LMFDB - Embedded newform 336.2.bu.a.107.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(11,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 6, 8]))

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

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

chi := DirichletCharacter("336.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.bu (of order $12$, degree $4$, 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:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$60$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			107.15
Character	$\chi$	$=$	336.107
Dual form			336.2.bu.a.179.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.985435 - 1.01436i) q^{2} +(-0.774639 + 1.54917i) q^{3} +(-0.0578377 + 1.99916i) q^{4} +(0.677113 + 2.52702i) q^{5} +(2.33477 - 0.740848i) q^{6} +(0.885088 + 2.49331i) q^{7} +(2.08486 - 1.91138i) q^{8} +(-1.79987 - 2.40010i) q^{9} +O(q^{10})$	\(q+(-0.985435 - 1.01436i) q^{2} +(-0.774639 + 1.54917i) q^{3} +(-0.0578377 + 1.99916i) q^{4} +(0.677113 + 2.52702i) q^{5} +(2.33477 - 0.740848i) q^{6} +(0.885088 + 2.49331i) q^{7} +(2.08486 - 1.91138i) q^{8} +(-1.79987 - 2.40010i) q^{9} +(1.89605 - 3.17705i) q^{10} +(0.874188 - 3.26252i) q^{11} +(-3.05225 - 1.63823i) q^{12} +(-3.62728 + 3.62728i) q^{13} +(1.65691 - 3.35479i) q^{14} +(-4.43931 - 0.908564i) q^{15} +(-3.99331 - 0.231254i) q^{16} +(-6.30359 + 3.63938i) q^{17} +(-0.660903 + 4.19085i) q^{18} +(5.63886 - 1.51093i) q^{19} +(-5.09109 + 1.20750i) q^{20} +(-4.54820 - 0.560266i) q^{21} +(-4.17081 + 2.32826i) q^{22} +(-0.902810 - 0.521238i) q^{23} +(1.34604 + 4.71043i) q^{24} +(-1.59722 + 0.922157i) q^{25} +(7.25380 + 0.104908i) q^{26} +(5.11241 - 0.929096i) q^{27} +(-5.03574 + 1.62523i) q^{28} +(0.164130 + 0.164130i) q^{29} +(3.45304 + 5.39837i) q^{30} +(-2.66713 + 1.53987i) q^{31} +(3.70057 + 4.27852i) q^{32} +(4.37702 + 3.88154i) q^{33} +(9.90341 + 2.80772i) q^{34} +(-5.70135 + 3.92489i) q^{35} +(4.90229 - 3.45942i) q^{36} +(2.95156 - 0.790868i) q^{37} +(-7.08935 - 4.23090i) q^{38} +(-2.80945 - 8.42911i) q^{39} +(6.24177 + 3.97426i) q^{40} -9.40208 q^{41} +(3.91364 + 5.16560i) q^{42} +(1.63803 - 1.63803i) q^{43} +(6.47174 + 1.93634i) q^{44} +(4.84638 - 6.17344i) q^{45} +(0.360940 + 1.42942i) q^{46} +(-2.82149 + 4.88697i) q^{47} +(3.45163 - 6.00719i) q^{48} +(-5.43324 + 4.41361i) q^{49} +(2.50935 + 0.711428i) q^{50} +(-0.755018 - 12.5846i) q^{51} +(-7.04173 - 7.46131i) q^{52} +(5.37060 + 1.43905i) q^{53} +(-5.98038 - 4.27025i) q^{54} +8.83637 q^{55} +(6.61095 + 3.50647i) q^{56} +(-2.02740 + 9.90600i) q^{57} +(0.00474693 - 0.328225i) q^{58} +(-0.969245 + 3.61727i) q^{59} +(2.07313 - 8.82235i) q^{60} +(1.36700 + 5.10170i) q^{61} +(4.19026 + 1.18798i) q^{62} +(4.39116 - 6.61194i) q^{63} +(0.693278 - 7.96990i) q^{64} +(-11.6223 - 6.71013i) q^{65} +(-0.375999 - 8.26486i) q^{66} +(-2.04193 + 7.62060i) q^{67} +(-6.91113 - 12.8124i) q^{68} +(1.50684 - 0.994837i) q^{69} +(9.59955 + 1.91548i) q^{70} -2.28487i q^{71} +(-8.33997 - 1.56364i) q^{72} +(9.32837 - 5.38574i) q^{73} +(-3.71079 - 2.21458i) q^{74} +(-0.191309 - 3.18871i) q^{75} +(2.69446 + 11.3604i) q^{76} +(8.90821 - 0.707986i) q^{77} +(-5.78159 + 11.1561i) q^{78} +(6.93760 + 4.00542i) q^{79} +(-2.11954 - 10.2478i) q^{80} +(-2.52095 + 8.63972i) q^{81} +(9.26514 + 9.53706i) q^{82} +(4.18395 - 4.18395i) q^{83} +(1.38312 - 9.06019i) q^{84} +(-13.4650 - 13.4650i) q^{85} +(-3.27572 - 0.0473750i) q^{86} +(-0.381406 + 0.127124i) q^{87} +(-4.41334 - 8.47279i) q^{88} +(3.04256 - 5.26988i) q^{89} +(-11.0379 + 1.16756i) q^{90} +(-12.2544 - 5.83349i) q^{91} +(1.09426 - 1.77472i) q^{92} +(-0.319458 - 5.32469i) q^{93} +(7.73753 - 1.95379i) q^{94} +(7.63630 + 13.2265i) q^{95} +(-9.49478 + 2.41851i) q^{96} -10.8329 q^{97} +(9.83107 + 1.16192i) q^{98} +(-9.40378 + 3.77396i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 2 q^{3} - 4 q^{4} - 8 q^{6} - 16 q^{7}+O(q^{10}) $ 240 * q - 2 * q^3 - 4 * q^4 - 8 * q^6 - 16 * q^7	$ 240 q - 2 q^{3} - 4 q^{4} - 8 q^{6} - 16 q^{7} - 4 q^{10} - 2 q^{12} - 16 q^{13} - 20 q^{16} + 16 q^{18} - 4 q^{19} + 2 q^{21} - 40 q^{22} - 22 q^{24} - 8 q^{27} - 4 q^{28} - 26 q^{30} - 4 q^{33} + 16 q^{36} - 4 q^{37} - 4 q^{39} + 8 q^{40} - 18 q^{42} - 16 q^{43} + 18 q^{45} - 20 q^{46} - 88 q^{48} - 16 q^{49} + 6 q^{51} + 8 q^{52} + 14 q^{54} - 32 q^{55} - 36 q^{58} - 42 q^{60} - 4 q^{61} - 64 q^{64} - 30 q^{66} - 36 q^{67} - 20 q^{69} + 116 q^{70} - 46 q^{72} - 24 q^{75} - 112 q^{76} - 92 q^{78} - 4 q^{81} - 32 q^{82} + 44 q^{84} - 56 q^{85} - 4 q^{87} - 20 q^{88} + 28 q^{90} - 40 q^{91} - 14 q^{93} + 72 q^{94} + 36 q^{96} - 32 q^{97} + 28 q^{99}+O(q^{100}) $ 240 * q - 2 * q^3 - 4 * q^4 - 8 * q^6 - 16 * q^7 - 4 * q^10 - 2 * q^12 - 16 * q^13 - 20 * q^16 + 16 * q^18 - 4 * q^19 + 2 * q^21 - 40 * q^22 - 22 * q^24 - 8 * q^27 - 4 * q^28 - 26 * q^30 - 4 * q^33 + 16 * q^36 - 4 * q^37 - 4 * q^39 + 8 * q^40 - 18 * q^42 - 16 * q^43 + 18 * q^45 - 20 * q^46 - 88 * q^48 - 16 * q^49 + 6 * q^51 + 8 * q^52 + 14 * q^54 - 32 * q^55 - 36 * q^58 - 42 * q^60 - 4 * q^61 - 64 * q^64 - 30 * q^66 - 36 * q^67 - 20 * q^69 + 116 * q^70 - 46 * q^72 - 24 * q^75 - 112 * q^76 - 92 * q^78 - 4 * q^81 - 32 * q^82 + 44 * q^84 - 56 * q^85 - 4 * q^87 - 20 * q^88 + 28 * q^90 - 40 * q^91 - 14 * q^93 + 72 * q^94 + 36 * q^96 - 32 * q^97 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.985435	−	1.01436i	−0.696807	−	0.717258i
$2$	−0.985435	−	1.01436i	−0.696807	−	0.717258i
$3$	−0.774639	+	1.54917i	−0.447238	+	0.894415i
$3$	−0.774639	+	1.54917i	−0.447238	+	0.894415i
$4$	−0.0578377	+	1.99916i	−0.0289188	+	0.999582i
$5$	0.677113	+	2.52702i	0.302814	+	1.13012i	0.934811	+	0.355147i	$0.115569\pi$
$5$	0.677113	+	2.52702i	0.302814	+	1.13012i	−0.631996	+	0.774971i	$0.717764\pi$
$6$	2.33477	−	0.740848i	0.953165	−	0.302450i
$7$	0.885088	+	2.49331i	0.334532	+	0.942384i
$7$	0.885088	+	2.49331i	0.334532	+	0.942384i
$8$	2.08486	−	1.91138i	0.737109	−	0.675774i
$9$	−1.79987	−	2.40010i	−0.599956	−	0.800033i
$10$	1.89605	−	3.17705i	0.599583	−	1.00467i
$11$	0.874188	−	3.26252i	0.263578	−	0.983686i	−0.699537	−	0.714596i	$-0.746611\pi$
$11$	0.874188	−	3.26252i	0.263578	−	0.983686i	0.963115	−	0.269090i	$-0.0867228\pi$
$12$	−3.05225	−	1.63823i	−0.881107	−	0.472916i
$13$	−3.62728	+	3.62728i	−1.00603	+	1.00603i	−0.00604406	+	0.999982i	$0.501924\pi$
$13$	−3.62728	+	3.62728i	−1.00603	+	1.00603i	−0.999982	+	0.00604406i	$0.998076\pi$
$14$	1.65691	−	3.35479i	0.442829	−	0.896606i
$15$	−4.43931	−	0.908564i	−1.14622	−	0.234590i
$16$	−3.99331	−	0.231254i	−0.998327	−	0.0578135i
$17$	−6.30359	+	3.63938i	−1.52885	+	0.882680i	−0.529435	+	0.848350i	$0.677596\pi$
$17$	−6.30359	+	3.63938i	−1.52885	+	0.882680i	−0.999411	+	0.0343291i	$0.989071\pi$
$18$	−0.660903	+	4.19085i	−0.155776	+	0.987792i
$19$	5.63886	−	1.51093i	1.29364	−	0.346631i	0.454601	−	0.890695i	$-0.349782\pi$
$19$	5.63886	−	1.51093i	1.29364	−	0.346631i	0.839043	+	0.544064i	$0.183115\pi$
$20$	−5.09109	+	1.20750i	−1.13840	+	0.270006i
$21$	−4.54820	−	0.560266i	−0.992498	−	0.122260i
$22$	−4.17081	+	2.32826i	−0.889219	+	0.496386i
$23$	−0.902810	−	0.521238i	−0.188249	−	0.108686i	0.402914	−	0.915238i	$-0.367998\pi$
$23$	−0.902810	−	0.521238i	−0.188249	−	0.108686i	−0.591163	+	0.806552i	$0.701331\pi$
$24$	1.34604	+	4.71043i	0.274759	+	0.961513i
$25$	−1.59722	+	0.922157i	−0.319444	+	0.184431i
$26$	7.25380	+	0.104908i	1.42259	+	0.0205741i
$27$	5.11241	−	0.929096i	0.983885	−	0.178805i
$28$	−5.03574	+	1.62523i	−0.951665	+	0.307139i
$29$	0.164130	+	0.164130i	0.0304781	+	0.0304781i	0.722182	−	0.691704i	$-0.243139\pi$
$29$	0.164130	+	0.164130i	0.0304781	+	0.0304781i	−0.691704	+	0.722182i	$0.743139\pi$
$30$	3.45304	+	5.39837i	0.630436	+	0.985603i
$31$	−2.66713	+	1.53987i	−0.479031	+	0.276569i	−0.720012	−	0.693961i	$-0.755864\pi$
$31$	−2.66713	+	1.53987i	−0.479031	+	0.276569i	0.240982	+	0.970530i	$0.422531\pi$
$32$	3.70057	+	4.27852i	0.654175	+	0.756343i
$33$	4.37702	+	3.88154i	0.761941	+	0.675689i
$34$	9.90341	+	2.80772i	1.69842	+	0.481520i
$35$	−5.70135	+	3.92489i	−0.963705	+	0.663428i
$36$	4.90229	−	3.45942i	0.817048	−	0.576569i
$37$	2.95156	−	0.790868i	0.485233	−	0.130018i	−0.00790499	−	0.999969i	$-0.502516\pi$
$37$	2.95156	−	0.790868i	0.485233	−	0.130018i	0.493138	+	0.869951i	$0.335850\pi$
$38$	−7.08935	−	4.23090i	−1.15004	−	0.686342i
$39$	−2.80945	−	8.42911i	−0.449871	−	1.34974i
$40$	6.24177	+	3.97426i	0.986911	+	0.628386i
$41$	−9.40208			−1.46836			−0.734179	−	0.678956i	$-0.762433\pi$
$41$	−9.40208			−1.46836			−0.734179	+	0.678956i	$0.762433\pi$
$42$	3.91364	+	5.16560i	0.603888	+	0.797069i
$43$	1.63803	−	1.63803i	0.249798	−	0.249798i	−0.571090	−	0.820888i	$-0.693479\pi$
$43$	1.63803	−	1.63803i	0.249798	−	0.249798i	0.820888	+	0.571090i	$0.193479\pi$
$44$	6.47174	+	1.93634i	0.975652	+	0.291915i
$45$	4.84638	−	6.17344i	0.722456	−	0.920282i
$46$	0.360940	+	1.42942i	0.0532176	+	0.210756i
$47$	−2.82149	+	4.88697i	−0.411557	+	0.712838i	−0.995060	−	0.0992728i	$-0.968348\pi$
$47$	−2.82149	+	4.88697i	−0.411557	+	0.712838i	0.583503	+	0.812111i	$0.301682\pi$
$48$	3.45163	−	6.00719i	0.498199	−	0.867063i
$49$	−5.43324	+	4.41361i	−0.776177	+	0.630515i
$50$	2.50935	+	0.711428i	0.354876	+	0.100611i
$51$	−0.755018	−	12.5846i	−0.105724	−	1.76219i
$52$	−7.04173	−	7.46131i	−0.976512	−	1.03470i
$53$	5.37060	+	1.43905i	0.737708	+	0.197668i	0.608059	−	0.793892i	$-0.291948\pi$
$53$	5.37060	+	1.43905i	0.737708	+	0.197668i	0.129649	+	0.991560i	$0.458615\pi$
$54$	−5.98038	−	4.27025i	−0.813827	−	0.581107i
$55$	8.83637			1.19150
$56$	6.61095	+	3.50647i	0.883425	+	0.468572i
$57$	−2.02740	+	9.90600i	−0.268535	+	1.31208i
$58$	0.00474693	−	0.328225i	0.000623303	−	0.0430980i
