LMFDB - Embedded newform 13.9.f.a.2.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [13,9,Mod(2,13)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(13, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 9, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("13.2"); S:= CuspForms(chi, 9); N := Newforms(S);

Level:	$ N $	$=$	$ 13 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	13.f (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.29592193079$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			2.6
Character	$\chi$	$=$	13.2
Dual form			13.9.f.a.7.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(8.65394 + 2.31882i) q^{2} +(-30.7307 - 53.2271i) q^{3} +(-152.189 - 87.8662i) q^{4} +(-612.629 + 612.629i) q^{5} +(-142.518 - 531.883i) q^{6} +(-968.610 + 259.538i) q^{7} +(-2735.08 - 2735.08i) q^{8} +(1391.75 - 2410.58i) q^{9} +(-6722.23 + 3881.08i) q^{10} +(0.564567 - 2.10699i) q^{11} +10800.8i q^{12} +(-19265.9 - 21084.5i) q^{13} -8984.12 q^{14} +(51435.0 + 13782.0i) q^{15} +(5166.67 + 8948.93i) q^{16} +(93462.5 + 53960.6i) q^{17} +(17633.8 - 17633.8i) q^{18} +(-23450.7 - 87519.3i) q^{19} +(147065. - 39405.8i) q^{20} +(43580.5 + 43580.5i) q^{21} +(9.77146 - 16.9247i) q^{22} +(-387384. + 223656. i) q^{23} +(-61529.5 + 229631. i) q^{24} -360004. i q^{25} +(-117835. - 227138. i) q^{26} -574326. q^{27} +(170216. + 45609.3i) q^{28} +(-435075. - 753572. i) q^{29} +(413158. + 238537. i) q^{30} +(-67934.2 + 67934.2i) q^{31} +(280245. + 1.04589e6i) q^{32} +(-129.499 + 34.6991i) q^{33} +(683695. + 683695. i) q^{34} +(434398. - 752399. i) q^{35} +(-423617. + 244575. i) q^{36} +(358192. - 1.33679e6i) q^{37} -811765. i q^{38} +(-530214. + 1.67341e6i) q^{39} +3.35118e6 q^{40} +(2.47751e6 + 663846. i) q^{41} +(276088. + 478199. i) q^{42} +(-3.47455e6 - 2.00603e6i) q^{43} +(-271.054 + 271.054i) q^{44} +(624165. + 2.32942e6i) q^{45} +(-3.87102e6 + 1.03724e6i) q^{46} +(-1.42343e6 - 1.42343e6i) q^{47} +(317551. - 550014. i) q^{48} +(-4.12162e6 + 2.37962e6i) q^{49} +(834783. - 3.11545e6i) q^{50} -6.63299e6i q^{51} +(1.07943e6 + 4.90164e6i) q^{52} +3.19498e6 q^{53} +(-4.97018e6 - 1.33176e6i) q^{54} +(944.935 + 1636.67i) q^{55} +(3.35908e6 + 1.93937e6i) q^{56} +(-3.93775e6 + 3.93775e6i) q^{57} +(-2.01772e6 - 7.53023e6i) q^{58} +(3.40589e6 - 912605. i) q^{59} +(-6.61686e6 - 6.61686e6i) q^{60} +(-6.50874e6 + 1.12735e7i) q^{61} +(-745426. + 430372. i) q^{62} +(-722424. + 2.69612e6i) q^{63} +7.05556e6i q^{64} +(2.47198e7 + 1.11415e6i) q^{65} -1201.14 q^{66} +(3.56413e7 + 9.55007e6i) q^{67} +(-9.48263e6 - 1.64244e7i) q^{68} +(2.38092e7 + 1.37462e7i) q^{69} +(5.50393e6 - 5.50393e6i) q^{70} +(-5.07414e6 - 1.89369e7i) q^{71} +(-1.03997e7 + 2.78658e6i) q^{72} +(-1.21226e7 - 1.21226e7i) q^{73} +(6.19955e6 - 1.07379e7i) q^{74} +(-1.91620e7 + 1.10632e7i) q^{75} +(-4.12105e6 + 1.53800e7i) q^{76} +2187.38i q^{77} +(-8.46877e6 + 1.32521e7i) q^{78} -6.64644e7 q^{79} +(-8.64763e6 - 2.31713e6i) q^{80} +(8.51817e6 + 1.47539e7i) q^{81} +(1.99009e7 + 1.14898e7i) q^{82} +(4.60062e7 - 4.60062e7i) q^{83} +(-2.80321e6 - 1.04617e7i) q^{84} +(-9.03157e7 + 2.42000e7i) q^{85} +(-2.54169e7 - 2.54169e7i) q^{86} +(-2.67403e7 + 4.63156e7i) q^{87} +(-7306.93 + 4218.66i) q^{88} +(2.83718e7 - 1.05885e8i) q^{89} +2.16060e7i q^{90} +(2.41334e7 + 1.54224e7i) q^{91} +7.86073e7 q^{92} +(5.70361e6 + 1.52828e6i) q^{93} +(-9.01760e6 - 1.56189e7i) q^{94} +(6.79835e7 + 3.92503e7i) q^{95} +(4.70575e7 - 4.70575e7i) q^{96} +(3.59877e7 + 1.34308e8i) q^{97} +(-4.11862e7 + 1.10358e7i) q^{98} +(-4293.34 - 4293.34i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 172 q^{5} - 2726 q^{6} - 2784 q^{7} - 10470 q^{8} - 21872 q^{9} - 26886 q^{10} + 6476 q^{11} + 14794 q^{13} + 216232 q^{14} - 127934 q^{15} + 195174 q^{16} + 97644 q^{17}+ \cdots - 359343776 q^{99}+O(q^{100}) $ 32 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 172 * q^5 - 2726 * q^6 - 2784 * q^7 - 10470 * q^8 - 21872 * q^9 - 26886 * q^10 + 6476 * q^11 + 14794 * q^13 + 216232 * q^14 - 127934 * q^15 + 195174 * q^16 + 97644 * q^17 - 475646 * q^18 + 373314 * q^19 + 685798 * q^20 - 213824 * q^21 + 167756 * q^22 - 711654 * q^23 - 1396830 * q^24 - 1041274 * q^26 + 3386272 * q^27 - 491836 * q^28 - 178394 * q^29 - 6200118 * q^30 + 1793468 * q^31 + 955004 * q^32 - 369536 * q^33 + 4592250 * q^34 + 1520488 * q^35 - 11372454 * q^36 + 247730 * q^37 + 14761942 * q^39 + 15044736 * q^40 - 2285272 * q^41 - 1024084 * q^42 + 18199452 * q^43 + 5629904 * q^44 - 10428746 * q^45 - 25708302 * q^46 - 8054836 * q^47 - 19983002 * q^48 - 18234288 * q^49 - 7208294 * q^50 - 26124488 * q^52 - 26091116 * q^53 + 85261048 * q^54 - 2240524 * q^55 + 84926940 * q^56 + 57257116 * q^57 - 68659210 * q^58 - 58197100 * q^59 - 64428232 * q^60 - 38537926 * q^61 + 2935614 * q^62 - 43972436 * q^63 + 44466032 * q^65 + 209850752 * q^66 + 30462126 * q^67 + 68365716 * q^68 + 163279656 * q^69 + 256782116 * q^70 - 113836054 * q^71 - 445647780 * q^72 - 30722748 * q^73 - 156843362 * q^74 - 364524840 * q^75 - 180633890 * q^76 + 252047848 * q^78 + 364818200 * q^79 + 372146084 * q^80 - 17174000 * q^81 + 272314014 * q^82 + 389373188 * q^83 - 464450276 * q^84 - 331999758 * q^85 - 32039076 * q^86 - 337693978 * q^87 - 1180586364 * q^88 - 333088936 * q^89 + 251459988 * q^91 + 1275961956 * q^92 + 637177780 * q^93 + 171539378 * q^94 + 318589986 * q^95 + 1019148280 * q^96 - 230031796 * q^97 - 1287859636 * q^98 - 359343776 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/13\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{12}\right)$

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 $

$2$	8.65394	+	2.31882i	0.540871	+	0.144926i	0.518904	−	0.854833i	$-0.326340\pi$
$2$	8.65394	+	2.31882i	0.540871	+	0.144926i	0.0219676	+	0.999759i	$0.493007\pi$
$3$	−30.7307	−	53.2271i	−0.379391	−	0.657125i	0.611582	−	0.791181i	$-0.290533\pi$
$3$	−30.7307	−	53.2271i	−0.379391	−	0.657125i	−0.990974	+	0.134056i	$0.957200\pi$
$4$	−152.189	−	87.8662i	−0.594487	−	0.343227i
$5$	−612.629	+	612.629i	−0.980207	+	0.980207i	−0.999808	−	0.0196013i	$-0.993760\pi$
$5$	−612.629	+	612.629i	−0.980207	+	0.980207i	0.0196013	+	0.999808i	$0.493760\pi$
$6$	−142.518	−	531.883i	−0.109967	−	0.410404i
$7$	−968.610	+	259.538i	−0.403419	+	0.108096i	−0.454823	−	0.890582i	$-0.650297\pi$
$7$	−968.610	+	259.538i	−0.403419	+	0.108096i	0.0514032	+	0.998678i	$0.483631\pi$
$8$	−2735.08	−	2735.08i	−0.667744	−	0.667744i
$9$	1391.75	−	2410.58i	0.212124	−	0.367410i
$10$	−6722.23	+	3881.08i	−0.672223	+	0.388108i
$11$	0.564567	−	2.10699i	3.85607e−5	−	0.000143910i	−0.965907	−	0.258891i	$-0.916643\pi$
$11$	0.564567	−	2.10699i	3.85607e−5	−	0.000143910i	0.965945	+	0.258747i	$0.0833096\pi$
$12$			10800.8i			0.520870i
$13$	−19265.9	−	21084.5i	−0.674552	−	0.738227i
$13$	−19265.9	−	21084.5i	−0.674552	−	0.738227i
$14$	−8984.12			−0.233864
$15$	51435.0	+	13782.0i	1.01600	+	0.272236i
$16$	5166.67	+	8948.93i	0.0788371	+	0.136550i
$17$	93462.5	+	53960.6i	1.11903	+	0.646072i	0.941153	−	0.337980i	$-0.109744\pi$
$17$	93462.5	+	53960.6i	1.11903	+	0.646072i	0.177877	+	0.984053i	$0.443077\pi$
$18$	17633.8	−	17633.8i	0.167979	−	0.167979i
$19$	−23450.7	−	87519.3i	−0.179946	−	0.671567i	−0.995656	−	0.0931067i	$-0.970320\pi$
$19$	−23450.7	−	87519.3i	−0.179946	−	0.671567i	0.815710	−	0.578461i	$-0.196346\pi$
$20$	147065.	−	39405.8i	0.919154	−	0.246286i
$21$	43580.5	+	43580.5i	0.224086	+	0.224086i
$22$	9.77146	−	16.9247i	4.17127e−5	−	7.22486e-5i
$23$	−387384.	+	223656.i	−1.38430	+	0.799227i	−0.992665	−	0.120894i	$-0.961424\pi$
$23$	−387384.	+	223656.i	−1.38430	+	0.799227i	−0.391635	+	0.920120i	$0.628091\pi$
$24$	−61529.5	+	229631.i	−0.185455	+	0.692127i
$25$		−	360004.i		−	0.921610i
$26$	−117835.	−	227138.i	−0.257858	−	0.497046i
$27$	−574326.			−1.08070
$28$	170216.	+	45609.3i	0.276929	+	0.0742029i
$29$	−435075.	−	753572.i	−0.615137	−	1.06545i	−0.990360	−	0.138514i	$-0.955767\pi$
$29$	−435075.	−	753572.i	−0.615137	−	1.06545i	0.375223	−	0.926935i	$-0.377566\pi$
$30$	413158.	+	238537.i	0.510071	+	0.294490i
$31$	−67934.2	+	67934.2i	−0.0735600	+	0.0735600i	−0.742930	−	0.669370i	$-0.766564\pi$
$31$	−67934.2	+	67934.2i	−0.0735600	+	0.0735600i	0.669370	+	0.742930i	$0.266564\pi$
$32$	280245.	+	1.04589e6i	0.267262	+	0.997437i
$33$	−129.499	+	34.6991i	−0.000109197	+	2.92592e-5i
$34$	683695.	+	683695.i	0.511619	+	0.511619i
$35$	434398.	−	752399.i	0.289478	−	0.501391i
$36$	−423617.	+	244575.i	−0.252210	+	0.145614i
$37$	358192.	−	1.33679e6i	0.191121	−	0.713274i	−0.802116	−	0.597169i	$-0.796292\pi$
$37$	358192.	−	1.33679e6i	0.191121	−	0.713274i	0.993237	−	0.116105i	$-0.0370411\pi$
$38$		−	811765.i		−	0.389311i
$39$	−530214.	+	1.67341e6i	−0.229189	+	0.723342i
$40$	3.35118e6			1.30905
$41$	2.47751e6	+	663846.i	0.876757	+	0.234926i	0.669007	−	0.743256i	$-0.266719\pi$
$41$	2.47751e6	+	663846.i	0.876757	+	0.234926i	0.207750	+	0.978182i	$0.433386\pi$
$42$	276088.	+	478199.i	0.0887259	+	0.153678i
$43$	−3.47455e6	−	2.00603e6i	−1.01631	−	0.586764i	−0.103274	−	0.994653i	$-0.532932\pi$
$43$	−3.47455e6	−	2.00603e6i	−1.01631	−	0.586764i	−0.913032	+	0.407889i	$0.866265\pi$
$44$	−271.054	+	271.054i	−7.23178e−5	+	7.23178e-5i
$45$	624165.	+	2.32942e6i	0.152212	+	0.568064i
$46$	−3.87102e6	+	1.03724e6i	−0.864558	+	0.231658i
$47$	−1.42343e6	−	1.42343e6i	−0.291705	−	0.291705i	0.546048	−	0.837754i	$-0.316131\pi$
$47$	−1.42343e6	−	1.42343e6i	−0.291705	−	0.291705i	−0.837754	+	0.546048i	$0.816131\pi$
$48$	317551.	−	550014.i	0.0598202	−	0.103612i
$49$	−4.12162e6	+	2.37962e6i	−0.714963	+	0.412784i
$50$	834783.	−	3.11545e6i	0.133565	−	0.498472i
$51$		−	6.63299e6i		−	0.980457i
$52$	1.07943e6	+	4.90164e6i	0.147633	+	0.670391i
$53$	3.19498e6			0.404916			0.202458	−	0.979291i	$-0.435107\pi$
$53$	3.19498e6			0.404916			0.202458	+	0.979291i	$0.435107\pi$
$54$	−4.97018e6	−	1.33176e6i	−0.584517	−	0.156621i
$55$	944.935	+	1636.67i	0.000103265	+	0.000178859i
$56$	3.35908e6	+	1.93937e6i	0.341561	+	0.197200i
$57$	−3.93775e6	+	3.93775e6i	−0.373034	+	0.373034i
$58$	−2.01772e6	−	7.53023e6i	−0.178299	−	0.665420i
$59$	3.40589e6	−	912605.i	0.281075	−	0.0753139i	−0.115527	−	0.993304i	$-0.536856\pi$
