LMFDB - Embedded newform 375.3.j.b.176.27

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [375,3,Mod(26,375)]

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, 4]))

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

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

chi := DirichletCharacter("375.26");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 375 = 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	375.j (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:	$144$
Relative dimension:	$36$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			176.27
Character	$\chi$	$=$	375.176
Dual form			375.3.j.b.326.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.37175 + 1.88806i) q^{2} +(-1.35589 + 2.67611i) q^{3} +(-0.446980 + 1.37566i) q^{4} +(-6.91259 + 1.11096i) q^{6} +12.5544 q^{7} +(5.66769 - 1.84155i) q^{8} +(-5.32311 - 7.25703i) q^{9} +O(q^{10})$	\(q+(1.37175 + 1.88806i) q^{2} +(-1.35589 + 2.67611i) q^{3} +(-0.446980 + 1.37566i) q^{4} +(-6.91259 + 1.11096i) q^{6} +12.5544 q^{7} +(5.66769 - 1.84155i) q^{8} +(-5.32311 - 7.25703i) q^{9} +(7.59880 + 10.4589i) q^{11} +(-3.07537 - 3.06142i) q^{12} +(4.02255 + 2.92256i) q^{13} +(17.2215 + 23.7033i) q^{14} +(15.9325 + 11.5756i) q^{16} +(-10.2460 + 3.32914i) q^{17} +(6.39968 - 20.0052i) q^{18} +(1.29722 + 3.99244i) q^{19} +(-17.0224 + 33.5969i) q^{21} +(-9.32322 + 28.6939i) q^{22} +(-12.8053 - 17.6249i) q^{23} +(-2.75661 + 17.6643i) q^{24} +11.6038i q^{26} +(26.6382 - 4.40547i) q^{27} +(-5.61156 + 17.2706i) q^{28} +(-26.0760 - 8.47261i) q^{29} +(-8.64023 - 26.5919i) q^{31} +22.1228i q^{32} +(-38.2922 + 6.15414i) q^{33} +(-20.3406 - 14.7783i) q^{34} +(12.3626 - 4.07906i) q^{36} +(-0.0279372 - 0.0202976i) q^{37} +(-5.75848 + 7.92586i) q^{38} +(-13.2752 + 6.80212i) q^{39} +(-44.4000 + 61.1113i) q^{41} +(-86.7832 + 13.9474i) q^{42} +43.3942 q^{43} +(-17.7844 + 5.77849i) q^{44} +(15.7112 - 48.3541i) q^{46} +(-4.67812 - 1.52001i) q^{47} +(-52.5803 + 26.9417i) q^{48} +108.612 q^{49} +(4.98338 - 31.9334i) q^{51} +(-5.81846 + 4.22736i) q^{52} +(-1.62699 - 0.528642i) q^{53} +(44.8587 + 44.2511i) q^{54} +(71.1543 - 23.1194i) q^{56} +(-12.4431 - 1.94181i) q^{57} +(-19.7731 - 60.8553i) q^{58} +(-28.0481 + 38.6049i) q^{59} +(-5.28161 + 3.83732i) q^{61} +(38.3547 - 52.7907i) q^{62} +(-66.8283 - 91.1074i) q^{63} +(21.9608 - 15.9555i) q^{64} +(-64.1467 - 63.8558i) q^{66} +(-1.27935 - 3.93744i) q^{67} -15.5831i q^{68} +(64.5288 - 10.3708i) q^{69} +(-51.8456 - 16.8457i) q^{71} +(-43.5339 - 31.3279i) q^{72} +(28.9970 - 21.0676i) q^{73} -0.0805904i q^{74} -6.07208 q^{76} +(95.3981 + 131.304i) q^{77} +(-31.0531 - 15.7335i) q^{78} +(-5.27573 + 16.2370i) q^{79} +(-24.3290 + 77.2600i) q^{81} -176.287 q^{82} +(54.4519 - 17.6925i) q^{83} +(-38.6093 - 38.4342i) q^{84} +(59.5261 + 81.9306i) q^{86} +(58.0299 - 58.2943i) q^{87} +(62.3281 + 45.2840i) q^{88} +(-44.4639 - 61.1993i) q^{89} +(50.5006 + 36.6908i) q^{91} +(29.9697 - 9.73774i) q^{92} +(82.8780 + 12.9335i) q^{93} +(-3.54736 - 10.9176i) q^{94} +(-59.2029 - 29.9961i) q^{96} +(9.23778 - 28.4310i) q^{97} +(148.989 + 205.066i) q^{98} +(35.4509 - 110.818i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 76 q^{4} + 10 q^{6} + 26 q^{9}+O(q^{10}) $ 144 * q + 76 * q^4 + 10 * q^6 + 26 * q^9	$ 144 q + 76 q^{4} + 10 q^{6} + 26 q^{9} + 44 q^{16} + 72 q^{19} + 108 q^{21} + 40 q^{24} - 252 q^{31} - 420 q^{34} - 426 q^{36} + 382 q^{39} - 420 q^{46} + 448 q^{49} - 120 q^{51} - 640 q^{54} + 588 q^{61} - 724 q^{64} - 940 q^{66} - 670 q^{69} - 32 q^{76} + 692 q^{79} + 1014 q^{81} + 912 q^{84} + 1076 q^{91} + 1120 q^{94} + 1480 q^{96} - 120 q^{99}+O(q^{100}) $ 144 * q + 76 * q^4 + 10 * q^6 + 26 * q^9 + 44 * q^16 + 72 * q^19 + 108 * q^21 + 40 * q^24 - 252 * q^31 - 420 * q^34 - 426 * q^36 + 382 * q^39 - 420 * q^46 + 448 * q^49 - 120 * q^51 - 640 * q^54 + 588 * q^61 - 724 * q^64 - 940 * q^66 - 670 * q^69 - 32 * q^76 + 692 * q^79 + 1014 * q^81 + 912 * q^84 + 1076 * q^91 + 1120 * q^94 + 1480 * q^96 - 120 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$-1$

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 $

$2$	1.37175	+	1.88806i	0.685876	+	0.944028i	0.999986	−	0.00535908i	$-0.00170586\pi$
$2$	1.37175	+	1.88806i	0.685876	+	0.944028i	−0.314109	+	0.949387i	$0.601706\pi$
$3$	−1.35589	+	2.67611i	−0.451964	+	0.892036i
$3$	−1.35589	+	2.67611i	−0.451964	+	0.892036i
$4$	−0.446980	+	1.37566i	−0.111745	+	0.343916i
$5$		0			0
$5$		0			0
$6$	−6.91259	+	1.11096i	−1.15210	+	0.185160i
$7$	12.5544			1.79348			0.896741	−	0.442556i	$-0.145928\pi$
$7$	12.5544			1.79348			0.896741	+	0.442556i	$0.145928\pi$
$8$	5.66769	−	1.84155i	0.708462	−	0.230193i
$9$	−5.32311	−	7.25703i	−0.591457	−	0.806337i
$10$		0			0
$11$	7.59880	+	10.4589i	0.690800	+	0.950805i	1.00000		0.000192365i	$-6.12317e-5\pi$
$11$	7.59880	+	10.4589i	0.690800	+	0.950805i	−0.309200	+	0.950997i	$0.600061\pi$
$12$	−3.07537	−	3.06142i	−0.256281	−	0.255118i
$13$	4.02255	+	2.92256i	0.309427	+	0.224812i	0.731651	−	0.681680i	$-0.238750\pi$
$13$	4.02255	+	2.92256i	0.309427	+	0.224812i	−0.422223	+	0.906492i	$0.638750\pi$
$14$	17.2215	+	23.7033i	1.23011	+	1.69310i
$15$		0			0
$16$	15.9325	+	11.5756i	0.995778	+	0.723475i
$17$	−10.2460	+	3.32914i	−0.602707	+	0.195831i	−0.594448	−	0.804134i	$-0.702629\pi$
$17$	−10.2460	+	3.32914i	−0.602707	+	0.195831i	−0.00825983	+	0.999966i	$0.502629\pi$
$18$	6.39968	−	20.0052i	0.355538	−	1.11140i
$19$	1.29722	+	3.99244i	0.0682748	+	0.210128i	0.979373	−	0.202061i	$-0.0647641\pi$
$19$	1.29722	+	3.99244i	0.0682748	+	0.210128i	−0.911098	+	0.412190i	$0.864764\pi$
$20$		0			0
$21$	−17.0224	+	33.5969i	−0.810589	+	1.59985i
$22$	−9.32322	+	28.6939i	−0.423783	+	1.30427i
$23$	−12.8053	−	17.6249i	−0.556751	−	0.766301i	0.434158	−	0.900837i	$-0.357046\pi$
$23$	−12.8053	−	17.6249i	−0.556751	−	0.766301i	−0.990909	+	0.134535i	$0.957046\pi$
$24$	−2.75661	+	17.6643i	−0.114859	+	0.736012i
$25$		0			0
$26$			11.6038i			0.446301i
$27$	26.6382	−	4.40547i	0.986599	−	0.163166i
$28$	−5.61156	+	17.2706i	−0.200413	+	0.616807i
$29$	−26.0760	−	8.47261i	−0.899172	−	0.292159i	−0.177277	−	0.984161i	$-0.556729\pi$
$29$	−26.0760	−	8.47261i	−0.899172	−	0.292159i	−0.721895	+	0.692002i	$0.756729\pi$
$30$		0			0
$31$	−8.64023	−	26.5919i	−0.278717	−	0.857803i	−0.988212	−	0.153092i	$-0.951077\pi$
$31$	−8.64023	−	26.5919i	−0.278717	−	0.857803i	0.709495	−	0.704711i	$-0.248923\pi$
$32$			22.1228i			0.691336i
$33$	−38.2922	+	6.15414i	−1.16037	+	0.186489i
$34$	−20.3406	−	14.7783i	−0.598253	−	0.434656i
$35$		0			0
$36$	12.3626	−	4.07906i	0.343404	−	0.113307i
$37$	−0.0279372	−	0.0202976i	−0.000755061	−	0.000548584i	0.587408	−	0.809291i	$-0.300149\pi$
$37$	−0.0279372	−	0.0202976i	−0.000755061	−	0.000548584i	−0.588163	+	0.808743i	$0.700149\pi$
$38$	−5.75848	+	7.92586i	−0.151539	+	0.208575i
$39$	−13.2752	+	6.80212i	−0.340390	+	0.174413i
$40$		0			0
$41$	−44.4000	+	61.1113i	−1.08293	+	1.49052i	−0.226668	+	0.973972i	$0.572783\pi$
$41$	−44.4000	+	61.1113i	−1.08293	+	1.49052i	−0.856258	+	0.516548i	$0.827217\pi$
$42$	−86.7832	+	13.9474i	−2.06627	+	0.332081i
$43$	43.3942			1.00917			0.504583	−	0.863363i	$-0.331646\pi$
$43$	43.3942			1.00917			0.504583	+	0.863363i	$0.331646\pi$
$44$	−17.7844	+	5.77849i	−0.404190	+	0.131329i
$45$		0			0
$46$	15.7112	−	48.3541i	0.341548	−	1.05118i
$47$	−4.67812	−	1.52001i	−0.0995346	−	0.0323407i	0.258826	−	0.965924i	$-0.416664\pi$
$47$	−4.67812	−	1.52001i	−0.0995346	−	0.0323407i	−0.358361	+	0.933583i	$0.616664\pi$
$48$	−52.5803	+	26.9417i	−1.09542	+	0.561285i
$49$	108.612			2.21658
$50$		0			0
$51$	4.98338	−	31.9334i	0.0977134	−	0.626146i
$52$	−5.81846	+	4.22736i	−0.111893	+	0.0812953i
$53$	−1.62699	−	0.528642i	−0.0306980	−	0.00997438i	0.293628	−	0.955920i	$-0.405137\pi$
$53$	−1.62699	−	0.528642i	−0.0306980	−	0.00997438i	−0.324326	+	0.945945i	$0.605137\pi$
$54$	44.8587	+	44.2511i	0.830717	+	0.819465i
$55$		0			0
$56$	71.1543	−	23.1194i	1.27061	−	0.412847i
$57$	−12.4431	−	1.94181i	−0.218300	−	0.0340668i
$58$	−19.7731	−	60.8553i	−0.340915	−	1.04923i
$59$	−28.0481	+	38.6049i	−0.475392	+	0.654321i	−0.977611	−	0.210420i	$-0.932517\pi$
$59$	−28.0481	+	38.6049i	−0.475392	+	0.654321i	0.502219	+	0.864740i	$0.332517\pi$
$60$		0			0
$61$	−5.28161	+	3.83732i	−0.0865838	+	0.0629068i	−0.630235	−	0.776404i	$-0.717041\pi$
$61$	−5.28161	+	3.83732i	−0.0865838	+	0.0629068i	0.543651	+	0.839311i	$0.317041\pi$
$62$	38.3547	−	52.7907i	0.618624	−	0.851463i
