LMFDB - Embedded newform 325.3.w.e.24.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [325,3,Mod(24,325)] 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([6, 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("325.24"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	325.w (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [40,0,-12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == 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			24.1
Character	$\chi$	$=$	325.24
Dual form			325.3.w.e.149.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.30742 - 0.886220i) q^{2} +(0.0285599 - 0.0164891i) q^{3} +(6.68953 + 3.86220i) q^{4} +(-0.109072 + 0.0292259i) q^{6} +(0.692695 - 0.185607i) q^{7} +(-9.01754 - 9.01754i) q^{8} +(-4.49946 + 7.79329i) q^{9} +(15.5985 + 4.17961i) q^{11} +0.254736 q^{12} +(-12.8191 - 2.16135i) q^{13} -2.45552 q^{14} +(6.38443 + 11.0582i) q^{16} +(-0.860444 + 1.49033i) q^{17} +(21.7882 - 21.7882i) q^{18} +(-6.58643 + 1.76483i) q^{19} +(0.0167228 - 0.0167228i) q^{21} +(-47.8868 - 27.6475i) q^{22} +(0.674114 + 1.16760i) q^{23} +(-0.406230 - 0.108849i) q^{24} +(40.4826 + 18.5090i) q^{26} +0.593570i q^{27} +(5.35066 + 1.43370i) q^{28} +(-23.7681 - 41.1675i) q^{29} +(-21.6495 - 21.6495i) q^{31} +(1.88656 + 7.04075i) q^{32} +(0.514410 - 0.137836i) q^{33} +(4.16661 - 4.16661i) q^{34} +(-60.1985 + 34.7556i) q^{36} +(-11.3078 + 42.2011i) q^{37} +23.3481 q^{38} +(-0.401750 + 0.149647i) q^{39} +(-14.6912 + 54.8283i) q^{41} +(-0.0701294 + 0.0404892i) q^{42} +(-13.1597 + 22.7934i) q^{43} +(88.2044 + 88.2044i) q^{44} +(-1.19483 - 4.45916i) q^{46} +(57.0372 + 57.0372i) q^{47} +(0.364677 + 0.210547i) q^{48} +(-41.9899 + 24.2429i) q^{49} +0.0567516i q^{51} +(-77.4061 - 63.9683i) q^{52} +31.8181i q^{53} +(0.526034 - 1.96319i) q^{54} +(-7.92012 - 4.57268i) q^{56} +(-0.159007 + 0.159007i) q^{57} +(42.1275 + 157.222i) q^{58} +(24.3081 + 90.7191i) q^{59} +(-21.4156 + 37.0929i) q^{61} +(52.4177 + 90.7902i) q^{62} +(-1.67026 + 6.23350i) q^{63} -76.0341i q^{64} -1.82352 q^{66} +(-95.4126 - 25.5657i) q^{67} +(-11.5119 + 6.64642i) q^{68} +(0.0385053 + 0.0222310i) q^{69} +(50.7246 - 13.5916i) q^{71} +(110.850 - 29.7022i) q^{72} +(-52.6480 - 52.6480i) q^{73} +(74.7989 - 129.556i) q^{74} +(-50.8763 - 13.6323i) q^{76} +11.5808 q^{77} +(1.46137 - 0.138905i) q^{78} -41.6643 q^{79} +(-40.4853 - 70.1226i) q^{81} +(97.1800 - 168.321i) q^{82} +(-8.45759 + 8.45759i) q^{83} +(0.176455 - 0.0472809i) q^{84} +(63.7247 - 63.7247i) q^{86} +(-1.35763 - 0.783826i) q^{87} +(-102.971 - 178.350i) q^{88} +(-91.6776 - 24.5649i) q^{89} +(-9.28087 + 0.882157i) q^{91} +10.4143i q^{92} +(-0.975287 - 0.261327i) q^{93} +(-138.098 - 239.194i) q^{94} +(0.169975 + 0.169975i) q^{96} +(37.8898 + 141.407i) q^{97} +(160.363 - 42.9690i) q^{98} +(-102.758 + 102.758i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 12 q^{3} - 12 q^{6} - 44 q^{7} + 36 q^{8} + 72 q^{9} - 12 q^{11} + 120 q^{12} - 36 q^{13} - 48 q^{14} + 128 q^{16} - 32 q^{17} + 136 q^{18} - 68 q^{19} - 48 q^{21} - 72 q^{22} - 28 q^{23} + 56 q^{24}+ \cdots + 76 q^{99}+O(q^{100}) $ 40 * q - 12 * q^3 - 12 * q^6 - 44 * q^7 + 36 * q^8 + 72 * q^9 - 12 * q^11 + 120 * q^12 - 36 * q^13 - 48 * q^14 + 128 * q^16 - 32 * q^17 + 136 * q^18 - 68 * q^19 - 48 * q^21 - 72 * q^22 - 28 * q^23 + 56 * q^24 - 84 * q^26 + 76 * q^28 - 28 * q^29 + 128 * q^31 + 84 * q^32 - 68 * q^33 + 28 * q^34 + 300 * q^36 - 260 * q^37 + 8 * q^38 + 88 * q^39 + 68 * q^41 - 480 * q^42 + 32 * q^43 + 240 * q^44 + 260 * q^46 - 152 * q^47 - 480 * q^48 + 132 * q^49 + 488 * q^52 - 152 * q^54 - 288 * q^56 + 252 * q^57 + 468 * q^58 - 492 * q^59 - 100 * q^61 - 8 * q^62 - 356 * q^63 - 456 * q^66 - 56 * q^67 + 12 * q^68 + 576 * q^69 - 132 * q^71 + 396 * q^72 - 424 * q^73 + 160 * q^74 - 992 * q^76 + 344 * q^77 + 12 * q^78 + 248 * q^79 + 248 * q^82 - 112 * q^83 - 1100 * q^84 + 852 * q^86 - 1068 * q^87 + 8 * q^88 - 168 * q^89 - 160 * q^91 - 24 * q^93 - 328 * q^94 + 124 * q^96 + 1020 * q^97 + 1404 * q^98 + 76 * q^99

Character values

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

$n$	$27$	$301$
$\chi(n)$	$-1$	$e\left(\frac{7}{12}\right)$

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 $

$2$	−3.30742	−	0.886220i	−1.65371	−	0.443110i	−0.693062	−	0.720878i	$-0.743739\pi$
$2$	−3.30742	−	0.886220i	−1.65371	−	0.443110i	−0.960648	+	0.277768i	$0.910405\pi$
$3$	0.0285599	−	0.0164891i	0.00951996	−	0.00549635i	−0.495232	−	0.868760i	$-0.664917\pi$
$3$	0.0285599	−	0.0164891i	0.00951996	−	0.00549635i	0.504752	+	0.863264i	$0.331584\pi$
$4$	6.68953	+	3.86220i	1.67238	+	0.965551i
$5$		0			0
$5$		0			0
$6$	−0.109072	+	0.0292259i	−0.0181787	+	0.00487098i
$7$	0.692695	−	0.185607i	0.0989564	−	0.0265153i	−0.209001	−	0.977915i	$-0.567021\pi$
$7$	0.692695	−	0.185607i	0.0989564	−	0.0265153i	0.307957	+	0.951400i	$0.400355\pi$
$8$	−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	0.884791	−	0.465988i	$-0.154301\pi$
$11$	15.5985	+	4.17961i	1.41805	+	0.379965i	0.533257	+	0.845953i	$0.320968\pi$
$12$	0.254736			0.0212280
$13$	−12.8191	−	2.16135i	−0.986082	−	0.166257i
$13$	−12.8191	−	2.16135i	−0.986082	−	0.166257i
$14$	−2.45552			−0.175394
$15$		0			0
$16$	6.38443	+	11.0582i	0.399027	+	0.691135i
$17$	−0.860444	+	1.49033i	−0.0506143	+	0.0876666i	−0.890223	−	0.455526i	$-0.849451\pi$
$17$	−0.860444	+	1.49033i	−0.0506143	+	0.0876666i	0.839608	+	0.543192i	$0.182785\pi$
$18$	21.7882	−	21.7882i	1.21045	−	1.21045i
$19$	−6.58643	+	1.76483i	−0.346654	+	0.0928857i	−0.427945	−	0.903805i	$-0.640762\pi$
$19$	−6.58643	+	1.76483i	−0.346654	+	0.0928857i	0.0812910	+	0.996690i	$0.474096\pi$
$20$		0			0
$21$	0.0167228	−	0.0167228i	0.000796324	−	0.000796324i
$22$	−47.8868	−	27.6475i	−2.17667	−	1.25670i
$23$	0.674114	+	1.16760i	0.0293093	+	0.0507652i	0.880308	−	0.474403i	$-0.157336\pi$
$23$	0.674114	+	1.16760i	0.0293093	+	0.0507652i	−0.850999	+	0.525168i	$0.824003\pi$
$24$	−0.406230	−	0.108849i	−0.0169263	−	0.00453538i
$25$		0			0
$26$	40.4826	+	18.5090i	1.55702	+	0.711884i
$27$			0.593570i			0.0219841i
$28$	5.35066	+	1.43370i	0.191095	+	0.0512037i
$29$	−23.7681	−	41.1675i	−0.819588	−	1.41957i	−0.905986	−	0.423308i	$-0.860869\pi$
$29$	−23.7681	−	41.1675i	−0.819588	−	1.41957i	0.0863974	−	0.996261i	$-0.472465\pi$
$30$		0			0
$31$	−21.6495	−	21.6495i	−0.698371	−	0.698371i	0.265688	−	0.964059i	$-0.414401\pi$
$31$	−21.6495	−	21.6495i	−0.698371	−	0.698371i	−0.964059	+	0.265688i	$0.914401\pi$
$32$	1.88656	+	7.04075i	0.0589551	+	0.220023i
$33$	0.514410	−	0.137836i	0.0155882	−	0.00417684i
$34$	4.16661	−	4.16661i	0.122547	−	0.122547i
$35$		0			0
$36$	−60.1985	+	34.7556i	−1.67218	+	0.965435i
$37$	−11.3078	+	42.2011i	−0.305615	+	1.14057i	0.626800	+	0.779180i	$0.284364\pi$
$37$	−11.3078	+	42.2011i	−0.305615	+	1.14057i	−0.932415	+	0.361390i	$0.882302\pi$
$38$	23.3481			0.614424
$39$	−0.401750	+	0.149647i	−0.0103013	+	0.00383709i
$40$		0			0
$41$	−14.6912	+	54.8283i	−0.358322	+	1.33728i	0.517930	+	0.855423i	$0.326703\pi$
$41$	−14.6912	+	54.8283i	−0.358322	+	1.33728i	−0.876252	+	0.481853i	$0.839964\pi$
$42$	−0.0701294	+	0.0404892i	−0.00166975	+	0.000964029i
$43$	−13.1597	+	22.7934i	−0.306041	+	0.530078i	−0.977492	−	0.210970i	$-0.932338\pi$
$43$	−13.1597	+	22.7934i	−0.306041	+	0.530078i	0.671452	+	0.741048i	$0.265671\pi$
$44$	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	$0.421636\pi$
$48$	0.364677	+	0.210547i	0.00759744	+	0.00438639i
$49$	−41.9899	+	24.2429i	−0.856936	+	0.494752i
$50$		0			0
$51$			0.0567516i			0.00111278i
$52$	−77.4061	−	63.9683i	−1.48858	−	1.23016i
$53$			31.8181i			0.600342i	0.953885	+	0.300171i	$0.0970438\pi$
$53$			31.8181i			0.600342i	−0.953885	+	0.300171i	$0.902956\pi$
$54$	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
$58$	42.1275	+	157.222i	0.726336	+	2.71072i
