LMFDB - Embedded newform 460.2.o.b.19.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(19,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 15]))

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

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

chi := DirichletCharacter("460.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.o (of order $22$, degree $10$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$640$
Relative dimension:	$64$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			19.14
Character	$\chi$	$=$	460.19
Dual form			460.2.o.b.339.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.09143 + 0.899318i) q^{2} +(2.94595 - 0.865009i) q^{3} +(0.382455 - 1.96309i) q^{4} +(-1.40285 + 1.74127i) q^{5} +(-2.43739 + 3.59345i) q^{6} +(-1.84920 + 0.265875i) q^{7} +(1.34802 + 2.48653i) q^{8} +(5.40662 - 3.47462i) q^{9} +O(q^{10})$	\(q+(-1.09143 + 0.899318i) q^{2} +(2.94595 - 0.865009i) q^{3} +(0.382455 - 1.96309i) q^{4} +(-1.40285 + 1.74127i) q^{5} +(-2.43739 + 3.59345i) q^{6} +(-1.84920 + 0.265875i) q^{7} +(1.34802 + 2.48653i) q^{8} +(5.40662 - 3.47462i) q^{9} +(-0.0348340 - 3.16209i) q^{10} +(1.12848 - 2.47102i) q^{11} +(-0.571400 - 6.11400i) q^{12} +(5.89774 + 0.847967i) q^{13} +(1.77918 - 1.95321i) q^{14} +(-2.62652 + 6.34316i) q^{15} +(-3.70746 - 1.50159i) q^{16} +(3.18087 + 3.67092i) q^{17} +(-2.77618 + 8.65459i) q^{18} +(-0.125139 + 0.144418i) q^{19} +(2.88174 + 3.41988i) q^{20} +(-5.21768 + 2.38283i) q^{21} +(0.990574 + 3.71181i) q^{22} +(3.29454 + 3.48511i) q^{23} +(6.12207 + 6.15915i) q^{24} +(-1.06402 - 4.88547i) q^{25} +(-7.19958 + 4.37844i) q^{26} +(6.89016 - 7.95166i) q^{27} +(-0.185299 + 3.73184i) q^{28} +(0.861428 + 0.994141i) q^{29} +(-2.83785 - 9.28521i) q^{30} +(1.93522 - 6.59074i) q^{31} +(5.39685 - 1.69530i) q^{32} +(1.18698 - 8.25563i) q^{33} +(-6.77303 - 1.14595i) q^{34} +(2.13120 - 3.59294i) q^{35} +(-4.75322 - 11.9426i) q^{36} +(-8.55057 + 5.49512i) q^{37} +(0.00670309 - 0.270162i) q^{38} +(18.1079 - 2.60353i) q^{39} +(-6.22079 - 1.14097i) q^{40} +(-1.59761 - 1.02672i) q^{41} +(3.55182 - 7.29306i) q^{42} +(-1.72117 - 5.86176i) q^{43} +(-4.41924 - 3.16035i) q^{44} +(-1.53443 + 14.2887i) q^{45} +(-6.73000 - 0.840923i) q^{46} -2.14717 q^{47} +(-12.2209 - 1.21661i) q^{48} +(-3.36759 + 0.988812i) q^{49} +(5.55490 + 4.37528i) q^{50} +(12.5461 + 8.06287i) q^{51} +(3.92025 - 11.2535i) q^{52} +(0.0654096 + 0.454933i) q^{53} +(-0.369074 + 14.8752i) q^{54} +(2.71962 + 5.43144i) q^{55} +(-3.15387 - 4.23970i) q^{56} +(-0.243729 + 0.533693i) q^{57} +(-1.83424 - 0.310341i) q^{58} +(-2.89098 - 0.415660i) q^{59} +(11.4477 + 7.58206i) q^{60} +(-0.274884 + 0.936168i) q^{61} +(3.81501 + 8.93373i) q^{62} +(-9.07413 + 7.86278i) q^{63} +(-4.36569 + 6.70379i) q^{64} +(-9.75019 + 9.07997i) q^{65} +(6.12893 + 10.0779i) q^{66} +(-0.285124 + 0.130212i) q^{67} +(8.42289 - 4.84038i) q^{68} +(12.7202 + 7.41715i) q^{69} +(0.905136 + 5.83808i) q^{70} +(-11.0414 + 5.04244i) q^{71} +(15.9280 + 8.75987i) q^{72} +(-10.6708 - 9.24627i) q^{73} +(4.39052 - 13.6872i) q^{74} +(-7.36053 - 13.4720i) q^{75} +(0.235645 + 0.300892i) q^{76} +(-1.42980 + 4.86945i) q^{77} +(-17.4222 + 19.1264i) q^{78} +(1.27938 - 8.89828i) q^{79} +(7.81567 - 4.34917i) q^{80} +(5.41035 - 11.8470i) q^{81} +(2.66703 - 0.316161i) q^{82} +(8.07052 + 12.5580i) q^{83} +(2.68220 + 11.1541i) q^{84} +(-10.8543 + 0.388991i) q^{85} +(7.15013 + 4.84985i) q^{86} +(3.39767 + 2.18355i) q^{87} +(7.66547 - 0.524989i) q^{88} +(0.772172 + 2.62978i) q^{89} +(-11.1754 - 16.9752i) q^{90} -11.1316 q^{91} +(8.10160 - 5.13459i) q^{92} -21.0900i q^{93} +(2.34349 - 1.93099i) q^{94} +(-0.0759188 - 0.420496i) q^{95} +(14.4324 - 9.66259i) q^{96} +(5.88063 + 3.77925i) q^{97} +(2.78624 - 4.10775i) q^{98} +(-2.48462 - 17.2809i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 640 q - 6 q^{4} - 22 q^{5} + 2 q^{6} - 100 q^{9}+O(q^{10}) $ 640 * q - 6 * q^4 - 22 * q^5 + 2 * q^6 - 100 * q^9	$ 640 q - 6 q^{4} - 22 q^{5} + 2 q^{6} - 100 q^{9} - 11 q^{10} - 22 q^{14} + 2 q^{16} - 11 q^{20} - 44 q^{21} - 8 q^{24} - 38 q^{25} - 46 q^{26} - 52 q^{29} - 11 q^{30} - 44 q^{34} + 18 q^{36} - 11 q^{40} - 76 q^{41} - 154 q^{44} - 30 q^{46} - 100 q^{49} + 21 q^{50} + 178 q^{54} + 242 q^{56} - 11 q^{60} - 44 q^{61} + 6 q^{64} - 22 q^{65} + 44 q^{66} - 12 q^{69} + 22 q^{70} - 22 q^{74} + 88 q^{76} - 110 q^{80} - 252 q^{81} - 374 q^{84} + 94 q^{85} - 198 q^{86} - 44 q^{89} - 242 q^{90} - 62 q^{94} + 372 q^{96}+O(q^{100}) $ 640 * q - 6 * q^4 - 22 * q^5 + 2 * q^6 - 100 * q^9 - 11 * q^10 - 22 * q^14 + 2 * q^16 - 11 * q^20 - 44 * q^21 - 8 * q^24 - 38 * q^25 - 46 * q^26 - 52 * q^29 - 11 * q^30 - 44 * q^34 + 18 * q^36 - 11 * q^40 - 76 * q^41 - 154 * q^44 - 30 * q^46 - 100 * q^49 + 21 * q^50 + 178 * q^54 + 242 * q^56 - 11 * q^60 - 44 * q^61 + 6 * q^64 - 22 * q^65 + 44 * q^66 - 12 * q^69 + 22 * q^70 - 22 * q^74 + 88 * q^76 - 110 * q^80 - 252 * q^81 - 374 * q^84 + 94 * q^85 - 198 * q^86 - 44 * q^89 - 242 * q^90 - 62 * q^94 + 372 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{15}{22}\right)$

Coefficient data

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

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

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

$2$	−1.09143	+	0.899318i	−0.771760	+	0.635914i
$2$	−1.09143	+	0.899318i	−0.771760	+	0.635914i
$3$	2.94595	−	0.865009i	1.70084	−	0.499413i	0.719962	−	0.694013i	$-0.244159\pi$
$3$	2.94595	−	0.865009i	1.70084	−	0.499413i	0.980883	+	0.194600i	$0.0623409\pi$
$4$	0.382455	−	1.96309i	0.191227	−	0.981546i
$5$	−1.40285	+	1.74127i	−0.627374	+	0.778718i
$5$	−1.40285	+	1.74127i	−0.627374	+	0.778718i
$6$	−2.43739	+	3.59345i	−0.995061	+	1.46702i
$7$	−1.84920	+	0.265875i	−0.698933	+	0.100491i	−0.482617	−	0.875832i	$-0.660314\pi$
$7$	−1.84920	+	0.265875i	−0.698933	+	0.100491i	−0.216317	+	0.976323i	$0.569404\pi$
$8$	1.34802	+	2.48653i	0.476597	+	0.879122i
$9$	5.40662	−	3.47462i	1.80221	−	1.15821i
$10$	−0.0348340	−	3.16209i	−0.0110155	−	0.999939i
$11$	1.12848	−	2.47102i	0.340248	−	0.745040i	−0.659731	−	0.751502i	$-0.729330\pi$
$11$	1.12848	−	2.47102i	0.340248	−	0.745040i	0.999979	+	0.00646227i	$0.00205702\pi$
$12$	−0.571400	−	6.11400i	−0.164949	−	1.76496i
$13$	5.89774	+	0.847967i	1.63574	+	0.235184i	0.898030	−	0.439935i	$-0.144998\pi$
$13$	5.89774	+	0.847967i	1.63574	+	0.235184i	0.737709	+	0.675119i	$0.235908\pi$
$14$	1.77918	−	1.95321i	0.475505	−	0.522017i
$15$	−2.62652	+	6.34316i	−0.678164	+	1.63780i
$16$	−3.70746	−	1.50159i	−0.926864	−	0.375397i
$17$	3.18087	+	3.67092i	0.771475	+	0.890329i	0.996463	−	0.0840323i	$-0.0267799\pi$
$17$	3.18087	+	3.67092i	0.771475	+	0.890329i	−0.224988	+	0.974361i	$0.572234\pi$
$18$	−2.77618	+	8.65459i	−0.654351	+	2.03991i
$19$	−0.125139	+	0.144418i	−0.0287088	+	0.0331317i	−0.769922	−	0.638138i	$-0.779705\pi$
$19$	−0.125139	+	0.144418i	−0.0287088	+	0.0331317i	0.741214	+	0.671269i	$0.234251\pi$
$20$	2.88174	+	3.41988i	0.644377	+	0.764708i
$21$	−5.21768	+	2.38283i	−1.13859	+	0.519977i
$22$	0.990574	+	3.71181i	0.211191	+	0.791360i
$23$	3.29454	+	3.48511i	0.686960	+	0.726695i
$23$	3.29454	+	3.48511i	0.686960	+	0.726695i
$24$	6.12207	+	6.15915i	1.24966	+	1.25723i
$25$	−1.06402	−	4.88547i	−0.212804	−	0.977095i
$26$	−7.19958	+	4.37844i	−1.41195	+	0.858683i
$27$	6.89016	−	7.95166i	1.32601	−	1.53030i
$28$	−0.185299	+	3.73184i	−0.0350182	+	0.705252i
$29$	0.861428	+	0.994141i	0.159963	+	0.184607i	0.830073	−	0.557654i	$-0.188299\pi$
$29$	0.861428	+	0.994141i	0.159963	+	0.184607i	−0.670110	+	0.742262i	$0.733753\pi$
$30$	−2.83785	−	9.28521i	−0.518118	−	1.69524i
$31$	1.93522	−	6.59074i	0.347575	−	1.18373i	−0.581409	−	0.813611i	$-0.697498\pi$
$31$	1.93522	−	6.59074i	0.347575	−	1.18373i	0.928984	−	0.370120i	$-0.120683\pi$
$32$	5.39685	−	1.69530i	0.954037	−	0.299690i
$33$	1.18698	−	8.25563i	0.206627	−	1.43712i
$34$	−6.77303	−	1.14595i	−1.16157	−	0.196529i
$35$	2.13120	−	3.59294i	0.360238	−	0.607318i
$36$	−4.75322	−	11.9426i	−0.792203	−	1.99043i
$37$	−8.55057	+	5.49512i	−1.40571	+	0.903392i	−0.999944	−	0.0105869i	$-0.996630\pi$
$37$	−8.55057	+	5.49512i	−1.40571	+	0.903392i	−0.405762	+	0.913979i	$0.632994\pi$
$38$	0.00670309	−	0.270162i	0.00108739	−	0.0438260i
$39$	18.1079	−	2.60353i	2.89959	−	0.416898i
$40$	−6.22079	−	1.14097i	−0.983593	−	0.180403i
$41$	−1.59761	−	1.02672i	−0.249505	−	0.160347i	0.409911	−	0.912126i	$-0.365560\pi$
$41$	−1.59761	−	1.02672i	−0.249505	−	0.160347i	−0.659416	+	0.751779i	$0.729196\pi$
$42$	3.55182	−	7.29306i	0.548058	−	1.12534i
$43$	−1.72117	−	5.86176i	−0.262476	−	0.893911i	−0.980271	−	0.197657i	$-0.936667\pi$
$43$	−1.72117	−	5.86176i	−0.262476	−	0.893911i	0.717796	−	0.696254i	$-0.245151\pi$
$44$	−4.41924	−	3.16035i	−0.666226	−	0.476441i
$45$	−1.53443	+	14.2887i	−0.228740	+	2.13004i
$46$	−6.73000	−	0.840923i	−0.992284	−	0.123987i
$47$	−2.14717			−0.313197			−0.156598	−	0.987662i	$-0.550053\pi$
$47$	−2.14717			−0.313197			−0.156598	+	0.987662i	$0.550053\pi$
$48$	−12.2209	−	1.21661i	−1.76393	−	0.175603i
$49$	−3.36759	+	0.988812i	−0.481084	+	0.141259i
$50$	5.55490	+	4.37528i	0.785582	+	0.618758i
$51$	12.5461	+	8.06287i	1.75680	+	1.12903i
$52$	3.92025	−	11.2535i	0.543641	−	1.56058i
$53$	0.0654096	+	0.454933i	0.00898469	+	0.0624899i	0.993821	−	0.110999i	$-0.0354050\pi$
$53$	0.0654096	+	0.454933i	0.00898469	+	0.0624899i	−0.984836	+	0.173489i	$0.944496\pi$
$54$	−0.369074	+	14.8752i	−0.0502246	+	2.02425i
$55$	2.71962	+	5.43144i	0.366713	+	0.732376i
$56$	−3.15387	−	4.23970i	−0.421454	−	0.566554i
$57$	−0.243729	+	0.533693i	−0.0322828	+	0.0706894i
$58$	−1.83424	−	0.310341i	−0.240848	−	0.0407498i
$59$	−2.89098	−	0.415660i	−0.376373	−	0.0541143i	−0.0484676	−	0.998825i	$-0.515434\pi$
