LMFDB - Embedded newform 37.8.c.a.10.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,8,Mod(10,37)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("37.10");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	37.c (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:	$11.5582459429$
Analytic rank:	$0$
Dimension:	$42$
Relative dimension:	$21$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			10.6
Character	$\chi$	$=$	37.10
Dual form			37.8.c.a.26.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.43537 + 12.8784i) q^{2} +(41.2618 + 71.4676i) q^{3} +(-46.5696 - 80.6609i) q^{4} +(62.4377 + 108.145i) q^{5} -1227.19 q^{6} +(308.286 + 533.967i) q^{7} -518.407 q^{8} +(-2311.58 + 4003.77i) q^{9} +O(q^{10})$	\(q+(-7.43537 + 12.8784i) q^{2} +(41.2618 + 71.4676i) q^{3} +(-46.5696 - 80.6609i) q^{4} +(62.4377 + 108.145i) q^{5} -1227.19 q^{6} +(308.286 + 533.967i) q^{7} -518.407 q^{8} +(-2311.58 + 4003.77i) q^{9} -1856.99 q^{10} +3470.89 q^{11} +(3843.09 - 6656.43i) q^{12} +(2820.96 + 4886.05i) q^{13} -9168.89 q^{14} +(-5152.58 + 8924.54i) q^{15} +(9815.45 - 17000.9i) q^{16} +(7968.92 - 13802.6i) q^{17} +(-34374.9 - 59539.0i) q^{18} +(-11515.5 - 19945.5i) q^{19} +(5815.39 - 10072.6i) q^{20} +(-25440.9 + 44065.0i) q^{21} +(-25807.4 + 44699.7i) q^{22} +5797.58 q^{23} +(-21390.4 - 37049.3i) q^{24} +(31265.6 - 54153.6i) q^{25} -83899.7 q^{26} -201040. q^{27} +(28713.5 - 49733.3i) q^{28} +141993. q^{29} +(-76622.8 - 132715. i) q^{30} +195491. q^{31} +(112785. + 195350. i) q^{32} +(143215. + 248056. i) q^{33} +(118504. + 205255. i) q^{34} +(-38497.3 + 66679.3i) q^{35} +430597. q^{36} +(-268410. - 151287. i) q^{37} +342489. q^{38} +(-232796. + 403215. i) q^{39} +(-32368.1 - 56063.2i) q^{40} +(372614. + 645386. i) q^{41} +(-378325. - 655279. i) q^{42} -670867. q^{43} +(-161638. - 279965. i) q^{44} -577318. q^{45} +(-43107.2 + 74663.8i) q^{46} -933867. q^{47} +1.62001e6 q^{48} +(221691. - 383979. i) q^{49} +(464943. + 805304. i) q^{50} +1.31525e6 q^{51} +(262742. - 455083. i) q^{52} +(-497063. + 860938. i) q^{53} +(1.49481e6 - 2.58909e6i) q^{54} +(216714. + 375360. i) q^{55} +(-159818. - 276812. i) q^{56} +(950303. - 1.64597e6i) q^{57} +(-1.05577e6 + 1.82864e6i) q^{58} +(-33272.3 + 57629.3i) q^{59} +959814. q^{60} +(-1.34985e6 - 2.33800e6i) q^{61} +(-1.45355e6 + 2.51762e6i) q^{62} -2.85051e6 q^{63} -841642. q^{64} +(-352269. + 610147. i) q^{65} -4.25944e6 q^{66} +(956948. + 1.65748e6i) q^{67} -1.48444e6 q^{68} +(239219. + 414339. i) q^{69} +(-572484. - 991572. i) q^{70} +(2.11404e6 + 3.66163e6i) q^{71} +(1.19834e6 - 2.07558e6i) q^{72} -5.73256e6 q^{73} +(3.94407e6 - 2.33184e6i) q^{74} +5.16030e6 q^{75} +(-1.07255e6 + 1.85770e6i) q^{76} +(1.07003e6 + 1.85334e6i) q^{77} +(-3.46186e6 - 5.99611e6i) q^{78} +(1.10294e6 + 1.91035e6i) q^{79} +2.45142e6 q^{80} +(-3.23987e6 - 5.61163e6i) q^{81} -1.10821e7 q^{82} +(1.14168e6 - 1.97745e6i) q^{83} +4.73909e6 q^{84} +1.99024e6 q^{85} +(4.98815e6 - 8.63973e6i) q^{86} +(5.85887e6 + 1.01479e7i) q^{87} -1.79934e6 q^{88} +(3.85134e6 - 6.67072e6i) q^{89} +(4.29257e6 - 7.43496e6i) q^{90} +(-1.73933e6 + 3.01261e6i) q^{91} +(-269991. - 467638. i) q^{92} +(8.06633e6 + 1.39713e7i) q^{93} +(6.94365e6 - 1.20268e7i) q^{94} +(1.43800e6 - 2.49070e6i) q^{95} +(-9.30744e6 + 1.61210e7i) q^{96} +1.61290e7 q^{97} +(3.29671e6 + 5.71006e6i) q^{98} +(-8.02324e6 + 1.38967e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q - 16 q^{2} - 68 q^{3} - 1126 q^{4} - 337 q^{5} + 252 q^{6} - 158 q^{7} + 6264 q^{8} - 12773 q^{9}+O(q^{10}) $ 42 * q - 16 * q^2 - 68 * q^3 - 1126 * q^4 - 337 * q^5 + 252 * q^6 - 158 * q^7 + 6264 * q^8 - 12773 * q^9	\( 42 q - 16 q^{2} - 68 q^{3} - 1126 q^{4} - 337 q^{5} + 252 q^{6} - 158 q^{7} + 6264 q^{8} - 12773 q^{9} + 10028 q^{10} + 14876 q^{11} - 4836 q^{12} - 5922 q^{13} + 20176 q^{14} - 8460 q^{15} - 36726 q^{16} - 19095 q^{17} - 7338 q^{18} - 34334 q^{19} - 75668 q^{20} - 32764 q^{21} + 18526 q^{22} - 99896 q^{23} - 203760 q^{24} - 322660 q^{25} + 101516 q^{26} + 846616 q^{27} - 73490 q^{28} + 168186 q^{29} - 88790 q^{30} - 38052 q^{31} - 172292 q^{32} - 54536 q^{33} + 90724 q^{34} - 247046 q^{35} + 352004 q^{36} + 740185 q^{37} + 1994976 q^{38} - 591380 q^{39} - 38962 q^{40} - 292827 q^{41} - 1499386 q^{42} + 630980 q^{43} - 1727390 q^{44} - 994286 q^{45} + 576988 q^{46} + 3394668 q^{47} - 79840 q^{48} + 728851 q^{49} - 69656 q^{50} - 3970200 q^{51} - 2043140 q^{52} + 584438 q^{53} - 2160774 q^{54} + 2019874 q^{55} - 658986 q^{56} + 4295748 q^{57} - 5684872 q^{58} - 1773152 q^{59} + 20208544 q^{60} - 3596569 q^{61} - 1538738 q^{62} + 11795092 q^{63} - 9622852 q^{64} - 5027290 q^{65} - 17464952 q^{66} - 3249754 q^{67} + 5608668 q^{68} + 9599384 q^{69} - 5102080 q^{70} - 1162530 q^{71} - 4730172 q^{72} - 5266532 q^{73} + 4052290 q^{74} + 35543072 q^{75} - 13781226 q^{76} + 121180 q^{77} - 7012890 q^{78} - 13545718 q^{79} - 17840888 q^{80} - 16689077 q^{81} - 43173544 q^{82} + 7359048 q^{83} + 41186680 q^{84} + 21047382 q^{85} + 6732838 q^{86} + 7672800 q^{87} + 42023140 q^{88} + 2955725 q^{89} - 14596808 q^{90} - 19887752 q^{91} + 13352900 q^{92} + 9156784 q^{93} + 690474 q^{94} - 5667270 q^{95} + 29986904 q^{96} + 52065982 q^{97} - 53664462 q^{98} - 35534038 q^{99}+O(q^{100}) \) 42 * q - 16 * q^2 - 68 * q^3 - 1126 * q^4 - 337 * q^5 + 252 * q^6 - 158 * q^7 + 6264 * q^8 - 12773 * q^9 + 10028 * q^10 + 14876 * q^11 - 4836 * q^12 - 5922 * q^13 + 20176 * q^14 - 8460 * q^15 - 36726 * q^16 - 19095 * q^17 - 7338 * q^18 - 34334 * q^19 - 75668 * q^20 - 32764 * q^21 + 18526 * q^22 - 99896 * q^23 - 203760 * q^24 - 322660 * q^25 + 101516 * q^26 + 846616 * q^27 - 73490 * q^28 + 168186 * q^29 - 88790 * q^30 - 38052 * q^31 - 172292 * q^32 - 54536 * q^33 + 90724 * q^34 - 247046 * q^35 + 352004 * q^36 + 740185 * q^37 + 1994976 * q^38 - 591380 * q^39 - 38962 * q^40 - 292827 * q^41 - 1499386 * q^42 + 630980 * q^43 - 1727390 * q^44 - 994286 * q^45 + 576988 * q^46 + 3394668 * q^47 - 79840 * q^48 + 728851 * q^49 - 69656 * q^50 - 3970200 * q^51 - 2043140 * q^52 + 584438 * q^53 - 2160774 * q^54 + 2019874 * q^55 - 658986 * q^56 + 4295748 * q^57 - 5684872 * q^58 - 1773152 * q^59 + 20208544 * q^60 - 3596569 * q^61 - 1538738 * q^62 + 11795092 * q^63 - 9622852 * q^64 - 5027290 * q^65 - 17464952 * q^66 - 3249754 * q^67 + 5608668 * q^68 + 9599384 * q^69 - 5102080 * q^70 - 1162530 * q^71 - 4730172 * q^72 - 5266532 * q^73 + 4052290 * q^74 + 35543072 * q^75 - 13781226 * q^76 + 121180 * q^77 - 7012890 * q^78 - 13545718 * q^79 - 17840888 * q^80 - 16689077 * q^81 - 43173544 * q^82 + 7359048 * q^83 + 41186680 * q^84 + 21047382 * q^85 + 6732838 * q^86 + 7672800 * q^87 + 42023140 * q^88 + 2955725 * q^89 - 14596808 * q^90 - 19887752 * q^91 + 13352900 * q^92 + 9156784 * q^93 + 690474 * q^94 - 5667270 * q^95 + 29986904 * q^96 + 52065982 * q^97 - 53664462 * q^98 - 35534038 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/37\mathbb{Z}\right)^\times$.

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

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 $

$2$	−7.43537	+	12.8784i	−0.657200	+	1.13830i	0.324137	+	0.946010i	$0.394926\pi$
$2$	−7.43537	+	12.8784i	−0.657200	+	1.13830i	−0.981337	+	0.192294i	$0.938407\pi$
$3$	41.2618	+	71.4676i	0.882316	+	1.52822i	0.848759	+	0.528779i	$0.177350\pi$
$3$	41.2618	+	71.4676i	0.882316	+	1.52822i	0.0335564	+	0.999437i	$0.489317\pi$
$4$	−46.5696	−	80.6609i	−0.363825	−	0.630163i
$5$	62.4377	+	108.145i	0.223384	+	0.386912i	0.955833	−	0.293909i	$-0.0949564\pi$
$5$	62.4377	+	108.145i	0.223384	+	0.386912i	−0.732450	+	0.680821i	$0.761623\pi$
$6$	−1227.19			−2.31943
$7$	308.286	+	533.967i	0.339712	+	0.588399i	0.984378	−	0.176065i	$-0.0563370\pi$
$7$	308.286	+	533.967i	0.339712	+	0.588399i	−0.644666	+	0.764464i	$0.723004\pi$
$8$	−518.407			−0.357978
$9$	−2311.58	+	4003.77i	−1.05696	+	1.83071i
$10$	−1856.99			−0.587232
$11$	3470.89			0.786261			0.393131	−	0.919483i	$-0.371392\pi$
$11$	3470.89			0.786261			0.393131	+	0.919483i	$0.371392\pi$
$12$	3843.09	−	6656.43i	0.642017	−	1.11201i
$13$	2820.96	+	4886.05i	0.356120	+	0.616817i	0.987309	−	0.158812i	$-0.0507662\pi$
$13$	2820.96	+	4886.05i	0.356120	+	0.616817i	−0.631189	+	0.775629i	$0.717433\pi$
$14$	−9168.89			−0.893036
$15$	−5152.58	+	8924.54i	−0.394190	+	0.682757i
$16$	9815.45	−	17000.9i	0.599088	−	1.03765i
$17$	7968.92	−	13802.6i	0.393394	−	0.681379i	−0.599500	−	0.800374i	$-0.704634\pi$
$17$	7968.92	−	13802.6i	0.393394	−	0.681379i	0.992895	+	0.118995i	$0.0379673\pi$
$18$	−34374.9	−	59539.0i	−1.38927	−	2.40629i
$19$	−11515.5	−	19945.5i	−0.385164	−	0.667124i	0.606628	−	0.794986i	$-0.292522\pi$
$19$	−11515.5	−	19945.5i	−0.385164	−	0.667124i	−0.991792	+	0.127862i	$0.959189\pi$
$20$	5815.39	−	10072.6i	0.162545	−	0.281536i
$21$	−25440.9	+	44065.0i	−0.599467	+	1.03831i
$22$	−25807.4	+	44699.7i	−0.516731	+	0.895005i
$23$	5797.58			0.0993572			0.0496786	−	0.998765i	$-0.484180\pi$
$23$	5797.58			0.0993572			0.0496786	+	0.998765i	$0.484180\pi$
$24$	−21390.4	−	37049.3i	−0.315849	−	0.547067i
$25$	31265.6	−	54153.6i	0.400199	−	0.693166i
$26$	−83899.7			−0.936168
$27$	−201040.			−1.96567
$28$	28713.5	−	49733.3i	0.247191	−	0.428148i
$29$	141993.			1.08112			0.540558	−	0.841307i	$-0.318213\pi$
$29$	141993.			1.08112			0.540558	+	0.841307i	$0.318213\pi$
$30$	−76622.8	−	132715.i	−0.518124	−	0.897417i
$31$	195491.			1.17859			0.589293	−	0.807919i	$-0.299406\pi$
$31$	195491.			1.17859			0.589293	+	0.807919i	$0.299406\pi$
$32$	112785.	+	195350.i	0.608453	+	1.05387i
$33$	143215.	+	248056.i	0.693731	+	1.20158i
$34$	118504.	+	205255.i	0.517078	+	0.895605i
$35$	−38497.3	+	66679.3i	−0.151772	+	0.262877i
$36$	430597.			1.53820
