LMFDB - Embedded newform 425.3.t.f.24.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [425,3,Mod(24,425)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("425.24"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(425, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([8, 11])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	425.t (of order $16$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [96,0,0,0,0,0,0,0,0,0,0,0,-24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.5804112353$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			24.5
Character	$\chi$	$=$	425.24
Dual form			425.3.t.f.124.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.808326 - 0.334820i) q^{2} +(2.20904 + 1.47604i) q^{3} +(-2.28714 - 2.28714i) q^{4} +(-1.29142 - 1.93275i) q^{6} +(11.7391 + 2.33505i) q^{7} +(2.42226 + 5.84784i) q^{8} +(-0.742961 - 1.79367i) q^{9} +(7.28271 - 4.86615i) q^{11} +(-1.67649 - 8.42829i) q^{12} +(-17.5907 - 17.5907i) q^{13} +(-8.70718 - 5.81795i) q^{14} +7.40003i q^{16} +(15.4018 + 7.19617i) q^{17} +1.69863i q^{18} +(-5.64227 + 13.6217i) q^{19} +(22.4855 + 22.4855i) q^{21} +(-7.51609 + 1.49504i) q^{22} +(4.10923 - 2.74570i) q^{23} +(-3.28075 + 16.4935i) q^{24} +(8.32930 + 20.1087i) q^{26} +(5.67111 - 28.5106i) q^{27} +(-21.5083 - 32.1895i) q^{28} +(21.8020 - 4.33668i) q^{29} +(17.4150 + 11.6363i) q^{31} +(12.1667 - 29.3730i) q^{32} +23.2704 q^{33} +(-10.0403 - 10.9737i) q^{34} +(-2.40311 + 5.80162i) q^{36} +(11.9671 + 7.99619i) q^{37} +(9.12160 - 9.12160i) q^{38} +(-12.8941 - 64.8230i) q^{39} +(11.6758 - 58.6981i) q^{41} +(-10.6470 - 25.7042i) q^{42} +(62.8891 - 26.0495i) q^{43} +(-27.7861 - 5.52701i) q^{44} +(-4.24091 + 0.843569i) q^{46} +(-56.8070 - 56.8070i) q^{47} +(-10.9227 + 16.3470i) q^{48} +(87.0832 + 36.0710i) q^{49} +(23.4014 + 38.6302i) q^{51} +80.4646i q^{52} +(61.3341 + 25.4054i) q^{53} +(-14.1300 + 21.1471i) q^{54} +(14.7800 + 74.3043i) q^{56} +(-32.5701 + 21.7626i) q^{57} +(-19.0751 - 3.79427i) q^{58} +(-86.4081 + 35.7914i) q^{59} +(64.7697 + 12.8835i) q^{61} +(-10.1809 - 15.2368i) q^{62} +(-4.53338 - 22.7908i) q^{63} +(1.26113 - 1.26113i) q^{64} +(-18.8101 - 7.79140i) q^{66} +40.8378 q^{67} +(-18.7674 - 51.6847i) q^{68} +13.1302 q^{69} +(-24.8785 + 37.2333i) q^{71} +(8.68944 - 8.68944i) q^{72} +(-44.6004 + 8.87157i) q^{73} +(-6.99607 - 10.4704i) q^{74} +(44.0593 - 18.2500i) q^{76} +(96.8549 - 40.1186i) q^{77} +(-11.2814 + 56.7153i) q^{78} +(-35.0256 + 23.4033i) q^{79} +(42.2551 - 42.2551i) q^{81} +(-29.0911 + 43.5380i) q^{82} +(8.72588 - 21.0661i) q^{83} -102.855i q^{84} -59.5569 q^{86} +(54.5625 + 22.6005i) q^{87} +(46.0970 + 30.8011i) q^{88} +(-36.9839 - 36.9839i) q^{89} +(-165.423 - 247.573i) q^{91} +(-15.6782 - 3.11858i) q^{92} +(21.2948 + 51.4102i) q^{93} +(26.8985 + 64.9388i) q^{94} +(70.2323 - 46.9277i) q^{96} +(2.53031 + 12.7207i) q^{97} +(-58.3143 - 58.3143i) q^{98} +(-14.1390 - 9.44739i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 24 q^{13} - 32 q^{14} + 64 q^{17} + 24 q^{19} + 48 q^{22} + 72 q^{23} + 336 q^{24} - 224 q^{26} - 64 q^{31} + 400 q^{32} - 256 q^{33} - 64 q^{34} + 192 q^{36} + 72 q^{37} + 496 q^{38} - 16 q^{39}+ \cdots + 160 q^{99}+O(q^{100}) $ 96 * q - 24 * q^13 - 32 * q^14 + 64 * q^17 + 24 * q^19 + 48 * q^22 + 72 * q^23 + 336 * q^24 - 224 * q^26 - 64 * q^31 + 400 * q^32 - 256 * q^33 - 64 * q^34 + 192 * q^36 + 72 * q^37 + 496 * q^38 - 16 * q^39 + 216 * q^41 - 248 * q^42 - 64 * q^43 + 32 * q^44 + 336 * q^46 + 32 * q^49 - 32 * q^51 - 104 * q^53 - 584 * q^54 - 40 * q^56 + 336 * q^57 + 1088 * q^58 - 544 * q^59 + 112 * q^61 + 152 * q^62 - 1184 * q^63 - 592 * q^64 - 24 * q^66 - 144 * q^67 + 520 * q^68 + 192 * q^69 - 336 * q^71 - 1040 * q^72 + 336 * q^74 - 1016 * q^76 + 720 * q^77 + 1568 * q^78 + 384 * q^79 - 928 * q^81 + 288 * q^82 - 1200 * q^83 + 64 * q^86 - 384 * q^87 + 576 * q^88 - 576 * q^89 + 336 * q^91 - 640 * q^92 - 672 * q^94 + 768 * q^96 + 1440 * q^97 - 408 * q^98 + 160 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$-1$	$e\left(\frac{11}{16}\right)$

Coefficient data

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

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

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

$2$	−0.808326	−	0.334820i	−0.404163	−	0.167410i	0.171335	−	0.985213i	$-0.445192\pi$
$2$	−0.808326	−	0.334820i	−0.404163	−	0.167410i	−0.575498	+	0.817803i	$0.695192\pi$
$3$	2.20904	+	1.47604i	0.736348	+	0.492012i	0.866310	−	0.499507i	$-0.166486\pi$
$3$	2.20904	+	1.47604i	0.736348	+	0.492012i	−0.129962	+	0.991519i	$0.541486\pi$
$4$	−2.28714	−	2.28714i	−0.571785	−	0.571785i
$5$		0			0
$5$		0			0
$6$	−1.29142	−	1.93275i	−0.215237	−	0.322125i
$7$	11.7391	+	2.33505i	1.67701	+	0.333578i	0.939706	−	0.341983i	$-0.111099\pi$
$7$	11.7391	+	2.33505i	1.67701	+	0.333578i	0.737304	+	0.675561i	$0.236099\pi$
$8$	2.42226	+	5.84784i	0.302782	+	0.730980i
$9$	−0.742961	−	1.79367i	−0.0825513	−	0.199296i
$10$		0			0
$11$	7.28271	−	4.86615i	0.662064	−	0.442377i	−0.178609	−	0.983920i	$-0.557160\pi$
$11$	7.28271	−	4.86615i	0.662064	−	0.442377i	0.840673	+	0.541543i	$0.182160\pi$
$12$	−1.67649	−	8.42829i	−0.139708	−	0.702357i
$13$	−17.5907	−	17.5907i	−1.35313	−	1.35313i	−0.882139	−	0.470989i	$-0.843897\pi$
$13$	−17.5907	−	17.5907i	−1.35313	−	1.35313i	−0.470989	−	0.882139i	$-0.656103\pi$
$14$	−8.70718	−	5.81795i	−0.621941	−	0.415568i
$15$		0			0
$16$			7.40003i			0.462502i
$17$	15.4018	+	7.19617i	0.905988	+	0.423304i
$17$	15.4018	+	7.19617i	0.905988	+	0.423304i
$18$			1.69863i			0.0943682i
$19$	−5.64227	+	13.6217i	−0.296962	+	0.716929i	0.703022	+	0.711168i	$0.251834\pi$
$19$	−5.64227	+	13.6217i	−0.296962	+	0.716929i	−0.999983	+	0.00576061i	$0.998166\pi$
$20$		0			0
$21$	22.4855	+	22.4855i	1.07074	+	1.07074i
$22$	−7.51609	+	1.49504i	−0.341640	+	0.0679565i
$23$	4.10923	−	2.74570i	0.178662	−	0.119378i	−0.463024	−	0.886346i	$-0.653235\pi$
$23$	4.10923	−	2.74570i	0.178662	−	0.119378i	0.641685	+	0.766968i	$0.278235\pi$
$24$	−3.28075	+	16.4935i	−0.136698	+	0.687228i
$25$		0			0
$26$	8.32930	+	20.1087i	0.320358	+	0.773412i
$27$	5.67111	−	28.5106i	0.210041	−	1.05595i
$28$	−21.5083	−	32.1895i	−0.768154	−	1.14962i
$29$	21.8020	−	4.33668i	0.751792	−	0.149541i	0.195702	−	0.980663i	$-0.437301\pi$
$29$	21.8020	−	4.33668i	0.751792	−	0.149541i	0.556089	+	0.831123i	$0.312301\pi$
$30$		0			0
$31$	17.4150	+	11.6363i	0.561773	+	0.375365i	0.803795	−	0.594906i	$-0.202811\pi$
$31$	17.4150	+	11.6363i	0.561773	+	0.375365i	−0.242022	+	0.970271i	$0.577811\pi$
$32$	12.1667	−	29.3730i	0.380209	−	0.917906i
$33$	23.2704			0.705164
$34$	−10.0403	−	10.9737i	−0.295302	−	0.322755i
$35$		0			0
$36$	−2.40311	+	5.80162i	−0.0667531	+	0.161156i
$37$	11.9671	+	7.99619i	0.323436	+	0.216113i	0.706679	−	0.707535i	$-0.250193\pi$
$37$	11.9671	+	7.99619i	0.323436	+	0.216113i	−0.383243	+	0.923648i	$0.625193\pi$
$38$	9.12160	−	9.12160i	0.240042	−	0.240042i
$39$	−12.8941	−	64.8230i	−0.330618	−	1.66213i
$40$		0			0
$41$	11.6758	−	58.6981i	0.284775	−	1.43166i	−0.528079	−	0.849195i	$-0.677088\pi$
$41$	11.6758	−	58.6981i	0.284775	−	1.43166i	0.812854	−	0.582467i	$-0.197912\pi$
$42$	−10.6470	−	25.7042i	−0.253501	−	0.612005i
$43$	62.8891	−	26.0495i	1.46254	−	0.605803i	0.497395	−	0.867524i	$-0.334290\pi$
$43$	62.8891	−	26.0495i	1.46254	−	0.605803i	0.965144	+	0.261721i	$0.0842901\pi$
$44$	−27.7861	−	5.52701i	−0.631503	−	0.125614i
$45$		0			0
$46$	−4.24091	+	0.843569i	−0.0921937	+	0.0183385i
$47$	−56.8070	−	56.8070i	−1.20866	−	1.20866i	−0.971461	−	0.237199i	$-0.923771\pi$
$47$	−56.8070	−	56.8070i	−1.20866	−	1.20866i	−0.237199	−	0.971461i	$-0.576229\pi$
$48$	−10.9227	+	16.3470i	−0.227556	+	0.340562i
$49$	87.0832	+	36.0710i	1.77721	+	0.736144i
$50$		0			0
$51$	23.4014	+	38.6302i	0.458851	+	0.757455i
$52$			80.4646i			1.54740i
$53$	61.3341	+	25.4054i	1.15725	+	0.479347i	0.876957	−	0.480568i	$-0.159570\pi$
$53$	61.3341	+	25.4054i	1.15725	+	0.479347i	0.280289	+	0.959916i	$0.409570\pi$
$54$	−14.1300	+	21.1471i	−0.261667	+	0.391613i
$55$		0			0
$56$	14.7800	+	74.3043i	0.263929	+	1.32686i
$57$	−32.5701	+	21.7626i	−0.571404	+	0.381800i
$58$	−19.0751	−	3.79427i	−0.328881	−	0.0654185i
$59$	−86.4081	+	35.7914i	−1.46454	+	0.606634i	−0.965607	−	0.260005i	$-0.916276\pi$
$59$	−86.4081	+	35.7914i	−1.46454	+	0.606634i	−0.498936	+	0.866639i	$0.666276\pi$
$60$		0			0
$61$	64.7697	+	12.8835i	1.06180	+	0.211205i	0.694937	−	0.719071i	$-0.255432\pi$
