LMFDB - Embedded newform 230.2.l.a.103.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,2,Mod(7,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([11, 38]))

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

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

chi := DirichletCharacter("230.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.l (of order $44$, degree $20$, 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:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			103.5
Character	$\chi$	$=$	230.103
Dual form			230.2.l.a.67.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.212565 + 0.977147i) q^{2} +(2.04540 - 1.53116i) q^{3} +(-0.909632 - 0.415415i) q^{4} +(-2.20119 - 0.393381i) q^{5} +(1.06139 + 2.32412i) q^{6} +(0.361036 - 5.04795i) q^{7} +(0.599278 - 0.800541i) q^{8} +(0.993984 - 3.38520i) q^{9} +O(q^{10})$	\(q+(-0.212565 + 0.977147i) q^{2} +(2.04540 - 1.53116i) q^{3} +(-0.909632 - 0.415415i) q^{4} +(-2.20119 - 0.393381i) q^{5} +(1.06139 + 2.32412i) q^{6} +(0.361036 - 5.04795i) q^{7} +(0.599278 - 0.800541i) q^{8} +(0.993984 - 3.38520i) q^{9} +(0.852288 - 2.06727i) q^{10} +(-1.44535 + 2.24901i) q^{11} +(-2.49663 + 0.543108i) q^{12} +(6.05938 - 0.433376i) q^{13} +(4.85584 + 1.42580i) q^{14} +(-5.10464 + 2.56577i) q^{15} +(0.654861 + 0.755750i) q^{16} +(-0.522224 + 1.40014i) q^{17} +(3.09655 + 1.69084i) q^{18} +(-0.914739 + 2.00300i) q^{19} +(1.83886 + 1.27224i) q^{20} +(-6.99077 - 10.8779i) q^{21} +(-1.89038 - 1.89038i) q^{22} +(-4.59200 + 1.38330i) q^{23} -2.55502i q^{24} +(4.69050 + 1.73181i) q^{25} +(-0.864543 + 6.01303i) q^{26} +(-0.471543 - 1.26426i) q^{27} +(-2.42540 + 4.44179i) q^{28} +(5.74476 - 2.62354i) q^{29} +(-1.42206 - 5.53338i) q^{30} +(0.449243 + 3.12456i) q^{31} +(-0.877679 + 0.479249i) q^{32} +(0.487289 + 6.81318i) q^{33} +(-1.25713 - 0.807911i) q^{34} +(-2.78047 + 10.9695i) q^{35} +(-2.31042 + 2.66637i) q^{36} +(1.44686 + 2.64972i) q^{37} +(-1.76278 - 1.31960i) q^{38} +(11.7303 - 10.1643i) q^{39} +(-1.63404 + 1.52640i) q^{40} +(3.21204 - 0.943140i) q^{41} +(12.1153 - 4.51876i) q^{42} +(0.0653473 + 0.0872938i) q^{43} +(2.24901 - 1.44535i) q^{44} +(-3.51962 + 7.06046i) q^{45} +(-0.375584 - 4.78110i) q^{46} +(-1.68806 + 1.68806i) q^{47} +(2.49663 + 0.543108i) q^{48} +(-18.4227 - 2.64878i) q^{49} +(-2.68927 + 4.21519i) q^{50} +(1.07569 + 3.66345i) q^{51} +(-5.69184 - 2.12295i) q^{52} +(10.0271 + 0.717153i) q^{53} +(1.33560 - 0.192030i) q^{54} +(4.06621 - 4.38193i) q^{55} +(-3.82473 - 3.31415i) q^{56} +(1.19592 + 5.49754i) q^{57} +(1.34245 + 6.17114i) q^{58} +(-9.39124 - 8.13756i) q^{59} +(5.70921 - 0.213361i) q^{60} +(-2.07603 + 0.298488i) q^{61} +(-3.14864 - 0.225195i) q^{62} +(-16.7294 - 6.23976i) q^{63} +(-0.281733 - 0.959493i) q^{64} +(-13.5084 - 1.42970i) q^{65} +(-6.76106 - 0.972094i) q^{66} +(3.81092 + 0.829015i) q^{67} +(1.05667 - 1.05667i) q^{68} +(-7.27441 + 9.86050i) q^{69} +(-10.1278 - 5.04866i) q^{70} +(-3.32031 + 2.13383i) q^{71} +(-2.11432 - 2.82440i) q^{72} +(-7.56617 + 2.82203i) q^{73} +(-2.89672 + 0.850554i) q^{74} +(12.2456 - 3.63969i) q^{75} +(1.66415 - 1.44200i) q^{76} +(10.8311 + 8.10803i) q^{77} +(7.43860 + 13.6228i) q^{78} +(0.225753 - 0.260533i) q^{79} +(-1.14418 - 1.92116i) q^{80} +(6.00383 + 3.85843i) q^{81} +(0.238818 + 3.33911i) q^{82} +(-2.21632 + 1.21020i) q^{83} +(1.84021 + 12.7989i) q^{84} +(1.70030 - 2.87654i) q^{85} +(-0.0991894 + 0.0452983i) q^{86} +(7.73323 - 14.1623i) q^{87} +(0.934258 + 2.50484i) q^{88} +(-1.49958 + 10.4298i) q^{89} +(-6.15096 - 4.94000i) q^{90} -30.7439i q^{91} +(4.75167 + 0.649296i) q^{92} +(5.70309 + 5.70309i) q^{93} +(-1.29066 - 2.00831i) q^{94} +(2.80146 - 4.04915i) q^{95} +(-1.06139 + 2.32412i) q^{96} +(3.80751 + 2.07906i) q^{97} +(6.50427 - 17.4386i) q^{98} +(6.17669 + 7.12828i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 8 q^{3} - 8 q^{6}+O(q^{10}) $ 240 * q - 8 * q^3 - 8 * q^6	$ 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46} - 80 q^{47} + 8 q^{48} + 8 q^{50} + 16 q^{52} - 44 q^{56} - 88 q^{57} - 176 q^{61} - 32 q^{62} - 176 q^{66} + 24 q^{70} - 336 q^{71} + 16 q^{72} - 88 q^{73} - 36 q^{75} - 24 q^{77} + 40 q^{78} - 136 q^{81} + 40 q^{82} - 100 q^{85} - 44 q^{86} + 40 q^{87} + 8 q^{92} + 56 q^{93} + 52 q^{95} + 8 q^{96} + 132 q^{97} + 24 q^{98}+O(q^{100}) $ 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{9}{22}\right)$

Coefficient data

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

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

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

$2$	−0.212565	+	0.977147i	−0.150306	+	0.690947i
$2$	−0.212565	+	0.977147i	−0.150306	+	0.690947i
$3$	2.04540	−	1.53116i	1.18091	−	0.884018i	0.185780	−	0.982591i	$-0.440519\pi$
$3$	2.04540	−	1.53116i	1.18091	−	0.884018i	0.995130	+	0.0985731i	$0.0314278\pi$
$4$	−0.909632	−	0.415415i	−0.454816	−	0.207708i
$5$	−2.20119	−	0.393381i	−0.984404	−	0.175925i
$5$	−2.20119	−	0.393381i	−0.984404	−	0.175925i
$6$	1.06139	+	2.32412i	0.433312	+	0.948820i
$7$	0.361036	−	5.04795i	0.136459	−	1.90794i	−0.223057	−	0.974805i	$-0.571603\pi$
$7$	0.361036	−	5.04795i	0.136459	−	1.90794i	0.359515	−	0.933139i	$-0.382942\pi$
$8$	0.599278	−	0.800541i	0.211877	−	0.283034i
$9$	0.993984	−	3.38520i	0.331328	−	1.12840i
$10$	0.852288	−	2.06727i	0.269517	−	0.653728i
$11$	−1.44535	+	2.24901i	−0.435790	+	0.678102i	−0.987799	−	0.155736i	$-0.950225\pi$
$11$	−1.44535	+	2.24901i	−0.435790	+	0.678102i	0.552009	+	0.833838i	$0.313861\pi$
$12$	−2.49663	+	0.543108i	−0.720714	+	0.156782i
$13$	6.05938	−	0.433376i	1.68057	−	0.120197i	0.801847	−	0.597529i	$-0.203851\pi$
$13$	6.05938	−	0.433376i	1.68057	−	0.120197i	0.878723	+	0.477332i	$0.158396\pi$
$14$	4.85584	+	1.42580i	1.29778	+	0.381062i
$15$	−5.10464	+	2.56577i	−1.31801	+	0.662479i
$16$	0.654861	+	0.755750i	0.163715	+	0.188937i
$17$	−0.522224	+	1.40014i	−0.126658	+	0.339583i	−0.984766	−	0.173886i	$-0.944367\pi$
$17$	−0.522224	+	1.40014i	−0.126658	+	0.339583i	0.858108	+	0.513470i	$0.171640\pi$
$18$	3.09655	+	1.69084i	0.729863	+	0.398536i
$19$	−0.914739	+	2.00300i	−0.209856	+	0.459520i	−0.985065	−	0.172185i	$-0.944917\pi$
$19$	−0.914739	+	2.00300i	−0.209856	+	0.459520i	0.775209	+	0.631705i	$0.217644\pi$
$20$	1.83886	+	1.27224i	0.411182	+	0.284482i
$21$	−6.99077	−	10.8779i	−1.52551	−	2.37374i
$22$	−1.89038	−	1.89038i	−0.403031	−	0.403031i
$23$	−4.59200	+	1.38330i	−0.957499	+	0.288437i
$23$	−4.59200	+	1.38330i	−0.957499	+	0.288437i
$24$		−	2.55502i		−	0.521541i
$25$	4.69050	+	1.73181i	0.938101	+	0.346363i
$26$	−0.864543	+	6.01303i	−0.169551	+	1.17925i
$27$	−0.471543	−	1.26426i	−0.0907485	−	0.243306i
$28$	−2.42540	+	4.44179i	−0.458358	+	0.839420i
$29$	5.74476	−	2.62354i	1.06677	−	0.487180i	0.196885	−	0.980427i	$-0.436917\pi$
$29$	5.74476	−	2.62354i	1.06677	−	0.487180i	0.869889	+	0.493247i	$0.164190\pi$
$30$	−1.42206	−	5.53338i	−0.259632	−	1.01025i
$31$	0.449243	+	3.12456i	0.0806865	+	0.561187i	0.989561	+	0.144117i	$0.0460340\pi$
$31$	0.449243	+	3.12456i	0.0806865	+	0.561187i	−0.908874	+	0.417070i	$0.863057\pi$
$32$	−0.877679	+	0.479249i	−0.155153	+	0.0847201i
$33$	0.487289	+	6.81318i	0.0848261	+	1.18602i
$34$	−1.25713	−	0.807911i	−0.215597	−	0.138556i
$35$	−2.78047	+	10.9695i	−0.469986	+	1.85418i
$36$	−2.31042	+	2.66637i	−0.385070	+	0.444395i
$37$	1.44686	+	2.64972i	0.237862	+	0.435612i	0.969155	−	0.246452i	$-0.0792647\pi$
$37$	1.44686	+	2.64972i	0.237862	+	0.435612i	−0.731293	+	0.682063i	$0.761083\pi$
$38$	−1.76278	−	1.31960i	−0.285961	−	0.214068i
$39$	11.7303	−	10.1643i	1.87835	−	1.62760i
$40$	−1.63404	+	1.52640i	−0.258365	+	0.241345i
$41$	3.21204	−	0.943140i	0.501636	−	0.147294i	−0.0211182	−	0.999777i	$-0.506723\pi$
$41$	3.21204	−	0.943140i	0.501636	−	0.147294i	0.522754	+	0.852483i	$0.324904\pi$
$42$	12.1153	−	4.51876i	1.86943	−	0.697260i
$43$	0.0653473	+	0.0872938i	0.00996537	+	0.0133122i	0.805496	−	0.592601i	$-0.201899\pi$
$43$	0.0653473	+	0.0872938i	0.00996537	+	0.0133122i	−0.795531	+	0.605913i	$0.792808\pi$
$44$	2.24901	−	1.44535i	0.339051	−	0.217895i
$45$	−3.51962	+	7.06046i	−0.524674	+	1.05251i
$46$	−0.375584	−	4.78110i	−0.0553768	−	0.704935i
$47$	−1.68806	+	1.68806i	−0.246229	+	0.246229i	−0.819421	−	0.573192i	$-0.805705\pi$
$47$	−1.68806	+	1.68806i	−0.246229	+	0.246229i	0.573192	+	0.819421i	$0.305705\pi$
$48$	2.49663	+	0.543108i	0.360357	+	0.0783909i
$49$	−18.4227	−	2.64878i	−2.63181	−	0.378397i
$50$	−2.68927	+	4.21519i	−0.380321	+	0.596118i
$51$	1.07569	+	3.66345i	0.150626	+	0.512985i
$52$	−5.69184	−	2.12295i	−0.789316	−	0.294400i
$53$	10.0271	+	0.717153i	1.37733	+	0.0985085i	0.740272	−	0.672308i	$-0.234697\pi$
$53$	10.0271	+	0.717153i	1.37733	+	0.0985085i	0.637058	+	0.770816i	$0.280151\pi$
$54$	1.33560	−	0.192030i	0.181752	−	0.0261320i
$55$	4.06621	−	4.38193i	0.548288	−	0.590860i
$56$	−3.82473	−	3.31415i	−0.511101	−	0.442871i
$57$	1.19592	+	5.49754i	0.158403	+	0.728167i
$58$	1.34245	+	6.17114i	0.176272	+	0.810311i
$59$	−9.39124	−	8.13756i	−1.22264	−	1.05942i	−0.996350	−	0.0853584i	$-0.972796\pi$
$59$	−9.39124	−	8.13756i	−1.22264	−	1.05942i	−0.226285	−	0.974061i	$-0.572658\pi$
$60$	5.70921	−	0.213361i	0.737055	−	0.0275448i
$61$	−2.07603	+	0.298488i	−0.265808	+	0.0382175i	−0.273930	−	0.961750i	$-0.588324\pi$
$61$	−2.07603	+	0.298488i	−0.265808	+	0.0382175i	0.00812199	+	0.999967i	$0.497415\pi$
$62$	−3.14864	−	0.225195i	−0.399878	−	0.0285999i
$63$	−16.7294	−	6.23976i	−2.10771	−	0.786135i
$64$	−0.281733	−	0.959493i	−0.0352166	−	0.119937i
$65$	−13.5084	−	1.42970i	−1.67550	−	0.177332i