$37$	−268410.	−	151287.i	−0.871151	−	0.491015i
$37$	−268410.	−	151287.i	−0.871151	−	0.491015i
$38$	342489.			1.01252
$39$	−232796.	+	403215.i	−0.628420	+	1.08846i
$40$	−32368.1	−	56063.2i	−0.0799664	−	0.138506i
$41$	372614.	+	645386.i	0.844336	+	1.46243i	0.886196	+	0.463310i	$0.153338\pi$
$41$	372614.	+	645386.i	0.844336	+	1.46243i	−0.0418599	+	0.999123i	$0.513328\pi$
$42$	−378325.	−	655279.i	−0.787940	−	1.36475i
$43$	−670867.			−1.28676			−0.643379	−	0.765548i	$-0.722468\pi$
$43$	−670867.			−1.28676			−0.643379	+	0.765548i	$0.722468\pi$
$44$	−161638.	−	279965.i	−0.286061	−	0.495473i
$45$	−577318.			−0.944433
$46$	−43107.2	+	74663.8i	−0.0652976	+	0.113099i
$47$	−933867.			−1.31203			−0.656013	−	0.754750i	$-0.727758\pi$
$47$	−933867.			−1.31203			−0.656013	+	0.754750i	$0.727758\pi$
$48$	1.62001e6			2.11434
$49$	221691.	−	383979.i	0.269191	−	0.466253i
$50$	464943.	+	805304.i	0.526022	+	0.911098i
$51$	1.31525e6			1.38839
$52$	262742.	−	455083.i	0.259130	−	0.448827i
$53$	−497063.	+	860938.i	−0.458612	+	0.794340i	−0.998888	−	0.0471482i	$-0.984987\pi$
$53$	−497063.	+	860938.i	−0.458612	+	0.794340i	0.540275	+	0.841488i	$0.318320\pi$
$54$	1.49481e6	−	2.58909e6i	1.29184	−	2.23753i
$55$	216714.	+	375360.i	0.175638	+	0.304214i
$56$	−159818.	−	276812.i	−0.121609	−	0.210634i
$57$	950303.	−	1.64597e6i	0.679673	−	1.17723i
$58$	−1.05577e6	+	1.82864e6i	−0.710510	+	1.23064i
$59$	−33272.3	+	57629.3i	−0.0210912	+	0.0365310i	−0.876378	−	0.481623i	$-0.840047\pi$
$59$	−33272.3	+	57629.3i	−0.0210912	+	0.0365310i	0.855287	+	0.518154i	$0.173381\pi$
$60$	959814.			0.573664
$61$	−1.34985e6	−	2.33800e6i	−0.761430	−	1.31884i	−0.942113	−	0.335295i	$-0.891164\pi$
$61$	−1.34985e6	−	2.33800e6i	−0.761430	−	1.31884i	0.180683	−	0.983541i	$-0.442169\pi$
$62$	−1.45355e6	+	2.51762e6i	−0.774567	+	1.34159i
$63$	−2.85051e6			−1.43625
$64$	−841642.			−0.401326
$65$	−352269.	+	610147.i	−0.159103	+	0.275574i
$66$	−4.25944e6			−1.82368
$67$	956948.	+	1.65748e6i	0.388711	+	0.673267i	0.992276	−	0.124047i	$-0.0395872\pi$
$67$	956948.	+	1.65748e6i	0.388711	+	0.673267i	−0.603566	+	0.797313i	$0.706254\pi$
$68$	−1.48444e6			−0.572507
$69$	239219.	+	414339.i	0.0876645	+	0.151839i
$70$	−572484.	−	991572.i	−0.199490	−	0.345526i
$71$	2.11404e6	+	3.66163e6i	0.700986	+	1.21414i	0.968121	+	0.250484i	$0.0805896\pi$
$71$	2.11404e6	+	3.66163e6i	0.700986	+	1.21414i	−0.267135	+	0.963659i	$0.586077\pi$
$72$	1.19834e6	−	2.07558e6i	0.378369	−	0.655354i
$73$	−5.73256e6			−1.72472			−0.862359	−	0.506297i	$-0.831014\pi$
$73$	−5.73256e6			−1.72472			−0.862359	+	0.506297i	$0.831014\pi$
$74$	3.94407e6	−	2.33184e6i	1.13145	−	0.668940i
$75$	5.16030e6			1.41241
$76$	−1.07255e6	+	1.85770e6i	−0.280265	+	0.485433i
$77$	1.07003e6	+	1.85334e6i	0.267103	+	0.462635i
$78$	−3.46186e6	−	5.99611e6i	−0.825996	−	1.43067i
$79$	1.10294e6	+	1.91035e6i	0.251686	+	0.435932i	0.963990	−	0.265938i	$-0.0856818\pi$
$79$	1.10294e6	+	1.91035e6i	0.251686	+	0.435932i	−0.712304	+	0.701871i	$0.752348\pi$
$80$	2.45142e6			0.535306
$81$	−3.23987e6	−	5.61163e6i	−0.677377	−	1.17325i
$82$	−1.10821e7			−2.21959
$83$	1.14168e6	−	1.97745e6i	0.219165	−	0.379606i	−0.735388	−	0.677647i	$-0.763000\pi$
$83$	1.14168e6	−	1.97745e6i	0.219165	−	0.379606i	0.954553	+	0.298041i	$0.0963332\pi$
$84$	4.73909e6			0.872404
$85$	1.99024e6			0.351512
$86$	4.98815e6	−	8.63973e6i	0.845658	−	1.46472i
$87$	5.85887e6	+	1.01479e7i	0.953886	+	1.65218i
$88$	−1.79934e6			−0.281464
$89$	3.85134e6	−	6.67072e6i	0.579091	−	1.00302i	−0.416492	−	0.909139i	$-0.636741\pi$
$89$	3.85134e6	−	6.67072e6i	0.579091	−	1.00302i	0.995584	−	0.0938765i	$-0.0299259\pi$
$90$	4.29257e6	−	7.43496e6i	0.620682	−	1.07505i
$91$	−1.73933e6	+	3.01261e6i	−0.241956	+	0.419081i
$92$	−269991.	−	467638.i	−0.0361486	−	0.0626113i
$93$	8.06633e6	+	1.39713e7i	1.03989	+	1.80113i
$94$	6.94365e6	−	1.20268e7i	0.862264	−	1.49348i
$95$	1.43800e6	−	2.49070e6i	0.172079	−	0.298049i
$96$	−9.30744e6	+	1.61210e7i	−1.07370	+	1.85969i
$97$	1.61290e7			1.79435			0.897175	−	0.441676i	$-0.145616\pi$
$97$	1.61290e7			1.79435			0.897175	+	0.441676i	$0.145616\pi$
$98$	3.29671e6	+	5.71006e6i	0.353825	+	0.612843i
$99$	−8.02324e6	+	1.38967e7i	−0.831049	+	1.43942i
$100$	−5.82410e6			−0.582410
$101$	7.19904e6			0.695264			0.347632	−	0.937631i	$-0.386986\pi$
$101$	7.19904e6			0.695264			0.347632	+	0.937631i	$0.386986\pi$
$102$	−9.77937e6	+	1.69384e7i	−0.912452	+	1.58041i
$103$	−1.94396e7			−1.75290			−0.876448	−	0.481496i	$-0.840093\pi$
$103$	−1.94396e7			−1.75290			−0.876448	+	0.481496i	$0.840093\pi$
$104$	−1.46241e6	−	2.53296e6i	−0.127483	−	0.220807i
$105$	−6.35388e6			−0.535645
$106$	−7.39170e6	−	1.28028e7i	−0.602801	−	1.04408i
$107$	3.80477e6	+	6.59006e6i	0.300252	+	0.520051i	0.976193	−	0.216904i	$-0.0695960\pi$
$107$	3.80477e6	+	6.59006e6i	0.300252	+	0.520051i	−0.675941	+	0.736956i	$0.736263\pi$
$108$	9.36236e6	+	1.62161e7i	0.715159	+	1.23869i
$109$	3.19239e6	−	5.52939e6i	0.236115	−	0.408963i	−0.723481	−	0.690344i	$-0.757459\pi$
$109$	3.19239e6	−	5.52939e6i	0.236115	−	0.408963i	0.959596	+	0.281381i	$0.0907925\pi$
$110$	−6.44541e6			−0.461718
$111$	−263006.	−	2.54250e7i	−0.0182531	−	1.76454i
$112$	1.21039e7			0.814070
$113$	1.27044e6	−	2.20047e6i	0.0828287	−	0.143463i	−0.821635	−	0.570014i	$-0.806938\pi$
$113$	1.27044e6	−	2.20047e6i	0.0828287	−	0.143463i	0.904464	+	0.426550i	$0.140271\pi$
$114$	1.41317e7	+	2.44768e7i	0.893363	+	1.54735i
$115$	361987.	+	626981.i	0.0221948	+	0.0384425i
$116$	−6.61253e6	−	1.14532e7i	−0.393337	−	0.681280i
$117$	−2.60835e7			−1.50562
$118$	−494784.	−	856991.i	−0.0277222	−	0.0480163i
$119$	9.82683e6			0.534563
$120$	2.67113e6	−	4.62654e6i	0.141111	−	0.244412i
$121$	−7.44006e6			−0.381793
$122$	4.01465e7			2.00165
$123$	−3.07495e7	+	5.32596e7i	−1.48994	+	2.58066i
$124$	−9.10394e6	−	1.57685e7i	−0.428799	−	0.742702i
$125$	1.75645e7			0.804360
$126$	2.11946e7	−	3.67101e7i	0.943905	−	1.63489i
$127$	1.64545e7	−	2.85001e7i	0.712808	−	1.23462i	−0.250991	−	0.967989i	$-0.580756\pi$
$127$	1.64545e7	−	2.85001e7i	0.712808	−	1.23462i	0.963799	−	0.266630i	$-0.0859102\pi$
$128$	−8.17857e6	+	1.41657e7i	−0.344701	+	0.597040i
$129$	−2.76812e7	−	4.79453e7i	−1.13533	−	1.96644i
$130$	−5.23850e6	−	9.07335e6i	−0.209125	−	0.362215i
$131$	6.60768e6	−	1.14448e7i	0.256803	−	0.444795i	−0.708581	−	0.705629i	$-0.750664\pi$
$131$	6.60768e6	−	1.14448e7i	0.256803	−	0.444795i	0.965384	+	0.260834i	$0.0839977\pi$
$132$	1.33390e7	−	2.31038e7i	0.504793	−	0.874327i
$133$	7.10015e6	−	1.22978e7i	0.261690	−	0.453260i
$134$	−2.84611e7			−1.02184
$135$	−1.25525e7	−	2.17415e7i	−0.439098	−	0.760540i
$136$	−4.13114e6	+	7.15535e6i	−0.140826	+	0.243918i
$137$	−2.26909e7			−0.753929			−0.376964	−	0.926228i	$-0.623032\pi$
$137$	−2.26909e7			−0.753929			−0.376964	+	0.926228i	$0.623032\pi$
$138$	−7.11473e6			−0.230452
$139$	−2.80727e7	+	4.86233e7i	−0.886608	+	1.53565i	−0.0427493	+	0.999086i	$0.513612\pi$
$139$	−2.80727e7	+	4.86233e7i	−0.886608	+	1.53565i	−0.843859	+	0.536565i	$0.819722\pi$
$140$	7.17122e6			0.220874
$141$	−3.85330e7	−	6.67412e7i	−1.15762	−	2.00506i
$142$	−6.28747e7			−1.84275
$143$	9.79127e6	+	1.69590e7i	0.280003	+	0.484980i
$144$	4.53784e7	+	7.85976e7i	1.26643	+	2.19352i
$145$	8.86568e6	+	1.53558e7i	0.241504	+	0.418297i
$146$	4.26237e7	−	7.38264e7i	1.13349	−	1.96326i
$147$	3.65894e7			0.950047
$148$	296838.	+	2.86956e7i	0.00752669	+	0.727611i
$149$	−7.61573e6			−0.188608			−0.0943039	−	0.995543i	$-0.530063\pi$
$149$	−7.61573e6			−0.188608			−0.0943039	+	0.995543i	$0.530063\pi$
$150$	−3.83688e7	+	6.64566e7i	−0.928236	+	1.60775i
$151$	−5.38485e6	−	9.32684e6i	−0.127278	−	0.220453i	0.795343	−	0.606160i	$-0.207291\pi$
$151$	−5.38485e6	−	9.32684e6i	−0.127278	−	0.220453i	−0.922621	+	0.385707i	$0.873957\pi$
$152$	5.96973e6	+	1.03399e7i	0.137880	+	0.238815i
$153$	3.68415e7	+	6.38114e7i	0.831606	+	1.44038i
$154$	−3.18243e7			−0.702160
$155$	1.22060e7	+	2.11414e7i	0.263277	+	0.456009i
$156$	4.33649e7			0.914539
$157$	843441.	−	1.46088e6i	0.0173943	−	0.0301277i	−0.857197	−	0.514988i	$-0.827796\pi$
$157$	843441.	−	1.46088e6i	0.0173943	−	0.0301277i	0.874592	+	0.484860i	$0.161130\pi$
$158$	−3.28032e7			−0.661631
$159$	−8.20389e7			−1.61856
$160$	−1.40841e7	+	2.43943e7i	−0.271837	+	0.470835i
$161$	1.78731e6	+	3.09572e6i	0.0337529	+	0.0584617i
$162$	9.63587e7			1.78069
$163$	3.05055e7	−	5.28370e7i	0.551723	−	0.955612i	−0.446428	−	0.894820i	$-0.647304\pi$
$163$	3.05055e7	−	5.28370e7i	0.551723	−	0.955612i	0.998150	−	0.0607921i	$-0.0193627\pi$
$164$	3.47049e7	−	6.01107e7i	0.614381	−	1.06414i
$165$	−1.78841e7	+	3.09761e7i	−0.309936	+	0.536826i
$166$	1.69777e7	+	2.94062e7i	0.288071	+	0.498954i
$167$	1.58175e7	+	2.73966e7i	0.262802	+	0.455187i	0.966985	−	0.254831i	$-0.0820200\pi$
$167$	1.58175e7	+	2.73966e7i	0.262802	+	0.455187i	−0.704183	+	0.710018i	$0.748687\pi$
$168$	1.31887e7	−	2.28436e7i	0.214596	−	0.371691i
$169$	1.54586e7	−	2.67750e7i	0.246358	−	0.426704i
$170$	−1.47982e7	+	2.56312e7i	−0.231014	+	0.400127i
$171$	1.06476e8			1.62842
$172$	3.12420e7	+	5.41127e7i	0.468155	+	0.810868i
$173$	1.58462e7	−	2.74465e7i	0.232683	−	0.403019i	−0.725914	−	0.687786i	$-0.758583\pi$
$173$	1.58462e7	−	2.74465e7i	0.232683	−	0.403019i	0.958597	+	0.284767i	$0.0919163\pi$
$174$	−1.74252e8			−2.50758
$175$	3.85550e7			0.543810
$176$	3.40684e7	−	5.90082e7i	0.471040	−	0.815865i
$177$	−5.49150e6			−0.0744363
$178$	5.72723e7	+	9.91986e7i	0.761158	+	1.31836i
$179$	1.68829e7			0.220019			0.110010	−	0.993931i	$-0.464912\pi$
$179$	1.68829e7			0.220019			0.110010	+	0.993931i	$0.464912\pi$
$180$	2.68854e7	+	4.65670e7i	0.343608	+	0.595147i
$181$	6.07977e7	+	1.05305e8i	0.762101	+	1.32000i	0.941766	+	0.336269i	$0.109165\pi$
