LMFDB - Embedded newform 325.3.t.d.201.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [325,3,Mod(76,325)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(325, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 7])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("325.76"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	325.t (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [40,0,0,0,0,-12,40,-36] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)

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

Self dual:	no
Analytic conductor:	$8.85560859171$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			201.1
Character	$\chi$	$=$	325.201
Dual form			325.3.t.d.76.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.886220 - 3.30742i) q^{2} +(0.0164891 - 0.0285599i) q^{3} +(-6.68953 + 3.86220i) q^{4} +(-0.109072 - 0.0292259i) q^{6} +(-0.185607 + 0.692695i) q^{7} +(9.01754 + 9.01754i) q^{8} +(4.49946 + 7.79329i) q^{9} +(15.5985 - 4.17961i) q^{11} +0.254736i q^{12} +(2.16135 + 12.8191i) q^{13} +2.45552 q^{14} +(6.38443 - 11.0582i) q^{16} +(1.49033 - 0.860444i) q^{17} +(21.7882 - 21.7882i) q^{18} +(6.58643 + 1.76483i) q^{19} +(0.0167228 + 0.0167228i) q^{21} +(-27.6475 - 47.8868i) q^{22} +(-1.16760 - 0.674114i) q^{23} +(0.406230 - 0.108849i) q^{24} +(40.4826 - 18.5090i) q^{26} +0.593570 q^{27} +(-1.43370 - 5.35066i) q^{28} +(23.7681 - 41.1675i) q^{29} +(-21.6495 + 21.6495i) q^{31} +(7.04075 + 1.88656i) q^{32} +(0.137836 - 0.514410i) q^{33} +(-4.16661 - 4.16661i) q^{34} +(-60.1985 - 34.7556i) q^{36} +(42.2011 - 11.3078i) q^{37} -23.3481i q^{38} +(0.401750 + 0.149647i) q^{39} +(-14.6912 - 54.8283i) q^{41} +(0.0404892 - 0.0701294i) q^{42} +(-22.7934 + 13.1597i) q^{43} +(-88.2044 + 88.2044i) q^{44} +(-1.19483 + 4.45916i) q^{46} +(57.0372 + 57.0372i) q^{47} +(-0.210547 - 0.364677i) q^{48} +(41.9899 + 24.2429i) q^{49} -0.0567516i q^{51} +(-63.9683 - 77.4061i) q^{52} -31.8181 q^{53} +(-0.526034 - 1.96319i) q^{54} +(-7.92012 + 4.57268i) q^{56} +(0.159007 - 0.159007i) q^{57} +(-157.222 - 42.1275i) q^{58} +(-24.3081 + 90.7191i) q^{59} +(-21.4156 - 37.0929i) q^{61} +(90.7902 + 52.4177i) q^{62} +(-6.23350 + 1.67026i) q^{63} -76.0341i q^{64} -1.82352 q^{66} +(-25.5657 - 95.4126i) q^{67} +(-6.64642 + 11.5119i) q^{68} +(-0.0385053 + 0.0222310i) q^{69} +(50.7246 + 13.5916i) q^{71} +(-29.7022 + 110.850i) q^{72} +(52.6480 + 52.6480i) q^{73} +(-74.7989 - 129.556i) q^{74} +(-50.8763 + 13.6323i) q^{76} +11.5808i q^{77} +(0.138905 - 1.46137i) q^{78} +41.6643 q^{79} +(-40.4853 + 70.1226i) q^{81} +(-168.321 + 97.1800i) q^{82} +(-8.45759 + 8.45759i) q^{83} +(-0.176455 - 0.0472809i) q^{84} +(63.7247 + 63.7247i) q^{86} +(-0.783826 - 1.35763i) q^{87} +(178.350 + 102.971i) q^{88} +(91.6776 - 24.5649i) q^{89} +(-9.28087 - 0.882157i) q^{91} +10.4143 q^{92} +(0.261327 + 0.975287i) q^{93} +(138.098 - 239.194i) q^{94} +(0.169975 - 0.169975i) q^{96} +(141.407 + 37.8898i) q^{97} +(42.9690 - 160.363i) q^{98} +(102.758 + 102.758i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 12 q^{6} + 40 q^{7} - 36 q^{8} - 72 q^{9} - 12 q^{11} + 12 q^{13} + 48 q^{14} + 128 q^{16} - 60 q^{17} + 136 q^{18} + 68 q^{19} - 48 q^{21} + 48 q^{22} + 48 q^{23} - 56 q^{24} - 84 q^{26} - 24 q^{27}+ \cdots - 76 q^{99}+O(q^{100}) $ 40 * q - 12 * q^6 + 40 * q^7 - 36 * q^8 - 72 * q^9 - 12 * q^11 + 12 * q^13 + 48 * q^14 + 128 * q^16 - 60 * q^17 + 136 * q^18 + 68 * q^19 - 48 * q^21 + 48 * q^22 + 48 * q^23 - 56 * q^24 - 84 * q^26 - 24 * q^27 + 16 * q^28 + 28 * q^29 + 128 * q^31 + 408 * q^32 - 136 * q^33 - 28 * q^34 + 300 * q^36 - 56 * q^37 - 88 * q^39 + 68 * q^41 + 320 * q^42 + 372 * q^43 - 240 * q^44 + 260 * q^46 - 152 * q^47 - 424 * q^48 - 132 * q^49 - 372 * q^52 + 288 * q^53 + 152 * q^54 - 288 * q^56 - 252 * q^57 - 492 * q^58 + 492 * q^59 - 100 * q^61 - 120 * q^62 - 844 * q^63 - 456 * q^66 + 20 * q^67 - 72 * q^68 - 576 * q^69 - 132 * q^71 + 780 * q^72 + 424 * q^73 - 160 * q^74 - 992 * q^76 + 60 * q^78 - 248 * q^79 - 600 * q^82 - 112 * q^83 + 1100 * q^84 + 852 * q^86 + 160 * q^87 + 1188 * q^88 + 168 * q^89 - 160 * q^91 - 1192 * q^92 + 1008 * q^93 + 328 * q^94 + 124 * q^96 + 1008 * q^97 + 636 * q^98 - 76 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$1$	$e\left(\frac{5}{12}\right)$

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 $

$2$	−0.886220	−	3.30742i	−0.443110	−	1.65371i	−0.720878	−	0.693062i	$-0.756261\pi$
$2$	−0.886220	−	3.30742i	−0.443110	−	1.65371i	0.277768	−	0.960648i	$-0.410405\pi$
$3$	0.0164891	−	0.0285599i	0.00549635	−	0.00951996i	−0.863264	−	0.504752i	$-0.831584\pi$
$3$	0.0164891	−	0.0285599i	0.00549635	−	0.00951996i	0.868760	+	0.495232i	$0.164917\pi$
$4$	−6.68953	+	3.86220i	−1.67238	+	0.965551i
$5$		0			0
$5$		0			0
$6$	−0.109072	−	0.0292259i	−0.0181787	−	0.00487098i
$7$	−0.185607	+	0.692695i	−0.0265153	+	0.0989564i	−0.977915	−	0.209001i	$-0.932979\pi$
$7$	−0.185607	+	0.692695i	−0.0265153	+	0.0989564i	0.951400	+	0.307957i	$0.0996455\pi$
$8$	9.01754	+	9.01754i	1.12719	+	1.12719i
$9$	4.49946	+	7.79329i	0.499940	+	0.865921i
$10$		0			0
$11$	15.5985	−	4.17961i	1.41805	−	0.379965i	0.533257	−	0.845953i	$-0.320968\pi$
$11$	15.5985	−	4.17961i	1.41805	−	0.379965i	0.884791	+	0.465988i	$0.154301\pi$
$12$			0.254736i			0.0212280i
$13$	2.16135	+	12.8191i	0.166257	+	0.986082i
$13$	2.16135	+	12.8191i	0.166257	+	0.986082i
$14$	2.45552			0.175394
$15$		0			0
$16$	6.38443	−	11.0582i	0.399027	−	0.691135i
$17$	1.49033	−	0.860444i	0.0876666	−	0.0506143i	−0.455526	−	0.890223i	$-0.650549\pi$
$17$	1.49033	−	0.860444i	0.0876666	−	0.0506143i	0.543192	+	0.839608i	$0.317215\pi$
$18$	21.7882	−	21.7882i	1.21045	−	1.21045i
$19$	6.58643	+	1.76483i	0.346654	+	0.0928857i	0.427945	−	0.903805i	$-0.359238\pi$
$19$	6.58643	+	1.76483i	0.346654	+	0.0928857i	−0.0812910	+	0.996690i	$0.525904\pi$
$20$		0			0
$21$	0.0167228	+	0.0167228i	0.000796324	+	0.000796324i
$22$	−27.6475	−	47.8868i	−1.25670	−	2.17667i
$23$	−1.16760	−	0.674114i	−0.0507652	−	0.0293093i	0.474403	−	0.880308i	$-0.342664\pi$
$23$	−1.16760	−	0.674114i	−0.0507652	−	0.0293093i	−0.525168	+	0.850999i	$0.675997\pi$
$24$	0.406230	−	0.108849i	0.0169263	−	0.00453538i
$25$		0			0
$26$	40.4826	−	18.5090i	1.55702	−	0.711884i
$27$	0.593570			0.0219841
$28$	−1.43370	−	5.35066i	−0.0512037	−	0.191095i
$29$	23.7681	−	41.1675i	0.819588	−	1.41957i	−0.0863974	−	0.996261i	$-0.527535\pi$
$29$	23.7681	−	41.1675i	0.819588	−	1.41957i	0.905986	−	0.423308i	$-0.139131\pi$
$30$		0			0
$31$	−21.6495	+	21.6495i	−0.698371	+	0.698371i	−0.964059	−	0.265688i	$-0.914401\pi$
$31$	−21.6495	+	21.6495i	−0.698371	+	0.698371i	0.265688	+	0.964059i	$0.414401\pi$
$32$	7.04075	+	1.88656i	0.220023	+	0.0589551i
$33$	0.137836	−	0.514410i	0.00417684	−	0.0155882i
$34$	−4.16661	−	4.16661i	−0.122547	−	0.122547i
$35$		0			0
$36$	−60.1985	−	34.7556i	−1.67218	−	0.965435i
$37$	42.2011	−	11.3078i	1.14057	−	0.305615i	0.361390	−	0.932415i	$-0.382302\pi$
$37$	42.2011	−	11.3078i	1.14057	−	0.305615i	0.779180	+	0.626800i	$0.215636\pi$
$38$		−	23.3481i		−	0.614424i
$39$	0.401750	+	0.149647i	0.0103013	+	0.00383709i
$40$		0			0
$41$	−14.6912	−	54.8283i	−0.358322	−	1.33728i	−0.876252	−	0.481853i	$-0.839964\pi$
$41$	−14.6912	−	54.8283i	−0.358322	−	1.33728i	0.517930	−	0.855423i	$-0.326703\pi$
$42$	0.0404892	−	0.0701294i	0.000964029	−	0.00166975i
$43$	−22.7934	+	13.1597i	−0.530078	+	0.306041i	−0.741048	−	0.671452i	$-0.765671\pi$
$43$	−22.7934	+	13.1597i	−0.530078	+	0.306041i	0.210970	+	0.977492i	$0.432338\pi$
$44$	−88.2044	+	88.2044i	−2.00465	+	2.00465i
$45$		0			0
$46$	−1.19483	+	4.45916i	−0.0259745	+	0.0969382i
$47$	57.0372	+	57.0372i	1.21356	+	1.21356i	0.969848	+	0.243710i	$0.0783643\pi$
$47$	57.0372	+	57.0372i	1.21356	+	1.21356i	0.243710	+	0.969848i	$0.421636\pi$
$48$	−0.210547	−	0.364677i	−0.00438639	−	0.00759744i
$49$	41.9899	+	24.2429i	0.856936	+	0.494752i
$50$		0			0
$51$		−	0.0567516i		−	0.00111278i
$52$	−63.9683	−	77.4061i	−1.23016	−	1.48858i
$53$	−31.8181			−0.600342			−0.300171	−	0.953885i	$-0.597044\pi$
$53$	−31.8181			−0.600342			−0.300171	+	0.953885i	$0.597044\pi$
$54$	−0.526034	−	1.96319i	−0.00974137	−	0.0363553i
$55$		0			0
$56$	−7.92012	+	4.57268i	−0.141431	+	0.0816551i
$57$	0.159007	−	0.159007i	0.00278960	−	0.00278960i
$58$	−157.222	−	42.1275i	−2.71072	−	0.726336i
$59$	−24.3081	+	90.7191i	−0.412002	+	1.53761i	0.378764	+	0.925493i	$0.376349\pi$
$59$	−24.3081	+	90.7191i	−0.412002	+	1.53761i	−0.790766	+	0.612119i	$0.790317\pi$
