LMFDB - Embedded newform 91.2.k.b.4.1

Newspace parameters

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	91.k (of order $6$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$0.726638658394$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.2346760387617129.1
Defining polynomial:	$ x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + 16 x^{2} - 96 x + 64 $ x^12 - 3x^11 + x^10 + 10x^9 - 15x^8 - 10x^7 + 45x^6 - 20x^5 - 60x^4 + 80x^3 + 16x^2 - 96x + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			4.1
Root			$1.32725 - 0.488273i$ of defining polynomial
Character	$\chi$	$=$	91.4
Dual form			91.2.k.b.23.6

$q$-expansion

$f(q)$	$=$	$q-2.58860i q^{2} +(-0.259233 - 0.449005i) q^{3} -4.70085 q^{4} +(-1.39608 + 0.806027i) q^{5} +(-1.16229 + 0.671051i) q^{6} +(1.06153 - 2.42346i) q^{7} +6.99143i q^{8} +(1.36560 - 2.36528i) q^{9} +O(q^{10})$	\(q-2.58860i q^{2} +(-0.259233 - 0.449005i) q^{3} -4.70085 q^{4} +(-1.39608 + 0.806027i) q^{5} +(-1.16229 + 0.671051i) q^{6} +(1.06153 - 2.42346i) q^{7} +6.99143i q^{8} +(1.36560 - 2.36528i) q^{9} +(2.08648 + 3.61389i) q^{10} +(2.34256 - 1.35248i) q^{11} +(1.21862 + 2.11070i) q^{12} +(2.36840 + 2.71858i) q^{13} +(-6.27337 - 2.74787i) q^{14} +(0.723819 + 0.417897i) q^{15} +8.69632 q^{16} -3.12661 q^{17} +(-6.12277 - 3.53498i) q^{18} +(3.18828 + 1.84075i) q^{19} +(6.56276 - 3.78901i) q^{20} +(-1.36333 + 0.151611i) q^{21} +(-3.50103 - 6.06396i) q^{22} -1.98604 q^{23} +(3.13918 - 1.81241i) q^{24} +(-1.20064 + 2.07957i) q^{25} +(7.03732 - 6.13084i) q^{26} -2.97143 q^{27} +(-4.99008 + 11.3923i) q^{28} +(2.68636 - 4.65290i) q^{29} +(1.08177 - 1.87368i) q^{30} +(9.07425 + 5.23902i) q^{31} -8.52843i q^{32} +(-1.21454 - 0.701214i) q^{33} +8.09354i q^{34} +(0.471400 + 4.23896i) q^{35} +(-6.41947 + 11.1188i) q^{36} +5.95346i q^{37} +(4.76497 - 8.25317i) q^{38} +(0.606687 - 1.76817i) q^{39} +(-5.63528 - 9.76059i) q^{40} +(-6.66970 - 3.85075i) q^{41} +(0.392460 + 3.52911i) q^{42} +(-1.67800 - 2.90638i) q^{43} +(-11.0120 + 6.35780i) q^{44} +4.40283i q^{45} +5.14106i q^{46} +(0.913730 - 0.527542i) q^{47} +(-2.25437 - 3.90469i) q^{48} +(-4.74633 - 5.14513i) q^{49} +(5.38318 + 3.10798i) q^{50} +(0.810520 + 1.40386i) q^{51} +(-11.1335 - 12.7796i) q^{52} +(-3.63284 + 6.29226i) q^{53} +7.69184i q^{54} +(-2.18027 + 3.77633i) q^{55} +(16.9435 + 7.42158i) q^{56} -1.90873i q^{57} +(-12.0445 - 6.95390i) q^{58} +11.4241i q^{59} +(-3.40257 - 1.96447i) q^{60} +(1.46254 - 2.53319i) q^{61} +(13.5617 - 23.4896i) q^{62} +(-4.28255 - 5.82028i) q^{63} -4.68406 q^{64} +(-5.49772 - 1.88636i) q^{65} +(-1.81516 + 3.14395i) q^{66} +(11.7622 - 6.79091i) q^{67} +14.6977 q^{68} +(0.514846 + 0.891740i) q^{69} +(10.9730 - 1.22027i) q^{70} +(1.17009 - 0.675554i) q^{71} +(16.5367 + 9.54747i) q^{72} +(-7.88374 - 4.55168i) q^{73} +15.4111 q^{74} +1.24498 q^{75} +(-14.9876 - 8.65311i) q^{76} +(-0.790989 - 7.11280i) q^{77} +(-4.57708 - 1.57047i) q^{78} +(3.10289 + 5.37436i) q^{79} +(-12.1407 + 7.00946i) q^{80} +(-3.32650 - 5.76166i) q^{81} +(-9.96806 + 17.2652i) q^{82} +2.69672i q^{83} +(6.40880 - 0.712700i) q^{84} +(4.36499 - 2.52013i) q^{85} +(-7.52346 + 4.34367i) q^{86} -2.78557 q^{87} +(9.45576 + 16.3779i) q^{88} +1.75988i q^{89} +11.3972 q^{90} +(9.10249 - 2.85388i) q^{91} +9.33607 q^{92} -5.43251i q^{93} +(-1.36560 - 2.36528i) q^{94} -5.93478 q^{95} +(-3.82930 + 2.21085i) q^{96} +(-13.4078 + 7.74102i) q^{97} +(-13.3187 + 12.2863i) q^{98} -7.38776i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{3} - 8 q^{4} - 3 q^{5} - 9 q^{6} - 3 q^{7} - q^{9}+O(q^{10}) $ 12 * q - 3 * q^3 - 8 * q^4 - 3 * q^5 - 9 * q^6 - 3 * q^7 - q^9	$ 12 q - 3 q^{3} - 8 q^{4} - 3 q^{5} - 9 q^{6} - 3 q^{7} - q^{9} + 12 q^{10} + 12 q^{11} - q^{12} - 2 q^{13} + 4 q^{14} - 12 q^{15} + 16 q^{16} - 34 q^{17} + 3 q^{18} + 9 q^{19} - 3 q^{20} + 21 q^{21} - 15 q^{22} - 6 q^{23} + 15 q^{24} - 5 q^{25} - 6 q^{26} + 12 q^{27} - 9 q^{28} - q^{29} + 11 q^{30} + 18 q^{31} - 6 q^{33} - 6 q^{35} - 13 q^{36} + 19 q^{38} - 4 q^{39} - q^{40} - 6 q^{41} - 8 q^{42} + 11 q^{43} - 33 q^{44} - 15 q^{47} + 19 q^{48} - 3 q^{49} + 18 q^{50} + 4 q^{51} - 7 q^{52} - 8 q^{53} - 15 q^{55} + 27 q^{56} - 24 q^{58} - 30 q^{60} + 5 q^{61} + 41 q^{62} - 30 q^{63} + 2 q^{64} + 21 q^{65} - 34 q^{66} + 15 q^{67} + 22 q^{68} + 7 q^{69} + 3 q^{70} + 30 q^{71} + 57 q^{72} + 42 q^{73} + 66 q^{74} - 2 q^{75} - 45 q^{76} - 19 q^{77} + 44 q^{78} - 35 q^{79} - 63 q^{80} + 14 q^{81} + 5 q^{82} - 12 q^{84} - 21 q^{85} - 57 q^{86} - 20 q^{87} - 14 q^{88} - 7 q^{91} - 66 q^{92} + q^{94} - 4 q^{95} + 21 q^{96} - 3 q^{97} - 18 q^{98}+O(q^{100}) $ 12 * q - 3 * q^3 - 8 * q^4 - 3 * q^5 - 9 * q^6 - 3 * q^7 - q^9 + 12 * q^10 + 12 * q^11 - q^12 - 2 * q^13 + 4 * q^14 - 12 * q^15 + 16 * q^16 - 34 * q^17 + 3 * q^18 + 9 * q^19 - 3 * q^20 + 21 * q^21 - 15 * q^22 - 6 * q^23 + 15 * q^24 - 5 * q^25 - 6 * q^26 + 12 * q^27 - 9 * q^28 - q^29 + 11 * q^30 + 18 * q^31 - 6 * q^33 - 6 * q^35 - 13 * q^36 + 19 * q^38 - 4 * q^39 - q^40 - 6 * q^41 - 8 * q^42 + 11 * q^43 - 33 * q^44 - 15 * q^47 + 19 * q^48 - 3 * q^49 + 18 * q^50 + 4 * q^51 - 7 * q^52 - 8 * q^53 - 15 * q^55 + 27 * q^56 - 24 * q^58 - 30 * q^60 + 5 * q^61 + 41 * q^62 - 30 * q^63 + 2 * q^64 + 21 * q^65 - 34 * q^66 + 15 * q^67 + 22 * q^68 + 7 * q^69 + 3 * q^70 + 30 * q^71 + 57 * q^72 + 42 * q^73 + 66 * q^74 - 2 * q^75 - 45 * q^76 - 19 * q^77 + 44 * q^78 - 35 * q^79 - 63 * q^80 + 14 * q^81 + 5 * q^82 - 12 * q^84 - 21 * q^85 - 57 * q^86 - 20 * q^87 - 14 * q^88 - 7 * q^91 - 66 * q^92 + q^94 - 4 * q^95 + 21 * q^96 - 3 * q^97 - 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		−	2.58860i		−	1.83042i	−0.402981	−	0.915209i	$-0.632026\pi$
$2$		−	2.58860i		−	1.83042i	0.402981	−	0.915209i	$-0.367974\pi$
$3$	−0.259233	−	0.449005i	−0.149668	−	0.259233i	0.781437	−	0.623985i	$-0.214487\pi$
$3$	−0.259233	−	0.449005i	−0.149668	−	0.259233i	−0.931105	+	0.364752i	$0.881154\pi$
$4$	−4.70085			−2.35043
$5$	−1.39608	+	0.806027i	−0.624346	+	0.360466i	−0.778559	−	0.627571i	$-0.784049\pi$
$5$	−1.39608	+	0.806027i	−0.624346	+	0.360466i	0.154213	+	0.988038i	$0.450716\pi$
$6$	−1.16229	+	0.671051i	−0.474504	+	0.273955i
$7$	1.06153	−	2.42346i	0.401219	−	0.915982i
$7$	1.06153	−	2.42346i	0.401219	−	0.915982i
$8$			6.99143i			2.47184i
$9$	1.36560	−	2.36528i	0.455199	−	0.788428i
$10$	2.08648	+	3.61389i	0.659803	+	1.14281i
$11$	2.34256	−	1.35248i	0.706309	−	0.407788i	−0.103384	−	0.994642i	$-0.532967\pi$
$11$	2.34256	−	1.35248i	0.706309	−	0.407788i	0.809693	+	0.586854i	$0.199634\pi$
$12$	1.21862	+	2.11070i	0.351784	+	0.609308i
$13$	2.36840	+	2.71858i	0.656876	+	0.753998i
$13$	2.36840	+	2.71858i	0.656876	+	0.753998i
$14$	−6.27337	−	2.74787i	−1.67663	−	0.734398i
$15$	0.723819	+	0.417897i	0.186889	+	0.107901i
$16$	8.69632			2.17408
$17$	−3.12661			−0.758314			−0.379157	−	0.925332i	$-0.623786\pi$
$17$	−3.12661			−0.758314			−0.379157	+	0.925332i	$0.623786\pi$
$18$	−6.12277	−	3.53498i	−1.44315	−	0.833204i
$19$	3.18828	+	1.84075i	0.731441	+	0.422297i	0.818949	−	0.573866i	$-0.194557\pi$
$19$	3.18828	+	1.84075i	0.731441	+	0.422297i	−0.0875083	+	0.996164i	$0.527890\pi$
$20$	6.56276	−	3.78901i	1.46748	−	0.847249i
$21$	−1.36333	+	0.151611i	−0.297502	+	0.0330842i
$22$	−3.50103	−	6.06396i	−0.746421	−	1.29284i
$23$	−1.98604			−0.414117			−0.207059	−	0.978329i	$-0.566389\pi$
$23$	−1.98604			−0.414117			−0.207059	+	0.978329i	$0.566389\pi$