$181$	6.07977e7	+	1.05305e8i	0.762101	+	1.32000i	−0.179665	+	0.983728i	$0.557501\pi$
$182$	−2.58651e7	−	4.47997e7i	−0.318028	−	0.550840i
$183$	1.11394e8	−	1.92941e8i	1.34364	−	2.32726i
$184$	−3.00551e6			−0.0355677
$185$	−397983.	−	3.84733e7i	−0.00462129	−	0.446744i
$186$	−2.39905e8			−2.73365
$187$	2.76593e7	−	4.79073e7i	0.309311	−	0.535742i
$188$	4.34898e7	+	7.53265e7i	0.477348	+	0.826790i
$189$	−6.19780e7	−	1.07349e8i	−0.667761	−	1.15660i
$190$	2.13842e7	+	3.70385e7i	0.226181	+	0.391756i
$191$	1.06879e8			1.10988			0.554940	−	0.831890i	$-0.312741\pi$
$191$	1.06879e8			1.10988			0.554940	+	0.831890i	$0.312741\pi$
$192$	−3.47277e7	−	6.01501e7i	−0.354096	−	0.613313i
$193$	−5.66679e7			−0.567396			−0.283698	−	0.958914i	$-0.591561\pi$
$193$	−5.66679e7			−0.567396			−0.283698	+	0.958914i	$0.591561\pi$
$194$	−1.19925e8	+	2.07717e8i	−1.17925	+	2.04252i
$195$	−5.81410e7			−0.561515
$196$	−4.12962e7			−0.391754
$197$	6.59503e7	−	1.14229e8i	0.614589	−	1.06450i	−0.375867	−	0.926673i	$-0.622655\pi$
$197$	6.59503e7	−	1.14229e8i	0.614589	−	1.06450i	0.990456	−	0.137826i	$-0.0440115\pi$
$198$	−1.19312e8	−	2.06654e8i	−1.09233	−	1.89197i
$199$	−1.29305e7			−0.116314			−0.0581568	−	0.998307i	$-0.518522\pi$
$199$	−1.29305e7			−0.116314			−0.0581568	+	0.998307i	$0.518522\pi$
$200$	−1.62083e7	+	2.80736e7i	−0.143262	+	0.248138i
$201$	−7.89708e7	+	1.36782e8i	−0.685931	+	1.18807i
$202$	−5.35276e7	+	9.27125e7i	−0.456928	+	0.791423i
$203$	4.37744e7	+	7.58194e7i	0.367268	+	0.636128i
$204$	−6.12506e7	−	1.06089e8i	−0.505132	−	0.874914i
$205$	−4.65303e7	+	8.05928e7i	−0.377222	+	0.653368i
$206$	1.44540e8	−	2.50351e8i	1.15200	−	1.99533i
$207$	−1.34016e7	+	2.32122e7i	−0.105017	+	0.181895i
$208$	1.10756e8			0.853388
$209$	−3.99692e7	−	6.92286e7i	−0.302840	−	0.524534i
$210$	4.72435e7	−	8.18281e7i	0.352026	−	0.609727i
$211$	5.99880e7			0.439618			0.219809	−	0.975543i	$-0.429457\pi$
$211$	5.99880e7			0.439618			0.219809	+	0.975543i	$0.429457\pi$
$212$	9.25920e7			0.667418
$213$	−1.74458e8	+	3.02171e8i	−1.23698	+	2.14251i
$214$	−1.13160e8			−0.789302
$215$	−4.18874e7	−	7.25511e7i	−0.287441	−	0.497862i
$216$	1.04221e8			0.703665
$217$	6.02673e7	+	1.04386e8i	0.400380	+	0.693479i
$218$	4.74733e7	+	8.22261e7i	0.310350	+	0.537542i
$219$	−2.36536e8	−	4.09692e8i	−1.52175	−	2.63574i
$220$	2.01846e7	−	3.49608e7i	0.127803	−	0.221361i
$221$	8.99202e7			0.560382
$222$	3.29390e8	+	1.85657e8i	2.02058	+	1.13888i
$223$	6.76986e7			0.408802			0.204401	−	0.978887i	$-0.434475\pi$
$223$	6.76986e7			0.408802			0.204401	+	0.978887i	$0.434475\pi$
$224$	−6.95402e7	+	1.20447e8i	−0.413398	+	0.716026i
$225$	1.44546e8	+	2.50360e8i	0.845992	+	1.46530i
$226$	1.88924e7	+	3.27227e7i	0.108870	+	0.188569i
$227$	−6.45957e7	−	1.11883e8i	−0.366533	−	0.634853i	0.622488	−	0.782629i	$-0.286122\pi$
$227$	−6.45957e7	−	1.11883e8i	−0.366533	−	0.634853i	−0.989021	+	0.147776i	$0.952789\pi$
$228$	−1.77021e8			−0.989128
$229$	−4.07825e7	−	7.06373e7i	−0.224414	−	0.388696i	0.731730	−	0.681595i	$-0.238713\pi$
$229$	−4.07825e7	−	7.06373e7i	−0.224414	−	0.388696i	−0.956143	+	0.292899i	$0.905380\pi$
$230$	−1.07660e7			−0.0583457
$231$	−8.83027e7	+	1.52945e8i	−0.471338	+	0.816381i
$232$	−7.36099e7			−0.387015
$233$	−3.15337e8			−1.63316			−0.816581	−	0.577231i	$-0.804133\pi$
$233$	−3.15337e8			−1.63316			−0.816581	+	0.577231i	$0.804133\pi$
$234$	1.93941e8	−	3.35915e8i	0.989494	−	1.71385i
$235$	−5.83084e7	−	1.00993e8i	−0.293085	−	0.507638i
$236$	6.19790e6			0.0306940
$237$	−9.10189e7	+	1.57649e8i	−0.444132	+	0.769260i
$238$	−7.30662e7	+	1.26554e8i	−0.351315	+	0.608496i
$239$	1.18277e8	−	2.04862e8i	0.560412	−	0.970663i	−0.437048	−	0.899438i	$-0.643976\pi$
$239$	1.18277e8	−	2.04862e8i	0.560412	−	0.970663i	0.997460	−	0.0712245i	$-0.0226907\pi$
$240$	1.01150e8	+	1.75197e8i	0.472309	+	0.818063i
$241$	−6.99817e7	−	1.21212e8i	−0.322051	−	0.557809i	0.658860	−	0.752266i	$-0.271039\pi$
$241$	−6.99817e7	−	1.21212e8i	−0.322051	−	0.557809i	−0.980911	+	0.194457i	$0.937706\pi$
$242$	5.53197e7	−	9.58165e7i	0.250914	−	0.434597i
$243$	4.75286e7	−	8.23220e7i	0.212487	−	0.368039i
$244$	−1.25724e8	+	2.17760e8i	−0.554055	+	0.959651i
$245$	5.53674e7			0.240532
$246$	−4.57267e8	−	7.92010e8i	−1.95838	−	3.39202i
$247$	6.49697e7	−	1.12531e8i	0.274329	−	0.475152i
$248$	−1.01344e8			−0.421907
$249$	1.88432e8			0.773493
$250$	−1.30598e8	+	2.26203e8i	−0.528625	+	0.915606i
$251$	1.93959e8			0.774197			0.387098	−	0.922038i	$-0.373477\pi$
$251$	1.93959e8			0.774197			0.387098	+	0.922038i	$0.373477\pi$
$252$	1.32747e8	+	2.29925e8i	0.522544	+	0.905073i
$253$	2.01228e7			0.0781208
$254$	2.44691e8	+	4.23818e8i	0.936915	+	1.62279i
$255$	8.21211e7	+	1.42238e8i	0.310144	+	0.537186i
$256$	−1.75487e8	−	3.03952e8i	−0.653738	−	1.13231i
$257$	−2.41723e8	+	4.18676e8i	−0.888284	+	1.53855i	−0.0463815	+	0.998924i	$0.514769\pi$
$257$	−2.41723e8	+	4.18676e8i	−0.888284	+	1.53855i	−0.841903	+	0.539629i	$0.818564\pi$
$258$	8.23281e8			2.98455
$259$	−1.96504e6	−	1.89962e8i	−0.00702785	−	0.679388i
$260$	6.56200e7			0.231542
$261$	−3.28227e8	+	5.68505e8i	−1.14270	+	1.97921i
$262$	9.82611e7	+	1.70193e8i	0.337541	+	0.584639i
$263$	−6.78201e7	−	1.17468e8i	−0.229886	−	0.398175i	0.727888	−	0.685696i	$-0.240502\pi$
$263$	−6.78201e7	−	1.17468e8i	−0.229886	−	0.398175i	−0.957774	+	0.287521i	$0.907169\pi$
$264$	−7.42439e7	−	1.28594e8i	−0.248340	−	0.430138i
$265$	−1.24142e8			−0.409786
$266$	1.05585e8	+	1.82878e8i	0.343965	+	0.595766i
$267$	6.35654e8			2.04377
$268$	8.91293e7	−	1.54376e8i	0.282845	−	0.489902i
$269$	4.18804e8			1.31183			0.655915	−	0.754835i	$-0.272283\pi$
$269$	4.18804e8			1.31183			0.655915	+	0.754835i	$0.272283\pi$
$270$	3.73330e8			1.15430
$271$	7.82596e7	−	1.35550e8i	0.238861	−	0.413719i	−0.721527	−	0.692386i	$-0.756559\pi$
$271$	7.82596e7	−	1.35550e8i	0.238861	−	0.413719i	0.960388	+	0.278667i	$0.0898927\pi$
$272$	−1.56437e8	−	2.70957e8i	−0.471356	−	0.816412i
$273$	−2.87072e8			−0.853927
$274$	1.68716e8	−	2.92224e8i	0.495482	−	0.858201i
$275$	1.08520e8	−	1.87961e8i	0.314661	−	0.545009i
$276$	2.22806e7	−	3.85912e7i	0.0637890	−	0.110486i
$277$	−1.25354e8	−	2.17120e8i	−0.354373	−	0.613792i	0.632638	−	0.774448i	$-0.281972\pi$
$277$	−1.25354e8	−	2.17120e8i	−0.354373	−	0.613792i	−0.987010	+	0.160656i	$0.948639\pi$
$278$	−4.17462e8	−	7.23065e8i	−1.16536	−	2.01846i
$279$	−4.51893e8	+	7.82702e8i	−1.24572	+	2.15765i
$280$	1.99573e7	−	3.45670e7i	0.0543311	−	0.0941042i
$281$	−2.91612e8	+	5.05088e8i	−0.784032	+	1.35798i	0.145543	+	0.989352i	$0.453507\pi$
$281$	−2.91612e8	+	5.05088e8i	−0.784032	+	1.35798i	−0.929575	+	0.368632i	$0.879826\pi$
$282$	1.14603e9			3.04316
$283$	−8.97016e7	−	1.55368e8i	−0.235260	−	0.407482i	0.724088	−	0.689707i	$-0.242261\pi$
$283$	−8.97016e7	−	1.55368e8i	−0.235260	−	0.407482i	−0.959348	+	0.282225i	$0.908927\pi$
$284$	1.96900e8	−	3.41041e8i	0.510072	−	0.883470i
$285$	2.37339e8			0.607312
$286$	−2.91207e8			−0.736073
$287$	−2.29743e8	+	3.97927e8i	−0.573663	+	0.993613i
$288$	−1.04285e9			−2.57245
$289$	7.81620e7	+	1.35380e8i	0.190482	+	0.329924i
$290$	−2.63679e8			−0.634866
$291$	6.65513e8	+	1.15270e9i	1.58318	+	2.74215i
$292$	2.66963e8	+	4.62393e8i	0.627496	+	1.08685i
$293$	1.14586e8	+	1.98469e8i	0.266132	+	0.460953i	0.967859	−	0.251492i	$-0.0809211\pi$
$293$	1.14586e8	+	1.98469e8i	0.266132	+	0.460953i	−0.701728	+	0.712445i	$0.747588\pi$
$294$	−2.72056e8	+	4.71215e8i	−0.624371	+	1.08144i
$295$	−8.30977e6			−0.0188457
$296$	1.39146e8	+	7.84281e7i	0.311853	+	0.175772i
$297$	−6.97790e8			−1.54553
$298$	5.66258e7	−	9.80788e7i	0.123953	−	0.214693i
$299$	1.63548e7	+	2.83273e7i	0.0353831	+	0.0612852i
$300$	−2.40313e8	−	4.16234e8i	−0.513870	−	0.890048i
$301$	−2.06819e8	−	3.58221e8i	−0.437127	−	0.757127i
$302$	1.60154e8			0.334590
$303$	2.97046e8	+	5.14498e8i	0.613443	+	1.06251i
$304$	−4.52120e8			−0.922989
$305$	1.68563e8	−	2.91959e8i	0.340182	−	0.589213i
$306$	−1.09572e9			−2.18613
$307$	−1.34743e8			−0.265779			−0.132889	−	0.991131i	$-0.542426\pi$
$307$	−1.34743e8			−0.265779			−0.132889	+	0.991131i	$0.542426\pi$
$308$	9.96616e7	−	1.72619e8i	0.194357	−	0.336636i
$309$	−8.02112e8	−	1.38930e9i	−1.54661	−	2.67880i
$310$	−3.63025e8			−0.692103
$311$	−6.46102e7	+	1.11908e8i	−0.121798	+	0.210960i	−0.920477	−	0.390797i	$-0.872199\pi$
$311$	−6.46102e7	+	1.11908e8i	−0.121798	+	0.210960i	0.798679	+	0.601758i	$0.205533\pi$
$312$	1.20683e8	−	2.09029e8i	0.224960	−	0.389643i
$313$	3.16255e8	−	5.47769e8i	0.582951	−	1.00970i	−0.412177	−	0.911104i	$-0.635231\pi$
$313$	3.16255e8	−	5.47769e8i	0.582951	−	1.00970i	0.995128	−	0.0985964i	$-0.0314353\pi$
$314$	1.25426e7	+	2.17244e7i	0.0228630	+	0.0395999i
$315$	−1.77979e8	−	3.08269e8i	−0.320835	−	0.555703i
$316$	1.02727e8	−	1.77929e8i	0.183139	−	0.317206i
$317$	9.58922e7	−	1.66090e8i	0.169074	−	0.292844i	−0.769021	−	0.639224i	$-0.779256\pi$
$317$	9.58922e7	−	1.66090e8i	0.169074	−	0.292844i	0.938094	+	0.346380i	$0.112589\pi$
$318$	6.09990e8	−	1.05653e9i	1.06372	−	1.84242i
$319$	4.92841e8			0.850040
$320$	−5.25501e7	−	9.10195e7i	−0.0896497	−	0.155278i
$321$	−3.13984e8	+	5.43836e8i	−0.529834	+	0.917699i
$322$	−5.31574e7			−0.0887296
$323$	−3.67065e8			−0.606086
$324$	−3.01759e8	+	5.22662e8i	−0.492893	+	0.853716i
$325$	3.52796e8			0.570075
$326$	4.53639e8	+	7.85726e8i	0.725185	+	1.25606i
$327$	5.26896e8			0.833312
$328$	−1.93166e8	−	3.34573e8i	−0.302253	−	0.523518i
$329$	−2.87898e8	−	4.98654e8i	−0.445711	−	0.771994i
$330$	−2.65950e8	−	4.60638e8i	−0.407381	−	0.705604i
$331$	6.38283e8	−	1.10554e9i	0.967421	−	1.67562i	0.264454	−	0.964398i	$-0.414808\pi$
$331$	6.38283e8	−	1.10554e9i	0.967421	−	1.67562i	0.702966	−	0.711223i	$-0.251859\pi$
$332$	−2.12671e8			−0.318951
$333$	1.22617e9	−	7.24942e8i	1.81968	−	1.07584i
