LMFDB - Embedded newform 76.6.f.a.27.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,6,Mod(27,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("76.27");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	76.f (of order $6$, 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:	$12.1891703058$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			27.11
Character	$\chi$	$=$	76.27
Dual form			76.6.f.a.31.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.57989 - 3.32033i) q^{2} +(14.1896 - 24.5772i) q^{3} +(9.95083 + 30.4135i) q^{4} +(24.5038 - 42.4418i) q^{5} +(-146.591 + 65.4465i) q^{6} +6.61611i q^{7} +(55.4091 - 172.331i) q^{8} +(-281.192 - 487.038i) q^{9} +O(q^{10})$	\(q+(-4.57989 - 3.32033i) q^{2} +(14.1896 - 24.5772i) q^{3} +(9.95083 + 30.4135i) q^{4} +(24.5038 - 42.4418i) q^{5} +(-146.591 + 65.4465i) q^{6} +6.61611i q^{7} +(55.4091 - 172.331i) q^{8} +(-281.192 - 487.038i) q^{9} +(-253.145 + 113.018i) q^{10} -102.400i q^{11} +(888.677 + 186.993i) q^{12} +(718.961 - 415.092i) q^{13} +(21.9677 - 30.3011i) q^{14} +(-695.399 - 1204.47i) q^{15} +(-825.962 + 605.279i) q^{16} +(-44.3616 + 76.8365i) q^{17} +(-329.300 + 3164.23i) q^{18} +(-1229.01 + 982.672i) q^{19} +(1534.64 + 322.915i) q^{20} +(162.605 + 93.8802i) q^{21} +(-340.003 + 468.983i) q^{22} +(1774.70 - 1024.62i) q^{23} +(-3449.16 - 3807.11i) q^{24} +(361.630 + 626.361i) q^{25} +(-4671.01 - 486.109i) q^{26} -9063.87 q^{27} +(-201.219 + 65.8358i) q^{28} +(-1344.24 + 776.096i) q^{29} +(-814.373 + 7825.29i) q^{30} -9082.58 q^{31} +(5792.54 - 29.6480i) q^{32} +(-2516.71 - 1453.02i) q^{33} +(458.294 - 204.608i) q^{34} +(280.799 + 162.120i) q^{35} +(12014.4 - 13398.5i) q^{36} +13310.4i q^{37} +(8891.51 - 419.830i) q^{38} -23560.0i q^{39} +(-5956.29 - 6574.41i) q^{40} +(4422.70 + 2553.45i) q^{41} +(-433.001 - 969.864i) q^{42} +(6152.55 + 3552.18i) q^{43} +(3114.36 - 1018.97i) q^{44} -27561.0 q^{45} +(-11530.0 - 1199.92i) q^{46} +(12584.9 - 7265.91i) q^{47} +(3155.95 + 28888.5i) q^{48} +16763.2 q^{49} +(423.500 - 4069.40i) q^{50} +(1258.95 + 2180.56i) q^{51} +(19778.7 + 17735.6i) q^{52} +(20292.1 - 11715.7i) q^{53} +(41511.5 + 30095.0i) q^{54} +(-4346.06 - 2509.20i) q^{55} +(1140.16 + 366.593i) q^{56} +(6712.16 + 44149.2i) q^{57} +(8733.35 + 908.875i) q^{58} +(-8821.95 + 15280.1i) q^{59} +(29712.3 - 33135.0i) q^{60} +(-21243.9 - 36795.5i) q^{61} +(41597.3 + 30157.2i) q^{62} +(3222.30 - 1860.39i) q^{63} +(-26627.7 - 19097.4i) q^{64} -40685.3i q^{65} +(6701.75 + 15011.0i) q^{66} +(-26113.8 - 45230.5i) q^{67} +(-2778.30 - 584.604i) q^{68} -58156.1i q^{69} +(-747.741 - 1674.84i) q^{70} +(-35903.7 + 62187.0i) q^{71} +(-99512.2 + 21471.6i) q^{72} +(28690.5 - 49693.4i) q^{73} +(44194.8 - 60960.1i) q^{74} +20525.6 q^{75} +(-42116.1 - 27600.0i) q^{76} +677.492 q^{77} +(-78227.1 + 107902. i) q^{78} +(29171.1 - 50525.8i) q^{79} +(5449.94 + 49886.9i) q^{80} +(-60283.4 + 104414. i) q^{81} +(-11777.2 - 26379.3i) q^{82} -57869.7i q^{83} +(-1237.17 + 5879.58i) q^{84} +(2174.05 + 3765.57i) q^{85} +(-16383.6 - 36697.1i) q^{86} +44050.1i q^{87} +(-17646.7 - 5673.91i) q^{88} +(92288.0 - 53282.5i) q^{89} +(126227. + 91511.7i) q^{90} +(2746.30 + 4756.72i) q^{91} +(48822.1 + 43778.9i) q^{92} +(-128879. + 223224. i) q^{93} +(-81762.8 - 8509.01i) q^{94} +(11591.1 + 76240.4i) q^{95} +(81465.4 - 142785. i) q^{96} +(100168. + 57831.9i) q^{97} +(-76773.8 - 55659.4i) q^{98} +(-49872.9 + 28794.1i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 3 q^{2} - 11 q^{4} - 2 q^{5} - 27 q^{6} - 3588 q^{9}+O(q^{10}) $ 96 * q - 3 * q^2 - 11 * q^4 - 2 * q^5 - 27 * q^6 - 3588 * q^9	$ 96 q - 3 q^{2} - 11 q^{4} - 2 q^{5} - 27 q^{6} - 3588 q^{9} + 648 q^{10} - 354 q^{13} + 2154 q^{14} - 611 q^{16} - 1006 q^{17} + 10524 q^{20} + 7824 q^{21} + 93 q^{22} - 5311 q^{24} - 25002 q^{25} - 13428 q^{26} + 1556 q^{28} - 6 q^{29} - 12656 q^{30} - 30453 q^{32} + 8586 q^{33} + 30102 q^{34} - 2306 q^{36} + 29846 q^{38} - 1392 q^{40} + 29064 q^{41} + 18616 q^{42} + 9155 q^{44} + 13464 q^{45} + 38217 q^{48} - 116224 q^{49} + 36858 q^{52} + 26262 q^{53} - 26355 q^{54} + 53974 q^{57} - 112740 q^{58} - 108810 q^{60} - 77370 q^{61} - 106848 q^{62} + 337966 q^{64} + 166855 q^{66} + 175796 q^{68} + 148122 q^{70} - 259842 q^{72} - 52040 q^{73} + 103690 