LMFDB - Embedded newform 95.2.e.c.11.4

Newspace parameters

Level:	$ N $	$=$	$ 95 = 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	95.e (of order $3$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$0.758578819202$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.4601315889.1
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} - 3x^{5} + 26x^{4} - 14x^{3} + 31x^{2} + 12x + 9 $ x^8 - x^7 + 6x^6 - 3x^5 + 26x^4 - 14x^3 + 31x^2 + 12x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			11.4
Root			$1.07988 - 1.87040i$ of defining polynomial
Character	$\chi$	$=$	95.11
Dual form			95.2.e.c.26.4

$q$-expansion

$f(q)$	$=$	$q+(0.832272 - 1.44154i) q^{2} +(0.579878 - 1.00438i) q^{3} +(-0.385355 - 0.667454i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.965233 - 1.67183i) q^{6} -2.43525 q^{7} +2.04621 q^{8} +(0.827483 + 1.43324i) q^{9} +O(q^{10})$	\(q+(0.832272 - 1.44154i) q^{2} +(0.579878 - 1.00438i) q^{3} +(-0.385355 - 0.667454i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.965233 - 1.67183i) q^{6} -2.43525 q^{7} +2.04621 q^{8} +(0.827483 + 1.43324i) q^{9} +(0.832272 + 1.44154i) q^{10} -5.75477 q^{11} -0.893835 q^{12} +(0.797505 + 1.38132i) q^{13} +(-2.02680 + 3.51051i) q^{14} +(0.579878 + 1.00438i) q^{15} +(2.47371 - 4.28460i) q^{16} +(2.99203 - 5.18234i) q^{17} +2.75477 q^{18} +(0.149412 + 4.35634i) q^{19} +0.770710 q^{20} +(-1.41215 + 2.44592i) q^{21} +(-4.78953 + 8.29572i) q^{22} +(0.470022 + 0.814102i) q^{23} +(1.18655 - 2.05517i) q^{24} +(-0.500000 - 0.866025i) q^{25} +2.65497 q^{26} +5.39862 q^{27} +(0.938437 + 1.62542i) q^{28} +(-1.30917 - 2.26755i) q^{29} +1.93047 q^{30} -5.26913 q^{31} +(-2.07140 - 3.58777i) q^{32} +(-3.33706 + 5.77996i) q^{33} +(-4.98037 - 8.62625i) q^{34} +(1.21763 - 2.10899i) q^{35} +(0.637749 - 1.10461i) q^{36} -2.89384 q^{37} +(6.40418 + 3.41028i) q^{38} +1.84982 q^{39} +(-1.02310 + 1.77207i) q^{40} +(3.15767 - 5.46925i) q^{41} +(2.35059 + 4.07134i) q^{42} +(-2.26961 + 3.93108i) q^{43} +(2.21763 + 3.84104i) q^{44} -1.65497 q^{45} +1.56475 q^{46} +(-4.47718 - 7.75471i) q^{47} +(-2.86890 - 4.96909i) q^{48} -1.06953 q^{49} -1.66454 q^{50} +(-3.47002 - 6.01025i) q^{51} +(0.614645 - 1.06460i) q^{52} +(1.09819 + 1.90213i) q^{53} +(4.49313 - 7.78232i) q^{54} +(2.87738 - 4.98377i) q^{55} -4.98304 q^{56} +(4.46205 + 2.37608i) q^{57} -4.35834 q^{58} +(5.39939 - 9.35202i) q^{59} +(0.446918 - 0.774084i) q^{60} +(5.26434 + 9.11811i) q^{61} +(-4.38535 + 7.59566i) q^{62} +(-2.01513 - 3.49031i) q^{63} +2.99898 q^{64} -1.59501 q^{65} +(5.55469 + 9.62100i) q^{66} +(-0.504789 - 0.874320i) q^{67} -4.61197 q^{68} +1.09022 q^{69} +(-2.02680 - 3.51051i) q^{70} +(-4.41694 + 7.65036i) q^{71} +(1.69320 + 2.93271i) q^{72} +(5.12499 - 8.87674i) q^{73} +(-2.40846 + 4.17157i) q^{74} -1.15976 q^{75} +(2.85008 - 1.77846i) q^{76} +14.0143 q^{77} +(1.53956 - 2.66659i) q^{78} +(-3.80229 + 6.58577i) q^{79} +(2.47371 + 4.28460i) q^{80} +(0.648093 - 1.12253i) q^{81} +(-5.25609 - 9.10381i) q^{82} +3.11355 q^{83} +2.17672 q^{84} +(2.99203 + 5.18234i) q^{85} +(3.77787 + 6.54346i) q^{86} -3.03663 q^{87} -11.7755 q^{88} +(5.55706 + 9.62511i) q^{89} +(-1.37738 + 2.38570i) q^{90} +(-1.94213 - 3.36387i) q^{91} +(0.362251 - 0.627436i) q^{92} +(-3.05545 + 5.29220i) q^{93} -14.9049 q^{94} +(-3.84741 - 2.04877i) q^{95} -4.80463 q^{96} +(-2.02888 + 3.51412i) q^{97} +(-0.890144 + 1.54177i) q^{98} +(-4.76197 - 8.24798i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} - 3 q^{3} - 5 q^{4} - 4 q^{5} - 2 q^{6} - 8 q^{7} + 24 q^{8} - q^{9}+O(q^{10}) $ 8 * q - q^2 - 3 * q^3 - 5 * q^4 - 4 * q^5 - 2 * q^6 - 8 * q^7 + 24 * q^8 - q^9	\( 8 q - q^{2} - 3 q^{3} - 5 q^{4} - 4 q^{5} - 2 q^{6} - 8 q^{7} + 24 q^{8} - q^{9} - q^{10} - 4 q^{11} + 12 q^{12} - 7 q^{13} + q^{14} - 3 q^{15} - 7 q^{16} + q^{17} - 20 q^{18} + 5 q^{19} + 10 q^{20} + 4 q^{21} - 2 q^{22} - 2 q^{23} - 23 q^{24} - 4 q^{25} + 6 q^{26} + 24 q^{27} + 19 q^{28} + q^{29} + 4 q^{30} - 30 q^{32} - 19 q^{33} - 15 q^{34} + 4 q^{35} + 7 q^{36} - 4 q^{37} + 13 q^{38} + 30 q^{39} - 12 q^{40} + 8 q^{41} + 15 q^{42} - q^{43} + 12 q^{44} + 2 q^{45} + 24 q^{46} + 12 q^{47} - 23 q^{48} - 20 q^{49} + 2 q^{50} - 22 q^{51} + 3 q^{52} + 5 q^{53} + 34 q^{54} + 2 q^{55} - 82 q^{56} + 7 q^{57} - 54 q^{58} + 5 q^{59} - 6 q^{60} - 37 q^{62} + 3 q^{63} + 112 q^{64} + 14 q^{65} + 31 q^{66} - 4 q^{67} + 32 q^{68} - 18 q^{69} + q^{70} - 20 q^{71} - 17 q^{72} + 20 q^{73} - 25 q^{74} + 6 q^{75} + 63 q^{76} + 28 q^{77} + 18 q^{78} - 17 q^{79} - 7 q^{80} - 12 q^{81} - 21 q^{82} + 2 q^{83} - 40 q^{84} + q^{85} - 8 q^{86} - 32 q^{87} - 14 q^{88} - 11 q^{89} + 10 q^{90} - 6 q^{91} + q^{92} + 8 q^{93} - 62 q^{94} - 4 q^{95} + 42 q^{96} - q^{97} - 9 q^{98} - 38 q^{99}+O(q^{100}) \) 8 * q - q^2 - 3 * q^3 - 5 * q^4 - 4 * q^5 - 2 * q^6 - 8 * q^7 + 24 * q^8 - q^9 - q^10 - 4 * q^11 + 12 * q^12 - 7 * q^13 + q^14 - 3 * q^15 - 7 * q^16 + q^17 - 20 * q^18 + 5 * q^19 + 10 * q^20 + 4 * q^21 - 2 * q^22 - 2 * q^23 - 23 * q^24 - 4 * q^25 + 6 * q^26 + 24 * q^27 + 19 * q^28 + q^29 + 4 * q^30 - 30 * q^32 - 19 * q^33 - 15 * q^34 + 4 * q^35 + 7 * q^36 - 4 * q^37 + 13 * q^38 + 30 * q^39 - 12 * q^40 + 8 * q^41 + 15 * q^42 - q^43 + 12 * q^44 + 2 * q^45 + 24 * q^46 + 12 * q^47 - 23 * q^48 - 20 * q^49 + 2 * q^50 - 22 * q^51 + 3 * q^52 + 5 * q^53 + 34 * q^54 + 2 * q^55 - 82 * q^56 + 7 * q^57 - 54 * q^58 + 5 * q^59 - 6 * q^60 - 37 * q^62 + 3 * q^63 + 112 * q^64 + 14 * q^65 + 31 * q^66 - 4 * q^67 + 32 * q^68 - 18 * q^69 + q^70 - 20 * q^71 - 17 * q^72 + 20 * q^73 - 25 * q^74 + 6 * q^75 + 63 * q^76 + 28 * q^77 + 18 * q^78 - 17 * q^79 - 7 * q^80 - 12 * q^81 - 21 * q^82 + 2 * q^83 - 40 * q^84 + q^85 - 8 * q^86 - 32 * q^87 - 14 * q^88 - 11 * q^89 + 10 * q^90 - 6 * q^91 + q^92 + 8 * q^93 - 62 * q^94 - 4 * q^95 + 42 * q^96 - q^97 - 9 * q^98 - 38 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/95\mathbb{Z}\right)^\times$.

