LMFDB - Embedded newform 380.2.bb.a.219.14

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			219.14
Character	$\chi$	$=$	380.219
Dual form			380.2.bb.a.59.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.997360 - 1.00263i) q^{2} +(0.300395 + 0.357997i) q^{3} +(-0.0105474 + 1.99997i) q^{4} +(-1.26326 + 1.84504i) q^{5} +(0.0593378 - 0.658238i) q^{6} +(-1.68031 + 2.91038i) q^{7} +(2.01576 - 1.98412i) q^{8} +(0.483020 - 2.73934i) q^{9} +O(q^{10})$	\(q+(-0.997360 - 1.00263i) q^{2} +(0.300395 + 0.357997i) q^{3} +(-0.0105474 + 1.99997i) q^{4} +(-1.26326 + 1.84504i) q^{5} +(0.0593378 - 0.658238i) q^{6} +(-1.68031 + 2.91038i) q^{7} +(2.01576 - 1.98412i) q^{8} +(0.483020 - 2.73934i) q^{9} +(3.10982 - 0.573580i) q^{10} +(-0.107274 + 0.0619346i) q^{11} +(-0.719153 + 0.597006i) q^{12} +(-4.63813 - 3.89185i) q^{13} +(4.59392 - 1.21796i) q^{14} +(-1.04000 + 0.101997i) q^{15} +(-3.99978 - 0.0421890i) q^{16} +(-5.27335 + 0.929834i) q^{17} +(-3.22830 + 2.24782i) q^{18} +(-4.35738 - 0.115147i) q^{19} +(-3.67670 - 2.54595i) q^{20} +(-1.54667 + 0.272719i) q^{21} +(0.169088 + 0.0457853i) q^{22} +(2.96562 - 1.07940i) q^{23} +(1.31583 + 0.125617i) q^{24} +(-1.80834 - 4.66153i) q^{25} +(0.723781 + 8.53191i) q^{26} +(2.33994 - 1.35096i) q^{27} +(-5.80296 - 3.39127i) q^{28} +(3.07901 + 0.542912i) q^{29} +(1.13952 + 0.941008i) q^{30} +(-3.24345 + 5.61782i) q^{31} +(3.94692 + 4.05239i) q^{32} +(-0.0543970 - 0.0197989i) q^{33} +(6.19171 + 4.35986i) q^{34} +(-3.24710 - 6.77681i) q^{35} +(5.47351 + 0.994919i) q^{36} +4.80607 q^{37} +(4.23042 + 4.48370i) q^{38} -2.82953i q^{39} +(1.11434 + 6.22561i) q^{40} +(1.73589 + 2.06876i) q^{41} +(1.81602 + 1.27874i) q^{42} +(-11.3069 - 4.11538i) q^{43} +(-0.122736 - 0.215198i) q^{44} +(4.44401 + 4.35170i) q^{45} +(-4.04003 - 1.89688i) q^{46} +(-1.96698 + 11.1553i) q^{47} +(-1.18641 - 1.44458i) q^{48} +(-2.14689 - 3.71852i) q^{49} +(-2.87024 + 6.46233i) q^{50} +(-1.91697 - 1.60853i) q^{51} +(7.83251 - 9.23507i) q^{52} +(0.110513 - 0.0402236i) q^{53} +(-3.68828 - 0.998703i) q^{54} +(0.0212432 - 0.276164i) q^{55} +(2.38744 + 9.20056i) q^{56} +(-1.26771 - 1.59452i) q^{57} +(-2.52653 - 3.62859i) q^{58} +(0.756119 + 4.28817i) q^{59} +(-0.193022 - 2.08104i) q^{60} +(-6.90121 + 2.51183i) q^{61} +(8.86750 - 2.35100i) q^{62} +(7.16091 + 6.00872i) q^{63} +(0.126564 - 7.99900i) q^{64} +(13.0398 - 3.64110i) q^{65} +(0.0344024 + 0.0742869i) q^{66} +(1.55757 + 0.274642i) q^{67} +(-1.80402 - 10.5564i) q^{68} +(1.27728 + 0.737438i) q^{69} +(-3.55613 + 10.0146i) q^{70} +(-2.80683 - 1.02160i) q^{71} +(-4.46152 - 6.48022i) q^{72} +(4.12772 + 4.91923i) q^{73} +(-4.79338 - 4.81873i) q^{74} +(1.12560 - 2.04768i) q^{75} +(0.276250 - 8.71342i) q^{76} -0.416278i q^{77} +(-2.83698 + 2.82206i) q^{78} +(-8.67515 + 7.27931i) q^{79} +(5.13060 - 7.32645i) q^{80} +(-6.65500 - 2.42222i) q^{81} +(0.342895 - 3.80376i) q^{82} +(3.57061 - 6.18447i) q^{83} +(-0.529117 - 3.09617i) q^{84} +(4.94604 - 10.9042i) q^{85} +(7.15084 + 15.4412i) q^{86} +(0.730558 + 1.26536i) q^{87} +(-0.0933528 + 0.337689i) q^{88} +(-2.78066 + 3.31386i) q^{89} +(-0.0691245 - 8.79592i) q^{90} +(19.1203 - 6.95921i) q^{91} +(2.12748 + 5.94254i) q^{92} +(-2.98548 + 0.526421i) q^{93} +(13.1465 - 9.15370i) q^{94} +(5.71696 - 7.89407i) q^{95} +(-0.265108 + 2.63030i) q^{96} +(-1.90434 - 10.8000i) q^{97} +(-1.58709 + 5.86124i) q^{98} +(0.117845 + 0.323776i) 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 $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$-1$	$-1$

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 $

$2$	−0.997360	−	1.00263i	−0.705240	−	0.708969i
$2$	−0.997360	−	1.00263i	−0.705240	−	0.708969i
$3$	0.300395	+	0.357997i	0.173433	+	0.206690i	0.845758	−	0.533566i	$-0.179149\pi$
$3$	0.300395	+	0.357997i	0.173433	+	0.206690i	−0.672325	+	0.740256i	$0.734704\pi$
$4$	−0.0105474	+	1.99997i	−0.00527370	+	0.999986i
$5$	−1.26326	+	1.84504i	−0.564948	+	0.825127i
$5$	−1.26326	+	1.84504i	−0.564948	+	0.825127i
$6$	0.0593378	−	0.658238i	0.0242245	−	0.268725i
$7$	−1.68031	+	2.91038i	−0.635098	+	1.10002i	0.351397	+	0.936227i	$0.385707\pi$
$7$	−1.68031	+	2.91038i	−0.635098	+	1.10002i	−0.986494	+	0.163795i	$0.947627\pi$
$8$	2.01576	−	1.98412i	0.712678	−	0.701491i
$9$	0.483020	−	2.73934i	0.161007	−	0.913114i
$10$	3.10982	−	0.573580i	0.983413	−	0.181382i
$11$	−0.107274	+	0.0619346i	−0.0323443	+	0.0186740i	−0.516085	−	0.856537i	$-0.672611\pi$
$11$	−0.107274	+	0.0619346i	−0.0323443	+	0.0186740i	0.483741	+	0.875211i	$0.339278\pi$
$12$	−0.719153	+	0.597006i	−0.207602	+	0.172341i
$13$	−4.63813	−	3.89185i	−1.28638	−	1.07941i	−0.992330	−	0.123616i	$-0.960551\pi$
$13$	−4.63813	−	3.89185i	−1.28638	−	1.07941i	−0.294055	−	0.955789i	$-0.595005\pi$
$14$	4.59392	−	1.21796i	1.22778	−	0.325514i
$15$	−1.04000	+	0.101997i	−0.268526	+	0.0263356i
$16$	−3.99978	−	0.0421890i	−0.999944	−	0.0105473i
$17$	−5.27335	+	0.929834i	−1.27898	+	0.225518i	−0.771545	−	0.636175i	$-0.780516\pi$
$17$	−5.27335	+	0.929834i	−1.27898	+	0.225518i	−0.507431	+	0.861693i	$0.669405\pi$
$18$	−3.22830	+	2.24782i	−0.760918	+	0.529816i
$19$	−4.35738	−	0.115147i	−0.999651	−	0.0264166i
$19$	−4.35738	−	0.115147i	−0.999651	−	0.0264166i
$20$	−3.67670	−	2.54595i	−0.822136	−	0.569291i
$21$	−1.54667	+	0.272719i	−0.337510	+	0.0595122i
$22$	0.169088	+	0.0457853i	0.0360498	+	0.00976146i
$23$	2.96562	−	1.07940i	0.618374	−	0.225070i	−0.0137891	−	0.999905i	$-0.504389\pi$
$23$	2.96562	−	1.07940i	0.618374	−	0.225070i	0.632163	+	0.774835i	$0.282167\pi$
$24$	1.31583	+	0.125617i	0.268593	+	0.0256414i
$25$	−1.80834	−	4.66153i	−0.361668	−	0.932307i
$26$	0.723781	+	8.53191i	0.141945	+	1.67325i
$27$	2.33994	−	1.35096i	0.450321	−	0.259993i
$28$	−5.80296	−	3.39127i	−1.09666	−	0.640890i
$29$	3.07901	+	0.542912i	0.571757	+	0.100816i	0.452049	−	0.891993i	$-0.350693\pi$
$29$	3.07901	+	0.542912i	0.571757	+	0.100816i	0.119708	+	0.992809i	$0.461804\pi$
$30$	1.13952	+	0.941008i	0.208046	+	0.171804i
$31$	−3.24345	+	5.61782i	−0.582541	+	1.00899i	0.412636	+	0.910896i	$0.364608\pi$
$31$	−3.24345	+	5.61782i	−0.582541	+	1.00899i	−0.995177	+	0.0980944i	$0.968725\pi$
$32$	3.94692	+	4.05239i	0.697723	+	0.716368i
$33$	−0.0543970	−	0.0197989i	−0.00946931	−	0.00344655i
$34$	6.19171	+	4.35986i	1.06187	+	0.747710i
$35$	−3.24710	−	6.77681i	−0.548860	−	1.14549i
$36$	5.47351	+	0.994919i	0.912252	+	0.165820i
$37$	4.80607			0.790113			0.395057	−	0.918657i	$-0.370725\pi$
$37$	4.80607			0.790113			0.395057	+	0.918657i	$0.370725\pi$
$38$	4.23042	+	4.48370i	0.686265	+	0.727351i
$39$		−	2.82953i		−	0.453087i
$40$	1.11434	+	6.22561i	0.176193	+	0.984356i
$41$	1.73589	+	2.06876i	0.271101	+	0.323086i	0.884368	−	0.466790i	$-0.154590\pi$
$41$	1.73589	+	2.06876i	0.271101	+	0.323086i	−0.613267	+	0.789876i	$0.710145\pi$
$42$	1.81602	+	1.27874i	0.280218	+	0.197314i
$43$	−11.3069	−	4.11538i	−1.72429	−	0.627589i	−0.726090	−	0.687600i	$-0.758664\pi$
$43$	−11.3069	−	4.11538i	−1.72429	−	0.627589i	−0.998198	+	0.0600104i	$0.980887\pi$
$44$	−0.122736	−	0.215198i	−0.0185032	−	0.0324423i
$45$	4.44401	+	4.35170i	0.662474	+	0.648712i
$46$	−4.04003	−	1.89688i	−0.595670	−	0.279680i
$47$	−1.96698	+	11.1553i	−0.286914	+	1.62717i	0.411453	+	0.911431i	$0.365021\pi$
$47$	−1.96698	+	11.1553i	−0.286914	+	1.62717i	−0.698367	+	0.715739i	$0.746090\pi$
$48$	−1.18641	−	1.44458i	−0.171244	−	0.208508i
$49$	−2.14689	−	3.71852i	−0.306698	−	0.531217i
$50$	−2.87024	+	6.46233i	−0.405914	+	0.913911i
$51$	−1.91697	−	1.60853i	−0.268429	−	0.225239i
$52$	7.83251	−	9.23507i	1.08617	−	1.28067i
$53$	0.110513	−	0.0402236i	0.0151802	−	0.00552513i	−0.334419	−	0.942425i	$-0.608540\pi$
$53$	0.110513	−	0.0402236i	0.0151802	−	0.00552513i	0.349599	+	0.936899i	$0.386318\pi$
$54$	−3.68828	−	0.998703i	−0.501912	−	0.135906i
$55$	0.0212432	−	0.276164i	0.00286443	−	0.0372380i
$56$	2.38744	+	9.20056i	0.319035	+	1.22948i
$57$	−1.26771	−	1.59452i	−0.167913	−	0.211199i
$58$	−2.52653	−	3.62859i	−0.331750	−	0.476457i
$59$	0.756119	+	4.28817i	0.0984383	+	0.558272i	0.993639	+	0.112609i	$0.0359208\pi$
$59$	0.756119	+	4.28817i	0.0984383	+	0.558272i	−0.895201	+	0.445663i	$0.852968\pi$
$60$	−0.193022	−	2.08104i	−0.0249191	−	0.268661i
$61$	−6.90121	+	2.51183i	−0.883609	+	0.321607i	−0.743665	−	0.668552i	$-0.766914\pi$
$61$	−6.90121	+	2.51183i	−0.883609	+	0.321607i	−0.139944	+	0.990159i	$0.544692\pi$
$62$	8.86750	−	2.35100i	1.12617	−	0.298577i
$63$	7.16091	+	6.00872i	0.902190	+	0.757027i
$64$	0.126564	−	7.99900i	0.0158205	−	0.999875i
$65$	13.0398	−	3.64110i	1.61739	−	0.451623i
$66$	0.0344024	+	0.0742869i	0.00423464	+	0.00914408i
$67$	1.55757	+	0.274642i	0.190288	+	0.0335529i	0.267980	−	0.963425i	$-0.413644\pi$
$67$	1.55757	+	0.274642i	0.190288	+	0.0335529i	−0.0776919	+	0.996977i	$0.524755\pi$
$68$	−1.80402	−	10.5564i	−0.218770	−	1.28015i
$69$	1.27728	+	0.737438i	0.153766	+	0.0887771i
$70$	−3.55613	+	10.0146i	−0.425039	+	1.19697i
$71$	−2.80683	−	1.02160i	−0.333110	−	0.121242i	0.170050	−	0.985435i	$-0.445607\pi$
$71$	−2.80683	−	1.02160i	−0.333110	−	0.121242i	−0.503160	+	0.864193i	$0.667829\pi$
$72$	−4.46152	−	6.48022i	−0.525795	−	0.763701i
$73$	4.12772	+	4.91923i	0.483114	+	0.575752i	0.951452	−	0.307797i	$-0.0995917\pi$
$73$	4.12772	+	4.91923i	0.483114	+	0.575752i	−0.468339	+	0.883549i	$0.655147\pi$
$74$	−4.79338	−	4.81873i	−0.557219	−	0.560166i
$75$	1.12560	−	2.04768i	0.129973	−	0.236446i
