LMFDB - Embedded newform 77.2.e.a.67.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [77,2,Mod(23,77)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(77, 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("77.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 77 = 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	77.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:	$0.614848095564$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.2
Root			$0.939693 + 0.342020i$ of defining polynomial
Character	$\chi$	$=$	77.67
Dual form			77.2.e.a.23.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173648 + 0.300767i) q^{2} +(0.266044 - 0.460802i) q^{3} +(0.939693 - 1.62760i) q^{4} +(-0.0603074 - 0.104455i) q^{5} +0.184793 q^{6} +(-2.47178 + 0.943555i) q^{7} +1.34730 q^{8} +(1.35844 + 2.35289i) q^{9} +O(q^{10})$	\(q+(0.173648 + 0.300767i) q^{2} +(0.266044 - 0.460802i) q^{3} +(0.939693 - 1.62760i) q^{4} +(-0.0603074 - 0.104455i) q^{5} +0.184793 q^{6} +(-2.47178 + 0.943555i) q^{7} +1.34730 q^{8} +(1.35844 + 2.35289i) q^{9} +(0.0209445 - 0.0362770i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(-0.500000 - 0.866025i) q^{12} -1.22668 q^{13} +(-0.713011 - 0.579585i) q^{14} -0.0641778 q^{15} +(-1.64543 - 2.84997i) q^{16} +(-3.08512 + 5.34359i) q^{17} +(-0.471782 + 0.817150i) q^{18} +(-3.20574 - 5.55250i) q^{19} -0.226682 q^{20} +(-0.222811 + 1.39003i) q^{21} -0.347296 q^{22} +(1.01114 + 1.75135i) q^{23} +(0.358441 - 0.620838i) q^{24} +(2.49273 - 4.31753i) q^{25} +(-0.213011 - 0.368946i) q^{26} +3.04189 q^{27} +(-0.786989 + 4.90971i) q^{28} +3.24897 q^{29} +(-0.0111444 - 0.0193026i) q^{30} +(-2.43969 + 4.22567i) q^{31} +(1.91875 - 3.32337i) q^{32} +(0.266044 + 0.460802i) q^{33} -2.14290 q^{34} +(0.247626 + 0.201288i) q^{35} +5.10607 q^{36} +(-1.18479 - 2.05212i) q^{37} +(1.11334 - 1.92836i) q^{38} +(-0.326352 + 0.565258i) q^{39} +(-0.0812519 - 0.140732i) q^{40} +8.29086 q^{41} +(-0.456767 + 0.174362i) q^{42} +2.22668 q^{43} +(0.939693 + 1.62760i) q^{44} +(0.163848 - 0.283793i) q^{45} +(-0.351167 + 0.608239i) q^{46} +(-4.61721 - 7.99724i) q^{47} -1.75103 q^{48} +(5.21941 - 4.66452i) q^{49} +1.73143 q^{50} +(1.64156 + 2.84326i) q^{51} +(-1.15270 + 1.99654i) q^{52} +(-4.84002 + 8.38316i) q^{53} +(0.528218 + 0.914901i) q^{54} +0.120615 q^{55} +(-3.33022 + 1.27125i) q^{56} -3.41147 q^{57} +(0.564178 + 0.977185i) q^{58} +(4.87211 - 8.43874i) q^{59} +(-0.0603074 + 0.104455i) q^{60} +(0.716881 + 1.24168i) q^{61} -1.69459 q^{62} +(-5.57785 - 4.53406i) q^{63} -5.24897 q^{64} +(0.0739780 + 0.128134i) q^{65} +(-0.0923963 + 0.160035i) q^{66} +(1.53209 - 2.65366i) q^{67} +(5.79813 + 10.0427i) q^{68} +1.07604 q^{69} +(-0.0175410 + 0.109431i) q^{70} -8.49525 q^{71} +(1.83022 + 3.17004i) q^{72} +(-1.76604 + 3.05888i) q^{73} +(0.411474 - 0.712694i) q^{74} +(-1.32635 - 2.29731i) q^{75} -12.0496 q^{76} +(0.418748 - 2.61240i) q^{77} -0.226682 q^{78} +(-4.54576 - 7.87349i) q^{79} +(-0.198463 + 0.343748i) q^{80} +(-3.26604 + 5.65695i) q^{81} +(1.43969 + 2.49362i) q^{82} -7.02229 q^{83} +(2.05303 + 1.66885i) q^{84} +0.744223 q^{85} +(0.386659 + 0.669713i) q^{86} +(0.864370 - 1.49713i) q^{87} +(-0.673648 + 1.16679i) q^{88} +(3.43969 + 5.95772i) q^{89} +0.113808 q^{90} +(3.03209 - 1.15744i) q^{91} +3.80066 q^{92} +(1.29813 + 2.24843i) q^{93} +(1.60354 - 2.77741i) q^{94} +(-0.386659 + 0.669713i) q^{95} +(-1.02094 - 1.76833i) q^{96} +16.5321 q^{97} +(2.30928 + 0.759842i) q^{98} -2.71688 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{3} - 6 q^{5} - 6 q^{6} + 6 q^{8}+O(q^{10}) $ 6 * q - 3 * q^3 - 6 * q^5 - 6 * q^6 + 6 * q^8	$ 6 q - 3 q^{3} - 6 q^{5} - 6 q^{6} + 6 q^{8} - 3 q^{10} - 3 q^{11} - 3 q^{12} + 6 q^{13} - 12 q^{14} + 18 q^{15} + 6 q^{16} + 3 q^{17} + 12 q^{18} - 9 q^{19} + 12 q^{20} - 12 q^{21} - 6 q^{24} - 3 q^{25} - 9 q^{26} + 12 q^{27} + 3 q^{28} - 6 q^{29} + 6 q^{30} - 9 q^{31} + 9 q^{32} - 3 q^{33} - 12 q^{34} - 15 q^{35} + 6 q^{36} - 3 q^{39} - 3 q^{40} + 18 q^{41} - 18 q^{42} - 3 q^{45} + 24 q^{46} + 3 q^{47} - 36 q^{48} + 30 q^{50} + 18 q^{51} - 9 q^{52} - 9 q^{53} + 18 q^{54} + 12 q^{55} + 3 q^{56} - 15 q^{58} - 6 q^{60} - 12 q^{61} - 6 q^{62} + 6 q^{63} - 6 q^{64} - 15 q^{65} + 3 q^{66} + 21 q^{68} + 42 q^{69} + 45 q^{70} - 18 q^{71} - 12 q^{72} - 6 q^{73} - 18 q^{74} - 9 q^{75} - 18 q^{76} + 12 q^{78} + 3 q^{79} + 27 q^{80} - 15 q^{81} + 3 q^{82} - 30 q^{83} - 54 q^{85} + 9 q^{86} + 24 q^{87} - 3 q^{88} + 15 q^{89} - 72 q^{90} + 9 q^{91} - 6 q^{92} - 6 q^{93} - 9 q^{95} - 3 q^{96} + 90 q^{97} - 6 q^{98}+O(q^{100}) $ 6 * q - 3 * q^3 - 6 * q^5 - 6 * q^6 + 6 * q^8 - 3 * q^10 - 3 * q^11 - 3 * q^12 + 6 * q^13 - 12 * q^14 + 18 * q^15 + 6 * q^16 + 3 * q^17 + 12 * q^18 - 9 * q^19 + 12 * q^20 - 12 * q^21 - 6 * q^24 - 3 * q^25 - 9 * q^26 + 12 * q^27 + 3 * q^28 - 6 * q^29 + 6 * q^30 - 9 * q^31 + 9 * q^32 - 3 * q^33 - 12 * q^34 - 15 * q^35 + 6 * q^36 - 3 * q^39 - 3 * q^40 + 18 * q^41 - 18 * q^42 - 3 * q^45 + 24 * q^46 + 3 * q^47 - 36 * q^48 + 30 * q^50 + 18 * q^51 - 9 * q^52 - 9 * q^53 + 18 * q^54 + 12 * q^55 + 3 * q^56 - 15 * q^58 - 6 * q^60 - 12 * q^61 - 6 * q^62 + 6 * q^63 - 6 * q^64 - 15 * q^65 + 3 * q^66 + 21 * q^68 + 42 * q^69 + 45 * q^70 - 18 * q^71 - 12 * q^72 - 6 * q^73 - 18 * q^74 - 9 * q^75 - 18 * q^76 + 12 * q^78 + 3 * q^79 + 27 * q^80 - 15 * q^81 + 3 * q^82 - 30 * q^83 - 54 * q^85 + 9 * q^86 + 24 * q^87 - 3 * q^88 + 15 * q^89 - 72 * q^90 + 9 * q^91 - 6 * q^92 - 6 * q^93 - 9 * q^95 - 3 * q^96 + 90 * q^97 - 6 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/77\mathbb{Z}\right)^\times$.

$n$	$45$	$57$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.173648	+	0.300767i	0.122788	+	0.212675i	0.920866	−	0.389879i	$-0.127483\pi$
$2$	0.173648	+	0.300767i	0.122788	+	0.212675i	−0.798078	+	0.602554i	$0.794150\pi$
$3$	0.266044	−	0.460802i	0.153601	−	0.266044i	−0.778948	−	0.627089i	$-0.784246\pi$
$3$	0.266044	−	0.460802i	0.153601	−	0.266044i	0.932549	+	0.361044i	$0.117580\pi$
$4$	0.939693	−	1.62760i	0.469846	−	0.813798i
$5$	−0.0603074	−	0.104455i	−0.0269703	−	0.0467139i	0.852225	−	0.523175i	$-0.175253\pi$
$5$	−0.0603074	−	0.104455i	−0.0269703	−	0.0467139i	−0.879196	+	0.476461i	$0.841919\pi$
$6$	0.184793			0.0754412
$7$	−2.47178	+	0.943555i	−0.934246	+	0.356630i
$7$	−2.47178	+	0.943555i	−0.934246	+	0.356630i
$8$	1.34730			0.476341
$9$	1.35844	+	2.35289i	0.452814	+	0.784296i
$10$	0.0209445	−	0.0362770i	0.00662324	−	0.0114718i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	−1.22668			−0.340220			−0.170110	−	0.985425i	$-0.554412\pi$
$13$	−1.22668			−0.340220			−0.170110	+	0.985425i	$0.554412\pi$
$14$	−0.713011	−	0.579585i	−0.190560	−	0.154901i
$15$	−0.0641778			−0.0165706
$16$	−1.64543	−	2.84997i	−0.411357	−	0.712492i
$17$	−3.08512	+	5.34359i	−0.748252	+	1.29601i	0.200408	+	0.979713i	$0.435773\pi$
$17$	−3.08512	+	5.34359i	−0.748252	+	1.29601i	−0.948660	+	0.316298i	$0.897560\pi$
$18$	−0.471782	+	0.817150i	−0.111200	+	0.192604i
$19$	−3.20574	−	5.55250i	−0.735447	−	1.27383i	−0.954527	−	0.298124i	$-0.903639\pi$
$19$	−3.20574	−	5.55250i	−0.735447	−	1.27383i	0.219081	−	0.975707i	$-0.429694\pi$
$20$	−0.226682			−0.0506875
$21$	−0.222811	+	1.39003i	−0.0486214	+	0.303330i
$22$	−0.347296			−0.0740438
$23$	1.01114	+	1.75135i	0.210838	+	0.365182i	0.951977	−	0.306169i	$-0.0990474\pi$
$23$	1.01114	+	1.75135i	0.210838	+	0.365182i	−0.741139	+	0.671352i	$0.765714\pi$
$24$	0.358441	−	0.620838i	0.0731664	−	0.126728i
$25$	2.49273	−	4.31753i	0.498545	−	0.863506i
$26$	−0.213011	−	0.368946i	−0.0417749	−	0.0723562i
$27$	3.04189			0.585412
$28$	−0.786989	+	4.90971i	−0.148727	+	0.927848i
$29$	3.24897			0.603319			0.301659	−	0.953416i	$-0.402459\pi$
$29$	3.24897			0.603319			0.301659	+	0.953416i	$0.402459\pi$
$30$	−0.0111444	−	0.0193026i	−0.00203467	−	0.00352415i
$31$	−2.43969	+	4.22567i	−0.438182	+	0.758953i	−0.997549	−	0.0699667i	$-0.977711\pi$
$31$	−2.43969	+	4.22567i	−0.438182	+	0.758953i	0.559368	+	0.828920i	$0.311044\pi$
$32$	1.91875	−	3.32337i	0.339190	−	0.587494i
$33$	0.266044	+	0.460802i	0.0463124	+	0.0802154i
$34$	−2.14290			−0.367505
$35$	0.247626	+	0.201288i	0.0418565	+	0.0340238i
$36$	5.10607			0.851011
$37$	−1.18479	−	2.05212i	−0.194779	−	0.337367i	0.752049	−	0.659107i	$-0.229066\pi$
$37$	−1.18479	−	2.05212i	−0.194779	−	0.337367i	−0.946828	+	0.321740i	$0.895732\pi$
$38$	1.11334	−	1.92836i	0.180608	−	0.312822i
$39$	−0.326352	+	0.565258i	−0.0522581	+	0.0905137i
$40$	−0.0812519	−	0.140732i	−0.0128471	−	0.0222518i
$41$	8.29086			1.29481			0.647407	−	0.762144i	$-0.275853\pi$
$41$	8.29086			1.29481			0.647407	+	0.762144i	$0.275853\pi$
$42$	−0.456767	+	0.174362i	−0.0704806	+	0.0269046i
$43$	2.22668			0.339566			0.169783	−	0.985481i	$-0.445693\pi$
$43$	2.22668			0.339566			0.169783	+	0.985481i	$0.445693\pi$
$44$	0.939693	+	1.62760i	0.141664	+	0.245369i
$45$	0.163848	−	0.283793i	0.0244250	−	0.0423054i
$46$	−0.351167	+	0.608239i	−0.0517767	+	0.0896799i
$47$	−4.61721	−	7.99724i	−0.673489	−	1.16652i	−0.976908	−	0.213661i	$-0.931461\pi$
$47$	−4.61721	−	7.99724i	−0.673489	−	1.16652i	0.303418	−	0.952857i	$-0.401872\pi$
$48$	−1.75103			−0.252739
$49$	5.21941	−	4.66452i	0.745630	−	0.666361i
$50$	1.73143			0.244861
$51$	1.64156	+	2.84326i	0.229864	+	0.398137i
$52$	−1.15270	+	1.99654i	−0.159851	+	0.276870i
$53$	−4.84002	+	8.38316i	−0.664828	+	1.15152i	0.314504	+	0.949256i	$0.398162\pi$
