LMFDB - Embedded newform 380.2.bb.a.59.14

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			59.14
Character	$\chi$	$=$	380.59
Dual form			380.2.bb.a.219.14

$q$-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 $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.997360	+	1.00263i	−0.705240	+	0.708969i
$2$	−0.997360	+	1.00263i	−0.705240	+	0.708969i
$3$	0.300395	−	0.357997i	0.173433	−	0.206690i	−0.672325	−	0.740256i	$-0.734704\pi$
$3$	0.300395	−	0.357997i	0.173433	−	0.206690i	0.845758	+	0.533566i	$0.179149\pi$
$4$	−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	−0.986494	−	0.163795i	$-0.947627\pi$
$7$	−1.68031	−	2.91038i	−0.635098	−	1.10002i	0.351397	−	0.936227i	$-0.385707\pi$
$8$	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	0.483741	−	0.875211i	$-0.339278\pi$
$11$	−0.107274	−	0.0619346i	−0.0323443	−	0.0186740i	−0.516085	+	0.856537i	$0.672611\pi$
$12$	−0.719153	−	0.597006i	−0.207602	−	0.172341i
$13$	−4.63813	+	3.89185i	−1.28638	+	1.07941i	−0.294055	+	0.955789i	$0.595005\pi$
$13$	−4.63813	+	3.89185i	−1.28638	+	1.07941i	−0.992330	+	0.123616i	$0.960551\pi$
$14$	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	−0.507431	−	0.861693i	$-0.669405\pi$
$17$	−5.27335	−	0.929834i	−1.27898	−	0.225518i	−0.771545	+	0.636175i	$0.780516\pi$
$18$	−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	0.632163	−	0.774835i	$-0.282167\pi$
$23$	2.96562	+	1.07940i	0.618374	+	0.225070i	−0.0137891	+	0.999905i	$0.504389\pi$
$24$	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	0.119708	−	0.992809i	$-0.461804\pi$
$29$	3.07901	−	0.542912i	0.571757	−	0.100816i	0.452049	+	0.891993i	$0.350693\pi$
$30$	1.13952	−	0.941008i	0.208046	−	0.171804i
$31$	−3.24345	−	5.61782i	−0.582541	−	1.00899i	−0.995177	−	0.0980944i	$-0.968725\pi$
$31$	−3.24345	−	5.61782i	−0.582541	−	1.00899i	0.412636	−	0.910896i	$-0.364608\pi$
$32$	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	−0.613267	−	0.789876i	$-0.710145\pi$
$41$	1.73589	−	2.06876i	0.271101	−	0.323086i	0.884368	+	0.466790i	$0.154590\pi$
$42$	1.81602	−	1.27874i	0.280218	−	0.197314i
$43$	−11.3069	+	4.11538i	−1.72429	+	0.627589i	−0.998198	−	0.0600104i	$-0.980887\pi$
$43$	−11.3069	+	4.11538i	−1.72429	+	0.627589i	−0.726090	+	0.687600i	$0.758664\pi$
$44$	−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	−0.698367	−	0.715739i	$-0.746090\pi$
$47$	−1.96698	−	11.1553i	−0.286914	−	1.62717i	0.411453	−	0.911431i	$-0.365021\pi$
$48$	−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	0.349599	−	0.936899i	$-0.386318\pi$
$53$	0.110513	+	0.0402236i	0.0151802	+	0.00552513i	−0.334419	+	0.942425i	$0.608540\pi$
$54$	−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	−0.895201	−	0.445663i	$-0.852968\pi$
$59$	0.756119	−	4.28817i	0.0984383	−	0.558272i	0.993639	−	0.112609i	$-0.0359208\pi$
$60$	−0.193022	+	2.08104i	−0.0249191	+	0.268661i
$61$	−6.90121	−	2.51183i	−0.883609	−	0.321607i	−0.139944	−	0.990159i	$-0.544692\pi$
$61$	−6.90121	−	2.51183i	−0.883609	−	0.321607i	−0.743665	+	0.668552i	$0.766914\pi$
$62$	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	−0.0776919	−	0.996977i	$-0.524755\pi$
$67$	1.55757	−	0.274642i	0.190288	−	0.0335529i	0.267980	+	0.963425i	$0.413644\pi$
$68$	−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	−0.503160	−	0.864193i	$-0.667829\pi$
$71$	−2.80683	+	1.02160i	−0.333110	+	0.121242i	0.170050	+	0.985435i	$0.445607\pi$
$72$	−4.46152	+	6.48022i	−0.525795	+	0.763701i
$73$	4.12772	−	4.91923i	0.483114	−	0.575752i	−0.468339	−	0.883549i	$-0.655147\pi$
$73$	4.12772	−	4.91923i	0.483114	−	0.575752i	0.951452	+	0.307797i	$0.0995917\pi$
$74$	−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	0.00745528	−	0.999972i	$-0.497627\pi$
$79$	−8.67515	−	7.27931i	−0.976031	−	0.818987i	−0.983486	+	0.180985i	$0.942071\pi$
$80$	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	0.992703	−	0.120582i	$-0.0384760\pi$
