LMFDB - Embedded newform 57.2.i.b.16.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [57,2,Mod(4,57)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(57, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([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("57.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 57 = 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	57.i (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.455147291521$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 33 x^{10} - 110 x^{9} + 318 x^{8} - 678 x^{7} + 1225 x^{6} - 1698 x^{5} + 1905 x^{4} + \cdots + 57 $ x^12 - 6x^11 + 33x^10 - 110x^9 + 318x^8 - 678x^7 + 1225x^6 - 1698x^5 + 1905x^4 - 1584x^3 + 936x^2 - 342*x + 57
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			16.1
Root			$0.500000 + 1.74095i$ of defining polynomial
Character	$\chi$	$=$	57.16
Dual form			57.2.i.b.25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.958464 - 0.804247i) q^{2} +(-0.939693 + 0.342020i) q^{3} +(-0.0754558 - 0.427931i) q^{4} +(0.755623 - 4.28535i) q^{5} +(1.17573 + 0.427931i) q^{6} +(0.898157 + 1.55565i) q^{7} +(-1.52303 + 2.63796i) q^{8} +(0.766044 - 0.642788i) q^{9} +O(q^{10})$	\(q+(-0.958464 - 0.804247i) q^{2} +(-0.939693 + 0.342020i) q^{3} +(-0.0754558 - 0.427931i) q^{4} +(0.755623 - 4.28535i) q^{5} +(1.17573 + 0.427931i) q^{6} +(0.898157 + 1.55565i) q^{7} +(-1.52303 + 2.63796i) q^{8} +(0.766044 - 0.642788i) q^{9} +(-4.17072 + 3.49965i) q^{10} +(-0.667129 + 1.15550i) q^{11} +(0.217266 + 0.376316i) q^{12} +(1.88330 + 0.685465i) q^{13} +(0.390278 - 2.21338i) q^{14} +(0.755623 + 4.28535i) q^{15} +(2.76469 - 1.00626i) q^{16} +(3.43091 + 2.87887i) q^{17} -1.25119 q^{18} +(1.57962 - 4.06261i) q^{19} -1.89085 q^{20} +(-1.37606 - 1.15465i) q^{21} +(1.56873 - 0.570970i) q^{22} +(0.479691 + 2.72047i) q^{23} +(0.528942 - 2.99978i) q^{24} +(-13.0948 - 4.76612i) q^{25} +(-1.25379 - 2.17163i) q^{26} +(-0.500000 + 0.866025i) q^{27} +(0.597941 - 0.501732i) q^{28} +(1.22770 - 1.03016i) q^{29} +(2.72224 - 4.71507i) q^{30} +(2.36453 + 4.09548i) q^{31} +(2.26557 + 0.824601i) q^{32} +(0.231691 - 1.31399i) q^{33} +(-0.973078 - 5.51860i) q^{34} +(7.34519 - 2.67343i) q^{35} +(-0.332871 - 0.279312i) q^{36} -2.66325 q^{37} +(-4.78135 + 2.62346i) q^{38} -2.00416 q^{39} +(10.1538 + 8.52001i) q^{40} +(-5.35044 + 1.94740i) q^{41} +(0.390278 + 2.21338i) q^{42} +(0.139578 - 0.791584i) q^{43} +(0.544813 + 0.198296i) q^{44} +(-2.17573 - 3.76848i) q^{45} +(1.72816 - 2.99326i) q^{46} +(-3.77421 + 3.16694i) q^{47} +(-2.25379 + 1.89116i) q^{48} +(1.88663 - 3.26774i) q^{49} +(8.71778 + 15.0996i) q^{50} +(-4.20863 - 1.53182i) q^{51} +(0.151226 - 0.857644i) q^{52} +(0.260602 + 1.47795i) q^{53} +(1.17573 - 0.427931i) q^{54} +(4.44763 + 3.73201i) q^{55} -5.47167 q^{56} +(-0.0948636 + 4.35787i) q^{57} -2.00521 q^{58} +(-4.81575 - 4.04089i) q^{59} +(1.77682 - 0.646709i) q^{60} +(2.07618 + 11.7746i) q^{61} +(1.02746 - 5.82704i) q^{62} +(1.68798 + 0.614376i) q^{63} +(-4.45040 - 7.70833i) q^{64} +(4.36052 - 7.55265i) q^{65} +(-1.27884 + 1.07307i) q^{66} +(-4.13346 + 3.46838i) q^{67} +(0.973078 - 1.68542i) q^{68} +(-1.38122 - 2.39234i) q^{69} +(-9.19021 - 3.34496i) q^{70} +(0.844267 - 4.78807i) q^{71} +(0.528942 + 2.99978i) q^{72} +(-5.39836 + 1.96484i) q^{73} +(2.55263 + 2.14191i) q^{74} +13.9352 q^{75} +(-1.85771 - 0.369421i) q^{76} -2.39675 q^{77} +(1.92092 + 1.61184i) q^{78} +(-3.84337 + 1.39887i) q^{79} +(-2.22313 - 12.6080i) q^{80} +(0.173648 - 0.984808i) q^{81} +(6.69440 + 2.43656i) q^{82} +(1.32418 + 2.29354i) q^{83} +(-0.390278 + 0.675982i) q^{84} +(14.9295 - 12.5273i) q^{85} +(-0.770410 + 0.646450i) q^{86} +(-0.801324 + 1.38793i) q^{87} +(-2.03211 - 3.51972i) q^{88} +(11.0474 + 4.02092i) q^{89} +(-0.945426 + 5.36178i) q^{90} +(0.625153 + 3.54542i) q^{91} +(1.12798 - 0.410550i) q^{92} +(-3.62267 - 3.03978i) q^{93} +6.16445 q^{94} +(-16.2161 - 9.83904i) q^{95} -2.41097 q^{96} +(-7.22847 - 6.06541i) q^{97} +(-4.43633 + 1.61469i) q^{98} +(0.231691 + 1.31399i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} - 3 q^{4} + 6 q^{5} - 3 q^{6} - 9 q^{7} + 3 q^{8}+O(q^{10}) $ 12 * q - 3 * q^2 - 3 * q^4 + 6 * q^5 - 3 * q^6 - 9 * q^7 + 3 * q^8	\( 12 q - 3 q^{2} - 3 q^{4} + 6 q^{5} - 3 q^{6} - 9 q^{7} + 3 q^{8} - 18 q^{10} - 9 q^{11} - 6 q^{12} - 3 q^{13} - 3 q^{14} + 6 q^{15} + 33 q^{16} + 12 q^{17} - 9 q^{19} - 18 q^{20} - 24 q^{22} + 9 q^{23} + 30 q^{24} - 12 q^{25} - 6 q^{27} + 30 q^{28} - 6 q^{30} - 3 q^{32} - 9 q^{33} + 21 q^{34} + 30 q^{35} - 3 q^{36} - 12 q^{37} + 18 q^{38} + 6 q^{39} - 3 q^{40} - 18 q^{41} - 3 q^{42} + 15 q^{43} + 15 q^{44} - 9 q^{45} + 27 q^{46} - 9 q^{47} - 12 q^{48} - 9 q^{49} + 9 q^{50} - 15 q^{51} - 27 q^{52} - 30 q^{53} - 3 q^{54} + 15 q^{55} - 78 q^{56} - 3 q^{57} - 24 q^{58} - 30 q^{59} - 15 q^{60} + 21 q^{61} + 3 q^{62} + 9 q^{63} - 21 q^{64} + 21 q^{65} + 30 q^{66} + 3 q^{67} - 21 q^{68} - 6 q^{69} + 18 q^{70} - 30 q^{71} + 30 q^{72} - 24 q^{73} + 39 q^{74} + 30 q^{75} - 60 q^{76} + 96 q^{77} + 9 q^{78} + 24 q^{79} + 42 q^{80} - 33 q^{82} + 3 q^{83} + 3 q^{84} + 3 q^{85} + 51 q^{86} + 15 q^{87} + 42 q^{88} + 3 q^{89} - 9 q^{90} + 24 q^{91} + 69 q^{92} - 6 q^{93} + 18 q^{94} - 54 q^{95} - 42 q^{96} - 27 q^{97} - 3 q^{98} - 9 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 - 3 * q^4 + 6 * q^5 - 3 * q^6 - 9 * q^7 + 3 * q^8 - 18 * q^10 - 9 * q^11 - 6 * q^12 - 3 * q^13 - 3 * q^14 + 6 * q^15 + 33 * q^16 + 12 * q^17 - 9 * q^19 - 18 * q^20 - 24 * q^22 + 9 * q^23 + 30 * q^24 - 12 * q^25 - 6 * q^27 + 30 * q^28 - 6 * q^30 - 3 * q^32 - 9 * q^33 + 21 * q^34 + 30 * q^35 - 3 * q^36 - 12 * q^37 + 18 * q^38 + 6 * q^39 - 3 * q^40 - 18 * q^41 - 3 * q^42 + 15 * q^43 + 15 * q^44 - 9 * q^45 + 27 * q^46 - 9 * q^47 - 12 * q^48 - 9 * q^49 + 9 * q^50 - 15 * q^51 - 27 * q^52 - 30 * q^53 - 3 * q^54 + 15 * q^55 - 78 * q^56 - 3 * q^57 - 24 * q^58 - 30 * q^59 - 15 * q^60 + 21 * q^61 + 3 * q^62 + 9 * q^63 - 21 * q^64 + 21 * q^65 + 30 * q^66 + 3 * q^67 - 21 * q^68 - 6 * q^69 + 18 * q^70 - 30 * q^71 + 30 * q^72 - 24 * q^73 + 39 * q^74 + 30 * q^75 - 60 * q^76 + 96 * q^77 + 9 * q^78 + 24 * q^79 + 42 * q^80 - 33 * q^82 + 3 * q^83 + 3 * q^84 + 3 * q^85 + 51 * q^86 + 15 * q^87 + 42 * q^88 + 3 * q^89 - 9 * q^90 + 24 * q^91 + 69 * q^92 - 6 * q^93 + 18 * q^94 - 54 * q^95 - 42 * q^96 - 27 * q^97 - 3 * q^98 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/57\mathbb{Z}\right)^\times$.

$n$	$20$	$40$
$\chi(n)$	$1$	$e\left(\frac{2}{9}\right)$

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 $

$2$	−0.958464	−	0.804247i	−0.677737	−	0.568689i	0.237607	−	0.971361i	$-0.423637\pi$
$2$	−0.958464	−	0.804247i	−0.677737	−	0.568689i	−0.915344	+	0.402673i	$0.868081\pi$
$3$	−0.939693	+	0.342020i	−0.542532	+	0.197465i
$3$	−0.939693	+	0.342020i	−0.542532	+	0.197465i
$4$	−0.0754558	−	0.427931i	−0.0377279	−	0.213965i
$5$	0.755623	−	4.28535i	0.337925	−	1.91647i	−0.0582683	−	0.998301i	$-0.518558\pi$
$5$	0.755623	−	4.28535i	0.337925	−	1.91647i	0.396193	−	0.918167i	$-0.370331\pi$
$6$	1.17573	+	0.427931i	0.479990	+	0.174702i
$7$	0.898157	+	1.55565i	0.339471	+	0.587982i	0.984333	−	0.176317i	$-0.0564185\pi$
$7$	0.898157	+	1.55565i	0.339471	+	0.587982i	−0.644862	+	0.764299i	$0.723085\pi$
$8$	−1.52303	+	2.63796i	−0.538471	+	0.932660i
$9$	0.766044	−	0.642788i	0.255348	−	0.214263i
$10$	−4.17072	+	3.49965i	−1.31890	+	1.10669i
$11$	−0.667129	+	1.15550i	−0.201147	+	0.348397i	−0.948898	−	0.315582i	$-0.897800\pi$
$11$	−0.667129	+	1.15550i	−0.201147	+	0.348397i	0.747751	+	0.663979i	$0.231134\pi$
$12$	0.217266	+	0.376316i	0.0627194	+	0.108633i
$13$	1.88330	+	0.685465i	0.522333	+	0.190114i	0.589712	−	0.807614i	$-0.299241\pi$
$13$	1.88330	+	0.685465i	0.522333	+	0.190114i	−0.0673786	+	0.997727i	$0.521464\pi$
$14$	0.390278	−	2.21338i	0.104306	−	0.591550i
$15$	0.755623	+	4.28535i	0.195101	+	1.10647i
$16$	2.76469	−	1.00626i	0.691171	−	0.251566i
$17$	3.43091	+	2.87887i	0.832118	+	0.698230i	0.955776	−	0.294095i	$-0.0950183\pi$
$17$	3.43091	+	2.87887i	0.832118	+	0.698230i	−0.123658	+	0.992325i	$0.539463\pi$
$18$	−1.25119			−0.294907
$19$	1.57962	−	4.06261i	0.362390	−	0.932027i
$19$	1.57962	−	4.06261i	0.362390	−	0.932027i
$20$	−1.89085			−0.422807
$21$	−1.37606	−	1.15465i	−0.300280	−	0.251965i
$22$	1.56873	−	0.570970i	0.334454	−	0.121731i
$23$	0.479691	+	2.72047i	0.100023	+	0.567256i	0.993092	+	0.117338i	$0.0374359\pi$
$23$	0.479691	+	2.72047i	0.100023	+	0.567256i	−0.893070	+	0.449919i	$0.851453\pi$
$24$	0.528942	−	2.99978i	0.107970	−	0.612327i
$25$	−13.0948	−	4.76612i	−2.61896	−	0.953225i
$26$	−1.25379	−	2.17163i	−0.245889	−	0.425892i
$27$	−0.500000	+	0.866025i	−0.0962250	+	0.166667i
$28$	0.597941	−	0.501732i	0.113000	−	0.0948185i
$29$	1.22770	−	1.03016i	0.227978	−	0.191296i	−0.521642	−	0.853164i	$-0.674680\pi$
$29$	1.22770	−	1.03016i	0.227978	−	0.191296i	0.749620	+	0.661868i	$0.230236\pi$
$30$	2.72224	−	4.71507i	0.497012	−	0.860849i
$31$	2.36453	+	4.09548i	0.424682	+	0.735570i	0.996391	−	0.0848863i	$-0.0270527\pi$
$31$	2.36453	+	4.09548i	0.424682	+	0.735570i	−0.571709	+	0.820456i	$0.693719\pi$
$32$	2.26557	+	0.824601i	0.400500	+	0.145770i
$33$	0.231691	−	1.31399i	0.0403323	−	0.228736i
$34$	−0.973078	−	5.51860i	−0.166881	−	0.946432i
$35$	7.34519	−	2.67343i	1.24156	−	0.451892i
$36$	−0.332871	−	0.279312i	−0.0554785	−	0.0465520i
$37$	−2.66325			−0.437836			−0.218918	−	0.975743i	$-0.570253\pi$
$37$	−2.66325			−0.437836			−0.218918	+	0.975743i	$0.570253\pi$
$38$	−4.78135	+	2.62346i	−0.775638	+	0.425582i
$39$	−2.00416			−0.320923
$40$	10.1538	+	8.52001i	1.60545	+	1.34713i
$41$	−5.35044	+	1.94740i	−0.835599	+	0.304133i	−0.724155	−	0.689638i	$-0.757770\pi$
$41$	−5.35044	+	1.94740i	−0.835599	+	0.304133i	−0.111444	+	0.993771i	$0.535548\pi$
$42$	0.390278	+	2.21338i	0.0602213	+	0.341532i
