LMFDB - Embedded newform 77.2.i.a.10.2

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			10.2
Root			$-1.43898 - 0.830794i$ of defining polynomial
Character	$\chi$	$=$	77.10
Dual form			77.2.i.a.54.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.43898 + 0.830794i) q^{2} +(-1.97141 - 1.13819i) q^{3} +(0.380438 - 0.658939i) q^{4} +(2.80150 - 1.61745i) q^{5} +3.78242 q^{6} +(2.23530 - 1.41542i) q^{7} -2.05891i q^{8} +(1.09097 + 1.88962i) q^{9} +O(q^{10})$	\(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} +(-3.17611 - 0.955145i) 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} +(5.17428 + 5.49802i) 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} +(-1.83770 + 1.72949i) 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} +(-12.0134 - 3.61276i) 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} +(-8.45151 + 2.36050i) 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} +(-1.96656 + 6.53934i) 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	−0.913382	−	0.407104i	$-0.866539\pi$
$2$	−1.43898	+	0.830794i	−1.01751	+	0.587460i	−0.104129	+	0.994564i	$0.533205\pi$
$3$	−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
$11$	−3.17611	−	0.955145i	−0.957634	−	0.287987i
$11$	−3.17611	−	0.955145i	−0.957634	−	0.287987i
$12$	−1.50000	+	0.866025i	−0.433013	+	0.250000i
$13$	0.904465			0.250853			0.125427	−	0.992103i	$-0.459970\pi$
$13$	0.904465			0.250853			0.125427	+	0.992103i	$0.459970\pi$
$14$	−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	−0.564626	−	0.825347i	$-0.690980\pi$
$17$	1.78307	−	3.08837i	0.432458	−	0.749040i	0.997084	+	0.0763071i	$0.0243130\pi$
$18$	−3.13977	−	1.81275i	−0.740050	−	0.427268i
$19$	1.99935	+	3.46298i	0.458682	+	0.794461i	0.998892	−	0.0470697i	$-0.0149883\pi$
$19$	1.99935	+	3.46298i	0.458682	+	0.794461i	−0.540209	+	0.841531i	$0.681655\pi$
$20$		−	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	$0.238915\pi$
$29$			7.34599i			1.36412i	−0.731298	+	0.682058i	$0.761085\pi$
$30$	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
$33$	5.17428	+	5.49802i	0.900727	+	0.957082i
$34$			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	$-0.432041\pi$
$41$	2.71339			0.423761			0.211881	+	0.977296i	$0.432041\pi$
$42$	8.45486	−	5.35372i	1.30461	−	0.826097i
$43$			2.15392i			0.328470i	0.986421	+	0.164235i	$0.0525156\pi$
$43$			2.15392i			0.328470i	−0.986421	+	0.164235i	$0.947484\pi$
$44$	−1.83770	+	1.72949i	−0.277043	+	0.260730i
$45$	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	0.711583	−	0.702602i	$-0.247979\pi$
$61$	−1.97349	−	3.41819i	−0.252680	−	0.437654i	−0.964263	+	0.264948i	$0.914645\pi$
$62$	−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
$66$	−12.0134	−	3.61276i	−1.47875	−	0.444700i
$67$	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	−0.996876	−	0.0789770i	$-0.974835\pi$
$73$	−3.67428	+	6.36404i	−0.430042	+	0.744855i	0.566834	+	0.823832i	$0.308168\pi$
$74$	−3.56614	−	2.05891i	−0.414556	−	0.239344i
$75$	−10.7729	+	6.21975i	−1.24395	+	0.718194i
$76$	3.04252			0.349001
$77$	−8.45151	+	2.36050i	−0.963139	+	0.269004i
$78$	3.42107			0.387360
