LMFDB - Embedded newform 77.2.i.a.10.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [77,2,Mod(10,77)]

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([1, 3]))

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

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

chi := DirichletCharacter("77.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 77 = 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	77.i (of order $6$, 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:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 8x^{10} + 47x^{8} - 122x^{6} + 233x^{4} - 119x^{2} + 49 $ x^12 - 8x^10 + 47x^8 - 122x^6 + 233x^4 - 119*x^2 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			10.5
Root			$1.43898 + 0.830794i$ of defining polynomial
Character	$\chi$	$=$	77.10
Dual form			77.2.i.a.54.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.43898 - 0.830794i) q^{2} +(-1.97141 - 1.13819i) q^{3} +(0.380438 - 0.658939i) q^{4} +(2.80150 - 1.61745i) q^{5} -3.78242 q^{6} +(-2.23530 + 1.41542i) q^{7} +2.05891i q^{8} +(1.09097 + 1.88962i) q^{9} +O(q^{10})$	\(q+(1.43898 - 0.830794i) q^{2} +(-1.97141 - 1.13819i) q^{3} +(0.380438 - 0.658939i) q^{4} +(2.80150 - 1.61745i) q^{5} -3.78242 q^{6} +(-2.23530 + 1.41542i) q^{7} +2.05891i q^{8} +(1.09097 + 1.88962i) q^{9} +(2.68754 - 4.65495i) q^{10} +(2.41524 + 2.27302i) q^{11} +(-1.50000 + 0.866025i) q^{12} -0.904465 q^{13} +(-2.04063 + 3.89384i) q^{14} -7.36389 q^{15} +(2.47141 + 4.28061i) q^{16} +(-1.78307 + 3.08837i) q^{17} +(3.13977 + 1.81275i) q^{18} +(-1.99935 - 3.46298i) q^{19} -2.46136i q^{20} +(6.01772 - 0.246167i) q^{21} +(5.36389 + 1.26426i) q^{22} +(-3.09097 - 5.35372i) q^{23} +(2.34344 - 4.05896i) q^{24} +(2.73229 - 4.73246i) q^{25} +(-1.30150 + 0.751424i) q^{26} +1.86221i q^{27} +(0.0822807 + 2.01141i) q^{28} -7.34599i q^{29} +(-10.5965 + 6.11788i) q^{30} +(0.358685 + 0.207087i) q^{31} +(3.54647 + 2.04755i) q^{32} +(-2.17428 - 7.23007i) q^{33} +5.92546i q^{34} +(-3.97284 + 7.58080i) q^{35} +1.66019 q^{36} +(1.23912 + 2.14622i) q^{37} +(-5.75404 - 3.32210i) q^{38} +(1.78307 + 1.02946i) q^{39} +(3.33019 + 5.76806i) q^{40} -2.71339 q^{41} +(8.45486 - 5.35372i) q^{42} -2.15392i q^{43} +(2.41663 - 0.726748i) q^{44} +(6.11273 + 3.52918i) q^{45} +(-8.89568 - 5.13592i) q^{46} +(-3.11273 + 1.79713i) q^{47} -11.2518i q^{48} +(2.99316 - 6.32779i) q^{49} -9.07987i q^{50} +(7.03033 - 4.05896i) q^{51} +(-0.344093 + 0.595987i) q^{52} +(-4.39248 + 7.60799i) q^{53} +(1.54712 + 2.67969i) q^{54} +(10.4428 + 2.46136i) q^{55} +(-2.91423 - 4.60230i) q^{56} +9.10259i q^{57} +(-6.10301 - 10.5707i) q^{58} +(9.29987 + 5.36928i) q^{59} +(-2.80150 + 4.85235i) q^{60} +(1.97349 + 3.41819i) q^{61} +0.688186 q^{62} +(-5.11326 - 2.67969i) q^{63} -3.08126 q^{64} +(-2.53386 + 1.46293i) q^{65} +(-9.13544 - 8.59753i) q^{66} +(0.660190 - 1.14348i) q^{67} +(1.35670 + 2.34987i) q^{68} +14.0725i q^{69} +(0.581257 + 14.2092i) q^{70} +4.70370 q^{71} +(-3.89056 + 2.24622i) q^{72} +(3.67428 - 6.36404i) q^{73} +(3.56614 + 2.05891i) q^{74} +(-10.7729 + 6.21975i) q^{75} -3.04252 q^{76} +(-8.61607 - 1.66232i) q^{77} +3.42107 q^{78} +(5.67363 - 3.27567i) q^{79} +(13.8473 + 7.99476i) q^{80} +(5.39248 - 9.34004i) q^{81} +(-3.90451 + 2.25427i) q^{82} -15.0780 q^{83} +(2.12716 - 4.05896i) q^{84} +11.5361i q^{85} +(-1.78947 - 3.09945i) q^{86} +(-8.36117 + 14.4820i) q^{87} +(-4.67996 + 4.97276i) q^{88} +(-2.41586 + 1.39480i) q^{89} +11.7281 q^{90} +(2.02175 - 1.28020i) q^{91} -4.70370 q^{92} +(-0.471410 - 0.816506i) q^{93} +(-2.98610 + 5.17207i) q^{94} +(-11.2024 - 6.46769i) q^{95} +(-4.66103 - 8.07314i) q^{96} -6.82916i q^{97} +(-0.949999 - 11.5923i) q^{98} +(-1.66019 + 7.04368i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{3} + 4 q^{4} - 4 q^{9}+O(q^{10}) $ 12 * q - 6 * q^3 + 4 * q^4 - 4 * q^9	$ 12 q - 6 q^{3} + 4 q^{4} - 4 q^{9} - 4 q^{11} - 18 q^{12} + 8 q^{14} - 20 q^{15} + 12 q^{16} - 4 q^{22} - 20 q^{23} + 14 q^{25} + 18 q^{26} + 6 q^{31} + 18 q^{33} - 12 q^{36} + 16 q^{37} - 48 q^{38} + 16 q^{42} + 20 q^{44} + 54 q^{45} - 18 q^{47} + 16 q^{49} - 2 q^{53} + 18 q^{56} - 6 q^{58} - 12 q^{59} + 28 q^{64} - 42 q^{66} - 24 q^{67} - 58 q^{70} + 20 q^{71} - 78 q^{75} - 50 q^{77} + 8 q^{78} + 30 q^{80} + 14 q^{81} + 54 q^{82} - 38 q^{86} - 4 q^{88} - 66 q^{89} + 22 q^{91} - 20 q^{92} + 12 q^{93} + 12 q^{99}+O(q^{100}) $ 12 * q - 6 * q^3 + 4 * q^4 - 4 * q^9 - 4 * q^11 - 18 * q^12 + 8 * q^14 - 20 * q^15 + 12 * q^16 - 4 * q^22 - 20 * q^23 + 14 * q^25 + 18 * q^26 + 6 * q^31 + 18 * q^33 - 12 * q^36 + 16 * q^37 - 48 * q^38 + 16 * q^42 + 20 * q^44 + 54 * q^45 - 18 * q^47 + 16 * q^49 - 2 * q^53 + 18 * q^56 - 6 * q^58 - 12 * q^59 + 28 * q^64 - 42 * q^66 - 24 * q^67 - 58 * q^70 + 20 * q^71 - 78 * q^75 - 50 * q^77 + 8 * q^78 + 30 * q^80 + 14 * q^81 + 54 * q^82 - 38 * q^86 - 4 * q^88 - 66 * q^89 + 22 * q^91 - 20 * q^92 + 12 * q^93 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$45$	$57$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	1.43898	−	0.830794i	1.01751	−	0.587460i	0.104129	−	0.994564i	$-0.466795\pi$
$2$	1.43898	−	0.830794i	1.01751	−	0.587460i	0.913382	+	0.407104i	$0.133461\pi$
$3$	−1.97141	−	1.13819i	−1.13819	−	0.657137i	−0.192211	−	0.981354i	$-0.561566\pi$
$3$	−1.97141	−	1.13819i	−1.13819	−	0.657137i	−0.945983	+	0.324217i	$0.894899\pi$
$4$	0.380438	−	0.658939i	0.190219	−	0.329469i
$5$	2.80150	−	1.61745i	1.25287	−	0.723345i	0.281192	−	0.959651i	$-0.409270\pi$
$5$	2.80150	−	1.61745i	1.25287	−	0.723345i	0.971679	+	0.236306i	$0.0759368\pi$
$6$	−3.78242			−1.54417
$7$	−2.23530	+	1.41542i	−0.844865	+	0.534979i
$7$	−2.23530	+	1.41542i	−0.844865	+	0.534979i
$8$			2.05891i			0.727936i
$9$	1.09097	+	1.88962i	0.363657	+	0.629873i
$10$	2.68754	−	4.65495i	0.849873	−	1.47202i
$11$	2.41524	+	2.27302i	0.728221	+	0.685342i
$11$	2.41524	+	2.27302i	0.728221	+	0.685342i
$12$	−1.50000	+	0.866025i	−0.433013	+	0.250000i
$13$	−0.904465			−0.250853			−0.125427	−	0.992103i	$-0.540030\pi$
$13$	−0.904465			−0.250853			−0.125427	+	0.992103i	$0.540030\pi$
$14$	−2.04063	+	3.89384i	−0.545381	+	1.04067i
$15$	−7.36389			−1.90135
$16$	2.47141	+	4.28061i	0.617853	+	1.07015i
$17$	−1.78307	+	3.08837i	−0.432458	+	0.749040i	−0.997084	−	0.0763071i	$-0.975687\pi$
$17$	−1.78307	+	3.08837i	−0.432458	+	0.749040i	0.564626	+	0.825347i	$0.309020\pi$
$18$	3.13977	+	1.81275i	0.740050	+	0.427268i
$19$	−1.99935	−	3.46298i	−0.458682	−	0.794461i	0.540209	−	0.841531i	$-0.318345\pi$
$19$	−1.99935	−	3.46298i	−0.458682	−	0.794461i	−0.998892	+	0.0470697i	$0.985012\pi$
$20$		−	2.46136i		−	0.550377i
$21$	6.01772	−	0.246167i	1.31318	−	0.0537180i
$22$	5.36389	+	1.26426i	1.14358	+	0.269542i
$23$	−3.09097	−	5.35372i	−0.644512	−	1.11633i	−0.984414	−	0.175867i	$-0.943727\pi$
$23$	−3.09097	−	5.35372i	−0.644512	−	1.11633i	0.339902	−	0.940461i	$-0.389606\pi$
$24$	2.34344	−	4.05896i	0.478353	−	0.828532i
$25$	2.73229	−	4.73246i	0.546457	−	0.946492i
$26$	−1.30150	+	0.751424i	−0.255246	+	0.147366i
$27$			1.86221i			0.358383i
$28$	0.0822807	+	2.01141i	0.0155496	+	0.380120i
$29$		−	7.34599i		−	1.36412i	−0.731298	−	0.682058i	$-0.761085\pi$
$29$		−	7.34599i		−	1.36412i	0.731298	−	0.682058i	$-0.238915\pi$
$30$	−10.5965	+	6.11788i	−1.93464	+	1.11697i
$31$	0.358685	+	0.207087i	0.0644217	+	0.0371939i	0.531865	−	0.846829i	$-0.321491\pi$
$31$	0.358685	+	0.207087i	0.0644217	+	0.0371939i	−0.467443	+	0.884023i	$0.654825\pi$
$32$	3.54647	+	2.04755i	0.626933	+	0.361960i
$33$	−2.17428	−	7.23007i	−0.378494	−	1.25859i
$34$			5.92546i			1.01621i
$35$	−3.97284	+	7.58080i	−0.671533	+	1.28139i
$36$	1.66019			0.276698
$37$	1.23912	+	2.14622i	0.203711	+	0.352837i	0.949721	−	0.313097i	$-0.101367\pi$
$37$	1.23912	+	2.14622i	0.203711	+	0.352837i	−0.746011	+	0.665934i	$0.768033\pi$
$38$	−5.75404	−	3.32210i	−0.933429	−	0.538915i
$39$	1.78307	+	1.02946i	0.285520	+	0.164845i
$40$	3.33019	+	5.76806i	0.526549	+	0.912010i
$41$	−2.71339			−0.423761			−0.211881	−	0.977296i	$-0.567959\pi$
$41$	−2.71339			−0.423761			−0.211881	+	0.977296i	$0.567959\pi$
$42$	8.45486	−	5.35372i	1.30461	−	0.826097i
$43$		−	2.15392i		−	0.328470i	−0.986421	−	0.164235i	$-0.947484\pi$
$43$		−	2.15392i		−	0.328470i	0.986421	−	0.164235i	$-0.0525156\pi$
$44$	2.41663	−	0.726748i	0.364321	−	0.109561i
$45$	6.11273	+	3.52918i	0.911231	+	0.526100i
$46$	−8.89568	−	5.13592i	−1.31160	−	0.757251i
$47$	−3.11273	+	1.79713i	−0.454038	+	0.262139i	−0.709534	−	0.704671i	$-0.751094\pi$
$47$	−3.11273	+	1.79713i	−0.454038	+	0.262139i	0.255496	+	0.966810i	$0.417761\pi$
$48$		−	11.2518i		−	1.62405i
$49$	2.99316	−	6.32779i	0.427595	−	0.903971i
$50$		−	9.07987i		−	1.28409i
$51$	7.03033	−	4.05896i	0.984443	−	0.568368i
$52$	−0.344093	+	0.595987i	−0.0477171	+	0.0826485i
$53$	−4.39248	+	7.60799i	−0.603353	+	1.04504i	0.388956	+	0.921256i	$0.372836\pi$
$53$	−4.39248	+	7.60799i	−0.603353	+	1.04504i	−0.992309	+	0.123782i	$0.960498\pi$
$54$	1.54712	+	2.67969i	0.210536	+	0.364659i
$55$	10.4428	+	2.46136i	1.40811	+	0.331890i
$56$	−2.91423	−	4.60230i	−0.389430	−	0.615008i
$57$			9.10259i			1.20567i
$58$	−6.10301	−	10.5707i	−0.801364	−	1.38800i
$59$	9.29987	+	5.36928i	1.21074	+	0.699021i	0.962921	−	0.269785i	$-0.0869527\pi$
