LMFDB - Embedded newform 494.2.g.b.419.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [494,2,Mod(191,494)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(494, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("494.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 494 = 2 \cdot 13 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	494.g (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:	$3.94460985985$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.771147.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 5x^{4} + 6x^{3} + 15x^{2} + 4x + 1 $ x^6 - x^5 + 5x^4 + 6x^3 + 15x^2 + 4x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			419.1
Root			$1.32555 + 2.29591i$ of defining polynomial
Character	$\chi$	$=$	494.419
Dual form			494.2.g.b.191.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.825547 - 1.42989i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.27389 q^{5} +(-0.825547 + 1.42989i) q^{6} +(1.32555 - 2.29591i) q^{7} +1.00000 q^{8} +(0.136945 - 0.237196i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.825547 - 1.42989i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.27389 q^{5} +(-0.825547 + 1.42989i) q^{6} +(1.32555 - 2.29591i) q^{7} +1.00000 q^{8} +(0.136945 - 0.237196i) q^{9} +(-0.636945 - 1.10322i) q^{10} +(1.63695 + 2.83527i) q^{11} +1.65109 q^{12} +(3.47664 + 0.955496i) q^{13} -2.65109 q^{14} +(-1.05166 - 1.82152i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.65109 - 4.59183i) q^{17} -0.273891 q^{18} +(-0.500000 + 0.866025i) q^{19} +(-0.636945 + 1.10322i) q^{20} -4.37720 q^{21} +(1.63695 - 2.83527i) q^{22} +(-3.20275 - 5.54732i) q^{23} +(-0.825547 - 1.42989i) q^{24} -3.37720 q^{25} +(-0.910836 - 3.48861i) q^{26} -5.40550 q^{27} +(1.32555 + 2.29591i) q^{28} +(3.74026 + 6.47832i) q^{29} +(-1.05166 + 1.82152i) q^{30} +2.47277 q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.70275 - 4.68130i) q^{33} -5.30219 q^{34} +(1.68860 - 2.92474i) q^{35} +(0.136945 + 0.237196i) q^{36} +(-1.10331 - 1.91099i) q^{37} +1.00000 q^{38} +(-1.50388 - 5.76002i) q^{39} +1.27389 q^{40} +(-1.94834 - 3.37463i) q^{41} +(2.18860 + 3.79077i) q^{42} +(3.15109 - 5.45785i) q^{43} -3.27389 q^{44} +(0.174453 - 0.302162i) q^{45} +(-3.20275 + 5.54732i) q^{46} -12.3305 q^{47} +(-0.825547 + 1.42989i) q^{48} +(-0.0141481 - 0.0245053i) q^{49} +(1.68860 + 2.92474i) q^{50} -8.75441 q^{51} +(-2.56580 + 2.53311i) q^{52} -2.47277 q^{53} +(2.70275 + 4.68130i) q^{54} +(2.08529 + 3.61183i) q^{55} +(1.32555 - 2.29591i) q^{56} +1.65109 q^{57} +(3.74026 - 6.47832i) q^{58} +(-4.76855 + 8.25938i) q^{59} +2.10331 q^{60} +(2.83969 - 4.91850i) q^{61} +(-1.23638 - 2.14148i) q^{62} +(-0.363055 - 0.628829i) q^{63} +1.00000 q^{64} +(4.42886 + 1.21720i) q^{65} -5.40550 q^{66} +(0.103312 + 0.178942i) q^{67} +(2.65109 + 4.59183i) q^{68} +(-5.28804 + 9.15915i) q^{69} -3.37720 q^{70} +(1.50000 - 2.59808i) q^{71} +(0.136945 - 0.237196i) q^{72} +9.41325 q^{73} +(-1.10331 + 1.91099i) q^{74} +(2.78804 + 4.82902i) q^{75} +(-0.500000 - 0.866025i) q^{76} +8.67939 q^{77} +(-4.23638 + 4.18240i) q^{78} -12.2555 q^{79} +(-0.636945 - 1.10322i) q^{80} +(4.05166 + 7.01767i) q^{81} +(-1.94834 + 3.37463i) q^{82} +7.79045 q^{83} +(2.18860 - 3.79077i) q^{84} +(3.37720 - 5.84949i) q^{85} -6.30219 q^{86} +(6.17551 - 10.6963i) q^{87} +(1.63695 + 2.83527i) q^{88} +(7.06580 + 12.2383i) q^{89} -0.348907 q^{90} +(6.80219 - 6.71551i) q^{91} +6.40550 q^{92} +(-2.04138 - 3.53578i) q^{93} +(6.16524 + 10.6785i) q^{94} +(-0.636945 + 1.10322i) q^{95} +1.65109 q^{96} +(5.65109 - 9.78798i) q^{97} +(-0.0141481 + 0.0245053i) q^{98} +0.896688 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} + 2 q^{3} - 3 q^{4} + 4 q^{5} + 2 q^{6} + q^{7} + 6 q^{8} - q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 + 2 * q^3 - 3 * q^4 + 4 * q^5 + 2 * q^6 + q^7 + 6 * q^8 - q^9	\( 6 q - 3 q^{2} + 2 q^{3} - 3 q^{4} + 4 q^{5} + 2 q^{6} + q^{7} + 6 q^{8} - q^{9} - 2 q^{10} + 8 q^{11} - 4 q^{12} - 2 q^{14} - 3 q^{15} - 3 q^{16} + 2 q^{17} + 2 q^{18} - 3 q^{19} - 2 q^{20} - 16 q^{21} + 8 q^{22} - 2 q^{23} + 2 q^{24} - 10 q^{25} + 2 q^{27} + q^{28} + 14 q^{29} - 3 q^{30} - 10 q^{31} - 3 q^{32} - q^{33} - 4 q^{34} + 5 q^{35} - q^{36} + 6 q^{38} - 13 q^{39} + 4 q^{40} - 15 q^{41} + 8 q^{42} + 5 q^{43} - 16 q^{44} + 8 q^{45} - 2 q^{46} - 22 q^{47} + 2 q^{48} + 12 q^{49} + 5 q^{50} - 32 q^{51} + 10 q^{53} - q^{54} + 14 q^{55} + q^{56} - 4 q^{57} + 14 q^{58} + 4 q^{59} + 6 q^{60} - 2 q^{61} + 5 q^{62} - 4 q^{63} + 6 q^{64} + 13 q^{65} + 2 q^{66} - 6 q^{67} + 2 q^{68} - 16 q^{69} - 10 q^{70} + 9 q^{71} - q^{72} + 30 q^{73} + q^{75} - 3 q^{76} + 14 q^{77} - 13 q^{78} - 4 q^{79} - 2 q^{80} + 21 q^{81} - 15 q^{82} + 10 q^{83} + 8 q^{84} + 10 q^{85} - 10 q^{86} - 5 q^{87} + 8 q^{88} + 27 q^{89} - 16 q^{90} + 13 q^{91} + 4 q^{92} - 25 q^{93} + 11 q^{94} - 2 q^{95} - 4 q^{96} + 20 q^{97} + 12 q^{98} + 12 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 + 2 * q^3 - 3 * q^4 + 4 * q^5 + 2 * q^6 + q^7 + 6 * q^8 - q^9 - 2 * q^10 + 8 * q^11 - 4 * q^12 - 2 * q^14 - 3 * q^15 - 3 * q^16 + 2 * q^17 + 2 * q^18 - 3 * q^19 - 2 * q^20 - 16 * q^21 + 8 * q^22 - 2 * q^23 + 2 * q^24 - 10 * q^25 + 2 * q^27 + q^28 + 14 * q^29 - 3 * q^30 - 10 * q^31 - 3 * q^32 - q^33 - 4 * q^34 + 5 * q^35 - q^36 + 6 * q^38 - 13 * q^39 + 4 * q^40 - 15 * q^41 + 8 * q^42 + 5 * q^43 - 16 * q^44 + 8 * q^45 - 2 * q^46 - 22 * q^47 + 2 * q^48 + 12 * q^49 + 5 * q^50 - 32 * q^51 + 10 * q^53 - q^54 + 14 * q^55 + q^56 - 4 * q^57 + 14 * q^58 + 4 * q^59 + 6 * q^60 - 2 * q^61 + 5 * q^62 - 4 * q^63 + 6 * q^64 + 13 * q^65 + 2 * q^66 - 6 * q^67 + 2 * q^68 - 16 * q^69 - 10 * q^70 + 9 * q^71 - q^72 + 30 * q^73 + q^75 - 3 * q^76 + 14 * q^77 - 13 * q^78 - 4 * q^79 - 2 * q^80 + 21 * q^81 - 15 * q^82 + 10 * q^83 + 8 * q^84 + 10 * q^85 - 10 * q^86 - 5 * q^87 + 8 * q^88 + 27 * q^89 - 16 * q^90 + 13 * q^91 + 4 * q^92 - 25 * q^93 + 11 * q^94 - 2 * q^95 - 4 * q^96 + 20 * q^97 + 12 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/494\mathbb{Z}\right)^\times$.

$n$	$287$	$457$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−0.825547	−	1.42989i	−0.476630	−	0.825547i	0.523012	−	0.852325i	$-0.324808\pi$
$3$	−0.825547	−	1.42989i	−0.476630	−	0.825547i	−0.999641	+	0.0267788i	$0.991475\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.27389			0.569701			0.284851	−	0.958572i	$-0.408056\pi$
$5$	1.27389			0.569701			0.284851	+	0.958572i	$0.408056\pi$
$6$	−0.825547	+	1.42989i	−0.337028	+	0.583750i
$7$	1.32555	−	2.29591i	0.501010	−	0.867774i	−0.498990	−	0.866608i	$-0.666295\pi$
$7$	1.32555	−	2.29591i	0.501010	−	0.867774i	0.999999	−	0.00116613i	$-0.000371192\pi$
$8$	1.00000			0.353553
$9$	0.136945	−	0.237196i	0.0456484	−	0.0790654i
$10$	−0.636945	−	1.10322i	−0.201420	−	0.348869i
$11$	1.63695	+	2.83527i	0.493558	+	0.854867i	0.999972	−	0.00742317i	$-0.00236289\pi$
$11$	1.63695	+	2.83527i	0.493558	+	0.854867i	−0.506415	+	0.862290i	$0.669030\pi$
$12$	1.65109			0.476630
$13$	3.47664	+	0.955496i	0.964246	+	0.265007i
$13$	3.47664	+	0.955496i	0.964246	+	0.265007i
$14$	−2.65109			−0.708535
$15$	−1.05166	−	1.82152i	−0.271536	−	0.470315i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.65109	−	4.59183i	0.642985	−	1.11368i	−0.341778	−	0.939781i	$-0.611029\pi$
$17$	2.65109	−	4.59183i	0.642985	−	1.11368i	0.984763	−	0.173901i	$-0.0556374\pi$
$18$	−0.273891			−0.0645566
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i
$20$	−0.636945	+	1.10322i	−0.142425	+	0.246688i
$21$	−4.37720			−0.955184
$22$	1.63695	−	2.83527i	0.348998	−	0.604482i
$23$	−3.20275	−	5.54732i	−0.667819	−	1.15670i	−0.978513	−	0.206187i	$-0.933894\pi$
$23$	−3.20275	−	5.54732i	−0.667819	−	1.15670i	0.310693	−	0.950510i	$-0.399439\pi$
$24$	−0.825547	−	1.42989i	−0.168514	−	0.291875i
$25$	−3.37720			−0.675441
$26$	−0.910836	−	3.48861i	−0.178630	−	0.684172i
$27$	−5.40550			−1.04029
$28$	1.32555	+	2.29591i	0.250505	+	0.433887i
$29$	3.74026	+	6.47832i	0.694548	+	1.20299i	0.970333	+	0.241774i	$0.0777291\pi$
$29$	3.74026	+	6.47832i	0.694548	+	1.20299i	−0.275784	+	0.961220i	$0.588938\pi$
$30$	−1.05166	+	1.82152i	−0.192005	+	0.332563i
$31$	2.47277			0.444122			0.222061	−	0.975033i	$-0.428722\pi$
$31$	2.47277			0.444122			0.222061	+	0.975033i	$0.428722\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	2.70275	−	4.68130i	0.470488	−	0.814910i
$34$	−5.30219			−0.909318
$35$	1.68860	−	2.92474i	0.285426	−	0.494372i
$36$	0.136945	+	0.237196i	0.0228242	+	0.0395327i
$37$	−1.10331	−	1.91099i	−0.181383	−	0.314165i	0.760968	−	0.648789i	$-0.224724\pi$
$37$	−1.10331	−	1.91099i	−0.181383	−	0.314165i	−0.942352	+	0.334624i	$0.891391\pi$
$38$	1.00000			0.162221
$39$	−1.50388	−	5.76002i	−0.240813	−	0.922341i
$40$	1.27389			0.201420
$41$	−1.94834	−	3.37463i	−0.304280	−	0.527029i	0.672821	−	0.739806i	$-0.265083\pi$
$41$	−1.94834	−	3.37463i	−0.304280	−	0.527029i	−0.977101	+	0.212777i	$0.931749\pi$
$42$	2.18860	+	3.79077i	0.337709	+	0.584928i
$43$	3.15109	−	5.45785i	0.480537	−	0.832315i	−0.519213	−	0.854645i	$-0.673775\pi$