$59$	−2.89098	−	0.415660i	−0.376373	−	0.0541143i	−0.327906	+	0.944710i	$0.606343\pi$
$60$	11.4477	+	7.58206i	1.47789	+	0.978840i
$61$	−0.274884	+	0.936168i	−0.0351952	+	0.119864i	−0.975217	−	0.221250i	$-0.928986\pi$
$61$	−0.274884	+	0.936168i	−0.0351952	+	0.119864i	0.940022	+	0.341114i	$0.110804\pi$
$62$	3.81501	+	8.93373i	0.484507	+	1.13458i
$63$	−9.07413	+	7.86278i	−1.14323	+	0.990617i
$64$	−4.36569	+	6.70379i	−0.545711	+	0.837974i
$65$	−9.75019	+	9.07997i	−1.20936	+	1.12623i
$66$	6.12893	+	10.0779i	0.754419	+	1.24051i
$67$	−0.285124	+	0.130212i	−0.0348334	+	0.0159079i	−0.432756	−	0.901511i	$-0.642459\pi$
$67$	−0.285124	+	0.130212i	−0.0348334	+	0.0159079i	0.397922	+	0.917419i	$0.369731\pi$
$68$	8.42289	−	4.84038i	1.02143	−	0.586982i
$69$	12.7202	+	7.41715i	1.53133	+	0.892920i
$70$	0.905136	+	5.83808i	0.108184	+	0.697784i
$71$	−11.0414	+	5.04244i	−1.31037	+	0.598427i	−0.943355	−	0.331786i	$-0.892349\pi$
$71$	−11.0414	+	5.04244i	−1.31037	+	0.598427i	−0.367019	+	0.930214i	$0.619621\pi$
$72$	15.9280	+	8.75987i	1.87713	+	1.03236i
$73$	−10.6708	−	9.24627i	−1.24892	−	1.08219i	−0.993318	−	0.115412i	$-0.963181\pi$
$73$	−10.6708	−	9.24627i	−1.24892	−	1.08219i	−0.255601	−	0.966782i	$-0.582273\pi$
$74$	4.39052	−	13.6872i	0.510388	−	1.59111i
$75$	−7.36053	−	13.4720i	−0.849921	−	1.55561i
$76$	0.235645	+	0.300892i	0.0270304	+	0.0345146i
$77$	−1.42980	+	4.86945i	−0.162941	+	0.554925i
$78$	−17.4222	+	19.1264i	−1.97268	+	2.16564i
$79$	1.27938	−	8.89828i	0.143941	−	1.00113i	−0.781949	−	0.623342i	$-0.785774\pi$
$79$	1.27938	−	8.89828i	0.143941	−	1.00113i	0.925890	−	0.377792i	$-0.123317\pi$
$80$	7.81567	−	4.34917i	0.873819	−	0.486252i
$81$	5.41035	−	11.8470i	0.601150	−	1.31634i
$82$	2.66703	−	0.316161i	0.294525	−	0.0349141i
$83$	8.07052	+	12.5580i	0.885855	+	1.37842i	0.925316	+	0.379196i	$0.123799\pi$
$83$	8.07052	+	12.5580i	0.885855	+	1.37842i	−0.0394614	+	0.999221i	$0.512564\pi$
$84$	2.68220	+	11.1541i	0.292652	+	1.21701i
$85$	−10.8543	+	0.388991i	−1.17732	+	0.0421920i
$86$	7.15013	+	4.84985i	0.771018	+	0.522972i
$87$	3.39767	+	2.18355i	0.364268	+	0.234101i
$88$	7.66547	−	0.524989i	0.817142	−	0.0559640i
$89$	0.772172	+	2.62978i	0.0818501	+	0.278756i	0.990241	−	0.139366i	$-0.0445066\pi$
$89$	0.772172	+	2.62978i	0.0818501	+	0.278756i	−0.908391	+	0.418122i	$0.862688\pi$
$90$	−11.1754	−	16.9752i	−1.17799	−	1.78934i
$91$	−11.1316			−1.16691
$92$	8.10160	−	5.13459i	0.844650	−	0.535319i
$93$		−	21.0900i		−	2.18693i
$94$	2.34349	−	1.93099i	0.241713	−	0.199166i
$95$	−0.0759188	−	0.420496i	−0.00778911	−	0.0431420i
$96$	14.4324	−	9.66259i	1.47300	−	0.986184i
$97$	5.88063	+	3.77925i	0.597087	+	0.383725i	0.803995	−	0.594636i	$-0.202704\pi$
$97$	5.88063	+	3.77925i	0.597087	+	0.383725i	−0.206908	+	0.978360i	$0.566340\pi$
$98$	2.78624	−	4.10775i	0.281453	−	0.414946i
$99$	−2.48462	−	17.2809i	−0.249713	−	1.73679i
$100$	−9.99757	+	0.220296i	−0.999757	+	0.0220296i
$101$	−0.657542	+	0.422577i	−0.0654279	+	0.0420480i	−0.572946	−	0.819593i	$-0.694199\pi$
$101$	−0.657542	+	0.422577i	−0.0654279	+	0.0420480i	0.507518	+	0.861641i	$0.330563\pi$
$102$	−20.9443	+	2.48282i	−2.07379	+	0.245836i
$103$	−10.9524	−	5.00179i	−1.07917	−	0.492841i	−0.205151	−	0.978730i	$-0.565769\pi$
$103$	−10.9524	−	5.00179i	−1.07917	−	0.492841i	−0.874020	+	0.485889i	$0.838496\pi$
$104$	5.84177	+	15.8080i	0.572833	+	1.55010i
$105$	3.17047	−	12.4281i	0.309407	−	1.21286i
$106$	−0.480520	−	0.437706i	−0.0466722	−	0.0425137i
$107$	4.73987	−	16.1425i	0.458221	−	1.56056i	−0.329274	−	0.944235i	$-0.606804\pi$
$107$	4.73987	−	16.1425i	0.458221	−	1.56056i	0.787494	−	0.616322i	$-0.211378\pi$
$108$	−12.9747	−	16.5672i	−1.24849	−	1.59418i
$109$	−7.15645	+	6.20110i	−0.685463	+	0.593957i	−0.926381	−	0.376588i	$-0.877097\pi$
$109$	−7.15645	+	6.20110i	−0.685463	+	0.593957i	0.240917	+	0.970546i	$0.422552\pi$
$110$	−7.85288	−	3.48226i	−0.748742	−	0.332021i
$111$	−20.4362	+	23.5847i	−1.93972	+	2.23856i
$112$	7.25508	+	1.79102i	0.685541	+	0.169235i
$113$	0.359998	+	0.788286i	0.0338658	+	0.0741557i	0.925809	−	0.377992i	$-0.123385\pi$
$113$	0.359998	+	0.788286i	0.0338658	+	0.0741557i	−0.891943	+	0.452148i	$0.850658\pi$
$114$	−0.213945	−	0.801681i	−0.0200378	−	0.0750843i
$115$	−10.6903	+	0.847591i	−0.996872	+	0.0790383i
$116$	2.28105	−	1.31085i	0.211790	−	0.121709i
$117$	34.8332	−	15.9078i	3.22033	−	1.47068i
$118$	3.52912	−	2.14624i	0.324882	−	0.197578i
$119$	−6.85809	−	5.94257i	−0.628680	−	0.544754i
$120$	−19.3131	+	2.01979i	−1.76303	+	0.184381i
$121$	2.37100	+	2.73628i	0.215546	+	0.248753i
$122$	−0.541895	−	1.26897i	−0.0490609	−	0.114887i
$123$	−5.59460	−	1.64272i	−0.504448	−	0.148119i
$124$	−12.1981	−	6.31966i	−1.09542	−	0.567522i
$125$	9.99958	+	5.00085i	0.894389	+	0.447290i
$126$	2.83267	−	16.7422i	0.252354	−	1.49152i
$127$	−2.15143	+	4.71097i	−0.190908	+	0.418031i	−0.980747	−	0.195284i	$-0.937437\pi$
$127$	−2.15143	+	4.71097i	−0.190908	+	0.418031i	0.789838	+	0.613315i	$0.210164\pi$
$128$	−1.26398	−	11.2429i	−0.111721	−	0.993740i
$129$	−10.1410	−	15.7796i	−0.892861	−	1.38932i
$130$	2.47590	−	18.6787i	0.217151	−	1.63823i
$131$	−1.02596	+	0.147510i	−0.0896384	+	0.0128881i	−0.186988	−	0.982362i	$-0.559873\pi$
$131$	−1.02596	+	0.147510i	−0.0896384	+	0.0128881i	0.0973497	+	0.995250i	$0.468963\pi$
$132$	−15.7526	−	5.48756i	−1.37109	−	0.477630i
$133$	0.193010	−	0.300329i	0.0167361	−	0.0260418i
$134$	0.194092	−	0.398535i	0.0167670	−	0.0344281i
$135$	4.18011	+	23.1526i	0.359766	+	1.99266i
$136$	−4.83999	+	12.8578i	−0.415025	+	1.10255i
$137$	−11.5823			−0.989541			−0.494770	−	0.869024i	$-0.664748\pi$
$137$	−11.5823			−0.989541			−0.494770	+	0.869024i	$0.664748\pi$
$138$	−20.5536	+	3.34419i	−1.74964	+	0.284676i
$139$		−	10.5712i		−	0.896640i	−0.893873	−	0.448320i	$-0.852022\pi$
$139$		−	10.5712i		−	0.896640i	0.893873	−	0.448320i	$-0.147978\pi$
$140$	−6.23819	−	5.55787i	−0.527223	−	0.469726i
$141$	−6.32546	+	1.85732i	−0.532699	+	0.156415i
$142$	7.51620	−	15.4332i	0.630745	−	1.29513i
$143$	8.75080	−	13.6165i	0.731778	−	1.13867i
$144$	−25.2623	+	4.76351i	−2.10519	+	0.396959i
$145$	−2.93952	+	0.105345i	−0.244114	+	0.00874840i
$146$	19.9618	+	0.495280i	1.65205	+	0.0409896i
$147$	−9.06541	+	5.82598i	−0.747702	+	0.480519i
$148$	7.51722	+	18.8872i	0.617911	+	1.55252i
$149$	−15.5985	−	7.12360i	−1.27788	−	0.583588i	−0.343261	−	0.939240i	$-0.611532\pi$
$149$	−15.5985	−	7.12360i	−1.27788	−	0.583588i	−0.934619	+	0.355652i	$0.884259\pi$
$150$	20.1491	+	8.08431i	1.64517	+	0.660081i
$151$	23.3874	+	3.36261i	1.90324	+	0.273645i	0.990776	−	0.135507i	$-0.0432662\pi$
$151$	23.3874	+	3.36261i	1.90324	+	0.273645i	0.912466	+	0.409152i	$0.134175\pi$
$152$	−0.527788	−	0.116483i	−0.0428093	−	0.00944804i
$153$	29.9528	+	8.79494i	2.42154	+	0.711029i
$154$	−2.81865	−	6.60052i	−0.227133	−	0.531885i
$155$	8.76141	+	12.6155i	0.703734	+	1.01331i
$156$	1.81450	−	36.5433i	0.145276	−	2.92580i
$157$	−7.78779	+	8.98759i	−0.621534	+	0.717288i	−0.975998	−	0.217782i	$-0.930118\pi$
$157$	−7.78779	+	8.98759i	−0.621534	+	0.717288i	0.354464	+	0.935070i	$0.384663\pi$
$158$	6.60602	+	10.8624i	0.525547	+	0.864170i
$159$	0.586215	+	1.28363i	0.0464899	+	0.101799i
$160$	−4.61900	+	11.7756i	−0.365164	+	0.930943i
$161$	−7.01889	−	5.56874i	−0.553166	−	0.438878i
$162$	4.74919	+	17.7959i	0.373132	+	1.39817i
$163$	6.14934	+	13.4652i	0.481654	+	1.05467i	0.982006	+	0.188852i	$0.0604767\pi$
$163$	6.14934	+	13.4652i	0.481654	+	1.05467i	−0.500352	+	0.865822i	$0.666796\pi$
$164$	−2.62656	+	2.74358i	−0.205100	+	0.214238i
$165$	12.7101	+	13.6483i	0.989480	+	1.06252i
$166$	−20.1021	−	6.44823i	−1.56022	−	0.500480i
$167$	−9.76467	−	11.2690i	−0.755613	−	0.872024i	0.239487	−	0.970900i	$-0.423021\pi$
$167$	−9.76467	−	11.2690i	−0.755613	−	0.872024i	−0.995100	+	0.0988760i	$0.968475\pi$
$168$	−12.9585	−	9.76182i	−0.999772	−	0.753141i
$169$	21.5909	+	6.33965i	1.66084	+	0.487666i
$170$	11.4970	−	10.1861i	0.881777	−	0.781235i
$171$	−0.174780	+	1.21562i	−0.0133658	+	0.0929608i
$172$	−12.1654	+	1.13695i	−0.927607	+	0.0866920i
$173$	6.43435	+	2.93847i	0.489195	+	0.223408i	0.644712	−	0.764425i	$-0.276977\pi$
$173$	6.43435	+	2.93847i	0.489195	+	0.223408i	−0.155517	+	0.987833i	$0.549705\pi$
$174$	−5.67203	+	0.672385i	−0.429995	+	0.0509734i
$175$	3.26652	+	8.75134i	0.246925	+	0.661539i
$176$	−7.89422	+	7.46669i	−0.595049	+	0.562823i
$177$	−8.87623	+	1.27621i	−0.667178	+	0.0959257i
$178$	−3.20778	−	2.17580i	−0.240433	−	0.163083i
$179$	−3.02559	+	4.70791i	−0.226143	+	0.351886i	−0.935721	−	0.352741i	$-0.885250\pi$
$179$	−3.02559	+	4.70791i	−0.226143	+	0.351886i	0.709577	+	0.704627i	$0.248886\pi$
$180$	27.4633	+	8.47703i	2.04699	+	0.631841i
$181$	−2.64998	−	9.02500i	−0.196971	−	0.670823i	−0.997444	−	0.0714535i	$-0.977236\pi$
$181$	−2.64998	−	9.02500i	−0.196971	−	0.670823i	0.800473	−	0.599369i	$-0.204582\pi$
$182$	12.1494	−	10.0108i	0.900572	−	0.742052i
$183$			2.99568i			0.221447i
$184$	−4.22473	+	12.8900i	−0.311451	+	0.950262i
$185$	2.42671	−	22.5977i	0.178415	−	1.66141i
$186$	18.9666	+	23.0183i	1.39070	+	1.68778i
$187$	12.6604	−	3.71744i	0.925823	−	0.271846i
$188$	−0.821195	+	4.21509i	−0.0598918	+	0.307417i
$189$	−10.6272	+	16.5362i	−0.773012	+	1.20283i
$190$	0.461020	+	0.390668i	0.0334459	+	0.0283421i
$191$	−2.56585	−	17.8459i	−0.185658	−	1.29128i	−0.843092	−	0.537769i	$-0.819267\pi$
$191$	−2.56585	−	17.8459i	−0.185658	−	1.29128i	0.657434	−	0.753512i	$-0.271642\pi$
$192$	−7.06225	+	23.5254i	−0.509674	+	1.69780i
$193$	−6.52564	−	10.1541i	−0.469726	−	0.730908i	0.522864	−	0.852416i	$-0.324863\pi$
$193$	−6.52564	−	10.1541i	−0.469726	−	0.730908i	−0.992590	+	0.121508i	$0.961227\pi$
$194$	−9.81706	+	1.16375i	−0.704824	+	0.0835526i
$195$	−20.8693	+	35.1831i	−1.49448	+	2.51952i
