LMFDB - Embedded newform 460.2.o.b.19.6

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			19.6
Character	$\chi$	$=$	460.19
Dual form			460.2.o.b.339.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39440 + 0.235922i) q^{2} +(-2.94595 + 0.865009i) q^{3} +(1.88868 - 0.657939i) q^{4} +(-1.40285 + 1.74127i) q^{5} +(3.90375 - 1.90118i) q^{6} +(1.84920 - 0.265875i) q^{7} +(-2.47835 + 1.36301i) q^{8} +(5.40662 - 3.47462i) q^{9} +O(q^{10})$	\(q+(-1.39440 + 0.235922i) q^{2} +(-2.94595 + 0.865009i) q^{3} +(1.88868 - 0.657939i) q^{4} +(-1.40285 + 1.74127i) q^{5} +(3.90375 - 1.90118i) q^{6} +(1.84920 - 0.265875i) q^{7} +(-2.47835 + 1.36301i) q^{8} +(5.40662 - 3.47462i) q^{9} +(1.54533 - 2.75898i) q^{10} +(-1.12848 + 2.47102i) q^{11} +(-4.99484 + 3.57198i) q^{12} +(5.89774 + 0.847967i) q^{13} +(-2.51580 + 0.807004i) q^{14} +(2.62652 - 6.34316i) q^{15} +(3.13423 - 2.48527i) q^{16} +(3.18087 + 3.67092i) q^{17} +(-6.71923 + 6.12054i) q^{18} +(0.125139 - 0.144418i) q^{19} +(-1.50389 + 4.21169i) 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} +(-8.42384 + 0.209007i) q^{26} +(-6.89016 + 7.95166i) q^{27} +(3.31763 - 1.71882i) q^{28} +(0.861428 + 0.994141i) q^{29} +(-2.16591 + 9.46454i) q^{30} +(-1.93522 + 6.59074i) q^{31} +(-3.78403 + 4.20489i) q^{32} +(1.18698 - 8.25563i) q^{33} +(-5.30145 - 4.36828i) q^{34} +(-2.13120 + 3.59294i) q^{35} +(7.92529 - 10.1197i) q^{36} +(-8.55057 + 5.49512i) q^{37} +(-0.140421 + 0.230898i) q^{38} +(-18.1079 + 2.60353i) q^{39} +(1.10339 - 6.22756i) q^{40} +(-1.59761 - 1.02672i) q^{41} +(6.71335 - 4.55358i) q^{42} +(1.72117 + 5.86176i) q^{43} +(-0.505553 + 5.40943i) q^{44} +(-1.53443 + 14.2887i) q^{45} +(5.41611 + 4.08237i) q^{46} +2.14717 q^{47} +(-7.08351 + 10.0326i) q^{48} +(-3.36759 + 0.988812i) q^{49} +(2.63626 + 6.56126i) q^{50} +(-12.5461 - 8.06287i) q^{51} +(11.6969 - 2.27881i) q^{52} +(0.0654096 + 0.454933i) q^{53} +(7.73163 - 12.7133i) q^{54} +(-2.71962 - 5.43144i) q^{55} +(-4.22058 + 3.17941i) q^{56} +(-0.243729 + 0.533693i) q^{57} +(-1.43571 - 1.18300i) q^{58} +(2.89098 + 0.415660i) q^{59} +(0.787240 - 13.7083i) q^{60} +(-0.274884 + 0.936168i) q^{61} +(1.14355 - 9.64666i) q^{62} +(9.07413 - 7.86278i) q^{63} +(4.28441 - 6.75602i) q^{64} +(-9.75019 + 9.07997i) q^{65} +(0.292568 + 11.7917i) q^{66} +(0.285124 - 0.130212i) q^{67} +(8.42289 + 4.84038i) q^{68} +(12.7202 + 7.41715i) q^{69} +(2.12408 - 5.51278i) q^{70} +(11.0414 - 5.04244i) q^{71} +(-8.66354 + 15.9806i) q^{72} +(-10.6708 - 9.24627i) q^{73} +(10.6265 - 9.67965i) q^{74} +(7.36053 + 13.4720i) q^{75} +(0.141329 - 0.355092i) q^{76} +(-1.42980 + 4.86945i) q^{77} +(24.6354 - 7.90242i) q^{78} +(-1.27938 + 8.89828i) q^{79} +(-0.0693383 + 8.94400i) q^{80} +(5.41035 - 11.8470i) q^{81} +(2.46993 + 1.05474i) q^{82} +(-8.07052 - 12.5580i) q^{83} +(-8.28677 + 7.93333i) q^{84} +(-10.8543 + 0.388991i) q^{85} +(-3.78291 - 7.76756i) q^{86} +(-3.39767 - 2.18355i) q^{87} +(-0.571265 - 7.66216i) q^{88} +(0.772172 + 2.62978i) q^{89} +(-1.23143 - 20.2862i) q^{90} +11.1316 q^{91} +(-8.51533 - 4.41465i) q^{92} -21.0900i q^{93} +(-2.99401 + 0.506566i) q^{94} +(0.0759188 + 0.420496i) q^{95} +(7.51030 - 15.6606i) q^{96} +(5.88063 + 3.77925i) q^{97} +(4.46246 - 2.17328i) 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 $

$2$	−1.39440	+	0.235922i	−0.985987	+	0.166822i
$2$	−1.39440	+	0.235922i	−0.985987	+	0.166822i
$3$	−2.94595	+	0.865009i	−1.70084	+	0.499413i	−0.980883	−	0.194600i	$-0.937659\pi$
$3$	−2.94595	+	0.865009i	−1.70084	+	0.499413i	−0.719962	+	0.694013i	$0.755841\pi$
$4$	1.88868	−	0.657939i	0.944341	−	0.328969i
$5$	−1.40285	+	1.74127i	−0.627374	+	0.778718i
$5$	−1.40285	+	1.74127i	−0.627374	+	0.778718i
$6$	3.90375	−	1.90118i	1.59370	−	0.776154i
$7$	1.84920	−	0.265875i	0.698933	−	0.100491i	0.216317	−	0.976323i	$-0.430596\pi$
$7$	1.84920	−	0.265875i	0.698933	−	0.100491i	0.482617	+	0.875832i	$0.339686\pi$
$8$	−2.47835	+	1.36301i	−0.876228	+	0.481897i
$9$	5.40662	−	3.47462i	1.80221	−	1.15821i
$10$	1.54533	−	2.75898i	0.488675	−	0.872466i
$11$	−1.12848	+	2.47102i	−0.340248	+	0.745040i	−0.999979	−	0.00646227i	$-0.997943\pi$
$11$	−1.12848	+	2.47102i	−0.340248	+	0.745040i	0.659731	+	0.751502i	$0.270670\pi$
$12$	−4.99484	+	3.57198i	−1.44189	+	1.03114i
$13$	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	$0.235908\pi$
$14$	−2.51580	+	0.807004i	−0.672375	+	0.215681i
$15$	2.62652	−	6.34316i	0.678164	−	1.63780i
$16$	3.13423	−	2.48527i	0.783558	−	0.621318i
$17$	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	$0.572234\pi$
$18$	−6.71923	+	6.12054i	−1.58374	+	1.44263i
$19$	0.125139	−	0.144418i	0.0287088	−	0.0331317i	−0.741214	−	0.671269i	$-0.765749\pi$
$19$	0.125139	−	0.144418i	0.0287088	−	0.0331317i	0.769922	+	0.638138i	$0.220295\pi$
$20$	−1.50389	+	4.21169i	−0.336280	+	0.941762i
$21$	−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
$26$	−8.42384	+	0.209007i	−1.65205	+	0.0409897i
$27$	−6.89016	+	7.95166i	−1.32601	+	1.53030i
$28$	3.31763	−	1.71882i	0.626973	−	0.324826i
$29$	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	$0.733753\pi$
$30$	−2.16591	+	9.46454i	−0.395439	+	1.72798i
$31$	−1.93522	+	6.59074i	−0.347575	+	1.18373i	0.581409	+	0.813611i	$0.302502\pi$
$31$	−1.93522	+	6.59074i	−0.347575	+	1.18373i	−0.928984	+	0.370120i	$0.879317\pi$
$32$	−3.78403	+	4.20489i	−0.668928	+	0.743327i
$33$	1.18698	−	8.25563i	0.206627	−	1.43712i
$34$	−5.30145	−	4.36828i	−0.909191	−	0.749154i
$35$	−2.13120	+	3.59294i	−0.360238	+	0.607318i
$36$	7.92529	−	10.1197i	1.32088	−	1.68661i
$37$	−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	$0.632994\pi$
$38$	−0.140421	+	0.230898i	−0.0227794	+	0.0374567i
$39$	−18.1079	+	2.60353i	−2.89959	+	0.416898i
$40$	1.10339	−	6.22756i	0.174461	−	0.984664i
$41$	−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	$0.729196\pi$
$42$	6.71335	−	4.55358i	1.03589	−	0.702633i
$43$	1.72117	+	5.86176i	0.262476	+	0.893911i	0.980271	+	0.197657i	$0.0633331\pi$
$43$	1.72117	+	5.86176i	0.262476	+	0.893911i	−0.717796	+	0.696254i	$0.754849\pi$
$44$	−0.505553	+	5.40943i	−0.0762150	+	0.815502i
$45$	−1.53443	+	14.2887i	−0.228740	+	2.13004i
$46$	5.41611	+	4.08237i	0.798562	+	0.601912i
$47$	2.14717			0.313197			0.156598	−	0.987662i	$-0.449947\pi$
$47$	2.14717			0.313197			0.156598	+	0.987662i	$0.449947\pi$
$48$	−7.08351	+	10.0326i	−1.02242	+	1.44809i
$49$	−3.36759	+	0.988812i	−0.481084	+	0.141259i
$50$	2.63626	+	6.56126i	0.372823	+	0.927902i
$51$	−12.5461	−	8.06287i	−1.75680	−	1.12903i
$52$	11.6969	−	2.27881i	1.62206	−	0.316014i
$53$	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	$0.944496\pi$
$54$	7.73163	−	12.7133i	1.05214	−	1.73006i
$55$	−2.71962	−	5.43144i	−0.366713	−	0.732376i
$56$	−4.22058	+	3.17941i	−0.563999	+	0.424867i
$57$	−0.243729	+	0.533693i	−0.0322828	+	0.0706894i
$58$	−1.43571	−	1.18300i	−0.188518	−	0.155335i
$59$	2.89098	+	0.415660i	0.376373	+	0.0541143i	0.327906	−	0.944710i	$-0.393657\pi$
$59$	2.89098	+	0.415660i	0.376373	+	0.0541143i	0.0484676	+	0.998825i	$0.484566\pi$
$60$	0.787240	−	13.7083i	0.101632	−	1.76973i
$61$	−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	$0.110804\pi$
$62$	1.14355	−	9.64666i	0.145231	−	1.22513i
$63$	9.07413	−	7.86278i	1.14323	−	0.990617i
$64$	4.28441	−	6.75602i	0.535551	−	0.844503i
$65$	−9.75019	+	9.07997i	−1.20936	+	1.12623i
$66$	0.292568	+	11.7917i	0.0360126	+	1.45145i
$67$	0.285124	−	0.130212i	0.0348334	−	0.0159079i	−0.397922	−	0.917419i	$-0.630269\pi$
$67$	0.285124	−	0.130212i	0.0348334	−	0.0159079i	0.432756	+	0.901511i	$0.357541\pi$
$68$	8.42289	+	4.84038i	1.02143	+	0.586982i
$69$	12.7202	+	7.41715i	1.53133	+	0.892920i
$70$	2.12408	−	5.51278i	0.253876	−	0.658903i
$71$	11.0414	−	5.04244i	1.31037	−	0.598427i	0.367019	−	0.930214i	$-0.380379\pi$
$71$	11.0414	−	5.04244i	1.31037	−	0.598427i	0.943355	+	0.331786i	$0.107651\pi$
$72$	−8.66354	+	15.9806i	−1.02101	+	1.88333i
$73$	−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	$-0.582273\pi$
