LMFDB - Embedded newform 37.9.d.a.6.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,9,Mod(6,37)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("37.6");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	37.d (of order $4$, 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:	$15.0730085723$
Analytic rank:	$0$
Dimension:	$50$
Relative dimension:	$25$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			6.1
Character	$\chi$	$=$	37.6
Dual form			37.9.d.a.31.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-21.1416 + 21.1416i) q^{2} -117.640i q^{3} -637.931i q^{4} +(228.288 + 228.288i) q^{5} +(2487.09 + 2487.09i) q^{6} +1007.48 q^{7} +(8074.63 + 8074.63i) q^{8} -7278.14 q^{9} +O(q^{10})$	\(q+(-21.1416 + 21.1416i) q^{2} -117.640i q^{3} -637.931i q^{4} +(228.288 + 228.288i) q^{5} +(2487.09 + 2487.09i) q^{6} +1007.48 q^{7} +(8074.63 + 8074.63i) q^{8} -7278.14 q^{9} -9652.73 q^{10} -19912.6i q^{11} -75046.2 q^{12} +(19557.2 + 19557.2i) q^{13} +(-21299.6 + 21299.6i) q^{14} +(26855.8 - 26855.8i) q^{15} -178110. q^{16} +(-16374.2 - 16374.2i) q^{17} +(153871. - 153871. i) q^{18} +(138401. + 138401. i) q^{19} +(145632. - 145632. i) q^{20} -118519. i q^{21} +(420984. + 420984. i) q^{22} +(-356959. - 356959. i) q^{23} +(949898. - 949898. i) q^{24} -286394. i q^{25} -826940. q^{26} +84364.2i q^{27} -642701. i q^{28} +(-231078. + 231078. i) q^{29} +1.13555e6i q^{30} +(874183. - 874183. i) q^{31} +(1.69842e6 - 1.69842e6i) q^{32} -2.34252e6 q^{33} +692354. q^{34} +(229995. + 229995. i) q^{35} +4.64295e6i q^{36} +(-926672. + 1.62904e6i) q^{37} -5.85201e6 q^{38} +(2.30071e6 - 2.30071e6i) q^{39} +3.68668e6i q^{40} -4.74005e6i q^{41} +(2.50569e6 + 2.50569e6i) q^{42} +(-2.78296e6 - 2.78296e6i) q^{43} -1.27029e7 q^{44} +(-1.66151e6 - 1.66151e6i) q^{45} +1.50933e7 q^{46} +81765.7 q^{47} +2.09528e7i q^{48} -4.74979e6 q^{49} +(6.05482e6 + 6.05482e6i) q^{50} +(-1.92626e6 + 1.92626e6i) q^{51} +(1.24762e7 - 1.24762e7i) q^{52} -1.60221e6 q^{53} +(-1.78359e6 - 1.78359e6i) q^{54} +(4.54582e6 - 4.54582e6i) q^{55} +(8.13500e6 + 8.13500e6i) q^{56} +(1.62814e7 - 1.62814e7i) q^{57} -9.77071e6i q^{58} +(-8.49171e6 - 8.49171e6i) q^{59} +(-1.71321e7 - 1.71321e7i) q^{60} +(-5.93111e6 + 5.93111e6i) q^{61} +3.69632e7i q^{62} -7.33256e6 q^{63} +2.62183e7i q^{64} +8.92936e6i q^{65} +(4.95246e7 - 4.95246e7i) q^{66} +1.12538e7i q^{67} +(-1.04456e7 + 1.04456e7i) q^{68} +(-4.19926e7 + 4.19926e7i) q^{69} -9.72490e6 q^{70} -1.60515e7 q^{71} +(-5.87683e7 - 5.87683e7i) q^{72} +1.74048e7i q^{73} +(-1.48491e7 - 5.40317e7i) q^{74} -3.36914e7 q^{75} +(8.82901e7 - 8.82901e7i) q^{76} -2.00615e7i q^{77} +9.72812e7i q^{78} +(1.75230e7 + 1.75230e7i) q^{79} +(-4.06604e7 - 4.06604e7i) q^{80} -3.78273e7 q^{81} +(1.00212e8 + 1.00212e8i) q^{82} +4.77509e7 q^{83} -7.56073e7 q^{84} -7.47609e6i q^{85} +1.17672e8 q^{86} +(2.71840e7 + 2.71840e7i) q^{87} +(1.60787e8 - 1.60787e8i) q^{88} +(7.10666e7 - 7.10666e7i) q^{89} +7.02540e7 q^{90} +(1.97034e7 + 1.97034e7i) q^{91} +(-2.27715e8 + 2.27715e8i) q^{92} +(-1.02839e8 - 1.02839e8i) q^{93} +(-1.72865e6 + 1.72865e6i) q^{94} +6.31904e7i q^{95} +(-1.99802e8 - 1.99802e8i) q^{96} +(-6.63089e7 - 6.63089e7i) q^{97} +(1.00418e8 - 1.00418e8i) q^{98} +1.44927e8i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q + 4 q^{2} + 124 q^{5} + 510 q^{6} - 4 q^{7} - 5256 q^{8} - 93534 q^{9}+O(q^{10}) $ 50 * q + 4 * q^2 + 124 * q^5 + 510 * q^6 - 4 * q^7 - 5256 * q^8 - 93534 * q^9	\( 50 q + 4 q^{2} + 124 q^{5} + 510 q^{6} - 4 q^{7} - 5256 q^{8} - 93534 q^{9} - 10756 q^{10} - 45440 q^{12} + 63592 q^{13} - 80206 q^{14} - 124346 q^{15} - 639128 q^{16} - 178796 q^{17} - 45882 q^{18} + 264774 q^{19} + 469204 q^{20} + 714574 q^{22} - 654272 q^{23} - 1573644 q^{24} + 1841660 q^{26} - 1683686 q^{29} + 1766336 q^{31} - 4332632 q^{32} - 1438888 q^{33} - 5838452 q^{34} - 650482 q^{35} - 2870078 q^{37} - 2281528 q^{38} + 11036546 q^{39} - 7453902 q^{42} + 5097830 q^{43} - 14992464 q^{44} - 15078446 q^{45} + 28776464 q^{46} + 13992320 q^{47} + 4370314 q^{49} + 7603288 q^{50} + 19417938 q^{51} + 54318452 q^{52} + 28075952 q^{53} - 19197122 q^{54} - 6104306 q^{55} + 47803128 q^{56} + 17462426 q^{57} - 677072 q^{59} + 24953316 q^{60} + 4206386 q^{61} - 18098032 q^{63} - 56061730 q^{66} - 52579760 q^{68} + 88118984 q^{69} - 295493636 q^{70} - 37172476 q^{71} - 74582504 q^{72} - 224754524 q^{74} - 144364996 q^{75} + 189294548 q^{76} + 271163438 q^{79} - 312998084 q^{80} + 41535626 q^{81} - 177494710 q^{82} - 74250268 q^{83} - 82088924 q^{84} + 112964036 q^{86} - 142771908 q^{87} + 224951860 q^{88} + 84928780 q^{89} + 716592116 q^{90} - 40969098 q^{91} - 701292428 q^{92} - 83761576 q^{93} + 553881406 q^{94} - 7259376 q^{96} + 467792674 q^{97} + 538649310 q^{98}+O(q^{100}) \) 50 * q + 4 * q^2 + 124 * q^5 + 510 * q^6 - 4 * q^7 - 5256 * q^8 - 93534 * q^9 - 10756 * q^10 - 45440 * q^12 + 63592 * q^13 - 80206 * q^14 - 124346 * q^15 - 639128 * q^16 - 178796 * q^17 - 45882 * q^18 + 264774 * q^19 + 469204 * q^20 + 714574 * q^22 - 654272 * q^23 - 1573644 * q^24 + 1841660 * q^26 - 1683686 * q^29 + 1766336 * q^31 - 4332632 * q^32 - 1438888 * q^33 - 5838452 * q^34 - 650482 * q^35 - 2870078 * q^37 - 2281528 * q^38 + 11036546 * q^39 - 7453902 * q^42 + 5097830 * q^43 - 14992464 * q^44 - 15078446 * q^45 + 28776464 * q^46 + 13992320 * q^47 + 4370314 * q^49 + 7603288 * q^50 + 19417938 * q^51 + 54318452 * q^52 + 28075952 * q^53 - 19197122 * q^54 - 6104306 * q^55 + 47803128 * q^56 + 17462426 * q^57 - 677072 * q^59 + 24953316 * q^60 + 4206386 * q^61 - 18098032 * q^63 - 56061730 * q^66 - 52579760 * q^68 + 88118984 * q^69 - 295493636 * q^70 - 37172476 * q^71 - 74582504 * q^72 - 224754524 * q^74 - 144364996 * q^75 + 189294548 * q^76 + 271163438 * q^79 - 312998084 * q^80 + 41535626 * q^81 - 177494710 * q^82 - 74250268 * q^83 - 82088924 * q^84 + 112964036 * q^86 - 142771908 * q^87 + 224951860 * q^88 + 84928780 * q^89 + 716592116 * q^90 - 40969098 * q^91 - 701292428 * q^92 - 83761576 * q^93 + 553881406 * q^94 - 7259376 * q^96 + 467792674 * q^97 + 538649310 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−21.1416	+	21.1416i	−1.32135	+	1.32135i	−0.408662	+	0.912686i	$0.634004\pi$
$2$	−21.1416	+	21.1416i	−1.32135	+	1.32135i	−0.912686	+	0.408662i	$0.865996\pi$
$3$		−	117.640i		−	1.45234i	−0.687513	−	0.726172i	$-0.741298\pi$
$3$		−	117.640i		−	1.45234i	0.687513	−	0.726172i	$-0.258702\pi$
$4$		−	637.931i		−	2.49192i
$5$	228.288	+	228.288i	0.365261	+	0.365261i	0.865745	−	0.500485i	$-0.166845\pi$
$5$	228.288	+	228.288i	0.365261	+	0.365261i	−0.500485	+	0.865745i	$0.666845\pi$
$6$	2487.09	+	2487.09i	1.91905	+	1.91905i
$7$	1007.48			0.419607			0.209804	−	0.977744i	$-0.432718\pi$
$7$	1007.48			0.419607			0.209804	+	0.977744i	$0.432718\pi$
$8$	8074.63	+	8074.63i	1.97134	+	1.97134i
$9$	−7278.14			−1.10930
$10$	−9652.73			−0.965273
$11$		−	19912.6i		−	1.36006i	−0.733184	−	0.680030i	$-0.761967\pi$
$11$		−	19912.6i		−	1.36006i	0.733184	−	0.680030i	$-0.238033\pi$
$12$	−75046.2			−3.61912
$13$	19557.2	+	19557.2i	0.684753	+	0.684753i	0.961067	−	0.276315i	$-0.0891132\pi$
$13$	19557.2	+	19557.2i	0.684753	+	0.684753i	−0.276315	+	0.961067i	$0.589113\pi$
$14$	−21299.6	+	21299.6i	−0.554447	+	0.554447i
$15$	26855.8	−	26855.8i	0.530485	−	0.530485i
$16$	−178110.			−2.71774
$17$	−16374.2	−	16374.2i	−0.196049	−	0.196049i	0.602255	−	0.798304i	$-0.294269\pi$
$17$	−16374.2	−	16374.2i	−0.196049	−	0.196049i	−0.798304	+	0.602255i	$0.794269\pi$
$18$	153871.	−	153871.i	1.46578	−	1.46578i
$19$	138401.	+	138401.i	1.06200	+	1.06200i	0.997947	+	0.0640509i	$0.0204020\pi$
$19$	138401.	+	138401.i	1.06200	+	1.06200i	0.0640509	+	0.997947i	$0.479598\pi$
$20$	145632.	−	145632.i	0.910201	−	0.910201i
$21$		−	118519.i		−	0.609414i
$22$	420984.	+	420984.i	1.79711	+	1.79711i
$23$	−356959.	−	356959.i	−1.27558	−	1.27558i	−0.943117	−	0.332461i	$-0.892121\pi$
$23$	−356959.	−	356959.i	−1.27558	−	1.27558i	−0.332461	−	0.943117i	$-0.607879\pi$
$24$	949898.	−	949898.i	2.86307	−	2.86307i
$25$		−	286394.i		−	0.733169i
$26$	−826940.			−1.80959
$27$			84364.2i			0.158746i
$28$		−	642701.i		−	1.04563i
$29$	−231078.	+	231078.i	−0.326713	+	0.326713i	−0.851335	−	0.524622i	$-0.824207\pi$
$29$	−231078.	+	231078.i	−0.326713	+	0.326713i	0.524622	+	0.851335i	$0.324207\pi$
$30$			1.13555e6i			1.40191i
$31$	874183.	−	874183.i	0.946576	−	0.946576i	−0.0520678	−	0.998644i	$-0.516581\pi$
$31$	874183.	−	874183.i	0.946576	−	0.946576i	0.998644	+	0.0520678i	$0.0165812\pi$
$32$	1.69842e6	−	1.69842e6i	1.61974	−	1.61974i
$33$	−2.34252e6			−1.97528
$34$	692354.			0.518099
$35$	229995.	+	229995.i	0.153266	+	0.153266i
$36$			4.64295e6i			2.76429i
$37$	−926672.	+	1.62904e6i	−0.494446	+	0.869208i
$37$	−926672.	+	1.62904e6i	−0.494446	+	0.869208i
$38$	−5.85201e6			−2.80654
$39$	2.30071e6	−	2.30071e6i	0.994497	−	0.994497i
$40$			3.68668e6i			1.44011i
$41$		−	4.74005e6i		−	1.67744i	−0.544561	−	0.838721i	$-0.683304\pi$
$41$		−	4.74005e6i		−	1.67744i	0.544561	−	0.838721i	$-0.316696\pi$
$42$	2.50569e6	+	2.50569e6i	0.805248	+	0.805248i
$43$	−2.78296e6	−	2.78296e6i	−0.814015	−	0.814015i	0.171218	−	0.985233i	$-0.445230\pi$