$60$		0			0
$61$	−21.4156	−	37.0929i	−0.351075	−	0.608080i	0.635363	−	0.772214i	$-0.280850\pi$
$61$	−21.4156	−	37.0929i	−0.351075	−	0.608080i	−0.986438	+	0.164134i	$0.947517\pi$
$62$	90.7902	+	52.4177i	1.46436	+	0.845447i
$63$	−6.23350	+	1.67026i	−0.0989445	+	0.0265121i
$64$		−	76.0341i		−	1.18803i
$65$		0			0
$66$	−1.82352			−0.0276291
$67$	−25.5657	−	95.4126i	−0.381578	−	1.42407i	−0.843491	−	0.537143i	$-0.819504\pi$
$67$	−25.5657	−	95.4126i	−0.381578	−	1.42407i	0.461913	−	0.886925i	$-0.347163\pi$
$68$	−6.64642	+	11.5119i	−0.0977415	+	0.169293i
$69$	−0.0385053	+	0.0222310i	−0.000558047	+	0.000322189i
$70$		0			0
$71$	50.7246	+	13.5916i	0.714431	+	0.191431i	0.597685	−	0.801731i	$-0.296087\pi$
$71$	50.7246	+	13.5916i	0.714431	+	0.191431i	0.116745	+	0.993162i	$0.462754\pi$
$72$	−29.7022	+	110.850i	−0.412531	+	1.53959i
$73$	52.6480	+	52.6480i	0.721205	+	0.721205i	0.968851	−	0.247646i	$-0.0796568\pi$
$73$	52.6480	+	52.6480i	0.721205	+	0.721205i	−0.247646	+	0.968851i	$0.579657\pi$
$74$	−74.7989	−	129.556i	−1.01080	−	1.75075i
$75$		0			0
$76$	−50.8763	+	13.6323i	−0.669425	+	0.179372i
$77$			11.5808i			0.150400i
$78$	0.138905	−	1.46137i	0.00178084	−	0.0187356i
$79$	41.6643			0.527397			0.263698	−	0.964605i	$-0.415058\pi$
$79$	41.6643			0.527397			0.263698	+	0.964605i	$0.415058\pi$
$80$		0			0
$81$	−40.4853	+	70.1226i	−0.499819	+	0.865711i
$82$	−168.321	+	97.1800i	−2.05269	+	1.18512i
$83$	−8.45759	+	8.45759i	−0.101899	+	0.101899i	−0.756218	−	0.654320i	$-0.772955\pi$
$83$	−8.45759	+	8.45759i	−0.101899	+	0.101899i	0.654320	+	0.756218i	$0.272955\pi$
$84$	−0.176455	−	0.0472809i	−0.00210065	−	0.000562868i
$85$		0			0
$86$	63.7247	+	63.7247i	0.740985	+	0.740985i
$87$	−0.783826	−	1.35763i	−0.00900949	−	0.0156049i
$88$	178.350	+	102.971i	2.02671	+	1.17012i
$89$	91.6776	−	24.5649i	1.03009	−	0.276011i	0.296087	−	0.955161i	$-0.404318\pi$
$89$	91.6776	−	24.5649i	1.03009	−	0.276011i	0.733999	+	0.679150i	$0.237652\pi$
$90$		0			0
$91$	−9.28087	−	0.882157i	−0.101988	−	0.00969403i
$92$	10.4143			0.113199
$93$	0.261327	+	0.975287i	0.00280997	+	0.0104870i
$94$	138.098	−	239.194i	1.46913	−	2.54461i
$95$		0			0
$96$	0.169975	−	0.169975i	0.00177058	−	0.00177058i
$97$	141.407	+	37.8898i	1.45780	+	0.390616i	0.898729	−	0.438504i	$-0.144492\pi$
$97$	141.407	+	37.8898i	1.45780	+	0.390616i	0.559070	+	0.829120i	$0.311158\pi$
$98$	42.9690	−	160.363i	0.438460	−	1.63635i
$99$	102.758	+	102.758i	1.03796	+	1.03796i
$100$		0			0
$101$	78.2407	+	45.1723i	0.774660	+	0.447250i	0.834535	−	0.550956i	$-0.185737\pi$
$101$	78.2407	+	45.1723i	0.774660	+	0.447250i	−0.0598743	+	0.998206i	$0.519070\pi$
$102$	−0.187701	+	0.0502944i	−0.00184021	+	0.000493083i
$103$		−	106.662i		−	1.03555i	−0.855516	−	0.517777i	$-0.826760\pi$
$103$		−	106.662i		−	1.03555i	0.855516	−	0.517777i	$-0.173240\pi$
$104$	−96.1064	+	135.086i	−0.924100	+	1.29891i
$105$		0			0
$106$	28.1979	+	105.236i	0.266018	+	0.992792i
$107$	64.4638	−	111.655i	0.602465	−	1.04350i	−0.389982	−	0.920823i	$-0.627519\pi$
$107$	64.4638	−	111.655i	0.602465	−	1.04350i	0.992447	−	0.122677i	$-0.0391480\pi$
$108$	−3.97071	+	2.29249i	−0.0367658	+	0.0212268i
$109$	−80.6778	+	80.6778i	−0.740164	+	0.740164i	−0.972609	−	0.232446i	$-0.925327\pi$
$109$	−80.6778	+	80.6778i	−0.740164	+	0.740164i	0.232446	+	0.972609i	$0.425327\pi$
$110$		0			0
$111$	0.372908	−	1.39171i	0.00335953	−	0.0125380i
$112$	6.47494	+	6.47494i	0.0578119	+	0.0578119i
$113$	71.2477	+	123.405i	0.630510	+	1.09208i	0.987448	+	0.157947i	$0.0504877\pi$
$113$	71.2477	+	123.405i	0.630510	+	1.09208i	−0.356937	+	0.934128i	$0.616179\pi$
$114$	−0.666819	−	0.384988i	−0.00584929	−	0.00337709i
$115$		0			0
$116$			367.189i			3.16542i
$117$	−90.1778	+	74.5228i	−0.770751	+	0.636947i
$118$	321.589			2.72533
$119$	0.319409	+	1.19205i	0.00268411	+	0.0100172i
$120$		0			0
$121$	121.056	−	69.8917i	1.00046	−	0.577617i
$122$	−103.703	+	103.703i	−0.850022	+	0.850022i
$123$	−1.80813	−	0.484488i	−0.0147003	−	0.00393893i
$124$	61.2103	−	228.440i	0.493631	−	1.84226i
$125$		0			0
$126$	11.0485	+	19.1366i	0.0876866	+	0.151878i
$127$	−85.7085	−	49.4838i	−0.674870	−	0.389636i	0.123049	−	0.992401i	$-0.460733\pi$
$127$	−85.7085	−	49.4838i	−0.674870	−	0.389636i	−0.797919	+	0.602764i	$0.794066\pi$
$128$	−223.314	+	59.8367i	−1.74464	+	0.467474i
$129$			0.867967i			0.00672843i
$130$		0			0
$131$	−96.5698			−0.737174			−0.368587	−	0.929593i	$-0.620158\pi$
$131$	−96.5698			−0.737174			−0.368587	+	0.929593i	$0.620158\pi$
$132$	1.06470	+	3.97352i	0.00806591	+	0.0301024i
$133$	−2.44497	+	4.23482i	−0.0183833	+	0.0318408i
$134$	−292.913	+	169.113i	−2.18591	+	1.26204i
$135$		0			0
$136$	21.1982	+	5.68004i	0.155869	+	0.0417650i
$137$	−35.9585	+	134.199i	−0.262471	+	0.979555i	0.701309	+	0.712857i	$0.252599\pi$
$137$	−35.9585	+	134.199i	−0.262471	+	0.979555i	−0.963780	+	0.266698i	$0.914068\pi$
$138$	0.107651	+	0.107651i	0.000780083	+	0.000780083i
$139$	−36.5951	−	63.3846i	−0.263274	−	0.456005i	0.703836	−	0.710363i	$-0.251469\pi$
$139$	−36.5951	−	63.3846i	−0.263274	−	0.456005i	−0.967110	+	0.254358i	$0.918136\pi$
$140$		0			0
$141$	2.56947	−	0.688486i	0.0182232	−	0.00488288i
$142$		−	179.813i		−	1.26629i
$143$	87.2926	+	190.925i	0.610438	+	1.33514i
$144$	114.906			0.797958
$145$		0			0
$146$	127.471	−	220.787i	0.873091	−	1.51224i
$147$	1.38475	−	0.799484i	0.00942005	−	0.00543867i
$148$	−238.633	+	238.633i	−1.61238	+	1.61238i
$149$	−157.836	−	42.2920i	−1.05930	−	0.283839i	−0.313210	−	0.949684i	$-0.601405\pi$
$149$	−157.836	−	42.2920i	−1.05930	−	0.283839i	−0.746090	+	0.665845i	$0.768071\pi$
$150$		0			0
$151$	−183.510	−	183.510i	−1.21530	−	1.21530i	−0.969261	−	0.246036i	$-0.920872\pi$
$151$	−183.510	−	183.510i	−1.21530	−	1.21530i	−0.246036	−	0.969261i	$-0.579128\pi$
$152$	43.4790	+	75.3078i	0.286046	+	0.495446i
$153$	13.4114	+	7.74306i	0.0876560	+	0.0506082i
$154$	38.3025	−	10.2631i	0.248718	−	0.0666437i
$155$		0			0
$156$	−3.26548	+	0.550573i	−0.0209326	+	0.00352932i
$157$	21.3368			0.135903			0.0679516	−	0.997689i	$-0.478354\pi$
$157$	21.3368			0.135903			0.0679516	+	0.997689i	$0.478354\pi$
$158$	−36.9238	−	137.801i	−0.233695	−	0.872161i
$159$	−0.524651	+	0.908722i	−0.00329969	+	0.00571524i
$160$		0			0
$161$	0.683670	−	0.683670i	0.00424640	−	0.00424640i
$162$	267.804	+	71.7578i	1.65311	+	0.442950i
$163$	19.9108	−	74.3081i	0.122152	−	0.455878i	−0.877570	−	0.479448i	$-0.840837\pi$
$163$	19.9108	−	74.3081i	0.122152	−	0.455878i	0.999722	+	0.0235705i	$0.00750342\pi$
$164$	310.036	+	310.036i	1.89046	+	1.89046i
$165$		0			0
$166$	35.4681	+	20.4775i	0.213663	+	0.123358i
$167$	−238.687	+	63.9559i	−1.42926	+	0.382969i	−0.888759	−	0.458374i	$-0.848432\pi$
$167$	−238.687	+	63.9559i	−1.42926	+	0.382969i	−0.540501	+	0.841343i	$0.681765\pi$
$168$			0.301597i			0.00179522i
$169$	−159.657	+	55.4129i	−0.944717	+	0.327887i
$170$		0			0
$171$	15.8815	+	59.2707i	0.0928745	+	0.346612i
$172$	101.651	−	176.065i	0.590996	−	1.02363i
$173$	−95.6665	+	55.2331i	−0.552986	+	0.319266i	−0.750325	−	0.661069i	$-0.770103\pi$
$173$	−95.6665	+	55.2331i	−0.552986	+	0.319266i	0.197340	+	0.980335i	$0.436770\pi$
$174$	−3.79560	+	3.79560i	−0.0218138	+	0.0218138i
$175$		0			0
$176$	53.3689	−	199.176i	0.303233	−	1.13168i
$177$	2.19011	+	2.19011i	0.0123735	+	0.0123735i
$178$	−162.493	−	281.446i	−0.912883	−	1.58116i
$179$	183.778	+	106.104i	1.02669	+	0.592761i	0.916035	−	0.401098i	$-0.131371\pi$
$179$	183.778	+	106.104i	1.02669	+	0.592761i	0.110656	+	0.993859i	$0.464705\pi$
$180$		0			0
$181$			51.8213i			0.286306i	0.989701	+	0.143153i	$0.0457240\pi$
$181$			51.8213i			0.286306i	−0.989701	+	0.143153i	$0.954276\pi$
$182$	5.30723	+	31.4775i	0.0291606	+	0.172953i
$183$	−1.41249			−0.00771853
$184$	−4.45003	−	16.6077i	−0.0241849	−	0.0902594i
$185$		0			0
$186$	2.99409	−	1.72864i	0.0160973	−	0.00929375i
$187$	19.6507	−	19.6507i	0.105084	−	0.105084i
$188$	−601.842	−	161.263i	−3.20129	−	0.857782i
$189$	−0.110171	+	0.411163i	−0.000582914	+	0.00217547i
$190$		0			0
$191$	−95.3560	−	165.161i	−0.499246	−	0.864720i	0.500753	−	0.865590i	$-0.333056\pi$
$191$	−95.3560	−	165.161i	−0.499246	−	0.864720i	−1.00000		0.000870149i	$0.999723\pi$
$192$	−2.17152	−	1.25373i	−0.0113100	−	0.00652984i
$193$	21.9641	−	5.88526i	0.113804	−	0.0304936i	−0.201468	−	0.979495i	$-0.564571\pi$
$193$	21.9641	−	5.88526i	0.113804	−	0.0304936i	0.315271	+	0.949002i	$0.397904\pi$
$194$		−	501.269i		−	2.58386i