$24$	3.13918	−	1.81241i	0.640783	−	0.369956i
$25$	−1.20064	+	2.07957i	−0.240128	+	0.415914i
$26$	7.03732	−	6.13084i	1.38013	−	1.20236i
$27$	−2.97143			−0.571852
$28$	−4.99008	+	11.3923i	−0.943036	+	2.15295i
$29$	2.68636	−	4.65290i	0.498844	−	0.864023i	−0.501155	−	0.865357i	$-0.667092\pi$
$29$	2.68636	−	4.65290i	0.498844	−	0.864023i	0.999999	+	0.00133469i	$0.000424845\pi$
$30$	1.08177	−	1.87368i	0.197503	−	0.342086i
$31$	9.07425	+	5.23902i	1.62978	+	0.940956i	0.984156	+	0.177303i	$0.0567372\pi$
$31$	9.07425	+	5.23902i	1.62978	+	0.940956i	0.645627	+	0.763653i	$0.276596\pi$
$32$		−	8.52843i		−	1.50763i
$33$	−1.21454	−	0.701214i	−0.211424	−	0.122066i
$34$			8.09354i			1.38803i
$35$	0.471400	+	4.23896i	0.0796811	+	0.716515i
$36$	−6.41947	+	11.1188i	−1.06991	+	1.85314i
$37$			5.95346i			0.978743i	0.872075	+	0.489371i	$0.162774\pi$
$37$			5.95346i			0.978743i	−0.872075	+	0.489371i	$0.837226\pi$
$38$	4.76497	−	8.25317i	0.772981	−	1.33884i
$39$	0.606687	−	1.76817i	0.0971477	−	0.283134i
$40$	−5.63528	−	9.76059i	−0.891016	−	1.54329i
$41$	−6.66970	−	3.85075i	−1.04163	−	0.601386i	−0.121337	−	0.992611i	$-0.538718\pi$
$41$	−6.66970	−	3.85075i	−1.04163	−	0.601386i	−0.920295	+	0.391225i	$0.872051\pi$
$42$	0.392460	+	3.52911i	0.0605579	+	0.544554i
$43$	−1.67800	−	2.90638i	−0.255892	−	0.443219i	0.709245	−	0.704962i	$-0.249036\pi$
$43$	−1.67800	−	2.90638i	−0.255892	−	0.443219i	−0.965138	+	0.261743i	$0.915703\pi$
$44$	−11.0120	+	6.35780i	−1.66013	+	0.958475i
$45$			4.40283i			0.656335i
$46$			5.14106i			0.758008i
$47$	0.913730	−	0.527542i	0.133281	−	0.0769500i	−0.431877	−	0.901933i	$-0.642148\pi$
$47$	0.913730	−	0.527542i	0.133281	−	0.0769500i	0.565158	+	0.824983i	$0.308815\pi$
$48$	−2.25437	−	3.90469i	−0.325390	−	0.563593i
$49$	−4.74633	−	5.14513i	−0.678046	−	0.735019i
$50$	5.38318	+	3.10798i	0.761297	+	0.439535i
$51$	0.810520	+	1.40386i	0.113495	+	0.196580i
$52$	−11.1335	−	12.7796i	−1.54394	−	1.77222i
$53$	−3.63284	+	6.29226i	−0.499009	+	0.864308i	−0.999999	−	0.00114437i	$-0.999636\pi$
$53$	−3.63284	+	6.29226i	−0.499009	+	0.864308i	0.500991	+	0.865453i	$0.332969\pi$
$54$			7.69184i			1.04673i
$55$	−2.18027	+	3.77633i	−0.293987	+	0.509201i
$56$	16.9435	+	7.42158i	2.26416	+	0.991751i
$57$		−	1.90873i		−	0.252818i
$58$	−12.0445	−	6.95390i	−1.58152	−	0.913092i
$59$			11.4241i			1.48729i	0.668577	+	0.743643i	$0.266904\pi$
$59$			11.4241i			1.48729i	−0.668577	+	0.743643i	$0.733096\pi$
$60$	−3.40257	−	1.96447i	−0.439270	−	0.253613i
$61$	1.46254	−	2.53319i	0.187259	−	0.324341i	−0.757077	−	0.653326i	$-0.773373\pi$
$61$	1.46254	−	2.53319i	0.187259	−	0.324341i	0.944335	+	0.328985i	$0.106706\pi$
$62$	13.5617	−	23.4896i	1.72234	−	2.98318i
$63$	−4.28255	−	5.82028i	−0.539551	−	0.733286i
$64$	−4.68406			−0.585507
$65$	−5.49772	−	1.88636i	−0.681909	−	0.233974i
$66$	−1.81516	+	3.14395i	−0.223431	+	0.386994i
$67$	11.7622	−	6.79091i	1.43698	−	0.829642i	0.439343	−	0.898320i	$-0.355211\pi$
$67$	11.7622	−	6.79091i	1.43698	−	0.829642i	0.997639	+	0.0686778i	$0.0218780\pi$
$68$	14.6977			1.78236
$69$	0.514846	+	0.891740i	0.0619802	+	0.107353i
$70$	10.9730	−	1.22027i	1.31152	−	0.145850i
$71$	1.17009	−	0.675554i	0.138865	−	0.0801736i	−0.428958	−	0.903324i	$-0.641119\pi$
$71$	1.17009	−	0.675554i	0.138865	−	0.0801736i	0.567823	+	0.823151i	$0.307786\pi$
$72$	16.5367	+	9.54747i	1.94887	+	1.12518i
$73$	−7.88374	−	4.55168i	−0.922721	−	0.532733i	−0.0382192	−	0.999269i	$-0.512169\pi$
$73$	−7.88374	−	4.55168i	−0.922721	−	0.532733i	−0.884502	+	0.466536i	$0.845502\pi$
$74$	15.4111			1.79151
$75$	1.24498			0.143758
$76$	−14.9876	−	8.65311i	−1.71920	−	0.992579i
$77$	−0.790989	−	7.11280i	−0.0901416	−	0.810578i
$78$	−4.57708	−	1.57047i	−0.518252	−	0.177821i
$79$	3.10289	+	5.37436i	0.349102	+	0.604663i	0.986090	−	0.166211i	$-0.0531532\pi$
$79$	3.10289	+	5.37436i	0.349102	+	0.604663i	−0.636988	+	0.770874i	$0.719820\pi$
$80$	−12.1407	+	7.00946i	−1.35738	+	0.783682i
$81$	−3.32650	−	5.76166i	−0.369611	−	0.640185i
$82$	−9.96806	+	17.2652i	−1.10079	+	1.90662i
$83$			2.69672i			0.296003i	0.988987	+	0.148002i	$0.0472841\pi$
$83$			2.69672i			0.296003i	−0.988987	+	0.148002i	$0.952716\pi$
$84$	6.40880	−	0.712700i	0.699258	−	0.0777620i
$85$	4.36499	−	2.52013i	0.473450	−	0.273346i
$86$	−7.52346	+	4.34367i	−0.811275	+	0.468390i
$87$	−2.78557			−0.298644
$88$	9.45576	+	16.3779i	1.00799	+	1.74589i
$89$			1.75988i			0.186546i	0.995641	+	0.0932732i	$0.0297330\pi$
$89$			1.75988i			0.186546i	−0.995641	+	0.0932732i	$0.970267\pi$
$90$	11.3972			1.20137
$91$	9.10249	−	2.85388i	0.954200	−	0.299168i
$92$	9.33607			0.973353
$93$		−	5.43251i		−	0.563325i
$94$	−1.36560	−	2.36528i	−0.140851	−	0.243960i
$95$	−5.93478			−0.608896
$96$	−3.82930	+	2.21085i	−0.390827	+	0.225644i
$97$	−13.4078	+	7.74102i	−1.36136	+	0.785981i	−0.989805	−	0.142430i	$-0.954509\pi$
$97$	−13.4078	+	7.74102i	−1.36136	+	0.785981i	−0.371555	+	0.928411i	$0.621175\pi$
$98$	−13.3187	+	12.2863i	−1.34539	+	1.24111i
$99$		−	7.38776i		−	0.742498i
$100$	5.64404	−	9.77576i	0.564404	−	0.977576i
$101$	−0.639651	−	1.10791i	−0.0636477	−	0.110241i	0.832446	−	0.554107i	$-0.186940\pi$
$101$	−0.639651	−	1.10791i	−0.0636477	−	0.110241i	−0.896093	+	0.443866i	$0.853607\pi$
$102$	3.63404	−	2.09811i	0.359823	−	0.207744i
$103$	−5.73367	−	9.93101i	−0.564956	−	0.978532i	−0.997054	−	0.0767054i	$-0.975560\pi$
$103$	−5.73367	−	9.93101i	−0.564956	−	0.978532i	0.432098	−	0.901827i	$-0.357773\pi$
$104$	−19.0068	+	16.5585i	−1.86377	+	1.62370i
$105$	1.78111	−	1.31054i	0.173819	−	0.127896i
$106$	16.2881	+	9.40397i	1.58204	+	0.913394i
$107$	−5.13525			−0.496444			−0.248222	−	0.968703i	$-0.579846\pi$
$107$	−5.13525			−0.496444			−0.248222	+	0.968703i	$0.579846\pi$
$108$	13.9682			1.34410
$109$	1.49635	+	0.863916i	0.143324	+	0.0827481i	0.569947	−	0.821681i	$-0.306964\pi$
$109$	1.49635	+	0.863916i	0.143324	+	0.0827481i	−0.426623	+	0.904429i	$0.640297\pi$
$110$	9.77542	+	5.64384i	0.932050	+	0.538119i
$111$	2.67313	−	1.54333i	0.253722	−	0.146487i
$112$	9.23136	−	21.0752i	0.872282	−	1.99142i
$113$	4.29556	+	7.44014i	0.404093	+	0.699909i	0.994215	−	0.107404i	$-0.0342540\pi$
$113$	4.29556	+	7.44014i	0.404093	+	0.699909i	−0.590123	+	0.807314i	$0.700921\pi$
$114$	−4.94095			−0.462762
$115$	2.77267	−	1.60080i	0.258552	−	0.149275i
$116$	−12.6282	+	21.8726i	−1.17250	+	2.03082i
$117$	9.66449	−	1.88945i	0.893482	−	0.174680i
$118$	29.5723			2.72235
$119$	−3.31897	+	7.57721i	−0.304250	+	0.694602i
$120$	−2.92170	+	5.06053i	−0.266714	+	0.461961i
$121$	−1.84160	+	3.18975i	−0.167419	+	0.289977i
$122$	−6.55741	−	3.78592i	−0.593680	−	0.342761i
$123$			3.99297i			0.360034i
$124$	−42.6567	−	24.6279i	−3.83069	−	2.21165i
$125$		−	11.9313i		−	1.06716i
$126$	−15.0664	+	11.0858i	−1.34222	+	0.987603i
$127$	−1.56206	+	2.70556i	−0.138610	+	0.240080i	−0.926971	−	0.375133i	$-0.877597\pi$
$127$	−1.56206	+	2.70556i	−0.138610	+	0.240080i	0.788361	+	0.615214i	$0.210930\pi$
$128$		−	4.93170i		−	0.435904i
$129$	−0.869985	+	1.50686i	−0.0765979	+	0.132671i
$130$	−4.88303	+	14.2314i	−0.428270	+	1.24818i
$131$	−5.10460	−	8.84142i	−0.445991	−	0.772479i	0.552130	−	0.833758i	$-0.313815\pi$
$131$	−5.10460	−	8.84142i	−0.445991	−	0.772479i	−0.998121	+	0.0612793i	$0.980482\pi$
$132$	5.70937	+	3.29630i	0.496936	+	0.286906i
$133$	7.84543	−	5.77266i	0.680285	−	0.500553i
$134$	−17.5790	−	30.4476i	−1.51859	−	2.63028i