$43$	−2.78296e6	−	2.78296e6i	−0.814015	−	0.814015i	−0.985233	+	0.171218i	$0.945230\pi$
$44$	−1.27029e7			−3.38916
$45$	−1.66151e6	−	1.66151e6i	−0.405185	−	0.405185i
$46$	1.50933e7			3.37096
$47$	81765.7			0.0167564			0.00837818	−	0.999965i	$-0.497333\pi$
$47$	81765.7			0.0167564			0.00837818	+	0.999965i	$0.497333\pi$
$48$			2.09528e7i			3.94710i
$49$	−4.74979e6			−0.823930
$50$	6.05482e6	+	6.05482e6i	0.968771	+	0.968771i
$51$	−1.92626e6	+	1.92626e6i	−0.284731	+	0.284731i
$52$	1.24762e7	−	1.24762e7i	1.70635	−	1.70635i
$53$	−1.60221e6			−0.203055			−0.101528	−	0.994833i	$-0.532373\pi$
$53$	−1.60221e6			−0.203055			−0.101528	+	0.994833i	$0.532373\pi$
$54$	−1.78359e6	−	1.78359e6i	−0.209759	−	0.209759i
$55$	4.54582e6	−	4.54582e6i	0.496777	−	0.496777i
$56$	8.13500e6	+	8.13500e6i	0.827190	+	0.827190i
$57$	1.62814e7	−	1.62814e7i	1.54239	−	1.54239i
$58$		−	9.77071e6i		−	0.863404i
$59$	−8.49171e6	−	8.49171e6i	−0.700789	−	0.700789i	0.263791	−	0.964580i	$-0.415027\pi$
$59$	−8.49171e6	−	8.49171e6i	−0.700789	−	0.700789i	−0.964580	+	0.263791i	$0.915027\pi$
$60$	−1.71321e7	−	1.71321e7i	−1.32192	−	1.32192i
$61$	−5.93111e6	+	5.93111e6i	−0.428367	+	0.428367i	−0.888072	−	0.459704i	$-0.847955\pi$
$61$	−5.93111e6	+	5.93111e6i	−0.428367	+	0.428367i	0.459704	+	0.888072i	$0.347955\pi$
$62$			3.69632e7i			2.50151i
$63$	−7.33256e6			−0.465472
$64$			2.62183e7i			1.56273i
$65$			8.92936e6i			0.500227i
$66$	4.95246e7	−	4.95246e7i	2.61003	−	2.61003i
$67$			1.12538e7i			0.558471i	0.960223	+	0.279236i	$0.0900810\pi$
$67$			1.12538e7i			0.558471i	−0.960223	+	0.279236i	$0.909919\pi$
$68$	−1.04456e7	+	1.04456e7i	−0.488540	+	0.488540i
$69$	−4.19926e7	+	4.19926e7i	−1.85258	+	1.85258i
$70$	−9.72490e6			−0.405036
$71$	−1.60515e7			−0.631657			−0.315828	−	0.948816i	$-0.602282\pi$
$71$	−1.60515e7			−0.631657			−0.315828	+	0.948816i	$0.602282\pi$
$72$	−5.87683e7	−	5.87683e7i	−2.18682	−	2.18682i
$73$			1.74048e7i			0.612884i	0.951889	+	0.306442i	$0.0991385\pi$
$73$			1.74048e7i			0.612884i	−0.951889	+	0.306442i	$0.900861\pi$
$74$	−1.48491e7	−	5.40317e7i	−0.495191	−	1.80186i
$75$	−3.36914e7			−1.06481
$76$	8.82901e7	−	8.82901e7i	2.64641	−	2.64641i
$77$		−	2.00615e7i		−	0.570691i
$78$			9.72812e7i			2.62815i
$79$	1.75230e7	+	1.75230e7i	0.449883	+	0.449883i	0.895315	−	0.445433i	$-0.146950\pi$
$79$	1.75230e7	+	1.75230e7i	0.449883	+	0.449883i	−0.445433	+	0.895315i	$0.646950\pi$
$80$	−4.06604e7	−	4.06604e7i	−0.992685	−	0.992685i
$81$	−3.78273e7			−0.878749
$82$	1.00212e8	+	1.00212e8i	2.21649	+	2.21649i
$83$	4.77509e7			1.00617			0.503083	−	0.864238i	$-0.332199\pi$
$83$	4.77509e7			1.00617			0.503083	+	0.864238i	$0.332199\pi$
$84$	−7.56073e7			−1.51861
$85$		−	7.47609e6i		−	0.143218i
$86$	1.17672e8			2.15119
$87$	2.71840e7	+	2.71840e7i	0.474500	+	0.474500i
$88$	1.60787e8	−	1.60787e8i	2.68115	−	2.68115i
$89$	7.10666e7	−	7.10666e7i	1.13268	−	1.13268i	0.142944	−	0.989731i	$-0.454343\pi$
$89$	7.10666e7	−	7.10666e7i	1.13268	−	1.13268i	0.989731	−	0.142944i	$-0.0456570\pi$
$90$	7.02540e7			1.07078
$91$	1.97034e7	+	1.97034e7i	0.287327	+	0.287327i
$92$	−2.27715e8	+	2.27715e8i	−3.17864	+	3.17864i
$93$	−1.02839e8	−	1.02839e8i	−1.37475	−	1.37475i
$94$	−1.72865e6	+	1.72865e6i	−0.0221410	+	0.0221410i
$95$			6.31904e7i			0.775812i
$96$	−1.99802e8	−	1.99802e8i	−2.35242	−	2.35242i
$97$	−6.63089e7	−	6.63089e7i	−0.749005	−	0.749005i	0.225287	−	0.974292i	$-0.427668\pi$
$97$	−6.63089e7	−	6.63089e7i	−0.749005	−	0.749005i	−0.974292	+	0.225287i	$0.927668\pi$
$98$	1.00418e8	−	1.00418e8i	1.08870	−	1.08870i
$99$			1.44927e8i			1.50872i
$100$	−1.82700e8			−1.82700
$101$		−	1.16327e7i		−	0.111788i	−0.998437	−	0.0558941i	$-0.982199\pi$
$101$		−	1.16327e7i		−	0.111788i	0.998437	−	0.0558941i	$-0.0178009\pi$
$102$		−	8.14485e7i		−	0.752458i
$103$	9.63630e7	−	9.63630e7i	0.856173	−	0.856173i	−0.134712	−	0.990885i	$-0.543011\pi$
$103$	9.63630e7	−	9.63630e7i	0.856173	−	0.856173i	0.990885	+	0.134712i	$0.0430108\pi$
$104$			3.15835e8i			2.69977i
$105$	2.70566e7	−	2.70566e7i	0.222595	−	0.222595i
$106$	3.38731e7	−	3.38731e7i	0.268307	−	0.268307i
$107$	1.17063e8			0.893065			0.446533	−	0.894767i	$-0.352659\pi$
$107$	1.17063e8			0.893065			0.446533	+	0.894767i	$0.352659\pi$
$108$	5.38186e7			0.395583
$109$	4.16601e7	+	4.16601e7i	0.295131	+	0.295131i	0.839103	−	0.543972i	$-0.183080\pi$
$109$	4.16601e7	+	4.16601e7i	0.295131	+	0.295131i	−0.543972	+	0.839103i	$0.683080\pi$
$110$			1.92211e8i			1.31283i
$111$	1.91640e8	+	1.09014e8i	1.26239	+	0.718106i
$112$	−1.79442e8			−1.14038
$113$	−2.16641e8	+	2.16641e8i	−1.32870	+	1.32870i	−0.422197	+	0.906504i	$0.638741\pi$
$113$	−2.16641e8	+	2.16641e8i	−1.32870	+	1.32870i	−0.906504	+	0.422197i	$0.861259\pi$
$114$			6.88430e8i			4.07606i
$115$		−	1.62979e8i		−	0.931838i
$116$	1.47412e8	+	1.47412e8i	0.814143	+	0.814143i
$117$	−1.42340e8	−	1.42340e8i	−0.759599	−	0.759599i
$118$	3.59056e8			1.85197
$119$	−1.64967e7	−	1.64967e7i	−0.0822638	−	0.0822638i
$120$	4.33701e8			2.09154
$121$	−1.82155e8			−0.849765
$122$		−	2.50786e8i		−	1.13204i
$123$	−5.57619e8			−2.43622
$124$	−5.57668e8	−	5.57668e8i	−2.35879	−	2.35879i
$125$	1.54555e8	−	1.54555e8i	0.633059	−	0.633059i
$126$	1.55022e8	−	1.55022e8i	0.615050	−	0.615050i
$127$	1.26145e8			0.484902			0.242451	−	0.970164i	$-0.422049\pi$
$127$	1.26145e8			0.484902			0.242451	+	0.970164i	$0.422049\pi$
$128$	−1.19501e8	−	1.19501e8i	−0.445176	−	0.445176i
$129$	−3.27387e8	+	3.27387e8i	−1.18223	+	1.18223i
$130$	−1.88781e8	−	1.88781e8i	−0.660974	−	0.660974i
$131$	−1.11299e7	+	1.11299e7i	−0.0377926	+	0.0377926i	−0.725751	−	0.687958i	$-0.758507\pi$
$131$	−1.11299e7	+	1.11299e7i	−0.0377926	+	0.0377926i	0.687958	+	0.725751i	$0.258507\pi$
$132$			1.49437e9i			4.92223i
$133$	1.39435e8	+	1.39435e8i	0.445622	+	0.445622i
$134$	−2.37923e8	−	2.37923e8i	−0.737935	−	0.737935i
$135$	−1.92593e7	+	1.92593e7i	−0.0579838	+	0.0579838i
$136$		−	2.64432e8i		−	0.772962i
$137$	−1.19120e8			−0.338144			−0.169072	−	0.985604i	$-0.554077\pi$
$137$	−1.19120e8			−0.338144			−0.169072	+	0.985604i	$0.554077\pi$
$138$		−	1.77558e9i		−	4.89580i
$139$		−	7.08492e7i		−	0.189791i	−0.995487	−	0.0948955i	$-0.969748\pi$
$139$		−	7.08492e7i		−	0.189791i	0.995487	−	0.0948955i	$-0.0302517\pi$
$140$	1.46721e8	−	1.46721e8i	0.381927	−	0.381927i
$141$		−	9.61890e6i		−	0.0243360i
$142$	3.39353e8	−	3.39353e8i	0.834638	−	0.834638i
$143$	3.89436e8	−	3.89436e8i	0.931305	−	0.931305i
$144$	1.29631e9			3.01480
$145$	−1.05505e8			−0.238671
$146$	−3.67965e8	−	3.67965e8i	−0.809833	−	0.809833i
$147$			5.58765e8i			1.19663i
$148$	1.03921e9	+	5.91153e8i	2.16600	+	1.23212i
$149$	−4.68218e8			−0.949955			−0.474977	−	0.879998i	$-0.657544\pi$
$149$	−4.68218e8			−0.949955			−0.474977	+	0.879998i	$0.657544\pi$
$150$	7.12288e8	−	7.12288e8i	1.40699	−	1.40699i
$151$		−	8.28605e8i		−	1.59382i	−0.604097	−	0.796911i	$-0.706466\pi$
$151$		−	8.28605e8i		−	1.59382i	0.604097	−	0.796911i	$-0.293534\pi$
$152$			2.23507e9i			4.18713i
$153$	1.19174e8	+	1.19174e8i	0.217478	+	0.217478i
$154$	4.24132e8	+	4.24132e8i	0.754081	+	0.754081i
$155$	3.99131e8			0.691494
$156$	−1.46769e9	−	1.46769e9i	−2.47821	−	2.47821i
$157$	1.11410e9			1.83369			0.916845	−	0.399244i	$-0.130727\pi$
$157$	1.11410e9			1.83369			0.916845	+	0.399244i	$0.130727\pi$
$158$	−7.40926e8			−1.18890
$159$			1.88483e8i			0.294906i
$160$	7.75458e8			1.18325
$161$	−3.59628e8	−	3.59628e8i	−0.535242	−	0.535242i
$162$	7.99728e8	−	7.99728e8i	1.16113	−	1.16113i
$163$	−6.83340e7	+	6.83340e7i	−0.0968025	+	0.0968025i	−0.753850	−	0.657047i	$-0.771805\pi$
$163$	−6.83340e7	+	6.83340e7i	−0.0968025	+	0.0968025i	0.657047	+	0.753850i	$0.271805\pi$
$164$	−3.02383e9			−4.18005
$165$	−5.34770e8	−	5.34770e8i	−0.721491	−	0.721491i
$166$	−1.00953e9	+	1.00953e9i	−1.32949	+	1.32949i
$167$	1.09562e9	+	1.09562e9i	1.40862	+	1.40862i	0.767139	+	0.641480i	$0.221679\pi$
$167$	1.09562e9	+	1.09562e9i	1.40862	+	1.40862i	0.641480	+	0.767139i	$0.278321\pi$
$168$	9.57000e8	−	9.57000e8i	1.20136	−	1.20136i
$169$		−	5.07609e7i		−	0.0622275i
$170$	1.58056e8	+	1.58056e8i	0.189241	+	0.189241i
$171$	−1.00730e9	−	1.00730e9i	−1.17808	−	1.17808i
$172$	−1.77534e9	+	1.77534e9i	−2.02846	+	2.02846i
$173$		−	1.55053e9i		−	1.73100i	−0.500910	−	0.865499i	$-0.667001\pi$
$173$		−	1.55053e9i		−	1.73100i	0.500910	−	0.865499i	$-0.332999\pi$
$174$	−1.14942e9			−1.25396
$175$		−	2.88535e8i		−	0.307643i
$176$			3.54664e9i			3.69629i
$177$	−9.98964e8	+	9.98964e8i	−1.01779	+	1.01779i
$178$			3.00492e9i			2.99332i
$179$	−1.84828e8	+	1.84828e8i	−0.180034	+	0.180034i	−0.791371	−	0.611337i	$-0.790632\pi$
$179$	−1.84828e8	+	1.84828e8i	−0.180034	+	0.180034i	0.611337	+	0.791371i	$0.290632\pi$
$180$	−1.05993e9	+	1.05993e9i	−1.00969	+	1.00969i
$181$	1.11275e9			1.03677			0.518384	−	0.855148i	$-0.326534\pi$
$181$	1.11275e9			1.03677			0.518384	+	0.855148i	$0.326534\pi$
$182$	−8.33123e8			−0.759318
$183$	6.97735e8	+	6.97735e8i	0.622137	+	0.622137i
$184$		−	5.76462e9i		−	5.02921i
$185$	−5.83438e8	+	1.60341e8i	−0.498090	+	0.136886i
$186$	4.34834e9			3.63306
$187$	−3.26055e8	+	3.26055e8i	−0.266639	+	0.266639i
$188$		−	5.21609e7i		−	0.0417555i