$196$	0.653181	+	6.98905i	0.0466558	+	0.499218i
$197$	−1.02153	−	0.146873i	−0.0727808	−	0.0104643i	0.105828	−	0.994384i	$-0.466251\pi$
$197$	−1.02153	−	0.146873i	−0.0727808	−	0.0104643i	−0.178609	+	0.983920i	$0.557160\pi$
$198$	18.2528	+	16.6265i	1.29717	+	1.18159i
$199$	−2.05684	−	0.603943i	−0.145806	−	0.0428124i	0.208015	−	0.978126i	$-0.433300\pi$
$199$	−2.05684	−	0.603943i	−0.145806	−	0.0428124i	−0.353821	+	0.935313i	$0.615118\pi$
$200$	10.7136	−	9.23144i	0.757564	−	0.652761i
$201$	−0.727327	+	0.630232i	−0.0513017	+	0.0444531i
$202$	0.337633	−	1.05255i	0.0237558	−	0.0740575i
$203$	−1.85727	−	1.60934i	−0.130355	−	0.112953i
$204$	20.6264	−	21.5454i	1.44414	−	1.50848i
$205$	4.02900	−	1.34153i	0.281398	−	0.0936964i
$206$	16.4520	−	4.39056i	1.14627	−	0.305905i
$207$	29.9218	+	7.39536i	2.07971	+	0.514013i
$208$	−20.5923	−	11.9998i	−1.42782	−	0.832034i
$209$	0.215643	+	0.472191i	0.0149163	+	0.0326622i
$210$	7.71648	+	16.4157i	0.532487	+	1.13279i
$211$	−7.27174	−	6.30100i	−0.500607	−	0.433779i	0.367597	−	0.929985i	$-0.380180\pi$
$211$	−7.27174	−	6.30100i	−0.500607	−	0.433779i	−0.868205	+	0.496206i	$0.834726\pi$
$212$	0.918092	+	0.0455864i	0.0630548	+	0.00313089i
$213$	−28.1657	+	24.4057i	−1.92988	+	1.67225i
$214$	9.34400	+	21.8811i	0.638743	+	1.49576i
$215$	12.6214	+	5.22616i	0.860775	+	0.356421i
$216$	29.0601	+	6.41360i	1.97729	+	0.436390i
$217$	−1.82629	+	12.7021i	−0.123977	+	0.862278i
$218$	2.23403	−	13.2040i	0.151308	−	0.894288i
$219$	−39.4336	−	18.0087i	−2.66468	−	1.21692i
$220$	11.7026	−	3.26158i	0.788986	−	0.219895i
$221$	15.6471	+	24.3474i	1.05254	+	1.63778i
$222$	1.09467	−	44.1198i	0.0734697	−	2.96112i
$223$	−0.181933	−	1.26537i	−0.0121831	−	0.0847355i	0.982823	−	0.184552i	$-0.0590835\pi$
$223$	−0.181933	−	1.26537i	−0.0121831	−	0.0847355i	−0.995006	+	0.0998166i	$0.968174\pi$
$224$	−9.52913	+	4.56985i	−0.636692	+	0.305336i
$225$	−22.7279	−	22.7168i	−1.51520	−	1.51446i
$226$	−1.10183	−	0.536609i	−0.0732929	−	0.0356947i
$227$	−2.67267	−	9.10227i	−0.177391	−	0.604139i	−0.999399	−	0.0346627i	$-0.988964\pi$
$227$	−2.67267	−	9.10227i	−0.177391	−	0.604139i	0.822008	−	0.569476i	$-0.192854\pi$
$228$	0.954473	+	0.682577i	0.0632115	+	0.0452047i
$229$		−	19.1841i		−	1.26772i	−0.773446	−	0.633862i	$-0.781469\pi$
$229$		−	19.1841i		−	1.26772i	0.773446	−	0.633862i	$-0.218531\pi$
$230$	10.9055	−	10.5390i	0.719084	−	0.694923i
$231$			15.5819i			1.02522i
$232$	−1.31074	+	3.48209i	−0.0860544	+	0.228610i
$233$	5.92006	+	20.1619i	0.387836	+	1.32085i	0.889954	+	0.456050i	$0.150736\pi$
$233$	5.92006	+	20.1619i	0.387836	+	1.32085i	−0.502118	+	0.864799i	$0.667446\pi$
$234$	−23.7120	+	48.6884i	−1.55010	+	3.18286i
$235$	3.01216	−	3.73880i	0.196492	−	0.243892i
$236$	−1.92165	+	5.51628i	−0.125089	+	0.359080i
$237$	−3.92810	−	27.3206i	−0.255158	−	1.77466i
$238$	12.8294	+	0.318316i	0.831607	+	0.0206333i
$239$	13.0022	+	20.2318i	0.841041	+	1.30869i	0.949239	+	0.314556i	$0.101856\pi$
$239$	13.0022	+	20.2318i	0.841041	+	1.30869i	−0.108198	+	0.994129i	$0.534508\pi$
$240$	19.2625	−	19.5731i	1.24339	−	1.26344i
$241$	9.04472	+	4.13058i	0.582622	+	0.266074i	0.684847	−	0.728687i	$-0.259869\pi$
$241$	9.04472	+	4.13058i	0.582622	+	0.266074i	−0.102225	+	0.994761i	$0.532596\pi$
$242$	−5.04858	−	0.854185i	−0.324535	−	0.0549091i
$243$	1.19873	−	8.33732i	0.0768983	−	0.534839i
$244$	1.73265	+	0.897663i	0.110922	+	0.0574670i
$245$	3.00243	−	7.25102i	0.191818	−	0.463251i
$246$	7.58347	−	3.23840i	0.483504	−	0.206473i
$247$	−0.860496	+	0.745624i	−0.0547521	+	0.0474429i
$248$	18.9968	−	4.07247i	1.20630	−	0.258602i
$249$	34.6381	+	30.0141i	2.19510	+	1.90207i
$250$	−15.4112	+	3.53470i	−0.974692	+	0.223554i
$251$	3.62829	+	7.94485i	0.229016	+	0.501475i	0.988900	−	0.148584i	$-0.0474716\pi$
$251$	3.62829	+	7.94485i	0.229016	+	0.501475i	−0.759884	+	0.650059i	$0.774744\pi$
$252$	11.9649	+	20.8205i	0.753718	+	1.31157i
$253$	12.3296	−	4.20801i	0.775154	−	0.264555i
$254$	−1.88852	−	7.07652i	−0.118496	−	0.444021i
$255$	−31.6399	+	10.5350i	−1.98137	+	0.659730i
$256$	11.4905	+	11.1341i	0.718155	+	0.695883i
$257$	11.9125	+	10.3222i	0.743079	+	0.643881i	0.941800	−	0.336175i	$-0.109133\pi$
$257$	11.9125	+	10.3222i	0.743079	+	0.643881i	−0.198721	+	0.980056i	$0.563679\pi$
$258$	25.2591	+	8.10248i	1.57256	+	0.504438i
$259$	14.3507	−	12.4350i	0.891711	−	0.772672i
$260$	14.0958	+	22.6132i	0.874185	+	1.40241i
$261$	8.11168	+	2.38180i	0.502101	+	0.147430i
$262$	0.987106	−	1.08366i	0.0609836	−	0.0669488i
$263$	3.68571	+	0.529925i	0.227271	+	0.0326766i	0.255009	−	0.966939i	$-0.417921\pi$
$263$	3.68571	+	0.529925i	0.227271	+	0.0326766i	−0.0277385	+	0.999615i	$0.508831\pi$
$264$	22.1280	−	8.17729i	1.36188	−	0.503277i
$265$	−0.883920	−	0.524308i	−0.0542988	−	0.0322080i
$266$	0.0594339	+	0.501366i	0.00364413	+	0.0307407i
$267$	4.54956	+	7.07925i	0.278429	+	0.433243i
$268$	0.146571	+	0.609524i	0.00895323	+	0.0372326i
$269$	−3.34253	−	23.2478i	−0.203798	−	1.41744i	−0.792883	−	0.609374i	$-0.791421\pi$
$269$	−3.34253	−	23.2478i	−0.203798	−	1.41744i	0.589085	−	0.808071i	$-0.299488\pi$
$270$	−25.3839	−	21.5103i	−1.54481	−	1.30907i
$271$	4.39395	−	6.83712i	0.266913	−	0.415325i	−0.681763	−	0.731573i	$-0.738787\pi$
$271$	4.39395	−	6.83712i	0.266913	−	0.415325i	0.948677	+	0.316248i	$0.102423\pi$
$272$	−6.28074	−	18.3861i	−0.380826	−	1.11482i
$273$	−32.7931	+	9.62891i	−1.98473	+	0.582768i
$274$	12.6413	−	10.4161i	0.763688	−	0.629263i
$275$	−13.2728	−	2.88393i	−0.800381	−	0.173907i
$276$	19.4254	−	22.1342i	1.16927	−	1.33232i
$277$			12.8423i			0.771616i	0.922579	+	0.385808i	$0.126077\pi$
$277$			12.8423i			0.771616i	−0.922579	+	0.385808i	$0.873923\pi$
$278$	9.50690	+	11.5378i	0.570186	+	0.691991i
$279$	−12.4374	−	42.3578i	−0.744605	−	2.53589i
$280$	11.8069	+	0.455935i	0.705595	+	0.0272473i
$281$	−10.1588	+	15.8074i	−0.606022	+	0.942989i	0.393696	+	0.919241i	$0.371196\pi$
$281$	−10.1588	+	15.8074i	−0.606022	+	0.942989i	−0.999718	+	0.0237481i	$0.992440\pi$
$282$	5.23349	−	7.71574i	0.311650	−	0.459466i
$283$	−18.5616	+	2.66876i	−1.10337	+	0.158641i	−0.669847	−	0.742499i	$-0.733640\pi$
$283$	−18.5616	+	2.66876i	−1.10337	+	0.158641i	−0.433528	+	0.901140i	$0.642731\pi$
$284$	5.67594	+	23.6038i	0.336805	+	1.40063i
$285$	−0.587386	−	1.17309i	−0.0347937	−	0.0694878i
$286$	2.69465	+	22.7313i	0.159338	+	1.34413i
$287$	3.22729	+	1.47385i	0.190501	+	0.0869988i
$288$	23.2882	−	27.9179i	1.37227	−	1.64508i
$289$	−0.938367	+	6.52649i	−0.0551981	+	0.383911i
$290$	3.11355	−	2.75854i	0.182834	−	0.161987i
$291$	20.5931	+	6.04668i	1.20719	+	0.354463i
$292$	−22.2324	+	17.4114i	−1.30105	+	1.01893i
$293$	−12.1589	−	14.0322i	−0.710333	−	0.819768i	0.279777	−	0.960065i	$-0.409740\pi$
$293$	−12.1589	−	14.0322i	−0.710333	−	0.819768i	−0.990109	+	0.140297i	$0.955194\pi$
$294$	4.65488	−	14.5114i	0.271478	−	0.846319i
$295$	4.77939	−	4.45086i	0.278267	−	0.259139i
$296$	−25.1901	−	13.8537i	−1.46415	−	0.805233i
$297$	−11.8733	−	25.9990i	−0.688960	−	1.50861i
$298$	23.4311	−	6.25308i	1.35733	−	0.362231i
$299$	16.4751	+	23.3479i	0.952780	+	1.35025i
$300$	−29.2618	+	9.29697i	−1.68943	+	0.536761i
$301$	4.74129	+	10.3820i	0.273283	+	0.598407i
$302$	−28.5499	+	17.3627i	−1.64286	+	0.999110i
$303$	−1.57155	+	1.81367i	−0.0902834	+	0.104193i
$304$	0.680801	−	0.347516i	0.0390466	−	0.0199314i
$305$	−1.24450	−	1.79195i	−0.0712597	−	0.102607i
$306$	−40.6010	+	17.3380i	−2.32100	+	0.991149i
$307$	−7.90623	−	2.32148i	−0.451233	−	0.132494i	0.0482169	−	0.998837i	$-0.484646\pi$
$307$	−7.90623	−	2.32148i	−0.451233	−	0.132494i	−0.499449	+	0.866343i	$0.666464\pi$
$308$	9.01234	+	4.66917i	0.513526	+	0.266051i
$309$	−36.5918	−	5.26111i	−2.08163	−	0.299294i
$310$	−20.9079	−	5.88973i	−1.18749	−	0.334514i
$311$	−22.4600	−	10.2571i	−1.27359	−	0.581629i	−0.340153	−	0.940370i	$-0.610479\pi$
$311$	−22.4600	−	10.2571i	−1.27359	−	0.581629i	−0.933437	+	0.358741i	$0.883206\pi$
$312$	30.8836	+	41.5164i	1.74844	+	2.35040i
$313$	2.65152	−	1.70403i	0.149873	−	0.0963173i	−0.463555	−	0.886068i	$-0.653426\pi$
$313$	2.65152	−	1.70403i	0.149873	−	0.0963173i	0.613428	+	0.789751i	$0.289790\pi$
$314$	0.417156	−	16.8131i	0.0235415	−	0.948816i
$315$	−0.961544	−	26.8308i	−0.0541769	−	1.51174i
$316$	−16.9788	−	5.91473i	−0.955134	−	0.332729i
$317$	−2.85543	+	4.44313i	−0.160377	+	0.249551i	−0.912137	−	0.409885i	$-0.865569\pi$
$317$	−2.85543	+	4.44313i	−0.160377	+	0.249551i	0.751760	+	0.659436i	$0.229205\pi$
$318$	−1.79421	−	0.873805i	−0.100614	−	0.0490005i
$319$	3.42864	−	1.00674i	0.191967	−	0.0563666i
$320$	−5.54868	−	17.0062i	−0.310181	−	0.950678i
$321$		−	51.6551i		−	2.88311i
$322$	12.6687	−	0.234302i	0.706000	−	0.0130572i
$323$	−0.928195			−0.0516462
$324$	−21.1876	−	15.1520i	−1.17709	−	0.841775i
$325$	−2.13259	−	29.7155i	−0.118295	−	1.64832i
$326$	−18.8211	−	9.16614i	−1.04240	−	0.507665i
$327$	−15.7185	+	24.4585i	−0.869237	+	1.35256i
$328$	0.399367	−	5.35655i	0.0220513	−	0.295766i
$329$	3.97056	−	0.570880i	0.218904	−	0.0314736i
$330$	−26.1464	−	3.46576i	−1.43931	−	0.190784i
$331$	0.326709	+	0.508369i	0.0179575	+	0.0279425i	0.850116	−	0.526595i	$-0.176532\pi$
$331$	0.326709	+	0.508369i	0.0179575	+	0.0279425i	−0.832159	+	0.554537i	$0.812895\pi$
$332$	27.7391	−	11.0403i	1.52238	−	0.605916i
$333$	−27.1362	+	59.4200i	−1.48706	+	3.25620i
$334$	20.7919	+	3.51785i	1.13768	+	0.192488i
$335$	0.173253	−	0.679144i	0.00946582	−	0.0371056i
$336$	22.9223	−	0.999459i	1.25052	−	0.0545250i
$337$	21.9866	+	6.45586i	1.19769	+	0.351673i	0.818968	−	0.573839i	$-0.194546\pi$
$337$	21.9866	+	6.45586i	1.19769	+	0.351673i	0.378719	+	0.925512i	$0.376365\pi$
$338$	−29.2664	+	12.4978i	−1.59188	+	0.679788i
$339$	1.74241	+	2.01085i	0.0946347	+	0.109214i
