LMFDB - Embedded newform 315.2.l.c.121.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(121,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0, 2]))

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

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

chi := DirichletCharacter("315.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.l (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.12
Character	$\chi$	$=$	315.121
Dual form			315.2.l.c.151.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.831231 q^{2} +(-0.611026 + 1.62069i) q^{3} -1.30905 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.507903 + 1.34717i) q^{6} +(-2.57526 - 0.606656i) q^{7} -2.75059 q^{8} +(-2.25330 - 1.98057i) q^{9} +O(q^{10})$	\(q+0.831231 q^{2} +(-0.611026 + 1.62069i) q^{3} -1.30905 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.507903 + 1.34717i) q^{6} +(-2.57526 - 0.606656i) q^{7} -2.75059 q^{8} +(-2.25330 - 1.98057i) q^{9} +(-0.415616 - 0.719867i) q^{10} +(-1.06048 + 1.83681i) q^{11} +(0.799866 - 2.12158i) q^{12} +(0.552087 - 0.956243i) q^{13} +(-2.14064 - 0.504271i) q^{14} +(1.70907 - 0.281183i) q^{15} +0.331734 q^{16} +(-3.19669 - 5.53684i) q^{17} +(-1.87301 - 1.64631i) q^{18} +(-2.76722 + 4.79297i) q^{19} +(0.654527 + 1.13367i) q^{20} +(2.55675 - 3.80303i) q^{21} +(-0.881504 + 1.52681i) q^{22} +(3.82515 + 6.62536i) q^{23} +(1.68068 - 4.45786i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(0.458912 - 0.794859i) q^{26} +(4.58672 - 2.44172i) q^{27} +(3.37116 + 0.794145i) q^{28} +(-0.160759 - 0.278443i) q^{29} +(1.42064 - 0.233728i) q^{30} -10.8110 q^{31} +5.77693 q^{32} +(-2.32892 - 2.84105i) q^{33} +(-2.65719 - 4.60239i) q^{34} +(0.762251 + 2.53357i) q^{35} +(2.94969 + 2.59268i) q^{36} +(1.76248 - 3.05270i) q^{37} +(-2.30020 + 3.98406i) q^{38} +(1.21244 + 1.47905i) q^{39} +(1.37529 + 2.38208i) q^{40} +(-5.63436 + 9.75900i) q^{41} +(2.12525 - 3.16119i) q^{42} +(-4.52334 - 7.83465i) q^{43} +(1.38823 - 2.40448i) q^{44} +(-0.588576 + 2.94170i) q^{45} +(3.17959 + 5.50720i) q^{46} +2.35967 q^{47} +(-0.202698 + 0.537640i) q^{48} +(6.26394 + 3.12459i) q^{49} +(-0.415616 + 0.719867i) q^{50} +(10.9268 - 1.79771i) q^{51} +(-0.722712 + 1.25177i) q^{52} +(5.02990 + 8.71204i) q^{53} +(3.81262 - 2.02964i) q^{54} +2.12096 q^{55} +(7.08349 + 1.66866i) q^{56} +(-6.07709 - 7.41345i) q^{57} +(-0.133628 - 0.231450i) q^{58} +5.51699 q^{59} +(-2.23727 + 0.368084i) q^{60} -5.97973 q^{61} -8.98641 q^{62} +(4.60130 + 6.46746i) q^{63} +4.13849 q^{64} -1.10417 q^{65} +(-1.93587 - 2.36157i) q^{66} +0.240571 q^{67} +(4.18465 + 7.24802i) q^{68} +(-13.0749 + 2.15114i) q^{69} +(0.633607 + 2.10598i) q^{70} +3.28400 q^{71} +(6.19789 + 5.44774i) q^{72} +(-3.39398 - 5.87854i) q^{73} +(1.46503 - 2.53750i) q^{74} +(-1.09805 - 1.33951i) q^{75} +(3.62245 - 6.27426i) q^{76} +(3.84532 - 4.08691i) q^{77} +(1.00782 + 1.22943i) q^{78} -5.18040 q^{79} +(-0.165867 - 0.287290i) q^{80} +(1.15468 + 8.92562i) q^{81} +(-4.68345 + 8.11198i) q^{82} +(-2.94842 - 5.10682i) q^{83} +(-3.34693 + 4.97837i) q^{84} +(-3.19669 + 5.53684i) q^{85} +(-3.75994 - 6.51241i) q^{86} +(0.549499 - 0.0904055i) q^{87} +(2.91695 - 5.05230i) q^{88} +(2.74411 - 4.75294i) q^{89} +(-0.489243 + 2.44523i) q^{90} +(-2.00188 + 2.12765i) q^{91} +(-5.00733 - 8.67296i) q^{92} +(6.60578 - 17.5213i) q^{93} +1.96143 q^{94} +5.53444 q^{95} +(-3.52985 + 9.36263i) q^{96} +(-8.61631 - 14.9239i) q^{97} +(5.20678 + 2.59726i) q^{98} +(6.02750 - 2.03851i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - q^{3} + 44 q^{4} - 18 q^{5} - 4 q^{6} - q^{7} - 9 q^{9}+O(q^{10}) $ 36 * q - q^3 + 44 * q^4 - 18 * q^5 - 4 * q^6 - q^7 - 9 * q^9	\( 36 q - q^{3} + 44 q^{4} - 18 q^{5} - 4 q^{6} - q^{7} - 9 q^{9} + q^{11} + 8 q^{12} + 2 q^{13} + 9 q^{14} - q^{15} + 60 q^{16} - 5 q^{17} - 21 q^{18} - 2 q^{19} - 22 q^{20} - 23 q^{21} - 19 q^{22} - 3 q^{23} - 32 q^{24} - 18 q^{25} - 4 q^{26} + 17 q^{27} + 5 q^{28} - 8 q^{29} + 2 q^{30} - 20 q^{32} - 35 q^{33} + 10 q^{34} - q^{35} - 44 q^{36} - 15 q^{37} - 22 q^{38} + 7 q^{39} - 4 q^{41} + 57 q^{42} - 29 q^{43} - 7 q^{44} + 6 q^{45} - 24 q^{46} + 46 q^{47} - 19 q^{48} - 7 q^{49} + 42 q^{51} - 7 q^{52} + 21 q^{54} - 2 q^{55} - 12 q^{56} + 21 q^{57} - 20 q^{58} + 10 q^{59} - 13 q^{60} + 6 q^{61} - 12 q^{62} + 2 q^{63} + 128 q^{64} - 4 q^{65} - 12 q^{66} + 70 q^{67} - 17 q^{68} - 50 q^{69} - 3 q^{70} + 24 q^{71} - 10 q^{72} - 10 q^{73} + 22 q^{74} + 2 q^{75} + 10 q^{76} + 35 q^{77} + 66 q^{78} + 56 q^{79} - 30 q^{80} - 49 q^{81} - 8 q^{82} - 22 q^{83} - 86 q^{84} - 5 q^{85} + 19 q^{86} - 42 q^{87} - 50 q^{88} - 4 q^{89} + 3 q^{90} + 7 q^{91} - 50 q^{92} - q^{93} + 4 q^{94} + 4 q^{95} - 179 q^{96} + 16 q^{97} + 16 q^{98} - 89 q^{99}+O(q^{100}) \) 36 * q - q^3 + 44 * q^4 - 18 * q^5 - 4 * q^6 - q^7 - 9 * q^9 + q^11 + 8 * q^12 + 2 * q^13 + 9 * q^14 - q^15 + 60 * q^16 - 5 * q^17 - 21 * q^18 - 2 * q^19 - 22 * q^20 - 23 * q^21 - 19 * q^22 - 3 * q^23 - 32 * q^24 - 18 * q^25 - 4 * q^26 + 17 * q^27 + 5 * q^28 - 8 * q^29 + 2 * q^30 - 20 * q^32 - 35 * q^33 + 10 * q^34 - q^35 - 44 * q^36 - 15 * q^37 - 22 * q^38 + 7 * q^39 - 4 * q^41 + 57 * q^42 - 29 * q^43 - 7 * q^44 + 6 * q^45 - 24 * q^46 + 46 * q^47 - 19 * q^48 - 7 * q^49 + 42 * q^51 - 7 * q^52 + 21 * q^54 - 2 * q^55 - 12 * q^56 + 21 * q^57 - 20 * q^58 + 10 * q^59 - 13 * q^60 + 6 * q^61 - 12 * q^62 + 2 * q^63 + 128 * q^64 - 4 * q^65 - 12 * q^66 + 70 * q^67 - 17 * q^68 - 50 * q^69 - 3 * q^70 + 24 * q^71 - 10 * q^72 - 10 * q^73 + 22 * q^74 + 2 * q^75 + 10 * q^76 + 35 * q^77 + 66 * q^78 + 56 * q^79 - 30 * q^80 - 49 * q^81 - 8 * q^82 - 22 * q^83 - 86 * q^84 - 5 * q^85 + 19 * q^86 - 42 * q^87 - 50 * q^88 - 4 * q^89 + 3 * q^90 + 7 * q^91 - 50 * q^92 - q^93 + 4 * q^94 + 4 * q^95 - 179 * q^96 + 16 * q^97 + 16 * q^98 - 89 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.831231			0.587769			0.293885	−	0.955841i	$-0.405052\pi$
$2$	0.831231			0.587769			0.293885	+	0.955841i	$0.405052\pi$
$3$	−0.611026	+	1.62069i	−0.352776	+	0.935708i
$3$	−0.611026	+	1.62069i	−0.352776	+	0.935708i
$4$	−1.30905			−0.654527
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−0.507903	+	1.34717i	−0.207351	+	0.549980i
$7$	−2.57526	−	0.606656i	−0.973357	−	0.229294i
$7$	−2.57526	−	0.606656i	−0.973357	−	0.229294i
$8$	−2.75059			−0.972480
$9$	−2.25330	−	1.98057i	−0.751099	−	0.660190i
$10$	−0.415616	−	0.719867i	−0.131429	−	0.227642i
$11$	−1.06048	+	1.83681i	−0.319747	+	0.553818i	−0.980435	−	0.196843i	$-0.936931\pi$
$11$	−1.06048	+	1.83681i	−0.319747	+	0.553818i	0.660688	+	0.750660i	$0.270265\pi$
$12$	0.799866	−	2.12158i	0.230901	−	0.612446i
$13$	0.552087	−	0.956243i	0.153121	−	0.265214i	−0.779252	−	0.626711i	$-0.784401\pi$
$13$	0.552087	−	0.956243i	0.153121	−	0.265214i	0.932373	+	0.361497i	$0.117734\pi$
$14$	−2.14064	−	0.504271i	−0.572109	−	0.134772i
$15$	1.70907	−	0.281183i	0.441281	−	0.0726012i
$16$	0.331734			0.0829336
$17$	−3.19669	−	5.53684i	−0.775312	−	1.34288i	−0.934619	−	0.355651i	$-0.884259\pi$
$17$	−3.19669	−	5.53684i	−0.775312	−	1.34288i	0.159306	−	0.987229i	$-0.449074\pi$
$18$	−1.87301	−	1.64631i	−0.441473	−	0.388039i
$19$	−2.76722	+	4.79297i	−0.634844	+	1.09958i	0.351704	+	0.936111i	$0.385602\pi$
$19$	−2.76722	+	4.79297i	−0.634844	+	1.09958i	−0.986548	+	0.163471i	$0.947731\pi$
$20$	0.654527	+	1.13367i	0.146357	+	0.253497i
$21$	2.55675	−	3.80303i	0.557929	−	0.829889i
$22$	−0.881504	+	1.52681i	−0.187937	+	0.325517i
$23$	3.82515	+	6.62536i	0.797599	+	1.38148i	0.921175	+	0.389147i	$0.127230\pi$
$23$	3.82515	+	6.62536i	0.797599	+	1.38148i	−0.123576	+	0.992335i	$0.539436\pi$
$24$	1.68068	−	4.45786i	0.343067	−	0.909957i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	0.458912	−	0.794859i	0.0900000	−	0.155885i
$27$	4.58672	−	2.44172i	0.882714	−	0.469910i
$28$	3.37116	+	0.794145i	0.637089	+	0.150079i
$29$	−0.160759	−	0.278443i	−0.0298522	−	0.0517055i	0.850713	−	0.525630i	$-0.176170\pi$
$29$	−0.160759	−	0.278443i	−0.0298522	−	0.0517055i	−0.880566	+	0.473924i	$0.842837\pi$
$30$	1.42064	−	0.233728i	0.259371	−	0.0426727i
$31$	−10.8110			−1.94171			−0.970853	−	0.239674i	$-0.922960\pi$
$31$	−10.8110			−1.94171			−0.970853	+	0.239674i	$0.922960\pi$
$32$	5.77693			1.02123
$33$	−2.32892	−	2.84105i	−0.405413	−	0.494563i
$34$	−2.65719	−	4.60239i	−0.455705	−	0.789304i
$35$	0.762251	+	2.53357i	0.128844	+	0.428251i
$36$	2.94969	+	2.59268i	0.491615	+	0.432113i
$37$	1.76248	−	3.05270i	0.289749	−	0.501861i	−0.684000	−	0.729482i	$-0.739761\pi$
$37$	1.76248	−	3.05270i	0.289749	−	0.501861i	0.973750	+	0.227621i	$0.0730947\pi$
$38$	−2.30020	+	3.98406i	−0.373142	+	0.646301i
$39$	1.21244	+	1.47905i	0.194145	+	0.236838i
$40$	1.37529	+	2.38208i	0.217453	+	0.376640i
$41$	−5.63436	+	9.75900i	−0.879939	+	1.52410i	−0.0285326	+	0.999593i	$0.509083\pi$
$41$	−5.63436	+	9.75900i	−0.879939	+	1.52410i	−0.851406	+	0.524506i	$0.824250\pi$
$42$	2.12525	−	3.16119i	0.327934	−	0.487783i
$43$	−4.52334	−	7.83465i	−0.689803	−	1.19477i	−0.971901	−	0.235388i	$-0.924364\pi$
$43$	−4.52334	−	7.83465i	−0.689803	−	1.19477i	0.282099	−	0.959385i	$-0.408969\pi$
$44$	1.38823	−	2.40448i	0.209283	−	0.362489i
$45$	−0.588576	+	2.94170i	−0.0877398	+	0.438522i
$46$	3.17959	+	5.50720i	0.468804	+	0.811993i
$47$	2.35967			0.344193			0.172096	−	0.985080i	$-0.444946\pi$
$47$	2.35967			0.344193			0.172096	+	0.985080i	$0.444946\pi$
$48$	−0.202698	+	0.537640i	−0.0292570	+	0.0776016i
