LMFDB - Embedded newform 603.2.e.b.202.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [603,2,Mod(202,603)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(603, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("603.202");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 603 = 3^{2} \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	603.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.81497924188$
Analytic rank:	$0$
Dimension:	$66$
Relative dimension:	$33$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			202.20
Character	$\chi$	$=$	603.202
Dual form			603.2.e.b.403.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.341820 + 0.592049i) q^{2} +(1.72544 + 0.151135i) q^{3} +(0.766318 - 1.32730i) q^{4} +(0.565440 - 0.979371i) q^{5} +(0.500312 + 1.07321i) q^{6} +(-2.29004 - 3.96647i) q^{7} +2.41505 q^{8} +(2.95432 + 0.521550i) q^{9} +O(q^{10})$	\(q+(0.341820 + 0.592049i) q^{2} +(1.72544 + 0.151135i) q^{3} +(0.766318 - 1.32730i) q^{4} +(0.565440 - 0.979371i) q^{5} +(0.500312 + 1.07321i) q^{6} +(-2.29004 - 3.96647i) q^{7} +2.41505 q^{8} +(2.95432 + 0.521550i) q^{9} +0.773115 q^{10} +(0.758004 + 1.31290i) q^{11} +(1.52284 - 2.17437i) q^{12} +(-2.91789 + 5.05393i) q^{13} +(1.56556 - 2.71164i) q^{14} +(1.12365 - 1.60439i) q^{15} +(-0.707125 - 1.22478i) q^{16} -1.62236 q^{17} +(0.701060 + 1.92738i) q^{18} -1.46277 q^{19} +(-0.866615 - 1.50102i) q^{20} +(-3.35187 - 7.19003i) q^{21} +(-0.518202 + 0.897551i) q^{22} +(4.35592 - 7.54467i) q^{23} +(4.16704 + 0.364999i) q^{24} +(1.86055 + 3.22257i) q^{25} -3.98956 q^{26} +(5.01868 + 1.34641i) q^{27} -7.01961 q^{28} +(-0.499517 - 0.865189i) q^{29} +(1.33397 + 0.116845i) q^{30} +(0.954196 - 1.65272i) q^{31} +(2.89847 - 5.02030i) q^{32} +(1.10947 + 2.37990i) q^{33} +(-0.554554 - 0.960515i) q^{34} -5.17953 q^{35} +(2.95620 - 3.52160i) q^{36} +4.29839 q^{37} +(-0.500004 - 0.866033i) q^{38} +(-5.79847 + 8.27927i) q^{39} +(1.36557 - 2.36523i) q^{40} +(-2.59366 + 4.49234i) q^{41} +(3.11112 - 4.44217i) q^{42} +(2.48085 + 4.29695i) q^{43} +2.32349 q^{44} +(2.18128 - 2.59847i) q^{45} +5.95576 q^{46} +(3.78552 + 6.55672i) q^{47} +(-1.03500 - 2.22015i) q^{48} +(-6.98859 + 12.1046i) q^{49} +(-1.27195 + 2.20308i) q^{50} +(-2.79929 - 0.245195i) q^{51} +(4.47206 + 7.74583i) q^{52} -14.2165 q^{53} +(0.918347 + 3.43154i) q^{54} +1.71442 q^{55} +(-5.53057 - 9.57923i) q^{56} +(-2.52393 - 0.221076i) q^{57} +(0.341490 - 0.591478i) q^{58} +(-2.35033 + 4.07089i) q^{59} +(-1.26844 - 2.72090i) q^{60} +(6.70236 + 11.6088i) q^{61} +1.30465 q^{62} +(-4.69680 - 12.9126i) q^{63} +1.13452 q^{64} +(3.29978 + 5.71539i) q^{65} +(-1.02978 + 1.47036i) q^{66} +(0.500000 - 0.866025i) q^{67} +(-1.24324 + 2.15336i) q^{68} +(8.65616 - 12.3596i) q^{69} +(-1.77047 - 3.06654i) q^{70} +5.27337 q^{71} +(7.13482 + 1.25957i) q^{72} -11.5626 q^{73} +(1.46928 + 2.54486i) q^{74} +(2.72324 + 5.84157i) q^{75} +(-1.12095 + 1.94154i) q^{76} +(3.47172 - 6.01320i) q^{77} +(-6.88377 - 0.602963i) q^{78} +(-0.528994 - 0.916245i) q^{79} -1.59935 q^{80} +(8.45597 + 3.08165i) q^{81} -3.54625 q^{82} +(3.12353 + 5.41011i) q^{83} +(-12.1119 - 1.06091i) q^{84} +(-0.917346 + 1.58889i) q^{85} +(-1.69601 + 2.93757i) q^{86} +(-0.731129 - 1.56833i) q^{87} +(1.83062 + 3.17072i) q^{88} +0.567051 q^{89} +(2.28403 + 0.403218i) q^{90} +26.7283 q^{91} +(-6.67604 - 11.5632i) q^{92} +(1.89620 - 2.70746i) q^{93} +(-2.58793 + 4.48243i) q^{94} +(-0.827110 + 1.43260i) q^{95} +(5.75989 - 8.22418i) q^{96} +(-0.747876 - 1.29536i) q^{97} -9.55535 q^{98} +(1.55464 + 4.27406i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q + 7 q^{2} - 33 q^{4} + 18 q^{5} - 3 q^{6} - 48 q^{8} + 4 q^{9}+O(q^{10}) $ 66 * q + 7 * q^2 - 33 * q^4 + 18 * q^5 - 3 * q^6 - 48 * q^8 + 4 * q^9	\( 66 q + 7 q^{2} - 33 q^{4} + 18 q^{5} - 3 q^{6} - 48 q^{8} + 4 q^{9} + 12 q^{11} + q^{12} + 9 q^{14} + 3 q^{15} - 33 q^{16} - 62 q^{17} + 7 q^{18} + 43 q^{20} + 17 q^{21} + 19 q^{23} - 17 q^{24} - 33 q^{25} - 28 q^{26} - 3 q^{27} + 54 q^{28} + 25 q^{29} + 24 q^{30} + 45 q^{32} - 32 q^{33} - 6 q^{34} - 50 q^{35} + 53 q^{36} - 24 q^{37} + 34 q^{38} + 19 q^{39} - 6 q^{40} + 34 q^{41} - 107 q^{42} - 98 q^{44} + 9 q^{45} + 12 q^{46} + 26 q^{47} + 49 q^{48} - 33 q^{49} + 39 q^{50} - 50 q^{51} + 9 q^{52} - 104 q^{53} + 70 q^{54} + 60 q^{55} + 16 q^{56} + 6 q^{57} + 3 q^{58} + 21 q^{59} - 161 q^{60} - 54 q^{62} + q^{63} - 12 q^{64} + 52 q^{65} + 52 q^{66} + 33 q^{67} + 98 q^{68} + 2 q^{69} - 6 q^{70} - 62 q^{71} + 66 q^{72} + 27 q^{74} + 21 q^{75} - 6 q^{76} + 85 q^{77} - 107 q^{78} - 172 q^{80} + 72 q^{81} + 102 q^{82} + 71 q^{83} - 54 q^{84} - 27 q^{85} + 9 q^{86} + 3 q^{87} - 12 q^{88} - 82 q^{89} + 153 q^{90} - 60 q^{91} + 67 q^{92} - 47 q^{93} + 15 q^{94} + 58 q^{95} - 136 q^{96} - 12 q^{97} - 172 q^{98} + 96 q^{99}+O(q^{100}) \) 66 * q + 7 * q^2 - 33 * q^4 + 18 * q^5 - 3 * q^6 - 48 * q^8 + 4 * q^9 + 12 * q^11 + q^12 + 9 * q^14 + 3 * q^15 - 33 * q^16 - 62 * q^17 + 7 * q^18 + 43 * q^20 + 17 * q^21 + 19 * q^23 - 17 * q^24 - 33 * q^25 - 28 * q^26 - 3 * q^27 + 54 * q^28 + 25 * q^29 + 24 * q^30 + 45 * q^32 - 32 * q^33 - 6 * q^34 - 50 * q^35 + 53 * q^36 - 24 * q^37 + 34 * q^38 + 19 * q^39 - 6 * q^40 + 34 * q^41 - 107 * q^42 - 98 * q^44 + 9 * q^45 + 12 * q^46 + 26 * q^47 + 49 * q^48 - 33 * q^49 + 39 * q^50 - 50 * q^51 + 9 * q^52 - 104 * q^53 + 70 * q^54 + 60 * q^55 + 16 * q^56 + 6 * q^57 + 3 * q^58 + 21 * q^59 - 161 * q^60 - 54 * q^62 + q^63 - 12 * q^64 + 52 * q^65 + 52 * q^66 + 33 * q^67 + 98 * q^68 + 2 * q^69 - 6 * q^70 - 62 * q^71 + 66 * q^72 + 27 * q^74 + 21 * q^75 - 6 * q^76 + 85 * q^77 - 107 * q^78 - 172 * q^80 + 72 * q^81 + 102 * q^82 + 71 * q^83 - 54 * q^84 - 27 * q^85 + 9 * q^86 + 3 * q^87 - 12 * q^88 - 82 * q^89 + 153 * q^90 - 60 * q^91 + 67 * q^92 - 47 * q^93 + 15 * q^94 + 58 * q^95 - 136 * q^96 - 12 * q^97 - 172 * q^98 + 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/603\mathbb{Z}\right)^\times$.

$n$	$136$	$470$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.341820	+	0.592049i	0.241703	+	0.418642i	0.961200	−	0.275854i	$-0.0889607\pi$
$2$	0.341820	+	0.592049i	0.241703	+	0.418642i	−0.719496	+	0.694496i	$0.755627\pi$
$3$	1.72544	+	0.151135i	0.996186	+	0.0872579i
$3$	1.72544	+	0.151135i	0.996186	+	0.0872579i
$4$	0.766318	−	1.32730i	0.383159	−	0.663651i
$5$	0.565440	−	0.979371i	0.252873	−	0.437988i	−0.711443	−	0.702744i	$-0.751958\pi$
$5$	0.565440	−	0.979371i	0.252873	−	0.437988i	0.964316	+	0.264756i	$0.0852913\pi$
$6$	0.500312	+	1.07321i	0.204251	+	0.438136i
$7$	−2.29004	−	3.96647i	−0.865555	−	1.49918i	−0.866495	−	0.499185i	$-0.833633\pi$
$7$	−2.29004	−	3.96647i	−0.865555	−	1.49918i	0.000940588	−	1.00000i	$-0.499701\pi$
$8$	2.41505			0.853849
$9$	2.95432	+	0.521550i	0.984772	+	0.173850i
$10$	0.773115			0.244480
$11$	0.758004	+	1.31290i	0.228547	+	0.395855i	0.957378	−	0.288839i	$-0.0932693\pi$
$11$	0.758004	+	1.31290i	0.228547	+	0.395855i	−0.728831	+	0.684694i	$0.759936\pi$
$12$	1.52284	−	2.17437i	0.439607	−	0.627686i
$13$	−2.91789	+	5.05393i	−0.809276	+	1.40171i	0.104090	+	0.994568i	$0.466807\pi$
$13$	−2.91789	+	5.05393i	−0.809276	+	1.40171i	−0.913366	+	0.407139i	$0.866526\pi$
$14$	1.56556	−	2.71164i	0.418415	−	0.724715i
$15$	1.12365	−	1.60439i	0.290126	−	0.414253i
$16$	−0.707125	−	1.22478i	−0.176781	−	0.306194i
$17$	−1.62236			−0.393479			−0.196740	−	0.980456i	$-0.563035\pi$
$17$	−1.62236			−0.393479			−0.196740	+	0.980456i	$0.563035\pi$
$18$	0.701060	+	1.92738i	0.165242	+	0.454287i
$19$	−1.46277			−0.335583			−0.167791	−	0.985823i	$-0.553664\pi$
$19$	−1.46277			−0.335583			−0.167791	+	0.985823i	$0.553664\pi$
$20$	−0.866615	−	1.50102i	−0.193781	−	0.335638i
$21$	−3.35187	−	7.19003i	−0.731438	−	1.56899i
$22$	−0.518202	+	0.897551i	−0.110481	+	0.191359i
$23$	4.35592	−	7.54467i	0.908272	−	1.57317i	0.0918083	−	0.995777i	$-0.470735\pi$
$23$	4.35592	−	7.54467i	0.908272	−	1.57317i	0.816464	−	0.577397i	$-0.195931\pi$
$24$	4.16704	+	0.364999i	0.850593	+	0.0745051i
$25$	1.86055	+	3.22257i	0.372111	+	0.644515i
$26$	−3.98956			−0.782418
$27$	5.01868	+	1.34641i	0.965846	+	0.259116i
$28$	−7.01961			−1.32658
$29$	−0.499517	−	0.865189i	−0.0927580	−	0.160662i	0.815913	−	0.578175i	$-0.196235\pi$
$29$	−0.499517	−	0.865189i	−0.0927580	−	0.160662i	−0.908671	+	0.417514i	$0.862902\pi$
$30$	1.33397	+	0.116845i	0.243548	+	0.0213328i
$31$	0.954196	−	1.65272i	0.171379	−	0.296836i	−0.767523	−	0.641021i	$-0.778511\pi$
$31$	0.954196	−	1.65272i	0.171379	−	0.296836i	0.938902	+	0.344184i	$0.111845\pi$
$32$	2.89847	−	5.02030i	0.512382	−	0.887471i
$33$	1.10947	+	2.37990i	0.193134	+	0.414287i
$34$	−0.554554	−	0.960515i	−0.0951052	−	0.164727i
$35$	−5.17953			−0.875500
$36$	2.95620	−	3.52160i	0.492700	−	0.586933i
$37$	4.29839			0.706651			0.353326	−	0.935500i	$-0.385051\pi$
$37$	4.29839			0.706651			0.353326	+	0.935500i	$0.385051\pi$
$38$	−0.500004	−	0.866033i	−0.0811114	−	0.140489i
$39$	−5.79847	+	8.27927i	−0.928499	+	1.32574i
$40$	1.36557	−	2.36523i	0.215915	−	0.373976i
$41$	−2.59366	+	4.49234i	−0.405061	+	0.701586i	−0.994329	−	0.106352i	$-0.966083\pi$
$41$	−2.59366	+	4.49234i	−0.405061	+	0.701586i	0.589268	+	0.807938i	$0.299416\pi$
$42$	3.11112	−	4.44217i	0.480056	−	0.685441i
$43$	2.48085	+	4.29695i	0.378326	+	0.655279i	0.990819	−	0.135197i	$-0.0431666\pi$
