LMFDB - Embedded newform 425.3.u.c.226.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [425,3,Mod(126,425)] 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("425.126"); 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([0, 11])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	425.u (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [96,0,0,0,0,0,0,0,0,0,0,-96] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(12)] == 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			226.8
Character	$\chi$	$=$	425.226
Dual form			425.3.u.c.126.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.334820 + 0.808326i) q^{2} +(1.47604 + 2.20904i) q^{3} +(2.28714 - 2.28714i) q^{4} +(-1.29142 + 1.93275i) q^{6} +(-2.33505 - 11.7391i) q^{7} +(5.84784 + 2.42226i) q^{8} +(0.742961 - 1.79367i) q^{9} +(7.28271 + 4.86615i) q^{11} +(8.42829 + 1.67649i) q^{12} +(-17.5907 - 17.5907i) q^{13} +(8.70718 - 5.81795i) q^{14} -7.40003i q^{16} +(-7.19617 - 15.4018i) q^{17} +1.69863 q^{18} +(5.64227 + 13.6217i) q^{19} +(22.4855 - 22.4855i) q^{21} +(-1.49504 + 7.51609i) q^{22} +(-2.74570 + 4.10923i) q^{23} +(3.28075 + 16.4935i) q^{24} +(8.32930 - 20.1087i) q^{26} +(28.5106 - 5.67111i) q^{27} +(-32.1895 - 21.5083i) q^{28} +(-21.8020 - 4.33668i) q^{29} +(17.4150 - 11.6363i) q^{31} +(29.3730 - 12.1667i) q^{32} +23.2704i q^{33} +(10.0403 - 10.9737i) q^{34} +(-2.40311 - 5.80162i) q^{36} +(-7.99619 - 11.9671i) q^{37} +(-9.12160 + 9.12160i) q^{38} +(12.8941 - 64.8230i) q^{39} +(11.6758 + 58.6981i) q^{41} +(25.7042 + 10.6470i) q^{42} +(-26.0495 + 62.8891i) q^{43} +(27.7861 - 5.52701i) q^{44} +(-4.24091 - 0.843569i) q^{46} +(56.8070 + 56.8070i) q^{47} +(16.3470 - 10.9227i) q^{48} +(-87.0832 + 36.0710i) q^{49} +(23.4014 - 38.6302i) q^{51} -80.4646 q^{52} +(25.4054 + 61.3341i) q^{53} +(14.1300 + 21.1471i) q^{54} +(14.7800 - 74.3043i) q^{56} +(-21.7626 + 32.5701i) q^{57} +(-3.79427 - 19.0751i) q^{58} +(86.4081 + 35.7914i) q^{59} +(64.7697 - 12.8835i) q^{61} +(15.2368 + 10.1809i) q^{62} +(-22.7908 - 4.53338i) q^{63} +(-1.26113 - 1.26113i) q^{64} +(-18.8101 + 7.79140i) q^{66} -40.8378i q^{67} +(-51.6847 - 18.7674i) q^{68} -13.1302 q^{69} +(-24.8785 - 37.2333i) q^{71} +(8.68944 - 8.68944i) q^{72} +(8.87157 - 44.6004i) q^{73} +(6.99607 - 10.4704i) q^{74} +(44.0593 + 18.2500i) q^{76} +(40.1186 - 96.8549i) q^{77} +(56.7153 - 11.2814i) q^{78} +(35.0256 + 23.4033i) q^{79} +(42.2551 + 42.2551i) q^{81} +(-43.5380 + 29.0911i) q^{82} +(-21.0661 + 8.72588i) q^{83} -102.855i q^{84} -59.5569 q^{86} +(-22.6005 - 54.5625i) q^{87} +(30.8011 + 46.0970i) q^{88} +(36.9839 - 36.9839i) q^{89} +(-165.423 + 247.573i) q^{91} +(3.11858 + 15.6782i) q^{92} +(51.4102 + 21.2948i) q^{93} +(-26.8985 + 64.9388i) q^{94} +(70.2323 + 46.9277i) q^{96} +(-12.7207 - 2.53031i) q^{97} +(-58.3143 - 58.3143i) q^{98} +(14.1390 - 9.44739i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 96 q^{12} - 24 q^{13} + 32 q^{14} + 8 q^{17} + 64 q^{18} - 24 q^{19} + 96 q^{22} + 56 q^{23} - 336 q^{24} - 224 q^{26} - 144 q^{27} + 480 q^{28} - 64 q^{31} - 40 q^{32} + 64 q^{34} + 192 q^{36} + 128 q^{37}+ \cdots - 160 q^{99}+O(q^{100}) $ 96 * q - 96 * q^12 - 24 * q^13 + 32 * q^14 + 8 * q^17 + 64 * q^18 - 24 * q^19 + 96 * q^22 + 56 * q^23 - 336 * q^24 - 224 * q^26 - 144 * q^27 + 480 * q^28 - 64 * q^31 - 40 * q^32 + 64 * q^34 + 192 * q^36 + 128 * q^37 - 496 * q^38 + 16 * q^39 + 216 * q^41 + 432 * q^42 - 592 * q^43 - 32 * q^44 + 336 * q^46 - 160 * q^48 - 32 * q^49 - 32 * q^51 + 96 * q^53 + 584 * q^54 - 40 * q^56 + 1120 * q^57 + 256 * q^58 + 544 * q^59 + 112 * q^61 + 560 * q^62 + 312 * q^63 + 592 * q^64 - 24 * q^66 - 192 * q^69 - 336 * q^71 - 1040 * q^72 - 336 * q^74 - 1016 * q^76 - 960 * q^77 - 384 * q^79 - 928 * q^81 - 1200 * q^82 - 144 * q^83 + 64 * q^86 - 672 * q^87 - 832 * q^88 + 576 * q^89 + 336 * q^91 - 1008 * q^92 - 512 * q^93 + 672 * q^94 + 768 * q^96 - 128 * q^97 - 408 * q^98 - 160 * q^99

Character values

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

$n$	$52$	$326$
$\chi(n)$	$1$	$e\left(\frac{5}{16}\right)$

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 $

$2$	0.334820	+	0.808326i	0.167410	+	0.404163i	0.985213	−	0.171335i	$-0.0548081\pi$
$2$	0.334820	+	0.808326i	0.167410	+	0.404163i	−0.817803	+	0.575498i	$0.804808\pi$
$3$	1.47604	+	2.20904i	0.492012	+	0.736348i	0.991519	−	0.129962i	$-0.0414856\pi$
$3$	1.47604	+	2.20904i	0.492012	+	0.736348i	−0.499507	+	0.866310i	$0.666486\pi$
$4$	2.28714	−	2.28714i	0.571785	−	0.571785i
$5$		0			0
$5$		0			0
$6$	−1.29142	+	1.93275i	−0.215237	+	0.322125i
$7$	−2.33505	−	11.7391i	−0.333578	−	1.67701i	−0.675561	−	0.737304i	$-0.736099\pi$
$7$	−2.33505	−	11.7391i	−0.333578	−	1.67701i	0.341983	−	0.939706i	$-0.388901\pi$
$8$	5.84784	+	2.42226i	0.730980	+	0.302782i
$9$	0.742961	−	1.79367i	0.0825513	−	0.199296i
$10$		0			0
$11$	7.28271	+	4.86615i	0.662064	+	0.442377i	0.840673	−	0.541543i	$-0.182160\pi$
$11$	7.28271	+	4.86615i	0.662064	+	0.442377i	−0.178609	+	0.983920i	$0.557160\pi$
$12$	8.42829	+	1.67649i	0.702357	+	0.139708i
$13$	−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
$17$	−7.19617	−	15.4018i	−0.423304	−	0.905988i
$17$	−7.19617	−	15.4018i	−0.423304	−	0.905988i
$18$	1.69863			0.0943682
$19$	5.64227	+	13.6217i	0.296962	+	0.716929i	0.999983	+	0.00576061i	$0.00183367\pi$
$19$	5.64227	+	13.6217i	0.296962	+	0.716929i	−0.703022	+	0.711168i	$0.748166\pi$
$20$		0			0
$21$	22.4855	−	22.4855i	1.07074	−	1.07074i
$22$	−1.49504	+	7.51609i	−0.0679565	+	0.341640i
$23$	−2.74570	+	4.10923i	−0.119378	+	0.178662i	−0.886346	−	0.463024i	$-0.846765\pi$
$23$	−2.74570	+	4.10923i	−0.119378	+	0.178662i	0.766968	+	0.641685i	$0.221765\pi$
$24$	3.28075	+	16.4935i	0.136698	+	0.687228i
$25$		0			0
$26$	8.32930	−	20.1087i	0.320358	−	0.773412i
$27$	28.5106	−	5.67111i	1.05595	−	0.210041i
$28$	−32.1895	−	21.5083i	−1.14962	−	0.768154i
$29$	−21.8020	−	4.33668i	−0.751792	−	0.149541i	−0.195702	−	0.980663i	$-0.562699\pi$
$29$	−21.8020	−	4.33668i	−0.751792	−	0.149541i	−0.556089	+	0.831123i	$0.687699\pi$
$30$		0			0
$31$	17.4150	−	11.6363i	0.561773	−	0.375365i	−0.242022	−	0.970271i	$-0.577811\pi$
$31$	17.4150	−	11.6363i	0.561773	−	0.375365i	0.803795	+	0.594906i	$0.202811\pi$
$32$	29.3730	−	12.1667i	0.917906	−	0.380209i
$33$			23.2704i			0.705164i
$34$	10.0403	−	10.9737i	0.295302	−	0.322755i
$35$		0			0
$36$	−2.40311	−	5.80162i	−0.0667531	−	0.161156i
$37$	−7.99619	−	11.9671i	−0.216113	−	0.323436i	0.707535	−	0.706679i	$-0.249807\pi$
$37$	−7.99619	−	11.9671i	−0.216113	−	0.323436i	−0.923648	+	0.383243i	$0.874807\pi$
$38$	−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	0.812854	+	0.582467i	$0.197912\pi$
$41$	11.6758	+	58.6981i	0.284775	+	1.43166i	−0.528079	+	0.849195i	$0.677088\pi$
$42$	25.7042	+	10.6470i	0.612005	+	0.253501i
$43$	−26.0495	+	62.8891i	−0.605803	+	1.46254i	0.261721	+	0.965144i	$0.415710\pi$
$43$	−26.0495	+	62.8891i	−0.605803	+	1.46254i	−0.867524	+	0.497395i	$0.834290\pi$
$44$	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	$0.0762295\pi$
$47$	56.8070	+	56.8070i	1.20866	+	1.20866i	0.237199	+	0.971461i	$0.423771\pi$
$48$	16.3470	−	10.9227i	0.340562	−	0.227556i
$49$	−87.0832	+	36.0710i	−1.77721	+	0.736144i
$50$		0			0
$51$	23.4014	−	38.6302i	0.458851	−	0.757455i
$52$	−80.4646			−1.54740
$53$	25.4054	+	61.3341i	0.479347	+	1.15725i	0.959916	+	0.280289i	$0.0904304\pi$
$53$	25.4054	+	61.3341i	0.479347	+	1.15725i	−0.480568	+	0.876957i	$0.659570\pi$
$54$	14.1300	+	21.1471i	0.261667	+	0.391613i
$55$		0			0
$56$	14.7800	−	74.3043i	0.263929	−	1.32686i
$57$	−21.7626	+	32.5701i	−0.381800	+	0.571404i
$58$	−3.79427	−	19.0751i	−0.0654185	−	0.328881i
$59$	86.4081	+	35.7914i	1.46454	+	0.606634i	0.965607	−	0.260005i	$-0.0837242\pi$
$59$	86.4081	+	35.7914i	1.46454	+	0.606634i	0.498936	+	0.866639i	$0.333724\pi$
$60$		0			0
$61$	64.7697	−	12.8835i	1.06180	−	0.211205i	0.366861	−	0.930276i	$-0.380432\pi$
