LMFDB - Embedded newform 290.2.l.b.109.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [290,2,Mod(9,290)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("290.9"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(290, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([7, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 290 = 2 \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	290.l (of order $14$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$2.31566165862$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			109.3
Character	$\chi$	$=$	290.109
Dual form			290.2.l.b.149.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.222521 + 0.974928i) q^{2} +(-0.893741 - 0.430403i) q^{3} +(-0.900969 + 0.433884i) q^{4} +(2.22348 + 0.236969i) q^{5} +(0.220736 - 0.967106i) q^{6} +(1.53438 - 3.18618i) q^{7} +(-0.623490 - 0.781831i) q^{8} +(-1.25694 - 1.57616i) q^{9} +(0.263743 + 2.22046i) q^{10} +(4.95449 + 3.95107i) q^{11} +0.991977 q^{12} +(-3.09664 - 2.46949i) q^{13} +(3.44773 + 0.786921i) q^{14} +(-1.88522 - 1.16878i) q^{15} +(0.623490 - 0.781831i) q^{16} +4.53324 q^{17} +(1.25694 - 1.57616i) q^{18} +(1.27735 + 2.65245i) q^{19} +(-2.10610 + 0.751229i) q^{20} +(-2.74268 + 2.18721i) q^{21} +(-2.74953 + 5.70946i) q^{22} +(1.28657 + 0.293650i) q^{23} +(0.220736 + 0.967106i) q^{24} +(4.88769 + 1.05379i) q^{25} +(1.71850 - 3.56851i) q^{26} +(1.10721 + 4.85099i) q^{27} +3.53639i q^{28} +(-4.74063 + 2.55468i) q^{29} +(0.719974 - 2.09803i) q^{30} +(-0.562161 + 0.128310i) q^{31} +(0.900969 + 0.433884i) q^{32} +(-2.72747 - 5.66366i) q^{33} +(1.00874 + 4.41958i) q^{34} +(4.16669 - 6.72079i) q^{35} +(1.81634 + 0.874701i) q^{36} +(-4.36485 - 5.47334i) q^{37} +(-2.30171 + 1.83555i) q^{38} +(1.70472 + 3.53988i) q^{39} +(-1.20105 - 1.88613i) q^{40} -9.51792i q^{41} +(-2.74268 - 2.18721i) q^{42} +(0.135073 - 0.591795i) q^{43} +(-6.17815 - 1.41012i) q^{44} +(-2.42128 - 3.80240i) q^{45} +1.31965i q^{46} +(-2.94835 + 3.69712i) q^{47} +(-0.893741 + 0.430403i) q^{48} +(-3.43297 - 4.30481i) q^{49} +(0.0602468 + 4.99964i) q^{50} +(-4.05154 - 1.95112i) q^{51} +(3.86144 + 0.881350i) q^{52} +(-11.0126 + 2.51355i) q^{53} +(-4.48299 + 2.15889i) q^{54} +(10.0799 + 9.95917i) q^{55} +(-3.44773 + 0.786921i) q^{56} -2.92038i q^{57} +(-3.54552 - 4.05330i) q^{58} -0.894046 q^{59} +(2.20564 + 0.235067i) q^{60} +(-3.29299 + 6.83797i) q^{61} +(-0.250185 - 0.519515i) q^{62} +(-6.95055 + 1.58642i) q^{63} +(-0.222521 + 0.974928i) q^{64} +(-6.30011 - 6.22465i) q^{65} +(4.91474 - 3.91937i) q^{66} +(-4.57829 + 3.65107i) q^{67} +(-4.08431 + 1.96690i) q^{68} +(-1.02347 - 0.816188i) q^{69} +(7.47946 + 2.56670i) q^{70} +(3.91813 - 4.91318i) q^{71} +(-0.448598 + 1.96544i) q^{72} +(1.00575 - 4.40648i) q^{73} +(4.36485 - 5.47334i) q^{74} +(-3.91478 - 3.04549i) q^{75} +(-2.30171 - 1.83555i) q^{76} +(20.1909 - 9.72342i) q^{77} +(-3.07179 + 2.44967i) q^{78} +(-2.01282 + 1.60517i) q^{79} +(1.57158 - 1.59064i) q^{80} +(-0.247471 + 1.08424i) q^{81} +(9.27928 - 2.11794i) q^{82} +(2.99634 + 6.22196i) q^{83} +(1.52207 - 3.16062i) q^{84} +(10.0796 + 1.07424i) q^{85} +0.607015 q^{86} +(5.33644 - 0.242843i) q^{87} -6.33703i q^{88} +(2.22074 - 0.506870i) q^{89} +(3.16828 - 3.20669i) q^{90} +(-12.6197 + 6.07730i) q^{91} +(-1.28657 + 0.293650i) q^{92} +(0.557651 + 0.127280i) q^{93} +(-4.26049 - 2.05175i) q^{94} +(2.21162 + 6.20035i) q^{95} +(-0.618488 - 0.775559i) q^{96} +(-6.40893 + 3.08638i) q^{97} +(3.43297 - 4.30481i) q^{98} -12.7753i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 8 q^{2} - 4 q^{3} - 8 q^{4} + 8 q^{5} - 3 q^{6} + 7 q^{7} + 8 q^{8} - 8 q^{9} - q^{10} + 10 q^{12} - 10 q^{15} - 8 q^{16} - 30 q^{17} + 8 q^{18} - 13 q^{20} + 7 q^{21} + 7 q^{23} - 3 q^{24} - 12 q^{25}+ \cdots - 27 q^{98}+O(q^{100}) $ 48 * q + 8 * q^2 - 4 * q^3 - 8 * q^4 + 8 * q^5 - 3 * q^6 + 7 * q^7 + 8 * q^8 - 8 * q^9 - q^10 + 10 * q^12 - 10 * q^15 - 8 * q^16 - 30 * q^17 + 8 * q^18 - 13 * q^20 + 7 * q^21 + 7 * q^23 - 3 * q^24 - 12 * q^25 + 21 * q^26 + 11 * q^27 - 10 * q^29 - 18 * q^30 + 14 * q^31 + 8 * q^32 - 14 * q^33 - 33 * q^34 - q^36 - 44 * q^37 - 28 * q^38 - 14 * q^39 - 8 * q^40 + 7 * q^42 - 8 * q^43 + 14 * q^44 + 25 * q^45 - 6 * q^47 - 4 * q^48 + 27 * q^49 + 5 * q^50 + 24 * q^51 + 77 * q^53 + 10 * q^54 - 32 * q^55 + 10 * q^58 - 24 * q^59 + 4 * q^60 + 56 * q^61 - 8 * q^64 - 34 * q^65 + 42 * q^67 - 2 * q^68 + 28 * q^69 - 30 * q^71 + 22 * q^72 - 29 * q^73 + 44 * q^74 - 32 * q^75 - 28 * q^76 - 30 * q^77 + 14 * q^78 + q^80 - 130 * q^81 - 42 * q^82 - 42 * q^84 + 28 * q^85 - 62 * q^86 + 32 * q^87 + 31 * q^90 - 106 * q^91 - 7 * q^92 - 70 * q^93 + 27 * q^94 + 165 * q^95 + 4 * q^96 - 49 * q^97 - 27 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/290\mathbb{Z}\right)^\times$.

$n$	$31$	$117$
$\chi(n)$	$e\left(\frac{13}{14}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.222521	+	0.974928i	0.157346	+	0.689378i
$2$	0.222521	+	0.974928i	0.157346	+	0.689378i
$3$	−0.893741	−	0.430403i	−0.516001	−	0.248493i	0.157713	−	0.987485i	$-0.449588\pi$
$3$	−0.893741	−	0.430403i	−0.516001	−	0.248493i	−0.673714	+	0.738992i	$0.735302\pi$
$4$	−0.900969	+	0.433884i	−0.450484	+	0.216942i
$5$	2.22348	+	0.236969i	0.994369	+	0.105976i
$5$	2.22348	+	0.236969i	0.994369	+	0.105976i
$6$	0.220736	−	0.967106i	0.0901150	−	0.394819i
$7$	1.53438	−	3.18618i	0.579942	−	1.20426i	−0.380240	−	0.924888i	$-0.624159\pi$
$7$	1.53438	−	3.18618i	0.579942	−	1.20426i	0.960182	−	0.279374i	$-0.0901270\pi$
$8$	−0.623490	−	0.781831i	−0.220437	−	0.276419i
$9$	−1.25694	−	1.57616i	−0.418981	−	0.525386i
$10$	0.263743	+	2.22046i	0.0834028	+	0.702171i
$11$	4.95449	+	3.95107i	1.49383	+	1.19129i	0.931158	+	0.364616i	$0.118800\pi$
$11$	4.95449	+	3.95107i	1.49383	+	1.19129i	0.562676	+	0.826677i	$0.309772\pi$
$12$	0.991977			0.286359
$13$	−3.09664	−	2.46949i	−0.858853	−	0.684912i	0.0915950	−	0.995796i	$-0.470803\pi$
$13$	−3.09664	−	2.46949i	−0.858853	−	0.684912i	−0.950448	+	0.310884i	$0.899375\pi$
$14$	3.44773	+	0.786921i	0.921444	+	0.210313i
$15$	−1.88522	−	1.16878i	−0.486761	−	0.301777i
$16$	0.623490	−	0.781831i	0.155872	−	0.195458i
$17$	4.53324			1.09947			0.549736	−	0.835338i	$-0.314728\pi$
$17$	4.53324			1.09947			0.549736	+	0.835338i	$0.314728\pi$
$18$	1.25694	−	1.57616i	0.296264	−	0.371504i
$19$	1.27735	+	2.65245i	0.293045	+	0.608514i	0.994563	−	0.104138i	$-0.0332083\pi$
$19$	1.27735	+	2.65245i	0.293045	+	0.608514i	−0.701518	+	0.712652i	$0.747494\pi$
$20$	−2.10610	+	0.751229i	−0.470938	+	0.167980i
$21$	−2.74268	+	2.18721i	−0.598502	+	0.477289i
$22$	−2.74953	+	5.70946i	−0.586202	+	1.21726i
$23$	1.28657	+	0.293650i	0.268267	+	0.0612303i	0.354538	−	0.935041i	$-0.384638\pi$
$23$	1.28657	+	0.293650i	0.268267	+	0.0612303i	−0.0862711	+	0.996272i	$0.527495\pi$
$24$	0.220736	+	0.967106i	0.0450575	+	0.197410i
$25$	4.88769	+	1.05379i	0.977538	+	0.210758i
$26$	1.71850	−	3.56851i	0.337026	−	0.699843i
$27$	1.10721	+	4.85099i	0.213082	+	0.933573i
$28$			3.53639i			0.668315i
$29$	−4.74063	+	2.55468i	−0.880313	+	0.474393i
$29$	−4.74063	+	2.55468i	−0.880313	+	0.474393i
$30$	0.719974	−	2.09803i	0.131449	−	0.383046i
$31$	−0.562161	+	0.128310i	−0.100967	+	0.0230451i	−0.272706	−	0.962097i	$-0.587919\pi$
$31$	−0.562161	+	0.128310i	−0.100967	+	0.0230451i	0.171739	+	0.985143i	$0.445061\pi$
$32$	0.900969	+	0.433884i	0.159270	+	0.0767005i
$33$	−2.72747	−	5.66366i	−0.474792	−	0.985916i
$34$	1.00874	+	4.41958i	0.172998	+	0.757952i
$35$	4.16669	−	6.72079i	0.704299	−	1.13602i
$36$	1.81634	+	0.874701i	0.302723	+	0.145784i
$37$	−4.36485	−	5.47334i	−0.717576	−	0.899812i	0.280622	−	0.959818i	$-0.409459\pi$
$37$	−4.36485	−	5.47334i	−0.717576	−	0.899812i	−0.998198	+	0.0600064i	$0.980888\pi$
$38$	−2.30171	+	1.83555i	−0.373387	+	0.297766i
$39$	1.70472	+	3.53988i	0.272973	+	0.566835i
$40$	−1.20105	−	1.88613i	−0.189902	−	0.298224i
$41$		−	9.51792i		−	1.48645i	−0.669042	−	0.743225i	$-0.733295\pi$
$41$		−	9.51792i		−	1.48645i	0.669042	−	0.743225i	$-0.266705\pi$
$42$	−2.74268	−	2.18721i	−0.423205	−	0.337494i
$43$	0.135073	−	0.591795i	0.0205985	−	0.0902480i	−0.963584	−	0.267406i	$-0.913833\pi$
$43$	0.135073	−	0.591795i	0.0205985	−	0.0902480i	0.984182	+	0.177158i	$0.0566905\pi$
$44$	−6.17815	−	1.41012i	−0.931390	−	0.212584i
$45$	−2.42128	−	3.80240i	−0.360944	−	0.566829i
$46$			1.31965i			0.194572i
$47$	−2.94835	+	3.69712i	−0.430061	+	0.539280i	−0.948894	−	0.315596i	$-0.897796\pi$
$47$	−2.94835	+	3.69712i	−0.430061	+	0.539280i	0.518832	+	0.854876i	$0.326367\pi$
$48$	−0.893741	+	0.430403i	−0.129000	+	0.0621233i
$49$	−3.43297	−	4.30481i	−0.490424	−	0.614973i
$50$	0.0602468	+	4.99964i	0.00852018	+	0.707055i
$51$	−4.05154	−	1.95112i	−0.567329	−	0.273211i
$52$	3.86144	+	0.881350i	0.535486	+	0.122221i
$53$	−11.0126	+	2.51355i	−1.51270	+	0.345263i	−0.896755	−	0.442528i	$-0.854082\pi$
$53$	−11.0126	+	2.51355i	−1.51270	+	0.345263i	−0.615942	+	0.787791i	$0.711225\pi$
$54$	−4.48299	+	2.15889i	−0.610057	+	0.293788i
$55$	10.0799	+	9.95917i	1.35917	+	1.34289i
$56$	−3.44773	+	0.786921i	−0.460722	+	0.105157i
$57$		−	2.92038i		−	0.386814i
$58$	−3.54552	−	4.05330i	−0.465550	−	0.532225i
$59$	−0.894046			−0.116395			−0.0581974	−	0.998305i	$-0.518535\pi$
$59$	−0.894046			−0.116395			−0.0581974	+	0.998305i	$0.518535\pi$
$60$	2.20564	+	0.235067i	0.284747	+	0.0303471i
$61$	−3.29299	+	6.83797i	−0.421624	+	0.875512i	0.576661	+	0.816983i	$0.304355\pi$