$59$	24.3081	+	90.7191i	0.412002	+	1.53761i	0.790766	+	0.612119i	$0.209683\pi$
$59$	24.3081	+	90.7191i	0.412002	+	1.53761i	−0.378764	+	0.925493i	$0.623651\pi$
$60$		0			0
$61$	−21.4156	+	37.0929i	−0.351075	+	0.608080i	−0.986438	−	0.164134i	$-0.947517\pi$
$61$	−21.4156	+	37.0929i	−0.351075	+	0.608080i	0.635363	+	0.772214i	$0.280850\pi$
$62$	52.4177	+	90.7902i	0.845447	+	1.46436i
$63$	−1.67026	+	6.23350i	−0.0265121	+	0.0989445i
$64$		−	76.0341i		−	1.18803i
$65$		0			0
$66$	−1.82352			−0.0276291
$67$	−95.4126	−	25.5657i	−1.42407	−	0.381578i	−0.537143	−	0.843491i	$-0.680496\pi$
$67$	−95.4126	−	25.5657i	−1.42407	−	0.381578i	−0.886925	+	0.461913i	$0.847163\pi$
$68$	−11.5119	+	6.64642i	−0.169293	+	0.0977415i
$69$	0.0385053	+	0.0222310i	0.000558047	+	0.000322189i
$70$		0			0
$71$	50.7246	−	13.5916i	0.714431	−	0.191431i	0.116745	−	0.993162i	$-0.462754\pi$
$71$	50.7246	−	13.5916i	0.714431	−	0.191431i	0.597685	+	0.801731i	$0.296087\pi$
$72$	110.850	−	29.7022i	1.53959	−	0.412531i
$73$	−52.6480	−	52.6480i	−0.721205	−	0.721205i	0.247646	−	0.968851i	$-0.420343\pi$
$73$	−52.6480	−	52.6480i	−0.721205	−	0.721205i	−0.968851	+	0.247646i	$0.920343\pi$
$74$	74.7989	−	129.556i	1.01080	−	1.75075i
$75$		0			0
$76$	−50.8763	−	13.6323i	−0.669425	−	0.179372i
$77$	11.5808			0.150400
$78$	1.46137	−	0.138905i	0.0187356	−	0.00178084i
$79$	−41.6643			−0.527397			−0.263698	−	0.964605i	$-0.584942\pi$
$79$	−41.6643			−0.527397			−0.263698	+	0.964605i	$0.584942\pi$
$80$		0			0
$81$	−40.4853	−	70.1226i	−0.499819	−	0.865711i
$82$	97.1800	−	168.321i	1.18512	−	2.05269i
$83$	−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
$87$	−1.35763	−	0.783826i	−0.0156049	−	0.00900949i
$88$	−102.971	−	178.350i	−1.17012	−	2.02671i
$89$	−91.6776	−	24.5649i	−1.03009	−	0.276011i	−0.296087	−	0.955161i	$-0.595682\pi$
$89$	−91.6776	−	24.5649i	−1.03009	−	0.276011i	−0.733999	+	0.679150i	$0.762348\pi$
$90$		0			0
$91$	−9.28087	+	0.882157i	−0.101988	+	0.00969403i
$92$			10.4143i			0.113199i
$93$	−0.975287	−	0.261327i	−0.0104870	−	0.00280997i
$94$	−138.098	−	239.194i	−1.46913	−	2.54461i
$95$		0			0
$96$	0.169975	+	0.169975i	0.00177058	+	0.00177058i
$97$	37.8898	+	141.407i	0.390616	+	1.45780i	0.829120	+	0.559070i	$0.188842\pi$
$97$	37.8898	+	141.407i	0.390616	+	1.45780i	−0.438504	+	0.898729i	$0.644492\pi$
$98$	160.363	−	42.9690i	1.63635	−	0.438460i
$99$	−102.758	+	102.758i	−1.03796	+	1.03796i
$100$		0			0
$101$	78.2407	−	45.1723i	0.774660	−	0.447250i	−0.0598743	−	0.998206i	$-0.519070\pi$
$101$	78.2407	−	45.1723i	0.774660	−	0.447250i	0.834535	+	0.550956i	$0.185737\pi$
$102$	0.0502944	−	0.187701i	0.000493083	−	0.00184021i
$103$	106.662			1.03555			0.517777	−	0.855516i	$-0.326760\pi$
$103$	106.662			1.03555			0.517777	+	0.855516i	$0.326760\pi$
$104$	96.1064	+	135.086i	0.924100	+	1.29891i
$105$		0			0
$106$	28.1979	−	105.236i	0.266018	−	0.992792i
$107$	−111.655	+	64.4638i	−1.04350	+	0.602465i	−0.920823	−	0.389982i	$-0.872481\pi$
$107$	−111.655	+	64.4638i	−1.04350	+	0.602465i	−0.122677	+	0.992447i	$0.539148\pi$
$108$	−2.29249	+	3.97071i	−0.0212268	+	0.0367658i
$109$	80.6778	+	80.6778i	0.740164	+	0.740164i	0.972609	−	0.232446i	$-0.0746728\pi$
$109$	80.6778	+	80.6778i	0.740164	+	0.740164i	−0.232446	+	0.972609i	$0.574673\pi$
$110$		0			0
$111$	0.372908	+	1.39171i	0.00335953	+	0.0125380i
$112$	6.47494	+	6.47494i	0.0578119	+	0.0578119i
$113$	−123.405	−	71.2477i	−1.09208	−	0.630510i	−0.157947	−	0.987448i	$-0.550488\pi$
$113$	−123.405	−	71.2477i	−1.09208	−	0.630510i	−0.934128	+	0.356937i	$0.883821\pi$
$114$	0.666819	−	0.384988i	0.00584929	−	0.00337709i
$115$		0			0
$116$		−	367.189i		−	3.16542i
$117$	74.5228	−	90.1778i	0.636947	−	0.770751i
$118$		−	321.589i		−	2.72533i
$119$	−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
$123$	0.484488	+	1.80813i	0.00393893	+	0.0147003i
$124$	−61.2103	−	228.440i	−0.493631	−	1.84226i
$125$		0			0
$126$	11.0485	−	19.1366i	0.0876866	−	0.151878i
$127$	−49.4838	−	85.7085i	−0.389636	−	0.674870i	0.602764	−	0.797919i	$-0.294066\pi$
$127$	−49.4838	−	85.7085i	−0.389636	−	0.674870i	−0.992401	+	0.123049i	$0.960733\pi$
$128$	−59.8367	+	223.314i	−0.467474	+	1.74464i
$129$			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	$0.620158\pi$
$132$	3.97352	+	1.06470i	0.0301024	+	0.00806591i
$133$	−4.23482	+	2.44497i	−0.0318408	+	0.0183833i
$134$	292.913	+	169.113i	2.18591	+	1.26204i
$135$		0			0
$136$	21.1982	−	5.68004i	0.155869	−	0.0417650i
$137$	134.199	−	35.9585i	0.979555	−	0.262471i	0.266698	−	0.963780i	$-0.414068\pi$
$137$	134.199	−	35.9585i	0.979555	−	0.262471i	0.712857	+	0.701309i	$0.247401\pi$
$138$	−0.107651	−	0.107651i	−0.000780083	−	0.000780083i
$139$	36.5951	−	63.3846i	0.263274	−	0.456005i	−0.703836	−	0.710363i	$-0.748531\pi$
$139$	36.5951	−	63.3846i	0.263274	−	0.456005i	0.967110	+	0.254358i	$0.0818642\pi$
$140$		0			0
$141$	2.56947	+	0.688486i	0.0182232	+	0.00488288i
$142$	−179.813			−1.26629
$143$	−190.925	−	87.2926i	−1.33514	−	0.610438i
$144$	−114.906			−0.797958
$145$		0			0
$146$	127.471	+	220.787i	0.873091	+	1.51224i
$147$	−0.799484	+	1.38475i	−0.00543867	+	0.00942005i
$148$	−238.633	+	238.633i	−1.61238	+	1.61238i
$149$	157.836	−	42.2920i	1.05930	−	0.283839i	0.313210	−	0.949684i	$-0.398595\pi$
$149$	157.836	−	42.2920i	1.05930	−	0.283839i	0.746090	+	0.665845i	$0.231929\pi$
$150$		0			0
$151$	−183.510	+	183.510i	−1.21530	+	1.21530i	−0.246036	+	0.969261i	$0.579128\pi$
$151$	−183.510	+	183.510i	−1.21530	+	1.21530i	−0.969261	+	0.246036i	$0.920872\pi$
$152$	75.3078	+	43.4790i	0.495446	+	0.286046i
$153$	−7.74306	−	13.4114i	−0.0506082	−	0.0876560i
$154$	−38.3025	−	10.2631i	−0.248718	−	0.0666437i
$155$		0			0
$156$	−3.26548	−	0.550573i	−0.0209326	−	0.00352932i
$157$			21.3368i			0.135903i	0.997689	+	0.0679516i	$0.0216463\pi$
$157$			21.3368i			0.135903i	−0.997689	+	0.0679516i	$0.978354\pi$
$158$	137.801	+	36.9238i	0.872161	+	0.233695i
$159$	0.524651	+	0.908722i	0.00329969	+	0.00571524i
$160$		0			0
$161$	0.683670	+	0.683670i	0.00424640	+	0.00424640i
$162$	71.7578	+	267.804i	0.442950	+	1.65311i
$163$	74.3081	−	19.9108i	0.455878	−	0.122152i	−0.0235705	−	0.999722i	$-0.507503\pi$
$163$	74.3081	−	19.9108i	0.455878	−	0.122152i	0.479448	+	0.877570i	$0.340837\pi$
$164$	−310.036	+	310.036i	−1.89046	+	1.89046i
$165$		0			0
$166$	35.4681	−	20.4775i	0.213663	−	0.123358i
$167$	63.9559	−	238.687i	0.382969	−	1.42926i	−0.458374	−	0.888759i	$-0.651568\pi$
$167$	63.9559	−	238.687i	0.382969	−	1.42926i	0.841343	−	0.540501i	$-0.181765\pi$
$168$	−0.301597			−0.00179522
$169$	159.657	+	55.4129i	0.944717	+	0.327887i
$170$		0			0
$171$	15.8815	−	59.2707i	0.0928745	−	0.346612i
$172$	−176.065	+	101.651i	−1.02363	+	0.590996i
$173$	−55.2331	+	95.6665i	−0.319266	+	0.552986i	−0.980335	−	0.197340i	$-0.936770\pi$
$173$	−55.2331	+	95.6665i	−0.319266	+	0.552986i	0.661069	+	0.750325i	$0.270103\pi$
$174$	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
$178$	281.446	+	162.493i	1.58116	+	0.912883i
$179$	−183.778	+	106.104i	−1.02669	+	0.592761i	−0.916035	−	0.401098i	$-0.868629\pi$
$179$	−183.778	+	106.104i	−1.02669	+	0.592761i	−0.110656	+	0.993859i	$0.535295\pi$
$180$		0			0
$181$		−	51.8213i		−	0.286306i	−0.989701	−	0.143153i	$-0.954276\pi$
$181$		−	51.8213i		−	0.286306i	0.989701	−	0.143153i	$-0.0457240\pi$
$182$	31.4775	+	5.30723i	0.172953	+	0.0291606i
$183$			1.41249i			0.00771853i
$184$	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
$188$	161.263	+	601.842i	0.857782	+	3.20129i
$189$	0.110171	+	0.411163i	0.000582914	+	0.00217547i
$190$		0			0
$191$	−95.3560	+	165.161i	−0.499246	+	0.864720i	−1.00000		0.000870149i	$-0.999723\pi$
$191$	−95.3560	+	165.161i	−0.499246	+	0.864720i	0.500753	+	0.865590i	$0.333056\pi$
$192$	−1.25373	−	2.17152i	−0.00652984	−	0.0113100i