$n$	$21$	$77$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.832272	−	1.44154i	0.588506	−	1.01932i	−0.405923	−	0.913907i	$-0.633050\pi$
$2$	0.832272	−	1.44154i	0.588506	−	1.01932i	0.994428	−	0.105414i	$-0.0336168\pi$
$3$	0.579878	−	1.00438i	0.334793	−	0.579878i	−0.648652	−	0.761085i	$-0.724667\pi$
$3$	0.579878	−	1.00438i	0.334793	−	0.579878i	0.983445	+	0.181207i	$0.0580004\pi$
$4$	−0.385355	−	0.667454i	−0.192677	−	0.333727i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	−0.965233	−	1.67183i	−0.394055	−	0.682523i
$7$	−2.43525			−0.920440			−0.460220	−	0.887805i	$-0.652229\pi$
$7$	−2.43525			−0.920440			−0.460220	+	0.887805i	$0.652229\pi$
$8$	2.04621			0.723444
$9$	0.827483	+	1.43324i	0.275828	+	0.477748i
$10$	0.832272	+	1.44154i	0.263188	+	0.455854i
$11$	−5.75477			−1.73513			−0.867564	−	0.497326i	$-0.834315\pi$
$11$	−5.75477			−1.73513			−0.867564	+	0.497326i	$0.834315\pi$
$12$	−0.893835			−0.258028
$13$	0.797505	+	1.38132i	0.221188	+	0.383109i	0.955169	−	0.296061i	$-0.0956732\pi$
$13$	0.797505	+	1.38132i	0.221188	+	0.383109i	−0.733981	+	0.679170i	$0.762340\pi$
$14$	−2.02680	+	3.51051i	−0.541684	+	0.938224i
$15$	0.579878	+	1.00438i	0.149724	+	0.259329i
$16$	2.47371	−	4.28460i	0.618428	−	1.07115i
$17$	2.99203	−	5.18234i	0.725673	−	1.25690i	−0.233023	−	0.972471i	$-0.574862\pi$
$17$	2.99203	−	5.18234i	0.725673	−	1.25690i	0.958696	−	0.284432i	$-0.0918050\pi$
$18$	2.75477			0.649305
$19$	0.149412	+	4.35634i	0.0342775	+	0.999412i
$19$	0.149412	+	4.35634i	0.0342775	+	0.999412i
$20$	0.770710			0.172336
$21$	−1.41215	+	2.44592i	−0.308156	+	0.533743i
$22$	−4.78953	+	8.29572i	−1.02113	+	1.76865i
$23$	0.470022	+	0.814102i	0.0980064	+	0.169752i	0.910859	−	0.412717i	$-0.135420\pi$
$23$	0.470022	+	0.814102i	0.0980064	+	0.169752i	−0.812853	+	0.582469i	$0.802087\pi$
$24$	1.18655	−	2.05517i	0.242204	−	0.419509i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	2.65497			0.520682
$27$	5.39862			1.03897
$28$	0.938437	+	1.62542i	0.177348	+	0.307176i
$29$	−1.30917	−	2.26755i	−0.243106	−	0.421073i	0.718491	−	0.695536i	$-0.244833\pi$
$29$	−1.30917	−	2.26755i	−0.243106	−	0.421073i	−0.961598	+	0.274463i	$0.911500\pi$
$30$	1.93047			0.352453
$31$	−5.26913			−0.946364			−0.473182	−	0.880965i	$-0.656895\pi$
$31$	−5.26913			−0.946364			−0.473182	+	0.880965i	$0.656895\pi$
$32$	−2.07140	−	3.58777i	−0.366175	−	0.634233i
$33$	−3.33706	+	5.77996i	−0.580908	+	1.00616i
$34$	−4.98037	−	8.62625i	−0.854126	−	1.47939i
$35$	1.21763	−	2.10899i	0.205817	−	0.356485i
$36$	0.637749	−	1.10461i	0.106292	−	0.184102i
$37$	−2.89384			−0.475744			−0.237872	−	0.971297i	$-0.576450\pi$
$37$	−2.89384			−0.475744			−0.237872	+	0.971297i	$0.576450\pi$
$38$	6.40418	+	3.41028i	1.03889	+	0.553220i
$39$	1.84982			0.296209
$40$	−1.02310	+	1.77207i	−0.161767	+	0.280189i
$41$	3.15767	−	5.46925i	0.493145	−	0.854153i	−0.506823	−	0.862050i	$-0.669180\pi$
$41$	3.15767	−	5.46925i	0.493145	−	0.854153i	0.999969	+	0.00789701i	$0.00251372\pi$
$42$	2.35059	+	4.07134i	0.362704	+	0.628221i
$43$	−2.26961	+	3.93108i	−0.346113	+	0.599485i	−0.985555	−	0.169354i	$-0.945832\pi$
$43$	−2.26961	+	3.93108i	−0.346113	+	0.599485i	0.639443	+	0.768839i	$0.279165\pi$
$44$	2.21763	+	3.84104i	0.334320	+	0.579059i
$45$	−1.65497			−0.246708
$46$	1.56475			0.230709
$47$	−4.47718	−	7.75471i	−0.653064	−	1.13114i	−0.982375	−	0.186919i	$-0.940150\pi$
$47$	−4.47718	−	7.75471i	−0.653064	−	1.13114i	0.329311	−	0.944221i	$-0.393184\pi$
$48$	−2.86890	−	4.96909i	−0.414090	−	0.717226i
$49$	−1.06953			−0.152791
$50$	−1.66454			−0.235402
$51$	−3.47002	−	6.01025i	−0.485900	−	0.841604i
$52$	0.614645	−	1.06460i	0.0852359	−	0.147633i
$53$	1.09819	+	1.90213i	0.150848	+	0.261277i	0.931540	−	0.363640i	$-0.118466\pi$
$53$	1.09819	+	1.90213i	0.150848	+	0.261277i	−0.780691	+	0.624917i	$0.785133\pi$
$54$	4.49313	−	7.78232i	0.611437	−	1.05904i
$55$	2.87738	−	4.98377i	0.387986	−	0.672012i
$56$	−4.98304			−0.665887
$57$	4.46205	+	2.37608i	0.591013	+	0.314719i
$58$	−4.35834			−0.572278
$59$	5.39939	−	9.35202i	0.702941	−	1.21753i	−0.264489	−	0.964389i	$-0.585203\pi$
$59$	5.39939	−	9.35202i	0.702941	−	1.21753i	0.967430	−	0.253140i	$-0.0814634\pi$
$60$	0.446918	−	0.774084i	0.0576968	−	0.0999338i
$61$	5.26434	+	9.11811i	0.674030	+	1.16745i	0.976751	+	0.214375i	$0.0687716\pi$
$61$	5.26434	+	9.11811i	0.674030	+	1.16745i	−0.302721	+	0.953079i	$0.597895\pi$
$62$	−4.38535	+	7.59566i	−0.556941	+	0.964649i
$63$	−2.01513	−	3.49031i	−0.253883	−	0.439738i
$64$	2.99898			0.374873
$65$	−1.59501			−0.197837
$66$	5.55469	+	9.62100i	0.683735	+	1.18426i
$67$	−0.504789	−	0.874320i	−0.0616698	−	0.106815i	0.833542	−	0.552456i	$-0.186309\pi$
$67$	−0.504789	−	0.874320i	−0.0616698	−	0.106815i	−0.895212	+	0.445641i	$0.852976\pi$
$68$	−4.61197			−0.559284
$69$	1.09022			0.131247
$70$	−2.02680	−	3.51051i	−0.242248	−	0.419587i
$71$	−4.41694	+	7.65036i	−0.524194	+	0.907931i	0.475409	+	0.879765i	$0.342300\pi$
$71$	−4.41694	+	7.65036i	−0.524194	+	0.907931i	−0.999603	+	0.0281662i	$0.991033\pi$
$72$	1.69320	+	2.93271i	0.199546	+	0.345624i
$73$	5.12499	−	8.87674i	0.599835	−	1.03894i	−0.393011	−	0.919534i	$-0.628566\pi$
$73$	5.12499	−	8.87674i	0.599835	−	1.03894i	0.992845	−	0.119410i	$-0.0381003\pi$
$74$	−2.40846	+	4.17157i	−0.279978	+	0.484936i
$75$	−1.15976			−0.133917
$76$	2.85008	−	1.77846i	0.326927	−	0.204004i
$77$	14.0143			1.59708
$78$	1.53956	−	2.66659i	0.174320	−	0.301932i
$79$	−3.80229	+	6.58577i	−0.427792	+	0.740957i	−0.996677	−	0.0814604i	$-0.974042\pi$
$79$	−3.80229	+	6.58577i	−0.427792	+	0.740957i	0.568885	+	0.822417i	$0.307375\pi$
$80$	2.47371	+	4.28460i	0.276570	+	0.479032i
$81$	0.648093	−	1.12253i	0.0720103	−	0.124726i
$82$	−5.25609	−	9.10381i	−0.580438	−	1.00535i
$83$	3.11355			0.341756			0.170878	−	0.985292i	$-0.445340\pi$
$83$	3.11355			0.341756			0.170878	+	0.985292i	$0.445340\pi$
$84$	2.17672			0.237499
$85$	2.99203	+	5.18234i	0.324531	+	0.562104i
$86$	3.77787	+	6.54346i	0.407378	+	0.705600i
$87$	−3.03663			−0.325561
$88$	−11.7755			−1.25527
$89$	5.55706	+	9.62511i	0.589047	+	1.02026i	0.994358	+	0.106081i	$0.0338302\pi$
$89$	5.55706	+	9.62511i	0.589047	+	1.02026i	−0.405310	+	0.914179i	$0.632837\pi$
$90$	−1.37738	+	2.38570i	−0.145189	+	0.251475i
$91$	−1.94213	−	3.36387i	−0.203590	−	0.352629i
$92$	0.362251	−	0.627436i	0.0377672	−	0.0654148i
$93$	−3.05545	+	5.29220i	−0.316836	+	0.548776i
$94$	−14.9049			−1.53733
$95$	−3.84741	−	2.04877i	−0.394735	−	0.210200i
$96$	−4.80463			−0.490371
$97$	−2.02888	+	3.51412i	−0.206002	+	0.356805i	−0.950451	−	0.310873i	$-0.899379\pi$
$97$	−2.02888	+	3.51412i	−0.206002	+	0.356805i	0.744450	+	0.667678i	$0.232712\pi$
$98$	−0.890144	+	1.54177i	−0.0899181	+	0.155743i
$99$	−4.76197	−	8.24798i	−0.478596	−	0.828953i
$100$	−0.385355	+	0.667454i	−0.0385355	+	0.0667454i
$101$	5.56503	+	9.63892i	0.553741	+	0.959108i	0.998000	+	0.0632098i	$0.0201337\pi$
$101$	5.56503	+	9.63892i	0.553741	+	0.959108i	−0.444259	+	0.895898i	$0.646533\pi$
$102$	−11.5520			−1.14382
$103$	11.5791			1.14092			0.570460	−	0.821326i	$-0.306765\pi$
$103$	11.5791			1.14092			0.570460	+	0.821326i	$0.306765\pi$
$104$	1.63186	+	2.82647i	0.160017	+	0.277158i
$105$	−1.41215	−	2.44592i	−0.137812	−	0.238697i
$106$	3.65598			0.355101
$107$	17.9177			1.73217			0.866086	−	0.499894i	$-0.166628\pi$
$107$	17.9177			1.73217			0.866086	+	0.499894i	$0.166628\pi$
$108$	−2.08039	−	3.60333i	−0.200185	−	0.346731i
$109$	−2.81235	+	4.87113i	−0.269374	+	0.466570i	−0.968700	−	0.248233i	$-0.920150\pi$
$109$	−2.81235	+	4.87113i	−0.269374	+	0.466570i	0.699326	+	0.714803i	$0.253484\pi$