$189$			8.49950e7i			0.0666110i
$190$	−1.33594e9	−	1.33594e9i	−1.02512	−	1.02512i
$191$	−8.55766e8	−	8.55766e8i	−0.643015	−	0.643015i	0.308280	−	0.951296i	$-0.400247\pi$
$191$	−8.55766e8	−	8.55766e8i	−0.643015	−	0.643015i	−0.951296	+	0.308280i	$0.900247\pi$
$192$	3.08432e9			2.26963
$193$	8.47846e8	+	8.47846e8i	0.611065	+	0.611065i	0.943224	−	0.332158i	$-0.107777\pi$
$193$	8.47846e8	+	8.47846e8i	0.611065	+	0.611065i	−0.332158	+	0.943224i	$0.607777\pi$
$194$	2.80375e9			1.97939
$195$	1.05045e9			0.726502
$196$			3.03004e9i			2.05317i
$197$	−1.01911e9			−0.676637			−0.338318	−	0.941032i	$-0.609858\pi$
$197$	−1.01911e9			−0.676637			−0.338318	+	0.941032i	$0.609858\pi$
$198$	−3.06398e9	−	3.06398e9i	−1.99354	−	1.99354i
$199$	−7.11085e8	+	7.11085e8i	−0.453429	+	0.453429i	−0.896491	−	0.443062i	$-0.853892\pi$
$199$	−7.11085e8	+	7.11085e8i	−0.453429	+	0.453429i	0.443062	+	0.896491i	$0.353892\pi$
$200$	2.31253e9	−	2.31253e9i	1.44533	−	1.44533i
$201$	1.32390e9			0.811092
$202$	2.45934e8	+	2.45934e8i	0.147711	+	0.147711i
$203$	−2.32806e8	+	2.32806e8i	−0.137091	+	0.137091i
$204$	1.22882e9	+	1.22882e9i	0.709528	+	0.709528i
$205$	1.08210e9	−	1.08210e9i	0.612704	−	0.612704i
$206$			4.07453e9i			2.26260i
$207$	2.59800e9	+	2.59800e9i	1.41500	+	1.41500i
$208$	−3.48334e9	−	3.48334e9i	−1.86098	−	1.86098i
$209$	2.75592e9	−	2.75592e9i	1.44438	−	1.44438i
$210$			1.14404e9i			0.588251i
$211$	−1.18323e9			−0.596953			−0.298476	−	0.954417i	$-0.596478\pi$
$211$	−1.18323e9			−0.596953			−0.298476	+	0.954417i	$0.596478\pi$
$212$			1.02210e9i			0.505998i
$213$			1.88829e9i			0.917383i
$214$	−2.47489e9	+	2.47489e9i	−1.18005	+	1.18005i
$215$		−	1.27063e9i		−	0.594656i
$216$	−6.81210e8	+	6.81210e8i	−0.312943	+	0.312943i
$217$	8.80719e8	−	8.80719e8i	0.397190	−	0.397190i
$218$	−1.76152e9			−0.779941
$219$	2.04750e9			0.890118
$220$	−2.89992e9	−	2.89992e9i	−1.23793	−	1.23793i
$221$		−	6.40470e8i		−	0.268491i
$222$	−6.35628e9	+	1.74684e9i	−2.61692	+	0.719187i
$223$	6.58610e8			0.266323			0.133161	−	0.991094i	$-0.457487\pi$
$223$	6.58610e8			0.266323			0.133161	+	0.991094i	$0.457487\pi$
$224$	1.71112e9	−	1.71112e9i	0.679654	−	0.679654i
$225$			2.08442e9i			0.813307i
$226$		−	9.16027e9i		−	3.51135i
$227$	2.02484e9	+	2.02484e9i	0.762583	+	0.762583i	0.976789	−	0.214205i	$-0.0687162\pi$
$227$	2.02484e9	+	2.02484e9i	0.762583	+	0.762583i	−0.214205	+	0.976789i	$0.568716\pi$
$228$	−1.03864e10	−	1.03864e10i	−3.84350	−	3.84350i
$229$	1.30973e9			0.476257			0.238128	−	0.971234i	$-0.423466\pi$
$229$	1.30973e9			0.476257			0.238128	+	0.971234i	$0.423466\pi$
$230$	3.44563e9	+	3.44563e9i	1.23128	+	1.23128i
$231$	−2.36004e9			−0.828840
$232$	−3.73174e9			−1.28813
$233$			2.88731e9i			0.979647i	0.871822	+	0.489824i	$0.162939\pi$
$233$			2.88731e9i			0.979647i	−0.871822	+	0.489824i	$0.837061\pi$
$234$	6.01859e9			2.00739
$235$	1.86661e7	+	1.86661e7i	0.00612044	+	0.00612044i
$236$	−5.41713e9	+	5.41713e9i	−1.74631	+	1.74631i
$237$	2.06140e9	−	2.06140e9i	0.653384	−	0.653384i
$238$	6.97531e8			0.217398
$239$	−1.36406e9	−	1.36406e9i	−0.418063	−	0.418063i	0.466473	−	0.884536i	$-0.345525\pi$
$239$	−1.36406e9	−	1.36406e9i	−0.418063	−	0.418063i	−0.884536	+	0.466473i	$0.845525\pi$
$240$	−4.78328e9	+	4.78328e9i	−1.44172	+	1.44172i
$241$	5.39696e7	+	5.39696e7i	0.0159986	+	0.0159986i	0.715061	−	0.699062i	$-0.246399\pi$
$241$	5.39696e7	+	5.39696e7i	0.0159986	+	0.0159986i	−0.699062	+	0.715061i	$0.746399\pi$
$242$	3.85103e9	−	3.85103e9i	1.12283	−	1.12283i
$243$			5.00351e9i			1.43499i
$244$	3.78364e9	+	3.78364e9i	1.06746	+	1.06746i
$245$	−1.08432e9	−	1.08432e9i	−0.300949	−	0.300949i
$246$	1.17889e10	−	1.17889e10i	3.21910	−	3.21910i
$247$			5.41346e9i			1.45441i
$248$	1.41174e10			3.73205
$249$		−	5.61741e9i		−	1.46130i
$250$			6.53509e9i			1.67298i
$251$	−3.65099e8	+	3.65099e8i	−0.0919846	+	0.0919846i	−0.751602	−	0.659617i	$-0.770718\pi$
$251$	−3.65099e8	+	3.65099e8i	−0.0919846	+	0.0919846i	0.659617	+	0.751602i	$0.270718\pi$
$252$			4.67767e9i			1.15992i
$253$	−7.10800e9	+	7.10800e9i	−1.73486	+	1.73486i
$254$	−2.66690e9	+	2.66690e9i	−0.640724	+	0.640724i
$255$	−8.79487e8			−0.208002
$256$	−1.65902e9			−0.386270
$257$	2.50164e9	+	2.50164e9i	0.573447	+	0.573447i	0.933090	−	0.359643i	$-0.117102\pi$
$257$	2.50164e9	+	2.50164e9i	0.573447	+	0.573447i	−0.359643	+	0.933090i	$0.617102\pi$
$258$		−	1.38429e10i		−	3.12428i
$259$	−9.33601e8	+	1.64122e9i	−0.207473	+	0.364726i
$260$	5.69632e9			1.24653
$261$	1.68182e9	−	1.68182e9i	0.362424	−	0.362424i
$262$		−	4.70608e8i		−	0.0998743i
$263$		−	2.19762e9i		−	0.459335i	−0.973269	−	0.229668i	$-0.926236\pi$
$263$		−	2.19762e9i		−	0.459335i	0.973269	−	0.229668i	$-0.0737639\pi$
$264$	−1.89150e10	−	1.89150e10i	−3.89395	−	3.89395i
$265$	−3.65764e8	−	3.65764e8i	−0.0741682	−	0.0741682i
$266$	−5.89576e9			−1.17764
$267$	−8.36026e9	−	8.36026e9i	−1.64503	−	1.64503i
$268$	7.17917e9			1.39167
$269$	2.52173e9			0.481602			0.240801	−	0.970574i	$-0.422590\pi$
$269$	2.52173e9			0.481602			0.240801	+	0.970574i	$0.422590\pi$
$270$		−	8.14345e8i		−	0.153233i
$271$	−6.90611e8			−0.128043			−0.0640215	−	0.997949i	$-0.520393\pi$
$271$	−6.90611e8			−0.128043			−0.0640215	+	0.997949i	$0.520393\pi$
$272$	2.91642e9	+	2.91642e9i	0.532812	+	0.532812i
$273$	2.31791e9	−	2.31791e9i	0.417298	−	0.417298i
$274$	2.51838e9	−	2.51838e9i	0.446805	−	0.446805i
$275$	−5.70286e9			−0.997154
$276$	2.67884e10	+	2.67884e10i	4.61648	+	4.61648i
$277$	2.38276e9	−	2.38276e9i	0.404726	−	0.404726i	−0.475169	−	0.879895i	$-0.657613\pi$
$277$	2.38276e9	−	2.38276e9i	0.404726	−	0.404726i	0.879895	+	0.475169i	$0.157613\pi$
$278$	1.49786e9	+	1.49786e9i	0.250780	+	0.250780i
$279$	−6.36242e9	+	6.36242e9i	−1.05004	+	1.05004i
$280$			3.71425e9i			0.604280i
$281$	−3.37304e9	−	3.37304e9i	−0.540999	−	0.540999i	0.382823	−	0.923822i	$-0.374952\pi$
$281$	−3.37304e9	−	3.37304e9i	−0.540999	−	0.540999i	−0.923822	+	0.382823i	$0.874952\pi$
$282$	2.03359e8	+	2.03359e8i	0.0321563	+	0.0321563i
$283$	−4.44586e7	+	4.44586e7i	−0.00693123	+	0.00693123i	−0.710564	−	0.703633i	$-0.751560\pi$
$283$	−4.44586e7	+	4.44586e7i	−0.00693123	+	0.00693123i	0.703633	+	0.710564i	$0.251560\pi$
$284$			1.02397e10i			1.57404i
$285$	7.43371e9			1.12675
$286$			1.64666e10i			2.46116i
$287$		−	4.77549e9i		−	0.703867i
$288$	−1.23613e10	+	1.23613e10i	−1.79678	+	1.79678i
$289$		−	6.43953e9i		−	0.923129i
$290$	2.23054e9	−	2.23054e9i	0.315368	−	0.315368i
$291$	−7.80057e9	+	7.80057e9i	−1.08781	+	1.08781i
$292$	1.11031e10			1.52726
$293$	6.33911e9			0.860117			0.430059	−	0.902801i	$-0.358493\pi$
$293$	6.33911e9			0.860117			0.430059	+	0.902801i	$0.358493\pi$
$294$	−1.18132e10	−	1.18132e10i	−1.58116	−	1.58116i
$295$		−	3.87711e9i		−	0.511942i
$296$	−2.06364e10	+	5.67133e9i	−2.68823	+	0.738784i
$297$	1.67991e9			0.215904
$298$	9.89886e9	−	9.89886e9i	1.25522	−	1.25522i
$299$		−	1.39623e10i		−	1.74691i
$300$			2.14928e10i			2.65343i
$301$	−2.80376e9	−	2.80376e9i	−0.341567	−	0.341567i
$302$	1.75180e10	+	1.75180e10i	2.10599	+	2.10599i
$303$	−1.36847e9			−0.162355
$304$	−2.46505e10	−	2.46505e10i	−2.88624	−	2.88624i
$305$	−2.70800e9			−0.312932
$306$	−5.03905e9			−0.574729
$307$			3.52830e9i			0.397203i	0.980080	+	0.198601i	$0.0636399\pi$
$307$			3.52830e9i			0.397203i	−0.980080	+	0.198601i	$0.936360\pi$
$308$	−1.27979e10			−1.42212
$309$	−1.13361e10	−	1.13361e10i	−1.24346	−	1.24346i
$310$	−8.43825e9	+	8.43825e9i	−0.913704	+	0.913704i
$311$	−4.45239e9	+	4.45239e9i	−0.475939	+	0.475939i	−0.903830	−	0.427891i	$-0.859257\pi$
$311$	−4.45239e9	+	4.45239e9i	−0.475939	+	0.475939i	0.427891	+	0.903830i	$0.359257\pi$
$312$	3.71547e10			3.92099
$313$	−6.03884e9	−	6.03884e9i	−0.629182	−	0.629182i	0.318680	−	0.947862i	$-0.396760\pi$
$313$	−6.03884e9	−	6.03884e9i	−0.629182	−	0.629182i	−0.947862	+	0.318680i	$0.896760\pi$
$314$	−2.35538e10	+	2.35538e10i	−2.42294	+	2.42294i
$315$	−1.67394e9	−	1.67394e9i	−0.170019	−	0.170019i
$316$	1.11784e10	−	1.11784e10i	1.12107	−	1.12107i
$317$			6.33979e9i			0.627824i	0.949452	+	0.313912i	$0.101640\pi$
$317$			6.33979e9i			0.627824i	−0.949452	+	0.313912i	$0.898360\pi$
$318$	−3.98483e9	−	3.98483e9i	−0.389674	−	0.389674i
$319$	4.60138e9	+	4.60138e9i	0.444350	+	0.444350i
$320$	−5.98533e9	+	5.98533e9i	−0.570806	+	0.570806i
$321$		−	1.37712e10i		−	1.29704i
$322$	1.52062e10			1.41448
$323$		−	4.53241e9i		−	0.416408i
$324$			2.41312e10i			2.18977i
$325$	5.60107e9	−	5.60107e9i	0.502039	−	0.502039i
$326$		−	2.88938e9i		−	0.255819i
$327$	4.90089e9	−	4.90089e9i	0.428631	−	0.428631i
$328$	3.82742e10	−	3.82742e10i	3.30682	−	3.30682i
$329$	8.23770e7			0.00703109
$330$	2.26117e10			1.90668
$331$	8.04158e9	+	8.04158e9i	0.669930	+	0.669930i	0.957700	−	0.287770i	$-0.0929138\pi$
$331$	8.04158e9	+	8.04158e9i	0.669930	+	0.669930i	−0.287770	+	0.957700i	$0.592914\pi$
$332$		−	3.04618e10i		−	2.50728i
$333$	6.74445e9	−	1.18564e10i	0.548491	−	0.964216i
$334$	−4.63262e10			−3.72255
$335$	−2.56911e9	+	2.56911e9i	−0.203988	+	0.203988i
$336$			2.11095e10i			1.65623i
$337$			1.48816e10i			1.15380i	0.816815	+	0.576899i	$0.195737\pi$
$337$			1.48816e10i			1.15380i	−0.816815	+	0.576899i	$0.804263\pi$