$193$	5.88526	−	21.9641i	0.0304936	−	0.113804i	−0.949002	−	0.315271i	$-0.897904\pi$
$193$	5.88526	−	21.9641i	0.0304936	−	0.113804i	0.979495	+	0.201468i	$0.0645711\pi$
$194$		−	501.269i		−	2.58386i
$195$		0			0
$196$	−374.524			−1.91083
$197$	119.041	+	31.8969i	0.604267	+	0.161913i	0.547966	−	0.836501i	$-0.315402\pi$
$197$	119.041	+	31.8969i	0.604267	+	0.161913i	0.0563018	+	0.998414i	$0.482069\pi$
$198$	430.929	−	248.797i	2.17641	−	1.25655i
$199$	−23.6042	−	13.6279i	−0.118614	−	0.0684820i	0.439519	−	0.898233i	$-0.355149\pi$
$199$	−23.6042	−	13.6279i	−0.118614	−	0.0684820i	−0.558133	+	0.829751i	$0.688482\pi$
$200$		0			0
$201$	−3.14653	+	0.843109i	−0.0156544	+	0.00419457i
$202$	−298.807	+	80.0652i	−1.47924	+	0.396362i
$203$	−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
$207$	−12.1326			−0.0586116
$208$	−57.9420	−	155.554i	−0.278567	−	0.747857i
$209$	−110.115			−0.526866
$210$		0			0
$211$	13.7251	+	23.7725i	0.0650477	+	0.112666i	0.896715	−	0.442608i	$-0.145947\pi$
$211$	13.7251	+	23.7725i	0.0650477	+	0.112666i	−0.831667	+	0.555274i	$0.812613\pi$
$212$	−122.888	+	212.849i	−0.579661	+	1.00400i
$213$	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
$217$	−19.0148	−	10.9782i	−0.0876258	−	0.0505908i
$218$	−195.337	−	338.334i	−0.896042	−	1.55199i
$219$	−2.37174	−	0.635505i	−0.0108298	−	0.00290185i
$220$		0			0
$221$	14.2512	−	17.2450i	0.0644851	−	0.0780315i
$222$		−	4.93346i		−	0.0222228i
$223$	−29.2747	−	7.84413i	−0.131277	−	0.0351755i	0.192582	−	0.981281i	$-0.438314\pi$
$223$	−29.2747	−	7.84413i	−0.131277	−	0.0351755i	−0.323859	+	0.946105i	$0.604980\pi$
$224$	2.61362	+	4.52693i	0.0116680	+	0.0202095i
$225$		0			0
$226$	345.010	+	345.010i	1.52659	+	1.52659i
$227$	−97.2358	−	362.889i	−0.428351	−	1.59863i	−0.756494	−	0.654001i	$-0.773089\pi$
$227$	−97.2358	−	362.889i	−0.428351	−	1.59863i	0.328142	−	0.944628i	$-0.393577\pi$
$228$	−1.67780	+	0.449566i	−0.00735879	+	0.00197178i
$229$	165.325	−	165.325i	0.721942	−	0.721942i	−0.247059	−	0.969001i	$-0.579464\pi$
$229$	165.325	−	165.325i	0.721942	−	0.721942i	0.969001	+	0.247059i	$0.0794640\pi$
$230$		0			0
$231$	0.330746	−	0.190956i	0.00143180	−	0.000826651i
$232$	−156.900	+	585.559i	−0.676293	+	2.52396i
$233$	116.211			0.498759			0.249379	−	0.968406i	$-0.419773\pi$
$233$	116.211			0.498759			0.249379	+	0.968406i	$0.419773\pi$
$234$	−326.396	+	232.212i	−1.39485	+	0.992360i
$235$		0			0
$236$	−187.766	+	700.752i	−0.795618	+	2.96929i
$237$	−1.18993	+	0.687006i	−0.00502080	+	0.00289876i
$238$	2.11284	−	3.65954i	0.00887747	−	0.0153762i
$239$	224.962	+	224.962i	0.941263	+	0.941263i	0.998368	−	0.0571055i	$-0.0181871\pi$
$239$	224.962	+	224.962i	0.941263	+	0.941263i	−0.0571055	+	0.998368i	$0.518187\pi$
$240$		0			0
$241$	−44.9894	−	167.903i	−0.186678	−	0.696692i	−0.994265	−	0.106944i	$-0.965894\pi$
$241$	−44.9894	−	167.903i	−0.186678	−	0.696692i	0.807587	−	0.589748i	$-0.200773\pi$
$242$	−338.444	−	338.444i	−1.39853	−	1.39853i
$243$	−6.93893	−	4.00620i	−0.0285553	−	0.0164864i
$244$	−286.520	+	165.423i	−1.17426	+	0.677962i
$245$		0			0
$246$		−	6.40962i		−	0.0260554i
$247$	88.2463	−	8.38791i	0.357272	−	0.0339592i
$248$			390.450i			1.57440i
$249$	−0.102090	+	0.381005i	−0.000410000	+	0.00153014i
$250$		0			0
$251$	145.005	+	83.7187i	0.577709	+	0.333541i	0.760223	−	0.649663i	$-0.225090\pi$
$251$	145.005	+	83.7187i	0.577709	+	0.333541i	−0.182513	+	0.983203i	$0.558423\pi$
$252$	−35.2483	+	35.2483i	−0.139874	+	0.139874i
$253$	5.63508	+	21.0304i	0.0222730	+	0.0831241i
$254$	87.7071	+	327.327i	0.345304	+	1.28869i
$255$		0			0
$256$	243.742	−	422.173i	0.952117	−	1.64911i
$257$	−93.3719	−	161.725i	−0.363315	−	0.629279i	0.625190	−	0.780473i	$-0.285022\pi$
$257$	−93.3719	−	161.725i	−0.363315	−	0.629279i	−0.988504	+	0.151194i	$0.951688\pi$
$258$	0.769210	−	2.87073i	0.00298144	−	0.0111269i
$259$			31.3313i			0.120970i
$260$		0			0
$261$	427.773			1.63898
$262$	319.397	+	85.5821i	1.21907	+	0.326649i
$263$	121.329	−	70.0491i	0.461326	−	0.266346i	−0.251276	−	0.967915i	$-0.580850\pi$
$263$	121.329	−	70.0491i	0.461326	−	0.266346i	0.712601	+	0.701569i	$0.247517\pi$
$264$	−5.88165	−	3.39577i	−0.0222790	−	0.0128628i
$265$		0			0
$266$	16.1731	−	4.33357i	0.0608012	−	0.0162916i
$267$	−3.02336	+	0.810106i	−0.0113234	+	0.00303410i
$268$	−539.526	−	539.526i	−2.01316	−	2.01316i
$269$	−24.6298	+	42.6600i	−0.0915604	+	0.158587i	−0.908168	−	0.418606i	$-0.862519\pi$
$269$	−24.6298	+	42.6600i	−0.0915604	+	0.158587i	0.816607	+	0.577193i	$0.195852\pi$
$270$		0			0
$271$	−450.532	−	120.720i	−1.66248	−	0.445460i	−0.699412	−	0.714718i	$-0.746555\pi$
$271$	−450.532	−	120.720i	−1.66248	−	0.445460i	−0.963068	+	0.269258i	$0.913222\pi$
$272$	−21.9738			−0.0807859
$273$	−0.250515	+	0.178227i	−0.000917636	+	0.000652846i
$274$	−475.719			−1.73620
$275$		0			0
$276$	0.171721	+	0.297430i	0.000622179	+	0.00107765i
$277$	11.0619	−	19.1597i	0.0399345	−	0.0691686i	−0.845367	−	0.534185i	$-0.820618\pi$
$277$	11.0619	−	19.1597i	0.0399345	−	0.0691686i	0.885302	+	0.465017i	$0.153952\pi$
$278$	−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	−0.216943	−	0.976184i	$-0.569609\pi$
$281$	213.347	−	213.347i	0.759241	−	0.759241i	0.976184	+	0.216943i	$0.0696086\pi$
$282$	−7.88815	−	4.55423i	−0.0279722	−	0.0161497i
$283$	−1.31656	−	2.28036i	−0.00465217	−	0.00805779i	0.863690	−	0.504023i	$-0.168148\pi$
$283$	−1.31656	−	2.28036i	−0.00465217	−	0.00805779i	−0.868342	+	0.495966i	$0.834814\pi$
$284$	391.817	+	104.987i	1.37964	+	0.369673i
$285$		0			0
$286$	554.109	+	457.915i	1.93744	+	1.60110i
$287$			40.7061i			0.141833i
$288$	−63.3591	−	16.9770i	−0.219997	−	0.0589480i
$289$	143.019	+	247.717i	0.494876	+	0.857151i
$290$		0			0
$291$	3.41379	+	3.41379i	0.0117312	+	0.0117312i
$292$	−148.853	−	555.528i	−0.509771	−	1.90249i
$293$	102.990	−	27.5961i	0.351502	−	0.0941847i	−0.0787477	−	0.996895i	$-0.525092\pi$
$293$	102.990	−	27.5961i	0.351502	−	0.0941847i	0.430250	+	0.902710i	$0.358425\pi$
$294$	3.87142	−	3.87142i	0.0131681	−	0.0131681i
$295$		0			0
$296$	482.518	−	278.582i	1.63013	−	0.941155i
$297$	−2.48089	+	9.25882i	−0.00835318	+	0.0311745i
$298$	−559.509			−1.87755
$299$	−6.11793	−	16.4245i	−0.0204613	−	0.0549316i
$300$		0			0
$301$	−4.88508	+	18.2314i	−0.0162295	+	0.0605694i
$302$	769.574	−	444.314i	2.54826	−	1.47124i
$303$	1.48970	−	2.58023i	0.00491649	−	0.00851561i
$304$	−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	$0.638773\pi$
$308$	77.4701	+	44.7274i	0.251526	+	0.145219i
$309$	3.04626	−	1.75876i	0.00985843	−	0.00569177i
$310$		0			0
$311$			158.134i			0.508469i	0.967143	+	0.254234i	$0.0818235\pi$
$311$			158.134i			0.508469i	−0.967143	+	0.254234i	$0.918177\pi$
$312$	4.97224	+	2.27335i	0.0159367	+	0.00728638i
$313$		−	145.003i		−	0.463269i	−0.972803	−	0.231634i	$-0.925593\pi$
$313$		−	145.003i		−	0.463269i	0.972803	−	0.231634i	$-0.0744073\pi$
$314$	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	$0.579585\pi$
$317$	−385.578	+	385.578i	−1.21633	+	1.21633i	−0.968907	+	0.247427i	$0.920415\pi$
$318$	−0.929913	−	3.47048i	−0.00292425	−	0.0109135i
$319$	−198.683	−	741.494i	−0.622830	−	2.32443i
$320$		0			0
$321$	−2.12589	+	3.68215i	−0.00662272	+	0.0114709i
$322$	−1.65530	−	2.86707i	−0.00514069	−	0.00890394i
$323$	3.03707	−	11.3345i	0.00940269	−	0.0350913i
$324$		−	625.450i		−	1.93040i
$325$		0			0
$326$	−263.413			−0.808017
$327$	3.63445	+	0.973848i	0.0111145	+	0.00297813i
$328$	626.895	−	361.938i	1.91127	−	1.10347i
$329$	50.0959	+	28.9229i	0.152267	+	0.0879115i
$330$		0			0
$331$	71.9790	−	19.2867i	0.217459	−	0.0582680i	−0.148444	−	0.988921i	$-0.547427\pi$
$331$	71.9790	−	19.2867i	0.217459	−	0.0582680i	0.365904	+	0.930653i	$0.380760\pi$
$332$	−89.2422	+	23.9124i	−0.268802	+	0.0720253i
$333$	−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