$110$	−4.78953	−	8.29572i	−0.456664	−	0.790965i
$111$	−1.67807	+	2.90650i	−0.159275	+	0.275873i
$112$	−6.02412	+	10.4341i	−0.569226	+	0.985928i
$113$	−15.6789			−1.47494			−0.737472	−	0.675378i	$-0.763981\pi$
$113$	−15.6789			−1.47494			−0.737472	+	0.675378i	$0.763981\pi$
$114$	7.13885	−	4.45467i	0.668614	−	0.417218i
$115$	−0.940044			−0.0876595
$116$	−1.00899	+	1.74762i	−0.0936822	+	0.162262i
$117$	−1.31984	+	2.28604i	−0.122020	+	0.211344i
$118$	−8.98753	−	15.5669i	−0.827369	−	1.43304i
$119$	−7.28635	+	12.6203i	−0.667939	+	1.15690i
$120$	1.18655	+	2.05517i	0.108317	+	0.187610i
$121$	22.1173			2.01067
$122$	17.5255			1.58668
$123$	−3.66213	−	6.34299i	−0.330203	−	0.571928i
$124$	2.03049	+	3.51691i	0.182343	+	0.315827i
$125$	1.00000			0.0894427
$126$	−6.70856			−0.597646
$127$	−3.05996	−	5.30000i	−0.271527	−	0.470299i	0.697726	−	0.716365i	$-0.254195\pi$
$127$	−3.05996	−	5.30000i	−0.271527	−	0.470299i	−0.969253	+	0.246066i	$0.920862\pi$
$128$	6.63877	−	11.4987i	0.586790	−	1.01635i
$129$	2.63220	+	4.55910i	0.231752	+	0.401406i
$130$	−1.32748	+	2.29927i	−0.116428	+	0.201659i
$131$	7.44055	−	12.8874i	0.650084	−	1.12598i	−0.333018	−	0.942920i	$-0.608067\pi$
$131$	7.44055	−	12.8874i	0.650084	−	1.12598i	0.983102	−	0.183058i	$-0.0585997\pi$
$132$	5.14381			0.447711
$133$	−0.363857	−	10.6088i	−0.0315504	−	0.919899i
$134$	−1.68049			−0.145172
$135$	−2.69931	+	4.67535i	−0.232320	+	0.402390i
$136$	6.12231	−	10.6042i	0.524984	−	0.909299i
$137$	−8.67518	−	15.0258i	−0.741170	−	1.28374i	−0.951963	−	0.306214i	$-0.900938\pi$
$137$	−8.67518	−	15.0258i	−0.741170	−	1.28374i	0.210793	−	0.977531i	$-0.432396\pi$
$138$	0.907361	−	1.57160i	0.0772397	−	0.133783i
$139$	3.35267	+	5.80700i	0.284370	+	0.492543i	0.972456	−	0.233086i	$-0.0748823\pi$
$139$	3.35267	+	5.80700i	0.284370	+	0.492543i	−0.688086	+	0.725629i	$0.741549\pi$
$140$	−1.87687			−0.158625
$141$	−10.3849			−0.874564
$142$	7.35219	+	12.7344i	0.616982	+	1.06864i
$143$	−4.58946	−	7.94917i	−0.383790	−	0.664743i
$144$	8.18782			0.682319
$145$	2.61834			0.217441
$146$	−8.53077	−	14.7757i	−0.706012	−	1.22285i
$147$	−0.620199	+	1.07422i	−0.0511532	+	0.0885999i
$148$	1.11515	+	1.93150i	0.0916651	+	0.158769i
$149$	−7.19642	+	12.4646i	−0.589553	+	1.02114i	0.404737	+	0.914433i	$0.367363\pi$
$149$	−7.19642	+	12.4646i	−0.589553	+	1.02114i	−0.994291	+	0.106704i	$0.965970\pi$
$150$	−0.965233	+	1.67183i	−0.0788109	+	0.136505i
$151$	12.7219			1.03529			0.517645	−	0.855595i	$-0.326809\pi$
$151$	12.7219			1.03529			0.517645	+	0.855595i	$0.326809\pi$
$152$	0.305729	+	8.91398i	0.0247979	+	0.723019i
$153$	9.90341			0.800644
$154$	11.6637	−	20.2022i	0.939890	−	1.62794i
$155$	2.63457	−	4.56320i	0.211614	−	0.366525i
$156$	−0.712838	−	1.23467i	−0.0570727	−	0.0988529i
$157$	1.68765	−	2.92309i	0.134689	−	0.233288i	−0.790790	−	0.612088i	$-0.790330\pi$
$157$	1.68765	−	2.92309i	0.134689	−	0.233288i	0.925479	+	0.378800i	$0.123663\pi$
$158$	6.32909	+	10.9623i	0.503515	+	0.872114i
$159$	2.54727			0.202012
$160$	4.14280			0.327517
$161$	−1.14462	−	1.98255i	−0.0902089	−	0.156246i
$162$	−1.07878	−	1.86850i	−0.0847569	−	0.146803i
$163$	0.307960			0.0241213			0.0120607	−	0.999927i	$-0.496161\pi$
$163$	0.307960			0.0241213			0.0120607	+	0.999927i	$0.496161\pi$
$164$	−4.86730			−0.380072
$165$	−3.33706	−	5.77996i	−0.259790	−	0.449969i
$166$	2.59132	−	4.48830i	0.201125	−	0.348359i
$167$	−7.13215	−	12.3532i	−0.551902	−	0.955923i	−0.998137	−	0.0610070i	$-0.980569\pi$
$167$	−7.13215	−	12.3532i	−0.551902	−	0.955923i	0.446235	−	0.894916i	$-0.352765\pi$
$168$	−2.88955	+	5.00486i	−0.222934	+	0.386133i
$169$	5.22797	−	9.05511i	0.402152	−	0.696547i
$170$	9.96073			0.763953
$171$	−6.12005	+	3.81894i	−0.468012	+	0.292042i
$172$	3.49842			0.266752
$173$	−6.67357	+	11.5590i	−0.507382	+	0.878811i	0.492581	+	0.870266i	$0.336053\pi$
$173$	−6.67357	+	11.5590i	−0.507382	+	0.878811i	−0.999963	+	0.00854514i	$0.997280\pi$
$174$	−2.52730	+	4.37742i	−0.191594	+	0.331851i
$175$	1.21763	+	2.10899i	0.0920440	+	0.159425i
$176$	−14.2356	+	24.6569i	−1.07305	+	1.85858i
$177$	−6.26197	−	10.8461i	−0.470679	−	0.815239i
$178$	18.5000			1.38663
$179$	−14.2207			−1.06291			−0.531454	−	0.847087i	$-0.678354\pi$
$179$	−14.2207			−1.06291			−0.531454	+	0.847087i	$0.678354\pi$
$180$	0.637749	+	1.10461i	0.0475350	+	0.0823331i
$181$	−4.94132	−	8.55861i	−0.367285	−	0.636157i	0.621855	−	0.783133i	$-0.286379\pi$
$181$	−4.94132	−	8.55861i	−0.367285	−	0.636157i	−0.989140	+	0.146976i	$0.953046\pi$
$182$	−6.46552			−0.479256
$183$	12.2107			0.902641
$184$	0.961763	+	1.66582i	0.0709021	+	0.122806i
$185$	1.44692	−	2.50613i	0.106379	−	0.184255i
$186$	5.08594	+	8.80911i	0.372919	+	0.645915i
$187$	−17.2184	+	29.8232i	−1.25914	+	2.18089i
$188$	−3.45061	+	5.97663i	−0.251661	+	0.435891i
$189$	−13.1470			−0.956305
$190$	−6.15548	+	3.84104i	−0.446565	+	0.278659i
$191$	−12.9942			−0.940228			−0.470114	−	0.882606i	$-0.655787\pi$
$191$	−12.9942			−0.940228			−0.470114	+	0.882606i	$0.655787\pi$
$192$	1.73904	−	3.01211i	0.125505	−	0.217380i
$193$	−7.25795	+	12.5711i	−0.522439	+	0.904890i	0.477221	+	0.878784i	$0.341644\pi$
$193$	−7.25795	+	12.5711i	−0.522439	+	0.904890i	−0.999659	+	0.0261066i	$0.991689\pi$
$194$	3.37716	+	5.84942i	0.242466	+	0.419964i
$195$	−0.924911	+	1.60199i	−0.0662343	+	0.114721i
$196$	0.412150	+	0.713865i	0.0294393	+	0.0509904i
$197$	−25.0010			−1.78125			−0.890624	−	0.454740i	$-0.849732\pi$
$197$	−25.0010			−1.78125			−0.890624	+	0.454740i	$0.849732\pi$
$198$	−15.8530			−1.12663
$199$	1.12769	+	1.95322i	0.0799401	+	0.138460i	0.903224	−	0.429170i	$-0.141194\pi$
$199$	1.12769	+	1.95322i	0.0799401	+	0.138460i	−0.823284	+	0.567630i	$0.807860\pi$
$200$	−1.02310	−	1.77207i	−0.0723444	−	0.125304i
$201$	−1.17086			−0.0825864
$202$	18.5265			1.30352
$203$	3.18816	+	5.52205i	0.223765	+	0.387572i
$204$	−2.67438	+	4.63216i	−0.187244	+	0.324316i
$205$	3.15767	+	5.46925i	0.220541	+	0.381989i
$206$	9.63694	−	16.6917i	0.671437	−	1.16296i
$207$	−0.777871	+	1.34731i	−0.0540657	+	0.0936446i
$208$	7.89120			0.547156
$209$	−0.859833	−	25.0697i	−0.0594759	−	1.73411i
$210$	−4.70118			−0.324412
$211$	−11.1081	+	19.2397i	−0.764710	+	1.32452i	0.175689	+	0.984446i	$0.443785\pi$
$211$	−11.1081	+	19.2397i	−0.764710	+	1.32452i	−0.940400	+	0.340071i	$0.889549\pi$
$212$	0.846388	−	1.46599i	0.0581302	−	0.100684i
$213$	5.12257	+	8.87255i	0.350993	+	0.607937i
$214$	14.9124	−	25.8291i	1.01939	−	1.76564i
$215$	−2.26961	−	3.93108i	−0.154786	−	0.268098i
$216$	11.0467			0.751634
$217$	12.8317			0.871071
$218$	4.68128	+	8.10822i	0.317057	+	0.549158i
$219$	−5.94373	−	10.2949i	−0.401640	−	0.695662i
$220$	−4.43525			−0.299025
$221$	9.54463			0.642041
$222$	2.79322	+	4.83801i	0.187469	+	0.324706i
$223$	−5.10799	+	8.84730i	−0.342056	+	0.592459i	−0.984814	−	0.173610i	$-0.944457\pi$
$223$	−5.10799	+	8.84730i	−0.342056	+	0.592459i	0.642758	+	0.766069i	$0.277790\pi$
$224$	5.04438	+	8.73712i	0.337042	+	0.583774i
$225$	0.827483	−	1.43324i	0.0551656	−	0.0955495i
$226$	−13.0491	+	22.6017i	−0.868012	+	1.50344i
$227$	4.15180			0.275565			0.137782	−	0.990463i	$-0.456003\pi$
$227$	4.15180			0.275565			0.137782	+	0.990463i	$0.456003\pi$
$228$	−0.133550	−	3.89385i	−0.00884456	−	0.257876i
$229$	6.53286			0.431703			0.215852	−	0.976426i	$-0.430747\pi$
$229$	6.53286			0.431703			0.215852	+	0.976426i	$0.430747\pi$
$230$	−0.782373	+	1.35511i	−0.0515881	+	0.0893533i
$231$	8.12660	−	14.0757i	0.534691	−	0.926111i
$232$	−2.67883	−	4.63987i	−0.175874	−	0.304623i