$338$	1.07316e9	+	1.07316e9i	0.0822241	+	0.0822241i
$339$	2.54856e10	+	2.54856e10i	1.92973	+	1.92973i
$340$	−4.76923e9			−0.356889
$341$	−1.74073e10	−	1.74073e10i	−1.28740	−	1.28740i
$342$	4.25917e10			3.11330
$343$	−1.05932e10			−0.765334
$344$		−	4.49427e10i		−	3.20941i
$345$	−1.91728e10			−1.35335
$346$	3.27807e10	+	3.27807e10i	2.28725	+	2.28725i
$347$	−1.46961e10	+	1.46961e10i	−1.01364	+	1.01364i	−0.0137335	+	0.999906i	$0.504372\pi$
$347$	−1.46961e10	+	1.46961e10i	−1.01364	+	1.01364i	−0.999906	+	0.0137335i	$0.995628\pi$
$348$	1.73415e10	−	1.73415e10i	1.18242	−	1.18242i
$349$	2.55490e10			1.72216			0.861079	−	0.508471i	$-0.169789\pi$
$349$	2.55490e10			1.72216			0.861079	+	0.508471i	$0.169789\pi$
$350$	6.10009e9	+	6.10009e9i	0.406503	+	0.406503i
$351$	−1.64993e9	+	1.64993e9i	−0.108702	+	0.108702i
$352$	−3.38200e10	−	3.38200e10i	−2.20294	−	2.20294i
$353$	1.18774e9	−	1.18774e9i	0.0764930	−	0.0764930i	−0.667825	−	0.744318i	$-0.732775\pi$
$353$	1.18774e9	−	1.18774e9i	0.0764930	−	0.0764930i	0.744318	+	0.667825i	$0.232775\pi$
$354$		−	4.22393e10i		−	2.68970i
$355$	−3.66436e9	−	3.66436e9i	−0.230719	−	0.230719i
$356$	−4.53356e10	−	4.53356e10i	−2.82254	−	2.82254i
$357$	−1.94067e9	+	1.94067e9i	−0.119475	+	0.119475i
$358$		−	7.81509e9i		−	0.475775i
$359$	−2.49653e9			−0.150300			−0.0751499	−	0.997172i	$-0.523944\pi$
$359$	−2.49653e9			−0.150300			−0.0751499	+	0.997172i	$0.523944\pi$
$360$		−	2.68322e10i		−	1.59752i
$361$			2.13259e10i			1.25568i
$362$	−2.35252e10	+	2.35252e10i	−1.36993	+	1.36993i
$363$			2.14286e10i			1.23415i
$364$	1.25694e10	−	1.25694e10i	0.715996	−	0.715996i
$365$	−3.97331e9	+	3.97331e9i	−0.223863	+	0.223863i
$366$	−2.95024e10			−1.64412
$367$	1.42017e10			0.782848			0.391424	−	0.920210i	$-0.371983\pi$
$367$	1.42017e10			0.782848			0.391424	+	0.920210i	$0.371983\pi$
$368$	6.35780e10	+	6.35780e10i	3.46669	+	3.46669i
$369$			3.44988e10i			1.86079i
$370$	8.94492e9	−	1.57247e10i	0.477276	−	0.839024i
$371$	−1.61418e9			−0.0852035
$372$	−6.56041e10	+	6.56041e10i	−3.42578	+	3.42578i
$373$		−	1.49886e9i		−	0.0774327i	−0.999250	−	0.0387164i	$-0.987673\pi$
$373$		−	1.49886e9i		−	0.0774327i	0.999250	−	0.0387164i	$-0.0123269\pi$
$374$		−	1.37866e10i		−	0.704646i
$375$	−1.81819e10	−	1.81819e10i	−0.919419	−	0.919419i
$376$	6.60227e8	+	6.60227e8i	0.0330325	+	0.0330325i
$377$	−9.03849e9			−0.447436
$378$	−1.79693e9	−	1.79693e9i	−0.0880163	−	0.0880163i
$379$	−1.96668e10			−0.953187			−0.476593	−	0.879124i	$-0.658129\pi$
$379$	−1.96668e10			−0.953187			−0.476593	+	0.879124i	$0.658129\pi$
$380$	4.03111e10			1.93326
$381$		−	1.48396e10i		−	0.704245i
$382$	3.61845e10			1.69929
$383$	3.77865e9	+	3.77865e9i	0.175607	+	0.175607i	0.789438	−	0.613831i	$-0.210372\pi$
$383$	3.77865e9	+	3.77865e9i	0.175607	+	0.175607i	−0.613831	+	0.789438i	$0.710372\pi$
$384$	−1.40581e10	+	1.40581e10i	−0.646549	+	0.646549i
$385$	4.57981e9	−	4.57981e9i	0.208451	−	0.208451i
$386$	−3.58496e10			−1.61486
$387$	2.02547e10	+	2.02547e10i	0.902990	+	0.902990i
$388$	−4.23005e10	+	4.23005e10i	−1.86646	+	1.86646i
$389$	1.21970e10	+	1.21970e10i	0.532666	+	0.532666i	0.921365	−	0.388699i	$-0.127075\pi$
$389$	1.21970e10	+	1.21970e10i	0.532666	+	0.532666i	−0.388699	+	0.921365i	$0.627075\pi$
$390$	−2.22081e10	+	2.22081e10i	−0.959961	+	0.959961i
$391$			1.16899e10i			0.500153i
$392$	−3.83528e10	−	3.83528e10i	−1.62425	−	1.62425i
$393$	1.30932e9	+	1.30932e9i	0.0548879	+	0.0548879i
$394$	2.15455e10	−	2.15455e10i	0.894072	−	0.894072i
$395$			8.00057e9i			0.328649i
$396$	9.24535e10			3.75961
$397$			7.51869e8i			0.0302677i	0.999885	+	0.0151339i	$0.00481745\pi$
$397$			7.51869e8i			0.0302677i	−0.999885	+	0.0151339i	$0.995183\pi$
$398$		−	3.00669e10i		−	1.19828i
$399$	1.64032e10	−	1.64032e10i	0.647196	−	0.647196i
$400$			5.10097e10i			1.99256i
$401$	2.90038e10	−	2.90038e10i	1.12170	−	1.12170i	0.130217	−	0.991486i	$-0.458433\pi$
$401$	2.90038e10	−	2.90038e10i	1.12170	−	1.12170i	0.991486	−	0.130217i	$-0.0415674\pi$
$402$	−2.79893e10	+	2.79893e10i	−1.07174	+	1.07174i
$403$	3.41932e10			1.29634
$404$	−7.42088e9			−0.278567
$405$	−8.63552e9	−	8.63552e9i	−0.320973	−	0.320973i
$406$		−	9.84376e9i		−	0.362290i
$407$	3.24384e10	+	1.84525e10i	1.18218	+	0.672477i
$408$	−3.11077e10			−1.12261
$409$	−4.40863e9	+	4.40863e9i	−0.157547	+	0.157547i	−0.781479	−	0.623932i	$-0.785534\pi$
$409$	−4.40863e9	+	4.40863e9i	−0.157547	+	0.157547i	0.623932	+	0.781479i	$0.285534\pi$
$410$			4.57545e10i			1.61919i
$411$			1.40132e10i			0.491101i
$412$	−6.14730e10	−	6.14730e10i	−2.13351	−	2.13351i
$413$	−8.55520e9	−	8.55520e9i	−0.294056	−	0.294056i
$414$	−1.09851e11			−3.73942
$415$	1.09010e10	+	1.09010e10i	0.367513	+	0.367513i
$416$	6.64327e10			2.21824
$417$	−8.33469e9			−0.275642
$418$			1.16529e11i			3.81706i
$419$	4.86854e10			1.57958			0.789791	−	0.613376i	$-0.210189\pi$
$419$	4.86854e10			1.57958			0.789791	+	0.613376i	$0.210189\pi$
$420$	−1.72602e10	−	1.72602e10i	−0.554689	−	0.554689i
$421$	3.31738e10	−	3.31738e10i	1.05601	−	1.05601i	0.0576726	−	0.998336i	$-0.481632\pi$
$421$	3.31738e10	−	3.31738e10i	1.05601	−	1.05601i	0.998336	−	0.0576726i	$-0.0183680\pi$
$422$	2.50154e10	−	2.50154e10i	0.788782	−	0.788782i
$423$	−5.95102e8			−0.0185879
$424$	−1.29372e10	−	1.29372e10i	−0.400292	−	0.400292i
$425$	−4.68949e9	+	4.68949e9i	−0.143737	+	0.143737i
$426$	−3.99214e10	−	3.99214e10i	−1.21218	−	1.21218i
$427$	−5.97545e9	+	5.97545e9i	−0.179746	+	0.179746i
$428$		−	7.46779e10i		−	2.22545i
$429$	−4.58132e10	−	4.58132e10i	−1.35258	−	1.35258i
$430$	2.68631e10	+	2.68631e10i	0.785748	+	0.785748i
$431$	−1.60301e9	+	1.60301e9i	−0.0464543	+	0.0464543i	−0.729952	−	0.683498i	$-0.760458\pi$
$431$	−1.60301e9	+	1.60301e9i	−0.0464543	+	0.0464543i	0.683498	+	0.729952i	$0.260458\pi$
$432$		−	1.50261e10i		−	0.431431i
$433$	−6.58246e9			−0.187256			−0.0936282	−	0.995607i	$-0.529846\pi$
$433$	−6.58246e9			−0.187256			−0.0936282	+	0.995607i	$0.529846\pi$
$434$			3.72395e10i			1.04965i
$435$			1.24116e10i			0.346633i
$436$	2.65763e10	−	2.65763e10i	0.735442	−	0.735442i
$437$		−	9.88067e10i		−	2.70932i
$438$	−4.32874e10	+	4.32874e10i	−1.17616	+	1.17616i
$439$	−2.78084e10	+	2.78084e10i	−0.748718	+	0.748718i	−0.974238	−	0.225520i	$-0.927592\pi$
$439$	−2.78084e10	+	2.78084e10i	−0.748718	+	0.748718i	0.225520	+	0.974238i	$0.427592\pi$
$440$	7.34116e10			1.95864
$441$	3.45696e10			0.913988
$442$	1.35405e10	+	1.35405e10i	0.354770	+	0.354770i
$443$		−	4.50837e10i		−	1.17059i	−0.810821	−	0.585294i	$-0.800979\pi$
$443$		−	4.50837e10i		−	1.17059i	0.810821	−	0.585294i	$-0.199021\pi$
$444$	6.95432e10	−	1.22253e11i	1.78946	−	3.14577i
$445$	3.24473e10			0.827444
$446$	−1.39240e10	+	1.39240e10i	−0.351905	+	0.351905i
$447$			5.50811e10i			1.37966i
$448$			2.64144e10i			0.655734i
$449$	3.11138e10	+	3.11138e10i	0.765541	+	0.765541i	0.977318	−	0.211777i	$-0.0679251\pi$
$449$	3.11138e10	+	3.11138e10i	0.765541	+	0.765541i	−0.211777	+	0.977318i	$0.567925\pi$
$450$	−4.40678e10	−	4.40678e10i	−1.07466	−	1.07466i
$451$	−9.43870e10			−2.28142
$452$	1.38202e11	+	1.38202e11i	3.31102	+	3.31102i
$453$	−9.74770e10			−2.31478
$454$	−8.56166e10			−2.01528
$455$			8.99612e9i			0.209899i
$456$	2.62933e11			6.08115
$457$	2.72913e10	+	2.72913e10i	0.625691	+	0.625691i	0.946981	−	0.321290i	$-0.104116\pi$
$457$	2.72913e10	+	2.72913e10i	0.625691	+	0.625691i	−0.321290	+	0.946981i	$0.604116\pi$
$458$	−2.76898e10	+	2.76898e10i	−0.629300	+	0.629300i
$459$	1.38140e9	−	1.38140e9i	0.0311221	−	0.0311221i
$460$	−1.03969e11			−2.32206
$461$	−3.38626e10	−	3.38626e10i	−0.749751	−	0.749751i	0.224681	−	0.974432i	$-0.427866\pi$
$461$	−3.38626e10	−	3.38626e10i	−0.749751	−	0.749751i	−0.974432	+	0.224681i	$0.927866\pi$
$462$	4.98948e10	−	4.98948e10i	1.09519	−	1.09519i
$463$	4.94574e10	+	4.94574e10i	1.07624	+	1.07624i	0.996843	+	0.0793923i	$0.0252980\pi$
$463$	4.94574e10	+	4.94574e10i	1.07624	+	1.07624i	0.0793923	+	0.996843i	$0.474702\pi$
$464$	4.11573e10	−	4.11573e10i	0.887923	−	0.887923i
$465$		−	4.69537e10i		−	1.00429i
$466$	−6.10422e10	−	6.10422e10i	−1.29445	−	1.29445i
$467$	−1.24254e10	−	1.24254e10i	−0.261243	−	0.261243i	0.564316	−	0.825559i	$-0.309140\pi$
$467$	−1.24254e10	−	1.24254e10i	−0.261243	−	0.261243i	−0.825559	+	0.564316i	$0.809140\pi$
$468$	−9.08033e10	+	9.08033e10i	−1.89286	+	1.89286i
$469$			1.13380e10i			0.234338i
$470$	−7.89262e8			−0.0161745
$471$		−	1.31063e11i		−	2.66315i
$472$		−	1.37135e11i		−	2.76299i
$473$	−5.54160e10	+	5.54160e10i	−1.10711	+	1.10711i
$474$			8.71624e10i			1.72670i
$475$	3.96371e10	−	3.96371e10i	0.778624	−	0.778624i
$476$	−1.05237e10	+	1.05237e10i	−0.204995	+	0.204995i
$477$	1.16611e10			0.225250
$478$	5.76767e10			1.10481
$479$	5.54243e10	+	5.54243e10i	1.05283	+	1.05283i	0.998524	+	0.0543048i	$0.0172943\pi$
$479$	5.54243e10	+	5.54243e10i	1.05283	+	1.05283i	0.0543048	+	0.998524i	$0.482706\pi$
$480$		−	9.12248e10i		−	1.71849i
$481$	−4.99826e10	+	1.37363e10i	−0.933766	+	0.256619i
$482$	−2.28200e9			−0.0422793
$483$	−4.23066e10	+	4.23066e10i	−0.777355	+	0.777355i
$484$			1.16202e11i			2.11754i
$485$		−	3.02751e10i		−	0.547165i
$486$	−1.05782e11	−	1.05782e11i	−1.89612	−	1.89612i