$74$	10.6265	−	9.67965i	1.23530	−	1.12524i
$75$	7.36053	+	13.4720i	0.849921	+	1.55561i
$76$	0.141329	−	0.355092i	0.0162115	−	0.0407319i
$77$	−1.42980	+	4.86945i	−0.162941	+	0.554925i
$78$	24.6354	−	7.90242i	2.78941	−	0.894773i
$79$	−1.27938	+	8.89828i	−0.143941	+	1.00113i	0.781949	+	0.623342i	$0.214226\pi$
$79$	−1.27938	+	8.89828i	−0.143941	+	1.00113i	−0.925890	+	0.377792i	$0.876683\pi$
$80$	−0.0693383	+	8.94400i	−0.00775226	+	0.999970i
$81$	5.41035	−	11.8470i	0.601150	−	1.31634i
$82$	2.46993	+	1.05474i	0.272758	+	0.116477i
$83$	−8.07052	−	12.5580i	−0.885855	−	1.37842i	−0.925316	−	0.379196i	$-0.876201\pi$
$83$	−8.07052	−	12.5580i	−0.885855	−	1.37842i	0.0394614	−	0.999221i	$-0.487436\pi$
$84$	−8.28677	+	7.93333i	−0.904161	+	0.865597i
$85$	−10.8543	+	0.388991i	−1.17732	+	0.0421920i
$86$	−3.78291	−	7.76756i	−0.407922	−	0.837597i
$87$	−3.39767	−	2.18355i	−0.364268	−	0.234101i
$88$	−0.571265	−	7.66216i	−0.0608971	−	0.816789i
$89$	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	$0.862688\pi$
$90$	−1.23143	−	20.2862i	−0.129804	−	2.13835i
$91$	11.1316			1.16691
$92$	−8.51533	−	4.41465i	−0.887785	−	0.460259i
$93$		−	21.0900i		−	2.18693i
$94$	−2.99401	+	0.506566i	−0.308808	+	0.0522483i
$95$	0.0759188	+	0.420496i	0.00778911	+	0.0431420i
$96$	7.51030	−	15.6606i	0.766517	−	1.59836i
$97$	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	$0.566340\pi$
$98$	4.46246	−	2.17328i	0.450777	−	0.219535i
$99$	2.48462	+	17.2809i	0.249713	+	1.73679i
$100$	−5.22394	−	8.52704i	−0.522394	−	0.852704i
$101$	−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	$0.330563\pi$
$102$	19.3964	+	8.28293i	1.92053	+	0.820133i
$103$	10.9524	+	5.00179i	1.07917	+	0.492841i	0.874020	−	0.485889i	$-0.161504\pi$
$103$	10.9524	+	5.00179i	1.07917	+	0.492841i	0.205151	+	0.978730i	$0.434231\pi$
$104$	−15.7724	+	5.93712i	−1.54661	+	0.582182i
$105$	3.17047	−	12.4281i	0.309407	−	1.21286i
$106$	−0.198536	−	0.618926i	−0.0192835	−	0.0601154i
$107$	−4.73987	+	16.1425i	−0.458221	+	1.56056i	0.329274	+	0.944235i	$0.393196\pi$
$107$	−4.73987	+	16.1425i	−0.458221	+	1.56056i	−0.787494	+	0.616322i	$0.788622\pi$
$108$	−7.78160	+	19.5515i	−0.748785	+	1.88134i
$109$	−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	$0.422552\pi$
$110$	5.07362	+	6.93197i	0.483751	+	0.660937i
$111$	20.4362	−	23.5847i	1.93972	−	2.23856i
$112$	5.13506	−	5.42909i	0.485218	−	0.513001i
$113$	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
$118$	−4.12923	+	0.102452i	−0.380127	+	0.00943148i
$119$	6.85809	+	5.94257i	0.628680	+	0.544754i
$120$	2.13637	+	19.3005i	0.195023	+	1.76189i
$121$	2.37100	+	2.73628i	0.215546	+	0.248753i
$122$	0.162434	−	1.37024i	0.0147061	−	0.124056i
$123$	5.59460	+	1.64272i	0.504448	+	0.148119i
$124$	0.681297	+	13.7211i	0.0611823	+	1.23219i
$125$	9.99958	+	5.00085i	0.894389	+	0.447290i
$126$	−10.7979	+	13.1046i	−0.961955	+	1.16745i
$127$	2.15143	−	4.71097i	0.190908	−	0.418031i	−0.789838	−	0.613315i	$-0.789836\pi$
$127$	2.15143	−	4.71097i	0.190908	−	0.418031i	0.980747	+	0.195284i	$0.0625629\pi$
$128$	−4.38027	+	10.4314i	−0.387165	+	0.922011i
$129$	−10.1410	−	15.7796i	−0.892861	−	1.38932i
$130$	11.4535	−	14.9614i	1.00453	−	1.31220i
$131$	1.02596	−	0.147510i	0.0896384	−	0.0128881i	−0.0973497	−	0.995250i	$-0.531037\pi$
$131$	1.02596	−	0.147510i	0.0896384	−	0.0128881i	0.186988	+	0.982362i	$0.440127\pi$
$132$	−3.18987	−	16.3732i	−0.277643	−	1.42511i
$133$	0.193010	−	0.300329i	0.0167361	−	0.0260418i
$134$	−0.366856	+	0.248834i	−0.0316915	+	0.0214960i
$135$	−4.18011	−	23.1526i	−0.359766	−	1.99266i
$136$	−12.8868	−	4.76226i	−1.10503	−	0.408360i
$137$	−11.5823			−0.989541			−0.494770	−	0.869024i	$-0.664748\pi$
$137$	−11.5823			−0.989541			−0.494770	+	0.869024i	$0.664748\pi$
$138$	−19.4869	−	7.34146i	−1.65883	−	0.624946i
$139$			10.5712i			0.896640i	0.893873	+	0.448320i	$0.147978\pi$
$139$			10.5712i			0.896640i	−0.893873	+	0.448320i	$0.852022\pi$
$140$	−1.66122	+	8.18812i	−0.140398	+	0.692022i
$141$	−6.32546	+	1.85732i	−0.532699	+	0.156415i
$142$	−14.2065	+	9.63607i	−1.19218	+	0.808641i
$143$	−8.75080	+	13.6165i	−0.731778	+	1.13867i
$144$	8.31022	−	24.3272i	0.692518	−	2.02727i
$145$	−2.93952	+	0.105345i	−0.244114	+	0.00874840i
$146$	17.0607	+	10.3755i	1.41195	+	0.858682i
$147$	9.06541	−	5.82598i	0.747702	−	0.480519i
$148$	−12.5339	+	16.0043i	−1.03028	+	1.31554i
$149$	−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	$0.884259\pi$
$150$	−13.4418	−	17.0488i	−1.09752	−	1.39203i
$151$	−23.3874	−	3.36261i	−1.90324	−	0.273645i	−0.912466	−	0.409152i	$-0.865825\pi$
$151$	−23.3874	−	3.36261i	−1.90324	−	0.273645i	−0.990776	+	0.135507i	$0.956734\pi$
$152$	−0.113294	+	0.528482i	−0.00918938	+	0.0428656i
$153$	29.9528	+	8.79494i	2.42154	+	0.711029i
$154$	0.844894	−	7.12726i	0.0680835	−	0.574331i
$155$	−8.76141	−	12.6155i	−0.703734	−	1.01331i
$156$	−32.4872	+	16.8312i	−2.60106	+	1.34757i
$157$	−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	$0.384663\pi$
$158$	−0.315342	−	12.7096i	−0.0250873	−	1.01112i
$159$	−0.586215	−	1.28363i	−0.0464899	−	0.101799i
$160$	−2.01341	−	12.4878i	−0.159174	−	0.987251i
$161$	−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	$-0.939523\pi$
$163$	−6.14934	−	13.4652i	−0.481654	−	1.05467i	0.500352	−	0.865822i	$-0.333204\pi$
$164$	−3.69290	−	0.888020i	−0.288367	−	0.0693427i
$165$	12.7101	+	13.6483i	0.989480	+	1.06252i
$166$	14.2162	+	15.6068i	1.10339	+	1.21132i
$167$	9.76467	+	11.2690i	0.755613	+	0.872024i	0.995100	−	0.0988760i	$-0.0315247\pi$
$167$	9.76467	+	11.2690i	0.755613	+	0.872024i	−0.239487	+	0.970900i	$0.576979\pi$
$168$	9.68339	−	13.0172i	0.747090	−	1.00430i
$169$	21.5909	+	6.33965i	1.66084	+	0.487666i
$170$	15.0435	−	3.10319i	1.15378	−	0.238004i
$171$	0.174780	−	1.21562i	0.0133658	−	0.0929608i
$172$	7.10742	+	9.93858i	0.541936	+	0.757810i
$173$	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	$0.549705\pi$
$174$	5.25284	+	2.24314i	0.398217	+	0.170052i
$175$	−3.26652	−	8.75134i	−0.246925	−	0.661539i
$176$	2.60425	+	10.5493i	0.196302	+	0.795184i
$177$	−8.87623	+	1.27621i	−0.667178	+	0.0959257i
$178$	−1.69714	−	3.48478i	−0.127206	−	0.261195i
$179$	3.02559	−	4.70791i	0.226143	−	0.351886i	−0.709577	−	0.704627i	$-0.751114\pi$
$179$	3.02559	−	4.70791i	0.226143	−	0.351886i	0.935721	+	0.352741i	$0.114750\pi$
$180$	6.50306	+	27.9964i	0.484710	+	2.08673i
$181$	−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	$-0.204582\pi$
$182$	−15.5218	+	2.62619i	−1.15055	+	0.194666i
$183$		−	2.99568i		−	0.221447i
$184$	12.9153	+	4.14682i	0.952126	+	0.305707i
$185$	2.42671	−	22.5977i	0.178415	−	1.66141i
$186$	4.97560	+	29.4078i	0.364828	+	2.15628i
$187$	−12.6604	+	3.71744i	−0.925823	+	0.271846i
$188$	4.05532	−	1.41271i	0.295765	−	0.103032i
$189$	−10.6272	+	16.5362i	−0.773012	+	1.20283i
$190$	−0.205065	−	0.568427i	−0.0148770	−	0.0412380i
$191$	2.56585	+	17.8459i	0.185658	+	1.29128i	0.843092	+	0.537769i	$0.180733\pi$
$191$	2.56585	+	17.8459i	0.185658	+	1.29128i	−0.657434	+	0.753512i	$0.728358\pi$
$192$	−6.77764	+	23.6090i	−0.489134	+	1.70383i
$193$	−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	$0.961227\pi$
$194$	−9.09153	−	3.88240i	−0.652734	−	0.278740i
$195$	20.8693	−	35.1831i	1.49448	−	2.51952i
$196$	−5.70972	+	4.08322i	−0.407837	+	0.291658i
$197$	−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	$0.557160\pi$
$198$	−7.54148	−	23.5102i	−0.535950	−	1.67080i
$199$	2.05684	+	0.603943i	0.145806	+	0.0428124i	0.353821	−	0.935313i	$-0.384882\pi$
$199$	2.05684	+	0.603943i	0.145806	+	0.0428124i	−0.208015	+	0.978126i	$0.566700\pi$
$200$	9.29596	+	10.6576i	0.657324	+	0.753609i
$201$	−0.727327	+	0.630232i	−0.0513017	+	0.0444531i
$202$	0.817179	−	0.744368i	0.0574965	−	0.0523736i
$203$	1.85727	+	1.60934i	0.130355	+	0.112953i
$204$	−29.0004	−	6.97364i	−2.03043	−	0.488253i
$205$	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
$210$	−1.48882	+	18.0777i	−0.102739	+	1.24748i
$211$	7.27174	+	6.30100i	0.500607	+	0.433779i	0.868205	−	0.496206i	$-0.165274\pi$