$337$	−127.419			−0.378098			−0.189049	−	0.981968i	$-0.560541\pi$
$337$	−127.419			−0.378098			−0.189049	+	0.981968i	$0.560541\pi$
$338$	−478.945	−	324.765i	−1.41700	−	0.960843i
$339$	−4.69923			−0.0138620
$340$		0			0
$341$	−247.214	−	428.187i	−0.724967	−	1.25568i
$342$	−105.054	+	181.958i	−0.307175	+	0.532042i
$343$	−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
$347$	−244.481	−	141.151i	−0.704557	−	0.406776i	0.104486	−	0.994526i	$-0.466680\pi$
$347$	−244.481	−	141.151i	−0.704557	−	0.406776i	−0.809042	+	0.587750i	$0.800014\pi$
$348$	−6.05459	−	10.4869i	−0.0173983	−	0.0301347i
$349$	−146.454	−	39.2423i	−0.419640	−	0.112442i	0.0428192	−	0.999083i	$-0.486366\pi$
$349$	−146.454	−	39.2423i	−0.419640	−	0.112442i	−0.462459	+	0.886641i	$0.653033\pi$
$350$		0			0
$351$	1.28291	−	7.60902i	0.00365501	−	0.0216781i
$352$			117.710i			0.334405i
$353$	420.878	+	112.774i	1.19229	+	0.319473i	0.799790	−	0.600280i	$-0.204944\pi$
$353$	420.878	+	112.774i	1.19229	+	0.319473i	0.392499	+	0.919753i	$0.371611\pi$
$354$	−5.30269	−	9.18453i	−0.0149794	−	0.0259450i
$355$		0			0
$356$	−518.406	−	518.406i	−1.45620	−	1.45620i
$357$	0.0105335	+	0.0393116i	2.95056e−5	+	0.000110116i
$358$	701.862	−	188.063i	1.96051	−	0.525316i
$359$	121.061	−	121.061i	0.337217	−	0.337217i	−0.518102	−	0.855319i	$-0.673361\pi$
$359$	121.061	−	121.061i	0.337217	−	0.337217i	0.855319	+	0.518102i	$0.173361\pi$
$360$		0			0
$361$	−272.369	+	157.252i	−0.754484	+	0.435602i
$362$	−45.9251	+	171.395i	−0.126865	+	0.473466i
$363$	4.60979			0.0126992
$364$	−65.4918	−	29.9434i	−0.179922	−	0.0822621i
$365$		0			0
$366$	1.25178	−	4.67170i	0.00342016	−	0.0127642i
$367$	540.000	−	311.769i	1.47139	−	0.849507i	0.471907	−	0.881648i	$-0.343566\pi$
$367$	540.000	−	311.769i	1.47139	−	0.849507i	0.999483	+	0.0321410i	$0.0102326\pi$
$368$	−8.60767	+	14.9089i	−0.0233904	+	0.0405134i
$369$	−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
$373$	577.015	+	333.140i	1.54696	+	0.893136i	0.998372	+	0.0570403i	$0.0181664\pi$
$373$	577.015	+	333.140i	1.54696	+	0.893136i	0.548584	+	0.836095i	$0.315167\pi$
$374$	82.4078	−	47.5782i	0.220342	−	0.127214i
$375$		0			0
$376$		−	1028.67i		−	2.73583i
$377$	215.707	+	579.100i	0.572168	+	1.53607i
$378$		−	1.45752i		−	0.00385588i
$379$	−99.5832	+	371.649i	−0.262752	+	0.980605i	0.700859	+	0.713299i	$0.252800\pi$
$379$	−99.5832	+	371.649i	−0.262752	+	0.980605i	−0.963612	+	0.267306i	$0.913867\pi$
$380$		0			0
$381$	−2.82650	−	1.63188i	−0.00741864	−	0.00428316i
$382$	461.752	−	461.752i	1.20877	−	1.20877i
$383$	−1.92147	−	7.17101i	−0.00501689	−	0.0187233i	0.963372	−	0.268169i	$-0.0864184\pi$
$383$	−1.92147	−	7.17101i	−0.00501689	−	0.0187233i	−0.968389	+	0.249445i	$0.919752\pi$
$384$	1.97330	+	7.36446i	0.00513881	+	0.0191783i
$385$		0			0
$386$	−38.9300	+	67.4288i	−0.100855	+	0.174686i
$387$	−118.423	−	205.115i	−0.306004	−	0.530014i
$388$	−292.676	+	1092.28i	−0.754320	+	2.81516i
$389$		−	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
$392$	597.256	+	160.034i	1.52361	+	0.408251i
$393$	−2.75802	+	1.59235i	−0.00701787	+	0.00405177i
$394$	−365.450	−	210.993i	−0.927538	−	0.535514i
$395$		0			0
$396$	−1084.27	+	290.530i	−2.73807	+	0.733663i
$397$	181.452	−	48.6200i	0.457059	−	0.122469i	−0.0229416	−	0.999737i	$-0.507303\pi$
$397$	181.452	−	48.6200i	0.457059	−	0.122469i	0.480000	+	0.877268i	$0.340637\pi$
$398$	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	0.605317	−	0.795985i	$-0.293046\pi$
$401$	293.349	+	78.6027i	0.731544	+	0.196017i	0.126227	+	0.992001i	$0.459713\pi$
$402$	11.1541			0.0277464
$403$	230.734	+	324.318i	0.572542	+	0.804761i
$404$	697.858			1.72737
$405$		0			0
$406$	58.3630	+	101.088i	0.143751	+	0.248984i
$407$	−352.769	+	611.013i	−0.866753	+	1.50126i
$408$	0.511760	−	0.511760i	0.00125431	−	0.00125431i
$409$	124.212	−	33.2825i	0.303697	−	0.0813753i	−0.103752	−	0.994603i	$-0.533085\pi$
$409$	124.212	−	33.2825i	0.303697	−	0.0813753i	0.407449	+	0.913228i	$0.366418\pi$
$410$		0			0
$411$	3.23979	−	3.23979i	0.00788269	−	0.00788269i
$412$	713.519	+	411.951i	1.73184	+	0.999880i
$413$	33.6762	+	58.3289i	0.0815405	+	0.141232i
$414$	40.1276	+	10.7521i	0.0969265	+	0.0259714i
$415$		0			0
$416$	−8.96649	−	94.3334i	−0.0215541	−	0.226763i
$417$		−	2.41368i		−	0.00578819i
$418$	364.196	+	97.5861i	0.871283	+	0.233460i
$419$	−82.0055	−	142.038i	−0.195717	−	0.338992i	0.751418	−	0.659826i	$-0.229370\pi$
$419$	−82.0055	−	142.038i	−0.195717	−	0.338992i	−0.947135	+	0.320834i	$0.896037\pi$
$420$		0			0
$421$	32.1013	+	32.1013i	0.0762501	+	0.0762501i	0.744203	−	0.667953i	$-0.232829\pi$
$421$	32.1013	+	32.1013i	0.0762501	+	0.0762501i	−0.667953	+	0.744203i	$0.732829\pi$
$422$	−24.3269	−	90.7891i	−0.0576466	−	0.215140i
$423$	−701.144	+	187.871i	−1.65755	+	0.444139i
$424$	286.921	−	286.921i	0.676701	−	0.676701i
$425$		0			0
$426$	−5.13543	+	2.96494i	−0.0120550	+	0.00695996i
$427$	−7.94976	+	29.6689i	−0.0186177	+	0.0694822i
$428$	−995.889			−2.32684
$429$	−6.89217	+	0.655109i	−0.0160657	+	0.00152706i
$430$		0			0
$431$	−60.7510	+	226.726i	−0.140953	+	0.526046i	0.858949	+	0.512062i	$0.171118\pi$
$431$	−60.7510	+	226.726i	−0.140953	+	0.526046i	−0.999902	+	0.0139840i	$0.995549\pi$
$432$	−6.56379	+	3.78961i	−0.0151940	+	0.00877224i
$433$	−43.3111	+	75.0171i	−0.100026	+	0.173250i	−0.911695	−	0.410868i	$-0.865226\pi$
$433$	−43.3111	+	75.0171i	−0.100026	+	0.173250i	0.811669	+	0.584117i	$0.198559\pi$
$434$	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
$438$	7.28113	+	4.20376i	0.0166236	+	0.00959763i
$439$	−94.1234	+	54.3422i	−0.214404	+	0.123786i	−0.603357	−	0.797472i	$-0.706170\pi$
$439$	−94.1234	+	54.3422i	−0.214404	+	0.123786i	0.388952	+	0.921258i	$0.372837\pi$
$440$		0			0
$441$		−	436.319i		−	0.989385i
$442$	−62.4176	+	44.4066i	−0.141216	+	0.100467i
$443$			355.262i			0.801945i	0.916090	+	0.400973i	$0.131328\pi$
$443$			355.262i			0.801945i	−0.916090	+	0.400973i	$0.868672\pi$
$444$	−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
$448$	−14.1125	−	52.6684i	−0.0315010	−	0.117563i
$449$	−54.9003	−	204.891i	−0.122272	−	0.456327i	0.877455	−	0.479658i	$-0.159239\pi$
$449$	−54.9003	−	204.891i	−0.122272	−	0.456327i	−0.999728	+	0.0233313i	$0.992573\pi$
$450$		0			0
$451$	−458.323	+	793.838i	−1.01624	+	1.76017i
$452$	−550.346	−	953.227i	−1.21758	−	2.10891i
$453$	−2.21512	+	8.26692i	−0.00488988	+	0.0182493i
$454$			1286.40i			2.83348i
$455$		0			0
$456$	2.86771			0.00628883
$457$	304.417	+	81.5684i	0.666121	+	0.178487i	0.576007	−	0.817445i	$-0.304610\pi$
$457$	304.417	+	81.5684i	0.666121	+	0.178487i	0.0901143	+	0.995931i	$0.471277\pi$
$458$	−693.312	+	400.284i	−1.51378	+	0.873983i
$459$	−0.884617	−	0.510734i	−0.00192727	−	0.00111271i
$460$		0			0
$461$	673.308	−	180.412i	1.46054	−	0.391350i	0.560862	−	0.827909i	$-0.310470\pi$
$461$	673.308	−	180.412i	1.46054	−	0.391350i	0.899676	+	0.436559i	$0.143803\pi$
$462$	−1.26315	+	0.338459i	−0.00273408	+	0.000732595i
$463$	645.269	+	645.269i	1.39367	+	1.39367i	0.816923	+	0.576746i	$0.195678\pi$
$463$	645.269	+	645.269i	1.39367	+	1.39367i	0.576746	+	0.816923i	$0.304322\pi$
$464$	303.491	−	525.662i	0.654076	−	1.13289i
$465$		0			0
$466$	−384.358	−	102.988i	−0.824802	−	0.221005i
$467$	−571.015			−1.22273			−0.611365	−	0.791349i	$-0.709379\pi$
$467$	−571.015			−1.22273			−0.611365	+	0.791349i	$0.709379\pi$
$468$	846.808	−	315.425i	1.80942	−	0.673986i
$469$	−70.8370			−0.151038
$470$		0			0
$471$	0.351824	+	0.609376i	0.000746972	+	0.00129379i
$472$	598.864	−	1037.26i	1.26878	−	2.19759i
$473$	−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
$477$	−247.968	−	143.164i	−0.519849	−	0.300135i
$478$	−544.677	−	943.409i	−1.13949	−	1.97366i
$479$	−40.3383	−	10.8086i	−0.0842137	−	0.0225650i	0.216466	−	0.976290i	$-0.430547\pi$