$61$	64.7697	−	12.8835i	1.06180	−	0.211205i	0.694937	+	0.719071i	$0.255432\pi$
$62$	15.2368	+	10.1809i	0.245755	+	0.164208i
$63$	−22.7908	−	4.53338i	−0.361759	−	0.0719584i
$64$	−1.26113	−	1.26113i	−0.0197051	−	0.0197051i
$65$		0			0
$66$	−18.8101	+	7.79140i	−0.285001	+	0.118051i
$67$		−	40.8378i		−	0.609520i	−0.952429	−	0.304760i	$-0.901424\pi$
$67$		−	40.8378i		−	0.609520i	0.952429	−	0.304760i	$-0.0985762\pi$
$68$	−51.6847	−	18.7674i	−0.760069	−	0.275991i
$69$	−13.1302			−0.190293
$70$		0			0
$71$	−24.8785	−	37.2333i	−0.350402	−	0.524413i	0.613842	−	0.789429i	$-0.289623\pi$
$71$	−24.8785	−	37.2333i	−0.350402	−	0.524413i	−0.964244	+	0.265015i	$0.914623\pi$
$72$	8.68944	−	8.68944i	0.120687	−	0.120687i
$73$	8.87157	−	44.6004i	0.121528	−	0.610964i	−0.871234	−	0.490868i	$-0.836680\pi$
$73$	8.87157	−	44.6004i	0.121528	−	0.610964i	0.992762	−	0.120096i	$-0.0383203\pi$
$74$	6.99607	−	10.4704i	0.0945415	−	0.141491i
$75$		0			0
$76$	44.0593	+	18.2500i	0.579727	+	0.240131i
$77$	40.1186	−	96.8549i	0.521021	−	1.25786i
$78$	56.7153	−	11.2814i	0.727120	−	0.144633i
$79$	35.0256	+	23.4033i	0.443361	+	0.296245i	0.757141	−	0.653251i	$-0.226595\pi$
$79$	35.0256	+	23.4033i	0.443361	+	0.296245i	−0.313780	+	0.949496i	$0.601595\pi$
$80$		0			0
$81$	42.2551	+	42.2551i	0.521668	+	0.521668i
$82$	−43.5380	+	29.0911i	−0.530951	+	0.354770i
$83$	−21.0661	+	8.72588i	−0.253809	+	0.105131i	−0.505960	−	0.862557i	$-0.668862\pi$
$83$	−21.0661	+	8.72588i	−0.253809	+	0.105131i	0.252152	+	0.967688i	$0.418862\pi$
$84$		−	102.855i		−	1.22446i
$85$		0			0
$86$	−59.5569			−0.692522
$87$	−22.6005	−	54.5625i	−0.259776	−	0.627156i
$88$	30.8011	+	46.0970i	0.350012	+	0.523830i
$89$	36.9839	−	36.9839i	0.415550	−	0.415550i	−0.468117	−	0.883667i	$-0.655067\pi$
$89$	36.9839	−	36.9839i	0.415550	−	0.415550i	0.883667	+	0.468117i	$0.155067\pi$
$90$		0			0
$91$	−165.423	+	247.573i	−1.81784	+	2.72058i
$92$	3.11858	+	15.6782i	0.0338976	+	0.170415i
$93$	51.4102	+	21.2948i	0.552798	+	0.228976i
$94$	−26.8985	+	64.9388i	−0.286154	+	0.690838i
$95$		0			0
$96$	70.2323	+	46.9277i	0.731587	+	0.488831i
$97$	−12.7207	−	2.53031i	−0.131142	−	0.0260857i	0.129083	−	0.991634i	$-0.458797\pi$
$97$	−12.7207	−	2.53031i	−0.131142	−	0.0260857i	−0.260225	+	0.965548i	$0.583797\pi$
$98$	−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	$-0.882372\pi$
$101$		−	72.9595i		−	0.722371i	0.932494	−	0.361186i	$-0.117628\pi$
$102$	39.0611	+	5.98182i	0.382952	+	0.0586453i
$103$	69.3005			0.672820			0.336410	−	0.941716i	$-0.390787\pi$
$103$	69.3005			0.672820			0.336410	+	0.941716i	$0.390787\pi$
$104$	−60.2583	−	145.477i	−0.579407	−	1.39881i
$105$		0			0
$106$	−41.0717	+	41.0717i	−0.387469	+	0.387469i
$107$	−5.56128	+	27.9584i	−0.0519745	+	0.261294i	−0.998032	−	0.0627049i	$-0.980027\pi$
$107$	−5.56128	+	27.9584i	−0.0519745	+	0.261294i	0.946058	+	0.323999i	$0.105027\pi$
$108$	52.2371	−	78.1784i	0.483677	−	0.723874i
$109$	14.0628	+	70.6985i	0.129017	+	0.648610i	0.990125	+	0.140188i	$0.0447708\pi$
$109$	14.0628	+	70.6985i	0.129017	+	0.648610i	−0.861108	+	0.508422i	$0.830229\pi$
$110$		0			0
$111$	14.6333	−	35.3278i	0.131831	−	0.318269i
$112$	−86.8695	+	17.2794i	−0.775620	+	0.154280i
$113$	23.2356	+	15.5255i	0.205625	+	0.137394i	0.654119	−	0.756392i	$-0.273040\pi$
$113$	23.2356	+	15.5255i	0.205625	+	0.137394i	−0.448494	+	0.893786i	$0.648040\pi$
$114$	−33.6138	−	6.68620i	−0.294858	−	0.0586509i
$115$		0			0
$116$	−59.7827	+	39.9455i	−0.515368	+	0.344358i
$117$	−44.6210	+	18.4826i	−0.381376	+	0.157971i
$118$			81.8296i			0.693471i
$119$	−163.999	+	120.440i	−1.37815	+	1.01210i
$120$		0			0
$121$	−16.9463	−	40.9119i	−0.140052	−	0.338115i
$122$	32.1002	+	48.0414i	0.263117	+	0.393782i
$123$	−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
$127$	53.2959	+	22.0759i	0.419652	+	0.173826i	0.582509	−	0.812824i	$-0.302071\pi$
$127$	53.2959	+	22.0759i	0.419652	+	0.173826i	−0.162857	+	0.986650i	$0.552071\pi$
$128$	49.2639	−	118.934i	0.384875	−	0.929169i
$129$	−177.375	+	35.2820i	−1.37500	+	0.273504i
$130$		0			0
$131$	−228.910	−	45.5330i	−1.74740	−	0.347580i	−0.785061	−	0.619418i	$-0.787369\pi$
$131$	−228.910	−	45.5330i	−1.74740	−	0.347580i	−0.962343	+	0.271837i	$0.912369\pi$
$132$	53.2227	+	53.2227i	0.403202	+	0.403202i
$133$	146.731	−	98.0422i	1.10324	−	0.737159i
$134$	33.0103	−	13.6733i	0.246345	−	0.102040i
$135$		0			0
$136$	−4.77498	−	107.498i	−0.0351102	−	0.790428i
$137$	−133.676			−0.975739			−0.487870	−	0.872916i	$-0.662226\pi$
$137$	−133.676			−0.975739			−0.487870	+	0.872916i	$0.662226\pi$
$138$	−4.39625	−	10.6135i	−0.0318569	−	0.0769093i
$139$	0.828008	+	1.23920i	0.00595689	+	0.00891512i	0.834436	−	0.551105i	$-0.185794\pi$
$139$	0.828008	+	1.23920i	0.00595689	+	0.00891512i	−0.828479	+	0.560020i	$0.810794\pi$
$140$		0			0
$141$	−41.6400	+	209.338i	−0.295319	+	1.48467i
$142$	21.7669	−	32.5764i	0.153288	−	0.229411i
$143$	−42.5089	−	213.706i	−0.297265	−	1.49445i
$144$	−13.2732	−	5.49794i	−0.0921750	−	0.0381801i
$145$		0			0
$146$	39.0220	−	7.76197i	0.267274	−	0.0531642i
$147$	−208.220	−	139.128i	−1.41646	−	0.946451i
$148$	−45.6589	−	9.08212i	−0.308506	−	0.0613657i
$149$	44.2723	+	44.2723i	0.297129	+	0.297129i	0.839888	−	0.542759i	$-0.182620\pi$
$149$	44.2723	+	44.2723i	0.297129	+	0.297129i	−0.542759	+	0.839888i	$0.682620\pi$
$150$		0			0
$151$	−96.5922	+	40.0098i	−0.639683	+	0.264965i	−0.678861	−	0.734267i	$-0.737526\pi$
$151$	−96.5922	+	40.0098i	−0.639683	+	0.264965i	0.0391778	+	0.999232i	$0.487526\pi$
$152$			93.3243i			0.613975i
$153$	−32.9722	+	1.46460i	−0.215504	+	0.00957253i
$154$	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	$0.100917\pi$
$158$	−7.19028	+	36.1480i	−0.0455081	+	0.228785i
$159$	−97.9903	+	146.653i	−0.616291	+	0.922345i
$160$		0			0
$161$	54.6498	+	22.6367i	0.339440	+	0.140601i
$162$	−20.0081	+	48.3037i	−0.123507	+	0.298171i
$163$	−22.6005	+	4.49551i	−0.138653	+	0.0275798i	−0.263929	−	0.964542i	$-0.585018\pi$
$163$	−22.6005	+	4.49551i	−0.138653	+	0.0275798i	0.125276	+	0.992122i	$0.460018\pi$
$164$	160.955	+	107.547i	0.981433	+	0.655773i
$165$		0			0
$166$	−14.1067	−	14.1067i	−0.0849802	−	0.0849802i
$167$	−156.497	+	104.568i	−0.937108	+	0.626156i	−0.927510	−	0.373798i	$-0.878055\pi$
$167$	−156.497	+	104.568i	−0.937108	+	0.626156i	−0.00959805	+	0.999954i	$0.503055\pi$
$168$	185.957	−	77.0260i	1.10689	−	0.458488i
$169$			449.863i			2.66191i
$170$		0			0
$171$	28.6247			0.167396
$172$	84.2573	+	203.415i	0.489868	+	1.18265i
$173$	−122.377	−	183.149i	−0.707379	−	1.05867i	−0.994897	−	0.100892i	$-0.967830\pi$
$173$	−122.377	−	183.149i	−0.707379	−	1.05867i	0.287519	−	0.957775i	$-0.407170\pi$
$174$	36.5372	−	36.5372i	0.209984	−	0.209984i
$175$		0			0
$176$	36.0097	−	53.8923i	0.204600	−	0.306206i
$177$	48.4766	+	243.708i	0.273879	+	1.37688i
$178$	42.2781	+	17.5121i	0.237517	+	0.0983828i
$179$	65.5165	−	158.171i	0.366014	−	0.883636i	−0.628381	−	0.777906i	$-0.716282\pi$
$179$	65.5165	−	158.171i	0.366014	−	0.883636i	0.994395	−	0.105730i	$-0.0337180\pi$
$180$		0			0
$181$	−5.80388	−	3.87803i	−0.0320656	−	0.0214256i	0.539434	−	0.842028i	$-0.318638\pi$
$181$	−5.80388	−	3.87803i	−0.0320656	−	0.0214256i	−0.571500	+	0.820602i	$0.693638\pi$
$182$	−255.507	−	50.8235i	−1.40388	−	0.279250i
$183$	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
$187$	22.5398	−	147.184i	0.120534	−	0.787082i
$188$	259.851			1.38219
$189$	−133.147	−	321.446i	−0.704482	−	1.70077i
$190$		0			0
$191$	82.3988	−	82.3988i	0.431407	−	0.431407i	−0.457700	−	0.889107i	$-0.651326\pi$
$191$	82.3988	−	82.3988i	0.431407	−	0.431407i	0.889107	+	0.457700i	$0.151326\pi$
$192$	0.924416	−	4.64735i	0.00481467	−	0.0242050i
$193$	−92.2635	+	138.082i	−0.478049	+	0.715451i	−0.989607	−	0.143798i	$-0.954069\pi$
$193$	−92.2635	+	138.082i	−0.478049	+	0.715451i	0.511558	+	0.859249i	$0.329069\pi$
$194$	−2.21384	−	11.1297i	−0.0114115	−	0.0573696i
$195$		0			0
$196$	−116.672	+	281.671i	−0.595265	+	1.43710i