$66$	−6.76106	−	0.972094i	−0.832229	−	0.119657i
$67$	3.81092	+	0.829015i	0.465578	+	0.101280i	0.439234	−	0.898373i	$-0.355250\pi$
$67$	3.81092	+	0.829015i	0.465578	+	0.101280i	0.0263438	+	0.999653i	$0.491614\pi$
$68$	1.05667	−	1.05667i	0.128140	−	0.128140i
$69$	−7.27441	+	9.86050i	−0.875736	+	1.18706i
$70$	−10.1278	−	5.04866i	−1.21050	−	0.603431i
$71$	−3.32031	+	2.13383i	−0.394048	+	0.253239i	−0.722628	−	0.691237i	$-0.757066\pi$
$71$	−3.32031	+	2.13383i	−0.394048	+	0.253239i	0.328580	+	0.944476i	$0.393430\pi$
$72$	−2.11432	−	2.82440i	−0.249175	−	0.332858i
$73$	−7.56617	+	2.82203i	−0.885553	+	0.330294i	−0.750756	−	0.660579i	$-0.770311\pi$
$73$	−7.56617	+	2.82203i	−0.885553	+	0.330294i	−0.134796	+	0.990873i	$0.543038\pi$
$74$	−2.89672	+	0.850554i	−0.336737	+	0.0988748i
$75$	12.2456	−	3.63969i	1.41400	−	0.420275i
$76$	1.66415	−	1.44200i	0.190891	−	0.165408i
$77$	10.8311	+	8.10803i	1.23431	+	0.923995i
$78$	7.43860	+	13.6228i	0.842256	+	1.54248i
$79$	0.225753	−	0.260533i	0.0253992	−	0.0293122i	−0.742908	−	0.669394i	$-0.766554\pi$
$79$	0.225753	−	0.260533i	0.0253992	−	0.0293122i	0.768307	+	0.640081i	$0.221099\pi$
$80$	−1.14418	−	1.92116i	−0.127923	−	0.214792i
$81$	6.00383	+	3.85843i	0.667092	+	0.428714i
$82$	0.238818	+	3.33911i	0.0263730	+	0.368743i
$83$	−2.21632	+	1.21020i	−0.243273	+	0.132837i	−0.596261	−	0.802791i	$-0.703347\pi$
$83$	−2.21632	+	1.21020i	−0.243273	+	0.132837i	0.352988	+	0.935628i	$0.385166\pi$
$84$	1.84021	+	12.7989i	0.200783	+	1.39648i
$85$	1.70030	−	2.87654i	0.184424	−	0.312005i
$86$	−0.0991894	+	0.0452983i	−0.0106959	+	0.00488464i
$87$	7.73323	−	14.1623i	0.829089	−	1.51836i
$88$	0.934258	+	2.50484i	0.0995923	+	0.267017i
$89$	−1.49958	+	10.4298i	−0.158955	+	1.10556i	0.741608	+	0.670834i	$0.234064\pi$
$89$	−1.49958	+	10.4298i	−0.158955	+	1.10556i	−0.900563	+	0.434725i	$0.856846\pi$
$90$	−6.15096	−	4.94000i	−0.648368	−	0.520721i
$91$		−	30.7439i		−	3.22284i
$92$	4.75167	+	0.649296i	0.495396	+	0.0676937i
$93$	5.70309	+	5.70309i	0.591383	+	0.591383i
$94$	−1.29066	−	2.00831i	−0.133122	−	0.207141i
$95$	2.80146	−	4.04915i	0.287424	−	0.415434i
$96$	−1.06139	+	2.32412i	−0.108328	+	0.237205i
$97$	3.80751	+	2.07906i	0.386594	+	0.211096i	0.660779	−	0.750581i	$-0.270226\pi$
$97$	3.80751	+	2.07906i	0.386594	+	0.211096i	−0.274185	+	0.961677i	$0.588408\pi$
$98$	6.50427	−	17.4386i	0.657030	−	1.76157i
$99$	6.17669	+	7.12828i	0.620780	+	0.716419i
$100$	−3.54721	−	3.52382i	−0.354721	−	0.352382i
$101$	8.81345	+	2.58786i	0.876971	+	0.257502i	0.689078	−	0.724688i	$-0.258016\pi$
$101$	8.81345	+	2.58786i	0.876971	+	0.257502i	0.187893	+	0.982189i	$0.439834\pi$
$102$	−3.80838	+	0.272381i	−0.377086	+	0.0269697i
$103$	3.62890	−	0.789419i	0.357566	−	0.0777837i	−0.0301940	−	0.999544i	$-0.509613\pi$
$103$	3.62890	−	0.789419i	0.357566	−	0.0777837i	0.387760	+	0.921760i	$0.373249\pi$
$104$	3.28432	−	5.11050i	0.322054	−	0.501126i
$105$	11.1089	+	26.6943i	1.08412	+	2.60510i
$106$	−2.83218	+	9.64552i	−0.275086	+	0.936855i
$107$	−2.57909	+	3.44526i	−0.249330	+	0.333066i	−0.907693	−	0.419634i	$-0.862158\pi$
$107$	−2.57909	+	3.44526i	−0.249330	+	0.333066i	0.658363	+	0.752701i	$0.271249\pi$
$108$	−0.0962602	+	1.34589i	−0.00926264	+	0.129509i
$109$	−7.87227	−	17.2379i	−0.754027	−	1.65109i	−0.758991	−	0.651101i	$-0.774307\pi$
$109$	−7.87227	−	17.2379i	−0.754027	−	1.65109i	0.00496401	−	0.999988i	$-0.498420\pi$
$110$	3.41745	+	4.90473i	0.325842	+	0.467648i
$111$	7.01656	+	3.20435i	0.665982	+	0.304144i
$112$	4.05141	−	3.03285i	0.382822	−	0.286577i
$113$	0.859449	−	3.95082i	0.0808502	−	0.371662i	−0.918889	−	0.394517i	$-0.870912\pi$
$113$	0.859449	−	3.95082i	0.0808502	−	0.371662i	0.999739	+	0.0228548i	$0.00727553\pi$
$114$	−5.62612			−0.526934
$115$	10.6520	−	1.23850i	0.993309	−	0.115491i
$116$	−6.31547			−0.586377
$117$	4.55586	−	20.9430i	0.421190	−	1.93618i
$118$	9.94784	−	7.44686i	0.915773	−	0.685539i
$119$	6.87928	+	3.14166i	0.630622	+	0.287996i
$120$	−1.00509	+	5.62409i	−0.0917521	+	0.513406i
$121$	1.60056	+	3.50474i	0.145505	+	0.318613i
$122$	0.149625	−	2.09203i	0.0135464	−	0.189404i
$123$	5.12579	−	6.84726i	0.462177	−	0.617396i
$124$	0.889342	−	3.02882i	0.0798652	−	0.271996i
$125$	−9.64344	−	5.65721i	−0.862536	−	0.505996i
$126$	9.65325	−	15.0208i	0.859980	−	1.33816i
$127$	4.69834	−	1.02206i	0.416910	−	0.0906933i	0.000783161	−	1.00000i	$-0.499751\pi$
$127$	4.69834	−	1.02206i	0.416910	−	0.0906933i	0.416127	+	0.909306i	$0.363387\pi$
$128$	0.997452	−	0.0713392i	0.0881631	−	0.00630555i
$129$	0.267322	+	0.0784929i	0.0235364	+	0.00691092i
$130$	4.26843	−	12.8957i	0.374366	−	1.13103i
$131$	−0.618549	−	0.713844i	−0.0540429	−	0.0623688i	0.728084	−	0.685487i	$-0.240411\pi$
$131$	−0.618549	−	0.713844i	−0.0540429	−	0.0623688i	−0.782127	+	0.623119i	$0.785865\pi$
$132$	2.38705	−	6.39992i	0.207766	−	0.557041i
$133$	9.78078	+	5.34071i	0.848101	+	0.463098i
$134$	−1.62014	+	3.54761i	−0.139959	+	0.306467i
$135$	0.540624	+	2.96837i	0.0465295	+	0.255476i
$136$	0.807911	+	1.25713i	0.0692778	+	0.107798i
$137$	7.84543	+	7.84543i	0.670280	+	0.670280i	0.957781	−	0.287500i	$-0.0928243\pi$
$137$	7.84543	+	7.84543i	0.670280	+	0.670280i	−0.287500	+	0.957781i	$0.592824\pi$
$138$	−8.08887	−	9.20417i	−0.688570	−	0.783511i
$139$			16.2597i			1.37913i	0.724222	+	0.689567i	$0.242199\pi$
$139$			16.2597i			1.37913i	−0.724222	+	0.689567i	$0.757801\pi$
$140$	7.08610	−	8.82314i	0.598884	−	0.745692i
$141$	−0.868056	+	6.03746i	−0.0731035	+	0.508446i
$142$	−1.37929	−	3.69801i	−0.115747	−	0.310330i
$143$	−7.78327	+	14.2540i	−0.650869	+	1.19198i
$144$	3.20928	−	1.46563i	0.267440	−	0.122136i
$145$	−13.6774	+	3.51505i	−1.13584	+	0.291909i
$146$	−1.14924	−	7.99312i	−0.0951116	−	0.661515i
$147$	−41.7374	+	22.7903i	−3.44244	+	1.87972i
$148$	−0.215374	−	3.01132i	−0.0177036	−	0.247529i
$149$	−4.92416	−	3.16457i	−0.403403	−	0.259252i	0.323169	−	0.946341i	$-0.395252\pi$
$149$	−4.92416	−	3.16457i	−0.403403	−	0.259252i	−0.726573	+	0.687090i	$0.758888\pi$
$150$	0.953514	+	12.7394i	0.0778541	+	1.04017i
$151$	4.81874	−	5.56113i	0.392144	−	0.452558i	−0.525007	−	0.851098i	$-0.675937\pi$
$151$	4.81874	−	5.56113i	0.392144	−	0.452558i	0.917151	+	0.398540i	$0.130483\pi$
$152$	1.05530	+	1.93264i	0.0855962	+	0.156758i
$153$	4.22066	+	3.15955i	0.341220	+	0.255434i
$154$	−10.2250	+	8.86005i	−0.823957	+	0.713963i
$155$	0.240268	−	7.05448i	0.0192988	−	0.566629i
$156$	−14.8926	+	4.37288i	−1.19237	+	0.350110i
$157$	−6.54720	+	2.44198i	−0.522523	+	0.194891i	−0.596865	−	0.802342i	$-0.703587\pi$
$157$	−6.54720	+	2.44198i	−0.522523	+	0.194891i	0.0743417	+	0.997233i	$0.476314\pi$
$158$	0.206591	+	0.275974i	0.0164355	+	0.0219553i
$159$	21.6075	−	13.8863i	1.71359	−	1.10125i
$160$	2.12047	−	0.709658i	0.167638	−	0.0561034i
$161$	5.32493	+	23.6796i	0.419663	+	1.86621i
$162$	−5.04646	+	5.04646i	−0.396487	+	0.396487i
$163$	−24.1528	−	5.25411i	−1.89179	−	0.411534i	−0.892566	−	0.450917i	$-0.851097\pi$
$163$	−24.1528	−	5.25411i	−1.89179	−	0.411534i	−0.999224	+	0.0393833i	$0.987461\pi$
$164$	−3.31357	−	0.476419i	−0.258746	−	0.0372021i
$165$	1.60756	−	15.1888i	0.125148	−	1.18245i
$166$	−0.711432	−	2.42292i	−0.0552179	−	0.188055i
$167$	1.02825	+	0.383519i	0.0795687	+	0.0296776i	0.388933	−	0.921266i	$-0.372844\pi$
$167$	1.02825	+	0.383519i	0.0795687	+	0.0296776i	−0.309365	+	0.950943i	$0.600116\pi$
$168$	−12.8976	−	0.922454i	−0.995071	−	0.0711689i
$169$	23.6606	−	3.40188i	1.82005	−	0.261683i
$170$	2.44938	+	2.27290i	0.187859	+	0.174323i
$171$	5.87131	+	5.08752i	0.448990	+	0.389052i
$172$	−0.0231789	−	0.106551i	−0.00176737	−	0.00812447i
$173$	−2.88426	−	13.2587i	−0.219287	−	1.00804i	−0.946768	−	0.321917i	$-0.895673\pi$
$173$	−2.88426	−	13.2587i	−0.219287	−	1.00804i	0.727481	−	0.686127i	$-0.240691\pi$
$174$	12.1949	+	10.5669i	0.924491	+	0.801076i
$175$	10.4355	−	23.0522i	0.788853	−	1.74258i
$176$	−2.64619	+	0.380465i	−0.199464	+	0.0286786i
$177$	−31.6687	−	2.26499i	−2.38037	−	0.170247i
$178$	−9.87271	−	3.68233i	−0.739991	−	0.276002i
$179$	−1.11402	−	3.79400i	−0.0832656	−	0.283577i	0.907326	−	0.420428i	$-0.138120\pi$
$179$	−1.11402	−	3.79400i	−0.0832656	−	0.283577i	−0.990592	+	0.136851i	$0.956302\pi$
$180$	6.13458	−	4.96032i	0.457245	−	0.369720i
$181$	−8.77727	−	1.26198i	−0.652409	−	0.0938023i	−0.191840	−	0.981426i	$-0.561446\pi$
$181$	−8.77727	−	1.26198i	−0.652409	−	0.0938023i	−0.460569	+	0.887624i	$0.652355\pi$
$182$	30.0413	+	6.53509i	2.22681	+	0.484413i
$183$	−3.78927	+	3.78927i	−0.280111	+	0.280111i
$184$	−1.64450	+	4.50507i	−0.121234	+	0.332118i
$185$	−2.14246	−	6.40172i	−0.157517	−	0.470664i
$186$	−6.78504	+	4.36048i	−0.497503	+	0.319726i
$187$	−2.39413	−	3.19818i	−0.175076	−	0.233874i
$188$	2.23676	−	0.834270i	0.163133	−	0.0608454i
$189$	−6.55214	+	1.92388i	−0.476598	+	0.139942i
$190$	3.36112	+	3.59814i	0.243841	+	0.261037i
$191$	2.62080	−	2.27093i	0.189634	−	0.164319i	−0.554869	−	0.831938i	$-0.687232\pi$
$191$	2.62080	−	2.27093i	0.189634	−	0.164319i	0.744504	+	0.667619i	$0.232686\pi$
$192$	−2.04540	−	1.53116i	−0.147614	−	0.110502i
$193$	8.78037	+	16.0800i	0.632025	+	1.15747i	0.975852	+	0.218434i	$0.0700949\pi$
$193$	8.78037	+	16.0800i	0.632025	+	1.15747i	−0.343827	+	0.939033i	$0.611723\pi$
$194$	−2.84089	+	3.27856i	−0.203964	+	0.235387i
$195$	−29.8190	+	17.7592i	−2.13539	+	1.27176i
$196$	15.6575	+	10.0625i	1.11839	+	0.718748i
$197$	−1.16070	−	16.2287i	−0.0826963	−	1.15625i	−0.854173	−	0.519988i	$-0.825936\pi$
$197$	−1.16070	−	16.2287i	−0.0826963	−	1.15625i	0.771477	−	0.636257i	$-0.219518\pi$
$198$	−8.27832	+	4.52031i	−0.588315	+	0.321244i