$233$	−2.57410	+	4.45848i	−0.168635	+	0.292084i	−0.937940	−	0.346797i	$-0.887269\pi$
$233$	−2.57410	+	4.45848i	−0.168635	+	0.292084i	0.769305	+	0.638882i	$0.220603\pi$
$234$	2.19694	+	3.80521i	0.143618	+	0.248755i
$235$	8.95437			0.584118
$236$	−8.32272			−0.541763
$237$	4.40973	+	7.63788i	0.286443	+	0.496134i
$238$	12.1285	+	21.0071i	0.786171	+	1.36169i
$239$	13.9962			0.905338			0.452669	−	0.891679i	$-0.350472\pi$
$239$	13.9962			0.905338			0.452669	+	0.891679i	$0.350472\pi$
$240$	5.73781			0.370374
$241$	−7.61285	−	13.1858i	−0.490387	−	0.849375i	0.509552	−	0.860440i	$-0.329811\pi$
$241$	−7.61285	−	13.1858i	−0.490387	−	0.849375i	−0.999939	+	0.0110652i	$0.996478\pi$
$242$	18.4076	−	31.8830i	1.18329	−	2.04952i
$243$	7.34631	+	12.7242i	0.471266	+	0.816256i
$244$	4.05728	−	7.02742i	0.259741	−	0.449884i
$245$	0.534767	−	0.926244i	0.0341650	−	0.0591756i
$246$	−12.1916			−0.777305
$247$	−5.89834	+	3.68059i	−0.375302	+	0.234190i
$248$	−10.7817			−0.684642
$249$	1.80548	−	3.12718i	0.114417	−	0.198177i
$250$	0.832272	−	1.44154i	0.0526375	−	0.0911709i
$251$	3.05630	+	5.29366i	0.192912	+	0.334133i	0.946214	−	0.323542i	$-0.104874\pi$
$251$	3.05630	+	5.29366i	0.192912	+	0.334133i	−0.753302	+	0.657674i	$0.771540\pi$
$252$	−1.55308	+	2.69002i	−0.0978350	+	0.169455i
$253$	−2.70487	−	4.68497i	−0.170053	−	0.294541i
$254$	−10.1869			−0.639181
$255$	6.94004			0.434602
$256$	−8.05154	−	13.9457i	−0.503221	−	0.871605i
$257$	−0.0613414	−	0.106246i	−0.00382637	−	0.00662747i	0.864106	−	0.503310i	$-0.167885\pi$
$257$	−0.0613414	−	0.106246i	−0.00382637	−	0.00662747i	−0.867932	+	0.496683i	$0.834551\pi$
$258$	8.76281			0.545549
$259$	7.04723			0.437893
$260$	0.614645	+	1.06460i	0.0381187	+	0.0660235i
$261$	2.16663	−	3.75271i	0.134111	−	0.232287i
$262$	−12.3851	−	21.4517i	−0.765156	−	1.32529i
$263$	5.03027	−	8.71267i	0.310179	−	0.537247i	−0.668222	−	0.743962i	$-0.732944\pi$
$263$	5.03027	−	8.71267i	0.310179	−	0.537247i	0.978401	+	0.206716i	$0.0662775\pi$
$264$	−6.82832	+	11.8270i	−0.420254	+	0.727902i
$265$	−2.19639			−0.134923
$266$	−15.5958	−	8.30489i	−0.956240	−	0.509206i
$267$	12.8897			0.788835
$268$	−0.389046	+	0.673847i	−0.0237648	+	0.0411618i
$269$	−2.85614	+	4.94698i	−0.174142	+	0.301623i	−0.939864	−	0.341549i	$-0.889049\pi$
$269$	−2.85614	+	4.94698i	−0.174142	+	0.301623i	0.765722	+	0.643172i	$0.222382\pi$
$270$	4.49313	+	7.78232i	0.273443	+	0.473617i
$271$	6.35560	−	11.0082i	0.386075	−	0.668702i	−0.605843	−	0.795585i	$-0.707164\pi$
$271$	6.35560	−	11.0082i	0.386075	−	0.668702i	0.991918	+	0.126883i	$0.0404972\pi$
$272$	−14.8028	−	25.6393i	−0.897554	−	1.55461i
$273$	−4.50479			−0.272642
$274$	−28.8804			−1.74473
$275$	2.87738	+	4.98377i	0.173513	+	0.300533i
$276$	−0.420122	−	0.727673i	−0.0252884	−	0.0438008i
$277$	17.6019			1.05760			0.528799	−	0.848747i	$-0.322642\pi$
$277$	17.6019			1.05760			0.528799	+	0.848747i	$0.322642\pi$
$278$	11.1613			0.669413
$279$	−4.36012	−	7.55195i	−0.261034	−	0.452123i
$280$	2.49152	−	4.31544i	0.148897	−	0.257897i
$281$	10.2502	+	17.7539i	0.611476	+	1.05911i	0.990992	+	0.133922i	$0.0427571\pi$
$281$	10.2502	+	17.7539i	0.611476	+	1.05911i	−0.379516	+	0.925185i	$0.623910\pi$
$282$	−8.64305	+	14.9702i	−0.514686	+	0.891462i
$283$	5.92805	−	10.2677i	0.352386	−	0.610350i	−0.634281	−	0.773103i	$-0.718704\pi$
$283$	5.92805	−	10.2677i	0.352386	−	0.610350i	0.986667	+	0.162752i	$0.0520371\pi$
$284$	6.80836			0.404002
$285$	−4.28877	+	2.67621i	−0.254045	+	0.158525i
$286$	−15.2787			−0.903449
$287$	−7.68973	+	13.3190i	−0.453911	+	0.786196i
$288$	3.42809	−	5.93763i	0.202002	−	0.349878i
$289$	−9.40447	−	16.2890i	−0.553204	−	0.958177i
$290$	2.17917	−	3.77443i	0.127965	−	0.221642i
$291$	2.35301	+	4.07552i	0.137936	+	0.238911i
$292$	−7.89976			−0.462298
$293$	−24.9814			−1.45943			−0.729715	−	0.683751i	$-0.760347\pi$
$293$	−24.9814			−1.45943			−0.729715	+	0.683751i	$0.760347\pi$
$294$	1.03235	+	1.78808i	0.0602079	+	0.104283i
$295$	5.39939	+	9.35202i	0.314365	+	0.544495i
$296$	−5.92139			−0.344174
$297$	−31.0678			−1.80274
$298$	11.9788	+	20.7478i	0.693911	+	1.20189i
$299$	−0.749690	+	1.29850i	−0.0433557	+	0.0750943i
$300$	0.446918	+	0.774084i	0.0258028	+	0.0446918i
$301$	5.52708	−	9.57319i	0.318576	−	0.551789i
$302$	10.5881	−	18.3391i	0.609274	−	1.05529i
$303$	12.9082			0.741554
$304$	19.0348	+	10.1362i	1.09172	+	0.581348i
$305$	−10.5287			−0.602871
$306$	8.24234	−	14.2761i	0.471183	−	0.816113i
$307$	−8.45997	+	14.6531i	−0.482836	+	0.836296i	−0.999806	−	0.0197074i	$-0.993727\pi$
$307$	−8.45997	+	14.6531i	−0.482836	+	0.836296i	0.516970	+	0.856003i	$0.327060\pi$
$308$	−5.40049	−	9.35392i	−0.307721	−	0.532989i
$309$	6.71444	−	11.6298i	0.381971	−	0.661594i
$310$	−4.38535	−	7.59566i	−0.249071	−	0.431404i
$311$	−15.2133			−0.862670			−0.431335	−	0.902192i	$-0.641957\pi$
$311$	−15.2133			−0.862670			−0.431335	+	0.902192i	$0.641957\pi$
$312$	3.78512			0.214290
$313$	−12.4637	−	21.5877i	−0.704488	−	1.22021i	−0.966876	−	0.255246i	$-0.917844\pi$
$313$	−12.4637	−	21.5877i	−0.704488	−	1.22021i	0.262389	−	0.964962i	$-0.415490\pi$
$314$	−2.80917	−	4.86562i	−0.158531	−	0.274583i
$315$	4.03027			0.227080
$316$	5.86093			0.329703
$317$	12.6152	+	21.8502i	0.708541	+	1.22723i	0.965398	+	0.260780i	$0.0839798\pi$
$317$	12.6152	+	21.8502i	0.708541	+	1.22723i	−0.256857	+	0.966449i	$0.582687\pi$
$318$	2.12002	−	3.67199i	0.118885	−	0.205915i
$319$	7.53396	+	13.0492i	0.421821	+	0.730615i
$320$	−1.49949	+	2.59720i	−0.0838241	+	0.145188i
$321$	10.3901	−	17.9962i	0.579919	−	1.00445i
$322$	−3.81055			−0.212354
$323$	23.0231	+	12.2600i	1.28104	+	0.682163i
$324$	−0.998983			−0.0554991
$325$	0.797505	−	1.38132i	0.0442376	−	0.0766218i
$326$	0.256307	−	0.443937i	0.0141955	−	0.0245874i
$327$	3.26164	+	5.64933i	0.180369	+	0.312408i
$328$	6.46125	−	11.1912i	0.356763	−	0.617932i
$329$	10.9031	+	18.8847i	0.601106	+	1.04115i
$330$	−11.1094			−0.611551
$331$	−20.2063			−1.11064			−0.555320	−	0.831637i	$-0.687404\pi$
$331$	−20.2063			−1.11064			−0.555320	+	0.831637i	$0.687404\pi$
$332$	−1.19982	−	2.07815i	−0.0658487	−	0.114053i
$333$	−2.39460	−	4.14757i	−0.131223	−	0.227285i
$334$	−23.7436			−1.29919
$335$	1.00958			0.0551592
$336$	6.98651	+	12.1010i	0.381145	+	0.660163i
$337$	15.9123	−	27.5610i	0.866800	−	1.50134i	0.00155051	−	0.999999i	$-0.499506\pi$
$337$	15.9123	−	27.5610i	0.866800	−	1.50134i	0.865249	−	0.501342i	$-0.167160\pi$
$338$	−8.70219	−	15.0726i	−0.473337	−	0.819843i
$339$	−9.09183	+	15.7475i	−0.493800	+	0.855287i
$340$	2.30599	−	3.99408i	0.125060	−	0.216610i
$341$	30.3226			1.64206
$342$	0.411596	+	12.0007i	0.0222566	+	0.648923i
$343$	19.6514			1.06107
$344$	−4.64410	+	8.04382i	−0.250393	+	0.433693i
$345$	−0.545111	+	0.944159i	−0.0293478	+	0.0508318i
$346$	11.1085	+	19.2404i	0.597194	+	1.03437i
$347$	1.65128	−	2.86009i	0.0886451	−	0.153538i	−0.818294	−	0.574801i	$-0.805080\pi$
$347$	1.65128	−	2.86009i	0.0886451	−	0.153538i	0.906939	+	0.421263i	$0.138413\pi$
$348$	1.17018	+	2.02681i	0.0627283	+	0.108649i
$349$	17.8486			0.955416			0.477708	−	0.878519i	$-0.341468\pi$
$349$	17.8486			0.955416			0.477708	+	0.878519i	$0.341468\pi$
$350$	4.05359			0.216674
$351$	4.30543	+	7.45723i	0.229807	+	0.398037i
$352$	11.9204	+	20.6468i	0.635360	+	1.10048i
$353$	−8.29523			−0.441511			−0.220755	−	0.975329i	$-0.570852\pi$
$353$	−8.29523			−0.441511			−0.220755	+	0.975329i	$0.570852\pi$
$354$	−20.8467			−1.10799
$355$	−4.41694	−	7.65036i	−0.234427	−	0.406039i
$356$	4.28288	−	7.41817i	0.226992	−	0.393162i
$357$	8.45039	+	14.6365i	0.447242	+	0.774646i