$43$	2.48085	+	4.29695i	0.378326	+	0.655279i	−0.612493	+	0.790476i	$0.709833\pi$
$44$	2.32349			0.350279
$45$	2.18128	−	2.59847i	0.325166	−	0.387357i
$46$	5.95576			0.878129
$47$	3.78552	+	6.55672i	0.552175	+	0.956396i	0.998117	+	0.0613338i	$0.0195354\pi$
$47$	3.78552	+	6.55672i	0.552175	+	0.956396i	−0.445942	+	0.895062i	$0.647131\pi$
$48$	−1.03500	−	2.22015i	−0.149389	−	0.320452i
$49$	−6.98859	+	12.1046i	−0.998370	+	1.72923i
$50$	−1.27195	+	2.20308i	−0.179881	+	0.311563i
$51$	−2.79929	−	0.245195i	−0.391979	−	0.0343342i
$52$	4.47206	+	7.74583i	0.620163	+	1.07415i
$53$	−14.2165			−1.95279			−0.976395	−	0.215993i	$-0.930701\pi$
$53$	−14.2165			−1.95279			−0.976395	+	0.215993i	$0.930701\pi$
$54$	0.918347	+	3.43154i	0.124971	+	0.466973i
$55$	1.71442			0.231173
$56$	−5.53057	−	9.57923i	−0.739053	−	1.28008i
$57$	−2.52393	−	0.221076i	−0.334303	−	0.0292822i
$58$	0.341490	−	0.591478i	0.0448398	−	0.0776648i
$59$	−2.35033	+	4.07089i	−0.305987	+	0.529985i	−0.977481	−	0.211026i	$-0.932320\pi$
$59$	−2.35033	+	4.07089i	−0.305987	+	0.529985i	0.671494	+	0.741010i	$0.265653\pi$
$60$	−1.26844	−	2.72090i	−0.163755	−	0.351267i
$61$	6.70236	+	11.6088i	0.858149	+	1.48636i	0.873693	+	0.486478i	$0.161719\pi$
$61$	6.70236	+	11.6088i	0.858149	+	1.48636i	−0.0155439	+	0.999879i	$0.504948\pi$
$62$	1.30465			0.165691
$63$	−4.69680	−	12.9126i	−0.591741	−	1.62683i
$64$	1.13452			0.141815
$65$	3.29978	+	5.71539i	0.409287	+	0.708907i
$66$	−1.02978	+	1.47036i	−0.126757	+	0.180988i
$67$	0.500000	−	0.866025i	0.0610847	−	0.105802i
$67$	0.500000	−	0.866025i	0.0610847	−	0.105802i
$68$	−1.24324	+	2.15336i	−0.150765	+	0.261133i
$69$	8.65616	−	12.3596i	1.04208	−	1.48792i
$70$	−1.77047	−	3.06654i	−0.211611	−	0.366521i
$71$	5.27337			0.625834			0.312917	−	0.949780i	$-0.398694\pi$
$71$	5.27337			0.625834			0.312917	+	0.949780i	$0.398694\pi$
$72$	7.13482	+	1.25957i	0.840847	+	0.148442i
$73$	−11.5626			−1.35330			−0.676652	−	0.736303i	$-0.736570\pi$
$73$	−11.5626			−1.35330			−0.676652	+	0.736303i	$0.736570\pi$
$74$	1.46928	+	2.54486i	0.170800	+	0.295834i
$75$	2.72324	+	5.84157i	0.314453	+	0.674526i
$76$	−1.12095	+	1.94154i	−0.128582	+	0.222710i
$77$	3.47172	−	6.01320i	0.395640	−	0.685268i
$78$	−6.88377	−	0.602963i	−0.779434	−	0.0682721i
$79$	−0.528994	−	0.916245i	−0.0595165	−	0.103086i	0.834732	−	0.550656i	$-0.185623\pi$
$79$	−0.528994	−	0.916245i	−0.0595165	−	0.103086i	−0.894248	+	0.447571i	$0.852289\pi$
$80$	−1.59935			−0.178812
$81$	8.45597	+	3.08165i	0.939552	+	0.342405i
$82$	−3.54625			−0.391618
$83$	3.12353	+	5.41011i	0.342852	+	0.593837i	0.984961	−	0.172776i	$-0.0552737\pi$
$83$	3.12353	+	5.41011i	0.342852	+	0.593837i	−0.642109	+	0.766613i	$0.721940\pi$
$84$	−12.1119	−	1.06091i	−1.32152	−	0.115755i
$85$	−0.917346	+	1.58889i	−0.0995002	+	0.172339i
$86$	−1.69601	+	2.93757i	−0.182885	+	0.316766i
$87$	−0.731129	−	1.56833i	−0.0783852	−	0.168143i
$88$	1.83062	+	3.17072i	0.195145	+	0.338000i
$89$	0.567051			0.0601072			0.0300536	−	0.999548i	$-0.490432\pi$
$89$	0.567051			0.0601072			0.0300536	+	0.999548i	$0.490432\pi$
$90$	2.28403	+	0.403218i	0.240757	+	0.0425029i
$91$	26.7283			2.80189
$92$	−6.67604	−	11.5632i	−0.696026	−	1.20555i
$93$	1.89620	−	2.70746i	0.196626	−	0.280750i
$94$	−2.58793	+	4.48243i	−0.266925	+	0.462328i
$95$	−0.827110	+	1.43260i	−0.0848597	+	0.146981i
$96$	5.75989	−	8.22418i	0.587866	−	0.839377i
$97$	−0.747876	−	1.29536i	−0.0759353	−	0.131524i	0.825557	−	0.564318i	$-0.190861\pi$
$97$	−0.747876	−	1.29536i	−0.0759353	−	0.131524i	−0.901493	+	0.432795i	$0.857528\pi$
$98$	−9.55535			−0.965237
$99$	1.55464	+	4.27406i	0.156247	+	0.429560i
$100$	5.70311			0.570311
$101$	−4.30619	−	7.45853i	−0.428481	−	0.742152i	0.568257	−	0.822851i	$-0.307618\pi$
$101$	−4.30619	−	7.45853i	−0.428481	−	0.742152i	−0.996738	+	0.0806994i	$0.974285\pi$
$102$	−0.811684	−	1.74113i	−0.0803687	−	0.172397i
$103$	−3.14904	+	5.45429i	−0.310284	+	0.537428i	−0.978424	−	0.206608i	$-0.933757\pi$
$103$	−3.14904	+	5.45429i	−0.310284	+	0.537428i	0.668140	+	0.744036i	$0.267091\pi$
$104$	−7.04684	+	12.2055i	−0.691000	+	1.19685i
$105$	−8.93699	−	0.782808i	−0.872161	−	0.0763943i
$106$	−4.85949	−	8.41688i	−0.471995	−	0.817520i
$107$	14.7000			1.42110			0.710551	−	0.703646i	$-0.248446\pi$
$107$	14.7000			1.42110			0.710551	+	0.703646i	$0.248446\pi$
$108$	5.63300	−	5.62954i	0.542036	−	0.541702i
$109$	−9.00582			−0.862601			−0.431300	−	0.902208i	$-0.641945\pi$
$109$	−9.00582			−0.862601			−0.431300	+	0.902208i	$0.641945\pi$
$110$	0.586024	+	1.01502i	0.0558752	+	0.0967787i
$111$	7.41664	+	0.649638i	0.703956	+	0.0616609i
$112$	−3.23869	+	5.60958i	−0.306028	+	0.530055i
$113$	2.41444	−	4.18193i	0.227131	−	0.393403i	−0.729825	−	0.683634i	$-0.760399\pi$
$113$	2.41444	−	4.18193i	0.227131	−	0.393403i	0.956957	+	0.290231i	$0.0937320\pi$
$114$	−0.731842	−	1.56986i	−0.0685433	−	0.147031i
$115$	−4.92603	−	8.53213i	−0.459354	−	0.795625i
$116$	−1.53116			−0.142164
$117$	−11.2562	+	13.4091i	−1.04064	+	1.23967i
$118$	−3.21356			−0.295832
$119$	3.71527	+	6.43503i	0.340578	+	0.589898i
$120$	2.71368	−	3.87469i	0.247724	−	0.353709i
$121$	4.35086	−	7.53591i	0.395533	−	0.685083i
$122$	−4.58200	+	7.93625i	−0.414834	+	0.718514i
$123$	−5.15416	+	7.35930i	−0.464735	+	0.663565i
$124$	−1.46244	−	2.53301i	−0.131331	−	0.227471i
$125$	9.86253			0.882132
$126$	6.03943	−	7.19451i	0.538035	−	0.640938i
$127$	−15.5376			−1.37874			−0.689370	−	0.724410i	$-0.742112\pi$
$127$	−15.5376			−1.37874			−0.689370	+	0.724410i	$0.742112\pi$
$128$	−5.40914	−	9.36890i	−0.478105	−	0.828102i
$129$	3.63114	+	7.78910i	0.319704	+	0.685792i
$130$	−2.25586	+	3.90727i	−0.197852	+	0.342690i
$131$	−1.39141	+	2.41000i	−0.121568	+	0.210563i	−0.920386	−	0.391010i	$-0.872126\pi$
$131$	−1.39141	+	2.41000i	−0.121568	+	0.210563i	0.798818	+	0.601573i	$0.205459\pi$
$132$	4.00905	+	0.351161i	0.348943	+	0.0305646i
$133$	3.34981	+	5.80204i	0.290465	+	0.503101i
$134$	0.683640			0.0590575
$135$	4.15640	−	4.15384i	0.357726	−	0.357506i
$136$	−3.91807			−0.335972
$137$	−6.64792	−	11.5145i	−0.567970	−	0.983753i	−0.996767	−	0.0803521i	$-0.974396\pi$
$137$	−6.64792	−	11.5145i	−0.567970	−	0.983753i	0.428796	−	0.903401i	$-0.358938\pi$
$138$	10.2763	+	0.900124i	0.874779	+	0.0766236i
$139$	−11.0299	+	19.1043i	−0.935542	+	1.62041i	−0.161879	+	0.986811i	$0.551755\pi$
$139$	−11.0299	+	19.1043i	−0.935542	+	1.62041i	−0.773664	+	0.633596i	$0.781578\pi$
$140$	−3.96917	+	6.87480i	−0.335456	+	0.581027i
$141$	5.54076	+	11.8854i	0.466616	+	1.00093i
$142$	1.80254	+	3.12210i	0.151266	+	0.262001i
$143$	−8.84708			−0.739830
$144$	−1.45029	−	3.98718i	−0.120857	−	0.332265i
$145$	−1.12979			−0.0938239
$146$	−3.95234	−	6.84565i	−0.327098	−	0.566550i
$147$	−13.8879	+	19.8296i	−1.14545	+	1.63552i
$148$	3.29394	−	5.70527i	0.270760	−	0.468970i
$149$	10.7229	−	18.5726i	0.878452	−	1.52152i	0.0254131	−	0.999677i	$-0.491910\pi$
$149$	10.7229	−	18.5726i	0.878452	−	1.52152i	0.853039	−	0.521847i	$-0.174757\pi$
$150$	−2.52764	+	3.60906i	−0.206381	+	0.294678i
$151$	−2.89462	−	5.01363i	−0.235561	−	0.408004i	0.723875	−	0.689932i	$-0.242359\pi$
$151$	−2.89462	−	5.01363i	−0.235561	−	0.408004i	−0.959436	+	0.281928i	$0.909026\pi$
$152$	−3.53267			−0.286537
$153$	−4.79296	−	0.846141i	−0.387488	−	0.0684064i
$154$	4.74681			0.382509
$155$	−1.07908	−	1.86902i	−0.0866739	−	0.150124i
$156$	6.54562	+	14.0409i	0.524069	+	1.12417i
$157$	−2.73157	+	4.73122i	−0.218003	+	0.377593i	−0.954197	−	0.299178i	$-0.903288\pi$
$157$	−2.73157	+	4.73122i	−0.218003	+	0.377593i	0.736194	+	0.676770i	$0.236621\pi$
$158$	0.361641	−	0.626381i	0.0287706	−	0.0498322i
$159$	−24.5298	−	2.14861i	−1.94534	−	0.170396i
$160$	−3.27782	−	5.67736i	−0.259135	−	0.448834i
$161$	−39.9010			−3.14464
$162$	1.06593	+	6.05972i	0.0837474	+	0.476097i
$163$	−17.5776			−1.37679			−0.688393	−	0.725338i	$-0.741684\pi$
$163$	−17.5776			−1.37679			−0.688393	+	0.725338i	$0.741684\pi$
$164$	3.97513	+	6.88513i	0.310406	+	0.537638i
$165$	2.95814	+	0.259110i	0.230291	+	0.0201717i
$166$	−2.13537	+	3.69857i	−0.165737	+	0.287065i
$167$	11.5450	−	19.9966i	0.893381	−	1.54738i	0.0575855	−	0.998341i	$-0.481660\pi$
$167$	11.5450	−	19.9966i	0.893381	−	1.54738i	0.835796	−	0.549041i	$-0.185007\pi$
$168$	−8.09493	−	17.3643i	−0.624538	−	1.33968i
$169$	−10.5281	−	18.2352i	−0.809855	−	1.40271i
$170$	−1.25427			−0.0961980
$171$	−4.32149	−	0.762909i	−0.330473	−	0.0583411i
$172$	7.60447			0.579836
$173$	2.23341	+	3.86837i	0.169803	+	0.294107i	0.938350	−	0.345685i	$-0.112354\pi$
$173$	2.23341	+	3.86837i	0.169803	+	0.294107i	−0.768548	+	0.639793i	$0.779020\pi$
$174$	0.678615	−	0.968951i	0.0514456	−	0.0734560i
$175$	8.52150	−	14.7597i	0.644165	−	1.11573i
$176$	1.07201	−	1.85677i	0.0808055	−	0.139959i
$177$	−4.67062	+	6.66887i	−0.351065	+	0.501263i
$178$	0.193829	+	0.335722i	0.0145281	+	0.0251634i
$179$	1.53976			0.115087			0.0575434	−	0.998343i	$-0.481673\pi$
$179$	1.53976			0.115087			0.0575434	+	0.998343i	$0.481673\pi$
$180$	−1.77740	−	4.88647i	−0.132479	−	0.364216i
$181$	21.6583			1.60985			0.804924	−	0.593378i	$-0.202206\pi$
$181$	21.6583			1.60985			0.804924	+	0.593378i	$0.202206\pi$
$182$	9.13627	+	15.8245i	0.677226	+	1.17299i
$183$	9.81004	+	21.0433i	0.725179	+	1.55557i
$184$	10.5198	−	18.2208i	0.775527	−	1.34325i