$79$	−5.67363	+	3.27567i	−0.638333	+	0.368542i	−0.783972	−	0.620796i	$-0.786810\pi$
$79$	−5.67363	+	3.27567i	−0.638333	+	0.368542i	0.145639	+	0.989338i	$0.453476\pi$
$80$	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	$-0.189756\pi$
$83$	15.0780			1.65502			0.827511	+	0.561450i	$0.189756\pi$
$84$	−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
$88$	−1.96656	+	6.53934i	−0.209636	+	0.697096i
$89$	−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	−0.795629	−	0.605784i	$-0.792860\pi$
$101$	1.27442	−	2.20735i	0.126809	−	0.219640i	0.922439	+	0.386144i	$0.126193\pi$
$102$	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	−0.999320	−	0.0368767i	$-0.988259\pi$
$107$	−15.1752	+	8.76142i	−1.46704	+	0.846998i	−0.467724	+	0.883875i	$0.654926\pi$
$108$	1.22708	+	0.708458i	0.118076	+	0.0681714i
$109$	−1.80275	−	1.04082i	−0.172672	−	0.0996921i	0.411173	−	0.911557i	$-0.365119\pi$
$109$	−1.80275	−	1.04082i	−0.172672	−	0.0996921i	−0.583845	+	0.811865i	$0.698452\pi$
$110$	12.9821	−	12.2177i	1.23779	−	1.16491i
$111$		−	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
$121$	9.17540	+	6.06730i	0.834127	+	0.551573i
$122$	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	$0.0925565\pi$
$127$			6.46177i			0.573389i	−0.958022	+	0.286695i	$0.907444\pi$
$128$	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	0.661466	−	0.749975i	$-0.269934\pi$
$131$	−3.64842	−	6.31925i	−0.318764	−	0.552116i	−0.980230	+	0.197859i	$0.936601\pi$
$132$	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	$-0.417942\pi$
$139$	6.01154			0.509892			0.254946	+	0.966955i	$0.417942\pi$
$140$	−3.48386	−	5.50189i	−0.294440	−	0.464994i
$141$	8.18194			0.689044
$142$	−6.76852	+	3.90780i	−0.568001	+	0.327936i
$143$	−2.87268	−	0.863895i	−0.240226	−	0.0722426i
$144$	−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	−0.540120	−	0.841588i	$-0.681621\pi$
$149$	−0.992929	+	0.573268i	−0.0813439	+	0.0469639i	0.458776	+	0.888552i	$0.348288\pi$
$150$	10.3347	−	17.9002i	0.843821	−	1.46154i
$151$	14.2449	+	8.22429i	1.15923	+	0.669283i	0.951120	−	0.308821i	$-0.0999345\pi$
$151$	14.2449	+	8.22429i	1.15923	+	0.669283i	0.208113	+	0.978105i	$0.433268\pi$
$152$	7.12997	−	4.11649i	0.578317	−	0.333891i
$153$	7.78112			0.629066
$154$	10.2004	−	10.4182i	0.821976	−	0.839520i
$155$	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
$165$	23.3885	+	7.03358i	1.82080	+	0.547564i
$166$	−21.6969	+	12.5267i	−1.68400	+	0.972260i
$167$	−19.8559			−1.53650			−0.768249	−	0.640152i	$-0.778872\pi$
$167$	−19.8559			−1.53650			−0.768249	+	0.640152i	$0.778872\pi$
$168$	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	$-0.922188\pi$
$173$	−9.13782	−	15.8272i	−0.694735	−	1.20332i	0.275534	−	0.961291i	$-0.411145\pi$
$174$			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
$187$	−8.61308	+	8.10592i	−0.629851	+	0.592764i
$188$			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	−0.143327	−	0.989675i	$-0.545780\pi$
$193$	−14.8937	−	8.59890i	−1.07207	−	0.618962i	−0.928747	+	0.370713i	$0.879113\pi$
$194$	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	$0.104573\pi$
$197$			9.05715i			0.645296i	−0.946519	+	0.322648i	$0.895427\pi$