$135$	4.14835	−	2.39505i	0.357033	−	0.206133i
$136$		−	21.8595i		−	1.87443i
$137$		−	9.99261i		−	0.853726i	−0.904316	−	0.426863i	$-0.859619\pi$
$137$		−	9.99261i		−	0.853726i	0.904316	−	0.426863i	$-0.140381\pi$
$138$	2.30836	−	1.33273i	0.196501	−	0.113450i
$139$	0.832100	+	1.44124i	0.0705778	+	0.122244i	0.899155	−	0.437631i	$-0.144182\pi$
$139$	0.832100	+	1.44124i	0.0705778	+	0.122244i	−0.828577	+	0.559875i	$0.810849\pi$
$140$	−2.21598	−	19.9267i	−0.187285	−	1.68412i
$141$	−0.473738	−	0.273513i	−0.0398959	−	0.0230339i
$142$	−1.74874	−	3.02891i	−0.146751	−	0.254180i
$143$	9.22495	+	3.16523i	0.771429	+	0.264690i
$144$	11.8757	−	20.5692i	0.989638	−	1.71410i
$145$			8.66110i			0.719265i
$146$	−11.7825	+	20.4078i	−0.975124	+	1.68897i
$147$	−1.07978	+	3.46491i	−0.0890591	+	0.285781i
$148$		−	27.9863i		−	2.30046i
$149$	17.1456	+	9.89902i	1.40462	+	0.810959i	0.994863	−	0.101234i	$-0.0322792\pi$
$149$	17.1456	+	9.89902i	1.40462	+	0.810959i	0.409760	+	0.912193i	$0.365613\pi$
$150$		−	3.22276i		−	0.263138i
$151$	−6.52544	−	3.76746i	−0.531033	−	0.306592i	0.210404	−	0.977614i	$-0.432522\pi$
$151$	−6.52544	−	3.76746i	−0.531033	−	0.306592i	−0.741437	+	0.671023i	$0.765855\pi$
$152$	−12.8695	+	22.2906i	−1.04385	+	1.80801i
$153$	−4.26968	+	7.39531i	−0.345183	+	0.597875i
$154$	−18.4122	+	2.04755i	−1.48370	+	0.164997i
$155$	−16.8912			−1.35673
$156$	−2.85195	+	8.31190i	−0.228339	+	0.665485i
$157$	−7.00223	+	12.1282i	−0.558839	+	0.967938i	0.438755	+	0.898607i	$0.355420\pi$
$157$	−7.00223	+	12.1282i	−0.558839	+	0.967938i	−0.997594	+	0.0693309i	$0.977914\pi$
$158$	13.9121	−	8.03214i	1.10679	−	0.639003i
$159$	3.76700			0.298743
$160$	6.87414	+	11.9064i	0.543448	+	0.941280i
$161$	−2.10823	+	4.81308i	−0.166152	+	0.379324i
$162$	−14.9146	+	8.61097i	−1.17181	+	0.676542i
$163$	6.20936	+	3.58498i	0.486355	+	0.280797i	0.723061	−	0.690784i	$-0.242735\pi$
$163$	6.20936	+	3.58498i	0.486355	+	0.280797i	−0.236706	+	0.971581i	$0.576068\pi$
$164$	31.3533	+	18.1018i	2.44828	+	1.41351i
$165$	2.26079			0.176002
$166$	6.98072			0.541809
$167$	15.5716	+	8.99027i	1.20497	+	0.695688i	0.961656	−	0.274260i	$-0.0884328\pi$
$167$	15.5716	+	8.99027i	1.20497	+	0.695688i	0.243312	+	0.969948i	$0.421766\pi$
$168$	−1.05998	−	9.53161i	−0.0817790	−	0.735380i
$169$	−1.78135	+	12.8774i	−0.137027	+	0.990567i
$170$	−6.52361	−	11.2992i	−0.500338	−	0.866611i
$171$	8.70780	−	5.02745i	0.665902	−	0.384459i
$172$	7.88803	+	13.6625i	0.601456	+	1.04175i
$173$	−6.40579	+	11.0952i	−0.487023	+	0.843549i	−0.999889	−	0.0149198i	$-0.995251\pi$
$173$	−6.40579	+	11.0952i	−0.487023	+	0.843549i	0.512865	+	0.858469i	$0.328584\pi$
$174$			7.21072i			0.546643i
$175$	3.76525	+	5.11723i	0.284626	+	0.386826i
$176$	20.3717	−	11.7616i	1.53557	−	0.886562i
$177$	5.12945	−	2.96149i	0.385553	−	0.222599i
$178$	4.55561			0.341458
$179$	0.920110	+	1.59368i	0.0687723	+	0.119117i	0.898361	−	0.439258i	$-0.144758\pi$
$179$	0.920110	+	1.59368i	0.0687723	+	0.119117i	−0.829589	+	0.558375i	$0.811425\pi$
$180$		−	20.6971i		−	1.54267i
$181$	−3.29928			−0.245234			−0.122617	−	0.992454i	$-0.539129\pi$
$181$	−3.29928			−0.245234			−0.122617	+	0.992454i	$0.539129\pi$
$182$	−7.38757	−	23.5627i	−0.547603	−	1.74658i
$183$	−1.51655			−0.112107
$184$		−	13.8852i		−	1.02363i
$185$	−4.79865	−	8.31150i	−0.352804	−	0.611074i
$186$	−14.0626			−1.03112
$187$	−7.32427	+	4.22867i	−0.535604	+	0.309231i
$188$	−4.29531	+	2.47990i	−0.313268	+	0.180865i
$189$	−3.15425	+	7.20114i	−0.229438	+	0.523806i
$190$			15.3628i			1.11453i
$191$	−2.44807	+	4.24018i	−0.177136	+	0.306809i	−0.940898	−	0.338689i	$-0.890017\pi$
$191$	−2.44807	+	4.24018i	−0.177136	+	0.306809i	0.763762	+	0.645498i	$0.223350\pi$
$192$	1.21426	+	2.10316i	0.0876318	+	0.151783i
$193$	2.61462	−	1.50955i	0.188204	−	0.108660i	−0.402937	−	0.915228i	$-0.632011\pi$
$193$	2.61462	−	1.50955i	0.188204	−	0.108660i	0.591142	+	0.806568i	$0.298677\pi$
$194$	20.0384	+	34.7075i	1.43867	+	2.49186i
$195$	0.578207	+	2.95751i	0.0414063	+	0.211792i
$196$	22.3118	+	24.1865i	1.59370	+	1.72761i
$197$	4.02694	+	2.32496i	0.286908	+	0.165646i	0.636546	−	0.771238i	$-0.280362\pi$
$197$	4.02694	+	2.32496i	0.286908	+	0.165646i	−0.349639	+	0.936885i	$0.613696\pi$
$198$	−19.1240			−1.35908
$199$	−0.410721			−0.0291152			−0.0145576	−	0.999894i	$-0.504634\pi$
$199$	−0.410721			−0.0291152			−0.0145576	+	0.999894i	$0.504634\pi$
$200$	−14.5392	−	8.39420i	−1.02808	−	0.593560i
$201$	−6.09830	−	3.52085i	−0.430141	−	0.248342i
$202$	−2.86793	+	1.65580i	−0.201787	+	0.116502i
$203$	−8.42450	−	11.4495i	−0.591284	−	0.803594i
$204$	−3.81013	−	6.59934i	−0.266763	−	0.462047i
$205$	12.4152			0.867118
$206$	−25.7074	+	14.8422i	−1.79112	+	1.03410i
$207$	−2.71213	+	4.69754i	−0.188506	+	0.326502i
$208$	20.5964	+	23.6416i	1.42810	+	1.63925i
$209$	9.95831			0.688831
$210$	−3.39246	−	4.61059i	−0.234102	−	0.318161i
$211$	3.75800	−	6.50905i	0.258711	−	0.448101i	−0.707186	−	0.707028i	$-0.750035\pi$
$211$	3.75800	−	6.50905i	0.258711	−	0.448101i	0.965897	+	0.258927i	$0.0833688\pi$
$212$	17.0774	−	29.5790i	1.17288	−	2.03149i
$213$	−0.606654	−	0.350252i	−0.0415672	−	0.0239989i
$214$			13.2931i			0.908699i
$215$	4.68524	+	2.70502i	0.319531	+	0.184481i
$216$		−	20.7745i		−	1.41353i
$217$	22.3291	−	16.4297i	1.51580	−	1.11532i
$218$	2.23633	−	3.87344i	0.151464	−	0.262343i
$219$			4.71978i			0.318933i
$220$	10.2491	−	17.7520i	0.690996	−	1.19684i
$221$	−7.40506	−	8.49993i	−0.498118	−	0.571767i
$222$	−3.99507	−	6.91967i	−0.268132	−	0.464418i
$223$	−19.5544	−	11.2897i	−1.30946	−	0.756016i	−0.327452	−	0.944868i	$-0.606190\pi$
$223$	−19.5544	−	11.2897i	−1.30946	−	0.756016i	−0.982006	+	0.188852i	$0.939523\pi$
$224$	−20.6683	−	9.05315i	−1.38096	−	0.604889i
$225$	3.27918	+	5.67971i	0.218612	+	0.378648i
$226$	19.2595	−	11.1195i	1.28113	−	0.739658i
$227$		−	13.6717i		−	0.907424i	−0.891148	−	0.453712i	$-0.850099\pi$
$227$		−	13.6717i		−	0.907424i	0.891148	−	0.453712i	$-0.149901\pi$
$228$			8.97268i			0.594230i
$229$	6.86832	−	3.96543i	0.453872	−	0.262043i	−0.255592	−	0.966785i	$-0.582270\pi$
$229$	6.86832	−	3.96543i	0.453872	−	0.262043i	0.709464	+	0.704742i	$0.248937\pi$
$230$	−4.14383	−	7.17733i	−0.273236	−	0.473259i
$231$	−2.98863	+	2.19903i	−0.196637	+	0.144685i
$232$	32.5305	+	18.7815i	2.13573	+	1.23306i
$233$	−3.28585	−	5.69127i	−0.215263	−	0.372847i	0.738091	−	0.674702i	$-0.235728\pi$
$233$	−3.28585	−	5.69127i	−0.215263	−	0.372847i	−0.953354	+	0.301854i	$0.902394\pi$
$234$	−4.89104	−	25.0175i	−0.319738	−	1.63545i
$235$	−0.850427	+	1.47298i	−0.0554757	+	0.0960868i
$236$		−	53.7028i		−	3.49576i
$237$	1.60874	−	2.78642i	0.104499	−	0.180998i
$238$	19.6144	+	8.59150i	1.27141	+	0.556904i
$239$			9.39284i			0.607572i	0.952740	+	0.303786i	$0.0982508\pi$
$239$			9.39284i			0.607572i	−0.952740	+	0.303786i	$0.901749\pi$
$240$	6.29456	+	3.63417i	0.406312	+	0.234584i
$241$		−	10.0858i		−	0.649686i	−0.945768	−	0.324843i	$-0.894689\pi$
$241$		−	10.0858i		−	0.649686i	0.945768	−	0.324843i	$-0.105311\pi$
$242$	8.25699	+	4.76718i	0.530780	+	0.306446i
$243$	−6.18182	+	10.7072i	−0.396564	+	0.686869i
$244$	−6.87517	+	11.9081i	−0.440137	+	0.762340i
$245$	10.7734	+	3.35735i	0.688285	+	0.214493i
$246$	10.3362			0.659012
$247$	2.54689	+	13.0272i	0.162054	+	0.828902i
$248$	−36.6282	+	63.4420i	−2.32590	+	4.02857i
$249$	1.21084	−	0.699078i	0.0767337	−	0.0443022i
$250$	−30.8853			−1.95336