$59$	3.40589e6	−	912605.i	0.281075	−	0.0753139i	0.396603	+	0.917990i	$0.370189\pi$
$60$	−6.61686e6	−	6.61686e6i	−0.510560	−	0.510560i
$61$	−6.50874e6	+	1.12735e7i	−0.470086	+	0.814214i	−0.999415	−	0.0342033i	$-0.989111\pi$
$61$	−6.50874e6	+	1.12735e7i	−0.470086	+	0.814214i	0.529328	+	0.848417i	$0.322444\pi$
$62$	−745426.	+	430372.i	−0.0504473	+	0.0291258i
$63$	−722424.	+	2.69612e6i	−0.0458596	+	0.171150i
$64$			7.05556e6i			0.420544i
$65$	2.47198e7	+	1.11415e6i	1.38482	+	0.0624151i
$66$	−1201.14			−6.33018e−5
$67$	3.56413e7	+	9.55007e6i	1.76870	+	0.473922i	0.988451	−	0.151543i	$-0.0484242\pi$
$67$	3.56413e7	+	9.55007e6i	1.76870	+	0.473922i	0.780252	+	0.625465i	$0.215091\pi$
$68$	−9.48263e6	−	1.64244e7i	−0.443499	−	0.768163i
$69$	2.38092e7	+	1.37462e7i	1.05038	+	0.606439i
$70$	5.50393e6	−	5.50393e6i	0.229235	−	0.229235i
$71$	−5.07414e6	−	1.89369e7i	−0.199677	−	0.745206i	−0.991006	−	0.133816i	$-0.957277\pi$
$71$	−5.07414e6	−	1.89369e7i	−0.199677	−	0.745206i	0.791329	−	0.611391i	$-0.209390\pi$
$72$	−1.03997e7	+	2.78658e6i	−0.386981	+	0.103691i
$73$	−1.21226e7	−	1.21226e7i	−0.426878	−	0.426878i	0.460686	−	0.887563i	$-0.347604\pi$
$73$	−1.21226e7	−	1.21226e7i	−0.426878	−	0.426878i	−0.887563	+	0.460686i	$0.847604\pi$
$74$	6.19955e6	−	1.07379e7i	0.206744	−	0.358091i
$75$	−1.91620e7	+	1.10632e7i	−0.605613	+	0.349651i
$76$	−4.12105e6	+	1.53800e7i	−0.123525	+	0.461000i
$77$			2187.38i			6.22245e-5i
$78$	−8.46877e6	+	1.32521e7i	−0.228793	+	0.358020i
$79$	−6.64644e7			−1.70640			−0.853200	−	0.521584i	$-0.825341\pi$
$79$	−6.64644e7			−1.70640			−0.853200	+	0.521584i	$0.825341\pi$
$80$	−8.64763e6	−	2.31713e6i	−0.211124	−	0.0565704i
$81$	8.51817e6	+	1.47539e7i	0.197882	+	0.342742i
$82$	1.99009e7	+	1.14898e7i	0.440166	+	0.254130i
$83$	4.60062e7	−	4.60062e7i	0.969403	−	0.969403i	−0.0301431	−	0.999546i	$-0.509596\pi$
$83$	4.60062e7	−	4.60062e7i	0.969403	−	0.969403i	0.999546	+	0.0301431i	$0.00959629\pi$
$84$	−2.80321e6	−	1.04617e7i	−0.0563039	−	0.210129i
$85$	−9.03157e7	+	2.42000e7i	−1.73017	+	0.463596i
$86$	−2.54169e7	−	2.54169e7i	−0.464653	−	0.464653i
$87$	−2.67403e7	+	4.63156e7i	−0.466755	+	0.808444i
$88$	−7306.93	+	4218.66i	−0.000121844	+	7.03466e-5i
$89$	2.83718e7	−	1.05885e8i	0.452196	−	1.68762i	−0.244009	−	0.969773i	$-0.578463\pi$
$89$	2.83718e7	−	1.05885e8i	0.452196	−	1.68762i	0.696204	−	0.717844i	$-0.254871\pi$
$90$			2.16060e7i			0.329309i
$91$	2.41334e7	+	1.54224e7i	0.351927	+	0.224899i
$92$	7.86073e7			1.09727
$93$	5.70361e6	+	1.52828e6i	0.0762462	+	0.0204301i
$94$	−9.01760e6	−	1.56189e7i	−0.115499	−	0.200051i
$95$	6.79835e7	+	3.92503e7i	0.834659	+	0.481891i
$96$	4.70575e7	−	4.70575e7i	0.554044	−	0.554044i
$97$	3.59877e7	+	1.34308e8i	0.406506	+	1.51710i	0.801260	+	0.598316i	$0.204163\pi$
$97$	3.59877e7	+	1.34308e8i	0.406506	+	1.51710i	−0.394754	+	0.918787i	$0.629170\pi$
$98$	−4.11862e7	+	1.10358e7i	−0.446526	+	0.119646i
$99$	−4293.34	−	4293.34i	−4.46945e−5	−	4.46945e-5i
$100$	−3.16322e7	+	5.47885e7i	−0.316322	+	0.547885i
$101$	5.58274e7	−	3.22319e7i	0.536490	−	0.309743i	−0.207165	−	0.978306i	$-0.566424\pi$
$101$	5.58274e7	−	3.22319e7i	0.536490	−	0.309743i	0.743655	+	0.668563i	$0.233090\pi$
$102$	1.53807e7	−	5.74015e7i	0.142094	−	0.530301i
$103$		−	1.17668e8i		−	1.04547i	−0.852496	−	0.522733i	$-0.824912\pi$
$103$		−	1.17668e8i		−	1.04547i	0.852496	−	0.522733i	$-0.175088\pi$
$104$	−4.97411e6	+	1.10362e8i	−0.0425189	+	0.943375i
$105$	−5.33974e7			−0.439302
$106$	2.76492e7	+	7.40858e6i	0.219008	+	0.0586829i
$107$	−6.07873e7	−	1.05287e8i	−0.463744	−	0.803227i	0.535400	−	0.844598i	$-0.320161\pi$
$107$	−6.07873e7	−	1.05287e8i	−0.463744	−	0.803227i	−0.999144	+	0.0413710i	$0.986827\pi$
$108$	8.74059e7	+	5.04638e7i	0.642459	+	0.370924i
$109$	1.72260e7	−	1.72260e7i	0.122033	−	0.122033i	−0.643453	−	0.765486i	$-0.722499\pi$
$109$	1.72260e7	−	1.72260e7i	0.122033	−	0.122033i	0.765486	+	0.643453i	$0.222499\pi$
$110$	4382.26	+	16354.8i	2.99314e−5	+	0.000111706i
$111$	−8.21610e7	+	2.20150e7i	−0.541220	+	0.145019i
$112$	−7.32708e6	−	7.32708e6i	−0.0465649	−	0.0465649i
$113$	−1.17357e8	+	2.03269e8i	−0.719773	+	1.24668i	0.241316	+	0.970447i	$0.422421\pi$
$113$	−1.17357e8	+	2.03269e8i	−0.719773	+	1.24668i	−0.961089	+	0.276238i	$0.910912\pi$
$114$	−4.32079e7	+	2.49461e7i	−0.255826	+	0.147701i
$115$	1.00304e8	−	3.74341e8i	0.573494	−	2.14031i
$116$			1.52913e8i			0.844527i
$117$	−7.76391e7	+	1.70976e7i	−0.414321	+	0.0912413i
$118$	3.15905e7			0.162940
$119$	−1.04534e8	−	2.80097e7i	−0.521276	−	0.139676i
$120$	−1.02984e8	−	1.78374e8i	−0.496644	−	0.860212i
$121$	1.85640e8	+	1.07179e8i	0.866025	+	0.500000i
$122$	−8.24674e7	+	8.24674e7i	−0.372257	+	0.372257i
$123$	−4.08009e7	−	1.52271e8i	−0.178258	−	0.665268i
$124$	1.63079e7	−	4.36970e6i	0.0689783	−	0.0184827i
$125$	−1.87594e7	−	1.87594e7i	−0.0768387	−	0.0768387i
$126$	−1.25036e7	+	2.16569e7i	−0.0496082	+	0.0859240i
$127$	−3.51916e8	+	2.03179e8i	−1.35277	+	0.781022i	−0.988637	−	0.150325i	$-0.951968\pi$
$127$	−3.51916e8	+	2.03179e8i	−1.35277	+	0.781022i	−0.364133	+	0.931347i	$0.618635\pi$
$128$	5.53821e7	−	2.06689e8i	0.206315	−	0.769976i
$129$			2.46587e8i			0.890453i
$130$	2.11340e8	+	6.69625e7i	0.739962	+	0.234454i
$131$	−6.71055e7			−0.227863			−0.113931	−	0.993489i	$-0.536344\pi$
$131$	−6.71055e7			−0.227863			−0.113931	+	0.993489i	$0.536344\pi$
$132$	22757.1	+	6097.75i	7.49586e−5	+	2.00851e-5i
$133$	4.54292e7	+	7.86857e7i	0.145187	+	0.251472i
$134$	2.86293e8	+	1.65291e8i	0.887957	+	0.512662i
$135$	3.51849e8	−	3.51849e8i	1.05930	−	1.05930i
$136$	−1.08041e8	−	4.03214e8i	−0.315815	−	1.17864i
$137$	−1.25868e8	+	3.37262e7i	−0.357299	+	0.0957381i	−0.433003	−	0.901392i	$-0.642546\pi$
$137$	−1.25868e8	+	3.37262e7i	−0.357299	+	0.0957381i	0.0757041	+	0.997130i	$0.475880\pi$
$138$	1.74168e8	+	1.74168e8i	0.480234	+	0.480234i
$139$	9.56859e6	−	1.65733e7i	0.0256324	−	0.0443965i	−0.852925	−	0.522034i	$-0.825173\pi$
$139$	9.56859e6	−	1.65733e7i	0.0256324	−	0.0443965i	0.878557	+	0.477637i	$0.158507\pi$
$140$	−1.32221e8	+	7.63378e7i	−0.344182	+	0.198713i
$141$	−3.20221e7	+	1.19508e8i	−0.0810164	+	0.302357i
$142$		−	1.75645e8i		−	0.431999i
$143$	−55301.8	+	28689.4i	−0.000132250	+	6.86085e-5i
$144$	2.87628e7			0.0668931
$145$	7.28200e8	+	1.95120e8i	1.64732	+	0.441399i
$146$	−7.67981e7	−	1.33018e8i	−0.169020	−	0.292752i
$147$	2.53320e8	+	1.46255e8i	0.542502	+	0.313213i
$148$	−1.71971e8	+	1.71971e8i	−0.358434	+	0.358434i
$149$	1.29391e8	+	4.82894e8i	0.262518	+	0.979730i	0.963752	+	0.266799i	$0.0859661\pi$
$149$	1.29391e8	+	4.82894e8i	0.262518	+	0.979730i	−0.701234	+	0.712931i	$0.747367\pi$
$150$	−1.91480e8	+	5.13069e7i	−0.378232	+	0.101347i
$151$	−4.26930e8	−	4.26930e8i	−0.821200	−	0.821200i	0.165080	−	0.986280i	$-0.447212\pi$
$151$	−4.26930e8	−	4.26930e8i	−0.821200	−	0.821200i	−0.986280	+	0.165080i	$0.947212\pi$
$152$	−1.75233e8	+	3.03512e8i	−0.328277	+	0.568593i
$153$	2.60153e8	−	1.50199e8i	0.474747	−	0.274096i
$154$	−5072.13	+	18929.5i	−9.01795e−6	+	3.36555e-5i
$155$		−	8.32370e7i		−	0.144208i
$156$	2.27729e8	−	2.08086e8i	0.384520	−	0.351354i
$157$	7.13472e7			0.117430			0.0587149	−	0.998275i	$-0.481300\pi$
$157$	7.13472e7			0.117430			0.0587149	+	0.998275i	$0.481300\pi$
$158$	−5.75179e8	−	1.54119e8i	−0.922943	−	0.247302i
$159$	−9.81841e7	−	1.70060e8i	−0.153622	−	0.266081i
$160$	−8.12428e8	−	4.69055e8i	−1.23967	−	0.715722i
$161$	3.17177e8	−	3.17177e8i	0.472061	−	0.472061i
$162$	3.95042e7	+	1.47432e8i	0.0573565	+	0.214057i
$163$	−3.48858e8	+	9.34763e7i	−0.494195	+	0.132419i	−0.497305	−	0.867576i	$-0.665677\pi$
$163$	−3.48858e8	+	9.34763e7i	−0.494195	+	0.132419i	0.00310949	+	0.999995i	$0.499010\pi$
$164$	−3.18719e8	−	3.18719e8i	−0.440588	−	0.440588i
$165$	58077.0	−	100592.i	7.83553e−5	−	0.000135715i
$166$	5.04815e8	−	2.91455e8i	0.664814	−	0.383830i
$167$	−2.16753e8	+	8.08933e8i	−0.278676	+	1.04003i	0.674662	+	0.738127i	$0.264289\pi$
$167$	−2.16753e8	+	8.08933e8i	−0.278676	+	1.04003i	−0.953338	+	0.301905i	$0.902377\pi$
$168$		−	2.38392e8i		−	0.299265i
$169$	−7.33826e7	+	8.12423e8i	−0.0899593	+	0.995945i
$170$	−8.37702e8			−1.00298
$171$	−2.43610e8	−	6.52751e7i	−0.284912	−	0.0763419i
$172$	3.52524e8	+	6.10590e8i	0.402787	+	0.697647i
$173$	−7.09432e6	−	4.09591e6i	−0.00792002	−	0.00457263i	0.496035	−	0.868303i	$-0.334789\pi$
$173$	−7.09432e6	−	4.09591e6i	−0.00792002	−	0.00457263i	−0.503955	+	0.863730i	$0.668122\pi$
$174$	−3.38806e8	+	3.38806e8i	−0.369619	+	0.369619i
$175$	9.34347e7	+	3.48703e8i	0.0996222	+	0.371795i
$176$	21772.3	−	5833.86i	2.26910e−5	−	6.08003e-6i
$177$	−1.53241e8	−	1.53241e8i	−0.156128	−	0.156128i
$178$	4.91055e8	−	8.50533e8i	0.489159	−	0.847249i
$179$	1.64181e8	−	9.47897e7i	0.159923	−	0.0923313i	−0.417903	−	0.908492i	$-0.637235\pi$
$179$	1.64181e8	−	9.47897e7i	0.159923	−	0.0923313i	0.577825	+	0.816160i	$0.303901\pi$
$180$	1.09686e8	−	4.09354e8i	0.104487	−	0.389950i
$181$		−	1.58416e9i		−	1.47599i	−0.674806	−	0.737995i	$-0.735773\pi$
$181$		−	1.58416e9i		−	1.47599i	0.674806	−	0.737995i	$-0.264227\pi$
$182$	1.73087e8	+	1.89426e8i	0.157753	+	0.172645i
$183$	8.00073e8			0.713387
$184$	1.67124e9	+	4.47808e8i	1.45804	+	0.390680i
$185$	5.99518e8	+	1.03840e9i	0.511818	+	0.886494i
$186$	4.58149e7	+	2.64513e7i	0.0382785	+	0.0221001i
$187$	166460.	−	166460.i	0.000136127	−	0.000136127i
$188$	9.15585e7	+	3.41701e8i	0.0732938	+	0.273536i
$189$	5.56298e8	−	1.49059e8i	0.435973	−	0.116819i
$190$	4.97311e8	+	4.97311e8i	0.381605	+	0.381605i
$191$	8.32362e8	−	1.44169e9i	0.625430	−	1.08328i	−0.363028	−	0.931778i	$-0.618257\pi$
$191$	8.32362e8	−	1.44169e9i	0.625430	−	1.08328i	0.988458	−	0.151498i	$-0.0484097\pi$
$192$	3.75547e8	−	2.16822e8i	0.276350	−	0.159551i
$193$	−6.40823e8	+	2.39158e9i	−0.461858	+	1.72368i	0.205243	+	0.978711i	$0.434201\pi$
$193$	−6.40823e8	+	2.39158e9i	−0.461858	+	1.72368i	−0.667101	+	0.744967i	$0.732465\pi$
$194$			1.24574e9i			0.879471i
$195$	−7.00355e8	−	1.35000e9i	−0.484373	−	0.933677i
$196$	8.36352e8			0.566715
$197$	−1.40727e9	−	3.77077e8i	−0.934358	−	0.250360i	−0.240646	−	0.970613i	$-0.577359\pi$
$197$	−1.40727e9	−	3.77077e8i	−0.934358	−	0.250360i	−0.693712	+	0.720253i	$0.744026\pi$