$197$	132.204	−	26.2969i	0.671084	−	0.133487i	0.152224	−	0.988346i	$-0.451356\pi$
$197$	132.204	−	26.2969i	0.671084	−	0.133487i	0.518860	+	0.854859i	$0.326356\pi$
$198$	12.3706	+	8.26577i	0.0624778	+	0.0417463i
$199$	103.420	+	20.5715i	0.519697	+	0.103374i	0.447967	−	0.894050i	$-0.352148\pi$
$199$	103.420	+	20.5715i	0.519697	+	0.103374i	0.0717299	+	0.997424i	$0.477148\pi$
$200$		0			0
$201$	90.2125	−	60.2780i	0.448818	−	0.299891i
$202$	58.9751	−	24.4283i	0.291956	−	0.120932i
$203$			266.061i			1.31065i
$204$	−34.8304	−	141.875i	−0.170737	−	0.695466i
$205$		0			0
$206$	23.2032	+	56.0174i	0.112637	+	0.271929i
$207$	5.33064	+	7.97786i	0.0257519	+	0.0385404i
$208$	−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	−0.967729	−	0.251995i	$-0.918913\pi$
$211$	−35.8907	−	180.435i	−0.170098	−	0.855141i	0.797631	−	0.603146i	$-0.206087\pi$
$212$	198.385	+	82.1739i	0.935780	+	0.387613i
$213$	45.5285	−	109.915i	0.213749	−	0.516035i
$214$	−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
$218$	−52.4390	+	35.0386i	−0.240546	+	0.160727i
$219$	111.619	−	46.2341i	0.509675	−	0.211114i
$220$		0			0
$221$	−144.342	+	397.513i	−0.653133	+	1.79870i
$222$	33.4559			0.150702
$223$	29.0827	+	70.2118i	0.130416	+	0.314851i	0.975576	−	0.219661i	$-0.0704953\pi$
$223$	29.0827	+	70.2118i	0.130416	+	0.314851i	−0.845161	+	0.534512i	$0.820495\pi$
$224$	−211.413	−	316.402i	−0.943808	−	1.41251i
$225$		0			0
$226$	−4.76996	+	23.9802i	−0.0211060	+	0.106107i
$227$	69.8522	−	104.541i	0.307719	−	0.460534i	−0.645089	−	0.764107i	$-0.723180\pi$
$227$	69.8522	−	104.541i	0.307719	−	0.460534i	0.952808	+	0.303574i	$0.0981798\pi$
$228$	24.7181	+	124.266i	0.108413	+	0.545028i
$229$	304.241	+	126.021i	1.32856	+	0.550309i	0.930245	−	0.366938i	$-0.119594\pi$
$229$	304.241	+	126.021i	1.32856	+	0.550309i	0.398318	+	0.917247i	$0.369594\pi$
$230$		0			0
$231$	273.173	−	54.3375i	1.18257	−	0.235227i
$232$	−116.990	−	78.1701i	−0.504267	−	0.336940i
$233$	−215.466	−	42.8588i	−0.924746	−	0.183943i	−0.290322	−	0.956929i	$-0.593762\pi$
$233$	−215.466	−	42.8588i	−0.924746	−	0.183943i	−0.634424	+	0.772986i	$0.718762\pi$
$234$	−29.8800	−	29.8800i	−0.127692	−	0.127692i
$235$		0			0
$236$	279.487	−	115.767i	1.18427	−	0.490540i
$237$			111.917i			0.472224i
$238$	−152.265	−	92.2392i	−0.639770	−	0.387560i
$239$	−100.337			−0.419822			−0.209911	−	0.977721i	$-0.567317\pi$
$239$	−100.337			−0.419822			−0.209911	+	0.977721i	$0.567317\pi$
$240$		0			0
$241$	−38.3073	−	57.3310i	−0.158952	−	0.237888i	0.743442	−	0.668800i	$-0.233192\pi$
$241$	−38.3073	−	57.3310i	−0.158952	−	0.237888i	−0.902394	+	0.430912i	$0.858192\pi$
$242$	27.3963	−	27.3963i	0.113208	−	0.113208i
$243$	20.0667	−	100.882i	0.0825792	−	0.415153i
$244$	118.671	−	177.604i	0.486357	−	0.727884i
$245$		0			0
$246$	−128.527	−	53.2377i	−0.522468	−	0.216413i
$247$	140.363	−	338.865i	0.568270	−	1.37192i
$248$	130.026	−	25.8638i	0.524299	−	0.104289i
$249$	−50.3702	−	33.6563i	−0.202290	−	0.135166i
$250$		0			0
$251$	−265.197	−	265.197i	−1.05656	−	1.05656i	−0.998301	−	0.0582606i	$-0.981445\pi$
$251$	−265.197	−	265.197i	−1.05656	−	1.05656i	−0.0582606	−	0.998301i	$-0.518555\pi$
$252$	−62.4943	+	41.7573i	−0.247993	+	0.165704i
$253$	−39.9922	+	16.5653i	−0.158072	+	0.0654755i
$254$			50.4719i			0.198708i
$255$		0			0
$256$	105.498			0.412101
$257$	116.695	+	281.727i	0.454066	+	1.09621i	0.970762	+	0.240044i	$0.0771619\pi$
$257$	116.695	+	281.727i	0.454066	+	1.09621i	−0.516696	+	0.856169i	$0.672838\pi$
$258$	−87.9080	−	131.564i	−0.340729	−	0.509937i
$259$	−121.812	+	121.812i	−0.470315	+	0.470315i
$260$		0			0
$261$	−23.9766	+	35.8835i	−0.0918643	+	0.137485i
$262$	−39.8380	−	200.279i	−0.152054	−	0.764425i
$263$	307.894	+	127.534i	1.17070	+	0.484919i	0.881423	−	0.472327i	$-0.156586\pi$
$263$	307.894	+	127.534i	1.17070	+	0.484919i	0.289275	+	0.957246i	$0.406586\pi$
$264$	−56.3669	+	136.082i	−0.213511	+	0.515461i
$265$		0			0
$266$	128.378	+	85.7797i	0.482626	+	0.322480i
$267$	136.289	+	27.1095i	0.510445	+	0.101534i
$268$	−93.4018	−	93.4018i	−0.348514	−	0.348514i
$269$	249.325	−	166.594i	0.926859	−	0.619308i	0.00215658	−	0.999998i	$-0.499314\pi$
$269$	249.325	−	166.594i	0.926859	−	0.619308i	0.924703	+	0.380690i	$0.124314\pi$
$270$		0			0
$271$		−	139.013i		−	0.512963i	−0.966549	−	0.256481i	$-0.917437\pi$
$271$		−	139.013i		−	0.512963i	0.966549	−	0.256481i	$-0.0825633\pi$
$272$	−113.974	+	53.2519i	−0.419021	+	0.195779i
$273$	−791.070			−2.89769
$274$	−44.7575	−	108.054i	−0.163348	−	0.394358i
$275$		0			0
$276$	−30.0306	+	30.0306i	−0.108807	+	0.108807i
$277$	19.2699	−	96.8761i	0.0695662	−	0.349733i	−0.930288	−	0.366831i	$-0.880443\pi$
$277$	19.2699	−	96.8761i	0.0695662	−	0.349733i	0.999854	+	0.0170979i	$0.00544271\pi$
$278$	−0.724446	+	1.08421i	−0.00260592	+	0.00390003i
$279$	−7.93302	−	39.8820i	−0.0284338	−	0.142946i
$280$		0			0
$281$	−0.465552	+	1.12394i	−0.00165677	+	0.00399979i	−0.924706	−	0.380683i	$-0.875689\pi$
$281$	−0.465552	+	1.12394i	−0.00165677	+	0.00399979i	0.923049	+	0.384682i	$0.125689\pi$
$282$	−183.156	+	36.4319i	−0.649488	+	0.129191i
$283$	128.017	+	85.5380i	0.452355	+	0.302254i	0.760798	−	0.648989i	$-0.224808\pi$
$283$	128.017	+	85.5380i	0.452355	+	0.302254i	−0.308443	+	0.951243i	$0.599808\pi$
$284$	−142.059	−	28.2572i	−0.500206	−	0.0994972i
$285$		0			0
$286$	158.512	−	105.914i	0.554237	−	0.370329i
$287$	661.798	−	274.126i	2.30592	−	0.955142i
$288$		−	61.7248i		−	0.214322i
$289$	−185.430	+	221.668i	−0.641627	+	0.767016i
$290$		0			0
$291$	−13.1867	−	31.8355i	−0.0453151	−	0.109400i
$292$	−81.7168	−	122.298i	−0.279852	−	0.418828i
$293$	−132.488	+	132.488i	−0.452176	+	0.452176i	−0.896076	−	0.443900i	$-0.853594\pi$
$293$	−132.488	+	132.488i	−0.452176	+	0.452176i	0.443900	+	0.896076i	$0.353594\pi$
$294$	42.7449	−	214.893i	0.145391	−	0.730928i
$295$		0			0
$296$	−17.7730	−	89.3507i	−0.0600438	−	0.301861i
$297$	235.231	+	97.4358i	0.792023	+	0.328067i
$298$	−20.9632	+	50.6097i	−0.0703463	+	0.169831i
$299$	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
$303$	161.171	−	107.691i	0.531916	−	0.355415i
$304$	100.801	−	41.7530i	0.331581	−	0.137345i
$305$		0			0
$306$	−12.2236	−	26.1619i	−0.0399464	−	0.0854964i
$307$	502.910			1.63814			0.819072	−	0.573691i	$-0.194489\pi$
$307$	502.910			1.63814			0.819072	+	0.573691i	$0.194489\pi$
$308$	−129.764	−	313.277i	−0.421311	−	1.01713i
$309$	102.290	+	153.088i	0.331035	+	0.495429i
$310$		0			0
$311$	−18.4534	+	92.7716i	−0.0593358	+	0.298301i	−0.999046	−	0.0436707i	$-0.986095\pi$
$311$	−18.4534	+	92.7716i	−0.0593358	+	0.298301i	0.939710	+	0.341972i	$0.111095\pi$
$312$	232.420	−	347.842i	0.744937	−	1.11488i
$313$	82.7611	+	416.068i	0.264413	+	1.32929i	0.853445	+	0.521182i	$0.174509\pi$
$313$	82.7611	+	416.068i	0.264413	+	1.32929i	−0.589033	+	0.808109i	$0.700491\pi$
$314$	114.577	+	47.4595i	0.364896	+	0.151145i
$315$		0			0
$316$	133.635	−	26.5817i	0.422896	−	0.0841192i
$317$	−175.798	−	117.464i	−0.554567	−	0.370550i	0.246483	−	0.969147i	$-0.420725\pi$
$317$	−175.798	−	117.464i	−0.554567	−	0.370550i	−0.801050	+	0.598597i	$0.795725\pi$
$318$	−151.352	−	30.1059i	−0.475951	−	0.0946726i
$319$	−137.674	−	137.674i	−0.431581	−	0.431581i
$320$		0			0
$321$	−69.9700	+	28.9825i	−0.217975	+	0.0902882i
$322$			51.7541i			0.160727i
$323$	169.195	−	184.925i	0.523824	−	0.572523i
$324$	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
$328$	−73.9037	+	371.539i	−0.225316	+	1.13274i
$329$	534.215	−	799.509i	1.62375	−	2.43012i
$330$		0			0
$331$	212.770	+	88.1322i	0.642810	+	0.266260i	0.680185	−	0.733041i	$-0.261900\pi$
$331$	212.770	+	88.1322i	0.642810	+	0.266260i	−0.0373750	+	0.999301i	$0.511900\pi$
$332$	−28.2239	+	68.1385i	−0.0850117	+	0.205236i
$333$	−27.4059	+	5.45138i	−0.0823001	+	0.0163705i
$334$	−136.923	−	91.4893i	−0.409950	−	0.273920i
$335$		0			0
$336$	−166.393	−	166.393i	−0.495218	−	0.495218i
$337$	−513.952	+	343.412i	−1.52508	+	1.01903i	−0.541056	+	0.840987i	$0.681975\pi$