$61$	−3.29299	+	6.83797i	−0.421624	+	0.875512i	−0.998286	+	0.0585287i	$0.981359\pi$
$62$	−0.250185	−	0.519515i	−0.0317735	−	0.0659784i
$63$	−6.95055	+	1.58642i	−0.875687	+	0.199870i
$64$	−0.222521	+	0.974928i	−0.0278151	+	0.121866i
$65$	−6.30011	−	6.22465i	−0.781433	−	0.772073i
$66$	4.91474	−	3.91937i	0.604963	−	0.482442i
$67$	−4.57829	+	3.65107i	−0.559327	+	0.446049i	−0.861900	−	0.507077i	$-0.830726\pi$
$67$	−4.57829	+	3.65107i	−0.559327	+	0.446049i	0.302573	+	0.953126i	$0.402154\pi$
$68$	−4.08431	+	1.96690i	−0.495295	+	0.238522i
$69$	−1.02347	−	0.816188i	−0.123211	−	0.0982575i
$70$	7.47946	+	2.56670i	0.893967	+	0.306780i
$71$	3.91813	−	4.91318i	0.464997	−	0.583087i	−0.492941	−	0.870062i	$-0.664078\pi$
$71$	3.91813	−	4.91318i	0.464997	−	0.583087i	0.957938	+	0.286975i	$0.0926498\pi$
$72$	−0.448598	+	1.96544i	−0.0528678	+	0.231629i
$73$	1.00575	−	4.40648i	0.117714	−	0.515740i	−0.881349	−	0.472466i	$-0.843364\pi$
$73$	1.00575	−	4.40648i	0.117714	−	0.515740i	0.999063	−	0.0432740i	$-0.0137788\pi$
$74$	4.36485	−	5.47334i	0.507403	−	0.636263i
$75$	−3.91478	−	3.04549i	−0.452039	−	0.351663i
$76$	−2.30171	−	1.83555i	−0.264024	−	0.210552i
$77$	20.1909	−	9.72342i	2.30097	−	1.10809i
$78$	−3.07179	+	2.44967i	−0.347812	+	0.277371i
$79$	−2.01282	+	1.60517i	−0.226460	+	0.180595i	−0.730146	−	0.683291i	$-0.760548\pi$
$79$	−2.01282	+	1.60517i	−0.226460	+	0.180595i	0.503687	+	0.863886i	$0.331977\pi$
$80$	1.57158	−	1.59064i	0.175708	−	0.177839i
$81$	−0.247471	+	1.08424i	−0.0274968	+	0.120471i
$82$	9.27928	−	2.11794i	1.02473	−	0.233887i
$83$	2.99634	+	6.22196i	0.328891	+	0.682949i	0.998196	−	0.0600387i	$-0.0191224\pi$
$83$	2.99634	+	6.22196i	0.328891	+	0.682949i	−0.669305	+	0.742988i	$0.733408\pi$
$84$	1.52207	−	3.16062i	0.166072	−	0.344851i
$85$	10.0796	+	1.07424i	1.09328	+	0.116517i
$86$	0.607015			0.0654561
$87$	5.33644	−	0.242843i	0.572126	−	0.0260355i
$88$		−	6.33703i		−	0.675529i
$89$	2.22074	−	0.506870i	0.235398	−	0.0537281i	−0.103194	−	0.994661i	$-0.532906\pi$
$89$	2.22074	−	0.506870i	0.235398	−	0.0537281i	0.338592	+	0.940933i	$0.390049\pi$
$90$	3.16828	−	3.20669i	0.333966	−	0.338015i
$91$	−12.6197	+	6.07730i	−1.32290	+	0.637074i
$92$	−1.28657	+	0.293650i	−0.134134	+	0.0306151i
$93$	0.557651	+	0.127280i	0.0578257	+	0.0131983i
$94$	−4.26049	−	2.05175i	−0.439436	−	0.211621i
$95$	2.21162	+	6.20035i	0.226907	+	0.636143i
$96$	−0.618488	−	0.775559i	−0.0631241	−	0.0791552i
$97$	−6.40893	+	3.08638i	−0.650728	+	0.313374i	−0.729968	−	0.683482i	$-0.760465\pi$
$97$	−6.40893	+	3.08638i	−0.650728	+	0.313374i	0.0792399	+	0.996856i	$0.474751\pi$
$98$	3.43297	−	4.30481i	0.346782	−	0.434851i
$99$		−	12.7753i		−	1.28397i
$100$	−4.86088	+	1.17126i	−0.486088	+	0.117126i
$101$	−11.1260	−	2.53944i	−1.10708	−	0.252684i	−0.370365	−	0.928886i	$-0.620767\pi$
$101$	−11.1260	−	2.53944i	−1.10708	−	0.252684i	−0.736716	+	0.676203i	$0.763624\pi$
$102$	1.00065	−	4.38413i	0.0990789	−	0.434093i
$103$	−6.60262	−	5.26541i	−0.650575	−	0.518816i	0.241675	−	0.970357i	$-0.422303\pi$
$103$	−6.60262	−	5.26541i	−0.650575	−	0.518816i	−0.892250	+	0.451541i	$0.850875\pi$
$104$			3.96075i			0.388383i
$105$	−6.61658	+	4.21329i	−0.645712	+	0.411175i
$106$	−4.90107	−	10.1772i	−0.476034	−	0.988495i
$107$	−7.09658	+	5.65933i	−0.686052	+	0.547108i	−0.903301	−	0.429008i	$-0.858863\pi$
$107$	−7.09658	+	5.65933i	−0.686052	+	0.547108i	0.217249	+	0.976116i	$0.430292\pi$
$108$	−3.10232	−	3.89019i	−0.298521	−	0.374334i
$109$	15.4390	+	7.43501i	1.47878	+	0.712145i	0.987318	−	0.158752i	$-0.0507471\pi$
$109$	15.4390	+	7.43501i	1.47878	+	0.712145i	0.491465	+	0.870897i	$0.336461\pi$
$110$	−7.46648	+	12.0433i	−0.711901	+	1.14828i
$111$	1.54530	+	6.77039i	0.146673	+	0.642617i
$112$	−1.53438	−	3.18618i	−0.144986	−	0.301066i
$113$	10.6158	+	5.11229i	0.998649	+	0.480924i	0.860480	−	0.509485i	$-0.170164\pi$
$113$	10.6158	+	5.11229i	0.998649	+	0.480924i	0.138169	+	0.990409i	$0.455878\pi$
$114$	2.84716	−	0.649846i	0.266661	−	0.0608636i
$115$	2.79106	+	0.957799i	0.260268	+	0.0893153i
$116$	3.16273	−	4.35857i	0.293652	−	0.404683i
$117$			7.98479i			0.738195i
$118$	−0.198944	−	0.871630i	−0.0183143	−	0.0802401i
$119$	6.95572	−	14.4437i	0.637630	−	1.32405i
$120$	0.261627	+	2.20265i	0.0238832	+	0.201073i
$121$	6.48825	+	28.4269i	0.589841	+	2.58426i
$122$	−7.39928	−	1.68884i	−0.669900	−	0.152900i
$123$	−4.09654	+	8.50655i	−0.369372	+	0.767010i
$124$	0.450818	−	0.359515i	0.0404846	−	0.0322854i
$125$	10.6180	+	3.50130i	0.949698	+	0.313166i
$126$	−3.09329	−	6.42327i	−0.275572	−	0.572231i
$127$	−8.27480	+	10.3763i	−0.734270	+	0.920745i	−0.999051	−	0.0435636i	$-0.986129\pi$
$127$	−8.27480	+	10.3763i	−0.734270	+	0.920745i	0.264781	+	0.964309i	$0.414700\pi$
$128$	−1.00000			−0.0883883
$129$	−0.375431	+	0.470776i	−0.0330549	+	0.0414495i
$130$	4.66668	−	7.52727i	0.409295	−	0.660185i
$131$	17.8759	+	4.08005i	1.56182	+	0.356475i	0.914128	−	0.405426i	$-0.132877\pi$
$131$	17.8759	+	4.08005i	1.56182	+	0.356475i	0.647693	+	0.761901i	$0.275734\pi$
$132$	4.91474	+	3.91937i	0.427773	+	0.341138i
$133$	10.4111			0.902759
$134$	−4.57829	−	3.65107i	−0.395504	−	0.315404i
$135$	1.31232	+	11.0484i	0.112946	+	0.950897i
$136$	−2.82643	−	3.54423i	−0.242364	−	0.303915i
$137$	−13.5970	−	17.0501i	−1.16167	−	1.45669i	−0.865042	−	0.501699i	$-0.832708\pi$
$137$	−13.5970	−	17.0501i	−1.16167	−	1.45669i	−0.296630	−	0.954992i	$-0.595863\pi$
$138$	0.567982	−	1.17943i	0.0483498	−	0.100399i
$139$	1.89743	−	8.31319i	0.160938	−	0.705115i	−0.828480	−	0.560019i	$-0.810794\pi$
$139$	1.89743	−	8.31319i	0.160938	−	0.705115i	0.989418	−	0.145096i	$-0.0463492\pi$
$140$	−0.838013	+	7.86308i	−0.0708250	+	0.664552i
$141$	4.22631	−	2.03528i	0.355920	−	0.171402i
$142$	5.66186	+	2.72661i	0.475133	+	0.228812i
$143$	−5.58514	−	24.4701i	−0.467053	−	2.04629i
$144$	−2.01598			−0.167998
$145$	−11.1461	+	4.55690i	−0.925630	+	0.378430i
$146$	4.51980			0.374062
$147$	1.21538	+	5.32494i	0.100243	+	0.439194i
$148$	6.30738	+	3.03748i	0.518464	+	0.249679i
$149$	−11.0804	+	5.33606i	−0.907746	+	0.437147i	−0.828680	−	0.559722i	$-0.810908\pi$
$149$	−11.0804	+	5.33606i	−0.907746	+	0.437147i	−0.0790653	+	0.996869i	$0.525194\pi$
$150$	2.09801	−	4.49431i	0.171302	−	0.366959i
$151$	−5.32613	+	23.3353i	−0.433435	+	1.89900i	0.00449027	+	0.999990i	$0.498571\pi$
$151$	−5.32613	+	23.3353i	−0.433435	+	1.89900i	−0.437925	+	0.899012i	$0.644286\pi$
$152$	1.27735	−	2.65245i	0.103607	−	0.215142i
$153$	−5.69803	−	7.14510i	−0.460658	−	0.577647i
$154$	13.9725	+	17.5210i	1.12594	+	1.41188i
$155$	−1.28036	+	0.152079i	−0.102841	+	0.0122153i
$156$	−3.07179	−	2.44967i	−0.245940	−	0.196131i
$157$	8.14461			0.650010			0.325005	−	0.945712i	$-0.394634\pi$
$157$	8.14461			0.650010			0.325005	+	0.945712i	$0.394634\pi$
$158$	−2.01282	−	1.60517i	−0.160131	−	0.127700i
$159$	10.9243	+	2.49339i	0.866349	+	0.197739i
$160$	1.90047	+	1.17823i	0.150245	+	0.0931474i
$161$	2.90970	−	3.64865i	0.229317	−	0.287554i
$162$	−1.11212			−0.0873767
$163$	−4.98364	+	6.24928i	−0.390348	+	0.489481i	−0.937712	−	0.347413i	$-0.887060\pi$
$163$	−4.98364	+	6.24928i	−0.390348	+	0.489481i	0.547364	+	0.836895i	$0.315631\pi$
$164$	4.12967	+	8.57535i	0.322473	+	0.669622i
$165$	−4.72237	−	13.2393i	−0.367636	−	1.03068i
$166$	−5.39921	+	4.30573i	−0.419060	+	0.334189i
$167$	−1.72597	+	3.58402i	−0.133560	+	0.277340i	−0.957013	−	0.290044i	$-0.906330\pi$
$167$	−1.72597	+	3.58402i	−0.133560	+	0.277340i	0.823454	+	0.567384i	$0.192044\pi$
$168$	3.42007	+	0.780608i	0.263864	+	0.0602252i
$169$	0.598032	+	2.62015i	0.0460025	+	0.201550i
$170$	1.19561	+	10.0659i	0.0916991	+	0.772018i
$171$	2.57512	−	5.34729i	0.196924	−	0.408918i
$172$	0.135073	+	0.591795i	0.0102993	+	0.0451240i
$173$			13.4871i			1.02541i	0.858566	+	0.512703i	$0.171356\pi$
$173$			13.4871i			1.02541i	−0.858566	+	0.512703i	$0.828644\pi$
$174$	1.42422	+	5.14861i	0.107970	+	0.390315i
$175$	10.8571	−	13.9561i	0.820723	−	1.05499i
$176$	6.17815	−	1.41012i	0.465695	−	0.106292i
$177$	0.799045	+	0.384800i	0.0600599	+	0.0289233i
$178$	0.988323	+	2.05227i	0.0740779	+	0.153824i
$179$	−4.07599	−	17.8581i	−0.304654	−	1.33478i	−0.863015	−	0.505178i	$-0.831427\pi$
$179$	−4.07599	−	17.8581i	−0.304654	−	1.33478i	0.558361	−	0.829598i	$-0.311430\pi$
$180$	3.83130	+	2.37529i	0.285569	+	0.177044i
$181$	−2.51845	−	1.21282i	−0.187195	−	0.0901484i	0.337939	−	0.941168i	$-0.390270\pi$
$181$	−2.51845	−	1.21282i	−0.187195	−	0.0901484i	−0.525134	+	0.851020i	$0.675985\pi$
$182$	−8.73307	−	10.9509i	−0.647338	−	0.811736i
$183$	5.88616	−	4.69406i	0.435118	−	0.346995i
$184$	−0.572575	−	1.18897i	−0.0422108	−	0.0876517i
$185$	−8.40812	−	13.2042i	−0.618177	−	0.970790i
$186$			0.571992i			0.0419405i
$187$	22.4599	+	17.9112i	1.64243	+	1.30979i
$188$	1.05226	−	4.61023i	0.0767436	−	0.336236i
$189$	17.1550	+	3.91551i	1.24784	+	0.284812i
$190$	−5.55277	+	3.53588i	−0.402840	+	0.256519i
$191$		−	3.22743i		−	0.233529i	−0.993160	−	0.116764i	$-0.962748\pi$
$191$		−	3.22743i		−	0.233529i	0.993160	−	0.116764i	$-0.0372522\pi$
$192$	0.618488	−	0.775559i	0.0446355	−	0.0559712i
$193$	−3.05193	+	1.46973i	−0.219683	+	0.105794i	−0.540489	−	0.841351i	$-0.681761\pi$
$193$	−3.05193	+	1.46973i	−0.219683	+	0.105794i	0.320806	+	0.947145i	$0.396046\pi$
$194$	−4.43511	−	5.56146i	−0.318423	−	0.399289i
$195$	2.95156	+	8.27481i	0.211365	+	0.592571i
$196$	4.96079	+	2.38899i	0.354342	+	0.170642i
