LMFDB - Embedded newform 250.2.g.b.231.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [250,2,Mod(11,250)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(250, base_ring=CyclotomicField(50))

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

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

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

chi := DirichletCharacter("250.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 250 = 2 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	250.g (of order $25$, 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:	$1.99626005053$
Analytic rank:	$0$
Dimension:	$140$
Relative dimension:	$7$ over $\Q(\zeta_{25})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{25}]$

Embedding invariants

Embedding label			231.1
Character	$\chi$	$=$	250.231
Dual form			250.2.g.b.171.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.535827 - 0.844328i) q^{2} +(-2.25183 + 2.11461i) q^{3} +(-0.425779 - 0.904827i) q^{4} +(2.21119 + 0.332605i) q^{5} +(0.578833 + 3.03435i) q^{6} +(-1.80742 + 1.31317i) q^{7} +(-0.992115 - 0.125333i) q^{8} +(0.410795 - 6.52940i) q^{9} +O(q^{10})$	\(q+(0.535827 - 0.844328i) q^{2} +(-2.25183 + 2.11461i) q^{3} +(-0.425779 - 0.904827i) q^{4} +(2.21119 + 0.332605i) q^{5} +(0.578833 + 3.03435i) q^{6} +(-1.80742 + 1.31317i) q^{7} +(-0.992115 - 0.125333i) q^{8} +(0.410795 - 6.52940i) q^{9} +(1.46564 - 1.68875i) q^{10} +(-2.82920 + 4.45811i) q^{11} +(2.87214 + 1.13716i) q^{12} +(-0.371622 + 5.90677i) q^{13} +(0.140280 + 2.22969i) q^{14} +(-5.68256 + 3.92684i) q^{15} +(-0.637424 + 0.770513i) q^{16} +(-0.204009 + 0.433542i) q^{17} +(-5.29284 - 3.84547i) q^{18} +(0.678227 + 0.636898i) q^{19} +(-0.640530 - 2.14236i) q^{20} +(1.29317 - 6.77902i) q^{21} +(2.24815 + 4.77755i) q^{22} +(-1.45580 - 0.373786i) q^{23} +(2.49910 - 1.81571i) q^{24} +(4.77875 + 1.47091i) q^{25} +(4.78812 + 3.47878i) q^{26} +(6.97495 + 8.43127i) q^{27} +(1.95775 + 1.07628i) q^{28} +(0.297979 + 0.163815i) q^{29} +(0.270671 + 6.90205i) q^{30} +(4.71174 - 10.0130i) q^{31} +(0.309017 + 0.951057i) q^{32} +(-3.05628 - 16.0216i) q^{33} +(0.256738 + 0.404554i) q^{34} +(-4.43333 + 2.30251i) q^{35} +(-6.08288 + 2.40838i) q^{36} +(-3.37945 + 4.08505i) q^{37} +(0.901163 - 0.231379i) q^{38} +(-11.6537 - 14.0869i) q^{39} +(-2.15207 - 0.607118i) q^{40} +(-0.698377 + 0.179313i) q^{41} +(-5.03080 - 4.72424i) q^{42} +(0.123080 - 0.378802i) q^{43} +(5.23844 + 0.661769i) q^{44} +(3.08006 - 14.3011i) q^{45} +(-1.09566 + 1.02889i) q^{46} +(12.0959 - 1.52806i) q^{47} +(-0.193964 - 3.08297i) q^{48} +(-0.620757 + 1.91049i) q^{49} +(3.80251 - 3.24668i) q^{50} +(-0.457377 - 1.40766i) q^{51} +(5.50283 - 2.17873i) q^{52} +(1.22315 - 6.41197i) q^{53} +(10.8561 - 1.37145i) q^{54} +(-7.73871 + 8.91674i) q^{55} +(1.95775 - 1.07628i) q^{56} -2.87404 q^{57} +(0.297979 - 0.163815i) q^{58} +(-0.125821 - 0.0498162i) q^{59} +(5.97262 + 3.46977i) q^{60} +(4.07695 + 1.04678i) q^{61} +(-5.92955 - 9.34347i) q^{62} +(7.83172 + 12.3408i) q^{63} +(0.968583 + 0.248690i) q^{64} +(-2.78635 + 12.9374i) q^{65} +(-15.1651 - 6.00429i) q^{66} +(4.70962 - 2.58914i) q^{67} +0.479143 q^{68} +(4.06863 - 2.23675i) q^{69} +(-0.431419 + 4.97693i) q^{70} +(10.3241 - 1.30424i) q^{71} +(-1.22591 + 6.42642i) q^{72} +(-8.35969 + 3.30983i) q^{73} +(1.63832 + 5.04224i) q^{74} +(-13.8713 + 6.79295i) q^{75} +(0.287507 - 0.884856i) q^{76} +(-0.740689 - 11.7729i) q^{77} +(-18.1383 + 2.29140i) q^{78} +(-8.55999 + 8.03837i) q^{79} +(-1.66574 + 1.49174i) q^{80} +(-14.0631 - 1.77658i) q^{81} +(-0.222810 + 0.685740i) q^{82} +(1.90714 + 1.79092i) q^{83} +(-6.68445 + 1.71627i) q^{84} +(-0.595302 + 0.890790i) q^{85} +(-0.253883 - 0.306892i) q^{86} +(-1.01740 + 0.261225i) q^{87} +(3.36565 - 4.06837i) q^{88} +(5.41949 - 2.14573i) q^{89} +(-10.4245 - 10.2635i) q^{90} +(-7.08491 - 11.1640i) q^{91} +(0.281638 + 1.47640i) q^{92} +(10.5635 + 32.5110i) q^{93} +(5.19110 - 11.0317i) q^{94} +(1.28786 + 1.63388i) q^{95} +(-2.70697 - 1.48817i) q^{96} +(-2.44262 - 1.34284i) q^{97} +(1.28046 + 1.54782i) q^{98} +(27.9466 + 20.3044i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q - 5 q^{5} - 10 q^{7} - 10 q^{9}+O(q^{10}) $ 140 * q - 5 * q^5 - 10 * q^7 - 10 * q^9	$ 140 q - 5 q^{5} - 10 q^{7} - 10 q^{9} + 20 q^{10} - 10 q^{11} + 20 q^{12} + 20 q^{14} - 10 q^{15} - 5 q^{17} - 50 q^{18} + 40 q^{19} - 10 q^{20} - 5 q^{21} - 10 q^{22} + 10 q^{23} - 5 q^{24} - 5 q^{25} - 35 q^{26} + 30 q^{27} - 5 q^{28} - 10 q^{29} - 10 q^{30} + 35 q^{31} - 35 q^{32} - 55 q^{33} - 15 q^{34} - 25 q^{35} - 10 q^{36} - 25 q^{37} - 30 q^{39} + 25 q^{41} - 5 q^{42} - 45 q^{43} + 40 q^{44} - 5 q^{45} + 90 q^{47} - 5 q^{48} - 65 q^{49} + 30 q^{50} - 80 q^{51} - 50 q^{53} - 5 q^{54} - 35 q^{55} - 5 q^{56} + 40 q^{57} - 10 q^{58} + 45 q^{59} + 15 q^{60} + 45 q^{61} - 45 q^{62} - 75 q^{63} - 60 q^{65} + 15 q^{66} - 45 q^{67} + 10 q^{68} - 125 q^{69} - 15 q^{70} - 5 q^{71} - 5 q^{72} - 50 q^{73} + 20 q^{74} - 130 q^{75} - 5 q^{76} + 10 q^{77} + 10 q^{78} - 50 q^{79} - 5 q^{80} + 15 q^{81} + 40 q^{82} + 25 q^{83} - 50 q^{84} - 95 q^{85} - 10 q^{86} + 80 q^{87} - 10 q^{88} - 65 q^{89} - 10 q^{90} + 65 q^{91} - 25 q^{92} - 10 q^{93} - 35 q^{94} + 80 q^{95} - 40 q^{97} - 25 q^{98} + 90 q^{99}+O(q^{100}) $ 140 * q - 5 * q^5 - 10 * q^7 - 10 * q^9 + 20 * q^10 - 10 * q^11 + 20 * q^12 + 20 * q^14 - 10 * q^15 - 5 * q^17 - 50 * q^18 + 40 * q^19 - 10 * q^20 - 5 * q^21 - 10 * q^22 + 10 * q^23 - 5 * q^24 - 5 * q^25 - 35 * q^26 + 30 * q^27 - 5 * q^28 - 10 * q^29 - 10 * q^30 + 35 * q^31 - 35 * q^32 - 55 * q^33 - 15 * q^34 - 25 * q^35 - 10 * q^36 - 25 * q^37 - 30 * q^39 + 25 * q^41 - 5 * q^42 - 45 * q^43 + 40 * q^44 - 5 * q^45 + 90 * q^47 - 5 * q^48 - 65 * q^49 + 30 * q^50 - 80 * q^51 - 50 * q^53 - 5 * q^54 - 35 * q^55 - 5 * q^56 + 40 * q^57 - 10 * q^58 + 45 * q^59 + 15 * q^60 + 45 * q^61 - 45 * q^62 - 75 * q^63 - 60 * q^65 + 15 * q^66 - 45 * q^67 + 10 * q^68 - 125 * q^69 - 15 * q^70 - 5 * q^71 - 5 * q^72 - 50 * q^73 + 20 * q^74 - 130 * q^75 - 5 * q^76 + 10 * q^77 + 10 * q^78 - 50 * q^79 - 5 * q^80 + 15 * q^81 + 40 * q^82 + 25 * q^83 - 50 * q^84 - 95 * q^85 - 10 * q^86 + 80 * q^87 - 10 * q^88 - 65 * q^89 - 10 * q^90 + 65 * q^91 - 25 * q^92 - 10 * q^93 - 35 * q^94 + 80 * q^95 - 40 * q^97 - 25 * q^98 + 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/250\mathbb{Z}\right)^\times$.

$n$	$127$
$\chi(n)$	$e\left(\frac{17}{25}\right)$

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 $

$2$	0.535827	−	0.844328i	0.378887	−	0.597030i
$2$	0.535827	−	0.844328i	0.378887	−	0.597030i
$3$	−2.25183	+	2.11461i	−1.30009	+	1.22087i	−0.340251	+	0.940335i	$0.610512\pi$
$3$	−2.25183	+	2.11461i	−1.30009	+	1.22087i	−0.959844	+	0.280535i	$0.909488\pi$
$4$	−0.425779	−	0.904827i	−0.212890	−	0.452414i
$5$	2.21119	+	0.332605i	0.988876	+	0.148746i
$5$	2.21119	+	0.332605i	0.988876	+	0.148746i
$6$	0.578833	+	3.03435i	0.236307	+	1.23877i
$7$	−1.80742	+	1.31317i	−0.683141	+	0.496331i	−0.874398	−	0.485209i	$-0.838744\pi$
$7$	−1.80742	+	1.31317i	−0.683141	+	0.496331i	0.191257	+	0.981540i	$0.438744\pi$
$8$	−0.992115	−	0.125333i	−0.350766	−	0.0443120i
$9$	0.410795	−	6.52940i	0.136932	−	2.17647i
$10$	1.46564	−	1.68875i	0.463477	−	0.534031i
$11$	−2.82920	+	4.45811i	−0.853037	+	1.34417i	0.0845490	+	0.996419i	$0.473055\pi$
$11$	−2.82920	+	4.45811i	−0.853037	+	1.34417i	−0.937586	+	0.347752i	$0.886945\pi$
$12$	2.87214	+	1.13716i	0.829115	+	0.328270i
$13$	−0.371622	+	5.90677i	−0.103070	+	1.63824i	0.518638	+	0.854994i	$0.326439\pi$
$13$	−0.371622	+	5.90677i	−0.103070	+	1.63824i	−0.621708	+	0.783249i	$0.713561\pi$
$14$	0.140280	+	2.22969i	0.0374914	+	0.595909i
$15$	−5.68256	+	3.92684i	−1.46723	+	1.01391i
$16$	−0.637424	+	0.770513i	−0.159356	+	0.192628i
$17$	−0.204009	+	0.433542i	−0.0494795	+	0.105149i	−0.928038	−	0.372485i	$-0.878506\pi$
$17$	−0.204009	+	0.433542i	−0.0494795	+	0.105149i	0.878559	+	0.477635i	$0.158506\pi$
$18$	−5.29284	−	3.84547i	−1.24753	−	0.906386i
$19$	0.678227	+	0.636898i	0.155596	+	0.146114i	0.758435	−	0.651748i	$-0.225964\pi$
$19$	0.678227	+	0.636898i	0.155596	+	0.146114i	−0.602840	+	0.797862i	$0.705964\pi$
$20$	−0.640530	−	2.14236i	−0.143227	−	0.479047i
$21$	1.29317	−	6.77902i	0.282192	−	1.47930i
$22$	2.24815	+	4.77755i	0.479306	+	1.01858i
$23$	−1.45580	−	0.373786i	−0.303556	−	0.0779398i	0.0938398	−	0.995587i	$-0.470086\pi$
$23$	−1.45580	−	0.373786i	−0.303556	−	0.0779398i	−0.397395	+	0.917647i	$0.630086\pi$
$24$	2.49910	−	1.81571i	0.510127	−	0.370629i
$25$	4.77875	+	1.47091i	0.955750	+	0.294182i
$26$	4.78812	+	3.47878i	0.939029	+	0.682244i
$27$	6.97495	+	8.43127i	1.34233	+	1.62260i
$28$	1.95775	+	1.07628i	0.369981	+	0.203399i
$29$	0.297979	+	0.163815i	0.0553333	+	0.0304197i	0.509180	−	0.860660i	$-0.329949\pi$
$29$	0.297979	+	0.163815i	0.0553333	+	0.0304197i	−0.453847	+	0.891080i	$0.649949\pi$
$30$	0.270671	+	6.90205i	0.0494176	+	1.26014i
$31$	4.71174	−	10.0130i	0.846254	−	1.79838i	0.322288	−	0.946642i	$-0.395548\pi$
$31$	4.71174	−	10.0130i	0.846254	−	1.79838i	0.523966	−	0.851739i	$-0.324452\pi$
$32$	0.309017	+	0.951057i	0.0546270	+	0.168125i
$33$	−3.05628	−	16.0216i	−0.532030	−	2.78900i
$34$	0.256738	+	0.404554i	0.0440302	+	0.0693805i
$35$	−4.43333	+	2.30251i	−0.749369	+	0.389196i
$36$	−6.08288	+	2.40838i	−1.01381	+	0.401397i
$37$	−3.37945	+	4.08505i	−0.555578	+	0.671579i	−0.971285	−	0.237920i	$-0.923534\pi$
$37$	−3.37945	+	4.08505i	−0.555578	+	0.671579i	0.415707	+	0.909499i	$0.363534\pi$
$38$	0.901163	−	0.231379i	0.146188	−	0.0375347i
$39$	−11.6537	−	14.0869i	−1.86608	−	2.25570i
$40$	−2.15207	−	0.607118i	−0.340272	−	0.0959938i
$41$	−0.698377	+	0.179313i	−0.109068	+	0.0280039i	−0.302829	−	0.953045i	$-0.597931\pi$
$41$	−0.698377	+	0.179313i	−0.109068	+	0.0280039i	0.193761	+	0.981049i	$0.437931\pi$
$42$	−5.03080	−	4.72424i	−0.776270	−	0.728966i
$43$	0.123080	−	0.378802i	0.0187695	−	0.0577667i	−0.941233	−	0.337758i	$-0.890332\pi$
$43$	0.123080	−	0.378802i	0.0187695	−	0.0577667i	0.960003	+	0.279991i	$0.0903315\pi$