$63$	−66.8283	−	91.1074i	−1.06077	−	1.44615i
$64$	21.9608	−	15.9555i	0.343138	−	0.249304i
$65$		0			0
$66$	−64.1467	−	63.8558i	−0.971920	−	0.967512i
$67$	−1.27935	−	3.93744i	−0.0190948	−	0.0587677i	0.941055	−	0.338253i	$-0.109836\pi$
$67$	−1.27935	−	3.93744i	−0.0190948	−	0.0587677i	−0.960150	+	0.279486i	$0.909836\pi$
$68$		−	15.5831i		−	0.229164i
$69$	64.5288	−	10.3708i	0.935200	−	0.150301i
$70$		0			0
$71$	−51.8456	−	16.8457i	−0.730220	−	0.237263i	−0.0797717	−	0.996813i	$-0.525419\pi$
$71$	−51.8456	−	16.8457i	−0.730220	−	0.237263i	−0.650449	+	0.759550i	$0.725419\pi$
$72$	−43.5339	−	31.3279i	−0.604638	−	0.435109i
$73$	28.9970	−	21.0676i	0.397220	−	0.288597i	−0.371188	−	0.928558i	$-0.621049\pi$
$73$	28.9970	−	21.0676i	0.397220	−	0.288597i	0.768408	+	0.639961i	$0.221049\pi$
$74$		−	0.0805904i		−	0.00108906i
$75$		0			0
$76$	−6.07208			−0.0798958
$77$	95.3981	+	131.304i	1.23894	+	1.70525i
$78$	−31.0531	−	15.7335i	−0.398117	−	0.201712i
$79$	−5.27573	+	16.2370i	−0.0667813	+	0.205532i	−0.978879	−	0.204442i	$-0.934462\pi$
$79$	−5.27573	+	16.2370i	−0.0667813	+	0.205532i	0.912097	+	0.409974i	$0.134462\pi$
$80$		0			0
$81$	−24.3290	+	77.2600i	−0.300358	+	0.953827i
$82$	−176.287			−2.14985
$83$	54.4519	−	17.6925i	0.656046	−	0.213162i	0.0379682	−	0.999279i	$-0.487911\pi$
$83$	54.4519	−	17.6925i	0.656046	−	0.213162i	0.618078	+	0.786117i	$0.287911\pi$
$84$	−38.6093	−	38.4342i	−0.459635	−	0.457550i
$85$		0			0
$86$	59.5261	+	81.9306i	0.692164	+	0.952682i
$87$	58.0299	−	58.2943i	0.667010	−	0.670049i
$88$	62.3281	+	45.2840i	0.708274	+	0.514591i
$89$	−44.4639	−	61.1993i	−0.499595	−	0.687633i	0.482527	−	0.875881i	$-0.339719\pi$
$89$	−44.4639	−	61.1993i	−0.499595	−	0.687633i	−0.982121	+	0.188248i	$0.939719\pi$
$90$		0			0
$91$	50.5006	+	36.6908i	0.554952	+	0.403196i
$92$	29.9697	−	9.73774i	0.325757	−	0.105845i
$93$	82.8780	+	12.9335i	0.891161	+	0.139070i
$94$	−3.54736	−	10.9176i	−0.0377378	−	0.116145i
$95$		0			0
$96$	−59.2029	−	29.9961i	−0.616697	−	0.312459i
$97$	9.23778	−	28.4310i	0.0952349	−	0.293103i	−0.892080	−	0.451878i	$-0.850754\pi$
$97$	9.23778	−	28.4310i	0.0952349	−	0.293103i	0.987315	+	0.158775i	$0.0507544\pi$
$98$	148.989	+	205.066i	1.52030	+	2.09251i
$99$	35.4509	−	110.818i	0.358090	−	1.11938i
$100$		0			0
$101$		−	26.0891i		−	0.258308i	−0.991625	−	0.129154i	$-0.958774\pi$
$101$		−	26.0891i		−	0.258308i	0.991625	−	0.129154i	$-0.0412261\pi$
$102$	67.1280	−	34.3959i	0.658118	−	0.337214i
$103$	−14.5421	+	44.7560i	−0.141185	+	0.434524i	−0.996501	−	0.0835838i	$-0.973363\pi$
$103$	−14.5421	+	44.7560i	−0.141185	+	0.434524i	0.855315	+	0.518108i	$0.173363\pi$
$104$	28.1806	+	9.15644i	0.270967	+	0.0880427i
$105$		0			0
$106$	−1.23373	−	3.79702i	−0.0116389	−	0.0358209i
$107$		−	149.068i		−	1.39316i	−0.717478	−	0.696581i	$-0.754704\pi$
$107$		−	149.068i		−	1.39316i	0.717478	−	0.696581i	$-0.245296\pi$
$108$	−5.84629	+	38.6143i	−0.0541323	+	0.357540i
$109$	−120.472	−	87.5279i	−1.10525	−	0.803008i	−0.123338	−	0.992365i	$-0.539360\pi$
$109$	−120.472	−	87.5279i	−1.10525	−	0.803008i	−0.981908	+	0.189357i	$0.939360\pi$
$110$		0			0
$111$	0.0921985	−	0.0472417i	0.000830617	−	0.000425601i
$112$	200.022	+	145.324i	1.78591	+	1.29754i
$113$	−34.3689	+	47.3048i	−0.304150	+	0.418626i	−0.933546	−	0.358458i	$-0.883302\pi$
$113$	−34.3689	+	47.3048i	−0.304150	+	0.418626i	0.629396	+	0.777085i	$0.283302\pi$
$114$	−13.4026	−	26.1569i	−0.117567	−	0.229447i
$115$		0			0
$116$	23.3109	−	32.0847i	0.200956	−	0.276592i
$117$	−0.203422	−	44.7489i	−0.00173865	−	0.382469i
$118$	−111.363			−0.943757
$119$	−128.632	+	41.7952i	−1.08094	+	0.351220i
$120$		0			0
$121$	−14.2548	+	43.8716i	−0.117808	+	0.362575i
$122$	−14.4901	−	4.70813i	−0.118772	−	0.0385912i
$123$	−103.339	−	201.679i	−0.840154	−	1.63967i
$124$	40.4435			0.326157
$125$		0			0
$126$	80.3440	−	251.152i	0.637651	−	1.99327i
$127$	107.773	−	78.3016i	0.848605	−	0.616548i	−0.0761557	−	0.997096i	$-0.524265\pi$
$127$	107.773	−	78.3016i	0.848605	−	0.616548i	0.924761	+	0.380548i	$0.124265\pi$
$128$	144.410	+	46.9215i	1.12820	+	0.366574i
$129$	−58.8378	+	116.128i	−0.456107	+	0.900213i
$130$		0			0
$131$	201.121	−	65.3482i	1.53528	−	0.498841i	0.585208	−	0.810883i	$-0.301013\pi$
$131$	201.121	−	65.3482i	1.53528	−	0.498841i	0.950068	+	0.312042i	$0.101013\pi$
$132$	8.64983	−	55.4279i	0.0655290	−	0.419909i
$133$	16.2858	+	50.1225i	0.122450	+	0.376861i
$134$	5.67915	−	7.81668i	0.0423817	−	0.0583334i
$135$		0			0
$136$	−51.9406	+	37.7370i	−0.381916	+	0.277478i
$137$	112.794	−	155.247i	0.823312	−	1.13319i	−0.165819	−	0.986156i	$-0.553027\pi$
$137$	112.794	−	155.247i	0.823312	−	1.13319i	0.989131	−	0.147036i	$-0.0469733\pi$
$138$	108.098	+	107.608i	0.783320	+	0.779767i
$139$	−82.6077	+	60.0180i	−0.594300	+	0.431784i	−0.843851	−	0.536577i	$-0.819717\pi$
$139$	−82.6077	+	60.0180i	−0.594300	+	0.431784i	0.249551	+	0.968362i	$0.419717\pi$
$140$		0			0
$141$	10.4108	−	10.4582i	0.0738352	−	0.0741716i
$142$	−39.3138	−	120.996i	−0.276858	−	0.852081i
$143$			64.2792i			0.449505i
$144$	−0.805710	−	177.240i	−0.00559521	−	1.23084i
$145$		0			0
$146$	79.5535	+	25.8485i	0.544887	+	0.177045i
$147$	−147.266	+	290.658i	−1.00181	+	1.97727i
$148$	0.0404101	−	0.0293596i	0.000273041	−	0.000198376i
$149$		−	114.565i		−	0.768892i	−0.923148	−	0.384446i	$-0.874393\pi$
$149$		−	114.565i		−	0.768892i	0.923148	−	0.384446i	$-0.125607\pi$
$150$		0			0
$151$	−163.992			−1.08604			−0.543019	−	0.839720i	$-0.682719\pi$
$151$	−163.992			−1.08604			−0.543019	+	0.839720i	$0.682719\pi$
$152$	14.7045	+	20.2390i	0.0967402	+	0.133151i
$153$	78.7004	+	56.6344i	0.514382	+	0.370159i
$154$	−117.047	+	360.234i	−0.760046	+	2.33918i
$155$		0			0
$156$	−3.42366	−	21.3027i	−0.0219466	−	0.136556i
$157$	73.2155			0.466341			0.233170	−	0.972436i	$-0.425090\pi$
$157$	73.2155			0.466341			0.233170	+	0.972436i	$0.425090\pi$
$158$	−37.8934	+	12.3123i	−0.239831	+	0.0779260i
$159$	3.62073	−	3.63723i	0.0227719	−	0.0228756i
$160$		0			0
$161$	−160.762	−	221.270i	−0.998522	−	1.37435i
$162$	−179.244	+	60.0471i	−1.10645	+	0.370661i
$163$	−15.7750	−	11.4612i	−0.0967790	−	0.0703141i	0.538343	−	0.842726i	$-0.319050\pi$
$163$	−15.7750	−	11.4612i	−0.0967790	−	0.0703141i	−0.635122	+	0.772412i	$0.719050\pi$
$164$	−64.2227	−	88.3950i	−0.391602	−	0.538994i
$165$		0			0
$166$	108.099	+	78.5384i	0.651198	+	0.473123i
$167$	−86.5934	+	28.1359i	−0.518523	+	0.168478i	−0.556575	−	0.830797i	$-0.687885\pi$
$167$	−86.5934	+	28.1359i	−0.518523	+	0.168478i	0.0380519	+	0.999276i	$0.487885\pi$
$168$	−34.6075	+	221.764i	−0.205997	+	1.32002i
$169$	−44.5843	−	137.216i	−0.263812	−	0.811931i
$170$		0			0
$171$	22.0680	−	30.6662i	0.129053	−	0.179334i
$172$	−19.3963	+	59.6958i	−0.112769	+	0.347069i
$173$	−25.4472	−	35.0251i	−0.147094	−	0.202457i	0.729112	−	0.684394i	$-0.239933\pi$
$173$	−25.4472	−	35.0251i	−0.147094	−	0.202457i	−0.876206	+	0.481937i	$0.839933\pi$
$174$	189.665	+	29.5983i	1.09003	+	0.170105i
$175$		0			0
$176$			254.596i			1.44657i
$177$	−65.2807	−	127.404i	−0.368818	−	0.719796i
$178$	54.5542	−	167.901i	0.306485	−	0.943262i
$179$	−86.3556	−	28.0587i	−0.482434	−	0.156752i	0.0576956	−	0.998334i	$-0.481625\pi$
$179$	−86.3556	−	28.0587i	−0.482434	−	0.156752i	−0.540129	+	0.841582i	$0.681625\pi$
$180$		0			0
$181$	−34.0023	−	104.648i	−0.187858	−	0.578168i	0.812128	−	0.583480i	$-0.198309\pi$
$181$	−34.0023	−	104.648i	−0.187858	−	0.578168i	−0.999986	+	0.00531154i	$0.998309\pi$
$182$			145.679i			0.800433i
$183$	−3.10778	−	19.3372i	−0.0169824	−	0.105668i
$184$	−105.033	−	76.3112i	−0.570834	−	0.414735i
$185$		0			0
$186$	89.2688	+	174.220i	0.479940	+	0.936666i
$187$	−112.676	−	81.8642i	−0.602548	−	0.437777i
$188$	4.18206	−	5.75611i	0.0222450	−	0.0306176i
$189$	334.425	−	55.3079i	1.76945	−	0.292634i
$190$		0			0
$191$	−57.8437	+	79.6151i	−0.302847	+	0.416833i	−0.933134	−	0.359529i	$-0.882937\pi$
$191$	−57.8437	+	79.6151i	−0.302847	+	0.416833i	0.630287	+	0.776362i	$0.282937\pi$
$192$	12.9221	+	80.4034i	0.0673024	+	0.418768i
$193$	−183.115			−0.948784			−0.474392	−	0.880314i	$-0.657332\pi$
$193$	−183.115			−0.948784			−0.474392	+	0.880314i	$0.657332\pi$
$194$	66.3512	−	21.5588i	0.342017	−	0.111128i
$195$		0			0
$196$	−48.5475	+	149.414i	−0.247691	+	0.762316i
$197$	321.562	+	104.482i	1.63229	+	0.530365i	0.974797	−	0.223092i	$-0.0716152\pi$
$197$	321.562	+	104.482i	1.63229	+	0.530365i	0.657497	+	0.753457i	$0.271615\pi$