$43$	0.139578	−	0.791584i	0.0212854	−	0.120715i	−0.972314	−	0.233679i	$-0.924923\pi$
$43$	0.139578	−	0.791584i	0.0212854	−	0.120715i	0.993599	+	0.112964i	$0.0360345\pi$
$44$	0.544813	+	0.198296i	0.0821337	+	0.0298942i
$45$	−2.17573	−	3.76848i	−0.324339	−	0.561771i
$46$	1.72816	−	2.99326i	0.254803	−	0.441332i
$47$	−3.77421	+	3.16694i	−0.550526	+	0.461946i	−0.875119	−	0.483908i	$-0.839217\pi$
$47$	−3.77421	+	3.16694i	−0.550526	+	0.461946i	0.324593	+	0.945854i	$0.394773\pi$
$48$	−2.25379	+	1.89116i	−0.325307	+	0.272965i
$49$	1.88663	−	3.26774i	0.269518	−	0.466819i
$50$	8.71778	+	15.0996i	1.23288	+	2.13541i
$51$	−4.20863	−	1.53182i	−0.589327	−	0.214497i
$52$	0.151226	−	0.857644i	0.0209712	−	0.118934i
$53$	0.260602	+	1.47795i	0.0357964	+	0.203012i	0.997461	−	0.0712176i	$-0.0226885\pi$
$53$	0.260602	+	1.47795i	0.0357964	+	0.203012i	−0.961664	+	0.274229i	$0.911577\pi$
$54$	1.17573	−	0.427931i	0.159997	−	0.0582340i
$55$	4.44763	+	3.73201i	0.599718	+	0.503224i
$56$	−5.47167			−0.731183
$57$	−0.0948636	+	4.35787i	−0.0125650	+	0.577214i
$58$	−2.00521			−0.263297
$59$	−4.81575	−	4.04089i	−0.626957	−	0.526079i	0.273025	−	0.962007i	$-0.411976\pi$
$59$	−4.81575	−	4.04089i	−0.626957	−	0.526079i	−0.899982	+	0.435928i	$0.856420\pi$
$60$	1.77682	−	0.646709i	0.229386	−	0.0834898i
$61$	2.07618	+	11.7746i	0.265827	+	1.50758i	0.766668	+	0.642043i	$0.221913\pi$
$61$	2.07618	+	11.7746i	0.265827	+	1.50758i	−0.500841	+	0.865539i	$0.666976\pi$
$62$	1.02746	−	5.82704i	0.130488	−	0.740034i
$63$	1.68798	+	0.614376i	0.212666	+	0.0774040i
$64$	−4.45040	−	7.70833i	−0.556301	−	0.963541i
$65$	4.36052	−	7.55265i	0.540856	−	0.936791i
$66$	−1.27884	+	1.07307i	−0.157414	+	0.132086i
$67$	−4.13346	+	3.46838i	−0.504982	+	0.423730i	−0.859359	−	0.511372i	$-0.829137\pi$
$67$	−4.13346	+	3.46838i	−0.504982	+	0.423730i	0.354377	+	0.935103i	$0.384693\pi$
$68$	0.973078	−	1.68542i	0.118003	−	0.204387i
$69$	−1.38122	−	2.39234i	−0.166279	−	0.288004i
$70$	−9.19021	−	3.34496i	−1.09844	−	0.399799i
$71$	0.844267	−	4.78807i	0.100196	−	0.568240i	−0.892835	−	0.450384i	$-0.851287\pi$
$71$	0.844267	−	4.78807i	0.100196	−	0.568240i	0.993031	−	0.117855i	$-0.0376020\pi$
$72$	0.528942	+	2.99978i	0.0623364	+	0.353527i
$73$	−5.39836	+	1.96484i	−0.631830	+	0.229967i	−0.638028	−	0.770014i	$-0.720249\pi$
$73$	−5.39836	+	1.96484i	−0.631830	+	0.229967i	0.00619766	+	0.999981i	$0.498027\pi$
$74$	2.55263	+	2.14191i	0.296737	+	0.248992i
$75$	13.9352			1.60910
$76$	−1.85771	−	0.369421i	−0.213094	−	0.0423755i
$77$	−2.39675			−0.273135
$78$	1.92092	+	1.61184i	0.217501	+	0.182505i
$79$	−3.84337	+	1.39887i	−0.432413	+	0.157386i	−0.549051	−	0.835789i	$-0.685011\pi$
$79$	−3.84337	+	1.39887i	−0.432413	+	0.157386i	0.116637	+	0.993175i	$0.462788\pi$
$80$	−2.22313	−	12.6080i	−0.248554	−	1.40962i
$81$	0.173648	−	0.984808i	0.0192942	−	0.109423i
$82$	6.69440	+	2.43656i	0.739273	+	0.269073i
$83$	1.32418	+	2.29354i	0.145347	+	0.251749i	0.929503	−	0.368816i	$-0.120237\pi$
$83$	1.32418	+	2.29354i	0.145347	+	0.251749i	−0.784155	+	0.620565i	$0.786903\pi$
$84$	−0.390278	+	0.675982i	−0.0425829	+	0.0737557i
$85$	14.9295	−	12.5273i	1.61933	−	1.35878i
$86$	−0.770410	+	0.646450i	−0.0830754	+	0.0697085i
$87$	−0.801324	+	1.38793i	−0.0859109	+	0.148802i
$88$	−2.03211	−	3.51972i	−0.216624	−	0.375203i
$89$	11.0474	+	4.02092i	1.17102	+	0.426216i	0.853022	−	0.521875i	$-0.174767\pi$
$89$	11.0474	+	4.02092i	1.17102	+	0.426216i	0.317998	+	0.948091i	$0.396990\pi$
$90$	−0.945426	+	5.36178i	−0.0996566	+	0.565181i
$91$	0.625153	+	3.54542i	0.0655338	+	0.371661i
$92$	1.12798	−	0.410550i	0.117600	−	0.0428028i
$93$	−3.62267	−	3.03978i	−0.375653	−	0.315210i
$94$	6.16445			0.635815
$95$	−16.2161	−	9.83904i	−1.66374	−	1.00946i
$96$	−2.41097			−0.246069
$97$	−7.22847	−	6.06541i	−0.733940	−	0.615849i	0.197263	−	0.980351i	$-0.436795\pi$
$97$	−7.22847	−	6.06541i	−0.733940	−	0.615849i	−0.931203	+	0.364502i	$0.881239\pi$
$98$	−4.43633	+	1.61469i	−0.448137	+	0.163109i
$99$	0.231691	+	1.31399i	0.0232859	+	0.132061i
$100$	−1.05149	+	5.96331i	−0.105149	+	0.596331i
$101$	3.91168	+	1.42373i	0.389227	+	0.141667i	0.529218	−	0.848486i	$-0.322485\pi$
$101$	3.91168	+	1.42373i	0.389227	+	0.141667i	−0.139992	+	0.990153i	$0.544708\pi$
$102$	2.80187	+	4.85297i	0.277426	+	0.480516i
$103$	−7.69722	+	13.3320i	−0.758429	+	1.31364i	0.185222	+	0.982697i	$0.440700\pi$
$103$	−7.69722	+	13.3320i	−0.758429	+	1.31364i	−0.943651	+	0.330941i	$0.892634\pi$
$104$	−4.67654	+	3.92409i	−0.458573	+	0.384788i
$105$	−5.98786	+	5.02441i	−0.584355	+	0.490332i
$106$	0.938856	−	1.62615i	0.0911898	−	0.157945i
$107$	−7.60826	−	13.1779i	−0.735518	−	1.27395i	−0.954496	−	0.298225i	$-0.903605\pi$
$107$	−7.60826	−	13.1779i	−0.735518	−	1.27395i	0.218977	−	0.975730i	$-0.429728\pi$
$108$	0.408327	+	0.148619i	0.0392913	+	0.0143009i
$109$	1.92789	−	10.9336i	0.184658	−	1.04725i	−0.741736	−	0.670692i	$-0.765997\pi$
$109$	1.92789	−	10.9336i	0.184658	−	1.04725i	0.926394	−	0.376555i	$-0.122892\pi$
$110$	−1.26144	−	7.15399i	−0.120274	−	0.682106i
$111$	2.50264	−	0.910885i	0.237540	−	0.0864574i
$112$	4.04852	+	3.39711i	0.382549	+	0.320997i
$113$	14.6263			1.37593			0.687965	−	0.725744i	$-0.258504\pi$
$113$	14.6263			1.37593			0.687965	+	0.725744i	$0.258504\pi$
$114$	3.59573	−	4.10057i	0.336771	−	0.384053i
$115$	12.0206			1.12093
$116$	−0.533475	−	0.447639i	−0.0495319	−	0.0415622i
$117$	1.88330	−	0.685465i	0.174111	−	0.0633712i
$118$	1.36585	+	7.74610i	0.125736	+	0.713087i
$119$	−1.39704	+	7.92299i	−0.128066	+	0.726299i
$120$	−12.4554	−	4.53340i	−1.13702	−	0.413841i
$121$	4.60988	+	7.98454i	0.419080	+	0.725868i
$122$	7.47974	−	12.9553i	0.677184	−	1.17292i
$123$	4.36172	−	3.65992i	0.393283	−	0.330004i
$124$	1.57417	−	1.32088i	0.141364	−	0.118619i
$125$	−19.4406	+	33.6721i	−1.73882	+	3.01173i
$126$	−1.12376	−	1.94641i	−0.100113	−	0.173400i
$127$	−8.35124	−	3.03960i	−0.741053	−	0.269721i	−0.0562170	−	0.998419i	$-0.517904\pi$
$127$	−8.35124	−	3.03960i	−0.741053	−	0.269721i	−0.684836	+	0.728697i	$0.740126\pi$
$128$	−1.09652	+	6.21869i	−0.0969199	+	0.549660i
$129$	0.139578	+	0.791584i	0.0122891	+	0.0696951i
$130$	−10.2536	+	3.73201i	−0.899300	+	0.327319i
$131$	7.35881	+	6.17478i	0.642942	+	0.539493i	0.904920	−	0.425581i	$-0.139930\pi$
$131$	7.35881	+	6.17478i	0.642942	+	0.539493i	−0.261978	+	0.965074i	$0.584375\pi$
$132$	−0.579778			−0.0504632
$133$	7.73876	−	1.19152i	0.671036	−	0.103318i
$134$	6.75121			0.583215
$135$	3.33341	+	2.79707i	0.286894	+	0.240733i
$136$	−12.8197	+	4.66600i	−1.09928	+	0.400106i
$137$	−1.21039	−	6.86448i	−0.103411	−	0.586472i	−0.991843	−	0.127465i	$-0.959316\pi$
$137$	−1.21039	−	6.86448i	−0.103411	−	0.586472i	0.888432	−	0.459008i	$-0.151795\pi$
$138$	−0.600183	+	3.40381i	−0.0510910	+	0.289752i
$139$	14.8192	+	5.39376i	1.25695	+	0.457493i	0.882745	−	0.469852i	$-0.155693\pi$
$139$	14.8192	+	5.39376i	1.25695	+	0.457493i	0.374207	+	0.927345i	$0.377915\pi$
$140$	−1.69828	−	2.94151i	−0.143531	−	0.248603i
$141$	2.46344	−	4.26681i	0.207459	−	0.359330i
$142$	−4.65999	+	3.91020i	−0.391058	+	0.328137i
$143$	−2.04846	+	1.71886i	−0.171301	+	0.143738i
$144$	1.47106	−	2.54795i	0.122588	−	0.212329i
$145$	−3.48693	−	6.03954i	−0.289574	−	0.501556i
$146$	6.75435	+	2.45838i	0.558994	+	0.203457i
$147$	−0.655219	+	3.71593i	−0.0540416	+	0.306485i
$148$	0.200958	+	1.13969i	0.0165186	+	0.0936817i
$149$	−4.38503	+	1.59602i	−0.359235	+	0.130751i	−0.515332	−	0.856991i	$-0.672331\pi$
$149$	−4.38503	+	1.59602i	−0.359235	+	0.130751i	0.156096	+	0.987742i	$0.450109\pi$
$150$	−13.3564	−	11.2074i	−1.09055	−	0.915077i
$151$	−6.85898			−0.558176			−0.279088	−	0.960266i	$-0.590032\pi$
$151$	−6.85898			−0.558176			−0.279088	+	0.960266i	$0.590032\pi$
$152$	8.31120	+	10.3544i	0.674127	+	0.839856i
$153$	4.47873			0.362084
$154$	2.29720	+	1.92758i	0.185113	+	0.155328i
$155$	19.3373	−	7.03819i	1.55321	−	0.565321i
$156$	0.151226	+	0.857644i	0.0121078	+	0.0686665i
$157$	0.136510	−	0.774188i	0.0108947	−	0.0617869i	−0.978876	−	0.204456i	$-0.934457\pi$
$157$	0.136510	−	0.774188i	0.0108947	−	0.0617869i	0.989770	+	0.142669i	$0.0455685\pi$
$158$	4.80878	+	1.75025i	0.382566	+	0.139243i
$159$	−0.750373	−	1.29968i	−0.0595084	−	0.103072i
$160$	5.24563	−	9.08569i	0.414703	−	0.718287i
$161$	−3.80126	+	3.18964i	−0.299582	+	0.251379i
$162$	−0.958464	+	0.804247i	−0.0753041	+	0.0631876i
$163$	10.6979	−	18.5293i	0.837922	−	1.45132i	−0.0537071	−	0.998557i	$-0.517104\pi$
$163$	10.6979	−	18.5293i	0.837922	−	1.45132i	0.891629	−	0.452767i	$-0.149563\pi$
$164$	1.23708	+	2.14268i	0.0965994	+	0.167315i
$165$	−5.45583	−	1.98576i	−0.424736	−	0.154591i
$166$	0.575398	−	3.26325i	0.0446596	−	0.253277i
$167$	−3.86253	−	21.9055i	−0.298891	−	1.69510i	−0.650952	−	0.759119i	$-0.725630\pi$
$167$	−3.86253	−	21.9055i	−0.298891	−	1.69510i	0.352061	−	0.935977i	$-0.385481\pi$
$168$	5.14169	−	1.87142i	0.396690	−	0.144383i
$169$	−6.88162	−	5.77437i	−0.529356	−	0.444182i
$170$	−24.3844			−1.87020
$171$	−1.40134	−	4.12750i	−0.107163	−	0.315638i
$172$	−0.349275			−0.0266320
$173$	3.23129	+	2.71137i	0.245670	+	0.206142i	0.757305	−	0.653061i	$-0.226516\pi$
$173$	3.23129	+	2.71137i	0.245670	+	0.206142i	−0.511635	+	0.859203i	$0.670960\pi$
$174$	1.88428	−	0.685823i	0.142847	−	0.0519921i
$175$	−4.34677	−	24.6517i	−0.328585	−	1.86350i
$176$	−0.681663	+	3.86590i	−0.0513823	+	0.291403i
$177$	5.90739	+	2.15011i	0.444027	+	0.161612i
$178$	−7.35471	−	12.7387i	−0.551259	−	0.954808i
$179$	−8.71498	+	15.0948i	−0.651388	+	1.12824i	0.331398	+	0.943491i	$0.392480\pi$
$179$	−8.71498	+	15.0948i	−0.651388	+	1.12824i	−0.982786	+	0.184747i	$0.940854\pi$
$180$	−1.44848	+	1.21542i	−0.107963	+	0.0905917i
$181$	9.65206	−	8.09904i	0.717432	−	0.601997i	−0.209241	−	0.977864i	$-0.567099\pi$
$181$	9.65206	−	8.09904i	0.717432	−	0.601997i	0.926674	+	0.375867i	$0.122655\pi$
$182$	2.25220	−	3.90093i	0.166944	−	0.289156i