$334$	−4.70435e8			−0.690855
$335$	−1.19499e8	+	2.06979e8i	−0.173663	+	0.300794i
$336$	4.99428e8	+	8.65035e8i	0.718267	+	1.24407i
$337$	−6.11965e8	−	1.05995e9i	−0.871008	−	1.50863i	−0.860955	−	0.508680i	$-0.830134\pi$
$337$	−6.11965e8	−	1.05995e9i	−0.871008	−	1.50863i	−0.0100524	−	0.999949i	$-0.503200\pi$
$338$	2.29881e8	+	3.98165e8i	0.323813	+	0.560860i
$339$	2.09683e8			0.292324
$340$	−9.26848e7	−	1.60535e8i	−0.127889	−	0.221510i
$341$	6.78529e8			0.926677
$342$	−7.91689e8	+	1.37125e9i	−1.07020	+	1.85363i
$343$	7.81151e8			1.04521
$344$	3.47782e8			0.460631
$345$	−2.98725e7	+	5.17407e7i	−0.0391656	+	0.0678369i
$346$	2.35645e8	+	4.08149e8i	0.305839	+	0.529728i
$347$	1.04321e9			1.34035			0.670174	−	0.742204i	$-0.266220\pi$
$347$	1.04321e9			1.34035			0.670174	+	0.742204i	$0.266220\pi$
$348$	5.45690e8	−	9.45163e8i	0.694095	−	1.20221i
$349$	−4.62265e8	+	8.00667e8i	−0.582106	+	1.00824i	0.413123	+	0.910675i	$0.364438\pi$
$349$	−4.62265e8	+	8.00667e8i	−0.582106	+	1.00824i	−0.995229	+	0.0975626i	$0.968895\pi$
$350$	−2.86671e8	+	4.96528e8i	−0.357392	+	0.619022i
$351$	−5.67128e8	−	9.82294e8i	−0.700013	−	1.21246i
$352$	3.91465e8	+	6.78038e8i	0.478403	+	0.828618i
$353$	−6.06158e8	+	1.04990e9i	−0.733456	+	1.27038i	0.221942	+	0.975060i	$0.428761\pi$
$353$	−6.06158e8	+	1.04990e9i	−0.733456	+	1.27038i	−0.955397	+	0.295323i	$0.904573\pi$
$354$	4.08314e7	−	7.07220e7i	0.0489196	−	0.0847312i
$355$	−2.63991e8	+	4.57247e8i	−0.313178	+	0.542439i
$356$	−7.17422e8			−0.842751
$357$	4.05473e8	+	7.02300e8i	0.471654	+	0.816928i
$358$	−1.25531e8	+	2.17425e8i	−0.144597	+	0.250449i
$359$	−1.45334e9			−1.65782			−0.828909	−	0.559384i	$-0.811038\pi$
$359$	−1.45334e9			−1.65782			−0.828909	+	0.559384i	$0.811038\pi$
$360$	2.99286e8			0.338086
$361$	1.81721e8	−	3.14751e8i	0.203297	−	0.352121i
$362$	−1.80822e9			−2.00341
$363$	−3.06991e8	−	5.31723e8i	−0.336862	−	0.583462i
$364$	3.23999e8			0.352119
$365$	−3.57927e8	−	6.19948e8i	−0.385274	−	0.667314i
$366$	1.65652e9	+	2.86917e9i	1.76609	+	3.05895i
$367$	3.72786e8	+	6.45684e8i	0.393666	+	0.681850i	0.992930	−	0.118702i	$-0.0378733\pi$
$367$	3.72786e8	+	6.45684e8i	0.393666	+	0.681850i	−0.599264	+	0.800552i	$0.704540\pi$
$368$	5.69059e7	−	9.85639e7i	0.0595237	−	0.103098i
$369$	−3.44530e9			−3.56973
$370$	4.98435e8	+	2.80938e8i	0.511567	+	0.288340i
$371$	−6.12951e8			−0.623185
$372$	7.51291e8	−	1.30127e9i	0.756672	−	1.31059i
$373$	−3.15391e8	−	5.46273e8i	−0.314679	−	0.545041i	0.664690	−	0.747119i	$-0.268564\pi$
$373$	−3.15391e8	−	5.46273e8i	−0.314679	−	0.545041i	−0.979369	+	0.202079i	$0.935230\pi$
$374$	4.11314e8	+	7.12417e8i	0.406559	+	0.704180i
$375$	7.24743e8	+	1.25529e9i	0.709699	+	1.22924i
$376$	4.84123e8			0.469676
$377$	4.00556e8	+	6.93783e8i	0.385007	+	0.666851i
$378$	1.84332e9			1.75541
$379$	−5.25267e8	+	9.09789e8i	−0.495613	+	0.858427i	−0.999987	−	0.00505834i	$-0.998390\pi$
$379$	−5.25267e8	+	9.09789e8i	−0.495613	+	0.858427i	0.504374	+	0.863485i	$0.331723\pi$
$380$	−2.67869e8			−0.250426
$381$	2.71578e9			2.51569
$382$	−7.94686e8	+	1.37644e9i	−0.729414	+	1.26338i
$383$	−1.41510e8	−	2.45102e8i	−0.128704	−	0.222921i	0.794471	−	0.607302i	$-0.207748\pi$
$383$	−1.41510e8	−	2.45102e8i	−0.128704	−	0.222921i	−0.923175	+	0.384381i	$0.874415\pi$
$384$	−1.34985e9			−1.21654
$385$	−1.33620e8	+	2.31437e8i	−0.119333	+	0.206690i
$386$	4.21347e8	−	7.29794e8i	0.372893	−	0.645869i
$387$	1.55076e9	−	2.68600e9i	1.36006	−	2.35569i
$388$	−7.51122e8	−	1.30098e9i	−0.652829	−	1.13073i
$389$	−2.32308e7	−	4.02368e7i	−0.0200097	−	0.0346577i	0.855847	−	0.517229i	$-0.173036\pi$
$389$	−2.32308e7	−	4.02368e7i	−0.0200097	−	0.0346577i	−0.875857	+	0.482571i	$0.839703\pi$
$390$	4.32300e8	−	7.48766e8i	0.369028	−	0.639175i
$391$	4.62005e7	−	8.00216e7i	0.0390866	−	0.0676999i
$392$	−1.14926e8	+	1.99058e8i	−0.0963645	+	0.166908i
$393$	1.09058e9			0.906324
$394$	9.80730e8	+	1.69867e9i	0.807816	+	1.39918i
$395$	−1.37730e8	+	2.38556e8i	−0.112445	+	0.194760i
$396$	1.49456e9			1.20942
$397$	2.33980e9			1.87677			0.938387	−	0.345587i	$-0.112320\pi$
$397$	2.33980e9			1.87677			0.938387	+	0.345587i	$0.112320\pi$
$398$	9.61433e7	−	1.66525e8i	0.0764413	−	0.132400i
$399$	1.17186e9			0.923573
$400$	−6.13772e8	−	1.06308e9i	−0.479509	−	0.830534i
$401$	2.83600e7			0.0219634			0.0109817	−	0.999940i	$-0.496504\pi$
$401$	2.83600e7			0.0219634			0.0109817	+	0.999940i	$0.496504\pi$
$402$	−1.17436e9	−	2.03404e9i	−0.901589	−	1.56160i
$403$	5.51474e8	+	9.55181e8i	0.419718	+	0.726972i
$404$	−3.35256e8	−	5.80681e8i	−0.252954	−	0.438130i
$405$	4.04580e8	−	7.00754e8i	0.302630	−	0.524171i
$406$	−1.30191e9			−0.965476
$407$	−9.31624e8	−	5.25100e8i	−0.684952	−	0.386066i
$408$	−6.81834e8			−0.497013
$409$	−4.15218e7	+	7.19178e7i	−0.0300085	+	0.0519763i	−0.880640	−	0.473787i	$-0.842887\pi$
$409$	−4.15218e7	+	7.19178e7i	−0.0300085	+	0.0519763i	0.850631	+	0.525763i	$0.176220\pi$
$410$	−6.91940e8	−	1.19848e9i	−0.495821	−	0.858787i
$411$	−9.36269e8	−	1.62167e9i	−0.665203	−	1.15217i
$412$	9.05292e8	+	1.56801e9i	0.637747	+	1.10461i
$413$	−4.10296e7			−0.0286597
$414$	−1.99291e8	−	3.45182e8i	−0.138034	−	0.239082i
$415$	2.85136e8			0.195832
$416$	−6.36326e8	+	1.10215e9i	−0.433364	+	0.750608i
$417$	−4.63332e9			−3.12907
$418$	1.18874e9			0.796106
$419$	−1.40076e9	+	2.42619e9i	−0.930282	+	1.61130i	−0.147444	+	0.989070i	$0.547105\pi$
$419$	−1.40076e9	+	2.42619e9i	−0.930282	+	1.61130i	−0.782838	+	0.622225i	$0.786229\pi$
$420$	2.95898e8	+	5.12510e8i	0.194881	+	0.337543i
$421$	−3.79961e8			−0.248171			−0.124086	−	0.992272i	$-0.539600\pi$
$421$	−3.79961e8			−0.248171			−0.124086	+	0.992272i	$0.539600\pi$
$422$	−4.46033e8	+	7.72552e8i	−0.288917	+	0.500419i
$423$	2.15870e9	−	3.73899e9i	1.38676	−	2.40194i
$424$	2.57681e8	−	4.46316e8i	0.164173	−	0.284356i
$425$	−4.98306e8	−	8.63091e8i	−0.314872	−	0.545375i
$426$	−2.59433e9	−	4.49351e9i	−1.62589	−	2.81612i
$427$	8.32279e8	−	1.44155e9i	0.517334	−	0.896049i
$428$	3.54373e8	−	6.13792e8i	0.218478	−	0.378415i
$429$	−8.08011e8	+	1.39952e9i	−0.494102	+	0.855810i
$430$	1.24579e9			0.755625
$431$	1.31278e8	+	2.27381e8i	0.0789810	+	0.136799i	0.902811	−	0.430039i	$-0.141500\pi$
$431$	1.31278e8	+	2.27381e8i	0.0789810	+	0.136799i	−0.823830	+	0.566838i	$0.808167\pi$
$432$	−1.97330e9	+	3.41786e9i	−1.17761	+	2.03968i
$433$	−2.57461e9			−1.52407			−0.762034	−	0.647537i	$-0.775799\pi$
$433$	−2.57461e9			−1.52407			−0.762034	+	0.647537i	$0.775799\pi$
$434$	−1.79244e9			−1.05252
$435$	−7.31628e8	+	1.26722e9i	−0.426165	+	0.738140i
$436$	−5.94673e8			−0.343618
$437$	−6.67622e7	−	1.15635e8i	−0.0382689	−	0.0662836i
$438$	7.03493e9			4.00037
$439$	−1.10868e8	−	1.92030e8i	−0.0625435	−	0.108329i	0.833058	−	0.553185i	$-0.186588\pi$
$439$	−1.10868e8	−	1.92030e8i	−0.0625435	−	0.108329i	−0.895602	+	0.444857i	$0.853255\pi$
$440$	−1.12346e8	−	1.94589e8i	−0.0628745	−	0.108902i
$441$	1.02491e9	+	1.77520e9i	0.569050	+	0.985624i
$442$	−6.68590e8	+	1.15803e9i	−0.368283	+	0.637885i
$443$	3.73489e8			0.204110			0.102055	−	0.994779i	$-0.467458\pi$
$443$	3.73489e8			0.204110			0.102055	+	0.994779i	$0.467458\pi$
$444$	−2.03856e9	+	1.20525e9i	−1.10531	+	0.653485i
$445$	9.61875e8			0.517438
$446$	−5.03365e8	+	8.71853e8i	−0.268665	+	0.465341i
$447$	−3.14239e8	−	5.44278e8i	−0.166412	−	0.288233i
$448$	−2.59467e8	−	4.49409e8i	−0.136335	−	0.236140i
$449$	4.55690e8	+	7.89278e8i	0.237578	+	0.411498i	0.960019	−	0.279935i	$-0.0903130\pi$
$449$	4.55690e8	+	7.89278e8i	0.237578	+	0.411498i	−0.722440	+	0.691433i	$0.756980\pi$
$450$	−4.29900e9			−2.22394
$451$	1.29330e9	+	2.24007e9i	0.663869	+	1.14986i
$452$	−2.36656e8			−0.120541
$453$	4.44378e8	−	7.69685e8i	0.224599	−	0.389018i
$454$	1.92117e9			0.963542
$455$	−4.34399e8			−0.216196
$456$	−4.92644e8	+	8.53284e8i	−0.243308	+	0.421421i
$457$	3.58505e8	+	6.20948e8i	0.175707	+	0.304333i	0.940406	−	0.340055i	$-0.110446\pi$
$457$	3.58505e8	+	6.20948e8i	0.175707	+	0.304333i	−0.764699	+	0.644388i	$0.777112\pi$
$458$	1.21293e9			0.589939
$459$	−1.60207e9	+	2.77487e9i	−0.773283	+	1.33937i
$460$	3.37152e7	−	5.83964e7i	0.0161500	−	0.0279727i
$461$	1.70400e9	−	2.95141e9i	0.810058	−	1.40306i	−0.102764	−	0.994706i	$-0.532769\pi$
$461$	1.70400e9	−	2.95141e9i	0.810058	−	1.40306i	0.912823	−	0.408357i	$-0.133898\pi$
$462$	−1.31313e9	−	2.27440e9i	−0.619527	−	1.07305i
$463$	3.17615e8	+	5.50126e8i	0.148719	+	0.257590i	0.930754	−	0.365645i	$-0.119152\pi$
$463$	3.17615e8	+	5.50126e8i	0.148719	+	0.257590i	−0.782035	+	0.623235i	$0.785818\pi$
$464$	1.39372e9	−	2.41400e9i	0.647684	−	1.12182i
$465$	−1.00728e9	+	1.74467e9i	−0.464587	+	0.804688i
$466$	2.34465e9	−	4.06105e9i	1.07331	−	1.85904i
$467$	−8.90990e8			−0.404821			−0.202411	−	0.979301i	$-0.564878\pi$
$467$	−8.90990e8			−0.404821			−0.202411	+	0.979301i	$0.564878\pi$
$468$	1.21470e9	+	2.10392e9i	0.547782	+	0.948786i
$469$	−5.90028e8	+	1.02196e9i	−0.264099	+	0.457434i
$470$	1.73418e9			0.770463
$471$	1.39208e8			0.0613889
$472$	1.72486e7	−	2.98754e7i	0.00755016	−	0.0130773i
$473$	−2.32851e9			−1.01173
$474$	−1.35352e9	−	2.34436e9i	−0.583768	−	1.01112i
$475$	−1.44016e9			−0.616570
$476$	−4.57632e8	−	7.92641e8i	−0.194487	−	0.336862i
$477$	−2.29800e9	−	3.98025e9i	−0.969472	−	1.67918i
$478$	1.75887e9	+	3.04645e9i	0.736606	+	1.27584i
$479$	−3.01159e8	+	5.21623e8i	−0.125205	+	0.216861i	−0.921813	−	0.387635i	$-0.873292\pi$
$479$	−3.01159e8	+	5.21623e8i	−0.125205	+	0.216861i	0.796608	+	0.604496i	$0.206626\pi$
$480$	−2.32454e9			−0.959384
$481$	−1.79811e7	−	1.73824e9i	−0.00736728	−	0.712201i
$482$	2.08136e9			0.846608
$483$	−1.47496e8	+	2.55470e8i	−0.0595614	+	0.103163i
$484$	3.46481e8	+	6.00122e8i	0.138906	+	0.240592i
$485$	1.00706e9	+	1.74428e9i	0.400829	+	0.694255i
$486$	7.06786e8	+	1.22419e9i	0.279294	+	0.483751i