q^{74} - 194709 q^{76} + 197584 q^{77} + 253206 q^{78} - 171934 q^{80} - 313100 q^{81} + 63919 q^{82} - 161762 q^{85} - 38442 q^{86} + 10482 q^{89} - 372450 q^{90} + 64544 q^{92} + 94012 q^{93} + 537614 q^{96} + 177180 q^{97} - 509397 q^{98}+O(q^{100}) $ 96 * q - 3 * q^2 - 11 * q^4 - 2 * q^5 - 27 * q^6 - 3588 * q^9 + 648 * q^10 - 354 * q^13 + 2154 * q^14 - 611 * q^16 - 1006 * q^17 + 10524 * q^20 + 7824 * q^21 + 93 * q^22 - 5311 * q^24 - 25002 * q^25 - 13428 * q^26 + 1556 * q^28 - 6 * q^29 - 12656 * q^30 - 30453 * q^32 + 8586 * q^33 + 30102 * q^34 - 2306 * q^36 + 29846 * q^38 - 1392 * q^40 + 29064 * q^41 + 18616 * q^42 + 9155 * q^44 + 13464 * q^45 + 38217 * q^48 - 116224 * q^49 + 36858 * q^52 + 26262 * q^53 - 26355 * q^54 + 53974 * q^57 - 112740 * q^58 - 108810 * q^60 - 77370 * q^61 - 106848 * q^62 + 337966 * q^64 + 166855 * q^66 + 175796 * q^68 + 148122 * q^70 - 259842 * q^72 - 52040 * q^73 + 103690 * q^74 - 194709 * q^76 + 197584 * q^77 + 253206 * q^78 - 171934 * q^80 - 313100 * q^81 + 63919 * q^82 - 161762 * q^85 - 38442 * q^86 + 10482 * q^89 - 372450 * q^90 + 64544 * q^92 + 94012 * q^93 + 537614 * q^96 + 177180 * q^97 - 509397 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−4.57989	−	3.32033i	−0.809618	−	0.586957i
$2$	−4.57989	−	3.32033i	−0.809618	−	0.586957i
$3$	14.1896	−	24.5772i	0.910266	−	1.57663i	0.0965771	−	0.995326i	$-0.469211\pi$
$3$	14.1896	−	24.5772i	0.910266	−	1.57663i	0.813689	−	0.581301i	$-0.197456\pi$
$4$	9.95083	+	30.4135i	0.310963	+	0.950422i
$5$	24.5038	−	42.4418i	0.438337	−	0.759222i	−0.559224	−	0.829016i	$-0.688901\pi$
$5$	24.5038	−	42.4418i	0.438337	−	0.759222i	0.997561	+	0.0697945i	$0.0222343\pi$
$6$	−146.591	+	65.4465i	−1.66238	+	0.742179i
$7$			6.61611i			0.0510338i	0.999674	+	0.0255169i	$0.00812316\pi$
$7$			6.61611i			0.0510338i	−0.999674	+	0.0255169i	$0.991877\pi$
$8$	55.4091	−	172.331i	0.306095	−	0.952001i
$9$	−281.192	−	487.038i	−1.15717	−	2.00427i
$10$	−253.145	+	113.018i	−0.800516	+	0.357395i
$11$		−	102.400i		−	0.255164i	−0.991828	−	0.127582i	$-0.959278\pi$
$11$		−	102.400i		−	0.255164i	0.991828	−	0.127582i	$-0.0407217\pi$
$12$	888.677	+	186.993i	1.78152	+	0.374863i
$13$	718.961	−	415.092i	1.17990	−	0.681218i	0.223912	−	0.974609i	$-0.428117\pi$
$13$	718.961	−	415.092i	1.17990	−	0.681218i	0.955992	+	0.293391i	$0.0947838\pi$
$14$	21.9677	−	30.3011i	0.0299546	−	0.0413179i
$15$	−695.399	−	1204.47i	−0.798006	−	1.38219i
$16$	−825.962	+	605.279i	−0.806603	+	0.591093i
$17$	−44.3616	+	76.8365i	−0.0372293	+	0.0644830i	−0.884040	−	0.467412i	$-0.845187\pi$
$17$	−44.3616	+	76.8365i	−0.0372293	+	0.0644830i	0.846810	+	0.531895i	$0.178520\pi$
$18$	−329.300	+	3164.23i	−0.239558	+	2.30190i
$19$	−1229.01	+	982.672i	−0.781034	+	0.624489i
$19$	−1229.01	+	982.672i	−0.781034	+	0.624489i
$20$	1534.64	+	322.915i	0.857888	+	0.180515i
$21$	162.605	+	93.8802i	0.0804612	+	0.0464543i
$22$	−340.003	+	468.983i	−0.149770	+	0.206586i
$23$	1774.70	−	1024.62i	0.699528	−	0.403872i	−0.107644	−	0.994190i	$-0.534331\pi$
$23$	1774.70	−	1024.62i	0.699528	−	0.403872i	0.807171	+	0.590317i	$0.200997\pi$
$24$	−3449.16	−	3807.11i	−1.22232	−	1.34917i
$25$	361.630	+	626.361i	0.115722	+	0.200436i
$26$	−4671.01	−	486.109i	−1.35512	−	0.141026i
$27$	−9063.87			−2.39279
$28$	−201.219	+	65.8358i	−0.0485036	+	0.0158696i
$29$	−1344.24	+	776.096i	−0.296812	+	0.171364i	−0.641010	−	0.767533i	$-0.721484\pi$
$29$	−1344.24	+	776.096i	−0.296812	+	0.171364i	0.344198	+	0.938897i	$0.388151\pi$
$30$	−814.373	+	7825.29i	−0.165204	+	1.58744i
$31$	−9082.58			−1.69748			−0.848741	−	0.528809i	$-0.822639\pi$
$31$	−9082.58			−1.69748			−0.848741	+	0.528809i	$0.822639\pi$
$32$	5792.54	−	29.6480i	0.999987	−	0.00511824i
$33$	−2516.71	−	1453.02i	−0.402299	−	0.232267i
$34$	458.294	−	204.608i	0.0679902	−	0.0303546i
$35$	280.799	+	162.120i	0.0387459	+	0.0223700i
$36$	12014.4	−	13398.5i	1.54507	−	1.72305i
$37$			13310.4i			1.59840i	0.601064	+	0.799201i	$0.294743\pi$
$37$			13310.4i			1.59840i	−0.601064	+	0.799201i	$0.705257\pi$
$38$	8891.51	−	419.830i	0.998887	−	0.0471644i
$39$		−	23560.0i		−	2.48036i
$40$	−5956.29	−	6574.41i	−0.588607	−	0.649691i
$41$	4422.70	+	2553.45i	0.410892	+	0.237229i	0.691173	−	0.722689i	$-0.257094\pi$
$41$	4422.70	+	2553.45i	0.410892	+	0.237229i	−0.280281	+	0.959918i	$0.590428\pi$
