LMFDB - Embedded newform 750.2.o.b.229.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(19,750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, base_ring=CyclotomicField(50))

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

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

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

chi := DirichletCharacter("750.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.o (of order $50$, 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:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$280$
Relative dimension:	$14$ over $\Q(\zeta_{50})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label			229.8
Character	$\chi$	$=$	750.229
Dual form			750.2.o.b.619.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.248690 + 0.968583i) q^{2} +(-0.982287 + 0.187381i) q^{3} +(-0.876307 + 0.481754i) q^{4} +(-2.01220 - 0.975220i) q^{5} +(-0.425779 - 0.904827i) q^{6} +(2.44257 - 3.36191i) q^{7} +(-0.684547 - 0.728969i) q^{8} +(0.929776 - 0.368125i) q^{9} +O(q^{10})$	\(q+(0.248690 + 0.968583i) q^{2} +(-0.982287 + 0.187381i) q^{3} +(-0.876307 + 0.481754i) q^{4} +(-2.01220 - 0.975220i) q^{5} +(-0.425779 - 0.904827i) q^{6} +(2.44257 - 3.36191i) q^{7} +(-0.684547 - 0.728969i) q^{8} +(0.929776 - 0.368125i) q^{9} +(0.444168 - 2.19151i) q^{10} +(-3.71130 + 0.952899i) q^{11} +(0.770513 - 0.637424i) q^{12} +(1.92375 + 4.85885i) q^{13} +(3.86373 + 1.52976i) q^{14} +(2.15930 + 0.580897i) q^{15} +(0.535827 - 0.844328i) q^{16} +(-3.45774 + 6.28960i) q^{17} +(0.587785 + 0.809017i) q^{18} +(-0.396812 + 2.08016i) q^{19} +(2.23312 - 0.114793i) q^{20} +(-1.76934 + 3.76005i) q^{21} +(-1.84592 - 3.35772i) q^{22} +(2.73714 + 0.172206i) q^{23} +(0.809017 + 0.587785i) q^{24} +(3.09789 + 3.92467i) q^{25} +(-4.22778 + 3.07166i) q^{26} +(-0.844328 + 0.535827i) q^{27} +(-0.520828 + 4.12278i) q^{28} +(-0.368452 - 0.0465463i) q^{29} +(-0.0256523 + 2.23592i) q^{30} +(7.58536 + 4.17009i) q^{31} +(0.951057 + 0.309017i) q^{32} +(3.46701 - 1.63145i) q^{33} +(-6.95190 - 1.78495i) q^{34} +(-8.19353 + 4.38278i) q^{35} +(-0.637424 + 0.770513i) q^{36} +(-3.48268 - 2.21017i) q^{37} +(-2.11349 + 0.132970i) q^{38} +(-2.80014 - 4.41231i) q^{39} +(0.666541 + 2.13441i) q^{40} +(0.404604 + 6.43100i) q^{41} +(-4.08194 - 0.778671i) q^{42} +(-11.9369 + 3.87853i) q^{43} +(2.79317 - 2.62296i) q^{44} +(-2.22990 - 0.165996i) q^{45} +(0.513902 + 2.69397i) q^{46} +(2.39238 - 2.54763i) q^{47} +(-0.368125 + 0.929776i) q^{48} +(-3.17315 - 9.76596i) q^{49} +(-3.03096 + 3.97659i) q^{50} +(2.21794 - 6.82611i) q^{51} +(-4.02657 - 3.33107i) q^{52} +(-2.84307 - 1.33785i) q^{53} +(-0.728969 - 0.684547i) q^{54} +(8.39716 + 1.70191i) q^{55} +(-4.12278 + 0.520828i) q^{56} -2.11767i q^{57} +(-0.0465463 - 0.368452i) q^{58} +(-7.23904 - 8.75050i) q^{59} +(-2.17205 + 0.531204i) q^{60} +(-0.380118 + 6.04180i) q^{61} +(-2.15267 + 8.38411i) q^{62} +(1.03344 - 4.02499i) q^{63} +(-0.0627905 + 0.998027i) q^{64} +(0.867468 - 11.6531i) q^{65} +(2.44240 + 2.95236i) q^{66} +(1.09380 + 8.65835i) q^{67} -7.17739i q^{68} +(-2.72092 + 0.343732i) q^{69} +(-6.28274 - 6.84616i) q^{70} +(10.9807 + 10.3116i) q^{71} +(-0.904827 - 0.425779i) q^{72} +(-2.15979 - 1.78673i) q^{73} +(1.27463 - 3.92291i) q^{74} +(-3.77843 - 3.27467i) q^{75} +(-0.654397 - 2.01403i) q^{76} +(-5.86154 + 14.8046i) q^{77} +(3.57732 - 3.80946i) q^{78} +(2.85082 + 14.9445i) q^{79} +(-1.90160 + 1.17641i) q^{80} +(0.728969 - 0.684547i) q^{81} +(-6.12833 + 1.99122i) q^{82} +(11.0091 + 2.10010i) q^{83} +(-0.260929 - 4.14734i) q^{84} +(13.0914 - 9.28387i) q^{85} +(-6.72526 - 10.5973i) q^{86} +(0.370647 - 0.0233191i) q^{87} +(3.23519 + 2.05312i) q^{88} +(0.121414 - 0.146765i) q^{89} +(-0.393772 - 2.20112i) q^{90} +(21.0339 + 5.40058i) q^{91} +(-2.48153 + 1.16772i) q^{92} +(-8.23240 - 2.67487i) q^{93} +(3.06255 + 1.68365i) q^{94} +(2.82708 - 3.79872i) q^{95} +(-0.992115 - 0.125333i) q^{96} +(0.416952 - 3.30052i) q^{97} +(8.67002 - 5.50216i) q^{98} +(-3.09989 + 2.25220i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 280 q+O(q^{10}) $ 280 * q	$ 280 q - 10 q^{11} - 20 q^{13} + 30 q^{17} + 10 q^{19} + 20 q^{22} + 60 q^{23} + 70 q^{24} + 20 q^{25} + 20 q^{29} + 10 q^{30} + 20 q^{31} + 20 q^{33} - 10 q^{34} + 30 q^{35} - 20 q^{37} + 90 q^{38} - 40 q^{41} - 10 q^{46} - 100 q^{47} + 120 q^{49} - 20 q^{50} - 30 q^{51} + 80 q^{52} - 30 q^{53} - 10 q^{55} + 30 q^{58} + 20 q^{59} + 60 q^{61} - 50 q^{62} - 10 q^{63} + 20 q^{65} + 40 q^{66} + 50 q^{67} + 10 q^{69} + 20 q^{70} + 80 q^{71} - 20 q^{73} + 80 q^{75} - 30 q^{76} - 100 q^{77} - 100 q^{79} + 100 q^{82} + 30 q^{83} - 20 q^{86} - 10 q^{87} - 60 q^{89} - 10 q^{90} + 70 q^{91} - 120 q^{92} + 50 q^{93} + 30 q^{94} - 20 q^{95} + 10 q^{97} + 40 q^{98} + 20 q^{99}+O(q^{100}) $ 280 * q - 10 * q^11 - 20 * q^13 + 30 * q^17 + 10 * q^19 + 20 * q^22 + 60 * q^23 + 70 * q^24 + 20 * q^25 + 20 * q^29 + 10 * q^30 + 20 * q^31 + 20 * q^33 - 10 * q^34 + 30 * q^35 - 20 * q^37 + 90 * q^38 - 40 * q^41 - 10 * q^46 - 100 * q^47 + 120 * q^49 - 20 * q^50 - 30 * q^51 + 80 * q^52 - 30 * q^53 - 10 * q^55 + 30 * q^58 + 20 * q^59 + 60 * q^61 - 50 * q^62 - 10 * q^63 + 20 * q^65 + 40 * q^66 + 50 * q^67 + 10 * q^69 + 20 * q^70 + 80 * q^71 - 20 * q^73 + 80 * q^75 - 30 * q^76 - 100 * q^77 - 100 * q^79 + 100 * q^82 + 30 * q^83 - 20 * q^86 - 10 * q^87 - 60 * q^89 - 10 * q^90 + 70 * q^91 - 120 * q^92 + 50 * q^93 + 30 * q^94 - 20 * q^95 + 10 * q^97 + 40 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{21}{50}\right)$	$1$

Coefficient data

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

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

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

$2$	0.248690	+	0.968583i	0.175850	+	0.684892i
$2$	0.248690	+	0.968583i	0.175850	+	0.684892i
$3$	−0.982287	+	0.187381i	−0.567124	+	0.108185i
$3$	−0.982287	+	0.187381i	−0.567124	+	0.108185i
$4$	−0.876307	+	0.481754i	−0.438153	+	0.240877i
$5$	−2.01220	−	0.975220i	−0.899883	−	0.436132i
$5$	−2.01220	−	0.975220i	−0.899883	−	0.436132i
$6$	−0.425779	−	0.904827i	−0.173824	−	0.369394i
$7$	2.44257	−	3.36191i	0.923204	−	1.27068i	−0.0392486	−	0.999229i	$-0.512496\pi$
$7$	2.44257	−	3.36191i	0.923204	−	1.27068i	0.962452	−	0.271451i	$-0.0875036\pi$
$8$	−0.684547	−	0.728969i	−0.242024	−	0.257729i
$9$	0.929776	−	0.368125i	0.309925	−	0.122708i
$10$	0.444168	−	2.19151i	0.140458	−	0.693016i
$11$	−3.71130	+	0.952899i	−1.11900	+	0.287310i	−0.762501	−	0.646986i	$-0.776029\pi$
$11$	−3.71130	+	0.952899i	−1.11900	+	0.287310i	−0.356497	+	0.934296i	$0.616029\pi$
$12$	0.770513	−	0.637424i	0.222428	−	0.184008i
$13$	1.92375	+	4.85885i	0.533553	+	1.34760i	0.907461	+	0.420136i	$0.138018\pi$
$13$	1.92375	+	4.85885i	0.533553	+	1.34760i	−0.373908	+	0.927466i	$0.621982\pi$
$14$	3.86373	+	1.52976i	1.03262	+	0.408845i
$15$	2.15930	+	0.580897i	0.557528	+	0.149987i
$16$	0.535827	−	0.844328i	0.133957	−	0.211082i
$17$	−3.45774	+	6.28960i	−0.838624	+	1.52545i	0.0121537	+	0.999926i	$0.496131\pi$
$17$	−3.45774	+	6.28960i	−0.838624	+	1.52545i	−0.850778	+	0.525525i	$0.823869\pi$
$18$	0.587785	+	0.809017i	0.138542	+	0.190687i
$19$	−0.396812	+	2.08016i	−0.0910349	+	0.477222i	0.907348	+	0.420380i	$0.138103\pi$
$19$	−0.396812	+	2.08016i	−0.0910349	+	0.477222i	−0.998383	+	0.0568421i	$0.981897\pi$
$20$	2.23312	−	0.114793i	0.499341	−	0.0256685i
$21$	−1.76934	+	3.76005i	−0.386103	+	0.820510i
$22$	−1.84592	−	3.35772i	−0.393552	−	0.715869i
$23$	2.73714	+	0.172206i	0.570732	+	0.0359074i	0.345535	−	0.938406i	$-0.387697\pi$
$23$	2.73714	+	0.172206i	0.570732	+	0.0359074i	0.225197	+	0.974313i	$0.427697\pi$
$24$	0.809017	+	0.587785i	0.165140	+	0.119981i
$25$	3.09789	+	3.92467i	0.619579	+	0.784935i
$26$	−4.22778	+	3.07166i	−0.829136	+	0.602402i
$27$	−0.844328	+	0.535827i	−0.162491	+	0.103120i
$28$	−0.520828	+	4.12278i	−0.0984272	+	0.779131i
$29$	−0.368452	−	0.0465463i	−0.0684197	−	0.00864342i	0.0910488	−	0.995846i	$-0.470978\pi$
$29$	−0.368452	−	0.0465463i	−0.0684197	−	0.00864342i	−0.159469	+	0.987203i	$0.550978\pi$
$30$	−0.0256523	+	2.23592i	−0.00468345	+	0.408221i
$31$	7.58536	+	4.17009i	1.36237	+	0.748970i	0.984249	−	0.176787i	$-0.0565702\pi$
$31$	7.58536	+	4.17009i	1.36237	+	0.748970i	0.378121	+	0.925756i	$0.376570\pi$
$32$	0.951057	+	0.309017i	0.168125	+	0.0546270i
$33$	3.46701	−	1.63145i	0.603528	−	0.283999i
$34$	−6.95190	−	1.78495i	−1.19224	−	0.306116i
$35$	−8.19353	+	4.38278i	−1.38496	+	0.740826i
$36$	−0.637424	+	0.770513i	−0.106237	+	0.128419i
$37$	−3.48268	−	2.21017i	−0.572549	−	0.363350i	0.217813	−	0.975990i	$-0.430108\pi$
$37$	−3.48268	−	2.21017i	−0.572549	−	0.363350i	−0.790362	+	0.612640i	$0.790108\pi$
$38$	−2.11349	+	0.132970i	−0.342854	+	0.0215705i
$39$	−2.80014	−	4.41231i	−0.448381	−	0.706535i
$40$	0.666541	+	2.13441i	0.105389	+	0.337480i
$41$	0.404604	+	6.43100i	0.0631885	+	1.00435i	0.894077	+	0.447914i	$0.147833\pi$
$41$	0.404604	+	6.43100i	0.0631885	+	1.00435i	−0.830888	+	0.556439i	$0.812167\pi$
$42$	−4.08194	−	0.778671i	−0.629857	−	0.120152i
$43$	−11.9369	+	3.87853i	−1.82036	+	0.591470i	−0.820556	+	0.571566i	$0.806336\pi$
$43$	−11.9369	+	3.87853i	−1.82036	+	0.591470i	−0.999802	+	0.0199037i	$0.993664\pi$
$44$	2.79317	−	2.62296i	0.421087	−	0.395427i
$45$	−2.22990	−	0.165996i	−0.332414	−	0.0247453i
$46$	0.513902	+	2.69397i	0.0757707	+	0.397204i
$47$	2.39238	−	2.54763i	0.348965	−	0.371610i	−0.530409	−	0.847742i	$-0.677962\pi$
$47$	2.39238	−	2.54763i	0.348965	−	0.371610i	0.879374	+	0.476132i	$0.157962\pi$
$48$	−0.368125	+	0.929776i	−0.0531342	+	0.134202i
$49$	−3.17315	−	9.76596i	−0.453308	−	1.39514i
$50$	−3.03096	+	3.97659i	−0.428642	+	0.562375i
$51$	2.21794	−	6.82611i	0.310573	−	0.955846i
$52$	−4.02657	−	3.33107i	−0.558384	−	0.461936i
$53$	−2.84307	−	1.33785i	−0.390525	−	0.183767i	0.220484	−	0.975391i	$-0.429236\pi$