$251$	−5.17427	−	8.96209i	−0.326597	−	0.565682i	0.655237	−	0.755423i	$-0.272569\pi$
$251$	−5.17427	−	8.96209i	−0.326597	−	0.565682i	−0.981834	+	0.189741i	$0.939235\pi$
$252$	20.1317	+	27.3603i	1.26818	+	1.72354i
$253$	−4.65242	+	2.68607i	−0.292495	+	0.168872i
$254$	7.00363	+	4.04355i	0.439447	+	0.253715i
$255$	−2.26310	−	1.30660i	−0.141721	−	0.0818225i
$256$	−22.1343			−1.38339
$257$	−7.98658			−0.498189			−0.249095	−	0.968479i	$-0.580133\pi$
$257$	−7.98658			−0.498189			−0.249095	+	0.968479i	$0.580133\pi$
$258$	3.90065	+	2.25204i	0.242844	+	0.140206i
$259$	14.4280	+	6.31975i	0.896511	+	0.392690i
$260$	25.8440	+	8.86749i	1.60278	+	0.549939i
$261$	−7.33696	−	12.7080i	−0.454146	−	0.786604i
$262$	−22.8869	+	13.2138i	−1.41396	+	0.816349i
$263$	−2.52967	−	4.38152i	−0.155986	−	0.270176i	0.777431	−	0.628968i	$-0.216522\pi$
$263$	−2.52967	−	4.38152i	−0.155986	−	0.270176i	−0.933418	+	0.358792i	$0.883189\pi$
$264$	4.90249	−	8.49136i	0.301727	−	0.522607i
$265$		−	11.7127i		−	0.719503i
$266$	−14.9431	−	20.3087i	−0.916220	−	1.24521i
$267$	0.790192	−	0.456218i	0.0483590	−	0.0279201i
$268$	−55.2924	+	31.9231i	−3.37752	+	1.95001i
$269$	13.8902			0.846902			0.423451	−	0.905919i	$-0.360819\pi$
$269$	13.8902			0.846902			0.423451	+	0.905919i	$0.360819\pi$
$270$	−6.19983	−	10.7384i	−0.377310	−	0.653519i
$271$		−	8.32721i		−	0.505842i	−0.967487	−	0.252921i	$-0.918609\pi$
$271$		−	8.32721i		−	0.505842i	0.967487	−	0.252921i	$-0.0813913\pi$
$272$	−27.1900			−1.64863
$273$	−3.64107	−	3.34724i	−0.220368	−	0.202584i
$274$	−25.8669			−1.56267
$275$			6.49537i			0.391685i
$276$	−2.42022	−	4.19194i	−0.145680	−	0.252325i
$277$	23.2116			1.39465			0.697325	−	0.716755i	$-0.254374\pi$
$277$	23.2116			1.39465			0.697325	+	0.716755i	$0.254374\pi$
$278$	3.73080	−	2.15398i	0.223758	−	0.129187i
$279$	24.7835	−	14.3088i	1.48375	−	0.856644i
$280$	−29.6364	+	3.29576i	−1.77111	+	0.196959i
$281$			27.1595i			1.62020i	0.586292	+	0.810100i	$0.300587\pi$
$281$			27.1595i			1.62020i	−0.586292	+	0.810100i	$0.699413\pi$
$282$	−0.708015	+	1.22632i	−0.0421617	+	0.0730262i
$283$	−8.07563	−	13.9874i	−0.480046	−	0.831464i	0.519692	−	0.854354i	$-0.326047\pi$
$283$	−8.07563	−	13.9874i	−0.480046	−	0.831464i	−0.999738	+	0.0228894i	$0.992713\pi$
$284$	−5.50044	+	3.17568i	−0.326391	+	0.188442i
$285$	1.53849	+	2.66474i	0.0911323	+	0.157846i
$286$	8.19351	−	23.8797i	0.484493	−	1.41204i
$287$	−16.4122	+	12.0761i	−0.968782	+	0.712828i
$288$	−20.1721	−	11.6464i	−1.18865	−	0.686270i
$289$	−7.22433			−0.424960
$290$	22.4201			1.31656
$291$	6.95151	+	4.01345i	0.407504	+	0.235273i
$292$	37.0603	+	21.3968i	2.16879	+	1.25215i
$293$	−12.6831	+	7.32260i	−0.740956	+	0.427791i	−0.822417	−	0.568885i	$-0.807375\pi$
$293$	−12.6831	+	7.32260i	−0.740956	+	0.427791i	0.0814609	+	0.996677i	$0.474041\pi$
$294$	8.96927	+	2.79513i	0.523098	+	0.163015i
$295$	−9.20810	−	15.9489i	−0.536116	−	0.928580i
$296$	−41.6232			−2.41930
$297$	−6.96075	+	4.01879i	−0.403904	+	0.233194i
$298$	25.6246	−	44.3831i	1.48439	−	2.57104i
$299$	−4.70373	−	5.39920i	−0.272024	−	0.312244i
$300$	−5.85248			−0.337893
$301$	−8.82474	+	0.981368i	−0.508649	+	0.0565651i
$302$	−9.75246	+	16.8918i	−0.561191	+	0.972011i
$303$	−0.331637	+	0.574412i	−0.0190521	+	0.0329991i
$304$	27.7263	+	16.0078i	1.59021	+	0.918108i
$305$			4.71537i			0.270001i
$306$	19.1435	+	11.0525i	1.09436	+	0.631830i
$307$		−	8.97844i		−	0.512427i	−0.966620	−	0.256213i	$-0.917525\pi$
$307$		−	8.97844i		−	0.512427i	0.966620	−	0.256213i	$-0.0824750\pi$
$308$	3.71832	+	33.4362i	0.211871	+	1.90521i
$309$	−2.97271	+	5.14889i	−0.169112	+	0.292910i
$310$			43.7245i			2.48338i
$311$	6.09080	−	10.5496i	0.345378	−	0.598212i	−0.640045	−	0.768338i	$-0.721084\pi$
$311$	6.09080	−	10.5496i	0.345378	−	0.598212i	0.985422	+	0.170126i	$0.0544175\pi$
$312$	12.3620	+	4.24161i	0.699862	+	0.240134i
$313$	−6.56198	−	11.3657i	−0.370905	−	0.642427i	0.618800	−	0.785549i	$-0.287619\pi$
$313$	−6.56198	−	11.3657i	−0.370905	−	0.642427i	−0.989705	+	0.143122i	$0.954286\pi$
$314$	31.3951	+	18.1260i	1.77173	+	1.02291i
$315$	10.6701	+	4.67372i	0.601191	+	0.263334i
$316$	−14.5862	−	25.2641i	−0.820540	−	1.42122i
$317$	14.4761	−	8.35775i	0.813056	−	0.469418i	−0.0349599	−	0.999389i	$-0.511130\pi$
$317$	14.4761	−	8.35775i	0.813056	−	0.469418i	0.848016	+	0.529971i	$0.177797\pi$
$318$		−	9.75127i		−	0.546824i
$319$		−	14.5330i		−	0.813689i
$320$	6.53932	−	3.77548i	0.365559	−	0.211056i
$321$	1.33123	+	2.30575i	0.0743018	+	0.128695i
$322$	12.4592	+	5.45737i	0.694321	+	0.304127i
$323$	−9.96849	−	5.75531i	−0.554661	−	0.320234i
$324$	15.6374	+	27.0847i	0.868743	+	1.50471i
$325$	−8.49708	+	1.66122i	−0.471333	+	0.0921480i
$326$	9.28007	−	16.0736i	0.513976	−	0.890232i
$327$		−	0.895821i		−	0.0495390i
$328$	26.9223	−	46.6307i	1.48653	−	2.57475i
$329$	−0.308530	−	2.77439i	−0.0170098	−	0.152957i
$330$		−	5.85228i		−	0.322157i
$331$	−3.43522	−	1.98332i	−0.188817	−	0.109013i	0.402612	−	0.915371i	$-0.368102\pi$
$331$	−3.43522	−	1.98332i	−0.188817	−	0.109013i	−0.591428	+	0.806357i	$0.701436\pi$
$332$		−	12.6769i		−	0.695733i
$333$	14.0816	+	8.13002i	0.771668	+	0.445523i
$334$	23.2722	−	40.3087i	1.27340	−	2.20559i
$335$	−10.9473	+	18.9613i	−0.598116	+	1.03597i
$336$	−11.8559	+	1.31846i	−0.646794	+	0.0719276i
$337$	−13.7032			−0.746461			−0.373230	−	0.927739i	$-0.621750\pi$
$337$	−13.7032			−0.746461			−0.373230	+	0.927739i	$0.621750\pi$
$338$	33.3344	+	4.61121i	1.81315	+	0.250817i
$339$	2.22710	−	3.85746i	0.120960	−	0.209508i
$340$	−20.5192	+	11.8468i	−1.11281	+	0.642481i
$341$	28.3426			1.53484
$342$	−13.0141	−	22.5410i	−0.703720	−	1.21888i
$343$	−17.5074	+	6.04084i	−0.945309	+	0.326175i
$344$	20.3197	−	11.7316i	1.09557	−	0.632526i
$345$	−1.43753	−	0.829960i	−0.0773942	−	0.0446835i
$346$	28.7209	+	16.5820i	1.54405	+	0.891456i
$347$	−26.3979			−1.41711			−0.708556	−	0.705655i	$-0.750653\pi$
$347$	−26.3979			−1.41711			−0.708556	+	0.705655i	$0.750653\pi$
$348$	13.0945			0.701941
$349$	−4.23507	−	2.44512i	−0.226698	−	0.130884i	0.382350	−	0.924018i	$-0.375115\pi$
$349$	−4.23507	−	2.44512i	−0.226698	−	0.130884i	−0.609048	+	0.793133i	$0.708448\pi$
$350$	13.2465	−	9.74673i	0.708053	−	0.520984i
$351$	−7.03753	−	8.07806i	−0.375636	−	0.431175i
$352$	−11.5345	−	19.9784i	−0.614792	−	1.06485i
$353$	−11.7413	+	6.77886i	−0.624928	+	0.360802i	−0.778785	−	0.627291i	$-0.784164\pi$
$353$	−11.7413	+	6.77886i	−0.624928	+	0.360802i	0.153857	+	0.988093i	$0.450830\pi$
$354$	−7.66612	−	13.2781i	−0.407450	−	0.705724i
$355$	−1.08903	+	1.88626i	−0.0577997	+	0.100112i
$356$		−	8.27291i		−	0.438464i
$357$	4.26259	−	0.474028i	0.225600	−	0.0250882i
$358$	4.12540	−	2.38180i	0.218034	−	0.125882i
$359$	7.43541	−	4.29284i	0.392426	−	0.226567i	−0.290785	−	0.956789i	$-0.593916\pi$
$359$	7.43541	−	4.29284i	0.392426	−	0.226567i	0.683211	+	0.730221i	$0.260583\pi$
$360$	−30.7821			−1.62236
$361$	−2.72326	−	4.71683i	−0.143330	−	0.248254i
$362$			8.54053i			0.448880i
$363$	1.90962			0.100229
$364$	−42.7895	+	13.4157i	−2.24278	+	0.703173i
$365$	14.6751			0.768130
$366$			3.92574i			0.205202i
$367$	0.831612	+	1.44039i	0.0434098	+	0.0751880i	0.886914	−	0.461935i	$-0.152845\pi$
$367$	0.831612	+	1.44039i	0.0434098	+	0.0751880i	−0.843504	+	0.537123i	$0.819511\pi$
$368$	−17.2712			−0.900324
$369$	−18.2162	+	10.5171i	−0.948299	+	0.547501i
$370$	−21.5152	+	12.4218i	−1.11852	+	0.645778i
$371$	11.3927	+	15.4834i	0.591479	+	0.803860i