$59$	−0.969245	+	3.61727i	−0.126185	+	0.470929i	−0.999879	−	0.0155470i	$-0.995051\pi$
$59$	−0.969245	+	3.61727i	−0.126185	+	0.470929i	0.873694	+	0.486475i	$0.161718\pi$
$60$	2.07313	−	8.82235i	0.267640	−	1.13896i
$61$	1.36700	+	5.10170i	0.175026	+	0.653206i	0.996547	+	0.0830278i	$0.0264590\pi$
$61$	1.36700	+	5.10170i	0.175026	+	0.653206i	−0.821521	+	0.570178i	$0.806874\pi$
$62$	4.19026	+	1.18798i	0.532163	+	0.150874i
$63$	4.39116	−	6.61194i	0.553234	−	0.833026i
$64$	0.693278	−	7.96990i	0.0866598	−	0.996238i
$65$	−11.6223	−	6.71013i	−1.44157	−	0.832289i
$66$	−0.375999	−	8.26486i	−0.0462823	−	1.01733i
$67$	−2.04193	+	7.62060i	−0.249462	+	0.931005i	0.721626	+	0.692283i	$0.243395\pi$
$67$	−2.04193	+	7.62060i	−0.249462	+	0.931005i	−0.971088	+	0.238722i	$0.923272\pi$
$68$	−6.91113	−	12.8124i	−0.838098	−	1.55373i
$69$	1.50684	−	0.994837i	0.181402	−	0.119764i
$70$	9.59955	+	1.91548i	1.14737	+	0.228944i
$71$		−	2.28487i		−	0.271165i	−0.990766	−	0.135582i	$-0.956709\pi$
$71$		−	2.28487i		−	0.271165i	0.990766	−	0.135582i	$-0.0432905\pi$
$72$	−8.33997	−	1.56364i	−0.982874	−	0.184277i
$73$	9.32837	−	5.38574i	1.09180	−	0.630353i	0.157747	−	0.987480i	$-0.449577\pi$
$73$	9.32837	−	5.38574i	1.09180	−	0.630353i	0.934056	+	0.357127i	$0.116244\pi$
$74$	−3.71079	−	2.21458i	−0.431371	−	0.257440i
$75$	−0.191309	−	3.18871i	−0.0220904	−	0.368201i
$76$	2.69446	+	11.3604i	0.309075	+	1.30313i
$77$	8.90821	−	0.707986i	1.01519	−	0.0806825i
$78$	−5.78159	+	11.1561i	−0.654637	+	1.26318i
$79$	6.93760	+	4.00542i	0.780541	+	0.450645i	0.836622	−	0.547781i	$-0.184527\pi$
$79$	6.93760	+	4.00542i	0.780541	+	0.450645i	−0.0560811	+	0.998426i	$0.517861\pi$
$80$	−2.11954	−	10.2478i	−0.236972	−	1.14573i
$81$	−2.52095	+	8.63972i	−0.280105	+	0.959969i
$82$	9.26514	+	9.53706i	1.02316	+	1.05319i
$83$	4.18395	−	4.18395i	0.459248	−	0.459248i	−0.439161	−	0.898409i	$-0.644724\pi$
$83$	4.18395	−	4.18395i	0.459248	−	0.459248i	0.898409	+	0.439161i	$0.144724\pi$
$84$	1.38312	−	9.06019i	0.150911	−	0.988547i
$85$	−13.4650	−	13.4650i	−1.46049	−	1.46049i
$86$	−3.27572	−	0.0473750i	−0.353230	−	0.00510857i
$87$	−0.381406	+	0.127124i	−0.0408910	+	0.0136291i
$88$	−4.41334	−	8.47279i	−0.470463	−	0.903202i
$89$	3.04256	−	5.26988i	0.322511	−	0.558606i	−0.658494	−	0.752586i	$-0.728806\pi$
$89$	3.04256	−	5.26988i	0.322511	−	0.558606i	0.981006	+	0.193980i	$0.0621397\pi$
$90$	−11.0379	+	1.16756i	−1.16349	+	0.123072i
$91$	−12.2544	−	5.83349i	−1.28461	−	0.611515i
$92$	1.09426	−	1.77472i	0.114084	−	0.185027i
$93$	−0.319458	−	5.32469i	−0.0331262	−	0.552144i
$94$	7.73753	−	1.95379i	0.798065	−	0.201518i
$95$	7.63630	+	13.2265i	0.783467	+	1.35701i
$96$	−9.49478	+	2.41851i	−0.969057	+	0.246838i
$97$	−10.8329			−1.09991			−0.549956	−	0.835193i	$-0.685356\pi$
$97$	−10.8329			−1.09991			−0.549956	+	0.835193i	$0.685356\pi$
$98$	9.83107	+	1.16192i	0.993088	+	0.117372i
$99$	−9.40378	+	3.77396i	−0.945116	+	0.379297i
$100$	−1.75116	−	3.24644i	−0.175116	−	0.324644i
$101$	14.4895	+	3.88246i	1.44176	+	0.386319i	0.893151	−	0.449758i	$-0.148490\pi$
$101$	14.4895	+	3.88246i	1.44176	+	0.386319i	0.548612	+	0.836077i	$0.315156\pi$
$102$	−12.0212	+	13.1671i	−1.19028	+	1.30374i
$103$	7.78320	−	13.4809i	0.766901	−	1.32831i	−0.172334	−	0.985039i	$-0.555131\pi$
$103$	7.78320	−	13.4809i	0.766901	−	1.32831i	0.939236	−	0.343273i	$-0.111536\pi$
$104$	−0.629270	+	14.4955i	−0.0617050	+	1.42140i
$105$	−1.66384	−	11.8728i	−0.162374	−	1.15866i
$106$	−3.83267	−	6.86579i	−0.372261	−	0.666864i
$107$	9.78826	−	2.62276i	0.946266	−	0.253551i	0.247489	−	0.968891i	$-0.420395\pi$
$107$	9.78826	−	2.62276i	0.946266	−	0.253551i	0.698777	+	0.715339i	$0.253728\pi$
$108$	1.56172	+	10.2743i	0.150277	+	0.988644i
$109$	−0.509537	−	0.136530i	−0.0488048	−	0.0130772i	0.234334	−	0.972156i	$-0.424709\pi$
$109$	−0.509537	−	0.136530i	−0.0488048	−	0.0130772i	−0.283139	+	0.959079i	$0.591376\pi$
$110$	−8.70766	−	8.96323i	−0.830243	−	0.854610i
$111$	−1.06120	+	5.18511i	−0.100725	+	0.492149i
$112$	−2.95784	−	10.1613i	−0.279490	−	0.960149i
$113$			6.87732i			0.646963i	0.946234	+	0.323482i	$0.104853\pi$
$113$			6.87732i			0.646963i	−0.946234	+	0.323482i	$0.895147\pi$
$114$	12.0461	−	7.70521i	1.12822	−	0.721659i
$115$	0.705874	−	2.63436i	0.0658231	−	0.245655i
$116$	−0.337615	+	0.318629i	−0.0313467	+	0.0295839i
$117$	15.2344	+	2.17720i	1.40843	+	0.201282i
$118$	4.62433	−	2.58142i	0.425704	−	0.237639i
$119$	−14.6534	−	12.4957i	−1.34327	−	1.14548i
$120$	−10.9919	+	6.59096i	−1.00342	+	0.601670i
$121$	−0.353524	−	0.204107i	−0.0321385	−	0.0185552i
$122$	3.82786	−	6.41401i	0.346558	−	0.580697i
$123$	7.28322	−	14.5654i	0.656706	−	1.31332i
$124$	−2.92419	−	5.42109i	−0.262600	−	0.486828i
$125$	5.83773	+	5.83773i	0.522142	+	0.522142i
$126$	−11.0341	+	2.06143i	−0.982992	+	0.183647i
$127$			4.45854i			0.395631i	0.980239	+	0.197816i	$0.0633848\pi$
$127$			4.45854i			0.395631i	−0.980239	+	0.197816i	$0.936615\pi$
$128$	−8.76750	+	7.15059i	−0.774945	+	0.632029i
$129$	1.26871	+	3.80648i	0.111704	+	0.335142i
$130$	4.64654	+	18.4015i	0.407528	+	1.61392i
$131$	1.14586	+	4.27640i	0.100114	+	0.373631i	0.997745	−	0.0671169i	$-0.0213800\pi$
$131$	1.14586	+	4.27640i	0.100114	+	0.373631i	−0.897631	+	0.440748i	$0.854713\pi$
$132$	−8.01299	+	8.52588i	−0.697441	+	0.742082i
$133$	8.75811	+	12.7222i	0.759425	+	1.10315i
$134$	9.74220	−	5.43836i	0.841598	−	0.469802i
$135$	5.80953	+	12.2901i	0.500004	+	1.05776i
$136$	−6.18588	+	19.6361i	−0.530435	+	1.68378i
$137$	11.1596	+	19.3289i	0.953425	+	1.65138i	0.737931	+	0.674876i	$0.235803\pi$
$137$	11.1596	+	19.3289i	0.953425	+	1.65138i	0.215494	+	0.976505i	$0.430864\pi$
$138$	−2.49401	−	0.548125i	−0.212304	−	0.0466595i
$139$	9.56395	−	9.56395i	0.811204	−	0.811204i	−0.173611	−	0.984814i	$-0.555543\pi$
$139$	9.56395	−	9.56395i	0.811204	−	0.811204i	0.984814	+	0.173611i	$0.0555434\pi$
$140$	−7.51675	−	11.6249i	−0.635281	−	0.982487i
$141$	−5.38512	−	8.15662i	−0.453509	−	0.686911i
$142$	−2.31768	+	2.25159i	−0.194495	+	0.188950i
$143$	8.66313	+	15.0050i	0.724447	+	1.25478i
$144$	6.63240	+	10.0006i	0.552700	+	0.833380i
$145$	−0.303624	+	0.525893i	−0.0252146	+	0.0436730i
$146$	−14.6556	−	4.15500i	−1.21290	−	0.343870i
$147$	−2.62864	−	11.8360i	−0.216806	−	0.976215i
$148$	1.41036	+	5.94639i	0.115931	+	0.488790i
$149$	1.16559	+	4.35004i	0.0954888	+	0.356369i	0.997093	−	0.0761927i	$-0.0242764\pi$
$149$	1.16559	+	4.35004i	0.0954888	+	0.356369i	−0.901604	+	0.432562i	$0.857610\pi$
$150$	−3.04597	+	3.33632i	−0.248702	+	0.272409i
$151$	4.83337	+	8.37165i	0.393334	+	0.681275i	0.992887	−	0.119060i	$-0.0379881\pi$
$151$	4.83337	+	8.37165i	0.393334	+	0.681275i	−0.599553	+	0.800335i	$0.704655\pi$
$152$	8.86828	−	13.9281i	0.719313	−	1.12972i
$153$	20.0805	+	8.57884i	1.62341	+	0.693558i
$154$	−9.49661	−	8.33843i	−0.765259	−	0.671930i
$155$	−5.69723	−	5.69723i	−0.457612	−	0.457612i
$156$	17.0137	−	5.12902i	1.36218	−	0.410650i
$157$	−4.24524	−	1.13751i	−0.338807	−	0.0907831i	0.0854039	−	0.996346i	$-0.472782\pi$
$157$	−4.24524	−	1.13751i	−0.338807	−	0.0907831i	−0.424211	+	0.905563i	$0.639449\pi$
$158$	−2.77362	−	10.9843i	−0.220657	−	0.873862i
$159$	−6.38961	+	7.20524i	−0.506729	+	0.571413i
$160$	−8.30621	+	12.2485i	−0.656664	+	0.968326i
$161$	0.500543	−	2.71233i	0.0394484	−	0.213762i
$162$	11.2480	−	5.95674i	0.883725	−	0.468006i
$163$	−14.4959	+	3.88416i	−1.13541	+	0.304231i	−0.777102	−	0.629374i	$-0.783311\pi$
$163$	−14.4959	+	3.88416i	−1.13541	+	0.304231i	−0.358303	+	0.933605i	$0.616645\pi$
$164$	0.543795	−	18.7963i	0.0424632	−	1.46774i
$165$	−6.84500	+	13.6891i	−0.532882	+	1.06569i
$166$	−8.36702	−	0.121008i	−0.649407	−	0.00939201i
$167$			10.6269i			0.822332i	0.911561	+	0.411166i	$0.134878\pi$
$167$			10.6269i			0.822332i	−0.911561	+	0.411166i	$0.865122\pi$
$168$	−10.5532	+	7.52524i	−0.814200	+	0.580585i
$169$		−	13.3143i		−	1.02418i
$170$	−0.389434	+	26.9273i	−0.0298682	+	2.06523i
$171$	−13.7756	−	10.8144i	−1.05345	−	0.826994i
$172$	3.17995	+	3.36943i	0.242469	+	0.256917i
$173$	−1.26462	+	0.338854i	−0.0961474	+	0.0257626i	−0.306572	−	0.951847i	$-0.599182\pi$
$173$	−1.26462	+	0.338854i	−0.0961474	+	0.0257626i	0.210425	+	0.977610i	$0.432515\pi$
$174$	0.504799	+	0.261609i	0.0382687	+	0.0198326i
$175$	−3.71291	−	3.16619i	−0.280670	−	0.239341i
$176$	−4.24537	+	12.8261i	−0.320007	+	0.966802i
$177$	−4.85296	−	4.30361i	−0.364771	−	0.323479i
$178$	−8.34378	+	2.10687i	−0.625393	+	0.157917i
$179$	−10.5050	−	2.81479i	−0.785177	−	0.210388i	−0.156111	−	0.987739i	$-0.549896\pi$
$179$	−10.5050	−	2.81479i	−0.785177	−	0.210388i	−0.629066	+	0.777352i	$0.716562\pi$
$180$	12.0614	+	10.0458i	0.899005	+	0.748767i
$181$	−5.73837	−	5.73837i	−0.426530	−	0.426530i	0.460915	−	0.887444i	$-0.347521\pi$
$181$	−5.73837	−	5.73837i	−0.426530	−	0.426530i	−0.887444	+	0.460915i	$0.847521\pi$
$182$	6.15868	+	18.1789i	0.456512	+	1.34751i
$183$	−8.96234	−	1.83426i	−0.662515	−	0.135593i
$184$	−2.87851	+	0.638903i	−0.212207	+	0.0471006i
$185$	3.99708	+	6.92314i	0.293871	+	0.509000i
$186$	−5.08633	+	5.57117i	−0.372947	+	0.408498i
$187$	6.36301	+	23.7471i	0.465309	+	1.73656i
$188$	−9.60667	−	5.92328i	−0.700638	−	0.432000i
$189$	6.84147	+	11.9245i	0.497643	+	0.867382i
$190$	5.89127	−	20.7797i	0.427397	−	1.50752i
$191$	6.72903	−	11.6550i	0.486896	−	0.843328i	−0.512991	−	0.858394i	$-0.671463\pi$
$191$	6.72903	−	11.6550i	0.486896	−	0.843328i	0.999886	+	0.0150661i	$0.00479588\pi$
$192$	11.8097	+	7.24781i	0.852293	+	0.523065i
$193$	6.12985	+	10.6172i	0.441236	+	0.764243i	0.997781	−	0.0665740i	$-0.0212068\pi$
$193$	6.12985	+	10.6172i	0.441236	+	0.764243i	−0.556546	+	0.830817i	$0.687874\pi$
$194$	10.6751	+	10.9884i	0.766427	+	0.788921i
$195$	19.3982	−	12.8070i	1.38914	−	0.917127i