$53$	−2.84307	−	1.33785i	−0.390525	−	0.183767i	−0.611009	+	0.791623i	$0.709236\pi$
$54$	−0.728969	−	0.684547i	−0.0992001	−	0.0931551i
$55$	8.39716	+	1.70191i	1.13227	+	0.229485i
$56$	−4.12278	+	0.520828i	−0.550929	+	0.0695985i
$57$		−	2.11767i		−	0.280492i
$58$	−0.0465463	−	0.368452i	−0.00611182	−	0.0483801i
$59$	−7.23904	−	8.75050i	−0.942443	−	1.13922i	−0.990101	−	0.140354i	$-0.955176\pi$
$59$	−7.23904	−	8.75050i	−0.942443	−	1.13922i	0.0476582	−	0.998864i	$-0.484824\pi$
$60$	−2.17205	+	0.531204i	−0.280411	+	0.0685782i
$61$	−0.380118	+	6.04180i	−0.0486691	+	0.773573i	0.895695	+	0.444670i	$0.146679\pi$
$61$	−0.380118	+	6.04180i	−0.0486691	+	0.773573i	−0.944364	+	0.328903i	$0.893321\pi$
$62$	−2.15267	+	8.38411i	−0.273390	+	1.06478i
$63$	1.03344	−	4.02499i	0.130201	−	0.507101i
$64$	−0.0627905	+	0.998027i	−0.00784881	+	0.124753i
$65$	0.867468	−	11.6531i	0.107596	−	1.44538i
$66$	2.44240	+	2.95236i	0.300639	+	0.363410i
$67$	1.09380	+	8.65835i	0.133629	+	1.05779i	0.906198	+	0.422854i	$0.138972\pi$
$67$	1.09380	+	8.65835i	0.133629	+	1.05779i	−0.772569	+	0.634931i	$0.781028\pi$
$68$		−	7.17739i		−	0.870387i
$69$	−2.72092	+	0.343732i	−0.327560	+	0.0413805i
$70$	−6.28274	−	6.84616i	−0.750931	−	0.818273i
$71$	10.9807	+	10.3116i	1.30317	+	1.22376i	0.958518	+	0.285033i	$0.0920046\pi$
$71$	10.9807	+	10.3116i	1.30317	+	1.22376i	0.344656	+	0.938729i	$0.387995\pi$
$72$	−0.904827	−	0.425779i	−0.106635	−	0.0501786i
$73$	−2.15979	−	1.78673i	−0.252784	−	0.209121i	0.502398	−	0.864637i	$-0.332451\pi$
$73$	−2.15979	−	1.78673i	−0.252784	−	0.209121i	−0.755182	+	0.655516i	$0.772451\pi$
$74$	1.27463	−	3.92291i	0.148173	−	0.456029i
$75$	−3.77843	−	3.27467i	−0.436296	−	0.378126i
$76$	−0.654397	−	2.01403i	−0.0750644	−	0.231025i
$77$	−5.86154	+	14.8046i	−0.667984	+	1.68714i
$78$	3.57732	−	3.80946i	0.405052	−	0.431337i
$79$	2.85082	+	14.9445i	0.320743	+	1.68139i	0.668424	+	0.743780i	$0.266969\pi$
$79$	2.85082	+	14.9445i	0.320743	+	1.68139i	−0.347682	+	0.937613i	$0.613031\pi$
$80$	−1.90160	+	1.17641i	−0.212605	+	0.131526i
$81$	0.728969	−	0.684547i	0.0809965	−	0.0760608i
$82$	−6.12833	+	1.99122i	−0.676761	+	0.219893i
$83$	11.0091	+	2.10010i	1.20841	+	0.230516i	0.751945	−	0.659225i	$-0.229116\pi$
$83$	11.0091	+	2.10010i	1.20841	+	0.230516i	0.456464	+	0.889742i	$0.349116\pi$
$84$	−0.260929	−	4.14734i	−0.0284697	−	0.452512i
$85$	13.0914	−	9.28387i	1.41996	−	1.00698i
$86$	−6.72526	−	10.5973i	−0.725203	−	1.14274i
$87$	0.370647	−	0.0233191i	0.0397376	−	0.00250007i
$88$	3.23519	+	2.05312i	0.344873	+	0.218863i
$89$	0.121414	−	0.146765i	0.0128699	−	0.0155570i	−0.764039	−	0.645170i	$-0.776787\pi$
$89$	0.121414	−	0.146765i	0.0128699	−	0.0155570i	0.776909	+	0.629613i	$0.216787\pi$
$90$	−0.393772	−	2.20112i	−0.0415072	−	0.232019i
$91$	21.0339	+	5.40058i	2.20495	+	0.566135i
$92$	−2.48153	+	1.16772i	−0.258717	+	0.121743i
$93$	−8.23240	−	2.67487i	−0.853660	−	0.277371i
$94$	3.06255	+	1.68365i	0.315878	+	0.173655i
$95$	2.82708	−	3.79872i	0.290052	−	0.389741i
$96$	−0.992115	−	0.125333i	−0.101257	−	0.0127918i
$97$	0.416952	−	3.30052i	0.0423351	−	0.335117i	−0.956695	−	0.291091i	$-0.905982\pi$
$97$	0.416952	−	3.30052i	0.0423351	−	0.335117i	0.999030	−	0.0440255i	$-0.0140183\pi$
$98$	8.67002	−	5.50216i	0.875804	−	0.555802i
$99$	−3.09989	+	2.25220i	−0.311551	+	0.226355i
$100$	−4.60543	−	1.94680i	−0.460543	−	0.194680i
$101$	5.36725	+	3.89953i	0.534061	+	0.388018i	0.821875	−	0.569668i	$-0.192928\pi$
$101$	5.36725	+	3.89953i	0.534061	+	0.388018i	−0.287814	+	0.957686i	$0.592928\pi$
$102$	7.16323	+	0.450672i	0.709266	+	0.0446232i
$103$	−6.69461	−	12.1775i	−0.659640	−	1.19988i	−0.968557	−	0.248791i	$-0.919967\pi$
$103$	−6.69461	−	12.1775i	−0.659640	−	1.19988i	0.308917	−	0.951089i	$-0.400033\pi$
$104$	2.22505	−	4.72847i	0.218184	−	0.463664i
$105$	7.22715	−	5.84047i	0.705297	−	0.569971i
$106$	0.588773	−	3.08645i	0.0571866	−	0.299783i
$107$	−7.28043	−	10.0206i	−0.703826	−	0.968733i	−0.999908	−	0.0135704i	$-0.995680\pi$
$107$	−7.28043	−	10.0206i	−0.703826	−	0.968733i	0.296082	−	0.955162i	$-0.404320\pi$
$108$	0.481754	−	0.876307i	0.0463568	−	0.0843226i
$109$	10.8215	−	17.0520i	1.03651	−	1.63329i	0.303817	−	0.952730i	$-0.401739\pi$
$109$	10.8215	−	17.0520i	1.03651	−	1.63329i	0.732697	−	0.680555i	$-0.238261\pi$
$110$	0.439849	+	8.55659i	0.0419380	+	0.815839i
$111$	3.83513	+	1.51844i	0.364015	+	0.144124i
$112$	−1.52976	−	3.86373i	−0.144549	−	0.365088i
$113$	−14.2537	+	11.7917i	−1.34087	+	1.10927i	−0.356283	+	0.934378i	$0.615956\pi$
$113$	−14.2537	+	11.7917i	−1.34087	+	1.10927i	−0.984588	+	0.174887i	$0.944044\pi$
$114$	2.05114	−	0.526644i	0.192107	−	0.0493247i
$115$	−5.33972	−	3.01582i	−0.497932	−	0.281227i
$116$	0.345300	−	0.136714i	0.0320603	−	0.0126936i
$117$	3.57732	+	3.80946i	0.330724	+	0.352185i
$118$	6.67531	−	9.18778i	0.614512	−	0.845803i
$119$	12.6993	+	26.9873i	1.16414	+	2.47393i
$120$	−1.05468	−	1.97171i	−0.0962790	−	0.179992i
$121$	3.22634	−	1.77370i	0.293304	−	0.161245i
$122$	−5.94651	+	1.13436i	−0.538372	+	0.102700i
$123$	−1.60249	−	6.24127i	−0.144491	−	0.562756i
$124$	−8.65605			−0.777337
$125$	−2.40616	−	10.9184i	−0.215213	−	0.976567i
$126$	4.15554			0.370205
$127$	−1.28626	−	5.00965i	−0.114137	−	0.444535i	0.885667	−	0.464321i	$-0.153702\pi$
$127$	−1.28626	−	5.00965i	−0.114137	−	0.444535i	−0.999804	+	0.0197859i	$0.993702\pi$
$128$	−0.982287	+	0.187381i	−0.0868227	+	0.0165623i
$129$	10.9987	−	6.04658i	0.968380	−	0.532372i
$130$	11.5027	−	2.05778i	1.00885	−	0.180479i
$131$	5.09115	+	10.8192i	0.444816	+	0.945282i	0.993979	+	0.109567i	$0.0349464\pi$
$131$	5.09115	+	10.8192i	0.444816	+	0.945282i	−0.549163	+	0.835715i	$0.685054\pi$
$132$	−2.25220	+	3.09989i	−0.196029	+	0.269811i
$133$	6.02407	+	6.41498i	0.522353	+	0.556249i
$134$	−8.11431	+	3.21268i	−0.700970	+	0.277533i
$135$	2.22151	−	0.254785i	0.191197	−	0.0219284i
$136$	6.95190	−	1.78495i	0.596121	−	0.153058i
$137$	−6.15210	+	5.08946i	−0.525610	+	0.434822i	−0.862006	−	0.506899i	$-0.830792\pi$
$137$	−6.15210	+	5.08946i	−0.525610	+	0.434822i	0.336396	+	0.941721i	$0.390792\pi$
$138$	−1.00960	−	2.54996i	−0.0859428	−	0.217067i
$139$	14.1671	+	5.60917i	1.20164	+	0.475763i	0.881762	−	0.471695i	$-0.156358\pi$
$139$	14.1671	+	5.60917i	1.20164	+	0.475763i	0.319879	+	0.947458i	$0.396358\pi$
$140$	5.06862	−	7.78793i	0.428377	−	0.658200i
$141$	−1.87263	+	2.95079i	−0.157704	+	0.248501i
$142$	−7.25684	+	13.2002i	−0.608981	+	1.10773i
$143$	−11.7696	−	16.1995i	−0.984225	−	1.35467i
$144$	0.187381	−	0.982287i	0.0156151	−	0.0818573i
$145$	0.696005	+	0.452982i	0.0578001	+	0.0376181i
$146$	1.19348	−	2.53628i	0.0987732	−	0.209904i
$147$	4.94691	+	8.99839i	0.408014	+	0.742175i
$148$	4.11665	+	0.258998i	0.338387	+	0.0212895i
$149$	2.50678	+	1.82128i	0.205363	+	0.149205i	0.685713	−	0.727872i	$-0.259490\pi$
$149$	2.50678	+	1.82128i	0.205363	+	0.149205i	−0.480350	+	0.877077i	$0.659490\pi$
$150$	2.23213	−	4.47410i	0.182253	−	0.365309i
$151$	−6.47196	+	4.70216i	−0.526681	+	0.382656i	−0.819115	−	0.573630i	$-0.805535\pi$
$151$	−6.47196	+	4.70216i	−0.526681	+	0.382656i	0.292434	+	0.956286i	$0.405535\pi$
$152$	1.78801	−	1.13471i	0.145027	−	0.0920367i
$153$	−0.899566	+	7.12080i	−0.0727256	+	0.575682i
$154$	−15.7971	−	1.99564i	−1.27297	−	0.160814i
$155$	−11.1965	−	15.7884i	−0.899325	−	1.26816i
$156$	4.57942	+	2.51756i	0.366647	+	0.201566i
$157$	−19.8083	−	6.43611i	−1.58088	−	0.513658i	−0.618594	−	0.785711i	$-0.712297\pi$
$157$	−19.8083	−	6.43611i	−1.58088	−	0.513658i	−0.962282	+	0.272053i	$0.912297\pi$
$158$	−13.7661	+	6.47782i	−1.09517	+	0.515348i
$159$	3.04339	+	0.781411i	0.241357	+	0.0619699i
$160$	−1.61236	−	1.54929i	−0.127468	−	0.122482i
$161$	7.26458	−	8.78137i	0.572529	−	0.692069i
$162$	0.844328	+	0.535827i	0.0663367	+	0.0420985i
$163$	2.99381	−	0.188355i	0.234493	−	0.0147531i	0.0548910	−	0.998492i	$-0.482519\pi$
$163$	2.99381	−	0.188355i	0.234493	−	0.0147531i	0.179602	+	0.983739i	$0.442519\pi$
$164$	−3.45271	−	5.44060i	−0.269612	−	0.424840i
$165$	−8.56733	−	0.0982915i	−0.666966	−	0.00765198i
$166$	0.703734	+	11.1855i	0.0546204	+	0.868166i
$167$	4.70285	+	0.897117i	0.363918	+	0.0694210i	0.366097	−	0.930577i	$-0.380694\pi$
$167$	4.70285	+	0.897117i	0.363918	+	0.0694210i	−0.00217950	+	0.999998i	$0.500694\pi$
$168$	3.95216	−	1.28413i	0.304916	−	0.0990731i
$169$	−10.4310	+	9.79534i	−0.802383	+	0.753488i
$170$	12.2479	+	10.3713i	0.939371	+	0.795442i
$171$	0.396812	+	2.08016i	0.0303450	+	0.159074i
$172$	8.59188	−	9.14942i	0.655124	−	0.697637i
$173$	−4.38075	+	11.0645i	−0.333062	+	0.841218i	0.662669	+	0.748913i	$0.269424\pi$
$173$	−4.38075	+	11.0645i	−0.333062	+	0.841218i	−0.995731	+	0.0923057i	$0.970576\pi$
$174$	0.114763	+	0.353203i	0.00870014	+	0.0267763i
$175$	20.7612	−	0.828545i	1.56940	−	0.0626321i
$176$	−1.18405	+	3.64414i	−0.0892514	+	0.274688i
$177$	8.75050	+	7.23904i	0.657728	+	0.544120i
$178$	0.172349	+	0.0811011i	0.0129181	+	0.00607878i
$179$	−12.2778	−	11.5297i	−0.917688	−	0.861767i	0.0730811	−	0.997326i	$-0.476717\pi$
$179$	−12.2778	−	11.5297i	−0.917688	−	0.861767i	−0.990769	+	0.135559i	$0.956717\pi$
$180$	2.03404	−	0.928798i	0.151609	−	0.0692285i
$181$	−7.12157	+	0.899664i	−0.529342	+	0.0668715i	−0.385462	−	0.922724i	$-0.625958\pi$
$181$	−7.12157	+	0.899664i	−0.529342	+	0.0668715i	−0.143880	+	0.989595i	$0.545958\pi$
$182$			21.7161i			1.60971i
$183$	−0.758735	−	6.00601i	−0.0560873	−	0.443977i
$184$	−1.74817	−	2.11317i	−0.128876	−	0.155785i
$185$	4.85244	+	7.84369i	0.356758	+	0.576679i
$186$	0.543518	−	8.63897i	0.0398527	−	0.633440i
$187$	6.83933	−	26.6374i	0.500142	−	1.94792i
$188$	−0.869132	+	3.38504i	−0.0633879	+	0.246880i
$189$	−0.260929	+	4.14734i	−0.0189798	+	0.301675i
$190$	4.38244	+	1.79356i	0.317936	+	0.130118i
$191$	−3.03102	−	3.66387i	−0.219317	−	0.265109i	0.649367	−	0.760475i	$-0.275034\pi$