$211$	7.27174	+	6.30100i	0.500607	+	0.433779i	−0.367597	+	0.929985i	$0.619820\pi$
$212$	0.422856	+	0.816189i	0.0290419	+	0.0560561i
$213$	−28.1657	+	24.4057i	−1.92988	+	1.67225i
$214$	2.80088	−	23.6273i	0.191464	−	1.61513i
$215$	−12.6214	−	5.22616i	−0.860775	−	0.356421i
$216$	6.23801	−	29.0983i	0.424443	−	1.97989i
$217$	−1.82629	+	12.7021i	−0.123977	+	0.862278i
$218$	8.51595	−	10.3352i	0.576773	−	0.699985i
$219$	39.4336	+	18.0087i	2.66468	+	1.21692i
$220$	−8.71005	−	8.46893i	−0.587231	−	0.570975i
$221$	15.6471	+	24.3474i	1.05254	+	1.63778i
$222$	−22.9320	+	37.7077i	−1.53910	+	2.53078i
$223$	0.181933	+	1.26537i	0.0121831	+	0.0847355i	0.995006	−	0.0998166i	$-0.0318256\pi$
$223$	0.181933	+	1.26537i	0.0121831	+	0.0847355i	−0.982823	+	0.184552i	$0.940917\pi$
$224$	−5.87947	+	8.78178i	−0.392838	+	0.586758i
$225$	−22.7279	−	22.7168i	−1.51520	−	1.51446i
$226$	−0.687954	−	1.01425i	−0.0457620	−	0.0674670i
$227$	2.67267	+	9.10227i	0.177391	+	0.604139i	0.999399	+	0.0346627i	$0.0110357\pi$
$227$	2.67267	+	9.10227i	0.177391	+	0.604139i	−0.822008	+	0.569476i	$0.807146\pi$
$228$	−0.109190	+	1.16834i	−0.00723128	+	0.0773749i
$229$		−	19.1841i		−	1.26772i	−0.773446	−	0.633862i	$-0.781469\pi$
$229$		−	19.1841i		−	1.26772i	0.773446	−	0.633862i	$-0.218531\pi$
$230$	−14.7065	+	3.70395i	−0.969717	+	0.244231i
$231$		−	15.5819i		−	1.02522i
$232$	−3.48994	−	1.28969i	−0.229126	−	0.0846724i
$233$	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	$0.667446\pi$
$234$	−44.8183	+	30.3997i	−2.92986	+	1.98729i
$235$	−3.01216	+	3.73880i	−0.196492	+	0.243892i
$236$	5.73362	−	1.11704i	0.373227	−	0.0727130i
$237$	−3.92810	−	27.3206i	−0.255158	−	1.77466i
$238$	−10.9649	−	6.66831i	−0.710747	−	0.432243i
$239$	−13.0022	−	20.2318i	−0.841041	−	1.30869i	−0.949239	−	0.314556i	$-0.898144\pi$
$239$	−13.0022	−	20.2318i	−0.841041	−	1.30869i	0.108198	−	0.994129i	$-0.465492\pi$
$240$	−7.53238	−	26.4086i	−0.486213	−	1.70467i
$241$	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	$0.532596\pi$
$242$	−3.95166	−	3.25609i	−0.254023	−	0.209309i
$243$	−1.19873	+	8.33732i	−0.0768983	+	0.534839i
$244$	0.0967734	+	1.94898i	0.00619528	+	0.124771i
$245$	3.00243	−	7.25102i	0.191818	−	0.463251i
$246$	−8.18865	−	0.970715i	−0.522089	−	0.0618905i
$247$	0.860496	−	0.745624i	0.0547521	−	0.0474429i
$248$	−4.18710	−	18.9719i	−0.265881	−	1.20471i
$249$	34.6381	+	30.0141i	2.19510	+	1.90207i
$250$	−15.1232	−	4.61404i	−0.956474	−	0.291818i
$251$	−3.62829	−	7.94485i	−0.229016	−	0.501475i	0.759884	−	0.650059i	$-0.225256\pi$
$251$	−3.62829	−	7.94485i	−0.229016	−	0.501475i	−0.988900	+	0.148584i	$0.952528\pi$
$252$	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
$256$	3.64684	−	15.5789i	0.227927	−	0.973678i
$257$	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	$0.563679\pi$
$258$	17.8633	+	19.6106i	1.11212	+	1.22090i
$259$	−14.3507	+	12.4350i	−0.891711	+	0.772672i
$260$	−12.4409	+	23.5642i	−0.771554	+	1.46139i
$261$	8.11168	+	2.38180i	0.502101	+	0.147430i
$262$	−1.39579	+	0.447735i	−0.0862322	+	0.0276611i
$263$	−3.68571	−	0.529925i	−0.227271	−	0.0326766i	0.0277385	−	0.999615i	$-0.491169\pi$
$263$	−3.68571	−	0.529925i	−0.227271	−	0.0326766i	−0.255009	+	0.966939i	$0.582079\pi$
$264$	8.31076	+	22.0782i	0.511492	+	1.35882i
$265$	−0.883920	−	0.524308i	−0.0542988	−	0.0322080i
$266$	−0.198278	+	0.464313i	−0.0121572	+	0.0284688i
$267$	−4.54956	−	7.07925i	−0.278429	−	0.433243i
$268$	0.452837	−	0.433523i	0.0276614	−	0.0264816i
$269$	−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	$-0.299488\pi$
$270$	11.2909	+	31.2977i	0.687145	+	1.90472i
$271$	−4.39395	+	6.83712i	−0.266913	+	0.415325i	−0.948677	−	0.316248i	$-0.897577\pi$
$271$	−4.39395	+	6.83712i	−0.266913	+	0.415325i	0.681763	+	0.731573i	$0.261213\pi$
$272$	19.0928	+	3.60019i	1.15767	+	0.218294i
$273$	−32.7931	+	9.62891i	−1.98473	+	0.582768i
$274$	16.1503	−	2.73252i	0.975674	−	0.165078i
$275$	13.2728	+	2.88393i	0.800381	+	0.173907i
$276$	28.9045	+	5.63951i	1.73984	+	0.339458i
$277$			12.8423i			0.771616i	0.922579	+	0.385808i	$0.126077\pi$
$277$			12.8423i			0.771616i	−0.922579	+	0.385808i	$0.873923\pi$
$278$	−2.49399	−	14.7405i	−0.149580	−	0.884076i
$279$	12.4374	+	42.3578i	0.744605	+	2.53589i
$280$	0.384634	−	11.8094i	0.0229863	−	0.705746i
$281$	−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	$0.992440\pi$
$282$	8.38201	−	4.08216i	0.499141	−	0.243089i
$283$	18.5616	−	2.66876i	1.10337	−	0.158641i	0.433528	−	0.901140i	$-0.357269\pi$
$283$	18.5616	−	2.66876i	1.10337	−	0.158641i	0.669847	+	0.742499i	$0.266360\pi$
$284$	17.5361	−	16.7881i	1.04057	−	0.996192i
$285$	−0.587386	−	1.17309i	−0.0347937	−	0.0694878i
$286$	8.98964	−	21.0513i	0.531568	−	1.24479i
$287$	−3.22729	−	1.47385i	−0.190501	−	0.0869988i
$288$	−5.84840	+	35.8823i	−0.344620	+	2.11439i
$289$	−0.938367	+	6.52649i	−0.0551981	+	0.383911i
$290$	4.07400	−	0.840391i	0.239234	−	0.0493495i
$291$	−20.5931	−	6.04668i	−1.20719	−	0.354463i
$292$	−26.2371	−	10.4425i	−1.53541	−	0.611104i
$293$	−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	$0.955194\pi$
$294$	−11.2663	+	10.2625i	−0.657063	+	0.598519i
$295$	−4.77939	+	4.45086i	−0.278267	+	0.259139i
$296$	13.7014	−	25.2733i	0.796377	−	1.46898i
$297$	−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
$300$	22.7654	+	20.6015i	1.31436	+	1.18943i
$301$	4.74129	+	10.3820i	0.273283	+	0.598407i
$302$	33.4047	−	0.828817i	1.92222	−	0.0476931i
$303$	1.57155	−	1.81367i	0.0902834	−	0.104193i
$304$	0.0332963	−	0.763642i	0.00190967	−	0.0437979i
$305$	−1.24450	−	1.79195i	−0.0712597	−	0.102607i
$306$	−43.8410	−	5.19709i	−2.50623	−	0.297098i
$307$	7.90623	+	2.32148i	0.451233	+	0.132494i	0.499449	−	0.866343i	$-0.333536\pi$
$307$	7.90623	+	2.32148i	0.451233	+	0.132494i	−0.0482169	+	0.998837i	$0.515354\pi$
$308$	0.503364	+	10.1376i	0.0286818	+	0.577641i
$309$	−36.5918	−	5.26111i	−2.08163	−	0.299294i
$310$	15.1932	+	15.5241i	0.862914	+	0.881707i
$311$	22.4600	+	10.2571i	1.27359	+	0.581629i	0.933437	−	0.358741i	$-0.116794\pi$
$311$	22.4600	+	10.2571i	1.27359	+	0.581629i	0.340153	+	0.940370i	$0.389521\pi$
$312$	41.3291	−	31.1338i	2.33980	−	1.76260i
$313$	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	$0.289790\pi$
$314$	8.73890	−	14.3696i	0.493164	−	0.810922i
$315$	0.961544	+	26.8308i	0.0541769	+	1.51174i
$316$	3.43818	+	17.6478i	0.193413	+	0.992764i
$317$	−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	$0.229205\pi$
$318$	1.12025	+	1.65159i	0.0628207	+	0.0926165i
$319$	−3.42864	+	1.00674i	−0.191967	+	0.0563666i
$320$	5.75365	+	16.9380i	0.321639	+	0.946862i
$321$		−	51.6551i		−	2.88311i
$322$	11.1009	+	6.10912i	0.618629	+	0.340448i
$323$	0.928195			0.0516462
$324$	2.42382	−	25.9349i	0.134657	−	1.44083i
$325$	−2.13259	−	29.7155i	−0.118295	−	1.64832i
$326$	11.7514	+	17.3250i	0.650847	+	0.959545i
$327$	15.7185	−	24.4585i	0.869237	−	1.35256i
$328$	5.35886	+	0.367015i	0.295894	+	0.0202650i
$329$	3.97056	−	0.570880i	0.218904	−	0.0314736i
$330$	−20.9429	−	16.0325i	−1.15287	−	0.882560i
$331$	−0.326709	−	0.508369i	−0.0179575	−	0.0279425i	0.832159	−	0.554537i	$-0.187105\pi$
$331$	−0.326709	−	0.508369i	−0.0179575	−	0.0279425i	−0.850116	+	0.526595i	$0.823468\pi$
$332$	−23.5050	−	18.4081i	−1.29001	−	1.01028i
$333$	−27.1362	+	59.4200i	−1.48706	+	3.25620i
$334$	−16.2744	−	13.4098i	−0.890497	−	0.733751i
$335$	−0.173253	+	0.679144i	−0.00946582	+	0.0371056i
$336$	−10.4314	+	20.4357i	−0.569081	+	1.11486i
$337$	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	$0.376365\pi$
$338$	−31.6019	−	3.74622i	−1.71892	−	0.203767i
$339$	−1.74241	−	2.01085i	−0.0946347	−	0.109214i
$340$	−20.2445	+	7.87617i	−1.09791	+	0.427145i
$341$	−14.1020	−	12.2194i	−0.763665	−	0.661720i
$342$	0.0430798	+	1.73629i	0.00232949	+	0.0938879i
$343$	−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	0.818255	−	0.574856i	$-0.194942\pi$
$347$	−2.83211	−	6.20145i	−0.152035	−	0.332911i	−0.970290	+	0.241945i	$0.922215\pi$
$348$	−7.85375	−	1.88857i	−0.421005	−	0.101238i