$198$	257.861	−	85.0820i	1.30233	−	0.429707i
$199$	12.6514			0.0635749			0.0317875	−	0.999495i	$-0.489880\pi$
$199$	12.6514			0.0635749			0.0317875	+	0.999495i	$0.489880\pi$
$200$		0			0
$201$	12.2717	+	1.91506i	0.0610531	+	0.00952767i
$202$	49.2577	−	35.7878i	0.243850	−	0.177167i
$203$	−327.368	−	106.368i	−1.61265	−	0.523981i
$204$	41.7022	+	21.1291i	0.204422	+	0.103574i
$205$		0			0
$206$	−104.450	+	33.9378i	−0.507038	+	0.164747i
$207$	−59.7408	+	186.748i	−0.288603	+	0.902163i
$208$	30.2588	+	93.1270i	0.145475	+	0.447726i
$209$	−31.8990	+	43.9052i	−0.152627	+	0.210073i
$210$		0			0
$211$	293.037	−	212.904i	1.38880	−	1.00902i	0.392808	−	0.919621i	$-0.371504\pi$
$211$	293.037	−	212.904i	1.38880	−	1.00902i	0.995995	−	0.0894038i	$-0.0284962\pi$
$212$	1.45447	−	2.00190i	0.00686069	−	0.00944294i
$213$	115.378	−	115.904i	0.541681	−	0.544149i
$214$	281.449	−	204.485i	1.31518	−	0.955537i
$215$		0			0
$216$	142.864	−	74.0242i	0.661408	−	0.342705i
$217$	−108.473	−	333.844i	−0.499874	−	1.53845i
$218$		−	347.524i		−	1.59415i
$219$	17.0623	+	106.165i	0.0779099	+	0.484770i
$220$		0			0
$221$	−50.9448	−	16.5530i	−0.230519	−	0.0749003i
$222$	0.215669	+	0.109272i	0.000971480	+	0.000492216i
$223$	−184.609	+	134.126i	−0.827842	+	0.601462i	−0.918948	−	0.394379i	$-0.870960\pi$
$223$	−184.609	+	134.126i	−0.827842	+	0.601462i	0.0911062	+	0.995841i	$0.470960\pi$
$224$			277.737i			1.23990i
$225$		0			0
$226$	−136.460			−0.603804
$227$	−182.632	−	251.371i	−0.804545	−	1.10736i	−0.992142	−	0.125115i	$-0.960070\pi$
$227$	−182.632	−	251.371i	−0.804545	−	1.10736i	0.187598	−	0.982246i	$-0.439930\pi$
$228$	8.23309	−	16.2496i	0.0361101	−	0.0712700i
$229$	−37.5038	+	115.425i	−0.163772	+	0.504039i	−0.998944	−	0.0459508i	$-0.985368\pi$
$229$	−37.5038	+	115.425i	−0.163772	+	0.504039i	0.835172	+	0.549989i	$0.185368\pi$
$230$		0			0
$231$	−480.734	+	77.2613i	−2.08110	+	0.334464i
$232$	−163.393			−0.704282
$233$	382.465	−	124.270i	1.64148	−	0.533350i	0.664612	−	0.747188i	$-0.268597\pi$
$233$	382.465	−	124.270i	1.64148	−	0.533350i	0.976869	+	0.213839i	$0.0685968\pi$
$234$	84.2093	−	61.7685i	0.359869	−	0.263968i
$235$		0			0
$236$	−40.5704	−	55.8404i	−0.171909	−	0.236612i
$237$	−36.2987	−	36.1341i	−0.153159	−	0.152464i
$238$	−255.363	−	185.532i	−1.07296	−	0.779548i
$239$	115.387	+	158.817i	0.482792	+	0.664507i	0.979038	−	0.203675i	$-0.0652887\pi$
$239$	115.387	+	158.817i	0.482792	+	0.664507i	−0.496246	+	0.868182i	$0.665289\pi$
$240$		0			0
$241$	−291.933	−	212.102i	−1.21134	−	0.880091i	−0.215989	−	0.976396i	$-0.569298\pi$
$241$	−291.933	−	212.102i	−1.21134	−	0.880091i	−0.995352	+	0.0963050i	$0.969298\pi$
$242$	−102.386	+	33.2672i	−0.423083	+	0.137468i
$243$	−173.769	−	169.863i	−0.715097	−	0.699025i
$244$	−2.91808	−	8.98093i	−0.0119594	−	0.0368071i
$245$		0			0
$246$	239.027	−	471.764i	0.971653	−	1.91774i
$247$	−6.44998	+	19.8510i	−0.0261133	+	0.0803684i
$248$	−97.9403	−	134.803i	−0.394921	−	0.543562i
$249$	−26.4839	+	169.708i	−0.106361	+	0.681559i
$250$		0			0
$251$			337.441i			1.34439i	0.740376	+	0.672193i	$0.234647\pi$
$251$			337.441i			1.34439i	−0.740376	+	0.672193i	$0.765353\pi$
$252$	155.204	−	51.2101i	0.615889	−	0.203215i
$253$	87.0319	−	267.857i	0.344000	−	1.05872i
$254$	295.676	+	96.0708i	1.16408	+	0.378231i
$255$		0			0
$256$	75.9506	+	233.752i	0.296682	+	0.913094i
$257$			190.928i			0.742911i	0.928451	+	0.371455i	$0.121141\pi$
$257$			190.928i			0.742911i	−0.928451	+	0.371455i	$0.878859\pi$
$258$	−299.966	+	48.2091i	−1.16266	+	0.186857i
$259$	−0.350735	−	0.254824i	−0.00135419	−	0.000983875i
$260$		0			0
$261$	77.3195	+	234.335i	0.296243	+	0.897835i
$262$	399.270	+	290.086i	1.52393	+	1.10720i
$263$	−161.231	+	221.916i	−0.613047	+	0.843787i	−0.996824	−	0.0796388i	$-0.974623\pi$
$263$	−161.231	+	221.916i	−0.613047	+	0.843787i	0.383776	+	0.923426i	$0.374623\pi$
$264$	−205.695	+	105.397i	−0.779148	+	0.399229i
$265$		0			0
$266$	−72.2940	+	99.5042i	−0.271782	+	0.374076i
$267$	224.064	−	36.0105i	0.839192	−	0.134871i
$268$	5.98844			0.0223449
$269$	132.545	−	43.0665i	0.492733	−	0.160099i	−0.0521023	−	0.998642i	$-0.516592\pi$
$269$	132.545	−	43.0665i	0.492733	−	0.160099i	0.544835	+	0.838543i	$0.316592\pi$
$270$		0			0
$271$	−108.618	+	334.292i	−0.400805	+	1.23355i	0.523543	+	0.851999i	$0.324610\pi$
$271$	−108.618	+	334.292i	−0.400805	+	1.23355i	−0.924348	+	0.381551i	$0.875390\pi$
$272$	−201.781	−	65.5626i	−0.741842	−	0.241039i
$273$	−166.662	+	85.3963i	−0.610484	+	0.312807i
$274$	447.841			1.63446
$275$		0			0
$276$	−14.5764	+	93.4054i	−0.0528131	+	0.338426i
$277$	−322.437	+	234.264i	−1.16403	+	0.845719i	−0.990282	−	0.139071i	$-0.955588\pi$
$277$	−322.437	+	234.264i	−1.16403	+	0.845719i	−0.173750	+	0.984790i	$0.555588\pi$
$278$	−226.635	−	73.6381i	−0.815233	−	0.264885i
$279$	−146.985	+	204.254i	−0.526829	+	0.732093i
$280$		0			0
$281$	167.897	−	54.5530i	0.597498	−	0.194139i	0.00537353	−	0.999986i	$-0.498290\pi$
$281$	167.897	−	54.5530i	0.597498	−	0.194139i	0.592124	+	0.805847i	$0.298290\pi$
$282$	34.0266	+	5.31004i	0.120662	+	0.0188299i
$283$	99.6099	+	306.568i	0.351979	+	1.08328i	0.957741	+	0.287633i	$0.0928683\pi$
$283$	99.6099	+	306.568i	0.351979	+	1.08328i	−0.605762	+	0.795646i	$0.707132\pi$
$284$	46.3480	−	63.7925i	0.163197	−	0.224621i
$285$		0			0
$286$	−121.363	+	88.1752i	−0.424345	+	0.308305i
$287$	−557.414	+	767.214i	−1.94221	+	2.67322i
$288$	160.545	−	117.762i	0.557450	−	0.408895i
$289$	−139.908	+	101.649i	−0.484111	+	0.351727i
$290$		0			0
$291$	63.5589	+	63.2706i	0.218416	+	0.217425i
$292$	16.0208	+	49.3070i	0.0548658	+	0.168860i
$293$			330.675i			1.12858i	0.825575	+	0.564292i	$0.190851\pi$
$293$			330.675i			1.12858i	−0.825575	+	0.564292i	$0.809149\pi$
$294$	−750.792	+	120.664i	−2.55371	+	0.410421i
$295$		0			0
$296$	−0.195719	−	0.0635929i	−0.000661212	−	0.000214841i
$297$	248.494	+	245.128i	0.836681	+	0.825348i
$298$	216.305	−	157.155i	0.725855	−	0.527365i
$299$		−	108.321i		−	0.362279i
$300$		0			0
$301$	544.787			1.80992
$302$	−224.956	−	309.626i	−0.744888	−	1.02525i
$303$	69.8173	+	35.3740i	0.230420	+	0.116746i
$304$	−25.5470	+	78.6254i	−0.0840360	+	0.258636i
$305$		0			0
$306$	1.02863	+	226.279i	0.00336154	+	0.739474i
$307$	−169.985			−0.553697			−0.276849	−	0.960914i	$-0.589290\pi$
$307$	−169.985			−0.553697			−0.276849	+	0.960914i	$0.589290\pi$
$308$	−223.272	+	72.5454i	−0.724908	+	0.235537i
$309$	−100.054	−	99.6005i	−0.323800	−	0.322332i
$310$		0			0
$311$	−269.449	−	370.864i	−0.866394	−	1.19249i	−0.980007	−	0.198964i	$-0.936242\pi$
$311$	−269.449	−	370.864i	−0.866394	−	1.19249i	0.113613	−	0.993525i	$-0.463758\pi$
$312$	−62.7135	+	62.9992i	−0.201005	+	0.201921i
$313$	258.542	+	187.842i	0.826012	+	0.600133i	0.918428	−	0.395587i	$-0.129459\pi$
$313$	258.542	+	187.842i	0.826012	+	0.600133i	−0.0924161	+	0.995720i	$0.529459\pi$
$314$	100.434	+	138.235i	0.319852	+	0.440239i
$315$		0			0
$316$	−19.9785	−	14.5153i	−0.0632232	−	0.0459343i
$317$	233.444	−	75.8505i	0.736415	−	0.239276i	0.0832897	−	0.996525i	$-0.473457\pi$
$317$	233.444	−	75.8505i	0.736415	−	0.239276i	0.653126	+	0.757249i	$0.273457\pi$
$318$	11.8340	+	1.84676i	0.0372139	+	0.00580743i
$319$	−109.533	−	337.107i	−0.343362	−	1.05676i
$320$		0			0
$321$	398.923	+	202.121i	1.24275	+	0.629659i
$322$	197.244	−	607.055i	0.612560	−	1.88526i
$323$	−26.5827	−	36.5880i	−0.0822995	−	0.113276i
$324$	−95.4092	−	68.0022i	−0.294473	−	0.209883i
$325$		0			0
$326$		−	45.5060i		−	0.139589i
$327$	397.581	−	203.717i	1.21584	−	0.622988i
$328$	−139.106	+	428.125i	−0.424104	+	1.30526i
$329$	−58.7309	−	19.0828i	−0.178513	−	0.0580025i
$330$		0			0
$331$	−46.4064	−	142.824i	−0.140200	−	0.431493i	0.856162	−	0.516707i	$-0.172842\pi$
$331$	−46.4064	−	142.824i	−0.140200	−	0.431493i	−0.996363	+	0.0852145i	$0.972842\pi$
$332$			82.8156i			0.249445i
$333$	0.00141280	+	0.310788i	4.24264e−6	+	0.000933297i
$334$	−171.907	−	124.898i	−0.514691	−	0.373945i
$335$		0			0
$336$	−660.112	+	338.236i	−1.96462	+	1.00665i
$337$	511.058	+	371.305i	1.51649	+	1.10180i	0.963192	+	0.268816i	$0.0866322\pi$
$337$	511.058	+	371.305i	1.51649	+	1.10180i	0.553301	+	0.832981i	$0.313368\pi$
$338$	197.913	−	272.404i	0.585542	−	0.805930i
$339$	−79.9922	−	156.115i	−0.235965	−	0.460517i
$340$		0			0
$341$	212.465	−	292.433i	0.623065	−	0.857575i
$342$	88.1712	−	0.400814i	0.257811	−	0.00117197i
$343$	748.394			2.18191
$344$	245.945	−	79.9123i	0.714956	−	0.232303i
$345$		0			0