$49$	6.26394	+	3.12459i	0.894848	+	0.446370i
$50$	−0.415616	+	0.719867i	−0.0587769	+	0.101805i
$51$	10.9268	−	1.79771i	1.53006	−	0.251730i
$52$	−0.722712	+	1.25177i	−0.100222	+	0.173590i
$53$	5.02990	+	8.71204i	0.690909	+	1.19669i	0.971540	+	0.236875i	$0.0761230\pi$
$53$	5.02990	+	8.71204i	0.690909	+	1.19669i	−0.280631	+	0.959816i	$0.590544\pi$
$54$	3.81262	−	2.02964i	0.518832	−	0.276198i
$55$	2.12096			0.285990
$56$	7.08349	+	1.66866i	0.946571	+	0.222984i
$57$	−6.07709	−	7.41345i	−0.804930	−	0.981935i
$58$	−0.133628	−	0.231450i	−0.0175462	−	0.0303909i
$59$	5.51699			0.718251			0.359125	−	0.933289i	$-0.383075\pi$
$59$	5.51699			0.718251			0.359125	+	0.933289i	$0.383075\pi$
$60$	−2.23727	+	0.368084i	−0.288831	+	0.0475195i
$61$	−5.97973			−0.765626			−0.382813	−	0.923826i	$-0.625045\pi$
$61$	−5.97973			−0.765626			−0.382813	+	0.923826i	$0.625045\pi$
$62$	−8.98641			−1.14128
$63$	4.60130	+	6.46746i	0.579709	+	0.814823i
$64$	4.13849			0.517311
$65$	−1.10417			−0.136956
$66$	−1.93587	−	2.36157i	−0.238289	−	0.290689i
$67$	0.240571			0.0293905			0.0146952	−	0.999892i	$-0.495322\pi$
$67$	0.240571			0.0293905			0.0146952	+	0.999892i	$0.495322\pi$
$68$	4.18465	+	7.24802i	0.507463	+	0.878952i
$69$	−13.0749	+	2.15114i	−1.57404	+	0.258966i
$70$	0.633607	+	2.10598i	0.0757305	+	0.251713i
$71$	3.28400			0.389739			0.194870	−	0.980829i	$-0.437572\pi$
$71$	3.28400			0.389739			0.194870	+	0.980829i	$0.437572\pi$
$72$	6.19789	+	5.44774i	0.730428	+	0.642022i
$73$	−3.39398	−	5.87854i	−0.397235	−	0.688032i	0.596148	−	0.802874i	$-0.296697\pi$
$73$	−3.39398	−	5.87854i	−0.397235	−	0.688032i	−0.993384	+	0.114843i	$0.963364\pi$
$74$	1.46503	−	2.53750i	0.170306	−	0.294978i
$75$	−1.09805	−	1.33951i	−0.126792	−	0.154673i
$76$	3.62245	−	6.27426i	0.415523	−	0.719707i
$77$	3.84532	−	4.08691i	0.438215	−	0.465746i
$78$	1.00782	+	1.22943i	0.114113	+	0.139206i
$79$	−5.18040			−0.582841			−0.291420	−	0.956595i	$-0.594128\pi$
$79$	−5.18040			−0.582841			−0.291420	+	0.956595i	$0.594128\pi$
$80$	−0.165867	−	0.287290i	−0.0185445	−	0.0321201i
$81$	1.15468	+	8.92562i	0.128298	+	0.991736i
$82$	−4.68345	+	8.11198i	−0.517201	+	0.895819i
$83$	−2.94842	−	5.10682i	−0.323632	−	0.560546i	0.657603	−	0.753365i	$-0.271571\pi$
$83$	−2.94842	−	5.10682i	−0.323632	−	0.560546i	−0.981234	+	0.192818i	$0.938237\pi$
$84$	−3.34693	+	4.97837i	−0.365180	+	0.543185i
$85$	−3.19669	+	5.53684i	−0.346730	+	0.600554i
$86$	−3.75994	−	6.51241i	−0.405445	−	0.702251i
$87$	0.549499	−	0.0904055i	0.0589124	−	0.00969249i
$88$	2.91695	−	5.05230i	0.310947	−	0.538577i
$89$	2.74411	−	4.75294i	0.290875	−	0.503811i	−0.683142	−	0.730286i	$-0.739387\pi$
$89$	2.74411	−	4.75294i	0.290875	−	0.503811i	0.974017	+	0.226475i	$0.0727202\pi$
$90$	−0.489243	+	2.44523i	−0.0515707	+	0.257750i
$91$	−2.00188	+	2.12765i	−0.209854	+	0.223038i
$92$	−5.00733	−	8.67296i	−0.522051	−	0.904218i
$93$	6.60578	−	17.5213i	0.684987	−	1.81687i
$94$	1.96143			0.202306
$95$	5.53444			0.567822
$96$	−3.52985	+	9.36263i	−0.360264	+	0.955569i
$97$	−8.61631	−	14.9239i	−0.874854	−	1.51529i	−0.856918	−	0.515452i	$-0.827624\pi$
$97$	−8.61631	−	14.9239i	−0.874854	−	1.51529i	−0.0179356	−	0.999839i	$-0.505709\pi$
$98$	5.20678	+	2.59726i	0.525964	+	0.262363i
$99$	6.02750	−	2.03851i	0.605786	−	0.204878i
$100$	0.654527	−	1.13367i	0.0654527	−	0.113367i
$101$	1.02405	−	1.77372i	0.101897	−	0.176491i	−0.810569	−	0.585643i	$-0.800842\pi$
$101$	1.02405	−	1.77372i	0.101897	−	0.176491i	0.912466	+	0.409152i	$0.134175\pi$
$102$	9.08268	−	1.49432i	0.899319	−	0.147959i
$103$	0.616096	+	1.06711i	0.0607057	+	0.105145i	0.894781	−	0.446505i	$-0.147332\pi$
$103$	0.616096	+	1.06711i	0.0607057	+	0.105145i	−0.834075	+	0.551651i	$0.813998\pi$
$104$	−1.51856	+	2.63023i	−0.148908	+	0.257915i
$105$	−4.57189	−	0.312700i	−0.446171	−	0.0305163i
$106$	4.18101	+	7.24172i	0.406095	+	0.703378i
$107$	−1.52561	+	2.64244i	−0.147486	+	0.255454i	−0.930298	−	0.366805i	$-0.880452\pi$
$107$	−1.52561	+	2.64244i	−0.147486	+	0.255454i	0.782811	+	0.622259i	$0.213785\pi$
$108$	−6.00427	+	3.19635i	−0.577761	+	0.307569i
$109$	−5.57983	−	9.66454i	−0.534450	−	0.925695i	−0.999190	−	0.0402476i	$-0.987185\pi$
$109$	−5.57983	−	9.66454i	−0.534450	−	0.925695i	0.464739	−	0.885448i	$-0.346148\pi$
$110$	1.76301			0.168096
$111$	3.87057	+	4.72171i	0.367378	+	0.448165i
$112$	−0.854303	−	0.201249i	−0.0807240	−	0.0190162i
$113$	2.28068	−	3.95026i	0.214549	−	0.371609i	−0.738584	−	0.674161i	$-0.764505\pi$
$113$	2.28068	−	3.95026i	0.214549	−	0.371609i	0.953133	+	0.302552i	$0.0978386\pi$
$114$	−5.05147	−	6.16229i	−0.473113	−	0.577151i
$115$	3.82515	−	6.62536i	0.356697	−	0.617818i
$116$	0.210442	+	0.364497i	0.0195391	+	0.0338427i
$117$	−3.13792	+	1.06125i	−0.290101	+	0.0981126i
$118$	4.58589			0.422166
$119$	4.87337	+	16.1981i	0.446741	+	1.48488i
$120$	−4.70096	+	0.773419i	−0.429137	+	0.0706032i
$121$	3.25076	+	5.63049i	0.295524	+	0.511862i
$122$	−4.97054			−0.450011
$123$	−12.3736	−	15.0946i	−1.11569	−	1.36103i
$124$	14.1521			1.27090
$125$	1.00000			0.0894427
$126$	3.82474	+	5.37595i	0.340735	+	0.478928i
$127$	−0.733050			−0.0650477			−0.0325238	−	0.999471i	$-0.510354\pi$
$127$	−0.733050			−0.0650477			−0.0325238	+	0.999471i	$0.510354\pi$
$128$	−8.11381			−0.717166
$129$	15.4614	−	2.54377i	1.36130	−	0.223967i
$130$	−0.917824			−0.0804985
$131$	−3.88263	−	6.72492i	−0.339227	−	0.587559i	0.645060	−	0.764132i	$-0.276832\pi$
$131$	−3.88263	−	6.72492i	−0.339227	−	0.587559i	−0.984288	+	0.176573i	$0.943499\pi$
$132$	3.04868	+	3.71909i	0.265354	+	0.323705i
$133$	10.0340	−	10.6644i	0.870058	−	0.924720i
$134$	0.199971			0.0172748
$135$	−4.40795	−	2.75135i	−0.379376	−	0.236799i
$136$	8.79279	+	15.2296i	0.753976	+	1.30592i
$137$	−5.57452	+	9.65536i	−0.476264	+	0.824913i	−0.999630	−	0.0271948i	$-0.991343\pi$
$137$	−5.57452	+	9.65536i	−0.476264	+	0.824913i	0.523366	+	0.852108i	$0.324676\pi$
$138$	−10.8683	+	1.78809i	−0.925171	+	0.152212i
$139$	−4.63912	+	8.03519i	−0.393485	+	0.681536i	−0.992907	−	0.118898i	$-0.962064\pi$
$139$	−4.63912	+	8.03519i	−0.393485	+	0.681536i	0.599422	+	0.800433i	$0.295397\pi$
$140$	−0.997829	−	3.31658i	−0.0843319	−	0.280302i
$141$	−1.44182	+	3.82430i	−0.121423	+	0.322064i
$142$	2.72976			0.229077
$143$	1.17095	+	2.02815i	0.0979202	+	0.169603i
$144$	−0.747496	−	0.657024i	−0.0622913	−	0.0547520i
$145$	−0.160759	+	0.278443i	−0.0133503	+	0.0231234i
$146$	−2.82118	−	4.88643i	−0.233483	−	0.404404i
$147$	−8.89143	+	8.24272i	−0.733353	+	0.679848i
$148$	−2.30718	+	3.99615i	−0.189649	+	0.328482i
$149$	−5.02802	−	8.70879i	−0.411912	−	0.713452i	0.583187	−	0.812338i	$-0.301805\pi$
$149$	−5.02802	−	8.70879i	−0.411912	−	0.713452i	−0.995099	+	0.0988860i	$0.968472\pi$
$150$	−0.912733	−	1.11344i	−0.0745243	−	0.0909122i
$151$	−9.91366	+	17.1710i	−0.806762	+	1.39735i	0.108333	+	0.994115i	$0.465449\pi$
$151$	−9.91366	+	17.1710i	−0.806762	+	1.39735i	−0.915095	+	0.403238i	$0.867885\pi$
$152$	7.61149	−	13.1835i	0.617373	−	1.06932i
$153$	−3.76300	+	18.8074i	−0.304220	+	1.52049i
$154$	3.19635	−	3.39716i	0.257569	−	0.273751i
$155$	5.40548	+	9.36257i	0.434179	+	0.752020i
$156$	−1.58715	−	1.93616i	−0.127073	−	0.155017i
$157$	−22.9870			−1.83456			−0.917279	−	0.398245i	$-0.869620\pi$
$157$	−22.9870			−1.83456			−0.917279	+	0.398245i	$0.869620\pi$
$158$	−4.30611			−0.342576
$159$	−17.1929	+	2.82864i	−1.36349	+	0.224326i
$160$	−2.88846	−	5.00297i	−0.228353	−	0.395519i
$161$	−5.83145	−	19.3826i	−0.459583	−	1.52756i
$162$	0.959808	+	7.41925i	0.0754096	+	0.582912i
$163$	10.3381	−	17.9061i	0.809742	−	1.40251i	−0.103301	−	0.994650i	$-0.532941\pi$
$163$	10.3381	−	17.9061i	0.809742	−	1.40251i	0.913043	−	0.407864i	$-0.133726\pi$
$164$	7.37569	−	12.7751i	0.575944	−	0.997565i
$165$	−1.29596	+	3.43743i	−0.100890	+	0.267603i
$166$	−2.45082	−	4.24495i	−0.190221	−	0.329472i
$167$	−1.91031	+	3.30875i	−0.147824	+	0.256039i	−0.930423	−	0.366487i	$-0.880560\pi$
$167$	−1.91031	+	3.30875i	−0.147824	+	0.256039i	0.782599	+	0.622526i	$0.213894\pi$
$168$	−7.03258	+	10.4606i	−0.542575	+	0.807050i
$169$	5.89040	+	10.2025i	0.453108	+	0.784806i
$170$	−2.65719	+	4.60239i	−0.203797	+	0.352987i
$171$	15.7282	−	5.31930i	1.20276	−	0.406777i
$172$	5.92130	+	10.2560i	0.451495	+	0.782012i
$173$	−6.81400			−0.518058			−0.259029	−	0.965869i	$-0.583403\pi$
$173$	−6.81400			−0.518058			−0.259029	+	0.965869i	$0.583403\pi$
$174$	0.456760	−	0.0751479i	0.0346269	−	0.00569694i
$175$	1.81301	−	1.92691i	0.137051	−	0.145661i
$176$	−0.351798	+	0.609332i	−0.0265178	+	0.0459301i
$177$	−3.37102	+	8.94135i	−0.253382	+	0.672073i
$178$	2.28099	−	3.95079i	0.170968	−	0.296124i
$179$	6.33162	+	10.9667i	0.473247	+	0.819688i	0.999531	−	0.0306206i	$-0.00974837\pi$
$179$	6.33162	+	10.9667i	0.473247	+	0.819688i	−0.526284	+	0.850309i	$0.676415\pi$
$180$	0.770479	−	3.85084i	0.0574281	−	0.287025i
$181$	−6.50939			−0.483839			−0.241920	−	0.970296i	$-0.577777\pi$
$181$	−6.50939			−0.483839			−0.241920	+	0.970296i	$0.577777\pi$
$182$	−1.66402	+	1.76857i	−0.123346	+	0.131095i
$183$	3.65377	−	9.69131i	0.270094	−	0.716402i
$184$	−10.5214	−	18.2236i	−0.775649	−	1.34346i
$185$	−3.52495			−0.259160
$186$	5.49093	−	14.5642i	0.402614	−	1.06790i
$187$	13.5601			0.991615
$188$	−3.08893			−0.225284
$189$	−13.2933	+	3.50551i	−0.966944	+	0.254989i
$190$	4.60040			0.333748
$191$	1.98888			0.143910			0.0719552	−	0.997408i	$-0.477076\pi$
