LMFDB - Embedded newform 74.8.c.b.47.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,8,Mod(47,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, 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("74.47");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	74.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:	$23.1164918858$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			47.1
Character	$\chi$	$=$	74.47
Dual form			74.8.c.b.63.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.00000 - 6.92820i) q^{2} +(-42.3772 - 73.3994i) q^{3} +(-32.0000 - 55.4256i) q^{4} +(46.6582 + 80.8144i) q^{5} -678.035 q^{6} +(-404.125 - 699.965i) q^{7} -512.000 q^{8} +(-2498.15 + 4326.92i) q^{9} +O(q^{10})$	\(q+(4.00000 - 6.92820i) q^{2} +(-42.3772 - 73.3994i) q^{3} +(-32.0000 - 55.4256i) q^{4} +(46.6582 + 80.8144i) q^{5} -678.035 q^{6} +(-404.125 - 699.965i) q^{7} -512.000 q^{8} +(-2498.15 + 4326.92i) q^{9} +746.531 q^{10} -991.685 q^{11} +(-2712.14 + 4697.56i) q^{12} +(418.305 + 724.525i) q^{13} -6466.00 q^{14} +(3954.49 - 6849.37i) q^{15} +(-2048.00 + 3547.24i) q^{16} +(-16340.2 + 28302.1i) q^{17} +(19985.2 + 34615.4i) q^{18} +(-26727.5 - 46293.4i) q^{19} +(2986.13 - 5172.12i) q^{20} +(-34251.4 + 59325.1i) q^{21} +(-3966.74 + 6870.59i) q^{22} +91623.6 q^{23} +(21697.1 + 37580.5i) q^{24} +(34708.5 - 60116.9i) q^{25} +6692.87 q^{26} +238100. q^{27} +(-25864.0 + 44797.8i) q^{28} +129930. q^{29} +(-31635.9 - 54795.0i) q^{30} +4834.74 q^{31} +(16384.0 + 28377.9i) q^{32} +(42024.8 + 72789.1i) q^{33} +(130722. + 226417. i) q^{34} +(37711.5 - 65318.3i) q^{35} +319763. q^{36} +(-252512. + 176549. i) q^{37} -427640. q^{38} +(35453.1 - 61406.6i) q^{39} +(-23889.0 - 41377.0i) q^{40} +(99117.8 + 171677. i) q^{41} +(274011. + 474601. i) q^{42} -537088. q^{43} +(31733.9 + 54964.7i) q^{44} -466237. q^{45} +(366495. - 634787. i) q^{46} -476890. q^{47} +347154. q^{48} +(85137.2 - 147462. i) q^{49} +(-277668. - 480935. i) q^{50} +2.76981e6 q^{51} +(26771.5 - 46369.6i) q^{52} +(-499325. + 864856. i) q^{53} +(952401. - 1.64961e6i) q^{54} +(-46270.2 - 80142.4i) q^{55} +(206912. + 358382. i) q^{56} +(-2.26527e6 + 3.92357e6i) q^{57} +(519722. - 900184. i) q^{58} +(-1.27869e6 + 2.21476e6i) q^{59} -506174. q^{60} +(120915. + 209430. i) q^{61} +(19339.0 - 33496.1i) q^{62} +4.03826e6 q^{63} +262144. q^{64} +(-39034.7 + 67610.1i) q^{65} +672397. q^{66} +(-982266. - 1.70133e6i) q^{67} +2.09155e6 q^{68} +(-3.88275e6 - 6.72512e6i) q^{69} +(-301692. - 522546. i) q^{70} +(-408757. - 707988. i) q^{71} +(1.27905e6 - 2.21538e6i) q^{72} -108352. q^{73} +(213119. + 2.45565e6i) q^{74} -5.88340e6 q^{75} +(-1.71056e6 + 2.96278e6i) q^{76} +(400765. + 694145. i) q^{77} +(-283625. - 491253. i) q^{78} +(2.33583e6 + 4.04577e6i) q^{79} -382224. q^{80} +(-4.62656e6 - 8.01343e6i) q^{81} +1.58588e6 q^{82} +(-2.59233e6 + 4.49005e6i) q^{83} +4.38417e6 q^{84} -3.04962e6 q^{85} +(-2.14835e6 + 3.72105e6i) q^{86} +(-5.50608e6 - 9.53682e6i) q^{87} +507743. q^{88} +(-838747. + 1.45275e6i) q^{89} +(-1.86495e6 + 3.23018e6i) q^{90} +(338095. - 585598. i) q^{91} +(-2.93196e6 - 5.07830e6i) q^{92} +(-204883. - 354867. i) q^{93} +(-1.90756e6 + 3.30399e6i) q^{94} +(2.49412e6 - 4.31994e6i) q^{95} +(1.38862e6 - 2.40515e6i) q^{96} -7.12045e6 q^{97} +(-681097. - 1.17970e6i) q^{98} +(2.47738e6 - 4.29094e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 96 q^{2} + 40 q^{3} - 768 q^{4} - 136 q^{5} + 640 q^{6} + 536 q^{7} - 12288 q^{8} - 12014 q^{9}+O(q^{10}) $ 24 * q + 96 * q^2 + 40 * q^3 - 768 * q^4 - 136 * q^5 + 640 * q^6 + 536 * q^7 - 12288 * q^8 - 12014 * q^9	\( 24 q + 96 q^{2} + 40 q^{3} - 768 q^{4} - 136 q^{5} + 640 q^{6} + 536 q^{7} - 12288 q^{8} - 12014 q^{9} - 2176 q^{10} - 3448 q^{11} + 2560 q^{12} + 186 q^{13} + 8576 q^{14} + 10628 q^{15} - 49152 q^{16} - 1212 q^{17} + 96112 q^{18} + 15980 q^{19} - 8704 q^{20} + 6994 q^{21} - 13792 q^{22} - 62464 q^{23} - 20480 q^{24} - 48368 q^{25} + 2976 q^{26} - 323648 q^{27} + 34304 q^{28} + 200084 q^{29} - 85024 q^{30} + 609672 q^{31} + 393216 q^{32} + 131560 q^{33} + 9696 q^{34} + 43132 q^{35} + 1537792 q^{36} - 557790 q^{37} + 255680 q^{38} - 694460 q^{39} + 69632 q^{40} + 377724 q^{41} - 55952 q^{42} - 304456 q^{43} + 110336 q^{44} + 3686244 q^{45} - 249856 q^{46} - 2156696 q^{47} - 327680 q^{48} - 2929078 q^{49} + 386944 q^{50} + 968912 q^{51} + 11904 q^{52} + 2071746 q^{53} - 1294592 q^{54} - 2492580 q^{55} - 274432 q^{56} - 1669714 q^{57} + 800336 q^{58} + 479512 q^{59} - 1360384 q^{60} + 6713104 q^{61} + 2438688 q^{62} - 7785864 q^{63} + 6291456 q^{64} + 6788906 q^{65} + 2104960 q^{66} + 1823780 q^{67} + 155136 q^{68} - 3604080 q^{69} - 345056 q^{70} - 3510960 q^{71} + 6151168 q^{72} - 27590128 q^{73} + 5276496 q^{74} - 16709392 q^{75} + 1022720 q^{76} - 65144 q^{77} + 5555680 q^{78} + 1130192 q^{79} + 1114112 q^{80} - 10442988 q^{81} + 6043584 q^{82} - 3888560 q^{83} - 895232 q^{84} + 8161728 q^{85} - 1217824 q^{86} - 17683256 q^{87} + 1765376 q^{88} - 14427556 q^{89} + 14744976 q^{90} + 3386000 q^{91} + 1998848 q^{92} - 20025152 q^{93} - 8626784 q^{94} + 21486568 q^{95} - 1310720 q^{96} - 11913436 q^{97} + 23432624 q^{98} + 16388620 q^{99}+O(q^{100}) \) 24 * q + 96 * q^2 + 40 * q^3 - 768 * q^4 - 136 * q^5 + 640 * q^6 + 536 * q^7 - 12288 * q^8 - 12014 * q^9 - 2176 * q^10 - 3448 * q^11 + 2560 * q^12 + 186 * q^13 + 8576 * q^14 + 10628 * q^15 - 49152 * q^16 - 1212 * q^17 + 96112 * q^18 + 15980 * q^19 - 8704 * q^20 + 6994 * q^21 - 13792 * q^22 - 62464 * q^23 - 20480 * q^24 - 48368 * q^25 + 2976 * q^26 - 323648 * q^27 + 34304 * q^28 + 200084 * q^29 - 85024 * q^30 + 609672 * q^31 + 393216 * q^32 + 131560 * q^33 + 9696 * q^34 + 43132 * q^35 + 1537792 * q^36 - 557790 * q^37 + 255680 * q^38 - 694460 * q^39 + 69632 * q^40 + 377724 * q^41 - 55952 * q^42 - 304456 * q^43 + 110336 * q^44 + 3686244 * q^45 - 249856 * q^46 - 2156696 * q^47 - 327680 * q^48 - 2929078 * q^49 + 386944 * q^50 + 968912 * q^51 + 11904 * q^52 + 2071746 * q^53 - 1294592 * q^54 - 2492580 * q^55 - 274432 * q^56 - 1669714 * q^57 + 800336 * q^58 + 479512 * q^59 - 1360384 * q^60 + 6713104 * q^61 + 2438688 * q^62 - 7785864 * q^63 + 6291456 * q^64 + 6788906 * q^65 + 2104960 * q^66 + 1823780 * q^67 + 155136 * q^68 - 3604080 * q^69 - 345056 * q^70 - 3510960 * q^71 + 6151168 * q^72 - 27590128 * q^73 + 5276496 * q^74 - 16709392 * q^75 + 1022720 * q^76 - 65144 * q^77 + 5555680 * q^78 + 1130192 * q^79 + 1114112 * q^80 - 10442988 * q^81 + 6043584 * q^82 - 3888560 * q^83 - 895232 * q^84 + 8161728 * q^85 - 1217824 * q^86 - 17683256 * q^87 + 1765376 * q^88 - 14427556 * q^89 + 14744976 * q^90 + 3386000 * q^91 + 1998848 * q^92 - 20025152 * q^93 - 8626784 * q^94 + 21486568 * q^95 - 1310720 * q^96 - 11913436 * q^97 + 23432624 * q^98 + 16388620 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	4.00000	−	6.92820i	0.353553	−	0.612372i
$2$	4.00000	−	6.92820i	0.353553	−	0.612372i
$3$	−42.3772	−	73.3994i	−0.906166	−	1.56952i	−0.819345	−	0.573301i	$-0.805663\pi$
$3$	−42.3772	−	73.3994i	−0.906166	−	1.56952i	−0.0868205	−	0.996224i	$-0.527671\pi$
$4$	−32.0000	−	55.4256i	−0.250000	−	0.433013i
$5$	46.6582	+	80.8144i	0.166930	+	0.289130i	0.937339	−	0.348419i	$-0.113281\pi$
$5$	46.6582	+	80.8144i	0.166930	+	0.289130i	−0.770409	+	0.637550i	$0.779948\pi$
$6$	−678.035			−1.28151
$7$	−404.125	−	699.965i	−0.445321	−	0.771318i	0.552754	−	0.833345i	$-0.313577\pi$
$7$	−404.125	−	699.965i	−0.445321	−	0.771318i	−0.998074	+	0.0620266i	$0.980244\pi$
$8$	−512.000			−0.353553
$9$	−2498.15	+	4326.92i	−1.14227	+	1.97847i
$10$	746.531			0.236074
$11$	−991.685			−0.224646			−0.112323	−	0.993672i	$-0.535829\pi$
$11$	−991.685			−0.224646			−0.112323	+	0.993672i	$0.535829\pi$
$12$	−2712.14	+	4697.56i	−0.453083	+	0.784762i
$13$	418.305	+	724.525i	0.0528069	+	0.0914643i	0.891221	−	0.453570i	$-0.149850\pi$
$13$	418.305	+	724.525i	0.0528069	+	0.0914643i	−0.838414	+	0.545035i	$0.816517\pi$
$14$	−6466.00			−0.629778
$15$	3954.49	−	6849.37i	0.302532	−	0.524000i
$16$	−2048.00	+	3547.24i	−0.125000	+	0.216506i
$17$	−16340.2	+	28302.1i	−0.806652	+	1.39716i	0.108518	+	0.994095i	$0.465390\pi$
$17$	−16340.2	+	28302.1i	−0.806652	+	1.39716i	−0.915170	+	0.403068i	$0.867944\pi$
$18$	19985.2	+	34615.4i	0.807708	+	1.39899i
$19$	−26727.5	−	46293.4i	−0.893966	−	1.54839i	−0.835079	−	0.550130i	$-0.814578\pi$
$19$	−26727.5	−	46293.4i	−0.893966	−	1.54839i	−0.0588867	−	0.998265i	$-0.518755\pi$
$20$	2986.13	−	5172.12i	0.0834648	−	0.144565i
$21$	−34251.4	+	59325.1i	−0.807068	+	1.39788i
$22$	−3966.74	+	6870.59i	−0.0794245	+	0.137567i
$23$	91623.6			1.57022			0.785109	−	0.619357i	$-0.212607\pi$
$23$	91623.6			1.57022			0.785109	+	0.619357i	$0.212607\pi$
$24$	21697.1	+	37580.5i	0.320378	+	0.554911i
$25$	34708.5	−	60116.9i	0.444269	−	0.769497i
$26$	6692.87			0.0746803
$27$	238100.			2.32802
$28$	−25864.0	+	44797.8i	−0.222660	+	0.385659i
$29$	129930.			0.989277			0.494638	−	0.869099i	$-0.335300\pi$
$29$	129930.			0.989277			0.494638	+	0.869099i	$0.335300\pi$
$30$	−31635.9	−	54795.0i	−0.213922	−	0.370524i
$31$	4834.74			0.0291479			0.0145740	−	0.999894i	$-0.495361\pi$
$31$	4834.74			0.0291479			0.0145740	+	0.999894i	$0.495361\pi$
$32$	16384.0	+	28377.9i	0.0883883	+	0.153093i
$33$	42024.8	+	72789.1i	0.203567	+	0.352588i
$34$	130722.	+	226417.i	0.570389	+	0.987943i
$35$	37711.5	−	65318.3i	0.148674	−	0.257511i
$36$	319763.			1.14227
$37$	−252512.	+	176549.i	−0.819551	+	0.573006i
$37$	−252512.	+	176549.i	−0.819551	+	0.573006i
$38$	−427640.			−1.26426
$39$	35453.1	−	61406.6i	0.0957037	−	0.165764i
$40$	−23889.0	−	41377.0i	−0.0590185	−	0.102223i
$41$	99117.8	+	171677.i	0.224599	+	0.389017i	0.956199	−	0.292717i	$-0.0945594\pi$