$197$	−8.67021	−	1.97892i	−0.617727	−	0.140992i	−0.0978045	−	0.995206i	$-0.531182\pi$
$197$	−8.67021	−	1.97892i	−0.617727	−	0.140992i	−0.519922	+	0.854214i	$0.674039\pi$
$198$	12.4550	−	2.84278i	0.885140	−	0.202027i
$199$	5.92732	−	2.85445i	0.420177	−	0.202346i	−0.211835	−	0.977306i	$-0.567944\pi$
$199$	5.92732	−	2.85445i	0.420177	−	0.202346i	0.632011	+	0.774959i	$0.282230\pi$
$200$	−2.22354	−	4.47838i	−0.157228	−	0.316669i
$201$	5.66323	−	1.29260i	0.399454	−	0.0911727i
$202$		−	11.4121i		−	0.802956i
$203$	0.865733	+	19.0244i	0.0607625	+	1.33525i
$204$	4.49687			0.314844
$205$	2.25545	−	21.1629i	0.157527	−	1.47808i
$206$	3.66418	−	7.60874i	0.255295	−	0.530126i
$207$	−1.15430	−	2.39693i	−0.0802295	−	0.166598i
$208$	−3.86144	+	0.881350i	−0.267743	+	0.0611106i
$209$	−4.15139	+	18.1884i	−0.287158	+	1.25812i
$210$	−5.57998	−	5.51315i	−0.385055	−	0.380443i
$211$	9.55111	−	7.61675i	0.657525	−	0.524359i	−0.236924	−	0.971528i	$-0.576139\pi$
$211$	9.55111	−	7.61675i	0.657525	−	0.524359i	0.894449	+	0.447169i	$0.147568\pi$
$212$	8.83142	−	7.04282i	0.606544	−	0.483703i
$213$	−5.61644	+	2.70473i	−0.384832	+	0.185325i
$214$	−7.09658	−	5.65933i	−0.485112	−	0.386864i
$215$	0.440569	−	1.28383i	0.0300466	−	0.0875568i
$216$	3.10232	−	3.89019i	0.211086	−	0.264694i
$217$	−0.453753	+	1.98802i	−0.0308027	+	0.134956i
$218$	−3.81311	+	16.7063i	−0.258256	+	1.13149i
$219$	−2.79544	+	3.50537i	−0.188899	+	0.236871i
$220$	−13.4028	−	4.59940i	−0.903617	−	0.310091i
$221$	−14.0378	−	11.1948i	−0.944285	−	0.753042i
$222$	−6.25678	+	3.01311i	−0.419928	+	0.202227i
$223$	−4.11429	+	3.28104i	−0.275513	+	0.219715i	−0.751492	−	0.659742i	$-0.770665\pi$
$223$	−4.11429	+	3.28104i	−0.275513	+	0.219715i	0.475979	+	0.879457i	$0.342094\pi$
$224$	2.76486	−	2.20490i	0.184735	−	0.147321i
$225$	−4.48262	−	9.02832i	−0.298841	−	0.601888i
$226$	−2.62188	+	11.4872i	−0.174405	+	0.764118i
$227$	27.4631	−	6.26826i	1.82279	−	0.416039i	0.832378	−	0.554208i	$-0.186979\pi$
$227$	27.4631	−	6.26826i	1.82279	−	0.416039i	0.990409	+	0.138169i	$0.0441217\pi$
$228$	1.26711	+	2.63117i	0.0839161	+	0.174254i
$229$	−4.63438	+	9.62339i	−0.306249	+	0.635932i	−0.996120	−	0.0879998i	$-0.971953\pi$
$229$	−4.63438	+	9.62339i	−0.306249	+	0.635932i	0.689872	+	0.723931i	$0.257667\pi$
$230$	−0.312716	+	2.93421i	−0.0206199	+	0.193476i
$231$	−22.2304			−1.46265
$232$	4.95307	+	2.11356i	0.325185	+	0.138762i
$233$		−	13.7943i		−	0.903696i	−0.892095	−	0.451848i	$-0.850765\pi$
$233$		−	13.7943i		−	0.903696i	0.892095	−	0.451848i	$-0.149235\pi$
$234$	−7.78460	+	1.77678i	−0.508895	+	0.116152i
$235$	−7.43169	+	7.52179i	−0.484790	+	0.490667i
$236$	0.805507	−	0.387912i	0.0524341	−	0.0252509i
$237$	2.48980	−	0.568282i	0.161730	−	0.0369139i
$238$	15.6294	+	3.56730i	1.01310	+	0.231234i
$239$	−23.7017	−	11.4141i	−1.53314	−	0.738320i	−0.538586	−	0.842571i	$-0.681041\pi$
$239$	−23.7017	−	11.4141i	−1.53314	−	0.738320i	−0.994551	+	0.104251i	$0.966756\pi$
$240$	−2.08920	+	0.745202i	−0.134857	+	0.0481026i
$241$	−13.1526	−	16.4929i	−0.847234	−	1.06240i	−0.997279	−	0.0737191i	$-0.976513\pi$
$241$	−13.1526	−	16.4929i	−0.847234	−	1.06240i	0.150045	−	0.988679i	$-0.452058\pi$
$242$	−26.2704	+	12.6511i	−1.68872	+	0.813247i
$243$	9.99480	−	12.5331i	0.641167	−	0.803998i
$244$		−	7.58957i		−	0.485873i
$245$	−6.61303	−	10.3851i	−0.422491	−	0.663483i
$246$	−9.20484	−	2.10094i	−0.586879	−	0.133951i
$247$	2.59469	−	11.3681i	0.165096	−	0.723334i
$248$	0.450818	+	0.359515i	0.0286270	+	0.0228292i
$249$		−	6.85045i		−	0.434130i
$250$	−1.05080	+	11.1308i	−0.0664584	+	0.703977i
$251$	11.5425	+	23.9684i	0.728559	+	1.51287i	0.853720	+	0.520732i	$0.174341\pi$
$251$	11.5425	+	23.9684i	0.728559	+	1.51287i	−0.125161	+	0.992136i	$0.539945\pi$
$252$	5.57391	−	4.44504i	0.351123	−	0.280011i
$253$	5.21404	+	6.53820i	0.327804	+	0.411053i
$254$	−11.9574	−	5.75839i	−0.750276	−	0.361314i
$255$	−8.54615	−	5.29836i	−0.535181	−	0.331796i
$256$	−0.222521	−	0.974928i	−0.0139076	−	0.0609330i
$257$	−1.35126	−	2.80592i	−0.0842893	−	0.175029i	0.854564	−	0.519346i	$-0.173825\pi$
$257$	−1.35126	−	2.80592i	−0.0842893	−	0.175029i	−0.938853	+	0.344318i	$0.888110\pi$
$258$	−0.542514	−	0.261261i	−0.0337754	−	0.0162654i
$259$	−24.1364	+	5.50897i	−1.49976	+	0.342311i
$260$	8.37698	+	2.87470i	0.519518	+	0.178281i
$261$	9.98529	+	4.26089i	0.618074	+	0.263742i
$262$			18.3356i			1.13278i
$263$	1.02780	+	4.50310i	0.0633771	+	0.277673i	0.996680	−	0.0814165i	$-0.0259444\pi$
$263$	1.02780	+	4.50310i	0.0633771	+	0.277673i	−0.933303	+	0.359090i	$0.883087\pi$
$264$	−2.72747	+	5.66366i	−0.167864	+	0.348574i
$265$	−25.0819	+	2.97919i	−1.54077	+	0.183010i
$266$	2.31669	+	10.1501i	0.142046	+	0.622343i
$267$	−2.20292	−	0.502803i	−0.134817	−	0.0307711i
$268$	2.54076	−	5.27594i	0.155202	−	0.322280i
$269$	24.0782	−	19.2017i	1.46807	−	1.17075i	0.519384	−	0.854541i	$-0.326161\pi$
$269$	24.0782	−	19.2017i	1.46807	−	1.17075i	0.948690	−	0.316209i	$-0.102410\pi$
$270$	−10.4794	+	3.73792i	−0.637756	+	0.227482i
$271$	−9.39962	−	19.5185i	−0.570986	−	1.18567i	−0.963943	−	0.266108i	$-0.914262\pi$
$271$	−9.39962	−	19.5185i	−0.570986	−	1.18567i	0.392957	−	0.919557i	$-0.371452\pi$
$272$	2.82643	−	3.54423i	0.171377	−	0.214901i
$273$	13.8944			0.840926
$274$	13.5970	−	17.0501i	0.821427	−	1.03004i
$275$	20.0524	+	24.5326i	1.20921	+	1.47937i
$276$	1.27624	+	0.291294i	0.0768208	+	0.0175339i
$277$	−13.1912	−	10.5196i	−0.792582	−	0.632063i	0.141170	−	0.989985i	$-0.454914\pi$
$277$	−13.1912	−	10.5196i	−0.792582	−	0.632063i	−0.933751	+	0.357923i	$0.883485\pi$
$278$	8.52698			0.511414
$279$	0.908840	+	0.724776i	0.0544109	+	0.0433912i
$280$	−7.85241	+	0.932697i	−0.469271	+	0.0557393i
$281$	4.86195	+	6.09670i	0.290040	+	0.363699i	0.905409	−	0.424541i	$-0.139564\pi$
$281$	4.86195	+	6.09670i	0.290040	+	0.363699i	−0.615369	+	0.788239i	$0.710993\pi$
$282$	2.92470	+	3.66746i	0.174163	+	0.218394i
$283$	2.36786	−	4.91691i	0.140755	−	0.292280i	−0.818660	−	0.574278i	$-0.805283\pi$
$283$	2.36786	−	4.91691i	0.140755	−	0.292280i	0.959415	+	0.281998i	$0.0909971\pi$
$284$	−1.39836	+	6.12664i	−0.0829777	+	0.363549i
$285$	0.692038	−	6.49339i	0.0409928	−	0.384635i
$286$	22.6138	−	10.8902i	1.33718	−	0.643952i
$287$	−30.3258	−	14.6041i	−1.79007	−	0.862054i
$288$	−0.448598	−	1.96544i	−0.0264339	−	0.115814i
$289$	3.55027			0.208840
$290$	−6.92288	−	9.85260i	−0.406525	−	0.578565i
$291$	7.05630			0.413648
$292$	1.00575	+	4.40648i	0.0588571	+	0.257870i
$293$	17.5692	+	8.46086i	1.02640	+	0.494289i	0.869816	−	0.493376i	$-0.164237\pi$
$293$	17.5692	+	8.46086i	1.02640	+	0.494289i	0.156585	+	0.987665i	$0.449952\pi$
$294$	−4.92099	+	2.36982i	−0.286998	+	0.138211i
$295$	−1.98789	−	0.211861i	−0.115739	−	0.0123350i
$296$	−1.55780	+	6.82515i	−0.0905450	+	0.396704i
$297$	−13.6810	+	28.4088i	−0.793850	+	1.64845i
$298$	−7.66791	−	9.61525i	−0.444190	−	0.556997i
$299$	−3.25886	−	4.08648i	−0.188465	−	0.236327i
$300$	4.84848	+	1.04533i	0.279927	+	0.0603523i
$301$	−1.67831	−	1.33841i	−0.0967363	−	0.0771446i
$302$	−23.9354			−1.37733
$303$	8.85079	+	7.05827i	0.508465	+	0.405487i
$304$	2.87019	+	0.655101i	0.164616	+	0.0375726i
$305$	−8.94227	+	14.4237i	−0.512033	+	0.825900i
$306$	5.69803	−	7.14510i	0.325735	−	0.408458i
$307$	0.137900			0.00787034			0.00393517	−	0.999992i	$-0.498747\pi$
$307$	0.137900			0.00787034			0.00393517	+	0.999992i	$0.498747\pi$
$308$	−13.9725	+	17.5210i	−0.796159	+	0.998352i
$309$	3.63478	+	7.54769i	0.206775	+	0.429373i
$310$	−0.433172	−	1.21441i	−0.0246025	−	0.0689741i
$311$	−12.8314	+	10.2327i	−0.727603	+	0.580244i	−0.915679	−	0.401910i	$-0.868346\pi$
$311$	−12.8314	+	10.2327i	−0.727603	+	0.580244i	0.188076	+	0.982154i	$0.439775\pi$
$312$	1.70472	−	3.53988i	0.0965106	−	0.200406i
$313$	24.0830	+	5.49678i	1.36125	+	0.310696i	0.839944	−	0.542673i	$-0.182588\pi$
$313$	24.0830	+	5.49678i	1.36125	+	0.310696i	0.521306	+	0.853370i	$0.325445\pi$
$314$	1.81235	+	7.94041i	0.102277	+	0.448103i
$315$	−15.8303	+	1.88030i	−0.891937	+	0.105943i
$316$	1.11703	−	2.31953i	0.0628378	−	0.130484i
$317$	0.0372518	+	0.163211i	0.00209227	+	0.00916682i	0.975963	−	0.217935i	$-0.0699321\pi$
$317$	0.0372518	+	0.163211i	0.00209227	+	0.00916682i	−0.973871	+	0.227102i	$0.927075\pi$
$318$			11.2052i			0.628356i
$319$	−33.5811	−	6.07343i	−1.88018	−	0.340047i
$320$	−0.725797	+	2.11500i	−0.0405733	+	0.118232i
$321$	8.77829	−	2.00359i	0.489956	−	0.111829i
$322$	4.20464	+	2.02485i	0.234316	+	0.112840i
$323$	5.79055	+	12.0242i	0.322195	+	0.669044i
$324$	−0.247471	−	1.08424i	−0.0137484	−	0.0602356i
$325$	−12.5331	−	15.3333i	−0.695211	−	0.850538i
$326$	−7.20156	−	3.46809i	−0.398858	−	0.192080i
$327$	−10.5984	−	13.2899i	−0.586091	−	0.734935i
$328$	−7.44141	+	5.93432i	−0.410883	+	0.327668i
$329$	7.25577	+	15.0668i	0.400024	+	0.830658i
$330$	11.8566	−	7.55000i	0.652683	−	0.415614i
$331$		−	11.9201i		−	0.655186i	−0.944819	−	0.327593i	$-0.893762\pi$
$331$		−	11.9201i		−	0.655186i	0.944819	−	0.327593i	$-0.106238\pi$
$332$	−5.39921	−	4.30573i	−0.296320	−	0.236308i
$333$	−3.14049	+	13.7594i	−0.172098	+	0.754009i
$334$	−3.87823	−	0.885180i	−0.212207	−	0.0484349i
$335$	−11.0449	+	7.03315i	−0.603448	+	0.384262i
$336$			3.50802i			0.191378i
$337$	−5.61591	+	7.04212i	−0.305918	+	0.383609i	−0.910898	−	0.412632i	$-0.864610\pi$
$337$	−5.61591	+	7.04212i	−0.305918	+	0.383609i	0.604980	+	0.796241i	$0.293181\pi$
$338$	−2.42138	+	1.16608i	−0.131706	+	0.0634262i
$339$	−7.28741	−	9.13813i	−0.395798	−	0.496315i