$191$	1.98888			0.143910			0.0719552	+	0.997408i	$0.477076\pi$
$192$	−2.52872	+	6.70723i	−0.182495	+	0.484052i
$193$	0.406947			0.0292927			0.0146463	−	0.999893i	$-0.495338\pi$
$193$	0.406947			0.0292927			0.0146463	+	0.999893i	$0.495338\pi$
$194$	−7.16215	−	12.4052i	−0.514212	−	0.890642i
$195$	0.674679	−	1.78953i	0.0483147	−	0.128151i
$196$	−8.19984	−	4.09026i	−0.585703	−	0.292162i
$197$	−1.94157			−0.138331			−0.0691656	−	0.997605i	$-0.522034\pi$
$197$	−1.94157			−0.138331			−0.0691656	+	0.997605i	$0.522034\pi$
$198$	5.01024	−	1.69447i	0.356063	−	0.120421i
$199$	2.67995	+	4.64181i	0.189977	+	0.329049i	0.945242	−	0.326370i	$-0.105825\pi$
$199$	2.67995	+	4.64181i	0.189977	+	0.329049i	−0.755266	+	0.655419i	$0.772492\pi$
$200$	1.37529	−	2.38208i	0.0972480	−	0.168439i
$201$	−0.146995	+	0.389893i	−0.0103683	+	0.0275009i
$202$	0.851226	−	1.47437i	0.0598921	−	0.103736i
$203$	0.245078	+	0.814588i	0.0172011	+	0.0571729i
$204$	−14.3038	+	2.35331i	−1.00146	+	0.164764i
$205$	11.2687			0.787041
$206$	0.512118	+	0.887014i	0.0356809	+	0.0618012i
$207$	4.50279	−	22.5049i	0.312965	−	1.56420i
$208$	0.183146	−	0.317219i	0.0126989	−	0.0219952i
$209$	−5.86917	−	10.1657i	−0.405979	−	0.703176i
$210$	−3.80030	−	0.259926i	−0.262246	−	0.0179366i
$211$	−0.945993	+	1.63851i	−0.0651249	+	0.112800i	−0.896749	−	0.442539i	$-0.854078\pi$
$211$	−0.945993	+	1.63851i	−0.0651249	+	0.112800i	0.831625	+	0.555338i	$0.187411\pi$
$212$	−6.58441	−	11.4045i	−0.452219	−	0.783267i
$213$	−2.00661	+	5.32236i	−0.137491	+	0.364682i
$214$	−1.26814	+	2.19648i	−0.0866880	+	0.150148i
$215$	−4.52334	+	7.83465i	−0.308489	+	0.534319i
$216$	−12.6162	+	6.71618i	−0.858422	+	0.456978i
$217$	27.8411	+	6.55853i	1.88997	+	0.445222i
$218$	−4.63812	−	8.03347i	−0.314133	−	0.544095i
$219$	11.6011	−	1.90866i	0.783932	−	0.128975i
$220$	−2.77645			−0.187188
$221$	−7.05941			−0.474868
$222$	3.21734	+	3.92483i	0.215934	+	0.263418i
$223$	3.79437	+	6.57205i	0.254090	+	0.440097i	0.964648	−	0.263542i	$-0.0848907\pi$
$223$	3.79437	+	6.57205i	0.254090	+	0.440097i	−0.710558	+	0.703639i	$0.751557\pi$
$224$	−14.8771	−	3.50460i	−0.994018	−	0.234161i
$225$	2.84187	−	0.961126i	0.189458	−	0.0640751i
$226$	1.89577	−	3.28358i	0.126105	−	0.218420i
$227$	−3.48509	+	6.03635i	−0.231314	+	0.400647i	−0.958195	−	0.286116i	$-0.907636\pi$
$227$	−3.48509	+	6.03635i	−0.231314	+	0.400647i	0.726881	+	0.686763i	$0.240969\pi$
$228$	7.95525	+	9.70461i	0.526849	+	0.642703i
$229$	7.30881	+	12.6592i	0.482980	+	0.836545i	0.999809	−	0.0195432i	$-0.00622119\pi$
$229$	7.30881	+	12.6592i	0.482980	+	0.836545i	−0.516829	+	0.856088i	$0.672888\pi$
$230$	3.17959	−	5.50720i	0.209656	−	0.363134i
$231$	4.27404	+	8.72929i	0.281211	+	0.574345i
$232$	0.442182	+	0.765882i	0.0290307	+	0.0502826i
$233$	−3.71696	+	6.43796i	−0.243506	+	0.421765i	−0.961711	−	0.274067i	$-0.911631\pi$
$233$	−3.71696	+	6.43796i	−0.243506	+	0.421765i	0.718204	+	0.695832i	$0.244964\pi$
$234$	−2.60834	+	0.882144i	−0.170512	+	0.0576676i
$235$	−1.17983	−	2.04353i	−0.0769638	−	0.133305i
$236$	−7.22204			−0.470115
$237$	3.16536	−	8.39584i	0.205612	−	0.545368i
$238$	4.05090	+	13.4644i	0.262581	+	0.872765i
$239$	6.56544	−	11.3717i	0.424683	−	0.735573i	−0.571708	−	0.820458i	$-0.693719\pi$
$239$	6.56544	−	11.3717i	0.424683	−	0.735573i	0.996391	+	0.0848845i	$0.0270521\pi$
$240$	0.566959	−	0.0932782i	0.0365970	−	0.00602108i
$241$	7.00745	−	12.1373i	0.451390	−	0.781830i	−0.547083	−	0.837078i	$-0.684262\pi$
$241$	7.00745	−	12.1373i	0.451390	−	0.781830i	0.998473	+	0.0552484i	$0.0175951\pi$
$242$	2.70214	+	4.68024i	0.173700	+	0.300857i
$243$	−15.1712	−	3.58240i	−0.973235	−	0.229811i
$244$	7.82780			0.501123
$245$	−0.425992	−	6.98703i	−0.0272157	−	0.446385i
$246$	−10.2853	−	12.5471i	−0.655768	−	0.799972i
$247$	3.05549	+	5.29227i	0.194416	+	0.336739i
$248$	29.7365			1.88827
$249$	10.0782	−	1.65809i	0.638677	−	0.105077i
$250$	0.831231			0.0525717
$251$	1.41785			0.0894937			0.0447468	−	0.998998i	$-0.485752\pi$
$251$	1.41785			0.0894937			0.0447468	+	0.998998i	$0.485752\pi$
$252$	−6.02335	−	8.46626i	−0.379436	−	0.533324i
$253$	−16.2260			−1.02012
$254$	−0.609334			−0.0382330
$255$	−7.02026	−	8.56401i	−0.439625	−	0.536299i
$256$	−15.0214			−0.938840
$257$	4.07173	+	7.05245i	0.253988	+	0.439920i	0.964620	−	0.263644i	$-0.0849244\pi$
$257$	4.07173	+	7.05245i	0.253988	+	0.439920i	−0.710632	+	0.703564i	$0.751591\pi$
$258$	12.8520	−	2.11446i	0.800133	−	0.131641i
$259$	−6.39078	+	6.79228i	−0.397103	+	0.422052i
$260$	1.44542			0.0896414
$261$	−0.189238	+	0.945809i	−0.0117135	+	0.0585441i
$262$	−3.22736	−	5.58996i	−0.199387	−	0.345349i
$263$	−6.13077	+	10.6188i	−0.378039	+	0.654783i	−0.990777	−	0.135503i	$-0.956735\pi$
$263$	−6.13077	+	10.6188i	−0.378039	+	0.654783i	0.612738	+	0.790286i	$0.290068\pi$
$264$	6.40590	+	7.81456i	0.394256	+	0.480953i
$265$	5.02990	−	8.71204i	0.308984	−	0.535176i
$266$	8.34057	−	8.86458i	0.511393	−	0.543522i
$267$	6.02634	+	7.35153i	0.368806	+	0.449906i
$268$	−0.314921			−0.0192369
$269$	−1.57030	−	2.71984i	−0.0957431	−	0.165832i	0.814175	−	0.580619i	$-0.197189\pi$
$269$	−1.57030	−	2.71984i	−0.0957431	−	0.165832i	−0.909918	+	0.414787i	$0.863856\pi$
$270$	−3.66403	−	2.28701i	−0.222986	−	0.139183i
$271$	3.45065	−	5.97670i	0.209612	−	0.363059i	−0.741980	−	0.670422i	$-0.766113\pi$
$271$	3.45065	−	5.97670i	0.209612	−	0.363059i	0.951592	+	0.307363i	$0.0994466\pi$
$272$	−1.06045	−	1.83676i	−0.0642995	−	0.111370i
$273$	−2.22507	−	4.54448i	−0.134667	−	0.275044i
$274$	−4.63372	+	8.02583i	−0.279933	+	0.484858i
$275$	−1.06048	−	1.83681i	−0.0639494	−	0.110764i
$276$	17.1158	−	2.81596i	1.03025	−	0.169501i
$277$	−5.69126	+	9.85756i	−0.341955	+	0.592283i	−0.984796	−	0.173717i	$-0.944422\pi$
$277$	−5.69126	+	9.85756i	−0.341955	+	0.592283i	0.642841	+	0.766000i	$0.277756\pi$
$278$	−3.85618	+	6.67910i	−0.231278	+	0.400586i
$279$	24.3603	+	21.4119i	1.45841	+	1.28190i
$280$	−2.09664	−	6.96881i	−0.125298	−	0.416466i
$281$	−6.28431	−	10.8847i	−0.374890	−	0.649329i	0.615420	−	0.788199i	$-0.288986\pi$
$281$	−6.28431	−	10.8847i	−0.374890	−	0.649329i	−0.990311	+	0.138870i	$0.955653\pi$
$282$	−1.19848	+	3.17887i	−0.0713686	+	0.189299i
$283$	5.83880			0.347081			0.173540	−	0.984827i	$-0.444479\pi$
$283$	5.83880			0.347081			0.173540	+	0.984827i	$0.444479\pi$
$284$	−4.29894			−0.255095
$285$	−3.38169	+	8.96964i	−0.200314	+	0.531316i
$286$	0.973334	+	1.68586i	0.0575544	+	0.0996872i
$287$	20.4303	−	21.7138i	1.20596	−	1.28173i
$288$	−13.0171	−	11.4416i	−0.767041	−	0.674203i
$289$	−11.9377	+	20.6767i	−0.702218	+	1.21628i
$290$	−0.133628	+	0.231450i	−0.00784690	+	0.0135912i
$291$	29.4518	−	4.84552i	1.72650	−	0.284050i
$292$	4.44291	+	7.69534i	0.260001	+	0.450336i
$293$	−13.0397	+	22.5854i	−0.761787	+	1.31945i	0.180141	+	0.983641i	$0.442345\pi$
$293$	−13.0397	+	22.5854i	−0.761787	+	1.31945i	−0.941928	+	0.335814i	$0.890989\pi$
$294$	−7.39084	+	6.85160i	−0.431042	+	0.399594i
$295$	−2.75849	−	4.77785i	−0.160606	−	0.278177i
$296$	−4.84785	+	8.39672i	−0.281776	+	0.488050i
$297$	−0.379155	+	11.0143i	−0.0220008	+	0.639115i
$298$	−4.17945	−	7.23902i	−0.242109	−	0.419345i
$299$	8.44727			0.488518
$300$	1.43741	+	1.75349i	0.0829887	+	0.101238i
$301$	6.89584	+	22.9204i	0.397470	+	1.32111i
$302$	−8.24054	+	14.2730i	−0.474190	+	0.821321i
$303$	2.24893	+	2.74346i	0.129197	+	0.157608i
$304$	−0.917983	+	1.58999i	−0.0526499	+	0.0911924i
$305$	2.98987	+	5.17860i	0.171199	+	0.296526i
$306$	−3.12792	+	15.6333i	−0.178811	+	0.893696i
$307$	20.6929			1.18101			0.590503	−	0.807035i	$-0.298929\pi$
$307$	20.6929			1.18101			0.590503	+	0.807035i	$0.298929\pi$
$308$	−5.03374	+	5.34999i	−0.286824	+	0.304844i
$309$	−2.10591	+	0.346471i	−0.119801	+	0.0197101i
$310$	4.49321	+	7.78246i	0.255197	+	0.442014i
$311$	−18.7276			−1.06194			−0.530972	−	0.847390i	$-0.678173\pi$
$311$	−18.7276			−1.06194			−0.530972	+	0.847390i	$0.678173\pi$
$312$	−3.33492	−	4.06827i	−0.188802	−	0.230320i
$313$	32.8728			1.85808			0.929040	−	0.369980i	$-0.120636\pi$
$313$	32.8728			1.85808			0.929040	+	0.369980i	$0.120636\pi$
$314$	−19.1075			−1.07830
$315$	3.30033	−	7.21857i	0.185953	−	0.406720i
$316$	6.78143			0.381485
$317$	26.6829			1.49866			0.749329	−	0.662198i	$-0.230376\pi$
$317$	26.6829			1.49866			0.749329	+	0.662198i	$0.230376\pi$
$318$	−14.2913	+	2.35126i	−0.801417	+	0.131852i
$319$	0.681927			0.0381806
$320$	−2.06925	−	3.58404i	−0.115674	−	0.200354i
$321$	−3.35039	−	4.08715i	−0.187001	−	0.228122i
$322$	−4.84729	−	16.1114i	−0.270129	−	0.897853i
$323$	35.3839			1.96881
$324$	−1.51154	−	11.6841i	−0.0839746	−	0.649118i
$325$	0.552087	+	0.956243i	0.0306243	+	0.0530428i
$326$	8.59334	−	14.8841i	0.475941	−	0.824354i
$327$	19.0727	−	3.13791i	1.05472	−	0.173527i
$328$	15.4978	−	26.8430i	0.855723	−	1.48216i
$329$	−6.07676	−	1.43150i	−0.335022	−	0.0789214i
$330$	−1.07724	+	2.85730i	−0.0593003	+	0.157289i
$331$	−15.1335			−0.831812			−0.415906	−	0.909408i	$-0.636536\pi$
$331$	−15.1335			−0.831812			−0.415906	+	0.909408i	$0.636536\pi$
$332$	3.85965	+	6.68511i	0.211826	+	0.366893i
$333$	−10.0175	+	3.38793i	−0.548954	+	0.185657i
$334$	−1.58791	+	2.75034i	−0.0868864	+	0.150492i
$335$	−0.120286	−	0.208341i	−0.00657191	−	0.0113829i
$336$	0.848163	−	1.26160i	0.0462711	−	0.0688257i
$337$	−2.53300	+	4.38728i	−0.137981	+	0.238990i	−0.926732	−	0.375722i	$-0.877395\pi$
$337$	−2.53300	+	4.38728i	−0.137981	+	0.238990i	0.788751	+	0.614713i	$0.210728\pi$