$196$	−8.50927	−	11.1172i	−0.607805	−	0.794086i
$197$	−7.79286	+	7.79286i	−0.555219	+	0.555219i	−0.927942	−	0.372724i	$-0.878424\pi$
$197$	−7.79286	+	7.79286i	−0.555219	+	0.555219i	0.372724	+	0.927942i	$0.378424\pi$
$198$	13.0950	+	5.81980i	0.930618	+	0.413595i
$199$	1.47583	+	2.55620i	0.104618	+	0.181204i	0.913582	−	0.406654i	$-0.133305\pi$
$199$	1.47583	+	2.55620i	0.104618	+	0.181204i	−0.808964	+	0.587858i	$0.799971\pi$
$200$	−1.56740	+	4.97546i	−0.110832	+	0.351818i
$201$	−10.2239	−	9.06653i	−0.721136	−	0.639503i
$202$	−10.3403	−	18.5235i	−0.727540	−	1.30331i
$203$	−0.263958	+	0.554496i	−0.0185262	+	0.0389180i
$204$	25.2023	−	0.781543i	1.76451	−	0.0547190i
$205$	−6.36627	−	23.7593i	−0.444640	−	1.65942i
$206$	−21.3443	+	5.38960i	−1.48713	+	0.375511i
$207$	0.373918	+	3.10499i	0.0259891	+	0.215812i
$208$	15.3237	−	13.6460i	1.06250	−	0.946181i
$209$		−	19.7177i		−	1.36390i
$210$	−10.4036	+	13.3875i	−0.717916	+	0.923828i
$211$	11.9004	+	11.9004i	0.819254	+	0.819254i	0.986000	−	0.166745i	$-0.0533258\pi$
$211$	11.9004	+	11.9004i	0.819254	+	0.819254i	−0.166745	+	0.986000i	$0.553326\pi$
$212$	−3.18751	+	10.6535i	−0.218919	+	0.731683i
$213$	3.53966	+	1.76995i	0.242534	+	0.121275i
$214$	−12.3061	−	7.34423i	−0.841227	−	0.502041i
$215$	5.24847	+	3.03021i	0.357943	+	0.206658i
$216$	8.88281	−	11.7088i	0.604399	−	0.796682i
$217$	−6.20002	−	5.28708i	−0.420885	−	0.358910i
$218$	0.363625	+	0.651393i	0.0246278	+	0.0441179i
$219$	1.11731	+	18.6233i	0.0755010	+	1.25844i
$220$	−0.511075	+	17.6653i	−0.0344567	+	1.19100i
$221$	9.66384	−	36.0659i	0.650060	−	2.42606i
$222$	6.30530	−	4.03315i	0.423184	−	0.270687i
$223$		−	7.42867i		−	0.497461i	−0.968573	−	0.248730i	$-0.919987\pi$
$223$		−	7.42867i		−	0.497461i	0.968573	−	0.248730i	$-0.0800133\pi$
$224$	−7.39238	+	13.0136i	−0.493924	+	0.869505i
$225$	5.08806	+	2.17373i	0.339204	+	0.144915i
$226$	6.97605	−	6.77714i	0.464040	−	0.450809i
$227$	5.46376	+	1.46401i	0.362642	+	0.0971698i	0.435539	−	0.900170i	$-0.356558\pi$
$227$	5.46376	+	1.46401i	0.362642	+	0.0971698i	−0.0728968	+	0.997339i	$0.523224\pi$
$228$	−19.6864	−	4.62603i	−1.30377	−	0.306367i
$229$	1.80894	−	0.484703i	0.119538	−	0.0320301i	−0.198554	−	0.980090i	$-0.563625\pi$
$229$	1.80894	−	0.484703i	0.119538	−	0.0320301i	0.318092	+	0.948060i	$0.396958\pi$
$230$	−3.36777	+	1.87998i	−0.222064	+	0.123962i
$231$	−5.80386	+	14.3488i	−0.381866	+	0.944081i
$232$	0.655900	+	0.0284736i	0.0430620	+	0.00186939i
$233$	2.84179	−	4.92212i	0.186172	−	0.322459i	−0.757799	−	0.652488i	$-0.773725\pi$
$233$	2.84179	−	4.92212i	0.186172	−	0.322459i	0.943971	+	0.330029i	$0.107059\pi$
$234$	−12.8041	−	17.5986i	−0.837030	−	1.15046i
$235$	−14.2599	−	3.82094i	−0.930217	−	0.249251i
$236$	−7.17546	−	2.14689i	−0.467082	−	0.139751i
$237$	−11.5792	+	7.64478i	−0.752152	+	0.496582i
$238$	1.76486	+	27.1774i	0.114399	+	1.76165i
$239$	14.1287			0.913909			0.456954	−	0.889490i	$-0.348940\pi$
$239$	14.1287			0.913909			0.456954	+	0.889490i	$0.348940\pi$
$240$	17.5174	+	4.65478i	1.13074	+	0.300465i
$241$	−10.5955	−	18.3519i	−0.682513	−	1.18215i	−0.974211	−	0.225637i	$-0.927554\pi$
$241$	−10.5955	−	18.3519i	−0.682513	−	1.18215i	0.291698	−	0.956510i	$-0.405780\pi$
$242$	0.141337	+	0.559734i	0.00908551	+	0.0359810i
$243$	−11.4316	−	10.5980i	−0.733337	−	0.679865i
$244$	−10.2782	+	2.43778i	−0.657994	+	0.156063i
$245$	−14.8322	−	10.7414i	−0.947594	−	0.686243i
$246$	−21.9517	+	6.96551i	−1.39959	+	0.444105i
$247$	−14.9732	+	25.9343i	−0.952720	+	1.65016i
$248$	−2.61732	+	8.30830i	−0.166200	+	0.527578i
$249$	3.24060	+	9.72270i	0.205365	+	0.616151i
$250$	0.168838	−	11.6742i	0.0106783	−	0.738343i
$251$	−10.6988	−	10.6988i	−0.675301	−	0.675301i	0.283632	−	0.958933i	$-0.408461\pi$
$251$	−10.6988	−	10.6988i	−0.675301	−	0.675301i	−0.958933	+	0.283632i	$0.908461\pi$
$252$	12.9644	+	9.16107i	0.816679	+	0.577093i
$253$	−2.48977	+	2.48977i	−0.156531	+	0.156531i
$254$	4.52255	−	4.39360i	0.283770	−	0.275679i
$255$	31.2902	−	10.4291i	1.95947	−	0.653096i
$256$	15.8930	+	1.84694i	0.993315	+	0.115434i
$257$	−14.9863	−	8.65236i	−0.934821	−	0.539719i	−0.0464880	−	0.998919i	$-0.514803\pi$
$257$	−14.9863	−	8.65236i	−0.934821	−	0.539719i	−0.888333	+	0.459200i	$0.848136\pi$
$258$	2.61089	−	5.03796i	0.162547	−	0.313650i
$259$	4.58427	+	6.65918i	0.284853	+	0.413781i
$260$	14.0868	−	22.8467i	0.873629	−	1.41689i
$261$	0.0985155	−	0.689339i	0.00609795	−	0.0426690i
$262$	3.20862	−	5.37642i	0.198229	−	0.332156i
$263$	−14.9718	+	8.64397i	−0.923201	+	0.533010i	−0.884655	−	0.466246i	$-0.845606\pi$
$263$	−14.9718	+	8.64397i	−0.923201	+	0.533010i	−0.0385461	+	0.999257i	$0.512273\pi$
$264$	16.5446	−	0.273663i	1.01825	−	0.0168428i
$265$			14.5460i			0.893554i
$266$	4.27426	−	21.4207i	0.262071	−	1.31339i
$267$	5.80706	+	8.79571i	0.355386	+	0.538289i
$268$	−15.1167	−	4.52292i	−0.923401	−	0.276281i
$269$	−5.83702	+	21.7841i	−0.355889	+	1.32820i	0.523472	+	0.852043i	$0.324636\pi$
$269$	−5.83702	+	21.7841i	−0.355889	+	1.32820i	−0.879362	+	0.476155i	$0.842030\pi$
$270$	6.74160	−	18.0040i	0.410281	−	1.09569i
$271$	−0.996893	−	0.575557i	−0.0605570	−	0.0349626i	0.469416	−	0.882977i	$-0.344465\pi$
$271$	−0.996893	−	0.575557i	−0.0605570	−	0.0349626i	−0.529973	+	0.848015i	$0.677798\pi$
$272$	26.0138	−	13.0754i	1.57732	−	0.792815i
$273$	18.5298	−	14.4653i	1.12148	−	0.875482i
$274$	8.60940	−	30.3672i	0.520113	−	1.83455i
$275$	1.61228	+	6.01710i	0.0972240	+	0.362845i
$276$	1.90169	+	3.06996i	0.114468	+	0.184790i
$277$	3.60302	−	13.4467i	0.216485	−	0.807932i	−0.769154	−	0.639063i	$-0.779322\pi$
$277$	3.60302	−	13.4467i	0.216485	−	0.807932i	0.985639	−	0.168868i	$-0.0540112\pi$
$278$	−19.1259	−	0.276607i	−1.14710	−	0.0165898i
$279$	8.49632	+	3.62982i	0.508661	+	0.217311i
$280$	−4.38457	+	19.0803i	−0.262028	+	1.14026i
$281$	−30.9858			−1.84846			−0.924229	−	0.381839i	$-0.875291\pi$
$281$	−30.9858			−1.84846			−0.924229	+	0.381839i	$0.875291\pi$
$282$	−2.96704	+	13.5002i	−0.176684	+	0.803928i
$283$	8.80706	+	2.35985i	0.523526	+	0.140278i	0.510897	−	0.859642i	$-0.329313\pi$
$283$	8.80706	+	2.35985i	0.523526	+	0.140278i	0.0126287	+	0.999920i	$0.495980\pi$
$284$	4.56784	+	0.132152i	0.271051	+	0.00784177i
$285$	−26.4054	+	1.58421i	−1.56412	+	0.0938405i
$286$	6.68345	−	23.5739i	0.395201	−	1.39395i
$287$	−8.32167	−	23.4424i	−0.491213	−	1.38376i
$288$	3.60834	−	16.5825i	0.212623	−	0.977134i
$289$	17.9902	−	31.1599i	1.05825	−	1.83294i
$290$	0.832645	−	0.210250i	0.0488946	−	0.0123463i
$291$	8.39157	−	16.7820i	0.491923	−	0.983778i
$292$	10.2274	+	18.9604i	0.598515	+	1.10958i
$293$	−0.312653	+	0.312653i	−0.0182654	+	0.0182654i	−0.716180	−	0.697915i	$-0.754111\pi$
$293$	−0.312653	+	0.312653i	−0.0182654	+	0.0182654i	0.697915	+	0.716180i	$0.254111\pi$
$294$	−9.41555	+	14.3300i	−0.549126	+	0.835740i
$295$	−9.79720			−0.570415
$296$	4.64194	−	7.29039i	0.269807	−	0.423745i
$297$	1.43802	−	17.4915i	0.0834426	−	1.01496i
$298$	3.26388	−	5.46900i	0.189071	−	0.316811i
$299$	5.16542	−	1.38407i	0.298724	−	0.0800428i
$300$	6.38582	−	0.198030i	0.368685	−	0.0114332i
$301$	5.53393	+	2.63433i	0.318971	+	0.151840i
$302$	3.72886	−	13.1525i	0.214572	−	0.756840i
$303$	−17.2388	+	19.4393i	−0.990341	+	1.11676i
$304$	−22.8671	+	4.72960i	−1.31152	+	0.271261i
$305$	−11.9665	+	6.90885i	−0.685199	+	0.395600i
$306$	−11.0860	−	28.8227i	−0.633746	−	1.64768i
$307$	−5.18531	−	5.18531i	−0.295941	−	0.295941i	0.543480	−	0.839422i	$-0.317106\pi$
$307$	−5.18531	−	5.18531i	−0.295941	−	0.295941i	−0.839422	+	0.543480i	$0.817106\pi$
$308$	0.900150	+	17.8499i	0.0512908	+	1.01709i
$309$	14.8551	+	22.5003i	0.845075	+	1.28000i
$310$	−0.164774	+	11.3933i	−0.00935856	+	0.647094i
$311$	23.6785	−	13.6708i	1.34268	−	0.775198i	0.355482	−	0.934683i	$-0.384317\pi$
$311$	23.6785	−	13.6708i	1.34268	−	0.775198i	0.987200	+	0.159485i	$0.0509834\pi$
$312$	−21.9685	−	12.2036i	−1.24372	−	0.690893i
$313$	−5.63063	−	3.25085i	−0.318262	−	0.183749i	0.332356	−	0.943154i	$-0.392157\pi$
$313$	−5.63063	−	3.25085i	−0.318262	−	0.183749i	−0.650618	+	0.759405i	$0.725490\pi$
$314$	3.02957	+	5.42713i	0.170968	+	0.306271i
$315$	19.6818	+	6.61952i	1.10894	+	0.372968i
$316$	−8.40875	+	13.6377i	−0.473029	+	0.767182i
$317$	25.4876	−	6.82939i	1.43153	−	0.383577i	0.541969	−	0.840399i	$-0.317679\pi$
$317$	25.4876	−	6.82939i	1.43153	−	0.383577i	0.889558	+	0.456822i	$0.151012\pi$
$318$	13.6052	−	0.618952i	0.762943	−	0.0347091i
$319$	0.678955	−	0.391995i	0.0380142	−	0.0219475i
$320$	20.6095	−	3.64460i	1.15211	−	0.203739i
$321$	−3.51927	+	17.1954i	−0.196426	+	0.959753i
$322$	−3.24452	+	2.16510i	−0.180810	+	0.120656i
$323$	−30.0463	+	30.0463i	−1.67182	+	1.67182i
$324$	−17.1264	−	5.53949i	−0.951468	−	0.307749i
$325$	2.44865	−	9.13849i	0.135827	−	0.506912i
$326$	18.2247	+	10.8764i	1.00937	+	0.602389i
$327$	0.606215	−	0.683599i	0.0335238	−	0.0378031i
$328$	−19.6020	+	17.9709i	−1.08234	+	0.992278i
$329$	−14.6820	−	2.70948i	−0.809447	−	0.149378i
$330$	20.6309	−	6.54640i	1.13569	−	0.360368i
$331$	2.34355	+	8.74625i	0.128813	+	0.480737i	0.999947	−	0.0103085i	$-0.00328136\pi$
$331$	2.34355	+	8.74625i	0.128813	+	0.480737i	−0.871134	+	0.491046i	$0.836615\pi$
$332$	8.12240	+	8.60638i	0.445775	+	0.472337i
$333$	−7.21058	−	5.66058i	−0.395137	−	0.310198i
$334$	10.7794	−	10.4721i	0.589824	−	0.573007i
$335$	−20.6400			−1.12769
$336$	18.0328	+	3.28910i	0.983770	+	0.179435i
$337$	12.1331			0.660930			0.330465	−	0.943818i	$-0.392794\pi$
$337$	12.1331			0.660930			0.330465	+	0.943818i	$0.392794\pi$
$338$	−13.5054	+	13.1204i	−0.734599	+	0.713653i
$339$	−10.6541	−	5.32744i	−0.578654	−	0.289347i
$340$	27.6976	−	26.1400i	1.50211	−	1.41764i
$341$	2.69227	+	10.0477i	0.145795	+	0.544113i