$183$	−5.97812	−	10.3544i	−0.441915	−	0.765420i
$184$	−7.90706	−	2.87794i	−0.582916	−	0.212164i
$185$	−2.01241	+	11.4130i	−0.147956	+	0.839098i
$186$	1.02746	+	5.82704i	0.0753373	+	0.427259i
$187$	−5.61540	+	2.04384i	−0.410639	+	0.149460i
$188$	1.64002	+	1.37614i	0.119611	+	0.100365i
$189$	−1.79631			−0.130663
$190$	7.62956	+	22.4721i	0.553506	+	1.63030i
$191$	−9.46558			−0.684905			−0.342453	−	0.939535i	$-0.611258\pi$
$191$	−9.46558			−0.684905			−0.342453	+	0.939535i	$0.611258\pi$
$192$	6.81841	+	5.72133i	0.492077	+	0.412901i
$193$	−8.96561	+	3.26322i	−0.645359	+	0.234891i	−0.643903	−	0.765108i	$-0.722686\pi$
$193$	−8.96561	+	3.26322i	−0.645359	+	0.234891i	−0.00145636	+	0.999999i	$0.500464\pi$
$194$	2.05015	+	11.6270i	0.147192	+	0.834766i
$195$	−1.51439	+	8.58855i	−0.108448	+	0.615039i
$196$	−1.54072	−	0.560777i	−0.110052	−	0.0400555i
$197$	1.30312	+	2.25706i	0.0928432	+	0.160809i	0.908706	−	0.417436i	$-0.137071\pi$
$197$	1.30312	+	2.25706i	0.0928432	+	0.160809i	−0.815863	+	0.578245i	$0.803738\pi$
$198$	0.834703	−	1.44575i	0.0593197	−	0.102745i
$199$	−5.77230	+	4.84354i	−0.409188	+	0.343349i	−0.824032	−	0.566543i	$-0.808280\pi$
$199$	−5.77230	+	4.84354i	−0.409188	+	0.343349i	0.414844	+	0.909892i	$0.363836\pi$
$200$	32.5166	−	27.2847i	2.29927	−	1.92932i
$201$	2.69792	−	4.67294i	0.190297	−	0.329604i
$202$	−2.60417	−	4.51056i	−0.183229	−	0.317362i
$203$	2.70524	+	0.984628i	0.189871	+	0.0691073i
$204$	−0.337946	+	1.91659i	−0.0236610	+	0.134188i
$205$	4.30239	+	24.4000i	0.300492	+	1.70417i
$206$	18.0997	−	6.58775i	1.26107	−	0.458991i
$207$	2.11615	+	1.77566i	0.147082	+	0.123417i
$208$	5.89649			0.408848
$209$	3.64054	+	4.53554i	0.251821	+	0.313730i
$210$	9.78001			0.674885
$211$	−0.344649	−	0.289195i	−0.0237266	−	0.0199090i	0.630847	−	0.775907i	$-0.282707\pi$
$211$	−0.344649	−	0.289195i	−0.0237266	−	0.0199090i	−0.654574	+	0.755998i	$0.727152\pi$
$212$	0.612795	−	0.223039i	0.0420869	−	0.0153184i
$213$	0.844267	+	4.78807i	0.0578482	+	0.328073i
$214$	−3.30604	+	18.7495i	−0.225996	+	1.28169i
$215$	−3.28675	−	1.19628i	−0.224154	−	0.0815856i
$216$	−1.52303	−	2.63796i	−0.103629	−	0.179490i
$217$	−4.24743	+	7.35677i	−0.288335	+	0.499410i
$218$	−10.6411	+	8.92895i	−0.720707	+	0.604745i
$219$	4.40078	−	3.69269i	0.297377	−	0.249529i
$220$	1.26144	−	2.18488i	0.0850464	−	0.147305i
$221$	4.48806	+	7.77355i	0.301900	+	0.522905i
$222$	−3.13126	−	1.13969i	−0.210157	−	0.0764908i
$223$	−1.28343	+	7.27869i	−0.0859448	+	0.487417i	0.911204	+	0.411956i	$0.135154\pi$
$223$	−1.28343	+	7.27869i	−0.0859448	+	0.487417i	−0.997149	+	0.0754616i	$0.975957\pi$
$224$	0.752046	+	4.26507i	0.0502482	+	0.284972i
$225$	−13.0948	+	4.76612i	−0.872988	+	0.317742i
$226$	−14.0188	−	11.7632i	−0.932519	−	0.782476i
$227$	−13.8034			−0.916164			−0.458082	−	0.888910i	$-0.651463\pi$
$227$	−13.8034			−0.916164			−0.458082	+	0.888910i	$0.651463\pi$
$228$	1.87202	−	0.288231i	0.123978	−	0.0190886i
$229$	−18.8593			−1.24626			−0.623128	−	0.782120i	$-0.714138\pi$
$229$	−18.8593			−1.24626			−0.623128	+	0.782120i	$0.714138\pi$
$230$	−11.5213	−	9.66755i	−0.759694	−	0.637459i
$231$	2.25220	−	0.819735i	0.148184	−	0.0539346i
$232$	0.847707	+	4.80759i	0.0556547	+	0.315634i
$233$	0.511665	−	2.90180i	0.0335203	−	0.190103i	−0.963450	−	0.267889i	$-0.913674\pi$
$233$	0.511665	−	2.90180i	0.0335203	−	0.190103i	0.996970	+	0.0777859i	$0.0247850\pi$
$234$	−2.35636	−	0.857644i	−0.154040	−	0.0560660i
$235$	10.7196	+	18.5669i	0.699268	+	1.21117i
$236$	−1.36585	+	2.36572i	−0.0889091	+	0.153995i
$237$	3.13315	−	2.62902i	0.203520	−	0.170773i
$238$	7.71105	−	6.47034i	0.499833	−	0.419410i
$239$	−2.68089	+	4.64344i	−0.173412	+	0.300359i	−0.939611	−	0.342245i	$-0.888813\pi$
$239$	−2.68089	+	4.64344i	−0.173412	+	0.300359i	0.766198	+	0.642604i	$0.222146\pi$
$240$	6.40125	+	11.0873i	0.413199	+	0.715682i
$241$	26.1970	+	9.53492i	1.68750	+	0.614198i	0.994307	−	0.106557i	$-0.0339826\pi$
$241$	26.1970	+	9.53492i	1.68750	+	0.614198i	0.693190	+	0.720755i	$0.256205\pi$
$242$	2.00314	−	11.3604i	0.128767	−	0.730273i
$243$	0.173648	+	0.984808i	0.0111395	+	0.0631754i
$244$	4.88205	−	1.77692i	0.312542	−	0.113756i
$245$	−12.5778	−	10.5540i	−0.803567	−	0.674273i
$246$	−7.12403			−0.454212
$247$	5.75967	−	6.56833i	0.366479	−	0.417933i
$248$	−14.4050			−0.914716
$249$	−2.02876	−	1.70233i	−0.128567	−	0.107881i
$250$	45.7139	−	16.6385i	2.89120	−	1.05231i
$251$	−5.35050	−	30.3442i	−0.337721	−	1.91531i	−0.398520	−	0.917160i	$-0.630476\pi$
$251$	−5.35050	−	30.3442i	−0.337721	−	1.91531i	0.0607990	−	0.998150i	$-0.480635\pi$
$252$	0.135542	−	0.768698i	0.00853836	−	0.0484234i
$253$	−3.46352	−	1.26062i	−0.217749	−	0.0792543i
$254$	5.55977	+	9.62981i	0.348851	+	0.604228i
$255$	−9.74452	+	16.8780i	−0.610225	+	1.05694i
$256$	−7.58448	+	6.36414i	−0.474030	+	0.397759i
$257$	2.76099	−	2.31674i	0.172226	−	0.144514i	−0.552601	−	0.833446i	$-0.686364\pi$
$257$	2.76099	−	2.31674i	0.172226	−	0.144514i	0.724826	+	0.688932i	$0.241920\pi$
$258$	0.502849	−	0.870960i	0.0313060	−	0.0542236i
$259$	−2.39202	−	4.14309i	−0.148633	−	0.257439i
$260$	−3.56104	−	1.29611i	−0.220846	−	0.0803815i
$261$	0.278297	−	1.57830i	0.0172261	−	0.0976943i
$262$	−2.08711	−	11.8366i	−0.128942	−	0.731268i
$263$	−15.0105	+	5.46336i	−0.925585	+	0.336885i	−0.760458	−	0.649387i	$-0.775025\pi$
$263$	−15.0105	+	5.46336i	−0.925585	+	0.336885i	−0.165127	+	0.986272i	$0.552803\pi$
$264$	3.11337	+	2.61243i	0.191615	+	0.160784i
$265$	6.53044			0.401162
$266$	−8.37560	−	5.08185i	−0.513541	−	0.311588i
$267$	−11.7564			−0.719478
$268$	1.79612	+	1.50712i	0.109716	+	0.0920623i
$269$	−2.67936	+	0.975208i	−0.163364	+	0.0594595i	−0.422407	−	0.906406i	$-0.638815\pi$
$269$	−2.67936	+	0.975208i	−0.163364	+	0.0594595i	0.259044	+	0.965866i	$0.416593\pi$
$270$	−0.945426	−	5.36178i	−0.0575368	−	0.326307i
$271$	2.83687	−	16.0887i	0.172328	−	0.977319i	−0.768856	−	0.639422i	$-0.779174\pi$
$271$	2.83687	−	16.0887i	0.172328	−	0.977319i	0.941183	−	0.337896i	$-0.109715\pi$
$272$	12.3823	+	4.50678i	0.750787	+	0.273264i
$273$	−1.80005	−	3.11779i	−0.108944	−	0.188697i
$274$	−4.36062	+	7.55282i	−0.263435	+	0.456283i
$275$	14.2432	−	11.9515i	0.858897	−	0.720700i
$276$	−0.919534	+	0.771581i	−0.0553495	+	0.0464437i
$277$	−5.97613	+	10.3510i	−0.359071	+	0.621929i	−0.987806	−	0.155691i	$-0.950240\pi$
$277$	−5.97613	+	10.3510i	−0.359071	+	0.621929i	0.628735	+	0.777620i	$0.283573\pi$
$278$	−9.86580	−	17.0881i	−0.591711	−	1.02487i
$279$	4.44386	+	1.61743i	0.266047	+	0.0968331i
$280$	−4.13452	+	23.4480i	−0.247085	+	1.40129i
$281$	−2.02301	−	11.4731i	−0.120683	−	0.684427i	−0.983779	−	0.179386i	$-0.942589\pi$
$281$	−2.02301	−	11.4731i	−0.120683	−	0.684427i	0.863096	−	0.505040i	$-0.168522\pi$
$282$	−5.79269	+	2.10837i	−0.344950	+	0.125551i
$283$	−17.9607	−	15.0708i	−1.06765	−	0.895867i	−0.0728155	−	0.997345i	$-0.523198\pi$
$283$	−17.9607	−	15.0708i	−1.06765	−	0.895867i	−0.994838	+	0.101478i	$0.967643\pi$
$284$	−2.11267			−0.125364
$285$	18.6033	+	3.69943i	1.10197	+	0.219135i
$286$	3.34576			0.197839
$287$	−7.83502	−	6.57436i	−0.462487	−	0.388072i
$288$	2.26557	−	0.824601i	0.133500	−	0.0485901i
$289$	0.531199	+	3.01258i	0.0312470	+	0.177211i
$290$	−1.51518	+	8.59304i	−0.0889747	+	0.504601i
$291$	8.86703	+	3.22734i	0.519795	+	0.189190i
$292$	1.24815	+	2.16187i	0.0730427	+	0.126514i
$293$	8.59825	−	14.8926i	0.502315	−	0.870035i	−0.497681	−	0.867360i	$-0.665815\pi$
$293$	8.59825	−	14.8926i	0.502315	−	0.870035i	0.999996	−	0.00267515i	$-0.000851528\pi$
$294$	3.61653	−	3.03463i	0.210920	−	0.176983i
$295$	−20.9555	+	17.5838i	−1.22008	+	1.02377i
$296$	4.05620	−	7.02555i	0.235762	−	0.408352i
$297$	−0.667129	−	1.15550i	−0.0387107	−	0.0670490i
$298$	5.48649	+	1.99692i	0.317824	+	0.115678i
$299$	−0.961381	+	5.45226i	−0.0555981	+	0.315312i
$300$	−1.05149	−	5.96331i	−0.0607079	−	0.344292i
$301$	1.35679	−	0.493832i	0.0782043	−	0.0284640i
$302$	6.57409	+	5.51632i	0.378296	+	0.317428i
$303$	−4.16272			−0.239142
$304$	0.279100	−	12.8214i	0.0160075	−	0.735355i
$305$	52.0271			2.97906
$306$	−4.29271	−	3.60201i	−0.245398	−	0.205913i
$307$	16.7507	−	6.09675i	0.956012	−	0.347960i	0.183542	−	0.983012i	$-0.441244\pi$
$307$	16.7507	−	6.09675i	0.956012	−	0.347960i	0.772469	+	0.635052i	$0.219021\pi$
$308$	0.180848	+	1.02564i	0.0103048	+	0.0584414i
$309$	2.67322	−	15.1606i	0.152074	−	0.862454i
$310$	−24.1945	−	8.80609i	−1.37416	−	0.500152i
$311$	16.2959	+	28.2254i	0.924057	+	1.60051i	0.793071	+	0.609129i	$0.208481\pi$
$311$	16.2959	+	28.2254i	0.924057	+	1.60051i	0.130986	+	0.991384i	$0.458186\pi$
$312$	3.05240	−	5.28691i	0.172808	−	0.299312i
$313$	−3.77417	+	3.16690i	−0.213328	+	0.179004i	−0.743190	−	0.669080i	$-0.766688\pi$
$313$	−3.77417	+	3.16690i	−0.213328	+	0.179004i	0.529862	+	0.848084i	$0.322244\pi$
$314$	−0.753479	+	0.632244i	−0.0425213	+	0.0356796i
$315$	3.90830	−	6.76937i	0.220208	−	0.381411i
$316$	0.888626	+	1.53915i	0.0499891	+	0.0865837i
$317$	0.811093	+	0.295214i	0.0455555	+	0.0165808i	0.364697	−	0.931126i	$-0.381172\pi$
$317$	0.811093	+	0.295214i	0.0455555	+	0.0165808i	−0.319142	+	0.947707i	$0.603395\pi$
$318$	−0.326061	+	1.84919i	−0.0182846	+	0.103697i
$319$	0.371320	+	2.10586i	0.0207899	+	0.117905i
$320$	−36.3957	+	13.2470i	−2.03458	+	0.740528i
$321$	11.6565	+	9.78099i	0.650604	+	0.545922i
$322$	6.20863			0.345994
$323$	17.1153	−	9.39091i	0.952320	−	0.522524i
$324$	−0.434532			−0.0241407
$325$	−21.3945	−	17.9521i	−1.18675	−	0.995802i
$326$	−25.1556	+	9.15590i	−1.39324	+	0.507098i
$327$	1.92789	+	10.9336i	0.106612	+	0.604628i
$328$	3.01170	−	17.0802i	0.166293	−	0.943096i
$329$	−8.31650	−	3.02696i	−0.458503	−	0.166882i
$330$	3.63218	+	6.29111i	0.199945	+	0.346314i
$331$	9.42126	−	16.3181i	0.517839	−	0.896924i	−0.481946	−	0.876201i	$-0.660070\pi$
$331$	9.42126	−	16.3181i	0.517839	−	0.896924i	0.999785	−	0.0207232i	$-0.00659687\pi$