$76$	0.276250	−	8.71342i	0.0316880	−	0.999498i
$77$		−	0.416278i		−	0.0474392i
$78$	−2.83698	+	2.82206i	−0.321225	+	0.319535i
$79$	−8.67515	+	7.27931i	−0.976031	+	0.818987i	−0.983486	−	0.180985i	$-0.942071\pi$
$79$	−8.67515	+	7.27931i	−0.976031	+	0.818987i	0.00745528	+	0.999972i	$0.497627\pi$
$80$	5.13060	−	7.32645i	0.573619	−	0.819122i
$81$	−6.65500	−	2.42222i	−0.739445	−	0.269136i
$82$	0.342895	−	3.80376i	0.0378664	−	0.420055i
$83$	3.57061	−	6.18447i	0.391925	−	0.678834i	−0.600778	−	0.799416i	$-0.705143\pi$
$83$	3.57061	−	6.18447i	0.391925	−	0.678834i	0.992703	+	0.120582i	$0.0384760\pi$
$84$	−0.529117	−	3.09617i	−0.0577314	−	0.337819i
$85$	4.94604	−	10.9042i	0.536474	−	1.18272i
$86$	7.15084	+	15.4412i	0.771095	+	1.66507i
$87$	0.730558	+	1.26536i	0.0783240	+	0.135661i
$88$	−0.0933528	+	0.337689i	−0.00995144	+	0.0359978i
$89$	−2.78066	+	3.31386i	−0.294749	+	0.351268i	−0.893013	−	0.450031i	$-0.851413\pi$
$89$	−2.78066	+	3.31386i	−0.294749	+	0.351268i	0.598264	+	0.801299i	$0.295857\pi$
$90$	−0.0691245	−	8.79592i	−0.00728636	−	0.927172i
$91$	19.1203	−	6.95921i	2.00435	−	0.729523i
$92$	2.12748	+	5.94254i	0.221806	+	0.619553i
$93$	−2.98548	+	0.526421i	−0.309580	+	0.0545873i
$94$	13.1465	−	9.15370i	1.35596	−	0.944132i
$95$	5.71696	−	7.89407i	0.586548	−	0.809915i
$96$	−0.265108	+	2.63030i	−0.0270575	+	0.268454i
$97$	−1.90434	−	10.8000i	−0.193356	−	1.09658i	−0.914740	−	0.404043i	$-0.867605\pi$
$97$	−1.90434	−	10.8000i	−0.193356	−	1.09658i	0.721384	−	0.692536i	$-0.243506\pi$
$98$	−1.58709	+	5.86124i	−0.160320	+	0.592075i
$99$	0.117845	+	0.323776i	0.0118438	+	0.0325407i
$100$	9.34201	−	3.56747i	0.934201	−	0.356747i
$101$	8.07286	+	6.77394i	0.803280	+	0.674032i	0.948994	−	0.315295i	$-0.102103\pi$
$101$	8.07286	+	6.77394i	0.803280	+	0.674032i	−0.145714	+	0.989327i	$0.546548\pi$
$102$	0.299144	+	3.52630i	0.0296196	+	0.349155i
$103$	11.2211	−	6.47850i	1.10565	−	0.638346i	0.167949	−	0.985796i	$-0.446286\pi$
$103$	11.2211	−	6.47850i	1.10565	−	0.638346i	0.937698	+	0.347450i	$0.112952\pi$
$104$	−17.0712	+	1.35755i	−1.67397	+	0.133119i
$105$	1.45067	−	3.19818i	0.141571	−	0.312110i
$106$	−0.150551	−	0.0706870i	−0.0146228	−	0.00686573i
$107$	−10.3559	−	5.97895i	−1.00114	−	0.578007i	−0.0925532	−	0.995708i	$-0.529503\pi$
$107$	−10.3559	−	5.97895i	−1.00114	−	0.578007i	−0.908585	+	0.417700i	$0.862836\pi$
$108$	2.67721	+	4.69406i	0.257615	+	0.451686i
$109$	0.337802	−	0.928104i	0.0323556	−	0.0888963i	−0.922463	−	0.386085i	$-0.873827\pi$
$109$	0.337802	−	0.928104i	0.0323556	−	0.0888963i	0.954819	+	0.297189i	$0.0960492\pi$
$110$	−0.298079	+	0.254136i	−0.0284207	+	0.0242309i
$111$	1.44372	+	1.72056i	0.137032	+	0.163308i
$112$	6.84365	−	11.5700i	0.646665	−	1.09326i
$113$	8.40598			0.790768			0.395384	−	0.918516i	$-0.370612\pi$
$113$	8.40598			0.790768			0.395384	+	0.918516i	$0.370612\pi$
$114$	−0.334351	+	2.86136i	−0.0313149	+	0.267991i
$115$	−1.75482	+	6.83525i	−0.163638	+	0.637390i
$116$	−1.11828	+	6.15220i	−0.103830	+	0.571217i
$117$	−12.9014	+	10.8256i	−1.19274	+	1.00082i
$118$	3.54533	−	5.03495i	0.326375	−	0.463505i
$119$	6.15470	−	16.9099i	0.564200	−	1.55013i
$120$	−1.89401	+	2.26908i	−0.172899	+	0.207137i
$121$	−5.49233	+	9.51299i	−0.499303	+	0.864817i
$122$	9.40144	+	4.41418i	0.851166	+	0.399641i
$123$	−0.219155	+	1.24289i	−0.0197606	+	0.112068i
$124$	−11.2013	−	6.54606i	−1.00590	−	0.587854i
$125$	10.8851	+	2.55228i	0.973595	+	0.228282i
$126$	−1.11746	−	13.1726i	−0.0995515	−	1.17351i
$127$	−12.2881	+	14.6443i	−1.09039	+	1.29947i	−0.139405	+	0.990235i	$0.544519\pi$
$127$	−12.2881	+	14.6443i	−1.09039	+	1.29947i	−0.950984	+	0.309239i	$0.899926\pi$
$128$	−8.14629	+	7.85098i	−0.720037	+	0.693935i
$129$	−1.92325	−	5.28408i	−0.169333	−	0.465238i
$130$	−16.6560	−	9.44263i	−1.46083	−	0.828174i
$131$	−6.09336	+	1.07442i	−0.532380	+	0.0938729i	−0.433374	−	0.901214i	$-0.642677\pi$
$131$	−6.09336	+	1.07442i	−0.532380	+	0.0938729i	−0.0990053	+	0.995087i	$0.531566\pi$
$132$	0.0401710	−	0.108584i	0.00349644	−	0.00945100i
$133$	7.65687	−	12.4882i	0.663935	−	1.08286i
$134$	−1.27810	−	1.83559i	−0.110411	−	0.158571i
$135$	−0.463372	+	6.02390i	−0.0398807	+	0.518455i
$136$	−8.78490	+	12.3373i	−0.753299	+	1.05791i
$137$	1.29187	+	3.54938i	0.110372	+	0.303244i	0.982566	−	0.185917i	$-0.0595254\pi$
$137$	1.29187	+	3.54938i	0.110372	+	0.303244i	−0.872194	+	0.489161i	$0.837303\pi$
$138$	−0.534527	−	2.01613i	−0.0455020	−	0.171625i
$139$	4.33196	−	5.16262i	0.367432	−	0.437888i	−0.550374	−	0.834918i	$-0.685515\pi$
$139$	4.33196	−	5.16262i	0.367432	−	0.437888i	0.917805	+	0.397030i	$0.129959\pi$
$140$	13.5877	−	6.42263i	1.14837	−	0.542812i
$141$	−4.58445	+	2.64683i	−0.386080	+	0.222903i
$142$	1.77513	+	3.83313i	0.148965	+	0.321669i
$143$	0.738590	+	0.130233i	0.0617640	+	0.0108907i
$144$	−2.04754	+	10.9364i	−0.170629	+	0.911365i
$145$	−4.89128	+	4.99505i	−0.406199	+	0.414816i
$146$	0.815359	−	9.04483i	0.0674796	−	0.748556i
$147$	0.686304	−	1.88560i	0.0566054	−	0.155522i
$148$	−0.0506915	+	9.61201i	−0.00416682	+	0.790102i
$149$	12.5667	−	10.5448i	1.02951	−	0.863860i	0.0387155	−	0.999250i	$-0.487673\pi$
$149$	12.5667	−	10.5448i	1.02951	−	0.863860i	0.990792	+	0.135391i	$0.0432289\pi$
$150$	−3.17570	+	0.913715i	−0.259295	+	0.0746045i
$151$	12.5228			1.01909			0.509544	−	0.860445i	$-0.329814\pi$
$151$	12.5228			1.01909			0.509544	+	0.860445i	$0.329814\pi$
$152$	−9.01189	+	8.41344i	−0.730960	+	0.682420i
$153$			14.8946i			1.20416i
$154$	−0.417374	+	0.415179i	−0.0336329	+	0.0334560i
$155$	−6.26777	−	13.0811i	−0.503440	−	1.05070i
$156$	5.65898	+	0.0298442i	0.453081	+	0.00238945i
$157$	1.45751	−	4.00446i	0.116322	−	0.319591i	−0.867845	−	0.496834i	$-0.834496\pi$
$157$	1.45751	−	4.00446i	0.116322	−	0.319591i	0.984167	+	0.177243i	$0.0567179\pi$
$158$	15.9507	+	1.43790i	1.26897	+	0.114393i
$159$	0.0475976	+	0.0274805i	0.00377474	+	0.00217934i
$160$	−12.4628	+	2.16299i	−0.985271	+	0.170999i
$161$	−1.84170	+	10.4448i	−0.145146	+	0.823166i
$162$	4.20883	+	9.08835i	0.330677	+	0.714048i
$163$	−5.11904	−	8.86644i	−0.400954	−	0.694474i	0.592887	−	0.805286i	$-0.297988\pi$
$163$	−5.11904	−	8.86644i	−0.400954	−	0.694474i	−0.993841	+	0.110812i	$0.964655\pi$
$164$	−4.15577	+	3.44992i	−0.324511	+	0.269394i
$165$	0.105247	−	0.0753535i	0.00819350	−	0.00586626i
$166$	−9.76194	+	2.58813i	−0.757673	+	0.200878i
$167$	5.66187	+	15.5558i	0.438128	+	1.20375i	0.940708	+	0.339217i	$0.110162\pi$
$167$	5.66187	+	15.5558i	0.438128	+	1.20375i	−0.502580	+	0.864531i	$0.667616\pi$
$168$	−2.57660	+	3.61850i	−0.198789	+	0.279174i
$169$	4.10829	+	23.2993i	0.316022	+	1.79225i
$170$	−15.8659	+	5.91631i	−1.21686	+	0.453760i
$171$	−2.42013	+	11.8807i	−0.185072	+	0.908542i
$172$	8.34990	−	22.5701i	0.636674	−	1.72095i
$173$	1.69136	+	9.59221i	0.128592	+	0.729282i	0.979109	+	0.203335i	$0.0651779\pi$
$173$	1.69136	+	9.59221i	0.128592	+	0.729282i	−0.850517	+	0.525947i	$0.823711\pi$
$174$	0.540067	−	1.99450i	0.0409423	−	0.151203i
$175$	16.6054	+	2.56986i	1.25525	+	0.194263i
$176$	0.431685	−	0.243199i	0.0325395	−	0.0183318i
$177$	−1.30802	+	1.55883i	−0.0983166	+	0.117169i
$178$	6.09590	−	0.517129i	0.456907	−	0.0387604i
$179$	7.26304	+	12.5800i	0.542865	+	0.940270i	0.998738	+	0.0502250i	$0.0159939\pi$
$179$	7.26304	+	12.5800i	0.542865	+	0.940270i	−0.455873	+	0.890045i	$0.650673\pi$
$180$	−8.75014	+	8.84200i	−0.652197	+	0.659044i
$181$	−21.1417	−	3.72785i	−1.57145	−	0.277089i	−0.681039	−	0.732247i	$-0.738471\pi$
$181$	−21.1417	−	3.72785i	−1.57145	−	0.277089i	−0.890410	+	0.455159i	$0.849583\pi$
$182$	−26.0473	−	12.2298i	−1.93076	−	0.906532i
$183$	−2.97232	−	1.71607i	−0.219720	−	0.126856i
$184$	3.83632	−	8.05994i	0.282817	−	0.594187i
$185$	−6.07132	+	8.86739i	−0.446373	+	0.651943i
$186$	3.50541	+	2.46831i	0.257029	+	0.180985i
$187$	0.508104	−	0.426350i	0.0371563	−	0.0311778i
$188$	−22.2896	−	4.05157i	−1.62563	−	0.295491i
$189$			9.08016i			0.660484i
$190$	−13.6167	+	2.14122i	−0.987861	+	0.155340i
$191$		−	14.5924i		−	1.05587i	−0.849285	−	0.527935i	$-0.822967\pi$
$191$		−	14.5924i		−	1.05587i	0.849285	−	0.527935i	$-0.177033\pi$
$192$	2.90164	−	2.35755i	0.209408	−	0.170142i
$193$	1.87190	−	1.57071i	0.134743	−	0.113062i	−0.572926	−	0.819607i	$-0.694192\pi$
$193$	1.87190	−	1.57071i	0.134743	−	0.113062i	0.707668	+	0.706545i	$0.249747\pi$
$194$	−8.92918	+	12.6809i	−0.641077	+	0.910435i
$195$	5.22059	+	3.57444i	0.373855	+	0.255971i
$196$	7.45957	−	4.25449i	0.532827	−	0.303892i
$197$	−20.7890	−	12.0025i	−1.48116	−	0.855146i	−0.481384	−	0.876510i	$-0.659866\pi$
$197$	−20.7890	−	12.0025i	−1.48116	−	0.855146i	−0.999772	+	0.0213642i	$0.993199\pi$
$198$	0.207095	−	0.441076i	0.0147176	−	0.0313459i
$199$	−0.465640	−	0.0821049i	−0.0330083	−	0.00582026i	0.157120	−	0.987580i	$-0.449779\pi$
$199$	−0.465640	−	0.0821049i	−0.0330083	−	0.00582026i	−0.190128	+	0.981759i	$0.560890\pi$
$200$	−12.8942	−	5.80857i	−0.911758	−	0.410728i
$201$	0.369567	+	0.640109i	0.0260672	+	0.0451498i
$202$	−1.25977	−	14.8502i	−0.0886373	−	1.04485i
$203$	−6.75377	+	8.04882i	−0.474021	+	0.564917i
$204$	3.23723	−	3.81692i	0.226651	−	0.267238i
$205$	−6.00983	+	0.589411i	−0.419745	+	0.0411662i
$206$	−17.6870	−	4.78925i	−1.23231	−	0.333683i
$207$	−1.52438	−	8.64522i	−0.105952	−	0.600884i
$208$	18.3873	+	15.7622i	1.27493	+	1.09291i
$209$	0.474565	−	0.257520i	0.0328263	−	0.0178131i
$210$	−4.65344	+	1.73525i	−0.321118	+	0.119743i