$199$	−1.95798	−	13.6180i	−0.138797	−	0.965357i	−0.933556	−	0.358431i	$-0.883312\pi$
$199$	−1.95798	−	13.6180i	−0.138797	−	0.965357i	0.794759	−	0.606925i	$-0.207597\pi$
$200$	4.19730	−	2.71710i	0.296794	−	0.192128i
$201$	9.06420	−	4.13948i	0.639339	−	0.291976i
$202$	−4.40215	+	8.06194i	−0.309734	+	0.567236i
$203$	−11.1694	−	29.9464i	−0.783941	−	2.10183i
$204$	0.543373	−	3.77925i	0.0380438	−	0.264600i
$205$	−7.44133	+	0.812479i	−0.519725	+	0.0567460i
$206$			3.71377i			0.258751i
$207$	0.118358	+	16.9198i	0.00822645	+	1.17601i
$208$	4.29557	+	4.29557i	0.297845	+	0.297845i
$209$	−3.18265	−	4.95229i	−0.220148	−	0.342557i
$210$	−28.4456	+	5.18075i	−1.96293	+	0.357506i
$211$	−2.89442	+	6.33789i	−0.199260	+	0.436319i	−0.982714	−	0.185132i	$-0.940729\pi$
$211$	−2.89442	+	6.33789i	−0.199260	+	0.436319i	0.783454	+	0.621450i	$0.213456\pi$
$212$	−8.82306	−	4.81776i	−0.605971	−	0.330885i
$213$	−3.52410	+	9.44847i	−0.241467	+	0.647398i
$214$	−2.81830	−	3.25250i	−0.192655	−	0.222336i
$215$	−0.109502	−	0.217857i	−0.00746800	−	0.0148577i
$216$	−1.29467	−	0.380151i	−0.0880914	−	0.0258660i
$217$	15.9348	−	1.13968i	1.08172	−	0.0773664i
$218$	18.5173	−	4.02819i	1.25415	−	0.272824i
$219$	−11.1548	+	17.3572i	−0.753772	+	1.17289i
$220$	−5.51908	+	2.29678i	−0.372096	+	0.154849i
$221$	−2.55757	+	8.71029i	−0.172041	+	0.585917i
$222$	−4.62260	+	6.17507i	−0.310249	+	0.414444i
$223$	0.662018	−	9.25623i	0.0443320	−	0.619843i	−0.925916	−	0.377730i	$-0.876705\pi$
$223$	0.662018	−	9.25623i	0.0443320	−	0.619843i	0.970248	−	0.242113i	$-0.0778405\pi$
$224$	2.10235	+	4.60350i	0.140469	+	0.307584i
$225$	10.5248	−	14.1569i	0.701654	−	0.943792i
$226$	3.67785	+	1.67962i	0.244647	+	0.111726i
$227$	17.5668	−	13.1504i	1.16595	−	0.872820i	0.172268	−	0.985050i	$-0.444890\pi$
$227$	17.5668	−	13.1504i	1.16595	−	0.872820i	0.993682	+	0.112230i	$0.0357994\pi$
$228$	1.19592	−	5.49754i	0.0792016	−	0.364084i
$229$	−18.9693			−1.25352			−0.626762	−	0.779211i	$-0.715620\pi$
$229$	−18.9693			−1.25352			−0.626762	+	0.779211i	$0.715620\pi$
$230$	−1.05406	+	10.6719i	−0.0695026	+	0.703683i
$231$	34.5685			2.27444
$232$	1.34245	−	6.17114i	0.0881362	−	0.405155i
$233$	−7.45267	+	5.57900i	−0.488241	+	0.365492i	−0.814855	−	0.579666i	$-0.803183\pi$
$233$	−7.45267	+	5.57900i	−0.488241	+	0.365492i	0.326614	+	0.945158i	$0.394092\pi$
$234$	19.4959	+	8.90350i	1.27449	+	0.582040i
$235$	4.37981	−	3.05170i	0.285707	−	0.199071i
$236$	5.16211	+	11.3034i	0.336025	+	0.735791i
$237$	0.0628356	−	0.878557i	0.00408161	−	0.0570684i
$238$	−4.53216	+	6.05426i	−0.293776	+	0.392439i
$239$	−5.44678	+	18.5500i	−0.352323	+	1.19990i	0.572628	+	0.819816i	$0.305924\pi$
$239$	−5.44678	+	18.5500i	−0.352323	+	1.19990i	−0.924951	+	0.380087i	$0.875894\pi$
$240$	−5.28191	−	2.17761i	−0.340946	−	0.140564i
$241$	−11.3253	+	17.6225i	−0.729526	+	1.13516i	0.256170	+	0.966632i	$0.417539\pi$
$241$	−11.3253	+	17.6225i	−0.729526	+	1.13516i	−0.985696	+	0.168533i	$0.946097\pi$
$242$	−3.76487	+	0.818997i	−0.242015	+	0.0526471i
$243$	22.2258	−	1.58962i	1.42578	−	0.101974i
$244$	2.01242	+	0.590899i	0.128832	+	0.0378285i
$245$	39.5099	+	13.0776i	2.52419	+	0.835497i
$246$	5.60121	+	6.46414i	0.357120	+	0.412138i
$247$	−4.67470	+	12.5334i	−0.297444	+	0.797479i
$248$	2.77056	+	1.51284i	0.175931	+	0.0960654i
$249$	−2.68023	+	5.86889i	−0.169853	+	0.371926i
$250$	7.57778	−	8.22053i	0.479261	−	0.519912i
$251$	−3.16368	−	4.92278i	−0.199690	−	0.310723i	0.726938	−	0.686703i	$-0.240943\pi$
$251$	−3.16368	−	4.92278i	−0.199690	−	0.310723i	−0.926628	+	0.375980i	$0.877306\pi$
$252$	12.6255	+	12.6255i	0.795334	+	0.795334i
$253$	3.52601	−	12.3268i	0.221678	−	0.774980i
$254$			4.80823i			0.301695i
$255$	−0.926662	−	8.48711i	−0.0580298	−	0.531483i
$256$	−0.142315	+	0.989821i	−0.00889468	+	0.0618638i
$257$	−5.48751	−	14.7126i	−0.342302	−	0.917746i	−0.988041	−	0.154189i	$-0.950724\pi$
$257$	−5.48751	−	14.7126i	−0.342302	−	0.917746i	0.645740	−	0.763558i	$-0.276549\pi$
$258$	−0.133523	+	0.244528i	−0.00831275	+	0.0152237i
$259$	13.8980	−	6.34701i	0.863581	−	0.394384i
$260$	11.6937	+	6.91207i	0.725213	+	0.428669i
$261$	−3.17101	−	22.0549i	−0.196281	−	1.36516i
$262$	0.829013	−	0.452675i	0.0512166	−	0.0279664i
$263$	1.92646	+	26.9354i	0.118790	+	1.66091i	0.611897	+	0.790938i	$0.290407\pi$
$263$	1.92646	+	26.9354i	0.118790	+	1.66091i	−0.493106	+	0.869969i	$0.664139\pi$
$264$	5.74626	+	3.69289i	0.353658	+	0.227282i
$265$	−21.7895	−	5.52306i	−1.33852	−	0.339279i
$266$	−7.29771	+	8.42201i	−0.447451	+	0.516386i
$267$	12.9025	+	23.6292i	0.789622	+	1.44609i
$268$	−3.12215	−	2.33721i	−0.190716	−	0.142768i
$269$	−2.83201	+	2.45395i	−0.172671	+	0.149620i	−0.736909	−	0.675992i	$-0.763715\pi$
$269$	−2.83201	+	2.45395i	−0.172671	+	0.149620i	0.564238	+	0.825612i	$0.309170\pi$
$270$	−3.01545	−	0.102703i	−0.183514	−	0.00625031i
$271$	−18.8259	+	5.52779i	−1.14359	+	0.335789i	−0.798037	−	0.602609i	$-0.794128\pi$
$271$	−18.8259	+	5.52779i	−1.14359	+	0.335789i	−0.345556	+	0.938398i	$0.612310\pi$
$272$	−1.40014	+	0.522224i	−0.0848958	+	0.0316645i
$273$	−47.0740	−	62.8835i	−2.84905	−	3.80588i
$274$	−9.33380	+	5.99847i	−0.563876	+	0.362381i
$275$	−10.6743	+	8.04591i	−0.643684	+	0.485187i
$276$	10.7132	−	5.94753i	0.644861	−	0.357999i
$277$	−17.9663	+	17.9663i	−1.07949	+	1.07949i	−0.0829338	+	0.996555i	$0.526429\pi$
$277$	−17.9663	+	17.9663i	−1.07949	+	1.07949i	−0.996555	+	0.0829338i	$0.973571\pi$
$278$	−15.8882	−	3.45626i	−0.952908	−	0.207292i
$279$	11.0238	+	1.58498i	0.659976	+	0.0948903i
$280$	7.11525	+	8.79965i	0.425217	+	0.525880i
$281$	−4.54209	−	15.4689i	−0.270959	−	0.922800i	−0.976750	−	0.214381i	$-0.931227\pi$
$281$	−4.54209	−	15.4689i	−0.270959	−	0.922800i	0.705792	−	0.708419i	$-0.250591\pi$
$282$	−5.71497	−	2.13157i	−0.340322	−	0.126933i
$283$	−9.13772	−	0.653543i	−0.543181	−	0.0388491i	−0.202947	−	0.979190i	$-0.565052\pi$
$283$	−9.13772	−	0.653543i	−0.543181	−	0.0388491i	−0.340234	+	0.940341i	$0.610506\pi$
$284$	3.90668	−	0.561696i	0.231819	−	0.0333305i
$285$	−0.469819	−	12.5716i	−0.0278296	−	0.744678i
$286$	−12.2738	−	10.6353i	−0.725764	−	0.628878i
$287$	−3.60126	−	16.5547i	−0.212575	−	0.977194i
$288$	0.749954	+	3.44748i	0.0441915	+	0.203145i
$289$	11.1601	+	9.67026i	0.656475	+	0.568839i
$290$	−0.527384	−	14.1120i	−0.0309691	−	0.828684i
$291$	10.9712	−	1.57743i	0.643145	−	0.0924703i
$292$	8.05474	+	0.576087i	0.471368	+	0.0337129i
$293$	0.231165	+	0.0862200i	0.0135048	+	0.00503703i	0.356208	−	0.934407i	$-0.384070\pi$
$293$	0.231165	+	0.0862200i	0.0135048	+	0.00503703i	−0.342703	+	0.939444i	$0.611342\pi$
$294$	−13.3976	−	45.6280i	−0.781363	−	2.66108i
$295$	17.4708	+	21.6067i	1.01719	+	1.25799i
$296$	2.98828	+	0.429650i	0.173690	+	0.0249729i
$297$	3.52487	+	0.766788i	0.204534	+	0.0444936i
$298$	4.13895	−	4.13895i	0.239763	−	0.239763i
$299$	−27.2252	+	10.3720i	−1.57447	+	0.599828i
$300$	−12.6510	−	1.77624i	−0.730406	−	0.102551i
$301$	0.464247	−	0.298354i	0.0267588	−	0.0171968i
$302$	4.40974	+	5.89072i	0.253752	+	0.338973i
$303$	21.9894	−	8.20163i	1.26326	−	0.471172i
$304$	−2.11279	+	0.620372i	−0.121177	+	0.0355808i
$305$	4.68716	+	0.159640i	0.268386	+	0.00914095i
$306$	−3.98451	+	3.45259i	−0.227779	+	0.197372i
$307$	−3.55238	−	2.65928i	−0.202745	−	0.151773i	0.493081	−	0.869983i	$-0.335871\pi$
$307$	−3.55238	−	2.65928i	−0.202745	−	0.151773i	−0.695826	+	0.718210i	$0.744962\pi$
$308$	−6.48408	−	11.8747i	−0.369465	−	0.676624i
$309$	6.21381	−	7.17112i	0.353491	−	0.407951i
$310$	6.84219	+	1.73431i	0.388610	+	0.0985024i
$311$	−27.4631	−	17.6495i	−1.55729	−	1.00081i	−0.983310	−	0.181940i	$-0.941762\pi$
$311$	−27.4631	−	17.6495i	−1.55729	−	1.00081i	−0.573980	−	0.818870i	$-0.694601\pi$
$312$	−1.10728	−	15.4818i	−0.0626875	−	0.876486i
$313$	27.2379	−	14.8730i	1.53958	−	0.840672i	0.539576	−	0.841937i	$-0.318584\pi$
$313$	27.2379	−	14.8730i	1.53958	−	0.840672i	0.999999	+	0.00126495i	$0.000402647\pi$
$314$	−0.994464	−	6.91665i	−0.0561209	−	0.390329i
$315$	34.3701	+	20.3159i	1.93654	+	1.14467i
$316$	−0.313581	+	0.143208i	−0.0176403	+	0.00805606i
$317$	−2.54426	+	4.65947i	−0.142900	+	0.261702i	−0.939320	−	0.343042i	$-0.888543\pi$
$317$	−2.54426	+	4.65947i	−0.142900	+	0.261702i	0.796420	+	0.604744i	$0.206724\pi$
$318$	8.97594	+	24.0654i	0.503346	+	1.34952i
$319$	−2.40282	+	16.7119i	−0.134532	+	0.935689i
$320$	0.242702	+	2.22286i	0.0135675	+	0.124262i
$321$			10.9959i			0.613734i
$322$	−24.2703	+	0.169777i	−1.35253	+	0.00946128i
$323$	−2.32678	−	2.32678i	−0.129465	−	0.129465i
$324$	−3.85843	−	6.00383i	−0.214357	−	0.333546i
$325$	29.1721	+	8.46097i	1.61818	+	0.469330i
$326$	10.2681	−	22.4840i	0.568696	−	1.24527i
$327$	−42.4959	−	23.2045i	−2.35003	−	1.28321i
$328$	1.16988	−	3.13657i	0.0645959	−	0.173188i
$329$	7.91181	+	9.13071i	0.436192	+	0.503392i
$330$	14.5000	+	4.79944i	0.798199	+	0.264200i
$331$	−9.66573	−	2.83811i	−0.531276	−	0.155997i	0.00508211	−	0.999987i	$-0.498382\pi$
$331$	−9.66573	−	2.83811i	−0.531276	−	0.155997i	−0.536358	+	0.843990i	$0.680200\pi$
$332$	2.51877	−	0.180146i	0.138236	−	0.00988680i
$333$	10.4080	−	2.26412i	0.570354	−	0.124073i
$334$	−0.593325	+	0.923232i	−0.0324653	+	0.0505170i
$335$	−8.06245	−	3.32396i	−0.440499	−	0.181608i
$336$	3.64295	−	12.4068i	0.198739	−	0.676844i
$337$	−13.3522	+	17.8365i	−0.727341	+	0.971614i	0.272614	+	0.962124i	$0.412112\pi$
$337$	−13.3522	+	17.8365i	−0.727341	+	0.971614i	−0.999955	+	0.00949047i	$0.996979\pi$
$338$	−1.70529	+	23.8430i	−0.0927554	+	1.29689i
$339$	−4.29145	−	9.39696i	−0.233079	−	0.510373i