$53$	−4.84002	+	8.38316i	−0.664828	+	1.15152i	−0.979332	+	0.202260i	$0.935171\pi$
$54$	0.528218	+	0.914901i	0.0718814	+	0.124502i
$55$	0.120615			0.0162637
$56$	−3.33022	+	1.27125i	−0.445020	+	0.169878i
$57$	−3.41147			−0.451861
$58$	0.564178	+	0.977185i	0.0740802	+	0.128311i
$59$	4.87211	−	8.43874i	0.634295	−	1.09863i	−0.352369	−	0.935861i	$-0.614624\pi$
$59$	4.87211	−	8.43874i	0.634295	−	1.09863i	0.986664	−	0.162770i	$-0.0520428\pi$
$60$	−0.0603074	+	0.104455i	−0.00778565	+	0.0134851i
$61$	0.716881	+	1.24168i	0.0917873	+	0.158980i	0.908263	−	0.418399i	$-0.137409\pi$
$61$	0.716881	+	1.24168i	0.0917873	+	0.158980i	−0.816476	+	0.577379i	$0.804075\pi$
$62$	−1.69459			−0.215213
$63$	−5.57785	−	4.53406i	−0.702743	−	0.571238i
$64$	−5.24897			−0.656121
$65$	0.0739780	+	0.128134i	0.00917584	+	0.0158930i
$66$	−0.0923963	+	0.160035i	−0.0113732	+	0.0196989i
$67$	1.53209	−	2.65366i	0.187174	−	0.324196i	−0.757133	−	0.653261i	$-0.773400\pi$
$67$	1.53209	−	2.65366i	0.187174	−	0.324196i	0.944307	+	0.329066i	$0.106734\pi$
$68$	5.79813	+	10.0427i	0.703127	+	1.21785i
$69$	1.07604			0.129540
$70$	−0.0175410	+	0.109431i	−0.00209655	+	0.0130795i
$71$	−8.49525			−1.00820			−0.504100	−	0.863645i	$-0.668176\pi$
$71$	−8.49525			−1.00820			−0.504100	+	0.863645i	$0.668176\pi$
$72$	1.83022	+	3.17004i	0.215694	+	0.373593i
$73$	−1.76604	+	3.05888i	−0.206700	+	0.358015i	−0.950673	−	0.310195i	$-0.899606\pi$
$73$	−1.76604	+	3.05888i	−0.206700	+	0.358015i	0.743973	+	0.668210i	$0.232939\pi$
$74$	0.411474	−	0.712694i	0.0478329	−	0.0828490i
$75$	−1.32635	−	2.29731i	−0.153154	−	0.265270i
$76$	−12.0496			−1.38219
$77$	0.418748	−	2.61240i	0.0477208	−	0.297711i
$78$	−0.226682			−0.0256666
$79$	−4.54576	−	7.87349i	−0.511438	−	0.885836i	−0.999912	−	0.0132581i	$-0.995780\pi$
$79$	−4.54576	−	7.87349i	−0.511438	−	0.885836i	0.488474	−	0.872578i	$-0.337554\pi$
$80$	−0.198463	+	0.343748i	−0.0221888	+	0.0384322i
$81$	−3.26604	+	5.65695i	−0.362894	+	0.628551i
$82$	1.43969	+	2.49362i	0.158987	+	0.275374i
$83$	−7.02229			−0.770796			−0.385398	−	0.922750i	$-0.625936\pi$
$83$	−7.02229			−0.770796			−0.385398	+	0.922750i	$0.625936\pi$
$84$	2.05303	+	1.66885i	0.224004	+	0.182086i
$85$	0.744223			0.0807223
$86$	0.386659	+	0.669713i	0.0416945	+	0.0722171i
$87$	0.864370	−	1.49713i	0.0926702	−	0.160510i
$88$	−0.673648	+	1.16679i	−0.0718111	+	0.124381i
$89$	3.43969	+	5.95772i	0.364607	+	0.631517i	0.988713	−	0.149822i	$-0.0478701\pi$
$89$	3.43969	+	5.95772i	0.364607	+	0.631517i	−0.624106	+	0.781339i	$0.714537\pi$
$90$	0.113808			0.0119964
$91$	3.03209	−	1.15744i	0.317849	−	0.121333i
$92$	3.80066			0.396246
$93$	1.29813	+	2.24843i	0.134610	+	0.233152i
$94$	1.60354	−	2.77741i	0.165393	−	0.286468i
$95$	−0.386659	+	0.669713i	−0.0396704	+	0.0687111i
$96$	−1.02094	−	1.76833i	−0.104200	−	0.180479i
$97$	16.5321			1.67858			0.839290	−	0.543685i	$-0.182971\pi$
$97$	16.5321			1.67858			0.839290	+	0.543685i	$0.182971\pi$
$98$	2.30928	+	0.759842i	0.233272	+	0.0767556i
$99$	−2.71688			−0.273057
$100$	−4.68479	−	8.11430i	−0.468479	−	0.811430i
$101$	3.40033	−	5.88954i	0.338345	−	0.586032i	−0.645776	−	0.763527i	$-0.723466\pi$
$101$	3.40033	−	5.88954i	0.338345	−	0.586032i	0.984122	+	0.177495i	$0.0567994\pi$
$102$	−0.570108	+	0.987455i	−0.0564491	+	0.0977726i
$103$	4.58512	+	7.94166i	0.451786	+	0.782515i	0.998497	−	0.0548055i	$-0.0174539\pi$
$103$	4.58512	+	7.94166i	0.451786	+	0.782515i	−0.546712	+	0.837321i	$0.684121\pi$
$104$	−1.65270			−0.162061
$105$	0.158633	−	0.0605553i	0.0154810	−	0.00590959i
$106$	−3.36184			−0.326531
$107$	4.06031	+	7.03266i	0.392525	+	0.679873i	0.992782	−	0.119934i	$-0.0382684\pi$
$107$	4.06031	+	7.03266i	0.392525	+	0.679873i	−0.600257	+	0.799807i	$0.704935\pi$
$108$	2.85844	−	4.95096i	0.275054	−	0.476407i
$109$	3.24510	−	5.62068i	0.310824	−	0.538363i	−0.667717	−	0.744415i	$-0.732728\pi$
$109$	3.24510	−	5.62068i	0.310824	−	0.538363i	0.978541	+	0.206052i	$0.0660616\pi$
$110$	0.0209445	+	0.0362770i	0.00199698	+	0.00345888i
$111$	−1.26083			−0.119673
$112$	6.75624	+	5.49194i	0.638405	+	0.518940i
$113$	−10.8648			−1.02208			−0.511039	−	0.859558i	$-0.670739\pi$
$113$	−10.8648			−1.02208			−0.511039	+	0.859558i	$0.670739\pi$
$114$	−0.592396	−	1.02606i	−0.0554830	−	0.0960994i
$115$	0.121959	−	0.211239i	0.0113727	−	0.0196981i
$116$	3.05303	−	5.28801i	0.283467	−	0.490979i
$117$	−1.66637	−	2.88624i	−0.154056	−	0.266833i
$118$	3.38413			0.311535
$119$	2.58378	−	16.1192i	0.236855	−	1.47764i
$120$	−0.0864665			−0.00789327
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	−0.248970	+	0.431229i	−0.0225407	+	0.0390417i
$123$	2.20574	−	3.82045i	0.198885	−	0.344478i
$124$	4.58512	+	7.94166i	0.411756	+	0.713183i
$125$	−1.20439			−0.107724
$126$	0.395115	−	2.46497i	0.0351997	−	0.219597i
$127$	2.68004			0.237816			0.118908	−	0.992905i	$-0.462061\pi$
$127$	2.68004			0.237816			0.118908	+	0.992905i	$0.462061\pi$
$128$	−4.74897	−	8.22546i	−0.419754	−	0.727035i
$129$	0.592396	−	1.02606i	0.0521576	−	0.0903396i
$130$	−0.0256923	+	0.0445003i	−0.00225336	+	0.00390294i
$131$	7.01367	+	12.1480i	0.612787	+	1.06138i	0.990768	+	0.135565i	$0.0432851\pi$
$131$	7.01367	+	12.1480i	0.612787	+	1.06138i	−0.377981	+	0.925813i	$0.623382\pi$
$132$	1.00000			0.0870388
$133$	13.1630	+	10.6998i	1.14137	+	0.927788i
$134$	1.06418			0.0919310
$135$	−0.183448	−	0.317742i	−0.0157887	−	0.0273469i
$136$	−4.15657	+	7.19940i	−0.356423	+	0.617343i
$137$	−7.32042	+	12.6793i	−0.625426	+	1.08327i	0.363032	+	0.931776i	$0.381741\pi$
$137$	−7.32042	+	12.6793i	−0.625426	+	1.08327i	−0.988458	+	0.151493i	$0.951592\pi$
$138$	0.186852	+	0.323637i	0.0159059	+	0.0275498i
$139$	11.0155			0.934321			0.467160	−	0.884173i	$-0.345277\pi$
$139$	11.0155			0.934321			0.467160	+	0.884173i	$0.345277\pi$
$140$	0.560307	−	0.213887i	0.0473546	−	0.0180767i
$141$	−4.91353			−0.413794
$142$	−1.47519	−	2.55510i	−0.123795	−	0.214419i
$143$	0.613341	−	1.06234i	0.0512901	−	0.0888371i
$144$	4.47044	−	7.74302i	0.372536	−	0.645252i
$145$	−0.195937	−	0.339373i	−0.0162717	−	0.0281834i
$146$	−1.22668			−0.101521
$147$	−0.760830	−	3.64609i	−0.0627522	−	0.300724i
$148$	−4.45336			−0.366064
$149$	−7.36484	−	12.7563i	−0.603351	−	1.04503i	−0.992310	−	0.123779i	$-0.960498\pi$
$149$	−7.36484	−	12.7563i	−0.603351	−	1.04503i	0.388959	−	0.921255i	$-0.372835\pi$
$150$	0.460637	−	0.797847i	0.0376109	−	0.0651439i
$151$	−11.6211	+	20.1283i	−0.945710	+	1.63802i	−0.191387	+	0.981515i	$0.561299\pi$
$151$	−11.6211	+	20.1283i	−0.945710	+	1.63802i	−0.754323	+	0.656504i	$0.772035\pi$
$152$	−4.31908	−	7.48086i	−0.350323	−	0.606778i
$153$	−16.7638			−1.35527
$154$	0.858441	−	0.327693i	0.0691751	−	0.0264063i
$155$	0.588526			0.0472715
$156$	0.613341	+	1.06234i	0.0491066	+	0.0850551i
$157$	−8.03209	+	13.9120i	−0.641030	+	1.11030i	0.344173	+	0.938906i	$0.388159\pi$
$157$	−8.03209	+	13.9120i	−0.641030	+	1.11030i	−0.985203	+	0.171391i	$0.945174\pi$
$158$	1.57873	−	2.73443i	0.125597	−	0.217540i
$159$	2.57532	+	4.46059i	0.204236	+	0.353748i
$160$	−0.462859			−0.0365922
$161$	−4.15183	−	3.37489i	−0.327210	−	0.265979i
$162$	−2.26857			−0.178236
$163$	5.30066	+	9.18101i	0.415180	+	0.719112i	0.995447	−	0.0953135i	$-0.0303854\pi$
$163$	5.30066	+	9.18101i	0.415180	+	0.719112i	−0.580268	+	0.814426i	$0.697052\pi$
$164$	7.79086	−	13.4942i	0.608364	−	1.05372i
$165$	0.0320889	−	0.0555796i	0.00249812	−	0.00432686i
$166$	−1.21941	−	2.11208i	−0.0946444	−	0.163929i
$167$	−21.1361			−1.63556			−0.817780	−	0.575531i	$-0.804795\pi$
$167$	−21.1361			−1.63556			−0.817780	+	0.575531i	$0.804795\pi$
$168$	−0.300193	+	1.87278i	−0.0231604	+	0.144488i
$169$	−11.4953			−0.884250
$170$	0.129233	+	0.223838i	0.00991171	+	0.0171676i
$171$	8.70961	−	15.0855i	0.666040	−	1.15362i
$172$	2.09240	−	3.62414i	0.159544	−	0.276338i
$173$	−1.15998	−	2.00914i	−0.0881915	−	0.152752i	0.818555	−	0.574428i	$-0.194775\pi$
$173$	−1.15998	−	2.00914i	−0.0881915	−	0.152752i	−0.906747	+	0.421676i	$0.861442\pi$
$174$	0.600385			0.0455151
$175$	−2.08765	+	13.0240i	−0.157811	+	0.984523i
$176$	3.29086			0.248058
$177$	−2.59240	−	4.49016i	−0.194856	−	0.337501i
$178$	−1.19459	+	2.06910i	−0.0895385	+	0.155085i
$179$	−5.70961	+	9.88933i	−0.426756	+	0.739163i	−0.996583	−	0.0826018i	$-0.973677\pi$
$179$	−5.70961	+	9.88933i	−0.426756	+	0.739163i	0.569827	+	0.821765i	$0.307010\pi$
$180$	−0.307934	−	0.533356i	−0.0229520	−	0.0397540i
$181$	16.4679			1.22405			0.612025	−	0.790838i	$-0.290355\pi$
$181$	16.4679			1.22405			0.612025	+	0.790838i	$0.290355\pi$
$182$	0.874638	+	0.710966i	0.0648324	+	0.0527003i
$183$	0.762889			0.0563944
$184$	1.36231	+	2.35959i	0.100431	+	0.173951i
$185$	−0.142903	+	0.247516i	−0.0105065	+	0.0181977i
$186$	−0.450837	+	0.780873i	−0.0330570	+	0.0572564i
$187$	−3.08512	−	5.34359i	−0.225606	−	0.390762i
$188$	−17.3550			−1.26575
$189$	−7.51889	+	2.87019i	−0.546918	+	0.208776i
$190$	−0.268571			−0.0194842
$191$	5.58378	+	9.67139i	0.404028	+	0.699797i	0.994208	−	0.107475i	$-0.0342765\pi$
$191$	5.58378	+	9.67139i	0.404028	+	0.699797i	−0.590180	+	0.807272i	$0.700943\pi$
$192$	−1.39646	+	2.41874i	−0.100781	+	0.174557i
$193$	10.0248	−	17.3635i	0.721602	−	1.24985i	−0.238755	−	0.971080i	$-0.576739\pi$
$193$	10.0248	−	17.3635i	0.721602	−	1.24985i	0.960357	−	0.278772i	$-0.0899272\pi$
$194$	2.87077	+	4.97231i	0.206109	+	0.356991i