$211$	1.27499	+	7.23082i	0.0877739	+	0.497791i	0.996723	+	0.0808845i	$0.0257745\pi$
$211$	1.27499	+	7.23082i	0.0877739	+	0.497791i	−0.908950	+	0.416906i	$0.863114\pi$
$212$	0.0792804	+	0.221448i	0.00544500	+	0.0152091i
$213$	−0.477428	−	1.31172i	−0.0327128	−	0.0898778i
$214$	4.33381	+	16.3463i	0.296253	+	1.11741i
$215$	21.8766	−	15.6629i	1.49197	−	1.06820i
$216$	2.03628	−	7.36593i	0.138551	−	0.501188i
$217$	−10.9000	−	18.8794i	−0.739941	−	1.28161i
$218$	−1.26746	+	0.586962i	−0.0858431	+	0.0397541i
$219$	−0.521122	+	2.95543i	−0.0352141	+	0.199709i
$220$	0.552097	+	0.0453986i	0.0372224	+	0.00306077i
$221$	28.0773	+	16.2104i	1.88868	+	1.09043i
$222$	0.285182	−	3.16354i	0.0191401	−	0.212323i
$223$	−3.52244	+	9.67782i	−0.235880	+	0.648075i	0.764116	+	0.645079i	$0.223176\pi$
$223$	−3.52244	+	9.67782i	−0.235880	+	0.648075i	−0.999996	+	0.00299548i	$0.999047\pi$
$224$	−18.4260	+	4.67777i	−1.23114	+	0.312547i
$225$	−13.6430	+	2.70205i	−0.909533	+	0.180137i
$226$	−8.38378	−	8.42811i	−0.557681	−	0.560630i
$227$			9.41783i			0.625083i	0.949904	+	0.312542i	$0.101180\pi$
$227$			9.41783i			0.625083i	−0.949904	+	0.312542i	$0.898820\pi$
$228$	3.20236	−	2.51857i	0.212082	−	0.166797i
$229$	−11.7727			−0.777959			−0.388979	−	0.921246i	$-0.627172\pi$
$229$	−11.7727			−0.777959			−0.388979	+	0.921246i	$0.627172\pi$
$230$	8.60343	−	5.05776i	0.567294	−	0.333498i
$231$	0.149026	−	0.125048i	0.00980521	−	0.00822755i
$232$	7.28373	−	5.01473i	0.478200	−	0.329233i
$233$	−0.145204	+	0.398944i	−0.00951262	+	0.0261357i	−0.944358	−	0.328919i	$-0.893316\pi$
$233$	−0.145204	+	0.398944i	−0.00951262	+	0.0261357i	0.934845	+	0.355055i	$0.115538\pi$
$234$	23.7214	+	2.13840i	1.55072	+	0.139792i
$235$	−18.0972	−	17.7212i	−1.18053	−	1.15601i
$236$	−8.58419	+	1.46699i	−0.558783	+	0.0954928i
$237$	−5.21195	−	0.919007i	−0.338552	−	0.0596959i
$238$	−23.0929	+	10.6943i	−1.49689	+	0.693211i
$239$	26.0654	−	15.0489i	1.68603	−	0.973432i	0.728528	−	0.685016i	$-0.240205\pi$
$239$	26.0654	−	15.0489i	1.68603	−	0.973432i	0.957505	−	0.288416i	$-0.0931285\pi$
$240$	4.16406	−	0.364090i	0.268789	−	0.0235019i
$241$	5.17036	−	6.16180i	0.333052	−	0.396916i	−0.573365	−	0.819300i	$-0.694362\pi$
$241$	5.17036	−	6.16180i	0.333052	−	0.396916i	0.906417	+	0.422384i	$0.138807\pi$
$242$	15.0159	−	3.98108i	0.965257	−	0.255914i
$243$	−3.90432	−	10.7270i	−0.250463	−	0.688140i
$244$	−4.95081	−	13.8287i	−0.316943	−	0.885293i
$245$	9.57289	+	0.736368i	0.611590	+	0.0470448i
$246$	1.46474	−	1.01988i	0.0933884	−	0.0650250i
$247$	19.7619	+	17.4923i	1.25742	+	1.11301i
$248$	4.60840	+	17.7595i	0.292634	+	1.12773i
$249$	3.28662	−	0.579519i	0.208281	−	0.0367255i
$250$	−8.29739	−	13.4593i	−0.524773	−	0.851242i
$251$	−1.40827	−	3.86919i	−0.0888892	−	0.244221i	0.887280	−	0.461231i	$-0.152592\pi$
$251$	−1.40827	−	3.86919i	−0.0888892	−	0.244221i	−0.976169	+	0.217010i	$0.930370\pi$
$252$	−12.0928	+	14.2582i	−0.761775	+	0.898185i
$253$	−0.251282	+	0.299466i	−0.0157979	+	0.0188273i
$254$	26.9385	−	2.28525i	1.69027	−	0.143390i
$255$	5.38943	−	1.50489i	0.337499	−	0.0942400i
$256$	15.9964	+	0.337493i	0.999778	+	0.0210933i
$257$	−1.39435	+	7.90776i	−0.0869773	+	0.493273i	0.909935	+	0.414751i	$0.136131\pi$
$257$	−1.39435	+	7.90776i	−0.0869773	+	0.493273i	−0.996912	+	0.0785220i	$0.974980\pi$
$258$	−3.37983	+	7.19845i	−0.210419	+	0.448156i
$259$	−8.07569	+	13.9875i	−0.501799	+	0.869141i
$260$	7.14457	+	26.1176i	0.443087	+	1.61975i
$261$	2.97444	−	8.17221i	0.184113	−	0.505847i
$262$	7.15453	+	5.03782i	0.442008	+	0.311238i
$263$	−4.76930	+	4.00192i	−0.294088	+	0.246769i	−0.777878	−	0.628415i	$-0.783704\pi$
$263$	−4.76930	+	4.00192i	−0.294088	+	0.246769i	0.483791	+	0.875184i	$0.339260\pi$
$264$	−0.148935	+	0.0680202i	−0.00916629	+	0.00418636i
$265$	−0.0653932	+	0.254714i	−0.00401707	+	0.0156470i
$266$	−20.1577	+	4.77815i	−1.23595	+	0.292967i
$267$	−2.02165			−0.123723
$268$	−0.565705	+	3.11221i	−0.0345560	+	0.190108i
$269$	−15.8691	−	18.9121i	−0.967558	−	1.15309i	−0.988179	−	0.153303i	$-0.951009\pi$
$269$	−15.8691	−	18.9121i	−0.967558	−	1.15309i	0.0206212	−	0.999787i	$-0.493436\pi$
$270$	6.50191	−	5.54340i	0.395694	−	0.337361i
$271$	−6.22615	+	17.1062i	−0.378212	+	1.03913i	0.593886	+	0.804549i	$0.297593\pi$
$271$	−6.22615	+	17.1062i	−0.378212	+	1.03913i	−0.972097	+	0.234578i	$0.924629\pi$
$272$	21.1315	−	3.49665i	1.28128	−	0.212016i
$273$	8.23502	+	4.75449i	0.498406	+	0.287755i
$274$	2.27027	−	4.83528i	0.137152	−	0.292110i
$275$	0.482698	+	0.388062i	0.0291078	+	0.0234010i
$276$	−1.48833	+	2.54675i	−0.0895867	+	0.153296i
$277$	−4.03598	+	2.33018i	−0.242499	+	0.140007i	−0.616325	−	0.787492i	$-0.711379\pi$
$277$	−4.03598	+	2.33018i	−0.242499	+	0.140007i	0.373826	+	0.927499i	$0.378046\pi$
$278$	−9.49674	+	0.805629i	−0.569576	+	0.0483184i
$279$	13.8225	+	11.5984i	0.827530	+	0.694380i
$280$	−19.9914	−	7.21779i	−1.19471	−	0.431346i
$281$	−6.97083	−	19.1522i	−0.415845	−	1.14252i	−0.954034	−	0.299700i	$-0.903114\pi$
$281$	−6.97083	−	19.1522i	−0.415845	−	1.14252i	0.538189	−	0.842824i	$-0.319109\pi$
$282$	7.22614	+	1.95668i	0.430310	+	0.116518i
$283$	−2.17388	−	12.3287i	−0.129224	−	0.732864i	−0.978709	−	0.205252i	$-0.934199\pi$
$283$	−2.17388	−	12.3287i	−0.129224	−	0.732864i	0.849486	−	0.527612i	$-0.176912\pi$
$284$	2.07278	−	5.60281i	0.122997	−	0.332466i
$285$	4.54340	−	0.324688i	0.269128	−	0.0192328i
$286$	−0.606064	−	0.870425i	−0.0358373	−	0.0514693i
$287$	−8.93772	+	1.57596i	−0.527577	+	0.0930261i
$288$	13.0073	−	8.85457i	0.766463	−	0.521761i
$289$	10.9689	−	3.99235i	0.645228	−	0.234844i
$290$	9.88657	−	0.0776955i	0.580559	−	0.00456244i
$291$	3.29433	−	3.92603i	0.193117	−	0.230148i
$292$	−9.88186	+	8.20345i	−0.578292	+	0.480070i
$293$	−1.10918	−	1.92115i	−0.0647987	−	0.112235i	0.831806	−	0.555067i	$-0.187307\pi$
$293$	−1.10918	−	1.92115i	−0.0647987	−	0.112235i	−0.896605	+	0.442832i	$0.853974\pi$
$294$	−2.57506	+	1.19251i	−0.150181	+	0.0695489i
$295$	−8.86701	−	4.02200i	−0.516257	−	0.234170i
$296$	9.68788	−	9.53580i	0.563096	−	0.554257i
$297$	−0.167343	+	0.289846i	−0.00971022	+	0.0168186i
$298$	−23.1061	−	2.08293i	−1.33850	−	0.120661i
$299$	−17.9558	−	6.53537i	−1.03841	−	0.377950i
$300$	4.08344	+	2.27276i	0.235758	+	0.131218i
$301$	30.9764	−	25.9923i	1.78545	−	1.49817i
$302$	−12.4897	−	12.5557i	−0.718701	−	0.722501i
$303$			4.92492i			0.282929i
$304$	17.4237	+	0.644396i	0.999317	+	0.0369587i
$305$	4.08360	−	15.9061i	0.233826	−	0.910781i
$306$	14.9339	−	14.8553i	0.853712	−	0.849222i
$307$	−6.48351	−	7.72675i	−0.370033	−	0.440989i	0.548609	−	0.836079i	$-0.315158\pi$
$307$	−6.48351	−	7.72675i	−0.370033	−	0.440989i	−0.918642	+	0.395091i	$0.870713\pi$
$308$	0.832544	+	0.00439065i	0.0474386	+	0.000250180i
$309$	5.69005	+	2.07101i	0.323696	+	0.117816i
$310$	−6.86429	+	19.3308i	−0.389865	+	1.09792i
$311$	−0.331975	−	0.191666i	−0.0188246	−	0.0108684i	0.490558	−	0.871408i	$-0.336793\pi$
$311$	−0.331975	−	0.191666i	−0.0188246	−	0.0108684i	−0.509383	+	0.860540i	$0.670126\pi$
$312$	−5.61412	−	5.70365i	−0.317837	−	0.322906i
$313$	22.5307	+	3.97277i	1.27351	+	0.224554i	0.769222	−	0.638982i	$-0.220644\pi$
$313$	22.5307	+	3.97277i	1.27351	+	0.224554i	0.504287	+	0.863536i	$0.331755\pi$
$314$	−5.46867	+	2.53255i	−0.308615	+	0.142920i
$315$	−20.1324	+	5.62158i	−1.13433	+	0.316740i
$316$	−14.4669	−	17.4268i	−0.813828	−	0.980336i
$317$	21.8398	+	18.3258i	1.22665	+	1.02928i	0.998450	+	0.0556648i	$0.0177278\pi$
$317$	21.8398	+	18.3258i	1.22665	+	1.02928i	0.228198	+	0.973615i	$0.426717\pi$
$318$	−0.0199191	−	0.0751309i	−0.00111701	−	0.00421313i
$319$	−0.363922	+	0.132457i	−0.0203757	+	0.00741616i
$320$	14.5986	+	10.3383i	0.816086	+	0.577931i
$321$	−0.970401	−	5.50342i	−0.0541625	−	0.307171i
$322$	12.3092	−	8.57068i	0.685962	−	0.477625i
$323$	23.0851	−	3.44443i	1.28449	−	0.191653i
$324$	4.91457	−	13.2843i	0.273032	−	0.738015i
$325$	−9.75468	+	28.6586i	−0.541092	+	1.58969i
$326$	−3.78427	+	13.9756i	−0.209591	+	0.774035i
$327$	0.433733	−	0.157866i	0.0239855	−	0.00873001i
$328$	7.60380	+	0.725901i	0.419850	+	0.0400812i
$329$	−29.1611	−	24.4691i	−1.60770	−	1.34902i
$330$	−0.180521	−	0.0303701i	−0.00993738	−	0.00167182i
$331$	−9.80984	−	16.9911i	−0.539198	−	0.933918i	−0.998947	−	0.0458692i	$-0.985394\pi$
$331$	−9.80984	−	16.9911i	−0.539198	−	0.933918i	0.459750	−	0.888048i	$-0.347939\pi$
$332$	12.3311	+	7.20634i	0.676758	+	0.395499i
$333$	2.32143	−	13.1655i	0.127213	−	0.721463i
$334$	9.94990	−	21.1916i	0.544434	−	1.15955i
$335$	−2.47435	+	2.52684i	−0.135188	+	0.138056i
$336$	6.19783	−	1.02556i	0.338119	−	0.0559491i
$337$	8.99330	+	3.27329i	0.489896	+	0.178308i	0.575144	−	0.818052i	$-0.304946\pi$
$337$	8.99330	+	3.27329i	0.489896	+	0.178308i	−0.0852479	+	0.996360i	$0.527168\pi$
$338$	19.2632	−	27.3569i	1.04778	−	1.48802i
$339$	2.52512	+	3.00932i	0.137145	+	0.163444i
$340$	21.7559	+	10.0070i	1.17988	+	0.542703i
$341$		−	0.803528i		−	0.0435135i
$342$	14.3258	−	9.42286i	0.774648	−	0.509530i
$343$	−9.09460			−0.491062
$344$	−30.9574	+	14.1386i	−1.66911	+	0.762303i
$345$	−2.97414	+	1.42505i	−0.160122	+	0.0767224i
$346$	7.93057	−	11.2627i	0.426350	−	0.605486i
$347$	−8.64421	−	3.14623i	−0.464045	−	0.168899i	0.0994077	−	0.995047i	$-0.468305\pi$
$347$	−8.64421	−	3.14623i	−0.464045	−	0.168899i	−0.563453	+	0.826148i	$0.690527\pi$
$348$	−2.53840	+	1.44775i	−0.136072	+	0.0776075i
$349$	−14.5699	+	25.2358i	−0.779908	+	1.35084i	0.152086	+	0.988367i	$0.451401\pi$