$43$	3.15109	−	5.45785i	0.480537	−	0.832315i	0.999751	+	0.0223297i	$0.00710836\pi$
$44$	−3.27389			−0.493558
$45$	0.174453	−	0.302162i	0.0260060	−	0.0450436i
$46$	−3.20275	+	5.54732i	−0.472220	+	0.817908i
$47$	−12.3305			−1.79859			−0.899293	−	0.437347i	$-0.855918\pi$
$47$	−12.3305			−1.79859			−0.899293	+	0.437347i	$0.855918\pi$
$48$	−0.825547	+	1.42989i	−0.119157	+	0.206387i
$49$	−0.0141481	−	0.0245053i	−0.00202116	−	0.00350075i
$50$	1.68860	+	2.92474i	0.238804	+	0.413621i
$51$	−8.75441			−1.22586
$52$	−2.56580	+	2.53311i	−0.355813	+	0.351279i
$53$	−2.47277			−0.339660			−0.169830	−	0.985473i	$-0.554322\pi$
$53$	−2.47277			−0.339660			−0.169830	+	0.985473i	$0.554322\pi$
$54$	2.70275	+	4.68130i	0.367798	+	0.637044i
$55$	2.08529	+	3.61183i	0.281180	+	0.487019i
$56$	1.32555	−	2.29591i	0.177134	−	0.306804i
$57$	1.65109			0.218693
$58$	3.74026	−	6.47832i	0.491120	−	0.850645i
$59$	−4.76855	+	8.25938i	−0.620813	+	1.07528i	0.368522	+	0.929619i	$0.379864\pi$
$59$	−4.76855	+	8.25938i	−0.620813	+	1.07528i	−0.989335	+	0.145660i	$0.953469\pi$
$60$	2.10331			0.271536
$61$	2.83969	−	4.91850i	0.363586	−	0.629749i	−0.624962	−	0.780655i	$-0.714886\pi$
$61$	2.83969	−	4.91850i	0.363586	−	0.629749i	0.988548	+	0.150906i	$0.0482191\pi$
$62$	−1.23638	−	2.14148i	−0.157021	−	0.271968i
$63$	−0.363055	−	0.628829i	−0.0457406	−	0.0792250i
$64$	1.00000			0.125000
$65$	4.42886	+	1.21720i	0.549332	+	0.150975i
$66$	−5.40550			−0.665371
$67$	0.103312	+	0.178942i	0.0126216	+	0.0218613i	0.872267	−	0.489030i	$-0.162649\pi$
$67$	0.103312	+	0.178942i	0.0126216	+	0.0218613i	−0.859646	+	0.510891i	$0.829316\pi$
$68$	2.65109	+	4.59183i	0.321492	+	0.556841i
$69$	−5.28804	+	9.15915i	−0.636605	+	1.10263i
$70$	−3.37720			−0.403653
$71$	1.50000	−	2.59808i	0.178017	−	0.308335i	−0.763184	−	0.646181i	$-0.776365\pi$
$71$	1.50000	−	2.59808i	0.178017	−	0.308335i	0.941201	+	0.337846i	$0.109698\pi$
$72$	0.136945	−	0.237196i	0.0161392	−	0.0279538i
$73$	9.41325			1.10174			0.550869	−	0.834592i	$-0.314296\pi$
$73$	9.41325			1.10174			0.550869	+	0.834592i	$0.314296\pi$
$74$	−1.10331	+	1.91099i	−0.128257	+	0.222148i
$75$	2.78804	+	4.82902i	0.321935	+	0.557608i
$76$	−0.500000	−	0.866025i	−0.0573539	−	0.0993399i
$77$	8.67939			0.989108
$78$	−4.23638	+	4.18240i	−0.479676	+	0.473564i
$79$	−12.2555			−1.37885			−0.689424	−	0.724358i	$-0.742136\pi$
$79$	−12.2555			−1.37885			−0.689424	+	0.724358i	$0.742136\pi$
$80$	−0.636945	−	1.10322i	−0.0712126	−	0.123344i
$81$	4.05166	+	7.01767i	0.450184	+	0.779742i
$82$	−1.94834	+	3.37463i	−0.215159	+	0.372666i
$83$	7.79045			0.855113			0.427557	−	0.903989i	$-0.359374\pi$
$83$	7.79045			0.855113			0.427557	+	0.903989i	$0.359374\pi$
$84$	2.18860	−	3.79077i	0.238796	−	0.413607i
$85$	3.37720	−	5.84949i	0.366309	−	0.634466i
$86$	−6.30219			−0.679582
$87$	6.17551	−	10.6963i	0.662085	−	1.14676i
$88$	1.63695	+	2.83527i	0.174499	+	0.302241i
$89$	7.06580	+	12.2383i	0.748974	+	1.29726i	0.948315	+	0.317330i	$0.102786\pi$
$89$	7.06580	+	12.2383i	0.748974	+	1.29726i	−0.199341	+	0.979930i	$0.563880\pi$
$90$	−0.348907			−0.0367780
$91$	6.80219	−	6.71551i	0.713063	−	0.703977i
$92$	6.40550			0.667819
$93$	−2.04138	−	3.53578i	−0.211682	−	0.366643i
$94$	6.16524	+	10.6785i	0.635896	+	1.10140i
$95$	−0.636945	+	1.10322i	−0.0653492	+	0.113188i
$96$	1.65109			0.168514
$97$	5.65109	−	9.78798i	0.573782	−	0.993819i	−0.422391	−	0.906414i	$-0.638809\pi$
$97$	5.65109	−	9.78798i	0.573782	−	0.993819i	0.996173	−	0.0874053i	$-0.0278575\pi$
$98$	−0.0141481	+	0.0245053i	−0.00142918	+	0.00247541i
$99$	0.896688			0.0901205
$100$	1.68860	−	2.92474i	0.168860	−	0.292474i
$101$	6.90550	+	11.9607i	0.687123	+	1.19013i	0.972765	+	0.231795i	$0.0744599\pi$
$101$	6.90550	+	11.9607i	0.687123	+	1.19013i	−0.285642	+	0.958336i	$0.592207\pi$
$102$	4.37720	+	7.58154i	0.433408	+	0.750684i
$103$	15.4904			1.52631			0.763157	−	0.646214i	$-0.223648\pi$
$103$	15.4904			1.52631			0.763157	+	0.646214i	$0.223648\pi$
$104$	3.47664	+	0.955496i	0.340913	+	0.0936941i
$105$	−5.57608			−0.544169
$106$	1.23638	+	2.14148i	0.120088	+	0.207999i
$107$	0.948344	+	1.64258i	0.0916799	+	0.158794i	0.908218	−	0.418497i	$-0.137443\pi$
$107$	0.948344	+	1.64258i	0.0916799	+	0.158794i	−0.816538	+	0.577291i	$0.804110\pi$
$108$	2.70275	−	4.68130i	0.260072	−	0.450458i
$109$	12.9066			1.23622			0.618112	−	0.786090i	$-0.287898\pi$
$109$	12.9066			1.23622			0.618112	+	0.786090i	$0.287898\pi$
$110$	2.08529	−	3.61183i	0.198825	−	0.344374i
$111$	−1.82167	+	3.15523i	−0.172905	+	0.299481i
$112$	−2.65109			−0.250505
$113$	−10.0761	+	17.4523i	−0.947878	+	1.64177i	−0.197993	+	0.980203i	$0.563442\pi$
$113$	−10.0761	+	17.4523i	−0.947878	+	1.64177i	−0.749884	+	0.661569i	$0.769891\pi$
$114$	−0.825547	−	1.42989i	−0.0773195	−	0.133921i
$115$	−4.07995	−	7.06668i	−0.380458	−	0.658972i
$116$	−7.48052			−0.694548
$117$	0.702750	−	0.693795i	0.0649692	−	0.0641414i
$118$	9.53711			0.877962
$119$	−7.02830	−	12.1734i	−0.644283	−	1.11593i
$120$	−1.05166	−	1.82152i	−0.0960026	−	0.166281i
$121$	0.140820	−	0.243908i	0.0128018	−	0.0221734i
$122$	−5.67939			−0.514188
$123$	−3.21690	+	5.57183i	−0.290058	+	0.502395i
$124$	−1.23638	+	2.14148i	−0.111030	+	0.192310i
$125$	−10.6716			−0.954500
$126$	−0.363055	+	0.628829i	−0.0323435	+	0.0560206i
$127$	3.85918	+	6.68430i	0.342447	+	0.593135i	0.984887	−	0.173201i	$-0.0554110\pi$
$127$	3.85918	+	6.68430i	0.342447	+	0.593135i	−0.642440	+	0.766336i	$0.722078\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−10.4055			−0.916153
$130$	−1.16031	−	4.44410i	−0.101765	−	0.389774i
$131$	−8.97170			−0.783861			−0.391931	−	0.919995i	$-0.628193\pi$
$131$	−8.97170			−0.783861			−0.391931	+	0.919995i	$0.628193\pi$
$132$	2.70275	+	4.68130i	0.235244	+	0.407455i
$133$	1.32555	+	2.29591i	0.114939	+	0.199081i
$134$	0.103312	−	0.178942i	0.00892482	−	0.0154582i
$135$	−6.88601			−0.592654
$136$	2.65109	−	4.59183i	0.227329	−	0.393746i
$137$	−6.95716	+	12.0501i	−0.594390	+	1.02951i	0.399243	+	0.916845i	$0.369273\pi$
$137$	−6.95716	+	12.0501i	−0.594390	+	1.02951i	−0.993633	+	0.112668i	$0.964060\pi$
$138$	10.5761			0.900295
$139$	7.71690	−	13.3661i	0.654539	−	1.13369i	−0.327471	−	0.944861i	$-0.606196\pi$
$139$	7.71690	−	13.3661i	0.654539	−	1.13369i	0.982009	−	0.188833i	$-0.0604705\pi$
$140$	1.68860	+	2.92474i	0.142713	+	0.247186i
$141$	10.1794	+	17.6312i	0.857259	+	1.48482i
$142$	−3.00000			−0.251754
$143$	2.98198	+	11.4213i	0.249365	+	0.955099i
$144$	−0.273891			−0.0228242
$145$	4.76468	+	8.25267i	0.395685	+	0.685347i
$146$	−4.70662	−	8.15211i	−0.389523	−	0.674674i
$147$	−0.0233599	+	0.0404605i	−0.00192669	+	0.00333713i
$148$	2.20662			0.181383
$149$	10.2027	−	17.6717i	0.835842	−	1.44772i	−0.0575014	−	0.998345i	$-0.518313\pi$
$149$	10.2027	−	17.6717i	0.835842	−	1.44772i	0.893343	−	0.449375i	$-0.148353\pi$
$150$	2.78804	−	4.82902i	0.227642	−	0.394288i
$151$	−3.04672			−0.247939			−0.123969	−	0.992286i	$-0.539562\pi$
$151$	−3.04672			−0.247939			−0.123969	+	0.992286i	$0.539562\pi$
$152$	−0.500000	+	0.866025i	−0.0405554	+	0.0702439i
$153$	−0.726109	−	1.25766i	−0.0587025	−	0.101676i
$154$	−4.33969	−	7.51657i	−0.349703	−	0.605703i
$155$	3.15003			0.253017
$156$	5.74026	+	1.57761i	0.459588	+	0.126310i
$157$	−2.17833			−0.173850			−0.0869248	−	0.996215i	$-0.527704\pi$
$157$	−2.17833			−0.173850			−0.0869248	+	0.996215i	$0.527704\pi$
$158$	6.12773	+	10.6135i	0.487496	+	0.844368i
$159$	2.04138	+	3.53578i	0.161892	+	0.280406i
$160$	−0.636945	+	1.10322i	−0.0503549	+	0.0872173i
$161$	−16.9816			−1.33834
$162$	4.05166	−	7.01767i	0.318328	−	0.551361i
$163$	−0.136945	+	0.237196i	−0.0107264	+	0.0185786i	−0.871339	−	0.490682i	$-0.836748\pi$
$163$	−0.136945	+	0.237196i	−0.0107264	+	0.0185786i	0.860612	+	0.509261i	$0.170081\pi$
$164$	3.89669			0.304280
$165$	3.44301	−	5.96346i	0.268038	−	0.464255i
$166$	−3.89523	−	6.74673i	−0.302328	−	0.523648i
$167$	−1.06193	−	1.83932i	−0.0821746	−	0.142330i	0.822009	−	0.569474i	$-0.192853\pi$
$167$	−1.06193	−	1.83932i	−0.0821746	−	0.142330i	−0.904184	+	0.427144i	$0.859520\pi$
$168$	−4.37720			−0.337709
$169$	11.1741	+	6.64383i	0.859543	+	0.511064i
$170$	−6.75441			−0.518039
$171$	0.136945	+	0.237196i	0.0104725	+	0.0181388i
$172$	3.15109	+	5.45785i	0.240269	+	0.416157i
$173$	−12.1560	+	21.0549i	−0.924206	+	1.60077i	−0.131372	+	0.991333i	$0.541938\pi$
$173$	−12.1560	+	21.0549i	−0.924206	+	1.60077i	−0.792833	+	0.609438i	$0.791395\pi$
$174$	−12.3510			−0.936329
$175$	−4.47664	+	7.75377i	−0.338402	+	0.586130i
$176$	1.63695	−	2.83527i	0.123389	−	0.213717i
$177$	15.7467			1.18359
$178$	7.06580	−	12.2383i	0.529604	−	0.917302i
$179$	−5.13307	−	8.89074i	−0.383664	−	0.664525i	0.607919	−	0.793999i	$-0.292004\pi$
$179$	−5.13307	−	8.89074i	−0.383664	−	0.664525i	−0.991583	+	0.129474i	$0.958671\pi$
$180$	0.174453	+	0.302162i	0.0130030	+	0.0225218i
$181$	−25.6893			−1.90947			−0.954734	−	0.297461i	$-0.903860\pi$
$181$	−25.6893			−1.90947			−0.954734	+	0.297461i	$0.903860\pi$
$182$	−9.21690	−	2.53311i	−0.683202	−	0.187767i
$183$	−9.37720			−0.693183
$184$	−3.20275	−	5.54732i	−0.236110	−	0.408954i
