LMFDB - Embedded newform 91.8.e.b.53.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,8,Mod(53,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("91.53");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	91.e (of order $3$, degree $2$, 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:	$28.4270373191$
Analytic rank:	$0$
Dimension:	$58$
Relative dimension:	$29$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			53.16
Character	$\chi$	$=$	91.53
Dual form			91.8.e.b.79.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0355890 - 0.0616420i) q^{2} +(-26.4772 + 45.8599i) q^{3} +(63.9975 - 110.847i) q^{4} +(184.974 + 320.384i) q^{5} +3.76919 q^{6} +(-905.689 - 57.1831i) q^{7} -18.2212 q^{8} +(-308.586 - 534.486i) q^{9} +O(q^{10})$	\(q+(-0.0355890 - 0.0616420i) q^{2} +(-26.4772 + 45.8599i) q^{3} +(63.9975 - 110.847i) q^{4} +(184.974 + 320.384i) q^{5} +3.76919 q^{6} +(-905.689 - 57.1831i) q^{7} -18.2212 q^{8} +(-308.586 - 534.486i) q^{9} +(13.1661 - 22.8043i) q^{10} +(-714.139 + 1236.92i) q^{11} +(3388.95 + 5869.83i) q^{12} -2197.00 q^{13} +(28.7077 + 57.8636i) q^{14} -19590.3 q^{15} +(-8191.03 - 14187.3i) q^{16} +(-903.069 + 1564.16i) q^{17} +(-21.9645 + 38.0437i) q^{18} +(27422.3 + 47496.8i) q^{19} +47351.4 q^{20} +(26602.5 - 40020.8i) q^{21} +101.662 q^{22} +(-7490.56 - 12974.0i) q^{23} +(482.447 - 835.623i) q^{24} +(-29367.9 + 50866.7i) q^{25} +(78.1891 + 135.427i) q^{26} -83129.4 q^{27} +(-64300.4 + 96733.2i) q^{28} -186368. q^{29} +(697.201 + 1207.59i) q^{30} +(88913.9 - 154003. i) q^{31} +(-1749.18 + 3029.67i) q^{32} +(-37816.8 - 65500.6i) q^{33} +128.557 q^{34} +(-149208. - 300745. i) q^{35} -78994.8 q^{36} +(-185341. - 321020. i) q^{37} +(1951.86 - 3380.73i) q^{38} +(58170.4 - 100754. i) q^{39} +(-3370.44 - 5837.78i) q^{40} -828388. q^{41} +(-3413.72 - 215.534i) q^{42} -177329. q^{43} +(91406.2 + 158320. i) q^{44} +(114160. - 197732. i) q^{45} +(-533.163 + 923.466i) q^{46} +(-511002. - 885081. i) q^{47} +867502. q^{48} +(817003. + 103580. i) q^{49} +4180.70 q^{50} +(-47821.5 - 82829.2i) q^{51} +(-140602. + 243531. i) q^{52} +(-636768. + 1.10291e6i) q^{53} +(2958.49 + 5124.26i) q^{54} -528387. q^{55} +(16502.8 + 1041.95i) q^{56} -2.90426e6 q^{57} +(6632.65 + 11488.1i) q^{58} +(564552. - 977833. i) q^{59} +(-1.25373e6 + 2.17153e6i) q^{60} +(844239. + 1.46227e6i) q^{61} -12657.4 q^{62} +(248919. + 501724. i) q^{63} -2.09665e6 q^{64} +(-406387. - 703883. i) q^{65} +(-2691.73 + 4662.21i) q^{66} +(757013. - 1.31118e6i) q^{67} +(115588. + 200205. i) q^{68} +793316. q^{69} +(-13228.4 + 19900.7i) q^{70} -3.47517e6 q^{71} +(5622.81 + 9738.99i) q^{72} +(-155345. + 269065. i) q^{73} +(-13192.2 + 22849.6i) q^{74} +(-1.55516e6 - 2.69362e6i) q^{75} +7.01982e6 q^{76} +(717519. - 1.07943e6i) q^{77} -8280.92 q^{78} +(2.10806e6 + 3.65127e6i) q^{79} +(3.03025e6 - 5.24854e6i) q^{80} +(2.87591e6 - 4.98122e6i) q^{81} +(29481.5 + 51063.5i) q^{82} -3.50541e6 q^{83} +(-2.73368e6 - 5.51003e6i) q^{84} -668175. q^{85} +(6310.97 + 10930.9i) q^{86} +(4.93450e6 - 8.54681e6i) q^{87} +(13012.5 - 22538.3i) q^{88} +(1.88836e6 + 3.27073e6i) q^{89} -16251.4 q^{90} +(1.98980e6 + 125631. i) q^{91} -1.91751e6 q^{92} +(4.70839e6 + 8.15516e6i) q^{93} +(-36372.1 + 62998.4i) q^{94} +(-1.01448e7 + 1.75713e7i) q^{95} +(-92626.8 - 160434. i) q^{96} +1.31315e7 q^{97} +(-22691.5 - 54048.0i) q^{98} +881492. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 58 q - 31 q^{2} - 1893 q^{4} + 48 q^{5} - 4602 q^{6} + 85 q^{7} + 11436 q^{8} - 25535 q^{9}+O(q^{10}) $ 58 * q - 31 * q^2 - 1893 * q^4 + 48 * q^5 - 4602 * q^6 + 85 * q^7 + 11436 * q^8 - 25535 * q^9	\( 58 q - 31 q^{2} - 1893 q^{4} + 48 q^{5} - 4602 q^{6} + 85 q^{7} + 11436 q^{8} - 25535 q^{9} + 3029 q^{10} - 15843 q^{11} + 10995 q^{12} - 127426 q^{13} - 65720 q^{14} + 115668 q^{15} - 154909 q^{16} + 43475 q^{17} - 67288 q^{18} + 64641 q^{19} + 40146 q^{20} - 321354 q^{21} + 170964 q^{22} - 96894 q^{23} + 501382 q^{24} - 637413 q^{25} + 68107 q^{26} + 156816 q^{27} - 877133 q^{28} + 155846 q^{29} - 335448 q^{30} + 393806 q^{31} - 1827215 q^{32} + 299052 q^{33} - 38692 q^{34} - 133704 q^{35} + 5417220 q^{36} - 597180 q^{37} - 502034 q^{38} + 1223016 q^{40} - 1436280 q^{41} - 2542432 q^{42} + 3496372 q^{43} - 2679210 q^{44} - 2509582 q^{45} + 2358719 q^{46} + 2368643 q^{47} - 843698 q^{48} + 995403 q^{49} + 3451796 q^{50} - 2396956 q^{51} + 4158921 q^{52} - 1919163 q^{53} - 4029674 q^{54} + 6075808 q^{55} + 3653181 q^{56} + 11452960 q^{57} - 4051049 q^{58} + 48733 q^{59} - 2792030 q^{60} + 1417921 q^{61} - 10244784 q^{62} + 7636291 q^{63} + 30707792 q^{64} - 105456 q^{65} - 22397813 q^{66} - 7025007 q^{67} + 5107354 q^{68} - 19729612 q^{69} - 13744304 q^{70} + 29267486 q^{71} - 7267524 q^{72} - 2417490 q^{73} + 2601511 q^{74} + 17567528 q^{75} - 19814476 q^{76} - 824982 q^{77} + 10110594 q^{78} - 7837082 q^{79} - 7428483 q^{80} - 24976533 q^{81} - 11520562 q^{82} - 38573688 q^{83} - 14286428 q^{84} + 41189436 q^{85} + 17943598 q^{86} - 37502020 q^{87} - 2949879 q^{88} + 15969588 q^{89} - 114635026 q^{90} - 186745 q^{91} + 83440638 q^{92} - 14525204 q^{93} - 30315990 q^{94} - 8678760 q^{95} + 23478593 q^{96} - 14169276 q^{97} + 14221151 q^{98} + 83443706 q^{99}+O(q^{100}) \) 58 * q - 31 * q^2 - 1893 * q^4 + 48 * q^5 - 4602 * q^6 + 85 * q^7 + 11436 * q^8 - 25535 * q^9 + 3029 * q^10 - 15843 * q^11 + 10995 * q^12 - 127426 * q^13 - 65720 * q^14 + 115668 * q^15 - 154909 * q^16 + 43475 * q^17 - 67288 * q^18 + 64641 * q^19 + 40146 * q^20 - 321354 * q^21 + 170964 * q^22 - 96894 * q^23 + 501382 * q^24 - 637413 * q^25 + 68107 * q^26 + 156816 * q^27 - 877133 * q^28 + 155846 * q^29 - 335448 * q^30 + 393806 * q^31 - 1827215 * q^32 + 299052 * q^33 - 38692 * q^34 - 133704 * q^35 + 5417220 * q^36 - 597180 * q^37 - 502034 * q^38 + 1223016 * q^40 - 1436280 * q^41 - 2542432 * q^42 + 3496372 * q^43 - 2679210 * q^44 - 2509582 * q^45 + 2358719 * q^46 + 2368643 * q^47 - 843698 * q^48 + 995403 * q^49 + 3451796 * q^50 - 2396956 * q^51 + 4158921 * q^52 - 1919163 * q^53 - 4029674 * q^54 + 6075808 * q^55 + 3653181 * q^56 + 11452960 * q^57 - 4051049 * q^58 + 48733 * q^59 - 2792030 * q^60 + 1417921 * q^61 - 10244784 * q^62 + 7636291 * q^63 + 30707792 * q^64 - 105456 * q^65 - 22397813 * q^66 - 7025007 * q^67 + 5107354 * q^68 - 19729612 * q^69 - 13744304 * q^70 + 29267486 * q^71 - 7267524 * q^72 - 2417490 * q^73 + 2601511 * q^74 + 17567528 * q^75 - 19814476 * q^76 - 824982 * q^77 + 10110594 * q^78 - 7837082 * q^79 - 7428483 * q^80 - 24976533 * q^81 - 11520562 * q^82 - 38573688 * q^83 - 14286428 * q^84 + 41189436 * q^85 + 17943598 * q^86 - 37502020 * q^87 - 2949879 * q^88 + 15969588 * q^89 - 114635026 * q^90 - 186745 * q^91 + 83440638 * q^92 - 14525204 * q^93 - 30315990 * q^94 - 8678760 * q^95 + 23478593 * q^96 - 14169276 * q^97 + 14221151 * q^98 + 83443706 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.0355890	−	0.0616420i	−0.00314566	−	0.00544843i	0.864448	−	0.502722i	$-0.167668\pi$
$2$	−0.0355890	−	0.0616420i	−0.00314566	−	0.00544843i	−0.867594	+	0.497273i	$0.834335\pi$
$3$	−26.4772	+	45.8599i	−0.566171	+	0.980638i	0.430768	+	0.902463i	$0.358243\pi$
$3$	−26.4772	+	45.8599i	−0.566171	+	0.980638i	−0.996940	+	0.0781750i	$0.975091\pi$
$4$	63.9975	−	110.847i	0.499980	−	0.865991i
$5$	184.974	+	320.384i	0.661781	+	1.14624i	0.980147	+	0.198271i	$0.0635327\pi$
$5$	184.974	+	320.384i	0.661781	+	1.14624i	−0.318366	+	0.947968i	$0.603134\pi$
$6$	3.76919			0.00712392
$7$	−905.689	−	57.1831i	−0.998013	−	0.0630122i
$7$	−905.689	−	57.1831i	−0.998013	−	0.0630122i
$8$	−18.2212			−0.0125824
$9$	−308.586	−	534.486i	−0.141100	−	0.244392i
$10$	13.1661	−	22.8043i	0.00416347	−	0.00721135i
$11$	−714.139	+	1236.92i	−0.161774	+	0.280200i	−0.935505	−	0.353314i	$-0.885055\pi$
$11$	−714.139	+	1236.92i	−0.161774	+	0.280200i	0.773731	+	0.633514i	$0.218388\pi$
$12$	3388.95	+	5869.83i	0.566149	+	0.980599i
$13$	−2197.00			−0.277350
$13$	−2197.00			−0.277350
$14$	28.7077	+	57.8636i	0.00279609	+	0.00563582i
$15$	−19590.3			−1.49873
$16$	−8191.03	−	14187.3i	−0.499941	−	0.865923i
$17$	−903.069	+	1564.16i	−0.0445810	+	0.0772165i	−0.887455	−	0.460895i	$-0.847529\pi$
$17$	−903.069	+	1564.16i	−0.0445810	+	0.0772165i	0.842874	+	0.538111i	$0.180862\pi$
$18$	−21.9645	+	38.0437i	−0.000887704	+	0.00153755i
$19$	27422.3	+	47496.8i	0.917204	+	1.58864i	0.803642	+	0.595112i	$0.202892\pi$
$19$	27422.3	+	47496.8i	0.917204	+	1.58864i	0.113561	+	0.993531i	$0.463774\pi$
$20$	47351.4			1.32351
$21$	26602.5	−	40020.8i	0.626838	−	0.943013i
$22$	101.662			0.00203554
$23$	−7490.56	−	12974.0i	−0.128371	−	0.222345i	0.794675	−	0.607036i	$-0.207641\pi$
$23$	−7490.56	−	12974.0i	−0.128371	−	0.222345i	−0.923046	+	0.384691i	$0.874308\pi$
$24$	482.447	−	835.623i	0.00712378	−	0.0123387i
$25$	−29367.9	+	50866.7i	−0.375909	+	0.651094i
$26$	78.1891	+	135.427i	0.000872448	+	0.00151112i
$27$	−83129.4			−0.812796
$28$	−64300.4	+	96733.2i	−0.553555	+	0.832765i
$29$	−186368.			−1.41899			−0.709493	−	0.704712i	$-0.751076\pi$
$29$	−186368.			−1.41899			−0.709493	+	0.704712i	$0.751076\pi$
$30$	697.201	+	1207.59i	0.00471448	+	0.00816572i
$31$	88913.9	−	154003.i	0.536048	−	0.928463i	−0.463064	−	0.886325i	$-0.653250\pi$
$31$	88913.9	−	154003.i	0.536048	−	0.928463i	0.999112	−	0.0421376i	$-0.0134168\pi$
$32$	−1749.18	+	3029.67i	−0.00943647	+	0.0163444i
$33$	−37816.8	−	65500.6i	−0.183183	−	0.317283i
$34$	128.557			0.000560945
$35$	−149208.	−	300745.i	−0.588239	−	1.18566i
$36$	−78994.8			−0.282189
$37$	−185341.	−	321020.i	−0.601541	−	1.04190i	−0.992588	−	0.121529i	$-0.961220\pi$
$37$	−185341.	−	321020.i	−0.601541	−	1.04190i	0.391047	−	0.920371i	$-0.372113\pi$
$38$	1951.86	−	3380.73i	0.00577041	−	0.00999465i
$39$	58170.4	−	100754.i	0.157028	−	0.271980i
$40$	−3370.44	−	5837.78i	−0.00832678	−	0.0144224i
$41$	−828388.			−1.87711			−0.938557	−	0.345125i	$-0.887837\pi$