$198$	8.24083	+	8.75642i	0.585650	+	0.622292i
$199$	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	$-0.696742\pi$
$211$		−	23.6769i		−	1.62998i	0.579474	−	0.814991i	$-0.303258\pi$
$212$	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
$220$	−2.35096	+	7.81756i	−0.158501	+	0.527060i
$221$	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	−0.918594	−	0.395203i	$-0.870674\pi$
$227$	−1.76340	+	3.05429i	−0.117041	+	0.202720i	0.801553	+	0.597924i	$0.204007\pi$
$228$	−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
$231$	19.3481	+	4.96595i	1.27301	+	0.326735i
$232$	15.1248			0.992989
$233$	25.0638	−	14.4706i	1.64199	−	0.948001i	0.661859	−	0.749628i	$-0.269768\pi$
$233$	25.0638	−	14.4706i	1.64199	−	0.948001i	0.980127	−	0.198373i	$-0.0635657\pi$
$234$	−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	$-0.822875\pi$
$239$		−	16.3309i		−	1.05636i	0.849134	−	0.528178i	$-0.177125\pi$
$240$	−18.1992	−	31.5219i	−1.17475	−	2.03473i
$241$	4.95959	−	8.59026i	0.319475	−	0.553347i	−0.660904	−	0.750471i	$-0.729827\pi$
$241$	4.95959	−	8.59026i	0.319475	−	0.553347i	0.980379	+	0.197124i	$0.0631601\pi$
$242$	−18.2439	−	1.10784i	−1.17276	−	0.0712149i
$243$	−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	0.922864	−	0.385126i	$-0.125842\pi$
$263$	17.0406	+	9.83838i	1.05077	+	0.606660i	0.127903	+	0.991787i	$0.459175\pi$
$264$	11.3199	−	10.6534i	0.696694	−	0.655671i
$265$			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	0.995480	−	0.0949687i	$-0.0302751\pi$
$271$	6.83991	+	11.8471i	0.415495	+	0.719658i	−0.579985	+	0.814627i	$0.696942\pi$
$272$	17.6268			1.06878
$273$	−5.44282	+	0.222649i	−0.329414	+	0.0134754i
$274$		−	25.2434i		−	1.52501i
$275$	−13.1982	+	12.4211i	−0.795884	+	0.749020i
$276$	9.27292	+	5.35372i	0.558164	+	0.322256i
$277$	−8.95829	−	5.17207i	−0.538251	−	0.310759i	0.206119	−	0.978527i	$-0.433917\pi$
$277$	−8.95829	−	5.17207i	−0.538251	−	0.310759i	−0.744370	+	0.667768i	$0.767250\pi$
$278$	−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	$0.275433\pi$
$281$			25.5230i			1.52258i	−0.648414	+	0.761288i	$0.724567\pi$
$282$	−11.7736	+	6.79751i	−0.701110	+	0.404786i
$283$	−2.39516	+	4.14854i	−0.142377	+	0.246605i	−0.928391	−	0.371604i	$-0.878808\pi$
$283$	−2.39516	+	4.14854i	−0.142377	+	0.246605i	0.786014	+	0.618209i	$0.212141\pi$
$284$	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	$-0.519208\pi$
$293$	−2.06456			−0.120613			−0.0603064	+	0.998180i	$0.519208\pi$
$294$	11.3214	−	23.9344i	0.660278	−	1.39588i
$295$	34.7382			2.02253
$296$	4.41889	−	2.55125i	0.256843	−	0.148288i
$297$	1.77869	−	5.91460i	0.103210	−	0.343200i
$298$	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	$-0.629280\pi$
$307$	−13.8444			−0.790140			−0.395070	+	0.918651i	$0.629280\pi$
$308$	−1.65985	+	6.46705i	−0.0945790	+	0.368494i
$309$	−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
$319$	7.01649	−	23.3317i	0.392848	−	1.30633i
$320$	−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	$0.00446551\pi$
$337$			0.515053i			0.0280567i	−0.999902	+	0.0140284i	$0.995534\pi$
$338$	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