$349$	−14.5699	+	25.2358i	−0.779908	+	1.35084i	−0.931994	+	0.362473i	$0.881933\pi$
$350$	−13.9850	−	19.2122i	−0.747527	−	1.02694i
$351$	−16.1107	−	2.84075i	−0.859924	−	0.151628i
$352$	−0.674385	−	0.190265i	−0.0359448	−	0.0101411i
$353$	−11.6342	+	6.71703i	−0.619228	+	0.357512i	−0.776568	−	0.630033i	$-0.783041\pi$
$353$	−11.6342	+	6.71703i	−0.619228	+	0.357512i	0.157340	+	0.987544i	$0.449708\pi$
$354$	2.86750	−	0.243257i	0.152406	−	0.0129289i
$355$	5.43066	−	3.88816i	0.288230	−	0.206362i
$356$	−6.59829	−	5.59619i	−0.349709	−	0.296597i
$357$	7.90253	−	2.87629i	0.418246	−	0.152229i
$358$	5.36922	−	19.8289i	0.283772	−	1.04799i
$359$	−31.1619	+	5.49469i	−1.64466	+	0.289998i	−0.917877	−	0.396866i	$-0.870098\pi$
$359$	−31.1619	+	5.49469i	−1.64466	+	0.289998i	−0.726786	+	0.686864i	$0.758987\pi$
$360$	17.5923	−	0.0454730i	0.927197	−	0.00239664i
$361$	18.9735	+	1.00348i	0.998604	+	0.0528147i
$362$	17.3482	+	24.9154i	0.911801	+	1.30952i
$363$	−5.05549	+	0.891420i	−0.265345	+	0.0467874i
$364$	13.7166	+	38.3134i	0.718943	+	2.00817i
$365$	−14.2906	+	1.40154i	−0.748002	+	0.0733600i
$366$	1.24388	+	4.69169i	0.0650188	+	0.245238i
$367$	3.00569	+	2.52207i	0.156896	+	0.131651i	0.717856	−	0.696192i	$-0.245124\pi$
$367$	3.00569	+	2.52207i	0.156896	+	0.131651i	−0.560960	+	0.827843i	$0.689568\pi$
$368$	−11.9074	+	4.19223i	−0.620714	+	0.218535i
$369$	6.50551	−	3.75596i	0.338663	−	0.195527i
$370$	14.9460	−	2.75667i	0.777007	−	0.143312i
$371$	−0.0686307	+	0.389224i	−0.00356313	+	0.0202075i
$372$	−1.02134	−	5.97643i	−0.0529539	−	0.309864i
$373$	−0.240112	+	0.415886i	−0.0124325	+	0.0215337i	−0.872175	−	0.489194i	$-0.837291\pi$
$373$	−0.240112	+	0.415886i	−0.0124325	+	0.0215337i	0.859742	+	0.510728i	$0.170624\pi$
$374$	−0.934236	−	0.0842179i	−0.0483082	−	0.00435480i
$375$	2.35613	+	4.66354i	0.121670	+	0.240824i
$376$	18.1685	+	26.3891i	0.936968	+	1.36092i
$377$	−12.1679	−	14.5011i	−0.626678	−	0.746846i
$378$	9.10407	−	9.05618i	0.468263	−	0.465800i
$379$	−12.0512			−0.619030			−0.309515	−	0.950895i	$-0.600167\pi$
$379$	−12.0512			−0.619030			−0.309515	+	0.950895i	$0.600167\pi$
$380$	15.7276	+	11.5170i	0.806810	+	0.590811i
$381$	−8.93391			−0.457698
$382$	−14.6308	+	14.5539i	−0.748579	+	0.744641i
$383$	−5.15486	−	6.14332i	−0.263401	−	0.313909i	0.618092	−	0.786105i	$-0.287906\pi$
$383$	−5.15486	−	6.14332i	−0.263401	−	0.313909i	−0.881493	+	0.472196i	$0.843461\pi$
$384$	−5.25774	−	0.557952i	−0.268308	−	0.0284729i
$385$	0.768049	+	0.525868i	0.0391434	+	0.0268007i
$386$	−3.44181	−	0.310267i	−0.175184	−	0.0157922i
$387$	−16.7349	+	28.9857i	−0.850682	+	1.47343i
$388$	21.6199	−	3.69471i	1.09758	−	0.187571i
$389$	0.0952729	−	0.540320i	0.00483053	−	0.0273953i	−0.982297	−	0.187329i	$-0.940017\pi$
$389$	0.0952729	−	0.540320i	0.00483053	−	0.0273953i	0.987128	+	0.159934i	$0.0511281\pi$
$390$	−1.62296	−	8.79934i	−0.0821819	−	0.445572i
$391$	−14.6351	+	8.44958i	−0.740129	+	0.427313i
$392$	−11.7056	−	3.23596i	−0.591221	−	0.163441i
$393$	−2.21506	−	1.85866i	−0.111735	−	0.0937568i
$394$	8.69997	+	32.8146i	0.438298	+	1.65318i
$395$	−2.47164	−	25.2017i	−0.124362	−	1.26803i
$396$	−0.648785	+	0.232271i	−0.0326027	+	0.0116721i
$397$	12.2046	−	2.15200i	0.612532	−	0.108006i	0.141228	−	0.989977i	$-0.454895\pi$
$397$	12.2046	−	2.15200i	0.612532	−	0.108006i	0.471303	+	0.881971i	$0.343784\pi$
$398$	0.382089	+	0.548754i	0.0191524	+	0.0275066i
$399$	6.77081	−	1.01025i	0.338965	−	0.0505756i
$400$	7.03630	+	18.7214i	0.351815	+	0.936070i
$401$	25.1953	−	4.44261i	1.25819	−	0.221853i	0.495496	−	0.868610i	$-0.334986\pi$
$401$	25.1953	−	4.44261i	1.25819	−	0.221853i	0.762696	+	0.646757i	$0.223875\pi$
$402$	0.273203	−	1.00896i	0.0136261	−	0.0503223i
$403$	36.9072	−	13.4331i	1.83848	−	0.669152i
$404$	−13.6328	+	16.0741i	−0.678259	+	0.799714i
$405$	12.8761	−	9.21884i	0.639819	−	0.458088i
$406$	14.8060	−	1.25602i	0.734807	−	0.0623353i
$407$	−0.515566	+	0.297662i	−0.0255557	+	0.0147546i
$408$	−7.05565	+	0.561086i	−0.349307	+	0.0277779i
$409$	24.2784	+	4.28093i	1.20049	+	0.211679i	0.737910	−	0.674899i	$-0.235813\pi$
$409$	24.2784	+	4.28093i	1.20049	+	0.211679i	0.462579	+	0.886578i	$0.346924\pi$
$410$	6.58492	+	5.43780i	0.325206	+	0.268554i
$411$	−0.882597	+	1.52870i	−0.0435353	+	0.0754053i
$412$	12.8385	+	22.5102i	0.632506	+	1.10900i
$413$	−13.7507	−	5.00485i	−0.676629	−	0.246273i
$414$	−7.14762	+	10.1508i	−0.351286	+	0.498884i
$415$	6.89998	+	14.4005i	0.338707	+	0.706893i
$416$	−2.53501	−	34.1563i	−0.124289	−	1.67465i
$417$	3.14950			0.154232
$418$	−0.731510	−	0.218974i	−0.0357793	−	0.0107104i
$419$		−	7.31772i		−	0.357494i	−0.983895	−	0.178747i	$-0.942796\pi$
$419$		−	7.31772i		−	0.357494i	0.983895	−	0.178747i	$-0.0572044\pi$
$420$	6.38096	+	2.93503i	0.311359	+	0.143215i
$421$	−12.4412	−	14.8269i	−0.606348	−	0.722618i	0.372311	−	0.928108i	$-0.378566\pi$
$421$	−12.4412	−	14.8269i	−0.606348	−	0.722618i	−0.978659	+	0.205490i	$0.934121\pi$
$422$	5.97824	−	8.49008i	0.291016	−	0.413291i
$423$	29.6081	+	10.7765i	1.43960	+	0.523970i
$424$	0.142960	−	0.300352i	0.00694275	−	0.0145864i
$425$	13.8705	+	22.9005i	0.672817	+	1.11084i
$426$	−0.839010	+	1.78695i	−0.0406502	+	0.0865778i
$427$	4.28577	−	24.3058i	0.207403	−	1.17624i
$428$	12.0670	−	20.6484i	0.583279	−	0.998076i
$429$	0.175246	+	0.303535i	0.00846095	+	0.0146548i
$430$	−37.5230	−	6.31269i	−1.80952	−	0.304425i
$431$	−17.1074	−	14.3548i	−0.824032	−	0.691445i	0.129880	−	0.991530i	$-0.458541\pi$
$431$	−17.1074	−	14.3548i	−0.824032	−	0.691445i	−0.953913	+	0.300085i	$0.902985\pi$
$432$	−9.41623	+	5.30484i	−0.453039	+	0.255229i
$433$	−19.6537	+	7.15338i	−0.944499	+	0.343769i	−0.767941	−	0.640521i	$-0.778718\pi$
$433$	−19.6537	+	7.15338i	−0.944499	+	0.343769i	−0.176558	+	0.984290i	$0.556496\pi$
$434$	−8.05785	+	29.7582i	−0.386789	+	1.42844i
$435$	−3.25753	−	0.250577i	−0.156187	−	0.0120142i
$436$	1.85262	+	0.685384i	0.0887244	+	0.0328240i
$437$	−13.0466	+	4.36186i	−0.624104	+	0.208656i
$438$	3.48296	−	2.42513i	0.166422	−	0.115877i
$439$	−3.98417	−	22.5954i	−0.190154	−	1.07842i	−0.919152	−	0.393903i	$-0.871125\pi$
$439$	−3.98417	−	22.5954i	−0.190154	−	1.07842i	0.728998	−	0.684516i	$-0.239986\pi$
$440$	−0.505121	−	0.598829i	−0.0240807	−	0.0285481i
$441$	−11.2233	+	4.08494i	−0.534442	+	0.194521i
$442$	−11.7500	−	44.3188i	−0.558891	−	2.10803i
$443$	−1.68095	−	1.41048i	−0.0798641	−	0.0670139i	0.601982	−	0.798510i	$-0.294378\pi$
$443$	−1.68095	−	1.41048i	−0.0798641	−	0.0670139i	−0.681846	+	0.731496i	$0.738822\pi$
$444$	−3.45630	+	2.86925i	−0.164029	+	0.136169i
$445$	−2.60150	−	9.31669i	−0.123323	−	0.441653i
$446$	13.2164	−	6.12055i	0.625817	−	0.289817i
$447$	7.54998	+	1.33127i	0.357102	+	0.0629667i
$448$	23.0675	+	13.8092i	1.08984	+	0.652421i
$449$	7.27665	+	4.20118i	0.343406	+	0.198266i	0.661777	−	0.749700i	$-0.269802\pi$
$449$	7.27665	+	4.20118i	0.343406	+	0.198266i	−0.318371	+	0.947966i	$0.603136\pi$
$450$	16.3161	+	10.9840i	0.769150	+	0.517791i
$451$	−0.314344	−	0.114412i	−0.0148019	−	0.00538744i
$452$	−0.0886612	+	16.8117i	−0.00417027	+	0.790757i
$453$	3.76178	+	4.48311i	0.176744	+	0.210635i
$454$	9.44263	−	9.39297i	0.443165	−	0.440834i
$455$	−11.3139	+	44.0689i	−0.530403	+	2.06598i
$456$	−5.71912	−	0.698873i	−0.267822	−	0.0327277i
$457$			5.17318i			0.241991i	0.992653	+	0.120996i	$0.0386087\pi$
$457$			5.17318i			0.241991i	−0.992653	+	0.120996i	$0.961391\pi$
$458$	11.7416	+	11.8037i	0.548648	+	0.551549i
$459$	−11.0831	+	9.29986i	−0.517317	+	0.434081i
$460$	−13.6518	−	3.58169i	−0.636518	−	0.166997i
$461$	−33.6010	−	12.2297i	−1.56495	−	0.569596i	−0.593088	−	0.805137i	$-0.702091\pi$
$461$	−33.6010	−	12.2297i	−1.56495	−	0.569596i	−0.971864	+	0.235541i	$0.924314\pi$
$462$	−0.274010	−	0.0247010i	−0.0127481	−	0.00114919i
$463$	−12.9520	+	22.4334i	−0.601928	+	1.04257i	0.390601	+	0.920560i	$0.372267\pi$
$463$	−12.9520	+	22.4334i	−0.601928	+	1.04257i	−0.992529	+	0.122010i	$0.961066\pi$
$464$	−12.2924	−	2.30143i	−0.570662	−	0.106841i
$465$	2.80018	−	6.17334i	0.129855	−	0.286282i
$466$	0.544816	−	0.252305i	0.0252381	−	0.0116878i
$467$	−6.29519	−	10.9036i	−0.291306	−	0.504558i	0.682812	−	0.730594i	$-0.260757\pi$
$467$	−6.29519	−	10.9036i	−0.291306	−	0.504558i	−0.974119	+	0.226036i	$0.927423\pi$
$468$	−21.5148	−	25.9167i	−0.994520	−	1.19800i
$469$	−3.41652	+	4.07165i	−0.157760	+	0.188012i
$470$	0.281493	+	35.8193i	0.0129843	+	1.65222i
$471$	1.87142	−	0.681140i	0.0862303	−	0.0313853i
$472$	10.0324	+	7.14368i	0.461777	+	0.328814i
$473$	1.46782	−	0.258817i	0.0674905	−	0.0119004i
$474$	4.27676	+	6.14225i	0.196438	+	0.282123i
$475$	7.34286	+	20.5203i	0.336914	+	0.941536i
$476$	33.7544	+	12.4876i	1.54713	+	0.572367i
$477$	−0.0568059	−	0.322163i	−0.00260097	−	0.0147508i
$478$	−41.0851	−	11.1249i	−1.87919	−	0.508842i
$479$	−9.04170	−	24.8419i	−0.413126	−	1.13505i	−0.955519	−	0.294929i	$-0.904704\pi$
$479$	−9.04170	−	24.8419i	−0.413126	−	1.13505i	0.542393	−	0.840125i	$-0.317518\pi$
$480$	−4.51811	−	3.81190i	−0.206223	−	0.173988i
$481$	−22.2912	−	18.7045i	−1.01639	−	0.852852i
$482$	−11.3347	+	0.961551i	−0.516283	+	0.0437974i
$483$	−4.29245	+	2.47825i	−0.195313	+	0.112764i
$484$	−18.9678	−	11.0848i	−0.862172	−	0.503856i
$485$	22.3322	+	10.1297i	1.01405	+	0.459966i
$486$	−6.86128	+	14.6133i	−0.311234	+	0.662874i
$487$	12.9509	+	7.47722i	0.586862	+	0.338825i	0.763856	−	0.645387i	$-0.223304\pi$