$59$	9.29987	+	5.36928i	1.21074	+	0.699021i	0.247819	+	0.968806i	$0.420286\pi$
$60$	−2.80150	+	4.85235i	−0.361673	+	0.626436i
$61$	1.97349	+	3.41819i	0.252680	+	0.437654i	0.964263	−	0.264948i	$-0.0853548\pi$
$61$	1.97349	+	3.41819i	0.252680	+	0.437654i	−0.711583	+	0.702602i	$0.752021\pi$
$62$	0.688186			0.0873997
$63$	−5.11326	−	2.67969i	−0.644210	−	0.337609i
$64$	−3.08126			−0.385157
$65$	−2.53386	+	1.46293i	−0.314287	+	0.181454i
$66$	−9.13544	−	8.59753i	−1.12450	−	1.05828i
$67$	0.660190	−	1.14348i	0.0806550	−	0.139699i	−0.822876	−	0.568220i	$-0.807632\pi$
$67$	0.660190	−	1.14348i	0.0806550	−	0.139699i	0.903531	+	0.428522i	$0.140965\pi$
$68$	1.35670	+	2.34987i	0.164524	+	0.284963i
$69$			14.0725i			1.69413i
$70$	0.581257	+	14.2092i	0.0694734	+	1.69833i
$71$	4.70370			0.558226			0.279113	−	0.960258i	$-0.409960\pi$
$71$	4.70370			0.558226			0.279113	+	0.960258i	$0.409960\pi$
$72$	−3.89056	+	2.24622i	−0.458507	+	0.264719i
$73$	3.67428	−	6.36404i	0.430042	−	0.744855i	−0.566834	−	0.823832i	$-0.691832\pi$
$73$	3.67428	−	6.36404i	0.430042	−	0.744855i	0.996876	+	0.0789770i	$0.0251654\pi$
$74$	3.56614	+	2.05891i	0.414556	+	0.239344i
$75$	−10.7729	+	6.21975i	−1.24395	+	0.718194i
$76$	−3.04252			−0.349001
$77$	−8.61607	−	1.66232i	−0.981893	−	0.189439i
$78$	3.42107			0.387360
$79$	5.67363	−	3.27567i	0.638333	−	0.368542i	−0.145639	−	0.989338i	$-0.546524\pi$
$79$	5.67363	−	3.27567i	0.638333	−	0.368542i	0.783972	+	0.620796i	$0.213190\pi$
$80$	13.8473	+	7.99476i	1.54818	+	0.893842i
$81$	5.39248	−	9.34004i	0.599164	−	1.03778i
$82$	−3.90451	+	2.25427i	−0.431182	+	0.248943i
$83$	−15.0780			−1.65502			−0.827511	−	0.561450i	$-0.810244\pi$
$83$	−15.0780			−1.65502			−0.827511	+	0.561450i	$0.810244\pi$
$84$	2.12716	−	4.05896i	0.232093	−	0.442869i
$85$			11.5361i			1.25127i
$86$	−1.78947	−	3.09945i	−0.192963	−	0.334222i
$87$	−8.36117	+	14.4820i	−0.896411	+	1.55263i
$88$	−4.67996	+	4.97276i	−0.498885	+	0.530098i
$89$	−2.41586	+	1.39480i	−0.256081	+	0.147849i	−0.622546	−	0.782584i	$-0.713901\pi$
$89$	−2.41586	+	1.39480i	−0.256081	+	0.147849i	0.366464	+	0.930432i	$0.380568\pi$
$90$	11.7281			1.23625
$91$	2.02175	−	1.28020i	0.211937	−	0.134201i
$92$	−4.70370			−0.490394
$93$	−0.471410	−	0.816506i	−0.0488829	−	0.0846677i
$94$	−2.98610	+	5.17207i	−0.307992	+	0.533458i
$95$	−11.2024	−	6.46769i	−1.14934	−	0.663571i
$96$	−4.66103	−	8.07314i	−0.475714	−	0.823961i
$97$		−	6.82916i		−	0.693397i	−0.937977	−	0.346698i	$-0.887303\pi$
$97$		−	6.82916i		−	0.693397i	0.937977	−	0.346698i	$-0.112697\pi$
$98$	−0.949999	−	11.5923i	−0.0959644	−	1.17099i
$99$	−1.66019	+	7.04368i	−0.166855	+	0.707916i
$100$	−2.07893	−	3.60082i	−0.207893	−	0.360082i
$101$	−1.27442	+	2.20735i	−0.126809	+	0.219640i	−0.922439	−	0.386144i	$-0.873807\pi$
$101$	−1.27442	+	2.20735i	−0.126809	+	0.219640i	0.795629	+	0.605784i	$0.207140\pi$
$102$	6.74433	−	11.6815i	0.667788	−	1.15664i
$103$	12.9903	−	7.49994i	1.27997	−	0.738991i	0.303128	−	0.952950i	$-0.401969\pi$
$103$	12.9903	−	7.49994i	1.27997	−	0.738991i	0.976843	+	0.213958i	$0.0686357\pi$
$104$		−	1.86221i		−	0.182605i
$105$	16.4605	−	10.4230i	1.60638	−	1.01718i
$106$			14.5970i			1.41778i
$107$	15.1752	−	8.76142i	1.46704	−	0.846998i	0.467724	−	0.883875i	$-0.345074\pi$
$107$	15.1752	−	8.76142i	1.46704	−	0.846998i	0.999320	+	0.0368767i	$0.0117409\pi$
$108$	1.22708	+	0.708458i	0.118076	+	0.0681714i
$109$	1.80275	+	1.04082i	0.172672	+	0.0996921i	0.583845	−	0.811865i	$-0.301548\pi$
$109$	1.80275	+	1.04082i	0.172672	+	0.0996921i	−0.411173	+	0.911557i	$0.634881\pi$
$110$	17.0718	−	5.13397i	1.62774	−	0.489505i
$111$		−	5.64145i		−	0.535463i
$112$	−11.5832	−	6.07037i	−1.09451	−	0.573596i
$113$	0.138436			0.0130230			0.00651150	−	0.999979i	$-0.497927\pi$
$113$	0.138436			0.0130230			0.00651150	+	0.999979i	$0.497927\pi$
$114$	7.56238	+	13.0984i	0.708282	+	1.22678i
$115$	−17.3187	−	9.99898i	−1.61498	−	0.932410i
$116$	−4.84056	−	2.79470i	−0.449435	−	0.259481i
$117$	−0.986746	−	1.70909i	−0.0912247	−	0.158006i
$118$	17.8431			1.64259
$119$	−0.385640	−	9.42724i	−0.0353516	−	0.864194i
$120$		−	15.1616i		−	1.38406i
$121$	0.666738	+	10.9798i	0.0606126	+	0.998161i
$122$	5.67962	+	3.27913i	0.514209	+	0.296879i
$123$	5.34921	+	3.08837i	0.482322	+	0.278469i
$124$	0.272915	−	0.157568i	0.0245085	−	0.0141500i
$125$		−	1.50285i		−	0.134419i
$126$	−9.58414	+	0.392058i	−0.853823	+	0.0349273i
$127$		−	6.46177i		−	0.573389i	−0.958022	−	0.286695i	$-0.907444\pi$
$127$		−	6.46177i		−	0.573389i	0.958022	−	0.286695i	$-0.0925565\pi$
$128$	−11.5268	+	6.65500i	−1.01883	+	0.588224i
$129$	−2.45158	+	4.24626i	−0.215850	+	0.373863i
$130$	−2.43078	+	4.21024i	−0.213194	+	0.369262i
$131$	3.64842	+	6.31925i	0.318764	+	0.552116i	0.980230	−	0.197859i	$-0.0633989\pi$
$131$	3.64842	+	6.31925i	0.318764	+	0.552116i	−0.661466	+	0.749975i	$0.730066\pi$
$132$	−5.59135	−	1.31788i	−0.486665	−	0.114706i
$133$	9.37072	+	4.91088i	0.812545	+	0.425827i
$134$		−	2.19393i		−	0.189527i
$135$	3.01204	+	5.21700i	0.259235	+	0.449008i
$136$	−6.35868	−	3.67119i	−0.545253	−	0.314802i
$137$	−7.59617	+	13.1570i	−0.648985	+	1.12407i	0.334381	+	0.942438i	$0.391473\pi$
$137$	−7.59617	+	13.1570i	−0.648985	+	1.12407i	−0.983366	+	0.181637i	$0.941860\pi$
$138$	11.6914	+	20.2500i	0.995234	+	1.72380i
$139$	−6.01154			−0.509892			−0.254946	−	0.966955i	$-0.582058\pi$
$139$	−6.01154			−0.509892			−0.254946	+	0.966955i	$0.582058\pi$
$140$	3.48386	+	5.50189i	0.294440	+	0.464994i
$141$	8.18194			0.689044
$142$	6.76852	−	3.90780i	0.568001	−	0.327936i
$143$	−2.18450	−	2.05587i	−0.182677	−	0.171920i
$144$	−5.39248	+	9.34004i	−0.449373	+	0.778337i
$145$	−11.8818	−	20.5798i	−0.986728	−	1.70906i
$146$		−	12.2103i		−	1.01053i
$147$	−13.1030	+	9.06787i	−1.08072	+	0.747906i
$148$	1.88564			0.154999
$149$	0.992929	−	0.573268i	0.0813439	−	0.0469639i	−0.458776	−	0.888552i	$-0.651712\pi$
$149$	0.992929	−	0.573268i	0.0813439	−	0.0469639i	0.540120	+	0.841588i	$0.318379\pi$
$150$	−10.3347	+	17.9002i	−0.843821	+	1.46154i
$151$	−14.2449	−	8.22429i	−1.15923	−	0.669283i	−0.208113	−	0.978105i	$-0.566732\pi$
$151$	−14.2449	−	8.22429i	−1.15923	−	0.669283i	−0.951120	+	0.308821i	$0.900065\pi$
$152$	7.12997	−	4.11649i	0.578317	−	0.333891i
$153$	−7.78112			−0.629066
$154$	−13.7794	+	4.76615i	−1.11037	+	0.384067i
$155$	1.33981			0.107616
$156$	1.35670	−	0.783290i	0.108623	−	0.0627134i
$157$	−5.76320	−	3.32738i	−0.459953	−	0.265554i	0.252071	−	0.967709i	$-0.418888\pi$
$157$	−5.76320	−	3.32738i	−0.459953	−	0.265554i	−0.712025	+	0.702154i	$0.752222\pi$
$158$	5.44282	−	9.42724i	0.433008	−	0.749991i
$159$	17.3187	−	9.99898i	1.37347	−	0.792971i
$160$	13.2473			1.04729
$161$	14.4870	+	7.59216i	1.14174	+	0.598346i
$162$		−	17.9202i		−	1.40794i
$163$	−1.55718	−	2.69711i	−0.121968	−	0.211254i	0.798576	−	0.601894i	$-0.205587\pi$
$163$	−1.55718	−	2.69711i	−0.121968	−	0.211254i	−0.920544	+	0.390640i	$0.872254\pi$
$164$	−1.03228	+	1.78796i	−0.0806075	+	0.139616i
$165$	−17.7855	−	16.7383i	−1.38460	−	1.30307i
$166$	−21.6969	+	12.5267i	−1.68400	+	0.972260i
$167$	19.8559			1.53650			0.768249	−	0.640152i	$-0.221128\pi$
$167$	19.8559			1.53650			0.768249	+	0.640152i	$0.221128\pi$
$168$	0.506837	+	12.3900i	0.0391033	+	0.955907i
$169$	−12.1819			−0.937073
$170$	9.58414	+	16.6002i	0.735070	+	1.27318i
$171$	4.36247	−	7.55602i	0.333606	−	0.577823i
$172$	−1.41930	−	0.819435i	−0.108221	−	0.0624813i
$173$	9.13782	+	15.8272i	0.694735	+	1.20332i	0.970270	+	0.242026i	$0.0778119\pi$
$173$	9.13782	+	15.8272i	0.694735	+	1.20332i	−0.275534	+	0.961291i	$0.588855\pi$
$174$			27.7856i			2.10642i
$175$	0.590935	+	14.4458i	0.0446705	+	1.09200i
$176$	−3.76088	+	15.9563i	−0.283487	+	1.20275i
$177$	−12.2226	−	21.1701i	−0.918705	−	1.59124i
$178$	−2.31758	+	4.01417i	−0.173710	+	0.300875i
$179$	−5.89248	+	10.2061i	−0.440424	+	0.762837i	−0.997721	−	0.0674762i	$-0.978505\pi$
$179$	−5.89248	+	10.2061i	−0.440424	+	0.762837i	0.557297	+	0.830314i	$0.311839\pi$
$180$	4.65103	−	2.68527i	0.346667	−	0.200148i
$181$		−	9.38956i		−	0.697921i	−0.937137	−	0.348960i	$-0.886535\pi$
$181$		−	9.38956i		−	0.697921i	0.937137	−	0.348960i	$-0.113465\pi$
$182$	1.84568	−	3.52184i	0.136811	−	0.261056i
$183$		−	8.98486i		−	0.664180i
$184$	11.0228	−	6.36404i	0.812615	−	0.469163i
$185$	6.94282	+	4.00844i	0.510446	+	0.294706i
$186$	−1.35670	−	0.783290i	−0.0994779	−	0.0574336i
$187$	−11.3265	+	3.40618i	−0.828274	+	0.249085i
$188$			2.73479i			0.199455i
$189$	−2.63582	−	4.16261i	−0.191728	−	0.302786i
$190$	−21.4933			−1.55929
$191$	−3.56758	−	6.17924i	−0.258141	−	0.447114i	0.707603	−	0.706610i	$-0.249777\pi$
$191$	−3.56758	−	6.17924i	−0.258141	−	0.447114i	−0.965744	+	0.259497i	$0.916443\pi$
$192$	6.07442	+	3.50707i	0.438384	+	0.253101i
$193$	14.8937	+	8.59890i	1.07207	+	0.618962i	0.928747	−	0.370713i	$-0.120887\pi$
$193$	14.8937	+	8.59890i	1.07207	+	0.618962i	0.143327	+	0.989675i	$0.454220\pi$
$194$	−5.67363	−	9.82702i	−0.407343	−	0.705539i
$195$	6.66038			0.476959
$196$	−3.03091	−	4.37965i	−0.216494	−	0.312832i
$197$		−	9.05715i		−	0.645296i	−0.946519	−	0.322648i	$-0.895427\pi$
$197$		−	9.05715i		−	0.645296i	0.946519	−	0.322648i	$-0.104573\pi$
$198$	3.46287	+	11.5150i	0.246096	+	0.818334i
