LMFDB - Embedded newform 637.2.bl.b.235.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(53,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([10, 0]))

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

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

chi := DirichletCharacter("637.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bl (of order $21$, degree $12$, 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$348$
Relative dimension:	$29$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			235.22
Character	$\chi$	$=$	637.235
Dual form			637.2.bl.b.534.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.40276 + 0.211433i) q^{2} +(0.102437 - 0.0698406i) q^{3} +(0.0118965 + 0.00366960i) q^{4} +(-0.300677 - 4.01226i) q^{5} +(0.158462 - 0.0763113i) q^{6} +(-2.12848 - 1.57148i) q^{7} +(-2.54033 - 1.22336i) q^{8} +(-1.09041 + 2.77831i) q^{9} +O(q^{10})$	\(q+(1.40276 + 0.211433i) q^{2} +(0.102437 - 0.0698406i) q^{3} +(0.0118965 + 0.00366960i) q^{4} +(-0.300677 - 4.01226i) q^{5} +(0.158462 - 0.0763113i) q^{6} +(-2.12848 - 1.57148i) q^{7} +(-2.54033 - 1.22336i) q^{8} +(-1.09041 + 2.77831i) q^{9} +(0.426543 - 5.69183i) q^{10} +(1.89016 + 4.81604i) q^{11} +(0.00147494 - 0.000454958i) q^{12} +(0.623490 - 0.781831i) q^{13} +(-2.65350 - 2.65445i) q^{14} +(-0.311019 - 0.390006i) q^{15} +(-3.32540 - 2.26722i) q^{16} +(-5.69421 - 5.28345i) q^{17} +(-2.11701 + 3.66677i) q^{18} +(-1.02653 - 1.77801i) q^{19} +(0.0111464 - 0.0488354i) q^{20} +(-0.327789 - 0.0123238i) q^{21} +(1.63318 + 7.15541i) q^{22} +(3.63941 - 3.37688i) q^{23} +(-0.345665 + 0.0521006i) q^{24} +(-11.0637 + 1.66758i) q^{25} +(1.03991 - 0.964899i) q^{26} +(0.165105 + 0.723373i) q^{27} +(-0.0195549 - 0.0265059i) q^{28} +(0.896286 - 3.92689i) q^{29} +(-0.353827 - 0.612846i) q^{30} +(2.31386 - 4.00773i) q^{31} +(-0.0516250 - 0.0479010i) q^{32} +(0.529978 + 0.361333i) q^{33} +(-6.87053 - 8.61537i) q^{34} +(-5.66521 + 9.01254i) q^{35} +(-0.0231674 + 0.0290510i) q^{36} +(0.738392 - 0.227764i) q^{37} +(-1.06405 - 2.71117i) q^{38} +(0.00926506 - 0.123634i) q^{39} +(-4.14462 + 10.5603i) q^{40} +(-2.99562 - 1.44262i) q^{41} +(-0.457205 - 0.0865928i) q^{42} +(2.98655 - 1.43825i) q^{43} +(0.00481340 + 0.0642304i) q^{44} +(11.4752 + 3.53962i) q^{45} +(5.81922 - 3.96748i) q^{46} +(3.76008 + 0.566741i) q^{47} -0.498989 q^{48} +(2.06089 + 6.68975i) q^{49} -15.8723 q^{50} +(-0.952299 - 0.143536i) q^{51} +(0.0102864 - 0.00701314i) q^{52} +(7.50905 + 2.31623i) q^{53} +(0.0786589 + 1.04963i) q^{54} +(18.7549 - 9.03188i) q^{55} +(3.48457 + 6.59599i) q^{56} +(-0.229332 - 0.110441i) q^{57} +(2.08755 - 5.31899i) q^{58} +(-0.0920752 + 1.22866i) q^{59} +(-0.00226889 - 0.00578104i) q^{60} +(8.62818 - 2.66144i) q^{61} +(4.09317 - 5.13267i) q^{62} +(6.68698 - 4.20004i) q^{63} +(4.95648 + 6.21523i) q^{64} +(-3.32438 - 2.26652i) q^{65} +(0.667036 + 0.618919i) q^{66} +(-0.288736 + 0.500105i) q^{67} +(-0.0483532 - 0.0837503i) q^{68} +(0.136968 - 0.600097i) q^{69} +(-9.85249 + 11.4447i) q^{70} +(-1.12923 - 4.94750i) q^{71} +(6.16887 - 5.72388i) q^{72} +(-5.81137 + 0.875923i) q^{73} +(1.08395 - 0.163379i) q^{74} +(-1.01687 + 0.943517i) q^{75} +(-0.00568762 - 0.0249191i) q^{76} +(3.54515 - 13.2212i) q^{77} +(0.0391369 - 0.171470i) q^{78} +(-6.37906 - 11.0489i) q^{79} +(-8.09680 + 14.0241i) q^{80} +(-6.49623 - 6.02762i) q^{81} +(-3.89714 - 2.65702i) q^{82} +(9.72033 + 12.1889i) q^{83} +(-0.00385434 - 0.00134947i) q^{84} +(-19.4865 + 24.4353i) q^{85} +(4.49352 - 1.38607i) q^{86} +(-0.182443 - 0.464857i) q^{87} +(1.09012 - 14.5467i) q^{88} +(1.54024 - 3.92446i) q^{89} +(15.3486 + 7.39148i) q^{90} +(-2.55572 + 0.684313i) q^{91} +(0.0556882 - 0.0268180i) q^{92} +(-0.0428762 - 0.572143i) q^{93} +(5.15467 + 1.59001i) q^{94} +(-6.82517 + 4.65333i) q^{95} +(-0.00863377 - 0.00130133i) q^{96} +3.54214 q^{97} +(1.47651 + 9.81988i) q^{98} -15.4415 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9}+O(q^{10}) $ 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9	\( 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9} - 5 q^{10} + 2 q^{11} - 40 q^{12} - 58 q^{13} - 45 q^{14} - 14 q^{15} + 27 q^{16} - 12 q^{17} - 59 q^{18} - 24 q^{19} - 99 q^{20} - 2 q^{21} - 10 q^{22} - 14 q^{23} + 28 q^{25} + 3 q^{26} - 9 q^{27} - 37 q^{28} - 26 q^{29} - 83 q^{30} - 49 q^{31} + 33 q^{32} + 2 q^{33} - 130 q^{34} - 38 q^{35} - 74 q^{36} - 4 q^{37} + 92 q^{38} + 24 q^{40} + 20 q^{41} - 52 q^{42} + 2 q^{43} + 226 q^{44} - 23 q^{45} + 71 q^{46} + 24 q^{47} + 86 q^{48} + 25 q^{49} + 114 q^{50} - 54 q^{51} + 31 q^{52} + 36 q^{53} + 75 q^{54} + 38 q^{55} + 126 q^{56} + 27 q^{57} - 33 q^{58} + q^{59} - 179 q^{60} - 15 q^{61} + 158 q^{62} - 5 q^{63} - 24 q^{64} + q^{65} - 150 q^{66} - 151 q^{67} + 140 q^{68} - 98 q^{69} - 126 q^{70} - 31 q^{71} - 149 q^{72} - 9 q^{73} + 39 q^{74} + 85 q^{75} - 81 q^{76} + 46 q^{77} - 25 q^{78} - 69 q^{79} - 64 q^{80} + 71 q^{81} - 52 q^{82} - q^{83} - 47 q^{84} + 62 q^{85} + 97 q^{86} + 150 q^{87} - 12 q^{88} + 23 q^{89} + 107 q^{90} - q^{91} - 43 q^{92} + 316 q^{93} - 86 q^{94} - 29 q^{95} + 177 q^{96} + 114 q^{97} - 336 q^{98} + 102 q^{99}+O(q^{100}) \) 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9 - 5 * q^10 + 2 * q^11 - 40 * q^12 - 58 * q^13 - 45 * q^14 - 14 * q^15 + 27 * q^16 - 12 * q^17 - 59 * q^18 - 24 * q^19 - 99 * q^20 - 2 * q^21 - 10 * q^22 - 14 * q^23 + 28 * q^25 + 3 * q^26 - 9 * q^27 - 37 * q^28 - 26 * q^29 - 83 * q^30 - 49 * q^31 + 33 * q^32 + 2 * q^33 - 130 * q^34 - 38 * q^35 - 74 * q^36 - 4 * q^37 + 92 * q^38 + 24 * q^40 + 20 * q^41 - 52 * q^42 + 2 * q^43 + 226 * q^44 - 23 * q^45 + 71 * q^46 + 24 * q^47 + 86 * q^48 + 25 * q^49 + 114 * q^50 - 54 * q^51 + 31 * q^52 + 36 * q^53 + 75 * q^54 + 38 * q^55 + 126 * q^56 + 27 * q^57 - 33 * q^58 + q^59 - 179 * q^60 - 15 * q^61 + 158 * q^62 - 5 * q^63 - 24 * q^64 + q^65 - 150 * q^66 - 151 * q^67 + 140 * q^68 - 98 * q^69 - 126 * q^70 - 31 * q^71 - 149 * q^72 - 9 * q^73 + 39 * q^74 + 85 * q^75 - 81 * q^76 + 46 * q^77 - 25 * q^78 - 69 * q^79 - 64 * q^80 + 71 * q^81 - 52 * q^82 - q^83 - 47 * q^84 + 62 * q^85 + 97 * q^86 + 150 * q^87 - 12 * q^88 + 23 * q^89 + 107 * q^90 - q^91 - 43 * q^92 + 316 * q^93 - 86 * q^94 - 29 * q^95 + 177 * q^96 + 114 * q^97 - 336 * q^98 + 102 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{17}{21}\right)$

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 $

$2$	1.40276	+	0.211433i	0.991904	+	0.149505i	0.624892	−	0.780711i	$-0.285143\pi$
$2$	1.40276	+	0.211433i	0.991904	+	0.149505i	0.367011	+	0.930216i	$0.380381\pi$
$3$	0.102437	−	0.0698406i	0.0591422	−	0.0403225i	−0.533388	−	0.845871i	$-0.679081\pi$
$3$	0.102437	−	0.0698406i	0.0591422	−	0.0403225i	0.592530	+	0.805548i	$0.298129\pi$
$4$	0.0118965	+	0.00366960i	0.00594827	+	0.00183480i
$5$	−0.300677	−	4.01226i	−0.134467	−	1.79434i	−0.502553	−	0.864546i	$-0.667606\pi$
$5$	−0.300677	−	4.01226i	−0.134467	−	1.79434i	0.368086	−	0.929792i	$-0.380013\pi$
$6$	0.158462	−	0.0763113i	0.0646918	−	0.0311539i
$7$	−2.12848	−	1.57148i	−0.804491	−	0.593964i
$7$	−2.12848	−	1.57148i	−0.804491	−	0.593964i
$8$	−2.54033	−	1.22336i	−0.898143	−	0.432523i
$9$	−1.09041	+	2.77831i	−0.363469	+	0.926104i
$10$	0.426543	−	5.69183i	0.134885	−	1.79991i
$11$	1.89016	+	4.81604i	0.569904	+	1.45209i	0.867518	+	0.497405i	$0.165714\pi$
$11$	1.89016	+	4.81604i	0.569904	+	1.45209i	−0.297615	+	0.954686i	$0.596191\pi$
$12$	0.00147494		0.000454958i	0.000425778		0.000131335i
$13$	0.623490	−	0.781831i	0.172925	−	0.216841i
$13$	0.623490	−	0.781831i	0.172925	−	0.216841i
$14$	−2.65350	−	2.65445i	−0.709177	−	0.709431i
$15$	−0.311019	−	0.390006i	−0.0803048	−	0.100699i
$16$	−3.32540	−	2.26722i	−0.831350	−	0.566805i
$17$	−5.69421	−	5.28345i	−1.38105	−	1.28142i	−0.918827	−	0.394660i	$-0.870862\pi$
$17$	−5.69421	−	5.28345i	−1.38105	−	1.28142i	−0.462220	−	0.886765i	$-0.652947\pi$
$18$	−2.11701	+	3.66677i	−0.498984	+	0.864266i
$19$	−1.02653	−	1.77801i	−0.235503	−	0.407903i	0.723916	−	0.689888i	$-0.242340\pi$
$19$	−1.02653	−	1.77801i	−0.235503	−	0.407903i	−0.959419	+	0.281985i	$0.909007\pi$
$20$	0.0111464	−	0.0488354i	0.00249240	−	0.0109199i
$21$	−0.327789	−	0.0123238i	−0.0715295	−	0.00268927i
$22$	1.63318	+	7.15541i	0.348194	+	1.52554i
$23$	3.63941	−	3.37688i	0.758870	−	0.704128i	−0.202532	−	0.979276i	$-0.564917\pi$
$23$	3.63941	−	3.37688i	0.758870	−	0.704128i	0.961402	+	0.275147i	$0.0887266\pi$
$24$	−0.345665	+	0.0521006i	−0.0705586	+	0.0106350i
$25$	−11.0637	+	1.66758i	−2.21274	+	0.333516i
$26$	1.03991	−	0.964899i	0.203944	−	0.189232i
$27$	0.165105	+	0.723373i	0.0317745	+	0.139213i
$28$	−0.0195549	−	0.0265059i	−0.00369553	−	0.00500914i
$29$	0.896286	−	3.92689i	0.166436	−	0.729204i	−0.820967	−	0.570976i	$-0.806565\pi$
$29$	0.896286	−	3.92689i	0.166436	−	0.729204i	0.987403	−	0.158228i	$-0.0505781\pi$
$30$	−0.353827	−	0.612846i	−0.0645996	−	0.111890i
$31$	2.31386	−	4.00773i	0.415582	−	0.719810i	−0.579907	−	0.814683i	$-0.696911\pi$
$31$	2.31386	−	4.00773i	0.415582	−	0.719810i	0.995489	+	0.0948730i	$0.0302445\pi$
$32$	−0.0516250	−	0.0479010i	−0.00912611	−	0.00846779i
$33$	0.529978	+	0.361333i	0.0922573	+	0.0629000i
$34$	−6.87053	−	8.61537i	−1.17829	−	1.47752i
$35$	−5.66521	+	9.01254i	−0.957595	+	1.52340i
$36$	−0.0231674	+	0.0290510i	−0.00386123	+	0.00484183i
$37$	0.738392	−	0.227764i	0.121391	−	0.0374442i	−0.233465	−	0.972365i	$-0.575006\pi$
$37$	0.738392	−	0.227764i	0.121391	−	0.0374442i	0.354855	+	0.934921i	$0.384530\pi$
$38$	−1.06405	−	2.71117i	−0.172612	−	0.439809i
$39$	0.00926506	−	0.123634i	0.00148360	−	0.0197972i
$40$	−4.14462	+	10.5603i	−0.655321	+	1.66973i
$41$	−2.99562	−	1.44262i	−0.467838	−	0.225299i	0.185086	−	0.982722i	$-0.440744\pi$
$41$	−2.99562	−	1.44262i	−0.467838	−	0.225299i	−0.652924	+	0.757423i	$0.726458\pi$
$42$	−0.457205	−	0.0865928i	−0.0705483	−	0.0133616i
$43$	2.98655	−	1.43825i	0.455445	−	0.219331i	−0.192073	−	0.981381i	$-0.561521\pi$
$43$	2.98655	−	1.43825i	0.455445	−	0.219331i	0.647518	+	0.762050i	$0.275807\pi$
$44$	0.00481340	+	0.0642304i	0.000725647	+	0.00968309i
$45$	11.4752	+	3.53962i	1.71062	+	0.527656i
$46$	5.81922	−	3.96748i	0.857997	−	0.584972i
