LMFDB - Embedded newform 570.2.bb.b.41.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(41,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 13]))

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

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

chi := DirichletCharacter("570.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bb (of order $18$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$14$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			41.7
Character	$\chi$	$=$	570.41
Dual form			570.2.bb.b.431.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 - 0.642788i) q^{2} +(0.0507095 + 1.73131i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.984808 + 0.173648i) q^{5} +(1.07402 - 1.35885i) q^{6} +(0.847833 + 1.46849i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.99486 + 0.175587i) q^{9} +O(q^{10})$	\(q+(-0.766044 - 0.642788i) q^{2} +(0.0507095 + 1.73131i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.984808 + 0.173648i) q^{5} +(1.07402 - 1.35885i) q^{6} +(0.847833 + 1.46849i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.99486 + 0.175587i) q^{9} +(-0.642788 - 0.766044i) q^{10} +(2.48350 + 1.43385i) q^{11} +(-1.69620 + 0.350578i) q^{12} +(-1.37377 + 3.77439i) q^{13} +(0.294449 - 1.66990i) q^{14} +(-0.250699 + 1.71381i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(1.41017 - 1.68058i) q^{17} +(2.40706 + 1.79055i) q^{18} +(3.83513 - 2.07166i) q^{19} +1.00000i q^{20} +(-2.49941 + 1.54233i) q^{21} +(-0.980811 - 2.69476i) q^{22} +(-5.59374 + 0.986328i) q^{23} +(1.52471 + 0.821738i) q^{24} +(0.939693 + 0.342020i) q^{25} +(3.47850 - 2.00831i) q^{26} +(-0.455864 - 5.17612i) q^{27} +(-1.29895 + 1.08995i) q^{28} +(-4.26078 + 3.57522i) q^{29} +(1.29366 - 1.15171i) q^{30} +(0.657784 - 0.379772i) q^{31} +(0.939693 + 0.342020i) q^{32} +(-2.35650 + 4.37241i) q^{33} +(-2.16051 + 0.380957i) q^{34} +(0.579952 + 1.59340i) q^{35} +(-0.692971 - 2.91887i) q^{36} +7.06283i q^{37} +(-4.26952 - 0.878196i) q^{38} +(-6.60430 - 2.18702i) q^{39} +(0.642788 - 0.766044i) q^{40} +(-2.36400 + 0.860427i) q^{41} +(2.90605 + 0.425102i) q^{42} +(-0.907694 + 5.14779i) q^{43} +(-0.980811 + 2.69476i) q^{44} +(-2.97985 - 0.347132i) q^{45} +(4.91906 + 2.84002i) q^{46} +(0.302030 + 0.359945i) q^{47} +(-0.639794 - 1.60955i) q^{48} +(2.06236 - 3.57211i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(2.98111 + 2.35623i) q^{51} +(-3.95560 - 0.697479i) q^{52} +(2.36349 + 13.4040i) q^{53} +(-2.97793 + 4.25816i) q^{54} +(2.19679 + 1.84332i) q^{55} +1.69567 q^{56} +(3.78115 + 6.53475i) q^{57} +5.56205 q^{58} +(-1.73040 - 1.45198i) q^{59} +(-1.73131 + 0.0507095i) q^{60} +(-0.413907 - 2.34738i) q^{61} +(-0.748004 - 0.131893i) q^{62} +(-2.79699 - 4.24905i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-2.00831 + 3.47850i) q^{65} +(4.61572 - 1.83474i) q^{66} +(-0.208994 - 0.249070i) q^{67} +(1.89992 + 1.09692i) q^{68} +(-1.99129 - 9.63448i) q^{69} +(0.579952 - 1.59340i) q^{70} +(0.321939 - 1.82581i) q^{71} +(-1.34537 + 2.68142i) q^{72} +(13.1053 - 4.76996i) q^{73} +(4.53990 - 5.41044i) q^{74} +(-0.544491 + 1.64424i) q^{75} +(2.70615 + 3.41713i) q^{76} +4.86266i q^{77} +(3.65340 + 5.92051i) q^{78} +(-4.21257 - 11.5739i) q^{79} +(-0.984808 + 0.173648i) q^{80} +(8.93834 - 1.05172i) q^{81} +(2.36400 + 0.860427i) q^{82} +(-0.347171 + 0.200439i) q^{83} +(-1.95291 - 2.19362i) q^{84} +(1.68058 - 1.41017i) q^{85} +(4.00427 - 3.35998i) q^{86} +(-6.40587 - 7.19543i) q^{87} +(2.48350 - 1.43385i) q^{88} +(3.05820 + 1.11309i) q^{89} +(2.05956 + 2.18133i) q^{90} +(-6.70738 + 1.18269i) q^{91} +(-1.94269 - 5.33749i) q^{92} +(0.690858 + 1.11957i) q^{93} -0.469875i q^{94} +(4.13661 - 1.37422i) q^{95} +(-0.544491 + 1.64424i) q^{96} +(-5.17546 + 6.16787i) q^{97} +(-3.87597 + 1.41074i) q^{98} +(-7.68949 - 3.85810i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 6 q^{6} + 42 q^{8}+O(q^{10}) $ 84 * q - 6 * q^6 + 42 * q^8	$ 84 q - 6 q^{6} + 42 q^{8} + 24 q^{13} - 24 q^{14} + 12 q^{17} - 12 q^{19} + 36 q^{22} + 24 q^{27} - 12 q^{28} - 12 q^{29} + 36 q^{33} + 12 q^{34} + 6 q^{36} + 18 q^{38} + 12 q^{39} + 6 q^{41} + 24 q^{43} + 36 q^{44} + 12 q^{47} - 12 q^{48} - 54 q^{49} - 42 q^{50} + 96 q^{51} + 12 q^{52} - 60 q^{53} - 18 q^{54} - 96 q^{57} - 24 q^{58} - 18 q^{59} - 48 q^{61} - 12 q^{62} - 114 q^{63} - 42 q^{64} - 24 q^{66} + 6 q^{67} - 54 q^{68} - 48 q^{69} + 48 q^{71} + 84 q^{73} + 24 q^{74} - 12 q^{79} - 36 q^{81} - 6 q^{82} + 36 q^{83} + 18 q^{84} + 12 q^{86} + 6 q^{87} - 12 q^{89} - 24 q^{90} + 24 q^{91} - 6 q^{93} - 12 q^{95} - 42 q^{97} + 36 q^{98} - 6 q^{99}+O(q^{100}) $ 84 * q - 6 * q^6 + 42 * q^8 + 24 * q^13 - 24 * q^14 + 12 * q^17 - 12 * q^19 + 36 * q^22 + 24 * q^27 - 12 * q^28 - 12 * q^29 + 36 * q^33 + 12 * q^34 + 6 * q^36 + 18 * q^38 + 12 * q^39 + 6 * q^41 + 24 * q^43 + 36 * q^44 + 12 * q^47 - 12 * q^48 - 54 * q^49 - 42 * q^50 + 96 * q^51 + 12 * q^52 - 60 * q^53 - 18 * q^54 - 96 * q^57 - 24 * q^58 - 18 * q^59 - 48 * q^61 - 12 * q^62 - 114 * q^63 - 42 * q^64 - 24 * q^66 + 6 * q^67 - 54 * q^68 - 48 * q^69 + 48 * q^71 + 84 * q^73 + 24 * q^74 - 12 * q^79 - 36 * q^81 - 6 * q^82 + 36 * q^83 + 18 * q^84 + 12 * q^86 + 6 * q^87 - 12 * q^89 - 24 * q^90 + 24 * q^91 - 6 * q^93 - 12 * q^95 - 42 * q^97 + 36 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{13}{18}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.766044	−	0.642788i	−0.541675	−	0.454519i
$2$	−0.766044	−	0.642788i	−0.541675	−	0.454519i
$3$	0.0507095	+	1.73131i	0.0292771	+	0.999571i
$3$	0.0507095	+	1.73131i	0.0292771	+	0.999571i
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	0.984808	+	0.173648i	0.440419	+	0.0776578i
$5$	0.984808	+	0.173648i	0.440419	+	0.0776578i
$6$	1.07402	−	1.35885i	0.438466	−	0.554750i
$7$	0.847833	+	1.46849i	0.320451	+	0.555037i	0.980581	−	0.196114i	$-0.0628324\pi$
$7$	0.847833	+	1.46849i	0.320451	+	0.555037i	−0.660130	+	0.751151i	$0.729499\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	−2.99486	+	0.175587i	−0.998286	+	0.0585292i
$10$	−0.642788	−	0.766044i	−0.203267	−	0.242245i
$11$	2.48350	+	1.43385i	0.748804	+	0.432322i	0.825261	−	0.564751i	$-0.191028\pi$
$11$	2.48350	+	1.43385i	0.748804	+	0.432322i	−0.0764579	+	0.997073i	$0.524361\pi$
$12$	−1.69620	+	0.350578i	−0.489651	+	0.101203i
$13$	−1.37377	+	3.77439i	−0.381014	+	1.04683i	0.589916	+	0.807465i	$0.299161\pi$
$13$	−1.37377	+	3.77439i	−0.381014	+	1.04683i	−0.970930	+	0.239363i	$0.923061\pi$
$14$	0.294449	−	1.66990i	0.0786948	−	0.446301i
$15$	−0.250699	+	1.71381i	−0.0647303	+	0.442504i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	1.41017	−	1.68058i	0.342018	−	0.407601i	−0.567428	−	0.823423i	$-0.692062\pi$
$17$	1.41017	−	1.68058i	0.342018	−	0.407601i	0.909446	+	0.415822i	$0.136506\pi$
$18$	2.40706	+	1.79055i	0.567349	+	0.422036i
$19$	3.83513	−	2.07166i	0.879840	−	0.475270i
$19$	3.83513	−	2.07166i	0.879840	−	0.475270i
$20$			1.00000i			0.223607i
$21$	−2.49941	+	1.54233i	−0.545417	+	0.336563i
$22$	−0.980811	−	2.69476i	−0.209110	−	0.574524i
$23$	−5.59374	+	0.986328i	−1.16638	+	0.205664i	−0.723114	−	0.690729i	$-0.757290\pi$
$23$	−5.59374	+	0.986328i	−1.16638	+	0.205664i	−0.443262	+	0.896392i	$0.646179\pi$
$24$	1.52471	+	0.821738i	0.311230	+	0.167737i
$25$	0.939693	+	0.342020i	0.187939	+	0.0684040i
$26$	3.47850	−	2.00831i	0.682190	−	0.393862i
$27$	−0.455864	−	5.17612i	−0.0877310	−	0.996144i
$28$	−1.29895	+	1.08995i	−0.245479	+	0.205982i
$29$	−4.26078	+	3.57522i	−0.791207	+	0.663902i	−0.946044	−	0.324039i	$-0.894959\pi$
$29$	−4.26078	+	3.57522i	−0.791207	+	0.663902i	0.154837	+	0.987940i	$0.450515\pi$
$30$	1.29366	−	1.15171i	0.236190	−	0.210272i
$31$	0.657784	−	0.379772i	0.118142	−	0.0682090i	−0.439765	−	0.898113i	$-0.644938\pi$
$31$	0.657784	−	0.379772i	0.118142	−	0.0682090i	0.557906	+	0.829904i	$0.311605\pi$
$32$	0.939693	+	0.342020i	0.166116	+	0.0604612i
$33$	−2.35650	+	4.37241i	−0.410214	+	0.761140i
$34$	−2.16051	+	0.380957i	−0.370525	+	0.0653335i
$35$	0.579952	+	1.59340i	0.0980297	+	0.269334i
$36$	−0.692971	−	2.91887i	−0.115495	−	0.486478i
$37$			7.06283i			1.16112i	0.814217	+	0.580561i	$0.197167\pi$
$37$			7.06283i			1.16112i	−0.814217	+	0.580561i	$0.802833\pi$
$38$	−4.26952	−	0.878196i	−0.692607	−	0.142462i
$39$	−6.60430	−	2.18702i	−1.05753	−	0.350203i
$40$	0.642788	−	0.766044i	0.101634	−	0.121122i
$41$	−2.36400	+	0.860427i	−0.369195	+	0.134376i	−0.519953	−	0.854195i	$-0.674051\pi$
$41$	−2.36400	+	0.860427i	−0.369195	+	0.134376i	0.150758	+	0.988571i	$0.451829\pi$
$42$	2.90605	+	0.425102i	0.448413	+	0.0655947i
$43$	−0.907694	+	5.14779i	−0.138422	+	0.785030i	0.833993	+	0.551774i	$0.186049\pi$
$43$	−0.907694	+	5.14779i	−0.138422	+	0.785030i	−0.972415	+	0.233256i	$0.925062\pi$
$44$	−0.980811	+	2.69476i	−0.147863	+	0.406250i
$45$	−2.97985	−	0.347132i	−0.444210	−	0.0517473i
$46$	4.91906	+	2.84002i	0.725275	+	0.418738i
$47$	0.302030	+	0.359945i	0.0440556	+	0.0525034i	0.787622	−	0.616158i	$-0.211312\pi$
$47$	0.302030	+	0.359945i	0.0440556	+	0.0525034i	−0.743567	+	0.668662i	$0.766867\pi$
$48$	−0.639794	−	1.60955i	−0.0923463	−	0.232319i
$49$	2.06236	−	3.57211i	0.294623	−	0.510302i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	2.98111	+	2.35623i	0.417439	+	0.329938i
$52$	−3.95560	−	0.697479i	−0.548543	−	0.0967230i
$53$	2.36349	+	13.4040i	0.324650	+	1.84118i	0.512125	+	0.858911i	$0.328858\pi$
$53$	2.36349	+	13.4040i	0.324650	+	1.84118i	−0.187475	+	0.982269i	$0.560030\pi$
$54$	−2.97793	+	4.25816i	−0.405245	+	0.579462i
$55$	2.19679	+	1.84332i	0.296214	+	0.248553i
$56$	1.69567			0.226593
$57$	3.78115	+	6.53475i	0.500826	+	0.865548i
$58$	5.56205			0.730333