$358$	−11.8355	+	20.4997i	−0.625527	+	1.08344i
$359$	−4.17511	+	7.23150i	−0.220354	+	0.381664i	−0.954915	−	0.296878i	$-0.904055\pi$
$359$	−4.17511	+	7.23150i	−0.220354	+	0.381664i	0.734562	+	0.678542i	$0.237388\pi$
$360$	−3.38641			−0.178479
$361$	−18.9554	+	1.30178i	−0.997650	+	0.0685148i
$362$	−16.4501			−0.864598
$363$	12.8254	−	22.2142i	0.673156	−	1.16594i
$364$	−1.49682	+	2.59256i	−0.0784545	+	0.135887i
$365$	5.12499	+	8.87674i	0.268254	+	0.464630i
$366$	10.1626	−	17.6022i	0.531209	−	0.920082i
$367$	−7.20988	−	12.4879i	−0.376353	−	0.651862i	0.614176	−	0.789169i	$-0.289489\pi$
$367$	−7.20988	−	12.4879i	−0.376353	−	0.651862i	−0.990528	+	0.137307i	$0.956155\pi$
$368$	4.65080			0.242440
$369$	10.4517			0.544093
$370$	−2.40846	−	4.17157i	−0.125210	−	0.216870i
$371$	−2.67438	−	4.63216i	−0.138847	−	0.240490i
$372$	4.70974			0.244188
$373$	−24.1157			−1.24866			−0.624332	−	0.781159i	$-0.714629\pi$
$373$	−24.1157			−1.24866			−0.624332	+	0.781159i	$0.714629\pi$
$374$	28.6608	+	49.6420i	1.48202	+	2.56693i
$375$	0.579878	−	1.00438i	0.0299448	−	0.0518659i
$376$	−9.16125	−	15.8678i	−0.472455	−	0.818317i
$377$	2.08814	−	3.61676i	0.107545	−	0.186273i
$378$	−10.9419	+	18.9519i	−0.562791	+	0.974783i
$379$	16.6757			0.856571			0.428285	−	0.903644i	$-0.359118\pi$
$379$	16.6757			0.856571			0.428285	+	0.903644i	$0.359118\pi$
$380$	0.115154	+	3.35747i	0.00590725	+	0.172235i
$381$	−7.09760			−0.363621
$382$	−10.8147	+	18.7316i	−0.553329	+	0.958395i
$383$	5.43895	−	9.42053i	0.277917	−	0.481367i	−0.692950	−	0.720986i	$-0.743689\pi$
$383$	5.43895	−	9.42053i	0.277917	−	0.481367i	0.970867	+	0.239619i	$0.0770226\pi$
$384$	−7.69935	−	13.3357i	−0.392906	−	0.680533i
$385$	−7.00716	+	12.1368i	−0.357118	+	0.618546i
$386$	12.0812	+	20.9252i	0.614916	+	1.06507i
$387$	−7.51226			−0.381870
$388$	3.12736			0.158767
$389$	−18.2272	−	31.5704i	−0.924154	−	1.60068i	−0.792917	−	0.609330i	$-0.791438\pi$
$389$	−18.2272	−	31.5704i	−0.924154	−	1.60068i	−0.131237	−	0.991351i	$-0.541895\pi$
$390$	1.53956	+	2.66659i	0.0779585	+	0.135028i
$391$	5.62528			0.284482
$392$	−2.18849			−0.110535
$393$	−8.62922	−	14.9463i	−0.435287	−	0.753939i
$394$	−20.8077	+	36.0399i	−1.04827	+	1.81566i
$395$	−3.80229	−	6.58577i	−0.191314	−	0.331366i
$396$	−3.67010	+	6.35680i	−0.184429	+	0.319441i
$397$	−4.29191	+	7.43380i	−0.215405	+	0.373092i	−0.953398	−	0.301717i	$-0.902440\pi$
$397$	−4.29191	+	7.43380i	−0.215405	+	0.373092i	0.737993	+	0.674808i	$0.235774\pi$
$398$	3.75419			0.188181
$399$	−10.8662	−	5.78635i	−0.543992	−	0.289680i
$400$	−4.94743			−0.247371
$401$	8.52785	−	14.7707i	0.425860	−	0.737612i	−0.570640	−	0.821200i	$-0.693305\pi$
$401$	8.52785	−	14.7707i	0.425860	−	0.737612i	0.996500	+	0.0835885i	$0.0266381\pi$
$402$	−0.974478	+	1.68785i	−0.0486026	+	0.0841821i
$403$	−4.20216	−	7.27836i	−0.209325	−	0.362561i
$404$	4.28903	−	7.42881i	0.213387	−	0.369597i
$405$	0.648093	+	1.12253i	0.0322040	+	0.0557790i
$406$	10.6137			0.526747
$407$	16.6533			0.825476
$408$	−7.10039	−	12.2982i	−0.351522	−	0.608853i
$409$	5.89702	+	10.2139i	0.291589	+	0.505047i	0.974186	−	0.225749i	$-0.0724828\pi$
$409$	5.89702	+	10.2139i	0.291589	+	0.505047i	−0.682597	+	0.730795i	$0.739149\pi$
$410$	10.5122			0.519159
$411$	−20.1222			−0.992553
$412$	−4.46205	−	7.72850i	−0.219829	−	0.380756i
$413$	−13.1489	+	22.7745i	−0.647015	+	1.12066i
$414$	1.29480	+	2.24266i	0.0636360	+	0.110221i
$415$	−1.55677	+	2.69641i	−0.0764190	+	0.132362i
$416$	3.30390	−	5.72252i	0.161987	−	0.280570i
$417$	7.77656			0.380820
$418$	−36.8546	−	19.6253i	−1.80261	−	0.959907i
$419$	1.14280			0.0558292			0.0279146	−	0.999610i	$-0.491113\pi$
$419$	1.14280			0.0558292			0.0279146	+	0.999610i	$0.491113\pi$
$420$	−1.08836	+	1.88509i	−0.0531064	+	0.0919830i
$421$	−9.75944	+	16.9039i	−0.475646	+	0.823843i	−0.999611	−	0.0278967i	$-0.991119\pi$
$421$	−9.75944	+	16.9039i	−0.475646	+	0.823843i	0.523965	+	0.851740i	$0.324452\pi$
$422$	18.4899	+	32.0254i	0.900072	+	1.55897i
$423$	7.40959	−	12.8338i	0.360266	−	0.624000i
$424$	2.24713	+	3.89215i	0.109130	+	0.189019i
$425$	−5.98406			−0.290269
$426$	17.0535			0.826245
$427$	−12.8200	−	22.2049i	−0.620404	−	1.07457i
$428$	−6.90469	−	11.9593i	−0.333751	−	0.578073i
$429$	−10.6453			−0.513960
$430$	−7.55574			−0.364370
$431$	18.4392	+	31.9377i	0.888187	+	1.53838i	0.842017	+	0.539451i	$0.181368\pi$
$431$	18.4392	+	31.9377i	0.888187	+	1.53838i	0.0461694	+	0.998934i	$0.485299\pi$
$432$	13.3546	−	23.1309i	0.642526	−	1.11289i
$433$	−0.184467	−	0.319506i	−0.00886490	−	0.0153545i	0.861559	−	0.507658i	$-0.169488\pi$
$433$	−0.184467	−	0.319506i	−0.00886490	−	0.0153545i	−0.870424	+	0.492303i	$0.836155\pi$
$434$	10.6795	−	18.4974i	0.512630	−	0.887902i
$435$	1.51832	−	2.62980i	0.0727976	−	0.126089i
$436$	4.33501			0.207609
$437$	−3.47628	+	2.16921i	−0.166293	+	0.103767i
$438$	−19.7872			−0.945470
$439$	1.13220	−	1.96102i	0.0540367	−	0.0935944i	−0.837742	−	0.546067i	$-0.816125\pi$
$439$	1.13220	−	1.96102i	0.0540367	−	0.0935944i	0.891778	+	0.452472i	$0.149458\pi$
$440$	5.88773	−	10.1978i	0.280686	−	0.486163i
$441$	−0.885022	−	1.53290i	−0.0421439	−	0.0729954i
$442$	7.94373	−	13.7590i	0.377845	−	0.654447i
$443$	8.23137	+	14.2572i	0.391084	+	0.677378i	0.992593	−	0.121488i	$-0.0387667\pi$
$443$	8.23137	+	14.2572i	0.391084	+	0.677378i	−0.601508	+	0.798866i	$0.705433\pi$
$444$	2.58661			0.122755
$445$	−11.1141			−0.526860
$446$	8.50248	+	14.7267i	0.402604	+	0.697331i
$447$	8.34609	+	14.4558i	0.394756	+	0.683738i
$448$	−7.30329			−0.345048
$449$	14.1613			0.668315			0.334158	−	0.942517i	$-0.391548\pi$
$449$	14.1613			0.668315			0.334158	+	0.942517i	$0.391548\pi$
$450$	−1.37738	−	2.38570i	−0.0649305	−	0.112463i
$451$	−18.1717	+	31.4742i	−0.855670	+	1.48206i
$452$	6.04193	+	10.4649i	0.284188	+	0.492229i
$453$	7.37713	−	12.7776i	0.346608	−	0.600342i
$454$	3.45543	−	5.98498i	0.162171	−	0.280889i
$455$	3.88426			0.182097
$456$	9.13029	+	4.86195i	0.427565	+	0.227682i
$457$	1.22073			0.0571033			0.0285516	−	0.999592i	$-0.490910\pi$
$457$	1.22073			0.0571033			0.0285516	+	0.999592i	$0.490910\pi$
$458$	5.43712	−	9.41736i	0.254060	−	0.440045i
$459$	16.1528	−	27.9775i	0.753950	−	1.30588i
$460$	0.362251	+	0.627436i	0.0168900	+	0.0292544i
$461$	4.34580	−	7.52714i	0.202404	−	0.350574i	−0.746898	−	0.664938i	$-0.768458\pi$
$461$	4.34580	−	7.52714i	0.202404	−	0.350574i	0.949303	+	0.314364i	$0.101791\pi$
$462$	−13.5271	−	23.4296i	−0.629337	−	1.09004i
$463$	−19.7149			−0.916229			−0.458114	−	0.888893i	$-0.651475\pi$
$463$	−19.7149			−0.916229			−0.458114	+	0.888893i	$0.651475\pi$
$464$	−12.9540			−0.601375
$465$	−3.05545	−	5.29220i	−0.141693	−	0.245420i
$466$	4.28471	+	7.42133i	0.198485	+	0.343787i
$467$	−11.4795			−0.531207			−0.265604	−	0.964082i	$-0.585571\pi$
$467$	−11.4795			−0.531207			−0.265604	+	0.964082i	$0.585571\pi$
$468$	2.03443			0.0940418
$469$	1.22929	+	2.12919i	0.0567633	+	0.0983170i
$470$	7.45247	−	12.9081i	0.343757	−	0.595404i
$471$	−1.95726	−	3.39008i	−0.0901858	−	0.156206i
$472$	11.0483	−	19.1362i	0.508538	−	0.880814i
$473$	13.0611	−	22.6225i	0.600549	−	1.04018i
$474$	14.6804			0.674293
$475$	3.69799	−	2.30756i	0.169676	−	0.105878i
$476$	11.2313			0.514787
$477$	−1.81747	+	3.14796i	−0.0832164	+	0.144135i
$478$	11.6486	−	20.1760i	0.532796	−	0.922830i
$479$	−19.6316	−	34.0029i	−0.896989	−	1.55363i	−0.831324	−	0.555789i	$-0.812416\pi$
$479$	−19.6316	−	34.0029i	−0.896989	−	1.55363i	−0.0656652	−	0.997842i	$-0.520917\pi$
$480$	2.40232	−	4.16093i	0.109650	−	0.189920i
$481$	−2.30785	−	3.99731i	−0.105229	−	0.182262i