$337$	−513.952	+	343.412i	−1.52508	+	1.01903i	−0.984023	+	0.178039i	$0.943025\pi$
$338$	−363.636	+	150.623i	−1.07585	+	0.445630i
$339$			74.2446i			0.219011i
$340$		0			0
$341$	183.452			0.537983
$342$	9.58412	+	23.1381i	0.0280237	+	0.0676553i
$343$	300.951	+	450.405i	0.877408	+	1.31313i
$344$	−304.667	+	304.667i	−0.885660	+	0.885660i
$345$		0			0
$346$	107.070	−	160.242i	0.309452	−	0.463128i
$347$	119.037	+	598.438i	0.343045	+	1.72460i	0.638829	+	0.769349i	$0.279419\pi$
$347$	119.037	+	598.438i	0.343045	+	1.72460i	−0.295783	+	0.955255i	$0.595581\pi$
$348$	−176.483	−	73.1016i	−0.507134	−	0.210062i
$349$	−68.1756	+	164.590i	−0.195345	+	0.471606i	−0.990953	−	0.134206i	$-0.957152\pi$
$349$	−68.1756	+	164.590i	−0.195345	+	0.471606i	0.795608	+	0.605812i	$0.207152\pi$
$350$		0			0
$351$	−601.279	−	401.762i	−1.71305	−	1.14462i
$352$	273.120	+	54.3269i	0.775909	+	0.154338i
$353$	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
$357$	−508.126	−	184.507i	−1.42332	−	0.516828i
$358$	149.790			0.418408
$359$	87.7860	+	211.934i	0.244529	+	0.590346i	0.997722	−	0.0674536i	$-0.0214875\pi$
$359$	87.7860	+	211.934i	0.244529	+	0.590346i	−0.753193	+	0.657799i	$0.771487\pi$
$360$		0			0
$361$	101.551	−	101.551i	0.281306	−	0.281306i
$362$	1.19146	−	5.98987i	0.00329132	−	0.0165466i
$363$	65.3629	−	97.8225i	0.180063	−	0.269484i
$364$	187.889	+	944.580i	0.516177	+	2.59500i
$365$		0			0
$366$	−58.7444	+	141.822i	−0.160504	+	0.387491i
$367$	−633.227	+	125.957i	−1.72541	+	0.343206i	−0.955511	−	0.294956i	$-0.904695\pi$
$367$	−633.227	+	125.957i	−1.72541	+	0.343206i	−0.769902	+	0.638162i	$0.779695\pi$
$368$	30.4084	+	20.3182i	0.0826315	+	0.0552126i
$369$	113.960	+	22.6680i	0.308834	+	0.0614308i
$370$		0			0
$371$	660.682	−	441.454i	1.78081	−	1.18990i
$372$	166.287	−	68.8781i	0.447007	−	0.185156i
$373$			17.3537i			0.0465246i	0.999729	+	0.0232623i	$0.00740529\pi$
$373$			17.3537i			0.0465246i	−0.999729	+	0.0232623i	$0.992595\pi$
$374$	126.520	−	31.0607i	0.338288	−	0.0830500i
$375$		0			0
$376$	194.597	+	469.800i	0.517546	+	1.24947i
$377$	307.226	+	459.796i	0.814923	+	1.21962i
$378$	215.253	−	215.253i	0.569452	−	0.569452i
$379$	28.2844	−	142.195i	0.0746289	−	0.375185i	−0.925363	−	0.379081i	$-0.876240\pi$
$379$	28.2844	−	142.195i	0.0746289	−	0.375185i	0.999992	+	0.00389606i	$0.00124016\pi$
$380$		0			0
$381$	29.9000	+	150.318i	0.0784778	+	0.394534i
$382$	94.1939	+	39.0164i	0.246581	+	0.102137i
$383$	−5.20255	+	12.5601i	−0.0135837	+	0.0327939i	−0.930526	−	0.366226i	$-0.880650\pi$
$383$	−5.20255	+	12.5601i	−0.0135837	+	0.0327939i	0.916942	+	0.399020i	$0.130650\pi$
$384$	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
$388$	−34.8813	+	23.3069i	−0.0899002	+	0.0600694i
$389$	−527.645	+	218.558i	−1.35641	+	0.561845i	−0.938070	−	0.346445i	$-0.887389\pi$
$389$	−527.645	+	218.558i	−1.35641	+	0.561845i	−0.418343	+	0.908289i	$0.637389\pi$
$390$		0			0
$391$	83.0479	+	12.7180i	0.212399	+	0.0325268i
$392$	−596.622			−1.52199
$393$	−237.295	−	572.880i	−0.603804	−	1.45771i
$394$	65.5209	+	98.0590i	0.166297	+	0.248881i
$395$		0			0
$396$	10.7304	−	53.9454i	0.0270970	−	0.136226i
$397$	412.128	−	616.794i	1.03811	−	1.55364i	0.222583	−	0.974914i	$-0.428551\pi$
$397$	412.128	−	616.794i	1.03811	−	1.55364i	0.815524	−	0.578723i	$-0.196449\pi$
$398$	17.9985	+	90.4847i	0.0452224	+	0.227348i
$399$	433.159	+	179.420i	1.08561	+	0.449675i
$400$		0			0
$401$	−272.971	+	54.2973i	−0.680726	+	0.135405i	−0.523329	−	0.852131i	$-0.675310\pi$
$401$	−272.971	+	54.2973i	−0.680726	+	0.135405i	−0.157397	+	0.987535i	$0.550310\pi$
$402$	78.9293	+	52.7388i	0.196341	+	0.131191i
$403$	−511.031	−	101.650i	−1.26807	−	0.252234i
$404$	−166.869	−	166.869i	−0.413041	−	0.413041i
$405$		0			0
$406$	−215.064	+	89.0825i	−0.529715	+	0.219415i
$407$		−	126.064i		−	0.309739i
$408$	230.420	−	169.219i	0.564755	−	0.414753i
$409$	−417.503			−1.02079			−0.510395	−	0.859940i	$-0.670501\pi$
$409$	−417.503			−1.02079			−0.510395	+	0.859940i	$0.670501\pi$
$410$		0			0
$411$	−197.311	−	295.297i	−0.480075	−	0.718483i
$412$	158.500	−	158.500i	0.384708	−	0.384708i
$413$	218.391	−	1097.92i	0.528791	−	2.65841i
$414$	−4.66391	+	6.98004i	−0.0112655	+	0.0168600i
$415$		0			0
$416$	−730.711	−	302.670i	−1.75652	−	0.727573i
$417$	−1.51528	+	3.65821i	−0.00363376	+	0.00877268i
$418$	−110.817	+	22.0429i	−0.265112	+	0.0527341i
$419$	−453.352	−	302.920i	−1.08199	−	0.722960i	−0.119104	−	0.992882i	$-0.538002\pi$
$419$	−453.352	−	302.920i	−1.08199	−	0.722960i	−0.962882	+	0.269921i	$0.913002\pi$
$420$		0			0
$421$	−362.826	−	362.826i	−0.861820	−	0.861820i	0.129730	−	0.991549i	$-0.458589\pi$
$421$	−362.826	−	362.826i	−0.861820	−	0.861820i	−0.991549	+	0.129730i	$0.958589\pi$
$422$	133.833	−	89.4245i	0.317140	−	0.211906i
$423$	144.098	−	59.6875i	0.340658	−	0.141105i
$424$			420.210i			0.991062i
$425$		0			0
$426$	104.091			0.244346
$427$	−302.480	−	730.252i	−0.708385	−	1.71019i
$428$	51.2254	+	76.6642i	0.119686	+	0.179122i
$429$	409.342	−	409.342i	0.954178	−	0.954178i
$430$		0			0
$431$	−157.395	+	235.558i	−0.365185	+	0.546538i	−0.967873	−	0.251439i	$-0.919096\pi$
$431$	−157.395	+	235.558i	−0.365185	+	0.546538i	0.602688	+	0.797977i	$0.294096\pi$
$432$	−41.9664	−	210.979i	−0.0971445	−	0.488378i
$433$	288.914	+	119.672i	0.667238	+	0.276379i	0.690481	−	0.723351i	$-0.257399\pi$
$433$	288.914	+	119.672i	0.667238	+	0.276379i	−0.0232429	+	0.999730i	$0.507399\pi$
$434$	83.9358	−	202.639i	0.193400	−	0.466910i
$435$		0			0
$436$	193.861	+	129.534i	0.444635	+	0.297096i
$437$	−71.4664	−	14.2156i	−0.163539	−	0.0325299i
$438$	74.7444	+	74.7444i	0.170649	+	0.170649i
$439$	63.4957	−	42.4264i	0.144637	−	0.0966434i	−0.481146	−	0.876640i	$-0.659779\pi$
$439$	63.4957	−	42.4264i	0.144637	−	0.0966434i	0.625783	+	0.779997i	$0.284779\pi$
$440$		0			0
$441$			182.998i			0.414961i
$442$	−369.649	+	16.4195i	−0.836310	+	0.0371482i
$443$	167.822			0.378830			0.189415	−	0.981897i	$-0.439341\pi$
$443$	167.822			0.378830			0.189415	+	0.981897i	$0.439341\pi$
$444$	−47.3314	−	114.268i	−0.106602	−	0.257360i
$445$		0			0
$446$	−47.0166	+	47.0166i	−0.105418	+	0.105418i
$447$	−32.4519	+	163.147i	−0.0725993	+	0.364981i
$448$	−11.8597	+	17.7492i	−0.0264725	+	0.0396189i
$449$	7.23934	+	36.3946i	0.0161233	+	0.0810571i	0.988009	−	0.154395i	$-0.0493429\pi$
$449$	7.23934	+	36.3946i	0.0161233	+	0.0810571i	−0.971886	+	0.235452i	$0.924343\pi$
$450$		0			0
$451$	−200.603	+	484.297i	−0.444795	+	1.07383i
$452$	88.6521	−	17.6340i	0.196133	−	0.0390133i
$453$	−230.957	−	154.320i	−0.509838	−	0.340663i
$454$	107.891	+	21.4609i	0.237646	+	0.0472707i
$455$		0			0
$456$	−206.157	+	137.750i	−0.452099	+	0.302083i
$457$	−304.553	+	126.150i	−0.666418	+	0.276039i	−0.690136	−	0.723679i	$-0.742449\pi$
$457$	−304.553	+	126.150i	−0.666418	+	0.276039i	0.0237185	+	0.999719i	$0.492449\pi$
$458$			288.120i			0.629084i
$459$	−292.512	−	398.304i	−0.637282	−	0.867765i
$460$		0			0
$461$	199.727	+	482.184i	0.433248	+	1.04595i	0.978233	+	0.207507i	$0.0665351\pi$
$461$	199.727	+	482.184i	0.433248	+	1.04595i	−0.544986	+	0.838445i	$0.683465\pi$
$462$	135.386	+	202.620i	0.293044	+	0.438571i
$463$	195.559	−	195.559i	0.422373	−	0.422373i	−0.463647	−	0.886020i	$-0.653459\pi$
$463$	195.559	−	195.559i	0.422373	−	0.422373i	0.886020	+	0.463647i	$0.153459\pi$
$464$	−32.0916	+	161.335i	−0.0691629	+	0.347705i
$465$		0			0
$466$	−37.4983	−	188.517i	−0.0804684	−	0.404542i
$467$	439.119	+	181.889i	0.940298	+	0.389484i	0.799576	−	0.600565i	$-0.205058\pi$
$467$	439.119	+	181.889i	0.940298	+	0.389484i	0.140722	+	0.990049i	$0.455058\pi$
$468$	−59.7821	+	144.327i	−0.127740	+	0.308391i
$469$	−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
$473$	−495.739	+	331.242i	−1.04807	+	0.700301i
$474$	−90.4655	+	37.4720i	−0.190856	+	0.0790550i
$475$		0			0
$476$	−99.6257	+	650.553i	−0.209298	+	1.36671i
$477$	128.888			0.270206
$478$	−33.5949	−	81.1053i	−0.0702823	−	0.169676i