$61$	64.7697	+	12.8835i	1.06180	+	0.211205i	0.366861	+	0.930276i	$0.380432\pi$
$62$	−10.1809	−	15.2368i	−0.164208	−	0.245755i
$63$	−4.53338	−	22.7908i	−0.0719584	−	0.361759i
$64$	1.26113	−	1.26113i	0.0197051	−	0.0197051i
$65$		0			0
$66$	−18.8101	−	7.79140i	−0.285001	−	0.118051i
$67$	40.8378			0.609520			0.304760	−	0.952429i	$-0.401424\pi$
$67$	40.8378			0.609520			0.304760	+	0.952429i	$0.401424\pi$
$68$	−18.7674	−	51.6847i	−0.275991	−	0.760069i
$69$	13.1302			0.190293
$70$		0			0
$71$	−24.8785	+	37.2333i	−0.350402	+	0.524413i	−0.964244	−	0.265015i	$-0.914623\pi$
$71$	−24.8785	+	37.2333i	−0.350402	+	0.524413i	0.613842	+	0.789429i	$0.289623\pi$
$72$	8.68944	−	8.68944i	0.120687	−	0.120687i
$73$	−44.6004	+	8.87157i	−0.610964	+	0.121528i	−0.490868	−	0.871234i	$-0.663320\pi$
$73$	−44.6004	+	8.87157i	−0.610964	+	0.121528i	−0.120096	+	0.992762i	$0.538320\pi$
$74$	−6.99607	−	10.4704i	−0.0945415	−	0.141491i
$75$		0			0
$76$	44.0593	−	18.2500i	0.579727	−	0.240131i
$77$	96.8549	−	40.1186i	1.25786	−	0.521021i
$78$	−11.2814	+	56.7153i	−0.144633	+	0.727120i
$79$	−35.0256	+	23.4033i	−0.443361	+	0.296245i	−0.757141	−	0.653251i	$-0.773405\pi$
$79$	−35.0256	+	23.4033i	−0.443361	+	0.296245i	0.313780	+	0.949496i	$0.398405\pi$
$80$		0			0
$81$	42.2551	−	42.2551i	0.521668	−	0.521668i
$82$	−29.0911	+	43.5380i	−0.354770	+	0.530951i
$83$	8.72588	−	21.0661i	0.105131	−	0.253809i	−0.862557	−	0.505960i	$-0.831138\pi$
$83$	8.72588	−	21.0661i	0.105131	−	0.253809i	0.967688	+	0.252152i	$0.0811382\pi$
$84$		−	102.855i		−	1.22446i
$85$		0			0
$86$	−59.5569			−0.692522
$87$	54.5625	+	22.6005i	0.627156	+	0.259776i
$88$	46.0970	+	30.8011i	0.523830	+	0.350012i
$89$	−36.9839	−	36.9839i	−0.415550	−	0.415550i	0.468117	−	0.883667i	$-0.344933\pi$
$89$	−36.9839	−	36.9839i	−0.415550	−	0.415550i	−0.883667	+	0.468117i	$0.844933\pi$
$90$		0			0
$91$	−165.423	−	247.573i	−1.81784	−	2.72058i
$92$	−15.6782	−	3.11858i	−0.170415	−	0.0338976i
$93$	21.2948	+	51.4102i	0.228976	+	0.552798i
$94$	26.8985	+	64.9388i	0.286154	+	0.690838i
$95$		0			0
$96$	70.2323	−	46.9277i	0.731587	−	0.488831i
$97$	2.53031	+	12.7207i	0.0260857	+	0.131142i	0.991634	−	0.129083i	$-0.0412034\pi$
$97$	2.53031	+	12.7207i	0.0260857	+	0.131142i	−0.965548	+	0.260225i	$0.916203\pi$
$98$	−58.3143	−	58.3143i	−0.595044	−	0.595044i
$99$	−14.1390	−	9.44739i	−0.142818	−	0.0954282i
$100$		0			0
$101$			72.9595i			0.722371i	0.932494	+	0.361186i	$0.117628\pi$
$101$			72.9595i			0.722371i	−0.932494	+	0.361186i	$0.882372\pi$
$102$	−5.98182	−	39.0611i	−0.0586453	−	0.382952i
$103$			69.3005i			0.672820i	0.941716	+	0.336410i	$0.109213\pi$
$103$			69.3005i			0.672820i	−0.941716	+	0.336410i	$0.890787\pi$
$104$	60.2583	−	145.477i	0.579407	−	1.39881i
$105$		0			0
$106$	−41.0717	−	41.0717i	−0.387469	−	0.387469i
$107$	−27.9584	+	5.56128i	−0.261294	+	0.0519745i	−0.323999	−	0.946058i	$-0.605027\pi$
$107$	−27.9584	+	5.56128i	−0.261294	+	0.0519745i	0.0627049	+	0.998032i	$0.480027\pi$
$108$	−78.1784	+	52.2371i	−0.723874	+	0.483677i
$109$	−14.0628	+	70.6985i	−0.129017	+	0.648610i	0.861108	+	0.508422i	$0.169771\pi$
$109$	−14.0628	+	70.6985i	−0.129017	+	0.648610i	−0.990125	+	0.140188i	$0.955229\pi$
$110$		0			0
$111$	14.6333	+	35.3278i	0.131831	+	0.318269i
$112$	−17.2794	+	86.8695i	−0.154280	+	0.775620i
$113$	15.5255	+	23.2356i	0.137394	+	0.205625i	0.893786	−	0.448494i	$-0.148040\pi$
$113$	15.5255	+	23.2356i	0.137394	+	0.205625i	−0.756392	+	0.654119i	$0.773040\pi$
$114$	33.6138	−	6.68620i	0.294858	−	0.0586509i
$115$		0			0
$116$	−59.7827	−	39.9455i	−0.515368	−	0.344358i
$117$	−18.4826	+	44.6210i	−0.157971	+	0.381376i
$118$	81.8296			0.693471
$119$	163.999	+	120.440i	1.37815	+	1.01210i
$120$		0			0
$121$	−16.9463	+	40.9119i	−0.140052	+	0.338115i
$122$	−48.0414	−	32.1002i	−0.393782	−	0.263117i
$123$	112.433	−	112.433i	0.914088	−	0.914088i
$124$	−13.2166	−	66.4443i	−0.106585	−	0.535841i
$125$		0			0
$126$	−3.96637	+	19.9403i	−0.0314791	+	0.158256i
$127$	−22.0759	−	53.2959i	−0.173826	−	0.419652i	0.812824	−	0.582509i	$-0.197929\pi$
$127$	−22.0759	−	53.2959i	−0.173826	−	0.419652i	−0.986650	+	0.162857i	$0.947929\pi$
$128$	−118.934	+	49.2639i	−0.929169	+	0.384875i
$129$	177.375	+	35.2820i	1.37500	+	0.273504i
$130$		0			0
$131$	−228.910	+	45.5330i	−1.74740	+	0.347580i	−0.962343	−	0.271837i	$-0.912369\pi$
$131$	−228.910	+	45.5330i	−1.74740	+	0.347580i	−0.785061	+	0.619418i	$0.787369\pi$
$132$	−53.2227	−	53.2227i	−0.403202	−	0.403202i
$133$	−98.0422	+	146.731i	−0.737159	+	1.10324i
$134$	−33.0103	−	13.6733i	−0.246345	−	0.102040i
$135$		0			0
$136$	−4.77498	+	107.498i	−0.0351102	+	0.790428i
$137$			133.676i			0.975739i	0.872916	+	0.487870i	$0.162226\pi$
$137$			133.676i			0.975739i	−0.872916	+	0.487870i	$0.837774\pi$
$138$	−10.6135	−	4.39625i	−0.0769093	−	0.0318569i
$139$	−0.828008	+	1.23920i	−0.00595689	+	0.00891512i	−0.834436	−	0.551105i	$-0.814206\pi$
$139$	−0.828008	+	1.23920i	−0.00595689	+	0.00891512i	0.828479	+	0.560020i	$0.189206\pi$
$140$		0			0
$141$	−41.6400	−	209.338i	−0.295319	−	1.48467i
$142$	32.5764	−	21.7669i	0.229411	−	0.153288i
$143$	−213.706	−	42.5089i	−1.49445	−	0.297265i
$144$	13.2732	−	5.49794i	0.0921750	−	0.0381801i
$145$		0			0
$146$	39.0220	+	7.76197i	0.267274	+	0.0531642i
$147$	139.128	+	208.220i	0.946451	+	1.41646i
$148$	−9.08212	−	45.6589i	−0.0613657	−	0.308506i
$149$	−44.2723	+	44.2723i	−0.297129	+	0.297129i	−0.839888	−	0.542759i	$-0.817380\pi$
$149$	−44.2723	+	44.2723i	−0.297129	+	0.297129i	0.542759	+	0.839888i	$0.317380\pi$
$150$		0			0
$151$	−96.5922	−	40.0098i	−0.639683	−	0.264965i	0.0391778	−	0.999232i	$-0.487526\pi$
$151$	−96.5922	−	40.0098i	−0.639683	−	0.264965i	−0.678861	+	0.734267i	$0.737526\pi$
$152$	−93.3243			−0.613975
$153$	1.46460	−	32.9722i	0.00957253	−	0.215504i
$154$	−91.7229			−0.595603
$155$		0			0
$156$	−118.769	+	177.750i	−0.761337	+	1.13942i
$157$	100.230	−	100.230i	0.638406	−	0.638406i	−0.311756	−	0.950162i	$-0.600917\pi$
$157$	100.230	−	100.230i	0.638406	−	0.638406i	0.950162	+	0.311756i	$0.100917\pi$
$158$	36.1480	−	7.19028i	0.228785	−	0.0455081i
$159$	97.9903	+	146.653i	0.616291	+	0.922345i
$160$		0			0
$161$	54.6498	−	22.6367i	0.339440	−	0.140601i
$162$	−48.3037	+	20.0081i	−0.298171	+	0.123507i
$163$	4.49551	−	22.6005i	0.0275798	−	0.138653i	−0.964542	−	0.263929i	$-0.914982\pi$
$163$	4.49551	−	22.6005i	0.0275798	−	0.138653i	0.992122	+	0.125276i	$0.0399816\pi$
$164$	−160.955	+	107.547i	−0.981433	+	0.655773i
$165$		0			0
$166$	−14.1067	+	14.1067i	−0.0849802	+	0.0849802i
$167$	−104.568	+	156.497i	−0.626156	+	0.937108i	0.373798	+	0.927510i	$0.378055\pi$
$167$	−104.568	+	156.497i	−0.626156	+	0.937108i	−0.999954	+	0.00959805i	$0.996945\pi$
$168$	−77.0260	+	185.957i	−0.458488	+	1.10689i
$169$			449.863i			2.66191i
$170$		0			0
$171$	28.6247			0.167396
$172$	−203.415	−	84.2573i	−1.18265	−	0.489868i
$173$	−183.149	−	122.377i	−1.05867	−	0.707379i	−0.100892	−	0.994897i	$-0.532170\pi$
$173$	−183.149	−	122.377i	−1.05867	−	0.707379i	−0.957775	+	0.287519i	$0.907170\pi$
$174$	−36.5372	−	36.5372i	−0.209984	−	0.209984i
$175$		0			0
$176$	36.0097	+	53.8923i	0.204600	+	0.306206i
$177$	−243.708	−	48.4766i	−1.37688	−	0.273879i
$178$	17.5121	+	42.2781i	0.0983828	+	0.237517i
$179$	−65.5165	−	158.171i	−0.366014	−	0.883636i	−0.994395	−	0.105730i	$-0.966282\pi$
$179$	−65.5165	−	158.171i	−0.366014	−	0.883636i	0.628381	−	0.777906i	$-0.283718\pi$
$180$		0			0
$181$	−5.80388	+	3.87803i	−0.0320656	+	0.0214256i	−0.571500	−	0.820602i	$-0.693638\pi$
$181$	−5.80388	+	3.87803i	−0.0320656	+	0.0214256i	0.539434	+	0.842028i	$0.318638\pi$
$182$	50.8235	+	255.507i	0.279250	+	1.40388i
$183$	124.063	+	124.063i	0.677937	+	0.677937i
$184$	26.0100	+	17.3793i	0.141359	+	0.0944528i
$185$		0			0
$186$		−	48.6862i		−	0.261754i
$187$	147.184	−	22.5398i	0.787082	−	0.120534i
$188$			259.851i			1.38219i
$189$	133.147	−	321.446i	0.704482	−	1.70077i
$190$		0			0
$191$	82.3988	+	82.3988i	0.431407	+	0.431407i	0.889107	−	0.457700i	$-0.151326\pi$
$191$	82.3988	+	82.3988i	0.431407	+	0.431407i	−0.457700	+	0.889107i	$0.651326\pi$
$192$	4.64735	−	0.924416i	0.0242050	−	0.00481467i
$193$	138.082	−	92.2635i	0.715451	−	0.478049i	−0.143798	−	0.989607i	$-0.545931\pi$
$193$	138.082	−	92.2635i	0.715451	−	0.478049i	0.859249	+	0.511558i	$0.170931\pi$
$194$	2.21384	−	11.1297i	0.0114115	−	0.0573696i
$195$		0			0
$196$	−116.672	−	281.671i	−0.595265	−	1.43710i