$342$	2.60533	+	24.6302i	0.140880	+	1.33185i
$343$	−15.8134	−	9.64035i	−0.853844	−	0.520530i
$344$	0.284170	−	6.54596i	0.0153214	−	0.352935i
$345$	3.53427	+	3.13420i	0.190279	+	0.168739i
$346$	1.58992	+	0.948858i	0.0854746	+	0.0510109i
$347$	−0.509606	+	1.90188i	−0.0273571	+	0.102098i	−0.978254	−	0.207408i	$-0.933497\pi$
$347$	−0.509606	+	1.90188i	−0.0273571	+	0.102098i	0.950897	+	0.309506i	$0.100164\pi$
$348$	−0.232081	−	0.769845i	−0.0124409	−	0.0412680i
$349$	17.8288	−	17.8288i	0.954351	−	0.954351i	−0.0446512	−	0.999003i	$-0.514218\pi$
$349$	17.8288	−	17.8288i	0.954351	−	0.954351i	0.999003	+	0.0446512i	$0.0142176\pi$
$350$	0.447185	+	6.88628i	0.0239031	+	0.368087i
$351$	−15.1741	+	21.9142i	−0.809931	+	1.16970i
$352$	17.1938	−	8.33293i	0.916430	−	0.444147i
$353$	18.7066	−	10.8003i	0.995654	−	0.574841i	0.0886947	−	0.996059i	$-0.471730\pi$
$353$	18.7066	−	10.8003i	0.995654	−	0.574841i	0.906960	+	0.421218i	$0.138397\pi$
$354$	0.416884	+	9.16355i	0.0221571	+	0.487037i
$355$	5.77392	−	1.54712i	0.306448	−	0.0821125i
$356$	10.3594	+	6.38738i	0.549046	+	0.338531i
$357$	30.7090	−	13.0209i	1.62529	−	0.689141i
$358$	7.49674	+	13.4296i	0.396215	+	0.709774i
$359$	−1.46649	−	0.846678i	−0.0773983	−	0.0446859i	0.460801	−	0.887503i	$-0.347562\pi$
$359$	−1.46649	−	0.846678i	−0.0773983	−	0.0446859i	−0.538200	+	0.842817i	$0.680895\pi$
$360$	−1.69575	−	22.1340i	−0.0893736	−	1.16657i
$361$	13.0594	−	7.53985i	0.687337	−	0.396834i
$362$	−0.165964	+	11.4755i	−0.00872289	+	0.603141i
$363$	0.590051	−	0.389560i	0.0309696	−	0.0204466i
$364$	12.3709	−	24.1612i	0.648409	−	1.26639i
$365$	19.9262	+	19.9262i	1.04299	+	1.04299i
$366$	6.97120	+	10.8986i	0.364391	+	0.569676i
$367$	−25.2699	+	14.5896i	−1.31908	+	0.761570i	−0.983580	−	0.180471i	$-0.942238\pi$
$367$	−25.2699	+	14.5896i	−1.31908	+	0.761570i	−0.335498	+	0.942041i	$0.608904\pi$
$368$	3.48466	+	2.29024i	0.181651	+	0.119387i
$369$	16.9225	+	22.5659i	0.880951	+	1.17474i
$370$	3.08368	−	10.8768i	0.160313	−	0.565456i
$371$	1.16545	+	14.6643i	0.0605073	+	0.761331i
$372$	10.6634	−	0.330681i	0.552871	−	0.0171450i
$373$	9.97716	−	2.67337i	0.516598	−	0.138422i	0.00890526	−	0.999960i	$-0.497165\pi$
$373$	9.97716	−	2.67337i	0.516598	−	0.138422i	0.507692	+	0.861538i	$0.330499\pi$
$374$	17.8177	−	29.8555i	0.921330	−	1.54379i
$375$	−13.5658	+	4.52151i	−0.700534	+	0.233490i
$376$	3.45842	+	15.5816i	0.178355	+	0.803559i
$377$	−1.19069			−0.0613235
$378$	5.35390	−	18.6905i	0.275375	−	0.961337i
$379$	15.1494	−	15.1494i	0.778170	−	0.778170i	−0.201349	−	0.979520i	$-0.564533\pi$
$379$	15.1494	−	15.1494i	0.778170	−	0.778170i	0.979520	+	0.201349i	$0.0645326\pi$
$380$	−26.8835	+	14.5012i	−1.37909	+	0.743897i
$381$	−6.90705	−	3.45376i	−0.353859	−	0.176941i
$382$	−18.4534	+	4.65963i	−0.944156	+	0.238407i
$383$	17.5315	−	30.3655i	0.895820	−	1.55161i	0.0630335	−	0.998011i	$-0.479922\pi$
$383$	17.5315	−	30.3655i	0.895820	−	1.55161i	0.832786	−	0.553594i	$-0.186744\pi$
$384$	−4.28584	−	19.1215i	−0.218711	−	0.975790i
$385$	7.82096	+	22.0318i	0.398593	+	1.12285i
$386$	4.72907	−	16.6804i	0.240703	−	0.849010i
$387$	−6.87968	−	0.983196i	−0.349714	−	0.0499787i
$388$	0.626549	−	21.6567i	0.0318082	−	1.09945i
$389$	−20.2950	−	5.43803i	−1.02900	−	0.275719i	−0.295451	−	0.955358i	$-0.595470\pi$
$389$	−20.2950	−	5.43803i	−1.02900	−	0.275719i	−0.733547	+	0.679639i	$0.762136\pi$
$390$	−32.1065	−	7.05626i	−1.62578	−	0.357307i
$391$	7.58793			0.383738
$392$	−2.89148	+	19.5867i	−0.146042	+	0.989278i
$393$	−7.51250	−	1.53753i	−0.378956	−	0.0775584i
$394$	15.5841	+	0.225384i	0.785116	+	0.0113547i
$395$	−5.42425	+	20.2436i	−0.272924	+	1.01856i
$396$	−7.00087	−	19.0180i	−0.351807	−	0.955689i
$397$	6.54620	+	24.4308i	0.328545	+	1.22614i	0.910700	+	0.413068i	$0.135543\pi$
$397$	6.54620	+	24.4308i	0.328545	+	1.22614i	−0.582156	+	0.813077i	$0.697791\pi$
$398$	1.13857	−	4.01598i	0.0570715	−	0.201303i
$399$	−26.4932	+	3.71274i	−1.32632	+	0.185870i
$400$	6.59146	−	3.31309i	0.329573	−	0.165655i
$401$	1.87721	+	1.08381i	0.0937434	+	0.0541228i	0.546139	−	0.837695i	$-0.316097\pi$
$401$	1.87721	+	1.08381i	0.0937434	+	0.0541228i	−0.452395	+	0.891817i	$0.649430\pi$
$402$	0.878261	+	19.3051i	0.0438037	+	0.962851i
$403$	4.08889	−	15.2600i	0.203682	−	0.760152i
$404$	−8.59971	+	28.7424i	−0.427852	+	1.42999i
$405$	−23.5397	−	0.520413i	−1.16970	−	0.0258595i
$406$	0.822569	−	0.278672i	0.0408234	−	0.0138303i
$407$		−	10.3209i		−	0.511587i
$408$	−25.6279	−	24.7939i	−1.26877	−	1.22748i
$409$	−20.0783	+	11.5922i	−0.992809	+	0.573199i	−0.906113	−	0.423036i	$-0.860964\pi$
$409$	−20.0783	+	11.5922i	−0.992809	+	0.573199i	−0.0866966	+	0.996235i	$0.527631\pi$
$410$	−17.8268	+	29.8709i	−0.880403	+	1.47522i
$411$	−38.5885	+	2.31514i	−1.90343	+	0.114197i
$412$	26.5003	+	16.3396i	1.30558	+	0.804994i
$413$	−9.87686	+	0.784970i	−0.486009	+	0.0386259i
$414$	2.78110	−	3.43905i	0.136684	−	0.169020i
$415$	13.4059	+	7.73991i	0.658071	+	0.379937i
$416$	−28.9424	−	2.09640i	−1.41902	−	0.102784i
$417$	7.40760	+	22.2248i	0.362751	+	1.08835i
$418$	−20.0008	+	19.4305i	−0.978271	+	0.950378i
$419$	8.05061	−	8.05061i	0.393298	−	0.393298i	−0.482563	−	0.875861i	$-0.660294\pi$
$419$	8.05061	−	8.05061i	0.393298	−	0.393298i	0.875861	+	0.482563i	$0.160294\pi$
$420$	23.8318	−	2.63960i	1.16287	−	0.128799i
$421$	0.873466	+	0.873466i	0.0425701	+	0.0425701i	0.728071	−	0.685501i	$-0.240417\pi$
$421$	0.873466	+	0.873466i	0.0425701	+	0.0425701i	−0.685501	+	0.728071i	$0.740417\pi$
$422$	0.344181	−	23.7982i	0.0167544	−	1.15848i
$423$	16.8075	−	2.02404i	0.817210	−	0.0984123i
$424$	13.9475	−	7.26502i	0.677351	−	0.352821i
$425$	6.71216	−	11.6258i	0.325588	−	0.563934i
$426$	−1.69274	−	5.33465i	−0.0820137	−	0.258465i
$427$	−11.5102	+	7.92380i	−0.557019	+	0.383460i
$428$	4.67719	+	19.7200i	0.226080	+	0.953203i
$429$	−29.9561	+	1.79723i	−1.44629	+	0.0867713i
$430$	−2.09832	−	8.30989i	−0.101190	−	0.400739i
$431$	−10.4850	−	18.1606i	−0.505047	−	0.874766i	−0.999983	−	0.00583707i	$-0.998142\pi$
$431$	−10.4850	−	18.1606i	−0.505047	−	0.874766i	0.494936	−	0.868929i	$-0.335191\pi$
$432$	−20.6303	+	2.52790i	−0.992576	+	0.121624i
$433$	−16.4987			−0.792877			−0.396438	−	0.918061i	$-0.629754\pi$
$433$	−16.4987			−0.792877			−0.396438	+	0.918061i	$0.629754\pi$
$434$	0.746735	+	11.4991i	0.0358444	+	0.551974i
$435$	−0.579499	−	0.877744i	−0.0277849	−	0.0420846i
$436$	0.302416	−	1.01075i	0.0144831	−	0.0484062i
$437$	−5.87838	−	1.57511i	−0.281201	−	0.0753476i
$438$	17.7896	−	19.4853i	0.850019	−	0.931046i
$439$	−2.57666	+	4.46290i	−0.122977	+	0.213003i	−0.920940	−	0.389703i	$-0.872578\pi$
$439$	−2.57666	+	4.46290i	−0.122977	+	0.213003i	0.797963	+	0.602706i	$0.205911\pi$
$440$	18.4226	−	16.8896i	0.878262	−	0.805181i
$441$	20.3722	+	5.09640i	0.970105	+	0.242686i
$442$	−46.1068	+	25.7380i	−2.19308	+	1.22423i
$443$	9.26646	−	2.48294i	0.440263	−	0.117968i	−0.0318768	−	0.999492i	$-0.510148\pi$
$443$	9.26646	−	2.48294i	0.440263	−	0.117968i	0.472140	+	0.881524i	$0.343482\pi$
$444$	−10.3045	−	2.42141i	−0.489030	−	0.114915i
$445$	15.3772	+	4.12032i	0.728951	+	0.195322i
$446$	−7.53532	+	7.32047i	−0.356808	+	0.346634i
$447$	−7.64187	−	1.56401i	−0.361448	−	0.0739752i
$448$	20.4851	−	5.32550i	0.967830	−	0.251606i
$449$			0.701207i			0.0330920i	0.999863	+	0.0165460i	$0.00526699\pi$
$449$			0.701207i			0.0330920i	−0.999863	+	0.0165460i	$0.994733\pi$
$450$	−2.80901	−	7.30317i	−0.132418	−	0.344275i
$451$	−8.21919	+	30.6744i	−0.387027	+	1.44440i
$452$	−13.7489	−	0.397768i	−0.646693	−	0.0187094i
$453$	−16.7132	+	1.00272i	−0.785257	+	0.0471120i
$454$	−3.89915	−	6.98489i	−0.182996	−	0.327817i
$455$	6.44372	−	34.9171i	0.302086	−	1.63694i
$456$	14.7073	+	24.5277i	0.688730	+	1.14862i
$457$	−0.359990	−	0.207840i	−0.0168396	−	0.00972235i	0.491557	−	0.870846i	$-0.336428\pi$
$457$	−0.359990	−	0.207840i	−0.0168396	−	0.00972235i	−0.508396	+	0.861123i	$0.669761\pi$
$458$	−2.27425	−	1.35726i	−0.106269	−	0.0634207i
$459$	−28.8452	+	24.4627i	−1.34638	+	1.14182i
$460$	5.22568	+	1.56352i	0.243649	+	0.0728996i
$461$	13.2059	+	13.2059i	0.615061	+	0.615061i	0.944260	−	0.329200i	$-0.106779\pi$
$461$	13.2059	+	13.2059i	0.615061	+	0.615061i	−0.329200	+	0.944260i	$0.606779\pi$
$462$	20.2741	−	8.25261i	0.943237	−	0.383946i
$463$		−	24.2762i		−	1.12821i	−0.825704	−	0.564104i	$-0.809222\pi$
$463$		−	24.2762i		−	1.12821i	0.825704	−	0.564104i	$-0.190778\pi$
$464$	−0.617464	−	0.693376i	−0.0286651	−	0.0321892i
$465$	13.2393	−	4.41269i	0.613957	−	0.204634i
$466$	−7.79318	+	1.96784i	−0.361012	+	0.0911585i
$467$	4.20865	+	15.7069i	0.194753	+	0.726829i	0.992331	+	0.123612i	$0.0394479\pi$
$467$	4.20865	+	15.7069i	0.194753	+	0.726829i	−0.797577	+	0.603217i	$0.793885\pi$
$468$	−5.23371	+	30.3302i	−0.241928	+	1.40202i
$469$	−20.8079	+	1.65372i	−0.960818	+	0.0763616i
$470$	10.1764	+	18.2300i	0.469405	+	0.840885i
$471$	5.05073	−	5.69545i	0.232725	−	0.262433i
$472$	4.89323	+	9.39409i	0.225229	+	0.432398i
$473$	−3.91216	−	6.77606i	−0.179881	−	0.311563i
$474$	19.1651	+	4.21204i	0.880282	+	0.193465i
$475$	−7.61321	+	7.61321i	−0.349318	+	0.349318i
$476$	25.8284	−	28.5717i	1.18384	−	1.30958i
$477$	−6.21251	−	15.4801i	−0.284451	−	0.708783i
$478$	−13.9229	−	14.3315i	−0.636819	−	0.655509i
$479$	−2.20778	−	3.82399i	−0.100876	−	0.174723i	0.811170	−	0.584811i	$-0.198831\pi$
$479$	−2.20778	−	3.82399i	−0.100876	−	0.174723i	−0.912046	+	0.410088i	$0.865498\pi$
$480$	−12.5407	−	22.3559i	−0.572400	−	1.02040i
$481$	−7.83743	+	13.5748i	−0.357356	+	0.618959i
$482$	−8.17421	+	28.8321i	−0.372325	+	1.31327i
$483$	3.81413	+	2.87651i	0.173549	+	0.130886i
$484$	0.428491	−	0.694947i	0.0194768	−	0.0315885i
$485$	−7.33509	−	27.3749i	−0.333069	−	1.24303i
$486$	0.514892	+	22.0394i	0.0233560	+	0.999727i