$41$	−828388.			−1.87711			−0.938557	+	0.345125i	$0.887837\pi$
$42$	−3413.72	−	215.534i	−0.00710976	−	0.000448894i
$43$	−177329.			−0.340126			−0.170063	−	0.985433i	$-0.554397\pi$
$43$	−177329.			−0.340126			−0.170063	+	0.985433i	$0.554397\pi$
$44$	91406.2	+	158320.i	0.161767	+	0.280189i
$45$	114160.	−	197732.i	0.186755	−	0.323469i
$46$	−533.163	+	923.466i	−0.000807621	+	0.00139884i
$47$	−511002.	−	885081.i	−0.717927	−	1.24349i	−0.961820	−	0.273683i	$-0.911758\pi$
$47$	−511002.	−	885081.i	−0.717927	−	1.24349i	0.243893	−	0.969802i	$-0.421575\pi$
$48$	867502.			1.13221
$49$	817003.	+	103580.i	0.992059	+	0.125774i
$50$	4180.70			0.00472993
$51$	−47821.5	−	82829.2i	−0.0504809	−	0.0874355i
$52$	−140602.	+	243531.i	−0.138670	+	0.240183i
$53$	−636768.	+	1.10291e6i	−0.587510	+	1.01760i	0.407047	+	0.913407i	$0.366558\pi$
$53$	−636768.	+	1.10291e6i	−0.587510	+	1.01760i	−0.994557	+	0.104190i	$0.966775\pi$
$54$	2958.49	+	5124.26i	0.00255677	+	0.00442846i
$55$	−528387.			−0.428236
$56$	16502.8	+	1041.95i	0.0125574	+	0.000792843i
$57$	−2.90426e6			−2.07718
$58$	6632.65	+	11488.1i	0.00446364	+	0.00773125i
$59$	564552.	−	977833.i	0.357867	−	0.619844i	−0.629737	−	0.776808i	$-0.716837\pi$
$59$	564552.	−	977833.i	0.357867	−	0.619844i	0.987604	+	0.156964i	$0.0501707\pi$
$60$	−1.25373e6	+	2.17153e6i	−0.749334	+	1.29788i
$61$	844239.	+	1.46227e6i	0.476224	+	0.824844i	0.999629	−	0.0272401i	$-0.00867185\pi$
$61$	844239.	+	1.46227e6i	0.476224	+	0.824844i	−0.523405	+	0.852084i	$0.675339\pi$
$62$	−12657.4			−0.00674489
$63$	248919.	+	501724.i	0.125420	+	0.252798i
$64$	−2.09665e6			−0.999763
$65$	−406387.	−	703883.i	−0.183545	−	0.317910i
$66$	−2691.73	+	4662.21i	−0.00115246	+	0.00199613i
$67$	757013.	−	1.31118e6i	0.307497	−	0.532601i	−0.670317	−	0.742075i	$-0.733842\pi$
$67$	757013.	−	1.31118e6i	0.307497	−	0.532601i	0.977814	+	0.209474i	$0.0671751\pi$
$68$	115588.	+	200205.i	0.0445792	+	0.0772134i
$69$	793316.			0.290720
$70$	−13228.4	+	19900.7i	−0.00460960	+	0.00693467i
$71$	−3.47517e6			−1.15232			−0.576158	−	0.817339i	$-0.695449\pi$
$71$	−3.47517e6			−1.15232			−0.576158	+	0.817339i	$0.695449\pi$
$72$	5622.81	+	9738.99i	0.00177537	+	0.00307503i
$73$	−155345.	+	269065.i	−0.0467376	+	0.0809519i	−0.888448	−	0.458978i	$-0.848216\pi$
$73$	−155345.	+	269065.i	−0.0467376	+	0.0809519i	0.841710	+	0.539930i	$0.181549\pi$
$74$	−13192.2	+	22849.6i	−0.00378448	+	0.00655491i
$75$	−1.55516e6	−	2.69362e6i	−0.425658	−	0.737262i
$76$	7.01982e6			1.83433
$77$	717519.	−	1.07943e6i	0.179108	−	0.269450i
$78$	−8280.92			−0.00197582
$79$	2.10806e6	+	3.65127e6i	0.481048	+	0.833200i	0.999763	−	0.0217473i	$-0.00692293\pi$
$79$	2.10806e6	+	3.65127e6i	0.481048	+	0.833200i	−0.518715	+	0.854947i	$0.673590\pi$
$80$	3.03025e6	−	5.24854e6i	0.661703	−	1.14610i
$81$	2.87591e6	−	4.98122e6i	0.601282	−	1.04145i
$82$	29481.5	+	51063.5i	0.00590475	+	0.0102273i
$83$	−3.50541e6			−0.672924			−0.336462	−	0.941697i	$-0.609230\pi$
$83$	−3.50541e6			−0.672924			−0.336462	+	0.941697i	$0.609230\pi$
$84$	−2.73368e6	−	5.51003e6i	−0.503234	−	1.01432i
$85$	−668175.			−0.118011
$86$	6310.97	+	10930.9i	0.00106992	+	0.00185316i
$87$	4.93450e6	−	8.54681e6i	0.803389	−	1.39151i
$88$	13012.5	−	22538.3i	0.00203550	−	0.00352559i
$89$	1.88836e6	+	3.27073e6i	0.283935	+	0.491790i	0.972350	−	0.233527i	$-0.0750266\pi$
$89$	1.88836e6	+	3.27073e6i	0.283935	+	0.491790i	−0.688415	+	0.725317i	$0.741693\pi$
$90$	−16251.4			−0.00234986
$91$	1.98980e6	+	125631.i	0.276799	+	0.0174764i
$92$	−1.91751e6			−0.256732
$93$	4.70839e6	+	8.15516e6i	0.606990	+	1.05134i
$94$	−36372.1	+	62998.4i	−0.00451670	+	0.00782315i
$95$	−1.01448e7	+	1.75713e7i	−1.21398	+	2.10267i
$96$	−92626.8	−	160434.i	−0.0106853	−	0.0185075i
$97$	1.31315e7			1.46088			0.730439	−	0.682978i	$-0.239316\pi$
$97$	1.31315e7			1.46088			0.730439	+	0.682978i	$0.239316\pi$
$98$	−22691.5	−	54048.0i	−0.00243540	−	0.00580081i
$99$	881492.			0.0913051
$100$	3.75895e6	+	6.51069e6i	0.375895	+	0.651069i
$101$	−5.36484e6	+	9.29217e6i	−0.518122	+	0.897413i	0.481656	+	0.876360i	$0.340035\pi$
$101$	−5.36484e6	+	9.29217e6i	−0.518122	+	0.897413i	−0.999778	+	0.0210533i	$0.993298\pi$
$102$	−3403.84	+	5895.62i	−0.000317591	+	0.000550084i
$103$	−1.97739e6	−	3.42495e6i	−0.178305	−	0.308833i	0.762995	−	0.646404i	$-0.223728\pi$
$103$	−1.97739e6	−	3.42495e6i	−0.178305	−	0.308833i	−0.941300	+	0.337571i	$0.890395\pi$
$104$	40032.0			0.00348972
$105$	1.77428e7	+	1.12024e6i	1.49575	+	0.0944381i
$106$	90647.7			0.00739242
$107$	−303196.	−	525151.i	−0.0239266	−	0.0414421i	0.853814	−	0.520578i	$-0.174283\pi$
$107$	−303196.	−	525151.i	−0.0239266	−	0.0414421i	−0.877741	+	0.479136i	$0.840950\pi$
$108$	−5.32007e6	+	9.21463e6i	−0.406382	+	0.703874i
$109$	−5.28909e6	+	9.16097e6i	−0.391190	+	0.677561i	−0.992607	−	0.121374i	$-0.961270\pi$
$109$	−5.28909e6	+	9.16097e6i	−0.391190	+	0.677561i	0.601417	+	0.798936i	$0.294603\pi$
$110$	18804.8	+	32570.8i	0.00134708	+	0.00233321i
$111$	1.96292e7			1.36230
$112$	6.60725e6	+	1.33177e7i	0.444383	+	0.895704i
$113$	−1.69725e6			−0.110655			−0.0553274	−	0.998468i	$-0.517620\pi$
$113$	−1.69725e6			−0.110655			−0.0553274	+	0.998468i	$0.517620\pi$
$114$	103360.	+	179024.i	0.00653409	+	0.0113174i
$115$	2.77111e6	−	4.79970e6i	0.169907	−	0.294288i
$116$	−1.19271e7	+	2.06583e7i	−0.709465	+	1.22883i
$117$	677963.	+	1.17427e6i	0.0391341	+	0.0677822i
$118$	−80367.5			−0.00450291
$119$	907343.	−	1.36500e6i	0.0493580	−	0.0742539i
$120$	356960.			0.0188575
$121$	8.72360e6	+	1.51097e7i	0.447658	+	0.775367i
$122$	60091.3	−	104081.i	0.00299607	−	0.00518935i
$123$	2.19334e7	−	3.79898e7i	1.06277	−	1.84077i
$124$	−1.13805e7	−	1.97117e7i	−0.536027	−	0.928426i
$125$	7.17296e6			0.328483
$126$	22068.5	−	33199.7i	0.000982824	−	0.00147856i
$127$	5.62537e6			0.243690			0.121845	−	0.992549i	$-0.461119\pi$
$127$	5.62537e6			0.243690			0.121845	+	0.992549i	$0.461119\pi$
$128$	298513.	+	517039.i	0.0125814	+	0.0217916i
$129$	4.69518e6	−	8.13229e6i	0.192570	−	0.333541i
$130$	−28925.8	+	50101.0i	−0.00115474	+	0.00200007i
$131$	−9.87310e6	−	1.71007e7i	−0.383711	−	0.664607i	0.607879	−	0.794030i	$-0.292021\pi$
$131$	−9.87310e6	−	1.71007e7i	−0.383711	−	0.664607i	−0.991589	+	0.129423i	$0.958687\pi$
$132$	−9.68072e6			−0.366352
$133$	−2.21200e7	−	4.45854e7i	−0.815277	−	1.64328i
$134$	−107765.			−0.00386912
$135$	−1.53767e7	−	2.66333e7i	−0.537893	−	0.931658i
$136$	16455.0	−	28500.9i	0.000560934	−	0.000971567i
$137$	−7.02416e6	+	1.21662e7i	−0.233385	+	0.404234i	−0.958802	−	0.284075i	$-0.908314\pi$
$137$	−7.02416e6	+	1.21662e7i	−0.233385	+	0.404234i	0.725417	+	0.688309i	$0.241647\pi$
$138$	−28233.4	−	48901.6i	−0.000914504	−	0.00158397i
$139$	3.65525e7			1.15442			0.577211	−	0.816595i	$-0.304141\pi$
$139$	3.65525e7			1.15442			0.577211	+	0.816595i	$0.304141\pi$
$140$	−4.28856e7	−	2.70770e6i	−1.32088	−	0.0833973i
$141$	5.41196e7			1.62588
$142$	123678.	+	214216.i	0.00362479	+	0.00627831i
$143$	1.56896e6	−	2.71752e6i	0.0448680	−	0.0777136i
$144$	−5.05527e6	+	8.75598e6i	−0.141083	+	0.244363i
$145$	−3.44731e7	−	5.97092e7i	−0.939059	−	1.62650i
$146$	22114.3			0.000588082
$147$	−2.63821e7	+	3.47252e7i	−0.685014	+	0.901641i
$148$	−4.74454e7			−1.20303
$149$	1.77478e7	+	3.07401e7i	0.439535	+	0.761296i	0.997654	−	0.0684647i	$-0.0218101\pi$
$149$	1.77478e7	+	3.07401e7i	0.439535	+	0.761296i	−0.558119	+	0.829761i	$0.688477\pi$
$150$	−110693.	+	191727.i	−0.00267795	+	0.00463834i
$151$	−1.63115e7	+	2.82524e7i	−0.385545	+	0.667784i	−0.991845	−	0.127453i	$-0.959320\pi$
$151$	−1.63115e7	+	2.82524e7i	−0.385545	+	0.667784i	0.606299	+	0.795236i	$0.292653\pi$
$152$	−499667.	−	865449.i	−0.0115406	−	0.0199889i
$153$	1.11470e6			0.0251615
$154$	−92074.2	−	5813.35i	−0.00203149	−	0.000128264i
$155$	6.57869e7			1.41899
$156$	−7.44552e6	−	1.28960e7i	−0.157021	−	0.271969i
$157$	−4.15051e7	+	7.18890e7i	−0.855959	+	1.48256i	0.0197934	+	0.999804i	$0.493699\pi$
$157$	−4.15051e7	+	7.18890e7i	−0.855959	+	1.48256i	−0.875752	+	0.482760i	$0.839634\pi$
$158$	150048.	−	259890.i	0.00302642	−	0.00524192i
$159$	−3.37197e7	−	5.84042e7i	−0.665263	−	1.15227i
$160$	−1.29421e6			−0.0249795
$161$	6.04222e6	+	1.21788e7i	0.114105	+	0.229992i
$162$	−409403.			−0.00756570
$163$	−2.71508e7	−	4.70266e7i	−0.491051	−	0.850525i	0.508896	−	0.860828i	$-0.330054\pi$
$163$	−2.71508e7	−	4.70266e7i	−0.491051	−	0.850525i	−0.999947	+	0.0103031i	$0.996720\pi$
$164$	−5.30148e7	+	9.18243e7i	−0.938520	+	1.62556i
$165$	1.39902e7	−	2.42318e7i	0.242455	−	0.419944i
$166$	124754.	+	216081.i	0.00211679	+	0.00366638i
$167$	−8.87901e7			−1.47522			−0.737610	−	0.675227i	$-0.764046\pi$
$167$	−8.87901e7			−1.47522			−0.737610	+	0.675227i	$0.764046\pi$
$168$	−484731.	+	729227.i	−0.00788711	+	0.0118653i
$169$	4.82681e6			0.0769231
$170$	23779.7	+	41187.7i	0.000371223	+	0.000642978i
$171$	1.69242e7	−	2.93136e7i	0.258835	−	0.448315i
$172$	−1.13486e7	+	1.96564e7i	−0.170056	+	0.294546i
$173$	4.68903e7	+	8.12165e7i	0.688529	+	1.19257i	0.972314	+	0.233679i	$0.0750764\pi$
$173$	4.68903e7	+	8.12165e7i	0.688529	+	1.19257i	−0.283785	+	0.958888i	$0.591590\pi$
$174$	−702457.			−0.0101087
$175$	2.95069e7	−	4.43901e7i	0.416189	−	0.626114i
$176$	2.33981e7			0.323509
$177$	2.98955e7	+	5.17806e7i	0.405229	+	0.701876i
$178$	134410.	−	232804.i	0.00178632	−	0.00309400i
$179$	5.60102e6	−	9.70125e6i	0.0729930	−	0.126428i	−0.827219	−	0.561880i	$-0.810078\pi$
$179$	5.60102e6	−	9.70125e6i	0.0729930	−	0.126428i	0.900212	+	0.435452i	$0.143412\pi$
$180$	−1.46119e7	−	2.53086e7i	−0.186747	−	0.323456i
$181$	−5.06010e7			−0.634284			−0.317142	−	0.948378i	$-0.602723\pi$
$181$	−5.06010e7			−0.634284			−0.317142	+	0.948378i	$0.602723\pi$
$182$	−63070.9	−	127126.i	−0.000775495	−	0.00156310i
$183$	−8.94124e7			−1.07850
$184$	136487.	+	236403.i	0.00161521	+	0.00279763i
$185$	6.85663e7	−	1.18760e8i	0.796177	−	1.37902i
$186$	335134.	−	580469.i	0.00381876	−	0.00661429i