$332$	0.881561	−	0.739718i	0.0483820	−	0.0405973i
$333$	−2.04017	+	1.71190i	−0.111800	+	0.0938118i
$334$	−13.9153	+	24.1020i	−0.761412	+	1.31880i
$335$	11.7399	+	20.3341i	0.641419	+	1.11097i
$336$	−4.96624	−	1.80756i	−0.270931	−	0.0986107i
$337$	−5.70858	+	32.3750i	−0.310966	+	1.76358i	0.283033	+	0.959110i	$0.408659\pi$
$337$	−5.70858	+	32.3750i	−0.310966	+	1.76358i	−0.593999	+	0.804466i	$0.702452\pi$
$338$	1.95177	+	11.0691i	0.106162	+	0.602077i
$339$	−13.7443	+	5.00250i	−0.746486	+	0.271699i
$340$	−6.48734	−	5.44352i	−0.351825	−	0.295217i
$341$	−6.30978			−0.341694
$342$	−1.97640	+	5.08308i	−0.106871	+	0.274862i
$343$	19.3522			1.04492
$344$	1.87559	+	1.57380i	0.101125	+	0.0848538i
$345$	−11.2957	+	4.11129i	−0.608139	+	0.221345i
$346$	−0.916461	−	5.19751i	−0.0492692	−	0.279420i
$347$	1.35342	−	7.67563i	0.0726554	−	0.412049i	−0.926688	−	0.375830i	$-0.877358\pi$
$347$	1.35342	−	7.67563i	0.0726554	−	0.412049i	0.999344	−	0.0362189i	$-0.0115313\pi$
$348$	0.654404	+	0.238184i	0.0350798	+	0.0127680i
$349$	−0.0364745	−	0.0631757i	−0.00195244	−	0.00338172i	0.865048	−	0.501690i	$-0.167288\pi$
$349$	−0.0364745	−	0.0631757i	−0.00195244	−	0.00338172i	−0.867000	+	0.498308i	$0.833955\pi$
$350$	−15.6599	+	27.1237i	−0.837055	+	1.44982i
$351$	−1.53528	+	1.28825i	−0.0819472	+	0.0687618i
$352$	−2.46426	+	2.06776i	−0.131345	+	0.110212i
$353$	7.28303	−	12.6146i	0.387636	−	0.671406i	−0.604495	−	0.796609i	$-0.706625\pi$
$353$	7.28303	−	12.6146i	0.387636	−	0.671406i	0.992131	+	0.125203i	$0.0399583\pi$
$354$	−3.93280	−	6.81181i	−0.209026	−	0.362044i
$355$	−19.8806	−	7.23596i	−1.05515	−	0.384045i
$356$	0.887086	−	5.03092i	0.0470155	−	0.266638i
$357$	−1.39704	−	7.92299i	−0.0739390	−	0.419329i
$358$	20.4929	−	7.45882i	1.08309	−	0.394211i
$359$	6.90318	+	5.79246i	0.364336	+	0.305714i	0.806516	−	0.591212i	$-0.201350\pi$
$359$	6.90318	+	5.79246i	0.364336	+	0.305714i	−0.442180	+	0.896926i	$0.645795\pi$
$360$	13.2548			0.698589
$361$	−14.0096	−	12.8348i	−0.737347	−	0.675514i
$362$	−15.7648			−0.828579
$363$	−7.06274	−	5.92635i	−0.370698	−	0.311052i
$364$	1.47002	−	0.535044i	0.0770501	−	0.0280439i
$365$	4.34091	+	24.6185i	0.227214	+	1.28859i
$366$	−2.59769	+	14.7322i	−0.135783	+	0.770065i
$367$	25.5445	+	9.29743i	1.33341	+	0.485322i	0.907731	−	0.419552i	$-0.137813\pi$
$367$	25.5445	+	9.29743i	1.33341	+	0.485322i	0.425680	+	0.904874i	$0.360035\pi$
$368$	4.06370	+	7.03853i	0.211835	+	0.366909i
$369$	−2.84691	+	4.93100i	−0.148204	+	0.256697i
$370$	11.1077	−	9.32044i	0.577460	−	0.484547i
$371$	−2.06511	+	1.73283i	−0.107215	+	0.0899643i
$372$	−1.02746	+	1.77962i	−0.0532715	+	0.0922690i
$373$	−5.14836	−	8.91723i	−0.266572	−	0.461717i	0.701402	−	0.712766i	$-0.252558\pi$
$373$	−5.14836	−	8.91723i	−0.266572	−	0.461717i	−0.967974	+	0.251049i	$0.919224\pi$
$374$	7.02591	+	2.55722i	0.363301	+	0.132231i
$375$	6.75166	−	38.2906i	0.348654	−	1.97732i
$376$	−2.60604	−	14.7796i	−0.134396	−	0.762198i
$377$	3.01827	−	1.09856i	0.155449	−	0.0565786i
$378$	1.72170	+	1.44468i	0.0885549	+	0.0743063i
$379$	5.97688			0.307012			0.153506	−	0.988148i	$-0.450944\pi$
$379$	5.97688			0.307012			0.153506	+	0.988148i	$0.450944\pi$
$380$	−2.98683	+	7.68179i	−0.153221	+	0.394068i
$381$	8.88720			0.455305
$382$	9.07242	+	7.61267i	0.464186	+	0.389498i
$383$	18.2122	−	6.62870i	0.930600	−	0.338711i	0.168153	−	0.985761i	$-0.446220\pi$
$383$	18.2122	−	6.62870i	0.930600	−	0.338711i	0.762448	+	0.647050i	$0.223998\pi$
$384$	−1.09652	−	6.21869i	−0.0559567	−	0.317346i
$385$	−1.81104	+	10.2709i	−0.0922990	+	0.523454i
$386$	11.2177	+	4.08289i	0.570964	+	0.207814i
$387$	−0.401898	−	0.696107i	−0.0204296	−	0.0353851i
$388$	−2.05015	+	3.55096i	−0.104080	+	0.180272i
$389$	−9.24537	+	7.75779i	−0.468759	+	0.393335i	−0.846342	−	0.532640i	$-0.821200\pi$
$389$	−9.24537	+	7.75779i	−0.468759	+	0.393335i	0.377583	+	0.925976i	$0.376755\pi$
$390$	8.35881	−	7.01388i	0.423265	−	0.355161i
$391$	−6.18610	+	10.7146i	−0.312845	+	0.541863i
$392$	5.74677	+	9.95370i	0.290256	+	0.502738i
$393$	−9.02692	−	3.28553i	−0.455348	−	0.165733i
$394$	0.566246	−	3.21134i	0.0285271	−	0.161785i
$395$	3.09052	+	17.5272i	0.155501	+	0.881891i
$396$	0.544813	−	0.198296i	0.0273779	−	0.00996474i
$397$	4.84717	+	4.06726i	0.243273	+	0.204130i	0.756269	−	0.654261i	$-0.227020\pi$
$397$	4.84717	+	4.06726i	0.243273	+	0.204130i	−0.512996	+	0.858391i	$0.671465\pi$
$398$	9.42795			0.472580
$399$	−6.86453	+	3.76647i	−0.343657	+	0.188560i
$400$	−40.9990			−2.04995
$401$	−9.02068	−	7.56925i	−0.450471	−	0.377990i	0.389140	−	0.921179i	$-0.372772\pi$
$401$	−9.02068	−	7.56925i	−0.450471	−	0.377990i	−0.839611	+	0.543189i	$0.817217\pi$
$402$	−6.34406	+	2.30905i	−0.316413	+	0.115165i
$403$	1.64580	+	9.33382i	0.0819833	+	0.464951i
$404$	0.314101	−	1.78136i	0.0156271	−	0.0886258i
$405$	−4.08904	−	1.48829i	−0.203186	−	0.0739536i
$406$	−1.80099	−	3.11941i	−0.0893819	−	0.154814i
$407$	1.77673	−	3.07739i	0.0880693	−	0.152540i
$408$	10.4507	−	8.76921i	0.517388	−	0.434140i
$409$	19.2620	−	16.1628i	0.952447	−	0.799198i	−0.0272614	−	0.999628i	$-0.508679\pi$
$409$	19.2620	−	16.1628i	0.952447	−	0.799198i	0.979708	+	0.200431i	$0.0642342\pi$
$410$	15.5000	−	26.8468i	0.765489	−	1.32587i
$411$	3.48519	+	6.03653i	0.171912	+	0.297760i
$412$	6.28596	+	2.28790i	0.309687	+	0.112717i
$413$	1.96093	−	11.1210i	0.0964911	−	0.547228i
$414$	−0.600183	−	3.40381i	−0.0294974	−	0.167288i
$415$	10.8292	−	3.94151i	0.531586	−	0.193481i
$416$	3.70152	+	3.10594i	0.181482	+	0.152281i
$417$	−15.7703			−0.772276
$418$	0.158366	−	7.27504i	0.00774592	−	0.355834i
$419$	−24.0675			−1.17577			−0.587887	−	0.808943i	$-0.700040\pi$
$419$	−24.0675			−1.17577			−0.587887	+	0.808943i	$0.700040\pi$
$420$	2.60192	+	2.18327i	0.126961	+	0.106533i
$421$	−18.8056	+	6.84468i	−0.916529	+	0.333589i	−0.756857	−	0.653581i	$-0.773266\pi$
$421$	−18.8056	+	6.84468i	−0.916529	+	0.333589i	−0.159672	+	0.987170i	$0.551044\pi$
$422$	0.0977497	+	0.554366i	0.00475838	+	0.0269861i
$423$	−0.855545	+	4.85204i	−0.0415980	+	0.235914i
$424$	−4.29567	−	1.56349i	−0.208616	−	0.0759300i
$425$	−31.2061	−	54.0505i	−1.51372	−	2.62183i
$426$	3.04160	−	5.26820i	0.147366	−	0.255245i
$427$	−16.4525	+	13.8053i	−0.796190	+	0.668083i
$428$	−5.06514	+	4.25016i	−0.244833	+	0.205439i
$429$	1.33704	−	2.31581i	0.0645527	−	0.111809i
$430$	2.18813	+	3.78995i	0.105521	+	0.182768i
$431$	11.7762	+	4.28618i	0.567238	+	0.206458i	0.609689	−	0.792641i	$-0.291294\pi$
$431$	11.7762	+	4.28618i	0.567238	+	0.206458i	−0.0424507	+	0.999099i	$0.513517\pi$
$432$	−0.510893	+	2.89742i	−0.0245804	+	0.139402i
$433$	4.46094	+	25.2993i	0.214379	+	1.21581i	0.881980	+	0.471286i	$0.156210\pi$
$433$	4.46094	+	25.2993i	0.214379	+	1.21581i	−0.667601	+	0.744519i	$0.732679\pi$
$434$	9.98768	−	3.63522i	0.479424	−	0.174496i
$435$	5.34229	+	4.48271i	0.256143	+	0.214930i
$436$	−4.82429			−0.231041
$437$	11.8099	+	2.34850i	0.564945	+	0.112344i
$438$	−7.18783			−0.343448
$439$	14.4704	+	12.1421i	0.690635	+	0.579512i	0.919092	−	0.394042i	$-0.128924\pi$
$439$	14.4704	+	12.1421i	0.690635	+	0.579512i	−0.228457	+	0.973554i	$0.573368\pi$
$440$	−16.6187	+	6.04873i	−0.792268	+	0.288362i
$441$	−0.655219	−	3.71593i	−0.0312009	−	0.176949i
$442$	1.95021	−	11.0602i	0.0927619	−	0.526079i
$443$	−22.0347	−	8.01999i	−1.04690	−	0.381041i	−0.239409	−	0.970919i	$-0.576954\pi$
$443$	−22.0347	−	8.01999i	−1.04690	−	0.381041i	−0.807493	+	0.589878i	$0.799176\pi$
$444$	−0.578634	−	1.00222i	−0.0274608	−	0.0475634i
$445$	25.5787	−	44.3036i	1.21255	−	2.10019i
$446$	7.08399	−	5.94417i	0.335437	−	0.281465i
$447$	3.57471	−	2.99954i	0.169078	−	0.141873i
$448$	7.99432	−	13.8466i	0.377696	−	0.654189i
$449$	−12.6719	−	21.9485i	−0.598026	−	1.03581i	−0.993112	−	0.117168i	$-0.962619\pi$
$449$	−12.6719	−	21.9485i	−0.598026	−	1.03581i	0.395086	−	0.918644i	$-0.370715\pi$
$450$	16.3841	+	5.96331i	0.772352	+	0.281113i
$451$	1.31921	−	7.48161i	0.0621192	−	0.352295i
$452$	−1.10364	−	6.25907i	−0.0519110	−	0.294402i
$453$	6.44534	−	2.34591i	0.302828	−	0.110220i
$454$	13.2301	+	11.1013i	0.620918	+	0.521012i
$455$	15.6657			0.734421
$456$	−11.3514	−	6.88739i	−0.531578	−	0.322532i
$457$	14.5788			0.681969			0.340985	−	0.940069i	$-0.389240\pi$
$457$	14.5788			0.681969			0.340985	+	0.940069i	$0.389240\pi$
$458$	18.0759	+	15.1675i	0.844634	+	0.708732i
$459$	−4.20863	+	1.53182i	−0.196442	+	0.0714991i
$460$	−0.907025	−	5.14400i	−0.0422903	−	0.239840i
$461$	−4.49158	+	25.4730i	−0.209194	+	1.18640i	0.681508	+	0.731810i	$0.261324\pi$
$461$	−4.49158	+	25.4730i	−0.209194	+	1.18640i	−0.890702	+	0.454587i	$0.849787\pi$
$462$	−2.81793	−	1.02564i	−0.131102	−	0.0477172i
$463$	−13.0500	−	22.6033i	−0.606487	−	1.05047i	−0.991815	−	0.127686i	$-0.959245\pi$
$463$	−13.0500	−	22.6033i	−0.606487	−	1.05047i	0.385328	−	0.922780i	$-0.374088\pi$
$464$	2.35759	−	4.08346i	0.109448	−	0.189570i
$465$	−15.7639	+	13.2275i	−0.731033	+	0.613409i
$466$	−2.82418	+	2.36977i	−0.130827	+	0.109777i
$467$	−12.8612	+	22.2763i	−0.595146	+	1.03082i	0.398380	+	0.917221i	$0.369573\pi$
$467$	−12.8612	+	22.2763i	−0.595146	+	1.03082i	−0.993526	+	0.113603i	$0.963761\pi$
$468$	−0.435437	−	0.754200i	−0.0201281	−	0.0348629i
$469$	−9.10809	−	3.31507i	−0.420573	−	0.153076i
$470$	4.65800	−	26.4169i	0.214858	−	1.21852i
$471$	0.136510	+	0.774188i	0.00629006	+	0.0356727i
$472$	17.9942	−	6.54936i	0.828252	−	0.301459i
$473$	0.821560	+	0.689371i	0.0377754	+	0.0316973i
$474$	−5.11739			−0.235050
$475$	−40.0478	+	45.6705i	−1.83752	+	2.09550i
$476$	3.49591			0.160235
$477$	1.14964	+	0.964661i	0.0526383	+	0.0441688i
$478$	6.30401	−	2.29447i	0.288339	−	0.104947i
$479$	3.16337	+	17.9403i	0.144538	+	0.819715i	0.967737	+	0.251962i	$0.0810760\pi$
$479$	3.16337	+	17.9403i	0.144538	+	0.819715i	−0.823199	+	0.567753i	$0.807813\pi$
$480$	−1.82179	+	10.3319i	−0.0831528	+	0.471583i
$481$	−5.01570	−	1.82556i	−0.228696	−	0.0832386i