$59$	−1.73040	−	1.45198i	−0.225279	−	0.189032i	0.523161	−	0.852234i	$-0.324753\pi$
$59$	−1.73040	−	1.45198i	−0.225279	−	0.189032i	−0.748440	+	0.663202i	$0.769197\pi$
$60$	−1.73131	+	0.0507095i	−0.223511	+	0.00654657i
$61$	−0.413907	−	2.34738i	−0.0529953	−	0.300551i	0.946777	−	0.321890i	$-0.104318\pi$
$61$	−0.413907	−	2.34738i	−0.0529953	−	0.300551i	−0.999772	+	0.0213389i	$0.993207\pi$
$62$	−0.748004	−	0.131893i	−0.0949967	−	0.0167505i
$63$	−2.79699	−	4.24905i	−0.352387	−	0.535329i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−2.00831	+	3.47850i	−0.249100	+	0.431455i
$66$	4.61572	−	1.83474i	0.568155	−	0.225840i
$67$	−0.208994	−	0.249070i	−0.0255327	−	0.0304287i	0.753127	−	0.657875i	$-0.228545\pi$
$67$	−0.208994	−	0.249070i	−0.0255327	−	0.0304287i	−0.778660	+	0.627446i	$0.784100\pi$
$68$	1.89992	+	1.09692i	0.230399	+	0.133021i
$69$	−1.99129	−	9.63448i	−0.239724	−	1.15985i
$70$	0.579952	−	1.59340i	0.0693175	−	0.190448i
$71$	0.321939	−	1.82581i	0.0382071	−	0.216683i	−0.959727	−	0.280936i	$-0.909355\pi$
$71$	0.321939	−	1.82581i	0.0382071	−	0.216683i	0.997934	+	0.0642526i	$0.0204663\pi$
$72$	−1.34537	+	2.68142i	−0.158553	+	0.316008i
$73$	13.1053	−	4.76996i	1.53387	−	0.558281i	0.569301	−	0.822129i	$-0.307214\pi$
$73$	13.1053	−	4.76996i	1.53387	−	0.558281i	0.964564	+	0.263848i	$0.0849917\pi$
$74$	4.53990	−	5.41044i	0.527753	−	0.628951i
$75$	−0.544491	+	1.64424i	−0.0628724	+	0.189861i
$76$	2.70615	+	3.41713i	0.310416	+	0.391972i
$77$			4.86266i			0.554151i
$78$	3.65340	+	5.92051i	0.413666	+	0.670366i
$79$	−4.21257	−	11.5739i	−0.473951	−	1.30217i	−0.914552	−	0.404468i	$-0.867457\pi$
$79$	−4.21257	−	11.5739i	−0.473951	−	1.30217i	0.440601	−	0.897703i	$-0.354765\pi$
$80$	−0.984808	+	0.173648i	−0.110105	+	0.0194145i
$81$	8.93834	−	1.05172i	0.993149	−	0.116858i
$82$	2.36400	+	0.860427i	0.261060	+	0.0950182i
$83$	−0.347171	+	0.200439i	−0.0381069	+	0.0220010i	−0.518932	−	0.854815i	$-0.673670\pi$
$83$	−0.347171	+	0.200439i	−0.0381069	+	0.0220010i	0.480826	+	0.876816i	$0.340337\pi$
$84$	−1.95291	−	2.19362i	−0.213080	−	0.239344i
$85$	1.68058	−	1.41017i	0.182285	−	0.152955i
$86$	4.00427	−	3.35998i	0.431791	−	0.362316i
$87$	−6.40587	−	7.19543i	−0.686781	−	0.771431i
$88$	2.48350	−	1.43385i	0.264742	−	0.152849i
$89$	3.05820	+	1.11309i	0.324169	+	0.117988i	0.498978	−	0.866614i	$-0.333709\pi$
$89$	3.05820	+	1.11309i	0.324169	+	0.117988i	−0.174809	+	0.984602i	$0.555931\pi$
$90$	2.05956	+	2.18133i	0.217097	+	0.229932i
$91$	−6.70738	+	1.18269i	−0.703124	+	0.123980i
$92$	−1.94269	−	5.33749i	−0.202539	−	0.556472i
$93$	0.690858	+	1.11957i	0.0716386	+	0.116094i
$94$		−	0.469875i		−	0.0484639i
$95$	4.13661	−	1.37422i	0.424407	−	0.140992i
$96$	−0.544491	+	1.64424i	−0.0555719	+	0.167815i
$97$	−5.17546	+	6.16787i	−0.525488	+	0.626252i	−0.961869	−	0.273510i	$-0.911815\pi$
$97$	−5.17546	+	6.16787i	−0.525488	+	0.626252i	0.436381	+	0.899762i	$0.356260\pi$
$98$	−3.87597	+	1.41074i	−0.391532	+	0.142506i
$99$	−7.68949	−	3.85810i	−0.772823	−	0.387754i
$100$	−0.173648	+	0.984808i	−0.0173648	+	0.0984808i
$101$	2.59290	−	7.12393i	0.258003	−	0.708857i	−0.741287	−	0.671188i	$-0.765784\pi$
$101$	2.59290	−	7.12393i	0.258003	−	0.708857i	0.999290	−	0.0376693i	$-0.0119934\pi$
$102$	−0.769112	−	3.72120i	−0.0761534	−	0.368453i
$103$	12.6640	+	7.31158i	1.24782	+	0.720431i	0.970675	−	0.240396i	$-0.0772772\pi$
$103$	12.6640	+	7.31158i	1.24782	+	0.720431i	0.277149	+	0.960827i	$0.410611\pi$
$104$	2.58184	+	3.07691i	0.253170	+	0.301716i
$105$	−2.72926	+	1.08488i	−0.266349	+	0.105873i
$106$	6.80539	−	11.7873i	0.660998	−	1.14488i
$107$	−6.54964	−	11.3443i	−0.633178	−	1.09670i	−0.986898	−	0.161345i	$-0.948417\pi$
$107$	−6.54964	−	11.3443i	−0.633178	−	1.09670i	0.353720	−	0.935351i	$-0.384917\pi$
$108$	5.01832	−	1.34776i	0.482888	−	0.129688i
$109$	19.0212	+	3.35394i	1.82190	+	0.321249i	0.976928	−	0.213568i	$-0.0685084\pi$
$109$	19.0212	+	3.35394i	1.82190	+	0.321249i	0.844968	+	0.534817i	$0.179620\pi$
$110$	−0.497971	−	2.82413i	−0.0474796	−	0.269270i
$111$	−12.2279	+	0.358153i	−1.16062	+	0.0339943i
$112$	−1.29895	−	1.08995i	−0.122740	−	0.102991i
$113$	−15.2644			−1.43596			−0.717978	−	0.696065i	$-0.754932\pi$
$113$	−15.2644			−1.43596			−0.717978	+	0.696065i	$0.754932\pi$
$114$	1.30392	−	7.43638i	0.122124	−	0.696481i
$115$	−5.68004			−0.529666
$116$	−4.26078	−	3.57522i	−0.395604	−	0.331951i
$117$	3.45150	−	11.5450i	0.319091	−	1.06733i
$118$	0.392251	+	2.22456i	0.0361096	+	0.204788i
$119$	3.66351	+	0.645975i	0.335833	+	0.0592164i
$120$	1.35885	+	1.07402i	0.124046	+	0.0980440i
$121$	−1.38815	−	2.40435i	−0.126196	−	0.218577i
$122$	−1.19180	+	2.06425i	−0.107900	+	0.186889i
$123$	−1.60954	−	4.04919i	−0.145127	−	0.365103i
$124$	0.488225	+	0.581844i	0.0438439	+	0.0522512i
$125$	0.866025	+	0.500000i	0.0774597	+	0.0447214i
$126$	−0.588619	+	5.05283i	−0.0524383	+	0.450142i
$127$	3.79242	−	10.4196i	0.336523	−	0.924590i	−0.649849	−	0.760063i	$-0.725168\pi$
$127$	3.79242	−	10.4196i	0.336523	−	0.924590i	0.986373	−	0.164527i	$-0.0526098\pi$
$128$	−0.173648	+	0.984808i	−0.0153485	+	0.0870455i
$129$	−8.95844	−	1.31046i	−0.788746	−	0.115379i
$130$	3.77439	−	1.37377i	0.331036	−	0.120487i
$131$	9.57778	−	11.4144i	0.836814	−	0.997277i	−0.163129	−	0.986605i	$-0.552159\pi$
$131$	9.57778	−	11.4144i	0.836814	−	0.997277i	0.999943	−	0.0106718i	$-0.00339701\pi$
$132$	−4.71519	−	1.56144i	−0.410405	−	0.135906i
$133$	6.29375	+	3.87543i	0.545738	+	0.336043i
$134$			0.325137i			0.0280876i
$135$	0.449885	−	5.17664i	0.0387199	−	0.445534i
$136$	−0.750338	−	2.06154i	−0.0643410	−	0.176775i
$137$	13.3417	−	2.35251i	1.13986	−	0.200988i	0.428316	−	0.903629i	$-0.359107\pi$
$137$	13.3417	−	2.35251i	1.13986	−	0.200988i	0.711545	+	0.702640i	$0.247996\pi$
$138$	−4.66750	+	8.66042i	−0.397324	+	0.737224i
$139$	−6.17007	−	2.24572i	−0.523338	−	0.190480i	0.0668232	−	0.997765i	$-0.478714\pi$
$139$	−6.17007	−	2.24572i	−0.523338	−	0.190480i	−0.590161	+	0.807285i	$0.700936\pi$
$140$	−1.46849	+	0.847833i	−0.124110	+	0.0716549i
$141$	−0.607860	+	0.541159i	−0.0511911	+	0.0455738i
$142$	−1.42022	+	1.19171i	−0.119183	+	0.100006i
$143$	−8.82366	+	7.40393i	−0.737871	+	0.619148i
$144$	2.75419	−	1.18930i	0.229516	−	0.0991083i
$145$	−4.81688	+	2.78103i	−0.400020	+	0.230952i
$146$	−13.1053	−	4.76996i	−1.08461	−	0.394764i
$147$	6.28901	+	3.38944i	0.518709	+	0.279556i
$148$	−6.95553	+	1.22645i	−0.571741	+	0.100813i
$149$	4.26842	+	11.7274i	0.349683	+	0.960746i	0.982470	+	0.186420i	$0.0596886\pi$
$149$	4.26842	+	11.7274i	0.349683	+	0.960746i	−0.632787	+	0.774326i	$0.718089\pi$
$150$	1.47400	−	0.909570i	0.120352	−	0.0742661i
$151$		−	4.63978i		−	0.377580i	−0.982018	−	0.188790i	$-0.939543\pi$
$151$		−	4.63978i		−	0.377580i	0.982018	−	0.188790i	$-0.0604565\pi$
$152$	0.123460	−	4.35715i	0.0100140	−	0.353412i
$153$	−3.92818	+	5.28071i	−0.317575	+	0.426920i
$154$	3.12566	−	3.72501i	0.251873	−	0.300170i
$155$	0.713738	−	0.259779i	0.0573288	−	0.0208660i
$156$	1.00697	−	6.88374i	0.0806217	−	0.551140i
$157$	1.81510	−	10.2939i	0.144860	−	0.821544i	−0.822619	−	0.568593i	$-0.807488\pi$
$157$	1.81510	−	10.2939i	0.144860	−	0.821544i	0.967479	−	0.252951i	$-0.0814011\pi$
$158$	−4.21257	+	11.5739i	−0.335134	+	0.920774i
$159$	−23.0866	+	4.77163i	−1.83089	+	0.378415i
$160$	0.866025	+	0.500000i	0.0684653	+	0.0395285i
$161$	−6.19097	−	7.37811i	−0.487917	−	0.581476i
$162$	−7.52320	−	4.93979i	−0.591078	−	0.388107i
$163$	1.59132	−	2.75625i	0.124642	−	0.215886i	−0.796951	−	0.604044i	$-0.793555\pi$
$163$	1.59132	−	2.75625i	0.124642	−	0.215886i	0.921593	+	0.388158i	$0.126888\pi$
$164$	−1.25786	−	2.17868i	−0.0982224	−	0.170126i
$165$	−3.07996	+	3.89679i	−0.239775	+	0.303364i
$166$	0.394788	+	0.0696118i	0.0306415	+	0.00540292i
$167$	0.294207	+	1.66853i	0.0227664	+	0.129115i	0.994073	−	0.108717i	$-0.0346743\pi$
$167$	0.294207	+	1.66853i	0.0227664	+	0.129115i	−0.971306	+	0.237832i	$0.923563\pi$
$168$	0.0859863	+	2.93572i	0.00663399	+	0.226496i
$169$	−2.40022	−	2.01402i	−0.184632	−	0.154925i
$170$	−2.19384			−0.168260
$171$	−11.1219	+	6.87771i	−0.850514	+	0.525952i
$172$	−5.22720			−0.398570
$173$	11.7595	+	9.86736i	0.894055	+	0.750202i	0.969019	−	0.246985i	$-0.0794398\pi$
$173$	11.7595	+	9.86736i	0.894055	+	0.750202i	−0.0749640	+	0.997186i	$0.523884\pi$
$174$	0.282049	+	9.62963i	0.0213821	+	0.730020i
$175$	0.294449	+	1.66990i	0.0222583	+	0.126233i
$176$	−2.82413	−	0.497971i	−0.212877	−	0.0375360i
$177$	2.42608	−	3.06949i	0.182355	−	0.230717i
$178$	−1.62724	−	2.81846i	−0.121966	−	0.211252i
$179$	7.98310	−	13.8271i	0.596685	−	1.03349i	−0.396622	−	0.917982i	$-0.629818\pi$
$179$	7.98310	−	13.8271i	0.596685	−	1.03349i	0.993307	−	0.115506i	$-0.0368491\pi$
$180$	−0.175587	−	2.99486i	−0.0130875	−	0.223223i
$181$	−12.7512	−	15.1963i	−0.947790	−	1.12953i	−0.991450	−	0.130486i	$-0.958346\pi$
$181$	−12.7512	−	15.1963i	−0.947790	−	1.12953i	0.0436597	−	0.999046i	$-0.486098\pi$
$182$	5.89837	+	3.40542i	0.437216	+	0.252427i
$183$	4.04305	−	0.835634i	0.298871	−	0.0617719i
$184$	−1.94269	+	5.33749i	−0.143217	+	0.393485i
$185$	−1.22645	+	6.95553i	−0.0901703	+	0.511381i
$186$	0.190417	−	1.30171i	0.0139621	−	0.0954463i
$187$	5.91187	−	2.15174i	0.432319	−	0.157351i
$188$	−0.302030	+	0.359945i	−0.0220278	+	0.0262517i
$189$	7.21458	−	5.05791i	0.524783	−	0.367909i
$190$	−4.05216	−	1.60625i	−0.293974	−	0.116529i
$191$		−	12.4540i		−	0.901140i	−0.892741	−	0.450570i	$-0.851221\pi$
$191$		−	12.4540i		−	0.901140i	0.892741	−	0.450570i	$-0.148779\pi$
$192$	1.47400	−	0.909570i	0.106377	−	0.0656426i
$193$	−8.90144	−	24.4565i	−0.640739	−	1.76042i	−0.649391	−	0.760454i	$-0.724976\pi$
$193$	−8.90144	−	24.4565i	−0.640739	−	1.76042i	0.00865183	−	0.999963i	$-0.497246\pi$