$44$	5.23844	+	0.661769i	0.789724	+	0.0997654i
$45$	3.08006	−	14.3011i	0.459148	−	2.13189i
$46$	−1.09566	+	1.02889i	−0.161546	+	0.151701i
$47$	12.0959	−	1.52806i	1.76436	−	0.222891i	0.824838	−	0.565369i	$-0.191266\pi$
$47$	12.0959	−	1.52806i	1.76436	−	0.222891i	0.939526	+	0.342478i	$0.111266\pi$
$48$	−0.193964	−	3.08297i	−0.0279963	−	0.444988i
$49$	−0.620757	+	1.91049i	−0.0886796	+	0.272928i
$50$	3.80251	−	3.24668i	0.537756	−	0.459150i
$51$	−0.457377	−	1.40766i	−0.0640456	−	0.197112i
$52$	5.50283	−	2.17873i	0.763106	−	0.302135i
$53$	1.22315	−	6.41197i	0.168012	−	0.880752i	−0.794035	−	0.607872i	$-0.792024\pi$
$53$	1.22315	−	6.41197i	0.168012	−	0.880752i	0.962048	−	0.272881i	$-0.0879764\pi$
$54$	10.8561	−	1.37145i	1.47733	−	0.186630i
$55$	−7.73871	+	8.91674i	−1.04349	+	1.20233i
$56$	1.95775	−	1.07628i	0.261616	−	0.143825i
$57$	−2.87404			−0.380676
$58$	0.297979	−	0.163815i	0.0391265	−	0.0215100i
$59$	−0.125821	−	0.0498162i	−0.0163805	−	0.00648552i	0.359920	−	0.932983i	$-0.382804\pi$
$59$	−0.125821	−	0.0498162i	−0.0163805	−	0.00648552i	−0.376301	+	0.926498i	$0.622804\pi$
$60$	5.97262	+	3.46977i	0.771063	+	0.447945i
$61$	4.07695	+	1.04678i	0.522000	+	0.134027i	0.500491	−	0.865742i	$-0.333153\pi$
$61$	4.07695	+	1.04678i	0.522000	+	0.134027i	0.0215094	+	0.999769i	$0.493153\pi$
$62$	−5.92955	−	9.34347i	−0.753053	−	1.18662i
$63$	7.83172	+	12.3408i	0.986704	+	1.55480i
$64$	0.968583	+	0.248690i	0.121073	+	0.0310862i
$65$	−2.78635	+	12.9374i	−0.345604	+	1.60469i
$66$	−15.1651	−	6.00429i	−1.86669	−	0.739077i
$67$	4.70962	−	2.58914i	0.575372	−	0.316313i	−0.167367	−	0.985895i	$-0.553526\pi$
$67$	4.70962	−	2.58914i	0.575372	−	0.316313i	0.742739	+	0.669581i	$0.233526\pi$
$68$	0.479143			0.0581047
$69$	4.06863	−	2.23675i	0.489805	−	0.269273i
$70$	−0.431419	+	4.97693i	−0.0515645	+	0.594857i
$71$	10.3241	−	1.30424i	1.22524	−	0.154784i	0.514037	−	0.857768i	$-0.328149\pi$
$71$	10.3241	−	1.30424i	1.22524	−	0.154784i	0.711206	+	0.702984i	$0.248149\pi$
$72$	−1.22591	+	6.42642i	−0.144474	+	0.757361i
$73$	−8.35969	+	3.30983i	−0.978427	+	0.387387i	−0.802261	−	0.596974i	$-0.796370\pi$
$73$	−8.35969	+	3.30983i	−0.978427	+	0.387387i	−0.176166	+	0.984360i	$0.556370\pi$
$74$	1.63832	+	5.04224i	0.190451	+	0.586149i
$75$	−13.8713	+	6.79295i	−1.60172	+	0.784382i
$76$	0.287507	−	0.884856i	0.0329793	−	0.101500i
$77$	−0.740689	−	11.7729i	−0.0844094	−	1.34165i
$78$	−18.1383	+	2.29140i	−2.05376	+	0.259450i
$79$	−8.55999	+	8.03837i	−0.963074	+	0.904387i	−0.995469	−	0.0950880i	$-0.969687\pi$
$79$	−8.55999	+	8.03837i	−0.963074	+	0.904387i	0.0323944	+	0.999475i	$0.489687\pi$
$80$	−1.66574	+	1.49174i	−0.186236	+	0.166782i
$81$	−14.0631	−	1.77658i	−1.56256	−	0.197398i
$82$	−0.222810	+	0.685740i	−0.0246053	+	0.0757273i
$83$	1.90714	+	1.79092i	0.209336	+	0.196579i	0.782122	−	0.623126i	$-0.214137\pi$
$83$	1.90714	+	1.79092i	0.209336	+	0.196579i	−0.572786	+	0.819705i	$0.694137\pi$
$84$	−6.68445	+	1.71627i	−0.729333	+	0.187261i
$85$	−0.595302	+	0.890790i	−0.0645696	+	0.0966198i
$86$	−0.253883	−	0.306892i	−0.0273769	−	0.0330930i
$87$	−1.01740	+	0.261225i	−0.109077	+	0.0280062i
$88$	3.36565	−	4.06837i	0.358779	−	0.433689i
$89$	5.41949	−	2.14573i	0.574464	−	0.227447i	−0.0628859	−	0.998021i	$-0.520030\pi$
$89$	5.41949	−	2.14573i	0.574464	−	0.227447i	0.637350	+	0.770574i	$0.280030\pi$
$90$	−10.4245	−	10.2635i	−1.09883	−	1.08187i
$91$	−7.08491	−	11.1640i	−0.742700	−	1.17031i
$92$	0.281638	+	1.47640i	0.0293628	+	0.153925i
$93$	10.5635	+	32.5110i	1.09538	+	3.37123i
$94$	5.19110	−	11.0317i	0.535422	−	1.13783i
$95$	1.28786	+	1.63388i	0.132131	+	0.167633i
$96$	−2.70697	−	1.48817i	−0.276279	−	0.151885i
$97$	−2.44262	−	1.34284i	−0.248011	−	0.136345i	0.352900	−	0.935661i	$-0.385195\pi$
$97$	−2.44262	−	1.34284i	−0.248011	−	0.136345i	−0.600911	+	0.799316i	$0.705195\pi$
$98$	1.28046	+	1.54782i	0.129346	+	0.156353i
$99$	27.9466	+	20.3044i	2.80874	+	2.04067i
$100$	−0.703775	−	4.95022i	−0.0703775	−	0.495022i
$101$	2.44796	−	1.77855i	0.243581	−	0.176972i	−0.459296	−	0.888283i	$-0.651898\pi$
$101$	2.44796	−	1.77855i	0.243581	−	0.176972i	0.702877	+	0.711311i	$0.251898\pi$
$102$	−1.43360	−	0.368087i	−0.141948	−	0.0364460i
$103$	−3.84504	−	8.17112i	−0.378863	−	0.805124i	−0.999774	−	0.0212438i	$-0.993237\pi$
$103$	−3.84504	−	8.17112i	−0.378863	−	0.805124i	0.620912	−	0.783881i	$-0.286763\pi$
$104$	1.10901	−	5.81362i	0.108747	−	0.570072i
$105$	5.11418	−	14.5596i	0.499093	−	1.42087i
$106$	−4.75841	−	4.46845i	−0.462178	−	0.434014i
$107$	2.11207	+	1.53451i	0.204181	+	0.148346i	0.685177	−	0.728377i	$-0.259725\pi$
$107$	2.11207	+	1.53451i	0.204181	+	0.148346i	−0.480996	+	0.876723i	$0.659725\pi$
$108$	4.65905	−	9.90098i	0.448317	−	0.952722i
$109$	−10.6633	+	12.8897i	−1.02136	+	1.23461i	−0.0495640	+	0.998771i	$0.515783\pi$
$109$	−10.6633	+	12.8897i	−1.02136	+	1.23461i	−0.971793	+	0.235837i	$0.924217\pi$
$110$	3.38205	+	11.3118i	0.322465	+	1.07854i
$111$	−1.02834	−	16.3451i	−0.0976061	−	1.55140i
$112$	0.140280	−	2.22969i	0.0132552	−	0.210686i
$113$	17.2030	+	6.81116i	1.61833	+	0.640740i	0.990487	−	0.137604i	$-0.0439400\pi$
$113$	17.2030	+	6.81116i	1.61833	+	0.640740i	0.627838	+	0.778344i	$0.283940\pi$
$114$	−1.53999	+	2.42663i	−0.144233	+	0.227275i
$115$	−3.09474	−	1.31072i	−0.288586	−	0.122225i
$116$	0.0213513	−	0.339368i	0.00198241	−	0.0315096i
$117$	38.4150	+	4.85294i	3.55147	+	0.448654i
$118$	−0.109480	+	0.0795416i	−0.0100784	+	0.00732240i
$119$	−0.200583	−	1.05149i	−0.0183874	−	0.0963901i
$120$	6.12991	−	3.18366i	0.559582	−	0.290627i
$121$	−7.18680	−	15.2727i	−0.653346	−	1.38843i
$122$	3.06837	−	2.88139i	0.277797	−	0.260869i
$123$	1.19345	−	1.88058i	0.107610	−	0.169566i
$124$	−11.0662			−0.993771
$125$	10.0775	+	4.84190i	0.901359	+	0.433072i
$126$	14.6161			1.30211
$127$	−7.58090	+	11.9456i	−0.672696	+	1.06000i	0.320911	+	0.947109i	$0.396011\pi$
$127$	−7.58090	+	11.9456i	−0.672696	+	1.06000i	−0.993607	+	0.112890i	$0.963989\pi$
$128$	0.728969	−	0.684547i	0.0644323	−	0.0605060i
$129$	0.523862	+	1.11326i	0.0461235	+	0.0980173i
$130$	9.43041	+	9.28480i	0.827102	+	0.814331i
$131$	0.501509	+	2.62900i	0.0438170	+	0.229697i	0.997459	−	0.0712478i	$-0.0226981\pi$
$131$	0.501509	+	2.62900i	0.0438170	+	0.229697i	−0.953642	+	0.300945i	$0.902698\pi$
$132$	−13.1955	+	9.58706i	−1.14852	+	0.834446i
$133$	−2.06220	−	0.260516i	−0.178815	−	0.0225896i
$134$	0.337461	−	5.36379i	0.0291522	−	0.463361i
$135$	12.6187	+	20.9631i	1.08604	+	1.80421i
$136$	0.256738	−	0.404554i	0.0220151	−	0.0346902i
$137$	−20.8632	−	8.26032i	−1.78246	−	0.705727i	−0.996127	−	0.0879282i	$-0.971975\pi$
$137$	−20.8632	−	8.26032i	−1.78246	−	0.705727i	−0.786336	−	0.617799i	$-0.788025\pi$
$138$	0.291532	−	4.63377i	0.0248168	−	0.394452i
$139$	−0.0579855	−	0.921654i	−0.00491827	−	0.0781737i	0.994802	−	0.101829i	$-0.0324695\pi$
$139$	−0.0579855	−	0.921654i	−0.00491827	−	0.0781737i	−0.999720	+	0.0236555i	$0.992470\pi$
$140$	3.97099	+	3.03103i	0.335610	+	0.256169i
$141$	−24.0066	+	29.0190i	−2.02172	+	2.44384i
$142$	4.43072	−	9.41576i	0.371818	−	0.790153i
$143$	−25.2817	−	18.3682i	−2.11416	−	1.53603i
$144$	4.76914	+	4.47852i	0.397428	+	0.373210i
$145$	0.604403	+	0.461336i	0.0501929	+	0.0383119i
$146$	−1.68476	+	8.83181i	−0.139432	+	0.730926i
$147$	−2.64211	−	5.61476i	−0.217917	−	0.463098i
$148$	5.13517	+	1.31849i	0.422108	+	0.108379i
$149$	8.02109	−	5.82766i	0.657113	−	0.477421i	−0.208574	−	0.978007i	$-0.566882\pi$
$149$	8.02109	−	5.82766i	0.657113	−	0.477421i	0.865687	+	0.500586i	$0.166882\pi$
$150$	−1.69715	+	15.3518i	−0.138572	+	1.25347i
$151$	16.1798	+	11.7553i	1.31669	+	0.956631i	0.999967	+	0.00811262i	$0.00258235\pi$
$151$	16.1798	+	11.7553i	1.31669	+	0.956631i	0.316722	+	0.948518i	$0.397418\pi$
$152$	−0.593055	−	0.716880i	−0.0481031	−	0.0581466i
$153$	2.74696	+	1.51015i	0.222079	+	0.122089i
$154$	−10.3371	−	5.68286i	−0.832986	−	0.457938i
$155$	13.7489	−	20.5734i	1.10434	−	1.65250i
$156$	−7.78429	+	16.5425i	−0.623242	+	1.32446i
$157$	−2.01468	−	6.20055i	−0.160789	−	0.494858i	0.837912	−	0.545805i	$-0.183776\pi$
$157$	−2.01468	−	6.20055i	−0.160789	−	0.494858i	−0.998701	+	0.0509472i	$0.983776\pi$
$158$	2.20035	+	11.5346i	0.175050	+	0.917645i
$159$	10.8045	+	17.0252i	0.856852	+	1.35018i
$160$	0.366970	+	2.20575i	0.0290115	+	0.174380i
$161$	3.12209	−	1.23612i	0.246055	−	0.0974202i
$162$	−9.03539	+	10.9219i	−0.709887	+	0.858106i
$163$	−6.90721	+	1.77347i	−0.541014	+	0.138909i	−0.509302	−	0.860588i	$-0.670096\pi$
$163$	−6.90721	+	1.77347i	−0.541014	+	0.138909i	−0.0317129	+	0.999497i	$0.510096\pi$
$164$	0.459602	+	0.555563i	0.0358889	+	0.0433822i
$165$	−1.42916	−	36.4433i	−0.111260	−	2.83711i
$166$	2.53402	−	0.650626i	0.196678	−	0.0504984i
$167$	−0.280539	−	0.263444i	−0.0217088	−	0.0203859i	0.673617	−	0.739081i	$-0.264740\pi$
$167$	−0.280539	−	0.263444i	−0.0217088	−	0.0203859i	−0.695326	+	0.718695i	$0.744740\pi$
$168$	−2.13261	+	6.56349i	−0.164534	+	0.506384i
$169$	−21.8543	−	2.76084i	−1.68110	−	0.212373i
$170$	0.433140	+	0.979940i	0.0332203	+	0.0751579i
$171$	4.43717	−	4.16678i	0.339319	−	0.318641i
$172$	−0.395155	+	0.0499197i	−0.0301303	+	0.00380634i
$173$	0.517106	+	8.21916i	0.0393148	+	0.624891i	0.967516	+	0.252811i	$0.0813552\pi$
$173$	0.517106	+	8.21916i	0.0393148	+	0.624891i	−0.928201	+	0.372080i	$0.878645\pi$
$174$	−0.324592	+	0.998993i	−0.0246073	+	0.0757334i
$175$	−10.5688	+	3.61675i	−0.798924	+	0.273401i
$176$	−1.63163	−	5.02165i	−0.122989	−	0.378521i
$177$	0.388670	−	0.153885i	0.0292142	−	0.0115667i
$178$	1.09221	−	5.72556i	0.0818645	−	0.429149i
$179$	5.12170	−	0.647021i	0.382814	−	0.0483606i	0.0684284	−	0.997656i	$-0.478202\pi$
$179$	5.12170	−	0.647021i	0.382814	−	0.0483606i	0.314386	+	0.949295i	$0.398202\pi$
$180$	−14.2515	+	3.30220i	−1.06224	+	0.246132i
$181$	9.94405	−	5.46679i	0.739136	−	0.406343i	−0.0672478	−	0.997736i	$-0.521422\pi$
$181$	9.94405	−	5.46679i	0.739136	−	0.406343i	0.806383	+	0.591393i	$0.201422\pi$
$182$	−13.2224			−0.980108