$187$	−1.28983e6	−	2.23406e6i	−0.0144241	−	0.0249832i
$188$	−1.30811e8			−1.43580
$189$	7.52894e7	+	4.75360e6i	0.811180	+	0.0512160i
$190$	1.44417e6			0.0152750
$191$	−6.18476e7	−	1.07123e8i	−0.642252	−	1.11241i	−0.984929	−	0.172960i	$-0.944667\pi$
$191$	−6.18476e7	−	1.07123e8i	−0.642252	−	1.11241i	0.342676	−	0.939454i	$-0.388667\pi$
$192$	5.55136e7	−	9.61523e7i	0.566037	−	0.980405i
$193$	−8.03602e7	+	1.39188e8i	−0.804619	+	1.39364i	0.111929	+	0.993716i	$0.464297\pi$
$193$	−8.03602e7	+	1.39188e8i	−0.804619	+	1.39364i	−0.916548	+	0.399925i	$0.869036\pi$
$194$	−467338.	−	809453.i	−0.00459542	−	0.00795950i
$195$	4.30400e7			0.415672
$196$	6.37677e7	−	8.39334e7i	0.604929	−	0.796230i
$197$	9.90276e7			0.922836			0.461418	−	0.887183i	$-0.347341\pi$
$197$	9.90276e7			0.922836			0.461418	+	0.887183i	$0.347341\pi$
$198$	−31371.4	−	54336.9i	−0.000287214	−	0.000497470i
$199$	−8.26686e7	+	1.43186e8i	−0.743627	+	1.28800i	0.207207	+	0.978297i	$0.433563\pi$
$199$	−8.26686e7	+	1.43186e8i	−0.743627	+	1.28800i	−0.950834	+	0.309702i	$0.899771\pi$
$200$	535119.	−	926854.i	0.00472983	−	0.00819231i
$201$	4.00872e7	+	6.94330e7i	0.348192	+	0.603087i
$202$	763718.			0.00651933
$203$	1.68791e8	+	1.06571e7i	1.41617	+	0.0894134i
$204$	−1.22418e7			−0.100958
$205$	−1.53230e8	−	2.65402e8i	−1.24224	−	2.15162i
$206$	−140747.	+	243781.i	−0.00112177	+	0.00194296i
$207$	−4.62296e6	+	8.00720e6i	−0.0362263	+	0.0627457i
$208$	1.79957e7	+	3.11694e7i	0.138659	+	0.240164i
$209$	−7.83332e7			−0.593518
$210$	−562394.	−	1.13357e6i	−0.00419057	−	0.00844656i
$211$	1.48346e8			1.08715			0.543573	−	0.839362i	$-0.317071\pi$
$211$	1.48346e8			1.08715			0.543573	+	0.839362i	$0.317071\pi$
$212$	8.15030e7	+	1.41167e8i	0.587487	+	1.01756i
$213$	9.20127e7	−	1.59371e8i	0.652408	−	1.13000i
$214$	−21580.9	+	37379.2i	−0.000150530	+	0.000260725i
$215$	−3.28012e7	−	5.68133e7i	−0.225089	−	0.389866i
$216$	1.51472e6			0.0102269
$217$	−8.93348e7	+	1.34395e8i	−0.593487	+	0.892840i
$218$	752934.			0.00492220
$219$	−8.22619e6	−	1.42482e7i	−0.0529230	−	0.0916653i
$220$	−3.38154e7	+	5.85701e7i	−0.214109	+	0.370848i
$221$	1.98404e6	−	3.43646e6i	0.0123645	−	0.0214160i
$222$	−698586.	−	1.20999e6i	−0.00428533	−	0.00742241i
$223$	−1.46498e8			−0.884638			−0.442319	−	0.896858i	$-0.645844\pi$
$223$	−1.46498e8			−0.884638			−0.442319	+	0.896858i	$0.645844\pi$
$224$	1.75746e6	−	2.64391e6i	0.0104476	−	0.0157173i
$225$	3.62501e7			0.212163
$226$	60403.4	+	104622.i	0.000348082	+	0.000602896i
$227$	1.63644e7	−	2.83439e7i	0.0928557	−	0.160831i	−0.815856	−	0.578255i	$-0.803734\pi$
$227$	1.63644e7	−	2.83439e7i	0.0928557	−	0.160831i	0.908712	+	0.417424i	$0.137067\pi$
$228$	−1.85865e8	+	3.21928e8i	−1.03855	+	1.79882i
$229$	1.35913e8	+	2.35408e8i	0.747886	+	1.29538i	0.948834	+	0.315775i	$0.102265\pi$
$229$	1.35913e8	+	2.35408e8i	0.747886	+	1.29538i	−0.200948	+	0.979602i	$0.564402\pi$
$230$	−394484.			−0.00213788
$231$	3.05048e7	+	6.14857e7i	0.162827	+	0.328195i
$232$	3.39585e6			0.0178542
$233$	−4.62244e7	−	8.00631e7i	−0.239401	−	0.414655i	0.721142	−	0.692788i	$-0.243618\pi$
$233$	−4.62244e7	−	8.00631e7i	−0.239401	−	0.414655i	−0.960543	+	0.278133i	$0.910284\pi$
$234$	48256.1	−	83581.9i	0.000246205	−	0.000426439i
$235$	1.89044e8	−	3.27433e8i	0.950221	−	1.64583i
$236$	−7.22598e7	−	1.25158e8i	−0.357853	−	0.619820i
$237$	−2.23262e8			−1.08942
$238$	−116433.	−	7351.31i	−0.000559831	−	3.53464e-5i
$239$	4.10071e8			1.94297			0.971487	−	0.237093i	$-0.0761948\pi$
$239$	4.10071e8			1.94297			0.971487	+	0.237093i	$0.0761948\pi$
$240$	1.60465e8	+	2.77933e8i	0.749274	+	1.29778i
$241$	1.43313e8	−	2.48225e8i	0.659516	−	1.14231i	−0.321225	−	0.947003i	$-0.604095\pi$
$241$	1.43313e8	−	2.48225e8i	0.659516	−	1.14231i	0.980741	−	0.195312i	$-0.0625720\pi$
$242$	620929.	−	1.07548e6i	0.00281636	−	0.00487808i
$243$	6.13902e7	+	1.06331e8i	0.274459	+	0.475377i
$244$	2.16117e8			0.952410
$245$	1.17939e8	+	2.80914e8i	0.512359	+	1.22037i
$246$	−3.12236e6			−0.0133724
$247$	−6.02467e7	−	1.04350e8i	−0.254387	−	0.440610i
$248$	−1.62012e6	+	2.80613e6i	−0.00674476	+	0.0116823i
$249$	9.28136e7	−	1.60758e8i	0.380990	−	0.659894i
$250$	−255279.	−	442156.i	−0.00103330	−	0.00178972i
$251$	4.49573e8			1.79449			0.897247	−	0.441530i	$-0.145564\pi$
$251$	4.49573e8			1.79449			0.897247	+	0.441530i	$0.145564\pi$
$252$	7.15447e7	+	4.51717e6i	0.281628	+	0.0177813i
$253$	2.13972e7			0.0830682
$254$	−200201.	−	346759.i	−0.000766566	−	0.00132773i
$255$	1.76914e7	−	3.06424e7i	0.0668147	−	0.115726i
$256$	−1.34165e8	+	2.32380e8i	−0.499802	+	0.865683i
$257$	4.76805e7	+	8.25850e7i	0.175216	+	0.303484i	0.940236	−	0.340523i	$-0.110604\pi$
$257$	4.76805e7	+	8.25850e7i	0.175216	+	0.303484i	−0.765020	+	0.644007i	$0.777271\pi$
$258$	−668387.			−0.00242303
$259$	1.49504e8	+	3.01343e8i	0.534693	+	1.07773i
$260$	−1.04031e8			−0.367076
$261$	5.75105e7	+	9.96110e7i	0.200219	+	0.346789i
$262$	−702748.	+	1.21720e6i	−0.00241404	+	0.00418125i
$263$	3.98694e7	−	6.90559e7i	0.135143	−	0.234075i	−0.790509	−	0.612451i	$-0.790184\pi$
$263$	3.98694e7	−	6.90559e7i	0.135143	−	0.234075i	0.925652	+	0.378375i	$0.123517\pi$
$264$	689068.	+	1.19350e6i	0.00230488	+	0.00399217i
$265$	−4.71141e8			−1.55521
$266$	−1.96110e6	+	2.95027e6i	−0.00638873	+	0.00961118i
$267$	−1.99994e8			−0.643024
$268$	−9.68938e7	−	1.67825e8i	−0.307485	−	0.532580i
$269$	−3.80868e7	+	6.59683e7i	−0.119300	+	0.206634i	−0.919491	−	0.393112i	$-0.871398\pi$
$269$	−3.80868e7	+	6.59683e7i	−0.119300	+	0.206634i	0.800190	+	0.599746i	$0.204732\pi$
$270$	−1.09449e6	+	1.89571e6i	−0.00338405	+	0.00586135i
$271$	3.11274e7	+	5.39142e7i	0.0950057	+	0.164555i	0.909611	−	0.415461i	$-0.136380\pi$
$271$	3.11274e7	+	5.39142e7i	0.0950057	+	0.164555i	−0.814605	+	0.580016i	$0.803046\pi$
$272$	2.95882e7			0.0891513
$273$	−5.84458e7	+	8.79256e7i	−0.173854	+	0.261545i
$274$	999933.			0.00293659
$275$	−4.19456e7	−	7.26518e7i	−0.121625	−	0.210660i
$276$	5.07702e7	−	8.79366e7i	0.145354	−	0.251761i
$277$	1.05965e8	−	1.83537e8i	0.299560	−	0.518852i	−0.676476	−	0.736465i	$-0.736494\pi$
$277$	1.05965e8	−	1.83537e8i	0.299560	−	0.518852i	0.976035	+	0.217613i	$0.0698269\pi$
$278$	−1.30087e6	−	2.25317e6i	−0.00363142	−	0.00628980i
$279$	−1.09750e8			−0.302546
$280$	2.71875e6	+	5.47995e6i	0.00740145	+	0.0149184i
$281$	−4.37727e8			−1.17688			−0.588439	−	0.808541i	$-0.700257\pi$
$281$	−4.37727e8			−1.17688			−0.588439	+	0.808541i	$0.700257\pi$
$282$	−1.92606e6	−	3.33604e6i	−0.00511445	−	0.00885849i
$283$	1.81369e8	−	3.14141e8i	0.475676	−	0.823894i	−0.523936	−	0.851758i	$-0.675537\pi$
$283$	1.81369e8	−	3.14141e8i	0.475676	−	0.823894i	0.999612	+	0.0278632i	$0.00887029\pi$
$284$	−2.22402e8	+	3.85211e8i	−0.576135	+	0.997895i
$285$	−5.37212e8	−	9.30478e8i	−1.37464	−	2.38094i
$286$	−223351.			−0.000564557
$287$	7.50263e8	+	4.73698e7i	1.87338	+	0.118281i
$288$	2.15909e6			0.00532594
$289$	2.03538e8	+	3.52539e8i	0.496025	+	0.859141i
$290$	−2.45373e6	+	4.24999e6i	−0.00590791	+	0.0102328i
$291$	−3.47686e8	+	6.02210e8i	−0.827107	+	1.43259i
$292$	1.98833e7	+	3.44390e7i	0.0467358	+	0.0809487i
$293$	−7.96195e8			−1.84920			−0.924598	−	0.380944i	$-0.875599\pi$
$293$	−7.96195e8			−1.84920			−0.924598	+	0.380944i	$0.875599\pi$
$294$	3.07944e6	+	390414.i	0.00706735	+	0.000896003i
$295$	4.17709e8			0.947320
$296$	3.37714e6	+	5.84937e6i	0.00756881	+	0.0131096i
$297$	5.93659e7	−	1.02825e8i	0.131489	−	0.227746i
$298$	1.26326e6	−	2.18802e6i	0.00276525	−	0.00478955i
$299$	1.64568e7	+	2.85039e7i	0.0356037	+	0.0616674i
$300$	−3.98106e8			−0.851283
$301$	1.60605e8	+	1.01402e7i	0.339450	+	0.0214321i
$302$	2.32205e6			0.00485117
$303$	−2.84092e8	−	4.92062e8i	−0.586692	−	1.01618i
$304$	4.49233e8	−	7.78095e8i	0.917095	−	1.58845i
$305$	−3.12324e8	+	5.40961e8i	−0.630312	+	1.09173i
$306$	−39670.9	−	68712.1i	−7.91494e−5	−	0.000137091i
$307$	6.01182e6			0.0118583			0.00592913	−	0.999982i	$-0.498113\pi$
$307$	6.01182e6			0.0118583			0.00592913	+	0.999982i	$0.498113\pi$
$308$	−7.37323e7	−	1.48616e8i	−0.143791	−	0.289826i
$309$	2.09423e8			0.403804
$310$	−2.34129e6	−	4.05524e6i	−0.00446364	−	0.00773126i
$311$	−1.60492e8	+	2.77980e8i	−0.302546	+	0.524024i	−0.976712	−	0.214555i	$-0.931170\pi$
$311$	−1.60492e8	+	2.77980e8i	−0.302546	+	0.524024i	0.674166	+	0.738580i	$0.264503\pi$
$312$	−1.05994e6	+	1.83586e6i	−0.00197578	+	0.00342215i
$313$	−4.14879e8	−	7.18591e8i	−0.764743	−	1.32457i	−0.940382	−	0.340120i	$-0.889532\pi$
$313$	−4.14879e8	−	7.18591e8i	−0.764743	−	1.32457i	0.175639	−	0.984455i	$-0.443801\pi$
$314$	5.90851e6			0.0107702
$315$	−1.14701e8	+	1.72555e8i	−0.206766	+	0.311058i
$316$	5.39642e8			0.962058
$317$	1.61104e8	+	2.79041e8i	0.284053	+	0.491995i	0.972379	−	0.233407i	$-0.0749874\pi$
$317$	1.61104e8	+	2.79041e8i	0.284053	+	0.491995i	−0.688326	+	0.725402i	$0.741654\pi$
$318$	−2.40010e6	+	4.15709e6i	−0.00418537	+	0.00724928i
$319$	1.33093e8	−	2.30523e8i	0.229555	−	0.397601i
$320$	−3.87826e8	−	6.71734e8i	−0.661624	−	1.14597i
$321$	3.21112e7			0.0541862
$322$	535687.	−	805885.i	0.000894160	−	0.00134517i
$323$	−9.90568e7			−0.163559
$324$	−3.68102e8	−	6.37571e8i	−0.601258	−	1.04141i
$325$	6.45213e7	−	1.11754e8i	0.104259	−	0.180581i
$326$	−1.93254e6	+	3.34726e6i	−0.00308935	+	0.00535092i
$327$	−2.80081e8	−	4.85114e8i	−0.442961	−	0.767232i
$328$	1.50942e7			0.0236185
$329$	4.12197e8	+	8.30829e8i	0.638145	+	1.28625i
$330$	−1.99159e6			−0.00305072
$331$	2.18643e8	+	3.78701e8i	0.331389	+	0.573983i	0.982784	−	0.184756i	$-0.0591494\pi$
$331$	2.18643e8	+	3.78701e8i	0.331389	+	0.573983i	−0.651395	+	0.758738i	$0.725816\pi$
$332$	−2.24338e8	+	3.88564e8i	−0.336449	+	0.582746i
$333$	−1.14387e8	+	1.98124e8i	−0.169755	+	0.294024i
$334$	3.15995e6	+	5.47320e6i	0.00464054	+	0.00803764i
$335$	5.60109e8			0.813984
$336$	−7.85688e8	−	4.96065e7i	−1.12996	−	0.0713429i
$337$	−1.13525e8			−0.161580			−0.0807902	−	0.996731i	$-0.525744\pi$
$337$	−1.13525e8			−0.161580			−0.0807902	+	0.996731i	$0.525744\pi$