$185$	2.43048	−	4.20972i	0.178693	−	0.309505i
$186$	2.25110	+	0.197179i	0.165059	+	0.0144578i
$187$	−1.22975	−	2.12999i	−0.0899285	−	0.155761i
$188$	11.6037			0.846284
$189$	−6.15252	−	22.9898i	−0.447530	−	1.67226i
$190$	−1.13089			−0.0820434
$191$	2.79884	+	4.84774i	0.202517	+	0.350770i	0.949339	−	0.314254i	$-0.101754\pi$
$191$	2.79884	+	4.84774i	0.202517	+	0.350770i	−0.746822	+	0.665024i	$0.768421\pi$
$192$	1.95755	+	0.171465i	0.141274	+	0.0123744i
$193$	−3.43585	+	5.95106i	−0.247318	+	0.428367i	−0.962781	−	0.270284i	$-0.912882\pi$
$193$	−3.43585	+	5.95106i	−0.247318	+	0.428367i	0.715463	+	0.698651i	$0.246216\pi$
$194$	0.511277	−	0.885558i	0.0367076	−	0.0635794i
$195$	4.82979	+	10.3603i	0.345869	+	0.741916i
$196$	10.7110	+	18.5519i	0.765069	+	1.32514i
$197$	−11.0832			−0.789644			−0.394822	−	0.918758i	$-0.629194\pi$
$197$	−11.0832			−0.789644			−0.394822	+	0.918758i	$0.629194\pi$
$198$	−1.99905	+	2.38138i	−0.142066	+	0.169237i
$199$	0.537635			0.0381119			0.0190560	−	0.999818i	$-0.493934\pi$
$199$	0.537635			0.0381119			0.0190560	+	0.999818i	$0.493934\pi$
$200$	4.49333	+	7.78268i	0.317727	+	0.550319i
$201$	0.993609	−	1.41871i	0.0700838	−	0.100068i
$202$	2.94388	−	5.09895i	0.207131	−	0.358761i
$203$	−2.28783	+	3.96264i	−0.160574	+	0.278123i
$204$	−2.47059	+	3.52760i	−0.172976	+	0.246982i
$205$	2.93312	+	5.08031i	0.204858	+	0.354824i
$206$	−4.30561			−0.299986
$207$	16.8037	−	20.0175i	1.16794	−	1.39131i
$208$	8.25324			0.572259
$209$	−1.10879	−	1.92048i	−0.0766964	−	0.132842i
$210$	−2.59138	−	5.55872i	−0.178822	−	0.383588i
$211$	−7.79071	+	13.4939i	−0.536335	+	0.928959i	0.462763	+	0.886482i	$0.346858\pi$
$211$	−7.79071	+	13.4939i	−0.536335	+	0.928959i	−0.999097	+	0.0424768i	$0.986475\pi$
$212$	−10.8944	+	18.8696i	−0.748229	+	1.29597i
$213$	9.09891	+	0.796992i	0.623447	+	0.0546090i
$214$	5.02475	+	8.70312i	0.343485	+	0.594933i
$215$	5.61108			0.382673
$216$	12.1204	+	3.25164i	0.824687	+	0.221246i
$217$	−8.74060			−0.593350
$218$	−3.07837	−	5.33189i	−0.208493	−	0.361121i
$219$	−19.9507	−	1.74752i	−1.34814	−	0.118086i
$220$	1.31379	−	2.27556i	0.0885760	−	0.153418i
$221$	4.73385	−	8.19927i	0.318433	−	0.551543i
$222$	2.15054	+	4.61307i	0.144334	+	0.309609i
$223$	−3.26384	−	5.65313i	−0.218563	−	0.378562i	0.735806	−	0.677192i	$-0.236803\pi$
$223$	−3.26384	−	5.65313i	−0.218563	−	0.378562i	−0.954369	+	0.298631i	$0.903470\pi$
$224$	−26.5505			−1.77398
$225$	3.81593	+	10.4909i	0.254395	+	0.699392i
$226$	3.30121			0.219593
$227$	−1.10241	−	1.90942i	−0.0731692	−	0.126733i	0.827119	−	0.562026i	$-0.189978\pi$
$227$	−1.10241	−	1.90942i	−0.0731692	−	0.126733i	−0.900289	+	0.435293i	$0.856645\pi$
$228$	−2.22757	+	3.18061i	−0.147524	+	0.210641i
$229$	3.06469	−	5.30820i	0.202520	−	0.350776i	−0.746819	−	0.665027i	$-0.768420\pi$
$229$	3.06469	−	5.30820i	0.202520	−	0.350776i	0.949340	+	0.314251i	$0.101753\pi$
$230$	3.36763	−	5.83290i	0.222055	−	0.384610i
$231$	6.89907	−	9.85074i	0.453925	−	0.648131i
$232$	−1.20636	−	2.08948i	−0.0792014	−	0.137181i
$233$	−10.2211			−0.669606			−0.334803	−	0.942288i	$-0.608670\pi$
$233$	−10.2211			−0.669606			−0.334803	+	0.942288i	$0.608670\pi$
$234$	−11.7864	−	2.08076i	−0.770503	−	0.136023i
$235$	8.56195			0.558520
$236$	3.60220	+	6.23919i	0.234483	+	0.406137i
$237$	−0.774273	−	1.66088i	−0.0502944	−	0.107886i
$238$	−2.53990	+	4.39924i	−0.164638	+	0.285161i
$239$	−4.94283	+	8.56123i	−0.319725	+	0.553780i	−0.980431	−	0.196865i	$-0.936924\pi$
$239$	−4.94283	+	8.56123i	−0.319725	+	0.553780i	0.660706	+	0.750645i	$0.270257\pi$
$240$	−2.75959	−	0.241717i	−0.178130	−	0.0156028i
$241$	6.83386	+	11.8366i	0.440208	+	0.762462i	0.997705	−	0.0677171i	$-0.0215715\pi$
$241$	6.83386	+	11.8366i	0.440208	+	0.762462i	−0.557497	+	0.830179i	$0.688238\pi$
$242$	5.94884			0.382406
$243$	14.1246	+	6.59521i	0.906091	+	0.423083i
$244$	20.5446			1.31523
$245$	7.90326	+	13.6889i	0.504921	+	0.874549i
$246$	−6.11886	−	0.535963i	−0.390124	−	0.0341717i
$247$	4.26820	−	7.39274i	0.271579	−	0.470389i
$248$	2.30443	−	3.99139i	0.146332	−	0.253454i
$249$	4.57182	+	9.80693i	0.289727	+	0.621489i
$250$	3.37121	+	5.83911i	0.213214	+	0.369298i
$251$	−10.0426			−0.633883			−0.316941	−	0.948445i	$-0.602656\pi$
$251$	−10.0426			−0.633883			−0.316941	+	0.948445i	$0.602656\pi$
$252$	−20.7381	−	3.66108i	−1.30638	−	0.230626i
$253$	13.2072			0.830331
$254$	−5.31106	−	9.19903i	−0.333246	−	0.577198i
$255$	−1.82297	+	2.60290i	−0.114159	+	0.163000i
$256$	4.83242	−	8.36999i	0.302026	−	0.523125i
$257$	13.3402	−	23.1059i	0.832140	−	1.44131i	−0.0641976	−	0.997937i	$-0.520449\pi$
$257$	13.3402	−	23.1059i	0.832140	−	1.44131i	0.896338	−	0.443372i	$-0.146218\pi$
$258$	−3.37033	+	4.81228i	−0.209828	+	0.299600i
$259$	−9.84350	−	17.0494i	−0.611645	−	1.05940i
$260$	10.1147			0.627289
$261$	−1.02449	−	2.81657i	−0.0634145	−	0.174341i
$262$	−1.90245			−0.117534
$263$	−5.83114	−	10.0998i	−0.359564	−	0.622783i	0.628324	−	0.777952i	$-0.283741\pi$
$263$	−5.83114	−	10.0998i	−0.359564	−	0.622783i	−0.987888	+	0.155169i	$0.950408\pi$
$264$	2.67942	+	5.74758i	0.164907	+	0.353739i
$265$	−8.03860	+	13.9233i	−0.493807	+	0.855299i
$266$	−2.29006	+	3.96651i	−0.140413	+	0.243202i
$267$	0.978414	+	0.0857012i	0.0598780	+	0.00524483i
$268$	−0.766318	−	1.32730i	−0.0468103	−	0.0810779i
$269$	3.18753			0.194347			0.0971736	−	0.995267i	$-0.469020\pi$
$269$	3.18753			0.194347			0.0971736	+	0.995267i	$0.469020\pi$
$270$	3.88002	+	1.04093i	0.236130	+	0.0633488i
$271$	−17.0932			−1.03834			−0.519169	−	0.854671i	$-0.673759\pi$
$271$	−17.0932			−1.03834			−0.519169	+	0.854671i	$0.673759\pi$
$272$	1.14721	+	1.98702i	0.0695598	+	0.120481i
$273$	46.1182	+	4.03959i	2.79120	+	0.244487i
$274$	4.54478	−	7.87179i	0.274560	−	0.475552i
$275$	−2.82062	+	4.88545i	−0.170089	+	0.294604i
$276$	−9.77153	−	20.9607i	−0.588177	−	1.26169i
$277$	14.8162	+	25.6625i	0.890221	+	1.54191i	0.839610	+	0.543190i	$0.182784\pi$
$277$	14.8162	+	25.6625i	0.890221	+	1.54191i	0.0506112	+	0.998718i	$0.483883\pi$
$278$	−15.0809			−0.904494
$279$	3.68097	−	4.38498i	0.220374	−	0.262522i
$280$	−12.5088			−0.747545
$281$	14.9318	+	25.8626i	0.890757	+	1.54284i	0.838970	+	0.544178i	$0.183158\pi$
$281$	14.9318	+	25.8626i	0.890757	+	1.54284i	0.0517866	+	0.998658i	$0.483508\pi$
$282$	−5.14279	+	7.34306i	−0.306249	+	0.437273i
$283$	4.17461	−	7.23064i	0.248155	−	0.429817i	−0.714859	−	0.699269i	$-0.753509\pi$
$283$	4.17461	−	7.23064i	0.248155	−	0.429817i	0.963014	+	0.269452i	$0.0868425\pi$
$284$	4.04108	−	6.99936i	0.239794	−	0.415336i
$285$	−1.64365	+	2.34686i	−0.0973613	+	0.139016i
$286$	−3.02411	−	5.23790i	−0.178819	−	0.309724i
$287$	23.7583			1.40241
$288$	11.1813	−	13.3198i	0.658866	−	0.784879i
$289$	−14.3680			−0.845174
$290$	−0.386184	−	0.668891i	−0.0226775	−	0.0392786i
$291$	−1.09464	−	2.34810i	−0.0641691	−	0.137648i
$292$	−8.86066	+	15.3471i	−0.518531	+	0.898121i
$293$	7.83210	−	13.5656i	0.457556	−	0.792511i	−0.541275	−	0.840846i	$-0.682058\pi$
$293$	7.83210	−	13.5656i	0.457556	−	0.792511i	0.998831	+	0.0483350i	$0.0153915\pi$
$294$	−16.4872	−	1.44415i	−0.961555	−	0.0842245i
$295$	2.65794	+	4.60369i	0.154751	+	0.268037i
$296$	10.3808			0.603374
$297$	2.03648	+	7.60962i	0.118169	+	0.441555i
$298$	14.6612			0.849299
$299$	25.4202	+	44.0290i	1.47009	+	2.54626i
$300$	9.84040	+	0.861939i	0.568136	+	0.0497641i
$301$	11.3625	−	19.6804i	0.654923	−	1.13436i
$302$	1.97888	−	3.42752i	0.113872	−	0.197232i
$303$	−6.30284	−	13.5201i	−0.362089	−	0.776709i
$304$	1.03436	+	1.79157i	0.0593247	+	0.102753i
$305$	15.1591			0.868009
$306$	−1.13737	−	3.12689i	−0.0650191	−	0.178753i
$307$	−7.59977			−0.433742			−0.216871	−	0.976200i	$-0.569585\pi$
$307$	−7.59977			−0.433742			−0.216871	+	0.976200i	$0.569585\pi$
$308$	−5.32089	−	9.21605i	−0.303186	−	0.525133i
$309$	−6.25783	+	8.93515i	−0.355995	+	0.508303i
$310$	0.737703	−	1.27774i	0.0418987	−	0.0725707i
$311$	6.99970	−	12.1238i	0.396916	−	0.687479i	−0.596427	−	0.802667i	$-0.703414\pi$
$311$	6.99970	−	12.1238i	0.396916	−	0.687479i	0.993344	+	0.115188i	$0.0367470\pi$
$312$	−14.0036	+	19.9949i	−0.792798	+	1.13199i
$313$	−10.0051	−	17.3293i	−0.565520	−	0.979510i	−0.997001	−	0.0773877i	$-0.975342\pi$
$313$	−10.0051	−	17.3293i	−0.565520	−	0.979510i	0.431481	−	0.902122i	$-0.357991\pi$
$314$	−3.73482			−0.210768
$315$	−15.3020	−	2.70139i	−0.862168	−	0.152206i
$316$	−1.62151			−0.0912172
$317$	−7.61117	−	13.1829i	−0.427486	−	0.740428i	0.569163	−	0.822225i	$-0.307267\pi$
$317$	−7.61117	−	13.1829i	−0.427486	−	0.740428i	−0.996649	+	0.0817971i	$0.973934\pi$
$318$	−7.11269	−	15.2573i	−0.398860	−	0.855587i
$319$	0.757272	−	1.31163i	0.0423991	−	0.0734374i
$320$	0.641502	−	1.11111i	0.0358611	−	0.0621132i
$321$	25.3640	+	2.22168i	1.41568	+	0.124002i
$322$	−13.6389	−	23.6233i	−0.760068	−	1.31648i
$323$	2.37314			0.132045
$324$	10.5702	−	8.86211i	0.587236	−	0.492339i
$325$	−21.7155			−1.20456
$326$	−6.00838	−	10.4068i	−0.332774	−	0.576381i
$327$	−15.5390	−	1.36109i	−0.859311	−	0.0752687i
$328$	−6.26381	+	10.8492i	−0.345861	+	0.599049i
$329$	17.3380	−	30.0303i	0.955876	−	1.65563i
$330$	0.857746	+	1.83994i	0.0472174	+	0.101285i
$331$	−6.23215	−	10.7944i	−0.342550	−	0.593314i	0.642356	−	0.766407i	$-0.277957\pi$
$331$	−6.23215	−	10.7944i	−0.342550	−	0.593314i	−0.984906	+	0.173093i	$0.944624\pi$