$340$	−2.74161	+	1.91026i	−0.148685	+	0.103598i
$341$	−7.67647	−	3.50573i	−0.415704	−	0.189846i
$342$	−6.21929	+	4.65570i	−0.336301	+	0.251752i
$343$	−12.4918	+	57.4241i	−0.674496	+	3.10061i
$344$	0.109043			0.00587923
$345$	19.8913	−	18.8433i	1.07091	−	1.01449i
$346$	13.5688			0.729465
$347$	−1.45805	+	6.70255i	−0.0782722	+	0.359811i	−0.999579	−	0.0290257i	$-0.990760\pi$
$347$	−1.45805	+	6.70255i	−0.0782722	+	0.359811i	0.921306	+	0.388837i	$0.127123\pi$
$348$	−12.9176	+	9.67003i	−0.692458	+	0.518368i
$349$	−2.31295	−	1.05629i	−0.123810	−	0.0565419i	0.352547	−	0.935794i	$-0.385316\pi$
$349$	−2.31295	−	1.05629i	−0.123810	−	0.0565419i	−0.476357	+	0.879252i	$0.658043\pi$
$350$	20.3071	+	15.0971i	1.08546	+	0.806977i
$351$	−3.40516	−	7.45625i	−0.181754	−	0.397985i
$352$	0.190718	−	2.66659i	0.0101653	−	0.142130i
$353$	−1.01333	+	1.35366i	−0.0539343	+	0.0720478i	−0.826697	−	0.562647i	$-0.809783\pi$
$353$	−1.01333	+	1.35366i	−0.0539343	+	0.0720478i	0.772763	+	0.634695i	$0.218874\pi$
$354$	8.94491	−	30.4636i	0.475416	−	1.61912i
$355$	8.14805	−	3.39083i	0.432453	−	0.179967i
$356$	5.69677	−	8.86435i	0.301928	−	0.469810i
$357$	18.8813	−	4.10737i	0.999302	−	0.217385i
$358$	3.94409	−	0.282087i	0.208452	−	0.0149088i
$359$	13.7653	+	4.04187i	0.726507	+	0.213322i	0.624015	−	0.781412i	$-0.285500\pi$
$359$	13.7653	+	4.04187i	0.726507	+	0.213322i	0.102492	+	0.994734i	$0.467318\pi$
$360$	3.54296	+	7.04878i	0.186730	+	0.371503i
$361$	9.26710	+	10.6948i	0.487742	+	0.562884i
$362$	3.09888	−	8.30843i	0.162874	−	0.436681i
$363$	8.64011	+	4.71786i	0.453488	+	0.247623i
$364$	−12.7715	+	27.9656i	−0.669407	+	1.46580i
$365$	17.7647	−	3.23546i	0.929848	−	0.169352i
$366$	−2.89720	−	4.50814i	−0.151439	−	0.235644i
$367$	14.3713	+	14.3713i	0.750177	+	0.750177i	0.974512	−	0.224335i	$-0.0720210\pi$
$367$	14.3713	+	14.3713i	0.750177	+	0.750177i	−0.224335	+	0.974512i	$0.572021\pi$
$368$	−4.05255	−	2.56454i	−0.211254	−	0.133686i
$369$		−	11.8109i		−	0.614848i
$370$	6.71083	−	0.732720i	0.348879	−	0.0380923i
$371$	7.24030	−	50.3574i	0.375898	−	2.61443i
$372$	−2.81856	−	7.55686i	−0.146136	−	0.391805i
$373$	6.09315	−	11.1588i	0.315491	−	0.577779i	−0.671027	−	0.741433i	$-0.734146\pi$
$373$	6.09315	−	11.1588i	0.315491	−	0.577779i	0.986518	+	0.163654i	$0.0523282\pi$
$374$	3.63400	−	1.65959i	0.187910	−	0.0858154i
$375$	−28.3868	+	3.19446i	−1.46589	+	0.164961i
$376$	0.339746	+	2.36298i	0.0175211	+	0.121862i
$377$	33.6727	−	18.3867i	1.73423	−	0.946962i
$378$	−0.487158	−	6.81135i	−0.0250567	−	0.350338i
$379$	−7.89258	−	5.07226i	−0.405415	−	0.260544i	0.322004	−	0.946738i	$-0.395644\pi$
$379$	−7.89258	−	5.07226i	−0.405415	−	0.260544i	−0.727418	+	0.686194i	$0.759280\pi$
$380$	−4.23037	+	2.51947i	−0.217014	+	0.129246i
$381$	8.04503	−	9.28446i	0.412159	−	0.475657i
$382$	1.66195	+	3.04363i	0.0850325	+	0.155725i
$383$	−13.5597	−	10.1506i	−0.692867	−	0.518674i	0.193824	−	0.981036i	$-0.437911\pi$
$383$	−13.5597	−	10.1506i	−0.692867	−	0.518674i	−0.886691	+	0.462363i	$0.847002\pi$
$384$	1.93095	−	1.67318i	0.0985385	−	0.0853841i
$385$	−20.6517	−	22.1081i	−1.05251	−	1.12673i
$386$	−17.5790	+	5.16165i	−0.894746	+	0.262721i
$387$	0.360461	−	0.134445i	0.0183233	−	0.00683422i
$388$	−2.59976	−	3.47287i	−0.131983	−	0.176308i
$389$	6.77960	−	4.35699i	0.343739	−	0.220908i	−0.357368	−	0.933964i	$-0.616326\pi$
$389$	6.77960	−	4.35699i	0.343739	−	0.220908i	0.701107	+	0.713056i	$0.252689\pi$
$390$	−11.0149	−	32.9126i	−0.557759	−	1.66659i
$391$	0.461249	−	7.15183i	0.0233264	−	0.361683i
$392$	−13.1608	+	13.1608i	−0.664718	+	0.664718i
$393$	−2.35819	−	0.512993i	−0.118955	−	0.0258771i
$394$	16.1045	+	2.31548i	0.811334	+	0.116652i
$395$	−0.599414	+	0.484676i	−0.0301598	+	0.0243867i
$396$	−2.65732	−	9.04999i	−0.133535	−	0.454779i
$397$	20.3191	+	7.57863i	1.01979	+	0.380361i	0.803077	−	0.595876i	$-0.203195\pi$
$397$	20.3191	+	7.57863i	1.01979	+	0.380361i	0.216709	+	0.976236i	$0.430468\pi$
$398$	13.7230	+	0.981489i	0.687873	+	0.0491976i
$399$	28.1831	−	4.05211i	1.41092	−	0.202859i
$400$	1.76281	+	4.67894i	0.0881405	+	0.233947i
$401$	−13.8658	−	12.0148i	−0.692424	−	0.599989i	0.235893	−	0.971779i	$-0.424199\pi$
$401$	−13.8658	−	12.0148i	−0.692424	−	0.599989i	−0.928317	+	0.371791i	$0.878744\pi$
$402$	2.11815	+	9.73696i	0.105644	+	0.485636i
$403$	4.07624	+	18.7382i	0.203052	+	0.933416i
$404$	−6.94196	−	6.01524i	−0.345375	−	0.299269i
$405$	−11.6978	−	10.8549i	−0.581266	−	0.539386i
$406$	31.6363	−	4.54861i	1.57008	−	0.225744i
$407$	−8.05047	−	0.575781i	−0.399047	−	0.0285404i
$408$	3.57738	+	1.33429i	0.177106	+	0.0660573i
$409$	−6.01969	−	20.5012i	−0.297654	−	1.01372i	−0.963518	−	0.267644i	$-0.913755\pi$
$409$	−6.01969	−	20.5012i	−0.297654	−	1.01372i	0.665863	−	0.746074i	$-0.268063\pi$
$410$	0.787857	−	7.44398i	0.0389095	−	0.367632i
$411$	28.0597	+	4.03437i	1.38408	+	0.199001i
$412$	−3.62890	−	0.789419i	−0.178783	−	0.0388919i
$413$	−44.4685	+	44.4685i	−2.18815	+	2.18815i
$414$	−16.5583	−	3.48091i	−0.813796	−	0.171077i
$415$	5.35462	−	1.79203i	0.262848	−	0.0879674i
$416$	−5.11050	+	3.28432i	−0.250563	+	0.161027i
$417$	24.8963	+	33.2576i	1.21918	+	1.62863i
$418$	5.51564	−	2.05723i	0.269779	−	0.100622i
$419$	−2.83441	+	0.832259i	−0.138470	+	0.0406585i	−0.350233	−	0.936663i	$-0.613898\pi$
$419$	−2.83441	+	0.832259i	−0.138470	+	0.0406585i	0.211763	+	0.977321i	$0.432079\pi$
$420$	0.984195	−	28.8968i	0.0480238	−	1.41002i
$421$	14.9928	−	12.9913i	0.730705	−	0.633160i	−0.207901	−	0.978150i	$-0.566663\pi$
$421$	14.9928	−	12.9913i	0.730705	−	0.633160i	0.938606	+	0.344990i	$0.112118\pi$
$422$	−5.57780	−	4.17549i	−0.271523	−	0.203260i
$423$	4.03652	+	7.39234i	0.196262	+	0.359428i
$424$	6.58313	−	7.59734i	0.319705	−	0.368960i
$425$	−4.87427	+	5.66296i	−0.236437	+	0.274694i
$426$	−8.48344	−	5.45198i	−0.411024	−	0.264149i
$427$	0.757229	+	10.5874i	0.0366449	+	0.512363i
$428$	3.77724	−	2.06253i	0.182580	−	0.0996961i
$429$	5.90534	+	41.0725i	0.285112	+	1.98300i
$430$	0.236155	−	0.0606911i	0.0113884	−	0.00292679i
$431$	−26.9595	+	12.3120i	−1.29859	+	0.593047i	−0.940231	−	0.340536i	$-0.889391\pi$
$431$	−26.9595	+	12.3120i	−1.29859	+	0.593047i	−0.358361	+	0.933583i	$0.616664\pi$
$432$	0.646666	−	1.18428i	0.0311127	−	0.0569787i
$433$	1.59278	+	4.27040i	0.0765441	+	0.205223i	0.969586	−	0.244751i	$-0.0787062\pi$
$433$	1.59278	+	4.27040i	0.0765441	+	0.205223i	−0.893042	+	0.449973i	$0.851433\pi$
$434$	−2.27355	+	15.8129i	−0.109134	+	0.759043i
$435$	−22.5935	+	28.1320i	−1.08328	+	1.34882i
$436$			18.9504i			0.907559i
$437$	1.42974	−	10.4631i	0.0683938	−	0.500520i
$438$	−14.5894	−	14.5894i	−0.697110	−	0.697110i
$439$	7.92659	+	12.3340i	0.378315	+	0.588670i	0.977240	−	0.212135i	$-0.0680416\pi$
$439$	7.92659	+	12.3340i	0.378315	+	0.588670i	−0.598925	+	0.800805i	$0.704405\pi$
$440$	−1.07113	−	5.88116i	−0.0510640	−	0.280374i
$441$	−27.2785	+	59.7315i	−1.29898	+	2.84436i
$442$	−7.96758	−	4.35063i	−0.378979	−	0.206938i
$443$	10.1847	−	27.3061i	0.483887	−	1.29735i	−0.434144	−	0.900844i	$-0.642949\pi$
$443$	10.1847	−	27.3061i	0.483887	−	1.29735i	0.918031	−	0.396509i	$-0.129778\pi$
$444$	−5.05135	−	5.82957i	−0.239726	−	0.276659i
$445$	7.40376	−	22.3681i	0.350972	−	1.06035i
$446$	8.90397	+	2.61444i	0.421615	+	0.123797i
$447$	−14.9173	+	1.06691i	−0.705566	+	0.0504631i
$448$	−4.94519	+	1.07576i	−0.233638	+	0.0508248i
$449$	−1.67825	+	2.61141i	−0.0792017	+	0.123240i	−0.878595	−	0.477568i	$-0.841518\pi$
$449$	−1.67825	+	2.61141i	−0.0792017	+	0.123240i	0.799393	+	0.600809i	$0.205155\pi$
$450$	11.5961	+	13.2936i	0.546648	+	0.626664i
$451$	−2.52139	+	8.58707i	−0.118728	+	0.404350i
$452$	−2.42301	+	3.23677i	−0.113969	+	0.152245i
$453$	1.34124	−	18.7530i	0.0630170	−	0.881093i
$454$	9.11573	+	19.9607i	0.427823	+	0.936801i
$455$	−12.0941	+	67.6733i	−0.566978	+	3.17257i
$456$	5.11770	+	2.33717i	0.239658	+	0.109448i
$457$	14.4015	−	10.7808i	0.673672	−	0.504304i	−0.206812	−	0.978381i	$-0.566309\pi$
$457$	14.4015	−	10.7808i	0.673672	−	0.504304i	0.880484	+	0.474076i	$0.157218\pi$
$458$	4.03221	−	18.5358i	0.188413	−	0.866119i
$459$	2.01638			0.0941167
$460$	−10.2039	−	3.29844i	−0.475761	−	0.153791i
$461$	14.8385			0.691097			0.345549	−	0.938401i	$-0.387693\pi$
$461$	14.8385			0.691097			0.345549	+	0.938401i	$0.387693\pi$
$462$	−7.34807	+	33.7785i	−0.341863	+	1.57152i
$463$	14.0518	−	10.5190i	0.653041	−	0.488860i	−0.220643	−	0.975355i	$-0.570816\pi$
$463$	14.0518	−	10.5190i	0.653041	−	0.488860i	0.873684	+	0.486495i	$0.161725\pi$
$464$	5.74476	+	2.62354i	0.266694	+	0.121795i
$465$	−10.3101	−	14.7971i	−0.478120	−	0.686199i
$466$	−3.86732	−	8.46825i	−0.179150	−	0.392284i
$467$	0.757931	−	10.5973i	0.0350729	−	0.490383i	−0.949310	−	0.314342i	$-0.898216\pi$
$467$	0.757931	−	10.5973i	0.0350729	−	0.490383i	0.984383	−	0.176041i	$-0.0563292\pi$
$468$	−12.8442	+	17.1578i	−0.593723	+	0.793121i
$469$	5.56070	−	18.9380i	0.256769	−	0.874476i
$470$	2.05097	+	4.92840i	0.0946041	+	0.227330i
$471$	−9.65254	+	15.0196i	−0.444766	+	0.692069i
$472$	−12.1424	+	2.64142i	−0.558900	+	0.121581i
$473$	−0.290774	+	0.0207966i	−0.0133698	+	0.000956228i
$474$	0.845122	+	0.248150i	0.0388178	+	0.0113979i
$475$	−7.75941	+	7.81092i	−0.356026	+	0.358389i
$476$	−4.95252	−	5.71551i	−0.226998	−	0.261970i
$477$	12.3945	−	33.2309i	0.567505	−	1.52154i
$478$	−16.9683	−	9.26540i	−0.776113	−	0.423790i
$479$	−1.27738	+	2.79707i	−0.0583649	+	0.127801i	−0.936567	−	0.350488i	$-0.886016\pi$
$479$	−1.27738	+	2.79707i	−0.0583649	+	0.127801i	0.878202	+	0.478289i	$0.158743\pi$
$480$	3.25060	−	4.69832i	0.148369	−	0.214448i