$479$	−40.3383	−	10.8086i	−0.0842137	−	0.0225650i	−0.300680	+	0.953725i	$0.597214\pi$
$480$		0			0
$481$	236.166	−	516.539i	0.490990	−	1.07389i
$482$			595.196i			1.23485i
$483$	0.0307986	+	0.00825247i	6.37653e−5	+	1.70859e-5i
$484$	539.872	+	935.086i	1.11544	+	1.93200i
$485$		0			0
$486$	19.3996	+	19.3996i	0.0399169	+	0.0399169i
$487$	95.2286	+	355.398i	0.195541	+	0.729770i	0.992126	+	0.125243i	$0.0399711\pi$
$487$	95.2286	+	355.398i	0.195541	+	0.729770i	−0.796585	+	0.604527i	$0.793362\pi$
$488$	527.602	−	141.371i	1.08115	−	0.289694i
$489$	1.79392	−	1.79392i	0.00366855	−	0.00366855i
$490$		0			0
$491$	274.278	−	158.355i	0.558612	−	0.322515i	−0.193976	−	0.981006i	$-0.562138\pi$
$491$	274.278	−	158.355i	0.558612	−	0.322515i	0.752588	+	0.658491i	$0.228805\pi$
$492$	−3.74239	+	13.9668i	−0.00760648	+	0.0283878i
$493$	81.8043			0.165932
$494$	−299.301	−	50.4633i	−0.605872	−	0.102152i
$495$		0			0
$496$	101.184	−	377.623i	0.204000	−	0.761337i
$497$	32.6140	−	18.8297i	0.0656217	−	0.0378867i
$498$	0.675309	−	1.16967i	0.00135604	−	0.00234873i
$499$	−426.657	−	426.657i	−0.855023	−	0.855023i	0.135723	−	0.990747i	$-0.456664\pi$
$499$	−426.657	−	426.657i	−0.855023	−	0.855023i	−0.990747	+	0.135723i	$0.956664\pi$
$500$		0			0
$501$	−2.10914	−	7.87143i	−0.00420987	−	0.0157114i
$502$	−405.399	−	405.399i	−0.807568	−	0.807568i
$503$	−638.951	−	368.899i	−1.27028	−	0.733397i	−0.295240	−	0.955423i	$-0.595400\pi$
$503$	−638.951	−	368.899i	−1.27028	−	0.733397i	−0.975041	+	0.222026i	$0.928733\pi$
$504$	71.2725	−	41.1492i	0.141414	−	0.0816452i
$505$		0			0
$506$		−	74.5502i		−	0.147332i
$507$	5.47350	−	1.05001i	0.0107959	−	0.00207103i
$508$		−	764.466i		−	1.50486i
$509$	21.0926	−	78.7186i	0.0414392	−	0.154653i	−0.942106	−	0.335315i	$-0.891157\pi$
$509$	21.0926	−	78.7186i	0.0414392	−	0.154653i	0.983545	+	0.180662i	$0.0578239\pi$
$510$		0			0
$511$	−46.2408	−	26.6972i	−0.0904908	−	0.0522449i
$512$	−526.388	+	526.388i	−1.02810	+	1.02810i
$513$	−1.04755	−	3.90951i	−0.00204201	−	0.00762087i
$514$	165.496	+	617.640i	0.321977	+	1.20163i
$515$		0			0
$516$	−3.35227	+	5.80630i	−0.00649664	+	0.0112525i
$517$	651.303	+	1128.09i	1.25977	+	2.18199i
$518$	27.7664	−	103.626i	0.0536031	−	0.200050i
$519$			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	$0.354007\pi$
$522$	−1414.83	−	379.102i	−2.71040	−	0.726248i
$523$	515.982	−	297.903i	0.986582	−	0.569603i	0.0823312	−	0.996605i	$-0.473763\pi$
$523$	515.982	−	297.903i	0.986582	−	0.569603i	0.904251	+	0.427002i	$0.140430\pi$
$524$	−646.007	−	372.972i	−1.23284	−	0.711779i
$525$		0			0
$526$	−463.364	+	124.158i	−0.880919	+	0.236042i
$527$	50.8931	−	13.6368i	0.0965714	−	0.0258762i
$528$	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
$532$	−37.7720			−0.0709999
$533$	306.831	−	671.095i	0.575667	−	1.25909i
$534$	10.7174			0.0200701
$535$		0			0
$536$	629.847	+	1090.93i	1.17509	+	2.03531i
$537$	−3.49911	+	6.06064i	−0.00651604	+	0.0112861i
$538$	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	−0.427359	−	0.904082i	$-0.640556\pi$
$541$	257.907	−	257.907i	0.476723	−	0.476723i	0.904082	+	0.427359i	$0.140556\pi$
$542$	1383.11	+	798.542i	2.55187	+	1.47332i
$543$	−0.854485	−	1.48001i	−0.00157364	−	0.00272562i
$544$	−12.1163	−	3.24656i	−0.0222727	−	0.00596794i
$545$		0			0
$546$	0.986505	−	0.367460i	0.00180679	−	0.000673005i
$547$		−	700.642i		−	1.28088i	−0.768007	−	0.640441i	$-0.778752\pi$
$547$		−	700.642i		−	1.28088i	0.768007	−	0.640441i	$-0.221248\pi$
$548$	1036.61	+	277.758i	1.89162	+	0.506858i
$549$	−192.717	−	333.795i	−0.351033	−	0.608006i
$550$		0			0
$551$	229.200	+	229.200i	0.415971	+	0.415971i
$552$	−0.146754	−	0.547692i	−0.000265858	−	0.000992195i
$553$	−28.8607	+	7.73320i	−0.0521893	+	0.0139841i
$554$	−53.5660	+	53.5660i	−0.0966894	+	0.0966894i
$555$		0			0
$556$	489.609	−	282.676i	0.880591	−	0.508410i
$557$	93.6252	−	349.414i	0.168088	−	0.627314i	−0.829538	−	0.558451i	$-0.811396\pi$
$557$	93.6252	−	349.414i	0.168088	−	0.627314i	0.997626	−	0.0688635i	$-0.0219373\pi$
$558$	−943.405			−1.69069
$559$	217.960	−	263.747i	0.389911	−	0.471819i
$560$		0			0
$561$	−0.237200	+	0.885242i	−0.000422816	+	0.00157797i
$562$	−894.700	+	516.555i	−1.59199	+	0.919137i
$563$	416.253	−	720.971i	0.739348	−	1.28059i	−0.213441	−	0.976956i	$-0.568467\pi$
$563$	416.253	−	720.971i	0.739348	−	1.28059i	0.952789	−	0.303632i	$-0.0981995\pi$
$564$	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
$568$	−579.974	−	334.848i	−1.02108	−	0.589521i
$569$	744.104	−	429.609i	1.30774	−	0.755024i	0.326021	−	0.945362i	$-0.394292\pi$
$569$	744.104	−	429.609i	1.30774	−	0.755024i	0.981719	+	0.190338i	$0.0609585\pi$
$570$		0			0
$571$			835.548i			1.46331i	0.681677	+	0.731654i	$0.261251\pi$
$571$			835.548i			1.46331i	−0.681677	+	0.731654i	$0.738749\pi$
$572$	−940.058	−	1321.34i	−1.64346	−	2.31003i
$573$			6.28932i			0.0109761i
$574$	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	−0.792699	−	0.609613i	$-0.791325\pi$
$577$	−105.641	+	105.641i	−0.183087	+	0.183087i	0.609613	+	0.792699i	$0.291325\pi$
$578$	−253.493	−	946.049i	−0.438570	−	1.63676i
$579$	−0.194085	−	0.724334i	−0.000335207	−	0.00125101i
$580$		0			0
$581$	−4.28874	+	7.42831i	−0.00738165	+	0.0127854i
$582$	−8.26546	−	14.3162i	−0.0142018	−	0.0245983i
$583$	−132.988	+	496.316i	−0.228109	+	0.851314i
$584$			949.510i			1.62587i
$585$		0			0
$586$	−365.088			−0.623017
$587$	−335.366	−	89.8610i	−0.571322	−	0.153085i	−0.0384190	−	0.999262i	$-0.512232\pi$
$587$	−335.366	−	89.8610i	−0.571322	−	0.153085i	−0.532903	+	0.846177i	$0.678899\pi$
$588$	−10.6964	+	6.17554i	−0.0181911	+	0.0105026i
$589$	180.800	+	104.385i	0.306962	+	0.177224i
$590$		0			0
$591$	3.92574	−	1.05190i	0.00664253	−	0.00177986i
$592$	−538.860	+	144.387i	−0.910237	+	0.243897i
$593$	−143.809	−	143.809i	−0.242511	−	0.242511i	0.575377	−	0.817888i	$-0.304855\pi$
$593$	−143.809	−	143.809i	−0.242511	−	0.242511i	−0.817888	+	0.575377i	$0.804855\pi$
$594$	16.4107	−	28.4242i	0.0276275	−	0.0478522i
$595$		0			0
$596$	1219.19	+	326.680i	2.04562	+	0.548122i
$597$	−0.898846			−0.00150560
$598$	5.67880	+	59.7447i	0.00949632	+	0.0999075i
$599$	927.612			1.54860			0.774300	−	0.632818i	$-0.218102\pi$
$599$	927.612			1.54860			0.774300	+	0.632818i	$0.218102\pi$
$600$		0			0
$601$	53.2308	+	92.1984i	0.0885703	+	0.153408i	0.906907	−	0.421331i	$-0.138437\pi$
$601$	53.2308	+	92.1984i	0.0885703	+	0.153408i	−0.818337	+	0.574739i	$0.805104\pi$
$602$	32.3140	−	55.9696i	0.0536778	−	0.0929727i
$603$	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
$607$	−1023.85	−	591.121i	−1.68674	−	0.973841i	−0.956987	−	0.290132i	$-0.906301\pi$
$607$	−1023.85	−	591.121i	−1.68674	−	0.973841i	−0.729755	−	0.683709i	$-0.760366\pi$
$608$	−24.8514	−	43.0439i	−0.0408740	−	0.0707959i
$609$	−1.08590	−	0.290967i	−0.00178309	−	0.000477779i
$610$		0			0
$611$	−607.887	−	854.441i	−0.994905	−	1.39843i
$612$		−	119.621i		−	0.195459i
$613$	−690.777	−	185.093i	−1.12688	−	0.301947i	−0.353215	−	0.935542i	$-0.614912\pi$
$613$	−690.777	−	185.093i	−1.12688	−	0.301947i	−0.773665	+	0.633595i	$0.781578\pi$
$614$	−359.890	−	623.348i	−0.586140	−	1.01522i
$615$		0			0
$616$	−104.430	−	104.430i	−0.169530	−	0.169530i
$617$	190.111	+	709.503i	0.308121	+	1.14992i	0.930225	+	0.366989i	$0.119611\pi$
$617$	190.111	+	709.503i	0.308121	+	1.14992i	−0.622104	+	0.782934i	$0.713722\pi$
$618$	−11.6339	+	3.11729i	−0.0188251	+	0.00504416i
$619$	−446.560	+	446.560i	−0.721421	+	0.721421i	−0.968895	−	0.247474i	$-0.920400\pi$
$619$	−446.560	+	446.560i	−0.721421	+	0.721421i	0.247474	+	0.968895i	$0.420400\pi$
$620$		0			0
$621$	−0.693053	+	0.400134i	−0.00111603	+	0.000644338i
$622$	140.141	−	523.015i	0.225308	−	0.840860i
$623$	−68.0641			−0.109252
$624$	−4.21976	−	3.48720i	−0.00676244	−	0.00558847i
$625$		0			0
$626$	−128.505	+	479.586i	−0.205279	+	0.766112i