$194$	7.92926	−	1.39814i	0.569288	−	0.100381i
$195$	−6.12419	−	3.30061i	−0.438563	−	0.236362i
$196$	3.87597	+	1.41074i	0.276855	+	0.100767i
$197$	2.43158	−	1.40388i	0.173243	−	0.100022i	−0.410871	−	0.911693i	$-0.634775\pi$
$197$	2.43158	−	1.40388i	0.173243	−	0.100022i	0.584114	+	0.811672i	$0.301442\pi$
$198$	3.41055	+	7.89819i	0.242378	+	0.561300i
$199$	7.91258	−	6.63944i	0.560908	−	0.470658i	−0.317707	−	0.948189i	$-0.602913\pi$
$199$	7.91258	−	6.63944i	0.560908	−	0.470658i	0.878615	+	0.477531i	$0.158468\pi$
$200$	0.766044	−	0.642788i	0.0541675	−	0.0454519i
$201$	0.420618	−	0.374463i	0.0296681	−	0.0264126i
$202$	−6.56545	+	3.79056i	−0.461943	+	0.266703i
$203$	−8.86260	−	3.22572i	−0.622032	−	0.226401i
$204$	−1.80276	+	3.34498i	−0.126219	+	0.234195i
$205$	−2.47750	+	0.436850i	−0.173036	+	0.0305109i
$206$	−5.00142	−	13.7413i	−0.348465	−	0.957400i
$207$	16.5793	−	3.93610i	1.15234	−	0.273578i
$208$		−	4.01662i		−	0.278503i
$209$	12.4950	+	0.354047i	0.864297	+	0.0244900i
$210$	2.78808	+	0.923274i	0.192396	+	0.0637120i
$211$	−13.5851	+	16.1901i	−0.935239	+	1.11457i	0.0579806	+	0.998318i	$0.481534\pi$
$211$	−13.5851	+	16.1901i	−0.935239	+	1.11457i	−0.993219	+	0.116256i	$0.962911\pi$
$212$	−12.7899	+	4.65516i	−0.878417	+	0.319718i
$213$	3.17736	+	0.464790i	0.217709	+	0.0318469i
$214$	−2.27467	+	12.9003i	−0.155493	+	0.881845i
$215$	−1.78781	+	4.91196i	−0.121928	+	0.334993i
$216$	−4.71058	−	2.19327i	−0.320514	−	0.149233i
$217$	1.11538	+	0.643966i	0.0757170	+	0.0437152i
$218$	−12.4152	−	14.7958i	−0.840862	−	1.00210i
$219$	8.92283	+	22.4475i	0.602949	+	1.51686i
$220$	−1.43385	+	2.48350i	−0.0966701	+	0.167438i
$221$	4.40592	+	7.63127i	0.296374	+	0.513335i
$222$	9.59736	+	7.58561i	0.644133	+	0.509113i
$223$	6.59149	+	1.16226i	0.441399	+	0.0778305i	0.389931	−	0.920844i	$-0.372499\pi$
$223$	6.59149	+	1.16226i	0.441399	+	0.0778305i	0.0514680	+	0.998675i	$0.483610\pi$
$224$	0.294449	+	1.66990i	0.0196737	+	0.111575i
$225$	−2.87430	−	0.859303i	−0.191620	−	0.0572869i
$226$	11.6932	+	9.81179i	0.777822	+	0.652670i
$227$	6.67953			0.443336			0.221668	−	0.975122i	$-0.428850\pi$
$227$	6.67953			0.443336			0.221668	+	0.975122i	$0.428850\pi$
$228$	−5.77888	+	4.85845i	−0.382716	+	0.321759i
$229$	17.4931			1.15597			0.577987	−	0.816046i	$-0.303838\pi$
$229$	17.4931			1.15597			0.577987	+	0.816046i	$0.303838\pi$
$230$	4.35116	+	3.65106i	0.286907	+	0.240744i
$231$	−8.41876	+	0.246583i	−0.553914	+	0.0162240i
$232$	0.965841	+	5.47755i	0.0634105	+	0.359619i
$233$	11.5601	+	2.03835i	0.757325	+	0.133537i	0.538961	−	0.842331i	$-0.318817\pi$
$233$	11.5601	+	2.03835i	0.757325	+	0.133537i	0.218364	+	0.975867i	$0.429928\pi$
$234$	−10.0650	+	6.62539i	−0.657968	+	0.433115i
$235$	0.234937	+	0.406924i	0.0153256	+	0.0265448i
$236$	1.12944	−	1.95625i	0.0735203	−	0.127341i
$237$	19.8245	−	7.88017i	1.28774	−	0.511872i
$238$	−2.39118	−	2.84970i	−0.154997	−	0.184719i
$239$	22.2705	+	12.8579i	1.44056	+	0.831707i	0.997887	−	0.0649770i	$-0.0206974\pi$
$239$	22.2705	+	12.8579i	1.44056	+	0.831707i	0.442672	+	0.896684i	$0.354031\pi$
$240$	−0.350578	−	1.69620i	−0.0226297	−	0.109489i
$241$	−7.13935	+	19.6152i	−0.459886	+	1.26353i	0.465685	+	0.884951i	$0.345808\pi$
$241$	−7.13935	+	19.6152i	−0.459886	+	1.26353i	−0.925571	+	0.378575i	$0.876414\pi$
$242$	−0.482100	+	2.73412i	−0.0309905	+	0.175756i
$243$	2.27411	+	15.4217i	0.145884	+	0.989302i
$244$	2.23984	−	0.815237i	0.143391	−	0.0521902i
$245$	2.65132	−	3.15972i	0.169387	−	0.201867i
$246$	−1.36979	+	4.13645i	−0.0873344	+	0.263730i
$247$	2.55066	+	17.3213i	0.162295	+	1.10213i
$248$		−	0.759544i		−	0.0482311i
$249$	−0.364627	−	0.590895i	−0.0231073	−	0.0374465i
$250$	−0.342020	−	0.939693i	−0.0216313	−	0.0594314i
$251$	14.5596	−	2.56725i	0.918994	−	0.162043i	0.305909	−	0.952061i	$-0.401040\pi$
$251$	14.5596	−	2.56725i	0.918994	−	0.162043i	0.613085	+	0.790017i	$0.289928\pi$
$252$	3.69880	−	3.49233i	0.233003	−	0.219996i
$253$	−15.3063	−	5.57104i	−0.962299	−	0.350248i
$254$	−9.60276	+	5.54415i	−0.602530	+	0.347871i
$255$	2.52667	+	2.83809i	0.158226	+	0.177728i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−5.78311	+	4.85260i	−0.360740	+	0.302697i	−0.805086	−	0.593159i	$-0.797881\pi$
$257$	−5.78311	+	4.85260i	−0.360740	+	0.302697i	0.444345	+	0.895856i	$0.353436\pi$
$258$	6.02022	+	6.76224i	0.374802	+	0.420999i
$259$	−10.3717	+	5.98810i	−0.644466	+	0.372082i
$260$	−3.77439	−	1.37377i	−0.234078	−	0.0851974i
$261$	12.1327	−	11.4554i	0.750993	−	0.709072i
$262$	−14.6740	+	2.58742i	−0.906563	+	0.159852i
$263$	−7.27377	−	19.9845i	−0.448520	−	1.23230i	−0.933755	−	0.357914i	$-0.883488\pi$
$263$	−7.27377	−	19.9845i	−0.448520	−	1.23230i	0.485235	−	0.874384i	$-0.338734\pi$
$264$	2.60837	+	4.22700i	0.160534	+	0.260154i
$265$			13.6108i			0.836103i
$266$	−2.33021	−	7.01430i	−0.142875	−	0.430074i
$267$	−1.77203	+	5.35114i	−0.108447	+	0.327484i
$268$	0.208994	−	0.249070i	0.0127663	−	0.0152143i
$269$	26.4097	−	9.61234i	1.61023	−	0.586075i	0.628742	−	0.777614i	$-0.283570\pi$
$269$	26.4097	−	9.61234i	1.61023	−	0.586075i	0.981485	+	0.191539i	$0.0613480\pi$
$270$	−3.67211	+	3.67636i	−0.223478	+	0.223736i
$271$	−2.35946	+	13.3812i	−0.143327	+	0.812847i	0.825368	+	0.564594i	$0.190967\pi$
$271$	−2.35946	+	13.3812i	−0.143327	+	0.812847i	−0.968695	+	0.248253i	$0.920144\pi$
$272$	−0.750338	+	2.06154i	−0.0454959	+	0.124999i
$273$	−2.38773	−	11.5526i	−0.144512	−	0.699193i
$274$	−11.7325	−	6.77378i	−0.708788	−	0.409219i
$275$	1.84332	+	2.19679i	0.111156	+	0.132471i
$276$	9.14232	−	3.63405i	0.550303	−	0.218744i
$277$	3.36662	−	5.83116i	0.202281	−	0.350360i	−0.746982	−	0.664844i	$-0.768498\pi$
$277$	3.36662	−	5.83116i	0.202281	−	0.350360i	0.949263	+	0.314484i	$0.101831\pi$
$278$	3.28302	+	5.68636i	0.196903	+	0.341045i
$279$	−1.90329	+	1.25286i	−0.113947	+	0.0750068i
$280$	1.66990	+	0.294449i	0.0997959	+	0.0175967i
$281$	3.49792	+	19.8377i	0.208668	+	1.18342i	0.891562	+	0.452899i	$0.149610\pi$
$281$	3.49792	+	19.8377i	0.208668	+	1.18342i	−0.682894	+	0.730518i	$0.739279\pi$
$282$	0.813498	−	0.0238271i	0.0484431	−	0.00141888i
$283$	8.81181	+	7.39399i	0.523808	+	0.439527i	0.865957	−	0.500119i	$-0.166710\pi$
$283$	8.81181	+	7.39399i	0.523808	+	0.439527i	−0.342149	+	0.939646i	$0.611155\pi$
$284$	1.85397			0.110013
$285$	2.58896	+	7.09206i	0.153357	+	0.420097i
$286$	11.5185			0.681101
$287$	−3.26781	−	2.74201i	−0.192893	−	0.161856i
$288$	−2.87430	−	0.859303i	−0.169370	−	0.0506349i
$289$	2.11626	+	12.0019i	0.124486	+	0.705995i
$290$	5.47755	+	0.965841i	0.321653	+	0.0567161i
$291$	−10.9409	−	8.64754i	−0.641369	−	0.506928i
$292$	6.97321	+	12.0780i	0.408076	+	0.706809i
$293$	−15.5673	+	26.9634i	−0.909454	+	1.57522i	−0.0946304	+	0.995512i	$0.530167\pi$
$293$	−15.5673	+	26.9634i	−0.909454	+	1.57522i	−0.814824	+	0.579709i	$0.803166\pi$
$294$	−2.63897	−	6.63896i	−0.153908	−	0.387192i
$295$	−1.45198	−	1.73040i	−0.0845376	−	0.100748i
$296$	6.11659	+	3.53142i	0.355520	+	0.205259i
$297$	6.28964	−	13.5085i	0.364962	−	0.783844i
$298$	4.26842	−	11.7274i	0.247263	−	0.679350i
$299$	3.96171	−	22.4680i	0.229111	−	1.29936i
$300$	−1.71381	−	0.250699i	−0.0989470	−	0.0144741i
$301$	−8.32904	+	3.03152i	−0.480078	+	0.174734i
$302$	−2.98239	+	3.55428i	−0.171617	+	0.204526i
$303$	12.4652	+	4.12785i	0.716107	+	0.237139i
$304$	−2.89530	+	3.25841i	−0.166057	+	0.186883i
$305$		−	2.38359i		−	0.136484i
$306$	6.40353	−	1.52027i	0.366066	−	0.0869080i
$307$	−3.82934	−	10.5210i	−0.218552	−	0.600466i	0.781163	−	0.624327i	$-0.214627\pi$
$307$	−3.82934	−	10.5210i	−0.218552	−	0.600466i	−0.999715	+	0.0238602i	$0.992404\pi$
$308$	−4.78878	+	0.844392i	−0.272866	+	0.0481137i
$309$	−12.0164	+	22.2961i	−0.683590	+	1.26838i
$310$	−0.713738	−	0.259779i	−0.0405376	−	0.0147545i
$311$	−17.6981	+	10.2180i	−1.00357	+	0.579409i	−0.909301	−	0.416138i	$-0.863383\pi$
$311$	−17.6981	+	10.2180i	−1.00357	+	0.579409i	−0.0942642	+	0.995547i	$0.530050\pi$
$312$	−5.19616	+	4.62598i	−0.294175	+	0.261895i
$313$	−22.4994	+	18.8792i	−1.27174	+	1.06712i	−0.277413	+	0.960751i	$0.589477\pi$
$313$	−22.4994	+	18.8792i	−1.27174	+	1.06712i	−0.994327	+	0.106366i	$0.966078\pi$
$314$	−8.00725	+	6.71888i	−0.451875	+	0.379168i
$315$	−2.01665	−	4.67018i	−0.113626	−	0.263135i
$316$	10.6666	−	6.15837i	0.600044	−	0.346435i
$317$	6.35655	+	2.31360i	0.357019	+	0.129944i	0.514302	−	0.857609i	$-0.328051\pi$
$317$	6.35655	+	2.31360i	0.357019	+	0.129944i	−0.157282	+	0.987554i	$0.550273\pi$
$318$	20.7525	+	11.1845i	1.16374	+	0.627195i
$319$	−15.7080	+	2.76974i	−0.879478	+	0.155076i
$320$	−0.342020	−	0.939693i	−0.0191195	−	0.0525304i
$321$	19.3084	−	11.9147i	1.07769	−	0.665015i
$322$			9.63144i			0.536739i
$323$	1.92662	−	9.36664i	0.107200	−	0.521174i
$324$	2.58787	+	8.61992i	0.143770	+	0.478884i
$325$	−2.58184	+	3.07691i	−0.143214	+	0.170676i
$326$	−2.99071	+	1.08853i	−0.165640	+	0.0602880i
$327$	−4.84216	+	33.1016i	−0.267772	+	1.83052i
$328$	−0.436850	+	2.47750i	−0.0241210	+	0.136797i
$329$	−0.272505	+	0.748701i	−0.0150237	+	0.0412772i
$330$	4.86419	−	1.00535i	0.267765	−	0.0553428i
$331$	−19.6284	−	11.3325i	−1.07887	−	0.622888i	−0.148281	−	0.988945i	$-0.547374\pi$
$331$	−19.6284	−	11.3325i	−1.07887	−	0.622888i	−0.930592	+	0.366057i	$0.880707\pi$
$332$	−0.257680	−	0.307091i	−0.0141420	−	0.0168538i
$333$	−1.24015	−	21.1522i	−0.0679595	−	1.15913i
$334$	0.847136	−	1.46728i	0.0463532	−	0.0802861i
$335$	−0.162569	−	0.281577i	−0.00888207	−	0.0153842i
$336$	1.82117	−	2.30416i	0.0993532	−	0.125702i
$337$	−5.40271	−	0.952644i	−0.294305	−	0.0518938i	0.0245464	−	0.999699i	$-0.492186\pi$
$337$	−5.40271	−	0.952644i	−0.294305	−	0.0518938i	−0.318851	+	0.947805i	$0.603297\pi$