$195$	0.0787257			0.00563766
$196$	−2.68732	−	12.8783i	−0.191951	−	0.919879i
$197$	15.9932			1.13947			0.569734	−	0.821829i	$-0.307046\pi$
$197$	15.9932			1.13947			0.569734	+	0.821829i	$0.307046\pi$
$198$	−0.471782	−	0.817150i	−0.0335281	−	0.0580723i
$199$	−3.13429	+	5.42874i	−0.222184	+	0.384833i	−0.955471	−	0.295086i	$-0.904652\pi$
$199$	−3.13429	+	5.42874i	−0.222184	+	0.384833i	0.733287	+	0.679919i	$0.237985\pi$
$200$	3.35844	−	5.81699i	0.237478	−	0.411323i
$201$	−0.815207	−	1.41198i	−0.0575003	−	0.0995934i
$202$	2.36184			0.166179
$203$	−8.03074	+	3.06558i	−0.563648	+	0.215162i
$204$	6.17024			0.432004
$205$	−0.500000	−	0.866025i	−0.0349215	−	0.0604858i
$206$	−1.59240	+	2.75811i	−0.110948	+	0.192167i
$207$	−2.74716	+	4.75822i	−0.190941	+	0.330719i
$208$	2.01842	+	3.49600i	0.139952	+	0.242404i
$209$	6.41147			0.443491
$210$	0.0457595	+	0.0371965i	0.00315770	+	0.00256680i
$211$	11.0642			0.761689			0.380845	−	0.924639i	$-0.375633\pi$
$211$	11.0642			0.761689			0.380845	+	0.924639i	$0.375633\pi$
$212$	9.09627	+	15.7552i	0.624734	+	1.08207i
$213$	−2.26011	+	3.91463i	−0.154861	+	0.268226i
$214$	−1.41013	+	2.44242i	−0.0963945	+	0.166960i
$215$	−0.134285	−	0.232589i	−0.00915818	−	0.0158624i
$216$	4.09833			0.278856
$217$	2.04323	−	12.7469i	0.138704	−	0.865317i
$218$	2.25402			0.152662
$219$	0.939693	+	1.62760i	0.0634985	+	0.109983i
$220$	0.113341	−	0.196312i	0.00764144	−	0.0132354i
$221$	3.78446	−	6.55488i	0.254571	−	0.440929i
$222$	−0.218941	−	0.379217i	−0.0146943	−	0.0254514i
$223$	9.25671			0.619875			0.309938	−	0.950757i	$-0.399692\pi$
$223$	9.25671			0.619875			0.309938	+	0.950757i	$0.399692\pi$
$224$	−1.60694	+	10.0251i	−0.107368	+	0.669829i
$225$	13.5449			0.902992
$226$	−1.88666	−	3.26779i	−0.125499	−	0.217370i
$227$	10.2528	−	17.7584i	0.680505	−	1.17867i	−0.294322	−	0.955706i	$-0.595094\pi$
$227$	10.2528	−	17.7584i	0.680505	−	1.17867i	0.974827	−	0.222963i	$-0.0715729\pi$
$228$	−3.20574	+	5.55250i	−0.212305	+	0.367723i
$229$	−13.0321	−	22.5722i	−0.861185	−	1.49162i	−0.870786	−	0.491662i	$-0.836390\pi$
$229$	−13.0321	−	22.5722i	−0.861185	−	1.49162i	0.00960162	−	0.999954i	$-0.496944\pi$
$230$	0.0847118			0.00558573
$231$	−1.09240	−	0.887975i	−0.0718744	−	0.0584245i
$232$	4.37733			0.287386
$233$	−1.39393	−	2.41436i	−0.0913196	−	0.158170i	0.816747	−	0.576996i	$-0.195775\pi$
$233$	−1.39393	−	2.41436i	−0.0913196	−	0.158170i	−0.908067	+	0.418826i	$0.862442\pi$
$234$	0.578726	−	1.00238i	0.0378325	−	0.0655278i
$235$	−0.556904	+	0.964586i	−0.0363284	+	0.0629226i
$236$	−9.15657	−	15.8597i	−0.596042	−	1.03238i
$237$	−4.83750			−0.314229
$238$	5.29679	−	2.02195i	0.343340	−	0.131063i
$239$	−11.2199			−0.725753			−0.362877	−	0.931837i	$-0.618205\pi$
$239$	−11.2199			−0.725753			−0.362877	+	0.931837i	$0.618205\pi$
$240$	0.105600	+	0.182905i	0.00681645	+	0.0118064i
$241$	−5.12789	+	8.88176i	−0.330316	+	0.572125i	−0.982574	−	0.185873i	$-0.940489\pi$
$241$	−5.12789	+	8.88176i	−0.330316	+	0.572125i	0.652257	+	0.757997i	$0.273822\pi$
$242$	0.173648	−	0.300767i	0.0111625	−	0.0193341i
$243$	6.30066	+	10.9131i	0.404187	+	0.700073i
$244$	2.69459			0.172504
$245$	−0.802004	−	0.263890i	−0.0512381	−	0.0168593i
$246$	1.53209			0.0976824
$247$	3.93242	+	6.81115i	0.250214	+	0.433383i
$248$	−3.28699	+	5.69323i	−0.208724	+	0.361521i
$249$	−1.86824	+	3.23589i	−0.118395	+	0.205066i
$250$	−0.209141	−	0.362242i	−0.0132272	−	0.0229102i
$251$	29.1215			1.83814			0.919068	−	0.394099i	$-0.128943\pi$
$251$	29.1215			1.83814			0.919068	+	0.394099i	$0.128943\pi$
$252$	−12.6211	+	4.81786i	−0.795053	+	0.303496i
$253$	−2.02229			−0.127140
$254$	0.465385	+	0.806070i	0.0292008	+	0.0505773i
$255$	0.197996	−	0.342940i	0.0123990	−	0.0214757i
$256$	−3.59967	+	6.23481i	−0.224979	+	0.389676i
$257$	−4.19846	−	7.27195i	−0.261893	−	0.453612i	0.704852	−	0.709354i	$-0.251013\pi$
$257$	−4.19846	−	7.27195i	−0.261893	−	0.453612i	−0.966745	+	0.255743i	$0.917680\pi$
$258$	0.411474			0.0256173
$259$	4.86484	+	3.95448i	0.302286	+	0.245719i
$260$	0.278066			0.0172449
$261$	4.41353	+	7.64446i	0.273191	+	0.473180i
$262$	−2.43582	+	4.21897i	−0.150486	+	0.260649i
$263$	12.1814	−	21.0988i	0.751137	−	1.30101i	−0.196136	−	0.980577i	$-0.562839\pi$
$263$	12.1814	−	21.0988i	0.751137	−	1.30101i	0.947272	−	0.320430i	$-0.103827\pi$
$264$	0.358441	+	0.620838i	0.0220605	+	0.0382099i
$265$	1.16756			0.0717224
$266$	−0.932419	+	5.81699i	−0.0571703	+	0.356663i
$267$	3.66044			0.224016
$268$	−2.87939	−	4.98724i	−0.175886	−	0.304644i
$269$	−14.5954	+	25.2800i	−0.889897	+	1.54135i	−0.0499001	+	0.998754i	$0.515890\pi$
$269$	−14.5954	+	25.2800i	−0.889897	+	1.54135i	−0.839996	+	0.542592i	$0.817443\pi$
$270$	0.0637109	−	0.110351i	0.00387732	−	0.00671572i
$271$	−4.78312	−	8.28460i	−0.290554	−	0.503254i	0.683387	−	0.730056i	$-0.260506\pi$
$271$	−4.78312	−	8.28460i	−0.290554	−	0.503254i	−0.973941	+	0.226802i	$0.927173\pi$
$272$	20.3054			1.23120
$273$	0.273318	−	1.70513i	0.0165420	−	0.103199i
$274$	−5.08471			−0.307179
$275$	2.49273	+	4.31753i	0.150317	+	0.260357i
$276$	1.01114	−	1.75135i	0.0608637	−	0.105419i
$277$	10.1407	−	17.5642i	0.609295	−	1.05533i	−0.382062	−	0.924137i	$-0.624786\pi$
$277$	10.1407	−	17.5642i	0.609295	−	1.05533i	0.991357	−	0.131193i	$-0.0418806\pi$
$278$	1.91282	+	3.31310i	0.114723	+	0.198706i
$279$	−13.2567			−0.793659
$280$	0.333626	+	0.271194i	0.0199380	+	0.0162070i
$281$	−5.52528			−0.329611			−0.164805	−	0.986326i	$-0.552700\pi$
$281$	−5.52528			−0.329611			−0.164805	+	0.986326i	$0.552700\pi$
$282$	−0.853226	−	1.47783i	−0.0508089	−	0.0880036i
$283$	−2.03343	+	3.52201i	−0.120875	+	0.209362i	−0.920113	−	0.391653i	$-0.871903\pi$
$283$	−2.03343	+	3.52201i	−0.120875	+	0.209362i	0.799238	+	0.601015i	$0.205237\pi$
$284$	−7.98293	+	13.8268i	−0.473699	+	0.820472i
$285$	0.205737	+	0.356347i	0.0121868	+	0.0211082i
$286$	0.426022			0.0251912
$287$	−20.4932	+	7.82288i	−1.20967	+	0.461770i
$288$	10.4260			0.614359
$289$	−10.5360	−	18.2488i	−0.619762	−	1.07346i
$290$	0.0680482	−	0.117863i	0.00399593	−	0.00692115i
$291$	4.39827	−	7.61803i	0.257831	−	0.446577i
$292$	3.31908	+	5.74881i	0.194234	+	0.336424i
$293$	−23.2567			−1.35867			−0.679336	−	0.733828i	$-0.737732\pi$
$293$	−23.2567			−1.35867			−0.679336	+	0.733828i	$0.737732\pi$
$294$	0.964508	−	0.861969i	0.0562512	−	0.0502711i
$295$	−1.17530			−0.0684284
$296$	−1.59627	−	2.76481i	−0.0927811	−	0.160702i
$297$	−1.52094	+	2.63435i	−0.0882542	+	0.152861i
$298$	2.55778	−	4.43021i	0.148168	−	0.256635i
$299$	−1.24035	−	2.14835i	−0.0717314	−	0.124242i
$300$	−4.98545			−0.287835
$301$	−5.50387	+	2.10100i	−0.317238	+	0.121099i
$302$	−8.07192			−0.464487
$303$	−1.80928	−	3.13376i	−0.103940	−	0.180030i
$304$	−10.5496	+	18.2725i	−0.605063	+	1.04800i
$305$	0.0864665	−	0.149764i	0.00495106	−	0.00857548i
$306$	−2.91101	−	5.04201i	−0.166411	−	0.288233i
$307$	−15.3131			−0.873968			−0.436984	−	0.899469i	$-0.643953\pi$
$307$	−15.3131			−0.873968			−0.436984	+	0.899469i	$0.643953\pi$
$308$	−3.85844	−	3.13641i	−0.219855	−	0.178713i
$309$	4.87939			0.277579
$310$	0.102196	+	0.177009i	0.00580437	+	0.0100535i
$311$	3.53596	−	6.12446i	0.200506	−	0.347286i	−0.748186	−	0.663489i	$-0.769075\pi$
$311$	3.53596	−	6.12446i	0.200506	−	0.347286i	0.948692	+	0.316203i	$0.102408\pi$
$312$	−0.439693	+	0.761570i	−0.0248927	+	0.0431154i
$313$	−13.1989	−	22.8612i	−0.746048	−	1.29219i	−0.949704	−	0.313150i	$-0.898616\pi$
$313$	−13.1989	−	22.8612i	−0.746048	−	1.29219i	0.203656	−	0.979042i	$-0.434718\pi$
$314$	−5.57903			−0.314843
$315$	−0.137222	+	0.856074i	−0.00773159	+	0.0482343i
$316$	−17.0865			−0.961189
$317$	0.0859997	+	0.148956i	0.00483022	+	0.00836619i	0.868430	−	0.495811i	$-0.165129\pi$
$317$	0.0859997	+	0.148956i	0.00483022	+	0.00836619i	−0.863600	+	0.504177i	$0.831796\pi$
$318$	−0.894400	+	1.54915i	−0.0501555	+	0.0868718i
$319$	−1.62449	+	2.81369i	−0.0909537	+	0.157536i
$320$	0.316552	+	0.548284i	0.0176958	+	0.0306500i
$321$	4.32089			0.241168
$322$	0.294101	−	1.83478i	0.0163896	−	0.102248i
$323$	39.5604			2.20120
$324$	6.13816	+	10.6316i	0.341009	+	0.590644i
$325$	−3.05778	+	5.29623i	−0.169615	+	0.293782i
$326$	−1.84090	+	3.18853i	−0.101958	+	0.176596i
$327$	−1.72668	−	2.99070i	−0.0954857	−	0.165386i
$328$	11.1702			0.616774
$329$	18.9586	+	15.4108i	1.04522	+	0.849628i
$330$	0.0222887			0.00122695
$331$	0.0543776	+	0.0941848i	0.00298886	+	0.00517686i	0.867516	−	0.497409i	$-0.165715\pi$
$331$	0.0543776	+	0.0941848i	0.00298886	+	0.00517686i	−0.864527	+	0.502586i	$0.832382\pi$
$332$	−6.59879	+	11.4294i	−0.362156	+	0.627272i
$333$	3.21894	−	5.57537i	0.176397	−	0.305528i
$334$	−3.67024	−	6.35705i	−0.200827	−	0.347842i
$335$	−0.369585			−0.0201926
$336$	4.32816	−	1.65219i	0.236121	−	0.0901345i
$337$	−4.69728			−0.255877			−0.127939	−	0.991782i	$-0.540836\pi$
$337$	−4.69728			−0.255877			−0.127939	+	0.991782i	$0.540836\pi$
$338$	−1.99613	−	3.45740i	−0.108575	−	0.188058i
$339$	−2.89053	+	5.00654i	−0.156992	+	0.271918i
$340$	0.699340	−	1.21129i	0.0379271	−	0.0656916i
$341$	−2.43969	−	4.22567i	−0.132117	−	0.228833i
$342$	6.04963			0.327127
$343$	−8.50000	+	16.4545i	−0.458957	+	0.888459i
$344$	3.00000			0.161749
$345$	−0.0648930	−	0.112398i	−0.00349372	−	0.00605130i
$346$	0.402856	−	0.697767i	0.0216577	−	0.0375122i
$347$	−2.07785	+	3.59894i	−0.111545	+	0.193201i	−0.916393	−	0.400279i	$-0.868913\pi$