$183$	−11.3941	+	6.26398i	−0.842279	+	0.463047i
$184$	1.39747	+	0.553299i	0.103023	+	0.0407898i
$185$	−8.83132	+	7.90882i	−0.649292	+	0.581468i
$186$	33.1101	+	8.50123i	2.42775	+	0.623340i
$187$	−1.35560	−	2.13608i	−0.0991309	−	0.156205i
$188$	−6.53280	−	10.2941i	−0.476454	−	0.750771i
$189$	−23.6784	−	6.07957i	−1.72235	−	0.442224i
$190$	2.06960	−	0.211893i	0.150145	−	0.0153723i
$191$	9.55306	+	3.78232i	0.691235	+	0.273679i	0.687364	−	0.726313i	$-0.258768\pi$
$191$	9.55306	+	3.78232i	0.691235	+	0.273679i	0.00387121	+	0.999993i	$0.498768\pi$
$192$	−2.70697	+	1.48817i	−0.195358	+	0.107399i
$193$	−5.67962			−0.408828			−0.204414	−	0.978885i	$-0.565529\pi$
$193$	−5.67962			−0.408828			−0.204414	+	0.978885i	$0.565529\pi$
$194$	−2.44262	+	1.34284i	−0.175370	+	0.0964106i
$195$	−21.0832	−	35.0249i	−1.50980	−	2.50818i
$196$	1.99297	−	0.251771i	0.142355	−	0.0179836i
$197$	0.332125	−	1.74106i	0.0236629	−	0.124045i	−0.968496	−	0.249030i	$-0.919888\pi$
$197$	0.332125	−	1.74106i	0.0236629	−	0.124045i	0.992159	+	0.124985i	$0.0398882\pi$
$198$	32.1181	−	12.7164i	2.28253	−	0.903718i
$199$	6.09376	+	18.7547i	0.431975	+	1.32948i	0.896155	+	0.443742i	$0.146349\pi$
$199$	6.09376	+	18.7547i	0.431975	+	1.32948i	−0.464180	+	0.885741i	$0.653651\pi$
$200$	−4.55671	−	2.05825i	−0.322208	−	0.145540i
$201$	−5.13026	+	15.7893i	−0.361860	+	1.11369i
$202$	−0.189994	−	3.01987i	−0.0133680	−	0.212478i
$203$	−0.753691	+	0.0952133i	−0.0528987	+	0.00668266i
$204$	−1.07895	+	1.01320i	−0.0755416	+	0.0709383i
$205$	−1.60389	+	0.164211i	−0.112020	+	0.0114690i
$206$	−8.95938	−	1.13183i	−0.624230	−	0.0788585i
$207$	−3.03863	+	9.35196i	−0.211200	+	0.650006i
$208$	−4.31436	−	4.05146i	−0.299147	−	0.280918i
$209$	−4.75820	+	1.22170i	−0.329132	+	0.0845067i
$210$	−9.55277	−	12.1195i	−0.659204	−	0.836323i
$211$	4.48040	+	5.41587i	0.308443	+	0.372844i	0.901843	−	0.432064i	$-0.142215\pi$
$211$	4.48040	+	5.41587i	0.308443	+	0.372844i	−0.593400	+	0.804908i	$0.702215\pi$
$212$	−6.32252	+	1.62335i	−0.434232	+	0.111492i
$213$	−20.4901	+	24.7683i	−1.40396	+	1.69710i
$214$	2.42733	−	0.961047i	0.165929	−	0.0656958i
$215$	0.398145	−	0.796666i	0.0271533	−	0.0543322i
$216$	−5.86323	−	9.23898i	−0.398942	−	0.628633i
$217$	4.63260	+	24.2850i	0.314482	+	1.64857i
$218$	5.16945	+	15.9099i	0.350120	+	1.07756i
$219$	11.8256	−	25.1306i	0.799099	−	1.69817i
$220$	11.3631	+	3.20563i	0.766099	+	0.216123i
$221$	−2.48502	−	1.36615i	−0.167160	−	0.0918972i
$222$	−14.3516	−	7.88986i	−0.963216	−	0.529533i
$223$	−8.16345	−	9.86791i	−0.546665	−	0.660804i	0.422746	−	0.906248i	$-0.361066\pi$
$223$	−8.16345	−	9.86791i	−0.546665	−	0.660804i	−0.969411	+	0.245444i	$0.921066\pi$
$224$	−1.80742	−	1.31317i	−0.120763	−	0.0877398i
$225$	11.5672	−	30.5981i	0.771148	−	2.03987i
$226$	14.9687	−	10.8754i	0.995703	−	0.723421i
$227$	18.9984	+	4.87795i	1.26096	+	0.323761i	0.819272	−	0.573405i	$-0.194378\pi$
$227$	18.9984	+	4.87795i	1.26096	+	0.323761i	0.441693	+	0.897166i	$0.354378\pi$
$228$	1.22371	+	2.60051i	0.0810420	+	0.172223i
$229$	2.64251	−	13.8525i	0.174622	−	0.915400i	−0.781826	−	0.623497i	$-0.785711\pi$
$229$	2.64251	−	13.8525i	0.174622	−	0.915400i	0.956448	−	0.291903i	$-0.0942886\pi$
$230$	−2.76492	+	1.91065i	−0.182313	+	0.125985i
$231$	26.5630	+	24.9443i	1.74772	+	1.64122i
$232$	−0.275098	−	0.199870i	−0.0180610	−	0.0131221i
$233$	7.37380	−	15.6701i	0.483074	−	1.02658i	−0.503610	−	0.863931i	$-0.667995\pi$
$233$	7.37380	−	15.6701i	0.483074	−	1.02658i	0.986683	−	0.162653i	$-0.0520050\pi$
$234$	24.6812	−	29.8345i	1.61346	−	1.95034i
$235$	27.2545	+	0.644304i	1.77789	+	0.0420298i
$236$	0.00849708	+	0.135057i	0.000553113	+	0.00879148i
$237$	2.27764	−	36.2021i	0.147949	−	2.35158i
$238$	−0.995282	−	0.394060i	−0.0645145	−	0.0255431i
$239$	−8.04015	+	12.6693i	−0.520074	+	0.819506i	−0.998273	−	0.0587459i	$-0.981290\pi$
$239$	−8.04015	+	12.6693i	−0.520074	+	0.819506i	0.478199	+	0.878252i	$0.341290\pi$
$240$	0.596519	−	6.88155i	0.0385051	−	0.444202i
$241$	0.0210243	−	0.334171i	0.00135429	−	0.0215259i	−0.997292	−	0.0735498i	$-0.976567\pi$
$241$	0.0210243	−	0.334171i	0.00135429	−	0.0215259i	0.998646	+	0.0520239i	$0.0165672\pi$
$242$	−16.7461	−	2.11552i	−1.07648	−	0.135991i
$243$	8.86664	−	6.44199i	0.568795	−	0.413254i
$244$	−0.788724	−	4.13464i	−0.0504929	−	0.264693i
$245$	−2.00805	+	4.01800i	−0.128290	+	0.256701i
$246$	−0.948340	−	2.01533i	−0.0604640	−	0.128492i
$247$	−4.01405	+	3.76944i	−0.255408	+	0.239844i
$248$	−5.92955	+	9.34347i	−0.376526	+	0.593311i
$249$	−8.08165			−0.512154
$250$	9.48794	−	5.91430i	0.600070	−	0.374053i
$251$	2.07602			0.131037			0.0655185	−	0.997851i	$-0.479130\pi$
$251$	2.07602			0.131037			0.0655185	+	0.997851i	$0.479130\pi$
$252$	7.83172	−	12.3408i	0.493352	−	0.777398i
$253$	5.78514	−	5.43261i	0.363709	−	0.341545i
$254$	6.02394	+	12.8015i	0.377976	+	0.803240i
$255$	−0.543154	−	3.26474i	−0.0340136	−	0.204446i
$256$	−0.187381	−	0.982287i	−0.0117113	−	0.0613930i
$257$	−4.50802	+	3.27526i	−0.281202	+	0.204305i	−0.719442	−	0.694553i	$-0.755602\pi$
$257$	−4.50802	+	3.27526i	−0.281202	+	0.204305i	0.438239	+	0.898858i	$0.355602\pi$
$258$	1.22066	+	0.154205i	0.0759949	+	0.00960038i
$259$	0.743727	−	11.8212i	0.0462130	−	0.734534i
$260$	12.8925	−	2.98731i	0.799558	−	0.185265i
$261$	1.19202	−	1.87833i	0.0737844	−	0.116266i
$262$	2.48846	+	0.985251i	0.153738	+	0.0608690i
$263$	1.32090	−	20.9952i	0.0814504	−	1.29462i	−0.718912	−	0.695101i	$-0.755360\pi$
$263$	1.32090	−	20.9952i	0.0814504	−	1.29462i	0.800363	−	0.599516i	$-0.204640\pi$
$264$	1.02414	+	16.2783i	0.0630317	+	1.00186i
$265$	4.83727	−	13.7713i	0.297151	−	0.845963i
$266$	−1.32494	+	1.60158i	−0.0812374	+	0.0981991i
$267$	−7.66639	+	16.2919i	−0.469175	+	0.997048i
$268$	−4.34798	−	3.15899i	−0.265595	−	0.192966i
$269$	14.3096	+	13.4376i	0.872469	+	0.819303i	0.984678	−	0.174382i	$-0.0557927\pi$
$269$	14.3096	+	13.4376i	0.872469	+	0.819303i	−0.112209	+	0.993685i	$0.535793\pi$
$270$	24.4611	+	0.578267i	1.48866	+	0.0351922i
$271$	−1.48521	+	7.78576i	−0.0902203	+	0.472951i	0.908288	+	0.418346i	$0.137390\pi$
$271$	−1.48521	+	7.78576i	−0.0902203	+	0.472951i	−0.998508	+	0.0546053i	$0.982610\pi$
$272$	−0.204009	−	0.433542i	−0.0123699	−	0.0262873i
$273$	39.5616	+	10.1577i	2.39437	+	0.614771i
$274$	−18.1535	+	13.1893i	−1.09669	+	0.796793i
$275$	−20.0775	+	17.1427i	−1.21072	+	1.03374i
$276$	−3.75621	−	2.72904i	−0.226097	−	0.164269i
$277$	−6.03129	−	7.29058i	−0.362385	−	0.438048i	0.557535	−	0.830153i	$-0.311747\pi$
$277$	−6.03129	−	7.29058i	−0.362385	−	0.438048i	−0.919921	+	0.392105i	$0.871747\pi$
$278$	−0.809248	−	0.444888i	−0.0485355	−	0.0266826i
$279$	−63.4430	−	34.8781i	−3.79823	−	2.08810i
$280$	4.68695	−	1.72871i	0.280099	−	0.103310i
$281$	6.91256	−	14.6899i	0.412369	−	0.876328i	−0.585475	−	0.810690i	$-0.699092\pi$
$281$	6.91256	−	14.6899i	0.412369	−	0.876328i	0.997844	−	0.0656373i	$-0.0209080\pi$
$282$	11.6382	+	35.8186i	0.693042	+	2.13296i
$283$	−6.22433	−	32.6291i	−0.369998	−	1.93960i	−0.341138	−	0.940013i	$-0.610812\pi$
$283$	−6.22433	−	32.6291i	−0.369998	−	1.93960i	−0.0288600	−	0.999583i	$-0.509188\pi$
$284$	−5.57589	−	8.78619i	−0.330868	−	0.521365i
$285$	−6.35506	−	0.955920i	−0.376441	−	0.0566238i
$286$	−29.0554	+	11.5038i	−1.71808	+	0.680236i
$287$	1.02679	−	1.24118i	0.0606098	−	0.0732646i
$288$	6.33677	−	1.62701i	0.373398	−	0.0958722i
$289$	10.6899	+	12.9218i	0.628816	+	0.760108i
$290$	0.713374	−	0.263118i	0.0418908	−	0.0154508i
$291$	8.33996	−	2.14134i	0.488897	−	0.125527i
$292$	6.55421	+	6.15481i	0.383556	+	0.360183i
$293$	6.39458	−	19.6805i	0.373575	−	1.14975i	−0.570860	−	0.821048i	$-0.693390\pi$
$293$	6.39458	−	19.6805i	0.373575	−	1.14975i	0.944435	−	0.328699i	$-0.106610\pi$
$294$	−6.15641	−	0.777736i	−0.359049	−	0.0453585i
$295$	−0.261646	−	0.152002i	−0.0152336	−	0.00884990i
$296$	3.86479	−	3.62928i	0.224637	−	0.210948i
$297$	−57.3211	+	7.24134i	−3.32611	+	0.420185i
$298$	−0.622544	−	9.89505i	−0.0360630	−	0.573205i
$299$	2.74888	−	8.46018i	0.158972	−	0.489265i
$300$	12.0526	+	9.65885i	0.695855	+	0.557654i
$301$	0.274973	+	0.846280i	0.0158492	+	0.0487787i
$302$	18.5949	−	7.36222i	1.07001	−	0.423648i
$303$	−1.75146	+	9.18146i	−0.100619	+	0.527461i
$304$	−0.923056	+	0.116609i	−0.0529409	+	0.00668799i
$305$	8.66676	+	3.67066i	0.496258	+	0.210181i
$306$	2.74696	−	1.51015i	0.157033	−	0.0863298i
$307$	12.3482			0.704750			0.352375	−	0.935859i	$-0.385374\pi$
$307$	12.3482			0.704750			0.352375	+	0.935859i	$0.385374\pi$
$308$	−10.3371	+	5.68286i	−0.589010	+	0.323811i
$309$	25.9371	+	10.2692i	1.47551	+	0.584196i
$310$	−10.0037	−	22.6324i	−0.568171	−	1.28543i
$311$	−23.4737	−	6.02701i	−1.33107	−	0.341761i	−0.484851	−	0.874597i	$-0.661126\pi$
$311$	−23.4737	−	6.02701i	−1.33107	−	0.341761i	−0.846218	+	0.532836i	$0.821126\pi$
$312$	9.79623	+	15.4364i	0.554602	+	0.873913i
$313$	2.26314	+	3.56613i	0.127920	+	0.201570i	0.902251	−	0.431211i	$-0.141914\pi$
$313$	2.26314	+	3.56613i	0.127920	+	0.201570i	−0.774331	+	0.632781i	$0.781914\pi$
$314$	−6.31482	−	1.62137i	−0.356366	−	0.0914992i
$315$	13.2128	+	29.8928i	0.744458	+	1.68427i
$316$	10.9180	+	4.32274i	0.614186	+	0.243173i
$317$	−3.36127	+	1.84788i	−0.188788	+	0.103787i	−0.573345	−	0.819314i	$-0.694354\pi$
$317$	−3.36127	+	1.84788i	−0.188788	+	0.103787i	0.384557	+	0.923101i	$0.374354\pi$
$318$	20.1641			1.13075
$319$	−1.57335	+	0.864957i	−0.0880907	+	0.0484283i
$320$	2.05901	+	0.872057i	0.115102	+	0.0487495i
$321$	−8.00089	+	1.01075i	−0.446566	+	0.0564144i
$322$	0.629207	−	3.29842i	0.0350643	−	0.183814i
$323$	−0.414486	+	0.164107i	−0.0230626	+	0.00913115i
$324$	4.38027	+	13.4811i	0.243348	+	0.748949i
$325$	−10.4642	+	27.6803i	−0.580450	+	1.53543i
$326$	−2.20368	+	6.78222i	−0.122050	+	0.375633i
$327$	−3.24476	−	51.5740i	−0.179436	−	2.85205i
$328$	0.715344	−	0.0903690i	0.0394983	−	0.00498979i
$329$	−19.8557	+	18.6458i	−1.09468	+	1.02798i
$330$	−31.5359	−	18.3206i	−1.73599	−	1.00852i
$331$	−34.6842	−	4.38163i	−1.90642	−	0.240836i	−0.918454	−	0.395529i	$-0.870561\pi$