$338$	−171781.	−	297534.i	−0.000241973	−	0.000419110i
$339$	4.49384e7	−	7.78355e7i	0.0626496	−	0.108512i
$340$	−4.27615e7	+	7.40651e7i	−0.0590034	+	0.102197i
$341$	1.26994e8	+	2.19960e8i	0.173437	+	0.300402i
$342$	−2.40927e6			−0.00325682
$343$	−7.34028e8	−	1.40530e8i	−0.982162	−	0.188036i
$344$	3.23115e6			0.00427960
$345$	1.46743e8	+	2.54166e8i	0.192393	+	0.333234i
$346$	3.33756e6	−	5.78083e6i	0.00433175	−	0.00750281i
$347$	1.40680e8	−	2.43665e8i	0.180751	−	0.313069i	−0.761386	−	0.648299i	$-0.775481\pi$
$347$	1.40680e8	−	2.43665e8i	0.180751	−	0.313069i	0.942136	+	0.335230i	$0.108814\pi$
$348$	−6.31591e8	−	1.09395e9i	−0.803357	−	1.39146i
$349$	3.95817e8			0.498431			0.249215	−	0.968448i	$-0.419827\pi$
$349$	3.95817e8			0.498431			0.249215	+	0.968448i	$0.419827\pi$
$350$	−3.78642e6	−	239066.i	−0.00472053	−	0.000298043i
$351$	1.82635e8			0.225429
$352$	−2.49831e6	−	4.32721e6i	−0.00305315	−	0.00528821i
$353$	−8.16603e8	+	1.41440e9i	−0.988096	+	1.71143i	−0.360822	+	0.932635i	$0.617504\pi$
$353$	−8.16603e8	+	1.41440e9i	−0.988096	+	1.71143i	−0.627274	+	0.778798i	$0.715830\pi$
$354$	2.12791e6	−	3.68564e6i	0.00254942	−	0.00441572i
$355$	−6.42814e8	−	1.11339e9i	−0.762581	−	1.32083i
$356$	4.83400e8			0.567848
$357$	3.85750e7	+	7.77521e7i	0.0448711	+	0.0904427i
$358$	−797339.			−0.000918443
$359$	−3.53540e8	−	6.12349e8i	−0.403281	−	0.698503i	0.590839	−	0.806790i	$-0.298797\pi$
$359$	−3.53540e8	−	6.12349e8i	−0.403281	−	0.698503i	−0.994120	+	0.108286i	$0.965464\pi$
$360$	−2.08014e6	+	3.60291e6i	−0.00234982	+	0.00407000i
$361$	−1.05703e9	+	1.83082e9i	−1.18253	+	2.04819i
$362$	1.80084e6	+	3.11914e6i	0.00199524	+	0.00345585i
$363$	−9.23906e8			−1.01381
$364$	1.41268e8	−	2.12523e8i	0.153528	−	0.230968i
$365$	−1.14939e8			−0.123720
$366$	3.18210e6	+	5.51156e6i	0.00339258	+	0.00587612i
$367$	−7.45171e7	+	1.29067e8i	−0.0786910	+	0.136297i	−0.902685	−	0.430301i	$-0.858407\pi$
$367$	−7.45171e7	+	1.29067e8i	−0.0786910	+	0.136297i	0.823994	+	0.566598i	$0.191741\pi$
$368$	−1.22711e8	+	2.12541e8i	−0.128356	+	0.222319i
$369$	2.55629e8	+	4.42762e8i	0.264861	+	0.458752i
$370$	−9.76084e6			−0.0100180
$371$	6.39782e8	−	9.62485e8i	0.650464	−	0.978555i
$372$	1.20530e9			1.21393
$373$	−1.42427e8	−	2.46691e8i	−0.142106	−	0.246134i	0.786184	−	0.617993i	$-0.212054\pi$
$373$	−1.42427e8	−	2.46691e8i	−0.142106	−	0.246134i	−0.928289	+	0.371859i	$0.878721\pi$
$374$	−91807.8	+	159016.i	−9.07463e−5	+	0.000157177i
$375$	−1.89920e8	+	3.28951e8i	−0.185978	+	0.322123i
$376$	9.31108e6	+	1.61273e7i	0.00903322	+	0.0156460i
$377$	4.09450e8			0.393556
$378$	−2.38645e6	−	4.81016e6i	−0.00227265	−	0.00458077i
$379$	2.65524e8			0.250534			0.125267	−	0.992123i	$-0.460021\pi$
$379$	2.65524e8			0.250534			0.125267	+	0.992123i	$0.460021\pi$
$380$	1.29848e9	+	2.24904e9i	1.21393	+	2.10259i
$381$	−1.48944e8	+	2.57979e8i	−0.137970	+	0.238972i
$382$	−4.40219e6	+	7.62481e6i	−0.00404061	+	0.00699854i
$383$	8.67256e7	+	1.50213e8i	0.0788773	+	0.136619i	0.902766	−	0.430132i	$-0.141533\pi$
$383$	8.67256e7	+	1.50213e8i	0.0788773	+	0.136619i	−0.823889	+	0.566752i	$0.808200\pi$
$384$	−3.16152e7			−0.0284929
$385$	4.78555e8	+	3.02148e7i	0.427385	+	0.0269841i
$386$	1.14398e7			0.0101242
$387$	5.47212e7	+	9.47799e7i	0.0479918	+	0.0831243i
$388$	8.40384e8	−	1.45559e9i	0.730410	−	1.26511i
$389$	−1.11656e8	+	1.93394e8i	−0.0961742	+	0.166579i	−0.910098	−	0.414393i	$-0.863994\pi$
$389$	−1.11656e8	+	1.93394e8i	−0.0961742	+	0.166579i	0.813924	+	0.580972i	$0.197327\pi$
$390$	−1.53175e6	−	2.65307e6i	−0.00130756	−	0.00226476i
$391$	2.70579e7			0.0228916
$392$	−1.48868e7	−	1.88736e6i	−0.0124825	−	0.00158253i
$393$	1.04565e9			0.868984
$394$	−3.52430e6	−	6.10426e6i	−0.00290292	−	0.00502801i
$395$	−7.79871e8	+	1.35078e9i	−0.636697	+	1.10279i
$396$	5.64133e7	−	9.77106e7i	0.0456508	−	0.0790694i
$397$	−8.75632e8	−	1.51664e9i	−0.702352	−	1.21651i	−0.967639	−	0.252340i	$-0.918800\pi$
$397$	−8.75632e8	−	1.51664e9i	−0.702352	−	1.21651i	0.265287	−	0.964170i	$-0.414533\pi$
$398$	1.17684e7			0.00935677
$399$	2.63036e9	+	1.66075e8i	2.07305	+	0.130888i
$400$	9.62214e8			0.751730
$401$	−8.57293e8	−	1.48488e9i	−0.663933	−	1.14997i	−0.979574	−	0.201086i	$-0.935553\pi$
$401$	−8.57293e8	−	1.48488e9i	−0.663933	−	1.14997i	0.315641	−	0.948879i	$-0.397781\pi$
$402$	2.85333e6	−	4.94211e6i	0.00219059	−	0.00379421i
$403$	−1.95344e8	+	3.38345e8i	−0.148673	+	0.257509i
$404$	6.86672e8	+	1.18935e9i	0.518101	+	0.897378i
$405$	2.12787e9			1.59167
$406$	−5.35020e6	−	1.07839e7i	−0.00396761	−	0.00799715i
$407$	5.29437e8			0.389254
$408$	871366.	+	1.50925e6i	0.000635170	+	0.00110015i
$409$	9.99871e8	−	1.73183e9i	0.722624	−	1.25162i	−0.237321	−	0.971431i	$-0.576269\pi$
$409$	9.99871e8	−	1.73183e9i	0.722624	−	1.25162i	0.959945	−	0.280190i	$-0.0903974\pi$
$410$	−1.09066e7	+	1.88908e7i	−0.00781531	+	0.0135365i
$411$	−3.71961e8	−	6.44255e8i	−0.264272	−	0.457732i
$412$	−5.06193e8			−0.356595
$413$	−5.67224e8	+	8.53330e8i	−0.396214	+	0.596063i
$414$	658106.			0.000455821
$415$	−6.48409e8	−	1.12308e9i	−0.445328	−	0.771332i
$416$	3.84295e6	−	6.65618e6i	0.00261721	−	0.00453313i
$417$	−9.67807e8	+	1.67629e9i	−0.653601	+	1.13207i
$418$	2.78780e6	+	4.82862e6i	0.00186700	+	0.00323375i
$419$	−6.82242e8			−0.453095			−0.226548	−	0.974000i	$-0.572744\pi$
$419$	−6.82242e8			−0.453095			−0.226548	+	0.974000i	$0.572744\pi$
$420$	1.25967e9	−	1.89504e9i	0.829627	−	1.24809i
$421$	−1.51725e9			−0.990991			−0.495496	−	0.868610i	$-0.665014\pi$
$421$	−1.51725e9			−0.990991			−0.495496	+	0.868610i	$0.665014\pi$
$422$	−5.27950e6	−	9.14436e6i	−0.00341979	−	0.00592324i
$423$	−3.15376e8	+	5.46247e8i	−0.202599	+	0.350911i
$424$	1.16027e7	−	2.00964e7i	0.00739227	−	0.0128038i
$425$	−5.30425e7	−	9.18723e7i	−0.0335168	−	0.0580528i
$426$	−1.30986e7			−0.00820900
$427$	−6.81002e8	−	1.37263e9i	−0.423302	−	0.853213i
$428$	−7.76152e7			−0.0478513
$429$	8.30835e7	+	1.43905e8i	0.0508059	+	0.0879985i
$430$	−2.33472e6	+	4.04386e6i	−0.00141611	+	0.00245277i
$431$	−1.34952e9	+	2.33743e9i	−0.811909	+	1.40627i	0.0996168	+	0.995026i	$0.468238\pi$
$431$	−1.34952e9	+	2.33743e9i	−0.811909	+	1.40627i	−0.911526	+	0.411242i	$0.865095\pi$
$432$	6.80915e8	+	1.17938e9i	0.406350	+	0.703818i
$433$	−5.02648e8			−0.297547			−0.148774	−	0.988871i	$-0.547533\pi$
$433$	−5.02648e8			−0.297547			−0.148774	+	0.988871i	$0.547533\pi$
$434$	1.14637e7	+	723792.i	0.00673149	+	0.000425010i
$435$	3.65101e9			2.12667
$436$	6.76976e8	+	1.17256e9i	0.391175	+	0.677535i
$437$	4.10816e8	−	7.11554e8i	0.235485	−	0.407871i
$438$	−585524.	+	1.01416e6i	−0.000332955	+	0.000576695i
$439$	1.11007e9	+	1.92270e9i	0.626216	+	1.08464i	0.988304	+	0.152495i	$0.0487307\pi$
$439$	1.11007e9	+	1.92270e9i	0.626216	+	1.08464i	−0.362088	+	0.932144i	$0.617936\pi$
$440$	9.62786e6			0.00538822
$441$	−1.96753e8	−	4.68640e8i	−0.109241	−	0.260198i
$442$	−282440.			−0.000155578
$443$	−4.40357e8	−	7.62721e8i	−0.240653	−	0.416824i	0.720247	−	0.693718i	$-0.244028\pi$
$443$	−4.40357e8	−	7.62721e8i	−0.240653	−	0.416824i	−0.960901	+	0.276894i	$0.910695\pi$
$444$	1.25622e9	−	2.17584e9i	0.681124	−	1.17974i
$445$	−6.98592e8	+	1.21000e9i	−0.375806	+	0.650915i
$446$	5.21373e6	+	9.03045e6i	0.00278277	+	0.00481989i
$447$	−1.87965e9			−0.995408
$448$	1.89892e9	+	1.19893e8i	0.997776	+	0.0629972i
$449$	−2.26355e9			−1.18012			−0.590062	−	0.807358i	$-0.700897\pi$
$449$	−2.26355e9			−1.18012			−0.590062	+	0.807358i	$0.700897\pi$
$450$	−1.29011e6	−	2.23453e6i	−0.000667392	−	0.00115596i
$451$	5.91584e8	−	1.02465e9i	0.303668	−	0.525968i
$452$	−1.08620e8	+	1.88135e8i	−0.0553252	+	0.0958261i
$453$	−8.63768e8	−	1.49609e9i	−0.436569	−	0.756160i
$454$	−2.32957e6			−0.00116837
$455$	3.27810e8	+	6.60738e8i	0.163148	+	0.328843i
$456$	5.29192e7			0.0261358
$457$	7.98854e7	+	1.38366e8i	0.0391526	+	0.0678143i	0.884938	−	0.465709i	$-0.154201\pi$
$457$	7.98854e7	+	1.38366e8i	0.0391526	+	0.0678143i	−0.845785	+	0.533524i	$0.820867\pi$
$458$	9.67399e6	−	1.67559e7i	0.00470518	−	0.00814962i
$459$	7.50715e7	−	1.30028e8i	0.0362352	−	0.0627612i
$460$	−3.54688e8	−	6.14338e8i	−0.169900	−	0.294276i
$461$	3.82844e9			1.81999			0.909994	−	0.414621i	$-0.136086\pi$
$461$	3.82844e9			1.81999			0.909994	+	0.414621i	$0.136086\pi$
$462$	2.70447e6	−	4.06859e6i	0.00127595	−	0.00191954i
$463$	−7.05011e8			−0.330113			−0.165056	−	0.986284i	$-0.552781\pi$
$463$	−7.05011e8			−0.330113			−0.165056	+	0.986284i	$0.552781\pi$
$464$	1.52654e9	+	2.64405e9i	0.709409	+	1.22873i
$465$	−1.74185e9	+	3.01698e9i	−0.803390	+	1.39151i
$466$	−3.29017e6	+	5.69873e6i	−0.00150615	+	0.00260872i
$467$	9.78344e8	+	1.69454e9i	0.444511	+	0.769915i	0.998018	−	0.0629290i	$-0.0200442\pi$
$467$	9.78344e8	+	1.69454e9i	0.444511	+	0.769915i	−0.553507	+	0.832844i	$0.686711\pi$
$468$	1.73552e8			0.0782651
$469$	−7.60596e8	+	1.14424e9i	−0.340447	+	0.512167i
$470$	−2.69115e7			−0.0119563
$471$	−2.19788e9	−	3.80684e9i	−0.969239	−	1.67877i
$472$	−1.02868e7	+	1.78173e7i	−0.00450282	+	0.00779911i
$473$	1.26638e8	−	2.19343e8i	0.0550235	−	0.0953036i
$474$	7.94569e6	+	1.37623e7i	0.00342695	+	0.00593565i
$475$	−3.22134e9			−1.37914
$476$	−9.32387e7	−	1.87933e8i	−0.0396252	−	0.0798690i
$477$	7.85989e8			0.331591
$478$	−1.45940e7	−	2.52776e7i	−0.00611193	−	0.0105862i
$479$	−2.52221e8	+	4.36860e8i	−0.104859	+	0.181622i	−0.913681	−	0.406433i	$-0.866773\pi$
$479$	−2.52221e8	+	4.36860e8i	−0.104859	+	0.181622i	0.808821	+	0.588054i	$0.200106\pi$
$480$	3.42670e7	−	5.93522e7i	0.0141427	−	0.0244959i
$481$	4.07194e8	+	7.05281e8i	0.166837	+	0.288971i
$482$	−2.04014e7			−0.00829844
$483$	−7.18498e8	−	4.53643e7i	−0.290142	−	0.0183189i
$484$	2.23315e9			0.895281
$485$	2.42898e9	+	4.20712e9i	0.966782	+	1.67452i
$486$	4.36964e6	−	7.56844e6i	0.00172671	−	0.00299074i
$487$	−1.01079e9	+	1.75073e9i	−0.396559	+	0.686861i	−0.993299	−	0.115574i	$-0.963129\pi$