$199$	14.3393	+	8.27877i	1.01648	+	0.586867i	0.913083	−	0.407773i	$-0.133695\pi$
$199$	14.3393	+	8.27877i	1.01648	+	0.586867i	0.103400	+	0.994640i	$0.467028\pi$
$200$	9.74372	+	5.62554i	0.688985	+	0.397786i
$201$	−2.60301	+	1.50285i	−0.183602	+	0.106003i
$202$			4.23511i			0.297981i
$203$	10.3977	+	16.4205i	0.729774	+	1.15249i
$204$		−	6.17674i		−	0.432458i
$205$	−7.60159	+	4.38878i	−0.530918	+	0.306526i
$206$	12.4618	−	21.5845i	0.868256	−	1.50386i
$207$	6.74433	−	11.6815i	0.468763	−	0.811921i
$208$	−2.23530	−	3.87166i	−0.154990	−	0.268451i
$209$	3.04252	−	12.9085i	0.210455	−	0.892898i
$210$	15.0270	−	28.6738i	1.03696	−	1.97868i
$211$			23.6769i			1.62998i	0.579474	+	0.814991i	$0.303258\pi$
$211$			23.6769i			1.62998i	−0.579474	+	0.814991i	$0.696742\pi$
$212$	3.34213	+	5.78874i	0.229539	+	0.397573i
$213$	−9.27292	−	5.35372i	−0.635370	−	0.366831i
$214$	14.5579	−	25.2150i	0.995155	−	1.72366i
$215$	−3.48386	−	6.03423i	−0.237597	−	0.411531i
$216$	−3.83414			−0.260880
$217$	−1.09488	+	0.0447885i	−0.0743256	+	0.00304044i
$218$	3.45882			0.234261
$219$	−14.4870	+	8.36409i	−0.978943	+	0.565193i
$220$	5.59473	−	5.94477i	0.377196	−	0.400796i
$221$	1.61273	−	2.79332i	0.108484	−	0.187899i
$222$	−4.68689	−	8.11792i	−0.314563	−	0.544839i
$223$		−	22.1205i		−	1.48130i	−0.671892	−	0.740649i	$-0.734518\pi$
$223$		−	22.1205i		−	1.48130i	0.671892	−	0.740649i	$-0.265482\pi$
$224$	−10.8256	+	0.442842i	−0.723315	+	0.0295886i
$225$	11.9234			0.794893
$226$	0.199207	−	0.115012i	0.0132511	−	0.00765050i
$227$	1.76340	−	3.05429i	0.117041	−	0.202720i	−0.801553	−	0.597924i	$-0.795993\pi$
$227$	1.76340	−	3.05429i	0.117041	−	0.202720i	0.918594	+	0.395203i	$0.129326\pi$
$228$	5.99805	+	3.46298i	0.397231	+	0.229341i
$229$	−9.78263	+	5.64800i	−0.646454	+	0.373231i	−0.787096	−	0.616830i	$-0.788417\pi$
$229$	−9.78263	+	5.64800i	−0.646454	+	0.373231i	0.140642	+	0.990061i	$0.455083\pi$
$230$	−33.2284			−2.19102
$231$	15.0938	+	13.0839i	0.993097	+	0.860855i
$232$	15.1248			0.992989
$233$	−25.0638	+	14.4706i	−1.64199	+	0.948001i	−0.661859	+	0.749628i	$0.730232\pi$
$233$	−25.0638	+	14.4706i	−1.64199	+	0.948001i	−0.980127	+	0.198373i	$0.936434\pi$
$234$	−2.83981	−	1.63957i	−0.185644	−	0.107182i
$235$	−5.81354	+	10.0694i	−0.379234	+	0.656852i
$236$	7.07605	−	4.08536i	0.460612	−	0.265934i
$237$	−14.9134			−0.968730
$238$	−8.38703	−	13.2452i	−0.543650	−	0.858559i
$239$			16.3309i			1.05636i	0.849134	+	0.528178i	$0.177125\pi$
$239$			16.3309i			1.05636i	−0.849134	+	0.528178i	$0.822875\pi$
$240$	−18.1992	−	31.5219i	−1.17475	−	2.03473i
$241$	−4.95959	+	8.59026i	−0.319475	+	0.553347i	−0.980379	−	0.197124i	$-0.936840\pi$
$241$	−4.95959	+	8.59026i	−0.319475	+	0.553347i	0.660904	+	0.750471i	$0.270173\pi$
$242$	10.0814	+	15.2457i	0.648054	+	0.980033i
$243$	−16.4234	+	9.48205i	−1.05356	+	0.608274i
$244$	3.00317			0.192258
$245$	−1.84953	−	22.5686i	−0.118162	−	1.44186i
$246$	10.2632			0.654358
$247$	1.80834	+	3.13214i	0.115062	+	0.199293i
$248$	−0.426374	+	0.738501i	−0.0270748	+	0.0468949i
$249$	29.7249	+	17.1617i	1.88374	+	1.08758i
$250$	−1.24856	−	2.16257i	−0.0789657	−	0.136773i
$251$			20.4564i			1.29119i	0.763678	+	0.645597i	$0.223392\pi$
$251$			20.4564i			1.29119i	−0.763678	+	0.645597i	$0.776608\pi$
$252$	−3.71103	+	2.34987i	−0.233773	+	0.148028i
$253$	4.70370	−	19.9563i	0.295719	−	1.25464i
$254$	−5.36840	−	9.29834i	−0.336843	−	0.583430i
$255$	13.1303	−	22.7424i	0.822253	−	1.42418i
$256$	−7.97661	+	13.8159i	−0.498538	+	0.863494i
$257$	−2.79016	+	1.61090i	−0.174045	+	0.100485i	−0.584492	−	0.811400i	$-0.698706\pi$
$257$	−2.79016	+	1.61090i	−0.174045	+	0.100485i	0.410447	+	0.911885i	$0.365373\pi$
$258$			8.14704i			0.507213i
$259$	−5.80763	−	3.04358i	−0.360869	−	0.189119i
$260$			2.22621i			0.138064i
$261$	13.8811	−	8.01427i	0.859220	−	0.496071i
$262$	10.5000	+	6.06218i	0.648692	+	0.374523i
$263$	−17.0406	−	9.83838i	−1.05077	−	0.606660i	−0.127903	−	0.991787i	$-0.540825\pi$
$263$	−17.0406	−	9.83838i	−1.05077	−	0.606660i	−0.922864	+	0.385126i	$0.874158\pi$
$264$	14.8861	−	4.47666i	0.916175	−	0.275519i
$265$			28.4184i			1.74573i
$266$	17.5642	−	0.718498i	1.07693	−	0.0440540i
$267$	6.35021			0.388627
$268$	−0.502323	−	0.870049i	−0.0306843	−	0.0531467i
$269$	−1.47304	−	0.850463i	−0.0898131	−	0.0518536i	0.454421	−	0.890787i	$-0.349846\pi$
$269$	−1.47304	−	0.850463i	−0.0898131	−	0.0518536i	−0.544234	+	0.838934i	$0.683180\pi$
$270$	8.66851	+	5.00477i	0.527549	+	0.304581i
$271$	−6.83991	−	11.8471i	−0.415495	−	0.719658i	0.579985	−	0.814627i	$-0.303058\pi$
$271$	−6.83991	−	11.8471i	−0.415495	−	0.719658i	−0.995480	+	0.0949687i	$0.969725\pi$
$272$	−17.6268			−1.06878
$273$	−5.44282	+	0.222649i	−0.329414	+	0.0134754i
$274$			25.2434i			1.52501i
$275$	17.3561	−	5.21946i	1.04661	−	0.314745i
$276$	9.27292	+	5.35372i	0.558164	+	0.322256i
$277$	8.95829	+	5.17207i	0.538251	+	0.310759i	0.744370	−	0.667768i	$-0.232750\pi$
$277$	8.95829	+	5.17207i	0.538251	+	0.310759i	−0.206119	+	0.978527i	$0.566083\pi$
$278$	−8.65047	+	4.99435i	−0.518821	+	0.299541i
$279$			0.903703i			0.0541033i
$280$	−15.6082	−	8.17973i	−0.932769	−	0.488833i
$281$		−	25.5230i		−	1.52258i	−0.648414	−	0.761288i	$-0.724567\pi$
$281$		−	25.5230i		−	1.52258i	0.648414	−	0.761288i	$-0.275433\pi$
$282$	11.7736	−	6.79751i	0.701110	−	0.404786i
$283$	2.39516	−	4.14854i	0.142377	−	0.246605i	−0.786014	−	0.618209i	$-0.787859\pi$
$283$	2.39516	−	4.14854i	0.142377	−	0.246605i	0.928391	+	0.371604i	$0.121192\pi$
$284$	1.78947	−	3.09945i	0.106185	−	0.183918i
$285$	14.7230	+	25.5010i	0.872114	+	1.51055i
$286$	−4.85145	−	1.14348i	−0.286872	−	0.0676155i
$287$	6.06526	−	3.84060i	0.358021	−	0.226703i
$288$			8.93529i			0.526517i
$289$	2.14132	+	3.70887i	0.125960	+	0.218169i
$290$	−34.1952	−	19.7426i	−2.00801	−	1.15933i
$291$	−7.77292	+	13.4631i	−0.455656	+	0.789220i
$292$	−2.79568	−	4.84225i	−0.163605	−	0.283371i
$293$	2.06456			0.120613			0.0603064	−	0.998180i	$-0.480792\pi$
$293$	2.06456			0.120613			0.0603064	+	0.998180i	$0.480792\pi$
$294$	−11.3214	+	23.9344i	−0.660278	+	1.39588i
$295$	34.7382			2.02253
$296$	−4.41889	+	2.55125i	−0.256843	+	0.148288i
$297$	−4.23286	+	4.49769i	−0.245615	+	0.260982i
$298$	0.952535	−	1.64984i	0.0551789	−	0.0955726i
$299$	2.79568	+	4.84225i	0.161678	+	0.280035i
$300$			9.46492i			0.546457i
$301$	3.04871	+	4.81467i	0.175725	+	0.277513i
$302$	−27.3308			−1.57271
$303$	5.02480	−	2.90107i	0.288667	−	0.166662i
$304$	9.88243	−	17.1169i	0.566796	−	0.981719i
$305$	11.0575	+	6.38404i	0.633150	+	0.365549i
$306$	−11.1969	+	6.46451i	−0.640082	+	0.369551i
$307$	13.8444			0.790140			0.395070	−	0.918651i	$-0.370720\pi$
$307$	13.8444			0.790140			0.395070	+	0.918651i	$0.370720\pi$
$308$	−4.37325	+	5.04505i	−0.249189	+	0.287469i
$309$	−34.1456			−1.94247
$310$	1.92796	−	1.11311i	0.109501	−	0.0632202i
$311$	11.4811	+	6.62863i	0.651035	+	0.375875i	0.788853	−	0.614582i	$-0.210675\pi$
$311$	11.4811	+	6.62863i	0.651035	+	0.375875i	−0.137818	+	0.990458i	$0.544009\pi$
$312$	−2.11956	+	3.67119i	−0.119997	+	0.207840i
$313$	−12.7535	+	7.36323i	−0.720870	+	0.416194i	−0.815073	−	0.579359i	$-0.803303\pi$
$313$	−12.7535	+	7.36323i	−0.720870	+	0.416194i	0.0942031	+	0.995553i	$0.469970\pi$
$314$	−11.0575			−0.624010
$315$	−18.6591	+	0.763287i	−1.05132	+	0.0430063i
$316$		−	4.98477i		−	0.280415i
$317$	−5.08809	−	8.81284i	−0.285776	−	0.494978i	0.687021	−	0.726637i	$-0.258918\pi$
$317$	−5.08809	−	8.81284i	−0.285776	−	0.494978i	−0.972797	+	0.231659i	$0.925585\pi$
$318$	16.6142	−	28.7766i	0.931678	−	1.61371i
$319$	16.6976	−	17.7423i	0.934887	−	0.993379i
$320$	−8.63216	+	4.98378i	−0.482552	+	0.278602i
$321$	−39.8888			−2.22637
$322$	27.1540	−	1.11079i	1.51324	−	0.0619019i
$323$	14.2599			0.793444
$324$	−4.10301	−	7.10662i	−0.227945	−	0.394812i
$325$	−2.47126	+	4.28034i	−0.137081	+	0.237431i
$326$	−4.48150	−	2.58739i	−0.248207	−	0.143302i
$327$	−2.36930	−	4.10375i	−0.131023	−	0.226938i
$328$		−	5.58664i		−	0.308471i
$329$	4.41418	−	8.42296i	0.243362	−	0.464373i
$330$	−39.4991	−	9.30990i	−2.17435	−	0.512493i
$331$	1.62476	+	2.81417i	0.0893051	+	0.154681i	0.907218	−	0.420662i	$-0.138202\pi$
$331$	1.62476	+	2.81417i	0.0893051	+	0.154681i	−0.817913	+	0.575343i	$0.804869\pi$
$332$	−5.73624	+	9.93545i	−0.314817	+	0.545279i
$333$	−2.70370	+	4.68294i	−0.148162	+	0.256624i
$334$	28.5722	−	16.4962i	1.56340	−	0.902631i
$335$		−	4.27130i		−	0.233366i
$336$	15.9260	+	25.1511i	0.868835	+	1.37211i
$337$		−	0.515053i		−	0.0280567i	−0.999902	−	0.0140284i	$-0.995534\pi$
$337$		−	0.515053i		−	0.0280567i	0.999902	−	0.0140284i	$-0.00446551\pi$
$338$	−17.5295	+	10.1207i	−0.953482	+	0.550493i
$339$	−0.272915	−	0.157568i	−0.0148227	−	0.00855789i
$340$	7.60159	+	4.38878i	0.412254	+	0.238015i
$341$	0.395596	+	1.31546i	0.0214227	+	0.0712363i
$342$		−	14.4973i		−	0.783922i
$343$	2.26587	+	18.3811i	0.122345	+	0.992488i
$344$	4.43474			0.239105
$345$	22.7616	+	39.4242i	1.22544	+	2.12253i
$346$	26.2982	+	15.1833i	1.41380	+	0.816259i
$347$	−2.79568	−	1.61408i	−0.150080	−	0.0866486i	0.423080	−	0.906093i	$-0.360949\pi$
$347$	−2.79568	−	1.61408i	−0.150080	−	0.0866486i	−0.573159	+	0.819444i	$0.694282\pi$
$348$	6.36182	+	11.0190i	0.341029	+	0.590680i