$487$	−20.3373	−	35.2252i	−0.921569	−	1.59620i	−0.796989	−	0.603994i	$-0.793575\pi$
$487$	−20.3373	−	35.2252i	−0.921569	−	1.59620i	−0.124580	−	0.992210i	$-0.539758\pi$
$488$	12.6013	+	8.02348i	0.570432	+	0.363206i
$489$	5.21185	−	25.4654i	0.235688	−	1.15159i
$490$	3.72055	+	25.6301i	0.168077	+	1.15785i
$491$	9.25599	+	9.25599i	0.417717	+	0.417717i	0.884416	−	0.466699i	$-0.154557\pi$
$491$	9.25599	+	9.25599i	0.417717	+	0.417717i	−0.466699	+	0.884416i	$0.654557\pi$
$492$	28.6975	+	15.4028i	1.29378	+	0.694411i
$493$	−1.63194	−	0.437276i	−0.0734987	−	0.0196939i
$494$	41.0617	−	10.3684i	1.84745	−	0.466497i
$495$	−15.9043	−	21.2082i	−0.714845	−	0.953236i
$496$	11.0068	−	5.53239i	0.494219	−	0.248412i
$497$	5.69691	−	2.02232i	0.255541	−	0.0907132i
$498$	6.66888	−	12.8682i	0.298840	−	0.576638i
$499$	−24.5381	+	6.57495i	−1.09847	+	0.294335i	−0.762143	−	0.647408i	$-0.775853\pi$
$499$	−24.5381	+	6.57495i	−1.09847	+	0.294335i	−0.336331	+	0.941744i	$0.609186\pi$
$500$	−12.0082	+	11.3329i	−0.537024	+	0.506824i
$501$	−16.4628	−	8.23199i	−0.735506	−	0.367778i
$502$	−0.309429	+	21.3953i	−0.0138105	+	0.954921i
$503$			5.54151i			0.247084i	0.992339	+	0.123542i	$0.0394253\pi$
$503$			5.54151i			0.247084i	−0.992339	+	0.123542i	$0.960575\pi$
$504$	−3.48295	−	22.1781i	−0.155143	−	0.987892i
$505$			39.2442i			1.74634i
$506$	4.97903	+	0.0720089i	0.221345	+	0.00320119i
$507$	20.6261	+	10.3138i	0.916038	+	0.458050i
$508$	−8.91335	−	0.257872i	−0.395466	−	0.0114412i
$509$	−38.5250	+	10.3227i	−1.70759	+	0.457548i	−0.974832	−	0.222940i	$-0.928435\pi$
$509$	−38.5250	+	10.3227i	−1.70759	+	0.457548i	−0.732759	+	0.680488i	$0.761768\pi$
$510$	−41.4133	−	21.4622i	−1.83381	−	0.950362i
$511$	21.6848	+	18.4917i	0.959278	+	0.818025i
$512$	−13.7881	−	17.9412i	−0.609354	−	0.792899i
$513$	27.4244	−	12.9635i	1.21082	−	0.572354i
$514$	5.99147	+	23.7278i	0.264272	+	1.04659i
$515$	39.3366	+	10.5402i	1.73338	+	0.464457i
$516$	−7.68315	+	2.31620i	−0.338232	+	0.101965i
$517$	13.4773	+	13.4773i	0.592731	+	0.592731i
$518$	2.23728	−	11.2123i	0.0983005	−	0.492639i
$519$	0.454681	−	2.22161i	0.0199583	−	0.0975177i
$520$	−37.0564	+	8.22488i	−1.62503	+	0.360685i
$521$	3.33292	+	5.77279i	0.146018	+	0.252910i	0.929752	−	0.368186i	$-0.120021\pi$
$521$	3.33292	+	5.77279i	0.146018	+	0.252910i	−0.783734	+	0.621096i	$0.786688\pi$
$522$	−0.796315	+	0.579368i	−0.0348538	+	0.0253583i
$523$	−8.26355	−	30.8400i	−0.361340	−	1.34854i	−0.872316	−	0.488943i	$-0.837383\pi$
$523$	−8.26355	−	30.8400i	−0.361340	−	1.34854i	0.510976	−	0.859595i	$-0.329284\pi$
$524$	−8.61549	+	2.04342i	−0.376370	+	0.0892672i
$525$	7.78114	−	3.29928i	0.339597	−	0.143992i
$526$	23.5218	+	6.66867i	1.02560	+	0.290768i
$527$	11.2083	−	19.4134i	0.488243	−	0.845661i
$528$	−16.5812	−	16.5124i	−0.721603	−	0.718610i
$529$	−10.9566	−	18.9774i	−0.476375	−	0.825106i
$530$	14.7548	−	14.3341i	0.640909	−	0.622635i
$531$	10.4263	−	4.18433i	0.452464	−	0.181584i
$532$	−25.9402	+	16.7731i	−1.12465	+	0.727205i
$533$	34.1040	−	34.1040i	1.47721	−	1.47721i
$534$	3.19951	−	14.5580i	0.138456	−	0.629987i
$535$	13.2555	+	22.9592i	0.573086	+	0.992614i
$536$	10.3087	+	19.7908i	0.445268	+	0.854832i
$537$	12.4981	−	14.0935i	0.539335	−	0.608181i
$538$	27.8488	−	15.5459i	1.20065	−	0.670233i
$539$	9.64978	+	21.5844i	0.415646	+	0.929704i
$540$	−24.9059	+	10.9034i	−1.07178	+	0.469206i
$541$	−0.708732	−	2.64502i	−0.0304708	−	0.113718i	0.949015	−	0.315229i	$-0.102081\pi$
$541$	−0.708732	−	2.64502i	−0.0304708	−	0.113718i	−0.979486	+	0.201511i	$0.935415\pi$
$542$	0.398554	+	1.57838i	0.0171193	+	0.0677972i
$543$	13.3349	−	4.44456i	0.572255	−	0.190734i
$544$	−38.8981	−	13.5023i	−1.66774	−	0.578906i
$545$		−	1.38006i		−	0.0591151i
$546$	−32.9329	−	4.54119i	−1.40940	−	0.194345i
$547$	9.50732	+	9.50732i	0.406504	+	0.406504i	0.880517	−	0.474014i	$-0.157195\pi$
$547$	9.50732	+	9.50732i	0.406504	+	0.406504i	−0.474014	+	0.880517i	$0.657195\pi$
$548$	−39.2871	+	21.1918i	−1.67826	+	0.905270i
$549$	9.78417	−	12.4633i	0.417578	−	0.531921i
$550$	4.51469	−	7.56488i	0.192507	−	0.322568i
$551$	1.17349	+	0.677516i	0.0499924	+	0.0288631i
$552$	1.24004	−	4.95423i	0.0527796	−	0.210866i
$553$	−3.84640	+	20.8428i	−0.163566	+	0.886325i
$554$	−17.1902	+	9.59606i	−0.730344	+	0.407697i
$555$	−13.8214	+	0.829226i	−0.586687	+	0.0351987i
$556$	18.5667	+	19.6731i	0.787405	+	0.834323i
$557$	8.27911	−	30.8981i	0.350797	−	1.30919i	−0.534894	−	0.844919i	$-0.679649\pi$
$557$	8.27911	−	30.8981i	0.350797	−	1.30919i	0.885691	−	0.464274i	$-0.153685\pi$
$558$	−4.69064	−	12.1952i	−0.198571	−	0.516266i
$559$			11.8832i			0.502606i
$560$	23.6749	−	14.3548i	1.00045	−	0.606603i
$561$	−41.7173	−	8.53802i	−1.76131	−	0.360475i
$562$	30.5345	+	31.4306i	1.28802	+	1.32582i
$563$	3.89411	+	1.04342i	0.164117	+	0.0439750i	0.339942	−	0.940446i	$-0.389593\pi$
$563$	3.89411	+	1.04342i	0.164117	+	0.0439750i	−0.175825	+	0.984421i	$0.556259\pi$
$564$	16.6179	−	10.2940i	0.699739	−	0.433455i
$565$	−17.3791	+	4.65672i	−0.731145	+	0.195910i
$566$	−6.28506	−	11.2590i	−0.264181	−	0.473250i
$567$	−23.7728	+	1.36140i	−0.998364	+	0.0571735i
$568$	−4.36726	−	4.76364i	−0.183246	−	0.199878i
$569$	2.48807	−	4.30946i	0.104305	−	0.180662i	−0.809149	−	0.587604i	$-0.800071\pi$
$569$	2.48807	−	4.30946i	0.104305	−	0.180662i	0.913454	+	0.406942i	$0.133405\pi$
$570$	27.6278	+	25.2234i	1.15720	+	1.05649i
$571$	29.3271	+	7.85817i	1.22730	+	0.328854i	0.813528	−	0.581526i	$-0.197544\pi$
$571$	29.3271	+	7.85817i	1.22730	+	0.328854i	0.413773	+	0.910380i	$0.364211\pi$
$572$	−30.4985	+	16.4512i	−1.27520	+	0.687857i
$573$	12.8431	+	19.4529i	0.536527	+	0.812655i
$574$	−15.5784	+	31.5420i	−0.650232	+	1.31654i
$575$	1.92265			0.0801801
$576$	−20.3764	+	12.6808i	−0.849015	+	0.528368i
$577$	0.860428	+	1.49031i	0.0358201	+	0.0620422i	0.883380	−	0.468658i	$-0.155262\pi$
$577$	0.860428	+	1.49031i	0.0358201	+	0.0620422i	−0.847560	+	0.530700i	$0.821929\pi$
$578$	−49.3354	+	12.4576i	−2.05208	+	0.518168i
$579$	−21.1963	+	1.27168i	−0.880888	+	0.0528494i
$580$	−1.03378	−	0.637411i	−0.0429256	−	0.0264671i
$581$	14.1351	+	6.72874i	0.586421	+	0.279155i
$582$	−25.2923	+	8.02552i	−1.04840	+	0.332668i
$583$	9.38983	−	16.2637i	0.388887	−	0.673572i
$584$	9.15417	−	29.0585i	0.378802	−	1.20245i
$585$	4.81361	+	39.9720i	0.199018	+	1.65264i
$586$	0.625240	+	0.00904250i	0.0258284	+	0.000373542i
$587$	−15.5903	−	15.5903i	−0.643480	−	0.643480i	0.307930	−	0.951409i	$-0.400364\pi$
$587$	−15.5903	−	15.5903i	−0.643480	−	0.643480i	−0.951409	+	0.307930i	$0.900364\pi$
$588$	23.8141	−	4.57051i	0.982076	−	0.188485i
$589$	−12.7130	+	12.7130i	−0.523828	+	0.523828i
$590$	9.65450	+	9.93786i	0.397470	+	0.409135i
$591$	−6.03583	−	18.1091i	−0.248281	−	0.744911i
$592$	−11.9694	+	2.47562i	−0.491939	+	0.101747i
$593$	24.8897	+	14.3701i	1.02210	+	0.590109i	0.914711	−	0.404109i	$-0.132418\pi$
$593$	24.8897	+	14.3701i	1.02210	+	0.590109i	0.107387	+	0.994217i	$0.465752\pi$
$594$	−19.1597	+	15.7781i	−0.786133	+	0.647383i
$595$	21.6548	−	45.4903i	0.887762	−	1.86492i
$596$	−8.76385	+	2.07861i	−0.358981	+	0.0851431i
$597$	−5.10323	+	0.306172i	−0.208861	+	0.0125308i
$598$	−6.49412	−	3.87566i	−0.265564	−	0.158488i
$599$	−25.1110	+	14.4978i	−1.02601	+	0.592365i	−0.915838	−	0.401547i	$-0.868472\pi$
$599$	−25.1110	+	14.4978i	−1.02601	+	0.592365i	−0.110169	+	0.993913i	$0.535139\pi$
$600$	−6.49368	−	6.28235i	−0.265103	−	0.256476i
$601$		−	25.2326i		−	1.02926i	−0.857413	−	0.514629i	$-0.827930\pi$
$601$		−	25.2326i		−	1.02926i	0.857413	−	0.514629i	$-0.172070\pi$
$602$	−2.78118	−	8.20934i	−0.113352	−	0.334588i
$603$	21.9654	−	8.81524i	0.894501	−	0.358984i
$604$	−17.0158	+	9.17851i	−0.692365	+	0.373468i
$605$	0.276407	−	1.03157i	0.0112376	−	0.0419391i
$606$	36.7060	−	1.66989i	1.49108	−	0.0678348i
$607$	3.05575	+	1.76424i	0.124029	+	0.0716083i	0.560731	−	0.827998i	$-0.310520\pi$
$607$	3.05575	+	1.76424i	0.124029	+	0.0716083i	−0.436702	+	0.899606i	$0.643854\pi$
$608$	27.3316	+	18.5347i	1.10844	+	0.751682i
$609$	−0.654537	−	0.838450i	−0.0265232	−	0.0339757i
$610$	18.8002	+	5.33006i	0.761199	+	0.215808i
$611$	−7.49206	−	27.9608i	−0.303096	−	1.13117i
$612$	−18.3119	+	39.6480i	−0.740215	+	1.60268i
$613$	−2.28645	+	8.53316i	−0.0923489	+	0.344651i	−0.996604	−	0.0823414i	$-0.973760\pi$
$613$	−2.28645	+	8.53316i	−0.0923489	+	0.344651i	0.904255	+	0.426992i	$0.140427\pi$
$614$	−0.149969	+	10.3695i	−0.00605225	+	0.418481i
$615$	41.7387	+	8.54239i	1.68307	+	0.344463i
$616$	17.2191	−	18.5030i	0.693779	−	0.745507i
$617$	0.165107			0.00664695			0.00332347	−	0.999994i	$-0.498942\pi$
$617$	0.165107			0.00664695			0.00332347	+	0.999994i	$0.498942\pi$
$618$	8.18468	−	37.2409i	0.329236	−	1.49805i
$619$	16.3052	+	4.36898i	0.655363	+	0.175604i	0.571152	−	0.820844i	$-0.306496\pi$
$619$	16.3052	+	4.36898i	0.655363	+	0.175604i	0.0842106	+	0.996448i	$0.473163\pi$
$620$	11.7192	−	11.0602i	0.470655	−	0.444187i
$621$	−5.09982	−	1.82599i	−0.204649	−	0.0732743i
$622$	−37.2006	−	10.5468i	−1.49161	−	0.422886i
$623$	15.8324	+	2.92177i	0.634312	+	0.117058i
$624$	9.26972	+	34.3097i	0.371086	+	1.37349i
$625$	−15.4100	+	26.6910i	−0.616402	+	1.06764i
$626$	2.25110	+	8.91497i	0.0899721	+	0.356314i
$627$	30.5461	+	15.2741i	1.21990	+	0.609989i
$628$	2.51960	−	8.42115i	0.100543	−	0.336040i
$629$	−15.7272	+	15.7272i	−0.627083	+	0.627083i
$630$	−12.6806	−	26.4875i	−0.505207	−	1.05529i
$631$	46.9954			1.87086			0.935428	−	0.353517i	$-0.115014\pi$
$631$	46.9954			1.87086			0.935428	+	0.353517i	$0.115014\pi$
$632$	22.1198	−	4.90962i	0.879878	−	0.195294i
$633$	−27.6542	+	9.21722i	−1.09916	+	0.366352i
$634$	−32.0438	−	19.1236i	−1.27262	−	0.759496i
$635$	−11.2668	+	3.01894i	−0.447110	+	0.119803i