$47$	3.76008	+	0.566741i	0.548464	+	0.0826676i	0.417428	−	0.908710i	$-0.362932\pi$
$47$	3.76008	+	0.566741i	0.548464	+	0.0826676i	0.131036	+	0.991378i	$0.458170\pi$
$48$	−0.498989			−0.0720229
$49$	2.06089	+	6.68975i	0.294413	+	0.955678i
$50$	−15.8723			−2.24468
$51$	−0.952299	−	0.143536i	−0.133348	−	0.0200990i
$52$	0.0102864	−	0.00701314i	0.00142646	−	0.000972547i
$53$	7.50905	+	2.31623i	1.03145	+	0.318159i	0.763865	−	0.645376i	$-0.223299\pi$
$53$	7.50905	+	2.31623i	1.03145	+	0.318159i	0.267582	+	0.963535i	$0.413775\pi$
$54$	0.0786589	+	1.04963i	0.0107041	+	0.142837i
$55$	18.7549	−	9.03188i	2.52891	−	1.21786i
$56$	3.48457	+	6.59599i	0.465645	+	0.881426i
$57$	−0.229332	−	0.110441i	−0.0303758	−	0.0146282i
$58$	2.08755	−	5.31899i	0.274109	−	0.698417i
$59$	−0.0920752	+	1.22866i	−0.0119872	+	0.159958i	0.987998	+	0.154468i	$0.0493664\pi$
$59$	−0.0920752	+	1.22866i	−0.0119872	+	0.159958i	−0.999985	+	0.00548947i	$0.998253\pi$
$60$	−0.00226889	−	0.00578104i	−0.000292912	−	0.000746329i
$61$	8.62818	−	2.66144i	1.10473	−	0.340763i	0.311841	−	0.950134i	$-0.399054\pi$
$61$	8.62818	−	2.66144i	1.10473	−	0.340763i	0.792885	+	0.609372i	$0.208578\pi$
$62$	4.09317	−	5.13267i	0.519833	−	0.651850i
$63$	6.68698	−	4.20004i	0.842481	−	0.529155i
$64$	4.95648	+	6.21523i	0.619561	+	0.776904i
$65$	−3.32438	−	2.26652i	−0.412339	−	0.281128i
$66$	0.667036	+	0.618919i	0.0821065	+	0.0761837i
$67$	−0.288736	+	0.500105i	−0.0352747	+	0.0610976i	−0.883124	−	0.469140i	$-0.844564\pi$
$67$	−0.288736	+	0.500105i	−0.0352747	+	0.0610976i	0.847849	+	0.530238i	$0.177897\pi$
$68$	−0.0483532	−	0.0837503i	−0.00586369	−	0.0101562i
$69$	0.136968	−	0.600097i	0.0164890	−	0.0722432i
$70$	−9.85249	+	11.4447i	−1.17760	+	1.36790i
$71$	−1.12923	−	4.94750i	−0.134015	−	0.587160i	−0.996683	−	0.0813878i	$-0.974065\pi$
$71$	−1.12923	−	4.94750i	−0.134015	−	0.587160i	0.862667	−	0.505772i	$-0.168792\pi$
$72$	6.16887	−	5.72388i	0.727008	−	0.674565i
$73$	−5.81137	+	0.875923i	−0.680170	+	0.102519i	−0.480035	−	0.877249i	$-0.659376\pi$
$73$	−5.81137	+	0.875923i	−0.680170	+	0.102519i	−0.200135	+	0.979768i	$0.564138\pi$
$74$	1.08395	−	0.163379i	0.126006	−	0.0189924i
$75$	−1.01687	+	0.943517i	−0.117418	+	0.108948i
$76$	−0.00568762	−	0.0249191i	−0.000652415	−	0.00285842i
$77$	3.54515	−	13.2212i	0.404008	−	1.50670i
$78$	0.0391369	−	0.171470i	0.00443138	−	0.0194151i
$79$	−6.37906	−	11.0489i	−0.717700	−	1.24309i	−0.961909	−	0.273371i	$-0.911861\pi$
$79$	−6.37906	−	11.0489i	−0.717700	−	1.24309i	0.244208	−	0.969723i	$-0.421472\pi$
$80$	−8.09680	+	14.0241i	−0.905250	+	1.56794i
$81$	−6.49623	−	6.02762i	−0.721803	−	0.669736i
$82$	−3.89714	−	2.65702i	−0.430367	−	0.293419i
$83$	9.72033	+	12.1889i	1.06694	+	1.33791i	0.938148	+	0.346236i	$0.112540\pi$
$83$	9.72033	+	12.1889i	1.06694	+	1.33791i	0.128797	+	0.991671i	$0.458888\pi$
$84$	−0.00385434	−	0.00134947i	−0.000420543	−	0.000147239i
$85$	−19.4865	+	24.4353i	−2.11360	+	2.65038i
$86$	4.49352	−	1.38607i	0.484549	−	0.149464i
$87$	−0.182443	−	0.464857i	−0.0195599	−	0.0498379i
$88$	1.09012	−	14.5467i	0.116208	−	1.55068i
$89$	1.54024	−	3.92446i	0.163265	−	0.415992i	−0.825706	−	0.564100i	$-0.809223\pi$
$89$	1.54024	−	3.92446i	0.163265	−	0.415992i	0.988971	+	0.148108i	$0.0473184\pi$
$90$	15.3486	+	7.39148i	1.61788	+	0.779131i
$91$	−2.55572	+	0.684313i	−0.267912	+	0.0717355i
$92$	0.0556882	−	0.0268180i	0.00580590	−	0.00279597i
$93$	−0.0428762	−	0.572143i	−0.00444605	−	0.0593285i
$94$	5.15467	+	1.59001i	0.531664	+	0.163997i
$95$	−6.82517	+	4.65333i	−0.700248	+	0.477421i
$96$	−0.00863377	−	0.00130133i	−0.000881180	−	0.000132817i
$97$	3.54214			0.359649			0.179825	−	0.983699i	$-0.442447\pi$
$97$	3.54214			0.359649			0.179825	+	0.983699i	$0.442447\pi$
$98$	1.47651	+	9.81988i	0.149150	+	0.991957i
$99$	−15.4415			−1.55193
$100$	−0.137739	−	0.0207608i	−0.0137739	−	0.00207608i
$101$	−8.22918	+	5.61056i	−0.818834	+	0.558272i	−0.898715	−	0.438533i	$-0.855498\pi$
$101$	−8.22918	+	5.61056i	−0.818834	+	0.558272i	0.0798810	+	0.996804i	$0.474546\pi$
$102$	−1.30550	−	0.402694i	−0.129264	−	0.0398726i
$103$	−0.803134	−	10.7171i	−0.0791352	−	1.05599i	−0.885522	−	0.464597i	$-0.846199\pi$
$103$	−0.803134	−	10.7171i	−0.0791352	−	1.05599i	0.806387	−	0.591388i	$-0.201420\pi$
$104$	−2.54033	+	1.22336i	−0.249100	+	0.119960i
$105$	0.0491126	+	1.31888i	0.00479290	+	0.128710i
$106$	10.0437	+	4.83679i	0.975530	+	0.469790i
$107$	3.61389	−	9.20804i	0.349368	−	0.890175i	−0.642888	−	0.765961i	$-0.722264\pi$
$107$	3.61389	−	9.20804i	0.349368	−	0.890175i	0.992255	−	0.124214i	$-0.0396410\pi$
$108$	−0.000690307		0.00921151i	−6.64249e−5		0.000886378i
$109$	1.01446	+	2.58481i	0.0971679	+	0.247580i	0.971190	−	0.238306i	$-0.0765922\pi$
$109$	1.01446	+	2.58481i	0.0971679	+	0.247580i	−0.874022	+	0.485886i	$0.838497\pi$
$110$	28.2183	−	8.70420i	2.69051	−	0.829913i
$111$	0.0597318	−	0.0749013i	0.00566949	−	0.00710932i
$112$	3.51517	+	10.0515i	0.332152	+	0.949782i
$113$	10.2783	+	12.8886i	0.966901	+	1.21246i	0.977159	+	0.212508i	$0.0681631\pi$
$113$	10.2783	+	12.8886i	0.966901	+	1.21246i	−0.0102585	+	0.999947i	$0.503265\pi$
$114$	−0.298348	−	0.203410i	−0.0279429	−	0.0190511i
$115$	−14.6432	−	13.5869i	−1.36549	−	1.26699i
$116$	0.0250728	−	0.0434274i	0.00232795	−	0.00403213i
$117$	1.49231	+	2.58476i	0.137965	+	0.238962i
$118$	−0.388938	+	1.70405i	−0.0358047	+	0.156870i
$119$	3.81718	+	20.1941i	0.349920	+	1.85119i
$120$	0.312975	+	1.37123i	0.0285706	+	0.125176i
$121$	−11.5580	+	10.7242i	−1.05073	+	0.974932i
$122$	12.6660	−	1.90910i	1.14673	−	0.172841i
$123$	−0.407617	+	0.0614384i	−0.0367536	+	0.00553971i
$124$	0.0422337	−	0.0391872i	0.00379270	−	0.00351911i
$125$	5.54079	+	24.2758i	0.495584	+	2.17129i
$126$	10.2683	−	4.47782i	0.914771	−	0.398916i
$127$	1.67437	−	7.33590i	0.148576	−	0.650956i	−0.844705	−	0.535232i	$-0.820224\pi$
$127$	1.67437	−	7.33590i	0.148576	−	0.650956i	0.993281	−	0.115724i	$-0.0369188\pi$
$128$	5.70910	+	9.88845i	0.504618	+	0.874023i
$129$	0.205486	−	0.355913i	0.0180921	−	0.0313364i
$130$	−4.18410	−	3.88228i	−0.366970	−	0.340499i
$131$	−12.2044	−	8.32082i	−1.06630	−	0.726994i	−0.102804	−	0.994702i	$-0.532781\pi$
$131$	−12.2044	−	8.32082i	−1.06630	−	0.726994i	−0.963500	+	0.267708i	$0.913734\pi$
$132$	0.00497896	+	0.00624342i	0.000433363	+	0.000543420i
$133$	−0.609147	+	5.39764i	−0.0528197	+	0.468035i
$134$	−0.510767	+	0.640481i	−0.0441235	+	0.0553291i
$135$	2.85272	−	0.879947i	0.245523	−	0.0757338i
$136$	8.00161	+	20.3878i	0.686133	+	1.74824i
$137$	−0.182870	+	2.44024i	−0.0156237	+	0.208483i	0.983929	+	0.178562i	$0.0571446\pi$
$137$	−0.182870	+	2.44024i	−0.0156237	+	0.208483i	−0.999552	+	0.0299211i	$0.990474\pi$
$138$	0.319014	−	0.812835i	0.0271563	−	0.0691931i
$139$	−7.88428	−	3.79687i	−0.668736	−	0.322046i	0.0685299	−	0.997649i	$-0.478169\pi$
$139$	−7.88428	−	3.79687i	−0.668736	−	0.322046i	−0.737266	+	0.675603i	$0.763883\pi$
$140$	−0.100469	+	0.0864291i	−0.00849116	+	0.00730459i
$141$	0.424754	−	0.204551i	0.0357707	−	0.0172263i
$142$	−0.537986	−	7.17893i	−0.0451468	−	0.602442i
$143$	4.94383	+	1.52497i	0.413424	+	0.127524i
$144$	9.92508	−	6.76681i	0.827090	−	0.563901i
$145$	−16.0252	−	2.41541i	−1.33082	−	0.200589i
$146$	−8.33718			−0.689990
$147$	0.678328	+	0.541346i	0.0559476	+	0.0446495i
$148$	0.00962012			0.000790769
$149$	−15.9763	−	2.40804i	−1.30883	−	0.197275i	−0.542683	−	0.839938i	$-0.682591\pi$
$149$	−15.9763	−	2.40804i	−1.30883	−	0.197275i	−0.766149	+	0.642663i	$0.777829\pi$
$150$	−1.62592	+	1.10853i	−0.132756	+	0.0905112i
$151$	−16.0658	−	4.95564i	−1.30741	−	0.403284i	−0.438716	−	0.898626i	$-0.644567\pi$
$151$	−16.0658	−	4.95564i	−1.30741	−	0.403284i	−0.868698	+	0.495342i	$0.835043\pi$
$152$	0.432593	+	5.77255i	0.0350879	+	0.468215i
$153$	20.8881	−	10.0592i	1.68870	−	0.813236i
$154$	7.76841	−	17.7967i	0.625996	−	1.43410i
$155$	−16.7758	−	8.07879i	−1.34746	−	0.648904i
$156$	0.000563908	−	0.00143681i	4.51488e−5	−	0.000115037i
$157$	1.26832	−	16.9245i	0.101223	−	1.35072i	−0.683080	−	0.730344i	$-0.739360\pi$
$157$	1.26832	−	16.9245i	0.101223	−	1.35072i	0.784302	−	0.620379i	$-0.213021\pi$
$158$	−6.61223	−	16.8477i	−0.526041	−	1.34033i
$159$	0.930974	−	0.287167i	0.0738310	−	0.0227739i
$160$	−0.176669	+	0.221536i	−0.0139669	+	0.0175140i
$161$	−13.0531	+	1.46837i	−1.02873	+	0.115724i
$162$	−7.83824	−	9.82884i	−0.615830	−	0.772227i
$163$	6.15730	+	4.19797i	0.482277	+	0.328811i	0.779934	−	0.625862i	$-0.215253\pi$
$163$	6.15730	+	4.19797i	0.482277	+	0.328811i	−0.297657	+	0.954673i	$0.596205\pi$
$164$	−0.0303438	−	0.0281549i	−0.00236945	−	0.00219853i
$165$	1.29041	−	2.23505i	0.100458	−	0.173999i
$166$	11.0582	+	19.1534i	0.858282	+	1.48659i
$167$	−2.74710	+	12.0358i	−0.212577	+	0.931361i	0.750231	+	0.661175i	$0.229942\pi$
$167$	−2.74710	+	12.0358i	−0.212577	+	0.931361i	−0.962808	+	0.270185i	$0.912915\pi$
$168$	0.817618	+	0.432311i	0.0630806	+	0.0333535i
$169$	−0.222521	−	0.974928i	−0.0171170	−	0.0749945i
$170$	−32.5013	+	30.1568i	−2.49274	+	2.31292i
$171$	6.05920	−	0.913277i	0.463359	−	0.0698401i
$172$	0.0408075	−	0.00615073i	0.00311154	−	0.000468989i
$173$	1.91529	−	1.77713i	0.145617	−	0.135113i	−0.604001	−	0.796984i	$-0.706428\pi$
$173$	1.91529	−	1.77713i	0.145617	−	0.135113i	0.749618	+	0.661871i	$0.230237\pi$
$174$	−0.157638	−	0.690659i	−0.0119505	−	0.0523587i
$175$	26.1694	+	13.8369i	1.97822	+	1.04598i
$176$	4.63349	−	20.3007i	0.349263	−	1.53022i
$177$	0.0763783	+	0.132291i	0.00574094	+	0.00994360i
$178$	2.99035	−	5.17944i	0.224136	−	0.388215i
$179$	14.0903	+	13.0739i	1.05316	+	0.977190i	0.999771	−	0.0213835i	$-0.00680710\pi$
$179$	14.0903	+	13.0739i	1.05316	+	0.977190i	0.0533893	+	0.998574i	$0.482998\pi$
$180$	0.123526	+	0.0842186i	0.00920708	+	0.00627728i
$181$	12.5003	+	15.6748i	0.929138	+	1.16510i	0.986004	+	0.166720i	$0.0533177\pi$
$181$	12.5003	+	15.6748i	0.929138	+	1.16510i	−0.0568662	+	0.998382i	$0.518111\pi$
$182$	−3.72976	+	0.419567i	−0.276468	+	0.0311004i
$183$	0.697971	−	0.875229i	0.0515955	−	0.0646988i
$184$	−13.3765	+	4.12609i	−0.986125	+	0.304179i
$185$	−1.13587	−	2.89414i	−0.0835105	−	0.212781i
$186$	0.0608245	−	0.811647i	0.00445987	−	0.0595128i
