LMFDB - Embedded newform 336.2.bo.a.173.48

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(5,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 6, 10]))

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

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

chi := DirichletCharacter("336.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.bo (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$60$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			173.48
Character	$\chi$	$=$	336.173
Dual form			336.2.bo.a.101.48

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.16732 + 0.798357i) q^{2} +(1.06648 - 1.36478i) q^{3} +(0.725251 + 1.86387i) q^{4} +(0.729016 + 2.72073i) q^{5} +(2.33450 - 0.741703i) q^{6} +(0.617966 - 2.57257i) q^{7} +(-0.641437 + 2.75473i) q^{8} +(-0.725259 - 2.91101i) q^{9} +O(q^{10})$	\(q+(1.16732 + 0.798357i) q^{2} +(1.06648 - 1.36478i) q^{3} +(0.725251 + 1.86387i) q^{4} +(0.729016 + 2.72073i) q^{5} +(2.33450 - 0.741703i) q^{6} +(0.617966 - 2.57257i) q^{7} +(-0.641437 + 2.75473i) q^{8} +(-0.725259 - 2.91101i) q^{9} +(-1.32112 + 3.75796i) q^{10} +(-0.126836 + 0.473358i) q^{11} +(3.31724 + 0.997962i) q^{12} +(-1.61659 + 1.61659i) q^{13} +(2.77519 - 2.50964i) q^{14} +(4.49068 + 1.90664i) q^{15} +(-2.94802 + 2.70355i) q^{16} +(0.919117 + 1.59196i) q^{17} +(1.47742 - 3.97709i) q^{18} +(-2.02262 - 7.54853i) q^{19} +(-4.54236 + 3.33200i) q^{20} +(-2.85195 - 3.58697i) q^{21} +(-0.525966 + 0.451297i) q^{22} +(-1.49868 + 2.59579i) q^{23} +(3.07553 + 3.81328i) q^{24} +(-2.54076 + 1.46691i) q^{25} +(-3.17769 + 0.596454i) q^{26} +(-4.74637 - 2.11470i) q^{27} +(5.24312 - 0.713952i) q^{28} +(-2.89744 + 2.89744i) q^{29} +(3.71986 + 5.81081i) q^{30} +(9.09536 - 5.25121i) q^{31} +(-5.59967 + 0.802318i) q^{32} +(0.510763 + 0.677928i) q^{33} +(-0.198051 + 2.59210i) q^{34} +(7.44977 - 0.194130i) q^{35} +(4.89975 - 3.46300i) q^{36} +(-0.460312 - 1.71791i) q^{37} +(3.66539 - 10.4263i) q^{38} +(0.482239 + 3.93035i) q^{39} +(-7.96249 + 0.263071i) q^{40} -6.10153i q^{41} +(-0.465443 - 6.46401i) q^{42} +(-6.34740 + 6.34740i) q^{43} +(-0.974265 + 0.106898i) q^{44} +(7.39134 - 4.09541i) q^{45} +(-3.82180 + 1.83363i) q^{46} +(-0.607881 + 1.05288i) q^{47} +(0.545759 + 6.90667i) q^{48} +(-6.23624 - 3.17952i) q^{49} +(-4.13698 - 0.316089i) q^{50} +(3.15289 + 0.443389i) q^{51} +(-4.18555 - 1.84068i) q^{52} +(0.913867 - 3.41060i) q^{53} +(-3.85222 - 6.25783i) q^{54} -1.38034 q^{55} +(6.69036 + 3.35247i) q^{56} +(-12.4592 - 5.28989i) q^{57} +(-5.69542 + 1.06904i) q^{58} +(-3.84178 - 1.02940i) q^{59} +(-0.296860 + 9.75283i) q^{60} +(1.66094 + 6.19872i) q^{61} +(14.8095 + 1.13153i) q^{62} +(-7.93697 + 0.0668744i) q^{63} +(-7.17712 - 3.53398i) q^{64} +(-5.57682 - 3.21978i) q^{65} +(0.0549927 + 1.19913i) q^{66} +(-0.532520 + 1.98739i) q^{67} +(-2.30061 + 2.86768i) q^{68} +(1.94438 + 4.81372i) q^{69} +(8.85121 + 5.72096i) q^{70} -4.11592 q^{71} +(8.48428 - 0.130664i) q^{72} +(-2.86263 - 4.95823i) q^{73} +(0.834176 - 2.37284i) q^{74} +(-0.707648 + 5.03200i) q^{75} +(12.6026 - 9.24449i) q^{76} +(1.13937 + 0.618813i) q^{77} +(-2.57490 + 4.97296i) q^{78} +(-4.97869 + 8.62335i) q^{79} +(-9.50477 - 6.04983i) q^{80} +(-7.94800 + 4.22248i) q^{81} +(4.87120 - 7.12241i) q^{82} +(9.94175 + 9.94175i) q^{83} +(4.61727 - 7.91712i) q^{84} +(-3.66123 + 3.66123i) q^{85} +(-12.4769 + 2.34192i) q^{86} +(0.864325 + 7.04443i) q^{87} +(-1.22262 - 0.653028i) q^{88} +(-12.6823 - 7.32215i) q^{89} +(11.8976 + 1.12030i) q^{90} +(3.15980 + 5.15779i) q^{91} +(-5.92514 - 0.910746i) q^{92} +(2.53323 - 18.0135i) q^{93} +(-1.55016 + 0.743738i) q^{94} +(19.0630 - 11.0060i) q^{95} +(-4.87692 + 8.49798i) q^{96} +1.90345i q^{97} +(-4.74126 - 8.69025i) q^{98} +(1.46994 + 0.0259136i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 6 q^{3} - 4 q^{4}+O(q^{10}) $ 240 * q - 6 * q^3 - 4 * q^4	$ 240 q - 6 q^{3} - 4 q^{4} - 12 q^{10} - 6 q^{12} - 16 q^{15} - 20 q^{16} - 4 q^{18} - 12 q^{19} + 2 q^{21} - 40 q^{22} - 6 q^{24} - 12 q^{28} + 22 q^{30} - 24 q^{31} - 12 q^{33} - 64 q^{36} - 4 q^{37} + 48 q^{40} - 18 q^{42} - 16 q^{43} - 6 q^{45} + 12 q^{46} - 16 q^{49} - 10 q^{51} - 48 q^{52} - 90 q^{54} - 4 q^{58} - 18 q^{60} - 12 q^{61} - 36 q^{63} + 32 q^{64} - 66 q^{66} - 36 q^{67} - 76 q^{70} - 46 q^{72} + 24 q^{75} - 76 q^{78} - 8 q^{79} - 4 q^{81} + 72 q^{82} - 24 q^{84} + 24 q^{85} + 12 q^{88} - 88 q^{91} - 14 q^{93} + 24 q^{94} + 96 q^{96} + 28 q^{99}+O(q^{100}) $ 240 * q - 6 * q^3 - 4 * q^4 - 12 * q^10 - 6 * q^12 - 16 * q^15 - 20 * q^16 - 4 * q^18 - 12 * q^19 + 2 * q^21 - 40 * q^22 - 6 * q^24 - 12 * q^28 + 22 * q^30 - 24 * q^31 - 12 * q^33 - 64 * q^36 - 4 * q^37 + 48 * q^40 - 18 * q^42 - 16 * q^43 - 6 * q^45 + 12 * q^46 - 16 * q^49 - 10 * q^51 - 48 * q^52 - 90 * q^54 - 4 * q^58 - 18 * q^60 - 12 * q^61 - 36 * q^63 + 32 * q^64 - 66 * q^66 - 36 * q^67 - 76 * q^70 - 46 * q^72 + 24 * q^75 - 76 * q^78 - 8 * q^79 - 4 * q^81 + 72 * q^82 - 24 * q^84 + 24 * q^85 + 12 * q^88 - 88 * q^91 - 14 * q^93 + 24 * q^94 + 96 * q^96 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	1.16732	+	0.798357i	0.825417	+	0.564524i
$2$	1.16732	+	0.798357i	0.825417	+	0.564524i
$3$	1.06648	−	1.36478i	0.615730	−	0.787957i
$3$	1.06648	−	1.36478i	0.615730	−	0.787957i
$4$	0.725251	+	1.86387i	0.362626	+	0.931935i
$5$	0.729016	+	2.72073i	0.326026	+	1.21675i	0.913276	+	0.407340i	$0.133544\pi$
$5$	0.729016	+	2.72073i	0.326026	+	1.21675i	−0.587250	+	0.809405i	$0.699790\pi$
$6$	2.33450	−	0.741703i	0.953055	−	0.302799i
$7$	0.617966	−	2.57257i	0.233569	−	0.972340i
$7$	0.617966	−	2.57257i	0.233569	−	0.972340i
$8$	−0.641437	+	2.75473i	−0.226782	+	0.973945i
$9$	−0.725259	−	2.91101i	−0.241753	−	0.970338i
$10$	−1.32112	+	3.75796i	−0.417775	+	1.18837i
$11$	−0.126836	+	0.473358i	−0.0382424	+	0.142723i	−0.982407	−	0.186750i	$-0.940204\pi$
$11$	−0.126836	+	0.473358i	−0.0382424	+	0.142723i	0.944165	+	0.329473i	$0.106871\pi$
$12$	3.31724	+	0.997962i	0.957604	+	0.288087i
$13$	−1.61659	+	1.61659i	−0.448362	+	0.448362i	−0.894810	−	0.446448i	$-0.852689\pi$
$13$	−1.61659	+	1.61659i	−0.448362	+	0.448362i	0.446448	+	0.894810i	$0.352689\pi$
$14$	2.77519	−	2.50964i	0.741701	−	0.670731i
$15$	4.49068	+	1.90664i	1.15949	+	0.492292i
$16$	−2.94802	+	2.70355i	−0.737005	+	0.675887i
$17$	0.919117	+	1.59196i	0.222919	+	0.386106i	0.955693	−	0.294365i	$-0.0951083\pi$
$17$	0.919117	+	1.59196i	0.222919	+	0.386106i	−0.732774	+	0.680472i	$0.761775\pi$
$18$	1.47742	−	3.97709i	0.348232	−	0.937408i
$19$	−2.02262	−	7.54853i	−0.464022	−	1.73175i	−0.660113	−	0.751166i	$-0.729492\pi$
$19$	−2.02262	−	7.54853i	−0.464022	−	1.73175i	0.196091	−	0.980586i	$-0.437175\pi$
$20$	−4.54236	+	3.33200i	−1.01570	+	0.745058i
$21$	−2.85195	−	3.58697i	−0.622347	−	0.782741i
$22$	−0.525966	+	0.451297i	−0.112136	+	0.0962169i
$23$	−1.49868	+	2.59579i	−0.312497	+	0.541260i	−0.978902	−	0.204329i	$-0.934499\pi$
$23$	−1.49868	+	2.59579i	−0.312497	+	0.541260i	0.666406	+	0.745589i	$0.267832\pi$
$24$	3.07553	+	3.81328i	0.627791	+	0.778382i
$25$	−2.54076	+	1.46691i	−0.508151	+	0.293381i
$26$	−3.17769	+	0.596454i	−0.623196	+	0.116974i
$27$	−4.74637	−	2.11470i	−0.913439	−	0.406975i
$28$	5.24312	−	0.713952i	0.990856	−	0.134924i
$29$	−2.89744	+	2.89744i	−0.538042	+	0.538042i	−0.922953	−	0.384912i	$-0.874232\pi$
$29$	−2.89744	+	2.89744i	−0.538042	+	0.538042i	0.384912	+	0.922953i	$0.374232\pi$
$30$	3.71986	+	5.81081i	0.679150	+	1.06090i
$31$	9.09536	−	5.25121i	1.63357	−	0.943145i	0.650597	−	0.759423i	$-0.274519\pi$
$31$	9.09536	−	5.25121i	1.63357	−	0.943145i	0.982978	−	0.183721i	$-0.0588145\pi$
$32$	−5.59967	+	0.802318i	−0.989891	+	0.141831i
$33$	0.510763	+	0.677928i	0.0889124	+	0.118012i
$34$	−0.198051	+	2.59210i	−0.0339655	+	0.444541i
$35$	7.44977	−	0.194130i	1.25924	−	0.0328140i
$36$	4.89975	−	3.46300i	0.816626	−	0.577167i
$37$	−0.460312	−	1.71791i	−0.0756749	−	0.282423i	0.917711	−	0.397250i	$-0.130035\pi$
$37$	−0.460312	−	1.71791i	−0.0756749	−	0.282423i	−0.993385	+	0.114827i	$0.963369\pi$
$38$	3.66539	−	10.4263i	0.594604	−	1.69137i
$39$	0.482239	+	3.93035i	0.0772201	+	0.629359i
$40$	−7.96249	+	0.263071i	−1.25898	+	0.0415952i
$41$		−	6.10153i		−	0.952899i	−0.879202	−	0.476449i	$-0.841924\pi$
$41$		−	6.10153i		−	0.952899i	0.879202	−	0.476449i	$-0.158076\pi$
$42$	−0.465443	−	6.46401i	−0.0718193	−	0.997418i
$43$	−6.34740	+	6.34740i	−0.967969	+	0.967969i	−0.999503	−	0.0315339i	$-0.989961\pi$
$43$	−6.34740	+	6.34740i	−0.967969	+	0.967969i	0.0315339	+	0.999503i	$0.489961\pi$
$44$	−0.974265	+	0.106898i	−0.146876	+	0.0161154i
$45$	7.39134	−	4.09541i	1.10184	−	0.610507i
$46$	−3.82180	+	1.83363i	−0.563494	+	0.270353i
$47$	−0.607881	+	1.05288i	−0.0886686	+	0.153579i	−0.906949	−	0.421241i	$-0.861595\pi$
$47$	−0.607881	+	1.05288i	−0.0886686	+	0.153579i	0.818280	+	0.574820i	$0.194928\pi$
$48$	0.545759	+	6.90667i	0.0787736	+	0.996893i
$49$	−6.23624	−	3.17952i	−0.890891	−	0.454217i
$50$	−4.13698	−	0.316089i	−0.585057	−	0.0447017i
$51$	3.15289	+	0.443389i	0.441493	+	0.0620869i
$52$	−4.18555	−	1.84068i	−0.580431	−	0.255256i
$53$	0.913867	−	3.41060i	0.125529	−	0.468481i	−0.874329	−	0.485334i	$-0.838698\pi$
$53$	0.913867	−	3.41060i	0.125529	−	0.468481i	0.999858	+	0.0168527i	$0.00536463\pi$
$54$	−3.85222	−	6.25783i	−0.524221	−	0.851582i
$55$	−1.38034			−0.186125
$56$	6.69036	+	3.35247i	0.894037	+	0.447993i
$57$	−12.4592	−	5.28989i	−1.65026	−	0.700663i
$58$	−5.69542	+	1.06904i	−0.747846	+	0.140371i
$59$	−3.84178	−	1.02940i	−0.500157	−	0.134017i	−8.42898e−5	−	1.00000i	$-0.500027\pi$
$59$	−3.84178	−	1.02940i	−0.500157	−	0.134017i	−0.500073	+	0.865983i	$0.666693\pi$
$60$	−0.296860	+	9.75283i	−0.0383245	+	1.25908i