$331$	−34.6842	−	4.38163i	−1.90642	−	0.240836i	−0.987963	+	0.154692i	$0.950561\pi$
$332$	0.808455	−	2.48817i	0.0443697	−	0.136556i
$333$	25.2847	+	23.7439i	1.38559	+	1.30116i
$334$	−0.372754	+	0.0957069i	−0.0203962	+	0.00523685i
$335$	11.2750	−	4.15864i	0.616021	−	0.227211i
$336$	4.39903	+	5.31752i	0.239987	+	0.290094i
$337$	26.1648	−	6.71798i	1.42529	−	0.365952i	0.544220	−	0.838942i	$-0.316826\pi$
$337$	26.1648	−	6.71798i	1.42529	−	0.365952i	0.881068	+	0.472991i	$0.156826\pi$
$338$	−14.0412	+	16.9729i	−0.763740	+	0.923203i
$339$	−53.1412	+	21.0401i	−2.88624	+	1.14274i
$340$	1.05948	+	0.159366i	0.0574583	+	0.00864281i
$341$	31.3084	+	49.3342i	1.69545	+	2.67160i
$342$	−1.14057	−	5.97910i	−0.0616752	−	0.323312i
$343$	−6.21945	−	19.1415i	−0.335819	−	1.03354i
$344$	−0.169586	+	0.360389i	−0.00914347	+	0.0194309i
$345$	9.74048	−	3.59263i	0.524410	−	0.193421i
$346$	7.21675	+	3.96744i	0.387975	+	0.213291i
$347$	−0.344299	−	0.189280i	−0.0184829	−	0.0101611i	0.472485	−	0.881338i	$-0.343357\pi$
$347$	−0.344299	−	0.189280i	−0.0184829	−	0.0101611i	−0.490968	+	0.871177i	$0.663357\pi$
$348$	0.669552	+	0.809349i	0.0358918	+	0.0433857i
$349$	−13.0271	−	9.46473i	−0.697324	−	0.506636i	0.181736	−	0.983347i	$-0.441829\pi$
$349$	−13.0271	−	9.46473i	−0.697324	−	0.506636i	−0.879060	+	0.476712i	$0.841829\pi$
$350$	−2.60930	+	10.8615i	−0.139473	+	0.580569i
$351$	−52.3936	+	38.0662i	−2.79656	+	2.03182i
$352$	−5.11419	−	1.31310i	−0.272587	−	0.0699885i
$353$	8.81483	+	18.7325i	0.469166	+	0.997029i	0.989696	+	0.143185i	$0.0457345\pi$
$353$	8.81483	+	18.7325i	0.469166	+	0.997029i	−0.520530	+	0.853844i	$0.674266\pi$
$354$	0.0783301	−	0.410621i	0.00416320	−	0.0218243i
$355$	23.2623	+	0.549927i	1.23464	+	0.0291871i
$356$	−4.24902	−	3.99009i	−0.225197	−	0.211474i
$357$	2.67517	+	1.94363i	0.141585	+	0.102868i
$358$	2.19805	−	4.67109i	0.116170	−	0.246875i
$359$	11.1768	−	13.5105i	0.589890	−	0.713055i	−0.388121	−	0.921609i	$-0.626876\pi$
$359$	11.1768	−	13.5105i	0.589890	−	0.713055i	0.978011	+	0.208554i	$0.0668756\pi$
$360$	−4.84818	+	13.8023i	−0.255521	+	0.727446i
$361$	−1.13867	−	18.0986i	−0.0599298	−	0.952557i
$362$	0.712527	−	11.3253i	0.0374496	−	0.595244i
$363$	48.4793	+	19.1943i	2.54450	+	1.00744i
$364$	−7.08491	+	11.1640i	−0.371350	+	0.585154i
$365$	−19.5857	+	4.53821i	−1.02516	+	0.237541i
$366$	−0.816431	+	12.9768i	−0.0426755	+	0.678308i
$367$	−5.28707	−	0.667912i	−0.275983	−	0.0348647i	−0.0138763	−	0.999904i	$-0.504417\pi$
$367$	−5.28707	−	0.667912i	−0.275983	−	0.0348647i	−0.262106	+	0.965039i	$0.584417\pi$
$368$	1.21597	−	0.883454i	0.0633868	−	0.0460532i
$369$	0.883914	+	4.63364i	0.0460147	+	0.241218i
$370$	1.94558	+	11.6943i	0.101146	+	0.607957i
$371$	6.20926	+	13.1953i	0.322369	+	0.685068i
$372$	24.9191	−	23.4006i	1.29200	−	1.21326i
$373$	−6.44850	+	10.1612i	−0.333891	+	0.526128i	−0.969246	−	0.246092i	$-0.920853\pi$
$373$	−6.44850	+	10.1612i	−0.333891	+	0.526128i	0.635356	+	0.772220i	$0.280853\pi$
$374$	−2.52991			−0.130819
$375$	−32.9315	+	10.4068i	−1.70058	+	0.537407i
$376$	−12.1920			−0.628755
$377$	−1.07835	+	1.69921i	−0.0555381	+	0.0875140i
$378$	−17.8206	+	16.7347i	−0.916595	+	0.860740i
$379$	7.11276	+	15.1154i	0.365358	+	0.776425i	0.999993	+	0.00361347i	$0.00115021\pi$
$379$	7.11276	+	15.1154i	0.365358	+	0.776425i	−0.634636	+	0.772812i	$0.718850\pi$
$380$	0.930041	−	1.86096i	0.0477101	−	0.0954653i
$381$	−8.18935	−	42.9301i	−0.419553	−	2.19937i
$382$	8.31231	−	6.03924i	0.425295	−	0.308995i
$383$	−7.24182	−	0.914855i	−0.370040	−	0.0467469i	−0.0618855	−	0.998083i	$-0.519711\pi$
$383$	−7.24182	−	0.914855i	−0.370040	−	0.0467469i	−0.308154	+	0.951336i	$0.599711\pi$
$384$	−0.193964	+	3.08297i	−0.00989817	+	0.157327i
$385$	2.27793	−	26.2785i	0.116094	−	1.33928i
$386$	−3.04329	+	4.79546i	−0.154899	+	0.244082i
$387$	−2.42279	−	0.959249i	−0.123157	−	0.0487613i
$388$	−0.175023	+	2.78191i	−0.00888544	+	0.141230i
$389$	0.0630117	+	1.00154i	0.00319482	+	0.0507802i	0.999301	−	0.0373801i	$-0.0119012\pi$
$389$	0.0630117	+	1.00154i	0.00319482	+	0.0507802i	−0.996106	+	0.0881603i	$0.971901\pi$
$390$	−40.8694	−	0.966162i	−2.06950	−	0.0489235i
$391$	0.459049	−	0.554895i	0.0232151	−	0.0280623i
$392$	0.855310	−	1.81763i	0.0431997	−	0.0918040i
$393$	−6.68862	−	4.85956i	−0.337396	−	0.245133i
$394$	−1.29206	−	1.21333i	−0.0650933	−	0.0611267i
$395$	−21.6014	+	14.9273i	−1.08688	+	0.751073i
$396$	6.47287	−	33.9320i	0.325274	−	1.70515i
$397$	6.82415	+	14.5021i	0.342494	+	0.727837i	0.999664	−	0.0259051i	$-0.00824676\pi$
$397$	6.82415	+	14.5021i	0.342494	+	0.727837i	−0.657170	+	0.753742i	$0.728247\pi$
$398$	19.1003	+	4.90412i	0.957411	+	0.245821i
$399$	5.19460	−	3.77410i	0.260056	−	0.188941i
$400$	−4.17944	+	2.74450i	−0.208972	+	0.137225i
$401$	2.42717	+	1.76344i	0.121207	+	0.0880621i	0.646737	−	0.762713i	$-0.276133\pi$
$401$	2.42717	+	1.76344i	0.121207	+	0.0880621i	−0.525530	+	0.850775i	$0.676133\pi$
$402$	10.5824	+	12.7919i	0.527803	+	0.638004i
$403$	57.3933	+	31.5522i	2.85896	+	1.57173i
$404$	−2.65157	−	1.45771i	−0.131920	−	0.0725239i
$405$	−30.5053	−	8.60581i	−1.51582	−	0.427626i
$406$	−0.323456	+	0.687380i	−0.0160529	+	0.0341141i
$407$	−8.65047	−	26.6234i	−0.428788	−	1.31967i
$408$	0.277344	+	1.45389i	0.0137306	+	0.0719781i
$409$	6.77039	+	10.6684i	0.334774	+	0.527520i	0.969460	−	0.245251i	$-0.0788704\pi$
$409$	6.77039	+	10.6684i	0.334774	+	0.527520i	−0.634686	+	0.772771i	$0.718870\pi$
$410$	−0.720757	+	1.44220i	−0.0355957	+	0.0712249i
$411$	64.4477	−	25.5167i	3.17897	−	1.25864i
$412$	−5.75631	+	6.95819i	−0.283593	+	0.342805i
$413$	0.292829	−	0.0751858i	0.0144092	−	0.00369965i
$414$	6.26794	+	7.57663i	0.308052	+	0.372371i
$415$	3.62138	+	4.59440i	0.177767	+	0.225530i
$416$	−5.73251	+	1.47186i	−0.281059	+	0.0721638i
$417$	2.07951	+	1.95279i	0.101834	+	0.0956286i
$418$	−1.51806	+	4.67210i	−0.0742507	+	0.228520i
$419$	15.6314	+	1.97471i	0.763644	+	0.0964707i	0.497502	−	0.867463i	$-0.334251\pi$
$419$	15.6314	+	1.97471i	0.763644	+	0.0964707i	0.266142	+	0.963934i	$0.414251\pi$
$420$	−15.3514	+	1.57173i	−0.749074	+	0.0766927i
$421$	−13.2081	+	12.4032i	−0.643722	+	0.604495i	−0.936069	−	0.351817i	$-0.885564\pi$
$421$	−13.2081	+	12.4032i	−0.643722	+	0.604495i	0.292347	+	0.956312i	$0.405564\pi$
$422$	6.97349	−	0.880956i	0.339464	−	0.0428843i
$423$	−5.00841	−	79.6064i	−0.243517	−	3.87060i
$424$	−2.01714	+	6.20811i	−0.0979609	+	0.301493i
$425$	−1.61261	+	1.77171i	−0.0782231	+	0.0859405i
$426$	9.93342	+	30.5719i	0.481276	+	1.48121i
$427$	−8.74338	+	3.46175i	−0.423122	+	0.167526i
$428$	0.489188	−	2.56441i	0.0236458	−	0.123956i
$429$	95.7715	−	12.0988i	4.62389	−	0.584133i
$430$	−0.459311	−	0.763040i	−0.0221499	−	0.0367971i
$431$	−3.94682	+	2.16978i	−0.190111	+	0.104515i	−0.573967	−	0.818879i	$-0.694596\pi$
$431$	−3.94682	+	2.16978i	−0.190111	+	0.104515i	0.383855	+	0.923393i	$0.374596\pi$
$432$	−10.9424			−0.526467
$433$	27.2919	−	15.0038i	1.31156	−	0.721038i	0.336230	−	0.941780i	$-0.390848\pi$
$433$	27.2919	−	15.0038i	1.31156	−	0.721038i	0.975332	+	0.220742i	$0.0708479\pi$
$434$	22.9867	+	9.10110i	1.10340	+	0.436867i
$435$	−2.33656	+	0.239225i	−0.112029	+	0.0114699i
$436$	16.2031	+	4.16026i	0.775990	+	0.199240i
$437$	−0.749300	−	1.18071i	−0.0358439	−	0.0564809i
$438$	−14.8820	−	23.4503i	−0.711091	−	1.12050i
$439$	28.1575	+	7.22962i	1.34389	+	0.345051i	0.851056	−	0.525075i	$-0.175963\pi$
$439$	28.1575	+	7.22962i	1.34389	+	0.345051i	0.492829	+	0.870126i	$0.335963\pi$
$440$	8.79525	−	7.87651i	0.419297	−	0.375498i
$441$	12.2194	+	4.83799i	0.581874	+	0.230380i
$442$	−2.48502	+	1.36615i	−0.118200	+	0.0649811i
$443$	−17.3079			−0.822322			−0.411161	−	0.911563i	$-0.634877\pi$
$443$	−17.3079			−0.822322			−0.411161	+	0.911563i	$0.634877\pi$
$444$	−14.3516	+	7.88986i	−0.681097	+	0.374436i
$445$	12.6972	−	2.94207i	0.601905	−	0.139467i
$446$	−12.7060	+	1.60513i	−0.601644	+	0.0760053i
$447$	−5.73890	+	30.0844i	−0.271441	+	1.42294i
$448$	−2.07721	+	0.822426i	−0.0981390	+	0.0388560i
$449$	−0.672017	−	2.06826i	−0.0317144	−	0.0976070i	0.933946	−	0.357413i	$-0.116341\pi$
$449$	−0.672017	−	2.06826i	−0.0317144	−	0.0976070i	−0.965661	+	0.259806i	$0.916341\pi$
$450$	−19.6368	−	26.1618i	−0.925687	−	1.23328i
$451$	1.17646	−	3.62076i	0.0553971	−	0.170495i
$452$	−1.16177	−	18.4658i	−0.0546451	−	0.868559i
$453$	−61.2919	+	7.74296i	−2.87974	+	0.363796i
$454$	14.2984	−	13.4271i	0.671058	−	0.630165i
$455$	−11.9529	−	27.0423i	−0.560360	−	1.26776i
$456$	2.85138	+	0.360213i	0.133528	+	0.0168685i
$457$	−7.04970	+	21.6967i	−0.329771	+	1.01493i	0.639470	+	0.768816i	$0.279154\pi$
$457$	−7.04970	+	21.6967i	−0.329771	+	1.01493i	−0.969241	+	0.246115i	$0.920846\pi$
$458$	−10.2801	−	9.65370i	−0.480360	−	0.451088i
$459$	−5.07826	+	1.30388i	−0.237033	+	0.0608597i
$460$	0.131699	+	3.35828i	0.00614048	+	0.156581i
$461$	−6.57370	−	7.94624i	−0.306168	−	0.370093i	0.594879	−	0.803815i	$-0.297200\pi$
$461$	−6.57370	−	7.94624i	−0.306168	−	0.370093i	−0.901047	+	0.433722i	$0.857200\pi$
$462$	35.2944	−	9.06206i	1.64204	−	0.421605i
$463$	−8.34297	+	10.0849i	−0.387731	+	0.468686i	−0.927878	−	0.372885i	$-0.878369\pi$
$463$	−8.34297	+	10.0849i	−0.387731	+	0.468686i	0.540147	+	0.841571i	$0.318369\pi$
$464$	−0.316161	+	0.125177i	−0.0146774	+	0.00581119i
$465$	12.5445	+	75.4015i	0.581738	+	3.49666i
$466$	−9.27964	−	14.6224i	−0.429871	−	0.677369i
$467$	−5.07120	−	26.5841i	−0.234667	−	1.23017i	−0.883206	−	0.468986i	$-0.844620\pi$
$467$	−5.07120	−	26.5841i	−0.234667	−	1.23017i	0.648539	−	0.761182i	$-0.275380\pi$
$468$	−11.9652	−	36.8252i	−0.553093	−	1.70224i
$469$	−5.11230	+	10.8642i	−0.236064	+	0.501662i
$470$	15.1477	−	22.6665i	0.698712	−	1.04553i
$471$	17.6484	+	9.70232i	0.813198	+	0.447059i
$472$	0.118586	+	0.0651930i	0.00545835	+	0.00300075i
$473$	1.34052	+	1.62041i	0.0616373	+	0.0745067i
$474$	−29.3460	−	21.3211i	−1.34791	−	0.979311i
$475$	2.30426	+	4.04118i	0.105727	+	0.185422i
$476$	−0.866015	+	0.629196i	−0.0396937	+	0.0288392i
$477$	−41.3638	−	10.6204i	−1.89392	−	0.486276i
$478$	6.38887	+	13.5770i	0.292220	+	0.621000i