$187$	14.6824	−	37.4101i	1.07368	−	2.73570i
$188$	0.0426522	+	0.0205402i	0.00311073	+	0.00149805i
$189$	0.785344	−	1.79915i	0.0571254	−	0.130869i
$190$	−10.5580	+	5.08445i	−0.765956	+	0.368865i
$191$	−1.75560	−	23.4268i	−0.127031	−	1.69510i	−0.588939	−	0.808177i	$-0.700454\pi$
$191$	−1.75560	−	23.4268i	−0.127031	−	1.69510i	0.461909	−	0.886927i	$-0.347165\pi$
$192$	0.941805	+	0.290508i	0.0679689	+	0.0209656i
$193$	16.3407	−	11.1409i	1.17623	−	0.801941i	0.192449	−	0.981307i	$-0.438357\pi$
$193$	16.3407	−	11.1409i	1.17623	−	0.801941i	0.983782	+	0.179366i	$0.0574045\pi$
$194$	4.96878	+	0.748923i	0.356738	+	0.0537695i
$195$	−0.498836			−0.0357224
$196$	−3.12127e−5		0.0871475i	−2.22948e−6		0.00622482i
$197$	−13.5337			−0.964233			−0.482117	−	0.876107i	$-0.660132\pi$
$197$	−13.5337			−0.964233			−0.482117	+	0.876107i	$0.660132\pi$
$198$	−21.6608	−	3.26484i	−1.53937	−	0.232022i
$199$	15.0846	−	10.2845i	1.06932	−	0.729051i	0.105184	−	0.994453i	$-0.466457\pi$
$199$	15.0846	−	10.2845i	1.06932	−	0.729051i	0.964138	+	0.265401i	$0.0855045\pi$
$200$	30.1455	+	9.29865i	2.13161	+	0.657514i
$201$	0.00535031	+	0.0713949i	0.000377382	+	0.00503581i
$202$	−12.7299	+	6.13037i	−0.895669	+	0.431332i
$203$	−8.07876	+	6.94982i	−0.567018	+	0.487781i
$204$	−0.0108023	−	0.00520213i	−0.000756315	−	0.000364222i
$205$	−4.88744	+	12.4530i	−0.341354	+	0.869755i
$206$	1.13933	−	15.2033i	0.0793811	−	1.05927i
$207$	5.41359	+	13.7936i	0.376270	+	0.958722i
$208$	−3.84594	+	1.18631i	−0.266668	+	0.0822561i
$209$	6.62265	−	8.30454i	0.458098	−	0.574437i
$210$	−0.209961	+	1.86046i	−0.0144887	+	0.128384i
$211$	7.10999	+	8.91564i	0.489472	+	0.613778i	0.963818	−	0.266560i	$-0.0858871\pi$
$211$	7.10999	+	8.91564i	0.489472	+	0.613778i	−0.474347	+	0.880338i	$0.657316\pi$
$212$	0.0808321	+	0.0551104i	0.00555157	+	0.00378500i
$213$	−0.461212	−	0.427942i	−0.0316017	−	0.0293221i
$214$	7.01631	−	12.1526i	0.479625	−	0.830735i
$215$	−6.66862	−	11.5504i	−0.454796	−	0.787730i
$216$	0.465523	−	2.03959i	0.0316749	−	0.138777i
$217$	−11.2231	+	4.89420i	−0.761874	+	0.332240i
$218$	0.876538	+	3.84036i	0.0593667	+	0.260102i
$219$	−0.534126	+	0.495597i	−0.0360929	+	0.0334893i
$220$	0.256262	−	0.0386252i	0.0172772	−	0.00260411i
$221$	−7.68105	+	1.15773i	−0.516683	+	0.0778775i
$222$	0.0996261	−	0.0924396i	0.00668647	−	0.00620414i
$223$	5.56423	+	24.3785i	0.372608	+	1.63250i	0.719424	+	0.694571i	$0.244406\pi$
$223$	5.56423	+	24.3785i	0.372608	+	1.63250i	−0.346816	+	0.937933i	$0.612737\pi$
$224$	0.0346075	+	0.183084i	0.00231231	+	0.0122328i
$225$	7.43086	−	32.5567i	0.495390	−	2.17045i
$226$	11.6930	+	20.2528i	0.777804	+	1.34720i
$227$	3.21169	−	5.56281i	0.213167	−	0.369217i	−0.739537	−	0.673116i	$-0.764955\pi$
$227$	3.21169	−	5.56281i	0.213167	−	0.369217i	0.952704	+	0.303900i	$0.0982887\pi$
$228$	−0.00232299	−	0.00215542i	−0.000153844	−	0.000142746i
$229$	−12.0514	−	8.21651i	−0.796379	−	0.542962i	0.0953969	−	0.995439i	$-0.469588\pi$
$229$	−12.0514	−	8.21651i	−0.796379	−	0.542962i	−0.891776	+	0.452477i	$0.850540\pi$
$230$	−17.6683	−	22.1553i	−1.16501	−	1.46088i
$231$	−0.560222	−	1.60194i	−0.0368599	−	0.105400i
$232$	−7.08085	+	8.87911i	−0.464881	+	0.582942i
$233$	22.4795	−	6.93400i	1.47268	−	0.454262i	0.548478	−	0.836165i	$-0.315208\pi$
$233$	22.4795	−	6.93400i	1.47268	−	0.454262i	0.924202	+	0.381904i	$0.124731\pi$
$234$	1.54686	+	3.94134i	0.101121	+	0.257653i
$235$	1.14334	−	15.2568i	0.0745833	−	0.995245i
$236$	−0.00560406	+	0.0142789i	−0.000364793	+	0.000929478i
$237$	−1.42511	−	0.686298i	−0.0925710	−	0.0445799i
$238$	1.08492	+	29.1346i	0.0703246	+	1.88852i
$239$	−12.0285	+	5.79262i	−0.778059	+	0.374693i	−0.780381	−	0.625304i	$-0.784975\pi$
$239$	−12.0285	+	5.79262i	−0.778059	+	0.374693i	0.00232251	+	0.999997i	$0.499261\pi$
$240$	0.150035	+	2.00207i	0.00968470	+	0.129233i
$241$	−2.44202	−	0.753263i	−0.157304	−	0.0485219i	0.215103	−	0.976591i	$-0.430991\pi$
$241$	−2.44202	−	0.753263i	−0.157304	−	0.0485219i	−0.372407	+	0.928069i	$0.621467\pi$
$242$	−18.4806	+	12.5999i	−1.18798	+	0.809949i
$243$	−3.28750	−	0.495510i	−0.210893	−	0.0317870i
$244$	0.112412			0.00719644
$245$	26.2214	−	10.2803i	1.67522	−	0.656783i
$246$	−0.584780			−0.0372842
$247$	−2.03013	−	0.305994i	−0.129174	−	0.0194699i
$248$	−10.7809	+	7.35028i	−0.684586	+	0.466743i
$249$	1.84701	+	0.569726i	0.117049	+	0.0361049i
$250$	2.63973	+	35.2247i	0.166951	+	2.22781i
$251$	−10.6805	+	5.14348i	−0.674150	+	0.324653i	−0.739449	−	0.673212i	$-0.764914\pi$
$251$	−10.6805	+	5.14348i	−0.674150	+	0.324653i	0.0652996	+	0.997866i	$0.479200\pi$
$252$	0.0949644	−	0.0254274i	0.00598220	−	0.00160178i
$253$	23.1423	+	11.1447i	1.45494	+	0.700663i
$254$	3.89980	−	9.93652i	0.244695	−	0.623473i
$255$	−0.289569	+	3.86403i	−0.0181335	+	0.241975i
$256$	0.109157	+	0.278126i	0.00682229	+	0.0173829i
$257$	−24.0984	+	7.43336i	−1.50321	+	0.463680i	−0.933626	−	0.358250i	$-0.883374\pi$
$257$	−24.0984	+	7.43336i	−1.50321	+	0.463680i	−0.569588	+	0.821930i	$0.692897\pi$
$258$	0.363500	−	0.455815i	0.0226306	−	0.0283778i
$259$	−1.92958	−	0.675578i	−0.119898	−	0.0419784i
$260$	−0.0312314	−	0.0391630i	−0.00193689	−	0.00242878i
$261$	9.93280	+	6.77207i	0.614825	+	0.419180i
$262$	−15.3606	−	14.2526i	−0.948981	−	0.880526i
$263$	−1.03470	+	1.79215i	−0.0638022	+	0.110509i	−0.896162	−	0.443727i	$-0.853656\pi$
$263$	−1.03470	+	1.79215i	−0.0638022	+	0.110509i	0.832360	+	0.554236i	$0.186989\pi$
$264$	−0.904280	−	1.56626i	−0.0556546	−	0.0963965i
$265$	7.03554	−	30.8247i	0.432190	−	1.89355i
$266$	−1.99573	+	7.44282i	−0.122366	+	0.456348i
$267$	−0.116309	−	0.509583i	−0.00711799	−	0.0311859i
$268$	−0.00527014	+	0.00488998i	−0.000321925	+	0.000298703i
$269$	8.72640	−	1.31529i	0.532058	−	0.0801948i	0.122482	−	0.992471i	$-0.460915\pi$
$269$	8.72640	−	1.31529i	0.532058	−	0.0801948i	0.409576	+	0.912276i	$0.365677\pi$
$270$	4.18774	−	0.631200i	0.254858	−	0.0384136i
$271$	−13.1341	+	12.1867i	−0.797840	+	0.740288i	−0.969559	−	0.244858i	$-0.921259\pi$
$271$	−13.1341	+	12.1867i	−0.797840	+	0.740288i	0.171718	+	0.985146i	$0.445068\pi$
$272$	6.95677	+	30.4796i	0.421816	+	1.84810i
$273$	−0.214009	+	0.248592i	−0.0129524	+	0.0150455i
$274$	−0.772470	+	3.38441i	−0.0466666	+	0.204460i
$275$	−28.9432	−	50.1312i	−1.74534	−	3.02302i
$276$	0.00383157	−	0.00663647i	0.000230633	−	0.000399468i
$277$	17.5773	+	16.3094i	1.05612	+	0.979936i	0.999829	−	0.0184789i	$-0.00588235\pi$
$277$	17.5773	+	16.3094i	1.05612	+	0.979936i	0.0562901	+	0.998414i	$0.482073\pi$
$278$	−10.2570	−	6.99310i	−0.615174	−	0.419418i
$279$	8.61167	+	10.7987i	0.515567	+	0.646501i
$280$	25.4171	−	15.9643i	1.51896	−	0.954047i
$281$	2.64697	−	3.31920i	0.157905	−	0.198007i	−0.696585	−	0.717474i	$-0.745298\pi$
$281$	2.64697	−	3.31920i	0.157905	−	0.198007i	0.854490	+	0.519467i	$0.173870\pi$
$282$	0.639078	−	0.197129i	0.0380565	−	0.0117389i
$283$	5.50401	+	14.0240i	0.327180	+	0.833640i	0.995928	+	0.0901515i	$0.0287351\pi$
$283$	5.50401	+	14.0240i	0.327180	+	0.833640i	−0.668748	+	0.743489i	$0.733170\pi$
$284$	0.00472134	−	0.0630020i	0.000280160	−	0.00373848i
$285$	−0.374162	+	0.953348i	−0.0221634	+	0.0564715i
$286$	6.61259	+	3.18446i	0.391011	+	0.188301i
$287$	4.10909	+	7.77816i	0.242552	+	0.459130i
$288$	0.189376	−	0.0911989i	0.0111591	−	0.00537394i
$289$	3.23871	+	43.2176i	0.190513	+	2.54221i
$290$	−21.9688	−	6.77649i	−1.29006	−	0.397929i
$291$	0.362847	−	0.247385i	0.0212705	−	0.0145020i
$292$	−0.0723495	−	0.0109049i	−0.00423394	−	0.000638163i
$293$	−13.0960			−0.765079			−0.382540	−	0.923939i	$-0.624950\pi$
$293$	−13.0960			−0.765079			−0.382540	+	0.923939i	$0.624950\pi$
$294$	0.837076	+	0.902801i	0.0488192	+	0.0526524i
$295$	4.95738			0.288630
$296$	−2.15440	−	0.324723i	−0.125222	−	0.0188742i
$297$	−3.17172	+	2.16244i	−0.184042	+	0.125478i
$298$	−21.9019	−	6.75583i	−1.26874	−	0.391355i
$299$	−0.371016	−	4.95086i	−0.0214564	−	0.286316i
$300$	−0.0155596	+	0.00749309i	−0.000898331	+	0.000432614i
$301$	−8.61701	−	1.63202i	−0.496676	−	0.0940684i
$302$	−21.4887	−	10.3484i	−1.23654	−	0.595484i
$303$	−0.451131	+	1.14946i	−0.0259168	+	0.0660349i
$304$	−0.617500	+	8.23996i	−0.0354160	+	0.472594i
$305$	−13.2727	−	33.8183i	−0.759993	−	1.93643i
$306$	31.4279	−	9.69422i	1.79661	−	0.554181i
$307$	3.14836	−	3.94792i	0.179686	−	0.225319i	−0.683829	−	0.729643i	$-0.739686\pi$
$307$	3.14836	−	3.94792i	0.179686	−	0.225319i	0.863515	+	0.504323i	$0.168258\pi$
$308$	0.0906916	−	0.144278i	0.00516763	−	0.00822097i
$309$	−0.830758	−	1.04174i	−0.0472602	−	0.0592624i
$310$	−21.8243	−	14.8796i	−1.23954	−	0.845104i
$311$	−11.4254	−	10.6012i	−0.647876	−	0.601141i	0.286219	−	0.958164i	$-0.407601\pi$
$311$	−11.4254	−	10.6012i	−0.647876	−	0.601141i	−0.934096	+	0.357023i	$0.883792\pi$
$312$	−0.174785	+	0.302736i	−0.00989523	+	0.0171390i
$313$	−1.66874	−	2.89035i	−0.0943229	−	0.163372i	0.815003	−	0.579457i	$-0.196735\pi$
$313$	−1.66874	−	2.89035i	−0.0943229	−	0.163372i	−0.909326	+	0.416085i	$0.863402\pi$
$314$	5.35754	−	23.4729i	0.302343	−	1.32465i
$315$	−18.8623	−	25.5671i	−1.06277	−	1.44054i
$316$	−0.0353439	−	0.154852i	−0.00198825	−	0.00871110i
$317$	−10.2472	+	9.50800i	−0.575539	+	0.534022i	−0.913341	−	0.407195i	$-0.866507\pi$
$317$	−10.2472	+	9.50800i	−0.575539	+	0.534022i	0.337802	+	0.941217i	$0.390317\pi$
$318$	1.36665	−	0.205990i	0.0766381	−	0.0115513i
$319$	20.6062	−	3.10588i	1.15372	−	0.173896i
$320$	23.4468	−	21.7555i	1.31072	−	1.21617i
$321$	−0.272898	−	1.19564i	−0.0152317	−	0.0667343i
$322$	−18.6209	−	0.700085i	−1.03770	−	0.0390142i
$323$	−3.54872	+	15.5480i	−0.197456	+	0.865112i
$324$	−0.0551637	−	0.0955464i	−0.00306465	−	0.00530813i
$325$	−5.59432	+	9.68965i	−0.310317	+	0.537485i
$326$	7.74964	+	7.19062i	0.429213	+	0.398252i
$327$	0.284443	+	0.193930i	0.0157297	+	0.0107244i
$328$	5.84504	+	7.32945i	0.322738	+	0.404701i
$329$	−7.11265	−	7.11519i	−0.392133	−	0.392273i
$330$	2.28270	−	2.86242i	0.125659	−	0.157571i
$331$	23.9417	−	7.38503i	1.31595	−	0.405918i	0.444229	−	0.895913i	$-0.353478\pi$
$331$	23.9417	−	7.38503i	1.31595	−	0.405918i	0.871725	+	0.489995i	$0.163001\pi$
$332$	0.0709099	+	0.180676i	0.00389169	+	0.00991586i