$340$	−9.54746	+	3.40550i	−0.517784	+	0.184689i
$341$	−3.29218	−	1.58543i	−0.178281	−	0.0858558i
$342$	5.78624	+	1.32067i	0.312884	+	0.0714138i
$343$	5.15070	−	1.17561i	0.278112	−	0.0634772i
$344$	−0.546901	+	0.263374i	−0.0294869	+	0.0142002i
$345$	−2.08225	−	2.05730i	−0.112104	−	0.110762i
$346$	−13.1490	+	3.00116i	−0.706893	+	0.161344i
$347$		−	29.4761i		−	1.58236i	−0.611583	−	0.791180i	$-0.709467\pi$
$347$		−	29.4761i		−	1.58236i	0.611583	−	0.791180i	$-0.290533\pi$
$348$	−4.70260	+	2.53419i	−0.252086	+	0.135847i
$349$	−10.2372			−0.547985			−0.273992	−	0.961732i	$-0.588344\pi$
$349$	−10.2372			−0.547985			−0.273992	+	0.961732i	$0.588344\pi$
$350$	16.0222	+	7.47940i	0.856421	+	0.399791i
$351$	8.55083	−	17.7560i	0.456410	−	0.947744i
$352$	2.74953	+	5.70946i	0.146551	+	0.304315i
$353$	19.9218	−	4.54702i	1.06033	−	0.242014i	0.343423	−	0.939181i	$-0.388414\pi$
$353$	19.9218	−	4.54702i	1.06033	−	0.242014i	0.716909	+	0.697167i	$0.245556\pi$
$354$	−0.197348	+	0.864637i	−0.0104889	+	0.0459549i
$355$	9.87614	−	9.99586i	0.524171	−	0.530525i
$356$	−1.78090	+	1.42022i	−0.0943873	+	0.0752714i
$357$	−12.4332	+	9.91517i	−0.658036	+	0.524766i
$358$	16.5034	−	7.94760i	0.872229	−	0.420043i
$359$	21.0103	+	16.7552i	1.10888	+	0.884305i	0.994033	−	0.109077i	$-0.0347897\pi$
$359$	21.0103	+	16.7552i	1.10888	+	0.884305i	0.114851	+	0.993383i	$0.463361\pi$
$360$	−1.46319	+	4.26380i	−0.0771171	+	0.224722i
$361$	6.44244	−	8.07857i	0.339076	−	0.425188i
$362$	0.622006	−	2.72519i	0.0326919	−	0.143233i
$363$	6.43619	−	28.1988i	0.337813	−	1.48005i
$364$	8.73307	−	10.9509i	0.457737	−	0.573984i
$365$	3.28046	−	9.55938i	0.171707	−	0.500361i
$366$	5.88616	+	4.69406i	0.307675	+	0.245362i
$367$	−0.602074	+	0.289944i	−0.0314280	+	0.0151349i	−0.449532	−	0.893264i	$-0.648409\pi$
$367$	−0.602074	+	0.289944i	−0.0314280	+	0.0151349i	0.418104	+	0.908399i	$0.362695\pi$
$368$	1.03175	−	0.822789i	0.0537834	−	0.0428909i
$369$	−15.0017	+	11.9635i	−0.780959	+	0.622794i
$370$	11.0021	−	11.1355i	0.571974	−	0.578908i
$371$	−8.88891	+	38.9449i	−0.461489	+	2.02192i
$372$	−0.557651	+	0.127280i	−0.0289128	+	0.00659917i
$373$	−7.66435	−	15.9152i	−0.396845	−	0.824057i	−0.999657	−	0.0261740i	$-0.991668\pi$
$373$	−7.66435	−	15.9152i	−0.396845	−	0.824057i	0.602813	−	0.797883i	$-0.294047\pi$
$374$	−12.4643	+	25.8824i	−0.644513	+	1.33835i
$375$	−7.98272	−	7.69925i	−0.412226	−	0.397588i
$376$	4.72879			0.243869
$377$	20.9888	+	3.79600i	1.08098	+	0.195504i
$378$			17.5962i			0.905049i
$379$	27.8274	−	6.35143i	1.42940	−	0.326251i	0.563353	−	0.826216i	$-0.309511\pi$
$379$	27.8274	−	6.35143i	1.42940	−	0.326251i	0.866045	+	0.499965i	$0.166654\pi$
$380$	−4.68283	−	4.62674i	−0.240224	−	0.237347i
$381$	11.8615	−	5.71220i	0.607683	−	0.292645i
$382$	3.14651	−	0.718171i	0.160990	−	0.0367448i
$383$	−11.8180	−	2.69738i	−0.603872	−	0.137830i	−0.0903555	−	0.995910i	$-0.528800\pi$
$383$	−11.8180	−	2.69738i	−0.603872	−	0.137830i	−0.513516	+	0.858080i	$0.671657\pi$
$384$	0.893741	+	0.430403i	0.0456085	+	0.0219639i
$385$	47.1981	−	16.8352i	2.40544	−	0.858001i
$386$	−2.11200	−	2.64837i	−0.107498	−	0.134798i
$387$	−1.10254	+	0.530957i	−0.0560454	+	0.0269900i
$388$	4.43511	−	5.56146i	0.225159	−	0.282340i
$389$		−	13.1845i		−	0.668482i	−0.942488	−	0.334241i	$-0.891520\pi$
$389$		−	13.1845i		−	0.668482i	0.942488	−	0.334241i	$-0.108480\pi$
$390$	−7.41056	+	4.71887i	−0.375248	+	0.238949i
$391$	5.83231	+	1.33119i	0.294953	+	0.0673210i
$392$	−1.22521	+	5.36801i	−0.0618826	+	0.271125i
$393$	−14.2203	−	11.3403i	−0.717320	−	0.572044i
$394$		−	8.89318i		−	0.448032i
$395$	−4.85582	+	3.09208i	−0.244323	+	0.155579i
$396$	5.54301	+	11.5102i	0.278547	+	0.578408i
$397$	3.57200	−	2.84858i	0.179274	−	0.142966i	−0.529742	−	0.848159i	$-0.677711\pi$
$397$	3.57200	−	2.84858i	0.179274	−	0.142966i	0.709015	+	0.705193i	$0.249140\pi$
$398$	4.10183	+	5.14354i	0.205606	+	0.257822i
$399$	−9.30485	−	4.48098i	−0.465825	−	0.224330i
$400$	3.87131	−	3.16433i	0.193566	−	0.158216i
$401$	−3.72824	−	16.3345i	−0.186180	−	0.815706i	−0.978607	−	0.205740i	$-0.934040\pi$
$401$	−3.72824	−	16.3345i	−0.186180	−	0.815706i	0.792427	−	0.609967i	$-0.208817\pi$
$402$	2.52038	+	5.23362i	0.125705	+	0.261029i
$403$	2.05767	+	0.990920i	0.102500	+	0.0493613i
$404$	11.1260	−	2.53944i	0.553540	−	0.126342i
$405$	−0.807176	+	2.35214i	−0.0401089	+	0.116879i
$406$	−18.3547	+	5.07734i	−0.910930	+	0.251984i
$407$		−	44.3634i		−	2.19901i
$408$	1.00065	+	4.38413i	0.0495395	+	0.217047i
$409$	−8.09661	+	16.8128i	−0.400352	+	0.831338i	0.599176	+	0.800617i	$0.295495\pi$
$409$	−8.09661	+	16.8128i	−0.400352	+	0.831338i	−0.999528	+	0.0307215i	$0.990220\pi$
$410$	21.1341	−	2.51028i	1.04374	−	0.123974i
$411$	4.81379	+	21.0906i	0.237447	+	1.04032i
$412$	8.23333	+	1.87920i	0.405627	+	0.0925817i
$413$	−1.37181	+	2.84859i	−0.0675023	+	0.140170i
$414$	2.07998	−	1.65873i	0.102225	−	0.0815220i
$415$	5.18788	+	14.5444i	0.254663	+	0.713957i
$416$	−1.71850	−	3.56851i	−0.0842566	−	0.174961i
$417$	−5.27383	+	6.61317i	−0.258261	+	0.323849i
$418$	−18.6562			−0.912505
$419$	−0.588859	+	0.738406i	−0.0287676	+	0.0360735i	−0.796007	−	0.605287i	$-0.793058\pi$
$419$	−0.588859	+	0.738406i	−0.0287676	+	0.0360735i	0.767240	+	0.641361i	$0.221630\pi$
$420$	4.13326	−	6.66687i	0.201682	−	0.325310i
$421$	−15.3732	−	3.50883i	−0.749243	−	0.171010i	−0.169184	−	0.985584i	$-0.554113\pi$
$421$	−15.3732	−	3.50883i	−0.749243	−	0.171010i	−0.580059	+	0.814575i	$0.696970\pi$
$422$	9.55111	+	7.61675i	0.464941	+	0.370778i
$423$	9.53315			0.463518
$424$	8.83142	+	7.04282i	0.428892	+	0.342030i
$425$	22.1571	+	4.77707i	1.07478	+	0.231722i
$426$	−3.88670	−	4.87376i	−0.188311	−	0.236135i
$427$	16.7343	+	20.9841i	0.809828	+	1.01549i
$428$	3.93830	−	8.17797i	0.190365	−	0.395297i
$429$	−5.54033	+	24.2738i	−0.267490	+	1.17195i
$430$	1.34968	+	0.143843i	0.0650875	+	0.00693674i
$431$	9.79531	−	4.71717i	0.471823	−	0.227218i	−0.182834	−	0.983144i	$-0.558527\pi$
$431$	9.79531	−	4.71717i	0.471823	−	0.227218i	0.654657	+	0.755926i	$0.272813\pi$
$432$	4.48299	+	2.15889i	0.215688	+	0.103870i
$433$	6.11707	+	26.8006i	0.293968	+	1.28796i	0.878951	+	0.476912i	$0.158244\pi$
$433$	6.11707	+	26.8006i	0.293968	+	1.28796i	−0.584983	+	0.811045i	$0.698899\pi$
$434$	−2.03915			−0.0978821
$435$	11.9230	+	0.724613i	0.571664	+	0.0347425i
$436$	−17.1359			−0.820663
$437$	0.864505	+	3.78765i	0.0413549	+	0.181188i
$438$	−4.03953	−	1.94534i	−0.193016	−	0.0929517i
$439$	11.2268	−	5.40653i	0.535825	−	0.258040i	−0.146345	−	0.989234i	$-0.546751\pi$
$439$	11.2268	−	5.40653i	0.535825	−	0.258040i	0.682169	+	0.731194i	$0.261037\pi$
$440$	1.50168	−	14.0902i	0.0715896	−	0.671725i
$441$	−2.47001	+	10.8218i	−0.117619	+	0.515324i
$442$	7.79039	−	16.1769i	0.370551	−	0.769458i
$443$	16.3572	+	20.5113i	0.777156	+	0.974523i	1.00000		0.000331450i	$-0.000105504\pi$
$443$	16.3572	+	20.5113i	0.777156	+	0.974523i	−0.222844	+	0.974854i	$0.571534\pi$
$444$	−4.32983	−	5.42943i	−0.205484	−	0.257669i
$445$	5.05788	−	0.600767i	0.239766	−	0.0284791i
$446$	−4.11429	−	3.28104i	−0.194817	−	0.155362i
$447$	12.1997			0.577026
$448$	2.76486	+	2.20490i	0.130627	+	0.104172i
$449$	10.7698	+	2.45813i	0.508257	+	0.116006i	0.468957	−	0.883221i	$-0.344630\pi$
$449$	10.7698	+	2.45813i	0.508257	+	0.116006i	0.0393002	+	0.999227i	$0.487487\pi$
$450$	7.80449	−	6.37922i	0.367907	−	0.300719i
$451$	37.6060	−	47.1564i	1.77080	−	2.22051i
$452$	−11.7826			−0.554208
$453$	14.8038	−	18.5633i	0.695542	−	0.872182i
$454$	12.2222	+	25.3797i	0.573617	+	1.19113i
$455$	−29.4996	+	10.5223i	−1.38296	+	0.493292i
$456$	−2.28324	+	1.82083i	−0.106923	+	0.0852680i
$457$	−2.40328	+	4.99046i	−0.112421	+	0.233444i	−0.949586	−	0.313505i	$-0.898497\pi$
$457$	−2.40328	+	4.99046i	−0.112421	+	0.233444i	0.837166	+	0.546949i	$0.184211\pi$
$458$	−10.4134	−	2.37678i	−0.486584	−	0.111060i
$459$	5.01923	+	21.9907i	0.234278	+	1.02644i
$460$	−2.93023	+	0.348049i	−0.136623	+	0.0162278i
$461$	−0.158861	+	0.329878i	−0.00739888	+	0.0153639i	−0.904636	−	0.426186i	$-0.859857\pi$
$461$	−0.158861	+	0.329878i	−0.00739888	+	0.0153639i	0.897237	+	0.441550i	$0.145571\pi$
$462$	−4.94673	−	21.6731i	−0.230143	−	1.00832i
$463$		−	4.77114i		−	0.221734i	−0.993835	−	0.110867i	$-0.964637\pi$
$463$		−	4.77114i		−	0.221734i	0.993835	−	0.110867i	$-0.0353627\pi$
$464$	−0.958404	+	5.29919i	−0.0444928	+	0.246009i
$465$	1.20976	+	0.415150i	0.0561013	+	0.0192521i
$466$	13.4485	−	3.06952i	0.622988	−	0.142193i
$467$	−1.23620	−	0.595324i	−0.0572047	−	0.0275483i	0.405063	−	0.914289i	$-0.367250\pi$
$467$	−1.23620	−	0.595324i	−0.0572047	−	0.0275483i	−0.462267	+	0.886741i	$0.652964\pi$
$468$	−3.46447	−	7.19405i	−0.160145	−	0.332545i
$469$	4.60810	+	20.1894i	0.212782	+	0.932259i
$470$	−8.98691	−	5.57161i	−0.414535	−	0.256999i
$471$	−7.27917	−	3.50546i	−0.335406	−	0.161523i
$472$	0.557428	+	0.698993i	0.0256577	+	0.0321738i
$473$	3.00745	−	2.39836i	0.138283	−	0.110277i
$474$	1.10807	+	2.30093i	0.0508952	+	0.105685i
$475$	3.44819	+	14.3104i	0.158214	+	0.656607i
$476$			16.0313i			0.734794i
$477$	17.8040	+	14.1982i	0.815188	+	0.650091i
$478$	5.85384	−	25.6474i	0.267749	−	1.17308i
$479$	18.4057	+	4.20097i	0.840976	+	0.191947i	0.621248	−	0.783614i	$-0.286626\pi$
$479$	18.4057	+	4.20097i	0.840976	+	0.191947i	0.219728	+	0.975561i	$0.429483\pi$
$480$	−1.19141	−	1.87100i	−0.0543802	−	0.0853990i
$481$			27.7279i			1.26428i