$341$	−0.941426	−	1.00033i	−0.0509811	−	0.0541708i
$342$		−	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	0.573159	−	0.819444i	$-0.305718\pi$
$347$	2.79568	+	1.61408i	0.150080	+	0.0866486i	−0.423080	+	0.906093i	$0.639051\pi$
$348$	−6.36182	−	11.0190i	−0.341029	−	0.590680i
$349$	1.55330			0.0831463			0.0415731	−	0.999135i	$-0.486763\pi$
$349$	1.55330			0.0831463			0.0415731	+	0.999135i	$0.486763\pi$
$350$	12.8518	+	20.2963i	0.686960	+	1.08488i
$351$			1.68431i			0.0899017i
$352$	9.30827	+	9.89065i	0.496132	+	0.527174i
$353$	−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	−0.301699	−	0.953403i	$-0.597554\pi$
$359$	7.06968	−	4.08168i	0.373123	−	0.215423i	0.674822	+	0.737980i	$0.264220\pi$
$360$	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	−0.845929	−	0.533296i	$-0.820953\pi$
$373$	−15.5866	+	8.99894i	−0.807045	+	0.465947i	0.0388839	+	0.999244i	$0.487620\pi$
$374$	5.65968	−	18.8199i	0.292655	−	0.973156i
$375$	−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
$385$	−19.8590	+	20.2828i	−1.01211	+	1.03371i
$386$	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
$396$	−5.27295	−	1.58572i	−0.264976	−	0.0796856i
$397$	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	−0.946459	−	0.322825i	$-0.895367\pi$
$409$	−3.91642	+	6.78344i	−0.193654	+	0.335419i	0.752804	+	0.658245i	$0.228701\pi$
$410$	−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
$418$	15.1024	+	16.0473i	0.738683	+	0.784899i
$419$			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
$429$	4.67996	+	4.97276i	0.225950	+	0.240087i
$430$	−10.0264	−	5.78874i	−0.483516	−	0.279158i
$431$	−16.2748	−	9.39626i	−0.783930	−	0.452602i	0.0538914	−	0.998547i	$-0.482838\pi$
$431$	−16.2748	−	9.39626i	−0.783930	−	0.452602i	−0.837821	+	0.545945i	$0.816171\pi$
$432$	−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	$0.165587\pi$
$439$	18.1096	+	31.3667i	0.864324	+	1.49705i	−0.00339323	+	0.999994i	$0.501080\pi$
$440$	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
$451$	−8.61805	−	2.59169i	−0.405808	−	0.122038i
$452$	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	−0.474173	−	0.880432i	$-0.657253\pi$
$457$	1.09488	−	0.632132i	0.0512166	−	0.0295699i	0.525390	+	0.850862i	$0.323920\pi$
$458$	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	$-0.738662\pi$
$461$	−29.2638			−1.36295			−0.681476	+	0.731840i	$0.738662\pi$
$462$	−31.9672	+	8.92840i	−1.48725	+	0.415387i
$463$	−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
$473$	2.05731	−	6.84110i	0.0945952	−	0.314554i
$474$	−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	−0.683292	−	0.730146i	$-0.739452\pi$
$479$	6.36182	−	11.0190i	0.290679	−	0.503471i	0.973970	+	0.226675i	$0.0727855\pi$
$480$	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	$-0.883317\pi$
$491$		−	15.8840i		−	0.716833i	0.933562	−	0.358417i	$-0.116683\pi$
$492$	−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
$495$	−16.0438	−	17.0476i	−0.721116	−	0.766234i
$496$			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	$-0.622959\pi$
$503$	−16.8993			−0.753501			−0.376750	+	0.926315i	$0.622959\pi$
$504$	5.51724	−	10.5278i	0.245757	−	0.468944i