$481$	9.91539	+	15.4286i	0.452103	+	0.703486i
$482$	−14.8124	−	14.8124i	−0.674687	−	0.674687i
$483$	47.1490	+	40.2808i	2.14535	+	1.83284i
$484$		−	3.85292i		−	0.175133i
$485$	−7.56320	−	6.07420i	−0.343427	−	0.275815i
$486$	−3.17114	+	22.0558i	−0.143846	+	1.00047i
$487$	−8.19970	−	21.9843i	−0.371564	−	0.996202i	−0.979363	−	0.202111i	$-0.935220\pi$
$487$	−8.19970	−	21.9843i	−0.371564	−	0.996202i	0.607799	−	0.794091i	$-0.292053\pi$
$488$	−1.00517	+	1.84082i	−0.0455017	+	0.0833302i
$489$	−57.4469	+	26.2351i	−2.59784	+	1.18639i
$490$	−21.1772	+	35.8271i	−0.956687	+	1.61850i
$491$	2.18016	+	15.1633i	0.0983892	+	0.684312i	0.977998	+	0.208614i	$0.0668953\pi$
$491$	2.18016	+	15.1633i	0.0983892	+	0.684312i	−0.879609	+	0.475698i	$0.842196\pi$
$492$	−7.50704	+	4.09915i	−0.338443	+	0.184804i
$493$	0.673269	+	9.41353i	0.0303225	+	0.423964i
$494$	−11.2533	−	7.23203i	−0.506308	−	0.325384i
$495$	−10.7920	−	18.1205i	−0.485062	−	0.814456i
$496$	−2.06719	+	2.38566i	−0.0928196	+	0.107120i
$497$	9.57272	+	17.5311i	0.429395	+	0.786379i
$498$	−5.16505	−	3.86650i	−0.231451	−	0.173262i
$499$	4.57960	−	3.96824i	0.205011	−	0.177643i	−0.546304	−	0.837587i	$-0.683966\pi$
$499$	4.57960	−	3.96824i	0.205011	−	0.177643i	0.751315	+	0.659944i	$0.229420\pi$
$500$	6.42189	+	9.15201i	0.287196	+	0.409290i
$501$	2.69042	−	0.789978i	0.120199	−	0.0352936i
$502$	5.48277	−	2.04497i	0.244708	−	0.0912714i
$503$	−20.9730	−	28.0167i	−0.935142	−	1.24920i	−0.968309	−	0.249754i	$-0.919650\pi$
$503$	−20.9730	−	28.0167i	−0.935142	−	1.24920i	0.0331673	−	0.999450i	$-0.489441\pi$
$504$	−15.0208	+	9.65325i	−0.669078	+	0.429990i
$505$	−18.3821	−	9.16342i	−0.817992	−	0.407767i
$506$	11.2956	+	6.06568i	0.502150	+	0.269652i
$507$	43.1865	−	43.1865i	1.91798	−	1.91798i
$508$	−4.69834	−	1.02206i	−0.208455	−	0.0453467i
$509$	−36.1706	−	5.20054i	−1.60323	−	0.230510i	−0.718130	−	0.695909i	$-0.755002\pi$
$509$	−36.1706	−	5.20054i	−1.60323	−	0.230510i	−0.885101	+	0.465399i	$0.845911\pi$
$510$	8.49013	+	0.898580i	0.375949	+	0.0397898i
$511$	11.5138	+	39.2125i	0.509341	+	1.73466i
$512$	−0.936950	−	0.349464i	−0.0414077	−	0.0154443i
$513$	2.96364	+	0.211964i	0.130848	+	0.00935843i
$514$	15.5428	−	2.23472i	0.685564	−	0.0985693i
$515$	−8.29845	+	0.310125i	−0.365673	+	0.0136657i
$516$	−0.210558	−	0.182449i	−0.00926929	−	0.00803189i
$517$	−1.35663	−	6.23632i	−0.0596644	−	0.274273i
$518$	3.24773	+	14.9296i	0.142697	+	0.655967i
$519$	−26.2008	−	22.7031i	−1.15009	−	0.996556i
$520$	−9.23979	+	9.95721i	−0.405191	+	0.436652i
$521$	−36.2761	+	5.21572i	−1.58929	+	0.228505i	−0.879495	−	0.475908i	$-0.842120\pi$
$521$	−36.2761	+	5.21572i	−1.58929	+	0.228505i	−0.709791	+	0.704412i	$0.751211\pi$
$522$	22.2249	+	1.58956i	0.972758	+	0.0695730i
$523$	18.4612	+	6.88568i	0.807253	+	0.301090i	0.719002	−	0.695008i	$-0.244599\pi$
$523$	18.4612	+	6.88568i	0.807253	+	0.301090i	0.0882514	+	0.996098i	$0.471872\pi$
$524$	0.266111	+	0.906290i	0.0116251	+	0.0395915i
$525$	−13.9518	−	63.1293i	−0.608908	−	2.75519i
$526$	−26.7293	−	3.84310i	−1.16545	−	0.167567i
$527$	−4.60942	−	1.00272i	−0.200789	−	0.0436790i
$528$	−4.82996	+	4.82996i	−0.210197	+	0.210197i
$529$	19.1730	−	12.7042i	0.833608	−	0.552357i
$530$	10.0285	−	20.1175i	0.435612	−	0.873849i
$531$	−36.8820	+	23.7026i	−1.60054	+	1.02861i
$532$	−6.67830	−	8.92116i	−0.289541	−	0.386781i
$533$	19.0542	−	7.10686i	0.825331	−	0.307832i
$534$	−25.8319	+	7.58492i	−1.11785	+	0.328231i
$535$	7.03238	−	6.56913i	0.304036	−	0.284008i
$536$	2.94746	−	2.55399i	0.127311	−	0.110315i
$537$	−8.08784	−	6.05448i	−0.349016	−	0.261270i
$538$	−1.79588	−	3.28891i	−0.0774260	−	0.141795i
$539$	32.5843	−	37.6043i	1.40351	−	1.61973i
$540$	0.741336	−	2.92470i	0.0319020	−	0.125859i
$541$	−16.5959	−	10.6656i	−0.713515	−	0.458548i	0.132860	−	0.991135i	$-0.457584\pi$
$541$	−16.5959	−	10.6656i	−0.713515	−	0.458548i	−0.846376	+	0.532586i	$0.821220\pi$
$542$	−1.39972	−	19.5707i	−0.0601233	−	0.840634i
$543$	−19.8853	+	10.8582i	−0.853359	+	0.465969i
$544$	−0.212669	−	1.47915i	−0.00911812	−	0.0634179i
$545$	10.5473	+	41.0407i	0.451799	+	1.75799i
$546$	71.4527	−	32.6313i	3.05789	−	1.39649i
$547$	−6.13911	+	11.2429i	−0.262489	+	0.480713i	−0.975371	−	0.220571i	$-0.929208\pi$
$547$	−6.13911	+	11.2429i	−0.262489	+	0.480713i	0.712882	+	0.701284i	$0.247390\pi$
$548$	−3.87734	−	10.3956i	−0.165632	−	0.444076i
$549$	−1.05310	+	7.32446i	−0.0449451	+	0.312600i
$550$	−5.59305	−	12.1406i	−0.238489	−	0.517678i
$551$			13.9066i			0.592441i
$552$	3.53435	+	11.7326i	0.150432	+	0.499374i
$553$	−1.23365	−	1.23365i	−0.0524601	−	0.0524601i
$554$	−13.7367	−	21.3747i	−0.583616	−	0.908124i
$555$	−14.1843	−	9.81358i	−0.602089	−	0.416563i
$556$	6.75454	−	14.7904i	0.286456	−	0.627252i
$557$	35.3285	+	19.2908i	1.49692	+	0.817378i	0.998764	−	0.0497110i	$-0.0158300\pi$
$557$	35.3285	+	19.2908i	1.49692	+	0.817378i	0.498153	+	0.867089i	$0.334012\pi$
$558$	−3.89203	+	10.4349i	−0.164763	+	0.441746i
$559$	0.433795	+	0.500627i	0.0183476	+	0.0211742i
$560$	−10.1110	+	5.08214i	−0.427268	+	0.214760i
$561$	−9.79387	−	2.87574i	−0.413498	−	0.121414i
$562$	16.0809	−	1.15013i	0.678333	−	0.0485153i
$563$	32.2952	−	7.02540i	1.36108	−	0.296085i	0.528005	−	0.849241i	$-0.322940\pi$
$563$	32.2952	−	7.02540i	1.36108	−	0.296085i	0.833078	+	0.553156i	$0.186577\pi$
$564$	3.29766	−	5.13127i	0.138857	−	0.216065i
$565$	−3.44599	+	8.35844i	−0.144974	+	0.351642i
$566$	2.58097	−	8.78998i	0.108486	−	0.369470i
$567$	21.6447	−	28.9140i	0.908994	−	1.21427i
$568$	−0.281566	+	3.93680i	−0.0118142	+	0.165185i
$569$	12.0809	+	26.4536i	0.506459	+	1.10899i	0.974316	+	0.225187i	$0.0722993\pi$
$569$	12.0809	+	26.4536i	0.506459	+	1.10899i	−0.467856	+	0.883805i	$0.654973\pi$
$570$	12.3842	+	2.21321i	0.518716	+	0.0927010i
$571$	28.6120	+	13.0667i	1.19737	+	0.546823i	0.911443	−	0.411427i	$-0.134969\pi$
$571$	28.6120	+	13.0667i	1.19737	+	0.546823i	0.285932	+	0.958250i	$0.407697\pi$
$572$	13.0012	−	9.73260i	0.543609	−	0.406940i
$573$	1.88340	−	8.65783i	0.0786800	−	0.361686i
$574$	16.9419			0.707141
$575$	−23.9344	−	1.46413i	−0.998134	−	0.0610585i
$576$	−3.52811			−0.147005
$577$	−7.92490	+	36.4302i	−0.329918	+	1.51661i	0.451313	+	0.892366i	$0.350956\pi$
$577$	−7.92490	+	36.4302i	−0.329918	+	1.51661i	−0.781231	+	0.624242i	$0.785408\pi$
$578$	−11.8215	+	8.84947i	−0.491710	+	0.368089i
$579$	42.5805	+	19.4459i	1.76959	+	0.808143i
$580$	13.9016	+	2.48438i	0.577231	+	0.103158i
$581$	5.30886	+	11.6248i	0.220249	+	0.482278i
$582$	−0.790727	+	11.0558i	−0.0327767	+	0.458278i
$583$	−16.1056	+	21.5145i	−0.667025	+	0.891041i
$584$	−2.27508	+	7.74821i	−0.0941435	+	0.320623i
$585$	−18.2669	+	44.3073i	−0.755243	+	1.83188i
$586$	−0.133387	+	0.207555i	−0.00551018	+	0.00857400i
$587$	18.9854	−	4.13003i	0.783613	−	0.170465i	0.197077	−	0.980388i	$-0.436855\pi$
$587$	18.9854	−	4.13003i	0.783613	−	0.170465i	0.586536	+	0.809923i	$0.300491\pi$
$588$	47.4331	−	3.39248i	1.95611	−	0.139904i
$589$	−6.66942	−	1.95832i	−0.274809	−	0.0806912i
$590$	−24.8266	+	12.4787i	−1.02209	+	0.513740i
$591$	−27.2229	−	31.4168i	−1.11980	−	1.29232i
$592$	−1.05504	+	2.82866i	−0.0433617	+	0.116257i
$593$	0.515436	+	0.281449i	0.0211664	+	0.0115577i	0.489797	−	0.871836i	$-0.337071\pi$
$593$	0.515436	+	0.281449i	0.0211664	+	0.0115577i	−0.468631	+	0.883394i	$0.655253\pi$
$594$	−1.49853	+	3.28132i	−0.0614854	+	0.134634i
$595$	−13.9068	−	9.62158i	−0.570121	−	0.394446i
$596$	3.16457	+	4.92416i	0.129626	+	0.201702i
$597$	−24.8563	−	24.8563i	−1.01730	−	1.01730i
$598$	−4.34782	−	28.8078i	−0.177796	−	1.17804i
$599$			34.0230i			1.39014i	0.718942	+	0.695070i	$0.244627\pi$
$599$			34.0230i			1.39014i	−0.718942	+	0.695070i	$0.755373\pi$
$600$	4.42481	−	11.9843i	0.180642	−	0.489258i
$601$	0.509294	−	3.54222i	0.0207745	−	0.144490i	−0.976794	−	0.214180i	$-0.931292\pi$
$601$	0.509294	−	3.54222i	0.0207745	−	0.144490i	0.997569	+	0.0696902i	$0.0222011\pi$
$602$	0.192852	+	0.517057i	0.00786008	+	0.0210737i
$603$	6.59437	−	12.0767i	0.268543	−	0.491801i
$604$	−6.69346	+	3.05680i	−0.272353	+	0.124379i
$605$	−2.14445	−	8.34424i	−0.0871842	−	0.339241i
$606$	3.34001	+	23.2303i	0.135679	+	0.943666i
$607$	30.6806	−	16.7528i	1.24529	−	0.679977i	0.284874	−	0.958565i	$-0.408048\pi$
$607$	30.6806	−	16.7528i	1.24529	−	0.679977i	0.960411	+	0.278588i	$0.0898663\pi$
$608$	−0.157088	−	2.19638i	−0.00637076	−	0.0890749i
$609$	−68.6988	−	44.1500i	−2.78382	−	1.78905i
$610$	−1.15232	+	4.54611i	−0.0466560	+	0.184067i
$611$	−9.49706	+	10.9602i	−0.384210	+	0.443402i
$612$	−2.52672	−	4.62735i	−0.102137	−	0.187050i
$613$	14.7760	+	11.0612i	0.596798	+	0.446758i	0.854489	−	0.519470i	$-0.173871\pi$
$613$	14.7760	+	11.0612i	0.596798	+	0.446758i	−0.257690	+	0.966228i	$0.582961\pi$
$614$	3.35362	−	2.90593i	0.135341	−	0.117274i
$615$	−13.9764	+	13.0557i	−0.563584	+	0.526458i
$616$	12.9816	−	3.81175i	0.523044	−	0.153580i
$617$	−8.40827	+	3.13612i	−0.338504	+	0.126256i	−0.512967	−	0.858408i	$-0.671454\pi$
$617$	−8.40827	+	3.13612i	−0.338504	+	0.126256i	0.174463	+	0.984664i	$0.444181\pi$
$618$	5.68639	+	7.59613i	0.228740	+	0.305561i
$619$	38.3335	−	24.6355i	1.54075	−	0.990183i	0.553175	−	0.833065i	$-0.313416\pi$
$619$	38.3335	−	24.6355i	1.54075	−	0.990183i	0.987580	−	0.157118i	$-0.0502203\pi$
$620$	−3.14909	+	6.31717i	−0.126471	+	0.253704i
$621$	3.91417	+	5.15318i	0.157070	+	0.206790i
$622$	23.0838	−	23.0838i	0.925577	−	0.925577i
$623$	52.1078	+	11.3354i	2.08765	+	0.454141i
$624$	15.3634	+	2.20892i	0.615028	+	0.0884276i
$625$	19.0016	+	16.2462i	0.760066	+	0.649846i
$626$	8.74328	+	29.7769i	0.349452	+	1.19012i