$482$	13.1526	−	16.4929i	0.599085	−	0.751229i
$483$	−4.17091	+	2.00861i	−0.189783	+	0.0913947i
$484$	−18.1797	−	22.7966i	−0.826348	−	1.03621i
$485$	−14.9815	+	5.34377i	−0.680273	+	0.242648i
$486$	14.4429	+	6.95534i	0.655144	+	0.315501i
$487$	−14.0692	−	3.21120i	−0.637536	−	0.145513i	−0.108477	−	0.994099i	$-0.534598\pi$
$487$	−14.0692	−	3.21120i	−0.637536	−	0.145513i	−0.529058	+	0.848586i	$0.677455\pi$
$488$	7.39928	−	1.68884i	0.334950	−	0.0764501i
$489$	7.14379	−	3.44027i	0.323053	−	0.155574i
$490$	8.65323	−	8.75814i	0.390913	−	0.395652i
$491$	−33.4574	+	7.63643i	−1.50991	+	0.344627i	−0.895751	−	0.444556i	$-0.853362\pi$
$491$	−33.4574	+	7.63643i	−1.50991	+	0.344627i	−0.614159	+	0.789183i	$0.710504\pi$
$492$		−	9.44156i		−	0.425658i
$493$	−21.4904	+	11.5810i	−0.967880	+	0.521582i
$494$	11.6604			0.524628
$495$	3.02735	−	28.4056i	0.136069	−	1.27674i
$496$	−0.250185	+	0.519515i	−0.0112336	+	0.0233269i
$497$	−9.64236	−	20.0226i	−0.432519	−	0.898134i
$498$	6.67870	−	1.52437i	0.299280	−	0.0683086i
$499$	−1.02908	+	4.50870i	−0.0460680	+	0.201837i	−0.992725	−	0.120407i	$-0.961580\pi$
$499$	−1.02908	+	4.50870i	−0.0460680	+	0.201837i	0.946657	+	0.322244i	$0.104437\pi$
$500$	−11.0856	+	1.45239i	−0.495763	+	0.0649530i
$501$	3.08514	−	2.46032i	0.137834	−	0.109919i
$502$	−20.7990	+	16.5866i	−0.928303	+	0.740297i
$503$	23.7103	−	11.4183i	1.05719	−	0.509115i	0.177232	−	0.984169i	$-0.443286\pi$
$503$	23.7103	−	11.4183i	1.05719	−	0.509115i	0.879957	+	0.475054i	$0.157571\pi$
$504$	5.57391	+	4.44504i	0.248282	+	0.197998i
$505$	−24.1367	−	8.28290i	−1.07407	−	0.368584i
$506$	−5.21404	+	6.53820i	−0.231792	+	0.290658i
$507$	0.593234	−	2.59913i	0.0263464	−	0.115431i
$508$	2.95324	−	12.9390i	0.131029	−	0.574075i
$509$	−22.1498	+	27.7750i	−0.981772	+	1.23110i	−0.00885236	+	0.999961i	$0.502818\pi$
$509$	−22.1498	+	27.7750i	−0.981772	+	1.23110i	−0.972920	+	0.231143i	$0.925754\pi$
$510$	3.26382	−	9.51088i	0.144524	−	0.421149i
$511$	−12.4966	−	9.96573i	−0.552818	−	0.440858i
$512$	0.900969	−	0.433884i	0.0398176	−	0.0191751i
$513$	−11.4527	+	9.13323i	−0.505650	+	0.403242i
$514$	2.43489	−	1.94176i	0.107398	−	0.0856473i
$515$	−13.4330	−	13.2721i	−0.591930	−	0.584840i
$516$	0.133990	−	0.587048i	0.00589857	−	0.0258433i
$517$	−29.2152	+	6.66817i	−1.28488	+	0.293266i
$518$	−10.7417	−	22.3054i	−0.471963	−	0.980042i
$519$	5.80489	−	12.0540i	0.254806	−	0.529111i
$520$	−0.938573	+	8.80663i	−0.0411591	+	0.386196i
$521$	14.8662			0.651298			0.325649	−	0.945491i	$-0.394417\pi$
$521$	14.8662			0.651298			0.325649	+	0.945491i	$0.394417\pi$
$522$	−1.93212	+	10.6831i	−0.0845668	+	0.467586i
$523$			12.9256i			0.565198i	0.959238	+	0.282599i	$0.0911966\pi$
$523$			12.9256i			0.565198i	−0.959238	+	0.282599i	$0.908803\pi$
$524$	−17.8759	+	4.08005i	−0.780911	+	0.178238i
$525$	−15.7102	+	7.80023i	−0.685651	+	0.340430i
$526$	−4.16149	+	2.00407i	−0.181450	+	0.0873815i
$527$	−2.54841	+	0.581658i	−0.111010	+	0.0253374i
$528$	−6.12858	−	1.39881i	−0.266712	−	0.0608753i
$529$	−19.1533	−	9.22373i	−0.832751	−	0.401032i
$530$	−8.48574	−	23.7901i	−0.368597	−	1.03338i
$531$	1.12377	+	1.40916i	0.0487673	+	0.0611522i
$532$	−9.38010	+	4.51722i	−0.406679	+	0.195846i
$533$	−23.5044	+	29.4735i	−1.01809	+	1.27664i
$534$		−	2.25958i		−	0.0977815i
$535$	−17.1201	+	10.9017i	−0.740169	+	0.471322i
$536$	5.70904	+	1.30305i	0.246593	+	0.0562832i
$537$	−4.04329	+	17.7148i	−0.174481	+	0.764451i
$538$	24.0782	+	19.2017i	1.03808	+	0.827845i
$539$		−	34.8920i		−	1.50291i
$540$	−5.97609	−	9.38490i	−0.257170	−	0.403862i
$541$	−10.9737	−	22.7872i	−0.471797	−	0.979697i	−0.992069	−	0.125696i	$-0.959884\pi$
$541$	−10.9737	−	22.7872i	−0.471797	−	0.979697i	0.520272	−	0.854001i	$-0.325831\pi$
$542$	16.9375	−	13.5072i	0.727529	−	0.580185i
$543$	1.72884	+	2.16790i	0.0741917	+	0.0930334i
$544$	4.08431	+	1.96690i	0.175113	+	0.0843301i
$545$	32.5663	+	20.1901i	1.39499	+	0.864849i
$546$	3.09179	+	13.5460i	0.132316	+	0.579716i
$547$	−5.47777	−	11.3747i	−0.234212	−	0.486347i	0.750426	−	0.660955i	$-0.229849\pi$
$547$	−5.47777	−	11.3747i	−0.234212	−	0.486347i	−0.984638	+	0.174608i	$0.944134\pi$
$548$	19.6483	+	9.46211i	0.839333	+	0.404201i
$549$	14.9168	−	3.40467i	0.636634	−	0.145308i
$550$	−19.4554	+	25.0087i	−0.829583	+	1.06637i
$551$	−12.8316	−	9.31106i	−0.546646	−	0.396665i
$552$			1.30906i			0.0557175i
$553$	2.02592	+	8.87613i	0.0861509	+	0.377452i
$554$	7.32056	−	15.2013i	0.311021	−	0.645841i
$555$	1.83156	+	15.4200i	0.0777455	+	0.654542i
$556$	1.89743	+	8.31319i	0.0804690	+	0.352558i
$557$	29.7439	+	6.78885i	1.26029	+	0.287653i	0.799937	−	0.600084i	$-0.204866\pi$
$557$	29.7439	+	6.78885i	1.26029	+	0.287653i	0.460352	+	0.887737i	$0.347723\pi$
$558$	−0.504368	+	1.04733i	−0.0213516	+	0.0443371i
$559$	−1.87970	+	1.49901i	−0.0795030	+	0.0634016i
$560$	−2.65664	−	7.44799i	−0.112263	−	0.314735i
$561$	−12.3643	−	25.6747i	−0.522021	−	1.08399i
$562$	−4.86195	+	6.09670i	−0.205089	+	0.257174i
$563$	−11.8127			−0.497846			−0.248923	−	0.968523i	$-0.580077\pi$
$563$	−11.8127			−0.497846			−0.248923	+	0.968523i	$0.580077\pi$
$564$	−2.92470	+	3.66746i	−0.123152	+	0.154428i
$565$	22.3925	+	13.8827i	0.942059	+	0.584048i
$566$	5.32054	+	1.21438i	0.223639	+	0.0510441i
$567$	3.07487	+	2.45213i	0.129132	+	0.102980i
$568$	−6.28419			−0.263679
$569$	11.3249	+	9.03132i	0.474765	+	0.378613i	0.831439	−	0.555616i	$-0.187518\pi$
$569$	11.3249	+	9.03132i	0.474765	+	0.378613i	−0.356673	+	0.934229i	$0.616089\pi$
$570$	6.48458	−	0.770229i	0.271609	−	0.0322613i
$571$	−1.31792	−	1.65262i	−0.0551532	−	0.0691599i	0.753490	−	0.657460i	$-0.228369\pi$
$571$	−1.31792	−	1.65262i	−0.0551532	−	0.0691599i	−0.808643	+	0.588300i	$0.799798\pi$
$572$	15.6492	+	19.6235i	0.654326	+	0.820499i
$573$	−1.38910	+	2.88449i	−0.0580303	+	0.120501i
$574$	7.48985	−	32.8152i	0.312620	−	1.36968i
$575$	5.97889	+	2.79104i	0.249337	+	0.116394i
$576$	1.81634	−	0.874701i	0.0756807	−	0.0364459i
$577$	17.7651	+	8.55524i	0.739572	+	0.356159i	0.765441	−	0.643506i	$-0.222521\pi$
$577$	17.7651	+	8.55524i	0.739572	+	0.356159i	−0.0258688	+	0.999665i	$0.508235\pi$
$578$	0.790010	+	3.46126i	0.0328601	+	0.143969i
$579$	3.36021			0.139646
$580$	8.06509	−	8.94172i	0.334885	−	0.371285i
$581$	24.4218			1.01319
$582$	1.57017	+	6.87939i	0.0650858	+	0.285160i
$583$	−64.4930	−	31.0582i	−2.67103	−	1.28630i
$584$	−4.07220	+	1.96107i	−0.168509	+	0.0811496i
$585$	−1.89214	+	17.7540i	−0.0782306	+	0.734038i
$586$	−4.33922	+	19.0114i	−0.179252	+	0.785353i
$587$	−18.8257	+	39.0920i	−0.777021	+	1.61350i	0.0126119	+	0.999920i	$0.495985\pi$
$587$	−18.8257	+	39.0920i	−0.777021	+	1.61350i	−0.789633	+	0.613580i	$0.789729\pi$
$588$	−3.40543	−	4.27027i	−0.140438	−	0.176103i
$589$	−1.05841	−	1.32721i	−0.0436111	−	0.0546866i
$590$	−0.235798	−	1.98519i	−0.00970765	−	0.0817291i
$591$	6.89719	+	5.50032i	0.283712	+	0.226253i
$592$	−7.00067			−0.287726
$593$	−12.1376	−	9.67945i	−0.498433	−	0.397487i	0.341749	−	0.939791i	$-0.388981\pi$
$593$	−12.1376	−	9.67945i	−0.498433	−	0.397487i	−0.840182	+	0.542304i	$0.817552\pi$
$594$	−30.7408	−	7.01640i	−1.26131	−	0.287886i
$595$	18.8886	−	30.4670i	0.774357	−	1.24902i
$596$	7.66791	−	9.61525i	0.314090	−	0.393856i
$597$	−6.52605			−0.267093
$598$	3.25886	−	4.08648i	0.133265	−	0.167109i
$599$	−3.83434	−	7.96209i	−0.156667	−	0.325322i	0.807830	−	0.589415i	$-0.200642\pi$
$599$	−3.83434	−	7.96209i	−0.156667	−	0.325322i	−0.964497	+	0.264093i	$0.914927\pi$
$600$	0.0597634	+	4.95953i	0.00243983	+	0.202472i
$601$	20.9343	−	16.6945i	0.853926	−	0.680983i	−0.0953443	−	0.995444i	$-0.530395\pi$
$601$	20.9343	−	16.6945i	0.853926	−	0.680983i	0.949270	+	0.314461i	$0.101824\pi$
$602$	0.931393	−	1.93406i	0.0379607	−	0.0788263i
$603$	11.5093	+	2.62693i	0.468695	+	0.106977i
$604$	−5.32613	−	23.3353i	−0.216717	−	0.949501i
$605$	7.69019	+	64.7440i	0.312651	+	2.63222i
$606$	−4.91182	+	10.1995i	−0.199529	+	0.414326i
$607$	5.44215	+	23.8436i	0.220890	+	0.967783i	0.956810	+	0.290714i	$0.0938929\pi$
$607$	5.44215	+	23.8436i	0.220890	+	0.967783i	−0.735920	+	0.677069i	$0.763250\pi$
$608$			2.94400i			0.119395i
$609$	7.41440	−	17.3755i	0.300447	−	0.704089i
$610$	−16.0519	−	5.50849i	−0.649924	−	0.223032i
$611$	18.2600	−	4.16772i	0.738719	−	0.168608i
$612$	8.23389	+	3.96523i	0.332835	+	0.160285i
$613$	4.15361	+	8.62506i	0.167763	+	0.348363i	0.967853	−	0.251517i	$-0.0809294\pi$
$613$	4.15361	+	8.62506i	0.167763	+	0.348363i	−0.800090	+	0.599880i	$0.795215\pi$
$614$	0.0306855	+	0.134442i	0.00123837	+	0.00542564i
$615$	−11.1243	+	17.9434i	−0.448577	+	0.723546i
$616$	−20.1909	−	9.72342i	−0.813514	−	0.391768i
$617$	−8.63777	−	10.8314i	−0.347743	−	0.436056i	0.576944	−	0.816784i	$-0.304245\pi$
$617$	−8.63777	−	10.8314i	−0.347743	−	0.436056i	−0.924687	+	0.380727i	$0.875674\pi$
$618$	−6.54964	+	5.22317i	−0.263465	+	0.210107i
$619$	−17.8500	−	37.0660i	−0.717454	−	1.48981i	−0.865543	−	0.500834i	$-0.833027\pi$
$619$	−17.8500	−	37.0660i	−0.717454	−	1.48981i	0.148089	−	0.988974i	$-0.452688\pi$
$620$	1.08758	−	0.692544i	0.0436781	−	0.0278132i
$621$			6.56624i			0.263494i
$622$	−12.8314	−	10.2327i	−0.514493	−	0.410294i
$623$	1.79249	−	7.85341i	0.0718146	−	0.314640i
$624$	3.83047	+	0.874279i	0.153341	+	0.0349992i
$625$	22.7791	+	10.3012i	0.911163	+	0.412047i
$626$			24.7023i			0.987303i
$627$	11.5386	−	14.4690i	0.460808	−	0.577836i
$628$	−7.33804	+	3.53381i	−0.292820	+	0.141014i
$629$	−19.7869	−	24.8120i	−0.788955	−	0.989318i