$41$	99117.8	+	171677.i	0.224599	+	0.389017i	−0.731600	+	0.681734i	$0.761226\pi$
$42$	274011.	+	474601.i	0.570684	+	0.988453i
$43$	−537088.			−1.03016			−0.515081	−	0.857141i	$-0.672238\pi$
$43$	−537088.			−1.03016			−0.515081	+	0.857141i	$0.672238\pi$
$44$	31733.9	+	54964.7i	0.0561616	+	0.0972747i
$45$	−466237.			−0.762716
$46$	366495.	−	634787.i	0.555156	−	0.961559i
$47$	−476890.			−0.670001			−0.335001	−	0.942218i	$-0.608737\pi$
$47$	−476890.			−0.670001			−0.335001	+	0.942218i	$0.608737\pi$
$48$	347154.			0.453083
$49$	85137.2	−	147462.i	0.103379	−	0.179058i
$50$	−277668.	−	480935.i	−0.314146	−	0.544116i
$51$	2.76981e6			2.92384
$52$	26771.5	−	46369.6i	0.0264035	−	0.0457321i
$53$	−499325.	+	864856.i	−0.460699	+	0.797955i	−0.998996	−	0.0448009i	$-0.985735\pi$
$53$	−499325.	+	864856.i	−0.460699	+	0.797955i	0.538297	+	0.842755i	$0.319068\pi$
$54$	952401.	−	1.64961e6i	0.823079	−	1.42561i
$55$	−46270.2	−	80142.4i	−0.0375001	−	0.0649521i
$56$	206912.	+	358382.i	0.157445	+	0.272702i
$57$	−2.26527e6	+	3.92357e6i	−1.62016	+	2.80620i
$58$	519722.	−	900184.i	0.349762	−	0.605806i
$59$	−1.27869e6	+	2.21476e6i	−0.810558	+	1.40393i	0.101916	+	0.994793i	$0.467503\pi$
$59$	−1.27869e6	+	2.21476e6i	−0.810558	+	1.40393i	−0.912474	+	0.409135i	$0.865831\pi$
$60$	−506174.			−0.302532
$61$	120915.	+	209430.i	0.0682063	+	0.118137i	0.898112	−	0.439767i	$-0.144939\pi$
$61$	120915.	+	209430.i	0.0682063	+	0.118137i	−0.829905	+	0.557904i	$0.811606\pi$
$62$	19339.0	−	33496.1i	0.0103053	−	0.0178494i
$63$	4.03826e6			2.03471
$64$	262144.			0.125000
$65$	−39034.7	+	67610.1i	−0.0176301	+	0.0305362i
$66$	672397.			0.287887
$67$	−982266.	−	1.70133e6i	−0.398995	−	0.691079i	0.594607	−	0.804016i	$-0.297308\pi$
$67$	−982266.	−	1.70133e6i	−0.398995	−	0.691079i	−0.993602	+	0.112937i	$0.963974\pi$
$68$	2.09155e6			0.806652
$69$	−3.88275e6	−	6.72512e6i	−1.42288	−	2.46450i
$70$	−301692.	−	522546.i	−0.105129	−	0.182088i
$71$	−408757.	−	707988.i	−0.135538	−	0.234759i	0.790265	−	0.612765i	$-0.209943\pi$
$71$	−408757.	−	707988.i	−0.135538	−	0.234759i	−0.925803	+	0.378007i	$0.876610\pi$
$72$	1.27905e6	−	2.21538e6i	0.403854	−	0.699496i
$73$	−108352.			−0.0325991			−0.0162996	−	0.999867i	$-0.505189\pi$
$73$	−108352.			−0.0325991			−0.0162996	+	0.999867i	$0.505189\pi$
$74$	213119.	+	2.45565e6i	0.0611380	+	0.704459i
$75$	−5.88340e6			−1.61033
$76$	−1.71056e6	+	2.96278e6i	−0.446983	+	0.774197i
$77$	400765.	+	694145.i	0.100040	+	0.173274i
$78$	−283625.	−	491253.i	−0.0676727	−	0.117213i
$79$	2.33583e6	+	4.04577e6i	0.533023	+	0.923223i	0.999256	+	0.0385613i	$0.0122775\pi$
$79$	2.33583e6	+	4.04577e6i	0.533023	+	0.923223i	−0.466233	+	0.884662i	$0.654389\pi$
$80$	−382224.			−0.0834648
$81$	−4.62656e6	−	8.01343e6i	−0.967299	−	1.67541i
$82$	1.58588e6			0.317631
$83$	−2.59233e6	+	4.49005e6i	−0.497642	+	0.861941i	−0.999996	−	0.00272089i	$-0.999134\pi$
$83$	−2.59233e6	+	4.49005e6i	−0.497642	+	0.861941i	0.502355	+	0.864662i	$0.332467\pi$
$84$	4.38417e6			0.807068
$85$	−3.04962e6			−0.538616
$86$	−2.14835e6	+	3.72105e6i	−0.364218	+	0.630843i
$87$	−5.50608e6	−	9.53682e6i	−0.896449	−	1.55269i
$88$	507743.			0.0794245
$89$	−838747.	+	1.45275e6i	−0.126115	+	0.218437i	−0.922168	−	0.386789i	$-0.873584\pi$
$89$	−838747.	+	1.45275e6i	−0.126115	+	0.218437i	0.796053	+	0.605226i	$0.206917\pi$
$90$	−1.86495e6	+	3.23018e6i	−0.269661	+	0.467066i
$91$	338095.	−	585598.i	0.0470320	−	0.0814619i
$92$	−2.93196e6	−	5.07830e6i	−0.392555	−	0.679925i
$93$	−204883.	−	354867.i	−0.0264128	−	0.0457484i
$94$	−1.90756e6	+	3.30399e6i	−0.236881	+	0.410290i
$95$	2.49412e6	−	4.31994e6i	0.298459	−	0.516945i
$96$	1.38862e6	−	2.40515e6i	0.160189	−	0.277455i
$97$	−7.12045e6			−0.792148			−0.396074	−	0.918218i	$-0.629628\pi$
$97$	−7.12045e6			−0.792148			−0.396074	+	0.918218i	$0.629628\pi$
$98$	−681097.	−	1.17970e6i	−0.0731001	−	0.126613i
$99$	2.47738e6	−	4.29094e6i	0.256607	−	0.444457i
$100$	−4.44269e6			−0.444269
$101$	−4.61773e6			−0.445968			−0.222984	−	0.974822i	$-0.571580\pi$
$101$	−4.61773e6			−0.445968			−0.222984	+	0.974822i	$0.571580\pi$
$102$	1.10792e7	−	1.91898e7i	1.03373	−	1.79048i
$103$	9.06950e6			0.817811			0.408906	−	0.912577i	$-0.365910\pi$
$103$	9.06950e6			0.817811			0.408906	+	0.912577i	$0.365910\pi$
$104$	−214172.	−	370957.i	−0.0186701	−	0.0323375i
$105$	−6.39243e6			−0.538894
$106$	3.99460e6	+	6.91885e6i	0.325764	+	0.564239i
$107$	−6.76194e6	−	1.17120e7i	−0.533615	−	0.924248i	−0.999229	−	0.0392602i	$-0.987500\pi$
$107$	−6.76194e6	−	1.17120e7i	−0.533615	−	0.924248i	0.465614	−	0.884988i	$-0.345833\pi$
$108$	−7.61920e6	−	1.31968e7i	−0.582005	−	1.00806i
$109$	−1.31258e6	+	2.27346e6i	−0.0970807	+	0.168149i	−0.910475	−	0.413564i	$-0.864284\pi$
$109$	−1.31258e6	+	2.27346e6i	−0.0970807	+	0.168149i	0.813394	+	0.581713i	$0.197617\pi$
$110$	−740324.			−0.0530331
$111$	2.36593e7	+	1.10526e7i	1.64200	+	0.767067i
$112$	3.31059e6			0.222660
$113$	−8.03611e6	+	1.39189e7i	−0.523927	+	0.907469i	0.475685	+	0.879616i	$0.342200\pi$
$113$	−8.03611e6	+	1.39189e7i	−0.523927	+	0.907469i	−0.999612	+	0.0278530i	$0.991133\pi$
$114$	1.81222e7	+	3.13885e7i	1.14563	+	1.98429i
$115$	4.27500e6	+	7.40451e6i	0.262116	+	0.453998i
$116$	−4.15777e6	−	7.20147e6i	−0.247319	−	0.428369i
$117$	−4.17995e6			−0.241280
$118$	1.02295e7	+	1.77181e7i	0.573151	+	0.992727i
$119$	2.64140e7			1.43688
$120$	−2.02470e6	+	3.50688e6i	−0.106961	+	0.185262i
$121$	−1.85037e7			−0.949534
$122$	1.93464e6			0.0964583
$123$	8.40066e6	−	1.45504e7i	0.407048	−	0.705028i
$124$	−154712.	−	267969.i	−0.00728698	−	0.0126214i
$125$	1.37681e7			0.630506
$126$	1.61530e7	−	2.79779e7i	0.719378	−	1.24600i
$127$	2.12379e7	−	3.67851e7i	0.920021	−	1.59352i	0.120642	−	0.992696i	$-0.461505\pi$
$127$	2.12379e7	−	3.67851e7i	0.920021	−	1.59352i	0.799379	−	0.600827i	$-0.205162\pi$
$128$	1.04858e6	−	1.81619e6i	0.0441942	−	0.0765466i
$129$	2.27603e7	+	3.94219e7i	0.933498	+	1.61687i
$130$	312278.	+	540881.i	0.0124663	+	0.0215923i
$131$	−2.28564e7	+	3.95884e7i	−0.888297	+	1.53858i	−0.0464091	+	0.998923i	$0.514778\pi$
$131$	−2.28564e7	+	3.95884e7i	−0.888297	+	1.53858i	−0.841888	+	0.539653i	$0.818556\pi$
$132$	2.68959e6	−	4.65850e6i	0.101783	−	0.176294i
$133$	−2.16025e7	+	3.74167e7i	−0.796203	+	1.37906i
$134$	−1.57163e7			−0.564264
$135$	1.11093e7	+	1.92419e7i	0.388615	+	0.673101i
$136$	8.36619e6	−	1.44907e7i	0.285195	−	0.493972i
$137$	6.65125e6			0.220994			0.110497	−	0.993876i	$-0.464756\pi$
$137$	6.65125e6			0.220994			0.110497	+	0.993876i	$0.464756\pi$
$138$	−6.21240e7			−2.01225
$139$	−1.65375e7	+	2.86438e7i	−0.522297	+	0.904645i	0.477367	+	0.878704i	$0.341591\pi$
$139$	−1.65375e7	+	2.86438e7i	−0.522297	+	0.904645i	−0.999663	+	0.0259406i	$0.991742\pi$
$140$	−4.82707e6			−0.148674
$141$	2.02092e7	+	3.50034e7i	0.607132	+	1.05158i
$142$	−6.54012e6			−0.191680
$143$	−414826.	−	718500.i	−0.0118629	−	0.0205471i
$144$	−1.02324e7	−	1.77231e7i	−0.285568	−	0.494618i
$145$	6.06232e6	+	1.05002e7i	0.165140	+	0.286030i
$146$	−433407.	+	750683.i	−0.0115255	+	0.0199628i
$147$	−1.44315e7			−0.374714
$148$	1.78657e7	+	8.34607e6i	0.453007	+	0.211625i
$149$	4.34793e7			1.07679			0.538395	−	0.842693i	$-0.319031\pi$
$149$	4.34793e7			1.07679			0.538395	+	0.842693i	$0.319031\pi$
$150$	−2.35336e7	+	4.07614e7i	−0.569336	+	0.986119i
$151$	4.33912e6	+	7.51558e6i	0.102561	+	0.177641i	0.912739	−	0.408543i	$-0.133963\pi$
$151$	4.33912e6	+	7.51558e6i	0.102561	+	0.177641i	−0.810178	+	0.586184i	$0.800630\pi$
$152$	1.36845e7	+	2.37022e7i	0.316065	+	0.547440i
$153$	−8.16405e7	−	1.41406e8i	−1.84283	−	3.19188i
$154$	6.41224e6			0.141477
$155$	225580.	+	390717.i	0.00486565	+	0.00842755i
$156$	−4.53800e6			−0.0957037
$157$	−2.24538e7	+	3.88911e7i	−0.463063	+	0.802049i	−0.999112	−	0.0421381i	$-0.986583\pi$
$157$	−2.24538e7	+	3.88911e7i	−0.463063	+	0.802049i	0.536049	+	0.844187i	$0.319916\pi$
$158$	3.73733e7			0.753809
$159$	8.46399e7			1.66988
$160$	−1.52890e6	+	2.64813e6i	−0.0295092	+	0.0511115i
$161$	−3.70274e7	−	6.41334e7i	−0.699251	−	1.21114i
$162$	−7.40249e7			−1.36797
$163$	−1.79021e7	+	3.10073e7i	−0.323778	+	0.560800i	−0.981264	−	0.192667i	$-0.938286\pi$
$163$	−1.79021e7	+	3.10073e7i	−0.323778	+	0.560800i	0.657486	+	0.753466i	$0.271620\pi$
$164$	6.34354e6	−	1.09873e7i	0.112300	−	0.194509i
$165$	−3.92160e6	+	6.79242e6i	−0.0679626	+	0.117715i
$166$	2.07386e7	+	3.59204e7i	0.351886	+	0.609484i
$167$	−2.94598e7	−	5.10259e7i	−0.489466	−	0.847781i	0.510460	−	0.859901i	$-0.329475\pi$
$167$	−2.94598e7	−	5.10259e7i	−0.489466	−	0.847781i	−0.999927	+	0.0121208i	$0.996142\pi$
$168$	1.75367e7	−	3.03745e7i	0.285342	−	0.494226i
$169$	3.10243e7	−	5.37357e7i	0.494423	−	0.856366i
$170$	−1.21985e7	+	2.11284e7i	−0.190430	+	0.329834i
$171$	2.67077e8			4.08461
$172$	1.71868e7	+	2.97684e7i	0.257541	+	0.446074i
$173$	3.09767e7	−	5.36532e7i	0.454856	−	0.787833i	−0.543824	−	0.839199i	$-0.683024\pi$
$173$	3.09767e7	−	5.36532e7i	0.454856	−	0.787833i	0.998680	+	0.0513661i	$0.0163575\pi$
$174$	−8.80973e7			−1.26777
$175$	−5.61064e7			−0.791369
$176$	2.03097e6	−	3.51774e6i	0.0280808	−	0.0486373i
$177$	2.16750e8			2.93800
$178$	6.70998e6	+	1.16220e7i	0.0891766	+	0.154458i
$179$	−1.28394e8			−1.67324			−0.836620	−	0.547783i	$-0.815472\pi$
$179$	−1.28394e8			−1.67324			−0.836620	+	0.547783i	$0.815472\pi$
$180$	1.49196e7	+	2.58415e7i	0.190679	+	0.330266i
$181$	−3.38149e7	−	5.85691e7i	−0.423870	−	0.734165i	0.572444	−	0.819944i	$-0.305995\pi$
$181$	−3.38149e7	−	5.85691e7i	−0.423870	−	0.734165i	−0.996314	+	0.0857792i	$0.972662\pi$
$182$	−2.70476e6	−	4.68478e6i	−0.0332567	−	0.0576022i
$183$	1.02480e7	−	1.77501e7i	0.123612	−	0.214103i
$184$	−4.69113e7			−0.555156
