LMFDB - Embedded newform 375.3.h.a.74.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [375,3,Mod(74,375)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(375, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("375.74");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 375 = 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	375.h (of order $10$, degree $4$, not 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:	$10.2180099135$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			74.4
Character	$\chi$	$=$	375.74
Dual form			375.3.h.a.299.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.05424 + 1.49250i) q^{2} +(-2.06574 + 2.17548i) q^{3} +(0.756307 - 2.32767i) q^{4} +(0.996648 - 7.55208i) q^{6} -6.97211i q^{7} +(-1.21820 - 3.74924i) q^{8} +(-0.465411 - 8.98796i) q^{9} +O(q^{10})$	\(q+(-2.05424 + 1.49250i) q^{2} +(-2.06574 + 2.17548i) q^{3} +(0.756307 - 2.32767i) q^{4} +(0.996648 - 7.55208i) q^{6} -6.97211i q^{7} +(-1.21820 - 3.74924i) q^{8} +(-0.465411 - 8.98796i) q^{9} +(7.98507 + 10.9905i) q^{11} +(3.50147 + 6.45371i) q^{12} +(-0.259763 + 0.357533i) q^{13} +(10.4058 + 14.3224i) q^{14} +(16.0184 + 11.6380i) q^{16} +(7.94771 + 24.4605i) q^{17} +(14.3706 + 17.7688i) q^{18} +(-3.70606 - 11.4061i) q^{19} +(15.1677 + 14.4026i) q^{21} +(-32.8065 - 10.6595i) q^{22} +(19.1473 - 13.9113i) q^{23} +(10.6729 + 5.09479i) q^{24} -1.12216i q^{26} +(20.5145 + 17.5543i) q^{27} +(-16.2288 - 5.27306i) q^{28} +(-32.2785 - 10.4879i) q^{29} +(7.00881 + 21.5709i) q^{31} -34.5066 q^{32} +(-40.4047 - 5.33221i) q^{33} +(-52.8338 - 38.3860i) q^{34} +(-21.2730 - 5.71433i) q^{36} +(24.1765 - 33.2760i) q^{37} +(24.6367 + 17.8996i) q^{38} +(-0.241202 - 1.30368i) q^{39} +(-11.1774 + 15.3843i) q^{41} +(-52.6539 - 6.94875i) q^{42} +40.7478i q^{43} +(31.6215 - 10.2744i) q^{44} +(-18.5706 + 57.1545i) q^{46} +(-7.83781 + 24.1223i) q^{47} +(-58.4081 + 10.8064i) q^{48} +0.389632 q^{49} +(-69.6313 - 33.2391i) q^{51} +(0.635761 + 0.875050i) q^{52} +(-22.0806 + 67.9572i) q^{53} +(-68.3416 - 5.44301i) q^{54} +(-26.1401 + 8.49344i) q^{56} +(32.4694 + 15.4996i) q^{57} +(81.9612 - 26.6308i) q^{58} +(-16.0556 + 22.0987i) q^{59} +(77.8653 - 56.5725i) q^{61} +(-46.5923 - 33.8513i) q^{62} +(-62.6651 + 3.24490i) q^{63} +(6.81151 - 4.94885i) q^{64} +(90.9594 - 49.3502i) q^{66} +(-92.0681 + 29.9148i) q^{67} +62.9471 q^{68} +(-9.28961 + 70.3918i) q^{69} +(15.2176 + 4.94450i) q^{71} +(-33.1310 + 12.6941i) q^{72} +(23.6157 + 32.5042i) q^{73} +104.440i q^{74} -29.3526 q^{76} +(76.6270 - 55.6728i) q^{77} +(2.44123 + 2.31809i) q^{78} +(-3.55591 + 10.9440i) q^{79} +(-80.5668 + 8.36620i) q^{81} -48.2853i q^{82} +(-9.61536 - 29.5930i) q^{83} +(44.9960 - 24.4126i) q^{84} +(-60.8159 - 83.7059i) q^{86} +(89.4954 - 48.5559i) q^{87} +(31.4786 - 43.3265i) q^{88} +(35.6526 + 49.0716i) q^{89} +(2.49276 + 1.81110i) q^{91} +(-17.8998 - 55.0899i) q^{92} +(-61.4054 - 29.3124i) q^{93} +(-19.9017 - 61.2510i) q^{94} +(71.2817 - 75.0683i) q^{96} +(125.919 + 40.9136i) q^{97} +(-0.800399 + 0.581524i) q^{98} +(95.0658 - 76.8845i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 5 q^{3} - 38 q^{4} + 5 q^{6} - 13 q^{9}+O(q^{10}) $ 72 * q + 5 * q^3 - 38 * q^4 + 5 * q^6 - 13 * q^9	$ 72 q + 5 q^{3} - 38 q^{4} + 5 q^{6} - 13 q^{9} + 45 q^{12} + 10 q^{13} + 22 q^{16} - 36 q^{19} + 54 q^{21} + 50 q^{22} - 20 q^{24} - 100 q^{27} - 270 q^{28} - 126 q^{31} - 20 q^{33} + 210 q^{34} - 213 q^{36} - 110 q^{37} - 191 q^{39} + 175 q^{42} - 210 q^{46} - 150 q^{48} - 224 q^{49} - 60 q^{51} + 320 q^{52} + 320 q^{54} + 70 q^{58} + 294 q^{61} - 795 q^{63} + 362 q^{64} - 470 q^{66} + 260 q^{67} + 335 q^{69} - 215 q^{72} + 150 q^{73} - 16 q^{76} + 1295 q^{78} - 346 q^{79} + 507 q^{81} - 456 q^{84} + 430 q^{87} + 1710 q^{88} + 538 q^{91} - 560 q^{94} + 740 q^{96} + 150 q^{97} + 60 q^{99}+O(q^{100}) $ 72 * q + 5 * q^3 - 38 * q^4 + 5 * q^6 - 13 * q^9 + 45 * q^12 + 10 * q^13 + 22 * q^16 - 36 * q^19 + 54 * q^21 + 50 * q^22 - 20 * q^24 - 100 * q^27 - 270 * q^28 - 126 * q^31 - 20 * q^33 + 210 * q^34 - 213 * q^36 - 110 * q^37 - 191 * q^39 + 175 * q^42 - 210 * q^46 - 150 * q^48 - 224 * q^49 - 60 * q^51 + 320 * q^52 + 320 * q^54 + 70 * q^58 + 294 * q^61 - 795 * q^63 + 362 * q^64 - 470 * q^66 + 260 * q^67 + 335 * q^69 - 215 * q^72 + 150 * q^73 - 16 * q^76 + 1295 * q^78 - 346 * q^79 + 507 * q^81 - 456 * q^84 + 430 * q^87 + 1710 * q^88 + 538 * q^91 - 560 * q^94 + 740 * q^96 + 150 * q^97 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/375\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$-1$

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 $

$2$	−2.05424	+	1.49250i	−1.02712	+	0.746248i	−0.967731	−	0.251987i	$-0.918916\pi$
$2$	−2.05424	+	1.49250i	−1.02712	+	0.746248i	−0.0593914	+	0.998235i	$0.518916\pi$
$3$	−2.06574	+	2.17548i	−0.688581	+	0.725159i
$3$	−2.06574	+	2.17548i	−0.688581	+	0.725159i
$4$	0.756307	−	2.32767i	0.189077	−	0.581919i
$5$		0			0
$5$		0			0
$6$	0.996648	−	7.55208i	0.166108	−	1.25868i
$7$		−	6.97211i		−	0.996016i	−0.867172	−	0.498008i	$-0.834065\pi$
$7$		−	6.97211i		−	0.996016i	0.867172	−	0.498008i	$-0.165935\pi$
$8$	−1.21820	−	3.74924i	−0.152275	−	0.468655i
$9$	−0.465411	−	8.98796i	−0.0517124	−	0.998662i
$10$		0			0
$11$	7.98507	+	10.9905i	0.725915	+	0.999136i	0.999307	+	0.0372335i	$0.0118545\pi$
$11$	7.98507	+	10.9905i	0.725915	+	0.999136i	−0.273392	+	0.961903i	$0.588145\pi$
$12$	3.50147	+	6.45371i	0.291789	+	0.537809i
$13$	−0.259763	+	0.357533i	−0.0199818	+	0.0275026i	−0.818891	−	0.573949i	$-0.805411\pi$
$13$	−0.259763	+	0.357533i	−0.0199818	+	0.0275026i	0.798909	+	0.601452i	$0.205411\pi$
$14$	10.4058	+	14.3224i	0.743275	+	1.02303i
$15$		0			0
$16$	16.0184	+	11.6380i	1.00115	+	0.727376i
$17$	7.94771	+	24.4605i	0.467512	+	1.43885i	0.855795	+	0.517314i	$0.173068\pi$
$17$	7.94771	+	24.4605i	0.467512	+	1.43885i	−0.388283	+	0.921540i	$0.626932\pi$
$18$	14.3706	+	17.7688i	0.798364	+	0.987158i
$19$	−3.70606	−	11.4061i	−0.195056	−	0.600320i	−0.999976	−	0.00693679i	$-0.997792\pi$
$19$	−3.70606	−	11.4061i	−0.195056	−	0.600320i	0.804920	−	0.593383i	$-0.202208\pi$
$20$		0			0
$21$	15.1677	+	14.4026i	0.722271	+	0.685838i
$22$	−32.8065	−	10.6595i	−1.49121	−	0.484522i
$23$	19.1473	−	13.9113i	0.832491	−	0.604840i	−0.0877718	−	0.996141i	$-0.527975\pi$
$23$	19.1473	−	13.9113i	0.832491	−	0.604840i	0.920263	+	0.391300i	$0.127975\pi$
$24$	10.6729	+	5.09479i	0.444703	+	0.212283i
$25$		0			0
$26$		−	1.12216i		−	0.0431599i
$27$	20.5145	+	17.5543i	0.759797	+	0.650160i
$28$	−16.2288	−	5.27306i	−0.579600	−	0.188324i
$29$	−32.2785	−	10.4879i	−1.11305	−	0.361653i	−0.305941	−	0.952051i	$-0.598971\pi$
$29$	−32.2785	−	10.4879i	−1.11305	−	0.361653i	−0.807112	+	0.590398i	$0.798971\pi$
$30$		0			0
$31$	7.00881	+	21.5709i	0.226091	+	0.695835i	0.998179	+	0.0603203i	$0.0192122\pi$
$31$	7.00881	+	21.5709i	0.226091	+	0.695835i	−0.772088	+	0.635515i	$0.780788\pi$
$32$	−34.5066			−1.07833
$33$	−40.4047	−	5.33221i	−1.22438	−	0.161582i
$34$	−52.8338	−	38.3860i	−1.55393	−	1.12900i
$35$		0			0
$36$	−21.2730	−	5.71433i	−0.590918	−	0.158731i
$37$	24.1765	−	33.2760i	0.653418	−	0.899353i	−0.345823	−	0.938300i	$-0.612400\pi$
$37$	24.1765	−	33.2760i	0.653418	−	0.899353i	0.999241	+	0.0389470i	$0.0124004\pi$
$38$	24.6367	+	17.8996i	0.648333	+	0.471042i
$39$	−0.241202	−	1.30368i	−0.00618467	−	0.0334277i
$40$		0			0
$41$	−11.1774	+	15.3843i	−0.272619	+	0.375227i	−0.923272	−	0.384148i	$-0.874495\pi$
$41$	−11.1774	+	15.3843i	−0.272619	+	0.375227i	0.650653	+	0.759375i	$0.274495\pi$
$42$	−52.6539	−	6.94875i	−1.25367	−	0.165446i
$43$			40.7478i			0.947623i	0.880626	+	0.473811i	$0.157122\pi$
$43$			40.7478i			0.947623i	−0.880626	+	0.473811i	$0.842878\pi$
$44$	31.6215	−	10.2744i	0.718670	−	0.233510i
$45$		0			0
$46$	−18.5706	+	57.1545i	−0.403709	+	1.24249i
$47$	−7.83781	+	24.1223i	−0.166762	+	0.513240i	−0.999162	−	0.0409351i	$-0.986966\pi$
$47$	−7.83781	+	24.1223i	−0.166762	+	0.513240i	0.832400	+	0.554175i	$0.186966\pi$
$48$	−58.4081	+	10.8064i	−1.21683	+	0.225134i
$49$	0.389632			0.00795167
$50$		0			0
$51$	−69.6313	−	33.2391i	−1.36532	−	0.651747i
$52$	0.635761	+	0.875050i	0.0122262	+	0.0168279i
$53$	−22.0806	+	67.9572i	−0.416616	+	1.28221i	0.494182	+	0.869358i	$0.335468\pi$
$53$	−22.0806	+	67.9572i	−0.416616	+	1.28221i	−0.910798	+	0.412853i	$0.864532\pi$
$54$	−68.3416	−	5.44301i	−1.26559	−	0.100797i
$55$		0			0
$56$	−26.1401	+	8.49344i	−0.466788	+	0.151668i
$57$	32.4694	+	15.4996i	0.569639	+	0.271922i
$58$	81.9612	−	26.6308i	1.41312	−	0.459152i