$42$	−433.001	−	969.864i	−0.0378762	−	0.0848375i
$43$	6152.55	+	3552.18i	0.507439	+	0.292970i	0.731780	−	0.681540i	$-0.238690\pi$
$43$	6152.55	+	3552.18i	0.507439	+	0.292970i	−0.224341	+	0.974511i	$0.572023\pi$
$44$	3114.36	−	1018.97i	0.242514	−	0.0793468i
$45$	−27561.0			−2.02892
$46$	−11530.0	−	1199.92i	−0.803406	−	0.0836100i
$47$	12584.9	−	7265.91i	0.831010	−	0.479784i	−0.0231886	−	0.999731i	$-0.507382\pi$
$47$	12584.9	−	7265.91i	0.831010	−	0.479784i	0.854198	+	0.519947i	$0.174048\pi$
$48$	3155.95	+	28888.5i	0.197709	+	1.80976i
$49$	16763.2			0.997396
$50$	423.500	−	4069.40i	0.0239568	−	0.230200i
$51$	1258.95	+	2180.56i	0.0677770	+	0.117393i
$52$	19778.7	+	17735.6i	1.01435	+	0.909573i
$53$	20292.1	−	11715.7i	0.992288	−	0.572898i	0.0863305	−	0.996267i	$-0.472486\pi$
$53$	20292.1	−	11715.7i	0.992288	−	0.572898i	0.905957	+	0.423369i	$0.139153\pi$
$54$	41511.5	+	30095.0i	1.93724	+	1.40446i
$55$	−4346.06	−	2509.20i	−0.193726	−	0.111848i
$56$	1140.16	+	366.593i	0.0485842	+	0.0156212i
$57$	6712.16	+	44149.2i	0.273637	+	1.79985i
$58$	8733.35	+	908.875i	0.340887	+	0.0354759i
$59$	−8821.95	+	15280.1i	−0.329940	+	0.571472i	−0.982500	−	0.186265i	$-0.940362\pi$
$59$	−8821.95	+	15280.1i	−0.329940	+	0.571472i	0.652560	+	0.757737i	$0.273695\pi$
$60$	29712.3	−	33135.0i	1.06551	−	1.18825i
$61$	−21243.9	−	36795.5i	−0.730987	−	1.26611i	−0.956462	−	0.291857i	$-0.905727\pi$
$61$	−21243.9	−	36795.5i	−0.730987	−	1.26611i	0.225475	−	0.974249i	$-0.427606\pi$
$62$	41597.3	+	30157.2i	1.37431	+	0.996349i
$63$	3222.30	−	1860.39i	0.102286	−	0.0590546i
$64$	−26627.7	−	19097.4i	−0.812612	−	0.582805i
$65$		−	40685.3i		−	1.19441i
$66$	6701.75	+	15011.0i	0.189378	+	0.424180i
$67$	−26113.8	−	45230.5i	−0.710696	−	1.23096i	−0.964596	−	0.263731i	$-0.915047\pi$
$67$	−26113.8	−	45230.5i	−0.710696	−	1.23096i	0.253901	−	0.967230i	$-0.418286\pi$
$68$	−2778.30	−	584.604i	−0.0728630	−	0.0153317i
$69$		−	58156.1i		−	1.47053i
$70$	−747.741	−	1674.84i	−0.0182392	−	0.0408533i
$71$	−35903.7	+	62187.0i	−0.845265	+	1.46404i	0.0401258	+	0.999195i	$0.487224\pi$
$71$	−35903.7	+	62187.0i	−0.845265	+	1.46404i	−0.885391	+	0.464847i	$0.846109\pi$
$72$	−99512.2	+	21471.6i	−2.26227	+	0.488127i
$73$	28690.5	−	49693.4i	0.630131	−	1.09142i	−0.357394	−	0.933954i	$-0.616335\pi$
$73$	28690.5	−	49693.4i	0.630131	−	1.09142i	0.987525	−	0.157465i	$-0.0503320\pi$
$74$	44194.8	−	60960.1i	0.938192	−	1.29409i
$75$	20525.6			0.421349
$76$	−42116.1	−	27600.0i	−0.836401	−	0.548118i
$77$	677.492			0.0130220
$78$	−78227.1	+	107902.i	−1.45586	+	2.00814i
$79$	29171.1	−	50525.8i	0.525878	−	0.910848i	−0.473667	−	0.880704i	$-0.657070\pi$
$79$	29171.1	−	50525.8i	0.525878	−	0.910848i	0.999546	−	0.0301438i	$-0.00959653\pi$
$80$	5449.94	+	49886.9i	0.0952066	+	0.871489i
$81$	−60283.4	+	104414.i	−1.02091	+	1.76826i
$82$	−11777.2	−	26379.3i	−0.193423	−	0.433240i
$83$		−	57869.7i		−	0.922054i	−0.887386	−	0.461027i	$-0.847481\pi$
$83$		−	57869.7i		−	0.922054i	0.887386	−	0.461027i	$-0.152519\pi$
$84$	−1237.17	+	5879.58i	−0.0191307	+	0.0909176i
$85$	2174.05	+	3765.57i	0.0326379	+	0.0565305i
$86$	−16383.6	−	36697.1i	−0.238871	−	0.535039i
$87$			44050.1i			0.623948i
$88$	−17646.7	−	5673.91i	−0.242917	−	0.0781045i
$89$	92288.0	−	53282.5i	1.23501	−	0.713033i	0.266940	−	0.963713i	$-0.413988\pi$
$89$	92288.0	−	53282.5i	1.23501	−	0.713033i	0.968070	+	0.250680i	$0.0806542\pi$
$90$	126227.	+	91511.7i	1.64265	+	1.19089i
$91$	2746.30	+	4756.72i	0.0347651	+	0.0602150i
$92$	48822.1	+	43778.9i	0.601377	+	0.539257i
$93$	−128879.	+	223224.i	−1.54516	+	2.67630i
$94$	−81762.8	−	8509.01i	−0.954413	−	0.0993252i
$95$	11591.1	+	76240.4i	0.131770	+	0.866714i
$96$	81465.4	−	142785.i	0.902184	−	1.58126i
$97$	100168.	+	57831.9i	1.08093	+	0.624077i	0.931148	−	0.364642i	$-0.118809\pi$
$97$	100168.	+	57831.9i	1.08093	+	0.624077i	0.149785	+	0.988719i	$0.452142\pi$
$98$	−76773.8	−	55659.4i	−0.807510	−	0.585428i
$99$	−49872.9	+	28794.1i	−0.511419	+	0.295268i
$100$	−15451.3	+	17231.2i	−0.154513	+	0.172312i
$101$	28261.3	+	48950.0i	0.275669	+	0.477474i	0.970304	−	0.241889i	$-0.0777671\pi$
$101$	28261.3	+	48950.0i	0.275669	+	0.477474i	−0.694634	+	0.719363i	$0.744434\pi$
$102$	1474.34	−	14166.9i	0.0140313	−	0.134826i
$103$	−19738.5			−0.183325			−0.0916623	−	0.995790i	$-0.529218\pi$