$479$	−220.245	−	329.620i	−0.459802	−	0.688142i	0.527038	−	0.849842i	$-0.323303\pi$
$479$	−220.245	−	329.620i	−0.459802	−	0.688142i	−0.986840	+	0.161699i	$0.948303\pi$
$480$		0			0
$481$	−69.8517	+	351.168i	−0.145222	+	0.730079i
$482$	33.5161	−	50.1604i	0.0695354	−	0.104067i
$483$	30.6596	+	154.136i	0.0634775	+	0.319123i
$484$	−132.330	−	54.8128i	−0.273409	−	0.113250i
$485$		0			0
$486$	88.2646	−	17.5569i	0.181614	−	0.0361253i
$487$	−228.096	−	152.409i	−0.468369	−	0.312954i	0.298895	−	0.954286i	$-0.403382\pi$
$487$	−228.096	−	152.409i	−0.468369	−	0.312954i	−0.767263	+	0.641332i	$0.778382\pi$
$488$	409.970	+	81.5481i	0.840102	+	0.167107i
$489$	−43.2898	−	43.2898i	−0.0885273	−	0.0885273i
$490$		0			0
$491$	−439.630	+	182.101i	−0.895378	+	0.370878i	−0.782441	−	0.622725i	$-0.786026\pi$
$491$	−439.630	+	182.101i	−0.895378	+	0.370878i	−0.112937	+	0.993602i	$0.536026\pi$
$492$			514.299i			1.04532i
$493$	90.0979	+	366.997i	0.182754	+	0.744415i
$494$	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
$498$	10.3403	−	51.9844i	0.0207637	−	0.104386i
$499$	−266.019	+	398.126i	−0.533104	+	0.797847i	−0.996074	−	0.0885272i	$-0.971784\pi$
$499$	−266.019	+	398.126i	−0.533104	+	0.797847i	0.462969	+	0.886374i	$0.346784\pi$
$500$		0			0
$501$	−461.990	−	191.363i	−0.922136	−	0.381961i
$502$	125.573	−	303.159i	0.250145	−	0.603902i
$503$	−5.45243	+	1.08456i	−0.0108398	+	0.00215617i	−0.200507	−	0.979692i	$-0.564259\pi$
$503$	−5.45243	+	1.08456i	−0.0108398	+	0.00215617i	0.189667	+	0.981848i	$0.439259\pi$
$504$	−122.296	−	81.7157i	−0.242651	−	0.162134i
$505$		0			0
$506$	−26.7804	−	26.7804i	−0.0529256	−	0.0529256i
$507$	−993.767	+	664.014i	−1.96009	+	1.30969i
$508$	172.386	−	71.4045i	0.339342	−	0.140560i
$509$		−	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
$512$	−161.733	−	390.458i	−0.315885	−	0.762613i
$513$	238.115	+	356.364i	0.464161	+	0.694666i
$514$	−188.655	+	188.655i	−0.367034	+	0.367034i
$515$		0			0
$516$	−324.986	+	486.376i	−0.629818	+	0.942589i
$517$	137.277	+	690.141i	0.265527	+	1.33489i
$518$	−139.248	−	57.6786i	−0.268819	−	0.111349i
$519$	223.953	−	540.670i	0.431508	−	1.04175i
$520$		0			0
$521$	814.191	+	544.025i	1.56275	+	1.04419i	0.971302	+	0.237849i	$0.0764422\pi$
$521$	814.191	+	544.025i	1.56275	+	1.04419i	0.591445	+	0.806346i	$0.298558\pi$
$522$	−37.0334	−	7.36640i	−0.0709452	−	0.0141119i
$523$	−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
$527$	−304.541	−	184.485i	−0.577877	−	0.350066i
$528$	172.202			0.326140
$529$	193.093	+	466.167i	0.365014	+	0.881223i
$530$		0			0
$531$	128.396	−	128.396i	0.241800	−	0.241800i
$532$	111.357	−	559.829i	0.209318	−	1.05231i
$533$	827.155	−	1237.92i	1.55188	−	2.32256i
$534$	23.7188	+	119.243i	0.0444173	+	0.223301i
$535$		0			0
$536$	98.9196	−	238.813i	0.184551	−	0.445547i
$537$	446.111	−	88.7370i	0.830746	−	0.165246i
$538$	218.141	+	145.757i	0.405467	+	0.270924i
$539$	−809.728	−	161.065i	−1.50228	−	0.298822i
$540$		0			0
$541$	−423.296	+	282.838i	−0.782433	+	0.522805i	−0.881448	−	0.472281i	$-0.843431\pi$
$541$	−423.296	+	282.838i	−0.782433	+	0.522805i	0.0990149	+	0.995086i	$0.468431\pi$
$542$	112.368	−	46.5443i	0.207321	−	0.0858751i
$543$		−	18.5451i		−	0.0341531i
$544$	−398.762	−	364.843i	−0.733018	−	0.670668i
$545$		0			0
$546$	−264.866	−	639.442i	−0.485102	−	1.17114i
$547$	−290.720	−	435.093i	−0.531481	−	0.795417i	0.464444	−	0.885602i	$-0.346254\pi$
$547$	−290.720	−	435.093i	−0.531481	−	0.795417i	−0.995925	+	0.0901850i	$0.971254\pi$
$548$	−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
$552$	−76.7833	−	31.8047i	−0.139100	−	0.0576172i
$553$	192.947	−	465.815i	0.348910	−	0.842342i
$554$	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	0.558496	−	0.829507i	$-0.311379\pi$
$557$	−150.954	−	150.954i	−0.271012	−	0.271012i	−0.829507	+	0.558496i	$0.811379\pi$
$558$	29.5815	−	19.7657i	0.0530135	−	0.0354225i
$559$	1564.49	−	648.033i	2.79873	−	1.15927i
$560$		0			0
$561$	358.406	−	167.458i	0.638870	−	0.298499i
$562$	−1.06439			−0.00189393
$563$	169.562	+	409.360i	0.301176	+	0.727104i	0.999931	+	0.0117427i	$0.00373790\pi$
$563$	169.562	+	409.360i	0.301176	+	0.727104i	−0.698755	+	0.715361i	$0.746262\pi$
$564$	383.550	+	574.023i	0.680052	+	1.01777i
$565$		0			0
$566$	−26.2801	+	132.119i	−0.0464313	+	0.233426i
$567$	397.368	−	594.703i	0.700825	−	1.04886i
$568$	−55.2970	−	277.997i	−0.0973539	−	0.489431i
$569$	795.099	+	329.341i	1.39736	+	0.578806i	0.949065	−	0.315079i	$-0.102031\pi$
$569$	795.099	+	329.341i	1.39736	+	0.578806i	0.448296	+	0.893885i	$0.352031\pi$
$570$		0			0
$571$	−751.766	+	149.535i	−1.31658	+	0.261883i	−0.802907	−	0.596104i	$-0.796714\pi$
$571$	−751.766	+	149.535i	−1.31658	+	0.261883i	−0.513670	+	0.857988i	$0.671714\pi$
$572$	−586.000	−	391.553i	−1.02448	−	0.684533i
$573$	303.646	+	60.3989i	0.529923	+	0.105408i
$574$	443.166	+	443.166i	0.772066	+	0.772066i
$575$		0			0
$576$	−3.19901	+	1.32507i	−0.00555384	+	0.00230048i
$577$			970.916i			1.68270i	0.540493	+	0.841349i	$0.318238\pi$
$577$			970.916i			1.68270i	−0.540493	+	0.841349i	$0.681762\pi$
$578$	−241.266	−	75.6695i	−0.417415	−	0.130916i
$579$	−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
$583$	−113.441	+	570.304i	−0.194581	+	0.978224i
$584$	159.913	−	239.327i	0.273824	−	0.409806i
$585$		0			0
$586$	−151.453	−	62.7337i	−0.258452	−	0.107054i
$587$	38.4507	−	92.8282i	0.0655038	−	0.158140i	−0.887738	−	0.460349i	$-0.847724\pi$
$587$	38.4507	−	92.8282i	0.0655038	−	0.158140i	0.953242	+	0.302209i	$0.0977241\pi$
$588$	−794.435	+	158.023i	−1.35108	+	0.268746i
$589$	256.766	+	171.565i	0.435935	+	0.291283i
$590$		0			0
$591$	253.228	+	253.228i	0.428474	+	0.428474i
$592$	−88.5572	+	59.1720i	−0.149590	+	0.0999528i
$593$	−171.814	+	71.1679i	−0.289738	+	0.120013i	−0.522818	−	0.852444i	$-0.675119\pi$
$593$	−171.814	+	71.1679i	−0.289738	+	0.120013i	0.233081	+	0.972457i	$0.425119\pi$
$594$			222.767i			0.375028i
$595$		0			0
$596$	202.514			0.339788
$597$	107.208	+	258.823i	0.179578	+	0.433539i
$598$	59.7615	+	89.4394i	0.0999356	+	0.149564i
$599$	−210.427	+	210.427i	−0.351297	+	0.351297i	−0.860592	−	0.509295i	$-0.829906\pi$
$599$	−210.427	+	210.427i	−0.351297	+	0.351297i	0.509295	+	0.860592i	$0.329906\pi$
$600$		0			0
$601$	−285.040	+	426.592i	−0.474276	+	0.709804i	−0.989060	−	0.147516i	$-0.952872\pi$
$601$	−285.040	+	426.592i	−0.474276	+	0.709804i	0.514784	+	0.857320i	$0.327872\pi$
$602$	139.068	+	699.142i	0.231010	+	1.16137i
$603$	−73.2495	−	30.3409i	−0.121475	−	0.0503166i
$604$	−129.412	+	312.428i	−0.214258	+	0.517264i
$605$		0			0
$606$	141.012	+	94.2215i	0.232694	+	0.155481i
$607$	−943.017	−	187.578i	−1.55357	−	0.309024i	−0.657679	−	0.753298i	$-0.728462\pi$
$607$	−943.017	−	187.578i	−1.55357	−	0.309024i	−0.895891	+	0.444274i	$0.853462\pi$
$608$	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
$612$	−72.0622	+	78.7617i	−0.117749	+	0.128696i
$613$	757.810			1.23623			0.618116	−	0.786087i	$-0.287896\pi$
$613$	757.810			1.23623			0.618116	+	0.786087i	$0.287896\pi$
$614$	168.384	+	406.516i	0.274242	+	0.662078i
$615$		0			0
$616$	469.214	−	469.214i	0.761712	−	0.761712i
$617$	−43.8045	+	220.220i	−0.0709959	+	0.356921i	−0.999911	−	0.0133733i	$-0.995743\pi$
$617$	−43.8045	+	220.220i	−0.0709959	+	0.356921i	0.928915	+	0.370294i	$0.120743\pi$
$618$	−89.4961	+	133.940i	−0.144816	+	0.216732i
$619$	−231.722	−	1164.94i	−0.374348	−	1.88198i	−0.463726	−	0.885979i	$-0.653488\pi$
$619$	−231.722	−	1164.94i	−0.374348	−	1.88198i	0.0893776	−	0.995998i	$-0.471512\pi$
$620$		0			0
$621$	−54.9776	+	132.728i	−0.0885308	+	0.213732i
$622$	−81.1684	+	16.1454i	−0.130496	+	0.0259572i
$623$	−520.516	−	347.798i	−0.835499	−	0.558263i
$624$	−479.692	−	95.4167i	−0.768737	−	0.152911i
$625$		0			0
$626$	−308.609	+	206.206i	−0.492986	+	0.329402i
$627$	−316.981	+	131.298i	−0.505553	+	0.209407i
$628$		−	458.479i		−	0.730062i
$629$	−126.773	+	209.273i	−0.201548	+	0.332708i
$630$		0			0