$198$	−27198.8	−	47109.8i	−1.76966e−5	−	3.06514e-5i
$199$	−1.76068e9	−	1.01653e9i	−1.12271	−	0.648197i	−0.180619	−	0.983553i	$-0.557810\pi$
$199$	−1.76068e9	−	1.01653e9i	−1.12271	−	0.648197i	−0.942092	+	0.335356i	$0.891143\pi$
$200$	−9.84639e8	+	9.84639e8i	−0.615399	+	0.615399i
$201$	−5.86960e8	−	2.19057e9i	−0.359604	−	1.34206i
$202$	5.57867e8	−	1.49480e8i	0.335062	−	0.0897796i
$203$	6.16998e8	+	6.16998e8i	0.363329	+	0.363329i
$204$	−5.82815e8	+	1.00947e9i	−0.336520	+	0.582869i
$205$	−1.92448e9	+	1.11110e9i	−1.08968	+	0.629127i
$206$	2.72851e8	−	1.01829e9i	0.151515	−	0.565463i
$207$			1.24509e9i			0.678142i
$208$	8.91435e7	−	2.81346e8i	0.0476251	−	0.150310i
$209$	−197642.			−0.000103584
$210$	−4.62098e8	−	1.23819e8i	−0.237606	−	0.0636663i
$211$	−8.27593e8	−	1.43343e9i	−0.417529	−	0.723182i	0.578161	−	0.815923i	$-0.303771\pi$
$211$	−8.27593e8	−	1.43343e9i	−0.417529	−	0.723182i	−0.995690	+	0.0927407i	$0.970437\pi$
$212$	−4.86240e8	−	2.80731e8i	−0.240717	−	0.138978i
$213$	−8.52027e8	+	8.52027e8i	−0.413938	+	0.413938i
$214$	−2.81909e8	−	1.05210e9i	−0.134417	−	0.501651i
$215$	3.35756e9	−	8.99655e8i	1.57134	−	0.421039i
$216$	1.57083e9	+	1.57083e9i	0.721628	+	0.721628i
$217$	4.81702e7	−	8.34333e7i	0.0217240	−	0.0376271i
$218$	1.89017e8	−	1.09129e8i	0.0836901	−	0.0483185i
$219$	−2.72715e8	+	1.01779e9i	−0.118558	+	0.442466i
$220$		−	332111.i		−	0.000141773i
$221$	−6.62904e8	−	3.01021e9i	−0.277896	−	1.26191i
$222$	−7.62066e8			−0.313748
$223$	−7.53278e8	−	2.01840e8i	−0.304604	−	0.0816185i	0.103279	−	0.994652i	$-0.467066\pi$
$223$	−7.53278e8	−	2.01840e8i	−0.304604	−	0.0816185i	−0.407884	+	0.913034i	$0.633733\pi$
$224$	−5.42896e8	−	9.40323e8i	−0.215638	−	0.373495i
$225$	−8.67818e8	−	5.01035e8i	−0.338609	−	0.195496i
$226$	−1.48694e9	+	1.48694e9i	−0.569982	+	0.569982i
$227$	8.61131e8	+	3.21379e9i	0.324314	+	1.21036i	0.914999	+	0.403455i	$0.132191\pi$
$227$	8.61131e8	+	3.21379e9i	0.324314	+	1.21036i	−0.590685	+	0.806902i	$0.701143\pi$
$228$	9.45275e8	−	2.53286e8i	0.349799	−	0.0937284i
$229$	−4.02746e8	−	4.02746e8i	−0.146450	−	0.146450i	0.630080	−	0.776530i	$-0.283022\pi$
$229$	−4.02746e8	−	4.02746e8i	−0.146450	−	0.146450i	−0.776530	+	0.630080i	$0.783022\pi$
$230$	1.73606e9	−	3.00694e9i	0.620373	−	1.07452i
$231$	116428.	−	67219.7i	4.08893e−5	−	2.36074e-5i
$232$	−8.71114e8	+	3.25104e9i	−0.300693	+	1.12220i
$233$			4.47396e8i			0.151799i	0.997115	+	0.0758995i	$0.0241828\pi$
$233$			4.47396e8i			0.151799i	−0.997115	+	0.0758995i	$0.975817\pi$
$234$	−7.11531e8	−	3.20694e7i	−0.237318	−	0.0106962i
$235$	1.74407e9			0.571863
$236$	−5.98525e8	−	1.60374e8i	−0.192945	−	0.0516995i
$237$	2.04250e9	+	3.53771e9i	0.647393	+	1.12132i
$238$	−8.39678e8	−	4.84788e8i	−0.261701	−	0.151093i
$239$	1.23011e9	−	1.23011e9i	0.377008	−	0.377008i	−0.493013	−	0.870022i	$-0.664105\pi$
$239$	1.23011e9	−	1.23011e9i	0.377008	−	0.377008i	0.870022	+	0.493013i	$0.164105\pi$
$240$	1.42414e8	+	5.31495e8i	0.0429247	+	0.160197i
$241$	5.38249e9	−	1.44223e9i	1.59557	−	0.427531i	0.651868	−	0.758333i	$-0.273986\pi$
$241$	5.38249e9	−	1.44223e9i	1.59557	−	0.427531i	0.943700	+	0.330801i	$0.107319\pi$
$242$	1.35799e9	+	1.35799e9i	0.395945	+	0.395945i
$243$	−1.36054e9	+	2.35652e9i	−0.390198	+	0.675843i
$244$	1.98111e9	−	1.14380e9i	0.558921	−	0.322693i
$245$	1.06720e9	−	3.98285e9i	0.296198	−	1.10543i
$246$		−	1.41235e9i		−	0.385659i
$247$	−1.39350e9	+	2.18058e9i	−0.374387	+	0.585848i
$248$	3.71611e8			0.0982385
$249$	−3.86258e9	−	1.03498e9i	−1.00480	−	0.269236i
$250$	−1.18843e8	−	2.05843e8i	−0.0304239	−	0.0526958i
$251$	−2.71055e9	−	1.56494e9i	−0.682909	−	0.394277i	0.118041	−	0.993009i	$-0.462338\pi$
$251$	−2.71055e9	−	1.56494e9i	−0.682909	−	0.394277i	−0.800950	+	0.598731i	$0.795672\pi$
$252$	3.46843e8	−	3.46843e8i	0.0860063	−	0.0860063i
$253$	252538.	+	942484.i	6.16374e−5	+	0.000230034i
$254$	−3.51659e9	+	9.42268e8i	−0.844865	+	0.226381i
$255$	4.06356e9	+	4.06356e9i	0.961051	+	0.961051i
$256$	1.86166e9	−	3.22449e9i	0.433451	−	0.750760i
$257$	5.28505e9	−	3.05133e9i	1.21148	−	0.699449i	0.248400	−	0.968658i	$-0.420095\pi$
$257$	5.28505e9	−	3.05133e9i	1.21148	−	0.699449i	0.963082	+	0.269208i	$0.0867621\pi$
$258$	−5.71790e8	+	2.13395e9i	−0.129050	+	0.481621i
$259$			1.38779e9i			0.308408i
$260$	−3.66418e9	−	2.34160e9i	−0.801832	−	0.512411i
$261$	−2.42206e9			−0.521943
$262$	−5.80727e8	−	1.55605e8i	−0.123244	−	0.0330232i
$263$	2.88065e9	+	4.98943e9i	0.602098	+	1.04286i	0.992503	+	0.122221i	$0.0390017\pi$
$263$	2.88065e9	+	4.98943e9i	0.602098	+	1.04286i	−0.390405	+	0.920643i	$0.627665\pi$
$264$	449094.	+	259284.i	9.24531e−5	+	5.33778e-5i
$265$	−1.95734e9	+	1.95734e9i	−0.396901	+	0.396901i
$266$	2.10684e8	+	7.86284e8i	0.0420829	+	0.157055i
$267$	−6.50783e9	+	1.74377e9i	−1.28053	+	0.343118i
$268$	−4.58508e9	−	4.58508e9i	−0.888808	−	0.888808i
$269$	1.94483e8	−	3.36855e8i	0.0371427	−	0.0643330i	−0.846856	−	0.531821i	$-0.821508\pi$
$269$	1.94483e8	−	3.36855e8i	0.0371427	−	0.0643330i	0.883999	+	0.467488i	$0.154841\pi$
$270$	3.86075e9	−	2.22901e9i	0.726469	−	0.419427i
$271$	−3.55920e8	+	1.32831e9i	−0.0659896	+	0.246277i	−0.991040	−	0.133569i	$-0.957356\pi$
$271$	−3.55920e8	+	1.32831e9i	−0.0659896	+	0.246277i	0.925050	+	0.379846i	$0.124023\pi$
$272$			1.11519e9i			0.203738i
$273$	7.92570e7	−	1.75849e9i	0.0142688	−	0.316584i
$274$	−1.16746e9			−0.207128
$275$	−758525.	−	203246.i	−0.000132629	−	3.55379e-5i
$276$	−2.41566e9	−	4.18404e9i	−0.416293	−	0.721040i
$277$	−5.10846e8	−	2.94937e8i	−0.0867702	−	0.0500968i	0.455987	−	0.889986i	$-0.349286\pi$
$277$	−5.10846e8	−	2.94937e8i	−0.0867702	−	0.0500968i	−0.542757	+	0.839890i	$0.682620\pi$
$278$	1.21236e8	−	1.21236e8i	0.0202980	−	0.0202980i
$279$	6.92135e7	+	2.58308e8i	0.0114228	+	0.0426306i
$280$	−3.24598e9	+	8.69759e8i	−0.528098	+	0.141503i
$281$	−3.32744e9	−	3.32744e9i	−0.533685	−	0.533685i	0.387982	−	0.921667i	$-0.373172\pi$
$281$	−3.32744e9	−	3.32744e9i	−0.533685	−	0.533685i	−0.921667	+	0.387982i	$0.873172\pi$
$282$	−5.54234e8	+	9.59962e8i	−0.0876389	+	0.151795i
$283$	−1.15402e9	+	6.66274e8i	−0.179915	+	0.103874i	−0.587253	−	0.809404i	$-0.699791\pi$
$283$	−1.15402e9	+	6.66274e8i	−0.179915	+	0.103874i	0.407338	+	0.913278i	$0.366457\pi$
$284$	−8.91690e8	+	3.32783e9i	−0.137069	+	0.511550i
$285$		−	4.82476e9i		−	0.731300i
$286$	−545104.	+	120042.i	−8.14733e−5	+	1.79419e-5i
$287$	−2.57203e9			−0.379095
$288$	2.91123e9	+	7.80061e8i	0.423161	+	0.113386i
$289$	2.33562e9	+	4.04541e9i	0.334819	+	0.579924i
$290$	5.84935e9	+	3.37712e9i	0.827019	+	0.477480i
$291$	6.04290e9	−	6.04290e9i	0.842701	−	0.842701i
$292$	7.79755e8	+	2.91008e9i	0.107257	+	0.400289i
$293$	8.54392e9	−	2.28934e9i	1.15928	−	0.310627i	0.372599	−	0.927993i	$-0.378467\pi$
$293$	8.54392e9	−	2.28934e9i	1.15928	−	0.310627i	0.786676	+	0.617366i	$0.211800\pi$
$294$	1.85308e9	+	1.85308e9i	0.248031	+	0.248031i
$295$	−1.52746e9	+	2.64564e9i	−0.201689	+	0.349335i
$296$	−4.63591e9	+	2.67654e9i	−0.603904	+	0.348664i
$297$	−324245.	+	1.21010e6i	−4.16723e−5	+	0.000155523i
$298$			4.47897e9i			0.567954i
$299$	1.21790e10	+	3.85887e9i	1.52379	+	0.482809i
$300$	3.88831e9			0.480039
$301$	3.88612e9	+	1.04128e9i	0.473424	+	0.126854i
$302$	−2.70466e9	−	4.68460e9i	−0.325151	−	0.563177i
$303$	−3.43123e9	−	1.98102e9i	−0.407079	−	0.235027i
$304$	6.62043e8	−	6.62043e8i	0.0775160	−	0.0775160i
$305$	−2.91901e9	−	1.08939e10i	−0.337316	−	1.25888i
$306$	2.59963e9	−	6.96569e8i	0.296501	−	0.0794472i
$307$	−7.98681e8	−	7.98681e8i	−0.0899124	−	0.0899124i	0.660720	−	0.750632i	$-0.270251\pi$
$307$	−7.98681e8	−	7.98681e8i	−0.0899124	−	0.0899124i	−0.750632	+	0.660720i	$0.770251\pi$
$308$	192197.	−	332894.i	2.13571e−5	−	3.69917e-5i
$309$	−6.26314e9	+	3.61603e9i	−0.687002	+	0.396641i
$310$	1.93011e8	−	7.20328e8i	0.0208995	−	0.0779980i
$311$			8.87167e9i			0.948340i	0.880433	+	0.474170i	$0.157252\pi$
$311$			8.87167e9i			0.948340i	−0.880433	+	0.474170i	$0.842748\pi$
$312$	6.02708e9	−	3.12673e9i	0.636046	−	0.329968i
$313$	−4.34504e9			−0.452706			−0.226353	−	0.974045i	$-0.572680\pi$
$313$	−4.34504e9			−0.452706			−0.226353	+	0.974045i	$0.572680\pi$
$314$	6.17435e8	+	1.65441e8i	0.0635145	+	0.0170186i
$315$	−1.20915e9	−	2.09430e9i	−0.122811	−	0.212714i
$316$	1.01151e10	+	5.83997e9i	1.01443	+	0.585683i
$317$	−3.59612e9	+	3.59612e9i	−0.356121	+	0.356121i	−0.862381	−	0.506260i	$-0.831028\pi$
$317$	−3.59612e9	+	3.59612e9i	−0.356121	+	0.356121i	0.506260	+	0.862381i	$0.331028\pi$
$318$	−4.55342e8	−	1.69936e9i	−0.0445276	−	0.166179i
$319$	−1.83340e6	+	491258.i	−0.000177049	+	4.74402e-5i
$320$	−4.32244e9	−	4.32244e9i	−0.412220	−	0.412220i
$321$	−3.73607e9	+	6.47107e9i	−0.351881	+	0.609475i
$322$	3.48030e9	−	2.00935e9i	0.323738	−	0.186910i
$323$	2.53083e9	−	9.44520e9i	0.232516	−	0.867762i
$324$		−	2.99384e9i		−	0.271674i
$325$	−7.59050e9	+	6.93579e9i	−0.680357	+	0.621674i
$326$	−3.23575e9			−0.286487
$327$	−1.44626e9	−	3.87523e8i	−0.126489	−	0.0338927i
$328$	−4.96050e9	−	8.59184e9i	−0.428579	−	0.742320i
$329$	1.74818e9	+	1.00931e9i	0.149212	+	0.0861474i
$330$	735850.	−	735850.i	6.20489e−5	−	6.20489e-5i
$331$	−3.06546e9	−	1.14405e10i	−0.255378	−	0.953084i	−0.967880	−	0.251414i	$-0.919105\pi$
$331$	−3.06546e9	−	1.14405e10i	−0.255378	−	0.953084i	0.712502	−	0.701670i	$-0.247562\pi$
$332$	−1.10440e10	+	2.95923e9i	−0.909023	+	0.243572i
$333$	−2.72393e9	−	2.72393e9i	−0.221523	−	0.221523i
$334$	−3.75154e9	+	6.49785e9i	−0.301456	+	0.522136i
$335$	−2.76856e10	+	1.59843e10i	−2.19824	+	1.26915i
$336$	−1.64833e8	+	6.15165e8i	−0.0129326	+	0.0482653i
$337$		−	1.80707e10i		−	1.40106i	−0.713625	−	0.700528i	$-0.752948\pi$
$337$		−	1.80707e10i		−	1.40106i	0.713625	−	0.700528i	$-0.247052\pi$
$338$	−2.51891e9	+	6.86050e9i	−0.192995	+	0.525641i
$339$	1.44259e10			1.09230
$340$	1.58714e10	+	4.25273e9i	1.18768	+	0.318238i
$341$	104783.	+	181490.i	7.74953e−6	+	1.34226e-5i
$342$	−1.95682e9	−	1.12977e9i	−0.143037	−	0.0825823i
$343$	7.46230e9	−	7.46230e9i	0.539133	−	0.539133i
$344$	4.01651e9	+	1.49898e10i	0.286823	+	1.07044i
$345$	−2.30075e10	+	6.16485e9i	−1.62403	+	0.435157i
$346$	−5.18962e7	−	5.18962e7i	−0.00362102	−	0.00362102i