$479$	−2.73039	+	14.3132i	−0.124755	+	0.653988i	0.863886	+	0.503688i	$0.168024\pi$
$479$	−2.73039	+	14.3132i	−0.124755	+	0.653988i	−0.988640	+	0.150300i	$0.951976\pi$
$480$	−5.49065	−	4.19097i	−0.250613	−	0.191291i
$481$	−22.8736	−	21.4797i	−1.04295	−	0.979391i
$482$	−0.270885	−	0.196809i	−0.0123385	−	0.00896442i
$483$	−4.41650	+	9.38555i	−0.200958	+	0.427057i
$484$	−10.7592	+	13.0056i	−0.489054	+	0.591165i
$485$	−4.95448	−	3.78172i	−0.224971	−	0.171719i
$486$	−0.688170	−	10.9381i	−0.0312160	−	0.496164i
$487$	−1.16769	+	18.5599i	−0.0529131	+	0.841029i	0.878654	+	0.477459i	$0.158442\pi$
$487$	−1.16769	+	18.5599i	−0.0529131	+	0.841029i	−0.931567	+	0.363570i	$0.881558\pi$
$488$	−3.91361	−	1.54951i	−0.177161	−	0.0701429i
$489$	11.8037	−	18.5996i	0.533780	−	0.841103i
$490$	2.31654	+	3.84841i	0.104651	+	0.173853i
$491$	1.46014	−	23.2083i	0.0658954	−	1.04738i	−0.816645	−	0.577140i	$-0.804168\pi$
$491$	1.46014	−	23.2083i	0.0658954	−	1.04738i	0.882540	−	0.470237i	$-0.155832\pi$
$492$	−2.20974	−	0.279155i	−0.0996229	−	0.0125853i
$493$	−0.131811	+	0.0957665i	−0.00593648	+	0.00431311i
$494$	1.03181	+	5.40894i	0.0464234	+	0.243360i
$495$	55.0419	+	54.1920i	2.47395	+	2.43575i
$496$	4.71174	+	10.0130i	0.211563	+	0.449595i
$497$	−16.9473	+	15.9146i	−0.760190	+	0.713866i
$498$	−4.33036	+	6.82356i	−0.194048	+	0.305771i
$499$	−28.3008			−1.26692			−0.633459	−	0.773776i	$-0.718365\pi$
$499$	−28.3008			−1.26692			−0.633459	+	0.773776i	$0.718365\pi$
$500$	0.0902877	−	11.1800i	0.00403779	−	0.499984i
$501$	1.18881			0.0531120
$502$	1.11239	−	1.75284i	0.0496482	−	0.0782330i
$503$	−19.7612	+	18.5570i	−0.881107	+	0.827414i	−0.985944	−	0.167075i	$-0.946568\pi$
$503$	−19.7612	+	18.5570i	−0.881107	+	0.827414i	0.104837	+	0.994489i	$0.466568\pi$
$504$	−6.22325	−	13.2251i	−0.277206	−	0.589092i
$505$	6.00447	−	3.11851i	0.267195	−	0.138772i
$506$	−1.48707	−	7.79550i	−0.0661084	−	0.346552i
$507$	55.0503	−	39.9964i	2.44487	−	1.77630i
$508$	14.0365	+	1.77322i	0.622768	+	0.0786739i
$509$	0.145526	−	2.31307i	0.00645032	−	0.102525i	−0.993484	−	0.113970i	$-0.963643\pi$
$509$	0.145526	−	2.31307i	0.00645032	−	0.102525i	0.999935	+	0.0114452i	$0.00364319\pi$
$510$	−3.04755	−	1.29073i	−0.134948	−	0.0571547i
$511$	10.7631	−	16.9599i	0.476132	−	0.750264i
$512$	−0.929776	−	0.368125i	−0.0410907	−	0.0162690i
$513$	−0.639253	+	10.1606i	−0.0282237	+	0.448603i
$514$	0.349882	+	5.56122i	0.0154326	+	0.245295i
$515$	−5.78436	−	19.3468i	−0.254889	−	0.852522i
$516$	0.784261	−	0.948009i	0.0345252	−	0.0417338i
$517$	−27.4094	+	58.2480i	−1.20546	+	2.56174i
$518$	−9.58246	−	6.96207i	−0.421029	−	0.305896i
$519$	−18.5447	−	17.4147i	−0.814024	−	0.764419i
$520$	4.38587	−	12.4862i	0.192333	−	0.547555i
$521$	−0.227918	+	1.19479i	−0.00998526	+	0.0523446i	−0.986931	−	0.161143i	$-0.948482\pi$
$521$	−0.227918	+	1.19479i	−0.00998526	+	0.0523446i	0.976946	+	0.213487i	$0.0684821\pi$
$522$	−0.947206	−	2.01292i	−0.0414581	−	0.0881029i
$523$	20.9684	+	5.38378i	0.916886	+	0.235416i	0.677512	−	0.735511i	$-0.263058\pi$
$523$	20.9684	+	5.38378i	0.916886	+	0.235416i	0.239373	+	0.970928i	$0.423058\pi$
$524$	2.16526	−	1.57315i	0.0945897	−	0.0687235i
$525$	16.1510	−	30.4931i	0.704889	−	1.33083i
$526$	−17.0190	−	12.3650i	−0.742065	−	0.539142i
$527$	3.37980	+	4.08548i	0.147226	+	0.177966i
$528$	14.2930	+	7.85763i	0.622022	+	0.341960i
$529$	−18.1754	−	9.99202i	−0.790235	−	0.434436i
$530$	−9.03554	−	11.4633i	−0.392479	−	0.497933i
$531$	−0.376956	+	0.801073i	−0.0163585	+	0.0347636i
$532$	0.642319	+	1.97685i	0.0278480	+	0.0857075i
$533$	−0.799626	−	4.19179i	−0.0346357	−	0.181567i
$534$	9.64785	+	15.2026i	0.417503	+	0.657880i
$535$	4.15980	+	4.09557i	0.179844	+	0.177067i
$536$	−4.99699	+	1.97845i	−0.215837	+	0.0854560i
$537$	−10.1650	+	12.2874i	−0.438652	+	0.530239i
$538$	19.0132	−	4.88175i	0.819715	−	0.210467i
$539$	−6.76095	−	8.17258i	−0.291215	−	0.352018i
$540$	13.5952	−	20.3434i	0.585043	−	0.875439i
$541$	−36.7879	+	9.44553i	−1.58164	+	0.406095i	−0.934409	−	0.356202i	$-0.884072\pi$
$541$	−36.7879	+	9.44553i	−1.58164	+	0.406095i	−0.647227	+	0.762297i	$0.724072\pi$
$542$	5.77792	+	5.42583i	0.248183	+	0.233059i
$543$	−10.8322	+	33.3381i	−0.464854	+	1.43067i
$544$	−0.475365	−	0.0600526i	−0.0203811	−	0.00257473i
$545$	−27.8657	+	24.9549i	−1.19364	+	1.06895i
$546$	29.7746	−	27.9602i	1.27423	−	1.19658i
$547$	26.2019	−	3.31007i	1.12031	−	0.141528i	0.456711	−	0.889615i	$-0.349027\pi$
$547$	26.2019	−	3.31007i	1.12031	−	0.141528i	0.663601	+	0.748087i	$0.269027\pi$
$548$	1.40895	+	22.3947i	0.0601875	+	0.956652i
$549$	8.50966	−	26.1900i	0.363183	−	1.11776i
$550$	3.71598	+	26.1375i	0.158450	+	1.11451i
$551$	0.0977638	+	0.300886i	0.00416488	+	0.0128182i
$552$	−4.31689	+	1.70918i	−0.183739	+	0.0727474i
$553$	4.91578	−	25.7694i	0.209040	−	1.09583i
$554$	−9.38737	+	1.18590i	−0.398831	+	0.0503841i
$555$	3.16258	−	36.4841i	0.134244	−	1.54866i
$556$	−0.809248	+	0.444888i	−0.0343198	+	0.0188675i
$557$	27.3117			1.15723			0.578616	−	0.815600i	$-0.303593\pi$
$557$	27.3117			1.15723			0.578616	+	0.815600i	$0.303593\pi$
$558$	−63.4430	+	34.8781i	−2.68576	+	1.47651i
$559$	2.19175	+	0.867777i	0.0927013	+	0.0367031i
$560$	1.05179	−	4.88361i	0.0444463	−	0.206370i
$561$	7.56953	+	1.94353i	0.319586	+	0.0820557i
$562$	−8.69919	−	13.7077i	−0.366953	−	0.578225i
$563$	−18.4917	−	29.1383i	−0.779333	−	1.22803i	−0.969213	−	0.246225i	$-0.920810\pi$
$563$	−18.4917	−	29.1383i	−0.779333	−	1.22803i	0.189880	−	0.981807i	$-0.439190\pi$
$564$	36.4787	+	9.36613i	1.53603	+	0.394385i
$565$	35.7738	+	20.7826i	1.50502	+	0.874331i
$566$	−30.8848	−	12.2282i	−1.29818	−	0.513988i
$567$	27.7509	−	15.2562i	1.16543	−	0.640699i
$568$	−10.4061			−0.436632
$569$	16.3589	−	8.99337i	0.685800	−	0.377022i	−0.100440	−	0.994943i	$-0.532025\pi$
$569$	16.3589	−	8.99337i	0.685800	−	0.377022i	0.786240	+	0.617921i	$0.212025\pi$
$570$	−4.21232	+	4.85354i	−0.176435	+	0.203293i
$571$	6.41884	−	0.810888i	0.268620	−	0.0339346i	0.0101306	−	0.999949i	$-0.496775\pi$
$571$	6.41884	−	0.810888i	0.268620	−	0.0339346i	0.258489	+	0.966014i	$0.416775\pi$
$572$	−5.85564	+	30.6963i	−0.244836	+	1.28348i
$573$	−29.5100	+	11.6838i	−1.23280	+	0.488099i
$574$	−0.497780	−	1.53201i	−0.0207769	−	0.0639448i
$575$	−6.40710	−	3.92758i	−0.267195	−	0.163791i
$576$	2.02168	−	6.22210i	0.0842368	−	0.259254i
$577$	1.21567	+	19.3226i	0.0506091	+	0.804409i	0.938699	+	0.344738i	$0.112032\pi$
$577$	1.21567	+	19.3226i	0.0506091	+	0.804409i	−0.888090	+	0.459670i	$0.847968\pi$
$578$	16.6382	−	2.10189i	0.692057	−	0.0874271i
$579$	12.7895	−	12.0102i	0.531515	−	0.499125i
$580$	0.160087	−	0.743308i	0.00664727	−	0.0308642i
$581$	−5.79879	−	0.732557i	−0.240574	−	0.0303916i
$582$	2.66078	−	8.18905i	0.110293	−	0.339447i
$583$	25.1248	+	23.5937i	1.04056	+	0.977152i
$584$	8.70860	−	2.23599i	0.360364	−	0.0925258i
$585$	83.3288	+	23.5078i	3.44522	+	0.971928i
$586$	−13.1904	−	15.9445i	−0.544890	−	0.658659i
$587$	1.02699	−	0.263685i	0.0423883	−	0.0108835i	−0.227436	−	0.973793i	$-0.573034\pi$
$587$	1.02699	−	0.263685i	0.0423883	−	0.0108835i	0.269824	+	0.962910i	$0.413034\pi$
$588$	−3.95544	+	4.78130i	−0.163119	+	0.197177i
$589$	9.57286	−	3.79016i	0.394443	−	0.156171i
$590$	−0.268537	+	0.139468i	−0.0110555	+	0.00574182i
$591$	2.93377	+	4.62289i	0.120679	+	0.190160i
$592$	−0.993445	−	5.20782i	−0.0408303	−	0.214040i
$593$	−5.60684	−	17.2561i	−0.230245	−	0.708622i	−0.997717	−	0.0675391i	$-0.978485\pi$
$593$	−5.60684	−	17.2561i	−0.230245	−	0.708622i	0.767471	−	0.641083i	$-0.221515\pi$
$594$	−24.6001	+	52.2779i	−1.00936	+	2.14499i
$595$	−0.0937958	−	2.39177i	−0.00384525	−	0.0980529i
$596$	−8.68824	−	4.77640i	−0.355884	−	0.195649i
$597$	−53.3809	−	29.3464i	−2.18473	−	1.20107i
$598$	−5.67024	−	6.85414i	−0.231873	−	0.280287i
$599$	−17.5592	−	12.7575i	−0.717450	−	0.521258i	0.168118	−	0.985767i	$-0.446231\pi$
$599$	−17.5592	−	12.7575i	−0.717450	−	0.521258i	−0.885569	+	0.464509i	$0.846231\pi$
$600$	14.6133	−	5.00085i	0.596586	−	0.204159i
$601$	24.3855	−	17.7171i	0.994703	−	0.722694i	0.0337572	−	0.999430i	$-0.489253\pi$
$601$	24.3855	−	17.7171i	0.994703	−	0.722694i	0.960946	+	0.276736i	$0.0892527\pi$
$602$	0.861875	+	0.221292i	0.0351274	+	0.00901919i
$603$	−14.9708	−	31.8146i	−0.609659	−	1.29559i
$604$	3.74749	−	19.6450i	0.152483	−	0.799345i
$605$	−10.8116	−	36.1613i	−0.439555	−	1.47017i
$606$	6.81369	+	6.39848i	0.276787	+	0.259920i
$607$	−24.7609	−	17.9898i	−1.00501	−	0.730185i	−0.0418563	−	0.999124i	$-0.513327\pi$
$607$	−24.7609	−	17.9898i	−1.00501	−	0.730185i	−0.963157	+	0.268939i	$0.913327\pi$
$608$	−0.396142	+	0.841844i	−0.0160657	+	0.0341413i
$609$	1.49584	−	1.80816i	0.0606147	−	0.0732705i
$610$	7.74312	−	5.35076i	0.313510	−	0.216646i
$611$	4.53082	+	72.0154i	0.183297	+	2.91343i
$612$	0.196830	−	3.12852i	0.00795637	−	0.126463i
$613$	−21.8250	−	8.64112i	−0.881502	−	0.349011i	−0.116616	−	0.993177i	$-0.537205\pi$
$613$	−21.8250	−	8.64112i	−0.881502	−	0.349011i	−0.764886	+	0.644166i	$0.777205\pi$
$614$	6.61651	−	10.4259i	0.267020	−	0.420757i
$615$	3.26444	−	3.76137i	0.131635	−	0.151673i
$616$	−0.740689	+	11.7729i	−0.0298432	+	0.474344i
$617$	32.1866	+	4.06612i	1.29578	+	0.163696i	0.742810	−	0.669502i	$-0.233493\pi$
$617$	32.1866	+	4.06612i	1.29578	+	0.163696i	0.552975	+	0.833198i	$0.313493\pi$
$618$	22.5684	−	16.3969i	0.907833	−	0.659579i
$619$	−5.89375	−	30.8961i	−0.236890	−	1.24182i	−0.879601	−	0.475711i	$-0.842191\pi$
$619$	−5.89375	−	30.8961i	−0.236890	−	1.24182i	0.642712	−	0.766108i	$-0.277809\pi$
$620$	−24.4694	−	3.68066i	−0.982715	−	0.147819i
$621$	−7.00265	−	14.8814i	−0.281007	−	0.597170i
$622$	−17.6666	+	16.5900i	−0.708366	+	0.665200i
$623$	−6.97760	+	10.9949i	−0.279552	+	0.440503i
$624$	18.2825			0.731884
$625$	20.6729	+	14.0582i	0.826914	+	0.562328i
$626$	4.22363			0.168810
$627$	8.13125	−	12.8128i	0.324731	−	0.511694i
$628$	−4.75261	+	4.46300i	−0.189650	+	0.178093i
$629$	−1.08160	−	2.29852i	−0.0431263	−	0.0916481i
$630$	32.3191	+	4.86140i	1.28762	+	0.193683i