$487$	4.41705e9			1.73293			0.866465	−	0.499238i	$-0.166387\pi$
$487$	4.41705e9			1.73293			0.866465	+	0.499238i	$0.166387\pi$
$488$	6.99770e8	+	1.21204e9i	0.272575	+	0.472114i
$489$	5.03484e9			1.94717
$490$	−4.11677e8	+	7.13046e8i	−0.158078	+	0.273799i
$491$	−4.34187e8			−0.165536			−0.0827679	−	0.996569i	$-0.526376\pi$
$491$	−4.34187e8			−0.165536			−0.0827679	+	0.996569i	$0.526376\pi$
$492$	5.72796e9			2.16831
$493$	1.13153e9	−	1.95986e9i	0.425305	−	0.736650i
$494$	9.66149e8	+	1.67342e9i	0.360578	+	0.624540i
$495$	−2.00381e9			−0.742571
$496$	1.91884e9	−	3.32352e9i	0.706077	−	1.22296i
$497$	−1.30346e9	+	2.25766e9i	−0.476267	+	0.824918i
$498$	−1.40106e9	+	2.42671e9i	−0.508340	+	0.880470i
$499$	5.29755e8	+	9.17563e8i	0.190864	+	0.330586i	0.945537	−	0.325515i	$-0.105538\pi$
$499$	5.29755e8	+	9.17563e8i	0.190864	+	0.330586i	−0.754673	+	0.656101i	$0.772204\pi$
$500$	−8.17970e8	−	1.41677e9i	−0.292646	−	0.506878i
$501$	−1.30531e9	+	2.26087e9i	−0.463749	+	0.803237i
$502$	−1.44216e9	+	2.49789e9i	−0.508803	+	0.881272i
$503$	2.09685e9	−	3.63185e9i	0.734648	−	1.27245i	−0.220229	−	0.975448i	$-0.570681\pi$
$503$	2.09685e9	−	3.63185e9i	0.734648	−	1.27245i	0.954877	−	0.297000i	$-0.0959861\pi$
$504$	1.47772e9			0.514146
$505$	4.49491e8	+	7.78542e8i	0.155311	+	0.269006i
$506$	−1.49620e8	+	2.59150e8i	−0.0513410	+	0.0889252i
$507$	2.55140e9			0.869461
$508$	−3.06512e9			−1.03735
$509$	−9.69454e8	+	1.67914e9i	−0.325848	+	0.564385i	−0.981684	−	0.190519i	$-0.938983\pi$
$509$	−9.69454e8	+	1.67914e9i	−0.325848	+	0.564385i	0.655836	+	0.754904i	$0.272316\pi$
$510$	−2.44240e9			−0.815308
$511$	−1.76727e9	−	3.06100e9i	−0.585908	−	1.01482i
$512$	3.12552e9			1.02915
$513$	2.31508e9	+	4.00984e9i	0.757105	+	1.31134i
$514$	−3.59460e9	−	6.22603e9i	−1.16756	−	2.02228i
$515$	−1.21376e9	−	2.10229e9i	−0.391568	−	0.678216i
$516$	−2.57820e9	+	4.46558e9i	−0.826121	+	1.43088i
$517$	−3.24135e9			−1.03160
$518$	2.46103e9	+	1.38713e9i	0.777969	+	0.438494i
$519$	2.61538e9			0.821199
$520$	1.82619e8	−	3.16305e8i	0.0569552	−	0.0986493i
$521$	−1.72149e9	−	2.98171e9i	−0.533302	−	0.923706i	−0.999243	−	0.0388908i	$-0.987618\pi$
$521$	−1.72149e9	−	2.98171e9i	−0.533302	−	0.923706i	0.465941	−	0.884816i	$-0.345716\pi$
$522$	−4.88098e9	−	8.45410e9i	−1.50197	−	2.60148i
$523$	−4.56511e8	−	7.90700e8i	−0.139539	−	0.241688i	0.787783	−	0.615953i	$-0.211229\pi$
$523$	−4.56511e8	−	7.90700e8i	−0.139539	−	0.241688i	−0.927322	+	0.374264i	$0.877895\pi$
$524$	−1.23087e9			−0.373725
$525$	1.59085e9	+	2.75543e9i	0.479813	+	0.831060i
$526$	2.01707e9			0.604326
$527$	1.55785e9	−	2.69828e9i	0.463649	−	0.803064i
$528$	5.62290e9			1.66242
$529$	−3.37121e9			−0.990128
$530$	9.23040e8	−	1.59875e9i	0.269312	−	0.466461i
$531$	−1.53823e8	−	2.66429e8i	−0.0445851	−	0.0772237i
$532$	−1.32260e9			−0.380837
$533$	−2.10226e9	+	3.64122e9i	−0.601369	+	1.04160i
$534$	−4.72632e9	+	8.18623e9i	−1.34316	+	2.32643i
$535$	−4.75122e8	+	8.22936e8i	−0.134143	+	0.232342i
$536$	−4.96088e8	−	8.59250e8i	−0.139150	−	0.241014i
$537$	6.96619e8	+	1.20658e9i	0.194127	+	0.336237i
$538$	−3.11396e9	+	5.39354e9i	−0.862135	+	1.49326i
$539$	7.69465e8	−	1.33275e9i	0.211655	−	0.366597i
$540$	−1.16913e9	+	2.02499e9i	−0.319510	+	0.553407i
$541$	1.14479e9			0.310838			0.155419	−	0.987849i	$-0.450327\pi$
$541$	1.14479e9			0.310838			0.155419	+	0.987849i	$0.450327\pi$
$542$	1.16378e9	+	2.01572e9i	0.313959	+	0.543793i
$543$	−5.01725e9	+	8.69013e9i	−1.34483	+	2.32931i
$544$	3.59510e9			0.957448
$545$	7.97302e8			0.210977
$546$	2.13448e9	−	3.69704e9i	0.561202	−	0.972030i
$547$	−2.98336e9			−0.779382			−0.389691	−	0.920946i	$-0.627418\pi$
$547$	−2.98336e9			−0.779382			−0.389691	+	0.920946i	$0.627418\pi$
$548$	1.05671e9	+	1.83027e9i	0.274298	+	0.475098i
$549$	1.24811e10			3.21921
$550$	1.61377e9	+	2.79513e9i	0.413591	+	0.716361i
$551$	−1.63512e9	−	2.83211e9i	−0.416407	−	0.721239i
$552$	−1.24013e8	−	2.14796e8i	−0.0313819	−	0.0543551i
$553$	−6.80044e8	+	1.17787e9i	−0.171001	+	0.296183i
$554$	3.72823e9			0.931576
$555$	2.73317e9	−	1.61592e9i	0.678643	−	0.401231i
$556$	5.22933e9			1.29028
$557$	1.67429e9	−	2.89996e9i	0.410523	−	0.711047i	−0.584424	−	0.811449i	$-0.698679\pi$
$557$	1.67429e9	−	2.89996e9i	0.410523	−	0.711047i	0.994947	+	0.100401i	$0.0320127\pi$
$558$	−6.71999e9	−	1.16394e10i	−1.63738	−	2.83602i
$559$	−1.89249e9	−	3.27789e9i	−0.458240	−	0.793695i
$560$	7.55738e8	+	1.30898e9i	0.181850	+	0.314973i
$561$	4.56509e9			1.09164
$562$	−4.33650e9	−	7.51103e9i	−1.03053	−	1.78494i
$563$	−3.82732e9			−0.903889			−0.451945	−	0.892046i	$-0.649270\pi$
$563$	−3.82732e9			−0.903889			−0.451945	+	0.892046i	$0.649270\pi$
$564$	−3.58894e9	+	6.21622e9i	−0.842343	+	1.45898i
$565$	3.17294e8			0.0740103
$566$	2.66786e9			0.618451
$567$	1.99762e9	−	3.45997e9i	0.460226	−	0.797136i
$568$	−1.09593e9	−	1.89821e9i	−0.250937	−	0.434636i
$569$	−3.06524e9			−0.697544			−0.348772	−	0.937208i	$-0.613401\pi$
$569$	−3.06524e9			−0.697544			−0.348772	+	0.937208i	$0.613401\pi$
$570$	−1.76470e9	+	3.05655e9i	−0.399125	+	0.691306i
$571$	−3.73218e9	+	6.46432e9i	−0.838949	+	1.45310i	0.0518248	+	0.998656i	$0.483496\pi$
$571$	−3.73218e9	+	6.46432e9i	−0.838949	+	1.45310i	−0.890774	+	0.454447i	$0.849837\pi$
$572$	9.11950e8	−	1.57954e9i	0.203744	−	0.352895i
$573$	4.41003e9	+	7.63839e9i	0.979265	+	1.69614i
$574$	−3.41646e9	−	5.91748e9i	−0.754023	−	1.30601i
$575$	1.81265e8	−	3.13960e8i	0.0397627	−	0.0688710i
$576$	1.94552e9	−	3.36974e9i	0.424187	−	0.734713i
$577$	−6.75691e8	+	1.17033e9i	−0.146431	+	0.253626i	−0.929906	−	0.367798i	$-0.880112\pi$
$577$	−6.75691e8	+	1.17033e9i	−0.146431	+	0.253626i	0.783475	+	0.621423i	$0.213445\pi$
$578$	−2.32465e9			−0.500738
$579$	−2.33822e9	−	4.04992e9i	−0.500623	−	0.867104i
$580$	8.25742e8	−	1.43023e9i	0.175730	−	0.304374i
$581$	1.40786e9			0.297813
$582$	−1.97934e10			−4.16187
$583$	−1.72525e9	+	2.98823e9i	−0.360589	+	0.624559i
$584$	2.97180e9			0.617411
$585$	−1.62859e9	−	2.82081e9i	−0.336331	−	0.582543i
$586$	−3.40797e9			−0.699607
$587$	−6.80180e8	−	1.17811e9i	−0.138800	−	0.240409i	0.788242	−	0.615365i	$-0.210991\pi$
$587$	−6.80180e8	−	1.17811e9i	−0.138800	−	0.240409i	−0.927043	+	0.374956i	$0.877658\pi$
$588$	−1.70396e9	−	2.95134e9i	−0.345651	−	0.598685i
$589$	−2.25118e9	−	3.89916e9i	−0.453949	−	0.786263i
$590$	6.17863e7	−	1.07017e8i	0.0123854	−	0.0214521i
$591$	1.08849e10			2.16905
$592$	−5.20658e9	+	3.07826e9i	−1.03140	+	0.609789i
$593$	3.25835e9			0.641662			0.320831	−	0.947137i	$-0.396038\pi$
$593$	3.25835e9			0.641662			0.320831	+	0.947137i	$0.396038\pi$
$594$	5.18833e9	−	8.98645e9i	1.01572	−	1.75928i
$595$	6.13564e8	+	1.06272e9i	0.119413	+	0.206829i
$596$	3.54661e8	+	6.14292e8i	0.0686202	+	0.118854i
$597$	−5.33537e8	−	9.24113e8i	−0.102625	−	0.177752i
$598$	−4.86415e8			−0.0930150
$599$	4.77244e9	+	8.26612e9i	0.907292	+	1.57148i	0.817811	+	0.575487i	$0.195188\pi$
$599$	4.77244e9	+	8.26612e9i	0.907292	+	1.57148i	0.0894811	+	0.995989i	$0.471479\pi$
$600$	−2.67514e9			−0.505611
$601$	8.37595e8	−	1.45076e9i	0.157389	−	0.272605i	−0.776538	−	0.630071i	$-0.783026\pi$
$601$	8.37595e8	−	1.45076e9i	0.157389	−	0.272605i	0.933926	+	0.357466i	$0.116359\pi$
$602$	6.15111e9			1.14912
$603$	−8.84824e9			−1.64341
$604$	−5.01541e8	+	8.68694e8i	−0.0926141	+	0.160412i
$605$	−4.64540e8	−	8.04607e8i	−0.0852863	−	0.147720i
$606$	−8.83458e9			−1.61262
$607$	−1.20388e9	+	2.08517e9i	−0.218485	+	0.378427i	−0.954345	−	0.298707i	$-0.903445\pi$
$607$	−1.20388e9	+	2.08517e9i	−0.218485	+	0.378427i	0.735860	+	0.677134i	$0.236778\pi$
$608$	2.59756e9	−	4.49910e9i	0.468709	−	0.811827i
$609$	−3.61242e9	+	6.25689e9i	−0.648094	+	1.12253i
$610$	2.50665e9	+	4.34165e9i	0.447136	+	0.774462i
$611$	−2.63440e9	−	4.56292e9i	−0.467238	−	0.809280i
$612$	3.43139e9	−	5.94334e9i	0.605118	−	1.04810i
$613$	2.37717e8	−	4.11738e8i	0.0416820	−	0.0721953i	−0.844432	−	0.535663i	$-0.820062\pi$
$613$	2.37717e8	−	4.11738e8i	0.0416820	−	0.0721953i	0.886114	+	0.463468i	$0.153395\pi$
$614$	1.00186e9	−	1.73527e9i	0.174670	−	0.302537i
$615$	−7.67970e9			−1.33132
$616$	−5.54710e8	−	9.60787e8i	−0.0956167	−	0.165613i
$617$	1.24227e9	−	2.15167e9i	0.212920	−	0.368788i	−0.739707	−	0.672929i	$-0.765036\pi$
$617$	1.24227e9	−	2.15167e9i	0.212920	−	0.368788i	0.952627	+	0.304141i	$0.0983693\pi$
$618$	2.38560e10			4.06573
$619$	−2.81879e7			−0.00477689			−0.00238844	−	0.999997i	$-0.500760\pi$
$619$	−2.81879e7			−0.00477689			−0.00238844	+	0.999997i	$0.500760\pi$
$620$	1.13686e9	−	1.96910e9i	0.191573	−	0.331815i
$621$	−1.16555e9			−0.195303
$622$	−9.60802e8	−	1.66416e9i	−0.160091	−	0.277286i
$623$	4.74926e9			0.786897
$624$	4.57000e9	+	7.91548e9i	0.752957	+	1.30416i
$625$	−1.34594e9	−	2.33123e9i	−0.220519	−	0.381949i
$626$	4.70294e9	+	8.14574e9i	0.766231	+	1.32715i
$627$	3.29840e9	−	5.71300e9i	0.534401	−	0.925609i
$628$	−1.57115e8			−0.0253138
$629$	−4.22709e9	+	2.49916e9i	−0.677274	+	0.400422i
$630$	5.29337e9			0.843412
$631$	−3.48456e9	+	6.03544e9i	−0.552135	+	0.956326i	0.445985	+	0.895040i	$0.352853\pi$
$631$	−3.48456e9	+	6.03544e9i	−0.552135	+	0.956326i	−0.998120	+	0.0612859i	$0.980480\pi$
$632$	−5.71773e8	−	9.90340e8i	−0.0900978	−	0.156054i
$633$	2.47521e9	+	4.28720e9i	0.387882	+	0.671832i
$634$	1.42599e9	+	2.46988e9i	0.222230	+	0.384914i
$635$	4.10953e9			0.636919
$636$	3.82052e9	+	6.61733e9i	0.588874	+	1.01996i
$637$	2.50153e9			0.383457
$638$	−3.66446e9	+	6.34703e9i	−0.558647	+	0.967605i
$639$	−1.95471e10			−2.96366
$640$	−2.04260e9			−0.308002
$641$	−8.94375e8	+	1.54910e9i	−0.134127	+	0.232315i	−0.925264	−	0.379325i	$-0.876156\pi$
$641$	−8.94375e8	+	1.54910e9i	−0.134127	+	0.232315i	0.791137	+	0.611640i	$0.209490\pi$
$642$	−4.66917e9	−	8.08724e9i	−0.696414	−	1.20622i