$482$	−17.4404	−	30.2077i	−0.794390	−	1.37592i
$483$	2.48110	−	4.29739i	0.112894	−	0.195538i
$484$	3.06899	−	2.57519i	0.139500	−	0.117054i
$485$	−31.4544	+	26.3934i	−1.42827	+	1.19846i
$486$	0.625593	−	1.08356i	0.0283775	−	0.0491512i
$487$	11.0302	+	19.1049i	0.499828	+	0.865727i	1.00000		0.000199053i	$-6.33604e-5\pi$
$487$	11.0302	+	19.1049i	0.499828	+	0.865727i	−0.500172	+	0.865926i	$0.666730\pi$
$488$	−34.2230	−	12.4562i	−1.54920	−	0.563863i
$489$	−3.71533	+	21.0707i	−0.168013	+	0.952850i
$490$	3.56733	+	20.2313i	0.161156	+	0.913959i
$491$	13.6931	−	4.98388i	0.617960	−	0.224919i	−0.0140224	−	0.999902i	$-0.504464\pi$
$491$	13.6931	−	4.98388i	0.617960	−	0.224919i	0.631983	+	0.774983i	$0.282241\pi$
$492$	−1.89531	−	1.59035i	−0.0854472	−	0.0716987i
$493$	7.17783			0.323273
$494$	−10.8030	+	1.66331i	−0.486050	+	0.0748360i
$495$	5.80597			0.260959
$496$	10.6583	+	8.94338i	0.478572	+	0.401570i
$497$	8.20687	−	2.98706i	0.368128	−	0.133988i
$498$	0.575398	+	3.26325i	0.0257842	+	0.146230i
$499$	1.65383	−	9.37936i	0.0740358	−	0.419878i	−0.925153	−	0.379596i	$-0.876063\pi$
$499$	1.65383	−	9.37936i	0.0740358	−	0.419878i	0.999188	−	0.0402824i	$-0.0128257\pi$
$500$	15.8763	+	5.77849i	0.710008	+	0.258422i
$501$	11.1217	+	19.2633i	0.496881	+	0.860623i
$502$	−19.2760	+	33.3870i	−0.860329	+	1.49013i
$503$	11.6302	−	9.75894i	0.518567	−	0.435130i	−0.345565	−	0.938395i	$-0.612313\pi$
$503$	11.6302	−	9.75894i	0.518567	−	0.435130i	0.864132	+	0.503265i	$0.167868\pi$
$504$	−4.19154	+	3.51712i	−0.186706	+	0.156665i
$505$	9.05696	−	15.6871i	0.403029	−	0.698067i
$506$	2.30581	+	3.99378i	0.102506	+	0.177545i
$507$	8.44156	+	3.07248i	0.374903	+	0.136454i
$508$	−0.670591	+	3.80311i	−0.0297527	+	0.168736i
$509$	−5.39871	−	30.6176i	−0.239294	−	1.35710i	−0.833380	−	0.552701i	$-0.813597\pi$
$509$	−5.39871	−	30.6176i	−0.239294	−	1.35710i	0.594086	−	0.804401i	$-0.297514\pi$
$510$	22.9139	−	8.33996i	1.01464	−	0.369300i
$511$	−7.90519	−	6.63324i	−0.349705	−	0.293437i
$512$	25.0171			1.10561
$513$	2.72851	+	3.39930i	0.120467	+	0.150083i
$514$	−4.50954			−0.198907
$515$	51.3160	+	43.0592i	2.26125	+	1.89742i
$516$	0.328211	−	0.119459i	0.0144487	−	0.00525890i
$517$	−1.14152	−	6.47386i	−0.0502039	−	0.284720i
$518$	−1.03941	+	5.89478i	−0.0456690	+	0.259002i
$519$	−3.96376	−	1.44269i	−0.173990	−	0.0633271i
$520$	13.2824	+	23.0058i	0.582471	+	1.00887i
$521$	9.72487	−	16.8440i	0.426054	−	0.737948i	−0.570464	−	0.821323i	$-0.693237\pi$
$521$	9.72487	−	16.8440i	0.426054	−	0.737948i	0.996518	+	0.0833749i	$0.0265699\pi$
$522$	−1.53608	+	1.28892i	−0.0672324	+	0.0564147i
$523$	−19.6368	+	16.4772i	−0.858656	+	0.720498i	−0.961678	−	0.274181i	$-0.911593\pi$
$523$	−19.6368	+	16.4772i	−0.858656	+	0.720498i	0.103022	+	0.994679i	$0.467149\pi$
$524$	2.08711	−	3.61499i	0.0911760	−	0.157921i
$525$	12.5160	+	21.6784i	0.546244	+	0.946122i
$526$	18.7809	+	6.83568i	0.818885	+	0.298050i
$527$	−3.67790	+	20.8584i	−0.160212	+	0.908606i
$528$	−0.681663	−	3.86590i	−0.0296656	−	0.168242i
$529$	14.4421	−	5.25650i	0.627917	−	0.228543i
$530$	−6.25919	−	5.25209i	−0.271882	−	0.228136i
$531$	−6.28651			−0.272811
$532$	−1.09382	−	3.22175i	−0.0474232	−	0.139681i
$533$	−11.4114			−0.494281
$534$	11.2681	+	9.45503i	0.487617	+	0.409159i
$535$	−62.2209	+	22.6466i	−2.69004	+	0.979096i
$536$	−2.85409	−	16.1863i	−0.123278	−	0.699143i
$537$	3.02668	−	17.1652i	0.130611	−	0.740732i
$538$	3.35238	+	1.22017i	0.144531	+	0.0526051i
$539$	2.51725	+	4.36000i	0.108426	+	0.187799i
$540$	0.945426	−	1.63753i	0.0406846	−	0.0704679i
$541$	−4.52022	+	3.79292i	−0.194340	+	0.163070i	−0.734765	−	0.678322i	$-0.762708\pi$
$541$	−4.52022	+	3.79292i	−0.194340	+	0.163070i	0.540426	+	0.841392i	$0.318263\pi$
$542$	−15.6583	+	13.1389i	−0.672583	+	0.564364i
$543$	−6.29994	+	10.9118i	−0.270356	+	0.468271i
$544$	5.39905	+	9.35143i	0.231482	+	0.400939i
$545$	−45.3975	−	16.5233i	−1.94461	−	0.707782i
$546$	−0.782182	+	4.43598i	−0.0334743	+	0.189842i
$547$	−6.84978	−	38.8470i	−0.292875	−	1.66098i	−0.675715	−	0.737163i	$-0.736165\pi$
$547$	−6.84978	−	38.8470i	−0.292875	−	1.66098i	0.382839	−	0.923815i	$-0.374946\pi$
$548$	−2.84619	+	1.03593i	−0.121583	+	0.0442527i
$549$	9.15901	+	7.68532i	0.390897	+	0.328002i
$550$	−23.2635			−0.991960
$551$	−2.24585	−	6.61493i	−0.0956763	−	0.281805i
$552$	8.41452			0.358146
$553$	−5.62812	−	4.72255i	−0.239332	−	0.200823i
$554$	14.0526	−	5.11474i	0.597039	−	0.217305i
$555$	−2.01241	−	11.4130i	−0.0854222	−	0.484453i
$556$	1.18996	−	6.74861i	0.0504656	−	0.286205i
$557$	−22.7681	−	8.28690i	−0.964714	−	0.351127i	−0.188835	−	0.982009i	$-0.560471\pi$
$557$	−22.7681	−	8.28690i	−0.964714	−	0.351127i	−0.775879	+	0.630882i	$0.782693\pi$
$558$	−2.95846	−	5.12421i	−0.125242	−	0.216925i
$559$	0.805470	−	1.39511i	0.0340677	−	0.0590070i
$560$	17.6170	−	14.7824i	0.744453	−	0.624670i
$561$	4.57772	−	3.84116i	0.193271	−	0.162174i
$562$	−7.28821	+	12.6235i	−0.307434	+	0.532492i
$563$	−6.78813	−	11.7574i	−0.286086	−	0.495515i	0.686786	−	0.726859i	$-0.259021\pi$
$563$	−6.78813	−	11.7574i	−0.286086	−	0.495515i	−0.972872	+	0.231345i	$0.925688\pi$
$564$	−2.01178	−	0.732228i	−0.0847112	−	0.0308324i
$565$	11.0520	−	62.6790i	0.464961	−	2.63693i
$566$	5.09403	+	28.8897i	0.214118	+	1.21432i
$567$	1.68798	−	0.614376i	0.0708886	−	0.0258013i
$568$	11.3449	+	9.51951i	0.476022	+	0.399430i
$569$	2.89524			0.121375			0.0606875	−	0.998157i	$-0.480671\pi$
$569$	2.89524			0.121375			0.0606875	+	0.998157i	$0.480671\pi$
$570$	−14.8554	−	18.5074i	−0.622223	−	0.775191i
$571$	25.6378			1.07291			0.536455	−	0.843929i	$-0.319763\pi$
$571$	25.6378			1.07291			0.536455	+	0.843929i	$0.319763\pi$
$572$	0.890122	+	0.746901i	0.0372179	+	0.0312295i
$573$	8.89474	−	3.23742i	0.371583	−	0.135245i
$574$	2.22218	+	12.6026i	0.0927518	+	0.526022i
$575$	6.68460	−	37.9103i	0.278767	−	1.58097i
$576$	−8.36402	−	3.04426i	−0.348501	−	0.126844i
$577$	−18.5390	−	32.1104i	−0.771787	−	1.33677i	−0.936583	−	0.350446i	$-0.886030\pi$
$577$	−18.5390	−	32.1104i	−0.771787	−	1.33677i	0.164796	−	0.986328i	$-0.447303\pi$
$578$	1.91372	−	3.31467i	0.0796004	−	0.137872i
$579$	7.30883	−	6.13284i	0.303745	−	0.254872i
$580$	−2.32140	+	1.94788i	−0.0963908	+	0.0808815i
$581$	−2.37864	+	4.11992i	−0.0986826	+	0.170923i
$582$	−5.90316	−	10.2246i	−0.244694	−	0.423822i
$583$	−1.88162	−	0.684855i	−0.0779289	−	0.0283638i
$584$	3.03867	−	17.2332i	0.125741	−	0.713113i
$585$	−1.51439	−	8.58855i	−0.0626125	−	0.355093i
$586$	−20.2184	+	7.35891i	−0.835216	+	0.303994i
$587$	−11.5922	−	9.72703i	−0.478462	−	0.401478i	0.371408	−	0.928470i	$-0.378875\pi$
$587$	−11.5922	−	9.72703i	−0.478462	−	0.401478i	−0.849870	+	0.526992i	$0.823320\pi$
$588$	1.63960			0.0676161
$589$	20.3734	−	3.13684i	0.839471	−	0.129251i
$590$	34.2269			1.40910
$591$	−1.99649	−	1.67525i	−0.0821246	−	0.0689107i
$592$	−7.36305	+	2.67993i	−0.302619	+	0.110144i
$593$	3.86573	+	21.9237i	0.158747	+	0.900297i	0.955280	+	0.295703i	$0.0955537\pi$
$593$	3.86573	+	21.9237i	0.158747	+	0.900297i	−0.796533	+	0.604595i	$0.793335\pi$
$594$	−0.289889	+	1.64404i	−0.0118943	+	0.0674559i
$595$	32.8972	+	11.9736i	1.34865	+	0.490869i
$596$	1.01386	+	1.75606i	0.0415294	+	0.0719310i
$597$	3.76760	−	6.52568i	0.154198	−	0.267078i
$598$	5.30642	−	4.45261i	0.216995	−	0.182081i
$599$	−16.6376	+	13.9606i	−0.679792	+	0.570413i	−0.915946	−	0.401303i	$-0.868558\pi$
$599$	−16.6376	+	13.9606i	−0.679792	+	0.570413i	0.236154	+	0.971716i	$0.424113\pi$
$600$	−21.2237	+	36.7605i	−0.866454	+	1.50074i
$601$	−3.06235	−	5.30415i	−0.124916	−	0.216361i	0.796784	−	0.604264i	$-0.206533\pi$
$601$	−3.06235	−	5.30415i	−0.124916	−	0.216361i	−0.921700	+	0.387903i	$0.873199\pi$
$602$	−1.69760	−	0.617876i	−0.0691891	−	0.0251828i
$603$	−0.936978	+	5.31387i	−0.0381567	+	0.216397i
$604$	0.517550	+	2.93517i	0.0210588	+	0.119430i
$605$	37.6999	−	13.7216i	1.53272	−	0.557864i
$606$	3.98982	+	3.34786i	0.162075	+	0.135997i
$607$	32.4439			1.31686			0.658429	−	0.752643i	$-0.271221\pi$
$607$	32.4439			1.31686			0.658429	+	0.752643i	$0.271221\pi$
$608$	6.92878	−	7.90158i	0.280999	−	0.320451i
$609$	−2.87886			−0.116657
$610$	−49.8661	−	41.8427i	−2.01902	−	1.69416i
$611$	−9.27880	+	3.37721i	−0.375380	+	0.136627i
$612$	−0.337946	−	1.91659i	−0.0136607	−	0.0774735i
$613$	−5.25862	+	29.8231i	−0.212394	+	1.20454i	0.672978	+	0.739662i	$0.265015\pi$
$613$	−5.25862	+	29.8231i	−0.212394	+	1.20454i	−0.885372	+	0.464883i	$0.846096\pi$
$614$	−20.9582	−	7.62817i	−0.845805	−	0.307848i
$615$	−12.3882	−	21.4570i	−0.499541	−	0.865231i
$616$	3.65031	−	6.32252i	0.147075	−	0.254742i
$617$	−9.92207	+	8.32561i	−0.399448	+	0.335176i	−0.820280	−	0.571962i	$-0.806182\pi$
$617$	−9.92207	+	8.32561i	−0.399448	+	0.335176i	0.420833	+	0.907138i	$0.361738\pi$
$618$	−14.7550	+	12.3809i	−0.593534	+	0.498034i
$619$	−0.298469	+	0.516963i	−0.0119965	+	0.0207785i	−0.871961	−	0.489575i	$-0.837152\pi$
$619$	−0.298469	+	0.516963i	−0.0119965	+	0.0207785i	0.859965	+	0.510353i	$0.170485\pi$
$620$	−4.47097	−	7.74395i	−0.179558	−	0.311004i
$621$	−2.59584	−	0.944808i	−0.104167	−	0.0379138i
$622$	7.08111	−	40.1590i	0.283927	−	1.61023i
$623$	3.66713	+	20.7973i	0.146920	+	0.833227i
$624$	−5.54089	+	2.01672i	−0.221813	+	0.0807333i
$625$	76.2323	+	63.9665i	3.04929	+	2.55866i
$626$	6.16437			0.246378
$627$	−4.97223	−	3.01687i	−0.198572	−	0.120482i
$628$	−0.341600			−0.0136313
$629$	−9.13737	−	7.66716i	−0.364331	−	0.305710i
$630$	−9.19021	+	3.34496i	−0.366147	+	0.133266i
$631$	−4.62457	−	26.2273i	−0.184101	−	1.04409i	−0.927105	−	0.374803i	$-0.877710\pi$
$631$	−4.62457	−	26.2273i	−0.184101	−	1.04409i	0.743003	−	0.669288i	$-0.233401\pi$
$632$	2.16339	−	12.2692i	0.0860550	−	0.488042i
$633$	0.422775	+	0.153877i	0.0168038	+	0.00611608i
$634$	−0.539979	−	0.935271i	−0.0214453	−	0.0371443i
$635$	−19.3362	+	33.4912i	−0.767332	+	1.32906i