$487$	8.18350e9	+	8.18350e9i	0.145487	+	0.145487i	0.776098	−	0.630612i	$-0.217196\pi$
$487$	8.18350e9	+	8.18350e9i	0.145487	+	0.145487i	−0.630612	+	0.776098i	$0.717196\pi$
$488$	−9.57830e10			−1.68892
$489$	8.03880e9	+	8.03880e9i	0.140591	+	0.140591i
$490$	4.58485e10			0.795318
$491$	−2.19397e10			−0.377489			−0.188744	−	0.982026i	$-0.560442\pi$
$491$	−2.19397e10			−0.377489			−0.188744	+	0.982026i	$0.560442\pi$
$492$			3.55723e11i			6.07088i
$493$	7.56746e9			0.128104
$494$	−1.14449e11	−	1.14449e11i	−1.92178	−	1.92178i
$495$	−3.30851e10	+	3.30851e10i	−0.551076	+	0.551076i
$496$	−1.55701e11	+	1.55701e11i	−2.57255	+	2.57255i
$497$	−1.61715e10			−0.265048
$498$	1.18761e11	+	1.18761e11i	1.93088	+	1.93088i
$499$	7.16278e10	−	7.16278e10i	1.15526	−	1.15526i	0.169776	−	0.985483i	$-0.445695\pi$
$499$	7.16278e10	−	7.16278e10i	1.15526	−	1.15526i	0.985483	−	0.169776i	$-0.0543045\pi$
$500$	−9.85957e10	−	9.85957e10i	−1.57753	−	1.57753i
$501$	1.28889e11	−	1.28889e11i	2.04580	−	2.04580i
$502$		−	1.54375e10i		−	0.243087i
$503$	4.50998e10	+	4.50998e10i	0.704535	+	0.704535i	0.965381	−	0.260846i	$-0.0840013\pi$
$503$	4.50998e10	+	4.50998e10i	0.704535	+	0.704535i	−0.260846	+	0.965381i	$0.584001\pi$
$504$	−5.92076e10	−	5.92076e10i	−0.917605	−	0.917605i
$505$	2.65561e9	−	2.65561e9i	0.0408319	−	0.0408319i
$506$		−	3.00548e11i		−	4.58472i
$507$	−5.97150e9			−0.0903757
$508$		−	8.04717e10i		−	1.20834i
$509$		−	2.40425e10i		−	0.358186i	−0.983832	−	0.179093i	$-0.942684\pi$
$509$		−	2.40425e10i		−	0.358186i	0.983832	−	0.179093i	$-0.0573163\pi$
$510$	1.85937e10	−	1.85937e10i	0.274844	−	0.274844i
$511$			1.75350e10i			0.257170i
$512$	6.56664e10	−	6.56664e10i	0.955572	−	0.955572i
$513$	−1.16761e10	+	1.16761e10i	−0.168588	+	0.168588i
$514$	−1.05777e11			−1.51545
$515$	4.39971e10			0.625453
$516$	2.08850e11	+	2.08850e11i	2.94602	+	2.94602i
$517$		−	1.62817e9i		−	0.0227897i
$518$	−1.49601e10	−	5.44356e10i	−0.207785	−	0.756074i
$519$	−1.82405e11			−2.51401
$520$	−7.21013e10	+	7.21013e10i	−0.986119	+	0.986119i
$521$		−	6.44883e10i		−	0.875246i	−0.899159	−	0.437623i	$-0.855820\pi$
$521$		−	6.44883e10i		−	0.875246i	0.899159	−	0.437623i	$-0.144180\pi$
$522$			7.11126e10i			0.957777i
$523$	2.72664e10	+	2.72664e10i	0.364436	+	0.364436i	0.865443	−	0.501007i	$-0.167037\pi$
$523$	2.72664e10	+	2.72664e10i	0.364436	+	0.364436i	−0.501007	+	0.865443i	$0.667037\pi$
$524$	7.10012e9	+	7.10012e9i	0.0941761	+	0.0941761i
$525$	−3.39433e10			−0.446803
$526$	4.64611e10	+	4.64611e10i	0.606941	+	0.606941i
$527$	−2.86282e10			−0.371151
$528$	4.17226e11			5.36829
$529$			1.76529e11i			2.25420i
$530$	1.54657e10			0.196004
$531$	6.18039e10	+	6.18039e10i	0.777388	+	0.777388i
$532$	8.89502e10	−	8.89502e10i	1.11045	−	1.11045i
$533$	9.27023e10	−	9.27023e10i	1.14863	−	1.14863i
$534$	3.53498e11			4.34732
$535$	2.67240e10	+	2.67240e10i	0.326202	+	0.326202i
$536$	−9.08704e10	+	9.08704e10i	−1.10094	+	1.10094i
$537$	2.17431e10	+	2.17431e10i	0.261471	+	0.261471i
$538$	−5.33132e10	+	5.33132e10i	−0.636364	+	0.636364i
$539$			9.45809e10i			1.12059i
$540$	1.22861e10	+	1.22861e10i	0.144491	+	0.144491i
$541$	4.60005e10	+	4.60005e10i	0.536999	+	0.536999i	0.922646	−	0.385647i	$-0.126022\pi$
$541$	4.60005e10	+	4.60005e10i	0.536999	+	0.536999i	−0.385647	+	0.922646i	$0.626022\pi$
$542$	1.46006e10	−	1.46006e10i	0.169189	−	0.169189i
$543$		−	1.30903e11i		−	1.50574i
$544$	−5.56207e10			−0.635098
$545$			1.90210e10i			0.215600i
$546$			9.80085e10i			1.10279i
$547$	−7.01239e10	+	7.01239e10i	−0.783280	+	0.783280i	−0.980383	−	0.197103i	$-0.936847\pi$
$547$	−7.01239e10	+	7.01239e10i	−0.783280	+	0.783280i	0.197103	+	0.980383i	$0.436847\pi$
$548$			7.59901e10i			0.842626i
$549$	4.31674e10	−	4.31674e10i	0.475190	−	0.475190i
$550$	1.20567e11	−	1.20567e11i	1.31759	−	1.31759i
$551$	−6.39627e10			−0.693938
$552$	−6.78149e11			−7.30414
$553$	1.76540e10	+	1.76540e10i	0.188774	+	0.188774i
$554$			1.00751e11i			1.06957i
$555$	1.88625e10	+	6.86355e10i	0.198805	+	0.723398i
$556$	−4.51969e10			−0.472944
$557$	−7.75232e10	+	7.75232e10i	−0.805398	+	0.805398i	−0.983934	−	0.178535i	$-0.942864\pi$
$557$	−7.75232e10	+	7.75232e10i	−0.805398	+	0.805398i	0.178535	+	0.983934i	$0.442864\pi$
$558$		−	2.69023e11i		−	2.77494i
$559$		−	1.08854e11i		−	1.11480i
$560$	−4.09644e10	−	4.09644e10i	−0.416538	−	0.416538i
$561$	3.83570e10	+	3.83570e10i	0.387252	+	0.387252i
$562$	1.42623e11			1.42969
$563$	−6.22479e10	−	6.22479e10i	−0.619571	−	0.619571i	0.325850	−	0.945421i	$-0.394350\pi$
$563$	−6.22479e10	−	6.22479e10i	−0.619571	−	0.619571i	−0.945421	+	0.325850i	$0.894350\pi$
$564$	−6.13620e9			−0.0606433
$565$	−9.89132e10			−0.970645
$566$		−	1.87985e9i		−	0.0183171i
$567$	−3.81101e10			−0.368729
$568$	−1.29609e11	−	1.29609e11i	−1.24521	−	1.24521i
$569$	−8.16998e10	+	8.16998e10i	−0.779421	+	0.779421i	−0.979732	−	0.200312i	$-0.935805\pi$
$569$	−8.16998e10	+	8.16998e10i	−0.779421	+	0.779421i	0.200312	+	0.979732i	$0.435805\pi$
$570$	−1.57160e11	+	1.57160e11i	−1.48882	+	1.48882i
$571$	−1.87719e11			−1.76589			−0.882947	−	0.469473i	$-0.844444\pi$
$571$	−1.87719e11			−1.76589			−0.882947	+	0.469473i	$0.844444\pi$
$572$	−2.48433e11	−	2.48433e11i	−2.32074	−	2.32074i
$573$	−1.00672e11	+	1.00672e11i	−0.933880	+	0.933880i
$574$	1.00961e11	+	1.00961e11i	0.930053	+	0.930053i
$575$	−1.02231e11	+	1.02231e11i	−0.935214	+	0.935214i
$576$		−	1.90821e11i		−	1.73355i
$577$	−6.33330e10	−	6.33330e10i	−0.571383	−	0.571383i	0.361132	−	0.932515i	$-0.382390\pi$
$577$	−6.33330e10	−	6.33330e10i	−0.571383	−	0.571383i	−0.932515	+	0.361132i	$0.882390\pi$
$578$	1.36142e11	+	1.36142e11i	1.21977	+	1.21977i
$579$	9.97405e10	−	9.97405e10i	0.887477	−	0.887477i
$580$			6.73048e10i			0.594750i
$581$	4.81079e10			0.422194
$582$		−	3.29833e11i		−	2.87476i
$583$			3.19041e10i			0.276168i
$584$	−1.40537e11	+	1.40537e11i	−1.20820	+	1.20820i
$585$		−	6.49891e10i		−	0.554903i
$586$	−1.34019e11	+	1.34019e11i	−1.13651	+	1.13651i
$587$	−4.56517e10	+	4.56517e10i	−0.384507	+	0.384507i	−0.872723	−	0.488216i	$-0.837648\pi$
$587$	−4.56517e10	+	4.56517e10i	−0.384507	+	0.384507i	0.488216	+	0.872723i	$0.337648\pi$
$588$	3.56454e11			2.98190
$589$	2.41975e11			2.01052
$590$	8.19683e10	+	8.19683e10i	0.676453	+	0.676453i
$591$			1.19888e11i			0.982709i
$592$	1.65050e11	−	2.90148e11i	1.34378	−	2.36228i
$593$	1.99252e11			1.61133			0.805665	−	0.592372i	$-0.201808\pi$
$593$	1.99252e11			1.61133			0.805665	+	0.592372i	$0.201808\pi$
$594$	−3.55160e10	+	3.55160e10i	−0.285285	+	0.285285i
$595$		−	7.53199e9i		−	0.0600955i
$596$			2.98691e11i			2.36721i
$597$	8.36520e10	+	8.36520e10i	0.658535	+	0.658535i
$598$	2.95184e11	+	2.95184e11i	2.30828	+	2.30828i
$599$	1.12117e10			0.0870888			0.0435444	−	0.999051i	$-0.486135\pi$
$599$	1.12117e10			0.0870888			0.0435444	+	0.999051i	$0.486135\pi$
$600$	−2.72045e11	−	2.72045e11i	−2.09911	−	2.09911i
$601$	1.18897e11			0.911321			0.455660	−	0.890154i	$-0.349403\pi$
$601$	1.18897e11			0.911321			0.455660	+	0.890154i	$0.349403\pi$
$602$	1.18552e11			0.902657
$603$		−	8.19069e10i		−	0.619514i
$604$	−5.28593e11			−3.97168
$605$	−4.15837e10	−	4.15837e10i	−0.310386	−	0.310386i
$606$	2.89316e10	−	2.89316e10i	0.214527	−	0.214527i
$607$	8.88056e10	−	8.88056e10i	0.654162	−	0.654162i	−0.299830	−	0.953993i	$-0.596930\pi$
$607$	8.88056e10	−	8.88056e10i	0.654162	−	0.654162i	0.953993	+	0.299830i	$0.0969300\pi$
$608$	4.70125e11			3.44032
$609$	2.73873e10	+	2.73873e10i	0.199104	+	0.199104i
$610$	5.72514e10	−	5.72514e10i	0.413492	−	0.413492i
$611$	1.59911e9	+	1.59911e9i	0.0114740	+	0.0114740i
$612$	7.60249e10	−	7.60249e10i	0.541939	−	0.541939i
$613$			2.95344e10i			0.209164i	0.994516	+	0.104582i	$0.0333504\pi$
$613$			2.95344e10i			0.209164i	−0.994516	+	0.104582i	$0.966650\pi$
$614$	−7.45938e10	−	7.45938e10i	−0.524843	−	0.524843i
$615$	−1.27298e11	−	1.27298e11i	−0.889858	−	0.889858i
$616$	1.61989e11	−	1.61989e11i	1.12503	−	1.12503i
$617$			4.55611e10i			0.314379i	0.987568	+	0.157189i	$0.0502433\pi$
$617$			4.55611e10i			0.314379i	−0.987568	+	0.157189i	$0.949757\pi$
$618$	4.79327e11			3.28608
$619$		−	2.95039e9i		−	0.0200963i	−0.999950	−	0.0100482i	$-0.996802\pi$
$619$		−	2.95039e9i		−	0.0200963i	0.999950	−	0.0100482i	$-0.00319849\pi$
$620$		−	2.54618e11i		−	1.72315i
$621$	3.01146e10	−	3.01146e10i	0.202493	−	0.202493i
$622$		−	1.88261e11i		−	1.25776i
$623$	7.15979e10	−	7.15979e10i	0.475278	−	0.475278i
$624$	−4.09779e11	+	4.09779e11i	−2.70279	+	2.70279i
$625$	−4.13064e10			−0.270705
$626$	2.55341e11			1.66274
$627$	−3.24206e11	−	3.24206e11i	−2.09774	−	2.09774i
$628$		−	7.10720e11i		−	4.56941i
$629$	4.18478e10	−	1.15007e10i	0.267344	−	0.0734718i
$630$	7.07792e10			0.449307
$631$	−5.71115e10	+	5.71115e10i	−0.360252	+	0.360252i	−0.863905	−	0.503654i	$-0.831989\pi$
$631$	−5.71115e10	+	5.71115e10i	−0.360252	+	0.360252i	0.503654	+	0.863905i	$0.331989\pi$
$632$			2.82983e11i			1.77375i
$633$			1.39195e11i			0.866981i
$634$	−1.34033e11	−	1.34033e11i	−0.829573	−	0.829573i
$635$	2.87973e10	+	2.87973e10i	0.177116	+	0.177116i
$636$	1.20239e11			0.734883
$637$	−9.28927e10	−	9.28927e10i	−0.564188	−	0.564188i
$638$	−1.94561e11			−1.17428
$639$	1.16825e11			0.700699