$338$	0.544086	+	3.08566i	0.0295944	+	0.167838i
$339$	−0.774051	−	26.4274i	−0.0420407	−	1.43534i
$340$	1.68058	+	1.41017i	0.0911423	+	0.0764774i
$341$	2.17814			0.117953
$342$	12.9408	+	1.88040i	0.699758	+	0.101680i
$343$	18.8638			1.01855
$344$	4.00427	+	3.35998i	0.215896	+	0.181158i
$345$	−0.288032	−	9.83389i	−0.0155071	−	0.529439i
$346$	−2.66565	−	15.1177i	−0.143306	−	0.812731i
$347$	13.0833	+	2.30694i	0.702349	+	0.123843i	0.513407	−	0.858145i	$-0.328383\pi$
$347$	13.0833	+	2.30694i	0.702349	+	0.123843i	0.188942	+	0.981988i	$0.439494\pi$
$348$	5.97374	−	7.55802i	0.320226	−	0.405153i
$349$	7.49687	+	12.9850i	0.401298	+	0.695069i	0.993883	−	0.110439i	$-0.0352257\pi$
$349$	7.49687	+	12.9850i	0.401298	+	0.695069i	−0.592585	+	0.805508i	$0.701892\pi$
$350$	0.847833	−	1.46849i	0.0453186	−	0.0784940i
$351$	20.1629	+	5.39017i	1.07622	+	0.287706i
$352$	1.84332	+	2.19679i	0.0982494	+	0.117089i
$353$	−21.5572	−	12.4461i	−1.14737	−	0.662437i	−0.199128	−	0.979974i	$-0.563811\pi$
$353$	−21.5572	−	12.4461i	−1.14737	−	0.662437i	−0.948246	+	0.317537i	$0.897144\pi$
$354$	−3.83151	+	0.791913i	−0.203643	+	0.0420897i
$355$	0.634095	−	1.74216i	0.0336543	−	0.0924644i
$356$	−0.565133	+	3.20503i	−0.0299520	+	0.169866i
$357$	−0.932607	+	6.37541i	−0.0493588	+	0.337423i
$358$	−15.0033	+	5.46076i	−0.792950	+	0.288610i
$359$	−8.99178	+	10.7160i	−0.474568	+	0.565568i	−0.949223	−	0.314604i	$-0.898128\pi$
$359$	−8.99178	+	10.7160i	−0.474568	+	0.565568i	0.474655	+	0.880172i	$0.342573\pi$
$360$	−1.79055	+	2.40706i	−0.0943702	+	0.126863i
$361$	10.4165	−	15.8901i	0.548236	−	0.836323i
$362$			19.8374i			1.04263i
$363$	4.09227	−	2.52524i	0.214789	−	0.132541i
$364$	−2.32945	−	6.40010i	−0.122096	−	0.335457i
$365$	13.7345	−	2.42177i	0.718899	−	0.126761i
$366$	−3.63429	−	1.95869i	−0.189967	−	0.102382i
$367$	−29.6233	−	10.7820i	−1.54632	−	0.562816i	−0.578772	−	0.815490i	$-0.696468\pi$
$367$	−29.6233	−	10.7820i	−1.54632	−	0.562816i	−0.967551	+	0.252674i	$0.918690\pi$
$368$	4.91906	−	2.84002i	0.256423	−	0.148046i
$369$	6.92877	−	2.99194i	0.360697	−	0.155754i
$370$	5.41044	−	4.53990i	0.281276	−	0.236018i
$371$	−17.6798	+	14.8351i	−0.917888	+	0.770200i
$372$	−0.982594	+	0.874773i	−0.0509451	+	0.0453549i
$373$	−11.1914	+	6.46136i	−0.579469	+	0.334556i	−0.760922	−	0.648843i	$-0.775253\pi$
$373$	−11.1914	+	6.46136i	−0.579469	+	0.334556i	0.181454	+	0.983400i	$0.441920\pi$
$374$	−5.91187	−	2.15174i	−0.305695	−	0.111264i
$375$	−0.821738	+	1.52471i	−0.0424344	+	0.0787358i
$376$	0.462736	−	0.0815929i	0.0238638	−	0.00420783i
$377$	−7.64096	−	20.9934i	−0.393530	−	1.08121i
$378$	−8.77785	−	0.762855i	−0.451484	−	0.0392370i
$379$		−	12.5935i		−	0.646885i	−0.946248	−	0.323443i	$-0.895160\pi$
$379$		−	12.5935i		−	0.646885i	0.946248	−	0.323443i	$-0.104840\pi$
$380$	2.07166	+	3.83513i	0.106274	+	0.196738i
$381$	18.2319	+	6.03748i	0.934046	+	0.309310i
$382$	−8.00528	+	9.54032i	−0.409586	+	0.488125i
$383$	4.85226	−	1.76608i	0.247939	−	0.0902425i	−0.215061	−	0.976601i	$-0.568995\pi$
$383$	4.85226	−	1.76608i	0.247939	−	0.0902425i	0.463000	+	0.886358i	$0.346773\pi$
$384$	−1.71381	−	0.250699i	−0.0874576	−	0.0127935i
$385$	−0.844392	+	4.78878i	−0.0430342	+	0.244059i
$386$	−8.90144	+	24.4565i	−0.453071	+	1.24480i
$387$	1.81453	−	15.5763i	0.0922376	−	0.791786i
$388$	−6.97287	−	4.02579i	−0.353994	−	0.204379i
$389$	9.92835	+	11.8321i	0.503387	+	0.599913i	0.956569	−	0.291504i	$-0.0941558\pi$
$389$	9.92835	+	11.8321i	0.503387	+	0.599913i	−0.453182	+	0.891418i	$0.649711\pi$
$390$	2.56981	+	6.46497i	0.130127	+	0.327367i
$391$	−6.23055	+	10.7916i	−0.315092	+	0.545756i
$392$	−2.06236	−	3.57211i	−0.104165	−	0.180419i
$393$	20.2474	+	16.0033i	1.02135	+	0.807258i
$394$	−2.76509	−	0.487561i	−0.139303	−	0.0245630i
$395$	−2.13878	−	12.1296i	−0.107614	−	0.610307i
$396$	2.46422	−	8.24263i	0.123832	−	0.414208i
$397$	−13.9716	−	11.7236i	−0.701216	−	0.588390i	0.220904	−	0.975296i	$-0.429099\pi$
$397$	−13.9716	−	11.7236i	−0.701216	−	0.588390i	−0.922119	+	0.386906i	$0.873544\pi$
$398$	−10.3291			−0.517753
$399$	−6.39042	+	11.0929i	−0.319921	+	0.555342i
$400$	−1.00000			−0.0500000
$401$	−6.96398	−	5.84347i	−0.347765	−	0.291809i	0.452127	−	0.891954i	$-0.350665\pi$
$401$	−6.96398	−	5.84347i	−0.347765	−	0.291809i	−0.799892	+	0.600144i	$0.795110\pi$
$402$	−0.562913	+	0.0164875i	−0.0280755	+	0.000822324i
$403$	0.529766	+	3.00445i	0.0263895	+	0.149662i
$404$	7.46595	+	1.31645i	0.371445	+	0.0654958i
$405$	8.98517	+	0.516385i	0.446477	+	0.0256594i
$406$	4.71569	+	8.16782i	0.234036	+	0.405362i
$407$	−10.1270	+	17.5406i	−0.501979	+	0.869453i
$408$	3.53111	−	1.40361i	0.174816	−	0.0694889i
$409$	5.64043	+	6.72200i	0.278901	+	0.332382i	0.887251	−	0.461288i	$-0.152612\pi$
$409$	5.64043	+	6.72200i	0.278901	+	0.332382i	−0.608349	+	0.793669i	$0.708168\pi$
$410$	2.17868	+	1.25786i	0.107597	+	0.0621213i
$411$	4.74947	+	22.9794i	0.234274	+	1.13349i
$412$	−5.00142	+	13.7413i	−0.246402	+	0.676984i
$413$	0.665126	−	3.77211i	0.0327287	−	0.185614i
$414$	−15.2305	−	7.64172i	−0.748540	−	0.375570i
$415$	−0.376702	+	0.137108i	−0.0184916	+	0.00673039i
$416$	−2.58184	+	3.07691i	−0.126585	+	0.150858i
$417$	3.57515	−	10.7962i	0.175076	−	0.528691i
$418$	−9.34415	−	8.30284i	−0.457037	−	0.406105i
$419$		−	21.0563i		−	1.02867i	−0.857590	−	0.514335i	$-0.828039\pi$
$419$		−	21.0563i		−	1.02867i	0.857590	−	0.514335i	$-0.171961\pi$
$420$	−1.54233	−	2.49941i	−0.0752578	−	0.121959i
$421$	−9.66292	−	26.5486i	−0.470942	−	1.29390i	−0.916996	−	0.398896i	$-0.869393\pi$
$421$	−9.66292	−	26.5486i	−0.470942	−	1.29390i	0.446055	−	0.895006i	$-0.352829\pi$
$422$	20.8136	−	3.67000i	1.01319	−	0.178653i
$423$	−0.967738	−	1.02495i	−0.0470530	−	0.0498348i
$424$	12.7899	+	4.65516i	0.621134	+	0.226074i
$425$	1.89992	−	1.09692i	0.0921598	−	0.0532085i
$426$	−2.13524	−	2.39842i	−0.103453	−	0.116204i
$427$	3.09618	−	2.59800i	0.149835	−	0.125726i
$428$	10.0346	−	8.42006i	0.485042	−	0.406999i
$429$	−13.2659	−	14.9010i	−0.640485	−	0.719428i
$430$	4.52689	−	2.61360i	0.218306	−	0.126039i
$431$	−8.45233	−	3.07640i	−0.407134	−	0.148185i	0.130331	−	0.991471i	$-0.458396\pi$
$431$	−8.45233	−	3.07640i	−0.407134	−	0.148185i	−0.537466	+	0.843286i	$0.680618\pi$
$432$	2.19871	+	4.70804i	0.105785	+	0.226516i
$433$	12.8871	−	2.27235i	0.619316	−	0.109202i	0.144817	−	0.989458i	$-0.453741\pi$
$433$	12.8871	−	2.27235i	0.619316	−	0.109202i	0.474498	+	0.880256i	$0.342629\pi$
$434$	−0.440499	−	1.21026i	−0.0211446	−	0.0580943i
$435$	−5.05908	−	8.19848i	−0.242564	−	0.393087i
$436$			19.3146i			0.925001i
$437$	−19.4094	+	15.3710i	−0.928478	+	0.735295i
$438$	7.59370	−	22.9313i	0.362841	−	1.09570i
$439$	−13.2640	+	15.8075i	−0.633058	+	0.754450i	−0.983257	−	0.182226i	$-0.941670\pi$
$439$	−13.2640	+	15.8075i	−0.633058	+	0.754450i	0.350198	+	0.936676i	$0.386114\pi$
$440$	2.69476	−	0.980811i	0.128467	−	0.0467583i
$441$	−5.54926	+	11.0601i	−0.264250	+	0.526671i
$442$	1.53016	−	8.67797i	0.0727823	−	0.412769i
$443$	13.0334	−	35.8091i	0.619238	−	1.70134i	−0.0896071	−	0.995977i	$-0.528561\pi$
$443$	13.0334	−	35.8091i	0.619238	−	1.70134i	0.708845	−	0.705364i	$-0.249217\pi$
$444$	−2.47607	−	11.9800i	−0.117509	−	0.568545i
$445$	2.81846	+	1.62724i	0.133608	+	0.0771384i
$446$	−4.30229	−	5.12727i	−0.203719	−	0.242783i
$447$	−20.0873	+	7.98465i	−0.950097	+	0.377661i
$448$	0.847833	−	1.46849i	0.0400563	−	0.0693796i
$449$	−4.54811	−	7.87756i	−0.214639	−	0.371765i	0.738522	−	0.674229i	$-0.235524\pi$
$449$	−4.54811	−	7.87756i	−0.214639	−	0.371765i	−0.953161	+	0.302464i	$0.902191\pi$
$450$	1.64949	+	2.50583i	0.0777578	+	0.118126i
$451$	−7.10473	−	1.25275i	−0.334548	−	0.0589899i
$452$	−2.65064	−	15.0325i	−0.124676	−	0.707071i
$453$	8.03289	−	0.235281i	0.377418	−	0.0110545i
$454$	−5.11681	−	4.29352i	−0.240144	−	0.201505i
$455$	−6.81085			−0.319297
$456$	7.54983	−	0.00720080i	0.353553	−	0.000337208i
$457$	18.8931			0.883784			0.441892	−	0.897068i	$-0.354307\pi$
$457$	18.8931			0.883784			0.441892	+	0.897068i	$0.354307\pi$
$458$	−13.4005	−	11.2443i	−0.626162	−	0.525413i
$459$	−9.34173	−	6.53311i	−0.436035	−	0.304940i
$460$	−0.986328	−	5.59374i	−0.0459878	−	0.260810i
$461$	1.25907	+	0.222008i	0.0586408	+	0.0103399i	0.202892	−	0.979201i	$-0.434966\pi$
$461$	1.25907	+	0.222008i	0.0586408	+	0.0103399i	−0.144251	+	0.989541i	$0.546077\pi$
$462$	6.60764	+	5.22258i	0.307415	+	0.242976i
$463$	−1.56970	−	2.71880i	−0.0729502	−	0.126353i	0.827243	−	0.561844i	$-0.189908\pi$
$463$	−1.56970	−	2.71880i	−0.0729502	−	0.126353i	−0.900193	+	0.435491i	$0.856575\pi$
$464$	2.78103	−	4.81688i	0.129106	−	0.223618i
$465$	0.485951	+	1.22253i	0.0225354	+	0.0566933i
$466$	−7.54530	−	8.99214i	−0.349529	−	0.416553i
$467$	−25.4638	−	14.7015i	−1.17832	−	0.680306i	−0.222698	−	0.974888i	$-0.571486\pi$
$467$	−25.4638	−	14.7015i	−1.17832	−	0.680306i	−0.955626	+	0.294582i	$0.904820\pi$
$468$	11.9689	+	1.39430i	0.553264	+	0.0644514i
$469$	0.188564	−	0.518075i	0.00870707	−	0.0239225i
$470$	0.0815929	−	0.462736i	0.00376360	−	0.0213444i
$471$	17.9140	+	2.62049i	0.825433	+	0.120746i
$472$	−2.12265	+	0.772583i	−0.0977031	+	0.0355610i
$473$	−9.63541	+	11.4830i	−0.443037	+	0.527991i
$474$	−20.2517	−	6.70635i	−0.930191	−	0.308033i
$475$	4.31239	−	0.635026i	0.197866	−	0.0291370i
$476$			3.72002i			0.170507i
$477$	−9.43188	−	39.7280i	−0.431856	−	1.81902i
$478$	−8.79530	−	24.1649i	−0.402288	−	1.10528i
$479$	−20.4921	+	3.61331i	−0.936308	+	0.165096i	−0.620927	−	0.783869i	$-0.713244\pi$
$479$	−20.4921	+	3.61331i	−0.936308	+	0.165096i	−0.315381	+	0.948965i	$0.602132\pi$
$480$	−0.821738	+	1.52471i	−0.0375071	+	0.0695933i
$481$	−26.6579	−	9.70268i	−1.21550	−	0.442404i
$482$	18.0775	−	10.4370i	0.823406	−	0.475393i