$191$	−3.03102	−	3.66387i	−0.219317	−	0.265109i	−0.868684	+	0.495366i	$0.835034\pi$
$192$	−0.125333	−	0.992115i	−0.00904515	−	0.0715997i
$193$		−	8.95811i		−	0.644819i	−0.946600	−	0.322409i	$-0.895507\pi$
$193$		−	8.95811i		−	0.644819i	0.946600	−	0.322409i	$-0.104493\pi$
$194$	3.30052	−	0.416952i	0.236963	−	0.0299354i
$195$	1.33146	+	11.6092i	0.0953480	+	0.831352i
$196$	7.48544	+	7.02930i	0.534675	+	0.502093i
$197$	−6.51790	−	3.06709i	−0.464381	−	0.218521i	0.179331	−	0.983789i	$-0.442607\pi$
$197$	−6.51790	−	3.06709i	−0.464381	−	0.218521i	−0.643712	+	0.765268i	$0.722607\pi$
$198$	−2.95236	−	2.44240i	−0.209815	−	0.173574i
$199$	3.22107	−	9.91344i	0.228336	−	0.702745i	−0.769600	−	0.638526i	$-0.779544\pi$
$199$	3.22107	−	9.91344i	0.228336	−	0.702745i	0.997936	−	0.0642188i	$-0.0204556\pi$
$200$	0.740310	−	4.94489i	0.0523478	−	0.349657i
$201$	−2.69684	−	8.30002i	−0.190221	−	0.585439i
$202$	−2.44224	+	6.16840i	−0.171836	+	0.434007i
$203$	−1.05645	+	1.12501i	−0.0741484	+	0.0789600i
$204$	1.34491	+	7.05026i	0.0941625	+	0.493617i
$205$	5.45749	−	13.3350i	0.381168	−	0.931358i
$206$	10.1300	−	9.51270i	0.705790	−	0.662781i
$207$	2.60832	−	0.847494i	0.181291	−	0.0589049i
$208$	5.13326	+	0.979222i	0.355928	+	0.0678968i
$209$	−0.509497	−	8.09822i	−0.0352426	−	0.560166i
$210$	7.45430	+	5.54763i	0.514395	+	0.382823i
$211$	7.07484	+	11.1482i	0.487052	+	0.767471i	0.995614	−	0.0935541i	$-0.0298228\pi$
$211$	7.07484	+	11.1482i	0.487052	+	0.767471i	−0.508562	+	0.861025i	$0.669823\pi$
$212$	3.13591	−	0.197295i	0.215375	−	0.0135503i
$213$	−12.7184	−	8.07137i	−0.871453	−	0.553041i
$214$	7.89526	−	9.54373i	0.539709	−	0.652396i
$215$	27.8018	+	3.83671i	1.89607	+	0.261662i
$216$	0.968583	+	0.248690i	0.0659037	+	0.0169212i
$217$	32.5472	−	15.3155i	2.20945	−	1.03969i
$218$	19.2075	+	6.24089i	1.30089	+	0.422686i
$219$	2.45633	+	1.35038i	0.165984	+	0.0912502i
$220$	−8.17839	+	2.55397i	−0.551387	+	0.172189i
$221$	−37.2120	−	4.70097i	−2.50315	−	0.316222i
$222$	−0.516974	+	4.09227i	−0.0346970	+	0.274655i
$223$	2.00698	−	1.27367i	0.134397	−	0.0852912i	−0.466928	−	0.884295i	$-0.654639\pi$
$223$	2.00698	−	1.27367i	0.134397	−	0.0852912i	0.601326	+	0.799004i	$0.294639\pi$
$224$	3.36191	−	2.44257i	0.224627	−	0.163201i
$225$	4.32512	+	2.50866i	0.288341	+	0.167244i
$226$	−14.9659	−	10.8734i	−0.995519	−	0.723287i
$227$	1.63388	+	0.102795i	0.108444	+	0.00682274i	0.116920	−	0.993141i	$-0.462698\pi$
$227$	1.63388	+	0.102795i	0.108444	+	0.00682274i	−0.00847558	+	0.999964i	$0.502698\pi$
$228$	1.02020	+	1.85573i	0.0675641	+	0.122899i
$229$	1.49143	−	3.16946i	0.0985568	−	0.209444i	−0.849468	−	0.527640i	$-0.823077\pi$
$229$	1.49143	−	3.16946i	0.0985568	−	0.209444i	0.948025	+	0.318196i	$0.103077\pi$
$230$	1.59314	−	5.92197i	0.105048	−	0.390483i
$231$	2.98362	−	15.6407i	0.196308	−	1.02908i
$232$	0.218292	+	0.300453i	0.0143316	+	0.0197257i
$233$	−3.26586	+	5.94058i	−0.213954	+	0.389180i	−0.961405	−	0.275136i	$-0.911277\pi$
$233$	−3.26586	+	5.94058i	−0.213954	+	0.389180i	0.747452	+	0.664316i	$0.231277\pi$
$234$	−2.80014	+	4.41231i	−0.183051	+	0.288442i
$235$	−7.29845	+	2.79324i	−0.476098	+	0.182211i
$236$	10.5592	+	4.18069i	0.687346	+	0.272139i
$237$	−5.60066	−	14.1456i	−0.363802	−	0.918858i
$238$	−22.9813	+	19.0118i	−1.48966	+	1.23235i
$239$	14.1342	−	3.62904i	0.914263	−	0.234743i	0.237881	−	0.971294i	$-0.423547\pi$
$239$	14.1342	−	3.62904i	0.914263	−	0.234743i	0.676382	+	0.736551i	$0.263547\pi$
$240$	1.64748	−	1.51189i	0.106344	−	0.0975923i
$241$	−23.0888	+	9.14151i	−1.48728	+	0.588856i	−0.964611	−	0.263678i	$-0.915064\pi$
$241$	−23.0888	+	9.14151i	−1.48728	+	0.588856i	−0.522671	+	0.852535i	$0.675064\pi$
$242$	2.52033	+	2.68388i	0.162013	+	0.172526i
$243$	−0.587785	+	0.809017i	−0.0377064	+	0.0518985i
$244$	−2.57756	−	5.47759i	−0.165011	−	0.350667i
$245$	−3.13894	+	22.7456i	−0.200540	+	1.45316i
$246$	5.64667	−	3.10428i	0.360018	−	0.197922i
$247$	−10.8706	+	2.07367i	−0.691677	+	0.131944i
$248$	−2.15267	−	8.38411i	−0.136695	−	0.532391i
$249$	−11.2077			−0.710256
$250$	9.97694	−	5.04585i	0.630997	−	0.319128i
$251$	27.9616			1.76492			0.882459	−	0.470390i	$-0.155887\pi$
$251$	27.9616			1.76492			0.882459	+	0.470390i	$0.155887\pi$
$252$	1.03344	+	4.02499i	0.0651007	+	0.253551i
$253$	−10.3224	+	1.96911i	−0.648965	+	0.123797i
$254$	4.53239	−	2.49170i	0.284387	−	0.156343i
$255$	−11.1199	+	11.5725i	−0.696354	+	0.724699i
$256$	−0.425779	−	0.904827i	−0.0266112	−	0.0565517i
$257$	−2.64925	+	3.64639i	−0.165256	+	0.227455i	−0.883611	−	0.468221i	$-0.844895\pi$
$257$	−2.64925	+	3.64639i	−0.165256	+	0.227455i	0.718356	+	0.695676i	$0.244895\pi$
$258$	8.59188	+	9.14942i	0.534907	+	0.569618i
$259$	−15.9371	+	6.30993i	−0.990281	+	0.392080i
$260$	4.85373	+	10.6296i	0.301016	+	0.659217i
$261$	−0.359712	+	0.0923585i	−0.0222656	+	0.00571685i
$262$	−9.21322	+	7.62184i	−0.569195	+	0.470879i
$263$	7.79565	+	19.6896i	0.480701	+	1.21411i	0.944600	+	0.328223i	$0.106450\pi$
$263$	7.79565	+	19.6896i	0.480701	+	1.21411i	−0.463899	+	0.885888i	$0.653550\pi$
$264$	−3.56260	−	1.41053i	−0.219263	−	0.0868124i
$265$	4.41612	+	5.46462i	0.271280	+	0.335689i
$266$	−4.71532	+	7.43015i	−0.289115	+	0.455572i
$267$	−0.0917629	+	0.166916i	−0.00561580	+	0.0102151i
$268$	−5.12970	−	7.06042i	−0.313346	−	0.431284i
$269$	3.11582	−	16.3337i	0.189975	−	0.995882i	−0.751738	−	0.659462i	$-0.770784\pi$
$269$	3.11582	−	16.3337i	0.189975	−	0.995882i	0.941712	−	0.336419i	$-0.109216\pi$
$270$	0.799246	+	2.08835i	0.0486406	+	0.127093i
$271$	8.26162	−	17.5568i	0.501858	−	1.06650i	−0.480067	−	0.877232i	$-0.659388\pi$
$271$	8.26162	−	17.5568i	0.501858	−	1.06650i	0.981925	−	0.189271i	$-0.0606123\pi$
$272$	3.45774	+	6.28960i	0.209656	+	0.381363i
$273$	−21.6733	−	1.36357i	−1.31173	−	0.0825269i
$274$	−6.45953	−	4.69312i	−0.390235	−	0.283522i
$275$	−15.2370	−	11.6137i	−0.918827	−	0.700330i
$276$	2.21877	−	1.61203i	0.133554	−	0.0970327i
$277$	−15.0331	+	9.54032i	−0.903254	+	0.573222i	−0.904357	−	0.426777i	$-0.859649\pi$
$277$	−15.0331	+	9.54032i	−0.903254	+	0.573222i	0.00110311	+	0.999999i	$0.499649\pi$
$278$	−1.90972	+	15.1170i	−0.114537	+	0.906657i
$279$	8.58780	+	1.08489i	0.514138	+	0.0649507i
$280$	8.80377	+	2.97260i	0.526126	+	0.177647i
$281$	−1.65909	−	0.912091i	−0.0989728	−	0.0544108i	0.431498	−	0.902114i	$-0.357985\pi$
$281$	−1.65909	−	0.912091i	−0.0989728	−	0.0544108i	−0.530471	+	0.847703i	$0.677985\pi$
$282$	−3.32379	−	1.07997i	−0.197929	−	0.0643110i
$283$	14.9242	−	7.02280i	0.887152	−	0.417462i	0.0724702	−	0.997371i	$-0.476912\pi$
$283$	14.9242	−	7.02280i	0.887152	−	0.417462i	0.814681	+	0.579909i	$0.196912\pi$
$284$	−14.5901	−	3.74611i	−0.865766	−	0.222291i
$285$	−2.06520	+	4.26118i	−0.122332	+	0.252410i
$286$	12.7636	−	15.4285i	0.754725	−	0.912306i
$287$	22.6087	+	14.3479i	1.33455	+	0.846930i
$288$	0.998027	−	0.0627905i	0.0588093	−	0.00369997i
$289$	−18.4941	−	29.1420i	−1.08789	−	1.71423i
$290$	−0.265661	+	0.786791i	−0.0156001	+	0.0462020i
$291$	0.208888	+	3.32018i	0.0122452	+	0.194633i
$292$	2.75340	+	0.525239i	0.161131	+	0.0307373i
$293$	17.0348	−	5.53493i	0.995182	−	0.323354i	0.234243	−	0.972178i	$-0.424739\pi$
$293$	17.0348	−	5.53493i	0.995182	−	0.323354i	0.760939	+	0.648824i	$0.224739\pi$
$294$	−7.48544	+	7.02930i	−0.436560	+	0.409957i
$295$	6.03274	+	24.6674i	0.351240	+	1.43619i
$296$	0.772909	+	4.05173i	0.0449244	+	0.235502i
$297$	2.62296	−	2.79317i	0.152200	−	0.162076i
$298$	−1.14065	+	2.88096i	−0.0660762	+	0.166889i
$299$	4.42885	+	13.6306i	0.256127	+	0.788278i
$300$	4.88865	+	1.04934i	0.282246	+	0.0605837i
$301$	−16.1174	+	49.6042i	−0.928991	+	2.85914i
$302$	−6.16394	−	5.09926i	−0.354695	−	0.293429i
$303$	−6.00288	−	2.82474i	−0.344856	−	0.162277i
$304$	1.54372	+	1.44965i	0.0885382	+	0.0831429i
$305$	6.65695	−	11.7866i	0.381176	−	0.674899i
$306$	−7.12080	+	0.899566i	−0.407069	+	0.0514248i
$307$		−	0.465275i		−	0.0265546i	−0.999912	−	0.0132773i	$-0.995774\pi$
$307$		−	0.465275i		−	0.0265546i	0.999912	−	0.0132773i	$-0.00422643\pi$
$308$	−1.99564	−	15.7971i	−0.113712	−	0.900126i
$309$	8.85786	+	10.7073i	0.503906	+	0.609118i
$310$	12.5080	−	14.7712i	0.710404	−	0.838946i
$311$	0.901668	−	14.3316i	0.0511289	−	0.812670i	−0.886000	−	0.463686i	$-0.846527\pi$
$311$	0.901668	−	14.3316i	0.0511289	−	0.812670i	0.937129	−	0.348984i	$-0.113473\pi$
$312$	−1.29961	+	5.06164i	−0.0735759	+	0.286559i
$313$	3.57594	−	13.9274i	0.202124	−	0.787221i	−0.783937	−	0.620840i	$-0.786792\pi$
$313$	3.57594	−	13.9274i	0.202124	−	0.787221i	0.986061	−	0.166381i	$-0.0532083\pi$
$314$	1.30778	−	20.7866i	0.0738024	−	1.17306i
$315$	−6.00474	+	7.09125i	−0.338329	+	0.399547i
$316$	−9.69779	−	11.7226i	−0.545543	−	0.659448i
$317$	1.52707	+	12.0880i	0.0857690	+	0.678932i	0.975115	+	0.221698i	$0.0711598\pi$
$317$	1.52707	+	12.0880i	0.0857690	+	0.678932i	−0.889346	+	0.457234i	$0.848840\pi$
$318$			3.14211i			0.176201i
$319$	1.41179	−	0.178350i	0.0790449	−	0.00998570i
$320$	1.09964	−	1.94699i	0.0614719	−	0.108840i
$321$	9.02915	+	8.47894i	0.503958	+	0.473248i
$322$	10.3121	+	4.85251i	0.574671	+	0.270420i
$323$	−11.7113	−	9.68844i	−0.651635	−	0.539079i
$324$	−0.309017	+	0.951057i	−0.0171676	+	0.0528365i
$325$	−13.1098	+	22.6023i	−0.727201	+	1.25375i
$326$	0.926968	+	2.85291i	0.0513400	+	0.158008i
$327$	−7.43462	+	18.7777i	−0.411136	+	1.03841i
$328$	4.41102	−	4.69726i	0.243558	−	0.259363i
$329$	−2.72133	−	14.2657i	−0.150032	−	0.786495i
$330$	−2.03540	−	8.32261i	−0.112045	−	0.458145i
$331$	−12.7328	+	11.9569i	−0.699858	+	0.657210i	−0.950448	−	0.310883i	$-0.899375\pi$
$331$	−12.7328	+	11.9569i	−0.699858	+	0.657210i	0.250591	+	0.968093i	$0.419375\pi$
$332$	−10.6591	+	3.46336i	−0.584995	+	0.190076i
$333$	−4.05173	−	0.772909i	−0.222033	−	0.0423552i
$334$	0.300619	+	4.77821i	0.0164492	+	0.261452i
$335$	6.24284	−	18.4890i	0.341083	−	1.01016i
$336$	2.22665	+	3.50864i	0.121474	+	0.191412i