$340$	−3.38767	+	21.4568i	−0.183722	+	1.16366i
$341$	−14.1020	−	12.2194i	−0.763665	−	0.661720i
$342$	−0.902469	−	1.48395i	−0.0487999	−	0.0802429i
$343$	17.8602	−	8.15648i	0.964360	−	0.440408i
$344$	12.2553	−	12.1815i	0.660761	−	0.656783i
$345$	−30.7598	+	11.7441i	−1.65605	+	0.632283i
$346$	−9.66529	+	2.57938i	−0.519609	+	0.138668i
$347$	2.83211	+	6.20145i	0.152035	+	0.332911i	0.970290	−	0.241945i	$-0.0777853\pi$
$347$	2.83211	+	6.20145i	0.152035	+	0.332911i	−0.818255	+	0.574856i	$0.805058\pi$
$348$	5.58596	−	5.83482i	0.299439	−	0.312779i
$349$	9.76190	−	11.2658i	0.522542	−	0.603046i	−0.431723	−	0.902006i	$-0.642094\pi$
$349$	9.76190	−	11.2658i	0.522542	−	0.603046i	0.954266	+	0.298960i	$0.0966397\pi$
$350$	−11.4354	−	6.61387i	−0.611249	−	0.353526i
$351$	47.3791	−	41.0542i	2.52891	−	2.19131i
$352$	1.90109	−	15.2488i	0.101329	−	0.812764i
$353$	−6.95670	+	23.6923i	−0.370268	+	1.26102i	0.538113	+	0.842873i	$0.319137\pi$
$353$	−6.95670	+	23.6923i	−0.370268	+	1.26102i	−0.908381	+	0.418143i	$0.862681\pi$
$354$	8.54010	−	9.37545i	0.453901	−	0.498299i
$355$	6.70921	−	26.2998i	0.356088	−	1.39585i
$356$	5.45781	−	0.510075i	0.289264	−	0.0270339i
$357$	−25.3440	−	11.5742i	−1.34134	−	0.612571i
$358$	−0.931678	−	7.85935i	−0.0492407	−	0.415379i
$359$	−21.2236	+	13.6396i	−1.12014	+	0.719868i	−0.963479	−	0.267784i	$-0.913709\pi$
$359$	−21.2236	+	13.6396i	−1.12014	+	0.719868i	−0.156658	+	0.987653i	$0.550072\pi$
$360$	−37.5979	+	15.4461i	−1.98158	+	0.814081i
$361$	2.69879	+	18.7705i	0.142041	+	0.987919i
$362$	11.0086	+	7.46701i	0.578600	+	0.392458i
$363$	9.35176	+	6.01001i	0.490840	+	0.315444i
$364$	−4.25732	+	21.8523i	−0.223144	+	1.14537i
$365$	31.0697	−	5.60951i	1.62626	−	0.293615i
$366$	−2.69407	−	3.26959i	−0.140821	−	0.170904i
$367$			10.1040i			0.527425i	0.964601	+	0.263712i	$0.0849470\pi$
$367$			10.1040i			0.527425i	−0.964601	+	0.263712i	$0.915053\pi$
$368$	−6.98119	−	17.8679i	−0.363919	−	0.931430i
$369$	−12.2051			−0.635374
$370$	17.6739	+	26.8462i	0.918822	+	1.39567i
$371$	−0.241911	−	0.823874i	−0.0125594	−	0.0427734i
$372$	−41.4015	−	8.06595i	−2.14657	−	0.418200i
$373$	0.209399	+	0.134572i	0.0108423	+	0.00696790i	0.546051	−	0.837752i	$-0.316131\pi$
$373$	0.209399	+	0.134572i	0.0108423	+	0.00696790i	−0.535208	+	0.844720i	$0.679767\pi$
$374$	−10.4749	+	15.4431i	−0.541643	+	0.798544i
$375$	33.7840	+	6.08253i	1.74460	+	0.314101i
$376$	−2.89443	−	5.33901i	−0.149269	−	0.275338i
$377$	4.23748	+	6.59365i	0.218241	+	0.339590i
$378$	−3.27245	−	27.6053i	−0.168316	−	1.41986i
$379$	0.993358	−	2.17515i	0.0510254	−	0.111730i	−0.882402	−	0.470496i	$-0.844075\pi$
$379$	0.993358	−	2.17515i	0.0510254	−	0.111730i	0.933428	+	0.358766i	$0.116802\pi$
$380$	−0.854508	−	0.0117850i	−0.0438353	−	0.000604555i
$381$	−2.26297	+	15.7393i	−0.115935	+	0.806347i
$382$	18.8495	+	17.1700i	0.964427	+	0.878496i
$383$	−3.84588	+	13.0978i	−0.196515	+	0.669269i	0.800990	+	0.598677i	$0.204307\pi$
$383$	−3.84588	+	13.0978i	−0.196515	+	0.669269i	−0.997505	+	0.0705914i	$0.977511\pi$
$384$	−13.4488	−	32.0276i	−0.686307	−	1.63440i
$385$	−6.47321	−	9.32077i	−0.329906	−	0.475030i
$386$	16.2541	+	5.21390i	0.827310	+	0.265380i
$387$	−29.6731	−	25.7119i	−1.50837	−	1.30701i
$388$	9.66808	−	10.0988i	0.490823	−	0.512690i
$389$	23.6813	−	10.8149i	1.20069	−	0.548338i	0.288254	−	0.957554i	$-0.406925\pi$
$389$	23.6813	−	10.8149i	1.20069	−	0.548338i	0.912437	+	0.409216i	$0.134198\pi$
$390$	−8.86336	−	57.1682i	−0.448813	−	2.89482i
$391$	−2.31404	+	23.1797i	−0.117026	+	1.17225i
$392$	−6.99828	−	7.04067i	−0.353467	−	0.355608i
$393$	−2.89482	+	1.32202i	−0.146025	+	0.0666872i
$394$	1.24701	−	0.758375i	0.0628237	−	0.0382064i
$395$	13.6995	+	14.7107i	0.689297	+	0.740176i
$396$	−34.8742	−	1.73162i	−1.75249	−	0.0870173i
$397$	10.9072	−	9.45114i	0.547416	−	0.474339i	−0.336696	−	0.941613i	$-0.609309\pi$
$397$	10.9072	−	9.45114i	0.547416	−	0.474339i	0.884112	+	0.467274i	$0.154764\pi$
$398$	2.78804	−	1.19059i	0.139752	−	0.0596789i
$399$	0.308810	−	1.05171i	0.0154598	−	0.0526513i
$400$	−3.39116	+	19.7104i	−0.169558	+	0.985520i
$401$	11.4183	+	1.64171i	0.570203	+	0.0819829i	0.421385	−	0.906882i	$-0.361544\pi$
$401$	11.4183	+	1.64171i	0.570203	+	0.0819829i	0.148818	+	0.988865i	$0.452453\pi$
$402$	0.227050	−	1.34195i	0.0113242	−	0.0669306i
$403$	17.0021	−	37.2295i	0.846936	−	1.85453i
$404$	0.578077	+	1.45243i	0.0287604	+	0.0722612i
$405$	13.0389	+	26.0405i	0.647908	+	1.29396i
$406$	3.47440	+	0.0862047i	0.172431	+	0.00427827i
$407$	3.92942	+	27.3297i	0.194774	+	1.35468i
$408$	−3.13623	+	42.0651i	−0.155267	+	2.08253i
$409$	23.6484	+	15.1979i	1.16934	+	0.751488i	0.973397	−	0.229127i	$-0.0735872\pi$
$409$	23.6484	+	15.1979i	1.16934	+	0.751488i	0.195942	+	0.980615i	$0.437224\pi$
$410$	−3.19093	+	5.08754i	−0.157589	+	0.251256i
$411$	−34.1208	+	10.0188i	−1.68306	+	0.494190i
$412$	−14.0078	+	19.5876i	−0.690113	+	0.965011i
$413$	5.45652			0.268498
$414$	−39.3084	+	18.8377i	−1.93190	+	0.925820i
$415$	−33.1885	−	3.56404i	−1.62916	−	0.174952i
$416$	33.2668	−	5.42210i	1.63104	−	0.265840i
$417$	−9.14421	−	31.1423i	−0.447794	−	1.52505i
$418$	−0.660010	−	0.321434i	−0.0322821	−	0.0157219i
$419$	5.30330	+	3.40823i	0.259083	+	0.166503i	0.663734	−	0.747968i	$-0.268971\pi$
$419$	5.30330	+	3.40823i	0.259083	+	0.166503i	−0.404651	+	0.914471i	$0.632607\pi$
$420$	−23.1850	−	10.9771i	−1.13131	−	0.535629i
$421$	−1.68685	+	0.242533i	−0.0822122	+	0.0118203i	−0.183298	−	0.983057i	$-0.558677\pi$
$421$	−1.68685	+	0.242533i	−0.0822122	+	0.0118203i	0.101086	+	0.994878i	$0.467768\pi$
$422$	13.6032	+	0.337515i	0.662194	+	0.0164300i
$423$	−11.6089	+	7.46061i	−0.564446	+	0.362747i
$424$	−1.04303	+	0.775902i	−0.0506542	+	0.0376811i
$425$	14.5497	−	19.4460i	0.705763	−	0.943269i
$426$	8.79248	−	51.9671i	0.425997	−	2.51781i
$427$	0.259412	−	1.80425i	0.0125538	−	0.0873138i
$428$	−29.8765	−	15.4786i	−1.44413	−	0.748186i
$429$	14.0010	−	47.6831i	0.675975	−	2.30216i
$430$	−18.4754	+	5.64667i	−0.890965	+	0.272307i
$431$	−0.00869822	−	0.0100383i	−0.000418979	−	0.000483527i	0.755540	−	0.655102i	$-0.227375\pi$
$431$	−0.00869822	−	0.0100383i	−0.000418979	−	0.000483527i	−0.755959	+	0.654619i	$0.772829\pi$
$432$	−37.4851	+	19.1343i	−1.80350	+	0.920599i
$433$	20.6582	−	23.8408i	0.992769	−	1.14572i	0.00344341	−	0.999994i	$-0.498904\pi$
$433$	20.6582	−	23.8408i	0.992769	−	1.14572i	0.989326	−	0.145722i	$-0.0465506\pi$
$434$	−9.42999	−	15.5060i	−0.452654	−	0.744310i
$435$	−8.56856	+	2.85305i	−0.410831	+	0.136793i
$436$	9.43631	+	16.4204i	0.451917	+	0.786395i
$437$	−0.915586	+	0.0396685i	−0.0437984	+	0.00189760i
$438$	59.2348	−	15.8080i	2.83035	−	0.755337i
$439$	24.2205	−	11.0611i	1.15598	−	0.527920i	0.257219	−	0.966353i	$-0.417194\pi$
$439$	24.2205	−	11.0611i	1.15598	−	0.527920i	0.898764	+	0.438434i	$0.144467\pi$
$440$	−9.83937	+	14.0841i	−0.469073	+	0.671434i
$441$	−14.7715	+	17.0472i	−0.703405	+	0.811773i
$442$	−38.9739	−	12.5018i	−1.85380	−	0.594652i
$443$	−10.4002	−	12.0025i	−0.494128	−	0.570254i	0.452836	−	0.891594i	$-0.350412\pi$
$443$	−10.4002	−	12.0025i	−0.494128	−	0.570254i	−0.946964	+	0.321340i	$0.895867\pi$
$444$	38.4829	+	49.1383i	1.82632	+	2.33200i
$445$	−5.66239	−	2.34463i	−0.268423	−	0.111146i
$446$	1.33654	+	1.21745i	0.0632870	+	0.0576481i
$447$	−52.1144	−	7.49292i	−2.46493	−	0.354403i
$448$	6.29067	−	13.5574i	0.297206	−	0.640527i
$449$	−1.30746	+	2.86293i	−0.0617026	+	0.135110i	−0.937971	−	0.346713i	$-0.887298\pi$
$449$	−1.30746	+	2.86293i	−0.0617026	+	0.135110i	0.876269	+	0.481823i	$0.160025\pi$
$450$	45.2357	+	4.35428i	2.13243	+	0.205263i
$451$	−4.33991	+	2.78909i	−0.204358	+	0.131333i
$452$	1.68516	−	0.405226i	0.0792633	−	0.0190602i
$453$	71.8069	−	10.3243i	3.37378	−	0.485077i
$454$	11.1029	+	7.53094i	0.521084	+	0.353445i
$455$	15.6159	−	19.3830i	0.732087	−	0.908691i
$456$	−1.65560	+	0.113388i	−0.0775304	+	0.00530986i
$457$	22.1289	−	6.49763i	1.03515	−	0.303946i	0.280344	−	0.959899i	$-0.409551\pi$
$457$	22.1289	−	6.49763i	1.03515	−	0.303946i	0.754802	+	0.655953i	$0.227733\pi$
$458$	17.2526	+	20.9382i	0.806163	+	0.978378i
$459$	51.1066			2.38545
$460$	−2.42464	+	21.3101i	−0.113049	+	0.993589i
$461$	37.2090			1.73300			0.866498	−	0.499180i	$-0.166365\pi$
$461$	37.2090			1.73300			0.866498	+	0.499180i	$0.166365\pi$
$462$	−14.0131	−	17.0067i	−0.651949	−	0.791221i
$463$	−15.7655	+	4.62916i	−0.732683	+	0.215135i	−0.626731	−	0.779236i	$-0.715607\pi$
$463$	−15.7655	+	4.62916i	−0.732683	+	0.215135i	−0.105953	+	0.994371i	$0.533789\pi$
$464$	−1.70092	−	4.97925i	−0.0789632	−	0.231156i
$465$	36.7232	+	29.5861i	1.70300	+	1.37202i
$466$	−24.5933	−	16.6813i	−1.13926	−	0.772748i
$467$	−3.22356	+	0.463478i	−0.149169	+	0.0214472i	−0.216495	−	0.976284i	$-0.569462\pi$
$467$	−3.22356	+	0.463478i	−0.149169	+	0.0214472i	0.0673259	+	0.997731i	$0.478553\pi$
$468$	−17.9063	−	74.4648i	−0.827721	−	3.44214i
$469$	0.492632	−	0.316596i	0.0227476	−	0.0146190i
$470$	0.0747945	+	6.78954i	0.00345001	+	0.313178i
$471$	−15.1681	+	33.2135i	−0.698909	+	1.53040i
$472$	−2.86354	−	7.74883i	−0.131805	−	0.356669i
$473$	−16.4268	−	2.36182i	−0.755306	−	0.108597i
$474$	28.8571	+	26.2860i	1.32545	+	1.20735i
$475$	0.838699	+	0.457698i	0.0384821	+	0.0210006i
$476$	−14.2887	+	11.1903i	−0.654922	+	0.512906i
$477$	1.93437	+	2.23238i	0.0885686	+	0.102214i
$478$	−32.3858	−	10.3886i	−1.48129	−	0.475161i
$479$	2.66660	−	3.07742i	0.121840	−	0.140611i	−0.691552	−	0.722326i	$-0.743073\pi$
$479$	2.66660	−	3.07742i	0.121840	−	0.140611i	0.813392	+	0.581715i	$0.197618\pi$
$480$	−3.42134	+	38.6858i	−0.156162	+	1.76576i
$481$	−55.0887	+	25.1582i	−2.51183	+	1.14711i
$482$	−13.5864	+	3.62582i	−0.618844	+	0.165152i
$483$	−25.4943	−	10.3338i	−1.16003	−	0.470205i