$346$	31.2221	−	96.0916i	0.0902371	−	0.277721i
$347$	−546.463	−	177.557i	−1.57482	−	0.511690i	−0.614105	−	0.789224i	$-0.710483\pi$
$347$	−546.463	−	177.557i	−1.57482	−	0.511690i	−0.960716	+	0.277534i	$0.910483\pi$
$348$	54.2551	+	105.886i	0.155905	+	0.304270i
$349$	−461.206			−1.32151			−0.660754	−	0.750603i	$-0.729763\pi$
$349$	−461.206			−1.32151			−0.660754	+	0.750603i	$0.729763\pi$
$350$		0			0
$351$	120.029	+	60.1303i	0.341962	+	0.171311i
$352$	−231.379	+	168.106i	−0.657326	+	0.477575i
$353$	−167.093	−	54.2919i	−0.473352	−	0.153801i	0.0626196	−	0.998037i	$-0.480055\pi$
$353$	−167.093	−	54.2919i	−0.473352	−	0.153801i	−0.535971	+	0.844236i	$0.680055\pi$
$354$	150.997	−	298.020i	0.426544	−	0.841865i
$355$		0			0
$356$	104.064	−	33.8125i	0.292315	−	0.0949790i
$357$	62.5632	−	400.904i	0.175247	−	1.12298i
$358$	−65.4823	−	201.534i	−0.182911	−	0.562944i
$359$	−271.386	+	373.531i	−0.755950	+	1.04048i	0.241590	+	0.970379i	$0.422331\pi$
$359$	−271.386	+	373.531i	−0.755950	+	1.04048i	−0.997540	+	0.0700981i	$0.977669\pi$
$360$		0			0
$361$	277.798	−	201.832i	0.769525	−	0.559092i
$362$	150.939	−	207.750i	0.416959	−	0.573895i
$363$	−98.0773	−	97.6324i	−0.270185	−	0.268960i
$364$	−73.0471	+	53.0718i	−0.200679	+	0.145802i
$365$		0			0
$366$	32.2465	−	32.3935i	0.0881053	−	0.0885067i
$367$	121.946	+	375.313i	0.332279	+	1.02265i	0.968047	+	0.250770i	$0.0806837\pi$
$367$	121.946	+	375.313i	0.332279	+	1.02265i	−0.635768	+	0.771881i	$0.719316\pi$
$368$		−	429.037i		−	1.16586i
$369$	679.833	−	3.09042i	1.84236	−	0.00837513i
$370$		0			0
$371$	−20.4259	−	6.63677i	−0.0550562	−	0.0178889i
$372$	−54.8370	+	108.231i	−0.147411	+	0.290944i
$373$	−279.732	+	203.237i	−0.749951	+	0.544871i	−0.895812	−	0.444434i	$-0.853405\pi$
$373$	−279.732	+	203.237i	−0.749951	+	0.544871i	0.145861	+	0.989305i	$0.453405\pi$
$374$		−	325.037i		−	0.869082i
$375$		0			0
$376$	−29.3133			−0.0779610
$377$	−80.1304	−	110.290i	−0.212548	−	0.292547i
$378$	563.173	+	555.545i	1.48988	+	1.46970i
$379$	115.909	−	356.732i	0.305829	−	0.941245i	−0.673537	−	0.739153i	$-0.735226\pi$
$379$	115.909	−	356.732i	0.305829	−	0.941245i	0.979367	−	0.202092i	$-0.0647741\pi$
$380$		0			0
$381$	63.4151	+	394.580i	0.166444	+	1.03564i
$382$	−229.665			−0.601217
$383$	120.889	−	39.2793i	0.315638	−	0.102557i	−0.146914	−	0.989149i	$-0.546934\pi$
$383$	120.889	−	39.2793i	0.315638	−	0.102557i	0.462552	+	0.886592i	$0.346934\pi$
$384$	−321.371	+	322.835i	−0.836903	+	0.840716i
$385$		0			0
$386$	−251.189	−	345.732i	−0.650748	−	0.895678i
$387$	−230.992	−	314.913i	−0.596879	−	0.813728i
$388$	34.9824	+	25.4162i	0.0901607	+	0.0655056i
$389$	−157.269	−	216.462i	−0.404291	−	0.556458i	0.557524	−	0.830161i	$-0.311752\pi$
$389$	−157.269	−	216.462i	−0.404291	−	0.556458i	−0.961814	+	0.273703i	$0.911752\pi$
$390$		0			0
$391$	189.879	+	137.955i	0.485624	+	0.352826i
$392$	615.581	−	200.014i	1.57036	−	0.510240i
$393$	−97.8197	+	626.827i	−0.248905	+	1.59498i
$394$	243.836	+	750.450i	0.618873	+	1.90470i
$395$		0			0
$396$	136.603	+	98.3022i	0.344957	+	0.248238i
$397$	22.2941	−	68.6142i	0.0561564	−	0.172832i	−0.919044	−	0.394155i	$-0.871037\pi$
$397$	22.2941	−	68.6142i	0.0561564	−	0.172832i	0.975201	+	0.221323i	$0.0710375\pi$
$398$	17.3546	+	23.8866i	0.0436045	+	0.0600165i
$399$	−156.215	−	24.3782i	−0.391517	−	0.0610983i
$400$		0			0
$401$		−	255.533i		−	0.637239i	−0.947883	−	0.318620i	$-0.896781\pi$
$401$		−	255.533i		−	0.637239i	0.947883	−	0.318620i	$-0.103219\pi$
$402$	13.2180	+	25.7966i	0.0328805	+	0.0641706i
$403$	42.9605	−	132.219i	0.106602	−	0.328086i
$404$	35.8898	+	11.6613i	0.0888362	+	0.0288646i
$405$		0			0
$406$	−248.238	−	763.999i	−0.611425	−	1.88177i
$407$		−	0.446429i		−	0.00109688i
$408$	−30.5626	−	190.166i	−0.0749082	−	0.466093i
$409$	577.930	+	419.891i	1.41303	+	1.02663i	0.992873	+	0.119178i	$0.0380259\pi$
$409$	577.930	+	419.891i	1.41303	+	1.02663i	0.420160	+	0.907450i	$0.361974\pi$
$410$		0			0
$411$	262.522	+	512.347i	0.638741	+	1.24659i
$412$	−55.0691	−	40.0101i	−0.133663	−	0.0971118i
$413$	−352.126	+	484.660i	−0.852606	+	1.17351i
$414$	−434.540	+	143.378i	−1.04961	+	0.346323i
$415$		0			0
$416$	−64.6550	+	88.9900i	−0.155421	+	0.213918i
$417$	−48.6076	−	302.445i	−0.116565	−	0.725288i
$418$	−126.653			−0.302997
$419$	−4.75627	+	1.54540i	−0.0113515	+	0.00368832i	−0.314687	−	0.949195i	$-0.601900\pi$
$419$	−4.75627	+	1.54540i	−0.0113515	+	0.00368832i	0.303336	+	0.952884i	$0.401900\pi$
$420$		0			0
$421$	−34.6754	+	106.720i	−0.0823643	+	0.253491i	−0.983755	−	0.179515i	$-0.942547\pi$
$421$	−34.6754	+	106.720i	−0.0823643	+	0.253491i	0.901391	+	0.433006i	$0.142547\pi$
$422$	803.950	+	261.219i	1.90509	+	0.619003i
$423$	13.8714	+	42.0405i	0.0327929	+	0.0993865i
$424$	−10.1948			−0.0240444
$425$		0			0
$426$	377.103	+	58.8489i	0.885217	+	0.138143i
$427$	−66.3073	+	48.1751i	−0.155287	+	0.112822i
$428$	205.068	+	66.6306i	0.479131	+	0.155679i
$429$	−172.018	−	87.1557i	−0.400975	−	0.203160i
$430$		0			0
$431$	−418.838	+	136.089i	−0.971783	+	0.315751i	−0.751535	−	0.659693i	$-0.770686\pi$
$431$	−418.838	+	136.089i	−0.971783	+	0.315751i	−0.220247	+	0.975444i	$0.570686\pi$
$432$	475.407	+	238.163i	1.10048	+	0.551303i
$433$	−227.890	−	701.374i	−0.526305	−	1.61980i	−0.761720	−	0.647906i	$-0.775645\pi$
$433$	−227.890	−	701.374i	−0.526305	−	1.61980i	0.235415	−	0.971895i	$-0.424355\pi$
$434$	481.519	−	662.754i	1.10949	−	1.52708i
$435$		0			0
$436$	174.257	−	126.605i	0.399673	−	0.290380i
$437$	53.7552	−	73.9877i	0.123010	−	0.169308i
$438$	−177.039	+	177.846i	−0.404200	+	0.406041i
$439$	150.664	−	109.464i	0.343199	−	0.249349i	−0.402811	−	0.915283i	$-0.631967\pi$
$439$	150.664	−	109.464i	0.343199	−	0.249349i	0.746010	+	0.665934i	$0.231967\pi$
$440$		0			0
$441$	−578.155	−	788.202i	−1.31101	−	1.78731i
$442$	−38.6307	−	118.893i	−0.0873998	−	0.268989i
$443$		−	474.687i		−	1.07153i	−0.844368	−	0.535764i	$-0.820024\pi$
$443$		−	474.687i		−	1.07153i	0.844368	−	0.535764i	$-0.179976\pi$
$444$	0.0237779	+	0.147950i	5.35537e−5	+	0.000333221i
$445$		0			0
$446$	−506.475	−	164.564i	−1.13559	−	0.368977i
$447$	306.588	+	155.338i	0.685879	+	0.347511i
$448$	275.704	−	200.311i	0.615411	−	0.447122i
$449$		−	211.075i		−	0.470100i	−0.971983	−	0.235050i	$-0.924475\pi$
$449$		−	211.075i		−	0.470100i	0.971983	−	0.235050i	$-0.0755254\pi$
$450$		0			0
$451$	−976.541			−2.16528
$452$	−49.7133	−	68.4244i	−0.109985	−	0.151381i
$453$	222.355	−	438.860i	0.490850	−	0.968786i
$454$	224.077	−	689.637i	0.493561	−	1.51902i
$455$		0			0
$456$	−74.0995	+	11.9089i	−0.162499	+	0.0261161i
$457$	353.601			0.773743			0.386872	−	0.922134i	$-0.373556\pi$
$457$	353.601			0.773743			0.386872	+	0.922134i	$0.373556\pi$
$458$	−269.374	+	87.5251i	−0.588154	+	0.191103i
$459$	−258.269	+	133.821i	−0.562677	+	0.291548i
$460$		0			0
$461$	175.509	+	241.567i	0.380713	+	0.524007i	0.955773	−	0.294104i	$-0.0950214\pi$
$461$	175.509	+	241.567i	0.380713	+	0.524007i	−0.575060	+	0.818111i	$0.695021\pi$
$462$	−805.322	−	801.669i	−1.74312	−	1.73521i
$463$	−419.957	−	305.117i	−0.907035	−	0.659000i	0.0332279	−	0.999448i	$-0.489421\pi$
$463$	−419.957	−	305.117i	−0.907035	−	0.659000i	−0.940263	+	0.340448i	$0.889421\pi$
$464$	−317.379	−	436.835i	−0.684007	−	0.941454i
$465$		0			0
$466$	759.277	+	551.647i	1.62935	+	1.18379i
$467$	−405.664	+	131.808i	−0.868659	+	0.282244i	−0.709240	−	0.704967i	$-0.750962\pi$
$467$	−405.664	+	131.808i	−0.868659	+	0.282244i	−0.159419	+	0.987211i	$0.550962\pi$
$468$	61.6503	+	19.7220i	0.131732	+	0.0421411i
$469$	−16.0615	−	49.4321i	−0.0342462	−	0.105399i
$470$		0			0
$471$	−99.2724	+	195.933i	−0.210769	+	0.415993i
$472$	−87.8754	+	270.453i	−0.186177	+	0.572993i
$473$	329.744	+	453.853i	0.697133	+	0.959521i
$474$	18.4303	−	118.101i	0.0388824	−	0.249158i
$475$		0			0
$476$		−	195.637i		−	0.411001i
$477$	4.82429	+	14.6212i	0.0101138	+	0.0306523i
$478$	−141.573	+	435.715i	−0.296177	+	0.911539i
$479$	280.502	+	91.1407i	0.585600	+	0.190273i	0.586808	−	0.809726i	$-0.300384\pi$
$479$	280.502	+	91.1407i	0.585600	+	0.190273i	−0.00120777	+	0.999999i	$0.500384\pi$
$480$		0			0
$481$	−0.0530582	−	0.163296i	−0.000110308	−	0.000339493i
$482$		−	842.137i		−	1.74717i
$483$	810.118	−	130.198i	1.67726	−	0.269562i
$484$	−53.9810	−	39.2195i	−0.111531	−	0.0810320i
$485$		0			0
$486$	82.3436	−	561.095i	0.169431	−	1.15452i
$487$	−536.625	−	389.881i	−1.10190	−	0.800576i	−0.120530	−	0.992710i	$-0.538459\pi$