$332$	9.57448			0.525468
$333$	12.6988	+	2.24183i	0.695890	+	0.122851i
$334$	15.7853			0.863732
$335$	−0.565440	−	0.979371i	−0.0308933	−	0.0535088i
$336$	−6.43599	+	9.18953i	−0.351112	+	0.501330i
$337$	13.6038	−	23.5624i	0.741045	−	1.28353i	−0.210975	−	0.977491i	$-0.567664\pi$
$337$	13.6038	−	23.5624i	0.741045	−	1.28353i	0.952020	−	0.306036i	$-0.0990028\pi$
$338$	7.19744	−	12.4663i	0.391489	−	0.678079i
$339$	4.79802	−	6.85078i	0.260593	−	0.372084i
$340$	1.40596	+	2.43519i	0.0762488	+	0.132067i
$341$	2.89314			0.156672
$342$	−1.02549	−	2.81931i	−0.0554522	−	0.152451i
$343$	31.9561			1.72547
$344$	5.99137	+	10.3774i	0.323033	+	0.559510i
$345$	−7.21008	−	15.4662i	−0.388178	−	0.832673i
$346$	−1.52685	+	2.64457i	−0.0820837	+	0.142173i
$347$	3.95817	−	6.85575i	0.212486	−	0.368036i	−0.740006	−	0.672600i	$-0.765177\pi$
$347$	3.95817	−	6.85575i	0.212486	−	0.368036i	0.952492	+	0.304564i	$0.0985108\pi$
$348$	−2.64193	−	0.231411i	−0.141622	−	0.0124050i
$349$	−7.81285	−	13.5322i	−0.418212	−	0.724365i	0.577548	−	0.816357i	$-0.304010\pi$
$349$	−7.81285	−	13.5322i	−0.418212	−	0.724365i	−0.995760	+	0.0919924i	$0.970676\pi$
$350$	11.6513			0.622786
$351$	−21.4486	+	21.4354i	−1.14484	+	1.14414i
$352$	8.78820			0.468413
$353$	−16.9539	−	29.3649i	−0.902362	−	1.56294i	−0.824419	−	0.565980i	$-0.808498\pi$
$353$	−16.9539	−	29.3649i	−0.902362	−	1.56294i	−0.0779433	−	0.996958i	$-0.524835\pi$
$354$	−5.54481	−	0.485681i	−0.294703	−	0.0258136i
$355$	2.98178	−	5.16459i	0.158256	−	0.274108i
$356$	0.434541	−	0.752648i	0.0230306	−	0.0398902i
$357$	5.43793	+	11.6648i	0.287806	+	0.617366i
$358$	0.526319	+	0.911612i	0.0278168	+	0.0481802i
$359$	6.94576			0.366583			0.183292	−	0.983059i	$-0.441325\pi$
$359$	6.94576			0.366583			0.183292	+	0.983059i	$0.441325\pi$
$360$	5.26790	−	6.27543i	0.277643	−	0.330744i
$361$	−16.8603			−0.887384
$362$	7.40323	+	12.8228i	0.389105	+	0.673950i
$363$	8.64611	−	12.3452i	0.453803	−	0.647956i
$364$	20.4824	−	35.4766i	1.07357	−	1.85948i
$365$	−6.53798	+	11.3241i	−0.342213	+	0.592731i
$366$	−9.10543	+	13.0011i	−0.475948	+	0.679576i
$367$	−0.592024	−	1.02542i	−0.0309034	−	0.0535263i	0.850160	−	0.526524i	$-0.176505\pi$
$367$	−0.592024	−	1.02542i	−0.0309034	−	0.0535263i	−0.881063	+	0.472998i	$0.843172\pi$
$368$	−12.3207			−0.642262
$369$	−10.0055	+	11.9191i	−0.520864	+	0.620483i
$370$	3.32315			0.172762
$371$	32.5564	+	56.3894i	1.69025	+	2.92759i
$372$	−2.14052	−	4.59160i	−0.110981	−	0.238063i
$373$	6.45736	−	11.1845i	0.334349	−	0.579110i	−0.649010	−	0.760780i	$-0.724817\pi$
$373$	6.45736	−	11.1845i	0.334349	−	0.579110i	0.983360	+	0.181670i	$0.0581501\pi$
$374$	0.840708	−	1.45615i	0.0434720	−	0.0752957i
$375$	17.0173	+	1.49057i	0.878767	+	0.0769729i
$376$	9.14223	+	15.8348i	0.471474	+	0.816618i
$377$	5.83014			0.300267
$378$	11.5080	−	11.5010i	0.591909	−	0.591546i
$379$	−10.9162			−0.560728			−0.280364	−	0.959894i	$-0.590455\pi$
$379$	−10.9162			−0.560728			−0.280364	+	0.959894i	$0.590455\pi$
$380$	1.26766	+	2.19565i	0.0650296	+	0.112635i
$381$	−26.8093	−	2.34828i	−1.37348	−	0.120306i
$382$	−1.91340	+	3.31411i	−0.0978981	+	0.169564i
$383$	8.30806	−	14.3900i	0.424522	−	0.735294i	−0.571853	−	0.820356i	$-0.693775\pi$
$383$	8.30806	−	14.3900i	0.424522	−	0.735294i	0.996376	+	0.0850617i	$0.0271087\pi$
$384$	−7.91720	−	16.9830i	−0.404023	−	0.866661i
$385$	−3.92610	−	6.80021i	−0.200093	−	0.346571i
$386$	−4.69776			−0.239110
$387$	5.08813	+	13.9884i	0.258644	+	0.711073i
$388$	−2.29244			−0.116381
$389$	15.4454	+	26.7523i	0.783114	+	1.35639i	0.930119	+	0.367258i	$0.119703\pi$
$389$	15.4454	+	26.7523i	0.783114	+	1.35639i	−0.147005	+	0.989136i	$0.546963\pi$
$390$	−4.48289	+	6.40083i	−0.227000	+	0.324119i
$391$	−7.06686	+	12.2402i	−0.357386	+	0.619011i
$392$	−16.8778	+	29.2332i	−0.852458	+	1.47650i
$393$	−2.76504	+	3.94803i	−0.139478	+	0.199152i
$394$	−3.78845	−	6.56179i	−0.190859	−	0.330578i
$395$	−1.19646			−0.0602004
$396$	6.86432	+	1.21182i	0.344945	+	0.0608961i
$397$	−29.6731			−1.48925			−0.744624	−	0.667484i	$-0.767371\pi$
$397$	−29.6731			−1.48925			−0.744624	+	0.667484i	$0.767371\pi$
$398$	0.183774	+	0.318307i	0.00921178	+	0.0159553i
$399$	4.90302	+	10.5174i	0.245458	+	0.526527i
$400$	2.63129	−	4.55752i	0.131564	−	0.227876i
$401$	−10.6761	+	18.4915i	−0.533137	+	0.923420i	0.466114	+	0.884725i	$0.345654\pi$
$401$	−10.6761	+	18.4915i	−0.533137	+	0.923420i	−0.999251	+	0.0386955i	$0.987680\pi$
$402$	1.17958	+	0.103322i	0.0588322	+	0.00515323i
$403$	5.56847	+	9.64487i	0.277385	+	0.480445i
$404$	−13.1996			−0.656706
$405$	7.79943	−	6.53905i	0.387557	−	0.324928i
$406$	−3.12810			−0.155245
$407$	3.25820	+	5.64336i	0.161503	+	0.279731i
$408$	−6.76042	−	0.592158i	−0.334691	−	0.0293162i
$409$	5.97066	−	10.3415i	0.295230	−	0.511354i	−0.679808	−	0.733390i	$-0.737937\pi$
$409$	5.97066	−	10.3415i	0.295230	−	0.511354i	0.975038	+	0.222036i	$0.0712704\pi$
$410$	−2.00519	+	3.47310i	−0.0990295	+	0.171524i
$411$	−9.73037	−	20.8724i	−0.479964	−	1.02956i
$412$	4.82633	+	8.35945i	0.237776	+	0.411841i
$413$	21.5294			1.05939
$414$	17.5952	+	3.10623i	0.864757	+	0.152663i
$415$	7.06468			0.346792
$416$	16.9148	+	29.2973i	0.829316	+	1.43642i
$417$	−21.9188	+	31.2964i	−1.07337	+	1.53259i
$418$	0.758011	−	1.31291i	0.0370755	−	0.0642167i
$419$	−13.5464	+	23.4631i	−0.661785	+	1.14625i	0.318361	+	0.947970i	$0.396868\pi$
$419$	−13.5464	+	23.4631i	−0.661785	+	1.14625i	−0.980146	+	0.198276i	$0.936466\pi$
$420$	−7.88760	+	11.2622i	−0.384876	+	0.549540i
$421$	−11.0136	−	19.0761i	−0.536770	−	0.929712i	−0.999075	−	0.0429917i	$-0.986311\pi$
$421$	−11.0136	−	19.0761i	−0.536770	−	0.929712i	0.462306	−	0.886721i	$-0.347022\pi$
$422$	−10.6521			−0.518535
$423$	7.76397	+	21.3450i	0.377497	+	1.03783i
$424$	−34.3336			−1.66739
$425$	−3.01848	−	5.22817i	−0.146418	−	0.253603i
$426$	2.63833	+	5.65943i	0.127828	+	0.274200i
$427$	30.6974	−	53.1694i	1.48555	−	2.57305i
$428$	11.2649	−	19.5113i	0.544508	−	0.943116i
$429$	−15.2651	−	1.33710i	−0.737008	−	0.0645559i
$430$	1.91798	+	3.32204i	0.0924932	+	0.160203i
$431$	−15.3761			−0.740642			−0.370321	−	0.928904i	$-0.620752\pi$
$431$	−15.3761			−0.740642			−0.370321	+	0.928904i	$0.620752\pi$
$432$	−1.89979	−	7.09884i	−0.0914036	−	0.341543i
$433$	21.8572			1.05039			0.525195	−	0.850982i	$-0.323992\pi$
$433$	21.8572			1.05039			0.525195	+	0.850982i	$0.323992\pi$
$434$	−2.98771	−	5.17486i	−0.143415	−	0.248401i
$435$	−1.94939	−	0.170751i	−0.0934660	−	0.00818687i
$436$	−6.90132	+	11.9534i	−0.330513	+	0.572466i
$437$	−6.37172	+	11.0361i	−0.304801	+	0.527930i
$438$	−5.78492	−	12.4091i	−0.276414	−	0.592931i
$439$	15.5943	+	27.0101i	0.744275	+	1.28912i	0.950533	+	0.310625i	$0.100538\pi$
$439$	15.5943	+	27.0101i	0.744275	+	1.28912i	−0.206257	+	0.978498i	$0.566128\pi$
$440$	4.14042			0.197387
$441$	−26.9597	+	32.1159i	−1.28379	+	1.52933i
$442$	6.47250			0.307865
$443$	16.7350	+	28.9858i	0.795103	+	1.37716i	0.922774	+	0.385342i	$0.125916\pi$
$443$	16.7350	+	28.9858i	0.795103	+	1.37716i	−0.127671	+	0.991817i	$0.540750\pi$
$444$	6.54577	−	9.34629i	0.310648	−	0.443555i
$445$	0.320633	−	0.555353i	0.0151995	−	0.0263263i
$446$	2.23129	−	3.86470i	0.105655	−	0.182999i
$447$	21.3087	−	30.4253i	1.00787	−	1.43907i
$448$	−2.59809	−	4.50003i	−0.122748	−	0.212606i
$449$	14.7216			0.694754			0.347377	−	0.937726i	$-0.387072\pi$
$449$	14.7216			0.694754			0.347377	+	0.937726i	$0.387072\pi$
$450$	−4.90676	+	5.84521i	−0.231307	+	0.275546i
$451$	−7.86401			−0.370302
$452$	−3.70046	−	6.40938i	−0.174055	−	0.301472i
$453$	−4.23677	−	9.08823i	−0.199061	−	0.427002i
$454$	0.753648	−	1.30536i	0.0353705	−	0.0612634i
$455$	15.1133	−	26.1770i	0.708521	−	1.22719i
$456$	−6.09542	−	0.533910i	−0.285444	−	0.0250026i
$457$	−7.33156	−	12.6986i	−0.342956	−	0.594017i	0.642024	−	0.766684i	$-0.278095\pi$
$457$	−7.33156	−	12.6986i	−0.342956	−	0.594017i	−0.984980	+	0.172667i	$0.944761\pi$
$458$	4.19029			0.195799
$459$	−8.14210	−	2.18435i	−0.380041	−	0.101957i
$460$	−15.0996			−0.704023
$461$	1.23804	+	2.14436i	0.0576615	+	0.0998726i	0.893415	−	0.449232i	$-0.148302\pi$
$461$	1.23804	+	2.14436i	0.0576615	+	0.0998726i	−0.835754	+	0.549104i	$0.814969\pi$
$462$	8.19036	+	0.717410i	0.381050	+	0.0333769i
$463$	−2.71730	+	4.70650i	−0.126284	+	0.218730i	−0.922234	−	0.386632i	$-0.873638\pi$
$463$	−2.71730	+	4.70650i	−0.126284	+	0.218730i	0.795950	+	0.605362i	$0.206972\pi$
$464$	−0.706442	+	1.22359i	−0.0327957	+	0.0568039i
$465$	−1.57942	−	3.38798i	−0.0732439	−	0.157114i
$466$	−3.49377	−	6.05139i	−0.161846	−	0.280325i
$467$	−5.00087			−0.231412			−0.115706	−	0.993283i	$-0.536913\pi$
$467$	−5.00087			−0.231412			−0.115706	+	0.993283i	$0.536913\pi$
$468$	9.17204	+	25.2160i	0.423978	+	1.16561i
$469$	−4.58009			−0.211489
$470$	2.92664	+	5.06910i	0.134996	+	0.233820i
$471$	−5.42823	+	7.75062i	−0.250120	+	0.357130i
$472$	−5.67616	+	9.83140i	−0.261267	+	0.452527i
$473$	−3.76098	+	6.51421i	−0.172930	+	0.299524i
$474$	0.718660	−	1.02613i	0.0330092	−	0.0471317i
$475$	−2.72157	−	4.71389i	−0.124874	−	0.216288i
$476$	11.3883			0.521982
$477$	−42.0001	−	7.41463i	−1.92305	−	0.339493i
$478$	−6.75822			−0.309114
$479$	−21.2766	−	36.8522i	−0.972154	−	1.68382i	−0.689023	−	0.724740i	$-0.741960\pi$