$197$	26.2969	−	132.204i	0.133487	−	0.671084i	−0.854859	−	0.518860i	$-0.826356\pi$
$197$	26.2969	−	132.204i	0.133487	−	0.671084i	0.988346	−	0.152224i	$-0.0486435\pi$
$198$	8.26577	+	12.3706i	0.0417463	+	0.0624778i
$199$	−103.420	+	20.5715i	−0.519697	+	0.103374i	−0.447967	−	0.894050i	$-0.647852\pi$
$199$	−103.420	+	20.5715i	−0.519697	+	0.103374i	−0.0717299	+	0.997424i	$0.522852\pi$
$200$		0			0
$201$	90.2125	+	60.2780i	0.448818	+	0.299891i
$202$	24.4283	−	58.9751i	0.120932	−	0.291956i
$203$	266.061			1.31065
$204$	34.8304	−	141.875i	0.170737	−	0.695466i
$205$		0			0
$206$	23.2032	−	56.0174i	0.112637	−	0.271929i
$207$	−7.97786	−	5.33064i	−0.0385404	−	0.0257519i
$208$	130.172	−	130.172i	0.625825	−	0.625825i
$209$	25.1940	+	126.659i	0.120545	+	0.606022i
$210$		0			0
$211$	−35.8907	+	180.435i	−0.170098	+	0.855141i	0.797631	+	0.603146i	$0.206087\pi$
$211$	−35.8907	+	180.435i	−0.170098	+	0.855141i	−0.967729	+	0.251995i	$0.918913\pi$
$212$	−82.1739	−	198.385i	−0.387613	−	0.935780i
$213$	−109.915	+	45.5285i	−0.516035	+	0.213749i
$214$	24.4616	+	4.86571i	0.114306	+	0.0227369i
$215$		0			0
$216$	180.462	−	35.8962i	0.835474	−	0.166186i
$217$	177.264	+	177.264i	0.816886	+	0.816886i
$218$	35.0386	−	52.4390i	0.160727	−	0.240546i
$219$	−111.619	−	46.2341i	−0.509675	−	0.211114i
$220$		0			0
$221$	−144.342	−	397.513i	−0.653133	−	1.79870i
$222$		−	33.4559i		−	0.150702i
$223$	70.2118	+	29.0827i	0.314851	+	0.130416i	0.534512	−	0.845161i	$-0.320495\pi$
$223$	70.2118	+	29.0827i	0.314851	+	0.130416i	−0.219661	+	0.975576i	$0.570495\pi$
$224$	211.413	−	316.402i	0.943808	−	1.41251i
$225$		0			0
$226$	−4.76996	−	23.9802i	−0.0211060	−	0.106107i
$227$	104.541	−	69.8522i	0.460534	−	0.307719i	−0.303574	−	0.952808i	$-0.598180\pi$
$227$	104.541	−	69.8522i	0.460534	−	0.307719i	0.764107	+	0.645089i	$0.223180\pi$
$228$	124.266	+	24.7181i	0.545028	+	0.108413i
$229$	−304.241	+	126.021i	−1.32856	+	0.550309i	−0.930245	−	0.366938i	$-0.880406\pi$
$229$	−304.241	+	126.021i	−1.32856	+	0.550309i	−0.398318	+	0.917247i	$0.630406\pi$
$230$		0			0
$231$	273.173	+	54.3375i	1.18257	+	0.235227i
$232$	78.1701	+	116.990i	0.336940	+	0.504267i
$233$	−42.8588	−	215.466i	−0.183943	−	0.924746i	−0.956929	−	0.290322i	$-0.906238\pi$
$233$	−42.8588	−	215.466i	−0.183943	−	0.924746i	0.772986	−	0.634424i	$-0.218762\pi$
$234$	29.8800	−	29.8800i	0.127692	−	0.127692i
$235$		0			0
$236$	279.487	+	115.767i	1.18427	+	0.490540i
$237$	−111.917			−0.472224
$238$	−92.2392	−	152.265i	−0.387560	−	0.639770i
$239$	100.337			0.419822			0.209911	−	0.977721i	$-0.432683\pi$
$239$	100.337			0.419822			0.209911	+	0.977721i	$0.432683\pi$
$240$		0			0
$241$	−38.3073	+	57.3310i	−0.158952	+	0.237888i	−0.902394	−	0.430912i	$-0.858192\pi$
$241$	−38.3073	+	57.3310i	−0.158952	+	0.237888i	0.743442	+	0.668800i	$0.233192\pi$
$242$	27.3963	−	27.3963i	0.113208	−	0.113208i
$243$	−100.882	+	20.0667i	−0.415153	+	0.0825792i
$244$	−118.671	−	177.604i	−0.486357	−	0.727884i
$245$		0			0
$246$	−128.527	+	53.2377i	−0.522468	+	0.216413i
$247$	338.865	−	140.363i	1.37192	−	0.568270i
$248$	−25.8638	+	130.026i	−0.104289	+	0.524299i
$249$	50.3702	−	33.6563i	0.202290	−	0.135166i
$250$		0			0
$251$	−265.197	+	265.197i	−1.05656	+	1.05656i	−0.0582606	+	0.998301i	$0.518555\pi$
$251$	−265.197	+	265.197i	−1.05656	+	1.05656i	−0.998301	+	0.0582606i	$0.981445\pi$
$252$	−41.7573	+	62.4943i	−0.165704	+	0.247993i
$253$	16.5653	−	39.9922i	0.0654755	−	0.158072i
$254$			50.4719i			0.198708i
$255$		0			0
$256$	105.498			0.412101
$257$	−281.727	−	116.695i	−1.09621	−	0.454066i	−0.240044	−	0.970762i	$-0.577162\pi$
$257$	−281.727	−	116.695i	−1.09621	−	0.454066i	−0.856169	+	0.516696i	$0.827162\pi$
$258$	−131.564	−	87.9080i	−0.509937	−	0.340729i
$259$	121.812	+	121.812i	0.470315	+	0.470315i
$260$		0			0
$261$	−23.9766	−	35.8835i	−0.0918643	−	0.137485i
$262$	200.279	+	39.8380i	0.764425	+	0.152054i
$263$	127.534	+	307.894i	0.484919	+	1.17070i	0.957246	+	0.289275i	$0.0934141\pi$
$263$	127.534	+	307.894i	0.484919	+	1.17070i	−0.472327	+	0.881423i	$0.656586\pi$
$264$	56.3669	+	136.082i	0.213511	+	0.515461i
$265$		0			0
$266$	128.378	−	85.7797i	0.482626	−	0.322480i
$267$	−27.1095	−	136.289i	−0.101534	−	0.510445i
$268$	−93.4018	−	93.4018i	−0.348514	−	0.348514i
$269$	−249.325	−	166.594i	−0.926859	−	0.619308i	−0.00215658	−	0.999998i	$-0.500686\pi$
$269$	−249.325	−	166.594i	−0.926859	−	0.619308i	−0.924703	+	0.380690i	$0.875686\pi$
$270$		0			0
$271$			139.013i			0.512963i	0.966549	+	0.256481i	$0.0825633\pi$
$271$			139.013i			0.512963i	−0.966549	+	0.256481i	$0.917437\pi$
$272$	−53.2519	+	113.974i	−0.195779	+	0.419021i
$273$		−	791.070i		−	2.89769i
$274$	44.7575	−	108.054i	0.163348	−	0.394358i
$275$		0			0
$276$	−30.0306	−	30.0306i	−0.108807	−	0.108807i
$277$	96.8761	−	19.2699i	0.349733	−	0.0695662i	−0.0170979	−	0.999854i	$-0.505443\pi$
$277$	96.8761	−	19.2699i	0.349733	−	0.0695662i	0.366831	+	0.930288i	$0.380443\pi$
$278$	1.08421	−	0.724446i	0.00390003	−	0.00260592i
$279$	7.93302	−	39.8820i	0.0284338	−	0.142946i
$280$		0			0
$281$	−0.465552	−	1.12394i	−0.00165677	−	0.00399979i	0.923049	−	0.384682i	$-0.125689\pi$
$281$	−0.465552	−	1.12394i	−0.00165677	−	0.00399979i	−0.924706	+	0.380683i	$0.875689\pi$
$282$	−36.4319	+	183.156i	−0.129191	+	0.649488i
$283$	85.5380	+	128.017i	0.302254	+	0.452355i	0.951243	−	0.308443i	$-0.0998078\pi$
$283$	85.5380	+	128.017i	0.302254	+	0.452355i	−0.648989	+	0.760798i	$0.724808\pi$
$284$	142.059	−	28.2572i	0.500206	−	0.0994972i
$285$		0			0
$286$	158.512	+	105.914i	0.554237	+	0.370329i
$287$	274.126	−	661.798i	0.955142	−	2.30592i
$288$	−61.7248			−0.214322
$289$	185.430	+	221.668i	0.641627	+	0.767016i
$290$		0			0
$291$	−13.1867	+	31.8355i	−0.0453151	+	0.109400i
$292$	122.298	+	81.7168i	0.418828	+	0.279852i
$293$	132.488	−	132.488i	0.452176	−	0.452176i	−0.443900	−	0.896076i	$-0.646406\pi$
$293$	132.488	−	132.488i	0.452176	−	0.452176i	0.896076	+	0.443900i	$0.146406\pi$
$294$	−42.7449	−	214.893i	−0.145391	−	0.730928i
$295$		0			0
$296$	−17.7730	+	89.3507i	−0.0600438	+	0.301861i
$297$	−97.4358	−	235.231i	−0.328067	−	0.792023i
$298$	50.6097	−	20.9632i	0.169831	−	0.0703463i
$299$	−120.583	−	23.9854i	−0.403286	−	0.0802187i
$300$		0			0
$301$	799.087	−	158.948i	2.65477	−	0.528067i
$302$	64.6819	+	64.6819i	0.214179	+	0.214179i
$303$	−107.691	+	161.171i	−0.355415	+	0.531916i
$304$	−100.801	−	41.7530i	−0.331581	−	0.137345i
$305$		0			0
$306$	−12.2236	+	26.1619i	−0.0399464	+	0.0854964i
$307$		−	502.910i		−	1.63814i	−0.573691	−	0.819072i	$-0.694489\pi$
$307$		−	502.910i		−	1.63814i	0.573691	−	0.819072i	$-0.305511\pi$
$308$	−313.277	−	129.764i	−1.01713	−	0.421311i
$309$	−102.290	+	153.088i	−0.331035	+	0.495429i
$310$		0			0
$311$	−18.4534	−	92.7716i	−0.0593358	−	0.298301i	0.939710	−	0.341972i	$-0.111095\pi$
$311$	−18.4534	−	92.7716i	−0.0593358	−	0.298301i	−0.999046	+	0.0436707i	$0.986095\pi$
$312$	347.842	−	232.420i	1.11488	−	0.744937i
$313$	416.068	+	82.7611i	1.32929	+	0.264413i	0.808109	−	0.589033i	$-0.200491\pi$
$313$	416.068	+	82.7611i	1.32929	+	0.264413i	0.521182	+	0.853445i	$0.325491\pi$
$314$	−114.577	+	47.4595i	−0.364896	+	0.151145i
$315$		0			0
$316$	133.635	+	26.5817i	0.422896	+	0.0841192i
$317$	117.464	+	175.798i	0.370550	+	0.554567i	0.969147	−	0.246483i	$-0.0792749\pi$
$317$	117.464	+	175.798i	0.370550	+	0.554567i	−0.598597	+	0.801050i	$0.704275\pi$
$318$	−30.1059	−	151.352i	−0.0946726	−	0.475951i
$319$	137.674	−	137.674i	0.431581	−	0.431581i
$320$		0			0
$321$	−69.9700	−	28.9825i	−0.217975	−	0.0902882i
$322$	−51.7541			−0.160727
$323$	−184.925	+	169.195i	−0.572523	+	0.523824i
$324$	−193.287			−0.596563
$325$		0			0
$326$	−11.2009	+	16.7634i	−0.0343587	+	0.0514214i
$327$	−135.419	+	135.419i	−0.414125	+	0.414125i
$328$	371.539	−	73.9037i	1.13274	−	0.225316i
$329$	−534.215	−	799.509i	−1.62375	−	2.43012i
$330$		0			0
$331$	212.770	−	88.1322i	0.642810	−	0.266260i	−0.0373750	−	0.999301i	$-0.511900\pi$
$331$	212.770	−	88.1322i	0.642810	−	0.266260i	0.680185	+	0.733041i	$0.261900\pi$
$332$	−68.1385	+	28.2239i	−0.205236	+	0.0850117i
$333$	5.45138	−	27.4059i	0.0163705	−	0.0823001i
$334$	136.923	−	91.4893i	0.409950	−	0.273920i
$335$		0			0
$336$	−166.393	+	166.393i	−0.495218	+	0.495218i
$337$	−343.412	+	513.952i	−1.01903	+	1.52508i	−0.178039	+	0.984023i	$0.556975\pi$
$337$	−343.412	+	513.952i	−1.01903	+	1.52508i	−0.840987	+	0.541056i	$0.818025\pi$