$337$	−6.53559	+	0.411185i	−0.356016	+	0.0223987i	−0.239792	−	0.970824i	$-0.577079\pi$
$337$	−6.53559	+	0.411185i	−0.356016	+	0.0223987i	−0.116225	+	0.993223i	$0.537079\pi$
$338$	−12.0817	−	7.66727i	−0.657157	−	0.417044i
$339$	11.7917	−	14.2537i	0.640435	−	0.774153i
$340$	−6.99954	+	14.4423i	−0.379603	+	0.783246i
$341$	−32.1252	−	8.24835i	−1.73968	−	0.446673i
$342$	−1.91613	+	0.901661i	−0.103612	+	0.0487562i
$343$	−12.9178	−	4.19724i	−0.697495	−	0.226630i
$344$	10.9987	+	6.04658i	0.593009	+	0.326010i
$345$	5.81025	+	1.96184i	0.312813	+	0.105622i
$346$	−11.8063	−	1.49149i	−0.634712	−	0.0801828i
$347$	−0.0755065	+	0.597695i	−0.00405340	+	0.0320860i	−0.994012	−	0.109274i	$-0.965147\pi$
$347$	−0.0755065	+	0.597695i	−0.00405340	+	0.0320860i	0.989958	+	0.141360i	$0.0451475\pi$
$348$	−0.313567	+	0.198995i	−0.0168089	+	0.0106673i
$349$	6.90133	−	5.01411i	0.369420	−	0.268399i	−0.387550	−	0.921848i	$-0.626679\pi$
$349$	6.90133	−	5.01411i	0.369420	−	0.268399i	0.756970	+	0.653449i	$0.226679\pi$
$350$	5.96561	+	19.9029i	0.318875	+	1.06385i
$351$	−4.22778	−	3.07166i	−0.225662	−	0.163953i
$352$	−3.82412	−	0.240593i	−0.203826	−	0.0128237i
$353$	−7.77570	−	14.1439i	−0.413859	−	0.752806i	0.584420	−	0.811451i	$-0.301322\pi$
$353$	−7.77570	−	14.1439i	−0.413859	−	0.752806i	−0.998279	+	0.0586451i	$0.981322\pi$
$354$	−4.83545	+	10.2759i	−0.257001	+	0.546156i
$355$	−12.0394	−	31.4576i	−0.638983	−	1.66960i
$356$	−0.0356918	+	0.187103i	−0.00189166	+	0.00991643i
$357$	−17.5313	−	24.1297i	−0.927853	−	1.27708i
$358$	8.11405	−	14.7594i	0.428841	−	0.780059i
$359$	−0.286684	+	0.451741i	−0.0151306	+	0.0238420i	−0.851809	−	0.523852i	$-0.824494\pi$
$359$	−0.286684	+	0.451741i	−0.0151306	+	0.0238420i	0.836678	+	0.547694i	$0.184494\pi$
$360$	1.40546	+	1.73916i	0.0740745	+	0.0916617i
$361$	13.4961	+	5.34350i	0.710323	+	0.281237i
$362$	−2.64246	−	6.67410i	−0.138885	−	0.350783i
$363$	−2.83684	+	2.34684i	−0.148895	+	0.123177i
$364$	−21.0339	+	5.40058i	−1.10248	+	0.283067i
$365$	2.60347	+	5.70153i	0.136272	+	0.298432i
$366$	5.62863	−	2.22853i	0.294213	−	0.116487i
$367$	−6.50271	−	6.92468i	−0.339439	−	0.361466i	0.536489	−	0.843907i	$-0.319750\pi$
$367$	−6.50271	−	6.92468i	−0.339439	−	0.361466i	−0.875928	+	0.482441i	$0.839750\pi$
$368$	1.61203	−	2.21877i	0.0840328	−	0.115661i
$369$	2.74360	+	5.83044i	0.142826	+	0.303521i
$370$	−6.39051	+	6.65063i	−0.332227	+	0.345750i
$371$	−11.4421	+	6.29034i	−0.594044	+	0.326578i
$372$	8.50273	−	1.62198i	0.440846	−	0.0840959i
$373$	4.10796	+	15.9994i	0.212702	+	0.828419i	0.981899	+	0.189407i	$0.0606566\pi$
$373$	4.10796	+	15.9994i	0.212702	+	0.828419i	−0.769197	+	0.639012i	$0.779343\pi$
$374$	27.5015			1.42207
$375$	4.40944	+	10.2741i	0.227702	+	0.530552i
$376$	−3.49484			−0.180233
$377$	−0.482649	−	1.87979i	−0.0248577	−	0.0968143i
$378$	−4.08194	+	0.778671i	−0.209952	+	0.0400505i
$379$	−12.7731	+	7.02205i	−0.656108	+	0.360698i	−0.774776	−	0.632236i	$-0.782137\pi$
$379$	−12.7731	+	7.02205i	−0.656108	+	0.360698i	0.118668	+	0.992934i	$0.462137\pi$
$380$	−0.647341	+	4.69080i	−0.0332079	+	0.240633i
$381$	2.20219	+	4.67990i	0.112822	+	0.239758i
$382$	2.79498	−	3.84696i	0.143004	−	0.196828i
$383$	−6.49427	−	6.91569i	−0.331842	−	0.353375i	0.541311	−	0.840823i	$-0.317928\pi$
$383$	−6.49427	−	6.91569i	−0.331842	−	0.353375i	−0.873153	+	0.487447i	$0.837928\pi$
$384$	0.929776	−	0.368125i	0.0474475	−	0.0187858i
$385$	26.2323	−	24.0734i	1.33692	−	1.22690i
$386$	8.67667	−	2.22779i	0.441631	−	0.113392i
$387$	−9.67085	+	8.00042i	−0.491597	+	0.406684i
$388$	1.22466	+	3.09313i	0.0621726	+	0.157030i
$389$	−6.52234	−	2.58238i	−0.330696	−	0.130932i	0.196909	−	0.980422i	$-0.436910\pi$
$389$	−6.52234	−	2.58238i	−0.330696	−	0.130932i	−0.527605	+	0.849490i	$0.676910\pi$
$390$	−10.9133	+	4.17672i	−0.552619	+	0.211496i
$391$	−10.5474	+	16.6200i	−0.533405	+	0.840512i
$392$	−4.94691	+	8.99839i	−0.249857	+	0.454487i
$393$	−7.02830	−	9.67362i	−0.354531	−	0.487970i
$394$	1.34980	−	7.07588i	0.0680018	−	0.356478i
$395$	8.83779	−	32.8516i	0.444677	−	1.65294i
$396$	1.63145	−	3.46701i	0.0819834	−	0.174224i
$397$	5.03931	+	9.16648i	0.252916	+	0.460052i	0.972035	−	0.234834i	$-0.0754547\pi$
$397$	5.03931	+	9.16648i	0.252916	+	0.460052i	−0.719120	+	0.694886i	$0.755455\pi$
$398$	10.4030	+	0.654503i	0.521457	+	0.0328073i
$399$	−7.11941	−	5.17256i	−0.356416	−	0.258952i
$400$	4.97365	−	0.512693i	0.248682	−	0.0256346i
$401$	2.78130	−	2.02074i	0.138892	−	0.100911i	−0.516170	−	0.856486i	$-0.672643\pi$
$401$	2.78130	−	2.02074i	0.138892	−	0.100911i	0.655062	+	0.755576i	$0.272643\pi$
$402$	7.36859	−	4.67625i	0.367512	−	0.233230i
$403$	−5.66945	+	44.8783i	−0.282415	+	2.23555i
$404$	−6.58197	−	0.831496i	−0.327465	−	0.0413685i
$405$	−2.13441	+	0.666541i	−0.106060	+	0.0331207i
$406$	−1.35239	−	0.743484i	−0.0671181	−	0.0368985i
$407$	15.0313	+	4.88397i	0.745075	+	0.242090i
$408$	−6.49430	+	3.05599i	−0.321516	+	0.151294i
$409$	−3.41879	−	0.877797i	−0.169049	−	0.0434043i	0.163217	−	0.986590i	$-0.447813\pi$
$409$	−3.41879	−	0.877797i	−0.169049	−	0.0434043i	−0.332265	+	0.943186i	$0.607813\pi$
$410$	14.2733	+	1.96975i	0.704908	+	0.0972789i
$411$	5.08946	−	6.15210i	0.251045	−	0.303461i
$412$	11.7331	+	7.44603i	0.578047	+	0.366840i
$413$	−47.1002	+	2.96329i	−2.31765	+	0.145814i
$414$	1.46953	+	2.31561i	0.0722235	+	0.113806i
$415$	−20.1045	−	14.9622i	−0.986892	−	0.734463i
$416$	0.328132	+	5.21551i	0.0160880	+	0.255711i
$417$	−14.9673	−	2.85516i	−0.732950	−	0.139818i
$418$	7.71710	−	2.50744i	0.377455	−	0.122643i
$419$	15.6543	−	14.7004i	0.764765	−	0.718162i	−0.200426	−	0.979709i	$-0.564233\pi$
$419$	15.6543	−	14.7004i	0.764765	−	0.718162i	0.965191	+	0.261547i	$0.0842326\pi$
$420$	−3.51953	+	8.59974i	−0.171736	+	0.419625i
$421$	3.65116	+	19.1400i	0.177947	+	0.932829i	0.953465	+	0.301504i	$0.0974886\pi$
$421$	3.65116	+	19.1400i	0.177947	+	0.932829i	−0.775518	+	0.631325i	$0.782511\pi$
$422$	−9.03848	+	9.62501i	−0.439986	+	0.468538i
$423$	1.28654	−	3.24942i	0.0625536	−	0.157992i
$424$	0.970965	+	2.98832i	0.0471542	+	0.145126i
$425$	−35.3963	+	5.91402i	−1.71697	+	0.286872i
$426$	4.65484	−	14.3261i	0.225528	−	0.694104i
$427$	19.3835	+	16.0354i	0.938032	+	0.776008i
$428$	11.2074	+	5.27379i	0.541729	+	0.254918i
$429$	14.5966	+	13.7071i	0.704732	+	0.661787i
$430$	3.19785	+	27.8825i	0.154214	+	1.34461i
$431$	−15.8619	+	2.00382i	−0.764041	+	0.0965208i	−0.497690	−	0.867355i	$-0.665818\pi$
$431$	−15.8619	+	2.00382i	−0.764041	+	0.0965208i	−0.266351	+	0.963876i	$0.585818\pi$
$432$			1.00000i			0.0481125i
$433$	3.80135	+	30.0908i	0.182681	+	1.44607i	0.770686	+	0.637215i	$0.219914\pi$
$433$	3.80135	+	30.0908i	0.182681	+	1.44607i	−0.588005	+	0.808858i	$0.700086\pi$
$434$	22.9285	+	27.7158i	1.10060	+	1.33040i
$435$	−0.768557	−	0.314540i	−0.0368495	−	0.0150810i
$436$	−1.26811	+	20.1561i	−0.0607316	+	0.965302i
$437$	−1.44434	+	5.62535i	−0.0690924	+	0.269097i
$438$	−0.697090	+	2.71499i	−0.0333083	+	0.129727i
$439$	−0.0486051	+	0.772556i	−0.00231980	+	0.0368721i	−0.999016	−	0.0443438i	$-0.985880\pi$
$439$	−0.0486051	+	0.772556i	−0.00231980	+	0.0368721i	0.996697	+	0.0812159i	$0.0258803\pi$
$440$	−4.50761	−	7.28630i	−0.214892	−	0.347361i
$441$	−6.54541	−	7.91205i	−0.311686	−	0.376764i
$442$	−4.70097	−	37.2120i	−0.223602	−	1.77000i
$443$		−	1.58257i		−	0.0751900i	−0.999293	−	0.0375950i	$-0.988030\pi$
$443$		−	1.58257i		−	0.0751900i	0.999293	−	0.0375950i	$-0.0119697\pi$
$444$	−4.09227	+	0.516974i	−0.194210	+	0.0245345i
$445$	−0.387438	+	0.176914i	−0.0183663	+	0.00838655i
$446$	1.73277	+	1.62718i	0.0820491	+	0.0770492i
$447$	−2.80365	−	1.31930i	−0.132608	−	0.0624006i
$448$	3.20190	+	2.64884i	0.151276	+	0.125146i
$449$	−9.38937	+	28.8975i	−0.443112	+	1.36376i	0.441430	+	0.897296i	$0.354471\pi$
$449$	−9.38937	+	28.8975i	−0.443112	+	1.36376i	−0.884541	+	0.466462i	$0.845529\pi$
$450$	−1.35423	+	4.81311i	−0.0638391	+	0.226892i
$451$	−7.62970	−	23.4818i	−0.359268	−	1.10571i
$452$	6.80990	−	17.1999i	0.320311	−	0.809013i
$453$	5.47623	−	5.83159i	0.257296	−	0.273992i
$454$	0.306764	+	1.60811i	0.0143971	+	0.0754725i
$455$	−37.0576	−	31.3797i	−1.73729	−	1.47110i
$456$	−1.54372	+	1.44965i	−0.0722911	+	0.0678859i
$457$	22.7208	−	7.38243i	1.06283	−	0.345335i	0.275140	−	0.961404i	$-0.411276\pi$
$457$	22.7208	−	7.38243i	1.06283	−	0.345335i	0.787692	+	0.616069i	$0.211276\pi$
$458$	3.44079	+	0.656366i	0.160778	+	0.0306700i
$459$	−0.450672	−	7.16323i	−0.0210356	−	0.334351i
$460$	6.13212	+	0.0703527i	0.285911	+	0.00328021i
$461$	−12.8146	−	20.1926i	−0.596838	−	0.940465i	−0.999682	−	0.0251972i	$-0.991979\pi$
$461$	−12.8146	−	20.1926i	−0.596838	−	0.940465i	0.402845	−	0.915268i	$-0.368021\pi$
$462$	15.8913	−	0.999795i	0.739329	−	0.0465147i
$463$	−2.65738	−	1.68642i	−0.123499	−	0.0783747i	0.472642	−	0.881254i	$-0.343300\pi$
$463$	−2.65738	−	1.68642i	−0.123499	−	0.0783747i	−0.596141	+	0.802880i	$0.703300\pi$
$464$	−0.236727	+	0.286153i	−0.0109898	+	0.0132843i
$465$	13.9566	+	13.4108i	0.647224	+	0.621909i
$466$	−6.56613	−	1.68590i	−0.304170	−	0.0780976i
$467$	27.7671	−	13.0662i	1.28491	−	0.604631i	0.342631	−	0.939470i	$-0.388682\pi$
$467$	27.7671	−	13.0662i	1.28491	−	0.604631i	0.942275	+	0.334839i	$0.108682\pi$
$468$	−4.97005	−	1.61487i	−0.229741	−	0.0746473i
$469$	31.7802	+	17.4713i	1.46747	+	0.806751i
$470$	−4.52054	−	6.37451i	−0.208517	−	0.294034i
$471$	20.6635	+	2.61040i	0.952122	+	0.120281i
$472$	−1.42337	+	11.2672i	−0.0655161	+	0.518613i
$473$	40.6055	−	25.7690i	1.86704	−	1.18486i
$474$	12.3084	−	8.94258i	0.565344	−	0.410746i
$475$	−9.39324	+	4.88676i	−0.430991	+	0.224220i
$476$	−24.1297	−	17.5313i	−1.10598	−	0.803544i
$477$	−3.13591	−	0.197295i	−0.143583	−	0.00903350i
$478$	7.03005	+	12.7876i	0.321547	+	0.584892i
$479$	−6.99901	+	14.8737i	−0.319793	+	0.679595i	−0.998496	−	0.0548178i	$-0.982542\pi$