$631$	−184.417	−	445.222i	−0.292262	−	0.705582i	0.707738	−	0.706475i	$-0.249716\pi$
$631$	−184.417	−	445.222i	−0.292262	−	0.705582i	−1.00000		0.000892895i	$0.999716\pi$
$632$	148.135	+	221.700i	0.234391	+	0.350791i
$633$	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
$637$	2166.36	+	897.338i	3.40089	+	1.40869i
$638$	65.1897	−	157.382i	0.102178	−	0.246680i
$639$	−85.2680	+	16.9609i	−0.133440	+	0.0265428i
$640$		0			0
$641$	−89.5481	−	17.8122i	−0.139701	−	0.0277882i	0.124745	−	0.992189i	$-0.460189\pi$
$641$	−89.5481	−	17.8122i	−0.139701	−	0.0277882i	−0.264445	+	0.964401i	$0.585189\pi$
$642$	−46.8547	−	46.8547i	−0.0729823	−	0.0729823i
$643$	−169.429	+	113.209i	−0.263498	+	0.176064i	−0.680300	−	0.732933i	$-0.738151\pi$
$643$	−169.429	+	113.209i	−0.263498	+	0.176064i	0.416803	+	0.908997i	$0.363151\pi$
$644$	176.765	−	73.2185i	0.274480	−	0.113693i
$645$		0			0
$646$	206.129	+	74.8484i	0.319086	+	0.115864i
$647$	−1013.82			−1.56696			−0.783478	−	0.621420i	$-0.786556\pi$
$647$	−1013.82			−1.56696			−0.783478	+	0.621420i	$0.786556\pi$
$648$	144.748	+	349.454i	0.223377	+	0.539280i
$649$	455.118	+	681.133i	0.701261	+	1.04951i
$650$		0			0
$651$	129.936	−	653.232i	0.199594	−	1.00343i
$652$	−41.4085	+	61.9723i	−0.0635100	+	0.0950495i
$653$	−60.1893	−	302.592i	−0.0921735	−	0.463387i	−0.999112	−	0.0421251i	$-0.986587\pi$
$653$	−60.1893	−	302.592i	−0.0921735	−	0.463387i	0.906939	−	0.421262i	$-0.138413\pi$
$654$	−154.803	−	64.1217i	−0.236703	−	0.0980454i
$655$		0			0
$656$	434.368	−	86.4012i	0.662147	−	0.131709i
$657$	−73.4070	−	49.0490i	−0.111731	−	0.0746560i
$658$	825.130	+	164.128i	1.25400	+	0.249435i
$659$	554.044	+	554.044i	0.840734	+	0.840734i	0.988954	−	0.148220i	$-0.0473544\pi$
$659$	554.044	+	554.044i	0.840734	+	0.840734i	−0.148220	+	0.988954i	$0.547354\pi$
$660$		0			0
$661$	−396.870	+	164.389i	−0.600409	+	0.248697i	−0.662121	−	0.749397i	$-0.730344\pi$
$661$	−396.870	+	164.389i	−0.600409	+	0.248697i	0.0617128	+	0.998094i	$0.480344\pi$
$662$			201.496i			0.304375i
$663$	−1091.18	+	267.885i	−1.64582	+	0.404050i
$664$	−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
$668$	−118.769	+	597.092i	−0.177798	+	0.893851i
$669$	−112.174	+	167.880i	−0.167674	+	0.250941i
$670$		0			0
$671$	534.392	+	221.352i	0.796411	+	0.329884i
$672$	386.892	−	934.041i	0.575733	−	1.38994i
$673$	−1023.84	+	203.655i	−1.52131	+	0.302607i	−0.883811	−	0.467845i	$-0.845031\pi$
$673$	−1023.84	+	203.655i	−1.52131	+	0.302607i	−0.637498	+	0.770452i	$0.720031\pi$
$674$	−449.670	−	300.460i	−0.667166	−	0.445786i
$675$		0			0
$676$	1028.90	+	1028.90i	1.52204	+	1.52204i
$677$	984.303	−	657.690i	1.45392	−	0.971477i	0.457300	−	0.889313i	$-0.348817\pi$
$677$	984.303	−	657.690i	1.45392	−	0.971477i	0.996619	−	0.0821649i	$-0.0261834\pi$
$678$	−60.0139	+	24.8586i	−0.0885161	+	0.0366646i
$679$			155.238i			0.228627i
$680$		0			0
$681$	334.040			0.490514
$682$	61.4234	+	148.289i	0.0900636	+	0.217433i
$683$	−218.936	−	327.661i	−0.320551	−	0.479738i	0.635843	−	0.771818i	$-0.280653\pi$
$683$	−218.936	−	327.661i	−0.320551	−	0.479738i	−0.956394	+	0.292080i	$0.905653\pi$
$684$	65.4687	−	65.4687i	0.0957145	−	0.0957145i
$685$		0			0
$686$	−263.310	+	394.071i	−0.383833	+	0.574447i
$687$	170.685	+	858.092i	0.248450	+	1.24904i
$688$	465.382	+	192.767i	0.676427	+	0.280185i
$689$	632.009	−	1525.80i	0.917285	−	2.21452i
$690$		0			0
$691$	−44.0092	−	29.4060i	−0.0636892	−	0.0425558i	0.523318	−	0.852137i	$-0.324694\pi$
$691$	−44.0092	−	29.4060i	−0.0636892	−	0.0425558i	−0.587007	+	0.809582i	$0.699694\pi$
$692$	−698.780	−	138.996i	−1.00980	−	0.200861i
$693$	−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
$697$	820.036	−	602.230i	1.17652	−	0.864031i
$698$	−155.869			−0.223308
$699$	−223.358	−	539.234i	−0.319539	−	0.771437i
$700$		0			0
$701$	581.552	−	581.552i	0.829603	−	0.829603i	−0.157859	−	0.987462i	$-0.550459\pi$
$701$	581.552	−	581.552i	0.829603	−	0.829603i	0.987462	+	0.157859i	$0.0504590\pi$
$702$	123.435	−	620.548i	0.175833	−	0.883971i
$703$	117.896	−	176.443i	0.167703	−	0.250986i
$704$	−3.04759	−	15.3213i	−0.00432896	−	0.0217631i
$705$		0			0
$706$	−116.674	+	281.676i	−0.165261	+	0.398975i
$707$	−856.476	+	170.364i	−1.21142	+	0.240967i
$708$	668.268	+	446.522i	0.943881	+	0.630681i
$709$	−222.555	−	44.2689i	−0.313900	−	0.0624385i	0.0356263	−	0.999365i	$-0.488657\pi$
$709$	−222.555	−	44.2689i	−0.313900	−	0.0624385i	−0.349526	+	0.936927i	$0.613657\pi$
$710$		0			0
$711$	68.0004	−	45.4364i	0.0956405	−	0.0639050i
$712$	305.861	−	126.692i	0.429580	−	0.177938i
$713$			103.512i			0.145178i
$714$	−20.9885	−	472.509i	−0.0293956	−	0.661777i
$715$		0			0
$716$	−211.913	−	511.604i	−0.295968	−	0.714531i
$717$	−148.101	−	221.650i	−0.206557	−	0.309135i
$718$	−141.919	+	141.919i	−0.197659	+	0.197659i
$719$	−158.183	+	795.241i	−0.220005	+	1.10604i	0.700004	+	0.714139i	$0.253182\pi$
$719$	−158.183	+	795.241i	−0.220005	+	1.10604i	−0.920008	+	0.391899i	$0.871818\pi$
$720$		0			0
$721$	−161.820	−	813.523i	−0.224438	−	1.12833i
$722$	116.088	+	48.0853i	0.160787	+	0.0666001i
$723$	70.1036	−	169.245i	0.0969621	−	0.234087i
$724$	−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	0.847626	−	0.530594i	$-0.178031\pi$
$727$	230.482	+	230.482i	0.317032	+	0.317032i	−0.530594	+	0.847626i	$0.678031\pi$
$728$	−1567.05	+	1047.07i	−2.15254	+	1.43828i
$729$	749.353	−	310.392i	1.02792	−	0.425778i
$730$		0			0
$731$	1156.06	−	51.3514i	1.58148	−	0.0702481i
$732$	567.497			0.775269
$733$	−99.7350	−	240.782i	−0.136064	−	0.328488i	0.841131	−	0.540832i	$-0.181890\pi$
$733$	−99.7350	−	240.782i	−0.136064	−	0.328488i	−0.977195	+	0.212344i	$0.931890\pi$
$734$	−313.831	−	469.681i	−0.427562	−	0.639892i
$735$		0			0
$736$	−30.6537	+	154.106i	−0.0416490	+	0.209384i
$737$	198.723	−	297.410i	0.269638	−	0.403541i
$738$	19.8328	+	99.7062i	0.0268737	+	0.135103i
$739$	152.235	+	63.0577i	0.206001	+	0.0853285i	0.483298	−	0.875456i	$-0.339439\pi$
$739$	152.235	+	63.0577i	0.206001	+	0.0853285i	−0.277297	+	0.960784i	$0.589439\pi$
$740$		0			0
$741$	955.748	−	190.110i	1.28981	−	0.256559i
$742$	578.048	+	386.239i	0.779040	+	0.520538i
$743$	−286.905	−	57.0690i	−0.386145	−	0.0768089i	−0.00179939	−	0.999998i	$-0.500573\pi$
$743$	−286.905	−	57.0690i	−0.386145	−	0.0768089i	−0.384345	+	0.923189i	$0.625573\pi$
$744$	249.057	+	249.057i	0.334754	+	0.334754i
$745$		0			0
$746$	−14.0274	+	5.81035i	−0.0188035	+	0.00778868i
$747$			44.2686i			0.0592619i
$748$	−285.079	−	388.183i	−0.381122	−	0.518961i
$749$	341.192			0.455530
$750$		0			0
$751$	−300.658	−	449.967i	−0.400344	−	0.599157i	0.575453	−	0.817835i	$-0.304826\pi$
$751$	−300.658	−	449.967i	−0.400344	−	0.599157i	−0.975797	+	0.218677i	$0.929826\pi$
$752$	420.374	−	420.374i	0.559008	−	0.559008i
$753$	194.391	−	977.272i	0.258156	−	1.29784i
$754$	−268.800	+	402.288i	−0.356499	+	0.533538i
$755$		0			0
$756$	−1039.72	−	430.665i	−1.37529	−	0.569663i
$757$	−99.0239	+	239.065i	−0.130811	+	0.315805i	−0.975691	−	0.219150i	$-0.929672\pi$
$757$	−99.0239	+	239.065i	−0.130811	+	0.315805i	0.844880	+	0.534955i	$0.179672\pi$
$758$	124.410	−	24.7467i	0.164130	−	0.0326474i
$759$	−95.6234	−	63.8935i	−0.125986	−	0.0841812i
$760$		0			0
$761$	176.582	+	176.582i	0.232039	+	0.232039i	0.813543	−	0.581504i	$-0.197536\pi$
$761$	176.582	+	176.582i	0.232039	+	0.232039i	−0.581504	+	0.813543i	$0.697536\pi$
$762$	−111.495	+	74.4983i	−0.146318	+	0.0977668i
$763$	797.097	−	330.168i	1.04469	−	0.432724i
$764$		−	376.915i		−	0.493344i
$765$		0			0
$766$	−11.8945			−0.0155281
$767$	−890.381	−	2149.57i	−1.16086	−	2.80257i
$768$	155.718	+	233.049i	0.202758	+	0.303449i
$769$	644.591	−	644.591i	0.838220	−	0.838220i	−0.150405	−	0.988624i	$-0.548058\pi$
$769$	644.591	−	644.591i	0.838220	−	0.838220i	0.988624	+	0.150405i	$0.0480577\pi$
$770$		0			0
$771$	−450.100	+	673.623i	−0.583788	+	0.873700i
$772$	104.793	+	526.832i	0.135743	+	0.682425i
$773$	−1016.27	−	420.952i	−1.31471	−	0.544569i	−0.388451	−	0.921469i	$-0.626990\pi$