$627$	−3.14487	+	1.81569i	−0.00501574	+	0.00289584i
$628$	−82.4071	+	142.733i	−0.131221	+	0.227282i
$629$	−53.1640	−	53.1640i	−0.0845214	−	0.0845214i
$630$		0			0
$631$	16.5174	+	61.6436i	0.0261765	+	0.0976920i	0.977778	−	0.209642i	$-0.0672298\pi$
$631$	16.5174	+	61.6436i	0.0261765	+	0.0976920i	−0.951602	+	0.307334i	$0.900563\pi$
$632$	375.710	+	375.710i	0.594477	+	0.594477i
$633$	0.783973	+	0.452627i	0.00123850	+	0.000715050i
$634$	1616.97	−	933.561i	2.55043	−	1.47249i
$635$		0			0
$636$			8.10524i			0.0127441i
$637$	590.668	−	220.016i	0.927266	−	0.345395i
$638$			2628.51i			4.11992i
$639$	−122.310	+	456.466i	−0.191408	+	0.714344i
$640$		0			0
$641$	581.799	+	335.902i	0.907643	+	0.524028i	0.879672	−	0.475581i	$-0.157762\pi$
$641$	581.799	+	335.902i	0.907643	+	0.524028i	0.0279707	+	0.999609i	$0.491096\pi$
$642$	10.2944	−	10.2944i	0.0160349	−	0.0160349i
$643$	143.059	+	533.905i	0.222487	+	0.830334i	0.983396	+	0.181475i	$0.0580870\pi$
$643$	143.059	+	533.905i	0.222487	+	0.830334i	−0.760908	+	0.648859i	$0.775246\pi$
$644$	1.93296	+	7.21391i	0.00300149	+	0.0112017i
$645$		0			0
$646$	−20.0897	+	34.7964i	−0.0310987	+	0.0538644i
$647$	−122.042	−	211.383i	−0.188628	−	0.326713i	0.756165	−	0.654381i	$-0.227071\pi$
$647$	−122.042	−	211.383i	−0.188628	−	0.326713i	−0.944793	+	0.327668i	$0.893737\pi$
$648$	−267.256	+	997.411i	−0.412431	+	1.53921i
$649$			1516.68i			2.33696i
$650$		0			0
$651$	−0.724081			−0.00111226
$652$	573.986	+	153.799i	0.880347	+	0.235888i
$653$	−957.406	+	552.758i	−1.46617	+	0.846491i	−0.999284	−	0.0378295i	$-0.987956\pi$
$653$	−957.406	+	552.758i	−1.46617	+	0.846491i	−0.466881	+	0.884320i	$0.654622\pi$
$654$	−11.1576	−	6.44185i	−0.0170606	−	0.00984992i
$655$		0			0
$656$	−700.095	+	187.590i	−1.06722	+	0.285960i
$657$	647.188	−	173.414i	0.985066	−	0.263948i
$658$	−140.056	−	140.056i	−0.212851	−	0.212851i
$659$	−352.219	+	610.061i	−0.534475	+	0.925737i	0.464714	+	0.885461i	$0.346157\pi$
$659$	−352.219	+	610.061i	−0.534475	+	0.925737i	−0.999189	+	0.0402762i	$0.987176\pi$
$660$		0			0
$661$	−1116.82	−	299.251i	−1.68959	−	0.452724i	−0.719307	−	0.694693i	$-0.755540\pi$
$661$	−1116.82	−	299.251i	−1.68959	−	0.452724i	−0.970284	+	0.241968i	$0.922207\pi$
$662$	−255.157			−0.385434
$663$	0.122660	−	0.727503i	0.000185007	−	0.00109729i
$664$	152.533			0.229719
$665$		0			0
$666$	673.109	+	1165.86i	1.01067	+	1.75054i
$667$	32.0448	−	55.5032i	0.0480432	−	0.0832132i
$668$	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
$672$	0.149290	+	0.0861924i	0.000222157	+	0.000128263i
$673$	463.497	+	802.800i	0.688703	+	1.19287i	0.972258	+	0.233912i	$0.0751528\pi$
$673$	463.497	+	802.800i	0.688703	+	1.19287i	−0.283555	+	0.958956i	$0.591514\pi$
$674$	421.429	+	112.921i	0.625265	+	0.167539i
$675$		0			0
$676$	854.016	+	987.315i	1.26334	+	1.46053i
$677$			168.337i			0.248651i	0.992241	+	0.124326i	$0.0396767\pi$
$677$			168.337i			0.248651i	−0.992241	+	0.124326i	$0.960323\pi$
$678$	15.5423	+	4.16455i	0.0229238	+	0.00614240i
$679$	52.4921	+	90.9190i	0.0773079	+	0.133901i
$680$		0			0
$681$	−8.76074	−	8.76074i	−0.0128645	−	0.0128645i
$682$	438.172	+	1635.28i	0.642481	+	2.39777i
$683$	−360.167	+	96.5064i	−0.527331	+	0.141298i	−0.512655	−	0.858595i	$-0.671338\pi$
$683$	−360.167	+	96.5064i	−0.527331	+	0.141298i	−0.0146753	+	0.999892i	$0.504671\pi$
$684$	335.156	−	335.156i	0.489994	−	0.489994i
$685$		0			0
$686$	207.308	−	119.689i	0.302198	−	0.174474i
$687$	1.99561	−	7.44770i	0.00290481	−	0.0108409i
$688$	−336.070			−0.488474
$689$	68.7700	−	407.879i	0.0998113	−	0.591987i
$690$		0			0
$691$	186.588	−	696.355i	0.270026	−	1.00775i	−0.689076	−	0.724689i	$-0.741984\pi$
$691$	186.588	−	696.355i	0.270026	−	1.00775i	0.959102	−	0.283061i	$-0.0913497\pi$
$692$	−738.967	+	426.643i	−1.06787	+	0.616536i
$693$	−52.1073	+	90.2524i	−0.0751909	+	0.130234i
$694$	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
$698$	449.608	+	259.581i	0.644138	+	0.371893i
$699$	3.31897	−	1.91621i	0.00474816	−	0.00274135i
$700$		0			0
$701$			589.719i			0.841254i	0.907234	+	0.420627i	$0.138190\pi$
$701$			589.719i			0.841254i	−0.907234	+	0.420627i	$0.861810\pi$
$702$	−10.9864	+	24.0293i	−0.0156501	+	0.0342297i
$703$		−	297.911i		−	0.423771i
$704$	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
$708$	6.19216	+	23.1095i	0.00874600	+	0.0326405i
$709$	40.7548	+	152.099i	0.0574821	+	0.214526i	0.988693	−	0.149955i	$-0.0479129\pi$
$709$	40.7548	+	152.099i	0.0574821	+	0.214526i	−0.931211	+	0.364481i	$0.881246\pi$
$710$		0			0
$711$	187.467	−	324.702i	0.263667	−	0.456684i
$712$	605.191	+	1048.22i	0.849988	+	1.47222i
$713$	10.6837	−	39.8722i	0.0149842	−	0.0559217i
$714$		−	0.139355i		−	0.000195175i
$715$		0			0
$716$	−1639.18			−2.28936
$717$	10.1343	+	2.71547i	0.0141343	+	0.00378727i
$718$	−507.685	+	293.112i	−0.707083	+	0.408234i
$719$	721.138	+	416.349i	1.00297	+	0.579067i	0.909127	−	0.416519i	$-0.136750\pi$
$719$	721.138	+	416.349i	1.00297	+	0.579067i	0.0938470	+	0.995587i	$0.470084\pi$
$720$		0			0
$721$	73.8843	−	19.7972i	0.102475	−	0.0274580i
$722$	1040.20	−	278.720i	1.44072	−	0.386039i
$723$	−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
$727$	61.3646			0.0844079			0.0422040	−	0.999109i	$-0.486562\pi$
$727$	61.3646			0.0844079			0.0422040	+	0.999109i	$0.486562\pi$
$728$	91.6454	+	75.7357i	0.125887	+	0.104033i
$729$	728.472			0.999275
$730$		0			0
$731$	−22.6464	−	39.2248i	−0.0309801	−	0.0536591i
$732$	−5.45533	+	9.44890i	−0.00745263	+	0.0129083i
$733$	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
$737$	−1381.44	−	797.576i	−1.87441	−	1.08219i
$738$	874.514	+	1514.70i	1.18498	+	2.05244i
$739$	−306.125	−	82.0259i	−0.414242	−	0.110996i	0.0456779	−	0.998956i	$-0.485455\pi$
$739$	−306.125	−	82.0259i	−0.414242	−	0.110996i	−0.459920	+	0.887960i	$0.652122\pi$
$740$		0			0
$741$	2.38199	−	1.69466i	0.00321457	−	0.00228698i
$742$		−	78.1301i		−	0.105297i
$743$	991.663	+	265.715i	1.33467	+	0.357625i	0.854456	−	0.519524i	$-0.173891\pi$
$743$	991.663	+	265.715i	1.33467	+	0.357625i	0.480219	+	0.877149i	$0.340557\pi$
$744$	6.43816	+	11.1512i	0.00865344	+	0.0149882i
$745$		0			0
$746$	−1613.19	−	1613.19i	−2.16246	−	2.16246i
$747$	−27.8579	−	103.967i	−0.0372930	−	0.139179i
$748$	−207.349	+	55.5589i	−0.277204	+	0.0742767i
$749$	−65.3776	+	65.3776i	−0.0872865	+	0.0872865i
$750$		0			0
$751$	−444.296	+	256.514i	−0.591605	+	0.341563i	−0.765732	−	0.643160i	$-0.777623\pi$
$751$	−444.296	+	256.514i	−0.591605	+	0.341563i	0.174127	+	0.984723i	$0.444290\pi$
$752$	−266.576	+	994.877i	−0.354490	+	1.32297i
$753$	5.52177			0.00733303
$754$	−200.224	−	2106.49i	−0.265550	−	2.79375i
$755$		0			0
$756$	−0.851004	+	3.17599i	−0.00112567	+	0.00420105i
$757$	0.322110	−	0.185970i	0.000425508	−	0.000245667i	−0.499787	−	0.866148i	$-0.666588\pi$
$757$	0.322110	−	0.185970i	0.000425508	−	0.000245667i	0.500213	+	0.865903i	$0.333255\pi$
$758$	658.727	−	1140.95i	0.869032	−	1.50521i
$759$	0.507708	+	0.507708i	0.000668918	+	0.000668918i
$760$		0			0
$761$	−100.429	−	374.806i	−0.131970	−	0.492518i	0.868022	−	0.496525i	$-0.165391\pi$
$761$	−100.429	−	374.806i	−0.131970	−	0.492518i	−0.999992	+	0.00400744i	$0.998724\pi$
$762$	7.90223	+	7.90223i	0.0103704	+	0.0103704i
$763$	70.8595	+	40.9107i	0.0928696	+	0.0536183i
$764$	−1275.78	+	736.569i	−1.66986	+	0.964096i
$765$		0			0
$766$			25.4204i			0.0331859i
$767$	−115.532	−	1215.47i	−0.150629	−	1.58471i
$768$		−	16.0763i		−	0.0209327i
$769$	290.354	−	1083.62i	0.377574	−	1.40913i	−0.471973	−	0.881613i	$-0.656458\pi$
$769$	290.354	−	1083.62i	0.377574	−	1.40913i	0.849547	−	0.527512i	$-0.176875\pi$
$770$		0			0
$771$	−5.33338	−	3.07923i	−0.00691748	−	0.00399381i
$772$	124.199	−	124.199i	0.160880	−	0.160880i
$773$	−252.729	−	943.196i	−0.326945	−	1.22018i	−0.912342	−	0.409429i	$-0.865728\pi$