$83$	3.57061	+	6.18447i	0.391925	+	0.678834i	−0.600778	+	0.799416i	$0.705143\pi$
$84$	−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	0.598264	−	0.801299i	$-0.295857\pi$
$89$	−2.78066	−	3.31386i	−0.294749	−	0.351268i	−0.893013	+	0.450031i	$0.851413\pi$
$90$	−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	0.721384	+	0.692536i	$0.243506\pi$
$97$	−1.90434	+	10.8000i	−0.193356	+	1.09658i	−0.914740	+	0.404043i	$0.867605\pi$
$98$	−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	−0.145714	−	0.989327i	$-0.546548\pi$
$101$	8.07286	−	6.77394i	0.803280	−	0.674032i	0.948994	+	0.315295i	$0.102103\pi$
$102$	0.299144	−	3.52630i	0.0296196	−	0.349155i
$103$	11.2211	+	6.47850i	1.10565	+	0.638346i	0.937698	−	0.347450i	$-0.112952\pi$
$103$	11.2211	+	6.47850i	1.10565	+	0.638346i	0.167949	+	0.985796i	$0.446286\pi$
$104$	−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	−0.908585	−	0.417700i	$-0.862836\pi$
$107$	−10.3559	+	5.97895i	−1.00114	+	0.578007i	−0.0925532	+	0.995708i	$0.529503\pi$
$108$	2.67721	−	4.69406i	0.257615	−	0.451686i
$109$	0.337802	+	0.928104i	0.0323556	+	0.0888963i	0.954819	−	0.297189i	$-0.0960492\pi$
$109$	0.337802	+	0.928104i	0.0323556	+	0.0888963i	−0.922463	+	0.386085i	$0.873827\pi$
$110$	−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	−0.950984	−	0.309239i	$-0.899926\pi$
$127$	−12.2881	−	14.6443i	−1.09039	−	1.29947i	−0.139405	−	0.990235i	$-0.544519\pi$
$128$	−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	−0.0990053	−	0.995087i	$-0.531566\pi$
$131$	−6.09336	−	1.07442i	−0.532380	−	0.0938729i	−0.433374	+	0.901214i	$0.642677\pi$
$132$	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	−0.872194	−	0.489161i	$-0.837303\pi$
$137$	1.29187	−	3.54938i	0.110372	−	0.303244i	0.982566	+	0.185917i	$0.0595254\pi$
$138$	−0.534527	+	2.01613i	−0.0455020	+	0.171625i
$139$	4.33196	+	5.16262i	0.367432	+	0.437888i	0.917805	−	0.397030i	$-0.129959\pi$
$139$	4.33196	+	5.16262i	0.367432	+	0.437888i	−0.550374	+	0.834918i	$0.685515\pi$
$140$	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	0.990792	−	0.135391i	$-0.0432289\pi$
$149$	12.5667	+	10.5448i	1.02951	+	0.863860i	0.0387155	+	0.999250i	$0.487673\pi$
$150$	−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	0.984167	−	0.177243i	$-0.0567179\pi$
$157$	1.45751	+	4.00446i	0.116322	+	0.319591i	−0.867845	+	0.496834i	$0.834496\pi$
$158$	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	−0.993841	−	0.110812i	$-0.964655\pi$
$163$	−5.11904	+	8.86644i	−0.400954	+	0.694474i	0.592887	+	0.805286i	$0.297988\pi$
$164$	−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	−0.502580	−	0.864531i	$-0.667616\pi$
$167$	5.66187	−	15.5558i	0.438128	−	1.20375i	0.940708	−	0.339217i	$-0.110162\pi$
$168$	−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	−0.850517	−	0.525947i	$-0.823711\pi$
$173$	1.69136	−	9.59221i	0.128592	−	0.729282i	0.979109	−	0.203335i	$-0.0651779\pi$
$174$	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	−0.455873	−	0.890045i	$-0.650673\pi$
$179$	7.26304	−	12.5800i	0.542865	−	0.940270i	0.998738	−	0.0502250i	$-0.0159939\pi$
$180$	−8.75014	−	8.84200i	−0.652197	−	0.659044i
$181$	−21.1417	+	3.72785i	−1.57145	+	0.277089i	−0.890410	−	0.455159i	$-0.849583\pi$
$181$	−21.1417	+	3.72785i	−1.57145	+	0.277089i	−0.681039	+	0.732247i	$0.738471\pi$
$182$	−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	$0.177033\pi$
$191$			14.5924i			1.05587i	−0.849285	+	0.527935i	$0.822967\pi$
$192$	2.90164	+	2.35755i	0.209408	+	0.170142i
$193$	1.87190	+	1.57071i	0.134743	+	0.113062i	0.707668	−	0.706545i	$-0.249747\pi$
$193$	1.87190	+	1.57071i	0.134743	+	0.113062i	−0.572926	+	0.819607i	$0.694192\pi$
$194$	−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	−0.999772	−	0.0213642i	$-0.993199\pi$
$197$	−20.7890	+	12.0025i	−1.48116	+	0.855146i	−0.481384	+	0.876510i	$0.659866\pi$