$59$	−16.0556	+	22.0987i	−0.272129	+	0.374554i	−0.923107	−	0.384543i	$-0.874359\pi$
$59$	−16.0556	+	22.0987i	−0.272129	+	0.374554i	0.650978	+	0.759097i	$0.274359\pi$
$60$		0			0
$61$	77.8653	−	56.5725i	1.27648	−	0.927418i	0.277040	−	0.960858i	$-0.410647\pi$
$61$	77.8653	−	56.5725i	1.27648	−	0.927418i	0.999441	+	0.0334407i	$0.0106465\pi$
$62$	−46.5923	−	33.8513i	−0.751488	−	0.545988i
$63$	−62.6651	+	3.24490i	−0.994684	+	0.0515064i
$64$	6.81151	−	4.94885i	0.106430	−	0.0773258i
$65$		0			0
$66$	90.9594	−	49.3502i	1.37817	−	0.747730i
$67$	−92.0681	+	29.9148i	−1.37415	+	0.446489i	−0.900742	−	0.434354i	$-0.856977\pi$
$67$	−92.0681	+	29.9148i	−1.37415	+	0.446489i	−0.473409	+	0.880843i	$0.656977\pi$
$68$	62.9471			0.925692
$69$	−9.28961	+	70.3918i	−0.134632	+	1.02017i
$70$		0			0
$71$	15.2176	+	4.94450i	0.214333	+	0.0696409i	0.414215	−	0.910179i	$-0.364056\pi$
$71$	15.2176	+	4.94450i	0.214333	+	0.0696409i	−0.199883	+	0.979820i	$0.564056\pi$
$72$	−33.1310	+	12.6941i	−0.460153	+	0.176307i
$73$	23.6157	+	32.5042i	0.323502	+	0.445263i	0.939533	−	0.342460i	$-0.111260\pi$
$73$	23.6157	+	32.5042i	0.323502	+	0.445263i	−0.616030	+	0.787723i	$0.711260\pi$
$74$			104.440i			1.41136i
$75$		0			0
$76$	−29.3526			−0.386218
$77$	76.6270	−	55.6728i	0.995156	−	0.723023i
$78$	2.44123	+	2.31809i	0.0312978	+	0.0297191i
$79$	−3.55591	+	10.9440i	−0.0450115	+	0.138531i	−0.971037	−	0.238931i	$-0.923203\pi$
$79$	−3.55591	+	10.9440i	−0.0450115	+	0.138531i	0.926025	+	0.377462i	$0.123203\pi$
$80$		0			0
$81$	−80.5668	+	8.36620i	−0.994652	+	0.103286i
$82$		−	48.2853i		−	0.588845i
$83$	−9.61536	−	29.5930i	−0.115848	−	0.356543i	0.876275	−	0.481811i	$-0.160021\pi$
$83$	−9.61536	−	29.5930i	−0.115848	−	0.356543i	−0.992123	+	0.125268i	$0.960021\pi$
$84$	44.9960	−	24.4126i	0.535667	−	0.290627i
$85$		0			0
$86$	−60.8159	−	83.7059i	−0.707162	−	0.973324i
$87$	89.4954	−	48.5559i	1.02868	−	0.558114i
$88$	31.4786	−	43.3265i	0.357711	−	0.492347i
$89$	35.6526	+	49.0716i	0.400591	+	0.551367i	0.960892	−	0.276923i	$-0.0893145\pi$
$89$	35.6526	+	49.0716i	0.400591	+	0.551367i	−0.560301	+	0.828289i	$0.689315\pi$
$90$		0			0
$91$	2.49276	+	1.81110i	0.0273930	+	0.0199022i
$92$	−17.8998	−	55.0899i	−0.194563	−	0.598803i
$93$	−61.4054	−	29.3124i	−0.660273	−	0.315187i
$94$	−19.9017	−	61.2510i	−0.211720	−	0.651606i
$95$		0			0
$96$	71.2817	−	75.0683i	0.742518	−	0.781962i
$97$	125.919	+	40.9136i	1.29813	+	0.421789i	0.874932	−	0.484246i	$-0.160906\pi$
$97$	125.919	+	40.9136i	1.29813	+	0.421789i	0.423202	+	0.906035i	$0.360906\pi$
$98$	−0.800399	+	0.581524i	−0.00816734	+	0.00593392i
$99$	95.0658	−	76.8845i	0.960261	−	0.776612i
$100$		0			0
$101$			182.040i			1.80238i	0.433423	+	0.901191i	$0.357306\pi$
$101$			182.040i			1.80238i	−0.433423	+	0.901191i	$0.642694\pi$
$102$	192.649	−	35.6431i	1.88871	−	0.349443i
$103$	−33.2817	−	10.8139i	−0.323123	−	0.104989i	0.142964	−	0.989728i	$-0.454337\pi$
$103$	−33.2817	−	10.8139i	−0.323123	−	0.104989i	−0.466087	+	0.884739i	$0.654337\pi$
$104$	1.65692	+	0.538366i	0.0159319	+	0.00517660i
$105$		0			0
$106$	−56.0668	−	172.556i	−0.528932	−	1.62789i
$107$	−142.508			−1.33185			−0.665925	−	0.746018i	$-0.731963\pi$
$107$	−142.508			−1.33185			−0.665925	+	0.746018i	$0.731963\pi$
$108$	56.3760	−	34.4747i	0.522000	−	0.319210i
$109$	116.368	+	84.5460i	1.06759	+	0.775651i	0.975478	−	0.220097i	$-0.0706375\pi$
$109$	116.368	+	84.5460i	1.06759	+	0.775651i	0.0921144	+	0.995748i	$0.470637\pi$
$110$		0			0
$111$	22.4490	+	121.335i	0.202243	+	1.09311i
$112$	81.1416	−	111.682i	0.724478	−	0.997159i
$113$	58.5612	+	42.5472i	0.518240	+	0.376524i	0.815941	−	0.578136i	$-0.196220\pi$
$113$	58.5612	+	42.5472i	0.518240	+	0.376524i	−0.297700	+	0.954659i	$0.596220\pi$
$114$	−89.8332	+	16.6206i	−0.788011	+	0.145795i
$115$		0			0
$116$	−48.8250	+	67.2018i	−0.420905	+	0.579326i
$117$	3.33439	+	2.16834i	0.0284991	+	0.0185328i
$118$		−	69.3590i		−	0.587788i
$119$	170.542	−	55.4123i	1.43312	−	0.465650i
$120$		0			0
$121$	−19.6388	+	60.4419i	−0.162304	+	0.499520i
$122$	−75.5202	+	232.427i	−0.619018	+	1.90514i
$123$	−10.3787	−	56.0962i	−0.0843796	−	0.456066i
$124$	55.5109			0.447668
$125$		0			0
$126$	123.886	−	100.193i	0.983225	−	0.795184i
$127$	104.138	+	143.334i	0.819984	+	1.12861i	0.989705	+	0.143119i	$0.0457132\pi$
$127$	104.138	+	143.334i	0.819984	+	1.12861i	−0.169721	+	0.985492i	$0.554287\pi$
$128$	36.0461	−	110.939i	0.281610	−	0.866707i
$129$	−88.6459	−	84.1745i	−0.687178	−	0.652515i
$130$		0			0
$131$	110.681	−	35.9623i	0.844891	−	0.274522i	0.145586	−	0.989346i	$-0.453493\pi$
$131$	110.681	−	35.9623i	0.844891	−	0.274522i	0.699304	+	0.714824i	$0.253493\pi$
$132$	−42.9700	+	90.0162i	−0.325530	+	0.681941i
$133$	−79.5245	+	25.8391i	−0.597928	+	0.194279i
$134$	144.483	−	198.864i	1.07823	−	1.48406i
$135$		0			0
$136$	82.0264	−	59.5957i	0.603135	−	0.438203i
$137$	82.1209	+	59.6643i	0.599423	+	0.435506i	0.845674	−	0.533700i	$-0.179199\pi$
$137$	82.1209	+	59.6643i	0.599423	+	0.435506i	−0.246251	+	0.969206i	$0.579199\pi$
$138$	−85.9763	−	158.467i	−0.623016	−	1.14831i
$139$	−13.3673	+	9.71192i	−0.0961677	+	0.0698699i	−0.634830	−	0.772652i	$-0.718930\pi$
$139$	−13.3673	+	9.71192i	−0.0961677	+	0.0698699i	0.538662	+	0.842522i	$0.318930\pi$
$140$		0			0
$141$	−36.2866	−	66.8815i	−0.257352	−	0.474337i
$142$	−38.6403	+	12.5550i	−0.272115	+	0.0884155i
$143$	−6.00370			−0.0419839
$144$	97.1469	−	149.389i	0.674631	−	1.03742i
$145$		0			0
$146$	−97.0248	−	31.5253i	−0.664553	−	0.215926i
$147$	−0.804880	+	0.847636i	−0.00547537	+	0.00576623i
$148$	−59.1710	−	81.4419i	−0.399804	−	0.550283i
$149$			163.472i			1.09713i	0.836109	+	0.548563i	$0.184825\pi$
$149$			163.472i			1.09713i	−0.836109	+	0.548563i	$0.815175\pi$
$150$		0			0
$151$	−94.5637			−0.626250			−0.313125	−	0.949712i	$-0.601376\pi$
$151$	−94.5637			−0.626250			−0.313125	+	0.949712i	$0.601376\pi$
$152$	−38.2494	+	27.7898i	−0.251641	+	0.182828i
$153$	216.151	−	82.8179i	1.41275	−	0.541293i
$154$	−74.3192	+	228.731i	−0.482592	+	1.48527i
$155$		0			0
$156$	−3.21697	−	0.424544i	−0.0206216	−	0.00272144i
$157$			105.152i			0.669756i	0.942262	+	0.334878i	$0.108695\pi$
$157$			105.152i			0.669756i	−0.942262	+	0.334878i	$0.891305\pi$
$158$	−9.02911	−	27.7887i	−0.0571462	−	0.175878i
$159$	−102.226	−	188.418i	−0.642934	−	1.18502i
$160$		0			0
$161$	−96.9913	−	133.497i	−0.602431	−	0.829175i
$162$	153.017	−	137.432i	0.944551	−	0.848344i
$163$	36.7479	−	50.5791i	0.225447	−	0.310301i	−0.681277	−	0.732026i	$-0.738575\pi$
$163$	36.7479	−	50.5791i	0.225447	−	0.310301i	0.906724	+	0.421725i	$0.138575\pi$
$164$	27.3562	+	37.6525i	0.166806	+	0.229589i
$165$		0			0
$166$	63.9198	+	46.4404i	0.385059	+	0.279762i
$167$	−37.6809	−	115.970i	−0.225634	−	0.694431i	−0.998227	−	0.0595283i	$-0.981040\pi$
$167$	−37.6809	−	115.970i	−0.225634	−	0.694431i	0.772592	−	0.634902i	$-0.218960\pi$
$168$	35.5215	−	74.4125i	0.211437	−	0.442932i
$169$	52.1635	+	160.543i	0.308660	+	0.949957i
$170$		0			0
$171$	−100.793	+	38.6184i	−0.589430	+	0.225839i
$172$	94.8476	+	30.8179i	0.551439	+	0.179174i
$173$	124.504	−	90.4577i	0.719678	−	0.522877i	−0.166603	−	0.986024i	$-0.553280\pi$
$173$	124.504	−	90.4577i	0.719678	−	0.522877i	0.886281	+	0.463147i	$0.153280\pi$
$174$	−111.376	+	233.317i	−0.640092	+	1.34090i
$175$		0			0
$176$			268.980i			1.52830i
$177$	−14.9084	−	80.5788i	−0.0842281	−	0.455247i
$178$	−146.478	−	47.5937i	−0.822912	−	0.267380i
$179$	−164.186	−	53.3472i	−0.917239	−	0.298029i	−0.187905	−	0.982187i	$-0.560170\pi$
$179$	−164.186	−	53.3472i	−0.917239	−	0.298029i	−0.729334	+	0.684158i	$0.760170\pi$
$180$		0			0
$181$	−23.8974	−	73.5485i	−0.132030	−	0.406345i	0.863087	−	0.505056i	$-0.168528\pi$
$181$	−23.8974	−	73.5485i	−0.132030	−	0.406345i	−0.995116	+	0.0987106i	$0.968528\pi$
$182$	−7.82380			−0.0429879
$183$	−37.7776	+	286.259i	−0.206435	+	1.56425i
$184$	−75.4821	−	54.8410i	−0.410229	−	0.298049i
$185$		0			0
$186$	169.890	−	31.4325i	0.913389	−	0.168992i
$187$	−205.370	+	282.668i	−1.09824	+	1.51159i
$188$	50.2211	+	36.4877i	0.267133	+	0.194084i
$189$	122.391	−	143.030i	0.647570	−	0.756770i
$190$		0			0
$191$	−51.5237	+	70.9163i	−0.269758	+	0.371290i	−0.922308	−	0.386456i	$-0.873699\pi$
$191$	−51.5237	+	70.9163i	−0.269758	+	0.371290i	0.652550	+	0.757746i	$0.273699\pi$
$192$	−3.30471	+	25.0414i	−0.0172120	+	0.130424i
$193$			32.0812i			0.166224i	0.996540	+	0.0831119i	$0.0264859\pi$
$193$			32.0812i			0.166224i	−0.996540	+	0.0831119i	$0.973514\pi$
$194$	−319.732	+	103.887i	−1.64810	+	0.535501i
$195$		0			0
$196$	0.294682	−	0.906937i	0.00150348	−	0.00462723i