$643$	5.45694e9			0.809489			0.404744	−	0.914430i	$-0.367360\pi$
$643$	5.45694e9			0.809489			0.404744	+	0.914430i	$0.367360\pi$
$644$	1.66469e8	−	2.88333e8i	0.0245603	−	0.0425396i
$645$	3.45670e9	−	5.98718e9i	0.507227	−	0.878544i
$646$	2.72927e9	−	4.72723e9i	0.398320	−	0.689910i
$647$	3.95929e9	+	6.85770e9i	0.574715	+	0.995436i	0.996073	+	0.0885411i	$0.0282204\pi$
$647$	3.95929e9	+	6.85770e9i	0.574715	+	0.995436i	−0.421357	+	0.906895i	$0.638446\pi$
$648$	1.67957e9	+	2.90911e9i	0.242486	+	0.419998i
$649$	−1.15485e8	+	2.00025e8i	−0.0165832	+	0.0287229i
$650$	−2.62317e9	+	4.54347e9i	−0.374654	+	0.648919i
$651$	−4.97348e9	+	8.61431e9i	−0.706523	+	1.22373i
$652$	−5.68250e9			−0.802922
$653$	−6.39537e9	−	1.10771e10i	−0.898813	−	1.55679i	−0.829013	−	0.559229i	$-0.811097\pi$
$653$	−6.39537e9	−	1.10771e10i	−0.898813	−	1.55679i	−0.0698002	−	0.997561i	$-0.522236\pi$
$654$	−3.91767e9	+	6.78560e9i	−0.547653	+	0.948563i
$655$	1.65027e9			0.229462
$656$	1.46295e10			2.02333
$657$	1.32512e10	−	2.29518e10i	1.82296	−	3.15747i
$658$	8.56252e9			1.17169
$659$	−1.28836e9	−	2.23150e9i	−0.175363	−	0.303737i	0.764924	−	0.644121i	$-0.222776\pi$
$659$	−1.28836e9	−	2.23150e9i	−0.175363	−	0.303737i	−0.940287	+	0.340383i	$0.889443\pi$
$660$	3.33141e9			0.451050
$661$	−3.65263e9	−	6.32654e9i	−0.491927	−	0.852042i	0.508030	−	0.861339i	$-0.330374\pi$
$661$	−3.65263e9	−	6.32654e9i	−0.491927	−	0.852042i	−0.999957	+	0.00929737i	$0.997041\pi$
$662$	9.49175e9	+	1.64402e10i	1.27158	+	2.20244i
$663$	3.71027e9	+	6.42638e9i	0.494434	+	0.856385i
$664$	−5.91856e8	+	1.02512e9i	−0.0784563	+	0.135890i
$665$	1.77327e9			0.233829
$666$	2.19108e8	+	2.11814e10i	0.0287408	+	2.77840i
$667$	8.23213e8			0.107417
$668$	1.47322e9	−	2.55170e9i	0.191228	−	0.331217i
$669$	2.79337e9	+	4.83826e9i	0.360692	+	0.624738i
$670$	−1.77704e9	−	3.07793e9i	−0.228263	−	0.395363i
$671$	−4.68518e9	−	8.11497e9i	−0.598683	−	1.03695i
$672$	−1.14774e10			−1.45899
$673$	2.97531e9	+	5.15339e9i	0.376252	+	0.651688i	0.990514	−	0.137414i	$-0.0438792\pi$
$673$	2.97531e9	+	5.15339e9i	0.376252	+	0.651688i	−0.614261	+	0.789103i	$0.710546\pi$
$674$	1.82008e10			2.28971
$675$	−6.28564e9	+	1.08871e10i	−0.786659	+	1.36253i
$676$	−2.87960e9			−0.358524
$677$	−1.27614e10			−1.58066			−0.790332	−	0.612679i	$-0.790092\pi$
$677$	−1.27614e10			−1.58066			−0.790332	+	0.612679i	$0.790092\pi$
$678$	−1.55907e9	+	2.70039e9i	−0.192116	+	0.332754i
$679$	4.97236e9	+	8.61238e9i	0.609562	+	1.05579i
$680$	−1.03176e9			−0.125833
$681$	5.33067e9	−	9.23299e9i	0.646795	−	1.12028i
$682$	−5.04512e9	+	8.73840e9i	−0.609012	+	1.05484i
$683$	1.84031e9	−	3.18751e9i	0.221013	−	0.382806i	−0.734103	−	0.679038i	$-0.762397\pi$
$683$	1.84031e9	−	3.18751e9i	0.221013	−	0.382806i	0.955116	+	0.296232i	$0.0957303\pi$
$684$	−4.95854e9	−	8.58845e9i	−0.592458	−	1.02617i
$685$	−1.41677e9	−	2.45391e9i	−0.168415	−	0.291704i
$686$	−5.80815e9	+	1.00600e10i	−0.686915	+	1.18977i
$687$	3.36552e9	−	5.82925e9i	0.396007	−	0.685905i
$688$	−6.58487e9	+	1.14053e10i	−0.770881	+	1.33521i
$689$	−5.60879e9			−0.653283
$690$	−4.44227e8	−	7.69423e8i	−0.0514793	−	0.0891648i
$691$	3.91705e9	−	6.78453e9i	0.451633	−	0.782251i	−0.546855	−	0.837228i	$-0.684175\pi$
$691$	3.91705e9	−	6.78453e9i	0.451633	−	0.782251i	0.998488	+	0.0549762i	$0.0175083\pi$
$692$	−2.95181e9			−0.338623
$693$	−9.89382e9			−1.12927
$694$	−7.75664e9	+	1.34349e10i	−0.880877	+	1.52572i
$695$	−7.01116e9			−0.792216
$696$	−3.03728e9	−	5.26072e9i	−0.341470	−	0.591443i
$697$	1.18773e10			1.32863
$698$	−6.87423e9	−	1.19065e10i	−0.765121	−	1.32523i
$699$	−1.30114e10	−	2.25364e10i	−1.44097	−	2.49582i
$700$	−1.79549e9	−	3.10988e9i	−0.197852	−	0.342689i
$701$	6.81257e9	−	1.17997e10i	0.746960	−	1.29377i	−0.202313	−	0.979321i	$-0.564846\pi$
$701$	6.81257e9	−	1.17997e10i	0.746960	−	1.29377i	0.949273	−	0.314452i	$-0.101821\pi$
$702$	1.68672e10			1.84019
$703$	7.34009e7	+	7.09572e9i	0.00796815	+	0.770287i
$704$	−2.92125e9			−0.315547
$705$	4.81183e9	−	8.33433e9i	0.517187	−	0.895795i
$706$	−9.01402e9	−	1.56127e10i	−0.964055	−	1.66979i
$707$	2.21937e9	+	3.84406e9i	0.236190	+	0.409093i
$708$	2.55737e8	+	4.42949e8i	0.0270818	+	0.0469070i
$709$	−4.97759e9			−0.524515			−0.262257	−	0.964998i	$-0.584467\pi$
$709$	−4.97759e9			−0.524515			−0.262257	+	0.964998i	$0.584467\pi$
$710$	−3.92575e9	−	6.79960e9i	−0.411641	−	0.712983i
$711$	−1.01982e10			−1.06409
$712$	−1.99656e9	+	3.45815e9i	−0.207302	+	0.359057i
$713$	1.13338e9			0.117101
$714$	−1.20594e10			−1.23988
$715$	−1.22269e9	+	2.11776e9i	−0.125096	+	0.216673i
$716$	−7.86229e8	−	1.36179e9i	−0.0800485	−	0.138648i
$717$	1.95213e10			1.97784
$718$	1.08061e10	−	1.87168e10i	1.08952	−	1.88710i
$719$	−3.06604e9	+	5.31054e9i	−0.307629	+	0.532829i	−0.977843	−	0.209339i	$-0.932869\pi$
$719$	−3.06604e9	+	5.31054e9i	−0.307629	+	0.532829i	0.670214	+	0.742168i	$0.266202\pi$
$720$	−5.66664e9	+	9.81490e9i	−0.565798	+	0.979991i
$721$	−5.99295e9	−	1.03801e10i	−0.595480	−	1.03140i
$722$	2.70233e9	+	4.68058e9i	0.267214	+	0.462828i
$723$	5.77514e9	−	1.00028e10i	0.568301	−	0.984327i
$724$	5.66265e9	−	9.80800e9i	0.554542	−	0.960496i
$725$	4.43948e9	−	7.68940e9i	0.432662	−	0.749393i
$726$	9.13036e9			0.885543
$727$	6.55319e9	+	1.13505e10i	0.632531	+	1.09558i	0.987032	+	0.160521i	$0.0513174\pi$
$727$	6.55319e9	+	1.13505e10i	0.632531	+	1.09558i	−0.354501	+	0.935056i	$0.615349\pi$
$728$	9.01680e8	−	1.56176e9i	0.0866149	−	0.150021i
$729$	−6.32674e9			−0.604830
$730$	1.06453e10			1.01281
$731$	−5.34609e9	+	9.25970e9i	−0.506204	+	0.876771i
$732$	−2.07503e10			−1.95540
$733$	7.07669e9	+	1.22572e10i	0.663692	+	1.14955i	0.979638	+	0.200771i	$0.0643447\pi$
$733$	7.07669e9	+	1.22572e10i	0.663692	+	1.14955i	−0.315946	+	0.948777i	$0.602322\pi$
$734$	−1.10872e10			−1.03487
$735$	2.28456e9	+	3.95697e9i	0.212225	+	0.367585i
$736$	6.53881e8	+	1.13255e9i	0.0604542	+	0.104710i
$737$	3.32146e9	+	5.75295e9i	0.305628	+	0.529364i
$738$	2.56171e10	−	4.43701e10i	2.34603	−	4.06344i
$739$	6.54252e9			0.596334			0.298167	−	0.954514i	$-0.403625\pi$
$739$	6.54252e9			0.596334			0.298167	+	0.954514i	$0.403625\pi$
$740$	−3.08476e9	+	1.82379e9i	−0.279840	+	0.165449i
$741$	1.07231e10			0.968180
$742$	4.55752e9	−	7.89385e9i	0.409557	−	0.709374i
$743$	5.04031e9	+	8.73008e9i	0.450813	+	0.780832i	0.998437	−	0.0558934i	$-0.0178007\pi$
$743$	5.04031e9	+	8.73008e9i	0.450813	+	0.780832i	−0.547623	+	0.836725i	$0.684467\pi$
$744$	−4.18164e9	−	7.24281e9i	−0.372256	−	0.644766i
$745$	−4.75508e8	−	8.23605e8i	−0.0421319	−	0.0729746i
$746$	9.38020e9			0.827230
$747$	5.27817e9	+	9.14207e9i	0.463299	+	0.802458i
$748$	−5.15232e9			−0.450140
$749$	−2.34592e9	+	4.06325e9i	−0.203998	+	0.353335i
$750$	−2.15549e10			−1.86566
$751$	7.19098e9			0.619510			0.309755	−	0.950816i	$-0.399753\pi$
$751$	7.19098e9			0.619510			0.309755	+	0.950816i	$0.399753\pi$
$752$	−9.16633e9	+	1.58765e10i	−0.786019	+	1.36142i
$753$	8.00309e9	+	1.38618e10i	0.683086	+	1.18314i
$754$	−1.19131e10			−1.01211
$755$	6.72435e8	−	1.16469e9i	0.0568638	−	0.0984911i
$756$	−5.77258e9	+	9.99840e9i	−0.485896	+	0.841597i
$757$	−9.11455e9	+	1.57869e10i	−0.763659	+	1.32270i	0.177294	+	0.984158i	$0.443266\pi$
$757$	−9.11455e9	+	1.57869e10i	−0.763659	+	1.32270i	−0.940953	+	0.338538i	$0.890068\pi$
$758$	−7.81111e9	−	1.35292e10i	−0.651434	−	1.12832i
$759$	8.30303e8	+	1.43813e9i	0.0689272	+	0.119385i
$760$	−7.45471e8	+	1.29119e9i	−0.0616004	+	0.106695i
$761$	8.15524e9	−	1.41253e10i	0.670796	−	1.16185i	−0.306883	−	0.951747i	$-0.599286\pi$
$761$	8.15524e9	−	1.41253e10i	0.670796	−	1.16185i	0.977679	−	0.210105i	$-0.0673807\pi$
$762$	−2.01928e10	+	3.49750e10i	−1.65331	+	2.86362i
$763$	3.93668e9			0.320844
$764$	−4.97731e9	−	8.62096e9i	−0.403802	−	0.699405i
$765$	−4.60060e9	+	7.96847e9i	−0.371535	+	0.643517i
$766$	4.20872e9			0.338337
$767$	−3.75440e8			−0.0300439
$768$	1.44818e10	−	2.50832e10i	1.15361	−	1.99811i
$769$	−1.13332e10			−0.898688			−0.449344	−	0.893359i	$-0.648342\pi$
$769$	−1.13332e10			−0.898688			−0.449344	+	0.893359i	$0.648342\pi$
$770$	−1.98703e9	−	3.44164e9i	−0.156851	−	0.271674i
$771$	−3.98957e10			−3.13499
$772$	2.63900e9	+	4.57088e9i	0.206433	+	0.357552i
$773$	−7.18286e9	−	1.24411e10i	−0.559331	−	0.968790i	−0.997552	−	0.0699230i	$-0.977725\pi$
$773$	−7.18286e9	−	1.24411e10i	−0.559331	−	0.968790i	0.438221	−	0.898867i	$-0.355609\pi$
$774$	2.30610e10	+	3.99428e10i	1.78766	+	3.09631i
$775$	6.11215e9	−	1.05865e10i	0.471670	−	0.816956i
$776$	−8.36140e9			−0.642337
$777$	1.34951e10	−	7.97862e9i	1.03205	−	0.610175i
$778$	6.90917e8			0.0526014
$779$	8.58169e9	−	1.48639e10i	0.650416	−	1.12655i
$780$	2.70760e9	+	4.68971e9i	0.204293	+	0.353846i
$781$	7.33761e9	+	1.27091e10i	0.551158	+	0.954634i
$782$	6.87035e8	+	1.18998e9i	0.0513754	+	0.0889849i
$783$	−2.85462e10			−2.12512
$784$	−4.35199e9	−	7.53787e9i	−0.322539	−	0.558653i
$785$	2.10650e8			0.0155424
$786$	−8.10887e9	+	1.40450e10i	−0.595636	+	1.03167i
$787$	2.41499e10			1.76605			0.883025	−	0.469326i	$-0.155503\pi$
$787$	2.41499e10			1.76605			0.883025	+	0.469326i	$0.155503\pi$
$788$	−1.22851e10			−0.894411
$789$	5.59676e9	−	9.69388e9i	0.405665	−	0.702632i
$790$	−2.04815e9	−	3.54751e9i	−0.147798	−	0.255993i
$791$	1.56664e9			0.112552
$792$	4.15930e9	−	7.20412e9i	0.297497	−	0.515280i
$793$	7.61574e9	−	1.31909e10i	0.542321	−	0.939327i
$794$	−1.73973e10	+	3.01330e10i	−1.23342	+	2.13634i
$795$	−5.12232e9	−	8.87211e9i	−0.361561	−	0.626242i
$796$	6.02169e8	+	1.04299e9i	0.0423178	+	0.0732965i
$797$	2.33855e9	−	4.05048e9i	0.163622	−	0.283402i	−0.772543	−	0.634962i	$-0.781016\pi$
$797$	2.33855e9	−	4.05048e9i	0.163622	−	0.283402i	0.936165	+	0.351561i	$0.114349\pi$
$798$	−8.71323e9	+	1.50918e10i	−0.606972	+	1.05131i