$347$	−2.07785	+	3.59894i	−0.111545	+	0.193201i	0.804849	+	0.593480i	$0.202247\pi$
$348$	−1.62449	−	2.81369i	−0.0870815	−	0.150830i
$349$	16.4730			0.881778			0.440889	−	0.897562i	$-0.354663\pi$
$349$	16.4730			0.881778			0.440889	+	0.897562i	$0.354663\pi$
$350$	−4.27972	+	1.63370i	−0.228760	+	0.0873249i
$351$	−3.73143			−0.199169
$352$	1.91875	+	3.32337i	0.102270	+	0.177136i
$353$	11.3011	−	19.5741i	0.601498	−	1.04183i	−0.391096	−	0.920350i	$-0.627904\pi$
$353$	11.3011	−	19.5741i	0.601498	−	1.04183i	0.992594	−	0.121476i	$-0.0387627\pi$
$354$	0.900330	−	1.55942i	0.0478520	−	0.0828821i
$355$	0.512326	+	0.887375i	0.0271915	+	0.0470970i
$356$	12.9290			0.685236
$357$	−6.74035	−	5.47903i	−0.356737	−	0.289981i
$358$	−3.96585			−0.209602
$359$	17.5364	+	30.3740i	0.925537	+	1.60308i	0.790695	+	0.612210i	$0.209719\pi$
$359$	17.5364	+	30.3740i	0.925537	+	1.60308i	0.134842	+	0.990867i	$0.456947\pi$
$360$	0.220752	−	0.382353i	0.0116346	−	0.0201518i
$361$	−11.0535	+	19.1452i	−0.581763	+	1.00764i
$362$	2.85962	+	4.95301i	0.150298	+	0.260325i
$363$	−0.532089			−0.0279274
$364$	0.965385	−	6.02265i	0.0505999	−	0.315673i
$365$	0.426022			0.0222990
$366$	0.132474	+	0.229452i	0.00692454	+	0.0119937i
$367$	5.92989	−	10.2709i	0.309538	−	0.536135i	−0.668723	−	0.743511i	$-0.733159\pi$
$367$	5.92989	−	10.2709i	0.309538	−	0.536135i	0.978261	+	0.207376i	$0.0664923\pi$
$368$	3.32753	−	5.76346i	0.173460	−	0.300441i
$369$	11.2626	+	19.5075i	0.586310	+	1.01552i
$370$	−0.0992597			−0.00516027
$371$	4.05350	−	25.2882i	0.210447	−	1.31290i
$372$	4.87939			0.252984
$373$	−14.5077	−	25.1281i	−0.751182	−	1.30109i	−0.947250	−	0.320496i	$-0.896151\pi$
$373$	−14.5077	−	25.1281i	−0.751182	−	1.30109i	0.196068	−	0.980590i	$-0.437183\pi$
$374$	1.07145	−	1.85581i	0.0554035	−	0.0959616i
$375$	−0.320422	+	0.554987i	−0.0165465	+	0.0286594i
$376$	−6.22075	−	10.7747i	−0.320811	−	0.555661i
$377$	−3.98545			−0.205261
$378$	−2.16890	−	1.76303i	−0.111556	−	0.0906806i
$379$	18.2695			0.938441			0.469221	−	0.883081i	$-0.344535\pi$
$379$	18.2695			0.938441			0.469221	+	0.883081i	$0.344535\pi$
$380$	0.726682	+	1.25865i	0.0372780	+	0.0645674i
$381$	0.713011	−	1.23497i	0.0365287	−	0.0632695i
$382$	−1.93923	+	3.35884i	−0.0992194	+	0.171853i
$383$	7.71941	+	13.3704i	0.394443	+	0.683196i	0.993030	−	0.117862i	$-0.0376041\pi$
$383$	7.71941	+	13.3704i	0.394443	+	0.683196i	−0.598587	+	0.801058i	$0.704271\pi$
$384$	−5.05375			−0.257898
$385$	−0.298133	+	0.113807i	−0.0151943	+	0.00580012i
$386$	6.96316			0.354416
$387$	3.02481	+	5.23913i	0.153760	+	0.266320i
$388$	15.5351	−	26.9076i	0.788674	−	1.36602i
$389$	12.0214	−	20.8217i	0.609510	−	1.05570i	−0.381812	−	0.924240i	$-0.624700\pi$
$389$	12.0214	−	20.8217i	0.609510	−	1.05570i	0.991321	−	0.131462i	$-0.0419670\pi$
$390$	0.0136706	+	0.0236781i	0.000692236	+	0.00119899i
$391$	−12.4780			−0.631040
$392$	7.03209	−	6.28450i	0.355174	−	0.317415i
$393$	7.46379			0.376499
$394$	2.77719	+	4.81023i	0.139913	+	0.242336i
$395$	−0.548286	+	0.949659i	−0.0275872	+	0.0477825i
$396$	−2.55303	+	4.42198i	−0.128295	+	0.222213i
$397$	4.57398	+	7.92236i	0.229561	+	0.397612i	0.957678	−	0.287841i	$-0.0929375\pi$
$397$	4.57398	+	7.92236i	0.229561	+	0.397612i	−0.728117	+	0.685453i	$0.759604\pi$
$398$	−2.17705			−0.109126
$399$	8.43242	−	3.21891i	0.422149	−	0.161147i
$400$	−16.4064			−0.820321
$401$	−4.01501	−	6.95421i	−0.200500	−	0.347277i	0.748189	−	0.663485i	$-0.230923\pi$
$401$	−4.01501	−	6.95421i	−0.200500	−	0.347277i	−0.948690	+	0.316208i	$0.897590\pi$
$402$	0.283119	−	0.490376i	0.0141207	−	0.0244577i
$403$	2.99273	−	5.18355i	0.149078	−	0.258211i
$404$	−6.39053	−	11.0687i	−0.317941	−	0.550689i
$405$	0.787866			0.0391494
$406$	−2.31655	−	1.88305i	−0.114969	−	0.0934544i
$407$	2.36959			0.117456
$408$	2.21167	+	3.83072i	0.109494	+	0.189649i
$409$	−0.907604	+	1.57202i	−0.0448781	+	0.0777312i	−0.887592	−	0.460631i	$-0.847623\pi$
$409$	−0.907604	+	1.57202i	−0.0448781	+	0.0777312i	0.842714	+	0.538362i	$0.180957\pi$
$410$	0.173648	−	0.300767i	0.00857587	−	0.0148538i
$411$	3.89512	+	6.74654i	0.192132	+	0.332782i
$412$	17.2344			0.849079
$413$	−4.08037	+	25.4558i	−0.200782	+	1.25260i
$414$	−1.90816			−0.0937808
$415$	0.423496	+	0.733516i	0.0207886	+	0.0360069i
$416$	−2.35369	+	4.07672i	−0.115399	+	0.199877i
$417$	2.93061	−	5.07596i	0.143512	−	0.248571i
$418$	1.11334	+	1.92836i	0.0544553	+	0.0943193i
$419$	−36.3756			−1.77706			−0.888531	−	0.458816i	$-0.848274\pi$
$419$	−36.3756			−1.77706			−0.888531	+	0.458816i	$0.848274\pi$
$420$	0.0505072	−	0.315094i	0.00246450	−	0.0153750i
$421$	−13.3432			−0.650307			−0.325153	−	0.945661i	$-0.605416\pi$
$421$	−13.3432			−0.650307			−0.325153	+	0.945661i	$0.605416\pi$
$422$	1.92127	+	3.32774i	0.0935262	+	0.161992i
$423$	12.5444	−	21.7276i	0.609930	−	1.05643i
$424$	−6.52094	+	11.2946i	−0.316685	+	0.548515i
$425$	15.3807	+	26.6402i	0.746075	+	1.29224i
$426$	−1.56986			−0.0760599
$427$	−2.94356	−	2.39273i	−0.142449	−	0.115792i
$428$	15.2618			0.737705
$429$	−0.326352	−	0.565258i	−0.0157564	−	0.0272909i
$430$	0.0466368	−	0.0807773i	0.00224903	−	0.00389543i
$431$	−5.39899	+	9.35132i	−0.260060	+	0.450437i	−0.966258	−	0.257578i	$-0.917076\pi$
$431$	−5.39899	+	9.35132i	−0.260060	+	0.450437i	0.706198	+	0.708015i	$0.250409\pi$
$432$	−5.00521	−	8.66929i	−0.240813	−	0.417101i
$433$	−17.8425			−0.857458			−0.428729	−	0.903433i	$-0.641039\pi$
$433$	−17.8425			−0.857458			−0.428729	+	0.903433i	$0.641039\pi$
$434$	4.18866	−	1.59894i	0.201062	−	0.0767517i
$435$	−0.208512			−0.00999737
$436$	−6.09879	−	10.5634i	−0.292079	−	0.505896i
$437$	6.48293	−	11.2288i	0.310120	−	0.537144i
$438$	−0.326352	+	0.565258i	−0.0155937	+	0.0270091i
$439$	4.64425	+	8.04407i	0.221658	+	0.383923i	0.955312	−	0.295601i	$-0.0955199\pi$
$439$	4.64425	+	8.04407i	0.221658	+	0.383923i	−0.733654	+	0.679524i	$0.762187\pi$
$440$	0.162504			0.00774707
$441$	18.0654	+	5.94420i	0.860255	+	0.283057i
$442$	2.62866			0.125033
$443$	−8.21095	−	14.2218i	−0.390114	−	0.675697i	0.602350	−	0.798232i	$-0.294231\pi$
$443$	−8.21095	−	14.2218i	−0.390114	−	0.675697i	−0.992464	+	0.122535i	$0.960898\pi$
$444$	−1.18479	+	2.05212i	−0.0562278	+	0.0973893i
$445$	0.414878	−	0.718589i	0.0196671	−	0.0340644i
$446$	1.60741	+	2.78412i	0.0761131	+	0.131832i
$447$	−7.83750			−0.370701
$448$	12.9743	−	4.95269i	0.612978	−	0.233993i
$449$	−36.5621			−1.72547			−0.862737	−	0.505654i	$-0.831251\pi$
$449$	−36.5621			−1.72547			−0.862737	+	0.505654i	$0.831251\pi$
$450$	2.35204	+	4.07386i	0.110876	+	0.192044i
$451$	−4.14543	+	7.18009i	−0.195201	+	0.338097i
$452$	−10.2096	+	17.6836i	−0.480220	+	0.831765i
$453$	6.18345	+	10.7100i	0.290524	+	0.503202i
$454$	7.12155			0.334231
$455$	−0.303758	−	0.246916i	−0.0142404	−	0.0115756i
$456$	−4.59627			−0.215240
$457$	4.49660	+	7.78833i	0.210342	+	0.364323i	0.951822	−	0.306653i	$-0.0992089\pi$
$457$	4.49660	+	7.78833i	0.210342	+	0.364323i	−0.741480	+	0.670975i	$0.765876\pi$
$458$	4.52600	−	7.83926i	0.211486	−	0.366304i
$459$	−9.38460	+	16.2546i	−0.438036	+	0.758700i
$460$	−0.229208	−	0.397000i	−0.0106869	−	0.0185102i
$461$	13.8844			0.646663			0.323331	−	0.946286i	$-0.395197\pi$
$461$	13.8844			0.646663			0.323331	+	0.946286i	$0.395197\pi$
$462$	0.0773815	−	0.482753i	0.00360011	−	0.0224597i
$463$	−11.0624			−0.514114			−0.257057	−	0.966396i	$-0.582753\pi$
$463$	−11.0624			−0.514114			−0.257057	+	0.966396i	$0.582753\pi$
$464$	−5.34595	−	9.25946i	−0.248180	−	0.429860i
$465$	0.156574	−	0.271194i	0.00726095	−	0.0125763i
$466$	0.484108	−	0.838499i	0.0224259	−	0.0388427i
$467$	−2.54829	−	4.41376i	−0.117921	−	0.204244i	0.801023	−	0.598634i	$-0.204289\pi$
$467$	−2.54829	−	4.41376i	−0.117921	−	0.204244i	−0.918943	+	0.394389i	$0.870956\pi$
$468$	−6.26352			−0.289531
$469$	−1.28312	+	8.00487i	−0.0592489	+	0.369630i
$470$	−0.386821			−0.0178427
$471$	4.27379	+	7.40241i	0.196926	+	0.341085i
$472$	6.56418	−	11.3695i	0.302141	−	0.523323i
$473$	−1.11334	+	1.92836i	−0.0511915	+	0.0886662i
$474$	−0.840022	−	1.45496i	−0.0385835	−	0.0668286i
$475$	−31.9641			−1.46661
$476$	−23.8075	−	19.3524i	−1.09122	−	0.887016i
$477$	−26.2995			−1.20417
$478$	−1.94831	−	3.37457i	−0.0891137	−	0.154349i
$479$	−9.49706	+	16.4494i	−0.433932	+	0.751592i	−0.997208	−	0.0746768i	$-0.976207\pi$
$479$	−9.49706	+	16.4494i	−0.433932	+	0.751592i	0.563276	+	0.826269i	$0.309541\pi$
$480$	−0.123141	+	0.213286i	−0.00562059	+	0.00973515i
$481$	1.45336	+	2.51730i	0.0662677	+	0.114779i
$482$	−3.56179			−0.162235
$483$	−2.65973	+	1.01530i	−0.121022	+	0.0461978i
$484$	−1.87939			−0.0854266
$485$	−0.997007	−	1.72687i	−0.0452718	−	0.0784130i
$486$	−2.18820	+	3.79007i	−0.0992586	+	0.171921i
$487$	9.36231	−	16.2160i	0.424247	−	0.734817i	−0.572103	−	0.820182i	$-0.693872\pi$
$487$	9.36231	−	16.2160i	0.424247	−	0.734817i	0.996350	+	0.0853648i	$0.0272056\pi$
$488$	0.965852	+	1.67290i	0.0437221	+	0.0757288i
$489$	5.64084			0.255088
$490$	−0.0598969	−	0.287041i	−0.00270586	−	0.0129672i
$491$	3.08378			0.139169			0.0695845	−	0.997576i	$-0.477833\pi$
$491$	3.08378			0.139169			0.0695845	+	0.997576i	$0.477833\pi$
$492$	−4.14543	−	7.18009i	−0.186890	−	0.323704i
$493$	−10.0235	+	17.3612i	−0.451434	+	0.781907i
$494$	−1.36571	+	2.36549i	−0.0614464	+	0.106428i
$495$	0.163848	+	0.283793i	0.00736442	+	0.0127555i
$496$	16.0574			0.720997
$497$	20.9984	−	8.01574i	0.941907	−	0.359555i