$195$		0			0
$196$	−374.524			−1.91083
$197$	31.8969	+	119.041i	0.161913	+	0.604267i	0.998414	+	0.0563018i	$0.0179309\pi$
$197$	31.8969	+	119.041i	0.161913	+	0.604267i	−0.836501	+	0.547966i	$0.815402\pi$
$198$	248.797	−	430.929i	1.25655	−	2.17641i
$199$	23.6042	−	13.6279i	0.118614	−	0.0684820i	−0.439519	−	0.898233i	$-0.644851\pi$
$199$	23.6042	−	13.6279i	0.118614	−	0.0684820i	0.558133	+	0.829751i	$0.311518\pi$
$200$		0			0
$201$	−3.14653	−	0.843109i	−0.0156544	−	0.00419457i
$202$	80.0652	−	298.807i	0.396362	−	1.47924i
$203$	24.1050	+	24.1050i	0.118744	+	0.118744i
$204$	0.219186	+	0.379642i	0.00107444	+	0.00186099i
$205$		0			0
$206$	−352.776	+	94.5261i	−1.71251	+	0.458864i
$207$		−	12.1326i		−	0.0586116i
$208$	155.554	+	57.9420i	0.747857	+	0.278567i
$209$	110.115			0.526866
$210$		0			0
$211$	13.7251	−	23.7725i	0.0650477	−	0.112666i	−0.831667	−	0.555274i	$-0.812613\pi$
$211$	13.7251	−	23.7725i	0.0650477	−	0.112666i	0.896715	+	0.442608i	$0.145947\pi$
$212$	212.849	−	122.888i	1.00400	−	0.579661i
$213$	1.22458	−	1.22458i	0.00574918	−	0.00574918i
$214$	−426.417	−	114.258i	−1.99260	−	0.533917i
$215$		0			0
$216$	5.35254	+	5.35254i	0.0247803	+	0.0247803i
$217$	−10.9782	−	19.0148i	−0.0505908	−	0.0876258i
$218$	338.334	+	195.337i	1.55199	+	0.896042i
$219$	2.37174	−	0.635505i	0.0108298	−	0.00290185i
$220$		0			0
$221$	14.2512	+	17.2450i	0.0644851	+	0.0780315i
$222$	−4.93346			−0.0222228
$223$	7.84413	+	29.2747i	0.0351755	+	0.131277i	0.981281	−	0.192582i	$-0.0616863\pi$
$223$	7.84413	+	29.2747i	0.0351755	+	0.131277i	−0.946105	+	0.323859i	$0.895020\pi$
$224$	−2.61362	+	4.52693i	−0.0116680	+	0.0202095i
$225$		0			0
$226$	345.010	−	345.010i	1.52659	−	1.52659i
$227$	−362.889	−	97.2358i	−1.59863	−	0.428351i	−0.654001	−	0.756494i	$-0.726911\pi$
$227$	−362.889	−	97.2358i	−1.59863	−	0.428351i	−0.944628	+	0.328142i	$0.893577\pi$
$228$	−0.449566	+	1.67780i	−0.00197178	+	0.00735879i
$229$	−165.325	−	165.325i	−0.721942	−	0.721942i	0.247059	−	0.969001i	$-0.420536\pi$
$229$	−165.325	−	165.325i	−0.721942	−	0.721942i	−0.969001	+	0.247059i	$0.920536\pi$
$230$		0			0
$231$	0.330746	+	0.190956i	0.00143180	+	0.000826651i
$232$	585.559	−	156.900i	2.52396	−	0.676293i
$233$		−	116.211i		−	0.498759i	−0.968406	−	0.249379i	$-0.919773\pi$
$233$		−	116.211i		−	0.498759i	0.968406	−	0.249379i	$-0.0802266\pi$
$234$	326.396	+	232.212i	1.39485	+	0.992360i
$235$		0			0
$236$	−187.766	−	700.752i	−0.795618	−	2.96929i
$237$	0.687006	−	1.18993i	0.00289876	−	0.00502080i
$238$	3.65954	−	2.11284i	0.0153762	−	0.00887747i
$239$	−224.962	+	224.962i	−0.941263	+	0.941263i	−0.998368	−	0.0571055i	$-0.981813\pi$
$239$	−224.962	+	224.962i	−0.941263	+	0.941263i	0.0571055	+	0.998368i	$0.481813\pi$
$240$		0			0
$241$	−44.9894	+	167.903i	−0.186678	+	0.696692i	0.807587	+	0.589748i	$0.200773\pi$
$241$	−44.9894	+	167.903i	−0.186678	+	0.696692i	−0.994265	+	0.106944i	$0.965894\pi$
$242$	−338.444	−	338.444i	−1.39853	−	1.39853i
$243$	4.00620	+	6.93893i	0.0164864	+	0.0285553i
$244$	286.520	+	165.423i	1.17426	+	0.677962i
$245$		0			0
$246$			6.40962i			0.0260554i
$247$	−8.38791	+	88.2463i	−0.0339592	+	0.357272i
$248$	−390.450			−1.57440
$249$	0.102090	+	0.381005i	0.000410000	+	0.00153014i
$250$		0			0
$251$	145.005	−	83.7187i	0.577709	−	0.333541i	−0.182513	−	0.983203i	$-0.558423\pi$
$251$	145.005	−	83.7187i	0.577709	−	0.333541i	0.760223	+	0.649663i	$0.225090\pi$
$252$	35.2483	−	35.2483i	0.139874	−	0.139874i
$253$	−21.0304	−	5.63508i	−0.0831241	−	0.0222730i
$254$	−87.7071	+	327.327i	−0.345304	+	1.28869i
$255$		0			0
$256$	243.742	+	422.173i	0.952117	+	1.64911i
$257$	−161.725	−	93.3719i	−0.629279	−	0.363315i	0.151194	−	0.988504i	$-0.451688\pi$
$257$	−161.725	−	93.3719i	−0.629279	−	0.363315i	−0.780473	+	0.625190i	$0.785022\pi$
$258$	2.87073	−	0.769210i	0.0111269	−	0.00298144i
$259$			31.3313i			0.120970i
$260$		0			0
$261$	427.773			1.63898
$262$	85.5821	+	319.397i	0.326649	+	1.21907i
$263$	70.0491	−	121.329i	0.266346	−	0.461326i	−0.701569	−	0.712601i	$-0.747517\pi$
$263$	70.0491	−	121.329i	0.266346	−	0.461326i	0.967915	+	0.251276i	$0.0808502\pi$
$264$	5.88165	−	3.39577i	0.0222790	−	0.0128628i
$265$		0			0
$266$	16.1731	+	4.33357i	0.0608012	+	0.0162916i
$267$	0.810106	−	3.02336i	0.00303410	−	0.0113234i
$268$	539.526	+	539.526i	2.01316	+	2.01316i
$269$	24.6298	+	42.6600i	0.0915604	+	0.158587i	0.908168	−	0.418606i	$-0.137481\pi$
$269$	24.6298	+	42.6600i	0.0915604	+	0.158587i	−0.816607	+	0.577193i	$0.804148\pi$
$270$		0			0
$271$	−450.532	+	120.720i	−1.66248	+	0.445460i	−0.963068	−	0.269258i	$-0.913222\pi$
$271$	−450.532	+	120.720i	−1.66248	+	0.445460i	−0.699412	+	0.714718i	$0.746555\pi$
$272$		−	21.9738i		−	0.0807859i
$273$	−0.178227	+	0.250515i	−0.000652846	+	0.000917636i
$274$	475.719			1.73620
$275$		0			0
$276$	0.171721	−	0.297430i	0.000622179	−	0.00107765i
$277$	−19.1597	+	11.0619i	−0.0691686	+	0.0399345i	−0.534185	−	0.845367i	$-0.679382\pi$
$277$	−19.1597	+	11.0619i	−0.0691686	+	0.0399345i	0.465017	+	0.885302i	$0.346048\pi$
$278$	−177.208	+	177.208i	−0.637440	+	0.637440i
$279$	−266.132	−	71.3098i	−0.953877	−	0.255591i
$280$		0			0
$281$	213.347	+	213.347i	0.759241	+	0.759241i	0.976184	−	0.216943i	$-0.0696086\pi$
$281$	213.347	+	213.347i	0.759241	+	0.759241i	−0.216943	+	0.976184i	$0.569609\pi$
$282$	−4.55423	−	7.88815i	−0.0161497	−	0.0279722i
$283$	2.28036	+	1.31656i	0.00805779	+	0.00465217i	0.504023	−	0.863690i	$-0.331852\pi$
$283$	2.28036	+	1.31656i	0.00805779	+	0.00465217i	−0.495966	+	0.868342i	$0.665186\pi$
$284$	−391.817	+	104.987i	−1.37964	+	0.369673i
$285$		0			0
$286$	554.109	−	457.915i	1.93744	−	1.60110i
$287$	40.7061			0.141833
$288$	16.9770	+	63.3591i	0.0589480	+	0.219997i
$289$	−143.019	+	247.717i	−0.494876	+	0.857151i
$290$		0			0
$291$	3.41379	−	3.41379i	0.0117312	−	0.0117312i
$292$	−555.528	−	148.853i	−1.90249	−	0.509771i
$293$	27.5961	−	102.990i	0.0941847	−	0.351502i	−0.902710	−	0.430250i	$-0.858425\pi$
$293$	27.5961	−	102.990i	0.0941847	−	0.351502i	0.996895	+	0.0787477i	$0.0250921\pi$
$294$	−3.87142	−	3.87142i	−0.0131681	−	0.0131681i
$295$		0			0
$296$	482.518	+	278.582i	1.63013	+	0.941155i
$297$	9.25882	−	2.48089i	0.0311745	−	0.00835318i
$298$			559.509i			1.87755i
$299$	6.11793	−	16.4245i	0.0204613	−	0.0549316i
$300$		0			0
$301$	−4.88508	−	18.2314i	−0.0162295	−	0.0605694i
$302$	−444.314	+	769.574i	−1.47124	+	2.54826i
$303$	2.58023	−	1.48970i	0.00851561	−	0.00491649i
$304$	61.5664	−	61.5664i	0.202521	−	0.202521i
$305$		0			0
$306$	13.7241	−	51.2191i	0.0448500	−	0.167383i
$307$	148.641	+	148.641i	0.484174	+	0.484174i	0.906462	−	0.422288i	$-0.138773\pi$
$307$	148.641	+	148.641i	0.484174	+	0.484174i	−0.422288	+	0.906462i	$0.638773\pi$
$308$	−44.7274	−	77.4701i	−0.145219	−	0.251526i
$309$	−3.04626	−	1.75876i	−0.00985843	−	0.00569177i
$310$		0			0
$311$		−	158.134i		−	0.508469i	−0.967143	−	0.254234i	$-0.918177\pi$
$311$		−	158.134i		−	0.508469i	0.967143	−	0.254234i	$-0.0818235\pi$
$312$	2.27335	+	4.97224i	0.00728638	+	0.0159367i
$313$	145.003			0.463269			0.231634	−	0.972803i	$-0.425593\pi$
$313$	145.003			0.463269			0.231634	+	0.972803i	$0.425593\pi$
$314$	−18.9091	−	70.5697i	−0.0602201	−	0.224744i
$315$		0			0
$316$	−278.715	+	160.916i	−0.882010	+	0.509229i
$317$	385.578	−	385.578i	1.21633	−	1.21633i	0.247427	−	0.968907i	$-0.420415\pi$
$317$	385.578	−	385.578i	1.21633	−	1.21633i	0.968907	−	0.247427i	$-0.0795851\pi$
$318$	3.47048	+	0.929913i	0.0109135	+	0.00292425i
$319$	198.683	−	741.494i	0.622830	−	2.32443i
$320$		0			0
$321$	−2.12589	−	3.68215i	−0.00662272	−	0.0114709i
$322$	−2.86707	−	1.65530i	−0.00890394	−	0.00514069i
$323$	11.3345	−	3.03707i	0.0350913	−	0.00940269i
$324$		−	625.450i		−	1.93040i
$325$		0			0
$326$	−263.413			−0.808017
$327$	0.973848	+	3.63445i	0.00297813	+	0.0111145i
$328$	361.938	−	626.895i	1.10347	−	1.91127i
$329$	−50.0959	+	28.9229i	−0.152267	+	0.0879115i
$330$		0			0
$331$	71.9790	+	19.2867i	0.217459	+	0.0582680i	0.365904	−	0.930653i	$-0.380760\pi$
$331$	71.9790	+	19.2867i	0.217459	+	0.0582680i	−0.148444	+	0.988921i	$0.547427\pi$
$332$	23.9124	−	89.2422i	0.0720253	−	0.268802i
$333$	278.007	+	278.007i	0.834854	+	0.834854i
$334$	423.058	+	732.758i	1.26664	+	2.19388i
$335$		0			0
$336$	0.291689	−	0.0781578i	0.000868122	−	0.000232613i
$337$		−	127.419i		−	0.378098i	−0.981968	−	0.189049i	$-0.939459\pi$
$337$		−	127.419i		−	0.378098i	0.981968	−	0.189049i	$-0.0605406\pi$
$338$	324.765	+	478.945i	0.960843	+	1.41700i