$487$	−1.01079e9	+	1.75073e9i	−0.396559	+	0.686861i	0.596740	+	0.802435i	$0.296463\pi$
$488$	−1.53831e7	−	2.66443e7i	−0.00599203	−	0.0103785i
$489$	2.87551e9			1.11208
$490$	1.31188e7	−	1.72674e7i	0.00503741	−	0.00663042i
$491$	−8.85632e8			−0.337651			−0.168826	−	0.985646i	$-0.553997\pi$
$491$	−8.85632e8			−0.337651			−0.168826	+	0.985646i	$0.553997\pi$
$492$	−2.80737e9	−	4.86250e9i	−1.06273	−	1.84070i
$493$	1.68303e8	−	2.91509e8i	0.0632598	−	0.109569i
$494$	−4.28824e6	+	7.42746e6i	−0.00160042	+	0.00277202i
$495$	1.63053e8	+	2.82416e8i	0.0604240	+	0.104658i
$496$	−2.91319e9			−1.07197
$497$	3.14742e9	+	1.98721e8i	1.15003	+	0.0726099i
$498$	−1.32126e7			−0.00479385
$499$	−6.48355e8	−	1.12298e9i	−0.233593	−	0.404596i	0.725270	−	0.688465i	$-0.241715\pi$
$499$	−6.48355e8	−	1.12298e9i	−0.233593	−	0.404596i	−0.958863	+	0.283869i	$0.908382\pi$
$500$	4.59051e8	−	7.95100e8i	0.164235	−	0.284464i
$501$	2.35092e9	−	4.07190e9i	0.835228	−	1.44666i
$502$	−1.59999e7	−	2.77126e7i	−0.00564486	−	0.00977718i
$503$	−3.84016e9			−1.34543			−0.672716	−	0.739901i	$-0.734872\pi$
$503$	−3.84016e9			−1.34543			−0.672716	+	0.739901i	$0.734872\pi$
$504$	−4.53561e6	−	9.14203e6i	−0.00157808	−	0.00318079i
$505$	−3.96941e9			−1.37153
$506$	−761505.	−	1.31897e6i	−0.000261304	−	0.000452592i
$507$	−1.27800e8	+	2.21357e8i	−0.0435516	+	0.0754337i
$508$	3.60010e8	−	6.23555e8i	0.121840	−	0.211034i
$509$	1.72347e9	+	2.98514e9i	0.579285	+	1.00335i	0.995562	+	0.0941131i	$0.0300015\pi$
$509$	1.72347e9	+	2.98514e9i	0.579285	+	1.00335i	−0.416276	+	0.909238i	$0.636665\pi$
$510$	−2.51848e6			−0.000840704
$511$	1.56080e8	−	2.34806e8i	0.0517457	−	0.0778460i
$512$	9.55184e7			0.0314516
$513$	−2.27960e9	−	3.94838e9i	−0.745499	−	1.29124i
$514$	3.39380e6	−	5.87824e6i	0.00110234	−	0.00190931i
$515$	7.31531e8	−	1.26705e9i	0.235997	−	0.408760i
$516$	−6.00959e8	−	1.04089e9i	−0.192562	−	0.333528i
$517$	1.45971e9			0.464567
$518$	1.32546e7	−	1.99402e7i	0.00419000	−	0.00630342i
$519$	−4.96610e9			−1.55930
$520$	7.40487e6	+	1.28256e7i	0.00230943	+	0.00400006i
$521$	−7.68618e8	+	1.33129e9i	−0.238110	+	0.412419i	−0.960172	−	0.279409i	$-0.909861\pi$
$521$	−7.68618e8	+	1.33129e9i	−0.238110	+	0.412419i	0.722062	+	0.691829i	$0.243195\pi$
$522$	4.09348e6	−	7.09012e6i	0.00125964	−	0.00218176i
$523$	−5.75700e8	−	9.97141e8i	−0.175971	−	0.304790i	0.764526	−	0.644593i	$-0.222973\pi$
$523$	−5.75700e8	−	9.97141e8i	−0.175971	−	0.304790i	−0.940497	+	0.339803i	$0.889640\pi$
$524$	−2.52741e9			−0.767391
$525$	1.25446e9	+	2.52851e9i	0.378356	+	0.762618i
$526$	−5.67566e6			−0.00170046
$527$	1.60591e8	+	2.78151e8i	0.0477951	+	0.0827835i
$528$	−6.19517e8	+	1.07304e9i	−0.183162	+	0.317245i
$529$	1.59020e9	−	2.75430e9i	0.467042	−	0.808940i
$530$	1.67674e7	+	2.90420e7i	0.00489216	+	0.00847348i
$531$	−6.96851e8			−0.201980
$532$	−6.35778e9	−	4.01415e8i	−1.83069	−	0.115585i
$533$	1.81997e9			0.520618
$534$	7.11758e6	+	1.23280e7i	0.00202273	+	0.00350347i
$535$	1.12167e8	−	1.94278e8i	0.0316683	−	0.0548512i
$536$	−1.37937e7	+	2.38914e7i	−0.00386905	+	0.00670138i
$537$	2.96599e8	+	5.13724e8i	0.0826531	+	0.143159i
$538$	5.42189e6			0.00150111
$539$	−7.11575e8	+	9.36601e8i	−0.195731	+	0.257628i
$540$	−3.93629e9			−1.07574
$541$	5.44375e8	+	9.42885e8i	0.147811	+	0.256017i	0.930418	−	0.366499i	$-0.119444\pi$
$541$	5.44375e8	+	9.42885e8i	0.147811	+	0.256017i	−0.782607	+	0.622516i	$0.786111\pi$
$542$	2.21558e6	−	3.83750e6i	0.000597710	−	0.00103526i
$543$	1.33977e9	−	2.32055e9i	0.359113	−	0.622003i
$544$	−3.15926e6	−	5.47200e6i	−0.000841374	−	0.00145730i
$545$	−3.91337e9			−1.03553
$546$	7.49994e6	+	473529.i	0.00197189	+	0.000124501i
$547$	2.04970e9			0.535471			0.267735	−	0.963493i	$-0.413725\pi$
$547$	2.04970e9			0.535471			0.267735	+	0.963493i	$0.413725\pi$
$548$	8.99057e8	+	1.55721e9i	0.233376	+	0.404218i
$549$	5.21040e8	−	9.02468e8i	0.134390	−	0.232771i
$550$	−2.98560e6	+	5.17122e6i	−0.000765178	+	0.00132533i
$551$	−5.11063e9	−	8.85187e9i	−1.30150	−	2.25426i
$552$	−1.44552e7			−0.00365794
$553$	−1.70046e9	−	3.42746e9i	−0.427590	−	0.861856i
$554$	−1.50848e7			−0.00376924
$555$	3.63089e9	+	6.28889e9i	0.901546	+	1.56152i
$556$	2.33927e9	−	4.05173e9i	0.577189	−	0.999720i
$557$	−5.85602e7	+	1.01429e8i	−0.0143585	+	0.0248697i	−0.873115	−	0.487514i	$-0.837904\pi$
$557$	−5.85602e7	+	1.01429e8i	−0.0143585	+	0.0248697i	0.858757	+	0.512383i	$0.171237\pi$
$558$	3.90590e6	+	6.76522e6i	0.000951704	+	0.00164840i
$559$	3.89592e8			0.0943341
$560$	−3.04459e9	+	4.58027e9i	−0.732606	+	1.10213i
$561$	1.36605e8			0.0326660
$562$	1.55783e7	+	2.69824e7i	0.00370205	+	0.00641214i
$563$	2.06581e9	−	3.57809e9i	0.487878	−	0.845029i	−0.512025	−	0.858970i	$-0.671105\pi$
$563$	2.06581e9	−	3.57809e9i	0.487878	−	0.845029i	0.999903	+	0.0139417i	$0.00443792\pi$
$564$	3.46352e9	−	5.99899e9i	0.812907	−	1.40800i
$565$	−3.13946e8	−	5.43770e8i	−0.0732293	−	0.126837i
$566$	−2.58190e7			−0.00598525
$567$	−2.88952e9	+	4.34699e9i	−0.665711	+	1.00149i
$568$	6.33218e7			0.0144989
$569$	7.84793e8	+	1.35930e9i	0.178592	+	0.309331i	0.941399	−	0.337296i	$-0.109512\pi$
$569$	7.84793e8	+	1.35930e9i	0.178592	+	0.309331i	−0.762806	+	0.646627i	$0.776179\pi$
$570$	−3.82377e7	+	6.62296e7i	−0.00864827	+	0.0149792i
$571$	−9.22048e7	+	1.59703e8i	−0.0207265	+	0.0358994i	−0.876203	−	0.481943i	$-0.839931\pi$
$571$	−9.22048e7	+	1.59703e8i	−0.0207265	+	0.0358994i	0.855476	+	0.517842i	$0.173265\pi$
$572$	−2.00819e8	−	3.47829e8i	−0.0448662	−	0.0777106i
$573$	6.55020e9			1.45450
$574$	−2.37811e7	−	4.79335e7i	−0.00524857	−	0.0105791i
$575$	8.79929e8			0.193023
$576$	6.46997e8	+	1.12063e9i	0.141066	+	0.244334i
$577$	−8.64629e7	+	1.49758e8i	−0.0187376	+	0.0324545i	−0.875242	−	0.483685i	$-0.839298\pi$
$577$	−8.64629e7	+	1.49758e8i	−0.0187376	+	0.0324545i	0.856505	+	0.516139i	$0.172631\pi$
$578$	1.44875e7	−	2.50930e7i	0.00312065	−	0.00540512i
$579$	−4.25543e9	−	7.37062e9i	−0.911105	−	1.57808i
$580$	−8.82477e9			−1.87804
$581$	3.17481e9	+	2.00450e8i	0.671586	+	0.0424024i
$582$	4.94952e7			0.0104072
$583$	−9.09481e8	−	1.57527e9i	−0.190088	−	0.329241i
$584$	2.83057e6	−	4.90269e6i	0.000588070	−	0.00101857i
$585$	−2.50810e8	+	4.34416e8i	−0.0517964	+	0.0897141i
$586$	2.83358e7	+	4.90791e7i	0.00581693	+	0.0100752i
$587$	−4.98206e9			−1.01666			−0.508330	−	0.861163i	$-0.669737\pi$
$587$	−4.98206e9			−1.01666			−0.508330	+	0.861163i	$0.669737\pi$
$588$	2.16078e9	+	5.14670e9i	0.438319	+	1.04402i
$589$	9.75289e9			1.96666
$590$	−1.48659e7	−	2.57484e7i	−0.00297994	−	0.00516141i
$591$	−2.62198e9	+	4.54140e9i	−0.522483	+	0.904968i
$592$	−3.03626e9	+	5.25896e9i	−0.601470	+	1.04178i
$593$	4.04163e9	+	7.00031e9i	0.795912	+	1.37856i	0.922258	+	0.386574i	$0.126342\pi$
$593$	4.04163e9	+	7.00031e9i	0.795912	+	1.37856i	−0.126346	+	0.991986i	$0.540325\pi$
$594$	−8.45110e6			−0.00165448
$595$	6.05159e8	+	3.82083e7i	0.117777	+	0.00743616i
$596$	4.54326e9			0.879034
$597$	−4.37767e9	−	7.58235e9i	−0.842040	−	1.45846i
$598$	1.17136e6	−	2.02885e6i	0.000223994	−	0.000387969i
$599$	5.25255e8	−	9.09769e8i	0.0998566	−	0.172957i	−0.811769	−	0.583979i	$-0.801495\pi$
$599$	5.25255e8	−	9.09769e8i	0.0998566	−	0.172957i	0.911625	+	0.411023i	$0.134828\pi$
$600$	2.83369e7	+	4.90810e7i	0.00535579	+	0.00927650i
$601$	7.89835e9			1.48414			0.742072	−	0.670320i	$-0.233843\pi$
$601$	7.89835e9			1.48414			0.742072	+	0.670320i	$0.233843\pi$
$602$	−5.09071e6	−	1.02609e7i	−0.000951023	−	0.00191689i
$603$	−9.34413e8			−0.173551
$604$	2.08779e9	+	3.61616e9i	0.385530	+	0.667757i
$605$	−3.22727e9	+	5.58979e9i	−0.592504	+	1.02625i
$606$	−2.02211e7	+	3.50240e7i	−0.00369106	+	0.00639310i
$607$	4.61027e9	+	7.98523e9i	0.836693	+	1.44920i	0.892644	+	0.450762i	$0.148848\pi$
$607$	4.61027e9	+	7.98523e9i	0.836693	+	1.44920i	−0.0559510	+	0.998434i	$0.517819\pi$
$608$	−1.91866e8			−0.0346207
$609$	−4.95786e9	+	7.45858e9i	−0.889475	+	1.33812i
$610$	4.44612e7			0.00793098
$611$	1.12267e9	+	1.94452e9i	0.199117	+	0.344881i
$612$	7.13377e7	−	1.23561e8i	0.0125802	−	0.0217896i
$613$	1.75817e9	−	3.04525e9i	0.308284	−	0.533963i	−0.669703	−	0.742629i	$-0.733579\pi$
$613$	1.75817e9	−	3.04525e9i	0.308284	−	0.533963i	0.977987	+	0.208666i	$0.0669121\pi$
$614$	−213955.	−	370580.i	−3.73020e−5	−	6.46090e-5i
$615$	1.62284e10			2.81328
$616$	−1.30741e7	+	1.96686e7i	−0.00225361	+	0.00339032i
$617$	−7.68163e9			−1.31661			−0.658303	−	0.752753i	$-0.728725\pi$
$617$	−7.68163e9			−1.31661			−0.658303	+	0.752753i	$0.728725\pi$
$618$	−7.45318e6	−	1.29093e7i	−0.00127023	−	0.00220010i
$619$	3.18698e9	−	5.52000e9i	0.540084	−	0.935453i	−0.458814	−	0.888532i	$-0.651726\pi$
$619$	3.18698e9	−	5.52000e9i	0.540084	−	0.935453i	0.998899	−	0.0469212i	$-0.0149410\pi$
$620$	4.21019e9	−	7.29227e9i	0.709465	−	1.22883i
$621$	6.22685e8	+	1.07852e9i	0.104339	+	0.180721i
$622$	2.28470e7			0.00380682
$623$	−1.52323e9	−	3.07025e9i	−0.252382	−	0.508704i
$624$	−1.90590e9			−0.314018
$625$	3.62118e9	+	6.27206e9i	0.593294	+	1.02761i
$626$	−2.95302e7	+	5.11479e7i	−0.00481124	+	0.00833331i
$627$	2.07405e9	−	3.59235e9i	0.336033	−	0.582026i
$628$	5.31245e9	+	9.20143e9i	0.855925	+	1.48251i
$629$	6.69502e8			0.107269
$630$	1.47187e7	+	929307.i	0.00234519	+	0.000148070i
$631$	−7.95831e9			−1.26101			−0.630504	−	0.776186i	$-0.717152\pi$
$631$	−7.95831e9			−1.26101			−0.630504	+	0.776186i	$0.717152\pi$
$632$	−3.84115e7	−	6.65306e7i	−0.00605272	−	0.0104836i
$633$	−3.92779e9	+	6.80314e9i	−0.615511	+	1.06610i
$634$	1.14671e7	−	1.98616e7i	0.00178707	−	0.00309529i
$635$	1.04054e9	+	1.80228e9i	0.161270	+	0.279327i
$636$	−8.63189e9			−1.33047
$637$	−1.79496e9	−	2.27566e8i	−0.275148	−	0.0348834i
$638$	−1.89465e7			−0.00288840
$639$	1.07239e9	+	1.85743e9i	0.162592	+	0.281617i
$640$	−1.10434e8	+	1.91277e8i	−0.0166522	+	0.0288425i
$641$	−9.09562e8	+	1.57541e9i	−0.136405	+	0.236260i	−0.926133	−	0.377197i	$-0.876888\pi$
$641$	−9.09562e8	+	1.57541e9i	−0.136405	+	0.236260i	0.789729	+	0.613456i	$0.210221\pi$