$505$		−	8.24522i		−	0.366907i
$506$	−23.3481	−	24.8089i	−1.03795	−	1.10289i
$507$	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	$-0.853816\pi$
$523$	−19.0290	−	32.9592i	−0.832081	−	1.44121i	0.0643034	−	0.997930i	$-0.479517\pi$
$524$	−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
$528$	−10.7471	+	35.7369i	−0.467707	+	1.55525i
$529$	−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
$539$	−15.5506	+	17.2389i	−0.669811	+	0.742531i
$540$	4.58358			0.197246
$541$	−31.0816	+	17.9449i	−1.33630	+	0.771513i	−0.986257	−	0.165220i	$-0.947167\pi$
$541$	−31.0816	+	17.9449i	−1.33630	+	0.771513i	−0.350044	+	0.936733i	$0.613833\pi$
$542$	−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	$-0.991888\pi$
$547$		−	1.19197i		−	0.0509651i	0.999675	−	0.0254826i	$-0.00811223\pi$
$548$	5.77975	+	10.0108i	0.246899	+	0.427641i
$549$	4.30605	−	7.45829i	0.183778	−	0.318312i
$550$	8.67260	−	28.8387i	0.369801	−	1.22969i
$551$	−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	0.685379	−	0.728186i	$-0.259636\pi$
$557$	9.37995	+	5.41552i	0.397441	+	0.229463i	−0.287938	+	0.957649i	$0.592970\pi$
$558$	−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	−0.715922	−	0.698181i	$-0.753993\pi$
$563$	5.85316	−	10.1380i	0.246681	−	0.427265i	0.962603	+	0.270916i	$0.0873265\pi$
$564$	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	−0.0821147	−	0.996623i	$-0.526167\pi$
$569$	17.6501	−	10.1903i	0.739929	−	0.427198i	0.822043	+	0.569425i	$0.192834\pi$
$570$	42.3721	+	24.4635i	1.77477	+	1.02467i
$571$	−2.14213	−	1.23676i	−0.0896455	−	0.0517569i	0.454507	−	0.890743i	$-0.349815\pi$
$571$	−2.14213	−	1.23676i	−0.0896455	−	0.0517569i	−0.544153	+	0.838986i	$0.683149\pi$
$572$	−1.66213	+	1.56426i	−0.0694973	+	0.0654051i
$573$			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
$583$	21.2177	−	19.9684i	0.878749	−	0.827006i
$584$	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	0.906733	−	0.421704i	$-0.138568\pi$
$593$	2.14684	+	3.71843i	0.0881601	+	0.152698i	−0.818573	+	0.574402i	$0.805235\pi$
$594$	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	$-0.584583\pi$
$601$	−12.8758			−0.525216			−0.262608	+	0.964903i	$0.584583\pi$
$602$	−8.38703	−	4.39536i	−0.341830	−	0.179141i
$603$	2.88099			0.117323
$604$	10.8386	−	6.25767i	0.441017	−	0.254621i
$605$	35.5185	+	2.15683i	1.44403	+	0.0876876i
$606$	4.82038	−	8.34914i	0.195815	−	0.339161i
$607$	−0.452232	−	0.783290i	−0.0183555	−	0.0317927i	0.856702	−	0.515812i	$-0.172510\pi$
$607$	−0.452232	−	0.783290i	−0.0183555	−	0.0317927i	−0.875057	+	0.484019i	$0.839176\pi$
$608$		−	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	0.753803	−	0.657101i	$-0.228217\pi$
$613$	13.9055	+	8.02835i	0.561638	+	0.324262i	−0.192165	+	0.981363i	$0.561551\pi$
$614$	19.9218	−	11.5018i	0.803977	−	0.464176i
$615$	−19.9811			−0.805717
$616$	4.86006	+	17.4009i	0.195818	+	0.701103i
$617$	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
$627$	−8.69430	+	28.9109i	−0.347217	+	1.15459i
$628$	−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
$649$	−24.4090	−	25.9362i	−0.958137	−	1.01808i