$349$	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	$0.0966397\pi$
$350$	6.61946	+	11.4322i	0.353825	+	0.611076i
$351$	−47.3791	+	41.0542i	−2.52891	+	2.19131i
$352$	−6.12017	−	14.0955i	−0.326206	−	0.751294i
$353$	−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	$0.862681\pi$
$354$	12.0759	−	3.87364i	0.641826	−	0.205882i
$355$	−6.70921	+	26.2998i	−0.356088	+	1.39585i
$356$	3.18862	+	4.45877i	0.168996	+	0.236314i
$357$	−25.3440	−	11.5742i	−1.34134	−	0.612571i
$358$	−3.10817	+	7.27850i	−0.164272	+	0.384681i
$359$	21.2236	−	13.6396i	1.12014	−	0.719868i	0.156658	−	0.987653i	$-0.449928\pi$
$359$	21.2236	−	13.6396i	1.12014	−	0.719868i	0.963479	+	0.267784i	$0.0862915\pi$
$360$	−15.6728	−	37.5039i	−0.826031	−	1.97663i
$361$	2.69879	+	18.7705i	0.142041	+	0.987919i
$362$	5.82432	+	11.9592i	0.306119	+	0.628563i
$363$	−9.35176	−	6.01001i	−0.490840	−	0.315444i
$364$	21.0240	−	7.32390i	1.10196	−	0.383876i
$365$	31.0697	−	5.60951i	1.62626	−	0.293615i
$366$	0.706748	+	4.17716i	0.0369423	+	0.218344i
$367$		−	10.1040i		−	0.527425i	−0.964601	−	0.263712i	$-0.915053\pi$
$367$		−	10.1040i		−	0.527425i	0.964601	−	0.263712i	$-0.0849470\pi$
$368$	−18.9873	−	2.73530i	−0.989782	−	0.142588i
$369$	−12.2051			−0.635374
$370$	1.94750	+	32.0826i	0.101246	+	1.66790i
$371$	0.241911	+	0.823874i	0.0125594	+	0.0427734i
$372$	−13.8759	−	39.8322i	−0.719432	−	2.06520i
$373$	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	$0.679767\pi$
$374$	16.7766	−	8.17047i	0.867500	−	0.422485i
$375$	−33.7840	−	6.08253i	−1.74460	−	0.314101i
$376$	−5.32143	+	2.92661i	−0.274432	+	0.150929i
$377$	4.23748	+	6.59365i	0.218241	+	0.339590i
$378$	10.9172	−	25.5652i	0.561521	−	1.31493i
$379$	−0.993358	+	2.17515i	−0.0510254	+	0.111730i	−0.933428	−	0.358766i	$-0.883198\pi$
$379$	−0.993358	+	2.17515i	−0.0510254	+	0.111730i	0.882402	+	0.470496i	$0.155925\pi$
$380$	0.420047	+	0.744233i	0.0215480	+	0.0381783i
$381$	−2.26297	+	15.7393i	−0.115935	+	0.806347i
$382$	−7.78804	−	24.2788i	−0.398471	−	1.24221i
$383$	3.84588	−	13.0978i	0.196515	−	0.669269i	−0.800990	−	0.598677i	$-0.795693\pi$
$383$	3.84588	−	13.0978i	0.196515	−	0.669269i	0.997505	−	0.0705914i	$-0.0224887\pi$
$384$	3.88083	−	34.5192i	0.198043	−	1.76155i
$385$	−6.47321	−	9.32077i	−0.329906	−	0.475030i
$386$	11.4949	+	12.6193i	0.585076	+	0.642305i
$387$	29.6731	+	25.7119i	1.50837	+	1.30701i
$388$	13.5931	+	3.26870i	0.690087	+	0.165943i
$389$	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	$0.134198\pi$
$390$	−20.7996	+	53.9828i	−1.05323	+	2.73352i
$391$	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
$394$	1.45906	−	0.0362014i	0.0735066	−	0.00182380i
$395$	−13.6995	−	14.7107i	−0.689297	−	0.740176i
$396$	16.0624	+	31.0033i	0.807166	+	1.55798i
$397$	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	$0.154764\pi$
$398$	−3.01053	−	0.356881i	−0.150904	−	0.0178888i
$399$	−0.308810	+	1.05171i	−0.0154598	+	0.0526513i
$400$	−15.4766	−	12.6678i	−0.773831	−	0.633392i
$401$	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	$0.452453\pi$
$402$	0.865495	−	1.05039i	0.0431670	−	0.0523885i
$403$	−17.0021	+	37.2295i	−0.846936	+	1.85453i
$404$	−0.963858	+	1.23074i	−0.0479537	+	0.0612314i
$405$	13.0389	+	26.0405i	0.647908	+	1.29396i
$406$	−2.96946	−	1.80588i	−0.147372	−	0.0896244i
$407$	−3.92942	−	27.3297i	−0.194774	−	1.35468i
$408$	42.0833	+	2.88218i	2.08343	+	0.142689i
$409$	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	$0.437224\pi$
$410$	−5.30153	+	2.82115i	−0.261824	+	0.139327i
$411$	34.1208	−	10.0188i	1.68306	−	0.494190i
$412$	23.9765	+	2.24078i	1.18123	+	0.110395i
$413$	5.45652			0.268498
$414$	43.4676	+	3.25284i	2.13631	+	0.159868i
$415$	33.1885	+	3.56404i	1.62916	+	0.174952i
$416$	−25.8828	+	21.5906i	−1.26901	+	1.05857i
$417$	−9.14421	−	31.1423i	−0.447794	−	1.52505i
$418$	−0.412092	−	0.607547i	−0.0201561	−	0.0297161i
$419$	−5.30330	−	3.40823i	−0.259083	−	0.166503i	0.404651	−	0.914471i	$-0.367393\pi$
$419$	−5.30330	−	3.40823i	−0.259083	−	0.166503i	−0.663734	+	0.747968i	$0.731029\pi$
$420$	−2.18893	−	25.5588i	−0.106809	−	1.24714i
$421$	−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	$0.467768\pi$
$422$	−11.6262	−	7.07052i	−0.565956	−	0.344188i
$423$	11.6089	−	7.46061i	0.564446	−	0.362747i
$424$	−0.782186	−	1.03833i	−0.0379863	−	0.0504257i
$425$	14.5497	−	19.4460i	0.705763	−	0.943269i
$426$	33.5162	−	40.6761i	1.62387	−	1.97076i
$427$	−0.259412	+	1.80425i	−0.0125538	+	0.0873138i
$428$	1.66868	+	33.6066i	0.0806588	+	1.62444i
$429$	14.0010	−	47.6831i	0.675975	−	2.30216i
$430$	18.8323	+	4.30966i	0.908172	+	0.207830i
$431$	0.00869822	+	0.0100383i	0.000418979	+	0.000483527i	0.755959	−	0.654619i	$-0.227171\pi$
$431$	0.00869822	+	0.0100383i	0.000418979	+	0.000483527i	−0.755540	+	0.655102i	$0.772625\pi$
$432$	−1.83330	+	42.0463i	−0.0882047	+	2.02295i
$433$	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	$-0.0465506\pi$
$434$	−0.450146	−	18.1427i	−0.0216077	−	0.870877i
$435$	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	−0.898764	−	0.438434i	$-0.855533\pi$
$439$	−24.2205	+	11.0611i	−1.15598	+	0.527920i	−0.257219	+	0.966353i	$0.582806\pi$
$440$	14.1433	+	9.75414i	0.674254	+	0.465011i
$441$	−14.7715	+	17.0472i	−0.703405	+	0.811773i
$442$	−27.5624	−	30.2584i	−1.31101	−	1.43925i
$443$	10.4002	+	12.0025i	0.494128	+	0.570254i	0.946964	−	0.321340i	$-0.104133\pi$
$443$	10.4002	+	12.0025i	0.494128	+	0.570254i	−0.452836	+	0.891594i	$0.649588\pi$
$444$	23.0803	−	57.9897i	1.09534	−	2.75207i
$445$	−5.66239	−	2.34463i	−0.268423	−	0.111146i
$446$	−0.552216	−	1.72151i	−0.0261482	−	0.0815157i
$447$	52.1144	+	7.49292i	2.46493	+	0.354403i
$448$	6.12649	−	13.6324i	0.289449	−	0.644070i
$449$	−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	$0.160025\pi$
$450$	37.0512	+	26.3142i	1.74661	+	1.24047i
$451$	4.33991	−	2.78909i	0.204358	−	0.131333i
$452$	1.19857	+	1.25196i	0.0563758	+	0.0588874i
$453$	71.8069	−	10.3243i	3.37378	−	0.485077i
$454$	−5.87419	−	12.0616i	−0.275689	−	0.566080i
$455$	−15.6159	+	19.3830i	−0.732087	+	0.908691i
$456$	−0.123383	−	1.65488i	−0.00577792	−	0.0774970i
$457$	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	$0.227733\pi$
$458$	4.52597	+	26.7503i	0.211485	+	1.24996i
$459$	−51.1066			−2.38545
$460$	19.6328	−	8.63436i	0.915385	−	0.402579i
$461$	37.2090			1.73300			0.866498	−	0.499180i	$-0.166365\pi$
$461$	37.2090			1.73300			0.866498	+	0.499180i	$0.166365\pi$
$462$	3.67613	+	21.7274i	0.171029	+	1.01085i
$463$	15.7655	−	4.62916i	0.732683	−	0.215135i	0.105953	−	0.994371i	$-0.466211\pi$
$463$	15.7655	−	4.62916i	0.732683	−	0.215135i	0.626731	+	0.779236i	$0.284393\pi$
$464$	5.17063	+	0.974986i	0.240040	+	0.0452626i
$465$	36.7232	+	29.5861i	1.70300	+	1.37202i
$466$	−13.0116	−	26.7170i	−0.602749	−	1.23764i
$467$	3.22356	−	0.463478i	0.149169	−	0.0214472i	−0.0673259	−	0.997731i	$-0.521447\pi$
$467$	3.22356	−	0.463478i	0.149169	−	0.0214472i	0.216495	+	0.976284i	$0.430538\pi$
$468$	55.3225	−	52.9629i	2.55728	−	2.44821i
$469$	0.492632	−	0.316596i	0.0227476	−	0.0146190i
$470$	3.31808	−	5.92400i	0.153051	−	0.273254i
$471$	15.1681	−	33.2135i	0.698909	−	1.53040i
$472$	−7.73140	+	2.91028i	−0.355866	+	0.133957i
$473$	−16.4268	−	2.36182i	−0.755306	−	0.108597i
$474$	11.9229	+	37.1690i	0.547635	+	1.70723i
$475$	−0.838699	−	0.457698i	−0.0384821	−	0.0210006i
$476$	16.8626	+	6.71141i	0.772895	+	0.307617i
$477$	1.93437	+	2.23238i	0.0885686	+	0.102214i
$478$	22.9033	+	25.1436i	1.04757	+	1.15004i
$479$	−2.66660	+	3.07742i	−0.121840	+	0.140611i	−0.813392	−	0.581715i	$-0.802382\pi$
$479$	−2.66660	+	3.07742i	−0.121840	+	0.140611i	0.691552	+	0.722326i	$0.256927\pi$
$480$	16.7335	+	35.0469i	0.763776	+	1.59967i
$481$	−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
$486$	−0.295463	−	11.9083i	−0.0134025	−	0.540173i
$487$	22.3104	−	25.7475i	1.01098	−	1.16673i	0.0250292	−	0.999687i	$-0.492032\pi$
$487$	22.3104	−	25.7475i	1.01098	−	1.16673i	0.985949	−	0.167045i	$-0.0534224\pi$
