	76.3281i	0.499366	−	2.50290i
$931$	1.71530	+	20.8973i	0.0562167	+	0.684882i
$932$	5.66121	−	3.29811i	0.185439	−	0.108033i
$933$	−3.61482	+	20.5007i	−0.118344	+	0.671162i
$934$	2.94602	+	8.04509i	0.0963966	+	0.263243i
$935$	−9.00803	−	0.219422i	−0.294594	−	0.00717586i
$936$	23.1898	+	62.5680i	0.757983	+	2.04510i
$937$	−18.7023	−	22.2886i	−0.610978	−	0.728135i	0.368513	−	0.929623i	$-0.379867\pi$
$937$	−18.7023	−	22.2886i	−0.610978	−	0.728135i	−0.979491	+	0.201487i	$0.935423\pi$
$938$	−11.9602	+	0.0234078i	−0.390515	+	0.000764291i
$939$	37.8180	−	65.5027i	1.23414	−	2.13760i
$940$	8.54013	−	14.1175i	0.278548	−	0.460462i
$941$	39.0059	−	6.87780i	1.27156	−	0.224210i	0.503166	−	0.864190i	$-0.332168\pi$
$941$	39.0059	−	6.87780i	1.27156	−	0.224210i	0.768392	+	0.639980i	$0.221057\pi$
$942$	−48.4542	+	28.1017i	−1.57872	+	0.915601i
$943$	38.3018	−	22.1136i	1.24728	−	0.720116i
$944$	−6.30581	−	34.1945i	−0.205237	−	1.11294i
$945$	−28.3802	−	35.5453i	−0.923207	−	1.15629i
$946$	−0.709004	+	0.597294i	−0.0230517	+	0.0194197i
$947$	−33.1194	−	27.7904i	−1.07623	−	0.903068i	−0.0806320	−	0.996744i	$-0.525694\pi$
$947$	−33.1194	−	27.7904i	−1.07623	−	0.903068i	−0.995603	+	0.0936757i	$0.970138\pi$
$948$	−9.33982	−	25.3518i	−0.303343	−	0.823387i
$949$			18.6060i			0.603977i
$950$	29.3158	+	9.51745i	0.951131	+	0.308787i
$951$			48.1575i			1.56161i
$952$	1.40838	−	8.27100i	0.0456458	−	0.268065i
$953$	35.6060	+	29.8770i	1.15339	+	0.967811i	0.999793	−	0.0203229i	$-0.00646942\pi$
$953$	35.6060	+	29.8770i	1.15339	+	0.967811i	0.153598	+	0.988133i	$0.450914\pi$
$954$	−4.52342	−	5.36943i	−0.146451	−	0.173842i
$955$	13.6803	+	17.1342i	0.442685	+	0.554450i
$956$	4.99985	−	13.9061i	0.161707	−	0.449755i
$957$	−71.2932	+	41.1612i	−2.30458	+	1.33055i
$958$	5.23430	+	9.02523i	0.169113	+	0.291592i
$959$	−34.4107	+	6.06754i	−1.11118	+	0.195931i
$960$	44.3591	−	24.8702i	1.43168	−	0.802683i
$961$	−21.9774	+	38.0660i	−0.708949	+	1.22794i
$962$	0.0477180	+	24.3816i	0.00153849	+	0.786094i
$963$	4.05255	+	4.82964i	0.130592	+	0.155633i
$964$	−17.2637	+	20.7384i	−0.556027	+	0.667940i
$965$	−40.3723	−	0.983408i	−1.29963	−	0.0316570i
$966$	56.4921	−	20.6868i	1.81760	−	0.665586i
$967$	8.67349	−	49.1898i	0.278921	−	1.58184i	−0.447305	−	0.894381i	$-0.647616\pi$
$967$	8.67349	−	49.1898i	0.278921	−	1.58184i	0.726226	−	0.687456i	$-0.241273\pi$
$968$	0.179279	+	30.5340i	0.00576226	+	0.981401i
$969$	−2.82378	+	10.3167i	−0.0907129	+	0.331419i