$631$	−6.14607	−	32.2188i	−0.244671	−	1.28261i	−0.866389	−	0.499370i	$-0.833565\pi$
$631$	−6.14607	−	32.2188i	−0.244671	−	1.28261i	0.621718	−	0.783241i	$-0.286435\pi$
$632$	9.49997	−	6.90213i	0.377889	−	0.274552i
$633$	−21.5415	−	2.72133i	−0.856199	−	0.108163i
$634$	−0.240847	+	3.82816i	−0.00956527	+	0.152036i
$635$	−20.7360	+	23.8926i	−0.822883	+	0.948147i
$636$	10.8045	−	17.0252i	0.428426	−	0.675091i
$637$	−11.0542	−	4.37665i	−0.437982	−	0.173409i
$638$	−0.112736	+	1.79189i	−0.00446327	+	0.0709416i
$639$	−4.27479	−	67.9458i	−0.169108	−	2.68789i
$640$	1.83957	−	1.27121i	0.0727155	−	0.0502489i
$641$	21.0729	−	25.4727i	0.832329	−	1.00611i	−0.167466	−	0.985878i	$-0.553559\pi$
$641$	21.0729	−	25.4727i	0.832329	−	1.00611i	0.999795	−	0.0202352i	$-0.00644150\pi$
$642$	−3.43369	+	7.29696i	−0.135517	+	0.287988i
$643$	4.12895	+	2.99986i	0.162830	+	0.118303i	0.666216	−	0.745759i	$-0.267913\pi$
$643$	4.12895	+	2.99986i	0.162830	+	0.118303i	−0.503386	+	0.864061i	$0.667913\pi$
$644$	−2.44780	−	2.29864i	−0.0964569	−	0.0905790i
$645$	0.788083	+	2.63588i	0.0310307	+	0.103788i
$646$	−0.0835330	+	0.437895i	−0.00328656	+	0.0172288i
$647$	−8.64311	−	18.3675i	−0.339796	−	0.722102i	0.659773	−	0.751465i	$-0.270652\pi$
$647$	−8.64311	−	18.3675i	−0.339796	−	0.722102i	−0.999569	+	0.0293623i	$0.990652\pi$
$648$	13.7295	+	3.52514i	0.539346	+	0.138481i
$649$	0.578061	−	0.419986i	0.0226909	−	0.0164859i
$650$	17.7643	+	23.6671i	0.696772	+	0.928299i
$651$	−61.7850	−	44.8894i	−2.42155	−	1.75936i
$652$	4.54563	+	5.49472i	0.178021	+	0.215190i
$653$	−14.0916	−	7.74691i	−0.551446	−	0.303160i	0.181562	−	0.983379i	$-0.441885\pi$
$653$	−14.0916	−	7.74691i	−0.551446	−	0.303160i	−0.733009	+	0.680219i	$0.761885\pi$
$654$	−45.2840	−	24.8951i	−1.77075	−	0.973476i
$655$	0.234513	+	5.98003i	0.00916320	+	0.233659i
$656$	0.306999	−	0.652407i	0.0119863	−	0.0254722i
$657$	18.1771	+	55.9434i	0.709156	+	2.18256i
$658$	5.10392	+	26.7557i	0.198971	+	1.04304i
$659$	7.67488	+	12.0937i	0.298971	+	0.471103i	0.960291	−	0.279001i	$-0.0900034\pi$
$659$	7.67488	+	12.0937i	0.298971	+	0.471103i	−0.661320	+	0.750104i	$0.730003\pi$
$660$	−32.3664	+	16.8100i	−1.25986	+	0.654327i
$661$	12.2384	−	4.84552i	0.476018	−	0.188469i	−0.117850	−	0.993031i	$-0.537600\pi$
$661$	12.2384	−	4.84552i	0.476018	−	0.188469i	0.593868	+	0.804563i	$0.297600\pi$
$662$	−22.2843	+	26.9370i	−0.866102	+	1.04694i
$663$	8.48471	−	2.17850i	0.329519	−	0.0846060i
$664$	−1.66764	−	2.01583i	−0.0647169	−	0.0782293i
$665$	−4.47327	−	1.26195i	−0.173466	−	0.0489363i
$666$	33.5958	−	8.62594i	1.30181	−	0.334248i
$667$	−0.372566	−	0.349863i	−0.0144258	−	0.0135467i
$668$	−0.118923	+	0.366009i	−0.00460129	+	0.0141613i
$669$	39.2495	+	4.95836i	1.51747	+	0.191701i
$670$	2.53022	−	11.7481i	0.0977508	−	0.453870i
$671$	−16.2012	+	15.2140i	−0.625441	+	0.587328i
$672$	6.84685	−	0.864958i	0.264123	−	0.0333665i
$673$	−1.08113	−	17.1840i	−0.0416744	−	0.662396i	−0.962307	−	0.271966i	$-0.912326\pi$
$673$	−1.08113	−	17.1840i	−0.0416744	−	0.662396i	0.920632	−	0.390430i	$-0.127674\pi$
$674$	8.34763	−	25.6914i	0.321539	−	0.989594i
$675$	20.9299	+	50.5504i	0.805593	+	1.94569i
$676$	6.80703	+	20.9499i	0.261809	+	0.805765i
$677$	−12.1359	+	4.80496i	−0.466422	+	0.184669i	−0.589567	−	0.807719i	$-0.700702\pi$
$677$	−12.1359	+	4.80496i	−0.466422	+	0.184669i	0.123146	+	0.992389i	$0.460702\pi$
$678$	−10.7098	+	56.1425i	−0.411306	+	2.15614i
$679$	6.17824	−	0.780493i	0.237099	−	0.0299526i
$680$	0.702254	−	0.809155i	0.0269302	−	0.0310297i
$681$	−53.0960	+	29.1898i	−2.03464	+	1.11855i
$682$	58.4301			2.23741
$683$	−28.5958	+	15.7207i	−1.09419	+	0.601536i	−0.923426	−	0.383776i	$-0.874623\pi$
$683$	−28.5958	+	15.7207i	−1.09419	+	0.601536i	−0.170764	+	0.985312i	$0.554623\pi$
$684$	−5.65947	−	2.24074i	−0.216395	−	0.0856769i
$685$	−43.3851	−	25.2044i	−1.65766	−	0.963010i
$686$	−19.4942	−	5.00527i	−0.744294	−	0.191102i
$687$	23.3422	+	36.7814i	0.890560	+	1.40330i
$688$	0.213417	+	0.336292i	0.00813647	+	0.0128210i
$689$	37.4195	+	9.60769i	1.42557	+	0.366024i
$690$	2.18585	−	10.1492i	0.0832138	−	0.386373i
$691$	26.8610	+	10.6350i	1.02184	+	0.404575i	0.818484	−	0.574529i	$-0.194815\pi$
$691$	26.8610	+	10.6350i	1.02184	+	0.404575i	0.203357	+	0.979105i	$0.434815\pi$
$692$	7.21675	−	3.96744i	0.274339	−	0.150819i
$693$	−77.1743			−2.93161
$694$	−0.344299	+	0.189280i	−0.0130694	+	0.00718497i
$695$	0.178330	−	2.05724i	0.00676442	−	0.0780356i
$696$	1.04212	−	0.131650i	0.0395015	−	0.00499020i
$697$	0.0647359	−	0.339357i	0.00245205	−	0.0128541i
$698$	−14.9716	+	5.92768i	−0.566683	+	0.224366i
$699$	16.5316	+	50.8791i	0.625284	+	1.92443i
$700$	7.77250	+	8.02297i	0.293773	+	0.303240i
$701$	−6.54292	+	20.1371i	−0.247123	+	0.760566i	0.748157	+	0.663522i	$0.230939\pi$
$701$	−6.54292	+	20.1371i	−0.247123	+	0.760566i	−0.995280	+	0.0970444i	$0.969061\pi$
$702$	4.06644	+	64.6342i	0.153478	+	2.43946i
$703$	−4.89379	+	0.618230i	−0.184573	+	0.0233170i
$704$	−3.84901	+	3.61446i	−0.145065	+	0.136225i
$705$	−62.7350	+	56.1818i	−2.36274	+	2.11593i
$706$	20.5396	+	2.59475i	0.773017	+	0.0976548i
$707$	−2.08896	+	6.42917i	−0.0785636	+	0.241794i
$708$	−0.304727	−	0.286158i	−0.0114524	−	0.0107545i
$709$	−13.9160	+	3.57301i	−0.522625	+	0.134187i	−0.500781	−	0.865574i	$-0.666954\pi$
$709$	−13.9160	+	3.57301i	−0.522625	+	0.134187i	−0.0218442	+	0.999761i	$0.506954\pi$
$710$	12.9289	−	19.3464i	0.485213	−	0.726056i
$711$	48.9693	+	59.1937i	1.83649	+	2.21994i
$712$	−5.64568	+	1.44956i	−0.211581	+	0.0543247i
$713$	−10.6021	+	12.8157i	−0.397051	+	0.479952i
$714$	3.07449	−	1.21728i	0.115060	−	0.0455554i
$715$	−49.7933	−	49.0244i	−1.86216	−	1.83341i
$716$	−2.76616	−	4.35877i	−0.103376	−	0.162895i
$717$	−8.68546	−	45.5308i	−0.324364	−	1.70038i
$718$	−5.41842	−	16.6762i	−0.202213	−	0.622349i
$719$	17.9961	−	38.2437i	0.671143	−	1.42625i	−0.221353	−	0.975194i	$-0.571047\pi$
$719$	17.9961	−	38.2437i	0.671143	−	1.42625i	0.892495	−	0.451057i	$-0.148953\pi$
$720$	9.05590	+	11.4891i	0.337494	+	0.428174i
$721$	17.6797	+	9.71948i	0.658425	+	0.361972i
$722$	−15.8913	−	8.73630i	−0.591412	−	0.325131i
$723$	0.659298	+	0.796955i	0.0245196	+	0.0296391i
$724$	−9.18047	−	6.67000i	−0.341189	−	0.247889i
$725$	1.18301	+	1.22113i	0.0439358	+	0.0453517i
$726$	42.1828	−	30.6476i	1.56555	−	1.13744i
$727$	3.44703	+	0.885047i	0.127843	+	0.0328246i	0.312069	−	0.950059i	$-0.398978\pi$
$727$	3.44703	+	0.885047i	0.127843	+	0.0328246i	−0.184226	+	0.982884i	$0.558978\pi$
$728$	5.62982	+	11.9640i	0.208655	+	0.443414i
$729$	1.62443	−	8.51557i	0.0601641	−	0.315391i
$730$	−6.66283	+	18.9685i	−0.246602	+	0.702055i
$731$	0.139117	+	0.130639i	0.00514543	+	0.00483188i
$732$	10.5192	+	7.64265i	0.388801	+	0.282481i
$733$	8.41204	−	17.8765i	0.310706	−	0.660283i	−0.687095	−	0.726567i	$-0.741114\pi$
$733$	8.41204	−	17.8765i	0.310706	−	0.660283i	0.997801	+	0.0662844i	$0.0211145\pi$
$734$	−3.39689	+	4.10613i	−0.125381	+	0.151560i
$735$	−3.97471	−	13.2941i	−0.146609	−	0.490360i
$736$	−0.0943755	−	1.50006i	−0.00347873	−	0.0552928i
$737$	−1.78182	+	28.3212i	−0.0656342	+	1.04323i
$738$	4.38594	+	1.73652i	0.161449	+	0.0639220i
$739$	−10.4661	+	16.4919i	−0.385002	+	0.606665i	−0.980459	−	0.196721i	$-0.936971\pi$
$739$	−10.4661	+	16.4919i	−0.385002	+	0.606665i	0.595458	+	0.803387i	$0.296971\pi$
$740$	10.9163	+	4.62341i	0.401291	+	0.169960i
$741$	1.06806	−	16.9763i	0.0392361	−	0.623640i
$742$	14.4683	+	1.82777i	0.531147	+	0.0670995i
$743$	10.9783	−	7.97619i	0.402754	−	0.292618i	−0.367908	−	0.929862i	$-0.619926\pi$
$743$	10.9783	−	7.97619i	0.402754	−	0.292618i	0.770662	+	0.637244i	$0.219926\pi$
$744$	−6.40545	−	33.5786i	−0.234835	−	1.23105i
$745$	19.6745	−	10.2182i	0.720817	−	0.374367i
$746$	5.12412	+	10.8893i	0.187607	+	0.398686i
$747$	12.4771	−	11.7168i	0.456513	−	0.428694i
$748$	−1.35560	+	2.13608i	−0.0495655	+	0.0781027i
$749$	−5.83246			−0.213113
$750$	−8.85881	+	33.3813i	−0.323478	+	1.21891i
$751$	−22.4648			−0.819754			−0.409877	−	0.912141i	$-0.634428\pi$
$751$	−22.4648			−0.819754			−0.409877	+	0.912141i	$0.634428\pi$
$752$	−6.53280	+	10.2941i	−0.238227	+	0.375385i
$753$	−4.67484	+	4.38996i	−0.170361	+	0.159979i
$754$	0.856883	+	1.82097i	0.0312058	+	0.0663158i
$755$	31.8667	+	31.3747i	1.15975	+	1.14184i
$756$	4.58080	+	24.0134i	0.166602	+	0.873358i
$757$	−20.5587	+	14.9368i	−0.747220	+	0.542887i	−0.894964	−	0.446139i	$-0.852799\pi$
$757$	−20.5587	+	14.9368i	−0.747220	+	0.542887i	0.147744	+	0.989026i	$0.452799\pi$
$758$	16.5735	+	2.09373i	0.601978	+	0.0760475i
$759$	−1.53931	+	24.4666i	−0.0558734	+	0.888082i
$760$	−1.07292	−	1.78241i	−0.0389189	−	0.0646549i
$761$	21.0982	−	33.2455i	0.764811	−	1.20515i	−0.209028	−	0.977910i	$-0.567030\pi$
$761$	21.0982	−	33.2455i	0.764811	−	1.20515i	0.973839	−	0.227239i	$-0.0729699\pi$
$762$	−40.6351	−	16.0886i	−1.47206	−	0.582828i
$763$	2.34670	−	37.2998i	0.0849564	−	1.35034i
$764$	−0.645146	−	10.2543i	−0.0233406	−	0.370988i
$765$	5.57178	+	4.25290i	0.201448	+	0.153764i
$766$	−4.65280	+	5.62427i	−0.168113	+	0.203213i
$767$	0.341011	−	0.724685i	0.0123132	−	0.0261669i
$768$	2.49910	+	1.81571i	0.0901786	+	0.0655186i
$769$	15.3726	+	14.4358i	0.554349	+	0.520568i	0.910307	−	0.413934i	$-0.135846\pi$
$769$	15.3726	+	14.4358i	0.554349	+	0.520568i	−0.355958	+	0.934502i	$0.615846\pi$
$770$	−20.9671	−	16.0041i	−0.755603	−	0.576747i
$771$	3.22538	−	16.9080i	0.116159	−	0.608928i
$772$	2.41826	+	5.13907i	0.0870352	+	0.184959i
$773$	29.4712	+	7.56691i	1.06000	+	0.272163i	0.738157	−	0.674629i	$-0.235696\pi$
$773$	29.4712	+	7.56691i	1.06000	+	0.272163i	0.321847	+	0.946792i	$0.395696\pi$
$774$	−2.10811	+	1.53163i	−0.0757746	+	0.0550535i
$775$	37.2444	−	40.9189i	1.33786	−	1.46985i
$776$	2.25506	+	1.63840i	0.0809520	+	0.0588150i
$777$	23.3225	+	28.1920i	0.836689	+	1.01138i
$778$	0.879394	+	0.483451i	0.0315278	+	0.0173325i
$779$	−0.587862	−	0.323180i	−0.0210623	−	0.0115791i
$780$	−22.7147	+	33.9895i	−0.813316	+	1.21702i
$781$	−23.3945	+	49.7159i	−0.837122	+	1.77897i
$782$	−0.222543	−	0.684916i	−0.00795811	−	0.0244925i