$61$	1.66094	+	6.19872i	0.212662	+	0.793665i	0.986977	+	0.160864i	$0.0514281\pi$
$61$	1.66094	+	6.19872i	0.212662	+	0.793665i	−0.774315	+	0.632801i	$0.781905\pi$
$62$	14.8095	+	1.13153i	1.88081	+	0.143704i
$63$	−7.93697	+	0.0668744i	−0.999965	+	0.00842538i
$64$	−7.17712	−	3.53398i	−0.897140	−	0.441747i
$65$	−5.57682	−	3.21978i	−0.691720	−	0.399364i
$66$	0.0549927	+	1.19913i	0.00676914	+	0.147602i
$67$	−0.532520	+	1.98739i	−0.0650577	+	0.242799i	−0.990795	−	0.135367i	$-0.956779\pi$
$67$	−0.532520	+	1.98739i	−0.0650577	+	0.242799i	0.925738	+	0.378166i	$0.123445\pi$
$68$	−2.30061	+	2.86768i	−0.278990	+	0.347758i
$69$	1.94438	+	4.81372i	0.234076	+	0.579504i
$70$	8.85121	+	5.72096i	1.05792	+	0.683786i
$71$	−4.11592			−0.488470			−0.244235	−	0.969716i	$-0.578537\pi$
$71$	−4.11592			−0.488470			−0.244235	+	0.969716i	$0.578537\pi$
$72$	8.48428	−	0.130664i	0.999881	−	0.0153989i
$73$	−2.86263	−	4.95823i	−0.335046	−	0.580316i	0.648448	−	0.761259i	$-0.275418\pi$
$73$	−2.86263	−	4.95823i	−0.335046	−	0.580316i	−0.983494	+	0.180943i	$0.942085\pi$
$74$	0.834176	−	2.37284i	0.0969709	−	0.275837i
$75$	−0.707648	+	5.03200i	−0.0817121	+	0.581045i
$76$	12.6026	−	9.24449i	1.44561	−	1.06042i
$77$	1.13937	+	0.618813i	0.129843	+	0.0705203i
$78$	−2.57490	+	4.97296i	−0.291550	+	0.563076i
$79$	−4.97869	+	8.62335i	−0.560147	+	0.970203i	0.437336	+	0.899298i	$0.355922\pi$
$79$	−4.97869	+	8.62335i	−0.560147	+	0.970203i	−0.997483	+	0.0709047i	$0.977411\pi$
$80$	−9.50477	−	6.04983i	−1.06267	−	0.676391i
$81$	−7.94800	+	4.22248i	−0.883111	+	0.469164i
$82$	4.87120	−	7.12241i	0.537934	−	0.786539i
$83$	9.94175	+	9.94175i	1.09125	+	1.09125i	0.995395	+	0.0958536i	$0.0305581\pi$
$83$	9.94175	+	9.94175i	1.09125	+	1.09125i	0.0958536	+	0.995395i	$0.469442\pi$
$84$	4.61727	−	7.91712i	0.503785	−	0.863829i
$85$	−3.66123	+	3.66123i	−0.397116	+	0.397116i
$86$	−12.4769	+	2.34192i	−1.34542	+	0.252536i
$87$	0.864325	+	7.04443i	0.0926654	+	0.755242i
$88$	−1.22262	−	0.653028i	−0.130331	−	0.0696130i
$89$	−12.6823	−	7.32215i	−1.34433	−	0.776147i	−0.356887	−	0.934148i	$-0.616162\pi$
$89$	−12.6823	−	7.32215i	−1.34433	−	0.776147i	−0.987439	+	0.158001i	$0.949495\pi$
$90$	11.8976	+	1.12030i	1.25412	+	0.118090i
$91$	3.15980	+	5.15779i	0.331237	+	0.540683i
$92$	−5.92514	−	0.910746i	−0.617738	−	0.0949518i
$93$	2.53323	−	18.0135i	0.262683	−	1.86791i
$94$	−1.55016	+	0.743738i	−0.159887	+	0.0767107i
$95$	19.0630	−	11.0060i	1.95582	−	1.12919i
$96$	−4.87692	+	8.49798i	−0.497749	+	0.867321i
$97$			1.90345i			0.193266i	0.995320	+	0.0966332i	$0.0308074\pi$
$97$			1.90345i			0.193266i	−0.995320	+	0.0966332i	$0.969193\pi$
$98$	−4.74126	−	8.69025i	−0.478940	−	0.877848i
$99$	1.46994	+	0.0259136i	0.147734	+	0.00260442i
$100$	−4.57681	−	3.67176i	−0.457681	−	0.367176i
$101$	12.9663	+	3.47431i	1.29020	+	0.345707i	0.837735	−	0.546077i	$-0.183879\pi$
$101$	12.9663	+	3.47431i	1.29020	+	0.345707i	0.452461	+	0.891784i	$0.350546\pi$
$102$	3.32643	+	3.03471i	0.329366	+	0.300481i
$103$	9.51505	−	16.4805i	0.937546	−	1.62388i	0.167515	−	0.985869i	$-0.446426\pi$
$103$	9.51505	−	16.4805i	0.937546	−	1.62388i	0.770030	−	0.638007i	$-0.220241\pi$
$104$	−3.41634	−	5.49022i	−0.334999	−	0.538360i
$105$	7.68005	−	10.3743i	0.749496	−	1.01243i
$106$	3.78965	−	3.25165i	0.368083	−	0.315828i
$107$	11.3816	−	3.04970i	1.10030	−	0.294825i	0.337415	−	0.941356i	$-0.390448\pi$
$107$	11.3816	−	3.04970i	1.10030	−	0.294825i	0.762888	+	0.646531i	$0.223781\pi$
$108$	0.499223	−	10.3803i	0.0480377	−	0.998846i
$109$	−3.70624	+	13.8319i	−0.354994	+	1.32486i	0.525498	+	0.850795i	$0.323879\pi$
$109$	−3.70624	+	13.8319i	−0.354994	+	1.32486i	−0.880492	+	0.474061i	$0.842788\pi$
$110$	−1.61129	−	1.10201i	−0.153631	−	0.105072i
$111$	−2.83548	−	1.20388i	−0.269132	−	0.114267i
$112$	5.13329	+	9.25469i	0.485050	+	0.874486i
$113$		−	9.34533i		−	0.879135i	−0.898210	−	0.439568i	$-0.855132\pi$
$113$		−	9.34533i		−	0.879135i	0.898210	−	0.439568i	$-0.144868\pi$
$114$	−10.3206	−	16.1218i	−0.966610	−	1.50995i
$115$	−8.15500	−	2.18513i	−0.760458	−	0.203764i
$116$	−7.50183	−	3.29908i	−0.696527	−	0.306312i
$117$	5.87836	+	3.53347i	0.543455	+	0.326669i
$118$	−3.66274	−	4.26875i	−0.337183	−	0.392970i
$119$	4.66340	−	1.38072i	0.427494	−	0.126570i
$120$	−8.13277	+	11.1476i	−0.742417	+	1.01763i
$121$	9.31830	+	5.37992i	0.847118	+	0.489084i
$122$	−3.00995	+	8.56189i	−0.272508	+	0.775157i
$123$	−8.32726	−	6.50713i	−0.750844	−	0.586728i
$124$	16.3840	+	13.1441i	1.47133	+	1.18038i
$125$	4.11524	+	4.11524i	0.368079	+	0.368079i
$126$	−9.31834	−	6.25848i	−0.830144	−	0.557549i
$127$	15.7494			1.39753			0.698766	−	0.715350i	$-0.253733\pi$
$127$	15.7494			1.39753			0.698766	+	0.715350i	$0.253733\pi$
$128$	−5.55658	−	9.85517i	−0.491137	−	0.871082i
$129$	1.89347	+	15.4322i	0.166711	+	1.35873i
$130$	−3.93938	−	8.21079i	−0.345506	−	0.720134i
$131$	−10.4023	+	2.78729i	−0.908853	+	0.243526i	−0.682814	−	0.730592i	$-0.739244\pi$
$131$	−10.4023	+	2.78729i	−0.908853	+	0.243526i	−0.226039	+	0.974118i	$0.572578\pi$
$132$	−0.893138	+	1.44366i	−0.0777376	+	0.125655i
$133$	−20.6690	+	0.538606i	−1.79223	+	0.0467031i
$134$	−2.20827	+	1.89477i	−0.190765	+	0.163683i
$135$	2.29335	−	14.4552i	0.197380	−	1.24411i
$136$	−4.97497	+	1.51078i	−0.426600	+	0.129548i
$137$	7.93476	+	13.7434i	0.677912	+	1.17418i	0.975609	+	0.219517i	$0.0704482\pi$
$137$	7.93476	+	13.7434i	0.677912	+	1.17418i	−0.297697	+	0.954660i	$0.596218\pi$
$138$	−1.57336	+	7.17145i	−0.133933	+	0.610474i
$139$	7.46731	+	7.46731i	0.633369	+	0.633369i	0.948911	−	0.315542i	$-0.102186\pi$
$139$	7.46731	+	7.46731i	0.633369	+	0.633369i	−0.315542	+	0.948911i	$0.602186\pi$
$140$	5.76478	+	13.7446i	0.487213	+	1.16163i
$141$	0.788663	+	1.95250i	0.0664174	+	0.164430i
$142$	−4.80458	−	3.28598i	−0.403192	−	0.275753i
$143$	−0.560184	−	0.970267i	−0.0468449	−	0.0811378i
$144$	10.0081	+	6.62096i	0.834012	+	0.551746i
$145$	−9.99543	−	5.77086i	−0.830075	−	0.479244i
$146$	0.616840	−	8.07322i	0.0510500	−	0.668144i
$147$	−10.9901	+	5.12022i	−0.906452	+	0.422309i
$148$	2.86812	−	2.10388i	0.235758	−	0.172938i
$149$	0.668648	−	0.179164i	0.0547778	−	0.0146777i	−0.231326	−	0.972876i	$-0.574306\pi$
$149$	0.668648	−	0.179164i	0.0547778	−	0.0146777i	0.286104	+	0.958199i	$0.407640\pi$
$150$	−4.84338	+	5.30898i	−0.395460	+	0.433476i
$151$	0.0758742	−	0.0438060i	0.00617455	−	0.00356488i	−0.496910	−	0.867802i	$-0.665532\pi$
$151$	0.0758742	−	0.0438060i	0.00617455	−	0.00356488i	0.503084	+	0.864237i	$0.332199\pi$
$152$	22.0916	−	0.729879i	1.79186	−	0.0592010i
$153$	3.96761	−	3.83014i	0.320762	−	0.309649i
$154$	0.835965	+	1.63197i	0.0673640	+	0.131508i
$155$	20.9178	+	20.9178i	1.68016	+	1.68016i
$156$	−6.97591	+	3.74932i	−0.558520	+	0.300186i
$157$	3.30329	+	0.885113i	0.263631	+	0.0706397i	0.388213	−	0.921570i	$-0.373092\pi$
$157$	3.30329	+	0.885113i	0.263631	+	0.0706397i	−0.124582	+	0.992209i	$0.539759\pi$
$158$	−12.6962	+	6.09139i	−1.01006	+	0.484605i
$159$	−3.68010	−	4.88455i	−0.291851	−	0.387370i
$160$	−6.26514	−	14.6503i	−0.495303	−	1.15820i
$161$	5.75172	+	5.45957i	0.453299	+	0.430275i
$162$	−12.6489	−	1.41638i	−0.993789	−	0.111281i
$163$	10.7095	−	2.86960i	0.838832	−	0.224764i	0.186269	−	0.982499i	$-0.440360\pi$
$163$	10.7095	−	2.86960i	0.838832	−	0.224764i	0.652563	+	0.757734i	$0.273694\pi$
$164$	11.3725	−	4.42514i	0.888040	−	0.345546i
$165$	−1.47210	+	1.88387i	−0.114603	+	0.146659i
$166$	3.66809	+	19.5422i	0.284699	+	1.51677i
$167$			22.7064i			1.75708i	0.477671	+	0.878539i	$0.341481\pi$
$167$			22.7064i			1.75708i	−0.477671	+	0.878539i	$0.658519\pi$
$168$	11.7105	−	5.55555i	0.903485	−	0.428620i
$169$			7.77327i			0.597944i
$170$	−7.19678	+	1.35084i	−0.551967	+	0.103605i
$171$	−20.5070	+	11.3625i	−1.56821	+	0.868914i
$172$	−16.4342	−	7.22726i	−1.25309	−	0.551074i
$173$	3.45957	−	0.926989i	0.263026	−	0.0704777i	−0.124896	−	0.992170i	$-0.539860\pi$
$173$	3.45957	−	0.926989i	0.263026	−	0.0704777i	0.387922	+	0.921692i	$0.373193\pi$
$174$	−4.61503	+	8.91311i	−0.349865	+	0.675701i
$175$	2.20362	+	7.44277i	0.166578	+	0.562621i
$176$	−0.905830	−	1.73838i	−0.0682795	−	0.131035i
$177$	−5.50208	+	4.14536i	−0.413561	+	0.311584i
$178$	−8.95860	−	18.6723i	−0.671475	−	1.39955i
$179$	−19.8857	−	5.32836i	−1.48633	−	0.398260i	−0.577832	−	0.816156i	$-0.696101\pi$
$179$	−19.8857	−	5.32836i	−1.48633	−	0.398260i	−0.908495	+	0.417896i	$0.862768\pi$
$180$	12.9939	+	10.8063i	0.968507	+	0.805454i
$181$	5.51392	+	5.51392i	0.409846	+	0.409846i	0.881685	−	0.471839i	$-0.156410\pi$
$181$	5.51392	+	5.51392i	0.409846	+	0.409846i	−0.471839	+	0.881685i	$0.656410\pi$
$182$	−0.429282	+	8.54342i	−0.0318205	+	0.633280i
$183$	10.2313	+	4.34396i	0.756316	+	0.321115i
$184$	−6.18941	−	5.79351i	−0.456289	−	0.427103i
$185$	4.33838	−	2.50477i	0.318964	−	0.184154i
$186$	17.3383	−	19.0050i	1.27130	−	1.39351i
$187$	−0.870142	+	0.233154i	−0.0636311	+	0.0170499i
$188$	−2.40330	−	0.369408i	−0.175279	−	0.0269419i
$189$	−8.37332	+	10.9036i	−0.609069	+	0.793117i
$190$	31.0392	+	2.37157i	2.25182	+	0.172052i
$191$	−15.0476	−	8.68776i	−1.08881	−	0.628625i	−0.155550	−	0.987828i	$-0.549715\pi$
$191$	−15.0476	−	8.68776i	−1.08881	−	0.628625i	−0.933259	+	0.359203i	$0.883048\pi$
$192$	−12.4773	+	6.02630i	−0.900474	+	0.434911i
$193$	6.16296	+	10.6746i	0.443620	+	0.768372i	0.997955	−	0.0639218i	$-0.0203608\pi$
$193$	6.16296	+	10.6746i	0.443620	+	0.768372i	−0.554335	+	0.832293i	$0.687027\pi$
$194$	−1.51964	+	2.22193i	−0.109104	+	0.159525i
$195$	−10.3418	+	4.17733i	−0.740595	+	0.299145i
$196$	1.40338	−	13.9295i	0.100241	−	0.994963i
$197$	−4.71405	−	4.71405i	−0.335862	−	0.335862i	0.518946	−	0.854807i	$-0.326325\pi$