$198$	0.207095	+	0.441076i	0.0147176	+	0.0313459i
$199$	−0.465640	+	0.0821049i	−0.0330083	+	0.00582026i	−0.190128	−	0.981759i	$-0.560890\pi$
$199$	−0.465640	+	0.0821049i	−0.0330083	+	0.00582026i	0.157120	+	0.987580i	$0.449779\pi$
$200$	−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	−0.908950	−	0.416906i	$-0.863114\pi$
$211$	1.27499	−	7.23082i	0.0877739	−	0.497791i	0.996723	−	0.0808845i	$-0.0257745\pi$
$212$	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	−0.999996	−	0.00299548i	$-0.999047\pi$
$223$	−3.52244	−	9.67782i	−0.235880	−	0.648075i	0.764116	−	0.645079i	$-0.223176\pi$
$224$	−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	$-0.898820\pi$
$227$		−	9.41783i		−	0.625083i	0.949904	−	0.312542i	$-0.101180\pi$
$228$	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	0.934845	−	0.355055i	$-0.115538\pi$
$233$	−0.145204	−	0.398944i	−0.00951262	−	0.0261357i	−0.944358	+	0.328919i	$0.893316\pi$
$234$	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	0.957505	+	0.288416i	$0.0931285\pi$
$239$	26.0654	+	15.0489i	1.68603	+	0.973432i	0.728528	+	0.685016i	$0.240205\pi$
$240$	4.16406	+	0.364090i	0.268789	+	0.0235019i
$241$	5.17036	+	6.16180i	0.333052	+	0.396916i	0.906417	−	0.422384i	$-0.138807\pi$
$241$	5.17036	+	6.16180i	0.333052	+	0.396916i	−0.573365	+	0.819300i	$0.694362\pi$
$242$	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	−0.976169	−	0.217010i	$-0.930370\pi$
$251$	−1.40827	+	3.86919i	−0.0888892	+	0.244221i	0.887280	+	0.461231i	$0.152592\pi$
$252$	−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	−0.996912	−	0.0785220i	$-0.974980\pi$
$257$	−1.39435	−	7.90776i	−0.0869773	−	0.493273i	0.909935	−	0.414751i	$-0.136131\pi$
$258$	−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	0.483791	−	0.875184i	$-0.339260\pi$
$263$	−4.76930	−	4.00192i	−0.294088	−	0.246769i	−0.777878	+	0.628415i	$0.783704\pi$
$264$	−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	0.0206212	+	0.999787i	$0.493436\pi$
$269$	−15.8691	+	18.9121i	−0.967558	+	1.15309i	−0.988179	+	0.153303i	$0.951009\pi$
$270$	6.50191	+	5.54340i	0.395694	+	0.337361i
$271$	−6.22615	−	17.1062i	−0.378212	−	1.03913i	−0.972097	−	0.234578i	$-0.924629\pi$
$271$	−6.22615	−	17.1062i	−0.378212	−	1.03913i	0.593886	−	0.804549i	$-0.297593\pi$
$272$	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	0.373826	−	0.927499i	$-0.378046\pi$
$277$	−4.03598	−	2.33018i	−0.242499	−	0.140007i	−0.616325	+	0.787492i	$0.711379\pi$
$278$	−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	0.538189	+	0.842824i	$0.319109\pi$
$281$	−6.97083	+	19.1522i	−0.415845	+	1.14252i	−0.954034	+	0.299700i	$0.903114\pi$
$282$	7.22614	−	1.95668i	0.430310	−	0.116518i
$283$	−2.17388	+	12.3287i	−0.129224	+	0.732864i	0.849486	+	0.527612i	$0.176912\pi$
$283$	−2.17388	+	12.3287i	−0.129224	+	0.732864i	−0.978709	+	0.205252i	$0.934199\pi$
$284$	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	−0.896605	−	0.442832i	$-0.853974\pi$
$293$	−1.10918	+	1.92115i	−0.0647987	+	0.112235i	0.831806	+	0.555067i	$0.187307\pi$
$294$	−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	−0.918642	−	0.395091i	$-0.870713\pi$
$307$	−6.48351	+	7.72675i	−0.370033	+	0.440989i	0.548609	+	0.836079i	$0.315158\pi$
$308$	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	−0.509383	−	0.860540i	$-0.670126\pi$
$311$	−0.331975	+	0.191666i	−0.0188246	+	0.0108684i	0.490558	+	0.871408i	$0.336793\pi$
$312$	−5.61412	+	5.70365i	−0.317837	+	0.322906i
$313$	22.5307	−	3.97277i	1.27351	−	0.224554i	0.504287	−	0.863536i	$-0.331755\pi$
$313$	22.5307	−	3.97277i	1.27351	−	0.224554i	0.769222	+	0.638982i	$0.220644\pi$
$314$	−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	0.228198	−	0.973615i	$-0.426717\pi$
$317$	21.8398	−	18.3258i	1.22665	−	1.02928i	0.998450	−	0.0556648i	$-0.0177278\pi$