$487$	12.9509	+	7.47722i	0.586862	+	0.338825i	−0.176994	+	0.984212i	$0.556637\pi$
$488$	−8.92740	+	18.7561i	−0.404124	+	0.849047i
$489$	1.63643	−	4.49604i	0.0740017	−	0.203318i
$490$	−8.80931	−	10.3325i	−0.397964	−	0.466776i
$491$	14.1447	+	16.8570i	0.638341	+	0.760745i	0.984107	−	0.177576i	$-0.0568255\pi$
$491$	14.1447	+	16.8570i	0.638341	+	0.760745i	−0.345767	+	0.938321i	$0.612381\pi$
$492$	−2.48344	−	0.451414i	−0.111962	−	0.0203513i
$493$	−16.7415			−0.753999
$494$	−2.17136	−	37.2601i	−0.0976943	−	1.67641i
$495$	−0.746248	−	0.191585i	−0.0335413	−	0.00861111i
$496$	13.2101	−	22.3332i	0.593150	−	1.00279i
$497$	7.68961	−	6.45235i	0.344926	−	0.289427i
$498$	−3.85898	−	2.71728i	−0.172925	−	0.121764i
$499$	10.3844	−	28.5310i	0.464870	−	1.27722i	−0.456912	−	0.889512i	$-0.651044\pi$
$499$	10.3844	−	28.5310i	0.464870	−	1.27722i	0.921782	−	0.387709i	$-0.126733\pi$
$500$	−5.21929	+	21.7430i	−0.233414	+	0.972378i
$501$	−3.86815	+	6.69984i	−0.172816	+	0.299327i
$502$	−2.47483	+	5.27095i	−0.110457	+	0.235254i
$503$	−2.58938	+	14.6851i	−0.115455	+	0.654778i	0.871069	+	0.491161i	$0.163427\pi$
$503$	−2.58938	+	14.6851i	−0.115455	+	0.654778i	−0.986524	+	0.163617i	$0.947684\pi$
$504$	26.3567	−	2.09596i	1.17402	−	0.0933614i
$505$	−22.6963	+	6.33750i	−1.00997	+	0.282015i
$506$	0.550873	−	0.0467317i	0.0244893	−	0.00207748i
$507$	−7.10697	+	8.46975i	−0.315632	+	0.376155i
$508$	−29.1587	−	24.7302i	−1.29371	−	1.09723i
$509$	1.62332	+	4.46003i	0.0719524	+	0.197688i	0.970456	−	0.241279i	$-0.0775669\pi$
$509$	1.62332	+	4.46003i	0.0719524	+	0.197688i	−0.898503	+	0.438967i	$0.855345\pi$
$510$	−6.88405	−	3.90270i	−0.304831	−	0.172815i
$511$	−21.2527	+	3.74742i	−0.940164	+	0.165776i
$512$	−15.6158	−	16.3752i	−0.690128	−	0.723687i
$513$	−10.3516	+	5.61722i	−0.457032	+	0.248006i
$514$	9.31926	−	6.48886i	0.411055	−	0.286211i
$515$	−2.22208	+	28.8874i	−0.0979167	+	1.27293i
$516$	10.5883	−	3.79071i	0.466124	−	0.166877i
$517$	−0.479894	−	1.31850i	−0.0211057	−	0.0579875i
$518$	22.0787	−	5.85362i	0.970083	−	0.257193i
$519$	−2.92591	+	3.48696i	−0.128433	+	0.153060i
$520$	19.0607	−	33.2120i	0.835866	−	1.45644i
$521$	30.2443	−	17.4615i	1.32502	−	0.765004i	0.340499	−	0.940245i	$-0.389404\pi$
$521$	30.2443	−	17.4615i	1.32502	−	0.765004i	0.984526	+	0.175241i	$0.0560705\pi$
$522$	−11.1603	+	5.16836i	−0.488474	+	0.226213i
$523$	−38.8181	−	6.84468i	−1.69740	−	0.299297i	−0.760613	−	0.649205i	$-0.775102\pi$
$523$	−38.8181	−	6.84468i	−1.69740	−	0.299297i	−0.936784	+	0.349908i	$0.886213\pi$
$524$	−2.08455	−	12.1979i	−0.0910640	−	0.532867i
$525$	4.06819	+	6.71667i	0.177550	+	0.293140i
$526$	8.76917	+	0.790508i	0.382354	+	0.0344678i
$527$	11.8802	−	32.6406i	0.517510	−	1.42185i
$528$	0.216741	+	0.0814861i	0.00943243	+	0.00354623i
$529$	−9.98922	+	8.38195i	−0.434314	+	0.364433i
$530$	0.320606	−	0.188476i	0.0139262	−	0.00818689i
$531$	12.1120			0.525615
$532$	24.8952	+	15.4452i	1.07934	+	0.669636i
$533$		−	16.3510i		−	0.708241i
$534$	2.01631	+	2.02697i	0.0872543	+	0.0877157i
$535$	24.1136	−	11.5540i	1.04252	−	0.499522i
$536$	3.68462	−	2.53680i	0.159151	−	0.109573i
$537$	−2.32181	+	6.37911i	−0.100193	+	0.275279i
$538$	−3.13467	+	34.7731i	−0.135145	+	1.49917i
$539$	0.460610	+	0.265933i	0.0198399	+	0.0114546i
$540$	−12.0427	−	0.990267i	−0.518237	−	0.0426143i
$541$	1.29084	−	7.32072i	0.0554976	−	0.314742i	−0.944404	−	0.328788i	$-0.893360\pi$
$541$	1.29084	−	7.32072i	0.0554976	−	0.314742i	0.999901	+	0.0140456i	$0.00447099\pi$
$542$	23.3610	−	10.8185i	1.00344	−	0.464694i
$543$	−5.01630	−	8.68849i	−0.215270	−	0.372859i
$544$	−24.5815	−	17.6997i	−1.05392	−	0.758868i
$545$	1.28566	+	1.79570i	0.0550715	+	0.0769192i
$546$	−3.44626	−	12.9986i	−0.147486	−	0.556290i
$547$	11.5905	+	31.8446i	0.495573	+	1.36158i	0.895513	+	0.445034i	$0.146809\pi$
$547$	11.5905	+	31.8446i	0.495573	+	1.36158i	−0.399941	+	0.916541i	$0.630969\pi$
$548$	−7.11229	+	2.54626i	−0.303822	+	0.108771i
$549$	3.54735	+	20.1180i	0.151397	+	0.858617i
$550$	−0.0923397	−	0.871007i	−0.00393738	−	0.0371399i
$551$	−13.3539	−	2.72021i	−0.568894	−	0.115885i
$552$	4.03785	−	1.04778i	0.171862	−	0.0445963i
$553$	−6.60865	−	37.4795i	−0.281028	−	1.59379i
$554$	6.36164	+	1.72259i	0.270280	+	0.0731858i
$555$	−4.99830	+	0.490206i	−0.212166	+	0.0208081i
$556$	10.2794	+	8.71824i	0.435944	+	0.369736i
$557$	−7.87765	+	9.38822i	−0.333787	+	0.397792i	−0.906667	−	0.421848i	$-0.861382\pi$
$557$	−7.87765	+	9.38822i	−0.333787	+	0.397792i	0.572880	+	0.819639i	$0.305826\pi$
$558$	−2.15700	−	25.4267i	−0.0913132	−	1.07640i
$559$	36.4264	+	63.0924i	1.54067	+	2.66853i
$560$	12.7018	+	27.2427i	0.536748	+	1.15122i
$561$	0.305264	+	0.0538263i	0.0128883	+	0.00227255i
$562$	−12.2502	+	26.0908i	−0.516744	+	1.10057i
$563$	3.27238	+	1.88931i	0.137915	+	0.0796250i	0.567370	−	0.823463i	$-0.307961\pi$
$563$	3.27238	+	1.88931i	0.137915	+	0.0796250i	−0.429455	+	0.903088i	$0.641294\pi$
$564$	−5.24523	−	9.19668i	−0.220864	−	0.387250i
$565$	−10.6189	+	15.5094i	−0.446742	+	0.652484i
$566$	−10.1930	+	14.4757i	−0.428444	+	0.608460i
$567$	18.2321	−	15.2985i	0.765675	−	0.642477i
$568$	−7.68488	+	3.50978i	−0.322450	+	0.147267i
$569$			5.11343i			0.214366i	0.994239	+	0.107183i	$0.0341831\pi$
$569$			5.11343i			0.214366i	−0.994239	+	0.107183i	$0.965817\pi$
$570$	−4.85695	−	4.23154i	−0.203435	−	0.177240i
$571$			15.0942i			0.631673i	0.948814	+	0.315836i	$0.102285\pi$
$571$			15.0942i			0.631673i	−0.948814	+	0.315836i	$0.897715\pi$
$572$	−0.268253	+	1.47579i	−0.0112162	+	0.0617057i
$573$	5.22404	−	4.38349i	0.218237	−	0.183123i
$574$	10.4942	+	7.38946i	0.438021	+	0.308430i
$575$	−10.3945	−	11.8724i	−0.433481	−	0.495114i
$576$	−21.8509	−	4.21038i	−0.910452	−	0.175432i
$577$	31.4897	+	18.1806i	1.31093	+	0.756867i	0.982250	−	0.187574i	$-0.0600624\pi$
$577$	31.4897	+	18.1806i	1.31093	+	0.756867i	0.328681	+	0.944441i	$0.393396\pi$
$578$	−14.9428	−	7.01596i	−0.621538	−	0.291825i
$579$	1.12462	+	0.198301i	0.0467377	+	0.00824112i
$580$	−9.93836	−	9.83511i	−0.412668	−	0.408381i
$581$	11.9995	+	20.7837i	0.497821	+	0.862252i
$582$	−7.22201	+	0.612659i	−0.299362	+	0.0253955i
$583$	−0.00936397	+	0.0111595i	−0.000387816	+	0.000462181i
$584$	18.0808	+	1.72609i	0.748190	+	0.0714263i
$585$	−3.67575	−	37.4791i	−0.151974	−	1.54957i
$586$	−0.819960	+	3.02817i	−0.0338722	+	0.125093i
$587$	−8.00064	−	45.3739i	−0.330222	−	1.87278i	−0.470100	−	0.882613i	$-0.655782\pi$
$587$	−8.00064	−	45.3739i	−0.330222	−	1.87278i	0.139878	−	0.990169i	$-0.455329\pi$
$588$	3.76392	+	1.39248i	0.155221	+	0.0574248i
$589$	14.7798	−	24.1055i	0.608992	−	0.993249i
$590$	4.81100	+	12.9017i	0.198066	+	0.531156i
$591$	−1.94805	−	11.0479i	−0.0801319	−	0.454451i
$592$	−19.2232	−	0.202763i	−0.790069	−	0.00833352i
$593$	−12.5909	−	34.5933i	−0.517047	−	1.42058i	−0.873758	−	0.486361i	$-0.838324\pi$
$593$	−12.5909	−	34.5933i	−0.517047	−	1.42058i	0.356711	−	0.934215i	$-0.383898\pi$
$594$	0.457511	−	0.121298i	0.0187719	−	0.00497690i
$595$	23.4244	+	32.7173i	0.960308	+	1.34128i
$596$	20.9567	+	25.2444i	0.858418	+	1.03405i
$597$	−0.110483	−	0.191362i	−0.00452176	−	0.00783192i
$598$	11.3558	+	24.5212i	0.464373	+	1.00274i
$599$	−0.850222	+	4.82185i	−0.0347391	+	0.197015i	−0.997238	−	0.0742695i	$-0.976337\pi$
$599$	−0.850222	+	4.82185i	−0.0347391	+	0.197015i	0.962499	+	0.271285i	$0.0874486\pi$
$600$	−1.79391	−	6.36096i	−0.0732360	−	0.259685i
$601$	1.65208	+	0.953830i	0.0673899	+	0.0389076i	0.533316	−	0.845916i	$-0.320946\pi$
$601$	1.65208	+	0.953830i	0.0673899	+	0.0389076i	−0.465926	+	0.884823i	$0.654279\pi$
$602$	−56.9554	−	5.13432i	−2.32133	−	0.209259i
$603$	1.50468	−	4.13407i	0.0612753	−	0.168352i
$604$	−0.132082	+	25.0452i	−0.00537436	+	1.01907i
$605$	−10.6136	−	22.1510i	−0.431504	−	0.900564i
$606$	4.93789	−	4.91192i	0.200588	−	0.199533i
$607$		−	16.1506i		−	0.655533i	−0.944759	−	0.327767i	$-0.893704\pi$
$607$		−	16.1506i		−	0.655533i	0.944759	−	0.327767i	$-0.106296\pi$
$608$	−16.7316	−	18.1123i	−0.678555	−	0.734549i
$609$	−4.91026			−0.198974
$610$	−20.0208	+	11.7698i	−0.810619	+	0.476544i
$611$	52.5379	−	44.0846i	2.12546	−	1.78347i
$612$	−29.7889	−	0.157100i	−1.20414	−	0.00635038i
$613$	−9.84341	+	27.0446i	−0.397572	+	1.09232i	0.565892	+	0.824480i	$0.308532\pi$
$613$	−9.84341	+	27.0446i	−0.397572	+	1.09232i	−0.963463	+	0.267840i	$0.913690\pi$
$614$	−1.28070	+	14.2069i	−0.0516849	+	0.573345i
$615$	−2.01633	−	1.97445i	−0.0813064	−	0.0796173i
$616$	−0.825943	−	0.839115i	−0.0332782	−	0.0338089i
$617$	−7.05674	−	1.24429i	−0.284094	−	0.0500934i	0.0297856	−	0.999556i	$-0.490518\pi$
$617$	−7.05674	−	1.24429i	−0.284094	−	0.0500934i	−0.313879	+	0.949463i	$0.601629\pi$
$618$	−3.59856	−	7.77057i	−0.144755	−	0.312578i
$619$	−18.0822	+	10.4398i	−0.726787	+	0.419610i	−0.817245	−	0.576290i	$-0.804500\pi$
$619$	−18.0822	+	10.4398i	−0.726787	+	0.419610i	0.0904588	+	0.995900i	$0.471167\pi$
$620$	26.2279	−	12.3974i	1.05334	−	0.497892i
$621$	5.48114	−	6.53217i	0.219951	−	0.262127i
$622$	0.138928	+	0.524009i	0.00557050	+	0.0210108i
$623$	−4.97223	−	13.6611i	−0.199208	−	0.547320i
$624$	−0.119375	+	11.3175i	−0.00477883	+	0.453062i
$625$	−18.4598	+	16.8593i	−0.738392	+	0.674372i
$626$	−18.4880	−	26.5523i	−0.738927	−	1.06124i
$627$	0.234749	+	0.0925349i	0.00937496	+	0.00369549i
$628$	7.99345	+	2.95721i	0.318973	+	0.118005i
$629$	−25.3441	+	4.46885i	−1.01054	+	0.178185i
$630$	25.7157	+	14.5787i	1.02454	+	0.580829i