$185$	−1.40550	−	2.43440i	−0.103334	−	0.178980i
$186$	−2.04138	+	3.53578i	−0.149681	+	0.259256i
$187$	17.3588			1.26940
$188$	6.16524	−	10.6785i	0.449646	−	0.778811i
$189$	−7.16524	+	12.4106i	−0.521195	+	0.902736i
$190$	1.27389			0.0924177
$191$	0.428859	−	0.742806i	0.0310311	−	0.0537475i	−0.850093	−	0.526633i	$-0.823454\pi$
$191$	0.428859	−	0.742806i	0.0310311	−	0.0537475i	0.881124	+	0.472885i	$0.156788\pi$
$192$	−0.825547	−	1.42989i	−0.0595787	−	0.103193i
$193$	5.04632	+	8.74048i	0.363242	+	0.629154i	0.988492	−	0.151271i	$-0.0483365\pi$
$193$	5.04632	+	8.74048i	0.363242	+	0.629154i	−0.625250	+	0.780424i	$0.715003\pi$
$194$	−11.3022			−0.811450
$195$	−1.91577	−	7.33763i	−0.137191	−	0.525459i
$196$	0.0282963			0.00202116
$197$	−4.84503	−	8.39184i	−0.345194	−	0.597894i	0.640195	−	0.768213i	$-0.278854\pi$
$197$	−4.84503	−	8.39184i	−0.345194	−	0.597894i	−0.985389	+	0.170319i	$0.945520\pi$
$198$	−0.448344	−	0.776554i	−0.0318624	−	0.0551873i
$199$	−12.0980	+	20.9543i	−0.857603	+	1.48541i	0.0166065	+	0.999862i	$0.494714\pi$
$199$	−12.0980	+	20.9543i	−0.857603	+	1.48541i	−0.874209	+	0.485549i	$0.838620\pi$
$200$	−3.37720			−0.238804
$201$	0.170578	−	0.295450i	0.0120317	−	0.0208395i
$202$	6.90550	−	11.9607i	0.485869	−	0.841550i
$203$	19.8315			1.39190
$204$	4.37720	−	7.58154i	0.306465	−	0.530814i
$205$	−2.48198	−	4.29891i	−0.173349	−	0.300249i
$206$	−7.74519	−	13.4151i	−0.539633	−	0.934672i
$207$	−1.75441			−0.121940
$208$	−0.910836	−	3.48861i	−0.0631551	−	0.241891i
$209$	−3.27389			−0.226460
$210$	2.78804	+	4.82902i	0.192393	+	0.333234i
$211$	−3.36412	−	5.82682i	−0.231595	−	0.401135i	0.726682	−	0.686974i	$-0.241061\pi$
$211$	−3.36412	−	5.82682i	−0.231595	−	0.401135i	−0.958278	+	0.285839i	$0.907728\pi$
$212$	1.23638	−	2.14148i	0.0849151	−	0.147077i
$213$	−4.95328			−0.339393
$214$	0.948344	−	1.64258i	0.0648275	−	0.112284i
$215$	4.01415	−	6.95271i	0.273763	−	0.474171i
$216$	−5.40550			−0.367798
$217$	3.27777	−	5.67726i	0.222509	−	0.385397i
$218$	−6.45328	−	11.1774i	−0.437071	−	0.757030i
$219$	−7.77108	−	13.4599i	−0.525121	−	0.909536i
$220$	−4.17058			−0.281180
$221$	13.6044	−	13.4310i	0.915129	−	0.903468i
$222$	3.64334			0.244525
$223$	7.52830	+	13.0394i	0.504132	+	0.873182i	0.999989	+	0.00477782i	$0.00152083\pi$
$223$	7.52830	+	13.0394i	0.504132	+	0.873182i	−0.495857	+	0.868404i	$0.665146\pi$
$224$	1.32555	+	2.29591i	0.0885668	+	0.153402i
$225$	−0.462492	+	0.801060i	−0.0308328	+	0.0534040i
$226$	20.1522			1.34050
$227$	0.382540	−	0.662578i	0.0253900	−	0.0439768i	−0.853051	−	0.521827i	$-0.825251\pi$
$227$	0.382540	−	0.662578i	0.0253900	−	0.0439768i	0.878441	+	0.477850i	$0.158584\pi$
$228$	−0.825547	+	1.42989i	−0.0546732	+	0.0946967i
$229$	10.8422			0.716474			0.358237	−	0.933631i	$-0.383378\pi$
$229$	10.8422			0.716474			0.358237	+	0.933631i	$0.383378\pi$
$230$	−4.07995	+	7.06668i	−0.269024	+	0.465963i
$231$	−7.16524	−	12.4106i	−0.471438	−	0.816555i
$232$	3.74026	+	6.47832i	0.245560	+	0.425322i
$233$	−15.9816			−1.04699			−0.523494	−	0.852029i	$-0.675372\pi$
$233$	−15.9816			−1.04699			−0.523494	+	0.852029i	$0.675372\pi$
$234$	−0.952219	−	0.261701i	−0.0622485	−	0.0171080i
$235$	−15.7077			−1.02466
$236$	−4.76855	−	8.25938i	−0.310406	−	0.537640i
$237$	10.1175	+	17.5240i	0.657200	+	1.13830i
$238$	−7.02830	+	12.1734i	−0.455577	+	0.789082i
$239$	−0.118812			−0.00768534			−0.00384267	−	0.999993i	$-0.501223\pi$
$239$	−0.118812			−0.00768534			−0.00384267	+	0.999993i	$0.501223\pi$
$240$	−1.05166	+	1.82152i	−0.0678841	+	0.117579i
$241$	−4.51415	+	7.81873i	−0.290782	+	0.503649i	−0.973995	−	0.226570i	$-0.927249\pi$
$241$	−4.51415	+	7.81873i	−0.290782	+	0.503649i	0.683213	+	0.730219i	$0.260582\pi$
$242$	−0.281641			−0.0181045
$243$	−1.41859	+	2.45706i	−0.0910023	+	0.157621i
$244$	2.83969	+	4.91850i	0.181793	+	0.314874i
$245$	−0.0180232	−	0.0312170i	−0.00115146	−	0.00199438i
$246$	6.43380			0.410204
$247$	−2.56580	+	2.53311i	−0.163258	+	0.161178i
$248$	2.47277			0.157021
$249$	−6.43138	−	11.1395i	−0.407572	−	0.705936i
$250$	5.33582	+	9.24191i	0.337467	+	0.584510i
$251$	−1.70275	+	2.94925i	−0.107477	+	0.186155i	−0.914747	−	0.404026i	$-0.867610\pi$
$251$	−1.70275	+	2.94925i	−0.107477	+	0.186155i	0.807271	+	0.590181i	$0.200944\pi$
$252$	0.726109			0.0457406
$253$	10.4855	−	18.1613i	0.659215	−	1.14179i
$254$	3.85918	−	6.68430i	0.242146	−	0.419410i
$255$	−11.1522			−0.698375
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−5.66137	−	9.80577i	−0.353146	−	0.611667i	0.633653	−	0.773618i	$-0.281555\pi$
$257$	−5.66137	−	9.80577i	−0.353146	−	0.611667i	−0.986799	+	0.161950i	$0.948222\pi$
$258$	5.20275	+	9.01143i	0.323909	+	0.561027i
$259$	−5.84997			−0.363499
$260$	−3.26855	+	3.22691i	−0.202707	+	0.200124i
$261$	2.04884			0.126820
$262$	4.48585	+	7.76972i	0.277137	+	0.480015i
$263$	14.7647	+	25.5732i	0.910429	+	1.57691i	0.813459	+	0.581622i	$0.197582\pi$
$263$	14.7647	+	25.5732i	0.910429	+	1.57691i	0.0969700	+	0.995287i	$0.469085\pi$
$264$	2.70275	−	4.68130i	0.166343	−	0.288114i
$265$	−3.15003			−0.193505
$266$	1.32555	−	2.29591i	0.0812745	−	0.140772i
$267$	11.6663	−	20.2066i	0.713966	−	1.23663i
$268$	−0.206625			−0.0126216
$269$	−7.90937	+	13.6994i	−0.482243	+	0.835269i	−0.999792	−	0.0203840i	$-0.993511\pi$
$269$	−7.90937	+	13.6994i	−0.482243	+	0.835269i	0.517549	+	0.855653i	$0.326844\pi$
$270$	3.44301	+	5.96346i	0.209535	+	0.362925i
$271$	−7.79685	−	13.5045i	−0.473625	−	0.820342i	0.525919	−	0.850535i	$-0.323721\pi$
$271$	−7.79685	−	13.5045i	−0.473625	−	0.820342i	−0.999544	+	0.0301921i	$0.990388\pi$
$272$	−5.30219			−0.321492
$273$	−15.2180	−	4.18240i	−0.921033	−	0.253130i
$274$	13.9143			0.840594
$275$	−5.52830	−	9.57529i	−0.333369	−	0.577412i
$276$	−5.28804	−	9.15915i	−0.318303	−	0.551316i
$277$	4.12667	−	7.14761i	0.247948	−	0.429458i	−0.715009	−	0.699116i	$-0.753577\pi$
$277$	4.12667	−	7.14761i	0.247948	−	0.429458i	0.962956	+	0.269658i	$0.0869106\pi$
$278$	−15.4338			−0.925658
$279$	0.338633	−	0.586530i	0.0202735	−	0.0351147i
$280$	1.68860	−	2.92474i	0.100913	−	0.174787i
$281$	−1.38708			−0.0827460			−0.0413730	−	0.999144i	$-0.513173\pi$
$281$	−1.38708			−0.0827460			−0.0413730	+	0.999144i	$0.513173\pi$
$282$	10.1794	−	17.6312i	0.606174	−	1.04992i
$283$	11.9494	+	20.6970i	0.710318	+	1.23031i	0.964738	+	0.263214i	$0.0847824\pi$
$283$	11.9494	+	20.6970i	0.710318	+	1.23031i	−0.254419	+	0.967094i	$0.581884\pi$
$284$	1.50000	+	2.59808i	0.0890086	+	0.154167i
$285$	2.10331			0.124589
$286$	8.40016	−	8.29313i	0.496712	−	0.490383i
$287$	−10.3305			−0.609789
$288$	0.136945	+	0.237196i	0.00806958	+	0.0139769i
$289$	−5.55659	−	9.62430i	−0.326858	−	0.566135i
$290$	4.76468	−	8.25267i	0.279792	−	0.484613i
$291$	−18.6610			−1.09393
$292$	−4.70662	+	8.15211i	−0.275434	+	0.477066i
$293$	0.399101	−	0.691263i	0.0233157	−	0.0403840i	−0.854132	−	0.520056i	$-0.825911\pi$
$293$	0.399101	−	0.691263i	0.0233157	−	0.0403840i	0.877448	+	0.479672i	$0.159244\pi$
$294$	0.0467198			0.00272475
$295$	−6.07462	+	10.5215i	−0.353678	+	0.612588i
$296$	−1.10331	−	1.91099i	−0.0641287	−	0.111074i
$297$	−8.84851	−	15.3261i	−0.513442	−	0.889308i
$298$	−20.4055			−1.18206
$299$	−5.83436	−	22.3463i	−0.337410	−	1.29232i
$300$	−5.57608			−0.321935
$301$	−8.35384	−	14.4693i	−0.481508	−	0.833995i
$302$	1.52336	+	2.63854i	0.0876595	+	0.151831i
$303$	11.4016	−	19.7482i	0.655006	−	1.13450i
$304$	1.00000			0.0573539
$305$	3.61746	−	6.26563i	0.207135	−	0.358769i
$306$	−0.726109	+	1.25766i	−0.0415089	+	0.0718955i
$307$	18.1522			1.03600			0.517999	−	0.855381i	$-0.326677\pi$
$307$	18.1522			1.03600			0.517999	+	0.855381i	$0.326677\pi$
$308$	−4.33969	+	7.51657i	−0.247277	+	0.428296i
$309$	−12.7880	−	22.1495i	−0.727486	−	1.26004i
$310$	−1.57502	−	2.72801i	−0.0894549	−	0.154940i
$311$	15.5011			0.878985			0.439492	−	0.898246i	$-0.355158\pi$
$311$	15.5011			0.878985			0.439492	+	0.898246i	$0.355158\pi$
$312$	−1.50388	−	5.76002i	−0.0851402	−	0.326097i
$313$	0.803248			0.0454023			0.0227011	−	0.999742i	$-0.492773\pi$
$313$	0.803248			0.0454023			0.0227011	+	0.999742i	$0.492773\pi$
$314$	1.08916	+	1.88649i	0.0614651	+	0.106461i
$315$	−0.462492	−	0.801060i	−0.0260585	−	0.0451346i
$316$	6.12773	−	10.6135i	0.344712	−	0.597059i
$317$	23.0820			1.29641			0.648206	−	0.761465i	$-0.275519\pi$
$317$	23.0820			1.29641			0.648206	+	0.761465i	$0.275519\pi$
$318$	2.04138	−	3.53578i	0.114475	−	0.198277i
$319$	−12.2452	+	21.2093i	−0.685599	+	1.18749i
$320$	1.27389			0.0712126
$321$	1.56580	−	2.71205i	0.0873947	−	0.151372i
$322$	8.49079	+	14.7065i	0.473173	+	0.819560i
$323$	2.65109	+	4.59183i	0.147511	+	0.255496i
$324$	−8.10331			−0.450184
$325$	−11.7413	−	3.22691i	−0.651291	−	0.178997i
$326$	0.273891			0.0151694
$327$	−10.6550	−	18.4549i	−0.589221	−	1.02056i
$328$	−1.94834	−	3.37463i	−0.107579	−	0.186333i
$329$	−16.3446	+	28.3097i	−0.901109	+	1.56077i
$330$	−6.88601			−0.379063
$331$	−3.83582	+	6.64383i	−0.210836	+	0.365178i	−0.951976	−	0.306172i	$-0.900952\pi$
$331$	−3.83582	+	6.64383i	−0.210836	+	0.365178i	0.741141	+	0.671350i	$0.234285\pi$
$332$	−3.89523	+	6.74673i	−0.213778	+	0.370275i