$349$	−1.55330			−0.0831463			−0.0415731	−	0.999135i	$-0.513237\pi$
$349$	−1.55330			−0.0831463			−0.0415731	+	0.999135i	$0.513237\pi$
$350$	12.8518	+	20.2963i	0.686960	+	1.08488i
$351$		−	1.68431i		−	0.0899017i
$352$	3.91142	+	13.0065i	0.208480	+	0.693250i
$353$	−7.70494	−	4.44845i	−0.410093	−	0.236767i	0.280737	−	0.959785i	$-0.409421\pi$
$353$	−7.70494	−	4.44845i	−0.410093	−	0.236767i	−0.690830	+	0.723018i	$0.742754\pi$
$354$	−35.1760	−	20.3089i	−1.86958	−	1.07941i
$355$	13.1774	−	7.60799i	0.699385	−	0.403790i
$356$			2.12254i			0.112495i
$357$	−9.96978	+	19.0239i	−0.527656	+	1.00685i
$358$			19.5817i			1.03493i
$359$	−7.06968	+	4.08168i	−0.373123	+	0.215423i	−0.674822	−	0.737980i	$-0.735780\pi$
$359$	−7.06968	+	4.08168i	−0.373123	+	0.215423i	0.301699	+	0.953403i	$0.402446\pi$
$360$	−7.26628	+	12.5856i	−0.382967	+	0.663318i
$361$	1.50520	−	2.60709i	0.0792211	−	0.137215i
$362$	−7.80080	−	13.5114i	−0.410001	−	0.710142i
$363$	11.1827	−	22.4045i	0.586940	−	1.17593i
$364$	−0.0744200	−	1.81925i	−0.00390067	−	0.0953545i
$365$		−	23.7719i		−	1.24428i
$366$	−7.46457	−	12.9290i	−0.390180	−	0.675811i
$367$	−13.7524	−	7.93995i	−0.717870	−	0.414462i	0.0960984	−	0.995372i	$-0.469364\pi$
$367$	−13.7524	−	7.93995i	−0.717870	−	0.414462i	−0.813968	+	0.580910i	$0.802697\pi$
$368$	15.2781	−	26.4625i	0.796427	−	1.37945i
$369$	−2.96024	−	5.12728i	−0.154104	−	0.266916i
$370$	13.3208			0.692513
$371$	−0.949999	−	23.2234i	−0.0493215	−	1.20570i
$372$	−0.717370			−0.0371939
$373$	15.5866	−	8.99894i	0.807045	−	0.465947i	−0.0388839	−	0.999244i	$-0.512380\pi$
$373$	15.5866	−	8.99894i	0.807045	−	0.465947i	0.845929	+	0.533296i	$0.179047\pi$
$374$	−13.4687	+	14.3114i	−0.696450	+	0.740024i
$375$	−1.71053	+	2.96273i	−0.0883316	+	0.152995i
$376$	−3.70014	−	6.40883i	−0.190820	−	0.330510i
$377$			6.64419i			0.342193i
$378$	−7.25116	−	3.80009i	−0.372960	−	0.195455i
$379$	−17.6810			−0.908212			−0.454106	−	0.890948i	$-0.650041\pi$
$379$	−17.6810			−0.908212			−0.454106	+	0.890948i	$0.650041\pi$
$380$	−8.52363	+	4.92112i	−0.437253	+	0.252448i
$381$	−7.35475	+	12.7388i	−0.376795	+	0.652628i
$382$	−10.2673	−	5.92786i	−0.525323	−	0.303296i
$383$	−18.9520	+	10.9419i	−0.968401	+	0.559107i	−0.898748	−	0.438465i	$-0.855522\pi$
$383$	−18.9520	+	10.9419i	−0.968401	+	0.559107i	−0.0696526	+	0.997571i	$0.522189\pi$
$384$	30.2987			1.54617
$385$	−26.8267	+	9.27908i	−1.36721	+	0.472905i
$386$	28.5757			1.45446
$387$	4.07009	−	2.34987i	0.206894	−	0.119451i
$388$	−4.50000	−	2.59808i	−0.228453	−	0.131897i
$389$	10.4399	−	18.0825i	0.529326	−	0.916820i	−0.470089	−	0.882619i	$-0.655778\pi$
$389$	10.4399	−	18.0825i	0.529326	−	0.916820i	0.999415	−	0.0342006i	$-0.0108885\pi$
$390$	9.58414	−	5.53340i	0.485312	−	0.280195i
$391$	22.0457			1.11490
$392$	13.0284	+	6.16266i	0.658032	+	0.311262i
$393$		−	16.6105i		−	0.837887i
$394$	−7.52463	−	13.0330i	−0.379085	−	0.656595i
$395$	10.5965	−	18.3536i	0.533166	−	0.923471i
$396$	4.00975	+	3.77365i	0.201498	+	0.189633i
$397$	28.4660	−	16.4348i	1.42867	−	0.824840i	0.431650	−	0.902041i	$-0.357932\pi$
$397$	28.4660	−	16.4348i	1.42867	−	0.824840i	0.997016	+	0.0772012i	$0.0245984\pi$
$398$	27.5118			1.37904
$399$	−12.8840	−	20.3471i	−0.645007	−	1.01863i
$400$	27.0104			1.35052
$401$	−13.0607	−	22.6219i	−0.652223	−	1.12968i	−0.982582	−	0.185828i	$-0.940503\pi$
$401$	−13.0607	−	22.6219i	−0.652223	−	1.12968i	0.330360	−	0.943855i	$-0.392830\pi$
$402$	−2.49712	+	4.32513i	−0.124545	+	0.215718i
$403$	−0.324418	−	0.187303i	−0.0161604	−	0.00933022i
$404$	0.969674	+	1.67952i	0.0482431	+	0.0835595i
$405$		−	34.8882i		−	1.73361i
$406$	28.6041	+	14.9904i	1.41960	+	0.743963i
$407$	−1.88564	+	8.00020i	−0.0934677	+	0.396555i
$408$	8.35705	+	14.4748i	0.413736	+	0.716611i
$409$	3.91642	−	6.78344i	0.193654	−	0.335419i	−0.752804	−	0.658245i	$-0.771299\pi$
$409$	3.91642	−	6.78344i	0.193654	−	0.335419i	0.946459	+	0.322825i	$0.104633\pi$
$410$	−7.29235	+	12.6307i	−0.360143	+	0.623786i
$411$	29.9503	−	17.2918i	1.47734	−	0.852944i
$412$		−	11.4131i		−	0.562281i
$413$	−28.3878	+	1.16126i	−1.39687	+	0.0571419i
$414$		−	22.4126i		−	1.10152i
$415$	−42.2410	+	24.3879i	−2.07353	+	1.19715i
$416$	−3.20765	−	1.85194i	−0.157268	−	0.0907988i
$417$	11.8512	+	6.84230i	0.580356	+	0.335069i
$418$	−6.34617	−	21.1027i	−0.310401	−	1.03217i
$419$			5.10769i			0.249527i	0.992187	+	0.124764i	$0.0398172\pi$
$419$			5.10769i			0.249527i	−0.992187	+	0.124764i	$0.960183\pi$
$420$	−0.605906	−	14.8118i	−0.0295652	−	0.722741i
$421$	12.3171			0.600299			0.300150	−	0.953892i	$-0.402963\pi$
$421$	12.3171			0.600299			0.300150	+	0.953892i	$0.402963\pi$
$422$	19.6706	+	34.0705i	0.957550	+	1.65852i
$423$	−6.79179	−	3.92124i	−0.330228	−	0.190657i
$424$	−15.6642	−	9.04373i	−0.760721	−	0.439202i
$425$	9.74372	+	16.8766i	0.472640	+	0.818636i
$426$	−17.7914			−0.861994
$427$	−9.24953	−	4.84736i	−0.447616	−	0.234580i
$428$		−	13.3327i		−	0.644461i
$429$	1.96656	+	6.53934i	0.0949465	+	0.315722i
$430$	−10.0264	−	5.78874i	−0.483516	−	0.279158i
$431$	16.2748	+	9.39626i	0.783930	+	0.452602i	0.837821	−	0.545945i	$-0.183829\pi$
$431$	16.2748	+	9.39626i	0.783930	+	0.452602i	−0.0538914	+	0.998547i	$0.517162\pi$
$432$	−7.97141	+	4.60230i	−0.383525	+	0.221428i
$433$			13.0281i			0.626089i	0.949739	+	0.313044i	$0.101349\pi$
$433$			13.0281i			0.626089i	−0.949739	+	0.313044i	$0.898651\pi$
$434$	−1.53831	+	0.974074i	−0.0738410	+	0.0467570i
$435$			54.0951i			2.59366i
$436$	1.37167	−	0.791933i	0.0656910	−	0.0379267i
$437$	−12.3599	+	21.4079i	−0.591253	+	1.02408i
$438$	−13.8977	+	24.0715i	−0.664057	+	1.15018i
$439$	−18.1096	−	31.3667i	−0.864324	−	1.49705i	−0.867717	−	0.497058i	$-0.834413\pi$
$439$	−18.1096	−	31.3667i	−0.864324	−	1.49705i	0.00339323	−	0.999994i	$-0.498920\pi$
$440$	−5.06773	+	21.5008i	−0.241594	+	1.02501i
$441$	15.2226	−	1.24751i	0.724884	−	0.0594051i
$442$		−	5.35937i		−	0.254919i
$443$	13.1517	+	22.7794i	0.624857	+	1.08228i	0.988568	+	0.150772i	$0.0481761\pi$
$443$	13.1517	+	22.7794i	0.624857	+	1.08228i	−0.363711	+	0.931512i	$0.618491\pi$
$444$	−3.71737	−	2.14622i	−0.176419	−	0.101855i
$445$	−4.51204	+	7.81508i	−0.213891	+	0.370470i
$446$	−18.3776	−	31.8309i	−0.870204	−	1.50724i
$447$	−2.60996			−0.123447
$448$	6.88754	−	4.36128i	0.325406	−	0.206051i
$449$	−34.9064			−1.64734			−0.823669	−	0.567072i	$-0.808076\pi$
$449$	−34.9064			−1.64734			−0.823669	+	0.567072i	$0.808076\pi$
$450$	17.1575	−	9.90588i	0.808812	−	0.466968i
$451$	−6.55349	−	6.16761i	−0.308592	−	0.290421i
$452$	0.0526665	−	0.0912211i	0.00247723	−	0.00429068i
$453$	18.7217	+	32.4269i	0.879621	+	1.52355i
$454$		−	5.86008i		−	0.275027i
$455$	3.59329	−	6.85657i	0.168456	−	0.321441i
$456$	−18.7414			−0.877649
$457$	−1.09488	+	0.632132i	−0.0512166	+	0.0295699i	−0.525390	−	0.850862i	$-0.676080\pi$
$457$	−1.09488	+	0.632132i	−0.0512166	+	0.0295699i	0.474173	+	0.880432i	$0.342747\pi$
$458$	−9.38466	+	16.2547i	−0.438516	+	0.759533i
$459$	−5.75121	−	3.32046i	−0.268443	−	0.154986i
$460$	−13.1774	+	7.60799i	−0.614401	+	0.354724i
$461$	29.2638			1.36295			0.681476	−	0.731840i	$-0.261338\pi$
$461$	29.2638			1.36295			0.681476	+	0.731840i	$0.261338\pi$
$462$	32.5896	+	6.28758i	1.51621	+	0.292525i
$463$	−2.91874			−0.135646			−0.0678228	−	0.997697i	$-0.521605\pi$
$463$	−2.91874			−0.135646			−0.0678228	+	0.997697i	$0.521605\pi$
$464$	31.4453	−	18.1550i	1.45981	−	0.842823i
$465$	−2.64132	−	1.52496i	−0.122488	−	0.0707185i
$466$	−24.0442	+	41.6458i	−1.11383	+	1.92920i
$467$	−0.349525	+	0.201799i	−0.0161741	+	0.00933812i	−0.508065	−	0.861319i	$-0.669639\pi$
$467$	−0.349525	+	0.201799i	−0.0161741	+	0.00933812i	0.491891	+	0.870657i	$0.336306\pi$
$468$	−1.50158			−0.0694107
$469$	0.142785	+	3.49048i	0.00659320	+	0.161175i
$470$			19.3194i			0.891139i
$471$	7.57442	+	13.1193i	0.349011	+	0.604505i
$472$	−11.0549	+	19.1476i	−0.508842	+	0.881341i
$473$	4.89591	−	5.20223i	0.225114	−	0.239199i
$474$	−21.4601	+	12.3900i	−0.985693	+	0.569090i
$475$	−21.8512			−1.00260
$476$	−6.35868	−	3.33237i	−0.291450	−	0.152739i
$477$	−19.1683			−0.877655
$478$	13.5676	+	23.4997i	0.620567	+	1.07485i
$479$	−6.36182	+	11.0190i	−0.290679	+	0.503471i	−0.973970	−	0.226675i	$-0.927214\pi$
$479$	−6.36182	+	11.0190i	−0.290679	+	0.503471i	0.683292	+	0.730146i	$0.260548\pi$
$480$	−26.1158	−	15.0780i	−1.19202	−	0.688211i
$481$	−1.12074	−	1.94118i	−0.0511015	−	0.0885104i
$482$			16.4816i			0.750716i
$483$	−19.9185	−	31.4563i	−0.906324	−	1.43131i
$484$	7.48865	+	3.73779i	0.340393	+	0.169899i
$485$	−11.0458	−	19.1319i	−0.501565	−	0.868737i
$486$	−15.7553	+	27.2889i	−0.714673	+	1.23785i
$487$	−4.11793	+	7.13246i	−0.186601	+	0.323203i	−0.944115	−	0.329617i	$-0.893081\pi$
$487$	−4.11793	+	7.13246i	−0.186601	+	0.323203i	0.757514	+	0.652819i	$0.226414\pi$
$488$	−7.03775	+	4.06325i	−0.318584	+	0.183935i
$489$			7.08949i			0.320598i
$490$	−21.4113	−	30.9392i	−0.967265	−	1.39769i
$491$			15.8840i			0.716833i	0.933562	+	0.358417i	$0.116683\pi$
$491$			15.8840i			0.716833i	−0.933562	+	0.358417i	$0.883317\pi$
$492$	4.07009	−	2.34987i	0.183494	−	0.105940i
$493$	22.6871	+	13.0984i	1.02178	+	0.589924i
$494$	5.20433	+	3.00472i	0.234154	+	0.135189i
$495$	6.74177	+	22.4182i	0.303020	+	1.00762i
$496$			2.04719i			0.0919214i