$970$	56.9000	+	11.3524i	1.82695	+	0.364504i
$971$	8.87908	−	50.3558i	0.284943	−	1.61599i	−0.420545	−	0.907272i	$-0.638161\pi$
$971$	8.87908	−	50.3558i	0.284943	−	1.61599i	0.705488	−	0.708722i	$-0.250728\pi$
$972$	−26.1392	−	4.50362i	−0.838415	−	0.144454i
$973$	1.41704	−	3.89328i	0.0454282	−	0.124813i
$974$	−2.13417	+	12.2436i	−0.0683833	+	0.392309i
$975$	64.3482	+	14.6086i	2.06079	+	0.467849i
$976$	17.6768	−	0.138386i	0.565819	−	0.00442962i
$977$	17.9690	−	31.1232i	0.574880	−	0.995721i	−0.421175	−	0.906979i	$-0.638382\pi$
$977$	17.9690	−	31.1232i	0.574880	−	0.995721i	0.996055	−	0.0887413i	$-0.0282844\pi$
$978$	55.9979	+	20.2575i	1.79061	+	0.647764i
$979$	6.68984	+	37.9400i	0.213808	+	1.21257i
$980$	20.3611	−	6.94295i	0.650411	−	0.221784i
$981$	−29.5912	+	17.0845i	−0.944775	+	0.545466i
$982$	5.42587	+	30.4234i	0.173147	+	0.970848i
$983$	2.77017	+	7.61099i	0.0883548	+	0.242753i	0.975998	−	0.217779i	$-0.0698811\pi$
$983$	2.77017	+	7.61099i	0.0883548	+	0.242753i	−0.887643	+	0.460531i	$0.847659\pi$
$984$	−27.4834	+	76.9120i	−0.876137	+	2.45186i
$985$	7.22429	−	18.4386i	0.230185	−	0.587503i
$986$	−4.85544	+	5.80954i	−0.154629	+	0.185014i
$987$			36.0454i			1.14734i
$988$	40.3101	+	3.58572i	1.28243	+	0.114077i
$989$	−0.611387			−0.0194410
$990$	69.9111	+	27.2336i	2.22192	+	0.865541i
$991$	42.8808	+	35.9813i	1.36215	+	1.14298i	0.975310	+	0.220838i	$0.0708793\pi$
$991$	42.8808	+	35.9813i	1.36215	+	1.14298i	0.386844	+	0.922145i	$0.373565\pi$
$992$	−48.1455	+	8.97598i	−1.52862	+	0.284988i
$993$	−18.9972	−	52.1943i	−0.602857	−	1.65633i
$994$	10.4324	−	1.86057i	0.330894	−	0.0590136i
$995$	−6.64619	+	7.53985i	−0.210698	+	0.239029i
$996$	0.143735	+	36.7207i	0.00455442	+	1.16354i
$997$	−43.7182	+	7.70870i	−1.38457	+	0.244137i	−0.815788	−	0.578352i	$-0.803696\pi$
$997$	−43.7182	+	7.70870i	−1.38457	+	0.244137i	−0.568782	+	0.822489i	$0.692585\pi$
$998$	−39.8656	−	14.4216i	−1.26192	−	0.456507i
$999$	19.0377	+	10.9914i	0.602327	+	0.347754i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.bb.a.59.16	✓	336
4.3	odd	2	inner	380.2.bb.a.59.35	yes	336
5.4	even	2	inner	380.2.bb.a.59.41	yes	336
19.10	odd	18	inner	380.2.bb.a.219.22	yes	336
20.19	odd	2	inner	380.2.bb.a.59.22	yes	336
76.67	even	18	inner	380.2.bb.a.219.41	yes	336
95.29	odd	18	inner	380.2.bb.a.219.35	yes	336
380.219	even	18	inner	380.2.bb.a.219.16	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.bb.a.59.16	✓	336	1.1	even	1	trivial