$488$	−0.594748	−	2.69482i	−0.0269230	−	0.121989i
$489$	29.7632	+	34.3485i	1.34594	+	1.55329i
$490$	−2.47590	+	10.8191i	−0.111850	+	0.488759i
$491$	−6.06186	+	20.6448i	−0.273568	+	0.931687i	0.702035	+	0.712143i	$0.252275\pi$
$491$	−6.06186	+	20.6448i	−0.273568	+	0.931687i	−0.975603	+	0.219544i	$0.929543\pi$
$492$	11.6472	−	0.578325i	0.525098	−	0.0260729i
$493$	−0.909322	+	6.32447i	−0.0409538	+	0.284840i
$494$	−1.02396	+	1.24271i	−0.0460703	+	0.0559120i
$495$	−33.5762	−	19.9161i	−1.50914	−	0.895163i
$496$	10.3144	+	25.4664i	0.463129	+	1.14348i
$497$	19.0771	−	12.2601i	0.855727	−	0.549942i
$498$	−55.3803	−	33.6796i	−2.48165	−	1.50922i
$499$	−33.3644	+	4.79708i	−1.49360	+	0.214747i	−0.840203	−	0.542273i	$-0.817564\pi$
$499$	−33.3644	+	4.79708i	−1.49360	+	0.214747i	−0.653393	+	0.757019i	$0.726655\pi$
$500$	22.1763	+	2.86590i	0.991753	+	0.128167i
$501$	−38.5140	−	24.7515i	−1.72068	−	1.10581i
$502$	6.93365	+	10.2223i	0.309464	+	0.456243i
$503$	−10.1068	−	34.4206i	−0.450640	−	1.53474i	−0.801316	−	0.598242i	$-0.795866\pi$
$503$	−10.1068	−	34.4206i	−0.450640	−	1.53474i	0.350676	−	0.936497i	$-0.385952\pi$
$504$	−11.7718	+	31.8548i	−0.524358	+	1.41893i
$505$	0.186615	−	1.73777i	0.00830425	−	0.0773297i
$506$	−16.1995	+	8.77646i	−0.720158	+	0.390161i
$507$	−69.0895			−3.06837
$508$	0.963831	−	10.3130i	0.0427631	−	0.457566i
$509$	−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	$0.551392\pi$
$510$	−41.6330	+	22.1546i	−1.84354	+	0.981022i
$511$	−22.1908	−	14.2611i	−0.981662	−	0.630876i
$512$	−1.40973	+	22.5835i	−0.0623020	+	0.998057i
$513$	0.286136	+	1.99012i	0.0126332	+	0.0878659i
$514$	−19.0459	−	11.5828i	−0.840080	−	0.510897i
$515$	−24.0740	+	12.0543i	−1.06083	+	0.531175i
$516$	−29.5351	−	23.1306i	−1.30021	−	1.01827i
$517$	−2.42303	+	5.30569i	−0.106565	+	0.233344i
$518$	17.0769	−	20.7250i	0.750317	−	0.910602i
$519$	−21.4971	−	3.09081i	−0.943617	−	0.135672i
$520$	11.7883	−	35.7929i	0.516950	−	1.56962i
$521$	−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	$0.984355\pi$
$522$	−11.8728	−	1.40745i	−0.519659	−	0.0616025i
$523$	−16.3794	+	14.1928i	−0.716220	+	0.620608i	−0.934785	−	0.355214i	$-0.884408\pi$
$523$	−16.3794	+	14.1928i	−0.716220	+	0.620608i	0.218565	+	0.975822i	$0.429862\pi$
$524$	1.84065	−	0.953618i	0.0804094	−	0.0416590i
$525$	17.1930	+	22.9555i	0.750363	+	1.00186i
$526$	5.26436	−	0.130616i	0.229537	−	0.00569514i
$527$	−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
$530$	1.35623	+	0.522557i	0.0589109	+	0.0226984i
$531$	17.0747	−	7.79775i	0.740978	−	0.338393i
$532$	0.166936	−	0.694214i	0.00723758	−	0.0300980i
$533$	−8.55166	−	7.41006i	−0.370414	−	0.320965i
$534$	8.01405	+	8.79794i	0.346802	+	0.380724i
$535$	−21.4591	−	30.8989i	−0.927758	−	1.33588i
$536$	−0.529156	+	0.711337i	−0.0228561	+	0.0307251i
$537$	−4.84086	+	16.4864i	−0.208898	+	0.711443i
$538$	10.1455	+	31.6281i	0.437404	+	1.36358i
$539$	1.35687	−	9.43721i	0.0584444	−	0.406489i
$540$	−23.1279	−	40.9776i	−0.995266	−	1.76340i
$541$	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	$-0.122444\pi$
$542$	4.51387	−	10.5703i	0.193888	−	0.454032i
$543$	15.6134	+	24.2949i	0.670036	+	1.04260i
$544$	−27.4723	−	0.515662i	−1.17787	−	0.0221088i
$545$	−0.758336	−	21.1605i	−0.0324836	−	0.906416i
$546$	43.4549	−	21.1631i	1.85970	−	0.905699i
$547$	18.7906	+	12.0760i	0.803430	+	0.516333i	0.876733	−	0.480977i	$-0.159718\pi$
$547$	18.7906	+	12.0760i	0.803430	+	0.516333i	−0.0733037	+	0.997310i	$0.523354\pi$
$548$	−21.8752	+	7.62043i	−0.934463	+	0.325529i
$549$	1.76664	+	6.01662i	0.0753983	+	0.256783i
$550$	−19.1879	−	0.889985i	−0.818176	−	0.0379491i
$551$	0.251369			0.0107087
$552$	−41.6347	−	1.04450i	−1.77209	−	0.0444567i
$553$			16.7949i			0.714191i
$554$	−3.02978	−	17.9072i	−0.128723	−	0.760803i
$555$	12.3982	+	68.6707i	0.526275	+	2.91491i
$556$	6.95522	+	19.9657i	0.294967	+	0.846734i
$557$	−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	$0.790431\pi$
$558$	−27.3358	−	56.1292i	−1.15721	−	2.37614i
$559$	5.18043	+	36.0307i	0.219109	+	1.52393i
$560$	2.24977	+	16.5577i	0.0950701	+	0.699691i
$561$	34.0814	−	21.9028i	1.43892	−	0.924737i
$562$	10.4361	−	24.4384i	0.440218	−	1.03087i
$563$	20.8241	+	9.51004i	0.877631	+	0.400800i	0.802696	−	0.596388i	$-0.203398\pi$
$563$	20.8241	+	9.51004i	0.877631	+	0.400800i	0.0749343	+	0.997188i	$0.476125\pi$
$564$	−10.7248	+	7.66965i	−0.451594	+	0.322951i
$565$	−1.87764	−	0.478995i	−0.0789929	−	0.0201515i
$566$	−25.2527	+	8.10042i	−1.06145	+	0.340486i
$567$	6.85501	−	23.3460i	0.287883	−	0.980441i
$568$	−20.4915	+	27.5464i	−0.859806	+	1.15582i
$569$	−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	$0.352038\pi$
$570$	1.09581	+	1.49717i	0.0458983	+	0.0627097i
$571$	3.35817	−	3.87553i	0.140535	−	0.162186i	−0.681119	−	0.732173i	$-0.738506\pi$
$571$	3.35817	−	3.87553i	0.140535	−	0.162186i	0.821654	+	0.569987i	$0.193052\pi$
$572$	−7.56864	+	31.4747i	−0.316461	+	1.31602i
$573$	−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	$0.538891\pi$
$578$	−0.231289	−	9.32189i	−0.00962037	−	0.387740i
$579$	28.0076	+	24.2687i	1.16396	+	1.00857i
$580$	−5.48251	+	2.13299i	−0.227649	+	0.0885675i
$581$	−18.2629	−	21.0765i	−0.757673	−	0.874401i
$582$	30.1415	+	3.57309i	1.24941	+	0.148110i
$583$	−1.19796	−	0.351753i	−0.0496145	−	0.0145681i
$584$	39.0486	+	8.37111i	1.61584	+	0.346399i
$585$	−21.1661	+	82.9702i	−0.875110	+	3.43039i
$586$	20.2649	+	16.6978i	0.837135	+	0.689781i
$587$	16.4892	−	36.1062i	0.680581	−	1.49026i	−0.181446	−	0.983401i	$-0.558078\pi$
$587$	16.4892	−	36.1062i	0.680581	−	1.49026i	0.862027	−	0.506863i	$-0.169195\pi$
$588$	13.2885	−	16.9679i	0.548009	−	0.699745i
$589$	0.709649	+	1.10423i	0.0292406	+	0.0454992i
$590$	5.61430	−	7.33382i	0.231137	−	0.301929i
$591$	3.13641	−	0.450948i	0.129015	−	0.0185495i
$592$	−13.1426	+	38.4735i	−0.540158	+	1.58125i
$593$	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	$0.0485559\pi$
$594$	22.6899	+	33.4517i	0.930976	+	1.37254i
$595$	−19.9685	+	3.60523i	−0.818627	+	0.147800i
$596$	−34.1475	−	3.19135i	−1.39874	−	0.130723i
$597$	−6.58176			−0.269374
$598$	28.4811	+	28.6694i	1.16468	+	1.17238i
$599$		−	8.27511i		−	0.338112i	−0.985606	−	0.169056i	$-0.945928\pi$
$599$		−	8.27511i		−	0.338112i	0.985606	−	0.169056i	$-0.0540718\pi$
$600$	−36.6044	−	23.3558i	−1.49437	−	0.953495i
$601$	−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	$0.485768\pi$
$602$	−9.06058	−	13.3580i	−0.369282	−	0.544432i
$603$	1.08912	−	1.69470i	0.0443524	−	0.0690137i
$604$	−46.3838	+	9.03661i	−1.88733	+	0.367695i
$605$	−8.09075	+	0.289951i	−0.328936	+	0.0117882i
$606$	−1.76348	+	2.89974i	−0.0716366	+	0.117794i
$607$	−9.55427	+	6.14016i	−0.387796	+	0.249221i	−0.719982	−	0.693992i	$-0.755850\pi$
$607$	−9.55427	+	6.14016i	−0.387796	+	0.249221i	0.332186	+	0.943214i	$0.392214\pi$
$608$	0.133732	+	1.07267i	0.00542355	+	0.0435027i
$609$	−6.86353	−	3.13447i	−0.278124	−	0.127015i
$610$	2.15808	+	2.20508i	0.0873782	+	0.0892812i
$611$	12.6635	+	1.82073i	0.512308	+	0.0736588i
$612$	62.3579	−	3.09628i	2.52067	−	0.125160i
$613$	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	$0.500604\pi$
$614$	−11.5721	−	1.37180i	−0.467012	−	0.0553615i
$615$	−10.7088	+	7.43720i	−0.431821	+	0.299897i
$616$	−3.09357	−	14.0170i	−0.124643	−	0.564762i
$617$	−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	$0.231822\pi$
$618$	52.2647	−	1.29676i	2.10239	−	0.0521634i
$619$	8.23908	+	18.0411i	0.331156	+	0.725131i	0.999830	−	0.0184245i	$-0.00586502\pi$
$619$	8.23908	+	18.0411i	0.331156	+	0.725131i	−0.668674	+	0.743556i	$0.733138\pi$
$620$	−24.8478	−	18.0623i	−0.997911	−	0.725398i
$621$	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
$624$	−50.2840	+	53.1633i	−2.01297	+	2.12823i
$625$	−22.7357	+	10.3965i	−0.909429	+	0.415859i
$626$	−3.29525	+	3.00164i	−0.131705	+	0.119970i
$627$	−1.04372	−	1.20452i	−0.0416822	−	0.0481039i
$628$	−8.79537	+	22.0986i	−0.350974	+	0.881830i
$629$	−47.3704	−	13.9092i	−1.88878	−	0.554597i