$799$	−7.44191e9	+	1.28898e10i	−0.516144	+	0.893987i
$800$	1.41052e10			0.974010
$801$	1.78053e10	+	3.08398e10i	1.22416	+	2.12030i
$802$	−2.10867e8	+	3.65232e8i	−0.0144344	+	0.0250011i
$803$	−1.98971e10			−1.35608
$804$	1.47106e10			0.998235
$805$	−2.23191e8	+	3.86579e8i	−0.0150797	+	0.0261188i
$806$	−1.64017e10			−1.10335
$807$	1.72806e10	+	2.99309e10i	1.15745	+	2.00476i
$808$	−3.73203e9			−0.248889
$809$	−7.19652e9	−	1.24647e10i	−0.477863	−	0.827682i	0.521815	−	0.853058i	$-0.325255\pi$
$809$	−7.19652e9	−	1.24647e10i	−0.477863	−	0.827682i	−0.999678	+	0.0253762i	$0.991922\pi$
$810$	6.01641e9	+	1.04207e10i	0.397777	+	0.688970i
$811$	6.93750e9	+	1.20161e10i	0.456699	+	0.791025i	0.998784	−	0.0492981i	$-0.0156984\pi$
$811$	6.93750e9	+	1.20161e10i	0.456699	+	0.791025i	−0.542085	+	0.840323i	$0.682365\pi$
$812$	4.07711e9	−	7.06175e9i	0.267243	−	0.462878i
$813$	1.29165e10			0.843003
$814$	1.36895e10	−	8.09356e9i	0.889612	−	0.525961i
$815$	7.61876e9			0.492984
$816$	1.29098e10	−	2.23604e10i	0.831769	−	1.44067i
$817$	7.72539e9	+	1.33808e10i	0.495613	+	0.858428i
$818$	−6.17460e8	−	1.06947e9i	−0.0394432	−	0.0683177i
$819$	−8.04119e9	−	1.39277e10i	−0.511477	−	0.885905i
$820$	8.66758e9			0.548971
$821$	−4.32100e9	−	7.48420e9i	−0.272511	−	0.472002i	0.696993	−	0.717078i	$-0.254521\pi$
$821$	−4.32100e9	−	7.48420e9i	−0.272511	−	0.472002i	−0.969504	+	0.245075i	$0.921187\pi$
$822$	2.78460e10			1.74869
$823$	9.48222e9	−	1.64237e10i	0.592940	−	1.02700i	−0.400894	−	0.916124i	$-0.631300\pi$
$823$	9.48222e9	−	1.64237e10i	0.592940	−	1.02700i	0.993834	−	0.110878i	$-0.0353662\pi$
$824$	1.00776e10			0.627497
$825$	1.79109e10			1.11052
$826$	3.05070e8	−	5.28397e8i	0.0188352	−	0.0326235i
$827$	5.84391e8	+	1.01220e9i	0.0359281	+	0.0622293i	0.883430	−	0.468563i	$-0.155228\pi$
$827$	5.84391e8	+	1.01220e9i	0.0359281	+	0.0622293i	−0.847502	+	0.530792i	$0.821895\pi$
$828$	2.49642e9			0.152831
$829$	2.05006e8	−	3.55081e8i	0.0124976	−	0.0216465i	−0.859709	−	0.510784i	$-0.829355\pi$
$829$	2.05006e8	−	3.55081e8i	0.0124976	−	0.0216465i	0.872207	+	0.489138i	$0.162688\pi$
$830$	−2.12009e9	+	3.67211e9i	−0.128701	+	0.222916i
$831$	1.03447e10	−	1.79176e10i	0.625337	−	1.08312i
$832$	−2.37424e9	−	4.11231e9i	−0.142920	−	0.247545i
$833$	−3.53327e9	−	6.11980e9i	−0.211797	−	0.366843i
$834$	3.44505e10	−	5.96699e10i	2.05643	−	3.56184i
$835$	−1.97521e9	+	3.42116e9i	−0.117411	+	0.203363i
$836$	−3.72269e9	+	6.44789e9i	−0.220361	+	0.381677i
$837$	−3.93016e10			−2.31671
$838$	−2.08304e10	−	3.60792e10i	−1.22276	−	2.11789i
$839$	2.80618e9	−	4.86045e9i	0.164040	−	0.284125i	−0.772274	−	0.635290i	$-0.780881\pi$
$839$	2.80618e9	−	4.86045e9i	0.164040	−	0.284125i	0.936314	+	0.351164i	$0.114214\pi$
$840$	3.29390e9			0.191749
$841$	2.91201e9			0.168813
$842$	2.82515e9	−	4.89331e9i	0.163098	−	0.282495i
$843$	−4.81299e10			−2.76706
$844$	−2.79362e9	−	4.83868e9i	−0.159944	−	0.277031i
$845$	3.86079e9			0.220129
$846$	3.21016e10	+	5.56015e10i	1.82276	+	3.15712i
$847$	−2.29367e9	−	3.97275e9i	−0.129700	−	0.224646i
$848$	9.75780e9	+	1.69010e10i	0.549498	+	0.951759i
$849$	7.40250e9	−	1.28215e10i	0.415147	−	0.719055i
$850$	1.48204e10			0.827737
$851$	−1.55613e9	−	8.77097e8i	−0.0865551	−	0.0487859i
$852$	3.24978e10			1.80018
$853$	−1.38060e10	+	2.39127e10i	−0.761635	+	1.31919i	0.180373	+	0.983598i	$0.442270\pi$
$853$	−1.38060e10	+	2.39127e10i	−0.761635	+	1.31919i	−0.942007	+	0.335592i	$0.891064\pi$
$854$	1.23766e10	+	2.14369e10i	0.679985	+	1.17777i
$855$	6.64811e9	+	1.15149e10i	0.363762	+	0.630054i
$856$	−1.97242e9	−	3.41633e9i	−0.107483	−	0.186167i
$857$	−2.73930e10			−1.48665			−0.743323	−	0.668933i	$-0.766751\pi$
$857$	−2.73930e10			−1.48665			−0.743323	+	0.668933i	$0.766751\pi$
$858$	−1.20157e10	−	2.08119e10i	−0.649449	−	1.12488i
$859$	8.61819e9			0.463917			0.231958	−	0.972726i	$-0.425487\pi$
$859$	8.61819e9			0.463917			0.231958	+	0.972726i	$0.425487\pi$
$860$	−3.90136e9	+	6.75735e9i	−0.209156	+	0.362269i
$861$	−3.79185e10			−2.02461
$862$	−3.90441e9			−0.207625
$863$	−3.22128e8	+	5.57942e8i	−0.0170605	+	0.0295496i	−0.874430	−	0.485152i	$-0.838764\pi$
$863$	−3.22128e8	+	5.57942e8i	−0.0170605	+	0.0295496i	0.857369	+	0.514702i	$0.172097\pi$
$864$	−2.26744e10	−	3.92731e10i	−1.19602	−	2.07156i
$865$	3.95760e9			0.207910
$866$	1.91432e10	−	3.31570e10i	1.00162	−	1.73485i
$867$	−6.45021e9	+	1.11721e10i	−0.336130	+	0.582194i
$868$	5.61324e9	−	9.72242e9i	0.291336	−	0.504609i
$869$	3.82820e9	+	6.63063e9i	0.197891	+	0.342757i
$870$	−1.08799e10	−	1.88445e10i	−0.560152	−	0.970212i
$871$	−5.39903e9	+	9.35140e9i	−0.276855	+	0.479527i
$872$	−1.65496e9	+	2.86647e9i	−0.0845239	+	0.146400i
$873$	−3.72835e10	+	6.45769e10i	−1.89656	+	3.28494i
$874$	1.98561e9			0.100601
$875$	5.41489e9	+	9.37886e9i	0.273251	+	0.473284i
$876$	−2.20307e10	+	3.81584e10i	−1.10730	+	1.91790i
$877$	−2.44546e9			−0.122423			−0.0612113	−	0.998125i	$-0.519496\pi$
$877$	−2.44546e9			−0.122423			−0.0612113	+	0.998125i	$0.519496\pi$
$878$	3.29739e9			0.164414
$879$	−9.45609e9	+	1.63784e10i	−0.469624	+	0.813413i
$880$	8.50860e9			0.420890
$881$	−1.19258e10	−	2.06561e10i	−0.587586	−	1.01773i	−0.994548	−	0.104283i	$-0.966745\pi$
$881$	−1.19258e10	−	2.06561e10i	−0.587586	−	1.01773i	0.406962	−	0.913445i	$-0.366588\pi$
$882$	−3.04824e10			−1.49592
$883$	4.19363e9	+	7.26359e9i	0.204988	+	0.355049i	0.950129	−	0.311858i	$-0.100951\pi$
$883$	4.19363e9	+	7.26359e9i	0.204988	+	0.355049i	−0.745141	+	0.666907i	$0.767618\pi$
$884$	−4.18754e9	−	7.25304e9i	−0.203881	−	0.353132i
$885$	−3.42876e8	−	5.93879e8i	−0.0166279	−	0.0288003i
$886$	−2.77703e9	+	4.80996e9i	−0.134141	+	0.232339i
$887$	9.28268e9			0.446623			0.223311	−	0.974747i	$-0.428313\pi$
$887$	9.28268e9			0.446623			0.223311	+	0.974747i	$0.428313\pi$
$888$	1.36344e8	+	1.31805e10i	0.00653419	+	0.631665i
$889$	2.02908e10			0.968598
$890$	−7.15190e9	+	1.23875e10i	−0.340061	+	0.589002i
$891$	−1.12453e10	−	1.94774e10i	−0.532596	−	0.922483i
$892$	−3.15270e9	−	5.46063e9i	−0.148732	−	0.257612i
$893$	1.07540e10	+	1.86264e10i	0.505345	+	0.875284i
$894$	9.34594e9			0.437463
$895$	1.05413e9	+	1.82580e9i	0.0491488	+	0.0851282i
$896$	−1.00854e10			−0.468397
$897$	−1.34966e9	+	2.33767e9i	−0.0624381	+	0.108146i
$898$	−1.35529e10			−0.624547
$899$	2.77583e10			1.27419
$900$	1.34629e10	−	2.33183e10i	0.615585	−	1.06623i
$901$	7.92211e9	+	1.37215e10i	0.360831	+	0.624978i
$902$	−3.84648e10			−1.74518
$903$	1.70675e10	−	2.95617e10i	0.771369	−	1.33605i
$904$	−6.58607e8	+	1.14074e9i	−0.0296508	+	0.0513567i
$905$	−7.59214e9	+	1.31500e10i	−0.340482	+	0.589732i
$906$	6.60823e9	+	1.14458e10i	0.295214	+	0.511325i
$907$	−2.12361e10	−	3.67821e10i	−0.945040	−	1.63686i	−0.755671	−	0.654952i	$-0.772689\pi$
$907$	−2.12361e10	−	3.67821e10i	−0.945040	−	1.63686i	−0.189369	−	0.981906i	$-0.560644\pi$
$908$	−6.01638e9	+	1.04207e10i	−0.266707	+	0.461951i
$909$	−1.66411e10	+	2.88233e10i	−0.734868	+	1.27283i
$910$	3.22992e9	−	5.59438e9i	0.142084	−	0.246097i
$911$	−4.54471e9			−0.199155			−0.0995777	−	0.995030i	$-0.531749\pi$
$911$	−4.54471e9			−0.199155			−0.0995777	+	0.995030i	$0.531749\pi$
$912$	−1.86553e10	−	3.23119e10i	−0.814368	−	1.41053i
$913$	3.96266e9	−	6.86353e9i	0.172321	−	0.298469i
$914$	−1.06625e10			−0.461898
$915$	2.78208e10			1.20059
$916$	−3.79844e9	+	6.57910e9i	−0.163295	+	0.282834i
$917$	8.14822e9			0.348956
$918$	−2.38240e10	−	4.12645e10i	−1.01640	−	1.76046i
$919$	−1.51248e10			−0.642814			−0.321407	−	0.946941i	$-0.604156\pi$
$919$	−1.51248e10			−0.642814			−0.321407	+	0.946941i	$0.604156\pi$
$920$	−1.87657e8	−	3.25031e8i	−0.00794524	−	0.0137616i
$921$	−5.55972e9	−	9.62973e9i	−0.234501	−	0.406168i
$922$	2.53398e10	+	4.38897e10i	1.06474	+	1.84419i
$923$	−1.19273e10	+	2.06586e10i	−0.499269	+	0.864760i
$924$	1.64489e10			0.685937
$925$	−1.65847e10	+	9.80532e9i	−0.688989	+	0.407348i
$926$	−9.44635e9			−0.390954
$927$	4.49360e10	−	7.78315e10i	1.85275	−	3.20905i
$928$	1.60146e10	+	2.77382e10i	0.657808	+	1.13936i
$929$	−7.57346e9	−	1.31176e10i	−0.309913	−	0.536785i	0.668430	−	0.743775i	$-0.266967\pi$
$929$	−7.57346e9	−	1.31176e10i	−0.309913	−	0.536785i	−0.978343	+	0.206990i	$0.933633\pi$
$930$	−1.49791e10	−	2.59445e10i	−0.610653	−	1.05768i
$931$	−1.02115e10			−0.414732
$932$	1.46851e10	+	2.54354e10i	0.594185	+	1.02916i
$933$	−1.06637e10			−0.429857
$934$	6.62484e9	−	1.14746e10i	0.266049	−	0.460810i
$935$	6.90792e9			0.276380
$936$	1.35219e10			0.538978
$937$	5.45023e9	−	9.44008e9i	0.216434	−	0.374875i	−0.737281	−	0.675586i	$-0.763891\pi$
$937$	5.45023e9	−	9.44008e9i	0.216434	−	0.374875i	0.953715	+	0.300711i	$0.0972239\pi$
$938$	−8.77415e9	−	1.51973e10i	−0.347133	−	0.601251i
$939$	5.21970e10			2.05739
$940$	−5.43080e9	+	9.40642e9i	−0.213263	+	0.369383i
$941$	4.34586e9	−	7.52724e9i	0.170025	−	0.294491i	−0.768404	−	0.639965i	$-0.778949\pi$
$941$	4.34586e9	−	7.52724e9i	0.170025	−	0.294491i	0.938428	+	0.345474i	$0.112282\pi$
$942$	−1.03506e9	+	1.79278e9i	−0.0403448	+	0.0698793i
$943$	2.16026e9	+	3.74168e9i	0.0838909	+	0.145303i
$944$	6.53165e8	+	1.13132e9i	0.0252709	+	0.0437705i
$945$	7.73952e9	−	1.34052e10i	0.298334	−	0.516730i
$946$	1.73133e10	−	2.99876e10i	0.664908	−	1.15166i
$947$	−1.49783e10	+	2.59432e10i	−0.573110	+	0.992656i	0.423134	+	0.906067i	$0.360930\pi$
$947$	−1.49783e10	+	2.59432e10i	−0.573110	+	0.992656i	−0.996244	+	0.0865891i	$0.972403\pi$
$948$	1.69548e10			0.646345
$949$	−1.61713e10	−	2.80096e10i	−0.614206	−	1.06384i
$950$	1.07081e10	−	1.85470e10i	0.405210	−	0.701844i
$951$	1.58267e10			0.596705
$952$	−5.09430e9			−0.191362
$953$	5.99194e9	−	1.03784e10i	0.224255	−	0.388421i	−0.731841	−	0.681476i	$-0.761338\pi$
$953$	5.99194e9	−	1.03784e10i	0.224255	−	0.388421i	0.956096	+	0.293055i	$0.0946717\pi$