$484$	6.27837	−	3.60799i	0.285380	−	0.163999i
$485$	−14.8303	+	4.93802i	−0.673410	+	0.224224i
$486$	6.18957	+	10.1777i	0.280765	+	0.461668i
$487$	−22.3104	+	25.7475i	−1.01098	+	1.16673i	−0.0250292	+	0.999687i	$0.507968\pi$
$487$	−22.3104	+	25.7475i	−1.01098	+	1.16673i	−0.985949	+	0.167045i	$0.946578\pi$
$488$	−2.69836	+	0.578465i	−0.122149	+	0.0261859i
$489$	29.7632	+	34.3485i	1.34594	+	1.55329i
$490$	3.24402	+	10.6141i	0.146550	+	0.479498i
$491$	6.06186	−	20.6448i	0.273568	−	0.931687i	−0.702035	−	0.712143i	$-0.747725\pi$
$491$	6.06186	−	20.6448i	0.273568	−	0.931687i	0.975603	−	0.219544i	$-0.0704570\pi$
$492$	−5.36450	+	10.3544i	−0.241850	+	0.466815i
$493$	−0.909322	+	6.32447i	−0.0409538	+	0.284840i
$494$	0.268621	−	1.58766i	0.0120858	−	0.0714322i
$495$	33.5762	+	19.9161i	1.50914	+	0.895163i
$496$	−17.0713	+	21.5290i	−0.766523	+	0.966680i
$497$	19.0771	−	12.2601i	0.855727	−	0.549942i
$498$	−64.7974	−	1.60772i	−2.90364	−	0.0720435i
$499$	33.3644	−	4.79708i	1.49360	−	0.214747i	0.653393	−	0.757019i	$-0.273345\pi$
$499$	33.3644	−	4.79708i	1.49360	−	0.214747i	0.840203	+	0.542273i	$0.182436\pi$
$500$	13.6415	−	17.7175i	0.610067	−	0.792350i
$501$	−38.5140	−	24.7515i	−1.72068	−	1.10581i
$502$	−11.1050	−	5.40829i	−0.495640	−	0.241384i
$503$	10.1068	+	34.4206i	0.450640	+	1.53474i	0.801316	+	0.598242i	$0.204134\pi$
$503$	10.1068	+	34.4206i	0.450640	+	1.53474i	−0.350676	+	0.936497i	$0.614048\pi$
$504$	−31.7831	−	11.9639i	−1.41573	−	0.532916i
$505$	0.186615	−	1.73777i	0.00830425	−	0.0773297i
$506$	−9.67257	+	15.6810i	−0.429998	+	0.697104i
$507$	69.0895			3.06837
$508$	8.42524	+	6.02518i	0.373809	+	0.267324i
$509$	−18.7165	+	5.49567i	−0.829596	+	0.243591i	−0.668844	−	0.743403i	$-0.733210\pi$
$509$	−18.7165	+	5.49567i	−0.829596	+	0.243591i	−0.160753	+	0.986995i	$0.551392\pi$
$510$	25.0584	−	39.9526i	1.10961	−	1.76913i
$511$	22.1908	+	14.2611i	0.981662	+	0.630876i
$512$	−22.5542	−	1.81858i	−0.996765	−	0.0803705i
$513$	0.286136	+	1.99012i	0.0126332	+	0.0878659i
$514$	−22.2846	−	0.552913i	−0.982932	−	0.0243879i
$515$	24.0740	−	12.0543i	1.06083	−	0.531175i
$516$	−34.8553	+	13.8726i	−1.53442	+	0.610709i
$517$	−2.42303	+	5.30569i	−0.106565	+	0.233344i
$518$	−4.47987	+	26.4778i	−0.196834	+	1.16337i
$519$	21.4971	+	3.09081i	0.943617	+	0.135672i
$520$	−35.7211	−	12.0042i	−1.56647	−	0.526418i
$521$	−4.22536	+	14.3902i	−0.185116	+	0.630448i	0.813676	+	0.581318i	$0.197463\pi$
$521$	−4.22536	+	14.3902i	−0.185116	+	0.630448i	−0.998792	+	0.0491296i	$0.984355\pi$
$522$	−10.9954	+	4.69540i	−0.481254	+	0.205512i
$523$	16.3794	−	14.1928i	0.716220	−	0.620608i	−0.218565	−	0.975822i	$-0.570138\pi$
$523$	16.3794	−	14.1928i	0.716220	−	0.620608i	0.934785	+	0.355214i	$0.115592\pi$
$524$	−0.102806	+	2.07047i	−0.00449109	+	0.0904487i
$525$	17.1930	+	22.9555i	0.750363	+	1.00186i
$526$	−4.49928	+	2.73625i	−0.196178	+	0.119306i
$527$	30.3497	−	13.8603i	1.32206	−	0.603763i
$528$	−16.7972	+	28.8251i	−0.731006	+	1.25445i
$529$	−1.29197	+	22.9637i	−0.0561725	+	0.998421i
$530$	1.43626	−	0.222678i	0.0623872	−	0.00967250i
$531$	−17.0747	+	7.79775i	−0.740978	+	0.338393i
$532$	−0.515756	−	0.493758i	−0.0223608	−	0.0214071i
$533$	−8.55166	−	7.41006i	−0.370414	−	0.320965i
$534$	−11.3320	−	3.63503i	−0.490386	−	0.157303i
$535$	21.4591	+	30.8989i	0.927758	+	1.33588i
$536$	−0.708128	−	0.533442i	−0.0305865	−	0.0230412i
$537$	−4.84086	+	16.4864i	−0.208898	+	0.711443i
$538$	24.5553	+	22.3675i	1.05866	+	0.964330i
$539$	−1.35687	+	9.43721i	−0.0584444	+	0.406489i
$540$	47.0494	+	0.648882i	2.02468	+	0.0279234i
$541$	14.0374	−	30.7375i	0.603513	−	1.32151i	−0.323410	−	0.946259i	$-0.604829\pi$
$541$	14.0374	−	30.7375i	0.603513	−	1.32151i	0.926923	−	0.375251i	$-0.122444\pi$
$542$	1.35304	+	11.4138i	0.0581180	+	0.490265i
$543$	−15.6134	−	24.2949i	−0.670036	−	1.04260i
$544$	23.3900	+	14.4189i	1.00284	+	0.618204i
$545$	−0.758336	−	21.1605i	−0.0324836	−	0.906416i
$546$	27.1320	−	40.0007i	1.16114	−	1.71187i
$547$	−18.7906	−	12.0760i	−0.803430	−	0.516333i	0.0733037	−	0.997310i	$-0.476646\pi$
$547$	−18.7906	−	12.0760i	−0.803430	−	0.516333i	−0.876733	+	0.480977i	$0.840282\pi$
$548$	−4.42969	+	22.7371i	−0.189227	+	0.971279i
$549$	1.76664	+	6.01662i	0.0753983	+	0.256783i
$550$	17.0800	−	8.78886i	0.728292	−	0.374758i
$551$	−0.251369			−0.0107087
$552$	−1.29588	+	41.6277i	−0.0551563	+	1.77179i
$553$			16.7949i			0.714191i
$554$	−11.5493	−	14.0165i	−0.490681	−	0.595502i
$555$	−12.3982	−	68.6707i	−0.526275	−	2.91491i
$556$	−20.7523	−	4.04302i	−0.880093	−	0.171462i
$557$	−13.2879	−	8.53959i	−0.563025	−	0.361834i	0.227959	−	0.973671i	$-0.426795\pi$
$557$	−13.2879	−	8.53959i	−0.563025	−	0.361834i	−0.790984	+	0.611837i	$0.790431\pi$
$558$	51.6676	+	35.0455i	2.18727	+	1.48360i
$559$	−5.18043	−	36.0307i	−0.219109	−	1.52393i
$560$	−13.2964	+	10.1205i	−0.561877	+	0.427669i
$561$	34.0814	−	21.9028i	1.43892	−	0.924737i
$562$	−3.12822	−	26.3887i	−0.131956	−	1.11314i
$563$	−20.8241	−	9.51004i	−0.877631	−	0.400800i	−0.0749343	−	0.997188i	$-0.523875\pi$
$563$	−20.8241	−	9.51004i	−0.877631	−	0.400800i	−0.802696	+	0.596388i	$0.796602\pi$
$564$	1.22689	+	13.1278i	0.0516615	+	0.552780i
$565$	−1.87764	−	0.478995i	−0.0789929	−	0.0201515i
$566$	17.8587	−	19.6056i	0.750658	−	0.824084i
$567$	−6.85501	+	23.3460i	−0.287883	+	0.980441i
$568$	−27.4222	−	20.6575i	−1.15061	−	0.866769i
$569$	−8.89087	+	7.70399i	−0.372725	+	0.322968i	−0.821000	−	0.570927i	$-0.806584\pi$
$569$	−8.89087	+	7.70399i	−0.372725	+	0.322968i	0.448276	+	0.893895i	$0.352038\pi$
$570$	1.69607	+	0.752103i	0.0710407	+	0.0315021i
$571$	−3.35817	+	3.87553i	−0.140535	+	0.162186i	−0.821654	−	0.569987i	$-0.806948\pi$
$571$	−3.35817	+	3.87553i	−0.140535	+	0.162186i	0.681119	+	0.732173i	$0.261494\pi$
$572$	−23.3837	−	22.3863i	−0.977720	−	0.936019i
$573$	−22.9957	−	50.3535i	−0.960658	−	2.10355i
$574$	−4.84783	+	1.29374i	−0.202345	+	0.0539999i
$575$	13.5210	−	19.8036i	0.563863	−	0.825869i
$576$	−0.310457	+	51.4140i	−0.0129357	+	2.14225i
$577$	−22.8631	+	10.4412i	−0.951805	+	0.434675i	−0.829928	−	0.557870i	$-0.811619\pi$
$577$	−22.8631	+	10.4412i	−0.951805	+	0.434675i	−0.121877	+	0.992545i	$0.538891\pi$
$578$	−4.84522	−	7.96712i	−0.201535	−	0.331388i
$579$	−28.0076	−	24.2687i	−1.16396	−	1.00857i
$580$	−0.917432	+	5.81084i	−0.0380943	+	0.241282i
$581$	−18.2629	−	21.0765i	−0.757673	−	0.874401i
$582$	−27.9139	+	11.9202i	−1.15707	+	0.494108i
$583$	1.19796	+	0.351753i	0.0496145	+	0.0145681i
$584$	8.60675	−	38.9974i	0.356150	−	1.61372i
$585$	−21.1661	+	82.9702i	−0.875110	+	3.43039i
$586$	25.8901	+	4.38042i	1.06951	+	0.180954i
$587$	−16.4892	+	36.1062i	−0.680581	+	1.49026i	0.181446	+	0.983401i	$0.441922\pi$
$587$	−16.4892	+	36.1062i	−0.680581	+	1.49026i	−0.862027	+	0.506863i	$0.830805\pi$
$588$	7.96983	+	20.0244i	0.328670	+	0.825792i
$589$	0.709649	+	1.10423i	0.0292406	+	0.0454992i
$590$	−1.21365	+	9.15600i	−0.0499651	+	0.376947i
$591$	−3.13641	+	0.450948i	−0.129015	+	0.0185495i
$592$	39.9523	−	7.53350i	1.64203	−	0.309625i
$593$	10.7044	−	16.6563i	0.439576	−	0.683994i	−0.548812	−	0.835946i	$-0.684920\pi$
$593$	10.7044	−	16.6563i	0.439576	−	0.683994i	0.988388	+	0.151952i	$0.0485559\pi$
$594$	36.3403	+	17.6982i	1.49106	+	0.726167i
$595$	19.9685	−	3.60523i	0.818627	−	0.147800i
$596$	−19.9500	+	27.8969i	−0.817184	+	1.14270i
$597$	−6.58176			−0.269374
$598$	−38.9787	−	10.6664i	−1.59396	−	0.436180i
$599$			8.27511i			0.338112i	0.985606	+	0.169056i	$0.0540718\pi$
$599$			8.27511i			0.338112i	−0.985606	+	0.169056i	$0.945928\pi$
$600$	23.5764	−	36.4627i	0.962501	−	1.48858i
$601$	−11.2232	+	3.29544i	−0.457805	+	0.134424i	−0.502500	−	0.864577i	$-0.667586\pi$
$601$	−11.2232	+	3.29544i	−0.457805	+	0.134424i	0.0446955	+	0.999001i	$0.485768\pi$
$602$	−14.5115	−	7.06731i	−0.591445	−	0.288042i
$603$	−1.08912	+	1.69470i	−0.0443524	+	0.0690137i
$604$	15.5457	−	44.6256i	0.632547	−	1.81579i
$605$	−8.09075	+	0.289951i	−0.328936	+	0.0117882i
$606$	0.0841809	−	3.39283i	0.00341961	−	0.137824i
$607$	9.55427	−	6.14016i	0.387796	−	0.249221i	−0.332186	−	0.943214i	$-0.607786\pi$
$607$	9.55427	−	6.14016i	0.387796	−	0.249221i	0.719982	+	0.693992i	$0.244150\pi$
$608$	−0.430522	+	0.991547i	−0.0174600	+	0.0402126i
$609$	−6.86353	−	3.13447i	−0.278124	−	0.127015i
$610$	2.96982	+	0.836595i	0.120244	+	0.0338727i
$611$	−12.6635	−	1.82073i	−0.512308	−	0.0736588i
$612$	28.7209	−	55.4365i	1.16097	−	2.24089i
$613$	13.2992	+	3.90499i	0.537149	+	0.157721i	0.539045	−	0.842277i	$-0.318785\pi$
$613$	13.2992	+	3.90499i	0.537149	+	0.157721i	−0.00189604	+	0.999998i	$0.500604\pi$
$614$	10.7169	−	4.57648i	0.432498	−	0.184692i
$615$	10.7088	−	7.43720i	0.431821	−	0.299897i
$616$	−14.0354	+	3.00887i	−0.565504	+	0.121231i
$617$	−0.464922	+	0.536548i	−0.0187170	+	0.0216006i	−0.765031	−	0.643994i	$-0.777276\pi$
$617$	−0.464922	+	0.536548i	−0.0187170	+	0.0216006i	0.746314	+	0.665594i	$0.231822\pi$
$618$	44.6689	−	27.1655i	1.79685	−	1.09276i
$619$	−8.23908	−	18.0411i	−0.331156	−	0.725131i	0.668674	−	0.743556i	$-0.266862\pi$
$619$	−8.23908	−	18.0411i	−0.331156	−	0.725131i	−0.999830	+	0.0184245i	$0.994135\pi$
$620$	28.1163	−	12.3746i	1.12918	−	0.496975i
$621$	50.4123	−	2.18416i	2.02298	−	0.0876473i
$622$	33.7381	−	9.00370i	1.35277	−	0.361016i
$623$	−2.12710	−	4.65769i	−0.0852203	−	0.186606i
$624$	−71.0439	−	17.5382i	−2.84403	−	0.702089i
$625$	−22.7357	+	10.3965i	−0.909429	+	0.415859i
$626$	−1.36149	+	4.24439i	−0.0544162	+	0.169640i
$627$	1.04372	+	1.20452i	0.0416822	+	0.0481039i
$628$	14.6650	+	18.7255i	0.585197	+	0.747229i
$629$	−47.3704	−	13.9092i	−1.88878	−	0.554597i
$630$	25.1789	+	28.4193i	1.00315	+	1.13225i
$631$	4.01375	−	27.9163i	0.159785	−	1.11133i	−0.739243	−	0.673438i	$-0.764817\pi$