$338$	4.89628	+	8.48061i	0.266323	+	0.461284i
$339$	5.00860	+	6.11000i	0.272030	+	0.331850i
$340$	4.18465	−	7.24802i	0.226944	−	0.393079i
$341$	11.4648	−	19.8576i	0.620855	−	1.07535i
$342$	13.0738	−	4.42157i	0.706948	−	0.239091i
$343$	−14.2357	−	11.8467i	−0.768657	−	0.639661i
$344$	12.4418	+	21.5499i	0.670819	+	1.16189i
$345$	8.40041	+	10.2477i	0.452263	+	0.551716i
$346$	−5.66400			−0.304499
$347$	18.4167			0.988662			0.494331	−	0.869274i	$-0.335413\pi$
$347$	18.4167			0.988662			0.494331	+	0.869274i	$0.335413\pi$
$348$	−0.719324	+	0.118346i	−0.0385598	+	0.00634400i
$349$	−0.379235	−	0.656854i	−0.0203000	−	0.0351606i	0.855697	−	0.517477i	$-0.173129\pi$
$349$	−0.379235	−	0.656854i	−0.0203000	−	0.0351606i	−0.875997	+	0.482317i	$0.839795\pi$
$350$	1.50703	−	1.60171i	0.0805541	−	0.0856150i
$351$	0.197388	−	5.73406i	0.0105358	−	0.306061i
$352$	−6.12632	+	10.6111i	−0.326534	+	0.565573i
$353$	9.00633	−	15.5994i	0.479359	−	0.830273i	−0.520361	−	0.853946i	$-0.674203\pi$
$353$	9.00633	−	15.5994i	0.479359	−	0.830273i	0.999720	+	0.0236728i	$0.00753600\pi$
$354$	−2.80210	+	7.43233i	−0.148930	+	0.395024i
$355$	−1.64200	−	2.84403i	−0.0871483	−	0.150945i
$356$	−3.59219	+	6.22186i	−0.190386	+	0.329758i
$357$	−29.2299	−	1.99921i	−1.54701	−	0.105809i
$358$	5.26304	+	9.11585i	0.278160	+	0.481788i
$359$	−12.0330	+	20.8418i	−0.635080	+	1.09999i	0.351418	+	0.936219i	$0.385699\pi$
$359$	−12.0330	+	20.8418i	−0.635080	+	1.09999i	−0.986498	+	0.163772i	$0.947634\pi$
$360$	1.61893	−	8.09140i	0.0853252	−	0.426454i
$361$	−5.81504	−	10.0719i	−0.306055	−	0.530102i
$362$	−5.41081			−0.284386
$363$	−11.1116	+	1.82812i	−0.583207	+	0.0959514i
$364$	2.62057	−	2.78521i	0.137355	−	0.145985i
$365$	−3.39398	+	5.87854i	−0.177649	+	0.307697i
$366$	3.03713	−	8.05572i	0.158753	−	0.421079i
$367$	−12.8661	+	22.2847i	−0.671605	+	1.16325i	0.305844	+	0.952082i	$0.401061\pi$
$367$	−12.8661	+	22.2847i	−0.671605	+	1.16325i	−0.977449	+	0.211172i	$0.932272\pi$
$368$	1.26893	+	2.19786i	0.0661478	+	0.114571i
$369$	32.0243	−	10.8307i	1.66712	−	0.563822i
$370$	−2.93005			−0.152326
$371$	−7.66809	−	25.4872i	−0.398107	−	1.32323i
$372$	−8.64732	+	22.9363i	−0.448343	+	1.18919i
$373$	−0.911806	−	1.57930i	−0.0472115	−	0.0817728i	0.841454	−	0.540329i	$-0.181700\pi$
$373$	−0.911806	−	1.57930i	−0.0472115	−	0.0817728i	−0.888665	+	0.458556i	$0.848367\pi$
$374$	11.2716			0.582840
$375$	−0.611026	+	1.62069i	−0.0315532	+	0.0836923i
$376$	−6.49047			−0.334721
$377$	−0.355012			−0.0182840
$378$	−11.0498	+	2.91389i	−0.568340	+	0.149874i
$379$	−1.81853			−0.0934118			−0.0467059	−	0.998909i	$-0.514872\pi$
$379$	−1.81853			−0.0934118			−0.0467059	+	0.998909i	$0.514872\pi$
$380$	−7.24489			−0.371655
$381$	0.447912	−	1.18805i	0.0229472	−	0.0608656i
$382$	1.65322			0.0845861
$383$	−1.77194	−	3.06909i	−0.0905419	−	0.156823i	0.817197	−	0.576358i	$-0.195527\pi$
$383$	−1.77194	−	3.06909i	−0.0905419	−	0.156823i	−0.907739	+	0.419535i	$0.862193\pi$
$384$	4.95775	−	13.1500i	0.252999	−	0.671058i
$385$	−5.46203	−	1.28669i	−0.278371	−	0.0655759i
$386$	0.338267			0.0172173
$387$	−5.32466	+	26.6126i	−0.270668	+	1.35279i
$388$	11.2792	+	19.5362i	0.572616	+	0.991800i
$389$	−2.90491	+	5.03144i	−0.147285	+	0.255104i	−0.930223	−	0.366995i	$-0.880387\pi$
$389$	−2.90491	+	5.03144i	−0.147285	+	0.255104i	0.782938	+	0.622099i	$0.213720\pi$
$390$	0.560814	−	1.48751i	0.0283979	−	0.0753231i
$391$	24.4557	−	42.3585i	1.23678	−	2.14216i
$392$	−17.2295	−	8.59447i	−0.870222	−	0.434086i
$393$	13.2714	−	2.18346i	0.669454	−	0.110141i
$394$	−1.61389			−0.0813069
$395$	2.59020	+	4.48636i	0.130327	+	0.225733i
$396$	−7.89033	+	2.66852i	−0.396504	+	0.134098i
$397$	2.08553	−	3.61224i	0.104670	−	0.181293i	−0.808933	−	0.587900i	$-0.799955\pi$
$397$	2.08553	−	3.61224i	0.104670	−	0.181293i	0.913603	+	0.406607i	$0.133288\pi$
$398$	2.22766	+	3.85842i	0.111662	+	0.193405i
$399$	11.1527	+	22.7783i	0.558333	+	1.14034i
$400$	−0.165867	+	0.287290i	−0.00829336	+	0.0143645i
$401$	6.90110	+	11.9530i	0.344624	+	0.596907i	0.985285	−	0.170917i	$-0.0546730\pi$
$401$	6.90110	+	11.9530i	0.344624	+	0.596907i	−0.640661	+	0.767824i	$0.721340\pi$
$402$	−0.122187	+	0.324091i	−0.00609414	+	0.0161642i
$403$	−5.96859	+	10.3379i	−0.297317	+	0.514968i
$404$	−1.34054	+	2.32189i	−0.0666946	+	0.115518i
$405$	7.15247	−	5.46279i	0.355409	−	0.271448i
$406$	0.203716	+	0.677111i	0.0101103	+	0.0336045i
$407$	3.73814	+	6.47466i	0.185293	+	0.320937i
$408$	−30.0551	+	4.94477i	−1.48795	+	0.244803i
$409$	16.1462			0.798379			0.399190	−	0.916868i	$-0.369291\pi$
$409$	16.1462			0.798379			0.399190	+	0.916868i	$0.369291\pi$
$410$	9.36691			0.462599
$411$	−12.2422	−	14.9343i	−0.603863	−	0.736653i
$412$	−0.806503	−	1.39690i	−0.0397335	−	0.0688205i
$413$	−14.2077	−	3.34691i	−0.699115	−	0.164691i
$414$	3.74286	−	18.7067i	0.183951	−	0.919387i
$415$	−2.94842	+	5.10682i	−0.144732	+	0.250684i
$416$	3.18937	−	5.52414i	0.156372	−	0.270843i
$417$	−10.1880	−	12.4283i	−0.498907	−	0.608616i
$418$	−4.87864	−	8.45004i	−0.238622	−	0.413305i
$419$	3.69695	−	6.40330i	0.180608	−	0.312822i	−0.761480	−	0.648188i	$-0.775527\pi$
$419$	3.69695	−	6.40330i	0.180608	−	0.312822i	0.942088	+	0.335367i	$0.108860\pi$
$420$	5.98486	+	0.409341i	0.292031	+	0.0199738i
$421$	−16.2111	−	28.0784i	−0.790080	−	1.36846i	−0.925917	−	0.377727i	$-0.876706\pi$
$421$	−16.2111	−	28.0784i	−0.790080	−	1.36846i	0.135837	−	0.990731i	$-0.456628\pi$
$422$	−0.786339	+	1.36198i	−0.0382784	+	0.0663001i
$423$	−5.31703	−	4.67348i	−0.258523	−	0.227233i
$424$	−13.8352	−	23.9632i	−0.671896	−	1.16376i
$425$	6.39339			0.310125
$426$	−1.66796	+	4.42411i	−0.0808127	+	0.214349i
$427$	15.3994	+	3.62764i	0.745228	+	0.175554i
$428$	1.99711	−	3.45910i	0.0965339	−	0.167202i
$429$	−4.00250	+	0.658506i	−0.193242	+	0.0317929i
$430$	−3.75994	+	6.51241i	−0.181320	+	0.314056i
$431$	−4.44098	−	7.69200i	−0.213914	−	0.370510i	0.739022	−	0.673681i	$-0.235288\pi$
$431$	−4.44098	−	7.69200i	−0.213914	−	0.370510i	−0.952936	+	0.303171i	$0.901955\pi$
$432$	1.52157	−	0.810004i	0.0732067	−	0.0389713i
$433$	−9.75786			−0.468933			−0.234467	−	0.972124i	$-0.575334\pi$
$433$	−9.75786			−0.468933			−0.234467	+	0.972124i	$0.575334\pi$
$434$	23.1424	+	5.45166i	1.11087	+	0.261688i
$435$	−0.353043	−	0.430677i	−0.0169271	−	0.0206494i
$436$	7.30430	+	12.6514i	0.349812	+	0.605893i
$437$	−42.3402			−2.02541
$438$	9.64322	−	1.58654i	0.460771	−	0.0758077i
$439$	−8.30025			−0.396149			−0.198075	−	0.980187i	$-0.563469\pi$
$439$	−8.30025			−0.396149			−0.198075	+	0.980187i	$0.563469\pi$
$440$	−5.83389			−0.278120
$441$	−7.92603	−	19.4468i	−0.377430	−	0.926038i
$442$	−5.86800			−0.279113
$443$	−20.7206			−0.984468			−0.492234	−	0.870463i	$-0.663820\pi$
$443$	−20.7206			−0.984468			−0.492234	+	0.870463i	$0.663820\pi$
$444$	−5.06679	−	6.18098i	−0.240459	−	0.293336i
$445$	−5.48822			−0.260167
$446$	3.15400	+	5.46289i	0.149346	+	0.258675i
$447$	17.1865	−	2.82759i	0.812895	−	0.133740i
$448$	−10.6577	−	2.51064i	−0.503529	−	0.118617i
$449$	−9.44816			−0.445886			−0.222943	−	0.974831i	$-0.571566\pi$
$449$	−9.44816			−0.445886			−0.222943	+	0.974831i	$0.571566\pi$
$450$	2.36225	−	0.798918i	0.111358	−	0.0376613i
$451$	−11.9503	−	20.6984i	−0.562716	−	0.974652i
$452$	−2.98554	+	5.17111i	−0.140428	+	0.243228i
$453$	−21.7714	−	26.5589i	−1.02291	−	1.24785i
$454$	−2.89691	+	5.01760i	−0.135959	+	0.235488i
$455$	2.84354	+	0.669853i	0.133307	+	0.0314032i
$456$	16.7156	+	20.3913i	0.782779	+	0.954912i
$457$	−21.3617			−0.999258			−0.499629	−	0.866240i	$-0.666530\pi$
$457$	−21.3617			−0.999258			−0.499629	+	0.866240i	$0.666530\pi$
$458$	6.07531	+	10.5227i	0.283880	+	0.491695i
$459$	−28.1818	−	17.5905i	−1.31541	−	0.821053i
$460$	−5.00733	+	8.67296i	−0.233468	+	0.404379i
$461$	15.9033	+	27.5453i	0.740690	+	1.28291i	0.952181	+	0.305533i	$0.0988347\pi$
$461$	15.9033	+	27.5453i	0.740690	+	1.28291i	−0.211491	+	0.977380i	$0.567832\pi$
$462$	3.55271	+	7.25606i	0.165287	+	0.337582i
$463$	−8.36330	+	14.4857i	−0.388675	+	0.673206i	−0.992272	−	0.124085i	$-0.960401\pi$
$463$	−8.36330	+	14.4857i	−0.388675	+	0.673206i	0.603596	+	0.797290i	$0.293734\pi$
$464$	−0.0533293	−	0.0923691i	−0.00247575	−	0.00428813i
$465$	−18.4767	+	3.03986i	−0.856839	+	0.140970i
$466$	−3.08965	+	5.35143i	−0.143125	+	0.247900i
$467$	−12.1438	+	21.0337i	−0.561950	+	0.973326i	0.435377	+	0.900248i	$0.356615\pi$
$467$	−12.1438	+	21.0337i	−0.561950	+	0.973326i	−0.997326	+	0.0730771i	$0.976718\pi$
$468$	4.10771	−	1.38924i	0.189879	−	0.0642174i
$469$	−0.619534	−	0.145944i	−0.0286074	−	0.00673907i
$470$	−0.980714	−	1.69865i	−0.0452370	−	0.0783527i
$471$	14.0456	−	37.2548i	0.647188	−	1.71661i
$472$	−15.1750			−0.698485
$473$	19.1876			0.882249
$474$	2.63114	−	6.97888i	0.120852	−	0.320551i
$475$	−2.76722	−	4.79297i	−0.126969	−	0.219917i
$476$	−6.37951	−	21.2042i	−0.292404	−	0.971893i
$477$	5.92096	−	29.5929i	0.271102	−	1.35496i
$478$	5.45740	−	9.45250i	0.249616	−	0.432347i
$479$	−11.6954	+	20.2570i	−0.534377	+	0.925568i	0.464817	+	0.885407i	$0.346120\pi$
$479$	−11.6954	+	20.2570i	−0.534377	+	0.925568i	−0.999193	+	0.0401605i	$0.987213\pi$
$480$	9.87320	−	1.62437i	0.450648	−	0.0741422i
$481$	−1.94608	−	3.37071i	−0.0887337	−	0.153691i
$482$	5.82481	−	10.0889i	0.265313	−	0.459536i
$483$	34.9764	+	2.39225i	1.59148	+	0.108851i
$484$	−4.25543	−	7.37062i	−0.193429	−	0.335028i
$485$	−8.61631	+	14.9239i	−0.391247	+	0.677659i