$627$	−14.0925	−	5.25625i	−0.562802	−	0.209914i
$628$	6.96997	+	0.498502i	0.278132	+	0.0198924i
$629$	−4.46556	+	0.642051i	−0.178054	+	0.0256002i
$630$	−27.1576	+	29.2662i	−1.08198	+	1.16599i
$631$	−28.5112	−	24.7051i	−1.13501	−	0.983493i	−0.135039	−	0.990840i	$-0.543116\pi$
$631$	−28.5112	−	24.7051i	−1.13501	−	0.983493i	−0.999973	+	0.00734723i	$0.997661\pi$
$632$	−0.0732785	−	0.336856i	−0.00291486	−	0.0133994i
$633$	3.78412	+	17.3953i	0.150405	+	0.691402i
$634$	−4.01216	−	3.47656i	−0.159343	−	0.138072i
$635$	−10.7440	+	0.401519i	−0.426363	+	0.0159338i
$636$	−25.4234	+	3.65534i	−1.00811	+	0.144944i
$637$	−112.778	−	8.06604i	−4.46842	−	0.319588i
$638$	−15.8193	−	5.90028i	−0.626291	−	0.233594i
$639$	3.92311	+	13.3609i	0.155196	+	0.528549i
$640$	−2.22365	−	0.235347i	−0.0878974	−	0.00930290i
$641$	35.8260	+	5.15100i	1.41504	+	0.203452i	0.807046	−	0.590489i	$-0.201065\pi$
$641$	35.8260	+	5.15100i	1.41504	+	0.203452i	0.607995	+	0.793941i	$0.291974\pi$
$642$	−10.7447	−	2.33736i	−0.424058	−	0.0922481i
$643$	17.7361	−	17.7361i	0.699443	−	0.699443i	−0.264847	−	0.964290i	$-0.585322\pi$
$643$	17.7361	−	17.7361i	0.699443	−	0.699443i	0.964290	+	0.264847i	$0.0853215\pi$
$644$	4.99314	−	23.7518i	0.196757	−	0.935951i
$645$	−0.557550	−	0.277937i	−0.0219535	−	0.0109438i
$646$	2.76819	−	1.77901i	0.108913	−	0.0699942i
$647$	−11.0638	−	14.7795i	−0.434963	−	0.581043i	0.528483	−	0.848944i	$-0.322761\pi$
$647$	−11.0638	−	14.7795i	−0.434963	−	0.581043i	−0.963447	+	0.267901i	$0.913670\pi$
$648$	6.68679	−	2.49404i	0.262682	−	0.0979753i
$649$	31.8751	−	9.35937i	1.25121	−	0.367387i
$650$	−14.4686	+	26.7069i	−0.567504	+	1.04753i
$651$	30.8479	−	26.7299i	1.20903	−	1.04763i
$652$	19.7875	+	14.8127i	0.774938	+	0.580111i
$653$	−2.13462	−	3.90927i	−0.0835343	−	0.152982i	0.832572	−	0.553916i	$-0.186867\pi$
$653$	−2.13462	−	3.90927i	−0.0835343	−	0.152982i	−0.916107	+	0.400935i	$0.868685\pi$
$654$	31.7074	−	36.5923i	1.23986	−	1.43087i
$655$	1.08073	+	1.81463i	0.0422278	+	0.0709036i
$656$	2.81622	+	1.80987i	0.109955	+	0.0706636i
$657$	2.03250	+	28.4180i	0.0792953	+	1.10869i
$658$	−10.6038	+	5.79012i	−0.413380	+	0.225723i
$659$	−1.62040	−	11.2702i	−0.0631220	−	0.439023i	−0.996735	−	0.0807404i	$-0.974272\pi$
$659$	−1.62040	−	11.2702i	−0.0631220	−	0.439023i	0.933613	−	0.358283i	$-0.116638\pi$
$660$	−7.77195	+	13.1484i	−0.302523	+	0.511802i
$661$	−20.3102	+	9.27535i	−0.789975	+	0.360769i	−0.769195	−	0.639015i	$-0.779342\pi$
$661$	−20.3102	+	9.27535i	−0.789975	+	0.360769i	−0.0207802	+	0.999784i	$0.506615\pi$
$662$	4.82785	−	8.84155i	0.187640	−	0.343637i
$663$	8.10564	+	21.7321i	0.314797	+	0.844003i
$664$	−0.359374	+	2.49950i	−0.0139464	+	0.0969995i
$665$	−19.4285	−	15.6035i	−0.753403	−	0.605078i
$666$			10.6514i			0.412733i
$667$	−22.7508	+	19.9940i	−0.880914	+	0.774171i
$668$	−0.776013	−	0.776013i	−0.0300249	−	0.0300249i
$669$	−12.8187	−	19.9463i	−0.495600	−	0.771169i
$670$	4.96180	−	7.17164i	0.191691	−	0.277065i
$671$	2.32929	−	5.10043i	0.0899211	−	0.196900i
$672$	11.3489	+	6.19695i	0.437792	+	0.239052i
$673$	1.35712	−	3.63857i	0.0523130	−	0.140256i	−0.908165	−	0.418612i	$-0.862517\pi$
$673$	1.35712	−	3.63857i	0.0523130	−	0.140256i	0.960478	+	0.278356i	$0.0897894\pi$
$674$	−14.5906	−	16.8385i	−0.562010	−	0.648594i
$675$	−0.0223193	−	6.74662i	−0.000859071	−	0.259678i
$676$	−22.9356	−	6.73451i	−0.882140	−	0.259020i
$677$	29.8372	−	2.13400i	1.14674	−	0.0820163i	0.514994	−	0.857194i	$-0.327794\pi$
$677$	29.8372	−	2.13400i	1.14674	−	0.0820163i	0.631744	+	0.775177i	$0.282339\pi$
$678$	10.0944	−	2.19591i	0.387674	−	0.0843333i
$679$	11.8696	−	18.4695i	0.455514	−	0.708793i
$680$	−1.28384	−	3.08501i	−0.0492328	−	0.118305i
$681$	15.7957	−	53.7954i	0.605294	−	2.06144i
$682$	5.05736	−	6.75584i	0.193656	−	0.258695i
$683$	2.77070	−	38.7394i	0.106018	−	1.48232i	−0.614517	−	0.788903i	$-0.710649\pi$
$683$	2.77070	−	38.7394i	0.106018	−	1.48232i	0.720535	−	0.693419i	$-0.243896\pi$
$684$	−3.22730	−	7.06680i	−0.123399	−	0.270206i
$685$	−14.1831	−	20.3555i	−0.541907	−	0.777745i
$686$	−53.4564	−	24.4127i	−2.04098	−	0.932082i
$687$	−38.7997	+	29.0451i	−1.48030	+	1.10814i
$688$	−0.0231789	+	0.106551i	−0.000883686	+	0.00406224i
$689$	61.0689			2.32654
$690$	14.1844	+	23.4422i	0.539992	+	0.892428i
$691$	−18.3136			−0.696681			−0.348341	−	0.937368i	$-0.613255\pi$
$691$	−18.3136			−0.696681			−0.348341	+	0.937368i	$0.613255\pi$
$692$	−2.88426	+	13.2587i	−0.109643	+	0.504022i
$693$	38.2132	−	28.6060i	1.45160	−	1.08665i
$694$	−6.23944	−	2.84946i	−0.236846	−	0.108164i
$695$	6.39627	−	35.7908i	0.242624	−	1.35762i
$696$	−6.70319	−	14.6779i	−0.254084	−	0.556366i
$697$	−0.356880	+	4.98983i	−0.0135178	+	0.189003i
$698$	1.52380	−	2.03556i	0.0576769	−	0.0770473i
$699$	−6.70130	+	22.8225i	−0.253466	+	0.863227i
$700$	−19.0687	+	16.6339i	−0.720730	+	0.628703i
$701$	−6.16429	+	9.59182i	−0.232822	+	0.362278i	−0.937932	−	0.346820i	$-0.887261\pi$
$701$	−6.16429	+	9.59182i	−0.232822	+	0.362278i	0.705110	+	0.709098i	$0.250898\pi$
$702$	8.00967	−	1.74240i	0.302306	−	0.0657626i
$703$	−6.63089	+	0.474250i	−0.250089	+	0.0178867i
$704$	2.56511	+	0.753185i	0.0966763	+	0.0283867i
$705$	4.28578	−	12.9481i	0.161412	−	0.487655i
$706$	−1.10732	−	1.27792i	−0.0416746	−	0.0480950i
$707$	16.2454	−	43.5555i	0.610970	−	1.63807i
$708$	27.8660	+	15.2160i	1.04727	+	0.571852i
$709$	−18.2633	+	39.9911i	−0.685893	+	1.50190i	0.170383	+	0.985378i	$0.445500\pi$
$709$	−18.2633	+	39.9911i	−0.685893	+	1.50190i	−0.856276	+	0.516519i	$0.827228\pi$
$710$	1.58135	+	8.68261i	0.0593470	+	0.325853i
$711$	−0.657560	−	1.02318i	−0.0246604	−	0.0383723i
$712$	7.45084	+	7.45084i	0.279232	+	0.279232i
$713$	−6.38512	−	13.7265i	−0.239125	−	0.514063i
$714$			19.3228i			0.723139i
$715$	22.7397	−	28.3140i	0.850417	−	1.05888i
$716$	−0.562737	+	3.91392i	−0.0210305	+	0.146270i
$717$	17.2623	+	46.2821i	0.644674	+	1.72844i
$718$	−6.87554	+	12.5916i	−0.256593	+	0.469914i
$719$	−0.0559333	+	0.0255439i	−0.00208596	+	0.000952626i	−0.416458	−	0.909155i	$-0.636729\pi$
$719$	−0.0559333	+	0.0255439i	−0.00208596	+	0.000952626i	0.414372	+	0.910108i	$0.364001\pi$
$720$	−7.64080	+	1.96367i	−0.284756	+	0.0731815i
$721$	−2.67478	−	18.6035i	−0.0996140	−	0.692831i
$722$	−12.4203	+	6.78197i	−0.462234	+	0.252399i
$723$	3.81823	+	53.3859i	0.142002	+	1.98544i
$724$	7.45984	+	4.79415i	0.277243	+	0.178173i
$725$	31.4893	−	2.35689i	1.16948	−	0.0875327i
$726$	−6.44663	+	7.43980i	−0.239257	+	0.276117i
$727$	−15.1545	−	27.7534i	−0.562050	−	1.02932i	−0.991973	−	0.126452i	$-0.959641\pi$
$727$	−15.1545	−	27.7534i	−0.562050	−	1.02932i	0.429923	−	0.902865i	$-0.358541\pi$
$728$	−24.6118	−	18.4241i	−0.912173	−	0.682844i
$729$	26.8457	−	23.2620i	0.994286	−	0.861554i
$730$	−0.614645	+	18.0465i	−0.0227490	+	0.667931i
$731$	−0.156349	+	0.0459083i	−0.00578279	+	0.00169798i
$732$	5.02096	−	1.87272i	0.185580	−	0.0692177i
$733$	20.4330	+	27.2954i	0.754712	+	1.00818i	0.999257	+	0.0385390i	$0.0122704\pi$
$733$	20.4330	+	27.2954i	0.754712	+	1.00818i	−0.244545	+	0.969638i	$0.578639\pi$
$734$	−17.0977	+	10.9880i	−0.631089	+	0.405576i
$735$	100.837	−	33.7473i	3.71944	−	1.24479i
$736$	3.36736	−	3.41480i	0.124123	−	0.125871i
$737$	−7.37258	+	7.37258i	−0.271572	+	0.271572i
$738$	11.5409	+	2.51058i	0.424828	+	0.0924156i
$739$	−12.7434	−	1.83222i	−0.468772	−	0.0673992i	−0.0961187	−	0.995370i	$-0.530643\pi$
$739$	−12.7434	−	1.83222i	−0.468772	−	0.0673992i	−0.372653	+	0.927971i	$0.621552\pi$
$740$	−0.710515	+	6.71322i	−0.0261190	+	0.246783i
$741$	9.62902	+	32.7934i	0.353731	+	1.20470i
$742$	47.6675	+	17.7791i	1.74993	+	0.652690i
$743$	−18.6797	−	1.33600i	−0.685290	−	0.0490129i	−0.275647	−	0.961259i	$-0.588892\pi$
$743$	−18.6797	−	1.33600i	−0.685290	−	0.0490129i	−0.409643	+	0.912246i	$0.634347\pi$
$744$	7.98329	−	1.14782i	0.292682	−	0.0420813i
$745$	9.59416	+	8.90290i	0.351503	+	0.326177i
$746$	9.60856	+	8.32586i	0.351794	+	0.304832i
$747$	1.89379	+	8.70560i	0.0692901	+	0.318521i
$748$	0.849202	+	3.90372i	0.0310499	+	0.142734i
$749$	16.4604	+	14.2630i	0.601449	+	0.521158i
$750$	2.91258	−	28.4171i	0.106352	−	1.03765i
$751$	42.8419	−	6.15973i	1.56332	−	0.224772i	0.694352	−	0.719636i	$-0.255691\pi$
$751$	42.8419	−	6.15973i	1.56332	−	0.224772i	0.868971	+	0.494864i	$0.164782\pi$
$752$	−2.38120	−	0.170307i	−0.0868335	−	0.00621045i
$753$	−14.0086	−	5.22493i	−0.510501	−	0.190407i
$754$	10.8088	+	36.8115i	0.393635	+	1.34060i
$755$	−12.7946	+	10.3455i	−0.465644	+	0.376512i
$756$	6.75924	+	0.971833i	0.245831	+	0.0353452i
$757$	24.9393	+	5.42522i	0.906435	+	0.197183i	0.641536	−	0.767093i	$-0.278298\pi$
$757$	24.9393	+	5.42522i	0.906435	+	0.197183i	0.264899	+	0.964276i	$0.414661\pi$
$758$	6.63403	−	6.63403i	0.240959	−	0.240959i
$759$	−11.6623	−	30.6121i	−0.423314	−	1.11115i
$760$	−1.56266	−	4.66925i	−0.0566836	−	0.169371i
$761$	30.5343	−	19.6232i	1.10687	−	0.711341i	0.146260	−	0.989246i	$-0.453276\pi$
$761$	30.5343	−	19.6232i	1.10687	−	0.711341i	0.960609	+	0.277905i	$0.0896401\pi$
$762$	7.36218	+	9.83473i	0.266704	+	0.356275i
$763$	−89.8580	+	33.5153i	−3.25308	+	1.21334i
$764$	−3.32734	+	0.976996i	−0.120379	+	0.0353465i
$765$	−8.04758	−	8.61510i	−0.290961	−	0.311480i
$766$	12.8010	−	11.0921i	0.462519	−	0.400775i
$767$	−60.4317	−	45.2386i	−2.18206	−	1.63347i
$768$	1.22449	+	2.24248i	0.0441849	+	0.0809187i
$769$	−19.3924	+	22.3800i	−0.699307	+	0.807043i	−0.988659	−	0.150180i	$-0.952015\pi$
$769$	−19.3924	+	22.3800i	−0.699307	+	0.807043i	0.289352	+	0.957223i	$0.406560\pi$
$770$	25.9927	−	15.4803i	0.936710	−	0.557873i