$482$	−25.3439			−1.15438
$483$	−2.65497			−0.120805
$484$	−8.52302	−	14.7623i	−0.387410	−	0.671014i
$485$	−2.02888	−	3.51412i	−0.0921267	−	0.159568i
$486$	24.4565			1.10937
$487$	31.5943			1.43168			0.715838	−	0.698266i	$-0.246045\pi$
$487$	31.5943			1.43168			0.715838	+	0.698266i	$0.246045\pi$
$488$	10.7719	+	18.6576i	0.487623	+	0.844588i
$489$	0.178579	−	0.309309i	0.00807564	−	0.0139874i
$490$	−0.890144	−	1.54177i	−0.0402126	−	0.0696503i
$491$	5.53187	−	9.58148i	0.249650	−	0.432406i	−0.713779	−	0.700371i	$-0.753018\pi$
$491$	5.53187	−	9.58148i	0.249650	−	0.432406i	0.963429	+	0.267965i	$0.0863511\pi$
$492$	−2.82244	+	4.88861i	−0.127245	+	0.220395i
$493$	−15.6683			−0.705663
$494$	0.396685	+	11.5659i	0.0178477	+	0.520376i
$495$	9.52395			0.428070
$496$	−13.0343	+	22.5761i	−0.585258	+	1.01370i
$497$	10.7564	−	18.6306i	0.482489	−	0.835696i
$498$	−3.00530	−	5.20533i	−0.134671	−	0.233256i
$499$	10.1868	−	17.6440i	0.456023	−	0.789854i	−0.542724	−	0.839911i	$-0.682607\pi$
$499$	10.1868	−	17.6440i	0.456023	−	0.789854i	0.998746	+	0.0500570i	$0.0159403\pi$
$500$	−0.385355	−	0.667454i	−0.0172336	−	0.0298495i
$501$	−16.5431			−0.739091
$502$	10.1747			0.454118
$503$	6.83622	+	11.8407i	0.304812	+	0.527950i	0.977219	−	0.212231i	$-0.0680730\pi$
$503$	6.83622	+	11.8407i	0.304812	+	0.527950i	−0.672407	+	0.740181i	$0.734740\pi$
$504$	−4.12338	−	7.14191i	−0.183670	−	0.318126i
$505$	−11.1301			−0.495281
$506$	−9.00474			−0.400310
$507$	−6.06317	−	10.5017i	−0.269275	−	0.466398i
$508$	−2.35834	+	4.08476i	−0.104634	+	0.181232i
$509$	3.86196	+	6.68912i	0.171179	+	0.296490i	0.938832	−	0.344375i	$-0.111909\pi$
$509$	3.86196	+	6.68912i	0.171179	+	0.296490i	−0.767654	+	0.640865i	$0.778576\pi$
$510$	5.77601	−	10.0043i	0.255766	−	0.443000i
$511$	−12.4807	+	21.6171i	−0.552112	+	0.956285i
$512$	−0.249240			−0.0110150
$513$	0.806621	+	23.5182i	0.0356132	+	1.03836i
$514$	−0.204211			−0.00900736
$515$	−5.78953	+	10.0278i	−0.255117	+	0.441876i
$516$	2.02866	−	3.51374i	0.0893067	−	0.154684i
$517$	25.7651	+	44.6265i	1.13315	+	1.96267i
$518$	5.86521	−	10.1588i	0.257703	−	0.446354i
$519$	7.73971	+	13.4056i	0.339736	+	0.588439i
$520$	−3.26372			−0.143124
$521$	−2.16876			−0.0950151			−0.0475075	−	0.998871i	$-0.515128\pi$
$521$	−2.16876			−0.0950151			−0.0475075	+	0.998871i	$0.515128\pi$
$522$	−3.60645	−	6.24656i	−0.157850	−	0.273404i
$523$	11.9466	+	20.6921i	0.522389	+	0.904804i	0.999661	+	0.0260485i	$0.00829243\pi$
$523$	11.9466	+	20.6921i	0.522389	+	0.904804i	−0.477272	+	0.878756i	$0.658374\pi$
$524$	−11.4690			−0.501026
$525$	2.82430			0.123263
$526$	−8.37310	−	14.5026i	−0.365085	−	0.632345i
$527$	−15.7654	+	27.3065i	−0.686751	+	1.18949i
$528$	16.5099	+	28.5959i	0.718500	+	1.24448i
$529$	11.0582	−	19.1533i	0.480790	−	0.832752i
$530$	−1.82799	+	3.16617i	−0.0794029	+	0.137530i
$531$	17.8716			0.775562
$532$	−6.94067	+	4.33101i	−0.300916	+	0.187773i
$533$	10.0730			0.436312
$534$	10.7277	−	18.5809i	0.464234	−	0.804076i
$535$	−8.95887	+	15.5172i	−0.387326	+	0.670868i
$536$	−1.03290	−	1.78904i	−0.0446147	−	0.0772749i
$537$	−8.24629	+	14.2830i	−0.355854	+	0.616356i
$538$	4.75418	+	8.23448i	0.204967	+	0.355013i
$539$	6.15492			0.265111
$540$	4.16077			0.179051
$541$	−21.2275	−	36.7671i	−0.912641	−	1.58074i	−0.810319	−	0.585990i	$-0.800706\pi$
$541$	−21.2275	−	36.7671i	−0.912641	−	1.58074i	−0.102323	−	0.994751i	$-0.532627\pi$
$542$	−10.5792	−	18.3237i	−0.454415	−	0.787069i
$543$	−11.4614			−0.491858
$544$	−24.7907			−1.06289
$545$	−2.81235	−	4.87113i	−0.120468	−	0.208656i
$546$	−3.74921	+	6.49383i	−0.160451	+	0.277910i
$547$	−6.01535	−	10.4189i	−0.257198	−	0.445480i	0.708292	−	0.705919i	$-0.249466\pi$
$547$	−6.01535	−	10.4189i	−0.257198	−	0.445480i	−0.965490	+	0.260439i	$0.916133\pi$
$548$	−6.68604	+	11.5806i	−0.285614	+	0.494697i
$549$	−8.71231	+	15.0902i	−0.371833	+	0.644033i
$550$	9.57907			0.408453
$551$	9.68259	−	6.04198i	0.412492	−	0.257397i
$552$	2.23082			0.0949500
$553$	9.25956	−	16.0380i	0.393756	−	0.682006i
$554$	14.6496	−	25.3739i	0.622403	−	1.07803i
$555$	−1.67807	−	2.90650i	−0.0712301	−	0.123374i
$556$	2.58394	−	4.47551i	0.109583	−	0.189804i
$557$	4.37635	+	7.58006i	0.185432	+	0.321178i	0.943722	−	0.330740i	$-0.107298\pi$
$557$	4.37635	+	7.58006i	0.185432	+	0.321178i	−0.758290	+	0.651917i	$0.773965\pi$
$558$	−14.5152			−0.614479
$559$	−7.24011			−0.306224
$560$	−6.02412	−	10.4341i	−0.254566	−	0.440921i
$561$	19.9692	+	34.5876i	0.843099	+	1.46029i
$562$	34.1238			1.43943
$563$	−35.9707			−1.51598			−0.757991	−	0.652265i	$-0.773819\pi$
$563$	−35.9707			−1.51598			−0.757991	+	0.652265i	$0.773819\pi$
$564$	4.00186	+	6.93143i	0.168509	+	0.291866i
$565$	7.83943	−	13.5783i	0.329807	−	0.571243i
$566$	−9.86750	−	17.0910i	−0.414762	−	0.718389i
$567$	−1.57827	+	2.73365i	−0.0662812	+	0.114802i
$568$	−9.03798	+	15.6542i	−0.379225	+	0.656837i
$569$	−20.3125			−0.851543			−0.425772	−	0.904831i	$-0.639997\pi$
$569$	−20.3125			−0.851543			−0.425772	+	0.904831i	$0.639997\pi$
$570$	0.288435	+	8.40976i	0.0120812	+	0.352246i
$571$	10.1773			0.425906			0.212953	−	0.977062i	$-0.431692\pi$
$571$	10.1773			0.425906			0.212953	+	0.977062i	$0.431692\pi$
$572$	−3.53714	+	6.12650i	−0.147895	+	0.256162i
$573$	−7.53505	+	13.0511i	−0.314781	+	0.545217i
$574$	12.7999	+	22.1701i	0.534258	+	0.925362i
$575$	0.470022	−	0.814102i	0.0196013	−	0.0339504i
$576$	2.48161	+	4.29827i	0.103400	+	0.179095i
$577$	−32.7441			−1.36316			−0.681578	−	0.731745i	$-0.738706\pi$
$577$	−32.7441			−1.36316			−0.681578	+	0.731745i	$0.738706\pi$
$578$	−31.3083			−1.30225
$579$	8.41745	+	14.5794i	0.349817	+	0.605901i
$580$	−1.00899	−	1.74762i	−0.0418960	−	0.0725660i
$581$	−7.58228			−0.314566
$582$	7.83337			0.324703
$583$	−6.31984	−	10.9463i	−0.261741	−	0.453349i
$584$	10.4868	−	18.1637i	0.433947	−	0.751618i
$585$	−1.31984	−	2.28604i	−0.0545689	−	0.0945160i
$586$	−20.7913	+	36.0117i	−0.858883	+	1.48763i
$587$	−4.38663	+	7.59786i	−0.181056	+	0.313597i	−0.942240	−	0.334938i	$-0.891285\pi$
$587$	−4.38663	+	7.59786i	−0.181056	+	0.313597i	0.761185	+	0.648535i	$0.224618\pi$
$588$	0.955987			0.0394243
$589$	−0.787274	−	22.9541i	−0.0324390	−	0.945808i
$590$	17.9751			0.740021
$591$	−14.4975	+	25.1105i	−0.596349	+	1.03291i
$592$	−7.15852	+	12.3989i	−0.294213	+	0.509592i
$593$	16.1603	+	27.9905i	0.663625	+	1.14943i	0.979656	+	0.200684i	$0.0643163\pi$
$593$	16.1603	+	27.9905i	0.663625	+	1.14943i	−0.316031	+	0.948749i	$0.602350\pi$
$594$	−25.8569	+	44.7855i	−1.06092	+	1.83757i
$595$	−7.28635	−	12.6203i	−0.298711	−	0.517383i
$596$	11.0927			0.454375
$597$	2.61570			0.107053
$598$	1.24789	+	2.16141i	0.0510301	+	0.0883868i
$599$	9.77520	+	16.9311i	0.399404	+	0.691787i	0.993652	−	0.112494i	$-0.0358839\pi$
$599$	9.77520	+	16.9311i	0.399404	+	0.691787i	−0.594249	+	0.804281i	$0.702551\pi$
$600$	−2.37310			−0.0968815
$601$	−0.401837			−0.0163913			−0.00819564	−	0.999966i	$-0.502609\pi$
$601$	−0.401837			−0.0163913			−0.00819564	+	0.999966i	$0.502609\pi$
$602$	−9.20008	−	15.9350i	−0.374967	−	0.649462i
$603$	0.835409	−	1.44697i	0.0340205	−	0.0589252i
$604$	−4.90243	−	8.49126i	−0.199477	−	0.345505i
$605$	−11.0587	+	19.1542i	−0.449599	+	0.778728i
$606$	10.7431	−	18.6076i	0.436409	−	0.755882i
$607$	13.4453			0.545727			0.272863	−	0.962053i	$-0.412029\pi$
$607$	13.4453			0.545727			0.272863	+	0.962053i	$0.412029\pi$
$608$	15.3200	−	9.55976i	0.621309	−	0.387700i
$609$	7.39497			0.299659
$610$	−8.76274	+	15.1775i	−0.354793	+	0.614519i
$611$	7.14115	−	12.3688i	0.288900	−	0.500390i