$497$	−10.5142	+	6.65771i	−0.471626	+	0.298639i
$498$	57.0312			2.55563
$499$	−18.2112	−	31.5428i	−0.815246	−	1.41205i	−0.909151	−	0.416467i	$-0.863268\pi$
$499$	−18.2112	−	31.5428i	−0.815246	−	1.41205i	0.0939047	−	0.995581i	$-0.470065\pi$
$500$	−0.990285	−	0.571741i	−0.0442869	−	0.0255690i
$501$	−39.1442	−	22.5999i	−1.74883	−	1.00969i
$502$	16.9950	+	29.4363i	0.758526	+	1.31380i
$503$	16.8993			0.753501			0.376750	−	0.926315i	$-0.377041\pi$
$503$	16.8993			0.753501			0.376750	+	0.926315i	$0.377041\pi$
$504$	5.51724	−	10.5278i	0.245757	−	0.468944i
$505$			8.24522i			0.366907i
$506$	−9.81111	−	32.6246i	−0.436157	−	1.45034i
$507$	24.0156	+	13.8654i	1.06657	+	0.615785i
$508$	−4.25791	−	2.45830i	−0.188914	−	0.109070i
$509$	14.2352	−	8.21868i	0.630963	−	0.364286i	−0.150162	−	0.988661i	$-0.547980\pi$
$509$	14.2352	−	8.21868i	0.630963	−	0.364286i	0.781125	+	0.624375i	$0.214646\pi$
$510$		−	43.6344i		−	1.93216i
$511$	0.794668	+	19.4262i	0.0351541	+	0.859366i
$512$		−	0.112296i		−	0.00496282i
$513$	6.44880	−	3.72322i	0.284722	−	0.164384i
$514$	−2.67665	+	4.63609i	−0.118062	+	0.204489i
$515$	24.2616	−	42.0223i	1.06909	−	1.85172i
$516$	1.86535	+	3.23088i	0.0821175	+	0.142232i
$517$	−11.6029	−	2.73479i	−0.510295	−	0.120276i
$518$	−10.8856	+	0.445299i	−0.478288	+	0.0195653i
$519$		−	41.6024i		−	1.82614i
$520$	−3.01204	−	5.21700i	−0.132087	−	0.228781i
$521$	−10.9331	−	6.31223i	−0.478988	−	0.276544i	0.241007	−	0.970523i	$-0.422522\pi$
$521$	−10.9331	−	6.31223i	−0.478988	−	0.276544i	−0.719995	+	0.693980i	$0.755856\pi$
$522$	13.3164	−	23.0647i	0.582844	−	1.00952i
$523$	19.0290	+	32.9592i	0.832081	+	1.44121i	0.896385	+	0.443277i	$0.146184\pi$
$523$	19.0290	+	32.9592i	0.832081	+	1.44121i	−0.0643034	+	0.997930i	$0.520483\pi$
$524$	5.55200			0.242540
$525$	15.2772	−	29.1512i	0.666750	−	1.27226i
$526$	−32.6947			−1.42556
$527$	−1.27912	+	0.738501i	−0.0557194	+	0.0321696i
$528$	25.5755	−	27.1757i	1.11303	−	1.18267i
$529$	−7.60821	+	13.1778i	−0.330792	+	0.572948i
$530$	23.6099	+	40.8935i	1.02555	+	1.77630i
$531$			23.4309i			1.01682i
$532$	6.80095	−	4.30644i	0.294859	−	0.186708i
$533$	2.45417			0.106302
$534$	9.13782	−	5.27572i	0.395432	−	0.228303i
$535$	28.3423	−	49.0903i	1.22534	−	2.12236i
$536$	2.35433	+	1.35927i	0.101692	+	0.0587117i
$537$	23.2330	−	13.4136i	1.00258	−	0.578838i
$538$	−2.82624			−0.121848
$539$	21.6124	−	8.47959i	0.930913	−	0.365242i
$540$	4.58358			0.197246
$541$	31.0816	−	17.9449i	1.33630	−	0.771513i	0.350044	−	0.936733i	$-0.386167\pi$
$541$	31.0816	−	17.9449i	1.33630	−	0.771513i	0.986257	+	0.165220i	$0.0528335\pi$
$542$	−19.6850	−	11.3651i	−0.845541	−	0.488173i
$543$	−10.6871	+	18.5107i	−0.458629	+	0.794369i
$544$	−12.6472	+	7.30187i	−0.542244	+	0.313065i
$545$	6.73387			0.288447
$546$	−7.64712	+	4.84225i	−0.327267	+	0.207229i
$547$			1.19197i			0.0509651i	0.999675	+	0.0254826i	$0.00811223\pi$
$547$			1.19197i			0.0509651i	−0.999675	+	0.0254826i	$0.991888\pi$
$548$	5.77975	+	10.0108i	0.246899	+	0.427641i
$549$	−4.30605	+	7.45829i	−0.183778	+	0.318312i
$550$	20.6388	−	21.9300i	0.880039	−	0.935100i
$551$	−25.4390	+	14.6872i	−1.08374	+	0.625696i
$552$	−28.9741			−1.23322
$553$	−8.04583	+	15.3527i	−0.342143	+	0.652863i
$554$	17.1877			0.730235
$555$	−9.12476	−	15.8046i	−0.387325	−	0.670866i
$556$	−2.28702	+	3.96124i	−0.0969913	+	0.167994i
$557$	−9.37995	−	5.41552i	−0.397441	−	0.229463i	0.287938	−	0.957649i	$-0.407030\pi$
$557$	−9.37995	−	5.41552i	−0.397441	−	0.229463i	−0.685379	+	0.728186i	$0.740364\pi$
$558$	0.750792	+	1.30041i	0.0317835	+	0.0550507i
$559$			1.94815i			0.0823979i
$560$	−42.2690	+	1.72910i	−1.78619	+	0.0730676i
$561$	26.2060	+	6.17674i	1.10642	+	0.260782i
$562$	−21.2044	−	36.7271i	−0.894453	−	1.54924i
$563$	−5.85316	+	10.1380i	−0.246681	+	0.427265i	−0.962603	−	0.270916i	$-0.912673\pi$
$563$	−5.85316	+	10.1380i	−0.246681	+	0.427265i	0.715922	+	0.698181i	$0.246007\pi$
$564$	3.11273	−	5.39140i	0.131069	−	0.227019i
$565$	0.387830	−	0.223914i	0.0163161	−	0.00942013i
$566$		−	7.95954i		−	0.334564i
$567$	1.16628	+	28.5105i	0.0489790	+	1.19733i
$568$			9.68450i			0.406353i
$569$	−17.6501	+	10.1903i	−0.739929	+	0.427198i	−0.822043	−	0.569425i	$-0.807166\pi$
$569$	−17.6501	+	10.1903i	−0.739929	+	0.427198i	0.0821147	+	0.996623i	$0.473833\pi$
$570$	42.3721	+	24.4635i	1.77477	+	1.02467i
$571$	2.14213	+	1.23676i	0.0896455	+	0.0517569i	0.544153	−	0.838986i	$-0.316851\pi$
$571$	2.14213	+	1.23676i	0.0896455	+	0.0517569i	−0.454507	+	0.890743i	$0.650185\pi$
$572$	−2.18576	+	0.657318i	−0.0913911	+	0.0274838i
$573$			16.2424i			0.678536i
$574$	5.53703	−	10.5655i	0.231111	−	0.440996i
$575$	−33.7817			−1.40879
$576$	−3.36156	−	5.82240i	−0.140065	−	0.242600i
$577$	19.1278	+	11.0434i	0.796300	+	0.459744i	0.842176	−	0.539203i	$-0.181275\pi$
$577$	19.1278	+	11.0434i	0.796300	+	0.459744i	−0.0458759	+	0.998947i	$0.514608\pi$
$578$	6.16261	+	3.55798i	0.256331	+	0.147993i
$579$	−19.5744	−	33.9039i	−0.813486	−	1.40900i
$580$	−18.0811			−0.750778
$581$	33.7038	−	21.3417i	1.39827	−	0.885402i
$582$			25.8308i			1.07072i
$583$	−27.9020	+	8.39091i	−1.15558	+	0.347516i
$584$	13.1030	+	7.56503i	0.542206	+	0.313043i
$585$	−5.52874	−	3.19202i	−0.228585	−	0.131974i
$586$	2.97085	−	1.71522i	0.122725	−	0.0708552i
$587$			30.0857i			1.24177i	0.783902	+	0.620885i	$0.213227\pi$
$587$			30.0857i			1.24177i	−0.783902	+	0.620885i	$0.786773\pi$
$588$	0.990285	+	12.0838i	0.0408387	+	0.498329i
$589$		−	1.65616i		−	0.0682407i
$590$	49.9875	−	28.8603i	2.05795	−	1.18816i
$591$	−10.3088	+	17.8554i	−0.424047	+	0.734472i
$592$	−6.12476	+	10.6084i	−0.251726	+	0.436003i
$593$	−2.14684	−	3.71843i	−0.0881601	−	0.152698i	0.818573	−	0.574402i	$-0.194765\pi$
$593$	−2.14684	−	3.71843i	−0.0881601	−	0.152698i	−0.906733	+	0.421704i	$0.861432\pi$
$594$	−2.35433	+	9.98871i	−0.0965994	+	0.409842i
$595$	−16.3285	−	25.7867i	−0.669402	−	1.05715i
$596$		−	0.872372i		−	0.0357338i
$597$	−18.8457	−	32.6417i	−0.771303	−	1.33594i
$598$	8.04583	+	4.64526i	0.329018	+	0.189959i
$599$	−4.62928	+	8.01814i	−0.189147	+	0.327612i	−0.944966	−	0.327168i	$-0.893906\pi$
$599$	−4.62928	+	8.01814i	−0.189147	+	0.327612i	0.755819	+	0.654781i	$0.227239\pi$
$600$	−12.8059	−	22.1805i	−0.522799	−	0.905515i
$601$	12.8758			0.525216			0.262608	−	0.964903i	$-0.415417\pi$
$601$	12.8758			0.525216			0.262608	+	0.964903i	$0.415417\pi$
$602$	8.38703	+	4.39536i	0.341830	+	0.179141i
$603$	2.88099			0.117323
$604$	−10.8386	+	6.25767i	−0.441017	+	0.254621i
$605$	19.6271	+	29.6815i	0.797955	+	1.20672i
$606$	4.82038	−	8.34914i	0.195815	−	0.339161i
$607$	0.452232	+	0.783290i	0.0183555	+	0.0317927i	0.875057	−	0.484019i	$-0.160824\pi$
$607$	0.452232	+	0.783290i	0.0183555	+	0.0317927i	−0.856702	+	0.515812i	$0.827490\pi$
$608$		−	16.3751i		−	0.664098i
$609$	−1.80834	−	44.2062i	−0.0732777	−	1.79132i
$610$	21.2153			0.858983
$611$	2.81535	−	1.62544i	0.113897	−	0.0657584i
$612$	−2.96024	+	5.12728i	−0.119660	+	0.207258i
$613$	−13.9055	−	8.02835i	−0.561638	−	0.324262i	0.192165	−	0.981363i	$-0.438449\pi$
$613$	−13.9055	−	8.02835i	−0.561638	−	0.324262i	−0.753803	+	0.657101i	$0.771783\pi$
$614$	19.9218	−	11.5018i	0.803977	−	0.464176i
$615$	19.9811			0.805717
$616$	3.42257	−	17.7397i	0.137899	−	0.714755i
$617$	33.0643			1.33112			0.665560	−	0.746345i	$-0.268193\pi$
$617$	33.0643			1.33112			0.665560	+	0.746345i	$0.268193\pi$
$618$	−49.1347	+	28.3679i	−1.97649	+	1.14113i
$619$	−18.8479	−	10.8818i	−0.757561	−	0.437378i	0.0708586	−	0.997486i	$-0.477426\pi$
$619$	−18.8479	−	10.8818i	−0.757561	−	0.437378i	−0.828419	+	0.560109i	$0.810759\pi$
$620$	0.509715	−	0.882853i	0.0204707	−	0.0354562i
$621$	9.96978	−	5.75605i	0.400073	−	0.230982i
$622$	22.0281			0.883247
$623$	3.42596	−	6.53727i	0.137258	−	0.261910i
$624$			10.1768i			0.407400i
$625$	11.2307	+	19.4521i	0.449226	+	0.778082i
$626$	−12.2347	+	21.1910i	−0.488995	+	0.846964i
$627$	−20.6904	+	21.9849i	−0.826295	+	0.877993i
$628$	−4.38508	+	2.53173i	−0.174984	+	0.101027i
$629$	−8.83778			−0.352385
$630$	−26.2159	+	16.6002i	−1.04447	+	0.661368i
$631$	−39.6317			−1.57771			−0.788857	−	0.614577i	$-0.789327\pi$
$631$	−39.6317			−1.57771			−0.788857	+	0.614577i	$0.789327\pi$
$632$	6.74433	+	11.6815i	0.268275	+	0.464666i
$633$	26.9489	−	46.6768i	1.07112	−	1.85524i
$634$	−14.6433	−	8.45432i	−0.581560	−	0.335764i
$635$	−10.4516	−	18.1027i	−0.414758	−	0.718383i
$636$		−	15.2160i		−	0.603353i
$637$	−2.70721	+	5.72327i	−0.107264	+	0.226764i
$638$	9.28728	−	39.4031i	0.367687	−	1.55998i
$639$	5.13160	+	8.88819i	0.203003	+	0.351611i
$640$	−21.5282	+	37.2880i	−0.850979	+	1.47394i
$641$	9.99153	−	17.3058i	0.394642	−	0.683539i	−0.598414	−	0.801187i	$-0.704202\pi$
$641$	9.99153	−	17.3058i	0.394642	−	0.683539i	0.993055	+	0.117648i	$0.0375354\pi$
$642$	−57.3991	+	33.1394i	−2.26536	+	1.30791i
$643$		−	34.9225i		−	1.37721i	−0.725137	−	0.688604i	$-0.758224\pi$
$643$		−	34.9225i		−	1.37721i	0.725137	−	0.688604i	$-0.241776\pi$
$644$	10.5142	−	6.65771i	0.414317	−	0.262351i
$645$			15.8612i			0.624536i
$646$	20.5197	−	11.8471i	0.807338	−	0.466117i
$647$	−30.9428	−	17.8648i	−1.21649	−	0.702340i	−0.252323	−	0.967643i	$-0.581194\pi$
$647$	−30.9428	−	17.8648i	−1.21649	−	0.702340i	−0.964165	+	0.265304i	$0.914528\pi$