$103$	−19738.5			−0.183325			−0.0916623	+	0.995790i	$0.529218\pi$
$104$	−31696.1	−	146899.i	−0.287358	−	1.33179i
$105$	7968.89	−	4600.84i	0.0705382	−	0.0407252i
$106$	−131836.	−	13720.0i	−1.13964	−	0.118602i
$107$	−105744.			−0.892891			−0.446445	−	0.894811i	$-0.647310\pi$
$107$	−105744.			−0.892891			−0.446445	+	0.894811i	$0.647310\pi$
$108$	−90193.0	−	275664.i	−0.744070	−	2.27416i
$109$	−54268.3	−	31331.8i	−0.437502	−	0.252592i	0.265035	−	0.964239i	$-0.414616\pi$
$109$	−54268.3	−	31331.8i	−0.437502	−	0.252592i	−0.702538	+	0.711647i	$0.747950\pi$
$110$	11573.1	+	25922.2i	0.0911945	+	0.204263i
$111$	327131.	+	188869.i	2.52008	+	1.45497i
$112$	−4004.59	−	5464.65i	−0.0301657	−	0.0411640i
$113$		−	4202.08i		−	0.0309576i	−0.999880	−	0.0154788i	$-0.995073\pi$
$113$		−	4202.08i		−	0.0309576i	0.999880	−	0.0154788i	$-0.00492726\pi$
$114$	115849.	−	224485.i	0.834892	−	1.61780i
$115$		−	100428.i		−	0.708129i
$116$	−36980.1	−	33160.2i	−0.255166	−	0.228808i
$117$	−404332.	−	233441.i	−2.73069	−	1.57657i
$118$	91138.4	−	40689.3i	0.602555	−	0.269014i
$119$	−508.358	−	293.501i	−0.00329081	−	0.00189995i
$120$	−246098.	+	53100.2i	−1.56011	+	0.336622i
$121$	150565.			0.934891
$122$	−24878.4	+	239056.i	−0.151329	+	1.45412i
$123$	125513.	−	72464.9i	0.748042	−	0.431882i
$124$	−90379.3	−	276233.i	−0.527855	−	1.61332i
$125$	188594.			1.07957
$126$	−20934.9	−	2178.68i	−0.117475	−	0.0122255i
$127$	−38925.4	−	67420.8i	−0.214153	−	0.370924i	0.738857	−	0.673862i	$-0.235366\pi$
$127$	−38925.4	−	67420.8i	−0.214153	−	0.370924i	−0.953010	+	0.302938i	$0.902032\pi$
$128$	58542.3	+	175876.i	0.315824	+	0.948818i
$129$	174605.	−	100808.i	0.923809	−	0.533362i
$130$	−135089.	+	186334.i	−0.701068	+	0.967018i
$131$	314648.	+	181662.i	1.60194	+	0.924881i	0.991099	+	0.133129i	$0.0425026\pi$
$131$	314648.	+	181662.i	1.60194	+	0.924881i	0.610843	+	0.791752i	$0.290831\pi$
$132$	19148.2	−	91000.9i	0.0956517	−	0.454580i
$133$	−6501.46	−	8131.23i	−0.0318700	−	0.0398591i
$134$	−30581.6	+	293857.i	−0.147129	+	1.41376i
$135$	−222099.	+	384687.i	−1.04885	+	1.81666i
$136$	10783.2	+	11902.3i	0.0499922	+	0.0551802i
$137$	68753.6	+	119085.i	0.312964	+	0.542069i	0.979003	−	0.203848i	$-0.0653448\pi$
$137$	68753.6	+	119085.i	0.312964	+	0.542069i	−0.666039	+	0.745917i	$0.732011\pi$
$138$	−193097.	+	266349.i	−0.863135	+	1.19056i
$139$	−277800.	+	160388.i	−1.21954	+	0.704101i	−0.964819	−	0.262914i	$-0.915317\pi$
$139$	−277800.	+	160388.i	−1.21954	+	0.704101i	−0.254720	+	0.967015i	$0.581983\pi$
$140$	−2136.44	+	10153.3i	−0.00921235	+	0.0437812i
$141$		−	412403.i		−	1.74692i
$142$	370916.	−	165598.i	1.54367	−	0.689181i
$143$	−42505.6	−	73621.9i	−0.173823	−	0.301070i
$144$	527048.	+	232076.i	2.11809	+	0.932660i
$145$			76069.1i			0.300461i
$146$	−296398.	+	132328.i	−1.15078	+	0.513773i
$147$	237864.	−	411993.i	0.907895	−	1.57252i
$148$	−404815.	+	132449.i	−1.51916	+	0.497044i
$149$	32934.8	−	57044.7i	0.121531	−	0.210499i	−0.798840	−	0.601543i	$-0.794553\pi$
$149$	32934.8	−	57044.7i	0.121531	−	0.210499i	0.920372	+	0.391044i	$0.127886\pi$
$150$	−94005.0	−	68151.7i	−0.341132	−	0.247314i
$151$	215525.			0.769230			0.384615	−	0.923077i	$-0.374334\pi$
$151$	215525.			0.769230			0.384615	+	0.923077i	$0.374334\pi$
$152$	101246.	+	266244.i	0.355443	+	0.934698i
$153$	49896.4			0.172322
$154$	−3102.84	−	2249.50i	−0.0105428	−	0.00764335i
$155$	−222558.	+	385481.i	−0.744069	+	1.28877i
$156$	716543.	−	234442.i	2.35739	−	0.771301i
$157$	−164208.	+	284416.i	−0.531673	+	0.920885i	0.467643	+	0.883917i	$0.345103\pi$
$157$	−164208.	+	284416.i	−0.531673	+	0.920885i	−0.999316	+	0.0369680i	$0.988230\pi$
$158$	−301363.	+	134545.i	−0.960389	+	0.428771i
$159$		−	664964.i		−	2.08596i
$160$	140681.	−	246572.i	0.434445	−	0.761455i
$161$	6779.01	+	11741.6i	0.0206111	+	0.0356995i
$162$	622780.	−	278044.i	1.86444	−	0.832388i
$163$		−	16950.9i		−	0.0499717i	−0.999688	−	0.0249859i	$-0.992046\pi$
$163$		−	16950.9i		−	0.0499717i	0.999688	−	0.0249859i	$-0.00795408\pi$
$164$	−33649.7	+	159919.i	−0.0976948	+	0.464290i
$165$	−123338.	+	71209.2i	−0.352685	+	0.203623i
$166$	−192147.	+	265037.i	−0.541206	+	0.746512i
$167$	−100621.	−	174280.i	−0.279187	−	0.483566i	0.691996	−	0.721902i	$-0.256732\pi$
$167$	−100621.	−	174280.i	−0.279187	−	0.483566i	−0.971183	+	0.238335i	$0.923398\pi$