$338$	150.623	−	363.636i	0.445630	−	1.07585i
$339$			74.2446i			0.219011i
$340$		0			0
$341$	183.452			0.537983
$342$	−23.1381	−	9.58412i	−0.0676553	−	0.0280237i
$343$	450.405	+	300.951i	1.31313	+	0.877408i
$344$	304.667	+	304.667i	0.885660	+	0.885660i
$345$		0			0
$346$	107.070	+	160.242i	0.309452	+	0.463128i
$347$	−598.438	−	119.037i	−1.72460	−	0.343045i	−0.769349	−	0.638829i	$-0.779419\pi$
$347$	−598.438	−	119.037i	−1.72460	−	0.343045i	−0.955255	+	0.295783i	$0.904419\pi$
$348$	−73.1016	−	176.483i	−0.210062	−	0.507134i
$349$	68.1756	+	164.590i	0.195345	+	0.471606i	0.990953	−	0.134206i	$-0.0428484\pi$
$349$	68.1756	+	164.590i	0.195345	+	0.471606i	−0.795608	+	0.605812i	$0.792848\pi$
$350$		0			0
$351$	−601.279	+	401.762i	−1.71305	+	1.14462i
$352$	−54.3269	−	273.120i	−0.154338	−	0.775909i
$353$	246.404	+	246.404i	0.698030	+	0.698030i	0.963985	−	0.265956i	$-0.0856874\pi$
$353$	246.404	+	246.404i	0.698030	+	0.698030i	−0.265956	+	0.963985i	$0.585687\pi$
$354$	180.765	+	120.783i	0.510636	+	0.341196i
$355$		0			0
$356$			169.175i			0.475210i
$357$	184.507	+	508.126i	0.516828	+	1.42332i
$358$			149.790i			0.418408i
$359$	−87.7860	+	211.934i	−0.244529	+	0.590346i	−0.997722	−	0.0674536i	$-0.978513\pi$
$359$	−87.7860	+	211.934i	−0.244529	+	0.590346i	0.753193	+	0.657799i	$0.228513\pi$
$360$		0			0
$361$	101.551	+	101.551i	0.281306	+	0.281306i
$362$	5.98987	−	1.19146i	0.0165466	−	0.00329132i
$363$	−97.8225	+	65.3629i	−0.269484	+	0.180063i
$364$	−187.889	+	944.580i	−0.516177	+	2.59500i
$365$		0			0
$366$	−58.7444	−	141.822i	−0.160504	−	0.387491i
$367$	−125.957	+	633.227i	−0.343206	+	1.72541i	0.294956	+	0.955511i	$0.404695\pi$
$367$	−125.957	+	633.227i	−0.343206	+	1.72541i	−0.638162	+	0.769902i	$0.720305\pi$
$368$	20.3182	+	30.4084i	0.0552126	+	0.0826315i
$369$	−113.960	+	22.6680i	−0.308834	+	0.0614308i
$370$		0			0
$371$	660.682	+	441.454i	1.78081	+	1.18990i
$372$	68.8781	−	166.287i	0.185156	−	0.447007i
$373$	17.3537			0.0465246			0.0232623	−	0.999729i	$-0.492595\pi$
$373$	17.3537			0.0465246			0.0232623	+	0.999729i	$0.492595\pi$
$374$	−126.520	−	31.0607i	−0.338288	−	0.0830500i
$375$		0			0
$376$	194.597	−	469.800i	0.517546	−	1.24947i
$377$	−459.796	−	307.226i	−1.21962	−	0.814923i
$378$	−215.253	+	215.253i	−0.569452	+	0.569452i
$379$	−28.2844	−	142.195i	−0.0746289	−	0.375185i	0.925363	−	0.379081i	$-0.123760\pi$
$379$	−28.2844	−	142.195i	−0.0746289	−	0.375185i	−0.999992	+	0.00389606i	$0.998760\pi$
$380$		0			0
$381$	29.9000	−	150.318i	0.0784778	−	0.394534i
$382$	−39.0164	−	94.1939i	−0.102137	−	0.246581i
$383$	12.5601	−	5.20255i	0.0327939	−	0.0135837i	−0.366226	−	0.930526i	$-0.619350\pi$
$383$	12.5601	−	5.20255i	0.0327939	−	0.0135837i	0.399020	+	0.916942i	$0.369350\pi$
$384$	−335.445	−	66.7241i	−0.873554	−	0.173761i
$385$		0			0
$386$	−142.507	+	28.3464i	−0.369189	+	0.0734363i
$387$	−93.4484	−	93.4484i	−0.241469	−	0.241469i
$388$	23.3069	−	34.8813i	0.0600694	−	0.0899002i
$389$	527.645	+	218.558i	1.35641	+	0.561845i	0.938070	−	0.346445i	$-0.112611\pi$
$389$	527.645	+	218.558i	1.35641	+	0.561845i	0.418343	+	0.908289i	$0.362611\pi$
$390$		0			0
$391$	83.0479	−	12.7180i	0.212399	−	0.0325268i
$392$			596.622i			1.52199i
$393$	−572.880	−	237.295i	−1.45771	−	0.603804i
$394$	−65.5209	+	98.0590i	−0.166297	+	0.248881i
$395$		0			0
$396$	10.7304	+	53.9454i	0.0270970	+	0.136226i
$397$	616.794	−	412.128i	1.55364	−	1.03811i	0.578723	−	0.815524i	$-0.303551\pi$
$397$	616.794	−	412.128i	1.55364	−	1.03811i	0.974914	−	0.222583i	$-0.0714489\pi$
$398$	90.4847	+	17.9985i	0.227348	+	0.0452224i
$399$	−433.159	+	179.420i	−1.08561	+	0.449675i
$400$		0			0
$401$	−272.971	−	54.2973i	−0.680726	−	0.135405i	−0.157397	−	0.987535i	$-0.550310\pi$
$401$	−272.971	−	54.2973i	−0.680726	−	0.135405i	−0.523329	+	0.852131i	$0.675310\pi$
$402$	−52.7388	−	78.9293i	−0.131191	−	0.196341i
$403$	−101.650	−	511.031i	−0.252234	−	1.26807i
$404$	166.869	−	166.869i	0.413041	−	0.413041i
$405$		0			0
$406$	−215.064	−	89.0825i	−0.529715	−	0.219415i
$407$	126.064			0.309739
$408$	−169.219	+	230.420i	−0.414753	+	0.564755i
$409$	417.503			1.02079			0.510395	−	0.859940i	$-0.329499\pi$
$409$	417.503			1.02079			0.510395	+	0.859940i	$0.329499\pi$
$410$		0			0
$411$	−197.311	+	295.297i	−0.480075	+	0.718483i
$412$	158.500	−	158.500i	0.384708	−	0.384708i
$413$	−1097.92	+	218.391i	−2.65841	+	0.528791i
$414$	4.66391	+	6.98004i	0.0112655	+	0.0168600i
$415$		0			0
$416$	−730.711	+	302.670i	−1.75652	+	0.727573i
$417$	−3.65821	+	1.51528i	−0.00877268	+	0.00363376i
$418$	22.0429	−	110.817i	0.0527341	−	0.265112i
$419$	453.352	−	302.920i	1.08199	−	0.722960i	0.119104	−	0.992882i	$-0.461998\pi$
$419$	453.352	−	302.920i	1.08199	−	0.722960i	0.962882	+	0.269921i	$0.0869977\pi$
$420$		0			0
$421$	−362.826	+	362.826i	−0.861820	+	0.861820i	−0.991549	−	0.129730i	$-0.958589\pi$
$421$	−362.826	+	362.826i	−0.861820	+	0.861820i	0.129730	+	0.991549i	$0.458589\pi$
$422$	89.4245	−	133.833i	0.211906	−	0.317140i
$423$	−59.6875	+	144.098i	−0.141105	+	0.340658i
$424$			420.210i			0.991062i
$425$		0			0
$426$	104.091			0.244346
$427$	730.252	+	302.480i	1.71019	+	0.708385i
$428$	76.6642	+	51.2254i	0.179122	+	0.119686i
$429$	−409.342	−	409.342i	−0.954178	−	0.954178i
$430$		0			0
$431$	−157.395	−	235.558i	−0.365185	−	0.546538i	0.602688	−	0.797977i	$-0.294096\pi$
$431$	−157.395	−	235.558i	−0.365185	−	0.546538i	−0.967873	+	0.251439i	$0.919096\pi$
$432$	210.979	+	41.9664i	0.488378	+	0.0971445i
$433$	119.672	+	288.914i	0.276379	+	0.667238i	0.999730	−	0.0232429i	$-0.00739910\pi$
$433$	119.672	+	288.914i	0.276379	+	0.667238i	−0.723351	+	0.690481i	$0.757399\pi$
$434$	−83.9358	−	202.639i	−0.193400	−	0.466910i
$435$		0			0
$436$	193.861	−	129.534i	0.444635	−	0.297096i
$437$	14.2156	+	71.4664i	0.0325299	+	0.163539i
$438$	74.7444	+	74.7444i	0.170649	+	0.170649i
$439$	−63.4957	−	42.4264i	−0.144637	−	0.0966434i	0.481146	−	0.876640i	$-0.340221\pi$
$439$	−63.4957	−	42.4264i	−0.144637	−	0.0966434i	−0.625783	+	0.779997i	$0.715221\pi$
$440$		0			0
$441$		−	182.998i		−	0.414961i
$442$	−16.4195	+	369.649i	−0.0371482	+	0.836310i
$443$			167.822i			0.378830i	0.981897	+	0.189415i	$0.0606591\pi$
$443$			167.822i			0.378830i	−0.981897	+	0.189415i	$0.939341\pi$
$444$	47.3314	−	114.268i	0.106602	−	0.257360i
$445$		0			0
$446$	−47.0166	−	47.0166i	−0.105418	−	0.105418i
$447$	−163.147	+	32.4519i	−0.364981	+	0.0725993i
$448$	17.7492	−	11.8597i	0.0396189	−	0.0264725i
$449$	−7.23934	+	36.3946i	−0.0161233	+	0.0810571i	−0.988009	−	0.154395i	$-0.950657\pi$
$449$	−7.23934	+	36.3946i	−0.0161233	+	0.0810571i	0.971886	+	0.235452i	$0.0756571\pi$
$450$		0			0
$451$	−200.603	−	484.297i	−0.444795	−	1.07383i
$452$	17.6340	−	88.6521i	0.0390133	−	0.196133i
$453$	−154.320	−	230.957i	−0.340663	−	0.509838i
$454$	−107.891	+	21.4609i	−0.237646	+	0.0472707i
$455$		0			0
$456$	−206.157	−	137.750i	−0.452099	−	0.302083i
$457$	−126.150	+	304.553i	−0.276039	+	0.666418i	−0.999719	−	0.0237185i	$-0.992449\pi$
$457$	−126.150	+	304.553i	−0.276039	+	0.666418i	0.723679	+	0.690136i	$0.242449\pi$
$458$	288.120			0.629084
$459$	292.512	−	398.304i	0.637282	−	0.867765i
$460$		0			0
$461$	199.727	−	482.184i	0.433248	−	1.04595i	−0.544986	−	0.838445i	$-0.683465\pi$
$461$	199.727	−	482.184i	0.433248	−	1.04595i	0.978233	−	0.207507i	$-0.0665351\pi$
$462$	−202.620	−	135.386i	−0.438571	−	0.293044i
$463$	−195.559	+	195.559i	−0.422373	+	0.422373i	−0.886020	−	0.463647i	$-0.846541\pi$
$463$	−195.559	+	195.559i	−0.422373	+	0.422373i	0.463647	+	0.886020i	$0.346541\pi$
$464$	32.0916	+	161.335i	0.0691629	+	0.347705i
$465$		0			0
$466$	−37.4983	+	188.517i	−0.0804684	+	0.404542i
$467$	−181.889	−	439.119i	−0.389484	−	0.940298i	−0.990049	−	0.140722i	$-0.955058\pi$
$467$	−181.889	−	439.119i	−0.389484	−	0.940298i	0.600565	−	0.799576i	$-0.294942\pi$
$468$	144.327	−	59.7821i	0.308391	−	0.127740i
$469$	479.398	+	95.3582i	1.02217	+	0.203322i
$470$		0			0
$471$	369.355	−	73.4692i	0.784192	−	0.155986i
$472$	−418.605	−	418.605i	−0.886874	−	0.886874i
$473$	331.242	−	495.739i	0.700301	−	1.04807i
$474$	90.4655	+	37.4720i	0.190856	+	0.0790550i
$475$		0			0
$476$	−99.6257	−	650.553i	−0.209298	−	1.36671i
$477$		−	128.888i		−	0.270206i
$478$	−81.1053	−	33.5949i	−0.169676	−	0.0702823i
$479$	220.245	−	329.620i	0.459802	−	0.688142i	−0.527038	−	0.849842i	$-0.676697\pi$
$479$	220.245	−	329.620i	0.459802	−	0.688142i	0.986840	+	0.161699i	$0.0516975\pi$