$487$	−536.625	−	389.881i	−1.10190	−	0.800576i	−0.981369	+	0.192133i	$0.938459\pi$
$488$	−22.8680	+	31.4751i	−0.0468606	+	0.0644981i
$489$	52.0606	−	26.6754i	0.106463	−	0.0545509i
$490$		0			0
$491$	315.408	−	434.122i	0.642379	−	0.884158i	−0.356361	−	0.934348i	$-0.615983\pi$
$491$	315.408	−	434.122i	0.642379	−	0.884158i	0.998740	+	0.0501900i	$0.0159827\pi$
$492$	323.634	−	52.0129i	0.657792	−	0.105717i
$493$	295.382			0.599152
$494$	−46.3276	+	15.0527i	−0.0937805	+	0.0304711i
$495$		0			0
$496$	170.157	−	523.690i	0.343059	−	1.05583i
$497$	−650.889	−	211.487i	−1.30964	−	0.425527i
$498$	−356.748	+	182.795i	−0.716361	+	0.367057i
$499$	791.222			1.58562			0.792808	−	0.609472i	$-0.208618\pi$
$499$	791.222			1.58562			0.792808	+	0.609472i	$0.208618\pi$
$500$		0			0
$501$	42.1166	−	269.882i	0.0840651	−	0.538688i
$502$	−637.107	+	462.885i	−1.26914	+	0.922082i
$503$	417.883	+	135.778i	0.830781	+	0.269937i	0.693374	−	0.720578i	$-0.256123\pi$
$503$	417.883	+	135.778i	0.830781	+	0.269937i	0.137407	+	0.990515i	$0.456123\pi$
$504$	−546.541	−	393.302i	−1.08441	−	0.780360i
$505$		0			0
$506$	625.115	−	203.112i	1.23540	−	0.401407i
$507$	427.657	+	66.7382i	0.843505	+	0.131633i
$508$	59.5443	+	183.259i	0.117213	+	0.360745i
$509$	311.605	−	428.888i	0.612191	−	0.842609i	−0.384564	−	0.923098i	$-0.625648\pi$
$509$	311.605	−	428.888i	0.612191	−	0.842609i	0.996755	+	0.0804893i	$0.0256483\pi$
$510$		0			0
$511$	364.040	−	264.490i	0.712406	−	0.517593i
$512$	19.8488	−	27.3195i	0.0387671	−	0.0533584i
$513$	52.1442	+	100.636i	0.101646	+	0.196172i
$514$	−360.483	+	261.906i	−0.701328	+	0.509545i
$515$		0			0
$516$	−133.453	−	132.848i	−0.258630	−	0.257457i
$517$	−19.6505	−	60.4781i	−0.0380088	−	0.116979i
$518$		−	1.01176i		−	0.00195321i
$519$	128.235	−	20.6093i	0.247080	−	0.0397096i
$520$		0			0
$521$	363.355	+	118.061i	0.697419	+	0.226605i	0.636206	−	0.771519i	$-0.280503\pi$
$521$	363.355	+	118.061i	0.697419	+	0.226605i	0.0612134	+	0.998125i	$0.480503\pi$
$522$	−336.374	+	467.433i	−0.644395	+	0.895466i
$523$	91.4124	−	66.4150i	0.174785	−	0.126988i	−0.496953	−	0.867777i	$-0.665548\pi$
$523$	91.4124	−	66.4150i	0.174785	−	0.126988i	0.671738	+	0.740789i	$0.265548\pi$
$524$			305.885i			0.583749i
$525$		0			0
$526$	−640.159			−1.21703
$527$	177.056	+	243.697i	0.335970	+	0.462422i
$528$	−681.326	−	345.205i	−1.29039	−	0.653797i
$529$	16.8065	−	51.7251i	0.0317703	−	0.0977790i
$530$		0			0
$531$	429.460	−	1.95227i	0.808777	−	0.00367658i
$532$	−76.2312			−0.143292
$533$	−357.202	+	116.062i	−0.670174	+	0.217753i
$534$	375.351	+	373.648i	0.702904	+	0.699716i
$535$		0			0
$536$	−14.5019	−	19.9602i	−0.0270559	−	0.0372392i
$537$	192.177	−	193.053i	0.357871	−	0.359502i
$538$	263.131	+	191.176i	0.489091	+	0.355346i
$539$	825.322	+	1135.96i	1.53121	+	2.10753i
$540$		0			0
$541$	−53.3470	−	38.7589i	−0.0986082	−	0.0716431i	0.537389	−	0.843335i	$-0.319411\pi$
$541$	−53.3470	−	38.7589i	−0.0986082	−	0.0716431i	−0.635997	+	0.771692i	$0.719411\pi$
$542$	−780.160	+	253.489i	−1.43941	+	0.467692i
$543$	326.154	+	50.8981i	0.600652	+	0.0937350i
$544$	−73.6496	−	226.670i	−0.135385	−	0.416673i
$545$		0			0
$546$	−389.852	−	197.525i	−0.714015	−	0.361767i
$547$	262.258	−	807.148i	0.479448	−	1.47559i	−0.360415	−	0.932792i	$-0.617365\pi$
$547$	262.258	−	807.148i	0.479448	−	1.47559i	0.839863	−	0.542798i	$-0.182635\pi$
$548$	163.152	+	224.559i	0.297722	+	0.409779i
$549$	55.9622	+	17.9024i	0.101935	+	0.0326090i
$550$		0			0
$551$		−	115.098i		−	0.208889i
$552$	346.631	−	177.611i	0.627955	−	0.321759i
$553$	−66.2334	+	203.845i	−0.119771	+	0.368617i
$554$	−884.607	−	287.426i	−1.59676	−	0.518820i
$555$		0			0
$556$	−45.6406	−	140.467i	−0.0820874	−	0.252639i
$557$			309.269i			0.555241i	0.960691	+	0.277621i	$0.0895458\pi$
$557$			309.269i			0.555241i	−0.960691	+	0.277621i	$0.910454\pi$
$558$	−587.270	+	2.66965i	−1.05246	+	0.00478431i
$559$	174.555	+	126.822i	0.312264	+	0.226873i
$560$		0			0
$561$	371.855	−	190.535i	0.662843	−	0.339635i
$562$	333.312	+	242.165i	0.593082	+	0.430899i
$563$	309.897	−	426.536i	0.550438	−	0.757614i	−0.439633	−	0.898177i	$-0.644892\pi$
$563$	309.897	−	426.536i	0.550438	−	0.757614i	0.990072	+	0.140564i	$0.0448915\pi$
$564$	9.73355	+	18.9963i	0.0172581	+	0.0336814i
$565$		0			0
$566$	−442.177	+	608.604i	−0.781231	+	1.07527i
$567$	−305.435	+	969.950i	−0.538686	+	1.71067i
$568$	−324.867			−0.571949
$569$	−619.336	+	201.235i	−1.08846	+	0.353663i	−0.797653	−	0.603117i	$-0.793925\pi$
$569$	−619.336	+	201.235i	−1.08846	+	0.353663i	−0.290811	+	0.956780i	$0.593925\pi$
$570$		0			0
$571$	−179.914	+	553.718i	−0.315086	+	0.969734i	0.660634	+	0.750708i	$0.270288\pi$
$571$	−179.914	+	553.718i	−0.315086	+	0.969734i	−0.975719	+	0.219025i	$0.929712\pi$
$572$	−88.4266	−	28.7315i	−0.154592	−	0.0502300i
$573$	−134.629	−	262.746i	−0.234954	−	0.458544i
$574$	−2213.18			−3.85571
$575$		0			0
$576$	−232.689	−	74.4376i	−0.403974	−	0.129232i
$577$	−187.010	+	135.871i	−0.324107	+	0.235478i	−0.737926	−	0.674881i	$-0.764195\pi$
$577$	−187.010	+	135.871i	−0.324107	+	0.235478i	0.413819	+	0.910359i	$0.364195\pi$
$578$	−383.838	−	124.717i	−0.664080	−	0.215773i
$579$	248.285	−	490.036i	0.428816	−	0.846349i
$580$		0			0
$581$	683.609	−	222.118i	1.17661	−	0.382303i
$582$	−32.2714	+	206.794i	−0.0554491	+	0.355317i
$583$	−6.83420	−	21.0335i	−0.0117225	−	0.0360781i
$584$	125.549	−	172.804i	0.214982	−	0.295897i
$585$		0			0
$586$	−624.333	+	453.604i	−1.06541	+	0.774069i
$587$	322.509	−	443.896i	0.549420	−	0.756212i	−0.440513	−	0.897746i	$-0.645204\pi$
$587$	322.509	−	443.896i	0.549420	−	0.756212i	0.989933	+	0.141534i	$0.0452036\pi$
$588$	−334.023	−	332.508i	−0.568066	−	0.565489i
$589$	94.9581	−	68.9911i	0.161219	−	0.117133i
$590$		0			0
$591$	−715.608	+	718.869i	−1.21084	+	1.21636i
$592$	−0.210152	−	0.646781i	−0.000354986	−	0.00109254i
$593$			1005.47i			1.69557i	0.530343	+	0.847783i	$0.322063\pi$
$593$			1005.47i			1.69557i	−0.530343	+	0.847783i	$0.677937\pi$
$594$	−121.943	+	805.426i	−0.205292	+	1.35594i
$595$		0			0
$596$	157.603	+	51.2082i	0.264434	+	0.0859199i
$597$	−17.1540	+	33.8565i	−0.0287336	+	0.0567111i
$598$	204.517	−	148.590i	0.342001	−	0.248478i
$599$			288.607i			0.481814i	0.970548	+	0.240907i	$0.0774449\pi$
$599$			288.607i			0.481814i	−0.970548	+	0.240907i	$0.922555\pi$
$600$		0			0
$601$	265.405			0.441605			0.220802	−	0.975319i	$-0.429132\pi$
$601$	265.405			0.441605			0.220802	+	0.975319i	$0.429132\pi$
$602$	747.312	+	1028.59i	1.24138	+	1.70862i
$603$	−21.7640	+	30.2437i	−0.0360928	+	0.0501554i
$604$	73.3011	−	225.598i	0.121359	−	0.373506i
$605$		0			0
$606$	28.9839	+	180.343i	0.0478282	+	0.297596i
$607$	357.546			0.589038			0.294519	−	0.955646i	$-0.404841\pi$
$607$	357.546			0.589038			0.294519	+	0.955646i	$0.404841\pi$
$608$	−88.3237	+	28.6981i	−0.145269	+	0.0472008i
$609$	728.528	−	731.848i	1.19627	−	1.20172i
$610$		0			0
$611$	−14.3757	−	19.7864i	−0.0235281	−	0.0323837i
$612$	−113.087	+	82.9508i	−0.184783	+	0.135541i
$613$	277.787	+	201.824i	0.453160	+	0.329240i	0.790842	−	0.612020i	$-0.209643\pi$
$613$	277.787	+	201.824i	0.453160	+	0.329240i	−0.337682	+	0.941260i	$0.609643\pi$
$614$	−233.178	−	320.941i	−0.379768	−	0.522706i
$615$		0			0
$616$	782.490	+	568.512i	1.27028	+	0.922910i
$617$	−146.541	+	47.6139i	−0.237505	+	0.0771701i	−0.425351	−	0.905028i	$-0.639849\pi$
$617$	−146.541	+	47.6139i	−0.237505	+	0.0771701i	0.187846	+	0.982198i	$0.439849\pi$
$618$	50.8015	−	325.535i	0.0822031	−	0.526756i
$619$	321.394	+	989.150i	0.519216	+	1.59798i	0.775479	+	0.631374i	$0.217509\pi$
$619$	321.394	+	989.150i	0.519216	+	1.59798i	−0.256263	+	0.966607i	$0.582491\pi$
$620$		0			0
$621$	−418.755	−	413.083i	−0.674323	−	0.665189i
$622$	330.595	−	1017.47i	0.531504	−	1.63580i
$623$	−558.216	−	768.319i	−0.896014	−	1.23326i
$624$	−290.245	−	45.2944i	−0.465137	−	0.0725871i
$625$		0			0
$626$			745.814i			1.19140i
$627$	−74.2434	−	144.896i	−0.118411	−	0.231094i
$628$	−32.7259	+	100.720i	−0.0521113	+	0.160382i
$629$	0.353819	+	0.114963i	0.000562511	+	0.000182771i
$630$		0			0
$631$	271.623	+	835.969i	0.430464	+	1.32483i	0.897664	+	0.440681i	$0.145263\pi$
$631$	271.623	+	835.969i	0.430464	+	1.32483i	−0.467200	+	0.884152i	$0.654737\pi$
$632$			101.742i			0.160984i
$633$	172.427	+	1072.88i	0.272397	+	1.69491i
$634$	463.437	+	336.707i	0.730973	+	0.531083i
$635$		0			0
$636$	3.38521	+	6.60668i	0.00532265	+	0.0103879i
$637$	436.898	+	317.425i	0.685869	+	0.498313i