$339$	4.69923			0.0138620
$340$		0			0
$341$	−247.214	+	428.187i	−0.724967	+	1.25568i
$342$	181.958	−	105.054i	0.532042	−	0.307175i
$343$	−49.4338	+	49.4338i	−0.144122	+	0.144122i
$344$	−324.208	−	86.8714i	−0.942466	−	0.252533i
$345$		0			0
$346$	267.461	+	267.461i	0.773008	+	0.773008i
$347$	−141.151	−	244.481i	−0.406776	−	0.704557i	0.587750	−	0.809042i	$-0.300014\pi$
$347$	−141.151	−	244.481i	−0.406776	−	0.704557i	−0.994526	+	0.104486i	$0.966680\pi$
$348$	10.4869	+	6.05459i	0.0301347	+	0.0173983i
$349$	146.454	−	39.2423i	0.419640	−	0.112442i	−0.0428192	−	0.999083i	$-0.513634\pi$
$349$	146.454	−	39.2423i	0.419640	−	0.112442i	0.462459	+	0.886641i	$0.346967\pi$
$350$		0			0
$351$	1.28291	+	7.60902i	0.00365501	+	0.0216781i
$352$	117.710			0.334405
$353$	−112.774	−	420.878i	−0.319473	−	1.19229i	−0.919753	−	0.392499i	$-0.871611\pi$
$353$	−112.774	−	420.878i	−0.319473	−	1.19229i	0.600280	−	0.799790i	$-0.295056\pi$
$354$	5.30269	−	9.18453i	0.0149794	−	0.0259450i
$355$		0			0
$356$	−518.406	+	518.406i	−1.45620	+	1.45620i
$357$	0.0393116	+	0.0105335i	0.000110116	+	2.95056e-5i
$358$	188.063	−	701.862i	0.525316	−	1.96051i
$359$	−121.061	−	121.061i	−0.337217	−	0.337217i	0.518102	−	0.855319i	$-0.326639\pi$
$359$	−121.061	−	121.061i	−0.337217	−	0.337217i	−0.855319	+	0.518102i	$0.826639\pi$
$360$		0			0
$361$	−272.369	−	157.252i	−0.754484	−	0.435602i
$362$	171.395	−	45.9251i	0.473466	−	0.126865i
$363$		−	4.60979i		−	0.0126992i
$364$	65.4918	−	29.9434i	0.179922	−	0.0822621i
$365$		0			0
$366$	1.25178	+	4.67170i	0.00342016	+	0.0127642i
$367$	−311.769	+	540.000i	−0.849507	+	1.47139i	0.0321410	+	0.999483i	$0.489767\pi$
$367$	−311.769	+	540.000i	−0.849507	+	1.47139i	−0.881648	+	0.471907i	$0.843566\pi$
$368$	−14.9089	+	8.60767i	−0.0405134	+	0.0233904i
$369$	361.190	−	361.190i	0.978836	−	0.978836i
$370$		0			0
$371$	5.90567	−	22.0403i	0.0159183	−	0.0594077i
$372$	−5.51492	−	5.51492i	−0.0148250	−	0.0148250i
$373$	−333.140	−	577.015i	−0.893136	−	1.54696i	−0.836095	−	0.548584i	$-0.815167\pi$
$373$	−333.140	−	577.015i	−0.893136	−	1.54696i	−0.0570403	−	0.998372i	$-0.518166\pi$
$374$	−82.4078	−	47.5782i	−0.220342	−	0.127214i
$375$		0			0
$376$			1028.67i			2.73583i
$377$	579.100	+	215.707i	1.53607	+	0.572168i
$378$	1.45752			0.00385588
$379$	99.5832	+	371.649i	0.262752	+	0.980605i	0.963612	+	0.267306i	$0.0861334\pi$
$379$	99.5832	+	371.649i	0.262752	+	0.980605i	−0.700859	+	0.713299i	$0.747200\pi$
$380$		0			0
$381$	−2.82650	+	1.63188i	−0.00741864	+	0.00428316i
$382$	−461.752	+	461.752i	−1.20877	+	1.20877i
$383$	7.17101	+	1.92147i	0.0187233	+	0.00501689i	0.268169	−	0.963372i	$-0.413582\pi$
$383$	7.17101	+	1.92147i	0.0187233	+	0.00501689i	−0.249445	+	0.968389i	$0.580248\pi$
$384$	−1.97330	+	7.36446i	−0.00513881	+	0.0191783i
$385$		0			0
$386$	−38.9300	−	67.4288i	−0.100855	−	0.174686i
$387$	−205.115	−	118.423i	−0.530014	−	0.306004i
$388$	−1092.28	+	292.676i	−2.81516	+	0.754320i
$389$		−	15.5965i		−	0.0400938i	−0.999799	−	0.0200469i	$-0.993618\pi$
$389$		−	15.5965i		−	0.0400938i	0.999799	−	0.0200469i	$-0.00638155\pi$
$390$		0			0
$391$	−2.32015			−0.00593389
$392$	160.034	+	597.256i	0.408251	+	1.52361i
$393$	−1.59235	+	2.75802i	−0.00405177	+	0.00701787i
$394$	365.450	−	210.993i	0.927538	−	0.535514i
$395$		0			0
$396$	−1084.27	−	290.530i	−2.73807	−	0.733663i
$397$	−48.6200	+	181.452i	−0.122469	+	0.457059i	−0.999737	−	0.0229416i	$-0.992697\pi$
$397$	−48.6200	+	181.452i	−0.122469	+	0.457059i	0.877268	+	0.480000i	$0.159363\pi$
$398$	−65.9918	−	65.9918i	−0.165809	−	0.165809i
$399$	0.0806307	+	0.139656i	0.000202082	+	0.000350016i
$400$		0			0
$401$	293.349	−	78.6027i	0.731544	−	0.196017i	0.126227	−	0.992001i	$-0.459713\pi$
$401$	293.349	−	78.6027i	0.731544	−	0.196017i	0.605317	+	0.795985i	$0.293046\pi$
$402$			11.1541i			0.0277464i
$403$	−324.318	−	230.734i	−0.804761	−	0.572542i
$404$	−697.858			−1.72737
$405$		0			0
$406$	58.3630	−	101.088i	0.143751	−	0.248984i
$407$	611.013	−	352.769i	1.50126	−	0.866753i
$408$	0.511760	−	0.511760i	0.00125431	−	0.00125431i
$409$	−124.212	−	33.2825i	−0.303697	−	0.0813753i	0.103752	−	0.994603i	$-0.466915\pi$
$409$	−124.212	−	33.2825i	−0.303697	−	0.0813753i	−0.407449	+	0.913228i	$0.633582\pi$
$410$		0			0
$411$	3.23979	+	3.23979i	0.00788269	+	0.00788269i
$412$	411.951	+	713.519i	0.999880	+	1.73184i
$413$	−58.3289	−	33.6762i	−0.141232	−	0.0815405i
$414$	−40.1276	+	10.7521i	−0.0969265	+	0.0259714i
$415$		0			0
$416$	−8.96649	+	94.3334i	−0.0215541	+	0.226763i
$417$	−2.41368			−0.00578819
$418$	−97.5861	−	364.196i	−0.233460	−	0.871283i
$419$	82.0055	−	142.038i	0.195717	−	0.338992i	−0.751418	−	0.659826i	$-0.770630\pi$
$419$	82.0055	−	142.038i	0.195717	−	0.338992i	0.947135	+	0.320834i	$0.103963\pi$
$420$		0			0
$421$	32.1013	−	32.1013i	0.0762501	−	0.0762501i	−0.667953	−	0.744203i	$-0.732829\pi$
$421$	32.1013	−	32.1013i	0.0762501	−	0.0762501i	0.744203	+	0.667953i	$0.232829\pi$
$422$	−90.7891	−	24.3269i	−0.215140	−	0.0576466i
$423$	−187.871	+	701.144i	−0.444139	+	1.65755i
$424$	−286.921	−	286.921i	−0.676701	−	0.676701i
$425$		0			0
$426$	−5.13543	−	2.96494i	−0.0120550	−	0.00695996i
$427$	29.6689	−	7.94976i	0.0694822	−	0.0186177i
$428$			995.889i			2.32684i
$429$	6.89217	+	0.655109i	0.0160657	+	0.00152706i
$430$		0			0
$431$	−60.7510	−	226.726i	−0.140953	−	0.526046i	−0.999902	−	0.0139840i	$-0.995549\pi$
$431$	−60.7510	−	226.726i	−0.140953	−	0.526046i	0.858949	−	0.512062i	$-0.171118\pi$
$432$	3.78961	−	6.56379i	0.00877224	−	0.0151940i
$433$	−75.0171	+	43.3111i	−0.173250	+	0.100026i	−0.584117	−	0.811669i	$-0.698559\pi$
$433$	−75.0171	+	43.3111i	−0.173250	+	0.100026i	0.410868	+	0.911695i	$0.365226\pi$
$434$	−53.1608	+	53.1608i	−0.122490	+	0.122490i
$435$		0			0
$436$	228.103	−	851.291i	0.523172	−	1.95250i
$437$	−6.50062	−	6.50062i	−0.0148756	−	0.0148756i
$438$	−4.20376	−	7.28113i	−0.00959763	−	0.0166236i
$439$	94.1234	+	54.3422i	0.214404	+	0.123786i	0.603357	−	0.797472i	$-0.293830\pi$
$439$	94.1234	+	54.3422i	0.214404	+	0.123786i	−0.388952	+	0.921258i	$0.627163\pi$
$440$		0			0
$441$			436.319i			0.989385i
$442$	44.4066	−	62.4176i	0.100467	−	0.141216i
$443$	−355.262			−0.801945			−0.400973	−	0.916090i	$-0.631328\pi$
$443$	−355.262			−0.801945			−0.400973	+	0.916090i	$0.631328\pi$
$444$	2.88050	+	10.7502i	0.00648760	+	0.0242121i
$445$		0			0
$446$	89.8721	−	51.8877i	0.201507	−	0.116340i
$447$	−3.81042	+	3.81042i	−0.00852442	+	0.00852442i
$448$	52.6684	+	14.1125i	0.117563	+	0.0315010i
$449$	54.9003	−	204.891i	0.122272	−	0.456327i	−0.877455	−	0.479658i	$-0.840761\pi$
$449$	54.9003	−	204.891i	0.122272	−	0.456327i	0.999728	+	0.0233313i	$0.00742726\pi$
$450$		0			0
$451$	−458.323	−	793.838i	−1.01624	−	1.76017i
$452$	−953.227	−	550.346i	−2.10891	−	1.21758i
$453$	−8.26692	+	2.21512i	−0.0182493	+	0.00488988i
$454$			1286.40i			2.83348i
$455$		0			0
$456$	2.86771			0.00628883
$457$	81.5684	+	304.417i	0.178487	+	0.666121i	0.995931	+	0.0901143i	$0.0287232\pi$
$457$	81.5684	+	304.417i	0.178487	+	0.666121i	−0.817445	+	0.576007i	$0.804610\pi$
$458$	−400.284	+	693.312i	−0.873983	+	1.51378i
$459$	0.884617	−	0.510734i	0.00192727	−	0.00111271i
$460$		0			0
$461$	673.308	+	180.412i	1.46054	+	0.391350i	0.899676	−	0.436559i	$-0.143803\pi$
$461$	673.308	+	180.412i	1.46054	+	0.391350i	0.560862	+	0.827909i	$0.310470\pi$
$462$	0.338459	−	1.26315i	0.000732595	−	0.00273408i
$463$	−645.269	−	645.269i	−1.39367	−	1.39367i	−0.816923	−	0.576746i	$-0.804322\pi$
$463$	−645.269	−	645.269i	−1.39367	−	1.39367i	−0.576746	−	0.816923i	$-0.695678\pi$
$464$	−303.491	−	525.662i	−0.654076	−	1.13289i
$465$		0			0
$466$	−384.358	+	102.988i	−0.824802	+	0.221005i
$467$		−	571.015i		−	1.22273i	−0.791349	−	0.611365i	$-0.790621\pi$
$467$		−	571.015i		−	1.22273i	0.791349	−	0.611365i	$-0.209379\pi$
$468$	315.425	−	846.808i	0.673986	−	1.80942i
$469$	70.8370			0.151038
$470$		0			0
$471$	0.351824	−	0.609376i	0.000746972	−	0.00129379i
$472$	−1037.26	+	598.864i	−2.19759	+	1.26878i
$473$	−300.540	+	300.540i	−0.635392	+	0.635392i
$474$	−4.54443	−	1.21768i	−0.00958741	−	0.00256894i
$475$		0			0
$476$	−6.74064	−	6.74064i	−0.0141610	−	0.0141610i
$477$	−143.164	−	247.968i	−0.300135	−	0.519849i
$478$	943.409	+	544.677i	1.97366	+	1.13949i
$479$	40.3383	−	10.8086i	0.0842137	−	0.0225650i	−0.216466	−	0.976290i	$-0.569453\pi$
$479$	40.3383	−	10.8086i	0.0842137	−	0.0225650i	0.300680	+	0.953725i	$0.402786\pi$
$480$		0			0