$480$		0			0
$481$	−69.8517	−	351.168i	−0.145222	−	0.730079i
$482$	50.1604	−	33.5161i	0.104067	−	0.0695354i
$483$	154.136	+	30.6596i	0.319123	+	0.0634775i
$484$	132.330	−	54.8128i	0.273409	−	0.113250i
$485$		0			0
$486$	88.2646	+	17.5569i	0.181614	+	0.0361253i
$487$	152.409	+	228.096i	0.312954	+	0.468369i	0.954286	−	0.298895i	$-0.0966179\pi$
$487$	152.409	+	228.096i	0.312954	+	0.468369i	−0.641332	+	0.767263i	$0.721618\pi$
$488$	81.5481	+	409.970i	0.167107	+	0.840102i
$489$	43.2898	−	43.2898i	0.0885273	−	0.0885273i
$490$		0			0
$491$	−439.630	−	182.101i	−0.895378	−	0.370878i	−0.112937	−	0.993602i	$-0.536026\pi$
$491$	−439.630	−	182.101i	−0.895378	−	0.370878i	−0.782441	+	0.622725i	$0.786026\pi$
$492$	−514.299			−1.04532
$493$	366.997	+	90.0979i	0.744415	+	0.182754i
$494$	−320.910			−0.649615
$495$		0			0
$496$	−86.1091	+	128.871i	−0.173607	+	0.259821i
$497$	−378.992	+	378.992i	−0.762560	+	0.762560i
$498$	−51.9844	+	10.3403i	−0.104386	+	0.0207637i
$499$	266.019	+	398.126i	0.533104	+	0.797847i	0.996074	−	0.0885272i	$-0.0282160\pi$
$499$	266.019	+	398.126i	0.533104	+	0.797847i	−0.462969	+	0.886374i	$0.653216\pi$
$500$		0			0
$501$	−461.990	+	191.363i	−0.922136	+	0.381961i
$502$	303.159	−	125.573i	0.603902	−	0.250145i
$503$	1.08456	−	5.45243i	0.00215617	−	0.0108398i	−0.979692	−	0.200507i	$-0.935741\pi$
$503$	1.08456	−	5.45243i	0.00215617	−	0.0108398i	0.981848	+	0.189667i	$0.0607410\pi$
$504$	122.296	−	81.7157i	0.242651	−	0.162134i
$505$		0			0
$506$	−26.7804	+	26.7804i	−0.0529256	+	0.0529256i
$507$	−664.014	+	993.767i	−1.30969	+	1.96009i
$508$	−71.4045	+	172.386i	−0.140560	+	0.339342i
$509$		−	460.670i		−	0.905049i	−0.891752	−	0.452524i	$-0.850524\pi$
$509$		−	460.670i		−	0.905049i	0.891752	−	0.452524i	$-0.149476\pi$
$510$		0			0
$511$	−544.282			−1.06513
$512$	390.458	+	161.733i	0.762613	+	0.315885i
$513$	356.364	+	238.115i	0.694666	+	0.464161i
$514$	188.655	+	188.655i	0.367034	+	0.367034i
$515$		0			0
$516$	−324.986	−	486.376i	−0.629818	−	0.942589i
$517$	−690.141	−	137.277i	−1.33489	−	0.265527i
$518$	−57.6786	−	139.248i	−0.111349	−	0.268819i
$519$	−223.953	−	540.670i	−0.431508	−	1.04175i
$520$		0			0
$521$	814.191	−	544.025i	1.56275	−	1.04419i	0.591445	−	0.806346i	$-0.298558\pi$
$521$	814.191	−	544.025i	1.56275	−	1.04419i	0.971302	−	0.237849i	$-0.0764422\pi$
$522$	7.36640	+	37.0334i	0.0141119	+	0.0709452i
$523$	−25.9709	−	25.9709i	−0.0496575	−	0.0496575i	0.681842	−	0.731499i	$-0.261179\pi$
$523$	−25.9709	−	25.9709i	−0.0496575	−	0.0496575i	−0.731499	+	0.681842i	$0.761179\pi$
$524$	627.690	+	419.409i	1.19788	+	0.800398i
$525$		0			0
$526$		−	291.579i		−	0.554333i
$527$	184.485	+	304.541i	0.350066	+	0.577877i
$528$			172.202i			0.326140i
$529$	−193.093	+	466.167i	−0.365014	+	0.881223i
$530$		0			0
$531$	128.396	+	128.396i	0.241800	+	0.241800i
$532$	559.829	−	111.357i	1.05231	−	0.209318i
$533$	−1237.92	+	827.155i	−2.32256	+	1.55188i
$534$	−23.7188	+	119.243i	−0.0444173	+	0.223301i
$535$		0			0
$536$	98.9196	+	238.813i	0.184551	+	0.445547i
$537$	88.7370	−	446.111i	0.165246	−	0.830746i
$538$	145.757	+	218.141i	0.270924	+	0.405467i
$539$	809.728	−	161.065i	1.50228	−	0.298822i
$540$		0			0
$541$	−423.296	−	282.838i	−0.782433	−	0.522805i	0.0990149	−	0.995086i	$-0.468431\pi$
$541$	−423.296	−	282.838i	−0.782433	−	0.522805i	−0.881448	+	0.472281i	$0.843431\pi$
$542$	46.5443	−	112.368i	0.0858751	−	0.207321i
$543$	−18.5451			−0.0341531
$544$	398.762	−	364.843i	0.733018	−	0.670668i
$545$		0			0
$546$	−264.866	+	639.442i	−0.485102	+	1.17114i
$547$	435.093	+	290.720i	0.795417	+	0.531481i	0.885602	−	0.464444i	$-0.153746\pi$
$547$	435.093	+	290.720i	0.795417	+	0.531481i	−0.0901850	+	0.995925i	$0.528746\pi$
$548$	305.736	−	305.736i	0.557913	−	0.557913i
$549$	−25.0127	−	125.747i	−0.0455604	−	0.229048i
$550$		0			0
$551$	−63.9399	+	321.447i	−0.116043	+	0.583389i
$552$	31.8047	+	76.7833i	0.0576172	+	0.139100i
$553$	−465.815	+	192.947i	−0.842342	+	0.348910i
$554$	−84.7594	−	16.8597i	−0.152995	−	0.0304327i
$555$		0			0
$556$	4.72800	−	0.940457i	0.00850359	−	0.00169147i
$557$	150.954	+	150.954i	0.271012	+	0.271012i	0.829507	−	0.558496i	$-0.188621\pi$
$557$	150.954	+	150.954i	0.271012	+	0.271012i	−0.558496	+	0.829507i	$0.688621\pi$
$558$	−19.7657	+	29.5815i	−0.0354225	+	0.0530135i
$559$	−1564.49	−	648.033i	−2.79873	−	1.15927i
$560$		0			0
$561$	358.406	+	167.458i	0.638870	+	0.298499i
$562$			1.06439i			0.00189393i
$563$	409.360	+	169.562i	0.727104	+	0.301176i	0.715361	−	0.698755i	$-0.246262\pi$
$563$	409.360	+	169.562i	0.727104	+	0.301176i	0.0117427	+	0.999931i	$0.496262\pi$
$564$	−383.550	+	574.023i	−0.680052	+	1.01777i
$565$		0			0
$566$	−26.2801	−	132.119i	−0.0464313	−	0.233426i
$567$	594.703	−	397.368i	1.04886	−	0.700825i
$568$	−277.997	−	55.2970i	−0.489431	−	0.0973539i
$569$	−795.099	+	329.341i	−1.39736	+	0.578806i	−0.949065	−	0.315079i	$-0.897969\pi$
$569$	−795.099	+	329.341i	−1.39736	+	0.578806i	−0.448296	+	0.893885i	$0.647969\pi$
$570$		0			0
$571$	−751.766	−	149.535i	−1.31658	−	0.261883i	−0.513670	−	0.857988i	$-0.671714\pi$
$571$	−751.766	−	149.535i	−1.31658	−	0.261883i	−0.802907	+	0.596104i	$0.796714\pi$
$572$	391.553	+	586.000i	0.684533	+	1.02448i
$573$	60.3989	+	303.646i	0.105408	+	0.529923i
$574$	−443.166	+	443.166i	−0.772066	+	0.772066i
$575$		0			0
$576$	−3.19901	−	1.32507i	−0.00555384	−	0.00230048i
$577$	−970.916			−1.68270			−0.841349	−	0.540493i	$-0.818238\pi$
$577$	−970.916			−1.68270			−0.841349	+	0.540493i	$0.818238\pi$
$578$	−75.6695	−	241.266i	−0.130916	−	0.417415i
$579$	441.213			0.762026
$580$		0			0
$581$	151.624	−	226.922i	0.260971	−	0.390571i
$582$	21.3183	−	21.3183i	0.0366294	−	0.0366294i
$583$	570.304	−	113.441i	0.978224	−	0.194581i
$584$	−159.913	−	239.327i	−0.273824	−	0.409806i
$585$		0			0
$586$	−151.453	+	62.7337i	−0.258452	+	0.107054i
$587$	92.8282	−	38.4507i	0.158140	−	0.0655038i	−0.302209	−	0.953242i	$-0.597724\pi$
$587$	92.8282	−	38.4507i	0.158140	−	0.0655038i	0.460349	+	0.887738i	$0.347724\pi$
$588$	158.023	−	794.435i	0.268746	−	1.35108i
$589$	−256.766	+	171.565i	−0.435935	+	0.291283i
$590$		0			0
$591$	253.228	−	253.228i	0.428474	−	0.428474i
$592$	−59.1720	+	88.5572i	−0.0999528	+	0.149590i
$593$	71.1679	−	171.814i	0.120013	−	0.289738i	−0.852444	−	0.522818i	$-0.824881\pi$
$593$	71.1679	−	171.814i	0.120013	−	0.289738i	0.972457	+	0.233081i	$0.0748806\pi$
$594$			222.767i			0.375028i
$595$		0			0
$596$	202.514			0.339788
$597$	−258.823	−	107.208i	−0.433539	−	0.179578i
$598$	89.4394	+	59.7615i	0.149564	+	0.0999356i
$599$	210.427	+	210.427i	0.351297	+	0.351297i	0.860592	−	0.509295i	$-0.170094\pi$
$599$	210.427	+	210.427i	0.351297	+	0.351297i	−0.509295	+	0.860592i	$0.670094\pi$
$600$		0			0
$601$	−285.040	−	426.592i	−0.474276	−	0.709804i	0.514784	−	0.857320i	$-0.327872\pi$
$601$	−285.040	−	426.592i	−0.474276	−	0.709804i	−0.989060	+	0.147516i	$0.952872\pi$
$602$	−699.142	−	139.068i	−1.16137	−	0.231010i
$603$	−30.3409	−	73.2495i	−0.0503166	−	0.121475i
$604$	129.412	+	312.428i	0.214258	+	0.517264i
$605$		0			0
$606$	141.012	−	94.2215i	0.232694	−	0.155481i
$607$	187.578	+	943.017i	0.309024	+	1.55357i	0.753298	+	0.657679i	$0.228462\pi$
$607$	187.578	+	943.017i	0.309024	+	1.55357i	−0.444274	+	0.895891i	$0.646538\pi$
$608$	331.461	+	331.461i	0.545166	+	0.545166i
$609$	587.740	+	392.715i	0.965090	+	0.644853i
$610$		0			0
$611$			1998.55i			3.27095i
$612$	−78.7617	+	72.0622i	−0.128696	+	0.117749i
$613$			757.810i			1.23623i	0.786087	+	0.618116i	$0.212104\pi$
$613$			757.810i			1.23623i	−0.786087	+	0.618116i	$0.787896\pi$
$614$	−168.384	+	406.516i	−0.274242	+	0.662078i
$615$		0			0
$616$	469.214	+	469.214i	0.761712	+	0.761712i
$617$	−220.220	+	43.8045i	−0.356921	+	0.0709959i	−0.370294	−	0.928915i	$-0.620743\pi$
$617$	−220.220	+	43.8045i	−0.356921	+	0.0709959i	0.0133733	+	0.999911i	$0.495743\pi$
$618$	133.940	−	89.4961i	0.216732	−	0.144816i
$619$	231.722	−	1164.94i	0.374348	−	1.88198i	−0.0893776	−	0.995998i	$-0.528488\pi$
$619$	231.722	−	1164.94i	0.374348	−	1.88198i	0.463726	−	0.885979i	$-0.346512\pi$
$620$		0			0
$621$	−54.9776	−	132.728i	−0.0885308	−	0.213732i
$622$	−16.1454	+	81.1684i	−0.0259572	+	0.130496i
$623$	−347.798	−	520.516i	−0.558263	−	0.835499i
$624$	479.692	−	95.4167i	0.768737	−	0.152911i
$625$		0			0
$626$	−308.609	−	206.206i	−0.492986	−	0.329402i
$627$	−131.298	+	316.981i	−0.209407	+	0.505553i