$648$	19.2303	+	11.1026i	0.755439	+	0.436153i
$649$	10.2569	+	34.1069i	0.402618	+	1.33881i
$650$			8.21243i			0.322118i
$651$	2.20944	+	1.15790i	0.0865950	+	0.0453815i
$652$	−2.36964			−0.0928024
$653$	19.3594	+	33.5314i	0.757591	+	1.31219i	0.944076	+	0.329728i	$0.106957\pi$
$653$	19.3594	+	33.5314i	0.757591	+	1.31219i	−0.186485	+	0.982458i	$0.559710\pi$
$654$	−6.81875	−	3.93680i	−0.266634	−	0.153941i
$655$	20.4421	+	11.8023i	0.798741	+	0.461153i
$656$	−6.70591	−	11.6150i	−0.261822	−	0.453489i
$657$	16.0341			0.625552
$658$	−0.645828	−	15.7877i	−0.0251770	−	0.615470i
$659$			23.9846i			0.934307i	0.884176	+	0.467154i	$0.154721\pi$
$659$			23.9846i			0.934307i	−0.884176	+	0.467154i	$0.845279\pi$
$660$	−17.7958	+	5.35169i	−0.692700	+	0.208314i
$661$	−23.1025	−	13.3382i	−0.898581	−	0.518796i	−0.0218417	−	0.999761i	$-0.506953\pi$
$661$	−23.1025	−	13.3382i	−0.898581	−	0.518796i	−0.876740	+	0.480965i	$0.840286\pi$
$662$	4.67600	+	2.69969i	0.181738	+	0.104926i
$663$	−6.35868	+	3.67119i	−0.246951	+	0.142577i
$664$		−	31.0442i		−	1.20475i
$665$	34.1952	−	1.39882i	1.32603	−	0.0542441i
$666$			8.98486i			0.348156i
$667$	−39.3284	+	22.7063i	−1.52280	+	0.879190i
$668$	7.55395	−	13.0838i	0.292271	−	0.506229i
$669$	−25.1774	+	43.6086i	−0.973416	+	1.68601i
$670$	−3.54857	−	6.14630i	−0.137093	−	0.237452i
$671$	−3.00317	+	12.7415i	−0.115936	+	0.491881i
$672$	21.8457	+	11.4486i	0.842716	+	0.441639i
$673$		−	44.9698i		−	1.73346i	−0.498780	−	0.866728i	$-0.666219\pi$
$673$		−	44.9698i		−	1.73346i	0.498780	−	0.866728i	$-0.333781\pi$
$674$	−0.427903	−	0.741150i	−0.0164822	−	0.0285480i
$675$	8.81285	+	5.08810i	0.339207	+	0.195841i
$676$	−4.63448	+	8.02715i	−0.178249	+	0.308737i
$677$	−9.04057	−	15.6587i	−0.347457	−	0.601814i	0.638340	−	0.769755i	$-0.279621\pi$
$677$	−9.04057	−	15.6587i	−0.347457	−	0.601814i	−0.985797	+	0.167941i	$0.946288\pi$
$678$	−0.523625			−0.0201097
$679$	9.66615	+	15.2653i	0.370953	+	0.585827i
$680$	−23.7518			−0.910842
$681$	−6.95275	+	4.01417i	−0.266430	+	0.153823i
$682$	1.66213	+	1.56426i	0.0636464	+	0.0598987i
$683$	−7.83297	+	13.5671i	−0.299720	+	0.519131i	−0.976072	−	0.217448i	$-0.930227\pi$
$683$	−7.83297	+	13.5671i	−0.299720	+	0.519131i	0.676351	+	0.736579i	$0.263560\pi$
$684$	−3.31930	−	5.74920i	−0.126917	−	0.219826i
$685$			49.1457i			1.87776i
$686$	18.5315	+	24.5676i	0.707535	+	0.937994i
$687$	25.7141			0.981054
$688$	9.22010	−	5.32323i	0.351513	−	0.202946i
$689$	3.97284	−	6.88116i	0.151353	−	0.262151i
$690$	65.5068	+	37.8204i	2.49380	+	1.43980i
$691$	−28.9396	+	16.7083i	−1.10091	+	0.635612i	−0.936461	−	0.350773i	$-0.885919\pi$
$691$	−28.9396	+	16.7083i	−1.10091	+	0.635612i	−0.164452	+	0.986385i	$0.552586\pi$
$692$	13.9055			0.528608
$693$	−6.25875	−	18.0946i	−0.237750	−	0.687358i
$694$	−5.36389			−0.203610
$695$	−16.8414	+	9.72336i	−0.638829	+	0.368828i
$696$	−29.8171	−	17.2149i	−1.13021	−	0.652530i
$697$	4.83818	−	8.37997i	0.183259	−	0.317414i
$698$	−2.23517	+	1.29047i	−0.0846023	+	0.0488451i
$699$	65.8814			2.49186
$700$	9.74372	+	5.10635i	0.368278	+	0.193002i
$701$		−	31.6783i		−	1.19647i	−0.801319	−	0.598237i	$-0.795868\pi$
$701$		−	31.6783i		−	1.19647i	0.801319	−	0.598237i	$-0.204132\pi$
$702$	−1.39931	−	2.42368i	−0.0528137	−	0.0914760i
$703$	4.95488	−	8.58211i	0.186877	−	0.323680i
$704$	−7.44196	−	7.00377i	−0.280480	−	0.263964i
$705$	22.9218	−	13.2339i	0.863283	−	0.498417i
$706$	−14.7830			−0.556365
$707$	−0.275629	−	6.73794i	−0.0103661	−	0.253406i
$708$	−18.5997			−0.699021
$709$	22.2547	+	38.5463i	0.835794	+	1.44764i	0.893382	+	0.449297i	$0.148326\pi$
$709$	22.2547	+	38.5463i	0.835794	+	1.44764i	−0.0575886	+	0.998340i	$0.518341\pi$
$710$	12.6414	−	21.8955i	0.474422	−	0.821722i
$711$	12.3795	+	7.14733i	0.464269	+	0.268046i
$712$	−2.87177	−	4.97406i	−0.107624	−	0.186411i
$713$		−	2.56040i		−	0.0958877i
$714$	1.45865	+	35.6578i	0.0545887	+	1.33446i
$715$	−9.44514	−	2.22621i	−0.353228	−	0.0832557i
$716$	4.48345	+	7.76556i	0.167554	+	0.290213i
$717$	18.5877	−	32.1948i	0.694170	−	1.20234i
$718$	−6.78207	+	11.7469i	−0.253105	+	0.438390i
$719$	10.0647	−	5.81086i	0.375350	−	0.216709i	−0.300443	−	0.953800i	$-0.597135\pi$
$719$	10.0647	−	5.81086i	0.375350	−	0.216709i	0.675793	+	0.737091i	$0.263801\pi$
$720$			34.8882i			1.30021i
$721$	−18.4216	+	35.1514i	−0.686058	+	1.30911i
$722$		−	5.00205i		−	0.186157i
$723$	19.5548	−	11.2899i	0.727249	−	0.419878i
$724$	−6.18715	−	3.57215i	−0.229943	−	0.132758i
$725$	−34.7646	−	20.0714i	−1.29113	−	0.745432i
$726$	−2.52188	−	41.5301i	−0.0935959	−	1.54133i
$727$		−	31.6745i		−	1.17474i	−0.809318	−	0.587371i	$-0.800163\pi$
$727$		−	31.6745i		−	1.17474i	0.809318	−	0.587371i	$-0.199837\pi$
$728$	2.63582	+	4.16261i	0.0976899	+	0.154277i
$729$	10.8148			0.400548
$730$	−19.7495	−	34.2072i	−0.730963	−	1.26606i
$731$	6.65211	+	3.84060i	0.246037	+	0.142050i
$732$	−5.92047	−	3.41819i	−0.218827	−	0.126340i
$733$	21.3834	+	37.0371i	0.789812	+	1.36800i	0.926082	+	0.377323i	$0.123155\pi$
$733$	21.3834	+	37.0371i	0.789812	+	1.36800i	−0.136269	+	0.990672i	$0.543511\pi$
$734$	−26.3859			−0.973921
$735$	−22.0413	+	46.5972i	−0.813006	+	1.71876i
$736$		−	25.3157i		−	0.933150i
$737$	4.19368	−	1.26115i	0.154476	−	0.0464552i
$738$	−8.51943	−	4.91870i	−0.313605	−	0.181060i
$739$	12.9694	+	7.48786i	0.477085	+	0.275445i	0.719201	−	0.694802i	$-0.244508\pi$
$739$	12.9694	+	7.48786i	0.477085	+	0.275445i	−0.242116	+	0.970247i	$0.577841\pi$
$740$	5.28263	−	3.04993i	0.194193	−	0.112118i
$741$		−	8.23297i		−	0.302446i
$742$	−20.6609	−	32.6287i	−0.758485	−	1.19784i
$743$			23.9164i			0.877409i	0.898631	+	0.438705i	$0.144563\pi$
$743$			23.9164i			0.877409i	−0.898631	+	0.438705i	$0.855437\pi$
$744$	1.68112	−	0.970592i	0.0616327	−	0.0355836i
$745$	1.85446	−	3.21203i	0.0679423	−	0.117679i
$746$	14.9525	−	25.8986i	0.547451	−	0.948213i
$747$	−16.4496	−	28.4916i	−0.601861	−	1.04245i
$748$	−2.06456	+	8.75929i	−0.0754877	+	0.320271i
$749$	−21.5201	+	41.0638i	−0.786328	+	1.50044i
$750$			5.68441i			0.207565i
$751$	14.2089	+	24.6105i	0.518490	+	0.898051i	0.999769	+	0.0214837i	$0.00683902\pi$
$751$	14.2089	+	24.6105i	0.518490	+	0.898051i	−0.481279	+	0.876567i	$0.659828\pi$
$752$	−15.3856	−	8.88290i	−0.561057	−	0.323926i
$753$	23.2833	−	40.3279i	0.848491	−	1.46963i
$754$	5.51996	+	9.56085i	0.201025	+	0.348186i
$755$	−53.2095			−1.93649
$756$	−3.74567	+	0.153224i	−0.136229	+	0.00557271i
$757$	8.67386			0.315257			0.157628	−	0.987498i	$-0.449615\pi$
$757$	8.67386			0.315257			0.157628	+	0.987498i	$0.449615\pi$
$758$	−25.4426	+	14.6893i	−0.924116	+	0.533538i
$759$	−31.9871	+	33.9884i	−1.16106	+	1.23370i
$760$	13.3164	−	23.0647i	0.483037	−	0.836645i
$761$	−2.61144	−	4.52314i	−0.0946646	−	0.163964i	0.814804	−	0.579737i	$-0.196845\pi$
$761$	−2.61144	−	4.52314i	−0.0946646	−	0.163964i	−0.909469	+	0.415773i	$0.863511\pi$
$762$			24.4411i			0.885409i
$763$	−5.50288	+	0.225106i	−0.199218	+	0.00814939i
$764$	−5.42898			−0.196414
$765$	−21.7988	+	12.5856i	−0.788139	+	0.455032i
$766$	−18.1810	+	31.4904i	−0.656906	+	1.13779i
$767$	−8.41141	−	4.85633i	−0.303718	−	0.175352i
$768$	31.4503	−	18.1579i	1.13487	−	0.655216i
$769$	−47.9896			−1.73055			−0.865275	−	0.501298i	$-0.832856\pi$
$769$	−47.9896			−1.73055			−0.865275	+	0.501298i	$0.832856\pi$
$770$	−30.8940	+	35.6398i	−1.11334	+	1.28437i
$771$	7.33405			0.264129
$772$	11.3323	−	6.54270i	0.407858	−	0.235477i
$773$	31.0739	+	17.9405i	1.11765	+	0.645275i	0.940800	−	0.338963i	$-0.110076\pi$
$773$	31.0739	+	17.9405i	1.11765	+	0.645275i	0.176849	+	0.984238i	$0.443409\pi$
$774$	3.90451	−	6.76282i	0.140345	−	0.243084i
$775$	1.96006	−	1.13164i	0.0704074	−	0.0406498i
$776$	14.0607			0.504748
$777$	7.98503	+	12.6104i	0.286461	+	0.452394i
$778$		−	34.6938i		−	1.24383i
$779$	5.42502	+	9.39642i	0.194372	+	0.336662i
$780$	2.53386	−	4.38878i	0.0907268	−	0.157143i
$781$	11.3605	+	10.6916i	0.406512	+	0.382576i
$782$	31.7233	−	18.3154i	1.13442	−	0.654959i
$783$	13.6798			0.488877
$784$	34.4841	−	2.82601i	1.23158	−	0.100929i
$785$	−21.5275			−0.768350
$786$	−13.7999	−	23.9021i	−0.492225	−	0.852559i
$787$	11.1507	−	19.3135i	0.397478	−	0.688452i	−0.595936	−	0.803032i	$-0.703219\pi$
$787$	11.1507	−	19.3135i	0.397478	−	0.688452i	0.993414	+	0.114580i	$0.0365521\pi$
$788$	−5.96811	−	3.44569i	−0.212605	−	0.122748i
$789$	22.3960	+	38.7909i	0.797317	+	1.38099i
$790$		−	35.2139i		−	1.25286i
$791$	−0.309447	+	0.195946i	−0.0110027	+	0.00696704i
$792$	−14.5023	−	3.41819i	−0.515318	−	0.121460i
$793$	−1.78495	−	3.09163i	−0.0633855	−	0.109787i
$794$	27.3079	−	47.2987i	0.969122	−	1.67857i
$795$	32.3457	−	56.0244i	1.14718	−	1.98698i
$796$	10.9104	−	6.29913i	0.386709	−	0.223267i
$797$		−	12.0564i		−	0.427061i	−0.976936	−	0.213531i	$-0.931504\pi$
$797$		−	12.0564i		−	0.427061i	0.976936	−	0.213531i	$-0.0684963\pi$
$798$	−35.4440	−	18.5750i	−1.25470	−	0.657548i
$799$		−	12.8177i		−	0.453456i
$800$	19.3799	−	11.1890i	0.685184	−	0.395591i
$801$	−5.27128	−	3.04338i	−0.186252	−	0.107532i
$802$	−37.5883	−	21.7016i	−1.32729	−	0.766310i
$803$	23.3399	−	7.01895i	0.823646	−	0.247693i
$804$			2.28696i			0.0806550i
$805$	52.8654	−	2.16257i	1.86326	−	0.0762204i
$806$	−0.622440			−0.0219245