$483$	12.4598	−	11.0926i	0.566942	−	0.504732i
$484$	2.12677	−	1.78457i	0.0966714	−	0.0811169i
$485$	−6.16787	+	5.17546i	−0.280069	+	0.235005i
$486$	8.17080	−	13.2755i	0.370635	−	0.602187i
$487$	35.5959	−	20.5513i	1.61300	−	0.931268i	0.624334	−	0.781158i	$-0.285371\pi$
$487$	35.5959	−	20.5513i	1.61300	−	0.931268i	0.988669	−	0.150110i	$-0.0479627\pi$
$488$	−2.23984	−	0.815237i	−0.101393	−	0.0369040i
$489$	4.85262	+	2.61530i	0.219443	+	0.118268i
$490$	−4.06206	+	0.716250i	−0.183505	+	0.0323569i
$491$	6.07581	+	16.6931i	0.274197	+	0.753351i	0.997992	+	0.0633358i	$0.0201739\pi$
$491$	6.07581	+	16.6931i	0.274197	+	0.753351i	−0.723795	+	0.690015i	$0.757604\pi$
$492$	3.70818	−	2.28822i	0.167178	−	0.103161i
$493$			12.2023i			0.549562i
$494$	9.17997	−	14.9084i	0.413026	−	0.670760i
$495$	−6.90272	−	5.13476i	−0.310254	−	0.230790i
$496$	−0.488225	+	0.581844i	−0.0219220	+	0.0261256i
$497$	2.95412	−	1.07521i	0.132511	−	0.0482299i
$498$	−0.100500	+	0.687030i	−0.00450351	+	0.0307865i
$499$	−2.93597	+	16.6507i	−0.131432	+	0.745387i	0.845846	+	0.533427i	$0.179096\pi$
$499$	−2.93597	+	16.6507i	−0.131432	+	0.745387i	−0.977278	+	0.211961i	$0.932015\pi$
$500$	−0.342020	+	0.939693i	−0.0152956	+	0.0420243i
$501$	−2.87382	+	0.593974i	−0.128393	+	0.0265368i
$502$	−12.8035	−	7.39210i	−0.571448	−	0.329926i
$503$	−15.5562	−	18.5391i	−0.693615	−	0.826618i	0.298173	−	0.954512i	$-0.403623\pi$
$503$	−15.5562	−	18.5391i	−0.693615	−	0.826618i	−0.991788	+	0.127894i	$0.959178\pi$
$504$	−5.07827	+	0.297738i	−0.226204	+	0.0132623i
$505$	3.79056	−	6.56545i	0.168678	−	0.292159i
$506$	8.14432	+	14.1064i	0.362059	+	0.627105i
$507$	3.36518	−	4.25765i	0.149453	−	0.189089i
$508$	10.9199	+	1.92546i	0.484490	+	0.0854287i
$509$	5.20884	+	29.5408i	0.230878	+	1.30937i	0.851123	+	0.524966i	$0.175922\pi$
$509$	5.20884	+	29.5408i	0.230878	+	1.30937i	−0.620245	+	0.784408i	$0.712967\pi$
$510$	−0.111249	−	3.79822i	−0.00492617	−	0.168188i
$511$	18.1158	+	15.2009i	0.801395	+	0.672450i
$512$	−1.00000			−0.0441942
$513$	−12.4714	−	18.9067i	−0.550627	−	0.834751i
$514$	7.54931			0.332986
$515$	11.2020	+	9.39959i	0.493619	+	0.414195i
$516$	−0.265069	−	9.04990i	−0.0116690	−	0.398400i
$517$	0.233984	+	1.32699i	0.0102906	+	0.0583609i
$518$	11.7943	+	2.07965i	0.518210	+	0.0913744i
$519$	−16.4871	+	20.8596i	−0.723705	+	0.915636i
$520$	2.00831	+	3.47850i	0.0880703	+	0.152542i
$521$	−18.2380	+	31.5892i	−0.799023	+	1.38395i	0.121230	+	0.992624i	$0.461316\pi$
$521$	−18.2380	+	31.5892i	−0.799023	+	1.38395i	−0.920253	+	0.391324i	$0.872017\pi$
$522$	−16.6576	+	0.976627i	−0.729081	+	0.0427458i
$523$	3.43128	+	4.08925i	0.150040	+	0.178810i	0.835829	−	0.548990i	$-0.184987\pi$
$523$	3.43128	+	4.08925i	0.150040	+	0.178810i	−0.685790	+	0.727800i	$0.740543\pi$
$524$	12.9041	+	7.45019i	0.563719	+	0.325463i
$525$	−2.87619	+	0.594462i	−0.125527	+	0.0259445i
$526$	−7.27377	+	19.9845i	−0.317151	+	0.871366i
$527$	0.289353	−	1.64100i	0.0126044	−	0.0714832i
$528$	0.718931	−	4.91470i	0.0312874	−	0.213885i
$529$	8.70419	−	3.16807i	0.378443	−	0.137742i
$530$	8.74884	−	10.4265i	0.380025	−	0.452896i
$531$	5.43726	+	4.04464i	0.235957	+	0.175522i
$532$	−2.72366	+	6.87110i	−0.118086	+	0.297900i
$533$		−	10.1047i		−	0.437683i
$534$	4.79710	−	2.96017i	0.207591	−	0.128099i
$535$	−4.48022	−	12.3093i	−0.193697	−	0.532178i
$536$	−0.320198	+	0.0564595i	−0.0138304	+	0.00243868i
$537$	24.3439	+	13.1200i	1.05051	+	0.566172i
$538$	−26.4097	−	9.61234i	−1.13860	−	0.414417i
$539$	10.2437	−	5.91423i	0.441229	−	0.254744i
$540$	5.17612	−	0.455864i	0.222745	−	0.0196173i
$541$	20.0043	−	16.7856i	0.860054	−	0.721671i	−0.101926	−	0.994792i	$-0.532500\pi$
$541$	20.0043	−	16.7856i	0.860054	−	0.721671i	0.961980	+	0.273121i	$0.0880560\pi$
$542$	10.4087	−	8.73393i	0.447091	−	0.375154i
$543$	25.6629	−	22.8469i	1.10130	−	0.980454i
$544$	1.89992	−	1.09692i	0.0814585	−	0.0470301i
$545$	18.1498	+	6.60598i	0.777451	+	0.282969i
$546$	−5.59674	+	10.3846i	−0.239518	+	0.444419i
$547$	−39.4258	+	6.95183i	−1.68572	+	0.297239i	−0.932673	−	0.360722i	$-0.882530\pi$
$547$	−39.4258	+	6.95183i	−1.68572	+	0.297239i	−0.753052	+	0.657961i	$0.771419\pi$
$548$	4.63354	+	12.7305i	0.197935	+	0.543822i
$549$	1.65176	+	6.95739i	0.0704955	+	0.296934i
$550$		−	2.86770i		−	0.122279i
$551$	−8.93404	+	22.5383i	−0.380603	+	0.960164i
$552$	−9.33935	−	3.09273i	−0.397509	−	0.131635i
$553$	13.4247	−	15.9989i	0.570875	−	0.680342i
$554$	−6.32718	+	2.30290i	−0.268816	+	0.0978410i
$555$	−12.1044	−	1.77065i	−0.513802	−	0.0751598i
$556$	1.14018	−	6.46629i	0.0483545	−	0.274232i
$557$	−9.14377	+	25.1223i	−0.387434	+	1.06447i	0.580719	+	0.814104i	$0.302772\pi$
$557$	−9.14377	+	25.1223i	−0.387434	+	1.06447i	−0.968152	+	0.250361i	$0.919451\pi$
$558$	2.26333	+	0.263662i	0.0958142	+	0.0111617i
$559$	−18.1828	−	10.4979i	−0.769051	−	0.444012i
$560$	−1.08995	−	1.29895i	−0.0460589	−	0.0548909i
$561$	4.02512	+	10.1262i	0.169941	+	0.427527i
$562$	10.0718	−	17.4450i	0.424855	−	0.735871i
$563$	−9.05749	−	15.6880i	−0.381728	−	0.661171i	0.609582	−	0.792723i	$-0.291337\pi$
$563$	−9.05749	−	15.6880i	−0.381728	−	0.661171i	−0.991309	+	0.131552i	$0.958004\pi$
$564$	−0.638492	−	0.504654i	−0.0268854	−	0.0212498i
$565$	−15.0325	−	2.65064i	−0.632423	−	0.111513i
$566$	−1.99747	−	11.3282i	−0.0839601	−	0.476162i
$567$	9.12265	+	12.2342i	0.383115	+	0.513787i
$568$	−1.42022	−	1.19171i	−0.0595913	−	0.0500030i
$569$	16.5022			0.691808			0.345904	−	0.938270i	$-0.387572\pi$
$569$	16.5022			0.691808			0.345904	+	0.938270i	$0.387572\pi$
$570$	2.57543	−	7.09698i	0.107873	−	0.297260i
$571$	27.8665			1.16618			0.583089	−	0.812408i	$-0.301844\pi$
$571$	27.8665			1.16618			0.583089	+	0.812408i	$0.301844\pi$
$572$	−8.82366	−	7.40393i	−0.368936	−	0.309574i
$573$	21.5617	−	0.631536i	0.900754	−	0.0263828i
$574$	0.740752	+	4.20101i	0.0309184	+	0.175347i
$575$	−5.59374	−	0.986328i	−0.233275	−	0.0411327i
$576$	1.64949	+	2.50583i	0.0687288	+	0.104410i
$577$	6.22594	+	10.7836i	0.259189	+	0.448929i	0.966025	−	0.258449i	$-0.0832114\pi$
$577$	6.22594	+	10.7836i	0.259189	+	0.448929i	−0.706836	+	0.707378i	$0.749878\pi$
$578$	6.09353	−	10.5543i	0.253457	−	0.439001i
$579$	41.8903	−	16.6513i	1.74090	−	0.692005i
$580$	−3.57522	−	4.26078i	−0.148453	−	0.176919i
$581$	−0.588685	−	0.339878i	−0.0244228	−	0.0141005i
$582$	2.82270	+	13.6571i	0.117005	+	0.566105i
$583$	−13.3496	+	36.6777i	−0.552884	+	1.51904i
$584$	2.42177	−	13.7345i	0.100214	−	0.568339i
$585$	5.40383	−	10.7702i	0.223421	−	0.445295i
$586$	29.2570	−	10.6487i	1.20860	−	0.439894i
$587$	−3.31969	+	3.95626i	−0.137018	+	0.163292i	−0.830190	−	0.557480i	$-0.811768\pi$
$587$	−3.31969	+	3.95626i	−0.137018	+	0.163292i	0.693172	+	0.720772i	$0.256213\pi$
$588$	−2.24587	+	6.78203i	−0.0926182	+	0.279686i
$589$	1.73593	−	2.81918i	0.0715279	−	0.116162i
$590$			2.25888i			0.0929967i
$591$	2.55384	+	4.13863i	0.105051	+	0.170240i
$592$	−2.41563	−	6.63689i	−0.0992818	−	0.272775i
$593$	−18.0306	+	3.17928i	−0.740427	+	0.130557i	−0.531125	−	0.847294i	$-0.678230\pi$
$593$	−18.0306	+	3.17928i	−0.740427	+	0.130557i	−0.209303	+	0.977851i	$0.567119\pi$
$594$	−13.5013	+	6.30523i	−0.553963	+	0.258707i
$595$	3.49568	+	1.27232i	0.143309	+	0.0521601i
$596$	−10.8080	+	6.24002i	−0.442714	+	0.255601i
$597$	11.8962	+	13.3624i	0.486878	+	0.546888i
$598$	−17.4770	+	14.6649i	−0.714686	+	0.599693i
$599$	−29.6316	+	24.8639i	−1.21071	+	1.01591i	−0.211456	+	0.977388i	$0.567821\pi$
$599$	−29.6316	+	24.8639i	−1.21071	+	1.01591i	−0.999258	+	0.0385220i	$0.987735\pi$
$600$	1.15171	+	1.29366i	0.0470183	+	0.0528136i
$601$	18.7134	−	10.8042i	0.763336	−	0.440712i	−0.0671564	−	0.997742i	$-0.521393\pi$
$601$	18.7134	−	10.8042i	0.763336	−	0.440712i	0.830492	+	0.557030i	$0.188059\pi$
$602$	8.32904	+	3.03152i	0.339466	+	0.123556i
$603$	0.669641	+	0.709231i	0.0272699	+	0.0288821i
$604$	4.56929	−	0.805689i	0.185922	−	0.0327830i
$605$	−0.949551	−	2.60887i	−0.0386047	−	0.106066i
$606$	−6.89556	−	11.1746i	−0.280113	−	0.453937i
$607$			25.2154i			1.02346i	0.859146	+	0.511730i	$0.170995\pi$
$607$			25.2154i			1.02346i	−0.859146	+	0.511730i	$0.829005\pi$
$608$	4.31239	−	0.635026i	0.174891	−	0.0257537i
$609$	5.13530	−	15.5075i	0.208093	−	0.628394i
$610$	−1.53214	+	1.82594i	−0.0620347	+	0.0739301i
$611$	−1.77349	+	0.645498i	−0.0717478	+	0.0261141i
$612$	−5.88260	−	2.95152i	−0.237790	−	0.119308i
$613$	4.39729	−	24.9383i	0.177605	−	1.00725i	−0.757489	−	0.652848i	$-0.773574\pi$
$613$	4.39729	−	24.9383i	0.177605	−	1.00725i	0.935094	−	0.354400i	$-0.115315\pi$
$614$	−3.82934	+	10.5210i	−0.154540	+	0.424594i
$615$	−0.881955	−	4.26716i	−0.0355639	−	0.172069i
$616$	4.21118	+	2.43133i	0.169673	+	0.0979610i
$617$	−22.8437	−	27.2241i	−0.919654	−	1.09600i	−0.995102	−	0.0988507i	$-0.968483\pi$
$617$	−22.8437	−	27.2241i	−0.919654	−	1.09600i	0.0754488	−	0.997150i	$-0.475961\pi$
$618$	23.5368	−	9.35580i	0.946788	−	0.376346i
$619$	21.7624	−	37.6936i	0.874706	−	1.51503i	0.0176300	−	0.999845i	$-0.494388\pi$
$619$	21.7624	−	37.6936i	0.874706	−	1.51503i	0.857076	−	0.515190i	$-0.172279\pi$
$620$	0.379772	+	0.657784i	0.0152520	+	0.0264172i
$621$	7.65533	+	28.5042i	0.307198	+	1.14384i
$622$	20.1255	+	3.54867i	0.806959	+	0.142289i
$623$	0.958277	+	5.43466i	0.0383925	+	0.217735i
$624$	6.95401	−	0.203681i	0.278383	−	0.00815376i
$625$	0.766044	+	0.642788i	0.0306418	+	0.0257115i
$626$	29.3709			1.17390
$627$	0.0206497	+	21.6506i	0.000824670	+	0.864643i
$628$	10.4527			0.417109
$629$	11.8697	+	9.95983i	0.473274	+	0.397124i
$630$	−1.45709	+	4.87385i	−0.0580519	+	0.194179i
$631$	−3.34829	−	18.9891i	−0.133294	−	0.755945i	−0.976033	−	0.217623i	$-0.930170\pi$
$631$	−3.34829	−	18.9891i	−0.133294	−	0.755945i	0.842739	−	0.538322i	$-0.180942\pi$