$630$	−7.67076	−	37.1859i	−0.305610	−	1.48152i
$631$	−4.01375	+	27.9163i	−0.159785	+	1.11133i	0.739243	+	0.673438i	$0.235183\pi$
$631$	−4.01375	+	27.9163i	−0.159785	+	1.11133i	−0.899028	+	0.437890i	$0.855726\pi$
$632$	−8.95769	−	23.7968i	−0.356318	−	0.946587i
$633$	−26.8726	−	12.2723i	−1.06809	−	0.487780i
$634$	2.93336	−	6.86914i	0.116499	−	0.272808i
$635$	5.18492	+	10.3550i	0.205757	+	0.410925i
$636$	−1.95172	−	2.03868i	−0.0773909	−	0.0808388i
$637$	−20.6996	+	2.97616i	−0.820149	+	0.117920i
$638$	4.54337	−	2.21269i	0.179874	−	0.0876011i
$639$	42.1761	−	65.6273i	1.66846	−	2.59617i
$640$	−12.0189	−	22.2609i	−0.475089	−	0.879938i
$641$	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	$0.828173\pi$
$642$	12.1866	+	72.0277i	0.480967	+	2.84270i
$643$			16.5072i			0.650979i	0.945546	+	0.325490i	$0.105529\pi$
$643$			16.5072i			0.650979i	−0.945546	+	0.325490i	$0.894471\pi$
$644$	−16.9203	−	5.89958i	−0.666754	−	0.232476i
$645$	41.7028	+	4.47836i	1.64205	+	0.176335i
$646$	−1.29427	+	0.218982i	−0.0509225	+	0.00861574i
$647$	7.81959	−	2.29604i	0.307420	−	0.0902666i	−0.124384	−	0.992234i	$-0.539695\pi$
$647$	7.81959	−	2.29604i	0.307420	−	0.0902666i	0.431804	+	0.901968i	$0.357877\pi$
$648$	2.73887	+	36.7354i	0.107593	+	1.44310i
$649$	−4.28950	+	6.67459i	−0.168378	+	0.262001i
$650$	9.98423	+	40.9321i	0.391614	+	1.60549i
$651$	−5.60730	−	38.9996i	−0.219767	−	1.52852i
$652$	−20.4734	−	21.3855i	−0.801801	−	0.837523i
$653$	−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	$0.979398\pi$
$654$	−16.1476	+	37.8132i	−0.631419	+	1.47861i
$655$	−1.18241	+	1.99340i	−0.0462006	+	0.0778887i
$656$	−7.55897	+	0.752512i	−0.295128	+	0.0293807i
$657$	−89.8201	−	12.9142i	−3.50421	−	0.503830i
$658$	−5.40184	+	1.73278i	−0.210586	+	0.0675506i
$659$	39.0497	+	11.4660i	1.52116	+	0.446652i	0.932331	−	0.361606i	$-0.117771\pi$
$659$	39.0497	+	11.4660i	1.52116	+	0.446652i	0.588828	+	0.808259i	$0.299590\pi$
$660$	32.9851	+	17.4148i	1.28394	+	0.677869i
$661$	−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	$0.276793\pi$
$662$	0.575497	+	0.631789i	0.0223673	+	0.0245552i
$663$	−67.1564	−	58.1913i	−2.60814	−	2.25996i
$664$	37.1182	+	20.1228i	1.44047	+	0.780917i
$665$	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
$670$	0.0813578	−	0.987871i	0.00314313	−	0.0381648i
$671$	−2.00309	−	1.73568i	−0.0773283	−	0.0670054i
$672$	9.72430	−	30.9565i	0.375123	−	1.19417i
$673$	−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	$0.276527\pi$
$674$	−32.1811	−	3.81488i	−1.23957	−	0.146944i
$675$	46.1789	+	25.2010i	1.77743	+	0.969985i
$676$	44.9494	−	2.23189i	1.72882	−	0.0858419i
$677$	−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	$0.758881\pi$
$678$	2.90401	+	2.39285i	0.111528	+	0.0918967i
$679$	11.8793	+	5.42509i	0.455885	+	0.208196i
$680$	26.3706	−	15.7586i	1.01127	−	0.604316i
$681$	−15.7471	−	24.5029i	−0.603430	−	0.938955i
$682$	22.5466	+	13.7118i	0.863353	+	0.525050i
$683$	2.99719	+	20.8459i	0.114684	+	0.797647i	0.963260	+	0.268572i	$0.0865519\pi$
$683$	2.99719	+	20.8459i	0.114684	+	0.797647i	−0.848575	+	0.529075i	$0.822539\pi$
$684$	−0.469701	−	2.41091i	−0.0179594	−	0.0921836i
$685$	16.2482	−	20.1678i	0.620812	−	0.770573i
$686$	22.9799	−	15.5870i	0.877376	−	0.595114i
$687$	16.5945	+	56.5155i	0.633118	+	2.15620i
$688$	19.9626	+	14.0946i	0.761068	+	0.537350i
$689$			2.73854i			0.104330i
$690$	40.1206	−	23.6329i	1.52737	−	0.899689i
$691$			44.0432i			1.67548i	0.546069	+	0.837740i	$0.316124\pi$
$691$			44.0432i			1.67548i	−0.546069	+	0.837740i	$0.683876\pi$
$692$	14.0858	+	1.31642i	0.535461	+	0.0500429i
$693$	9.18912	+	31.2953i	0.349066	+	1.18881i
$694$	5.41214	+	7.97912i	0.205442	+	0.302883i
$695$	−18.4073	−	14.8299i	−0.698230	−	0.562529i
$696$	11.3968	+	0.780537i	0.431994	+	0.0295862i
$697$	−1.31278	−	9.13057i	−0.0497250	−	0.345845i
$698$	−10.9541	+	18.0121i	−0.414618	+	0.681767i
$699$	−34.8804	−	54.2750i	−1.31930	−	2.05287i
$700$	−11.9273	−	14.3793i	−0.450808	−	0.543488i
$701$	−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	$0.674641\pi$
$702$	56.3796	−	68.4236i	2.12791	−	2.58248i
$703$	−0.276414	+	1.92250i	−0.0104252	+	0.0725086i
$704$	11.8594	+	18.2109i	0.446968	+	0.686347i
$705$	5.63958	−	13.6199i	0.212399	−	0.512953i
$706$	4.11084	−	34.6777i	0.154713	−	1.30511i
$707$	−1.10358	+	0.956255i	−0.0415043	+	0.0359637i
$708$	−15.9247	+	8.25037i	−0.598487	+	0.310068i
$709$	−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	$0.904994\pi$
$710$	3.15057	−	38.2552i	0.118239	−	1.43569i
$711$	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
$716$	2.61686	−	10.8824i	0.0977967	−	0.406695i
$717$	55.8044	+	48.3548i	2.08405	+	1.80584i
$718$	−26.3762	+	24.0261i	−0.984350	+	0.896645i
$719$	40.1407	−	34.7821i	1.49699	−	1.29715i	0.657990	−	0.753027i	$-0.271407\pi$
$719$	40.1407	−	34.7821i	1.49699	−	1.29715i	0.839004	−	0.544126i	$-0.183138\pi$
$720$	30.7022	+	48.5978i	1.14420	+	1.81113i
$721$	21.5831	+	6.33736i	0.803795	+	0.236016i
$722$	−8.19155	−	25.5368i	−0.304858	−	0.950380i
$723$	−30.2183	−	4.34473i	−1.12383	−	0.161582i
$724$	−10.9429	−	15.3018i	−0.406688	−	0.568688i
$725$	3.94028	−	5.26627i	0.146338	−	0.195584i
$726$	14.4579	+	6.17404i	0.536585	+	0.229140i
$727$	12.0147	+	18.6952i	0.445601	+	0.693368i	0.989297	−	0.145914i	$-0.0466122\pi$
$727$	12.0147	+	18.6952i	0.445601	+	0.693368i	−0.543697	+	0.839282i	$0.682976\pi$
$728$	−27.5879	+	15.1724i	−1.02248	+	0.562328i
$729$	1.88004	+	13.0760i	0.0696311	+	0.484295i
$730$	−42.0001	+	15.1519i	−1.55449	+	0.560798i
$731$	−16.0433	+	24.9638i	−0.593381	+	0.923319i
$732$	−1.97097	−	5.65788i	−0.0728493	−	0.209121i
$733$	−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	$0.554576\pi$
$734$	2.38376	+	14.0890i	0.0879863	+	0.520034i
$735$	−2.57282	+	23.9583i	−0.0949000	+	0.883714i
$736$	27.1212	−	0.665436i	0.999699	−	0.0245283i
$737$			0.851487i			0.0313649i
$738$	17.0188	−	2.87947i	0.626471	−	0.105995i
$739$	−12.1891	−	41.5123i	−0.448383	−	1.52705i	−0.805272	−	0.592906i	$-0.797981\pi$
$739$	−12.1891	−	41.5123i	−0.448383	−	1.52705i	0.356888	−	0.934147i	$-0.383838\pi$
$740$	−10.2846	−	44.2764i	−0.378069	−	1.62763i
$741$	−1.89001	+	2.94091i	−0.0694312	+	0.108037i
$742$	−0.531690	−	1.09173i	−0.0195190	−	0.0400788i
$743$	−32.1601	+	4.62392i	−1.17984	+	0.169635i	−0.704198	−	0.710004i	$-0.748693\pi$
$743$	−32.1601	+	4.62392i	−1.17984	+	0.169635i	−0.475641	+	0.879639i	$0.657784\pi$
$744$	28.7458	+	52.2682i	1.05387	+	1.91625i
$745$	34.2865	−	17.1678i	1.25616	−	0.628980i
$746$	−0.323733	−	0.138245i	−0.0118527	−	0.00506152i
$747$	−87.2685	−	39.8542i	−3.19299	−	1.45819i
$748$	−21.4657	+	15.3509i	−0.784863	+	0.561283i
$749$	−4.47309	+	31.1110i	−0.163443	+	1.13677i
$750$	48.5433	+	0.511048i	1.77255	+	0.0186608i
$751$	−25.1757	−	7.39225i	−0.918674	−	0.269747i	−0.211986	−	0.977273i	$-0.567993\pi$
$751$	−25.1757	−	7.39225i	−0.918674	−	0.269747i	−0.706688	+	0.707526i	$0.749811\pi$
$752$	6.72973	−	5.33630i	0.245408	−	0.194595i
$753$	17.5611	+	20.2666i	0.639963	+	0.738557i
$754$	−7.46432	−	8.19444i	−0.271834	−	0.298424i
$755$	38.6643	−	36.0065i	1.40714	−	1.31041i
$756$	−9.19152	+	38.2236i	−0.334292	+	1.39018i
$757$	−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
$760$	−0.761293	−	0.938657i	−0.0276150	−	0.0340487i
$761$	−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	$0.889131\pi$
$762$	−0.557777	−	22.4807i	−0.0202061	−	0.814389i
$763$	−11.5850	+	13.3698i	−0.419406	+	0.484020i
$764$	16.5875	+	32.0170i	0.600116	+	1.15833i
$765$	−57.3337	+	39.8179i	−2.07290	+	1.43962i
$766$	−2.27260	+	19.1709i	−0.0821123	+	0.692673i
$767$	16.6978	+	4.90291i	0.602922	+	0.177034i
$768$	2.73245	+	49.0491i	0.0985987	+	1.76991i
$769$	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	$0.253236\pi$
$770$	11.2252	+	11.4697i	0.404528	+	0.413338i
$771$	−44.0223	−	20.1043i	−1.58542	−	0.724039i
$772$	−19.0056	−	14.8844i	−0.684028	−	0.535701i
$773$	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	$0.218969\pi$
$774$	−47.4421	−	28.8520i	−1.70527	−	1.03706i