$636$	−0.499555	+	0.419176i	−0.0198086	+	0.0166214i
$637$	5.79300	−	4.86091i	0.229527	−	0.192596i
$638$	1.33773	−	2.31702i	0.0529614	−	0.0917318i
$639$	−2.43097	−	4.21056i	−0.0961677	−	0.166567i
$640$	25.8207	+	9.39798i	1.02065	+	0.371488i
$641$	−6.88310	+	39.0360i	−0.271866	+	1.54183i	0.476877	+	0.878970i	$0.341769\pi$
$641$	−6.88310	+	39.0360i	−0.271866	+	1.54183i	−0.748743	+	0.662860i	$0.769342\pi$
$642$	−3.30604	−	18.7495i	−0.130479	−	0.739982i
$643$	−32.1984	+	11.7193i	−1.26978	+	0.462163i	−0.887040	−	0.461693i	$-0.847242\pi$
$643$	−32.1984	+	11.7193i	−1.26978	+	0.462163i	−0.382742	+	0.923855i	$0.625020\pi$
$644$	1.65177	+	1.38600i	0.0650890	+	0.0546161i
$645$	3.49769			0.137721
$646$	−23.9570	−	4.76406i	−0.942576	−	0.187439i
$647$	−5.20523			−0.204639			−0.102319	−	0.994752i	$-0.532626\pi$
$647$	−5.20523			−0.204639			−0.102319	+	0.994752i	$0.532626\pi$
$648$	2.33341	+	1.95797i	0.0916651	+	0.0769162i
$649$	7.88198	−	2.86881i	0.309395	−	0.112611i
$650$	6.06791	+	34.4129i	0.238003	+	1.34978i
$651$	1.47512	−	8.36581i	0.0578144	−	0.327882i
$652$	−8.73646	−	3.17981i	−0.342146	−	0.124531i
$653$	21.4054	+	37.0752i	0.837658	+	1.45087i	0.891848	+	0.452335i	$0.149409\pi$
$653$	21.4054	+	37.0752i	0.837658	+	1.45087i	−0.0541904	+	0.998531i	$0.517258\pi$
$654$	6.94549	−	12.0299i	0.271590	−	0.470408i
$655$	32.0216	−	26.8693i	1.25119	−	1.04987i
$656$	−12.8327	+	10.7679i	−0.501032	+	0.420416i
$657$	−2.87241	+	4.97515i	−0.112063	+	0.194099i
$658$	5.53665	+	9.58975i	0.215841	+	0.373848i
$659$	22.7446	+	8.27834i	0.886002	+	0.322478i	0.744630	−	0.667478i	$-0.232626\pi$
$659$	22.7446	+	8.27834i	0.886002	+	0.322478i	0.141373	+	0.989956i	$0.454848\pi$
$660$	−0.438094	+	2.48455i	−0.0170528	+	0.0967112i
$661$	5.16240	+	29.2774i	0.200794	+	1.13876i	0.903922	+	0.427697i	$0.140675\pi$
$661$	5.16240	+	29.2774i	0.200794	+	1.13876i	−0.703128	+	0.711063i	$0.748214\pi$
$662$	−22.1537	+	8.06330i	−0.861029	+	0.313389i
$663$	−6.87611	−	5.76974i	−0.267046	−	0.224078i
$664$	−8.06703			−0.313062
$665$	0.741510	−	34.0637i	0.0287545	−	1.32093i
$666$	3.33222			0.129121
$667$	3.39144	+	2.84575i	0.131317	+	0.110188i
$668$	−9.08258	+	3.30579i	−0.351416	+	0.127905i
$669$	−1.28343	−	7.27869i	−0.0496203	−	0.281411i
$670$	5.10137	−	28.9313i	0.197083	−	1.11771i
$671$	−14.9906	−	5.45615i	−0.578707	−	0.210632i
$672$	−2.16543	−	3.75064i	−0.0835333	−	0.144684i
$673$	−25.3327	+	43.8776i	−0.976506	+	1.69136i	−0.301631	+	0.953425i	$0.597531\pi$
$673$	−25.3327	+	43.8776i	−0.976506	+	1.69136i	−0.674875	+	0.737932i	$0.735802\pi$
$674$	31.5089	−	26.4391i	1.21368	−	1.01840i
$675$	10.6750	−	8.95738i	0.410881	−	0.344770i
$676$	−1.95177	+	3.38057i	−0.0750682	+	0.130022i
$677$	10.8223	+	18.7448i	0.415935	+	0.720420i	0.995526	−	0.0944872i	$-0.0301212\pi$
$677$	10.8223	+	18.7448i	0.415935	+	0.720420i	−0.579591	+	0.814907i	$0.696788\pi$
$678$	17.1966	+	6.25907i	0.660433	+	0.240378i
$679$	2.94337	−	16.6927i	0.112956	−	0.640606i
$680$	10.3086	+	58.4628i	0.395315	+	2.24195i
$681$	12.9709	−	4.72104i	0.497048	−	0.180911i
$682$	6.04770	+	5.07462i	0.231578	+	0.194317i
$683$	9.17458			0.351055			0.175528	−	0.984474i	$-0.443837\pi$
$683$	9.17458			0.351055			0.175528	+	0.984474i	$0.443837\pi$
$684$	−1.66055	+	0.911119i	−0.0634926	+	0.0348375i
$685$	−30.3313			−1.15890
$686$	−18.5483	−	15.5639i	−0.708179	−	0.594233i
$687$	17.7219	−	6.45025i	0.676134	−	0.246093i
$688$	−0.410654	−	2.32893i	−0.0156560	−	0.0887897i
$689$	−0.522289	+	2.96205i	−0.0198976	+	0.112845i
$690$	14.1330	+	5.14400i	0.538035	+	0.195829i
$691$	4.95499	+	8.58229i	0.188497	+	0.326486i	0.944749	−	0.327794i	$-0.106305\pi$
$691$	4.95499	+	8.58229i	0.188497	+	0.326486i	−0.756253	+	0.654280i	$0.772972\pi$
$692$	0.916461	−	1.58736i	0.0348386	−	0.0603422i
$693$	−1.83601	+	1.54060i	−0.0697444	+	0.0585225i
$694$	−7.47031	+	6.26833i	−0.283569	+	0.237943i
$695$	34.3120	−	59.4300i	1.30153	−	2.25431i
$696$	−2.44088	−	4.22772i	−0.0925212	−	0.160251i
$697$	−23.9632	−	8.72190i	−0.907671	−	0.330365i
$698$	−0.0158494	+	0.0898862i	−0.000599907	+	0.00340224i
$699$	0.511665	+	2.90180i	0.0193530	+	0.109756i
$700$	−10.2213	+	3.72023i	−0.386327	+	0.140612i
$701$	−13.8999	−	11.6634i	−0.524993	−	0.440522i	0.341375	−	0.939927i	$-0.389107\pi$
$701$	−13.8999	−	11.6634i	−0.524993	−	0.440522i	−0.866368	+	0.499405i	$0.833552\pi$
$702$	2.50758			0.0946427
$703$	−4.20692	+	10.8197i	−0.158667	+	0.408074i
$704$	11.8760			0.447593
$705$	−16.4233	−	13.7808i	−0.618539	−	0.519016i
$706$	−17.1258	+	6.23327i	−0.644536	+	0.234592i
$707$	1.29846	+	7.36395i	0.0488338	+	0.276950i
$708$	0.474354	−	2.69019i	0.0178273	−	0.101104i
$709$	2.67289	+	0.972853i	0.100383	+	0.0365363i	0.391723	−	0.920083i	$-0.371879\pi$
$709$	2.67289	+	0.972853i	0.100383	+	0.0365363i	−0.291341	+	0.956619i	$0.594101\pi$
$710$	13.2354	+	22.9244i	0.496715	+	0.860336i
$711$	−2.04502	+	3.54207i	−0.0766941	+	0.132838i
$712$	−27.4325	+	23.0186i	−1.02808	+	0.862658i
$713$	−10.0074	+	8.39718i	−0.374779	+	0.314477i
$714$	−5.03303	+	8.71746i	−0.188356	+	0.326243i
$715$	5.81806	+	10.0772i	0.217583	+	0.376865i
$716$	7.11713	+	2.59042i	0.265979	+	0.0968086i
$717$	0.931063	−	5.28032i	0.0347712	−	0.197197i
$718$	−1.95789	−	11.1037i	−0.0730677	−	0.414387i
$719$	−5.56767	+	2.02647i	−0.207639	+	0.0755744i	−0.443746	−	0.896153i	$-0.646351\pi$
$719$	−5.56767	+	2.02647i	−0.207639	+	0.0755744i	0.236107	+	0.971727i	$0.424128\pi$
$720$	−9.80729	−	8.22929i	−0.365496	−	0.306688i
$721$	−27.6532			−1.02986
$722$	3.10538	+	23.5688i	0.115570	+	0.877142i
$723$	−27.8783			−1.03680
$724$	−4.19414	−	3.51930i	−0.155874	−	0.130794i
$725$	−20.9864	+	7.63842i	−0.779415	+	0.283684i
$726$	2.00314	+	11.3604i	0.0743436	+	0.421623i
$727$	2.28642	−	12.9669i	0.0847985	−	0.480916i	−0.912601	−	0.408850i	$-0.865930\pi$
$727$	2.28642	−	12.9669i	0.0847985	−	0.480916i	0.997400	−	0.0720656i	$-0.0229591\pi$
$728$	−10.3048	−	3.75064i	−0.381921	−	0.139008i
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$	15.6388	−	27.0872i	0.578817	−	1.00254i
$731$	2.75775	−	2.31403i	0.101999	−	0.0855874i
$732$	−3.97989	+	3.33952i	−0.147101	+	0.123432i
$733$	1.20077	−	2.07980i	0.0443516	−	0.0768193i	−0.842997	−	0.537918i	$-0.819211\pi$
$733$	1.20077	−	2.07980i	0.0443516	−	0.0768193i	0.887349	+	0.461098i	$0.152544\pi$
$734$	−17.0060	−	29.4553i	−0.627705	−	1.08722i
$735$	15.4290	+	5.61569i	0.569106	+	0.207138i
$736$	−1.15652	+	6.55897i	−0.0426300	+	0.241767i
$737$	−1.25017	−	7.09007i	−0.0460506	−	0.261166i
$738$	6.69440	−	2.43656i	0.246424	−	0.0896911i
$739$	−8.19485	−	6.87630i	−0.301452	−	0.252949i	0.479496	−	0.877544i	$-0.340819\pi$
$739$	−8.19485	−	6.87630i	−0.301452	−	0.252949i	−0.780949	+	0.624595i	$0.785264\pi$
$740$	5.03581			0.185120
$741$	−3.16582	+	8.14214i	−0.116299	+	0.299109i
$742$	3.37296			0.123825
$743$	23.4270	+	19.6576i	0.859453	+	0.721167i	0.961850	−	0.273577i	$-0.0882068\pi$
$743$	23.4270	+	19.6576i	0.859453	+	0.721167i	−0.102397	+	0.994744i	$0.532651\pi$
$744$	13.5362	−	4.92678i	0.496262	−	0.180625i
$745$	3.52608	+	19.9974i	0.129186	+	0.732647i
$746$	−2.23713	+	12.6874i	−0.0819072	+	0.464519i
$747$	2.48864	+	0.905791i	0.0910546	+	0.0331412i
$748$	1.29834	+	2.24878i	0.0474719	+	0.0822237i
$749$	13.6668	−	23.6716i	0.499375	−	0.864943i
$750$	−37.2663	+	31.2701i	−1.36077	+	1.14182i
$751$	38.8821	−	32.6259i	1.41883	−	1.19054i	0.466862	−	0.884330i	$-0.345384\pi$
$751$	38.8821	−	32.6259i	1.41883	−	1.19054i	0.951965	−	0.306207i	$-0.0990600\pi$
$752$	−7.24774	+	12.5534i	−0.264298	+	0.457777i
$753$	15.4062	+	26.6843i	0.561432	+	0.972428i
$754$	−3.77641	−	1.37450i	−0.137529	−	0.0500564i
$755$	−5.18281	+	29.3932i	−0.188622	+	1.06973i
$756$	0.135542	+	0.768698i	0.00492962	+	0.0279573i
$757$	8.09346	−	2.94578i	0.294162	−	0.107066i	−0.190724	−	0.981644i	$-0.561083\pi$
$757$	8.09346	−	2.94578i	0.294162	−	0.107066i	0.484886	+	0.874578i	$0.338861\pi$
$758$	−5.72863	−	4.80689i	−0.208073	−	0.174594i
$759$	3.68580			0.133786
$760$	50.6526	−	27.7924i	1.83736	−	1.00813i
$761$	18.7104			0.678250			0.339125	−	0.940741i	$-0.389869\pi$
$761$	18.7104			0.678250			0.339125	+	0.940741i	$0.389869\pi$
$762$	−8.51807	−	7.14751i	−0.308577	−	0.258927i
$763$	18.7404	−	6.82095i	0.678448	−	0.246935i
$764$	0.714233	+	4.05062i	0.0258400	+	0.146546i
$765$	3.38424	−	19.1930i	0.122357	−	0.693923i
$766$	−22.7869	−	8.29374i	−0.823323	−	0.299665i
$767$	−6.29961	−	10.9112i	−0.227466	−	0.393982i
$768$	4.95042	−	8.57438i	0.178633	−	0.309401i
$769$	−15.2986	+	12.8371i	−0.551682	+	0.462916i	−0.875510	−	0.483200i	$-0.839474\pi$
$769$	−15.2986	+	12.8371i	−0.551682	+	0.462916i	0.323828	+	0.946116i	$0.395030\pi$
$770$	9.99616	−	8.38777i	0.360237	−	0.302274i
$771$	−1.80211	+	3.12134i	−0.0649013	+	0.112412i
$772$	2.07294	+	3.59043i	0.0746067	+	0.129223i
$773$	−42.8017	−	15.5785i	−1.53947	−	0.560321i	−0.573551	−	0.819170i	$-0.694435\pi$
$773$	−42.8017	−	15.5785i	−1.53947	−	0.560321i	−0.965918	+	0.258849i	$0.916657\pi$
$774$	−0.174638	+	0.990419i	−0.00627722	+	0.0355999i
$775$	−11.4435	−	64.8992i	−0.411062	−	2.33125i
$776$	27.0095	−	9.83064i	0.969583	−	0.352899i
$777$	3.66478	+	3.07512i	0.131473	+	0.110319i
$778$	15.1005			0.541380
$779$	−0.540136	+	24.8129i	−0.0193524	+	0.889015i
$780$	3.78958			0.135689
$781$	4.96939	+	4.16981i	0.177819	+	0.149208i
$782$	14.5464	−	5.29445i	0.520177	−	0.189329i
$783$	0.278297	+	1.57830i	0.00994552	+	0.0564038i
$784$	1.92773	−	10.9327i	0.0688475	−	0.390454i
$785$	−3.21452	−	1.16999i	−0.114731	−	0.0417587i
$786$	6.00960	+	10.4089i	0.214355	+	0.371275i
$787$	−1.70544	+	2.95391i	−0.0607924	+	0.105296i	−0.894820	−	0.446427i	$-0.852696\pi$
$787$	−1.70544	+	2.95391i	−0.0607924	+	0.105296i	0.834027	+	0.551723i	$0.186029\pi$
$788$	0.867540	−	0.727952i	0.0309048	−	0.0259322i
$789$	12.2366	−	10.2678i	0.435636	−	0.365542i
$790$	11.1341	−	19.2848i	0.396132	−	0.686122i