$318$	−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	0.459750	+	0.888048i	$0.347939\pi$
$331$	−9.80984	+	16.9911i	−0.539198	+	0.933918i	−0.998947	+	0.0458692i	$0.985394\pi$
$332$	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	−0.0852479	−	0.996360i	$-0.527168\pi$
$337$	8.99330	−	3.27329i	0.489896	−	0.178308i	0.575144	+	0.818052i	$0.304946\pi$
$338$	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	−0.563453	−	0.826148i	$-0.690527\pi$
$347$	−8.64421	+	3.14623i	−0.464045	+	0.168899i	0.0994077	+	0.995047i	$0.468305\pi$
$348$	−2.53840	−	1.44775i	−0.136072	−	0.0776075i
$349$	−14.5699	−	25.2358i	−0.779908	−	1.35084i	−0.931994	−	0.362473i	$-0.881933\pi$
$349$	−14.5699	−	25.2358i	−0.779908	−	1.35084i	0.152086	−	0.988367i	$-0.451401\pi$
$350$	−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	0.157340	−	0.987544i	$-0.449708\pi$
$353$	−11.6342	−	6.71703i	−0.619228	−	0.357512i	−0.776568	+	0.630033i	$0.783041\pi$
$354$	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	−0.726786	−	0.686864i	$-0.758987\pi$
$359$	−31.1619	−	5.49469i	−1.64466	−	0.289998i	−0.917877	+	0.396866i	$0.870098\pi$
$360$	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	−0.560960	−	0.827843i	$-0.689568\pi$
$367$	3.00569	−	2.52207i	0.156896	−	0.131651i	0.717856	+	0.696192i	$0.245124\pi$
$368$	−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	0.859742	−	0.510728i	$-0.170624\pi$
$373$	−0.240112	−	0.415886i	−0.0124325	−	0.0215337i	−0.872175	+	0.489194i	$0.837291\pi$
$374$	−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	−0.881493	−	0.472196i	$-0.843461\pi$
$383$	−5.15486	+	6.14332i	−0.263401	+	0.313909i	0.618092	+	0.786105i	$0.287906\pi$
$384$	−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	0.987128	−	0.159934i	$-0.0511281\pi$
$389$	0.0952729	+	0.540320i	0.00483053	+	0.0273953i	−0.982297	+	0.187329i	$0.940017\pi$
$390$	−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	0.471303	−	0.881971i	$-0.343784\pi$
$397$	12.2046	+	2.15200i	0.612532	+	0.108006i	0.141228	+	0.989977i	$0.454895\pi$
$398$	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	0.762696	−	0.646757i	$-0.223875\pi$
$401$	25.1953	+	4.44261i	1.25819	+	0.221853i	0.495496	+	0.868610i	$0.334986\pi$
$402$	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	0.462579	−	0.886578i	$-0.346924\pi$
$409$	24.2784	−	4.28093i	1.20049	−	0.211679i	0.737910	+	0.674899i	$0.235813\pi$
$410$	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	$0.0572044\pi$
$419$			7.31772i			0.357494i	−0.983895	+	0.178747i	$0.942796\pi$
$420$	6.38096	−	2.93503i	0.311359	−	0.143215i
$421$	−12.4412	+	14.8269i	−0.606348	+	0.722618i	−0.978659	−	0.205490i	$-0.934121\pi$
$421$	−12.4412	+	14.8269i	−0.606348	+	0.722618i	0.372311	+	0.928108i	$0.378566\pi$
$422$	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	−0.953913	−	0.300085i	$-0.902985\pi$
$431$	−17.1074	+	14.3548i	−0.824032	+	0.691445i	0.129880	+	0.991530i	$0.458541\pi$
$432$	−9.41623	−	5.30484i	−0.453039	−	0.255229i
$433$	−19.6537	−	7.15338i	−0.944499	−	0.343769i	−0.176558	−	0.984290i	$-0.556496\pi$
$433$	−19.6537	−	7.15338i	−0.944499	−	0.343769i	−0.767941	+	0.640521i	$0.778718\pi$
$434$	−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	0.728998	+	0.684516i	$0.239986\pi$
$439$	−3.98417	+	22.5954i	−0.190154	+	1.07842i	−0.919152	+	0.393903i	$0.871125\pi$
$440$	−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	−0.681846	−	0.731496i	$-0.738822\pi$
$443$	−1.68095	+	1.41048i	−0.0798641	+	0.0670139i	0.601982	+	0.798510i	$0.294378\pi$
$444$	−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	−0.318371	−	0.947966i	$-0.603136\pi$
$449$	7.27665	−	4.20118i	0.343406	−	0.198266i	0.661777	+	0.749700i	$0.269802\pi$
$450$	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	$-0.961391\pi$
$457$		−	5.17318i		−	0.241991i	0.992653	−	0.120996i	$-0.0386087\pi$