$640$		−	5.45613e10i		−	0.325211i
$641$	−7.15088e10			−0.423572			−0.211786	−	0.977316i	$-0.567928\pi$
$641$	−7.15088e10			−0.423572			−0.211786	+	0.977316i	$0.567928\pi$
$642$	2.91145e11	+	2.91145e11i	1.71384	+	1.71384i
$643$	1.46673e11	−	1.46673e11i	0.858040	−	0.858040i	−0.133067	−	0.991107i	$-0.542482\pi$
$643$	1.46673e11	−	1.46673e11i	0.858040	−	0.858040i	0.991107	+	0.133067i	$0.0424825\pi$
$644$	−2.29418e11	+	2.29418e11i	−1.33378	+	1.33378i
$645$	−1.49477e11			−0.863645
$646$	9.58223e10	+	9.58223e10i	0.550220	+	0.550220i
$647$	−1.72797e10	+	1.72797e10i	−0.0986098	+	0.0986098i	−0.754691	−	0.656081i	$-0.772213\pi$
$647$	−1.72797e10	+	1.72797e10i	−0.0986098	+	0.0986098i	0.656081	+	0.754691i	$0.272213\pi$
$648$	−3.05441e11	−	3.05441e11i	−1.73232	−	1.73232i
$649$	−1.69092e11	+	1.69092e11i	−0.953115	+	0.953115i
$650$			2.36831e11i			1.32674i
$651$	−1.03608e11	−	1.03608e11i	−0.576856	−	0.576856i
$652$	4.35924e10	+	4.35924e10i	0.241224	+	0.241224i
$653$	2.15452e11	−	2.15452e11i	1.18494	−	1.18494i	0.206498	−	0.978447i	$-0.433793\pi$
$653$	2.15452e11	−	2.15452e11i	1.18494	−	1.18494i	0.978447	−	0.206498i	$-0.0662066\pi$
$654$			2.07225e11i			1.13274i
$655$	−5.08166e9			−0.0276083
$656$			8.44251e11i			4.55886i
$657$		−	1.26675e11i		−	0.679874i
$658$	−1.74158e9	+	1.74158e9i	−0.00929051	+	0.00929051i
$659$		−	1.33594e11i		−	0.708346i	−0.935180	−	0.354173i	$-0.884762\pi$
$659$		−	1.33594e11i		−	0.708346i	0.935180	−	0.354173i	$-0.115238\pi$
$660$	−3.41146e11	+	3.41146e11i	−1.79790	+	1.79790i
$661$	−1.24394e11	+	1.24394e11i	−0.651620	+	0.651620i	−0.953383	−	0.301763i	$-0.902425\pi$
$661$	−1.24394e11	+	1.24394e11i	−0.651620	+	0.651620i	0.301763	+	0.953383i	$0.402425\pi$
$662$	−3.40023e11			−1.77042
$663$	−7.53448e10			−0.389941
$664$	3.85571e11	+	3.85571e11i	1.98350	+	1.98350i
$665$			6.36629e10i			0.325536i
$666$	1.08074e11	+	3.93250e11i	0.549317	+	1.99881i
$667$	1.64971e11			0.833497
$668$	6.98930e11	−	6.98930e11i	3.51017	−	3.51017i
$669$		−	7.74787e10i		−	0.386793i
$670$		−	1.08630e11i		−	0.539077i
$671$	1.18104e11	+	1.18104e11i	0.582606	+	0.582606i
$672$	−2.01296e11	−	2.01296e11i	−0.987092	−	0.987092i
$673$	−3.25923e11			−1.58875			−0.794374	−	0.607428i	$-0.792201\pi$
$673$	−3.25923e11			−1.58875			−0.794374	+	0.607428i	$0.792201\pi$
$674$	−3.14620e11	−	3.14620e11i	−1.52457	−	1.52457i
$675$	2.41614e10			0.116388
$676$	−3.23819e10			−0.155066
$677$			6.68014e10i			0.318003i	0.987278	+	0.159001i	$0.0508274\pi$
$677$			6.68014e10i			0.318003i	−0.987278	+	0.159001i	$0.949173\pi$
$678$	−1.07761e12			−5.09969
$679$	−6.68047e10	−	6.68047e10i	−0.314288	−	0.314288i
$680$	6.03667e10	−	6.03667e10i	0.282333	−	0.282333i
$681$	2.38202e11	−	2.38202e11i	1.10753	−	1.10753i
$682$	7.36035e11			3.40221
$683$	1.45586e11	+	1.45586e11i	0.669018	+	0.669018i	0.957489	−	0.288471i	$-0.0931469\pi$
$683$	1.45586e11	+	1.45586e11i	0.669018	+	0.669018i	−0.288471	+	0.957489i	$0.593147\pi$
$684$	−6.42587e11	+	6.42587e11i	−2.93567	+	2.93567i
$685$	−2.71936e10	−	2.71936e10i	−0.123511	−	0.123511i
$686$	2.23957e11	−	2.23957e11i	1.01127	−	1.01127i
$687$		−	1.54077e11i		−	0.691688i
$688$	4.95672e11	+	4.95672e11i	2.21228	+	2.21228i
$689$	−3.13347e10	−	3.13347e10i	−0.139043	−	0.139043i
$690$	4.05344e11	−	4.05344e11i	1.78824	−	1.78824i
$691$			3.39132e11i			1.48750i	0.668460	+	0.743748i	$0.266954\pi$
$691$			3.39132e11i			1.48750i	−0.668460	+	0.743748i	$0.733046\pi$
$692$	−9.89134e11			−4.31351
$693$			1.46011e11i			0.633069i
$694$		−	6.21396e11i		−	2.67874i
$695$	1.61740e10	−	1.61740e10i	0.0693233	−	0.0693233i
$696$			4.39001e11i			1.87081i
$697$	−7.76148e10	+	7.76148e10i	−0.328862	+	0.328862i
$698$	−5.40147e11	+	5.40147e11i	−2.27557	+	2.27557i
$699$	3.39663e11			1.42278
$700$	−1.84066e11			−0.766621
$701$	9.23361e10	+	9.23361e10i	0.382384	+	0.382384i	0.871960	−	0.489576i	$-0.162849\pi$
$701$	9.23361e10	+	9.23361e10i	0.382384	+	0.382384i	−0.489576	+	0.871960i	$0.662849\pi$
$702$		−	6.97642e10i		−	0.287266i
$703$	−3.53711e11	+	9.72076e10i	−1.44820	+	0.397996i
$704$	5.22076e11			2.12541
$705$	2.19588e9	−	2.19588e9i	0.00888899	−	0.00888899i
$706$			5.02213e10i			0.202148i
$707$		−	1.17197e10i		−	0.0469071i
$708$	6.37271e11	+	6.37271e11i	2.53624	+	2.53624i
$709$	−1.28517e11	−	1.28517e11i	−0.508598	−	0.508598i	0.405498	−	0.914096i	$-0.367098\pi$
$709$	−1.28517e11	−	1.28517e11i	−0.508598	−	0.508598i	−0.914096	+	0.405498i	$0.867098\pi$
$710$	1.54940e11			0.609721
$711$	−1.27535e11	−	1.27535e11i	−0.499056	−	0.499056i
$712$	1.14767e12			4.46579
$713$	−6.24095e11			−2.41486
$714$		−	8.20574e10i		−	0.315737i
$715$	1.77807e11			0.680339
$716$	1.17907e11	+	1.17907e11i	0.448630	+	0.448630i
$717$	−1.60468e11	+	1.60468e11i	−0.607171	+	0.607171i
$718$	5.27805e10	−	5.27805e10i	0.198598	−	0.198598i
$719$	−2.68671e10			−0.100532			−0.0502661	−	0.998736i	$-0.516007\pi$
$719$	−2.68671e10			−0.100532			−0.0502661	+	0.998736i	$0.516007\pi$
$720$	2.95932e11	+	2.95932e11i	1.10119	+	1.10119i
$721$	9.70835e10	−	9.70835e10i	0.359256	−	0.359256i
$722$	−4.50862e11	−	4.50862e11i	−1.65919	−	1.65919i
$723$	6.34898e9	−	6.34898e9i	0.0232354	−	0.0232354i
$724$		−	7.09855e11i		−	2.58354i
$725$	6.61794e10	+	6.61794e10i	0.239536	+	0.239536i
$726$	−4.53035e11	−	4.53035e11i	−1.63074	−	1.63074i
$727$	2.90876e11	−	2.90876e11i	1.04129	−	1.04129i	0.0421772	−	0.999110i	$-0.486571\pi$
$727$	2.90876e11	−	2.90876e11i	1.04129	−	1.04129i	0.999110	−	0.0421772i	$-0.0134294\pi$
$728$			3.18196e11i			1.13284i
$729$	3.40427e11			1.20535
$730$		−	1.68004e11i		−	0.591600i
$731$			9.11377e10i			0.319175i
$732$	4.45107e11	−	4.45107e11i	1.55032	−	1.55032i
$733$			2.68229e11i			0.929157i	0.885532	+	0.464579i	$0.153794\pi$
$733$			2.68229e11i			0.929157i	−0.885532	+	0.464579i	$0.846206\pi$
$734$	−3.00247e11	+	3.00247e11i	−1.03441	+	1.03441i
$735$	−1.27559e11	+	1.27559e11i	−0.437082	+	0.437082i
$736$	−1.21253e12			−4.13221
$737$	2.24093e11			0.759555
$738$	−7.29358e11	−	7.29358e11i	−2.45875	−	2.45875i
$739$			3.21521e11i			1.07803i	0.842296	+	0.539015i	$0.181204\pi$
$739$			3.21521e11i			1.07803i	−0.842296	+	0.539015i	$0.818796\pi$
$740$	1.02287e11	+	3.72193e11i	0.341108	+	1.24120i
$741$	6.36839e11			2.11231
$742$	3.41264e10	−	3.41264e10i	0.112583	−	0.112583i
$743$			1.97899e11i			0.649364i	0.945823	+	0.324682i	$0.105257\pi$
$743$			1.97899e11i			0.649364i	−0.945823	+	0.324682i	$0.894743\pi$
$744$		−	1.66077e12i		−	5.42023i
$745$	−1.06889e11	−	1.06889e11i	−0.346981	−	0.346981i
$746$	3.16882e10	+	3.16882e10i	0.102316	+	0.102316i
$747$	−3.47538e11			−1.11614
$748$	2.08000e11	+	2.08000e11i	0.664443	+	0.664443i
$749$	1.17938e11			0.374737
$750$	7.68787e11			2.42975
$751$		−	4.12705e11i		−	1.29742i	−0.761036	−	0.648710i	$-0.775309\pi$
$751$		−	4.12705e11i		−	1.29742i	0.761036	−	0.648710i	$-0.224691\pi$
$752$	−1.45633e10			−0.0455395
$753$	4.29502e10	+	4.29502e10i	0.133593	+	0.133593i
$754$	1.91088e11	−	1.91088e11i	0.591218	−	0.591218i
$755$	1.89161e11	−	1.89161e11i	0.582161	−	0.582161i
$756$	5.42210e10			0.165989
$757$	−3.97532e11	−	3.97532e11i	−1.21056	−	1.21056i	−0.970841	−	0.239724i	$-0.922943\pi$
$757$	−3.97532e11	−	3.97532e11i	−1.21056	−	1.21056i	−0.239724	−	0.970841i	$-0.577057\pi$
$758$	4.15788e11	−	4.15788e11i	1.25949	−	1.25949i
$759$	8.36184e11	+	8.36184e11i	2.51962	+	2.51962i
$760$	−5.10239e11	+	5.10239e11i	−1.52939	+	1.52939i
$761$			4.47122e11i			1.33317i	0.745427	+	0.666587i	$0.232246\pi$
$761$			4.47122e11i			1.33317i	−0.745427	+	0.666587i	$0.767754\pi$
$762$	3.13733e11	+	3.13733e11i	0.930552	+	0.930552i
$763$	4.19716e10	+	4.19716e10i	0.123839	+	0.123839i
$764$	−5.45920e11	+	5.45920e11i	−1.60234	+	1.60234i
$765$			5.44120e10i			0.158873i
$766$	−1.59773e11			−0.464076
$767$		−	3.32149e11i		−	0.959734i
$768$			1.95166e11i			0.560996i
$769$	6.94275e10	−	6.94275e10i	0.198530	−	0.198530i	−0.600840	−	0.799370i	$-0.705167\pi$
$769$	6.94275e10	−	6.94275e10i	0.198530	−	0.198530i	0.799370	+	0.600840i	$0.205167\pi$
$770$			1.93649e11i			0.550873i
$771$	2.94293e11	−	2.94293e11i	0.832842	−	0.832842i
$772$	5.40868e11	−	5.40868e11i	1.52273	−	1.52273i
$773$	−3.62170e11			−1.01437			−0.507183	−	0.861839i	$-0.669313\pi$
$773$	−3.62170e11			−1.01437			−0.507183	+	0.861839i	$0.669313\pi$
$774$	−8.56434e11			−2.38633
$775$	−2.50361e11	−	2.50361e11i	−0.694000	−	0.694000i
$776$		−	1.07084e12i		−	2.95310i
$777$	1.93072e11	+	1.09829e11i	0.529707	+	0.301322i
$778$	−5.15727e11			−1.40767
$779$	6.56026e11	−	6.56026e11i	1.78144	−	1.78144i
$780$		−	6.70114e11i		−	1.81038i
$781$			3.19627e11i			0.859091i
$782$	−2.47142e11	−	2.47142e11i	−0.660876	−	0.660876i
$783$	−1.94947e10	−	1.94947e10i	−0.0518645	−	0.0518645i
$784$	8.45985e11			2.23923
$785$	2.54336e11	+	2.54336e11i	0.669775	+	0.669775i
$786$	−5.53622e10			−0.145052
$787$	4.31838e11			1.12570			0.562849	−	0.826560i	$-0.309705\pi$
$787$	4.31838e11			1.12570			0.562849	+	0.826560i	$0.309705\pi$
$788$			6.50121e11i			1.68612i
$789$	−2.58528e11			−0.667113
$790$	−1.69145e11	−	1.69145e11i	−0.434260	−	0.434260i
$791$	−2.18261e11	+	2.18261e11i	−0.557532	+	0.557532i
$792$	−1.17023e12	+	1.17023e12i	−2.97421	+	2.97421i