$197$	−4.71405	−	4.71405i	−0.335862	−	0.335862i	−0.854807	+	0.518946i	$0.826325\pi$
$198$	1.69519	+	1.20379i	0.120472	+	0.0855494i
$199$	−2.99274	−	5.18357i	−0.212150	−	0.367454i	0.740237	−	0.672346i	$-0.234713\pi$
$199$	−2.99274	−	5.18357i	−0.212150	−	0.367454i	−0.952387	+	0.304892i	$0.901380\pi$
$200$	−2.41120	−	7.94004i	−0.170498	−	0.561445i
$201$	2.14444	+	2.84628i	0.151257	+	0.200761i
$202$	12.3620	+	14.4074i	0.869789	+	1.01370i
$203$	5.66335	+	9.24439i	0.397490	+	0.648829i
$204$	1.46022	+	6.19814i	0.102236	+	0.433957i
$205$	16.6006	−	4.44812i	1.15944	−	0.310670i
$206$	24.2644	−	11.6416i	1.69058	−	0.811108i
$207$	8.64332	+	2.48006i	0.600752	+	0.172376i
$208$	0.395215	−	9.13627i	0.0274032	−	0.633487i
$209$	3.82970			0.264906
$210$	17.2475	−	5.97871i	1.19019	−	0.412570i
$211$	3.12823	+	3.12823i	0.215357	+	0.215357i	0.806538	−	0.591182i	$-0.201338\pi$
$211$	3.12823	+	3.12823i	0.215357	+	0.215357i	−0.591182	+	0.806538i	$0.701338\pi$
$212$	7.01969	−	0.770211i	0.482114	−	0.0528983i
$213$	−4.38953	+	5.61734i	−0.300766	+	0.384894i
$214$	15.7207	+	5.52664i	1.07464	+	0.377793i
$215$	−21.8969	−	12.6422i	−1.49335	−	0.862189i
$216$	8.86994	−	11.7185i	0.603523	−	0.797345i
$217$	−7.88848	−	26.6435i	−0.535505	−	1.80868i
$218$	−15.3692	+	13.1873i	−1.04093	+	0.893155i
$219$	−9.81983	−	1.38096i	−0.663562	−	0.0933164i
$220$	−1.00109	−	2.57278i	−0.0674938	−	0.173457i
$221$	−4.05938	−	1.08771i	−0.273063	−	0.0731671i
$222$	−2.34878	−	3.66904i	−0.157639	−	0.246250i
$223$		−	18.5643i		−	1.24316i	−0.783352	−	0.621579i	$-0.786492\pi$
$223$		−	18.5643i		−	1.24316i	0.783352	−	0.621579i	$-0.213508\pi$
$224$	−1.39638	+	14.9013i	−0.0932998	+	0.995638i
$225$	6.11289	+	6.33229i	0.407526	+	0.422153i
$226$	7.46092	−	10.9090i	0.496293	−	0.725653i
$227$	5.91349	−	22.0695i	0.392492	−	1.46480i	−0.433517	−	0.901145i	$-0.642728\pi$
$227$	5.91349	−	22.0695i	0.392492	−	1.46480i	0.826010	−	0.563656i	$-0.190606\pi$
$228$	0.823626	−	27.0588i	0.0545460	−	1.79201i
$229$	0.424470	−	0.113736i	0.0280497	−	0.00751591i	−0.244767	−	0.969582i	$-0.578711\pi$
$229$	0.424470	−	0.113736i	0.0280497	−	0.00751591i	0.272817	+	0.962066i	$0.412045\pi$
$230$	−7.77495	−	9.06134i	−0.512665	−	0.597487i
$231$	2.05965	−	0.895037i	0.135515	−	0.0588891i
$232$	−6.12315	−	9.84021i	−0.402005	−	0.646041i
$233$	−7.09072	+	12.2815i	−0.464528	+	0.804587i	−0.999180	−	0.0404856i	$-0.987109\pi$
$233$	−7.09072	+	12.2815i	−0.464528	+	0.804587i	0.534652	+	0.845073i	$0.320443\pi$
$234$	4.04094	+	8.81771i	0.264164	+	0.576432i
$235$	−3.30776	−	0.886311i	−0.215774	−	0.0578165i
$236$	−0.867584	−	7.90715i	−0.0564749	−	0.514712i
$237$	6.45934	+	15.9914i	0.419579	+	1.03875i
$238$	6.54597	+	2.11133i	0.424312	+	0.136857i
$239$			13.8034i			0.892868i	0.894816	+	0.446434i	$0.147306\pi$
$239$			13.8034i			0.892868i	−0.894816	+	0.446434i	$0.852694\pi$
$240$	−18.3933	+	6.51994i	−1.18728	+	0.420860i
$241$	1.99083	−	1.14941i	0.128241	−	0.0740399i	−0.434507	−	0.900668i	$-0.643077\pi$
$241$	1.99083	−	1.14941i	0.128241	−	0.0740399i	0.562748	+	0.826628i	$0.309744\pi$
$242$	6.58229	+	13.7194i	0.423126	+	0.881916i
$243$	−2.71358	+	15.3505i	−0.174076	+	0.984732i
$244$	−10.3490	+	7.59141i	−0.662527	+	0.485990i
$245$	4.10429	−	19.2850i	0.262213	−	1.23207i
$246$	−4.52552	−	14.2440i	−0.288537	−	0.908165i
$247$	15.4726	+	8.93313i	0.984501	+	0.568402i
$248$	8.63158	+	28.4236i	0.548106	+	1.80490i
$249$	24.1710	−	2.96569i	1.53177	−	0.187943i
$250$	1.51835	+	8.08922i	0.0960291	+	0.511607i
$251$	4.21799	−	4.21799i	0.266237	−	0.266237i	−0.561345	−	0.827582i	$-0.689716\pi$
$251$	4.21799	−	4.21799i	0.266237	−	0.266237i	0.827582	+	0.561345i	$0.189716\pi$
$252$	−5.88094	−	14.7450i	−0.370465	−	0.928847i
$253$	−1.03865	−	1.03865i	−0.0652995	−	0.0652995i
$254$	18.3845	+	12.5736i	1.15355	+	0.788941i
$255$	1.09217	+	8.90139i	0.0683942	+	0.557426i
$256$	1.38166	−	15.9402i	0.0863539	−	0.996265i
$257$	7.71764	−	13.3673i	0.481413	−	0.833832i	−0.518359	−	0.855163i	$-0.673457\pi$
$257$	7.71764	−	13.3673i	0.481413	−	0.833832i	0.999772	+	0.0213310i	$0.00679038\pi$
$258$	−10.1101	+	19.5259i	−0.629427	+	1.21563i
$259$	−4.70390	+	0.122577i	−0.292286	+	0.00761656i
$260$	1.95665	−	12.7296i	0.121346	−	0.789457i
$261$	10.5359	+	6.33310i	0.652155	+	0.392009i
$262$	−14.3680	−	5.05111i	−0.887659	−	0.312059i
$263$	−9.80895	−	16.9896i	−0.604846	−	1.04762i	−0.992076	−	0.125641i	$-0.959901\pi$
$263$	−9.80895	−	16.9896i	−0.604846	−	1.04762i	0.387230	−	0.921983i	$-0.373432\pi$
$264$	−2.19513	+	0.972167i	−0.135101	+	0.0598328i
$265$	9.94552			0.610948
$266$	−24.5573	−	15.8726i	−1.50570	−	0.973209i
$267$	−23.5186	+	9.49973i	−1.43931	+	0.581374i
$268$	−4.09045	+	0.448810i	−0.249864	+	0.0274155i
$269$	−5.02344	+	18.7477i	−0.306285	+	1.14307i	0.625549	+	0.780185i	$0.284875\pi$
$269$	−5.02344	+	18.7477i	−0.306285	+	1.14307i	−0.931834	+	0.362885i	$0.881792\pi$
$270$	14.2175	−	15.0429i	0.865249	−	0.915482i
$271$	2.16048	+	1.24735i	0.131240	+	0.0757713i	0.564182	−	0.825650i	$-0.309191\pi$
$271$	2.16048	+	1.24735i	0.131240	+	0.0757713i	−0.432943	+	0.901421i	$0.642525\pi$
$272$	−7.01351	−	2.20825i	−0.425256	−	0.133895i
$273$	10.4091	+	1.18823i	0.629988	+	0.0719147i
$274$	−1.70978	+	22.3777i	−0.103292	+	1.35188i
$275$	−0.372113	−	1.38874i	−0.0224392	−	0.0837443i
$276$	−7.56199	+	7.11523i	−0.455178	+	0.428287i
$277$	−3.44074	−	0.921943i	−0.206734	−	0.0553942i	0.153966	−	0.988076i	$-0.450795\pi$
$277$	−3.44074	−	0.921943i	−0.206734	−	0.0553942i	−0.360700	+	0.932682i	$0.617462\pi$
$278$	2.75513	+	14.6783i	0.165241	+	0.880345i
$279$	−21.8828	−	22.6682i	−1.31009	−	1.35711i
$280$	−4.24378	+	20.6466i	−0.253614	+	1.23387i
$281$	23.2099			1.38459			0.692295	−	0.721615i	$-0.256600\pi$
$281$	23.2099			1.38459			0.692295	+	0.721615i	$0.256600\pi$
$282$	−0.638173	+	2.90882i	−0.0380026	+	0.173217i
$283$	2.44522	−	9.12567i	0.145353	−	0.542465i	−0.854386	−	0.519638i	$-0.826067\pi$
$283$	2.44522	−	9.12567i	0.145353	−	0.542465i	0.999739	−	0.0228266i	$-0.00726656\pi$
$284$	−2.98508	−	7.67155i	−0.177132	−	0.455223i
$285$	5.30939	−	37.7544i	0.314501	−	2.23638i
$286$	0.120708	−	1.57983i	0.00713764	−	0.0934176i
$287$	−15.6966	−	3.77054i	−0.926542	−	0.222568i
$288$	6.39677	+	15.7188i	0.376933	+	0.926240i
$289$	6.81045	−	11.7960i	0.400615	−	0.693885i
$290$	−7.06061	−	14.7163i	−0.414613	−	0.864173i
$291$	2.59780	+	2.02999i	0.152286	+	0.119000i
$292$	7.16536	−	8.93153i	0.419321	−	0.522678i
$293$	−17.1560	+	17.1560i	−1.00227	+	1.00227i	−0.00226917	+	0.999997i	$0.500722\pi$
$293$	−17.1560	+	17.1560i	−1.00227	+	1.00227i	−0.999997	+	0.00226917i	$0.999278\pi$
$294$	−16.9167	−	2.79715i	−0.986604	−	0.163133i
$295$		−	11.2029i		−	0.652257i
$296$	5.02764	−	0.166107i	0.292226	−	0.00965478i
$297$	1.60302	−	1.97851i	0.0930167	−	0.114805i
$298$	0.923560	+	0.324679i	0.0535004	+	0.0188082i
$299$	−1.77358	−	6.61909i	−0.102569	−	0.382792i
$300$	−9.89221	+	2.33050i	−0.571127	+	0.134551i
$301$	12.4066	+	20.2516i	0.715107	+	1.16728i
$302$	0.123542	+	0.00943931i	0.00710904	+	0.000543171i
$303$	18.5699	−	13.9909i	1.06681	−	0.803757i
$304$	26.3706	+	16.7850i	1.51245	+	0.962685i
$305$	−15.6542	+	9.03794i	−0.896355	+	0.517511i
$306$	7.68928	−	1.30342i	0.439567	−	0.0745113i
$307$	0.664046	−	0.664046i	0.0378991	−	0.0378991i	−0.687903	−	0.725802i	$-0.741469\pi$
$307$	0.664046	−	0.664046i	0.0378991	−	0.0378991i	0.725802	+	0.687903i	$0.241469\pi$
$308$	−0.327060	+	2.57242i	−0.0186360	+	0.146577i
$309$	−12.3448	−	30.5621i	−0.702270	−	1.73862i
$310$	7.71778	+	41.1175i	0.438341	+	2.33532i
$311$	−22.5002	+	12.9905i	−1.27587	+	0.736625i	−0.976087	−	0.217382i	$-0.930248\pi$
$311$	−22.5002	+	12.9905i	−1.27587	+	0.736625i	−0.299785	+	0.954007i	$0.596915\pi$
$312$	−11.1364	−	1.19263i	−0.630474	−	0.0675195i
$313$	−1.14676	+	1.98624i	−0.0648186	+	0.112269i	−0.896613	−	0.442814i	$-0.853980\pi$
$313$	−1.14676	+	1.98624i	−0.0648186	+	0.112269i	0.831795	+	0.555083i	$0.187314\pi$
$314$	3.14934	+	3.67041i	0.177728	+	0.207133i
$315$	−5.96813	−	21.5456i	−0.336266	−	1.21396i
$316$	−19.6836	−	3.02554i	−1.10729	−	0.170200i
$317$	2.59148	+	9.67152i	0.145552	+	0.543207i	0.999730	+	0.0232267i	$0.00739394\pi$
$317$	2.59148	+	9.67152i	0.145552	+	0.543207i	−0.854178	+	0.519980i	$0.825939\pi$
$318$	−0.396229	−	8.63984i	−0.0222194	−	0.484498i
$319$	−1.00403	−	1.73903i	−0.0562147	−	0.0973667i
$320$	4.38275	−	22.1033i	0.245003	−	1.23561i
$321$	7.97605	−	18.7859i	0.445180	−	1.04852i
$322$	2.35539	+	10.9650i	0.131261	+	0.611054i
$323$	10.1579	−	10.1579i	0.565201	−	0.565201i
$324$	−13.6344	−	11.7517i	−0.757469	−	0.652871i
$325$	1.73598	−	6.47875i	0.0962946	−	0.359376i
$326$	14.7923	+	5.20027i	0.819271	+	0.288016i
$327$	14.9249	+	19.8096i	0.825349	+	1.09547i
$328$	16.8081	+	3.91375i	0.928072	+	0.216101i
$329$	2.33296	+	2.21446i	0.128620	+	0.122087i
$330$	−3.22240	+	1.02380i	−0.177387	+	0.0563585i
$331$	−8.84625	−	33.0147i	−0.486234	−	1.81465i	−0.574438	−	0.818548i	$-0.694779\pi$
$331$	−8.84625	−	33.0147i	−0.486234	−	1.81465i	0.0882039	−	0.996102i	$-0.471887\pi$
$332$	−11.3199	+	25.7404i	−0.621258	+	1.41269i
$333$	−4.66701	+	2.58591i	−0.255751	+	0.141707i
$334$	−18.1279	+	26.5056i	−0.991912	+	1.45032i
$335$	−5.79537			−0.316635
$336$	18.1052	+	2.86408i	0.987718	+	0.156249i
$337$	−5.64092			−0.307280			−0.153640	−	0.988127i	$-0.549100\pi$
$337$	−5.64092			−0.307280			−0.153640	+	0.988127i	$0.549100\pi$
$338$	−6.20585	+	9.07386i	−0.337554	+	0.493553i
$339$	−12.7543	−	9.96657i	−0.692721	−	0.541310i
$340$	−9.47936	−	4.16874i	−0.514091	−	0.226082i
$341$	1.33208	+	4.97140i	0.0721363	+	0.269216i
$342$	−33.0094	−	3.10822i	−1.78495	−	0.168073i
$343$	−12.0333	+	14.0783i	−0.649738	+	0.760158i