$333$	−0.172349	+	2.29984i	−0.00944468	+	0.126030i
$334$	−6.39830	+	16.3026i	−0.350099	+	0.892039i
$335$	2.09337	+	1.00811i	0.114373	+	0.0550791i
$336$	1.06209	+	0.784152i	0.0579418	+	0.0427790i
$337$	−15.3551	+	7.39462i	−0.836445	+	0.402811i	−0.802528	−	0.596614i	$-0.796512\pi$
$337$	−15.3551	+	7.39462i	−0.836445	+	0.402811i	−0.0339164	+	0.999425i	$0.510798\pi$
$338$	−0.106013	−	1.41464i	−0.00576633	−	0.0769464i
$339$	1.95303	+	0.602429i	0.106074	+	0.0327195i
$340$	−0.321489	+	0.219188i	−0.0174352	+	0.0118871i
$341$	23.6750	+	3.56843i	1.28207	+	0.193241i
$342$	8.69272			0.470049
$343$	6.12624	−	17.4777i	0.330786	−	0.943706i
$344$	−9.34633			−0.503920
$345$	−2.44893	−	0.369117i	−0.131846	−	0.0198726i
$346$	3.06244	−	2.08794i	0.164638	−	0.112248i
$347$	−5.57270	−	1.71895i	−0.299158	−	0.0922780i	0.141543	−	0.989932i	$-0.454794\pi$
$347$	−5.57270	−	1.71895i	−0.299158	−	0.0922780i	−0.440701	+	0.897654i	$0.645270\pi$
$348$	−0.000464602	−	0.00619968i	−2.49053e−5	−	0.000332338i
$349$	−2.61616	+	1.25988i	−0.140040	+	0.0674397i	−0.502591	−	0.864524i	$-0.667620\pi$
$349$	−2.61616	+	1.25988i	−0.140040	+	0.0674397i	0.362551	+	0.931964i	$0.381906\pi$
$350$	33.7840	+	24.9430i	1.80583	+	1.33326i
$351$	0.668497	+	0.321931i	0.0356817	+	0.0171834i
$352$	0.133114	−	0.339169i	0.00709500	−	0.0180778i
$353$	−0.707990	+	9.44747i	−0.0376825	+	0.502838i	0.946148	+	0.323735i	$0.104939\pi$
$353$	−0.707990	+	9.44747i	−0.0376825	+	0.502838i	−0.983830	+	0.179103i	$0.942680\pi$
$354$	0.0791700	+	0.201722i	0.00420784	+	0.0107214i
$355$	−19.5111	+	6.01838i	−1.03554	+	0.319423i
$356$	0.0327247	−	0.0410355i	0.00173441	−	0.00217488i
$357$	1.80139	+	1.80203i	0.0953396	+	0.0953737i
$358$	17.0011	+	21.3188i	0.898539	+	1.12673i
$359$	1.06621	+	0.726931i	0.0562725	+	0.0383660i	0.591130	−	0.806577i	$-0.298682\pi$
$359$	1.06621	+	0.726931i	0.0562725	+	0.0383660i	−0.534857	+	0.844943i	$0.679635\pi$
$360$	−24.8205	−	23.0301i	−1.30816	−	1.21379i
$361$	7.39246	−	12.8041i	0.389077	−	0.673901i
$362$	14.2208	+	24.6311i	0.747426	+	1.29458i
$363$	−0.434982	+	1.90578i	−0.0228306	+	0.100028i
$364$	−0.0329154	−	0.00123751i	−0.00172524	−	6.48632e-5i
$365$	5.26178	+	23.0534i	0.275414	+	1.20667i
$366$	1.16414	−	1.08016i	0.0608506	−	0.0564611i
$367$	16.7669	−	2.52720i	0.875225	−	0.131919i	0.303960	−	0.952685i	$-0.401691\pi$
$367$	16.7669	−	2.52720i	0.875225	−	0.131919i	0.571265	+	0.820766i	$0.306453\pi$
$368$	−19.7586	+	2.97813i	−1.02999	+	0.155246i
$369$	7.27449	−	6.74974i	0.378695	−	0.351378i
$370$	−0.981436	−	4.29995i	−0.0510224	−	0.223544i
$371$	−12.3430	−	16.7304i	−0.640815	−	0.868599i
$372$	0.00158946	−	0.00696386i	8.24095e−5	−	0.000361059i
$373$	−4.38014	−	7.58663i	−0.226795	−	0.392821i	0.730061	−	0.683382i	$-0.239491\pi$
$373$	−4.38014	−	7.58663i	−0.226795	−	0.392821i	−0.956856	+	0.290561i	$0.906158\pi$
$374$	28.5056	−	49.3732i	1.47399	−	2.55303i
$375$	2.26302	+	2.09978i	0.116862	+	0.108432i
$376$	−8.85852	−	6.03964i	−0.456843	−	0.311470i
$377$	−2.51134	−	3.14912i	−0.129340	−	0.162188i
$378$	1.48205	−	2.35773i	0.0762285	−	0.121269i
$379$	13.9696	−	17.5173i	0.717570	−	0.899804i	−0.280628	−	0.959817i	$-0.590543\pi$
$379$	13.9696	−	17.5173i	0.717570	−	0.899804i	0.998198	+	0.0600128i	$0.0191142\pi$
$380$	−0.0982718	+	0.0303128i	−0.00504124	+	0.00155502i
$381$	−0.340826	−	0.868409i	−0.0174610	−	0.0444900i
$382$	2.49050	−	33.2335i	0.127425	−	1.70037i
$383$	−3.27819	+	8.35269i	−0.167508	+	0.426803i	−0.989837	−	0.142210i	$-0.954579\pi$
$383$	−3.27819	+	8.35269i	−0.167508	+	0.426803i	0.822329	+	0.569013i	$0.192674\pi$
$384$	1.27544	+	0.614219i	0.0650870	+	0.0313443i
$385$	−54.1129	−	10.2488i	−2.75785	−	0.522325i
$386$	25.2777	−	12.1731i	1.28660	−	0.619595i
$387$	0.739344	+	9.86585i	0.0375829	+	0.501510i
$388$	0.0421392	+	0.0129982i	0.00213929	+	0.000659884i
$389$	−1.12199	+	0.764960i	−0.0568871	+	0.0387850i	−0.591430	−	0.806357i	$-0.701436\pi$
$389$	−1.12199	+	0.764960i	−0.0568871	+	0.0387850i	0.534543	+	0.845142i	$0.320484\pi$
$390$	−0.699749	−	0.105470i	−0.0354332	−	0.00534069i
$391$	−38.5651			−1.95032
$392$	2.94862	−	19.5154i	0.148928	−	0.985676i
$393$	−1.83132			−0.0923778
$394$	−18.9845	−	2.86146i	−0.956427	−	0.144158i
$395$	−42.4129	+	28.9166i	−2.13402	+	1.45495i
$396$	−0.183701	−	0.0566641i	−0.00923130	−	0.00284748i
$397$	−2.81346	−	37.5430i	−0.141203	−	1.88423i	−0.397458	−	0.917620i	$-0.630108\pi$
$397$	−2.81346	−	37.5430i	−0.141203	−	1.88423i	0.256255	−	0.966609i	$-0.417511\pi$
$398$	23.3347	−	11.2374i	1.16966	−	0.563279i
$399$	0.314575	+	0.595463i	0.0157484	+	0.0298104i
$400$	40.5719	+	19.5384i	2.02860	+	0.976921i
$401$	−13.1171	+	33.4217i	−0.655035	+	1.66900i	0.0849559	+	0.996385i	$0.472925\pi$
$401$	−13.1171	+	33.4217i	−0.655035	+	1.66900i	−0.739991	+	0.672617i	$0.765170\pi$
$402$	−0.00758999	+	0.101281i	−0.000378554	+	0.00505146i
$403$	−1.69070	−	4.30783i	−0.0842197	−	0.214588i
$404$	−0.118487	+	0.0365485i	−0.00589497	+	0.00181836i
$405$	−22.2311	+	27.8769i	−1.10467	+	1.38522i
$406$	−12.8020	+	8.04084i	−0.635353	+	0.399060i
$407$	2.49260	+	3.12562i	0.123553	+	0.154931i
$408$	2.24356	+	1.52963i	0.111073	+	0.0757281i
$409$	26.2744	+	24.3791i	1.29919	+	1.20547i	0.964786	+	0.263038i	$0.0847244\pi$
$409$	26.2744	+	24.3791i	1.29919	+	1.20547i	0.334401	+	0.942431i	$0.391466\pi$
$410$	−9.48889	+	16.4352i	−0.468623	+	0.811679i
$411$	0.151695	+	0.262743i	0.00748255	+	0.0129602i
$412$	0.0297729	−	0.130443i	0.00146680	−	0.00642649i
$413$	2.12679	−	2.47048i	0.104653	−	0.121565i
$414$	4.67757	+	20.4938i	0.229890	+	1.00721i
$415$	45.9824	−	42.6654i	2.25719	−	2.09436i
$416$	−0.0696382	+	0.0104963i	−0.00341430	+	0.000514622i
$417$	−1.07282	+	0.161702i	−0.0525362	+	0.00791856i
$418$	11.0459	−	10.2491i	0.540271	−	0.501298i
$419$	−5.57728	−	24.4357i	−0.272468	−	1.19376i	−0.907089	−	0.420938i	$-0.861701\pi$
$419$	−5.57728	−	24.4357i	−0.272468	−	1.19376i	0.634621	−	0.772823i	$-0.281156\pi$
$420$	−0.00425550	+	0.0158704i	−0.000207647	+	0.000774395i
$421$	1.09159	−	4.78257i	0.0532009	−	0.233088i	−0.941336	−	0.337469i	$-0.890429\pi$
$421$	1.09159	−	4.78257i	0.0532009	−	0.233088i	0.994537	+	0.104381i	$0.0332862\pi$
$422$	8.08857	+	14.0098i	0.393746	+	0.681987i
$423$	−5.67460	+	9.82870i	−0.275908	+	0.477888i
$424$	−16.2419	−	15.0703i	−0.788776	−	0.731877i
$425$	71.8095	+	48.9589i	3.48327	+	2.37485i
$426$	−0.556490	−	0.697817i	−0.0269620	−	0.0338093i
$427$	−22.5474	−	7.89420i	−1.09114	−	0.382027i
$428$	0.0767826	−	0.0962823i	0.00371143	−	0.00465398i
$429$	0.612937	−	0.189066i	0.0295929	−	0.00912820i
$430$	−6.91237	−	17.6124i	−0.333344	−	0.849346i
$431$	−0.794564	+	10.6027i	−0.0382728	+	0.510715i	0.944818	+	0.327596i	$0.106238\pi$
$431$	−0.794564	+	10.6027i	−0.0382728	+	0.510715i	−0.983091	+	0.183119i	$0.941381\pi$
$432$	1.09100	−	2.77983i	0.0524910	−	0.133745i
$433$	16.5808	+	7.98491i	0.796824	+	0.383730i	0.787569	−	0.616227i	$-0.211340\pi$
$433$	16.5808	+	7.98491i	0.796824	+	0.383730i	0.00925541	+	0.999957i	$0.497054\pi$
$434$	−16.7781	+	4.49247i	−0.805377	+	0.215646i
$435$	−1.81027	+	0.871780i	−0.0867958	+	0.0417987i
$436$	0.00258339	+	0.0344729i	0.000123722	+	0.00165095i
$437$	−9.74010	−	3.00442i	−0.465932	−	0.143721i
$438$	−0.854038	+	0.582274i	−0.0408075	+	0.0278221i
$439$	24.6912	+	3.72160i	1.17845	+	0.177622i	0.708916	−	0.705293i	$-0.249185\pi$
$439$	24.6912	+	3.72160i	1.17845	+	0.177622i	0.469532	+	0.882916i	$0.344423\pi$
$440$	−58.6929			−2.79807
$441$	−20.8334	−	1.56875i	−0.992068	−	0.0747025i
$442$	−11.0195			−0.524143
$443$	0.650488	+	0.0980453i	0.0309056	+	0.00465827i	0.164477	−	0.986381i	$-0.447406\pi$
$443$	0.650488	+	0.0980453i	0.0309056	+	0.00465827i	−0.133571	+	0.991039i	$0.542645\pi$
$444$	0.000985459	0	0.000671875i	4.67678e−5	0	3.18858e-5i
$445$	−16.2091	−	4.99984i	−0.768384	−	0.237015i
$446$	2.65089	+	35.3737i	0.125523	+	1.67499i
$447$	−1.80475	+	0.869122i	−0.0853618	+	0.0411081i
$448$	−0.782671	−	21.0181i	−0.0369777	−	0.993010i
$449$	−33.9786	−	16.3632i	−1.60355	−	0.772229i	−0.603858	−	0.797092i	$-0.706371\pi$
$449$	−33.9786	−	16.3632i	−1.60355	−	0.772229i	−0.999691	+	0.0248631i	$0.992085\pi$
$450$	17.3073	−	44.0982i	0.815873	−	2.07881i
$451$	1.28550	−	17.1538i	0.0605319	−	0.807742i
$452$	0.0749803	+	0.191047i	0.00352678	+	0.00898608i
$453$	−1.99184	+	0.614401i	−0.0935848	+	0.0288671i
$454$	5.68140	−	7.12425i	0.266641	−	0.334358i
$455$	3.51409	+	10.0485i	0.164743	+	0.471079i
$456$	0.447472	+	0.561112i	0.0209548	+	0.0262765i
$457$	8.70214	+	5.93302i	0.407069	+	0.277535i	0.749495	−	0.662010i	$-0.230296\pi$
$457$	8.70214	+	5.93302i	0.407069	+	0.277535i	−0.342426	+	0.939545i	$0.611249\pi$
$458$	−15.1680	−	14.0739i	−0.708756	−	0.657629i
$459$	2.88176	−	4.99136i	0.134509	−	0.232977i
$460$	−0.124345	−	0.215372i	−0.00579762	−	0.0100418i
$461$	3.94517	−	17.2849i	0.183745	−	0.805039i	−0.796082	−	0.605189i	$-0.793097\pi$
$461$	3.94517	−	17.2849i	0.183745	−	0.805039i	0.979827	−	0.199850i	$-0.0640454\pi$
$462$	−0.447156	−	2.36559i	−0.0208036	−	0.110057i
$463$	−1.96800	−	8.62236i	−0.0914606	−	0.400715i	0.908388	−	0.418129i	$-0.137314\pi$
$463$	−1.96800	−	8.62236i	−0.0914606	−	0.400715i	−0.999848	+	0.0174138i	$0.994457\pi$
$464$	−11.8836	+	11.0264i	−0.551683	+	0.511887i
$465$	−2.28269	+	0.344061i	−0.105857	+	0.0159554i
$466$	32.9995	−	4.97387i	1.52867	−	0.230410i
$467$	4.37882	−	4.06295i	0.202627	−	0.188011i	−0.572332	−	0.820022i	$-0.693961\pi$
$467$	4.37882	−	4.06295i	0.202627	−	0.188011i	0.774959	+	0.632012i	$0.217770\pi$
$468$	0.00826834	+	0.0362260i	0.000382204	+	0.00167455i
$469$	1.40048	−	0.610723i	0.0646679	−	0.0282006i
$470$	4.82963	−	21.1600i	0.222774	−	0.976037i
$471$	−1.05209	−	1.82228i	−0.0484779	−	0.0839663i
$472$	1.73699	−	3.00856i	0.0799515	−	0.138480i
$473$	12.5717	+	11.6648i	0.578048	+	0.536350i
$474$	−1.85399	−	1.26403i	−0.0851566	−	0.0580588i
$475$	14.3222	+	17.9595i	0.657148	+	0.824037i
$476$	−0.0286929	+	0.254247i	−0.00131514	+	0.0116534i
$477$	−14.6231	+	18.3368i	−0.669548	+	0.839586i
$478$	−18.0979	+	5.58246i	−0.827778	+	0.255336i
$479$	1.04706	+	2.66786i	0.0478412	+	0.121897i	0.952797	−	0.303608i	$-0.0981914\pi$