$636$	−14.0349	−	13.1906i	−0.556520	−	0.523041i
$637$	3.69849	−	35.7172i	0.146540	−	1.41517i
$638$	−1.06669	−	0.302417i	−0.0422306	−	0.0119728i
$639$	−5.48392	+	4.11247i	−0.216941	+	0.162687i
$640$	−24.0063	−	17.3139i	−0.948931	−	0.684392i
$641$	31.0249	−	17.9123i	1.22541	−	0.707491i	0.259345	−	0.965785i	$-0.416493\pi$
$641$	31.0249	−	17.9123i	1.22541	−	0.707491i	0.966067	+	0.258293i	$0.0831601\pi$
$642$	20.9103	−	13.3751i	0.825262	−	0.527874i
$643$	−7.82538	−	7.82538i	−0.308603	−	0.308603i	0.535765	−	0.844367i	$-0.320023\pi$
$643$	−7.82538	−	7.82538i	−0.308603	−	0.308603i	−0.844367	+	0.535765i	$0.820023\pi$
$644$	5.39344	+	1.15754i	0.212531	+	0.0456136i
$645$	−8.75999	+	5.78347i	−0.344924	+	0.227724i
$646$	60.0862	+	0.868994i	2.36406	+	0.0341901i
$647$	−21.1311	+	12.2001i	−0.830751	+	0.479634i	−0.854110	−	0.520093i	$-0.825897\pi$
$647$	−21.1311	+	12.2001i	−0.830751	+	0.479634i	0.0233589	+	0.999727i	$0.492564\pi$
$648$	11.2579	+	22.8311i	0.442254	+	0.896890i
$649$	10.9541	+	6.32435i	0.429986	+	0.248253i
$650$	−11.6827	+	6.52158i	−0.458232	+	0.255797i
$651$	12.9934	−	5.50932i	0.509250	−	0.215927i
$652$	−6.92667	−	29.2043i	−0.271269	−	1.14373i
$653$	−11.8286	+	3.16947i	−0.462890	+	0.124031i	−0.482724	−	0.875772i	$-0.660353\pi$
$653$	−11.8286	+	3.16947i	−0.462890	+	0.124031i	0.0198345	+	0.999803i	$0.493686\pi$
$654$	−1.29080	+	0.0587232i	−0.0504742	+	0.00229626i
$655$	−10.0307	+	5.79121i	−0.391931	+	0.226281i
$656$	37.5454	+	2.17427i	1.46590	+	0.0848909i
$657$	−29.7161	−	12.6954i	−1.15934	−	0.495294i
$658$	11.7198	+	17.5628i	0.456886	+	0.684670i
$659$	13.5753	−	13.5753i	0.528820	−	0.528820i	−0.391400	−	0.920220i	$-0.628009\pi$
$659$	13.5753	−	13.5753i	0.528820	−	0.528820i	0.920220	+	0.391400i	$0.128009\pi$
$660$	−26.9708	−	14.4760i	−1.04984	−	0.563478i
$661$	−5.69167	+	21.2416i	−0.221380	+	0.826203i	0.762442	+	0.647057i	$0.224000\pi$
$661$	−5.69167	+	21.2416i	−0.221380	+	0.826203i	−0.983822	+	0.179146i	$0.942666\pi$
$662$	6.56240	−	10.9961i	0.255055	−	0.427374i
$663$	48.3863	+	42.9090i	1.87917	+	1.66645i
$664$	0.725843	−	16.7200i	0.0281682	−	0.648863i
$665$	−26.2189	+	30.7463i	−1.01673	+	1.19229i
$666$	1.36371	+	12.8922i	0.0528429	+	0.499564i
$667$	−0.0626273	−	0.233728i	−0.00242494	−	0.00905000i
$668$	−21.2448	−	0.614633i	−0.821988	−	0.0237809i
$669$	11.5083	+	5.75454i	0.444936	+	0.222483i
$670$	20.3394	+	20.9364i	0.785780	+	0.808842i
$671$	17.8394			0.688682
$672$	−14.4338	−	21.5329i	−0.556797	−	0.830649i
$673$	−4.23796			−0.163361			−0.0816806	−	0.996659i	$-0.526029\pi$
$673$	−4.23796			−0.163361			−0.0816806	+	0.996659i	$0.526029\pi$
$674$	−11.9563	−	12.3073i	−0.460541	−	0.474058i
$675$	−7.30889	+	6.19842i	−0.281319	+	0.238577i
$676$	26.6174	+	0.770067i	1.02375	+	0.0296180i
$677$	7.71305	+	28.7855i	0.296436	+	1.10632i	0.940070	+	0.340982i	$0.110759\pi$
$677$	7.71305	+	28.7855i	0.296436	+	1.10632i	−0.643633	+	0.765334i	$0.722574\pi$
$678$	5.09504	+	16.0569i	0.195674	+	0.616663i
$679$	−9.58805	−	27.0098i	−0.367956	−	1.03654i
$680$	−53.8095	−	2.33595i	−2.06350	−	0.0895797i
$681$	−6.50045	+	7.33022i	−0.249098	+	0.280895i
$682$	7.53888	−	12.6323i	0.288679	−	0.483714i
$683$	9.96595	−	37.1934i	0.381336	−	1.42317i	−0.462525	−	0.886606i	$-0.653057\pi$
$683$	9.96595	−	37.1934i	0.381336	−	1.42317i	0.843862	−	0.536561i	$-0.180277\pi$
$684$	22.4164	−	26.9142i	0.857113	−	1.02909i
$685$	−41.2883	+	41.2883i	−1.57754	+	1.57754i
$686$	5.80433	+	25.5404i	0.221610	+	0.975135i
$687$	−0.650384	+	3.17782i	−0.0248137	+	0.121242i
$688$	−6.91997	+	6.16237i	−0.263821	+	0.234938i
$689$	−24.7005	+	14.2608i	−0.941013	+	0.543294i
$690$	−0.303605	−	6.67356i	−0.0115580	−	0.254058i
$691$	42.0172	−	11.2585i	1.59841	−	0.428293i	0.653849	−	0.756625i	$-0.273153\pi$
$691$	42.0172	−	11.2585i	1.59841	−	0.428293i	0.944562	+	0.328333i	$0.106487\pi$
$692$	−0.604282	−	2.54778i	−0.0229714	−	0.0968522i
$693$	−17.7328	−	20.1063i	−0.673615	−	0.763775i
$694$	2.43136	−	1.35725i	0.0922933	−	0.0515206i
$695$	30.6442	+	17.6924i	1.16240	+	0.671112i
$696$	−0.552197	+	0.994046i	−0.0209310	+	0.0376792i
$697$	59.2669	−	34.2178i	2.24489	−	1.29609i
$698$	−35.6538	−	0.515641i	−1.34952	−	0.0195173i
$699$	5.42385	+	8.21528i	0.205149	+	0.310731i
$700$	6.54447	−	7.23959i	0.247358	−	0.273631i
$701$	32.7611	+	32.7611i	1.23737	+	1.23737i	0.961073	+	0.276295i	$0.0891068\pi$
$701$	32.7611	+	32.7611i	1.23737	+	1.23737i	0.276295	+	0.961073i	$0.410893\pi$
$702$	37.1819	−	6.20314i	1.40334	−	0.234123i
$703$	15.4485	−	8.91920i	0.582651	−	0.336394i
$704$	−25.3959	−	9.22903i	−0.957143	−	0.347832i
$705$	16.9656	−	19.1313i	0.638962	−	0.720525i
$706$	−29.3895	−	8.33223i	−1.10609	−	0.313588i
$707$	3.14432	+	39.5633i	0.118254	+	1.48793i
$708$	8.88430	−	9.45295i	0.333892	−	0.355264i
$709$	15.1528	−	4.06017i	0.569074	−	0.152483i	0.0372022	−	0.999308i	$-0.488155\pi$
$709$	15.1528	−	4.06017i	0.569074	−	0.152483i	0.531872	+	0.846825i	$0.321489\pi$
$710$	−7.25915	−	4.33223i	−0.272431	−	0.162586i
$711$	−2.87335	−	23.8602i	−0.107759	−	0.894826i
$712$	−3.72940	−	16.8024i	−0.139765	−	0.629698i
$713$	3.21055			0.120236
$714$	−43.4696	−	18.3186i	−1.62681	−	0.685556i
$715$	−32.0520	+	32.0520i	−1.19868	+	1.19868i
$716$	6.23482	−	20.8383i	0.233006	−	0.778765i
$717$	−10.9446	+	21.8878i	−0.408735	+	0.817414i
$718$	0.586296	+	2.32189i	0.0218804	+	0.0866521i
$719$	−10.0861	+	17.4697i	−0.376149	+	0.651508i	−0.990498	−	0.137525i	$-0.956085\pi$
$719$	−10.0861	+	17.4697i	−0.376149	+	0.651508i	0.614350	+	0.789034i	$0.289418\pi$
$720$	−20.7807	+	23.5317i	−0.774453	+	0.876975i
$721$	40.5009	+	7.47419i	1.50833	+	0.278353i
$722$	−20.5173	−	5.81686i	−0.763574	−	0.216481i
$723$	36.6379	−	2.19811i	1.36258	−	0.0817486i
$724$	11.8038	−	11.1400i	0.438686	−	0.414017i
$725$	−0.413504	−	0.110798i	−0.0153572	−	0.00411494i
$726$	−0.976609	−	0.214636i	−0.0362454	−	0.00796588i
$727$	−17.7130			−0.656938			−0.328469	−	0.944515i	$-0.606533\pi$
$727$	−17.7130			−0.656938			−0.328469	+	0.944515i	$0.606533\pi$
$728$	−36.6987	+	11.2608i	−1.36014	+	0.417352i
$729$	25.2736	−	9.49985i	0.936058	−	0.351846i
$730$	0.576304	−	39.8483i	0.0213300	−	1.47485i
$731$	−4.36406	+	16.2869i	−0.161411	+	0.602393i
$732$	4.18535	−	17.8111i	0.154695	−	0.658317i
$733$	4.49895	+	16.7903i	0.166173	+	0.620164i	0.997888	+	0.0649619i	$0.0206926\pi$
$733$	4.49895	+	16.7903i	0.166173	+	0.620164i	−0.831715	+	0.555203i	$0.812641\pi$
$734$	39.7009	+	11.2556i	1.46539	+	0.415452i
$735$	28.1299	−	14.6569i	1.03759	−	0.540628i
$736$	−1.11079	−	5.79157i	−0.0409441	−	0.213480i
$737$	23.0773	+	13.3237i	0.850063	+	0.490784i
$738$	6.21386	−	39.4027i	0.228735	−	1.45043i
$739$	1.35659	−	5.06287i	0.0499031	−	0.186241i	−0.936475	−	0.350734i	$-0.885932\pi$
$739$	1.35659	−	5.06287i	0.0499031	−	0.186241i	0.986378	+	0.164493i	$0.0525988\pi$
$740$	−14.0717	+	7.59040i	−0.517285	+	0.279029i
$741$	−28.5779	−	43.2857i	−1.04983	−	1.59014i
$742$	13.7263	−	15.6329i	0.503909	−	0.573901i
$743$		−	47.2591i		−	1.73377i	−0.498511	−	0.866883i	$-0.666120\pi$
$743$		−	47.2591i		−	1.73377i	0.498511	−	0.866883i	$-0.333880\pi$
$744$	−10.8435	−	10.4906i	−0.397542	−	0.384605i
$745$	−10.2034	+	5.89094i	−0.373824	+	0.215827i
$746$	−12.5436	−	7.48596i	−0.459253	−	0.274080i
$747$	−17.5724	−	2.51133i	−0.642942	−	0.0918848i
$748$	−47.8423	+	11.3472i	−1.74929	+	0.414895i
$749$	15.2028	+	22.0838i	0.555499	+	0.806926i
$750$	17.9546	+	9.30488i	0.655610	+	0.339766i
$751$	−36.2802	−	20.9464i	−1.32388	−	0.764343i	−0.339536	−	0.940593i	$-0.610270\pi$
$751$	−36.2802	−	20.9464i	−1.32388	−	0.764343i	−0.984346	+	0.176250i	$0.943603\pi$
$752$	12.3972	−	18.8627i	0.452081	−	0.687852i
$753$	24.8620	−	8.28656i	0.906020	−	0.301979i
$754$	1.17334	+	1.20778i	0.0427307	+	0.0439848i
$755$	−17.8826	+	17.8826i	−0.650814	+	0.650814i
$756$	−24.2348	+	12.9875i	−0.881410	+	0.472352i
$757$	−14.1962	−	14.1962i	−0.515968	−	0.515968i	0.400381	−	0.916349i	$-0.368878\pi$
$757$	−14.1962	−	14.1962i	−0.515968	−	0.515968i	−0.916349	+	0.400381i	$0.868878\pi$
$758$	−30.2955	−	0.438148i	−1.10038	−	0.0159142i
$759$	−1.92841	−	5.78576i	−0.0699969	−	0.210010i
$760$	41.2013	+	12.9795i	1.49453	+	0.470814i
$761$	22.1520	−	38.3684i	0.803009	−	1.39085i	−0.114619	−	0.993410i	$-0.536565\pi$
$761$	22.1520	−	38.3684i	0.803009	−	1.39085i	0.917627	−	0.397442i	$-0.130102\pi$
$762$	3.30310	+	10.4097i	0.119659	+	0.377102i
$763$	−0.110573	−	1.39128i	−0.00400300	−	0.0503676i
$764$	22.9111	+	14.1265i	0.828895	+	0.511080i
$765$	−8.08212	+	56.5527i	−0.292210	+	2.04467i
$766$	−48.0776	+	12.1400i	−1.73712	+	0.438636i
$767$	−9.60512	−	16.6366i	−0.346821	−	0.600712i
$768$	−15.1726	+	23.1903i	−0.547494	+	0.836810i
$769$	1.96166			0.0707392			0.0353696	−	0.999374i	$-0.488739\pi$
$769$	1.96166			0.0707392			0.0353696	+	0.999374i	$0.488739\pi$
$770$	14.6411	−	29.6442i	0.527629	−	1.06830i
$771$	25.0130	−	16.5139i	0.900820	−	0.594735i
$772$	−21.5801	+	11.6405i	−0.776684	+	0.418950i
$773$	−50.0655	−	13.4150i	−1.80073	−	0.482505i	−0.806640	−	0.591043i	$-0.798716\pi$
$773$	−50.0655	−	13.4150i	−1.80073	−	0.482505i	−0.994092	+	0.108538i	$0.965383\pi$
$774$	5.78216	+	7.94732i	0.207836	+	0.285661i
$775$	2.84000	−	4.91902i	0.102016	−	0.176697i
$776$	−22.5850	+	20.7057i	−0.810756	+	0.743292i
$777$	−13.8674	+	1.94337i	−0.497489	+	0.0697179i
$778$	14.4833	+	25.9452i	0.519251	+	0.930180i
$779$	−53.0171	+	14.2059i	−1.89953	+	0.508978i
$780$	24.4813	+	39.5209i	0.876572	+	1.41508i
$781$	−7.45444	−	1.99741i	−0.266741	−	0.0714730i
$782$	−7.47741	−	7.69687i	−0.267392	−	0.275239i
$783$	0.991590	+	0.686606i	0.0354365	+	0.0245373i
$784$	22.7173	−	16.3684i	0.811331	−	0.584587i
$785$		−	11.4980i		−	0.410383i
$786$	5.84347	+	9.13550i	0.208430	+	0.325852i