$773$	−1016.27	−	420.952i	−1.31471	−	0.544569i	−0.926254	+	0.376900i	$0.876990\pi$
$774$	−44.2484	+	106.825i	−0.0571685	+	0.138017i
$775$		0			0
$776$	−68.2598	−	45.6097i	−0.0879636	−	0.0587754i
$777$	−448.885	−	89.2888i	−0.577716	−	0.114915i
$778$	−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
$782$	17.5258	+	71.3881i	0.0224115	+	0.0912891i
$783$	−646.181			−0.825263
$784$	266.927	+	644.418i	0.340468	+	0.821962i
$785$		0			0
$786$	383.623	−	383.623i	0.488070	−	0.488070i
$787$	261.903	−	1316.68i	0.332787	−	1.67303i	−0.345643	−	0.938366i	$-0.612339\pi$
$787$	261.903	−	1316.68i	0.332787	−	1.67303i	0.678430	−	0.734665i	$-0.262661\pi$
$788$	242.223	−	362.513i	0.307390	−	0.460042i
$789$	172.734	+	868.394i	0.218928	+	1.10063i
$790$		0			0
$791$	127.999	−	309.017i	0.161819	−	0.390666i
$792$	105.567	−	20.9985i	0.133291	−	0.0265133i
$793$	−1365.97	−	912.713i	−1.72254	−	1.15096i
$794$	636.560	+	126.620i	0.801712	+	0.159470i
$795$		0			0
$796$	283.585	−	189.486i	0.356263	−	0.238047i
$797$	665.304	−	275.578i	0.834761	−	0.345769i	0.0759753	−	0.997110i	$-0.475793\pi$
$797$	665.304	−	275.578i	0.834761	−	0.345769i	0.758786	+	0.651340i	$0.225793\pi$
$798$			410.207i			0.514044i
$799$	466.137	−	1283.72i	0.583401	−	1.60666i
$800$		0			0
$801$	−38.8592	−	93.8145i	−0.0485134	−	0.117122i
$802$	−135.286	−	202.470i	−0.168686	−	0.252456i
$803$	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
$807$	736.025	+	304.872i	0.912051	+	0.377784i
$808$	176.726	−	426.655i	0.218721	−	0.528039i
$809$	−1547.67	+	307.850i	−1.91306	+	0.380532i	−0.999649	−	0.0265023i	$-0.991563\pi$
$809$	−1547.67	+	307.850i	−1.91306	+	0.380532i	−0.913413	+	0.407034i	$0.866563\pi$
$810$		0			0
$811$	152.516	+	30.3374i	0.188059	+	0.0374073i	0.288221	−	0.957564i	$-0.406936\pi$
$811$	152.516	+	30.3374i	0.188059	+	0.0374073i	−0.100162	+	0.994971i	$0.531936\pi$
$812$	608.519	+	608.519i	0.749407	+	0.749407i
$813$	307.086	−	205.188i	0.377719	−	0.252384i
$814$	101.901	−	42.2087i	0.125185	−	0.0518534i
$815$		0			0
$816$	−285.865	−	173.171i	−0.350325	−	0.212220i
$817$	−1003.63			−1.22844
$818$	−139.788	−	337.479i	−0.170890	−	0.412566i
$819$	321.161	+	480.651i	0.392138	+	0.586876i
$820$		0			0
$821$	−219.728	+	1104.65i	−0.267634	+	1.34549i	0.579874	+	0.814707i	$0.303102\pi$
$821$	−219.728	+	1104.65i	−0.267634	+	1.34549i	−0.847508	+	0.530783i	$0.821898\pi$
$822$	172.632	−	258.363i	0.210015	−	0.314310i
$823$	250.771	+	1260.71i	0.304703	+	1.53185i	0.764971	+	0.644065i	$0.222753\pi$
$823$	250.771	+	1260.71i	0.304703	+	1.53185i	−0.460268	+	0.887780i	$0.652247\pi$
$824$	405.258	+	167.863i	0.491818	+	0.203718i
$825$		0			0
$826$	960.603	−	191.076i	1.16296	−	0.231327i
$827$	281.307	+	187.964i	0.340154	+	0.227284i	0.713900	−	0.700247i	$-0.246927\pi$
$827$	281.307	+	187.964i	0.340154	+	0.227284i	−0.373746	+	0.927531i	$0.621927\pi$
$828$	30.4384	+	6.05457i	0.0367613	+	0.00731229i
$829$	52.6400	+	52.6400i	0.0634982	+	0.0634982i	0.738143	−	0.674645i	$-0.235703\pi$
$829$	52.6400	+	52.6400i	0.0634982	+	0.0634982i	−0.674645	+	0.738143i	$0.735703\pi$
$830$		0			0
$831$	242.446	−	100.425i	0.291753	−	0.120848i
$832$			44.3681i			0.0533271i
$833$	1182.22	+	1081.66i	1.41924	+	1.29852i
$834$	−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
$838$	93.0672	−	467.881i	0.111059	−	0.558330i
$839$	676.864	−	1013.00i	0.806751	−	1.20739i	−0.168372	−	0.985723i	$-0.553851\pi$
$839$	676.864	−	1013.00i	0.806751	−	1.20739i	0.975123	−	0.221664i	$-0.0711489\pi$
$840$		0			0
$841$	−320.464	−	132.741i	−0.381051	−	0.157837i
$842$	171.801	−	414.763i	0.204039	−	0.492593i
$843$	−3.17000	+	0.630553i	−0.00376039	+	0.000747987i
$844$	−494.767	−	330.592i	−0.586216	−	0.391697i
$845$		0			0
$846$	96.4940	+	96.4940i	0.114059	+	0.114059i
$847$	−440.698	+	294.465i	−0.520304	+	0.347656i
$848$	453.874	−	188.001i	0.535229	−	0.221699i
$849$			409.051i			0.481803i
$850$		0			0
$851$	71.1308			0.0835849
$852$	−147.262	−	355.522i	−0.172843	−	0.417279i
$853$	548.333	+	820.639i	0.642829	+	0.962062i	0.999611	+	0.0278741i	$0.00887374\pi$
$853$	548.333	+	820.639i	0.642829	+	0.962062i	−0.356782	+	0.934187i	$0.616126\pi$
$854$	489.006	−	489.006i	0.572606	−	0.572606i
$855$		0			0
$856$	−100.244	+	150.026i	−0.117107	+	0.175264i
$857$	−169.587	−	852.570i	−0.197884	−	0.994831i	−0.944233	−	0.329277i	$-0.893195\pi$
$857$	−169.587	−	852.570i	−0.197884	−	0.994831i	0.746349	−	0.665555i	$-0.231805\pi$
$858$	467.938	+	193.826i	0.545382	+	0.225905i
$859$	194.793	−	470.272i	0.226767	−	0.547465i	−0.769013	−	0.639233i	$-0.779252\pi$
$859$	194.793	−	470.272i	0.226767	−	0.547465i	0.995780	+	0.0917683i	$0.0292519\pi$
$860$		0			0
$861$	1582.39	+	1057.32i	1.83785	+	1.22801i
$862$	−243.106	−	48.3569i	−0.282026	−	0.0560984i
$863$	−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
$867$	−763.375	−	82.4341i	−0.880479	−	0.0950797i
$868$	−810.856			−0.934166
$869$	141.197	+	340.879i	0.162482	+	0.392266i
$870$		0			0
$871$	−718.364	+	718.364i	−0.824758	+	0.824758i
$872$	−89.0127	+	447.497i	−0.102079	+	0.513185i
$873$	−13.9895	+	20.9368i	−0.0160247	+	0.0239826i
$874$	−12.4376	−	62.5278i	−0.0142306	−	0.0715421i
$875$		0			0
$876$	149.544	−	361.032i	0.170713	−	0.412137i
$877$	−968.898	+	192.726i	−1.10479	+	0.219756i	−0.713598	−	0.700555i	$-0.752936\pi$
$877$	−968.898	+	192.726i	−1.10479	+	0.219756i	−0.391188	+	0.920311i	$0.627936\pi$
$878$	55.5540	+	37.1200i	0.0632734	+	0.0422779i
$879$	−488.227	−	97.1144i	−0.555435	−	0.110483i
$880$		0			0
$881$	440.820	−	294.546i	0.500363	−	0.334332i	−0.279643	−	0.960104i	$-0.590216\pi$
$881$	440.820	−	294.546i	0.500363	−	0.334332i	0.780006	+	0.625772i	$0.215216\pi$
$882$	−147.922	+	61.2712i	−0.167712	+	0.0694685i
$883$			744.697i			0.843371i	0.906742	+	0.421686i	$0.138561\pi$
$883$			744.697i			0.843371i	−0.906742	+	0.421686i	$0.861439\pi$
$884$	579.037	+	1239.30i	0.655019	+	1.40192i
$885$		0			0
$886$	56.1900	+	135.655i	0.0634198	+	0.153109i
$887$	740.766	+	1108.63i	0.835136	+	1.24987i	0.966019	+	0.258472i	$0.0832189\pi$
$887$	740.766	+	1108.63i	0.835136	+	1.24987i	−0.130883	+	0.991398i	$0.541781\pi$
$888$	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
$892$	227.100	+	94.0680i	0.254597	+	0.105457i
$893$	−453.285	+	1094.33i	−0.507598	+	1.22545i
$894$	−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
$898$	−26.9949	+	18.0374i	−0.0300611	+	0.0200862i
$899$	−430.143	+	178.171i	−0.478469	+	0.198188i
$900$		0			0
$901$	761.833	−	832.659i	0.845541	−	0.924150i
$902$	−458.636			−0.508466
$903$	828.357	+	1999.83i	0.917339	+	2.21465i
$904$	98.2713	+	147.073i	0.108707	+	0.162692i
$905$		0			0
$906$	47.4123	−	238.358i	0.0523315	−	0.263088i
$907$	247.751	−	370.786i	0.273154	−	0.408804i	−0.669377	−	0.742923i	$-0.733439\pi$
$907$	247.751	−	370.786i	0.273154	−	0.408804i	0.942531	+	0.334119i	$0.108439\pi$
$908$	−79.3386	−	398.862i	−0.0873773	−	0.439275i
$909$	−130.865	−	54.2061i	−0.143966	−	0.0596327i
$910$		0			0
$911$	−700.509	+	139.340i	−0.768945	+	0.152953i	−0.563948	−	0.825810i	$-0.690718\pi$
$911$	−700.509	+	139.340i	−0.768945	+	0.152953i	−0.204996	+	0.978763i	$0.565718\pi$
$912$	241.019	+	161.044i	0.264276	+	0.176583i
$913$	−195.880	−	38.9629i	−0.214545	−	0.0426757i
$914$	−203.941	−	203.941i	−0.223130	−	0.223130i
$915$		0			0
$916$	984.069	−	407.615i	1.07431	−	0.444994i
$917$			2793.51i			3.04636i
$918$	224.021	−	369.806i	0.244031	−	0.402838i
$919$	−866.411			−0.942776			−0.471388	−	0.881926i	$-0.656247\pi$
$919$	−866.411			−0.942776			−0.471388	+	0.881926i	$0.656247\pi$
$920$		0			0
$921$	742.313	+	1110.95i	0.805986	+	1.20624i
$922$	−322.890	+	322.890i	−0.350206	+	0.350206i
$923$	−217.330	+	1092.59i	−0.235460	+	1.18374i
$924$	500.507	−	749.062i	0.541675	−	0.810673i
$925$		0			0
$926$	223.552	+	92.5984i	0.241417	+	0.0999983i
$927$	51.4876	−	124.302i	0.0555421	−	0.134091i
$928$	−693.152	+	137.877i	−0.746931	+	0.148574i