380.2.bb.a.59.22	yes	336	20.19	odd	2	inner
380.2.bb.a.59.35	yes	336	4.3	odd	2	inner
380.2.bb.a.59.41	yes	336	5.4	even	2	inner
380.2.bb.a.219.16	yes	336	380.219	even	18	inner
380.2.bb.a.219.22	yes	336	19.10	odd	18	inner
380.2.bb.a.219.35	yes	336	95.29	odd	18	inner
380.2.bb.a.219.41	yes	336	76.67	even	18	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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.bb (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.906917 + 1.08513i) q^{2} +(1.82738 - 2.17779i) q^{3} +(-0.355003 - 1.96824i) q^{4} +(1.74742 - 1.39518i) q^{5} +(0.705894 + 3.95801i) q^{6} +(1.71831 + 2.97619i) q^{7} +(2.45775 + 1.39981i) q^{8} +(-0.882491 - 5.00485i) q^{9} +O(q^{10})\)	\(q+(-0.906917 + 1.08513i) q^{2} +(1.82738 - 2.17779i) q^{3} +(-0.355003 - 1.96824i) q^{4} +(1.74742 - 1.39518i) q^{5} +(0.705894 + 3.95801i) q^{6} +(1.71831 + 2.97619i) q^{7} +(2.45775 + 1.39981i) q^{8} +(-0.882491 - 5.00485i) q^{9} +(-0.0708181 + 3.16148i) q^{10} +(4.04311 + 2.33429i) q^{11} +(-4.93513 - 2.82360i) q^{12} +(-3.55608 + 2.98391i) q^{13} +(-4.78791 - 0.834579i) q^{14} +(0.154799 - 6.35503i) q^{15} +(-3.74795 + 1.39746i) q^{16} +(-0.850042 - 0.149885i) q^{17} +(6.23125 + 3.58137i) q^{18} +(3.58397 - 2.48096i) q^{19} +(-3.36639 - 2.94405i) q^{20} +(9.62150 + 1.69653i) q^{21} +(-6.19976 + 2.27028i) q^{22} +(-4.09159 - 1.48922i) q^{23} +(7.53972 - 2.79448i) q^{24} +(1.10695 - 4.87593i) q^{25} +(-0.0128485 - 6.56496i) q^{26} +(-5.12608 - 2.95954i) q^{27} +(5.24786 - 4.43860i) q^{28} +(-6.10835 + 1.07707i) q^{29} +(6.75562 + 5.93146i) q^{30} +(-4.32882 - 7.49774i) q^{31} +(1.88265 - 5.33438i) q^{32} +(12.4719 - 4.53939i) q^{33} +(0.933562 - 0.786471i) q^{34} +(7.15492 + 2.80332i) q^{35} +(-9.53747 + 3.51369i) q^{36} -3.71390 q^{37} +(-0.558206 + 6.13909i) q^{38} +13.1971i q^{39} +(6.24770 - 0.982950i) q^{40} +(-6.52905 + 7.78102i) q^{41} +(-10.5669 + 8.90195i) q^{42} +(0.131946 - 0.0480244i) q^{43} +(3.15913 - 8.78649i) q^{44} +(-8.52475 - 7.51435i) q^{45} +(5.32672 - 3.08930i) q^{46} +(0.640662 + 3.63338i) q^{47} +(-3.80554 + 10.7159i) q^{48} +(-2.40515 + 4.16584i) q^{49} +(4.28709 + 5.62325i) q^{50} +(-1.87977 + 1.57731i) q^{51} +(7.13547 + 5.93993i) q^{52} +(-0.917952 - 0.334107i) q^{53} +(7.86041 - 2.87839i) q^{54} +(10.3218 - 1.56187i) q^{55} +(0.0570708 + 9.72004i) q^{56} +(1.14627 - 12.3388i) q^{57} +(4.37101 - 7.60514i) q^{58} +(-1.50948 + 