$197$	90.4803	−	278.470i	0.459291	−	1.41355i	−0.406732	−	0.913547i	$-0.633332\pi$
$197$	90.4803	−	278.470i	0.459291	−	1.41355i	0.866023	−	0.500004i	$-0.166668\pi$
$198$	−80.5385	+	299.825i	−0.406760	+	1.51427i
$199$	179.944			0.904241			0.452121	−	0.891957i	$-0.350668\pi$
$199$	179.944			0.904241			0.452121	+	0.891957i	$0.350668\pi$
$200$		0			0
$201$	125.110	−	262.088i	0.622439	−	1.30392i
$202$	−271.695	−	373.956i	−1.34502	−	1.85127i
$203$	−73.1231	+	225.050i	−0.360212	+	1.10862i
$204$	−130.032	+	136.940i	−0.637414	+	0.671274i
$205$		0			0
$206$	84.5083	−	27.4584i	0.410235	−	0.133293i
$207$	−133.946	−	165.621i	−0.647081	−	0.800100i
$208$	−8.32196	+	2.70397i	−0.0400094	+	0.0129999i
$209$	95.7654	−	131.810i	0.458208	−	0.630669i
$210$		0			0
$211$	−262.367	+	190.621i	−1.24344	+	0.903415i	−0.997823	−	0.0659506i	$-0.978992\pi$
$211$	−262.367	+	190.621i	−1.24344	+	0.903415i	−0.245621	+	0.969366i	$0.578992\pi$
$212$	141.482	+	102.793i	0.667370	+	0.484873i
$213$	−42.1923	+	22.8915i	−0.198086	+	0.107472i
$214$	292.746	−	212.693i	1.36797	−	0.993891i
$215$		0			0
$216$	40.8245	−	98.2985i	0.189002	−	0.455086i
$217$	150.395	−	48.8662i	0.693063	−	0.225190i
$218$	−365.232			−1.67538
$219$	−119.496	−	15.7699i	−0.545644	−	0.0720088i
$220$		0			0
$221$	−10.8100	−	3.51237i	−0.0489139	−	0.0158931i
$222$	−227.208	−	215.747i	−1.02346	−	0.971833i
$223$	157.480	+	216.752i	0.706187	+	0.971983i	0.999871	+	0.0160803i	$0.00511873\pi$
$223$	157.480	+	216.752i	0.706187	+	0.971983i	−0.293684	+	0.955903i	$0.594881\pi$
$224$			240.584i			1.07403i
$225$		0			0
$226$	−183.800			−0.813276
$227$	−19.7762	+	14.3683i	−0.0871199	+	0.0632963i	−0.630493	−	0.776195i	$-0.717147\pi$
$227$	−19.7762	+	14.3683i	−0.0871199	+	0.0632963i	0.543373	+	0.839492i	$0.317147\pi$
$228$	60.6348	−	63.8559i	0.265942	−	0.280070i
$229$	−54.2684	+	167.021i	−0.236980	+	0.729349i	0.759873	+	0.650072i	$0.225261\pi$
$229$	−54.2684	+	167.021i	−0.236980	+	0.729349i	−0.996853	+	0.0792770i	$0.974739\pi$
$230$		0			0
$231$	−37.1768	+	281.706i	−0.160938	+	1.21951i
$232$			133.796i			0.576708i
$233$	28.6275	+	88.1063i	0.122865	+	0.378139i	0.993506	−	0.113780i	$-0.0362958\pi$
$233$	28.6275	+	88.1063i	0.122865	+	0.378139i	−0.870641	+	0.491918i	$0.836296\pi$
$234$	−10.0859	+	0.522265i	−0.0431021	+	0.00223190i
$235$		0			0
$236$	39.2955	+	54.0856i	0.166506	+	0.229176i
$237$	−16.4628	−	30.3432i	−0.0694631	−	0.128030i
$238$	−267.631	+	368.363i	−1.12450	+	1.54774i
$239$	44.1110	+	60.7136i	0.184565	+	0.254032i	0.891266	−	0.453480i	$-0.149818\pi$
$239$	44.1110	+	60.7136i	0.184565	+	0.254032i	−0.706702	+	0.707512i	$0.749818\pi$
$240$		0			0
$241$	−25.5230	−	18.5436i	−0.105905	−	0.0769443i	0.533572	−	0.845754i	$-0.320849\pi$
$241$	−25.5230	−	18.5436i	−0.105905	−	0.0769443i	−0.639477	+	0.768810i	$0.720849\pi$
$242$	−49.8665	−	153.473i	−0.206060	−	0.634187i
$243$	148.230	−	192.554i	0.609999	−	0.792402i
$244$	−72.7922	−	224.031i	−0.298329	−	0.918161i
$245$		0			0
$246$	105.044	+	99.7450i	0.427007	+	0.405468i
$247$	5.04075	+	1.63784i	0.0204079	+	0.00663093i
$248$	72.3363	−	52.5554i	0.291679	−	0.211917i
$249$	84.2419	+	40.2136i	0.338321	+	0.161500i
$250$		0			0
$251$		−	349.893i		−	1.39400i	−0.717072	−	0.696999i	$-0.754518\pi$
$251$		−	349.893i		−	1.39400i	0.717072	−	0.696999i	$-0.245482\pi$
$252$	−39.8410	+	148.318i	−0.158099	+	0.588564i
$253$	305.785	+	99.3555i	1.20864	+	0.392710i
$254$	−427.850	−	139.017i	−1.68445	−	0.547310i
$255$		0			0
$256$	101.935	+	313.723i	0.398183	+	1.22548i
$257$	5.11640			0.0199082			0.00995408	−	0.999950i	$-0.496831\pi$
$257$	5.11640			0.0199082			0.00995408	+	0.999950i	$0.496831\pi$
$258$	307.730	+	40.6112i	1.19275	+	0.157408i
$259$	−232.004	−	168.561i	−0.895770	−	0.650815i
$260$		0			0
$261$	−79.2423	+	294.999i	−0.303610	+	1.13027i
$262$	−173.691	+	239.066i	−0.662945	+	0.912465i
$263$	239.867	+	174.274i	0.912043	+	0.662638i	0.941531	−	0.336927i	$-0.109387\pi$
$263$	239.867	+	174.274i	0.912043	+	0.662638i	−0.0294874	+	0.999565i	$0.509387\pi$
$264$	29.2293	+	157.982i	0.110717	+	0.598418i
$265$		0			0
$266$	124.798	−	171.770i	0.469165	−	0.645751i
$267$	−180.403	−	23.8079i	−0.675668	−	0.0891680i
$268$			236.929i			0.884065i
$269$	217.290	−	70.6018i	0.807769	−	0.262460i	0.124116	−	0.992268i	$-0.460390\pi$
$269$	217.290	−	70.6018i	0.807769	−	0.262460i	0.683653	+	0.729808i	$0.260390\pi$
$270$		0			0
$271$	77.2828	−	237.852i	0.285176	−	0.877682i	−0.701170	−	0.712995i	$-0.747338\pi$
$271$	77.2828	−	237.852i	0.285176	−	0.877682i	0.986346	−	0.164688i	$-0.0526616\pi$
$272$	−157.363	+	484.313i	−0.578540	+	1.78056i
$273$	−9.08942	+	1.68169i	−0.0332946	+	0.00616003i
$274$	−257.745			−0.940676
$275$		0			0
$276$	156.823	+	74.8610i	0.568200	+	0.271235i
$277$	−194.827	−	268.157i	−0.703348	−	0.968075i	−0.999915	−	0.0130633i	$-0.995842\pi$
$277$	−194.827	−	268.157i	−0.703348	−	0.968075i	0.296567	−	0.955012i	$-0.404158\pi$
$278$	12.9647	−	39.9013i	0.0466357	−	0.143530i
$279$	190.616	−	73.0342i	0.683213	−	0.261771i
$280$		0			0
$281$	460.102	−	149.496i	1.63737	−	0.532015i	0.661423	−	0.750013i	$-0.269953\pi$
$281$	460.102	−	149.496i	1.63737	−	0.532015i	0.975949	+	0.217998i	$0.0699526\pi$
$282$	174.362	+	83.2332i	0.618305	+	0.295153i
$283$	−473.697	+	153.914i	−1.67384	+	0.543864i	−0.983701	−	0.179811i	$-0.942451\pi$
$283$	−473.697	+	153.914i	−1.67384	+	0.543864i	−0.690141	+	0.723675i	$0.742451\pi$
$284$	23.0184	−	31.6821i	0.0810506	−	0.111557i
$285$		0			0
$286$	12.3331	−	8.96049i	0.0431226	−	0.0313304i
$287$	107.261	+	77.9298i	0.373732	+	0.271533i
$288$	16.0598	+	310.144i	0.0557630	+	1.07689i
$289$	−301.345	+	218.940i	−1.04272	+	0.757579i
$290$		0			0
$291$	−349.123	+	189.417i	−1.19974	+	0.650918i
$292$	93.5199	−	30.3865i	0.320274	−	0.104063i
$293$	−340.665			−1.16268			−0.581339	−	0.813662i	$-0.697471\pi$
$293$	−340.665			−1.16268			−0.581339	+	0.813662i	$0.697471\pi$
$294$	0.388326	−	2.94253i	0.00132084	−	0.0100086i
$295$		0			0
$296$	−154.212	−	50.1064i	−0.520985	−	0.169278i
$297$	−29.1209	+	365.637i	−0.0980501	+	1.23110i
$298$	−243.981	−	335.811i	−0.818728	−	1.12688i
$299$			10.4595i			0.0349814i
$300$		0			0
$301$	284.098			0.943848
$302$	194.257	−	141.136i	0.643235	−	0.467338i
$303$	−396.025	−	376.049i	−1.30701	−	1.24109i
$304$	73.3792	−	225.838i	0.241379	−	0.742888i
$305$		0			0
$306$	−320.422	+	492.733i	−1.04713	+	1.61024i
$307$		−	206.808i		−	0.673641i	−0.941569	−	0.336821i	$-0.890648\pi$
$307$		−	206.808i		−	0.673641i	0.941569	−	0.336821i	$-0.109352\pi$
$308$	−71.6346	−	220.469i	−0.232580	−	0.715807i
$309$	92.2767	−	50.0649i	0.298630	−	0.162022i
$310$		0			0
$311$	−114.814	−	158.028i	−0.369177	−	0.508128i	0.583500	−	0.812113i	$-0.301683\pi$
$311$	−114.814	−	158.028i	−0.369177	−	0.508128i	−0.952677	+	0.303985i	$0.901683\pi$
$312$	−4.59398	+	2.49247i	−0.0147243	+	0.00798869i
$313$	277.776	−	382.326i	0.887464	−	1.22149i	−0.0868331	−	0.996223i	$-0.527675\pi$
$313$	277.776	−	382.326i	0.887464	−	1.22149i	0.974297	−	0.225267i	$-0.0723253\pi$
$314$	−156.938	−	216.007i	−0.499804	−	0.687921i
$315$		0			0
$316$	22.7846	+	16.5540i	0.0721032	+	0.0523860i
$317$	15.1899	+	46.7499i	0.0479178	+	0.147476i	0.972153	−	0.234349i	$-0.0752958\pi$
$317$	15.1899	+	46.7499i	0.0479178	+	0.147476i	−0.924235	+	0.381825i	$0.875296\pi$
$318$	491.211	+	234.484i	1.54469	+	0.737371i
$319$	−142.479	−	438.504i	−0.446641	−	1.37462i
$320$		0			0
$321$	294.385	−	310.023i	0.917087	−	0.965804i
$322$	398.488	+	129.477i	1.23754	+	0.402101i
$323$	249.544	−	181.304i	0.772582	−	0.561314i
$324$	−41.4595	+	193.861i	−0.127961	+	0.598335i
$325$		0			0
$326$			158.748i			0.486957i
$327$	−424.313	+	78.5048i	−1.29759	+	0.240076i
$328$	71.2957	+	23.1654i	0.217365	+	0.0706262i
$329$	168.183	+	54.6461i	0.511196	+	0.166098i
$330$		0			0
$331$	6.07919	+	18.7098i	0.0183661	+	0.0565252i	0.959820	−	0.280618i	$-0.0905394\pi$
$331$	6.07919	+	18.7098i	0.0183661	+	0.0565252i	−0.941453	+	0.337143i	$0.890539\pi$
$332$	−76.1551			−0.229383
$333$	−310.336	−	201.810i	−0.931939	−	0.606036i
$334$	250.490	+	181.992i	0.749971	+	0.544886i
$335$		0			0
$336$	75.3437	+	407.228i	0.224237	+	1.21199i
$337$	−274.595	+	377.948i	−0.814822	+	1.12151i	0.175739	+	0.984437i	$0.443768\pi$
$337$	−274.595	+	377.948i	−0.814822	+	1.12151i	−0.990561	+	0.137070i	$0.956232\pi$
$338$	−346.766	−	251.940i	−1.02594	−	0.745385i
$339$	−213.533	+	39.5070i	−0.629890	+	0.116540i
$340$		0			0
$341$	−181.109	+	249.275i	−0.531112	+	0.731013i
$342$	149.415	−	229.764i	0.436885	−	0.671825i
$343$		−	344.350i		−	1.00394i