$787$	10.5381	−	39.3287i	0.375642	−	1.40192i	−0.476762	−	0.879033i	$-0.658190\pi$
$787$	10.5381	−	39.3287i	0.375642	−	1.40192i	0.852404	−	0.522884i	$-0.175144\pi$
$788$	−15.1285	−	16.0299i	−0.538930	−	0.571043i
$789$	−1.79326	−	29.8899i	−0.0638418	−	1.06411i
$790$	25.8794	−	14.4466i	0.920749	−	0.513987i
$791$	−17.1473	+	6.08703i	−0.609688	+	0.216430i
$792$	−12.3921	+	25.8424i	−0.440334	+	0.918268i
$793$	−23.4638	−	13.5468i	−0.833222	−	0.481061i
$794$	18.3306	−	30.7151i	0.650530	−	1.09004i
$795$	−22.5343	−	11.2679i	−0.799208	−	0.399631i
$796$	−5.19563	+	2.80257i	−0.184154	+	0.0993345i
$797$	−36.7521	−	36.7521i	−1.30183	−	1.30183i	−0.927160	−	0.374666i	$-0.877758\pi$
$797$	−36.7521	−	36.7521i	−1.30183	−	1.30183i	−0.374666	−	0.927160i	$-0.622242\pi$
$798$	29.8733	+	23.2149i	1.05750	+	0.821798i
$799$		−	41.0740i		−	1.45309i
$800$	−9.85610	−	3.42125i	−0.348466	−	0.120959i
$801$	−18.1244	+	2.18263i	−0.640396	+	0.0771194i
$802$	−0.750501	−	2.97218i	−0.0265011	−	0.104951i
$803$	−9.41630	−	35.1421i	−0.332294	−	1.24014i
$804$	18.7168	−	19.9148i	0.660090	−	0.702341i
$805$	7.19304	−	0.571672i	0.253521	−	0.0201488i
$806$	−19.5084	+	10.8901i	−0.687153	+	0.383587i
$807$	−29.2257	−	25.9173i	−1.02879	−	0.912333i
$808$	37.6295	−	19.6006i	1.32380	−	0.689546i
$809$	15.1841	+	26.2996i	0.533843	+	0.924643i	0.999218	+	0.0395298i	$0.0125860\pi$
$809$	15.1841	+	26.2996i	0.533843	+	0.924643i	−0.465375	+	0.885113i	$0.654081\pi$
$810$	22.6690	+	24.3905i	0.796506	+	0.856995i
$811$	14.9312	−	14.9312i	0.524304	−	0.524304i	−0.394564	−	0.918868i	$-0.629104\pi$
$811$	14.9312	−	14.9312i	0.524304	−	0.524304i	0.918868	+	0.394564i	$0.129104\pi$
$812$	−1.09326	−	0.559765i	−0.0383659	−	0.0196439i
$813$	1.66387	−	1.09851i	0.0583544	−	0.0385264i
$814$	−10.4690	+	10.1705i	−0.366940	+	0.356478i
$815$	−19.6307	−	34.0014i	−0.687634	−	1.19102i
$816$	0.104793	+	50.4286i	0.00366848	+	1.76536i
$817$	6.76169	−	11.7116i	0.236562	−	0.409737i
$818$	31.5445	+	8.94320i	1.10293	+	0.312692i
$819$	8.05538	+	39.9113i	0.281478	+	1.39461i
$820$	47.8668	−	11.3530i	1.67158	−	0.396465i
$821$	−2.08650	−	7.78694i	−0.0728195	−	0.271766i	0.919911	−	0.392128i	$-0.128261\pi$
$821$	−2.08650	−	7.78694i	−0.0728195	−	0.271766i	−0.992730	+	0.120362i	$0.961594\pi$
$822$	40.3748	+	36.8610i	1.40823	+	1.28568i
$823$	23.1086	+	40.0253i	0.805515	+	1.39519i	0.915943	+	0.401309i	$0.131445\pi$
$823$	23.1086	+	40.0253i	0.805515	+	1.39519i	−0.110428	+	0.993884i	$0.535222\pi$
$824$	−9.54019	−	42.9824i	−0.332348	−	1.49736i
$825$	−10.5705	−	2.16339i	−0.368016	−	0.0753195i
$826$	10.5292	+	9.24512i	0.366359	+	0.321679i
$827$	2.26431	+	2.26431i	0.0787379	+	0.0787379i	0.745379	−	0.666641i	$-0.232269\pi$
$827$	2.26431	+	2.26431i	0.0787379	+	0.0787379i	−0.666641	+	0.745379i	$0.732269\pi$
$828$	−6.22902	+	0.567937i	−0.216473	+	0.0197372i
$829$	−6.27079	−	1.68025i	−0.217794	−	0.0583576i	0.148272	−	0.988947i	$-0.452629\pi$
$829$	−6.27079	−	1.68025i	−0.217794	−	0.0583576i	−0.366066	+	0.930589i	$0.619296\pi$
$830$	−5.35963	−	21.2256i	−0.186035	−	0.736750i
$831$	18.0402	+	15.9980i	0.625806	+	0.554965i
$832$	26.3943	+	31.4238i	0.915059	+	1.08942i
$833$	18.1861	−	47.5952i	0.630112	−	1.64908i
$834$	15.2442	−	29.4150i	0.527863	−	1.01856i
$835$	−26.8543	+	7.19559i	−0.929332	+	0.249014i
$836$	39.4189	+	1.14043i	1.36333	+	0.0394425i
$837$	−12.2048	+	10.3505i	−0.421859	+	0.357764i
$838$	−16.0995	−	0.232839i	−0.556149	−	0.00804328i
$839$		−	5.18575i		−	0.179032i	−0.995985	−	0.0895160i	$-0.971468\pi$
$839$		−	5.18575i		−	0.179032i	0.995985	−	0.0895160i	$-0.0285320\pi$
$840$	−26.1622	−	21.5728i	−0.902681	−	0.744332i
$841$		−	28.9461i		−	0.998142i
$842$	0.0252623	−	1.74675i	0.000870596	−	0.0601970i
$843$	24.0028	−	48.0023i	0.826701	−	1.65329i
$844$	−24.4791	+	23.1025i	−0.842604	+	0.795220i
$845$	33.6455	−	9.01528i	1.15744	−	0.310135i
$846$	−18.6158	−	15.0543i	−0.640025	−	0.517576i
$847$	0.196004	−	1.06210i	0.00673476	−	0.0364942i
$848$	−21.1137	−	6.98853i	−0.725047	−	0.239987i
$849$	−10.4781	+	11.8156i	−0.359608	+	0.405511i
$850$	−18.4071	+	4.64794i	−0.631358	+	0.159423i
$851$	−3.07693	−	0.824461i	−0.105476	−	0.0282621i
$852$	−3.74315	+	6.97400i	−0.128238	+	0.238925i
$853$	40.1345	+	40.1345i	1.37418	+	1.37418i	0.854147	+	0.520032i	$0.174080\pi$
$853$	40.1345	+	40.1345i	1.37418	+	1.37418i	0.520032	+	0.854147i	$0.325920\pi$
$854$	19.3801	+	3.86709i	0.663175	+	0.132329i
$855$	18.0005	−	42.1337i	0.615603	−	1.44094i
$856$	15.3941	−	24.1771i	0.526158	−	0.826357i
$857$	11.6264	+	20.1374i	0.397149	+	0.687882i	0.993373	−	0.114936i	$-0.0366664\pi$
$857$	11.6264	+	20.1374i	0.397149	+	0.687882i	−0.596224	+	0.802818i	$0.703333\pi$
$858$	31.3428	+	28.6151i	1.07003	+	0.976903i
$859$	−7.81139	−	29.1525i	−0.266521	−	0.994671i	−0.961313	−	0.275459i	$-0.911170\pi$
$859$	−7.81139	−	29.1525i	−0.266521	−	0.994671i	0.694791	−	0.719211i	$-0.255497\pi$
$860$	−6.36144	+	10.3173i	−0.216923	+	0.351817i
$861$	42.7625	+	5.26766i	1.45734	+	0.179522i
$862$	−8.08902	+	28.5317i	−0.275513	+	0.971792i
$863$	−7.03655	+	12.1877i	−0.239527	+	0.414873i	−0.960579	−	0.278009i	$-0.910326\pi$
$863$	−7.03655	+	12.1877i	−0.239527	+	0.414873i	0.721052	+	0.692881i	$0.243659\pi$
$864$	22.8940	+	18.4354i	0.778870	+	0.627185i
$865$	−1.71258	−	2.96628i	−0.0582296	−	0.100857i
$866$	16.2584	+	16.7356i	0.552482	+	0.568697i
$867$	34.3362	+	52.0076i	1.16612	+	1.76627i
$868$	10.9283	−	12.0891i	0.370932	−	0.410330i
$869$	19.1325	−	19.1325i	0.649027	−	0.649027i
$870$	−0.319286	+	1.45278i	−0.0108248	+	0.0492538i
$871$	−20.2354	−	35.0487i	−0.685650	−	1.18758i
$872$	−1.32327	+	0.689271i	−0.0448117	+	0.0233417i
$873$	19.4978	+	26.0000i	0.659899	+	0.879966i
$874$	4.19504	+	7.51493i	0.141899	+	0.254196i
$875$	−9.38839	+	19.7222i	−0.317386	+	0.666732i
$876$	−37.2956	+	1.15657i	−1.26010	+	0.0390768i
$877$	3.45489	+	12.8938i	0.116663	+	0.435393i	0.999406	−	0.0344635i	$-0.0109723\pi$
$877$	3.45489	+	12.8938i	0.116663	+	0.435393i	−0.882743	+	0.469857i	$0.844306\pi$
$878$	7.06610	−	1.78425i	0.238469	−	0.0602154i
$879$	−0.242160	−	0.726546i	−0.00816785	−	0.0245058i
$880$	−35.2864	−	2.04345i	−1.18950	−	0.0688845i
$881$			8.31543i			0.280154i	0.990141	+	0.140077i	$0.0447350\pi$
$881$			8.31543i			0.280154i	−0.990141	+	0.140077i	$0.955265\pi$
$882$	−14.9059	−	25.6868i	−0.501908	−	0.864921i
$883$	−15.0386	−	15.0386i	−0.506088	−	0.506088i	0.407235	−	0.913323i	$-0.366493\pi$
$883$	−15.0386	−	15.0386i	−0.506088	−	0.506088i	−0.913323	+	0.407235i	$0.866493\pi$
$884$	71.5427	+	21.4056i	2.40624	+	0.719947i
$885$	7.58930	−	15.1776i	0.255111	−	0.510188i
$886$	−11.6501	−	6.95272i	−0.391392	−	0.233581i
$887$	3.51087	+	2.02700i	0.117884	+	0.0680601i	0.557782	−	0.829987i	$-0.311652\pi$
$887$	3.51087	+	2.02700i	0.117884	+	0.0680601i	−0.439899	+	0.898047i	$0.644986\pi$
$888$	7.69824	+	12.8386i	0.258336	+	0.430835i
$889$	−11.1165	+	3.94620i	−0.372837	+	0.132351i
$890$	−10.9738	−	19.6583i	−0.367842	−	0.658948i
$891$	25.9835	+	15.7774i	0.870478	+	0.528562i
$892$	14.8511	+	0.429657i	0.497253	+	0.0143860i
$893$	−8.52616	+	31.8201i	−0.285317	+	1.06482i
$894$	5.94410	+	9.29281i	0.198800	+	0.310798i
$895$		−	28.4522i		−	0.951051i
$896$	−25.5887	−	15.5312i	−0.854858	−	0.518863i
$897$	−1.85717	+	9.07428i	−0.0620092	+	0.302981i
$898$	0.711273	−	0.690993i	0.0237355	−	0.0230587i
$899$	−0.690493	−	0.185017i	−0.0230292	−	0.00617066i
$900$	−4.63992	+	10.0461i	−0.154664	+	0.334871i
$901$	−39.0913	+	10.4745i	−1.30232	+	0.348956i
$902$	39.2143	−	21.8905i	1.30569	−	0.728873i
$903$	−8.36783	+	6.53236i	−0.278464	+	0.217383i
$904$	13.1451	+	14.3382i	0.437201	+	0.476883i
$905$	10.6155	−	18.3865i	0.352870	−	0.611188i
$906$	17.4869	+	15.9651i	0.580964	+	0.530404i
$907$	−48.9410	−	13.1137i	−1.62506	−	0.435433i	−0.672577	−	0.740027i	$-0.734813\pi$
$907$	−48.9410	−	13.1137i	−1.62506	−	0.435433i	−0.952482	+	0.304594i	$0.901479\pi$
$908$	−3.24281	+	10.8383i	−0.107616	+	0.359681i
$909$	−16.7610	−	41.7642i	−0.555927	−	1.38523i
$910$	−41.7682	+	27.8722i	−1.38460	+	0.923956i
$911$	45.2661			1.49973			0.749866	−	0.661590i	$-0.230118\pi$
$911$	45.2661			1.49973			0.749866	+	0.661590i	$0.230118\pi$
$912$	10.3868	−	39.0889i	0.343942	−	1.29436i
$913$	−9.99263	−	17.3077i	−0.330708	−	0.572803i
$914$	0.143922	+	0.569971i	0.00476053	+	0.0188530i
$915$	−1.43330	−	23.8900i	−0.0473833	−	0.789780i
$916$	0.864376	+	3.64439i	0.0285598	+	0.120414i
$917$	−9.64822	+	6.64197i	−0.318612	+	0.219337i
$918$	53.2390	+	5.15300i	1.75715	+	0.170074i
$919$	−24.2461	+	41.9954i	−0.799804	+	1.38530i	0.119940	+	0.992781i	$0.461730\pi$
$919$	−24.2461	+	41.9954i	−0.799804	+	1.38530i	−0.919744	+	0.392519i	$0.871604\pi$
$920$	−3.56360	−	6.84145i	−0.117488	−	0.225556i
$921$	12.0497	−	4.01620i	0.397051	−	0.132338i
$922$	0.381940	−	26.4091i	0.0125785	−	0.869736i
$923$	8.28788	+	8.28788i	0.272799	+	0.272799i
$924$	−28.3499	−	12.4328i	−0.932643	−	0.409008i
$925$	−3.98499	+	3.98499i	−0.131026	+	0.131026i
$926$	−24.6247	+	23.9226i	−0.809217	+	0.786144i
$927$	−46.3642	+	5.58340i	−1.52280	+	0.183383i
$928$	−0.0948592	+	1.30961i	−0.00311391	+	0.0429899i
$929$	−27.0597	−	15.6230i	−0.887801	−	0.512572i	−0.0145787	−	0.999894i	$-0.504641\pi$
$929$	−27.0597	−	15.6230i	−0.887801	−	0.512572i	−0.873223	+	0.487321i	$0.837974\pi$
$930$	−17.5225	−	9.08093i	−0.574585	−	0.297775i
$931$	−23.9686	+	33.0970i	−0.785541	+	1.08471i
$932$	9.67576	+	5.96588i	0.316940	+	0.195419i
$933$	2.83611	+	47.2719i	0.0928500	+	1.54761i
$934$	11.7851	−	19.7472i	0.385619	−	0.646148i
$935$	−55.7009	+	32.1589i	−1.82161	+	1.05171i
$936$	35.9231	−	24.5796i	1.17418	−	0.803410i
$937$			27.8911i			0.911163i	0.890194	+	0.455581i	$0.150569\pi$
$937$			27.8911i			0.911163i	−0.890194	+	0.455581i	$0.849431\pi$