$372$			25.5374i			1.32405i
$373$	−6.98174	+	12.0927i	−0.361501	+	0.626138i	−0.988208	−	0.153117i	$-0.951069\pi$
$373$	−6.98174	+	12.0927i	−0.361501	+	0.626138i	0.626707	+	0.779255i	$0.284402\pi$
$374$	10.9463	+	18.9596i	0.566022	+	0.980378i
$375$	−5.35719	+	3.09298i	−0.276644	+	0.159721i
$376$	3.68828	+	6.38828i	0.190208	+	0.329450i
$377$	19.0117	−	3.71687i	0.979150	−	0.191429i
$378$	18.6409	+	8.16509i	0.958783	+	0.419967i
$379$	−27.3454	−	15.7879i	−1.40464	−	0.810969i	−0.409775	−	0.912187i	$-0.634393\pi$
$379$	−27.3454	−	15.7879i	−1.40464	−	0.810969i	−0.994864	+	0.101218i	$0.967726\pi$
$380$	27.8985			1.43116
$381$	1.61975			0.0829822
$382$	10.9761	+	6.33707i	0.561588	+	0.324233i
$383$	−27.6333	−	15.9541i	−1.41200	−	0.815217i	−0.416420	−	0.909172i	$-0.636716\pi$
$383$	−27.6333	−	15.9541i	−1.41200	−	0.815217i	−0.995576	+	0.0939554i	$0.970049\pi$
$384$	−2.21435	+	1.27846i	−0.113001	+	0.0652410i
$385$	6.83739	+	9.29247i	0.348466	+	0.473588i
$386$	−3.90762	−	6.76820i	−0.198893	−	0.344492i
$387$	−9.16588			−0.465928
$388$	63.0283	−	36.3894i	3.19978	−	1.84739i
$389$	−12.7075	+	22.0100i	−0.644296	+	1.11595i	0.340168	+	0.940365i	$0.389516\pi$
$389$	−12.7075	+	22.0100i	−0.644296	+	1.11595i	−0.984464	+	0.175589i	$0.943817\pi$
$390$	7.65581	−	1.49675i	0.387667	−	0.0757908i
$391$	6.20956			0.314031
$392$	35.9718	−	33.1836i	1.81685	−	1.67603i
$393$	−2.64656	+	4.58398i	−0.133501	+	0.231231i
$394$	6.01838	−	10.4241i	0.303202	−	0.525161i
$395$	−8.66376	−	5.00203i	−0.435921	−	0.251679i
$396$			34.7288i			1.74519i
$397$	−3.60178	−	2.07949i	−0.180768	−	0.104366i	0.406885	−	0.913479i	$-0.366615\pi$
$397$	−3.60178	−	2.07949i	−0.180768	−	0.104366i	−0.587653	+	0.809113i	$0.699948\pi$
$398$			1.06319i			0.0532930i
$399$	−4.62574	−	2.02617i	−0.231577	−	0.101435i
$400$	−10.4412	+	18.0846i	−0.522058	+	0.904231i
$401$		−	19.6013i		−	0.978844i	−0.872047	−	0.489422i	$-0.837208\pi$
$401$		−	19.6013i		−	0.978844i	0.872047	−	0.489422i	$-0.162792\pi$
$402$	−9.11409	+	15.7861i	−0.454569	+	0.787337i
$403$	7.24877	+	37.0772i	0.361087	+	1.84695i
$404$	3.00691	+	5.20811i	0.149599	+	0.259113i
$405$	9.28811	+	5.36249i	0.461530	+	0.266464i
$406$	−29.6381	+	21.8077i	−1.47091	+	1.08230i
$407$	8.05193	+	13.9463i	0.399119	+	0.691295i
$408$	−9.81500	+	5.66669i	−0.485915	+	0.280543i
$409$			17.6337i			0.871930i	0.899964	+	0.435965i	$0.143593\pi$
$409$			17.6337i			0.871930i	−0.899964	+	0.435965i	$0.856407\pi$
$410$		−	32.1381i		−	1.58719i
$411$	−4.48673	+	2.59041i	−0.221314	+	0.127776i
$412$	26.9532	+	46.6842i	1.32789	+	2.29997i
$413$	27.6858	+	12.1269i	1.36233	+	0.596727i
$414$	12.1601	+	7.02061i	0.597634	+	0.345044i
$415$	−2.17363	−	3.76483i	−0.106699	−	0.184808i
$416$	23.1852	−	20.1987i	1.13675	−	0.990324i
$417$	0.431416	−	0.747234i	0.0211265	−	0.0365922i
$418$		−	25.7781i		−	1.26085i
$419$	−14.9455	+	25.8864i	−0.730137	+	1.26463i	0.226688	+	0.973968i	$0.427210\pi$
$419$	−14.9455	+	25.8864i	−0.730137	+	1.26463i	−0.956824	+	0.290666i	$0.906123\pi$
$420$	−8.37274	+	6.16065i	−0.408548	+	0.300609i
$421$			12.8528i			0.626407i	0.949686	+	0.313203i	$0.101402\pi$
$421$			12.8528i			0.626407i	−0.949686	+	0.313203i	$0.898598\pi$
$422$	−16.8493	−	9.72796i	−0.820212	−	0.473550i
$423$		−	2.88164i		−	0.140110i
$424$	−43.9919	−	25.3987i	−2.13644	−	1.23347i
$425$	3.75393	−	6.50200i	0.182093	−	0.315394i
$426$	−0.906662	+	1.57038i	−0.0439279	+	0.0760854i
$427$	−4.58656	−	6.23344i	−0.221959	−	0.301657i
$428$	24.1401			1.16685
$429$	−0.970207	−	4.96257i	−0.0468421	−	0.239595i
$430$	7.00223	−	12.1282i	0.337677	−	0.584874i
$431$	7.76876	−	4.48530i	0.374208	−	0.216049i	−0.301087	−	0.953597i	$-0.597350\pi$
$431$	7.76876	−	4.48530i	0.374208	−	0.216049i	0.675295	+	0.737547i	$0.264016\pi$
$432$	−25.8405			−1.24325
$433$	−1.72531	−	2.98833i	−0.0829132	−	0.143610i	0.821587	−	0.570083i	$-0.193089\pi$
$433$	−1.72531	−	2.98833i	−0.0829132	−	0.143610i	−0.904500	+	0.426473i	$0.859756\pi$
$434$	−42.5300	−	57.8012i	−2.04151	−	2.77454i
$435$	3.88887	−	2.24524i	0.186457	−	0.107651i
$436$	−7.03410	−	4.06114i	−0.336872	−	0.194493i
$437$	−6.33204	−	3.65580i	−0.302902	−	0.174881i
$438$	12.2176			0.583780
$439$	38.5144			1.83819			0.919096	−	0.394034i	$-0.128921\pi$
$439$	38.5144			1.83819			0.919096	+	0.394034i	$0.128921\pi$
$440$	−26.4020	−	15.2432i	−1.25867	−	0.726691i
$441$	−18.6513	+	4.20023i	−0.888155	+	0.200011i
$442$	−22.0029	+	19.1687i	−1.04657	+	0.911764i
$443$	7.51997	+	13.0250i	0.357284	+	0.618835i	0.987506	−	0.157580i	$-0.0503693\pi$
$443$	7.51997	+	13.0250i	0.357284	+	0.618835i	−0.630222	+	0.776415i	$0.717036\pi$
$444$	−12.5660	+	7.25498i	−0.596356	+	0.344306i
$445$	−1.41851	−	2.45693i	−0.0672437	−	0.116469i
$446$	−29.2246	+	50.6185i	−1.38382	+	2.39685i
$447$		−	10.2646i		−	0.485499i
$448$	−4.97225	+	11.3516i	−0.234917	+	0.536314i
$449$	33.7087	−	19.4617i	1.59081	−	0.918456i	0.597646	−	0.801760i	$-0.296103\pi$
$449$	33.7087	−	19.4617i	1.59081	−	0.918456i	0.993168	−	0.116696i	$-0.0372304\pi$
$450$	14.7025	−	8.48850i	0.693083	−	0.400152i
$451$	−20.8322			−0.980952
$452$	−20.1928	−	34.9750i	−0.949790	−	1.64509i
$453$			3.90660i			0.183548i
$454$	−35.3906			−1.66097
$455$	−10.4075	+	11.3211i	−0.487911	+	0.530741i
$456$	13.3448			0.624927
$457$		−	13.9396i		−	0.652069i	−0.945358	−	0.326034i	$-0.894287\pi$
$457$		−	13.9396i		−	0.652069i	0.945358	−	0.326034i	$-0.105713\pi$
$458$	−10.2649	−	17.7793i	−0.479648	−	0.830774i
$459$	9.29049			0.433643
$460$	−13.0339	+	7.52512i	−0.607709	+	0.350861i
$461$	32.4443	−	18.7317i	1.51108	−	0.872424i	0.511167	−	0.859481i	$-0.329213\pi$
$461$	32.4443	−	18.7317i	1.51108	−	0.872424i	0.999916	−	0.0129430i	$-0.00412001\pi$
$462$	5.69241	+	7.73637i	0.264835	+	0.359928i
$463$		−	6.75275i		−	0.313827i	−0.987612	−	0.156913i	$-0.949846\pi$
$463$		−	6.75275i		−	0.313827i	0.987612	−	0.156913i	$-0.0501544\pi$
$464$	23.3614	−	40.4631i	1.08453	−	1.87845i
$465$	4.37875	+	7.58421i	0.203059	+	0.351709i
$466$	−14.7324	+	8.50576i	−0.682466	+	0.394022i
$467$	2.52516	+	4.37371i	0.116851	+	0.202391i	0.918518	−	0.395379i	$-0.129387\pi$
$467$	2.52516	+	4.37371i	0.116851	+	0.202391i	−0.801667	+	0.597770i	$0.796053\pi$
$468$	−45.4314	+	8.88205i	−2.10006	+	0.410573i
$469$	−3.97162	−	35.7140i	−0.183393	−	1.64912i
$470$	3.81296	+	2.20141i	0.175879	+	0.101544i
$471$	7.26084			0.334562
$472$	−79.8705			−3.67634
$473$	−7.86163	−	4.53892i	−0.361478	−	0.208700i
$474$	−7.21294	−	4.16439i	−0.331301	−	0.191277i
$475$	−7.65595	+	4.42017i	−0.351279	+	0.202811i
$476$	15.6020	−	35.6194i	0.715117	−	1.63261i
$477$	9.92198	+	17.1854i	0.454296	+	0.786864i
$478$	24.3143			1.11211
$479$	8.18670	−	4.72659i	0.374060	−	0.215964i	−0.301171	−	0.953570i	$-0.597377\pi$
$479$	8.18670	−	4.72659i	0.374060	−	0.215964i	0.675231	+	0.737607i	$0.264044\pi$
$480$	3.56401	−	6.17304i	0.162674	−	0.281759i
$481$	−16.1850	+	14.1002i	−0.737971	+	0.642913i
$482$	−26.1082			−1.18920
$483$	2.70762	−	0.301105i	0.123201	−	0.0137007i
$484$	8.65711	−	14.9946i	0.393505	−	0.681571i
$485$	12.4789	−	21.6142i	0.566639	−	0.981448i
$486$	27.7167	+	16.0023i	1.25726	+	0.725877i
$487$		−	39.9996i		−	1.81255i	−0.422684	−	0.906277i	$-0.638912\pi$
$487$		−	39.9996i		−	1.81255i	0.422684	−	0.906277i	$-0.361088\pi$
$488$	17.7106	+	10.2252i	0.801721	+	0.462874i
$489$		−	3.71737i		−	0.168105i
$490$	8.69084	−	27.8879i	0.392612	−	1.25985i