$347$	3.46648e9	−	6.00412e9i	0.239095	−	0.414125i	−0.721360	−	0.692561i	$-0.756483\pi$
$347$	3.46648e9	−	6.00412e9i	0.239095	−	0.414125i	0.960455	+	0.278436i	$0.0898159\pi$
$348$	8.13914e9	−	4.69914e9i	0.554960	−	0.320406i
$349$	5.93671e9	−	2.21561e10i	0.400170	−	1.49345i	−0.412624	−	0.910901i	$-0.635388\pi$
$349$	5.93671e9	−	2.21561e10i	0.400170	−	1.49345i	0.812794	−	0.582552i	$-0.197946\pi$
$350$			3.23432e9i			0.215531i
$351$	1.10649e10	+	1.21094e10i	0.728985	+	0.797799i
$352$	2.36190e6			0.000153847
$353$	2.44215e9	+	6.54371e8i	0.157280	+	0.0421430i	0.336600	−	0.941648i	$-0.390723\pi$
$353$	2.44215e9	+	6.54371e8i	0.157280	+	0.0421430i	−0.179320	+	0.983791i	$0.557390\pi$
$354$	−9.70799e8	−	1.68147e9i	−0.0618182	−	0.107072i
$355$	1.47099e10	+	8.49276e9i	0.926181	+	0.534731i
$356$	−1.36216e10	+	1.36216e10i	−0.848060	+	0.848060i
$357$	1.72151e9	+	6.42478e9i	0.105983	+	0.395535i
$358$	1.64061e9	−	4.39600e8i	0.0998788	−	0.0267624i
$359$	1.45545e9	+	1.45545e9i	0.0876233	+	0.0876233i	0.749560	−	0.661937i	$-0.230265\pi$
$359$	1.45545e9	+	1.45545e9i	0.0876233	+	0.0876233i	−0.661937	+	0.749560i	$0.730265\pi$
$360$	4.66400e9	−	8.07828e9i	0.277682	−	0.480960i
$361$	7.59850e9	−	4.38700e9i	0.447403	−	0.258308i
$362$	3.67337e9	−	1.37092e10i	0.213910	−	0.798321i
$363$		−	1.31748e10i		−	0.758783i
$364$	−2.31771e9	−	4.46763e9i	−0.132024	−	0.254490i
$365$	1.48533e10			0.836857
$366$	6.92379e9	+	1.85522e9i	0.385851	+	0.103388i
$367$	−6.17317e8	−	1.06922e9i	−0.0340286	−	0.0589392i	0.848510	−	0.529180i	$-0.177500\pi$
$367$	−6.17317e8	−	1.06922e9i	−0.0340286	−	0.0589392i	−0.882538	+	0.470241i	$0.844167\pi$
$368$	−4.00297e9	−	2.31112e9i	−0.218269	−	0.126017i
$369$	5.04832e9	−	5.04832e9i	0.272296	−	0.272296i
$370$	2.78035e9	+	1.03764e10i	0.148351	+	0.553655i
$371$	−3.09469e9	+	8.29220e8i	−0.163351	+	0.0437698i
$372$	−7.33741e8	−	7.33741e8i	−0.0383152	−	0.0383152i
$373$	−8.16859e9	+	1.41484e10i	−0.421999	+	0.730924i	−0.996135	−	0.0878361i	$-0.972005\pi$
$373$	−8.16859e9	+	1.41484e10i	−0.421999	+	0.730924i	0.574136	+	0.818760i	$0.305338\pi$
$374$	1.82653e6	−	1.05455e6i	9.33557e−5	−	5.38989e-5i
$375$	−4.22021e8	+	1.57500e9i	−0.0213407	+	0.0796446i
$376$			7.78638e9i			0.389569i
$377$	−7.50659e9	+	2.36916e10i	−0.371602	+	1.17281i
$378$	5.15981e9			0.252736
$379$	−1.96272e10	−	5.25909e9i	−0.951265	−	0.254891i	−0.250366	−	0.968151i	$-0.580551\pi$
$379$	−1.96272e10	−	5.25909e9i	−0.951265	−	0.254891i	−0.700899	+	0.713260i	$0.747218\pi$
$380$	−6.89755e9	−	1.19469e10i	−0.330796	−	0.572955i
$381$	2.16292e10	+	1.24876e10i	1.02646	+	0.592626i
$382$	1.05462e10	−	1.05462e10i	0.495272	−	0.495272i
$383$	3.93445e9	+	1.46836e10i	0.182847	+	0.682395i	0.995081	+	0.0990634i	$0.0315847\pi$
$383$	3.93445e9	+	1.46836e10i	0.182847	+	0.682395i	−0.812234	+	0.583332i	$0.801749\pi$
$384$	−1.27034e10	+	3.40386e9i	−0.584245	+	0.156548i
$385$	−1.34005e6	−	1.34005e6i	−6.09929e−5	−	6.09929e-5i
$386$	−1.10913e10	+	1.92107e10i	−0.499612	+	0.865353i
$387$	−9.67139e9	+	5.58378e9i	−0.431166	+	0.248934i
$388$	6.32421e9	−	2.36023e10i	0.279048	−	1.04142i
$389$		−	7.03366e9i		−	0.307173i	−0.988135	−	0.153586i	$-0.950918\pi$
$389$		−	7.03366e9i		−	0.307173i	0.988135	−	0.153586i	$-0.0490823\pi$
$390$	−2.93042e9	−	1.33069e10i	−0.126669	−	0.575197i
$391$	−4.82745e10			−2.06543
$392$	1.77814e10	+	4.76451e9i	0.753046	+	0.201778i
$393$	2.06220e9	+	3.57183e9i	0.0864491	+	0.149734i
$394$	−1.13041e10	−	6.52641e9i	−0.469084	−	0.270826i
$395$	4.07180e10	−	4.07180e10i	1.67262	−	1.67262i
$396$	276158.	+	1.03064e6i	1.12299e−5	+	4.19107e-5i
$397$	2.59930e10	−	6.96482e9i	1.04639	−	0.280380i	0.305633	−	0.952149i	$-0.401132\pi$
$397$	2.59930e10	−	6.96482e9i	1.04639	−	0.280380i	0.740761	+	0.671769i	$0.234465\pi$
$398$	−1.28797e10	−	1.28797e10i	−0.513301	−	0.513301i
$399$	2.79214e9	−	4.83613e9i	0.110166	−	0.190812i
$400$	3.22165e9	−	1.86002e9i	0.125846	−	0.0726570i
$401$	−8.86544e9	+	3.30863e10i	−0.342865	+	1.27959i	0.552222	+	0.833697i	$0.313780\pi$
$401$	−8.86544e9	+	3.30863e10i	−0.342865	+	1.27959i	−0.895087	+	0.445891i	$0.852887\pi$
$402$		−	2.03181e10i		−	0.777998i
$403$	2.74117e9	+	1.23547e8i	0.103924	+	0.00468396i
$404$	−1.13284e10			−0.425248
$405$	−1.42572e10	−	3.82019e9i	−0.529923	−	0.141992i
$406$	3.90876e9	+	6.77018e9i	0.143858	+	0.249170i
$407$	−2.61438e6	−	1.50942e6i	−9.52778e−5	−	5.50087e-5i
$408$	−1.81418e10	+	1.81418e10i	−0.654694	+	0.654694i
$409$	−4.89265e9	−	1.82596e10i	−0.174844	−	0.652527i	−0.996578	−	0.0826561i	$-0.973660\pi$
$409$	−4.89265e9	−	1.82596e10i	−0.174844	−	0.652527i	0.821734	−	0.569871i	$-0.193007\pi$
$410$	−1.92308e10	+	5.15288e9i	−0.680553	+	0.182354i
$411$	5.66315e9	+	5.66315e9i	0.198468	+	0.198468i
$412$	−1.03391e10	+	1.79078e10i	−0.358833	+	0.621516i
$413$	−3.06212e9	+	1.76792e9i	−0.105250	+	0.0607661i
$414$	−2.88714e9	+	1.07750e10i	−0.0982804	+	0.366788i
$415$			5.63695e10i			1.90043i
$416$	1.66529e10	−	2.60588e10i	0.556053	−	0.870123i
$417$	−1.17620e9			−0.0388988
$418$	−1.71038e6	−	458296.i	−5.60258e−5	−	1.50121e-5i
$419$	−1.36328e10	−	2.36128e10i	−0.442314	−	0.766110i	0.555547	−	0.831485i	$-0.312509\pi$
$419$	−1.36328e10	−	2.36128e10i	−0.442314	−	0.766110i	−0.997861	+	0.0653754i	$0.979176\pi$
$420$	8.12648e9	+	4.69182e9i	0.261159	+	0.150780i
$421$	−2.01867e10	+	2.01867e10i	−0.642595	+	0.642595i	−0.951193	−	0.308598i	$-0.900140\pi$
$421$	−2.01867e10	+	2.01867e10i	−0.642595	+	0.642595i	0.308598	+	0.951193i	$0.400140\pi$
$422$	−3.83807e9	−	1.43239e10i	−0.121022	−	0.451659i
$423$	−5.41234e9	+	1.45023e9i	−0.169053	+	0.0452977i
$424$	−8.73853e9	−	8.73853e9i	−0.270380	−	0.270380i
$425$	1.94260e10	−	3.36469e10i	0.595427	−	1.03131i
$426$	−9.34909e9	+	5.39770e9i	−0.283878	+	0.163897i
$427$	3.37853e9	−	1.26089e10i	0.101629	−	0.379284i
$428$			2.13646e10i			0.636678i
$429$	3.22652e6	+	2.06191e6i	9.52588e−5	+	6.08752e-5i
$430$	3.11423e10			0.910912
$431$	4.82111e9	+	1.29181e9i	0.139713	+	0.0374361i	0.327998	−	0.944678i	$-0.393626\pi$
$431$	4.82111e9	+	1.29181e9i	0.139713	+	0.0374361i	−0.188285	+	0.982114i	$0.560293\pi$
$432$	−2.96735e9	−	5.13960e9i	−0.0851989	−	0.147569i
$433$	3.40386e10	+	1.96522e10i	0.968322	+	0.559061i	0.898724	−	0.438514i	$-0.144495\pi$
$433$	3.40386e10	+	1.96522e10i	0.968322	+	0.559061i	0.0695981	+	0.997575i	$0.477828\pi$
$434$	6.10329e8	−	6.10329e8i	0.0172030	−	0.0172030i
$435$	−1.19924e10	−	4.47562e10i	−0.334926	−	1.24996i
$436$	−4.13518e9	+	1.10802e9i	−0.114432	+	0.0306620i
$437$	2.86587e10	+	2.86587e10i	0.785834	+	0.785834i
$438$	−4.72012e9	+	8.17548e9i	−0.128250	+	0.222135i
$439$	3.93395e10	−	2.27127e10i	1.05918	−	0.611520i	0.133977	−	0.990984i	$-0.457225\pi$
$439$	3.93395e10	−	2.27127e10i	1.05918	−	0.611520i	0.925206	+	0.379465i	$0.123892\pi$
$440$	1.89196e6	−	7.06091e6i	5.04780e−5	−	0.000188386i
$441$			1.32473e10i			0.350246i
$442$	1.24339e9	−	2.75873e10i	0.0325775	−	0.722805i
$443$	−1.80124e10			−0.467688			−0.233844	−	0.972274i	$-0.575130\pi$
$443$	−1.80124e10			−0.467688			−0.233844	+	0.972274i	$0.575130\pi$
$444$	1.44383e10	+	3.86874e9i	0.371523	+	0.0995493i
$445$	4.74868e10	+	8.22495e10i	1.21097	+	2.09746i
$446$	−6.05080e9	−	3.49343e9i	−0.152923	−	0.0882902i
$447$	2.17268e10	−	2.17268e10i	0.544208	−	0.544208i
$448$	−1.83119e9	−	6.83408e9i	−0.0454591	−	0.169656i
$449$	6.40994e10	−	1.71754e10i	1.57713	−	0.422592i	0.639097	−	0.769126i	$-0.279308\pi$
$449$	6.40994e10	−	1.71754e10i	1.57713	−	0.422592i	0.938038	+	0.346534i	$0.112641\pi$
$450$	−6.34824e9	−	6.34824e9i	−0.154811	−	0.154811i
$451$	2.79744e6	−	4.84530e6i	6.76167e−5	−	0.000117116i
$452$	3.57209e10	−	2.06235e10i	0.855792	−	0.494092i
$453$	−9.60441e9	+	3.58441e10i	−0.228075	+	0.851188i
$454$			2.98087e10i			0.701649i
$455$	−2.42330e10	+	5.33656e9i	−0.565408	+	0.124513i
$456$	2.15401e10			0.498182
$457$	−8.40866e10	−	2.25309e10i	−1.92780	−	0.516552i	−0.980654	−	0.195747i	$-0.937287\pi$
$457$	−8.40866e10	−	2.25309e10i	−1.92780	−	0.516552i	−0.947145	−	0.320805i	$-0.896047\pi$
$458$	−2.55145e9	−	4.41924e9i	−0.0579862	−	0.100435i
$459$	−5.36779e10	−	3.09910e10i	−1.20933	−	0.698208i
$460$	−4.81571e10	+	4.81571e10i	−1.07555	+	1.07555i
$461$	2.68844e9	+	1.00334e10i	0.0595246	+	0.222149i	0.989280	−	0.146028i	$-0.0466489\pi$
$461$	2.68844e9	+	1.00334e10i	0.0595246	+	0.222149i	−0.929756	+	0.368176i	$0.879982\pi$
$462$	1.16343e6	−	311740.i	2.55372e−5	−	6.84267e-6i
$463$	−1.00182e10	−	1.00182e10i	−0.218004	−	0.218004i	0.589653	−	0.807657i	$-0.299265\pi$
$463$	−1.00182e10	−	1.00182e10i	−0.218004	−	0.218004i	−0.807657	+	0.589653i	$0.799265\pi$
$464$	4.49578e9	−	7.78691e9i	0.0969913	−	0.167994i
$465$	−4.43046e9	+	2.55793e9i	−0.0947627	+	0.0547113i
$466$	−1.03743e9	+	3.87174e9i	−0.0219996	+	0.0821037i
$467$		−	8.21272e10i		−	1.72671i	−0.504598	−	0.863355i	$-0.668359\pi$
$467$		−	8.21272e10i		−	1.72671i	0.504598	−	0.863355i	$-0.331641\pi$
$468$	1.33181e10	+	4.21980e9i	0.277625	+	0.0879646i
$469$	−3.70012e10			−0.764758
$470$	1.50931e10	+	4.04417e9i	0.309304	+	0.0828779i
$471$	−2.19255e9	−	3.79761e9i	−0.0445519	−	0.0771661i
$472$	−1.18114e10	−	6.81933e9i	−0.237977	−	0.137396i
$473$	−6.18830e6	+	6.18830e6i	−0.000123631	+	0.000123631i
$474$	9.47235e9	+	3.53513e10i	0.187648	+	0.700313i
$475$	−3.15073e10	+	8.44235e9i	−0.618923	+	0.165840i
$476$	1.34477e10	+	1.34477e10i	0.261951	+	0.261951i
$477$	4.44661e9	−	7.70176e9i	0.0858926	−	0.148770i
$478$	1.34977e10	−	7.79288e9i	0.258551	−	0.149275i
$479$	2.51592e9	−	9.38952e9i	0.0477919	−	0.178362i	−0.937904	−	0.346894i	$-0.887236\pi$
$479$	2.51592e9	−	9.38952e9i	0.0477919	−	0.178362i	0.985696	+	0.168533i	$0.0539029\pi$
$480$			5.76576e10i			1.08615i
$481$	−3.50865e10	+	1.82021e10i	−0.655480	+	0.340050i
$482$	4.99241e10			0.924958
$483$	−2.66295e10	−	7.13534e9i	−0.489299	−	0.131107i
$484$	−1.88349e10	−	3.26230e10i	−0.343227	−	0.594487i
$485$	−1.04328e11	−	6.02339e10i	−1.88553	−	1.08861i
$486$	−1.72383e10	+	1.72383e10i	−0.308994	+	0.308994i
$487$	7.39962e9	+	2.76158e10i	0.131551	+	0.490954i	0.999988	−	0.00484446i	$-0.00154205\pi$
$487$	7.39962e9	+	2.76158e10i	0.131551	+	0.490954i	−0.868437	+	0.495799i	$0.834875\pi$