$168$	25188.2	−	22820.0i	0.0688533	−	0.0623797i
$169$	158957.	−	275321.i	0.428116	−	0.741519i
$170$	2546.00	−	24464.5i	0.00675673	−	0.0649252i
$171$	824185.	+	322254.i	2.15543	+	0.842767i
$172$	−46811.1	+	222468.i	−0.120650	+	0.573385i
$173$	−424703.	−	245202.i	−1.07887	−	0.622887i	−0.148280	−	0.988945i	$-0.547374\pi$
$173$	−424703.	−	245202.i	−1.07887	−	0.622887i	−0.930592	+	0.366058i	$0.880707\pi$
$174$	146261.	−	201745.i	0.366230	−	0.505160i
$175$	−4144.07	+	2392.58i	−0.0102290	+	0.00590570i
$176$	61980.8	+	84578.9i	0.150826	+	0.205816i
$177$	250360.	+	433637.i	0.600665	+	1.04038i
$178$	−599585.	−	62398.4i	−1.41841	−	0.147613i
$179$	759487.			1.77169			0.885845	−	0.463982i	$-0.153580\pi$
$179$	759487.			1.77169			0.885845	+	0.463982i	$0.153580\pi$
$180$	−274255.	−	838227.i	−0.630919	−	1.92833i
$181$	−152293.	+	87926.3i	−0.345528	+	0.199491i	−0.662714	−	0.748873i	$-0.730595\pi$
$181$	−152293.	+	87926.3i	−0.345528	+	0.199491i	0.317186	+	0.948363i	$0.397262\pi$
$182$	3216.15	−	30903.9i	0.00719710	−	0.0691567i
$183$	−1.20577e6			−2.66157
$184$	−78239.4	−	362608.i	−0.170365	−	0.789574i
$185$	564916.	+	326154.i	1.21354	+	0.700638i
$186$	1.33143e6	−	594424.i	2.82186	−	1.25984i
$187$	7868.09	+	4542.64i	0.0164538	+	0.00949958i
$188$	346212.	+	310450.i	0.714411	+	0.640615i
$189$		−	59967.5i		−	0.122113i
$190$	200057.	−	387659.i	0.402041	−	0.779051i
$191$			31022.2i			0.0615303i	0.999527	+	0.0307651i	$0.00979439\pi$
$191$			31022.2i			0.0615303i	−0.999527	+	0.0307651i	$0.990206\pi$
$192$	−847196.	+	383448.i	−1.65856	+	0.750678i
$193$	21949.6	+	12672.6i	0.0424164	+	0.0244891i	0.521058	−	0.853521i	$-0.325537\pi$
$193$	21949.6	+	12672.6i	0.0424164	+	0.0244891i	−0.478642	+	0.878010i	$0.658871\pi$
$194$	−266737.	−	597454.i	−0.508837	−	1.13972i
$195$	−999930.	−	577310.i	−1.88314	−	1.08723i
$196$	166808.	+	509828.i	0.310154	+	0.947947i
$197$	−474809.			−0.871672			−0.435836	−	0.900026i	$-0.643547\pi$
$197$	−474809.			−0.871672			−0.435836	+	0.900026i	$0.643547\pi$
$198$	324019.	+	33720.4i	0.587364	+	0.0611266i
$199$	−638300.	+	368523.i	−1.14259	+	0.659677i	−0.947072	−	0.321022i	$-0.895974\pi$
$199$	−638300.	+	368523.i	−1.14259	+	0.659677i	−0.195523	+	0.980699i	$0.562640\pi$
$200$	127979.	−	27613.8i	0.226237	−	0.0488147i
$201$	−1.48218e6			−2.58769
$202$	33096.4	−	318023.i	0.0570693	−	0.548377i
$203$	−5134.73	−	8893.62i	−0.00874536	−	0.0151474i
$204$	−53791.0	+	59987.5i	−0.0904970	+	0.100922i
$205$	216746.	−	125138.i	0.360218	−	0.207972i
$206$	90400.1	+	65538.3i	0.148423	+	0.107604i
$207$	−998061.	−	576231.i	−1.61894	−	0.934696i
$208$	−342588.	+	778022.i	−0.549052	+	1.24691i
$209$	100626.	+	125851.i	0.159347	+	0.199292i
$210$	−51772.9	−	5387.98i	−0.0810130	−	0.00843097i
$211$	19435.2	−	33662.8i	0.0300527	−	0.0520528i	−0.850608	−	0.525801i	$-0.823766\pi$
$211$	19435.2	−	33662.8i	0.0300527	−	0.0520528i	0.880661	+	0.473748i	$0.157099\pi$
$212$	558238.	+	500574.i	0.853060	+	0.764942i
$213$	1.01892e6	+	1.76482e6i	1.53883	+	2.66533i
$214$	484298.	+	351107.i	0.722901	+	0.524088i
$215$	301522.	−	174084.i	0.444859	−	0.256839i
$216$	−502221.	+	1.56198e6i	−0.732420	+	2.27794i
$217$		−	60091.4i		−	0.0866289i
$218$	144511.	+	323685.i	0.205949	+	0.461298i
$219$	−814215.	−	1.41026e6i	−1.14717	−	1.98696i
$220$	33066.6	−	157147.i	0.0460609	−	0.218902i
$221$			73656.5i			0.101445i
$222$	−871118.	−	1.95118e6i	−1.18630	−	2.65715i
$223$	7209.72	−	12487.6i	0.00970859	−	0.0168158i	−0.861130	−	0.508384i	$-0.830243\pi$
$223$	7209.72	−	12487.6i	0.00970859	−	0.0168158i	0.870839	+	0.491569i	$0.163576\pi$
$224$	196.155	+	38324.1i	0.000261203	+	0.0510331i
$225$	203375.	−	352255.i	0.267818	−	0.463875i
$226$	−13952.3	+	19245.1i	−0.0181708	+	0.0250639i
$227$	1.04832e6			1.35029			0.675147	−	0.737683i	$-0.264080\pi$
$227$	1.04832e6			1.35029			0.675147	+	0.737683i	$0.264080\pi$
$228$	−1.27594e6	+	643462.i	−1.62552	+	0.819758i
$229$	1.08418e6			1.36619			0.683094	−	0.730330i	$-0.260634\pi$
$229$	1.08418e6			1.36619			0.683094	+	0.730330i	$0.260634\pi$
$230$	−333456.	+	459952.i	−0.415641	+	0.573314i
$231$	9613.37	−	16650.8i	0.0118535	−	0.0205308i
$232$	59262.1	+	274656.i	0.0722864	+	0.335019i
$233$	379086.	−	656596.i	0.457455	−	0.792335i	−0.541371	−	0.840784i	$-0.682095\pi$