$185$	−2.60495e7	−	1.21691e7i	−0.302481	−	0.141306i
$186$	−3.27812e6			−0.0373534
$187$	1.62043e7	−	2.80667e7i	0.181211	−	0.313867i
$188$	1.52605e7	+	2.64319e7i	0.167500	+	0.290119i
$189$	−9.62223e7	−	1.66662e8i	−1.03671	−	1.79564i
$190$	−1.99529e7	−	3.45595e7i	−0.211042	−	0.365536i
$191$	−1.16091e8			−1.20554			−0.602769	−	0.797916i	$-0.705936\pi$
$191$	−1.16091e8			−1.20554			−0.602769	+	0.797916i	$0.705936\pi$
$192$	−1.11089e7	−	1.92412e7i	−0.113271	−	0.196191i
$193$	−3.85904e7			−0.386393			−0.193196	−	0.981160i	$-0.561885\pi$
$193$	−3.85904e7			−0.386393			−0.193196	+	0.981160i	$0.561885\pi$
$194$	−2.84818e7	+	4.93319e7i	−0.280067	+	0.485090i
$195$	6.61672e6			0.0639031
$196$	−1.08976e7			−0.103379
$197$	7.16273e7	−	1.24062e8i	0.667493	−	1.15613i	−0.311109	−	0.950374i	$-0.600701\pi$
$197$	7.16273e7	−	1.24062e8i	0.667493	−	1.15613i	0.978603	−	0.205758i	$-0.0659661\pi$
$198$	−1.98190e7	−	3.43275e7i	−0.181449	−	0.314278i
$199$	1.74140e8			1.56643			0.783216	−	0.621750i	$-0.213578\pi$
$199$	1.74140e8			1.56643			0.783216	+	0.621750i	$0.213578\pi$
$200$	−1.77708e7	+	3.07799e7i	−0.157073	+	0.272058i
$201$	−8.32513e7	+	1.44195e8i	−0.723111	+	1.25246i
$202$	−1.84709e7	+	3.19926e7i	−0.157673	+	0.273099i
$203$	−5.25082e7	−	9.09468e7i	−0.440545	−	0.763047i
$204$	−8.86338e7	−	1.53518e8i	−0.730960	−	1.26606i
$205$	−9.24932e6	+	1.60203e7i	−0.0749844	+	0.129877i
$206$	3.62780e7	−	6.28354e7i	0.289140	−	0.500805i
$207$	−2.28890e8	+	3.96448e8i	−1.79362	+	3.10664i
$208$	−3.42675e6			−0.0264035
$209$	2.65053e7	+	4.59085e7i	0.200826	+	0.347841i
$210$	−2.55697e7	+	4.42881e7i	−0.190528	+	0.330004i
$211$	−2.24916e8			−1.64828			−0.824141	−	0.566385i	$-0.808342\pi$
$211$	−2.24916e8			−1.64828			−0.824141	+	0.566385i	$0.808342\pi$
$212$	6.39136e7			0.460699
$213$	−3.46440e7	+	6.00051e7i	−0.245640	+	0.425461i
$214$	−1.08191e8			−0.754645
$215$	−2.50596e7	−	4.34044e7i	−0.171965	−	0.297851i
$216$	−1.21907e8			−0.823079
$217$	−1.95384e6	−	3.38415e6i	−0.0129802	−	0.0224823i
$218$	1.05006e7	+	1.81876e7i	0.0686465	+	0.118899i
$219$	4.59164e6	+	7.95295e6i	0.0295402	+	0.0511651i
$220$	−2.96130e6	+	5.12911e6i	−0.0187500	+	0.0324760i
$221$	−2.73407e7			−0.170387
$222$	1.71212e8	−	1.19706e8i	1.05026	−	0.734314i
$223$	−1.90128e8			−1.14810			−0.574049	−	0.818821i	$-0.694628\pi$
$223$	−1.90128e8			−1.14810			−0.574049	+	0.818821i	$0.694628\pi$
$224$	1.32424e7	−	2.29365e7i	0.0787223	−	0.136351i
$225$	1.73414e8	+	3.00362e8i	1.01495	+	1.75795i
$226$	6.42888e7	+	1.11352e8i	0.370473	+	0.641677i
$227$	1.09363e8	+	1.89422e8i	0.620554	+	1.07483i	0.989383	+	0.145334i	$0.0464258\pi$
$227$	1.09363e8	+	1.89422e8i	0.620554	+	1.07483i	−0.368828	+	0.929498i	$0.620241\pi$
$228$	2.89955e8			1.62016
$229$	−1.07833e7	−	1.86772e7i	−0.0593372	−	0.102775i	0.834831	−	0.550507i	$-0.185565\pi$
$229$	−1.07833e7	−	1.86772e7i	−0.0593372	−	0.102775i	−0.894168	+	0.447731i	$0.852232\pi$
$230$	6.83999e7			0.370688
$231$	3.39666e7	−	5.88318e7i	0.181305	−	0.314029i
$232$	−6.65244e7			−0.349762
$233$	−3.40563e8			−1.76381			−0.881905	−	0.471427i	$-0.843739\pi$
$233$	−3.40563e8			−1.76381			−0.881905	+	0.471427i	$0.843739\pi$
$234$	−1.67198e7	+	2.89595e7i	−0.0853052	+	0.147753i
$235$	−2.22508e7	−	3.85396e7i	−0.111843	−	0.193718i
$236$	1.63673e8			0.810558
$237$	1.97972e8	−	3.42897e8i	0.966015	−	1.67319i
$238$	1.05656e8	−	1.83001e8i	0.508012	−	0.879903i
$239$	2.08876e8	−	3.61783e8i	0.989681	−	1.71418i	0.370747	−	0.928734i	$-0.379102\pi$
$239$	2.08876e8	−	3.61783e8i	0.989681	−	1.71418i	0.618934	−	0.785443i	$-0.287565\pi$
$240$	1.61976e7	+	2.80550e7i	0.0756329	+	0.131000i
$241$	8.45650e7	+	1.46471e8i	0.389163	+	0.674049i	0.992337	−	0.123560i	$-0.0394311\pi$
$241$	8.45650e7	+	1.46471e8i	0.389163	+	0.674049i	−0.603175	+	0.797609i	$0.706098\pi$
$242$	−7.40149e7	+	1.28198e8i	−0.335711	+	0.581468i
$243$	−1.31758e8	+	2.28212e8i	−0.589056	+	1.02027i
$244$	7.73854e6	−	1.34035e7i	0.0341032	−	0.0590684i
$245$	1.58894e7			0.0690281
$246$	−6.72053e7	−	1.16403e8i	−0.287826	−	0.498530i
$247$	2.23605e7	−	3.87295e7i	0.0944152	−	0.163532i
$248$	−2.47539e6			−0.0103053
$249$	4.39422e8			1.80378
$250$	5.50724e7	−	9.53882e7i	0.222917	−	0.386104i
$251$	2.12103e8			0.846621			0.423310	−	0.905985i	$-0.360868\pi$
$251$	2.12103e8			0.846621			0.423310	+	0.905985i	$0.360868\pi$
$252$	−1.29224e8	−	2.23823e8i	−0.508677	−	0.881055i
$253$	−9.08618e7			−0.352744
$254$	−1.69903e8	−	2.94280e8i	−0.650553	−	1.12679i
$255$	1.29234e8	+	2.23840e8i	0.488075	+	0.845372i
$256$	−8.38861e6	−	1.45295e7i	−0.0312500	−	0.0541266i
$257$	2.22285e8	−	3.85009e8i	0.816855	−	1.41483i	−0.0911335	−	0.995839i	$-0.529049\pi$
$257$	2.22285e8	−	3.85009e8i	0.816855	−	1.41483i	0.907988	−	0.418995i	$-0.137618\pi$
$258$	3.64164e8			1.32017
$259$	2.25625e8	+	1.05402e8i	0.806933	+	0.376963i
$260$	4.99644e6			0.0176301
$261$	−3.24586e8	+	5.62199e8i	−1.13002	+	1.95726i
$262$	1.82851e8	+	3.16707e8i	0.628121	+	1.08794i
$263$	4.82776e7	+	8.36193e7i	0.163644	+	0.283440i	0.936173	−	0.351540i	$-0.114342\pi$
$263$	4.82776e7	+	8.36193e7i	0.163644	+	0.283440i	−0.772529	+	0.634980i	$0.781008\pi$
$264$	−2.15167e7	−	3.72680e7i	−0.0719717	−	0.124659i
$265$	−9.31904e7			−0.307617
$266$	1.72820e8	+	2.99333e8i	0.563000	+	0.975145i
$267$	1.42175e8			0.457123
$268$	−6.28650e7	+	1.08885e8i	−0.199497	+	0.345540i
$269$	−5.59732e7			−0.175326			−0.0876632	−	0.996150i	$-0.527940\pi$
$269$	−5.59732e7			−0.175326			−0.0876632	+	0.996150i	$0.527940\pi$
$270$	1.77749e8			0.549585
$271$	−2.34555e8	+	4.06261e8i	−0.715899	+	1.23997i	0.246713	+	0.969089i	$0.420650\pi$
$271$	−2.34555e8	+	4.06261e8i	−0.715899	+	1.23997i	−0.962612	+	0.270885i	$0.912684\pi$
$272$	−6.69295e7	−	1.15925e8i	−0.201663	−	0.349291i
$273$	−5.73100e7			−0.170475
$274$	2.66050e7	−	4.60812e7i	0.0781333	−	0.135331i
$275$	−3.44199e7	+	5.96170e7i	−0.0998034	+	0.172865i
$276$	−2.48496e8	+	4.30408e8i	−0.711439	+	1.23225i
$277$	−2.44569e8	−	4.23605e8i	−0.691388	−	1.19752i	−0.971383	−	0.237517i	$-0.923666\pi$
$277$	−2.44569e8	−	4.23605e8i	−0.691388	−	1.19752i	0.279996	−	0.960001i	$-0.409667\pi$
$278$	1.32300e8	+	2.29150e8i	0.369320	+	0.639680i
$279$	−1.20779e7	+	2.09195e7i	−0.0332948	+	0.0576684i
$280$	−1.93083e7	+	3.34430e7i	−0.0525643	+	0.0910440i
$281$	1.76349e8	−	3.05446e8i	0.474135	−	0.821225i	−0.525427	−	0.850839i	$-0.676094\pi$
$281$	1.76349e8	−	3.05446e8i	0.474135	−	0.821225i	0.999561	+	0.0296135i	$0.00942764\pi$
$282$	3.23348e8			0.858615
$283$	−1.30113e8	−	2.25362e8i	−0.341247	−	0.591056i	0.643418	−	0.765515i	$-0.277516\pi$
$283$	−1.30113e8	−	2.25362e8i	−0.341247	−	0.591056i	−0.984664	+	0.174459i	$0.944182\pi$
$284$	−2.61605e7	+	4.53113e7i	−0.0677690	+	0.117379i
$285$	−4.22774e8			−1.08181
$286$	−6.63722e6			−0.0167766
$287$	8.01120e7	−	1.38758e8i	0.200037	−	0.346475i
$288$	−1.63719e8			−0.403854
$289$	−3.28835e8	−	5.69560e8i	−0.801376	−	1.38802i
$290$	9.69971e7			0.233543
$291$	3.01745e8	+	5.22637e8i	0.717818	+	1.24330i
$292$	3.46725e6	+	6.00546e6i	0.00814978	+	0.0141158i
$293$	−2.16734e8	−	3.75395e8i	−0.503374	−	0.871870i	−0.999992	−	0.00390049i	$-0.998758\pi$
$293$	−2.16734e8	−	3.75395e8i	−0.503374	−	0.871870i	0.496618	−	0.867969i	$-0.334575\pi$
$294$	−5.77260e7	+	9.99843e7i	−0.132482	+	0.229465i
$295$	−2.38646e8			−0.541224
$296$	1.29286e8	−	9.03931e7i	0.289755	−	0.202588i
$297$	−2.36120e8			−0.522981
$298$	1.73917e8	−	3.01234e8i	0.380703	−	0.659396i
$299$	3.83266e7	+	6.63836e7i	0.0829184	+	0.143619i
$300$	1.88269e8	+	3.26091e8i	0.402581	+	0.697291i
$301$	2.17051e8	+	3.75943e8i	0.458753	+	0.794583i
$302$	6.94260e7			0.145043
$303$	1.95686e8	+	3.38939e8i	0.404121	+	0.699958i
$304$	2.18952e8			0.446983
$305$	−1.12833e7	+	1.95433e7i	−0.0227713	+	0.0394411i
$306$	−1.30625e9			−2.60616
$307$	−8.33011e8			−1.64311			−0.821555	−	0.570129i	$-0.806893\pi$
$307$	−8.33011e8			−1.64311			−0.821555	+	0.570129i	$0.806893\pi$
$308$	2.56489e7	−	4.44253e7i	0.0500198	−	0.0866369i
$309$	−3.84340e8	−	6.65696e8i	−0.741072	−	1.28358i
$310$	3.60929e6			0.00688106
$311$	−8.15212e7	+	1.41199e8i	−0.153677	+	0.266177i	−0.932577	−	0.360972i	$-0.882445\pi$
$311$	−8.15212e7	+	1.41199e8i	−0.153677	+	0.266177i	0.778899	+	0.627149i	$0.215778\pi$
$312$	−1.81520e7	+	3.14402e7i	−0.0338364	+	0.0586063i
$313$	7.12296e7	−	1.23373e8i	0.131297	−	0.227413i	−0.792880	−	0.609378i	$-0.791419\pi$
$313$	7.12296e7	−	1.23373e8i	0.131297	−	0.227413i	0.924177	+	0.381965i	$0.124752\pi$
$314$	1.79630e8	+	3.11128e8i	0.327435	+	0.567134i
$315$	1.88418e8	+	3.26350e8i	0.339653	+	0.588296i
$316$	1.49493e8	−	2.58930e8i	0.266512	−	0.461612i
$317$	−2.63484e8	+	4.56367e8i	−0.464565	+	0.804650i	−0.999182	−	0.0404442i	$-0.987123\pi$
$317$	−2.63484e8	+	4.56367e8i	−0.464565	+	0.804650i	0.534617	+	0.845095i	$0.320456\pi$
$318$	3.38559e8	−	5.86402e8i	0.590391	−	1.02259i
$319$	−1.28850e8			−0.222237
$320$	1.22312e7	+	2.11850e7i	0.0208662	+	0.0361413i
$321$	−5.73104e8	+	9.92644e8i	−0.967087	+	1.67504i
$322$	−5.92439e8			−0.988890
$323$	1.74693e9			2.88448
$324$	−2.96100e8	+	5.12860e8i	−0.483649	+	0.837705i
$325$	5.80749e7			0.0938420
$326$	1.43217e8	+	2.48059e8i	0.228945	+	0.396545i
$327$	2.22494e8			0.351885
$328$	−5.07483e7	−	8.78986e7i	−0.0794078	−	0.137538i
$329$	1.92723e8	+	3.33806e8i	0.298365	+	0.516784i
$330$	3.13728e7	+	5.43393e7i	0.0480568	+	0.0832368i
$331$	5.54533e8	−	9.60479e8i	0.840484	−	1.45576i	−0.0490020	−	0.998799i	$-0.515604\pi$
$331$	5.54533e8	−	9.60479e8i	0.840484	−	1.45576i	0.889486	−	0.456962i	$-0.151063\pi$
$332$	3.31818e8			0.497642
$333$	−1.33101e8	−	1.53365e9i	−0.197527	−	2.27599i
$334$	−4.71358e8			−0.692210
$335$	9.16616e7	−	1.58762e8i	0.133208	−	0.230723i
$336$	−1.40294e8	−	2.42996e8i	−0.201767	−	0.349471i