$481$	236.166	+	516.539i	0.490990	+	1.07389i
$482$	595.196			1.23485
$483$	−0.00825247	−	0.0307986i	−1.70859e−5	−	6.37653e-5i
$484$	−539.872	+	935.086i	−1.11544	+	1.93200i
$485$		0			0
$486$	19.3996	−	19.3996i	0.0399169	−	0.0399169i
$487$	355.398	+	95.2286i	0.729770	+	0.195541i	0.604527	−	0.796585i	$-0.293362\pi$
$487$	355.398	+	95.2286i	0.729770	+	0.195541i	0.125243	+	0.992126i	$0.460029\pi$
$488$	141.371	−	527.602i	0.289694	−	1.08115i
$489$	−1.79392	−	1.79392i	−0.00366855	−	0.00366855i
$490$		0			0
$491$	274.278	+	158.355i	0.558612	+	0.322515i	0.752588	−	0.658491i	$-0.228805\pi$
$491$	274.278	+	158.355i	0.558612	+	0.322515i	−0.193976	+	0.981006i	$0.562138\pi$
$492$	13.9668	−	3.74239i	0.0283878	−	0.00760648i
$493$		−	81.8043i		−	0.165932i
$494$	299.301	−	50.4633i	0.605872	−	0.102152i
$495$		0			0
$496$	101.184	+	377.623i	0.204000	+	0.761337i
$497$	−18.8297	+	32.6140i	−0.0378867	+	0.0656217i
$498$	1.16967	−	0.675309i	0.00234873	−	0.00135604i
$499$	426.657	−	426.657i	0.855023	−	0.855023i	−0.135723	−	0.990747i	$-0.543336\pi$
$499$	426.657	−	426.657i	0.855023	−	0.855023i	0.990747	+	0.135723i	$0.0433358\pi$
$500$		0			0
$501$	−2.10914	+	7.87143i	−0.00420987	+	0.0157114i
$502$	−405.399	−	405.399i	−0.807568	−	0.807568i
$503$	368.899	+	638.951i	0.733397	+	1.27028i	0.955423	+	0.295240i	$0.0953996\pi$
$503$	368.899	+	638.951i	0.733397	+	1.27028i	−0.222026	+	0.975041i	$0.571267\pi$
$504$	−71.2725	−	41.1492i	−0.141414	−	0.0816452i
$505$		0			0
$506$			74.5502i			0.147332i
$507$	−1.05001	+	5.47350i	−0.00207103	+	0.0107959i
$508$	764.466			1.50486
$509$	−21.0926	−	78.7186i	−0.0414392	−	0.154653i	0.942106	−	0.335315i	$-0.108843\pi$
$509$	−21.0926	−	78.7186i	−0.0414392	−	0.154653i	−0.983545	+	0.180662i	$0.942176\pi$
$510$		0			0
$511$	−46.2408	+	26.6972i	−0.0904908	+	0.0522449i
$512$	526.388	−	526.388i	1.02810	−	1.02810i
$513$	3.90951	+	1.04755i	0.00762087	+	0.00204201i
$514$	−165.496	+	617.640i	−0.321977	+	1.20163i
$515$		0			0
$516$	−3.35227	−	5.80630i	−0.00649664	−	0.0112525i
$517$	1128.09	+	651.303i	2.18199	+	1.25977i
$518$	103.626	−	27.7664i	0.200050	−	0.0536031i
$519$			3.64297i			0.00701920i
$520$		0			0
$521$	461.334			0.885477			0.442739	−	0.896651i	$-0.354007\pi$
$521$	461.334			0.885477			0.442739	+	0.896651i	$0.354007\pi$
$522$	−379.102	−	1414.83i	−0.726248	−	2.71040i
$523$	297.903	−	515.982i	0.569603	−	0.986582i	−0.427002	−	0.904251i	$-0.640430\pi$
$523$	297.903	−	515.982i	0.569603	−	0.986582i	0.996605	−	0.0823312i	$-0.0262365\pi$
$524$	646.007	−	372.972i	1.23284	−	0.711779i
$525$		0			0
$526$	−463.364	−	124.158i	−0.880919	−	0.236042i
$527$	−13.6368	+	50.8931i	−0.0258762	+	0.0965714i
$528$	−4.80843	−	4.80843i	−0.00910687	−	0.00910687i
$529$	−263.591	−	456.553i	−0.498282	−	0.863050i
$530$		0			0
$531$	−816.374	+	218.747i	−1.53743	+	0.411952i
$532$		−	37.7720i		−	0.0709999i
$533$	671.095	−	306.831i	1.25909	−	0.575667i
$534$	−10.7174			−0.0200701
$535$		0			0
$536$	629.847	−	1090.93i	1.17509	−	2.03531i
$537$	6.06064	−	3.49911i	0.0112861	−	0.00651604i
$538$	119.267	−	119.267i	0.221686	−	0.221686i
$539$	756.306	+	202.652i	1.40317	+	0.375977i
$540$		0			0
$541$	257.907	+	257.907i	0.476723	+	0.476723i	0.904082	−	0.427359i	$-0.140556\pi$
$541$	257.907	+	257.907i	0.476723	+	0.476723i	−0.427359	+	0.904082i	$0.640556\pi$
$542$	798.542	+	1383.11i	1.47332	+	2.55187i
$543$	1.48001	+	0.854485i	0.00272562	+	0.00157364i
$544$	12.1163	−	3.24656i	0.0222727	−	0.00596794i
$545$		0			0
$546$	0.986505	+	0.367460i	0.00180679	+	0.000673005i
$547$	−700.642			−1.28088			−0.640441	−	0.768007i	$-0.721248\pi$
$547$	−700.642			−1.28088			−0.640441	+	0.768007i	$0.721248\pi$
$548$	−277.758	−	1036.61i	−0.506858	−	1.89162i
$549$	192.717	−	333.795i	0.351033	−	0.608006i
$550$		0			0
$551$	229.200	−	229.200i	0.415971	−	0.415971i
$552$	−0.547692	−	0.146754i	−0.000992195	−	0.000265858i
$553$	−7.73320	+	28.8607i	−0.0139841	+	0.0521893i
$554$	53.5660	+	53.5660i	0.0966894	+	0.0966894i
$555$		0			0
$556$	489.609	+	282.676i	0.880591	+	0.508410i
$557$	−349.414	+	93.6252i	−0.627314	+	0.168088i	−0.558451	−	0.829538i	$-0.688604\pi$
$557$	−349.414	+	93.6252i	−0.627314	+	0.168088i	−0.0688635	+	0.997626i	$0.521937\pi$
$558$			943.405i			1.69069i
$559$	−217.960	−	263.747i	−0.389911	−	0.471819i
$560$		0			0
$561$	−0.237200	−	0.885242i	−0.000422816	−	0.00157797i
$562$	516.555	−	894.700i	0.919137	−	1.59199i
$563$	720.971	−	416.253i	1.28059	−	0.739348i	0.303632	−	0.952789i	$-0.401801\pi$
$563$	720.971	−	416.253i	1.28059	−	0.739348i	0.976956	+	0.213441i	$0.0684672\pi$
$564$	−14.5295	+	14.5295i	−0.0257615	+	0.0257615i
$565$		0			0
$566$	2.33353	−	8.70886i	0.00412285	−	0.0153867i
$567$	−41.0592	−	41.0592i	−0.0724149	−	0.0724149i
$568$	334.848	+	579.974i	0.589521	+	1.02108i
$569$	−744.104	−	429.609i	−1.30774	−	0.755024i	−0.326021	−	0.945362i	$-0.605708\pi$
$569$	−744.104	−	429.609i	−1.30774	−	0.755024i	−0.981719	+	0.190338i	$0.939041\pi$
$570$		0			0
$571$		−	835.548i		−	1.46331i	−0.681677	−	0.731654i	$-0.738749\pi$
$571$		−	835.548i		−	1.46331i	0.681677	−	0.731654i	$-0.261251\pi$
$572$	−1321.34	−	940.058i	−2.31003	−	1.64346i
$573$	−6.28932			−0.0109761
$574$	−36.0746	−	134.632i	−0.0628477	−	0.234551i
$575$		0			0
$576$	592.555	−	342.112i	1.02874	−	0.593944i
$577$	105.641	−	105.641i	0.183087	−	0.183087i	−0.609613	−	0.792699i	$-0.708675\pi$
$577$	105.641	−	105.641i	0.183087	−	0.183087i	0.792699	+	0.609613i	$0.208675\pi$
$578$	946.049	+	253.493i	1.63676	+	0.438570i
$579$	0.194085	−	0.724334i	0.000335207	−	0.00125101i
$580$		0			0
$581$	−4.28874	−	7.42831i	−0.00738165	−	0.0127854i
$582$	−14.3162	−	8.26546i	−0.0245983	−	0.0142018i
$583$	−496.316	+	132.988i	−0.851314	+	0.228109i
$584$			949.510i			1.62587i
$585$		0			0
$586$	−365.088			−0.623017
$587$	−89.8610	−	335.366i	−0.153085	−	0.571322i	−0.999262	−	0.0384190i	$-0.987768\pi$
$587$	−89.8610	−	335.366i	−0.153085	−	0.571322i	0.846177	−	0.532903i	$-0.178899\pi$
$588$	−6.17554	+	10.6964i	−0.0105026	+	0.0181911i
$589$	−180.800	+	104.385i	−0.306962	+	0.177224i
$590$		0			0
$591$	3.92574	+	1.05190i	0.00664253	+	0.00177986i
$592$	144.387	−	538.860i	0.243897	−	0.910237i
$593$	143.809	+	143.809i	0.242511	+	0.242511i	0.817888	−	0.575377i	$-0.195145\pi$
$593$	143.809	+	143.809i	0.242511	+	0.242511i	−0.575377	+	0.817888i	$0.695145\pi$
$594$	−16.4107	−	28.4242i	−0.0276275	−	0.0478522i
$595$		0			0
$596$	1219.19	−	326.680i	2.04562	−	0.548122i
$597$		−	0.898846i		−	0.00150560i
$598$	−59.7447	−	5.67880i	−0.0999075	−	0.00949632i
$599$	−927.612			−1.54860			−0.774300	−	0.632818i	$-0.781898\pi$
$599$	−927.612			−1.54860			−0.774300	+	0.632818i	$0.781898\pi$
$600$		0			0
$601$	53.2308	−	92.1984i	0.0885703	−	0.153408i	−0.818337	−	0.574739i	$-0.805104\pi$
$601$	53.2308	−	92.1984i	0.0885703	−	0.153408i	0.906907	+	0.421331i	$0.138437\pi$
$602$	−55.9696	+	32.3140i	−0.0929727	+	0.0536778i
$603$	628.546	−	628.546i	1.04236	−	1.04236i
$604$	1936.35	+	518.843i	3.20587	+	0.859011i
$605$		0			0
$606$	−7.21370	−	7.21370i	−0.0119038	−	0.0119038i
$607$	−591.121	−	1023.85i	−0.973841	−	1.68674i	−0.683709	−	0.729755i	$-0.739634\pi$
$607$	−591.121	−	1023.85i	−0.973841	−	1.68674i	−0.290132	−	0.956987i	$-0.593699\pi$
$608$	43.0439	+	24.8514i	0.0707959	+	0.0408740i
$609$	1.08590	−	0.290967i	0.00178309	−	0.000477779i
$610$		0			0
$611$	−607.887	+	854.441i	−0.994905	+	1.39843i
$612$	−119.621			−0.195459
$613$	185.093	+	690.777i	0.301947	+	1.12688i	0.935542	+	0.353215i	$0.114912\pi$
$613$	185.093	+	690.777i	0.301947	+	1.12688i	−0.633595	+	0.773665i	$0.718422\pi$
$614$	359.890	−	623.348i	0.586140	−	1.01522i
$615$		0			0
$616$	−104.430	+	104.430i	−0.169530	+	0.169530i
$617$	709.503	+	190.111i	1.14992	+	0.308121i	0.782934	−	0.622104i	$-0.213722\pi$
$617$	709.503	+	190.111i	1.14992	+	0.308121i	0.366989	+	0.930225i	$0.380389\pi$
$618$	−3.11729	+	11.6339i	−0.00504416	+	0.0188251i
$619$	446.560	+	446.560i	0.721421	+	0.721421i	0.968895	−	0.247474i	$-0.0796003\pi$
$619$	446.560	+	446.560i	0.721421	+	0.721421i	−0.247474	+	0.968895i	$0.579600\pi$
$620$		0			0
$621$	−0.693053	−	0.400134i	−0.00111603	−	0.000644338i
$622$	−523.015	+	140.141i	−0.840860	+	0.225308i
$623$			68.0641i			0.109252i
$624$	4.21976	−	3.48720i	0.00676244	−	0.00558847i
$625$		0			0
$626$	−128.505	−	479.586i	−0.205279	−	0.766112i
$627$	1.81569	−	3.14487i	0.00289584	−	0.00501574i
$628$	−142.733	+	82.4071i	−0.227282	+	0.131221i
$629$	53.1640	−	53.1640i	0.0845214	−	0.0845214i