$479$	1.04706	+	2.66786i	0.0478412	+	0.121897i	−0.904956	+	0.425506i	$0.860096\pi$
$480$	−0.00262530	+	0.0350322i	−0.000119828	+	0.00159899i
$481$	0.282307	−	0.719307i	0.0128721	−	0.0327976i
$482$	−3.26631	−	1.57297i	−0.148776	−	0.0716469i
$483$	−1.23458	+	1.06205i	−0.0561752	+	0.0483252i
$484$	−0.176854	+	0.0851683i	−0.00803881	+	0.00387129i
$485$	−1.06504	−	14.2120i	−0.0483610	−	0.645333i
$486$	−4.50681	−	1.39017i	−0.204433	−	0.0630593i
$487$	19.0855	−	13.0123i	0.864847	−	0.589643i	−0.0475867	−	0.998867i	$-0.515153\pi$
$487$	19.0855	−	13.0123i	0.864847	−	0.589643i	0.912434	+	0.409224i	$0.134201\pi$
$488$	−25.1744	−	3.79442i	−1.13959	−	0.171765i
$489$	0.923926			0.0417814
$490$	38.9560	−	8.87676i	1.75985	−	0.401011i
$491$	0.270745			0.0122185			0.00610927	−	0.999981i	$-0.498055\pi$
$491$	0.270745			0.0122185			0.00610927	+	0.999981i	$0.498055\pi$
$492$	−0.00507469		0.000764886i	−0.000228785		3.44837e-5i
$493$	−25.8511	+	17.6250i	−1.16428	+	0.793790i
$494$	−2.78310	−	0.858473i	−0.125218	−	0.0386245i
$495$	4.64291	+	61.9554i	0.208683	+	2.78469i
$496$	−16.7809	+	8.08127i	−0.753486	+	0.362860i
$497$	−5.37135	+	12.3052i	−0.240938	+	0.551966i
$498$	2.47045	+	1.18971i	0.110704	+	0.0533121i
$499$	8.14588	−	20.7554i	0.364660	−	0.929138i	−0.624331	−	0.781160i	$-0.714628\pi$
$499$	8.14588	−	20.7554i	0.364660	−	0.929138i	0.988991	−	0.147978i	$-0.0472765\pi$
$500$	−0.0231661	+	0.309131i	−0.00103602	+	0.0138247i
$501$	0.559184	+	1.42478i	0.0249825	+	0.0636544i
$502$	−16.0698	+	4.95687i	−0.717229	+	0.221236i
$503$	18.4646	−	23.1538i	0.823294	−	1.03238i	−0.175557	−	0.984469i	$-0.556173\pi$
$503$	18.4646	−	23.1538i	0.823294	−	1.03238i	0.998852	−	0.0479093i	$-0.0152559\pi$
$504$	−22.1253	+	2.48891i	−0.985540	+	0.110865i
$505$	24.9854	+	31.3307i	1.11183	+	1.39420i
$506$	30.1068	+	20.5264i	1.33841	+	0.912512i
$507$	−0.0908840	−	0.0843280i	−0.00403630	−	0.00374514i
$508$	0.0468391	−	0.0811276i	0.00207815	−	0.00359946i
$509$	4.25172	+	7.36420i	0.188454	+	0.326412i	0.944735	−	0.327835i	$-0.106319\pi$
$509$	4.25172	+	7.36420i	0.188454	+	0.326412i	−0.756281	+	0.654247i	$0.772986\pi$
$510$	−1.22318	+	5.35909i	−0.0541632	+	0.237305i
$511$	13.7459	+	7.26808i	0.608083	+	0.321521i
$512$	−4.98726	−	21.8506i	−0.220408	−	0.965670i
$513$	1.11668	−	1.03612i	0.0493025	−	0.0457460i
$514$	−35.3759	+	5.33207i	−1.56037	+	0.235187i
$515$	−42.7583	+	6.44477i	−1.88415	+	0.283991i
$516$	0.00375064	−	0.00348008i	0.000165113	−	0.000153202i
$517$	4.37769	+	19.1799i	0.192531	+	0.843532i
$518$	−2.56391	−	1.35565i	−0.112652	−	0.0595640i
$519$	0.0720815	−	0.315810i	0.00316403	−	0.0138625i
$520$	5.67226	+	9.82464i	0.248745	+	0.430839i
$521$	8.79176	−	15.2278i	0.385174	−	0.667141i	−0.606619	−	0.794993i	$-0.707475\pi$
$521$	8.79176	−	15.2278i	0.385174	−	0.667141i	0.991793	+	0.127851i	$0.0408081\pi$
$522$	12.5015	+	11.5997i	0.547177	+	0.507706i
$523$	−28.6851	−	19.5571i	−1.25431	−	0.855174i	−0.260415	−	0.965497i	$-0.583859\pi$
$523$	−28.6851	−	19.5571i	−1.25431	−	0.855174i	−0.993896	+	0.110323i	$0.964812\pi$
$524$	−0.114656	−	0.143774i	−0.00500878	−	0.00628081i
$525$	3.64711	−	0.410269i	0.159173	−	0.0179056i
$526$	−1.83036	+	2.29519i	−0.0798073	+	0.100075i
$527$	−34.3503	+	10.5957i	−1.49632	+	0.461554i
$528$	−0.943168	−	2.40315i	−0.0410461	−	0.104584i
$529$	0.123204	−	1.64404i	0.00535668	−	0.0714799i
$530$	16.3865	−	41.7522i	0.711786	−	1.81360i
$531$	−3.31320	−	1.59555i	−0.143780	−	0.0692410i
$532$	−0.0270539	+	0.0619779i	−0.00117294	+	0.00268708i
$533$	−2.99562	+	1.44262i	−0.129755	+	0.0624867i
$534$	−0.0554115	−	0.739415i	−0.00239789	−	0.0319976i
$535$	−38.0317	−	11.7312i	−1.64425	−	0.507185i
$536$	1.34529	−	0.917205i	0.0581078	−	0.0396172i
$537$	2.35647	+	0.355180i	0.101689	+	0.0153272i
$538$	12.5192			0.539740
$539$	−28.3227	+	22.5700i	−1.21995	+	0.972159i
$540$	0.0371666			0.00159939
$541$	29.0171	+	4.37362i	1.24754	+	0.188037i	0.739418	−	0.673247i	$-0.235101\pi$
$541$	29.0171	+	4.37362i	1.24754	+	0.188037i	0.508125	+	0.861284i	$0.330339\pi$
$542$	−21.0007	+	14.3180i	−0.902058	+	0.615013i
$543$	2.37524	+	0.732663i	0.101931	+	0.0314416i
$544$	0.0408808	+	0.545517i	0.00175275	+	0.0233888i
$545$	10.0659	−	4.84748i	0.431176	−	0.207643i
$546$	−0.352764	+	0.303468i	−0.0150969	+	0.0129872i
$547$	15.2879	+	7.36226i	0.653663	+	0.314787i	0.731161	−	0.682205i	$-0.238979\pi$
$547$	15.2879	+	7.36226i	0.653663	+	0.314787i	−0.0774982	+	0.996992i	$0.524693\pi$
$548$	−0.0111302	+	0.0283593i	−0.000475459	+	0.00121145i
$549$	−2.01392	+	26.8738i	−0.0859519	+	1.14695i
$550$	−30.0012	−	76.4417i	−1.27925	−	3.25949i
$551$	−7.90210	+	2.43747i	−0.336641	+	0.103840i
$552$	−1.08208	+	1.35689i	−0.0460564	+	0.0577529i
$553$	−3.78535	+	33.5419i	−0.160969	+	1.42635i
$554$	21.2085	+	26.5946i	0.901063	+	1.12990i
$555$	−0.318484	−	0.217138i	−0.0135189	−	0.00921701i
$556$	−0.0798627	−	0.0741017i	−0.00338693	−	0.00314261i
$557$	−1.59720	+	2.76643i	−0.0676755	+	0.117217i	−0.897878	−	0.440245i	$-0.854892\pi$
$557$	−1.59720	+	2.76643i	−0.0676755	+	0.117217i	0.830202	+	0.557462i	$0.188225\pi$
$558$	9.79695	+	16.9688i	0.414738	+	0.718347i
$559$	0.737618	−	3.23171i	0.0311979	−	0.136687i
$560$	39.2725	−	17.1260i	1.65957	−	0.723707i
$561$	−1.10872	−	4.85761i	−0.0468101	−	0.205089i
$562$	4.41486	−	4.09639i	0.186230	−	0.172796i
$563$	9.99929	−	1.50715i	0.421420	−	0.0635188i	0.0650907	−	0.997879i	$-0.479266\pi$
$563$	9.99929	−	1.50715i	0.421420	−	0.0635188i	0.356329	+	0.934361i	$0.384028\pi$
$564$	0.00580372		0.000874770i	0.000244381		3.68345e-5i
$565$	48.6219	−	45.1145i	2.04554	−	1.89798i
$566$	4.75570	+	20.8361i	0.199897	+	0.875806i
$567$	4.35483	+	23.0384i	0.182886	+	0.967522i
$568$	−3.18394	+	13.9497i	−0.133595	+	0.585318i
$569$	9.61914	+	16.6608i	0.403255	+	0.698459i	0.994117	−	0.108314i	$-0.0345453\pi$
$569$	9.61914	+	16.6608i	0.403255	+	0.698459i	−0.590861	+	0.806773i	$0.701212\pi$
$570$	−0.726429	+	1.25821i	−0.0304268	+	0.0527007i
$571$	0.417314	+	0.387211i	0.0174640	+	0.0162043i	0.688857	−	0.724898i	$-0.258113\pi$
$571$	0.417314	+	0.387211i	0.0174640	+	0.0162043i	−0.671392	+	0.741102i	$0.734303\pi$
$572$	0.0532184	+	0.0362837i	0.00222517	+	0.00151710i
$573$	−1.81598	−	2.27717i	−0.0758637	−	0.0951301i
$574$	4.11953	+	11.7797i	0.171946	+	0.491676i
$575$	−34.6341	+	43.4297i	−1.44434	+	1.81115i
$576$	−22.6725	+	6.99353i	−0.944685	+	0.291397i
$577$	−5.12224	−	13.0513i	−0.213242	−	0.543331i	0.783729	−	0.621102i	$-0.213315\pi$
$577$	−5.12224	−	13.0513i	−0.213242	−	0.543331i	−0.996971	+	0.0777711i	$0.975220\pi$
$578$	−4.59447	+	61.3089i	−0.191105	+	2.55011i
$579$	0.895812	−	2.28249i	0.0372287	−	0.0948572i
$580$	−0.181781	−	0.0875410i	−0.00754803	−	0.00363494i
$581$	−1.53492	−	41.2192i	−0.0636793	−	1.71006i
$582$	0.561294	−	0.270305i	0.0232664	−	0.0112045i
$583$	3.03820	+	40.5419i	0.125829	+	1.67908i
$584$	15.8344	+	4.88426i	0.655231	+	0.202112i
$585$	9.92205	−	6.76474i	0.410226	−	0.279687i
$586$	−18.3707	−	2.76893i	−0.758885	−	0.114383i
$587$	−11.9799			−0.494465			−0.247233	−	0.968956i	$-0.579521\pi$
$587$	−11.9799			−0.494465			−0.247233	+	0.968956i	$0.579521\pi$
$588$	0.00608324	+	0.00892934i	0.000250868	+	0.000368240i
$589$	−9.50103			−0.391483
$590$	6.95404	+	1.04815i	0.286293	+	0.0431517i
$591$	−1.38635	+	0.945199i	−0.0570269	+	0.0388803i
$592$	−2.97184	−	0.916691i	−0.122142	−	0.0376758i
$593$	0.459775	+	6.13527i	0.0188807	+	0.251945i	0.998655	+	0.0518413i	$0.0165090\pi$
$593$	0.459775	+	6.13527i	0.0188807	+	0.251945i	−0.979775	+	0.200104i	$0.935872\pi$
$594$	−4.90639	+	2.36279i	−0.201311	+	0.0969465i
$595$	79.8762	−	21.3874i	3.27460	−	0.876799i
$596$	−0.181226	−	0.0872741i	−0.00742333	−	0.00357488i
$597$	0.826953	−	2.10704i	0.0338449	−	0.0862354i
$598$	0.526326	−	7.02333i	0.0215231	−	0.287205i
$599$	2.93912	+	7.48875i	0.120089	+	0.305982i	0.978260	−	0.207382i	$-0.0664943\pi$
$599$	2.93912	+	7.48875i	0.120089	+	0.305982i	−0.858171	+	0.513364i	$0.828399\pi$
$600$	3.73744	−	1.15285i	0.152581	−	0.0470649i
$601$	9.77742	−	12.2605i	0.398829	−	0.500116i	−0.541349	−	0.840798i	$-0.682086\pi$
$601$	9.77742	−	12.2605i	0.398829	−	0.500116i	0.940179	+	0.340681i	$0.110658\pi$
$602$	−11.7426	−	4.11126i	−0.478591	−	0.167563i
$603$	−1.07461	−	1.34752i	−0.0437614	−	0.0548751i
$604$	−0.172942	−	0.117910i	−0.00703691	−	0.00479769i
$605$	46.5037	+	43.1491i	1.89065	+	1.75426i
$606$	−0.875863	+	1.51704i	−0.0355795	+	0.0616255i
$607$	−0.846769	−	1.46665i	−0.0343693	−	0.0595294i	0.848329	−	0.529469i	$-0.177609\pi$
$607$	−0.846769	−	1.46665i	−0.0343693	−	0.0595294i	−0.882698	+	0.469940i	$0.844276\pi$
$608$	−0.0321736	+	0.140962i	−0.00130481	+	0.00571675i
$609$	−0.342187	+	1.27615i	−0.0138661	+	0.0517120i
$610$	−11.4682	−	50.2454i	−0.464333	−	2.03437i
$611$	2.78747	−	2.58639i	0.112769	−	0.104634i
$612$	0.285409	−	0.0430185i	0.0115370	−	0.00173892i
$613$	−4.81243	+	0.725356i	−0.194372	+	0.0292969i	−0.245507	−	0.969395i	$-0.578954\pi$
$613$	−4.81243	+	0.725356i	−0.194372	+	0.0292969i	0.0511347	+	0.998692i	$0.483716\pi$
$614$	5.25112	−	4.87233i	0.211918	−	0.196631i
$615$	0.369068	+	1.61699i	0.0148823	+	0.0652034i
$616$	−25.1802	+	29.2493i	−1.01454	+	1.17849i
$617$	4.92365	−	21.5719i	0.198219	−	0.868452i	−0.773778	−	0.633457i	$-0.781635\pi$
$617$	4.92365	−	21.5719i	0.198219	−	0.868452i	0.971996	−	0.234995i	$-0.0755075\pi$
$618$	−0.945100	−	1.63696i	−0.0380175	−	0.0658483i
$619$	9.13703	−	15.8258i	0.367248	−	0.636092i	−0.621886	−	0.783108i	$-0.713633\pi$
$619$	9.13703	−	15.8258i	0.367248	−	0.636092i	0.989134	+	0.147015i	$0.0469666\pi$
$620$	−0.169928	−	0.157670i	−0.00682447	−	0.00633218i
$621$	3.04363	+	2.07511i	0.122137	+	0.0832714i
$622$	−13.7857	−	17.2867i	−0.552757	−	0.693135i
$623$	−9.44559	+	5.93270i	−0.378430	+	0.237689i
$624$	−0.311115	+	0.390125i	−0.0124546	+	0.0156175i
$625$	42.2770	−	13.0407i	1.69108	−	0.521629i
$626$	−1.72974	−	4.40730i	−0.0691342	−	0.176151i
$627$	0.0984126	−	1.31322i	0.00393022	−	0.0524451i
$628$	0.0771947	−	0.196689i	0.00308040	−	0.00784874i
$629$	−5.40794	−	2.60433i	−0.215629	−	0.103841i
$630$	−21.0536	−	39.8526i	−0.838796	−	1.58777i
$631$	37.2348	−	17.9313i	1.48229	−	0.713835i	0.494438	−	0.869213i	$-0.335374\pi$