$233$	379086.	−	656596.i	0.457455	−	0.792335i	0.998826	+	0.0484492i	$0.0154279\pi$
$234$	1.07669e6	+	2.41165e6i	1.28544	+	2.87922i
$235$		−	712169.i		−	0.841228i
$236$	−552506.	−	116257.i	−0.645739	−	0.135875i
$237$	−827855.	−	1.43389e6i	−0.957378	−	1.65823i
$238$	1353.71	+	3032.12i	0.00154911	+	0.00346980i
$239$			323053.i			0.365830i	0.983129	+	0.182915i	$0.0585533\pi$
$239$			323053.i			0.365830i	−0.983129	+	0.182915i	$0.941447\pi$
$240$	1.30341e6	+	573933.i	1.46068	+	0.643181i
$241$	−722458.	+	417112.i	−0.801254	+	0.462604i	−0.843909	−	0.536486i	$-0.819752\pi$
$241$	−722458.	+	417112.i	−0.801254	+	0.462604i	0.0426555	+	0.999090i	$0.486418\pi$
$242$	−689572.	−	499926.i	−0.756905	−	0.548741i
$243$	609540.	+	1.05576e6i	0.662196	+	1.14696i
$244$	907685.	−	1.01225e6i	0.976025	−	1.08846i
$245$	410762.	−	711461.i	0.437195	−	0.757244i
$246$	−815443.	−	84862.7i	−0.859124	−	0.0894085i
$247$	−475707.	+	1.21665e6i	−0.496132	+	1.26889i
$248$	−503258.	+	1.56521e6i	−0.519591	+	1.61600i
$249$	−1.42227e6	−	821151.i	−1.45373	−	0.839314i
$250$	−863739.	−	626193.i	−0.874043	−	0.633663i
$251$	−1.49827e6	+	865024.i	−1.50108	+	0.866650i	−0.501083	+	0.865399i	$0.667065\pi$
$251$	−1.49827e6	+	865024.i	−1.50108	+	0.866650i	−0.999999	+	0.00125049i	$0.999602\pi$
$252$	88645.7	+	79488.9i	0.0879338	+	0.0788506i
$253$	−104922.	−	181730.i	−0.103054	−	0.178495i
$254$	−45585.0	+	438025.i	−0.0443341	+	0.426005i
$255$	123396.			0.118837
$256$	315850.	−	999875.i	0.301218	−	0.953555i
$257$	991239.	−	572292.i	0.936150	−	0.540486i	0.0473985	−	0.998876i	$-0.484907\pi$
$257$	991239.	−	572292.i	0.936150	−	0.540486i	0.888751	+	0.458390i	$0.151574\pi$
$258$	−1.13439e6	−	118055.i	−1.06099	−	0.110417i
$259$	−88062.8			−0.0815724
$260$	1.23738e6	−	404853.i	1.13520	−	0.371419i
$261$	755976.	+	436463.i	0.686921	+	0.396594i
$262$	−837876.	−	1.87673e6i	−0.754096	−	1.68907i
$263$	471561.	+	272256.i	0.420386	+	0.242710i	0.695243	−	0.718775i	$-0.255297\pi$
$263$	471561.	+	272256.i	0.420386	+	0.242710i	−0.274856	+	0.961485i	$0.588630\pi$
$264$	−389849.	+	353196.i	−0.344260	+	0.311893i
$265$		−	1.14831e6i		−	1.00449i
$266$	2777.64	+	58827.2i	0.00240697	+	0.0509770i
$267$		−	3.02424e6i		−	2.59620i
$268$	1.11576e6	−	1.24429e6i	0.948932	−	1.05824i
$269$	136895.	+	79036.6i	0.115348	+	0.0665959i	0.556564	−	0.830805i	$-0.312119\pi$
$269$	136895.	+	79036.6i	0.115348	+	0.0665959i	−0.441216	+	0.897401i	$0.645453\pi$
$270$	2.29448e6	−	1.02438e6i	1.91546	−	0.855170i
$271$	246302.	+	142203.i	0.203725	+	0.117621i	0.598392	−	0.801203i	$-0.295807\pi$
$271$	246302.	+	142203.i	0.203725	+	0.117621i	−0.394667	+	0.918824i	$0.629140\pi$
$272$	−9866.56	−	90315.1i	−0.00808618	−	0.0740182i
$273$	155876.			0.126582
$274$	80516.4	−	773680.i	0.0647900	−	0.622566i
$275$	64139.6	−	37031.0i	0.0511440	−	0.0295280i
$276$	1.76873e6	−	578701.i	1.39762	−	0.457280i
$277$	−1.01914e6			−0.798057			−0.399029	−	0.916939i	$-0.630653\pi$
$277$	−1.01914e6			−0.798057			−0.399029	+	0.916939i	$0.630653\pi$
$278$	1.80484e6	+	187828.i	1.40064	+	0.145764i
$279$	2.55395e6	+	4.42357e6i	1.96427	+	3.40222i
$280$	43497.0	−	39407.4i	0.0331562	−	0.0300388i
$281$	−1.27084e6	+	733720.i	−0.960119	+	0.554325i	−0.896210	−	0.443631i	$-0.853690\pi$
$281$	−1.27084e6	+	733720.i	−0.960119	+	0.554325i	−0.0639091	+	0.997956i	$0.520357\pi$
$282$	−1.36931e6	+	1.88876e6i	−1.02537	+	1.41434i
$283$	1.93396e6	+	1.11657e6i	1.43543	+	0.828743i	0.997527	−	0.0702817i	$-0.0223898\pi$
$283$	1.93396e6	+	1.11657e6i	1.43543	+	0.828743i	0.437898	+	0.899025i	$0.355723\pi$
$284$	−2.24859e6	−	473144.i	−1.65430	−	0.348095i
$285$	2.03825e6	+	796947.i	1.48643	+	0.581189i
$286$	−49777.7	+	478313.i	−0.0359849	+	0.345778i
$287$	−16893.9	+	29261.0i	−0.0121067	+	0.0209694i
$288$	−1.64325e6	−	2.81285e6i	−1.16741	−	1.99832i
$289$	705993.	+	1.22282e6i	0.497228	+	0.861224i
$290$	252574.	−	348388.i	0.176358	−	0.243259i
$291$	2.84269e6	−	1.64123e6i	1.96787	−	1.13615i
$292$	1.79684e6	+	378088.i	1.23326	+	0.259499i
$293$			1.29944e6i			0.884278i	0.896947	+	0.442139i	$0.145780\pi$
$293$			1.29944e6i			0.884278i	−0.896947	+	0.442139i	$0.854220\pi$
$294$	−2.45734e6	+	1.09710e6i	−1.65805	+	0.740246i
$295$	432342.	+	748838.i	0.289249	+	0.500995i
$296$	2.29378e6	+	737515.i	1.52168	+	0.489262i
$297$			928144.i			0.610554i