$488$	4.86358e10	−	1.30319e10i	0.857584	−	0.229789i
$489$	1.56961e10	+	1.56961e10i	0.274509	+	0.274509i
$490$	1.84710e10	−	3.19927e10i	0.320410	−	0.554966i
$491$	−1.22139e10	+	7.05172e9i	−0.210150	+	0.121330i	−0.601381	−	0.798962i	$-0.705383\pi$
$491$	−1.22139e10	+	7.05172e9i	−0.210150	+	0.121330i	0.391231	+	0.920293i	$0.372049\pi$
$492$	−7.17003e9	+	2.67589e10i	−0.122366	+	0.456676i
$493$		−	9.39076e10i		−	1.58969i
$494$	−1.71157e10	+	1.56394e10i	−0.287400	+	0.262610i
$495$	5.26045e6			8.76197e−5
$496$	−9.58933e8	−	2.56945e8i	−0.0158439	−	0.00424535i
$497$	9.82972e9	+	1.70256e10i	0.161107	+	0.279046i
$498$	−3.10266e10	−	1.79132e10i	−0.504449	−	0.291244i
$499$	−1.31299e10	+	1.31299e10i	−0.211767	+	0.211767i	−0.805018	−	0.593251i	$-0.797844\pi$
$499$	−1.31299e10	+	1.31299e10i	−0.211767	+	0.211767i	0.593251	+	0.805018i	$0.297844\pi$
$500$	1.20665e9	+	4.50330e9i	0.0193065	+	0.0720527i
$501$	4.97182e10	−	1.33219e10i	0.789158	−	0.211454i
$502$	−1.98281e10	−	1.98281e10i	−0.312225	−	0.312225i
$503$	−5.51619e9	+	9.55432e9i	−0.0861722	+	0.149255i	−0.905890	−	0.423513i	$-0.860797\pi$
$503$	−5.51619e9	+	9.55432e9i	−0.0861722	+	0.149255i	0.819718	+	0.572767i	$0.194130\pi$
$504$	9.34999e9	−	5.39822e9i	0.144907	−	0.0836621i
$505$	−1.44552e10	+	5.39477e10i	−0.222259	+	0.829483i
$506$			8.74180e6i			0.000133352i
$507$	4.54981e10	−	2.10604e10i	0.688590	−	0.318739i
$508$	7.14101e10			1.07227
$509$	2.38665e10	+	6.39502e9i	0.355565	+	0.0952732i	0.432180	−	0.901788i	$-0.357745\pi$
$509$	2.38665e10	+	6.39502e9i	0.355565	+	0.0952732i	−0.0766152	+	0.997061i	$0.524411\pi$
$510$	2.57432e10	+	4.45885e10i	0.380524	+	0.659086i
$511$	1.48883e10	+	8.59578e9i	0.218355	+	0.126067i
$512$	−1.51468e10	+	1.51468e10i	−0.220416	+	0.220416i
$513$	1.34684e10	+	5.02646e10i	0.194467	+	0.725760i
$514$	5.28120e10	−	1.41509e10i	0.756624	−	0.202737i
$515$	7.20870e10	+	7.20870e10i	1.02477	+	1.02477i
$516$	2.16666e10	−	3.75277e10i	0.305628	−	0.529363i
$517$	−3.80278e6	+	2.19553e6i	−5.32278e−5	+	3.07311e-5i
$518$	−3.21804e9	+	1.20099e10i	−0.0446964	+	0.166809i
$519$			5.03480e8i			0.00693926i
$520$	−6.45634e10	−	7.06580e10i	−0.883025	−	0.966379i
$521$	4.68604e9			0.0635997			0.0317999	−	0.999494i	$-0.489876\pi$
$521$	4.68604e9			0.0635997			0.0317999	+	0.999494i	$0.489876\pi$
$522$	−2.09604e10	−	5.61631e9i	−0.282304	−	0.0756431i
$523$	2.79980e10	+	4.84940e10i	0.374214	+	0.648158i	0.990209	−	0.139592i	$-0.0445791\pi$
$523$	2.79980e10	+	4.84940e10i	0.374214	+	0.648158i	−0.615995	+	0.787750i	$0.711246\pi$
$524$	1.02127e10	+	5.89631e9i	0.135461	+	0.0782087i
$525$	1.56892e10	−	1.56892e10i	0.206520	−	0.206520i
$526$	1.33594e10	+	4.98579e10i	0.174519	+	0.651315i
$527$	−1.00151e10	+	2.68353e9i	−0.129841	+	0.0347908i
$528$	−979597.	−	979597.i	−1.26041e−5	−	1.26041e-5i
$529$	6.08888e10	−	1.05463e11i	0.777526	−	1.34671i
$530$	−2.14774e10	+	1.24000e10i	−0.272194	+	0.157151i
$531$	2.54023e9	−	9.48028e9i	0.0319518	−	0.119246i
$532$		−	1.59668e10i		−	0.199329i
$533$	−3.37345e10	−	6.50266e10i	−0.417989	−	0.805716i
$534$	−6.03619e10			−0.742331
$535$	1.01742e11	+	2.72616e10i	1.24189	+	0.332764i
$536$	−7.13617e10	−	1.23602e11i	−0.864582	−	1.49750i
$537$	−1.00908e10	−	5.82591e9i	−0.121346	−	0.0700594i
$538$	2.46415e9	−	2.46415e9i	0.0294129	−	0.0294129i
$539$	2.68691e6	+	1.00277e7i	3.18345e−5	+	0.000118808i
$540$	−8.44630e10	+	2.26318e10i	−0.993325	+	0.266161i
$541$	2.59605e10	+	2.59605e10i	0.303057	+	0.303057i	0.842209	−	0.539152i	$-0.181255\pi$
$541$	2.59605e10	+	2.59605e10i	0.303057	+	0.303057i	−0.539152	+	0.842209i	$0.681255\pi$
$542$	−6.16023e9	+	1.06698e10i	−0.0713838	+	0.123640i
$543$	−8.43201e10	+	4.86822e10i	−0.969911	+	0.559978i
$544$	−3.02444e10	+	1.12874e11i	−0.345342	+	1.28883i
$545$			2.11063e10i			0.239235i
$546$	4.76351e9	−	1.50341e10i	0.0535989	−	0.169164i
$547$	−2.92538e10			−0.326763			−0.163381	−	0.986563i	$-0.552240\pi$
$547$	−2.92538e10			−0.326763			−0.163381	+	0.986563i	$0.552240\pi$
$548$	2.21190e10	+	5.92678e9i	0.245270	+	0.0657198i
$549$	1.81171e10	+	3.13797e10i	0.199434	+	0.345429i
$550$	−6.09294e6	−	3.51776e6i	−6.65850e−5	−	3.84429e-5i
$551$	−5.57493e10	+	5.57493e10i	−0.604829	+	0.604829i
$552$	−2.75229e10	−	1.02717e11i	−0.296441	−	1.10633i
$553$	6.43781e10	−	1.72500e10i	0.688394	−	0.184455i
$554$	−3.73693e9	−	3.73693e9i	−0.0396712	−	0.0396712i
$555$	3.68472e10	−	6.38212e10i	0.388358	−	0.672656i
$556$	−2.91246e9	+	1.68151e9i	−0.0304762	+	0.0175954i
$557$	−1.39312e10	+	5.19920e10i	−0.144733	+	0.540152i	0.855034	+	0.518572i	$0.173536\pi$
$557$	−1.39312e10	+	5.19920e10i	−0.144733	+	0.540152i	−0.999767	+	0.0215796i	$0.993130\pi$
$558$			2.39588e9i			0.0247131i
$559$	2.46440e10	+	1.11907e11i	0.252385	+	1.14607i
$560$	8.97756e9			0.0912864
$561$	−1.39757e7	−	3.74477e6i	−0.000141098	−	3.78071e-5i
$562$	−2.10797e10	−	3.65112e10i	−0.211310	−	0.366000i
$563$	−1.31809e10	−	7.61002e9i	−0.131194	−	0.0757447i	0.432967	−	0.901410i	$-0.357467\pi$
$563$	−1.31809e10	−	7.61002e9i	−0.131194	−	0.0757447i	−0.564160	+	0.825665i	$0.690800\pi$
$564$	1.53741e10	−	1.53741e10i	0.151940	−	0.151940i
$565$	−5.26318e10	−	1.96425e11i	−0.516481	−	1.92753i
$566$	−1.15318e10	+	3.08994e9i	−0.112365	+	0.0301081i
$567$	−1.20800e10	−	1.20800e10i	−0.116878	−	0.116878i
$568$	−3.79159e10	+	6.56722e10i	−0.364274	+	0.630940i
$569$	−8.29129e10	+	4.78698e10i	−0.790994	+	0.456681i	−0.840312	−	0.542102i	$-0.817628\pi$
$569$	−8.29129e10	+	4.78698e10i	−0.790994	+	0.456681i	0.0493182	+	0.998783i	$0.484295\pi$
$570$	1.11877e10	−	4.17532e10i	0.105985	−	0.395540i
$571$		−	9.74996e10i		−	0.917188i	−0.888646	−	0.458594i	$-0.848353\pi$
$571$		−	9.74996e10i		−	0.917188i	0.888646	−	0.458594i	$-0.151647\pi$
$572$	1.09371e7	+	492948.i	0.000102169	+	4.60487e-6i
$573$	−1.02316e11			−0.949131
$574$	−2.22582e10	−	5.96407e9i	−0.205042	−	0.0549408i
$575$	8.05171e10	+	1.39460e11i	0.736575	+	1.27579i
$576$	1.70080e10	+	9.81956e9i	0.154512	+	0.0892077i
$577$	−8.77909e9	+	8.77909e9i	−0.0792039	+	0.0792039i	−0.745599	−	0.666395i	$-0.767836\pi$
$577$	−8.77909e9	+	8.77909e9i	−0.0792039	+	0.0792039i	0.666395	+	0.745599i	$0.267836\pi$
$578$	1.08317e10	+	4.04246e10i	0.0970481	+	0.362188i
$579$	1.46990e11	−	3.93859e10i	1.30790	−	0.350450i
$580$	−9.36792e10	−	9.36792e10i	−0.827811	−	0.827811i
$581$	−3.26217e10	+	5.65024e10i	−0.286287	+	0.495864i
$582$	6.63073e10	−	3.82825e10i	0.577922	−	0.333664i
$583$	1.80378e6	−	6.73181e6i	1.56138e−5	−	5.82717e-5i
$584$			6.63124e10i			0.570090i
$585$	3.70895e10	−	5.80385e10i	0.316685	−	0.495556i
$586$	7.92471e10			0.672037
$587$	−1.02094e11	−	2.73561e10i	−0.859902	−	0.230410i	−0.198186	−	0.980165i	$-0.563505\pi$
$587$	−1.02094e11	−	2.73561e10i	−0.859902	−	0.230410i	−0.661716	+	0.749755i	$0.730172\pi$
$588$	−2.57017e10	−	4.45166e10i	−0.215007	−	0.372403i
$589$	7.53867e9	+	4.35245e9i	0.0626373	+	0.0361637i
$590$	−1.93533e10	+	1.93533e10i	−0.159715	+	0.159715i
$591$	2.31757e10	+	8.64929e10i	0.189969	+	0.708975i
$592$	1.38135e10	−	3.70132e9i	0.112465	−	0.0301349i
$593$	3.01479e10	+	3.01479e10i	0.243803	+	0.243803i	0.818421	−	0.574618i	$-0.194850\pi$
$593$	3.01479e10	+	3.01479e10i	0.243803	+	0.243803i	−0.574618	+	0.818421i	$0.694850\pi$
$594$	−5.61200e6	+	9.72027e6i	−4.50788e−5	+	7.80787e-5i
$595$	8.11998e10	−	4.68808e10i	0.647869	−	0.374047i
$596$	2.27382e10	−	8.48600e10i	0.180207	−	0.672540i
$597$			1.24955e11i			0.983682i
$598$	9.64482e10	+	6.16353e10i	0.754205	+	0.481975i
$599$	3.76391e10			0.292369			0.146185	−	0.989257i	$-0.453301\pi$
$599$	3.76391e10			0.292369			0.146185	+	0.989257i	$0.453301\pi$
$600$	8.26681e10	+	2.21509e10i	0.637871	+	0.170917i
$601$	−2.66027e10	−	4.60773e10i	−0.203905	−	0.353174i	0.745878	−	0.666082i	$-0.232030\pi$
$601$	−2.66027e10	−	4.60773e10i	−0.203905	−	0.353174i	−0.949783	+	0.312908i	$0.898697\pi$
$602$	3.12157e10	+	1.80224e10i	0.237677	+	0.137223i
$603$	7.26250e10	−	7.26250e10i	0.549309	−	0.549309i
$604$	2.74612e10	+	1.02487e11i	0.206335	+	0.770051i
$605$	−1.79390e11	+	4.80674e10i	−1.33899	+	0.358780i
$606$	−2.51000e10	−	2.51000e10i	−0.186116	−	0.186116i
$607$	−6.97180e10	+	1.20755e11i	−0.513559	+	0.889510i	0.486318	+	0.873782i	$0.338340\pi$
$607$	−6.97180e10	+	1.20755e11i	−0.513559	+	0.889510i	−0.999876	+	0.0157277i	$0.994994\pi$
$608$	8.49635e10	−	4.90537e10i	0.621753	−	0.358969i
$609$	1.38803e10	−	5.18019e10i	0.100909	−	0.376596i
$610$		−	1.01044e11i		−	0.729778i
$611$	−2.58870e9	+	5.74359e10i	−0.0185745	+	0.412115i
$612$	−5.27897e10			−0.376308
$613$	−4.28834e10	−	1.14906e10i	−0.303701	−	0.0813766i	0.103750	−	0.994603i	$-0.466916\pi$
$613$	−4.28834e10	−	1.14906e10i	−0.303701	−	0.0813766i	−0.407452	+	0.913227i	$0.633582\pi$
$614$	−5.05974e9	−	8.76373e9i	−0.0356004	−	0.0616617i
$615$	1.18281e11	+	6.82898e10i	0.826830	+	0.477370i
$616$	5.98266e6	−	5.98266e6i	4.15500e−5	−	4.15500e-5i
$617$	2.00856e9	+	7.49606e9i	0.0138594	+	0.0517240i	0.972509	−	0.232864i	$-0.0748098\pi$
$617$	2.00856e9	+	7.49606e9i	0.0138594	+	0.0517240i	−0.958650	+	0.284588i	$0.908143\pi$
$618$	−6.25858e10	+	1.67698e10i	−0.429064	+	0.114967i
$619$	−1.54784e11	−	1.54784e11i	−1.05430	−	1.05430i	−0.998439	−	0.0558600i	$-0.982210\pi$
$619$	−1.54784e11	−	1.54784e11i	−1.05430	−	1.05430i	−0.0558600	−	0.998439i	$-0.517790\pi$
$620$	−7.31371e9	+	1.26677e10i	−0.0494961	+	0.0857298i
$621$	2.22485e11	−	1.28452e11i	1.49601	−	0.863720i
$622$	−2.05718e10	+	7.67750e10i	−0.137439	+	0.512930i
$623$			1.09925e11i			0.729698i
$624$	−1.77147e10	+	3.90110e9i	−0.116841	+	0.0257305i
$625$	1.63612e11			1.07225
$626$	−3.76017e10	−	1.00754e10i	−0.244856	−	0.0656090i
$627$	6.07368e6	+	1.05199e7i	3.92990e−5	+	6.80679e-5i
$628$	−1.08582e10	−	6.26901e9i	−0.0698105	−	0.0403051i
$629$	1.05612e11	−	1.05612e11i	0.674697	−	0.674697i
$630$	−5.60757e9	−	2.09277e10i	−0.0355969	−	0.132850i
$631$	−1.85734e11	+	4.97674e10i	−1.17159	+	0.313926i	−0.791585	−	0.611059i	$-0.790744\pi$
$631$	−1.85734e11	+	4.97674e10i	−1.17159	+	0.313926i	−0.380003	+	0.924985i	$0.624077\pi$
$632$	1.81785e11	+	1.81785e11i	1.13944	+	1.13944i
$633$	−5.08650e10	+	8.81008e10i	−0.316814	+	0.548738i
$634$	−3.94594e10	+	2.27819e10i	−0.244227	+	0.141004i