$631$	37.2348	−	17.9313i	1.48229	−	0.713835i	0.987855	+	0.155378i	$0.0496595\pi$
$632$	2.68821	+	35.8717i	0.106931	+	1.42690i
$633$	1.35100	+	0.416729i	0.0536975	+	0.0165635i
$634$	−16.3847	+	11.1709i	−0.650719	+	0.443653i
$635$	−29.9370	−	4.51228i	−1.18801	−	0.179064i
$636$	0.0121292			0.000480953
$637$	6.51520	+	2.55972i	0.258142	+	0.101420i
$638$	29.5623			1.17038
$639$	14.9770	+	2.25742i	0.592482	+	0.0893023i
$640$	37.9584	−	25.8796i	1.50044	−	1.02298i
$641$	35.4632	+	10.9389i	1.40071	+	0.432062i	0.900883	−	0.434062i	$-0.142920\pi$
$641$	35.4632	+	10.9389i	1.40071	+	0.432062i	0.499829	+	0.866124i	$0.333396\pi$
$642$	−0.130013	−	1.73490i	−0.00513121	−	0.0684712i
$643$	15.0203	−	7.23340i	0.592343	−	0.285258i	−0.113599	−	0.993527i	$-0.536238\pi$
$643$	15.0203	−	7.23340i	0.592343	−	0.285258i	0.705943	+	0.708269i	$0.250524\pi$
$644$	−0.160676	−	0.0304313i	−0.00633150	−	0.00119916i
$645$	−1.48980	−	0.717450i	−0.0586608	−	0.0282496i
$646$	−8.26537	+	21.0598i	−0.325197	+	0.828587i
$647$	2.13577	−	28.4999i	0.0839659	−	1.12045i	−0.782981	−	0.622046i	$-0.786302\pi$
$647$	2.13577	−	28.4999i	0.0839659	−	1.12045i	0.866947	−	0.498401i	$-0.166079\pi$
$648$	9.12863	+	23.2594i	0.358607	+	0.913715i
$649$	−6.09130	+	1.87892i	−0.239105	+	0.0737540i
$650$	−9.89622	+	12.4095i	−0.388162	+	0.486739i
$651$	−0.807851	+	1.28518i	−0.0316622	+	0.0503700i
$652$	0.0578457	+	0.0725362i	0.00226541	+	0.00284074i
$653$	31.6299	+	21.5649i	1.23778	+	0.843901i	0.992100	−	0.125451i	$-0.0400378\pi$
$653$	31.6299	+	21.5649i	1.23778	+	0.843901i	0.245676	+	0.969352i	$0.420990\pi$
$654$	0.358004	+	0.332179i	0.0139990	+	0.0129892i
$655$	−29.7157	+	51.4691i	−1.16109	+	2.01107i
$656$	6.69092	+	11.5890i	0.261237	+	0.452475i
$657$	3.90317	−	17.1009i	0.152277	−	0.667170i
$658$	−8.47298	−	11.4848i	−0.330311	−	0.447723i
$659$	1.03511	+	4.53509i	0.0403220	+	0.176662i	0.991079	−	0.133275i	$-0.0425492\pi$
$659$	1.03511	+	4.53509i	0.0403220	+	0.176662i	−0.950757	+	0.309937i	$0.899692\pi$
$660$	0.0235532	−	0.0218541i	0.000916806	−	0.000850671i
$661$	21.1957	−	3.19474i	0.824419	−	0.124261i	0.276735	−	0.960946i	$-0.410748\pi$
$661$	21.1957	−	3.19474i	0.824419	−	0.124261i	0.547684	+	0.836685i	$0.315510\pi$
$662$	35.1460	−	5.29740i	1.36599	−	0.205889i
$663$	−0.705969	+	0.655044i	−0.0274176	+	0.0254398i
$664$	−9.78145	−	42.8553i	−0.379594	−	1.66311i
$665$	21.8399	+	0.821108i	0.846915	+	0.0318412i
$666$	−0.728026	+	3.18969i	−0.0282105	+	0.123598i
$667$	−9.99867	−	17.3182i	−0.387150	−	0.670564i
$668$	−0.0768477	+	0.133104i	−0.00297333	+	0.00514995i
$669$	2.27259	+	2.10866i	0.0878635	+	0.0815254i
$670$	2.72335	+	1.85675i	0.105212	+	0.0717325i
$671$	29.1262	+	36.5231i	1.12441	+	1.40996i
$672$	0.0163318	+	0.0163377i	0.000630014	+	0.000630239i
$673$	−11.9658	+	15.0046i	−0.461247	+	0.578385i	−0.957004	−	0.290076i	$-0.906319\pi$
$673$	−11.9658	+	15.0046i	−0.461247	+	0.578385i	0.495757	+	0.868461i	$0.334891\pi$
$674$	−23.1030	+	7.12634i	−0.889895	+	0.274496i
$675$	−3.03295	−	7.72784i	−0.116738	−	0.297445i
$676$	0.000930363	−	0.0124148i	3.57832e−5	−	0.000477494i
$677$	−0.458544	+	1.16835i	−0.0176233	+	0.0449034i	−0.939415	−	0.342783i	$-0.888630\pi$
$677$	−0.458544	+	1.16835i	−0.0176233	+	0.0449034i	0.921791	+	0.387686i	$0.126726\pi$
$678$	2.61226	+	1.25800i	0.100323	+	0.0483132i
$679$	−7.53938	−	5.56640i	−0.289335	−	0.213619i
$680$	79.3952	−	38.2347i	3.04467	−	1.46623i
$681$	−0.0595130	−	0.794146i	−0.00228054	−	0.0304317i
$682$	32.4559	+	10.0113i	1.24280	+	0.383353i
$683$	41.7754	−	28.4820i	1.59849	−	1.08983i	0.656435	−	0.754383i	$-0.272064\pi$
$683$	41.7754	−	28.4820i	1.59849	−	1.08983i	0.942058	−	0.335451i	$-0.108889\pi$
$684$	0.0754349	+	0.0113700i	0.00288433	+	0.000434742i
$685$	9.84585			0.376191
$686$	12.2890	−	23.2218i	0.469197	−	0.886611i
$687$	−1.80836			−0.0689932
$688$	−13.1923	−	1.98842i	−0.502952	−	0.0758078i
$689$	6.49272	−	4.42666i	0.247353	−	0.168642i
$690$	−3.35723	−	1.03557i	−0.127807	−	0.0394234i
$691$	0.393981	+	5.25731i	0.0149877	+	0.199998i	0.999671	+	0.0256454i	$0.00816408\pi$
$691$	0.393981	+	5.25731i	0.0149877	+	0.199998i	−0.984683	+	0.174352i	$0.944217\pi$
$692$	0.0293067	−	0.0141134i	0.00111407	−	0.000536509i
$693$	32.8670	+	24.2661i	1.24851	+	0.921791i
$694$	−7.45374	−	3.58953i	−0.282940	−	0.136257i
$695$	−12.8634	+	32.7754i	−0.487937	+	1.24324i
$696$	−0.105222	+	1.40408i	−0.00398841	+	0.0532217i
$697$	9.43571	+	24.0418i	0.357403	+	0.910648i
$698$	−3.93624	+	1.21417i	−0.148989	+	0.0459570i
$699$	1.81846	−	2.28028i	0.0687806	−	0.0862481i
$700$	0.260550	+	0.260643i	0.00984786	+	0.00985139i
$701$	−3.12885	−	3.92346i	−0.118175	−	0.148187i	0.719225	−	0.694777i	$-0.244497\pi$
$701$	−3.12885	−	3.92346i	−0.118175	−	0.148187i	−0.837400	+	0.546590i	$0.815926\pi$
$702$	0.869677	+	0.592936i	0.0328238	+	0.0223789i
$703$	−1.16295	−	1.07906i	−0.0438615	−	0.0406975i
$704$	−20.5643	+	35.6184i	−0.775046	+	1.34242i
$705$	−0.948425	−	1.64272i	−0.0357197	−	0.0618684i
$706$	−2.99065	+	13.1029i	−0.112554	+	0.493133i
$707$	26.3326	+	0.990018i	0.990339	+	0.0372335i
$708$	0.000423183		0.00185408i	1.59042e−5		6.96807e-5i
$709$	−33.9893	+	31.5374i	−1.27649	+	1.18441i	−0.303692	+	0.952770i	$0.598220\pi$
$709$	−33.9893	+	31.5374i	−1.27649	+	1.18441i	−0.972801	+	0.231643i	$0.925590\pi$
$710$	−28.6420	+	4.31708i	−1.07491	+	0.162017i
$711$	37.6530	−	5.67527i	1.41210	−	0.212839i
$712$	−8.71374	+	8.08517i	−0.326561	+	0.303005i
$713$	−5.11252	−	22.3994i	−0.191466	−	0.838865i
$714$	2.14591	+	2.90870i	0.0803088	+	0.108855i
$715$	4.63208	−	20.2944i	0.173230	−	0.758969i
$716$	0.119650	+	0.207240i	0.00447154	+	0.00774493i
$717$	−0.827607	+	1.43346i	−0.0309076	+	0.0535335i
$718$	1.34195	+	1.24514i	0.0500810	+	0.0464684i
$719$	0.466169	+	0.317828i	0.0173852	+	0.0118530i	0.571981	−	0.820267i	$-0.306175\pi$
$719$	0.466169	+	0.317828i	0.0173852	+	0.0118530i	−0.554596	+	0.832120i	$0.687127\pi$
$720$	−30.1345	−	37.7874i	−1.12304	−	1.40825i
$721$	−15.1322	+	24.0733i	−0.563554	+	0.896535i
$722$	13.0771	−	16.3981i	0.486679	−	0.610276i
$723$	−0.302762	+	0.0933898i	−0.0112598	+	0.00347320i
$724$	0.0911897	+	0.232347i	0.00338904	+	0.00863513i
$725$	−3.36782	+	44.9404i	−0.125078	+	1.66905i
$726$	−1.01312	+	2.58139i	−0.0376004	+	0.0958044i
$727$	−23.7016	−	11.4141i	−0.879045	−	0.423326i	−0.0607692	−	0.998152i	$-0.519355\pi$
$727$	−23.7016	−	11.4141i	−0.879045	−	0.423326i	−0.818276	+	0.574826i	$0.805070\pi$
$728$	7.32954	+	1.38818i	0.271651	+	0.0514495i
$729$	23.5815	−	11.3563i	0.873389	−	0.420602i
$730$	2.50680	+	33.4509i	0.0927809	+	1.23807i
$731$	−24.6050	−	7.58962i	−0.910047	−	0.280712i
$732$	0.0115152	−	0.00785092i	0.000425614	−	0.000290178i
$733$	24.7208	+	3.72606i	0.913084	+	0.137625i	0.588748	−	0.808317i	$-0.299621\pi$
$733$	24.7208	+	3.72606i	0.913084	+	0.137625i	0.324336	+	0.945942i	$0.394859\pi$
$734$	24.0543			0.887861
$735$	1.96806	−	2.88440i	0.0725931	−	0.106393i
$736$	−0.349641			−0.0128879
$737$	−2.95428	−	0.445286i	−0.108822	−	0.0164023i
$738$	11.6315	−	7.93023i	0.428162	−	0.291916i
$739$	−44.7524	−	13.8043i	−1.64624	−	0.507799i	−0.673403	−	0.739276i	$-0.735168\pi$
$739$	−44.7524	−	13.8043i	−1.64624	−	0.507799i	−0.972840	+	0.231477i	$0.925644\pi$
$740$	−0.00289255	−	0.0385984i	−0.000106332	−	0.00141891i
$741$	−0.229332	+	0.110441i	−0.00842474	+	0.00405714i
$742$	−13.7769	−	26.0785i	−0.505767	−	0.957372i
$743$	−4.55800	−	2.19502i	−0.167217	−	0.0805274i	0.348403	−	0.937345i	$-0.386724\pi$
$743$	−4.55800	−	2.19502i	−0.167217	−	0.0805274i	−0.515620	+	0.856817i	$0.672438\pi$
$744$	−0.591017	+	1.50589i	−0.0216677	+	0.0552084i
$745$	−4.85798	+	64.8252i	−0.177983	+	2.37501i
$746$	−4.54024	−	11.5683i	−0.166230	−	0.423547i
$747$	−44.4637	+	13.7152i	−1.62684	+	0.501814i
$748$	0.311949	−	0.391172i	0.0114060	−	0.0143027i
$749$	−22.1624	+	13.9200i	−0.809795	+	0.508626i
$750$	2.73052	+	3.42397i	0.0997045	+	0.125026i
$751$	−0.325524	−	0.221939i	−0.0118786	−	0.00809866i	0.557366	−	0.830267i	$-0.311812\pi$
$751$	−0.325524	−	0.221939i	−0.0118786	−	0.00809866i	−0.569245	+	0.822168i	$0.692764\pi$
$752$	−11.2188	−	10.4096i	−0.409109	−	0.379598i
$753$	−0.734862	+	1.27282i	−0.0267799	+	0.0463841i
$754$	−2.85699	−	4.94845i	−0.104045	−	0.180212i
$755$	−15.0527	+	65.9502i	−0.547824	+	2.40017i
$756$	0.0159450	−	0.0185218i	0.000579915	−	0.000673630i
$757$	0.648480	+	2.84117i	0.0235694	+	0.103264i	0.985344	−	0.170577i	$-0.0545630\pi$
$757$	0.648480	+	2.84117i	0.0235694	+	0.103264i	−0.961775	+	0.273841i	$0.911706\pi$
$758$	23.2998	−	21.6190i	0.846285	−	0.785238i
$759$	3.14899	−	0.474633i	0.114301	−	0.0172281i
$760$	23.0309	−	3.47135i	0.835418	−	0.125919i
$761$	−12.5844	+	11.6767i	−0.456186	+	0.423279i	−0.874501	−	0.485023i	$-0.838811\pi$
$761$	−12.5844	+	11.6767i	−0.456186	+	0.423279i	0.418315	+	0.908302i	$0.362621\pi$
$762$	−0.294488	−	1.29023i	−0.0106682	−	0.0467403i
$763$	1.90271	−	7.09593i	0.0688828	−	0.256890i
$764$	0.0650814	−	0.285140i	0.00235456	−	0.0103160i
$765$	−46.6406	−	80.7839i	−1.68629	−	2.92075i
$766$	−6.36456	+	11.0237i	−0.229961	+	0.398304i
$767$	0.903196	+	0.838043i	0.0326125	+	0.0302600i
$768$	0.0306062	+	0.0208670i	0.00110441	+	0.000752972i
$769$	8.63649	+	10.8298i	0.311440	+	0.390533i	0.912774	−	0.408464i	$-0.133936\pi$
$769$	8.63649	+	10.8298i	0.311440	+	0.390533i	−0.601335	+	0.798997i	$0.705364\pi$
$770$	−73.7407	−	25.8178i	−2.65743	−	0.930410i
$771$	−1.94942	+	2.44450i	−0.0702067	+	0.0880364i
$772$	0.235281	−	0.0725746i	0.00846795	−	0.00261202i
$773$	16.5080	+	42.0617i	0.593751	+	1.51285i	0.839411	+	0.543497i	$0.182900\pi$
$773$	16.5080	+	42.0617i	0.593751	+	1.51285i	−0.245660	+	0.969356i	$0.579005\pi$
$774$	−1.04884	+	13.9958i	−0.0376997	+	0.503068i
$775$	−18.9166	+	48.1988i	−0.679506	+	1.73135i
$776$	−8.99820	−	4.33331i	−0.323017	−	0.155557i
$777$	−0.244844	+	0.0655588i	−0.00878373	+	0.00235191i
$778$	−1.73562	+	0.835832i	−0.0622251	+	0.0299660i
$779$	0.510124	+	6.80714i	0.0182771	+	0.243891i
$780$	−0.00593443	−	0.00183053i	−0.000212487	−	6.55434e-5i
$781$	21.6929	−	14.7900i	0.776234	−	0.529227i
$782$	−54.0978	−	8.15393i	−1.93453	−	0.291584i
$783$	2.98858			0.106803