$344$	152.773	−	49.6390i	0.444108	−	0.144299i
$345$		0			0
$346$	−120.755	+	371.644i	−0.349002	+	1.07412i
$347$	79.0960	−	243.432i	0.227942	−	0.701534i	−0.770037	−	0.637999i	$-0.779762\pi$
$347$	79.0960	−	243.432i	0.227942	−	0.701534i	0.997980	−	0.0635354i	$-0.0202376\pi$
$348$	−45.3363	−	245.039i	−0.130277	−	0.704136i
$349$	−17.4643			−0.0500411			−0.0250205	−	0.999687i	$-0.507965\pi$
$349$	−17.4643			−0.0500411			−0.0250205	+	0.999687i	$0.507965\pi$
$350$		0			0
$351$	−11.6052	+	2.77466i	−0.0330632	+	0.00790502i
$352$	−275.537	−	379.245i	−0.782776	−	1.07740i
$353$	−22.0131	+	67.7494i	−0.0623601	+	0.191925i	−0.977383	−	0.211478i	$-0.932172\pi$
$353$	−22.0131	+	67.7494i	−0.0623601	+	0.191925i	0.915023	+	0.403402i	$0.132172\pi$
$354$	150.889	+	143.278i	0.426240	+	0.404740i
$355$		0			0
$356$	141.187	−	45.8745i	0.396593	−	0.128861i
$357$	−231.747	+	485.477i	−0.649151	+	1.35988i
$358$	416.898	−	135.458i	1.16452	−	0.378375i
$359$	−90.9521	+	125.185i	−0.253348	+	0.348704i	−0.916680	−	0.399621i	$-0.869142\pi$
$359$	−90.9521	+	125.185i	−0.253348	+	0.348704i	0.663332	+	0.748325i	$0.269142\pi$
$360$		0			0
$361$	175.691	−	127.647i	0.486680	−	0.353594i
$362$	158.862	+	115.420i	0.438845	+	0.318840i
$363$	−90.9214	−	167.581i	−0.250472	−	0.461656i
$364$	6.10094	−	4.43260i	0.0167608	−	0.0121775i
$365$		0			0
$366$	−349.635	−	644.428i	−0.955288	−	1.76073i
$367$	421.585	−	136.981i	1.14873	−	0.373246i	0.328067	−	0.944654i	$-0.393603\pi$
$367$	421.585	−	136.981i	1.14873	−	0.373246i	0.820666	+	0.571408i	$0.193603\pi$
$368$	468.608			1.27339
$369$	143.476	+	93.3016i	0.388823	+	0.252850i
$370$		0			0
$371$	473.805	+	153.949i	1.27710	+	0.414956i
$372$	−114.671	+	120.763i	−0.308256	+	0.324631i
$373$	77.8079	+	107.093i	0.208600	+	0.287114i	0.900478	−	0.434901i	$-0.143216\pi$
$373$	77.8079	+	107.093i	0.208600	+	0.287114i	−0.691878	+	0.722014i	$0.743216\pi$
$374$		−	887.184i		−	2.37215i
$375$		0			0
$376$	99.9882			0.265926
$377$	12.1346	−	8.81628i	0.0321872	−	0.0233854i
$378$	−37.9493	+	476.485i	−0.100395	+	1.26054i
$379$	128.165	−	394.451i	0.338166	−	1.04077i	−0.626976	−	0.779039i	$-0.715707\pi$
$379$	128.165	−	394.451i	0.338166	−	1.04077i	0.965141	−	0.261729i	$-0.0842926\pi$
$380$		0			0
$381$	−526.941	−	69.5405i	−1.38305	−	0.182521i
$382$		−	222.578i		−	0.582666i
$383$	−101.612	−	312.730i	−0.265306	−	0.816527i	−0.991623	−	0.129167i	$-0.958770\pi$
$383$	−101.612	−	312.730i	−0.265306	−	0.816527i	0.726317	−	0.687360i	$-0.241230\pi$
$384$	166.882	+	307.588i	0.434589	+	0.801010i
$385$		0			0
$386$	−47.8811	−	65.9026i	−0.124044	−	0.170732i
$387$	366.239	−	18.9645i	0.946355	−	0.0490038i
$388$	190.467	−	262.155i	0.490894	−	0.675658i
$389$	88.8453	+	122.285i	0.228394	+	0.314358i	0.907799	−	0.419406i	$-0.137762\pi$
$389$	88.8453	+	122.285i	0.228394	+	0.314358i	−0.679404	+	0.733764i	$0.737762\pi$
$390$		0			0
$391$	492.455	+	357.790i	1.25948	+	0.915063i
$392$	−0.474650	−	1.46082i	−0.00121084	−	0.00372659i
$393$	−150.403	+	315.072i	−0.382704	+	0.801711i
$394$	229.746	+	707.086i	0.583112	+	1.79463i
$395$		0			0
$396$	−107.063	−	279.431i	−0.270362	−	0.705633i
$397$	559.798	+	181.889i	1.41007	+	0.458159i	0.912433	−	0.409226i	$-0.134201\pi$
$397$	559.798	+	181.889i	1.41007	+	0.458159i	0.497637	+	0.867386i	$0.334201\pi$
$398$	−369.649	+	268.566i	−0.928766	+	0.674788i
$399$	108.065	−	226.381i	0.270839	−	0.567370i
$400$		0			0
$401$		−	28.4184i		−	0.0708688i	−0.999372	−	0.0354344i	$-0.988719\pi$
$401$		−	28.4184i		−	0.0708688i	0.999372	−	0.0354344i	$-0.0112815\pi$
$402$	134.159	+	725.120i	0.333729	+	1.80378i
$403$	−9.53295	−	3.09744i	−0.0236550	−	0.00768596i
$404$	423.731	+	137.679i	1.04884	+	0.340789i
$405$		0			0
$406$	−185.673	−	571.443i	−0.457323	−	1.40749i
$407$	558.771			1.37290
$408$	−39.7964	+	301.556i	−0.0975402	+	0.739108i
$409$	−208.962	−	151.820i	−0.510910	−	0.371198i	0.302258	−	0.953226i	$-0.402259\pi$
$409$	−208.962	−	151.820i	−0.510910	−	0.371198i	−0.813169	+	0.582028i	$0.802259\pi$
$410$		0			0
$411$	−299.439	+	55.4011i	−0.728563	+	0.134796i
$412$	−50.3423	+	69.2903i	−0.122190	+	0.168180i
$413$	154.074	+	111.942i	0.373061	+	0.271045i
$414$	522.345	+	140.312i	1.26170	+	0.338917i
$415$		0			0
$416$	8.96354	−	12.3373i	0.0215470	−	0.0296569i
$417$	6.48536	−	49.1426i	0.0155524	−	0.117848i
$418$			413.699i			0.989710i
$419$	−225.854	+	73.3843i	−0.539030	+	0.175141i	−0.565864	−	0.824498i	$-0.691457\pi$
$419$	−225.854	+	73.3843i	−0.539030	+	0.175141i	0.0268343	+	0.999640i	$0.491457\pi$
$420$		0			0
$421$	132.441	−	407.611i	0.314586	−	0.968197i	−0.661338	−	0.750088i	$-0.730011\pi$
$421$	132.441	−	407.611i	0.314586	−	0.968197i	0.975924	−	0.218109i	$-0.0699889\pi$
$422$	254.465	−	783.163i	0.602997	−	1.85584i
$423$	220.458	+	59.2191i	0.521177	+	0.139998i
$424$	281.686			0.664354
$425$		0			0
$426$	52.5079	−	109.997i	0.123258	−	0.258208i
$427$	−394.430	−	542.886i	−0.923723	−	1.27140i
$428$	−107.780	+	331.712i	−0.251822	+	0.775029i
$429$	12.4021	−	13.0609i	0.0289093	−	0.0304450i
$430$		0			0
$431$	631.269	−	205.112i	1.46466	−	0.475898i	0.535172	−	0.844743i	$-0.320247\pi$
$431$	631.269	−	205.112i	1.46466	−	0.475898i	0.929491	+	0.368846i	$0.120247\pi$
$432$	124.312	+	519.940i	0.287758	+	1.20356i
$433$	559.669	−	181.848i	1.29254	−	0.419971i	0.419559	−	0.907728i	$-0.362185\pi$
$433$	559.669	−	181.848i	1.29254	−	0.419971i	0.872980	+	0.487756i	$0.162185\pi$
$434$	−236.015	+	324.847i	−0.543813	+	0.748495i
$435$		0			0
$436$	284.805	−	206.923i	0.653223	−	0.474594i
$437$	−229.635	−	166.839i	−0.525480	−	0.381783i
$438$	269.011	−	145.952i	0.614180	−	0.333224i
$439$	−248.454	+	180.512i	−0.565954	+	0.411190i	−0.833633	−	0.552318i	$-0.813743\pi$
$439$	−248.454	+	180.512i	−0.565954	+	0.411190i	0.267679	+	0.963508i	$0.413743\pi$
$440$		0			0
$441$	−0.181339	−	3.50200i	−0.000411200	−	0.00794103i
$442$	27.4485	−	8.91857i	0.0621008	−	0.0201778i
$443$	−567.297			−1.28058			−0.640290	−	0.768133i	$-0.721186\pi$
$443$	−567.297			−1.28058			−0.640290	+	0.768133i	$0.721186\pi$
$444$	299.407	+	39.5128i	0.674340	+	0.0889928i
$445$		0			0
$446$	−647.003	−	210.224i	−1.45068	−	0.471355i
$447$	−355.630	−	337.691i	−0.795592	−	0.755461i
$448$	−34.5040	−	47.4906i	−0.0770178	−	0.106006i
$449$			21.4607i			0.0477967i	0.999714	+	0.0238983i	$0.00760780\pi$
$449$			21.4607i			0.0477967i	−0.999714	+	0.0238983i	$0.992392\pi$
$450$		0			0
$451$	−258.333			−0.572801
$452$	143.326	−	104.133i	0.317093	−	0.230382i
$453$	195.344	−	205.721i	0.431224	−	0.454131i
$454$	19.1806	−	59.0318i	0.0422480	−	0.130026i
$455$		0			0
$456$	18.5573	−	140.617i	0.0406958	−	0.308371i
$457$		−	442.410i		−	0.968075i	−0.875047	−	0.484037i	$-0.839170\pi$
$457$		−	442.410i		−	0.968075i	0.875047	−	0.484037i	$-0.160830\pi$
$458$	−137.797	−	424.097i	−0.300868	−	0.925976i
$459$	−266.344	+	641.313i	−0.580271	+	1.39720i
$460$		0			0
$461$	−270.395	−	372.166i	−0.586540	−	0.807303i	0.407854	−	0.913047i	$-0.366277\pi$
$461$	−270.395	−	372.166i	−0.586540	−	0.807303i	−0.994393	+	0.105745i	$0.966277\pi$
$462$	−344.075	−	634.179i	−0.744751	−	1.37268i
$463$	−110.953	+	152.714i	−0.239640	+	0.329836i	−0.911849	−	0.410525i	$-0.865345\pi$
$463$	−110.953	+	152.714i	−0.239640	+	0.329836i	0.672209	+	0.740361i	$0.265345\pi$
$464$	−394.990	−	543.658i	−0.851272	−	1.17168i
$465$		0			0
$466$	−190.306	−	138.266i	−0.408382	−	0.296707i
$467$	38.8708	+	119.632i	0.0832352	+	0.256172i	0.984010	−	0.178116i	$-0.0570002\pi$
$467$	38.8708	+	119.632i	0.0832352	+	0.256172i	−0.900774	+	0.434288i	$0.857000\pi$
$468$	7.56902	−	6.12145i	0.0161731	−	0.0130800i
$469$	208.569	+	641.910i	0.444710	+	1.36868i
$470$		0			0
$471$	−228.755	−	217.216i	−0.485680	−	0.461181i
$472$	102.412	+	33.2757i	0.216975	+	0.0704994i
$473$	−447.839	+	325.374i	−0.946805	+	0.687894i
$474$	79.1056	+	37.7618i	0.166889	+	0.0796662i
$475$		0			0
$476$		−	438.874i		−	0.922004i
$477$	621.073	+	166.832i	1.30204	+	0.349752i
$478$	−181.229	−	58.8850i	−0.379141	−	0.123190i
$479$	−518.995	−	168.632i	−1.08350	−	0.352049i	−0.287766	−	0.957701i	$-0.592913\pi$
$479$	−518.995	−	168.632i	−1.08350	−	0.352049i	−0.795730	+	0.605651i	$0.792913\pi$
$480$		0			0
$481$	5.61714	+	17.2878i	0.0116781	+	0.0359413i
$482$	80.1068			0.166197
$483$	490.779	+	64.7682i	1.01611	+	0.134096i
$484$	125.836	+	91.4253i	0.259992	+	0.188895i
$485$		0			0
$486$	−17.1146	+	616.785i	−0.0352152	+	1.26910i
$487$	183.292	−	252.279i	0.376369	−	0.518027i	−0.578249	−	0.815860i	$-0.696264\pi$
$487$	183.292	−	252.279i	0.376369	−	0.518027i	0.954618	+	0.297833i	$0.0962638\pi$