$630$	−5.35573	−	15.0150i	−0.213378	−	0.598212i
$631$	−12.4176	−	5.97999i	−0.494336	−	0.238060i	0.170069	−	0.985432i	$-0.445601\pi$
$631$	−12.4176	−	5.97999i	−0.494336	−	0.238060i	−0.664405	+	0.747372i	$0.731315\pi$
$632$	2.50994	+	0.572878i	0.0998401	+	0.0227879i
$633$	−11.8145	+	2.69658i	−0.469583	+	0.107179i
$634$	−0.150829	+	0.0726356i	−0.00599020	+	0.00288473i
$635$	−20.8577	+	21.1105i	−0.827711	+	0.837745i
$636$	−10.9243	+	2.49339i	−0.433175	+	0.0988693i
$637$			21.8081i			0.864069i
$638$	−1.55135	−	34.0907i	−0.0614184	−	1.34966i
$639$	−12.6688			−0.501171
$640$	−2.22348	−	0.236969i	−0.0878906	−	0.00936700i
$641$	14.2991	−	29.6924i	0.564780	−	1.17278i	−0.401637	−	0.915799i	$-0.631559\pi$
$641$	14.2991	−	29.6924i	0.564780	−	1.17278i	0.966417	−	0.256979i	$-0.0827271\pi$
$642$	3.90671	+	8.11236i	0.154185	+	0.320169i
$643$	−32.5671	+	7.43322i	−1.28432	+	0.293138i	−0.809591	−	0.586994i	$-0.800311\pi$
$643$	−32.5671	+	7.43322i	−1.28432	+	0.293138i	−0.474729	+	0.880132i	$0.657454\pi$
$644$	−1.03846	+	4.54980i	−0.0409211	+	0.179287i
$645$	−0.946321	+	0.957793i	−0.0372614	+	0.0377131i
$646$	−10.4342	+	8.32100i	−0.410528	+	0.327385i
$647$	32.1793	−	25.6621i	1.26510	−	1.00888i	0.266109	−	0.963943i	$-0.414262\pi$
$647$	32.1793	−	25.6621i	1.26510	−	1.00888i	0.998990	−	0.0449392i	$-0.0143094\pi$
$648$	1.00199	−	0.482532i	0.0393618	−	0.0189557i
$649$	−4.42954	−	3.53244i	−0.173875	−	0.138660i
$650$	12.1600	−	15.6308i	0.476953	−	0.613092i
$651$	1.26119	−	1.58148i	0.0494298	−	0.0619830i
$652$	1.77864	−	7.79273i	0.0696569	−	0.305187i
$653$	1.26971	−	5.56295i	0.0496875	−	0.217695i	−0.943989	−	0.329977i	$-0.892959\pi$
$653$	1.26971	−	5.56295i	0.0496875	−	0.217695i	0.993676	+	0.112282i	$0.0358161\pi$
$654$	10.5984	−	13.2899i	0.414429	−	0.519678i
$655$	38.7797	+	13.3079i	1.51525	+	0.519983i
$656$	−7.44141	−	5.93432i	−0.290538	−	0.231696i
$657$	−8.20948	+	3.95348i	−0.320282	+	0.154240i
$658$	−13.0745	+	10.4265i	−0.509695	+	0.406468i
$659$	−8.82344	+	7.03645i	−0.343712	+	0.274101i	−0.780097	−	0.625659i	$-0.784830\pi$
$659$	−8.82344	+	7.03645i	−0.343712	+	0.274101i	0.436384	+	0.899760i	$0.356259\pi$
$660$	9.99904	+	9.87927i	0.389212	+	0.384550i
$661$	−0.865441	+	3.79175i	−0.0336618	+	0.147482i	−0.988966	−	0.148143i	$-0.952671\pi$
$661$	−0.865441	+	3.79175i	−0.0336618	+	0.147482i	0.955304	+	0.295624i	$0.0955277\pi$
$662$	11.6212	−	2.65246i	0.451671	−	0.103091i
$663$	7.72789	+	16.0471i	0.300127	+	0.623219i
$664$	2.99634	−	6.22196i	0.116280	−	0.241459i
$665$	23.1489	+	2.46711i	0.897676	+	0.0956704i
$666$	−14.1132			−0.546876
$667$	−6.84932	+	1.89468i	−0.265207	+	0.0733623i
$668$		−	3.97796i		−	0.153912i
$669$	5.08928	−	1.16159i	0.196763	−	0.0449098i
$670$	−9.31454	−	9.20297i	−0.359852	−	0.355542i
$671$	−43.3324	+	20.8678i	−1.67283	+	0.805592i
$672$	−3.42007	+	0.780608i	−0.131932	+	0.0301126i
$673$	−27.8014	−	6.34549i	−1.07167	−	0.244601i	−0.349935	−	0.936774i	$-0.613796\pi$
$673$	−27.8014	−	6.34549i	−1.07167	−	0.244601i	−0.721731	+	0.692173i	$0.756653\pi$
$674$	−8.11522	−	3.90808i	−0.312587	−	0.150534i
$675$	0.299772	+	24.8769i	0.0115382	+	0.957512i
$676$	−1.67565	−	2.10120i	−0.0644480	−	0.0808152i
$677$	30.1873	−	14.5375i	1.16019	−	0.558720i	0.248113	−	0.968731i	$-0.420189\pi$
$677$	30.1873	−	14.5375i	1.16019	−	0.558720i	0.912081	+	0.410011i	$0.134475\pi$
$678$	7.28741	−	9.13813i	0.279871	−	0.350948i
$679$			25.1557i			0.965386i
$680$	−5.44463	−	8.55029i	−0.208792	−	0.327889i
$681$	−27.2427	−	6.21797i	−1.04394	−	0.238273i
$682$	0.813101	−	3.56243i	0.0311352	−	0.136412i
$683$	−12.0647	−	9.62127i	−0.461643	−	0.368148i	0.364877	−	0.931056i	$-0.381111\pi$
$683$	−12.0647	−	9.62127i	−0.461643	−	0.368148i	−0.826520	+	0.562908i	$0.809682\pi$
$684$			5.93505i			0.226932i
$685$	−26.1923	−	41.1326i	−1.00076	−	1.57160i
$686$	2.29228	+	4.75996i	0.0875195	+	0.181736i
$687$	8.28387	−	6.60617i	0.316049	−	0.252041i
$688$	−0.378467	−	0.474583i	−0.0144289	−	0.0180933i
$689$	40.3092	+	19.4119i	1.53566	+	0.739535i
$690$	1.54238	−	2.48783i	0.0587174	−	0.0947102i
$691$	9.19750	+	40.2969i	0.349889	+	1.53296i	0.777430	+	0.628969i	$0.216523\pi$
$691$	9.19750	+	40.2969i	0.349889	+	1.53296i	−0.427541	+	0.903996i	$0.640620\pi$
$692$	−5.85184	−	12.1515i	−0.222454	−	0.461930i
$693$	−40.7045	−	19.6022i	−1.54623	−	0.744628i
$694$	28.7371	−	6.55905i	1.09084	−	0.248978i
$695$	6.18886	−	18.0345i	0.234757	−	0.684089i
$696$	−3.51708	−	4.02079i	−0.133314	−	0.152407i
$697$		−	43.1470i		−	1.63431i
$698$	−2.27799	−	9.98053i	−0.0862233	−	0.377769i
$699$	−5.93711	+	12.3285i	−0.224562	+	0.466308i
$700$	−3.72660	+	17.2848i	−0.140852	+	0.653304i
$701$	−6.95263	−	30.4615i	−0.262597	−	1.15051i	−0.918422	−	0.395601i	$-0.870536\pi$
$701$	−6.95263	−	30.4615i	−0.262597	−	1.15051i	0.655825	−	0.754913i	$-0.272321\pi$
$702$	19.2135	+	4.38537i	0.725168	+	0.165515i
$703$	8.94232	−	18.5689i	0.337266	−	0.700340i
$704$	−4.95449	+	3.95107i	−0.186729	+	0.148912i
$705$	9.87940	−	3.52390i	0.372080	−	0.132718i
$706$	8.86604	+	18.4105i	0.333678	+	0.692889i
$707$	−25.1627	+	31.5530i	−0.946340	+	1.18667i
$708$	−0.886873			−0.0333307
$709$	16.7023	−	20.9440i	0.627269	−	0.786570i	−0.362078	−	0.932148i	$-0.617933\pi$
$709$	16.7023	−	20.9440i	0.627269	−	0.786570i	0.989347	+	0.145578i	$0.0465041\pi$
$710$	11.9429	+	7.40423i	0.448209	+	0.277876i
$711$	5.05999	+	1.15491i	0.189765	+	0.0433125i
$712$	−1.78090	−	1.42022i	−0.0667419	−	0.0532249i
$713$	−0.760935			−0.0284972
$714$	−12.4332	−	9.91517i	−0.465302	−	0.371066i
$715$	−6.61978	−	55.7321i	−0.247566	−	2.08426i
$716$	11.4207	+	14.3211i	0.426811	+	0.535204i
$717$	16.2705	+	20.4026i	0.607633	+	0.761948i
$718$	−11.6599	+	24.2120i	−0.435142	+	0.903582i
$719$	5.31218	−	23.2742i	0.198111	−	0.867981i	−0.773949	−	0.633248i	$-0.781721\pi$
$719$	5.31218	−	23.2742i	0.198111	−	0.867981i	0.972060	−	0.234733i	$-0.0754215\pi$
$720$	−4.48249	−	0.477724i	−0.167052	−	0.0178037i
$721$	−26.9075	+	12.9580i	−1.00209	+	0.482579i
$722$	9.30960	+	4.48327i	0.346467	+	0.166850i
$723$	4.65645	+	20.4013i	0.173175	+	0.758731i
$724$	2.79527			0.103885
$725$	−25.8628	+	7.49088i	−0.960522	+	0.278204i
$726$	28.9240			1.07347
$727$	−1.59868	−	7.00429i	−0.0592919	−	0.259775i	0.936591	−	0.350425i	$-0.113963\pi$
$727$	−1.59868	−	7.00429i	−0.0592919	−	0.259775i	−0.995883	+	0.0906499i	$0.971106\pi$
$728$	12.6197	+	6.07730i	0.467715	+	0.225240i
$729$	−11.3211	+	5.45194i	−0.419299	+	0.201924i
$730$	10.0497	+	1.07105i	0.371955	+	0.0396414i
$731$	0.612320	−	2.68275i	0.0226475	−	0.0992251i
$732$	−3.26657	+	6.78311i	−0.120736	+	0.250711i
$733$	−5.02406	−	6.29997i	−0.185568	−	0.232695i	0.680342	−	0.732895i	$-0.261831\pi$
$733$	−5.02406	−	6.29997i	−0.185568	−	0.232695i	−0.865910	+	0.500200i	$0.833260\pi$
$734$	−0.416648	−	0.522460i	−0.0153788	−	0.0192844i
$735$	1.44053	+	12.1279i	0.0531348	+	0.447344i
$736$	1.03175	+	0.822789i	0.0380306	+	0.0303284i
$737$	−37.1087			−1.36692
$738$	−15.0017	−	11.9635i	−0.552222	−	0.440382i
$739$	−28.2754	−	6.45367i	−1.04013	−	0.237402i	−0.331846	−	0.943334i	$-0.607671\pi$
$739$	−28.2754	−	6.45367i	−1.04013	−	0.237402i	−0.708280	+	0.705932i	$0.750529\pi$
$740$	13.3045	+	8.24841i	0.489084	+	0.303217i
$741$	−7.21184	+	9.04336i	−0.264933	+	0.332216i
$742$	−39.9464			−1.46648
$743$	−24.9998	+	31.3488i	−0.917155	+	1.15008i	0.0711317	+	0.997467i	$0.477339\pi$
$743$	−24.9998	+	31.3488i	−0.917155	+	1.15008i	−0.988287	+	0.152609i	$0.951233\pi$
$744$	−0.248178	−	0.515347i	−0.00909864	−	0.0188935i
$745$	−25.9016	+	9.23889i	−0.948961	+	0.338487i
$746$	13.8107	−	11.0136i	0.505645	−	0.403238i
$747$	6.04056	−	12.5434i	0.221013	−	0.458937i
$748$	−28.0070	−	6.39242i	−1.02404	−	0.233730i
$749$	7.14277	+	31.2945i	0.260991	+	1.14348i
$750$	5.72989	−	9.49583i	0.209226	−	0.346739i
$751$	12.3576	−	25.6608i	0.450934	−	0.936375i	−0.544303	−	0.838889i	$-0.683206\pi$
$751$	12.3576	−	25.6608i	0.450934	−	0.936375i	0.995237	−	0.0974858i	$-0.0310800\pi$
$752$	1.05226	+	4.61023i	0.0383718	+	0.168118i
$753$		−	26.3894i		−	0.961684i
$754$	0.969618	+	21.3072i	0.0353114	+	0.775964i
$755$	−17.3723	+	50.6234i	−0.632242	+	1.84237i
$756$	−17.1550	+	3.91551i	−0.623921	+	0.142406i
$757$	15.4824	+	7.45592i	0.562717	+	0.270990i	0.693543	−	0.720415i	$-0.256049\pi$
$757$	15.4824	+	7.45592i	0.562717	+	0.270990i	−0.130826	+	0.991405i	$0.541763\pi$
$758$	12.3844	+	25.7164i	0.449820	+	0.934062i
$759$	−1.84594	−	8.08759i	−0.0670034	−	0.293561i
$760$	3.46871	−	5.59497i	0.125823	−	0.202951i
$761$	−8.20880	−	3.95315i	−0.297569	−	0.143302i	0.279142	−	0.960250i	$-0.409950\pi$
$761$	−8.20880	−	3.95315i	−0.297569	−	0.143302i	−0.576711	+	0.816948i	$0.695664\pi$
$762$	8.20841	+	10.2930i	0.297359	+	0.372877i
$763$	47.3785	−	37.7831i	1.71522	−	1.36784i
$764$	1.40033	+	2.90782i	0.0506622	+	0.105201i
$765$	−10.9763	−	17.2372i	−0.396848	−	0.623213i
$766$		−	12.1219i		−	0.437983i
$767$	2.76854	+	2.20783i	0.0999660	+	0.0797203i
$768$	−0.220736	+	0.967106i	−0.00796511	+	0.0348974i
$769$	15.7491	+	3.59463i	0.567927	+	0.129626i	0.496837	−	0.867844i	$-0.334495\pi$
$769$	15.7491	+	3.59463i	0.567927	+	0.129626i	0.0710908	+	0.997470i	$0.477352\pi$
$770$	26.9157	+	42.2686i	0.969973	+	1.52325i
$771$			3.08935i			0.111260i
$772$	2.11200	−	2.64837i	0.0760126	−	0.0953168i
$773$	23.7350	−	11.4302i	0.853690	−	0.411116i	0.0447443	−	0.998998i	$-0.485753\pi$
$773$	23.7350	−	11.4302i	0.853690	−	0.411116i	0.808946	+	0.587883i	$0.200038\pi$