$458$	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	−0.971864	−	0.235541i	$-0.924314\pi$
$461$	−33.6010	+	12.2297i	−1.56495	+	0.569596i	−0.593088	+	0.805137i	$0.702091\pi$
$462$	−0.274010	+	0.0247010i	−0.0127481	+	0.00114919i
$463$	−12.9520	−	22.4334i	−0.601928	−	1.04257i	−0.992529	−	0.122010i	$-0.961066\pi$
$463$	−12.9520	−	22.4334i	−0.601928	−	1.04257i	0.390601	−	0.920560i	$-0.372267\pi$
$464$	−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	−0.974119	−	0.226036i	$-0.927423\pi$
$467$	−6.29519	+	10.9036i	−0.291306	+	0.504558i	0.682812	+	0.730594i	$0.260757\pi$
$468$	−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	0.542393	+	0.840125i	$0.317518\pi$
$479$	−9.04170	+	24.8419i	−0.413126	+	1.13505i	−0.955519	+	0.294929i	$0.904704\pi$
$480$	−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	−0.176994	−	0.984212i	$-0.556637\pi$
$487$	12.9509	−	7.47722i	0.586862	−	0.338825i	0.763856	+	0.645387i	$0.223304\pi$
$488$	−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	−0.345767	−	0.938321i	$-0.612381\pi$
$491$	14.1447	−	16.8570i	0.638341	−	0.760745i	0.984107	+	0.177576i	$0.0568255\pi$
$492$	−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	0.921782	+	0.387709i	$0.126733\pi$
$499$	10.3844	+	28.5310i	0.464870	+	1.27722i	−0.456912	+	0.889512i	$0.651044\pi$
$500$	−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	−0.986524	−	0.163617i	$-0.947684\pi$
$503$	−2.58938	−	14.6851i	−0.115455	−	0.654778i	0.871069	−	0.491161i	$-0.163427\pi$
$504$	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	−0.898503	−	0.438967i	$-0.855345\pi$
$509$	1.62332	−	4.46003i	0.0719524	−	0.197688i	0.970456	+	0.241279i	$0.0775669\pi$
$510$	−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	0.984526	−	0.175241i	$-0.0560705\pi$
$521$	30.2443	+	17.4615i	1.32502	+	0.765004i	0.340499	+	0.940245i	$0.389404\pi$
$522$	−11.1603	−	5.16836i	−0.488474	−	0.226213i
$523$	−38.8181	+	6.84468i	−1.69740	+	0.299297i	−0.936784	−	0.349908i	$-0.886213\pi$
$523$	−38.8181	+	6.84468i	−1.69740	+	0.299297i	−0.760613	+	0.649205i	$0.775102\pi$
$524$	−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	0.999901	−	0.0140456i	$-0.00447099\pi$
$541$	1.29084	+	7.32072i	0.0554976	+	0.314742i	−0.944404	+	0.328788i	$0.893360\pi$
$542$	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	−0.399941	−	0.916541i	$-0.630969\pi$
$547$	11.5905	−	31.8446i	0.495573	−	1.36158i	0.895513	−	0.445034i	$-0.146809\pi$
$548$	−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	0.572880	−	0.819639i	$-0.305826\pi$
$557$	−7.87765	−	9.38822i	−0.333787	−	0.397792i	−0.906667	+	0.421848i	$0.861382\pi$
$558$	−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	−0.429455	−	0.903088i	$-0.641294\pi$
$563$	3.27238	−	1.88931i	0.137915	−	0.0796250i	0.567370	+	0.823463i	$0.307961\pi$
$564$	−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	$-0.965817\pi$
$569$		−	5.11343i		−	0.214366i	0.994239	−	0.107183i	$-0.0341831\pi$
$570$	−4.85695	+	4.23154i	−0.203435	+	0.177240i
$571$		−	15.0942i		−	0.631673i	−0.948814	−	0.315836i	$-0.897715\pi$
$571$		−	15.0942i		−	0.631673i	0.948814	−	0.315836i	$-0.102285\pi$
$572$	−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	0.328681	−	0.944441i	$-0.393396\pi$
$577$	31.4897	−	18.1806i	1.31093	−	0.756867i	0.982250	+	0.187574i	$0.0600624\pi$
$578$	−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	0.139878	+	0.990169i	$0.455329\pi$
$587$	−8.00064	+	45.3739i	−0.330222	+	1.87278i	−0.470100	+	0.882613i	$0.655782\pi$
$588$	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	0.356711	+	0.934215i	$0.383898\pi$
$593$	−12.5909	+	34.5933i	−0.517047	+	1.42058i	−0.873758	+	0.486361i	$0.838324\pi$
$594$	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	0.962499	−	0.271285i	$-0.0874486\pi$
$599$	−0.850222	−	4.82185i	−0.0347391	−	0.197015i	−0.997238	+	0.0742695i	$0.976337\pi$