$642$	−1.14281e6	−	1.97940e6i	−0.000170451	−	0.000295230i
$643$	1.24748e10			1.85053			0.925263	−	0.379326i	$-0.123844\pi$
$643$	1.24748e10			1.85053			0.925263	+	0.379326i	$0.123844\pi$
$644$	1.73667e9	+	1.09649e8i	0.256222	+	0.0161772i
$645$	3.47394e9			0.509757
$646$	3.52533e6	+	6.10606e6i	0.000514501	+	0.000891142i
$647$	1.39353e9	−	2.41366e9i	0.202279	−	0.350358i	−0.746983	−	0.664843i	$-0.768499\pi$
$647$	1.39353e9	−	2.41366e9i	0.202279	−	0.350358i	0.949262	+	0.314485i	$0.101832\pi$
$648$	−5.24026e7	+	9.07640e7i	−0.00756555	+	0.0131039i
$649$	8.06337e8	+	1.39662e9i	0.115787	+	0.200549i
$650$	−9.18501e6			−0.00131185
$651$	−3.79800e9	−	7.65528e9i	−0.539537	−	1.08750i
$652$	−6.95034e9			−0.982063
$653$	−5.29659e9	−	9.17396e9i	−0.744389	−	1.28932i	−0.950480	−	0.310787i	$-0.899408\pi$
$653$	−5.29659e9	−	9.17396e9i	−0.744389	−	1.28932i	0.206091	−	0.978533i	$-0.433926\pi$
$654$	−1.99356e7	+	3.45295e7i	−0.00278681	+	0.00482689i
$655$	3.65252e9	−	6.32636e9i	0.507865	−	0.879649i
$656$	6.78535e9	+	1.17526e10i	0.938445	+	1.62543i
$657$	1.91749e8			0.0263787
$658$	3.65443e7	−	5.49771e7i	0.00500068	−	0.00752300i
$659$	1.02874e9			0.140025			0.0700124	−	0.997546i	$-0.477696\pi$
$659$	1.02874e9			0.140025			0.0700124	+	0.997546i	$0.477696\pi$
$660$	−1.79068e9	−	3.10154e9i	−0.242445	−	0.419927i
$661$	2.78140e7	−	4.81753e7i	0.00374592	−	0.00648813i	−0.864146	−	0.503241i	$-0.832141\pi$
$661$	2.78140e7	−	4.81753e7i	0.00374592	−	0.00648813i	0.867892	+	0.496752i	$0.165474\pi$
$662$	1.55626e7	−	2.69552e7i	0.00208487	−	0.00361110i
$663$	1.05064e8	+	1.81976e8i	0.0140009	+	0.0242503i
$664$	6.38729e7			0.00846698
$665$	1.01928e10	−	1.53340e10i	1.34406	−	2.02200i
$666$	1.62837e7			0.00213596
$667$	1.39600e9	+	2.41794e9i	0.182157	+	0.315504i
$668$	−5.68234e9	+	9.84211e9i	−0.737581	+	1.27753i
$669$	3.87887e9	−	6.71840e9i	0.500857	−	0.867509i
$670$	−1.99337e7	−	3.45263e7i	−0.00256051	−	0.00443494i
$671$	−2.41162e9			−0.308162
$672$	7.47170e7	+	1.50600e8i	0.00949788	+	0.0191440i
$673$	7.41970e9			0.938282			0.469141	−	0.883123i	$-0.344564\pi$
$673$	7.41970e9			0.938282			0.469141	+	0.883123i	$0.344564\pi$
$674$	4.04026e6	+	6.99794e6i	0.000508276	+	0.000880360i
$675$	2.44134e9	−	4.22852e9i	0.305538	−	0.529207i
$676$	3.08904e8	−	5.35037e8i	0.0384600	−	0.0666147i
$677$	−2.10302e9	−	3.64254e9i	−0.260485	−	0.451174i	0.705886	−	0.708326i	$-0.250549\pi$
$677$	−2.10302e9	−	3.64254e9i	−0.260485	−	0.451174i	−0.966371	+	0.257152i	$0.917216\pi$
$678$	−6.39725e6			−0.000788296
$679$	−1.18931e10	−	7.50901e8i	−1.45797	−	0.0920531i
$680$	1.21750e7			0.00148486
$681$	8.66566e8	+	1.50094e9i	0.105144	+	0.182116i
$682$	9.03917e6	−	1.56563e7i	0.00109115	−	0.00188992i
$683$	−1.95283e9	+	3.38241e9i	−0.234527	+	0.406212i	−0.959135	−	0.282949i	$-0.908687\pi$
$683$	−1.95283e9	+	3.38241e9i	−0.234527	+	0.406212i	0.724608	+	0.689161i	$0.242021\pi$
$684$	−2.16622e9	−	3.75200e9i	−0.258825	−	0.448297i
$685$	−5.19714e9			−0.617799
$686$	1.74608e7	+	5.02483e7i	0.00206504	+	0.00594274i
$687$	−1.43943e10			−1.69373
$688$	1.45251e9	+	2.51582e9i	0.170043	+	0.294523i
$689$	1.39898e9	−	2.42310e9i	0.162946	−	0.282231i
$690$	1.04448e7	−	1.80910e7i	0.00121040	−	0.00209648i
$691$	−5.14588e9	−	8.91293e9i	−0.593317	−	1.02765i	−0.993782	−	0.111343i	$-0.964485\pi$
$691$	−5.14588e9	−	8.91293e9i	−0.593317	−	1.02765i	0.400465	−	0.916312i	$-0.368849\pi$
$692$	1.20035e10			1.37700
$693$	−7.98358e8	−	5.04064e7i	−0.0911237	−	0.00575334i
$694$	−2.00267e7			−0.00227432
$695$	6.76124e9	+	1.17108e10i	0.763976	+	1.32324i
$696$	−8.99127e7	+	1.55733e8i	−0.0101085	+	0.0175085i
$697$	7.48092e8	−	1.29573e9i	0.0836835	−	0.144944i
$698$	−1.40867e7	−	2.43989e7i	−0.00156789	−	0.00271567i
$699$	4.89558e9			0.542168
$700$	−3.03214e9	−	6.11161e9i	−0.334122	−	0.673461i
$701$	−3.92478e9			−0.430330			−0.215165	−	0.976578i	$-0.569029\pi$
$701$	−3.92478e9			−0.430330			−0.215165	+	0.976578i	$0.569029\pi$
$702$	−6.49981e6	−	1.12580e7i	−0.000709122	−	0.00122823i
$703$	1.01649e10	−	1.76062e10i	1.10347	−	1.91127i
$704$	1.49730e9	−	2.59340e9i	0.161735	−	0.280134i
$705$	1.00107e10	+	1.73390e10i	1.07598	+	1.86364i
$706$	1.16248e8			0.0124328
$707$	5.39023e9	−	8.10904e9i	0.573640	−	0.862982i
$708$	7.65296e9			0.810425
$709$	−6.27083e9	−	1.08614e10i	−0.660790	−	1.14452i	−0.980408	−	0.196975i	$-0.936888\pi$
$709$	−6.27083e9	−	1.08614e10i	−0.660790	−	1.14452i	0.319619	−	0.947546i	$-0.396445\pi$
$710$	−4.57542e7	+	7.92486e7i	−0.00479763	+	0.00830974i
$711$	1.30103e9	−	2.25346e9i	0.135752	−	0.235129i
$712$	−3.44082e7	−	5.95967e7i	−0.00357258	−	0.00618789i
$713$	−2.66406e9			−0.275252
$714$	3.41995e6	−	5.14496e6i	0.000351622	−	0.000528979i
$715$	1.16087e9			0.118771
$716$	−7.16902e8	−	1.24171e9i	−0.0729901	−	0.126423i
$717$	−1.08576e10	+	1.88058e10i	−1.10006	+	1.90535i
$718$	−2.51643e7	+	4.35858e7i	−0.00253717	+	0.00439450i
$719$	4.01542e9	+	6.95491e9i	0.402884	+	0.697815i	0.994073	−	0.108718i	$-0.0346745\pi$
$719$	4.01542e9	+	6.95491e9i	0.402884	+	0.697815i	−0.591189	+	0.806533i	$0.701341\pi$
$720$	−3.74036e9			−0.373465
$721$	1.59505e9	+	3.21501e9i	0.158490	+	0.319454i
$722$	1.50474e8			0.0148793
$723$	7.58904e9	+	1.31446e10i	0.746798	+	1.29349i
$724$	−3.23833e9	+	5.60896e9i	−0.317129	+	0.549284i
$725$	5.47324e9	−	9.47993e9i	0.533410	−	0.923894i
$726$	3.28809e7	+	5.69514e7i	0.00318908	+	0.00552365i
$727$	2.43384e9			0.234920			0.117460	−	0.993078i	$-0.462525\pi$
$727$	2.43384e9			0.234920			0.117460	+	0.993078i	$0.462525\pi$
$728$	−3.62566e7	−	2.28916e6i	−0.00348279	−	0.000219895i
$729$	6.07746e9			0.581000
$730$	4.09055e6	+	7.08505e6i	0.000389182	+	0.000674082i
$731$	1.60140e8	−	2.77371e8i	0.0151632	−	0.0262634i
$732$	−5.72217e9	+	9.91109e9i	−0.539227	+	0.933969i
$733$	4.04812e9	+	7.01154e9i	0.379655	+	0.657582i	0.991012	−	0.133773i	$-0.0427094\pi$
$733$	4.04812e9	+	7.01154e9i	0.379655	+	0.657582i	−0.611357	+	0.791355i	$0.709376\pi$
$734$	1.06080e7			0.000990139
$735$	−1.60054e10	−	2.02917e9i	−1.48683	−	0.188501i
$736$	5.24093e7			0.00484547
$737$	1.08122e9	+	1.87274e9i	0.0994900	+	0.172322i
$738$	1.81952e7	−	3.15149e7i	0.00166632	−	0.00288615i
$739$	−6.82902e9	+	1.18282e10i	−0.622448	+	1.07811i	0.366581	+	0.930386i	$0.380528\pi$
$739$	−6.82902e9	+	1.18282e10i	−0.622448	+	1.07811i	−0.989029	+	0.147725i	$0.952805\pi$
$740$	−8.77614e9	−	1.52007e10i	−0.796146	−	1.37897i
$741$	6.38066e9			0.576105
$742$	−8.20987e7	−	5.18352e6i	−0.00737773	−	0.000465812i
$743$	3.32577e9			0.297462			0.148731	−	0.988878i	$-0.452481\pi$
$743$	3.32577e9			0.297462			0.148731	+	0.988878i	$0.452481\pi$
$744$	−8.57925e7	−	1.48597e8i	−0.00763738	−	0.0132283i
$745$	−6.56575e9	+	1.13722e10i	−0.581752	+	1.00762i
$746$	−1.01377e7	+	1.75590e7i	−0.000894031	+	0.00154851i
$747$	1.08172e9	+	1.87359e9i	0.0949495	+	0.164457i
$748$	−3.30184e8			−0.0288470
$749$	2.44572e8	+	4.92962e8i	0.0212677	+	0.0428674i
$750$	2.70363e7			0.00234009
$751$	−4.59812e9	−	7.96418e9i	−0.396133	−	0.686122i	0.597112	−	0.802158i	$-0.296315\pi$
$751$	−4.59812e9	−	7.96418e9i	−0.396133	−	0.686122i	−0.993245	+	0.116036i	$0.962981\pi$
$752$	−8.37126e9	+	1.44995e10i	−0.717841	+	1.24334i
$753$	−1.19034e10	+	2.06173e10i	−1.01599	+	1.75975i
$754$	−1.45719e7	−	2.52393e7i	−0.00123799	−	0.00214426i
$755$	−1.20688e10			−1.02059
$756$	5.34525e9	−	8.04137e9i	0.449927	−	0.676868i
$757$	−5.40621e9			−0.452957			−0.226478	−	0.974016i	$-0.572721\pi$
$757$	−5.40621e9			−0.452957			−0.226478	+	0.974016i	$0.572721\pi$
$758$	−9.44973e6	−	1.63674e7i	−0.000788092	−	0.00136502i
$759$	−5.66538e8	+	9.81273e8i	−0.0470309	+	0.0814598i
$760$	1.84850e8	−	3.20170e8i	0.0152747	−	0.0264566i
$761$	−7.73959e8	−	1.34054e9i	−0.0636607	−	0.110264i	0.832438	−	0.554118i	$-0.186944\pi$
$761$	−7.73959e8	−	1.34054e9i	−0.0636607	−	0.110264i	−0.896099	+	0.443854i	$0.853611\pi$
$762$	2.12031e7			0.00173603
$763$	5.31412e9	−	7.99454e9i	0.433107	−	0.651565i
$764$	−1.58323e10			−1.28445
$765$	2.06189e8	+	3.57130e8i	0.0166514	+	0.0288411i
$766$	6.17296e6	−	1.06919e7i	0.000496241	−	0.000859515i
$767$	−1.24032e9	+	2.14830e9i	−0.0992546	+	0.171914i
$768$	−7.10461e9	−	1.23055e10i	−0.565947	−	0.980249i
$769$	−8.04692e9			−0.638099			−0.319049	−	0.947738i	$-0.603364\pi$
$769$	−8.04692e9			−0.638099			−0.319049	+	0.947738i	$0.603364\pi$
$770$	−1.51688e7	−	3.05744e7i	−0.00119738	−	0.00241346i
$771$	−5.04978e9			−0.396810
$772$	1.02857e10	+	1.78153e10i	0.804587	+	1.39359i
$773$	−6.45414e9	+	1.11789e10i	−0.502586	+	0.870504i	0.497410	+	0.867516i	$0.334284\pi$
$773$	−6.45414e9	+	1.11789e10i	−0.502586	+	0.870504i	−0.999996	+	0.00298809i	$0.999049\pi$
$774$	3.89495e6	−	6.74625e6i	0.000301931	−	0.000522961i
$775$	5.22243e9	+	9.04552e9i	0.403011	+	0.698036i
$776$	−2.39272e8			−0.0183813
$777$	−1.77780e10	−	1.12246e9i	−1.35959	−	0.0858416i
$778$	1.58949e7			0.00121012
$779$	−2.27163e10	−	3.93458e10i	−1.72170	−	2.98206i
$780$	2.75445e9	−	4.77085e9i	0.207828	−	0.359968i
$781$	2.48175e9	−	4.29852e9i	0.186414	−	0.322879i
$782$	−962966.	−	1.66791e6i	−7.20091e−5	−	0.000124723i
$783$	1.54926e10			1.15335
$784$	−5.22257e9	−	1.24395e10i	−0.387060	−	0.921926i
$785$	−3.07094e10			−2.26583
$786$	−3.72136e7	−	6.44559e7i	−0.00273352	−	0.00473460i
$787$	1.15699e10	−	2.00397e10i	0.846093	−	1.46548i	−0.0385749	−	0.999256i	$-0.512282\pi$
$787$	1.15699e10	−	2.00397e10i	0.846093	−	1.46548i	0.884668	−	0.466221i	$-0.154385\pi$
$788$	6.33752e9	−	1.09769e10i	0.461400	−	0.799168i
$789$	2.11126e9	+	3.65681e9i	0.153029	+	0.265053i
$790$	1.11019e8			0.00801132
$791$	1.53718e9	+	9.70539e7i	0.110435	+	0.00697261i
$792$	−1.60619e7			−0.00114884
$793$	−1.85479e9	−	3.21260e9i	−0.132081	−	0.228771i
$794$	−6.23258e7	+	1.07951e8i	−0.00441871	+	0.00765344i
$795$	1.24745e10	−	2.16065e10i	0.880517	−	1.52510i
$796$	1.05812e10	+	1.83271e10i	0.743597	+	1.28795i
$797$	2.57335e10			1.80051			0.900255	−	0.435363i	$-0.143380\pi$