$631$	−7.09703	−	19.4989i	−0.282528	−	0.776240i	−0.997059	−	0.0766361i	$-0.975582\pi$
$631$	−7.09703	−	19.4989i	−0.282528	−	0.776240i	0.714531	−	0.699604i	$-0.246640\pi$
$632$	−3.04400	+	31.8858i	−0.121084	+	1.26835i
$633$	−2.20561	+	2.62855i	−0.0876653	+	0.104475i
$634$	−3.40811	−	40.1748i	−0.135354	−	1.59554i
$635$	−11.4964	−	41.1716i	−0.456219	−	1.63384i
$636$	−0.0554623	+	0.0949041i	−0.00219922	+	0.00376319i
$637$	−4.51438	+	25.6023i	−0.178866	+	1.01440i
$638$	0.495767	+	0.232773i	0.0196276	+	0.00921558i
$639$	−4.15428	+	7.19542i	−0.164341	+	0.284646i
$640$	−4.19447	−	24.9481i	−0.165801	−	0.986159i
$641$	−7.23199	+	19.8697i	−0.285647	+	0.784808i	0.711016	+	0.703176i	$0.248235\pi$
$641$	−7.23199	+	19.8697i	−0.285647	+	0.784808i	−0.996663	+	0.0816317i	$0.973987\pi$
$642$	−4.55007	+	6.46184i	−0.179577	+	0.255029i
$643$	−10.6935	+	8.97290i	−0.421710	+	0.353856i	−0.828813	−	0.559526i	$-0.810983\pi$
$643$	−10.6935	+	8.97290i	−0.421710	+	0.353856i	0.407103	+	0.913382i	$0.366539\pi$
$644$	−20.8699	−	3.79352i	−0.822390	−	0.149486i
$645$	12.1789	+	3.12671i	0.479544	+	0.123114i
$646$	−26.4776	−	19.7105i	−1.04175	−	0.775500i
$647$	13.2331			0.520246			0.260123	−	0.965576i	$-0.416237\pi$
$647$	13.2331			0.520246			0.260123	+	0.965576i	$0.416237\pi$
$648$	−18.2208	+	8.32168i	−0.715782	+	0.326907i
$649$	−0.346698	−	0.413178i	−0.0136091	−	0.0162187i
$650$	38.4630	−	18.8025i	1.50864	−	0.737496i
$651$	3.48445	−	9.57344i	0.136566	−	0.375213i
$652$	17.7866	−	10.1444i	0.696578	−	0.397286i
$653$	10.2474	+	5.91634i	0.401012	+	0.231524i	0.686921	−	0.726732i	$-0.258962\pi$
$653$	10.2474	+	5.91634i	0.401012	+	0.231524i	−0.285908	+	0.958257i	$0.592295\pi$
$654$	−0.590869	−	0.277426i	−0.0231048	−	0.0108482i
$655$	5.71516	−	12.5998i	0.223310	−	0.492314i
$656$	−6.85591	−	8.34781i	−0.267678	−	0.325927i
$657$	15.4692	−	8.93116i	0.603512	−	0.348438i
$658$	4.55060	+	53.6424i	0.177401	+	2.09120i
$659$	7.77585	+	6.52471i	0.302904	+	0.254167i	0.781552	−	0.623840i	$-0.214428\pi$
$659$	7.77585	+	6.52471i	0.302904	+	0.254167i	−0.478648	+	0.878007i	$0.658873\pi$
$660$	0.149595	+	0.211287i	0.00582297	+	0.00822432i
$661$	1.60132	+	4.39958i	0.0622840	+	0.171124i	0.966931	−	0.255038i	$-0.0820878\pi$
$661$	1.60132	+	4.39958i	0.0622840	+	0.171124i	−0.904647	+	0.426161i	$0.859866\pi$
$662$	−7.25195	+	26.7820i	−0.281855	+	1.04091i
$663$	2.63099	+	14.9211i	0.102179	+	0.579488i
$664$	−5.07323	−	19.5509i	−0.196880	−	0.758722i
$665$	13.3685	+	29.9030i	0.518409	+	1.15959i
$666$	−15.5154	+	10.8032i	−0.601211	+	0.418614i
$667$	9.71718	−	1.71340i	0.376251	−	0.0663431i
$668$	−31.1710	+	11.1595i	−1.20604	+	0.431774i
$669$	−4.52276	+	1.64615i	−0.174860	+	0.0636438i
$670$	5.00131	−	0.0393038i	0.193218	−	0.00151844i
$671$	0.584750	−	0.696878i	0.0225740	−	0.0269027i
$672$	−7.20973	−	5.19129i	−0.278121	−	0.200259i
$673$	−9.59635	−	16.6214i	−0.369912	−	0.640706i	0.619639	−	0.784887i	$-0.287279\pi$
$673$	−9.59635	−	16.6214i	−0.369912	−	0.640706i	−0.989551	+	0.144180i	$0.953945\pi$
$674$	−5.68764	−	12.2816i	−0.219080	−	0.473071i
$675$	−10.5290	−	8.46470i	−0.405260	−	0.325806i
$676$	−46.6413	+	7.97072i	−1.79389	+	0.306566i
$677$	14.3635	−	24.8783i	0.552034	−	0.956150i	−0.446094	−	0.894986i	$-0.647185\pi$
$677$	14.3635	−	24.8783i	0.552034	−	0.956150i	0.998128	−	0.0611642i	$-0.0194813\pi$
$678$	0.498792	−	5.53314i	0.0191560	−	0.212499i
$679$	34.6322	+	12.6051i	1.32906	+	0.483738i
$680$	−11.6651	−	31.7937i	−0.447337	−	1.21923i
$681$	−3.37156	+	2.82907i	−0.129198	+	0.108410i
$682$	−0.805644	+	0.801406i	−0.0308497	+	0.0306874i
$683$			19.2351i			0.736010i	0.929824	+	0.368005i	$0.119959\pi$
$683$			19.2351i			0.736010i	−0.929824	+	0.368005i	$0.880041\pi$
$684$	−23.7356	−	4.96550i	−0.907553	−	0.189861i
$685$	−8.18071	−	2.10025i	−0.312569	−	0.0802463i
$686$	9.07059	+	9.11855i	0.346317	+	0.348148i
$687$	−3.53645	−	4.21458i	−0.134924	−	0.160796i
$688$	45.0515	+	16.9376i	1.71757	+	0.645741i
$689$	−0.669119	−	0.243539i	−0.0254914	−	0.00927811i
$690$	4.39509	+	1.56068i	0.167318	+	0.0594141i
$691$	−28.8741	−	16.6705i	−1.09842	−	0.634175i	−0.162617	−	0.986689i	$-0.551994\pi$
$691$	−28.8741	−	16.6705i	−1.09842	−	0.634175i	−0.935807	+	0.352514i	$0.885327\pi$
$692$	−19.2020	+	3.28151i	−0.729950	+	0.124744i
$693$	−1.14033	−	0.201070i	−0.0433174	−	0.00763803i
$694$	5.46686	+	11.8049i	0.207519	+	0.448108i
$695$	4.05285	+	14.5144i	0.153733	+	0.550562i
$696$	3.98326	+	1.10116i	0.150985	+	0.0417392i
$697$	−11.0776	−	9.29520i	−0.419593	−	0.352081i
$698$	39.8336	−	10.5609i	1.50773	−	0.399736i
$699$	−0.186440	+	0.0678585i	−0.00705179	+	0.00256664i
$700$	−5.31479	+	33.1833i	−0.200880	+	1.25421i
$701$	2.17829	+	12.3537i	0.0822728	+	0.466592i	0.997912	+	0.0645908i	$0.0205742\pi$
$701$	2.17829	+	12.3537i	0.0822728	+	0.466592i	−0.915639	+	0.402001i	$0.868315\pi$
$702$	13.2199	+	18.9864i	0.498954	+	0.716594i
$703$	−20.9419	−	0.553405i	−0.789837	−	0.0208721i
$704$	0.481838	+	0.865923i	0.0181600	+	0.0326357i
$705$	0.907846	−	11.8021i	0.0341914	−	0.444494i
$706$	18.3382	+	4.96558i	0.690169	+	0.186882i
$707$	−33.2797	+	12.1128i	−1.25161	+	0.455549i
$708$	−3.10383	−	2.63244i	−0.116649	−	0.0989331i
$709$	1.97546	+	1.65761i	0.0741900	+	0.0622528i	0.679129	−	0.734019i	$-0.262358\pi$
$709$	1.97546	+	1.65761i	0.0741900	+	0.0622528i	−0.604939	+	0.796272i	$0.706802\pi$
$710$	−9.31473	−	1.56706i	−0.349575	−	0.0588109i
$711$	15.7503	+	27.2803i	0.590681	+	1.02309i
$712$	0.969947	+	12.1971i	0.0363503	+	0.457105i
$713$	−3.55498	+	20.1613i	−0.133135	+	0.755046i
$714$	−10.7655	−	5.05465i	−0.402890	−	0.189166i
$715$	−1.17332	+	1.19821i	−0.0438796	+	0.0448105i
$716$	−25.2362	+	14.3932i	−0.943120	+	0.537899i
$717$	13.2174	+	4.81074i	0.493613	+	0.179660i
$718$	36.5888	+	25.7638i	1.36548	+	0.961496i
$719$	25.1654	+	29.9910i	0.938512	+	1.11848i	0.992780	+	0.119949i	$0.0382731\pi$
$719$	25.1654	+	29.9910i	0.938512	+	1.11848i	−0.0542677	+	0.998526i	$0.517282\pi$
$720$	−17.5915	−	17.5933i	−0.655595	−	0.655664i
$721$			43.5436i			1.62165i
$722$	−17.9173	−	20.0243i	−0.666812	−	0.745226i
$723$	3.75906			0.139801
$724$	7.67859	−	42.2435i	0.285372	−	1.56997i
$725$	−3.03709	−	15.3347i	−0.112795	−	0.569515i
$726$	5.93591	+	4.17974i	0.220302	+	0.155125i
$727$	−11.4446	−	4.16549i	−0.424456	−	0.154489i	0.120955	−	0.992658i	$-0.461404\pi$
$727$	−11.4446	−	4.16549i	−0.424456	−	0.154489i	−0.545411	+	0.838169i	$0.683626\pi$
$728$	24.7340	−	51.9649i	0.916702	−	1.92595i
$729$	−7.95574	+	13.7798i	−0.294657	+	0.510361i
$730$	15.6581	+	12.9304i	0.579531	+	0.478574i
$731$	63.4519	+	11.1883i	2.34685	+	0.413814i
$732$	3.46344	−	5.92646i	0.128013	−	0.219048i
$733$	−3.59670	+	2.07656i	−0.132847	+	0.0766993i	−0.564951	−	0.825125i	$-0.691105\pi$
$733$	−3.59670	+	2.07656i	−0.132847	+	0.0766993i	0.432104	+	0.901824i	$0.357771\pi$
$734$	−0.469039	−	5.52902i	−0.0173125	−	0.204080i
$735$	2.61203	+	3.64827i	0.0963463	+	0.134568i
$736$	16.0792	+	7.75755i	0.592687	+	0.285947i
$737$	−0.184097	+	0.0670058i	−0.00678130	+	0.00246819i
$738$	−10.2542	−	2.77660i	−0.377462	−	0.102208i
$739$	11.4880	−	2.02564i	0.422593	−	0.0745145i	0.0416921	−	0.999131i	$-0.486725\pi$
$739$	11.4880	−	2.02564i	0.422593	−	0.0745145i	0.380900	+	0.924616i	$0.375614\pi$
$740$	−17.6705	−	12.2360i	−0.649580	−	0.449804i
$741$	−0.325812	+	12.3293i	−0.0119690	+	0.452929i
$742$	0.458699	−	0.319385i	0.0168394	−	0.0117250i
$743$	30.8221	−	5.43476i	1.13075	−	0.199382i	0.423195	−	0.906039i	$-0.360908\pi$
$743$	30.8221	−	5.43476i	1.13075	−	0.199382i	0.707557	+	0.706656i	$0.249797\pi$
$744$	−4.97353	+	6.98468i	−0.182338	+	0.256071i
$745$	3.58040	+	36.5069i	0.131176	+	1.33751i
$746$	0.656459	−	0.174044i	0.0240347	−	0.00637219i
$747$	−15.2167	−	12.7683i	−0.556750	−	0.467169i
$748$	0.847329	+	1.02069i	0.0309814	+	0.0373202i
$749$	34.8021	−	20.0930i	1.27164	−	0.734182i
$750$	2.32590	−	7.01356i	0.0849300	−	0.256099i
$751$	−4.62967	+	26.2561i	−0.168939	+	0.958100i	0.775971	+	0.630769i	$0.217260\pi$
$751$	−4.62967	+	26.2561i	−0.168939	+	0.958100i	−0.944910	+	0.327331i	$0.893851\pi$
$752$	8.33813	−	44.5358i	0.304060	−	1.62405i
$753$	0.962121	−	1.66644i	0.0350616	−	0.0607286i
$754$	−2.40355	+	26.6628i	−0.0875321	+	0.971000i
$755$	−15.8195	+	23.1050i	−0.575731	+	0.840876i
$756$	−18.1601	−	0.0957720i	−0.660475	−	0.00348319i
$757$	−3.58939	−	4.27767i	−0.130459	−	0.155474i	0.696861	−	0.717207i	$-0.254580\pi$
$757$	−3.58939	−	4.27767i	−0.130459	−	0.155474i	−0.827319	+	0.561732i	$0.810135\pi$
$758$	12.0194	+	12.0830i	0.436565	+	0.438873i
$759$	−0.182692			−0.00663129
$760$	−4.13875	−	27.2557i	−0.150128	−	0.988667i
$761$	−13.6711			−0.495578			−0.247789	−	0.968814i	$-0.579704\pi$
$761$	−13.6711			−0.495578			−0.247789	+	0.968814i	$0.579704\pi$
$762$	8.91032	+	8.95743i	0.322787	+	0.324494i
$763$	2.13353	+	2.54264i	0.0772388	+	0.0920497i
$764$	29.1844	+	0.153912i	1.05585	+	0.00556834i
$765$	−27.4812	−	18.8158i	−0.993585	−	0.680288i
$766$	−1.01825	+	11.2955i	−0.0367909	+	0.408124i
$767$	13.1819	−	22.8318i	0.475972	−	0.824407i
$768$	4.68443	+	5.82806i	0.169035	+	0.210302i
$769$	−7.87761	+	44.6761i	−0.284074	+	1.61106i	0.424501	+	0.905427i	$0.360450\pi$
$769$	−7.87761	+	44.6761i	−0.284074	+	1.61106i	−0.708575	+	0.705636i	$0.750662\pi$
$770$	−0.238769	−	1.29455i	−0.00860462	−	0.0466524i
$771$	−3.24981	+	1.87628i	−0.117039	+	0.0675726i
$772$	3.12164	+	3.76032i	0.112350	+	0.135337i