$773$	−252.729	−	943.196i	−0.326945	−	1.22018i	0.585397	−	0.810747i	$-0.300939\pi$
$774$	209.899	+	783.352i	0.271187	+	1.01208i
$775$		0			0
$776$	933.466	−	1616.81i	1.20292	−	2.08352i
$777$	0.516623	+	0.894818i	0.000664895	+	0.00115163i
$778$	−13.8219	+	51.5841i	−0.0177660	+	0.0663035i
$779$		−	387.050i		−	0.496855i
$780$		0			0
$781$	848.037			1.08583
$782$	7.67371	+	2.05616i	0.00981293	+	0.00262937i
$783$	24.4358	−	14.1080i	0.0312079	−	0.0180179i
$784$	−536.163	−	309.554i	−0.683881	−	0.394839i
$785$		0			0
$786$	10.5331	−	2.82234i	0.0134009	−	0.00359076i
$787$	731.634	−	196.041i	0.929649	−	0.249099i	0.237944	−	0.971279i	$-0.423527\pi$
$787$	731.634	−	196.041i	0.929649	−	0.249099i	0.691705	+	0.722180i	$0.256860\pi$
$788$	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
$792$	1853.25			2.33996
$793$	354.698	−	429.210i	0.447287	−	0.541248i
$794$	−643.227			−0.810110
$795$		0			0
$796$	−105.268	−	182.329i	−0.132246	−	0.229056i
$797$	46.1830	−	79.9913i	0.0579460	−	0.100365i	−0.835597	−	0.549343i	$-0.814878\pi$
$797$	46.1830	−	79.9913i	0.0579460	−	0.100365i	0.893543	+	0.448977i	$0.148212\pi$
$798$	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
$802$	−900.569	−	519.944i	−1.12290	−	0.648309i
$803$	−601.183	−	1041.28i	−0.748671	−	1.29674i
$804$	−24.3051	−	6.51252i	−0.0302302	−	0.00810015i
$805$		0			0
$806$	−475.718	−	1277.14i	−0.590221	−	1.58454i
$807$			1.62449i			0.00201299i
$808$	−1112.88	−	298.196i	−1.37733	−	0.369054i
$809$	−23.1844	−	40.1565i	−0.0286580	−	0.0496372i	0.851341	−	0.524613i	$-0.175790\pi$
$809$	−23.1844	−	40.1565i	−0.0286580	−	0.0496372i	−0.879999	+	0.474976i	$0.842457\pi$
$810$		0			0
$811$	70.9896	+	70.9896i	0.0875334	+	0.0875334i	0.749518	−	0.661984i	$-0.230285\pi$
$811$	70.9896	+	70.9896i	0.0875334	+	0.0875334i	−0.661984	+	0.749518i	$0.730285\pi$
$812$	−68.1528	−	254.350i	−0.0839320	−	0.313238i
$813$	−14.8577	+	3.98111i	−0.0182752	+	0.00489681i
$814$	1708.25	−	1708.25i	2.09858	−	2.09858i
$815$		0			0
$816$	−0.627569	+	0.362327i	−0.000769079	+	0.000444028i
$817$	46.4494	−	173.351i	0.0568536	−	0.212181i
$818$	−440.317			−0.538285
$819$	34.8840	−	76.2977i	0.0425933	−	0.0931596i
$820$		0			0
$821$	−256.139	+	955.924i	−0.311984	+	1.16434i	0.614780	+	0.788698i	$0.289245\pi$
$821$	−256.139	+	955.924i	−0.311984	+	1.16434i	−0.926765	+	0.375643i	$0.877422\pi$
$822$	−13.5865	+	7.84417i	−0.0165286	+	0.00954278i
$823$	231.270	−	400.572i	0.281009	−	0.486722i	−0.690625	−	0.723213i	$-0.742664\pi$
$823$	231.270	−	400.572i	0.281009	−	0.486722i	0.971633	+	0.236492i	$0.0759977\pi$
$824$	−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	$0.457487\pi$
$828$	−81.1614	−	46.8586i	−0.0980210	−	0.0565925i
$829$	−385.154	+	222.369i	−0.464600	+	0.268237i	−0.713977	−	0.700170i	$-0.753108\pi$
$829$	−385.154	+	222.369i	−0.464600	+	0.268237i	0.249376	+	0.968407i	$0.419774\pi$
$830$		0			0
$831$		−	0.729599i		−	0.000877977i
$832$	−164.336	+	974.686i	−0.197519	+	1.17150i
$833$		−	83.4385i		−	0.100166i
$834$	−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
$838$	145.350	+	542.453i	0.173449	+	0.647319i
$839$	241.488	+	901.245i	0.287828	+	1.07419i	0.946748	+	0.321976i	$0.104347\pi$
$839$	241.488	+	901.245i	0.287828	+	1.07419i	−0.658920	+	0.752213i	$0.728986\pi$
$840$		0			0
$841$	−709.342	+	1228.62i	−0.843450	+	1.46090i
$842$	−77.7236	−	134.621i	−0.0923084	−	0.159883i
$843$	2.57527	−	9.61105i	0.00305489	−	0.0114010i
$844$			212.036i			0.251228i
$845$		0			0
$846$	2485.47			2.93791
$847$	96.8273	+	25.9448i	0.114318	+	0.0306314i
$848$	−351.850	+	203.141i	−0.414918	+	0.239553i
$849$	−0.0752018	−	0.0434178i	−8.85769e−5	−	5.11399e-5i
$850$		0			0
$851$	−56.8967	+	15.2454i	−0.0668587	+	0.0179147i
$852$	12.9214	−	3.46228i	0.0151660	−	0.00406371i
$853$	130.680	+	130.680i	0.153201	+	0.153201i	0.779546	−	0.626345i	$-0.215450\pi$
$853$	130.680	+	130.680i	0.153201	+	0.153201i	−0.626345	+	0.779546i	$0.715450\pi$
$854$	52.5864	−	91.0823i	0.0615766	−	0.106654i
$855$		0			0
$856$	1588.15	+	425.544i	1.85532	+	0.497131i
$857$	1553.51			1.81273			0.906365	−	0.422496i	$-0.138846\pi$
$857$	1553.51			1.81273			0.906365	+	0.422496i	$0.138846\pi$
$858$	23.3759	+	3.94126i	0.0272446	+	0.00459355i
$859$	781.729			0.910045			0.455023	−	0.890480i	$-0.349631\pi$
$859$	781.729			0.910045			0.455023	+	0.890480i	$0.349631\pi$
$860$		0			0
$861$	0.671205	+	1.16256i	0.000779565	+	0.00135025i
$862$	401.858	−	696.038i	0.466192	−	0.807469i
$863$	−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
$867$	8.16923	+	4.71651i	0.00942241	+	0.00544003i
$868$	−84.8001	−	146.878i	−0.0976960	−	0.169214i
$869$	−649.903	−	174.141i	−0.747874	−	0.200392i
$870$		0			0
$871$	1167.84	+	533.948i	1.34081	+	0.613029i
$872$		−	1455.03i		−	1.66861i
$873$	−1272.50	−	340.967i	−1.45762	−	0.390569i
$874$	15.7393	+	27.2613i	0.0180083	+	0.0311914i
$875$		0			0
$876$	−13.4114	−	13.4114i	−0.0153098	−	0.0153098i
$877$	−75.4171	−	281.460i	−0.0859944	−	0.320935i	0.909506	−	0.415690i	$-0.136460\pi$
$877$	−75.4171	−	281.460i	−0.0859944	−	0.320935i	−0.995501	+	0.0947548i	$0.969793\pi$
$878$	359.465	−	96.3183i	0.409413	−	0.109702i
$879$	2.48635	−	2.48635i	0.00282861	−	0.00282861i
$880$		0			0
$881$	−523.282	+	302.117i	−0.593964	+	0.342925i	−0.766663	−	0.642049i	$-0.778084\pi$
$881$	−523.282	+	302.117i	−0.593964	+	0.342925i	0.172699	+	0.984975i	$0.444751\pi$
$882$	−386.675	+	1443.09i	−0.438407	+	1.63616i
$883$	−1287.07			−1.45761			−0.728803	−	0.684724i	$-0.759923\pi$
$883$	−1287.07			−1.45761			−0.728803	+	0.684724i	$0.759923\pi$
$884$	161.938	−	60.3197i	0.183187	−	0.0682349i
$885$		0			0
$886$	314.840	−	1175.00i	0.355350	−	1.32618i
$887$	−190.472	+	109.969i	−0.214737	+	0.123979i	−0.603511	−	0.797355i	$-0.706232\pi$
$887$	−190.472	+	109.969i	−0.214737	+	0.123979i	0.388774	+	0.921333i	$0.372899\pi$
$888$	9.18711	−	15.9125i	0.0103458	−	0.0179195i
$889$	−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
$893$	−476.332	−	275.011i	−0.533407	−	0.307963i
$894$	−15.9795	+	9.22578i	−0.0178742	+	0.0103197i
$895$		0			0
$896$			165.794i			0.185038i
$897$	−0.445553	−	0.368204i	−0.000496714	−	0.000410484i
$898$			726.314i			0.808813i
$899$	−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
$903$	0.161101	+	0.601237i	0.000178406	+	0.000665821i
$904$	470.327	+	1755.28i	0.520273	+	1.94169i
$905$		0			0
$906$	14.6526	−	25.3791i	0.0161729	−	0.0280123i
$907$	−489.570	−	847.960i	−0.539768	−	0.934906i	−0.998916	−	0.0465461i	$-0.985179\pi$
$907$	−489.570	−	847.960i	−0.539768	−	0.934906i	0.459148	−	0.888360i	$-0.348155\pi$
$908$	751.089	−	2803.10i	0.827190	−	3.08712i
$909$			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	$0.421639\pi$
$912$	−2.77350	−	0.743157i	−0.00304112	−	0.000814865i
$913$	−167.275	+	96.5765i	−0.183215	+	0.105779i
$914$	−934.548	−	539.562i	−1.02248	−	0.590330i
$915$		0			0
$916$	1744.46	−	467.428i	1.90444	−	0.510292i
$917$	−66.8934	+	17.9240i	−0.0729481	+	0.0195464i
$918$	2.47318	+	2.47318i	0.00269409	+	0.00269409i
$919$	355.023	−	614.917i	0.386314	−	0.669115i	−0.605637	−	0.795741i	$-0.707081\pi$
$919$	355.023	−	614.917i	0.386314	−	0.669115i	0.991951	+	0.126626i	$0.0404148\pi$
$920$		0			0
$921$	6.69613	+	1.79422i	0.00727050	+	0.00194813i
$922$	−2386.80			−2.58872
$923$	−679.618	+	64.5985i	−0.736314	+	0.0699875i
$924$	2.95005			0.00319269
$925$		0			0
$926$	−1562.32	−	2706.03i	−1.68718	−	2.92227i
$927$	−479.921	+	831.248i	−0.517714	+	0.896707i
$928$	245.010	−	245.010i	0.264019	−	0.264019i
$929$	287.421	−	77.0142i	0.309387	−	0.0829001i	−0.100785	−	0.994908i	$-0.532135\pi$
$929$	287.421	−	77.0142i	0.309387	−	0.0829001i	0.410172	+	0.912008i	$0.365469\pi$
$930$		0			0
$931$	233.779	−	233.779i	0.251105	−	0.251105i
$932$	777.396	+	448.830i	0.834116	+	0.481577i