$486$	−12.6108	−	2.97780i	−0.572038	−	0.135076i
$487$	−20.2505	−	35.0749i	−0.917637	−	1.58939i	−0.802993	−	0.595988i	$-0.796761\pi$
$487$	−20.2505	−	35.0749i	−0.917637	−	1.58939i	−0.114644	−	0.993407i	$-0.536573\pi$
$488$	16.4478			0.744556
$489$	22.7035	+	27.6960i	1.02669	+	1.25245i
$490$	−0.354098	−	5.80783i	−0.0159965	−	0.262371i
$491$	2.66995	−	4.62449i	0.120493	−	0.208700i	−0.799469	−	0.600707i	$-0.794886\pi$
$491$	2.66995	−	4.62449i	0.120493	−	0.208700i	0.919962	+	0.392007i	$0.128219\pi$
$492$	16.1977	+	19.7596i	0.730250	+	0.890832i
$493$	−1.02780	+	1.78019i	−0.0462896	+	0.0801759i
$494$	2.53982	+	4.39910i	0.114272	+	0.197925i
$495$	−4.77915	−	4.20071i	−0.214807	−	0.188808i
$496$	−3.58637			−0.161033
$497$	−8.45716	−	1.99226i	−0.379355	−	0.0893649i
$498$	8.37728	−	1.37826i	0.375395	−	0.0617613i
$499$	−17.4767	−	30.2705i	−0.782363	−	1.35509i	−0.930562	−	0.366135i	$-0.880681\pi$
$499$	−17.4767	−	30.2705i	−0.782363	−	1.35509i	0.148198	−	0.988958i	$-0.452653\pi$
$500$	−1.30905			−0.0585427
$501$	−4.19522	−	5.11776i	−0.187429	−	0.228644i
$502$	1.17856			0.0526016
$503$	16.5844			0.739462			0.369731	−	0.929139i	$-0.379450\pi$
$503$	16.5844			0.739462			0.369731	+	0.929139i	$0.379450\pi$
$504$	−12.6563	−	17.7893i	−0.563756	−	0.792400i
$505$	−2.04811			−0.0911397
$506$	−13.4875			−0.599595
$507$	−20.1343	+	3.31256i	−0.894194	+	0.147116i
$508$	0.959603			0.0425755
$509$	−17.8172	−	30.8602i	−0.789732	−	1.36786i	−0.926131	−	0.377201i	$-0.876886\pi$
$509$	−17.8172	−	30.8602i	−0.789732	−	1.36786i	0.136400	−	0.990654i	$-0.456447\pi$
$510$	−5.83545	−	7.11867i	−0.258398	−	0.315220i
$511$	5.17413	+	17.1978i	0.228890	+	0.760784i
$512$	3.74134			0.165345
$513$	−0.989368	+	28.7408i	−0.0436817	+	1.26894i
$514$	3.38455	+	5.86221i	0.149286	+	0.258571i
$515$	0.616096	−	1.06711i	0.0271484	−	0.0470224i
$516$	−20.2399	+	3.32994i	−0.891011	+	0.146592i
$517$	−2.50238	+	4.33425i	−0.110055	+	0.190620i
$518$	−5.31221	+	5.64596i	−0.233405	+	0.248069i
$519$	4.16353	−	11.0434i	0.182758	−	0.484751i
$520$	3.03713			0.133187
$521$	8.85326	+	15.3343i	0.387868	+	0.671807i	0.992163	−	0.124954i	$-0.0398782\pi$
$521$	8.85326	+	15.3343i	0.387868	+	0.671807i	−0.604294	+	0.796761i	$0.706545\pi$
$522$	−0.157301	+	0.786186i	−0.00688486	+	0.0344104i
$523$	−14.4254	+	24.9856i	−0.630780	+	1.09254i	0.356613	+	0.934252i	$0.383931\pi$
$523$	−14.4254	+	24.9856i	−0.630780	+	1.09254i	−0.987393	+	0.158290i	$0.949402\pi$
$524$	5.08258	+	8.80328i	0.222033	+	0.384573i
$525$	2.01514	+	4.11573i	0.0879480	+	0.179625i
$526$	−5.09609	+	8.82668i	−0.222200	+	0.384861i
$527$	34.5594	+	59.8586i	1.50543	+	2.60748i
$528$	−0.772583	−	0.942474i	−0.0336223	−	0.0410159i
$529$	−17.7636	+	30.7674i	−0.772329	+	1.33771i
$530$	4.18101	−	7.24172i	0.181611	−	0.314560i
$531$	−12.4314	−	10.9268i	−0.539477	−	0.474182i
$532$	−13.1351	+	13.9603i	−0.569477	+	0.605255i
$533$	6.22131	+	10.7756i	0.269475	+	0.466744i
$534$	5.00928	+	6.11082i	0.216773	+	0.264441i
$535$	3.05122			0.131916
$536$	−0.661713			−0.0285817
$537$	−21.6424	+	3.56069i	−0.933939	+	0.153655i
$538$	−1.30528	−	2.26082i	−0.0562748	−	0.0974708i
$539$	−12.3821	+	8.19207i	−0.533333	+	0.352857i
$540$	5.77025	+	3.60167i	0.248312	+	0.154991i
$541$	−22.3771	+	38.7583i	−0.962068	+	1.66635i	−0.244775	+	0.969580i	$0.578714\pi$
$541$	−22.3771	+	38.7583i	−0.962068	+	1.66635i	−0.717293	+	0.696771i	$0.754619\pi$
$542$	2.86829	−	4.96802i	0.123203	−	0.213395i
$543$	3.97741	−	10.5497i	0.170687	−	0.452732i
$544$	−18.4671	−	31.9859i	−0.791769	−	1.37138i
$545$	−5.57983	+	9.66454i	−0.239013	+	0.413983i
$546$	−1.84954	−	3.77751i	−0.0791532	−	0.161663i
$547$	4.64026	+	8.03717i	0.198403	+	0.343645i	0.948011	−	0.318238i	$-0.103091\pi$
$547$	4.64026	+	8.03717i	0.198403	+	0.343645i	−0.749608	+	0.661883i	$0.769758\pi$
$548$	7.29736	−	12.6394i	0.311728	−	0.539928i
$549$	13.4741	+	11.8433i	0.575061	+	0.505459i
$550$	−0.881504	−	1.52681i	−0.0375875	−	0.0651034i
$551$	1.77942			0.0758060
$552$	35.9638	−	5.91689i	1.53072	−	0.251840i
$553$	13.3409	+	3.14272i	0.567312	+	0.133642i
$554$	−4.73076	+	8.19391i	−0.200991	+	0.348126i
$555$	2.15384	−	5.71287i	0.0914253	−	0.242498i
$556$	6.07286	−	10.5185i	0.257547	−	0.446084i
$557$	−5.99025	−	10.3754i	−0.253815	−	0.439621i	0.710758	−	0.703437i	$-0.248352\pi$
$557$	−5.99025	−	10.3754i	−0.253815	−	0.439621i	−0.964573	+	0.263816i	$0.915019\pi$
$558$	20.2490	+	17.7982i	0.857210	+	0.753459i
$559$	−9.98911			−0.422494
$560$	0.252865	+	0.840472i	0.0106855	+	0.0355164i
$561$	−8.28558	+	21.9768i	−0.349818	+	0.927862i
$562$	−5.22371	−	9.04774i	−0.220349	−	0.381656i
$563$	−1.19118			−0.0502023			−0.0251012	−	0.999685i	$-0.507991\pi$
$563$	−1.19118			−0.0502023			−0.0251012	+	0.999685i	$0.507991\pi$
$564$	1.88742	−	5.00621i	0.0794746	−	0.210800i
$565$	−4.56137			−0.191898
$566$	4.85340			0.204003
$567$	2.44117	−	23.6863i	0.102520	−	0.994731i
$568$	−9.03294			−0.379014
$569$	37.0794			1.55445			0.777224	−	0.629224i	$-0.216627\pi$
$569$	37.0794			1.55445			0.777224	+	0.629224i	$0.216627\pi$
$570$	−2.81096	+	7.45584i	−0.117738	+	0.312291i
$571$	−15.1618			−0.634503			−0.317252	−	0.948341i	$-0.602760\pi$
$571$	−15.1618			−0.634503			−0.317252	+	0.948341i	$0.602760\pi$
$572$	−1.53284	−	2.65496i	−0.0640914	−	0.111010i
$573$	−1.21526	+	3.22337i	−0.0507681	+	0.134658i
$574$	16.9823	−	18.0492i	0.708827	−	0.753360i
$575$	−7.65030			−0.319040
$576$	−9.32525	−	8.19657i	−0.388552	−	0.341524i
$577$	−1.35090	−	2.33983i	−0.0562387	−	0.0974084i	0.836535	−	0.547913i	$-0.184577\pi$
$577$	−1.35090	−	2.33983i	−0.0562387	−	0.0974084i	−0.892774	+	0.450504i	$0.851244\pi$
$578$	−9.92300	+	17.1871i	−0.412742	+	0.714891i
$579$	−0.248655	+	0.659536i	−0.0103338	+	0.0274094i
$580$	0.210442	−	0.364497i	0.00873815	−	0.0151349i
$581$	4.49488	+	14.9401i	0.186479	+	0.619819i
$582$	24.4813	−	4.02775i	1.01478	−	0.166956i
$583$	−21.3364			−0.883664
$584$	9.33544	+	16.1695i	0.386303	+	0.669097i
$585$	2.48803	+	2.18689i	0.102867	+	0.0904170i
$586$	−10.8390	+	18.7737i	−0.447755	+	0.775535i
$587$	−21.6593	−	37.5149i	−0.893973	−	1.54841i	−0.835070	−	0.550144i	$-0.814573\pi$
$587$	−21.6593	−	37.5149i	−0.893973	−	1.54841i	−0.0589034	−	0.998264i	$-0.518760\pi$
$588$	11.6394	−	10.7902i	0.480000	−	0.444979i
$589$	29.9163	−	51.8166i	1.23268	−	2.13507i
$590$	−2.29295	−	3.97150i	−0.0943991	−	0.163504i
$591$	1.18635	−	3.14669i	0.0487999	−	0.129438i
$592$	0.584674	−	1.01269i	0.0240300	−	0.0416211i
$593$	22.0807	−	38.2449i	0.906746	−	1.57053i	0.0881899	−	0.996104i	$-0.471892\pi$
$593$	22.0807	−	38.2449i	0.906746	−	1.57053i	0.818556	−	0.574427i	$-0.194775\pi$
$594$	−0.315165	+	9.15544i	−0.0129314	+	0.375652i
$595$	11.5913	−	12.3195i	0.475196	−	0.505051i
$596$	6.58196	+	11.4003i	0.269607	+	0.466974i
$597$	−9.16047	+	1.50711i	−0.374913	+	0.0616821i
$598$	7.02163			0.287136
$599$	18.7916			0.767803			0.383901	−	0.923374i	$-0.374580\pi$
$599$	18.7916			0.767803			0.383901	+	0.923374i	$0.374580\pi$
$600$	3.02028	+	3.68444i	0.123302	+	0.150417i
$601$	11.6864	+	20.2414i	0.476696	+	0.825663i	0.999643	−	0.0267027i	$-0.00850074\pi$
$601$	11.6864	+	20.2414i	0.476696	+	0.825663i	−0.522947	+	0.852365i	$0.675167\pi$
$602$	5.73204	+	19.0521i	0.233620	+	0.776507i
$603$	−0.542079	−	0.476469i	−0.0220752	−	0.0194033i
$604$	12.9775	−	22.4777i	0.528048	−	0.914606i
$605$	3.25076	−	5.63049i	0.132162	−	0.228912i
$606$	1.86938	+	2.28045i	0.0759382	+	0.0926371i
$607$	−8.05399	−	13.9499i	−0.326901	−	0.566210i	0.654994	−	0.755634i	$-0.272671\pi$
$607$	−8.05399	−	13.9499i	−0.326901	−	0.566210i	−0.981895	+	0.189424i	$0.939338\pi$
$608$	−15.9860	+	27.6886i	−0.648319	+	1.12292i
$609$	−1.46995	−	0.100539i	−0.0595653	−	0.00407403i
$610$	2.48527	+	4.30461i	0.100626	+	0.174289i
$611$	1.30274	−	2.25641i	0.0527033	−	0.0912847i
$612$	4.92597	−	24.6199i	0.199121	−	0.995202i
$613$	2.69429	+	4.66665i	0.108821	+	0.188484i	0.915293	−	0.402789i	$-0.131959\pi$
$613$	2.69429	+	4.66665i	0.108821	+	0.188484i	−0.806472	+	0.591273i	$0.798626\pi$
$614$	17.2006			0.694159
$615$	−6.88548	+	18.2631i	−0.277649	+	0.736441i
$616$	−10.5769	+	11.2414i	−0.426155	+	0.452929i
$617$	12.2729	−	21.2573i	0.494088	−	0.855785i	−0.505889	−	0.862599i	$-0.668835\pi$
$617$	12.2729	−	21.2573i	0.494088	−	0.855785i	0.999977	+	0.00681335i	$0.00216877\pi$
$618$	−1.75049	+	0.287998i	−0.0704152	+	0.0115850i
$619$	2.54774	−	4.41282i	0.102402	−	0.177366i	−0.810272	−	0.586055i	$-0.800680\pi$
$619$	2.54774	−	4.41282i	0.102402	−	0.177366i	0.912674	+	0.408689i	$0.134014\pi$
$620$	−7.07607	−	12.2561i	−0.284182	−	0.492218i
$621$	33.7222	+	21.0487i	1.35322	+	0.844655i
$622$	−15.5669			−0.624178
$623$	−9.95020	+	10.5753i	−0.398646	+	0.423692i
$624$	0.402207	+	0.490653i	0.0161012	+	0.0196418i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	27.3249			1.09212
$627$	20.0617	−	3.30062i	0.801187	−	0.131814i
$628$	30.0912			1.20077
$629$	−22.5364			−0.898585
$630$	2.74334	−	6.00030i	0.109297	−	0.239058i
$631$	30.2028			1.20236			0.601178	−	0.799115i	$-0.294698\pi$
$631$	30.2028			1.20236			0.601178	+	0.799115i	$0.294698\pi$
$632$	14.2492			0.566801
$633$	−2.07749	−	2.53434i	−0.0825730	−	0.100731i
$634$	22.1796			0.880865
$635$	0.366525	+	0.634840i	0.0145451	+	0.0251928i
$636$	22.5065	−	3.70285i	0.892441	−	0.146828i
$637$	6.44611	−	4.26480i	0.255404	−	0.168977i
$638$	0.566839			0.0224414
$639$	−7.39982	−	6.50419i	−0.292733	−	0.257302i