$333$	−0.604374			−0.0331195
$334$	−1.06193	+	1.83932i	−0.0581062	+	0.100643i
$335$	0.131609	+	0.227953i	0.00719054	+	0.0124544i
$336$	2.18860	+	3.79077i	0.119398	+	0.206803i
$337$	4.19887			0.228727			0.114364	−	0.993439i	$-0.463517\pi$
$337$	4.19887			0.228727			0.114364	+	0.993439i	$0.463517\pi$
$338$	0.166703	−	12.9989i	0.00906746	−	0.707049i
$339$	33.2731			1.80715
$340$	3.37720	+	5.84949i	0.183155	+	0.317233i
$341$	4.04778	+	7.01096i	0.219200	+	0.379665i
$342$	0.136945	−	0.237196i	0.00740515	−	0.0128261i
$343$	18.4826			0.997969
$344$	3.15109	−	5.45785i	0.169896	−	0.294268i
$345$	−6.73638	+	11.6678i	−0.362675	+	0.628171i
$346$	24.3121			1.30702
$347$	3.97024	−	6.87666i	0.213134	−	0.369159i	−0.739560	−	0.673091i	$-0.764966\pi$
$347$	3.97024	−	6.87666i	0.213134	−	0.369159i	0.952694	+	0.303932i	$0.0982997\pi$
$348$	6.17551	+	10.6963i	0.331042	+	0.573382i
$349$	10.9597	+	18.9827i	0.586658	+	1.01612i	0.994666	+	0.103143i	$0.0328901\pi$
$349$	10.9597	+	18.9827i	0.586658	+	1.01612i	−0.408008	+	0.912978i	$0.633777\pi$
$350$	8.95328			0.478573
$351$	−18.7930	−	5.16494i	−1.00309	−	0.275684i
$352$	−3.27389			−0.174499
$353$	−12.7983	−	22.1673i	−0.681185	−	1.17985i	−0.974619	−	0.223868i	$-0.928131\pi$
$353$	−12.7983	−	22.1673i	−0.681185	−	1.17985i	0.293434	−	0.955979i	$-0.405202\pi$
$354$	−7.87333	−	13.6370i	−0.418463	−	0.724799i
$355$	1.91084	−	3.30966i	0.101417	−	0.175659i
$356$	−14.1316			−0.748974
$357$	−11.6044	+	20.0994i	−0.614169	+	1.06377i
$358$	−5.13307	+	8.89074i	−0.271291	+	0.469890i
$359$	−9.51948			−0.502419			−0.251210	−	0.967933i	$-0.580828\pi$
$359$	−9.51948			−0.502419			−0.251210	+	0.967933i	$0.580828\pi$
$360$	0.174453	−	0.302162i	0.00919450	−	0.0159253i
$361$	−0.500000	−	0.866025i	−0.0263158	−	0.0455803i
$362$	12.8446	+	22.2476i	0.675099	+	1.16931i
$363$	−0.465015			−0.0244070
$364$	2.41471	+	9.24862i	0.126565	+	0.484760i
$365$	11.9914			0.627661
$366$	4.68860	+	8.12090i	0.245077	+	0.424486i
$367$	1.32061	+	2.28736i	0.0689353	+	0.119399i	0.898433	−	0.439111i	$-0.144706\pi$
$367$	1.32061	+	2.28736i	0.0689353	+	0.119399i	−0.829498	+	0.558510i	$0.811373\pi$
$368$	−3.20275	+	5.54732i	−0.166955	+	0.289174i
$369$	−1.06727			−0.0555596
$370$	−1.40550	+	2.43440i	−0.0730684	+	0.126558i
$371$	−3.27777	+	5.67726i	−0.170173	+	0.294748i
$372$	4.08277			0.211682
$373$	−12.4314	+	21.5318i	−0.643673	+	1.11487i	0.340934	+	0.940087i	$0.389257\pi$
$373$	−12.4314	+	21.5318i	−0.643673	+	1.11487i	−0.984606	+	0.174786i	$0.944077\pi$
$374$	−8.67939	−	15.0331i	−0.448801	−	0.777345i
$375$	8.80994	+	15.2593i	0.454943	+	0.787985i
$376$	−12.3305			−0.635896
$377$	6.81352	+	26.0966i	0.350914	+	1.34404i
$378$	14.3305			0.737081
$379$	−16.0796	−	27.8506i	−0.825951	−	1.43059i	−0.901190	−	0.433424i	$-0.857305\pi$
$379$	−16.0796	−	27.8506i	−0.825951	−	1.43059i	0.0752391	−	0.997166i	$-0.476028\pi$
$380$	−0.636945	−	1.10322i	−0.0326746	−	0.0565941i
$381$	6.37187	−	11.0364i	0.326441	−	0.565412i
$382$	−0.857718			−0.0438847
$383$	9.36905	−	16.2277i	0.478736	−	0.829195i	−0.520967	−	0.853577i	$-0.674428\pi$
$383$	9.36905	−	16.2277i	0.478736	−	0.829195i	0.999703	+	0.0243817i	$0.00776170\pi$
$384$	−0.825547	+	1.42989i	−0.0421285	+	0.0729687i
$385$	11.0566			0.563496
$386$	5.04632	−	8.74048i	0.256851	−	0.444879i
$387$	−0.863055	−	1.49485i	−0.0438715	−	0.0759877i
$388$	5.65109	+	9.78798i	0.286891	+	0.496909i
$389$	34.9426			1.77166			0.885830	−	0.464009i	$-0.153590\pi$
$389$	34.9426			1.77166			0.885830	+	0.464009i	$0.153590\pi$
$390$	−5.39669	+	5.32792i	−0.273272	+	0.269790i
$391$	−33.9632			−1.71759
$392$	−0.0141481	−	0.0245053i	−0.000714589	−	0.00123770i
$393$	7.40656	+	12.8285i	0.373612	+	0.647114i
$394$	−4.84503	+	8.39184i	−0.244089	+	0.422775i
$395$	−15.6121			−0.785531
$396$	−0.448344	+	0.776554i	−0.0225301	+	0.0390233i
$397$	12.6273	−	21.8712i	0.633748	−	1.09768i	−0.353031	−	0.935612i	$-0.614849\pi$
$397$	12.6273	−	21.8712i	0.633748	−	1.09768i	0.986779	−	0.162072i	$-0.0518176\pi$
$398$	24.1960			1.21283
$399$	2.18860	−	3.79077i	0.109567	−	0.189776i
$400$	1.68860	+	2.92474i	0.0844301	+	0.146237i
$401$	−0.471704	−	0.817015i	−0.0235558	−	0.0407998i	0.854007	−	0.520261i	$-0.174165\pi$
$401$	−0.471704	−	0.817015i	−0.0235558	−	0.0407998i	−0.877563	+	0.479461i	$0.840832\pi$
$402$	−0.341157			−0.0170153
$403$	8.59691	+	2.36272i	0.428243	+	0.117695i
$404$	−13.8110			−0.687123
$405$	5.16137	+	8.93975i	0.256470	+	0.444220i
$406$	−9.91577	−	17.1746i	−0.492112	−	0.852362i
$407$	3.61212	−	6.25638i	0.179046	−	0.310117i
$408$	−8.75441			−0.433408
$409$	−1.43661	+	2.48828i	−0.0710357	+	0.123038i	−0.899355	−	0.437218i	$-0.855964\pi$
$409$	−1.43661	+	2.48828i	−0.0710357	+	0.123038i	0.828320	+	0.560256i	$0.189297\pi$
$410$	−2.48198	+	4.29891i	−0.122576	+	0.212308i
$411$	22.9738			1.13322
$412$	−7.74519	+	13.4151i	−0.381578	+	0.660913i
$413$	12.6419	+	21.8964i	0.622066	+	1.07745i
$414$	0.877203	+	1.51936i	0.0431122	+	0.0746725i
$415$	9.92418			0.487159
$416$	−2.56580	+	2.53311i	−0.125799	+	0.124196i
$417$	−25.4826			−1.24789
$418$	1.63695	+	2.83527i	0.0800656	+	0.138678i
$419$	13.8977	+	24.0716i	0.678949	+	1.17597i	0.975298	+	0.220895i	$0.0708978\pi$
$419$	13.8977	+	24.0716i	0.678949	+	1.17597i	−0.296348	+	0.955080i	$0.595769\pi$
$420$	2.78804	−	4.82902i	0.136042	−	0.235632i
$421$	24.1599			1.17748			0.588741	−	0.808322i	$-0.299624\pi$
$421$	24.1599			1.17748			0.588741	+	0.808322i	$0.299624\pi$
$422$	−3.36412	+	5.82682i	−0.163763	+	0.283645i
$423$	−1.68860	+	2.92474i	−0.0821026	+	0.142206i
$424$	−2.47277			−0.120088
$425$	−8.95328	+	15.5075i	−0.434298	+	0.752226i
$426$	2.47664	+	4.28967i	0.119994	+	0.207835i
$427$	−7.52830	−	13.0394i	−0.364320	−	0.631020i
$428$	−1.89669			−0.0916799
$429$	13.8695	−	13.6927i	0.669623	−	0.661091i
$430$	−8.02830			−0.387159
$431$	5.04632	+	8.74048i	0.243073	+	0.421014i	0.961588	−	0.274497i	$-0.0885113\pi$
$431$	5.04632	+	8.74048i	0.243073	+	0.421014i	−0.718515	+	0.695511i	$0.755178\pi$
$432$	2.70275	+	4.68130i	0.130036	+	0.225229i
$433$	−2.34463	+	4.06102i	−0.112676	+	0.195160i	−0.916848	−	0.399236i	$-0.869275\pi$
$433$	−2.34463	+	4.06102i	−0.112676	+	0.195160i	0.804172	+	0.594396i	$0.202609\pi$
$434$	−6.55553			−0.314676
$435$	7.86693	−	13.6259i	0.377190	−	0.653313i
$436$	−6.45328	+	11.1774i	−0.309056	+	0.535301i
$437$	6.40550			0.306417
$438$	−7.77108	+	13.4599i	−0.371316	+	0.643139i
$439$	18.1185	+	31.3822i	0.864750	+	1.49779i	0.867295	+	0.497794i	$0.165856\pi$
$439$	18.1185	+	31.3822i	0.864750	+	1.49779i	−0.00254547	+	0.999997i	$0.500810\pi$
$440$	2.08529	+	3.61183i	0.0994123	+	0.172187i
$441$	−0.00775008			−0.000369051
$442$	−18.4338	−	5.06622i	−0.876806	−	0.240976i
$443$	1.13373			0.0538652			0.0269326	−	0.999637i	$-0.491426\pi$
$443$	1.13373			0.0538652			0.0269326	+	0.999637i	$0.491426\pi$
$444$	−1.82167	−	3.15523i	−0.0864527	−	0.149740i
$445$	9.00106	+	15.5903i	0.426691	+	0.739051i
$446$	7.52830	−	13.0394i	0.356475	−	0.617433i
$447$	−33.6914			−1.59355
$448$	1.32555	−	2.29591i	0.0626262	−	0.108472i
$449$	10.9972	−	19.0477i	0.518989	−	0.898916i	−0.480767	−	0.876848i	$-0.659642\pi$
$449$	10.9972	−	19.0477i	0.518989	−	0.898916i	0.999756	−	0.0220676i	$-0.00702489\pi$
$450$	0.924984			0.0436042
$451$	6.37866	−	11.0482i	0.300360	−	0.520238i
$452$	−10.0761	−	17.4523i	−0.473939	−	0.820886i
$453$	2.51521	+	4.35647i	0.118175	+	0.204685i
$454$	−0.765079			−0.0359069
$455$	8.66524	−	8.55483i	0.406233	−	0.401057i
$456$	1.65109			0.0773195
$457$	−8.38854	−	14.5294i	−0.392399	−	0.679655i	0.600366	−	0.799725i	$-0.295021\pi$
$457$	−8.38854	−	14.5294i	−0.392399	−	0.679655i	−0.992765	+	0.120070i	$0.961688\pi$
$458$	−5.42111	−	9.38964i	−0.253312	−	0.438749i
$459$	−14.3305	+	24.8211i	−0.668890	+	1.15855i
$460$	8.15990			0.380458
$461$	−17.4040	+	30.1447i	−0.810587	+	1.40398i	0.101867	+	0.994798i	$0.467518\pi$
$461$	−17.4040	+	30.1447i	−0.810587	+	1.40398i	−0.912454	+	0.409180i	$0.865815\pi$
$462$	−7.16524	+	12.4106i	−0.333357	+	0.577392i
$463$	0.842218			0.0391412			0.0195706	−	0.999808i	$-0.493770\pi$
$463$	0.842218			0.0391412			0.0195706	+	0.999808i	$0.493770\pi$
$464$	3.74026	−	6.47832i	0.173637	−	0.300748i
$465$	−2.60050	−	4.50420i	−0.120595	−	0.208877i
$466$	7.99079	+	13.8405i	0.370166	+	0.641147i
$467$	−30.5003			−1.41138			−0.705692	−	0.708519i	$-0.749364\pi$
$467$	−30.5003			−1.41138			−0.705692	+	0.708519i	$0.749364\pi$
$468$	0.249469	+	0.955496i	0.0115317	+	0.0441678i
$469$	0.547781			0.0252942
$470$	7.85384	+	13.6033i	0.362271	+	0.627471i
$471$	1.79831	+	3.11477i	0.0828618	+	0.143521i
$472$	−4.76855	+	8.25938i	−0.219490	+	0.380169i
$473$	20.6327			0.948691
$474$	10.1175	−	17.5240i	0.464710	−	0.804902i
$475$	1.68860	−	2.92474i	0.0774783	−	0.134196i
$476$	14.0566			0.644283
$477$	−0.338633	+	0.586530i	−0.0155050	+	0.0268554i
$478$	0.0594062	+	0.102895i	0.00271718	+	0.00470629i
$479$	8.92498	+	15.4585i	0.407793	+	0.706318i	0.994642	−	0.103378i	$-0.0329652\pi$
$479$	8.92498	+	15.4585i	0.407793	+	0.706318i	−0.586849	+	0.809696i	$0.699632\pi$
$480$	2.10331			0.0960026