$600$	−1.79391	+	6.36096i	−0.0732360	+	0.259685i
$601$	1.65208	−	0.953830i	0.0673899	−	0.0389076i	−0.465926	−	0.884823i	$-0.654279\pi$
$601$	1.65208	−	0.953830i	0.0673899	−	0.0389076i	0.533316	+	0.845916i	$0.320946\pi$
$602$	−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	$0.106296\pi$
$607$			16.1506i			0.655533i	−0.944759	+	0.327767i	$0.893704\pi$
$608$	−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	−0.963463	−	0.267840i	$-0.913690\pi$
$613$	−9.84341	−	27.0446i	−0.397572	−	1.09232i	0.565892	−	0.824480i	$-0.308532\pi$
$614$	−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	−0.313879	−	0.949463i	$-0.601629\pi$
$617$	−7.05674	+	1.24429i	−0.284094	+	0.0500934i	0.0297856	+	0.999556i	$0.490518\pi$
$618$	−3.59856	+	7.77057i	−0.144755	+	0.312578i
$619$	−18.0822	−	10.4398i	−0.726787	−	0.419610i	0.0904588	−	0.995900i	$-0.471167\pi$
$619$	−18.0822	−	10.4398i	−0.726787	−	0.419610i	−0.817245	+	0.576290i	$0.804500\pi$
$620$	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	0.714531	+	0.699604i	$0.246640\pi$
$631$	−7.09703	+	19.4989i	−0.282528	+	0.776240i	−0.997059	+	0.0766361i	$0.975582\pi$
$632$	−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	−0.996663	−	0.0816317i	$-0.973987\pi$
$641$	−7.23199	−	19.8697i	−0.285647	−	0.784808i	0.711016	−	0.703176i	$-0.248235\pi$
$642$	−4.55007	−	6.46184i	−0.179577	−	0.255029i
$643$	−10.6935	−	8.97290i	−0.421710	−	0.353856i	0.407103	−	0.913382i	$-0.366539\pi$
$643$	−10.6935	−	8.97290i	−0.421710	−	0.353856i	−0.828813	+	0.559526i	$0.810983\pi$
$644$	−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	−0.285908	−	0.958257i	$-0.592295\pi$
$653$	10.2474	−	5.91634i	0.401012	−	0.231524i	0.686921	+	0.726732i	$0.258962\pi$
$654$	−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	−0.478648	−	0.878007i	$-0.658873\pi$
$659$	7.77585	−	6.52471i	0.302904	−	0.254167i	0.781552	+	0.623840i	$0.214428\pi$
$660$	0.149595	−	0.211287i	0.00582297	−	0.00822432i
$661$	1.60132	−	4.39958i	0.0622840	−	0.171124i	−0.904647	−	0.426161i	$-0.859866\pi$
$661$	1.60132	−	4.39958i	0.0622840	−	0.171124i	0.966931	+	0.255038i	$0.0820878\pi$
$662$	−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	−0.989551	−	0.144180i	$-0.953945\pi$
$673$	−9.59635	+	16.6214i	−0.369912	+	0.640706i	0.619639	+	0.784887i	$0.287279\pi$
$674$	−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	0.998128	+	0.0611642i	$0.0194813\pi$
$677$	14.3635	+	24.8783i	0.552034	+	0.956150i	−0.446094	+	0.894986i	$0.647185\pi$
$678$	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	$-0.880041\pi$
$683$		−	19.2351i		−	0.736010i	0.929824	−	0.368005i	$-0.119959\pi$
$684$	−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	−0.935807	−	0.352514i	$-0.885327\pi$
$691$	−28.8741	+	16.6705i	−1.09842	+	0.634175i	−0.162617	+	0.986689i	$0.551994\pi$
$692$	−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	−0.915639	−	0.402001i	$-0.868315\pi$
$701$	2.17829	−	12.3537i	0.0822728	−	0.466592i	0.997912	−	0.0645908i	$-0.0205742\pi$
$702$	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	−0.604939	−	0.796272i	$-0.706802\pi$
$709$	1.97546	−	1.65761i	0.0741900	−	0.0622528i	0.679129	+	0.734019i	$0.262358\pi$
$710$	−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	−0.0542677	−	0.998526i	$-0.517282\pi$
$719$	25.1654	−	29.9910i	0.938512	−	1.11848i	0.992780	−	0.119949i	$-0.0382731\pi$
$720$	−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	−0.545411	−	0.838169i	$-0.683626\pi$
$727$	−11.4446	+	4.16549i	−0.424456	+	0.154489i	0.120955	+	0.992658i	$0.461404\pi$
$728$	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	0.432104	−	0.901824i	$-0.357771\pi$
$733$	−3.59670	−	2.07656i	−0.132847	−	0.0766993i	−0.564951	+	0.825125i	$0.691105\pi$
$734$	−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	0.380900	−	0.924616i	$-0.375614\pi$