$344$	−13.4139	−	21.5568i	−0.723231	−	1.16227i
$345$	−11.6793	+	8.79941i	−0.628794	+	0.473745i
$346$	4.77848	+	1.67988i	0.256893	+	0.0903112i
$347$	0.0672164	−	0.250855i	0.00360837	−	0.0134666i	−0.964098	−	0.265546i	$-0.914448\pi$
$347$	0.0672164	−	0.250855i	0.00360837	−	0.0134666i	0.967707	+	0.252079i	$0.0811144\pi$
$348$	−12.5030	+	6.71997i	−0.670234	+	0.360228i
$349$	−3.08135	+	3.08135i	−0.164941	+	0.164941i	−0.784751	−	0.619811i	$-0.787209\pi$
$349$	−3.08135	+	3.08135i	−0.164941	+	0.164941i	0.619811	+	0.784751i	$0.287209\pi$
$350$	−3.36967	+	10.4473i	−0.180117	+	0.558434i
$351$	11.0915	−	4.25433i	0.592023	−	0.227079i
$352$	0.330455	−	2.75241i	0.0176133	−	0.146704i
$353$	−8.65302	−	14.9875i	−0.460554	−	0.797702i	0.538435	−	0.842667i	$-0.319016\pi$
$353$	−8.65302	−	14.9875i	−0.460554	−	0.797702i	−0.998989	+	0.0449649i	$0.985682\pi$
$354$	−9.73214	+	0.446322i	−0.517257	+	0.0237218i
$355$	−3.00058	−	11.1983i	−0.159254	−	0.594344i
$356$	4.44966	−	28.9486i	0.235831	−	1.53427i
$357$	3.08903	−	7.83703i	0.163489	−	0.414780i
$358$	−18.9589	−	22.0958i	−1.00201	−	1.16780i
$359$	7.80783	−	13.5236i	0.412081	−	0.713746i	−0.583036	−	0.812447i	$-0.698135\pi$
$359$	7.80783	−	13.5236i	0.412081	−	0.713746i	0.995117	+	0.0987005i	$0.0314686\pi$
$360$	6.54068	+	22.9881i	0.344724	+	1.21158i
$361$	−36.4349	+	21.0357i	−1.91762	+	1.10714i
$362$	2.03441	+	10.8386i	0.106926	+	0.569662i
$363$	17.2802	−	6.97989i	0.906973	−	0.366349i
$364$	−7.32181	+	9.63014i	−0.383767	+	0.504757i
$365$	11.4031	−	11.4031i	0.596864	−	0.596864i
$366$	8.47507	+	13.2390i	0.442999	+	0.692012i
$367$	−15.5978	+	9.00537i	−0.814196	+	0.470077i	−0.848411	−	0.529338i	$-0.822440\pi$
$367$	−15.5978	+	9.00537i	−0.814196	+	0.470077i	0.0342146	+	0.999415i	$0.489107\pi$
$368$	−2.59970	−	11.7042i	−0.135519	−	0.610124i
$369$	−17.7616	+	4.42519i	−0.924634	+	0.230366i
$370$	7.06396	+	0.539727i	0.367238	+	0.0280591i
$371$	−8.20926	−	4.45862i	−0.426204	−	0.231480i
$372$	35.4120	−	8.34269i	1.83603	−	0.432548i
$373$	0.00510090	+	0.0190368i	0.000264115	+	0.000985690i	0.966058	−	0.258326i	$-0.0831709\pi$
$373$	0.00510090	+	0.0190368i	0.000264115	+	0.000985690i	−0.965794	+	0.259312i	$0.916504\pi$
$374$	−1.20187	−	0.422520i	−0.0621472	−	0.0218480i
$375$	10.0052	−	1.22760i	0.516667	−	0.0633932i
$376$	−2.51049	−	2.34991i	−0.129469	−	0.121187i
$377$		−	9.36796i		−	0.482474i
$378$	−18.4792	+	6.04299i	−0.950469	+	0.310818i
$379$	9.77906	−	9.77906i	0.502316	−	0.502316i	−0.409841	−	0.912157i	$-0.634416\pi$
$379$	9.77906	−	9.77906i	0.502316	−	0.502316i	0.912157	+	0.409841i	$0.134416\pi$
$380$	34.3392	+	27.5488i	1.76156	+	1.41322i
$381$	16.7963	−	21.4945i	0.860503	−	1.10120i
$382$	−10.6294	−	22.1548i	−0.543848	−	1.13354i
$383$	1.85747	−	3.21724i	0.0949124	−	0.164393i	−0.814660	−	0.579939i	$-0.803076\pi$
$383$	1.85747	−	3.21724i	0.0949124	−	0.164393i	0.909572	+	0.415546i	$0.136410\pi$
$384$	−19.3761	−	2.92678i	−0.988783	−	0.149356i
$385$	−0.853004	+	3.55103i	−0.0434731	+	0.180977i
$386$	−1.32799	+	17.3808i	−0.0675931	+	0.884661i
$387$	23.0809	+	13.8738i	1.17327	+	0.705247i
$388$	−3.54779	+	1.38048i	−0.180112	+	0.0700833i
$389$	−8.43541	+	31.4814i	−0.427693	+	1.59617i	0.330280	+	0.943883i	$0.392857\pi$
$389$	−8.43541	+	31.4814i	−0.427693	+	1.59617i	−0.757972	+	0.652287i	$0.773810\pi$
$390$	−15.4072	−	3.38022i	−0.780173	−	0.171164i
$391$	−5.50985			−0.278645
$392$	12.7589	−	15.1397i	0.644421	−	0.764671i
$393$	−7.28976	+	17.1694i	−0.367720	+	0.866084i
$394$	−1.73929	−	9.26627i	−0.0876239	−	0.466828i
$395$	−27.0913	−	7.25910i	−1.36311	−	0.365245i
$396$	1.01778	+	2.75857i	0.0511451	+	0.138623i
$397$	−4.64526	−	17.3364i	−0.233139	−	0.870087i	−0.978979	−	0.203961i	$-0.934618\pi$
$397$	−4.64526	−	17.3364i	−0.233139	−	0.870087i	0.745840	−	0.666125i	$-0.232048\pi$
$398$	0.644875	−	8.44014i	0.0323247	−	0.423066i
$399$	−21.3079	+	28.7831i	−1.06673	+	1.44096i
$400$	3.52435	−	11.1935i	0.176218	−	0.559676i
$401$	−2.02562	−	1.16949i	−0.101155	−	0.0584018i	0.448569	−	0.893748i	$-0.351934\pi$
$401$	−2.02562	−	1.16949i	−0.101155	−	0.0584018i	−0.549724	+	0.835346i	$0.685267\pi$
$402$	0.230887	+	5.03453i	0.0115156	+	0.251100i
$403$	−6.21442	+	23.1925i	−0.309562	+	1.15530i
$404$	2.92816	+	26.6873i	0.145682	+	1.32774i
$405$	−17.2824	−	18.5461i	−0.858771	−	0.921561i
$406$	−0.769409	+	15.3125i	−0.0381851	+	0.759947i
$407$	0.871569			0.0432021
$408$	−3.24380	+	8.40097i	−0.160592	+	0.415910i
$409$	−9.91575	−	17.1746i	−0.490302	−	0.849228i	0.509635	−	0.860390i	$-0.329780\pi$
$409$	−9.91575	−	17.1746i	−0.490302	−	0.849228i	−0.999938	+	0.0111620i	$0.996447\pi$
$410$	22.9293	+	8.06085i	1.13240	+	0.398097i
$411$	27.2190	+	3.82779i	1.34261	+	0.188811i
$412$	37.6184	+	5.78228i	1.85333	+	0.284872i
$413$	−5.02230	+	9.24712i	−0.247131	+	0.455021i
$414$	8.10951	+	9.79547i	0.398561	+	0.481421i
$415$	−19.8011	+	34.2965i	−0.971997	+	1.68355i
$416$	7.75535	−	10.3494i	0.380237	−	0.507421i
$417$	18.1550	−	2.22755i	0.889052	−	0.109083i
$418$	4.47046	+	3.05747i	0.218658	+	0.149546i
$419$	−13.1475	−	13.1475i	−0.642298	−	0.642298i	0.308822	−	0.951120i	$-0.400065\pi$
$419$	−13.1475	−	13.1475i	−0.642298	−	0.642298i	−0.951120	+	0.308822i	$0.900065\pi$
$420$	24.9064	+	6.79061i	1.21531	+	0.331348i
$421$	3.45061	−	3.45061i	0.168173	−	0.168173i	−0.618003	−	0.786176i	$-0.712058\pi$
$421$	3.45061	−	3.45061i	0.168173	−	0.168173i	0.786176	+	0.618003i	$0.212058\pi$
$422$	1.15419	+	6.14908i	0.0561850	+	0.299333i
$423$	3.50582	+	1.00594i	0.170459	+	0.0489104i
$424$	8.80910	+	4.70514i	0.427808	+	0.228502i
$425$	−4.67050	−	2.69652i	−0.226553	−	0.130800i
$426$	−9.60861	+	3.05279i	−0.465539	+	0.147908i
$427$	16.9730	−	0.442294i	0.821383	−	0.0214041i
$428$	13.9388	+	19.0021i	0.673756	+	0.918499i
$429$	−1.92163	−	0.270237i	−0.0927770	−	0.0130472i
$430$	−15.4676	−	32.2389i	−0.745914	−	1.55470i
$431$	−4.97763	+	2.87384i	−0.239764	+	0.138428i	−0.615068	−	0.788474i	$-0.710872\pi$
$431$	−4.97763	+	2.87384i	−0.239764	+	0.138428i	0.375304	+	0.926902i	$0.377538\pi$
$432$	19.7096	−	6.59784i	0.948279	−	0.317439i
$433$		−	9.18414i		−	0.441362i	−0.975346	−	0.220681i	$-0.929172\pi$
$433$		−	9.18414i		−	0.441362i	0.975346	−	0.220681i	$-0.0708279\pi$
$434$	12.0627	−	37.3992i	0.579028	−	1.79522i
$435$	−18.5359	+	7.48709i	−0.888726	+	0.358979i
$436$	−28.4688	+	3.12364i	−1.36341	+	0.149595i
$437$	22.6257	+	6.06253i	1.08233	+	0.290010i
$438$	−10.3603	−	9.45174i	−0.495036	−	0.451622i
$439$	5.53220	−	9.58206i	0.264038	−	0.457327i	−0.703273	−	0.710920i	$-0.748279\pi$
$439$	5.53220	−	9.58206i	0.264038	−	0.457327i	0.967311	+	0.253593i	$0.0816123\pi$
$440$	0.885403	−	3.80247i	0.0422099	−	0.181276i
$441$	−4.73274	+	20.4597i	−0.225368	+	0.974274i
$442$	−3.87020	−	4.51053i	−0.184086	−	0.214544i
$443$	11.2234	−	3.00730i	0.533239	−	0.142881i	0.0178553	−	0.999841i	$-0.494316\pi$
$443$	11.2234	−	3.00730i	0.533239	−	0.142881i	0.515383	+	0.856960i	$0.327650\pi$
$444$	0.187442	−	6.15809i	0.00889562	−	0.292250i
$445$	10.6759	−	39.8431i	0.506088	−	1.88875i
$446$	14.8209	−	21.6704i	0.701792	−	1.02612i
$447$	0.468577	−	1.10363i	0.0221629	−	0.0522000i
$448$	−13.5266	+	16.2798i	−0.639073	+	0.769146i
$449$		−	40.1346i		−	1.89407i	−0.321132	−	0.947035i	$-0.604063\pi$
$449$		−	40.1346i		−	1.89407i	0.321132	−	0.947035i	$-0.395937\pi$
$450$	2.08025	+	12.2721i	0.0980637	+	0.578510i
$451$	2.88821	+	0.773892i	0.136000	+	0.0364412i
$452$	17.4185	−	6.77771i	0.819297	−	0.318797i
$453$	0.0211324	−	0.150270i	0.000992885	−	0.00706029i
$454$	24.5222	−	21.0409i	1.15089	−	0.987500i
$455$	−11.7294	+	12.3571i	−0.549882	+	0.579308i
$456$	22.5640	−	30.9286i	1.05666	−	1.44836i
$457$	9.62796	+	5.55871i	0.450377	+	0.260025i	0.707989	−	0.706223i	$-0.249602\pi$
$457$	9.62796	+	5.55871i	0.450377	+	0.260025i	−0.257612	+	0.966248i	$0.582936\pi$
$458$	0.586292	+	0.206112i	0.0273956	+	0.00963100i
$459$	−0.995951	−	9.49968i	−0.0464870	−	0.443407i
$460$	−1.84163	−	16.7846i	−0.0858666	−	0.782587i
$461$	−5.26516	−	5.26516i	−0.245223	−	0.245223i	0.573784	−	0.819007i	$-0.305475\pi$
$461$	−5.26516	−	5.26516i	−0.245223	−	0.245223i	−0.819007	+	0.573784i	$0.805475\pi$
$462$	3.11882	+	0.599546i	0.145101	+	0.0278934i
$463$	12.5811			0.584693			0.292346	−	0.956312i	$-0.405564\pi$
$463$	12.5811			0.584693			0.292346	+	0.956312i	$0.405564\pi$
$464$	0.708350	−	16.3751i	0.0328843	−	0.760195i
$465$	50.8565	−	6.23990i	2.35841	−	0.289368i
$466$	−18.0821	+	8.67544i	−0.837638	+	0.401882i
$467$	−5.13222	+	1.37518i	−0.237491	+	0.0636355i	−0.375601	−	0.926781i	$-0.622564\pi$
$467$	−5.13222	+	1.37518i	−0.237491	+	0.0636355i	0.138110	+	0.990417i	$0.455897\pi$
$468$	−2.32264	+	13.5192i	−0.107364	+	0.624923i
$469$	4.78363	+	2.59809i	0.220887	+	0.119968i
$470$	−3.15360	−	3.67538i	−0.145465	−	0.169532i
$471$	4.73086	−	3.56431i	0.217986	−	0.164235i
$472$	5.29999	−	9.92279i	0.243952	−	0.456733i
$473$	−2.19951	−	3.80967i	−0.101134	−	0.175169i
$474$	−5.22679	+	23.8239i	−0.240074	+	1.09427i
$475$	16.2120	+	16.2120i	0.743857	+	0.743857i
$476$	5.95562	+	7.69061i	0.272975	+	0.352499i
$477$	−10.5911	−	0.186711i	−0.484932	−	0.00854889i
$478$	−11.0201	+	16.1129i	−0.504046	+	0.736988i
$479$	−8.65041	−	14.9830i	−0.395247	−	0.684589i	0.597885	−	0.801582i	$-0.296008\pi$
$479$	−8.65041	−	14.9830i	−0.395247	−	0.684589i	−0.993133	+	0.116993i	$0.962674\pi$
$480$	−26.6760	−	7.07360i	−1.21759	−	0.322864i
$481$	3.52129	+	2.03302i	0.160557	+	0.0926977i
$482$	3.24157	+	0.247674i	0.147649	+	0.0112813i
$483$	13.5852	−	2.02735i	0.618148	−	0.0922475i
$484$	−3.26937	+	21.2699i	−0.148608	+	0.966813i
$485$	−5.17878	+	1.38765i	−0.235156	+	0.0630099i
$486$	−15.4228	+	15.7524i	−0.699590	+	0.714544i