$784$	8.31384	−	26.9186i	0.296923	−	0.961378i
$785$	−68.2869			−2.43726
$786$	−2.56891	−	0.387200i	−0.0916298	−	0.0138110i
$787$	−4.57544	+	3.11948i	−0.163097	+	0.111197i	−0.642118	−	0.766606i	$-0.721944\pi$
$787$	−4.57544	+	3.11948i	−0.163097	+	0.111197i	0.479021	+	0.877803i	$0.340992\pi$
$788$	−0.161004	−	0.0496631i	−0.00573552	−	0.00176917i
$789$	0.0191731	+	0.255847i	0.000682579	+	0.00910839i
$790$	−65.6091	+	31.5957i	−2.33427	+	1.12412i
$791$	−1.62303	−	43.5853i	−0.0577083	−	1.54971i
$792$	39.2266	+	18.8905i	1.39386	+	0.671245i
$793$	3.29879	−	8.40517i	0.117143	−	0.298476i
$794$	3.99120	−	53.2588i	0.141642	−	1.89008i
$795$	−1.43211	−	3.64897i	−0.0507918	−	0.129415i
$796$	0.217195	−	0.0669959i	0.00769828	−	0.00237461i
$797$	−24.6413	+	30.8993i	−0.872841	+	1.09451i	0.121946	+	0.992537i	$0.461086\pi$
$797$	−24.6413	+	30.8993i	−0.872841	+	1.09451i	−0.994787	+	0.101971i	$0.967485\pi$
$798$	0.315374	+	0.901805i	0.0111641	+	0.0319236i
$799$	−18.4163	−	23.0933i	−0.651522	−	0.816983i
$800$	0.651042	+	0.443873i	0.0230178	+	0.0156933i
$801$	9.22390	+	8.55853i	0.325910	+	0.302401i
$802$	−25.4666	+	44.1094i	−0.899256	+	1.55756i
$803$	−15.2029	−	26.3322i	−0.536498	−	0.929242i
$804$	−0.000198340	0	0.000868986i	−6.99493e−6	0	3.06468e-5i
$805$	9.81626	+	51.9311i	0.345978	+	1.83033i
$806$	−1.46084	−	6.40034i	−0.0514557	−	0.225442i
$807$	0.802048	−	0.744192i	0.0282334	−	0.0261968i
$808$	27.7686	−	4.18544i	0.976895	−	0.147243i
$809$	−28.6041	+	4.31137i	−1.00567	+	0.151580i	−0.631166	−	0.775648i	$-0.717423\pi$
$809$	−28.6041	+	4.31137i	−1.00567	+	0.151580i	−0.374499	+	0.927227i	$0.622185\pi$
$810$	−37.0791	+	34.4044i	−1.30283	+	1.20885i
$811$	11.0618	+	48.4649i	0.388432	+	1.70183i	0.670059	+	0.742308i	$0.266269\pi$
$811$	11.0618	+	48.4649i	0.388432	+	1.70183i	−0.281627	+	0.959524i	$0.590874\pi$
$812$	−0.121612	+	0.0530330i	−0.00426776	+	0.00186109i
$813$	−0.494299	+	2.16566i	−0.0173358	+	0.0759532i
$814$	2.83567	+	4.91152i	0.0993901	+	0.172149i
$815$	14.9920	−	25.9669i	0.525147	−	0.909582i
$816$	2.84135	+	2.63638i	0.0994670	+	0.0922919i
$817$	−5.62301	−	3.83370i	−0.196724	−	0.134124i
$818$	31.7023	+	39.7534i	1.10844	+	1.38994i
$819$	0.885542	−	7.84678i	0.0309434	−	0.274189i
$820$	−0.103841	+	0.130213i	−0.00362629	+	0.00454722i
$821$	−29.3230	+	9.04496i	−1.02338	+	0.315671i	−0.760625	−	0.649191i	$-0.775108\pi$
$821$	−29.3230	+	9.04496i	−1.02338	+	0.315671i	−0.262756	+	0.964862i	$0.584631\pi$
$822$	0.157239	+	0.400640i	0.00548436	+	0.0139739i
$823$	0.829241	−	11.0655i	0.0289055	−	0.385718i	−0.963924	−	0.266178i	$-0.914239\pi$
$823$	0.829241	−	11.0655i	0.0289055	−	0.385718i	0.992829	−	0.119540i	$-0.0381418\pi$
$824$	−11.0706	+	28.2075i	−0.385663	+	0.982654i
$825$	−6.46606	−	3.11389i	−0.225119	−	0.108412i
$826$	3.50573	−	3.01583i	0.121980	−	0.104934i
$827$	7.30203	−	3.51647i	0.253916	−	0.122280i	−0.302596	−	0.953119i	$-0.597853\pi$
$827$	7.30203	−	3.51647i	0.253916	−	0.122280i	0.556513	+	0.830839i	$0.312139\pi$
$828$	0.0137860	+	0.183962i	0.000479098	+	0.00639312i
$829$	−28.0162	−	8.64185i	−0.973042	−	0.300144i	−0.232830	−	0.972517i	$-0.574799\pi$
$829$	−28.0162	−	8.64185i	−0.973042	−	0.300144i	−0.740212	+	0.672374i	$0.765275\pi$
$830$	73.5233	−	50.1273i	2.55203	−	1.73995i
$831$	2.93963	+	0.443078i	0.101975	+	0.0153702i
$832$	7.94958			0.275602
$833$	23.6098	−	48.9814i	0.818032	−	1.69711i
$834$	−1.53910			−0.0532947
$835$	49.1169	+	7.40318i	1.69976	+	0.256198i
$836$	0.109261	−	0.0744929i	0.00377887	−	0.00257639i
$837$	3.28112	+	1.01209i	0.113412	+	0.0349830i
$838$	−2.65711	−	35.4567i	−0.0917884	−	1.22483i
$839$	−45.7344	+	22.0245i	−1.57893	+	0.760372i	−0.998543	−	0.0539703i	$-0.982812\pi$
$839$	−45.7344	+	22.0245i	−1.57893	+	0.760372i	−0.580385	+	0.814342i	$0.697098\pi$
$840$	1.48870	−	3.41048i	0.0513652	−	0.117673i
$841$	11.5110	+	5.54340i	0.396931	+	0.191152i
$842$	2.54243	−	6.47802i	0.0876181	−	0.223247i
$843$	0.0393340	−	0.524875i	0.00135473	−	0.0180777i
$844$	0.0518674	+	0.132156i	0.00178535	+	0.00454900i
$845$	−3.84476	+	1.18595i	−0.132264	+	0.0407980i
$846$	−10.0382	+	12.5875i	−0.345121	+	0.432769i
$847$	41.4540	−	4.66322i	1.42438	−	0.160230i
$848$	−19.7192	−	24.7271i	−0.677159	−	0.849131i
$849$	1.54326	+	1.05218i	0.0529646	+	0.0361106i
$850$	90.3802	+	83.8606i	3.10001	+	2.87639i
$851$	1.91818	−	3.32239i	0.0657545	−	0.113890i
$852$	−0.00391645	−	0.00678349i	−0.000134175	−	0.000232399i
$853$	9.01947	−	39.5169i	0.308821	−	1.35303i	−0.547595	−	0.836744i	$-0.684456\pi$
$853$	9.01947	−	39.5169i	0.308821	−	1.35303i	0.856415	−	0.516288i	$-0.172686\pi$
$854$	−29.9595	−	15.8409i	−1.02519	−	0.542066i
$855$	−5.48617	−	24.0365i	−0.187623	−	0.822031i
$856$	−20.4452	+	18.9704i	−0.698803	+	0.648395i
$857$	15.6700	−	2.36187i	0.535277	−	0.0806801i	0.124160	−	0.992262i	$-0.460377\pi$
$857$	15.6700	−	2.36187i	0.535277	−	0.0806801i	0.411118	+	0.911582i	$0.365138\pi$
$858$	0.899781	−	0.135620i	0.0307180	−	0.00462999i
$859$	24.1399	−	22.3985i	0.823642	−	0.764228i	−0.150872	−	0.988553i	$-0.548208\pi$
$859$	24.1399	−	22.3985i	0.823642	−	0.764228i	0.974514	+	0.224325i	$0.0720177\pi$
$860$	−0.0369482	−	0.161881i	−0.00125992	−	0.00552009i
$861$	0.964156	+	0.509792i	0.0328583	+	0.0173737i
$862$	−3.35634	+	14.7051i	−0.114318	+	0.500858i
$863$	5.94176	+	10.2914i	0.202260	+	0.350324i	0.949256	−	0.314504i	$-0.101838\pi$
$863$	5.94176	+	10.2914i	0.202260	+	0.350324i	−0.746996	+	0.664828i	$0.768505\pi$
$864$	0.0261268	−	0.0452529i	0.000888851	−	0.00153953i
$865$	−7.70620	−	7.15030i	−0.262019	−	0.243118i
$866$	21.5707	+	14.7067i	0.733003	+	0.499753i
$867$	3.35011	+	4.20091i	0.113776	+	0.142670i
$868$	−0.151476	+	0.0170398i	−0.00514142	+	0.000578367i
$869$	41.1543	−	51.6059i	1.39607	−	1.75061i
$870$	−2.72370	+	0.840152i	−0.0923422	+	0.0284838i
$871$	0.210974	+	0.537553i	0.00714858	+	0.0182143i
$872$	0.585078	−	7.80732i	0.0198132	−	0.264389i
$873$	−3.86237	+	9.84116i	−0.130721	+	0.333073i
$874$	−13.0278	−	6.27387i	−0.440673	−	0.212217i
$875$	26.3555	−	60.3779i	0.890978	−	2.04115i
$876$	−0.00817290	+	0.00393586i	−0.000276137	+	0.000132980i
$877$	−2.79528	−	37.3004i	−0.0943899	−	1.25955i	−0.820371	−	0.571831i	$-0.806233\pi$
$877$	−2.79528	−	37.3004i	−0.0943899	−	1.25955i	0.725981	−	0.687714i	$-0.241386\pi$
$878$	33.8491	+	10.4411i	1.14235	+	0.352369i
$879$	−1.34152	+	0.914635i	−0.0452485	+	0.0308499i
$880$	−82.8448	−	12.4868i	−2.79270	−	0.420931i
$881$	−19.8214			−0.667798			−0.333899	−	0.942609i	$-0.608365\pi$
$881$	−19.8214			−0.667798			−0.333899	+	0.942609i	$0.608365\pi$
$882$	−28.8927	−	6.60545i	−0.972867	−	0.222417i
$883$	38.5417			1.29703			0.648515	−	0.761202i	$-0.275390\pi$
$883$	38.5417			1.29703			0.648515	+	0.761202i	$0.275390\pi$
$884$	−0.0956263	−	0.0144133i	−0.00321626	−	0.000484773i
$885$	0.507821	−	0.346226i	0.0170702	−	0.0116383i
$886$	0.891751	+	0.275069i	0.0299590	+	0.00924112i
$887$	−3.03353	−	40.4797i	−0.101856	−	1.35917i	−0.780707	−	0.624897i	$-0.785141\pi$
$887$	−3.03353	−	40.4797i	−0.101856	−	1.35917i	0.678851	−	0.734276i	$-0.262478\pi$
$888$	−0.243370	+	0.117201i	−0.00816695	+	0.00393300i
$889$	−15.0921	+	12.9831i	−0.506173	+	0.435440i
$890$	−21.6804	−	10.4407i	−0.726728	−	0.349974i
$891$	16.7504	−	42.6793i	0.561159	−	1.42981i
$892$	−0.0232641	+	0.310438i	−0.000778940	+	0.0103942i
$893$	−2.85218	−	7.26722i	−0.0954444	−	0.243188i
$894$	−2.71540	+	0.837590i	−0.0908166	+	0.0280132i
$895$	48.2193	−	60.4651i	1.61179	−	2.02113i
$896$	3.38779	−	30.0191i	0.113178	−	1.00287i
$897$	−0.383777	−	0.481241i	−0.0128139	−	0.0160682i
$898$	−44.2042	−	30.1379i	−1.47511	−	1.00572i
$899$	−13.6640	−	12.6784i	−0.455720	−	0.422847i
$900$	0.207872	−	0.360044i	0.00692905	−	0.0120015i
$901$	−30.5203	−	52.8628i	−1.01678	−	1.76112i
$902$	5.43013	−	23.7910i	0.180804	−	0.792153i
$903$	−0.996685	+	0.434637i	−0.0331676	+	0.0144638i
$904$	−10.3429	−	45.3153i	−0.344001	−	1.50716i
$905$	59.1330	−	54.8674i	1.96565	−	1.82386i
$906$	−2.92399	+	0.440720i	−0.0971429	+	0.0146419i
$907$	12.6898	−	1.91268i	0.421358	−	0.0635094i	0.0650586	−	0.997881i	$-0.479277\pi$
$907$	12.6898	−	1.91268i	0.421358	−	0.0635094i	0.356299	+	0.934372i	$0.384038\pi$
$908$	0.0586213	−	0.0543926i	0.00194542	−	0.00180508i
$909$	−6.61473	−	28.9810i	−0.219397	−	0.961240i
$910$	2.80487	+	14.8386i	0.0929804	+	0.491895i
$911$	−8.39664	+	36.7881i	−0.278193	+	1.21884i	0.621883	+	0.783110i	$0.286368\pi$
$911$	−8.39664	+	36.7881i	−0.278193	+	1.21884i	−0.900076	+	0.435733i	$0.856489\pi$
$912$	0.512229	+	0.887206i	0.0169616	+	0.0293783i
$913$	−40.3293	+	69.8525i	−1.33471	+	2.31178i
$914$	10.9526	+	10.1625i	0.362280	+	0.336147i
$915$	−3.72151	−	2.53728i	−0.123029	−	0.0838800i
$916$	−0.113219	−	0.141972i	−0.00374085	−	0.00469088i
$917$	12.9009	+	36.8897i	0.426024	+	1.21821i
$918$	5.09777	−	6.39240i	0.168251	−	0.210981i
$919$	34.6454	−	10.6867i	1.14285	−	0.352522i	0.335177	−	0.942155i	$-0.391204\pi$
$919$	34.6454	−	10.6867i	1.14285	−	0.352522i	0.807671	+	0.589634i	$0.200728\pi$
$920$	20.5769	+	52.4292i	0.678402	+	1.72854i
$921$	0.0467846	−	0.624297i	0.00154161	−	0.0205713i
$922$	9.18874	−	23.4125i	0.302615	−	0.771050i
$923$	−4.57218	−	2.20184i	−0.150495	−	0.0724746i
$924$	−0.000786220	−	0.0211134i	−2.58647e−5	−	0.000694578i
$925$	−7.78952	+	3.75124i	−0.256118	+	0.123340i
$926$	−0.937587	−	12.5112i	−0.0308110	−	0.411144i
$927$	30.6512	+	9.45463i	1.00672	+	0.310531i
$928$	−0.234373	+	0.159793i	−0.00769366	+	0.00524545i
$929$	−35.0191	−	5.27828i	−1.14894	−	0.173175i	−0.453160	−	0.891429i	$-0.649703\pi$
$929$	−35.0191	−	5.27828i	−1.14894	−	0.173175i	−0.695781	+	0.718254i	$0.744941\pi$
$930$	−3.27483			−0.107386
$931$	9.77885	−	10.5315i	0.320489	−	0.345157i
$932$	0.292873			0.00959338
$933$	−1.91079	−	0.288005i	−0.0625564	−	0.00942886i
$934$	7.00148	−	4.77353i	0.229096	−	0.156195i
$935$	−154.514	−	47.6612i	−5.05314	−	1.55869i
$936$	−0.628878	−	8.39180i	−0.0205555	−	0.274294i
$937$	8.57953	−	4.13169i	0.280281	−	0.134976i	−0.288462	−	0.957491i	$-0.593144\pi$
$937$	8.57953	−	4.13169i	0.280281	−	0.134976i	0.568743	+	0.822515i	$0.307430\pi$
$938$	2.09366	−	0.560593i	0.0683605	−	0.0183040i
$939$	−0.372805	−	0.179533i	−0.0121660	−	0.00585885i