$481$	−2.00987	−	7.69805i	−0.0916423	−	0.351001i
$482$	9.02830			0.411228
$483$	14.0191	+	24.2818i	0.637890	+	1.10486i
$484$	0.140820	+	0.243908i	0.00640092	+	0.0110867i
$485$	7.19887	−	12.4688i	0.326884	−	0.566180i
$486$	2.83717			0.128697
$487$	11.9338	−	20.6699i	0.540772	−	0.936644i	−0.458088	−	0.888907i	$-0.651466\pi$
$487$	11.9338	−	20.6699i	0.540772	−	0.936644i	0.998860	−	0.0477375i	$-0.0152011\pi$
$488$	2.83969	−	4.91850i	0.128547	−	0.222650i
$489$	0.452219			0.0204500
$490$	−0.0180232	+	0.0312170i	−0.000814204	+	0.00141024i
$491$	−1.93661	−	3.35431i	−0.0873979	−	0.151378i	0.819013	−	0.573776i	$-0.194522\pi$
$491$	−1.93661	−	3.35431i	−0.0873979	−	0.151378i	−0.906411	+	0.422398i	$0.861189\pi$
$492$	−3.21690	−	5.57183i	−0.145029	−	0.251198i
$493$	39.6631			1.78634
$494$	3.47664	+	0.955496i	0.156421	+	0.0429898i
$495$	1.14228			0.0513418
$496$	−1.23638	−	2.14148i	−0.0555152	−	0.0961552i
$497$	−3.97664	−	6.88774i	−0.178377	−	0.308957i
$498$	−6.43138	+	11.1395i	−0.288197	+	0.499172i
$499$	6.30219			0.282125			0.141062	−	0.990001i	$-0.454948\pi$
$499$	6.30219			0.282125			0.141062	+	0.990001i	$0.454948\pi$
$500$	5.33582	−	9.24191i	0.238625	−	0.413311i
$501$	−1.75334	+	3.03688i	−0.0783336	+	0.135678i
$502$	3.40550			0.151995
$503$	−16.3793	+	28.3698i	−0.730318	+	1.26495i	0.226429	+	0.974028i	$0.427295\pi$
$503$	−16.3793	+	28.3698i	−0.730318	+	1.26495i	−0.956747	+	0.290920i	$0.906039\pi$
$504$	−0.363055	−	0.628829i	−0.0161717	−	0.0280103i
$505$	8.79685	+	15.2366i	0.391455	+	0.678019i
$506$	−20.9709			−0.932270
$507$	0.275243	−	21.4624i	0.0122240	−	0.953181i
$508$	−7.71836			−0.342447
$509$	−12.3496	−	21.3901i	−0.547385	−	0.948099i	−0.998453	−	0.0556088i	$-0.982290\pi$
$509$	−12.3496	−	21.3901i	−0.547385	−	0.948099i	0.451068	−	0.892490i	$-0.351043\pi$
$510$	5.57608	+	9.65805i	0.246913	+	0.427666i
$511$	12.4777	−	21.6120i	0.551981	−	0.956059i
$512$	1.00000			0.0441942
$513$	2.70275	−	4.68130i	0.119329	−	0.206684i
$514$	−5.66137	+	9.80577i	−0.249712	+	0.432514i
$515$	19.7331			0.869542
$516$	5.20275	−	9.01143i	0.229038	−	0.396706i
$517$	−20.1843	−	34.9603i	−0.887706	−	1.53755i
$518$	2.92498	+	5.06622i	0.128516	+	0.222597i
$519$	40.1415			1.76202
$520$	4.42886	+	1.21720i	0.194218	+	0.0533777i
$521$	−5.82942			−0.255392			−0.127696	−	0.991813i	$-0.540758\pi$
$521$	−5.82942			−0.255392			−0.127696	+	0.991813i	$0.540758\pi$
$522$	−1.02442	−	1.77435i	−0.0448377	−	0.0776612i
$523$	−11.4027	−	19.7500i	−0.498605	−	0.863609i	0.501394	−	0.865219i	$-0.332821\pi$
$523$	−11.4027	−	19.7500i	−0.498605	−	0.863609i	−0.999999	+	0.00161050i	$0.999487\pi$
$524$	4.48585	−	7.76972i	0.195965	−	0.339422i
$525$	14.7827			0.645170
$526$	14.7647	−	25.5732i	0.643771	−	1.11504i
$527$	6.55553	−	11.3545i	0.285563	−	0.494610i
$528$	−5.40550			−0.235244
$529$	−9.01521	+	15.6148i	−0.391966	+	0.678904i
$530$	1.57502	+	2.72801i	0.0684143	+	0.118497i
$531$	1.30606	+	2.26217i	0.0566783	+	0.0981696i
$532$	−2.65109			−0.114939
$533$	−3.54924	−	13.5940i	−0.153735	−	0.588822i
$534$	−23.3326			−1.00970
$535$	1.20809	+	2.09247i	0.0522301	+	0.0904652i
$536$	0.103312	+	0.178942i	0.00446241	+	0.00772912i
$537$	−8.47518	+	14.6794i	−0.365731	+	0.633465i
$538$	15.8187			0.681995
$539$	0.0463194	−	0.0802276i	0.00199512	−	0.00345565i
$540$	3.44301	−	5.96346i	0.148163	−	0.256627i
$541$	−8.16203			−0.350913			−0.175456	−	0.984487i	$-0.556140\pi$
$541$	−8.16203			−0.350913			−0.175456	+	0.984487i	$0.556140\pi$
$542$	−7.79685	+	13.5045i	−0.334903	+	0.580070i
$543$	21.2077	+	36.7328i	0.910109	+	1.57635i
$544$	2.65109	+	4.59183i	0.113665	+	0.196873i
$545$	16.4415			0.704278
$546$	3.98691	+	15.2703i	0.170624	+	0.653510i
$547$	−32.9378			−1.40832			−0.704159	−	0.710042i	$-0.748676\pi$
$547$	−32.9378			−1.40832			−0.704159	+	0.710042i	$0.748676\pi$
$548$	−6.95716	−	12.0501i	−0.297195	−	0.514757i
$549$	−0.777766	−	1.34713i	−0.0331942	−	0.0574941i
$550$	−5.52830	+	9.57529i	−0.235727	+	0.408292i
$551$	−7.48052			−0.318681
$552$	−5.28804	+	9.15915i	−0.225074	+	0.389839i
$553$	−16.2452	+	28.1375i	−0.690816	+	1.19653i
$554$	−8.25334			−0.350651
$555$	−2.32061	+	4.01941i	−0.0985044	+	0.170615i
$556$	7.71690	+	13.3661i	0.327269	+	0.566847i
$557$	−6.34503	−	10.9899i	−0.268848	−	0.465658i	0.699717	−	0.714420i	$-0.253309\pi$
$557$	−6.34503	−	10.9899i	−0.268848	−	0.465658i	−0.968565	+	0.248762i	$0.919976\pi$
$558$	−0.677267			−0.0286710
$559$	16.1702	−	15.9641i	0.683926	−	0.675211i
$560$	−3.37720			−0.142713
$561$	−14.3305	−	24.8211i	−0.605033	−	1.04795i
$562$	0.693538	+	1.20124i	0.0292551	+	0.0506714i
$563$	−7.10196	+	12.3010i	−0.299312	+	0.518423i	−0.975979	−	0.217866i	$-0.930090\pi$
$563$	−7.10196	+	12.3010i	−0.299312	+	0.518423i	0.676667	+	0.736289i	$0.263424\pi$
$564$	−20.3588			−0.857259
$565$	−12.8358	+	22.2323i	−0.540007	+	0.935320i
$566$	11.9494	−	20.6970i	0.502271	−	0.869959i
$567$	21.4826			0.902186
$568$	1.50000	−	2.59808i	0.0629386	−	0.109013i
$569$	−7.32127	−	12.6808i	−0.306924	−	0.531607i	0.670764	−	0.741671i	$-0.265966\pi$
$569$	−7.32127	−	12.6808i	−0.306924	−	0.531607i	−0.977688	+	0.210063i	$0.932633\pi$
$570$	−1.05166	−	1.82152i	−0.0440490	−	0.0762952i
$571$	4.61505			0.193134			0.0965669	−	0.995327i	$-0.469214\pi$
$571$	4.61505			0.193134			0.0965669	+	0.995327i	$0.469214\pi$
$572$	−11.3821	−	3.12819i	−0.475911	−	0.130796i
$573$	−1.41617			−0.0591615
$574$	5.16524	+	8.94646i	0.215593	+	0.373418i
$575$	10.8163	+	18.7344i	0.451072	+	0.781280i
$576$	0.136945	−	0.237196i	0.00570605	−	0.00988317i
$577$	−42.8102			−1.78221			−0.891106	−	0.453795i	$-0.850070\pi$
$577$	−42.8102			−1.78221			−0.891106	+	0.453795i	$0.850070\pi$
$578$	−5.55659	+	9.62430i	−0.231124	+	0.400318i
$579$	8.33194	−	14.4314i	0.346264	−	0.599747i
$580$	−9.52936			−0.395685
$581$	10.3266	−	17.8862i	0.428420	−	0.742045i
$582$	9.33048	+	16.1609i	0.386761	+	0.669890i
$583$	−4.04778	−	7.01096i	−0.167642	−	0.290364i
$584$	9.41325			0.389523
$585$	0.895226	−	0.883819i	0.0370130	−	0.0365414i
$586$	−0.798202			−0.0329734
$587$	12.6571	+	21.9227i	0.522414	+	0.904848i	0.999660	+	0.0260779i	$0.00830179\pi$
$587$	12.6571	+	21.9227i	0.522414	+	0.904848i	−0.477246	+	0.878770i	$0.658365\pi$
$588$	−0.0233599	−	0.0404605i	−0.000963345	−	0.00166856i
$589$	−1.23638	+	2.14148i	−0.0509443	+	0.0882380i
$590$	12.1492			0.500176
$591$	−7.99960	+	13.8557i	−0.329060	+	0.569948i
$592$	−1.10331	+	1.91099i	−0.0453459	+	0.0785413i
$593$	1.13241			0.0465025			0.0232512	−	0.999730i	$-0.492598\pi$
$593$	1.13241			0.0465025			0.0232512	+	0.999730i	$0.492598\pi$
$594$	−8.84851	+	15.3261i	−0.363059	+	0.628836i
$595$	−8.95328	−	15.5075i	−0.367049	−	0.635747i
$596$	10.2027	+	17.6717i	0.417921	+	0.723860i
$597$	39.9498			1.63504
$598$	−16.4353	+	16.2258i	−0.672088	+	0.663524i
$599$	−5.91994			−0.241882			−0.120941	−	0.992660i	$-0.538591\pi$
$599$	−5.91994			−0.241882			−0.120941	+	0.992660i	$0.538591\pi$
$600$	2.78804	+	4.82902i	0.113821	+	0.197144i
$601$	−9.42751	−	16.3289i	−0.384556	−	0.666071i	0.607151	−	0.794586i	$-0.292312\pi$
$601$	−9.42751	−	16.3289i	−0.384556	−	0.666071i	−0.991707	+	0.128516i	$0.958979\pi$
$602$	−8.35384	+	14.4693i	−0.340477	+	0.589724i
$603$	0.0565925			0.00230463
$604$	1.52336	−	2.63854i	0.0619846	−	0.107361i
$605$	0.179390	−	0.310712i	0.00729323	−	0.0126322i
$606$	−22.8032			−0.926319
$607$	10.5375	−	18.2515i	0.427704	−	0.740806i	−0.568964	−	0.822362i	$-0.692656\pi$
$607$	10.5375	−	18.2515i	0.427704	−	0.740806i	0.996669	+	0.0815566i	$0.0259891\pi$
$608$	−0.500000	−	0.866025i	−0.0202777	−	0.0351220i
$609$	−16.3719	−	28.3569i	−0.663421	−	1.14908i
$610$	−7.23492			−0.292933
$611$	−42.8687	−	11.7817i	−1.73428	−	0.476638i
$612$	1.45222			0.0587025
$613$	12.0450	+	20.8625i	0.486492	+	0.842628i	0.999879	−	0.0155285i	$-0.00494307\pi$
$613$	12.0450	+	20.8625i	0.486492	+	0.842628i	−0.513388	+	0.858157i	$0.671610\pi$
$614$	−9.07608	−	15.7202i	−0.366281	−	0.634417i
$615$	−4.09798	+	7.09790i	−0.165246	+	0.286215i
$616$	8.67939			0.349703
$617$	−3.10050	+	5.37022i	−0.124821	+	0.216197i	−0.921663	−	0.387991i	$-0.873169\pi$
$617$	−3.10050	+	5.37022i	−0.124821	+	0.216197i	0.796842	+	0.604188i	$0.206502\pi$
$618$	−12.7880	+	22.1495i	−0.514410	+	0.890985i
$619$	−43.7437			−1.75821			−0.879105	−	0.476629i	$-0.841859\pi$
$619$	−43.7437			−1.75821			−0.879105	+	0.476629i	$0.841859\pi$
$620$	−1.57502	+	2.72801i	−0.0632542	+	0.109559i
$621$	17.3125	+	29.9861i	0.694725	+	1.20330i
$622$	−7.75053	−	13.4243i	−0.310768	−	0.538266i
$623$	37.4642			1.50097
$624$	−4.23638	+	4.18240i	−0.169591	+	0.167430i
$625$	3.29151			0.131661
$626$	−0.401624	−	0.695633i	−0.0160521	−	0.0278031i
$627$	2.70275	+	4.68130i	0.107937	+	0.186953i
$628$	1.08916	−	1.88649i	0.0434624	−	0.0752791i
$629$	−11.6999			−0.466507
$630$	−0.462492	+	0.801060i	−0.0184261	+	0.0319150i
$631$	−7.47170	+	12.9414i	−0.297444	+	0.515188i	−0.975550	−	0.219776i	$-0.929467\pi$
$631$	−7.47170	+	12.9414i	−0.297444	+	0.515188i	0.678107	+	0.734964i	$0.262801\pi$
$632$	−12.2555			−0.487496
$633$	−5.55447	+	9.62062i	−0.220770	+	0.382385i