$488$	−306.959	−	223.019i	−0.629015	−	0.457006i
$489$	34.1221	+	184.428i	0.0697793	+	0.377153i
$490$		0			0
$491$	−207.347	+	285.389i	−0.422296	+	0.581241i	−0.966163	−	0.257931i	$-0.916959\pi$
$491$	−207.347	+	285.389i	−0.422296	+	0.581241i	0.543867	+	0.839171i	$0.316959\pi$
$492$	−138.423	−	18.2677i	−0.281348	−	0.0371295i
$493$		−	872.905i		−	1.77060i
$494$	−12.7994	+	4.15878i	−0.0259097	+	0.00841858i
$495$		0			0
$496$	−138.773	+	427.099i	−0.279784	+	0.861087i
$497$	34.4736	−	106.099i	0.0693634	−	0.213479i
$498$	−233.072	+	43.1221i	−0.468016	+	0.0865905i
$499$	80.4065			0.161135			0.0805677	−	0.996749i	$-0.474327\pi$
$499$	80.4065			0.161135			0.0805677	+	0.996749i	$0.474327\pi$
$500$		0			0
$501$	330.129	+	157.590i	0.658940	+	0.314551i
$502$	522.214	+	718.766i	1.04027	+	1.43181i
$503$	−154.019	+	474.023i	−0.306201	+	0.942391i	0.673025	+	0.739620i	$0.264995\pi$
$503$	−154.019	+	474.023i	−0.306201	+	0.942391i	−0.979226	+	0.202771i	$0.935005\pi$
$504$	88.5046	+	230.993i	0.175604	+	0.458320i
$505$		0			0
$506$	−776.444	+	252.282i	−1.53448	+	0.498581i
$507$	−457.014	−	218.160i	−0.901408	−	0.430295i
$508$	412.394	−	133.995i	0.811800	−	0.263770i
$509$	−137.249	+	188.907i	−0.269645	+	0.371134i	−0.922270	−	0.386547i	$-0.873668\pi$
$509$	−137.249	+	188.907i	−0.269645	+	0.371134i	0.652625	+	0.757681i	$0.273668\pi$
$510$		0			0
$511$	226.623	−	164.651i	0.443489	−	0.322214i
$512$	−300.150	−	218.071i	−0.586230	−	0.425921i
$513$	124.198	−	299.048i	0.242101	−	0.582939i
$514$	−10.5103	+	7.63620i	−0.0204481	+	0.0148564i
$515$		0			0
$516$	−262.974	+	142.677i	−0.509640	+	0.276506i
$517$	−327.702	+	106.477i	−0.633852	+	0.205951i
$518$	728.170			1.40573
$519$	−60.4052	+	457.719i	−0.116388	+	0.881924i
$520$		0			0
$521$	−216.308	−	70.2826i	−0.415178	−	0.134899i	0.0939771	−	0.995574i	$-0.470042\pi$
$521$	−216.308	−	70.2826i	−0.415178	−	0.134899i	−0.509155	+	0.860675i	$0.670042\pi$
$522$	−277.502	−	724.270i	−0.531614	−	1.38749i
$523$	146.764	+	202.004i	0.280620	+	0.386241i	0.925939	−	0.377672i	$-0.123275\pi$
$523$	146.764	+	202.004i	0.280620	+	0.386241i	−0.645319	+	0.763913i	$0.723275\pi$
$524$		−	284.827i		−	0.543563i
$525$		0			0
$526$	−752.849			−1.43127
$527$	−471.932	+	342.878i	−0.895506	+	0.650623i
$528$	−585.160	−	555.644i	−1.10826	−	1.05236i
$529$	9.62402	−	29.6197i	0.0181929	−	0.0559918i
$530$		0			0
$531$	206.094	+	134.022i	0.388125	+	0.252396i
$532$			204.649i			0.384679i
$533$	−2.59694	−	7.99256i	−0.00487231	−	0.0149954i
$534$	406.126	−	220.344i	0.760535	−	0.412629i
$535$		0			0
$536$	224.315	+	308.743i	0.418498	+	0.576013i
$537$	455.221	−	246.981i	0.847712	−	0.459927i
$538$	−340.994	+	469.337i	−0.633817	+	0.872374i
$539$	3.11124	+	4.28225i	0.00577224	+	0.00794481i
$540$		0			0
$541$	95.2741	+	69.2207i	0.176107	+	0.127950i	0.672347	−	0.740236i	$-0.265286\pi$
$541$	95.2741	+	69.2207i	0.176107	+	0.127950i	−0.496240	+	0.868186i	$0.665286\pi$
$542$	196.235	+	603.950i	0.362058	+	1.11430i
$543$	209.369	+	99.9441i	0.385578	+	0.184059i
$544$	−274.248	−	844.049i	−0.504133	−	1.55156i
$545$		0			0
$546$	16.1620	−	17.0205i	0.0296007	−	0.0311731i
$547$	−689.808	−	224.132i	−1.26108	−	0.409748i	−0.399198	−	0.916865i	$-0.630711\pi$
$547$	−689.808	−	224.132i	−1.26108	−	0.409748i	−0.861877	+	0.507117i	$0.830711\pi$
$548$	200.988	−	146.026i	0.366766	−	0.266471i
$549$	−544.710	−	673.521i	−0.992187	−	1.22681i
$550$		0			0
$551$			407.040i			0.738730i
$552$	275.232	−	50.9224i	0.498609	−	0.0922507i
$553$	76.3025	+	24.7922i	0.137979	+	0.0448322i
$554$	800.446	+	260.081i	1.44485	+	0.469460i
$555$		0			0
$556$	12.4964	+	38.4600i	0.0224755	+	0.0691726i
$557$	66.5010			0.119391			0.0596957	−	0.998217i	$-0.480987\pi$
$557$	66.5010			0.119391			0.0596957	+	0.998217i	$0.480987\pi$
$558$	−282.569	+	434.524i	−0.506396	+	0.778717i
$559$	−14.5687	−	10.5848i	−0.0260621	−	0.0189352i
$560$		0			0
$561$	−190.696	−	1030.70i	−0.339921	−	1.83725i
$562$	−722.039	+	993.801i	−1.28477	+	1.76833i
$563$	−420.897	−	305.800i	−0.747598	−	0.543161i	0.147484	−	0.989064i	$-0.452883\pi$
$563$	−420.897	−	305.800i	−0.747598	−	0.543161i	−0.895081	+	0.445903i	$0.852883\pi$
$564$	−183.122	+	33.8805i	−0.324685	+	0.0600719i
$565$		0			0
$566$	743.374	−	1023.17i	1.31338	−	1.80772i
$567$	58.3301	+	561.721i	0.102875	+	0.990689i
$568$		−	63.0778i		−	0.111053i
$569$	−364.152	+	118.320i	−0.639985	+	0.207944i	−0.610993	−	0.791636i	$-0.709230\pi$
$569$	−364.152	+	118.320i	−0.639985	+	0.207944i	−0.0289921	+	0.999580i	$0.509230\pi$
$570$		0			0
$571$	−276.902	+	852.217i	−0.484942	+	1.49250i	0.347122	+	0.937820i	$0.387159\pi$
$571$	−276.902	+	852.217i	−0.484942	+	1.49250i	−0.832065	+	0.554679i	$0.812841\pi$
$572$	−4.54064	+	13.9747i	−0.00793818	+	0.0244312i
$573$	−47.8422	−	258.584i	−0.0834942	−	0.451280i
$574$	−336.651			−0.586499
$575$		0			0
$576$	−47.6502	−	58.9183i	−0.0827261	−	0.102289i
$577$	518.759	+	714.010i	0.899062	+	1.23745i	0.970766	+	0.240026i	$0.0771560\pi$
$577$	518.759	+	714.010i	0.899062	+	1.23745i	−0.0717049	+	0.997426i	$0.522844\pi$
$578$	292.270	−	899.513i	0.505657	−	1.55625i
$579$	−69.7920	−	66.2715i	−0.120539	−	0.114459i
$580$		0			0
$581$	−206.326	+	67.0394i	−0.355122	+	0.115386i
$582$	434.479	−	910.174i	0.746528	−	1.56387i
$583$	−923.199	+	299.965i	−1.58353	+	0.514520i
$584$	93.0973	−	128.137i	0.159413	−	0.219413i
$585$		0			0
$586$	699.808	−	508.440i	1.19421	−	0.867646i
$587$	−313.505	−	227.774i	−0.534079	−	0.388031i	0.287802	−	0.957690i	$-0.407075\pi$
$587$	−313.505	−	227.774i	−0.534079	−	0.388031i	−0.821881	+	0.569659i	$0.807075\pi$
$588$	1.36428	+	2.51457i	0.00232021	+	0.00427648i
$589$	220.064	−	159.886i	0.373624	−	0.271453i
$590$		0			0
$591$	418.896	+	772.085i	0.708791	+	1.30640i
$592$	774.534	−	251.661i	1.30834	−	0.425104i
$593$	134.959			0.227586			0.113793	−	0.993504i	$-0.463700\pi$
$593$	134.959			0.227586			0.113793	+	0.993504i	$0.463700\pi$
$594$	−485.891	−	794.571i	−0.817998	−	1.33766i
$595$		0			0
$596$	380.509	+	123.635i	0.638439	+	0.207441i
$597$	−371.718	+	391.464i	−0.622643	+	0.655719i
$598$	−15.6107	−	21.4863i	−0.0261048	−	0.0359302i
$599$			279.184i			0.466083i	0.972467	+	0.233041i	$0.0748678\pi$
$599$			279.184i			0.466083i	−0.972467	+	0.233041i	$0.925132\pi$
$600$		0			0
$601$	−135.279			−0.225089			−0.112545	−	0.993647i	$-0.535900\pi$
$601$	−135.279			−0.225089			−0.112545	+	0.993647i	$0.535900\pi$
$602$	−583.607	+	424.015i	−0.969447	+	0.704344i
$603$	311.722	+	813.582i	0.516952	+	1.34922i
$604$	−71.5193	+	220.114i	−0.118409	+	0.364427i
$605$		0			0
$606$	1374.78	+	181.430i	2.26862	+	0.299390i
$607$		−	206.038i		−	0.339436i	−0.985493	−	0.169718i	$-0.945714\pi$
$607$		−	206.038i		−	0.339436i	0.985493	−	0.169718i	$-0.0542857\pi$
$608$	127.883	+	393.585i	0.210335	+	0.647343i
$609$	−338.537	−	623.972i	−0.555890	−	1.02459i
$610$		0			0
$611$	−6.58855	−	9.06837i	−0.0107832	−	0.0148418i
$612$	−29.2963	−	565.766i	−0.0478697	−	0.924453i
$613$	−187.514	+	258.091i	−0.305896	+	0.421030i	−0.934096	−	0.357022i	$-0.883792\pi$
$613$	−187.514	+	258.091i	−0.305896	+	0.421030i	0.628200	+	0.778052i	$0.283792\pi$
$614$	308.660	+	424.834i	0.502703	+	0.691912i
$615$		0			0
$616$	−302.078	−	219.472i	−0.490386	−	0.356286i
$617$	134.643	+	414.390i	0.218223	+	0.671620i	0.998909	+	0.0466971i	$0.0148696\pi$
$617$	134.643	+	414.390i	0.218223	+	0.671620i	−0.780687	+	0.624923i	$0.785130\pi$
$618$	−114.837	+	240.568i	−0.185821	+	0.389269i
$619$	67.3502	+	207.283i	0.108805	+	0.334867i	0.990605	−	0.136757i	$-0.0436679\pi$
$619$	67.3502	+	207.283i	0.108805	+	0.334867i	−0.881800	+	0.471624i	$0.843668\pi$
$620$		0			0
$621$	637.002	+	50.7335i	1.02577	+	0.0816964i
$622$	471.712	+	153.268i	0.758379	+	0.246412i
$623$	342.133	−	248.574i	0.549170	−	0.398995i
$624$	11.3086	−	23.6899i	0.0181228	−	0.0379647i
$625$		0			0
$626$			1199.97i			1.91689i
$627$	88.9225	+	480.621i	0.141822	+	0.766540i
$628$	244.759	+	79.5270i	0.389743	+	0.126635i
$629$	1006.10	+	326.901i	1.59952	+	0.519715i
$630$		0			0
$631$	−327.690	−	1008.53i	−0.519319	−	1.59830i	−0.775283	−	0.631614i	$-0.782393\pi$
$631$	−327.690	−	1008.53i	−0.519319	−	1.59830i	0.255964	−	0.966686i	$-0.417607\pi$
$632$	45.3633			0.0717774
$633$	127.291	−	964.546i	0.201092	−	1.52377i
$634$	−100.978	−	73.3647i	−0.159271	−	0.115717i
$635$		0			0
$636$	−515.890	+	95.4480i	−0.811148	+	0.150076i
$637$	−0.101212	+	0.139306i	−0.000158889	+	0.000218691i
$638$	947.151	+	688.146i	1.48456	+	1.07860i
$639$	37.3585	−	139.076i	0.0584640	−	0.217647i
$640$		0			0