$498$	−1.29767			−0.0581498
$499$	−4.81433	−	8.33866i	−0.215519	−	0.373290i	0.737914	−	0.674895i	$-0.235811\pi$
$499$	−4.81433	−	8.33866i	−0.215519	−	0.373290i	−0.953433	+	0.301605i	$0.902478\pi$
$500$	−1.13176	+	1.96026i	−0.0506138	+	0.0876657i
$501$	−5.62314	+	9.73957i	−0.251223	+	0.435132i
$502$	5.05690	+	8.75881i	0.225701	+	0.390925i
$503$	−0.802414			−0.0357779			−0.0178889	−	0.999840i	$-0.505695\pi$
$503$	−0.802414			−0.0357779			−0.0178889	+	0.999840i	$0.505695\pi$
$504$	−7.51501	−	6.10873i	−0.334745	−	0.272104i
$505$	−0.820260			−0.0365011
$506$	−0.351167	−	0.608239i	−0.0156113	−	0.0270395i
$507$	−3.05825	+	5.29704i	−0.135822	+	0.235250i
$508$	2.51842	−	4.36203i	0.111737	−	0.193534i
$509$	7.32429	+	12.6860i	0.324644	+	0.562299i	0.981440	−	0.191769i	$-0.0614223\pi$
$509$	7.32429	+	12.6860i	0.324644	+	0.562299i	−0.656797	+	0.754068i	$0.728089\pi$
$510$	0.137527			0.00608979
$511$	1.47906	−	9.22724i	0.0654296	−	0.408189i
$512$	−21.4962			−0.950006
$513$	−9.75150	−	16.8901i	−0.430539	−	0.745716i
$514$	1.45811	−	2.52552i	0.0643145	−	0.111396i
$515$	0.553033	−	0.957882i	0.0243696	−	0.0422093i
$516$	−1.11334	−	1.92836i	−0.0490121	−	0.0848914i
$517$	9.23442			0.406129
$518$	−0.344608	+	2.14987i	−0.0151412	+	0.0944600i
$519$	−1.23442			−0.0541851
$520$	0.0996702	+	0.172634i	0.00437083	+	0.00757050i
$521$	−6.01620	+	10.4204i	−0.263574	+	0.456524i	−0.967189	−	0.254057i	$-0.918235\pi$
$521$	−6.01620	+	10.4204i	−0.263574	+	0.456524i	0.703615	+	0.710582i	$0.251568\pi$
$522$	−1.53280	+	2.65489i	−0.0670890	+	0.116202i
$523$	7.65136	+	13.2525i	0.334571	+	0.579493i	0.983402	−	0.181439i	$-0.0580754\pi$
$523$	7.65136	+	13.2525i	0.334571	+	0.579493i	−0.648832	+	0.760932i	$0.724742\pi$
$524$	26.3628			1.15166
$525$	5.44609	+	4.42696i	0.237687	+	0.193208i
$526$	8.46110			0.368922
$527$	−15.0535	−	26.0734i	−0.655741	−	1.13578i
$528$	0.875515	−	1.51644i	0.0381019	−	0.0659944i
$529$	9.45517	−	16.3768i	0.411095	−	0.712037i
$530$	0.202744	+	0.351163i	0.00880664	+	0.0152535i
$531$	26.4739			1.14887
$532$	29.7841	−	11.3695i	1.29130	−	0.492930i
$533$	−10.1702			−0.440522
$534$	0.635630	+	1.10094i	0.0275064	+	0.0476424i
$535$	0.489733	−	0.848242i	0.0211730	−	0.0366727i
$536$	2.06418	−	3.57526i	0.0891589	−	0.154428i
$537$	3.03802	+	5.26200i	0.131100	+	0.227072i
$538$	−10.1379			−0.437074
$539$	1.42989	+	6.85240i	0.0615898	+	0.295154i
$540$	−0.689540			−0.0296731
$541$	8.24304	+	14.2774i	0.354396	+	0.613832i	0.987014	−	0.160632i	$-0.0513532\pi$
$541$	8.24304	+	14.2774i	0.354396	+	0.613832i	−0.632618	+	0.774464i	$0.718020\pi$
$542$	1.66116	−	2.87721i	0.0713529	−	0.123587i
$543$	4.38120	−	7.58845i	0.188015	−	0.325652i
$544$	11.8391	+	20.5060i	0.507599	+	0.879188i
$545$	−0.782814			−0.0335321
$546$	0.560307	−	0.213887i	0.0239789	−	0.00915350i
$547$	−16.0060			−0.684367			−0.342183	−	0.939633i	$-0.611166\pi$
$547$	−16.0060			−0.684367			−0.342183	+	0.939633i	$0.611166\pi$
$548$	13.7579	+	23.8294i	0.587708	+	1.01794i
$549$	−1.94768	+	3.37348i	−0.0831250	+	0.143977i
$550$	−0.865715	+	1.49946i	−0.0369142	+	0.0639373i
$551$	−10.4153	−	18.0399i	−0.443709	−	0.768526i
$552$	1.44974			0.0617051
$553$	18.6652	+	15.1724i	0.793725	+	0.645195i
$554$	7.04364			0.299256
$555$	0.0760373	+	0.131701i	0.00322761	+	0.00559038i
$556$	10.3512	−	17.9287i	0.438987	−	0.760348i
$557$	−9.66431	+	16.7391i	−0.409490	+	0.709258i	−0.994833	−	0.101528i	$-0.967627\pi$
$557$	−9.66431	+	16.7391i	−0.409490	+	0.709258i	0.585342	+	0.810786i	$0.300960\pi$
$558$	−2.30200	−	3.98719i	−0.0974516	−	0.168791i
$559$	−2.73143			−0.115527
$560$	0.166212	−	1.03693i	0.00702374	−	0.0438183i
$561$	−3.28312			−0.138613
$562$	−0.959455	−	1.66182i	−0.0404722	−	0.0700999i
$563$	16.2306	−	28.1121i	0.684036	−	1.18479i	−0.289702	−	0.957117i	$-0.593556\pi$
$563$	16.2306	−	28.1121i	0.684036	−	1.18479i	0.973739	−	0.227669i	$-0.0731103\pi$
$564$	−4.61721	+	7.99724i	−0.194420	+	0.336745i
$565$	0.655230	+	1.13489i	0.0275657	+	0.0477452i
$566$	−1.41241			−0.0593679
$567$	2.73530	−	17.0644i	0.114872	−	0.716640i
$568$	−11.4456			−0.480248
$569$	2.22328	+	3.85083i	0.0932047	+	0.161435i	0.908858	−	0.417106i	$-0.136956\pi$
$569$	2.22328	+	3.85083i	0.0932047	+	0.161435i	−0.815653	+	0.578541i	$0.803622\pi$
$570$	−0.0714517	+	0.123758i	−0.00299278	+	0.00518365i
$571$	−3.88073	+	6.72162i	−0.162403	+	0.281291i	−0.935730	−	0.352717i	$-0.885258\pi$
$571$	−3.88073	+	6.72162i	−0.162403	+	0.281291i	0.773327	+	0.634008i	$0.218591\pi$
$572$	−1.15270	−	1.99654i	−0.0481970	−	0.0834796i
$573$	5.94213			0.248236
$574$	−5.91147	−	4.80526i	−0.246740	−	0.200568i
$575$	10.0820			0.420449
$576$	−7.13041	−	12.3502i	−0.297101	−	0.514593i
$577$	10.7652	−	18.6458i	0.448160	−	0.776235i	−0.550107	−	0.835094i	$-0.685413\pi$
$577$	10.7652	−	18.6458i	0.448160	−	0.776235i	0.998266	+	0.0588590i	$0.0187462\pi$
$578$	3.65910	−	6.33775i	0.152199	−	0.263616i
$579$	−5.33409	−	9.23892i	−0.221677	−	0.383956i
$580$	−0.736482			−0.0305807
$581$	17.3576	−	6.62592i	0.720113	−	0.274889i
$582$	3.05501			0.126634
$583$	−4.84002	−	8.38316i	−0.200453	−	0.347195i
$584$	−2.37939	+	4.12122i	−0.0984597	+	0.170537i
$585$	−0.200989	+	0.348124i	−0.00830989	+	0.0143931i
$586$	−4.03849	−	6.99486i	−0.166828	−	0.288955i
$587$	24.2523			1.00100			0.500499	−	0.865737i	$-0.333150\pi$
$587$	24.2523			1.00100			0.500499	+	0.865737i	$0.333150\pi$
$588$	−6.64930	−	2.18788i	−0.274213	−	0.0902266i
$589$	31.2841			1.28904
$590$	−0.204088	−	0.353491i	−0.00840218	−	0.0145530i
$591$	4.25490	−	7.36970i	0.175023	−	0.303149i
$592$	−3.89899	+	6.75324i	−0.160247	+	0.277557i
$593$	4.12923	+	7.15204i	0.169567	+	0.293699i	0.938268	−	0.345910i	$-0.112430\pi$
$593$	4.12923	+	7.15204i	0.169567	+	0.293699i	−0.768701	+	0.639609i	$0.779096\pi$
$594$	−1.05644			−0.0433461
$595$	−1.83956	+	0.702215i	−0.0754144	+	0.0287880i
$596$	−27.6827			−1.13393
$597$	1.66772	+	2.88857i	0.0682552	+	0.118221i
$598$	0.430770	−	0.746115i	0.0176155	−	0.0305109i
$599$	−7.24170	+	12.5430i	−0.295888	+	0.512493i	−0.975191	−	0.221365i	$-0.928949\pi$
$599$	−7.24170	+	12.5430i	−0.295888	+	0.512493i	0.679303	+	0.733858i	$0.262282\pi$
$600$	−1.78699	−	3.09516i	−0.0729535	−	0.126359i
$601$	−9.81109			−0.400203			−0.200101	−	0.979775i	$-0.564127\pi$
$601$	−9.81109			−0.400203			−0.200101	+	0.979775i	$0.564127\pi$
$602$	−1.58765	−	1.29055i	−0.0647077	−	0.0525989i
$603$	8.32501			0.339021
$604$	21.8405	+	37.8288i	0.888677	+	1.53923i
$605$	−0.0603074	+	0.104455i	−0.00245184	+	0.00424672i
$606$	0.628356	−	1.08834i	0.0255252	−	0.0442109i
$607$	17.5355	+	30.3725i	0.711746	+	1.23278i	0.964201	+	0.265172i	$0.0854286\pi$
$607$	17.5355	+	30.3725i	0.711746	+	1.23278i	−0.252455	+	0.967609i	$0.581238\pi$
$608$	−24.6040			−0.997824
$609$	−0.723907	+	4.51617i	−0.0293342	+	0.183004i
$610$	0.0600590			0.00243172
$611$	5.66385	+	9.81007i	0.229135	+	0.396873i
$612$	−15.7528	+	27.2847i	−0.636771	+	1.10292i
$613$	17.9094	−	31.0200i	0.723354	−	1.25289i	−0.236293	−	0.971682i	$-0.575933\pi$
$613$	17.9094	−	31.0200i	0.723354	−	1.25289i	0.959648	−	0.281205i	$-0.0907340\pi$
$614$	−2.65910	−	4.60570i	−0.107313	−	0.185871i
$615$	−0.532089			−0.0214559
$616$	0.564178	−	3.51968i	0.0227314	−	0.141812i
$617$	0.650015			0.0261686			0.0130843	−	0.999914i	$-0.495835\pi$
$617$	0.650015			0.0261686			0.0130843	+	0.999914i	$0.495835\pi$
$618$	0.847296	+	1.46756i	0.0340833	+	0.0590339i
$619$	−8.07873	+	13.9928i	−0.324711	+	0.562417i	−0.981454	−	0.191698i	$-0.938601\pi$
$619$	−8.07873	+	13.9928i	−0.324711	+	0.562417i	0.656743	+	0.754115i	$0.271934\pi$
$620$	0.553033	−	0.957882i	0.0222104	−	0.0384695i
$621$	3.07579	+	5.32742i	0.123427	+	0.213782i
$622$	2.45605			0.0984787
$623$	−14.1236	−	11.4806i	−0.565850	−	0.459962i
$624$	2.14796			0.0859871
$625$	−12.3910	−	21.4618i	−0.495640	−	0.858473i
$626$	4.58394	−	7.93962i	0.183211	−	0.317331i
$627$	1.70574	−	2.95442i	0.0681206	−	0.117988i
$628$	15.0954	+	26.1460i	0.602372	+	1.04334i
$629$	14.6209			0.582974
$630$	−0.281308	+	0.107384i	−0.0112076	+	0.00427827i
$631$	4.31584			0.171811			0.0859054	−	0.996303i	$-0.472622\pi$
$631$	4.31584			0.171811			0.0859054	+	0.996303i	$0.472622\pi$
$632$	−6.12449	−	10.6079i	−0.243619	−	0.421960i
$633$	2.94356	−	5.09840i	0.116996	−	0.202643i
$634$	−0.0298674	+	0.0517318i	−0.00118618	+	0.00205453i
$635$	−0.161626	−	0.279945i	−0.00641395	−	0.0111093i
$636$	9.68004			0.383839
$637$	−6.40255	+	5.72189i	−0.253678	+	0.226709i
$638$	−1.12836			−0.0446720
$639$	−11.5403	−	19.9884i	−0.456527	−	0.790728i
$640$	−0.572796	+	0.992112i	−0.0226417	+	0.0392167i
$641$	−6.45929	+	11.1878i	−0.255127	+	0.441892i	−0.964930	−	0.262508i	$-0.915451\pi$
$641$	−6.45929	+	11.1878i	−0.255127	+	0.441892i	0.709803	+	0.704400i	$0.248784\pi$
$642$	0.750314	+	1.29958i	0.0296126	+	0.0512904i
$643$	−42.4296			−1.67326			−0.836631	−	0.547767i	$-0.815478\pi$
$643$	−42.4296			−1.67326			−0.836631	+	0.547767i	$0.815478\pi$
$644$	−9.39440	+	3.58613i	−0.370191	+	0.141313i
$645$	−0.142903			−0.00562682
$646$	6.86959	+	11.8985i	0.270280	+	0.468139i
$647$	15.1215	−	26.1913i	0.594489	−	1.02969i	−0.399129	−	0.916895i	$-0.630688\pi$
$647$	15.1215	−	26.1913i	0.594489	−	1.02969i	0.993619	−	0.112791i	$-0.0359791\pi$
$648$	−4.40033	+	7.62159i	−0.172861	+	0.299405i
$649$	4.87211	+	8.43874i	0.191247	+	0.331250i
$650$	−2.12391			−0.0833067
$651$	−5.33022	−	4.33277i	−0.208908	−	0.169815i