$774$	−0.762983	−	0.956751i	−0.0274249	−	0.0343897i
$775$	−2.88288	+	0.0347394i	−0.103556	+	0.00124787i
$776$	6.40893	+	3.08638i	0.230067	+	0.110794i
$777$	23.9427	+	5.46478i	0.858941	+	0.196048i
$778$	12.8540	−	2.93384i	0.460837	−	0.105183i
$779$	25.2458	−	12.1577i	0.904525	−	0.435596i
$780$	−6.24957	−	6.17471i	−0.223770	−	0.221090i
$781$	38.8247	−	8.86147i	1.38926	−	0.317088i
$782$			5.98230i			0.213927i
$783$	−17.6416	−	20.1682i	−0.630459	−	0.720752i
$784$	−5.50606			−0.196645
$785$	18.1093	+	1.93002i	0.646350	+	0.0688852i
$786$	7.89168	−	16.3872i	0.281487	−	0.584514i
$787$	−19.4900	−	40.4714i	−0.694743	−	1.44265i	−0.887219	−	0.461348i	$-0.847366\pi$
$787$	−19.4900	−	40.4714i	−0.694743	−	1.44265i	0.192476	−	0.981302i	$-0.438348\pi$
$788$	8.67021	−	1.97892i	0.308863	−	0.0704961i
$789$	1.01956	−	4.46697i	0.0362972	−	0.159028i
$790$	−4.09508	−	4.04603i	−0.145696	−	0.143951i
$791$	32.5773	−	25.9796i	1.15832	−	0.923727i
$792$	−9.98815	+	7.96529i	−0.354914	+	0.283034i
$793$	27.0835	−	13.0427i	0.961762	−	0.463160i
$794$	3.57200	+	2.84858i	0.126766	+	0.101092i
$795$	23.6990	+	8.13269i	0.840515	+	0.288437i
$796$	−4.10183	+	5.14354i	−0.145386	+	0.182308i
$797$	5.57845	−	24.4408i	0.197599	−	0.865737i	−0.774762	−	0.632253i	$-0.782130\pi$
$797$	5.57845	−	24.4408i	0.197599	−	0.865737i	0.972361	−	0.233484i	$-0.0750126\pi$
$798$	2.29811	−	10.0687i	0.0813521	−	0.356427i
$799$	−13.3656	+	16.7599i	−0.472841	+	0.592924i
$800$	3.94644	+	3.07012i	0.139528	+	0.108545i
$801$	−3.59025	−	2.86313i	−0.126855	−	0.101164i
$802$	15.0954	−	7.26954i	0.533036	−	0.256696i
$803$	22.3933	−	17.8581i	0.790243	−	0.630198i
$804$	−4.54156	+	3.62177i	−0.160169	+	0.127730i
$805$	7.33427	−	7.42319i	0.258499	−	0.261633i
$806$	−0.508202	+	2.22658i	−0.0179006	+	0.0784278i
$807$	−29.7841	+	6.79804i	−1.04845	+	0.239302i
$808$	4.95154	+	10.2820i	0.174195	+	0.361719i
$809$	−7.77771	+	16.1506i	−0.273450	+	0.567824i	−0.991791	−	0.127866i	$-0.959187\pi$
$809$	−7.77771	+	16.1506i	−0.273450	+	0.567824i	0.718342	+	0.695690i	$0.244901\pi$
$810$	−2.47278	−	0.263538i	−0.0868846	−	0.00925979i
$811$	12.7959			0.449325			0.224663	−	0.974437i	$-0.427872\pi$
$811$	12.7959			0.449325			0.224663	+	0.974437i	$0.427872\pi$
$812$	−9.03436	−	16.7647i	−0.317044	−	0.588327i
$813$			21.4901i			0.753691i
$814$	43.2511	−	9.87179i	1.51595	−	0.346006i
$815$	−12.5619	+	12.7142i	−0.440023	+	0.445358i
$816$	−4.05154	+	1.95112i	−0.141832	+	0.0683028i
$817$	1.74224	−	0.397656i	0.0609534	−	0.0139122i
$818$	−18.1929	−	4.15241i	−0.636100	−	0.145186i
$819$	25.4410	+	12.2517i	0.888980	+	0.428110i
$820$	7.15013	+	20.0457i	0.249694	+	0.700026i
$821$	21.3526	+	26.7753i	0.745210	+	0.934464i	0.999466	−	0.0326727i	$-0.0104019\pi$
$821$	21.3526	+	26.7753i	0.745210	+	0.934464i	−0.254256	+	0.967137i	$0.581830\pi$
$822$	−19.4906	+	9.38620i	−0.679814	+	0.327381i
$823$	−7.22583	+	9.06090i	−0.251877	+	0.315843i	−0.891654	−	0.452717i	$-0.850455\pi$
$823$	−7.22583	+	9.06090i	−0.251877	+	0.315843i	0.639778	+	0.768560i	$0.279026\pi$
$824$			8.44506i			0.294198i
$825$	−7.36276	−	30.5564i	−0.256338	−	1.06384i
$826$	−3.08242	−	0.703543i	−0.107251	−	0.0244794i
$827$	−9.53963	+	41.7958i	−0.331725	+	1.45338i	0.484063	+	0.875033i	$0.339161\pi$
$827$	−9.53963	+	41.7958i	−0.331725	+	1.45338i	−0.815788	+	0.578351i	$0.803697\pi$
$828$	2.07998	+	1.65873i	0.0722843	+	0.0576448i
$829$		−	0.533028i		−	0.0185128i	−0.999957	−	0.00925642i	$-0.997054\pi$
$829$		−	0.533028i		−	0.0185128i	0.999957	−	0.00925642i	$-0.00294645\pi$
$830$	−13.0253	+	8.29424i	−0.452116	+	0.287897i
$831$	7.26183	+	15.0793i	0.251910	+	0.523096i
$832$	3.09664	−	2.46949i	0.107357	−	0.0856140i
$833$	−15.5625	−	19.5147i	−0.539208	−	0.676146i
$834$	−7.62091	−	3.67004i	−0.263890	−	0.127083i
$835$	−4.68696	+	7.55998i	−0.162199	+	0.261624i
$836$	−4.15139	−	18.1884i	−0.143579	−	0.629061i
$837$	−1.24486	−	2.58497i	−0.0430285	−	0.0893496i
$838$	−0.850926	−	0.409784i	−0.0293947	−	0.0141558i
$839$	11.4096	−	2.60418i	0.393905	−	0.0899062i	−0.0209807	−	0.999780i	$-0.506679\pi$
$839$	11.4096	−	2.60418i	0.393905	−	0.0899062i	0.414885	+	0.909874i	$0.363822\pi$
$840$	7.41945	+	2.54611i	0.255996	+	0.0878492i
$841$	15.9472	−	24.2216i	0.549903	−	0.835229i
$842$		−	15.7685i		−	0.543419i
$843$	−1.72129	−	7.54147i	−0.0592844	−	0.259742i
$844$	−5.30046	+	11.0065i	−0.182449	+	0.378860i
$845$	0.708817	+	5.96755i	0.0243840	+	0.205290i
$846$	2.12133	+	9.29414i	0.0729327	+	0.319539i
$847$	100.529	+	22.9450i	3.45420	+	0.788399i
$848$	−4.90107	+	10.1772i	−0.168303	+	0.349486i
$849$	−4.23251	+	3.37531i	−0.145259	+	0.115840i
$850$	0.273113	+	22.6646i	0.00936770	+	0.777388i
$851$	−4.00841	−	8.32355i	−0.137407	−	0.285328i
$852$	3.88670	−	4.87376i	0.133156	−	0.166972i
$853$	14.8149			0.507254			0.253627	−	0.967302i	$-0.418376\pi$
$853$	14.8149			0.507254			0.253627	+	0.967302i	$0.418376\pi$
$854$	−16.7343	+	20.9841i	−0.572635	+	0.718062i
$855$	6.99286	−	11.2794i	0.239151	−	0.385746i
$856$	8.84929	+	2.01979i	0.302462	+	0.0690351i
$857$	−23.5242	−	18.7600i	−0.803573	−	0.640828i	0.133073	−	0.991106i	$-0.457516\pi$
$857$	−23.5242	−	18.7600i	−0.803573	−	0.640828i	−0.936646	+	0.350278i	$0.886087\pi$
$858$	−24.8980			−0.850004
$859$	−4.99174	−	3.98078i	−0.170316	−	0.135823i	0.534622	−	0.845091i	$-0.320454\pi$
$859$	−4.99174	−	3.98078i	−0.170316	−	0.135823i	−0.704938	+	0.709269i	$0.749025\pi$
$860$	0.160096	+	1.34785i	0.00545922	+	0.0459613i
$861$	20.8177	+	26.1046i	0.709466	+	0.889642i
$862$	6.77856	+	8.50005i	0.230879	+	0.289513i
$863$	−3.00598	+	6.24198i	−0.102325	+	0.212479i	−0.945846	−	0.324617i	$-0.894765\pi$
$863$	−3.00598	+	6.24198i	−0.102325	+	0.212479i	0.843521	+	0.537096i	$0.180479\pi$
$864$	−1.10721	+	4.85099i	−0.0376679	+	0.165034i
$865$	−3.19602	+	29.9883i	−0.108668	+	1.01963i
$866$	−24.7675	+	11.9274i	−0.841635	+	0.405310i
$867$	−3.17302	−	1.52805i	−0.107761	−	0.0518952i
$868$	−0.453753	−	1.98802i	−0.0154014	−	0.0674778i
$869$	−16.3146			−0.553435
$870$	1.94667	+	11.7853i	0.0659983	+	0.399559i
$871$	23.1936			0.785884
$872$	−3.81311	−	16.7063i	−0.129128	−	0.565747i
$873$	12.9203	+	6.22208i	0.437285	+	0.210585i
$874$	−3.50031	+	1.68566i	−0.118400	+	0.0570183i
$875$	27.4478	−	28.4583i	0.927904	−	0.962068i
$876$	0.997682	−	4.37113i	0.0337085	−	0.147687i
$877$	1.71858	−	3.56866i	0.0580322	−	0.120505i	−0.869936	−	0.493165i	$-0.835840\pi$
$877$	1.71858	−	3.56866i	0.0580322	−	0.120505i	0.927968	+	0.372660i	$0.121554\pi$
$878$	7.76917	+	9.74223i	0.262197	+	0.328784i
$879$	−12.0607	−	15.1236i	−0.406797	−	0.510107i
$880$	14.0711	−	1.67135i	0.474337	−	0.0563410i
$881$	28.5537	+	22.7708i	0.961998	+	0.767168i	0.972530	−	0.232777i	$-0.0747811\pi$
$881$	28.5537	+	22.7708i	0.961998	+	0.767168i	−0.0105321	+	0.999945i	$0.503353\pi$
$882$	−11.1001			−0.373760
$883$	−24.7352	−	19.7256i	−0.832405	−	0.663821i	0.111599	−	0.993753i	$-0.464403\pi$
$883$	−24.7352	−	19.7256i	−0.832405	−	0.663821i	−0.944005	+	0.329932i	$0.892974\pi$
$884$	17.5049	+	3.99537i	0.588752	+	0.134379i
$885$	1.68547	+	1.04494i	0.0566565	+	0.0351253i
$886$	−16.3572	+	20.5113i	−0.549532	+	0.689092i
$887$	−30.4425			−1.02216			−0.511080	−	0.859533i	$-0.670755\pi$
$887$	−30.4425			−1.02216			−0.511080	+	0.859533i	$0.670755\pi$
$888$	4.32983	−	5.42943i	0.145299	−	0.182200i
$889$	20.3639	+	42.2861i	0.682984	+	1.41823i
$890$	1.71119	+	4.79738i	0.0573591	+	0.160809i
$891$	−5.51000	+	4.39408i	−0.184592	+	0.147207i
$892$	2.28326	−	4.74124i	0.0764492	−	0.158748i
$893$	−13.5725	−	3.09784i	−0.454187	−	0.103665i
$894$	2.71469	+	11.8938i	0.0907928	+	0.397789i
$895$	−4.83107	−	40.6729i	−0.161485	−	1.35955i
$896$	−1.53438	+	3.18618i	−0.0512601	+	0.106443i
$897$	1.15374	+	5.05488i	0.0385224	+	0.168778i
$898$			11.0467i			0.368634i
$899$	2.33721	−	2.04441i	0.0779502	−	0.0681849i
$900$	7.95594	+	6.18930i	0.265198	+	0.206310i
$901$	−49.9228	+	11.3945i	−1.66317	+	0.379607i
$902$	54.3422	+	26.1698i	1.80940	+	0.871360i
$903$	0.923920	+	1.91854i	0.0307461	+	0.0638450i
$904$	−2.62188	−	11.4872i	−0.0872025	−	0.382059i
$905$	−5.31232	−	3.29348i	−0.176587	−	0.109479i
$906$	21.3921	+	10.3019i	0.710704	+	0.342257i
$907$	12.2403	+	15.3489i	0.406433	+	0.509651i	0.942354	−	0.334617i	$-0.108607\pi$
$907$	12.2403	+	15.3489i	0.406433	+	0.509651i	−0.535921	+	0.844268i	$0.680036\pi$
$908$	−22.0237	+	17.5633i	−0.730881	+	0.582858i
$909$	9.98222	+	20.7283i	0.331089	+	0.687514i
$910$	−16.8227	−	26.4186i	−0.557669	−	0.875767i
$911$		−	13.9524i		−	0.462264i	−0.972922	−	0.231132i	$-0.925757\pi$
$911$		−	13.9524i		−	0.462264i	0.972922	−	0.231132i	$-0.0742429\pi$
$912$	−2.28324	−	1.82083i	−0.0756058	−	0.0602936i
$913$	−9.73809	+	42.6654i	−0.322284	+	1.41202i
$914$	−5.40011	−	1.23254i	−0.178620	−	0.0407688i
$915$	14.2001	−	9.04229i	0.469440	−	0.298929i
$916$		−	10.6812i		−	0.352915i
$917$	40.4282	−	50.6953i	1.33506	−	1.67411i
$918$	−20.3225	+	9.78678i	−0.670741	+	0.323012i
$919$	−0.879985	−	1.10347i	−0.0290280	−	0.0364000i	0.767106	−	0.641521i	$-0.221696\pi$
$919$	−0.879985	−	1.10347i	−0.0290280	−	0.0364000i	−0.796134	+	0.605121i	$0.793125\pi$
$920$	−0.991360	−	2.77932i	−0.0326842	−	0.0916314i
$921$	−0.123246	−	0.0593524i	−0.00406111	−	0.00195573i
$922$	−0.356957	−	0.0814730i	−0.0117557	−	0.00268317i
$923$	−24.2661	+	5.53857i	−0.798727	+	0.182304i
$924$	20.0289	−	9.64542i	0.658903	−	0.317311i
$925$	−15.5663	−	31.3516i	−0.511816	−	1.03084i