$631$	4.01375	−	27.9163i	0.159785	−	1.11133i	0.899028	−	0.437890i	$-0.144274\pi$
$632$	23.8505	−	8.81384i	0.948721	−	0.350596i
$633$	−26.8726	−	12.2723i	−1.06809	−	0.487780i
$634$	−0.879278	−	7.41732i	−0.0349206	−	0.294579i
$635$	−5.18492	−	10.3550i	−0.205757	−	0.410925i
$636$	2.74409	−	0.659863i	0.108810	−	0.0261653i
$637$	−20.6996	+	2.97616i	−0.820149	+	0.117920i
$638$	−2.83675	+	4.18223i	−0.112308	+	0.165576i
$639$	−42.1761	+	65.6273i	−1.66846	+	2.59617i
$640$	21.3500	+	13.5712i	0.843934	+	0.536447i
$641$	3.58758	+	12.2182i	0.141701	+	0.482589i	0.999507	−	0.0313840i	$-0.00999147\pi$
$641$	3.58758	+	12.2182i	0.141701	+	0.482589i	−0.857807	+	0.513973i	$0.828173\pi$
$642$	46.4543	+	56.3781i	1.83341	+	2.22507i
$643$		−	16.5072i		−	0.650979i	−0.945546	−	0.325490i	$-0.894471\pi$
$643$		−	16.5072i		−	0.650979i	0.945546	−	0.325490i	$-0.105529\pi$
$644$	−13.6164	+	11.6489i	−0.536559	+	0.459032i
$645$	41.7028	+	4.47836i	1.64205	+	0.176335i
$646$	1.01306	−	0.834743i	0.0398585	−	0.0328425i
$647$	−7.81959	+	2.29604i	−0.307420	+	0.0902666i	−0.431804	−	0.901968i	$-0.642123\pi$
$647$	−7.81959	+	2.29604i	−0.307420	+	0.0902666i	0.124384	+	0.992234i	$0.460305\pi$
$648$	36.7512	−	2.51700i	1.44373	−	0.0988771i
$649$	−4.28950	+	6.67459i	−0.168378	+	0.262001i
$650$	29.0513	+	30.5146i	1.13948	+	1.19688i
$651$	5.60730	+	38.9996i	0.219767	+	1.52852i
$652$	28.7852	−	6.92190i	1.12732	−	0.271083i
$653$	−13.4037	−	20.8565i	−0.524527	−	0.816179i	0.473379	−	0.880859i	$-0.343034\pi$
$653$	−13.4037	−	20.8565i	−0.524527	−	0.816179i	−0.997906	+	0.0646792i	$0.979398\pi$
$654$	−4.84025	−	40.8308i	−0.189269	−	1.59661i
$655$	1.18241	−	1.99340i	0.0462006	−	0.0778887i
$656$	4.38136	+	6.20548i	0.171063	+	0.242283i
$657$	−89.8201	−	12.9142i	−3.50421	−	0.503830i
$658$	−3.82020	+	4.19387i	−0.148927	+	0.163494i
$659$	−39.0497	−	11.4660i	−1.52116	−	0.446652i	−0.588828	−	0.808259i	$-0.700410\pi$
$659$	−39.0497	−	11.4660i	−1.52116	−	0.446652i	−0.932331	+	0.361606i	$0.882229\pi$
$660$	31.6538	−	19.7313i	1.23212	−	0.768038i
$661$	−0.496372	+	0.430109i	−0.0193066	+	0.0167293i	−0.664461	−	0.747323i	$-0.731339\pi$
$661$	−0.496372	+	0.430109i	−0.0193066	+	0.0167293i	0.645154	+	0.764053i	$0.276793\pi$
$662$	−0.813766	−	0.261036i	−0.0316279	−	0.0101454i
$663$	67.1564	+	58.1913i	2.60814	+	2.25996i
$664$	−20.3466	+	36.9960i	−0.789601	+	1.43572i
$665$	0.252189	+	0.757398i	0.00977947	+	0.0293706i
$666$	−23.8201	−	89.2571i	−0.923011	−	3.45864i
$667$	−0.626678	+	6.27741i	−0.0242651	+	0.243062i
$668$	−25.8567	+	14.8590i	−1.00042	+	0.574914i
$669$	−1.63052	−	3.57035i	−0.0630397	−	0.138038i
$670$	0.421673	+	0.897051i	0.0162906	+	0.0346561i
$671$	2.00309	+	1.73568i	0.0773283	+	0.0670054i
$672$	−24.1194	+	21.7053i	−0.930426	+	0.837301i
$673$	−0.468093	+	0.405604i	−0.0180436	+	0.0156349i	−0.663836	−	0.747878i	$-0.731073\pi$
$673$	−0.468093	+	0.405604i	−0.0180436	+	0.0156349i	0.645792	+	0.763513i	$0.276527\pi$
$674$	−29.8028	+	12.7268i	−1.14796	+	0.490219i
$675$	−46.1789	−	25.2010i	−1.77743	−	0.969985i
$676$	20.7029	−	39.9602i	0.796264	−	1.53693i
$677$	−5.80256	+	40.3577i	−0.223011	+	1.55107i	0.503548	+	0.863967i	$0.332028\pi$
$677$	−5.80256	+	40.3577i	−0.223011	+	1.55107i	−0.726558	+	0.687105i	$0.758881\pi$
$678$	−3.71012	−	0.627727i	−0.142486	−	0.0241077i
$679$	−11.8793	−	5.42509i	−0.455885	−	0.208196i
$680$	−15.5991	−	26.4653i	−0.598198	−	1.01490i
$681$	−15.7471	−	24.5029i	−0.603430	−	0.938955i
$682$	26.3805	+	0.654538i	1.01016	+	0.0250636i
$683$	−2.99719	−	20.8459i	−0.114684	−	0.797647i	−0.963260	−	0.268572i	$-0.913448\pi$
$683$	−2.99719	−	20.8459i	−0.114684	−	0.797647i	0.848575	−	0.529075i	$-0.177461\pi$
$684$	2.31953	+	0.808029i	0.0886894	+	0.0308957i
$685$	16.2482	−	20.1678i	0.620812	−	0.770573i
$686$	−12.1580	+	24.9643i	−0.464193	+	0.953140i
$687$	−16.5945	−	56.5155i	−0.633118	−	2.15620i
$688$	−2.42078	+	24.3167i	−0.0922915	+	0.927066i
$689$			2.73854i			0.104330i
$690$	23.0106	−	40.4808i	0.875997	−	1.54108i
$691$		−	44.0432i		−	1.67548i	−0.546069	−	0.837740i	$-0.683876\pi$
$691$		−	44.0432i		−	1.67548i	0.546069	−	0.837740i	$-0.316124\pi$
$692$	8.22933	−	11.5074i	0.312832	−	0.437445i
$693$	9.18912	+	31.2953i	0.349066	+	1.18881i
$694$	−8.66813	−	4.22150i	−0.329038	−	0.160246i
$695$	18.4073	+	14.8299i	0.698230	+	0.562529i
$696$	−0.849340	+	11.3919i	−0.0321941	+	0.431808i
$697$	−1.31278	−	9.13057i	−0.0497250	−	0.345845i
$698$	−0.522899	+	21.0750i	−0.0197920	+	0.797699i
$699$	34.8804	+	54.2750i	1.31930	+	2.05287i
$700$	18.4290	−	3.06548i	0.696550	−	0.115864i
$701$	−5.77836	−	2.63889i	−0.218246	−	0.0996695i	0.303292	−	0.952898i	$-0.401914\pi$
$701$	−5.77836	−	2.63889i	−0.218246	−	0.0996695i	−0.521538	+	0.853228i	$0.674641\pi$
$702$	−14.7903	+	87.4168i	−0.558225	+	3.29934i
$703$	0.276414	−	1.92250i	0.0104252	−	0.0725086i
$704$	11.6386	+	18.3527i	0.438647	+	0.691695i
$705$	5.63958	−	13.6199i	0.212399	−	0.512953i
$706$	−13.7142	−	32.1149i	−0.516140	−	1.20866i
$707$	1.10358	−	0.956255i	0.0415043	−	0.0359637i
$708$	−0.889438	+	17.9129i	−0.0334271	+	0.673210i
$709$	−21.3214	−	18.4751i	−0.800744	−	0.693848i	0.155044	−	0.987908i	$-0.450448\pi$
$709$	−21.3214	−	18.4751i	−0.800744	−	0.693848i	−0.955787	+	0.294059i	$0.904994\pi$
$710$	16.3292	+	34.7382i	0.612825	+	1.30370i
$711$	−24.0011	−	52.5550i	−0.900110	−	1.97097i
$712$	−5.49812	+	5.46502i	−0.206051	+	0.204810i
$713$	29.3451	−	14.9690i	1.09898	−	0.560595i
$714$	38.0701	−	10.1598i	1.42474	−	0.380221i
$715$	11.4339	+	34.3394i	0.427604	+	1.28422i
$716$	8.08491	+	7.74008i	0.302147	+	0.289260i
$717$	55.8044	+	48.3548i	2.08405	+	1.80584i
$718$	10.8978	−	33.9734i	0.406703	−	1.26788i
$719$	−40.1407	+	34.7821i	−1.49699	+	1.29715i	−0.657990	+	0.753027i	$0.728593\pi$
$719$	−40.1407	+	34.7821i	−1.49699	+	1.29715i	−0.839004	+	0.544126i	$0.816862\pi$
$720$	27.1446	−	50.6708i	1.01162	−	1.88839i
$721$	21.5831	+	6.33736i	0.803795	+	0.236016i
$722$	−19.8262	−	18.0596i	−0.737853	−	0.672110i
$723$	30.2183	+	4.34473i	1.12383	+	0.161582i
$724$	−18.7304	+	1.75050i	−0.696110	+	0.0650568i
$725$	3.94028	−	5.26627i	0.146338	−	0.195584i
$726$	−15.6117	+	1.85068i	−0.579406	+	0.0686851i
$727$	−12.0147	−	18.6952i	−0.445601	−	0.693368i	0.543697	−	0.839282i	$-0.317024\pi$
$727$	−12.0147	−	18.6952i	−0.445601	−	0.693368i	−0.989297	+	0.145914i	$0.953388\pi$
$728$	−15.0056	−	27.6790i	−0.556144	−	1.02585i
$729$	1.88004	+	13.0760i	0.0696311	+	0.484295i
$730$	−28.8658	+	34.0640i	−1.06837	+	1.26076i
$731$	16.0433	−	24.9638i	0.593381	−	0.923319i
$732$	5.88079	+	1.14571i	0.217360	+	0.0423467i
$733$	−22.9279	+	6.73223i	−0.846861	+	0.248661i	−0.676245	−	0.736677i	$-0.736394\pi$
$733$	−22.9279	+	6.73223i	−0.846861	+	0.248661i	−0.170616	+	0.985338i	$0.554576\pi$
$734$	−9.08672	−	11.0279i	−0.335397	−	0.407046i
$735$	2.57282	−	23.9583i	0.0949000	−	0.883714i
$736$	23.6885	+	13.2234i	0.873168	+	0.487419i
$737$			0.851487i			0.0313649i
$738$	13.3211	−	10.9763i	0.490357	−	0.404043i
$739$	12.1891	+	41.5123i	0.448383	+	1.52705i	0.805272	+	0.592906i	$0.202019\pi$
$739$	12.1891	+	41.5123i	0.448383	+	1.52705i	−0.356888	+	0.934147i	$0.616162\pi$
$740$	−43.4332	−	13.4064i	−1.59664	−	0.492830i
$741$	−1.89001	+	2.94091i	−0.0694312	+	0.108037i
$742$	1.00495	+	0.681649i	0.0368930	+	0.0250241i
$743$	32.1601	−	4.62392i	1.17984	−	0.169635i	0.475641	−	0.879639i	$-0.342216\pi$
$743$	32.1601	−	4.62392i	1.17984	−	0.169635i	0.704198	+	0.710004i	$0.251307\pi$
$744$	52.4409	−	28.4297i	1.92258	−	1.04228i
$745$	34.2865	−	17.1678i	1.25616	−	0.628980i
$746$	−0.349568	+	0.0414392i	−0.0127986	+	0.00151720i
$747$	87.2685	+	39.8542i	3.19299	+	1.45819i
$748$	−2.45563	−	26.2754i	−0.0897869	−	0.960722i
$749$	−4.47309	+	31.1110i	−0.163443	+	1.13677i
$750$	−42.3432	+	23.7439i	−1.54615	+	0.867005i
$751$	25.1757	+	7.39225i	0.918674	+	0.269747i	0.706688	−	0.707526i	$-0.250189\pi$
$751$	25.1757	+	7.39225i	0.918674	+	0.269747i	0.211986	+	0.977273i	$0.432007\pi$
$752$	7.96054	+	3.22416i	0.290291	+	0.117573i
$753$	17.5611	+	20.2666i	0.639963	+	0.738557i
$754$	−10.5547	−	3.38569i	−0.384380	−	0.123299i
$755$	−38.6643	+	36.0065i	−1.40714	+	1.31041i
$756$	28.3976	+	27.1864i	1.03281	+	0.988760i
$757$	−1.47274	−	3.22486i	−0.0535277	−	0.117209i	0.880978	−	0.473157i	$-0.156886\pi$
$757$	−1.47274	−	3.22486i	−0.0535277	−	0.117209i	−0.934506	+	0.355947i	$0.884158\pi$
$758$	0.871968	+	3.26738i	0.0316713	+	0.118676i
$759$	32.6823	−	23.0618i	1.18629	−	0.837090i
$760$	0.943237	−	0.755612i	0.0342148	−	0.0274089i
$761$	−1.83376	−	4.01538i	−0.0664738	−	0.145557i	0.873479	−	0.486862i	$-0.161859\pi$
$761$	−1.83376	−	4.01538i	−0.0664738	−	0.145557i	−0.939953	+	0.341305i	$0.889131\pi$
$762$	−11.6847	−	19.2135i	−0.423293	−	0.696032i
$763$	11.5850	−	13.3698i	0.419406	−	0.484020i
$764$	−36.0144	−	1.78824i	−1.30295	−	0.0646961i
$765$	−57.3337	+	39.8179i	−2.07290	+	1.43962i
$766$	−7.58161	−	17.7541i	−0.273935	−	0.641482i
$767$	−16.6978	−	4.90291i	−0.602922	−	0.177034i
$768$	43.4815	+	22.8612i	1.56900	+	0.824934i
$769$	43.6107	+	6.27027i	1.57264	+	0.226112i	0.872761	−	0.488148i	$-0.162327\pi$
$769$	43.6107	+	6.27027i	1.57264	+	0.226112i	0.699881	+	0.714260i	$0.253236\pi$
$770$	15.4474	+	4.35152i	0.556686	+	0.156818i
$771$	44.0223	+	20.1043i	1.58542	+	0.724039i
$772$	−22.4292	+	8.92695i	−0.807244	+	0.321288i
$773$	14.3454	−	9.21920i	0.515967	−	0.331592i	−0.256608	−	0.966516i	$-0.582605\pi$
$773$	14.3454	−	9.21920i	0.515967	−	0.331592i	0.772575	+	0.634924i	$0.218969\pi$
$774$	55.5094	+	1.37727i	1.99525	+	0.0495049i
$775$	−34.2580	−	2.44177i	−1.23058	−	0.0877110i
$776$	−1.47002	+	19.7169i	−0.0527708	+	0.707794i
$777$	31.5202	−	49.0464i	1.13078	−	1.75953i
$778$	−16.1206	+	33.1008i	−0.577951	+	1.18672i
$779$	0.348199	−	0.102241i	0.0124755	−	0.00366315i