$771$	−33.7515	−	21.6908i	−1.21553	−	0.781175i
$772$	−1.30701	−	18.2744i	−0.0470404	−	0.657711i
$773$	−8.17869	+	4.46590i	−0.294167	+	0.160627i	−0.619555	−	0.784953i	$-0.712687\pi$
$773$	−8.17869	+	4.46590i	−0.294167	+	0.160627i	0.325388	+	0.945581i	$0.394505\pi$
$774$	0.0547510	+	0.380802i	0.00196798	+	0.0136876i
$775$	−3.30397	+	15.4337i	−0.118682	+	0.554397i
$776$	3.94612	−	1.80213i	0.141658	−	0.0646928i
$777$	18.7086	−	34.2623i	0.671169	−	1.22915i
$778$	2.81631	+	7.55081i	0.100969	+	0.270710i
$779$	−1.04907	+	7.29644i	−0.0375868	+	0.261422i
$780$	34.5018	−	3.76707i	1.23536	−	0.134883i
$781$		−	10.5515i		−	0.377564i
$782$	6.89034	+	1.97094i	0.246398	+	0.0704806i
$783$	−6.02573	−	6.02573i	−0.215342	−	0.215342i
$784$	−10.0625	−	15.6575i	−0.359374	−	0.559197i
$785$	15.3723	−	2.79973i	0.548660	−	0.0999265i
$786$	1.00254	−	2.19525i	0.0357594	−	0.0783021i
$787$	−2.81587	−	1.53758i	−0.100375	−	0.0548089i	0.428277	−	0.903647i	$-0.359121\pi$
$787$	−2.81587	−	1.53758i	−0.100375	−	0.0548089i	−0.528652	+	0.848838i	$0.677302\pi$
$788$	−5.68583	+	15.2443i	−0.202549	+	0.543055i
$789$	45.1829	+	52.1438i	1.60855	+	1.85637i
$790$	−0.346185	−	0.688741i	−0.0123167	−	0.0245043i
$791$	−19.6333	−	5.76485i	−0.698078	−	0.204974i
$792$	9.40803	−	0.672875i	0.334300	−	0.0239096i
$793$	−12.4501	+	2.70835i	−0.442116	+	0.0961764i
$794$	−11.7246	+	18.2438i	−0.416089	+	0.647448i
$795$	−53.0249	+	22.0664i	−1.88060	+	0.782616i
$796$	−3.87610	+	13.2008i	−0.137385	+	0.467889i
$797$	17.5001	−	23.3774i	0.619886	−	0.828071i	−0.375215	−	0.926938i	$-0.622431\pi$
$797$	17.5001	−	23.3774i	0.619886	−	0.828071i	0.995101	+	0.0988673i	$0.0315219\pi$
$798$	−2.03123	+	28.4003i	−0.0719049	+	1.00536i
$799$	−1.48197	−	3.24507i	−0.0524285	−	0.114802i
$800$	−4.94673	+	0.727943i	−0.174893	+	0.0257367i
$801$	33.8164	+	15.4435i	1.19485	+	0.545668i
$802$	14.6876	−	10.9950i	0.518636	−	0.388246i
$803$	4.58898	−	21.0952i	0.161942	−	0.744434i
$804$	−9.96469			−0.351427
$805$	−2.40610	−	54.2181i	−0.0848040	−	1.91094i
$806$	−19.1764			−0.675461
$807$	−2.03518	+	9.35557i	−0.0716417	+	0.329332i
$808$	7.35339	−	5.50468i	0.258691	−	0.193654i
$809$	−35.0331	−	15.9991i	−1.23170	−	0.562497i	−0.310122	−	0.950697i	$-0.600370\pi$
$809$	−35.0331	−	15.9991i	−1.23170	−	0.562497i	−0.921575	+	0.388199i	$0.873097\pi$
$810$	13.0934	−	9.12305i	0.460055	−	0.320551i
$811$	−5.24208	−	11.4785i	−0.184074	−	0.403066i	0.794989	−	0.606624i	$-0.207477\pi$
$811$	−5.24208	−	11.4785i	−0.184074	−	0.403066i	−0.979063	+	0.203558i	$0.934749\pi$
$812$	−2.28011	+	31.8802i	−0.0800163	+	1.11877i
$813$	−30.0425	+	40.1321i	−1.05364	+	1.40749i
$814$	2.27387	−	7.74410i	0.0796992	−	0.271430i
$815$	51.0980	+	21.0665i	1.78989	+	0.737929i
$816$	−2.06423	+	3.21200i	−0.0722623	+	0.112442i
$817$	−0.234625	+	0.0510396i	−0.00820849	+	0.00178565i
$818$	21.3122	−	1.52428i	0.745165	−	0.0532952i
$819$	−104.074	−	30.5589i	−3.63665	−	1.06782i
$820$	7.10639	+	2.35218i	0.248166	+	0.0821418i
$821$	7.86979	+	9.08223i	0.274658	+	0.316972i	0.876274	−	0.481813i	$-0.160022\pi$
$821$	7.86979	+	9.08223i	0.274658	+	0.316972i	−0.601616	+	0.798785i	$0.705476\pi$
$822$	−9.90668	+	26.5608i	−0.345535	+	0.926415i
$823$	−7.78880	−	4.25301i	−0.271500	−	0.148250i	0.337732	−	0.941242i	$-0.390340\pi$
$823$	−7.78880	−	4.25301i	−0.271500	−	0.148250i	−0.609232	+	0.792992i	$0.708522\pi$
$824$	1.54276	−	3.37817i	0.0537445	−	0.117684i
$825$	−9.51353	+	32.8012i	−0.331219	+	1.14199i
$826$	−33.9998	−	52.9047i	−1.18300	−	1.84079i
$827$	25.8418	+	25.8418i	0.898608	+	0.898608i	0.995313	−	0.0967053i	$-0.0308304\pi$
$827$	25.8418	+	25.8418i	0.898608	+	0.898608i	−0.0967053	+	0.995313i	$0.530830\pi$
$828$	6.92108	−	15.4400i	0.240524	−	0.536576i
$829$		−	13.7882i		−	0.478885i	−0.970910	−	0.239443i	$-0.923035\pi$
$829$		−	13.7882i		−	0.478885i	0.970910	−	0.239443i	$-0.0769647\pi$
$830$	0.612872	+	5.61317i	0.0212731	+	0.194836i
$831$	−9.23883	+	64.2575i	−0.320491	+	2.22907i
$832$	−2.12295	−	5.69184i	−0.0735999	−	0.197329i
$833$	13.3294	−	24.4110i	0.461837	−	0.845792i
$834$	−37.7897	+	17.2580i	−1.30855	+	0.597594i
$835$	−2.11252	−	1.24869i	−0.0731067	−	0.0432129i
$836$	0.837779	+	5.82688i	0.0289752	+	0.201527i
$837$	3.73840	−	2.04132i	0.129218	−	0.0705584i
$838$	−0.210741	−	2.94655i	−0.00727994	−	0.101787i
$839$	16.2851	+	10.4658i	0.562226	+	0.361320i	0.790676	−	0.612235i	$-0.209729\pi$
$839$	16.2851	+	10.4658i	0.562226	+	0.361320i	−0.228450	+	0.973556i	$0.573366\pi$
$840$	28.0272	+	7.10416i	0.967031	+	0.245117i
$841$	7.12828	−	8.22648i	0.245803	−	0.283672i
$842$	9.50750	+	17.4117i	0.327650	+	0.600047i
$843$	−32.9759	−	24.6854i	−1.13575	−	0.850212i
$844$	5.26571	−	4.56276i	0.181253	−	0.157057i
$845$	−53.4198	−	1.81942i	−1.83770	−	0.0625901i
$846$	−8.08142	+	2.37292i	−0.277845	+	0.0815827i
$847$	18.2696	−	6.81421i	0.627751	−	0.234139i
$848$	6.02437	+	8.04762i	0.206878	+	0.276356i
$849$	−19.6909	+	12.6546i	−0.675792	+	0.434305i
$850$	−4.49744	−	5.96663i	−0.154261	−	0.204654i
$851$	−10.3093	−	10.1661i	−0.353399	−	0.348489i
$852$	7.13067	−	7.13067i	0.244293	−	0.244293i
$853$	17.4074	+	3.78675i	0.596019	+	0.129656i	0.500448	−	0.865767i	$-0.333169\pi$
$853$	17.4074	+	3.78675i	0.596019	+	0.129656i	0.0955711	+	0.995423i	$0.469532\pi$
$854$	−10.5065	−	1.51060i	−0.359523	−	0.0516917i
$855$	−10.9226	−	13.5083i	−0.373544	−	0.461973i
$856$	1.21248	+	4.12934i	0.0414418	+	0.141138i
$857$	−19.4392	−	7.25044i	−0.664030	−	0.247670i	−0.00522733	−	0.999986i	$-0.501664\pi$
$857$	−19.4392	−	7.25044i	−0.664030	−	0.247670i	−0.658802	+	0.752316i	$0.728937\pi$
$858$	−41.3891	−	2.96021i	−1.41300	−	0.101060i
$859$	44.1980	−	6.35471i	1.50801	−	0.216820i	0.661808	−	0.749674i	$-0.269790\pi$
$859$	44.1980	−	6.35471i	1.50801	−	0.216820i	0.846207	+	0.532854i	$0.178880\pi$
$860$	0.00910586	+	0.243659i	0.000310507	+	0.00830869i
$861$	−32.7140	−	28.3468i	−1.11489	−	0.966057i
$862$	−6.29996	−	28.9605i	−0.214578	−	0.986397i
$863$	1.92425	+	8.84564i	0.0655023	+	0.301109i	0.998230	−	0.0594725i	$-0.0189419\pi$
$863$	1.92425	+	8.84564i	0.0655023	+	0.301109i	−0.932728	+	0.360582i	$0.882578\pi$
$864$	1.01976	+	0.883624i	0.0346928	+	0.0300615i
$865$	1.13309	+	30.3197i	0.0385262	+	1.03090i
$866$	−4.51138	+	0.648639i	−0.153303	+	0.0220416i
$867$	37.6335	+	2.69160i	1.27810	+	0.0914116i
$868$	−14.9682	−	5.58286i	−0.508055	−	0.189495i
$869$	0.259648	+	0.884281i	0.00880797	+	0.0299972i
$870$	−22.6865	−	28.0571i	−0.769143	−	0.951224i
$871$	23.4511	+	3.37176i	0.794610	+	0.114248i
$872$	−18.5173	−	4.02819i	−0.627075	−	0.136412i
$873$	10.8226	−	10.8226i	0.366290	−	0.366290i
$874$	9.92010	+	3.62117i	0.335553	+	0.122488i
$875$	−32.0389	+	46.6371i	−1.08311	+	1.57662i
$876$	17.3572	−	11.1548i	0.586446	−	0.376886i
$877$	2.21883	+	2.96401i	0.0749245	+	0.100087i	0.836438	−	0.548062i	$-0.184634\pi$
$877$	2.21883	+	2.96401i	0.0749245	+	0.100087i	−0.761513	+	0.648149i	$0.775543\pi$
$878$	−13.7371	+	5.12366i	−0.463603	+	0.172915i
$879$	0.604841	−	0.177597i	0.0204008	−	0.00599021i
$880$	5.97445	+	0.203483i	0.201399	+	0.00685943i
$881$	12.5043	−	10.8350i	0.421280	−	0.365041i	−0.418271	−	0.908322i	$-0.637364\pi$
$881$	12.5043	−	10.8350i	0.421280	−	0.365041i	0.839551	+	0.543281i	$0.182818\pi$
$882$	−52.5680	−	39.3519i	−1.77006	−	1.32505i
$883$	11.1127	+	20.3514i	0.373972	+	0.684879i	0.995105	−	0.0988266i	$-0.0315089\pi$
$883$	11.1127	+	20.3514i	0.373972	+	0.684879i	−0.621132	+	0.783706i	$0.713327\pi$
$884$	5.94483	−	6.86070i	0.199946	−	0.230750i
$885$	68.8180	+	17.4436i	2.31329	+	0.586359i
$886$	24.5172	+	15.7562i	0.823671	+	0.529341i
$887$	−0.480726	−	6.72143i	−0.0161412	−	0.225684i	−0.999119	−	0.0419606i	$-0.986640\pi$
$887$	−0.480726	−	6.72143i	−0.0161412	−	0.225684i	0.982978	−	0.183723i	$-0.0588150\pi$
$888$	6.77008	−	3.69675i	0.227189	−	0.124055i
$889$	−3.46304	−	24.0860i	−0.116147	−	0.807818i
$890$	20.2832	+	11.9893i	0.679894	+	0.401881i
$891$	−17.3553	+	7.92589i	−0.581424	+	0.265527i
$892$	−4.44737	+	8.14475i	−0.148909	+	0.272706i
$893$	−1.83705	−	4.92533i	−0.0614746	−	0.164820i
$894$	2.12838	−	14.8032i	0.0711837	−	0.495094i
$895$	0.959684	+	8.78955i	0.0320787	+	0.293802i
$896$		−	5.06084i		−	0.169071i
$897$	−39.8051	+	62.9011i	−1.32905	+	2.10021i
$898$	−2.19500	−	2.19500i	−0.0732480	−	0.0732480i
$899$	10.7782	+	16.7712i	0.359473	+	0.559351i
$900$	−15.4547	+	8.50539i	−0.515156	+	0.283513i
$901$	−6.24051	+	13.6648i	−0.207902	+	0.455241i
$902$	−7.85487	−	4.28908i	−0.261539	−	0.142811i
$903$	0.492741	−	1.32109i	0.0163974	−	0.0439631i
$904$	−2.64775	−	3.05567i	−0.0880628	−	0.101630i
$905$	18.8240	+	6.23067i	0.625732	+	0.207114i
$906$	18.0393	+	5.29682i	0.599317	+	0.175975i
$907$	1.19517	−	0.0854802i	0.0396850	−	0.00283832i	−0.0514826	−	0.998674i	$-0.516395\pi$
$907$	1.19517	−	0.0854802i	0.0396850	−	0.00283832i	0.0911675	+	0.995836i	$0.470940\pi$
$908$	−21.4422	+	4.66446i	−0.711584	+	0.154796i
$909$	17.5208	−	27.2630i	0.581130	−	0.904255i
$910$	−63.5560	−	26.2027i	−2.10686	−	0.868610i
$911$	−8.44110	+	28.7478i	−0.279666	+	0.952455i	0.693134	+	0.720809i	$0.256229\pi$
$911$	−8.44110	+	28.7478i	−0.279666	+	0.952455i	−0.972800	+	0.231647i	$0.925589\pi$
$912$	−3.37161	+	4.50394i	−0.111645	+	0.149140i
$913$	0.481603	−	6.73369i	0.0159387	−	0.222853i
$914$	7.47317	+	16.3640i	0.247190	+	0.541272i
$915$	9.83154	−	6.85029i	0.325021	−	0.226463i
$916$	17.2550	+	7.88012i	0.570123	+	0.260366i
$917$	−3.82677	+	2.86468i	−0.126371	+	0.0946001i
$918$	−0.428613	+	1.97030i	−0.0141463	+	0.0650297i
$919$	−49.0141			−1.61683			−0.808413	−	0.588615i	$-0.799673\pi$