$926$	4.65151	−	1.06168i	0.152858	−	0.0348889i
$927$			17.0251i			0.559177i
$928$	−5.37960	+	0.244807i	−0.176594	+	0.00803618i
$929$	18.4473			0.605235			0.302618	−	0.953112i	$-0.402139\pi$
$929$	18.4473			0.605235			0.302618	+	0.953112i	$0.402139\pi$
$930$	−0.135544	+	1.27181i	−0.00444466	+	0.0417043i
$931$	7.03318	−	14.6045i	0.230503	−	0.478645i
$932$	5.98513	+	12.4283i	0.196049	+	0.407101i
$933$	15.8721	−	3.62271i	0.519631	−	0.118602i
$934$	0.305317	−	1.33768i	0.00999028	−	0.0437703i
$935$	45.6946	+	45.1473i	1.49437	+	1.47648i
$936$	6.24276	−	4.97844i	0.204051	−	0.162725i
$937$	3.57766	−	2.85309i	0.116877	−	0.0932065i	−0.563307	−	0.826248i	$-0.690471\pi$
$937$	3.57766	−	2.85309i	0.116877	−	0.0932065i	0.680184	+	0.733041i	$0.261900\pi$
$938$	−18.6578	+	8.98512i	−0.609199	+	0.293375i
$939$	−19.1581	−	15.2781i	−0.625201	−	0.498581i
$940$	3.43214	−	10.0014i	0.111944	−	0.326209i
$941$	−9.21232	+	11.5519i	−0.300313	+	0.376581i	−0.908976	−	0.416848i	$-0.863135\pi$
$941$	−9.21232	+	11.5519i	−0.300313	+	0.376581i	0.608663	+	0.793429i	$0.291706\pi$
$942$	1.79781	−	7.87670i	0.0585757	−	0.256637i
$943$	2.79494	−	12.2454i	0.0910157	−	0.398766i
$944$	−0.557428	+	0.698993i	−0.0181427	+	0.0227503i
$945$	37.2158	+	12.7712i	1.21063	+	0.415449i
$946$	3.00745	+	2.39836i	0.0977805	+	0.0779774i
$947$	−40.5817	+	19.5431i	−1.31873	+	0.635065i	−0.955046	−	0.296458i	$-0.904194\pi$
$947$	−40.5817	+	19.5431i	−1.31873	+	0.635065i	−0.363681	+	0.931524i	$0.618480\pi$
$948$	−1.99667	+	1.59229i	−0.0648488	+	0.0517152i
$949$	−13.9962	+	11.1616i	−0.454336	+	0.362321i
$950$	−13.1843	+	6.54610i	−0.427756	+	0.212384i
$951$	0.0369529	−	0.161901i	0.00119828	−	0.00525001i
$952$	−15.6294	+	3.56730i	−0.506551	+	0.115617i
$953$	−23.8612	−	49.5483i	−0.772941	−	1.60503i	−0.796002	−	0.605294i	$-0.793055\pi$
$953$	−23.8612	−	49.5483i	−0.772941	−	1.60503i	0.0230608	−	0.999734i	$-0.492659\pi$
$954$	−9.88046	+	20.5170i	−0.319892	+	0.664262i
$955$	0.764800	−	7.17612i	0.0247483	−	0.232214i
$956$	26.3069			0.850827
$957$	27.3988	+	19.8815i	0.885678	+	0.642677i
$958$			18.8790i			0.609952i
$959$	−75.1878	+	17.1611i	−2.42794	+	0.554162i
$960$	1.55898	−	1.57787i	0.0503157	−	0.0509257i
$961$	−27.6305	+	13.3061i	−0.891306	+	0.429230i
$962$	−27.0327	+	6.17004i	−0.871569	+	0.198930i
$963$	17.8400	+	4.07186i	0.574886	+	0.131214i
$964$	19.0061	+	9.15285i	0.612145	+	0.294793i
$965$	−7.13417	+	2.54470i	−0.229657	+	0.0819169i
$966$	−2.88636	−	3.61938i	−0.0928671	−	0.116452i
$967$	−25.6836	+	12.3686i	−0.825928	+	0.397746i	−0.798586	−	0.601880i	$-0.794418\pi$
$967$	−25.6836	+	12.3686i	−0.825928	+	0.397746i	−0.0273416	+	0.999626i	$0.508704\pi$
$968$	18.1797	−	22.7966i	0.584317	−	0.732710i
$969$		−	13.2388i		−	0.425291i
$970$	−8.54348	−	13.4168i	−0.274315	−	0.430786i
$971$	12.4456	+	2.84062i	0.399397	+	0.0911597i	0.417501	−	0.908676i	$-0.362906\pi$
$971$	12.4456	+	2.84062i	0.399397	+	0.0911597i	−0.0181043	+	0.999836i	$0.505763\pi$
$972$	−3.56710	+	15.6285i	−0.114415	+	0.501284i
$973$	−23.5759	−	18.8012i	−0.755809	−	0.602738i
$974$		−	14.4310i		−	0.462399i
$975$	4.60185	+	19.0983i	0.147377	+	0.611634i
$976$	3.29299	+	6.83797i	0.105406	+	0.218878i
$977$	34.3222	−	27.3711i	1.09807	−	0.875678i	0.105145	−	0.994457i	$-0.466469\pi$
$977$	34.3222	−	27.3711i	1.09807	−	0.875678i	0.992921	+	0.118779i	$0.0378979\pi$
$978$	4.94365	+	6.19914i	0.158081	+	0.198227i
$979$	13.0053	+	6.26303i	0.415652	+	0.200167i
$980$	10.4641	+	6.48741i	0.334263	+	0.207233i
$981$	−7.68715	−	33.6796i	−0.245432	−	1.07531i
$982$	−14.8899	−	30.9193i	−0.475157	−	0.986673i
$983$	12.0897	+	5.82210i	0.385602	+	0.185696i	0.616634	−	0.787250i	$-0.288496\pi$
$983$	12.0897	+	5.82210i	0.385602	+	0.185696i	−0.231032	+	0.972946i	$0.574210\pi$
$984$	9.20484	−	2.10094i	0.293440	−	0.0669757i
$985$	−18.8091	−	6.45465i	−0.599307	−	0.205662i
$986$	−16.0727	−	18.3746i	−0.511859	−	0.585167i
$987$		−	16.5887i		−	0.528024i
$988$	2.59469	+	11.3681i	0.0825481	+	0.361667i
$989$	0.347562	−	0.721719i	0.0110518	−	0.0229493i
$990$	28.3671	−	3.36940i	0.901566	−	0.107087i
$991$	2.29317	+	10.0470i	0.0728450	+	0.319155i	0.998202	−	0.0599424i	$-0.0190917\pi$
$991$	2.29317	+	10.0470i	0.0728450	+	0.319155i	−0.925357	+	0.379097i	$0.876235\pi$
$992$	−0.562161	−	0.128310i	−0.0178486	−	0.00407383i
$993$	−5.13043	+	10.6535i	−0.162809	+	0.338077i
$994$	17.3749	−	13.8560i	0.551099	−	0.439487i
$995$	13.8557	−	4.94221i	0.439254	−	0.156679i
$996$	2.97230	+	6.17204i	0.0941809	+	0.195569i
$997$	−22.7944	+	28.5833i	−0.721907	+	0.905243i	−0.998444	−	0.0557602i	$-0.982242\pi$
$997$	−22.7944	+	28.5833i	−0.721907	+	0.905243i	0.276537	+	0.961003i	$0.410813\pi$
$998$	−4.62465			−0.146391
$999$	21.7183	−	27.2339i	0.687138	−	0.861643i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	290.2.l.b.109.3	yes	48
5.4	even	2		290.2.l.a.109.6	✓	48
29.4	even	14		290.2.l.a.149.6	yes	48
145.4	even	14	inner	290.2.l.b.149.3	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
290.2.l.a.109.6	✓	48	5.4	even	2
290.2.l.a.149.6	yes	48	29.4	even	14
290.2.l.b.109.3	yes	48	1.1	even	1	trivial
290.2.l.b.149.3	yes	48	145.4	even	14	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 290 = 2 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	290.l (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.222521 + 0.974928i) q^{2} +(-0.893741 - 0.430403i) q^{3} +(-0.900969 + 0.433884i) q^{4} +(2.22348 + 0.236969i) q^{5} +(0.220736 - 0.967106i) q^{6} +(1.53438 - 3.18618i) q^{7} +(-0.623490 - 0.781831i) q^{8} +(-1.25694 - 1.57616i) q^{9} +(0.263743 + 2.22046i) q^{10} +(4.95449 + 3.95107i) q^{11} +0.991977 q^{12} +(-3.09664 - 2.46949i) q^{13} +(3.44773 + 0.786921i) q^{14} +(-1.88522 - 1.16878i) q^{15} +(0.623490 - 0.781831i) q^{16} +4.53324 q^{17} +(1.25694 - 1.57616i) q^{18} +(1.27735 + 2.65245i) q^{19} +(-2.10610 + 0.751229i) q^{20} +(-2.74268 + 2.18721i) q^{21} +(-2.74953 + 5.70946i) q^{22} +(1.28657 + 0.293650i) q^{23} +(0.220736 + 0.967106i) q^{24} +(4.88769 + 1.05379i) q^{25} +(1.71850 - 3.56851i) q^{26} +(1.10721 + 4.85099i) q^{27} +3.53639i q^{28} +(-4.74063 + 2.55468i) q^{29} +(0.719974 - 2.09803i) q^{30} +(-0.562161 + 0.128310i) q^{31} +(0.900969 + 0.433884i) q^{32} +(-2.72747 - 5.66366i) q^{33} +(1.00874 + 4.41958i) q^{34} +(4.16669 - 6.72079i) q^{35} +(1.81634 + 0.874701i) q^{36} +(-4.36485 - 5.47334i) q^{37} +(-2.30171 + 1.83555i) q^{38} +(1.70472 + 3.53988i) q^{39} +(-1.20105 - 1.88613i) q^{40} -9.51792i q^{41} +(-2.74268 - 2.18721i) q^{42} +(0.135073 - 0.591795i) q^{43} +(-6.17815 - 1.41012i) q^{44} +(-2.42128 - 3.80240i) q^{45} +1.31965i q^{46} +(-2.94835 + 3.69712i) q^{47} +(-0.893741 + 0.430403i) q^{48} +(-3.43297 - 4.30481i) q^{49} +(0.0602468 + 4.99964i) q^{50} +(-4.05154 - 1.95112i) q^{51} +(3.86144 + 0.881350i) q^{52} +(-11.0126 + 2.51355i) q^{53} +(-4.48299 + 2.15889i) q^{54} +(10.0799 + 9.95917i) q^{55} +(-3.44773 + 0.786921i) q^{56} -2.92038i q^{57} +(-3.54552 - 4.05330i) q^{58} -0.894046 q^{59} +(2.20564 + 0.235067i) q^{60} +(-3.29299 + 6.83797i) q^{61} +(-0.250185 - 0.519515i) q^{62} +(-6.95055 + 1.58642i) q^{63} +(-0.222521 + 0.974928i) q^{64} +(-6.30011 - 6.22465i) q^{65} +(4.91474 - 3.91937i) q^{66} +(-4.57829 + 3.65107i) q^{67} +(-4.08431 + 1.96690i) q^{68} +(-1.02347 - 0.816188i) q^{69} +(7.47946 + 2.56670i) q^{70} +(3.91813 - 4.91318i) q^{71} +(-0.448598 + 1.96544i) q^{72} +(1.00575 - 4.40648i) q^{73} +(4.36485 - 5.47334i) q^{74} +(-3.91478 - 3.04549i) q^{75} +(-2.30171 - 1.83555i) q^{76} +(20.1909 - 9.72342i) q^{77} +(-3.07179 + 2.44967i) q^{78} +(-2.01282 + 1.60517i) q^{79} +(1.57158 - 1.59064i) q^{80} +(-0.247471 + 1.08424i) q^{81} +(9.27928 - 2.11794i) q^{82} +(2.99634 + 6.22196i) q^{83} +(1.52207 - 3.16062i) q^{84} +(10.0796 + 1.07424i) q^{85} +0.607015 q^{86} +(5.33644 - 0.242843i) q^{87} -6.33703i q^{88} +(2.22074 - 0.506870i) q^{89} +(3.16828 - 3.20669i) q^{90} +(-12.6197 + 6.07730i) q^{91} +(-1.28657 + 0.293650i) q^{92} +(0.557651 + 0.127280i) q^{93} +(-4.26049 - 2.05175i) q^{94} +(2.21162 + 6.20035i) q^{95} +(-0.618488 - 0.775559i) q^{96} +(-6.40893 + 3.08638i) q^{97} +(3.43297 - 4.30481i) q^{98} -12.7753i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 8 q^{2} - 4 q^{3} - 8 q^{4} + 8 q^{5} - 3 q^{6} + 7 q^{7} + 8 q^{8} - 8 q^{9} - q^{10} + 10 q^{12} - 10 q^{15} - 8 q^{16} - 30 q^{17} + 8 q^{18} - 13 q^{20} + 7 q^{21} + 7 q^{23} - 3 q^{24} - 12 q^{25}+ \cdots - 27 q^{98}+O(q^{100}) \) 48 * q + 8 * q^2 - 4 * q^3 - 8 * q^4 + 8 * q^5 - 3 * q^6 + 7 * q^7 + 8 * q^8 - 8 * q^9 - q^10 + 10 * q^12 - 10 * q^15 - 8 * q^16 - 30 * q^17 + 8 * q^18 - 13 * q^20 + 7 * q^21 + 7 * q^23 - 3 * q^24 - 12 * q^25 + 21 * q^26 + 11 * q^27 - 10 * q^29 - 18 * q^30 + 14 * q^31 + 8 * q^32 - 14 * q^33 - 33 * q^34 - q^36 - 44 * q^37 - 28 * q^38 - 14 * q^39 - 8 * q^40 + 7 * q^42 - 8 * q^43 + 14 * q^44 + 25 * q^45 - 6 * q^47 - 4 * q^48 + 27 * q^49 + 5 * q^50 + 24 * q^51 + 77 * q^53 + 10 * q^54 - 32 * q^55 + 10 * q^58 - 24 * q^59 + 4 * q^60 + 56 * q^61 - 8 * q^64 - 34 * q^65 + 42 * q^67 - 2 * q^68 + 28 * q^69 - 30 * q^71 + 22 * q^72 - 29 * q^73 + 44 * q^74 - 32 * q^75 - 28 * q^76 - 30 * q^77 + 14 * q^78 + q^80 - 130 * q^81 - 42 * q^82 - 42 * q^84 + 28 * q^85 - 62 * q^86 + 32 * q^87 + 31 * q^90 - 106 * q^91 - 7 * q^92 - 70 * q^93 + 27 * q^94 + 165 * q^95 + 4 * q^96 - 49 * q^97 - 27 * q^98

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