$479$	−6.99901	+	14.8737i	−0.319793	+	0.679595i	0.678703	+	0.734412i	$0.262542\pi$
$480$	1.87411	+	1.21973i	0.0855408	+	0.0556726i
$481$	4.03909	−	21.1736i	0.184166	−	0.965434i
$482$	−14.5963	−	20.0900i	−0.664842	−	0.915076i
$483$	−5.49044	+	9.98707i	−0.249824	+	0.454427i
$484$	−1.97278	+	3.10860i	−0.0896718	+	0.141300i
$485$	−4.05772	+	6.23468i	−0.184252	+	0.283102i
$486$	−0.929776	−	0.368125i	−0.0421755	−	0.0166985i
$487$	−1.06541	−	2.69092i	−0.0482783	−	0.121937i	0.903636	−	0.428301i	$-0.140888\pi$
$487$	−1.06541	−	2.69092i	−0.0482783	−	0.121937i	−0.951915	+	0.306364i	$0.900888\pi$
$488$	4.66449	−	3.85880i	0.211151	−	0.174680i
$489$	−2.90549	+	0.746003i	−0.131391	+	0.0337354i
$490$	−22.8116	+	2.61627i	−1.03052	+	0.118191i
$491$	20.3985	−	8.07634i	0.920571	−	0.364480i	0.140435	−	0.990090i	$-0.455150\pi$
$491$	20.3985	−	8.07634i	0.920571	−	0.364480i	0.780136	+	0.625610i	$0.215150\pi$
$492$	4.41102	+	4.69726i	0.198864	+	0.211769i
$493$	1.56677	−	2.15647i	0.0705636	−	0.0971224i
$494$	−4.71192	−	10.0133i	−0.211999	−	0.450521i
$495$	8.43399	−	1.50881i	0.379080	−	0.0678158i
$496$	7.58536	−	4.17009i	0.340593	−	0.187242i
$497$	61.4878	−	11.7294i	2.75811	−	0.526137i
$498$	−2.78723	−	10.8555i	−0.124899	−	0.486449i
$499$	−33.2687			−1.48931			−0.744655	−	0.667449i	$-0.767386\pi$
$499$	−33.2687			−1.48931			−0.744655	+	0.667449i	$0.767386\pi$
$500$	7.36849	+	8.40865i	0.329529	+	0.376046i
$501$	−4.78766			−0.213897
$502$	6.95375	+	27.0831i	0.310361	+	1.20878i
$503$	−0.560235	+	0.106871i	−0.0249797	+	0.00476512i	−0.199856	−	0.979825i	$-0.564047\pi$
$503$	−0.560235	+	0.106871i	−0.0249797	+	0.00476512i	0.174876	+	0.984590i	$0.444047\pi$
$504$	−3.64153	+	2.00195i	−0.162207	+	0.0891739i
$505$	−6.99707	−	13.0809i	−0.311366	−	0.582092i
$506$	−4.47433	−	9.50843i	−0.198908	−	0.422701i
$507$	8.41075	−	11.5764i	0.373535	−	0.514126i
$508$	3.54058	+	3.77033i	0.157088	+	0.167281i
$509$	21.5376	−	8.52735i	0.954638	−	0.377968i	0.161407	−	0.986888i	$-0.448397\pi$
$509$	21.5376	−	8.52735i	0.954638	−	0.377968i	0.793232	+	0.608920i	$0.208397\pi$
$510$	−13.9743	−	7.89257i	−0.618794	−	0.349489i
$511$	−11.2823	+	2.89679i	−0.499097	+	0.128146i
$512$	0.770513	−	0.637424i	0.0340522	−	0.0281704i
$513$	−0.779567	−	1.96896i	−0.0344187	−	0.0869318i
$514$	−4.19067	−	1.65920i	−0.184843	−	0.0731843i
$515$	1.59520	+	31.0322i	0.0702930	+	1.36744i
$516$	−6.72526	+	10.5973i	−0.296063	+	0.466521i
$517$	−6.45121	+	11.7347i	−0.283724	+	0.516092i
$518$	−10.0751	−	13.8672i	−0.442674	−	0.609288i
$519$	2.22987	−	11.6894i	0.0978804	−	0.513107i
$520$	−9.08853	+	7.34471i	−0.398559	+	0.322087i
$521$	3.57356	−	7.59419i	0.156560	−	0.332708i	−0.811123	−	0.584875i	$-0.801143\pi$
$521$	3.57356	−	7.59419i	0.156560	−	0.332708i	0.967684	+	0.252168i	$0.0811435\pi$
$522$	−0.178914	−	0.325443i	−0.00783084	−	0.0142442i
$523$	−15.3924	−	0.968411i	−0.673065	−	0.0423456i	−0.277419	−	0.960749i	$-0.589479\pi$
$523$	−15.3924	−	0.968411i	−0.673065	−	0.0423456i	−0.395645	+	0.918403i	$0.629479\pi$
$524$	−9.67362	−	7.02830i	−0.422594	−	0.307033i
$525$	−20.2382	+	4.70413i	−0.883267	+	0.205305i
$526$	−17.1323	+	12.4473i	−0.747003	+	0.542730i
$527$	−52.4563	+	33.2898i	−2.28503	+	1.45013i
$528$	0.480236	−	3.80146i	0.0208996	−	0.165437i
$529$	−15.3564	−	1.93996i	−0.667669	−	0.0843462i
$530$	−4.19470	+	5.63638i	−0.182206	+	0.244829i
$531$	−9.95197	−	5.47114i	−0.431879	−	0.237427i
$532$	−8.36937	−	2.71937i	−0.362858	−	0.117900i
$533$	−30.4689	+	14.3376i	−1.31975	+	0.621029i
$534$	−0.184493	−	0.0473697i	−0.00798378	−	0.00204989i
$535$	4.87734	+	27.2636i	0.210866	+	1.17871i
$536$	5.56290	−	6.72439i	0.240281	−	0.290450i
$537$	14.2208	+	9.02479i	0.613673	+	0.389449i
$538$	16.5954	−	1.04409i	0.715478	−	0.0450141i
$539$	21.0825	+	33.2207i	0.908088	+	1.43092i
$540$	−1.82398	+	1.29349i	−0.0784914	+	0.0556629i
$541$	1.39635	+	22.1943i	0.0600336	+	0.954207i	0.906618	+	0.421952i	$0.138655\pi$
$541$	1.39635	+	22.1943i	0.0600336	+	0.954207i	−0.846584	+	0.532255i	$0.821345\pi$
$542$	19.0598	+	3.63586i	0.818691	+	0.156174i
$543$	6.82685	−	2.21818i	0.292968	−	0.0951911i
$544$	−5.23209	+	4.91326i	−0.224324	+	0.210654i
$545$	−38.4045	+	23.7587i	−1.64507	+	1.01771i
$546$	−4.06920	−	21.3315i	−0.174146	−	0.912903i
$547$	−13.0372	+	13.8832i	−0.557429	+	0.593602i	−0.944526	−	0.328438i	$-0.893478\pi$
$547$	−13.0372	+	13.8832i	−0.557429	+	0.593602i	0.387097	+	0.922039i	$0.373478\pi$
$548$	2.93926	−	7.42373i	0.125559	−	0.317126i
$549$	1.87071	+	5.75745i	0.0798399	+	0.245722i
$550$	7.45949	−	17.6465i	0.318074	−	0.752450i
$551$	0.243030	−	0.747969i	0.0103534	−	0.0318645i
$552$	2.11317	+	1.74817i	0.0899424	+	0.0744069i
$553$	57.2055	+	26.9189i	2.43262	+	1.14471i
$554$	−12.9792	−	12.1883i	−0.551433	−	0.517830i
$555$	−6.23625	−	6.79550i	−0.264714	−	0.288453i
$556$	−15.1170	+	1.90972i	−0.641104	+	0.0809902i
$557$		−	10.2913i		−	0.436055i	−0.975943	−	0.218027i	$-0.930038\pi$
$557$		−	10.2913i		−	0.436055i	0.975943	−	0.218027i	$-0.0699622\pi$
$558$	1.08489	+	8.58780i	0.0459271	+	0.363550i
$559$	−41.8088	−	50.5382i	−1.76832	−	2.13754i
$560$	−0.689805	+	9.26644i	−0.0291496	+	0.391578i
$561$	−1.72683	+	27.4472i	−0.0729069	+	1.15882i
$562$	0.470838	−	1.83379i	0.0198611	−	0.0773538i
$563$	−7.00498	+	27.2826i	−0.295225	+	1.14982i	0.631894	+	0.775055i	$0.282278\pi$
$563$	−7.00498	+	27.2826i	−0.295225	+	1.14982i	−0.927118	+	0.374769i	$0.877722\pi$
$564$	0.219443	−	3.48794i	0.00924021	−	0.146869i
$565$	40.1807	−	9.82671i	1.69041	−	0.413413i
$566$	10.5137	+	12.7088i	0.441922	+	0.534192i
$567$	−0.520828	−	4.12278i	−0.0218727	−	0.173140i
$568$		−	15.0634i		−	0.632046i
$569$	12.8640	−	1.62511i	0.539289	−	0.0681280i	0.149029	−	0.988833i	$-0.452385\pi$
$569$	12.8640	−	1.62511i	0.539289	−	0.0681280i	0.390260	+	0.920705i	$0.372385\pi$
$570$	−4.64090	−	0.940601i	−0.194386	−	0.0393975i
$571$	7.10039	+	6.66771i	0.297142	+	0.279035i	0.818750	−	0.574151i	$-0.194668\pi$
$571$	7.10039	+	6.66771i	0.297142	+	0.279035i	−0.521608	+	0.853185i	$0.674668\pi$
$572$	18.1180	+	8.52566i	0.757550	+	0.356476i
$573$	3.66387	+	3.03102i	0.153061	+	0.126623i
$574$	−8.27459	+	25.4666i	−0.345375	+	1.06295i
$575$	7.80350	+	11.2758i	0.325428	+	0.470235i
$576$	0.309017	+	0.951057i	0.0128757	+	0.0396274i
$577$	2.31316	−	5.84239i	0.0962983	−	0.243222i	−0.873640	−	0.486573i	$-0.838247\pi$
$577$	2.31316	−	5.84239i	0.0962983	−	0.243222i	0.969938	+	0.243351i	$0.0782468\pi$
$578$	23.6271	−	25.1603i	0.982759	−	1.04653i
$579$	1.67858	+	8.79943i	0.0697595	+	0.365692i
$580$	−0.828140	−	0.0616477i	−0.0343866	−	0.00255978i
$581$	33.9509	−	31.8820i	1.40852	−	1.32269i
$582$	−3.16393	+	1.02802i	−0.131149	+	0.0426129i
$583$	11.8263	+	2.25599i	0.489795	+	0.0934334i
$584$	0.176005	+	2.79752i	0.00728314	+	0.115762i
$585$	−3.48322	−	11.1541i	−0.144014	−	0.461164i
$586$	9.59742	+	15.1231i	0.396466	+	0.624730i
$587$	−1.45970	+	0.0918365i	−0.0602482	+	0.00379050i	−0.0928860	−	0.995677i	$-0.529609\pi$
$587$	−1.45970	+	0.0918365i	−0.0602482	+	0.00379050i	0.0326378	+	0.999467i	$0.489609\pi$
$588$	−8.67002	−	5.50216i	−0.357545	−	0.226905i
$589$	−11.6844	+	14.1240i	−0.481448	+	0.581971i
$590$	−22.3922	+	11.9777i	−0.921870	+	0.493116i
$591$	6.97716	+	1.79143i	0.287002	+	0.0736896i
$592$	−3.73222	+	1.75625i	−0.153393	+	0.0721815i
$593$	−9.89748	−	3.21589i	−0.406441	−	0.132061i	0.0986595	−	0.995121i	$-0.468545\pi$
$593$	−9.89748	−	3.21589i	−0.406441	−	0.132061i	−0.505100	+	0.863061i	$0.668545\pi$
$594$	3.35772	+	1.84592i	0.137769	+	0.0757392i
$595$	0.765106	−	66.6885i	0.0313663	−	2.73396i
$596$	−3.07411	−	0.388351i	−0.125921	−	0.0159075i
$597$	−1.30642	+	10.3414i	−0.0534684	+	0.423246i
$598$	−12.1010	+	7.67951i	−0.494845	+	0.314038i
$599$	17.1016	−	12.4250i	0.698751	−	0.507672i	−0.180774	−	0.983525i	$-0.557860\pi$
$599$	17.1016	−	12.4250i	0.698751	−	0.507672i	0.879525	+	0.475852i	$0.157860\pi$
$600$	0.199383	+	4.99602i	0.00813978	+	0.203962i
$601$	27.9574	+	20.3122i	1.14041	+	0.828554i	0.987176	−	0.159637i	$-0.0510323\pi$
$601$	27.9574	+	20.3122i	1.14041	+	0.828554i	0.153231	+	0.988190i	$0.451032\pi$
$602$	−52.0541	−	3.27496i	−2.12157	−	0.133478i
$603$	4.20434	+	7.64767i	0.171214	+	0.311437i
$604$	3.40614	−	7.23843i	0.138594	−	0.294527i
$605$	−8.22179	+	0.422639i	−0.334263	+	0.0171827i
$606$	1.24314	−	6.51677i	0.0504991	−	0.264726i
$607$	−14.3924	−	19.8094i	−0.584168	−	0.804038i	0.409977	−	0.912096i	$-0.365537\pi$
$607$	−14.3924	−	19.8094i	−0.584168	−	0.804038i	−0.994145	+	0.108058i	$0.965537\pi$
$608$	−1.02020	+	1.85573i	−0.0413744	+	0.0752598i
$609$	0.826934	−	1.30304i	0.0335091	−	0.0528018i
$610$	13.0718	+	3.51660i	0.529262	+	0.142383i
$611$	16.9809	+	6.72321i	0.686974	+	0.271992i
$612$	−2.64217	−	6.67337i	−0.106804	−	0.269755i
$613$	8.46736	−	7.00481i	0.341994	−	0.282922i	−0.450532	−	0.892760i	$-0.648766\pi$
$613$	8.46736	−	7.00481i	0.341994	−	0.282922i	0.792526	+	0.609839i	$0.208766\pi$
$614$	0.450658	−	0.115709i	0.0181871	−	0.00466964i
$615$	−2.86209	+	14.1215i	−0.115411	+	0.569432i
$616$	14.8046	−	5.86154i	0.596492	−	0.236168i
$617$	2.14203	+	2.28103i	0.0862349	+	0.0918309i	0.770639	−	0.637272i	$-0.219937\pi$
$617$	2.14203	+	2.28103i	0.0862349	+	0.0918309i	−0.684404	+	0.729103i	$0.739937\pi$
$618$	−8.16806	+	11.2424i	−0.328568	+	0.452235i
$619$	12.9337	+	27.4856i	0.519851	+	1.10474i	0.976584	+	0.215136i	$0.0690194\pi$
$619$	12.9337	+	27.4856i	0.519851	+	1.10474i	−0.456733	+	0.889604i	$0.650981\pi$
$620$	17.4177	+	8.44155i	0.699512	+	0.339021i
$621$	−2.40331	+	1.32123i	−0.0964416	+	0.0530192i
$622$	14.1056	−	2.69078i	0.565582	−	0.107891i
$623$	−0.196847	−	0.766667i	−0.00788649	−	0.0307159i
$624$	−5.22582			−0.209200
$625$	−5.80612	+	24.3164i	−0.232245	+	0.972657i
$626$	14.3791			0.574705
$627$	2.01793	+	7.85931i	0.0805883	+	0.313871i
$628$	20.4588	−	3.90272i	0.816394	−	0.155736i