$775$	34.2580	+	2.44177i	1.23058	+	0.0877110i
$776$	−19.7254	−	1.35094i	−0.708100	−	0.0484960i
$777$	31.5202	−	49.0464i	1.13078	−	1.75953i
$778$	−30.4697	+	20.6672i	−1.09239	+	0.740956i
$779$	−0.348199	+	0.102241i	−0.0124755	+	0.00366315i
$780$	16.2671	−	80.1804i	0.582456	−	2.87092i
$781$			32.9738i			1.17989i
$782$	2.24192	+	32.8676i	0.0801709	+	1.17534i
$783$	−13.8405			−0.494617
$784$	−8.09733	+	11.4685i	−0.289190	+	0.409591i
$785$	−4.72468	−	26.1689i	−0.168631	−	0.934007i
$786$	3.72464	−	2.52638i	0.132853	−	0.0901128i
$787$	13.9201	−	21.6602i	0.496200	−	0.772102i	−0.499344	−	0.866404i	$-0.666426\pi$
$787$	13.9201	−	21.6602i	0.496200	−	0.772102i	0.995544	+	0.0943021i	$0.0300620\pi$
$788$	−2.02597	+	0.394705i	−0.0721723	+	0.0140608i
$789$	11.3163	−	1.62704i	0.402871	−	0.0579242i
$790$	22.5731	+	17.2805i	0.803115	+	0.614813i
$791$	0.875296	+	1.36199i	0.0311219	+	0.0484267i
$792$	−29.7117	−	39.4415i	−1.05576	−	1.40149i
$793$	−2.41503	+	5.28818i	−0.0857603	+	0.187789i
$794$	−12.9792	+	15.7519i	−0.460615	+	0.559013i
$795$	3.05752	+	0.779987i	0.108439	+	0.0276633i
$796$	4.28207	−	0.212619i	0.151774	−	0.00753610i
$797$	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	$0.376430\pi$
$798$	0.182481	−	1.53935i	0.00645976	−	0.0544925i
$799$	6.82987	+	7.88209i	0.241623	+	0.278848i
$800$	24.5692	+	14.0127i	0.868651	+	0.495424i
$801$	13.3123	+	11.5352i	0.470368	+	0.407576i
$802$	−16.3090	+	0.404649i	−0.575890	+	0.0142886i
$803$	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
$808$	1.05364	−	1.94353i	0.0370670	−	0.0683731i
$809$	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	$0.162968\pi$
$810$	−24.3249	−	33.2345i	−0.854691	−	1.16774i
$811$	8.84443	−	7.66374i	0.310570	−	0.269110i	−0.485603	−	0.874179i	$-0.661400\pi$
$811$	8.84443	−	7.66374i	0.310570	−	0.269110i	0.796173	+	0.605069i	$0.206855\pi$
$812$	4.56664	+	1.81755i	0.160258	+	0.0637836i
$813$	7.03018	−	23.9426i	0.246559	−	0.839704i
$814$	11.9269	+	37.1814i	0.418036	+	1.30321i
$815$	32.0731	+	8.18199i	1.12347	+	0.286603i
$816$	−59.3607	+	5.90949i	−2.07804	+	0.206874i
$817$	1.06193	+	0.484966i	0.0371521	+	0.0169668i
$818$	−36.5608	−	15.6127i	−1.27832	−	0.545886i
$819$	60.1842	−	38.6780i	2.10301	−	1.35152i
$820$	6.72686	−	5.18456i	0.234912	−	0.181053i
$821$	−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	$-0.174954\pi$
$822$	−45.2143	+	22.0200i	−1.57703	+	0.768036i
$823$	−23.4306	−	15.0579i	−0.816739	−	0.524886i	0.0642998	−	0.997931i	$-0.479519\pi$
$823$	−23.4306	−	15.0579i	−0.816739	−	0.524886i	−0.881039	+	0.473044i	$0.843155\pi$
$824$	−33.9613	+	2.53204i	−1.18310	+	0.0882079i
$825$	−41.5957	+	2.98519i	−1.44817	+	0.103931i
$826$	−7.60855	+	1.28732i	−0.264735	+	0.0447915i
$827$		−	24.6268i		−	0.856359i	−0.903694	−	0.428180i	$-0.859155\pi$
$827$		−	24.6268i		−	0.856359i	0.903694	−	0.428180i	$-0.140845\pi$
$828$	−61.3784	+	5.71922i	−2.13305	+	0.198757i
$829$	−26.1980			−0.909895			−0.454948	−	0.890518i	$-0.650342\pi$
$829$	−26.1980			−0.909895			−0.454948	+	0.890518i	$0.650342\pi$
$830$	−47.1188	+	2.86024i	−1.63552	+	0.0992804i
$831$	−11.1087	−	37.8326i	−0.385355	−	1.31240i
$832$	30.9972	−	36.2122i	1.07464	−	1.25543i
$833$	−14.3417	−	9.21685i	−0.496911	−	0.319345i
$834$	20.0978	+	41.2674i	0.695931	+	1.42897i
$835$	−33.3208	+	1.19413i	−1.15311	+	0.0413245i
$836$	0.717953	+	0.749939i	0.0248309	+	0.0259372i
$837$	−39.0734	−	60.7994i	−1.35057	−	2.10153i
$838$	8.19899	+	3.50125i	0.283229	+	0.120949i
$839$	−13.1788	+	28.8576i	−0.454984	+	0.996276i	0.533618	+	0.845725i	$0.320832\pi$
$839$	−13.1788	+	28.8576i	−0.454984	+	0.996276i	−0.988602	+	0.150550i	$0.951895\pi$
$840$	9.08212	+	35.1226i	0.313363	+	1.21185i
$841$	3.88087	−	26.9921i	0.133823	−	0.930761i
$842$	2.29492	−	0.736154i	0.0790883	−	0.0253695i
$843$	16.2537	−	55.3552i	0.559809	−	1.90653i
$844$	17.8797	+	7.11622i	0.615444	+	0.244950i
$845$	−41.3278	+	28.7019i	−1.42172	+	0.987375i
$846$	−14.4273	+	13.1419i	−0.496022	+	0.451826i
$847$	5.11197	+	4.42955i	0.175649	+	0.152201i
$848$	1.33564	+	1.26331i	0.0458662	+	0.0433821i
$849$	−52.3732	+	23.9180i	−1.79744	+	0.820864i
$850$	−15.7003	+	30.5480i	−0.538515	+	1.04779i
$851$	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	$0.109281\pi$
$854$	−0.0639400	−	2.57704i	−0.00218798	−	0.0881845i
$855$	1.87153	+	2.00967i	0.0640050	+	0.0687294i
$856$	−10.2554	−	46.4673i	−0.350521	−	1.58822i
$857$	−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	$0.340821\pi$
$858$	−8.27345	+	69.7922i	−0.282451	+	2.38267i
$859$	9.00293	−	30.6612i	0.307176	−	1.04615i	−0.650788	−	0.759259i	$-0.725562\pi$
$859$	9.00293	−	30.6612i	0.307176	−	1.04615i	0.957965	−	0.286887i	$-0.0926203\pi$
$860$	−27.2764	−	1.56643i	−0.930116	−	0.0534147i
$861$	10.7823	+	1.55026i	0.367461	+	0.0528328i
$862$	−0.0144970	−	0.0119452i	−0.000493771	−	0.000406857i
$863$	12.3604	−	27.0655i	0.420753	−	0.921320i	−0.573985	−	0.818866i	$-0.694603\pi$
$863$	12.3604	−	27.0655i	0.420753	−	0.921320i	0.994738	−	0.102454i	$-0.0326696\pi$
$864$	−7.36332	−	59.0617i	−0.250505	−	2.00932i
$865$	−14.1431	+	7.08169i	−0.480880	+	0.240785i
$866$	−23.1811	+	38.1173i	−0.787726	+	1.29528i
$867$	−2.88109	−	20.0384i	−0.0978469	−	0.680540i
$868$	4.90795	+	25.1919i	0.166587	+	0.855068i
$869$	−20.5440	−	13.2029i	−0.696909	−	0.447876i
$870$	−11.2749	+	5.99980i	−0.382254	+	0.203412i
$871$	1.79200	−	0.526179i	0.0607197	−	0.0178289i
$872$	9.28401	−	25.1228i	0.314396	−	0.850765i
$873$	44.9258			1.52051
$874$	1.26733	−	0.271321i	0.0428681	−	0.00917757i
$875$	19.8209	+	6.58895i	0.670067	+	0.222747i
$876$	86.3262	+	8.06785i	2.91669	+	0.272587i
$877$	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	$0.881175\pi$
$878$	31.1634	−	21.1378i	1.05172	−	0.713366i
$879$	47.9576	+	30.8205i	1.61757	+	1.03955i
$880$	−22.0225	−	10.2644i	−0.742380	−	0.346014i
$881$	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	$0.387486\pi$
$882$	16.5755	−	27.2555i	0.558126	−	0.917741i
$883$	−20.2532	+	13.0159i	−0.681573	+	0.438020i	−0.835081	−	0.550127i	$-0.814579\pi$
$883$	−20.2532	+	13.0159i	−0.681573	+	0.438020i	0.153508	+	0.988147i	$0.450943\pi$
$884$	45.5715	+	35.6896i	1.53274	+	1.20037i
$885$	10.2298	−	17.2462i	0.343871	−	0.579725i
$886$	−17.3336	−	14.2825i	−0.582335	−	0.479832i
$887$	2.83071	−	19.6880i	0.0950458	−	0.661058i	−0.885481	−	0.464675i	$-0.846171\pi$
$887$	2.83071	−	19.6880i	0.0950458	−	0.661058i	0.980527	−	0.196383i	$-0.0629197\pi$
$888$	−18.5019	+	86.3058i	−0.620885	+	2.89623i
$889$	2.72590	−	9.28355i	0.0914236	−	0.311360i
$890$	8.44876	+	1.93345i	0.283203	+	0.0648095i
$891$	23.1687	+	26.7381i	0.776182	+	0.895761i
$892$	1.17615	+	2.27018i	0.0393804	+	0.0760113i
$893$	0.268694	−	0.310089i	0.00899150	−	0.0103767i
$894$	−74.4359	+	1.84686i	−2.48951	+	0.0617682i
$895$	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
$900$	−57.8721	−	27.9513i	−1.92907	−	0.931709i
$901$	−1.46197	+	1.68720i	−0.0487051	+	0.0562087i
$902$	−5.39354	+	4.91298i	−0.179585	+	0.163584i
$903$	−22.9481	−	26.4835i	−0.763665	−	0.881317i
$904$	−1.96664	−	1.46297i	−0.0654095	−	0.0486575i
$905$	19.4325	+	8.04641i	0.645957	+	0.267472i
$906$	−97.6916	+	31.3370i	−3.24558	+	1.04110i
$907$	−52.6792	−	7.57412i	−1.74918	−	0.251494i	−0.807949	−	0.589252i	$-0.799423\pi$
$907$	−52.6792	−	7.57412i	−1.74918	−	0.251494i	−0.941233	+	0.337758i	$0.890332\pi$
$908$	11.0366	+	15.4328i	0.366261	+	0.512157i
$909$	−2.08679	+	4.56942i	−0.0692143	+	0.151558i
$910$	17.2019	−	30.7118i	0.570238	−	1.01809i
$911$	−6.99053	+	4.49254i	−0.231607	+	0.148844i	−0.651297	−	0.758823i	$-0.725775\pi$
$911$	−6.99053	+	4.49254i	−0.231607	+	0.148844i	0.419691	+	0.907667i	$0.362139\pi$
$912$	0.562468	+	2.27845i	0.0186252	+	0.0754471i
$913$	40.1384	−	5.77103i	1.32839	−	0.190993i
$914$	−29.3235	+	14.2810i	−0.969935	+	0.472373i
$915$	5.21628	+	4.20249i	0.172445	+	0.138930i
$916$	−12.6220	−	36.2327i	−0.417042	−	1.19716i
$917$	1.85799	−	0.545554i	0.0613561	−	0.0180158i