$612$	−3.81633	−	6.61008i	−0.154266	−	0.267196i
$613$	10.3527	−	17.9313i	0.418140	−	0.724239i	−0.577613	−	0.816311i	$-0.696016\pi$
$613$	10.3527	−	17.9313i	0.418140	−	0.724239i	0.995752	+	0.0920716i	$0.0293489\pi$
$614$	14.0820	+	24.3907i	0.568303	+	0.984330i
$615$	7.32425			0.295342
$616$	28.6762			1.15540
$617$	4.63936	+	8.03560i	0.186773	+	0.323501i	0.944173	−	0.329451i	$-0.106864\pi$
$617$	4.63936	+	8.03560i	0.186773	+	0.323501i	−0.757399	+	0.652952i	$0.773530\pi$
$618$	−11.1765	−	19.3583i	−0.449585	−	0.778703i
$619$	−2.89129			−0.116211			−0.0581053	−	0.998310i	$-0.518506\pi$
$619$	−2.89129			−0.116211			−0.0581053	+	0.998310i	$0.518506\pi$
$620$	−4.06097			−0.163093
$621$	2.53747	+	4.39503i	0.101825	+	0.176366i
$622$	−12.6616	+	21.9306i	−0.507686	+	0.879338i
$623$	−13.5329	−	23.4396i	−0.542183	−	0.939088i
$624$	4.57593	−	7.92574i	0.183184	−	0.317284i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−41.4926			−1.65838
$627$	−25.6781	−	13.6738i	−1.02548	−	0.546078i
$628$	−2.60138			−0.103806
$629$	−8.65844	+	14.9969i	−0.345234	+	0.597964i
$630$	3.35428	−	5.80978i	0.133638	−	0.231467i
$631$	−15.2270	−	26.3740i	−0.606178	−	1.04993i	−0.991864	−	0.127301i	$-0.959369\pi$
$631$	−15.2270	−	26.3740i	−0.606178	−	1.04993i	0.385686	−	0.922630i	$-0.373965\pi$
$632$	−7.78029	+	13.4759i	−0.309483	+	0.536041i
$633$	12.8826	+	22.3134i	0.512039	+	0.886877i
$634$	41.9972			1.66792
$635$	6.11991			0.242861
$636$	−0.981604	−	1.70019i	−0.0389231	−	0.0674168i
$637$	−0.852959	−	1.47737i	−0.0337955	−	0.0585355i
$638$	25.0812			0.992975
$639$	−14.6198			−0.578349
$640$	6.63877	+	11.4987i	0.262420	+	0.454525i
$641$	10.0369	−	17.3845i	0.396434	−	0.686645i	−0.596849	−	0.802354i	$-0.703581\pi$
$641$	10.0369	−	17.3845i	0.396434	−	0.686645i	0.993283	+	0.115709i	$0.0369141\pi$
$642$	−17.2948	−	29.9554i	−0.682571	−	1.18225i
$643$	1.04457	−	1.80924i	0.0411937	−	0.0713496i	−0.844693	−	0.535250i	$-0.820217\pi$
$643$	1.04457	−	1.80924i	0.0411937	−	0.0713496i	0.885887	+	0.463901i	$0.153551\pi$
$644$	−0.882172	+	1.52797i	−0.0347625	+	0.0602103i
$645$	−5.26439			−0.207285
$646$	36.8347	−	22.9850i	1.44924	−	0.904334i
$647$	−2.10623			−0.0828043			−0.0414021	−	0.999143i	$-0.513182\pi$
$647$	−2.10623			−0.0828043			−0.0414021	+	0.999143i	$0.513182\pi$
$648$	1.32613	−	2.29693i	0.0520954	−	0.0902319i
$649$	−31.0722	+	53.8187i	−1.21969	+	2.11257i
$650$	−1.32748	−	2.29927i	−0.0520682	−	0.0901847i
$651$	7.44081	−	12.8879i	0.291628	−	0.505115i
$652$	−0.118674	−	0.205549i	−0.00464763	−	0.00804994i
$653$	1.83067			0.0716395			0.0358197	−	0.999358i	$-0.488596\pi$
$653$	1.83067			0.0716395			0.0358197	+	0.999358i	$0.488596\pi$
$654$	10.8583			0.424593
$655$	7.44055	+	12.8874i	0.290726	+	0.503553i
$656$	−15.6223	−	27.0587i	−0.609950	−	1.05646i
$657$	16.9634			0.661804
$658$	36.2973			1.41502
$659$	−12.0268	−	20.8310i	−0.468497	−	0.811460i	0.530855	−	0.847463i	$-0.321871\pi$
$659$	−12.0268	−	20.8310i	−0.468497	−	0.811460i	−0.999352	+	0.0360024i	$0.988538\pi$
$660$	−2.57191	+	4.45467i	−0.100111	+	0.173398i
$661$	8.72110	+	15.1054i	0.339211	+	0.587531i	0.984285	−	0.176589i	$-0.0565065\pi$
$661$	8.72110	+	15.1054i	0.339211	+	0.587531i	−0.645073	+	0.764121i	$0.723173\pi$
$662$	−16.8172	+	29.1282i	−0.653617	+	1.13210i
$663$	5.53472	−	9.58642i	0.214951	−	0.372306i
$664$	6.37097			0.247241
$665$	9.36941	+	4.98929i	0.363330	+	0.193476i
$666$	−7.97184			−0.308902
$667$	1.23068	−	2.13159i	0.0476519	−	0.0825356i
$668$	−5.49682	+	9.52077i	−0.212678	+	0.368370i
$669$	5.92402	+	10.2607i	0.229036	+	0.396702i
$670$	0.840244	−	1.45535i	0.0324615	−	0.0562249i
$671$	−30.2951	−	52.4726i	−1.16953	−	2.02568i
$672$	11.7005			0.451357
$673$	47.5187			1.83171			0.915856	−	0.401506i	$-0.131513\pi$
$673$	47.5187			1.83171			0.915856	+	0.401506i	$0.131513\pi$
$674$	−26.4868	−	45.8765i	−1.02023	−	1.76709i
$675$	−2.69931	−	4.67535i	−0.103897	−	0.179954i
$676$	−8.05850			−0.309942
$677$	14.5531			0.559321			0.279661	−	0.960099i	$-0.409778\pi$
$677$	14.5531			0.559321			0.279661	+	0.960099i	$0.409778\pi$
$678$	15.1338	+	26.2124i	0.581208	+	1.00668i
$679$	4.94084	−	8.55778i	0.189612	−	0.328418i
$680$	6.12231	+	10.6042i	0.234780	+	0.406651i
$681$	2.40754	−	4.16998i	0.0922570	−	0.159794i
$682$	25.2367	−	43.7112i	0.966363	−	1.67379i
$683$	3.33714			0.127692			0.0638460	−	0.997960i	$-0.479663\pi$
$683$	3.33714			0.127692			0.0638460	+	0.997960i	$0.479663\pi$
$684$	4.90736	+	2.61321i	0.187638	+	0.0999185i
$685$	17.3504			0.662923
$686$	16.3553	−	28.3282i	0.624448	−	1.08158i
$687$	3.78826	−	6.56146i	0.144531	−	0.250335i
$688$	11.2287	+	19.4487i	0.428092	+	0.741476i
$689$	−1.75163	+	3.03391i	−0.0667318	+	0.115583i
$690$	0.907361	+	1.57160i	0.0345426	+	0.0598296i
$691$	−19.3318			−0.735415			−0.367708	−	0.929941i	$-0.619857\pi$
$691$	−19.3318			−0.735415			−0.367708	+	0.929941i	$0.619857\pi$
$692$	10.2868			0.391044
$693$	11.5966	+	20.0859i	0.440519	+	0.763001i
$694$	−2.74862	−	4.76075i	−0.104336	−	0.180716i
$695$	−6.70534			−0.254348
$696$	−6.21358			−0.235525
$697$	−18.8957	−	32.7283i	−0.715725	−	1.23967i
$698$	14.8549	−	25.7295i	0.562268	−	0.973876i
$699$	2.98533	+	5.17074i	0.112916	+	0.195575i
$700$	0.938437	−	1.62542i	0.0354696	−	0.0614351i
$701$	−4.96892	+	8.60643i	−0.187674	+	0.325060i	−0.944474	−	0.328586i	$-0.893428\pi$
$701$	−4.96892	+	8.60643i	−0.187674	+	0.325060i	0.756801	+	0.653646i	$0.226761\pi$
$702$	14.3332			0.540971
$703$	−0.432375	−	12.6065i	−0.0163073	−	0.475464i
$704$	−17.2584			−0.650452
$705$	5.19244	−	8.99357i	0.195559	−	0.338717i
$706$	−6.90389	+	11.9579i	−0.259831	+	0.450041i
$707$	−13.5523	−	23.4732i	−0.509686	−	0.882801i
$708$	−4.82616	+	8.35916i	−0.181378	+	0.314157i
$709$	−18.6059	−	32.2264i	−0.698760	−	1.21029i	−0.968897	−	0.247466i	$-0.920402\pi$
$709$	−18.6059	−	32.2264i	−0.698760	−	1.21029i	0.270136	−	0.962822i	$-0.412931\pi$
$710$	−14.7044			−0.551846
$711$	−12.5853			−0.471987
$712$	11.3709	+	19.6950i	0.426143	+	0.738101i
$713$	−2.47661	−	4.28961i	−0.0927497	−	0.160647i
$714$	28.1321			1.05282
$715$	9.17891			0.343272
$716$	5.48003	+	9.49169i	0.204798	+	0.354721i
$717$	8.11608	−	14.0575i	0.303100	−	0.524985i
$718$	6.94966	+	12.0372i	0.259359	+	0.449223i
$719$	1.32109	−	2.28819i	0.0492683	−	0.0853351i	−0.840340	−	0.542060i	$-0.817644\pi$
$719$	1.32109	−	2.28819i	0.0492683	−	0.0853351i	0.889608	+	0.456725i	$0.150978\pi$
$720$	−4.09391	+	7.09086i	−0.152571	+	0.264261i
$721$	−28.1980			−1.05015
$722$	−13.8995	+	28.4083i	−0.517284	+	1.05725i
$723$	−17.6581			−0.656711
$724$	−3.80832	+	6.59621i	−0.141535	+	0.245146i
$725$	−1.30917	+	2.26755i	−0.0486213	+	0.0842145i
$726$	−21.3484	−	36.9765i	−0.792313	−	1.37233i
$727$	5.08653	−	8.81013i	0.188649	−	0.326750i	−0.756151	−	0.654397i	$-0.772923\pi$
$727$	5.08653	−	8.81013i	0.188649	−	0.326750i	0.944800	+	0.327647i	$0.106256\pi$
$728$	−3.97400	−	6.88317i	−0.147286	−	0.255107i
$729$	20.9284			0.775126
$730$	17.0615			0.631476
$731$	13.5815	+	23.5238i	0.502329	+	0.870060i
$732$	−4.70546	−	8.15009i	−0.173919	−	0.301236i
$733$	14.8222			0.547472			0.273736	−	0.961805i	$-0.411741\pi$
$733$	14.8222			0.547472			0.273736	+	0.961805i	$0.411741\pi$
$734$	−24.0023			−0.885942
$735$	−0.620199	−	1.07422i	−0.0228764	−	0.0396231i
$736$	1.94720	−	3.37266i	0.0717749	−	0.124318i
$737$	2.90494	+	5.03151i	0.107005	+	0.185338i
$738$	8.69865	−	15.0665i	0.320202	−	0.554605i
$739$	−17.7433	+	30.7323i	−0.652697	+	1.13050i	0.329769	+	0.944062i	$0.393029\pi$
$739$	−17.7433	+	30.7323i	−0.652697	+	1.13050i	−0.982466	+	0.186443i	$0.940304\pi$