$638$	486.224	−	669.231i	0.762107	−	1.04895i
$639$	153.731	+	465.917i	0.240580	+	0.729134i
$640$		0			0
$641$	−305.155	+	420.009i	−0.476060	+	0.655241i	−0.977742	−	0.209812i	$-0.932715\pi$
$641$	−305.155	+	420.009i	−0.476060	+	0.655241i	0.501682	+	0.865052i	$0.332715\pi$
$642$	165.609	+	1030.45i	0.257957	+	1.60506i
$643$	−702.045			−1.09183			−0.545914	−	0.837842i	$-0.683817\pi$
$643$	−702.045			−1.09183			−0.545914	+	0.837842i	$0.683817\pi$
$644$	376.250	−	122.251i	0.584240	−	0.189831i
$645$		0			0
$646$	32.6152	−	100.379i	0.0504880	−	0.155386i
$647$	−294.138	−	95.5712i	−0.454618	−	0.147714i	0.0727520	−	0.997350i	$-0.476822\pi$
$647$	−294.138	−	95.5712i	−0.454618	−	0.147714i	−0.527370	+	0.849636i	$0.676822\pi$
$648$	4.38856	+	482.689i	0.00677247	+	0.744890i
$649$	−616.895			−0.950532
$650$		0			0
$651$	1040.48	+	162.373i	1.59828	+	0.249420i
$652$	22.8179	−	16.5781i	0.0349967	−	0.0254266i
$653$	−124.241	−	40.3685i	−0.190263	−	0.0618200i	0.212336	−	0.977197i	$-0.431893\pi$
$653$	−124.241	−	40.3685i	−0.190263	−	0.0618200i	−0.402598	+	0.915377i	$0.631893\pi$
$654$	930.012	+	471.205i	1.42204	+	0.720497i
$655$		0			0
$656$	−1414.80	+	459.697i	−2.15671	+	0.700757i
$657$	−307.243	−	98.2873i	−0.467645	−	0.149600i
$658$	−44.5348	−	137.064i	−0.0676821	−	0.208304i
$659$	−543.472	+	748.024i	−0.824691	+	1.13509i	0.164197	+	0.986428i	$0.447497\pi$
$659$	−543.472	+	748.024i	−0.824691	+	1.13509i	−0.988888	+	0.148663i	$0.952503\pi$
$660$		0			0
$661$	−723.767	+	525.847i	−1.09496	+	0.795533i	−0.980230	−	0.197864i	$-0.936600\pi$
$661$	−723.767	+	525.847i	−1.09496	+	0.795533i	−0.114728	+	0.993397i	$0.536600\pi$
$662$	206.002	−	283.537i	0.311181	−	0.428304i
$663$	113.373	−	113.890i	0.171000	−	0.171779i
$664$	276.035	−	200.551i	0.415715	−	0.302035i
$665$		0			0
$666$	−0.584847	+	0.428991i	−0.000878148	+	0.000644131i
$667$	184.581	+	568.082i	0.276733	+	0.851697i
$668$		−	131.700i		−	0.197155i
$669$	−108.626	−	675.893i	−0.162371	−	1.01030i
$670$		0			0
$671$	−80.2679	−	26.0806i	−0.119624	−	0.0388683i
$672$	−743.255	−	376.582i	−1.10603	−	0.560390i
$673$	−217.242	+	157.836i	−0.322797	+	0.234526i	−0.737368	−	0.675491i	$-0.763932\pi$
$673$	−217.242	+	157.836i	−0.322797	+	0.234526i	0.414571	+	0.910017i	$0.363932\pi$
$674$			1474.25i			2.18731i
$675$		0			0
$676$	208.692			0.308716
$677$	490.323	+	674.872i	0.724259	+	0.996857i	0.999372	+	0.0354451i	$0.0112849\pi$
$677$	490.323	+	674.872i	0.724259	+	0.996857i	−0.275113	+	0.961412i	$0.588715\pi$
$678$	185.025	−	365.181i	0.272898	−	0.538615i
$679$	115.975	−	356.933i	0.170802	−	0.525674i
$680$		0			0
$681$	920.325	−	147.910i	1.35143	−	0.217196i
$682$	843.580			1.23692
$683$	751.391	−	244.142i	1.10013	−	0.357455i	0.297980	−	0.954572i	$-0.403687\pi$
$683$	751.391	−	244.142i	1.10013	−	0.357455i	0.802154	+	0.597117i	$0.203687\pi$
$684$	32.3224	+	44.0653i	0.0472549	+	0.0644230i
$685$		0			0
$686$	1026.61	+	1413.01i	1.49652	+	2.05978i
$687$	−258.038	−	256.868i	−0.375602	−	0.373898i
$688$	691.376	+	502.314i	1.00491	+	0.730107i
$689$	−4.99968	−	6.88147i	−0.00725643	−	0.00998762i
$690$		0			0
$691$	−760.429	−	552.484i	−1.10048	−	0.799543i	−0.119339	−	0.992854i	$-0.538078\pi$
$691$	−760.429	−	552.484i	−1.10048	−	0.799543i	−0.981138	+	0.193310i	$0.938078\pi$
$692$	59.5572	−	19.3513i	0.0860653	−	0.0279643i
$693$	445.064	−	1391.25i	0.642228	−	2.00758i
$694$	−414.375	−	1275.32i	−0.597082	−	1.83763i
$695$		0			0
$696$	221.544	−	437.259i	0.318310	−	0.628245i
$697$	251.475	−	773.962i	0.360797	−	1.11042i
$698$	−632.661	−	870.783i	−0.906390	−	1.24754i
$699$	−186.020	+	1192.02i	−0.266124	+	1.70532i
$700$		0			0
$701$		−	959.479i		−	1.36873i	−0.729140	−	0.684365i	$-0.760080\pi$
$701$		−	959.479i		−	1.36873i	0.729140	−	0.684365i	$-0.239920\pi$
$702$	51.1203	+	309.105i	0.0728210	+	0.440320i
$703$	0.0447961	−	0.137868i	6.37213e−5	−	0.000196114i
$704$	333.752	+	108.443i	0.474079	+	0.154038i
$705$		0			0
$706$	−126.704	−	389.956i	−0.179468	−	0.552346i
$707$		−	327.532i		−	0.463271i
$708$	204.444	−	32.8573i	0.288763	−	0.0464086i
$709$	−394.579	−	286.678i	−0.556529	−	0.404342i	0.273658	−	0.961827i	$-0.411766\pi$
$709$	−394.579	−	286.678i	−0.556529	−	0.404342i	−0.830187	+	0.557485i	$0.811766\pi$
$710$		0			0
$711$	145.916	−	48.1453i	0.205226	−	0.0677150i
$712$	−364.709	−	264.977i	−0.512232	−	0.372158i
$713$	−358.040	+	492.799i	−0.502160	+	0.691163i
$714$	842.750	−	431.818i	1.18032	−	0.604788i
$715$		0			0
$716$	77.1985	−	106.255i	0.107819	−	0.148400i
$717$	−581.465	+	93.4502i	−0.810969	+	0.130335i
$718$	−1077.52			−1.50073
$719$	9.24954	−	3.00536i	0.0128644	−	0.00417991i	−0.302578	−	0.953125i	$-0.597847\pi$
$719$	9.24954	−	3.00536i	0.0128644	−	0.00417991i	0.315442	+	0.948945i	$0.397847\pi$
$720$		0			0
$721$	−182.567	+	561.883i	−0.253213	+	0.779311i
$722$	762.141	+	247.635i	1.05560	+	0.342984i
$723$	963.438	−	493.658i	1.33256	−	0.682790i
$724$	159.159			0.219834
$725$		0			0
$726$	49.7977	−	319.103i	0.0685919	−	0.439536i
$727$	−747.076	+	542.782i	−1.02761	+	0.746606i	−0.967830	−	0.251606i	$-0.919041\pi$
$727$	−747.076	+	542.782i	−1.02761	+	0.746606i	−0.0597846	+	0.998211i	$0.519041\pi$
$728$	353.790	+	114.953i	0.485975	+	0.157903i
$729$	690.184	−	234.707i	0.946754	−	0.321958i
$730$		0			0
$731$	−444.618	+	144.465i	−0.608232	+	0.197627i
$732$	27.9906	+	4.36808i	0.0382385	+	0.00596732i
$733$	171.428	+	527.602i	0.233872	+	0.719784i	0.997269	+	0.0738544i	$0.0235300\pi$
$733$	171.428	+	527.602i	0.233872	+	0.719784i	−0.763397	+	0.645929i	$0.776470\pi$
$734$	−541.331	+	745.078i	−0.737508	+	1.01509i
$735$		0			0
$736$	389.912	−	283.288i	0.529772	−	0.384902i
$737$	31.4596	−	43.3004i	0.0426860	−	0.0587522i
$738$	938.397	+	1279.32i	1.27154	+	1.73350i
$739$	−1100.89	+	799.845i	−1.48970	+	1.08233i	−0.515440	+	0.856925i	$0.672372\pi$
$739$	−1100.89	+	799.845i	−1.48970	+	1.08233i	−0.974264	+	0.225408i	$0.927628\pi$
$740$		0			0
$741$	−44.3779	−	44.1767i	−0.0598893	−	0.0596176i
$742$	−15.4887	−	47.6692i	−0.0208742	−	0.0642442i
$743$		−	124.104i		−	0.167031i	−0.996506	−	0.0835155i	$-0.973385\pi$
$743$		−	124.104i		−	0.167031i	0.996506	−	0.0835155i	$-0.0266148\pi$
$744$	493.545	−	79.3201i	0.663366	−	0.106613i
$745$		0			0
$746$	−767.445	−	249.358i	−1.02875	−	0.334260i
$747$	−418.248	−	300.980i	−0.559904	−	0.402918i
$748$	162.982	−	118.413i	0.217890	−	0.158306i
$749$		−	1871.46i		−	2.49861i
$750$		0			0
$751$	632.917			0.842766			0.421383	−	0.906883i	$-0.361545\pi$
$751$	632.917			0.842766			0.421383	+	0.906883i	$0.361545\pi$
$752$	−56.9389	−	78.3697i	−0.0757166	−	0.104215i
$753$	−903.028	−	457.534i	−1.19924	−	0.607614i
$754$	98.3147	−	302.581i	0.130391	−	0.401302i
$755$		0			0
$756$	−73.3965	+	484.778i	−0.0970853	+	0.641241i
$757$	−1271.62			−1.67981			−0.839904	−	0.542734i	$-0.817389\pi$
$757$	−1271.62			−1.67981			−0.839904	+	0.542734i	$0.817389\pi$
$758$	832.529	−	270.505i	1.09832	−	0.356867i
$759$	598.808	+	596.092i	0.788943	+	0.785365i
$760$		0			0
$761$	706.088	+	971.847i	0.927843	+	1.27707i	0.960695	+	0.277606i	$0.0895409\pi$
$761$	706.088	+	971.847i	0.927843	+	1.27707i	−0.0328525	+	0.999460i	$0.510459\pi$
$762$	−658.000	+	660.998i	−0.863517	+	0.867451i
$763$	−1512.45	−	1098.86i	−1.98224	−	1.44018i
$764$	−83.6686	−	115.160i	−0.109514	−	0.150733i
$765$		0			0
$766$	239.992	+	174.364i	0.313305	+	0.227629i
$767$	−225.650	+	73.3182i	−0.294198	+	0.0955908i
$768$	−728.527	−	113.690i	−0.948602	−	0.148034i
$769$	164.777	+	507.132i	0.214275	+	0.659469i	0.999204	+	0.0398846i	$0.0126990\pi$
$769$	164.777	+	507.132i	0.214275	+	0.659469i	−0.784930	+	0.619585i	$0.787301\pi$
$770$		0			0
$771$	−510.944	−	258.878i	−0.662703	−	0.335769i
$772$	81.8489	−	251.905i	0.106022	−	0.326302i
$773$	593.017	+	816.217i	0.767163	+	1.05591i	0.996584	+	0.0825815i	$0.0263165\pi$
$773$	593.017	+	816.217i	0.767163	+	1.05591i	−0.229422	+	0.973327i	$0.573684\pi$
$774$	277.709	−	868.108i	0.358797	−	1.12159i
$775$		0			0
$776$		−	178.150i		−	0.229575i
$777$	1.15749	−	0.593090i	0.00148970	−	0.000763308i
$778$	192.959	−	593.865i	0.248019	−	0.763323i
$779$	−301.580	−	97.9892i	−0.387137	−	0.125788i
$780$		0			0
$781$	−217.778	−	670.253i	−0.278846	−	0.858198i
$782$			547.742i			0.700437i
$783$	−731.943	−	110.818i	−0.934793	−	0.141530i
$784$	1730.46	+	1257.25i	2.20722	+	1.60364i
$785$		0			0
$786$	−1317.67	+	675.163i	−1.67642	+	0.858986i
$787$	726.430	+	527.782i	0.923037	+	0.670625i	0.944278	−	0.329149i	$-0.106762\pi$