$780$	61.0861	+	54.4243i	2.18723	+	1.94870i
$781$			32.9738i			1.17989i
$782$	−18.3203	−	27.3802i	−0.655132	−	0.979112i
$783$	13.8405			0.494617
$784$	13.9700	+	1.39074i	0.498927	+	0.0496693i
$785$	−4.72468	−	26.1689i	−0.168631	−	0.934007i
$786$	1.97059	−	4.04626i	0.0702886	−	0.144325i
$787$	−13.9201	+	21.6602i	−0.496200	+	0.772102i	−0.995544	−	0.0943021i	$-0.969938\pi$
$787$	−13.9201	+	21.6602i	−0.496200	+	0.772102i	0.499344	+	0.866404i	$0.333574\pi$
$788$	−0.679013	+	1.94918i	−0.0241889	+	0.0694366i
$789$	11.3163	−	1.62704i	0.402871	−	0.0579242i
$790$	−28.1817	−	3.73554i	−1.00266	−	0.132905i
$791$	−0.875296	−	1.36199i	−0.0311219	−	0.0484267i
$792$	39.6201	−	29.4730i	1.40784	−	1.04728i
$793$	−2.41503	+	5.28818i	−0.0857603	+	0.187789i
$794$	−3.40490	+	20.1243i	−0.120835	+	0.714186i
$795$	−3.05752	−	0.779987i	−0.108439	−	0.0276633i
$796$	−1.97224	+	3.80678i	−0.0699043	+	0.134928i
$797$	33.8035	+	9.92560i	1.19738	+	0.351583i	0.818851	−	0.574006i	$-0.194612\pi$
$797$	33.8035	+	9.92560i	1.19738	+	0.351583i	0.378530	+	0.925589i	$0.376430\pi$
$798$	0.608776	+	1.42559i	0.0215504	+	0.0504653i
$799$	−6.82987	−	7.88209i	−0.241623	−	0.278848i
$800$	−14.0247	−	24.5623i	−0.495848	−	0.868409i
$801$	13.3123	+	11.5352i	0.470368	+	0.407576i
$802$	−13.9387	+	8.47688i	−0.492194	+	0.299329i
$803$	−34.8894	+	15.9334i	−1.23122	+	0.562279i
$804$	0.959034	+	1.66884i	0.0338225	+	0.0588556i
$805$	19.5431	−	4.40965i	0.688804	−	0.155420i
$806$	14.9244	+	55.9238i	0.525691	+	1.96983i
$807$	−29.9565	−	65.5956i	−1.05452	−	2.30907i
$808$	−1.93713	−	1.06536i	−0.0681480	−	0.0374792i
$809$	7.47463	−	8.62618i	0.262794	−	0.303280i	−0.608983	−	0.793183i	$-0.708422\pi$
$809$	7.47463	−	8.62618i	0.262794	−	0.303280i	0.871777	+	0.489903i	$0.162968\pi$
$810$	−37.6497	−	16.6953i	−1.32288	−	0.586614i
$811$	−8.84443	+	7.66374i	−0.310570	+	0.269110i	−0.796173	−	0.605069i	$-0.793145\pi$
$811$	−8.84443	+	7.66374i	−0.310570	+	0.269110i	0.485603	+	0.874179i	$0.338600\pi$
$812$	−3.86960	+	3.03050i	−0.135796	+	0.106350i
$813$	7.03018	−	23.9426i	0.246559	−	0.839704i
$814$	−28.8668	−	26.2948i	−1.01178	−	0.921631i
$815$	−32.0731	−	8.18199i	−1.12347	−	0.286603i
$816$	−34.4069	−	48.7317i	−1.20448	−	1.70595i
$817$	1.06193	+	0.484966i	0.0371521	+	0.0169668i
$818$	−39.4784	+	4.67993i	−1.38033	+	0.163630i
$819$	−60.1842	+	38.6780i	−2.10301	+	1.35152i
$820$	−1.09263	−	8.42238i	−0.0381563	−	0.294122i
$821$	−3.22716	−	22.4454i	−0.112629	−	0.783351i	−0.965345	−	0.260976i	$-0.915956\pi$
$821$	−3.22716	−	22.4454i	−0.112629	−	0.783351i	0.852716	−	0.522374i	$-0.174954\pi$
$822$	28.2305	−	41.6203i	0.984653	−	1.45167i
$823$	23.4306	+	15.0579i	0.816739	+	0.524886i	0.881039	−	0.473044i	$-0.156845\pi$
$823$	23.4306	+	15.0579i	0.816739	+	0.524886i	−0.0642998	+	0.997931i	$0.520481\pi$
$824$	−2.32693	−	33.9760i	−0.0810624	−	1.18361i
$825$	−41.5957	+	2.98519i	−1.44817	+	0.103931i
$826$	−5.95543	+	4.90715i	−0.207216	+	0.170742i
$827$			24.6268i			0.856359i	0.903694	+	0.428180i	$0.140845\pi$
$827$			24.6268i			0.856359i	−0.903694	+	0.428180i	$0.859155\pi$
$828$	25.9615	−	55.9108i	0.902224	−	1.94304i
$829$	−26.1980			−0.909895			−0.454948	−	0.890518i	$-0.650342\pi$
$829$	−26.1980			−0.909895			−0.454948	+	0.890518i	$0.650342\pi$
$830$	39.4283	−	25.9571i	1.36858	−	0.900985i
$831$	11.1087	+	37.8326i	0.385355	+	1.31240i
$832$	−31.4323	+	35.8352i	−1.08972	+	1.24236i
$833$	−14.3417	−	9.21685i	−0.496911	−	0.319345i
$834$	37.9871	+	25.7662i	1.31539	+	0.892211i
$835$	33.3208	−	1.19413i	1.15311	−	0.0413245i
$836$	1.00943	−	0.242734i	0.0349118	−	0.00839514i
$837$	−39.0734	−	60.7994i	−1.35057	−	2.10153i
$838$	−8.85328	+	1.04950i	−0.305832	+	0.0362545i
$839$	13.1788	−	28.8576i	0.454984	−	0.996276i	−0.533618	−	0.845725i	$-0.679168\pi$
$839$	13.1788	−	28.8576i	0.454984	−	0.996276i	0.988602	−	0.150550i	$-0.0481046\pi$
$840$	35.1768	−	8.86988i	1.21372	−	0.306040i
$841$	3.88087	−	26.9921i	0.133823	−	0.930761i
$842$	1.62298	−	1.78173i	0.0559314	−	0.0614024i
$843$	−16.2537	+	55.3552i	−0.559809	+	1.90653i
$844$	−15.1505	+	11.8652i	−0.521503	+	0.408419i
$845$	−41.3278	+	28.7019i	−1.42172	+	0.987375i
$846$	5.96092	−	18.5829i	0.204941	−	0.638893i
$847$	−5.11197	−	4.42955i	−0.175649	−	0.152201i
$848$	0.440619	−	1.78486i	0.0151309	−	0.0612925i
$849$	−52.3732	+	23.9180i	−1.79744	+	0.820864i
$850$	1.60812	+	34.3088i	0.0551581	+	1.17678i
$851$	−47.3213	−	11.6958i	−1.62215	−	0.400926i
$852$	37.1385	+	64.6258i	1.27234	+	2.21404i
$853$	38.0817	−	17.3913i	1.30389	−	0.595468i	0.362250	−	0.932081i	$-0.382009\pi$
$853$	38.0817	−	17.3913i	1.30389	−	0.595468i	0.941643	+	0.336612i	$0.109281\pi$
$854$	1.33946	+	2.20251i	0.0458355	+	0.0753684i
$855$	−1.87153	−	2.00967i	−0.0640050	−	0.0687294i
$856$	46.5283	−	9.97459i	1.59031	−	0.340925i
$857$	−9.39376	+	8.13974i	−0.320885	+	0.278048i	−0.800376	−	0.599499i	$-0.795367\pi$
$857$	−9.39376	+	8.13974i	−0.320885	+	0.278048i	0.479491	+	0.877547i	$0.340821\pi$
$858$	27.6011	+	64.6343i	0.942285	+	2.20658i
$859$	−9.00293	+	30.6612i	−0.307176	+	1.04615i	0.650788	+	0.759259i	$0.274438\pi$
$859$	−9.00293	+	30.6612i	−0.307176	+	1.04615i	−0.957965	+	0.286887i	$0.907380\pi$
$860$	15.0866	−	22.7783i	0.514448	−	0.776732i
$861$	10.7823	+	1.55026i	0.367461	+	0.0528328i
$862$	0.0185211	+	0.00313365i	0.000630833	+	0.000106733i
$863$	−12.3604	+	27.0655i	−0.420753	+	0.921320i	0.573985	+	0.818866i	$0.305397\pi$
$863$	−12.3604	+	27.0655i	−0.420753	+	0.921320i	−0.994738	+	0.102454i	$0.967330\pi$
$864$	23.7047	−	54.5948i	0.806449	−	1.85735i
$865$	−14.1431	+	7.08169i	−0.480880	+	0.240785i
$866$	−1.10656	+	44.5989i	−0.0376025	+	1.51553i
$867$	2.88109	+	20.0384i	0.0978469	+	0.680540i
$868$	24.2370	+	8.44317i	0.822657	+	0.286580i
$869$	−20.5440	−	13.2029i	−0.696909	−	0.447876i
$870$	6.78621	−	10.8198i	0.230074	−	0.366825i
$871$	−1.79200	+	0.526179i	−0.0607197	+	0.0178289i
$872$	−25.0663	−	9.43554i	−0.848851	−	0.319528i
$873$	44.9258			1.52051
$874$	0.963626	−	0.866698i	0.0325951	−	0.0293165i
$875$	−19.8209	−	6.58895i	−0.670067	−	0.222747i
$876$	−50.4344	+	70.5243i	−1.70402	+	2.38280i
$877$	1.46153	+	4.97752i	0.0493525	+	0.168079i	0.980482	−	0.196610i	$-0.0629934\pi$
$877$	1.46153	+	4.97752i	0.0493525	+	0.168079i	−0.931129	+	0.364689i	$0.881175\pi$
$878$	−16.4876	+	33.8545i	−0.556430	+	1.14253i
$879$	−47.9576	−	30.8205i	−1.61757	−	1.03955i
$880$	−1.92708	−	24.2206i	−0.0649618	−	0.816476i
$881$	12.2875	−	1.76668i	0.413977	−	0.0595209i	0.0678202	−	0.997698i	$-0.478396\pi$
$881$	12.2875	−	1.76668i	0.413977	−	0.0595209i	0.346157	+	0.938177i	$0.387486\pi$
$882$	0.791241	−	31.8902i	0.0266425	−	1.07380i
$883$	20.2532	−	13.0159i	0.681573	−	0.438020i	−0.153508	−	0.988147i	$-0.549057\pi$
$883$	20.2532	−	13.0159i	0.681573	−	0.438020i	0.835081	+	0.550127i	$0.185421\pi$
$884$	53.7805	−	21.4050i	1.80883	−	0.719927i
$885$	10.2298	−	17.2462i	0.343871	−	0.579725i
$886$	22.1452	+	3.74681i	0.743981	+	0.125877i
$887$	−2.83071	+	19.6880i	−0.0950458	+	0.661058i	0.885481	+	0.464675i	$0.153829\pi$
$887$	−2.83071	+	19.6880i	−0.0950458	+	0.661058i	−0.980527	+	0.196383i	$0.937080\pi$
$888$	−86.1925	−	19.0227i	−2.89243	−	0.638362i
$889$	2.72590	−	9.28355i	0.0914236	−	0.311360i
$890$	8.28868	−	2.53328i	0.277837	−	0.0849157i
$891$	−23.1687	−	26.7381i	−0.776182	−	0.895761i
$892$	−2.55362	−	0.126796i	−0.0855016	−	0.00424544i
$893$	0.268694	−	0.310089i	0.00899150	−	0.0103767i
$894$	63.6179	−	38.6894i	2.12770	−	1.29397i
$895$	−3.95328	−	11.8729i	−0.132144	−	0.396866i
$896$	5.32657	+	20.4543i	0.177948	+	0.683331i
$897$	68.7310	+	54.5307i	2.29486	+	1.82073i
$898$	−1.14768	−	4.30051i	−0.0382986	−	0.143510i
$899$	8.21917	−	3.75357i	0.274125	−	0.125189i
$900$	−53.2876	+	35.9289i	−1.77625	+	1.19763i
$901$	−1.46197	+	1.68720i	−0.0487051	+	0.0562087i
$902$	2.22844	−	6.94707i	0.0741991	−	0.231312i
$903$	22.9481	+	26.4835i	0.763665	+	0.881317i
$904$	−1.47481	+	1.95777i	−0.0490516	+	0.0651145i
$905$	19.4325	+	8.04641i	0.645957	+	0.267472i
$906$	−69.0877	+	75.8455i	−2.29528	+	2.51980i
$907$	52.6792	+	7.57412i	1.74918	+	0.251494i	0.941233	−	0.337758i	$-0.109668\pi$
$907$	52.6792	+	7.57412i	1.74918	+	0.251494i	0.807949	+	0.589252i	$0.200577\pi$
$908$	−18.8908	+	1.76549i	−0.626912	+	0.0585897i
$909$	−2.08679	+	4.56942i	−0.0692143	+	0.151558i
$910$	0.387757	+	35.1990i	0.0128540	+	1.16684i
$911$	6.99053	−	4.49254i	0.231607	−	0.148844i	−0.419691	−	0.907667i	$-0.637861\pi$
$911$	6.99053	−	4.49254i	0.231607	−	0.148844i	0.651297	+	0.758823i	$0.274225\pi$
$912$	1.70500	−	1.61266i	0.0564583	−	0.0534006i
$913$	40.1384	−	5.77103i	1.32839	−	0.190993i
$914$	−18.3088	+	26.9926i	−0.605601	+	0.892837i
$915$	−5.21628	−	4.20249i	−0.172445	−	0.138930i
$916$	−37.6602	−	7.33706i	−1.24433	−	0.242423i
$917$	1.85799	−	0.545554i	0.0613561	−	0.0180158i
$918$	−55.7795	+	45.9611i	−1.84100	+	1.51694i
$919$	−37.4672			−1.23593			−0.617965	−	0.786206i	$-0.712043\pi$
$919$	−37.4672			−1.23593			−0.617965	+	0.786206i	$0.712043\pi$
$920$	−16.5182	−	25.4391i	−0.544590	−	0.838702i
$921$	−25.2995			−0.833646
$922$	−40.6112	+	33.4627i	−1.33746	+	1.10204i
$923$	−69.3951	+	20.3762i	−2.28417	+	0.670692i
$924$	30.5888	+	5.95938i	1.00630	+	0.196049i
$925$	35.9442	+	35.9267i	1.18184	+	1.18126i
$926$	13.0439	−	19.2306i	0.428648	−	0.631956i
$927$	−76.5948	+	11.0127i	−2.51570	+	0.361703i
$928$	6.33437	+	3.90485i	0.207936	+	0.128183i
$929$	−13.0713	+	8.40044i	−0.428857	+	0.275610i	−0.737212	−	0.675662i	$-0.763858\pi$
$929$	−13.0713	+	8.40044i	−0.428857	+	0.275610i	0.308355	+	0.951271i	$0.400222\pi$
$930$	−66.6883	+	0.734647i	−2.18679	+	0.0240900i
$931$	0.278613	−	0.610077i	0.00913117	−	0.0199945i
$932$	41.8438	−	3.91062i	1.37064	−	0.128097i
$933$	−75.0386	−	10.7889i	−2.45665	−	0.353213i