8.56070i) q^{59} +(-12.5632 + 1.95137i) q^{60} +(-4.15281 - 1.51150i) q^{61} +(12.0619 + 2.10250i) q^{62} +(13.3790 - 11.2263i) q^{63} +(4.08108 + 6.88076i) q^{64} +(-2.05089 + 10.1755i) q^{65} +(-6.38513 + 17.6504i) q^{66} +(2.42352 - 0.427332i) q^{67} +(0.00675722 + 1.72630i) q^{68} +(-10.7201 + 6.18924i) q^{69} +(-9.53087 + 5.22163i) q^{70} +(-2.04891 + 0.745741i) q^{71} +(4.83689 - 13.5360i) q^{72} +(2.57634 - 3.07036i) q^{73} +(3.36819 - 4.03005i) q^{74} +(-8.59590 - 11.3209i) q^{75} +(-6.15545 - 6.17337i) q^{76} +16.0441i q^{77} +(-14.3206 - 11.9687i) q^{78} +(3.64005 + 3.05437i) q^{79} +(-4.59952 + 7.67101i) q^{80} +(-1.48581 + 0.540791i) q^{81} +(-2.52209 - 14.1416i) q^{82} +(-3.22919 - 5.59312i) q^{83} +(-0.0764839 - 19.5397i) q^{84} +(-1.69450 + 0.924048i) q^{85} +(-0.0675514 + 0.186732i) q^{86} +(-8.81664 + 15.2709i) q^{87} +(6.66939 + 11.3967i) q^{88} +(5.30431 + 6.32142i) q^{89} +(15.8853 - 2.43555i) q^{90} +(-14.9911 - 5.45632i) q^{91} +(-1.47861 + 8.58191i) q^{92} +(-24.2389 - 4.27397i) q^{93} +(-4.52370 - 2.59997i) q^{94} +(2.80132 - 9.33556i) q^{95} +(-8.17683 - 13.8479i) q^{96} +(3.18610 - 18.0692i) q^{97} +(-2.33920 - 6.38796i) q^{98} +(8.11477 - 22.2951i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9}+O(q^{10}) \) 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9	\( 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9} - 15 q^{10} + 18 q^{14} - 6 q^{16} - 42 q^{20} + 12 q^{21} + 12 q^{24} - 12 q^{25} + 18 q^{26} - 24 q^{29} - 24 q^{30} + 12 q^{34} - 6 q^{36} - 48 q^{40} - 12 q^{41} - 36 q^{44} - 6 q^{45} - 18 q^{46} - 108 q^{49} - 36 q^{50} + 36 q^{54} - 30 q^{60} - 24 q^{61} + 18 q^{64} - 18 q^{65} - 48 q^{66} - 180 q^{69} - 21 q^{70} - 30 q^{74} - 48 q^{76} + 3 q^{80} - 60 q^{81} + 90 q^{84} - 36 q^{85} + 102 q^{86} - 48 q^{89} - 78 q^{90} + 24 q^{96}+O(q^{100}) \) 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9 - 15 * q^10 + 18 * q^14 - 6 * q^16 - 42 * q^20 + 12 * q^21 + 12 * q^24 - 12 * q^25 + 18 * q^26 - 24 * q^29 - 24 * q^30 + 12 * q^34 - 6 * q^36 - 48 * q^40 - 12 * q^41 - 36 * q^44 - 6 * q^45 - 18 * q^46 - 108 * q^49 - 36 * q^50 + 36 * q^54 - 30 * q^60 - 24 * q^61 + 18 * q^64 - 18 * q^65 - 48 * q^66 - 180 * q^69 - 21 * q^70 - 30 * q^74 - 48 * q^76 + 3 * q^80 - 60 * q^81 + 90 * q^84 - 36 * q^85 + 102 * q^86 - 48 * q^89 - 78 * q^90 + 24 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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