$791$	13.1368	+	22.7535i	0.467089	+	0.809022i
$792$	−3.81912	−	1.39005i	−0.135706	−	0.0493931i
$793$	−4.16101	+	23.5982i	−0.147762	+	0.837998i
$794$	−1.37476	−	7.79665i	−0.0487884	−	0.276693i
$795$	−6.13660	+	2.23354i	−0.217643	+	0.0792155i
$796$	2.50825	+	2.10467i	0.0889027	+	0.0745982i
$797$	13.4853			0.477674			0.238837	−	0.971060i	$-0.423234\pi$
$797$	13.4853			0.477674			0.238837	+	0.971060i	$0.423234\pi$
$798$	9.60859	+	1.91075i	0.340140	+	0.0676398i
$799$	−22.0662			−0.780646
$800$	−25.7371	−	21.5960i	−0.909944	−	0.763534i
$801$	11.0474	−	4.02092i	0.390340	−	0.142072i
$802$	2.55845	+	14.5097i	0.0903421	+	0.512356i
$803$	1.33102	−	7.54861i	0.0469708	−	0.266385i
$804$	−2.20327	−	0.801924i	−0.0777033	−	0.0282817i
$805$	10.7964	+	18.6999i	0.380523	+	0.659086i
$806$	5.92925	−	10.2698i	0.208849	−	0.361737i
$807$	2.18424	−	1.83279i	0.0768887	−	0.0645173i
$808$	−9.71335	+	8.15047i	−0.341714	+	0.286732i
$809$	21.5583	−	37.3400i	0.757949	−	1.31281i	−0.185946	−	0.982560i	$-0.559535\pi$
$809$	21.5583	−	37.3400i	0.757949	−	1.31281i	0.943895	−	0.330246i	$-0.107132\pi$
$810$	2.72224	+	4.71507i	0.0956499	+	0.165671i
$811$	18.2440	+	6.64026i	0.640632	+	0.233171i	0.641852	−	0.766828i	$-0.278166\pi$
$811$	18.2440	+	6.64026i	0.640632	+	0.233171i	−0.00122009	+	0.999999i	$0.500388\pi$
$812$	0.217227	−	1.23195i	0.00762316	−	0.0432331i
$813$	2.83687	+	16.0887i	0.0994934	+	0.564255i
$814$	−4.17791	+	1.52064i	−0.146436	+	0.0532983i
$815$	−71.3208	−	59.8453i	−2.49826	−	2.09629i
$816$	−13.1770			−0.461286
$817$	−2.99542	−	1.81745i	−0.104796	−	0.0635846i
$818$	−31.4608			−1.10000
$819$	2.75784	+	2.31411i	0.0963669	+	0.0808614i
$820$	10.1169	−	3.68225i	0.353297	−	0.128590i
$821$	−3.43230	−	19.4655i	−0.119788	−	0.679352i	−0.984268	−	0.176684i	$-0.943463\pi$
$821$	−3.43230	−	19.4655i	−0.119788	−	0.679352i	0.864480	−	0.502668i	$-0.167648\pi$
$822$	1.51443	−	8.58875i	0.0528218	−	0.299567i
$823$	−9.87191	−	3.59308i	−0.344113	−	0.125247i	0.164182	−	0.986430i	$-0.447502\pi$
$823$	−9.87191	−	3.59308i	−0.344113	−	0.125247i	−0.508295	+	0.861183i	$0.669724\pi$
$824$	−23.4461	−	40.6099i	−0.816785	−	1.41471i
$825$	−9.29658	+	16.1022i	−0.323666	+	0.560605i
$826$	−10.8235	+	9.08200i	−0.376598	+	0.316003i
$827$	−1.21767	+	1.02174i	−0.0423424	+	0.0355295i	−0.663713	−	0.747987i	$-0.731020\pi$
$827$	−1.21767	+	1.02174i	−0.0423424	+	0.0355295i	0.621371	+	0.783517i	$0.286576\pi$
$828$	0.600183	−	1.03955i	0.0208578	−	0.0361268i
$829$	16.6180	+	28.7832i	0.577166	+	0.999681i	0.995803	+	0.0915268i	$0.0291747\pi$
$829$	16.6180	+	28.7832i	0.577166	+	0.999681i	−0.418637	+	0.908154i	$0.637492\pi$
$830$	−13.5494	−	4.93157i	−0.470306	−	0.171177i
$831$	2.07549	−	11.7707i	0.0719979	−	0.408320i
$832$	−3.09766	−	17.5677i	−0.107392	−	0.609050i
$833$	15.8802	−	5.77994i	0.550218	−	0.200263i
$834$	15.1153	+	12.6832i	0.523399	+	0.439184i
$835$	−96.7913			−3.34960
$836$	1.66620	−	1.90013i	0.0576266	−	0.0657174i
$837$	−4.72905			−0.163460
$838$	23.0678	+	19.3562i	0.796865	+	0.668649i
$839$	45.5929	−	16.5945i	1.57404	−	0.572905i	0.600145	−	0.799891i	$-0.295110\pi$
$839$	45.5929	−	16.5945i	1.57404	−	0.572905i	0.973898	+	0.226987i	$0.0728873\pi$
$840$	−4.13452	−	23.4480i	−0.142655	−	0.809034i
$841$	−4.58979	+	26.0300i	−0.158268	+	0.897585i
$842$	23.5293	+	8.56397i	0.810873	+	0.295134i
$843$	5.82504	+	10.0893i	0.200625	+	0.347493i
$844$	−0.0977497	+	0.169307i	−0.00336468	+	0.00582780i
$845$	−29.9451	+	25.1269i	−1.03014	+	0.864393i
$846$	4.72224	−	3.96243i	0.162354	−	0.136231i
$847$	−8.28079	+	14.3427i	−0.284531	+	0.492823i
$848$	2.20768	+	3.82382i	0.0758122	+	0.131311i
$849$	22.0321	+	8.01902i	0.756139	+	0.275212i
$850$	−13.5600	+	76.9028i	−0.465106	+	2.63775i
$851$	−1.27754	−	7.24528i	−0.0437934	−	0.248365i
$852$	1.98526	−	0.722576i	0.0680139	−	0.0247550i
$853$	−30.0903	−	25.2487i	−1.03027	−	0.864500i	−0.0393881	−	0.999224i	$-0.512541\pi$
$853$	−30.0903	−	25.2487i	−1.03027	−	0.864500i	−0.990883	+	0.134724i	$0.956985\pi$
$854$	26.8719			0.919539
$855$	−18.7467	+	2.88638i	−0.641123	+	0.0987122i
$856$	46.3503			1.58422
$857$	27.9960	+	23.4914i	0.956324	+	0.802451i	0.980351	−	0.197260i	$-0.0632043\pi$
$857$	27.9960	+	23.4914i	0.956324	+	0.802451i	−0.0240271	+	0.999711i	$0.507649\pi$
$858$	−3.14399	+	1.14432i	−0.107334	+	0.0390664i
$859$	−2.14705	−	12.1765i	−0.0732563	−	0.415457i	−0.999278	−	0.0379875i	$-0.987905\pi$
$859$	−2.14705	−	12.1765i	−0.0732563	−	0.415457i	0.926022	−	0.377470i	$-0.123206\pi$
$860$	−0.263921	+	1.49677i	−0.00899962	+	0.0510394i
$861$	9.61108	+	3.49815i	0.327545	+	0.119216i
$862$	−7.83990	−	13.5791i	−0.267028	−	0.462506i
$863$	−5.42717	+	9.40013i	−0.184743	+	0.319984i	−0.943490	−	0.331401i	$-0.892479\pi$
$863$	−5.42717	+	9.40013i	−0.184743	+	0.319984i	0.758747	+	0.651386i	$0.225812\pi$
$864$	−1.84691	+	1.54974i	−0.0628332	+	0.0527233i
$865$	14.0608	−	11.7984i	0.478082	−	0.401159i
$866$	16.0712	−	27.8362i	0.546122	−	0.945911i
$867$	−1.52953	−	2.64922i	−0.0519455	−	0.0899722i
$868$	3.46868	+	1.26250i	0.117735	+	0.0428520i
$869$	0.947625	−	5.37425i	0.0321460	−	0.182309i
$870$	−1.51518	−	8.59304i	−0.0513696	−	0.291331i
$871$	−10.1620	+	3.69866i	−0.344326	+	0.125324i
$872$	25.9061	+	21.7378i	0.877292	+	0.736136i
$873$	−9.43610			−0.319363
$874$	−9.43061	−	11.7491i	−0.318995	−	0.397418i
$875$	−69.8429			−2.36112
$876$	−1.91228	−	1.60460i	−0.0646100	−	0.0542143i
$877$	29.2340	−	10.6403i	0.987161	−	0.359297i	0.202541	−	0.979274i	$-0.435080\pi$
$877$	29.2340	−	10.6403i	0.987161	−	0.359297i	0.784620	+	0.619977i	$0.212858\pi$
$878$	−4.10411	−	23.2756i	−0.138507	−	0.785513i
$879$	−2.98614	+	16.9352i	−0.100720	+	0.571211i
$880$	16.0517	+	5.84233i	0.541102	+	0.196945i
$881$	0.549118	+	0.951100i	0.0185003	+	0.0320434i	0.875127	−	0.483893i	$-0.160778\pi$
$881$	0.549118	+	0.951100i	0.0185003	+	0.0320434i	−0.856627	+	0.515936i	$0.827444\pi$
$882$	−2.36052	+	4.08855i	−0.0794830	+	0.137669i
$883$	30.4720	−	25.5690i	1.02546	−	0.860466i	0.0351590	−	0.999382i	$-0.488806\pi$
$883$	30.4720	−	25.5690i	1.02546	−	0.860466i	0.990304	+	0.138916i	$0.0443618\pi$
$884$	2.98789	−	2.50714i	0.100494	−	0.0843242i
$885$	13.6778	−	23.6906i	0.459773	−	0.796350i
$886$	14.6695	+	25.4082i	0.492830	+	0.853606i
$887$	35.5931	+	12.9548i	1.19510	+	0.434981i	0.861512	−	0.507738i	$-0.169518\pi$
$887$	35.5931	+	12.9548i	1.19510	+	0.434981i	0.333588	+	0.942719i	$0.391740\pi$
$888$	−1.40870	+	7.98916i	−0.0472730	+	0.268099i
$889$	−2.77216	−	15.7217i	−0.0929751	−	0.527288i
$890$	−60.1473	+	21.8918i	−2.01614	+	0.733816i
$891$	1.02210	+	0.857644i	0.0342417	+	0.0287322i
$892$	3.21162			0.107533
$893$	6.90422	+	20.3357i	0.231041	+	0.680509i
$894$	−5.83860			−0.195272
$895$	58.1013	+	48.7528i	1.94211	+	1.62962i
$896$	−10.6590	+	3.87955i	−0.356092	+	0.129607i
$897$	−0.961381	−	5.45226i	−0.0320996	−	0.182046i
$898$	−5.50637	+	31.2282i	−0.183750	+	1.04210i
$899$	7.12194	+	2.59217i	0.237530	+	0.0864538i
$900$	3.02765	+	5.24405i	0.100922	+	0.174802i
$901$	−3.36072	+	5.82094i	−0.111962	+	0.193924i
$902$	−7.28148	+	6.10989i	−0.242447	+	0.203437i
$903$	−1.10607	+	0.928101i	−0.0368076	+	0.0308853i
$904$	−22.2763	+	38.5837i	−0.740899	+	1.28328i
$905$	−27.4139	−	47.4823i	−0.911270	−	1.57837i
$906$	−8.06432	−	2.93517i	−0.267919	−	0.0975145i
$907$	4.72682	−	26.8071i	0.156951	−	0.890115i	−0.800029	−	0.599962i	$-0.795182\pi$
$907$	4.72682	−	26.8071i	0.156951	−	0.890115i	0.956980	−	0.290154i	$-0.0937064\pi$
$908$	1.04155	+	5.90690i	0.0345649	+	0.196027i
$909$	3.91168	−	1.42373i	0.129742	−	0.0472223i
$910$	−15.0151	−	12.5991i	−0.497744	−	0.417657i
$911$	−49.6157			−1.64384			−0.821920	−	0.569603i	$-0.807097\pi$
$911$	−49.6157			−1.64384			−0.821920	+	0.569603i	$0.807097\pi$
$912$	4.12289	+	12.1436i	0.136523	+	0.402114i
$913$	−3.53359			−0.116945
$914$	−13.9733	−	11.7250i	−0.462196	−	0.387828i
$915$	−48.8895	+	17.7943i	−1.61624	+	0.588262i
$916$	1.42304	+	8.07047i	0.0470186	+	0.266656i
$917$	−2.99644	+	16.9937i	−0.0989513	+	0.561181i
$918$	5.26578	+	1.91659i	0.173797	+	0.0632569i
$919$	14.5908	+	25.2719i	0.481305	+	0.833644i	0.999770	−	0.0214546i	$-0.00682974\pi$
$919$	14.5908	+	25.2719i	0.481305	+	0.833644i	−0.518465	+	0.855099i	$0.673496\pi$
$920$	−18.3077	+	31.7099i	−0.603588	+	1.04545i
$921$	−13.6553	+	11.4581i	−0.449957	+	0.377559i
$922$	24.7916	−	20.8027i	0.816469	−	0.685099i
$923$	4.87206	−	8.43866i	0.160366	−	0.277762i
$924$	−0.520732	−	0.901934i	−0.0171308	−	0.0296715i
$925$	34.8748	+	12.6934i	1.14668	+	0.417356i
$926$	−5.67067	+	32.1599i	−0.186350	+	1.05684i
$927$	2.67322	+	15.1606i	0.0877999	+	0.497938i
$928$	3.63091	−	1.32154i	0.119191	−	0.0433818i
$929$	20.4797	+	17.1845i	0.671917	+	0.563805i	0.913632	−	0.406542i	$-0.133266\pi$
$929$	20.4797	+	17.1845i	0.671917	+	0.563805i	−0.241715	+	0.970347i	$0.577710\pi$
$930$	25.7473			0.844287
$931$	−10.2954	−	12.8264i	−0.337417	−	0.420369i
$932$	−1.28038			−0.0419402
$933$	−24.9668	−	20.9496i	−0.817376	−	0.685860i
$934$	30.2427	−	11.0074i	0.989570	−	0.360174i
$935$	4.51544	+	25.6083i	0.147671	+	0.837482i
$936$	−1.06009	+	6.01205i	−0.0346500	+	0.196510i
$937$	−40.6617	−	14.7996i	−1.32836	−	0.483483i	−0.422231	−	0.906488i	$-0.638753\pi$
$937$	−40.6617	−	14.7996i	−1.32836	−	0.483483i	−0.906127	+	0.423005i	$0.860975\pi$
$938$	6.06364	+	10.5025i	0.197985	+	0.342920i
$939$	2.46341	−	4.26675i	0.0803904	−	0.139240i
$940$	7.13648	−	5.98821i	0.232766	−	0.195314i
$941$	41.1069	−	34.4928i	1.34005	−	1.12443i	0.358435	−	0.933555i	$-0.383311\pi$
$941$	41.1069	−	34.4928i	1.34005	−	1.12443i	0.981614	−	0.190879i	$-0.0611338\pi$
$942$	0.491798	−	0.851820i	0.0160237	−	0.0277538i
$943$	−7.86440	−	13.6215i	−0.256100	−	0.443579i
$944$	−17.3802	−	6.32589i	−0.565678	−	0.205890i
$945$	−1.35734	+	7.69784i	−0.0441542	+	0.250411i
$946$	−0.233012	−	1.32147i	−0.00757586	−	0.0429648i