$337$	1.61272e8	+	2.79332e8i	0.229538	+	0.397572i	0.957671	−	0.287864i	$-0.0929451\pi$
$337$	1.61272e8	+	2.79332e8i	0.229538	+	0.397572i	−0.728133	+	0.685436i	$0.759612\pi$
$338$	−2.48194e8	−	4.29885e8i	−0.349610	−	0.605542i
$339$	1.36219e9			1.89906
$340$	9.75878e7	+	1.69027e8i	0.134654	+	0.233228i
$341$	−4.79454e6			−0.00654797
$342$	1.06831e9	−	1.85037e9i	1.44413	−	2.50130i
$343$	−8.03253e8			−1.07479
$344$	2.74989e8			0.364218
$345$	3.62324e8	−	6.27564e8i	0.475041	−	0.822795i
$346$	−2.47813e8	−	4.29225e8i	−0.321631	−	0.557082i
$347$	−1.15231e9			−1.48052			−0.740261	−	0.672319i	$-0.765298\pi$
$347$	−1.15231e9			−1.48052			−0.740261	+	0.672319i	$0.765298\pi$
$348$	−3.52389e8	+	6.10356e8i	−0.448224	+	0.776347i
$349$	−2.21837e8	+	3.84233e8i	−0.279348	+	0.483844i	−0.971223	−	0.238173i	$-0.923451\pi$
$349$	−2.21837e8	+	3.84233e8i	−0.279348	+	0.483844i	0.691875	+	0.722017i	$0.256785\pi$
$350$	−2.24425e8	+	3.88716e8i	−0.279791	+	0.484612i
$351$	9.95984e7	+	1.72509e8i	0.122936	+	0.212931i
$352$	−1.62478e7	−	2.81420e7i	−0.0198561	−	0.0343918i
$353$	−1.90862e8	+	3.30582e8i	−0.230944	+	0.400007i	−0.958086	−	0.286480i	$-0.907515\pi$
$353$	−1.90862e8	+	3.30582e8i	−0.230944	+	0.400007i	0.727142	+	0.686487i	$0.240848\pi$
$354$	8.66998e8	−	1.50168e9i	1.03874	−	1.79915i
$355$	3.81438e7	−	6.60670e7i	0.0452506	−	0.0783764i
$356$	1.07360e8			0.126115
$357$	−1.11935e9	−	1.93877e9i	−1.30205	−	2.25521i
$358$	−5.13575e8	+	8.89538e8i	−0.591580	+	1.02465i
$359$	3.84165e8			0.438216			0.219108	−	0.975701i	$-0.429685\pi$
$359$	3.84165e8			0.438216			0.219108	+	0.975701i	$0.429685\pi$
$360$	2.38713e8			0.269661
$361$	−9.81784e8	+	1.70050e9i	−1.09835	+	1.90240i
$362$	−5.41038e8			−0.599443
$363$	7.84136e8	+	1.35816e9i	0.860435	+	1.49032i
$364$	−4.32761e7			−0.0470320
$365$	−5.05550e6	−	8.75638e6i	−0.00544175	−	0.00942539i
$366$	−8.19844e7	−	1.42001e8i	−0.0874072	−	0.151394i
$367$	1.66068e8	+	2.87639e8i	0.175370	+	0.303750i	0.940289	−	0.340376i	$-0.110555\pi$
$367$	1.66068e8	+	2.87639e8i	0.175370	+	0.303750i	−0.764919	+	0.644126i	$0.777221\pi$
$368$	−1.87645e8	+	3.25011e8i	−0.196277	+	0.339962i
$369$	−9.90444e8			−1.02621
$370$	−1.88508e8	+	1.31799e8i	−0.193475	+	0.135272i
$371$	8.07159e8			0.820635
$372$	−1.31125e7	+	2.27115e7i	−0.0132064	+	0.0228742i
$373$	−4.60228e8	−	7.97138e8i	−0.459189	−	0.795339i	0.539729	−	0.841839i	$-0.318527\pi$
$373$	−4.60228e8	−	7.97138e8i	−0.459189	−	0.795339i	−0.998918	+	0.0464995i	$0.985193\pi$
$374$	−1.29635e8	−	2.24534e8i	−0.128136	−	0.221938i
$375$	−5.83453e8	−	1.01057e9i	−0.571342	−	0.989594i
$376$	2.44168e8			0.236881
$377$	5.43505e7	+	9.41378e7i	0.0522407	+	0.0904835i
$378$	−1.53956e9			−1.46614
$379$	5.33491e8	−	9.24034e8i	0.503373	−	0.871868i	−0.496619	−	0.867968i	$-0.665426\pi$
$379$	5.33491e8	−	9.24034e8i	0.503373	−	0.871868i	0.999992	−	0.00389919i	$-0.00124115\pi$
$380$	−3.19247e8			−0.298459
$381$	−3.60000e9			−3.33477
$382$	−4.64363e8	+	8.04301e8i	−0.426222	+	0.738238i
$383$	−1.87483e8	−	3.24730e8i	−0.170516	−	0.295343i	0.768084	−	0.640349i	$-0.221210\pi$
$383$	−1.87483e8	−	3.24730e8i	−0.170516	−	0.295343i	−0.938600	+	0.345006i	$0.887877\pi$
$384$	−1.77743e8			−0.160189
$385$	−3.73979e7	+	6.47751e7i	−0.0333991	+	0.0578490i
$386$	−1.54362e8	+	2.67362e8i	−0.136610	+	0.236616i
$387$	1.34173e9	−	2.32394e9i	1.17673	−	2.03815i
$388$	2.27855e8	+	3.94656e8i	0.198037	+	0.343010i
$389$	4.33524e8	+	7.50886e8i	0.373413	+	0.646771i	0.990088	−	0.140447i	$-0.0448540\pi$
$389$	4.33524e8	+	7.50886e8i	0.373413	+	0.646771i	−0.616675	+	0.787218i	$0.711521\pi$
$390$	2.64669e7	−	4.58420e7i	0.0225931	−	0.0391325i
$391$	−1.49715e9	+	2.59314e9i	−1.26662	+	2.19385i
$392$	−4.35902e7	+	7.55005e7i	−0.0365500	+	0.0633065i
$393$	3.87436e9			3.21978
$394$	−5.73019e8	−	9.92498e8i	−0.471989	−	0.817509i
$395$	−2.17971e8	+	3.77537e8i	−0.177955	+	0.308226i
$396$	−3.17104e8			−0.256607
$397$	−4.81515e8			−0.386227			−0.193114	−	0.981176i	$-0.561859\pi$
$397$	−4.81515e8			−0.386227			−0.193114	+	0.981176i	$0.561859\pi$
$398$	6.96558e8	−	1.20647e9i	0.553817	−	0.959240i
$399$	3.66181e9			2.88597
$400$	1.42166e8	+	2.46239e8i	0.111067	+	0.192374i
$401$	1.01569e9			0.786607			0.393304	−	0.919409i	$-0.371332\pi$
$401$	1.01569e9			0.786607			0.393304	+	0.919409i	$0.371332\pi$
$402$	6.66010e8	+	1.15356e9i	0.511317	+	0.885626i
$403$	2.02240e6	+	3.50289e6i	0.00153921	+	0.00266599i
$404$	1.47767e8	+	2.55941e8i	0.111492	+	0.193110i
$405$	4.31734e8	−	7.47785e8i	0.322941	−	0.559351i
$406$	−8.40130e8			−0.623025
$407$	2.50412e8	−	1.75081e8i	0.184109	−	0.128724i
$408$	−1.41814e9			−1.03373
$409$	−6.03779e8	+	1.04578e9i	−0.436362	+	0.755800i	−0.997406	−	0.0719855i	$-0.977066\pi$
$409$	−6.03779e8	+	1.04578e9i	−0.436362	+	0.755800i	0.561044	+	0.827786i	$0.310400\pi$
$410$	7.39945e7	+	1.28162e8i	0.0530220	+	0.0918368i
$411$	−2.81861e8	−	4.88198e8i	−0.200257	−	0.346856i
$412$	−2.90224e8	−	5.02683e8i	−0.204453	−	0.354123i
$413$	2.06701e9			1.44383
$414$	1.83112e9	+	3.17159e9i	1.26828	+	2.19672i
$415$	−4.83814e8			−0.332284
$416$	−1.37070e7	+	2.37412e7i	−0.00933504	+	0.0161688i
$417$	2.80325e9			1.89315
$418$	4.24084e8			0.284011
$419$	−3.27916e8	+	5.67967e8i	−0.217778	+	0.377202i	−0.954128	−	0.299398i	$-0.903214\pi$
$419$	−3.27916e8	+	5.67967e8i	−0.217778	+	0.377202i	0.736350	+	0.676600i	$0.236547\pi$
$420$	2.04558e8	+	3.54304e8i	0.134724	+	0.233348i
$421$	−1.60159e9			−1.04608			−0.523040	−	0.852308i	$-0.675202\pi$
$421$	−1.60159e9			−1.04608			−0.523040	+	0.852308i	$0.675202\pi$
$422$	−8.99663e8	+	1.55826e9i	−0.582756	+	1.00936i
$423$	1.19134e9	−	2.06347e9i	0.765324	−	1.32558i
$424$	2.55654e8	−	4.42806e8i	0.162882	−	0.282120i
$425$	1.13429e9	+	1.96465e9i	0.716741	+	1.24143i
$426$	2.77152e8	+	4.80041e8i	0.173694	+	0.300846i
$427$	9.77294e7	−	1.69272e8i	0.0607474	−	0.105218i
$428$	−4.32764e8	+	7.49569e8i	−0.266807	+	0.462124i
$429$	−3.51583e7	+	6.08960e7i	−0.0214995	+	0.0372382i
$430$	−4.00953e8			−0.243195
$431$	8.14264e8	+	1.41035e9i	0.489886	+	0.848507i	0.999932	−	0.0116397i	$-0.00370512\pi$
$431$	8.14264e8	+	1.41035e9i	0.489886	+	0.848507i	−0.510046	+	0.860147i	$0.670372\pi$
$432$	−4.87629e8	+	8.44598e8i	−0.291002	+	0.504031i
$433$	−1.12112e9			−0.663656			−0.331828	−	0.943340i	$-0.607665\pi$
$433$	−1.12112e9			−0.663656			−0.331828	+	0.943340i	$0.607665\pi$
$434$	−3.12615e7			−0.0183567
$435$	5.13808e8	−	8.89942e8i	0.299287	−	0.518381i
$436$	1.68010e8			0.0970807
$437$	−2.44887e9	−	4.24157e9i	−1.40372	−	2.43132i
$438$	7.34662e7			0.0417761
$439$	1.58029e9	+	2.73714e9i	0.891479	+	1.54409i	0.838102	+	0.545513i	$0.183665\pi$
$439$	1.58029e9	+	2.73714e9i	0.891479	+	1.54409i	0.0533770	+	0.998574i	$0.483002\pi$
$440$	2.36904e7	+	4.10329e7i	0.0132583	+	0.0229640i
$441$	4.25371e8	+	7.36763e8i	0.236174	+	0.409066i
$442$	−1.09363e8	+	1.89422e8i	−0.0602410	+	0.104340i
$443$	1.46513e9			0.800688			0.400344	−	0.916365i	$-0.368891\pi$
$443$	1.46513e9			0.800688			0.400344	+	0.916365i	$0.368891\pi$
$444$	−1.44502e8	−	1.66502e9i	−0.0783491	−	0.902772i
$445$	−1.56538e8			−0.0842091
$446$	−7.60512e8	+	1.31725e9i	−0.405914	+	0.703064i
$447$	−1.84253e9	−	3.19136e9i	−0.975750	−	1.69005i
$448$	−1.05939e8	−	1.83492e8i	−0.0556651	−	0.0964147i
$449$	4.77002e8	+	8.26191e8i	0.248690	+	0.430743i	0.963163	−	0.268920i	$-0.0866667\pi$
$449$	4.77002e8	+	8.26191e8i	0.248690	+	0.430743i	−0.714473	+	0.699663i	$0.753333\pi$
$450$	2.77463e9			1.43536
$451$	−9.82936e7	−	1.70249e8i	−0.0504554	−	0.0873912i
$452$	1.02862e9			0.523927
$453$	3.67759e8	−	6.36978e8i	0.185875	−	0.321944i
$454$	1.74981e9			0.877597
$455$	6.30996e7			0.0314041
$456$	1.15982e9	−	2.00887e9i	0.572814	−	0.992143i
$457$	9.03209e8	+	1.56440e9i	0.442672	+	0.766730i	0.997887	−	0.0649770i	$-0.0206974\pi$
$457$	9.03209e8	+	1.56440e9i	0.442672	+	0.766730i	−0.555215	+	0.831707i	$0.687364\pi$
$458$	−1.72533e8			−0.0839155
$459$	−3.89061e9	+	6.73873e9i	−1.87790	+	3.25262i
$460$	2.73600e8	−	4.73889e8i	0.131058	−	0.226999i
$461$	1.48499e9	−	2.57208e9i	0.705944	−	1.22273i	−0.260405	−	0.965499i	$-0.583856\pi$
$461$	1.48499e9	−	2.57208e9i	0.705944	−	1.22273i	0.966350	−	0.257232i	$-0.0828105\pi$
$462$	−2.71732e8	−	4.70654e8i	−0.128202	−	0.222052i
$463$	3.26888e8	+	5.66186e8i	0.153061	+	0.265110i	0.932351	−	0.361553i	$-0.117753\pi$
$463$	3.26888e8	+	5.66186e8i	0.153061	+	0.265110i	−0.779290	+	0.626663i	$0.784420\pi$
$464$	−2.66098e8	+	4.60894e8i	−0.123660	+	0.214185i
$465$	1.91189e7	−	3.31149e7i	0.00881816	−	0.0152735i
$466$	−1.36225e9	+	2.35949e9i	−0.623601	+	1.08011i
$467$	−1.53186e9			−0.696002			−0.348001	−	0.937494i	$-0.613139\pi$
$467$	−1.53186e9			−0.696002			−0.348001	+	0.937494i	$0.613139\pi$
$468$	1.33758e8	+	2.31676e8i	0.0603199	+	0.104477i
$469$	−7.93917e8	+	1.37510e9i	−0.355361	+	0.615504i
$470$	−3.56013e8			−0.158170
$471$	3.80611e9			1.67845
$472$	6.54691e8	−	1.13396e9i	0.286576	−	0.496363i
$473$	5.32622e8			0.231422
$474$	−1.58377e9	−	2.74317e9i	−0.683075	−	1.18312i
$475$	−3.71069e9			−1.58865
$476$	−8.45247e8	−	1.46401e9i	−0.359219	−	0.622185i
$477$	−2.49477e9	−	4.32108e9i	−1.05249	−	1.82296i
$478$	−1.67100e9	−	2.89427e9i	−0.699810	−	1.21211i
$479$	−1.52305e9	+	2.63800e9i	−0.633198	+	1.09673i	0.353695	+	0.935361i	$0.384925\pi$
$479$	−1.52305e9	+	2.63800e9i	−0.633198	+	1.09673i	−0.986894	+	0.161371i	$0.948408\pi$
$480$	2.59161e8			0.106961
$481$	−2.33541e8	−	1.09100e8i	−0.0956876	−	0.0447010i
$482$	1.35304e9			0.550359
$483$	−3.13823e9	+	5.43558e9i	−1.26727	+	2.19498i
$484$	5.92119e8	+	1.02558e9i	0.237384	+	0.411160i
$485$	−3.32228e8	−	5.75435e8i	−0.132233	−	0.229034i
$486$	1.05407e9	+	1.82570e9i	0.416525	+	0.721443i
$487$	3.96129e9			1.55412			0.777062	−	0.629424i	$-0.216709\pi$