$630$		0			0
$631$	16.5174	−	61.6436i	0.0261765	−	0.0976920i	−0.951602	−	0.307334i	$-0.900563\pi$
$631$	16.5174	−	61.6436i	0.0261765	−	0.0976920i	0.977778	+	0.209642i	$0.0672298\pi$
$632$	375.710	+	375.710i	0.594477	+	0.594477i
$633$	−0.452627	−	0.783973i	−0.000715050	−	0.00123850i
$634$	−1616.97	−	933.561i	−2.55043	−	1.47249i
$635$		0			0
$636$		−	8.10524i		−	0.0127441i
$637$	−220.016	+	590.668i	−0.345395	+	0.927266i
$638$	−2628.51			−4.11992
$639$	122.310	+	456.466i	0.191408	+	0.714344i
$640$		0			0
$641$	581.799	−	335.902i	0.907643	−	0.524028i	0.0279707	−	0.999609i	$-0.491096\pi$
$641$	581.799	−	335.902i	0.907643	−	0.524028i	0.879672	+	0.475581i	$0.157762\pi$
$642$	−10.2944	+	10.2944i	−0.0160349	+	0.0160349i
$643$	−533.905	−	143.059i	−0.830334	−	0.222487i	−0.181475	−	0.983396i	$-0.558087\pi$
$643$	−533.905	−	143.059i	−0.830334	−	0.222487i	−0.648859	+	0.760908i	$0.724754\pi$
$644$	−1.93296	+	7.21391i	−0.00300149	+	0.0112017i
$645$		0			0
$646$	−20.0897	−	34.7964i	−0.0310987	−	0.0538644i
$647$	−211.383	−	122.042i	−0.326713	−	0.188628i	0.327668	−	0.944793i	$-0.393737\pi$
$647$	−211.383	−	122.042i	−0.326713	−	0.188628i	−0.654381	+	0.756165i	$0.727071\pi$
$648$	−997.411	+	267.256i	−1.53921	+	0.412431i
$649$			1516.68i			2.33696i
$650$		0			0
$651$	−0.724081			−0.00111226
$652$	153.799	+	573.986i	0.235888	+	0.880347i
$653$	−552.758	+	957.406i	−0.846491	+	1.46617i	0.0378295	+	0.999284i	$0.487956\pi$
$653$	−552.758	+	957.406i	−0.846491	+	1.46617i	−0.884320	+	0.466881i	$0.845378\pi$
$654$	11.1576	−	6.44185i	0.0170606	−	0.00984992i
$655$		0			0
$656$	−700.095	−	187.590i	−1.06722	−	0.285960i
$657$	−173.414	+	647.188i	−0.263948	+	0.985066i
$658$	140.056	+	140.056i	0.212851	+	0.212851i
$659$	352.219	+	610.061i	0.534475	+	0.925737i	0.999189	+	0.0402762i	$0.0128238\pi$
$659$	352.219	+	610.061i	0.534475	+	0.925737i	−0.464714	+	0.885461i	$0.653843\pi$
$660$		0			0
$661$	−1116.82	+	299.251i	−1.68959	+	0.452724i	−0.970284	−	0.241968i	$-0.922207\pi$
$661$	−1116.82	+	299.251i	−1.68959	+	0.452724i	−0.719307	+	0.694693i	$0.755540\pi$
$662$		−	255.157i		−	0.385434i
$663$	0.727503	−	0.122660i	0.00109729	−	0.000185007i
$664$	−152.533			−0.229719
$665$		0			0
$666$	673.109	−	1165.86i	1.01067	−	1.75054i
$667$	−55.5032	+	32.0448i	−0.0832132	+	0.0480432i
$668$	1349.69	−	1349.69i	2.02050	−	2.02050i
$669$	0.965424	+	0.258685i	0.00144309	+	0.000386674i
$670$		0			0
$671$	−489.085	−	489.085i	−0.728890	−	0.728890i
$672$	0.0861924	+	0.149290i	0.000128263	+	0.000222157i
$673$	−802.800	−	463.497i	−1.19287	−	0.688703i	−0.233912	−	0.972258i	$-0.575153\pi$
$673$	−802.800	−	463.497i	−1.19287	−	0.688703i	−0.958956	+	0.283555i	$0.908486\pi$
$674$	−421.429	+	112.921i	−0.625265	+	0.167539i
$675$		0			0
$676$	854.016	−	987.315i	1.26334	−	1.46053i
$677$	168.337			0.248651			0.124326	−	0.992241i	$-0.460323\pi$
$677$	168.337			0.248651			0.124326	+	0.992241i	$0.460323\pi$
$678$	−4.16455	−	15.5423i	−0.00614240	−	0.0229238i
$679$	−52.4921	+	90.9190i	−0.0773079	+	0.133901i
$680$		0			0
$681$	−8.76074	+	8.76074i	−0.0128645	+	0.0128645i
$682$	1635.28	+	438.172i	2.39777	+	0.642481i
$683$	−96.5064	+	360.167i	−0.141298	+	0.527331i	0.858595	+	0.512655i	$0.171338\pi$
$683$	−96.5064	+	360.167i	−0.141298	+	0.527331i	−0.999892	+	0.0146753i	$0.995329\pi$
$684$	−335.156	−	335.156i	−0.489994	−	0.489994i
$685$		0			0
$686$	207.308	+	119.689i	0.302198	+	0.174474i
$687$	−7.44770	+	1.99561i	−0.0108409	+	0.00290481i
$688$			336.070i			0.488474i
$689$	−68.7700	−	407.879i	−0.0998113	−	0.591987i
$690$		0			0
$691$	186.588	+	696.355i	0.270026	+	1.00775i	0.959102	+	0.283061i	$0.0913497\pi$
$691$	186.588	+	696.355i	0.270026	+	1.00775i	−0.689076	+	0.724689i	$0.741984\pi$
$692$	426.643	−	738.967i	0.616536	−	1.06787i
$693$	−90.2524	+	52.1073i	−0.130234	+	0.0751909i
$694$	−683.511	+	683.511i	−0.984886	+	0.984886i
$695$		0			0
$696$	5.17427	−	19.3106i	0.00743429	−	0.0277452i
$697$	−69.0715	−	69.0715i	−0.0990982	−	0.0990982i
$698$	−259.581	−	449.608i	−0.371893	−	0.644138i
$699$	−3.31897	−	1.91621i	−0.00474816	−	0.00274135i
$700$		0			0
$701$		−	589.719i		−	0.841254i	−0.907234	−	0.420627i	$-0.861810\pi$
$701$		−	589.719i		−	0.841254i	0.907234	−	0.420627i	$-0.138190\pi$
$702$	24.0293	−	10.9864i	0.0342297	−	0.0156501i
$703$	297.911			0.423771
$704$	−317.793	−	1186.02i	−0.451411	−	1.68469i
$705$		0			0
$706$	−1292.08	+	745.981i	−1.83014	+	1.05663i
$707$	−45.8126	+	45.8126i	−0.0647986	+	0.0647986i
$708$	−23.1095	−	6.19216i	−0.0326405	−	0.00874600i
$709$	−40.7548	+	152.099i	−0.0574821	+	0.214526i	−0.988693	−	0.149955i	$-0.952087\pi$
$709$	−40.7548	+	152.099i	−0.0574821	+	0.214526i	0.931211	+	0.364481i	$0.118754\pi$
$710$		0			0
$711$	187.467	+	324.702i	0.263667	+	0.456684i
$712$	1048.22	+	605.191i	1.47222	+	0.849988i
$713$	39.8722	−	10.6837i	0.0559217	−	0.0149842i
$714$		−	0.139355i		−	0.000195175i
$715$		0			0
$716$	−1639.18			−2.28936
$717$	2.71547	+	10.1343i	0.00378727	+	0.0141343i
$718$	−293.112	+	507.685i	−0.408234	+	0.707083i
$719$	−721.138	+	416.349i	−1.00297	+	0.579067i	−0.909127	−	0.416519i	$-0.863250\pi$
$719$	−721.138	+	416.349i	−1.00297	+	0.579067i	−0.0938470	+	0.995587i	$0.529916\pi$
$720$		0			0
$721$	73.8843	+	19.7972i	0.102475	+	0.0274580i
$722$	−278.720	+	1040.20i	−0.386039	+	1.44072i
$723$	4.05345	+	4.05345i	0.00560643	+	0.00560643i
$724$	−200.145	−	346.661i	−0.276443	−	0.478813i
$725$		0			0
$726$	−15.2465	+	4.08529i	−0.0210007	+	0.00562713i
$727$			61.3646i			0.0844079i	0.999109	+	0.0422040i	$0.0134379\pi$
$727$			61.3646i			0.0844079i	−0.999109	+	0.0422040i	$0.986562\pi$
$728$	−75.7357	−	91.6454i	−0.104033	−	0.125887i
$729$	−728.472			−0.999275
$730$		0			0
$731$	−22.6464	+	39.2248i	−0.0309801	+	0.0536591i
$732$	9.44890	−	5.45533i	0.0129083	−	0.00745263i
$733$	256.277	−	256.277i	0.349628	−	0.349628i	−0.510343	−	0.859971i	$-0.670482\pi$
$733$	256.277	−	256.277i	0.349628	−	0.349628i	0.859971	+	0.510343i	$0.170482\pi$
$734$	2062.30	+	552.592i	2.80968	+	0.752851i
$735$		0			0
$736$	−6.94902	−	6.94902i	−0.00944160	−	0.00944160i
$737$	−797.576	−	1381.44i	−1.08219	−	1.87441i
$738$	−1514.70	−	874.514i	−2.05244	−	1.18498i
$739$	306.125	−	82.0259i	0.414242	−	0.110996i	−0.0456779	−	0.998956i	$-0.514545\pi$
$739$	306.125	−	82.0259i	0.414242	−	0.110996i	0.459920	+	0.887960i	$0.347878\pi$
$740$		0			0
$741$	2.38199	+	1.69466i	0.00321457	+	0.00228698i
$742$	−78.1301			−0.105297
$743$	−265.715	−	991.663i	−0.357625	−	1.33467i	−0.877149	−	0.480219i	$-0.840557\pi$
$743$	−265.715	−	991.663i	−0.357625	−	1.33467i	0.519524	−	0.854456i	$-0.326109\pi$
$744$	−6.43816	+	11.1512i	−0.00865344	+	0.0149882i
$745$		0			0
$746$	−1613.19	+	1613.19i	−2.16246	+	2.16246i
$747$	−103.967	−	27.8579i	−0.139179	−	0.0372930i
$748$	−55.5589	+	207.349i	−0.0742767	+	0.277204i
$749$	65.3776	+	65.3776i	0.0872865	+	0.0872865i
$750$		0			0
$751$	−444.296	−	256.514i	−0.591605	−	0.341563i	0.174127	−	0.984723i	$-0.444290\pi$
$751$	−444.296	−	256.514i	−0.591605	−	0.341563i	−0.765732	+	0.643160i	$0.777623\pi$
$752$	994.877	−	266.576i	1.32297	−	0.354490i
$753$		−	5.52177i		−	0.00733303i
$754$	200.224	−	2106.49i	0.265550	−	2.79375i
$755$		0			0
$756$	−0.851004	−	3.17599i	−0.00112567	−	0.00420105i
$757$	−0.185970	+	0.322110i	−0.000245667	+	0.000425508i	−0.866148	−	0.499787i	$-0.833412\pi$
$757$	−0.185970	+	0.322110i	−0.000245667	+	0.000425508i	0.865903	+	0.500213i	$0.166745\pi$
$758$	1140.95	−	658.727i	1.50521	−	0.869032i
$759$	−0.507708	+	0.507708i	−0.000668918	+	0.000668918i
$760$		0			0
$761$	−100.429	+	374.806i	−0.131970	+	0.492518i	−0.999992	−	0.00400744i	$-0.998724\pi$
$761$	−100.429	+	374.806i	−0.131970	+	0.492518i	0.868022	+	0.496525i	$0.165391\pi$
$762$	7.90223	+	7.90223i	0.0103704	+	0.0103704i
$763$	−40.9107	−	70.8595i	−0.0536183	−	0.0928696i
$764$	1275.78	+	736.569i	1.66986	+	0.964096i
$765$		0			0
$766$		−	25.4204i		−	0.0331859i
$767$	−1215.47	−	115.532i	−1.58471	−	0.150629i
$768$	16.0763			0.0209327
$769$	−290.354	−	1083.62i	−0.377574	−	1.40913i	−0.849547	−	0.527512i	$-0.823125\pi$
$769$	−290.354	−	1083.62i	−0.377574	−	1.40913i	0.471973	−	0.881613i	$-0.343542\pi$
$770$		0			0
$771$	−5.33338	+	3.07923i	−0.00691748	+	0.00399381i
$772$	−124.199	+	124.199i	−0.160880	+	0.160880i
$773$	943.196	+	252.729i	1.22018	+	0.326945i	0.810747	−	0.585397i	$-0.199061\pi$
$773$	943.196	+	252.729i	1.22018	+	0.326945i	0.409429	+	0.912342i	$0.365728\pi$