$634$	−11.5410	−	19.9896i	−0.458351	−	0.793887i
$635$	4.91617	+	8.51506i	0.195092	+	0.337910i
$636$	−4.08277			−0.161892
$637$	−0.0257733	−	0.0987145i	−0.00102117	−	0.00391121i
$638$	24.4904			0.969584
$639$	−0.410836	−	0.711589i	−0.0162524	−	0.0281500i
$640$	−0.636945	−	1.10322i	−0.0251775	−	0.0436087i
$641$	12.5800	−	21.7891i	0.496878	−	0.860618i	−0.503115	−	0.864219i	$-0.667813\pi$
$641$	12.5800	−	21.7891i	0.496878	−	0.860618i	0.999994	+	0.00360095i	$0.00114622\pi$
$642$	−3.13161			−0.123595
$643$	−22.2647	+	38.5636i	−0.878033	+	1.52080i	−0.0245371	+	0.999699i	$0.507811\pi$
$643$	−22.2647	+	38.5636i	−0.878033	+	1.52080i	−0.853496	+	0.521099i	$0.825522\pi$
$644$	8.49079	−	14.7065i	0.334584	−	0.579516i
$645$	−13.2555			−0.521934
$646$	2.65109	−	4.59183i	0.104306	−	0.180663i
$647$	2.85143	+	4.93882i	0.112101	+	0.194165i	0.916617	−	0.399766i	$-0.130909\pi$
$647$	2.85143	+	4.93882i	0.112101	+	0.194165i	−0.804516	+	0.593931i	$0.797575\pi$
$648$	4.05166	+	7.01767i	0.159164	+	0.275680i
$649$	−31.2234			−1.22563
$650$	3.07608	+	11.7817i	0.120654	+	0.462118i
$651$	−10.8238			−0.424218
$652$	−0.136945	−	0.237196i	−0.00536319	−	0.00928932i
$653$	−4.43661	−	7.68443i	−0.173618	−	0.300715i	0.766064	−	0.642764i	$-0.222212\pi$
$653$	−4.43661	−	7.68443i	−0.173618	−	0.300715i	−0.939682	+	0.342049i	$0.888879\pi$
$654$	−10.6550	+	18.4549i	−0.416642	+	0.721646i
$655$	−11.4290			−0.446567
$656$	−1.94834	+	3.37463i	−0.0760700	+	0.131757i
$657$	1.28910	−	2.23279i	0.0502926	−	0.0871093i
$658$	32.6893			1.27436
$659$	−12.7374	+	22.0619i	−0.496180	+	0.859410i	−0.999990	−	0.00440493i	$-0.998598\pi$
$659$	−12.7374	+	22.0619i	−0.496180	+	0.859410i	0.503810	+	0.863815i	$0.331931\pi$
$660$	3.44301	+	5.96346i	0.134019	+	0.232127i
$661$	−13.3797	−	23.1744i	−0.520411	−	0.901378i	−0.999718	−	0.0237312i	$-0.992445\pi$
$661$	−13.3797	−	23.1744i	−0.520411	−	0.901378i	0.479307	−	0.877647i	$-0.340888\pi$
$662$	7.67164			0.298167
$663$	−30.4359	−	8.36480i	−1.18203	−	0.324862i
$664$	7.79045			0.302328
$665$	1.68860	+	2.92474i	0.0654812	+	0.113417i
$666$	0.302187	+	0.523403i	0.0117095	+	0.0202815i
$667$	23.9582	−	41.4968i	0.927666	−	1.60676i
$668$	2.12386			0.0821746
$669$	12.4299	−	21.5293i	0.480568	−	0.832369i
$670$	0.131609	−	0.227953i	0.00508448	−	0.00880658i
$671$	18.5937			0.717802
$672$	2.18860	−	3.79077i	0.0844271	−	0.146232i
$673$	−11.8099	−	20.4554i	−0.455240	−	0.788498i	0.543462	−	0.839434i	$-0.317113\pi$
$673$	−11.8099	−	20.4554i	−0.455240	−	0.788498i	−0.998702	+	0.0509354i	$0.983780\pi$
$674$	−2.09944	−	3.63633i	−0.0808673	−	0.140066i
$675$	18.2555			0.702653
$676$	−11.3408	+	6.35510i	−0.436183	+	0.244427i
$677$	0.317687			0.0122097			0.00610485	−	0.999981i	$-0.498057\pi$
$677$	0.317687			0.0122097			0.00610485	+	0.999981i	$0.498057\pi$
$678$	−16.6365	−	28.8153i	−0.638923	−	1.10665i
$679$	−14.9816	−	25.9489i	−0.574940	−	0.995826i
$680$	3.37720	−	5.84949i	0.129510	−	0.224318i
$681$	−1.26322			−0.0484066
$682$	4.04778	−	7.01096i	0.154998	−	0.268464i
$683$	9.74947	−	16.8866i	0.373053	−	0.646147i	−0.616980	−	0.786978i	$-0.711644\pi$
$683$	9.74947	−	16.8866i	0.373053	−	0.646147i	0.990034	+	0.140832i	$0.0449776\pi$
$684$	−0.273891			−0.0104725
$685$	−8.86265	+	15.3506i	−0.338625	+	0.586515i
$686$	−9.24132	−	16.0064i	−0.352835	−	0.611128i
$687$	−8.95076	−	15.5032i	−0.341493	−	0.591483i
$688$	−6.30219			−0.240269
$689$	−8.59691	−	2.36272i	−0.327516	−	0.0900124i
$690$	13.4728			0.512899
$691$	−1.84503	−	3.19569i	−0.0701883	−	0.121570i	0.828795	−	0.559552i	$-0.189027\pi$
$691$	−1.84503	−	3.19569i	−0.0701883	−	0.121570i	−0.898984	+	0.437982i	$0.855693\pi$
$692$	−12.1560	−	21.0549i	−0.462103	−	0.800386i
$693$	1.18860	−	2.05872i	0.0451512	−	0.0782042i
$694$	−7.94048			−0.301417
$695$	9.83048	−	17.0269i	0.372891	−	0.645867i
$696$	6.17551	−	10.6963i	0.234082	−	0.405442i
$697$	−20.6610			−0.782590
$698$	10.9597	−	18.9827i	0.414830	−	0.718507i
$699$	13.1935	+	22.8519i	0.499025	+	0.864337i
$700$	−4.47664	−	7.75377i	−0.169201	−	0.293065i
$701$	−13.7381			−0.518881			−0.259441	−	0.965759i	$-0.583538\pi$
$701$	−13.7381			−0.518881			−0.259441	+	0.965759i	$0.583538\pi$
$702$	4.92352	+	18.8577i	0.185826	+	0.711737i
$703$	2.20662			0.0832244
$704$	1.63695	+	2.83527i	0.0616947	+	0.106858i
$705$	12.9674	+	22.4602i	0.488382	+	0.845902i
$706$	−12.7983	+	22.1673i	−0.481671	+	0.834278i
$707$	36.6142			1.37702
$708$	−7.87333	+	13.6370i	−0.295898	+	0.512510i
$709$	8.09798	−	14.0261i	0.304126	−	0.526761i	−0.672940	−	0.739697i	$-0.734969\pi$
$709$	8.09798	−	14.0261i	0.304126	−	0.526761i	0.977066	+	0.212935i	$0.0683023\pi$
$710$	−3.82167			−0.143425
$711$	−1.67833	+	2.90695i	−0.0629422	+	0.109019i
$712$	7.06580	+	12.2383i	0.264802	+	0.458651i
$713$	−7.91965	−	13.7172i	−0.296593	−	0.513714i
$714$	23.2087			0.868566
$715$	3.79871	+	14.5495i	0.142064	+	0.544121i
$716$	10.2661			0.383664
$717$	0.0980852	+	0.169889i	0.00366306	+	0.00634461i
$718$	4.75974	+	8.24412i	0.177632	+	0.307668i
$719$	24.8520	−	43.0449i	0.926822	−	1.60530i	0.138219	−	0.990402i	$-0.455862\pi$
$719$	24.8520	−	43.0449i	0.926822	−	1.60530i	0.788604	−	0.614902i	$-0.210804\pi$
$720$	−0.348907			−0.0130030
$721$	20.5332	−	35.5646i	0.764698	−	1.32449i
$722$	−0.500000	+	0.866025i	−0.0186081	+	0.0322301i
$723$	14.9066			0.554381
$724$	12.8446	−	22.2476i	0.477367	−	0.826824i
$725$	−12.6316	−	21.8786i	−0.469126	−	0.812550i
$726$	0.232507	+	0.402715i	0.00862916	+	0.0149461i
$727$	−42.5470			−1.57798			−0.788990	−	0.614406i	$-0.789396\pi$
$727$	−42.5470			−1.57798			−0.788990	+	0.614406i	$0.789396\pi$
$728$	6.80219	−	6.71551i	0.252106	−	0.248893i
$729$	28.9944			1.07387
$730$	−5.99572	−	10.3849i	−0.221912	−	0.384362i
$731$	−16.7077	−	28.9386i	−0.617956	−	1.07033i
$732$	4.68860	−	8.12090i	0.173296	−	0.300157i
$733$	6.69569			0.247311			0.123655	−	0.992325i	$-0.460538\pi$
$733$	6.69569			0.247311			0.123655	+	0.992325i	$0.460538\pi$
$734$	1.32061	−	2.28736i	0.0487446	−	0.0844282i
$735$	−0.0297579	+	0.0515423i	−0.00109764	+	0.00190116i
$736$	6.40550			0.236110
$737$	−0.338233	+	0.585837i	−0.0124590	+	0.0215796i
$738$	0.533633	+	0.924279i	0.0196433	+	0.0340232i
$739$	13.7540	+	23.8226i	0.505949	+	0.876330i	0.999976	+	0.00688330i	$0.00219104\pi$
$739$	13.7540	+	23.8226i	0.505949	+	0.876330i	−0.494027	+	0.869447i	$0.664476\pi$
$740$	2.81100			0.103334
$741$	5.74026	+	1.57761i	0.210874	+	0.0579551i
$742$	6.55553			0.240661
$743$	1.05659	+	1.83007i	0.0387626	+	0.0671388i	0.884756	−	0.466055i	$-0.154325\pi$
$743$	1.05659	+	1.83007i	0.0387626	+	0.0671388i	−0.845993	+	0.533194i	$0.820992\pi$
$744$	−2.04138	−	3.53578i	−0.0748407	−	0.129628i
$745$	12.9972	−	22.5118i	0.476180	−	0.824768i
$746$	24.8628			0.910290
$747$	1.06687	−	1.84787i	0.0390346	−	0.0676099i
$748$	−8.67939	+	15.0331i	−0.317350	+	0.549666i
$749$	5.02830			0.183730
$750$	8.80994	−	15.2593i	0.321693	−	0.557189i
$751$	−1.36265	−	2.36019i	−0.0497240	−	0.0861244i	0.840092	−	0.542444i	$-0.182501\pi$
$751$	−1.36265	−	2.36019i	−0.0497240	−	0.0861244i	−0.889816	+	0.456319i	$0.849167\pi$
$752$	6.16524	+	10.6785i	0.224823	+	0.389405i
$753$	5.62280			0.204906
$754$	19.1935	−	18.9490i	0.698987	−	0.690081i
$755$	−3.88119			−0.141251
$756$	−7.16524	−	12.4106i	−0.260597	−	0.451368i
$757$	12.3114	+	21.3240i	0.447465	+	0.775033i	0.998220	−	0.0596342i	$-0.0189934\pi$
$757$	12.3114	+	21.3240i	0.447465	+	0.775033i	−0.550755	+	0.834667i	$0.685660\pi$
$758$	−16.0796	+	27.8506i	−0.584036	+	1.01158i
$759$	−34.6249			−1.25680
$760$	−0.636945	+	1.10322i	−0.0231044	+	0.0400181i
$761$	21.3744	−	37.0215i	0.774821	−	1.34203i	−0.160074	−	0.987105i	$-0.551173\pi$
$761$	21.3744	−	37.0215i	0.774821	−	1.34203i	0.934895	−	0.354924i	$-0.115493\pi$
$762$	−12.7437			−0.461657
$763$	17.1082	−	29.6324i	0.619360	−	1.07276i
$764$	0.428859	+	0.742806i	0.0155156	+	0.0268738i
$765$	−0.924984	−	1.60212i	−0.0334429	−	0.0579247i
$766$	−18.7381			−0.677035
$767$	−24.4704	+	24.1585i	−0.883573	+	0.872315i
$768$	1.65109			0.0595787
$769$	−10.9236	−	18.9203i	−0.393916	−	0.682283i	0.599046	−	0.800715i	$-0.295547\pi$
$769$	−10.9236	−	18.9203i	−0.393916	−	0.682283i	−0.992962	+	0.118432i	$0.962213\pi$
$770$	−5.52830	−	9.57529i	−0.199226	−	0.345069i
$771$	−9.34744	+	16.1902i	−0.336640	+	0.583078i
$772$	−10.0926			−0.363242
$773$	9.02936	−	15.6393i	0.324763	−	0.562507i	−0.656701	−	0.754151i	$-0.728049\pi$
$773$	9.02936	−	15.6393i	0.324763	−	0.562507i	0.981464	+	0.191644i	$0.0613820\pi$
$774$	−0.863055	+	1.49485i	−0.0310219	+	0.0537314i
$775$	−8.35103			−0.299978
$776$	5.65109	−	9.78798i	0.202862	−	0.351368i
$777$	4.82942	+	8.36480i	0.173255	+	0.300086i
$778$	−17.4713	−	30.2612i	−0.626377	−	1.08492i
$779$	3.89669			0.139613
$780$	7.31246	+	2.00971i	0.261828	+	0.0719591i
$781$	9.82167			0.351447
$782$	16.9816	+	29.4130i	0.607260	+	1.05181i
$783$	−20.2180	−	35.0185i	−0.722531	−	1.25146i
$784$	−0.0141481	+	0.0245053i	−0.000505290	+	0.000875189i
$785$	−2.77495			−0.0990423
$786$	7.40656	−	12.8285i	0.264183	−	0.457579i
$787$	−19.1546	+	33.1767i	−0.682787	+	1.18262i	0.291340	+	0.956619i	$0.405899\pi$