$807$	1.93598	+	3.35322i	0.0681498	+	0.118039i
$808$	−4.54475	−	2.62391i	−0.159884	−	0.0923089i
$809$	−7.28188	−	4.20419i	−0.256017	−	0.147812i	0.366499	−	0.930418i	$-0.380556\pi$
$809$	−7.28188	−	4.20419i	−0.256017	−	0.147812i	−0.622516	+	0.782607i	$0.713890\pi$
$810$	−28.9849	−	50.2034i	−1.01843	−	1.76397i
$811$	−12.6501			−0.444207			−0.222103	−	0.975023i	$-0.571292\pi$
$811$	−12.6501			−0.444207			−0.222103	+	0.975023i	$0.571292\pi$
$812$	14.7758	−	0.604433i	0.518529	−	0.0212115i
$813$			31.1406i			1.09215i
$814$	3.93312	+	13.0787i	0.137856	+	0.458408i
$815$	−8.72489	−	5.03732i	−0.305620	−	0.176450i
$816$	34.7496	+	20.0627i	1.21648	+	0.702336i
$817$	−7.45898	+	4.30644i	−0.260957	+	0.150663i
$818$		−	13.0150i		−	0.455057i
$819$	4.62476	+	2.42368i	0.161602	+	0.0846903i
$820$			6.67864i			0.233228i
$821$	0.465724	−	0.268886i	0.0162539	−	0.00938419i	−0.491851	−	0.870679i	$-0.663680\pi$
$821$	0.465724	−	0.268886i	0.0162539	−	0.00938419i	0.508105	+	0.861295i	$0.330346\pi$
$822$	28.7319	−	49.7652i	1.00214	−	1.73576i
$823$	3.30150	−	5.71837i	0.115083	−	0.199330i	−0.802730	−	0.596343i	$-0.796620\pi$
$823$	3.30150	−	5.71837i	0.115083	−	0.199330i	0.917813	+	0.397013i	$0.129953\pi$
$824$	15.4417	+	26.7459i	0.537938	+	0.931736i
$825$	−40.1568	−	9.46492i	−1.39808	−	0.329526i
$826$	−39.8847	+	25.2555i	−1.38777	+	0.878750i
$827$			33.0990i			1.15097i	0.817814	+	0.575483i	$0.195186\pi$
$827$			33.0990i			1.15097i	−0.817814	+	0.575483i	$0.804814\pi$
$828$	−5.13160	−	8.88819i	−0.178335	−	0.308886i
$829$	41.8080	+	24.1378i	1.45205	+	0.838342i	0.998598	−	0.0529390i	$-0.0168589\pi$
$829$	41.8080	+	24.1378i	1.45205	+	0.838342i	0.453452	+	0.891280i	$0.350192\pi$
$830$	−40.5226	+	70.1872i	−1.40656	+	2.43623i
$831$	−11.7736	−	20.3925i	−0.408423	−	0.707409i
$832$	2.78689			0.0966180
$833$	14.2055	+	20.5269i	0.492193	+	0.711215i
$834$	22.7382			0.787359
$835$	55.6265	−	32.1159i	1.92503	−	1.11142i
$836$	−7.34840	−	6.91571i	−0.254150	−	0.239185i
$837$	−0.385640	+	0.667948i	−0.0133297	+	0.0230877i
$838$	4.24344	+	7.34985i	0.146587	+	0.253896i
$839$		−	38.8499i		−	1.34125i	−0.741797	−	0.670624i	$-0.766026\pi$
$839$		−	38.8499i		−	1.34125i	0.741797	−	0.670624i	$-0.233974\pi$
$840$	21.4601	+	33.8908i	0.740442	+	1.16934i
$841$	−24.9636			−0.860815
$842$	17.7241	−	10.2330i	0.610811	−	0.352652i
$843$	−29.0502	+	50.3164i	−1.00054	+	1.73299i
$844$	15.6016	+	9.00758i	0.537029	+	0.310054i
$845$	−34.1278	+	19.7037i	−1.17403	+	0.677827i
$846$	−13.0310			−0.448014
$847$	−17.0314	−	23.5994i	−0.585205	−	0.810885i
$848$	−43.4224			−1.49113
$849$	−9.44369	+	5.45231i	−0.324106	+	0.187123i
$850$	28.0420	+	16.1901i	0.961833	+	0.555314i
$851$	7.66019	−	13.2678i	0.262588	−	0.454816i
$852$	−7.05555	+	4.07352i	−0.241719	+	0.139557i
$853$	−50.3833			−1.72509			−0.862545	−	0.505980i	$-0.831131\pi$
$853$	−50.3833			−1.72509			−0.862545	+	0.505980i	$0.831131\pi$
$854$	−17.3370	+	0.709206i	−0.593261	+	0.0242685i
$855$		−	28.2243i		−	0.965250i
$856$	18.0390	+	31.2445i	0.616560	+	1.06791i
$857$	28.9115	−	50.0761i	0.987597	−	1.71057i	0.357821	−	0.933790i	$-0.383520\pi$
$857$	28.9115	−	50.0761i	0.987597	−	1.71057i	0.629776	−	0.776777i	$-0.283147\pi$
$858$	8.26269	+	7.77616i	0.282083	+	0.265474i
$859$	23.1969	−	13.3927i	0.791467	−	0.456953i	−0.0490120	−	0.998798i	$-0.515607\pi$
$859$	23.1969	−	13.3927i	0.791467	−	0.456953i	0.840479	+	0.541845i	$0.182274\pi$
$860$	−5.30158			−0.180782
$861$	−16.3285	+	0.667948i	−0.556472	+	0.0227636i
$862$	31.2255			1.06354
$863$	−24.6242	−	42.6504i	−0.838218	−	1.45184i	−0.891383	−	0.453250i	$-0.850264\pi$
$863$	−24.6242	−	42.6504i	−0.838218	−	1.45184i	0.0531656	−	0.998586i	$-0.483069\pi$
$864$	−3.81298	+	6.60428i	−0.129720	+	0.224682i
$865$	51.1993	+	29.5599i	1.74083	+	1.00507i
$866$	10.8236	+	18.7471i	0.367802	+	0.637052i
$867$		−	9.74893i		−	0.331091i
$868$	−0.387023	+	0.738501i	−0.0131364	+	0.0250664i
$869$	21.1488	+	4.98477i	0.717425	+	0.169097i
$870$	44.9419	+	77.8416i	1.52367	+	2.63908i
$871$	−0.597119	+	1.03424i	−0.0202326	+	0.0350439i
$872$	−2.14295	+	3.71170i	−0.0725694	+	0.125694i
$873$	12.9045	−	7.45043i	0.436752	−	0.252159i
$874$			41.0740i			1.38935i
$875$	2.12716	+	3.35932i	0.0719113	+	0.113566i
$876$			12.7281i			0.430042i
$877$	38.4953	−	22.2253i	1.29989	−	0.750495i	0.319509	−	0.947583i	$-0.396482\pi$
$877$	38.4953	−	22.2253i	1.29989	−	0.750495i	0.980386	+	0.197089i	$0.0631487\pi$
$878$	−52.1186	−	30.0907i	−1.75892	−	1.01551i
$879$	−4.07009	−	2.34987i	−0.137281	−	0.0792591i
$880$	15.2723	+	50.7845i	0.514830	+	1.71195i
$881$		−	20.4252i		−	0.688144i	−0.938943	−	0.344072i	$-0.888194\pi$
$881$		−	20.4252i		−	0.688144i	0.938943	−	0.344072i	$-0.111806\pi$
$882$	20.8685	−	14.4420i	0.702680	−	0.486286i
$883$	−47.0941			−1.58484			−0.792422	−	0.609973i	$-0.791180\pi$
$883$	−47.0941			−1.58484			−0.792422	+	0.609973i	$0.791180\pi$
$884$	−1.22708	−	2.12537i	−0.0412713	−	0.0714840i
$885$	−68.4832	−	39.5388i	−2.30204	−	1.32908i
$886$	37.8501	+	21.8527i	1.27160	+	0.734157i
$887$	−19.3705	−	33.5507i	−0.650398	−	1.12652i	−0.983026	−	0.183465i	$-0.941269\pi$
$887$	−19.3705	−	33.5507i	−0.650398	−	1.12652i	0.332628	−	0.943058i	$-0.392065\pi$
$888$	11.6153			0.389783
$889$	9.14613	+	14.4440i	0.306751	+	0.484437i
$890$			14.9943i			0.502610i
$891$	34.2542	−	10.3012i	1.14756	−	0.345103i
$892$	−14.5761	−	8.41549i	−0.488042	−	0.281771i
$893$	12.4469	+	7.18619i	0.416518	+	0.240477i
$894$	−3.75567	+	2.16834i	−0.125609	+	0.0725201i
$895$			38.1231i			1.27432i
$896$	16.3463	−	31.1912i	0.546090	−	1.04203i
$897$		−	12.7281i		−	0.424978i
$898$	−50.2296	+	29.0001i	−1.67618	+	0.967745i
$899$	1.52126	−	2.63490i	0.0507368	−	0.0878787i
$900$	4.53611	−	7.85678i	0.151204	−	0.261893i
$901$	−15.6642	−	27.1312i	−0.521850	−	0.903871i
$902$	−14.5543	−	3.43045i	−0.484607	−	0.114221i
$903$	−0.530225	−	12.9617i	−0.0176448	−	0.431339i
$904$			0.285029i			0.00947991i
$905$	−15.1871	−	26.3049i	−0.504838	−	0.874405i
$906$	53.8802	+	31.1077i	1.79005	+	1.03349i
$907$	−5.63844	+	9.76606i	−0.187221	+	0.324277i	−0.944323	−	0.329021i	$-0.893281\pi$
$907$	−5.63844	+	9.76606i	−0.187221	+	0.324277i	0.757102	+	0.653297i	$0.226615\pi$
$908$	−1.34173	−	2.32394i	−0.0445268	−	0.0771226i
$909$	−5.56141			−0.184460
$910$	−0.525726	−	12.8517i	−0.0174276	−	0.426031i
$911$	42.7155			1.41523			0.707613	−	0.706600i	$-0.249772\pi$
$911$	42.7155			1.41523			0.707613	+	0.706600i	$0.249772\pi$
$912$	−38.9646	+	22.4962i	−1.29025	+	0.744925i
$913$	−36.4169	−	34.2726i	−1.20522	−	1.13426i
$914$	−1.05034	+	1.81925i	−0.0347423	+	0.0601754i
$915$	−14.5326	−	25.1711i	−0.480432	−	0.832132i
$916$			8.59487i			0.283982i
$917$	−17.0997	−	8.96139i	−0.564683	−	0.295931i
$918$	−11.0345			−0.364192
$919$	5.28661	−	3.05222i	0.174389	−	0.100684i	−0.410265	−	0.911966i	$-0.634564\pi$
$919$	5.28661	−	3.05222i	0.174389	−	0.100684i	0.584654	+	0.811283i	$0.301230\pi$
$920$	20.5870	−	35.6578i	0.678734	−	1.17560i
$921$	−27.2929	−	15.7576i	−0.899333	−	0.519230i
$922$	42.1100	−	24.3122i	1.38682	−	0.800681i
$923$	−4.25433			−0.140033
$924$	14.3637	−	4.96826i	0.472532	−	0.163444i
$925$	13.5426			0.445277
$926$	−4.20001	+	2.42488i	−0.138021	+	0.0796864i
$927$	28.3441	+	16.3645i	0.930941	+	0.537479i
$928$	15.0413	−	26.0523i	0.493755	−	0.855209i
$929$	−45.5728	+	26.3115i	−1.49519	+	0.863251i	−0.999985	−	0.00552241i	$-0.998242\pi$
$929$	−45.5728	+	26.3115i	−1.49519	+	0.863251i	−0.495210	+	0.868773i	$0.664909\pi$
$930$	−5.06773			−0.166177
$931$	−27.8974	+	2.28622i	−0.914299	+	0.0749279i
$932$			22.0207i			0.721312i
$933$	−15.0893	−	26.1355i	−0.494003	−	0.855638i
$934$	−0.335306	+	0.580767i	−0.0109716	+	0.0190033i
$935$	−26.2218	+	27.8624i	−0.857546	+	0.911199i
$936$	3.51887	−	2.03162i	0.115018	−	0.0664057i
$937$	−25.1006			−0.820000			−0.410000	−	0.912086i	$-0.634471\pi$
$937$	−25.1006			−0.820000			−0.410000	+	0.912086i	$0.634471\pi$
$938$	3.10533	+	4.90409i	0.101393	+	0.160124i
$939$	33.5231			1.09399
$940$	4.42339	+	7.66154i	0.144275	+	0.249892i
$941$	−26.2953	+	45.5448i	−0.857203	+	1.48472i	0.0173837	+	0.999849i	$0.494466\pi$
$941$	−26.2953	+	45.5448i	−0.857203	+	1.48472i	−0.874586	+	0.484870i	$0.838867\pi$
$942$	21.7988	+	12.5856i	0.710245	+	0.410060i
$943$	8.38703	+	14.5268i	0.273119	+	0.473056i
$944$			53.0788i			1.72757i
$945$	−14.1171	−	7.39828i	−0.459229	−	0.240666i
$946$	2.72313	−	11.5534i	0.0885365	−	0.375633i
$947$	9.47537	+	16.4118i	0.307908	+	0.533312i	0.977905	−	0.209052i	$-0.0670377\pi$
$947$	9.47537	+	16.4118i	0.307908	+	0.533312i	−0.669996	+	0.742364i	$0.733704\pi$
$948$	−5.67363	+	9.82702i	−0.184271	+	0.319167i
$949$	−3.32326	+	5.75605i	−0.107878	+	0.186849i
$950$	−31.4434	+	18.1538i	−1.02016	+	0.588988i
$951$			23.1650i			0.751175i
$952$	19.4099	−	0.793999i	0.629078	−	0.0257337i
$953$			43.3536i			1.40436i	0.711999	+	0.702181i	$0.247790\pi$
$953$			43.3536i			1.40436i	−0.711999	+	0.702181i	$0.752210\pi$
$954$	−27.5827	+	15.9249i	−0.893023	+	0.515587i
$955$	−19.9892	−	11.5408i	−0.646836	−	0.373451i
$956$	10.7610	+	6.21288i	0.348037	+	0.200939i
$957$	−53.1120	+	15.9723i	−1.71687	+	0.516310i
$958$			21.1414i			0.683049i
$959$	−1.64289	−	40.1616i	−0.0530517	−	1.29689i
$960$	22.6900			0.732317