$479$	−21.2766	−	36.8522i	−0.972154	−	1.68382i	−0.283132	−	0.959081i	$-0.591373\pi$
$480$	−4.79765	−	10.2914i	−0.218982	−	0.469734i
$481$	−12.5422	+	21.7238i	−0.571876	+	0.990518i
$482$	−4.67190	+	8.09196i	−0.212799	+	0.368579i
$483$	−68.8469	−	6.03043i	−3.13264	−	0.274394i
$484$	−6.66829	−	11.5498i	−0.303104	−	0.524992i
$485$	−1.69152			−0.0768078
$486$	0.923368	+	10.6168i	0.0418848	+	0.481588i
$487$	30.4585			1.38021			0.690104	−	0.723710i	$-0.257565\pi$
$487$	30.4585			1.38021			0.690104	+	0.723710i	$0.257565\pi$
$488$	16.1865	+	28.0359i	0.732730	+	1.26913i
$489$	−30.3292	−	2.65660i	−1.37154	−	0.120135i
$490$	−5.40298	+	9.35824i	−0.244082	+	0.422762i
$491$	10.8932	−	18.8675i	0.491602	−	0.851480i	−0.508351	−	0.861150i	$-0.669745\pi$
$491$	10.8932	−	18.8675i	0.491602	−	0.851480i	0.999953	+	0.00966996i	$0.00307809\pi$
$492$	5.81829	+	12.4807i	0.262309	+	0.562673i
$493$	0.810395	+	1.40365i	0.0364984	+	0.0632170i
$494$	5.83582			0.262566
$495$	5.06495	+	0.894158i	0.227653	+	0.0401894i
$496$	−2.69894			−0.121186
$497$	−12.0763	−	20.9167i	−0.541694	−	0.938241i
$498$	−4.24344	+	6.05894i	−0.190153	+	0.271508i
$499$	3.30197	−	5.71918i	0.147816	−	0.256026i	−0.782604	−	0.622520i	$-0.786109\pi$
$499$	3.30197	−	5.71918i	0.147816	−	0.256026i	0.930420	+	0.366495i	$0.119442\pi$
$500$	7.55784	−	13.0906i	0.337997	−	0.585428i
$501$	22.9425	−	32.7581i	1.02499	−	1.46352i
$502$	−3.43276	−	5.94571i	−0.153211	−	0.265370i
$503$	7.75221			0.345654			0.172827	−	0.984952i	$-0.444710\pi$
$503$	7.75221			0.345654			0.172827	+	0.984952i	$0.444710\pi$
$504$	−11.3430	−	31.1845i	−0.505257	−	1.38907i
$505$	−9.73956			−0.433405
$506$	4.51449	+	7.81932i	0.200694	+	0.347611i
$507$	−15.4097	−	33.0550i	−0.684368	−	1.46803i
$508$	−11.9068	+	20.6231i	−0.528277	+	0.915002i
$509$	−11.0389	+	19.1200i	−0.489291	+	0.847477i	−0.999924	−	0.0123215i	$-0.996078\pi$
$509$	−11.0389	+	19.1200i	−0.489291	+	0.847477i	0.510633	+	0.859799i	$0.329411\pi$
$510$	−2.16417	−	0.189564i	−0.0958311	−	0.00839403i
$511$	26.4789	+	45.8628i	1.17136	+	2.02885i
$512$	−15.0293			−0.664207
$513$	−7.34119	−	1.96949i	−0.324121	−	0.0869549i
$514$	18.2398			0.804523
$515$	3.56119	+	6.16816i	0.156925	+	0.271801i
$516$	13.1211	+	1.14930i	0.577624	+	0.0505952i
$517$	−5.73888	+	9.94004i	−0.252396	+	0.437162i
$518$	6.72941	−	11.6557i	0.295673	−	0.512121i
$519$	3.26897	+	7.01221i	0.143492	+	0.307802i
$520$	7.96914	+	13.8030i	0.349470	+	0.605299i
$521$	10.9723			0.480706			0.240353	−	0.970686i	$-0.422737\pi$
$521$	10.9723			0.480706			0.240353	+	0.970686i	$0.422737\pi$
$522$	1.31735	−	1.56931i	0.0576590	−	0.0686867i
$523$	15.3226			0.670010			0.335005	−	0.942216i	$-0.391262\pi$
$523$	15.3226			0.670010			0.335005	+	0.942216i	$0.391262\pi$
$524$	2.13253	+	3.69366i	0.0931602	+	0.161358i
$525$	16.9341	−	24.1791i	0.739063	−	1.05526i
$526$	3.98640	−	6.90465i	0.173815	−	0.301057i
$527$	−1.54805	+	2.68130i	−0.0674340	+	0.116799i
$528$	2.13031	−	3.04174i	0.0927099	−	0.132375i
$529$	−26.4481	−	45.8094i	−1.14992	−	1.99171i
$530$	−10.9910			−0.477419
$531$	−9.06679	+	10.8009i	−0.393465	+	0.468718i
$532$	10.2681			0.445178
$533$	−15.1360	−	26.2163i	−0.655612	−	1.13555i
$534$	0.283702	+	0.608564i	0.0122770	+	0.0263351i
$535$	8.31197	−	14.3967i	0.359358	−	0.622426i
$536$	1.20753	−	2.09150i	0.0521571	−	0.0903388i
$537$	2.65676	+	0.232711i	0.114648	+	0.0100422i
$538$	1.08956	+	1.88718i	0.0469743	+	0.0813619i
$539$	−21.1895			−0.912697
$540$	−2.32828	−	8.69997i	−0.100193	−	0.374387i
$541$	−10.1153			−0.434893			−0.217446	−	0.976072i	$-0.569773\pi$
$541$	−10.1153			−0.434893			−0.217446	+	0.976072i	$0.569773\pi$
$542$	−5.84280	−	10.1200i	−0.250970	−	0.434692i
$543$	37.3702	+	3.27333i	1.60371	+	0.140472i
$544$	−4.70235	+	8.14471i	−0.201612	+	0.349202i
$545$	−5.09225	+	8.82004i	−0.218128	+	0.377809i
$546$	13.3725	+	28.6851i	0.572290	+	1.22761i
$547$	−10.1985	−	17.6643i	−0.436055	−	0.755269i	0.561326	−	0.827595i	$-0.310291\pi$
$547$	−10.1985	−	17.6643i	−0.436055	−	0.755269i	−0.997381	+	0.0723254i	$0.976958\pi$
$548$	−20.3777			−0.870492
$549$	13.7463	+	37.7918i	0.586678	+	1.61291i
$550$	−3.85657			−0.164445
$551$	0.730680	+	1.26557i	0.0311280	+	0.0539153i
$552$	20.9051	−	29.8490i	0.889779	−	1.27046i
$553$	−2.42284	+	4.19648i	−0.103030	+	0.178452i
$554$	−10.1290	+	17.5439i	−0.430338	+	0.745368i
$555$	4.82990	−	6.89631i	0.205018	−	0.292732i
$556$	16.9048	+	29.2800i	0.716923	+	1.24175i
$557$	−10.3000			−0.436427			−0.218213	−	0.975901i	$-0.570023\pi$
$557$	−10.3000			−0.436427			−0.218213	+	0.975901i	$0.570023\pi$
$558$	3.85436	+	0.680442i	0.163168	+	0.0288054i
$559$	−28.9553			−1.22468
$560$	3.66257	+	6.34376i	0.154772	+	0.268073i
$561$	−1.79995	−	3.86105i	−0.0759941	−	0.163014i
$562$	−10.2080	+	17.6807i	−0.430597	+	0.745816i
$563$	6.49446	−	11.2487i	0.273709	−	0.474078i	−0.696100	−	0.717945i	$-0.745083\pi$
$563$	6.49446	−	11.2487i	0.273709	−	0.474078i	0.969809	+	0.243867i	$0.0784162\pi$
$564$	20.0215	+	1.75372i	0.843056	+	0.0738449i
$565$	−2.73044	−	4.72927i	−0.114871	−	0.198962i
$566$	5.70786			0.239919
$567$	−7.14127	−	40.5975i	−0.299905	−	1.70493i
$568$	12.7355			0.534368
$569$	7.97226	+	13.8084i	0.334215	+	0.578877i	0.983334	−	0.181810i	$-0.0581957\pi$
$569$	7.97226	+	13.8084i	0.334215	+	0.578877i	−0.649119	+	0.760687i	$0.724862\pi$
$570$	−1.95129	−	0.170917i	−0.0817305	−	0.00715893i
$571$	15.3875	−	26.6519i	0.643945	−	1.11535i	−0.340599	−	0.940209i	$-0.610630\pi$
$571$	15.3875	−	26.6519i	0.643945	−	1.11535i	0.984544	−	0.175137i	$-0.0560369\pi$
$572$	−6.77968	+	11.7427i	−0.283473	+	0.490989i
$573$	4.09658	+	8.78751i	0.171137	+	0.367103i
$574$	8.12107	+	14.0661i	0.338967	+	0.587108i
$575$	32.4177			1.35191
$576$	3.35172	+	0.591708i	0.139655	+	0.0246545i
$577$	−4.42536			−0.184230			−0.0921151	−	0.995748i	$-0.529363\pi$
$577$	−4.42536			−0.184230			−0.0921151	+	0.995748i	$0.529363\pi$
$578$	−4.91125	−	8.50654i	−0.204281	−	0.353825i
$579$	−6.82778	+	9.74895i	−0.283753	+	0.405152i
$580$	−0.865778	+	1.49957i	−0.0359495	+	0.0622663i
$581$	14.3060	−	24.7788i	0.593514	−	1.02800i
$582$	1.01602	−	1.45071i	0.0421154	−	0.0601339i
$583$	−10.7762	−	18.6649i	−0.446304	−	0.773021i
$584$	−27.9243			−1.15552
$585$	6.76773	+	18.6061i	0.279811	+	0.769266i
$586$	10.7087			0.442371
$587$	−2.20297	−	3.81565i	−0.0909263	−	0.157489i	0.816975	−	0.576673i	$-0.195649\pi$
$587$	−2.20297	−	3.81565i	−0.0909263	−	0.157489i	−0.907901	+	0.419184i	$0.862316\pi$
$588$	15.6773	+	33.6292i	0.646522	+	1.38684i
$589$	−1.39577	+	2.41755i	−0.0575117	+	0.0996133i
$590$	−1.81707	+	3.14726i	−0.0748078	+	0.129571i
$591$	−19.1234	−	1.67506i	−0.786632	−	0.0689026i
$592$	−3.03950	−	5.26457i	−0.124923	−	0.216372i
$593$	−3.73683			−0.153453			−0.0767267	−	0.997052i	$-0.524447\pi$
$593$	−3.73683			−0.153453			−0.0767267	+	0.997052i	$0.524447\pi$
$594$	−3.80916	+	3.80682i	−0.156292	+	0.156196i
$595$	8.40305			0.344491
$596$	−16.4343	−	28.4650i	−0.673174	−	1.16597i
$597$	0.927660	+	0.0812555i	0.0379666	+	0.00332557i
$598$	−17.3782	+	30.1000i	−0.710648	+	1.23088i
$599$	−18.6654	+	32.3295i	−0.762649	+	1.32095i	0.178832	+	0.983880i	$0.442768\pi$
$599$	−18.6654	+	32.3295i	−0.762649	+	1.32095i	−0.941481	+	0.337067i	$0.890565\pi$
$600$	6.57676	+	14.1077i	0.268495	+	0.575944i
$601$	−6.70996	−	11.6220i	−0.273705	−	0.474071i	0.696103	−	0.717942i	$-0.254916\pi$
$601$	−6.70996	−	11.6220i	−0.273705	−	0.474071i	−0.969808	+	0.243871i	$0.921583\pi$
$602$	15.5357			0.633188
$603$	1.92883	−	2.29774i	0.0785482	−	0.0935711i
$604$	−8.87281			−0.361030
$605$	−4.92030	−	8.52222i	−0.200039	−	0.346477i
$606$	5.85013	−	8.35303i	0.237645	−	0.339319i
$607$	−4.89664	+	8.48124i	−0.198749	+	0.344243i	−0.948123	−	0.317904i	$-0.897021\pi$
$607$	−4.89664	+	8.48124i	−0.198749	+	0.344243i	0.749374	+	0.662147i	$0.230354\pi$
$608$	−4.23980	+	7.34355i	−0.171947	+	0.297820i
$609$	−4.54642	+	6.49154i	−0.184230	+	0.263051i
$610$	5.18169	+	8.97495i	0.209801	+	0.363385i
$611$	−44.1829			−1.78745
$612$	−4.79602	+	5.71329i	−0.193867	+	0.230946i
$613$	−24.5062			−0.989797			−0.494898	−	0.868951i	$-0.664795\pi$
$613$	−24.5062			−0.989797			−0.494898	+	0.868951i	$0.664795\pi$
$614$	−2.59775	−	4.49944i	−0.104837	−	0.181583i
$615$	4.29312	+	9.20908i	0.173115	+	0.371346i
$616$	8.38439	−	14.5222i	0.337817	−	0.585115i
$617$	−8.89646	+	15.4091i	−0.358158	+	0.620348i	−0.987653	−	0.156657i	$-0.949928\pi$
$617$	−8.89646	+	15.4091i	−0.358158	+	0.620348i	0.629495	+	0.777004i	$0.283262\pi$
$618$	−7.42910	−	0.650729i	−0.298842	−	0.0261762i
$619$	14.5695	+	25.2352i	0.585599	+	1.01429i	0.994800	+	0.101843i	$0.0324739\pi$
$619$	14.5695	+	25.2352i	0.585599	+	1.01429i	−0.409202	+	0.912444i	$0.634193\pi$
$620$	−3.30768			−0.132840
$621$	32.0192	−	31.9995i	1.28489	−	1.28410i
$622$	9.57054			0.383744
$623$	−1.29857	−	2.24919i	−0.0520261	−	0.0901119i
$624$	14.2405	+	1.24735i	0.570076	+	0.0499341i
$625$	−3.72610	+	6.45379i	−0.149044	+	0.258152i
$626$	6.83987	−	11.8470i	0.273376	−	0.473501i
$627$	−1.62290	−	3.48125i	−0.0648123	−	0.139028i
$628$	4.18651	+	7.25125i	0.167060	+	0.289356i
$629$	−6.97353			−0.278053
$630$	−3.63116	−	9.98291i	−0.144669	−	0.397729i
$631$	26.8901			1.07048			0.535238	−	0.844701i	$-0.320222\pi$
$631$	26.8901			1.07048			0.535238	+	0.844701i	$0.320222\pi$
$632$	−1.27755	−	2.21278i	−0.0508181	−	0.0880195i