$487$	−21.4676	+	12.3943i	−0.972788	+	0.561639i	−0.900085	−	0.435714i	$-0.856496\pi$
$487$	−21.4676	+	12.3943i	−0.972788	+	0.561639i	−0.0727029	+	0.997354i	$0.523162\pi$
$488$	−18.1412	+	0.599363i	−0.821214	+	0.0271319i
$489$	7.50503	−	17.6765i	0.339389	−	0.799358i
$490$	20.1873	−	19.2350i	0.911970	−	0.868949i
$491$	1.12911	+	1.12911i	0.0509558	+	0.0509558i	0.732126	−	0.681170i	$-0.238528\pi$
$491$	1.12911	+	1.12911i	0.0509558	+	0.0509558i	−0.681170	+	0.732126i	$0.738528\pi$
$492$	6.08910	−	20.2402i	0.274518	−	0.912500i
$493$	−7.27569	−	1.94952i	−0.327681	−	0.0878018i
$494$	10.9296	+	22.7805i	0.491747	+	1.02494i
$495$	1.00111	+	4.01819i	0.0449964	+	0.180604i
$496$	−12.6164	+	40.0704i	−0.566494	+	1.79921i
$497$	−2.54350	+	10.5885i	−0.114092	+	0.474959i
$498$	30.5828	+	15.8352i	1.37045	+	0.709591i
$499$	28.7037	−	7.69113i	1.28495	−	0.344302i	0.449212	−	0.893425i	$-0.351705\pi$
$499$	28.7037	−	7.69113i	1.28495	−	0.344302i	0.835741	+	0.549123i	$0.185038\pi$
$500$	−4.68569	+	10.6549i	−0.209551	+	0.476500i
$501$	30.9893	+	24.2159i	1.38450	+	1.08189i
$502$	8.29119	−	1.55626i	0.370054	−	0.0694594i
$503$			5.00891i			0.223336i	0.993746	+	0.111668i	$0.0356194\pi$
$503$			5.00891i			0.223336i	−0.993746	+	0.111668i	$0.964381\pi$
$504$	4.90685	−	21.9071i	0.218568	−	0.975822i
$505$			37.8106i			1.68255i
$506$	−0.383219	−	2.04165i	−0.0170362	−	0.0907624i
$507$	10.6088	+	8.29000i	0.471154	+	0.368172i
$508$	11.4223	+	29.3548i	0.506781	+	1.30241i
$509$	−38.0367	+	10.1919i	−1.68595	+	0.451749i	−0.969339	−	0.245725i	$-0.920974\pi$
$509$	−38.0367	+	10.1919i	−1.68595	+	0.451749i	−0.716610	+	0.697474i	$0.754307\pi$
$510$	−5.83158	+	11.2627i	−0.258227	+	0.498719i
$511$	−14.5244	+	4.30031i	−0.642521	+	0.190235i
$512$	14.3388	−	17.5042i	0.633693	−	0.773585i
$513$	−6.36279	+	40.1054i	−0.280924	+	1.77070i
$514$	19.6808	−	9.44247i	0.868084	−	0.416490i
$515$	51.7757	+	13.8733i	2.28151	+	0.611328i
$516$	−27.3903	+	14.7214i	−1.20579	+	0.648072i
$517$	−0.421288	−	0.421288i	−0.0185282	−	0.0185282i
$518$	−5.58880	−	3.61231i	−0.245558	−	0.158716i
$519$	2.42441	−	5.71017i	0.106420	−	0.250649i
$520$	12.4468	−	13.2974i	0.545829	−	0.583128i
$521$	8.91205	−	5.14537i	0.390444	−	0.225423i	−0.291909	−	0.956446i	$-0.594290\pi$
$521$	8.91205	−	5.14537i	0.390444	−	0.225423i	0.682352	+	0.731023i	$0.260957\pi$
$522$	7.24263	+	15.8041i	0.317002	+	0.691728i
$523$	−13.0057	+	3.48486i	−0.568698	+	0.152382i	−0.531700	−	0.846933i	$-0.678446\pi$
$523$	−13.0057	+	3.48486i	−0.568698	+	0.152382i	−0.0369989	+	0.999315i	$0.511780\pi$
$524$	−12.7394	−	17.3671i	−0.556524	−	0.758683i
$525$	12.5079	+	4.93008i	0.545888	+	0.215166i
$526$	2.11363	−	27.6633i	0.0921588	−	1.20618i
$527$	16.7194	+	9.65295i	0.728308	+	0.420489i
$528$	−3.33855	−	0.617674i	−0.145292	−	0.0268808i
$529$	7.00791	+	12.1381i	0.304692	+	0.527742i
$530$	11.6096	+	7.94008i	0.504287	+	0.344895i
$531$	−0.210315	+	11.9301i	−0.00912691	+	0.517720i
$532$	−15.9941	−	38.1338i	−0.693434	−	1.65331i
$533$	9.86368	+	9.86368i	0.427243	+	0.427243i
$534$	−35.0378	−	7.68702i	−1.51623	−	0.332650i
$535$	16.5948	+	28.7430i	0.717455	+	1.24267i
$536$	−5.13316	−	2.74174i	−0.221719	−	0.118425i
$537$	−28.4797	+	21.4571i	−1.22899	+	0.925941i
$538$	−20.8313	+	17.8740i	−0.898103	+	0.770604i
$539$	2.29603	−	2.54869i	0.0988969	−	0.109780i
$540$	28.6059	−	6.20917i	1.23100	−	0.267200i
$541$	−11.8753	+	3.18197i	−0.510559	+	0.136804i	−0.504896	−	0.863180i	$-0.668469\pi$
$541$	−11.8753	+	3.18197i	−0.510559	+	0.136804i	−0.00566268	+	0.999984i	$0.501802\pi$
$542$	1.52613	+	3.18089i	0.0655527	+	0.136631i
$543$	13.4058	−	1.64484i	0.575296	−	0.0705867i
$544$	−6.42401	−	8.17701i	−0.275427	−	0.350586i
$545$	−40.3347			−1.72775
$546$	11.2021	+	9.69722i	0.479405	+	0.415003i
$547$	−19.4310	−	19.4310i	−0.830811	−	0.830811i	0.156817	−	0.987628i	$-0.449877\pi$
$547$	−19.4310	−	19.4310i	−0.830811	−	0.830811i	−0.987628	+	0.156817i	$0.949877\pi$
$548$	−19.8612	+	24.7568i	−0.848429	+	1.05756i
$549$	16.8399	−	9.33071i	0.718711	−	0.398225i
$550$	0.674340	−	1.91818i	0.0287540	−	0.0817915i
$551$	27.7319	+	16.0110i	1.18142	+	0.682092i
$552$	−14.5077	+	2.26856i	−0.617490	+	0.0965562i
$553$	19.1075	+	18.1370i	0.812534	+	0.771263i
$554$	−3.28039	−	3.82314i	−0.139370	−	0.162429i
$555$	1.20832	−	8.59222i	0.0512903	−	0.364720i
$556$	−8.50242	+	19.3338i	−0.360583	+	0.819935i
$557$	6.82673	+	1.82922i	0.289258	+	0.0775064i	0.400530	−	0.916284i	$-0.368826\pi$
$557$	6.82673	+	1.82922i	0.289258	+	0.0775064i	−0.111272	+	0.993790i	$0.535493\pi$
$558$	−7.44683	−	43.9313i	−0.315249	−	1.85976i
$559$		−	20.5223i		−	0.868000i
$560$	−21.4372	+	20.7131i	−0.905888	+	0.875288i
$561$	−0.609781	+	1.43621i	−0.0257450	+	0.0606367i
$562$	27.0933	+	18.5298i	1.14286	+	0.781634i
$563$	−2.26734	+	8.46183i	−0.0955570	+	0.356624i	−0.997103	−	0.0760590i	$-0.975766\pi$
$563$	−2.26734	+	8.46183i	−0.0955570	+	0.356624i	0.901546	+	0.432683i	$0.142433\pi$
$564$	−3.06722	+	2.88602i	−0.129153	+	0.121523i
$565$	25.4261	−	6.81290i	1.06968	−	0.286621i
$566$	10.1399	−	8.70038i	0.426211	−	0.365704i
$567$	5.95104	+	23.0561i	0.249920	+	0.968266i
$568$	2.64011	−	11.3383i	0.110776	−	0.475744i
$569$	−7.02366	+	12.1653i	−0.294447	+	0.509997i	−0.974856	−	0.222835i	$-0.928469\pi$
$569$	−7.02366	+	12.1653i	−0.294447	+	0.509997i	0.680409	+	0.732833i	$0.261802\pi$
$570$	36.3392	−	39.8325i	1.52208	−	1.66840i
$571$	−9.24419	−	2.47697i	−0.386857	−	0.103658i	0.0601478	−	0.998189i	$-0.480843\pi$
$571$	−9.24419	−	2.47697i	−0.386857	−	0.103658i	−0.447005	+	0.894531i	$0.647509\pi$
$572$	1.40218	−	1.74780i	0.0586280	−	0.0730791i
$573$	−27.9049	+	11.2715i	−1.16574	+	0.470872i
$574$	−15.3127	−	16.9329i	−0.639138	−	0.706766i
$575$		−	8.79370i		−	0.366723i
$576$	−5.08218	+	23.4557i	−0.211758	+	0.977322i
$577$	−6.71884	+	3.87913i	−0.279709	+	0.161490i	−0.633292	−	0.773913i	$-0.718297\pi$
$577$	−6.71884	+	3.87913i	−0.279709	+	0.161490i	0.353583	+	0.935403i	$0.384963\pi$
$578$	17.3674	−	8.33253i	0.722389	−	0.346588i
$579$	21.1411	+	2.97306i	0.878594	+	0.123556i
$580$	3.50694	−	22.8155i	0.145618	−	0.947362i
$581$	31.7195	−	19.4322i	1.31595	−	0.806183i
$582$	1.41180	+	4.44361i	0.0585208	+	0.184193i
$583$	1.49852	+	0.865171i	0.0620624	+	0.0358317i
$584$	15.4948	−	4.70540i	0.641179	−	0.194711i
$585$	−5.32818	+	18.5694i	−0.220293	+	0.767749i
$586$	−33.7232	+	6.32986i	−1.39309	+	0.261484i
$587$	11.3939	−	11.3939i	0.470275	−	0.470275i	−0.431729	−	0.902004i	$-0.642096\pi$
$587$	11.3939	−	11.3939i	0.470275	−	0.470275i	0.902004	+	0.431729i	$0.142096\pi$
$588$	−17.5140	−	16.7708i	−0.722267	−	0.691614i
$589$	−58.0354	−	58.0354i	−2.39131	−	2.39131i
$590$	8.94390	−	13.0773i	0.368215	−	0.538384i
$591$	−11.4611	+	1.40623i	−0.471445	+	0.0578445i
$592$	6.00146	+	3.81996i	0.246658	+	0.156999i
$593$	9.24151	−	16.0068i	0.379503	−	0.657319i	−0.611487	−	0.791255i	$-0.709428\pi$
$593$	9.24151	−	16.0068i	0.379503	−	0.657319i	0.990990	+	0.133936i	$0.0427616\pi$
$594$	3.45079	−	1.02976i	0.141588	−	0.0422517i
$595$	7.15625	+	11.6813i	0.293378	+	0.478886i
$596$	0.818875	+	1.11633i	0.0335424	+	0.0457268i
$597$	−10.2661	−	1.44372i	−0.420165	−	0.0590876i
$598$	3.21407	−	9.14251i	0.131433	−	0.373865i
$599$	−10.2397	−	17.7357i	−0.418384	−	0.724662i	0.577393	−	0.816466i	$-0.304070\pi$
$599$	−10.2397	−	17.7357i	−0.418384	−	0.724662i	−0.995777	+	0.0918041i	$0.970737\pi$
$600$	−13.4079	−	5.17709i	−0.547375	−	0.211354i
$601$	6.34934			0.258995			0.129498	−	0.991580i	$-0.458664\pi$
$601$	6.34934			0.258995			0.129498	+	0.991580i	$0.458664\pi$
$602$	−1.68554	+	33.5449i	−0.0686973	+	1.36719i
$603$	6.17154	+	0.108798i	0.251325	+	0.00443061i
$604$	0.136677	+	0.109649i	0.00556129	+	0.00446157i
$605$	−7.84410	+	29.2746i	−0.318908	+	1.19018i
$606$	32.8467	−	1.50637i	1.33431	−	0.0611922i
$607$	−18.6040	−	10.7410i	−0.755111	−	0.435964i	0.0724265	−	0.997374i	$-0.476926\pi$
$607$	−18.6040	−	10.7410i	−0.755111	−	0.435964i	−0.827538	+	0.561410i	$0.810259\pi$
$608$	17.3823	+	40.6465i	0.704947	+	1.64843i
$609$	18.6564	+	2.12968i	0.755996	+	0.0862989i
$610$	−25.4889	−	1.94749i	−1.03201	−	0.0788517i
$611$	−0.719383	−	2.68477i	−0.0291031	−	0.108614i
$612$	10.0164	+	4.61729i	0.404889	+	0.186643i
$613$	23.0988	+	6.18930i	0.932950	+	0.249983i	0.693112	−	0.720830i	$-0.256239\pi$
$613$	23.0988	+	6.18930i	0.932950	+	0.249983i	0.239838	+	0.970813i	$0.422906\pi$
$614$	1.30530	−	0.245005i	0.0526775	−	0.00988761i
$615$	11.6334	−	27.4000i	0.469105	−	1.10487i
$616$	−2.43550	+	2.74172i	−0.0981289	+	0.110467i
$617$	19.8821			0.800424			0.400212	−	0.916423i	$-0.368937\pi$
$617$	19.8821			0.800424			0.400212	+	0.916423i	$0.368937\pi$
$618$	9.98919	−	45.5311i	0.401824	−	1.83153i
$619$	−1.50208	+	5.60584i	−0.0603737	+	0.225318i	−0.989520	−	0.144394i	$-0.953877\pi$
$619$	−1.50208	+	5.60584i	−0.0603737	+	0.225318i	0.929147	+	0.369711i	$0.120543\pi$
$620$	−23.8174	+	54.1586i	−0.956528	+	2.17506i
$621$	12.6026	−	9.15132i	0.505726	−	0.367230i
$622$	−36.6360	−	2.79920i	−1.46897	−	0.112238i
$623$	−26.6740	+	28.1014i	−1.06867	+	1.12586i
$624$	−12.0475	−	10.2830i	−0.482287	−	0.411649i
$625$	−15.5309	+	26.9003i	−0.621236	+	1.07601i
$626$	−2.92436	+	1.40305i	−0.116881	+	0.0560771i
$627$	4.08428	−	5.22670i	0.163110	−	0.208734i
$628$	0.745977	+	6.79882i	0.0297677	+	0.271303i
$629$	2.31176	−	2.31176i	0.0921758	−	0.0921758i
$630$	10.2344	−	29.9152i	0.407747	−	1.19185i
$631$		−	0.968685i		−	0.0385628i	−0.999814	−	0.0192814i	$-0.993862\pi$
$631$		−	0.968685i		−	0.0385628i	0.999814	−	0.0192814i	$-0.00613783\pi$
$632$	−20.5615	−	19.2463i	−0.817893	−	0.765577i
$633$	7.60554	−	0.933172i	0.302293	−	0.0370903i
$634$	−4.69626	+	13.3586i	−0.186512	+	0.530539i