$934$	3.10149	−	3.40486i	0.101484	−	0.111410i
$935$	−11.2877	+	27.2602i	−0.369146	+	0.891505i
$936$	86.5111	+	65.1699i	2.82770	+	2.13014i
$937$	33.0058	+	38.0907i	1.07825	+	1.24437i	0.968129	+	0.250450i	$0.0805786\pi$
$937$	33.0058	+	38.0907i	1.07825	+	1.24437i	0.110122	+	0.993918i	$0.464876\pi$
$938$	−0.252955	+	0.788576i	−0.00825928	+	0.0257479i
$939$	6.33724	−	7.31356i	0.206808	−	0.238669i
$940$	−6.18758	−	7.34306i	−0.201817	−	0.239504i
$941$	38.0569	−	17.3800i	1.24062	−	0.566572i	0.316470	−	0.948603i	$-0.397502\pi$
$941$	38.0569	−	17.3800i	1.24062	−	0.566572i	0.924150	+	0.382031i	$0.124775\pi$
$942$	−13.3145	−	49.8913i	−0.433811	−	1.62555i
$943$	−1.68516	−	8.95042i	−0.0548763	−	0.291466i
$944$	10.0940	+	5.88210i	0.328533	+	0.191446i
$945$	−13.8856	−	41.7025i	−0.451698	−	1.35658i
$946$	20.0528	−	12.1952i	0.651973	−	0.396499i
$947$	−4.07388	+	4.70151i	−0.132383	+	0.152779i	−0.818071	−	0.575118i	$-0.804956\pi$
$947$	−4.07388	+	4.70151i	−0.132383	+	0.152779i	0.685687	+	0.727896i	$0.259502\pi$
$948$	−55.1351	−	2.73764i	−1.79070	−	0.0889145i
$949$	−55.0929	−	63.5805i	−1.78839	−	2.06391i
$950$	−1.32700	+	0.254709i	−0.0430536	+	0.00826387i
$951$	−4.56859	+	15.5592i	−0.148147	+	0.504542i
$952$	5.53155	−	25.0636i	0.179278	−	0.812314i
$953$	3.77201	−	26.2349i	0.122187	−	0.849833i	−0.832882	−	0.553451i	$-0.813311\pi$
$953$	3.77201	−	26.2349i	0.122187	−	0.849833i	0.955069	−	0.296382i	$-0.0957801\pi$
$954$	−4.11885	−	0.696882i	−0.133353	−	0.0225624i
$955$	34.6739	+	20.5672i	1.12202	+	0.665540i
$956$	44.6896	−	17.7867i	1.44536	−	0.575264i
$957$	9.22976	−	5.93161i	0.298356	−	0.191742i
$958$	−0.142837	+	5.75692i	−0.00461487	+	0.185998i
$959$	21.4180	−	3.07944i	0.691623	−	0.0994404i
$960$	−31.0567	−	45.2999i	−1.00235	−	1.46205i
$961$	−13.6139	−	8.74912i	−0.439158	−	0.282230i
$962$	37.5005	−	77.0008i	1.20906	−	2.48260i
$963$	−30.4625	−	103.746i	−0.981640	−	3.34316i
$964$	11.5679	−	16.1759i	0.372577	−	0.520989i
$965$	26.8355	+	2.88180i	0.863865	+	0.0927684i
$966$	37.1187	−	11.6488i	1.19428	−	0.374794i
$967$	0.198997			0.00639930			0.00319965	−	0.999995i	$-0.498982\pi$
$967$	0.198997			0.00639930			0.00319965	+	0.999995i	$0.498982\pi$
$968$	−3.60769	+	9.58413i	−0.115956	+	0.308046i
$969$	−2.73442	+	0.802897i	−0.0878421	+	0.0257928i
$970$	11.7455	−	18.7267i	0.377124	−	0.601278i
$971$	−21.8478	−	14.0407i	−0.701129	−	0.450588i	0.140898	−	0.990024i	$-0.455001\pi$
$971$	−21.8478	−	14.0407i	−0.701129	−	0.450588i	−0.842027	+	0.539436i	$0.818637\pi$
$972$	−15.9085	−	5.54185i	−0.510264	−	0.177755i
$973$	2.81063	+	19.5484i	0.0901047	+	0.626692i
$974$	1.19506	−	48.1658i	0.0382923	−	1.54333i
$975$	−31.9867	−	85.6957i	−1.02439	−	2.74446i
$976$	2.42486	−	3.05804i	0.0776177	−	0.0978855i
$977$	8.54515	−	18.7113i	0.273383	−	0.598626i	−0.722286	−	0.691595i	$-0.756908\pi$
$977$	8.54515	−	18.7113i	0.273383	−	0.598626i	0.995669	+	0.0929686i	$0.0296356\pi$
$978$	−63.3747	−	10.7226i	−2.02650	−	0.342870i
$979$	7.36960	+	1.05959i	0.235533	+	0.0338646i
$980$	−13.0861	−	8.66724i	−0.418021	−	0.276865i
$981$	−17.1457	+	58.3929i	−0.547421	+	1.86434i
$982$	11.9501	+	27.9840i	0.381344	+	0.893004i
$983$	21.8991	−	18.9757i	0.698473	−	0.605230i	−0.231510	−	0.972833i	$-0.574367\pi$
$983$	21.8991	−	18.9757i	0.698473	−	0.605230i	0.929983	+	0.367602i	$0.119821\pi$
$984$	−3.45695	−	16.1256i	−0.110204	−	0.514065i
$985$	1.68880	−	1.57271i	0.0538095	−	0.0501107i
$986$	−4.69525	−	7.72051i	−0.149527	−	0.245871i
$987$	11.2032	−	5.11635i	0.356603	−	0.162855i
$988$	1.13463	+	1.97440i	0.0360973	+	0.0628140i
$989$	14.7584	−	25.3103i	0.469290	−	0.804821i
$990$	−54.5571	+	8.45853i	−1.73394	+	0.268830i
$991$	−44.0477	+	20.1159i	−1.39922	+	0.639002i	−0.965107	−	0.261856i	$-0.915665\pi$
$991$	−44.0477	+	20.1159i	−1.39922	+	0.639002i	−0.434113	+	0.900858i	$0.642938\pi$
$992$	−0.729223	−	38.8500i	−0.0231528	−	1.23349i
$993$	1.40221	+	1.21502i	0.0444978	+	0.0385576i
$994$	−9.79567	+	30.5375i	−0.310700	+	0.968592i
$995$	3.93707	−	2.73427i	0.124813	−	0.0866821i
$996$	72.1679	−	56.5188i	2.28673	−	1.79087i
$997$	−4.08886	+	13.9254i	−0.129496	+	0.441021i	−0.998558	−	0.0536807i	$-0.982905\pi$
$997$	−4.08886	+	13.9254i	−0.129496	+	0.441021i	0.869063	+	0.494702i	$0.164723\pi$
$998$	−32.1009	+	35.2409i	−1.01614	+	1.11553i
$999$	−15.2194	+	105.854i	−0.481522	+	3.34906i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.o.b.19.14	yes	640
4.3	odd	2	inner	460.2.o.b.19.6	✓	640
5.4	even	2	inner	460.2.o.b.19.51	yes	640
20.19	odd	2	inner	460.2.o.b.19.59	yes	640
23.17	odd	22	inner	460.2.o.b.339.59	yes	640
92.63	even	22	inner	460.2.o.b.339.51	yes	640
115.109	odd	22	inner	460.2.o.b.339.6	yes	640
460.339	even	22	inner	460.2.o.b.339.14	yes	640

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.o.b.19.6	✓	640	4.3	odd	2	inner
460.2.o.b.19.14	yes	640	1.1	even	1	trivial
460.2.o.b.19.51	yes	640	5.4	even	2	inner
460.2.o.b.19.59	yes	640	20.19	odd	2	inner
460.2.o.b.339.6	yes	640	115.109	odd	22	inner
460.2.o.b.339.14	yes	640	460.339	even	22	inner
460.2.o.b.339.51	yes	640	92.63	even	22	inner
460.2.o.b.339.59	yes	640	23.17	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.o (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.09143 + 0.899318i) q^{2} +(2.94595 - 0.865009i) q^{3} +(0.382455 - 1.96309i) q^{4} +(-1.40285 + 1.74127i) q^{5} +(-2.43739 + 3.59345i) q^{6} +(-1.84920 + 0.265875i) q^{7} +(1.34802 + 2.48653i) q^{8} +(5.40662 - 3.47462i) q^{9} +O(q^{10})\)	\(q+(-1.09143 + 0.899318i) q^{2} +(2.94595 - 0.865009i) q^{3} +(0.382455 - 1.96309i) q^{4} +(-1.40285 + 1.74127i) q^{5} +(-2.43739 + 3.59345i) q^{6} +(-1.84920 + 0.265875i) q^{7} +(1.34802 + 2.48653i) q^{8} +(5.40662 - 3.47462i) q^{9} +(-0.0348340 - 3.16209i) q^{10} +(1.12848 - 2.47102i) q^{11} +(-0.571400 - 6.11400i) q^{12} +(5.89774 + 0.847967i) q^{13} +(1.77918 - 1.95321i) q^{14} +(-2.62652 + 6.34316i) q^{15} +(-3.70746 - 1.50159i) q^{16} +(3.18087 + 3.67092i) q^{17} +(-2.77618 + 8.65459i) q^{18} +(-0.125139 + 0.144418i) q^{19} +(2.88174 + 3.41988i) q^{20} +(-5.21768 + 2.38283i) q^{21} +(0.990574 + 3.71181i) q^{22} +(3.29454 + 3.48511i) q^{23} +(6.12207 + 6.15915i) q^{24} +(-1.06402 - 4.88547i) q^{25} +(-7.19958 + 4.37844i) q^{26} +(6.89016 - 7.95166i) q^{27} +(-0.185299 + 3.73184i) q^{28} +(0.861428 + 0.994141i) q^{29} +(-2.83785 - 9.28521i) q^{30} +(1.93522 - 6.59074i) q^{31} +(5.39685 - 1.69530i) q^{32} +(1.18698 - 8.25563i) q^{33} +(-6.77303 - 1.14595i) q^{34} +(2.13120 - 3.59294i) q^{35} +(-4.75322 - 11.9426i) q^{36} +(-8.55057 + 5.49512i) q^{37} +(0.00670309 - 0.270162i) q^{38} +(18.1079 - 2.60353i) q^{39} +(-6.22079 - 1.14097i) q^{40} +(-1.59761 - 1.02672i) q^{41} +(3.55182 - 7.29306i) q^{42} +(-1.72117 - 5.86176i) q^{43} +(-4.41924 - 3.16035i) q^{44} +(-1.53443 + 14.2887i) q^{45} +(-6.73000 - 0.840923i) q^{46} -2.14717 q^{47} +(-12.2209 - 1.21661i) q^{48} +(-3.36759 + 0.988812i) q^{49} +(5.55490 + 4.37528i) q^{50} +(12.5461 + 8.06287i) q^{51} +(3.92025 - 11.2535i) q^{52} +(0.0654096 + 0.454933i) q^{53} +(-0.369074 + 14.8752i) q^{54} +(2.71962 + 5.43144i) q^{55} +(-3.15387 - 4.23970i) q^{56} +(-0.243729 + 0.533693i) q^{57} +(-1.83424 - 0.310341i) q^{58} +(-2.89098 - 0.415660i) q^{59} +(11.4477 + 7.58206i) q^{60} +(-0.274884 + 0.936168i) q^{61} +(3.81501 + 8.93373i) q^{62} +(-9.07413 + 7.86278i) q^{63} +(-4.36569 + 6.70379i) q^{64} +(-9.75019 + 9.07997i) q^{65} +(6.12893 + 10.0779i) q^{66} +(-0.285124 + 0.130212i) q^{67} +(8.42289 - 4.84038i) q^{68} +(12.7202 + 7.41715i) q^{69} +(0.905136 + 5.83808i) q^{70} +(-11.0414 + 5.04244i) q^{71} +(15.9280 + 8.75987i) q^{72} +(-10.6708 - 9.24627i) q^{73} +(4.39052 - 13.6872i) q^{74} +(-7.36053 - 13.4720i) q^{75} +(0.235645 + 0.300892i) q^{76} +(-1.42980 + 4.86945i) q^{77} +(-17.4222 + 19.1264i) q^{78} +(1.27938 - 8.89828i) q^{79} +(7.81567 - 4.34917i) q^{80} +(5.41035 - 11.8470i) q^{81} +(2.66703 - 0.316161i) q^{82} +(8.07052 + 12.5580i) q^{83} +(2.68220 + 11.1541i) q^{84} +(-10.8543 + 0.388991i) q^{85} +(7.15013 + 4.84985i) q^{86} +(3.39767 + 2.18355i) q^{87} +(7.66547 - 0.524989i) q^{88} +(0.772172 + 2.62978i) q^{89} +(-11.1754 - 16.9752i) q^{90} -11.1316 q^{91} +(8.10160 - 5.13459i) q^{92} -21.0900i q^{93} +(2.34349 - 1.93099i) q^{94} +(-0.0759188 - 0.420496i) q^{95} +(14.4324 - 9.66259i) q^{96} +(5.88063 + 3.77925i) q^{97} +(2.78624 - 4.10775i) q^{98} +(-2.48462 - 17.2809i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 640 q - 6 q^{4} - 22 q^{5} + 2 q^{6} - 100 q^{9}+O(q^{10}) \) 640 * q - 6 * q^4 - 22 * q^5 + 2 * q^6 - 100 * q^9	\( 640 q - 6 q^{4} - 22 q^{5} + 2 q^{6} - 100 q^{9} - 11 q^{10} - 22 q^{14} + 2 q^{16} - 11 q^{20} - 44 q^{21} - 8 q^{24} - 38 q^{25} - 46 q^{26} - 52 q^{29} - 11 q^{30} - 44 q^{34} + 18 q^{36} - 11 q^{40} - 76 q^{41} - 154 q^{44} - 30 q^{46} - 100 q^{49} + 21 q^{50} + 178 q^{54} + 242 q^{56} - 11 q^{60} - 44 q^{61} + 6 q^{64} - 22 q^{65} + 44 q^{66} - 12 q^{69} + 22 q^{70} - 22 q^{74} + 88 q^{76} - 110 q^{80} - 252 q^{81} - 374 q^{84} + 94 q^{85} - 198 q^{86} - 44 q^{89} - 242 q^{90} - 62 q^{94} + 372 q^{96}+O(q^{100}) \) 640 * q - 6 * q^4 - 22 * q^5 + 2 * q^6 - 100 * q^9 - 11 * q^10 - 22 * q^14 + 2 * q^16 - 11 * q^20 - 44 * q^21 - 8 * q^24 - 38 * q^25 - 46 * q^26 - 52 * q^29 - 11 * q^30 - 44 * q^34 + 18 * q^36 - 11 * q^40 - 76 * q^41 - 154 * q^44 - 30 * q^46 - 100 * q^49 + 21 * q^50 + 178 * q^54 + 242 * q^56 - 11 * q^60 - 44 * q^61 + 6 * q^64 - 22 * q^65 + 44 * q^66 - 12 * q^69 + 22 * q^70 - 22 * q^74 + 88 * q^76 - 110 * q^80 - 252 * q^81 - 374 * q^84 + 94 * q^85 - 198 * q^86 - 44 * q^89 - 242 * q^90 - 62 * q^94 + 372 * q^96

Introduction

L-functions

Modular forms

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