$919$	−49.0141			−1.61683			−0.808413	+	0.588615i	$0.799673\pi$
$920$	5.39206	−	9.26961i	0.177771	−	0.305610i
$921$	−11.3378			−0.373594
$922$	−3.15415	+	14.4994i	−0.103876	+	0.477512i
$923$	−19.1943	+	14.3686i	−0.631787	+	0.472950i
$924$	−31.4446	−	14.3603i	−1.03445	−	0.472419i
$925$	2.19767	+	14.9342i	0.0722589	+	0.491034i
$926$	7.29171	+	15.9666i	0.239620	+	0.524695i
$927$	0.934728	−	13.0692i	0.0307005	−	0.429249i
$928$	−3.78472	+	5.05580i	−0.124240	+	0.165965i
$929$	−13.8322	+	47.1080i	−0.453818	+	1.54556i	0.341805	+	0.939771i	$0.388962\pi$
$929$	−13.8322	+	47.1080i	−0.453818	+	1.54556i	−0.795623	+	0.605792i	$0.792856\pi$
$930$	16.6505	−	6.92915i	0.545992	−	0.227216i
$931$	22.1574	−	34.4777i	0.726181	−	1.12996i
$932$	9.09678	−	1.97888i	0.297975	−	0.0648205i
$933$	−83.1971	+	5.95038i	−2.72375	+	0.194807i
$934$	10.1940	+	2.99322i	0.333557	+	0.0979411i
$935$	4.01183	+	7.98161i	0.131201	+	0.261027i
$936$	−14.0355	−	16.1978i	−0.458764	−	0.529442i
$937$	−12.2965	+	32.9681i	−0.401708	+	1.07702i	0.565881	+	0.824487i	$0.308536\pi$
$937$	−12.2965	+	32.9681i	−0.401708	+	1.07702i	−0.967588	+	0.252533i	$0.918736\pi$
$938$	17.3232	+	9.45919i	0.565623	+	0.308853i
$939$	32.9392	−	72.1268i	1.07493	−	2.35377i
$940$	−5.25174	+	0.956490i	−0.171293	+	0.0311973i
$941$	−17.1515	−	26.6882i	−0.559122	−	0.870010i	0.440493	−	0.897756i	$-0.354803\pi$
$941$	−17.1515	−	26.6882i	−0.559122	−	0.870010i	−0.999615	+	0.0277457i	$0.991167\pi$
$942$	−12.6246	−	12.6246i	−0.411332	−	0.411332i
$943$	−13.4451	+	8.77411i	−0.437831	+	0.285724i
$944$		−	12.4264i		−	0.404445i
$945$	15.1793	−	1.65735i	0.493784	−	0.0539136i
$946$	0.0414872	−	0.288550i	0.00134887	−	0.00938157i
$947$	13.4306	+	36.0088i	0.436436	+	1.17013i	0.950047	+	0.312107i	$0.101035\pi$
$947$	13.4306	+	36.0088i	0.436436	+	1.17013i	−0.513611	+	0.858023i	$0.671693\pi$
$948$	−0.422123	+	0.773061i	−0.0137099	+	0.0251078i
$949$	−44.6233	+	20.3788i	−1.44853	+	0.661523i
$950$	−5.98303	−	9.24241i	−0.194115	−	0.299863i
$951$	1.93039	+	13.4261i	0.0625971	+	0.435373i
$952$	6.63763	−	3.62442i	0.215127	−	0.117468i
$953$	1.03494	+	14.4704i	0.0335251	+	0.468742i	0.986289	+	0.165029i	$0.0527718\pi$
$953$	1.03494	+	14.4704i	0.0335251	+	0.468742i	−0.952764	+	0.303713i	$0.901774\pi$
$954$	29.8368	+	19.1750i	0.966003	+	0.620813i
$955$	−6.66222	+	3.96779i	−0.215585	+	0.128395i
$956$	12.6605	−	14.6110i	0.409471	−	0.472555i
$957$	20.6740	+	37.8617i	0.668296	+	1.22389i
$958$	−2.46162	−	1.84275i	−0.0795314	−	0.0595365i
$959$	42.4358	−	36.7708i	1.37032	−	1.18739i
$960$	3.89998	+	4.17501i	0.125871	+	0.134748i
$961$	20.1832	−	5.92634i	0.651073	−	0.191172i
$962$	−17.1837	+	6.40920i	−0.554025	+	0.206641i
$963$	9.09932	+	12.1553i	0.293222	+	0.391698i
$964$	17.6225	−	11.3253i	0.567582	−	0.364763i
$965$	−13.0017	−	38.8493i	−0.418540	−	1.25060i
$966$	−49.3825	+	37.5092i	−1.58886	+	1.20684i
$967$	−43.3258	+	43.3258i	−1.39327	+	1.39327i	−0.575376	+	0.817889i	$0.695144\pi$
$967$	−43.3258	+	43.3258i	−1.39327	+	1.39327i	−0.817889	+	0.575376i	$0.804856\pi$
$968$	3.76487	+	0.818997i	0.121007	+	0.0263236i
$969$	−8.32185	−	1.19650i	−0.267336	−	0.0384372i
$970$	7.54306	−	6.09919i	0.242193	−	0.195833i
$971$	−3.04477	−	10.3695i	−0.0977112	−	0.332774i	0.896101	−	0.443851i	$-0.146388\pi$
$971$	−3.04477	−	10.3695i	−0.0977112	−	0.332774i	−0.993812	+	0.111077i	$0.964570\pi$
$972$	−20.8776	−	7.78695i	−0.669650	−	0.249767i
$973$	82.0783	+	5.87036i	2.63131	+	0.188195i
$974$	23.2248	−	3.33923i	0.744171	−	0.106996i
$975$	72.6236	−	27.3612i	2.32582	−	0.876260i
$976$	−1.58509	−	1.37349i	−0.0507376	−	0.0439643i
$977$	−1.97324	−	9.07086i	−0.0631297	−	0.290202i	0.934749	−	0.355310i	$-0.115625\pi$
$977$	−1.97324	−	9.07086i	−0.0631297	−	0.290202i	−0.997878	+	0.0651074i	$0.979261\pi$
$978$	−13.4243	−	61.7107i	−0.429263	−	1.97329i
$979$	−21.2893	−	18.4473i	−0.680410	−	0.589579i
$980$	−30.5068	−	28.3088i	−0.974505	−	0.904291i
$981$	−66.1785	+	9.51503i	−2.11292	+	0.303792i
$982$	−15.2802	−	1.09286i	−0.487612	−	0.0348747i
$983$	17.3810	+	6.48276i	0.554366	+	0.206768i	0.611005	−	0.791627i	$-0.290766\pi$
$983$	17.3810	+	6.48276i	0.554366	+	0.206768i	−0.0566386	+	0.998395i	$0.518038\pi$
$984$	−2.40974	−	8.20681i	−0.0768196	−	0.261624i
$985$	−3.82912	+	36.1790i	−0.122006	+	1.15276i
$986$	−9.34151	−	1.34311i	−0.297494	−	0.0427732i
$987$	30.1634	+	6.56165i	0.960112	+	0.208859i
$988$	9.45881	−	9.45881i	0.300925	−	0.300925i
$989$	−0.420828	−	0.310459i	−0.0133816	−	0.00987201i
$990$	20.0004	−	6.69353i	0.635654	−	0.212734i
$991$	4.28081	−	2.75111i	0.135984	−	0.0873919i	−0.470880	−	0.882197i	$-0.656063\pi$
$991$	4.28081	−	2.75111i	0.135984	−	0.0873919i	0.606864	+	0.794805i	$0.292427\pi$
$992$	−1.89173	−	2.52706i	−0.0600626	−	0.0802342i
$993$	−24.1159	+	8.99475i	−0.765294	+	0.285440i
$994$	−19.1653	+	5.62744i	−0.607887	+	0.178492i
$995$	−1.04718	+	30.7461i	−0.0331979	+	0.974718i
$996$	4.87605	−	4.22512i	0.154504	−	0.133878i
$997$	−42.3705	−	31.7181i	−1.34189	−	1.00452i	−0.997848	−	0.0655683i	$-0.979114\pi$
$997$	−42.3705	−	31.7181i	−1.34189	−	1.00452i	−0.344039	−	0.938955i	$-0.611795\pi$
$998$	2.90409	+	5.31845i	0.0919274	+	0.168353i
$999$	2.66767	−	3.07866i	0.0844013	−	0.0974044i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.l.a.103.5	yes	240
5.2	odd	4	inner	230.2.l.a.57.2	✓	240
23.21	odd	22	inner	230.2.l.a.113.2	yes	240
115.67	even	44	inner	230.2.l.a.67.5	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.l.a.57.2	✓	240	5.2	odd	4	inner
230.2.l.a.67.5	yes	240	115.67	even	44	inner
230.2.l.a.103.5	yes	240	1.1	even	1	trivial
230.2.l.a.113.2	yes	240	23.21	odd	22	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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.212565 + 0.977147i) q^{2} +(2.04540 - 1.53116i) q^{3} +(-0.909632 - 0.415415i) q^{4} +(-2.20119 - 0.393381i) q^{5} +(1.06139 + 2.32412i) q^{6} +(0.361036 - 5.04795i) q^{7} +(0.599278 - 0.800541i) q^{8} +(0.993984 - 3.38520i) q^{9} +O(q^{10})\)	\(q+(-0.212565 + 0.977147i) q^{2} +(2.04540 - 1.53116i) q^{3} +(-0.909632 - 0.415415i) q^{4} +(-2.20119 - 0.393381i) q^{5} +(1.06139 + 2.32412i) q^{6} +(0.361036 - 5.04795i) q^{7} +(0.599278 - 0.800541i) q^{8} +(0.993984 - 3.38520i) q^{9} +(0.852288 - 2.06727i) q^{10} +(-1.44535 + 2.24901i) q^{11} +(-2.49663 + 0.543108i) q^{12} +(6.05938 - 0.433376i) q^{13} +(4.85584 + 1.42580i) q^{14} +(-5.10464 + 2.56577i) q^{15} +(0.654861 + 0.755750i) q^{16} +(-0.522224 + 1.40014i) q^{17} +(3.09655 + 1.69084i) q^{18} +(-0.914739 + 2.00300i) q^{19} +(1.83886 + 1.27224i) q^{20} +(-6.99077 - 10.8779i) q^{21} +(-1.89038 - 1.89038i) q^{22} +(-4.59200 + 1.38330i) q^{23} -2.55502i q^{24} +(4.69050 + 1.73181i) q^{25} +(-0.864543 + 6.01303i) q^{26} +(-0.471543 - 1.26426i) q^{27} +(-2.42540 + 4.44179i) q^{28} +(5.74476 - 2.62354i) q^{29} +(-1.42206 - 5.53338i) q^{30} +(0.449243 + 3.12456i) q^{31} +(-0.877679 + 0.479249i) q^{32} +(0.487289 + 6.81318i) q^{33} +(-1.25713 - 0.807911i) q^{34} +(-2.78047 + 10.9695i) q^{35} +(-2.31042 + 2.66637i) q^{36} +(1.44686 + 2.64972i) q^{37} +(-1.76278 - 1.31960i) q^{38} +(11.7303 - 10.1643i) q^{39} +(-1.63404 + 1.52640i) q^{40} +(3.21204 - 0.943140i) q^{41} +(12.1153 - 4.51876i) q^{42} +(0.0653473 + 0.0872938i) q^{43} +(2.24901 - 1.44535i) q^{44} +(-3.51962 + 7.06046i) q^{45} +(-0.375584 - 4.78110i) q^{46} +(-1.68806 + 1.68806i) q^{47} +(2.49663 + 0.543108i) q^{48} +(-18.4227 - 2.64878i) q^{49} +(-2.68927 + 4.21519i) q^{50} +(1.07569 + 3.66345i) q^{51} +(-5.69184 - 2.12295i) q^{52} +(10.0271 + 0.717153i) q^{53} +(1.33560 - 0.192030i) q^{54} +(4.06621 - 4.38193i) q^{55} +(-3.82473 - 3.31415i) q^{56} +(1.19592 + 5.49754i) q^{57} +(1.34245 + 6.17114i) q^{58} +(-9.39124 - 8.13756i) q^{59} +(5.70921 - 0.213361i) q^{60} +(-2.07603 + 0.298488i) q^{61} +(-3.14864 - 0.225195i) q^{62} +(-16.7294 - 6.23976i) q^{63} +(-0.281733 - 0.959493i) q^{64} +(-13.5084 - 1.42970i) q^{65} +(-6.76106 - 0.972094i) q^{66} +(3.81092 + 0.829015i) q^{67} +(1.05667 - 1.05667i) q^{68} +(-7.27441 + 9.86050i) q^{69} +(-10.1278 - 5.04866i) q^{70} +(-3.32031 + 2.13383i) q^{71} +(-2.11432 - 2.82440i) q^{72} +(-7.56617 + 2.82203i) q^{73} +(-2.89672 + 0.850554i) q^{74} +(12.2456 - 3.63969i) q^{75} +(1.66415 - 1.44200i) q^{76} +(10.8311 + 8.10803i) q^{77} +(7.43860 + 13.6228i) q^{78} +(0.225753 - 0.260533i) q^{79} +(-1.14418 - 1.92116i) q^{80} +(6.00383 + 3.85843i) q^{81} +(0.238818 + 3.33911i) q^{82} +(-2.21632 + 1.21020i) q^{83} +(1.84021 + 12.7989i) q^{84} +(1.70030 - 2.87654i) q^{85} +(-0.0991894 + 0.0452983i) q^{86} +(7.73323 - 14.1623i) q^{87} +(0.934258 + 2.50484i) q^{88} +(-1.49958 + 10.4298i) q^{89} +(-6.15096 - 4.94000i) q^{90} -30.7439i q^{91} +(4.75167 + 0.649296i) q^{92} +(5.70309 + 5.70309i) q^{93} +(-1.29066 - 2.00831i) q^{94} +(2.80146 - 4.04915i) q^{95} +(-1.06139 + 2.32412i) q^{96} +(3.80751 + 2.07906i) q^{97} +(6.50427 - 17.4386i) q^{98} +(6.17669 + 7.12828i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 8 q^{3} - 8 q^{6}+O(q^{10}) \) 240 * q - 8 * q^3 - 8 * q^6	\( 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46} - 80 q^{47} + 8 q^{48} + 8 q^{50} + 16 q^{52} - 44 q^{56} - 88 q^{57} - 176 q^{61} - 32 q^{62} - 176 q^{66} + 24 q^{70} - 336 q^{71} + 16 q^{72} - 88 q^{73} - 36 q^{75} - 24 q^{77} + 40 q^{78} - 136 q^{81} + 40 q^{82} - 100 q^{85} - 44 q^{86} + 40 q^{87} + 8 q^{92} + 56 q^{93} + 52 q^{95} + 8 q^{96} + 132 q^{97} + 24 q^{98}+O(q^{100}) \) 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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