$628$	−458.479			−0.730062
$629$	126.773	+	209.273i	0.201548	+	0.332708i
$630$		0			0
$631$	−184.417	+	445.222i	−0.292262	+	0.705582i	−1.00000		0.000892895i	$-0.999716\pi$
$631$	−184.417	+	445.222i	−0.292262	+	0.705582i	0.707738	+	0.706475i	$0.249716\pi$
$632$	−221.700	−	148.135i	−0.350791	−	0.234391i
$633$	−345.612	+	345.612i	−0.545991	+	0.545991i
$634$	−36.0890	−	181.431i	−0.0569227	−	0.286170i
$635$		0			0
$636$	111.298	−	559.533i	0.174997	−	0.879769i
$637$	−897.338	−	2166.36i	−1.40869	−	3.40089i
$638$	−157.382	+	65.1897i	−0.246680	+	0.102178i
$639$	85.2680	+	16.9609i	0.133440	+	0.0265428i
$640$		0			0
$641$	−89.5481	+	17.8122i	−0.139701	+	0.0277882i	−0.264445	−	0.964401i	$-0.585189\pi$
$641$	−89.5481	+	17.8122i	−0.139701	+	0.0277882i	0.124745	+	0.992189i	$0.460189\pi$
$642$	46.8547	+	46.8547i	0.0729823	+	0.0729823i
$643$	113.209	−	169.429i	0.176064	−	0.263498i	−0.732933	−	0.680300i	$-0.761849\pi$
$643$	113.209	−	169.429i	0.176064	−	0.263498i	0.908997	+	0.416803i	$0.136849\pi$
$644$	−176.765	−	73.2185i	−0.274480	−	0.113693i
$645$		0			0
$646$	206.129	−	74.8484i	0.319086	−	0.115864i
$647$			1013.82i			1.56696i	0.621420	+	0.783478i	$0.286556\pi$
$647$			1013.82i			1.56696i	−0.621420	+	0.783478i	$0.713444\pi$
$648$	349.454	+	144.748i	0.539280	+	0.223377i
$649$	−455.118	+	681.133i	−0.701261	+	1.04951i
$650$		0			0
$651$	129.936	+	653.232i	0.199594	+	1.00343i
$652$	−61.9723	+	41.4085i	−0.0950495	+	0.0635100i
$653$	−302.592	−	60.1893i	−0.463387	−	0.0921735i	−0.0421251	−	0.999112i	$-0.513413\pi$
$653$	−302.592	−	60.1893i	−0.463387	−	0.0921735i	−0.421262	+	0.906939i	$0.638413\pi$
$654$	154.803	−	64.1217i	0.236703	−	0.0980454i
$655$		0			0
$656$	434.368	+	86.4012i	0.662147	+	0.131709i
$657$	49.0490	+	73.4070i	0.0746560	+	0.111731i
$658$	164.128	+	825.130i	0.249435	+	1.25400i
$659$	−554.044	+	554.044i	−0.840734	+	0.840734i	−0.988954	−	0.148220i	$-0.952646\pi$
$659$	−554.044	+	554.044i	−0.840734	+	0.840734i	0.148220	+	0.988954i	$0.452646\pi$
$660$		0			0
$661$	−396.870	−	164.389i	−0.600409	−	0.248697i	0.0617128	−	0.998094i	$-0.480344\pi$
$661$	−396.870	−	164.389i	−0.600409	−	0.248697i	−0.662121	+	0.749397i	$0.730344\pi$
$662$	−201.496			−0.304375
$663$	267.885	−	1091.18i	0.404050	−	1.64582i
$664$	144.328			0.217361
$665$		0			0
$666$	−13.5825	+	20.3277i	−0.0203942	+	0.0305221i
$667$	77.6819	−	77.6819i	0.116465	−	0.116465i
$668$	597.092	−	118.769i	0.893851	−	0.177798i
$669$	112.174	+	167.880i	0.167674	+	0.250941i
$670$		0			0
$671$	534.392	−	221.352i	0.796411	−	0.329884i
$672$	934.041	−	386.892i	1.38994	−	0.575733i
$673$	203.655	−	1023.84i	0.302607	−	1.52131i	−0.467845	−	0.883811i	$-0.654969\pi$
$673$	203.655	−	1023.84i	0.302607	−	1.52131i	0.770452	−	0.637498i	$-0.220031\pi$
$674$	449.670	−	300.460i	0.667166	−	0.445786i
$675$		0			0
$676$	1028.90	−	1028.90i	1.52204	−	1.52204i
$677$	657.690	−	984.303i	0.971477	−	1.45392i	0.0821649	−	0.996619i	$-0.473817\pi$
$677$	657.690	−	984.303i	0.971477	−	1.45392i	0.889313	−	0.457300i	$-0.151183\pi$
$678$	24.8586	−	60.0139i	0.0366646	−	0.0885161i
$679$			155.238i			0.228627i
$680$		0			0
$681$	334.040			0.490514
$682$	−148.289	−	61.4234i	−0.217433	−	0.0900636i
$683$	−327.661	−	218.936i	−0.479738	−	0.320551i	0.292080	−	0.956394i	$-0.405653\pi$
$683$	−327.661	−	218.936i	−0.479738	−	0.320551i	−0.771818	+	0.635843i	$0.780653\pi$
$684$	−65.4687	−	65.4687i	−0.0957145	−	0.0957145i
$685$		0			0
$686$	−263.310	−	394.071i	−0.383833	−	0.574447i
$687$	−858.092	−	170.685i	−1.24904	−	0.248450i
$688$	192.767	+	465.382i	0.280185	+	0.676427i
$689$	−632.009	−	1525.80i	−0.917285	−	2.21452i
$690$		0			0
$691$	−44.0092	+	29.4060i	−0.0636892	+	0.0425558i	−0.587007	−	0.809582i	$-0.699694\pi$
$691$	−44.0092	+	29.4060i	−0.0636892	+	0.0425558i	0.523318	+	0.852137i	$0.324694\pi$
$692$	138.996	+	698.780i	0.200861	+	1.00980i
$693$	−143.919	−	143.919i	−0.207675	−	0.207675i
$694$	443.877	+	296.589i	0.639592	+	0.427362i
$695$		0			0
$696$			373.817i			0.537094i
$697$	602.230	−	820.036i	0.864031	−	1.17652i
$698$		−	155.869i		−	0.223308i
$699$	223.358	−	539.234i	0.319539	−	0.771437i
$700$		0			0
$701$	581.552	+	581.552i	0.829603	+	0.829603i	0.987462	−	0.157859i	$-0.0504590\pi$
$701$	581.552	+	581.552i	0.829603	+	0.829603i	−0.157859	+	0.987462i	$0.550459\pi$
$702$	620.548	−	123.435i	0.883971	−	0.175833i
$703$	−176.443	+	117.896i	−0.250986	+	0.167703i
$704$	3.04759	−	15.3213i	0.00432896	−	0.0217631i
$705$		0			0
$706$	−116.674	−	281.676i	−0.165261	−	0.398975i
$707$	−170.364	+	856.476i	−0.240967	+	1.21142i
$708$	446.522	+	668.268i	0.630681	+	0.943881i
$709$	222.555	−	44.2689i	0.313900	−	0.0624385i	−0.0356263	−	0.999365i	$-0.511343\pi$
$709$	222.555	−	44.2689i	0.313900	−	0.0624385i	0.349526	+	0.936927i	$0.386343\pi$
$710$		0			0
$711$	68.0004	+	45.4364i	0.0956405	+	0.0639050i
$712$	126.692	−	305.861i	0.177938	−	0.429580i
$713$	103.512			0.145178
$714$	20.9885	−	472.509i	0.0293956	−	0.661777i
$715$		0			0
$716$	−211.913	+	511.604i	−0.295968	+	0.714531i
$717$	221.650	+	148.101i	0.309135	+	0.206557i
$718$	141.919	−	141.919i	0.197659	−	0.197659i
$719$	158.183	+	795.241i	0.220005	+	1.10604i	0.920008	+	0.391899i	$0.128182\pi$
$719$	158.183	+	795.241i	0.220005	+	1.10604i	−0.700004	+	0.714139i	$0.746818\pi$
$720$		0			0
$721$	−161.820	+	813.523i	−0.224438	+	1.12833i
$722$	−48.0853	−	116.088i	−0.0666001	−	0.160787i
$723$	−169.245	+	70.1036i	−0.234087	+	0.0969621i
$724$	22.1439	+	4.40469i	0.0305855	+	0.00608383i
$725$		0			0
$726$	100.957	−	20.0817i	0.139060	−	0.0276607i
$727$	−230.482	−	230.482i	−0.317032	−	0.317032i	0.530594	−	0.847626i	$-0.321969\pi$
$727$	−230.482	−	230.482i	−0.317032	−	0.317032i	−0.847626	+	0.530594i	$0.821969\pi$
$728$	1047.07	−	1567.05i	1.43828	−	2.15254i
$729$	−749.353	−	310.392i	−1.02792	−	0.425778i
$730$		0			0
$731$	1156.06	+	51.3514i	1.58148	+	0.0702481i
$732$		−	567.497i		−	0.775269i
$733$	−240.782	−	99.7350i	−0.328488	−	0.136064i	0.212344	−	0.977195i	$-0.431890\pi$
$733$	−240.782	−	99.7350i	−0.328488	−	0.136064i	−0.540832	+	0.841131i	$0.681890\pi$
$734$	313.831	−	469.681i	0.427562	−	0.639892i
$735$		0			0
$736$	−30.6537	−	154.106i	−0.0416490	−	0.209384i
$737$	297.410	−	198.723i	0.403541	−	0.269638i
$738$	99.7062	+	19.8328i	0.135103	+	0.0268737i
$739$	−152.235	+	63.0577i	−0.206001	+	0.0853285i	−0.483298	−	0.875456i	$-0.660561\pi$
$739$	−152.235	+	63.0577i	−0.206001	+	0.0853285i	0.277297	+	0.960784i	$0.410561\pi$
$740$		0			0
$741$	955.748	+	190.110i	1.28981	+	0.256559i
$742$	−386.239	−	578.048i	−0.520538	−	0.779040i
$743$	−57.0690	−	286.905i	−0.0768089	−	0.386145i	−0.999998	−	0.00179939i	$-0.999427\pi$
$743$	−57.0690	−	286.905i	−0.0768089	−	0.386145i	0.923189	−	0.384345i	$-0.125573\pi$
$744$	−249.057	+	249.057i	−0.334754	+	0.334754i
$745$		0			0
$746$	−14.0274	−	5.81035i	−0.0188035	−	0.00778868i
$747$	−44.2686			−0.0592619
$748$	−388.183	−	285.079i	−0.518961	−	0.381122i
$749$	−341.192			−0.455530
$750$		0			0
$751$	−300.658	+	449.967i	−0.400344	+	0.599157i	−0.975797	−	0.218677i	$-0.929826\pi$
$751$	−300.658	+	449.967i	−0.400344	+	0.599157i	0.575453	+	0.817835i	$0.304826\pi$
$752$	420.374	−	420.374i	0.559008	−	0.559008i
$753$	−977.272	+	194.391i	−1.29784	+	0.258156i
$754$	268.800	+	402.288i	0.356499	+	0.533538i
$755$		0			0
$756$	−1039.72	+	430.665i	−1.37529	+	0.569663i
$757$	−239.065	+	99.0239i	−0.315805	+	0.130811i	−0.534955	−	0.844880i	$-0.679672\pi$
$757$	−239.065	+	99.0239i	−0.315805	+	0.130811i	0.219150	+	0.975691i	$0.429672\pi$
$758$	−24.7467	+	124.410i	−0.0326474	+	0.164130i
$759$	95.6234	−	63.8935i	0.125986	−	0.0841812i
$760$		0			0
$761$	176.582	−	176.582i	0.232039	−	0.232039i	−0.581504	−	0.813543i	$-0.697536\pi$
$761$	176.582	−	176.582i	0.232039	−	0.232039i	0.813543	+	0.581504i	$0.197536\pi$
$762$	−74.4983	+	111.495i	−0.0977668	+	0.146318i
$763$	−330.168	+	797.097i	−0.432724	+	1.04469i
$764$		−	376.915i		−	0.493344i
$765$		0			0
$766$	−11.8945			−0.0155281
$767$	2149.57	+	890.381i	2.80257	+	1.16086i
$768$	233.049	+	155.718i	0.303449	+	0.202758i
$769$	−644.591	−	644.591i	−0.838220	−	0.838220i	0.150405	−	0.988624i	$-0.451942\pi$
$769$	−644.591	−	644.591i	−0.838220	−	0.838220i	−0.988624	+	0.150405i	$0.951942\pi$
$770$		0			0
$771$	−450.100	−	673.623i	−0.583788	−	0.873700i
$772$	−526.832	−	104.793i	−0.682425	−	0.135743i
$773$	−420.952	−	1016.27i	−0.544569	−	1.31471i	−0.921469	−	0.388451i	$-0.873010\pi$