$487$	3.96129e9			1.55412			0.777062	+	0.629424i	$0.216709\pi$
$488$	−6.19083e7	−	1.07228e8i	−0.0241146	−	0.0417677i
$489$	3.03456e9			1.17359
$490$	6.35576e7	−	1.10085e8i	0.0244051	−	0.0422709i
$491$	−6.38497e8			−0.243430			−0.121715	−	0.992565i	$-0.538839\pi$
$491$	−6.38497e8			−0.243430			−0.121715	+	0.992565i	$0.538839\pi$
$492$	−1.07528e9			−0.407048
$493$	−2.12309e9	+	3.67730e9i	−0.798002	+	1.38218i
$494$	−1.78884e8	−	3.09836e8i	−0.0667616	−	0.115635i
$495$	4.62360e8			0.171341
$496$	−9.90155e6	+	1.71500e7i	−0.00364349	+	0.00631071i
$497$	−3.30378e8	+	5.72232e8i	−0.120716	+	0.209086i
$498$	1.75769e9	−	3.04441e9i	0.637734	−	1.10459i
$499$	−1.25424e9	−	2.17242e9i	−0.451888	−	0.782692i	0.546616	−	0.837384i	$-0.315916\pi$
$499$	−1.25424e9	−	2.17242e9i	−0.451888	−	0.782692i	−0.998503	+	0.0546914i	$0.982582\pi$
$500$	−4.40579e8	−	7.63105e8i	−0.157626	−	0.273017i
$501$	−2.49685e9	+	4.32467e9i	−0.887075	+	1.53646i
$502$	8.48412e8	−	1.46949e9i	0.299326	−	0.518447i
$503$	2.04961e9	−	3.55003e9i	0.718098	−	1.24378i	−0.243655	−	0.969862i	$-0.578346\pi$
$503$	2.04961e9	−	3.55003e9i	0.718098	−	1.24378i	0.961753	−	0.273919i	$-0.0883202\pi$
$504$	−2.06759e9			−0.719378
$505$	−2.15455e8	−	3.73179e8i	−0.0744452	−	0.128943i
$506$	−3.63447e8	+	6.29509e8i	−0.124714	+	0.216011i
$507$	−5.25889e9			−1.79212
$508$	−2.71845e9			−0.920021
$509$	1.97889e9	−	3.42754e9i	0.665135	−	1.15205i	−0.314114	−	0.949385i	$-0.601707\pi$
$509$	1.97889e9	−	3.42754e9i	0.665135	−	1.15205i	0.979249	−	0.202662i	$-0.0649593\pi$
$510$	2.06775e9			0.690243
$511$	4.37877e7	+	7.58424e7i	0.0145171	+	0.0251443i
$512$	−1.34218e8			−0.0441942
$513$	−6.36382e9	−	1.10225e10i	−2.08117	−	3.60469i
$514$	−1.77828e9	−	3.08008e9i	−0.577604	−	1.00044i
$515$	4.23167e8	+	7.32946e8i	0.136517	+	0.236454i
$516$	1.45666e9	−	2.52300e9i	0.466749	−	0.808433i
$517$	4.72925e8			0.150513
$518$	1.63274e9	−	1.14157e9i	0.516136	−	0.360867i
$519$	−5.25082e9			−1.64870
$520$	1.99858e7	−	3.46164e7i	0.00623317	−	0.0107962i
$521$	1.08228e8	+	1.87456e8i	0.0335279	+	0.0580721i	0.882302	−	0.470683i	$-0.155992\pi$
$521$	1.08228e8	+	1.87456e8i	0.0335279	+	0.0580721i	−0.848775	+	0.528755i	$0.822659\pi$
$522$	2.59668e9	+	4.49759e9i	0.799047	+	1.38399i
$523$	−2.68926e9	−	4.65793e9i	−0.822009	−	1.42376i	−0.904184	−	0.427143i	$-0.859520\pi$
$523$	−2.68926e9	−	4.65793e9i	−0.822009	−	1.42376i	0.0821754	−	0.996618i	$-0.473813\pi$
$524$	2.92562e9			0.888297
$525$	2.37763e9	+	4.11817e9i	0.717111	+	1.24207i
$526$	7.72442e8			0.231428
$527$	−7.90007e7	+	1.36833e8i	−0.0235122	+	0.0407244i
$528$	−3.44267e8			−0.101783
$529$	4.99007e9			1.46559
$530$	−3.72762e8	+	6.45642e8i	−0.108759	+	0.188376i
$531$	−6.38873e9	−	1.10656e10i	−1.85176	−	3.20733i
$532$	2.76512e9			0.796203
$533$	−8.29228e7	+	1.43627e8i	−0.0237208	+	0.0410856i
$534$	5.68700e8	−	9.85017e8i	0.161618	−	0.279930i
$535$	6.31000e8	−	1.09292e9i	0.178152	−	0.308569i
$536$	5.02920e8	+	8.71083e8i	0.141066	+	0.244333i
$537$	5.44097e9	+	9.42403e9i	1.51623	+	2.62619i
$538$	−2.23893e8	+	3.87794e8i	−0.0619873	+	0.107365i
$539$	−8.44292e7	+	1.46236e8i	−0.0232237	+	0.0402247i
$540$	7.10997e8	−	1.23148e9i	0.194308	−	0.336551i
$541$	5.16538e9			1.40253			0.701264	−	0.712901i	$-0.252619\pi$
$541$	5.16538e9			1.40253			0.701264	+	0.712901i	$0.252619\pi$
$542$	1.87644e9	+	3.25009e9i	0.506217	+	0.876794i
$543$	−2.86596e9	+	4.96398e9i	−0.768193	+	1.33055i
$544$	−1.07087e9			−0.285195
$545$	−2.44971e8			−0.0648226
$546$	−2.29240e8	+	3.97055e8i	−0.0602721	+	0.104394i
$547$	6.29612e9			1.64482			0.822408	−	0.568898i	$-0.192630\pi$
$547$	6.29612e9			1.64482			0.822408	+	0.568898i	$0.192630\pi$
$548$	−2.12840e8	−	3.68650e8i	−0.0552486	−	0.0956933i
$549$	−1.20825e9			−0.311641
$550$	2.75359e8	+	4.76936e8i	0.0705717	+	0.122234i
$551$	−3.47272e9	−	6.01492e9i	−0.884380	−	1.53179i
$552$	1.98797e9	+	3.44326e9i	0.503063	+	0.871331i
$553$	1.88793e9	−	3.27000e9i	0.474732	−	0.822261i
$554$	−3.91310e9			−0.977770
$555$	2.10694e8	+	2.42771e9i	0.0523151	+	0.602797i
$556$	2.11680e9			0.522297
$557$	−1.91693e9	+	3.32023e9i	−0.470018	+	0.814094i	−0.999412	−	0.0342813i	$-0.989086\pi$
$557$	−1.91693e9	+	3.32023e9i	−0.470018	+	0.814094i	0.529395	+	0.848376i	$0.322419\pi$
$558$	9.66233e7	+	1.67356e8i	0.0235430	+	0.0407777i
$559$	−2.24666e8	−	3.89134e8i	−0.0543997	−	0.0942231i
$560$	1.54466e8	+	2.67544e8i	0.0371686	+	0.0643779i
$561$	−2.74678e9			−0.656830
$562$	−1.41079e9	−	2.44357e9i	−0.335264	−	0.580694i
$563$	−1.77911e9			−0.420169			−0.210084	−	0.977683i	$-0.567374\pi$
$563$	−1.77911e9			−0.420169			−0.210084	+	0.977683i	$0.567374\pi$
$564$	1.29339e9	−	2.24022e9i	0.303566	−	0.525792i
$565$	−1.49980e9			−0.349836
$566$	−2.08181e9			−0.482595
$567$	−3.73942e9	+	6.47686e9i	−0.861516	+	1.49219i
$568$	2.09284e8	+	3.62490e8i	0.0479199	+	0.0829998i
$569$	1.58091e9			0.359762			0.179881	−	0.983688i	$-0.442429\pi$
$569$	1.58091e9			0.359762			0.179881	+	0.983688i	$0.442429\pi$
$570$	−1.69110e9	+	2.92907e9i	−0.382478	+	0.662472i
$571$	1.11657e9	−	1.93396e9i	0.250993	−	0.434732i	−0.712807	−	0.701361i	$-0.752576\pi$
$571$	1.11657e9	−	1.93396e9i	0.250993	−	0.434732i	0.963799	+	0.266628i	$0.0859096\pi$
$572$	−2.65489e7	+	4.59840e7i	−0.00593144	+	0.0102736i
$573$	4.91960e9	+	8.52100e9i	1.09242	+	1.89212i
$574$	−6.40896e8	−	1.11006e9i	−0.141448	−	0.244995i
$575$	3.18012e9	−	5.50813e9i	0.697600	−	1.20828i
$576$	−6.54875e8	+	1.13428e9i	−0.142784	+	0.247309i
$577$	−4.54104e8	+	7.86531e8i	−0.0984101	+	0.170451i	−0.911027	−	0.412347i	$-0.864709\pi$
$577$	−4.54104e8	+	7.86531e8i	−0.0984101	+	0.170451i	0.812617	+	0.582799i	$0.198042\pi$
$578$	−5.26137e9			−1.13332
$579$	1.63535e9	+	2.83251e9i	0.350136	+	0.606453i
$580$	3.87989e8	−	6.72016e8i	0.0825698	−	0.143015i
$581$	4.19050e9			0.886441
$582$	4.82791e9			1.01515
$583$	4.95173e8	−	8.57664e8i	0.103494	−	0.179258i
$584$	5.54761e7			0.0115255
$585$	−1.95029e8	−	3.37800e8i	−0.0402767	−	0.0697612i
$586$	−3.46775e9			−0.711879
$587$	−2.78225e9	−	4.81900e9i	−0.567757	−	0.983385i	−0.996787	−	0.0800944i	$-0.974478\pi$
$587$	−2.78225e9	−	4.81900e9i	−0.567757	−	0.983385i	0.429030	−	0.903290i	$-0.358856\pi$
$588$	4.61808e8	+	7.99874e8i	0.0936786	+	0.162256i
$589$	−1.29221e8	−	2.23817e8i	−0.0260572	−	0.0451325i
$590$	−9.54584e8	+	1.65339e9i	−0.191352	+	0.331431i
$591$	−1.21415e10			−2.41944
$592$	−1.09117e8	−	1.25729e9i	−0.0216156	−	0.249064i
$593$	−3.65445e9			−0.719665			−0.359832	−	0.933017i	$-0.617166\pi$
$593$	−3.65445e9			−0.719665			−0.359832	+	0.933017i	$0.617166\pi$
$594$	−9.44481e8	+	1.63589e9i	−0.184902	+	0.320259i
$595$	1.23243e9	+	2.13463e9i	0.239857	+	0.415444i
$596$	−1.39134e9	−	2.40987e9i	−0.269197	−	0.466264i
$597$	−7.37954e9	−	1.27817e10i	−1.41945	−	2.45855i
$598$	6.13226e8			0.117264
$599$	1.92795e9	+	3.33930e9i	0.366523	+	0.634836i	0.989019	−	0.147787i	$-0.0472149\pi$
$599$	1.92795e9	+	3.33930e9i	0.366523	+	0.634836i	−0.622497	+	0.782623i	$0.713882\pi$
$600$	3.01230e9			0.569336
$601$	−2.63560e8	+	4.56500e8i	−0.0495244	+	0.0857787i	−0.889725	−	0.456497i	$-0.849104\pi$
$601$	−2.63560e8	+	4.56500e8i	−0.0495244	+	0.0857787i	0.840201	+	0.542276i	$0.182437\pi$
$602$	3.47281e9			0.648774
$603$	9.81539e9			1.82304
$604$	2.77704e8	−	4.80997e8i	0.0512805	−	0.0888205i
$605$	−8.63351e8	−	1.49537e9i	−0.158505	−	0.274539i
$606$	3.13098e9			0.571513
$607$	−5.05115e9	+	8.74885e9i	−0.916706	+	1.58778i	−0.112321	+	0.993672i	$0.535828\pi$
$607$	−5.05115e9	+	8.74885e9i	−0.916706	+	1.58778i	−0.804385	+	0.594109i	$0.797505\pi$
$608$	8.75807e8	−	1.51694e9i	0.158032	−	0.273720i
$609$	−4.45029e9	+	7.70814e9i	−0.798414	+	1.38289i
$610$	9.02667e7	+	1.56346e8i	0.0161017	+	0.0278890i
$611$	−1.99485e8	−	3.45519e8i	−0.0353807	−	0.0612812i
$612$	−5.22499e9	+	9.04996e9i	−0.921416	+	1.59594i
$613$	1.40533e9	−	2.43410e9i	0.246414	−	0.426802i	−0.716114	−	0.697983i	$-0.754081\pi$
$613$	1.40533e9	−	2.43410e9i	0.246414	−	0.426802i	0.962528	+	0.271181i	$0.0874143\pi$
$614$	−3.33205e9	+	5.77127e9i	−0.580927	+	1.00620i
$615$	1.56784e9			0.271793
$616$	−2.05192e8	−	3.55402e8i	−0.0353693	−	0.0612615i
$617$	−2.48318e9	+	4.30099e9i	−0.425608	+	0.737175i	−0.996477	−	0.0838666i	$-0.973273\pi$
$617$	−2.48318e9	+	4.30099e9i	−0.425608	+	0.737175i	0.570869	+	0.821041i	$0.306606\pi$
$618$	−6.14944e9			−1.04803
$619$	1.17261e9			0.198717			0.0993585	−	0.995052i	$-0.468321\pi$
$619$	1.17261e9			0.198717			0.0993585	+	0.995052i	$0.468321\pi$
$620$	1.44372e7	−	2.50059e7i	0.00243282	−	0.00421377i
$621$	2.18156e10			3.65550
$622$	6.52169e8	+	1.12959e9i	0.108666	+	0.188215i
$623$	1.35584e9			0.224646
$624$	1.45216e8	+	2.51522e8i	0.0239259	+	0.0414409i
$625$	−2.06921e9	−	3.58397e9i	−0.339019	−	0.587198i
$626$	−5.69836e8	−	9.86986e8i	−0.0928411	−	0.160805i
$627$	2.24644e9	−	3.89094e9i	0.363963	−	0.630403i
$628$	2.87408e9			0.463063
$629$	−8.70602e8	−	1.00315e10i	−0.139490	−	1.60726i
$630$	3.01469e9			0.480342
$631$	6.17365e8	−	1.06931e9i	0.0978225	−	0.169434i	−0.812961	−	0.582319i	$-0.802146\pi$
$631$	6.17365e8	−	1.06931e9i	0.0978225	−	0.169434i	0.910783	+	0.412885i	$0.135479\pi$
$632$	−1.19594e9	−	2.07144e9i	−0.188452	−	0.326409i
$633$	9.53130e9	+	1.65087e10i	1.49362	+	2.58702i
$634$	2.10787e9	+	3.65094e9i	0.328497	+	0.568974i
$635$	3.96368e9			0.614315
$636$	−2.70848e9	−	4.69122e9i	−0.417470	−	0.723079i
$637$	1.42453e8			0.0218365
$638$	−5.15400e8	+	8.92699e8i	−0.0785728	+	0.136092i
$639$	4.08455e9			0.619285
$640$	1.95699e8			0.0295092
$641$	1.59902e9	−	2.76958e9i	0.239801	−	0.415347i	−0.720856	−	0.693085i	$-0.756251\pi$
$641$	1.59902e9	−	2.76958e9i	0.239801	−	0.415347i	0.960657	+	0.277738i	$0.0895846\pi$
$642$	4.58483e9	+	7.94116e9i	0.683834	+	1.18443i