$774$	−209.899	+	783.352i	−0.271187	+	1.01208i
$775$		0			0
$776$	933.466	+	1616.81i	1.20292	+	2.08352i
$777$	0.894818	+	0.516623i	0.00115163	+	0.000664895i
$778$	−51.5841	+	13.8219i	−0.0663035	+	0.0177660i
$779$		−	387.050i		−	0.496855i
$780$		0			0
$781$	848.037			1.08583
$782$	2.05616	+	7.67371i	0.00262937	+	0.00981293i
$783$	14.1080	−	24.4358i	0.0180179	−	0.0312079i
$784$	536.163	−	309.554i	0.683881	−	0.394839i
$785$		0			0
$786$	10.5331	+	2.82234i	0.0134009	+	0.00359076i
$787$	−196.041	+	731.634i	−0.249099	+	0.929649i	0.722180	+	0.691705i	$0.243140\pi$
$787$	−196.041	+	731.634i	−0.249099	+	0.929649i	−0.971279	+	0.237944i	$0.923527\pi$
$788$	−673.135	−	673.135i	−0.854232	−	0.854232i
$789$	−2.31009	−	4.00119i	−0.00292787	−	0.00507122i
$790$		0			0
$791$	−98.7058	+	26.4481i	−0.124786	+	0.0334363i
$792$			1853.25i			2.33996i
$793$	429.210	−	354.698i	0.541248	−	0.447287i
$794$	643.227			0.810110
$795$		0			0
$796$	−105.268	+	182.329i	−0.132246	+	0.229056i
$797$	−79.9913	+	46.1830i	−0.100365	+	0.0579460i	−0.549343	−	0.835597i	$-0.685122\pi$
$797$	−79.9913	+	46.1830i	−0.100365	+	0.0579460i	0.448977	+	0.893543i	$0.351788\pi$
$798$	0.390446	−	0.390446i	0.000489280	−	0.000489280i
$799$	134.082	+	35.9271i	0.167812	+	0.0449651i
$800$		0			0
$801$	603.941	+	603.941i	0.753984	+	0.753984i
$802$	−519.944	−	900.569i	−0.648309	−	1.12290i
$803$	1041.28	+	601.183i	1.29674	+	0.748671i
$804$	24.3051	−	6.51252i	0.0302302	−	0.00810015i
$805$		0			0
$806$	−475.718	+	1277.14i	−0.590221	+	1.58454i
$807$	1.62449			0.00201299
$808$	298.196	+	1112.88i	0.369054	+	1.37733i
$809$	23.1844	−	40.1565i	0.0286580	−	0.0496372i	−0.851341	−	0.524613i	$-0.824210\pi$
$809$	23.1844	−	40.1565i	0.0286580	−	0.0496372i	0.879999	+	0.474976i	$0.157543\pi$
$810$		0			0
$811$	70.9896	−	70.9896i	0.0875334	−	0.0875334i	−0.661984	−	0.749518i	$-0.730285\pi$
$811$	70.9896	−	70.9896i	0.0875334	−	0.0875334i	0.749518	+	0.661984i	$0.230285\pi$
$812$	−254.350	−	68.1528i	−0.313238	−	0.0839320i
$813$	−3.98111	+	14.8577i	−0.00489681	+	0.0182752i
$814$	−1708.25	−	1708.25i	−2.09858	−	2.09858i
$815$		0			0
$816$	−0.627569	−	0.362327i	−0.000769079	−	0.000444028i
$817$	−173.351	+	46.4494i	−0.212181	+	0.0568536i
$818$			440.317i			0.538285i
$819$	−34.8840	−	76.2977i	−0.0425933	−	0.0931596i
$820$		0			0
$821$	−256.139	−	955.924i	−0.311984	−	1.16434i	−0.926765	−	0.375643i	$-0.877422\pi$
$821$	−256.139	−	955.924i	−0.311984	−	1.16434i	0.614780	−	0.788698i	$-0.289245\pi$
$822$	7.84417	−	13.5865i	0.00954278	−	0.0165286i
$823$	400.572	−	231.270i	0.486722	−	0.281009i	−0.236492	−	0.971633i	$-0.575998\pi$
$823$	400.572	−	231.270i	0.486722	−	0.281009i	0.723213	+	0.690625i	$0.242664\pi$
$824$	961.829	−	961.829i	1.16727	−	1.16727i
$825$		0			0
$826$	−59.6891	+	222.763i	−0.0722628	+	0.269689i
$827$	929.759	+	929.759i	1.12426	+	1.12426i	0.991094	+	0.133161i	$0.0425127\pi$
$827$	929.759	+	929.759i	1.12426	+	1.12426i	0.133161	+	0.991094i	$0.457487\pi$
$828$	46.8586	+	81.1614i	0.0565925	+	0.0980210i
$829$	385.154	+	222.369i	0.464600	+	0.268237i	0.713977	−	0.700170i	$-0.246892\pi$
$829$	385.154	+	222.369i	0.464600	+	0.268237i	−0.249376	+	0.968407i	$0.580226\pi$
$830$		0			0
$831$			0.729599i			0.000877977i
$832$	974.686	−	164.336i	1.17150	−	0.197519i
$833$	83.4385			0.100166
$834$	2.13905	+	7.98304i	0.00256481	+	0.00957199i
$835$		0			0
$836$	−736.618	+	425.286i	−0.881121	+	0.508716i
$837$	−12.8505	+	12.8505i	−0.0153530	+	0.0153530i
$838$	−542.453	−	145.350i	−0.647319	−	0.173449i
$839$	−241.488	+	901.245i	−0.287828	+	1.07419i	0.658920	+	0.752213i	$0.271014\pi$
$839$	−241.488	+	901.245i	−0.287828	+	1.07419i	−0.946748	+	0.321976i	$0.895653\pi$
$840$		0			0
$841$	−709.342	−	1228.62i	−0.843450	−	1.46090i
$842$	−134.621	−	77.7236i	−0.159883	−	0.0923084i
$843$	9.61105	−	2.57527i	0.0114010	−	0.00305489i
$844$			212.036i			0.251228i
$845$		0			0
$846$	2485.47			2.93791
$847$	25.9448	+	96.8273i	0.0306314	+	0.114318i
$848$	−203.141	+	351.850i	−0.239553	+	0.414918i
$849$	0.0752018	−	0.0434178i	8.85769e−5	−	5.11399e-5i
$850$		0			0
$851$	−56.8967	−	15.2454i	−0.0668587	−	0.0179147i
$852$	−3.46228	+	12.9214i	−0.00406371	+	0.0151660i
$853$	−130.680	−	130.680i	−0.153201	−	0.153201i	0.626345	−	0.779546i	$-0.284550\pi$
$853$	−130.680	−	130.680i	−0.153201	−	0.153201i	−0.779546	+	0.626345i	$0.784550\pi$
$854$	−52.5864	−	91.0823i	−0.0615766	−	0.106654i
$855$		0			0
$856$	1588.15	−	425.544i	1.85532	−	0.497131i
$857$			1553.51i			1.81273i	0.422496	+	0.906365i	$0.361154\pi$
$857$			1553.51i			1.81273i	−0.422496	+	0.906365i	$0.638846\pi$
$858$	−3.94126	−	23.3759i	−0.00459355	−	0.0272446i
$859$	−781.729			−0.910045			−0.455023	−	0.890480i	$-0.650369\pi$
$859$	−781.729			−0.910045			−0.455023	+	0.890480i	$0.650369\pi$
$860$		0			0
$861$	0.671205	−	1.16256i	0.000779565	−	0.00135025i
$862$	−696.038	+	401.858i	−0.807469	+	0.466192i
$863$	−534.675	+	534.675i	−0.619554	+	0.619554i	−0.945417	−	0.325863i	$-0.894345\pi$
$863$	−534.675	+	534.675i	−0.619554	+	0.619554i	0.325863	+	0.945417i	$0.394345\pi$
$864$	4.17918	+	1.11981i	0.00483701	+	0.00129607i
$865$		0			0
$866$	209.730	+	209.730i	0.242182	+	0.242182i
$867$	4.71651	+	8.16923i	0.00544003	+	0.00942241i
$868$	146.878	+	84.8001i	0.169214	+	0.0976960i
$869$	649.903	−	174.141i	0.747874	−	0.200392i
$870$		0			0
$871$	1167.84	−	533.948i	1.34081	−	0.613029i
$872$	−1455.03			−1.66861
$873$	340.967	+	1272.50i	0.390569	+	1.45762i
$874$	−15.7393	+	27.2613i	−0.0180083	+	0.0311914i
$875$		0			0
$876$	−13.4114	+	13.4114i	−0.0153098	+	0.0153098i
$877$	−281.460	−	75.4171i	−0.320935	−	0.0859944i	0.0947548	−	0.995501i	$-0.469793\pi$
$877$	−281.460	−	75.4171i	−0.320935	−	0.0859944i	−0.415690	+	0.909506i	$0.636460\pi$
$878$	96.3183	−	359.465i	0.109702	−	0.409413i
$879$	−2.48635	−	2.48635i	−0.00282861	−	0.00282861i
$880$		0			0
$881$	−523.282	−	302.117i	−0.593964	−	0.342925i	0.172699	−	0.984975i	$-0.444751\pi$
$881$	−523.282	−	302.117i	−0.593964	−	0.342925i	−0.766663	+	0.642049i	$0.778084\pi$
$882$	1443.09	−	386.675i	1.63616	−	0.438407i
$883$			1287.07i			1.45761i	0.684724	+	0.728803i	$0.259923\pi$
$883$			1287.07i			1.45761i	−0.684724	+	0.728803i	$0.740077\pi$
$884$	−161.938	−	60.3197i	−0.183187	−	0.0682349i
$885$		0			0
$886$	314.840	+	1175.00i	0.355350	+	1.32618i
$887$	109.969	−	190.472i	0.123979	−	0.214737i	−0.797355	−	0.603511i	$-0.793768\pi$
$887$	109.969	−	190.472i	0.123979	−	0.214737i	0.921333	+	0.388774i	$0.127101\pi$
$888$	15.9125	−	9.18711i	0.0179195	−	0.0103458i
$889$	50.1853	−	50.1853i	0.0564514	−	0.0564514i
$890$		0			0
$891$	−338.426	+	1263.02i	−0.379827	+	1.41753i
$892$	−165.538	−	165.538i	−0.185581	−	0.185581i
$893$	275.011	+	476.332i	0.307963	+	0.533407i
$894$	15.9795	+	9.22578i	0.0178742	+	0.0103197i
$895$		0			0
$896$		−	165.794i		−	0.185038i
$897$	−0.368204	−	0.445553i	−0.000410484	−	0.000496714i
$898$	−726.314			−0.808813
$899$	376.689	+	1405.82i	0.419009	+	1.56376i
$900$		0			0
$901$	−47.4196	+	27.3777i	−0.0526300	+	0.0303859i
$902$	−2219.38	+	2219.38i	−2.46051	+	2.46051i
$903$	−0.601237	−	0.161101i	−0.000665821	−	0.000178406i
$904$	−470.327	+	1755.28i	−0.520273	+	1.94169i
$905$		0			0
$906$	14.6526	+	25.3791i	0.0161729	+	0.0280123i
$907$	−847.960	−	489.570i	−0.934906	−	0.539768i	−0.0465461	−	0.998916i	$-0.514821\pi$
$907$	−847.960	−	489.570i	−0.934906	−	0.539768i	−0.888360	+	0.459148i	$0.848155\pi$
$908$	2803.10	−	751.089i	3.08712	−	0.827190i
$909$			813.003i			0.894392i
$910$		0			0
$911$	444.018			0.487396			0.243698	−	0.969851i	$-0.421639\pi$
$911$	444.018			0.487396			0.243698	+	0.969851i	$0.421639\pi$
$912$	−0.743157	−	2.77350i	−0.000814865	−	0.00304112i
$913$	−96.5765	+	167.275i	−0.105779	+	0.183215i
$914$	934.548	−	539.562i	1.02248	−	0.590330i
$915$		0			0
$916$	1744.46	+	467.428i	1.90444	+	0.510292i
$917$	17.9240	−	66.8934i	0.0195464	−	0.0729481i
$918$	−2.47318	−	2.47318i	−0.00269409	−	0.00269409i
$919$	−355.023	−	614.917i	−0.386314	−	0.669115i	0.605637	−	0.795741i	$-0.292919\pi$
$919$	−355.023	−	614.917i	−0.386314	−	0.669115i	−0.991951	+	0.126626i	$0.959585\pi$
$920$		0			0
$921$	6.69613	−	1.79422i	0.00727050	−	0.00194813i
$922$		−	2386.80i		−	2.58872i
$923$	−64.5985	+	679.618i	−0.0699875	+	0.736314i
$924$	−2.95005			−0.00319269
$925$		0			0
$926$	−1562.32	+	2706.03i	−1.68718	+	2.92227i
$927$	831.248	−	479.921i	0.896707	−	0.517714i
$928$	245.010	−	245.010i	0.264019	−	0.264019i
$929$	−287.421	−	77.0142i	−0.309387	−	0.0829001i	0.100785	−	0.994908i	$-0.467865\pi$