$635$	9.11207e10	−	3.40067e11i	0.560431	−	2.09156i
$636$			3.45082e10i			0.210909i
$637$	1.29580e11	+	4.10569e10i	0.787008	+	0.249361i
$638$	−1.70053e7			−0.000102636
$639$	−5.27109e10	−	1.41239e10i	−0.316153	−	0.0847129i
$640$	9.26950e10	+	1.60552e11i	0.552505	+	0.956967i
$641$	−1.41496e11	−	8.16929e10i	−0.838132	−	0.483896i	0.0184967	−	0.999829i	$-0.494112\pi$
$641$	−1.41496e11	−	8.16929e10i	−0.838132	−	0.483896i	−0.856629	+	0.515933i	$0.827445\pi$
$642$	−4.73370e10	+	4.73370e10i	−0.278651	+	0.278651i
$643$	−3.27802e10	−	1.22337e11i	−0.191764	−	0.715673i	−0.993081	−	0.117433i	$-0.962533\pi$
$643$	−3.27802e10	−	1.22337e11i	−0.191764	−	0.715673i	0.801317	−	0.598240i	$-0.204133\pi$
$644$	−7.61398e10	+	2.04016e10i	−0.442658	+	0.118610i
$645$	−1.51066e11	−	1.51066e11i	−0.872828	−	0.872828i
$646$	4.38034e10	−	7.58697e10i	0.251523	−	0.435650i
$647$	−2.85066e11	+	1.64583e11i	−1.62678	+	0.939220i	−0.641731	+	0.766930i	$0.721783\pi$
$647$	−2.85066e11	+	1.64583e11i	−1.62678	+	0.939220i	−0.985046	+	0.172290i	$0.944883\pi$
$648$	1.70552e10	−	6.36510e10i	0.0967292	−	0.360998i
$649$		−	7.69141e6i		−	4.33538e-5i
$650$	−8.17706e10	+	4.24209e10i	−0.458083	+	0.237644i
$651$	−5.92122e9			−0.0329676
$652$	6.13057e10	+	1.64268e10i	0.339243	+	0.0908998i
$653$	−1.21647e11	−	2.10700e11i	−0.669037	−	1.15881i	−0.978174	−	0.207789i	$-0.933373\pi$
$653$	−1.21647e11	−	2.10700e11i	−0.669037	−	1.15881i	0.309136	−	0.951018i	$-0.399960\pi$
$654$	−1.16172e10	−	6.70721e9i	−0.0635026	−	0.0366632i
$655$	4.11108e10	−	4.11108e10i	0.223352	−	0.223352i
$656$	6.85974e9	+	2.56009e10i	0.0370418	+	0.138242i
$657$	−4.60940e10	+	1.23509e10i	−0.247391	+	0.0662881i
$658$	1.27883e10	+	1.27883e10i	0.0682193	+	0.0682193i
$659$	−1.26763e11	+	2.19561e11i	−0.672129	+	1.16416i	0.305171	+	0.952298i	$0.401286\pi$
$659$	−1.26763e11	+	2.19561e11i	−0.672129	+	1.16416i	−0.977299	+	0.211863i	$0.932047\pi$
$660$	−1.76773e7	+	1.02060e7i	−9.31624e−5	+	5.37874e-5i
$661$	6.30584e9	−	2.35337e10i	0.0330322	−	0.123278i	−0.947441	−	0.319930i	$-0.896340\pi$
$661$	6.30584e9	−	2.35337e10i	0.0330322	−	0.123278i	0.980473	+	0.196653i	$0.0630071\pi$
$662$		−	1.06113e11i		−	0.552507i
$663$	−1.39853e11	+	1.27790e11i	−0.723800	+	0.661369i
$664$	−2.51661e11			−1.29463
$665$	−7.60364e10	−	2.03739e10i	−0.388808	−	0.104181i
$666$	−1.72564e10	−	2.98890e10i	−0.0877109	−	0.151920i
$667$	3.37082e11	+	1.94615e11i	1.70307	+	0.983268i
$668$	1.04065e11	−	1.04065e11i	0.522637	−	0.522637i
$669$	1.24054e10	+	4.62975e10i	0.0619307	+	0.231128i
$670$	−2.76654e11	+	7.41292e10i	−1.37290	+	0.367866i
$671$	2.00785e7	+	2.00785e7i	9.90470e−5	+	9.90470e-5i
$672$	−3.33671e10	+	5.77936e10i	−0.163622	+	0.283402i
$673$	−7.14371e10	+	4.12442e10i	−0.348228	+	0.201049i	−0.663904	−	0.747817i	$-0.731102\pi$
$673$	−7.14371e10	+	4.12442e10i	−0.348228	+	0.201049i	0.315677	+	0.948867i	$0.397769\pi$
$674$	4.19027e10	−	1.56383e11i	0.203050	−	0.757792i
$675$			2.06759e11i			0.995979i
$676$	8.25525e10	−	1.17194e11i	0.395315	−	0.561200i
$677$	8.25644e10			0.393041			0.196521	−	0.980500i	$-0.437036\pi$
$677$	8.25644e10			0.393041			0.196521	+	0.980500i	$0.437036\pi$
$678$	1.24841e11	+	3.34510e10i	0.590796	+	0.158303i
$679$	−6.97161e10	−	1.20752e11i	−0.327985	−	0.568087i
$680$	3.13210e11	+	1.80832e11i	1.46487	+	0.845744i
$681$	1.44597e11	−	1.44597e11i	0.672314	−	0.672314i
$682$	485947.	+	1.81358e6i	2.24622e−6	+	8.38300e-6i
$683$	2.23120e11	−	5.97849e10i	1.02531	−	0.274732i	0.293298	−	0.956021i	$-0.405247\pi$
$683$	2.23120e11	−	5.97849e10i	1.02531	−	0.274732i	0.732014	+	0.681289i	$0.238580\pi$
$684$	3.13392e10	+	3.13392e10i	0.143174	+	0.143174i
$685$	5.64486e10	−	9.77719e10i	0.256384	−	0.444070i
$686$	8.18820e10	−	4.72746e10i	0.369736	−	0.213467i
$687$	−9.06035e9	+	3.38137e10i	−0.0406741	+	0.151798i
$688$		−	4.14580e10i		−	0.185035i
$689$	−6.15542e10	−	6.73647e10i	−0.273137	−	0.298920i
$690$	−2.13401e11			−0.941456
$691$	1.98667e11	+	5.32326e10i	0.871391	+	0.233489i	0.666689	−	0.745336i	$-0.267711\pi$
$691$	1.98667e11	+	5.32326e10i	0.871391	+	0.233489i	0.204702	+	0.978824i	$0.434377\pi$
$692$	7.19783e8	+	1.24670e9i	0.00313890	+	0.00543673i
$693$	5.27285e6	+	3.04428e6i	2.28619e−5	+	1.31993e-5i
$694$	4.39212e10	−	4.39212e10i	0.189337	−	0.189337i
$695$	4.29128e9	+	1.60153e10i	0.0183928	+	0.0686428i
$696$	1.99814e11	−	5.35399e10i	0.851507	−	0.228161i
$697$	1.95732e11	+	1.95732e11i	0.829338	+	0.829338i
$698$	1.02752e11	−	1.77972e11i	0.432881	−	0.749771i
$699$	2.38136e10	−	1.37488e10i	0.0997509	−	0.0575912i
$700$	1.64195e10	−	6.12784e10i	0.0683861	−	0.255220i
$701$		−	7.78379e10i		−	0.322344i	−0.986926	−	0.161172i	$-0.948473\pi$
$701$		−	7.78379e10i		−	0.322344i	0.986926	−	0.161172i	$-0.0515273\pi$
$702$	6.76755e10	+	1.30451e11i	0.278665	+	0.537156i
$703$	−1.25395e11			−0.513403
$704$	1.48660e7	+	3.98334e6i	6.05207e−5	+	1.62165e-5i
$705$	−5.35964e10	−	9.28317e10i	−0.216960	−	0.375785i
$706$	1.96168e10	+	1.13258e10i	0.0789605	+	0.0455879i
$707$	−4.57095e10	+	4.57095e10i	−0.182949	+	0.182949i
$708$	9.85683e9	+	3.67862e10i	0.0392287	+	0.146404i
$709$	5.37282e10	−	1.43964e10i	0.212627	−	0.0569731i	−0.150933	−	0.988544i	$-0.548228\pi$
$709$	5.37282e10	−	1.43964e10i	0.212627	−	0.0569731i	0.363560	+	0.931571i	$0.381561\pi$
$710$	1.07605e11	+	1.07605e11i	0.423449	+	0.423449i
$711$	−9.25017e10	+	1.60218e11i	−0.361969	+	0.626949i
$712$	−3.67202e11	+	2.12004e11i	−1.42885	+	0.824945i
$713$	1.11227e10	−	4.15106e10i	0.0430381	−	0.160620i
$714$			5.95915e10i			0.229294i
$715$	1.63035e7	−	5.14555e7i	6.23816e−5	−	0.000196883i
$716$	−3.33152e10			−0.126762
$717$	−1.03277e11	−	2.76730e10i	−0.390775	−	0.104708i
$718$	9.22046e9	+	1.59703e10i	0.0346940	+	0.0600918i
$719$	4.22957e11	+	2.44194e11i	1.58264	+	0.913735i	0.994473	+	0.104992i	$0.0334817\pi$
$719$	4.22957e11	+	2.44194e11i	1.58264	+	0.913735i	0.588162	+	0.808743i	$0.299852\pi$
$720$	−1.76209e10	+	1.76209e10i	−0.0655691	+	0.0655691i
$721$	3.05394e10	+	1.13975e11i	0.113011	+	0.421762i
$722$	7.59296e10	−	2.03453e10i	0.279423	−	0.0748712i
$723$	−2.42174e11	−	2.42174e11i	−0.886286	−	0.886286i
$724$	−1.39194e11	+	2.41091e11i	−0.506600	+	0.877457i
$725$	−2.71289e11	+	1.56629e11i	−0.981928	+	0.566916i
$726$	3.05499e10	−	1.14014e11i	0.109967	−	0.410404i
$727$		−	3.05062e11i		−	1.09207i	−0.837763	−	0.546035i	$-0.816137\pi$
$727$		−	3.05062e11i		−	1.09207i	0.837763	−	0.546035i	$-0.183863\pi$
$728$	−2.38251e10	−	1.08188e11i	−0.0848220	−	0.385172i
$729$	2.79016e11			0.987915
$730$	1.28540e11	+	3.44421e10i	0.452632	+	0.121282i
$731$	−2.16493e11	−	3.74977e11i	−0.758184	−	1.31321i
$732$	−1.21762e11	−	7.02993e10i	−0.424099	−	0.244854i
$733$	−2.30339e11	+	2.30339e11i	−0.797906	+	0.797906i	−0.982765	−	0.184859i	$-0.940817\pi$
$733$	−2.30339e11	+	2.30339e11i	−0.797906	+	0.797906i	0.184859	+	0.982765i	$0.440817\pi$
$734$	−2.86289e9	−	1.06844e10i	−0.00986326	−	0.0368102i
$735$	−2.44791e11	+	6.55916e10i	−0.838777	+	0.224750i
$736$	−3.42482e11	−	3.42482e11i	−1.16715	−	1.16715i
$737$	4.02438e7	−	6.97044e7i	0.000136405	−	0.000236260i
$738$	5.53940e10	−	3.19817e10i	0.186740	−	0.107814i
$739$	−3.63862e10	+	1.35795e11i	−0.122000	+	0.455309i	−0.999715	−	0.0238735i	$-0.992400\pi$
$739$	−3.63862e10	+	1.35795e11i	−0.122000	+	0.455309i	0.877715	+	0.479182i	$0.159067\pi$
$740$		−	2.10709e11i		−	0.702679i
$741$	1.58890e11	+	7.16132e9i	0.527015	+	0.0237531i
$742$	−2.87041e10			−0.0946953
$743$	1.97319e11	+	5.28714e10i	0.647460	+	0.173486i	0.567580	−	0.823318i	$-0.307880\pi$
$743$	1.97319e11	+	5.28714e10i	0.647460	+	0.173486i	0.0798800	+	0.996804i	$0.474546\pi$
$744$	−1.14199e10	−	1.97798e10i	−0.0372708	−	0.0645550i
$745$	−3.75103e11	−	2.16566e11i	−1.21766	−	0.703016i
$746$	−1.03498e11	+	1.03498e11i	−0.334177	+	0.334177i
$747$	−4.68725e10	−	1.74931e11i	−0.150535	−	0.561802i
$748$	−3.99596e7	+	1.07072e7i	−0.000127648	+	3.42033e-5i
$749$	8.62051e10	+	8.62051e10i	0.273909	+	0.273909i
$750$	−7.30429e9	+	1.26514e10i	−0.0230852	+	0.0399847i
$751$	3.98213e11	−	2.29908e11i	1.25186	−	0.722762i	0.280381	−	0.959889i	$-0.409539\pi$
$751$	3.98213e11	−	2.29908e11i	1.25186	−	0.722762i	0.971479	+	0.237127i	$0.0762058\pi$
$752$	5.38378e9	−	2.00926e10i	0.0168351	−	0.0628295i
$753$			1.92366e11i			0.598342i
$754$	−1.19898e11	+	1.87619e11i	−0.370960	+	0.580486i
$755$	5.23100e11			1.60989
$756$	−9.77595e10	−	2.61946e10i	−0.299276	−	0.0801907i
$757$	2.11611e11	+	3.66522e11i	0.644400	+	1.11613i	0.984440	+	0.175723i	$0.0562262\pi$
$757$	2.11611e11	+	3.66522e11i	0.644400	+	1.11613i	−0.340039	+	0.940411i	$0.610440\pi$
$758$	−1.57658e11	−	9.10238e10i	−0.477572	−	0.275726i
$759$	4.24051e7	−	4.24051e7i	0.000127776	−	0.000127776i
$760$	−7.85876e10	−	2.93293e11i	−0.235559	−	0.879118i
$761$	−2.28830e11	+	6.13147e10i	−0.682297	+	0.182821i	−0.583288	−	0.812266i	$-0.698234\pi$
$761$	−2.28830e11	+	6.13147e10i	−0.682297	+	0.182821i	−0.0990092	+	0.995087i	$0.531567\pi$
$762$	1.58222e11	+	1.58222e11i	0.469295	+	0.469295i
$763$	−1.22145e10	+	2.11561e10i	−0.0360393	+	0.0624218i
$764$	−2.53352e11	+	1.46273e11i	−0.743620	+	0.429329i
$765$	−6.73607e10	+	2.51393e11i	−0.196680	+	0.734021i
$766$			1.36194e11i			0.395588i
$767$	−8.48593e10	−	5.42294e10i	−0.245199	−	0.156694i
$768$	−2.28840e11			−0.657791
$769$	3.72249e10	+	9.97437e9i	0.106446	+	0.0285220i	0.311649	−	0.950197i	$-0.399119\pi$
$769$	3.72249e10	+	9.97437e9i	0.106446	+	0.0285220i	−0.205203	+	0.978719i	$0.565785\pi$
$770$	−8.48940e6	−	1.47041e7i	−2.41498e−5	−	4.18287e-5i
$771$	−3.24827e11	−	1.87539e11i	−0.919251	−	0.530730i
$772$	3.07665e11	−	3.07665e11i	0.866182	−	0.866182i
$773$	1.40934e11	+	5.25971e11i	0.394727	+	1.47314i	0.822245	+	0.569133i	$0.192721\pi$
$773$	1.40934e11	+	5.25971e11i	0.394727	+	1.47314i	−0.427518	+	0.904007i	$0.640612\pi$
$774$	−9.66434e10	+	2.58955e10i	−0.269283	+	0.0721541i
$775$	2.44566e10	+	2.44566e10i	0.0677936	+	0.0677936i
$776$	2.68914e11	−	4.65772e11i	0.741594	−	1.28448i
$777$	7.38682e10	−	4.26478e10i	0.202663	−	0.117007i
$778$	1.63098e10	−	6.08689e10i	0.0445173	−	0.166141i
$779$		−	2.32397e11i		−	0.631076i
$780$	−1.20336e10	+	2.66993e11i	−0.0325101	+	0.721309i