$938$	22.1822	+	19.4770i	0.724276	+	0.635945i
$939$	9.39783	−	6.20459i	0.306687	−	0.202479i
$940$	8.46345	−	28.2870i	0.276047	−	0.922619i
$941$	−5.07558	+	18.9423i	−0.165459	+	0.617503i	0.832522	+	0.553992i	$0.186896\pi$
$941$	−5.07558	+	18.9423i	−0.165459	+	0.617503i	−0.997981	+	0.0635104i	$0.979770\pi$
$942$	−10.7544	+	0.489257i	−0.350397	+	0.0159408i
$943$	8.48830	+	4.90072i	0.276417	+	0.159589i
$944$	4.70700	−	14.2207i	0.153200	−	0.462846i
$945$	−25.5011	+	25.3628i	−0.829550	+	0.825051i
$946$	−3.01816	+	10.6457i	−0.0981288	+	0.346121i
$947$	10.5144	+	39.2403i	0.341672	+	1.27514i	0.896452	+	0.443140i	$0.146136\pi$
$947$	10.5144	+	39.2403i	0.341672	+	1.27514i	−0.554780	+	0.831997i	$0.687198\pi$
$948$	−14.6134	−	23.5909i	−0.474623	−	0.766198i
$949$	−14.3010	+	53.3721i	−0.464231	+	1.73253i
$950$	15.2248	+	0.220188i	0.493958	+	0.00714385i
$951$	−9.16381	+	44.7750i	−0.297157	+	1.45193i
$952$	−54.4341	+	1.95637i	−1.76422	+	0.0634063i
$953$	−22.3127			−0.722778			−0.361389	−	0.932415i	$-0.617697\pi$
$953$	−22.3127			−0.722778			−0.361389	+	0.932415i	$0.617697\pi$
$954$	−9.58027	+	21.5563i	−0.310173	+	0.697911i
$955$	34.0088	+	9.11263i	1.10050	+	0.294878i
$956$	−0.817171	+	28.2456i	−0.0264292	+	0.913527i
$957$	0.0813224	+	1.35547i	0.00262878	+	0.0438162i
$958$	−1.70327	+	6.00777i	−0.0550300	+	0.194102i
$959$	−38.3159	+	44.9321i	−1.23728	+	1.45093i
$960$	−10.3188	+	34.7510i	−0.333039	+	1.12158i
$961$	−10.7576	+	18.6327i	−0.347020	+	0.601056i
$962$	21.4930	−	5.42716i	0.692962	−	0.174979i
$963$	−23.9124	−	18.7722i	−0.770568	−	0.604925i
$964$	37.3012	−	20.1206i	1.20139	−	0.648042i
$965$	−22.6793	+	22.6793i	−0.730072	+	0.730072i
$966$	−0.840771	−	6.70349i	−0.0270514	−	0.215681i
$967$	0.0670260			0.00215541			0.00107771	−	0.999999i	$-0.499657\pi$
$967$	0.0670260			0.00215541			0.00107771	+	0.999999i	$0.499657\pi$
$968$	−1.12717	+	0.250183i	−0.0362287	+	0.00804118i
$969$	−23.2718	−	69.8218i	−0.747598	−	2.24300i
$970$	−20.5397	+	34.4166i	−0.659489	+	1.10505i
$971$	−11.5620	+	3.09803i	−0.371043	+	0.0994206i	−0.439522	−	0.898232i	$-0.644852\pi$
$971$	−11.5620	+	3.09803i	−0.371043	+	0.0994206i	0.0684790	+	0.997653i	$0.478185\pi$
$972$	21.8484	−	22.2407i	0.700788	−	0.713370i
$973$	32.3109	+	15.3810i	1.03584	+	0.493092i
$974$	−15.6898	+	55.3413i	−0.502735	+	1.77325i
$975$	12.2603	+	10.8724i	0.392643	+	0.348196i
$976$	−4.27905	−	20.6888i	−0.136969	−	0.662232i
$977$	−25.5256	+	14.7372i	−0.816637	+	0.471485i	−0.849255	−	0.527982i	$-0.822949\pi$
$977$	−25.5256	+	14.7372i	−0.816637	+	0.471485i	0.0326185	+	0.999468i	$0.489615\pi$
$978$	−30.9670	+	19.8079i	−0.990215	+	0.633386i
$979$	−14.5333	−	14.5333i	−0.464486	−	0.464486i
$980$	22.3317	−	29.0307i	0.713359	−	0.927352i
$981$	0.589414	+	1.46867i	0.0188185	+	0.0468912i
$982$	0.267700	−	18.5100i	0.00854266	−	0.590679i
$983$	17.5590	−	10.1377i	0.560045	−	0.323342i	−0.193119	−	0.981175i	$-0.561860\pi$
$983$	17.5590	−	10.1377i	0.560045	−	0.323342i	0.753164	+	0.657833i	$0.228527\pi$
$984$	−12.6556	−	44.2879i	−0.403444	−	1.41185i
$985$	−24.9694	−	14.4161i	−0.795591	−	0.459334i
$986$	1.16461	+	2.08627i	0.0370888	+	0.0664404i
$987$	15.5707	−	20.6461i	0.495621	−	0.657174i
$988$	−50.9809	−	31.4338i	−1.62192	−	1.00004i
$989$	−2.33264	+	0.625028i	−0.0741735	+	0.0198747i
$990$	−5.83998	+	37.0319i	−0.185607	+	1.17695i
$991$	−22.1478	+	12.7871i	−0.703549	+	0.406194i	−0.808668	−	0.588265i	$-0.799811\pi$
$991$	−22.1478	+	12.7871i	−0.703549	+	0.406194i	0.105119	+	0.994460i	$0.466478\pi$
$992$	−16.4583	−	5.71299i	−0.522551	−	0.181388i
$993$	−15.3649	−	3.14462i	−0.487589	−	0.0997916i
$994$	−7.66528	−	3.78584i	−0.243128	−	0.120080i
$995$	−5.46028	+	5.46028i	−0.173102	+	0.173102i
$996$	−19.6247	+	5.91616i	−0.621832	+	0.187461i
$997$	1.96242	−	7.32386i	0.0621506	−	0.231949i	−0.927863	−	0.372921i	$-0.878356\pi$
$997$	1.96242	−	7.32386i	0.0621506	−	0.231949i	0.990014	+	0.140972i	$0.0450228\pi$
$998$	30.8500	+	18.4112i	0.976540	+	0.582795i
$999$	14.3548	−	6.78553i	0.454166	−	0.214685i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.bu.a.107.15	yes	240
3.2	odd	2	inner	336.2.bu.a.107.46	yes	240
7.4	even	3	inner	336.2.bu.a.11.56	yes	240
16.3	odd	4	inner	336.2.bu.a.275.5	yes	240
21.11	odd	6	inner	336.2.bu.a.11.5	✓	240
48.35	even	4	inner	336.2.bu.a.275.56	yes	240
112.67	odd	12	inner	336.2.bu.a.179.46	yes	240
336.179	even	12	inner	336.2.bu.a.179.15	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.bu.a.11.5	✓	240	21.11	odd	6	inner
336.2.bu.a.11.56	yes	240	7.4	even	3	inner
336.2.bu.a.107.15	yes	240	1.1	even	1	trivial
336.2.bu.a.107.46	yes	240	3.2	odd	2	inner
336.2.bu.a.179.15	yes	240	336.179	even	12	inner
336.2.bu.a.179.46	yes	240	112.67	odd	12	inner
336.2.bu.a.275.5	yes	240	16.3	odd	4	inner
336.2.bu.a.275.56	yes	240	48.35	even	4	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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.bu (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.985435 - 1.01436i) q^{2} +(-0.774639 + 1.54917i) q^{3} +(-0.0578377 + 1.99916i) q^{4} +(0.677113 + 2.52702i) q^{5} +(2.33477 - 0.740848i) q^{6} +(0.885088 + 2.49331i) q^{7} +(2.08486 - 1.91138i) q^{8} +(-1.79987 - 2.40010i) q^{9} +O(q^{10})\)	\(q+(-0.985435 - 1.01436i) q^{2} +(-0.774639 + 1.54917i) q^{3} +(-0.0578377 + 1.99916i) q^{4} +(0.677113 + 2.52702i) q^{5} +(2.33477 - 0.740848i) q^{6} +(0.885088 + 2.49331i) q^{7} +(2.08486 - 1.91138i) q^{8} +(-1.79987 - 2.40010i) q^{9} +(1.89605 - 3.17705i) q^{10} +(0.874188 - 3.26252i) q^{11} +(-3.05225 - 1.63823i) q^{12} +(-3.62728 + 3.62728i) q^{13} +(1.65691 - 3.35479i) q^{14} +(-4.43931 - 0.908564i) q^{15} +(-3.99331 - 0.231254i) q^{16} +(-6.30359 + 3.63938i) q^{17} +(-0.660903 + 4.19085i) q^{18} +(5.63886 - 1.51093i) q^{19} +(-5.09109 + 1.20750i) q^{20} +(-4.54820 - 0.560266i) q^{21} +(-4.17081 + 2.32826i) q^{22} +(-0.902810 - 0.521238i) q^{23} +(1.34604 + 4.71043i) q^{24} +(-1.59722 + 0.922157i) q^{25} +(7.25380 + 0.104908i) q^{26} +(5.11241 - 0.929096i) q^{27} +(-5.03574 + 1.62523i) q^{28} +(0.164130 + 0.164130i) q^{29} +(3.45304 + 5.39837i) q^{30} +(-2.66713 + 1.53987i) q^{31} +(3.70057 + 4.27852i) q^{32} +(4.37702 + 3.88154i) q^{33} +(9.90341 + 2.80772i) q^{34} +(-5.70135 + 3.92489i) q^{35} +(4.90229 - 3.45942i) q^{36} +(2.95156 - 0.790868i) q^{37} +(-7.08935 - 4.23090i) q^{38} +(-2.80945 - 8.42911i) q^{39} +(6.24177 + 3.97426i) q^{40} -9.40208 q^{41} +(3.91364 + 5.16560i) q^{42} +(1.63803 - 1.63803i) q^{43} +(6.47174 + 1.93634i) q^{44} +(4.84638 - 6.17344i) q^{45} +(0.360940 + 1.42942i) q^{46} +(-2.82149 + 4.88697i) q^{47} +(3.45163 - 6.00719i) q^{48} +(-5.43324 + 4.41361i) q^{49} +(2.50935 + 0.711428i) q^{50} +(-0.755018 - 12.5846i) q^{51} +(-7.04173 - 7.46131i) q^{52} +(5.37060 + 1.43905i) q^{53} +(-5.98038 - 4.27025i) q^{54} +8.83637 q^{55} +(6.61095 + 3.50647i) q^{56} +(-2.02740 + 9.90600i) q^{57} +(0.00474693 - 0.328225i) q^{58} +(-0.969245 + 3.61727i) q^{59} +(2.07313 - 8.82235i) q^{60} +(1.36700 + 5.10170i) q^{61} +(4.19026 + 1.18798i) q^{62} +(4.39116 - 6.61194i) q^{63} +(0.693278 - 7.96990i) q^{64} +(-11.6223 - 6.71013i) q^{65} +(-0.375999 - 8.26486i) q^{66} +(-2.04193 + 7.62060i) q^{67} +(-6.91113 - 12.8124i) q^{68} +(1.50684 - 0.994837i) q^{69} +(9.59955 + 1.91548i) q^{70} -2.28487i q^{71} +(-8.33997 - 1.56364i) q^{72} +(9.32837 - 5.38574i) q^{73} +(-3.71079 - 2.21458i) q^{74} +(-0.191309 - 3.18871i) q^{75} +(2.69446 + 11.3604i) q^{76} +(8.90821 - 0.707986i) q^{77} +(-5.78159 + 11.1561i) q^{78} +(6.93760 + 4.00542i) q^{79} +(-2.11954 - 10.2478i) q^{80} +(-2.52095 + 8.63972i) q^{81} +(9.26514 + 9.53706i) q^{82} +(4.18395 - 4.18395i) q^{83} +(1.38312 - 9.06019i) q^{84} +(-13.4650 - 13.4650i) q^{85} +(-3.27572 - 0.0473750i) q^{86} +(-0.381406 + 0.127124i) q^{87} +(-4.41334 - 8.47279i) q^{88} +(3.04256 - 5.26988i) q^{89} +(-11.0379 + 1.16756i) q^{90} +(-12.2544 - 5.83349i) q^{91} +(1.09426 - 1.77472i) q^{92} +(-0.319458 - 5.32469i) q^{93} +(7.73753 - 1.95379i) q^{94} +(7.63630 + 13.2265i) q^{95} +(-9.49478 + 2.41851i) q^{96} -10.8329 q^{97} +(9.83107 + 1.16192i) q^{98} +(-9.40378 + 3.77396i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 2 q^{3} - 4 q^{4} - 8 q^{6} - 16 q^{7}+O(q^{10}) \) 240 * q - 2 * q^3 - 4 * q^4 - 8 * q^6 - 16 * q^7	\( 240 q - 2 q^{3} - 4 q^{4} - 8 q^{6} - 16 q^{7} - 4 q^{10} - 2 q^{12} - 16 q^{13} - 20 q^{16} + 16 q^{18} - 4 q^{19} + 2 q^{21} - 40 q^{22} - 22 q^{24} - 8 q^{27} - 4 q^{28} - 26 q^{30} - 4 q^{33} + 16 q^{36} - 4 q^{37} - 4 q^{39} + 8 q^{40} - 18 q^{42} - 16 q^{43} + 18 q^{45} - 20 q^{46} - 88 q^{48} - 16 q^{49} + 6 q^{51} + 8 q^{52} + 14 q^{54} - 32 q^{55} - 36 q^{58} - 42 q^{60} - 4 q^{61} - 64 q^{64} - 30 q^{66} - 36 q^{67} - 20 q^{69} + 116 q^{70} - 46 q^{72} - 24 q^{75} - 112 q^{76} - 92 q^{78} - 4 q^{81} - 32 q^{82} + 44 q^{84} - 56 q^{85} - 4 q^{87} - 20 q^{88} + 28 q^{90} - 40 q^{91} - 14 q^{93} + 72 q^{94} + 36 q^{96} - 32 q^{97} + 28 q^{99}+O(q^{100}) \) 240 * q - 2 * q^3 - 4 * q^4 - 8 * q^6 - 16 * q^7 - 4 * q^10 - 2 * q^12 - 16 * q^13 - 20 * q^16 + 16 * q^18 - 4 * q^19 + 2 * q^21 - 40 * q^22 - 22 * q^24 - 8 * q^27 - 4 * q^28 - 26 * q^30 - 4 * q^33 + 16 * q^36 - 4 * q^37 - 4 * q^39 + 8 * q^40 - 18 * q^42 - 16 * q^43 + 18 * q^45 - 20 * q^46 - 88 * q^48 - 16 * q^49 + 6 * q^51 + 8 * q^52 + 14 * q^54 - 32 * q^55 - 36 * q^58 - 42 * q^60 - 4 * q^61 - 64 * q^64 - 30 * q^66 - 36 * q^67 - 20 * q^69 + 116 * q^70 - 46 * q^72 - 24 * q^75 - 112 * q^76 - 92 * q^78 - 4 * q^81 - 32 * q^82 + 44 * q^84 - 56 * q^85 - 4 * q^87 - 20 * q^88 + 28 * q^90 - 40 * q^91 - 14 * q^93 + 72 * q^94 + 36 * q^96 - 32 * q^97 + 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more