$635$	11.4816	+	42.8498i	0.455632	+	1.70044i
$636$	6.43516	−	10.4018i	0.255171	−	0.412457i
$637$	15.2214	−	4.94146i	0.603095	−	0.195788i
$638$	0.216348	−	2.83156i	0.00856529	−	0.112103i
$639$	2.98511	+	11.9815i	0.118089	+	0.473981i
$640$	22.7624	−	22.3025i	0.899762	−	0.881584i
$641$	1.48078	−	0.854929i	0.0584873	−	0.0337677i	−0.470471	−	0.882415i	$-0.655916\pi$
$641$	1.48078	−	0.854929i	0.0584873	−	0.0337677i	0.528959	+	0.848648i	$0.322583\pi$
$642$	24.3084	−	15.5613i	0.959376	−	0.614155i
$643$	−16.0992	+	16.0992i	−0.634891	+	0.634891i	−0.949291	−	0.314400i	$-0.898197\pi$
$643$	−16.0992	+	16.0992i	−0.634891	+	0.634891i	0.314400	+	0.949291i	$0.398197\pi$
$644$	−6.00449	+	14.6800i	−0.236610	+	0.578474i
$645$	−40.6063	+	16.4019i	−1.59887	+	0.645824i
$646$	19.9671	−	3.74784i	0.785596	−	0.147457i
$647$	14.9586	−	8.63636i	0.588084	−	0.339530i	−0.176256	−	0.984344i	$-0.556399\pi$
$647$	14.9586	−	8.63636i	0.588084	−	0.339530i	0.764340	+	0.644814i	$0.223065\pi$
$648$	−6.53367	−	24.6031i	−0.256667	−	0.966500i
$649$	0.974551	−	1.68797i	0.0382545	−	0.0662587i
$650$	7.19879	−	6.17682i	0.282360	−	0.242275i
$651$	−44.7755	−	17.6486i	−1.75489	−	0.691703i
$652$	13.1156	+	17.8799i	0.513648	+	0.700231i
$653$	−7.29070	−	27.2093i	−0.285307	−	1.06478i	−0.948615	−	0.316434i	$-0.897515\pi$
$653$	−7.29070	−	27.2093i	−0.285307	−	1.06478i	0.663307	−	0.748347i	$-0.269152\pi$
$654$	1.60693	+	35.0395i	0.0628360	+	1.37015i
$655$	−15.1669	−	26.2698i	−0.592620	−	1.02645i
$656$	16.4958	+	17.9874i	0.644052	+	0.702292i
$657$	−12.3573	+	11.9292i	−0.482105	+	0.465401i
$658$	0.955370	+	4.44751i	0.0372442	+	0.173382i
$659$	−18.1828	+	18.1828i	−0.708300	+	0.708300i	−0.966178	−	0.257877i	$-0.916977\pi$
$659$	−18.1828	+	18.1828i	−0.708300	+	0.708300i	0.257877	+	0.966178i	$0.416977\pi$
$660$	−4.57892	−	1.37753i	−0.178234	−	0.0536202i
$661$	−6.81556	+	25.4360i	−0.265095	+	0.989347i	0.697098	+	0.716976i	$0.254474\pi$
$661$	−6.81556	+	25.4360i	−0.265095	+	0.989347i	−0.962192	+	0.272371i	$0.912192\pi$
$662$	16.0311	−	45.6010i	0.623068	−	1.77233i
$663$	−5.81371	+	4.38015i	−0.225786	+	0.170111i
$664$	−33.7639	+	21.0099i	−1.31029	+	0.815341i
$665$	−16.5335	−	55.8421i	−0.641140	−	2.16547i
$666$	−7.51235	−	0.707375i	−0.291098	−	0.0274102i
$667$	−3.17882	−	11.8635i	−0.123084	−	0.459357i
$668$	−42.3219	+	16.4679i	−1.63748	+	0.637161i
$669$	−25.3362	−	19.7984i	−0.979555	−	0.765450i
$670$	−6.76502	−	4.62677i	−0.261356	−	0.178748i
$671$	−3.14488			−0.121407
$672$	18.8479	+	17.7977i	0.727073	+	0.686560i
$673$	35.7520			1.37814			0.689068	−	0.724696i	$-0.258020\pi$
$673$	35.7520			1.37814			0.689068	+	0.724696i	$0.258020\pi$
$674$	−6.58473	−	4.50347i	−0.253634	−	0.173467i
$675$	15.1614	−	1.58953i	0.583564	−	0.0611812i
$676$	−14.4884	+	5.63757i	−0.557245	+	0.216830i
$677$	−9.01261	−	33.6355i	−0.346383	−	1.29272i	−0.890988	−	0.454026i	$-0.849987\pi$
$677$	−9.01261	−	33.6355i	−0.346383	−	1.29272i	0.544605	−	0.838692i	$-0.316679\pi$
$678$	−6.93146	−	21.8167i	−0.266201	−	0.837864i
$679$	4.89677	+	1.17627i	0.187921	+	0.0451411i
$680$	−7.73726	−	12.4342i	−0.296710	−	0.476828i
$681$	−23.8134	−	31.6072i	−0.912532	−	1.21119i
$682$	−2.41399	+	6.86667i	−0.0924366	+	0.262938i
$683$	6.73524	−	25.1362i	0.257717	−	0.961812i	−0.708842	−	0.705367i	$-0.750782\pi$
$683$	6.73524	−	25.1362i	0.257717	−	0.961812i	0.966559	−	0.256445i	$-0.0825511\pi$
$684$	−36.0510	−	29.9816i	−1.37844	−	1.14638i
$685$	−31.6075	+	31.6075i	−1.20766	+	1.20766i
$686$	−25.2862	+	6.82695i	−0.965432	+	0.260654i
$687$	0.297461	−	0.700606i	0.0113489	−	0.0267298i
$688$	1.55177	−	35.8727i	0.0591608	−	1.36764i
$689$	4.03619	+	6.99089i	0.153767	+	0.266332i
$690$	−20.6585	+	0.947414i	−0.786457	+	0.0360674i
$691$	4.03539	+	15.0603i	0.153513	+	0.572920i	0.999228	+	0.0392846i	$0.0125079\pi$
$691$	4.03539	+	15.0603i	0.153513	+	0.572920i	−0.845715	+	0.533635i	$0.820825\pi$
$692$	4.23684	+	5.77589i	0.161061	+	0.219566i
$693$	0.975037	−	3.76551i	0.0370386	−	0.143040i
$694$	0.278735	−	0.239164i	0.0105806	−	0.00907856i
$695$	−14.8727	+	25.7603i	−0.564154	+	0.977144i
$696$	−19.9599	−	2.13757i	−0.756579	−	0.0810245i
$697$	9.71337	−	5.60802i	0.367920	−	0.212419i
$698$	−6.05693	+	1.13689i	−0.229258	+	0.0430319i
$699$	9.19947	+	22.7752i	0.347956	+	0.861437i
$700$	−12.2742	+	9.50514i	−0.463921	+	0.359261i
$701$	−24.2498	+	24.2498i	−0.915901	+	0.915901i	−0.996728	−	0.0808275i	$-0.974244\pi$
$701$	−24.2498	+	24.2498i	−0.915901	+	0.915901i	0.0808275	+	0.996728i	$0.474244\pi$
$702$	16.3438	+	3.88888i	0.616857	+	0.146776i
$703$	−12.0367	+	6.94937i	−0.453971	+	0.262100i
$704$	2.58315	−	2.94911i	0.0973562	−	0.111149i
$705$	−4.73726	+	3.56914i	−0.178416	+	0.134422i
$706$	1.86455	−	24.4033i	0.0701733	−	0.918430i
$707$	16.9506	−	31.2097i	0.637495	−	1.17376i
$708$	−11.7168	−	7.24872i	−0.440344	−	0.272424i
$709$	−5.28624	−	19.7285i	−0.198529	−	0.740920i	−0.991325	−	0.131433i	$-0.958042\pi$
$709$	−5.28624	−	19.7285i	−0.198529	−	0.740920i	0.792796	−	0.609487i	$-0.208625\pi$
$710$	5.43763	−	15.4675i	0.204071	−	0.580484i
$711$	28.7135	+	8.23888i	1.07684	+	0.308982i
$712$	28.3055	−	30.2398i	1.06079	−	1.13328i
$713$			31.4796i			1.17892i
$714$	9.86262	−	6.68214i	0.369099	−	0.250073i
$715$	2.23145	−	2.23145i	0.0834514	−	0.0834514i
$716$	−4.49076	−	40.9287i	−0.167828	−	1.52958i
$717$	18.8386	+	14.7210i	0.703542	+	0.549766i
$718$	19.9108	−	9.55282i	0.743066	−	0.356508i
$719$	8.76322	−	15.1783i	0.326813	−	0.566057i	−0.655065	−	0.755573i	$-0.727359\pi$
$719$	8.76322	−	15.1783i	0.326813	−	0.566057i	0.981878	+	0.189516i	$0.0606919\pi$
$720$	−10.7177	+	32.0562i	−0.399425	+	1.19466i
$721$	−36.5174	−	34.6625i	−1.35998	−	1.29090i
$722$	−59.3249	−	4.53276i	−2.20785	−	0.168692i
$723$	0.554484	−	3.94287i	0.0206215	−	0.146637i
$724$	−6.27825	+	14.2762i	−0.233329	+	0.530571i
$725$	3.11142	−	11.6120i	0.115555	−	0.431258i
$726$	25.7438	+	5.64801i	0.955444	+	0.209617i
$727$	8.67975			0.321914			0.160957	−	0.986961i	$-0.448542\pi$
$727$	8.67975			0.321914			0.160957	+	0.986961i	$0.448542\pi$
$728$	−16.2352	+	5.39600i	−0.601715	+	0.199989i
$729$	18.0561	+	20.0743i	0.668743	+	0.743494i
$730$	22.4147	−	4.20725i	0.829605	−	0.155717i
$731$	−15.9388	−	4.27078i	−0.589517	−	0.157961i
$732$	−0.676347	+	22.2202i	−0.0249985	+	0.821282i
$733$	10.1013	+	37.6985i	0.373100	+	1.39243i	0.856101	+	0.516808i	$0.172880\pi$
$733$	10.1013	+	37.6985i	0.373100	+	1.39243i	−0.483002	+	0.875620i	$0.660453\pi$
$734$	−25.3970	−	1.94048i	−0.937421	−	0.0716243i
$735$	−21.9427	−	26.1685i	−0.809369	−	0.965238i
$736$	6.30947	−	15.7380i	0.232570	−	0.580110i
$737$	−0.873205	−	0.504145i	−0.0321649	−	0.0185704i
$738$	−24.2663	−	9.01454i	−0.893256	−	0.331830i
$739$	12.2290	−	45.6392i	0.449851	−	1.67887i	−0.252951	−	0.967479i	$-0.581401\pi$
$739$	12.2290	−	45.6392i	0.449851	−	1.67887i	0.702801	−	0.711386i	$-0.251932\pi$
$740$	7.81498	+	6.26960i	0.287284	+	0.230475i
$741$	28.6930	−	11.5898i	1.05406	−	0.425762i
$742$	−6.02323	−	11.7585i	−0.221120	−	0.431669i
$743$	37.0600			1.35960			0.679801	−	0.733397i	$-0.262066\pi$
$743$	37.0600			1.35960			0.679801	+	0.733397i	$0.262066\pi$
$744$	47.9974	+	18.5329i	1.75967	+	0.679448i
$745$	0.974910	+	1.68859i	0.0357180	+	0.0618653i
$746$	−0.00924383	+	0.0262943i	−0.000338441	+	0.000962704i
$747$	21.7302	−	36.1509i	0.795067	−	1.32269i
$748$	−1.06564	−	1.45274i	−0.0389636	−	0.0531173i
$749$	−0.812106	−	31.1646i	−0.0296737	−	1.13873i
$750$	12.6593	+	6.55474i	0.462253	+	0.239345i
$751$	−8.77969	+	15.2069i	−0.320375	+	0.554907i	−0.980565	−	0.196192i	$-0.937142\pi$
$751$	−8.77969	+	15.2069i	−0.320375	+	0.554907i	0.660190	+	0.751099i	$0.270476\pi$
$752$	−1.05447	−	4.74735i	−0.0384525	−	0.173118i
$753$	−1.25825	−	10.2550i	−0.0458533	−	0.373714i
$754$	7.47898	−	10.9354i	0.272368	−	0.398242i
$755$	0.174498	+	0.174498i	0.00635062	+	0.00635062i
$756$	−26.3956	−	7.69896i	−0.959998	−	0.280008i
$757$	5.64053	−	5.64053i	0.205009	−	0.205009i	−0.597133	−	0.802142i	$-0.703694\pi$
$757$	5.64053	−	5.64053i	0.205009	−	0.205009i	0.802142	+	0.597133i	$0.203694\pi$
$758$	19.2224	−	3.60806i	0.698190	−	0.131051i
$759$	−2.52523	+	0.309836i	−0.0916600	+	0.0112463i
$760$	18.0909	+	59.5730i	0.656227	+	2.16094i
$761$	30.6169	+	17.6767i	1.10986	+	0.640780i	0.938794	−	0.344479i	$-0.111944\pi$
$761$	30.6169	+	17.6767i	1.10986	+	0.640780i	0.171069	+	0.985259i	$0.445278\pi$
$762$	36.7669	−	11.6814i	1.33192	−	0.423171i
$763$	33.2932	+	18.0822i	1.20529	+	0.654620i
$764$	5.27954	−	34.3477i	0.191007	−	1.24266i
$765$	13.3132	+	8.00254i	0.481341	+	0.289333i
$766$	4.73676	−	2.27260i	0.171146	−	0.0821125i
$767$	7.87471	−	4.54647i	0.284339	−	0.164163i
$768$	−20.2814	−	18.8855i	−0.731843	−	0.681473i
$769$			7.32298i			0.264074i	0.991245	+	0.132037i	$0.0421517\pi$
$769$			7.32298i			0.264074i	−0.991245	+	0.132037i	$0.957848\pi$
$770$	−3.83071	+	3.46417i	−0.138049	+	0.124840i
$771$	−10.0128	−	24.7888i	−0.360603	−	0.892748i
$772$	−15.4263	+	19.2287i	−0.555205	+	0.692056i
$773$	−44.0336	−	11.7988i	−1.58378	−	0.424372i	−0.643686	−	0.765290i	$-0.722596\pi$
$773$	−44.0336	−	11.7988i	−1.58378	−	0.424372i	−0.940093	+	0.340918i	$0.889262\pi$
$774$	15.8664	+	34.6219i	0.570305	+	1.24446i
$775$	−15.4061	+	26.6841i	−0.553402	+	0.958521i
$776$	−5.24351	−	1.22095i	−0.188231	−	0.0438294i
$777$	−4.84930	+	6.55052i	−0.173968	+	0.234999i
$778$	−34.9802	+	30.0142i	−1.25410	+	1.07606i
$779$	−46.0576	+	12.3411i	−1.65018	+	0.442166i
$780$	−15.2864	−	16.2462i	−0.547342	−	0.581708i
$781$	0.522047	−	1.94830i	0.0186803	−	0.0697158i
$782$	−6.43174	−	4.39883i	−0.229998	−	0.157302i
$783$	19.8796	−	7.62510i	0.710438	−	0.272499i
$784$	26.9805	−	7.48667i	0.963591	−	0.267381i