$739$	11.4880	+	2.02564i	0.422593	+	0.0745145i	0.0416921	+	0.999131i	$0.486725\pi$
$740$	−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	0.707557	−	0.706656i	$-0.249797\pi$
$743$	30.8221	+	5.43476i	1.13075	+	0.199382i	0.423195	+	0.906039i	$0.360908\pi$
$744$	−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	−0.944910	−	0.327331i	$-0.893851\pi$
$751$	−4.62967	−	26.2561i	−0.168939	−	0.958100i	0.775971	−	0.630769i	$-0.217260\pi$
$752$	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	−0.827319	−	0.561732i	$-0.810135\pi$
$757$	−3.58939	+	4.27767i	−0.130459	+	0.155474i	0.696861	+	0.717207i	$0.254580\pi$
$758$	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	−0.708575	−	0.705636i	$-0.750662\pi$
$769$	−7.87761	−	44.6761i	−0.284074	−	1.61106i	0.424501	−	0.905427i	$-0.360450\pi$
$770$	−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	0.590870	−	0.806767i	$-0.298784\pi$
$773$	41.3702	−	34.7137i	1.48798	−	1.24857i	0.897114	−	0.441800i	$-0.145660\pi$
$774$	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	0.925786	−	0.378048i	$-0.123405\pi$
$787$	29.7726	+	17.1892i	1.06128	+	0.612730i	0.135494	+	0.990778i	$0.456738\pi$
$788$	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	−0.834668	−	0.550754i	$-0.814340\pi$
$809$	1.69614	−	2.93780i	0.0596331	−	0.103288i	0.894301	+	0.447466i	$0.147674\pi$
$810$	−22.0852	+	3.71551i	−0.775996	+	0.130550i
$811$	30.5042	−	25.5961i	1.07115	−	0.898799i	0.0759913	−	0.997108i	$-0.475788\pi$
$811$	30.5042	−	25.5961i	1.07115	−	0.898799i	0.995156	+	0.0983093i	$0.0313434\pi$
$812$	−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	0.662347	−	0.749197i	$-0.269561\pi$
$821$	19.7179	+	7.17672i	0.688159	+	0.250469i	0.0258123	+	0.999667i	$0.491783\pi$
$822$	2.41299	+	0.639745i	0.0841629	+	0.0223137i
$823$	−17.9835	+	15.0900i	−0.626866	+	0.526003i	−0.899953	−	0.435987i	$-0.856400\pi$
$823$	−17.9835	+	15.0900i	−0.626866	+	0.526003i	0.273088	+	0.961989i	$0.411955\pi$
$824$	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	0.420515	−	0.907286i	$-0.361849\pi$
$827$	32.3805	−	5.70955i	1.12598	−	0.198541i	0.705465	+	0.708745i	$0.250738\pi$
$828$	17.3063	+	2.95754i	0.601434	+	0.102782i
$829$	42.2181	−	24.3746i	1.46629	−	0.846566i	0.467005	−	0.884254i	$-0.345333\pi$
$829$	42.2181	−	24.3746i	1.46629	−	0.846566i	0.999290	+	0.0376887i	$0.0119995\pi$
$830$	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	0.248855	−	0.968541i	$-0.419946\pi$
$839$	−19.1682	−	16.0840i	−0.661758	−	0.555281i	−0.910613	+	0.413260i	$0.864390\pi$
$840$	−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	0.426677	−	0.904404i	$-0.359684\pi$
$853$	15.1375	+	2.66915i	0.518298	+	0.0913899i	0.0916210	+	0.995794i	$0.470795\pi$
$854$	−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	−0.837692	−	0.546143i	$-0.816096\pi$
$857$	3.98933	−	22.6246i	0.136273	−	0.772841i	0.973965	−	0.226699i	$-0.0727933\pi$
$858$	0.129551	+	0.478441i	0.00442280	+	0.0163337i
$859$	−7.89087	+	21.6800i	−0.269233	+	0.739711i	0.729229	+	0.684270i	$0.239879\pi$
$859$	−7.89087	+	21.6800i	−0.269233	+	0.739711i	−0.998462	+	0.0554416i	$0.982343\pi$
$860$	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	0.460076	−	0.887880i	$-0.347822\pi$
$863$	−2.31528	−	1.33673i	−0.0788132	−	0.0455028i	−0.538889	+	0.842377i	$0.681156\pi$
$864$	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	0.639435	−	0.768845i	$-0.279168\pi$
$877$	−0.198222	−	0.166328i	−0.00669349	−	0.00561650i	−0.646128	+	0.763229i	$0.723613\pi$
$878$	−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	0.823363	−	0.567515i	$-0.192095\pi$
$881$	−2.36861	−	4.10255i	−0.0798004	−	0.138218i	−0.903164	+	0.429296i	$0.858762\pi$
$882$	15.2893	−	7.17868i	0.514819	−	0.241719i
$883$	−2.30439	−	13.0688i	−0.0775489	−	0.439801i	−0.998717	−	0.0506369i	$-0.983875\pi$
$883$	−2.30439	−	13.0688i	−0.0775489	−	0.439801i	0.921168	−	0.389165i	$-0.127236\pi$