$797$	2.57335e10			1.80051			0.900255	+	0.435363i	$0.143380\pi$
$798$	−8.33747e7	−	1.68051e8i	−0.00580797	−	0.0117066i
$799$	1.84588e9			0.128023
$800$	−1.02740e8	−	1.77950e8i	−0.00709451	−	0.0122881i
$801$	1.16544e9	−	2.01860e9i	0.0801265	−	0.138783i
$802$	−6.10205e7	+	1.05691e8i	−0.00417701	+	0.00723479i
$803$	−2.21875e8	−	3.84299e8i	−0.0151218	−	0.0261918i
$804$	1.02619e10			0.696357
$805$	−2.78423e9	+	4.18858e9i	−0.188113	+	0.282997i
$806$	2.78084e7			0.00187070
$807$	−2.01686e9	−	3.49331e9i	−0.135089	−	0.233981i
$808$	9.77539e7	−	1.69315e8i	0.00651920	−	0.0112916i
$809$	−5.70955e8	+	9.88924e8i	−0.0379125	+	0.0656664i	−0.884359	−	0.466807i	$-0.845404\pi$
$809$	−5.70955e8	+	9.88924e8i	−0.0379125	+	0.0656664i	0.846447	+	0.532474i	$0.178737\pi$
$810$	−7.57288e7	−	1.31166e8i	−0.00500684	−	0.00867210i
$811$	−1.62967e10			−1.07282			−0.536409	−	0.843958i	$-0.680219\pi$
$811$	−1.62967e10			−1.07282			−0.536409	+	0.843958i	$0.680219\pi$
$812$	1.19835e10	−	1.80280e10i	0.785486	−	1.18168i
$813$	−3.29666e9			−0.215158
$814$	−1.88421e7	−	3.26355e7i	−0.00122446	−	0.00212083i
$815$	1.00444e10	−	1.73974e10i	0.649937	−	1.12572i
$816$	−7.83414e8	+	1.35691e9i	−0.0504749	+	0.0874252i
$817$	−4.86277e9	−	8.42256e9i	−0.311965	−	0.540340i
$818$	−1.42338e8			−0.00909250
$819$	−5.46875e8	−	1.10229e9i	−0.0347852	−	0.0701135i
$820$	−3.92253e10			−2.48438
$821$	6.19480e9	+	1.07297e10i	0.390685	+	0.676686i	0.992540	−	0.121919i	$-0.0389049\pi$
$821$	6.19480e9	+	1.07297e10i	0.390685	+	0.676686i	−0.601855	+	0.798605i	$0.705572\pi$
$822$	−2.64754e7	+	4.58568e7i	−0.00166261	+	0.00287973i
$823$	3.37269e9	−	5.84166e9i	0.210900	−	0.365289i	−0.741097	−	0.671399i	$-0.765694\pi$
$823$	3.37269e9	−	5.84166e9i	0.210900	−	0.365289i	0.951996	+	0.306109i	$0.0990273\pi$
$824$	3.60305e7	+	6.24067e7i	0.00224350	+	0.00388585i
$825$	4.44241e9			0.275442
$826$	7.27879e7	+	4.59566e6i	0.00449396	+	0.000283738i
$827$	−4.27166e9			−0.262620			−0.131310	−	0.991341i	$-0.541918\pi$
$827$	−4.27166e9			−0.262620			−0.131310	+	0.991341i	$0.541918\pi$
$828$	5.91715e8	+	1.02488e9i	0.0362248	+	0.0627433i
$829$	−1.89946e8	+	3.28995e8i	−0.0115795	+	0.0200562i	−0.871757	−	0.489938i	$-0.837019\pi$
$829$	−1.89946e8	+	3.28995e8i	−0.0115795	+	0.0200562i	0.860178	+	0.509995i	$0.170353\pi$
$830$	−4.61525e7	+	7.99384e7i	−0.00280170	+	0.00485269i
$831$	5.61132e9	+	9.71908e9i	0.339204	+	0.587519i
$832$	4.60635e9			0.277284
$833$	−8.99826e8	+	1.18438e9i	−0.0539388	+	0.0709962i
$834$	1.37773e8			0.00822401
$835$	−1.64238e10	−	2.84469e10i	−0.976274	−	1.69096i
$836$	−5.01313e9	+	8.68299e9i	−0.296747	+	0.513982i
$837$	−7.39136e9	+	1.28022e10i	−0.435698	+	0.754650i
$838$	2.42803e7	+	4.20548e7i	0.00142528	+	0.00246866i
$839$	1.88987e10			1.10475			0.552376	−	0.833595i	$-0.313721\pi$
$839$	1.88987e10			1.10475			0.552376	+	0.833595i	$0.313721\pi$
$840$	−3.23295e8	−	2.04121e7i	−0.0188201	−	0.00118825i
$841$	1.74831e10			1.01352
$842$	5.39975e7	+	9.35263e7i	0.00311732	+	0.00539935i
$843$	1.15898e10	−	2.00741e10i	0.666315	−	1.15409i
$844$	9.49378e9	−	1.64437e10i	0.543551	−	0.941459i
$845$	8.92832e8	+	1.54643e9i	0.0509063	+	0.0881722i
$846$	4.48957e7			0.00254922
$847$	−7.03685e9	−	1.41835e10i	−0.397911	−	0.802034i
$848$	2.08631e10			1.17488
$849$	9.60430e9	+	1.66351e10i	0.538628	+	0.932931i
$850$	−3.77546e6	+	6.53929e6i	−0.000210865	+	0.000365228i
$851$	−2.77661e9	+	4.80924e9i	−0.154441	+	0.267499i
$852$	−1.17772e10	−	2.03986e10i	−0.652382	−	1.12996i
$853$	−1.77382e10			−0.978564			−0.489282	−	0.872126i	$-0.662741\pi$
$853$	−1.77382e10			−0.978564			−0.489282	+	0.872126i	$0.662741\pi$
$854$	−6.03757e7	+	9.08290e7i	−0.00331711	+	0.00499025i
$855$	1.25221e10			0.685168
$856$	5.52461e6	+	9.56890e6i	0.000301053	+	0.000521439i
$857$	−3.83407e9	+	6.64081e9i	−0.208079	+	0.360403i	−0.951109	−	0.308855i	$-0.900054\pi$
$857$	−3.83407e9	+	6.64081e9i	−0.208079	+	0.360403i	0.743031	+	0.669257i	$0.233388\pi$
$858$	5.91372e6	−	1.02429e7i	0.000319636	−	0.000553626i
$859$	1.31924e10	+	2.28500e10i	0.710148	+	1.23001i	0.964801	+	0.262980i	$0.0847052\pi$
$859$	1.31924e10	+	2.28500e10i	0.710148	+	1.23001i	−0.254654	+	0.967032i	$0.581961\pi$
$860$	−8.39677e9			−0.450161
$861$	−2.20372e10	+	3.31527e10i	−1.17665	+	1.77014i
$862$	1.92112e8			0.0102159
$863$	1.73792e10	+	3.01017e10i	0.920434	+	1.59424i	0.798745	+	0.601670i	$0.205498\pi$
$863$	1.73792e10	+	3.01017e10i	0.920434	+	1.59424i	0.121690	+	0.992568i	$0.461169\pi$
$864$	1.45408e8	−	2.51854e8i	0.00766992	−	0.0132847i
$865$	−1.73469e10	+	3.00458e10i	−0.911311	+	1.57844i
$866$	1.78887e7	+	3.09842e7i	0.000935982	+	0.00162117i
$867$	−2.15565e10			−1.12334
$868$	9.18005e9	+	1.85034e10i	0.476460	+	0.960357i
$869$	−6.02179e9			−0.311284
$870$	−1.29936e8	−	2.25056e8i	−0.00668978	−	0.0115870i
$871$	−1.66316e9	+	2.88067e9i	−0.0852844	+	0.147717i
$872$	9.63736e7	−	1.66924e8i	0.00492210	−	0.00852533i
$873$	−4.05220e9	−	7.01861e9i	−0.206130	−	0.357027i
$874$	−5.84822e7			−0.00296301
$875$	−6.49647e9	−	4.10172e8i	−0.327831	−	0.0206985i
$876$	−2.10582e9			−0.105842
$877$	1.69010e10	+	2.92735e10i	0.846087	+	1.46547i	0.884674	+	0.466210i	$0.154381\pi$
$877$	1.69010e10	+	2.92735e10i	0.846087	+	1.46547i	−0.0385871	+	0.999255i	$0.512286\pi$
$878$	7.90126e7	−	1.36854e8i	0.00393972	−	0.00682380i
$879$	2.10810e10	−	3.65134e10i	1.04696	−	1.81339i
$880$	4.32803e9	+	7.49637e9i	0.214092	+	0.370819i
$881$	3.25370e9			0.160311			0.0801553	−	0.996782i	$-0.474458\pi$
$881$	3.25370e9			0.160311			0.0801553	+	0.996782i	$0.474458\pi$
$882$	−2.18857e7	+	2.88067e7i	−0.00107404	+	0.00141369i
$883$	2.34447e10			1.14599			0.572997	−	0.819557i	$-0.305781\pi$
$883$	2.34447e10			1.14599			0.572997	+	0.819557i	$0.305781\pi$
$884$	−2.53947e8	−	4.39850e8i	−0.0123640	−	0.0214152i
$885$	−1.10598e10	+	1.91561e10i	−0.536345	+	0.928978i
$886$	−3.13438e7	+	5.42890e7i	−0.00151403	+	0.00262237i
$887$	1.90439e9	+	3.29849e9i	0.0916267	+	0.158702i	0.908196	−	0.418546i	$-0.137460\pi$
$887$	1.90439e9	+	3.29849e9i	0.0916267	+	0.158702i	−0.816569	+	0.577248i	$0.804127\pi$
$888$	−3.57669e8			−0.0171410
$889$	−5.09484e9	−	3.21676e8i	−0.243206	−	0.0153555i
$890$	9.94489e7			0.00472862
$891$	4.10760e9	+	7.11457e9i	0.194543	+	0.336959i
$892$	−9.37552e9	+	1.62389e10i	−0.442302	+	0.766089i
$893$	2.80257e10	−	4.85419e10i	1.31697	−	2.28106i
$894$	6.68950e7	+	1.15865e8i	0.00313121	+	0.00542341i
$895$	4.14416e9			0.193222
$896$	−2.40794e8	−	4.85347e8i	−0.0111832	−	0.0225411i
$897$	−1.74292e9			−0.0806312
$898$	8.05575e7	+	1.39530e8i	0.00371226	+	0.00642983i
$899$	−1.65707e10	+	2.87013e10i	−0.760645	+	1.31748i
$900$	2.31991e9	−	4.01821e9i	0.106077	−	0.183731i
$901$	−1.15009e9	−	1.99201e9i	−0.0523835	−	0.0907310i
$902$	−8.42156e7			−0.00382094
$903$	−4.71740e9	+	7.09684e9i	−0.213204	+	0.320744i
$904$	3.09259e7			0.00139230
$905$	−9.35984e9	−	1.62117e10i	−0.419757	−	0.727041i
$906$	−6.14813e7	+	1.06489e8i	−0.00274659	+	0.00475724i
$907$	−1.73148e10	+	2.99902e10i	−0.770536	+	1.33461i	0.166734	+	0.986002i	$0.446678\pi$
$907$	−1.73148e10	+	2.99902e10i	−0.770536	+	1.33461i	−0.937270	+	0.348605i	$0.886656\pi$
$908$	−2.09456e9	−	3.62788e9i	−0.0928520	−	0.160824i
$909$	6.62205e9			0.292428
$910$	2.90627e7	−	4.37219e7i	0.00127847	−	0.00192333i
$911$	4.41193e9			0.193337			0.0966684	−	0.995317i	$-0.469181\pi$
$911$	4.41193e9			0.193337			0.0966684	+	0.995317i	$0.469181\pi$
$912$	2.37889e10	+	4.12036e10i	1.03847	+	1.79868i
$913$	2.50335e9	−	4.33593e9i	0.108861	−	0.188554i
$914$	5.68609e6	−	9.84859e6i	0.000246321	−	0.000426641i
$915$	−1.65389e10	−	2.86463e10i	−0.713730	−	1.23622i
$916$	3.47923e10			1.49571
$917$	7.96409e9	+	1.60525e10i	0.341070	+	0.687464i
$918$	−1.06869e7			−0.000455934
$919$	1.90158e10	+	3.29364e10i	0.808186	+	1.39982i	0.914119	+	0.405446i	$0.132884\pi$
$919$	1.90158e10	+	3.29364e10i	0.808186	+	1.39982i	−0.105933	+	0.994373i	$0.533783\pi$
$920$	−5.04930e7	+	8.74564e7i	−0.00213783	+	0.00370284i
$921$	−1.59176e8	+	2.75701e8i	−0.00671381	+	0.0116287i
$922$	−1.36250e8	−	2.35993e8i	−0.00572505	−	0.00991609i
$923$	7.63494e9			0.319595
$924$	8.76773e9	+	5.53574e8i	0.365624	+	0.0230847i
$925$	2.17723e10			0.904500
$926$	2.50906e7	+	4.34583e7i	0.00103842	+	0.00179860i
$927$	−1.22039e9	+	2.11378e9i	−0.0503176	+	0.0871526i
$928$	3.25991e8	−	5.64633e8i	0.0133902	−	0.0231925i
$929$	−1.82728e10	−	3.16495e10i	−0.747741	−	1.29512i	−0.948903	−	0.315567i	$-0.897805\pi$
$929$	−1.82728e10	−	3.16495e10i	−0.747741	−	1.29512i	0.201163	−	0.979558i	$-0.435528\pi$
$930$	2.47963e8			0.0101087
$931$	1.74844e10	+	4.16454e10i	0.710110	+	1.69139i
$932$	−1.18330e10			−0.478783
$933$	−8.49874e9	−	1.47202e10i	−0.342585	−	0.593375i
$934$	6.96366e7	−	1.20614e8i	0.00279656	−	0.00484378i
$935$	4.77170e8	−	8.26482e8i	0.0190912	−	0.0330669i
$936$	−1.23533e7	−	2.13966e7i	−0.000492400	−	0.000852861i
$937$	4.30356e10			1.70899			0.854494	−	0.519462i	$-0.173868\pi$
$937$	4.30356e10			1.70899			0.854494	+	0.519462i	$0.173868\pi$
$938$	9.76020e7	+	6.16236e6i	0.00386143	+	0.000243802i
$939$	4.39393e10			1.73190
$940$	−2.41966e10	−	4.19098e10i	−0.950183	−	1.64577i
$941$	2.06339e10	−	3.57390e10i	0.807269	−	1.39823i	−0.107479	−	0.994207i	$-0.534278\pi$
$941$	2.06339e10	−	3.57390e10i	0.807269	−	1.39823i	0.914748	−	0.404024i	$-0.132389\pi$
$942$	−1.56441e8	+	2.70963e8i	−0.00609778	+	0.0105617i
$943$	6.20509e9	+	1.07475e10i	0.240967	+	0.417367i
$944$	−1.84971e10			−0.715650
$945$	1.24036e10	+	2.50008e10i	0.478118	+	0.963701i
$946$	−1.80276e7			−0.000692340
$947$	−1.63181e10	−	2.82638e10i	−0.624374	−	1.08145i	−0.988662	−	0.150161i	$-0.952021\pi$
$947$	−1.63181e10	−	2.82638e10i	−0.624374	−	1.08145i	0.364287	−	0.931287i	$-0.381313\pi$
$948$	−1.42882e10	+	2.47479e10i	−0.544690	+	0.943430i
$949$	3.41292e8	−	5.91136e8i	0.0129627	−	0.0224520i
$950$	1.14644e8	+	1.98570e8i	0.00433831	+	0.00751417i
$951$	−1.70624e10			−0.643291
$952$	−1.65329e7	+	2.48720e7i	−0.000621040	+	0.000934290i