$652$	19.9240			0.780283
$653$	5.10354	+	8.83959i	0.199717	+	0.345920i	0.948437	−	0.316967i	$-0.102664\pi$
$653$	5.10354	+	8.83959i	0.199717	+	0.345920i	−0.748720	+	0.662887i	$0.769331\pi$
$654$	0.599670	−	1.03866i	0.0234490	−	0.0406148i
$655$	0.845952	−	1.46523i	0.0330541	−	0.0572514i
$656$	−13.6420	−	23.6287i	−0.532632	−	0.922545i
$657$	−9.59627			−0.374386
$658$	−1.34296	+	8.37819i	−0.0523540	+	0.326616i
$659$	−27.9777			−1.08986			−0.544928	−	0.838483i	$-0.683443\pi$
$659$	−27.9777			−1.08986			−0.544928	+	0.838483i	$0.683443\pi$
$660$	−0.0603074	−	0.104455i	−0.00234746	−	0.00406592i
$661$	−4.08260	+	7.07126i	−0.158795	+	0.275040i	−0.934434	−	0.356136i	$-0.884094\pi$
$661$	−4.08260	+	7.07126i	−0.158795	+	0.275040i	0.775640	+	0.631176i	$0.217427\pi$
$662$	−0.0188851	+	0.0327100i	−0.000733992	+	0.00127131i
$663$	−2.01367	−	3.48778i	−0.0782045	−	0.135454i
$664$	−9.46110			−0.367162
$665$	0.323826	−	2.02022i	0.0125574	−	0.0783407i
$666$	2.23585			0.0866375
$667$	3.28518	+	5.69010i	0.127203	+	0.220321i
$668$	−19.8614	+	34.4010i	−0.768462	+	1.33102i
$669$	2.46270	−	4.26552i	0.0952133	−	0.164914i
$670$	−0.0641778	−	0.111159i	−0.00247940	−	0.00429445i
$671$	−1.43376			−0.0553498
$672$	4.19207	+	3.40760i	0.161712	+	0.131451i
$673$	17.6905			0.681918			0.340959	−	0.940078i	$-0.389248\pi$
$673$	17.6905			0.681918			0.340959	+	0.940078i	$0.389248\pi$
$674$	−0.815674	−	1.41279i	−0.0314186	−	0.0544186i
$675$	7.58260	−	13.1334i	0.291854	−	0.505506i
$676$	−10.8020	+	18.7096i	−0.415462	+	0.719601i
$677$	−22.5530	−	39.0630i	−0.866783	−	1.50131i	−0.865265	−	0.501314i	$-0.832850\pi$
$677$	−22.5530	−	39.0630i	−0.866783	−	1.50131i	−0.00151816	−	0.999999i	$-0.500483\pi$
$678$	−2.00774			−0.0771068
$679$	−40.8637	+	15.5989i	−1.56821	+	0.598632i
$680$	1.00269			0.0384513
$681$	−5.45542	−	9.44907i	−0.209052	−	0.362089i
$682$	0.847296	−	1.46756i	0.0324447	−	0.0561958i
$683$	5.30019	−	9.18020i	0.202806	−	0.351271i	−0.746625	−	0.665245i	$-0.768327\pi$
$683$	5.30019	−	9.18020i	0.202806	−	0.351271i	0.949432	+	0.313974i	$0.101661\pi$
$684$	−16.3687	−	28.3514i	−0.625873	−	1.08404i
$685$	1.76590			0.0674716
$686$	−6.42498	+	0.300767i	−0.245307	+	0.0114834i
$687$	−13.8685			−0.529115
$688$	−3.66385	−	6.34597i	−0.139683	−	0.241938i
$689$	5.93717	−	10.2835i	0.226188	−	0.391769i
$690$	0.0225371	−	0.0390354i	0.000857973	−	0.00148605i
$691$	−4.00000	−	6.92820i	−0.152167	−	0.263561i	0.779857	−	0.625958i	$-0.215292\pi$
$691$	−4.00000	−	6.92820i	−0.152167	−	0.263561i	−0.932024	+	0.362397i	$0.881959\pi$
$692$	−4.36009			−0.165746
$693$	6.71554	−	2.56353i	0.255102	−	0.0973803i
$694$	−1.44326			−0.0547853
$695$	−0.664315	−	1.15063i	−0.0251989	−	0.0436458i
$696$	1.16456	−	2.01708i	0.0441427	−	0.0764573i
$697$	−25.5783	+	44.3029i	−0.968848	+	1.67809i
$698$	2.86050	+	4.95453i	0.108272	+	0.187532i
$699$	−1.48339			−0.0561071
$700$	19.2361	+	15.6364i	0.727055	+	0.591001i
$701$	41.0533			1.55056			0.775280	−	0.631618i	$-0.217609\pi$
$701$	41.0533			1.55056			0.775280	+	0.631618i	$0.217609\pi$
$702$	−0.647956	−	1.12229i	−0.0244555	−	0.0423582i
$703$	−7.59627	+	13.1571i	−0.286499	+	0.496230i
$704$	2.62449	−	4.54574i	0.0989140	−	0.171324i
$705$	0.296322	+	0.513245i	0.0111601	+	0.0193299i
$706$	7.84968			0.295427
$707$	−2.84776	+	17.7661i	−0.107101	+	0.668162i
$708$	−9.74422			−0.366210
$709$	16.5535	+	28.6715i	0.621680	+	1.07678i	0.989173	+	0.146755i	$0.0468828\pi$
$709$	16.5535	+	28.6715i	0.621680	+	1.07678i	−0.367493	+	0.930026i	$0.619784\pi$
$710$	−0.177929	+	0.308182i	−0.00667756	+	0.0115659i
$711$	12.3503	−	21.3913i	0.463172	−	0.802238i
$712$	4.63429	+	8.02682i	0.173677	+	0.300818i
$713$	−9.86753			−0.369542
$714$	0.477463	−	2.97870i	0.0178686	−	0.111475i
$715$	−0.147956			−0.00553324
$716$	10.7306	+	18.5859i	0.401020	+	0.694586i
$717$	−2.98499	+	5.17015i	−0.111476	+	0.193083i
$718$	−6.09034	+	10.5488i	−0.227289	+	0.393677i
$719$	−13.7576	−	23.8288i	−0.513071	−	0.888666i	−0.999885	−	0.0151600i	$-0.995174\pi$
$719$	−13.7576	−	23.8288i	−0.513071	−	0.888666i	0.486814	−	0.873506i	$-0.338159\pi$
$720$	−1.07840			−0.0401896
$721$	−18.8268	−	15.3037i	−0.701147	−	0.569941i
$722$	−7.67768			−0.285734
$723$	2.72849	+	4.72589i	0.101474	+	0.175758i
$724$	15.4748	−	26.8031i	0.575115	−	0.996129i
$725$	8.09879	−	14.0275i	0.300782	−	0.520969i
$726$	−0.0923963	−	0.160035i	−0.00342915	−	0.00593946i
$727$	10.1111			0.375001			0.187500	−	0.982265i	$-0.439961\pi$
$727$	10.1111			0.375001			0.187500	+	0.982265i	$0.439961\pi$
$728$	4.08512	−	1.55942i	0.151405	−	0.0577958i
$729$	−12.8912			−0.477454
$730$	0.0739780	+	0.128134i	0.00273805	+	0.00474244i
$731$	−6.86959	+	11.8985i	−0.254081	+	0.440081i
$732$	0.716881	−	1.24168i	0.0264967	−	0.0458936i
$733$	−18.9354	−	32.7971i	−0.699395	−	1.21139i	−0.968676	−	0.248327i	$-0.920119\pi$
$733$	−18.9354	−	32.7971i	−0.699395	−	1.21139i	0.269281	−	0.963062i	$-0.413214\pi$
$734$	4.11886			0.152030
$735$	−0.334970	+	0.299359i	−0.0123556	+	0.0110420i
$736$	7.76053			0.286057
$737$	1.53209	+	2.65366i	0.0564352	+	0.0977487i
$738$	−3.91147	+	6.77487i	−0.143983	+	0.249386i
$739$	−0.441037	+	0.763898i	−0.0162238	+	0.0281004i	−0.874023	−	0.485884i	$-0.838498\pi$
$739$	−0.441037	+	0.763898i	−0.0162238	+	0.0281004i	0.857800	+	0.513984i	$0.171831\pi$
$740$	0.268571	+	0.465178i	0.00987285	+	0.0171003i
$741$	4.18479			0.153732
$742$	8.30974	−	3.17209i	0.305060	−	0.116451i
$743$	22.5800			0.828379			0.414189	−	0.910191i	$-0.364065\pi$
$743$	22.5800			0.828379			0.414189	+	0.910191i	$0.364065\pi$
$744$	1.74897	+	3.02931i	0.0641204	+	0.111060i
$745$	−0.888308	+	1.53859i	−0.0325451	+	0.0563697i
$746$	5.03849	−	8.72691i	0.184472	−	0.319515i
$747$	−9.53936	−	16.5227i	−0.349027	−	0.604533i
$748$	−11.5963			−0.424002
$749$	−16.6719	−	13.5521i	−0.609178	−	0.495182i
$750$	−0.222563			−0.00812684
$751$	19.7977	+	34.2907i	0.722429	+	1.25128i	0.960023	+	0.279920i	$0.0903078\pi$
$751$	19.7977	+	34.2907i	0.722429	+	1.25128i	−0.237594	+	0.971364i	$0.576359\pi$
$752$	−15.1946	+	26.3178i	−0.554090	+	0.959712i
$753$	7.74763	−	13.4193i	0.282339	−	0.489026i
$754$	−0.692066	−	1.19869i	−0.0252036	−	0.0436539i
$755$	2.80335			0.102024
$756$	−2.39393	+	14.9348i	−0.0870665	+	0.543173i
$757$	19.5253			0.709658			0.354829	−	0.934931i	$-0.384539\pi$
$757$	19.5253			0.709658			0.354829	+	0.934931i	$0.384539\pi$
$758$	3.17247	+	5.49487i	0.115229	+	0.199583i
$759$	−0.538019	+	0.931876i	−0.0195288	+	0.0338249i
$760$	−0.520945	+	0.902302i	−0.0188966	+	0.0327299i
$761$	11.6047	+	20.1000i	0.420671	+	0.728623i	0.996005	−	0.0892950i	$-0.0284614\pi$
$761$	11.6047	+	20.1000i	0.420671	+	0.728623i	−0.575334	+	0.817918i	$0.695128\pi$
$762$	0.495252			0.0179411
$763$	−2.71776	+	16.9550i	−0.0983895	+	0.613813i
$764$	20.9881			0.759324
$765$	1.01098	+	1.75107i	0.0365521	+	0.0633102i
$766$	−2.68092	+	4.64349i	−0.0968657	+	0.167776i
$767$	−5.97653	+	10.3517i	−0.215800	+	0.373777i
$768$	1.91534	+	3.31747i	0.0691140	+	0.119709i
$769$	37.2222			1.34227			0.671134	−	0.741336i	$-0.265807\pi$
$769$	37.2222			1.34227			0.671134	+	0.741336i	$0.265807\pi$
$770$	−0.0859997	−	0.0699065i	−0.00309921	−	0.00251925i
$771$	−4.46791			−0.160908
$772$	−18.8405	−	32.6327i	−0.678084	−	1.17448i
$773$	−20.6446	+	35.7574i	−0.742533	+	1.28610i	0.208806	+	0.977957i	$0.433042\pi$
$773$	−20.6446	+	35.7574i	−0.742533	+	1.28610i	−0.951339	+	0.308148i	$0.900291\pi$
$774$	−1.05051	+	1.81953i	−0.0377597	+	0.0654017i
$775$	12.1630	+	21.0669i	0.436907	+	0.756745i
$776$	22.2736			0.799576
$777$	3.11650	−	1.18966i	0.111804	−	0.0426789i
$778$	8.34998			0.299361
$779$	−26.5783	−	46.0350i	−0.952267	−	1.64937i
$780$	0.0739780	−	0.128134i	0.00264884	−	0.00458792i
$781$	4.24763	−	7.35710i	0.151992	−	0.263258i
$782$	−2.16678	−	3.75298i	−0.0774841	−	0.134206i
$783$	9.88301			0.353190
$784$	−21.8819	−	7.20000i	−0.781497	−	0.257143i
$785$	1.93758			0.0691551
$786$	1.29607	+	2.24487i	0.0462294	+	0.0800717i
$787$	11.2660	−	19.5134i	0.401591	−	0.695576i	−0.592327	−	0.805698i	$-0.701791\pi$
$787$	11.2660	−	19.5134i	0.401591	−	0.695576i	0.993918	+	0.110121i	$0.0351240\pi$
$788$	15.0287	−	26.0304i	0.535375	−	0.927296i
$789$	−6.48158	−	11.2264i	−0.230750	−	0.399671i
$790$	−0.380835			−0.0135495
$791$	26.8555	−	10.2516i	0.954872	−	0.364504i
$792$	−3.66044			−0.130068
$793$	−0.879385	−	1.52314i	−0.0312279	−	0.0540883i
$794$	−1.58853	+	2.75141i	−0.0563747	+	0.0976438i
$795$	0.310622	−	0.538013i	0.0110166	−	0.0190813i
$796$	5.89053	+	10.2027i	0.208784	+	0.361625i
$797$	−4.79528			−0.169858			−0.0849288	−	0.996387i	$-0.527066\pi$
$797$	−4.79528			−0.169858			−0.0849288	+	0.996387i	$0.527066\pi$
$798$	2.43242	+	1.97724i	0.0861067	+	0.0699935i
$799$	56.9786			2.01576
$800$	−9.56583	−	16.5685i	−0.338203	−	0.585785i
$801$	−9.34524	+	16.1864i	−0.330198	+	0.571919i
$802$	1.39440	−	2.41517i	0.0492380	−	0.0852827i
$803$	−1.76604	−	3.05888i	−0.0623224	−	0.107945i
$804$	−3.06418			−0.108065
$805$	−0.102140	+	0.637212i	−0.00359997	+	0.0224588i
$806$	2.07873			0.0732200
$807$	7.76604	+	13.4512i	0.273378	+	0.473504i
$808$	4.58125	−	7.93496i	0.161168	−	0.279151i
$809$	20.4590	−	35.4361i	0.719302	−	1.24587i	−0.241975	−	0.970282i	$-0.577795\pi$
$809$	20.4590	−	35.4361i	0.719302	−	1.24587i	0.961277	−	0.275585i	$-0.0888714\pi$
$810$	0.136812	+	0.236965i	0.00480707	+	0.00832609i