$491$	−3.38049	+	5.85517i	−0.152559	+	0.264240i	−0.932168	−	0.362027i	$-0.882085\pi$
$491$	−3.38049	+	5.85517i	−0.152559	+	0.264240i	0.779608	+	0.626267i	$0.215418\pi$
$492$		−	18.7704i		−	0.846233i
$493$	−8.39918	+	14.5478i	−0.378280	+	0.655200i
$494$	33.7223	−	6.59287i	1.51724	−	0.296627i
$495$	5.95473	+	10.3139i	0.267645	+	0.463575i
$496$	78.9125	+	45.5602i	3.54328	+	2.04571i
$497$	−0.395094	−	3.55280i	−0.0177224	−	0.159365i
$498$	−1.80963	−	3.13438i	−0.0810916	−	0.140455i
$499$	−9.83591	+	5.67877i	−0.440316	+	0.254217i	−0.703732	−	0.710466i	$-0.748484\pi$
$499$	−9.83591	+	5.67877i	−0.440316	+	0.254217i	0.263416	+	0.964682i	$0.415151\pi$
$500$			56.0871i			2.50829i
$501$		−	9.32230i		−	0.416490i
$502$	−23.1993	+	13.3941i	−1.03543	+	0.597808i
$503$	6.96423	+	12.0624i	0.310520	+	0.537836i	0.978475	−	0.206365i	$-0.0661635\pi$
$503$	6.96423	+	12.0624i	0.310520	+	0.537836i	−0.667955	+	0.744202i	$0.732830\pi$
$504$	40.6921	−	29.9412i	1.81257	−	1.33369i
$505$	1.78601	+	1.03115i	0.0794763	+	0.0458857i
$506$	6.95317	+	12.0432i	0.309106	+	0.535388i
$507$	6.24379	−	2.53840i	0.277296	−	0.112734i
$508$	7.34301	−	12.7185i	0.325793	−	0.564290i
$509$			19.8149i			0.878281i	0.898418	+	0.439141i	$0.144717\pi$
$509$			19.8149i			0.878281i	−0.898418	+	0.439141i	$0.855283\pi$
$510$	−3.38227	+	5.85826i	−0.149769	+	0.259408i
$511$	−19.3996	+	14.2742i	−0.858188	+	0.631453i
$512$			47.4335i			2.09628i
$513$	−9.47373	−	5.46966i	−0.418276	−	0.241491i
$514$			20.6741i			0.911894i
$515$	16.0093	+	9.24299i	0.705455	+	0.407295i
$516$	4.08967	−	7.08352i	0.180038	−	0.311835i
$517$	1.42698	−	2.47160i	0.0627585	−	0.108701i
$518$	16.3593	−	37.3483i	0.718787	−	1.64099i
$519$	6.64237			0.291568
$520$	13.1883	−	38.4370i	0.578347	−	1.68557i
$521$	15.5476	−	26.9292i	0.681151	−	1.17979i	−0.293479	−	0.955966i	$-0.594813\pi$
$521$	15.5476	−	26.9292i	0.681151	−	1.17979i	0.974630	−	0.223823i	$-0.0718537\pi$
$522$	−32.8959	+	18.9924i	−1.43981	+	0.831277i
$523$	22.7202			0.993485			0.496742	−	0.867898i	$-0.334529\pi$
$523$	22.7202			0.993485			0.496742	+	0.867898i	$0.334529\pi$
$524$	23.9960	+	41.5622i	1.04827	+	1.81565i
$525$	1.32158	−	3.01717i	0.0576786	−	0.131680i
$526$	−11.3420	+	6.54831i	−0.494535	+	0.285520i
$527$	−28.3716	−	16.3804i	−1.23589	−	0.713540i
$528$	−10.5620	−	6.09798i	−0.459652	−	0.265380i
$529$	−19.0557			−0.828507
$530$	−30.3194			−1.31699
$531$	27.0211	+	15.6007i	1.17262	+	0.677011i
$532$	−36.8802	+	27.1364i	−1.59896	+	1.17651i
$533$	−5.32794	−	27.2522i	−0.230779	−	1.18043i
$534$	−1.18097	−	2.04549i	−0.0511054	−	0.0885171i
$535$	7.16922	−	4.13915i	0.309952	−	0.178951i
$536$	47.4782	+	82.2346i	2.05074	+	3.55199i
$537$	0.477046	−	0.826267i	0.0205860	−	0.0356561i
$538$		−	35.9563i		−	1.55018i
$539$	−18.0772	−	5.63349i	−0.778642	−	0.242651i
$540$	−19.5008	+	11.2588i	−0.839180	+	0.484501i
$541$	1.81754	−	1.04936i	0.0781423	−	0.0451155i	−0.460420	−	0.887701i	$-0.652301\pi$
$541$	1.81754	−	1.04936i	0.0781423	−	0.0451155i	0.538562	+	0.842586i	$0.318968\pi$
$542$	−21.5558			−0.925902
$543$	0.855283	+	1.48139i	0.0367037	+	0.0635727i
$544$			26.6650i			1.14325i
$545$	−2.78536			−0.119312
$546$	−8.66467	+	9.42528i	−0.370813	+	0.403365i
$547$	25.3770			1.08504			0.542521	−	0.840042i	$-0.317470\pi$
$547$	25.3770			1.08504			0.542521	+	0.840042i	$0.317470\pi$
$548$			46.9738i			2.00662i
$549$	−3.99447	−	6.91862i	−0.170480	−	0.295280i
$550$	16.8139			0.716948
$551$	17.1297	−	9.88983i	0.729749	−	0.421321i
$552$	−6.23454	+	3.59951i	−0.265360	+	0.153205i
$553$	16.3184	−	1.81471i	0.693927	−	0.0771692i
$554$		−	60.0855i		−	2.55279i
$555$	−2.48794	+	4.30923i	−0.105607	+	0.182917i
$556$	−3.91158	−	6.77506i	−0.165888	−	0.287327i
$557$	−38.3219	+	22.1252i	−1.62375	+	0.937473i	−0.637846	+	0.770164i	$0.720174\pi$
$557$	−38.3219	+	22.1252i	−1.62375	+	0.937473i	−0.985904	+	0.167309i	$0.946492\pi$
$558$	−37.0397	−	64.1547i	−1.56802	−	2.71588i
$559$	3.92705	−	11.4452i	0.166097	−	0.484082i
$560$	4.09944	+	36.8634i	0.173233	+	1.55776i
$561$	3.79738	+	2.19242i	0.160326	+	0.0925641i
$562$	70.3051			2.96564
$563$	38.8907			1.63905			0.819523	−	0.573046i	$-0.194238\pi$
$563$	38.8907			1.63905			0.819523	+	0.573046i	$0.194238\pi$
$564$	2.22697	+	1.28574i	0.0937725	+	0.0541396i
$565$	−11.9939	−	6.92468i	−0.504587	−	0.291324i
$566$	−36.2078	+	20.9046i	−1.52193	+	0.878685i
$567$	−17.4943	+	1.94548i	−0.734693	+	0.0817026i
$568$	4.72309	+	8.18063i	0.198177	+	0.343252i
$569$	−46.1579			−1.93504			−0.967520	−	0.252796i	$-0.918650\pi$
$569$	−46.1579			−1.93504			−0.967520	+	0.252796i	$0.918650\pi$
$570$	6.89796	−	3.98254i	0.288924	−	0.166810i
$571$	10.5684	−	18.3050i	0.442274	−	0.766041i	−0.555584	−	0.831461i	$-0.687505\pi$
$571$	10.5684	−	18.3050i	0.442274	−	0.766041i	0.997858	+	0.0654194i	$0.0208385\pi$
$572$	−43.3651	−	14.8793i	−1.81319	−	0.622134i
$573$	2.53848			0.106047
$574$	31.2601	+	42.4846i	1.30477	+	1.77327i
$575$	2.38452	−	4.13011i	0.0994413	−	0.172237i
$576$	−6.39653	+	11.0791i	−0.266522	+	0.461630i
$577$	21.9368	+	12.6652i	0.913239	+	0.527259i	0.881472	−	0.472237i	$-0.156553\pi$
$577$	21.9368	+	12.6652i	0.913239	+	0.527259i	0.0317671	+	0.999495i	$0.489887\pi$
$578$			18.7009i			0.777855i
$579$	−1.35559	−	0.782650i	−0.0563364	−	0.0325258i
$580$		−	40.7146i		−	1.69058i
$581$	6.53539	+	2.86263i	0.271133	+	0.118762i
$582$	10.3892	−	17.9947i	0.430647	−	0.745903i
$583$			19.6533i			0.813958i
$584$	31.8227	−	55.1186i	1.31683	−	2.28082i
$585$	−11.9694	+	10.4277i	−0.494876	+	0.431131i
$586$	18.9553	+	32.8315i	0.783036	+	1.35626i
$587$	3.08554	+	1.78144i	0.127354	+	0.0735278i	0.562324	−	0.826917i	$-0.309908\pi$
$587$	3.08554	+	1.78144i	0.127354	+	0.0735278i	−0.434970	+	0.900445i	$0.643241\pi$
$588$	5.07591	−	16.2880i	0.209327	−	0.671707i
$589$	19.2875	+	33.4069i	0.794727	+	1.37651i
$590$	−41.2853	+	23.8361i	−1.69969	+	0.981316i
$591$		−	2.41082i		−	0.0991679i
$592$			51.7732i			2.12786i
$593$	21.9568	−	12.6768i	0.901659	−	0.520573i	0.0239212	−	0.999714i	$-0.492385\pi$
$593$	21.9568	−	12.6768i	0.901659	−	0.520573i	0.877738	+	0.479141i	$0.159052\pi$
$594$	10.4030	+	18.0186i	0.426842	+	0.739312i
$595$	−1.47388	−	13.2536i	−0.0604233	−	0.543343i
$596$	−80.5990	−	46.5338i	−3.30146	−	1.90610i
$597$	0.106472	+	0.184415i	0.00435762	+	0.00754762i
$598$	−13.9764	+	12.1761i	−0.571537	+	0.497917i
$599$	−5.46078	+	9.45835i	−0.223122	+	0.386458i	−0.955754	−	0.294166i	$-0.904958\pi$
$599$	−5.46078	+	9.45835i	−0.223122	+	0.386458i	0.732633	+	0.680624i	$0.238291\pi$
$600$			8.70421i			0.355348i
$601$	−12.1282	+	21.0067i	−0.494720	+	0.856880i	−0.999981	−	0.00608649i	$-0.998063\pi$
$601$	−12.1282	+	21.0067i	−0.494720	+	0.856880i	0.505262	+	0.862966i	$0.331396\pi$
$602$	2.54037	+	22.8437i	0.103538	+	0.931040i
$603$		−	37.0946i		−	1.51061i
$604$	30.6751	+	17.7103i	1.24815	+	0.720621i
$605$		−	5.93753i		−	0.241395i
$606$	1.48692	+	0.858476i	0.0604022	+	0.0348732i
$607$	4.92724	−	8.53422i	0.199990	−	0.346393i	−0.748535	−	0.663096i	$-0.769242\pi$
$607$	4.92724	−	8.53422i	0.199990	−	0.346393i	0.948525	+	0.316702i	$0.102576\pi$
$608$	15.6987	−	27.1910i	0.636667	−	1.10274i
$609$	−2.95695	+	6.75071i	−0.119822	+	0.273553i
$610$	12.2062			0.494215
$611$	3.59825	+	1.23462i	0.145569	+	0.0499472i
$612$	20.0712	−	34.7643i	0.811328	−	1.40526i
$613$	−3.18428	+	1.83844i	−0.128612	+	0.0742540i	−0.562926	−	0.826508i	$-0.690324\pi$