$793$	−2.31992e11			−0.586652
$794$	−1.58957e10	−	1.58957e10i	−0.0399942	−	0.0399942i
$795$	−4.30285e10	+	4.30285e10i	−0.107718	+	0.107718i
$796$	4.53624e11	+	4.53624e11i	1.12991	+	1.12991i
$797$	−2.44586e10	+	2.44586e10i	−0.0606176	+	0.0606176i	−0.736766	−	0.676148i	$-0.763648\pi$
$797$	−2.44586e10	+	2.44586e10i	−0.0606176	+	0.0606176i	0.676148	+	0.736766i	$0.263648\pi$
$798$			6.93577e11i			1.71034i
$799$	−1.33885e9	−	1.33885e9i	−0.00328507	−	0.00328507i
$800$	−4.86417e11	−	4.86417e11i	−1.18754	−	1.18754i
$801$	−5.17232e11	+	5.17232e11i	−1.25648	+	1.25648i
$802$			1.22637e12i			2.96432i
$803$	3.46576e11			0.833559
$804$		−	8.44556e11i		−	2.02118i
$805$		−	1.64198e11i		−	0.391006i
$806$	−7.22897e11	+	7.22897e11i	−1.71292	+	1.71292i
$807$		−	2.96655e11i		−	0.699452i
$808$	9.39299e10	−	9.39299e10i	0.220373	−	0.220373i
$809$	−3.07964e11	+	3.07964e11i	−0.718962	+	0.718962i	−0.968393	−	0.249431i	$-0.919756\pi$
$809$	−3.07964e11	+	3.07964e11i	−0.718962	+	0.718962i	0.249431	+	0.968393i	$0.419756\pi$
$810$	3.65137e11			0.848233
$811$	1.25639e11			0.290431			0.145215	−	0.989400i	$-0.453613\pi$
$811$	1.25639e11			0.290431			0.145215	+	0.989400i	$0.453613\pi$
$812$	1.48514e11	+	1.48514e11i	0.341620	+	0.341620i
$813$			8.12434e10i			0.185963i
$814$	−1.07591e12	+	2.95684e11i	−2.45064	+	0.673489i
$815$	−3.11997e10			−0.0707163
$816$	3.43087e11	−	3.43087e11i	0.773827	−	0.773827i
$817$		−	7.70326e11i		−	1.72896i
$818$		−	1.86411e11i		−	0.416349i
$819$	−1.43404e11	−	1.43404e11i	−0.318733	−	0.318733i
$820$	−6.90304e11	−	6.90304e11i	−1.52681	−	1.52681i
$821$	6.62905e11			1.45908			0.729540	−	0.683938i	$-0.239734\pi$
$821$	6.62905e11			1.45908			0.729540	+	0.683938i	$0.239734\pi$
$822$	−2.96261e11	−	2.96261e11i	−0.648915	−	0.648915i
$823$	1.14863e11			0.250369			0.125184	−	0.992134i	$-0.460048\pi$
$823$	1.14863e11			0.250369			0.125184	+	0.992134i	$0.460048\pi$
$824$	1.55619e12			3.37562
$825$			6.70884e11i			1.44821i
$826$	3.61741e11			0.777101
$827$	3.98235e11	+	3.98235e11i	0.851367	+	0.851367i	0.990302	−	0.138934i	$-0.0443677\pi$
$827$	3.98235e11	+	3.98235e11i	0.851367	+	0.851367i	−0.138934	+	0.990302i	$0.544368\pi$
$828$	1.65734e12	−	1.65734e12i	3.52607	−	3.52607i
$829$	−2.71211e11	+	2.71211e11i	−0.574234	+	0.574234i	−0.933309	−	0.359075i	$-0.883092\pi$
$829$	−2.71211e11	+	2.71211e11i	−0.574234	+	0.574234i	0.359075	+	0.933309i	$0.383092\pi$
$830$	−4.60927e11			−0.971225
$831$	−2.80308e11	−	2.80308e11i	−0.587801	−	0.587801i
$832$	−5.12758e11	+	5.12758e11i	−1.07009	+	1.07009i
$833$	7.77743e10	+	7.77743e10i	0.161531	+	0.161531i
$834$	1.76208e11	−	1.76208e11i	0.364219	−	0.364219i
$835$			5.00234e11i			1.02903i
$836$	−1.75809e12	−	1.75809e12i	−3.59928	−	3.59928i
$837$	7.37497e10	+	7.37497e10i	0.150265	+	0.150265i
$838$	−1.02928e12	+	1.02928e12i	−2.08718	+	2.08718i
$839$		−	5.53924e11i		−	1.11790i	−0.829202	−	0.558950i	$-0.811205\pi$
$839$		−	5.53924e11i		−	1.11790i	0.829202	−	0.558950i	$-0.188795\pi$
$840$	4.36943e11			0.877623
$841$			3.93452e11i			0.786517i
$842$			1.40269e12i			2.79071i
$843$	−3.96804e11	+	3.96804e11i	−0.785716	+	0.785716i
$844$			7.54821e11i			1.48756i
$845$	1.15881e10	−	1.15881e10i	0.0227293	−	0.0227293i
$846$	1.25814e10	−	1.25814e10i	0.0245611	−	0.0245611i
$847$	−1.83516e11			−0.356567
$848$	2.85369e11			0.551853
$849$	5.23011e9	+	5.23011e9i	0.0100665	+	0.0100665i
$850$		−	1.98286e11i		−	0.379854i
$851$	9.12283e11	−	2.50715e11i	1.73945	−	0.478038i
$852$	1.20460e12			2.28604
$853$	−5.56375e10	+	5.56375e10i	−0.105092	+	0.105092i	−0.757698	−	0.652605i	$-0.773676\pi$
$853$	−5.56375e10	+	5.56375e10i	−0.105092	+	0.105092i	0.652605	+	0.757698i	$0.273676\pi$
$854$		−	2.52661e11i		−	0.475014i
$855$		−	4.59909e11i		−	0.860611i
$856$	9.45237e11	+	9.45237e11i	1.76054	+	1.76054i
$857$	3.01352e11	+	3.01352e11i	0.558664	+	0.558664i	0.928927	−	0.370263i	$-0.120732\pi$
$857$	3.01352e11	+	3.01352e11i	0.558664	+	0.558664i	−0.370263	+	0.928927i	$0.620732\pi$
$858$	1.93713e12			3.57444
$859$	−5.75368e11	−	5.75368e11i	−1.05675	−	1.05675i	−0.998290	−	0.0584625i	$-0.981380\pi$
$859$	−5.75368e11	−	5.75368e11i	−1.05675	−	1.05675i	−0.0584625	−	0.998290i	$-0.518620\pi$
$860$	−8.10576e11			−1.48184
$861$	−5.61788e11			−1.02226
$862$		−	6.77801e10i		−	0.122765i
$863$	−3.16316e10			−0.0570267			−0.0285134	−	0.999593i	$-0.509077\pi$
$863$	−3.16316e10			−0.0570267			−0.0285134	+	0.999593i	$0.509077\pi$
$864$	1.43286e11	+	1.43286e11i	0.257127	+	0.257127i
$865$	3.53968e11	−	3.53968e11i	0.632266	−	0.632266i
$866$	1.39163e11	−	1.39163e11i	0.247431	−	0.247431i
$867$	−7.57545e11			−1.34070
$868$	−5.61838e11	−	5.61838e11i	−0.989765	−	0.989765i
$869$	3.48929e11	−	3.48929e11i	0.611868	−	0.611868i
$870$	−2.62400e11	−	2.62400e11i	−0.458023	−	0.458023i
$871$	−2.20093e11	+	2.20093e11i	−0.382415	+	0.382415i
$872$			6.72780e11i			1.16361i
$873$	4.82606e11	+	4.82606e11i	0.830874	+	0.830874i
$874$	2.08893e12	+	2.08893e12i	3.57996	+	3.57996i
$875$	1.55711e11	−	1.55711e11i	0.265636	−	0.265636i
$876$		−	1.30617e12i		−	2.21810i
$877$	−1.04398e12			−1.76480			−0.882399	−	0.470501i	$-0.844073\pi$
$877$	−1.04398e12			−1.76480			−0.882399	+	0.470501i	$0.844073\pi$
$878$		−	1.17583e12i		−	1.97863i
$879$		−	7.45732e11i		−	1.24919i
$880$	−8.09656e11	+	8.09656e11i	−1.35011	+	1.35011i
$881$		−	4.05150e11i		−	0.672532i	−0.941767	−	0.336266i	$-0.890836\pi$
$881$		−	4.05150e11i		−	0.672532i	0.941767	−	0.336266i	$-0.109164\pi$
$882$	−7.30856e11	+	7.30856e11i	−1.20770	+	1.20770i
$883$	8.14269e11	−	8.14269e11i	1.33945	−	1.33945i	0.442850	−	0.896596i	$-0.353968\pi$
$883$	8.14269e11	−	8.14269e11i	1.33945	−	1.33945i	0.896596	−	0.442850i	$-0.146032\pi$
$884$	−4.08576e11			−0.669058
$885$	−4.56103e11			−0.743516
$886$	9.53139e11	+	9.53139e11i	1.54675	+	1.54675i
$887$		−	1.65466e11i		−	0.267310i	−0.991028	−	0.133655i	$-0.957329\pi$
$887$		−	1.65466e11i		−	0.267310i	0.991028	−	0.133655i	$-0.0426714\pi$
$888$	6.67174e11	+	2.42766e12i	1.07297	+	3.90424i
$889$	1.27088e11			0.203468
$890$	−6.85987e11	+	6.85987e11i	−1.09334	+	1.09334i
$891$			7.53241e11i			1.19515i
$892$		−	4.20148e11i		−	0.663655i
$893$	1.13164e10	+	1.13164e10i	0.0177952	+	0.0177952i
$894$	−1.16450e12	−	1.16450e12i	−1.82301	−	1.82301i
$895$	−8.43879e10			−0.131519
$896$	−1.20394e11	−	1.20394e11i	−0.186799	−	0.186799i
$897$	−1.64252e12			−2.53712
$898$	−1.31559e12			−2.02309
$899$			4.04009e11i			0.618518i
$900$	1.32971e12			2.02669
$901$	2.62349e10	+	2.62349e10i	0.0398089	+	0.0398089i
$902$	1.99549e12	−	1.99549e12i	3.01455	−	3.01455i
$903$	−3.29834e11	+	3.29834e11i	−0.496072	+	0.496072i
$904$	−3.49859e12			−5.23865
$905$	2.54026e11	+	2.54026e11i	0.378691	+	0.378691i
$906$	2.06082e12	−	2.06082e12i	3.05863	−	3.05863i
$907$	−6.65068e11	−	6.65068e11i	−0.982736	−	0.982736i	0.0171170	−	0.999853i	$-0.494551\pi$
$907$	−6.65068e11	−	6.65068e11i	−0.982736	−	0.982736i	−0.999853	+	0.0171170i	$0.994551\pi$
$908$	1.29171e12	−	1.29171e12i	1.90030	−	1.90030i
$909$			8.46646e10i			0.124007i
$910$	−1.90192e11	−	1.90192e11i	−0.277349	−	0.277349i
$911$	4.38289e11	+	4.38289e11i	0.636337	+	0.636337i	0.949650	−	0.313313i	$-0.101439\pi$
$911$	4.38289e11	+	4.38289e11i	0.636337	+	0.636337i	−0.313313	+	0.949650i	$0.601439\pi$
$912$	−2.89988e12	+	2.89988e12i	−4.19181	+	4.19181i
$913$		−	9.50847e11i		−	1.36845i
$914$	−1.15396e12			−1.65351
$915$			3.18569e11i			0.454485i
$916$		−	8.35520e11i		−	1.18679i
$917$	−1.12131e10	+	1.12131e10i	−0.0158580	+	0.0158580i
$918$			5.84099e10i			0.0822462i
$919$	8.80670e11	−	8.80670e11i	1.23467	−	1.23467i	0.272521	−	0.962150i	$-0.412143\pi$
$919$	8.80670e11	−	8.80670e11i	1.23467	−	1.23467i	0.962150	−	0.272521i	$-0.0878573\pi$
$920$	1.31599e12	−	1.31599e12i	1.83697	−	1.83697i
$921$	4.15069e11			0.576875
$922$	1.43182e12			1.98136
$923$	−3.13922e11	−	3.13922e11i	−0.432529	−	0.432529i
$924$			1.50554e12i			2.06540i
$925$	4.66546e11	+	2.65393e11i	0.637276	+	0.362513i
$926$	−2.09121e12			−2.84416
$927$	−7.01344e11	+	7.01344e11i	−0.949756	+	0.949756i
$928$			7.84935e11i			1.05838i
$929$		−	5.33615e11i		−	0.716415i	−0.933642	−	0.358208i	$-0.883388\pi$
$929$		−	5.33615e11i		−	0.716415i	0.933642	−	0.358208i	$-0.116612\pi$
$930$	9.92675e11	+	9.92675e11i	1.32701	+	1.32701i
$931$	−6.57374e11	−	6.57374e11i	−0.875012	−	0.875012i
$932$	1.84191e12			2.44120
$933$	5.23778e11	+	5.23778e11i	0.691227	+	0.691227i
$934$	5.25386e11			0.690384
$935$	−1.48869e11			−0.194786
$936$		−	2.29869e12i		−	2.99486i
$937$	−1.91671e11			−0.248655			−0.124328	−	0.992241i	$-0.539677\pi$
$937$	−1.91671e11			−0.248655			−0.124328	+	0.992241i	$0.539677\pi$
$938$	−2.39702e11	−	2.39702e11i	−0.309643	−	0.309643i
$939$	−7.10409e11	+	7.10409e11i	−0.913789	+	0.913789i
$940$	1.19077e10	−	1.19077e10i	0.0152516	−	0.0152516i
$941$	1.90848e11			0.243405			0.121703	−	0.992567i	$-0.461165\pi$
$941$	1.90848e11			0.243405			0.121703	+	0.992567i	$0.461165\pi$
$942$	2.77087e12	+	2.77087e12i	3.51894	+	3.51894i
$943$	−1.69201e12	+	1.69201e12i	−2.13971	+	2.13971i
$944$	1.51246e12	+	1.51246e12i	1.90456	+	1.90456i
$945$	−1.94033e10	+	1.94033e10i	−0.0243304	+	0.0243304i
$946$		−	2.34316e12i		−	2.92576i