$643$	−4.89977e9			−0.726838			−0.363419	−	0.931626i	$-0.618391\pi$
$643$	−4.89977e9			−0.726838			−0.363419	+	0.931626i	$0.618391\pi$
$644$	−2.36976e9	+	4.10454e9i	−0.349625	+	0.605569i
$645$	−2.12391e9	+	3.67872e9i	−0.311657	+	0.539805i
$646$	6.98773e9	−	1.21031e10i	1.01982	−	1.76637i
$647$	−5.91728e8	−	1.02490e9i	−0.0858928	−	0.148771i	0.819878	−	0.572538i	$-0.194041\pi$
$647$	−5.91728e8	−	1.02490e9i	−0.0858928	−	0.148771i	−0.905771	+	0.423767i	$0.860708\pi$
$648$	2.36880e9	+	4.10288e9i	0.341992	+	0.592347i
$649$	1.26806e9	−	2.19634e9i	0.182089	−	0.315387i
$650$	2.32300e8	−	4.02355e8i	0.0331781	−	0.0574662i
$651$	−1.65597e8	+	2.86822e8i	−0.0235244	+	0.0407454i
$652$	2.29147e9			0.323778
$653$	1.12120e9	+	1.94198e9i	0.157576	+	0.272929i	0.933994	−	0.357289i	$-0.116299\pi$
$653$	1.12120e9	+	1.94198e9i	0.157576	+	0.272929i	−0.776418	+	0.630218i	$0.782966\pi$
$654$	8.89975e8	−	1.54148e9i	0.124410	−	0.215485i
$655$	−4.26575e9			−0.593132
$656$	−8.11973e8			−0.112300
$657$	2.70679e8	−	4.68829e8i	0.0372370	−	0.0644965i
$658$	3.08357e9			0.421952
$659$	−5.75294e9	−	9.96438e9i	−0.783052	−	1.35629i	−0.930156	−	0.367165i	$-0.880328\pi$
$659$	−5.75294e9	−	9.96438e9i	−0.783052	−	1.35629i	0.147104	−	0.989121i	$-0.453005\pi$
$660$	5.01965e8			0.0679626
$661$	4.25077e9	+	7.36255e9i	0.572483	+	0.991569i	0.996310	+	0.0858260i	$0.0273529\pi$
$661$	4.25077e9	+	7.36255e9i	0.572483	+	0.991569i	−0.423828	+	0.905743i	$0.639314\pi$
$662$	−4.43626e9	−	7.68384e9i	−0.594312	−	1.02938i
$663$	1.15862e9	+	2.00679e9i	0.154399	+	0.267427i
$664$	1.32727e9	−	2.29890e9i	0.175943	−	0.304742i
$665$	−4.03174e9			−0.531639
$666$	−1.11578e10	−	5.21243e9i	−1.46359	−	0.683724i
$667$	1.19047e10			1.55338
$668$	−1.88543e9	+	3.26566e9i	−0.244733	+	0.423890i
$669$	8.05709e9	+	1.39553e10i	1.04037	+	1.80197i
$670$	−7.33292e8	−	1.27010e9i	−0.0941923	−	0.163146i
$671$	−1.19909e8	−	2.07689e8i	−0.0153223	−	0.0265390i
$672$	−2.24470e9			−0.285342
$673$	−4.38125e8	−	7.58854e8i	−0.0554045	−	0.0959634i	0.836993	−	0.547214i	$-0.184312\pi$
$673$	−4.38125e8	−	7.58854e8i	−0.0554045	−	0.0959634i	−0.892397	+	0.451250i	$0.850978\pi$
$674$	2.58035e9			0.324616
$675$	8.26410e9	−	1.43138e10i	1.03427	−	1.79140i
$676$	−3.97111e9			−0.494423
$677$	−7.06314e9			−0.874858			−0.437429	−	0.899253i	$-0.644111\pi$
$677$	−7.06314e9			−0.874858			−0.437429	+	0.899253i	$0.644111\pi$
$678$	5.44876e9	−	9.43753e9i	0.671419	−	1.16293i
$679$	2.87755e9	+	4.98407e9i	0.352760	+	0.610998i
$680$	1.56141e9			0.190430
$681$	9.26899e9	−	1.60544e10i	1.12465	−	1.94795i
$682$	−1.91782e7	+	3.32176e7i	−0.00231506	+	0.00400980i
$683$	1.47199e9	−	2.54956e9i	0.176780	−	0.306191i	−0.763996	−	0.645221i	$-0.776765\pi$
$683$	1.47199e9	−	2.54956e9i	0.176780	−	0.306191i	0.940776	+	0.339030i	$0.110099\pi$
$684$	−8.54647e9	−	1.48029e10i	−1.02115	−	1.76869i
$685$	3.10335e8	+	5.37517e8i	0.0368905	+	0.0638962i
$686$	−3.21301e9	+	5.56510e9i	−0.379995	+	0.658171i
$687$	−9.13930e8	+	1.58297e9i	−0.107539	+	0.186262i
$688$	1.09996e9	−	1.90518e9i	0.128770	−	0.223037i
$689$	−8.35479e8			−0.0973125
$690$	−2.89860e9	−	5.02051e9i	−0.335904	−	0.581804i
$691$	6.37492e7	−	1.10417e8i	0.00735024	−	0.0127310i	−0.862327	−	0.506352i	$-0.830994\pi$
$691$	6.37492e7	−	1.10417e8i	0.00735024	−	0.0127310i	0.869677	+	0.493621i	$0.164327\pi$
$692$	−3.96502e9			−0.454856
$693$	−4.00468e9			−0.457090
$694$	−4.60923e9	+	7.98342e9i	−0.523444	+	0.906631i
$695$	−3.08644e9			−0.348747
$696$	2.81911e9	+	4.88285e9i	0.316942	+	0.548960i
$697$	−6.47842e9			−0.724693
$698$	1.77470e9	+	3.07386e9i	0.197529	+	0.342129i
$699$	1.44321e10	+	2.49971e10i	1.59830	+	2.76834i
$700$	1.79540e9	+	3.10973e9i	0.197842	+	0.342673i
$701$	−5.74814e9	+	9.95607e9i	−0.630252	+	1.09163i	0.357248	+	0.934010i	$0.383715\pi$
$701$	−5.74814e9	+	9.95607e9i	−0.630252	+	1.09163i	−0.987500	+	0.157619i	$0.949618\pi$
$702$	1.59357e9			0.173857
$703$	1.49221e10	+	6.97093e9i	1.61989	+	0.756741i
$704$	−2.59964e8			−0.0280808
$705$	−1.88585e9	+	3.26640e9i	−0.202697	+	0.351081i
$706$	1.52689e9	+	2.64466e9i	0.163302	+	0.282848i
$707$	1.86614e9	+	3.23225e9i	0.198599	+	0.343983i
$708$	−6.93598e9	−	1.20135e10i	−0.734500	−	1.27219i
$709$	6.77727e9			0.714156			0.357078	−	0.934075i	$-0.383773\pi$
$709$	6.77727e9			0.714156			0.357078	+	0.934075i	$0.383773\pi$
$710$	−3.05150e8	−	5.28536e8i	−0.0319970	−	0.0554205i
$711$	−2.33410e10			−2.43543
$712$	4.29438e8	−	7.43809e8i	0.0445883	−	0.0772292i
$713$	4.42977e8			0.0457686
$714$	−1.79096e10			−1.84137
$715$	3.87101e7	−	6.70479e7i	0.00396053	−	0.00685984i
$716$	4.10860e9	+	7.11631e9i	0.418310	+	0.724534i
$717$	−3.54062e10			−3.58726
$718$	1.53666e9	−	2.66158e9i	0.154933	−	0.268351i
$719$	−7.06511e8	+	1.22371e9i	−0.0708872	+	0.122780i	−0.899290	−	0.437352i	$-0.855916\pi$
$719$	−7.06511e8	+	1.22371e9i	−0.0708872	+	0.122780i	0.828403	+	0.560132i	$0.189250\pi$
$720$	9.54853e8	−	1.65385e9i	0.0953395	−	0.165133i
$721$	−3.66521e9	−	6.34834e9i	−0.364188	−	0.630793i
$722$	7.85427e9	+	1.36040e10i	0.776651	+	1.34520i
$723$	7.16725e9	−	1.24140e10i	0.705291	−	1.22160i
$724$	−2.16415e9	+	3.74842e9i	−0.211935	+	0.367082i
$725$	4.50969e9	−	7.81102e9i	0.439505	−	0.761245i
$726$	1.25462e10			1.21684
$727$	−8.63764e9	−	1.49608e10i	−0.833728	−	1.44406i	−0.895062	−	0.445943i	$-0.852869\pi$
$727$	−8.63764e9	−	1.49608e10i	−0.833728	−	1.44406i	0.0613331	−	0.998117i	$-0.480465\pi$
$728$	−1.73105e8	+	2.99826e8i	−0.0166283	+	0.0288011i
$729$	2.09762e9			0.200531
$730$	−8.08880e7			−0.00769580
$731$	8.77613e9	−	1.52007e10i	0.830983	−	1.43930i
$732$	−1.31175e9			−0.123612
$733$	4.46544e9	+	7.73436e9i	0.418793	+	0.725372i	0.995818	−	0.0913549i	$-0.0291198\pi$
$733$	4.46544e9	+	7.73436e9i	0.418793	+	0.725372i	−0.577025	+	0.816727i	$0.695786\pi$
$734$	2.65709e9			0.248011
$735$	−6.73347e8	−	1.16627e9i	−0.0625509	−	0.108341i
$736$	1.50116e9	+	2.60009e9i	0.138789	+	0.240390i
$737$	9.74098e8	+	1.68719e9i	0.0896327	+	0.155248i
$738$	−3.96177e9	+	6.86200e9i	−0.362821	+	0.628425i
$739$	1.77655e10			1.61928			0.809640	−	0.586927i	$-0.199663\pi$
$739$	1.77655e10			1.61928			0.809640	+	0.586927i	$0.199663\pi$
$740$	1.59100e8	+	1.83322e9i	0.0144331	+	0.166304i
$741$	−3.79030e9			−0.342223
$742$	3.22864e9	−	5.59216e9i	0.290138	−	0.502535i
$743$	−1.02587e10	−	1.77686e10i	−0.917553	−	1.58925i	−0.803120	−	0.595817i	$-0.796828\pi$
$743$	−1.02587e10	−	1.77686e10i	−0.917553	−	1.58925i	−0.114433	−	0.993431i	$-0.536505\pi$
$744$	1.04900e8	+	1.81692e8i	0.00933835	+	0.0161745i
$745$	2.02867e9	+	3.51376e9i	0.179748	+	0.311333i
$746$	−7.36364e9			−0.649392
$747$	−1.29520e10	−	2.24336e10i	−1.13688	−	1.96914i
$748$	−2.07415e9			−0.181211
$749$	−5.46534e9	+	9.46624e9i	−0.475259	+	0.823173i
$750$	−9.33525e9			−0.808000
$751$	−1.51278e10			−1.30328			−0.651639	−	0.758529i	$-0.725918\pi$
$751$	−1.51278e10			−1.30328			−0.651639	+	0.758529i	$0.725918\pi$
$752$	9.76671e8	−	1.69164e9i	0.0837502	−	0.145060i
$753$	−8.98833e9	−	1.55682e10i	−0.767179	−	1.32879i
$754$	8.69608e8			0.0738795
$755$	−4.04911e8	+	7.01327e8i	−0.0342409	+	0.0593071i
$756$	−6.15823e9	+	1.06664e10i	−0.518357	+	0.897821i
$757$	−9.97234e9	+	1.72726e10i	−0.835529	+	1.44718i	0.0580695	+	0.998313i	$0.481505\pi$
$757$	−9.97234e9	+	1.72726e10i	−0.835529	+	1.44718i	−0.893599	+	0.448867i	$0.851828\pi$
$758$	−4.26793e9	−	7.39227e9i	−0.355938	−	0.616503i
$759$	3.85046e9	+	6.66920e9i	0.319644	+	0.553640i
$760$	−1.27699e9	+	2.21181e9i	−0.105521	+	0.182768i
$761$	−7.91806e9	+	1.37145e10i	−0.651287	+	1.12806i	0.331524	+	0.943447i	$0.392437\pi$
$761$	−7.91806e9	+	1.37145e10i	−0.651287	+	1.12806i	−0.982811	+	0.184616i	$0.940896\pi$
$762$	−1.44000e10	+	2.49415e10i	−1.17902	+	2.04212i
$763$	2.12179e9			0.172928
$764$	3.71491e9	+	6.43440e9i	0.301385	+	0.522013i
$765$	7.61840e9	−	1.31955e10i	0.615246	−	1.06564i
$766$	−2.99972e9			−0.241146
$767$	−2.13953e9			−0.171212
$768$	−7.10971e8	+	1.23144e9i	−0.0566353	+	0.0980953i
$769$	5.88125e9			0.466367			0.233183	−	0.972433i	$-0.425086\pi$
$769$	5.88125e9			0.466367			0.233183	+	0.972433i	$0.425086\pi$
$770$	2.99184e8	+	5.18201e8i	0.0236168	+	0.0409054i
$771$	−3.76793e10			−2.96082
$772$	1.23489e9	+	2.13890e9i	0.0965982	+	0.167313i
$773$	1.26144e10	+	2.18488e10i	0.982287	+	1.70137i	0.653423	+	0.756993i	$0.273332\pi$
$773$	1.26144e10	+	2.18488e10i	0.982287	+	1.70137i	0.328864	+	0.944377i	$0.393334\pi$
$774$	−1.07338e10	−	1.85915e10i	−0.832071	−	1.44119i
$775$	1.67807e8	−	2.90650e8i	0.0129495	−	0.0224292i
$776$	3.64567e9			0.280067
$777$	−1.82490e9	−	2.10273e10i	−0.139562	−	1.60809i
$778$	6.93639e9			0.528086
$779$	5.29834e9	−	9.17700e9i	0.401568	−	0.695536i
$780$	−2.11735e8	−	3.66736e8i	−0.0159758	−	0.0276708i
$781$	4.05358e8	+	7.02101e8i	0.0304481	+	0.0527377i
$782$	1.19772e10	+	2.07451e10i	0.895636	+	1.55129i
$783$	3.09365e10			2.30306
$784$	3.48722e8	+	6.04004e8i	0.0258448	+	0.0447645i
$785$	−4.19061e9			−0.309196
$786$	1.54974e10	−	2.68423e10i	1.13836	−	1.97170i
$787$	−4.50807e8			−0.0329670			−0.0164835	−	0.999864i	$-0.505247\pi$
$787$	−4.50807e8			−0.0329670			−0.0164835	+	0.999864i	$0.505247\pi$
$788$	−9.16830e9			−0.667493
$789$	4.09174e9	−	7.08710e9i	0.296578	−	0.513687i
$790$	1.74377e9	+	3.02030e9i	0.125833	+	0.217949i
$791$	1.29904e10			0.933263
$792$	−1.26842e9	+	2.19696e9i	−0.0907243	+	0.157139i
$793$	−1.01158e8	+	1.75211e8i	−0.00720354	+	0.0124769i
$794$	−1.92606e9	+	3.33603e9i	−0.136552	+	0.236515i
$795$	3.94915e9	+	6.84012e9i	0.278752	+	0.482813i
$796$	−5.57246e9	−	9.65179e9i	−0.391608	−	0.678285i
$797$	1.84768e9	−	3.20028e9i	0.129278	−	0.223915i	−0.794119	−	0.607762i	$-0.792067\pi$
$797$	1.84768e9	−	3.20028e9i	0.129278	−	0.223915i	0.923397	+	0.383847i	$0.125401\pi$