$640$	4.05691	+	7.02677i	0.160363	+	0.277757i
$641$	−1.01732	+	1.76204i	−0.0401816	+	0.0695965i	−0.885417	−	0.464798i	$-0.846127\pi$
$641$	−1.01732	+	1.76204i	−0.0401816	+	0.0695965i	0.845235	+	0.534394i	$0.179460\pi$
$642$	−2.78495	−	3.39736i	−0.109913	−	0.134083i
$643$	−7.85890	+	13.6120i	−0.309925	+	0.536805i	−0.978346	−	0.206978i	$-0.933637\pi$
$643$	−7.85890	+	13.6120i	−0.309925	+	0.536805i	0.668421	+	0.743783i	$0.266971\pi$
$644$	7.63369	+	25.3729i	0.300810	+	0.999830i
$645$	−9.93370	−	12.1181i	−0.391139	−	0.477151i
$646$	29.4122			1.15721
$647$	−0.508715	−	0.881121i	−0.0199997	−	0.0346404i	0.855852	−	0.517220i	$-0.173033\pi$
$647$	−0.508715	−	0.881121i	−0.0199997	−	0.0346404i	−0.875852	+	0.482580i	$0.839700\pi$
$648$	−3.17606	−	24.5507i	−0.124767	−	0.964443i
$649$	−5.85066	+	10.1336i	−0.229658	+	0.397780i
$650$	0.458912	+	0.794859i	0.0180000	+	0.0311769i
$651$	−27.6410	+	41.1144i	−1.08334	+	1.61140i
$652$	−13.5331	+	23.4401i	−0.529998	+	0.917984i
$653$	−8.17390	−	14.1576i	−0.319869	−	0.554030i	0.660591	−	0.750746i	$-0.270306\pi$
$653$	−8.17390	−	14.1576i	−0.319869	−	0.554030i	−0.980461	+	0.196716i	$0.936972\pi$
$654$	15.8538	−	2.60833i	0.619933	−	0.101994i
$655$	−3.88263	+	6.72492i	−0.151707	+	0.262764i
$656$	−1.86911	+	3.23740i	−0.0729765	+	0.126399i
$657$	−3.99523	+	19.9681i	−0.155869	+	0.779030i
$658$	−5.05119	−	1.18991i	−0.196916	−	0.0463876i
$659$	−17.4617	−	30.2445i	−0.680210	−	1.17816i	−0.974917	−	0.222570i	$-0.928555\pi$
$659$	−17.4617	−	30.2445i	−0.680210	−	1.17816i	0.294707	−	0.955588i	$-0.404778\pi$
$660$	1.69648	−	4.49978i	0.0660356	−	0.175154i
$661$	39.3332			1.52988			0.764942	−	0.644099i	$-0.222767\pi$
$661$	39.3332			1.52988			0.764942	+	0.644099i	$0.222767\pi$
$662$	−12.5794			−0.488914
$663$	4.31348	−	11.4411i	0.167522	−	0.444337i
$664$	8.10991	+	14.0468i	0.314725	+	0.545120i
$665$	−14.2526	−	3.35750i	−0.552694	−	0.130198i
$666$	−8.32683	+	2.81615i	−0.322658	+	0.109124i
$667$	1.22986	−	2.13017i	0.0476202	−	0.0824806i
$668$	2.50070	−	4.33134i	0.0967549	−	0.167584i
$669$	−12.9697	+	2.13383i	−0.501439	+	0.0824986i
$670$	−0.0999853	−	0.173180i	−0.00386277	−	0.00669051i
$671$	6.34139	−	10.9836i	0.244807	−	0.424017i
$672$	14.7702	−	21.9698i	0.569772	−	0.847504i
$673$	−11.7856	−	20.4133i	−0.454301	−	0.786873i	0.544346	−	0.838861i	$-0.316778\pi$
$673$	−11.7856	−	20.4133i	−0.454301	−	0.786873i	−0.998648	+	0.0519875i	$0.983444\pi$
$674$	−2.10551	+	3.64684i	−0.0811010	+	0.140471i
$675$	−0.178766	+	5.19308i	−0.00688069	+	0.199882i
$676$	−7.71086	−	13.3556i	−0.296571	−	0.513677i
$677$	−10.2290			−0.393132			−0.196566	−	0.980491i	$-0.562979\pi$
$677$	−10.2290			−0.393132			−0.196566	+	0.980491i	$0.562979\pi$
$678$	4.16331	+	5.07882i	0.159891	+	0.195051i
$679$	13.1356	+	43.6600i	0.504098	+	1.67552i
$680$	8.79279	−	15.2296i	0.337188	−	0.584027i
$681$	−7.65360	−	9.33663i	−0.293287	−	0.357780i
$682$	9.52991	−	16.5063i	0.364919	−	0.632059i
$683$	−23.4175	−	40.5602i	−0.896044	−	1.55199i	−0.832507	−	0.554015i	$-0.813095\pi$
$683$	−23.4175	−	40.5602i	−0.896044	−	1.55199i	−0.0635371	−	0.997979i	$-0.520238\pi$
$684$	−20.5891	+	6.96325i	−0.787242	+	0.266247i
$685$	11.1490			0.425983
$686$	−11.8332	−	9.84734i	−0.451793	−	0.375973i
$687$	−24.9826	+	4.11023i	−0.953145	+	0.156815i
$688$	−1.50055	−	2.59902i	−0.0572078	−	0.0990869i
$689$	11.1078			0.423172
$690$	6.98268	+	8.51817i	0.265826	+	0.324281i
$691$	3.94268			0.149987			0.0749934	−	0.997184i	$-0.476106\pi$
$691$	3.94268			0.149987			0.0749934	+	0.997184i	$0.476106\pi$
$692$	8.91989			0.339083
$693$	−16.7591	+	1.59308i	−0.636624	+	0.0605161i
$694$	15.3086			0.581105
$695$	9.27824			0.351944
$696$	−1.51144	+	0.248668i	−0.0572912	+	0.00942575i
$697$	72.0453			2.72891
$698$	−0.315232	−	0.545997i	−0.0119317	−	0.0206663i
$699$	−8.16281	−	9.95781i	−0.308746	−	0.376639i
$700$	−2.37333	+	2.52244i	−0.0897034	+	0.0953391i
$701$	14.3063			0.540343			0.270172	−	0.962812i	$-0.412920\pi$
$701$	14.3063			0.540343			0.270172	+	0.962812i	$0.412920\pi$
$702$	0.164075	−	4.76633i	0.00619262	−	0.179893i
$703$	9.75433	+	16.8950i	0.367892	+	0.637207i
$704$	−4.38879	+	7.60161i	−0.165409	+	0.286496i
$705$	4.03285	−	0.663498i	0.151886	−	0.0249888i
$706$	7.48634	−	12.9667i	0.281752	−	0.488009i
$707$	−3.71324	+	3.94653i	−0.139651	+	0.148425i
$708$	4.41285	−	11.7047i	0.165845	−	0.439890i
$709$	−9.48107			−0.356069			−0.178035	−	0.984024i	$-0.556974\pi$
$709$	−9.48107			−0.356069			−0.178035	+	0.984024i	$0.556974\pi$
$710$	−1.36488	−	2.36404i	−0.0512231	−	0.0887210i
$711$	11.6730	+	10.2601i	0.437771	+	0.384786i
$712$	−7.54792	+	13.0734i	−0.282870	+	0.489946i
$713$	−41.3536	−	71.6265i	−1.54870	−	2.68243i
$714$	−24.2968	−	1.66181i	−0.909285	−	0.0621915i
$715$	1.17095	−	2.02815i	0.0437912	−	0.0758486i
$716$	−8.28843	−	14.3560i	−0.309753	−	0.536509i
$717$	14.4184	+	17.5890i	0.538464	+	0.656872i
$718$	−10.0022	+	17.3244i	−0.373280	+	0.646541i
$719$	−24.8737	+	43.0826i	−0.927634	+	1.60671i	−0.140365	+	0.990100i	$0.544828\pi$
$719$	−24.8737	+	43.0826i	−0.927634	+	1.60671i	−0.787269	+	0.616610i	$0.788506\pi$
$720$	−0.195251	+	0.975862i	−0.00727658	+	0.0363682i
$721$	−0.939239	−	3.12184i	−0.0349791	−	0.116263i
$722$	−4.83364	−	8.37211i	−0.179889	−	0.311578i
$723$	15.3891	+	18.7731i	0.572325	+	0.698180i
$724$	8.52115			0.316686
$725$	0.321518			0.0119409
$726$	−9.23630	+	1.51959i	−0.342791	+	0.0563973i
$727$	15.7849	+	27.3403i	0.585431	+	1.01400i	0.994822	+	0.101637i	$0.0324079\pi$
$727$	15.7849	+	27.3403i	0.585431	+	1.01400i	−0.409391	+	0.912359i	$0.634259\pi$
$728$	5.50634	−	5.85229i	0.204079	−	0.216900i
$729$	15.0760	−	22.3990i	0.558370	−	0.829592i
$730$	−2.82118	+	4.88643i	−0.104417	+	0.180855i
$731$	−28.9195	+	50.0900i	−1.06963	+	1.85265i
$732$	−4.78298	+	12.6865i	−0.176784	+	0.468905i
$733$	−13.0984	−	22.6870i	−0.483799	−	0.837965i	0.516027	−	0.856572i	$-0.327410\pi$
$733$	−13.0984	−	22.6870i	−0.483799	−	0.837965i	−0.999827	+	0.0186069i	$0.994077\pi$
$734$	−10.6947	+	18.5238i	−0.394749	+	0.683725i
$735$	11.5841	+	3.57885i	0.427287	+	0.132008i
$736$	22.0976	+	38.2742i	0.814529	+	1.41081i
$737$	−0.255121	+	0.441883i	−0.00939752	+	0.0162770i
$738$	26.6196	−	9.00278i	0.979879	−	0.331397i
$739$	−12.5214	−	21.6876i	−0.460606	−	0.797793i	0.538385	−	0.842699i	$-0.319034\pi$
$739$	−12.5214	−	21.6876i	−0.460606	−	0.797793i	−0.998991	+	0.0449061i	$0.985701\pi$
$740$	4.61436			0.169627
$741$	−10.4441	+	1.71831i	−0.383675	+	0.0631236i
$742$	−6.37396	−	21.1857i	−0.233995	−	0.777753i
$743$	−16.5633	+	28.6884i	−0.607648	+	1.05248i	0.383979	+	0.923342i	$0.374553\pi$
$743$	−16.5633	+	28.6884i	−0.607648	+	1.05248i	−0.991627	+	0.129135i	$0.958780\pi$
$744$	−18.1698	+	48.1938i	−0.666136	+	1.76687i
$745$	−5.02802	+	8.70879i	−0.184212	+	0.319065i
$746$	−0.757922	−	1.31276i	−0.0277495	−	0.0480635i
$747$	−3.47075	+	17.3467i	−0.126988	+	0.634684i
$748$	−17.7509			−0.649039
$749$	5.53190	−	5.87944i	0.202131	−	0.214830i
$750$	−0.507903	+	1.34717i	−0.0185460	+	0.0491917i
$751$	6.69238	+	11.5915i	0.244208	+	0.422981i	0.961909	−	0.273371i	$-0.0881386\pi$
$751$	6.69238	+	11.5915i	0.244208	+	0.422981i	−0.717700	+	0.696352i	$0.754805\pi$
$752$	0.782783			0.0285451
$753$	−0.866340	+	2.29789i	−0.0315712	+	0.0837399i
$754$	−0.295097			−0.0107468
$755$	19.8273			0.721590
$756$	17.4016	−	4.58891i	0.632891	−	0.166897i
$757$	17.7766			0.646100			0.323050	−	0.946382i	$-0.395292\pi$
$757$	17.7766			0.646100			0.323050	+	0.946382i	$0.395292\pi$
$758$	−1.51162			−0.0549046
$759$	9.91450	−	26.2974i	0.359873	−	0.954534i
$760$	−15.2230			−0.552196
$761$	22.8022	+	39.4945i	0.826577	+	1.43167i	0.900708	+	0.434425i	$0.143049\pi$
$761$	22.8022	+	39.4945i	0.826577	+	1.43167i	−0.0741305	+	0.997249i	$0.523618\pi$
$762$	0.372319	−	0.987543i	0.0134877	−	0.0357749i
$763$	8.50646	+	28.2737i	0.307955	+	1.02358i
$764$	−2.60355			−0.0941933
$765$	18.1692	−	6.14485i	0.656909	−	0.222168i
$766$	−1.47289	−	2.55112i	−0.0532178	−	0.0921759i
$767$	3.04586	−	5.27558i	0.109980	−	0.190490i
$768$	9.17848	−	24.3451i	0.331200	−	0.878480i
$769$	−3.57492	+	6.19195i	−0.128915	+	0.223287i	−0.923256	−	0.384184i	$-0.874483\pi$
$769$	−3.57492	+	6.19195i	−0.128915	+	0.223287i	0.794341	+	0.607471i	$0.207816\pi$
$770$	−4.54021	−	1.06954i	−0.163618	−	0.0385435i
$771$	−13.9178	+	2.28981i	−0.501237	+	0.0824653i
$772$	−0.532716			−0.0191729
$773$	−16.7854	−	29.0732i	−0.603730	−	1.04569i	−0.992251	−	0.124252i	$-0.960347\pi$
$773$	−16.7854	−	29.0732i	−0.603730	−	1.04569i	0.388520	−	0.921440i	$-0.372986\pi$
$774$	−4.42602	+	22.1212i	−0.159090	+	0.795130i
$775$	5.40548	−	9.36257i	0.194171	−	0.336314i
$776$	23.6999	+	41.0495i	0.850778	+	1.47359i
$777$	−7.10328	−	14.5077i	−0.254829	−	0.520463i
$778$	−2.41465	+	4.18229i	−0.0865693	+	0.149942i
$779$	−31.1830	−	54.0106i	−1.11725	−	1.93513i
$780$	−0.883191	+	2.34259i	−0.0316233	+	0.0838782i
$781$	−3.48262	+	6.03207i	−0.124618	+	0.215844i
$782$	20.3283	−	35.2097i	0.726939	−	1.25910i
$783$	−1.41724	−	0.884610i	−0.0506479	−	0.0316134i
$784$	2.07796	+	1.03654i	0.0742130	+	0.0370191i
$785$	11.4935	+	19.9073i	0.410220	+	0.710521i
$786$	11.0316	−	1.81496i	0.393485	−	0.0647375i
$787$	−28.8189			−1.02728			−0.513641	−	0.858005i	$-0.671704\pi$
$787$	−28.8189			−1.02728			−0.513641	+	0.858005i	$0.671704\pi$
$788$	2.54162			0.0905416
$789$	−13.4638	−	16.4245i	−0.479323	−	0.584726i