$940$	0.0695882	−	0.177308i	0.00226972	−	0.00578315i
$941$	−2.88773	+	38.5341i	−0.0941373	+	1.25617i	0.727477	+	0.686132i	$0.240693\pi$
$941$	−2.88773	+	38.5341i	−0.0941373	+	1.25617i	−0.821615	+	0.570043i	$0.806926\pi$
$942$	−1.09055	−	2.77868i	−0.0355320	−	0.0905342i
$943$	−15.7739	+	4.86559i	−0.513668	+	0.158445i
$944$	3.09182	−	3.87702i	0.100630	−	0.126186i
$945$	−7.45479	−	2.61004i	−0.242504	−	0.0849047i
$946$	15.1688	+	19.0211i	0.493181	+	0.618429i
$947$	10.2628	+	6.99705i	0.333496	+	0.227374i	0.718477	−	0.695551i	$-0.244840\pi$
$947$	10.2628	+	6.99705i	0.333496	+	0.227374i	−0.384981	+	0.922925i	$0.625792\pi$
$948$	−0.0144355	−	0.0133942i	−0.000468843	−	0.000435022i
$949$	−2.93851	+	5.08964i	−0.0953880	+	0.165217i
$950$	16.2934	+	28.2211i	0.528629	+	0.915613i
$951$	−0.385650	+	1.68964i	−0.0125056	+	0.0547905i
$952$	15.0077	−	55.9694i	0.486403	−	1.81398i
$953$	3.31051	+	14.5043i	0.107238	+	0.469840i	0.999820	+	0.0189555i	$0.00603409\pi$
$953$	3.31051	+	14.5043i	0.107238	+	0.469840i	−0.892583	+	0.450884i	$0.851109\pi$
$954$	−24.3898	+	22.6304i	−0.789650	+	0.732688i
$955$	−93.4666	+	14.0878i	−3.02451	+	0.455871i
$956$	−0.164354	+	0.0247724i	−0.00531559	+	0.000801197i
$957$	1.89392	−	1.75730i	0.0612219	−	0.0568056i
$958$	0.904701	+	3.96375i	0.0292296	+	0.128063i
$959$	4.22402	−	4.90663i	0.136401	−	0.158443i
$960$	0.882416	−	3.86612i	0.0284798	−	0.124778i
$961$	4.79206	+	8.30010i	0.154583	+	0.267745i
$962$	0.548095	−	0.949329i	0.0176713	−	0.0306076i
$963$	21.6422	+	20.0810i	0.697410	+	0.647102i
$964$	−0.0262874	−	0.0179225i	−0.000846661	−	0.000577243i
$965$	−49.6136	−	62.2135i	−1.59712	−	2.00272i
$966$	−1.95637	+	1.22878i	−0.0629453	+	0.0395354i
$967$	−23.3433	+	29.2716i	−0.750670	+	0.941310i	−0.999630	−	0.0272037i	$-0.991340\pi$
$967$	−23.3433	+	29.2716i	−0.750670	+	0.941310i	0.248960	+	0.968514i	$0.419911\pi$
$968$	42.4807	−	13.1036i	1.36538	−	0.421165i
$969$	0.722358	+	1.84054i	0.0232055	+	0.0591266i
$970$	1.51088	−	20.1612i	0.0485113	−	0.647338i
$971$	−12.2616	+	31.2422i	−0.393495	+	1.00261i	0.587612	+	0.809143i	$0.300068\pi$
$971$	−12.2616	+	31.2422i	−0.393495	+	1.00261i	−0.981107	+	0.193466i	$0.938027\pi$
$972$	−0.0372915	−	0.0179586i	−0.00119613	−	0.000576024i
$973$	10.8149	+	20.4716i	0.346708	+	0.656289i
$974$	29.5237	−	14.2179i	0.946000	−	0.455569i
$975$	0.103663	+	1.38329i	0.00331989	+	0.0443008i
$976$	−34.7262	−	10.7116i	−1.11156	−	0.342871i
$977$	−6.19559	+	4.22408i	−0.198214	+	0.135140i	−0.658360	−	0.752703i	$-0.728750\pi$
$977$	−6.19559	+	4.22408i	−0.198214	+	0.135140i	0.460146	+	0.887843i	$0.347797\pi$
$978$	1.29605	+	0.195348i	0.0414431	+	0.00624654i
$979$	21.8117			0.697104
$980$	0.349668	−	0.0260781i	0.0111697	−	0.000833033i
$981$	−8.28758			−0.264602
$982$	0.379791	+	0.0572442i	0.0121196	+	0.00182674i
$983$	33.1111	−	22.5747i	1.05608	−	0.720022i	0.0947712	−	0.995499i	$-0.469788\pi$
$983$	33.1111	−	22.5747i	1.05608	−	0.720022i	0.961308	+	0.275477i	$0.0888357\pi$
$984$	1.11064	+	0.342588i	0.0354060	+	0.0109213i
$985$	4.06927	+	54.3006i	0.129658	+	1.73016i
$986$	−39.9895	+	19.2579i	−1.27353	+	0.613298i
$987$	−1.22553	−	0.232110i	−0.0390090	−	0.00738814i
$988$	−0.0230287	−	0.0110900i	−0.000732641	−	0.000352821i
$989$	6.01250	−	15.3196i	0.191187	−	0.487135i
$990$	−6.58648	+	87.8904i	−0.209332	+	2.79334i
$991$	14.7171	+	37.4985i	0.467503	+	1.19118i	0.949153	+	0.314814i	$0.101942\pi$
$991$	14.7171	+	37.4985i	0.467503	+	1.19118i	−0.481650	+	0.876363i	$0.659963\pi$
$992$	−0.311428	+	0.0960628i	−0.00988784	+	0.00305000i
$993$	1.93675	−	2.42860i	0.0614608	−	0.0770694i
$994$	−10.1365	+	16.1257i	−0.321509	+	0.511475i
$995$	−45.7999	−	57.4312i	−1.45195	−	1.82069i
$996$	0.0198823	+	0.0135555i	0.000629995	+	0.000429524i
$997$	19.6804	+	18.2607i	0.623284	+	0.578323i	0.927288	−	0.374348i	$-0.122133\pi$
$997$	19.6804	+	18.2607i	0.623284	+	0.578323i	−0.304005	+	0.952671i	$0.598324\pi$
$998$	15.8151	−	27.3926i	0.500619	−	0.867097i
$999$	0.286671	+	0.496528i	0.00906986	+	0.0157095i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bl.b.235.22	✓	348
49.44	even	21	inner	637.2.bl.b.534.22	yes	348

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.bl.b.235.22	✓	348	1.1	even	1	trivial
637.2.bl.b.534.22	yes	348	49.44	even	21	inner

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.bl (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.40276 + 0.211433i) q^{2} +(0.102437 - 0.0698406i) q^{3} +(0.0118965 + 0.00366960i) q^{4} +(-0.300677 - 4.01226i) q^{5} +(0.158462 - 0.0763113i) q^{6} +(-2.12848 - 1.57148i) q^{7} +(-2.54033 - 1.22336i) q^{8} +(-1.09041 + 2.77831i) q^{9} +O(q^{10})\)	\(q+(1.40276 + 0.211433i) q^{2} +(0.102437 - 0.0698406i) q^{3} +(0.0118965 + 0.00366960i) q^{4} +(-0.300677 - 4.01226i) q^{5} +(0.158462 - 0.0763113i) q^{6} +(-2.12848 - 1.57148i) q^{7} +(-2.54033 - 1.22336i) q^{8} +(-1.09041 + 2.77831i) q^{9} +(0.426543 - 5.69183i) q^{10} +(1.89016 + 4.81604i) q^{11} +(0.00147494 - 0.000454958i) q^{12} +(0.623490 - 0.781831i) q^{13} +(-2.65350 - 2.65445i) q^{14} +(-0.311019 - 0.390006i) q^{15} +(-3.32540 - 2.26722i) q^{16} +(-5.69421 - 5.28345i) q^{17} +(-2.11701 + 3.66677i) q^{18} +(-1.02653 - 1.77801i) q^{19} +(0.0111464 - 0.0488354i) q^{20} +(-0.327789 - 0.0123238i) q^{21} +(1.63318 + 7.15541i) q^{22} +(3.63941 - 3.37688i) q^{23} +(-0.345665 + 0.0521006i) q^{24} +(-11.0637 + 1.66758i) q^{25} +(1.03991 - 0.964899i) q^{26} +(0.165105 + 0.723373i) q^{27} +(-0.0195549 - 0.0265059i) q^{28} +(0.896286 - 3.92689i) q^{29} +(-0.353827 - 0.612846i) q^{30} +(2.31386 - 4.00773i) q^{31} +(-0.0516250 - 0.0479010i) q^{32} +(0.529978 + 0.361333i) q^{33} +(-6.87053 - 8.61537i) q^{34} +(-5.66521 + 9.01254i) q^{35} +(-0.0231674 + 0.0290510i) q^{36} +(0.738392 - 0.227764i) q^{37} +(-1.06405 - 2.71117i) q^{38} +(0.00926506 - 0.123634i) q^{39} +(-4.14462 + 10.5603i) q^{40} +(-2.99562 - 1.44262i) q^{41} +(-0.457205 - 0.0865928i) q^{42} +(2.98655 - 1.43825i) q^{43} +(0.00481340 + 0.0642304i) q^{44} +(11.4752 + 3.53962i) q^{45} +(5.81922 - 3.96748i) q^{46} +(3.76008 + 0.566741i) q^{47} -0.498989 q^{48} +(2.06089 + 6.68975i) q^{49} -15.8723 q^{50} +(-0.952299 - 0.143536i) q^{51} +(0.0102864 - 0.00701314i) q^{52} +(7.50905 + 2.31623i) q^{53} +(0.0786589 + 1.04963i) q^{54} +(18.7549 - 9.03188i) q^{55} +(3.48457 + 6.59599i) q^{56} +(-0.229332 - 0.110441i) q^{57} +(2.08755 - 5.31899i) q^{58} +(-0.0920752 + 1.22866i) q^{59} +(-0.00226889 - 0.00578104i) q^{60} +(8.62818 - 2.66144i) q^{61} +(4.09317 - 5.13267i) q^{62} +(6.68698 - 4.20004i) q^{63} +(4.95648 + 6.21523i) q^{64} +(-3.32438 - 2.26652i) q^{65} +(0.667036 + 0.618919i) q^{66} +(-0.288736 + 0.500105i) q^{67} +(-0.0483532 - 0.0837503i) q^{68} +(0.136968 - 0.600097i) q^{69} +(-9.85249 + 11.4447i) q^{70} +(-1.12923 - 4.94750i) q^{71} +(6.16887 - 5.72388i) q^{72} +(-5.81137 + 0.875923i) q^{73} +(1.08395 - 0.163379i) q^{74} +(-1.01687 + 0.943517i) q^{75} +(-0.00568762 - 0.0249191i) q^{76} +(3.54515 - 13.2212i) q^{77} +(0.0391369 - 0.171470i) q^{78} +(-6.37906 - 11.0489i) q^{79} +(-8.09680 + 14.0241i) q^{80} +(-6.49623 - 6.02762i) q^{81} +(-3.89714 - 2.65702i) q^{82} +(9.72033 + 12.1889i) q^{83} +(-0.00385434 - 0.00134947i) q^{84} +(-19.4865 + 24.4353i) q^{85} +(4.49352 - 1.38607i) q^{86} +(-0.182443 - 0.464857i) q^{87} +(1.09012 - 14.5467i) q^{88} +(1.54024 - 3.92446i) q^{89} +(15.3486 + 7.39148i) q^{90} +(-2.55572 + 0.684313i) q^{91} +(0.0556882 - 0.0268180i) q^{92} +(-0.0428762 - 0.572143i) q^{93} +(5.15467 + 1.59001i) q^{94} +(-6.82517 + 4.65333i) q^{95} +(-0.00863377 - 0.00130133i) q^{96} +3.54214 q^{97} +(1.47651 + 9.81988i) q^{98} -15.4415 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9}+O(q^{10}) \) 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9	\( 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9} - 5 q^{10} + 2 q^{11} - 40 q^{12} - 58 q^{13} - 45 q^{14} - 14 q^{15} + 27 q^{16} - 12 q^{17} - 59 q^{18} - 24 q^{19} - 99 q^{20} - 2 q^{21} - 10 q^{22} - 14 q^{23} + 28 q^{25} + 3 q^{26} - 9 q^{27} - 37 q^{28} - 26 q^{29} - 83 q^{30} - 49 q^{31} + 33 q^{32} + 2 q^{33} - 130 q^{34} - 38 q^{35} - 74 q^{36} - 4 q^{37} + 92 q^{38} + 24 q^{40} + 20 q^{41} - 52 q^{42} + 2 q^{43} + 226 q^{44} - 23 q^{45} + 71 q^{46} + 24 q^{47} + 86 q^{48} + 25 q^{49} + 114 q^{50} - 54 q^{51} + 31 q^{52} + 36 q^{53} + 75 q^{54} + 38 q^{55} + 126 q^{56} + 27 q^{57} - 33 q^{58} + q^{59} - 179 q^{60} - 15 q^{61} + 158 q^{62} - 5 q^{63} - 24 q^{64} + q^{65} - 150 q^{66} - 151 q^{67} + 140 q^{68} - 98 q^{69} - 126 q^{70} - 31 q^{71} - 149 q^{72} - 9 q^{73} + 39 q^{74} + 85 q^{75} - 81 q^{76} + 46 q^{77} - 25 q^{78} - 69 q^{79} - 64 q^{80} + 71 q^{81} - 52 q^{82} - q^{83} - 47 q^{84} + 62 q^{85} + 97 q^{86} + 150 q^{87} - 12 q^{88} + 23 q^{89} + 107 q^{90} - q^{91} - 43 q^{92} + 316 q^{93} - 86 q^{94} - 29 q^{95} + 177 q^{96} + 114 q^{97} - 336 q^{98} + 102 q^{99}+O(q^{100}) \) 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9 - 5 * q^10 + 2 * q^11 - 40 * q^12 - 58 * q^13 - 45 * q^14 - 14 * q^15 + 27 * q^16 - 12 * q^17 - 59 * q^18 - 24 * q^19 - 99 * q^20 - 2 * q^21 - 10 * q^22 - 14 * q^23 + 28 * q^25 + 3 * q^26 - 9 * q^27 - 37 * q^28 - 26 * q^29 - 83 * q^30 - 49 * q^31 + 33 * q^32 + 2 * q^33 - 130 * q^34 - 38 * q^35 - 74 * q^36 - 4 * q^37 + 92 * q^38 + 24 * q^40 + 20 * q^41 - 52 * q^42 + 2 * q^43 + 226 * q^44 - 23 * q^45 + 71 * q^46 + 24 * q^47 + 86 * q^48 + 25 * q^49 + 114 * q^50 - 54 * q^51 + 31 * q^52 + 36 * q^53 + 75 * q^54 + 38 * q^55 + 126 * q^56 + 27 * q^57 - 33 * q^58 + q^59 - 179 * q^60 - 15 * q^61 + 158 * q^62 - 5 * q^63 - 24 * q^64 + q^65 - 150 * q^66 - 151 * q^67 + 140 * q^68 - 98 * q^69 - 126 * q^70 - 31 * q^71 - 149 * q^72 - 9 * q^73 + 39 * q^74 + 85 * q^75 - 81 * q^76 + 46 * q^77 - 25 * q^78 - 69 * q^79 - 64 * q^80 + 71 * q^81 - 52 * q^82 - q^83 - 47 * q^84 + 62 * q^85 + 97 * q^86 + 150 * q^87 - 12 * q^88 + 23 * q^89 + 107 * q^90 - q^91 - 43 * q^92 + 316 * q^93 - 86 * q^94 - 29 * q^95 + 177 * q^96 + 114 * q^97 - 336 * q^98 + 102 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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