$781$	−4.27647e7			−0.000114943
$782$	−4.17765e11	−	1.11940e11i	−1.11713	−	0.299335i
$783$	2.49875e11	+	4.32796e11i	0.664776	+	1.15143i
$784$	−4.25901e10	−	2.45894e10i	−0.112731	−	0.0650854i
$785$	−4.37094e10	+	4.37094e10i	−0.115106	+	0.115106i
$786$	9.56373e9	+	3.56923e10i	0.0250575	+	0.0935157i
$787$	3.07505e10	−	8.23956e9i	0.0801591	−	0.0214786i	−0.218517	−	0.975833i	$-0.570122\pi$
$787$	3.07505e10	−	8.23956e9i	0.0801591	−	0.0214786i	0.298676	+	0.954355i	$0.403455\pi$
$788$	1.81039e11	+	1.81039e11i	0.469533	+	0.469533i
$789$	1.77049e11	−	3.06657e11i	0.456862	−	0.791307i
$790$	4.46789e11	−	2.57954e11i	1.14708	−	0.662268i
$791$	6.09173e10	−	2.27347e11i	0.155609	−	0.580741i
$792$			2.34852e7i			5.96890e-5i
$793$	3.63092e11	−	7.99597e10i	0.918173	−	0.202199i
$794$	2.41093e11			0.606599
$795$	1.64334e11	+	4.40332e10i	0.411395	+	0.110233i
$796$	1.78637e11	+	3.09408e11i	0.444958	+	0.770690i
$797$	−1.23184e11	−	7.11204e10i	−0.305296	−	0.176263i	0.339523	−	0.940598i	$-0.389734\pi$
$797$	−1.23184e11	−	7.11204e10i	−0.305296	−	0.176263i	−0.644820	+	0.764335i	$0.723068\pi$
$798$	3.53772e10	−	3.53772e10i	0.0872392	−	0.0872392i
$799$	−5.62282e10	−	2.09846e11i	−0.137964	−	0.514890i
$800$	3.76524e11	−	1.00889e11i	0.919247	−	0.246312i
$801$	−2.15757e11	−	2.15757e11i	−0.524126	−	0.524126i
$802$	−1.53442e11	+	2.65769e11i	−0.370891	+	0.642403i
$803$	−3.23862e7	+	1.86982e7i	−7.78929e−5	+	4.49715e-5i
$804$	−1.03148e11	+	3.84953e11i	−0.246852	+	0.921264i
$805$			3.88623e11i			0.925434i
$806$	2.34355e10	+	7.42545e9i	0.0555307	+	0.0175947i
$807$	−2.39064e10			−0.0563664
$808$	−2.40849e11	−	6.45353e10i	−0.565067	−	0.151409i
$809$	4.44453e9	+	7.69815e9i	0.0103760	+	0.0179718i	0.871167	−	0.490987i	$-0.163364\pi$
$809$	4.44453e9	+	7.69815e9i	0.0103760	+	0.0179718i	−0.860791	+	0.508959i	$0.830030\pi$
$810$	−1.14522e11	−	6.61195e10i	−0.266042	−	0.153599i
$811$	−3.96090e11	+	3.96090e11i	−0.915610	+	0.915610i	−0.996706	−	0.0810966i	$-0.974158\pi$
$811$	−3.96090e11	+	3.96090e11i	−0.915610	+	0.915610i	0.0810966	+	0.996706i	$0.474158\pi$
$812$	−3.96869e10	−	1.48113e11i	−0.0912899	−	0.340699i
$813$	8.16400e10	−	2.18754e10i	0.186870	−	0.0500718i
$814$	−1.91247e7	−	1.91247e7i	−4.35609e−5	−	4.35609e-5i
$815$	1.56454e11	−	2.70987e11i	0.354615	−	0.614212i
$816$	5.93582e10	−	3.42705e10i	0.133881	−	0.0772964i
$817$	−9.40857e10	+	3.51133e11i	−0.211172	+	0.788103i
$818$		−	1.69363e11i		−	0.378273i
$819$	7.07645e10	−	3.67112e10i	0.157282	−	0.0815949i
$820$	3.90513e11			0.863734
$821$	4.13283e11	+	1.10739e11i	0.909652	+	0.243741i	0.683157	−	0.730272i	$-0.260607\pi$
$821$	4.13283e11	+	1.10739e11i	0.909652	+	0.243741i	0.226495	+	0.974012i	$0.427273\pi$
$822$	3.58768e10	+	6.21404e10i	0.0785825	+	0.136109i
$823$	−4.54097e11	−	2.62173e11i	−0.989804	−	0.571463i	−0.0845881	−	0.996416i	$-0.526957\pi$
$823$	−4.54097e11	−	2.62173e11i	−0.989804	−	0.571463i	−0.905216	+	0.424953i	$0.860291\pi$
$824$	−3.21832e11	+	3.21832e11i	−0.698104	+	0.698104i
$825$	1.24918e7	+	4.66200e7i	2.69655e−5	+	0.000100637i
$826$	−3.05989e10	+	8.19895e9i	−0.0657333	+	0.0176132i
$827$	−3.62472e11	−	3.62472e11i	−0.774913	−	0.774913i	0.204048	−	0.978961i	$-0.434590\pi$
$827$	−3.62472e11	−	3.62472e11i	−0.774913	−	0.774913i	−0.978961	+	0.204048i	$0.934590\pi$
$828$	1.09402e11	−	1.89489e11i	0.232757	−	0.403147i
$829$	2.56179e11	−	1.47905e11i	0.542408	−	0.313159i	−0.203646	−	0.979045i	$-0.565279\pi$
$829$	2.56179e11	−	1.47905e11i	0.542408	−	0.313159i	0.746054	+	0.665885i	$0.231946\pi$
$830$	−1.30711e11	+	4.87818e11i	−0.275422	+	1.02789i
$831$			3.62545e10i			0.0760252i
$832$	1.48763e11	−	1.35932e11i	0.310457	−	0.283679i
$833$	−5.13623e11			−1.06675
$834$	−1.01787e10	−	2.72739e9i	−0.0210392	−	0.00563745i
$835$	−3.62787e11	−	6.28365e11i	−0.746287	−	1.29261i
$836$	3.00789e7	+	1.73661e7i	6.15796e−5	+	3.55530e-5i
$837$	3.90164e10	−	3.90164e10i	0.0794960	−	0.0794960i
$838$	−6.32241e10	−	2.35956e11i	−0.128206	−	0.478470i
$839$	5.01346e11	−	1.34335e11i	1.01179	−	0.271108i	0.285412	−	0.958405i	$-0.407869\pi$
$839$	5.01346e11	−	1.34335e11i	1.01179	−	0.271108i	0.726377	+	0.687297i	$0.241203\pi$
$840$	1.46046e11	+	1.46046e11i	0.293341	+	0.293341i
$841$	−1.28457e11	+	2.22494e11i	−0.256788	+	0.444769i
$842$	−2.21504e11	+	1.27885e11i	−0.440690	+	0.254433i
$843$	−7.48555e10	+	2.79365e11i	−0.148222	+	0.553173i
$844$			2.90870e11i			0.573230i
$845$	−4.52758e11	−	5.42670e11i	−0.888054	−	1.06441i
$846$	−5.02009e10			−0.0980010
$847$	−2.07630e11	−	5.56343e10i	−0.403419	−	0.108096i
$848$	1.65074e10	+	2.85917e10i	0.0319224	+	0.0552913i
$849$	7.09277e10	+	4.09501e10i	0.136517	+	0.0788178i
$850$	2.46133e11	−	2.46133e11i	0.471513	−	0.471513i
$851$	1.60224e11	+	5.97963e11i	0.305498	+	1.14014i
$852$	2.04533e11	−	5.48045e10i	0.388155	−	0.104006i
$853$	5.18546e11	+	5.18546e11i	0.979471	+	0.979471i	0.999793	−	0.0203230i	$-0.00646944\pi$
$853$	5.18546e11	+	5.18546e11i	0.979471	+	0.979471i	−0.0203230	+	0.999793i	$0.506469\pi$
$854$	5.84753e10	−	1.01282e11i	0.109936	−	0.190415i
$855$	1.89232e11	−	1.09253e11i	0.354103	−	0.204442i
$856$	−1.21709e11	+	4.54226e11i	−0.226688	+	0.846012i
$857$		−	5.05907e11i		−	0.937880i	−0.883230	−	0.468940i	$-0.844636\pi$
$857$		−	5.05907e11i		−	0.937880i	0.883230	−	0.468940i	$-0.155364\pi$
$858$	2.31409e7	+	2.53254e7i	4.27004e−5	+	4.67311e-5i
$859$	−1.05348e12			−1.93488			−0.967440	−	0.253102i	$-0.918549\pi$
$859$	−1.05348e12			−1.93488			−0.967440	+	0.253102i	$0.918549\pi$
$860$	−5.90032e11	−	1.58099e11i	−1.07865	−	0.289024i
$861$	7.90403e10	+	1.36902e11i	0.143825	+	0.249113i
$862$	3.87261e10	+	2.23585e10i	0.0701415	+	0.0404962i
$863$	−3.72184e11	+	3.72184e11i	−0.670987	+	0.670987i	−0.957944	−	0.286957i	$-0.907356\pi$
$863$	−3.72184e11	+	3.72184e11i	−0.670987	+	0.670987i	0.286957	+	0.957944i	$0.407356\pi$
$864$	−1.60952e11	−	6.00681e11i	−0.288829	−	1.07793i
$865$	6.85546e9	−	1.83691e9i	0.0122454	−	0.00328114i
$866$	2.48998e11	+	2.48998e11i	0.442715	+	0.442715i
$867$	1.43550e11	−	2.48636e11i	0.254055	−	0.440036i
$868$	−1.46619e10	+	8.46507e9i	−0.0258293	+	0.0149125i
$869$	−3.75236e7	+	1.40040e8i	−6.57999e−5	+	0.000245569i
$870$		−	4.15125e11i		−	0.724607i
$871$	−4.85303e11	−	9.35471e11i	−0.843219	−	1.62539i
$872$	−9.42288e10			−0.162974
$873$	3.73846e11	+	1.00172e11i	0.643629	+	0.172460i
$874$	1.81556e11	+	3.14465e11i	0.311147	+	0.538923i
$875$	2.30394e10	+	1.33018e10i	0.0393042	+	0.0226923i
$876$	1.30933e11	−	1.30933e11i	0.222348	−	0.222348i
$877$	−8.76568e10	−	3.27139e11i	−0.148179	−	0.553012i	−0.999593	−	0.0285180i	$-0.990921\pi$
$877$	−8.76568e10	−	3.27139e11i	−0.148179	−	0.553012i	0.851414	−	0.524494i	$-0.175745\pi$
$878$	3.93109e11	−	1.05333e11i	0.661507	−	0.177250i
$879$	−3.84415e11	−	3.84415e11i	−0.643940	−	0.643940i
$880$	−9.76433e6	+	1.69123e7i	−1.62822e−5	+	2.82015e-5i
$881$	−3.22525e11	+	1.86210e11i	−0.535378	+	0.309100i	−0.743204	−	0.669065i	$-0.766695\pi$
$881$	−3.22525e11	+	1.86210e11i	−0.535378	+	0.309100i	0.207826	+	0.978166i	$0.433361\pi$
$882$	−3.07181e10	+	1.14642e11i	−0.0507598	+	0.189438i
$883$			8.54673e11i			1.40591i	0.711235	+	0.702954i	$0.248136\pi$
$883$			8.54673e11i			1.40591i	−0.711235	+	0.702954i	$0.751864\pi$
$884$	−1.63609e11	+	5.16367e11i	−0.267916	+	0.845569i
$885$	1.87759e11			0.306076
$886$	−1.55878e11	−	4.17674e10i	−0.252959	−	0.0677801i
$887$	1.38711e11	+	2.40254e11i	0.224086	+	0.388129i	0.956045	−	0.293220i	$-0.0947269\pi$
$887$	1.38711e11	+	2.40254e11i	0.224086	+	0.388129i	−0.731959	+	0.681349i	$0.761394\pi$
$888$	2.84930e11	+	1.64504e11i	0.458232	+	0.264561i
$889$	2.88136e11	−	2.88136e11i	0.461308	−	0.461308i
$890$	2.20226e11	+	8.21896e11i	0.351002	+	1.30996i
$891$	3.58954e7	−	9.61816e6i	5.69546e−5	−	1.52609e-5i
$892$	9.69055e10	+	9.69055e10i	0.153070	+	0.153070i
$893$	−9.11971e10	+	1.57958e11i	−0.143409	+	0.248391i
$894$	2.38403e11	−	1.37642e11i	0.373217	−	0.215477i
$895$	−4.25109e10	+	1.58653e11i	−0.0662534	+	0.247261i
$896$			2.14575e11i			0.332925i
$897$	−1.68872e11	−	7.66838e11i	−0.260848	−	1.18450i
$898$	5.94540e11			0.914272
$899$	8.07498e10	+	2.16368e10i	0.123624	+	0.0331249i
$900$	8.80480e10	+	1.52504e11i	0.134199	+	0.232440i
$901$	2.98611e11	+	1.72403e11i	0.453113	+	0.261605i
$902$	3.54442e7	−	3.54442e7i	5.35450e−5	−	5.35450e-5i
$903$	−6.39987e10	−	2.38846e11i	−0.0962543	−	0.359226i
$904$	8.76937e11	−	2.34974e11i	1.31309	−	0.351841i
$905$	9.70500e11	+	9.70500e11i	1.44678	+	1.44678i
$906$	−1.66232e11	+	2.87922e11i	−0.246719	+	0.427329i
$907$	7.87598e11	−	4.54720e11i	1.16379	−	0.671916i	0.211583	−	0.977360i	$-0.432138\pi$
$907$	7.87598e11	−	4.54720e11i	1.16379	−	0.671916i	0.952210	+	0.305444i	$0.0988049\pi$
$908$	1.51329e11	−	5.64766e11i	0.222627	−	0.830855i
$909$		−	1.79435e11i		−	0.262816i
$910$	−2.22086e11	−	1.00096e10i	−0.323858	−	0.0145966i
$911$	8.59012e11			1.24717			0.623585	−	0.781755i	$-0.285675\pi$
$911$	8.59012e11			1.24717			0.623585	+	0.781755i	$0.285675\pi$
$912$	−5.55837e10	−	1.48936e10i	−0.0803466	−	0.0215288i
$913$	−7.09612e7	−	1.22908e8i	−0.000102126	−	0.000176888i
$914$	−6.75435e11	−	3.89963e11i	−0.967830	−	0.558777i
$915$	−4.90148e11	+	4.90148e11i	−0.699267	+	0.699267i
$916$	2.59057e10	+	9.66812e10i	0.0367970	+	0.137328i
$917$	6.49991e10	−	1.74164e10i	0.0919242	−	0.0246310i
$918$	−3.92664e11	−	3.92664e11i	−0.552904	−	0.552904i
$919$	6.65977e11	−	1.15351e12i	0.933678	−	1.61718i	0.156704	−	0.987646i	$-0.449913\pi$
$919$	6.65977e11	−	1.15351e12i	0.933678	−	1.61718i	0.776974	−	0.629533i	$-0.216754\pi$
$920$	−1.29819e12	+	7.49512e11i	−1.81212	+	1.04623i
$921$	−1.79675e10	+	6.70555e10i	−0.0249717	+	0.0931957i
$922$			9.30623e10i			0.128781i
$923$	−3.01519e11	+	4.71823e11i	−0.415439	+	0.650088i
$924$	−2.36254e7			−3.24109e−5
$925$	−4.81250e11	−	1.28950e11i	−0.657360	−	0.176139i
$926$	−6.34663e10	−	1.09927e11i	−0.0863175	−	0.149506i
$927$	−2.83649e11	−	1.63765e11i	−0.384115	−	0.221769i
$928$	6.66224e11	−	6.66224e11i	0.898315	−	0.898315i
$929$	5.96720e10	+	2.22699e11i	0.0801139	+	0.298989i	0.994344	−	0.106206i	$-0.0338703\pi$
$929$	5.96720e10	+	2.22699e11i	0.0801139	+	0.298989i	−0.914230	+	0.405195i	$0.867204\pi$