$773$	41.3702	+	34.7137i	1.48798	+	1.24857i	0.897114	+	0.441800i	$0.145660\pi$
$773$	41.3702	+	34.7137i	1.48798	+	1.24857i	0.590870	+	0.806767i	$0.298784\pi$
$774$	45.7527	−	12.1302i	1.64455	−	0.436011i
$775$	32.0529	+	4.96052i	1.15138	+	0.178187i
$776$	−25.2672	−	17.9919i	−0.907041	−	0.645870i
$777$	−7.43339	+	1.31071i	−0.266671	+	0.0470213i
$778$	−0.636764	+	0.443369i	−0.0228291	+	0.0158956i
$779$	−7.32574	−	9.21424i	−0.262472	−	0.330135i
$780$	−7.20384	+	10.4033i	−0.257939	+	0.372499i
$781$	0.364373	−	0.0642487i	0.0130383	−	0.00229900i
$782$	23.0683	+	6.24637i	0.824920	+	0.223370i
$783$	7.93814	−	2.88925i	0.283686	−	0.103253i
$784$	8.43019	+	14.9638i	0.301078	+	0.534422i
$785$	5.54718	+	7.74784i	0.197988	+	0.276532i
$786$	0.345661	+	4.07464i	0.0123293	+	0.145338i
$787$	29.7726	−	17.1892i	1.06128	−	0.612730i	0.135494	−	0.990778i	$-0.456738\pi$
$787$	29.7726	−	17.1892i	1.06128	−	0.612730i	0.925786	+	0.378048i	$0.123405\pi$
$788$	24.2240	−	41.4508i	0.862945	−	1.47663i
$789$	−2.86535	−	0.505239i	−0.102009	−	0.0179870i
$790$	−22.8029	+	27.6133i	−0.811291	+	0.982436i
$791$	−14.1246	+	24.4646i	−0.502215	+	0.869861i
$792$	0.879955	+	0.418836i	0.0312678	+	0.0148827i
$793$	41.7844	+	15.2083i	1.48381	+	0.540061i
$794$	−14.3301	−	10.0904i	−0.508555	−	0.358096i
$795$	−0.110831	+	0.0531044i	−0.00393076	+	0.00188342i
$796$	0.169119	−	0.930401i	0.00599426	−	0.0329772i
$797$	28.0059			0.992019			0.496009	−	0.868317i	$-0.334798\pi$
$797$	28.0059			0.992019			0.496009	+	0.868317i	$0.334798\pi$
$798$	−7.76584	−	5.78107i	−0.274908	−	0.204647i
$799$		−	60.6549i		−	2.14582i
$800$	11.7530	−	25.7268i	0.415530	−	0.909579i
$801$	7.73468	+	9.21783i	0.273291	+	0.325696i
$802$	−29.5831	−	20.8308i	−1.04461	−	0.735559i
$803$	−0.747468	−	0.272056i	−0.0263776	−	0.00960065i
$804$	−1.28410	+	0.732372i	−0.0452866	+	0.0258288i
$805$	−16.9445	−	16.5925i	−0.597217	−	0.584810i
$806$	−50.2783	−	23.6068i	−1.77098	−	0.831513i
$807$	2.00346	−	11.3622i	0.0705253	−	0.399969i
$808$	29.7132	−	2.36288i	1.04531	−	0.0831258i
$809$	1.69614	+	2.93780i	0.0596331	+	0.103288i	0.894301	−	0.447466i	$-0.147674\pi$
$809$	1.69614	+	2.93780i	0.0596331	+	0.103288i	−0.834668	+	0.550754i	$0.814340\pi$
$810$	−22.0852	−	3.71551i	−0.775996	−	0.130550i
$811$	30.5042	+	25.5961i	1.07115	+	0.898799i	0.995156	−	0.0983093i	$-0.0313434\pi$
$811$	30.5042	+	25.5961i	1.07115	+	0.898799i	0.0759913	+	0.997108i	$0.475788\pi$
$812$	−16.0262	−	13.5922i	−0.562409	−	0.476994i
$813$	−7.99428	+	2.90968i	−0.280372	+	0.102047i
$814$	0.812651	+	0.220047i	0.0284834	+	0.00771266i
$815$	22.8256	+	1.75580i	0.799547	+	0.0615030i
$816$	7.59959	+	6.51463i	0.266039	+	0.228058i
$817$	48.7946	+	19.2342i	1.70711	+	0.672920i
$818$	−19.9221	−	28.6120i	−0.696559	−	1.00039i
$819$	−9.82818	−	55.7384i	−0.343424	−	1.94766i
$820$	−1.11542	−	12.0257i	−0.0389521	−	0.419956i
$821$	19.7179	−	7.17672i	0.688159	−	0.250469i	0.0258123	−	0.999667i	$-0.491783\pi$
$821$	19.7179	−	7.17672i	0.688159	−	0.250469i	0.662347	+	0.749197i	$0.269561\pi$
$822$	2.41299	−	0.639745i	0.0841629	−	0.0223137i
$823$	−17.9835	−	15.0900i	−0.626866	−	0.526003i	0.273088	−	0.961989i	$-0.411955\pi$
$823$	−17.9835	−	15.0900i	−0.626866	−	0.526003i	−0.899953	+	0.435987i	$0.856400\pi$
$824$	9.76491	−	35.3230i	0.340177	−	1.23054i
$825$	0.00607514	+	0.289377i	0.000211509	+	0.0100748i
$826$	8.69638	+	18.7786i	0.302586	+	0.653390i
$827$	32.3805	+	5.70955i	1.12598	+	0.198541i	0.705465	−	0.708745i	$-0.250738\pi$
$827$	32.3805	+	5.70955i	1.12598	+	0.198541i	0.420515	+	0.907286i	$0.361849\pi$
$828$	17.3063	−	2.95754i	0.601434	−	0.102782i
$829$	42.2181	+	24.3746i	1.46629	+	0.846566i	0.999290	−	0.0376887i	$-0.0119995\pi$
$829$	42.2181	+	24.3746i	1.46629	+	0.846566i	0.467005	+	0.884254i	$0.345333\pi$
$830$	7.55667	−	21.2806i	0.262296	−	0.738662i
$831$	−2.04659	−	0.744897i	−0.0709954	−	0.0258402i
$832$	−31.7179	+	36.6078i	−1.09962	+	1.26915i
$833$	14.7789	+	17.6128i	0.512058	+	0.610247i
$834$	−3.14119	−	3.15780i	−0.108770	−	0.109346i
$835$	−35.8536	−	9.20474i	−1.24076	−	0.318543i
$836$	0.510028	+	0.951832i	0.0176397	+	0.0329198i
$837$			17.5271i			0.605826i
$838$	−7.33699	+	7.29840i	−0.253452	+	0.252119i
$839$	−19.1682	+	16.0840i	−0.661758	+	0.555281i	−0.910613	−	0.413260i	$-0.864390\pi$
$839$	−19.1682	+	16.0840i	−0.661758	+	0.555281i	0.248855	+	0.968541i	$0.419946\pi$
$840$	−3.42136	−	9.32504i	−0.118048	−	0.321745i
$841$	−18.0656	−	6.57533i	−0.622951	−	0.226735i
$842$	−2.45754	+	27.2617i	−0.0846925	+	0.939501i
$843$	4.76243	−	8.24877i	0.164027	−	0.284103i
$844$	−14.4749	+	2.47368i	−0.498246	+	0.0851475i
$845$	−48.1779	−	21.8531i	−1.65737	−	0.751770i
$846$	−18.7251	−	40.4341i	−0.643782	−	1.39015i
$847$	−18.4576	−	31.9696i	−0.634212	−	1.09849i
$848$	−0.443726	+	0.156223i	−0.0152376	+	0.00536471i
$849$	3.76061	−	4.48172i	0.129064	−	0.153812i
$850$	9.12691	−	36.7470i	0.313050	−	1.26041i
$851$	14.2530	−	5.18766i	0.488586	−	0.177831i
$852$	2.62845	−	0.941008i	0.0900491	−	0.0322384i
$853$	15.1375	−	2.66915i	0.518298	−	0.0913899i	0.0916210	−	0.995794i	$-0.470795\pi$
$853$	15.1375	−	2.66915i	0.518298	−	0.0913899i	0.426677	+	0.904404i	$0.359684\pi$
$854$	−28.6443	+	19.9446i	−0.980187	+	0.682490i
$855$	−18.8632	−	19.4737i	−0.645106	−	0.665986i
$856$	−32.7378	+	8.49509i	−1.11896	+	0.290356i
$857$	3.98933	+	22.6246i	0.136273	+	0.772841i	0.973965	+	0.226699i	$0.0727933\pi$
$857$	3.98933	+	22.6246i	0.136273	+	0.772841i	−0.837692	+	0.546143i	$0.816096\pi$
$858$	0.129551	−	0.478441i	0.00442280	−	0.0163337i
$859$	−7.89087	−	21.6800i	−0.269233	−	0.739711i	−0.998462	−	0.0554416i	$-0.982343\pi$
$859$	−7.89087	−	21.6800i	−0.269233	−	0.739711i	0.729229	−	0.684270i	$-0.239879\pi$
$860$	31.0946	+	43.9178i	1.06032	+	1.49759i
$861$	−3.24904	−	2.72627i	−0.110727	−	0.0929110i
$862$	2.66961	+	31.4693i	0.0909272	+	1.07185i
$863$	−2.31528	+	1.33673i	−0.0788132	+	0.0455028i	−0.538889	−	0.842377i	$-0.681156\pi$
$863$	−2.31528	+	1.33673i	−0.0788132	+	0.0455028i	0.460076	+	0.887880i	$0.347822\pi$
$864$	14.7102	+	4.15020i	0.500450	+	0.141193i
$865$	−19.8346	−	8.99683i	−0.674398	−	0.305901i
$866$	26.7741	+	12.5710i	0.909820	+	0.427180i
$867$	4.72425	+	2.72755i	0.160444	+	0.0926323i
$868$	37.8732	−	21.6006i	1.28550	−	0.733171i
$869$	0.479776	−	1.31817i	0.0162753	−	0.0447160i
$870$	2.99769	+	3.51602i	0.101631	+	0.119204i
$871$	−6.15536	−	7.33567i	−0.208566	−	0.248560i
$872$	−1.16054	−	2.54107i	−0.0393008	−	0.0860516i
$873$	−30.5049			−1.03243
$874$	17.3855	+	8.73063i	0.588074	+	0.295318i
$875$	−25.7185	+	27.3913i	−0.869443	+	0.925994i
$876$	−5.90528	−	1.07340i	−0.199521	−	0.0362669i
$877$	−0.198222	+	0.166328i	−0.00669349	+	0.00561650i	−0.646128	−	0.763229i	$-0.723613\pi$
$877$	−0.198222	+	0.166328i	−0.00669349	+	0.00561650i	0.639435	+	0.768845i	$0.279168\pi$
$878$	−18.6812	+	26.5304i	−0.630461	+	0.895357i
$879$	0.354575	−	0.974185i	0.0119595	−	0.0328585i
$880$	−0.0966191	+	1.10370i	−0.00325703	+	0.0372057i
$881$	−2.36861	+	4.10255i	−0.0798004	+	0.138218i	−0.903164	−	0.429296i	$-0.858762\pi$
$881$	−2.36861	+	4.10255i	−0.0798004	+	0.138218i	0.823363	+	0.567515i	$0.192095\pi$
$882$	15.2893	+	7.17868i	0.514819	+	0.241719i
$883$	−2.30439	+	13.0688i	−0.0775489	+	0.439801i	0.921168	+	0.389165i	$0.127236\pi$
$883$	−2.30439	+	13.0688i	−0.0775489	+	0.439801i	−0.998717	+	0.0506369i	$0.983875\pi$
$884$	−32.7165	+	55.9827i	−1.10038	+	1.88290i
$885$	−1.22374	−	4.38256i	−0.0411357	−	0.147318i
$886$	0.262312	+	3.09213i	0.00881255	+	0.103882i
$887$	−5.32020	+	6.34036i	−0.178635	+	0.212889i	−0.847930	−	0.530108i	$-0.822152\pi$
$887$	−5.32020	+	6.34036i	−0.178635	+	0.212889i	0.669296	+	0.742996i	$0.266596\pi$
$888$	6.32398	+	0.603722i	0.212219	+	0.0202596i
$889$	−21.9729	−	60.3700i	−0.736947	−	2.02474i
$890$	−6.74659	+	11.9004i	−0.226146	+	0.398904i
$891$	0.863928	−	0.152334i	0.0289427	−	0.00510337i
$892$	−19.3182	−	7.14686i	−0.646822	−	0.239294i
$893$	9.85539	−	48.3814i	0.329798	−	1.61902i
$894$	−6.19528	−	8.89762i	−0.207201	−	0.297581i
$895$	−32.3856	−	2.49118i	−1.08253	−	0.0832708i
$896$	−9.16106	−	36.9009i	−0.306050	−	1.23277i
$897$	−3.05419	−	8.39131i	−0.101976	−	0.280178i
$898$	−3.04520	−	11.4859i	−0.101620	−	0.383289i
$899$	−13.0366	+	15.5364i	−0.434794	+	0.518168i
$900$	−5.26013	−	27.3141i	−0.175338	−	0.910471i
$901$	−0.545374	+	0.314872i	−0.0181691	+	0.0104899i
$902$	0.198801	+	0.429282i	0.00661935	+	0.0142935i
$903$	18.6104	+	3.28151i	0.619314	+	0.109202i
$904$	16.9444	−	16.6784i	0.563563	−	0.554716i
$905$	33.5855	−	34.2980i	1.11642	−	1.14010i
$906$	0.743072	−	8.24296i	0.0246869	−	0.273854i
$907$	5.86772	−	16.1214i	0.194834	−	0.535303i	−0.803352	−	0.595505i	$-0.796952\pi$
$907$	5.86772	−	16.1214i	0.194834	−	0.535303i	0.998186	+	0.0602014i	$0.0191743\pi$
$908$	−18.8354	−	0.0993336i	−0.625075	−	0.00329650i
$909$	22.4555	−	18.8424i	0.744801	−	0.624962i
$910$	55.4690	−	32.6089i	1.83878	−	1.08097i
$911$	−55.5736			−1.84123			−0.920617	−	0.390467i	$-0.872314\pi$
$911$	−55.5736			−1.84123			−0.920617	+	0.390467i	$0.872314\pi$
$912$	5.00330	+	6.43120i	0.165676	+	0.212958i
$913$			0.884577i			0.0292752i
$914$	5.18681	−	5.15953i	0.171564	−	0.170662i
$915$	6.92104	−	3.31620i	0.228802	−	0.109630i
$916$	0.124171	−	23.5450i	0.00410272	−	0.777948i
$917$	7.11176	−	19.5394i	0.234851	−	0.645247i
$918$	20.3782	+	1.83702i	0.672582	+	0.0606308i
$919$	13.6433	+	7.87694i	0.450050	+	0.259836i	0.707851	−	0.706362i	$-0.249665\pi$