$650$			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	$-0.845279\pi$
$659$		−	23.9846i		−	0.934307i	0.884176	−	0.467154i	$-0.154721\pi$
$660$	13.5326	−	12.7358i	0.526756	−	0.495739i
$661$	−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	$0.333781\pi$
$673$			44.9698i			1.73346i	−0.498780	+	0.866728i	$0.666219\pi$
$674$	−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	0.985797	−	0.167941i	$-0.0537119\pi$
$677$	9.04057	+	15.6587i	0.347457	+	0.601814i	−0.638340	+	0.769755i	$0.720379\pi$
$678$	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
$682$	2.18576	+	0.657318i	0.0836970	+	0.0251700i
$683$	−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
$693$	−13.6808	−	13.3949i	−0.519691	−	0.508830i
$694$	−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	$0.204132\pi$
$701$			31.6783i			1.19647i	−0.801319	+	0.598237i	$0.795868\pi$
$702$	−1.39931	−	2.42368i	−0.0528137	−	0.0914760i
$703$	−4.95488	+	8.58211i	−0.186877	+	0.323680i
$704$	9.78642	+	2.94305i	0.368840	+	0.110920i
$705$	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
$726$	34.7052	+	22.9491i	1.28803	+	0.851720i
$727$		−	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	$-0.876845\pi$
$733$	−21.3834	−	37.0371i	−0.789812	−	1.36800i	0.136269	−	0.990672i	$-0.456489\pi$
$734$	26.3859			0.973921
$735$	−22.0413	+	46.5972i	−0.813006	+	1.71876i
$736$			25.3157i			0.933150i
$737$	−3.18903	+	3.00125i	−0.117469	+	0.110553i
$738$	−8.51943	−	4.91870i	−0.313605	−	0.181060i
$739$	−12.9694	−	7.48786i	−0.477085	−	0.275445i	0.242116	−	0.970247i	$-0.422159\pi$
$739$	−12.9694	−	7.48786i	−0.477085	−	0.275445i	−0.719201	+	0.694802i	$0.755492\pi$
$740$	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	$-0.855437\pi$
$743$		−	23.9164i		−	0.877409i	0.898631	−	0.438705i	$-0.144563\pi$
$744$	−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
$759$	13.4413	−	44.6959i	0.487888	−	1.62236i
$760$	13.3164	−	23.0647i	0.483037	−	0.836645i
$761$	2.61144	+	4.52314i	0.0946646	+	0.163964i	0.909469	−	0.415773i	$-0.136489\pi$
$761$	2.61144	+	4.52314i	0.0946646	+	0.163964i	−0.814804	+	0.579737i	$0.803155\pi$
$762$			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	$-0.167144\pi$
$769$	47.9896			1.73055			0.865275	+	0.501298i	$0.167144\pi$
$770$	11.7257	−	45.6853i	0.422566	−	1.64638i
$771$	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
$781$	−14.9395	−	4.49271i	−0.534576	−	0.160762i
$782$	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	−0.993414	−	0.114580i	$-0.963448\pi$
$787$	−11.1507	+	19.3135i	−0.397478	+	0.688452i	0.595936	+	0.803032i	$0.296781\pi$
$788$	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
$803$	17.7485	−	16.7034i	0.626332	−	0.589452i
$804$			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	0.622516	−	0.782607i	$-0.286110\pi$
$809$	7.28188	+	4.20419i	0.256017	+	0.147812i	−0.366499	+	0.930418i	$0.619444\pi$
$810$	28.9849	+	50.2034i	1.01843	+	1.76397i
$811$	12.6501			0.444207			0.222103	−	0.975023i	$-0.428708\pi$
$811$	12.6501			0.444207			0.222103	+	0.975023i	$0.428708\pi$
$812$	14.7758	−	0.604433i	0.518529	−	0.0212115i
$813$		−	31.1406i		−	1.09215i
$814$	9.35991	+	9.94553i	0.328065	+	0.348590i