$933$	2.60748	+	4.51628i	0.00279472	+	0.00484060i
$934$	1888.58	+	506.045i	2.02204	+	0.541804i
$935$		0			0
$936$	−1485.19	+	141.169i	−1.58675	+	0.150822i
$937$			194.851i			0.207952i	0.994580	+	0.103976i	$0.0331565\pi$
$937$			194.851i			0.207952i	−0.994580	+	0.103976i	$0.966844\pi$
$938$	234.288	+	62.7772i	0.249774	+	0.0669266i
$939$	−2.39097	−	4.14127i	−0.00254629	−	0.00441030i
$940$		0			0
$941$	415.396	+	415.396i	0.441441	+	0.441441i	0.892496	−	0.451055i	$-0.148952\pi$
$941$	415.396	+	415.396i	0.441441	+	0.441441i	−0.451055	+	0.892496i	$0.648952\pi$
$942$	−0.623586	−	2.32726i	−0.000661981	−	0.00247055i
$943$	−73.9211	+	19.8071i	−0.0783893	+	0.0210044i
$944$	−847.993	+	847.993i	−0.898298	+	0.898298i
$945$		0			0
$946$	1260.36	−	727.668i	1.33230	−	0.769205i
$947$	214.904	−	802.031i	0.226931	−	0.846918i	−0.754691	−	0.656081i	$-0.772213\pi$
$947$	214.904	−	802.031i	0.226931	−	0.846918i	0.981622	−	0.190837i	$-0.0611202\pi$
$948$	−10.6134			−0.0111956
$949$	561.108	+	788.689i	0.591262	+	0.831073i
$950$		0			0
$951$	−4.65424	+	17.3699i	−0.00489405	+	0.0182648i
$952$	13.6296	−	7.86907i	0.0143168	−	0.00826583i
$953$	−523.182	+	906.178i	−0.548985	+	0.950869i	0.449360	+	0.893351i	$0.351652\pi$
$953$	−523.182	+	906.178i	−0.548985	+	0.950869i	−0.998344	+	0.0575183i	$0.981681\pi$
$954$	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
$958$	123.837	+	71.4973i	0.129266	+	0.0746319i
$959$	86.2848	−	49.8166i	0.0899737	−	0.0519464i
$960$		0			0
$961$		−	23.5985i		−	0.0245562i
$962$	−1238.87	+	1499.12i	−1.28780	+	1.55833i
$963$		−	1160.21i		−	1.20478i
$964$	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	−0.971477	−	0.237133i	$-0.923792\pi$
$967$	−710.111	+	710.111i	−0.734344	+	0.734344i	0.237133	+	0.971477i	$0.423792\pi$
$968$	−461.376	−	1721.88i	−0.476628	−	1.77880i
$969$	−0.100157	−	0.373790i	−0.000103361	−	0.000385749i
$970$		0			0
$971$	−759.207	+	1314.99i	−0.781882	+	1.35426i	0.148963	+	0.988843i	$0.452407\pi$
$971$	−759.207	+	1314.99i	−0.781882	+	1.35426i	−0.930844	+	0.365416i	$0.880927\pi$
$972$	−30.9455	−	53.5992i	−0.0318369	−	0.0551432i
$973$	13.5846	−	50.6985i	0.0139616	−	0.0521054i
$974$		−	1259.84i		−	1.29347i
$975$		0			0
$976$	−546.905			−0.560354
$977$	−169.508	−	45.4195i	−0.173498	−	0.0464887i	0.171024	−	0.985267i	$-0.445292\pi$
$977$	−169.508	−	45.4195i	−0.173498	−	0.0464887i	−0.344522	+	0.938778i	$0.611959\pi$
$978$	−7.52306	+	4.34344i	−0.00769229	+	0.00444114i
$979$	−1327.36	−	766.354i	−1.35584	−	0.782793i
$980$		0			0
$981$	−991.752	+	265.739i	−1.01096	+	0.270886i
$982$	−1047.49	+	280.674i	−1.06669	+	0.285819i
$983$	657.150	+	657.150i	0.668515	+	0.668515i	0.957372	−	0.288857i	$-0.0932753\pi$
$983$	657.150	+	657.150i	0.668515	+	0.668515i	−0.288857	+	0.957372i	$0.593275\pi$
$984$	11.9360	−	20.6738i	0.0121301	−	0.0210100i
$985$		0			0
$986$	−270.561	−	72.4967i	−0.274403	−	0.0735260i
$987$	1.90764			0.00193277
$988$	622.722	+	284.714i	0.630286	+	0.288172i
$989$	−35.4847			−0.0358794
$990$		0			0
$991$	−241.005	−	417.433i	−0.243194	−	0.421224i	0.718428	−	0.695601i	$-0.244862\pi$
$991$	−241.005	−	417.433i	−0.243194	−	0.421224i	−0.961622	+	0.274377i	$0.911528\pi$
$992$	111.586	−	193.272i	0.112485	−	0.194830i
$993$	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
$997$	−574.298	−	331.571i	−0.576026	−	0.332569i	0.183526	−	0.983015i	$-0.441249\pi$
$997$	−574.298	−	331.571i	−0.576026	−	0.332569i	−0.759553	+	0.650446i	$0.774582\pi$
$998$	1033.02	+	1789.24i	1.03509	+	1.79283i
$999$	−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.w.e.24.1		40
5.2	odd	4		65.3.p.a.11.10	yes	40
5.3	odd	4		325.3.t.d.76.1		40
5.4	even	2		325.3.w.f.24.10		40
13.6	odd	12		325.3.w.f.149.10		40
65.19	odd	12	inner	325.3.w.e.149.1		40
65.32	even	12		65.3.p.a.6.10	✓	40
65.58	even	12		325.3.t.d.201.1		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.3.p.a.6.10	✓	40	65.32	even	12
65.3.p.a.11.10	yes	40	5.2	odd	4
325.3.t.d.76.1		40	5.3	odd	4
325.3.t.d.201.1		40	65.58	even	12
325.3.w.e.24.1		40	1.1	even	1	trivial
325.3.w.e.149.1		40	65.19	odd	12	inner
325.3.w.f.24.10		40	5.4	even	2
325.3.w.f.149.10		40	13.6	odd	12

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.w (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-3.30742 - 0.886220i) q^{2} +(0.0285599 - 0.0164891i) q^{3} +(6.68953 + 3.86220i) q^{4} +(-0.109072 + 0.0292259i) q^{6} +(0.692695 - 0.185607i) q^{7} +(-9.01754 - 9.01754i) q^{8} +(-4.49946 + 7.79329i) q^{9} +(15.5985 + 4.17961i) q^{11} +0.254736 q^{12} +(-12.8191 - 2.16135i) q^{13} -2.45552 q^{14} +(6.38443 + 11.0582i) q^{16} +(-0.860444 + 1.49033i) q^{17} +(21.7882 - 21.7882i) q^{18} +(-6.58643 + 1.76483i) q^{19} +(0.0167228 - 0.0167228i) q^{21} +(-47.8868 - 27.6475i) q^{22} +(0.674114 + 1.16760i) q^{23} +(-0.406230 - 0.108849i) q^{24} +(40.4826 + 18.5090i) q^{26} +0.593570i q^{27} +(5.35066 + 1.43370i) q^{28} +(-23.7681 - 41.1675i) q^{29} +(-21.6495 - 21.6495i) q^{31} +(1.88656 + 7.04075i) q^{32} +(0.514410 - 0.137836i) q^{33} +(4.16661 - 4.16661i) q^{34} +(-60.1985 + 34.7556i) q^{36} +(-11.3078 + 42.2011i) q^{37} +23.3481 q^{38} +(-0.401750 + 0.149647i) q^{39} +(-14.6912 + 54.8283i) q^{41} +(-0.0701294 + 0.0404892i) q^{42} +(-13.1597 + 22.7934i) q^{43} +(88.2044 + 88.2044i) q^{44} +(-1.19483 - 4.45916i) q^{46} +(57.0372 + 57.0372i) q^{47} +(0.364677 + 0.210547i) q^{48} +(-41.9899 + 24.2429i) q^{49} +0.0567516i q^{51} +(-77.4061 - 63.9683i) q^{52} +31.8181i q^{53} +(0.526034 - 1.96319i) q^{54} +(-7.92012 - 4.57268i) q^{56} +(-0.159007 + 0.159007i) q^{57} +(42.1275 + 157.222i) q^{58} +(24.3081 + 90.7191i) q^{59} +(-21.4156 + 37.0929i) q^{61} +(52.4177 + 90.7902i) q^{62} +(-1.67026 + 6.23350i) q^{63} -76.0341i q^{64} -1.82352 q^{66} +(-95.4126 - 25.5657i) q^{67} +(-11.5119 + 6.64642i) q^{68} +(0.0385053 + 0.0222310i) q^{69} +(50.7246 - 13.5916i) q^{71} +(110.850 - 29.7022i) q^{72} +(-52.6480 - 52.6480i) q^{73} +(74.7989 - 129.556i) q^{74} +(-50.8763 - 13.6323i) q^{76} +11.5808 q^{77} +(1.46137 - 0.138905i) q^{78} -41.6643 q^{79} +(-40.4853 - 70.1226i) q^{81} +(97.1800 - 168.321i) q^{82} +(-8.45759 + 8.45759i) q^{83} +(0.176455 - 0.0472809i) q^{84} +(63.7247 - 63.7247i) q^{86} +(-1.35763 - 0.783826i) q^{87} +(-102.971 - 178.350i) q^{88} +(-91.6776 - 24.5649i) q^{89} +(-9.28087 + 0.882157i) q^{91} +10.4143i q^{92} +(-0.975287 - 0.261327i) q^{93} +(-138.098 - 239.194i) q^{94} +(0.169975 + 0.169975i) q^{96} +(37.8898 + 141.407i) q^{97} +(160.363 - 42.9690i) q^{98} +(-102.758 + 102.758i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 12 q^{3} - 12 q^{6} - 44 q^{7} + 36 q^{8} + 72 q^{9} - 12 q^{11} + 120 q^{12} - 36 q^{13} - 48 q^{14} + 128 q^{16} - 32 q^{17} + 136 q^{18} - 68 q^{19} - 48 q^{21} - 72 q^{22} - 28 q^{23} + 56 q^{24}+ \cdots + 76 q^{99}+O(q^{100}) \) 40 * q - 12 * q^3 - 12 * q^6 - 44 * q^7 + 36 * q^8 + 72 * q^9 - 12 * q^11 + 120 * q^12 - 36 * q^13 - 48 * q^14 + 128 * q^16 - 32 * q^17 + 136 * q^18 - 68 * q^19 - 48 * q^21 - 72 * q^22 - 28 * q^23 + 56 * q^24 - 84 * q^26 + 76 * q^28 - 28 * q^29 + 128 * q^31 + 84 * q^32 - 68 * q^33 + 28 * q^34 + 300 * q^36 - 260 * q^37 + 8 * q^38 + 88 * q^39 + 68 * q^41 - 480 * q^42 + 32 * q^43 + 240 * q^44 + 260 * q^46 - 152 * q^47 - 480 * q^48 + 132 * q^49 + 488 * q^52 - 152 * q^54 - 288 * q^56 + 252 * q^57 + 468 * q^58 - 492 * q^59 - 100 * q^61 - 8 * q^62 - 356 * q^63 - 456 * q^66 - 56 * q^67 + 12 * q^68 + 576 * q^69 - 132 * q^71 + 396 * q^72 - 424 * q^73 + 160 * q^74 - 992 * q^76 + 344 * q^77 + 12 * q^78 + 248 * q^79 + 248 * q^82 - 112 * q^83 - 1100 * q^84 + 852 * q^86 - 1068 * q^87 + 8 * q^88 - 168 * q^89 - 160 * q^91 - 24 * q^93 - 328 * q^94 + 124 * q^96 + 1020 * q^97 + 1404 * q^98 + 76 * q^99

Introduction

L-functions

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