$641$	−2.10516	+	2.89750i	−0.00328417	+	0.00452028i	−0.810656	−	0.585523i	$-0.800889\pi$
$641$	−2.10516	+	2.89750i	−0.00328417	+	0.00452028i	0.807372	+	0.590043i	$0.200889\pi$
$642$	−142.030	+	1076.23i	−0.221231	+	1.67637i
$643$			885.019i			1.37639i	0.725526	+	0.688195i	$0.241597\pi$
$643$			885.019i			1.37639i	−0.725526	+	0.688195i	$0.758403\pi$
$644$	−384.093	+	124.799i	−0.596418	+	0.193788i
$645$		0			0
$646$	−242.028	+	744.887i	−0.374657	+	1.15308i
$647$	−195.799	+	602.607i	−0.302626	+	0.931386i	0.677927	+	0.735129i	$0.262879\pi$
$647$	−195.799	+	602.607i	−0.302626	+	0.931386i	−0.980553	+	0.196257i	$0.937121\pi$
$648$	129.513	+	291.872i	0.199866	+	0.450420i
$649$	−371.081			−0.571773
$650$		0			0
$651$	−204.370	+	428.126i	−0.313932	+	0.657643i
$652$	−89.9390	−	123.790i	−0.137943	−	0.189863i
$653$	193.035	−	594.101i	0.295612	−	0.909802i	−0.687403	−	0.726277i	$-0.741249\pi$
$653$	193.035	−	594.101i	0.295612	−	0.909802i	0.983015	−	0.183525i	$-0.0587508\pi$
$654$	754.475	−	794.554i	1.15363	−	1.21491i
$655$		0			0
$656$	−358.086	+	116.349i	−0.545863	+	0.177362i
$657$	281.155	−	227.385i	0.427938	−	0.346095i
$658$	−427.049	+	138.757i	−0.649010	+	0.210876i
$659$	−319.722	+	440.059i	−0.485162	+	0.667768i	−0.979487	−	0.201509i	$-0.935415\pi$
$659$	−319.722	+	440.059i	−0.485162	+	0.667768i	0.494325	+	0.869277i	$0.335415\pi$
$660$		0			0
$661$	−138.017	+	100.275i	−0.208801	+	0.151703i	−0.687271	−	0.726401i	$-0.741191\pi$
$661$	−138.017	+	100.275i	−0.208801	+	0.151703i	0.478470	+	0.878104i	$0.341191\pi$
$662$	−40.4125	−	29.3614i	−0.0610461	−	0.0443526i
$663$	29.9717	−	16.2612i	0.0452062	−	0.0245267i
$664$	−99.2379	+	72.1005i	−0.149455	+	0.108585i
$665$		0			0
$666$	938.706	−	48.6078i	1.40947	−	0.0729846i
$667$	−763.948	+	248.222i	−1.14535	+	0.372146i
$668$	−298.439			−0.446764
$669$	−796.852	−	105.161i	−1.19111	−	0.157191i
$670$		0			0
$671$	1243.52	+	404.044i	1.85323	+	0.602152i
$672$	−523.385	−	496.984i	−0.778846	−	0.739560i
$673$	−251.764	−	346.524i	−0.374092	−	0.514894i	0.579915	−	0.814677i	$-0.303086\pi$
$673$	−251.764	−	346.524i	−0.374092	−	0.514894i	−0.954007	+	0.299783i	$0.903086\pi$
$674$		−	1186.23i		−	1.75998i
$675$		0			0
$676$	413.143			0.611158
$677$	391.318	−	284.309i	0.578018	−	0.419955i	−0.259991	−	0.965611i	$-0.583720\pi$
$677$	391.318	−	284.309i	0.578018	−	0.419955i	0.838009	+	0.545656i	$0.183720\pi$
$678$	379.684	−	399.854i	0.560006	−	0.589755i
$679$	285.254	−	877.922i	0.420109	−	1.29296i
$680$		0			0
$681$	9.59474	−	72.7039i	0.0140892	−	0.106760i
$682$		−	782.377i		−	1.14718i
$683$	354.430	+	1090.82i	0.518931	+	1.59711i	0.776013	+	0.630716i	$0.217239\pi$
$683$	354.430	+	1090.82i	0.518931	+	1.59711i	−0.257082	+	0.966389i	$0.582761\pi$
$684$	13.6610	+	263.820i	0.0199722	+	0.385701i
$685$		0			0
$686$	513.941	+	707.379i	0.749185	+	1.03117i
$687$	−251.246	−	463.082i	−0.365714	−	0.674064i
$688$	−474.223	+	652.713i	−0.689278	+	0.948710i
$689$	−18.5612	−	25.5473i	−0.0269394	−	0.0370789i
$690$		0			0
$691$	350.566	+	254.701i	0.507331	+	0.368597i	0.811810	−	0.583922i	$-0.198482\pi$
$691$	350.566	+	254.701i	0.507331	+	0.368597i	−0.304479	+	0.952519i	$0.598482\pi$
$692$	−116.393	−	358.219i	−0.168197	−	0.517658i
$693$	−536.048	−	662.810i	−0.773518	−	0.956435i
$694$	200.839	+	618.120i	0.289394	+	0.890663i
$695$		0			0
$696$	−291.071	−	276.389i	−0.418205	−	0.397110i
$697$	−465.143	−	151.134i	−0.667350	−	0.216835i
$698$	35.8760	−	26.0654i	0.0513983	−	0.0373430i
$699$	−250.810	−	119.727i	−0.358813	−	0.171283i
$700$		0			0
$701$		−	708.515i		−	1.01072i	−0.862909	−	0.505360i	$-0.831360\pi$
$701$		−	708.515i		−	1.01072i	0.862909	−	0.505360i	$-0.168640\pi$
$702$	19.6987	−	23.0205i	0.0280608	−	0.0327928i
$703$	−469.149	−	152.436i	−0.667352	−	0.216836i
$704$	108.781	+	35.3450i	0.154518	+	0.0502060i
$705$		0			0
$706$	−55.8954	−	172.028i	−0.0791719	−	0.243666i
$707$	1269.21			1.79520
$708$	−198.837	−	26.2405i	−0.280843	−	0.0370628i
$709$	869.199	+	631.510i	1.22595	+	0.890705i	0.996580	−	0.0826343i	$-0.0263333\pi$
$709$	869.199	+	631.510i	1.22595	+	0.890705i	0.229370	+	0.973339i	$0.426333\pi$
$710$		0			0
$711$	100.019	+	26.8669i	0.140673	+	0.0377875i
$712$	140.549	−	193.449i	0.197400	−	0.271698i
$713$	434.280	+	315.523i	0.609088	+	0.442528i
$714$	−248.508	−	1343.17i	−0.348050	−	1.88119i
$715$		0			0
$716$	−248.350	+	341.824i	−0.346857	+	0.477408i
$717$	−223.203	−	29.4561i	−0.311301	−	0.0410825i
$718$		−	392.906i		−	0.547223i
$719$	1266.77	−	411.597i	1.76184	−	0.572458i	0.764456	−	0.644676i	$-0.223008\pi$
$719$	1266.77	−	411.597i	1.76184	−	0.572458i	0.997389	+	0.0722178i	$0.0230077\pi$
$720$		0			0
$721$	−75.3955	+	232.044i	−0.104571	+	0.321836i
$722$	−170.400	+	524.437i	−0.236011	+	0.726367i
$723$	93.0652	−	17.2186i	0.128721	−	0.0238154i
$724$	−189.271			−0.261424
$725$		0			0
$726$	436.889	+	208.553i	0.601775	+	0.287263i
$727$	−319.388	−	439.600i	−0.439323	−	0.604676i	0.530738	−	0.847536i	$-0.321915\pi$
$727$	−319.388	−	439.600i	−0.439323	−	0.604676i	−0.970062	+	0.242859i	$0.921915\pi$
$728$	3.75355	−	11.5522i	0.00515598	−	0.0158685i
$729$	112.692	+	720.237i	0.154584	+	0.987980i
$730$		0			0
$731$	−996.712	+	323.851i	−1.36349	+	0.443025i
$732$	637.745	+	304.433i	0.871237	+	0.415893i
$733$	−803.163	+	260.963i	−1.09572	+	0.356021i	−0.800454	−	0.599394i	$-0.795408\pi$
$733$	−803.163	+	260.963i	−1.09572	+	0.356021i	−0.295266	+	0.955415i	$0.595408\pi$
$734$	−661.595	+	910.607i	−0.901355	+	1.24061i
$735$		0			0
$736$	−660.708	+	480.032i	−0.897701	+	0.652218i
$737$	−1063.95	−	773.004i	−1.44362	−	1.04885i
$738$	−433.986	+	22.4725i	−0.588057	+	0.0304506i
$739$	472.107	−	343.005i	0.638845	−	0.464148i	−0.220608	−	0.975363i	$-0.570804\pi$
$739$	472.107	−	343.005i	0.638845	−	0.464148i	0.859453	+	0.511214i	$0.170804\pi$
$740$		0			0
$741$	−13.9760	+	7.58269i	−0.0188610	+	0.0102331i
$742$	−1203.08	+	390.904i	−1.62140	+	0.526825i
$743$	−96.0790			−0.129312			−0.0646561	−	0.997908i	$-0.520595\pi$
$743$	−96.0790			−0.129312			−0.0646561	+	0.997908i	$0.520595\pi$
$744$	−35.0951	+	265.932i	−0.0471708	+	0.357435i
$745$		0			0
$746$	−319.673	−	103.868i	−0.428516	−	0.139233i
$747$	−261.506	+	100.195i	−0.350075	+	0.134130i
$748$	502.636	+	691.820i	0.671974	+	0.924893i
$749$			993.582i			1.32654i
$750$		0			0
$751$	−665.080			−0.885592			−0.442796	−	0.896622i	$-0.646013\pi$
$751$	−665.080			−0.885592			−0.442796	+	0.896622i	$0.646013\pi$
$752$	−406.285	+	295.183i	−0.540272	+	0.392531i
$753$	761.185	+	722.790i	1.01087	+	0.959880i
$754$	−11.7691	+	36.2216i	−0.0156089	+	0.0480392i
$755$		0			0
$756$	−240.361	−	393.060i	−0.317938	−	0.519921i
$757$			710.689i			0.938822i	0.882980	+	0.469411i	$0.155534\pi$
$757$			710.689i			0.938822i	−0.882980	+	0.469411i	$0.844466\pi$
$758$	325.434	+	1001.58i	0.429333	+	1.32135i
$759$	−847.819	+	459.985i	−1.11702	+	0.606041i
$760$		0			0
$761$	−89.4370	−	123.099i	−0.117526	−	0.161760i	0.746201	−	0.665721i	$-0.231876\pi$
$761$	−89.4370	−	123.099i	−0.117526	−	0.161760i	−0.863727	+	0.503960i	$0.831876\pi$
$762$	1186.26	−	643.605i	1.55677	−	0.844626i
$763$	589.464	−	811.328i	0.772561	−	1.06334i
$764$	126.102	+	173.565i	0.165055	+	0.227179i
$765$		0			0
$766$	675.484	+	490.768i	0.881832	+	0.640689i
$767$	−3.73035	−	11.4808i	−0.00486356	−	0.0149685i
$768$	−893.069	−	426.314i	−1.16285	−	0.555097i
$769$	−298.261	−	917.953i	−0.387856	−	1.19370i	−0.934387	−	0.356259i	$-0.884052\pi$
$769$	−298.261	−	917.953i	−0.387856	−	1.19370i	0.546532	−	0.837439i	$-0.315948\pi$
$770$		0			0
$771$	−10.5692	+	11.1306i	−0.0137084	+	0.0144366i
$772$	74.6746	+	24.2633i	0.0967288	+	0.0314291i
$773$	728.420	−	529.228i	0.942329	−	0.684642i	−0.00665109	−	0.999978i	$-0.502117\pi$
$773$	728.420	−	529.228i	0.942329	−	0.684642i	0.948980	+	0.315336i	$0.102117\pi$
$774$	−724.041	+	585.568i	−0.935453	+	0.756548i
$775$		0			0
$776$		−	521.941i		−	0.672605i
$777$	845.962	−	156.517i	1.08875	−	0.201437i
$778$	−365.020	−	118.602i	−0.469177	−	0.152445i
$779$	216.899	+	70.4747i	0.278432	+	0.0904681i
$780$		0			0
$781$	67.1711	+	206.731i	0.0860065	+	0.264701i
$782$	−1545.62			−1.97650
$783$	−478.070	−	781.783i	−0.610563	−	0.998445i
$784$	6.24126	+	4.53454i	0.00796080	+	0.00578386i
$785$		0			0
$786$	−161.281	−	871.711i	−0.205191	−	1.10905i
$787$	358.857	−	493.925i	0.455981	−	0.627605i	−0.517688	−	0.855570i	$-0.673207\pi$
$787$	358.857	−	493.925i	0.455981	−	0.627605i	0.973669	+	0.227965i	$0.0732071\pi$
$788$	−579.756	−	421.217i	−0.735731	−	0.534540i
$789$	−874.634	+	161.821i	−1.10853	+	0.205097i
$790$		0			0
$791$	296.644	−	408.295i	0.375024	−	0.516176i