$790$	2.15305	+	3.72920i	0.0766022	+	0.132679i
$791$	−8.26980	+	8.78936i	−0.294040	+	0.312514i
$792$	−16.5792	+	5.60710i	−0.589115	+	0.199240i
$793$	−3.30133	+	5.71807i	−0.117234	+	0.203055i
$794$	1.73356	−	3.00261i	0.0615216	−	0.106559i
$795$	11.0461	+	13.4752i	0.391766	+	0.477916i
$796$	−3.50820	−	6.07638i	−0.124345	−	0.215372i
$797$	20.2678	−	35.1049i	0.717923	−	1.24348i	−0.243899	−	0.969801i	$-0.578426\pi$
$797$	20.2678	−	35.1049i	0.717923	−	1.24348i	0.961821	−	0.273678i	$-0.0882402\pi$
$798$	9.27046	+	18.9340i	0.328171	+	0.670256i
$799$	−7.54313	−	13.0651i	−0.266857	−	0.462210i
$800$	−2.88846	+	5.00297i	−0.102123	+	0.176882i
$801$	−15.5968	+	5.27487i	−0.551087	+	0.186379i
$802$	5.73641	+	9.93575i	0.202560	+	0.350843i
$803$	14.3970			0.508059
$804$	0.192425	−	0.510391i	0.00678630	−	0.0180001i
$805$	−13.8701	+	14.7415i	−0.488856	+	0.519569i
$806$	−4.96128	+	8.59319i	−0.174754	+	0.302682i
$807$	5.36753	−	0.883086i	0.188946	−	0.0310861i
$808$	−2.81675	+	4.87876i	−0.0990931	+	0.171634i
$809$	−5.11406	−	8.85781i	−0.179801	−	0.311424i	0.762011	−	0.647564i	$-0.224212\pi$
$809$	−5.11406	−	8.85781i	−0.179801	−	0.311424i	−0.941812	+	0.336140i	$0.890879\pi$
$810$	5.94536	−	4.54084i	0.208899	−	0.159549i
$811$	−22.2632			−0.781767			−0.390883	−	0.920440i	$-0.627830\pi$
$811$	−22.2632			−0.781767			−0.390883	+	0.920440i	$0.627830\pi$
$812$	−0.320820	−	1.06634i	−0.0112586	−	0.0374212i
$813$	7.57797	+	9.24436i	0.265771	+	0.324214i
$814$	3.10726	+	5.38194i	0.108909	+	0.188637i
$815$	−20.6762			−0.724255
$816$	3.62479	−	0.596364i	0.126893	−	0.0208769i
$817$	50.0683			1.75167
$818$	13.4212			0.469263
$819$	8.72478	−	0.829359i	0.304868	−	0.0289802i
$820$	−14.7514			−0.515140
$821$	−49.1010			−1.71364			−0.856818	−	0.515619i	$-0.827562\pi$
$821$	−49.1010			−1.71364			−0.856818	+	0.515619i	$0.827562\pi$
$822$	−10.1761	−	12.4138i	−0.354932	−	0.432982i
$823$	40.3779			1.40749			0.703743	−	0.710455i	$-0.251511\pi$
$823$	40.3779			1.40749			0.703743	+	0.710455i	$0.251511\pi$
$824$	−1.69463	−	2.93518i	−0.0590351	−	0.102252i
$825$	3.62488	−	0.596378i	0.126202	−	0.0207632i
$826$	−11.8099	−	2.78206i	−0.410918	−	0.0968002i
$827$	−31.2502			−1.08668			−0.543339	−	0.839514i	$-0.682840\pi$
$827$	−31.2502			−1.08668			−0.543339	+	0.839514i	$0.682840\pi$
$828$	−5.89440	+	29.4601i	−0.204844	+	1.02381i
$829$	−6.35860	−	11.0134i	−0.220843	−	0.382512i	0.734221	−	0.678910i	$-0.237548\pi$
$829$	−6.35860	−	11.0134i	−0.220843	−	0.382512i	−0.955064	+	0.296399i	$0.904214\pi$
$830$	−2.45082	+	4.24495i	−0.0850693	+	0.147344i
$831$	−12.4986	−	15.2470i	−0.433571	−	0.528913i
$832$	2.28481	−	3.95740i	0.0792115	−	0.137198i
$833$	−2.72354	−	44.6708i	−0.0943649	−	1.54775i
$834$	−8.46855	−	10.3308i	−0.293242	−	0.357726i
$835$	3.82062			0.132218
$836$	7.68306	+	13.3075i	0.265724	+	0.460248i
$837$	−49.5869	+	26.3974i	−1.71397	+	0.912427i
$838$	3.07302	−	5.32262i	0.106156	−	0.183867i
$839$	13.8779	+	24.0373i	0.479120	+	0.829859i	0.999713	−	0.0239451i	$-0.00762269\pi$
$839$	13.8779	+	24.0373i	0.479120	+	0.829859i	−0.520594	+	0.853805i	$0.674289\pi$
$840$	12.5754	+	0.860108i	0.433893	+	0.0296765i
$841$	14.4483	−	25.0252i	0.498218	−	0.862938i
$842$	−13.4752	−	23.3396i	−0.464384	−	0.804337i
$843$	21.4807	−	3.53408i	0.739835	−	0.121720i
$844$	1.23836	−	2.14490i	0.0426260	−	0.0738304i
$845$	5.89040	−	10.2025i	0.202636	−	0.350976i
$846$	−4.41968	−	3.88475i	−0.151952	−	0.133560i
$847$	−4.95580	−	16.4721i	−0.170283	−	0.565987i
$848$	1.66859	+	2.89008i	0.0572996	+	0.0992459i
$849$	−3.56766	+	9.46291i	−0.122442	+	0.324766i
$850$	5.31438			0.182282
$851$	26.9670			0.924416
$852$	2.62676	−	6.96726i	0.0899913	−	0.238694i
$853$	16.1750	+	28.0158i	0.553820	+	0.959244i	0.997994	+	0.0633038i	$0.0201637\pi$
$853$	16.1750	+	28.0158i	0.553820	+	0.959244i	−0.444174	+	0.895940i	$0.646503\pi$
$854$	12.8004	+	3.01540i	0.438022	+	0.103185i
$855$	−12.4707	−	10.9614i	−0.426490	−	0.374870i
$856$	4.19633	−	7.26826i	0.143428	−	0.248424i
$857$	5.38683	−	9.33027i	0.184011	−	0.318716i	−0.759232	−	0.650820i	$-0.774425\pi$
$857$	5.38683	−	9.33027i	0.184011	−	0.318716i	0.943243	+	0.332104i	$0.107759\pi$
$858$	−3.32700	+	0.547370i	−0.113582	+	0.0186869i
$859$	14.5903	+	25.2711i	0.497814	+	0.862240i	0.999997	−	0.00252179i	$-0.000802711\pi$
$859$	14.5903	+	25.2711i	0.497814	+	0.862240i	−0.502182	+	0.864762i	$0.667469\pi$
$860$	5.92130	−	10.2560i	0.201915	−	0.349726i
$861$	22.7081	+	46.3790i	0.773889	+	1.58059i
$862$	−3.69148	−	6.39383i	−0.125732	−	0.217775i
$863$	−0.245453	+	0.425137i	−0.00835532	+	0.0144718i	−0.870173	−	0.492747i	$-0.835993\pi$
$863$	−0.245453	+	0.425137i	−0.00835532	+	0.0144718i	0.861818	+	0.507218i	$0.169326\pi$
$864$	26.4971	−	14.1057i	0.901451	−	0.479884i
$865$	3.40700	+	5.90109i	0.115841	+	0.200643i
$866$	−8.11104			−0.275624
$867$	−26.2164	−	31.9814i	−0.890355	−	1.08614i
$868$	−36.4455	−	8.58548i	−1.23704	−	0.291410i
$869$	5.49371	−	9.51539i	0.186361	−	0.322787i
$870$	−0.293460	−	0.357992i	−0.00994923	−	0.0121371i
$871$	0.132816	−	0.230045i	0.00450031	−	0.00779477i
$872$	15.3478	+	26.5832i	0.519742	+	0.900220i
$873$	−10.1427	+	50.6931i	−0.343279	+	1.71570i
$874$	−35.1945			−1.19047
$875$	−2.57526	−	0.606656i	−0.0870597	−	0.0205087i
$876$	−15.1865	+	2.49854i	−0.513105	+	0.0844179i
$877$	−18.1902	−	31.5064i	−0.614239	−	1.06389i	−0.990517	−	0.137387i	$-0.956130\pi$
$877$	−18.1902	−	31.5064i	−0.614239	−	1.06389i	0.376278	−	0.926507i	$-0.377204\pi$
$878$	−6.89942			−0.232844
$879$	−28.6365	−	34.9336i	−0.965884	−	1.17828i
$880$	0.703596			0.0237182
$881$	27.0041			0.909790			0.454895	−	0.890545i	$-0.349677\pi$
$881$	27.0041			0.909790			0.454895	+	0.890545i	$0.349677\pi$
$882$	−6.58836	−	16.1648i	−0.221842	−	0.544297i
$883$	43.0715			1.44947			0.724735	−	0.689028i	$-0.241962\pi$
$883$	43.0715			1.44947			0.724735	+	0.689028i	$0.241962\pi$
$884$	9.24116			0.310814
$885$	9.42895	−	1.55128i	0.316951	−	0.0521459i
$886$	−17.2236			−0.578640
$887$	9.31216	+	16.1291i	0.312672	+	0.541563i	0.978940	−	0.204149i	$-0.0654427\pi$
$887$	9.31216	+	16.1291i	0.312672	+	0.541563i	−0.666268	+	0.745712i	$0.732109\pi$
$888$	−10.6464	−	12.9875i	−0.357268	−	0.435832i
$889$	1.88779	+	0.444709i	0.0633146	+	0.0149151i
$890$	−4.56198			−0.152918
$891$	−17.6191	−	7.34452i	−0.590264	−	0.246051i
$892$	−4.96704	−	8.60317i	−0.166309	−	0.288055i
$893$	−6.52972	+	11.3098i	−0.218509	+	0.378468i
$894$	14.2860	−	2.35038i	0.477794	−	0.0786085i
$895$	6.33162	−	10.9667i	0.211643	−	0.366576i
$896$	20.8952	+	4.92229i	0.698059	+	0.164442i
$897$	−5.16150	+	13.6904i	−0.172337	+	0.457110i
$898$	−7.85361			−0.262078
$899$	1.73796	+	3.01024i	0.0579642	+	0.100397i
$900$	−3.72017	+	1.25817i	−0.124006	+	0.0419389i
$901$	32.1581	−	55.6994i	1.07134	−	1.85562i
$902$	−9.93342	−	17.2052i	−0.330747	−	0.572870i
$903$	−41.3605	−	2.82889i	−1.37639	−	0.0941396i
$904$	−6.27322	+	10.8655i	−0.208644	+	0.361383i
$905$	3.25470	+	5.63730i	0.108190	+	0.187390i
$906$	−18.0970	−	22.0766i	−0.601234	−	0.733445i
$907$	5.17170	−	8.95764i	0.171723	−	0.297434i	−0.767299	−	0.641289i	$-0.778400\pi$
$907$	5.17170	−	8.95764i	0.171723	−	0.297434i	0.939022	+	0.343856i	$0.111733\pi$
$908$	4.56217	−	7.90192i	0.151401	−	0.262234i
$909$	−5.82047	+	1.96849i	−0.193053	+	0.0652907i
$910$	2.36364	+	0.556803i	0.0783538	+	0.0184578i
$911$	−22.4053	−	38.8072i	−0.742322	−	1.28574i	−0.951436	−	0.307848i	$-0.900391\pi$
$911$	−22.4053	−	38.8072i	−0.742322	−	1.28574i	0.209114	−	0.977891i	$-0.432942\pi$
$912$	−2.01598	−	2.45930i	−0.0667558	−	0.0814354i
$913$	12.5070			0.413921
$914$	−17.7565			−0.587333
$915$	−10.2198	+	1.68140i	−0.337856	+	0.0555854i
$916$	−9.56763	−	16.5716i	−0.316123	−	0.547542i
$917$	5.91908	+	19.6738i	0.195465	+	0.649687i
$918$	−23.4256	−	14.6217i	−0.773159	−	0.482590i
$919$	9.08502	−	15.7357i	0.299687	−	0.519073i	−0.676377	−	0.736555i	$-0.736451\pi$
$919$	9.08502	−	15.7357i	0.299687	−	0.519073i	0.976064	+	0.217482i	$0.0697844\pi$
$920$	−10.5214	+	18.2236i	−0.346881	+	0.600816i
$921$	−12.6439	+	33.5369i	−0.416631	+	1.10508i
$922$	13.2193	+	22.8965i	0.435355	+	0.754057i
$923$	1.81305	−	3.14030i	0.0596774	−	0.103364i
$924$	−5.59495	−	11.4271i	−0.184060	−	0.375925i
$925$	1.76248	+	3.05270i	0.0579499	+	0.100372i
$926$	−6.95183	+	12.0409i	−0.228451	+	0.395689i
$927$	0.725239	−	3.62473i	0.0238200	−	0.119052i
$928$	−0.928693	−	1.60854i	−0.0304859	−	0.0528030i
$929$	−33.6857			−1.10519			−0.552597	−	0.833449i	$-0.686363\pi$
$929$	−33.6857			−1.10519			−0.552597	+	0.833449i	$0.686363\pi$
$930$	−15.3584	+	2.52683i	−0.503623	+	0.0828579i
$931$	−32.3098	+	21.3764i	−1.05891	+	0.700584i
$932$	4.86570	−	8.42765i	0.159381	−	0.276057i
$933$	11.4430	−	30.3517i	0.374628	−	0.993669i
$934$	−10.0943	+	17.4839i	−0.330297	+	0.572091i
$935$	−6.78006	−	11.7434i	−0.221732	−	0.384051i
$936$	8.63113	−	2.91906i	0.282117	−	0.0954126i
$937$	3.21860			0.105147			0.0525736	−	0.998617i	$-0.483258\pi$
$937$	3.21860			0.105147			0.0525736	+	0.998617i	$0.483258\pi$
$938$	−0.514976	−	0.121313i	−0.0168146	−	0.00396102i
$939$	−20.0861	+	53.2767i	−0.655485	+	1.73862i
$940$	1.54447	+	2.67509i	0.0503749	+	0.0872519i
$941$	−35.0105			−1.14131			−0.570655	−	0.821190i	$-0.693311\pi$
$941$	−35.0105			−1.14131			−0.570655	+	0.821190i	$0.693311\pi$
$942$	11.6752	−	30.9674i	0.380397	−	1.00897i
$943$	−86.2091			−2.80736
$944$	1.83018			0.0595671
$945$	9.68251	+	9.75956i	0.314972	+	0.317479i