$884$	−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	0.669296	−	0.742996i	$-0.266596\pi$
$887$	−5.32020	−	6.34036i	−0.178635	−	0.212889i	−0.847930	+	0.530108i	$0.822152\pi$
$888$	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	0.998186	−	0.0602014i	$-0.0191743\pi$
$907$	5.86772	+	16.1214i	0.194834	+	0.535303i	−0.803352	+	0.595505i	$0.796952\pi$
$908$	−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	−0.257801	−	0.966198i	$-0.582998\pi$
$919$	13.6433	−	7.87694i	0.450050	−	0.259836i	0.707851	+	0.706362i	$0.249665\pi$
$920$	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	−0.997100	−	0.0760962i	$-0.975754\pi$
$929$	−1.03954	+	5.89550i	−0.0341061	+	0.193425i	0.962994	+	0.269521i	$0.0868655\pi$
$930$	−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	0.963793	−	0.266653i	$-0.0859178\pi$
$937$	16.3408	+	19.4742i	0.533830	+	0.636193i	−0.429963	+	0.902847i	$0.641473\pi$
$938$	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	−0.239782	−	0.970827i	$-0.577076\pi$
$941$	−4.08175	+	0.719722i	−0.133061	+	0.0234623i	0.106721	+	0.994289i	$0.465965\pi$
$942$	−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	0.922557	−	0.385860i	$-0.126095\pi$
$947$	21.6263	+	18.1466i	0.702760	+	0.589686i	−0.219797	+	0.975546i	$0.570540\pi$
$948$	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	0.532327	−	0.846539i	$-0.321318\pi$
$953$	−6.44930	−	5.41160i	−0.208913	−	0.175299i	−0.741240	+	0.671240i	$0.765762\pi$
$954$	−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	−0.712926	−	0.701239i	$-0.752631\pi$
$967$	6.12116	−	34.7148i	0.196843	−	1.11635i	0.909769	−	0.415114i	$-0.136258\pi$
$968$	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	−0.866117	−	0.499841i	$-0.833392\pi$
$971$	3.69950	−	20.9809i	0.118723	−	0.673309i	0.984840	−	0.173468i	$-0.0554972\pi$
$972$	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	−0.676391	−	0.736543i	$-0.736457\pi$
$977$	9.36678	−	16.2237i	0.299670	−	0.519043i	0.976060	+	0.217500i	$0.0697902\pi$
$978$	−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	0.797039	−	0.603927i	$-0.206398\pi$
$983$	−6.32466	−	17.3769i	−0.201725	−	0.554235i	−0.998765	+	0.0496919i	$0.984176\pi$
$984$	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	0.794423	−	0.607365i	$-0.207774\pi$
$991$	10.5218	+	8.82881i	0.334235	+	0.280456i	−0.460188	+	0.887822i	$0.652218\pi$
$992$	−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	−0.668821	−	0.743423i	$-0.733201\pi$
$997$	−32.9344	+	5.80722i	−1.04304	+	0.183916i	−0.374221	+	0.927340i	$0.622090\pi$
$998$	−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.59.14	✓	336
4.3	odd	2	inner	380.2.bb.a.59.37	yes	336
5.4	even	2	inner	380.2.bb.a.59.43	yes	336
19.10	odd	18	inner	380.2.bb.a.219.20	yes	336
20.19	odd	2	inner	380.2.bb.a.59.20	yes	336
76.67	even	18	inner	380.2.bb.a.219.43	yes	336
95.29	odd	18	inner	380.2.bb.a.219.37	yes	336
380.219	even	18	inner	380.2.bb.a.219.14	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.bb.a.59.14	✓	336	1.1	even	1	trivial
380.2.bb.a.59.20	yes	336	20.19	odd	2	inner
380.2.bb.a.59.37	yes	336	4.3	odd	2	inner
380.2.bb.a.59.43	yes	336	5.4	even	2	inner
380.2.bb.a.219.14	yes	336	380.219	even	18	inner
380.2.bb.a.219.20	yes	336	19.10	odd	18	inner
380.2.bb.a.219.37	yes	336	95.29	odd	18	inner
380.2.bb.a.219.43	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)

\(f(q)\)	\(=\)	\(q+(-0.997360 + 1.00263i) q^{2} +(0.300395 - 0.357997i) q^{3} +(-0.0105474 - 1.99997i) q^{4} +(-1.26326 - 1.84504i) q^{5} +(0.0593378 + 0.658238i) q^{6} +(-1.68031 - 2.91038i) q^{7} +(2.01576 + 1.98412i) q^{8} +(0.483020 + 2.73934i) q^{9} +O(q^{10})\)	\(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

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Database

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