$613$	−3.18428	+	1.83844i	−0.128612	+	0.0742540i	0.434314	+	0.900762i	$0.356991\pi$
$614$	−23.2416			−0.937955
$615$	−3.21844	−	5.57450i	−0.129780	−	0.224785i
$616$	49.7286	−	5.53015i	2.00362	−	0.222816i
$617$	16.2352	−	9.37341i	0.653605	−	0.377359i	−0.136231	−	0.990677i	$-0.543499\pi$
$617$	16.2352	−	9.37341i	0.653605	−	0.377359i	0.789836	+	0.613318i	$0.210166\pi$
$618$	13.3284	+	7.69517i	0.536148	+	0.309545i
$619$	13.7650	+	7.94725i	0.553264	+	0.319427i	0.750437	−	0.660942i	$-0.229843\pi$
$619$	13.7650	+	7.94725i	0.553264	+	0.319427i	−0.197174	+	0.980369i	$0.563176\pi$
$620$	79.4029			3.18890
$621$	5.90137			0.236814
$622$	−27.3086	−	15.7667i	−1.09498	−	0.632185i
$623$	4.26499	+	1.86815i	0.170873	+	0.0748460i
$624$	5.27594	−	15.3765i	0.211207	−	0.615555i
$625$	3.61371	+	6.25913i	0.144549	+	0.250365i
$626$	−29.4212	+	16.9864i	−1.17591	+	0.678911i
$627$	−2.58152	−	4.47133i	−0.103096	−	0.178568i
$628$	32.9165	−	57.0130i	1.31351	−	2.27507i
$629$		−	18.6141i		−	0.742194i
$630$	12.0984	−	27.6206i	0.482011	−	1.10043i
$631$	−17.0998	+	9.87255i	−0.680731	+	0.393020i	−0.800130	−	0.599826i	$-0.795236\pi$
$631$	−17.0998	+	9.87255i	−0.680731	+	0.393020i	0.119400	+	0.992846i	$0.461903\pi$
$632$	−37.5745	+	21.6936i	−1.49463	+	0.862927i
$633$	−3.89679			−0.154883
$634$	−21.6349	−	37.4727i	−0.859231	−	1.48823i
$635$		−	5.03624i		−	0.199857i
$636$	−17.7081			−0.702173
$637$	2.74625	−	25.0890i	0.108811	−	0.994063i
$638$	−37.6200			−1.48939
$639$		−	3.69014i		−	0.145980i
$640$	3.97508	+	6.88504i	0.157129	+	0.272155i
$641$	29.7786			1.17618			0.588092	−	0.808794i	$-0.299879\pi$
$641$	29.7786			1.17618			0.588092	+	0.808794i	$0.299879\pi$
$642$	5.96867	−	3.44601i	0.235565	−	0.136003i
$643$	10.0220	−	5.78623i	0.395231	−	0.228187i	−0.289193	−	0.957271i	$-0.593387\pi$
$643$	10.0220	−	5.78623i	0.395231	−	0.228187i	0.684424	+	0.729084i	$0.260054\pi$
$644$	9.91048	−	22.6256i	0.390528	−	0.891574i
$645$		−	2.80493i		−	0.110444i
$646$	−14.8982	+	25.8044i	−0.586162	+	1.01526i
$647$	12.7533	+	22.0893i	0.501382	+	0.868420i	0.999999	+	0.00159698i	$0.000508335\pi$
$647$	12.7533	+	22.0893i	0.501382	+	0.868420i	−0.498616	+	0.866823i	$0.666158\pi$
$648$	40.2823	−	23.2570i	1.58244	−	0.913620i
$649$	15.4508	+	26.7616i	0.606497	+	1.05048i
$650$	4.30024	+	21.9956i	0.168669	+	0.862737i
$651$	−13.1655	−	5.76675i	−0.515995	−	0.226017i
$652$	−29.1893	−	16.8524i	−1.14314	−	0.659993i
$653$	−44.8293			−1.75430			−0.877152	−	0.480212i	$-0.840560\pi$
$653$	−44.8293			−1.75430			−0.877152	+	0.480212i	$0.840560\pi$
$654$	−2.31892			−0.0906771
$655$	14.2529	+	8.22889i	0.556905	+	0.321529i
$656$	−58.0018	−	33.4874i	−2.26459	−	1.30746i
$657$	−21.5320	+	12.4315i	−0.840043	+	0.484999i
$658$	−7.18179	+	0.798661i	−0.279975	+	0.0311350i
$659$	−20.5867	−	35.6572i	−0.801944	−	1.38901i	−0.918335	−	0.395805i	$-0.870466\pi$
$659$	−20.5867	−	35.6572i	−0.801944	−	1.38901i	0.116390	−	0.993204i	$-0.462868\pi$
$660$	−10.6276			−0.413680
$661$	−18.9606	+	10.9469i	−0.737481	+	0.425785i	−0.821153	−	0.570709i	$-0.806669\pi$
$661$	−18.9606	+	10.9469i	−0.737481	+	0.425785i	0.0836719	+	0.996493i	$0.473335\pi$
$662$	−5.13404	+	8.89241i	−0.199540	+	0.345613i
$663$	−1.89687	+	5.52837i	−0.0736684	+	0.214704i
$664$	−18.8539			−0.731673
$665$	−6.29993	+	14.3827i	−0.244301	+	0.557738i
$666$	21.0454	−	36.4517i	0.815492	−	1.41247i
$667$	−5.33520	+	9.24084i	−0.206580	+	0.357807i
$668$	−73.1999	−	42.2620i	−2.83219	−	1.63516i
$669$			11.7067i			0.452606i
$670$	49.0832	+	28.3382i	1.89625	+	1.09480i
$671$		−	7.91219i		−	0.305447i
$672$	1.29300	+	11.6270i	0.0498786	+	0.448523i
$673$	17.8344	−	30.8901i	0.687466	−	1.19073i	−0.285189	−	0.958471i	$-0.592056\pi$
$673$	17.8344	−	30.8901i	0.687466	−	1.19073i	0.972655	−	0.232254i	$-0.0746102\pi$
$674$			35.4721i			1.36633i
$675$	3.56762	−	6.17930i	0.137318	−	0.237841i
$676$	8.37388	−	60.5347i	0.322072	−	2.32826i
$677$	−1.27766	−	2.21297i	−0.0491044	−	0.0850514i	0.840428	−	0.541923i	$-0.182303\pi$
$677$	−1.27766	−	2.21297i	−0.0491044	−	0.0850514i	−0.889533	+	0.456871i	$0.848970\pi$
$678$	−9.98541	−	5.76508i	−0.383488	−	0.221407i
$679$	4.52729	+	40.7107i	0.173741	+	1.56233i
$680$	17.6193	+	30.5175i	0.675670	+	1.17029i
$681$	−6.13867	+	3.54416i	−0.235234	+	0.135813i
$682$		−	73.3678i		−	2.80940i
$683$			35.7399i			1.36755i	0.729693	+	0.683775i	$0.239663\pi$
$683$			35.7399i			1.36755i	−0.729693	+	0.683775i	$0.760337\pi$
$684$	−40.9341	+	23.6333i	−1.56515	+	0.903642i
$685$	8.05431	+	13.9505i	0.307739	+	0.533020i
$686$	15.6373	+	45.3196i	0.597036	+	1.73031i
$687$	−3.56099	−	2.05594i	−0.135860	−	0.0784390i
$688$	−14.5924	−	25.2748i	−0.556330	−	0.963592i
$689$	−25.7100	+	5.02643i	−0.979474	+	0.191492i
$690$	−2.14843	+	3.72120i	−0.0817895	+	0.141664i
$691$			26.0292i			0.990197i	0.868837	+	0.495099i	$0.164868\pi$
$691$			26.0292i			0.990197i	−0.868837	+	0.495099i	$0.835132\pi$
$692$	30.1127	−	52.1567i	1.14471	−	1.98270i
$693$	−17.9039	−	7.84230i	−0.680115	−	0.297904i
$694$			68.3335i			2.59391i
$695$	−2.32336	−	1.34139i	−0.0881299	−	0.0508818i
$696$		−	19.4751i		−	0.738202i
$697$	20.8535	+	12.0398i	0.789884	+	0.456040i
$698$	−6.32944	+	10.9629i	−0.239573	+	0.414952i
$699$	−1.70360	+	2.95073i	−0.0644362	+	0.111607i
$700$	−17.6999	−	24.0553i	−0.668993	−	0.909206i
$701$	−1.12731			−0.0425779			−0.0212890	−	0.999773i	$-0.506777\pi$
$701$	−1.12731			−0.0425779			−0.0212890	+	0.999773i	$0.506777\pi$
$702$	−20.9109	+	18.2174i	−0.789230	+	0.687570i
$703$	−10.9588	+	18.9813i	−0.413321	+	0.715892i
$704$	−10.9727	+	6.33509i	−0.413549	+	0.238763i
$705$	0.881834			0.0332118
$706$	17.5478	+	30.3936i	0.660419	+	1.14388i
$707$	−3.36398	+	0.374096i	−0.126515	+	0.0140693i
$708$	−24.1128	+	13.9215i	−0.906215	+	0.523203i
$709$	−5.23972	−	3.02515i	−0.196782	−	0.113612i	0.398372	−	0.917224i	$-0.369575\pi$
$709$	−5.23972	−	3.02515i	−0.196782	−	0.113612i	−0.595153	+	0.803612i	$0.702909\pi$
$710$	4.88276	+	2.81906i	0.183247	+	0.105798i
$711$	16.9492			0.635644
$712$	−12.3040			−0.461114
$713$	−18.0218	−	10.4049i	−0.674922	−	0.389666i
$714$	−1.22707	−	11.0341i	−0.0459219	−	0.412942i
$715$	−15.4300	+	3.01664i	−0.577050	+	0.112816i
$716$	−4.32530	−	7.49164i	−0.161644	−	0.279976i
$717$	4.21743	−	2.43493i	0.157503	−	0.0909342i
$718$	−11.1124	−	19.2473i	−0.414713	−	0.718304i
$719$	23.5589	−	40.8052i	0.878597	−	1.52178i	0.0257170	−	0.999669i	$-0.491813\pi$
$719$	23.5589	−	40.8052i	0.878597	−	1.52178i	0.852880	−	0.522106i	$-0.174854\pi$
$720$			38.2884i			1.42692i
$721$	−30.1539	+	3.35331i	−1.12299	+	0.124884i
$722$	−12.2100	+	7.04944i	−0.454409	+	0.262353i
$723$	−4.52859	+	2.61458i	−0.168420	+	0.0972374i
$724$	15.5095			0.576404
$725$	6.45070	+	11.1729i	0.239573	+	0.414953i
$726$		−	4.94324i		−	0.183461i
$727$	17.9215			0.664671			0.332335	−	0.943161i	$-0.392163\pi$
$727$	17.9215			0.664671			0.332335	+	0.943161i	$0.392163\pi$
$728$	19.9527	+	63.6394i	0.739498	+	2.35863i
$729$	−13.5489			−0.501810
$730$		−	37.9880i		−	1.40600i
$731$	5.24644	+	9.08711i	0.194047	+	0.336099i
$732$	7.12908			0.263498
$733$	−39.2037	+	22.6343i	−1.44802	+	0.836016i	−0.998364	−	0.0571848i	$-0.981788\pi$
$733$	−39.2037	+	22.6343i	−1.44802	+	0.836016i	−0.449658	+	0.893201i	$0.648454\pi$
$734$	3.72861	−	2.15271i	0.137625	−	0.0794581i
$735$	−1.28535	−	5.70762i	−0.0474107	−	0.210529i
$736$			16.9378i			0.624335i
$737$	18.3691	−	31.8163i	0.676635	−	1.17197i