$787$	726.430	+	527.782i	0.923037	+	0.670625i	−0.0212413	+	0.999774i	$0.506762\pi$
$788$	−287.464	+	395.660i	−0.364802	+	0.502107i
$789$	−375.259	−	732.367i	−0.475613	−	0.928222i
$790$		0			0
$791$	−431.480	+	593.882i	−0.545487	+	0.750799i
$792$	−3.15196	−	693.369i	−0.00397974	−	0.875466i
$793$	−32.4604			−0.0409336
$794$	160.129	−	52.0292i	0.201674	−	0.0655279i
$795$		0			0
$796$	−5.65493	+	17.4041i	−0.00710419	+	0.0218644i
$797$	74.0152	+	24.0490i	0.0928673	+	0.0301744i	0.355082	−	0.934835i	$-0.384453\pi$
$797$	74.0152	+	24.0490i	0.0928673	+	0.0301744i	−0.262215	+	0.965010i	$0.584453\pi$
$798$	−168.261	−	328.384i	−0.210854	−	0.411508i
$799$	52.9925			0.0663235
$800$		0			0
$801$	−207.439	+	648.447i	−0.258975	+	0.809547i
$802$	482.460	−	350.528i	0.601572	−	0.437067i
$803$	440.685	+	143.187i	0.548799	+	0.178316i
$804$	−8.11968	+	16.0257i	−0.0100991	+	0.0199325i
$805$		0			0
$806$	308.568	−	100.260i	0.382838	−	0.124392i
$807$	−64.4663	+	413.099i	−0.0798839	+	0.511894i
$808$	−48.0443	−	147.865i	−0.0594607	−	0.183001i
$809$	−503.318	+	692.758i	−0.622148	+	0.856314i	−0.997507	−	0.0705660i	$-0.977519\pi$
$809$	−503.318	+	692.758i	−0.622148	+	0.856314i	0.375359	+	0.926880i	$0.377519\pi$
$810$		0			0
$811$	859.986	−	624.817i	1.06040	−	0.770427i	0.0862396	−	0.996274i	$-0.472515\pi$
$811$	859.986	−	624.817i	1.06040	−	0.770427i	0.974163	+	0.225847i	$0.0725149\pi$
$812$	292.654	−	402.803i	0.360411	−	0.496063i
$813$	−747.328	−	743.938i	−0.919222	−	0.915053i
$814$	0.842883	−	0.612390i	0.00103548	−	0.000752322i
$815$		0			0
$816$	449.046	−	451.092i	0.550302	−	0.552809i
$817$	56.2919	+	173.249i	0.0689007	+	0.212055i
$818$			1667.15i			2.03808i
$819$	−2.55384	−	561.794i	−0.00311824	−	0.685951i
$820$		0			0
$821$	711.389	+	231.144i	0.866491	+	0.281540i	0.708337	−	0.705874i	$-0.249446\pi$
$821$	711.389	+	231.144i	0.866491	+	0.281540i	0.158154	+	0.987414i	$0.449446\pi$
$822$	−607.224	+	1198.47i	−0.738715	+	1.45799i
$823$	−630.647	+	458.192i	−0.766278	+	0.556733i	−0.900829	−	0.434173i	$-0.857041\pi$
$823$	−630.647	+	458.192i	−0.766278	+	0.556733i	0.134552	+	0.990907i	$0.457041\pi$
$824$			280.443i			0.340343i
$825$		0			0
$826$	−1398.10			−1.69261
$827$	400.497	+	551.236i	0.484276	+	0.666549i	0.979320	−	0.202319i	$-0.0648478\pi$
$827$	400.497	+	551.236i	0.484276	+	0.666549i	−0.495043	+	0.868868i	$0.664848\pi$
$828$	−230.199	−	165.656i	−0.278018	−	0.200067i
$829$	−131.487	+	404.674i	−0.158609	+	0.488147i	−0.998509	−	0.0545941i	$-0.982614\pi$
$829$	−131.487	+	404.674i	−0.158609	+	0.488147i	0.839900	+	0.542741i	$0.182614\pi$
$830$		0			0
$831$	−189.726	−	1180.51i	−0.228311	−	1.42059i
$832$	134.969			0.162223
$833$	−1112.84	+	361.585i	−1.33595	+	0.434075i
$834$	504.356	−	506.654i	0.604743	−	0.607499i
$835$		0			0
$836$	−46.1406	−	63.5070i	−0.0551921	−	0.0759653i
$837$	−347.310	−	670.295i	−0.414946	−	0.800830i
$838$	−9.44223	−	6.86018i	−0.0112676	−	0.00818637i
$839$	−795.202	−	1094.50i	−0.947797	−	1.30453i	−0.952499	−	0.304542i	$-0.901497\pi$
$839$	−795.202	−	1094.50i	−0.947797	−	1.30453i	0.00470187	−	0.999989i	$-0.498503\pi$
$840$		0			0
$841$	−72.2106	−	52.4640i	−0.0858627	−	0.0623829i
$842$	−249.059	+	80.9242i	−0.295795	+	0.0961095i
$843$	−81.6603	+	523.278i	−0.0968687	+	0.620733i
$844$	161.903	+	498.285i	0.191828	+	0.590385i
$845$		0			0
$846$	−60.3467	+	83.8591i	−0.0713318	+	0.0991242i
$847$	−178.959	+	550.780i	−0.211286	+	0.650272i
$848$	−19.8026	−	27.2560i	−0.0233522	−	0.0321415i
$849$	−955.469	−	149.106i	−1.12541	−	0.175626i
$850$		0			0
$851$			0.752308i			0.000884028i
$852$	107.873	+	210.528i	0.126611	+	0.247099i
$853$	374.784	−	1153.47i	0.439372	−	1.35225i	−0.449167	−	0.893448i	$-0.648279\pi$
$853$	374.784	−	1153.47i	0.439372	−	1.35225i	0.888539	−	0.458800i	$-0.151721\pi$
$854$	−181.915	−	59.1076i	−0.213015	−	0.0692127i
$855$		0			0
$856$	−274.516	−	844.873i	−0.320696	−	0.987002i
$857$		−	549.363i		−	0.641031i	−0.947243	−	0.320515i	$-0.896144\pi$
$857$		−	549.363i		−	0.641031i	0.947243	−	0.320515i	$-0.103856\pi$
$858$	−71.4115	−	444.336i	−0.0832302	−	0.517874i
$859$	−414.050	−	300.825i	−0.482013	−	0.350203i	0.320091	−	0.947387i	$-0.396286\pi$
$859$	−414.050	−	300.825i	−0.482013	−	0.350203i	−0.802105	+	0.597183i	$0.796286\pi$
$860$		0			0
$861$	−1297.35	−	2531.96i	−1.50680	−	2.94072i
$862$	−831.486	−	604.110i	−0.964601	−	0.700823i
$863$	249.038	−	342.771i	0.288572	−	0.397185i	−0.639978	−	0.768394i	$-0.721056\pi$
$863$	249.038	−	342.771i	0.288572	−	0.397185i	0.928550	+	0.371208i	$0.121056\pi$
$864$	97.4611	+	589.310i	0.112802	+	0.682071i
$865$		0			0
$866$	1011.62	−	1392.38i	1.16816	−	1.60783i
$867$	−82.3238	−	512.234i	−0.0949525	−	0.590812i
$868$	507.743			0.584957
$869$	−209.910	+	68.2038i	−0.241553	+	0.0784854i
$870$		0			0
$871$	6.36113	−	19.5775i	0.00730325	−	0.0224771i
$872$	−843.984	−	274.227i	−0.967871	−	0.314480i
$873$	−255.498	+	84.3024i	−0.292667	+	0.0965663i
$874$	213.432			0.244201
$875$		0			0
$876$	−153.673	−	23.9815i	−0.175426	−	0.0273762i
$877$	90.3501	−	65.6432i	0.103022	−	0.0748497i	−0.535082	−	0.844800i	$-0.679719\pi$
$877$	90.3501	−	65.6432i	0.103022	−	0.0748497i	0.638103	+	0.769951i	$0.279719\pi$
$878$	413.349	+	134.305i	0.470784	+	0.152967i
$879$	−884.922	−	448.360i	−1.00674	−	0.510079i
$880$		0			0
$881$	264.217	−	85.8494i	0.299906	−	0.0974454i	−0.155199	−	0.987883i	$-0.549602\pi$
$881$	264.217	−	85.8494i	0.299906	−	0.0974454i	0.455105	+	0.890438i	$0.349602\pi$
$882$	695.084	−	2172.81i	0.788077	−	2.46350i
$883$	324.514	+	998.750i	0.367513	+	1.13109i	0.948393	+	0.317098i	$0.102709\pi$
$883$	324.514	+	998.750i	0.367513	+	1.13109i	−0.580880	+	0.813989i	$0.697291\pi$
$884$	45.5426	−	62.6840i	0.0515188	−	0.0709095i
$885$		0			0
$886$	896.236	−	651.153i	1.01155	−	0.734936i
$887$	−383.313	+	527.586i	−0.432146	+	0.594798i	−0.968444	−	0.249231i	$-0.919822\pi$
$887$	−383.313	+	527.586i	−0.432146	+	0.594798i	0.536298	+	0.844029i	$0.319822\pi$
$888$	0.435555	−	0.437539i	0.000490490	−	0.000492725i
$889$	1353.02	−	983.027i	1.52196	−	1.10577i
$890$		0			0
$891$	−992.921	+	332.630i	−1.11439	+	0.373322i
$892$	−101.996	−	313.911i	−0.114345	−	0.351918i
$893$		−	20.6489i		−	0.0231231i
$894$	127.277	+	791.940i	0.142368	+	0.885839i
$895$		0			0
$896$	1812.97	+	589.070i	2.02341	+	0.657444i
$897$	289.880	+	146.872i	0.323166	+	0.163737i
$898$	398.521	−	289.543i	0.443788	−	0.322431i
$899$			766.615i			0.852742i
$900$		0			0
$901$	18.4301			0.0204552
$902$	−1339.57	−	1843.76i	−1.48511	−	2.04408i
$903$	−738.672	+	1457.91i	−0.818020	+	1.61452i
$904$	−107.679	+	331.401i	−0.119114	+	0.366594i
$905$		0			0
$906$	1133.61	−	182.188i	1.25122	−	0.201091i
$907$	−1.34888			−0.00148718			−0.000743592	−	1.00000i	$-0.500237\pi$
$907$	−1.34888			−0.00148718			−0.000743592		1.00000i	$0.500237\pi$
$908$	427.435	−	138.882i	0.470743	−	0.152954i
$909$	−189.329	+	138.875i	−0.208283	+	0.152778i
$910$		0			0
$911$	−460.782	−	634.213i	−0.505798	−	0.696172i	0.477405	−	0.878683i	$-0.341577\pi$
$911$	−460.782	−	634.213i	−0.505798	−	0.696172i	−0.983204	+	0.182511i	$0.941577\pi$
$912$	−175.771	−	174.974i	−0.192732	−	0.191857i
$913$	598.812	+	435.062i	0.655873	+	0.476519i
$914$	485.052	+	667.617i	0.530692	+	0.730435i
$915$		0			0
$916$	−142.022	−	103.185i	−0.155046	−	0.112648i
$917$	2524.95	−	820.406i	2.75349	−	0.894663i
$918$	−606.942	−	304.057i	−0.661157	−	0.331217i
$919$	−10.8003	−	33.2399i	−0.0117522	−	0.0361697i	0.945008	−	0.327046i	$-0.106053\pi$
$919$	−10.8003	−	33.2399i	−0.0117522	−	0.0361697i	−0.956761	+	0.290876i	$0.906053\pi$
$920$		0			0
$921$	230.482	−	454.899i	0.250251	−	0.493918i
$922$	−215.337	+	662.740i	−0.233555	+	0.718807i
$923$	−159.319	−	219.284i	−0.172610	−	0.237578i
$924$	108.593	−	695.863i	0.117525	−	0.753098i
$925$		0			0
$926$		−	1211.45i		−	1.30826i
$927$	402.205	−	132.709i	0.433878	−	0.143159i
$928$	187.437	−	576.873i	0.201980	−	0.621630i
$929$	317.359	+	103.116i	0.341613	+	0.110997i	0.474799	−	0.880094i	$-0.342521\pi$
$929$	317.359	+	103.116i	0.341613	+	0.110997i	−0.133186	+	0.991091i	$0.542521\pi$
$930$		0			0
$931$	140.894	+	433.627i	0.151336	+	0.465765i
$932$			581.690i			0.624131i
$933$	1357.82	−	218.222i	1.45532	−	0.233892i
$934$	−805.331	−	585.108i	−0.862239	−	0.626453i
$935$		0			0
$936$	−83.5600	−	253.248i	−0.0892735	−	0.270564i
$937$	−215.649	−	156.678i	−0.230148	−	0.167213i	0.466735	−	0.884397i	$-0.345430\pi$