$947$	−6.19977	+	2.25653i	−0.201465	+	0.0733274i	−0.440782	−	0.897614i	$-0.645299\pi$
$947$	−6.19977	+	2.25653i	−0.201465	+	0.0733274i	0.239317	+	0.970942i	$0.423077\pi$
$948$	−1.36145	−	1.14240i	−0.0442180	−	0.0371033i
$949$	−11.5136			−0.373746
$950$	75.1147	−	11.5652i	2.43704	−	0.375226i
$951$	−0.863147			−0.0279895
$952$	−18.7728	−	15.7523i	−0.608430	−	0.510533i
$953$	47.7146	−	17.3667i	1.54563	−	0.562563i	0.578241	−	0.815866i	$-0.303739\pi$
$953$	47.7146	−	17.3667i	1.54563	−	0.562563i	0.967387	+	0.253304i	$0.0815171\pi$
$954$	−0.326061	−	1.84919i	−0.0105566	−	0.0598696i
$955$	−7.15241	+	40.5634i	−0.231447	+	1.31260i
$956$	2.18936	+	0.796862i	0.0708089	+	0.0257723i
$957$	−1.06917	−	1.85186i	−0.0345614	−	0.0598622i
$958$	11.3965	−	19.7393i	0.368204	−	0.637748i
$959$	9.59164	−	8.04834i	0.309730	−	0.259894i
$960$	29.6701	−	24.8961i	0.957597	−	0.803520i
$961$	4.31802	−	7.47903i	0.139291	−	0.241259i
$962$	3.33916	+	5.78360i	0.107659	+	0.186471i
$963$	−14.2989	−	5.20436i	−0.460774	−	0.167708i
$964$	2.10358	−	11.9300i	0.0677516	−	0.384238i
$965$	7.20941	+	40.8866i	0.232079	+	1.31619i
$966$	−5.83421	+	2.12348i	−0.187713	+	0.0683218i
$967$	−1.70978	−	1.43467i	−0.0549827	−	0.0461360i	0.614882	−	0.788619i	$-0.289204\pi$
$967$	−1.70978	−	1.43467i	−0.0549827	−	0.0461360i	−0.669865	+	0.742483i	$0.733648\pi$
$968$	−28.0839			−0.902650
$969$	−12.8712	+	14.6783i	−0.413483	+	0.471536i
$970$	51.3747			1.64954
$971$	−35.0808	−	29.4363i	−1.12580	−	0.944654i	−0.126913	−	0.991914i	$-0.540507\pi$
$971$	−35.0808	−	29.4363i	−1.12580	−	0.944654i	−0.998883	+	0.0472596i	$0.984951\pi$
$972$	0.408327	−	0.148619i	0.0130971	−	0.00476695i
$973$	4.91918	+	27.8981i	0.157702	+	0.894371i
$974$	4.79299	−	27.1824i	0.153577	−	0.870981i
$975$	26.2442	+	9.55210i	0.840486	+	0.305912i
$976$	17.5883	+	30.4639i	0.562989	+	0.975125i
$977$	−21.3835	+	37.0374i	−0.684120	+	1.18493i	0.289593	+	0.957150i	$0.406480\pi$
$977$	−21.3835	+	37.0374i	−0.684120	+	1.18493i	−0.973712	+	0.227781i	$0.926853\pi$
$978$	20.5071	−	17.2075i	0.655743	−	0.550234i
$979$	−12.0162	+	10.0828i	−0.384039	+	0.322247i
$980$	−3.56733	+	6.17880i	−0.113954	+	0.197375i
$981$	−5.55112	−	9.61483i	−0.177234	−	0.306978i
$982$	−17.1326	−	6.23576i	−0.546723	−	0.198991i
$983$	9.41733	−	53.4083i	0.300366	−	1.70346i	−0.344187	−	0.938901i	$-0.611845\pi$
$983$	9.41733	−	53.4083i	0.300366	−	1.70346i	0.644553	−	0.764560i	$-0.277044\pi$
$984$	3.01170	+	17.0802i	0.0960095	+	0.544497i
$985$	10.6570	−	3.87882i	0.339560	−	0.123590i
$986$	−6.87970	−	5.77275i	−0.219094	−	0.183842i
$987$	8.85023			0.281706
$988$	−3.24539	−	1.96912i	−0.103250	−	0.0626462i
$989$	2.22043			0.0706056
$990$	−5.56482	−	4.66944i	−0.176861	−	0.148404i
$991$	−19.5371	+	7.11093i	−0.620617	+	0.225886i	−0.633142	−	0.774035i	$-0.718235\pi$
$991$	−19.5371	+	7.11093i	−0.620617	+	0.225886i	0.0125251	+	0.999922i	$0.496013\pi$
$992$	1.97987	+	11.2284i	0.0628609	+	0.356502i
$993$	−3.27197	+	18.5563i	−0.103833	+	0.588865i
$994$	−10.2683	−	3.73736i	−0.325691	−	0.118542i
$995$	16.3946	+	28.3962i	0.519743	+	0.900222i
$996$	−0.575398	+	0.996619i	−0.0182322	+	0.0315791i
$997$	−15.8005	+	13.2582i	−0.500406	+	0.419890i	−0.857738	−	0.514087i	$-0.828131\pi$
$997$	−15.8005	+	13.2582i	−0.500406	+	0.419890i	0.357332	+	0.933977i	$0.383686\pi$
$998$	−9.12847	+	7.65969i	−0.288957	+	0.242463i
$999$	1.33162	−	2.30644i	0.0421307	−	0.0729726i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	57.2.i.b.16.1	✓	12
3.2	odd	2		171.2.u.e.73.2		12
4.3	odd	2		912.2.bo.j.529.2		12
19.5	even	9		1083.2.a.q.1.2		6
19.6	even	9	inner	57.2.i.b.25.1	yes	12
19.14	odd	18		1083.2.a.p.1.5		6
57.5	odd	18		3249.2.a.bh.1.5		6
57.14	even	18		3249.2.a.bg.1.2		6
57.44	odd	18		171.2.u.e.82.2		12
76.63	odd	18		912.2.bo.j.481.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.2.i.b.16.1	✓	12	1.1	even	1	trivial
57.2.i.b.25.1	yes	12	19.6	even	9	inner
171.2.u.e.73.2		12	3.2	odd	2
171.2.u.e.82.2		12	57.44	odd	18
912.2.bo.j.481.2		12	76.63	odd	18
912.2.bo.j.529.2		12	4.3	odd	2
1083.2.a.p.1.5		6	19.14	odd	18
1083.2.a.q.1.2		6	19.5	even	9
3249.2.a.bg.1.2		6	57.14	even	18
3249.2.a.bh.1.5		6	57.5	odd	18

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:	\( N \)	\(=\)	\( 57 = 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	57.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.958464 - 0.804247i) q^{2} +(-0.939693 + 0.342020i) q^{3} +(-0.0754558 - 0.427931i) q^{4} +(0.755623 - 4.28535i) q^{5} +(1.17573 + 0.427931i) q^{6} +(0.898157 + 1.55565i) q^{7} +(-1.52303 + 2.63796i) q^{8} +(0.766044 - 0.642788i) q^{9} +O(q^{10})\)	\(q+(-0.958464 - 0.804247i) q^{2} +(-0.939693 + 0.342020i) q^{3} +(-0.0754558 - 0.427931i) q^{4} +(0.755623 - 4.28535i) q^{5} +(1.17573 + 0.427931i) q^{6} +(0.898157 + 1.55565i) q^{7} +(-1.52303 + 2.63796i) q^{8} +(0.766044 - 0.642788i) q^{9} +(-4.17072 + 3.49965i) q^{10} +(-0.667129 + 1.15550i) q^{11} +(0.217266 + 0.376316i) q^{12} +(1.88330 + 0.685465i) q^{13} +(0.390278 - 2.21338i) q^{14} +(0.755623 + 4.28535i) q^{15} +(2.76469 - 1.00626i) q^{16} +(3.43091 + 2.87887i) q^{17} -1.25119 q^{18} +(1.57962 - 4.06261i) q^{19} -1.89085 q^{20} +(-1.37606 - 1.15465i) q^{21} +(1.56873 - 0.570970i) q^{22} +(0.479691 + 2.72047i) q^{23} +(0.528942 - 2.99978i) q^{24} +(-13.0948 - 4.76612i) q^{25} +(-1.25379 - 2.17163i) q^{26} +(-0.500000 + 0.866025i) q^{27} +(0.597941 - 0.501732i) q^{28} +(1.22770 - 1.03016i) q^{29} +(2.72224 - 4.71507i) q^{30} +(2.36453 + 4.09548i) q^{31} +(2.26557 + 0.824601i) q^{32} +(0.231691 - 1.31399i) q^{33} +(-0.973078 - 5.51860i) q^{34} +(7.34519 - 2.67343i) q^{35} +(-0.332871 - 0.279312i) q^{36} -2.66325 q^{37} +(-4.78135 + 2.62346i) q^{38} -2.00416 q^{39} +(10.1538 + 8.52001i) q^{40} +(-5.35044 + 1.94740i) q^{41} +(0.390278 + 2.21338i) q^{42} +(0.139578 - 0.791584i) q^{43} +(0.544813 + 0.198296i) q^{44} +(-2.17573 - 3.76848i) q^{45} +(1.72816 - 2.99326i) q^{46} +(-3.77421 + 3.16694i) q^{47} +(-2.25379 + 1.89116i) q^{48} +(1.88663 - 3.26774i) q^{49} +(8.71778 + 15.0996i) q^{50} +(-4.20863 - 1.53182i) q^{51} +(0.151226 - 0.857644i) q^{52} +(0.260602 + 1.47795i) q^{53} +(1.17573 - 0.427931i) q^{54} +(4.44763 + 3.73201i) q^{55} -5.47167 q^{56} +(-0.0948636 + 4.35787i) q^{57} -2.00521 q^{58} +(-4.81575 - 4.04089i) q^{59} +(1.77682 - 0.646709i) q^{60} +(2.07618 + 11.7746i) q^{61} +(1.02746 - 5.82704i) q^{62} +(1.68798 + 0.614376i) q^{63} +(-4.45040 - 7.70833i) q^{64} +(4.36052 - 7.55265i) q^{65} +(-1.27884 + 1.07307i) q^{66} +(-4.13346 + 3.46838i) q^{67} +(0.973078 - 1.68542i) q^{68} +(-1.38122 - 2.39234i) q^{69} +(-9.19021 - 3.34496i) q^{70} +(0.844267 - 4.78807i) q^{71} +(0.528942 + 2.99978i) q^{72} +(-5.39836 + 1.96484i) q^{73} +(2.55263 + 2.14191i) q^{74} +13.9352 q^{75} +(-1.85771 - 0.369421i) q^{76} -2.39675 q^{77} +(1.92092 + 1.61184i) q^{78} +(-3.84337 + 1.39887i) q^{79} +(-2.22313 - 12.6080i) q^{80} +(0.173648 - 0.984808i) q^{81} +(6.69440 + 2.43656i) q^{82} +(1.32418 + 2.29354i) q^{83} +(-0.390278 + 0.675982i) q^{84} +(14.9295 - 12.5273i) q^{85} +(-0.770410 + 0.646450i) q^{86} +(-0.801324 + 1.38793i) q^{87} +(-2.03211 - 3.51972i) q^{88} +(11.0474 + 4.02092i) q^{89} +(-0.945426 + 5.36178i) q^{90} +(0.625153 + 3.54542i) q^{91} +(1.12798 - 0.410550i) q^{92} +(-3.62267 - 3.03978i) q^{93} +6.16445 q^{94} +(-16.2161 - 9.83904i) q^{95} -2.41097 q^{96} +(-7.22847 - 6.06541i) q^{97} +(-4.43633 + 1.61469i) q^{98} +(0.231691 + 1.31399i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - 3 q^{4} + 6 q^{5} - 3 q^{6} - 9 q^{7} + 3 q^{8}+O(q^{10}) \) 12 * q - 3 * q^2 - 3 * q^4 + 6 * q^5 - 3 * q^6 - 9 * q^7 + 3 * q^8	\( 12 q - 3 q^{2} - 3 q^{4} + 6 q^{5} - 3 q^{6} - 9 q^{7} + 3 q^{8} - 18 q^{10} - 9 q^{11} - 6 q^{12} - 3 q^{13} - 3 q^{14} + 6 q^{15} + 33 q^{16} + 12 q^{17} - 9 q^{19} - 18 q^{20} - 24 q^{22} + 9 q^{23} + 30 q^{24} - 12 q^{25} - 6 q^{27} + 30 q^{28} - 6 q^{30} - 3 q^{32} - 9 q^{33} + 21 q^{34} + 30 q^{35} - 3 q^{36} - 12 q^{37} + 18 q^{38} + 6 q^{39} - 3 q^{40} - 18 q^{41} - 3 q^{42} + 15 q^{43} + 15 q^{44} - 9 q^{45} + 27 q^{46} - 9 q^{47} - 12 q^{48} - 9 q^{49} + 9 q^{50} - 15 q^{51} - 27 q^{52} - 30 q^{53} - 3 q^{54} + 15 q^{55} - 78 q^{56} - 3 q^{57} - 24 q^{58} - 30 q^{59} - 15 q^{60} + 21 q^{61} + 3 q^{62} + 9 q^{63} - 21 q^{64} + 21 q^{65} + 30 q^{66} + 3 q^{67} - 21 q^{68} - 6 q^{69} + 18 q^{70} - 30 q^{71} + 30 q^{72} - 24 q^{73} + 39 q^{74} + 30 q^{75} - 60 q^{76} + 96 q^{77} + 9 q^{78} + 24 q^{79} + 42 q^{80} - 33 q^{82} + 3 q^{83} + 3 q^{84} + 3 q^{85} + 51 q^{86} + 15 q^{87} + 42 q^{88} + 3 q^{89} - 9 q^{90} + 24 q^{91} + 69 q^{92} - 6 q^{93} + 18 q^{94} - 54 q^{95} - 42 q^{96} - 27 q^{97} - 3 q^{98} - 9 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 - 3 * q^4 + 6 * q^5 - 3 * q^6 - 9 * q^7 + 3 * q^8 - 18 * q^10 - 9 * q^11 - 6 * q^12 - 3 * q^13 - 3 * q^14 + 6 * q^15 + 33 * q^16 + 12 * q^17 - 9 * q^19 - 18 * q^20 - 24 * q^22 + 9 * q^23 + 30 * q^24 - 12 * q^25 - 6 * q^27 + 30 * q^28 - 6 * q^30 - 3 * q^32 - 9 * q^33 + 21 * q^34 + 30 * q^35 - 3 * q^36 - 12 * q^37 + 18 * q^38 + 6 * q^39 - 3 * q^40 - 18 * q^41 - 3 * q^42 + 15 * q^43 + 15 * q^44 - 9 * q^45 + 27 * q^46 - 9 * q^47 - 12 * q^48 - 9 * q^49 + 9 * q^50 - 15 * q^51 - 27 * q^52 - 30 * q^53 - 3 * q^54 + 15 * q^55 - 78 * q^56 - 3 * q^57 - 24 * q^58 - 30 * q^59 - 15 * q^60 + 21 * q^61 + 3 * q^62 + 9 * q^63 - 21 * q^64 + 21 * q^65 + 30 * q^66 + 3 * q^67 - 21 * q^68 - 6 * q^69 + 18 * q^70 - 30 * q^71 + 30 * q^72 - 24 * q^73 + 39 * q^74 + 30 * q^75 - 60 * q^76 + 96 * q^77 + 9 * q^78 + 24 * q^79 + 42 * q^80 - 33 * q^82 + 3 * q^83 + 3 * q^84 + 3 * q^85 + 51 * q^86 + 15 * q^87 + 42 * q^88 + 3 * q^89 - 9 * q^90 + 24 * q^91 + 69 * q^92 - 6 * q^93 + 18 * q^94 - 54 * q^95 - 42 * q^96 - 27 * q^97 - 3 * q^98 - 9 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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