$632$	−12.1296	−	2.13878i	−0.482490	−	0.0850761i
$633$	−28.7190	−	22.6990i	−1.14148	−	0.902206i
$634$	−3.38225	−	5.85823i	−0.134326	−	0.232660i
$635$	5.54415	−	9.60276i	0.220013	−	0.381074i
$636$	−8.70809	−	21.9073i	−0.345298	−	0.868680i
$637$	10.6493	+	12.6914i	0.421943	+	0.502852i
$638$	13.8134	+	7.97515i	0.546876	+	0.315739i
$639$	−0.643572	+	5.52455i	−0.0254593	+	0.218548i
$640$	−0.342020	+	0.939693i	−0.0135195	+	0.0371446i
$641$	1.94043	−	11.0047i	0.0766423	−	0.434660i	−0.922207	−	0.386697i	$-0.873616\pi$
$641$	1.94043	−	11.0047i	0.0766423	−	0.434660i	0.998849	−	0.0479631i	$-0.0152730\pi$
$642$	−22.4497	−	3.28398i	−0.886019	−	0.129609i
$643$	27.7880	−	10.1140i	1.09585	−	0.398857i	0.270066	−	0.962842i	$-0.412955\pi$
$643$	27.7880	−	10.1140i	1.09585	−	0.398857i	0.825785	+	0.563985i	$0.190732\pi$
$644$	6.19097	−	7.37811i	0.243958	−	0.290738i
$645$	−8.59478	−	2.84616i	−0.338419	−	0.112068i
$646$	−7.49664	+	5.93686i	−0.294951	+	0.233582i
$647$		−	3.72775i		−	0.146553i	−0.997312	−	0.0732764i	$-0.976654\pi$
$647$		−	3.72775i		−	0.146553i	0.997312	−	0.0732764i	$-0.0233455\pi$
$648$	3.55835	−	8.26669i	0.139785	−	0.324746i
$649$	−2.21554	−	6.08713i	−0.0869674	−	0.238941i
$650$	3.95560	−	0.697479i	0.155151	−	0.0273574i
$651$	−1.05834	+	1.96372i	−0.0414797	+	0.0769644i
$652$	2.99071	+	1.08853i	0.117125	+	0.0426301i
$653$	11.3035	−	6.52609i	0.442341	−	0.255386i	−0.262249	−	0.965000i	$-0.584464\pi$
$653$	11.3035	−	6.52609i	0.442341	−	0.255386i	0.704590	+	0.709614i	$0.251131\pi$
$654$	24.9866	−	22.2448i	0.977053	−	0.869840i
$655$	11.4144	−	9.57778i	0.445996	−	0.374235i
$656$	1.92715	−	1.61707i	0.0752427	−	0.0631361i
$657$	−38.4111	+	16.5865i	−1.49856	+	0.647100i
$658$	0.690006	−	0.398375i	0.0268992	−	0.0155303i
$659$	38.2855	+	13.9348i	1.49139	+	0.542822i	0.953815	−	0.300394i	$-0.0971182\pi$
$659$	38.2855	+	13.9348i	1.49139	+	0.542822i	0.537575	+	0.843216i	$0.319340\pi$
$660$	−4.37241	−	2.35650i	−0.170196	−	0.0917266i
$661$	6.90014	−	1.21668i	0.268384	−	0.0473234i	−0.0378364	−	0.999284i	$-0.512047\pi$
$661$	6.90014	−	1.21668i	0.268384	−	0.0473234i	0.306221	+	0.951961i	$0.400935\pi$
$662$	7.75186	+	21.2980i	0.301284	+	0.827772i
$663$	−12.9887	+	8.01498i	−0.504438	+	0.311276i
$664$			0.400878i			0.0155571i
$665$	5.52518	+	4.90946i	0.214257	+	0.190381i
$666$	−12.6464	+	17.0007i	−0.490036	+	0.658762i
$667$	20.3074	−	24.2014i	0.786305	−	0.937081i
$668$	−1.59210	+	0.579475i	−0.0616000	+	0.0224206i
$669$	−1.67798	+	11.4708i	−0.0648743	+	0.443488i
$670$	−0.0564595	+	0.320198i	−0.00218122	+	0.0123703i
$671$	2.33785	−	6.42320i	0.0902518	−	0.247965i
$672$	−2.87619	+	0.594462i	−0.110951	+	0.0229319i
$673$	−41.5324	−	23.9787i	−1.60096	−	0.924312i	−0.991297	−	0.131648i	$-0.957973\pi$
$673$	−41.5324	−	23.9787i	−1.60096	−	0.924312i	−0.609659	−	0.792664i	$-0.708693\pi$
$674$	3.52637	+	4.20257i	0.135831	+	0.161877i
$675$	1.34196	−	5.01987i	0.0516522	−	0.193215i
$676$	1.56663	−	2.71349i	0.0602551	−	0.104365i
$677$	−13.1197	−	22.7239i	−0.504230	−	0.873352i	−0.999988	−	0.00489103i	$-0.998443\pi$
$677$	−13.1197	−	22.7239i	−0.504230	−	0.873352i	0.495758	−	0.868461i	$-0.334890\pi$
$678$	−16.3943	+	20.7421i	−0.629618	+	0.796597i
$679$	−13.4454	−	2.37078i	−0.515986	−	0.0909822i
$680$	−0.380957	−	2.16051i	−0.0146090	−	0.0828519i
$681$	0.338715	+	11.5643i	0.0129796	+	0.443146i
$682$	−1.66855	−	1.40008i	−0.0638922	−	0.0536120i
$683$	42.3997			1.62238			0.811190	−	0.584783i	$-0.198820\pi$
$683$	42.3997			1.62238			0.811190	+	0.584783i	$0.198820\pi$
$684$	−8.70453	−	9.75865i	−0.332826	−	0.373131i
$685$	13.5476			0.517625
$686$	−14.4505	−	12.1254i	−0.551723	−	0.462951i
$687$	0.887064	+	30.2859i	0.0338436	+	1.15548i
$688$	−0.907694	−	5.14779i	−0.0346055	−	0.196258i
$689$	−53.8388	−	9.49323i	−2.05109	−	0.361663i
$690$	−6.10046	+	7.71834i	−0.232241	+	0.293832i
$691$	−1.49957	−	2.59733i	−0.0570464	−	0.0988073i	0.836092	−	0.548589i	$-0.184835\pi$
$691$	−1.49957	−	2.59733i	−0.0570464	−	0.0988073i	−0.893138	+	0.449782i	$0.851502\pi$
$692$	−7.67544	+	13.2943i	−0.291777	+	0.505372i
$693$	−0.853822	−	14.5630i	−0.0324340	−	0.553201i
$694$	−8.53952	−	10.1770i	−0.324156	−	0.386314i
$695$	−5.68636	−	3.28302i	−0.215696	−	0.124532i
$696$	−9.43436	+	1.94993i	−0.357608	+	0.0739120i
$697$	−1.88764	+	5.18625i	−0.0714995	+	0.196443i
$698$	2.60364	−	14.7660i	0.0985491	−	0.558900i
$699$	−2.94281	+	20.1174i	−0.111307	+	0.760910i
$700$	−1.59340	+	0.579952i	−0.0602250	+	0.0219201i
$701$	−28.0973	+	33.4850i	−1.06122	+	1.26471i	−0.0982324	+	0.995164i	$0.531319\pi$
$701$	−28.0973	+	33.4850i	−1.06122	+	1.26471i	−0.962987	+	0.269548i	$0.913126\pi$
$702$	−11.9810	−	17.0896i	−0.452193	−	0.645005i
$703$	14.6318	+	27.0869i	0.551847	+	1.02160i
$704$		−	2.86770i		−	0.108080i
$705$	−0.692597	+	0.427384i	−0.0260847	+	0.0160962i
$706$	8.51360	+	23.3909i	0.320414	+	0.880329i
$707$	12.6597	−	2.23226i	0.476119	−	0.0839526i
$708$	3.44414	+	1.85621i	0.129439	+	0.0697606i
$709$	−8.59365	−	3.12783i	−0.322741	−	0.117468i	0.175569	−	0.984467i	$-0.443824\pi$
$709$	−8.59365	−	3.12783i	−0.322741	−	0.117468i	−0.498310	+	0.866999i	$0.666046\pi$
$710$	−1.60559	+	0.926986i	−0.0602566	+	0.0347891i
$711$	14.6483	+	33.9226i	0.549354	+	1.27220i
$712$	2.49307	−	2.09193i	0.0934318	−	0.0783986i
$713$	−3.30490	+	2.77314i	−0.123769	+	0.103855i
$714$	4.81246	−	4.28438i	0.180102	−	0.160339i
$715$	−9.97529	+	5.75923i	−0.373055	+	0.215383i
$716$	15.0033	+	5.46076i	0.560700	+	0.204078i
$717$	−21.1316	+	39.2091i	−0.789175	+	1.46429i
$718$	13.7762	−	2.42912i	0.514123	−	0.0906538i
$719$	−3.96878	−	10.9041i	−0.148011	−	0.406656i	0.843426	−	0.537246i	$-0.180535\pi$
$719$	−3.96878	−	10.9041i	−0.148011	−	0.406656i	−0.991436	+	0.130590i	$0.958313\pi$
$720$	2.91887	−	0.692971i	0.108780	−	0.0258255i
$721$			24.7960i			0.923451i
$722$	−18.1935	+	5.47697i	−0.677091	+	0.203832i
$723$	−34.3220	−	11.3657i	−1.27645	−	0.422696i
$724$	12.7512	−	15.1963i	0.473895	−	0.564766i
$725$	−5.22662	+	1.90233i	−0.194112	+	0.0706509i
$726$	−4.75806	−	0.696017i	−0.176588	−	0.0258316i
$727$	−0.332998	+	1.88853i	−0.0123502	+	0.0700416i	−0.990360	−	0.138518i	$-0.955766\pi$
$727$	−0.332998	+	1.88853i	−0.0123502	+	0.0700416i	0.978010	+	0.208559i	$0.0668774\pi$
$728$	−2.32945	+	6.40010i	−0.0863351	+	0.237204i
$729$	−26.5844	+	4.71921i	−0.984607	+	0.174785i
$730$	−12.0780	−	6.97321i	−0.447025	−	0.258090i
$731$	7.37127	+	8.78473i	0.272636	+	0.324915i
$732$	1.52501	+	3.83652i	0.0563659	+	0.141802i
$733$	−15.9349	+	27.6001i	−0.588570	+	1.01943i	0.405850	+	0.913940i	$0.366976\pi$
$733$	−15.9349	+	27.6001i	−0.588570	+	1.01943i	−0.994420	+	0.105494i	$0.966358\pi$
$734$	15.7622	+	27.3010i	0.581794	+	1.00770i
$735$	5.60489	+	4.43002i	0.206740	+	0.163404i
$736$	−5.59374	−	0.986328i	−0.206188	−	0.0363565i
$737$	−0.161909	−	0.918230i	−0.00596399	−	0.0338235i
$738$	−7.23093	−	2.16177i	−0.266174	−	0.0795757i
$739$	−34.3735	−	28.8428i	−1.26445	−	1.06100i	−0.995193	−	0.0979305i	$-0.968778\pi$
$739$	−34.3735	−	28.8428i	−1.26445	−	1.06100i	−0.269256	−	0.963069i	$-0.586778\pi$
$740$	−7.06283			−0.259635
$741$	−29.8591	+	5.29433i	−1.09690	+	0.194492i
$742$	23.0793			0.847268
$743$	5.86457	+	4.92096i	0.215150	+	0.180532i	0.743993	−	0.668187i	$-0.232930\pi$
$743$	5.86457	+	4.92096i	0.215150	+	0.180532i	−0.528843	+	0.848720i	$0.677374\pi$
$744$	1.31500	−	0.0385161i	0.0482104	−	0.00141207i
$745$	2.16714	+	12.2904i	0.0793977	+	0.450287i
$746$	12.7264	+	2.24401i	0.465946	+	0.0821589i
$747$	1.00453	−	0.661245i	0.0367539	−	0.0241937i
$748$	3.14564	+	5.44841i	0.115016	+	0.199213i
$749$	11.1060	−	19.2362i	0.405804	−	0.702874i
$750$	1.60955	−	0.639794i	0.0587726	−	0.0233620i
$751$	3.52021	+	4.19522i	0.128454	+	0.153086i	0.826438	−	0.563028i	$-0.190364\pi$
$751$	3.52021	+	4.19522i	0.128454	+	0.153086i	−0.697984	+	0.716114i	$0.745919\pi$
$752$	−0.406924	−	0.234937i	−0.0148390	−	0.00856729i
$753$	5.18301	+	25.0770i	0.188879	+	0.913856i
$754$	−7.64096	+	20.9934i	−0.278267	+	0.764533i
$755$	0.805689	−	4.56929i	0.0293220	−	0.166293i
$756$	6.23387	+	6.22667i	0.226724	+	0.226462i
$757$	8.57416	−	3.12074i	0.311633	−	0.113425i	−0.181469	−	0.983397i	$-0.558085\pi$
$757$	8.57416	−	3.12074i	0.311633	−	0.113425i	0.493102	+	0.869971i	$0.335863\pi$
$758$	−8.09495	+	9.64719i	−0.294022	+	0.350402i
$759$	8.86901	−	26.7824i	0.321925	−	0.972141i
$760$	0.878196	−	4.26952i	0.0318555	−	0.154872i
$761$		−	29.5607i		−	1.07158i	−0.844353	−	0.535788i	$-0.820015\pi$
$761$		−	29.5607i		−	1.07158i	0.844353	−	0.535788i	$-0.179985\pi$
$762$	−10.0856	−	16.3442i	−0.365362	−	0.592088i
$763$	11.2015	+	30.7759i	0.405522	+	1.11416i
$764$	12.2648	−	2.16262i	0.443725	−	0.0782407i
$765$	−4.78549	+	4.51836i	−0.173020	+	0.163362i
$766$	−4.85226	−	1.76608i	−0.175319	−	0.0638111i
$767$	7.85751	−	4.53654i	0.283718	−	0.163805i
$768$	1.15171	+	1.29366i	0.0415587	+	0.0466811i
$769$	−14.9764	+	12.5667i	−0.540063	+	0.453166i	−0.871559	−	0.490290i	$-0.836891\pi$
$769$	−14.9764	+	12.5667i	−0.540063	+	0.453166i	0.331497	+	0.943456i	$0.392446\pi$
$770$	3.72501	−	3.12566i	0.134240	−	0.112641i
$771$	−8.69461	−	9.76627i	−0.313129	−	0.351724i
$772$	22.5392	−	13.0130i	0.811205	−	0.468349i
$773$	−32.3367	−	11.7696i	−1.16307	−	0.423323i	−0.312877	−	0.949794i	$-0.601293\pi$
$773$	−32.3367	−	11.7696i	−1.16307	−	0.423323i	−0.850193	+	0.526471i	$0.823515\pi$
$774$	−11.4022	+	10.7658i	−0.409845	+	0.386967i
$775$	0.748004	−	0.131893i	0.0268691	−	0.00473775i
$776$	2.75380	+	7.56601i	0.0988558	+	0.271604i
$777$	−10.8932	−	17.6529i	−0.390791	−	0.633296i
$778$		−	15.4458i		−	0.553757i
$779$	−7.28376	+	8.19725i	−0.260968	+	0.293697i
$780$	2.18702	−	6.60430i	0.0783077	−	0.236472i