$815$	−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	−0.508105	−	0.861295i	$-0.669654\pi$
$821$	−0.465724	+	0.268886i	−0.0162539	+	0.00938419i	0.491851	+	0.870679i	$0.336320\pi$
$822$	−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	$-0.804814\pi$
$827$		−	33.0990i		−	1.15097i	0.817814	−	0.575483i	$-0.195186\pi$
$828$	−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
$836$	−9.66338	−	2.90605i	−0.334215	−	0.100508i
$837$	−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
$847$	29.0976	+	0.575204i	0.999805	+	0.0197643i
$848$	−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	$-0.168869\pi$
$853$	50.3833			1.72509			0.862545	+	0.505980i	$0.168869\pi$
$854$	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	$0.616480\pi$
$857$	−28.9115	+	50.0761i	−0.987597	+	1.71057i	−0.629776	+	0.776777i	$0.716853\pi$
$858$	−10.8657	−	3.26762i	−0.370949	−	0.111555i
$859$	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	−0.980386	−	0.197089i	$-0.936851\pi$
$877$	−38.4953	+	22.2253i	−1.29989	+	0.750495i	−0.319509	+	0.947583i	$0.603518\pi$
$878$	−52.1186	−	30.0907i	−1.75892	−	1.01551i
$879$	4.07009	+	2.34987i	0.137281	+	0.0792591i
$880$	−36.3445	−	38.6185i	−1.22517	−	1.30183i
$881$		−	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	$0.0587314\pi$
$887$	19.3705	+	33.5507i	0.650398	+	1.12652i	−0.332628	+	0.943058i	$0.607935\pi$
$888$	−11.6153			−0.389783
$889$	9.14613	+	14.4440i	0.306751	+	0.484437i
$890$		−	14.9943i		−	0.502610i
$891$	−26.0482	+	24.5144i	−0.872648	+	0.821265i
$892$	−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
$913$	−47.8893	−	14.4016i	−1.58491	−	0.476625i
$914$	−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	−0.584654	−	0.811283i	$-0.698770\pi$
$919$	−5.28661	+	3.05222i	−0.174389	+	0.100684i	0.410265	+	0.911966i	$0.365436\pi$
$920$	−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
$924$	10.6330	−	10.8600i	0.349800	−	0.357267i
$925$	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
$935$	−11.0187	+	36.6400i	−0.360349	+	1.19826i
$936$	3.51887	−	2.03162i	0.115018	−	0.0664057i
$937$	25.1006			0.820000			0.410000	−	0.912086i	$-0.365529\pi$
$937$	25.1006			0.820000			0.410000	+	0.912086i	$0.365529\pi$
$938$	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	$-0.505534\pi$
$941$	26.2953	−	45.5448i	0.857203	−	1.48472i	0.874586	−	0.484870i	$-0.161133\pi$
$942$	−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	$-0.752210\pi$
$953$		−	43.3536i		−	1.40436i	0.711999	−	0.702181i	$-0.247790\pi$
$954$	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
$957$	−40.3884	+	38.0102i	−1.30557	+	1.22870i
$958$			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	$-0.954573\pi$
$967$		−	8.84572i		−	0.284459i	0.989834	−	0.142230i	$-0.0454271\pi$
$968$	12.4920	−	18.8913i	0.401509	−	0.607191i
$969$	−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
$990$	37.2498	+	11.2020i	1.18388	+	0.356024i
$991$	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	−0.733635	−	0.679544i	$-0.762178\pi$
$997$	6.99976	−	12.1239i	0.221685	−	0.383969i	0.955320	+	0.295575i	$0.0955111\pi$