$633$	−15.4818	+	22.1055i	−0.615348	+	0.878616i
$634$	5.20330	−	9.01238i	0.206649	−	0.357927i
$635$	−8.78559	+	15.2171i	−0.348646	+	0.603872i
$636$	−21.6495	+	30.9120i	−0.858459	+	1.22574i
$637$	−40.7838	−	70.6396i	−1.61591	−	2.79884i
$638$	1.03540			0.0409920
$639$	15.5792	+	2.75033i	0.616304	+	0.108801i
$640$	−12.2342			−0.483598
$641$	22.4879	+	38.9501i	0.888217	+	1.53844i	0.841982	+	0.539506i	$0.181389\pi$
$641$	22.4879	+	38.9501i	0.888217	+	1.53844i	0.0462350	+	0.998931i	$0.485278\pi$
$642$	7.35458	+	15.7762i	0.290262	+	0.622635i
$643$	0.378613	−	0.655778i	0.0149311	−	0.0258614i	−0.858463	−	0.512875i	$-0.828580\pi$
$643$	0.378613	−	0.655778i	0.0149311	−	0.0258614i	0.873394	+	0.487014i	$0.161914\pi$
$644$	−30.5768	+	52.9607i	−1.20490	+	2.08694i
$645$	9.68161	+	0.848031i	0.381213	+	0.0333912i
$646$	0.811186	+	1.40501i	0.0319157	+	0.0552796i
$647$	25.0385			0.984364			0.492182	−	0.870492i	$-0.336199\pi$
$647$	25.0385			0.984364			0.492182	+	0.870492i	$0.336199\pi$
$648$	20.4216	+	7.44234i	0.802236	+	0.292363i
$649$	−7.12623			−0.279729
$650$	−7.42280	−	12.8567i	−0.291146	−	0.504280i
$651$	−15.0814	−	1.32101i	−0.591087	−	0.0517745i
$652$	−13.4701	+	23.3308i	−0.527529	+	0.913706i
$653$	−23.5157	+	40.7303i	−0.920239	+	1.59390i	−0.121194	+	0.992629i	$0.538672\pi$
$653$	−23.5157	+	40.7303i	−0.920239	+	1.59390i	−0.799045	+	0.601271i	$0.794661\pi$
$654$	−4.50572	−	9.66512i	−0.176187	−	0.377936i
$655$	1.57352	+	2.72542i	0.0614827	+	0.106491i
$656$	7.33615			0.286429
$657$	−34.1597	−	6.03049i	−1.33270	−	0.235272i
$658$	23.7059			0.924153
$659$	14.9507	+	25.8953i	0.582395	+	1.00874i	0.995195	+	0.0979158i	$0.0312176\pi$
$659$	14.9507	+	25.8953i	0.582395	+	1.00874i	−0.412800	+	0.910822i	$0.635449\pi$
$660$	2.61080	−	3.72779i	0.101625	−	0.145104i
$661$	−8.75982	+	15.1725i	−0.340717	+	0.590140i	−0.984566	−	0.175013i	$-0.944003\pi$
$661$	−8.75982	+	15.1725i	−0.340717	+	0.590140i	0.643849	+	0.765153i	$0.277337\pi$
$662$	4.26055	−	7.37948i	0.165591	−	0.286812i
$663$	9.40720	−	13.4319i	0.365345	−	0.521653i
$664$	7.54348	+	13.0657i	0.292744	+	0.507047i
$665$	7.57647			0.293803
$666$	3.01343	+	8.28462i	0.116768	+	0.321023i
$667$	−8.70343			−0.336998
$668$	−17.6943	−	30.6475i	−0.684614	−	1.18579i
$669$	−4.77718	−	10.2474i	−0.184697	−	0.396189i
$670$	0.386557	−	0.669537i	0.0149340	−	0.0258665i
$671$	−10.1608	+	17.5991i	−0.392254	+	0.679404i
$672$	−45.8114	−	4.01271i	−1.76721	−	0.154794i
$673$	12.3288	+	21.3541i	0.475241	+	0.823141i	0.999598	−	0.0283572i	$-0.00902760\pi$
$673$	12.3288	+	21.3541i	0.475241	+	0.823141i	−0.524357	+	0.851499i	$0.675694\pi$
$674$	18.6002			0.716452
$675$	4.99864	+	18.6781i	0.192398	+	0.718922i
$676$	−32.2715			−1.24121
$677$	−23.6309	−	40.9299i	−0.908208	−	1.57306i	−0.816552	−	0.577272i	$-0.804117\pi$
$677$	−23.6309	−	40.9299i	−0.908208	−	1.57306i	−0.0916568	−	0.995791i	$-0.529216\pi$
$678$	5.69606	+	0.498929i	0.218756	+	0.0191613i
$679$	−3.42533	+	5.93285i	−0.131452	+	0.227682i
$680$	−2.21544	+	3.83725i	−0.0849582	+	0.147152i
$681$	−1.61356	−	3.46121i	−0.0618317	−	0.132634i
$682$	0.988932	+	1.71288i	0.0378681	+	0.0655896i
$683$	15.6450			0.598640			0.299320	−	0.954153i	$-0.403240\pi$
$683$	15.6450			0.598640			0.299320	+	0.954153i	$0.403240\pi$
$684$	−4.32425	+	5.15129i	−0.165342	+	0.196965i
$685$	−15.0360			−0.574496
$686$	10.9232	+	18.9196i	0.417050	+	0.722353i
$687$	6.09021	−	8.69582i	0.232356	−	0.331766i
$688$	3.50854	−	6.07696i	0.133762	−	0.231682i
$689$	41.4822	−	71.8493i	1.58035	−	2.73724i
$690$	6.69221	−	9.55538i	0.254768	−	0.363767i
$691$	14.3282	+	24.8172i	0.545072	+	0.944092i	0.998602	+	0.0528514i	$0.0168310\pi$
$691$	14.3282	+	24.8172i	0.545072	+	0.944092i	−0.453531	+	0.891241i	$0.649836\pi$
$692$	6.84600			0.260246
$693$	13.3928	−	15.9542i	0.508749	−	0.606051i
$694$	5.41192			0.205434
$695$	12.4735	+	21.6047i	0.473146	+	0.819513i
$696$	−1.76571	−	3.78760i	−0.0669292	−	0.143568i
$697$	4.20784	−	7.28819i	0.159383	−	0.276060i
$698$	5.34117	−	9.25118i	0.202166	−	0.350162i
$699$	−17.6359	−	1.54477i	−0.667052	−	0.0584284i
$700$	−13.0604	−	22.6212i	−0.493635	−	0.855001i
$701$	−3.93002			−0.148435			−0.0742173	−	0.997242i	$-0.523646\pi$
$701$	−3.93002			−0.148435			−0.0742173	+	0.997242i	$0.523646\pi$
$702$	−20.0224	−	5.37158i	−0.755695	−	0.202737i
$703$	−6.28757			−0.237140
$704$	0.859969	+	1.48951i	0.0324113	+	0.0561380i
$705$	14.7732	+	1.29401i	0.556390	+	0.0487353i
$706$	11.5903	−	20.0750i	0.436208	−	0.755534i
$707$	−19.7227	+	34.1607i	−0.741748	+	1.28475i
$708$	5.27244	+	11.3098i	0.198150	+	0.425048i
$709$	5.31066	+	9.19833i	0.199446	+	0.345450i	0.948349	−	0.317229i	$-0.102752\pi$
$709$	5.31066	+	9.19833i	0.199446	+	0.345450i	−0.748903	+	0.662680i	$0.769419\pi$
$710$	4.07692			0.153004
$711$	−1.08495	−	2.98277i	−0.0406887	−	0.111863i
$712$	1.36946			0.0513225
$713$	−8.31280	−	14.3982i	−0.311317	−	0.539217i
$714$	−5.04734	+	7.20678i	−0.188892	+	0.269707i
$715$	−5.00249	+	8.66457i	−0.187083	+	0.324037i
$716$	1.17994	−	2.04372i	0.0440966	−	0.0763775i
$717$	−9.82247	+	14.0249i	−0.366827	+	0.523769i
$718$	2.37420	+	4.11223i	0.0886043	+	0.153467i
$719$	−3.65347			−0.136252			−0.0681258	−	0.997677i	$-0.521702\pi$
$719$	−3.65347			−0.136252			−0.0681258	+	0.997677i	$0.521702\pi$
$720$	−4.72498	−	0.834140i	−0.176090	−	0.0310866i
$721$	28.8457			1.07427
$722$	−5.76318	−	9.98213i	−0.214484	−	0.371496i
$723$	10.0025	+	21.4562i	0.371998	+	0.797965i
$724$	16.5971	−	28.7471i	0.616828	−	1.06838i
$725$	1.85876	−	3.21946i	0.0690325	−	0.119568i
$726$	10.2644	+	0.899078i	0.380947	+	0.0333679i
$727$	11.8655	+	20.5516i	0.440067	+	0.762218i	0.997694	−	0.0678735i	$-0.0216214\pi$
$727$	11.8655	+	20.5516i	0.440067	+	0.762218i	−0.557627	+	0.830092i	$0.688288\pi$
$728$	64.5503			2.39239
$729$	23.3744	+	13.5144i	0.865718	+	0.500533i
$730$	−8.93924			−0.330856
$731$	−4.02482	−	6.97119i	−0.148863	−	0.257839i
$732$	35.4485	+	3.10500i	1.31021	+	0.114764i
$733$	−19.3567	+	33.5267i	−0.714955	+	1.23834i	0.248022	+	0.968754i	$0.420219\pi$
$733$	−19.3567	+	33.5267i	−0.714955	+	1.23834i	−0.962977	+	0.269584i	$0.913114\pi$
$734$	0.404731	−	0.701015i	0.0149389	−	0.0258749i
$735$	11.5678	+	24.8138i	0.426684	+	0.915271i
$736$	−25.2510	−	43.7360i	−0.930764	−	1.61213i
$737$	1.51601			0.0558429
$738$	−10.4768	−	1.84955i	−0.385655	−	0.0680828i
$739$	41.9190			1.54202			0.771008	−	0.636825i	$-0.219753\pi$
$739$	41.9190			1.54202			0.771008	+	0.636825i	$0.219753\pi$
$740$	−3.72505	−	6.45197i	−0.136936	−	0.237179i
$741$	8.48185	−	12.1107i	0.311588	−	0.444897i
$742$	−22.2569	+	38.5500i	−0.817076	+	1.41522i
$743$	19.9571	−	34.5667i	0.732154	−	1.26813i	−0.223807	−	0.974634i	$-0.571848\pi$
$743$	19.9571	−	34.5667i	0.732154	−	1.26813i	0.955961	−	0.293494i	$-0.0948182\pi$
$744$	4.57941	−	6.53864i	0.167889	−	0.239718i
$745$	−12.1263	−	21.0034i	−0.444273	−	0.769504i
$746$	8.82901			0.323253
$747$	6.40625	+	17.6123i	0.234393	+	0.644399i
$748$	−3.76953			−0.137828
$749$	−33.6636	−	58.3071i	−1.23004	−	2.13049i
$750$	4.93434	+	10.5846i	0.180177	+	0.386494i
$751$	19.1649	−	33.1946i	0.699338	−	1.21129i	−0.269358	−	0.963040i	$-0.586811\pi$
$751$	19.1649	−	33.1946i	0.699338	−	1.21129i	0.968696	−	0.248249i	$-0.0798553\pi$
$752$	5.35367	−	9.27283i	0.195228	−	0.338145i
$753$	−17.3279	−	1.51779i	−0.631465	−	0.0553112i
$754$	1.99286	+	3.45173i	0.0725755	+	0.125705i
$755$	−6.54695			−0.238268
$756$	−35.2292	−	9.45125i	−1.28127	−	0.343738i
$757$	−18.0787			−0.657080			−0.328540	−	0.944490i	$-0.606557\pi$
$757$	−18.0787			−0.657080			−0.328540	+	0.944490i	$0.606557\pi$
$758$	−3.73138	−	6.46294i	−0.135530	−	0.234745i
$759$	22.7883	+	1.99607i	0.827164	+	0.0724529i
$760$	−1.99751	+	3.45979i	−0.0724574	+	0.125500i
$761$	−4.52544	+	7.83829i	−0.164047	+	0.284138i	−0.936316	−	0.351157i	$-0.885788\pi$
$761$	−4.52544	+	7.83829i	−0.164047	+	0.284138i	0.772269	+	0.635295i	$0.219122\pi$
$762$	−7.77365	−	16.6751i	−0.281609	−	0.604075i
$763$	20.6237	+	35.7213i	0.746628	+	1.29320i
$764$	8.57922			0.310385
$765$	−3.53882	+	4.21564i	−0.127946	+	0.152417i
$766$	11.3594			0.410433
$767$	−13.7160	−	23.7568i	−0.495255	−	0.857807i
$768$	9.60307	−	13.7116i	0.346521	−	0.494775i
$769$	−15.9747	+	27.6691i	−0.576064	+	0.997772i	0.419861	+	0.907588i	$0.362079\pi$
$769$	−15.9747	+	27.6691i	−0.576064	+	0.997772i	−0.995925	+	0.0901838i	$0.971255\pi$
$770$	2.68404	−	4.64889i	0.0967261	−	0.167535i
$771$	26.5099	−	37.8518i	0.954732	−	1.36320i
$772$	5.26590	+	9.12081i	0.189524	+	0.328265i
$773$	−9.79751			−0.352392			−0.176196	−	0.984355i	$-0.556379\pi$
$773$	−9.79751			−0.352392			−0.176196	+	0.984355i	$0.556379\pi$
$774$	−6.54262	+	7.79395i	−0.235170	+	0.280148i
$775$	7.10133			0.255087
$776$	−1.80616	−	3.12836i	−0.0648373	−	0.112301i
$777$	−14.4076	−	30.9056i	−0.516871	−	1.10873i
$778$	−10.5591	+	18.2889i	−0.378562	+	0.655689i
$779$	3.79393	−	6.57127i	0.135932	−	0.235440i
$780$	17.4524	+	1.52869i	0.624896	+	0.0547359i
$781$	3.99724	+	6.92342i	0.143032	+	0.247739i
$782$	−9.66237			−0.345526
$783$	−1.34202	−	5.01466i	−0.0479600	−	0.179209i
$784$	19.7672			0.705972
$785$	3.08908	+	5.35045i	0.110254	+	0.190966i
$786$	−3.28258	−	0.287527i	−0.117086	−	0.0102558i
$787$	17.9987	−	31.1747i	0.641585	−	1.11126i	−0.343494	−	0.939155i	$-0.611610\pi$