$961$	−15.4142	−	26.6982i	−0.497233	−	0.861233i
$962$	−3.22545	−	1.86221i	−0.103993	−	0.0600402i
$963$	33.1115	+	19.1169i	1.06700	+	0.616034i
$964$	3.77363	+	6.53613i	0.121541	+	0.210514i
$965$	55.6331			1.79089
$966$	−54.7960	−	28.7167i	−1.76303	−	0.923946i
$967$			8.84572i			0.284459i	0.989834	+	0.142230i	$0.0454271\pi$
$967$			8.84572i			0.284459i	−0.989834	+	0.142230i	$0.954573\pi$
$968$	−22.6064	+	1.37276i	−0.726597	+	0.0441221i
$969$	−28.1122	−	16.2306i	−0.903093	−	0.521401i
$970$	−31.7894	−	18.3536i	−1.02070	−	0.589299i
$971$	−11.5328	+	6.65849i	−0.370107	+	0.213681i	−0.673505	−	0.739183i	$-0.735212\pi$
$971$	−11.5328	+	6.65849i	−0.370107	+	0.213681i	0.303398	+	0.952864i	$0.401879\pi$
$972$			14.4293i			0.462821i
$973$	13.4376	−	8.50886i	0.430790	−	0.272782i
$974$			13.6846i			0.438483i
$975$	9.74372	−	5.62554i	0.312049	−	0.180162i
$976$	−9.75461	+	16.8955i	−0.312237	+	0.540811i
$977$	−18.8291	+	32.6130i	−0.602398	+	1.04338i	0.390059	+	0.920790i	$0.372455\pi$
$977$	−18.8291	+	32.6130i	−0.602398	+	1.04338i	−0.992457	+	0.122594i	$0.960879\pi$
$978$	5.88991	+	10.2016i	0.188339	+	0.326212i
$979$	−9.00530	−	2.12254i	−0.287811	−	0.0678367i
$980$	−15.5750	−	7.36725i	−0.497524	−	0.235338i
$981$			4.54200i			0.145015i
$982$	13.1963	+	22.8567i	0.421111	+	0.729386i
$983$	24.1283	+	13.9305i	0.769574	+	0.444314i	0.832723	−	0.553690i	$-0.186781\pi$
$983$	24.1283	+	13.9305i	0.769574	+	0.444314i	−0.0631485	+	0.998004i	$0.520114\pi$
$984$	−6.35868	+	11.0136i	−0.202707	+	0.351100i
$985$	−14.6495	−	25.3737i	−0.466772	−	0.808472i
$986$	43.5284			1.38623
$987$	−18.2891	+	11.5809i	−0.582149	+	0.368624i
$988$	2.75185			0.0875480
$989$	−11.5315	+	6.65771i	−0.366680	+	0.211703i
$990$	28.3261	+	26.6582i	0.900264	+	0.847254i
$991$	8.84050	−	15.3122i	0.280828	−	0.486408i	−0.690761	−	0.723083i	$-0.742724\pi$
$991$	8.84050	−	15.3122i	0.280828	−	0.486408i	0.971589	+	0.236675i	$0.0760577\pi$
$992$	0.848043	+	1.46885i	0.0269254	+	0.0466361i
$993$		−	7.39718i		−	0.234743i
$994$	−9.59850	+	18.3154i	−0.304446	+	0.580930i
$995$	53.5620			1.69803
$996$	22.6169	−	13.0579i	0.716645	−	0.413755i
$997$	−6.99976	+	12.1239i	−0.221685	+	0.383969i	−0.955320	−	0.295575i	$-0.904489\pi$
$997$	−6.99976	+	12.1239i	−0.221685	+	0.383969i	0.733635	+	0.679544i	$0.237822\pi$
$998$	−52.4111	−	30.2596i	−1.65904	−	0.957850i
$999$	−3.99673	+	2.30751i	−0.126451	+	0.0730065i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	77.2.i.a.10.5	yes	12
3.2	odd	2		693.2.bg.a.10.2		12
4.3	odd	2		1232.2.bn.a.241.6		12
7.2	even	3		539.2.i.c.362.2		12
7.3	odd	6		539.2.b.b.538.9		12
7.4	even	3		539.2.b.b.538.10		12
7.5	odd	6	inner	77.2.i.a.54.2	yes	12
7.6	odd	2		539.2.i.c.472.5		12
11.2	odd	10		847.2.r.b.766.5		48
11.3	even	5		847.2.r.b.717.2		48
11.4	even	5		847.2.r.b.94.5		48
11.5	even	5		847.2.r.b.360.2		48
11.6	odd	10		847.2.r.b.360.5		48
11.7	odd	10		847.2.r.b.94.2		48
11.8	odd	10		847.2.r.b.717.5		48
11.9	even	5		847.2.r.b.766.2		48
11.10	odd	2	inner	77.2.i.a.10.2	✓	12
21.5	even	6		693.2.bg.a.208.5		12
28.19	even	6		1232.2.bn.a.593.5		12
33.32	even	2		693.2.bg.a.10.5		12
44.43	even	2		1232.2.bn.a.241.5		12
77.5	odd	30		847.2.r.b.481.5		48
77.10	even	6		539.2.b.b.538.3		12
77.19	even	30		847.2.r.b.838.5		48
77.26	odd	30		847.2.r.b.215.5		48
77.32	odd	6		539.2.b.b.538.4		12
77.40	even	30		847.2.r.b.215.2		48
77.47	odd	30		847.2.r.b.838.2		48
77.54	even	6	inner	77.2.i.a.54.5	yes	12
77.61	even	30		847.2.r.b.481.2		48
77.65	odd	6		539.2.i.c.362.5		12
77.68	even	30		847.2.r.b.40.2		48
77.75	odd	30		847.2.r.b.40.5		48
77.76	even	2		539.2.i.c.472.2		12
231.131	odd	6		693.2.bg.a.208.2		12
308.131	odd	6		1232.2.bn.a.593.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.i.a.10.2	✓	12	11.10	odd	2	inner
77.2.i.a.10.5	yes	12	1.1	even	1	trivial
77.2.i.a.54.2	yes	12	7.5	odd	6	inner
77.2.i.a.54.5	yes	12	77.54	even	6	inner
539.2.b.b.538.3		12	77.10	even	6
539.2.b.b.538.4		12	77.32	odd	6
539.2.b.b.538.9		12	7.3	odd	6
539.2.b.b.538.10		12	7.4	even	3
539.2.i.c.362.2		12	7.2	even	3
539.2.i.c.362.5		12	77.65	odd	6
539.2.i.c.472.2		12	77.76	even	2
539.2.i.c.472.5		12	7.6	odd	2
693.2.bg.a.10.2		12	3.2	odd	2
693.2.bg.a.10.5		12	33.32	even	2
693.2.bg.a.208.2		12	231.131	odd	6
693.2.bg.a.208.5		12	21.5	even	6
847.2.r.b.40.2		48	77.68	even	30
847.2.r.b.40.5		48	77.75	odd	30
847.2.r.b.94.2		48	11.7	odd	10
847.2.r.b.94.5		48	11.4	even	5
847.2.r.b.215.2		48	77.40	even	30
847.2.r.b.215.5		48	77.26	odd	30
847.2.r.b.360.2		48	11.5	even	5
847.2.r.b.360.5		48	11.6	odd	10
847.2.r.b.481.2		48	77.61	even	30
847.2.r.b.481.5		48	77.5	odd	30
847.2.r.b.717.2		48	11.3	even	5
847.2.r.b.717.5		48	11.8	odd	10
847.2.r.b.766.2		48	11.9	even	5
847.2.r.b.766.5		48	11.2	odd	10
847.2.r.b.838.2		48	77.47	odd	30
847.2.r.b.838.5		48	77.19	even	30
1232.2.bn.a.241.5		12	44.43	even	2
1232.2.bn.a.241.6		12	4.3	odd	2
1232.2.bn.a.593.5		12	28.19	even	6
1232.2.bn.a.593.6		12	308.131	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 77 = 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	77.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.43898 - 0.830794i) q^{2} +(-1.97141 - 1.13819i) q^{3} +(0.380438 - 0.658939i) q^{4} +(2.80150 - 1.61745i) q^{5} -3.78242 q^{6} +(-2.23530 + 1.41542i) q^{7} +2.05891i q^{8} +(1.09097 + 1.88962i) q^{9} +O(q^{10})\)	\(q+(1.43898 - 0.830794i) q^{2} +(-1.97141 - 1.13819i) q^{3} +(0.380438 - 0.658939i) q^{4} +(2.80150 - 1.61745i) q^{5} -3.78242 q^{6} +(-2.23530 + 1.41542i) q^{7} +2.05891i q^{8} +(1.09097 + 1.88962i) q^{9} +(2.68754 - 4.65495i) q^{10} +(2.41524 + 2.27302i) q^{11} +(-1.50000 + 0.866025i) q^{12} -0.904465 q^{13} +(-2.04063 + 3.89384i) q^{14} -7.36389 q^{15} +(2.47141 + 4.28061i) q^{16} +(-1.78307 + 3.08837i) q^{17} +(3.13977 + 1.81275i) q^{18} +(-1.99935 - 3.46298i) q^{19} -2.46136i q^{20} +(6.01772 - 0.246167i) q^{21} +(5.36389 + 1.26426i) q^{22} +(-3.09097 - 5.35372i) q^{23} +(2.34344 - 4.05896i) q^{24} +(2.73229 - 4.73246i) q^{25} +(-1.30150 + 0.751424i) q^{26} +1.86221i q^{27} +(0.0822807 + 2.01141i) q^{28} -7.34599i q^{29} +(-10.5965 + 6.11788i) q^{30} +(0.358685 + 0.207087i) q^{31} +(3.54647 + 2.04755i) q^{32} +(-2.17428 - 7.23007i) q^{33} +5.92546i q^{34} +(-3.97284 + 7.58080i) q^{35} +1.66019 q^{36} +(1.23912 + 2.14622i) q^{37} +(-5.75404 - 3.32210i) q^{38} +(1.78307 + 1.02946i) q^{39} +(3.33019 + 5.76806i) q^{40} -2.71339 q^{41} +(8.45486 - 5.35372i) q^{42} -2.15392i q^{43} +(2.41663 - 0.726748i) q^{44} +(6.11273 + 3.52918i) q^{45} +(-8.89568 - 5.13592i) q^{46} +(-3.11273 + 1.79713i) q^{47} -11.2518i q^{48} +(2.99316 - 6.32779i) q^{49} -9.07987i q^{50} +(7.03033 - 4.05896i) q^{51} +(-0.344093 + 0.595987i) q^{52} +(-4.39248 + 7.60799i) q^{53} +(1.54712 + 2.67969i) q^{54} +(10.4428 + 2.46136i) q^{55} +(-2.91423 - 4.60230i) q^{56} +9.10259i q^{57} +(-6.10301 - 10.5707i) q^{58} +(9.29987 + 5.36928i) q^{59} +(-2.80150 + 4.85235i) q^{60} +(1.97349 + 3.41819i) q^{61} +0.688186 q^{62} +(-5.11326 - 2.67969i) q^{63} -3.08126 q^{64} +(-2.53386 + 1.46293i) q^{65} +(-9.13544 - 8.59753i) q^{66} +(0.660190 - 1.14348i) q^{67} +(1.35670 + 2.34987i) q^{68} +14.0725i q^{69} +(0.581257 + 14.2092i) q^{70} +4.70370 q^{71} +(-3.89056 + 2.24622i) q^{72} +(3.67428 - 6.36404i) q^{73} +(3.56614 + 2.05891i) q^{74} +(-10.7729 + 6.21975i) q^{75} -3.04252 q^{76} +(-8.61607 - 1.66232i) q^{77} +3.42107 q^{78} +(5.67363 - 3.27567i) q^{79} +(13.8473 + 7.99476i) q^{80} +(5.39248 - 9.34004i) q^{81} +(-3.90451 + 2.25427i) q^{82} -15.0780 q^{83} +(2.12716 - 4.05896i) q^{84} +11.5361i q^{85} +(-1.78947 - 3.09945i) q^{86} +(-8.36117 + 14.4820i) q^{87} +(-4.67996 + 4.97276i) q^{88} +(-2.41586 + 1.39480i) q^{89} +11.7281 q^{90} +(2.02175 - 1.28020i) q^{91} -4.70370 q^{92} +(-0.471410 - 0.816506i) q^{93} +(-2.98610 + 5.17207i) q^{94} +(-11.2024 - 6.46769i) q^{95} +(-4.66103 - 8.07314i) q^{96} -6.82916i q^{97} +(-0.949999 - 11.5923i) q^{98} +(-1.66019 + 7.04368i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{3} + 4 q^{4} - 4 q^{9}+O(q^{10}) \) 12 * q - 6 * q^3 + 4 * q^4 - 4 * q^9	\( 12 q - 6 q^{3} + 4 q^{4} - 4 q^{9} - 4 q^{11} - 18 q^{12} + 8 q^{14} - 20 q^{15} + 12 q^{16} - 4 q^{22} - 20 q^{23} + 14 q^{25} + 18 q^{26} + 6 q^{31} + 18 q^{33} - 12 q^{36} + 16 q^{37} - 48 q^{38} + 16 q^{42} + 20 q^{44} + 54 q^{45} - 18 q^{47} + 16 q^{49} - 2 q^{53} + 18 q^{56} - 6 q^{58} - 12 q^{59} + 28 q^{64} - 42 q^{66} - 24 q^{67} - 58 q^{70} + 20 q^{71} - 78 q^{75} - 50 q^{77} + 8 q^{78} + 30 q^{80} + 14 q^{81} + 54 q^{82} - 38 q^{86} - 4 q^{88} - 66 q^{89} + 22 q^{91} - 20 q^{92} + 12 q^{93} + 12 q^{99}+O(q^{100}) \) 12 * q - 6 * q^3 + 4 * q^4 - 4 * q^9 - 4 * q^11 - 18 * q^12 + 8 * q^14 - 20 * q^15 + 12 * q^16 - 4 * q^22 - 20 * q^23 + 14 * q^25 + 18 * q^26 + 6 * q^31 + 18 * q^33 - 12 * q^36 + 16 * q^37 - 48 * q^38 + 16 * q^42 + 20 * q^44 + 54 * q^45 - 18 * q^47 + 16 * q^49 - 2 * q^53 + 18 * q^56 - 6 * q^58 - 12 * q^59 + 28 * q^64 - 42 * q^66 - 24 * q^67 - 58 * q^70 + 20 * q^71 - 78 * q^75 - 50 * q^77 + 8 * q^78 + 30 * q^80 + 14 * q^81 + 54 * q^82 - 38 * q^86 - 4 * q^88 - 66 * q^89 + 22 * q^91 - 20 * q^92 + 12 * q^93 + 12 * q^99

Introduction

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