$937$	−215.649	−	156.678i	−0.230148	−	0.167213i	−0.696883	+	0.717185i	$0.745430\pi$
$938$	71.2981	−	98.1335i	0.0760108	−	0.104620i
$939$	−853.239	+	437.193i	−0.908668	+	0.465594i
$940$		0			0
$941$	−53.2570	+	73.3019i	−0.0565961	+	0.0778979i	−0.836377	−	0.548155i	$-0.815330\pi$
$941$	−53.2570	+	73.3019i	−0.0565961	+	0.0778979i	0.779781	+	0.626053i	$0.215330\pi$
$942$	−506.109	+	81.3394i	−0.537271	+	0.0863476i
$943$	1645.64			1.74511
$944$	−893.751	+	290.397i	−0.946770	+	0.307624i
$945$		0			0
$946$	−404.573	+	1245.15i	−0.427667	+	1.31622i
$947$	1251.99	+	406.796i	1.32206	+	0.429562i	0.883201	−	0.468995i	$-0.155384\pi$
$947$	1251.99	+	406.796i	1.32206	+	0.429562i	0.438856	+	0.898557i	$0.355384\pi$
$948$	65.9331	−	33.7836i	0.0695497	−	0.0356367i
$949$	178.213			0.187791
$950$		0			0
$951$	−113.541	+	727.566i	−0.119391	+	0.765053i
$952$	−652.081	+	473.765i	−0.684959	+	0.497652i
$953$	1641.62	+	533.396i	1.72259	+	0.559702i	0.992346	−	0.123488i	$-0.0394081\pi$
$953$	1641.62	+	533.396i	1.72259	+	0.559702i	0.730240	+	0.683190i	$0.239408\pi$
$954$	−20.9878	+	29.1651i	−0.0219998	+	0.0305714i
$955$		0			0
$956$	−270.055	+	87.7461i	−0.282484	+	0.0917846i
$957$	1050.65	+	163.959i	1.09786	+	0.171326i
$958$	212.701	+	654.627i	0.222026	+	0.683326i
$959$	1416.05	−	1949.03i	1.47660	−	2.03236i
$960$		0			0
$961$	144.991	−	105.342i	0.150875	−	0.109617i
$962$	0.235530	−	0.324179i	0.000244834	−	0.000336984i
$963$	−1081.79	+	793.507i	−1.12336	+	0.823995i
$964$	422.269	−	306.797i	0.438039	−	0.318254i
$965$		0			0
$966$	1357.10	+	1350.95i	1.40487	+	1.39850i
$967$	−224.851	−	692.020i	−0.232524	−	0.715636i	−0.997440	−	0.0715060i	$-0.977220\pi$
$967$	−224.851	−	692.020i	−0.232524	−	0.715636i	0.764916	−	0.644130i	$-0.222780\pi$
$968$			274.902i			0.283989i
$969$	133.957	−	21.5289i	0.138242	−	0.0222176i
$970$		0			0
$971$	−1094.40	−	355.593i	−1.12709	−	0.366213i	−0.314619	−	0.949218i	$-0.601877\pi$
$971$	−1094.40	−	355.593i	−1.12709	−	0.366213i	−0.812468	+	0.583005i	$0.801877\pi$
$972$	311.346	−	163.122i	0.320315	−	0.167821i
$973$	−1037.09	+	753.489i	−1.06587	+	0.774397i
$974$		−	1548.00i		−	1.58932i
$975$		0			0
$976$	−128.568			−0.131730
$977$	−155.757	−	214.381i	−0.159424	−	0.219428i	0.721831	−	0.692069i	$-0.243301\pi$
$977$	−155.757	−	214.381i	−0.159424	−	0.219428i	−0.881255	+	0.472641i	$0.843301\pi$
$978$	121.779	+	61.7012i	0.124518	+	0.0630892i
$979$	302.202	−	930.083i	0.308685	−	0.950034i
$980$		0			0
$981$	6.09231	+	1340.19i	0.00621030	+	1.36615i
$982$	1252.31			1.27526
$983$	−1540.75	+	500.620i	−1.56739	+	0.509277i	−0.958771	−	0.284181i	$-0.908278\pi$
$983$	−1540.75	+	500.620i	−1.56739	+	0.509277i	−0.608624	+	0.793459i	$0.708278\pi$
$984$	−957.095	−	952.754i	−0.972658	−	0.968246i
$985$		0			0
$986$	405.191	+	557.697i	0.410944	+	0.565616i
$987$	130.700	−	131.296i	0.132422	−	0.133025i
$988$	−24.4253	−	17.7460i	−0.0247219	−	0.0179615i
$989$	−555.674	−	764.819i	−0.561854	−	0.773326i
$990$		0			0
$991$	−262.932	−	191.031i	−0.265320	−	0.192766i	0.447169	−	0.894449i	$-0.352432\pi$
$991$	−262.932	−	191.031i	−0.265320	−	0.192766i	−0.712489	+	0.701683i	$0.752432\pi$
$992$	588.286	−	191.146i	0.593030	−	0.192687i
$993$	445.135	+	69.4657i	0.448273	+	0.0699554i
$994$	−493.560	−	1519.02i	−0.496540	−	1.52819i
$995$		0			0
$996$	−221.624	−	112.289i	−0.222514	−	0.112740i
$997$	−253.424	+	779.958i	−0.254186	+	0.782305i	0.739803	+	0.672824i	$0.234919\pi$
$997$	−253.424	+	779.958i	−0.254186	+	0.782305i	−0.993989	+	0.109481i	$0.965081\pi$
$998$	1085.36	+	1493.87i	1.08754	+	1.49687i
$999$	−0.833618	−	0.417614i	−0.000834452	−	0.000418032i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.3.j.b.176.27		144
3.2	odd	2	inner	375.3.j.b.176.9		144
5.2	odd	4		375.3.h.a.74.5		72
5.3	odd	4		75.3.h.a.14.14	yes	72
5.4	even	2	inner	375.3.j.b.176.10		144
15.2	even	4		375.3.h.a.74.14		72
15.8	even	4		75.3.h.a.14.5	✓	72
15.14	odd	2	inner	375.3.j.b.176.28		144
25.9	even	10	inner	375.3.j.b.326.28		144
25.12	odd	20		75.3.h.a.59.5	yes	72
25.13	odd	20		375.3.h.a.299.14		72
25.16	even	5	inner	375.3.j.b.326.9		144
75.38	even	20		375.3.h.a.299.5		72
75.41	odd	10	inner	375.3.j.b.326.27		144
75.59	odd	10	inner	375.3.j.b.326.10		144
75.62	even	20		75.3.h.a.59.14	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.3.h.a.14.5	✓	72	15.8	even	4
75.3.h.a.14.14	yes	72	5.3	odd	4
75.3.h.a.59.5	yes	72	25.12	odd	20
75.3.h.a.59.14	yes	72	75.62	even	20
375.3.h.a.74.5		72	5.2	odd	4
375.3.h.a.74.14		72	15.2	even	4
375.3.h.a.299.5		72	75.38	even	20
375.3.h.a.299.14		72	25.13	odd	20
375.3.j.b.176.9		144	3.2	odd	2	inner
375.3.j.b.176.10		144	5.4	even	2	inner
375.3.j.b.176.27		144	1.1	even	1	trivial
375.3.j.b.176.28		144	15.14	odd	2	inner
375.3.j.b.326.9		144	25.16	even	5	inner
375.3.j.b.326.10		144	75.59	odd	10	inner
375.3.j.b.326.27		144	75.41	odd	10	inner
375.3.j.b.326.28		144	25.9	even	10	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:	\( N \)	\(=\)	\( 375 = 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	375.j (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.37175 + 1.88806i) q^{2} +(-1.35589 + 2.67611i) q^{3} +(-0.446980 + 1.37566i) q^{4} +(-6.91259 + 1.11096i) q^{6} +12.5544 q^{7} +(5.66769 - 1.84155i) q^{8} +(-5.32311 - 7.25703i) q^{9} +O(q^{10})\)	\(q+(1.37175 + 1.88806i) q^{2} +(-1.35589 + 2.67611i) q^{3} +(-0.446980 + 1.37566i) q^{4} +(-6.91259 + 1.11096i) q^{6} +12.5544 q^{7} +(5.66769 - 1.84155i) q^{8} +(-5.32311 - 7.25703i) q^{9} +(7.59880 + 10.4589i) q^{11} +(-3.07537 - 3.06142i) q^{12} +(4.02255 + 2.92256i) q^{13} +(17.2215 + 23.7033i) q^{14} +(15.9325 + 11.5756i) q^{16} +(-10.2460 + 3.32914i) q^{17} +(6.39968 - 20.0052i) q^{18} +(1.29722 + 3.99244i) q^{19} +(-17.0224 + 33.5969i) q^{21} +(-9.32322 + 28.6939i) q^{22} +(-12.8053 - 17.6249i) q^{23} +(-2.75661 + 17.6643i) q^{24} +11.6038i q^{26} +(26.6382 - 4.40547i) q^{27} +(-5.61156 + 17.2706i) q^{28} +(-26.0760 - 8.47261i) q^{29} +(-8.64023 - 26.5919i) q^{31} +22.1228i q^{32} +(-38.2922 + 6.15414i) q^{33} +(-20.3406 - 14.7783i) q^{34} +(12.3626 - 4.07906i) q^{36} +(-0.0279372 - 0.0202976i) q^{37} +(-5.75848 + 7.92586i) q^{38} +(-13.2752 + 6.80212i) q^{39} +(-44.4000 + 61.1113i) q^{41} +(-86.7832 + 13.9474i) q^{42} +43.3942 q^{43} +(-17.7844 + 5.77849i) q^{44} +(15.7112 - 48.3541i) q^{46} +(-4.67812 - 1.52001i) q^{47} +(-52.5803 + 26.9417i) q^{48} +108.612 q^{49} +(4.98338 - 31.9334i) q^{51} +(-5.81846 + 4.22736i) q^{52} +(-1.62699 - 0.528642i) q^{53} +(44.8587 + 44.2511i) q^{54} +(71.1543 - 23.1194i) q^{56} +(-12.4431 - 1.94181i) q^{57} +(-19.7731 - 60.8553i) q^{58} +(-28.0481 + 38.6049i) q^{59} +(-5.28161 + 3.83732i) q^{61} +(38.3547 - 52.7907i) q^{62} +(-66.8283 - 91.1074i) q^{63} +(21.9608 - 15.9555i) q^{64} +(-64.1467 - 63.8558i) q^{66} +(-1.27935 - 3.93744i) q^{67} -15.5831i q^{68} +(64.5288 - 10.3708i) q^{69} +(-51.8456 - 16.8457i) q^{71} +(-43.5339 - 31.3279i) q^{72} +(28.9970 - 21.0676i) q^{73} -0.0805904i q^{74} -6.07208 q^{76} +(95.3981 + 131.304i) q^{77} +(-31.0531 - 15.7335i) q^{78} +(-5.27573 + 16.2370i) q^{79} +(-24.3290 + 77.2600i) q^{81} -176.287 q^{82} +(54.4519 - 17.6925i) q^{83} +(-38.6093 - 38.4342i) q^{84} +(59.5261 + 81.9306i) q^{86} +(58.0299 - 58.2943i) q^{87} +(62.3281 + 45.2840i) q^{88} +(-44.4639 - 61.1993i) q^{89} +(50.5006 + 36.6908i) q^{91} +(29.9697 - 9.73774i) q^{92} +(82.8780 + 12.9335i) q^{93} +(-3.54736 - 10.9176i) q^{94} +(-59.2029 - 29.9961i) q^{96} +(9.23778 - 28.4310i) q^{97} +(148.989 + 205.066i) q^{98} +(35.4509 - 110.818i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 76 q^{4} + 10 q^{6} + 26 q^{9}+O(q^{10}) \) 144 * q + 76 * q^4 + 10 * q^6 + 26 * q^9	\( 144 q + 76 q^{4} + 10 q^{6} + 26 q^{9} + 44 q^{16} + 72 q^{19} + 108 q^{21} + 40 q^{24} - 252 q^{31} - 420 q^{34} - 426 q^{36} + 382 q^{39} - 420 q^{46} + 448 q^{49} - 120 q^{51} - 640 q^{54} + 588 q^{61} - 724 q^{64} - 940 q^{66} - 670 q^{69} - 32 q^{76} + 692 q^{79} + 1014 q^{81} + 912 q^{84} + 1076 q^{91} + 1120 q^{94} + 1480 q^{96} - 120 q^{99}+O(q^{100}) \) 144 * q + 76 * q^4 + 10 * q^6 + 26 * q^9 + 44 * q^16 + 72 * q^19 + 108 * q^21 + 40 * q^24 - 252 * q^31 - 420 * q^34 - 426 * q^36 + 382 * q^39 - 420 * q^46 + 448 * q^49 - 120 * q^51 - 640 * q^54 + 588 * q^61 - 724 * q^64 - 940 * q^66 - 670 * q^69 - 32 * q^76 + 692 * q^79 + 1014 * q^81 + 912 * q^84 + 1076 * q^91 + 1120 * q^94 + 1480 * q^96 - 120 * q^99

Introduction

L-functions

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