$773$	−420.952	−	1016.27i	−0.544569	−	1.31471i	0.376900	−	0.926254i	$-0.376990\pi$
$774$	44.2484	+	106.825i	0.0571685	+	0.138017i
$775$		0			0
$776$	−68.2598	+	45.6097i	−0.0879636	+	0.0587754i
$777$	89.2888	+	448.885i	0.114915	+	0.577716i
$778$	−353.332	−	353.332i	−0.454154	−	0.454154i
$779$	733.688	+	490.234i	0.941833	+	0.629312i
$780$		0			0
$781$			392.222i			0.502205i
$782$	−71.3881	−	17.5258i	−0.0912891	−	0.0224115i
$783$		−	646.181i		−	0.825263i
$784$	−266.927	+	644.418i	−0.340468	+	0.821962i
$785$		0			0
$786$	383.623	+	383.623i	0.488070	+	0.488070i
$787$	1316.68	−	261.903i	1.67303	−	0.332787i	0.734665	−	0.678430i	$-0.237339\pi$
$787$	1316.68	−	261.903i	1.67303	−	0.332787i	0.938366	+	0.345643i	$0.112339\pi$
$788$	−362.513	+	242.223i	−0.460042	+	0.307390i
$789$	−172.734	+	868.394i	−0.218928	+	1.10063i
$790$		0			0
$791$	127.999	+	309.017i	0.161819	+	0.390666i
$792$	20.9985	−	105.567i	0.0265133	−	0.133291i
$793$	−912.713	−	1365.97i	−1.15096	−	1.72254i
$794$	−636.560	+	126.620i	−0.801712	+	0.159470i
$795$		0			0
$796$	283.585	+	189.486i	0.356263	+	0.238047i
$797$	275.578	−	665.304i	0.345769	−	0.834761i	−0.651340	−	0.758786i	$-0.725793\pi$
$797$	275.578	−	665.304i	0.345769	−	0.834761i	0.997110	−	0.0759753i	$-0.0242070\pi$
$798$	410.207			0.514044
$799$	−466.137	−	1283.72i	−0.583401	−	1.60666i
$800$		0			0
$801$	−38.8592	+	93.8145i	−0.0485134	+	0.117122i
$802$	202.470	+	135.286i	0.252456	+	0.168686i
$803$	−281.641	+	281.641i	−0.350736	+	0.350736i
$804$	−68.4642	−	344.193i	−0.0851545	−	0.428101i
$805$		0			0
$806$	−88.9367	+	447.115i	−0.110343	+	0.554733i
$807$	−304.872	−	736.025i	−0.377784	−	0.912051i
$808$	−426.655	+	176.726i	−0.528039	+	0.218721i
$809$	1547.67	+	307.850i	1.91306	+	0.380532i	0.999649	−	0.0265023i	$-0.00843694\pi$
$809$	1547.67	+	307.850i	1.91306	+	0.380532i	0.913413	+	0.407034i	$0.133437\pi$
$810$		0			0
$811$	152.516	−	30.3374i	0.188059	−	0.0374073i	−0.100162	−	0.994971i	$-0.531936\pi$
$811$	152.516	−	30.3374i	0.188059	−	0.0374073i	0.288221	+	0.957564i	$0.406936\pi$
$812$	−608.519	−	608.519i	−0.749407	−	0.749407i
$813$	−205.188	+	307.086i	−0.252384	+	0.377719i
$814$	−101.901	−	42.2087i	−0.125185	−	0.0518534i
$815$		0			0
$816$	−285.865	+	173.171i	−0.350325	+	0.212220i
$817$			1003.63i			1.22844i
$818$	−337.479	−	139.788i	−0.412566	−	0.170890i
$819$	−321.161	+	480.651i	−0.392138	+	0.586876i
$820$		0			0
$821$	−219.728	−	1104.65i	−0.267634	−	1.34549i	−0.847508	−	0.530783i	$-0.821898\pi$
$821$	−219.728	−	1104.65i	−0.267634	−	1.34549i	0.579874	−	0.814707i	$-0.303102\pi$
$822$	258.363	−	172.632i	0.314310	−	0.210015i
$823$	1260.71	+	250.771i	1.53185	+	0.304703i	0.887780	−	0.460268i	$-0.152247\pi$
$823$	1260.71	+	250.771i	1.53185	+	0.304703i	0.644065	+	0.764971i	$0.277247\pi$
$824$	−405.258	+	167.863i	−0.491818	+	0.203718i
$825$		0			0
$826$	960.603	+	191.076i	1.16296	+	0.231327i
$827$	−187.964	−	281.307i	−0.227284	−	0.340154i	0.700247	−	0.713900i	$-0.253073\pi$
$827$	−187.964	−	281.307i	−0.227284	−	0.340154i	−0.927531	+	0.373746i	$0.878073\pi$
$828$	6.05457	+	30.4384i	0.00731229	+	0.0367613i
$829$	−52.6400	+	52.6400i	−0.0634982	+	0.0634982i	−0.738143	−	0.674645i	$-0.764297\pi$
$829$	−52.6400	+	52.6400i	−0.0634982	+	0.0634982i	0.674645	+	0.738143i	$0.264297\pi$
$830$		0			0
$831$	242.446	+	100.425i	0.291753	+	0.120848i
$832$	−44.3681			−0.0533271
$833$	1081.66	+	1182.22i	1.29852	+	1.41924i
$834$	3.46437			0.00415392
$835$		0			0
$836$	232.064	−	347.308i	0.277588	−	0.415440i
$837$	430.521	−	430.521i	0.514362	−	0.514362i
$838$	−467.881	+	93.0672i	−0.558330	+	0.111059i
$839$	−676.864	−	1013.00i	−0.806751	−	1.20739i	−0.975123	−	0.221664i	$-0.928851\pi$
$839$	−676.864	−	1013.00i	−0.806751	−	1.20739i	0.168372	−	0.985723i	$-0.446149\pi$
$840$		0			0
$841$	−320.464	+	132.741i	−0.381051	+	0.157837i
$842$	414.763	−	171.801i	0.492593	−	0.204039i
$843$	0.630553	−	3.17000i	0.000747987	−	0.00376039i
$844$	494.767	−	330.592i	0.586216	−	0.391697i
$845$		0			0
$846$	96.4940	−	96.4940i	0.114059	−	0.114059i
$847$	−294.465	+	440.698i	−0.347656	+	0.520304i
$848$	−188.001	+	453.874i	−0.221699	+	0.535229i
$849$			409.051i			0.481803i
$850$		0			0
$851$	71.1308			0.0835849
$852$	355.522	+	147.262i	0.417279	+	0.172843i
$853$	820.639	+	548.333i	0.962062	+	0.642829i	0.934187	−	0.356782i	$-0.116126\pi$
$853$	820.639	+	548.333i	0.962062	+	0.642829i	0.0278741	+	0.999611i	$0.491126\pi$
$854$	−489.006	−	489.006i	−0.572606	−	0.572606i
$855$		0			0
$856$	−100.244	−	150.026i	−0.117107	−	0.175264i
$857$	852.570	+	169.587i	0.994831	+	0.197884i	0.665555	−	0.746349i	$-0.268195\pi$
$857$	852.570	+	169.587i	0.994831	+	0.197884i	0.329277	+	0.944233i	$0.393195\pi$
$858$	193.826	+	467.938i	0.225905	+	0.545382i
$859$	−194.793	−	470.272i	−0.226767	−	0.547465i	0.769013	−	0.639233i	$-0.220748\pi$
$859$	−194.793	−	470.272i	−0.226767	−	0.547465i	−0.995780	+	0.0917683i	$0.970748\pi$
$860$		0			0
$861$	1582.39	−	1057.32i	1.83785	−	1.22801i
$862$	48.3569	+	243.106i	0.0560984	+	0.282026i
$863$	−164.373	−	164.373i	−0.190467	−	0.190467i	0.605431	−	0.795898i	$-0.293001\pi$
$863$	−164.373	−	164.373i	−0.190467	−	0.190467i	−0.795898	+	0.605431i	$0.793001\pi$
$864$	−768.444	−	513.458i	−0.889402	−	0.594280i
$865$		0			0
$866$		−	273.605i		−	0.315941i
$867$	82.4341	+	763.375i	0.0950797	+	0.880479i
$868$		−	810.856i		−	0.934166i
$869$	−141.197	+	340.879i	−0.162482	+	0.392266i
$870$		0			0
$871$	−718.364	−	718.364i	−0.824758	−	0.824758i
$872$	−447.497	+	89.0127i	−0.513185	+	0.102079i
$873$	20.9368	−	13.9895i	0.0239826	−	0.0160247i
$874$	12.4376	−	62.5278i	0.0142306	−	0.0715421i
$875$		0			0
$876$	149.544	+	361.032i	0.170713	+	0.412137i
$877$	−192.726	+	968.898i	−0.219756	+	1.10479i	0.700555	+	0.713598i	$0.252936\pi$
$877$	−192.726	+	968.898i	−0.219756	+	1.10479i	−0.920311	+	0.391188i	$0.872064\pi$
$878$	37.1200	+	55.5540i	0.0422779	+	0.0632734i
$879$	488.227	−	97.1144i	0.555435	−	0.110483i
$880$		0			0
$881$	440.820	+	294.546i	0.500363	+	0.334332i	0.780006	−	0.625772i	$-0.215216\pi$
$881$	440.820	+	294.546i	0.500363	+	0.334332i	−0.279643	+	0.960104i	$0.590216\pi$
$882$	−61.2712	+	147.922i	−0.0694685	+	0.167712i
$883$	744.697			0.843371			0.421686	−	0.906742i	$-0.361439\pi$
$883$	744.697			0.843371			0.421686	+	0.906742i	$0.361439\pi$
$884$	−579.037	+	1239.30i	−0.655019	+	1.40192i
$885$		0			0
$886$	56.1900	−	135.655i	0.0634198	−	0.153109i
$887$	−1108.63	−	740.766i	−1.24987	−	0.835136i	−0.258472	−	0.966019i	$-0.583219\pi$
$887$	−1108.63	−	740.766i	−1.24987	−	0.835136i	−0.991398	+	0.130883i	$0.958219\pi$
$888$	−171.146	+	171.146i	−0.192732	+	0.192732i
$889$	−134.702	−	677.192i	−0.151521	−	0.761746i
$890$		0			0
$891$	102.112	−	513.351i	0.114604	−	0.576151i
$892$	−94.0680	−	227.100i	−0.105457	−	0.254597i
$893$	1094.33	−	453.285i	1.22545	−	0.507598i
$894$	142.741	+	28.3930i	0.159666	+	0.0317595i
$895$		0			0
$896$	−1511.20	+	300.597i	−1.68661	+	0.335488i
$897$	−230.969	−	230.969i	−0.257490	−	0.257490i
$898$	18.0374	−	26.9949i	0.0200862	−	0.0300611i
$899$	430.143	+	178.171i	0.478469	+	0.198188i
$900$		0			0
$901$	761.833	+	832.659i	0.845541	+	0.924150i
$902$			458.636i			0.508466i
$903$	1999.83	+	828.357i	2.21465	+	0.917339i
$904$	−98.2713	+	147.073i	−0.108707	+	0.162692i
$905$		0			0
$906$	47.4123	+	238.358i	0.0523315	+	0.263088i
$907$	370.786	−	247.751i	0.408804	−	0.273154i	−0.334119	−	0.942531i	$-0.608439\pi$
$907$	370.786	−	247.751i	0.408804	−	0.273154i	0.742923	+	0.669377i	$0.233439\pi$
$908$	−398.862	−	79.3386i	−0.439275	−	0.0873773i
$909$	130.865	−	54.2061i	0.143966	−	0.0596327i
$910$		0			0
$911$	−700.509	−	139.340i	−0.768945	−	0.152953i	−0.204996	−	0.978763i	$-0.565718\pi$
$911$	−700.509	−	139.340i	−0.768945	−	0.152953i	−0.563948	+	0.825810i	$0.690718\pi$
$912$	−161.044	−	241.019i	−0.176583	−	0.264276i
$913$	−38.9629	−	195.880i	−0.0426757	−	0.214545i
$914$	203.941	−	203.941i	0.223130	−	0.223130i
$915$		0			0
$916$	984.069	+	407.615i	1.07431	+	0.444994i
$917$	−2793.51			−3.04636
$918$	−369.806	+	224.021i	−0.402838	+	0.244031i
$919$	866.411			0.942776			0.471388	−	0.881926i	$-0.343753\pi$
$919$	866.411			0.942776			0.471388	+	0.881926i	$0.343753\pi$
$920$		0			0
$921$	742.313	−	1110.95i	0.805986	−	1.20624i
$922$	−322.890	+	322.890i	−0.350206	+	0.350206i
$923$	1092.59	−	217.330i	1.18374	−	0.235460i
$924$	−500.507	−	749.062i	−0.541675	−	0.810673i
$925$		0			0