$298$	−340245.	+	151904.i	−0.221948	+	0.0990899i
$299$	850626.	−	1.47333e6i	0.550251	−	0.953062i
$300$	204247.	+	624255.i	0.131024	+	0.400460i
$301$	−23501.6	+	40705.9i	−0.0149514	+	0.0258965i
$302$	−987083.	−	715615.i	−0.622782	−	0.451505i
$303$	1.60407e6			1.00373
$304$	420321.	−	1.55554e6i	0.260854	−	0.965378i
$305$	−2.08222e6			−1.28167
$306$	−228520.	−	165672.i	−0.139515	−	0.101146i
$307$	−1.07731e6	+	1.86595e6i	−0.652369	+	1.12994i	0.330177	+	0.943919i	$0.392891\pi$
$307$	−1.07731e6	+	1.86595e6i	−0.652369	+	1.12994i	−0.982546	+	0.186017i	$0.940442\pi$
$308$	6741.61	+	20604.9i	0.00404936	+	0.0123764i
$309$	−280082.	+	485116.i	−0.166874	+	0.289034i
$310$	2.29921e6	−	1.02650e6i	1.35886	−	0.606672i
$311$		−	1.05752e6i		−	0.619993i	−0.950738	−	0.309997i	$-0.899672\pi$
$311$		−	1.05752e6i		−	0.619993i	0.950738	−	0.309997i	$-0.100328\pi$
$312$	−4.06011e6	−	1.30544e6i	−2.36130	−	0.759225i
$313$	−241586.	−	418439.i	−0.139383	−	0.241419i	0.787880	−	0.615829i	$-0.211179\pi$
$313$	−241586.	−	418439.i	−0.139383	−	0.241419i	−0.927263	+	0.374410i	$0.877845\pi$
$314$	1.69641e6	−	757372.i	0.970972	−	0.433496i
$315$		−	182347.i		−	0.103543i
$316$	1.82694e6	+	384421.i	1.02922	+	0.216566i
$317$	−267998.	+	154729.i	−0.149790	+	0.0864814i	−0.573022	−	0.819540i	$-0.694229\pi$
$317$	−267998.	+	154729.i	−0.149790	+	0.0864814i	0.423232	+	0.906022i	$0.360896\pi$
$318$	−2.20790e6	+	3.04546e6i	−1.22437	+	1.68883i
$319$	79472.5	+	137650.i	0.0437260	+	0.0757357i
$320$	−1.46300e6	+	662168.i	−0.798676	+	0.361488i
$321$	−1.50048e6	+	2.59890e6i	−0.812768	+	1.40776i
$322$	7938.81	−	76283.8i	0.00426693	−	0.0410008i
$323$	−20984.5	−	138025.i	−0.0111916	−	0.0736126i
$324$	−3.77547e6	−	794425.i	−1.99806	−	0.420427i
$325$	519995.	+	300219.i	0.273081	+	0.157663i
$326$	−56282.7	+	77633.4i	−0.0293313	+	0.0404580i
$327$	−1.54010e6	+	889175.i	−0.796487	+	0.459852i
$328$	685094.	−	620682.i	0.351614	−	0.318555i
$329$	48072.1	+	83263.2i	0.0244852	+	0.0424095i
$330$	801313.	+	83392.1i	0.405058	+	0.0421541i
$331$	−1.87715e6			−0.941737			−0.470869	−	0.882203i	$-0.656059\pi$
$331$	−1.87715e6			−0.941737			−0.470869	+	0.882203i	$0.656059\pi$
$332$	1.76002e6	−	575852.i	0.876340	−	0.286725i
$333$	6.48266e6	−	3.74276e6i	3.20363	−	1.84962i
$334$	−117835.	+	1.13228e6i	−0.0577975	+	0.555375i
$335$	−2.55955e6			−1.24610
$336$	−191129.	+	20880.1i	−0.0923590	+	0.0100898i
$337$	−1.16105e6	−	670334.i	−0.556900	−	0.321526i	0.195000	−	0.980803i	$-0.437529\pi$
$337$	−1.16105e6	−	670334.i	−0.556900	−	0.321526i	−0.751900	+	0.659277i	$0.770863\pi$
$338$	−1.64216e6	+	733152.i	−0.781851	+	0.349062i
$339$	−103275.	−	59625.9i	−0.0488086	−	0.0281797i
$340$	−92890.5	+	103591.i	−0.0435787	+	0.0485987i
$341$			930060.i			0.433137i
$342$	−2.70469e6	−	4.21245e6i	−1.25041	−	1.94747i
$343$			222104.i			0.101935i
$344$	953056.	−	863450.i	0.434233	−	0.393406i
$345$	−2.46825e6	−	1.42504e6i	−1.11645	−	0.644585i
$346$	1.13094e6	+	2.53315e6i	0.507867	+	1.13755i
$347$	824436.	+	475988.i	0.367564	+	0.212213i	0.672394	−	0.740194i	$-0.265266\pi$
$347$	824436.	+	475988.i	0.367564	+	0.212213i	−0.304830	+	0.952407i	$0.598600\pi$
$348$	−1.33972e6	+	438335.i	−0.593014	+	0.194025i
$349$	−55711.0			−0.0244837			−0.0122419	−	0.999925i	$-0.503897\pi$
$349$	−55711.0			−0.0244837			−0.0122419	+	0.999925i	$0.503897\pi$
$350$	26923.6	+	2801.92i	0.0117480	+	0.00122260i
$351$	−6.51657e6	+	3.76234e6i	−2.82326	+	1.63001i
$352$	−3035.97	−	593159.i	−0.00130599	−	0.255161i
$353$	643210.			0.274736			0.137368	−	0.990520i	$-0.456136\pi$
$353$	643210.			0.274736			0.137368	+	0.990520i	$0.456136\pi$
$354$	293194.	−	2.81729e6i	0.124350	−	1.19488i
$355$	1.75955e6	+	3.04763e6i	0.741022	+	1.28349i
$356$	2.53885e6	+	2.27660e6i	1.06173	+	0.952053i
$357$	−14426.8	+	8329.34i	−0.00599102	+	0.00345892i
$358$	−3.47837e6	−	2.52175e6i	−1.43439	−	1.03991i
$359$	−2.07901e6	−	1.20031e6i	−0.851373	−	0.491540i	0.00974107	−	0.999953i	$-0.496899\pi$
$359$	−2.07901e6	−	1.20031e6i	−0.851373	−	0.491540i	−0.861114	+	0.508412i	$0.830233\pi$
$360$	−1.52713e6	+	4.74961e6i	−0.621041	+	1.93153i
$361$	544810.	−	2.41542e6i	0.220028	−	0.975494i
$362$	989429.	+	102969.i	0.396838	+	0.0412987i
$363$	2.13647e6	−	3.70047e6i	0.850999	−	1.47397i
$364$	−117341.	+	130858.i	−0.0464189	+	0.0517662i