$918$	71.2629	−	12.0572i	2.35203	−	0.397947i
$919$	37.4672			1.23593			0.617965	−	0.786206i	$-0.287957\pi$
$919$	37.4672			1.23593			0.617965	+	0.786206i	$0.287957\pi$
$920$	−25.3389	+	16.6715i	−0.835399	+	0.549645i
$921$	−25.2995			−0.833646
$922$	−51.8841	+	8.77844i	−1.70871	+	0.289103i
$923$	69.3951	−	20.3762i	2.28417	−	0.670692i
$924$	−10.2520	−	29.4293i	−0.337265	−	0.968153i
$925$	35.9442	+	35.9267i	1.18184	+	1.18126i
$926$	−20.8912	+	10.1743i	−0.686527	+	0.334348i
$927$	76.5948	−	11.0127i	2.51570	−	0.361703i
$928$	−7.43993	−	0.139649i	−0.244228	−	0.00458421i
$929$	−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	$0.400222\pi$
$930$	−58.1868	−	32.5909i	−1.90802	−	1.06870i
$931$	−0.278613	+	0.610077i	−0.00913117	+	0.0199945i
$932$	24.4464	+	34.1843i	0.800768	+	1.11974i
$933$	−75.0386	−	10.7889i	−2.45665	−	0.353213i
$934$	−4.38558	+	1.40678i	−0.143500	+	0.0460313i
$935$	11.2877	−	27.2602i	0.369146	−	0.891505i
$936$	−64.6463	+	86.9030i	−2.11303	+	2.84051i
$937$	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	$0.464876\pi$
$938$	−0.612232	+	0.557683i	−0.0199901	+	0.0182090i
$939$	−6.33724	+	7.31356i	−0.206808	+	0.238669i
$940$	−3.22911	+	9.04321i	−0.105322	+	0.294957i
$941$	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
$946$	23.4627	−	0.582143i	0.762838	−	0.0189271i
$947$	4.07388	−	4.70151i	0.132383	−	0.152779i	−0.685687	−	0.727896i	$-0.740498\pi$
$947$	4.07388	−	4.70151i	0.132383	−	0.152779i	0.818071	+	0.575118i	$0.195044\pi$
$948$	−25.3942	−	49.0154i	−0.824765	−	1.59195i
$949$	−55.0929	−	63.5805i	−1.78839	−	2.06391i
$950$	1.27746	+	0.440345i	0.0414463	+	0.0142867i
$951$	4.56859	−	15.5592i	0.148147	−	0.504542i
$952$	−25.0965	−	5.38010i	−0.813382	−	0.174370i
$953$	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	$-0.0957801\pi$
$954$	−3.22394	−	2.65646i	−0.104379	−	0.0860061i
$955$	−34.6739	−	20.5672i	−1.12202	−	0.665540i
$956$	−37.8682	−	29.6568i	−1.22475	−	0.959168i
$957$	9.22976	−	5.93161i	0.298356	−	0.191742i
$958$	2.99227	−	4.92026i	0.0966757	−	0.158966i
$959$	−21.4180	+	3.07944i	−0.691623	+	0.0994404i
$960$	−31.6015	−	44.9215i	−1.01993	−	1.44984i
$961$	−13.6139	−	8.74912i	−0.439158	−	0.282230i
$962$	70.8801	−	48.0771i	2.28527	−	1.55007i
$963$	30.4625	+	103.746i	0.981640	+	3.34316i
$964$	19.8003	+	1.85049i	0.637724	+	0.0596002i
$965$	26.8355	+	2.88180i	0.863865	+	0.0927684i
$966$	−37.9871	−	8.39477i	−1.22222	−	0.270097i
$967$	−0.198997			−0.00639930			−0.00319965	−	0.999995i	$-0.501018\pi$
$967$	−0.198997			−0.00639930			−0.00319965	+	0.999995i	$0.501018\pi$
$968$	−9.60574	−	3.54976i	−0.308740	−	0.114094i
$969$	−2.73442	+	0.802897i	−0.0878421	+	0.0257928i
$970$	19.5144	−	10.3844i	0.626568	−	0.333422i
$971$	21.8478	+	14.0407i	0.701129	+	0.450588i	0.842027	−	0.539436i	$-0.181363\pi$
$971$	21.8478	+	14.0407i	0.701129	+	0.450588i	−0.140898	+	0.990024i	$0.544999\pi$
$972$	3.22143	+	16.5352i	0.103328	+	0.530368i
$973$	2.81063	+	19.5484i	0.0901047	+	0.626692i
$974$	−25.0351	+	41.1658i	−0.802175	+	1.31904i
$975$	31.9867	+	85.6957i	1.02439	+	2.74446i
$976$	1.46508	+	3.61733i	0.0468962	+	0.115788i
$977$	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	$0.0296356\pi$
$978$	−49.6052	−	40.8736i	−1.58620	−	1.30699i
$979$	−7.36960	−	1.05959i	−0.235533	−	0.0338646i
$980$	0.899913	−	15.6703i	0.0287467	−	0.500569i
$981$	−17.1457	+	58.3929i	−0.547421	+	1.86434i
$982$	3.58206	−	30.2172i	0.114308	−	0.964268i
$983$	−21.8991	+	18.9757i	−0.698473	+	0.605230i	−0.929983	−	0.367602i	$-0.880179\pi$
$983$	−21.8991	+	18.9757i	−0.698473	+	0.605230i	0.231510	+	0.972833i	$0.425633\pi$
$984$	−16.1044	+	3.55426i	−0.513390	+	0.113306i
$985$	1.68880	−	1.57271i	0.0538095	−	0.0501107i
$986$	−0.224130	−	9.03335i	−0.00713776	−	0.287680i
$987$	−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
$990$	51.5171	+	19.8496i	1.63732	+	0.630861i
$991$	44.0477	−	20.1159i	1.39922	−	0.639002i	0.434113	−	0.900858i	$-0.357062\pi$
$991$	44.0477	−	20.1159i	1.39922	−	0.639002i	0.965107	+	0.261856i	$0.0843346\pi$
$992$	−20.3904	−	33.0769i	−0.647396	−	1.05019i
$993$	1.40221	+	1.21502i	0.0444978	+	0.0385576i
$994$	−23.7087	+	21.5962i	−0.751993	+	0.684990i
$995$	−3.93707	+	2.73427i	−0.124813	+	0.0866821i
$996$	85.1678	+	33.8973i	2.69865	+	1.07408i
$997$	−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	$0.164723\pi$
$998$	45.3914	−	14.5604i	1.43684	−	0.460902i
$999$	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.19.6	✓	640
4.3	odd	2	inner	460.2.o.b.19.14	yes	640
5.4	even	2	inner	460.2.o.b.19.59	yes	640
20.19	odd	2	inner	460.2.o.b.19.51	yes	640
23.17	odd	22	inner	460.2.o.b.339.51	yes	640
92.63	even	22	inner	460.2.o.b.339.59	yes	640
115.109	odd	22	inner	460.2.o.b.339.14	yes	640
460.339	even	22	inner	460.2.o.b.339.6	yes	640

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

\(f(q)\)	\(=\)	\(q+(-1.39440 + 0.235922i) q^{2} +(-2.94595 + 0.865009i) q^{3} +(1.88868 - 0.657939i) q^{4} +(-1.40285 + 1.74127i) q^{5} +(3.90375 - 1.90118i) q^{6} +(1.84920 - 0.265875i) q^{7} +(-2.47835 + 1.36301i) q^{8} +(5.40662 - 3.47462i) q^{9} +O(q^{10})\)	\(q+(-1.39440 + 0.235922i) q^{2} +(-2.94595 + 0.865009i) q^{3} +(1.88868 - 0.657939i) q^{4} +(-1.40285 + 1.74127i) q^{5} +(3.90375 - 1.90118i) q^{6} +(1.84920 - 0.265875i) q^{7} +(-2.47835 + 1.36301i) q^{8} +(5.40662 - 3.47462i) q^{9} +(1.54533 - 2.75898i) q^{10} +(-1.12848 + 2.47102i) q^{11} +(-4.99484 + 3.57198i) q^{12} +(5.89774 + 0.847967i) q^{13} +(-2.51580 + 0.807004i) q^{14} +(2.62652 - 6.34316i) q^{15} +(3.13423 - 2.48527i) q^{16} +(3.18087 + 3.67092i) q^{17} +(-6.71923 + 6.12054i) q^{18} +(0.125139 - 0.144418i) q^{19} +(-1.50389 + 4.21169i) 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} +(-8.42384 + 0.209007i) q^{26} +(-6.89016 + 7.95166i) q^{27} +(3.31763 - 1.71882i) q^{28} +(0.861428 + 0.994141i) q^{29} +(-2.16591 + 9.46454i) q^{30} +(-1.93522 + 6.59074i) q^{31} +(-3.78403 + 4.20489i) q^{32} +(1.18698 - 8.25563i) q^{33} +(-5.30145 - 4.36828i) q^{34} +(-2.13120 + 3.59294i) q^{35} +(7.92529 - 10.1197i) q^{36} +(-8.55057 + 5.49512i) q^{37} +(-0.140421 + 0.230898i) q^{38} +(-18.1079 + 2.60353i) q^{39} +(1.10339 - 6.22756i) q^{40} +(-1.59761 - 1.02672i) q^{41} +(6.71335 - 4.55358i) q^{42} +(1.72117 + 5.86176i) q^{43} +(-0.505553 + 5.40943i) q^{44} +(-1.53443 + 14.2887i) q^{45} +(5.41611 + 4.08237i) q^{46} +2.14717 q^{47} +(-7.08351 + 10.0326i) q^{48} +(-3.36759 + 0.988812i) q^{49} +(2.63626 + 6.56126i) q^{50} +(-12.5461 - 8.06287i) q^{51} +(11.6969 - 2.27881i) q^{52} +(0.0654096 + 0.454933i) q^{53} +(7.73163 - 12.7133i) q^{54} +(-2.71962 - 5.43144i) q^{55} +(-4.22058 + 3.17941i) q^{56} +(-0.243729 + 0.533693i) q^{57} +(-1.43571 - 1.18300i) q^{58} +(2.89098 + 0.415660i) q^{59} +(0.787240 - 13.7083i) q^{60} +(-0.274884 + 0.936168i) q^{61} +(1.14355 - 9.64666i) q^{62} +(9.07413 - 7.86278i) q^{63} +(4.28441 - 6.75602i) q^{64} +(-9.75019 + 9.07997i) q^{65} +(0.292568 + 11.7917i) q^{66} +(0.285124 - 0.130212i) q^{67} +(8.42289 + 4.84038i) q^{68} +(12.7202 + 7.41715i) q^{69} +(2.12408 - 5.51278i) q^{70} +(11.0414 - 5.04244i) q^{71} +(-8.66354 + 15.9806i) q^{72} +(-10.6708 - 9.24627i) q^{73} +(10.6265 - 9.67965i) q^{74} +(7.36053 + 13.4720i) q^{75} +(0.141329 - 0.355092i) q^{76} +(-1.42980 + 4.86945i) q^{77} +(24.6354 - 7.90242i) q^{78} +(-1.27938 + 8.89828i) q^{79} +(-0.0693383 + 8.94400i) q^{80} +(5.41035 - 11.8470i) q^{81} +(2.46993 + 1.05474i) q^{82} +(-8.07052 - 12.5580i) q^{83} +(-8.28677 + 7.93333i) q^{84} +(-10.8543 + 0.388991i) q^{85} +(-3.78291 - 7.76756i) q^{86} +(-3.39767 - 2.18355i) q^{87} +(-0.571265 - 7.66216i) q^{88} +(0.772172 + 2.62978i) q^{89} +(-1.23143 - 20.2862i) q^{90} +11.1316 q^{91} +(-8.51533 - 4.41465i) q^{92} -21.0900i q^{93} +(-2.99401 + 0.506566i) q^{94} +(0.0759188 + 0.420496i) q^{95} +(7.51030 - 15.6606i) q^{96} +(5.88063 + 3.77925i) q^{97} +(4.46246 - 2.17328i) 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

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