$787$	17.9987	−	31.1747i	0.641585	−	1.11126i	0.985079	−	0.172103i	$-0.0550562\pi$
$788$	−8.49324	+	14.7107i	−0.302559	+	0.524048i
$789$	−8.53487	−	18.3080i	−0.303850	−	0.651782i
$790$	−0.408973	−	0.708362i	−0.0145506	−	0.0252024i
$791$	−22.1167			−0.786378
$792$	3.75453	+	10.3221i	0.133412	+	0.366779i
$793$	−78.2268			−2.77792
$794$	−10.1428	−	17.5679i	−0.359956	−	0.623462i
$795$	−15.9744	+	22.8089i	−0.566555	+	0.808948i
$796$	0.412000	−	0.713605i	0.0146029	−	0.0252930i
$797$	12.2349	−	21.1914i	0.433382	−	0.750639i	−0.563780	−	0.825925i	$-0.690654\pi$
$797$	12.2349	−	21.1914i	0.433382	−	0.750639i	0.997162	+	0.0752857i	$0.0239869\pi$
$798$	−4.55085	+	6.49788i	−0.161098	+	0.230022i
$799$	−6.14147	−	10.6373i	−0.217270	−	0.376322i
$800$	21.5710			0.762651
$801$	1.67525	+	0.295745i	0.0591919	+	0.0104496i
$802$	−14.5972			−0.515443
$803$	−8.76452	−	15.1806i	−0.309293	−	0.535711i
$804$	−1.12164	−	2.40600i	−0.0395571	−	0.0848532i
$805$	−22.5616	+	39.0779i	−0.795193	+	1.37731i
$806$	−3.80683	+	6.59362i	−0.134090	+	0.232250i
$807$	5.49991	+	0.481748i	0.193606	+	0.0169583i
$808$	−10.3997	−	18.0127i	−0.365859	−	0.633686i
$809$	−44.7458			−1.57318			−0.786589	−	0.617476i	$-0.788155\pi$
$809$	−44.7458			−1.57318			−0.786589	+	0.617476i	$0.788155\pi$
$810$	6.53744	+	2.38247i	0.229702	+	0.0837114i
$811$	9.87608			0.346796			0.173398	−	0.984852i	$-0.444525\pi$
$811$	9.87608			0.346796			0.173398	+	0.984852i	$0.444525\pi$
$812$	3.50641	+	6.07329i	0.123051	+	0.213131i
$813$	−29.4934	−	2.58338i	−1.03438	−	0.0906032i
$814$	−2.22743	+	3.85803i	−0.0780715	+	0.135224i
$815$	−9.93911	+	17.2150i	−0.348152	+	0.603016i
$816$	1.67914	+	3.60188i	0.0587815	+	0.126091i
$817$	−3.62891	−	6.28546i	−0.126960	−	0.219900i
$818$	8.16356			0.285432
$819$	78.9639	+	13.9402i	2.75922	+	0.487109i
$820$	8.99080			0.313972
$821$	15.8307	+	27.4196i	0.552495	+	0.956950i	0.998094	+	0.0617170i	$0.0196576\pi$
$821$	15.8307	+	27.4196i	0.552495	+	0.956950i	−0.445598	+	0.895233i	$0.647009\pi$
$822$	9.03147	−	12.8955i	0.315009	−	0.449781i
$823$	5.86369	−	10.1562i	0.204395	−	0.354023i	−0.745545	−	0.666456i	$-0.767811\pi$
$823$	5.86369	−	10.1562i	0.204395	−	0.354023i	0.949940	+	0.312433i	$0.101144\pi$
$824$	−7.60509	+	13.1724i	−0.264936	+	0.458882i
$825$	−5.60518	+	8.00328i	−0.195147	+	0.278638i
$826$	7.35918	+	12.7465i	0.256059	+	0.443506i
$827$	32.2528			1.12154			0.560770	−	0.827972i	$-0.310505\pi$
$827$	32.2528			1.12154			0.560770	+	0.827972i	$0.310505\pi$
$828$	−13.6923	−	37.6434i	−0.475841	−	1.30820i
$829$	13.4996			0.468861			0.234430	−	0.972133i	$-0.424678\pi$
$829$	13.4996			0.468861			0.234430	+	0.972133i	$0.424678\pi$
$830$	2.41485	+	4.18264i	0.0838206	+	0.145182i
$831$	21.6861	+	46.5184i	0.752282	+	1.61371i
$832$	−3.31039	+	5.73377i	−0.114767	+	0.198783i
$833$	11.3380	−	19.6380i	0.392838	−	0.680415i
$834$	−26.0213	−	2.27926i	−0.901044	−	0.0789242i
$835$	−13.0560	−	22.6137i	−0.451823	−	0.782581i
$836$	−3.39874			−0.117548
$837$	7.01403	−	7.00972i	0.242441	−	0.242291i
$838$	−18.5217			−0.639822
$839$	−20.6031	−	35.6857i	−0.711299	−	1.23201i	−0.964370	−	0.264558i	$-0.914774\pi$
$839$	−20.6031	−	35.6857i	−0.711299	−	1.23201i	0.253071	−	0.967448i	$-0.418559\pi$
$840$	−21.5833	−	1.89052i	−0.744694	−	0.0652292i
$841$	14.0010	−	24.2504i	0.482792	−	0.836220i
$842$	7.52933	−	13.0412i	0.259478	−	0.449429i
$843$	21.8552	+	46.8813i	0.752735	+	1.61468i
$844$	11.9403	+	20.6813i	0.411003	+	0.711878i
$845$	−23.8121			−0.819160
$846$	−9.98339	+	11.8928i	−0.343236	+	0.408882i
$847$	−39.8546			−1.36942
$848$	10.0529	+	17.4121i	0.345216	+	0.597932i
$849$	8.29586	−	11.8451i	0.284713	−	0.406524i
$850$	2.06356	−	3.57418i	0.0707794	−	0.122593i
$851$	18.7234	−	32.4300i	0.641832	−	1.11168i
$852$	8.03051	−	11.4663i	0.275121	−	0.392828i
$853$	5.42186	+	9.39093i	0.185641	+	0.321539i	0.943792	−	0.330539i	$-0.107231\pi$
$853$	5.42186	+	9.39093i	0.185641	+	0.321539i	−0.758151	+	0.652079i	$0.773897\pi$
$854$	41.9719			1.43625
$855$	−3.19072	+	3.80097i	−0.109120	+	0.129990i
$856$	35.5012			1.21341
$857$	−6.94557	−	12.0301i	−0.237256	−	0.410940i	0.722670	−	0.691193i	$-0.242915\pi$
$857$	−6.94557	−	12.0301i	−0.237256	−	0.410940i	−0.959926	+	0.280254i	$0.909581\pi$
$858$	−4.42630	−	9.49476i	−0.151111	−	0.324146i
$859$	−1.26033	+	2.18296i	−0.0430020	+	0.0744817i	−0.886725	−	0.462297i	$-0.847026\pi$
$859$	−1.26033	+	2.18296i	−0.0430020	+	0.0744817i	0.843723	+	0.536778i	$0.180359\pi$
$860$	4.29988	−	7.44761i	0.146625	−	0.253961i
$861$	40.9937	+	3.59072i	1.39706	+	0.122371i
$862$	−5.25587	−	9.10343i	−0.179016	−	0.310064i
$863$	−3.14818			−0.107165			−0.0535827	−	0.998563i	$-0.517064\pi$
$863$	−3.14818			−0.107165			−0.0535827	+	0.998563i	$0.517064\pi$
$864$	21.3059	−	21.2928i	0.724840	−	0.724394i
$865$	5.05143			0.171754
$866$	7.47123	+	12.9405i	0.253883	+	0.439738i
$867$	−24.7911	−	2.17150i	−0.841950	−	0.0737481i
$868$	−6.69808	+	11.6014i	−0.227348	+	0.393778i
$869$	0.801959	−	1.38903i	0.0272046	−	0.0471198i
$870$	−0.565247	−	1.21250i	−0.0191637	−	0.0411076i
$871$	2.91789	+	5.05393i	0.0988688	+	0.171246i
$872$	−21.7495			−0.736531
$873$	−1.53387	−	4.21695i	−0.0519135	−	0.142722i
$874$	−8.71192			−0.294685
$875$	−22.5856	−	39.1194i	−0.763533	−	1.32248i
$876$	−17.6081	+	25.1414i	−0.594921	+	0.849450i
$877$	12.3100	−	21.3215i	0.415678	−	0.719976i	−0.579821	−	0.814744i	$-0.696878\pi$
$877$	12.3100	−	21.3215i	0.415678	−	0.719976i	0.995499	+	0.0947678i	$0.0302109\pi$
$878$	−10.6609	+	18.4652i	−0.359787	+	0.623170i
$879$	15.5641	−	22.2230i	0.524964	−	0.749562i
$880$	−1.21231	−	2.09979i	−0.0408670	−	0.0707838i
$881$	52.9627			1.78436			0.892180	−	0.451680i	$-0.149175\pi$
$881$	52.9627			1.78436			0.892180	+	0.451680i	$0.149175\pi$
$882$	−28.2295	−	4.98360i	−0.950538	−	0.167806i
$883$	−8.35550			−0.281185			−0.140592	−	0.990068i	$-0.544901\pi$
$883$	−8.35550			−0.281185			−0.140592	+	0.990068i	$0.544901\pi$
$884$	−7.25528	−	12.5665i	−0.244021	−	0.422657i
$885$	3.89035	+	8.34512i	0.130773	+	0.280518i
$886$	−11.4407	+	19.8159i	−0.384358	+	0.665727i
$887$	−6.03576	+	10.4542i	−0.202661	+	0.351019i	−0.949385	−	0.314115i	$-0.898292\pi$
$887$	−6.03576	+	10.4542i	−0.202661	+	0.351019i	0.746724	+	0.665134i	$0.231626\pi$
$888$	17.9115	+	1.56891i	0.601072	+	0.0526491i
$889$	35.5818	+	61.6295i	1.19337	+	2.06699i
$890$	0.438395			0.0146950
$891$	2.36376	+	13.4378i	0.0791889	+	0.450182i
$892$	−10.0046			−0.334977
$893$	−5.53736	−	9.59098i	−0.185301	−	0.320950i
$894$	25.2970	+	2.21582i	0.846059	+	0.0741080i
$895$	0.870641	−	1.50799i	0.0291023	−	0.0504067i
$896$	−24.7743	+	42.9104i	−0.827652	+	1.43353i
$897$	37.2067	+	79.8115i	1.24230	+	2.66483i
$898$	5.03212	+	8.71589i	0.167924	+	0.290853i
$899$	−1.90655			−0.0635870
$900$	16.8488	+	2.97446i	0.561626	+	0.0991486i
$901$	23.0643			0.768383
$902$	−2.68807	−	4.65588i	−0.0895030	−	0.155024i
$903$	22.5797	−	32.2402i	0.751407	−	1.07289i
$904$	5.83099	−	10.0996i	0.193936	−	0.335907i
$905$	12.2465	−	21.2115i	0.407086	−	0.705094i
$906$	3.93246	−	5.61492i	0.130647	−	0.186543i
$907$	25.2911	+	43.8055i	0.839778	+	1.45454i	0.890080	+	0.455804i	$0.150648\pi$
$907$	25.2911	+	43.8055i	0.839778	+	1.45454i	−0.0503021	+	0.998734i	$0.516018\pi$
$908$	−3.37917			−0.112142
$909$	−8.83184	−	24.2808i	−0.292933	−	0.805342i
$910$	20.6641			0.685007
$911$	−20.2465	−	35.0679i	−0.670796	−	1.16185i	−0.977679	−	0.210105i	$-0.932619\pi$
$911$	−20.2465	−	35.0679i	−0.670796	−	1.16185i	0.306883	−	0.951747i	$-0.400714\pi$
$912$	1.51397	+	3.24758i	0.0501324	+	0.107538i
$913$	−4.73530	+	8.20178i	−0.156715	+	0.271439i
$914$	5.01214	−	8.68129i	0.165787	−	0.287151i
$915$	26.1562	+	2.29108i	0.864699	+	0.0757406i
$916$	−4.69706	−	8.13554i	−0.155195	−	0.268806i
$917$	12.7456			0.420897
$918$	−1.48989	−	5.56718i	−0.0491736	−	0.183744i
$919$	11.4165			0.376596			0.188298	−	0.982112i	$-0.439703\pi$
$919$	11.4165			0.376596			0.188298	+	0.982112i	$0.439703\pi$
$920$	−11.8966	−	20.6055i	−0.392219	−	0.679344i
$921$	−13.1130	−	1.14859i	−0.432087	−	0.0378474i
$922$	−0.846376	+	1.46597i	−0.0278739	+	0.0482790i
$923$	−15.3871	+	26.6512i	−0.506473	+	0.877236i
$924$	−7.78803	−	16.7060i	−0.256207	−	0.549586i
$925$	7.99739	+	13.8519i	0.262953	+	0.455447i
$926$	−3.71531			−0.122093
$927$	−12.1479	+	14.4713i	−0.398991	+	0.475301i
$928$	−5.79134			−0.190110
$929$	−21.0644	−	36.4846i	−0.691100	−	1.19702i	−0.971478	−	0.237130i	$-0.923793\pi$
$929$	−21.0644	−	36.4846i	−0.691100	−	1.19702i	0.280378	−	0.959890i	$-0.409540\pi$
$930$	1.46598	−	2.09318i	0.0480713	−	0.0686379i
$931$	10.2227	−	17.7063i	0.335036	−	0.580299i
$932$	−7.83261	+	13.5665i	−0.256566	+	0.444385i
$933$	13.9099	−	19.8611i	0.455390	−	0.650223i
$934$	−1.70940	−	2.96076i	−0.0559331	−	0.0968790i
$935$	−2.78141			−0.0909618
$936$	−27.1844	+	32.3836i	−0.888549	+	1.05849i
$937$	−11.5551			−0.377489			−0.188745	−	0.982026i	$-0.560442\pi$
$937$	−11.5551			−0.377489			−0.188745	+	0.982026i	$0.560442\pi$
$938$	−1.56556	−	2.71164i	−0.0511175	−	0.0885381i
$939$	−14.6441	−	31.4129i	−0.477893	−	1.02512i
$940$	6.56118	−	11.3643i	0.214002	−	0.370662i
$941$	10.5574	−	18.2860i	0.344162	−	0.596105i	−0.641040	−	0.767508i	$-0.721497\pi$
$941$	10.5574	−	18.2860i	0.344162	−	0.596105i	0.985201	+	0.171403i	$0.0548299\pi$