$629$	25.9433	−	14.2624i	1.03443	−	0.568681i
$630$	−8.36178	−	4.05257i	−0.333141	−	0.161458i
$631$	−0.601724	−	1.27873i	−0.0239542	−	0.0509054i	0.892492	−	0.451063i	$-0.148955\pi$
$631$	−0.601724	−	1.27873i	−0.0239542	−	0.0509054i	−0.916446	+	0.400158i	$0.868955\pi$
$632$	8.94258	−	12.3084i	0.355717	−	0.489602i
$633$	−9.03848	−	9.62501i	−0.359247	−	0.382560i
$634$	−11.3285	+	4.48527i	−0.449912	+	0.178133i
$635$	−2.29730	+	11.3348i	−0.0911656	+	0.449808i
$636$	−3.04339	+	0.781411i	−0.120678	+	0.0309850i
$637$	41.3470	−	34.2052i	1.63823	−	1.35526i
$638$	0.523844	+	1.32308i	0.0207392	+	0.0523812i
$639$	14.0056	+	5.54520i	0.554053	+	0.219365i
$640$	2.15930	+	0.580897i	0.0853537	+	0.0229620i
$641$	11.9521	−	18.8336i	0.472081	−	0.743881i	−0.521950	−	0.852976i	$-0.674795\pi$
$641$	11.9521	−	18.8336i	0.472081	−	0.743881i	0.994031	+	0.109095i	$0.0347952\pi$
$642$	−5.96710	+	10.8541i	−0.235503	+	0.428378i
$643$	15.2473	+	20.9861i	0.601294	+	0.827610i	0.995826	−	0.0912725i	$-0.0290934\pi$
$643$	15.2473	+	20.9861i	0.601294	+	0.827610i	−0.394532	+	0.918882i	$0.629093\pi$
$644$	−2.13554	+	11.1949i	−0.0841522	+	0.441141i
$645$	−28.0283	+	1.44079i	−1.10361	+	0.0567309i
$646$	6.47157	−	13.7528i	0.254621	−	0.541096i
$647$	3.15125	+	5.73210i	0.123888	+	0.225352i	0.930977	−	0.365079i	$-0.118958\pi$
$647$	3.15125	+	5.73210i	0.123888	+	0.225352i	−0.807088	+	0.590431i	$0.798958\pi$
$648$	−0.998027	−	0.0627905i	−0.0392062	−	0.00246664i
$649$	35.2046	+	25.5776i	1.38190	+	1.00401i
$650$	−25.1525	−	7.07697i	−0.986561	−	0.277582i
$651$	−29.1008	+	21.1430i	−1.14055	+	0.828659i
$652$	−2.53276	+	1.60734i	−0.0991904	+	0.0629481i
$653$	−0.134718	+	1.06640i	−0.00527193	+	0.0417316i	−0.994531	−	0.104440i	$-0.966695\pi$
$653$	−0.134718	+	1.06640i	−0.00527193	+	0.0417316i	0.989259	+	0.146171i	$0.0466951\pi$
$654$	−20.0367	−	2.53122i	−0.783497	−	0.0989786i
$655$	0.306731	−	26.7355i	0.0119850	−	1.04464i
$656$	5.64667	+	3.10428i	0.220465	+	0.121202i
$657$	−2.66586	−	0.866190i	−0.104005	−	0.0337933i
$658$	13.1408	−	6.18358i	0.512281	−	0.241061i
$659$	10.6572	+	2.73631i	0.415147	+	0.106592i	0.450485	−	0.892784i	$-0.351251\pi$
$659$	10.6572	+	2.73631i	0.415147	+	0.106592i	−0.0353384	+	0.999375i	$0.511251\pi$
$660$	7.55496	−	4.04121i	0.294076	−	0.157304i
$661$	25.2224	−	30.4887i	0.981038	−	1.18587i	−0.00153579	−	0.999999i	$-0.500489\pi$
$661$	25.2224	−	30.4887i	0.981038	−	1.18587i	0.982574	−	0.185873i	$-0.0595111\pi$
$662$	−14.7478	−	9.35921i	−0.573188	−	0.363756i
$663$	37.4338	−	2.35513i	1.45381	−	0.0914658i
$664$	−6.00536	−	9.46294i	−0.233053	−	0.367233i
$665$	−5.86561	−	18.7830i	−0.227459	−	0.728374i
$666$	−0.258998	−	4.11665i	−0.0100360	−	0.159517i
$667$	−1.00049	−	0.190853i	−0.0387390	−	0.00738986i
$668$	−4.55333	+	1.47947i	−0.176174	+	0.0572423i
$669$	−1.73277	+	1.62718i	−0.0669928	+	0.0629104i
$670$	19.4607	+	1.44868i	0.751832	+	0.0559673i
$671$	−4.34649	−	22.7851i	−0.167795	−	0.879610i
$672$	−2.84467	+	3.02926i	−0.109735	+	0.116856i
$673$	10.4256	−	26.3320i	0.401877	−	1.01503i	−0.578109	−	0.815959i	$-0.696209\pi$
$673$	10.4256	−	26.3320i	0.401877	−	1.01503i	0.979986	−	0.199066i	$-0.0637908\pi$
$674$	−2.02360	−	6.22801i	−0.0779463	−	0.239894i
$675$	−4.71858	−	1.65378i	−0.181618	−	0.0636539i
$676$	4.42179	−	13.6089i	0.170069	−	0.523419i
$677$	−0.766117	−	0.633787i	−0.0294443	−	0.0243584i	0.622585	−	0.782552i	$-0.286082\pi$
$677$	−0.766117	−	0.633787i	−0.0294443	−	0.0243584i	−0.652030	+	0.758193i	$0.726082\pi$
$678$	16.7383	+	7.87646i	0.642831	+	0.302493i
$679$	−10.0776	−	9.46349i	−0.386742	−	0.363175i
$680$	−15.7293	−	3.18797i	−0.603192	−	0.122253i
$681$	−1.62420	+	0.205184i	−0.0622395	+	0.00786268i
$682$		−	33.1672i		−	1.27004i
$683$	−0.0617633	−	0.488907i	−0.00236331	−	0.0187075i	0.990889	−	0.134681i	$-0.0430011\pi$
$683$	−0.0617633	−	0.488907i	−0.00236331	−	0.0187075i	−0.993252	+	0.115974i	$0.963001\pi$
$684$	−1.34985	−	1.63169i	−0.0516130	−	0.0623894i
$685$	17.3426	−	4.24136i	0.662627	−	0.162054i
$686$	0.852856	−	13.5558i	0.0325622	−	0.517561i
$687$	−0.871120	+	3.39279i	−0.0332353	+	0.129443i
$688$	−3.12135	+	12.1569i	−0.119000	+	0.463476i
$689$	1.03103	−	16.3877i	0.0392790	−	0.624322i
$690$	−0.455253	+	6.11560i	−0.0173312	+	0.232817i
$691$	16.2630	+	19.6586i	0.618674	+	0.747849i	0.983037	−	0.183408i	$-0.0587131\pi$
$691$	16.2630	+	19.6586i	0.618674	+	0.747849i	−0.364362	+	0.931257i	$0.618713\pi$
$692$	−1.49149	−	11.8063i	−0.0566978	−	0.448810i
$693$			15.9227i			0.604853i
$694$	−0.597695	+	0.0755065i	−0.0226882	+	0.00286619i
$695$	−23.0369	−	25.1028i	−0.873841	−	0.952205i
$696$	−0.270724	−	0.254227i	−0.0102618	−	0.00963646i
$697$	−41.8474	−	19.6919i	−1.58508	−	0.745883i
$698$	6.57288	+	5.43756i	0.248787	+	0.205815i
$699$	2.09486	−	6.44732i	0.0792349	−	0.243860i
$700$	−17.7940	+	10.7278i	−0.672551	+	0.405474i
$701$	12.3374	+	37.9707i	0.465978	+	1.43413i	0.857748	+	0.514070i	$0.171863\pi$
$701$	12.3374	+	37.9707i	0.465978	+	1.43413i	−0.391771	+	0.920063i	$0.628137\pi$
$702$	1.92375	−	4.85885i	0.0726074	−	0.183385i
$703$	5.97949	−	6.36751i	0.225521	−	0.240155i
$704$	−0.717985	−	3.76381i	−0.0270601	−	0.141854i
$705$	6.64577	−	4.11136i	0.250294	−	0.154843i
$706$	11.7658	−	11.0489i	0.442813	−	0.415829i
$707$	26.2197	−	8.51930i	0.986094	−	0.320401i
$708$	−11.1556	−	2.12804i	−0.419251	−	0.0799765i
$709$	0.358063	+	5.69125i	0.0134473	+	0.213739i	0.999012	+	0.0444402i	$0.0141504\pi$
$709$	0.358063	+	5.69125i	0.0134473	+	0.213739i	−0.985565	+	0.169299i	$0.945850\pi$
$710$	27.4753	−	19.4843i	1.03113	−	0.731233i
$711$	8.15208	+	12.8456i	0.305727	+	0.481749i
$712$	−0.190101	+	0.0119601i	−0.00712433	+	0.000448225i
$713$	20.0440	+	12.7203i	0.750655	+	0.476380i
$714$	19.0118	−	22.9813i	0.711498	−	0.860054i
$715$	7.88476	+	44.0746i	0.294873	+	1.64830i
$716$	16.3136	+	4.18862i	0.609668	+	0.156536i
$717$	−13.2038	+	6.21323i	−0.493105	+	0.232038i
$718$	−0.508844	−	0.165334i	−0.0189899	−	0.00617019i
$719$	40.3790	+	22.1986i	1.50588	+	0.827866i	0.999409	−	0.0343884i	$-0.0109483\pi$
$719$	40.3790	+	22.1986i	1.50588	+	0.827866i	0.506475	+	0.862255i	$0.330948\pi$
$720$	−1.33499	+	1.79382i	−0.0497523	+	0.0668517i
$721$	−57.2915	−	7.23760i	−2.13365	−	0.269542i
$722$	−1.81927	+	14.4010i	−0.0677062	+	0.535950i
$723$	20.9669	−	13.3060i	0.779768	−	0.494856i
$724$	5.80726	−	4.21922i	0.215825	−	0.156806i
$725$	−0.958745	−	1.59025i	−0.0356069	−	0.0590603i
$726$	−2.97860	−	2.16408i	−0.110546	−	0.0803165i
$727$	−20.7688	−	1.30666i	−0.770272	−	0.0484614i	−0.327209	−	0.944952i	$-0.606108\pi$
$727$	−20.7688	−	1.30666i	−0.770272	−	0.0484614i	−0.443063	+	0.896491i	$0.646108\pi$
$728$	−10.4618	−	19.0300i	−0.387741	−	0.705299i
$729$	0.425779	−	0.904827i	0.0157696	−	0.0335121i
$730$	−4.87495	+	3.93959i	−0.180430	+	0.145811i
$731$	16.8802	−	88.4891i	0.624337	−	3.27289i
$732$	3.55830	+	4.89758i	0.131519	+	0.181020i
$733$	−14.7400	+	26.8120i	−0.544435	+	0.990324i	0.450781	+	0.892634i	$0.351145\pi$
$733$	−14.7400	+	26.8120i	−0.544435	+	0.990324i	−0.995217	+	0.0976901i	$0.968855\pi$
$734$	5.08997	−	8.02052i	0.187874	−	0.296043i
$735$	−1.17876	−	22.9309i	−0.0434791	−	0.845818i
$736$	2.54996	+	1.00960i	0.0939926	+	0.0372143i
$737$	−12.3100	−	31.0914i	−0.453443	−	1.14527i
$738$	−4.96496	+	4.10738i	−0.182763	+	0.151195i
$739$	36.0854	−	9.26515i	1.32742	−	0.340824i	0.482586	−	0.875849i	$-0.339698\pi$
$739$	36.0854	−	9.26515i	1.32742	−	0.340824i	0.844836	+	0.535025i	$0.179698\pi$
$740$	−8.03095	−	4.53580i	−0.295223	−	0.166739i
$741$	10.2894	−	4.07388i	0.377992	−	0.149658i
$742$	−8.93825	−	9.51827i	−0.328133	−	0.349427i
$743$	−6.32226	+	8.70185i	−0.231941	+	0.319240i	−0.909085	−	0.416611i	$-0.863218\pi$
$743$	−6.32226	+	8.70185i	−0.231941	+	0.319240i	0.677143	+	0.735851i	$0.263218\pi$
$744$	3.68557	+	7.83223i	0.135119	+	0.287144i
$745$	−3.26799	−	6.10944i	−0.119730	−	0.223832i
$746$	−14.4752	+	7.95779i	−0.529974	+	0.291355i
$747$	11.0091	−	2.10010i	0.402803	−	0.0768388i
$748$	6.83933	+	26.6374i	0.250071	+	0.973962i
$749$	−51.4714			−1.88072
$750$	−8.85473	+	6.82597i	−0.323329	+	0.249249i
$751$	−47.5526			−1.73522			−0.867609	−	0.497247i	$-0.834344\pi$
$751$	−47.5526			−1.73522			−0.867609	+	0.497247i	$0.834344\pi$
$752$	−0.869132	−	3.38504i	−0.0316940	−	0.123440i
$753$	−27.4663	+	5.23947i	−1.00093	+	0.190937i
$754$	1.70071	−	0.934971i	0.0619361	−	0.0340497i
$755$	17.6085	−	3.15009i	0.640840	−	0.114644i
$756$	−1.76934	−	3.76005i	−0.0643504	−	0.136752i
$757$	25.3987	−	34.9583i	0.923132	−	1.27058i	−0.0393465	−	0.999226i	$-0.512528\pi$
$757$	25.3987	−	34.9583i	0.923132	−	1.27058i	0.962479	−	0.271357i	$-0.0874724\pi$
$758$	−9.97797	−	10.6255i	−0.362416	−	0.385934i
$759$	9.77061	−	3.86846i	0.354651	−	0.140416i
$760$	−4.70442	+	0.539551i	−0.170647	+	0.0195716i
$761$	7.68340	−	1.97276i	0.278523	−	0.0715125i	−0.106845	−	0.994276i	$-0.534075\pi$
$761$	7.68340	−	1.97276i	0.278523	−	0.0715125i	0.385367	+	0.922763i	$0.374075\pi$
$762$	−3.98521	+	3.29685i	−0.144369	+	0.119432i
$763$	−30.8949	−	78.0316i	−1.11847	−	2.82493i
$764$	4.42119	+	1.75047i	0.159953	+	0.0633299i
$765$	8.75445	−	13.4512i	0.316518	−	0.486329i
$766$	5.08337	−	8.01010i	0.183669	−	0.289417i
$767$	28.5912	−	52.0072i	1.03237	−	1.87787i
$768$	0.587785	+	0.809017i	0.0212099	+	0.0291929i
$769$	−2.58782	+	13.5658i	−0.0933191	+	0.489196i	0.904687	+	0.426077i	$0.140105\pi$
$769$	−2.58782	+	13.5658i	−0.0933191	+	0.489196i	−0.998006	+	0.0631188i	$0.979895\pi$
$770$	29.8408	+	19.4213i	1.07539	+	0.699896i
$771$	1.91906	−	4.07822i	0.0691134	−	0.146873i
$772$	4.31560	+	7.85005i	0.155322	+	0.282529i
$773$	31.0357	+	1.95260i	1.11628	+	0.0702302i	0.610192	−	0.792253i	$-0.291092\pi$
$773$	31.0357	+	1.95260i	1.11628	+	0.0702302i	0.506085	+	0.862484i	$0.331092\pi$
$774$	−10.1541	−	7.37740i	−0.364982	−	0.265175i
$775$	7.13240	+	42.6885i	0.256204	+	1.53342i