$781$	3.41746	−	4.07278i	0.122287	−	0.145735i
$782$	11.7096	−	4.26195i	0.418735	−	0.152407i
$783$	20.4481	+	20.4245i	0.730755	+	0.729912i
$784$	−0.716250	+	4.06206i	−0.0255804	+	0.145073i
$785$	3.57504	−	9.82234i	0.127599	−	0.350574i
$786$	−5.22374	−	25.2740i	−0.186325	−	0.901495i
$787$	−1.72076	−	0.993482i	−0.0613385	−	0.0354138i	0.469017	−	0.883189i	$-0.344608\pi$
$787$	−1.72076	−	0.993482i	−0.0613385	−	0.0354138i	−0.530356	+	0.847775i	$0.677942\pi$
$788$	1.80479	+	2.15086i	0.0642929	+	0.0766213i
$789$	34.2305	−	13.6065i	1.21864	−	0.484406i
$790$	−6.15837	+	10.6666i	−0.219105	+	0.379501i
$791$	−12.9417	−	22.4157i	−0.460153	−	0.797009i
$792$	−7.18596	+	4.73025i	−0.255342	+	0.168082i
$793$	9.42854	+	1.66251i	0.334817	+	0.0590373i
$794$	3.16711	+	17.9616i	0.112397	+	0.637432i
$795$	−23.5644	+	0.690195i	−0.835745	+	0.0244787i
$796$	7.91258	+	6.63944i	0.280454	+	0.235329i
$797$	−35.7285			−1.26557			−0.632785	−	0.774327i	$-0.718088\pi$
$797$	−35.7285			−1.26557			−0.632785	+	0.774327i	$0.718088\pi$
$798$	12.0258	−	4.39001i	0.425707	−	0.155405i
$799$	1.03083			0.0364682
$800$	0.766044	+	0.642788i	0.0270838	+	0.0227260i
$801$	−9.35433	−	2.79658i	−0.330519	−	0.0988122i
$802$	1.57861	+	8.95272i	0.0557425	+	0.316132i
$803$	39.3865	+	6.94491i	1.38992	+	0.245081i
$804$	0.441814	+	0.349203i	0.0155816	+	0.0123154i
$805$	−4.81572	−	8.34107i	−0.169732	−	0.293984i
$806$	1.52540	−	2.64207i	0.0537299	−	0.0930630i
$807$	17.9811	+	45.2359i	0.632966	+	1.59238i
$808$	−4.87305	−	5.80748i	−0.171433	−	0.204306i
$809$	−3.86917	−	2.23387i	−0.136033	−	0.0785386i	0.430439	−	0.902620i	$-0.358359\pi$
$809$	−3.86917	−	2.23387i	−0.136033	−	0.0785386i	−0.566472	+	0.824081i	$0.691692\pi$
$810$	−6.55112	−	6.17113i	−0.230183	−	0.216831i
$811$	−13.4279	+	36.8928i	−0.471517	+	1.29548i	0.445016	+	0.895523i	$0.353198\pi$
$811$	−13.4279	+	36.8928i	−0.471517	+	1.29548i	−0.916533	+	0.399959i	$0.869024\pi$
$812$	1.63774	−	9.28810i	0.0574735	−	0.325948i
$813$	−23.2865	−	3.40640i	−0.816695	−	0.119468i
$814$	19.0326	−	6.92730i	0.667093	−	0.242802i
$815$	2.04576	−	2.43805i	0.0716600	−	0.0854011i
$816$	−3.60721	−	1.19453i	−0.126277	−	0.0418168i
$817$	7.18332	+	21.6229i	0.251312	+	0.756489i
$818$		−	8.77495i		−	0.306809i
$819$	19.8800	−	4.71972i	0.694662	−	0.164920i
$820$	−0.860427	−	2.36400i	−0.0300474	−	0.0825546i
$821$	−22.0415	+	3.88651i	−0.769254	+	0.135640i	−0.544483	−	0.838772i	$-0.683274\pi$
$821$	−22.0415	+	3.88651i	−0.769254	+	0.135640i	−0.224770	+	0.974412i	$0.572163\pi$
$822$	11.1325	−	20.6561i	0.388292	−	0.720465i
$823$	−5.85987	−	2.13282i	−0.204262	−	0.0743454i	0.237863	−	0.971299i	$-0.423553\pi$
$823$	−5.85987	−	2.13282i	−0.204262	−	0.0743454i	−0.442125	+	0.896953i	$0.645775\pi$
$824$	12.6640	−	7.31158i	0.441172	−	0.254711i
$825$	−3.70984	+	3.30276i	−0.129160	+	0.114987i
$826$	−2.93418	+	2.46207i	−0.102093	+	0.0856665i
$827$	27.2816	−	22.8919i	0.948673	−	0.796031i	−0.0304006	−	0.999538i	$-0.509678\pi$
$827$	27.2816	−	22.8919i	0.948673	−	0.796031i	0.979074	+	0.203507i	$0.0652339\pi$
$828$	6.75526	+	15.6439i	0.234762	+	0.543663i
$829$	−25.6548	+	14.8118i	−0.891030	+	0.514436i	−0.874279	−	0.485424i	$-0.838665\pi$
$829$	−25.6548	+	14.8118i	−0.891030	+	0.514436i	−0.0167504	+	0.999860i	$0.505332\pi$
$830$	0.376702	+	0.137108i	0.0130755	+	0.00475910i
$831$	10.2662	+	5.53296i	0.356132	+	0.191936i
$832$	3.95560	−	0.697479i	0.137136	−	0.0241807i
$833$	−3.09493	−	8.50326i	−0.107233	−	0.294621i
$834$	−9.67837	+	5.97228i	−0.335134	+	0.206803i
$835$			1.69427i			0.0586327i
$836$	1.82106	+	12.3666i	0.0629828	+	0.427709i
$837$	−2.26560	−	3.23164i	−0.0783107	−	0.111702i
$838$	−13.5347	+	16.1301i	−0.467550	+	0.557205i
$839$	5.33408	−	1.94145i	0.184153	−	0.0670261i	−0.248298	−	0.968684i	$-0.579871\pi$
$839$	5.33408	−	1.94145i	0.184153	−	0.0670261i	0.432451	+	0.901658i	$0.357649\pi$
$840$	−0.425102	+	2.90605i	−0.0146674	+	0.100268i
$841$	0.336260	−	1.90702i	0.0115952	−	0.0657594i
$842$	−9.66292	+	26.5486i	−0.333006	+	0.914927i
$843$	−34.1677	+	7.06193i	−1.17680	+	0.243226i
$844$	−18.3032	−	10.5674i	−0.630022	−	0.363743i
$845$	−2.01402	−	2.40022i	−0.0692845	−	0.0825701i
$846$	0.0825042	+	1.40721i	0.00283655	+	0.0483808i
$847$	2.35384	−	4.07697i	0.0808788	−	0.140086i
$848$	−6.80539	−	11.7873i	−0.233698	−	0.404777i
$849$	−12.3544	+	15.6309i	−0.424003	+	0.536451i
$850$	−2.16051	−	0.380957i	−0.0741050	−	0.0130667i
$851$	−6.96627	−	39.5077i	−0.238801	−	1.35431i
$852$	0.0940139	+	3.20980i	0.00322086	+	0.109966i
$853$	30.3606	+	25.4755i	1.03953	+	0.872266i	0.991954	−	0.126602i	$-0.0404070\pi$
$853$	30.3606	+	25.4755i	1.03953	+	0.872266i	0.0475725	+	0.998868i	$0.484851\pi$
$854$	−4.04178			−0.138307
$855$	−12.1473	+	4.84192i	−0.415427	+	0.165590i
$856$	−13.0993			−0.447724
$857$	39.5320	+	33.1713i	1.35039	+	1.13311i	0.978824	+	0.204702i	$0.0656225\pi$
$857$	39.5320	+	33.1713i	1.35039	+	1.13311i	0.371563	+	0.928408i	$0.378822\pi$
$858$	0.584096	+	19.9420i	0.0199407	+	0.680809i
$859$	0.127687	+	0.724149i	0.00435663	+	0.0247076i	0.986909	−	0.161281i	$-0.0515624\pi$
$859$	0.127687	+	0.724149i	0.00435663	+	0.0247076i	−0.982552	+	0.185988i	$0.940451\pi$
$860$	−5.14779	−	0.907694i	−0.175538	−	0.0309521i
$861$	4.58156	−	5.79663i	0.156139	−	0.197548i
$862$	4.49739	+	7.78971i	0.153182	+	0.265319i
$863$	22.3265	−	38.6707i	0.760004	−	1.31637i	−0.182844	−	0.983142i	$-0.558530\pi$
$863$	22.3265	−	38.6707i	0.760004	−	1.31637i	0.942848	−	0.333223i	$-0.108136\pi$
$864$	1.34196	−	5.01987i	0.0456546	−	0.170780i
$865$	9.86736	+	11.7595i	0.335500	+	0.399834i
$866$	−11.3327	−	6.54296i	−0.385102	−	0.222339i
$867$	−20.6717	+	4.27251i	−0.702047	+	0.145102i
$868$	−0.440499	+	1.21026i	−0.0149515	+	0.0410789i
$869$	6.13338	−	34.7841i	0.208061	−	1.17997i
$870$	−1.39440	+	9.53231i	−0.0472747	+	0.323176i
$871$	1.22719	−	0.446662i	0.0415819	−	0.0151346i
$872$	12.4152	−	14.7958i	0.420431	−	0.501050i
$873$	14.4168	−	19.3806i	0.487933	−	0.655935i
$874$	24.7488	+	0.701259i	0.837140	+	0.0237205i
$875$			1.69567i			0.0573239i
$876$	−20.5571	+	12.6852i	−0.694559	+	0.428595i
$877$	−11.7636	−	32.3204i	−0.397230	−	1.09138i	−0.963628	−	0.267249i	$-0.913885\pi$
$877$	−11.7636	−	32.3204i	−0.397230	−	1.09138i	0.566397	−	0.824132i	$-0.308337\pi$
$878$	20.3217	−	3.58326i	0.685824	−	0.120929i
$879$	−47.4714	−	25.5846i	−1.60117	−	0.862946i
$880$	−2.69476	−	0.980811i	−0.0908402	−	0.0330631i
$881$	−35.1477	+	20.2925i	−1.18416	+	0.683673i	−0.956972	−	0.290179i	$-0.906285\pi$
$881$	−35.1477	+	20.2925i	−1.18416	+	0.683673i	−0.227184	+	0.973852i	$0.572952\pi$
$882$	11.3603	−	4.90553i	0.382520	−	0.165178i
$883$	12.8646	−	10.7947i	0.432929	−	0.363271i	−0.400127	−	0.916460i	$-0.631034\pi$
$883$	12.8646	−	10.7947i	0.432929	−	0.363271i	0.833056	+	0.553189i	$0.186589\pi$
$884$	−6.75026	+	5.66414i	−0.227036	+	0.190506i
$885$	2.92223	−	2.60157i	0.0982298	−	0.0874510i
$886$	−33.0018	+	19.0536i	−1.10872	+	0.640119i
$887$	38.8078	+	14.1249i	1.30304	+	0.474267i	0.897985	−	0.440027i	$-0.145031\pi$
$887$	38.8078	+	14.1249i	1.30304	+	0.474267i	0.405052	+	0.914294i	$0.367253\pi$
$888$	−5.80380	+	10.7688i	−0.194763	+	0.361377i
$889$	18.5164	−	3.26494i	0.621020	−	0.109503i
$890$	−1.11309	−	3.05820i	−0.0373110	−	0.102511i
$891$	23.7064	+	10.2043i	0.794193	+	0.341857i
$892$			6.69317i			0.224104i
$893$	1.90401	+	0.754736i	0.0637151	+	0.0252563i
$894$	20.5202	+	6.79527i	0.686298	+	0.227268i
$895$	10.2629	−	12.2308i	0.343050	−	0.408831i
$896$	−1.59340	+	0.579952i	−0.0532319	+	0.0193748i
$897$	39.0999	+	5.71960i	1.30551	+	0.190972i
$898$	−1.57954	+	8.95803i	−0.0527100	+	0.298933i
$899$	−1.44491	+	3.96985i	−0.0481903	+	0.132402i
$900$	0.347132	−	2.97985i	0.0115711	−	0.0993283i
$901$	25.8594	+	14.9299i	0.861502	+	0.497388i
$902$	4.63728	+	5.52650i	0.154405	+	0.184012i
$903$	−5.67086	−	14.2664i	−0.188715	−	0.474757i
$904$	−7.63222	+	13.2194i	−0.253844	+	0.439670i
$905$	−9.91869	−	17.1797i	−0.329708	−	0.571071i
$906$	−6.30478	−	4.98320i	−0.209462	−	0.165556i
$907$	12.2947	+	2.16788i	0.408238	+	0.0719833i	0.373996	−	0.927430i	$-0.377987\pi$
$907$	12.2947	+	2.16788i	0.408238	+	0.0719833i	0.0342415	+	0.999414i	$0.489098\pi$
$908$	1.15989	+	6.57805i	0.0384922	+	0.218300i
$909$	−6.51448	+	21.7904i	−0.216072	+	0.722743i
$910$	5.21741	+	4.37793i	0.172956	+	0.145127i
$911$	15.2505			0.505272			0.252636	−	0.967561i	$-0.418702\pi$
$911$	15.2505			0.505272			0.252636	+	0.967561i	$0.418702\pi$
$912$	−5.78813	−	4.84742i	−0.191664	−	0.160514i
$913$	−1.14960			−0.0380461
$914$	−14.4730	−	12.1443i	−0.478724	−	0.401697i
$915$	4.12673	−	0.120871i	0.136426	−	0.00399586i
$916$	3.03764	+	17.2273i	0.100366	+	0.569206i
$917$	24.8822	+	4.38740i	0.821683	+	0.144885i
$918$	2.95678	+	11.0094i	0.0975881	+	0.363364i
$919$	21.5032	+	37.2447i	0.709326	+	1.22859i	0.965108	+	0.261854i	$0.0843338\pi$
$919$	21.5032	+	37.2447i	0.709326	+	1.22859i	−0.255782	+	0.966735i	$0.582333\pi$
$920$	−2.84002	+	4.91906i	−0.0936326	+	0.162176i
$921$	18.0209	−	7.16328i	0.593810	−	0.236038i
$922$	−0.821800	−	0.979383i	−0.0270645	−	0.0322543i
$923$	6.44903	+	3.72335i	0.212273	+	0.122556i
$924$	−1.70474	−	8.24804i	−0.0560818	−	0.271341i
$925$	−2.41563	+	6.63689i	−0.0794255	+	0.218220i
$926$	−0.545151	+	3.09171i	−0.0179148	+	0.101600i
$927$	−39.2108	−	19.6735i	−1.28785	−	0.646162i
$928$	−5.22662	+	1.90233i	−0.171572	+	0.0624472i
$929$	−17.8933	+	21.3244i	−0.587060	+	0.699630i	−0.975038	−	0.222038i	$-0.928729\pi$
$929$	−17.8933	+	21.3244i	−0.587060	+	0.699630i	0.387978	+	0.921668i	$0.373174\pi$
$930$	0.413565	−	1.24887i	0.0135613	−	0.0409522i
$931$	0.509240	−	17.9720i	0.0166897	−	0.589009i
$932$			11.7384i			0.384504i