$785$			9.63260i			0.343802i
$786$	−22.2168	+	14.2223i	−0.792447	+	0.507294i
$787$	41.3359	+	11.0759i	1.47347	+	0.394814i	0.904119	−	0.427282i	$-0.140529\pi$
$787$	41.3359	+	11.0759i	1.47347	+	0.394814i	0.569349	+	0.822096i	$0.307195\pi$
$788$	5.36750	−	12.2052i	0.191209	−	0.434793i
$789$	−33.6481	−	4.73192i	−1.19790	−	0.168461i
$790$	−25.8288	−	30.1022i	−0.918946	−	1.07099i
$791$	−24.0415	−	5.77510i	−0.854818	−	0.205339i
$792$	−1.01426	+	4.03267i	−0.0360401	+	0.143295i
$793$	−12.7059	−	7.33573i	−0.451198	−	0.260499i
$794$	8.41812	−	23.9456i	0.298748	−	0.849797i
$795$	10.6067	−	13.5735i	0.376179	−	0.481401i
$796$	7.49102	−	9.33747i	0.265512	−	0.330958i
$797$	16.5254	+	16.5254i	0.585359	+	0.585359i	0.936371	−	0.351012i	$-0.114162\pi$
$797$	16.5254	+	16.5254i	0.585359	+	0.585359i	−0.351012	+	0.936371i	$0.614162\pi$
$798$	−47.8523	+	16.5877i	−1.69395	+	0.587197i
$799$	−2.23486			−0.0790635
$800$	13.0505	−	10.2527i	0.461404	−	0.362487i
$801$	−12.1169	+	42.2289i	−0.428130	+	1.49209i
$802$	−1.43087	−	2.98234i	−0.0505257	−	0.105310i
$803$	2.71010	−	0.726169i	0.0956373	−	0.0256259i
$804$	−3.74984	+	6.06122i	−0.132247	+	0.213763i
$805$	−10.6609	+	19.6290i	−0.375747	+	0.691831i
$806$	−25.7701	+	22.1117i	−0.907714	+	0.778851i
$807$	20.2292	+	26.8499i	0.712102	+	0.945162i
$808$	−17.8879	+	33.4902i	−0.629293	+	1.17818i
$809$	−20.5919	−	35.6662i	−0.723973	−	1.25396i	−0.959395	−	0.282065i	$-0.908981\pi$
$809$	−20.5919	−	35.6662i	−0.723973	−	1.25396i	0.235422	−	0.971893i	$-0.424353\pi$
$810$	−5.36766	−	35.4467i	−0.188600	−	1.24547i
$811$	24.9078	+	24.9078i	0.874632	+	0.874632i	0.992973	−	0.118341i	$-0.0377575\pi$
$811$	24.9078	+	24.9078i	0.874632	+	0.874632i	−0.118341	+	0.992973i	$0.537757\pi$
$812$	−13.1230	+	17.2603i	−0.460527	+	0.605716i
$813$	4.00646	−	1.61831i	0.140513	−	0.0567566i
$814$	1.01740	+	0.695824i	0.0356597	+	0.0243886i
$815$	15.6148	+	27.0456i	0.546962	+	0.947366i
$816$	−10.4935	+	7.21687i	−0.367346	+	0.252641i
$817$	60.7519	+	35.0751i	2.12544	+	1.22712i
$818$	2.13665	−	27.9645i	0.0747060	−	0.977755i
$819$	12.7227	−	12.9389i	0.444568	−	0.452123i
$820$	20.3303	+	27.7153i	0.709965	+	0.967862i
$821$	4.61728	−	1.23720i	0.161144	−	0.0431785i	−0.177345	−	0.984149i	$-0.556751\pi$
$821$	4.61728	−	1.23720i	0.161144	−	0.0431785i	0.338489	+	0.940970i	$0.390084\pi$
$822$	28.7172	+	26.1987i	1.00163	+	0.913785i
$823$	−4.83785	+	2.79313i	−0.168637	+	0.0973624i	−0.581943	−	0.813230i	$-0.697707\pi$
$823$	−4.83785	+	2.79313i	−0.168637	+	0.0973624i	0.413306	+	0.910592i	$0.364374\pi$
$824$	39.2962	+	36.7827i	1.36895	+	1.28138i
$825$	−2.29218	−	0.973208i	−0.0798035	−	0.0338828i
$826$	−13.2451	+	6.78471i	−0.460856	+	0.236070i
$827$	21.2539	+	21.2539i	0.739069	+	0.739069i	0.972398	−	0.233329i	$-0.0749618\pi$
$827$	21.2539	+	21.2539i	0.739069	+	0.739069i	−0.233329	+	0.972398i	$0.574962\pi$
$828$	1.64607	+	17.9087i	0.0572049	+	0.622370i
$829$	−11.0282	−	2.95498i	−0.383023	−	0.102631i	0.0621692	−	0.998066i	$-0.480198\pi$
$829$	−11.0282	−	2.95498i	−0.383023	−	0.102631i	−0.445193	+	0.895435i	$0.646865\pi$
$830$	−50.4950	+	24.2265i	−1.75271	+	0.840913i
$831$	−4.92771	+	3.71263i	−0.170940	+	0.128790i
$832$	17.3155	−	5.88946i	0.600305	−	0.204180i
$833$	−0.670170	−	12.8502i	−0.0232200	−	0.445232i
$834$	22.9709	+	11.8939i	0.795419	+	0.411852i
$835$	−61.7780	+	16.5534i	−2.13792	+	0.572853i
$836$	2.77749	+	7.13806i	0.0960616	+	0.246875i
$837$	−54.2747	+	5.69019i	−1.87601	+	0.196682i
$838$	−4.85089	−	25.8437i	−0.167571	−	0.892757i
$839$			36.0214i			1.24360i	0.783177	+	0.621799i	$0.213598\pi$
$839$			36.0214i			1.24360i	−0.783177	+	0.621799i	$0.786402\pi$
$840$	23.6523	+	27.8110i	0.816081	+	0.959570i
$841$			12.2097i			0.421023i
$842$	6.78278	−	1.27313i	0.233750	−	0.0438750i
$843$	24.7528	−	31.6765i	0.852533	−	1.09100i
$844$	−3.56187	+	8.09938i	−0.122604	+	0.278792i
$845$	−21.1489	+	5.66684i	−0.727545	+	0.194945i
$846$	3.28930	+	3.97315i	0.113089	+	0.136600i
$847$	19.5986	−	20.6474i	0.673417	−	0.709452i
$848$	6.52661	+	12.5252i	0.224125	+	0.430117i
$849$	−9.84679	−	13.0695i	−0.337941	−	0.448544i
$850$	−3.29917	−	6.87642i	−0.113161	−	0.235859i
$851$	5.14920	+	1.37972i	0.176512	+	0.0472963i
$852$	−13.6535	−	4.10754i	−0.467761	−	0.140722i
$853$	−22.3241	−	22.3241i	−0.764362	−	0.764362i	0.212746	−	0.977108i	$-0.431759\pi$
$853$	−22.3241	−	22.3241i	−0.764362	−	0.764362i	−0.977108	+	0.212746i	$0.931759\pi$
$854$	20.1660	+	13.0343i	0.690067	+	0.446023i
$855$	−45.8642	−	47.5103i	−1.56852	−	1.62482i
$856$	1.10051	+	33.3095i	0.0376145	+	1.13850i
$857$	16.2500	−	9.38193i	0.555089	−	0.320481i	−0.196083	−	0.980587i	$-0.562822\pi$
$857$	16.2500	−	9.38193i	0.555089	−	0.320481i	0.751172	+	0.660107i	$0.229489\pi$
$858$	−2.02740	−	1.84960i	−0.0692142	−	0.0631442i
$859$	−31.5440	+	8.45219i	−1.07627	+	0.288385i	−0.753066	−	0.657945i	$-0.771426\pi$
$859$	−31.5440	+	8.45219i	−1.07627	+	0.288385i	−0.323201	+	0.946330i	$0.604759\pi$
$860$	7.68262	−	49.9817i	0.261975	−	1.70436i
$861$	−21.8860	+	17.4013i	−0.745874	+	0.593034i
$862$	−8.10481	−	0.619254i	−0.276051	−	0.0210919i
$863$	43.9830	+	25.3936i	1.49720	+	0.864409i	0.999995	−	0.00322368i	$-0.00102613\pi$
$863$	43.9830	+	25.3936i	1.49720	+	0.864409i	0.497206	+	0.867633i	$0.334359\pi$
$864$	28.2748	+	8.03354i	0.961927	+	0.273307i
$865$	5.04417	+	8.73675i	0.171507	+	0.297058i
$866$	7.33223	−	10.7208i	0.249159	−	0.364307i
$867$	−8.83585	−	21.8750i	−0.300081	−	0.742913i
$868$	43.9389	−	34.0264i	1.49138	−	1.15493i
$869$	−3.45045	−	3.45045i	−0.117049	−	0.117049i
$870$	−27.6146	−	6.05843i	−0.936221	−	0.205400i
$871$	−2.35193	−	4.07367i	−0.0796922	−	0.138031i
$872$	−35.7259	−	19.0820i	−1.20983	−	0.646198i
$873$	5.54098	−	1.38050i	0.187534	−	0.0467228i
$874$	21.5712	+	25.1403i	0.729658	+	0.850382i
$875$	13.1298	−	8.04367i	0.443869	−	0.271926i
$876$	−4.54791	−	19.3044i	−0.153660	−	0.652236i
$877$	28.4454	−	7.62193i	0.960534	−	0.257374i	0.255707	−	0.966754i	$-0.417692\pi$
$877$	28.4454	−	7.62193i	0.960534	−	0.257374i	0.704826	+	0.709380i	$0.251025\pi$
$878$	14.1077	−	6.76861i	0.476113	−	0.228430i
$879$	5.11775	+	41.7108i	0.172618	+	1.40687i
$880$	4.06928	−	3.73182i	0.137175	−	0.125800i
$881$	31.3950			1.05772			0.528862	−	0.848708i	$-0.322619\pi$
$881$	31.3950			1.05772			0.528862	+	0.848708i	$0.322619\pi$
$882$	−21.8588	+	20.1046i	−0.736024	+	0.676956i
$883$	24.1636	+	24.1636i	0.813171	+	0.813171i	0.985108	−	0.171937i	$-0.0550027\pi$
$883$	24.1636	+	24.1636i	0.813171	+	0.813171i	−0.171937	+	0.985108i	$0.555003\pi$
$884$	−0.916724	−	8.35501i	−0.0308328	−	0.281010i
$885$	−15.2895	−	11.9476i	−0.513951	−	0.401614i
$886$	15.5021	+	5.44980i	0.520804	+	0.183090i
$887$	5.53181	+	3.19379i	0.185740	+	0.107237i	0.589987	−	0.807413i	$-0.299133\pi$
$887$	5.53181	+	3.19379i	0.185740	+	0.107237i	−0.404247	+	0.914650i	$0.632466\pi$
$888$	5.13516	−	7.03879i	0.172325	−	0.236206i
$889$	9.73259	−	40.5164i	0.326420	−	1.35888i
$890$	44.2713	−	37.9863i	1.48398	−	1.27330i
$891$	−0.990652	−	4.29781i	−0.0331881	−	0.143982i
$892$	34.6014	−	13.4638i	1.15854	−	0.450801i
$893$	9.17722	+	2.45903i	0.307104	+	0.0822883i
$894$	1.42807	−	0.914195i	0.0477618	−	0.0305753i
$895$		−	57.9880i		−	1.93832i
$896$	−28.7869	+	8.20454i	−0.961703	+	0.274095i
$897$	−10.9251	−	4.63855i	−0.364778	−	0.154877i
$898$	32.0418	−	46.8497i	1.06925	−	1.56340i
$899$	−11.1382	+	41.5684i	−0.371480	+	1.38638i
$900$	−7.36918	+	15.9861i	−0.245639	+	0.532871i
$901$	6.26947	−	1.67990i	0.208866	−	0.0559656i
$902$	2.75361	+	3.20920i	0.0916850	+	0.106855i
$903$	40.8704	+	4.66546i	1.36008	+	0.155257i
$904$	25.7439	+	5.99445i	0.856230	+	0.199372i
$905$	−10.9821	+	19.0216i	−0.365058	+	0.632299i
$906$	0.144637	−	0.158541i	0.00480525	−	0.00526717i
$907$	−32.3226	−	8.66081i	−1.07325	−	0.287578i	−0.321425	−	0.946935i	$-0.604162\pi$
$907$	−32.3226	−	8.66081i	−1.07325	−	0.287578i	−0.751830	+	0.659358i	$0.770828\pi$
$908$	45.4234	−	4.98392i	1.50743	−	0.165397i
$909$	0.709831	−	40.2649i	0.0235436	−	1.33550i
$910$	−23.5572	+	5.06033i	−0.780915	+	0.167748i
$911$		−	11.5565i		−	0.382883i	−0.981504	−	0.191441i	$-0.938684\pi$
$911$		−	11.5565i		−	0.382883i	0.981504	−	0.191441i	$-0.0613162\pi$
$912$	51.0314	−	18.0893i	1.68982	−	0.598996i
$913$	−5.96697	+	3.44503i	−0.197478	+	0.114014i
$914$	6.80104	+	14.1753i	0.224958	+	0.468878i
$915$	−4.35997	+	31.0033i	−0.144136	+	1.02494i
$916$	0.519837	+	0.708669i	0.0171759	+	0.0234151i
$917$	0.742229	+	28.4831i	0.0245106	+	0.940595i
$918$	6.42155	−	11.8842i	0.211943	−	0.392239i
$919$	−26.4017	−	15.2430i	−0.870912	−	0.502821i	−0.00326070	−	0.999995i	$-0.501038\pi$
$919$	−26.4017	−	15.2430i	−0.870912	−	0.502821i	−0.867651	+	0.497173i	$0.834371\pi$
$920$	11.2504	−	21.0632i	0.370913	−	0.694434i
$921$	−0.198089	−	1.61447i	−0.00652726	−	0.0531985i
$922$	−1.94262	−	10.3496i	−0.0639769	−	0.340845i
$923$	6.65377	−	6.65377i	0.219011	−	0.219011i
$924$	3.16200	+	3.18979i	0.104022	+	0.104937i
$925$	3.68955	+	3.68955i	0.121312	+	0.121312i
$926$	14.6861	+	10.0442i	0.482615	+	0.330073i
$927$	−54.8760	−	15.7458i	−1.80236	−	0.517159i
$928$	13.9000	−	18.5494i	0.456291	−	0.608913i
$929$	1.52712	−	2.64506i	0.0501033	−	0.0867815i	−0.839886	−	0.542763i	$-0.817378\pi$
$929$	1.52712	−	2.64506i	0.0501033	−	0.0867815i	0.889989	+	0.455981i	$0.150712\pi$
$930$	64.3472	+	33.3177i	2.11003	+	1.09253i
$931$	−11.3872	+	53.5054i	−0.373199	+	1.75357i
$932$	−28.0336	−	4.30902i	−0.918273	−	0.141147i
$933$	−6.26673	+	44.5620i	−0.205164	+	1.45889i
$934$	−7.08881	−	2.49209i	−0.231953	−	0.0815435i
$935$	−1.26870	−	2.19744i	−0.0414908	−	0.0718641i
$936$	−13.5044	+	13.9268i	−0.441404	+	0.455213i