$929$	−287.421	−	77.0142i	−0.309387	−	0.0829001i	−0.410172	+	0.912008i	$0.634531\pi$
$930$		0			0
$931$	233.779	+	233.779i	0.251105	+	0.251105i
$932$	448.830	+	777.396i	0.481577	+	0.834116i
$933$	−4.51628	−	2.60748i	−0.00484060	−	0.00279472i
$934$	−1888.58	+	506.045i	−2.02204	+	0.541804i
$935$		0			0
$936$	−1485.19	−	141.169i	−1.58675	−	0.150822i
$937$	194.851			0.207952			0.103976	−	0.994580i	$-0.466844\pi$
$937$	194.851			0.207952			0.103976	+	0.994580i	$0.466844\pi$
$938$	−62.7772	−	234.288i	−0.0669266	−	0.249774i
$939$	2.39097	−	4.14127i	0.00254629	−	0.00441030i
$940$		0			0
$941$	415.396	−	415.396i	0.441441	−	0.441441i	−0.451055	−	0.892496i	$-0.648952\pi$
$941$	415.396	−	415.396i	0.441441	−	0.441441i	0.892496	+	0.451055i	$0.148952\pi$
$942$	−2.32726	−	0.623586i	−0.00247055	−	0.000661981i
$943$	−19.8071	+	73.9211i	−0.0210044	+	0.0783893i
$944$	847.993	+	847.993i	0.898298	+	0.898298i
$945$		0			0
$946$	1260.36	+	727.668i	1.33230	+	0.769205i
$947$	−802.031	+	214.904i	−0.846918	+	0.226931i	−0.656081	−	0.754691i	$-0.727787\pi$
$947$	−802.031	+	214.904i	−0.846918	+	0.226931i	−0.190837	+	0.981622i	$0.561120\pi$
$948$			10.6134i			0.0111956i
$949$	−561.108	+	788.689i	−0.591262	+	0.831073i
$950$		0			0
$951$	−4.65424	−	17.3699i	−0.00489405	−	0.0182648i
$952$	−7.86907	+	13.6296i	−0.00826583	+	0.0143168i
$953$	−906.178	+	523.182i	−0.950869	+	0.548985i	−0.893351	−	0.449360i	$-0.851652\pi$
$953$	−906.178	+	523.182i	−0.950869	+	0.548985i	−0.0575183	+	0.998344i	$0.518319\pi$
$954$	−693.259	+	693.259i	−0.726686	+	0.726686i
$955$		0			0
$956$	636.041	−	2373.74i	0.665315	−	2.48299i
$957$	−17.9009	−	17.9009i	−0.0187052	−	0.0187052i
$958$	−71.4973	−	123.837i	−0.0746319	−	0.129266i
$959$	−86.2848	−	49.8166i	−0.0899737	−	0.0519464i
$960$		0			0
$961$			23.5985i			0.0245562i
$962$	1499.12	−	1238.87i	1.55833	−	1.28780i
$963$	1160.21			1.20478
$964$	−347.517	−	1296.95i	−0.360495	−	1.34538i
$965$		0			0
$966$	−0.0945505	+	0.0545887i	−9.78783e−5	+	5.65101e-5i
$967$	710.111	−	710.111i	0.734344	−	0.734344i	−0.237133	−	0.971477i	$-0.576208\pi$
$967$	710.111	−	710.111i	0.734344	−	0.734344i	0.971477	+	0.237133i	$0.0762078\pi$
$968$	1721.88	+	461.376i	1.77880	+	0.476628i
$969$	0.100157	−	0.373790i	0.000103361	−	0.000385749i
$970$		0			0
$971$	−759.207	−	1314.99i	−0.781882	−	1.35426i	−0.930844	−	0.365416i	$-0.880927\pi$
$971$	−759.207	−	1314.99i	−0.781882	−	1.35426i	0.148963	−	0.988843i	$-0.452407\pi$
$972$	−53.5992	−	30.9455i	−0.0551432	−	0.0318369i
$973$	50.6985	−	13.5846i	0.0521054	−	0.0139616i
$974$		−	1259.84i		−	1.29347i
$975$		0			0
$976$	−546.905			−0.560354
$977$	−45.4195	−	169.508i	−0.0464887	−	0.173498i	0.938778	−	0.344522i	$-0.111959\pi$
$977$	−45.4195	−	169.508i	−0.0464887	−	0.173498i	−0.985267	+	0.171024i	$0.945292\pi$
$978$	−4.34344	+	7.52306i	−0.00444114	+	0.00769229i
$979$	1327.36	−	766.354i	1.35584	−	0.782793i
$980$		0			0
$981$	−991.752	−	265.739i	−1.01096	−	0.270886i
$982$	280.674	−	1047.49i	0.285819	−	1.06669i
$983$	−657.150	−	657.150i	−0.668515	−	0.668515i	0.288857	−	0.957372i	$-0.406725\pi$
$983$	−657.150	−	657.150i	−0.668515	−	0.668515i	−0.957372	+	0.288857i	$0.906725\pi$
$984$	−11.9360	−	20.6738i	−0.0121301	−	0.0210100i
$985$		0			0
$986$	−270.561	+	72.4967i	−0.274403	+	0.0735260i
$987$			1.90764i			0.00193277i
$988$	−284.714	−	622.722i	−0.288172	−	0.630286i
$989$	35.4847			0.0358794
$990$		0			0
$991$	−241.005	+	417.433i	−0.243194	+	0.421224i	−0.961622	−	0.274377i	$-0.911528\pi$
$991$	−241.005	+	417.433i	−0.243194	+	0.421224i	0.718428	+	0.695601i	$0.244862\pi$
$992$	−193.272	+	111.586i	−0.194830	+	0.112485i
$993$	1.73769	−	1.73769i	0.00174994	−	0.00174994i
$994$	124.555	+	33.3745i	0.125307	+	0.0335759i
$995$		0			0
$996$	−2.15446	−	2.15446i	−0.00216311	−	0.00216311i
$997$	−331.571	−	574.298i	−0.332569	−	0.576026i	0.650446	−	0.759553i	$-0.274582\pi$
$997$	−331.571	−	574.298i	−0.332569	−	0.576026i	−0.983015	+	0.183526i	$0.941249\pi$
$998$	−1789.24	−	1033.02i	−1.79283	−	1.03509i
$999$	25.0493	−	6.71194i	0.0250744	−	0.00671866i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.3.t.d.201.1		40
5.2	odd	4		325.3.w.f.149.10		40
5.3	odd	4		325.3.w.e.149.1		40
5.4	even	2		65.3.p.a.6.10	✓	40
13.11	odd	12	inner	325.3.t.d.76.1		40
65.24	odd	12		65.3.p.a.11.10	yes	40
65.37	even	12		325.3.w.e.24.1		40
65.63	even	12		325.3.w.f.24.10		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.3.p.a.6.10	✓	40	5.4	even	2
65.3.p.a.11.10	yes	40	65.24	odd	12
325.3.t.d.76.1		40	13.11	odd	12	inner
325.3.t.d.201.1		40	1.1	even	1	trivial
325.3.w.e.24.1		40	65.37	even	12
325.3.w.e.149.1		40	5.3	odd	4
325.3.w.f.24.10		40	65.63	even	12
325.3.w.f.149.10		40	5.2	odd	4

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:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	325.t (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.886220 - 3.30742i) q^{2} +(0.0164891 - 0.0285599i) q^{3} +(-6.68953 + 3.86220i) q^{4} +(-0.109072 - 0.0292259i) q^{6} +(-0.185607 + 0.692695i) q^{7} +(9.01754 + 9.01754i) q^{8} +(4.49946 + 7.79329i) q^{9} +(15.5985 - 4.17961i) q^{11} +0.254736i q^{12} +(2.16135 + 12.8191i) q^{13} +2.45552 q^{14} +(6.38443 - 11.0582i) q^{16} +(1.49033 - 0.860444i) q^{17} +(21.7882 - 21.7882i) q^{18} +(6.58643 + 1.76483i) q^{19} +(0.0167228 + 0.0167228i) q^{21} +(-27.6475 - 47.8868i) q^{22} +(-1.16760 - 0.674114i) q^{23} +(0.406230 - 0.108849i) q^{24} +(40.4826 - 18.5090i) q^{26} +0.593570 q^{27} +(-1.43370 - 5.35066i) q^{28} +(23.7681 - 41.1675i) q^{29} +(-21.6495 + 21.6495i) q^{31} +(7.04075 + 1.88656i) q^{32} +(0.137836 - 0.514410i) q^{33} +(-4.16661 - 4.16661i) q^{34} +(-60.1985 - 34.7556i) q^{36} +(42.2011 - 11.3078i) q^{37} -23.3481i q^{38} +(0.401750 + 0.149647i) q^{39} +(-14.6912 - 54.8283i) q^{41} +(0.0404892 - 0.0701294i) q^{42} +(-22.7934 + 13.1597i) q^{43} +(-88.2044 + 88.2044i) q^{44} +(-1.19483 + 4.45916i) q^{46} +(57.0372 + 57.0372i) q^{47} +(-0.210547 - 0.364677i) q^{48} +(41.9899 + 24.2429i) q^{49} -0.0567516i q^{51} +(-63.9683 - 77.4061i) q^{52} -31.8181 q^{53} +(-0.526034 - 1.96319i) q^{54} +(-7.92012 + 4.57268i) q^{56} +(0.159007 - 0.159007i) q^{57} +(-157.222 - 42.1275i) q^{58} +(-24.3081 + 90.7191i) q^{59} +(-21.4156 - 37.0929i) q^{61} +(90.7902 + 52.4177i) q^{62} +(-6.23350 + 1.67026i) q^{63} -76.0341i q^{64} -1.82352 q^{66} +(-25.5657 - 95.4126i) q^{67} +(-6.64642 + 11.5119i) q^{68} +(-0.0385053 + 0.0222310i) q^{69} +(50.7246 + 13.5916i) q^{71} +(-29.7022 + 110.850i) q^{72} +(52.6480 + 52.6480i) q^{73} +(-74.7989 - 129.556i) q^{74} +(-50.8763 + 13.6323i) q^{76} +11.5808i q^{77} +(0.138905 - 1.46137i) q^{78} +41.6643 q^{79} +(-40.4853 + 70.1226i) q^{81} +(-168.321 + 97.1800i) q^{82} +(-8.45759 + 8.45759i) q^{83} +(-0.176455 - 0.0472809i) q^{84} +(63.7247 + 63.7247i) q^{86} +(-0.783826 - 1.35763i) q^{87} +(178.350 + 102.971i) q^{88} +(91.6776 - 24.5649i) q^{89} +(-9.28087 - 0.882157i) q^{91} +10.4143 q^{92} +(0.261327 + 0.975287i) q^{93} +(138.098 - 239.194i) q^{94} +(0.169975 - 0.169975i) q^{96} +(141.407 + 37.8898i) q^{97} +(42.9690 - 160.363i) q^{98} +(102.758 + 102.758i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 12 q^{6} + 40 q^{7} - 36 q^{8} - 72 q^{9} - 12 q^{11} + 12 q^{13} + 48 q^{14} + 128 q^{16} - 60 q^{17} + 136 q^{18} + 68 q^{19} - 48 q^{21} + 48 q^{22} + 48 q^{23} - 56 q^{24} - 84 q^{26} - 24 q^{27}+ \cdots - 76 q^{99}+O(q^{100}) \) 40 * q - 12 * q^6 + 40 * q^7 - 36 * q^8 - 72 * q^9 - 12 * q^11 + 12 * q^13 + 48 * q^14 + 128 * q^16 - 60 * q^17 + 136 * q^18 + 68 * q^19 - 48 * q^21 + 48 * q^22 + 48 * q^23 - 56 * q^24 - 84 * q^26 - 24 * q^27 + 16 * q^28 + 28 * q^29 + 128 * q^31 + 408 * q^32 - 136 * q^33 - 28 * q^34 + 300 * q^36 - 56 * q^37 - 88 * q^39 + 68 * q^41 + 320 * q^42 + 372 * q^43 - 240 * q^44 + 260 * q^46 - 152 * q^47 - 424 * q^48 - 132 * q^49 - 372 * q^52 + 288 * q^53 + 152 * q^54 - 288 * q^56 - 252 * q^57 - 492 * q^58 + 492 * q^59 - 100 * q^61 - 120 * q^62 - 844 * q^63 - 456 * q^66 + 20 * q^67 - 72 * q^68 - 576 * q^69 - 132 * q^71 + 780 * q^72 + 424 * q^73 - 160 * q^74 - 992 * q^76 + 60 * q^78 - 248 * q^79 - 600 * q^82 - 112 * q^83 + 1100 * q^84 + 852 * q^86 + 160 * q^87 + 1188 * q^88 + 168 * q^89 - 160 * q^91 - 1192 * q^92 + 1008 * q^93 + 328 * q^94 + 124 * q^96 + 1008 * q^97 + 636 * q^98 - 76 * q^99

Introduction

L-functions

Modular forms

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