$946$	15.9494			0.518559
$947$	56.3848			1.83226			0.916130	−	0.400882i	$-0.131296\pi$
$947$	56.3848			1.83226			0.916130	+	0.400882i	$0.131296\pi$
$948$	−4.14363	+	10.9906i	−0.134579	+	0.356959i
$949$	−7.49509			−0.243301
$950$	−2.30020	−	3.98406i	−0.0746284	−	0.129260i
$951$	−16.3039	+	43.2447i	−0.528690	+	1.40231i
$952$	−13.4046	−	44.5543i	−0.434447	−	1.44401i
$953$	28.1189			0.910860			0.455430	−	0.890272i	$-0.349486\pi$
$953$	28.1189			0.910860			0.455430	+	0.890272i	$0.349486\pi$
$954$	4.92168	−	24.5985i	0.159345	−	0.796406i
$955$	−0.994440	−	1.72242i	−0.0321793	−	0.0557362i
$956$	−8.59453	+	14.8862i	−0.277967	+	0.481453i
$957$	−0.416675	+	1.10520i	−0.0134692	+	0.0357259i
$958$	−9.72158	+	16.8383i	−0.314090	+	0.544020i
$959$	20.2133	−	21.4833i	0.652722	−	0.693730i
$960$	7.07299	−	1.16367i	0.228280	−	0.0375574i
$961$	85.8770			2.77023
$962$	−1.61764	−	2.80184i	−0.0521549	−	0.0903350i
$963$	8.67119	−	2.93261i	0.279425	−	0.0945020i
$964$	−9.17314	+	15.8883i	−0.295447	+	0.511729i
$965$	−0.203474	−	0.352426i	−0.00655004	−	0.0113450i
$966$	29.0735	+	1.98851i	0.935423	+	0.0639792i
$967$	−3.66960	+	6.35593i	−0.118006	+	0.204393i	−0.918977	−	0.394310i	$-0.870984\pi$
$967$	−3.66960	+	6.35593i	−0.118006	+	0.204393i	0.800971	+	0.598703i	$0.204317\pi$
$968$	−8.94151	−	15.4872i	−0.287391	−	0.497776i
$969$	−21.6204	+	57.3464i	−0.694549	+	1.84223i
$970$	−7.16215	+	12.4052i	−0.229963	+	0.398307i
$971$	10.1628	−	17.6025i	0.326140	−	0.564891i	−0.655603	−	0.755106i	$-0.727585\pi$
$971$	10.1628	−	17.6025i	0.326140	−	0.564891i	0.981742	+	0.190215i	$0.0609187\pi$
$972$	19.8600	+	4.68955i	0.637009	+	0.150418i
$973$	16.8215	−	17.8784i	0.539274	−	0.573154i
$974$	−16.8328	−	29.1553i	−0.539359	−	0.934197i
$975$	−1.88712	+	0.310475i	−0.0604361	+	0.00994316i
$976$	−1.98368			−0.0634961
$977$	−10.6228			−0.339852			−0.169926	−	0.985457i	$-0.554353\pi$
$977$	−10.6228			−0.339852			−0.169926	+	0.985457i	$0.554353\pi$
$978$	18.8718	+	23.0217i	0.603454	+	0.736154i
$979$	5.82015	+	10.0808i	0.186013	+	0.322184i
$980$	0.557647	+	9.14640i	0.0178134	+	0.292171i
$981$	−6.56831	+	32.8283i	−0.209710	+	1.04813i
$982$	2.21935	−	3.84402i	0.0708222	−	0.122668i
$983$	8.73054	−	15.1217i	0.278461	−	0.482309i	−0.692541	−	0.721378i	$-0.743509\pi$
$983$	8.73054	−	15.1217i	0.278461	−	0.482309i	0.971002	+	0.239069i	$0.0768424\pi$
$984$	34.0347	+	41.5190i	1.08499	+	1.32358i
$985$	0.970786	+	1.68145i	0.0309318	+	0.0535755i
$986$	−0.854335	+	1.47975i	−0.0272076	+	0.0471249i
$987$	6.03308	−	8.97387i	0.192035	−	0.285642i
$988$	−3.99981	−	6.92787i	−0.127251	−	0.220405i
$989$	34.6049	−	59.9375i	1.10037	−	1.90590i
$990$	−3.97258	−	3.49176i	−0.126257	−	0.110975i
$991$	−15.3134	−	26.5235i	−0.486445	−	0.842547i	0.513434	−	0.858129i	$-0.328373\pi$
$991$	−15.3134	−	26.5235i	−0.486445	−	0.842547i	−0.999879	+	0.0155821i	$0.995040\pi$
$992$	−62.4542			−1.98292
$993$	9.24695	−	24.5268i	0.293443	−	0.778333i
$994$	−7.02985	−	1.65603i	−0.222973	−	0.0525260i
$995$	2.67995	−	4.64181i	0.0849601	−	0.147155i
$996$	−13.1929	+	2.17054i	−0.418032	+	0.0687761i
$997$	17.8327	−	30.8871i	0.564766	−	0.978204i	−0.432305	−	0.901727i	$-0.642300\pi$
$997$	17.8327	−	30.8871i	0.564766	−	0.978204i	0.997071	−	0.0764764i	$-0.0243670\pi$
$998$	−14.5272	−	25.1618i	−0.459849	−	0.796482i
$999$	0.630140	−	18.3054i	0.0199368	−	0.579156i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.l.c.121.12	yes	36
3.2	odd	2		945.2.l.c.226.7		36
7.4	even	3		315.2.k.c.256.7	yes	36
9.2	odd	6		945.2.k.c.856.12		36
9.7	even	3		315.2.k.c.16.7	✓	36
21.11	odd	6		945.2.k.c.361.12		36
63.11	odd	6		945.2.l.c.46.7		36
63.25	even	3	inner	315.2.l.c.151.12	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.k.c.16.7	✓	36	9.7	even	3
315.2.k.c.256.7	yes	36	7.4	even	3
315.2.l.c.121.12	yes	36	1.1	even	1	trivial
315.2.l.c.151.12	yes	36	63.25	even	3	inner
945.2.k.c.361.12		36	21.11	odd	6
945.2.k.c.856.12		36	9.2	odd	6
945.2.l.c.46.7		36	63.11	odd	6
945.2.l.c.226.7		36	3.2	odd	2

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.831231 q^{2} +(-0.611026 + 1.62069i) q^{3} -1.30905 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.507903 + 1.34717i) q^{6} +(-2.57526 - 0.606656i) q^{7} -2.75059 q^{8} +(-2.25330 - 1.98057i) q^{9} +O(q^{10})\)	\(q+0.831231 q^{2} +(-0.611026 + 1.62069i) q^{3} -1.30905 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.507903 + 1.34717i) q^{6} +(-2.57526 - 0.606656i) q^{7} -2.75059 q^{8} +(-2.25330 - 1.98057i) q^{9} +(-0.415616 - 0.719867i) q^{10} +(-1.06048 + 1.83681i) q^{11} +(0.799866 - 2.12158i) q^{12} +(0.552087 - 0.956243i) q^{13} +(-2.14064 - 0.504271i) q^{14} +(1.70907 - 0.281183i) q^{15} +0.331734 q^{16} +(-3.19669 - 5.53684i) q^{17} +(-1.87301 - 1.64631i) q^{18} +(-2.76722 + 4.79297i) q^{19} +(0.654527 + 1.13367i) q^{20} +(2.55675 - 3.80303i) q^{21} +(-0.881504 + 1.52681i) q^{22} +(3.82515 + 6.62536i) q^{23} +(1.68068 - 4.45786i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(0.458912 - 0.794859i) q^{26} +(4.58672 - 2.44172i) q^{27} +(3.37116 + 0.794145i) q^{28} +(-0.160759 - 0.278443i) q^{29} +(1.42064 - 0.233728i) q^{30} -10.8110 q^{31} +5.77693 q^{32} +(-2.32892 - 2.84105i) q^{33} +(-2.65719 - 4.60239i) q^{34} +(0.762251 + 2.53357i) q^{35} +(2.94969 + 2.59268i) q^{36} +(1.76248 - 3.05270i) q^{37} +(-2.30020 + 3.98406i) q^{38} +(1.21244 + 1.47905i) q^{39} +(1.37529 + 2.38208i) q^{40} +(-5.63436 + 9.75900i) q^{41} +(2.12525 - 3.16119i) q^{42} +(-4.52334 - 7.83465i) q^{43} +(1.38823 - 2.40448i) q^{44} +(-0.588576 + 2.94170i) q^{45} +(3.17959 + 5.50720i) q^{46} +2.35967 q^{47} +(-0.202698 + 0.537640i) q^{48} +(6.26394 + 3.12459i) q^{49} +(-0.415616 + 0.719867i) q^{50} +(10.9268 - 1.79771i) q^{51} +(-0.722712 + 1.25177i) q^{52} +(5.02990 + 8.71204i) q^{53} +(3.81262 - 2.02964i) q^{54} +2.12096 q^{55} +(7.08349 + 1.66866i) q^{56} +(-6.07709 - 7.41345i) q^{57} +(-0.133628 - 0.231450i) q^{58} +5.51699 q^{59} +(-2.23727 + 0.368084i) q^{60} -5.97973 q^{61} -8.98641 q^{62} +(4.60130 + 6.46746i) q^{63} +4.13849 q^{64} -1.10417 q^{65} +(-1.93587 - 2.36157i) q^{66} +0.240571 q^{67} +(4.18465 + 7.24802i) q^{68} +(-13.0749 + 2.15114i) q^{69} +(0.633607 + 2.10598i) q^{70} +3.28400 q^{71} +(6.19789 + 5.44774i) q^{72} +(-3.39398 - 5.87854i) q^{73} +(1.46503 - 2.53750i) q^{74} +(-1.09805 - 1.33951i) q^{75} +(3.62245 - 6.27426i) q^{76} +(3.84532 - 4.08691i) q^{77} +(1.00782 + 1.22943i) q^{78} -5.18040 q^{79} +(-0.165867 - 0.287290i) q^{80} +(1.15468 + 8.92562i) q^{81} +(-4.68345 + 8.11198i) q^{82} +(-2.94842 - 5.10682i) q^{83} +(-3.34693 + 4.97837i) q^{84} +(-3.19669 + 5.53684i) q^{85} +(-3.75994 - 6.51241i) q^{86} +(0.549499 - 0.0904055i) q^{87} +(2.91695 - 5.05230i) q^{88} +(2.74411 - 4.75294i) q^{89} +(-0.489243 + 2.44523i) q^{90} +(-2.00188 + 2.12765i) q^{91} +(-5.00733 - 8.67296i) q^{92} +(6.60578 - 17.5213i) q^{93} +1.96143 q^{94} +5.53444 q^{95} +(-3.52985 + 9.36263i) q^{96} +(-8.61631 - 14.9239i) q^{97} +(5.20678 + 2.59726i) q^{98} +(6.02750 - 2.03851i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - q^{3} + 44 q^{4} - 18 q^{5} - 4 q^{6} - q^{7} - 9 q^{9}+O(q^{10}) \) 36 * q - q^3 + 44 * q^4 - 18 * q^5 - 4 * q^6 - q^7 - 9 * q^9	\( 36 q - q^{3} + 44 q^{4} - 18 q^{5} - 4 q^{6} - q^{7} - 9 q^{9} + q^{11} + 8 q^{12} + 2 q^{13} + 9 q^{14} - q^{15} + 60 q^{16} - 5 q^{17} - 21 q^{18} - 2 q^{19} - 22 q^{20} - 23 q^{21} - 19 q^{22} - 3 q^{23} - 32 q^{24} - 18 q^{25} - 4 q^{26} + 17 q^{27} + 5 q^{28} - 8 q^{29} + 2 q^{30} - 20 q^{32} - 35 q^{33} + 10 q^{34} - q^{35} - 44 q^{36} - 15 q^{37} - 22 q^{38} + 7 q^{39} - 4 q^{41} + 57 q^{42} - 29 q^{43} - 7 q^{44} + 6 q^{45} - 24 q^{46} + 46 q^{47} - 19 q^{48} - 7 q^{49} + 42 q^{51} - 7 q^{52} + 21 q^{54} - 2 q^{55} - 12 q^{56} + 21 q^{57} - 20 q^{58} + 10 q^{59} - 13 q^{60} + 6 q^{61} - 12 q^{62} + 2 q^{63} + 128 q^{64} - 4 q^{65} - 12 q^{66} + 70 q^{67} - 17 q^{68} - 50 q^{69} - 3 q^{70} + 24 q^{71} - 10 q^{72} - 10 q^{73} + 22 q^{74} + 2 q^{75} + 10 q^{76} + 35 q^{77} + 66 q^{78} + 56 q^{79} - 30 q^{80} - 49 q^{81} - 8 q^{82} - 22 q^{83} - 86 q^{84} - 5 q^{85} + 19 q^{86} - 42 q^{87} - 50 q^{88} - 4 q^{89} + 3 q^{90} + 7 q^{91} - 50 q^{92} - q^{93} + 4 q^{94} + 4 q^{95} - 179 q^{96} + 16 q^{97} + 16 q^{98} - 89 q^{99}+O(q^{100}) \) 36 * q - q^3 + 44 * q^4 - 18 * q^5 - 4 * q^6 - q^7 - 9 * q^9 + q^11 + 8 * q^12 + 2 * q^13 + 9 * q^14 - q^15 + 60 * q^16 - 5 * q^17 - 21 * q^18 - 2 * q^19 - 22 * q^20 - 23 * q^21 - 19 * q^22 - 3 * q^23 - 32 * q^24 - 18 * q^25 - 4 * q^26 + 17 * q^27 + 5 * q^28 - 8 * q^29 + 2 * q^30 - 20 * q^32 - 35 * q^33 + 10 * q^34 - q^35 - 44 * q^36 - 15 * q^37 - 22 * q^38 + 7 * q^39 - 4 * q^41 + 57 * q^42 - 29 * q^43 - 7 * q^44 + 6 * q^45 - 24 * q^46 + 46 * q^47 - 19 * q^48 - 7 * q^49 + 42 * q^51 - 7 * q^52 + 21 * q^54 - 2 * q^55 - 12 * q^56 + 21 * q^57 - 20 * q^58 + 10 * q^59 - 13 * q^60 + 6 * q^61 - 12 * q^62 + 2 * q^63 + 128 * q^64 - 4 * q^65 - 12 * q^66 + 70 * q^67 - 17 * q^68 - 50 * q^69 - 3 * q^70 + 24 * q^71 - 10 * q^72 - 10 * q^73 + 22 * q^74 + 2 * q^75 + 10 * q^76 + 35 * q^77 + 66 * q^78 + 56 * q^79 - 30 * q^80 - 49 * q^81 - 8 * q^82 - 22 * q^83 - 86 * q^84 - 5 * q^85 + 19 * q^86 - 42 * q^87 - 50 * q^88 - 4 * q^89 + 3 * q^90 + 7 * q^91 - 50 * q^92 - q^93 + 4 * q^94 + 4 * q^95 - 179 * q^96 + 16 * q^97 + 16 * q^98 - 89 * q^99

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