$937$	41.3022			1.34929			0.674643	−	0.738144i	$-0.264298\pi$
$937$	41.3022			1.34929			0.674643	+	0.738144i	$0.264298\pi$
$938$	3.50980	+	6.85183i	0.114599	+	0.223720i
$939$	1.48780	+	3.68335i	0.0485525	+	0.120202i
$940$	−0.746987	−	6.80803i	−0.0243640	−	0.222053i
$941$	−6.03437	+	22.5206i	−0.196715	+	0.734150i	0.795101	+	0.606476i	$0.207418\pi$
$941$	−6.03437	+	22.5206i	−0.196715	+	0.734150i	−0.991816	+	0.127673i	$0.959249\pi$
$942$	8.36800	−	0.383762i	0.272644	−	0.0125036i
$943$	15.8383	+	9.14425i	0.515766	+	0.297778i
$944$	14.1087	−	7.35174i	0.459199	−	0.239279i
$945$	−35.7699	−	14.8326i	−1.16359	−	0.482506i
$946$	0.473950	−	6.20308i	0.0154095	−	0.201679i
$947$	−2.96452	−	11.0637i	−0.0963338	−	0.359523i	0.900885	−	0.434059i	$-0.142919\pi$
$947$	−2.96452	−	11.0637i	−0.0963338	−	0.359523i	−0.997218	+	0.0745362i	$0.976252\pi$
$948$	−25.1213	+	23.6372i	−0.815902	+	0.767699i
$949$	12.6431	+	3.38772i	0.410413	+	0.109970i
$950$	5.98154	+	31.8675i	0.194067	+	1.03392i
$951$	15.9633	+	6.77764i	0.517644	+	0.219780i
$952$	0.812229	+	13.7321i	0.0263245	+	0.445059i
$953$	15.4538			0.500596			0.250298	−	0.968169i	$-0.419471\pi$
$953$	15.4538			0.500596			0.250298	+	0.968169i	$0.419471\pi$
$954$	−12.2141	−	8.67342i	−0.395445	−	0.280812i
$955$	12.6670	−	47.2740i	0.409896	−	1.52975i
$956$	−25.7278	+	10.0109i	−0.832095	+	0.323777i
$957$	−3.44416	−	0.484351i	−0.111334	−	0.0156568i
$958$	1.86399	−	24.3960i	0.0602228	−	0.788198i
$959$	40.2593	−	11.9198i	1.30004	−	0.384909i
$960$	−25.4921	−	29.5541i	−0.822753	−	0.953855i
$961$	39.6504	−	68.6765i	1.27904	−	2.21537i
$962$	2.48738	+	5.18442i	0.0801965	+	0.167153i
$963$	−17.1323	−	30.9202i	−0.552082	−	0.996390i
$964$	3.58620	+	2.87705i	0.115504	+	0.0926634i
$965$	−24.5497	+	24.5497i	−0.790281	+	0.790281i
$966$	17.4768	+	8.47929i	0.562306	+	0.272817i
$967$		−	18.1600i		−	0.583986i	−0.956421	−	0.291993i	$-0.905682\pi$
$967$		−	18.1600i		−	0.583986i	0.956421	−	0.291993i	$-0.0943183\pi$
$968$	−20.7974	+	22.2186i	−0.668452	+	0.714131i
$969$	−3.03017	−	24.6965i	−0.0973431	−	0.793366i
$970$	−7.15310	−	2.51469i	−0.229672	−	0.0807418i
$971$	−10.5417	−	39.3420i	−0.338298	−	1.26255i	−0.900249	−	0.435375i	$-0.856616\pi$
$971$	−10.5417	−	39.3420i	−0.338298	−	1.26255i	0.561951	−	0.827171i	$-0.310051\pi$
$972$	−30.5793	+	6.07517i	−0.980831	+	0.194861i
$973$	23.8247	−	14.5956i	0.763786	−	0.467915i
$974$	−34.9545	−	2.67072i	−1.12001	−	0.0855755i
$975$	−6.99071	−	9.27866i	−0.223882	−	0.297155i
$976$	−21.6550	−	13.7835i	−0.693161	−	0.441200i
$977$	−29.9183	+	17.2733i	−0.957171	+	0.552623i	−0.895301	−	0.445461i	$-0.853040\pi$
$977$	−29.9183	+	17.2733i	−0.957171	+	0.552623i	−0.0618697	+	0.998084i	$0.519706\pi$
$978$	22.8729	−	14.6423i	0.731394	−	0.468210i
$979$	5.07457	−	5.07457i	0.162184	−	0.162184i
$980$	38.9214	−	6.33662i	1.24330	−	0.202416i
$981$	42.9528	+	0.757217i	1.37138	+	0.0241761i
$982$	0.416593	+	2.21945i	0.0132940	+	0.0708256i
$983$	4.97653	−	2.87320i	0.158727	−	0.0916409i	−0.418533	−	0.908202i	$-0.637455\pi$
$983$	4.97653	−	2.87320i	0.158727	−	0.0916409i	0.577259	+	0.816561i	$0.304122\pi$
$984$	23.2668	−	18.7655i	0.741720	−	0.598221i
$985$	9.38901	−	16.2622i	0.299159	−	0.518158i
$986$	−6.93662	−	8.08430i	−0.220907	−	0.257457i
$987$	5.51030	−	0.822314i	0.175395	−	0.0261745i
$988$	−5.42865	+	35.3178i	−0.172708	+	1.12361i
$989$	−6.96380	−	25.9892i	−0.221436	−	0.826410i
$990$	−2.03935	+	5.48974i	−0.0648147	+	0.174475i
$991$	−1.61163	−	2.79143i	−0.0511952	−	0.0886728i	0.839292	−	0.543681i	$-0.182970\pi$
$991$	−1.61163	−	2.79143i	−0.0511952	−	0.0886728i	−0.890487	+	0.455008i	$0.849636\pi$
$992$	−46.7179	+	36.7024i	−1.48329	+	1.16530i
$993$	−54.4921	−	23.1361i	−1.72926	−	0.734203i
$994$	−11.4225	+	10.3295i	−0.362299	+	0.327632i
$995$	11.9213	−	11.9213i	0.377932	−	0.377932i
$996$	23.0577	+	42.9007i	0.730610	+	1.35936i
$997$	13.1578	−	49.1057i	0.416712	−	1.55519i	−0.364668	−	0.931137i	$-0.618818\pi$
$997$	13.1578	−	49.1057i	0.416712	−	1.55519i	0.781381	−	0.624054i	$-0.214516\pi$
$998$	39.6465	+	13.9378i	1.25499	+	0.441194i
$999$	−1.44806	+	9.12726i	−0.0458145	+	0.288774i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.bo.a.173.48	yes	240
3.2	odd	2	inner	336.2.bo.a.173.13	yes	240
7.3	odd	6	inner	336.2.bo.a.269.9	yes	240
16.5	even	4	inner	336.2.bo.a.5.52	yes	240
21.17	even	6	inner	336.2.bo.a.269.52	yes	240
48.5	odd	4	inner	336.2.bo.a.5.9	✓	240
112.101	odd	12	inner	336.2.bo.a.101.13	yes	240
336.101	even	12	inner	336.2.bo.a.101.48	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.bo.a.5.9	✓	240	48.5	odd	4	inner
336.2.bo.a.5.52	yes	240	16.5	even	4	inner
336.2.bo.a.101.13	yes	240	112.101	odd	12	inner
336.2.bo.a.101.48	yes	240	336.101	even	12	inner
336.2.bo.a.173.13	yes	240	3.2	odd	2	inner
336.2.bo.a.173.48	yes	240	1.1	even	1	trivial
336.2.bo.a.269.9	yes	240	7.3	odd	6	inner
336.2.bo.a.269.52	yes	240	21.17	even	6	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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.bo (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.16732 + 0.798357i) q^{2} +(1.06648 - 1.36478i) q^{3} +(0.725251 + 1.86387i) q^{4} +(0.729016 + 2.72073i) q^{5} +(2.33450 - 0.741703i) q^{6} +(0.617966 - 2.57257i) q^{7} +(-0.641437 + 2.75473i) q^{8} +(-0.725259 - 2.91101i) q^{9} +O(q^{10})\)	\(q+(1.16732 + 0.798357i) q^{2} +(1.06648 - 1.36478i) q^{3} +(0.725251 + 1.86387i) q^{4} +(0.729016 + 2.72073i) q^{5} +(2.33450 - 0.741703i) q^{6} +(0.617966 - 2.57257i) q^{7} +(-0.641437 + 2.75473i) q^{8} +(-0.725259 - 2.91101i) q^{9} +(-1.32112 + 3.75796i) q^{10} +(-0.126836 + 0.473358i) q^{11} +(3.31724 + 0.997962i) q^{12} +(-1.61659 + 1.61659i) q^{13} +(2.77519 - 2.50964i) q^{14} +(4.49068 + 1.90664i) q^{15} +(-2.94802 + 2.70355i) q^{16} +(0.919117 + 1.59196i) q^{17} +(1.47742 - 3.97709i) q^{18} +(-2.02262 - 7.54853i) q^{19} +(-4.54236 + 3.33200i) q^{20} +(-2.85195 - 3.58697i) q^{21} +(-0.525966 + 0.451297i) q^{22} +(-1.49868 + 2.59579i) q^{23} +(3.07553 + 3.81328i) q^{24} +(-2.54076 + 1.46691i) q^{25} +(-3.17769 + 0.596454i) q^{26} +(-4.74637 - 2.11470i) q^{27} +(5.24312 - 0.713952i) q^{28} +(-2.89744 + 2.89744i) q^{29} +(3.71986 + 5.81081i) q^{30} +(9.09536 - 5.25121i) q^{31} +(-5.59967 + 0.802318i) q^{32} +(0.510763 + 0.677928i) q^{33} +(-0.198051 + 2.59210i) q^{34} +(7.44977 - 0.194130i) q^{35} +(4.89975 - 3.46300i) q^{36} +(-0.460312 - 1.71791i) q^{37} +(3.66539 - 10.4263i) q^{38} +(0.482239 + 3.93035i) q^{39} +(-7.96249 + 0.263071i) q^{40} -6.10153i q^{41} +(-0.465443 - 6.46401i) q^{42} +(-6.34740 + 6.34740i) q^{43} +(-0.974265 + 0.106898i) q^{44} +(7.39134 - 4.09541i) q^{45} +(-3.82180 + 1.83363i) q^{46} +(-0.607881 + 1.05288i) q^{47} +(0.545759 + 6.90667i) q^{48} +(-6.23624 - 3.17952i) q^{49} +(-4.13698 - 0.316089i) q^{50} +(3.15289 + 0.443389i) q^{51} +(-4.18555 - 1.84068i) q^{52} +(0.913867 - 3.41060i) q^{53} +(-3.85222 - 6.25783i) q^{54} -1.38034 q^{55} +(6.69036 + 3.35247i) q^{56} +(-12.4592 - 5.28989i) q^{57} +(-5.69542 + 1.06904i) q^{58} +(-3.84178 - 1.02940i) q^{59} +(-0.296860 + 9.75283i) q^{60} +(1.66094 + 6.19872i) q^{61} +(14.8095 + 1.13153i) q^{62} +(-7.93697 + 0.0668744i) q^{63} +(-7.17712 - 3.53398i) q^{64} +(-5.57682 - 3.21978i) q^{65} +(0.0549927 + 1.19913i) q^{66} +(-0.532520 + 1.98739i) q^{67} +(-2.30061 + 2.86768i) q^{68} +(1.94438 + 4.81372i) q^{69} +(8.85121 + 5.72096i) q^{70} -4.11592 q^{71} +(8.48428 - 0.130664i) q^{72} +(-2.86263 - 4.95823i) q^{73} +(0.834176 - 2.37284i) q^{74} +(-0.707648 + 5.03200i) q^{75} +(12.6026 - 9.24449i) q^{76} +(1.13937 + 0.618813i) q^{77} +(-2.57490 + 4.97296i) q^{78} +(-4.97869 + 8.62335i) q^{79} +(-9.50477 - 6.04983i) q^{80} +(-7.94800 + 4.22248i) q^{81} +(4.87120 - 7.12241i) q^{82} +(9.94175 + 9.94175i) q^{83} +(4.61727 - 7.91712i) q^{84} +(-3.66123 + 3.66123i) q^{85} +(-12.4769 + 2.34192i) q^{86} +(0.864325 + 7.04443i) q^{87} +(-1.22262 - 0.653028i) q^{88} +(-12.6823 - 7.32215i) q^{89} +(11.8976 + 1.12030i) q^{90} +(3.15980 + 5.15779i) q^{91} +(-5.92514 - 0.910746i) q^{92} +(2.53323 - 18.0135i) q^{93} +(-1.55016 + 0.743738i) q^{94} +(19.0630 - 11.0060i) q^{95} +(-4.87692 + 8.49798i) q^{96} +1.90345i q^{97} +(-4.74126 - 8.69025i) q^{98} +(1.46994 + 0.0259136i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 6 q^{3} - 4 q^{4}+O(q^{10}) \) 240 * q - 6 * q^3 - 4 * q^4	\( 240 q - 6 q^{3} - 4 q^{4} - 12 q^{10} - 6 q^{12} - 16 q^{15} - 20 q^{16} - 4 q^{18} - 12 q^{19} + 2 q^{21} - 40 q^{22} - 6 q^{24} - 12 q^{28} + 22 q^{30} - 24 q^{31} - 12 q^{33} - 64 q^{36} - 4 q^{37} + 48 q^{40} - 18 q^{42} - 16 q^{43} - 6 q^{45} + 12 q^{46} - 16 q^{49} - 10 q^{51} - 48 q^{52} - 90 q^{54} - 4 q^{58} - 18 q^{60} - 12 q^{61} - 36 q^{63} + 32 q^{64} - 66 q^{66} - 36 q^{67} - 76 q^{70} - 46 q^{72} + 24 q^{75} - 76 q^{78} - 8 q^{79} - 4 q^{81} + 72 q^{82} - 24 q^{84} + 24 q^{85} + 12 q^{88} - 88 q^{91} - 14 q^{93} + 24 q^{94} + 96 q^{96} + 28 q^{99}+O(q^{100}) \) 240 * q - 6 * q^3 - 4 * q^4 - 12 * q^10 - 6 * q^12 - 16 * q^15 - 20 * q^16 - 4 * q^18 - 12 * q^19 + 2 * q^21 - 40 * q^22 - 6 * q^24 - 12 * q^28 + 22 * q^30 - 24 * q^31 - 12 * q^33 - 64 * q^36 - 4 * q^37 + 48 * q^40 - 18 * q^42 - 16 * q^43 - 6 * q^45 + 12 * q^46 - 16 * q^49 - 10 * q^51 - 48 * q^52 - 90 * q^54 - 4 * q^58 - 18 * q^60 - 12 * q^61 - 36 * q^63 + 32 * q^64 - 66 * q^66 - 36 * q^67 - 76 * q^70 - 46 * q^72 + 24 * q^75 - 76 * q^78 - 8 * q^79 - 4 * q^81 + 72 * q^82 - 24 * q^84 + 24 * q^85 + 12 * q^88 - 88 * q^91 - 14 * q^93 + 24 * q^94 + 96 * q^96 + 28 * q^99

Introduction

L-functions

Modular forms

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Database

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