$933$	−18.5879	−	30.1227i	−0.608542	−	0.986172i
$934$	10.0564	+	27.6298i	0.329057	+	0.904076i
$935$	6.19570	−	1.09247i	0.202621	−	0.0357276i
$936$	−8.27250	−	8.76157i	−0.270395	−	0.286381i
$937$	2.47903	+	0.902292i	0.0809862	+	0.0294766i	0.382196	−	0.924081i	$-0.375168\pi$
$937$	2.47903	+	0.902292i	0.0809862	+	0.0294766i	−0.301209	+	0.953558i	$0.597390\pi$
$938$	−0.477460	+	0.275662i	−0.0155896	+	0.00900068i
$939$	−33.8267	−	37.9960i	−1.10389	−	1.23995i
$940$	−0.359945	+	0.302030i	−0.0117401	+	0.00985113i
$941$	41.5541	−	34.8681i	1.35463	−	1.13667i	0.377024	−	0.926203i	$-0.376947\pi$
$941$	41.5541	−	34.8681i	1.35463	−	1.13667i	0.977602	−	0.210463i	$-0.0674970\pi$
$942$	−12.0385	−	13.5223i	−0.392235	−	0.440580i
$943$	12.3750	−	7.14469i	0.402984	−	0.232663i
$944$	2.12265	+	0.772583i	0.0690865	+	0.0251454i
$945$	7.98327	−	3.72827i	0.259696	−	0.121281i
$946$	14.7623	−	2.60299i	0.479964	−	0.0846306i
$947$	−8.38878	−	23.0480i	−0.272599	−	0.748959i	−0.998150	−	0.0607915i	$-0.980638\pi$
$947$	−8.38878	−	23.0480i	−0.272599	−	0.748959i	0.725552	−	0.688168i	$-0.241585\pi$
$948$	11.2029	+	18.1549i	0.363854	+	0.589644i
$949$			56.0175i			1.81841i
$950$	−3.71167	−	2.28549i	−0.120423	−	0.0741512i
$951$	−3.68321	+	11.1225i	−0.119436	+	0.360671i
$952$	2.39118	−	2.84970i	0.0774987	−	0.0923594i
$953$	−27.4348	+	9.98547i	−0.888702	+	0.323461i	−0.745716	−	0.666264i	$-0.767892\pi$
$953$	−27.4348	+	9.98547i	−0.888702	+	0.323461i	−0.142986	+	0.989725i	$0.545670\pi$
$954$	−18.3115	+	36.4961i	−0.592855	+	1.18161i
$955$	2.16262	−	12.2648i	0.0699806	−	0.396880i
$956$	−8.79530	+	24.1649i	−0.284460	+	0.781549i
$957$	−5.59182	−	27.0549i	−0.180758	−	0.874561i
$958$	18.0204	+	10.4041i	0.582214	+	0.336142i
$959$	14.7662	+	17.5977i	0.476825	+	0.568258i
$960$	1.60955	−	0.639794i	0.0519481	−	0.0206493i
$961$	−15.2115	+	26.3472i	−0.490695	+	0.849909i
$962$	14.1844	+	24.5681i	0.457323	+	0.792106i
$963$	21.6072	+	32.8246i	0.696281	+	1.05776i
$964$	−20.5569	−	3.62474i	−0.662094	−	0.116745i
$965$	−4.51938	−	25.6307i	−0.145484	−	0.825080i
$966$	−16.6750	+	0.488405i	−0.536509	+	0.0157142i
$967$	−2.35517	−	1.97622i	−0.0757372	−	0.0635511i	0.604133	−	0.796883i	$-0.293520\pi$
$967$	−2.35517	−	1.97622i	−0.0757372	−	0.0635511i	−0.679870	+	0.733332i	$0.737964\pi$
$968$	−2.77630			−0.0892337
$969$	16.3142	+	2.86060i	0.524089	+	0.0918957i
$970$	8.05158			0.258521
$971$	4.93156	+	4.13807i	0.158261	+	0.132797i	0.718480	−	0.695548i	$-0.244838\pi$
$971$	4.93156	+	4.13807i	0.158261	+	0.132797i	−0.560218	+	0.828345i	$0.689283\pi$
$972$	−14.7925	+	4.91751i	−0.474470	+	0.157729i
$973$	−1.93337	−	10.9647i	−0.0619809	−	0.351511i
$974$	−40.4781	−	7.13739i	−1.29700	−	0.228697i
$975$	−5.45801	−	4.31393i	−0.174796	−	0.138156i
$976$	1.19180	+	2.06425i	0.0381485	+	0.0660751i
$977$	−25.3477	+	43.9034i	−0.810944	+	1.40460i	0.101261	+	0.994860i	$0.467712\pi$
$977$	−25.3477	+	43.9034i	−0.810944	+	1.40460i	−0.912204	+	0.409735i	$0.865621\pi$
$978$	−2.03624	−	5.12264i	−0.0651116	−	0.163804i
$979$	5.99904	+	7.14938i	0.191730	+	0.228495i
$980$	3.57211	+	2.06236i	0.114107	+	0.0658797i
$981$	−57.5545	−	6.70470i	−1.83758	−	0.214065i
$982$	6.07581	−	16.6931i	0.193887	−	0.532700i
$983$	−6.29561	+	35.7042i	−0.200799	+	1.13879i	0.703116	+	0.711075i	$0.251791\pi$
$983$	−6.29561	+	35.7042i	−0.200799	+	1.13879i	−0.903915	+	0.427712i	$0.859320\pi$
$984$	−4.31147	−	0.630690i	−0.137445	−	0.0201056i
$985$	2.63842	−	0.960307i	0.0840671	−	0.0305979i
$986$	7.84347	−	9.34748i	0.249787	−	0.297684i
$987$	−1.31005	−	0.433823i	−0.0416994	−	0.0138088i
$988$	−16.6152	+	5.51972i	−0.528600	+	0.175606i
$989$		−	29.6907i		−	0.944109i
$990$	1.98723	+	8.37044i	0.0631584	+	0.266030i
$991$	−10.9478	−	30.0787i	−0.347767	−	0.955483i	−0.983072	−	0.183221i	$-0.941348\pi$
$991$	−10.9478	−	30.0787i	−0.347767	−	0.955483i	0.635304	−	0.772262i	$-0.280875\pi$
$992$	0.748004	−	0.131893i	0.0237492	−	0.00418762i
$993$	18.6246	−	34.5575i	0.591035	−	1.09665i
$994$	−2.95412	−	1.07521i	−0.0936992	−	0.0341037i
$995$	8.94530	−	5.16457i	0.283585	−	0.163728i
$996$	0.518602	−	0.461695i	0.0164325	−	0.0146294i
$997$	−41.5102	+	34.8312i	−1.31464	+	1.10311i	−0.327229	+	0.944945i	$0.606115\pi$
$997$	−41.5102	+	34.8312i	−1.31464	+	1.10311i	−0.987412	+	0.158169i	$0.949441\pi$
$998$	12.9519	−	10.8680i	0.409986	−	0.344019i
$999$	36.5581	−	3.21969i	1.15665	−	0.101866i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bb.b.41.7	yes	84
3.2	odd	2		570.2.bb.a.41.11	✓	84
19.13	odd	18		570.2.bb.a.431.11	yes	84
57.32	even	18	inner	570.2.bb.b.431.7	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bb.a.41.11	✓	84	3.2	odd	2
570.2.bb.a.431.11	yes	84	19.13	odd	18
570.2.bb.b.41.7	yes	84	1.1	even	1	trivial
570.2.bb.b.431.7	yes	84	57.32	even	18	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.bb (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 - 0.642788i) q^{2} +(0.0507095 + 1.73131i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.984808 + 0.173648i) q^{5} +(1.07402 - 1.35885i) q^{6} +(0.847833 + 1.46849i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.99486 + 0.175587i) q^{9} +O(q^{10})\)	\(q+(-0.766044 - 0.642788i) q^{2} +(0.0507095 + 1.73131i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.984808 + 0.173648i) q^{5} +(1.07402 - 1.35885i) q^{6} +(0.847833 + 1.46849i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.99486 + 0.175587i) q^{9} +(-0.642788 - 0.766044i) q^{10} +(2.48350 + 1.43385i) q^{11} +(-1.69620 + 0.350578i) q^{12} +(-1.37377 + 3.77439i) q^{13} +(0.294449 - 1.66990i) q^{14} +(-0.250699 + 1.71381i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(1.41017 - 1.68058i) q^{17} +(2.40706 + 1.79055i) q^{18} +(3.83513 - 2.07166i) q^{19} +1.00000i q^{20} +(-2.49941 + 1.54233i) q^{21} +(-0.980811 - 2.69476i) q^{22} +(-5.59374 + 0.986328i) q^{23} +(1.52471 + 0.821738i) q^{24} +(0.939693 + 0.342020i) q^{25} +(3.47850 - 2.00831i) q^{26} +(-0.455864 - 5.17612i) q^{27} +(-1.29895 + 1.08995i) q^{28} +(-4.26078 + 3.57522i) q^{29} +(1.29366 - 1.15171i) q^{30} +(0.657784 - 0.379772i) q^{31} +(0.939693 + 0.342020i) q^{32} +(-2.35650 + 4.37241i) q^{33} +(-2.16051 + 0.380957i) q^{34} +(0.579952 + 1.59340i) q^{35} +(-0.692971 - 2.91887i) q^{36} +7.06283i q^{37} +(-4.26952 - 0.878196i) q^{38} +(-6.60430 - 2.18702i) q^{39} +(0.642788 - 0.766044i) q^{40} +(-2.36400 + 0.860427i) q^{41} +(2.90605 + 0.425102i) q^{42} +(-0.907694 + 5.14779i) q^{43} +(-0.980811 + 2.69476i) q^{44} +(-2.97985 - 0.347132i) q^{45} +(4.91906 + 2.84002i) q^{46} +(0.302030 + 0.359945i) q^{47} +(-0.639794 - 1.60955i) q^{48} +(2.06236 - 3.57211i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(2.98111 + 2.35623i) q^{51} +(-3.95560 - 0.697479i) q^{52} +(2.36349 + 13.4040i) q^{53} +(-2.97793 + 4.25816i) q^{54} +(2.19679 + 1.84332i) q^{55} +1.69567 q^{56} +(3.78115 + 6.53475i) q^{57} +5.56205 q^{58} +(-1.73040 - 1.45198i) q^{59} +(-1.73131 + 0.0507095i) q^{60} +(-0.413907 - 2.34738i) q^{61} +(-0.748004 - 0.131893i) q^{62} +(-2.79699 - 4.24905i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-2.00831 + 3.47850i) q^{65} +(4.61572 - 1.83474i) q^{66} +(-0.208994 - 0.249070i) q^{67} +(1.89992 + 1.09692i) q^{68} +(-1.99129 - 9.63448i) q^{69} +(0.579952 - 1.59340i) q^{70} +(0.321939 - 1.82581i) q^{71} +(-1.34537 + 2.68142i) q^{72} +(13.1053 - 4.76996i) q^{73} +(4.53990 - 5.41044i) q^{74} +(-0.544491 + 1.64424i) q^{75} +(2.70615 + 3.41713i) q^{76} +4.86266i q^{77} +(3.65340 + 5.92051i) q^{78} +(-4.21257 - 11.5739i) q^{79} +(-0.984808 + 0.173648i) q^{80} +(8.93834 - 1.05172i) q^{81} +(2.36400 + 0.860427i) q^{82} +(-0.347171 + 0.200439i) q^{83} +(-1.95291 - 2.19362i) q^{84} +(1.68058 - 1.41017i) q^{85} +(4.00427 - 3.35998i) q^{86} +(-6.40587 - 7.19543i) q^{87} +(2.48350 - 1.43385i) q^{88} +(3.05820 + 1.11309i) q^{89} +(2.05956 + 2.18133i) q^{90} +(-6.70738 + 1.18269i) q^{91} +(-1.94269 - 5.33749i) q^{92} +(0.690858 + 1.11957i) q^{93} -0.469875i q^{94} +(4.13661 - 1.37422i) q^{95} +(-0.544491 + 1.64424i) q^{96} +(-5.17546 + 6.16787i) q^{97} +(-3.87597 + 1.41074i) q^{98} +(-7.68949 - 3.85810i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 6 q^{6} + 42 q^{8}+O(q^{10}) \) 84 * q - 6 * q^6 + 42 * q^8	\( 84 q - 6 q^{6} + 42 q^{8} + 24 q^{13} - 24 q^{14} + 12 q^{17} - 12 q^{19} + 36 q^{22} + 24 q^{27} - 12 q^{28} - 12 q^{29} + 36 q^{33} + 12 q^{34} + 6 q^{36} + 18 q^{38} + 12 q^{39} + 6 q^{41} + 24 q^{43} + 36 q^{44} + 12 q^{47} - 12 q^{48} - 54 q^{49} - 42 q^{50} + 96 q^{51} + 12 q^{52} - 60 q^{53} - 18 q^{54} - 96 q^{57} - 24 q^{58} - 18 q^{59} - 48 q^{61} - 12 q^{62} - 114 q^{63} - 42 q^{64} - 24 q^{66} + 6 q^{67} - 54 q^{68} - 48 q^{69} + 48 q^{71} + 84 q^{73} + 24 q^{74} - 12 q^{79} - 36 q^{81} - 6 q^{82} + 36 q^{83} + 18 q^{84} + 12 q^{86} + 6 q^{87} - 12 q^{89} - 24 q^{90} + 24 q^{91} - 6 q^{93} - 12 q^{95} - 42 q^{97} + 36 q^{98} - 6 q^{99}+O(q^{100}) \) 84 * q - 6 * q^6 + 42 * q^8 + 24 * q^13 - 24 * q^14 + 12 * q^17 - 12 * q^19 + 36 * q^22 + 24 * q^27 - 12 * q^28 - 12 * q^29 + 36 * q^33 + 12 * q^34 + 6 * q^36 + 18 * q^38 + 12 * q^39 + 6 * q^41 + 24 * q^43 + 36 * q^44 + 12 * q^47 - 12 * q^48 - 54 * q^49 - 42 * q^50 + 96 * q^51 + 12 * q^52 - 60 * q^53 - 18 * q^54 - 96 * q^57 - 24 * q^58 - 18 * q^59 - 48 * q^61 - 12 * q^62 - 114 * q^63 - 42 * q^64 - 24 * q^66 + 6 * q^67 - 54 * q^68 - 48 * q^69 + 48 * q^71 + 84 * q^73 + 24 * q^74 - 12 * q^79 - 36 * q^81 - 6 * q^82 + 36 * q^83 + 18 * q^84 + 12 * q^86 + 6 * q^87 - 12 * q^89 - 24 * q^90 + 24 * q^91 - 6 * q^93 - 12 * q^95 - 42 * q^97 + 36 * q^98 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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