$798$	1.46473e10	−	2.53698e10i	1.02034	−	1.76729i
$799$	7.79248e9	−	1.34970e10i	0.540458	−	0.936101i
$800$	2.27466e9			0.157073
$801$	−4.19063e9	−	7.25838e9i	−0.288115	−	0.499029i
$802$	4.06278e9	−	7.03694e9i	0.278108	−	0.481697i
$803$	1.07451e8			0.00732327
$804$	1.06562e10			0.723111
$805$	3.45527e9	−	5.98470e9i	0.233451	−	0.404349i
$806$	3.23583e7			0.00217677
$807$	2.37199e9	+	4.10840e9i	0.158875	+	0.275179i
$808$	2.36428e9			0.157673
$809$	−5.03566e9	−	8.72202e9i	−0.334377	−	0.579158i	0.648988	−	0.760799i	$-0.275193\pi$
$809$	−5.03566e9	−	8.72202e9i	−0.334377	−	0.579158i	−0.983365	+	0.181641i	$0.941859\pi$
$810$	−3.45387e9	−	5.98228e9i	−0.228354	−	0.395521i
$811$	−1.29607e10	−	2.24486e10i	−0.853211	−	1.47780i	−0.878295	−	0.478119i	$-0.841319\pi$
$811$	−1.29607e10	−	2.24486e10i	−0.853211	−	1.47780i	0.0250838	−	0.999685i	$-0.492015\pi$
$812$	−3.36052e9	+	5.82059e9i	−0.220273	+	0.381523i
$813$	3.97591e10			2.59489
$814$	−2.11347e8	−	2.43523e9i	−0.0137344	−	0.158254i
$815$	−3.34112e9			−0.216192
$816$	−5.67256e9	+	9.82517e9i	−0.365480	+	0.633030i
$817$	1.43550e10	+	2.48636e10i	0.920930	+	1.59510i
$818$	4.83023e9	+	8.36621e9i	0.308554	+	0.534432i
$819$	1.68922e9	+	2.92582e9i	0.107447	+	0.186103i
$820$	1.18391e9			0.0749844
$821$	3.05111e9	+	5.28467e9i	0.192423	+	0.333286i	0.946053	−	0.324013i	$-0.105032\pi$
$821$	3.05111e9	+	5.28467e9i	0.192423	+	0.333286i	−0.753630	+	0.657299i	$0.771699\pi$
$822$	−4.50978e9			−0.283207
$823$	−2.74366e9	+	4.75215e9i	−0.171566	+	0.297160i	−0.938967	−	0.344006i	$-0.888216\pi$
$823$	−2.74366e9	+	4.75215e9i	−0.171566	+	0.297160i	0.767402	+	0.641167i	$0.221549\pi$
$824$	−4.64358e9			−0.289140
$825$	5.83447e9			0.361754
$826$	8.26803e9	−	1.43206e10i	0.510472	−	0.884163i
$827$	−2.13901e9	−	3.70488e9i	−0.131506	−	0.227774i	0.792752	−	0.609545i	$-0.208648\pi$
$827$	−2.13901e9	−	3.70488e9i	−0.131506	−	0.227774i	−0.924257	+	0.381770i	$0.875314\pi$
$828$	2.92979e10			1.79362
$829$	−3.29635e9	+	5.70945e9i	−0.200952	+	0.348059i	−0.948835	−	0.315771i	$-0.897737\pi$
$829$	−3.29635e9	+	5.70945e9i	−0.200952	+	0.348059i	0.747883	+	0.663830i	$0.231070\pi$
$830$	−1.93526e9	+	3.35196e9i	−0.117480	+	0.203482i
$831$	−2.07283e10	+	3.59024e10i	−1.25302	+	2.17030i
$832$	1.09656e8	+	1.89930e8i	0.00660087	+	0.0114330i
$833$	2.78232e9	+	4.81912e9i	0.166782	+	0.288875i
$834$	1.12130e10	−	1.94215e10i	0.669330	−	1.15931i
$835$	2.74909e9	−	4.76156e9i	0.163413	−	0.283039i
$836$	1.69634e9	−	2.93814e9i	0.100413	−	0.173921i
$837$	1.15115e9			0.0678569
$838$	2.62333e9	+	4.54374e9i	0.153992	+	0.266722i
$839$	1.37233e10	−	2.37695e10i	0.802218	−	1.38948i	−0.115935	−	0.993257i	$-0.536986\pi$
$839$	1.37233e10	−	2.37695e10i	0.802218	−	1.38948i	0.918153	−	0.396226i	$-0.129680\pi$
$840$	3.27292e9			0.190528
$841$	−3.67962e8			−0.0213313
$842$	−6.40637e9	+	1.10962e10i	−0.369845	+	0.640591i
$843$	−2.98927e10			−1.71858
$844$	7.19731e9	+	1.24661e10i	0.412070	+	0.713727i
$845$	5.79015e9			0.330135
$846$	−9.53074e9	−	1.65077e10i	−0.541166	−	0.937326i
$847$	7.47782e9	+	1.29520e10i	0.422847	+	0.732393i
$848$	−2.04523e9	−	3.54245e9i	−0.115175	−	0.199489i
$849$	−1.10276e10	+	1.91004e10i	−0.618452	+	1.07119i
$850$	1.81486e10			1.01363
$851$	−2.31361e10	+	1.61761e10i	−1.28687	+	0.899745i
$852$	4.43443e9			0.245640
$853$	1.13569e10	−	1.96707e10i	0.626524	−	1.08517i	−0.361720	−	0.932287i	$-0.617810\pi$
$853$	1.13569e10	−	1.96707e10i	0.626524	−	1.08517i	0.988244	−	0.152885i	$-0.0488564\pi$
$854$	−7.81835e8	−	1.35418e9i	−0.0429549	−	0.0744000i
$855$	1.24613e10	+	2.15837e10i	0.681842	+	1.18098i
$856$	3.46211e9	+	5.99655e9i	0.188661	+	0.326771i
$857$	−3.62135e10			−1.96534			−0.982669	−	0.185369i	$-0.940652\pi$
$857$	−3.62135e10			−1.96534			−0.982669	+	0.185369i	$0.940652\pi$
$858$	2.81267e8	+	4.87168e8i	0.0152024	+	0.0263314i
$859$	1.00264e10			0.539722			0.269861	−	0.962899i	$-0.413022\pi$
$859$	1.00264e10			0.539722			0.269861	+	0.962899i	$0.413022\pi$
$860$	−1.60381e9	+	2.77788e9i	−0.0859823	+	0.148926i
$861$	−1.35797e10			−0.725067
$862$	1.30282e10			0.692803
$863$	−1.87695e10	+	3.25097e10i	−0.994065	+	1.72177i	−0.402817	+	0.915281i	$0.631969\pi$
$863$	−1.87695e10	+	3.25097e10i	−0.994065	+	1.72177i	−0.591248	+	0.806490i	$0.701365\pi$
$864$	3.90103e9	+	6.75679e9i	0.205770	+	0.356404i
$865$	5.78127e9			0.303715
$866$	−4.48447e9	+	7.76732e9i	−0.234638	+	0.406405i
$867$	−2.78702e10	+	4.82726e10i	−1.45236	+	2.51556i
$868$	−1.25046e8	+	2.16586e8i	−0.00649008	+	0.0112412i
$869$	−2.31641e9	−	4.01213e9i	−0.119742	−	0.207399i
$870$	−4.11046e9	−	7.11953e9i	−0.211628	−	0.366551i
$871$	8.21773e8	−	1.42335e9i	0.0421394	−	0.0729876i
$872$	6.72041e8	−	1.16401e9i	0.0343232	−	0.0594496i
$873$	1.77880e10	−	3.08096e10i	0.904849	−	1.56724i
$874$	−3.91820e10			−1.98516
$875$	−5.56403e9	−	9.63719e9i	−0.280777	−	0.486320i
$876$	2.93865e8	−	5.08989e8i	0.0147701	−	0.0255826i
$877$	1.12809e10			0.564738			0.282369	−	0.959306i	$-0.408880\pi$
$877$	1.12809e10			0.564738			0.282369	+	0.959306i	$0.408880\pi$
$878$	2.52847e10			1.26074
$879$	−1.83692e10	+	3.18163e10i	−0.912281	+	1.58012i
$880$	3.79046e8			0.0187500
$881$	−1.46946e9	−	2.54519e9i	−0.0724008	−	0.125402i	0.827552	−	0.561389i	$-0.189733\pi$
$881$	−1.46946e9	−	2.54519e9i	−0.0724008	−	0.125402i	−0.899953	+	0.435987i	$0.856399\pi$
$882$	6.80593e9			0.334001
$883$	1.55098e9	+	2.68638e9i	0.0758131	+	0.131312i	0.901440	−	0.432905i	$-0.142511\pi$
$883$	1.55098e9	+	2.68638e9i	0.0758131	+	0.131312i	−0.825626	+	0.564217i	$0.809178\pi$
$884$	8.74904e8	+	1.51538e9i	0.0425968	+	0.0737799i
$885$	1.01131e10	+	1.75165e10i	0.490439	+	0.849465i
$886$	5.86052e9	−	1.01507e10i	0.283086	−	0.490319i
$887$	−1.27373e10			−0.612834			−0.306417	−	0.951897i	$-0.599130\pi$
$887$	−1.27373e10			−0.612834			−0.306417	+	0.951897i	$0.599130\pi$
$888$	−1.21136e10	−	5.65893e9i	−0.580533	−	0.271199i
$889$	−3.43310e10			−1.63882
$890$	−6.26151e8	+	1.08453e9i	−0.0297724	+	0.0515673i
$891$	4.58809e9	+	7.94680e9i	0.217300	+	0.376375i
$892$	6.08410e9	+	1.05380e10i	0.287025	+	0.497141i
$893$	1.27461e10	+	2.20769e10i	0.598958	+	1.03743i
$894$	−2.94805e10			−1.37992
$895$	−5.99063e9	−	1.03761e10i	−0.279313	−	0.483785i
$896$	−1.69502e9			−0.0787223
$897$	3.24835e9	−	5.62630e9i	0.150276	−	0.260285i
$898$	7.63203e9			0.351700
$899$	6.28180e8			0.0288354
$900$	1.10985e10	−	1.92232e10i	0.507476	−	0.878974i
$901$	−1.63181e10	−	2.82638e10i	−0.743248	−	1.28734i
$902$	−1.57270e9			−0.0713546
$903$	1.83960e10	−	3.18628e10i	0.831412	−	1.44005i
$904$	4.11449e9	−	7.12650e9i	0.185236	−	0.320839i
$905$	3.15548e9	−	5.46546e9i	0.141513	−	0.245107i
$906$	−2.94208e9	−	5.09582e9i	−0.131433	−	0.227649i
$907$	9.60445e9	+	1.66354e10i	0.427412	+	0.740300i	0.996642	−	0.0818785i	$-0.0260919\pi$
$907$	9.60445e9	+	1.66354e10i	0.427412	+	0.740300i	−0.569230	+	0.822178i	$0.692759\pi$
$908$	6.99923e9	−	1.21230e10i	0.310277	−	0.537416i
$909$	1.15358e10	−	1.99805e10i	0.509417	−	0.882336i
$910$	2.52398e8	−	4.37167e8i	0.0111030	−	0.0192310i
$911$	−2.23134e8			−0.00977803			−0.00488902	−	0.999988i	$-0.501556\pi$
$911$	−2.23134e8			−0.00977803			−0.00488902	+	0.999988i	$0.501556\pi$
$912$	−9.27856e9	−	1.60709e10i	−0.405041	−	0.701551i
$913$	2.57077e9	−	4.45271e9i	0.111793	−	0.193632i
$914$	1.44513e10			0.626032
$915$	1.91262e9			0.0825383
$916$	−6.90130e8	+	1.19534e9i	−0.0296686	+	0.0513875i
$917$	3.69474e10			1.58231
$918$	3.11248e10	+	5.39098e10i	1.32788	+	2.29995i
$919$	−2.97255e10			−1.26335			−0.631677	−	0.775232i	$-0.717633\pi$
$919$	−2.97255e10			−1.26335			−0.631677	+	0.775232i	$0.717633\pi$
$920$	−2.18880e9	−	3.79111e9i	−0.0926719	−	0.160513i
$921$	3.53007e10	+	6.11425e10i	1.48893	+	2.57890i
$922$	−1.18799e10	−	2.05766e10i	−0.499178	−	0.864602i
$923$	3.41970e8	−	5.92310e8i	0.0143147	−	0.0247938i
$924$	−4.34772e9			−0.181305
$925$	1.84926e9	+	2.13080e10i	0.0768250	+	0.885211i
$926$	5.23020e9			0.216461
$927$	−2.26570e10	+	3.92430e10i	−0.934163	+	1.61802i
$928$	2.12878e9	+	3.68716e9i	0.0874405	+	0.151451i
$929$	4.68552e8	+	8.11556e8i	0.0191736	+	0.0332096i	0.875453	−	0.483303i	$-0.160563\pi$
$929$	4.68552e8	+	8.11556e8i	0.0191736	+	0.0332096i	−0.856279	+	0.516513i	$0.827230\pi$
$930$	−1.52951e8	−	2.64920e8i	−0.00623538	−	0.0108000i
$931$	−9.10202e9			−0.369670
$932$	1.08980e10	+	1.88759e10i	0.440952	+	0.763752i
$933$	1.38185e10			0.557028
$934$	−6.12744e9	+	1.06130e10i	−0.246074	+	0.426212i
$935$	3.02426e9			0.120998
$936$	2.14013e9			0.0853052
$937$	−5.78172e9	+	1.00142e10i	−0.229598	+	0.397676i	−0.957689	−	0.287805i	$-0.907075\pi$
$937$	−5.78172e9	+	1.00142e10i	−0.229598	+	0.397676i	0.728091	+	0.685481i	$0.240408\pi$
$938$	6.35133e9	+	1.10008e10i	0.251278	+	0.435227i
$939$	−1.20740e10			−0.475908
$940$	−1.42405e9	+	2.46653e9i	−0.0559215	+	0.0968589i
$941$	7.55941e9	−	1.30933e10i	0.295750	−	0.512253i	−0.679409	−	0.733759i	$-0.737764\pi$
$941$	7.55941e9	−	1.30933e10i	0.295750	−	0.512253i	0.975159	+	0.221506i	$0.0710973\pi$
$942$	1.52244e10	−	2.63695e10i	0.593421	−	1.02784i
$943$	9.08153e9	+	1.57297e10i	0.352670	+	0.610842i
$944$	−5.23753e9	−	9.07166e9i	−0.202640	−	0.350982i
$945$	8.97912e9	−	1.55523e10i	0.346117	−	0.599491i
$946$	2.13049e9	−	3.69011e9i	0.0818201	−	0.141717i
$947$	2.33151e10	−	4.03829e10i	0.892097	−	1.54516i	0.0547395	−	0.998501i	$-0.482567\pi$
$947$	2.33151e10	−	4.03829e10i	0.892097	−	1.54516i	0.837357	−	0.546656i	$-0.184100\pi$
$948$	−2.53404e10			−0.966015
$949$	−4.53240e7	−	7.85035e7i	−0.00172146	−	0.00298165i
$950$	−1.48428e10	+	2.57084e10i	−0.561671	+	0.972843i
$951$	4.46628e10			1.68389
$952$	−1.35239e10			−0.508012
$953$	1.89496e10	−	3.28217e10i	0.709212	−	1.22839i	−0.255938	−	0.966693i	$-0.582384\pi$