$776$	−2.69140	+	1.95541i	−0.0966155	+	0.0701953i
$777$	14.4724	−	9.18447i	0.519195	−	0.329491i
$778$	0.879208	−	6.95964i	0.0315211	−	0.249515i
$779$	−13.5381	−	1.71026i	−0.485051	−	0.0612762i
$780$	−6.75954	−	9.53178i	−0.242030	−	0.341292i
$781$	−50.5787	−	27.8059i	−1.80985	−	0.994973i
$782$	−18.7209	−	6.08280i	−0.669459	−	0.217520i
$783$	0.336035	−	0.158126i	0.0120089	−	0.00565096i
$784$	−9.94594	−	2.55368i	−0.355212	−	0.0912029i
$785$	33.5817	+	32.2682i	1.19858	+	1.15170i
$786$	7.62184	−	9.21322i	0.271862	−	0.328625i
$787$	25.2422	+	16.0192i	0.899788	+	0.571023i	0.903318	−	0.428971i	$-0.141124\pi$
$787$	25.2422	+	16.0192i	0.899788	+	0.571023i	−0.00353022	+	0.999994i	$0.501124\pi$
$788$	7.18926	−	0.452310i	0.256107	−	0.0161129i
$789$	−11.3470	−	17.8801i	−0.403965	−	0.636547i
$790$	34.0174	+	0.390275i	1.21028	+	0.0138854i
$791$	4.82690	+	76.7214i	0.171625	+	2.72790i
$792$	3.76381	+	0.717985i	0.133741	+	0.0255125i
$793$	−30.0874	+	9.77599i	−1.06844	+	0.347156i
$794$	−7.62527	+	7.16061i	−0.270611	+	0.254120i
$795$	−5.36187	−	4.54033i	−0.190166	−	0.161029i
$796$	1.95319	+	10.2390i	0.0692289	+	0.362911i
$797$	11.4460	−	12.1888i	0.405439	−	0.431749i	−0.493551	−	0.869717i	$-0.664302\pi$
$797$	11.4460	−	12.1888i	0.405439	−	0.431749i	0.898991	+	0.437968i	$0.144302\pi$
$798$	3.23952	−	8.18210i	0.114678	−	0.289643i
$799$	7.75134	+	23.8562i	0.274223	+	0.843970i
$800$	1.73348	+	4.68989i	0.0612878	+	0.165813i
$801$	0.0588606	−	0.181154i	0.00207974	−	0.00640077i
$802$	2.64893	+	2.19139i	0.0935371	+	0.0773806i
$803$	9.71819	+	4.57303i	0.342948	+	0.161379i
$804$	6.36183	+	5.97415i	0.224364	+	0.210692i
$805$	−23.1815	+	10.5853i	−0.817042	+	0.373083i
$806$	−44.8783	+	5.66945i	−1.58077	+	0.199698i
$807$			16.6282i			0.585341i
$808$	−0.831496	−	6.58197i	−0.0292519	−	0.231553i
$809$	−17.8576	−	21.5861i	−0.627839	−	0.758927i	0.356676	−	0.934228i	$-0.383910\pi$
$809$	−17.8576	−	21.5861i	−0.627839	−	0.758927i	−0.984515	+	0.175301i	$0.943910\pi$
$810$	−1.17641	−	1.90160i	−0.0413347	−	0.0668153i
$811$	0.677321	−	10.7657i	0.0237839	−	0.378035i	−0.968072	−	0.250672i	$-0.919349\pi$
$811$	0.677321	−	10.7657i	0.0237839	−	0.378035i	0.991856	−	0.127363i	$-0.0406514\pi$
$812$	0.383800	−	1.49480i	0.0134687	−	0.0524572i
$813$	−4.82546	+	18.7939i	−0.169236	+	0.659132i
$814$	−0.992396	+	15.7737i	−0.0347835	+	0.552867i
$815$	−6.20783	−	2.54062i	−0.217451	−	0.0889939i
$816$	−4.57504	−	5.53028i	−0.160159	−	0.193598i
$817$	−3.33127	−	26.3697i	−0.116546	−	0.922559i
$818$		−	3.52969i		−	0.123413i
$819$	21.5449	−	2.72175i	0.752840	−	0.0951058i
$820$	1.64176	+	14.3147i	0.0573328	+	0.499892i
$821$	−1.45116	−	1.36273i	−0.0506459	−	0.0475597i	0.658811	−	0.752308i	$-0.271060\pi$
$821$	−1.45116	−	1.36273i	−0.0506459	−	0.0475597i	−0.709457	+	0.704749i	$0.751060\pi$
$822$	7.22452	+	3.39960i	0.251984	+	0.118575i
$823$	7.89837	+	6.53410i	0.275320	+	0.227764i	0.764828	−	0.644234i	$-0.222824\pi$
$823$	7.89837	+	6.53410i	0.275320	+	0.227764i	−0.489508	+	0.871999i	$0.662824\pi$
$824$	−4.29420	+	13.2162i	−0.149596	+	0.460408i
$825$	17.1433	+	8.55281i	0.596854	+	0.297771i
$826$	−14.5835	−	44.8835i	−0.507426	−	1.56170i
$827$	0.914264	−	2.30917i	0.0317921	−	0.0802976i	−0.913013	−	0.407930i	$-0.866251\pi$
$827$	0.914264	−	2.30917i	0.0317921	−	0.0802976i	0.944805	+	0.327632i	$0.106251\pi$
$828$	−1.87740	+	1.99923i	−0.0652443	+	0.0694781i
$829$	7.17789	+	37.6278i	0.249299	+	1.30687i	0.858074	+	0.513526i	$0.171661\pi$
$829$	7.17789	+	37.6278i	0.249299	+	1.30687i	−0.608775	+	0.793343i	$0.708339\pi$
$830$	9.49230	−	23.1938i	0.329483	−	0.805070i
$831$	12.9792	−	12.1883i	0.450243	−	0.422806i
$832$	−4.97005	+	1.61487i	−0.172306	+	0.0559855i
$833$	72.3959	+	13.8103i	2.50837	+	0.478497i
$834$	−0.956748	−	15.2071i	−0.0331295	−	0.526578i
$835$	−8.58819	−	6.39149i	−0.297207	−	0.221187i
$836$	4.34782	+	6.85107i	0.150373	+	0.236949i
$837$	−8.63897	+	0.543518i	−0.298607	+	0.0187867i
$838$	18.1316	+	11.5067i	0.626347	+	0.397492i
$839$	−5.33915	+	6.45392i	−0.184328	+	0.222814i	−0.854581	−	0.519319i	$-0.826186\pi$
$839$	−5.33915	+	6.45392i	−0.184328	+	0.222814i	0.670253	+	0.742133i	$0.266186\pi$
$840$	−9.20484	−	1.27029i	−0.317597	−	0.0438291i
$841$	−27.9553	−	7.17771i	−0.963977	−	0.247507i
$842$	−17.6307	+	8.29639i	−0.607595	+	0.285912i
$843$	1.80061	+	0.585053i	0.0620163	+	0.0201503i
$844$	−11.5704	−	6.36088i	−0.398270	−	0.218951i
$845$	30.5418	−	9.53768i	1.05067	−	0.328106i
$846$	3.46728	+	0.438020i	0.119208	+	0.0150594i
$847$	1.91756	−	15.1790i	0.0658881	−	0.521558i
$848$	−2.65297	+	1.68363i	−0.0911034	+	0.0578160i
$849$	−13.3439	+	9.69492i	−0.457962	+	0.332729i
$850$	−14.5309	−	32.8135i	−0.498407	−	1.12549i
$851$	−9.15195	−	6.64928i	−0.313725	−	0.227935i
$852$	15.0337	+	0.945838i	0.515045	+	0.0324039i
$853$	−8.49496	−	15.4523i	−0.290862	−	0.529076i	0.689993	−	0.723816i	$-0.257614\pi$
$853$	−8.49496	−	15.4523i	−0.290862	−	0.529076i	−0.980855	+	0.194740i	$0.937614\pi$
$854$	−10.7112	+	22.7624i	−0.366528	+	0.778912i
$855$	1.23015	−	4.57268i	0.0420702	−	0.156382i
$856$	−2.32094	+	12.1668i	−0.0793282	+	0.415853i
$857$	10.7667	+	14.8192i	0.367785	+	0.506213i	0.952297	−	0.305172i	$-0.0987140\pi$
$857$	10.7667	+	14.8192i	0.367785	+	0.506213i	−0.584512	+	0.811385i	$0.698714\pi$
$858$	−9.64648	+	17.5469i	−0.329325	+	0.599040i
$859$	−6.98765	+	11.0108i	−0.238416	+	0.375683i	−0.942376	−	0.334557i	$-0.891413\pi$
$859$	−6.98765	+	11.0108i	−0.238416	+	0.375683i	0.703960	+	0.710240i	$0.251413\pi$
$860$	−26.2113	+	10.0315i	−0.893797	+	0.342071i
$861$	−24.8967	−	9.85732i	−0.848479	−	0.335936i
$862$	−5.88557	−	14.8652i	−0.200463	−	0.506312i
$863$	−6.33314	+	5.23923i	−0.215583	+	0.178346i	−0.738947	−	0.673763i	$-0.764677\pi$
$863$	−6.33314	+	5.23923i	−0.215583	+	0.178346i	0.523364	+	0.852109i	$0.324677\pi$
$864$	−0.968583	+	0.248690i	−0.0329519	+	0.00846060i
$865$	19.6053	−	17.9918i	0.666599	−	0.611739i
$866$	−28.2001	+	11.1652i	−0.958279	+	0.379409i
$867$	23.6271	+	25.1603i	0.802419	+	0.854490i
$868$	−21.1430	+	29.1008i	−0.717640	+	0.987747i
$869$	−24.8209	−	52.7471i	−0.841992	−	1.78932i
$870$	0.113525	−	0.822635i	0.00384887	−	0.0278899i
$871$	−39.9654	+	21.9711i	−1.35417	+	0.744464i
$872$	−19.8382	+	3.78434i	−0.671807	+	0.128154i
$873$	−0.827329	−	3.22223i	−0.0280008	−	0.109056i
$874$	−5.80781			−0.196452
$875$	−42.5837	−	18.5795i	−1.43959	−	0.628103i
$876$	−2.80305			−0.0947063
$877$	−5.48587	−	21.3661i	−0.185245	−	0.721481i	−0.991522	−	0.129942i	$-0.958521\pi$
$877$	−5.48587	−	21.3661i	−0.185245	−	0.721481i	0.806277	−	0.591538i	$-0.201479\pi$
$878$	−0.760373	+	0.145049i	−0.0256613	+	0.00489516i
$879$	−15.6959	+	8.62889i	−0.529409	+	0.291045i
$880$	5.93639	−	6.17803i	0.200116	−	0.208261i
$881$	2.15684	+	4.58352i	0.0726658	+	0.154423i	0.937860	−	0.347015i	$-0.112805\pi$
$881$	2.15684	+	4.58352i	0.0726658	+	0.154423i	−0.865194	+	0.501438i	$0.832805\pi$
$882$	6.03570	−	8.30742i	0.203232	−	0.279726i
$883$	26.5345	+	28.2563i	0.892956	+	0.950901i	0.999055	−	0.0434541i	$-0.0138362\pi$
$883$	26.5345	+	28.2563i	0.892956	+	0.950901i	−0.106100	+	0.994356i	$0.533836\pi$
$884$	34.8739	−	13.8075i	1.17293	−	0.464398i
$885$	−10.5481	−	23.1001i	−0.354570	−	0.776500i
$886$	1.53285	−	0.393568i	0.0514970	−	0.0132222i
$887$	−19.3888	+	16.0398i	−0.651013	+	0.538565i	−0.903258	−	0.429099i	$-0.858831\pi$
$887$	−19.3888	+	16.0398i	−0.651013	+	0.538565i	0.252244	+	0.967664i	$0.418831\pi$
$888$	−1.51844	−	3.83513i	−0.0509554	−	0.128699i
$889$	−19.9838	−	7.91213i	−0.670234	−	0.265364i
$890$	−0.267708	−	0.331269i	−0.00897360	−	0.0111042i
$891$	−2.05312	+	3.23519i	−0.0687820	+	0.108383i
$892$	−1.14514	+	2.08300i	−0.0383420	+	0.0697439i
$893$	4.35015	+	5.98747i	0.145572	+	0.200363i
$894$	0.580610	−	3.04366i	0.0194185	−	0.101795i
$895$	13.4615	+	35.1735i	0.449968	+	1.17572i
$896$	−1.76934	+	3.76005i	−0.0591096	+	0.125614i
$897$	−6.90453	−	12.5593i	−0.230535	−	0.419342i
$898$	−30.3247	−	1.90787i	−1.01195	−	0.0636663i
$899$	−2.60074	−	1.88954i	−0.0867394	−	0.0630199i
$900$	−4.99868	−	0.114713i	−0.166623	−	0.00382377i
$901$	18.2451	−	13.2558i	0.607832	−	0.441616i
$902$	20.8466	−	13.2297i	0.694117	−	0.440500i
$903$	6.53700	−	51.7457i	0.217538	−	1.72199i
$904$	18.3530	+	2.31853i	0.610413	+	0.0771131i
$905$	15.2074	+	5.13479i	0.505511	+	0.170686i
$906$	7.01027	+	3.85393i	0.232901	+	0.128038i
$907$	−21.5279	−	6.99485i	−0.714824	−	0.232260i	−0.0710462	−	0.997473i	$-0.522634\pi$
$907$	−21.5279	−	6.99485i	−0.714824	−	0.232260i	−0.643778	+	0.765213i	$0.722634\pi$
$908$	−1.48130	+	0.697048i	−0.0491587	+	0.0231323i
$909$	6.42585	+	1.64988i	0.213132	+	0.0547230i
$910$	21.1780	−	43.6972i	0.702044	−	1.44855i
$911$	29.8794	−	36.1180i	0.989950	−	1.19664i	0.00948383	−	0.999955i	$-0.496981\pi$
$911$	29.8794	−	36.1180i	0.989950	−	1.19664i	0.980466	−	0.196689i	$-0.0630188\pi$
$912$	−1.78801	−	1.13471i	−0.0592069	−	0.0375738i
$913$	−42.8594	+	2.69648i	−1.41844	+	0.0892406i
$914$	12.8009	+	20.1710i	0.423417	+	0.667198i
$915$	−4.33045	+	12.8252i	−0.143160	+	0.423988i
$916$	0.219945	+	3.49592i	0.00726718	+	0.115509i
$917$	48.8088	+	9.31077i	1.61181	+	0.307469i
$918$	6.82611	−	2.21794i	0.225295	−	0.0732028i
$919$	−3.22836	+	3.03163i	−0.106494	+	0.100004i	−0.735965	−	0.677019i	$-0.763271\pi$
$919$	−3.22836	+	3.03163i	−0.106494	+	0.100004i	0.629472	+	0.777023i	$0.283271\pi$
$920$	1.45685	+	5.95696i	0.0480310	+	0.196395i
$921$	0.0871838	+	0.457034i	0.00287281	+	0.0150598i
$922$	16.3714	−	17.4338i	0.539163	−	0.574150i
$923$	−28.9783	+	73.1907i	−0.953831	+	2.40910i
$924$	4.92039	+	15.1434i	0.161869	+	0.498181i
$925$	−2.11475	−	20.5153i	−0.0695326	−	0.674537i
$926$	0.972578	−	2.99329i	0.0319609	−	0.0983655i
$927$	−10.7073	−	8.85786i	−0.351674	−	0.290930i
$928$	−0.336035	−	0.158126i	−0.0110309	−	0.00519074i
$929$	−4.07521	−	3.82688i	−0.133703	−	0.125556i	0.614811	−	0.788675i	$-0.289232\pi$