$926$	223.552	−	92.5984i	0.241417	−	0.0999983i
$927$	124.302	−	51.4876i	0.134091	−	0.0555421i
$928$	137.877	−	693.152i	0.148574	−	0.746931i
$929$	−215.616	+	144.070i	−0.232094	+	0.155081i	−0.666180	−	0.745791i	$-0.732072\pi$
$929$	−215.616	+	144.070i	−0.232094	+	0.155081i	0.434085	+	0.900872i	$0.357072\pi$
$930$		0			0
$931$	−982.694	+	982.694i	−1.05553	+	1.05553i
$932$	−394.776	+	590.824i	−0.423580	+	0.633932i
$933$	96.1698	−	232.174i	0.103076	−	0.248847i
$934$			415.851i			0.445237i
$935$		0			0
$936$	−305.706			−0.326609
$937$	−757.189	−	313.638i	−0.808099	−	0.334726i	−0.0599037	−	0.998204i	$-0.519079\pi$
$937$	−757.189	−	313.638i	−0.808099	−	0.334726i	−0.748195	+	0.663479i	$0.769079\pi$
$938$	−355.582	−	237.592i	−0.379085	−	0.253297i
$939$	796.954	+	796.954i	0.848727	+	0.848727i
$940$		0			0
$941$	366.641	+	548.717i	0.389629	+	0.583121i	0.973489	−	0.228733i	$-0.0734583\pi$
$941$	366.641	+	548.717i	0.389629	+	0.583121i	−0.583860	+	0.811854i	$0.698458\pi$
$942$	−323.158	−	64.2801i	−0.343055	−	0.0682379i
$943$	−113.189	−	273.262i	−0.120031	−	0.289779i
$944$	−264.857	−	639.423i	−0.280569	−	0.677354i
$945$		0			0
$946$	−433.735	+	289.813i	−0.458494	+	0.306356i
$947$	−295.518	−	1485.67i	−0.312057	−	1.56882i	−0.744792	−	0.667296i	$-0.767452\pi$
$947$	−295.518	−	1485.67i	−0.312057	−	1.56882i	0.432735	−	0.901521i	$-0.357548\pi$
$948$	255.970	+	255.970i	0.270011	+	0.270011i
$949$	940.607	+	628.494i	0.991156	+	0.662269i
$950$		0			0
$951$			561.727i			0.590669i
$952$	−307.067	+	1250.78i	−0.322549	+	1.31384i
$953$			341.348i			0.358182i	0.983832	+	0.179091i	$0.0573157\pi$
$953$			341.348i			0.358182i	−0.983832	+	0.179091i	$0.942684\pi$
$954$	−43.1543	+	104.184i	−0.0452351	+	0.109207i
$955$		0			0
$956$	−229.486	−	229.486i	−0.240048	−	0.240048i
$957$	507.341	−	100.916i	0.530136	−	0.105451i
$958$	−288.393	+	192.698i	−0.301037	+	0.201146i
$959$	−312.140	+	1569.24i	−0.325485	+	1.63632i
$960$		0			0
$961$	−199.881	−	482.556i	−0.207993	−	0.502140i
$962$	−61.1151	+	307.246i	−0.0635292	+	0.319383i
$963$	30.7471	+	46.0163i	0.0319285	+	0.0477843i
$964$	218.738	−	43.5097i	0.226907	−	0.0451346i
$965$		0			0
$966$	−114.327	−	76.3909i	−0.118351	−	0.0790796i
$967$	−392.886	+	948.511i	−0.406294	+	0.980880i	0.579810	+	0.814752i	$0.303127\pi$
$967$	−392.886	+	948.511i	−0.406294	+	0.980880i	−0.986104	+	0.166129i	$0.946873\pi$
$968$	−280.295			−0.289561
$969$	−658.245	+	100.804i	−0.679303	+	0.104029i
$970$		0			0
$971$	617.925	−	1491.80i	0.636380	−	1.53636i	−0.195089	−	0.980786i	$-0.562500\pi$
$971$	617.925	−	1491.80i	0.636380	−	1.53636i	0.831469	−	0.555571i	$-0.187500\pi$
$972$	276.627	+	184.836i	0.284596	+	0.190161i
$973$	−12.6136	+	12.6136i	−0.0129636	+	0.0129636i
$974$	−46.8250	−	235.405i	−0.0480749	−	0.241689i
$975$		0			0
$976$	−95.3383	+	479.298i	−0.0976827	+	0.491084i
$977$	−20.4799	−	49.4428i	−0.0209620	−	0.0506067i	0.913052	−	0.407843i	$-0.133719\pi$
$977$	−20.4799	−	49.4428i	−0.0209620	−	0.0506067i	−0.934014	+	0.357237i	$0.883719\pi$
$978$	−49.4866	+	20.4980i	−0.0505998	+	0.0209591i
$979$	−449.313	−	89.3738i	−0.458951	−	0.0912909i
$980$		0			0
$981$	137.258	−	27.3023i	0.139916	−	0.0278310i
$982$	294.394	+	294.394i	0.299790	+	0.299790i
$983$	−701.045	+	1049.19i	−0.713169	+	1.06733i	0.281022	+	0.959701i	$0.409327\pi$
$983$	−701.045	+	1049.19i	−0.713169	+	1.06733i	−0.994191	+	0.107632i	$0.965673\pi$
$984$	929.830	+	385.148i	0.944949	+	0.391411i
$985$		0			0
$986$	−266.487	−	195.706i	−0.270270	−	0.198485i
$987$		−	2554.67i		−	2.58832i
$988$	−1096.06	−	454.003i	−1.10937	−	0.459518i
$989$	186.902	−	279.718i	0.188980	−	0.282829i
$990$		0			0
$991$	48.3001	+	242.821i	0.0487387	+	0.245026i	0.997473	−	0.0710492i	$-0.0226347\pi$
$991$	48.3001	+	242.821i	0.0487387	+	0.245026i	−0.948734	+	0.316075i	$0.897635\pi$
$992$	553.676	−	369.955i	0.558141	−	0.372938i
$993$	600.104	+	119.368i	0.604334	+	0.120210i
$994$	433.244	−	179.455i	0.435859	−	0.180539i
$995$		0			0
$996$	−192.180	−	38.2270i	−0.192952	−	0.0383806i
$997$	295.683	+	442.522i	0.296573	+	0.443853i	0.949592	−	0.313489i	$-0.101498\pi$
$997$	295.683	+	442.522i	0.296573	+	0.443853i	−0.653019	+	0.757342i	$0.726498\pi$
$998$	−81.7299	−	410.884i	−0.0818937	−	0.411707i
$999$	295.843	−	295.843i	0.296139	−	0.296139i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.3.t.f.24.5		96
5.2	odd	4		425.3.u.c.126.8	✓	96
5.3	odd	4		425.3.u.d.126.5	yes	96
5.4	even	2		425.3.t.g.24.8		96
17.5	odd	16		425.3.t.g.124.8		96
85.22	even	16		425.3.u.c.226.8	yes	96
85.39	odd	16	inner	425.3.t.f.124.5		96
85.73	even	16		425.3.u.d.226.5	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.3.t.f.24.5		96	1.1	even	1	trivial
425.3.t.f.124.5		96	85.39	odd	16	inner
425.3.t.g.24.8		96	5.4	even	2
425.3.t.g.124.8		96	17.5	odd	16
425.3.u.c.126.8	✓	96	5.2	odd	4
425.3.u.c.226.8	yes	96	85.22	even	16
425.3.u.d.126.5	yes	96	5.3	odd	4
425.3.u.d.226.5	yes	96	85.73	even	16

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	425.t (of order \(16\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.808326 - 0.334820i) q^{2} +(2.20904 + 1.47604i) q^{3} +(-2.28714 - 2.28714i) q^{4} +(-1.29142 - 1.93275i) q^{6} +(11.7391 + 2.33505i) q^{7} +(2.42226 + 5.84784i) q^{8} +(-0.742961 - 1.79367i) q^{9} +(7.28271 - 4.86615i) q^{11} +(-1.67649 - 8.42829i) q^{12} +(-17.5907 - 17.5907i) q^{13} +(-8.70718 - 5.81795i) q^{14} +7.40003i q^{16} +(15.4018 + 7.19617i) q^{17} +1.69863i q^{18} +(-5.64227 + 13.6217i) q^{19} +(22.4855 + 22.4855i) q^{21} +(-7.51609 + 1.49504i) q^{22} +(4.10923 - 2.74570i) q^{23} +(-3.28075 + 16.4935i) q^{24} +(8.32930 + 20.1087i) q^{26} +(5.67111 - 28.5106i) q^{27} +(-21.5083 - 32.1895i) q^{28} +(21.8020 - 4.33668i) q^{29} +(17.4150 + 11.6363i) q^{31} +(12.1667 - 29.3730i) q^{32} +23.2704 q^{33} +(-10.0403 - 10.9737i) q^{34} +(-2.40311 + 5.80162i) q^{36} +(11.9671 + 7.99619i) q^{37} +(9.12160 - 9.12160i) q^{38} +(-12.8941 - 64.8230i) q^{39} +(11.6758 - 58.6981i) q^{41} +(-10.6470 - 25.7042i) q^{42} +(62.8891 - 26.0495i) q^{43} +(-27.7861 - 5.52701i) q^{44} +(-4.24091 + 0.843569i) q^{46} +(-56.8070 - 56.8070i) q^{47} +(-10.9227 + 16.3470i) q^{48} +(87.0832 + 36.0710i) q^{49} +(23.4014 + 38.6302i) q^{51} +80.4646i q^{52} +(61.3341 + 25.4054i) q^{53} +(-14.1300 + 21.1471i) q^{54} +(14.7800 + 74.3043i) q^{56} +(-32.5701 + 21.7626i) q^{57} +(-19.0751 - 3.79427i) q^{58} +(-86.4081 + 35.7914i) q^{59} +(64.7697 + 12.8835i) q^{61} +(-10.1809 - 15.2368i) q^{62} +(-4.53338 - 22.7908i) q^{63} +(1.26113 - 1.26113i) q^{64} +(-18.8101 - 7.79140i) q^{66} +40.8378 q^{67} +(-18.7674 - 51.6847i) q^{68} +13.1302 q^{69} +(-24.8785 + 37.2333i) q^{71} +(8.68944 - 8.68944i) q^{72} +(-44.6004 + 8.87157i) q^{73} +(-6.99607 - 10.4704i) q^{74} +(44.0593 - 18.2500i) q^{76} +(96.8549 - 40.1186i) q^{77} +(-11.2814 + 56.7153i) q^{78} +(-35.0256 + 23.4033i) q^{79} +(42.2551 - 42.2551i) q^{81} +(-29.0911 + 43.5380i) q^{82} +(8.72588 - 21.0661i) q^{83} -102.855i q^{84} -59.5569 q^{86} +(54.5625 + 22.6005i) q^{87} +(46.0970 + 30.8011i) q^{88} +(-36.9839 - 36.9839i) q^{89} +(-165.423 - 247.573i) q^{91} +(-15.6782 - 3.11858i) q^{92} +(21.2948 + 51.4102i) q^{93} +(26.8985 + 64.9388i) q^{94} +(70.2323 - 46.9277i) q^{96} +(2.53031 + 12.7207i) q^{97} +(-58.3143 - 58.3143i) q^{98} +(-14.1390 - 9.44739i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 24 q^{13} - 32 q^{14} + 64 q^{17} + 24 q^{19} + 48 q^{22} + 72 q^{23} + 336 q^{24} - 224 q^{26} - 64 q^{31} + 400 q^{32} - 256 q^{33} - 64 q^{34} + 192 q^{36} + 72 q^{37} + 496 q^{38} - 16 q^{39}+ \cdots + 160 q^{99}+O(q^{100}) \) 96 * q - 24 * q^13 - 32 * q^14 + 64 * q^17 + 24 * q^19 + 48 * q^22 + 72 * q^23 + 336 * q^24 - 224 * q^26 - 64 * q^31 + 400 * q^32 - 256 * q^33 - 64 * q^34 + 192 * q^36 + 72 * q^37 + 496 * q^38 - 16 * q^39 + 216 * q^41 - 248 * q^42 - 64 * q^43 + 32 * q^44 + 336 * q^46 + 32 * q^49 - 32 * q^51 - 104 * q^53 - 584 * q^54 - 40 * q^56 + 336 * q^57 + 1088 * q^58 - 544 * q^59 + 112 * q^61 + 152 * q^62 - 1184 * q^63 - 592 * q^64 - 24 * q^66 - 144 * q^67 + 520 * q^68 + 192 * q^69 - 336 * q^71 - 1040 * q^72 + 336 * q^74 - 1016 * q^76 + 720 * q^77 + 1568 * q^78 + 384 * q^79 - 928 * q^81 + 288 * q^82 - 1200 * q^83 + 64 * q^86 - 384 * q^87 + 576 * q^88 - 576 * q^89 + 336 * q^91 - 640 * q^92 - 672 * q^94 + 768 * q^96 + 1440 * q^97 - 408 * q^98 + 160 * q^99

Introduction

L-functions

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