$953$	1.89496e10	−	3.28217e10i	0.709212	−	1.22839i	0.965150	−	0.261698i	$-0.0842823\pi$
$954$	−3.99164e10			−1.48844
$955$	−5.41659e9	−	9.38181e9i	−0.201240	−	0.348558i
$956$	−2.67361e10			−0.989681
$957$	5.46030e9	+	9.45752e9i	0.201384	+	0.348807i
$958$	1.21844e10	+	2.11040e10i	0.447739	+	0.775506i
$959$	−2.68794e9	−	4.65564e9i	−0.0984133	−	0.170457i
$960$	1.03664e9	−	1.79552e9i	0.0378164	−	0.0655000i
$961$	−2.74892e10			−0.999150
$962$	−1.69003e9	+	1.18162e9i	−0.0612043	+	0.0427923i
$963$	6.75693e10			2.43813
$964$	5.41216e9	−	9.37414e9i	0.194581	−	0.337025i
$965$	−1.80056e9	−	3.11866e9i	−0.0645004	−	0.111718i
$966$	2.51059e10	+	4.34847e10i	0.896098	+	1.55209i
$967$	−1.27178e10	−	2.20278e10i	−0.452291	−	0.783391i	0.546237	−	0.837631i	$-0.316060\pi$
$967$	−1.27178e10	−	2.20278e10i	−0.452291	−	0.783391i	−0.998528	+	0.0542399i	$0.982726\pi$
$968$	9.47391e9			0.335711
$969$	−7.40300e10	−	1.28224e11i	−2.61381	−	4.52726i
$970$	−5.31564e9			−0.187006
$971$	−1.25914e10	+	2.18090e10i	−0.441375	+	0.764483i	−0.997792	−	0.0664199i	$-0.978842\pi$
$971$	−1.25914e10	+	2.18090e10i	−0.441375	+	0.764483i	0.556417	+	0.830903i	$0.312176\pi$
$972$	1.68651e10			0.589056
$973$	2.67328e10			0.930358
$974$	1.58452e10	−	2.74446e10i	0.549466	−	0.951703i
$975$	−2.46105e9	−	4.26267e9i	−0.0850363	−	0.147287i
$976$	−9.90533e8			−0.0341032
$977$	1.50875e10	−	2.61323e10i	0.517590	−	0.896493i	−0.482201	−	0.876061i	$-0.660162\pi$
$977$	1.50875e10	−	2.61323e10i	0.517590	−	0.896493i	0.999791	−	0.0204322i	$-0.00650422\pi$
$978$	1.21382e10	−	2.10240e10i	0.414925	−	0.718671i
$979$	8.31773e8	−	1.44067e9i	0.0283312	−	0.0490711i
$980$	−5.08461e8	−	8.80680e8i	−0.0172570	−	0.0298901i
$981$	−6.55804e9	−	1.13589e10i	−0.221785	−	0.384143i
$982$	−2.55399e9	+	4.42363e9i	−0.0860654	+	0.149070i
$983$	1.63474e10	−	2.83146e10i	0.548923	−	0.950763i	−0.449425	−	0.893318i	$-0.648371\pi$
$983$	1.63474e10	−	2.83146e10i	0.548923	−	0.950763i	0.998349	−	0.0574453i	$-0.0182955\pi$
$984$	−4.30114e9	+	7.44979e9i	−0.143913	+	0.249265i
$985$	1.33680e10			0.445697
$986$	1.69847e10	+	2.94184e10i	0.564273	+	0.977349i
$987$	1.63341e10	−	2.82915e10i	0.540737	−	0.936584i
$988$	−2.86214e9			−0.0944152
$989$	−4.92100e10			−1.61758
$990$	1.84944e9	−	3.20332e9i	0.0605783	−	0.104925i
$991$	2.65672e10			0.867138			0.433569	−	0.901120i	$-0.357254\pi$
$991$	2.65672e10			0.867138			0.433569	+	0.901120i	$0.357254\pi$
$992$	7.92124e7	+	1.37200e8i	0.00257634	+	0.00446234i
$993$	−9.39982e10			−3.04647
$994$	2.64303e9	+	4.57786e9i	0.0853590	+	0.147846i
$995$	8.12504e9	+	1.40730e10i	0.261484	+	0.452903i
$996$	−1.40615e10	−	2.43553e10i	−0.450946	−	0.781061i
$997$	−2.23978e9	+	3.87942e9i	−0.0715769	+	0.123975i	−0.899593	−	0.436730i	$-0.856136\pi$
$997$	−2.23978e9	+	3.87942e9i	−0.0715769	+	0.123975i	0.828016	+	0.560705i	$0.189470\pi$
$998$	−2.00679e10			−0.639065
$999$	−6.01232e10	+	4.20363e10i	−1.90793	+	1.33397i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.8.c.b.47.1	✓	24
37.26	even	3	inner	74.8.c.b.63.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.8.c.b.47.1	✓	24	1.1	even	1	trivial
74.8.c.b.63.1	yes	24	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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	74.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.00000 - 6.92820i) q^{2} +(-42.3772 - 73.3994i) q^{3} +(-32.0000 - 55.4256i) q^{4} +(46.6582 + 80.8144i) q^{5} -678.035 q^{6} +(-404.125 - 699.965i) q^{7} -512.000 q^{8} +(-2498.15 + 4326.92i) q^{9} +O(q^{10})\)	\(q+(4.00000 - 6.92820i) q^{2} +(-42.3772 - 73.3994i) q^{3} +(-32.0000 - 55.4256i) q^{4} +(46.6582 + 80.8144i) q^{5} -678.035 q^{6} +(-404.125 - 699.965i) q^{7} -512.000 q^{8} +(-2498.15 + 4326.92i) q^{9} +746.531 q^{10} -991.685 q^{11} +(-2712.14 + 4697.56i) q^{12} +(418.305 + 724.525i) q^{13} -6466.00 q^{14} +(3954.49 - 6849.37i) q^{15} +(-2048.00 + 3547.24i) q^{16} +(-16340.2 + 28302.1i) q^{17} +(19985.2 + 34615.4i) q^{18} +(-26727.5 - 46293.4i) q^{19} +(2986.13 - 5172.12i) q^{20} +(-34251.4 + 59325.1i) q^{21} +(-3966.74 + 6870.59i) q^{22} +91623.6 q^{23} +(21697.1 + 37580.5i) q^{24} +(34708.5 - 60116.9i) q^{25} +6692.87 q^{26} +238100. q^{27} +(-25864.0 + 44797.8i) q^{28} +129930. q^{29} +(-31635.9 - 54795.0i) q^{30} +4834.74 q^{31} +(16384.0 + 28377.9i) q^{32} +(42024.8 + 72789.1i) q^{33} +(130722. + 226417. i) q^{34} +(37711.5 - 65318.3i) q^{35} +319763. q^{36} +(-252512. + 176549. i) q^{37} -427640. q^{38} +(35453.1 - 61406.6i) q^{39} +(-23889.0 - 41377.0i) q^{40} +(99117.8 + 171677. i) q^{41} +(274011. + 474601. i) q^{42} -537088. q^{43} +(31733.9 + 54964.7i) q^{44} -466237. q^{45} +(366495. - 634787. i) q^{46} -476890. q^{47} +347154. q^{48} +(85137.2 - 147462. i) q^{49} +(-277668. - 480935. i) q^{50} +2.76981e6 q^{51} +(26771.5 - 46369.6i) q^{52} +(-499325. + 864856. i) q^{53} +(952401. - 1.64961e6i) q^{54} +(-46270.2 - 80142.4i) q^{55} +(206912. + 358382. i) q^{56} +(-2.26527e6 + 3.92357e6i) q^{57} +(519722. - 900184. i) q^{58} +(-1.27869e6 + 2.21476e6i) q^{59} -506174. q^{60} +(120915. + 209430. i) q^{61} +(19339.0 - 33496.1i) q^{62} +4.03826e6 q^{63} +262144. q^{64} +(-39034.7 + 67610.1i) q^{65} +672397. q^{66} +(-982266. - 1.70133e6i) q^{67} +2.09155e6 q^{68} +(-3.88275e6 - 6.72512e6i) q^{69} +(-301692. - 522546. i) q^{70} +(-408757. - 707988. i) q^{71} +(1.27905e6 - 2.21538e6i) q^{72} -108352. q^{73} +(213119. + 2.45565e6i) q^{74} -5.88340e6 q^{75} +(-1.71056e6 + 2.96278e6i) q^{76} +(400765. + 694145. i) q^{77} +(-283625. - 491253. i) q^{78} +(2.33583e6 + 4.04577e6i) q^{79} -382224. q^{80} +(-4.62656e6 - 8.01343e6i) q^{81} +1.58588e6 q^{82} +(-2.59233e6 + 4.49005e6i) q^{83} +4.38417e6 q^{84} -3.04962e6 q^{85} +(-2.14835e6 + 3.72105e6i) q^{86} +(-5.50608e6 - 9.53682e6i) q^{87} +507743. q^{88} +(-838747. + 1.45275e6i) q^{89} +(-1.86495e6 + 3.23018e6i) q^{90} +(338095. - 585598. i) q^{91} +(-2.93196e6 - 5.07830e6i) q^{92} +(-204883. - 354867. i) q^{93} +(-1.90756e6 + 3.30399e6i) q^{94} +(2.49412e6 - 4.31994e6i) q^{95} +(1.38862e6 - 2.40515e6i) q^{96} -7.12045e6 q^{97} +(-681097. - 1.17970e6i) q^{98} +(2.47738e6 - 4.29094e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 96 q^{2} + 40 q^{3} - 768 q^{4} - 136 q^{5} + 640 q^{6} + 536 q^{7} - 12288 q^{8} - 12014 q^{9}+O(q^{10}) \) 24 * q + 96 * q^2 + 40 * q^3 - 768 * q^4 - 136 * q^5 + 640 * q^6 + 536 * q^7 - 12288 * q^8 - 12014 * q^9	\( 24 q + 96 q^{2} + 40 q^{3} - 768 q^{4} - 136 q^{5} + 640 q^{6} + 536 q^{7} - 12288 q^{8} - 12014 q^{9} - 2176 q^{10} - 3448 q^{11} + 2560 q^{12} + 186 q^{13} + 8576 q^{14} + 10628 q^{15} - 49152 q^{16} - 1212 q^{17} + 96112 q^{18} + 15980 q^{19} - 8704 q^{20} + 6994 q^{21} - 13792 q^{22} - 62464 q^{23} - 20480 q^{24} - 48368 q^{25} + 2976 q^{26} - 323648 q^{27} + 34304 q^{28} + 200084 q^{29} - 85024 q^{30} + 609672 q^{31} + 393216 q^{32} + 131560 q^{33} + 9696 q^{34} + 43132 q^{35} + 1537792 q^{36} - 557790 q^{37} + 255680 q^{38} - 694460 q^{39} + 69632 q^{40} + 377724 q^{41} - 55952 q^{42} - 304456 q^{43} + 110336 q^{44} + 3686244 q^{45} - 249856 q^{46} - 2156696 q^{47} - 327680 q^{48} - 2929078 q^{49} + 386944 q^{50} + 968912 q^{51} + 11904 q^{52} + 2071746 q^{53} - 1294592 q^{54} - 2492580 q^{55} - 274432 q^{56} - 1669714 q^{57} + 800336 q^{58} + 479512 q^{59} - 1360384 q^{60} + 6713104 q^{61} + 2438688 q^{62} - 7785864 q^{63} + 6291456 q^{64} + 6788906 q^{65} + 2104960 q^{66} + 1823780 q^{67} + 155136 q^{68} - 3604080 q^{69} - 345056 q^{70} - 3510960 q^{71} + 6151168 q^{72} - 27590128 q^{73} + 5276496 q^{74} - 16709392 q^{75} + 1022720 q^{76} - 65144 q^{77} + 5555680 q^{78} + 1130192 q^{79} + 1114112 q^{80} - 10442988 q^{81} + 6043584 q^{82} - 3888560 q^{83} - 895232 q^{84} + 8161728 q^{85} - 1217824 q^{86} - 17683256 q^{87} + 1765376 q^{88} - 14427556 q^{89} + 14744976 q^{90} + 3386000 q^{91} + 1998848 q^{92} - 20025152 q^{93} - 8626784 q^{94} + 21486568 q^{95} - 1310720 q^{96} - 11913436 q^{97} + 23432624 q^{98} + 16388620 q^{99}+O(q^{100}) \) 24 * q + 96 * q^2 + 40 * q^3 - 768 * q^4 - 136 * q^5 + 640 * q^6 + 536 * q^7 - 12288 * q^8 - 12014 * q^9 - 2176 * q^10 - 3448 * q^11 + 2560 * q^12 + 186 * q^13 + 8576 * q^14 + 10628 * q^15 - 49152 * q^16 - 1212 * q^17 + 96112 * q^18 + 15980 * q^19 - 8704 * q^20 + 6994 * q^21 - 13792 * q^22 - 62464 * q^23 - 20480 * q^24 - 48368 * q^25 + 2976 * q^26 - 323648 * q^27 + 34304 * q^28 + 200084 * q^29 - 85024 * q^30 + 609672 * q^31 + 393216 * q^32 + 131560 * q^33 + 9696 * q^34 + 43132 * q^35 + 1537792 * q^36 - 557790 * q^37 + 255680 * q^38 - 694460 * q^39 + 69632 * q^40 + 377724 * q^41 - 55952 * q^42 - 304456 * q^43 + 110336 * q^44 + 3686244 * q^45 - 249856 * q^46 - 2156696 * q^47 - 327680 * q^48 - 2929078 * q^49 + 386944 * q^50 + 968912 * q^51 + 11904 * q^52 + 2071746 * q^53 - 1294592 * q^54 - 2492580 * q^55 - 274432 * q^56 - 1669714 * q^57 + 800336 * q^58 + 479512 * q^59 - 1360384 * q^60 + 6713104 * q^61 + 2438688 * q^62 - 7785864 * q^63 + 6291456 * q^64 + 6788906 * q^65 + 2104960 * q^66 + 1823780 * q^67 + 155136 * q^68 - 3604080 * q^69 - 345056 * q^70 - 3510960 * q^71 + 6151168 * q^72 - 27590128 * q^73 + 5276496 * q^74 - 16709392 * q^75 + 1022720 * q^76 - 65144 * q^77 + 5555680 * q^78 + 1130192 * q^79 + 1114112 * q^80 - 10442988 * q^81 + 6043584 * q^82 - 3888560 * q^83 - 895232 * q^84 + 8161728 * q^85 - 1217824 * q^86 - 17683256 * q^87 + 1765376 * q^88 - 14427556 * q^89 + 14744976 * q^90 + 3386000 * q^91 + 1998848 * q^92 - 20025152 * q^93 - 8626784 * q^94 + 21486568 * q^95 - 1310720 * q^96 - 11913436 * q^97 + 23432624 * q^98 + 16388620 * q^99

Introduction

L-functions

Modular forms

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