$792$	−404.068	−	262.763i	−0.510186	−	0.331772i
$793$			42.5349i			0.0536380i
$794$	−1421.43	+	461.851i	−1.79021	+	0.581676i
$795$		0			0
$796$	136.093	−	418.851i	0.170971	−	0.526195i
$797$	181.689	−	559.182i	0.227966	−	0.701608i	−0.770011	−	0.638031i	$-0.779749\pi$
$797$	181.689	−	559.182i	0.227966	−	0.701608i	0.997977	−	0.0635770i	$-0.0202509\pi$
$798$	115.881	+	626.327i	0.145214	+	0.784871i
$799$	−652.337			−0.816441
$800$		0			0
$801$	424.461	−	343.283i	0.529913	−	0.428568i
$802$	42.4143	+	58.3783i	0.0528857	+	0.0727909i
$803$	−168.665	+	519.096i	−0.210043	+	0.646446i
$804$	−515.435	−	489.435i	−0.641088	−	0.608750i
$805$		0			0
$806$	24.2059	−	7.86498i	0.0300322	−	0.00975804i
$807$	−295.272	+	618.554i	−0.365889	+	0.766486i
$808$	682.513	−	221.762i	0.844694	−	0.274458i
$809$	324.701	−	446.913i	0.401361	−	0.552426i	−0.559724	−	0.828679i	$-0.689093\pi$
$809$	324.701	−	446.913i	0.401361	−	0.552426i	0.961085	+	0.276253i	$0.0890927\pi$
$810$		0			0
$811$	−52.3347	+	38.0234i	−0.0645311	+	0.0468846i	−0.619583	−	0.784931i	$-0.712698\pi$
$811$	−52.3347	+	38.0234i	−0.0645311	+	0.0468846i	0.555052	+	0.831816i	$0.312698\pi$
$812$	468.539	+	340.413i	0.577018	+	0.419228i
$813$	357.795	+	659.468i	0.440093	+	0.811154i
$814$	−1147.85	+	833.963i	−1.41014	+	1.02453i
$815$		0			0
$816$	−728.541	−	1342.81i	−0.892820	−	1.64559i
$817$	464.772	−	151.014i	0.568877	−	0.184839i
$818$	655.850			0.801773
$819$	15.1179	−	23.2478i	0.0184590	−	0.0283855i
$820$		0			0
$821$	−253.051	−	82.2212i	−0.308223	−	0.100148i	0.150822	−	0.988561i	$-0.451808\pi$
$821$	−253.051	−	82.2212i	−0.308223	−	0.100148i	−0.459044	+	0.888413i	$0.651808\pi$
$822$	532.435	−	560.719i	0.647732	−	0.682140i
$823$	−215.463	−	296.559i	−0.261802	−	0.360339i	0.657799	−	0.753194i	$-0.271488\pi$
$823$	−215.463	−	296.559i	−0.261802	−	0.360339i	−0.919601	+	0.392854i	$0.871488\pi$
$824$			137.954i			0.167420i
$825$		0			0
$826$	−483.579			−0.585446
$827$	125.593	−	91.2487i	0.151866	−	0.110337i	−0.509258	−	0.860614i	$-0.670080\pi$
$827$	125.593	−	91.2487i	0.151866	−	0.110337i	0.661123	+	0.750277i	$0.270080\pi$
$828$	−486.815	+	186.522i	−0.587941	+	0.225268i
$829$	−255.989	+	787.854i	−0.308793	+	0.950367i	0.669441	+	0.742865i	$0.266533\pi$
$829$	−255.989	+	787.854i	−0.308793	+	0.950367i	−0.978235	+	0.207502i	$0.933467\pi$
$830$		0			0
$831$	985.833	+	130.100i	1.18632	+	0.156559i
$832$			3.72087i			0.00447220i
$833$	3.09668	+	9.53060i	0.00371750	+	0.0114413i
$834$	60.0227	+	110.630i	0.0719696	+	0.132650i
$835$		0			0
$836$	−234.382	−	322.599i	−0.280361	−	0.385884i
$837$	−234.880	+	565.552i	−0.280621	+	0.675689i
$838$	354.433	−	487.835i	0.422951	−	0.582142i
$839$	−555.403	−	764.447i	−0.661982	−	0.911140i	0.337563	−	0.941303i	$-0.390397\pi$
$839$	−555.403	−	764.447i	−0.661982	−	0.911140i	−0.999545	+	0.0301628i	$0.990397\pi$
$840$		0			0
$841$	251.524	+	182.743i	0.299077	+	0.217292i
$842$	336.292	+	1035.00i	0.399396	+	1.22922i
$843$	−625.226	+	1309.76i	−0.741668	+	1.55369i
$844$	245.273	+	754.872i	0.290608	+	0.894398i
$845$		0			0
$846$	−541.259	+	207.382i	−0.639786	+	0.245133i
$847$	421.408	+	136.924i	0.497530	+	0.161657i
$848$	−1144.58	+	831.588i	−1.34974	+	0.980646i
$849$	643.701	−	1348.46i	0.758187	−	1.58830i
$850$		0			0
$851$		−	973.473i		−	1.14392i
$852$	21.3736	+	115.523i	0.0250864	+	0.135590i
$853$	387.900	+	126.036i	0.454748	+	0.147757i	0.527430	−	0.849599i	$-0.323156\pi$
$853$	387.900	+	126.036i	0.454748	+	0.147757i	−0.0726819	+	0.997355i	$0.523156\pi$
$854$	1620.51	+	526.536i	1.89755	+	0.616552i
$855$		0			0
$856$	173.603	+	534.296i	0.202808	+	0.624178i
$857$	−1424.88			−1.66264			−0.831320	−	0.555795i	$-0.812414\pi$
$857$	−1424.88			−1.66264			−0.831320	+	0.555795i	$0.812414\pi$
$858$	−5.98358	+	45.3404i	−0.00697387	+	0.0528443i
$859$	796.733	+	578.860i	0.927512	+	0.673877i	0.945382	−	0.325964i	$-0.105689\pi$
$859$	796.733	+	578.860i	0.927512	+	0.673877i	−0.0178705	+	0.999840i	$0.505689\pi$
$860$		0			0
$861$	−391.109	+	72.3614i	−0.454249	+	0.0840435i
$862$	−990.653	+	1363.52i	−1.14925	+	1.58181i
$863$	−135.978	−	98.7941i	−0.157565	−	0.114478i	0.506209	−	0.862411i	$-0.331046\pi$
$863$	−135.978	−	98.7941i	−0.157565	−	0.114478i	−0.663774	+	0.747933i	$0.731046\pi$
$864$	−707.886	−	605.740i	−0.819313	−	0.701087i
$865$		0			0
$866$	−878.291	+	1208.86i	−1.01419	+	1.39592i
$867$	146.202	−	1107.84i	0.168630	−	1.27779i
$868$		−	387.028i		−	0.445885i
$869$	−148.674	+	48.3070i	−0.171086	+	0.0555892i
$870$		0			0
$871$	13.2204	−	40.6882i	0.0151784	−	0.0467143i
$872$	175.224	−	539.284i	0.200945	−	0.618445i
$873$	309.125	−	1150.80i	0.354095	−	1.31821i
$874$	720.733			0.824637
$875$		0			0
$876$	−127.083	+	266.221i	−0.145072	+	0.303905i
$877$	124.112	+	170.825i	0.141519	+	0.194784i	0.873893	−	0.486119i	$-0.161588\pi$
$877$	124.112	+	170.825i	0.141519	+	0.194784i	−0.732374	+	0.680902i	$0.761588\pi$
$878$	240.971	−	741.632i	0.274454	−	0.844684i
$879$	703.725	−	741.108i	0.800598	−	0.843127i
$880$		0			0
$881$	−1227.02	+	398.682i	−1.39276	+	0.452534i	−0.906841	−	0.421473i	$-0.861513\pi$
$881$	−1227.02	+	398.682i	−1.39276	+	0.452534i	−0.485914	+	0.874007i	$0.661513\pi$
$882$	5.59923	+	6.92331i	0.00634833	+	0.00784955i
$883$	−364.163	+	118.324i	−0.412416	+	0.134002i	−0.507874	−	0.861431i	$-0.669568\pi$
$883$	−364.163	+	118.324i	−0.412416	+	0.134002i	0.0954580	+	0.995433i	$0.469568\pi$
$884$	−16.3513	+	22.5057i	−0.0184970	+	0.0254589i
$885$		0			0
$886$	1165.37	−	846.689i	1.31531	−	0.955631i
$887$	−100.370	−	72.9232i	−0.113157	−	0.0822133i	0.529768	−	0.848143i	$-0.322279\pi$
$887$	−100.370	−	72.9232i	−0.113157	−	0.0822133i	−0.642925	+	0.765930i	$0.722279\pi$
$888$	427.567	−	231.977i	0.481494	−	0.261235i
$889$	999.338	−	726.062i	1.12412	−	0.816717i
$890$		0			0
$891$	−735.280	−	818.665i	−0.825230	−	0.918816i
$892$	623.632	−	202.630i	0.699139	−	0.227164i
$893$	304.188			0.340636
$894$	1234.55	+	162.924i	1.38093	+	0.182242i
$895$		0			0
$896$	−773.476	−	251.318i	−0.863254	−	0.280488i
$897$	−22.7543	−	21.6065i	−0.0253671	−	0.0240876i
$898$	−32.0300	−	44.0855i	−0.0356682	−	0.0490930i
$899$		−	769.785i		−	0.856268i
$900$		0			0
$901$	−1837.76			−2.03969
$902$	530.680	−	385.561i	0.588337	−	0.427452i
$903$	−586.874	+	618.049i	−0.649916	+	0.684440i
$904$	88.1802	−	271.391i	0.0975444	−	0.300211i
$905$		0			0
$906$	−94.2468	+	714.152i	−0.104025	+	0.788248i
$907$		−	479.783i		−	0.528978i	−0.964389	−	0.264489i	$-0.914797\pi$
$907$		−	479.783i		−	0.528978i	0.964389	−	0.264489i	$-0.0852033\pi$
$908$	18.4877	+	56.8994i	0.0203609	+	0.0626646i
$909$	1636.17	−	84.7237i	1.79997	−	0.0932054i
$910$		0			0
$911$	576.910	+	794.048i	0.633271	+	0.871623i	0.998234	−	0.0593992i	$-0.0189185\pi$
$911$	576.910	+	794.048i	0.633271	+	0.871623i	−0.364963	+	0.931022i	$0.618918\pi$
$912$	339.723	+	626.158i	0.372503	+	0.686576i
$913$	248.463	−	341.980i	0.272139	−	0.374567i
$914$	660.295	+	908.818i	0.722424	+	0.994331i
$915$		0			0
$916$	347.727	+	252.638i	0.379614	+	0.275806i
$917$	−250.733	−	771.678i	−0.273428	−	0.841525i
$918$	−410.020	−	1714.93i	−0.446645	−	1.86812i
$919$	−277.843	−	855.113i	−0.302332	−	0.930482i	−0.980659	−	0.195722i	$-0.937295\pi$
$919$	−277.843	−	855.113i	−0.302332	−	0.930482i	0.678327	−	0.734760i	$-0.262705\pi$
$920$		0			0
$921$	449.906	+	427.212i	0.488497	+	0.463857i
$922$	1110.91	+	360.958i	1.20490	+	0.391494i
$923$	−5.72080	+	4.15640i	−0.00619805	+	0.00450315i
$924$	627.603	+	299.592i	0.679224	+	0.324234i
$925$		0			0
$926$		−	479.309i		−	0.517613i
$927$	−81.7049	+	304.167i	−0.0881391	+	0.328120i
$928$	1113.82	+	361.903i	1.20024	+	0.389981i
$929$	−1487.83	−	483.425i	−1.60154	−	0.520371i	−0.634051	−	0.773291i	$-0.718609\pi$
$929$	−1487.83	−	483.425i	−1.60154	−	0.520371i	−0.967487	+	0.252920i	$0.918609\pi$
$930$		0			0
$931$	−1.44400	−	4.44417i	−0.00155102	−	0.00477355i
$932$	226.734			0.243277
$933$	580.962	+	76.6697i	0.622682	+	0.0821754i
$934$	−258.401	−	187.739i	−0.276660	−	0.201005i
$935$		0			0
$936$	4.06766	−	15.1429i	0.00434580	−	0.0161783i
$937$	374.955	−	516.081i	0.400165	−	0.550780i	−0.560620	−	0.828073i	$-0.689437\pi$
$937$	374.955	−	516.081i	0.400165	−	0.550780i	0.960785	+	0.277293i	$0.0894372\pi$
$938$	−1386.50	−	1007.35i	−1.47814	−	1.07393i
$939$	257.928	+	1394.08i	0.274684	+	1.48465i
$940$		0			0
$941$	−419.935	+	577.992i	−0.446265	+	0.614231i	−0.971590	−	0.236671i	$-0.923944\pi$
$941$	−419.935	+	577.992i	−0.446265	+	0.614231i	0.525325	+	0.850902i	$0.323944\pi$
$942$	794.113	+	104.799i	0.843008	+	0.111252i