$787$	−19.1546	+	33.1767i	−0.682787	+	1.18262i	−0.974127	+	0.226002i	$0.927435\pi$
$788$	9.69006			0.345194
$789$	24.3779	−	42.2237i	0.867875	−	1.50320i
$790$	7.80606	+	13.5205i	0.277727	+	0.481038i
$791$	26.7126	+	46.2676i	0.949792	+	1.64509i
$792$	0.896688			0.0318624
$793$	14.5722	−	14.3865i	0.517474	−	0.510880i
$794$	−25.2547			−0.896255
$795$	2.60050	+	4.50420i	0.0922302	+	0.159747i
$796$	−12.0980	−	20.9543i	−0.428801	−	0.742706i
$797$	13.5733	−	23.5096i	0.480790	−	0.832752i	−0.518967	−	0.854794i	$-0.673683\pi$
$797$	13.5733	−	23.5096i	0.480790	−	0.832752i	0.999757	+	0.0220419i	$0.00701673\pi$
$798$	−4.37720			−0.154951
$799$	−32.6893	+	56.6195i	−1.15646	+	2.00305i
$800$	1.68860	−	2.92474i	0.0597011	−	0.103405i
$801$	3.87051			0.136758
$802$	−0.471704	+	0.817015i	−0.0166564	+	0.0288498i
$803$	15.4090	+	26.6891i	0.543771	+	0.941839i
$804$	0.170578	+	0.295450i	0.00601583	+	0.0104197i
$805$	−21.6327			−0.762451
$806$	−2.25228	−	8.62651i	−0.0793333	−	0.303856i
$807$	26.1182			0.919405
$808$	6.90550	+	11.9607i	0.242935	+	0.420775i
$809$	−3.58916	−	6.21661i	−0.126188	−	0.218565i	0.796009	−	0.605285i	$-0.206941\pi$
$809$	−3.58916	−	6.21661i	−0.126188	−	0.218565i	−0.922197	+	0.386721i	$0.873608\pi$
$810$	5.16137	−	8.93975i	0.181352	−	0.314111i
$811$	6.01842			0.211335			0.105668	−	0.994401i	$-0.466302\pi$
$811$	6.01842			0.211335			0.105668	+	0.994401i	$0.466302\pi$
$812$	−9.91577	+	17.1746i	−0.347975	+	0.602711i
$813$	−12.8733	+	22.2973i	−0.451487	+	0.781999i
$814$	−7.22425			−0.253210
$815$	−0.174453	+	0.302162i	−0.00611083	+	0.0105843i
$816$	4.37720	+	7.58154i	0.153233	+	0.265407i
$817$	3.15109	+	5.45785i	0.110243	+	0.190946i
$818$	2.87322			0.100460
$819$	−0.661367	−	2.53311i	−0.0231100	−	0.0885140i
$820$	4.96395			0.173349
$821$	10.5035	+	18.1926i	0.366574	+	0.634924i	0.989027	−	0.147732i	$-0.0471974\pi$
$821$	10.5035	+	18.1926i	0.366574	+	0.634924i	−0.622454	+	0.782657i	$0.713864\pi$
$822$	−11.4869	−	19.8959i	−0.400652	−	0.693950i
$823$	10.3011	−	17.8421i	0.359075	−	0.621936i	−0.628732	−	0.777622i	$-0.716426\pi$
$823$	10.3011	−	17.8421i	0.359075	−	0.621936i	0.987806	+	0.155687i	$0.0497590\pi$
$824$	15.4904			0.539633
$825$	−9.12773	+	15.8097i	−0.317787	+	0.550423i
$826$	12.6419	−	21.8964i	0.439867	−	0.761873i
$827$	−27.0643			−0.941119			−0.470560	−	0.882368i	$-0.655948\pi$
$827$	−27.0643			−0.941119			−0.470560	+	0.882368i	$0.655948\pi$
$828$	0.877203	−	1.51936i	0.0304849	−	0.0528014i
$829$	−7.09023	−	12.2806i	−0.246254	−	0.426524i	0.716230	−	0.697865i	$-0.245866\pi$
$829$	−7.09023	−	12.2806i	−0.246254	−	0.426524i	−0.962483	+	0.271341i	$0.912533\pi$
$830$	−4.96209	−	8.59459i	−0.172237	−	0.298323i
$831$	−13.6270			−0.472717
$832$	3.47664	+	0.955496i	0.120531	+	0.0331259i
$833$	−0.150032			−0.00519830
$834$	12.7413	+	22.0686i	0.441196	+	0.764174i
$835$	−1.35278	−	2.34309i	−0.0468149	−	0.0810859i
$836$	1.63695	−	2.83527i	0.0566149	−	0.0980599i
$837$	−13.3665			−0.462015
$838$	13.8977	−	24.0716i	0.480090	−	0.831540i
$839$	−20.6171	+	35.7098i	−0.711780	+	1.23284i	0.252408	+	0.967621i	$0.418777\pi$
$839$	−20.6171	+	35.7098i	−0.711780	+	1.23284i	−0.964188	+	0.265218i	$0.914556\pi$
$840$	−5.57608			−0.192393
$841$	−13.4791	+	23.3464i	−0.464795	+	0.805048i
$842$	−12.0800	−	20.9231i	−0.416303	−	0.721057i
$843$	1.14510	+	1.98336i	0.0394392	+	0.0683107i
$844$	6.72823			0.231595
$845$	14.2345	+	8.46352i	0.489682	+	0.291154i
$846$	3.37720			0.116111
$847$	−0.373328	−	0.646623i	−0.0128277	−	0.0222182i
$848$	1.23638	+	2.14148i	0.0424576	+	0.0735386i
$849$	19.7296	−	34.1726i	0.677118	−	1.17280i
$850$	17.9066			0.614190
$851$	−7.06727	+	12.2409i	−0.242263	+	0.419611i
$852$	2.47664	−	4.28967i	0.0848483	−	0.146962i
$853$	−5.96900			−0.204375			−0.102187	−	0.994765i	$-0.532584\pi$
$853$	−5.96900			−0.204375			−0.102187	+	0.994765i	$0.532584\pi$
$854$	−7.52830	+	13.0394i	−0.257613	+	0.446199i
$855$	0.174453	+	0.302162i	0.00596618	+	0.0103337i
$856$	0.948344	+	1.64258i	0.0324137	+	0.0561422i
$857$	−39.2285			−1.34002			−0.670010	−	0.742352i	$-0.733710\pi$
$857$	−39.2285			−1.34002			−0.670010	+	0.742352i	$0.733710\pi$
$858$	−18.7930	−	5.16494i	−0.641582	−	0.176328i
$859$	6.83447			0.233189			0.116595	−	0.993180i	$-0.462802\pi$
$859$	6.83447			0.233189			0.116595	+	0.993180i	$0.462802\pi$
$860$	4.01415	+	6.95271i	0.136881	+	0.237085i
$861$	8.52830	+	14.7714i	0.290644	+	0.503409i
$862$	5.04632	−	8.74048i	0.171878	−	0.297702i
$863$	38.2760			1.30293			0.651465	−	0.758678i	$-0.274155\pi$
$863$	38.2760			1.30293			0.651465	+	0.758678i	$0.274155\pi$
$864$	2.70275	−	4.68130i	0.0919494	−	0.159261i
$865$	−15.4855	+	26.8216i	−0.526521	+	0.911961i
$866$	4.68926			0.159348
$867$	−9.17445	+	15.8906i	−0.311581	+	0.539674i
$868$	3.27777	+	5.67726i	0.111255	+	0.192699i
$869$	−20.0615	−	34.7476i	−0.680541	−	1.17873i
$870$	−15.7339			−0.533428
$871$	0.188201	+	0.720832i	0.00637695	+	0.0244245i
$872$	12.9066			0.437071
$873$	−1.54778	−	2.68084i	−0.0523845	−	0.0907325i
$874$	−3.20275	−	5.54732i	−0.108335	−	0.187641i
$875$	−14.1458	+	24.5012i	−0.478214	+	0.828291i
$876$	15.5422			0.525121
$877$	5.02402	−	8.70186i	0.169649	−	0.293841i	−0.768647	−	0.639673i	$-0.779070\pi$
$877$	5.02402	−	8.70186i	0.169649	−	0.293841i	0.938297	+	0.345832i	$0.112403\pi$
$878$	18.1185	−	31.3822i	0.611470	−	1.05910i
$879$	−1.31791			−0.0444519
$880$	2.08529	−	3.61183i	0.0702951	−	0.121755i
$881$	18.2784	+	31.6592i	0.615816	+	1.06662i	0.990241	+	0.139367i	$0.0445068\pi$
$881$	18.2784	+	31.6592i	0.615816	+	1.06662i	−0.374425	+	0.927257i	$0.622160\pi$
$882$	0.00387504	+	0.00671177i	0.000130479	+	0.000225997i
$883$	−10.0926			−0.339644			−0.169822	−	0.985475i	$-0.554319\pi$
$883$	−10.0926			−0.339644			−0.169822	+	0.985475i	$0.554319\pi$
$884$	4.82942	+	18.4972i	0.162431	+	0.622130i
$885$	20.0595			0.674293
$886$	−0.566866	−	0.981840i	−0.0190442	−	0.0329856i
$887$	−7.17979	−	12.4358i	−0.241074	−	0.417552i	0.719947	−	0.694029i	$-0.244166\pi$
$887$	−7.17979	−	12.4358i	−0.241074	−	0.417552i	−0.961020	+	0.276477i	$0.910833\pi$
$888$	−1.82167	+	3.15523i	−0.0611313	+	0.105883i
$889$	20.4621			0.686277
$890$	9.00106	−	15.5903i	0.301716	−	0.522588i
$891$	−13.2647	+	22.9751i	−0.444383	+	0.769695i
$892$	−15.0566			−0.504132
$893$	6.16524	−	10.6785i	0.206312	−	0.357343i
$894$	16.8457	+	29.1776i	0.563404	+	0.975845i
$895$	−6.53897	−	11.3258i	−0.218574	−	0.378581i
$896$	−2.65109			−0.0885668
$897$	−27.1361	+	26.7904i	−0.906049	+	0.894504i
$898$	−21.9944			−0.733962
$899$	9.24878	+	16.0194i	0.308464	+	0.534275i
$900$	−0.462492	−	0.801060i	−0.0154164	−	0.0267020i
$901$	−6.55553	+	11.3545i	−0.218396	+	0.378274i
$902$	−12.7573			−0.424773
$903$	−13.7930	+	23.8901i	−0.459001	+	0.795014i
$904$	−10.0761	+	17.4523i	−0.335125	+	0.580454i
$905$	−32.7253			−1.08783
$906$	2.51521	−	4.35647i	0.0835622	−	0.144734i
$907$	3.13055	+	5.42227i	0.103948	+	0.180043i	0.913308	−	0.407270i	$-0.133519\pi$
$907$	3.13055	+	5.42227i	0.103948	+	0.180043i	−0.809360	+	0.587313i	$0.800186\pi$
$908$	0.382540	+	0.662578i	0.0126950	+	0.0219884i
$909$	3.78270			0.125464
$910$	−11.7413	−	3.22691i	−0.389221	−	0.106971i
$911$	−34.5053			−1.14321			−0.571606	−	0.820528i	$-0.693679\pi$
$911$	−34.5053			−1.14321			−0.571606	+	0.820528i	$0.693679\pi$
$912$	−0.825547	−	1.42989i	−0.0273366	−	0.0473484i
$913$	12.7525	+	22.0881i	0.422048	+	0.731008i
$914$	−8.38854	+	14.5294i	−0.277468	+	0.480589i
$915$	−11.9455			−0.394907
$916$	−5.42111	+	9.38964i	−0.179118	+	0.310242i
$917$	−11.8924	+	20.5983i	−0.392722	+	0.680215i
$918$	28.6610			0.945953
$919$	28.1687	−	48.7896i	0.929200	−	1.60942i	0.144537	−	0.989499i	$-0.453831\pi$
$919$	28.1687	−	48.7896i	0.929200	−	1.60942i	0.784663	−	0.619923i	$-0.212836\pi$
$920$	−4.07995	−	7.06668i	−0.134512	−	0.232982i
$921$	−14.9855	−	25.9556i	−0.493787	−	0.855265i
$922$	34.8081			1.14634
$923$	7.69741	−	7.59933i	0.253363	−	0.250135i
$924$	14.3305			0.471438
$925$	3.72611	+	6.45381i	0.122514	+	0.212200i
$926$	−0.421109	−	0.729382i	−0.0138385	−	0.0239690i
$927$	2.12134	−	3.67426i	0.0696738	−	0.120679i
$928$	−7.48052			−0.245560
$929$	−8.98011	+	15.5540i	−0.294628	+	0.510311i	−0.974898	−	0.222651i	$-0.928529\pi$
$929$	−8.98011	+	15.5540i	−0.294628	+	0.510311i	0.680270	+	0.732961i	$0.261862\pi$
$930$	−2.60050	+	4.50420i	−0.0852737	+	0.147698i
$931$	0.0282963			0.000927373
$932$	7.99079	−	13.8405i	0.261747	−	0.453359i
$933$	−12.7969	−	22.1648i	−0.418950	−	0.725643i
$934$	15.2501	+	26.4140i	0.499000	+	0.864293i
$935$	22.1132			0.723178
$936$	0.702750	−	0.693795i	0.0229701	−	0.0226774i
$937$	−25.2886			−0.826142			−0.413071	−	0.910699i	$-0.635544\pi$
$937$	−25.2886			−0.826142			−0.413071	+	0.910699i	$0.635544\pi$
$938$	−0.273891	−	0.474392i	−0.00894284	−	0.0154895i
$939$	−0.663119	−	1.14856i	−0.0216401	−	0.0374817i
$940$	7.85384	−	13.6033i	0.256164	−	0.443689i
$941$	23.2095			0.756610			0.378305	−	0.925681i	$-0.376507\pi$
$941$	23.2095			0.756610			0.378305	+	0.925681i	$0.376507\pi$
$942$	1.79831	−	3.11477i	0.0585922	−	0.101485i
$943$	−12.4801	+	21.6162i	−0.406408	+	0.703920i