$811$	−30.8408			−1.08297			−0.541483	−	0.840711i	$-0.682137\pi$
$811$	−30.8408			−1.08297			−0.541483	+	0.840711i	$0.682137\pi$
$812$	−2.55690	+	15.9515i	−0.0897297	+	0.559788i
$813$	−5.09009			−0.178517
$814$	0.411474	+	0.712694i	0.0144222	+	0.0249799i
$815$	0.639338	−	1.10737i	0.0223950	−	0.0387893i
$816$	5.40214	−	9.35678i	0.189113	−	0.327553i
$817$	−7.13816	−	12.3636i	−0.249732	−	0.432549i
$818$	−0.630415			−0.0220419
$819$	6.84224	+	5.56185i	0.239087	+	0.194347i
$820$	−1.87939			−0.0656310
$821$	6.08260	+	10.5354i	0.212284	+	0.367687i	0.952429	−	0.304761i	$-0.0985765\pi$
$821$	6.08260	+	10.5354i	0.212284	+	0.367687i	−0.740145	+	0.672447i	$0.765243\pi$
$822$	−1.35276	+	2.34305i	−0.0471829	+	0.0817232i
$823$	12.8880	−	22.3227i	0.449248	−	0.778120i	−0.549090	−	0.835763i	$-0.685025\pi$
$823$	12.8880	−	22.3227i	0.449248	−	0.778120i	0.998337	+	0.0576439i	$0.0183588\pi$
$824$	6.17752	+	10.6998i	0.215204	+	0.372744i
$825$	2.65270			0.0923553
$826$	−8.36484	+	3.19312i	−0.291050	+	0.111103i
$827$	−23.6355			−0.821886			−0.410943	−	0.911661i	$-0.634800\pi$
$827$	−23.6355			−0.821886			−0.410943	+	0.911661i	$0.634800\pi$
$828$	5.16297	+	8.94253i	0.179426	+	0.310774i
$829$	5.09610	−	8.82671i	0.176995	−	0.306564i	−0.763855	−	0.645388i	$-0.776696\pi$
$829$	5.09610	−	8.82671i	0.176995	−	0.306564i	0.940850	+	0.338824i	$0.110029\pi$
$830$	−0.147079	+	0.254748i	−0.00510517	+	0.00884242i
$831$	−5.39574	−	9.34570i	−0.187176	−	0.324199i
$832$	6.43882			0.223226
$833$	8.82279	+	42.2810i	0.305691	+	1.46495i
$834$	2.03558			0.0704863
$835$	1.27466	+	2.20778i	0.0441115	+	0.0764034i
$836$	6.02481	−	10.4353i	0.208373	−	0.360912i
$837$	−7.42127	+	12.8540i	−0.256517	+	0.444300i
$838$	−6.31655	−	10.9406i	−0.218202	−	0.377936i
$839$	12.5193			0.432214			0.216107	−	0.976370i	$-0.430664\pi$
$839$	12.5193			0.432214			0.216107	+	0.976370i	$0.430664\pi$
$840$	0.213726	−	0.0815859i	0.00737426	−	0.00281498i
$841$	−18.4442			−0.636007
$842$	−2.31702	−	4.01319i	−0.0798497	−	0.138304i
$843$	−1.46997	+	2.54606i	−0.0506285	+	0.0876911i
$844$	10.3969	−	18.0080i	0.357877	−	0.619861i
$845$	0.693249	+	1.20074i	0.0238485	+	0.0413068i
$846$	8.71326			0.299568
$847$	2.05303	+	1.66885i	0.0705431	+	0.0573423i
$848$	31.8557			1.09393
$849$	1.08197	+	1.87402i	0.0371330	+	0.0643163i
$850$	−5.34167	+	9.25205i	−0.183218	+	0.317343i
$851$	2.39599	−	4.14998i	0.0821336	−	0.142260i
$852$	4.24763	+	7.35710i	0.145521	+	0.252050i
$853$	0.427777			0.0146468			0.00732340	−	0.999973i	$-0.497669\pi$
$853$	0.427777			0.0146468			0.00732340	+	0.999973i	$0.497669\pi$
$854$	0.208512	−	1.30082i	0.00713512	−	0.0445132i
$855$	−2.10101			−0.0718532
$856$	5.47044	+	9.47508i	0.186976	+	0.323851i
$857$	−22.8496	+	39.5766i	−0.780527	+	1.35191i	0.151109	+	0.988517i	$0.451716\pi$
$857$	−22.8496	+	39.5766i	−0.780527	+	1.35191i	−0.931635	+	0.363395i	$0.881618\pi$
$858$	0.113341	−	0.196312i	0.00386939	−	0.00670198i
$859$	−23.9511	−	41.4846i	−0.817202	−	1.41544i	−0.907736	−	0.419543i	$-0.862190\pi$
$859$	−23.9511	−	41.4846i	−0.817202	−	1.41544i	0.0905332	−	0.995893i	$-0.471143\pi$
$860$	−0.504748			−0.0172118
$861$	−1.84730	+	11.5245i	−0.0629557	+	0.392756i
$862$	−3.75010			−0.127729
$863$	−6.08765	−	10.5441i	−0.207226	−	0.358926i	0.743614	−	0.668610i	$-0.233110\pi$
$863$	−6.08765	−	10.5441i	−0.207226	−	0.358926i	−0.950840	+	0.309684i	$0.899777\pi$
$864$	5.83662	−	10.1093i	0.198566	−	0.343926i
$865$	−0.139910	+	0.242332i	−0.00475710	+	0.00823953i
$866$	−3.09833	−	5.36646i	−0.105285	−	0.182360i
$867$	−11.2121			−0.380784
$868$	−18.8268	−	15.3037i	−0.639024	−	0.519443i
$869$	9.09152			0.308409
$870$	−0.0362077	−	0.0627135i	−0.00122756	−	0.00212619i
$871$	−1.87939	+	3.25519i	−0.0636805	+	0.110298i
$872$	4.37211	−	7.57272i	0.148058	−	0.256445i
$873$	22.4579	+	38.8982i	0.760083	+	1.31650i
$874$	4.50299			0.152316
$875$	2.97700	−	1.13641i	0.100641	−	0.0384177i
$876$	3.53209			0.119338
$877$	6.55896	+	11.3605i	0.221480	+	0.383615i	0.955258	−	0.295775i	$-0.0955778\pi$
$877$	6.55896	+	11.3605i	0.221480	+	0.383615i	−0.733777	+	0.679390i	$0.762244\pi$
$878$	−1.61293	+	2.79368i	−0.0544338	+	0.0942820i
$879$	−6.18732	+	10.7168i	−0.208693	+	0.361467i
$880$	−0.198463	−	0.343748i	−0.00669019	−	0.0115877i
$881$	16.8571			0.567930			0.283965	−	0.958835i	$-0.408350\pi$
$881$	16.8571			0.567930			0.283965	+	0.958835i	$0.408350\pi$
$882$	1.34919	+	6.46567i	0.0454297	+	0.217711i
$883$	9.24030			0.310961			0.155480	−	0.987839i	$-0.450307\pi$
$883$	9.24030			0.310961			0.155480	+	0.987839i	$0.450307\pi$
$884$	−7.11246	−	12.3191i	−0.239218	−	0.414338i
$885$	−0.312681	+	0.541580i	−0.0105107	+	0.0182050i
$886$	2.85163	−	4.93917i	0.0958025	−	0.165935i
$887$	12.0091	+	20.8003i	0.403226	+	0.698407i	0.994113	−	0.108347i	$-0.0345557\pi$
$887$	12.0091	+	20.8003i	0.403226	+	0.698407i	−0.590888	+	0.806754i	$0.701222\pi$
$888$	−1.69871			−0.0570050
$889$	−6.62449	+	2.52877i	−0.222178	+	0.0848122i
$890$	0.288171			0.00965951
$891$	−3.26604	−	5.65695i	−0.109417	−	0.189515i
$892$	8.69846	−	15.0662i	0.291246	−	0.504453i
$893$	−29.6031	+	51.2741i	−0.990631	+	1.71582i
$894$	−1.36097	−	2.35726i	−0.0455175	−	0.0788387i
$895$	1.37733			0.0460389
$896$	19.4996	+	15.8506i	0.651436	+	0.529532i
$897$	−1.31996			−0.0440720
$898$	−6.34895	−	10.9967i	−0.211867	−	0.366964i
$899$	−7.92649	+	13.7291i	−0.264363	+	0.457891i
$900$	12.7280	−	22.0456i	0.424268	−	0.734853i
$901$	−29.8641	−	51.7262i	−0.994918	−	1.72325i
$902$	−2.87939			−0.0958730
$903$	−0.496130	+	3.09516i	−0.0165102	+	0.103000i
$904$	−14.6382			−0.486858
$905$	−0.993137	−	1.72016i	−0.0330130	−	0.0571802i
$906$	−2.14749	+	3.71956i	−0.0713455	+	0.123574i
$907$	−2.89693	+	5.01762i	−0.0961909	+	0.166607i	−0.910105	−	0.414378i	$-0.863999\pi$
$907$	−2.89693	+	5.01762i	−0.0961909	+	0.166607i	0.813914	+	0.580985i	$0.197333\pi$
$908$	−19.2690	−	33.3750i	−0.639465	−	1.10759i
$909$	18.4766			0.612830
$910$	0.0215172	−	0.134237i	0.000713288	−	0.00444992i
$911$	0.421903			0.0139783			0.00698914	−	0.999976i	$-0.497775\pi$
$911$	0.421903			0.0139783			0.00698914	+	0.999976i	$0.497775\pi$
$912$	5.61334	+	9.72259i	0.185876	+	0.321947i
$913$	3.51114	−	6.08148i	0.116202	−	0.201268i
$914$	−1.56165	+	2.70486i	−0.0516548	+	0.0894688i
$915$	−0.0460079	−	0.0796879i	−0.00152097	−	0.00263440i
$916$	−48.9846			−1.61850
$917$	−28.7986	−	23.4095i	−0.951014	−	0.773050i
$918$	−6.51847			−0.215142
$919$	0.236482	+	0.409598i	0.00780081	+	0.0135114i	0.869899	−	0.493229i	$-0.164184\pi$
$919$	0.236482	+	0.409598i	0.00780081	+	0.0135114i	−0.862099	+	0.506740i	$0.830850\pi$
$920$	0.164315	−	0.284602i	0.00541730	−	0.00938304i
$921$	−4.07398	+	7.05634i	−0.134242	+	0.232514i
$922$	2.41101	+	4.17599i	0.0794023	+	0.137529i
$923$	10.4210			0.343010
$924$	−2.47178	+	0.943555i	−0.0813156	+	0.0310407i
$925$	−11.8135			−0.388424
$926$	−1.92097	−	3.32722i	−0.0631270	−	0.109339i
$927$	−12.4572	+	21.5766i	−0.409149	+	0.708667i
$928$	6.23396	−	10.7975i	0.204640	−	0.354446i
$929$	3.49912	+	6.06066i	0.114802	+	0.198844i	0.917701	−	0.397272i	$-0.130043\pi$
$929$	3.49912	+	6.06066i	0.114802	+	0.198844i	−0.802898	+	0.596116i	$0.796710\pi$
$930$	0.108755			0.00356622
$931$	−42.6318	−	14.0275i	−1.39720	−	0.459733i
$932$	−5.23947			−0.171625
$933$	−1.88144	−	3.25876i	−0.0615957	−	0.106687i
$934$	0.885010	−	1.53288i	0.0289584	−	0.0501575i
$935$	−0.372111	+	0.644516i	−0.0121693	+	0.0210779i
$936$	−2.24510	−	3.88863i	−0.0733834	−	0.127104i
$937$	8.19017			0.267561			0.133781	−	0.991011i	$-0.457288\pi$
$937$	8.19017			0.267561			0.133781	+	0.991011i	$0.457288\pi$
$938$	−2.63041	+	1.00411i	−0.0858861	+	0.0327854i
$939$	−14.0460			−0.458374
$940$	1.04664	+	1.81283i	0.0341375	+	0.0591279i
$941$	−20.1853	+	34.9619i	−0.658021	+	1.13973i	0.323107	+	0.946363i	$0.395273\pi$
$941$	−20.1853	+	34.9619i	−0.658021	+	1.13973i	−0.981127	+	0.193363i	$0.938061\pi$
$942$	−1.48427	+	2.57083i	−0.0483601	+	0.0837622i
$943$	8.38326	+	14.5202i	0.272996	+	0.472844i
$944$	−32.0669			−1.04369
$945$	0.753251	+	0.612295i	0.0245033	+	0.0199180i
$946$	−0.773318			−0.0251428
$947$	20.9620	+	36.3072i	0.681173	+	1.17983i	0.974623	+	0.223852i	$0.0718631\pi$
$947$	20.9620	+	36.3072i	0.681173	+	1.17983i	−0.293450	+	0.955974i	$0.594804\pi$
$948$	−4.54576	+	7.87349i	−0.147639	+	0.255719i
$949$	2.16637	−	3.75227i	0.0703235	−	0.121804i
$950$	−5.55051	−	9.61376i	−0.180082	−	0.311912i
$951$	0.0915189			0.00296770
$952$	3.48111	−	21.7173i	0.112824	−	0.703862i
$953$	−38.6040			−1.25051			−0.625253	−	0.780422i	$-0.715004\pi$
$953$	−38.6040			−1.25051			−0.625253	+	0.780422i	$0.715004\pi$
$954$	−4.56687	−	7.91004i	−0.147858	−	0.256097i
$955$	0.673486	−	1.16651i	0.0217935	−	0.0377474i
$956$	−10.5432	+	18.2614i	−0.340993	+	0.590616i
$957$	0.864370	+	1.49713i	0.0279411	+	0.0483955i
$958$	−6.59659			−0.213126
$959$	6.13083	−	38.2478i	0.197975	−	1.23509i
$960$	0.336867			0.0108723
$961$	3.59580	+	6.22811i	0.115994	+	0.200907i
$962$	−0.504748	+	0.874249i	−0.0162737	+	0.0281869i
$963$	−11.0314	+	19.1069i	−0.355481	+	0.615711i
$964$	9.63728	+	16.6923i	0.310396	+	0.537621i
$965$	−2.41828			−0.0778472
$966$	−0.767226	−	0.623655i	−0.0246851	−	0.0200658i
$967$	−2.04364			−0.0657192			−0.0328596	−	0.999460i	$-0.510461\pi$
$967$	−2.04364			−0.0657192			−0.0328596	+	0.999460i	$0.510461\pi$
$968$	−0.673648	−	1.16679i	−0.0216519	−	0.0375021i