$919$	13.6433	+	7.87694i	0.450050	+	0.259836i	−0.257801	+	0.966198i	$0.582998\pi$
$920$	10.0246	+	17.2600i	0.330502	+	0.569045i
$921$	0.818537	−	4.64216i	0.0269717	−	0.152964i
$922$	21.2503	+	45.8869i	0.699841	+	1.51120i
$923$	9.04252	+	15.6621i	0.297638	+	0.515524i
$924$	0.248520	+	0.299367i	0.00817572	+	0.00984846i
$925$	−8.69101	−	22.4037i	−0.285759	−	0.736628i
$926$	35.4103	−	9.38815i	1.16365	−	0.308514i
$927$	−12.3268	−	33.8676i	−0.404866	−	1.11236i
$928$	9.95249	+	14.6202i	0.326706	+	0.479930i
$929$	−1.03954	−	5.89550i	−0.0341061	−	0.193425i	0.962994	−	0.269521i	$-0.0868655\pi$
$929$	−1.03954	−	5.89550i	−0.0341061	−	0.193425i	−0.997100	+	0.0760962i	$0.975754\pi$
$930$	−8.98238	+	3.34949i	−0.294544	+	0.109834i
$931$	8.92662	+	16.4502i	0.292558	+	0.539133i
$932$	−0.796346	−	0.294612i	−0.0260852	−	0.00965032i
$933$	−0.0311079	−	0.176422i	−0.00101843	−	0.00577578i
$934$	−4.65373	+	17.1866i	−0.152275	+	0.562361i
$935$	0.144764	+	1.47606i	0.00473430	+	0.0482725i
$936$	−4.52694	+	47.4196i	−0.147968	+	1.54996i
$937$	16.3408	−	19.4742i	0.533830	−	0.636193i	−0.429963	−	0.902847i	$-0.641473\pi$
$937$	16.3408	−	19.4742i	0.533830	−	0.636193i	0.963793	+	0.266653i	$0.0859178\pi$
$938$	7.48988	−	0.635383i	0.244553	−	0.0207460i
$939$	5.34587	+	9.25932i	0.174456	+	0.302166i
$940$	35.6329	−	36.0070i	1.16222	−	1.17442i
$941$	−4.08175	−	0.719722i	−0.133061	−	0.0234623i	0.106721	−	0.994289i	$-0.465965\pi$
$941$	−4.08175	−	0.719722i	−0.133061	−	0.0234623i	−0.239782	+	0.970827i	$0.577076\pi$
$942$	−2.54941	−	1.19700i	−0.0830642	−	0.0390004i
$943$	7.38101	+	4.26143i	0.240359	+	0.138771i
$944$	−2.84340	−	17.1836i	−0.0925446	−	0.559279i
$945$	−16.7532	−	11.4706i	−0.544983	−	0.373139i
$946$	−1.72344	−	1.21355i	−0.0560340	−	0.0394560i
$947$	21.6263	−	18.1466i	0.702760	−	0.589686i	−0.219797	−	0.975546i	$-0.570540\pi$
$947$	21.6263	−	18.1466i	0.702760	−	0.589686i	0.922557	+	0.385860i	$0.126095\pi$
$948$	1.89296	−	10.4141i	0.0614805	−	0.338233i
$949$		−	38.8805i		−	1.26211i
$950$	13.2509	−	27.8283i	0.429914	−	0.902870i
$951$			13.3236i			0.432047i
$952$	−21.1448	−	46.2979i	−0.685307	−	1.50052i
$953$	−6.44930	+	5.41160i	−0.208913	+	0.175299i	−0.741240	−	0.671240i	$-0.765762\pi$
$953$	−6.44930	+	5.41160i	−0.208913	+	0.175299i	0.532327	+	0.846539i	$0.321318\pi$
$954$	−0.266355	+	0.378267i	−0.00862356	+	0.0122469i
$955$	26.9236	+	18.4340i	0.871226	+	0.596511i
$956$	29.8224	+	52.2889i	0.964527	+	1.69114i
$957$	−0.156740	−	0.0904937i	−0.00506667	−	0.00292525i
$958$	−15.8895	+	33.8418i	−0.513365	+	1.09338i
$959$	−12.5008	−	2.20423i	−0.403672	−	0.0711782i
$960$	0.684249	+	8.33184i	0.0220840	+	0.268909i
$961$	−5.53993	−	9.59544i	−0.178708	−	0.309530i
$962$	3.47854	+	41.0050i	0.112153	+	1.32205i
$963$	−21.3805	+	25.4803i	−0.688976	+	0.821090i
$964$	12.2689	+	10.4056i	0.395154	+	0.335141i
$965$	0.533325	+	5.43796i	0.0171683	+	0.175054i
$966$	6.76589	+	1.83205i	0.217689	+	0.0589453i
$967$	6.12116	+	34.7148i	0.196843	+	1.11635i	0.909769	+	0.415114i	$0.136258\pi$
$967$	6.12116	+	34.7148i	0.196843	+	1.11635i	−0.712926	+	0.701239i	$0.752631\pi$
$968$	7.80368	+	30.0733i	0.250820	+	0.966593i
$969$	8.16774	+	7.22970i	0.262386	+	0.232251i
$970$	−12.1169	−	32.4940i	−0.389049	−	1.04332i
$971$	3.69950	+	20.9809i	0.118723	+	0.673309i	0.984840	+	0.173468i	$0.0554972\pi$
$971$	3.69950	+	20.9809i	0.118723	+	0.673309i	−0.866117	+	0.499841i	$0.833392\pi$
$972$	21.4950	−	7.69540i	0.689451	−	0.246830i
$973$	7.74618	+	21.2825i	0.248331	+	0.682284i
$974$	−5.41982	−	20.4425i	−0.173662	−	0.655020i
$975$	−13.1900	+	5.11676i	−0.422417	+	0.163867i
$976$	27.7093	−	9.75562i	0.886952	−	0.312270i
$977$	9.36678	+	16.2237i	0.299670	+	0.519043i	0.976060	−	0.217500i	$-0.0697902\pi$
$977$	9.36678	+	16.2237i	0.299670	+	0.519043i	−0.676391	+	0.736543i	$0.736457\pi$
$978$	−6.13999	+	2.84344i	−0.196335	+	0.0909231i
$979$	0.0930494	−	0.527710i	0.00297387	−	0.0168657i
$980$	−1.57369	+	19.1377i	−0.0502695	+	0.611333i
$981$	−2.37923	−	1.37365i	−0.0759630	−	0.0438572i
$982$	2.79403	−	30.9944i	0.0891611	−	0.989071i
$983$	−6.32466	+	17.3769i	−0.201725	+	0.554235i	−0.998765	−	0.0496919i	$-0.984176\pi$
$983$	−6.32466	+	17.3769i	−0.201725	+	0.554235i	0.797039	+	0.603927i	$0.206398\pi$
$984$	2.02428	+	2.94020i	0.0645316	+	0.0937301i
$985$	48.4071	−	23.1942i	1.54238	−	0.739029i
$986$	16.6973	+	16.7856i	0.531750	+	0.534562i
$987$		−	17.7900i		−	0.566262i
$988$	−35.1926	+	39.3388i	−1.11963	+	1.25153i
$989$	−37.9741			−1.20751
$990$	0.552188	+	0.939292i	0.0175497	+	0.0298527i
$991$	10.5218	−	8.82881i	0.334235	−	0.280456i	−0.460188	−	0.887822i	$-0.652218\pi$
$991$	10.5218	−	8.82881i	0.334235	−	0.280456i	0.794423	+	0.607365i	$0.207774\pi$
$992$	−35.5672	+	9.02935i	−1.12926	+	0.286682i
$993$	3.13595	−	8.61596i	0.0995164	−	0.273419i
$994$	−14.1386	−	1.27455i	−0.448451	−	0.0404262i
$995$	0.739712	−	0.755404i	0.0234504	−	0.0239479i
$996$	1.12436	+	6.57926i	0.0356266	+	0.208472i
$997$	−32.9344	−	5.80722i	−1.04304	−	0.183916i	−0.374221	−	0.927340i	$-0.622090\pi$
$997$	−32.9344	−	5.80722i	−1.04304	−	0.183916i	−0.668821	+	0.743423i	$0.733201\pi$
$998$	−38.9631	+	18.0439i	−1.23335	+	0.571168i
$999$	11.2459	−	6.49283i	0.355805	−	0.205424i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.bb.a.219.14	yes	336
4.3	odd	2	inner	380.2.bb.a.219.37	yes	336
5.4	even	2	inner	380.2.bb.a.219.43	yes	336
19.2	odd	18	inner	380.2.bb.a.59.20	yes	336
20.19	odd	2	inner	380.2.bb.a.219.20	yes	336
76.59	even	18	inner	380.2.bb.a.59.43	yes	336
95.59	odd	18	inner	380.2.bb.a.59.37	yes	336
380.59	even	18	inner	380.2.bb.a.59.14	✓	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.bb.a.59.14	✓	336	380.59	even	18	inner
380.2.bb.a.59.20	yes	336	19.2	odd	18	inner
380.2.bb.a.59.37	yes	336	95.59	odd	18	inner
380.2.bb.a.59.43	yes	336	76.59	even	18	inner
380.2.bb.a.219.14	yes	336	1.1	even	1	trivial
380.2.bb.a.219.20	yes	336	20.19	odd	2	inner
380.2.bb.a.219.37	yes	336	4.3	odd	2	inner
380.2.bb.a.219.43	yes	336	5.4	even	2	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)

\(f(q)\)	\(=\)	\(q+(-0.997360 - 1.00263i) q^{2} +(0.300395 + 0.357997i) q^{3} +(-0.0105474 + 1.99997i) q^{4} +(-1.26326 + 1.84504i) q^{5} +(0.0593378 - 0.658238i) q^{6} +(-1.68031 + 2.91038i) q^{7} +(2.01576 - 1.98412i) q^{8} +(0.483020 - 2.73934i) q^{9} +O(q^{10})\)	\(q+(-0.997360 - 1.00263i) q^{2} +(0.300395 + 0.357997i) q^{3} +(-0.0105474 + 1.99997i) q^{4} +(-1.26326 + 1.84504i) q^{5} +(0.0593378 - 0.658238i) q^{6} +(-1.68031 + 2.91038i) q^{7} +(2.01576 - 1.98412i) q^{8} +(0.483020 - 2.73934i) q^{9} +(3.10982 - 0.573580i) q^{10} +(-0.107274 + 0.0619346i) q^{11} +(-0.719153 + 0.597006i) q^{12} +(-4.63813 - 3.89185i) q^{13} +(4.59392 - 1.21796i) q^{14} +(-1.04000 + 0.101997i) q^{15} +(-3.99978 - 0.0421890i) q^{16} +(-5.27335 + 0.929834i) q^{17} +(-3.22830 + 2.24782i) q^{18} +(-4.35738 - 0.115147i) q^{19} +(-3.67670 - 2.54595i) q^{20} +(-1.54667 + 0.272719i) q^{21} +(0.169088 + 0.0457853i) q^{22} +(2.96562 - 1.07940i) q^{23} +(1.31583 + 0.125617i) q^{24} +(-1.80834 - 4.66153i) q^{25} +(0.723781 + 8.53191i) q^{26} +(2.33994 - 1.35096i) q^{27} +(-5.80296 - 3.39127i) q^{28} +(3.07901 + 0.542912i) q^{29} +(1.13952 + 0.941008i) q^{30} +(-3.24345 + 5.61782i) q^{31} +(3.94692 + 4.05239i) q^{32} +(-0.0543970 - 0.0197989i) q^{33} +(6.19171 + 4.35986i) q^{34} +(-3.24710 - 6.77681i) q^{35} +(5.47351 + 0.994919i) q^{36} +4.80607 q^{37} +(4.23042 + 4.48370i) q^{38} -2.82953i q^{39} +(1.11434 + 6.22561i) q^{40} +(1.73589 + 2.06876i) q^{41} +(1.81602 + 1.27874i) q^{42} +(-11.3069 - 4.11538i) q^{43} +(-0.122736 - 0.215198i) q^{44} +(4.44401 + 4.35170i) q^{45} +(-4.04003 - 1.89688i) q^{46} +(-1.96698 + 11.1553i) q^{47} +(-1.18641 - 1.44458i) q^{48} +(-2.14689 - 3.71852i) q^{49} +(-2.87024 + 6.46233i) q^{50} +(-1.91697 - 1.60853i) q^{51} +(7.83251 - 9.23507i) q^{52} +(0.110513 - 0.0402236i) q^{53} +(-3.68828 - 0.998703i) q^{54} +(0.0212432 - 0.276164i) q^{55} +(2.38744 + 9.20056i) q^{56} +(-1.26771 - 1.59452i) q^{57} +(-2.52653 - 3.62859i) q^{58} +(0.756119 + 4.28817i) q^{59} +(-0.193022 - 2.08104i) q^{60} +(-6.90121 + 2.51183i) q^{61} +(8.86750 - 2.35100i) q^{62} +(7.16091 + 6.00872i) q^{63} +(0.126564 - 7.99900i) q^{64} +(13.0398 - 3.64110i) q^{65} +(0.0344024 + 0.0742869i) q^{66} +(1.55757 + 0.274642i) q^{67} +(-1.80402 - 10.5564i) q^{68} +(1.27728 + 0.737438i) q^{69} +(-3.55613 + 10.0146i) q^{70} +(-2.80683 - 1.02160i) q^{71} +(-4.46152 - 6.48022i) q^{72} +(4.12772 + 4.91923i) q^{73} +(-4.79338 - 4.81873i) q^{74} +(1.12560 - 2.04768i) q^{75} +(0.276250 - 8.71342i) q^{76} -0.416278i q^{77} +(-2.83698 + 2.82206i) q^{78} +(-8.67515 + 7.27931i) q^{79} +(5.13060 - 7.32645i) q^{80} +(-6.65500 - 2.42222i) q^{81} +(0.342895 - 3.80376i) q^{82} +(3.57061 - 6.18447i) q^{83} +(-0.529117 - 3.09617i) q^{84} +(4.94604 - 10.9042i) q^{85} +(7.15084 + 15.4412i) q^{86} +(0.730558 + 1.26536i) q^{87} +(-0.0933528 + 0.337689i) q^{88} +(-2.78066 + 3.31386i) q^{89} +(-0.0691245 - 8.79592i) q^{90} +(19.1203 - 6.95921i) q^{91} +(2.12748 + 5.94254i) q^{92} +(-2.98548 + 0.526421i) q^{93} +(13.1465 - 9.15370i) q^{94} +(5.71696 - 7.89407i) q^{95} +(-0.265108 + 2.63030i) q^{96} +(-1.90434 - 10.8000i) q^{97} +(-1.58709 + 5.86124i) q^{98} +(0.117845 + 0.323776i) 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

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