$953$	1.82066e10			0.681403			0.340702	−	0.940171i	$-0.389335\pi$
$953$	1.82066e10			0.681403			0.340702	+	0.940171i	$0.389335\pi$
$954$	−2.79726e7	−	4.84500e7i	−0.00104307	−	0.00180665i
$955$	2.28803e10	−	3.96299e10i	0.850062	−	1.47235i
$956$	2.62435e10	−	4.54551e10i	0.971448	−	1.68260i
$957$	7.04784e9	+	1.22072e10i	0.259935	+	0.450220i
$958$	3.59052e7			0.00131941
$959$	7.05741e9	−	1.06171e10i	0.258393	−	0.388725i
$960$	4.10742e10			1.49837
$961$	−2.05506e9	−	3.55947e9i	−0.0746952	−	0.129376i
$962$	2.89833e7	−	5.02005e7i	0.00104963	−	0.00181801i
$963$	−1.87124e8	+	3.24108e8i	−0.00675208	+	0.0116949i
$964$	−1.83433e10	−	3.17715e10i	−0.659490	−	1.14227i
$965$	−5.94580e10			−2.12993
$966$	2.27743e7	+	4.59041e7i	0.000812878	+	0.00163844i
$967$	−1.69993e10			−0.604559			−0.302279	−	0.953219i	$-0.597748\pi$
$967$	−1.69993e10			−0.604559			−0.302279	+	0.953219i	$0.597748\pi$
$968$	−1.58955e8	−	2.75317e8i	−0.00563261	−	0.00975596i
$969$	2.62275e9	−	4.54273e9i	0.0926026	−	0.160392i
$970$	1.72890e8	−	2.99455e8i	0.00608232	−	0.0105349i
$971$	−1.13538e10	−	1.96653e10i	−0.397990	−	0.689339i	0.595488	−	0.803364i	$-0.296959\pi$
$971$	−1.13538e10	−	1.96653e10i	−0.397990	−	0.689339i	−0.993478	+	0.114025i	$0.963626\pi$
$972$	1.57153e10			0.548896
$973$	−3.31052e10	−	2.09018e9i	−1.15213	−	0.0727427i
$974$	1.43892e8			0.00498976
$975$	3.41669e9	+	5.91788e9i	0.118056	+	0.204480i
$976$	1.38304e10	−	2.39549e10i	0.476167	−	0.824746i
$977$	−7.51708e9	+	1.30200e10i	−0.257880	+	0.446662i	−0.965674	−	0.259758i	$-0.916357\pi$
$977$	−7.51708e9	+	1.30200e10i	−0.257880	+	0.446662i	0.707794	+	0.706419i	$0.249691\pi$
$978$	−1.02337e8	−	1.77252e8i	−0.00349821	−	0.00605907i
$979$	−5.39420e9			−0.183733
$980$	3.86862e10	+	4.90466e9i	1.31300	+	0.166463i
$981$	6.52855e9			0.220788
$982$	3.15188e7	+	5.45921e7i	0.00106213	+	0.00183967i
$983$	1.83346e10	−	3.17565e10i	0.615651	−	1.06634i	−0.374619	−	0.927179i	$-0.622227\pi$
$983$	1.83346e10	−	3.17565e10i	0.615651	−	1.06634i	0.990270	−	0.139159i	$-0.0444401\pi$
$984$	−3.99654e8	+	6.92220e8i	−0.0133721	+	0.0231612i
$985$	1.83175e10	+	3.17268e10i	0.610716	+	1.05779i
$986$	−2.39590e7			−0.000795974
$987$	−4.90156e10	−	3.09473e9i	−1.62265	−	0.102450i
$988$	−1.54226e10			−0.508753
$989$	1.32829e9	+	2.30067e9i	0.0436623	+	0.0756254i
$990$	1.16058e7	−	2.01018e7i	0.000380146	−	0.000658433i
$991$	−2.35444e10	+	4.07801e10i	−0.768474	+	1.33104i	0.169916	+	0.985459i	$0.445651\pi$
$991$	−2.35444e10	+	4.07801e10i	−0.768474	+	1.33104i	−0.938390	+	0.345578i	$0.887683\pi$
$992$	3.11053e8	+	5.38759e8i	0.0101168	+	0.0175228i
$993$	−2.31563e10			−0.750492
$994$	−9.97641e7	−	2.01086e8i	−0.00322197	−	0.00649424i
$995$	−6.11660e10			−1.96847
$996$	−1.18797e10	−	2.05762e10i	−0.380975	−	0.659868i
$997$	−2.99184e10	+	5.18202e10i	−0.956104	+	1.65602i	−0.224283	+	0.974524i	$0.572004\pi$
$997$	−2.99184e10	+	5.18202e10i	−0.956104	+	1.65602i	−0.731821	+	0.681497i	$0.761329\pi$
$998$	−4.61486e7	+	7.99318e7i	−0.00146961	+	0.00254544i
$999$	1.54073e10	+	2.66862e10i	0.488930	+	0.846851i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.e.b.53.16	✓	58
7.2	even	3	inner	91.8.e.b.79.16	yes	58

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.8.e.b.53.16	✓	58	1.1	even	1	trivial
91.8.e.b.79.16	yes	58	7.2	even	3	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:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	91.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0355890 - 0.0616420i) q^{2} +(-26.4772 + 45.8599i) q^{3} +(63.9975 - 110.847i) q^{4} +(184.974 + 320.384i) q^{5} +3.76919 q^{6} +(-905.689 - 57.1831i) q^{7} -18.2212 q^{8} +(-308.586 - 534.486i) q^{9} +O(q^{10})\)	\(q+(-0.0355890 - 0.0616420i) q^{2} +(-26.4772 + 45.8599i) q^{3} +(63.9975 - 110.847i) q^{4} +(184.974 + 320.384i) q^{5} +3.76919 q^{6} +(-905.689 - 57.1831i) q^{7} -18.2212 q^{8} +(-308.586 - 534.486i) q^{9} +(13.1661 - 22.8043i) q^{10} +(-714.139 + 1236.92i) q^{11} +(3388.95 + 5869.83i) q^{12} -2197.00 q^{13} +(28.7077 + 57.8636i) q^{14} -19590.3 q^{15} +(-8191.03 - 14187.3i) q^{16} +(-903.069 + 1564.16i) q^{17} +(-21.9645 + 38.0437i) q^{18} +(27422.3 + 47496.8i) q^{19} +47351.4 q^{20} +(26602.5 - 40020.8i) q^{21} +101.662 q^{22} +(-7490.56 - 12974.0i) q^{23} +(482.447 - 835.623i) q^{24} +(-29367.9 + 50866.7i) q^{25} +(78.1891 + 135.427i) q^{26} -83129.4 q^{27} +(-64300.4 + 96733.2i) q^{28} -186368. q^{29} +(697.201 + 1207.59i) q^{30} +(88913.9 - 154003. i) q^{31} +(-1749.18 + 3029.67i) q^{32} +(-37816.8 - 65500.6i) q^{33} +128.557 q^{34} +(-149208. - 300745. i) q^{35} -78994.8 q^{36} +(-185341. - 321020. i) q^{37} +(1951.86 - 3380.73i) q^{38} +(58170.4 - 100754. i) q^{39} +(-3370.44 - 5837.78i) q^{40} -828388. q^{41} +(-3413.72 - 215.534i) q^{42} -177329. q^{43} +(91406.2 + 158320. i) q^{44} +(114160. - 197732. i) q^{45} +(-533.163 + 923.466i) q^{46} +(-511002. - 885081. i) q^{47} +867502. q^{48} +(817003. + 103580. i) q^{49} +4180.70 q^{50} +(-47821.5 - 82829.2i) q^{51} +(-140602. + 243531. i) q^{52} +(-636768. + 1.10291e6i) q^{53} +(2958.49 + 5124.26i) q^{54} -528387. q^{55} +(16502.8 + 1041.95i) q^{56} -2.90426e6 q^{57} +(6632.65 + 11488.1i) q^{58} +(564552. - 977833. i) q^{59} +(-1.25373e6 + 2.17153e6i) q^{60} +(844239. + 1.46227e6i) q^{61} -12657.4 q^{62} +(248919. + 501724. i) q^{63} -2.09665e6 q^{64} +(-406387. - 703883. i) q^{65} +(-2691.73 + 4662.21i) q^{66} +(757013. - 1.31118e6i) q^{67} +(115588. + 200205. i) q^{68} +793316. q^{69} +(-13228.4 + 19900.7i) q^{70} -3.47517e6 q^{71} +(5622.81 + 9738.99i) q^{72} +(-155345. + 269065. i) q^{73} +(-13192.2 + 22849.6i) q^{74} +(-1.55516e6 - 2.69362e6i) q^{75} +7.01982e6 q^{76} +(717519. - 1.07943e6i) q^{77} -8280.92 q^{78} +(2.10806e6 + 3.65127e6i) q^{79} +(3.03025e6 - 5.24854e6i) q^{80} +(2.87591e6 - 4.98122e6i) q^{81} +(29481.5 + 51063.5i) q^{82} -3.50541e6 q^{83} +(-2.73368e6 - 5.51003e6i) q^{84} -668175. q^{85} +(6310.97 + 10930.9i) q^{86} +(4.93450e6 - 8.54681e6i) q^{87} +(13012.5 - 22538.3i) q^{88} +(1.88836e6 + 3.27073e6i) q^{89} -16251.4 q^{90} +(1.98980e6 + 125631. i) q^{91} -1.91751e6 q^{92} +(4.70839e6 + 8.15516e6i) q^{93} +(-36372.1 + 62998.4i) q^{94} +(-1.01448e7 + 1.75713e7i) q^{95} +(-92626.8 - 160434. i) q^{96} +1.31315e7 q^{97} +(-22691.5 - 54048.0i) q^{98} +881492. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 58 q - 31 q^{2} - 1893 q^{4} + 48 q^{5} - 4602 q^{6} + 85 q^{7} + 11436 q^{8} - 25535 q^{9}+O(q^{10}) \) 58 * q - 31 * q^2 - 1893 * q^4 + 48 * q^5 - 4602 * q^6 + 85 * q^7 + 11436 * q^8 - 25535 * q^9	\( 58 q - 31 q^{2} - 1893 q^{4} + 48 q^{5} - 4602 q^{6} + 85 q^{7} + 11436 q^{8} - 25535 q^{9} + 3029 q^{10} - 15843 q^{11} + 10995 q^{12} - 127426 q^{13} - 65720 q^{14} + 115668 q^{15} - 154909 q^{16} + 43475 q^{17} - 67288 q^{18} + 64641 q^{19} + 40146 q^{20} - 321354 q^{21} + 170964 q^{22} - 96894 q^{23} + 501382 q^{24} - 637413 q^{25} + 68107 q^{26} + 156816 q^{27} - 877133 q^{28} + 155846 q^{29} - 335448 q^{30} + 393806 q^{31} - 1827215 q^{32} + 299052 q^{33} - 38692 q^{34} - 133704 q^{35} + 5417220 q^{36} - 597180 q^{37} - 502034 q^{38} + 1223016 q^{40} - 1436280 q^{41} - 2542432 q^{42} + 3496372 q^{43} - 2679210 q^{44} - 2509582 q^{45} + 2358719 q^{46} + 2368643 q^{47} - 843698 q^{48} + 995403 q^{49} + 3451796 q^{50} - 2396956 q^{51} + 4158921 q^{52} - 1919163 q^{53} - 4029674 q^{54} + 6075808 q^{55} + 3653181 q^{56} + 11452960 q^{57} - 4051049 q^{58} + 48733 q^{59} - 2792030 q^{60} + 1417921 q^{61} - 10244784 q^{62} + 7636291 q^{63} + 30707792 q^{64} - 105456 q^{65} - 22397813 q^{66} - 7025007 q^{67} + 5107354 q^{68} - 19729612 q^{69} - 13744304 q^{70} + 29267486 q^{71} - 7267524 q^{72} - 2417490 q^{73} + 2601511 q^{74} + 17567528 q^{75} - 19814476 q^{76} - 824982 q^{77} + 10110594 q^{78} - 7837082 q^{79} - 7428483 q^{80} - 24976533 q^{81} - 11520562 q^{82} - 38573688 q^{83} - 14286428 q^{84} + 41189436 q^{85} + 17943598 q^{86} - 37502020 q^{87} - 2949879 q^{88} + 15969588 q^{89} - 114635026 q^{90} - 186745 q^{91} + 83440638 q^{92} - 14525204 q^{93} - 30315990 q^{94} - 8678760 q^{95} + 23478593 q^{96} - 14169276 q^{97} + 14221151 q^{98} + 83443706 q^{99}+O(q^{100}) \) 58 * q - 31 * q^2 - 1893 * q^4 + 48 * q^5 - 4602 * q^6 + 85 * q^7 + 11436 * q^8 - 25535 * q^9 + 3029 * q^10 - 15843 * q^11 + 10995 * q^12 - 127426 * q^13 - 65720 * q^14 + 115668 * q^15 - 154909 * q^16 + 43475 * q^17 - 67288 * q^18 + 64641 * q^19 + 40146 * q^20 - 321354 * q^21 + 170964 * q^22 - 96894 * q^23 + 501382 * q^24 - 637413 * q^25 + 68107 * q^26 + 156816 * q^27 - 877133 * q^28 + 155846 * q^29 - 335448 * q^30 + 393806 * q^31 - 1827215 * q^32 + 299052 * q^33 - 38692 * q^34 - 133704 * q^35 + 5417220 * q^36 - 597180 * q^37 - 502034 * q^38 + 1223016 * q^40 - 1436280 * q^41 - 2542432 * q^42 + 3496372 * q^43 - 2679210 * q^44 - 2509582 * q^45 + 2358719 * q^46 + 2368643 * q^47 - 843698 * q^48 + 995403 * q^49 + 3451796 * q^50 - 2396956 * q^51 + 4158921 * q^52 - 1919163 * q^53 - 4029674 * q^54 + 6075808 * q^55 + 3653181 * q^56 + 11452960 * q^57 - 4051049 * q^58 + 48733 * q^59 - 2792030 * q^60 + 1417921 * q^61 - 10244784 * q^62 + 7636291 * q^63 + 30707792 * q^64 - 105456 * q^65 - 22397813 * q^66 - 7025007 * q^67 + 5107354 * q^68 - 19729612 * q^69 - 13744304 * q^70 + 29267486 * q^71 - 7267524 * q^72 - 2417490 * q^73 + 2601511 * q^74 + 17567528 * q^75 - 19814476 * q^76 - 824982 * q^77 + 10110594 * q^78 - 7837082 * q^79 - 7428483 * q^80 - 24976533 * q^81 - 11520562 * q^82 - 38573688 * q^83 - 14286428 * q^84 + 41189436 * q^85 + 17943598 * q^86 - 37502020 * q^87 - 2949879 * q^88 + 15969588 * q^89 - 114635026 * q^90 - 186745 * q^91 + 83440638 * q^92 - 14525204 * q^93 - 30315990 * q^94 - 8678760 * q^95 + 23478593 * q^96 - 14169276 * q^97 + 14221151 * q^98 + 83443706 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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