$954$	6.83459e10			2.54855
$955$	6.67328e9	+	1.15585e10i	0.247929	+	0.429426i
$956$	−2.20324e10			−0.815568
$957$	2.03355e10	+	3.52222e10i	0.750004	+	1.29905i
$958$	−4.47846e9	−	7.75692e9i	−0.164570	−	0.285043i
$959$	−6.99530e9	−	1.21162e10i	−0.256119	−	0.443611i
$960$	4.33663e9	−	7.51126e9i	0.158199	−	0.274008i
$961$	1.07042e10			0.389066
$962$	2.25196e10	+	1.26929e10i	0.815544	+	0.459673i
$963$	−3.51801e10			−1.26942
$964$	−6.51803e9	+	1.12896e10i	−0.234340	+	0.405889i
$965$	−3.53821e9	−	6.12836e9i	−0.126747	−	0.219532i
$966$	−2.19337e9	−	3.79903e9i	−0.0782875	−	0.135598i
$967$	−4.06175e9	−	7.03516e9i	−0.144451	−	0.250197i	0.784717	−	0.619854i	$-0.212808\pi$
$967$	−4.06175e9	−	7.03516e9i	−0.144451	−	0.250197i	−0.929168	+	0.369658i	$0.879475\pi$
$968$	3.85698e9			0.136673
$969$	−1.51458e10	−	2.62333e10i	−0.534759	−	0.926230i
$970$	−2.99514e10			−1.05370
$971$	−1.25673e10	+	2.17671e10i	−0.440528	+	0.763017i	−0.997729	−	0.0673612i	$-0.978542\pi$
$971$	−1.25673e10	+	2.17671e10i	−0.440528	+	0.763017i	0.557201	+	0.830378i	$0.311875\pi$
$972$	−8.85355e9			−0.309233
$973$	−3.46177e10			−1.20477
$974$	−3.28424e10	+	5.68847e10i	−1.13888	+	1.97260i
$975$	1.45570e10	+	2.52135e10i	0.502987	+	0.871198i
$976$	−5.29975e10			−1.82465
$977$	−1.89253e10	+	3.27795e10i	−0.649249	+	1.12453i	0.334054	+	0.942554i	$0.391583\pi$
$977$	−1.89253e10	+	3.27795e10i	−0.649249	+	1.12453i	−0.983303	+	0.181978i	$0.941750\pi$
$978$	−3.74359e10	+	6.48410e10i	−1.27968	+	2.21648i
$979$	1.33676e10	−	2.31534e10i	0.455317	−	0.788633i
$980$	−2.57844e9	−	4.46598e9i	−0.0875115	−	0.151574i
$981$	1.47589e10	+	2.55632e10i	0.499129	+	0.864517i
$982$	3.22834e9	−	5.59166e9i	0.108790	−	0.188430i
$983$	2.11404e10	−	3.66162e10i	0.709864	−	1.22952i	−0.255043	−	0.966930i	$-0.582090\pi$
$983$	2.11404e10	−	3.66162e10i	0.709864	−	1.22952i	0.964907	−	0.262591i	$-0.0845769\pi$
$984$	1.59407e10	−	2.76102e10i	0.533366	−	0.923817i
$985$	1.64711e10			0.549157
$986$	1.68267e10	+	2.91446e10i	0.559022	+	0.968254i
$987$	2.37584e10	−	4.11508e10i	0.786516	−	1.36229i
$988$	−1.21025e10			−0.399231
$989$	−3.88941e9			−0.127849
$990$	1.48991e10	−	2.58059e10i	0.488018	−	0.845272i
$991$	−4.91340e10			−1.60370			−0.801852	−	0.597523i	$-0.796152\pi$
$991$	−4.91340e10			−1.60370			−0.801852	+	0.597523i	$0.796152\pi$
$992$	2.20485e10	+	3.81891e10i	0.717114	+	1.24208i
$993$	1.05347e11			3.41428
$994$	−1.93834e10	−	3.35731e10i	−0.626005	−	1.08427i
$995$	−8.07351e8	−	1.39837e9i	−0.0259826	−	0.0450031i
$996$	−8.77518e9	−	1.51991e10i	−0.281416	−	0.487426i
$997$	−1.40142e10	+	2.42733e10i	−0.447853	+	0.775704i	−0.998246	−	0.0592014i	$-0.981145\pi$
$997$	−1.40142e10	+	2.42733e10i	−0.447853	+	0.775704i	0.550393	+	0.834906i	$0.314478\pi$
$998$	−1.57557e10			−0.501743
$999$	5.39613e10	+	3.04148e10i	1.71239	+	0.965173i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.8.c.a.10.6	✓	42
37.26	even	3	inner	37.8.c.a.26.6	yes	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.8.c.a.10.6	✓	42	1.1	even	1	trivial
37.8.c.a.26.6	yes	42	37.26	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:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	37.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.43537 + 12.8784i) q^{2} +(41.2618 + 71.4676i) q^{3} +(-46.5696 - 80.6609i) q^{4} +(62.4377 + 108.145i) q^{5} -1227.19 q^{6} +(308.286 + 533.967i) q^{7} -518.407 q^{8} +(-2311.58 + 4003.77i) q^{9} +O(q^{10})\)	\(q+(-7.43537 + 12.8784i) q^{2} +(41.2618 + 71.4676i) q^{3} +(-46.5696 - 80.6609i) q^{4} +(62.4377 + 108.145i) q^{5} -1227.19 q^{6} +(308.286 + 533.967i) q^{7} -518.407 q^{8} +(-2311.58 + 4003.77i) q^{9} -1856.99 q^{10} +3470.89 q^{11} +(3843.09 - 6656.43i) q^{12} +(2820.96 + 4886.05i) q^{13} -9168.89 q^{14} +(-5152.58 + 8924.54i) q^{15} +(9815.45 - 17000.9i) q^{16} +(7968.92 - 13802.6i) q^{17} +(-34374.9 - 59539.0i) q^{18} +(-11515.5 - 19945.5i) q^{19} +(5815.39 - 10072.6i) q^{20} +(-25440.9 + 44065.0i) q^{21} +(-25807.4 + 44699.7i) q^{22} +5797.58 q^{23} +(-21390.4 - 37049.3i) q^{24} +(31265.6 - 54153.6i) q^{25} -83899.7 q^{26} -201040. q^{27} +(28713.5 - 49733.3i) q^{28} +141993. q^{29} +(-76622.8 - 132715. i) q^{30} +195491. q^{31} +(112785. + 195350. i) q^{32} +(143215. + 248056. i) q^{33} +(118504. + 205255. i) q^{34} +(-38497.3 + 66679.3i) q^{35} +430597. q^{36} +(-268410. - 151287. i) q^{37} +342489. q^{38} +(-232796. + 403215. i) q^{39} +(-32368.1 - 56063.2i) q^{40} +(372614. + 645386. i) q^{41} +(-378325. - 655279. i) q^{42} -670867. q^{43} +(-161638. - 279965. i) q^{44} -577318. q^{45} +(-43107.2 + 74663.8i) q^{46} -933867. q^{47} +1.62001e6 q^{48} +(221691. - 383979. i) q^{49} +(464943. + 805304. i) q^{50} +1.31525e6 q^{51} +(262742. - 455083. i) q^{52} +(-497063. + 860938. i) q^{53} +(1.49481e6 - 2.58909e6i) q^{54} +(216714. + 375360. i) q^{55} +(-159818. - 276812. i) q^{56} +(950303. - 1.64597e6i) q^{57} +(-1.05577e6 + 1.82864e6i) q^{58} +(-33272.3 + 57629.3i) q^{59} +959814. q^{60} +(-1.34985e6 - 2.33800e6i) q^{61} +(-1.45355e6 + 2.51762e6i) q^{62} -2.85051e6 q^{63} -841642. q^{64} +(-352269. + 610147. i) q^{65} -4.25944e6 q^{66} +(956948. + 1.65748e6i) q^{67} -1.48444e6 q^{68} +(239219. + 414339. i) q^{69} +(-572484. - 991572. i) q^{70} +(2.11404e6 + 3.66163e6i) q^{71} +(1.19834e6 - 2.07558e6i) q^{72} -5.73256e6 q^{73} +(3.94407e6 - 2.33184e6i) q^{74} +5.16030e6 q^{75} +(-1.07255e6 + 1.85770e6i) q^{76} +(1.07003e6 + 1.85334e6i) q^{77} +(-3.46186e6 - 5.99611e6i) q^{78} +(1.10294e6 + 1.91035e6i) q^{79} +2.45142e6 q^{80} +(-3.23987e6 - 5.61163e6i) q^{81} -1.10821e7 q^{82} +(1.14168e6 - 1.97745e6i) q^{83} +4.73909e6 q^{84} +1.99024e6 q^{85} +(4.98815e6 - 8.63973e6i) q^{86} +(5.85887e6 + 1.01479e7i) q^{87} -1.79934e6 q^{88} +(3.85134e6 - 6.67072e6i) q^{89} +(4.29257e6 - 7.43496e6i) q^{90} +(-1.73933e6 + 3.01261e6i) q^{91} +(-269991. - 467638. i) q^{92} +(8.06633e6 + 1.39713e7i) q^{93} +(6.94365e6 - 1.20268e7i) q^{94} +(1.43800e6 - 2.49070e6i) q^{95} +(-9.30744e6 + 1.61210e7i) q^{96} +1.61290e7 q^{97} +(3.29671e6 + 5.71006e6i) q^{98} +(-8.02324e6 + 1.38967e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q - 16 q^{2} - 68 q^{3} - 1126 q^{4} - 337 q^{5} + 252 q^{6} - 158 q^{7} + 6264 q^{8} - 12773 q^{9}+O(q^{10}) \) 42 * q - 16 * q^2 - 68 * q^3 - 1126 * q^4 - 337 * q^5 + 252 * q^6 - 158 * q^7 + 6264 * q^8 - 12773 * q^9	\( 42 q - 16 q^{2} - 68 q^{3} - 1126 q^{4} - 337 q^{5} + 252 q^{6} - 158 q^{7} + 6264 q^{8} - 12773 q^{9} + 10028 q^{10} + 14876 q^{11} - 4836 q^{12} - 5922 q^{13} + 20176 q^{14} - 8460 q^{15} - 36726 q^{16} - 19095 q^{17} - 7338 q^{18} - 34334 q^{19} - 75668 q^{20} - 32764 q^{21} + 18526 q^{22} - 99896 q^{23} - 203760 q^{24} - 322660 q^{25} + 101516 q^{26} + 846616 q^{27} - 73490 q^{28} + 168186 q^{29} - 88790 q^{30} - 38052 q^{31} - 172292 q^{32} - 54536 q^{33} + 90724 q^{34} - 247046 q^{35} + 352004 q^{36} + 740185 q^{37} + 1994976 q^{38} - 591380 q^{39} - 38962 q^{40} - 292827 q^{41} - 1499386 q^{42} + 630980 q^{43} - 1727390 q^{44} - 994286 q^{45} + 576988 q^{46} + 3394668 q^{47} - 79840 q^{48} + 728851 q^{49} - 69656 q^{50} - 3970200 q^{51} - 2043140 q^{52} + 584438 q^{53} - 2160774 q^{54} + 2019874 q^{55} - 658986 q^{56} + 4295748 q^{57} - 5684872 q^{58} - 1773152 q^{59} + 20208544 q^{60} - 3596569 q^{61} - 1538738 q^{62} + 11795092 q^{63} - 9622852 q^{64} - 5027290 q^{65} - 17464952 q^{66} - 3249754 q^{67} + 5608668 q^{68} + 9599384 q^{69} - 5102080 q^{70} - 1162530 q^{71} - 4730172 q^{72} - 5266532 q^{73} + 4052290 q^{74} + 35543072 q^{75} - 13781226 q^{76} + 121180 q^{77} - 7012890 q^{78} - 13545718 q^{79} - 17840888 q^{80} - 16689077 q^{81} - 43173544 q^{82} + 7359048 q^{83} + 41186680 q^{84} + 21047382 q^{85} + 6732838 q^{86} + 7672800 q^{87} + 42023140 q^{88} + 2955725 q^{89} - 14596808 q^{90} - 19887752 q^{91} + 13352900 q^{92} + 9156784 q^{93} + 690474 q^{94} - 5667270 q^{95} + 29986904 q^{96} + 52065982 q^{97} - 53664462 q^{98} - 35534038 q^{99}+O(q^{100}) \) 42 * q - 16 * q^2 - 68 * q^3 - 1126 * q^4 - 337 * q^5 + 252 * q^6 - 158 * q^7 + 6264 * q^8 - 12773 * q^9 + 10028 * q^10 + 14876 * q^11 - 4836 * q^12 - 5922 * q^13 + 20176 * q^14 - 8460 * q^15 - 36726 * q^16 - 19095 * q^17 - 7338 * q^18 - 34334 * q^19 - 75668 * q^20 - 32764 * q^21 + 18526 * q^22 - 99896 * q^23 - 203760 * q^24 - 322660 * q^25 + 101516 * q^26 + 846616 * q^27 - 73490 * q^28 + 168186 * q^29 - 88790 * q^30 - 38052 * q^31 - 172292 * q^32 - 54536 * q^33 + 90724 * q^34 - 247046 * q^35 + 352004 * q^36 + 740185 * q^37 + 1994976 * q^38 - 591380 * q^39 - 38962 * q^40 - 292827 * q^41 - 1499386 * q^42 + 630980 * q^43 - 1727390 * q^44 - 994286 * q^45 + 576988 * q^46 + 3394668 * q^47 - 79840 * q^48 + 728851 * q^49 - 69656 * q^50 - 3970200 * q^51 - 2043140 * q^52 + 584438 * q^53 - 2160774 * q^54 + 2019874 * q^55 - 658986 * q^56 + 4295748 * q^57 - 5684872 * q^58 - 1773152 * q^59 + 20208544 * q^60 - 3596569 * q^61 - 1538738 * q^62 + 11795092 * q^63 - 9622852 * q^64 - 5027290 * q^65 - 17464952 * q^66 - 3249754 * q^67 + 5608668 * q^68 + 9599384 * q^69 - 5102080 * q^70 - 1162530 * q^71 - 4730172 * q^72 - 5266532 * q^73 + 4052290 * q^74 + 35543072 * q^75 - 13781226 * q^76 + 121180 * q^77 - 7012890 * q^78 - 13545718 * q^79 - 17840888 * q^80 - 16689077 * q^81 - 43173544 * q^82 + 7359048 * q^83 + 41186680 * q^84 + 21047382 * q^85 + 6732838 * q^86 + 7672800 * q^87 + 42023140 * q^88 + 2955725 * q^89 - 14596808 * q^90 - 19887752 * q^91 + 13352900 * q^92 + 9156784 * q^93 + 690474 * q^94 - 5667270 * q^95 + 29986904 * q^96 + 52065982 * q^97 - 53664462 * q^98 - 35534038 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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