$930$	−4.42724e10	+	1.18627e10i	−0.0591835	+	0.0158582i
$931$	3.04918e11	+	3.04918e11i	0.405867	+	0.405867i
$932$	3.93110e10	−	6.80887e10i	0.0521015	−	0.0902425i
$933$	4.72214e11	−	2.72633e11i	0.623178	−	0.359792i
$934$	1.90438e11	−	7.10724e11i	0.250245	−	0.933928i
$935$			2.03957e8i			0.000266865i
$936$	2.59112e11	+	1.65586e11i	0.337586	+	0.215735i
$937$	−3.49817e11			−0.453819			−0.226909	−	0.973916i	$-0.572862\pi$
$937$	−3.49817e11			−0.453819			−0.226909	+	0.973916i	$0.572862\pi$
$938$	−3.20206e11	−	8.57989e10i	−0.413636	−	0.110833i
$939$	1.33526e11	+	2.31274e11i	0.171753	+	0.297485i
$940$	−2.65427e11	−	1.53245e11i	−0.339965	−	0.196279i
$941$	−9.61661e11	+	9.61661e11i	−1.22649	+	1.22649i	−0.261205	+	0.965283i	$0.584120\pi$
$941$	−9.61661e11	+	9.61661e11i	−1.22649	+	1.22649i	−0.965283	+	0.261205i	$0.915880\pi$
$942$	−1.01682e10	−	3.79484e10i	−0.0129135	−	0.0481937i
$943$	−1.10822e12	+	2.96947e11i	−1.40145	+	0.375519i
$944$	2.57639e10	+	2.57639e10i	0.0324433	+	0.0324433i
$945$	−2.49486e11	+	4.32122e11i	−0.312837	+	0.541850i
$946$	−6.79028e7	+	3.92037e7i	−8.47858e−5	+	4.89511e-5i
$947$	2.05151e11	−	7.65635e11i	0.255079	−	0.951967i	−0.712968	−	0.701197i	$-0.752649\pi$
$947$	2.05151e11	−	7.65635e11i	0.255079	−	0.951967i	0.968047	−	0.250771i	$-0.0806840\pi$
$948$		−	7.17866e11i		−	0.888812i
$949$	−2.20465e10	+	4.89151e11i	−0.0271816	+	0.603084i
$950$	−2.92239e11			−0.358792
$951$	3.01922e11	+	8.08999e10i	0.369125	+	0.0989067i
$952$	2.09299e11	+	3.62516e11i	0.254812	+	0.441346i
$953$	−2.17463e11	−	1.25552e11i	−0.263641	−	0.152213i	0.362353	−	0.932041i	$-0.381973\pi$
$953$	−2.17463e11	−	1.25552e11i	−0.263641	−	0.152213i	−0.625994	+	0.779828i	$0.715307\pi$
$954$	5.63397e10	−	5.63397e10i	0.0680176	−	0.0680176i
$955$	3.73294e11	+	1.39315e12i	0.448784	+	1.67488i
$956$	−2.95293e11	+	7.91235e10i	−0.353526	+	0.0947270i
$957$	8.24899e7	+	8.24899e7i	9.83451e−5	+	9.83451e-5i
$958$	4.35452e10	−	7.54225e10i	0.0516985	−	0.0895445i
$959$	1.13163e11	−	6.53350e10i	0.133793	−	0.0772452i
$960$	−9.72395e10	+	3.62903e11i	−0.114487	+	0.427273i
$961$			8.43661e11i			0.989178i
$962$	−3.45844e11	+	7.61612e10i	−0.403812	+	0.0889270i
$963$	−3.38403e11			−0.393485
$964$	−9.45878e11	−	2.53447e11i	−1.09528	−	0.293481i
$965$	−1.07257e12	−	1.85774e12i	−1.23684	−	2.14228i
$966$	−2.13904e11	−	1.23498e11i	−0.245647	−	0.141824i
$967$	9.76818e11	−	9.76818e11i	1.11714	−	1.11714i	0.124981	−	0.992159i	$-0.460113\pi$
$967$	9.76818e11	−	9.76818e11i	1.11714	−	1.11714i	0.992159	−	0.124981i	$-0.0398870\pi$
$968$	−2.14596e11	−	8.00885e11i	−0.244411	−	0.912155i
$969$	−5.80515e11	+	1.55549e11i	−0.658443	+	0.176429i
$970$	−7.63178e11	−	7.63178e11i	−0.862063	−	0.862063i
$971$	−3.68267e11	+	6.37858e11i	−0.414273	+	0.717541i	−0.995352	−	0.0963057i	$-0.969297\pi$
$971$	−3.68267e11	+	6.37858e11i	−0.414273	+	0.717541i	0.581079	+	0.813847i	$0.302631\pi$
$972$	4.14117e11	−	2.39090e11i	0.463936	−	0.267853i
$973$	−4.96683e9	+	1.85365e10i	−0.00554150	+	0.0206812i
$974$			2.56144e11i			0.284608i
$975$	6.02434e11	+	1.90879e11i	0.666639	+	0.211222i
$976$	−1.34514e11			−0.148241
$977$	3.53149e11	+	9.46260e10i	0.387596	+	0.103856i	0.447354	−	0.894357i	$-0.352366\pi$
$977$	3.53149e11	+	9.46260e10i	0.387596	+	0.103856i	−0.0597580	+	0.998213i	$0.519033\pi$
$978$	9.94370e10	+	1.72230e11i	0.108691	+	0.188258i
$979$	−2.07081e8	−	1.19558e8i	−0.000225429	−	0.000130151i
$980$	−5.12373e11	+	5.12373e11i	−0.555498	+	0.555498i
$981$	−1.75504e10	−	6.54988e10i	−0.0189500	−	0.0707225i
$982$	−1.22050e11	+	3.27033e10i	−0.131248	+	0.0351678i
$983$	6.09445e11	+	6.09445e11i	0.652710	+	0.652710i	0.953645	−	0.300935i	$-0.0972987\pi$
$983$	6.09445e11	+	6.09445e11i	0.652710	+	0.652710i	−0.300935	+	0.953645i	$0.597299\pi$
$984$	−3.04879e11	+	5.28067e11i	−0.325198	+	0.563259i
$985$	1.09314e12	−	6.31127e11i	1.16127	−	0.670459i
$986$	2.17755e11	−	8.12671e11i	0.230388	−	0.859820i
$987$		−	1.24068e11i		−	0.130734i
$988$	4.03675e11	−	2.09418e11i	0.423647	−	0.219779i
$989$	1.79464e12			1.87583
$990$	4.55236e7	+	1.21980e7i	4.73910e−5	+	1.26984e-5i
$991$	−2.62055e11	−	4.53893e11i	−0.271706	−	0.470608i	0.697593	−	0.716494i	$-0.254254\pi$
$991$	−2.62055e11	−	4.53893e11i	−0.271706	−	0.470608i	−0.969299	+	0.245886i	$0.920921\pi$
$992$	−9.00898e10	−	5.20134e10i	−0.0930313	−	0.0537116i
$993$	−5.14739e11	+	5.14739e11i	−0.529407	+	0.529407i
$994$	4.55867e10	+	1.70132e11i	0.0466973	+	0.174277i
$995$	1.70140e12	−	4.55888e11i	1.73586	−	0.465121i
$996$	4.96902e11	+	4.96902e11i	0.504932	+	0.504932i
$997$	−1.17867e11	+	2.04151e11i	−0.119292	+	0.206619i	−0.919487	−	0.393120i	$-0.871396\pi$
$997$	−1.17867e11	+	2.04151e11i	−0.119292	+	0.206619i	0.800196	+	0.599739i	$0.204729\pi$
$998$	−1.44071e11	+	8.31795e10i	−0.145230	+	0.0838483i
$999$	−2.05719e11	+	7.67753e11i	−0.206544	+	0.770832i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.9.f.a.2.6	✓	32
13.7	odd	12	inner	13.9.f.a.7.6	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.9.f.a.2.6	✓	32	1.1	even	1	trivial
13.9.f.a.7.6	yes	32	13.7	odd	12	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 13 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	13.f (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(8.65394 + 2.31882i) q^{2} +(-30.7307 - 53.2271i) q^{3} +(-152.189 - 87.8662i) q^{4} +(-612.629 + 612.629i) q^{5} +(-142.518 - 531.883i) q^{6} +(-968.610 + 259.538i) q^{7} +(-2735.08 - 2735.08i) q^{8} +(1391.75 - 2410.58i) q^{9} +(-6722.23 + 3881.08i) q^{10} +(0.564567 - 2.10699i) q^{11} +10800.8i q^{12} +(-19265.9 - 21084.5i) q^{13} -8984.12 q^{14} +(51435.0 + 13782.0i) q^{15} +(5166.67 + 8948.93i) q^{16} +(93462.5 + 53960.6i) q^{17} +(17633.8 - 17633.8i) q^{18} +(-23450.7 - 87519.3i) q^{19} +(147065. - 39405.8i) q^{20} +(43580.5 + 43580.5i) q^{21} +(9.77146 - 16.9247i) q^{22} +(-387384. + 223656. i) q^{23} +(-61529.5 + 229631. i) q^{24} -360004. i q^{25} +(-117835. - 227138. i) q^{26} -574326. q^{27} +(170216. + 45609.3i) q^{28} +(-435075. - 753572. i) q^{29} +(413158. + 238537. i) q^{30} +(-67934.2 + 67934.2i) q^{31} +(280245. + 1.04589e6i) q^{32} +(-129.499 + 34.6991i) q^{33} +(683695. + 683695. i) q^{34} +(434398. - 752399. i) q^{35} +(-423617. + 244575. i) q^{36} +(358192. - 1.33679e6i) q^{37} -811765. i q^{38} +(-530214. + 1.67341e6i) q^{39} +3.35118e6 q^{40} +(2.47751e6 + 663846. i) q^{41} +(276088. + 478199. i) q^{42} +(-3.47455e6 - 2.00603e6i) q^{43} +(-271.054 + 271.054i) q^{44} +(624165. + 2.32942e6i) q^{45} +(-3.87102e6 + 1.03724e6i) q^{46} +(-1.42343e6 - 1.42343e6i) q^{47} +(317551. - 550014. i) q^{48} +(-4.12162e6 + 2.37962e6i) q^{49} +(834783. - 3.11545e6i) q^{50} -6.63299e6i q^{51} +(1.07943e6 + 4.90164e6i) q^{52} +3.19498e6 q^{53} +(-4.97018e6 - 1.33176e6i) q^{54} +(944.935 + 1636.67i) q^{55} +(3.35908e6 + 1.93937e6i) q^{56} +(-3.93775e6 + 3.93775e6i) q^{57} +(-2.01772e6 - 7.53023e6i) q^{58} +(3.40589e6 - 912605. i) q^{59} +(-6.61686e6 - 6.61686e6i) q^{60} +(-6.50874e6 + 1.12735e7i) q^{61} +(-745426. + 430372. i) q^{62} +(-722424. + 2.69612e6i) q^{63} +7.05556e6i q^{64} +(2.47198e7 + 1.11415e6i) q^{65} -1201.14 q^{66} +(3.56413e7 + 9.55007e6i) q^{67} +(-9.48263e6 - 1.64244e7i) q^{68} +(2.38092e7 + 1.37462e7i) q^{69} +(5.50393e6 - 5.50393e6i) q^{70} +(-5.07414e6 - 1.89369e7i) q^{71} +(-1.03997e7 + 2.78658e6i) q^{72} +(-1.21226e7 - 1.21226e7i) q^{73} +(6.19955e6 - 1.07379e7i) q^{74} +(-1.91620e7 + 1.10632e7i) q^{75} +(-4.12105e6 + 1.53800e7i) q^{76} +2187.38i q^{77} +(-8.46877e6 + 1.32521e7i) q^{78} -6.64644e7 q^{79} +(-8.64763e6 - 2.31713e6i) q^{80} +(8.51817e6 + 1.47539e7i) q^{81} +(1.99009e7 + 1.14898e7i) q^{82} +(4.60062e7 - 4.60062e7i) q^{83} +(-2.80321e6 - 1.04617e7i) q^{84} +(-9.03157e7 + 2.42000e7i) q^{85} +(-2.54169e7 - 2.54169e7i) q^{86} +(-2.67403e7 + 4.63156e7i) q^{87} +(-7306.93 + 4218.66i) q^{88} +(2.83718e7 - 1.05885e8i) q^{89} +2.16060e7i q^{90} +(2.41334e7 + 1.54224e7i) q^{91} +7.86073e7 q^{92} +(5.70361e6 + 1.52828e6i) q^{93} +(-9.01760e6 - 1.56189e7i) q^{94} +(6.79835e7 + 3.92503e7i) q^{95} +(4.70575e7 - 4.70575e7i) q^{96} +(3.59877e7 + 1.34308e8i) q^{97} +(-4.11862e7 + 1.10358e7i) q^{98} +(-4293.34 - 4293.34i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 172 q^{5} - 2726 q^{6} - 2784 q^{7} - 10470 q^{8} - 21872 q^{9} - 26886 q^{10} + 6476 q^{11} + 14794 q^{13} + 216232 q^{14} - 127934 q^{15} + 195174 q^{16} + 97644 q^{17}+ \cdots - 359343776 q^{99}+O(q^{100}) \) 32 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 172 * q^5 - 2726 * q^6 - 2784 * q^7 - 10470 * q^8 - 21872 * q^9 - 26886 * q^10 + 6476 * q^11 + 14794 * q^13 + 216232 * q^14 - 127934 * q^15 + 195174 * q^16 + 97644 * q^17 - 475646 * q^18 + 373314 * q^19 + 685798 * q^20 - 213824 * q^21 + 167756 * q^22 - 711654 * q^23 - 1396830 * q^24 - 1041274 * q^26 + 3386272 * q^27 - 491836 * q^28 - 178394 * q^29 - 6200118 * q^30 + 1793468 * q^31 + 955004 * q^32 - 369536 * q^33 + 4592250 * q^34 + 1520488 * q^35 - 11372454 * q^36 + 247730 * q^37 + 14761942 * q^39 + 15044736 * q^40 - 2285272 * q^41 - 1024084 * q^42 + 18199452 * q^43 + 5629904 * q^44 - 10428746 * q^45 - 25708302 * q^46 - 8054836 * q^47 - 19983002 * q^48 - 18234288 * q^49 - 7208294 * q^50 - 26124488 * q^52 - 26091116 * q^53 + 85261048 * q^54 - 2240524 * q^55 + 84926940 * q^56 + 57257116 * q^57 - 68659210 * q^58 - 58197100 * q^59 - 64428232 * q^60 - 38537926 * q^61 + 2935614 * q^62 - 43972436 * q^63 + 44466032 * q^65 + 209850752 * q^66 + 30462126 * q^67 + 68365716 * q^68 + 163279656 * q^69 + 256782116 * q^70 - 113836054 * q^71 - 445647780 * q^72 - 30722748 * q^73 - 156843362 * q^74 - 364524840 * q^75 - 180633890 * q^76 + 252047848 * q^78 + 364818200 * q^79 + 372146084 * q^80 - 17174000 * q^81 + 272314014 * q^82 + 389373188 * q^83 - 464450276 * q^84 - 331999758 * q^85 - 32039076 * q^86 - 337693978 * q^87 - 1180586364 * q^88 - 333088936 * q^89 + 251459988 * q^91 + 1275961956 * q^92 + 637177780 * q^93 + 171539378 * q^94 + 318589986 * q^95 + 1019148280 * q^96 - 230031796 * q^97 - 1287859636 * q^98 - 359343776 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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