$783$	0.697217	+	3.65494i	0.0249165	+	0.130617i
$784$	−1.07638	−	1.69610i	−0.0384420	−	0.0605748i
$785$	−2.39251	−	14.3807i	−0.0853924	−	0.513269i
$786$	−7.68701	+	3.04350i	−0.274186	+	0.108558i
$787$	14.0678	−	17.0051i	0.501464	−	0.606166i	−0.457669	−	0.889123i	$-0.651315\pi$
$787$	14.0678	−	17.0051i	0.501464	−	0.606166i	0.959133	+	0.282957i	$0.0913154\pi$
$788$	−1.71677	+	0.440792i	−0.0611574	+	0.0157026i
$789$	41.4221	+	50.0707i	1.47467	+	1.78256i
$790$	1.02892	+	26.2371i	0.0366072	+	0.933474i
$791$	−40.0374	+	10.2798i	−1.42356	+	0.365509i
$792$	−25.1814	−	23.6469i	−0.894782	−	0.840256i
$793$	−7.69820	+	23.6926i	−0.273371	+	0.841349i
$794$	15.9010	+	2.00877i	0.564307	+	0.0712886i
$795$	18.2282	+	41.2395i	0.646486	+	1.46262i
$796$	14.3751	−	13.4991i	0.509513	−	0.478465i
$797$	11.6919	−	1.47704i	0.414150	−	0.0523193i	0.0845022	−	0.996423i	$-0.473070\pi$
$797$	11.6919	−	1.47704i	0.414150	−	0.0523193i	0.329648	+	0.944104i	$0.393070\pi$
$798$	−0.403171	−	6.40821i	−0.0142721	−	0.226848i
$799$	−1.80519	+	5.55581i	−0.0638631	+	0.196550i
$800$	0.0777977	+	4.99939i	0.00275056	+	0.176755i
$801$	−11.7840	−	36.2674i	−0.416367	−	1.28145i
$802$	2.78947	−	1.10443i	0.0984995	−	0.0389987i
$803$	8.89565	−	46.6326i	0.313921	−	1.64563i
$804$	16.4709	−	2.08076i	0.580885	−	0.0733829i
$805$	7.31469	−	1.69488i	0.257809	−	0.0597368i
$806$	57.3933	−	31.5522i	2.02159	−	1.11138i
$807$	−60.6379			−2.13455
$808$	−2.65157	+	1.45771i	−0.0932819	+	0.0512821i
$809$	−45.5644	−	18.0402i	−1.60196	−	0.634260i	−0.614046	−	0.789270i	$-0.710459\pi$
$809$	−45.5644	−	18.0402i	−1.60196	−	0.634260i	−0.987913	+	0.155010i	$0.950459\pi$
$810$	−23.6117	+	21.1452i	−0.829629	+	0.742967i
$811$	−16.9266	−	4.34601i	−0.594373	−	0.152609i	−0.0604921	−	0.998169i	$-0.519267\pi$
$811$	−16.9266	−	4.34601i	−0.594373	−	0.152609i	−0.533881	+	0.845560i	$0.679267\pi$
$812$	0.407057	+	0.641420i	0.0142849	+	0.0225094i
$813$	−13.1194	−	20.6729i	−0.460117	−	0.725029i
$814$	−27.1141	−	6.96171i	−0.950347	−	0.244008i
$815$	−15.8630	+	1.62411i	−0.555658	+	0.0568901i
$816$	1.37617	+	0.544863i	0.0481754	+	0.0190740i
$817$	0.324734	−	0.178524i	0.0113610	−	0.00624577i
$818$	12.6354			0.441786
$819$	−75.8048	+	41.6740i	−2.64883	+	1.45621i
$820$	0.831485	+	1.38132i	0.0290367	+	0.0482379i
$821$	−41.7002	+	5.26796i	−1.45535	+	0.183853i	−0.812867	−	0.582449i	$-0.802094\pi$
$821$	−41.7002	+	5.26796i	−1.45535	+	0.183853i	−0.642480	+	0.766302i	$0.722094\pi$
$822$	12.9884	−	68.0875i	0.453022	−	2.37482i
$823$	8.61682	−	3.41164i	0.300364	−	0.118922i	−0.213109	−	0.977028i	$-0.568359\pi$
$823$	8.61682	−	3.41164i	0.300364	−	0.118922i	0.513472	+	0.858106i	$0.328359\pi$
$824$	2.79061	+	8.58860i	0.0972153	+	0.299198i
$825$	8.96107	−	81.0586i	0.311985	−	2.82210i
$826$	0.0934244	−	0.287531i	0.00325065	−	0.0100045i
$827$	0.391913	+	6.22928i	0.0136282	+	0.216613i	0.998947	+	0.0458870i	$0.0146114\pi$
$827$	0.391913	+	6.22928i	0.0136282	+	0.216613i	−0.985318	+	0.170726i	$0.945389\pi$
$828$	9.75569	−	1.23243i	0.339034	−	0.0428299i
$829$	−40.0612	+	37.6200i	−1.39138	+	1.30660i	−0.491224	+	0.871033i	$0.663450\pi$
$829$	−40.0612	+	37.6200i	−1.39138	+	1.30660i	−0.900159	+	0.435562i	$0.856550\pi$
$830$	5.81961	−	0.595831i	0.202002	−	0.0206816i
$831$	28.9982	+	3.66332i	1.00593	+	0.127079i
$832$	−1.82890	+	5.62878i	−0.0634057	+	0.195143i
$833$	−0.701639	−	0.658883i	−0.0243103	−	0.0228289i
$834$	2.76305	−	0.709431i	0.0956767	−	0.0245656i
$835$	−0.532704	−	0.675835i	−0.0184350	−	0.0233882i
$836$	3.13137	+	3.78518i	0.108301	+	0.130913i
$837$	117.286	−	30.1140i	4.05400	−	1.04089i
$838$	10.0430	−	12.1399i	0.346930	−	0.419367i
$839$	7.89243	−	3.12483i	0.272477	−	0.107881i	−0.227913	−	0.973682i	$-0.573190\pi$
$839$	7.89243	−	3.12483i	0.272477	−	0.107881i	0.500390	+	0.865800i	$0.333190\pi$
$840$	−6.89866	+	13.8038i	−0.238026	+	0.476277i
$841$	−15.4770	−	24.3879i	−0.533690	−	0.840961i
$842$	3.39513	+	17.7979i	0.117004	+	0.613356i
$843$	15.4976	+	47.6966i	0.533764	+	1.64276i
$844$	2.99276	−	6.35995i	0.103015	−	0.218918i
$845$	−47.4059	−	13.3736i	−1.63081	−	0.460066i
$846$	−69.8976	−	38.4265i	−2.40313	−	1.32113i
$847$	33.0453	+	18.1668i	1.13545	+	0.624218i
$848$	4.16085	+	5.02960i	0.142884	+	0.172717i
$849$	83.0138	+	60.3131i	2.84903	+	2.06994i
$850$	0.631824	+	2.31090i	0.0216714	+	0.0792632i
$851$	6.44675	−	4.68383i	0.220992	−	0.160560i
$852$	31.1353	+	7.99419i	1.06668	+	0.273876i
$853$	1.79290	+	3.81010i	0.0613876	+	0.130455i	0.933167	−	0.359444i	$-0.117034\pi$
$853$	1.79290	+	3.81010i	0.0613876	+	0.130455i	−0.871779	+	0.489899i	$0.837034\pi$
$854$	−1.76209	+	9.23718i	−0.0602973	+	0.316090i
$855$	11.1973	−	7.73773i	0.382940	−	0.264625i
$856$	−1.90309	−	1.78712i	−0.0650462	−	0.0610824i
$857$	−21.7243	−	15.7837i	−0.742090	−	0.539160i	0.151275	−	0.988492i	$-0.451662\pi$
$857$	−21.7243	−	15.7837i	−0.742090	−	0.539160i	−0.893365	+	0.449332i	$0.851662\pi$
$858$	41.1016	−	87.3454i	1.40319	−	2.98192i
$859$	6.99982	−	8.46133i	0.238831	−	0.288697i	−0.637456	−	0.770487i	$-0.720013\pi$
$859$	6.99982	−	8.46133i	0.238831	−	0.288697i	0.876287	+	0.481790i	$0.160013\pi$
$860$	−0.890367	−	0.0210485i	−0.0303613	−	0.000717748i
$861$	0.312447	+	4.96620i	0.0106482	+	0.169248i
$862$	−0.282804	+	4.49503i	−0.00963233	+	0.153101i
$863$	41.1341	+	16.2862i	1.40022	+	0.554387i	0.942349	−	0.334631i	$-0.108612\pi$
$863$	41.1341	+	16.2862i	1.40022	+	0.554387i	0.457872	+	0.889018i	$0.348612\pi$
$864$	−5.86323	+	9.23898i	−0.199471	+	0.314316i
$865$	−1.59031	+	18.3461i	−0.0540723	+	0.623787i
$866$	1.95556	−	31.0827i	0.0664526	−	1.05623i
$867$	−51.3964	−	6.49287i	−1.74551	−	0.220510i
$868$	20.0012	−	14.5317i	0.678886	−	0.493239i
$869$	−11.6180	−	60.9036i	−0.394113	−	2.06601i
$870$	−1.05001	+	2.10100i	−0.0355985	+	0.0712307i
$871$	13.5432	+	28.7808i	0.458895	+	0.975201i
$872$	12.1947	−	11.4516i	0.412965	−	0.387800i
$873$	−9.77138	+	15.3972i	−0.330711	+	0.521117i
$874$	−1.39840			−0.0473016
$875$	−24.5725	+	4.48211i	−0.830703	+	0.151523i
$876$	−27.7740			−0.938396
$877$	22.5745	−	35.5718i	0.762288	−	1.20117i	−0.212308	−	0.977203i	$-0.568098\pi$
$877$	22.5745	−	35.5718i	0.762288	−	1.20117i	0.974596	−	0.223971i	$-0.0719020\pi$
$878$	21.1917	−	19.9004i	0.715186	−	0.671605i
$879$	27.2170	+	57.8391i	0.918007	+	1.95087i
$880$	−1.93763	−	11.6465i	−0.0653174	−	0.392604i
$881$	−4.81414	−	25.2366i	−0.162193	−	0.850244i	−0.966624	−	0.256198i	$-0.917530\pi$
$881$	−4.81414	−	25.2366i	−0.162193	−	0.850244i	0.804432	−	0.594045i	$-0.202470\pi$
$882$	10.6323	−	7.72483i	0.358009	−	0.260108i
$883$	−17.2594	−	2.18037i	−0.580826	−	0.0733754i	−0.170570	−	0.985346i	$-0.554561\pi$
$883$	−17.2594	−	2.18037i	−0.580826	−	0.0733754i	−0.410257	+	0.911970i	$0.634561\pi$
$884$	−0.178060	+	2.83019i	−0.00598882	+	0.0951896i
$885$	0.910608	−	0.210997i	0.0306097	−	0.00709257i
$886$	−9.27402	+	14.6135i	−0.311567	+	0.490951i
$887$	−9.68152	−	3.83319i	−0.325074	−	0.128706i	0.199919	−	0.979812i	$-0.435932\pi$
$887$	−9.68152	−	3.83319i	−0.325074	−	0.128706i	−0.524993	+	0.851107i	$0.675932\pi$
$888$	−1.02834	+	16.3451i	−0.0345090	+	0.548504i
$889$	−1.98469	−	31.5457i	−0.0665643	−	1.05801i
$890$	4.31944	−	12.2970i	0.144788	−	0.412198i
$891$	47.7075	−	57.6685i	1.59826	−	1.93197i
$892$	−5.45293	+	11.5881i	−0.182578	+	0.387997i
$893$	9.17697	+	6.66746i	0.307095	+	0.223118i
$894$	22.3260	+	20.9655i	0.746694	+	0.701192i
$895$	11.5403	+	0.272815i	0.385749	+	0.00911919i
$896$	−0.418628	+	2.19452i	−0.0139854	+	0.0733139i
$897$	11.7000	+	24.8637i	0.390650	+	0.830174i
$898$	−2.10637	−	0.540824i	−0.0702905	−	0.0180475i
$899$	3.04427	−	2.21180i	0.101532	−	0.0737675i
$900$	−32.6111	+	2.56170i	−1.08704	+	0.0853899i
$901$	2.53033	+	1.83839i	0.0842974	+	0.0612456i
$902$	−2.42673	−	2.93341i	−0.0808013	−	0.0976720i
$903$	−2.40874	−	1.32422i	−0.0801579	−	0.0440672i
$904$	−16.2137	−	8.91357i	−0.539260	−	0.296461i
$905$	23.8065	−	8.78068i	0.791355	−	0.291880i
$906$	−26.3042	+	55.8993i	−0.873899	+	1.85713i
$907$	−9.53156	−	29.3351i	−0.316490	−	0.974056i	−0.975137	−	0.221604i	$-0.928871\pi$
$907$	−9.53156	−	29.3351i	−0.316490	−	0.974056i	0.658647	−	0.752452i	$-0.271129\pi$
$908$	−3.67541	−	19.2672i	−0.121973	−	0.639403i
$909$	−10.6072	−	16.7143i	−0.351820	−	0.554379i
$910$	−29.2372	−	4.39783i	−0.969205	−	0.145787i
$911$	−36.0636	+	14.2786i	−1.19484	+	0.473071i	−0.879496	−	0.475906i	$-0.842120\pi$
$911$	−36.0636	+	14.2786i	−1.19484	+	0.473071i	−0.315345	+	0.948977i	$0.602120\pi$
$912$	1.83198	−	2.21449i	0.0606630	−	0.0733290i
$913$	−13.3798	+	3.43535i	−0.442807	+	0.113694i
$914$	14.5417	+	17.5780i	0.480998	+	0.581427i
$915$	−27.2781	+	10.0611i	−0.901785	+	0.332610i
$916$	−13.6593	+	3.50710i	−0.451315	+	0.115878i
$917$	−4.35876	−	4.09315i	−0.143939	−	0.135168i
$918$	−1.62017	+	4.98637i	−0.0534736	+	0.164575i
$919$	25.7412	+	3.25187i	0.849125	+	0.107269i	0.537840	−	0.843047i	$-0.319241\pi$
$919$	25.7412	+	3.25187i	0.849125	+	0.107269i	0.311285	+	0.950317i	$0.399241\pi$
$920$	2.90606	+	1.68826i	0.0958098	+	0.0556602i
$921$	−27.8061	+	26.1116i	−0.916241	+	0.860408i
$922$	−10.2316	+	1.29255i	−0.336960	+	0.0425679i
$923$	3.86715	+	61.4667i	0.127289	+	2.02320i
$924$	11.2603	−	34.6557i	0.370438	−	1.14009i
$925$	−22.1583	+	14.5506i	−0.728560	+	0.478420i
$926$	4.04459	+	12.4480i	0.132914	+	0.409066i
$927$	−54.9320	+	21.7491i	−1.80420	+	0.714335i
$928$	−0.0637170	+	0.334016i	−0.00209161	+	0.0109646i
$929$	−17.4261	+	2.20143i	−0.571732	+	0.0722266i	−0.405884	−	0.913925i	$-0.633036\pi$
$929$	−17.4261	+	2.20143i	−0.571732	+	0.0722266i	−0.165849	+	0.986151i	$0.553036\pi$
$930$	70.3853	+	29.8104i	2.30802	+	0.977523i
$931$	−1.63780	+	0.900390i	−0.0536768	+	0.0295091i
$932$	−17.3184			−0.567282
$933$	65.6035	−	36.0658i	2.14776	−	1.18074i
$934$	−25.1630	−	9.96274i	−0.823359	−	0.325991i
$935$	−2.28701	−	5.17415i	−0.0747933	−	0.169213i
$936$	−37.5038	−	9.62935i	−1.22585	−	0.314745i
$937$	2.03761	+	3.21076i	0.0665658	+	0.104891i	0.875980	−	0.482347i	$-0.160215\pi$