$738$	27.2247	+	47.1546i	1.00215	+	1.73578i
$739$	16.6808	−	9.63066i	0.613613	−	0.354270i	−0.160765	−	0.986993i	$-0.551396\pi$
$739$	16.6808	−	9.63066i	0.613613	−	0.354270i	0.774378	+	0.632723i	$0.218063\pi$
$740$	22.5577	+	39.0712i	0.829239	+	1.43628i
$741$	5.18905	−	4.52065i	0.190624	−	0.166070i
$742$	40.0804	−	29.4911i	1.47140	−	1.08265i
$743$	30.2115	+	17.4426i	1.10835	+	0.639908i	0.938402	−	0.345545i	$-0.112306\pi$
$743$	30.2115	+	17.4426i	1.10835	+	0.639908i	0.169951	+	0.985453i	$0.445639\pi$
$744$	37.9810			1.39245
$745$	−31.9155			−1.16929
$746$	31.3032	+	18.0729i	1.14609	+	0.661697i
$747$	6.37850	+	3.68263i	0.233377	+	0.134740i
$748$	34.4303	−	19.8784i	1.25890	−	0.726825i
$749$	−5.45120	+	12.4451i	−0.199183	+	0.454733i
$750$	8.00648	+	13.8676i	0.292355	+	0.506374i
$751$	24.9668			0.911051			0.455526	−	0.890223i	$-0.349451\pi$
$751$	24.9668			0.911051			0.455526	+	0.890223i	$0.349451\pi$
$752$	7.94609	−	4.58767i	0.289764	−	0.167295i
$753$	−2.68268	+	4.64654i	−0.0977623	+	0.169329i
$754$	−9.62150	−	49.2136i	−0.350394	−	1.79225i
$755$	12.1467			0.442064
$756$	14.8277	−	33.8515i	0.539277	−	1.23117i
$757$	5.30243	−	9.18408i	0.192720	−	0.333801i	−0.753431	−	0.657527i	$-0.771602\pi$
$757$	5.30243	−	9.18408i	0.192720	−	0.333801i	0.946151	+	0.323726i	$0.104936\pi$
$758$	−40.8685	+	70.7863i	−1.48441	+	2.57108i
$759$	2.41212	+	1.39264i	0.0875543	+	0.0505495i
$760$		−	41.4926i		−	1.50510i
$761$	28.2660	+	16.3194i	1.02464	+	0.591578i	0.915446	−	0.402442i	$-0.131838\pi$
$761$	28.2660	+	16.3194i	1.02464	+	0.591578i	0.109198	+	0.994020i	$0.465172\pi$
$762$		−	4.19288i		−	0.151892i
$763$	3.68208	−	2.70927i	0.133300	−	0.0980820i
$764$	11.5080	−	19.9325i	0.416345	−	0.721131i
$765$		−	13.7659i		−	0.497708i
$766$	−41.2988	+	71.5316i	−1.49219	+	2.58454i
$767$	−31.0572	+	27.0568i	−1.12141	+	0.976963i
$768$	5.73794	+	9.93841i	0.207050	+	0.358621i
$769$	−45.1851	−	26.0876i	−1.62942	−	0.940744i	−0.984267	−	0.176686i	$-0.943462\pi$
$769$	−45.1851	−	26.0876i	−1.62942	−	0.940744i	−0.645148	−	0.764057i	$-0.723204\pi$
$770$	24.0545	−	17.6993i	0.866864	−	0.637837i
$771$	2.07039	+	3.58601i	0.0745631	+	0.129147i
$772$	−12.2909	+	7.09618i	−0.442360	+	0.255397i
$773$			35.7057i			1.28425i	0.766602

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:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	91.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.58860i q^{2} +(-0.259233 - 0.449005i) q^{3} -4.70085 q^{4} +(-1.39608 + 0.806027i) q^{5} +(-1.16229 + 0.671051i) q^{6} +(1.06153 - 2.42346i) q^{7} +6.99143i q^{8} +(1.36560 - 2.36528i) q^{9} +O(q^{10})\)	\(q-2.58860i q^{2} +(-0.259233 - 0.449005i) q^{3} -4.70085 q^{4} +(-1.39608 + 0.806027i) q^{5} +(-1.16229 + 0.671051i) q^{6} +(1.06153 - 2.42346i) q^{7} +6.99143i q^{8} +(1.36560 - 2.36528i) q^{9} +(2.08648 + 3.61389i) q^{10} +(2.34256 - 1.35248i) q^{11} +(1.21862 + 2.11070i) q^{12} +(2.36840 + 2.71858i) q^{13} +(-6.27337 - 2.74787i) q^{14} +(0.723819 + 0.417897i) q^{15} +8.69632 q^{16} -3.12661 q^{17} +(-6.12277 - 3.53498i) q^{18} +(3.18828 + 1.84075i) q^{19} +(6.56276 - 3.78901i) q^{20} +(-1.36333 + 0.151611i) q^{21} +(-3.50103 - 6.06396i) q^{22} -1.98604 q^{23} +(3.13918 - 1.81241i) q^{24} +(-1.20064 + 2.07957i) q^{25} +(7.03732 - 6.13084i) q^{26} -2.97143 q^{27} +(-4.99008 + 11.3923i) q^{28} +(2.68636 - 4.65290i) q^{29} +(1.08177 - 1.87368i) q^{30} +(9.07425 + 5.23902i) q^{31} -8.52843i q^{32} +(-1.21454 - 0.701214i) q^{33} +8.09354i q^{34} +(0.471400 + 4.23896i) q^{35} +(-6.41947 + 11.1188i) q^{36} +5.95346i q^{37} +(4.76497 - 8.25317i) q^{38} +(0.606687 - 1.76817i) q^{39} +(-5.63528 - 9.76059i) q^{40} +(-6.66970 - 3.85075i) q^{41} +(0.392460 + 3.52911i) q^{42} +(-1.67800 - 2.90638i) q^{43} +(-11.0120 + 6.35780i) q^{44} +4.40283i q^{45} +5.14106i q^{46} +(0.913730 - 0.527542i) q^{47} +(-2.25437 - 3.90469i) q^{48} +(-4.74633 - 5.14513i) q^{49} +(5.38318 + 3.10798i) q^{50} +(0.810520 + 1.40386i) q^{51} +(-11.1335 - 12.7796i) q^{52} +(-3.63284 + 6.29226i) q^{53} +7.69184i q^{54} +(-2.18027 + 3.77633i) q^{55} +(16.9435 + 7.42158i) q^{56} -1.90873i q^{57} +(-12.0445 - 6.95390i) q^{58} +11.4241i q^{59} +(-3.40257 - 1.96447i) q^{60} +(1.46254 - 2.53319i) q^{61} +(13.5617 - 23.4896i) q^{62} +(-4.28255 - 5.82028i) q^{63} -4.68406 q^{64} +(-5.49772 - 1.88636i) q^{65} +(-1.81516 + 3.14395i) q^{66} +(11.7622 - 6.79091i) q^{67} +14.6977 q^{68} +(0.514846 + 0.891740i) q^{69} +(10.9730 - 1.22027i) q^{70} +(1.17009 - 0.675554i) q^{71} +(16.5367 + 9.54747i) q^{72} +(-7.88374 - 4.55168i) q^{73} +15.4111 q^{74} +1.24498 q^{75} +(-14.9876 - 8.65311i) q^{76} +(-0.790989 - 7.11280i) q^{77} +(-4.57708 - 1.57047i) q^{78} +(3.10289 + 5.37436i) q^{79} +(-12.1407 + 7.00946i) q^{80} +(-3.32650 - 5.76166i) q^{81} +(-9.96806 + 17.2652i) q^{82} +2.69672i q^{83} +(6.40880 - 0.712700i) q^{84} +(4.36499 - 2.52013i) q^{85} +(-7.52346 + 4.34367i) q^{86} -2.78557 q^{87} +(9.45576 + 16.3779i) q^{88} +1.75988i q^{89} +11.3972 q^{90} +(9.10249 - 2.85388i) q^{91} +9.33607 q^{92} -5.43251i q^{93} +(-1.36560 - 2.36528i) q^{94} -5.93478 q^{95} +(-3.82930 + 2.21085i) q^{96} +(-13.4078 + 7.74102i) q^{97} +(-13.3187 + 12.2863i) q^{98} -7.38776i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{3} - 8 q^{4} - 3 q^{5} - 9 q^{6} - 3 q^{7} - q^{9}+O(q^{10}) \) 12 * q - 3 * q^3 - 8 * q^4 - 3 * q^5 - 9 * q^6 - 3 * q^7 - q^9	\( 12 q - 3 q^{3} - 8 q^{4} - 3 q^{5} - 9 q^{6} - 3 q^{7} - q^{9} + 12 q^{10} + 12 q^{11} - q^{12} - 2 q^{13} + 4 q^{14} - 12 q^{15} + 16 q^{16} - 34 q^{17} + 3 q^{18} + 9 q^{19} - 3 q^{20} + 21 q^{21} - 15 q^{22} - 6 q^{23} + 15 q^{24} - 5 q^{25} - 6 q^{26} + 12 q^{27} - 9 q^{28} - q^{29} + 11 q^{30} + 18 q^{31} - 6 q^{33} - 6 q^{35} - 13 q^{36} + 19 q^{38} - 4 q^{39} - q^{40} - 6 q^{41} - 8 q^{42} + 11 q^{43} - 33 q^{44} - 15 q^{47} + 19 q^{48} - 3 q^{49} + 18 q^{50} + 4 q^{51} - 7 q^{52} - 8 q^{53} - 15 q^{55} + 27 q^{56} - 24 q^{58} - 30 q^{60} + 5 q^{61} + 41 q^{62} - 30 q^{63} + 2 q^{64} + 21 q^{65} - 34 q^{66} + 15 q^{67} + 22 q^{68} + 7 q^{69} + 3 q^{70} + 30 q^{71} + 57 q^{72} + 42 q^{73} + 66 q^{74} - 2 q^{75} - 45 q^{76} - 19 q^{77} + 44 q^{78} - 35 q^{79} - 63 q^{80} + 14 q^{81} + 5 q^{82} - 12 q^{84} - 21 q^{85} - 57 q^{86} - 20 q^{87} - 14 q^{88} - 7 q^{91} - 66 q^{92} + q^{94} - 4 q^{95} + 21 q^{96} - 3 q^{97} - 18 q^{98}+O(q^{100}) \) 12 * q - 3 * q^3 - 8 * q^4 - 3 * q^5 - 9 * q^6 - 3 * q^7 - q^9 + 12 * q^10 + 12 * q^11 - q^12 - 2 * q^13 + 4 * q^14 - 12 * q^15 + 16 * q^16 - 34 * q^17 + 3 * q^18 + 9 * q^19 - 3 * q^20 + 21 * q^21 - 15 * q^22 - 6 * q^23 + 15 * q^24 - 5 * q^25 - 6 * q^26 + 12 * q^27 - 9 * q^28 - q^29 + 11 * q^30 + 18 * q^31 - 6 * q^33 - 6 * q^35 - 13 * q^36 + 19 * q^38 - 4 * q^39 - q^40 - 6 * q^41 - 8 * q^42 + 11 * q^43 - 33 * q^44 - 15 * q^47 + 19 * q^48 - 3 * q^49 + 18 * q^50 + 4 * q^51 - 7 * q^52 - 8 * q^53 - 15 * q^55 + 27 * q^56 - 24 * q^58 - 30 * q^60 + 5 * q^61 + 41 * q^62 - 30 * q^63 + 2 * q^64 + 21 * q^65 - 34 * q^66 + 15 * q^67 + 22 * q^68 + 7 * q^69 + 3 * q^70 + 30 * q^71 + 57 * q^72 + 42 * q^73 + 66 * q^74 - 2 * q^75 - 45 * q^76 - 19 * q^77 + 44 * q^78 - 35 * q^79 - 63 * q^80 + 14 * q^81 + 5 * q^82 - 12 * q^84 - 21 * q^85 - 57 * q^86 - 20 * q^87 - 14 * q^88 - 7 * q^91 - 66 * q^92 + q^94 - 4 * q^95 + 21 * q^96 - 3 * q^97 - 18 * q^98

Introduction

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