$944$	9.53711			0.310406
$945$	−9.12773	+	15.8097i	−0.296925	+	0.514290i
$946$	−10.3163	−	17.8684i	−0.335413	−	0.580952i
$947$	27.6337	+	47.8630i	0.897976	+	1.55534i	0.830078	+	0.557647i	$0.188296\pi$
$947$	27.6337	+	47.8630i	0.897976	+	1.55534i	0.0678975	+	0.997692i	$0.478371\pi$
$948$	−20.2349			−0.657200
$949$	32.7265	+	8.99433i	1.06235	+	0.291968i
$950$	−3.37720			−0.109571
$951$	−19.0552	−	33.0046i	−0.617909	−	1.07025i
$952$	−7.02830	−	12.1734i	−0.227788	−	0.394541i
$953$	1.86346	−	3.22760i	0.0603632	−	0.104552i	−0.834265	−	0.551364i	$-0.814107\pi$
$953$	1.86346	−	3.22760i	0.0603632	−	0.104552i	0.894628	+	0.446812i	$0.147441\pi$
$954$	0.677267			0.0219273
$955$	0.546319	−	0.946253i	0.0176785	−	0.0306200i
$956$	0.0594062	−	0.102895i	0.00192133	−	0.00332785i
$957$	40.4359			1.30711
$958$	8.92498	−	15.4585i	0.288353	−	0.499442i
$959$	18.4441	+	31.9461i	0.595590	+	1.03159i
$960$	−1.05166	−	1.82152i	−0.0339421	−	0.0587894i
$961$	−24.8854			−0.802756
$962$	−5.66177	+	5.58962i	−0.182543	+	0.180217i
$963$	0.519485			0.0167402
$964$	−4.51415	−	7.81873i	−0.145391	−	0.251824i
$965$	6.42846	+	11.1344i	0.206939	+	0.358430i
$966$	14.0191	−	24.2818i	0.451057	−	0.781253i
$967$	8.11399			0.260928			0.130464	−	0.991453i	$-0.458353\pi$
$967$	8.11399			0.260928			0.130464	+	0.991453i	$0.458353\pi$
$968$	0.140820	−	0.243908i	0.00452614	−	0.00783950i
$969$	4.37720	−	7.58154i	0.140616	−	0.243554i
$970$	−14.3977			−0.462284
$971$	−3.37227	+	5.84094i	−0.108221	+	0.187445i	−0.915050	−	0.403341i	$-0.867849\pi$
$971$	−3.37227	+	5.84094i	−0.108221	+	0.187445i	0.806829	+	0.590786i	$0.201182\pi$
$972$	−1.41859	−	2.45706i	−0.0455012	−	0.0788103i
$973$	−20.4582	−	35.4347i	−0.655860	−	1.13598i
$974$	−23.8676			−0.764767
$975$	5.07889	+	19.4527i	0.162655	+	0.622986i
$976$	−5.67939			−0.181793
$977$	−23.1259	−	40.0552i	−0.739862	−	1.28148i	−0.952557	−	0.304360i	$-0.901557\pi$
$977$	−23.1259	−	40.0552i	−0.739862	−	1.28148i	0.212695	−	0.977119i	$-0.431776\pi$
$978$	−0.226109	−	0.391633i	−0.00723018	−	0.0125230i
$979$	−23.1327	+	40.0670i	−0.739323	+	1.28055i
$980$	0.0360463			0.00115146
$981$	1.76749	−	3.06139i	0.0564317	−	0.0977426i
$982$	−1.93661	+	3.35431i	−0.0617997	+	0.107040i
$983$	−26.7488			−0.853154			−0.426577	−	0.904451i	$-0.640281\pi$
$983$	−26.7488			−0.853154			−0.426577	+	0.904451i	$0.640281\pi$
$984$	−3.21690	+	5.57183i	−0.102551	+	0.177623i
$985$	−6.17204	−	10.6903i	−0.196658	−	0.340621i
$986$	−19.8315	−	34.3492i	−0.631565	−	1.09390i
$987$	53.9730			1.71798
$988$	−0.910836	−	3.48861i	−0.0289775	−	0.110987i
$989$	−40.3687			−1.28365
$990$	−0.571141	−	0.989245i	−0.0181521	−	0.0314403i
$991$	9.05019	+	15.6754i	0.287489	+	0.497945i	0.973210	−	0.229919i	$-0.0738462\pi$
$991$	9.05019	+	15.6754i	0.287489	+	0.497945i	−0.685721	+	0.727865i	$0.740513\pi$
$992$	−1.23638	+	2.14148i	−0.0392552	+	0.0679920i
$993$	12.6666			0.401962
$994$	−3.97664	+	6.88774i	−0.126131	+	0.218466i
$995$	−15.4115	+	26.6935i	−0.488577	+	0.846241i
$996$	12.8628			0.407572
$997$	6.30113	−	10.9139i	0.199559	−	0.345646i	−0.748827	−	0.662766i	$-0.769382\pi$
$997$	6.30113	−	10.9139i	0.199559	−	0.345646i	0.948385	+	0.317120i	$0.102716\pi$
$998$	−3.15109	−	5.45785i	−0.0997461	−	0.172765i
$999$	5.96395	+	10.3299i	0.188691	+	0.326823i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	494.2.g.b.419.1	yes	6
13.3	even	3		6422.2.a.u.1.3		3
13.9	even	3	inner	494.2.g.b.191.1	✓	6
13.10	even	6		6422.2.a.m.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
494.2.g.b.191.1	✓	6	13.9	even	3	inner
494.2.g.b.419.1	yes	6	1.1	even	1	trivial
6422.2.a.m.1.3		3	13.10	even	6
6422.2.a.u.1.3		3	13.3	even	3

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:	\( N \)	\(=\)	\( 494 = 2 \cdot 13 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	494.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.825547 - 1.42989i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.27389 q^{5} +(-0.825547 + 1.42989i) q^{6} +(1.32555 - 2.29591i) q^{7} +1.00000 q^{8} +(0.136945 - 0.237196i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.825547 - 1.42989i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.27389 q^{5} +(-0.825547 + 1.42989i) q^{6} +(1.32555 - 2.29591i) q^{7} +1.00000 q^{8} +(0.136945 - 0.237196i) q^{9} +(-0.636945 - 1.10322i) q^{10} +(1.63695 + 2.83527i) q^{11} +1.65109 q^{12} +(3.47664 + 0.955496i) q^{13} -2.65109 q^{14} +(-1.05166 - 1.82152i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.65109 - 4.59183i) q^{17} -0.273891 q^{18} +(-0.500000 + 0.866025i) q^{19} +(-0.636945 + 1.10322i) q^{20} -4.37720 q^{21} +(1.63695 - 2.83527i) q^{22} +(-3.20275 - 5.54732i) q^{23} +(-0.825547 - 1.42989i) q^{24} -3.37720 q^{25} +(-0.910836 - 3.48861i) q^{26} -5.40550 q^{27} +(1.32555 + 2.29591i) q^{28} +(3.74026 + 6.47832i) q^{29} +(-1.05166 + 1.82152i) q^{30} +2.47277 q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.70275 - 4.68130i) q^{33} -5.30219 q^{34} +(1.68860 - 2.92474i) q^{35} +(0.136945 + 0.237196i) q^{36} +(-1.10331 - 1.91099i) q^{37} +1.00000 q^{38} +(-1.50388 - 5.76002i) q^{39} +1.27389 q^{40} +(-1.94834 - 3.37463i) q^{41} +(2.18860 + 3.79077i) q^{42} +(3.15109 - 5.45785i) q^{43} -3.27389 q^{44} +(0.174453 - 0.302162i) q^{45} +(-3.20275 + 5.54732i) q^{46} -12.3305 q^{47} +(-0.825547 + 1.42989i) q^{48} +(-0.0141481 - 0.0245053i) q^{49} +(1.68860 + 2.92474i) q^{50} -8.75441 q^{51} +(-2.56580 + 2.53311i) q^{52} -2.47277 q^{53} +(2.70275 + 4.68130i) q^{54} +(2.08529 + 3.61183i) q^{55} +(1.32555 - 2.29591i) q^{56} +1.65109 q^{57} +(3.74026 - 6.47832i) q^{58} +(-4.76855 + 8.25938i) q^{59} +2.10331 q^{60} +(2.83969 - 4.91850i) q^{61} +(-1.23638 - 2.14148i) q^{62} +(-0.363055 - 0.628829i) q^{63} +1.00000 q^{64} +(4.42886 + 1.21720i) q^{65} -5.40550 q^{66} +(0.103312 + 0.178942i) q^{67} +(2.65109 + 4.59183i) q^{68} +(-5.28804 + 9.15915i) q^{69} -3.37720 q^{70} +(1.50000 - 2.59808i) q^{71} +(0.136945 - 0.237196i) q^{72} +9.41325 q^{73} +(-1.10331 + 1.91099i) q^{74} +(2.78804 + 4.82902i) q^{75} +(-0.500000 - 0.866025i) q^{76} +8.67939 q^{77} +(-4.23638 + 4.18240i) q^{78} -12.2555 q^{79} +(-0.636945 - 1.10322i) q^{80} +(4.05166 + 7.01767i) q^{81} +(-1.94834 + 3.37463i) q^{82} +7.79045 q^{83} +(2.18860 - 3.79077i) q^{84} +(3.37720 - 5.84949i) q^{85} -6.30219 q^{86} +(6.17551 - 10.6963i) q^{87} +(1.63695 + 2.83527i) q^{88} +(7.06580 + 12.2383i) q^{89} -0.348907 q^{90} +(6.80219 - 6.71551i) q^{91} +6.40550 q^{92} +(-2.04138 - 3.53578i) q^{93} +(6.16524 + 10.6785i) q^{94} +(-0.636945 + 1.10322i) q^{95} +1.65109 q^{96} +(5.65109 - 9.78798i) q^{97} +(-0.0141481 + 0.0245053i) q^{98} +0.896688 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} + 2 q^{3} - 3 q^{4} + 4 q^{5} + 2 q^{6} + q^{7} + 6 q^{8} - q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 + 2 * q^3 - 3 * q^4 + 4 * q^5 + 2 * q^6 + q^7 + 6 * q^8 - q^9	\( 6 q - 3 q^{2} + 2 q^{3} - 3 q^{4} + 4 q^{5} + 2 q^{6} + q^{7} + 6 q^{8} - q^{9} - 2 q^{10} + 8 q^{11} - 4 q^{12} - 2 q^{14} - 3 q^{15} - 3 q^{16} + 2 q^{17} + 2 q^{18} - 3 q^{19} - 2 q^{20} - 16 q^{21} + 8 q^{22} - 2 q^{23} + 2 q^{24} - 10 q^{25} + 2 q^{27} + q^{28} + 14 q^{29} - 3 q^{30} - 10 q^{31} - 3 q^{32} - q^{33} - 4 q^{34} + 5 q^{35} - q^{36} + 6 q^{38} - 13 q^{39} + 4 q^{40} - 15 q^{41} + 8 q^{42} + 5 q^{43} - 16 q^{44} + 8 q^{45} - 2 q^{46} - 22 q^{47} + 2 q^{48} + 12 q^{49} + 5 q^{50} - 32 q^{51} + 10 q^{53} - q^{54} + 14 q^{55} + q^{56} - 4 q^{57} + 14 q^{58} + 4 q^{59} + 6 q^{60} - 2 q^{61} + 5 q^{62} - 4 q^{63} + 6 q^{64} + 13 q^{65} + 2 q^{66} - 6 q^{67} + 2 q^{68} - 16 q^{69} - 10 q^{70} + 9 q^{71} - q^{72} + 30 q^{73} + q^{75} - 3 q^{76} + 14 q^{77} - 13 q^{78} - 4 q^{79} - 2 q^{80} + 21 q^{81} - 15 q^{82} + 10 q^{83} + 8 q^{84} + 10 q^{85} - 10 q^{86} - 5 q^{87} + 8 q^{88} + 27 q^{89} - 16 q^{90} + 13 q^{91} + 4 q^{92} - 25 q^{93} + 11 q^{94} - 2 q^{95} - 4 q^{96} + 20 q^{97} + 12 q^{98} + 12 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 + 2 * q^3 - 3 * q^4 + 4 * q^5 + 2 * q^6 + q^7 + 6 * q^8 - q^9 - 2 * q^10 + 8 * q^11 - 4 * q^12 - 2 * q^14 - 3 * q^15 - 3 * q^16 + 2 * q^17 + 2 * q^18 - 3 * q^19 - 2 * q^20 - 16 * q^21 + 8 * q^22 - 2 * q^23 + 2 * q^24 - 10 * q^25 + 2 * q^27 + q^28 + 14 * q^29 - 3 * q^30 - 10 * q^31 - 3 * q^32 - q^33 - 4 * q^34 + 5 * q^35 - q^36 + 6 * q^38 - 13 * q^39 + 4 * q^40 - 15 * q^41 + 8 * q^42 + 5 * q^43 - 16 * q^44 + 8 * q^45 - 2 * q^46 - 22 * q^47 + 2 * q^48 + 12 * q^49 + 5 * q^50 - 32 * q^51 + 10 * q^53 - q^54 + 14 * q^55 + q^56 - 4 * q^57 + 14 * q^58 + 4 * q^59 + 6 * q^60 - 2 * q^61 + 5 * q^62 - 4 * q^63 + 6 * q^64 + 13 * q^65 + 2 * q^66 - 6 * q^67 + 2 * q^68 - 16 * q^69 - 10 * q^70 + 9 * q^71 - q^72 + 30 * q^73 + q^75 - 3 * q^76 + 14 * q^77 - 13 * q^78 - 4 * q^79 - 2 * q^80 + 21 * q^81 - 15 * q^82 + 10 * q^83 + 8 * q^84 + 10 * q^85 - 10 * q^86 - 5 * q^87 + 8 * q^88 + 27 * q^89 - 16 * q^90 + 13 * q^91 + 4 * q^92 - 25 * q^93 + 11 * q^94 - 2 * q^95 - 4 * q^96 + 20 * q^97 + 12 * q^98 + 12 * q^99

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