$943$			450.060i			0.477264i
$944$	−514.369	+	167.129i	−0.544883	+	0.177043i
$945$		0			0
$946$	434.351	−	1336.79i	0.459145	−	1.41310i
$947$	85.6580	−	263.628i	0.0904520	−	0.278383i	−0.895590	−	0.444881i	$-0.853246\pi$
$947$	85.6580	−	263.628i	0.0904520	−	0.278383i	0.986042	+	0.166498i	$0.0532460\pi$
$948$	−83.0800	+	15.3711i	−0.0876371	+	0.0162143i
$949$	−17.7558			−0.0187100
$950$		0			0
$951$	−133.082	−	63.5278i	−0.139939	−	0.0668010i
$952$	−415.508	−	571.897i	−0.436458	−	0.600733i
$953$	230.629	−	709.802i	0.242003	−	0.744808i	−0.754112	−	0.656745i	$-0.771933\pi$
$953$	230.629	−	709.802i	0.242003	−	0.744808i	0.996115	−	0.0880621i	$-0.0280674\pi$
$954$	−1524.83	+	584.235i	−1.59836	+	0.612406i
$955$		0			0
$956$	174.683	−	56.7579i	0.182723	−	0.0593702i
$957$	1248.28	+	595.878i	1.30437	+	0.622652i
$958$	1317.82	−	428.187i	1.37560	−	0.446959i
$959$	415.987	−	572.556i	0.433771	−	0.597035i
$960$		0			0
$961$	361.285	−	262.489i	0.375947	−	0.273141i
$962$	−37.3409	−	27.1298i	−0.0388159	−	0.0282014i
$963$	66.3249	+	1280.86i	0.0688732	+	1.33007i
$964$	−62.4667	+	45.3847i	−0.0647995	+	0.0470796i
$965$		0			0
$966$	−1104.85	+	599.436i	−1.14373	+	0.620534i
$967$	1240.43	−	403.039i	1.28276	−	0.416793i	0.413207	−	0.910637i	$-0.364409\pi$
$967$	1240.43	−	403.039i	1.28276	−	0.416793i	0.869551	+	0.493844i	$0.164409\pi$
$968$	250.535			0.258817
$969$	−121.070	+	917.406i	−0.124943	+	0.946755i
$970$		0			0
$971$	721.884	+	234.554i	0.743444	+	0.241560i	0.656158	−	0.754624i	$-0.272181\pi$
$971$	721.884	+	234.554i	0.743444	+	0.241560i	0.0872862	+	0.996183i	$0.472181\pi$
$972$	−336.095	−	490.661i	−0.345777	−	0.504795i
$973$	67.7126	+	93.1984i	0.0695916	+	0.0957846i
$974$			791.805i			0.812942i
$975$		0			0
$976$	1905.67			1.95253
$977$	−961.944	+	698.893i	−0.984589	+	0.715346i	−0.958730	−	0.284319i	$-0.908232\pi$
$977$	−961.944	+	698.893i	−0.984589	+	0.715346i	−0.0258599	+	0.999666i	$0.508232\pi$
$978$	−345.352	−	327.932i	−0.353121	−	0.335309i
$979$	−254.633	+	783.680i	−0.260095	+	0.800491i
$980$		0			0
$981$	705.737	−	1085.26i	0.719406	−	1.10627i
$982$		−	895.724i		−	0.912143i
$983$	−441.654	−	1359.27i	−0.449292	−	1.38278i	−0.877708	−	0.479196i	$-0.840928\pi$
$983$	−441.654	−	1359.27i	−0.449292	−	1.38278i	0.428416	−	0.903581i	$-0.359072\pi$
$984$	−197.674	+	107.249i	−0.200889	+	0.108992i
$985$		0			0
$986$	1302.81	+	1793.16i	1.32131	+	1.81862i
$987$	−466.305	+	252.995i	−0.472447	+	0.256327i
$988$	7.62472	−	10.4945i	0.00771732	−	0.0106220i
$989$	566.856	+	780.210i	0.573160	+	0.788888i
$990$		0			0
$991$	−751.395	−	545.920i	−0.758219	−	0.550878i	0.140145	−	0.990131i	$-0.455243\pi$
$991$	−751.395	−	545.920i	−0.758219	−	0.550878i	−0.898363	+	0.439253i	$0.855243\pi$
$992$	−241.850	−	744.338i	−0.243800	−	0.750341i
$993$	−53.2609	−	25.4246i	−0.0536363	−	0.0256038i
$994$	87.5349	+	269.405i	0.0880633	+	0.271031i
$995$		0			0
$996$	157.317	−	165.674i	0.157949	−	0.166339i
$997$	695.228	+	225.893i	0.697320	+	0.226573i	0.636162	−	0.771555i	$-0.280521\pi$
$997$	695.228	+	225.893i	0.697320	+	0.226573i	0.0611574	+	0.998128i	$0.480521\pi$
$998$	−165.175	+	120.006i	−0.165506	+	0.120247i
$999$	1080.11	−	258.241i	1.08119	−	0.258500i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.3.h.a.74.4		72
3.2	odd	2	inner	375.3.h.a.74.15		72
5.2	odd	4		375.3.j.b.176.7		144
5.3	odd	4		375.3.j.b.176.30		144
5.4	even	2		75.3.h.a.14.15	yes	72
15.2	even	4		375.3.j.b.176.29		144
15.8	even	4		375.3.j.b.176.8		144
15.14	odd	2		75.3.h.a.14.4	✓	72
25.9	even	10	inner	375.3.h.a.299.15		72
25.12	odd	20		375.3.j.b.326.29		144
25.13	odd	20		375.3.j.b.326.8		144
25.16	even	5		75.3.h.a.59.4	yes	72
75.38	even	20		375.3.j.b.326.30		144
75.41	odd	10		75.3.h.a.59.15	yes	72
75.59	odd	10	inner	375.3.h.a.299.4		72
75.62	even	20		375.3.j.b.326.7		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.3.h.a.14.4	✓	72	15.14	odd	2
75.3.h.a.14.15	yes	72	5.4	even	2
75.3.h.a.59.4	yes	72	25.16	even	5
75.3.h.a.59.15	yes	72	75.41	odd	10
375.3.h.a.74.4		72	1.1	even	1	trivial
375.3.h.a.74.15		72	3.2	odd	2	inner
375.3.h.a.299.4		72	75.59	odd	10	inner
375.3.h.a.299.15		72	25.9	even	10	inner
375.3.j.b.176.7		144	5.2	odd	4
375.3.j.b.176.8		144	15.8	even	4
375.3.j.b.176.29		144	15.2	even	4
375.3.j.b.176.30		144	5.3	odd	4
375.3.j.b.326.7		144	75.62	even	20
375.3.j.b.326.8		144	25.13	odd	20
375.3.j.b.326.29		144	25.12	odd	20
375.3.j.b.326.30		144	75.38	even	20

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:	\( N \)	\(=\)	\( 375 = 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	375.h (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.05424 + 1.49250i) q^{2} +(-2.06574 + 2.17548i) q^{3} +(0.756307 - 2.32767i) q^{4} +(0.996648 - 7.55208i) q^{6} -6.97211i q^{7} +(-1.21820 - 3.74924i) q^{8} +(-0.465411 - 8.98796i) q^{9} +O(q^{10})\)	\(q+(-2.05424 + 1.49250i) q^{2} +(-2.06574 + 2.17548i) q^{3} +(0.756307 - 2.32767i) q^{4} +(0.996648 - 7.55208i) q^{6} -6.97211i q^{7} +(-1.21820 - 3.74924i) q^{8} +(-0.465411 - 8.98796i) q^{9} +(7.98507 + 10.9905i) q^{11} +(3.50147 + 6.45371i) q^{12} +(-0.259763 + 0.357533i) q^{13} +(10.4058 + 14.3224i) q^{14} +(16.0184 + 11.6380i) q^{16} +(7.94771 + 24.4605i) q^{17} +(14.3706 + 17.7688i) q^{18} +(-3.70606 - 11.4061i) q^{19} +(15.1677 + 14.4026i) q^{21} +(-32.8065 - 10.6595i) q^{22} +(19.1473 - 13.9113i) q^{23} +(10.6729 + 5.09479i) q^{24} -1.12216i q^{26} +(20.5145 + 17.5543i) q^{27} +(-16.2288 - 5.27306i) q^{28} +(-32.2785 - 10.4879i) q^{29} +(7.00881 + 21.5709i) q^{31} -34.5066 q^{32} +(-40.4047 - 5.33221i) q^{33} +(-52.8338 - 38.3860i) q^{34} +(-21.2730 - 5.71433i) q^{36} +(24.1765 - 33.2760i) q^{37} +(24.6367 + 17.8996i) q^{38} +(-0.241202 - 1.30368i) q^{39} +(-11.1774 + 15.3843i) q^{41} +(-52.6539 - 6.94875i) q^{42} +40.7478i q^{43} +(31.6215 - 10.2744i) q^{44} +(-18.5706 + 57.1545i) q^{46} +(-7.83781 + 24.1223i) q^{47} +(-58.4081 + 10.8064i) q^{48} +0.389632 q^{49} +(-69.6313 - 33.2391i) q^{51} +(0.635761 + 0.875050i) q^{52} +(-22.0806 + 67.9572i) q^{53} +(-68.3416 - 5.44301i) q^{54} +(-26.1401 + 8.49344i) q^{56} +(32.4694 + 15.4996i) q^{57} +(81.9612 - 26.6308i) q^{58} +(-16.0556 + 22.0987i) q^{59} +(77.8653 - 56.5725i) q^{61} +(-46.5923 - 33.8513i) q^{62} +(-62.6651 + 3.24490i) q^{63} +(6.81151 - 4.94885i) q^{64} +(90.9594 - 49.3502i) q^{66} +(-92.0681 + 29.9148i) q^{67} +62.9471 q^{68} +(-9.28961 + 70.3918i) q^{69} +(15.2176 + 4.94450i) q^{71} +(-33.1310 + 12.6941i) q^{72} +(23.6157 + 32.5042i) q^{73} +104.440i q^{74} -29.3526 q^{76} +(76.6270 - 55.6728i) q^{77} +(2.44123 + 2.31809i) q^{78} +(-3.55591 + 10.9440i) q^{79} +(-80.5668 + 8.36620i) q^{81} -48.2853i q^{82} +(-9.61536 - 29.5930i) q^{83} +(44.9960 - 24.4126i) q^{84} +(-60.8159 - 83.7059i) q^{86} +(89.4954 - 48.5559i) q^{87} +(31.4786 - 43.3265i) q^{88} +(35.6526 + 49.0716i) q^{89} +(2.49276 + 1.81110i) q^{91} +(-17.8998 - 55.0899i) q^{92} +(-61.4054 - 29.3124i) q^{93} +(-19.9017 - 61.2510i) q^{94} +(71.2817 - 75.0683i) q^{96} +(125.919 + 40.9136i) q^{97} +(-0.800399 + 0.581524i) q^{98} +(95.0658 - 76.8845i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 5 q^{3} - 38 q^{4} + 5 q^{6} - 13 q^{9}+O(q^{10}) \) 72 * q + 5 * q^3 - 38 * q^4 + 5 * q^6 - 13 * q^9	\( 72 q + 5 q^{3} - 38 q^{4} + 5 q^{6} - 13 q^{9} + 45 q^{12} + 10 q^{13} + 22 q^{16} - 36 q^{19} + 54 q^{21} + 50 q^{22} - 20 q^{24} - 100 q^{27} - 270 q^{28} - 126 q^{31} - 20 q^{33} + 210 q^{34} - 213 q^{36} - 110 q^{37} - 191 q^{39} + 175 q^{42} - 210 q^{46} - 150 q^{48} - 224 q^{49} - 60 q^{51} + 320 q^{52} + 320 q^{54} + 70 q^{58} + 294 q^{61} - 795 q^{63} + 362 q^{64} - 470 q^{66} + 260 q^{67} + 335 q^{69} - 215 q^{72} + 150 q^{73} - 16 q^{76} + 1295 q^{78} - 346 q^{79} + 507 q^{81} - 456 q^{84} + 430 q^{87} + 1710 q^{88} + 538 q^{91} - 560 q^{94} + 740 q^{96} + 150 q^{97} + 60 q^{99}+O(q^{100}) \) 72 * q + 5 * q^3 - 38 * q^4 + 5 * q^6 - 13 * q^9 + 45 * q^12 + 10 * q^13 + 22 * q^16 - 36 * q^19 + 54 * q^21 + 50 * q^22 - 20 * q^24 - 100 * q^27 - 270 * q^28 - 126 * q^31 - 20 * q^33 + 210 * q^34 - 213 * q^36 - 110 * q^37 - 191 * q^39 + 175 * q^42 - 210 * q^46 - 150 * q^48 - 224 * q^49 - 60 * q^51 + 320 * q^52 + 320 * q^54 + 70 * q^58 + 294 * q^61 - 795 * q^63 + 362 * q^64 - 470 * q^66 + 260 * q^67 + 335 * q^69 - 215 * q^72 + 150 * q^73 - 16 * q^76 + 1295 * q^78 - 346 * q^79 + 507 * q^81 - 456 * q^84 + 430 * q^87 + 1710 * q^88 + 538 * q^91 - 560 * q^94 + 740 * q^96 + 150 * q^97 + 60 * q^99

Introduction

L-functions

Modular forms

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