$942$	−6.44423	−	0.564463i	−0.209964	−	0.0183912i
$943$	22.5955	+	39.1366i	0.735811	+	1.27446i
$944$	6.64790			0.216371
$945$	−25.9944	−	6.97375i	−0.845599	−	0.226856i
$946$	−5.14231			−0.167191
$947$	−11.8557	−	20.5346i	−0.385258	−	0.667286i	0.606547	−	0.795048i	$-0.292554\pi$
$947$	−11.8557	−	20.5346i	−0.385258	−	0.667286i	−0.991805	+	0.127761i	$0.959221\pi$
$948$	−2.79783	−	0.245067i	−0.0908692	−	0.00795941i
$949$	33.7384	−	58.4367i	1.09520	−	1.89693i
$950$	1.86057	−	3.22260i	0.0603649	−	0.104555i
$951$	−11.1403	−	23.8967i	−0.361247	−	0.774905i
$952$	8.97256	+	15.5409i	0.290802	+	0.503684i
$953$	−11.0168			−0.356868			−0.178434	−	0.983952i	$-0.557103\pi$
$953$	−11.0168			−0.356868			−0.178434	+	0.983952i	$0.557103\pi$
$954$	−9.96664	−	27.4006i	−0.322682	−	0.887127i
$955$	6.33032			0.204844
$956$	7.57556	+	13.1212i	0.245011	+	0.424372i
$957$	1.50486	−	2.14870i	0.0486454	−	0.0694576i
$958$	14.5456	−	25.1936i	0.469946	−	0.813969i
$959$	−30.4480	+	52.7376i	−0.983219	+	1.70298i
$960$	1.27480	−	1.82021i	0.0411441	−	0.0587471i
$961$	13.6790	+	23.6928i	0.441259	+	0.764283i
$962$	−17.1487			−0.552897
$963$	43.4284	+	7.66678i	1.39946	+	0.247059i
$964$	20.9476			0.674678
$965$	3.88553	+	6.72994i	0.125080	+	0.216644i
$966$	−19.9629	−	42.8221i	−0.642296	−	1.37778i
$967$	−5.56079	+	9.63157i	−0.178823	+	0.309730i	−0.941478	−	0.337075i	$-0.890562\pi$
$967$	−5.56079	+	9.63157i	−0.178823	+	0.309730i	0.762655	+	0.646806i	$0.223896\pi$
$968$	10.5075	−	18.1996i	0.337725	−	0.584957i
$969$	4.09472	+	0.358664i	0.131541	+	0.0115220i
$970$	−0.578194	−	1.00146i	−0.0185647	−	0.0321550i
$971$	−0.261801			−0.00840159			−0.00420080	−	0.999991i	$-0.501337\pi$
$971$	−0.261801			−0.00840159			−0.00420080	+	0.999991i	$0.501337\pi$
$972$	19.5777	−	13.6935i	0.627956	−	0.439220i
$973$	101.036			3.23905
$974$	10.4113	+	18.0330i	0.333601	+	0.577813i
$975$	−37.4690	−	3.28198i	−1.19997	−	0.105107i
$976$	9.47880	−	16.4178i	0.303409	−	0.525520i
$977$	−17.3533	+	30.0568i	−0.555182	+	0.961603i	0.442707	+	0.896666i	$0.354018\pi$
$977$	−17.3533	+	30.0568i	−0.555182	+	0.961603i	−0.997889	+	0.0649372i	$0.979315\pi$
$978$	−8.79430	−	18.8645i	−0.281211	−	0.603220i
$979$	0.429827	+	0.744481i	0.0137373	+	0.0237937i
$980$	24.2257			0.773860
$981$	−26.6060	−	4.69699i	−0.849465	−	0.149963i
$982$	14.8940			0.475287
$983$	−12.2511	−	21.2196i	−0.390750	−	0.676799i	0.601799	−	0.798648i	$-0.294451\pi$
$983$	−12.2511	−	21.2196i	−0.390750	−	0.676799i	−0.992549	+	0.121849i	$0.961118\pi$
$984$	−12.4476	+	17.7731i	−0.396814	+	0.566585i
$985$	−6.26688	+	10.8545i	−0.199679	+	0.345855i
$986$	−0.554018	+	0.959588i	−0.0176435	+	0.0305595i
$987$	34.4544	−	49.1953i	1.09670	−	1.56590i
$988$	−6.54160	−	11.3304i	−0.208116	−	0.360468i
$989$	43.2255			1.37449
$990$	1.20192	+	3.30434i	0.0381994	+	0.105019i
$991$	−42.8474			−1.36109			−0.680546	−	0.732706i	$-0.738257\pi$
$991$	−42.8474			−1.36109			−0.680546	+	0.732706i	$0.738257\pi$
$992$	−5.53141	−	9.58069i	−0.175623	−	0.304187i
$993$	−9.12182	−	19.5670i	−0.289472	−	0.620941i
$994$	8.25580	−	14.2995i	0.261858	−	0.453552i
$995$	0.304001	−	0.526545i	0.00963747	−	0.0166926i
$996$	16.5202	+	1.44704i	0.523463	+	0.0458512i
$997$	18.4315	+	31.9243i	0.583732	+	1.01105i	0.995032	+	0.0995536i	$0.0317415\pi$
$997$	18.4315	+	31.9243i	0.583732	+	1.01105i	−0.411300	+	0.911500i	$0.634925\pi$
$998$	4.51472			0.142911
$999$	21.5723	+	5.78738i	0.682516	+	0.183105i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	603.2.e.b.202.20	✓	66
9.4	even	3		5427.2.a.n.1.14		33
9.5	odd	6		5427.2.a.q.1.20		33
9.7	even	3	inner	603.2.e.b.403.20	yes	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
603.2.e.b.202.20	✓	66	1.1	even	1	trivial
603.2.e.b.403.20	yes	66	9.7	even	3	inner
5427.2.a.n.1.14		33	9.4	even	3
5427.2.a.q.1.20		33	9.5	odd	6

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 603 = 3^{2} \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	603.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.341820 + 0.592049i) q^{2} +(1.72544 + 0.151135i) q^{3} +(0.766318 - 1.32730i) q^{4} +(0.565440 - 0.979371i) q^{5} +(0.500312 + 1.07321i) q^{6} +(-2.29004 - 3.96647i) q^{7} +2.41505 q^{8} +(2.95432 + 0.521550i) q^{9} +O(q^{10})\)	\(q+(0.341820 + 0.592049i) q^{2} +(1.72544 + 0.151135i) q^{3} +(0.766318 - 1.32730i) q^{4} +(0.565440 - 0.979371i) q^{5} +(0.500312 + 1.07321i) q^{6} +(-2.29004 - 3.96647i) q^{7} +2.41505 q^{8} +(2.95432 + 0.521550i) q^{9} +0.773115 q^{10} +(0.758004 + 1.31290i) q^{11} +(1.52284 - 2.17437i) q^{12} +(-2.91789 + 5.05393i) q^{13} +(1.56556 - 2.71164i) q^{14} +(1.12365 - 1.60439i) q^{15} +(-0.707125 - 1.22478i) q^{16} -1.62236 q^{17} +(0.701060 + 1.92738i) q^{18} -1.46277 q^{19} +(-0.866615 - 1.50102i) q^{20} +(-3.35187 - 7.19003i) q^{21} +(-0.518202 + 0.897551i) q^{22} +(4.35592 - 7.54467i) q^{23} +(4.16704 + 0.364999i) q^{24} +(1.86055 + 3.22257i) q^{25} -3.98956 q^{26} +(5.01868 + 1.34641i) q^{27} -7.01961 q^{28} +(-0.499517 - 0.865189i) q^{29} +(1.33397 + 0.116845i) q^{30} +(0.954196 - 1.65272i) q^{31} +(2.89847 - 5.02030i) q^{32} +(1.10947 + 2.37990i) q^{33} +(-0.554554 - 0.960515i) q^{34} -5.17953 q^{35} +(2.95620 - 3.52160i) q^{36} +4.29839 q^{37} +(-0.500004 - 0.866033i) q^{38} +(-5.79847 + 8.27927i) q^{39} +(1.36557 - 2.36523i) q^{40} +(-2.59366 + 4.49234i) q^{41} +(3.11112 - 4.44217i) q^{42} +(2.48085 + 4.29695i) q^{43} +2.32349 q^{44} +(2.18128 - 2.59847i) q^{45} +5.95576 q^{46} +(3.78552 + 6.55672i) q^{47} +(-1.03500 - 2.22015i) q^{48} +(-6.98859 + 12.1046i) q^{49} +(-1.27195 + 2.20308i) q^{50} +(-2.79929 - 0.245195i) q^{51} +(4.47206 + 7.74583i) q^{52} -14.2165 q^{53} +(0.918347 + 3.43154i) q^{54} +1.71442 q^{55} +(-5.53057 - 9.57923i) q^{56} +(-2.52393 - 0.221076i) q^{57} +(0.341490 - 0.591478i) q^{58} +(-2.35033 + 4.07089i) q^{59} +(-1.26844 - 2.72090i) q^{60} +(6.70236 + 11.6088i) q^{61} +1.30465 q^{62} +(-4.69680 - 12.9126i) q^{63} +1.13452 q^{64} +(3.29978 + 5.71539i) q^{65} +(-1.02978 + 1.47036i) q^{66} +(0.500000 - 0.866025i) q^{67} +(-1.24324 + 2.15336i) q^{68} +(8.65616 - 12.3596i) q^{69} +(-1.77047 - 3.06654i) q^{70} +5.27337 q^{71} +(7.13482 + 1.25957i) q^{72} -11.5626 q^{73} +(1.46928 + 2.54486i) q^{74} +(2.72324 + 5.84157i) q^{75} +(-1.12095 + 1.94154i) q^{76} +(3.47172 - 6.01320i) q^{77} +(-6.88377 - 0.602963i) q^{78} +(-0.528994 - 0.916245i) q^{79} -1.59935 q^{80} +(8.45597 + 3.08165i) q^{81} -3.54625 q^{82} +(3.12353 + 5.41011i) q^{83} +(-12.1119 - 1.06091i) q^{84} +(-0.917346 + 1.58889i) q^{85} +(-1.69601 + 2.93757i) q^{86} +(-0.731129 - 1.56833i) q^{87} +(1.83062 + 3.17072i) q^{88} +0.567051 q^{89} +(2.28403 + 0.403218i) q^{90} +26.7283 q^{91} +(-6.67604 - 11.5632i) q^{92} +(1.89620 - 2.70746i) q^{93} +(-2.58793 + 4.48243i) q^{94} +(-0.827110 + 1.43260i) q^{95} +(5.75989 - 8.22418i) q^{96} +(-0.747876 - 1.29536i) q^{97} -9.55535 q^{98} +(1.55464 + 4.27406i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 7 q^{2} - 33 q^{4} + 18 q^{5} - 3 q^{6} - 48 q^{8} + 4 q^{9}+O(q^{10}) \) 66 * q + 7 * q^2 - 33 * q^4 + 18 * q^5 - 3 * q^6 - 48 * q^8 + 4 * q^9	\( 66 q + 7 q^{2} - 33 q^{4} + 18 q^{5} - 3 q^{6} - 48 q^{8} + 4 q^{9} + 12 q^{11} + q^{12} + 9 q^{14} + 3 q^{15} - 33 q^{16} - 62 q^{17} + 7 q^{18} + 43 q^{20} + 17 q^{21} + 19 q^{23} - 17 q^{24} - 33 q^{25} - 28 q^{26} - 3 q^{27} + 54 q^{28} + 25 q^{29} + 24 q^{30} + 45 q^{32} - 32 q^{33} - 6 q^{34} - 50 q^{35} + 53 q^{36} - 24 q^{37} + 34 q^{38} + 19 q^{39} - 6 q^{40} + 34 q^{41} - 107 q^{42} - 98 q^{44} + 9 q^{45} + 12 q^{46} + 26 q^{47} + 49 q^{48} - 33 q^{49} + 39 q^{50} - 50 q^{51} + 9 q^{52} - 104 q^{53} + 70 q^{54} + 60 q^{55} + 16 q^{56} + 6 q^{57} + 3 q^{58} + 21 q^{59} - 161 q^{60} - 54 q^{62} + q^{63} - 12 q^{64} + 52 q^{65} + 52 q^{66} + 33 q^{67} + 98 q^{68} + 2 q^{69} - 6 q^{70} - 62 q^{71} + 66 q^{72} + 27 q^{74} + 21 q^{75} - 6 q^{76} + 85 q^{77} - 107 q^{78} - 172 q^{80} + 72 q^{81} + 102 q^{82} + 71 q^{83} - 54 q^{84} - 27 q^{85} + 9 q^{86} + 3 q^{87} - 12 q^{88} - 82 q^{89} + 153 q^{90} - 60 q^{91} + 67 q^{92} - 47 q^{93} + 15 q^{94} + 58 q^{95} - 136 q^{96} - 12 q^{97} - 172 q^{98} + 96 q^{99}+O(q^{100}) \) 66 * q + 7 * q^2 - 33 * q^4 + 18 * q^5 - 3 * q^6 - 48 * q^8 + 4 * q^9 + 12 * q^11 + q^12 + 9 * q^14 + 3 * q^15 - 33 * q^16 - 62 * q^17 + 7 * q^18 + 43 * q^20 + 17 * q^21 + 19 * q^23 - 17 * q^24 - 33 * q^25 - 28 * q^26 - 3 * q^27 + 54 * q^28 + 25 * q^29 + 24 * q^30 + 45 * q^32 - 32 * q^33 - 6 * q^34 - 50 * q^35 + 53 * q^36 - 24 * q^37 + 34 * q^38 + 19 * q^39 - 6 * q^40 + 34 * q^41 - 107 * q^42 - 98 * q^44 + 9 * q^45 + 12 * q^46 + 26 * q^47 + 49 * q^48 - 33 * q^49 + 39 * q^50 - 50 * q^51 + 9 * q^52 - 104 * q^53 + 70 * q^54 + 60 * q^55 + 16 * q^56 + 6 * q^57 + 3 * q^58 + 21 * q^59 - 161 * q^60 - 54 * q^62 + q^63 - 12 * q^64 + 52 * q^65 + 52 * q^66 + 33 * q^67 + 98 * q^68 + 2 * q^69 - 6 * q^70 - 62 * q^71 + 66 * q^72 + 27 * q^74 + 21 * q^75 - 6 * q^76 + 85 * q^77 - 107 * q^78 - 172 * q^80 + 72 * q^81 + 102 * q^82 + 71 * q^83 - 54 * q^84 - 27 * q^85 + 9 * q^86 + 3 * q^87 - 12 * q^88 - 82 * q^89 + 153 * q^90 - 60 * q^91 + 67 * q^92 - 47 * q^93 + 15 * q^94 + 58 * q^95 - 136 * q^96 - 12 * q^97 - 172 * q^98 + 96 * q^99

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