$998$	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.10.2	✓	12
3.2	odd	2		693.2.bg.a.10.5		12
4.3	odd	2		1232.2.bn.a.241.5		12
7.2	even	3		539.2.i.c.362.5		12
7.3	odd	6		539.2.b.b.538.3		12
7.4	even	3		539.2.b.b.538.4		12
7.5	odd	6	inner	77.2.i.a.54.5	yes	12
7.6	odd	2		539.2.i.c.472.2		12
11.2	odd	10		847.2.r.b.766.2		48
11.3	even	5		847.2.r.b.717.5		48
11.4	even	5		847.2.r.b.94.2		48
11.5	even	5		847.2.r.b.360.5		48
11.6	odd	10		847.2.r.b.360.2		48
11.7	odd	10		847.2.r.b.94.5		48
11.8	odd	10		847.2.r.b.717.2		48
11.9	even	5		847.2.r.b.766.5		48
11.10	odd	2	inner	77.2.i.a.10.5	yes	12
21.5	even	6		693.2.bg.a.208.2		12
28.19	even	6		1232.2.bn.a.593.6		12
33.32	even	2		693.2.bg.a.10.2		12
44.43	even	2		1232.2.bn.a.241.6		12
77.5	odd	30		847.2.r.b.481.2		48
77.10	even	6		539.2.b.b.538.9		12
77.19	even	30		847.2.r.b.838.2		48
77.26	odd	30		847.2.r.b.215.2		48
77.32	odd	6		539.2.b.b.538.10		12
77.40	even	30		847.2.r.b.215.5		48
77.47	odd	30		847.2.r.b.838.5		48
77.54	even	6	inner	77.2.i.a.54.2	yes	12
77.61	even	30		847.2.r.b.481.5		48
77.65	odd	6		539.2.i.c.362.2		12
77.68	even	30		847.2.r.b.40.5		48
77.75	odd	30		847.2.r.b.40.2		48
77.76	even	2		539.2.i.c.472.5		12
231.131	odd	6		693.2.bg.a.208.5		12
308.131	odd	6		1232.2.bn.a.593.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.i.a.10.2	✓	12	1.1	even	1	trivial
77.2.i.a.10.5	yes	12	11.10	odd	2	inner
77.2.i.a.54.2	yes	12	77.54	even	6	inner
77.2.i.a.54.5	yes	12	7.5	odd	6	inner
539.2.b.b.538.3		12	7.3	odd	6
539.2.b.b.538.4		12	7.4	even	3
539.2.b.b.538.9		12	77.10	even	6
539.2.b.b.538.10		12	77.32	odd	6
539.2.i.c.362.2		12	77.65	odd	6
539.2.i.c.362.5		12	7.2	even	3
539.2.i.c.472.2		12	7.6	odd	2
539.2.i.c.472.5		12	77.76	even	2
693.2.bg.a.10.2		12	33.32	even	2
693.2.bg.a.10.5		12	3.2	odd	2
693.2.bg.a.208.2		12	21.5	even	6
693.2.bg.a.208.5		12	231.131	odd	6
847.2.r.b.40.2		48	77.75	odd	30
847.2.r.b.40.5		48	77.68	even	30
847.2.r.b.94.2		48	11.4	even	5
847.2.r.b.94.5		48	11.7	odd	10
847.2.r.b.215.2		48	77.26	odd	30
847.2.r.b.215.5		48	77.40	even	30
847.2.r.b.360.2		48	11.6	odd	10
847.2.r.b.360.5		48	11.5	even	5
847.2.r.b.481.2		48	77.5	odd	30
847.2.r.b.481.5		48	77.61	even	30
847.2.r.b.717.2		48	11.8	odd	10
847.2.r.b.717.5		48	11.3	even	5
847.2.r.b.766.2		48	11.2	odd	10
847.2.r.b.766.5		48	11.9	even	5
847.2.r.b.838.2		48	77.19	even	30
847.2.r.b.838.5		48	77.47	odd	30
1232.2.bn.a.241.5		12	4.3	odd	2
1232.2.bn.a.241.6		12	44.43	even	2
1232.2.bn.a.593.5		12	308.131	odd	6
1232.2.bn.a.593.6		12	28.19	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.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} +(-3.17611 - 0.955145i) 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} +(5.17428 + 5.49802i) 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} +(-1.83770 + 1.72949i) 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} +(-12.0134 - 3.61276i) 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} +(-8.45151 + 2.36050i) 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} +(-1.96656 + 6.53934i) 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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