$947$	1.00197e12	+	1.00197e12i	1.24582	+	1.24582i	0.957550	+	0.288269i	$0.0930796\pi$
$947$	1.00197e12	+	1.00197e12i	1.24582	+	1.24582i	0.288269	+	0.957550i	$0.406920\pi$
$948$	−1.31503e12	−	1.31503e12i	−1.62818	−	1.62818i
$949$	−3.40390e11	+	3.40390e11i	−0.419674	+	0.419674i
$950$			1.67598e12i			2.05766i
$951$	7.45812e11			0.911816
$952$		−	2.66409e11i		−	0.324340i
$953$		−	8.14810e11i		−	0.987836i	−0.869509	−	0.493918i	$-0.835564\pi$
$953$		−	8.14810e11i		−	0.987836i	0.869509	−	0.493918i	$-0.164436\pi$
$954$	−2.46533e11	+	2.46533e11i	−0.297634	+	0.297634i
$955$		−	3.90722e11i		−	0.469737i
$956$	−8.70176e11	+	8.70176e11i	−1.04178	+	1.04178i
$957$	5.41305e11	−	5.41305e11i	0.645349	−	0.645349i
$958$	−2.34351e12			−2.78231
$959$	−1.20010e11			−0.141887
$960$	7.04114e11	+	7.04114e11i	0.829006	+	0.829006i
$961$		−	6.75499e11i		−	0.792011i
$962$	7.66303e11	−	1.34712e12i	0.894747	−	1.57291i
$963$	−8.51998e11			−0.990681
$964$	3.44289e10	−	3.44289e10i	0.0398671	−	0.0398671i
$965$			3.87106e11i			0.446397i
$966$		−	1.78885e12i		−	2.05431i
$967$	−4.53596e11	−	4.53596e11i	−0.518756	−	0.518756i	0.398439	−	0.917195i	$-0.369552\pi$
$967$	−4.53596e11	−	4.53596e11i	−0.518756	−	0.518756i	−0.917195	+	0.398439i	$0.869552\pi$
$968$	−1.47083e12	−	1.47083e12i	−1.67518	−	1.67518i
$969$	−5.33192e11			−0.604768
$970$	6.40062e11	+	6.40062e11i	0.722995	+	0.722995i
$971$	1.00326e11			0.112859			0.0564295	−	0.998407i	$-0.482028\pi$
$971$	1.00326e11			0.112859			0.0564295	+	0.998407i	$0.482028\pi$
$972$	3.19190e12			3.57589
$973$		−	7.13789e10i		−	0.0796377i
$974$	−3.46024e11			−0.384477
$975$	−6.58909e11	−	6.58909e11i	−0.729134	−	0.729134i
$976$	1.05639e12	−	1.05639e12i	1.16419	−	1.16419i
$977$	−4.04192e11	+	4.04192e11i	−0.443618	+	0.443618i	−0.893226	−	0.449608i	$-0.851564\pi$
$977$	−4.04192e11	+	4.04192e11i	−0.443618	+	0.443618i	0.449608	+	0.893226i	$0.351564\pi$
$978$	−3.39906e11			−0.371538
$979$	−1.41512e12	−	1.41512e12i	−1.54051	−	1.54051i
$980$	−6.91722e11	+	6.91722e11i	−0.749942	+	0.749942i
$981$	−3.03208e11	−	3.03208e11i	−0.327390	−	0.327390i
$982$	4.63839e11	−	4.63839e11i	0.498794	−	0.498794i
$983$		−	3.96691e11i		−	0.424853i	−0.977177	−	0.212426i	$-0.931863\pi$
$983$		−	3.96691e11i		−	0.424853i	0.977177	−	0.212426i	$-0.0681365\pi$
$984$	−4.50257e12	−	4.50257e12i	−4.80264	−	4.80264i
$985$	−2.32650e11	−	2.32650e11i	−0.247149	−	0.247149i
$986$	−1.59988e11	+	1.59988e11i	−0.169270	+	0.169270i
$987$		−	9.69082e9i		−	0.0102116i
$988$	3.45342e12			3.62428
$989$			1.98680e12i			2.07668i
$990$		−	1.39894e12i		−	1.45633i
$991$	7.62537e11	−	7.62537e11i	0.790617	−	0.790617i	−0.190977	−	0.981594i	$-0.561166\pi$
$991$	7.62537e11	−	7.62537e11i	0.790617	−	0.790617i	0.981594	+	0.190977i	$0.0611656\pi$
$992$		−	2.96946e12i		−	3.06641i
$993$	9.46010e11	−	9.46010e11i	0.972968	−	0.972968i
$994$	3.41890e11	−	3.41890e11i	0.350220	−	0.350220i
$995$	−3.24665e11			−0.331240
$996$	−3.58352e12			−3.64144
$997$	2.51946e11	+	2.51946e11i	0.254992	+	0.254992i	0.823014	−	0.568022i	$-0.192291\pi$
$997$	2.51946e11	+	2.51946e11i	0.254992	+	0.254992i	−0.568022	+	0.823014i	$0.692291\pi$
$998$			3.02865e12i			3.05300i
$999$	−1.37432e11	−	7.81780e10i	−0.137983	−	0.0784915i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.9.d.a.6.1	✓	50
37.31	odd	4	inner	37.9.d.a.31.1	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.9.d.a.6.1	✓	50	1.1	even	1	trivial
37.9.d.a.31.1	yes	50	37.31	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	37.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-21.1416 + 21.1416i) q^{2} -117.640i q^{3} -637.931i q^{4} +(228.288 + 228.288i) q^{5} +(2487.09 + 2487.09i) q^{6} +1007.48 q^{7} +(8074.63 + 8074.63i) q^{8} -7278.14 q^{9} +O(q^{10})\)	\(q+(-21.1416 + 21.1416i) q^{2} -117.640i q^{3} -637.931i q^{4} +(228.288 + 228.288i) q^{5} +(2487.09 + 2487.09i) q^{6} +1007.48 q^{7} +(8074.63 + 8074.63i) q^{8} -7278.14 q^{9} -9652.73 q^{10} -19912.6i q^{11} -75046.2 q^{12} +(19557.2 + 19557.2i) q^{13} +(-21299.6 + 21299.6i) q^{14} +(26855.8 - 26855.8i) q^{15} -178110. q^{16} +(-16374.2 - 16374.2i) q^{17} +(153871. - 153871. i) q^{18} +(138401. + 138401. i) q^{19} +(145632. - 145632. i) q^{20} -118519. i q^{21} +(420984. + 420984. i) q^{22} +(-356959. - 356959. i) q^{23} +(949898. - 949898. i) q^{24} -286394. i q^{25} -826940. q^{26} +84364.2i q^{27} -642701. i q^{28} +(-231078. + 231078. i) q^{29} +1.13555e6i q^{30} +(874183. - 874183. i) q^{31} +(1.69842e6 - 1.69842e6i) q^{32} -2.34252e6 q^{33} +692354. q^{34} +(229995. + 229995. i) q^{35} +4.64295e6i q^{36} +(-926672. + 1.62904e6i) q^{37} -5.85201e6 q^{38} +(2.30071e6 - 2.30071e6i) q^{39} +3.68668e6i q^{40} -4.74005e6i q^{41} +(2.50569e6 + 2.50569e6i) q^{42} +(-2.78296e6 - 2.78296e6i) q^{43} -1.27029e7 q^{44} +(-1.66151e6 - 1.66151e6i) q^{45} +1.50933e7 q^{46} +81765.7 q^{47} +2.09528e7i q^{48} -4.74979e6 q^{49} +(6.05482e6 + 6.05482e6i) q^{50} +(-1.92626e6 + 1.92626e6i) q^{51} +(1.24762e7 - 1.24762e7i) q^{52} -1.60221e6 q^{53} +(-1.78359e6 - 1.78359e6i) q^{54} +(4.54582e6 - 4.54582e6i) q^{55} +(8.13500e6 + 8.13500e6i) q^{56} +(1.62814e7 - 1.62814e7i) q^{57} -9.77071e6i q^{58} +(-8.49171e6 - 8.49171e6i) q^{59} +(-1.71321e7 - 1.71321e7i) q^{60} +(-5.93111e6 + 5.93111e6i) q^{61} +3.69632e7i q^{62} -7.33256e6 q^{63} +2.62183e7i q^{64} +8.92936e6i q^{65} +(4.95246e7 - 4.95246e7i) q^{66} +1.12538e7i q^{67} +(-1.04456e7 + 1.04456e7i) q^{68} +(-4.19926e7 + 4.19926e7i) q^{69} -9.72490e6 q^{70} -1.60515e7 q^{71} +(-5.87683e7 - 5.87683e7i) q^{72} +1.74048e7i q^{73} +(-1.48491e7 - 5.40317e7i) q^{74} -3.36914e7 q^{75} +(8.82901e7 - 8.82901e7i) q^{76} -2.00615e7i q^{77} +9.72812e7i q^{78} +(1.75230e7 + 1.75230e7i) q^{79} +(-4.06604e7 - 4.06604e7i) q^{80} -3.78273e7 q^{81} +(1.00212e8 + 1.00212e8i) q^{82} +4.77509e7 q^{83} -7.56073e7 q^{84} -7.47609e6i q^{85} +1.17672e8 q^{86} +(2.71840e7 + 2.71840e7i) q^{87} +(1.60787e8 - 1.60787e8i) q^{88} +(7.10666e7 - 7.10666e7i) q^{89} +7.02540e7 q^{90} +(1.97034e7 + 1.97034e7i) q^{91} +(-2.27715e8 + 2.27715e8i) q^{92} +(-1.02839e8 - 1.02839e8i) q^{93} +(-1.72865e6 + 1.72865e6i) q^{94} +6.31904e7i q^{95} +(-1.99802e8 - 1.99802e8i) q^{96} +(-6.63089e7 - 6.63089e7i) q^{97} +(1.00418e8 - 1.00418e8i) q^{98} +1.44927e8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 4 q^{2} + 124 q^{5} + 510 q^{6} - 4 q^{7} - 5256 q^{8} - 93534 q^{9}+O(q^{10}) \) 50 * q + 4 * q^2 + 124 * q^5 + 510 * q^6 - 4 * q^7 - 5256 * q^8 - 93534 * q^9	\( 50 q + 4 q^{2} + 124 q^{5} + 510 q^{6} - 4 q^{7} - 5256 q^{8} - 93534 q^{9} - 10756 q^{10} - 45440 q^{12} + 63592 q^{13} - 80206 q^{14} - 124346 q^{15} - 639128 q^{16} - 178796 q^{17} - 45882 q^{18} + 264774 q^{19} + 469204 q^{20} + 714574 q^{22} - 654272 q^{23} - 1573644 q^{24} + 1841660 q^{26} - 1683686 q^{29} + 1766336 q^{31} - 4332632 q^{32} - 1438888 q^{33} - 5838452 q^{34} - 650482 q^{35} - 2870078 q^{37} - 2281528 q^{38} + 11036546 q^{39} - 7453902 q^{42} + 5097830 q^{43} - 14992464 q^{44} - 15078446 q^{45} + 28776464 q^{46} + 13992320 q^{47} + 4370314 q^{49} + 7603288 q^{50} + 19417938 q^{51} + 54318452 q^{52} + 28075952 q^{53} - 19197122 q^{54} - 6104306 q^{55} + 47803128 q^{56} + 17462426 q^{57} - 677072 q^{59} + 24953316 q^{60} + 4206386 q^{61} - 18098032 q^{63} - 56061730 q^{66} - 52579760 q^{68} + 88118984 q^{69} - 295493636 q^{70} - 37172476 q^{71} - 74582504 q^{72} - 224754524 q^{74} - 144364996 q^{75} + 189294548 q^{76} + 271163438 q^{79} - 312998084 q^{80} + 41535626 q^{81} - 177494710 q^{82} - 74250268 q^{83} - 82088924 q^{84} + 112964036 q^{86} - 142771908 q^{87} + 224951860 q^{88} + 84928780 q^{89} + 716592116 q^{90} - 40969098 q^{91} - 701292428 q^{92} - 83761576 q^{93} + 553881406 q^{94} - 7259376 q^{96} + 467792674 q^{97} + 538649310 q^{98}+O(q^{100}) \) 50 * q + 4 * q^2 + 124 * q^5 + 510 * q^6 - 4 * q^7 - 5256 * q^8 - 93534 * q^9 - 10756 * q^10 - 45440 * q^12 + 63592 * q^13 - 80206 * q^14 - 124346 * q^15 - 639128 * q^16 - 178796 * q^17 - 45882 * q^18 + 264774 * q^19 + 469204 * q^20 + 714574 * q^22 - 654272 * q^23 - 1573644 * q^24 + 1841660 * q^26 - 1683686 * q^29 + 1766336 * q^31 - 4332632 * q^32 - 1438888 * q^33 - 5838452 * q^34 - 650482 * q^35 - 2870078 * q^37 - 2281528 * q^38 + 11036546 * q^39 - 7453902 * q^42 + 5097830 * q^43 - 14992464 * q^44 - 15078446 * q^45 + 28776464 * q^46 + 13992320 * q^47 + 4370314 * q^49 + 7603288 * q^50 + 19417938 * q^51 + 54318452 * q^52 + 28075952 * q^53 - 19197122 * q^54 - 6104306 * q^55 + 47803128 * q^56 + 17462426 * q^57 - 677072 * q^59 + 24953316 * q^60 + 4206386 * q^61 - 18098032 * q^63 - 56061730 * q^66 - 52579760 * q^68 + 88118984 * q^69 - 295493636 * q^70 - 37172476 * q^71 - 74582504 * q^72 - 224754524 * q^74 - 144364996 * q^75 + 189294548 * q^76 + 271163438 * q^79 - 312998084 * q^80 + 41535626 * q^81 - 177494710 * q^82 - 74250268 * q^83 - 82088924 * q^84 + 112964036 * q^86 - 142771908 * q^87 + 224951860 * q^88 + 84928780 * q^89 + 716592116 * q^90 - 40969098 * q^91 - 701292428 * q^92 - 83761576 * q^93 + 553881406 * q^94 - 7259376 * q^96 + 467792674 * q^97 + 538649310 * q^98

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