$929$	215.616	+	144.070i	0.232094	+	0.155081i	0.666180	−	0.745791i	$-0.267928\pi$
$929$	215.616	+	144.070i	0.232094	+	0.155081i	−0.434085	+	0.900872i	$0.642928\pi$
$930$		0			0
$931$	−982.694	−	982.694i	−1.05553	−	1.05553i
$932$	−590.824	+	394.776i	−0.633932	+	0.423580i
$933$	−232.174	+	96.1698i	−0.248847	+	0.103076i
$934$			415.851i			0.445237i
$935$		0			0
$936$	−305.706			−0.326609
$937$	313.638	+	757.189i	0.334726	+	0.808099i	0.998204	+	0.0599037i	$0.0190794\pi$
$937$	313.638	+	757.189i	0.334726	+	0.808099i	−0.663479	+	0.748195i	$0.730921\pi$
$938$	−237.592	−	355.582i	−0.253297	−	0.379085i
$939$	−796.954	+	796.954i	−0.848727	+	0.848727i
$940$		0			0
$941$	366.641	−	548.717i	0.389629	−	0.583121i	−0.583860	−	0.811854i	$-0.698458\pi$
$941$	366.641	−	548.717i	0.389629	−	0.583121i	0.973489	+	0.228733i	$0.0734583\pi$
$942$	64.2801	+	323.158i	0.0682379	+	0.343055i
$943$	−273.262	−	113.189i	−0.289779	−	0.120031i
$944$	264.857	−	639.423i	0.280569	−	0.677354i
$945$		0			0
$946$	−433.735	−	289.813i	−0.458494	−	0.306356i
$947$	1485.67	+	295.518i	1.56882	+	0.312057i	0.901521	−	0.432735i	$-0.142452\pi$
$947$	1485.67	+	295.518i	1.56882	+	0.312057i	0.667296	+	0.744792i	$0.267452\pi$
$948$	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
$952$	−1250.78	+	307.067i	−1.31384	+	0.322549i
$953$	341.348			0.358182			0.179091	−	0.983832i	$-0.442684\pi$
$953$	341.348			0.358182			0.179091	+	0.983832i	$0.442684\pi$
$954$	43.1543	+	104.184i	0.0452351	+	0.109207i
$955$		0			0
$956$	−229.486	+	229.486i	−0.240048	+	0.240048i
$957$	100.916	−	507.341i	0.105451	−	0.530136i
$958$	192.698	−	288.393i	0.201146	−	0.301037i
$959$	312.140	+	1569.24i	0.325485	+	1.63632i
$960$		0			0
$961$	−199.881	+	482.556i	−0.207993	+	0.502140i
$962$	−307.246	+	61.1151i	−0.319383	+	0.0635292i
$963$	46.0163	+	30.7471i	0.0477843	+	0.0319285i
$964$	−218.738	−	43.5097i	−0.226907	−	0.0451346i
$965$		0			0
$966$	−114.327	+	76.3909i	−0.118351	+	0.0790796i
$967$	−948.511	+	392.886i	−0.980880	+	0.406294i	−0.814752	−	0.579810i	$-0.803127\pi$
$967$	−948.511	+	392.886i	−0.980880	+	0.406294i	−0.166129	+	0.986104i	$0.553127\pi$
$968$		−	280.295i		−	0.289561i
$969$	658.245	+	100.804i	0.679303	+	0.104029i
$970$		0			0
$971$	617.925	+	1491.80i	0.636380	+	1.53636i	0.831469	+	0.555571i	$0.187500\pi$
$971$	617.925	+	1491.80i	0.636380	+	1.53636i	−0.195089	+	0.980786i	$0.562500\pi$
$972$	−184.836	−	276.627i	−0.190161	−	0.284596i
$973$	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
$977$	49.4428	+	20.4799i	0.0506067	+	0.0209620i	0.407843	−	0.913052i	$-0.366281\pi$
$977$	49.4428	+	20.4799i	0.0506067	+	0.0209620i	−0.357237	+	0.934014i	$0.616281\pi$
$978$	20.4980	−	49.4866i	0.0209591	−	0.0505998i
$979$	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
$983$	1049.19	−	701.045i	1.06733	−	0.713169i	0.107632	−	0.994191i	$-0.465673\pi$
$983$	1049.19	−	701.045i	1.06733	−	0.713169i	0.959701	+	0.281022i	$0.0906733\pi$
$984$	−929.830	+	385.148i	−0.944949	+	0.391411i
$985$		0			0
$986$	−266.487	+	195.706i	−0.270270	+	0.198485i
$987$	2554.67			2.58832
$988$	−454.003	−	1096.06i	−0.459518	−	1.10937i
$989$	−186.902	−	279.718i	−0.188980	−	0.282829i
$990$		0			0
$991$	48.3001	−	242.821i	0.0487387	−	0.245026i	−0.948734	−	0.316075i	$-0.897635\pi$
$991$	48.3001	−	242.821i	0.0487387	−	0.245026i	0.997473	+	0.0710492i	$0.0226347\pi$
$992$	369.955	−	553.676i	0.372938	−	0.558141i
$993$	119.368	+	600.104i	0.120210	+	0.604334i
$994$	−433.244	−	179.455i	−0.435859	−	0.180539i
$995$		0			0
$996$	−192.180	+	38.2270i	−0.192952	+	0.0383806i
$997$	−442.522	−	295.683i	−0.443853	−	0.296573i	0.313489	−	0.949592i	$-0.398502\pi$
$997$	−442.522	−	295.683i	−0.443853	−	0.296573i	−0.757342	+	0.653019i	$0.773502\pi$
$998$	−410.884	−	81.7299i	−0.411707	−	0.0818937i
$999$	−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.u.c.226.8	yes	96
5.2	odd	4		425.3.t.f.124.5		96
5.3	odd	4		425.3.t.g.124.8		96
5.4	even	2		425.3.u.d.226.5	yes	96
17.7	odd	16	inner	425.3.u.c.126.8	✓	96
85.7	even	16		425.3.t.g.24.8		96
85.24	odd	16		425.3.u.d.126.5	yes	96
85.58	even	16		425.3.t.f.24.5		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.3.t.f.24.5		96	85.58	even	16
425.3.t.f.124.5		96	5.2	odd	4
425.3.t.g.24.8		96	85.7	even	16
425.3.t.g.124.8		96	5.3	odd	4
425.3.u.c.126.8	✓	96	17.7	odd	16	inner
425.3.u.c.226.8	yes	96	1.1	even	1	trivial
425.3.u.d.126.5	yes	96	85.24	odd	16
425.3.u.d.226.5	yes	96	5.4	even	2

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.u (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.334820 + 0.808326i) q^{2} +(1.47604 + 2.20904i) q^{3} +(2.28714 - 2.28714i) q^{4} +(-1.29142 + 1.93275i) q^{6} +(-2.33505 - 11.7391i) q^{7} +(5.84784 + 2.42226i) q^{8} +(0.742961 - 1.79367i) q^{9} +(7.28271 + 4.86615i) q^{11} +(8.42829 + 1.67649i) q^{12} +(-17.5907 - 17.5907i) q^{13} +(8.70718 - 5.81795i) q^{14} -7.40003i q^{16} +(-7.19617 - 15.4018i) q^{17} +1.69863 q^{18} +(5.64227 + 13.6217i) q^{19} +(22.4855 - 22.4855i) q^{21} +(-1.49504 + 7.51609i) q^{22} +(-2.74570 + 4.10923i) q^{23} +(3.28075 + 16.4935i) q^{24} +(8.32930 - 20.1087i) q^{26} +(28.5106 - 5.67111i) q^{27} +(-32.1895 - 21.5083i) q^{28} +(-21.8020 - 4.33668i) q^{29} +(17.4150 - 11.6363i) q^{31} +(29.3730 - 12.1667i) q^{32} +23.2704i q^{33} +(10.0403 - 10.9737i) q^{34} +(-2.40311 - 5.80162i) q^{36} +(-7.99619 - 11.9671i) q^{37} +(-9.12160 + 9.12160i) q^{38} +(12.8941 - 64.8230i) q^{39} +(11.6758 + 58.6981i) q^{41} +(25.7042 + 10.6470i) q^{42} +(-26.0495 + 62.8891i) q^{43} +(27.7861 - 5.52701i) q^{44} +(-4.24091 - 0.843569i) q^{46} +(56.8070 + 56.8070i) q^{47} +(16.3470 - 10.9227i) q^{48} +(-87.0832 + 36.0710i) q^{49} +(23.4014 - 38.6302i) q^{51} -80.4646 q^{52} +(25.4054 + 61.3341i) q^{53} +(14.1300 + 21.1471i) q^{54} +(14.7800 - 74.3043i) q^{56} +(-21.7626 + 32.5701i) q^{57} +(-3.79427 - 19.0751i) q^{58} +(86.4081 + 35.7914i) q^{59} +(64.7697 - 12.8835i) q^{61} +(15.2368 + 10.1809i) q^{62} +(-22.7908 - 4.53338i) q^{63} +(-1.26113 - 1.26113i) q^{64} +(-18.8101 + 7.79140i) q^{66} -40.8378i q^{67} +(-51.6847 - 18.7674i) q^{68} -13.1302 q^{69} +(-24.8785 - 37.2333i) q^{71} +(8.68944 - 8.68944i) q^{72} +(8.87157 - 44.6004i) q^{73} +(6.99607 - 10.4704i) q^{74} +(44.0593 + 18.2500i) q^{76} +(40.1186 - 96.8549i) q^{77} +(56.7153 - 11.2814i) q^{78} +(35.0256 + 23.4033i) q^{79} +(42.2551 + 42.2551i) q^{81} +(-43.5380 + 29.0911i) q^{82} +(-21.0661 + 8.72588i) q^{83} -102.855i q^{84} -59.5569 q^{86} +(-22.6005 - 54.5625i) q^{87} +(30.8011 + 46.0970i) q^{88} +(36.9839 - 36.9839i) q^{89} +(-165.423 + 247.573i) q^{91} +(3.11858 + 15.6782i) q^{92} +(51.4102 + 21.2948i) q^{93} +(-26.8985 + 64.9388i) q^{94} +(70.2323 + 46.9277i) q^{96} +(-12.7207 - 2.53031i) q^{97} +(-58.3143 - 58.3143i) q^{98} +(14.1390 - 9.44739i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 96 q^{12} - 24 q^{13} + 32 q^{14} + 8 q^{17} + 64 q^{18} - 24 q^{19} + 96 q^{22} + 56 q^{23} - 336 q^{24} - 224 q^{26} - 144 q^{27} + 480 q^{28} - 64 q^{31} - 40 q^{32} + 64 q^{34} + 192 q^{36} + 128 q^{37}+ \cdots - 160 q^{99}+O(q^{100}) \) 96 * q - 96 * q^12 - 24 * q^13 + 32 * q^14 + 8 * q^17 + 64 * q^18 - 24 * q^19 + 96 * q^22 + 56 * q^23 - 336 * q^24 - 224 * q^26 - 144 * q^27 + 480 * q^28 - 64 * q^31 - 40 * q^32 + 64 * q^34 + 192 * q^36 + 128 * q^37 - 496 * q^38 + 16 * q^39 + 216 * q^41 + 432 * q^42 - 592 * q^43 - 32 * q^44 + 336 * q^46 - 160 * q^48 - 32 * q^49 - 32 * q^51 + 96 * q^53 + 584 * q^54 - 40 * q^56 + 1120 * q^57 + 256 * q^58 + 544 * q^59 + 112 * q^61 + 560 * q^62 + 312 * q^63 + 592 * q^64 - 24 * q^66 - 192 * q^69 - 336 * q^71 - 1040 * q^72 - 336 * q^74 - 1016 * q^76 - 960 * q^77 - 384 * q^79 - 928 * q^81 - 1200 * q^82 - 144 * q^83 + 64 * q^86 - 672 * q^87 - 832 * q^88 + 576 * q^89 + 336 * q^91 - 1008 * q^92 - 512 * q^93 + 672 * q^94 + 768 * q^96 - 128 * q^97 - 408 * q^98 - 160 * q^99

Introduction

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