$969$	10.5248	−	18.2295i	0.338106	−	0.585616i
$970$	0.346257	−	0.599735i	0.0111176	−	0.0192563i
$971$	4.77766	+	8.27514i	0.153322	+	0.265562i	0.932447	−	0.361307i	$-0.117669\pi$
$971$	4.77766	+	8.27514i	0.153322	+	0.265562i	−0.779125	+	0.626869i	$0.784336\pi$
$972$	23.6827			0.759624
$973$	−27.2279	+	10.3937i	−0.872885	+	0.333207i
$974$	6.50299			0.208369
$975$	1.62701	+	2.81807i	0.0521061	+	0.0902504i
$976$	2.35916	−	4.08618i	0.0755147	−	0.130795i
$977$	23.5979	−	40.8728i	0.754964	−	1.30764i	−0.190428	−	0.981701i	$-0.560988\pi$
$977$	23.5979	−	40.8728i	0.754964	−	1.30764i	0.945392	−	0.325935i	$-0.105679\pi$
$978$	0.979522	+	1.69658i	0.0313217	+	0.0542507i
$979$	−6.87939			−0.219866
$980$	−1.18314	+	1.05736i	−0.0377941	+	0.0337762i
$981$	17.6331			0.562982
$982$	0.535492	+	0.927500i	0.0170883	+	0.0295977i
$983$	−1.02687	+	1.77860i	−0.0327522	+	0.0567285i	−0.881937	−	0.471368i	$-0.843761\pi$
$983$	−1.02687	+	1.77860i	−0.0327522	+	0.0567285i	0.849185	+	0.528096i	$0.177094\pi$
$984$	2.97178	−	5.14728i	0.0947369	−	0.164089i
$985$	−0.964508	−	1.67058i	−0.0307318	−	0.0532290i
$986$	−6.96223			−0.221723
$987$	12.1452	−	4.63619i	0.386585	−	0.147572i
$988$	14.7811			0.470248
$989$	2.25150	+	3.89971i	0.0715934	+	0.124003i
$990$	−0.0569038	+	0.0985603i	−0.00180852	+	0.00313245i
$991$	−23.8489	+	41.3076i	−0.757587	+	1.31218i	0.186491	+	0.982457i	$0.440288\pi$
$991$	−23.8489	+	41.3076i	−0.757587	+	1.31218i	−0.944078	+	0.329722i	$0.893045\pi$
$992$	9.36231	+	16.2160i	0.297254	+	0.514858i
$993$	0.0578674			0.00183637
$994$	6.05721	+	4.92372i	0.192123	+	0.156171i
$995$	0.756082			0.0239694
$996$	3.51114	+	6.08148i	0.111255	+	0.192699i
$997$	23.3603	−	40.4611i	0.739827	−	1.28142i	−0.212747	−	0.977107i	$-0.568241\pi$
$997$	23.3603	−	40.4611i	0.739827	−	1.28142i	0.952573	−	0.304310i	$-0.0984258\pi$
$998$	1.67200	−	2.89599i	0.0529262	−	0.0916709i
$999$	−3.60401	−	6.24232i	−0.114026	−	0.197498i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	77.2.e.a.67.2	yes	6
3.2	odd	2		693.2.i.h.298.2		6
4.3	odd	2		1232.2.q.m.529.1		6
7.2	even	3	inner	77.2.e.a.23.2	✓	6
7.3	odd	6		539.2.a.g.1.2		3
7.4	even	3		539.2.a.j.1.2		3
7.5	odd	6		539.2.e.m.177.2		6
7.6	odd	2		539.2.e.m.67.2		6
11.2	odd	10		847.2.n.f.81.2		24
11.3	even	5		847.2.n.g.130.2		24
11.4	even	5		847.2.n.g.753.2		24
11.5	even	5		847.2.n.g.487.2		24
11.6	odd	10		847.2.n.f.487.2		24
11.7	odd	10		847.2.n.f.753.2		24
11.8	odd	10		847.2.n.f.130.2		24
11.9	even	5		847.2.n.g.81.2		24
11.10	odd	2		847.2.e.c.606.2		6
21.2	odd	6		693.2.i.h.100.2		6
21.11	odd	6		4851.2.a.bj.1.2		3
21.17	even	6		4851.2.a.bk.1.2		3
28.3	even	6		8624.2.a.co.1.1		3
28.11	odd	6		8624.2.a.ch.1.3		3
28.23	odd	6		1232.2.q.m.177.1		6
77.2	odd	30		847.2.n.f.807.2		24
77.9	even	15		847.2.n.g.807.2		24
77.10	even	6		5929.2.a.u.1.2		3
77.16	even	15		847.2.n.g.366.2		24
77.30	odd	30		847.2.n.f.9.2		24
77.32	odd	6		5929.2.a.x.1.2		3
77.37	even	15		847.2.n.g.632.2		24
77.51	odd	30		847.2.n.f.632.2		24
77.58	even	15		847.2.n.g.9.2		24
77.65	odd	6		847.2.e.c.485.2		6
77.72	odd	30		847.2.n.f.366.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.e.a.23.2	✓	6	7.2	even	3	inner
77.2.e.a.67.2	yes	6	1.1	even	1	trivial
539.2.a.g.1.2		3	7.3	odd	6
539.2.a.j.1.2		3	7.4	even	3
539.2.e.m.67.2		6	7.6	odd	2
539.2.e.m.177.2		6	7.5	odd	6
693.2.i.h.100.2		6	21.2	odd	6
693.2.i.h.298.2		6	3.2	odd	2
847.2.e.c.485.2		6	77.65	odd	6
847.2.e.c.606.2		6	11.10	odd	2
847.2.n.f.9.2		24	77.30	odd	30
847.2.n.f.81.2		24	11.2	odd	10
847.2.n.f.130.2		24	11.8	odd	10
847.2.n.f.366.2		24	77.72	odd	30
847.2.n.f.487.2		24	11.6	odd	10
847.2.n.f.632.2		24	77.51	odd	30
847.2.n.f.753.2		24	11.7	odd	10
847.2.n.f.807.2		24	77.2	odd	30
847.2.n.g.9.2		24	77.58	even	15
847.2.n.g.81.2		24	11.9	even	5
847.2.n.g.130.2		24	11.3	even	5
847.2.n.g.366.2		24	77.16	even	15
847.2.n.g.487.2		24	11.5	even	5
847.2.n.g.632.2		24	77.37	even	15
847.2.n.g.753.2		24	11.4	even	5
847.2.n.g.807.2		24	77.9	even	15
1232.2.q.m.177.1		6	28.23	odd	6
1232.2.q.m.529.1		6	4.3	odd	2
4851.2.a.bj.1.2		3	21.11	odd	6
4851.2.a.bk.1.2		3	21.17	even	6
5929.2.a.u.1.2		3	77.10	even	6
5929.2.a.x.1.2		3	77.32	odd	6
8624.2.a.ch.1.3		3	28.11	odd	6
8624.2.a.co.1.1		3	28.3	even	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:	\( N \)	\(=\)	\( 77 = 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	77.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 + 0.300767i) q^{2} +(0.266044 - 0.460802i) q^{3} +(0.939693 - 1.62760i) q^{4} +(-0.0603074 - 0.104455i) q^{5} +0.184793 q^{6} +(-2.47178 + 0.943555i) q^{7} +1.34730 q^{8} +(1.35844 + 2.35289i) q^{9} +O(q^{10})\)	\(q+(0.173648 + 0.300767i) q^{2} +(0.266044 - 0.460802i) q^{3} +(0.939693 - 1.62760i) q^{4} +(-0.0603074 - 0.104455i) q^{5} +0.184793 q^{6} +(-2.47178 + 0.943555i) q^{7} +1.34730 q^{8} +(1.35844 + 2.35289i) q^{9} +(0.0209445 - 0.0362770i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(-0.500000 - 0.866025i) q^{12} -1.22668 q^{13} +(-0.713011 - 0.579585i) q^{14} -0.0641778 q^{15} +(-1.64543 - 2.84997i) q^{16} +(-3.08512 + 5.34359i) q^{17} +(-0.471782 + 0.817150i) q^{18} +(-3.20574 - 5.55250i) q^{19} -0.226682 q^{20} +(-0.222811 + 1.39003i) q^{21} -0.347296 q^{22} +(1.01114 + 1.75135i) q^{23} +(0.358441 - 0.620838i) q^{24} +(2.49273 - 4.31753i) q^{25} +(-0.213011 - 0.368946i) q^{26} +3.04189 q^{27} +(-0.786989 + 4.90971i) q^{28} +3.24897 q^{29} +(-0.0111444 - 0.0193026i) q^{30} +(-2.43969 + 4.22567i) q^{31} +(1.91875 - 3.32337i) q^{32} +(0.266044 + 0.460802i) q^{33} -2.14290 q^{34} +(0.247626 + 0.201288i) q^{35} +5.10607 q^{36} +(-1.18479 - 2.05212i) q^{37} +(1.11334 - 1.92836i) q^{38} +(-0.326352 + 0.565258i) q^{39} +(-0.0812519 - 0.140732i) q^{40} +8.29086 q^{41} +(-0.456767 + 0.174362i) q^{42} +2.22668 q^{43} +(0.939693 + 1.62760i) q^{44} +(0.163848 - 0.283793i) q^{45} +(-0.351167 + 0.608239i) q^{46} +(-4.61721 - 7.99724i) q^{47} -1.75103 q^{48} +(5.21941 - 4.66452i) q^{49} +1.73143 q^{50} +(1.64156 + 2.84326i) q^{51} +(-1.15270 + 1.99654i) q^{52} +(-4.84002 + 8.38316i) q^{53} +(0.528218 + 0.914901i) q^{54} +0.120615 q^{55} +(-3.33022 + 1.27125i) q^{56} -3.41147 q^{57} +(0.564178 + 0.977185i) q^{58} +(4.87211 - 8.43874i) q^{59} +(-0.0603074 + 0.104455i) q^{60} +(0.716881 + 1.24168i) q^{61} -1.69459 q^{62} +(-5.57785 - 4.53406i) q^{63} -5.24897 q^{64} +(0.0739780 + 0.128134i) q^{65} +(-0.0923963 + 0.160035i) q^{66} +(1.53209 - 2.65366i) q^{67} +(5.79813 + 10.0427i) q^{68} +1.07604 q^{69} +(-0.0175410 + 0.109431i) q^{70} -8.49525 q^{71} +(1.83022 + 3.17004i) q^{72} +(-1.76604 + 3.05888i) q^{73} +(0.411474 - 0.712694i) q^{74} +(-1.32635 - 2.29731i) q^{75} -12.0496 q^{76} +(0.418748 - 2.61240i) q^{77} -0.226682 q^{78} +(-4.54576 - 7.87349i) q^{79} +(-0.198463 + 0.343748i) q^{80} +(-3.26604 + 5.65695i) q^{81} +(1.43969 + 2.49362i) q^{82} -7.02229 q^{83} +(2.05303 + 1.66885i) q^{84} +0.744223 q^{85} +(0.386659 + 0.669713i) q^{86} +(0.864370 - 1.49713i) q^{87} +(-0.673648 + 1.16679i) q^{88} +(3.43969 + 5.95772i) q^{89} +0.113808 q^{90} +(3.03209 - 1.15744i) q^{91} +3.80066 q^{92} +(1.29813 + 2.24843i) q^{93} +(1.60354 - 2.77741i) q^{94} +(-0.386659 + 0.669713i) q^{95} +(-1.02094 - 1.76833i) q^{96} +16.5321 q^{97} +(2.30928 + 0.759842i) q^{98} -2.71688 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{3} - 6 q^{5} - 6 q^{6} + 6 q^{8}+O(q^{10}) \) 6 * q - 3 * q^3 - 6 * q^5 - 6 * q^6 + 6 * q^8	\( 6 q - 3 q^{3} - 6 q^{5} - 6 q^{6} + 6 q^{8} - 3 q^{10} - 3 q^{11} - 3 q^{12} + 6 q^{13} - 12 q^{14} + 18 q^{15} + 6 q^{16} + 3 q^{17} + 12 q^{18} - 9 q^{19} + 12 q^{20} - 12 q^{21} - 6 q^{24} - 3 q^{25} - 9 q^{26} + 12 q^{27} + 3 q^{28} - 6 q^{29} + 6 q^{30} - 9 q^{31} + 9 q^{32} - 3 q^{33} - 12 q^{34} - 15 q^{35} + 6 q^{36} - 3 q^{39} - 3 q^{40} + 18 q^{41} - 18 q^{42} - 3 q^{45} + 24 q^{46} + 3 q^{47} - 36 q^{48} + 30 q^{50} + 18 q^{51} - 9 q^{52} - 9 q^{53} + 18 q^{54} + 12 q^{55} + 3 q^{56} - 15 q^{58} - 6 q^{60} - 12 q^{61} - 6 q^{62} + 6 q^{63} - 6 q^{64} - 15 q^{65} + 3 q^{66} + 21 q^{68} + 42 q^{69} + 45 q^{70} - 18 q^{71} - 12 q^{72} - 6 q^{73} - 18 q^{74} - 9 q^{75} - 18 q^{76} + 12 q^{78} + 3 q^{79} + 27 q^{80} - 15 q^{81} + 3 q^{82} - 30 q^{83} - 54 q^{85} + 9 q^{86} + 24 q^{87} - 3 q^{88} + 15 q^{89} - 72 q^{90} + 9 q^{91} - 6 q^{92} - 6 q^{93} - 9 q^{95} - 3 q^{96} + 90 q^{97} - 6 q^{98}+O(q^{100}) \) 6 * q - 3 * q^3 - 6 * q^5 - 6 * q^6 + 6 * q^8 - 3 * q^10 - 3 * q^11 - 3 * q^12 + 6 * q^13 - 12 * q^14 + 18 * q^15 + 6 * q^16 + 3 * q^17 + 12 * q^18 - 9 * q^19 + 12 * q^20 - 12 * q^21 - 6 * q^24 - 3 * q^25 - 9 * q^26 + 12 * q^27 + 3 * q^28 - 6 * q^29 + 6 * q^30 - 9 * q^31 + 9 * q^32 - 3 * q^33 - 12 * q^34 - 15 * q^35 + 6 * q^36 - 3 * q^39 - 3 * q^40 + 18 * q^41 - 18 * q^42 - 3 * q^45 + 24 * q^46 + 3 * q^47 - 36 * q^48 + 30 * q^50 + 18 * q^51 - 9 * q^52 - 9 * q^53 + 18 * q^54 + 12 * q^55 + 3 * q^56 - 15 * q^58 - 6 * q^60 - 12 * q^61 - 6 * q^62 + 6 * q^63 - 6 * q^64 - 15 * q^65 + 3 * q^66 + 21 * q^68 + 42 * q^69 + 45 * q^70 - 18 * q^71 - 12 * q^72 - 6 * q^73 - 18 * q^74 - 9 * q^75 - 18 * q^76 + 12 * q^78 + 3 * q^79 + 27 * q^80 - 15 * q^81 + 3 * q^82 - 30 * q^83 - 54 * q^85 + 9 * q^86 + 24 * q^87 - 3 * q^88 + 15 * q^89 - 72 * q^90 + 9 * q^91 - 6 * q^92 - 6 * q^93 - 9 * q^95 - 3 * q^96 + 90 * q^97 - 6 * q^98

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