$929$	−4.07521	−	3.82688i	−0.133703	−	0.125556i	−0.748514	+	0.663119i	$0.769232\pi$
$930$	−9.51856	+	16.8533i	−0.312126	+	0.552641i
$931$	21.5739	−	2.72542i	0.707057	−	0.0893221i
$932$		−	6.77911i		−	0.222057i
$933$	1.79978	+	14.2467i	0.0589220	+	0.466416i
$934$	19.5611	+	23.6453i	0.640058	+	0.773697i
$935$	−39.7395	+	46.9300i	−1.29962	+	1.53478i
$936$	0.328132	−	5.21551i	0.0107253	−	0.170474i
$937$	13.2015	−	51.4165i	0.431275	−	1.67970i	−0.266858	−	0.963736i	$-0.585985\pi$
$937$	13.2015	−	51.4165i	0.431275	−	1.67970i	0.698133	−	0.715968i	$-0.254015\pi$
$938$	−9.01901	+	35.1267i	−0.294481	+	1.14693i
$939$	−0.902872	+	14.3507i	−0.0294641	+	0.468319i
$940$	5.05003	−	5.96379i	0.164714	−	0.194517i
$941$	28.6046	+	34.5771i	0.932485	+	1.12718i	0.991653	+	0.128932i	$0.0411550\pi$
$941$	28.6046	+	34.5771i	0.932485	+	1.12718i	−0.0591688	+	0.998248i	$0.518845\pi$
$942$	2.61040	+	20.6635i	0.0850515	+	0.673252i
$943$			17.6722i			0.575485i
$944$	−11.2672	+	1.42337i	−0.366715	+	0.0463269i
$945$	4.56961	−	8.09082i	0.148649	−	0.263194i
$946$	35.0576	+	32.9213i	1.13982	+	1.07036i
$947$	25.5750	+	12.0347i	0.831075	+	0.391074i	0.793761	−	0.608229i	$-0.208120\pi$
$947$	25.5750	+	12.0347i	0.831075	+	0.391074i	0.0373137	+	0.999304i	$0.488120\pi$
$948$	11.7226	+	9.69779i	0.380733	+	0.314969i
$949$	4.52656	−	13.9313i	0.146938	−	0.452230i
$950$	−7.06924	−	7.88284i	−0.229356	−	0.255753i
$951$	−3.76510	−	11.5878i	−0.122092	−	0.375759i
$952$	10.9797	−	27.7315i	0.355853	−	0.898783i
$953$	13.8225	−	14.7195i	0.447755	−	0.476811i	−0.465004	−	0.885308i	$-0.653947\pi$
$953$	13.8225	−	14.7195i	0.447755	−	0.476811i	0.912759	+	0.408498i	$0.133947\pi$
$954$	−0.588773	−	3.08645i	−0.0190622	−	0.0999276i
$955$	2.52594	+	10.3284i	0.0817373	+	0.334218i
$956$	−10.6376	+	9.98933i	−0.344043	+	0.323078i
$957$	−1.35336	+	0.439734i	−0.0437480	+	0.0142146i
$958$	−16.1470	−	3.08020i	−0.521684	−	0.0995166i
$959$	2.08336	+	33.1141i	0.0672754	+	1.06931i
$960$	−0.715334	+	2.11856i	−0.0230873	+	0.0683762i
$961$	23.5374	+	37.0890i	0.759271	+	1.19642i
$962$	21.5129	−	1.35348i	0.693604	−	0.0436378i
$963$	−10.4580	−	6.63686i	−0.337005	−	0.213870i
$964$	15.8289	−	19.1339i	0.509816	−	0.616261i
$965$	−8.73612	+	18.0255i	−0.281226	+	0.580261i
$966$	−11.0387	−	2.83426i	−0.355165	−	0.0911909i
$967$	−2.35570	+	1.10851i	−0.0757541	+	0.0356472i	−0.463283	−	0.886210i	$-0.653329\pi$
$967$	−2.35570	+	1.10851i	−0.0757541	+	0.0356472i	0.387529	+	0.921858i	$0.373329\pi$
$968$	−3.50155	−	1.13772i	−0.112544	−	0.0365678i
$969$	13.3193	+	7.32235i	0.427878	+	0.235228i
$970$	−7.04792	−	2.37974i	−0.226295	−	0.0764088i
$971$	−54.6700	−	6.90643i	−1.75444	−	0.221638i	−0.818676	−	0.574256i	$-0.805292\pi$
$971$	−54.6700	−	6.90643i	−1.75444	−	0.221638i	−0.935767	+	0.352618i	$0.885292\pi$
$972$	0.125333	−	0.992115i	0.00402007	−	0.0318221i
$973$	53.4617	−	33.9278i	1.71390	−	1.08768i
$974$	2.34142	−	1.70114i	0.0750239	−	0.0545081i
$975$	8.64235	−	24.6585i	0.276777	−	0.789703i
$976$	4.89758	+	3.55830i	0.156768	+	0.113898i
$977$	18.8366	+	1.18510i	0.602636	+	0.0379146i	0.361178	−	0.932497i	$-0.382375\pi$
$977$	18.8366	+	1.18510i	0.602636	+	0.0379146i	0.241457	+	0.970411i	$0.422375\pi$
$978$	−1.44513	−	2.62868i	−0.0462102	−	0.0840560i
$979$	−0.310753	+	0.660384i	−0.00993171	+	0.0211060i
$980$	−8.20710	−	21.4443i	−0.262166	−	0.685013i
$981$	3.78434	−	19.8382i	0.120825	−	0.633385i
$982$	12.8955	+	17.7491i	0.411512	+	0.566398i
$983$	16.1656	−	29.4052i	0.515604	−	0.937880i	−0.482474	−	0.875910i	$-0.660262\pi$
$983$	16.1656	−	29.4052i	0.515604	−	0.937880i	0.998078	−	0.0619697i	$-0.0197382\pi$
$984$	−3.45271	+	5.44060i	−0.110068	+	0.173440i
$985$	10.1242	+	12.5280i	0.322585	+	0.399175i
$986$	2.47836	+	0.981251i	0.0789270	+	0.0312494i
$987$	5.34626	+	13.5031i	0.170173	+	0.429809i
$988$	8.52694	−	7.05410i	0.271278	−	0.224421i
$989$	−33.3408	+	8.56046i	−1.06017	+	0.272207i
$990$	3.55885	+	7.79380i	0.113108	+	0.247703i
$991$	48.9504	−	19.3808i	1.55496	−	0.615653i	0.575593	−	0.817736i	$-0.304771\pi$
$991$	48.9504	−	19.3808i	1.55496	−	0.615653i	0.979368	+	0.202084i	$0.0647712\pi$
$992$	5.92548	+	6.30999i	0.188134	+	0.200342i
$993$	10.2668	−	14.1310i	0.325806	−	0.448433i
$994$	26.6523	+	56.6391i	0.845361	+	1.79648i
$995$	−16.1492	+	16.8066i	−0.511965	+	0.532804i
$996$	9.82134	−	5.39933i	0.311201	−	0.171084i
$997$	−56.9748	+	10.8685i	−1.80441	+	0.344210i	−0.976311	−	0.216371i	$-0.930578\pi$
$997$	−56.9748	+	10.8685i	−1.80441	+	0.344210i	−0.828100	+	0.560580i	$0.810578\pi$
$998$	−8.27358	−	32.2235i	−0.261896	−	1.02002i
$999$	4.12479			0.130503

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.o.b.229.8	✓	280
125.119	even	50	inner	750.2.o.b.619.8	yes	280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
750.2.o.b.229.8	✓	280	1.1	even	1	trivial
750.2.o.b.619.8	yes	280	125.119	even	50	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:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.o (of order \(50\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.248690 + 0.968583i) q^{2} +(-0.982287 + 0.187381i) q^{3} +(-0.876307 + 0.481754i) q^{4} +(-2.01220 - 0.975220i) q^{5} +(-0.425779 - 0.904827i) q^{6} +(2.44257 - 3.36191i) q^{7} +(-0.684547 - 0.728969i) q^{8} +(0.929776 - 0.368125i) q^{9} +O(q^{10})\)	\(q+(0.248690 + 0.968583i) q^{2} +(-0.982287 + 0.187381i) q^{3} +(-0.876307 + 0.481754i) q^{4} +(-2.01220 - 0.975220i) q^{5} +(-0.425779 - 0.904827i) q^{6} +(2.44257 - 3.36191i) q^{7} +(-0.684547 - 0.728969i) q^{8} +(0.929776 - 0.368125i) q^{9} +(0.444168 - 2.19151i) q^{10} +(-3.71130 + 0.952899i) q^{11} +(0.770513 - 0.637424i) q^{12} +(1.92375 + 4.85885i) q^{13} +(3.86373 + 1.52976i) q^{14} +(2.15930 + 0.580897i) q^{15} +(0.535827 - 0.844328i) q^{16} +(-3.45774 + 6.28960i) q^{17} +(0.587785 + 0.809017i) q^{18} +(-0.396812 + 2.08016i) q^{19} +(2.23312 - 0.114793i) q^{20} +(-1.76934 + 3.76005i) q^{21} +(-1.84592 - 3.35772i) q^{22} +(2.73714 + 0.172206i) q^{23} +(0.809017 + 0.587785i) q^{24} +(3.09789 + 3.92467i) q^{25} +(-4.22778 + 3.07166i) q^{26} +(-0.844328 + 0.535827i) q^{27} +(-0.520828 + 4.12278i) q^{28} +(-0.368452 - 0.0465463i) q^{29} +(-0.0256523 + 2.23592i) q^{30} +(7.58536 + 4.17009i) q^{31} +(0.951057 + 0.309017i) q^{32} +(3.46701 - 1.63145i) q^{33} +(-6.95190 - 1.78495i) q^{34} +(-8.19353 + 4.38278i) q^{35} +(-0.637424 + 0.770513i) q^{36} +(-3.48268 - 2.21017i) q^{37} +(-2.11349 + 0.132970i) q^{38} +(-2.80014 - 4.41231i) q^{39} +(0.666541 + 2.13441i) q^{40} +(0.404604 + 6.43100i) q^{41} +(-4.08194 - 0.778671i) q^{42} +(-11.9369 + 3.87853i) q^{43} +(2.79317 - 2.62296i) q^{44} +(-2.22990 - 0.165996i) q^{45} +(0.513902 + 2.69397i) q^{46} +(2.39238 - 2.54763i) q^{47} +(-0.368125 + 0.929776i) q^{48} +(-3.17315 - 9.76596i) q^{49} +(-3.03096 + 3.97659i) q^{50} +(2.21794 - 6.82611i) q^{51} +(-4.02657 - 3.33107i) q^{52} +(-2.84307 - 1.33785i) q^{53} +(-0.728969 - 0.684547i) q^{54} +(8.39716 + 1.70191i) q^{55} +(-4.12278 + 0.520828i) q^{56} -2.11767i q^{57} +(-0.0465463 - 0.368452i) q^{58} +(-7.23904 - 8.75050i) q^{59} +(-2.17205 + 0.531204i) q^{60} +(-0.380118 + 6.04180i) q^{61} +(-2.15267 + 8.38411i) q^{62} +(1.03344 - 4.02499i) q^{63} +(-0.0627905 + 0.998027i) q^{64} +(0.867468 - 11.6531i) q^{65} +(2.44240 + 2.95236i) q^{66} +(1.09380 + 8.65835i) q^{67} -7.17739i q^{68} +(-2.72092 + 0.343732i) q^{69} +(-6.28274 - 6.84616i) q^{70} +(10.9807 + 10.3116i) q^{71} +(-0.904827 - 0.425779i) q^{72} +(-2.15979 - 1.78673i) q^{73} +(1.27463 - 3.92291i) q^{74} +(-3.77843 - 3.27467i) q^{75} +(-0.654397 - 2.01403i) q^{76} +(-5.86154 + 14.8046i) q^{77} +(3.57732 - 3.80946i) q^{78} +(2.85082 + 14.9445i) q^{79} +(-1.90160 + 1.17641i) q^{80} +(0.728969 - 0.684547i) q^{81} +(-6.12833 + 1.99122i) q^{82} +(11.0091 + 2.10010i) q^{83} +(-0.260929 - 4.14734i) q^{84} +(13.0914 - 9.28387i) q^{85} +(-6.72526 - 10.5973i) q^{86} +(0.370647 - 0.0233191i) q^{87} +(3.23519 + 2.05312i) q^{88} +(0.121414 - 0.146765i) q^{89} +(-0.393772 - 2.20112i) q^{90} +(21.0339 + 5.40058i) q^{91} +(-2.48153 + 1.16772i) q^{92} +(-8.23240 - 2.67487i) q^{93} +(3.06255 + 1.68365i) q^{94} +(2.82708 - 3.79872i) q^{95} +(-0.992115 - 0.125333i) q^{96} +(0.416952 - 3.30052i) q^{97} +(8.67002 - 5.50216i) q^{98} +(-3.09989 + 2.25220i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 280 q+O(q^{10}) \) 280 * q	\( 280 q - 10 q^{11} - 20 q^{13} + 30 q^{17} + 10 q^{19} + 20 q^{22} + 60 q^{23} + 70 q^{24} + 20 q^{25} + 20 q^{29} + 10 q^{30} + 20 q^{31} + 20 q^{33} - 10 q^{34} + 30 q^{35} - 20 q^{37} + 90 q^{38} - 40 q^{41} - 10 q^{46} - 100 q^{47} + 120 q^{49} - 20 q^{50} - 30 q^{51} + 80 q^{52} - 30 q^{53} - 10 q^{55} + 30 q^{58} + 20 q^{59} + 60 q^{61} - 50 q^{62} - 10 q^{63} + 20 q^{65} + 40 q^{66} + 50 q^{67} + 10 q^{69} + 20 q^{70} + 80 q^{71} - 20 q^{73} + 80 q^{75} - 30 q^{76} - 100 q^{77} - 100 q^{79} + 100 q^{82} + 30 q^{83} - 20 q^{86} - 10 q^{87} - 60 q^{89} - 10 q^{90} + 70 q^{91} - 120 q^{92} + 50 q^{93} + 30 q^{94} - 20 q^{95} + 10 q^{97} + 40 q^{98} + 20 q^{99}+O(q^{100}) \) 280 * q - 10 * q^11 - 20 * q^13 + 30 * q^17 + 10 * q^19 + 20 * q^22 + 60 * q^23 + 70 * q^24 + 20 * q^25 + 20 * q^29 + 10 * q^30 + 20 * q^31 + 20 * q^33 - 10 * q^34 + 30 * q^35 - 20 * q^37 + 90 * q^38 - 40 * q^41 - 10 * q^46 - 100 * q^47 + 120 * q^49 - 20 * q^50 - 30 * q^51 + 80 * q^52 - 30 * q^53 - 10 * q^55 + 30 * q^58 + 20 * q^59 + 60 * q^61 - 50 * q^62 - 10 * q^63 + 20 * q^65 + 40 * q^66 + 50 * q^67 + 10 * q^69 + 20 * q^70 + 80 * q^71 - 20 * q^73 + 80 * q^75 - 30 * q^76 - 100 * q^77 - 100 * q^79 + 100 * q^82 + 30 * q^83 - 20 * q^86 - 10 * q^87 - 60 * q^89 - 10 * q^90 + 70 * q^91 - 120 * q^92 + 50 * q^93 + 30 * q^94 - 20 * q^95 + 10 * q^97 + 40 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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