$937$	2.03761	+	3.21076i	0.0665658	+	0.104891i	−0.809415	+	0.587238i	$0.800215\pi$
$938$	6.43363	+	10.1378i	0.210066	+	0.331010i
$939$	−12.6372	−	3.24467i	−0.412398	−	0.105886i
$940$	−11.0214	−	24.9350i	−0.359480	−	0.813289i
$941$	15.8921	+	6.29214i	0.518069	+	0.205118i	0.612584	−	0.790405i	$-0.290130\pi$
$941$	15.8921	+	6.29214i	0.518069	+	0.205118i	−0.0945151	+	0.995523i	$0.530130\pi$
$942$	17.6484	−	9.70232i	0.575018	−	0.316119i
$943$	1.08372			0.0352909
$944$	0.118586	−	0.0651930i	0.00385963	−	0.00212185i
$945$	−50.3353	−	21.3186i	−1.63741	−	0.693495i
$946$	2.08645	−	0.263580i	0.0678363	−	0.00856971i
$947$	−3.88979	+	20.3910i	−0.126401	+	0.662618i	0.861528	+	0.507711i	$0.169508\pi$
$947$	−3.88979	+	20.3910i	−0.126401	+	0.662618i	−0.987929	+	0.154908i	$0.950492\pi$
$948$	−33.7264	+	13.3532i	−1.09538	+	0.433692i
$949$	−16.4438	−	50.6087i	−0.533788	−	1.64283i
$950$	4.64677	+	0.219824i	0.150761	+	0.00713204i
$951$	3.66148	−	11.2689i	0.118732	−	0.365418i
$952$	0.0672143	+	1.06834i	0.00217843	+	0.0346251i
$953$	40.8393	−	5.15920i	1.32291	−	0.167123i	0.568045	−	0.822998i	$-0.307700\pi$
$953$	40.8393	−	5.15920i	1.32291	−	0.167123i	0.754870	+	0.655875i	$0.227700\pi$
$954$	−31.1310	+	29.2339i	−1.00790	+	0.946484i
$955$	19.8656	+	11.5408i	0.642837	+	0.373453i
$956$	14.8868	+	1.88064i	0.481474	+	0.0608243i
$957$	1.71387	−	5.27475i	0.0554016	−	0.170509i
$958$	10.6220	+	9.97476i	0.343182	+	0.322270i
$959$	48.5558	−	12.4670i	1.56795	−	0.402581i
$960$	−6.48060	+	2.39027i	−0.209160	+	0.0771458i
$961$	−58.2987	−	70.4711i	−1.88060	−	2.27326i
$962$	−30.3922	+	7.80339i	−0.979884	+	0.251591i
$963$	10.8870	−	13.1601i	0.350829	−	0.424080i
$964$	−0.311319	+	0.123260i	−0.0100269	+	0.00396993i
$965$	−12.5587	−	1.88907i	−0.404280	−	0.0608113i
$966$	5.55800	+	8.75800i	0.178826	+	0.281784i
$967$	8.62820	+	45.2306i	0.277464	+	1.45452i	0.799022	+	0.601302i	$0.205351\pi$
$967$	8.62820	+	45.2306i	0.277464	+	1.45452i	−0.521558	+	0.853216i	$0.674649\pi$
$968$	5.21595	+	16.0531i	0.167647	+	0.515965i
$969$	0.586331	−	1.24602i	0.0188357	−	0.0400278i
$970$	−5.84775	+	2.15686i	−0.187760	+	0.0692525i
$971$	−10.4899	−	5.76688i	−0.336637	−	0.185068i	0.304465	−	0.952524i	$-0.401522\pi$
$971$	−10.4899	−	5.76688i	−0.336637	−	0.185068i	−0.641102	+	0.767456i	$0.721522\pi$
$972$	−9.60412	−	5.27991i	−0.308052	−	0.169353i
$973$	1.31509	+	1.58967i	0.0421599	+	0.0509626i
$974$	15.0450	+	10.9308i	0.482072	+	0.350245i
$975$	−34.9695	−	84.4591i	−1.11992	−	2.70486i
$976$	−3.40531	+	2.47410i	−0.109001	+	0.0791941i
$977$	51.5284	+	13.2302i	1.64854	+	0.423273i	0.954871	−	0.297022i	$-0.0959935\pi$
$977$	51.5284	+	13.2302i	1.64854	+	0.423273i	0.693668	+	0.720295i	$0.255993\pi$
$978$	−9.37944	−	19.9323i	−0.299921	−	0.637366i
$979$	−5.76694	+	30.2314i	−0.184312	+	0.966199i
$980$	4.49058	+	0.106159i	0.143446	+	0.00339111i
$981$	79.7814	+	74.9198i	2.54723	+	2.39200i
$982$	−18.8131	−	13.6685i	−0.600349	−	0.436179i
$983$	−13.6299	+	28.9650i	−0.434727	+	0.923841i	0.560674	+	0.828037i	$0.310542\pi$
$983$	−13.6299	+	28.9650i	−0.434727	+	0.923841i	−0.995400	+	0.0958040i	$0.969458\pi$
$984$	−1.41974	+	1.71617i	−0.0452596	+	0.0547094i
$985$	1.31348	−	3.73935i	0.0418509	−	0.119146i
$986$	0.0102303	+	0.162606i	0.000325800	+	0.00517844i
$987$	5.28321	−	83.9742i	0.168166	−	2.67293i
$988$	5.11980	+	2.02707i	0.162882	+	0.0644897i
$989$	−0.320771	+	0.505454i	−0.0101999	+	0.0160725i
$990$	75.2488	−	17.4359i	2.39156	−	0.554148i
$991$	−0.213160	+	3.38809i	−0.00677126	+	0.107626i	−0.999961	−	0.00888612i	$-0.997171\pi$
$991$	−0.213160	+	3.38809i	−0.00677126	+	0.107626i	0.993189	+	0.116512i	$0.0371714\pi$
$992$	10.9789	+	1.38696i	0.348580	+	0.0440359i
$993$	87.3684	−	63.4768i	2.77255	−	2.01438i
$994$	4.35630	+	22.8365i	0.138173	+	0.724331i
$995$	7.23658	+	43.4970i	0.229415	+	1.37895i
$996$	3.44100	+	7.31250i	0.109032	+	0.231705i
$997$	0.418251	−	0.392764i	0.0132461	−	0.0124390i	−0.677896	−	0.735158i	$-0.737108\pi$
$997$	0.418251	−	0.392764i	0.0132461	−	0.0124390i	0.691142	+	0.722719i	$0.257108\pi$
$998$	−15.1643	+	23.8952i	−0.480018	+	0.756388i
$999$	−58.0137			−1.83547

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	250.2.g.b.231.1	yes	140
125.46	even	25	inner	250.2.g.b.171.1	✓	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
250.2.g.b.171.1	✓	140	125.46	even	25	inner
250.2.g.b.231.1	yes	140	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 250 = 2 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	250.g (of order \(25\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.535827 - 0.844328i) q^{2} +(-2.25183 + 2.11461i) q^{3} +(-0.425779 - 0.904827i) q^{4} +(2.21119 + 0.332605i) q^{5} +(0.578833 + 3.03435i) q^{6} +(-1.80742 + 1.31317i) q^{7} +(-0.992115 - 0.125333i) q^{8} +(0.410795 - 6.52940i) q^{9} +O(q^{10})\)	\(q+(0.535827 - 0.844328i) q^{2} +(-2.25183 + 2.11461i) q^{3} +(-0.425779 - 0.904827i) q^{4} +(2.21119 + 0.332605i) q^{5} +(0.578833 + 3.03435i) q^{6} +(-1.80742 + 1.31317i) q^{7} +(-0.992115 - 0.125333i) q^{8} +(0.410795 - 6.52940i) q^{9} +(1.46564 - 1.68875i) q^{10} +(-2.82920 + 4.45811i) q^{11} +(2.87214 + 1.13716i) q^{12} +(-0.371622 + 5.90677i) q^{13} +(0.140280 + 2.22969i) q^{14} +(-5.68256 + 3.92684i) q^{15} +(-0.637424 + 0.770513i) q^{16} +(-0.204009 + 0.433542i) q^{17} +(-5.29284 - 3.84547i) q^{18} +(0.678227 + 0.636898i) q^{19} +(-0.640530 - 2.14236i) q^{20} +(1.29317 - 6.77902i) q^{21} +(2.24815 + 4.77755i) q^{22} +(-1.45580 - 0.373786i) q^{23} +(2.49910 - 1.81571i) q^{24} +(4.77875 + 1.47091i) q^{25} +(4.78812 + 3.47878i) q^{26} +(6.97495 + 8.43127i) q^{27} +(1.95775 + 1.07628i) q^{28} +(0.297979 + 0.163815i) q^{29} +(0.270671 + 6.90205i) q^{30} +(4.71174 - 10.0130i) q^{31} +(0.309017 + 0.951057i) q^{32} +(-3.05628 - 16.0216i) q^{33} +(0.256738 + 0.404554i) q^{34} +(-4.43333 + 2.30251i) q^{35} +(-6.08288 + 2.40838i) q^{36} +(-3.37945 + 4.08505i) q^{37} +(0.901163 - 0.231379i) q^{38} +(-11.6537 - 14.0869i) q^{39} +(-2.15207 - 0.607118i) q^{40} +(-0.698377 + 0.179313i) q^{41} +(-5.03080 - 4.72424i) q^{42} +(0.123080 - 0.378802i) q^{43} +(5.23844 + 0.661769i) q^{44} +(3.08006 - 14.3011i) q^{45} +(-1.09566 + 1.02889i) q^{46} +(12.0959 - 1.52806i) q^{47} +(-0.193964 - 3.08297i) q^{48} +(-0.620757 + 1.91049i) q^{49} +(3.80251 - 3.24668i) q^{50} +(-0.457377 - 1.40766i) q^{51} +(5.50283 - 2.17873i) q^{52} +(1.22315 - 6.41197i) q^{53} +(10.8561 - 1.37145i) q^{54} +(-7.73871 + 8.91674i) q^{55} +(1.95775 - 1.07628i) q^{56} -2.87404 q^{57} +(0.297979 - 0.163815i) q^{58} +(-0.125821 - 0.0498162i) q^{59} +(5.97262 + 3.46977i) q^{60} +(4.07695 + 1.04678i) q^{61} +(-5.92955 - 9.34347i) q^{62} +(7.83172 + 12.3408i) q^{63} +(0.968583 + 0.248690i) q^{64} +(-2.78635 + 12.9374i) q^{65} +(-15.1651 - 6.00429i) q^{66} +(4.70962 - 2.58914i) q^{67} +0.479143 q^{68} +(4.06863 - 2.23675i) q^{69} +(-0.431419 + 4.97693i) q^{70} +(10.3241 - 1.30424i) q^{71} +(-1.22591 + 6.42642i) q^{72} +(-8.35969 + 3.30983i) q^{73} +(1.63832 + 5.04224i) q^{74} +(-13.8713 + 6.79295i) q^{75} +(0.287507 - 0.884856i) q^{76} +(-0.740689 - 11.7729i) q^{77} +(-18.1383 + 2.29140i) q^{78} +(-8.55999 + 8.03837i) q^{79} +(-1.66574 + 1.49174i) q^{80} +(-14.0631 - 1.77658i) q^{81} +(-0.222810 + 0.685740i) q^{82} +(1.90714 + 1.79092i) q^{83} +(-6.68445 + 1.71627i) q^{84} +(-0.595302 + 0.890790i) q^{85} +(-0.253883 - 0.306892i) q^{86} +(-1.01740 + 0.261225i) q^{87} +(3.36565 - 4.06837i) q^{88} +(5.41949 - 2.14573i) q^{89} +(-10.4245 - 10.2635i) q^{90} +(-7.08491 - 11.1640i) q^{91} +(0.281638 + 1.47640i) q^{92} +(10.5635 + 32.5110i) q^{93} +(5.19110 - 11.0317i) q^{94} +(1.28786 + 1.63388i) q^{95} +(-2.70697 - 1.48817i) q^{96} +(-2.44262 - 1.34284i) q^{97} +(1.28046 + 1.54782i) q^{98} +(27.9466 + 20.3044i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q - 5 q^{5} - 10 q^{7} - 10 q^{9}+O(q^{10}) \) 140 * q - 5 * q^5 - 10 * q^7 - 10 * q^9	\( 140 q - 5 q^{5} - 10 q^{7} - 10 q^{9} + 20 q^{10} - 10 q^{11} + 20 q^{12} + 20 q^{14} - 10 q^{15} - 5 q^{17} - 50 q^{18} + 40 q^{19} - 10 q^{20} - 5 q^{21} - 10 q^{22} + 10 q^{23} - 5 q^{24} - 5 q^{25} - 35 q^{26} + 30 q^{27} - 5 q^{28} - 10 q^{29} - 10 q^{30} + 35 q^{31} - 35 q^{32} - 55 q^{33} - 15 q^{34} - 25 q^{35} - 10 q^{36} - 25 q^{37} - 30 q^{39} + 25 q^{41} - 5 q^{42} - 45 q^{43} + 40 q^{44} - 5 q^{45} + 90 q^{47} - 5 q^{48} - 65 q^{49} + 30 q^{50} - 80 q^{51} - 50 q^{53} - 5 q^{54} - 35 q^{55} - 5 q^{56} + 40 q^{57} - 10 q^{58} + 45 q^{59} + 15 q^{60} + 45 q^{61} - 45 q^{62} - 75 q^{63} - 60 q^{65} + 15 q^{66} - 45 q^{67} + 10 q^{68} - 125 q^{69} - 15 q^{70} - 5 q^{71} - 5 q^{72} - 50 q^{73} + 20 q^{74} - 130 q^{75} - 5 q^{76} + 10 q^{77} + 10 q^{78} - 50 q^{79} - 5 q^{80} + 15 q^{81} + 40 q^{82} + 25 q^{83} - 50 q^{84} - 95 q^{85} - 10 q^{86} + 80 q^{87} - 10 q^{88} - 65 q^{89} - 10 q^{90} + 65 q^{91} - 25 q^{92} - 10 q^{93} - 35 q^{94} + 80 q^{95} - 40 q^{97} - 25 q^{98} + 90 q^{99}+O(q^{100}) \) 140 * q - 5 * q^5 - 10 * q^7 - 10 * q^9 + 20 * q^10 - 10 * q^11 + 20 * q^12 + 20 * q^14 - 10 * q^15 - 5 * q^17 - 50 * q^18 + 40 * q^19 - 10 * q^20 - 5 * q^21 - 10 * q^22 + 10 * q^23 - 5 * q^24 - 5 * q^25 - 35 * q^26 + 30 * q^27 - 5 * q^28 - 10 * q^29 - 10 * q^30 + 35 * q^31 - 35 * q^32 - 55 * q^33 - 15 * q^34 - 25 * q^35 - 10 * q^36 - 25 * q^37 - 30 * q^39 + 25 * q^41 - 5 * q^42 - 45 * q^43 + 40 * q^44 - 5 * q^45 + 90 * q^47 - 5 * q^48 - 65 * q^49 + 30 * q^50 - 80 * q^51 - 50 * q^53 - 5 * q^54 - 35 * q^55 - 5 * q^56 + 40 * q^57 - 10 * q^58 + 45 * q^59 + 15 * q^60 + 45 * q^61 - 45 * q^62 - 75 * q^63 - 60 * q^65 + 15 * q^66 - 45 * q^67 + 10 * q^68 - 125 * q^69 - 15 * q^70 - 5 * q^71 - 5 * q^72 - 50 * q^73 + 20 * q^74 - 130 * q^75 - 5 * q^76 + 10 * q^77 + 10 * q^78 - 50 * q^79 - 5 * q^80 + 15 * q^81 + 40 * q^82 + 25 * q^83 - 50 * q^84 - 95 * q^85 - 10 * q^86 + 80 * q^87 - 10 * q^88 - 65 * q^89 - 10 * q^90 + 65 * q^91 - 25 * q^92 - 10 * q^93 - 35 * q^94 + 80 * q^95 - 40 * q^97 - 25 * q^98 + 90 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more