$740$	−2.23031			−0.0819877
$741$	0.276386	+	8.05845i	0.0101533	+	0.296035i
$742$	−8.90325			−0.326849
$743$	4.36941	−	7.56804i	0.160298	−	0.277645i	−0.774677	−	0.632357i	$-0.782088\pi$
$743$	4.36941	−	7.56804i	0.160298	−	0.277645i	0.934976	+	0.354712i	$0.115421\pi$
$744$	−6.25210	+	10.8289i	−0.229213	+	0.397009i
$745$	−7.19642	−	12.4646i	−0.263656	−	0.456666i
$746$	−20.0708	+	34.7637i	−0.734846	+	1.27279i
$747$	2.57641	+	4.46247i	0.0942658	+	0.163273i
$748$	26.5408			0.970428
$749$	−43.6342			−1.59436
$750$	−0.965233	−	1.67183i	−0.0352453	−	0.0610467i
$751$	−6.54957	−	11.3442i	−0.238997	−	0.413955i	0.721430	−	0.692488i	$-0.243485\pi$
$751$	−6.54957	−	11.3442i	−0.238997	−	0.413955i	−0.960427	+	0.278533i	$0.910152\pi$
$752$	−44.3011			−1.61549
$753$	7.08911			0.258342
$754$	−3.47580	−	6.02026i	−0.126581	−	0.219245i
$755$	−6.36093	+	11.0175i	−0.231498	+	0.400966i
$756$	5.06627	+	8.77504i	0.184258	+	0.319145i
$757$	8.21901	−	14.2357i	0.298725	−	0.517407i	−0.677119	−	0.735873i	$-0.736772\pi$
$757$	8.21901	−	14.2357i	0.298725	−	0.517407i	0.975845	+	0.218466i	$0.0701053\pi$
$758$	13.8787	−	24.0386i	0.504097	−	0.873121i
$759$	−6.27397			−0.227731
$760$	−7.87259	−	4.19222i	−0.285569	−	0.152068i
$761$	16.3918			0.594203			0.297101	−	0.954846i	$-0.403980\pi$
$761$	16.3918			0.594203			0.297101	+	0.954846i	$0.403980\pi$
$762$	−5.90714	+	10.2315i	−0.213993	+	0.370647i
$763$	6.84879	−	11.8625i	0.247943	−	0.429450i
$764$	5.00738	+	8.67304i	0.181161	+	0.313780i
$765$	−4.95171	+	8.57661i	−0.179029	+	0.310088i
$766$	−9.05337	−	15.6809i	−0.327112	−	0.566574i
$767$	17.2242			0.621929
$768$	−18.6756			−0.673899
$769$	25.0210	+	43.3377i	0.902282	+	1.56280i	0.824525	+	0.565825i	$0.191442\pi$
$769$	25.0210	+	43.3377i	0.902282	+	1.56280i	0.0777564	+	0.996972i	$0.475224\pi$
$770$	11.6637	+	20.2022i	0.420332	+	0.728036i
$771$	−0.142282			−0.00512416
$772$	11.1875			0.402649
$773$	−24.3436	−	42.1644i	−0.875580	−	1.51655i	−0.856144	−	0.516737i	$-0.827146\pi$
$773$	−24.3436	−	42.1644i	−0.875580	−	1.51655i	−0.0194356	−	0.999811i	$-0.506187\pi$
$774$	−6.25225	+	10.8292i	−0.224732	+	0.389248i

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:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	95.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.832272 - 1.44154i) q^{2} +(0.579878 - 1.00438i) q^{3} +(-0.385355 - 0.667454i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.965233 - 1.67183i) q^{6} -2.43525 q^{7} +2.04621 q^{8} +(0.827483 + 1.43324i) q^{9} +O(q^{10})\)	\(q+(0.832272 - 1.44154i) q^{2} +(0.579878 - 1.00438i) q^{3} +(-0.385355 - 0.667454i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.965233 - 1.67183i) q^{6} -2.43525 q^{7} +2.04621 q^{8} +(0.827483 + 1.43324i) q^{9} +(0.832272 + 1.44154i) q^{10} -5.75477 q^{11} -0.893835 q^{12} +(0.797505 + 1.38132i) q^{13} +(-2.02680 + 3.51051i) q^{14} +(0.579878 + 1.00438i) q^{15} +(2.47371 - 4.28460i) q^{16} +(2.99203 - 5.18234i) q^{17} +2.75477 q^{18} +(0.149412 + 4.35634i) q^{19} +0.770710 q^{20} +(-1.41215 + 2.44592i) q^{21} +(-4.78953 + 8.29572i) q^{22} +(0.470022 + 0.814102i) q^{23} +(1.18655 - 2.05517i) q^{24} +(-0.500000 - 0.866025i) q^{25} +2.65497 q^{26} +5.39862 q^{27} +(0.938437 + 1.62542i) q^{28} +(-1.30917 - 2.26755i) q^{29} +1.93047 q^{30} -5.26913 q^{31} +(-2.07140 - 3.58777i) q^{32} +(-3.33706 + 5.77996i) q^{33} +(-4.98037 - 8.62625i) q^{34} +(1.21763 - 2.10899i) q^{35} +(0.637749 - 1.10461i) q^{36} -2.89384 q^{37} +(6.40418 + 3.41028i) q^{38} +1.84982 q^{39} +(-1.02310 + 1.77207i) q^{40} +(3.15767 - 5.46925i) q^{41} +(2.35059 + 4.07134i) q^{42} +(-2.26961 + 3.93108i) q^{43} +(2.21763 + 3.84104i) q^{44} -1.65497 q^{45} +1.56475 q^{46} +(-4.47718 - 7.75471i) q^{47} +(-2.86890 - 4.96909i) q^{48} -1.06953 q^{49} -1.66454 q^{50} +(-3.47002 - 6.01025i) q^{51} +(0.614645 - 1.06460i) q^{52} +(1.09819 + 1.90213i) q^{53} +(4.49313 - 7.78232i) q^{54} +(2.87738 - 4.98377i) q^{55} -4.98304 q^{56} +(4.46205 + 2.37608i) q^{57} -4.35834 q^{58} +(5.39939 - 9.35202i) q^{59} +(0.446918 - 0.774084i) q^{60} +(5.26434 + 9.11811i) q^{61} +(-4.38535 + 7.59566i) q^{62} +(-2.01513 - 3.49031i) q^{63} +2.99898 q^{64} -1.59501 q^{65} +(5.55469 + 9.62100i) q^{66} +(-0.504789 - 0.874320i) q^{67} -4.61197 q^{68} +1.09022 q^{69} +(-2.02680 - 3.51051i) q^{70} +(-4.41694 + 7.65036i) q^{71} +(1.69320 + 2.93271i) q^{72} +(5.12499 - 8.87674i) q^{73} +(-2.40846 + 4.17157i) q^{74} -1.15976 q^{75} +(2.85008 - 1.77846i) q^{76} +14.0143 q^{77} +(1.53956 - 2.66659i) q^{78} +(-3.80229 + 6.58577i) q^{79} +(2.47371 + 4.28460i) q^{80} +(0.648093 - 1.12253i) q^{81} +(-5.25609 - 9.10381i) q^{82} +3.11355 q^{83} +2.17672 q^{84} +(2.99203 + 5.18234i) q^{85} +(3.77787 + 6.54346i) q^{86} -3.03663 q^{87} -11.7755 q^{88} +(5.55706 + 9.62511i) q^{89} +(-1.37738 + 2.38570i) q^{90} +(-1.94213 - 3.36387i) q^{91} +(0.362251 - 0.627436i) q^{92} +(-3.05545 + 5.29220i) q^{93} -14.9049 q^{94} +(-3.84741 - 2.04877i) q^{95} -4.80463 q^{96} +(-2.02888 + 3.51412i) q^{97} +(-0.890144 + 1.54177i) q^{98} +(-4.76197 - 8.24798i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} - 3 q^{3} - 5 q^{4} - 4 q^{5} - 2 q^{6} - 8 q^{7} + 24 q^{8} - q^{9}+O(q^{10}) \) 8 * q - q^2 - 3 * q^3 - 5 * q^4 - 4 * q^5 - 2 * q^6 - 8 * q^7 + 24 * q^8 - q^9	\( 8 q - q^{2} - 3 q^{3} - 5 q^{4} - 4 q^{5} - 2 q^{6} - 8 q^{7} + 24 q^{8} - q^{9} - q^{10} - 4 q^{11} + 12 q^{12} - 7 q^{13} + q^{14} - 3 q^{15} - 7 q^{16} + q^{17} - 20 q^{18} + 5 q^{19} + 10 q^{20} + 4 q^{21} - 2 q^{22} - 2 q^{23} - 23 q^{24} - 4 q^{25} + 6 q^{26} + 24 q^{27} + 19 q^{28} + q^{29} + 4 q^{30} - 30 q^{32} - 19 q^{33} - 15 q^{34} + 4 q^{35} + 7 q^{36} - 4 q^{37} + 13 q^{38} + 30 q^{39} - 12 q^{40} + 8 q^{41} + 15 q^{42} - q^{43} + 12 q^{44} + 2 q^{45} + 24 q^{46} + 12 q^{47} - 23 q^{48} - 20 q^{49} + 2 q^{50} - 22 q^{51} + 3 q^{52} + 5 q^{53} + 34 q^{54} + 2 q^{55} - 82 q^{56} + 7 q^{57} - 54 q^{58} + 5 q^{59} - 6 q^{60} - 37 q^{62} + 3 q^{63} + 112 q^{64} + 14 q^{65} + 31 q^{66} - 4 q^{67} + 32 q^{68} - 18 q^{69} + q^{70} - 20 q^{71} - 17 q^{72} + 20 q^{73} - 25 q^{74} + 6 q^{75} + 63 q^{76} + 28 q^{77} + 18 q^{78} - 17 q^{79} - 7 q^{80} - 12 q^{81} - 21 q^{82} + 2 q^{83} - 40 q^{84} + q^{85} - 8 q^{86} - 32 q^{87} - 14 q^{88} - 11 q^{89} + 10 q^{90} - 6 q^{91} + q^{92} + 8 q^{93} - 62 q^{94} - 4 q^{95} + 42 q^{96} - q^{97} - 9 q^{98} - 38 q^{99}+O(q^{100}) \) 8 * q - q^2 - 3 * q^3 - 5 * q^4 - 4 * q^5 - 2 * q^6 - 8 * q^7 + 24 * q^8 - q^9 - q^10 - 4 * q^11 + 12 * q^12 - 7 * q^13 + q^14 - 3 * q^15 - 7 * q^16 + q^17 - 20 * q^18 + 5 * q^19 + 10 * q^20 + 4 * q^21 - 2 * q^22 - 2 * q^23 - 23 * q^24 - 4 * q^25 + 6 * q^26 + 24 * q^27 + 19 * q^28 + q^29 + 4 * q^30 - 30 * q^32 - 19 * q^33 - 15 * q^34 + 4 * q^35 + 7 * q^36 - 4 * q^37 + 13 * q^38 + 30 * q^39 - 12 * q^40 + 8 * q^41 + 15 * q^42 - q^43 + 12 * q^44 + 2 * q^45 + 24 * q^46 + 12 * q^47 - 23 * q^48 - 20 * q^49 + 2 * q^50 - 22 * q^51 + 3 * q^52 + 5 * q^53 + 34 * q^54 + 2 * q^55 - 82 * q^56 + 7 * q^57 - 54 * q^58 + 5 * q^59 - 6 * q^60 - 37 * q^62 + 3 * q^63 + 112 * q^64 + 14 * q^65 + 31 * q^66 - 4 * q^67 + 32 * q^68 - 18 * q^69 + q^70 - 20 * q^71 - 17 * q^72 + 20 * q^73 - 25 * q^74 + 6 * q^75 + 63 * q^76 + 28 * q^77 + 18 * q^78 - 17 * q^79 - 7 * q^80 - 12 * q^81 - 21 * q^82 + 2 * q^83 - 40 * q^84 + q^85 - 8 * q^86 - 32 * q^87 - 14 * q^88 - 11 * q^89 + 10 * q^90 - 6 * q^91 + q^92 + 8 * q^93 - 62 * q^94 - 4 * q^95 + 42 * q^96 - q^97 - 9 * q^98 - 38 * q^99

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