$365$	−1.40605e6	−	2.43535e6i	−0.552419	−	0.956818i
$366$	5.52231e6	+	4.00356e6i	2.15485	+	1.56223i
$367$	1.40886e6	−	813405.i	0.546012	−	0.315240i	−0.201500	−	0.979489i	$-0.564582\pi$
$367$	1.40886e6	−	813405.i	0.546012	−	0.315240i	0.747512	+	0.664248i	$0.231248\pi$
$368$	−845651.	+	1.92049e6i	−0.325515	+	0.739251i
$369$		−	2.87203e6i		−	1.09805i
$370$	−1.50431e6	−	3.36946e6i	−0.571261	−	1.27955i
$371$	77512.1	+	134255.i	0.0292371	+	0.0506402i
$372$	−8.07148e6	−	1.69838e6i	−3.02410	−	0.636324i
$373$			829777.i			0.308808i	0.988008	+	0.154404i	$0.0493458\pi$
$373$			829777.i			0.308808i	−0.988008	+	0.154404i	$0.950654\pi$
$374$	−20951.9	−	46929.5i	−0.00774542	−	0.0173487i
$375$	2.67608e6	−	4.63510e6i	0.982699	−	1.70208i
$376$	−554819.	−	2.57137e6i	−0.202387	−	0.937981i
$377$	−644302.	+	1.11596e6i	−0.233473	+	0.404387i
$378$	−199112.	+	274645.i	−0.0716750	+	0.0988649i
$379$	1.60971e6			0.575637			0.287819	−	0.957685i	$-0.407070\pi$
$379$	1.60971e6			0.575637			0.287819	+	0.957685i	$0.407070\pi$
$380$	−2.20340e6	+	1.11118e6i	−0.782769	+	0.394753i
$381$	−2.20935e6			−0.779744
$382$	103004.	−	142078.i	0.0361156	−	0.0498160i
$383$	−759653.	+	1.31576e6i	−0.264617	+	0.458330i	−0.967463	−	0.253012i	$-0.918579\pi$
$383$	−759653.	+	1.31576e6i	−0.264617	+	0.458330i	0.702846	+	0.711342i	$0.251912\pi$
$384$	5.15324e6	+	1.05682e6i	1.78341	+	0.365740i
$385$	16601.1	−	28754.0i	0.00570802	−	0.00988658i
$386$	−58449.6	−	130919.i	−0.0199670	−	0.0447234i
$387$		−	3.99537e6i		−	1.35606i
$388$	−762118.	+	3.62193e6i	−0.257006	+	1.22141i
$389$	96471.0	+	167093.i	0.0323238	+	0.0559865i	0.881735	−	0.471745i	$-0.156376\pi$
$389$	96471.0	+	167093.i	0.0323238	+	0.0559865i	−0.849411	+	0.527732i	$0.823043\pi$
$390$	2.66271e6	+	5.96411e6i	0.886468	+	1.98557i
$391$			181815.i			0.0601435i
$392$	928835.	−	2.88882e6i	0.305298	−	0.949522i
$393$	8.92948e6	−	5.15544e6i	2.91638	−	1.68378i
$394$	2.17457e6	+	1.57652e6i	0.705721	+	0.511634i
$395$	−1.42960e6	−	2.47615e6i	−0.461024	−	0.798516i
$396$	−1.37201e6	−	1.23028e6i	−0.439662	−	0.394246i
$397$	−2.48991e6	+	4.31264e6i	−0.792879	+	1.37331i	0.131299	+	0.991343i	$0.458085\pi$
$397$	−2.48991e6	+	4.31264e6i	−0.792879	+	1.37331i	−0.924178	+	0.381963i	$0.875248\pi$
$398$	4.14696e6	+	431572.i	1.31227	+	0.136567i
$399$	−292096.	+	44408.4i	−0.0918531	+	0.0139647i
$400$	−677816.	−	298463.i	−0.211817	−	0.0932698i
$401$	−2.29680e6	−	1.32606e6i	−0.713284	−	0.411815i	0.0989918	−	0.995088i	$-0.468438\pi$
$401$	−2.29680e6	−	1.32606e6i	−0.713284	−	0.411815i	−0.812276	+	0.583274i	$0.801772\pi$
$402$	6.78824e6	+	4.92134e6i	2.09504	+	1.51886i
$403$	−6.53002e6	+	3.77011e6i	−2.00287	+	1.15636i
$404$	−1.20752e6	+	1.34662e6i	−0.368078	+	0.410479i
$405$	2.95434e6	+	5.11707e6i	0.895001	+	1.55019i
$406$	−6013.21	+	57780.8i	−0.00181047	+	0.0173968i
$407$	1.36299e6			0.407855
$408$	445535.	−	96132.4i	0.132505	−	0.0285903i
$409$	−2.71166e6	+	1.56558e6i	−0.801544	+	0.462771i	−0.844011	−	0.536326i	$-0.819812\pi$
$409$	−2.71166e6	+	1.56558e6i	−0.801544	+	0.462771i	0.0424671	+	0.999098i	$0.486478\pi$
$410$	−1.40817e6	−	146547.i	−0.413710	−	0.0430545i
$411$	3.90236e6			1.13952
$412$	−196414.	−	600316.i	−0.0570073	−	0.174236i
$413$	−101095.	−	58367.0i	−0.0291644	−	0.0168381i
$414$	2.65774e6	+	5.95296e6i	0.762098	+	1.70700i
$415$	−2.45609e6	−	1.41803e6i	−0.700043	−	0.404170i
$416$	4.15230e6	−	2.42576e6i	1.17640	−	0.687248i
$417$			9.10339e6i			2.56368i
$418$	−42990.7	−	910494.i	−0.0120347	−	0.254880i
$419$		−	627746.i		−	0.174682i	−0.996178	−	0.0873411i	$-0.972163\pi$
$419$		−	627746.i		−	0.174682i	0.996178	−	0.0873411i	$-0.0278370\pi$
$420$	219225.	+	196580.i	0.0606410	+	0.0543770i
$421$	1.03608e6	+	598181.i	0.284897	+	0.164485i	0.635638	−	0.771987i	$-0.280737\pi$
$421$	1.03608e6	+	598181.i	0.284897	+	0.164485i	−0.350741	+	0.936472i	$0.614070\pi$
$422$	−200783.	+	89640.7i	−0.0548840	+	0.0245033i
$423$	−7.07755e6	−	4.08623e6i	−1.92323	−	1.11038i
$424$	−894599.	−	4.14611e6i	−0.241665	−	1.12002i
$425$	−64169.8			−0.0172329
$426$	1.19324e6	−	1.14658e7i	0.318570	−	3.06113i
$427$	243443.	−	140552.i	0.0646141	−	0.0373050i
$428$	−1.05225e6	−	3.21606e6i	−0.277656	−	0.848623i
$429$	−2.41256e6			−0.632899
$430$	−1.95895e6	−	203867.i	−0.510919	−	0.0531711i
$431$	190195.	+	329427.i	0.0493180	+	0.0854213i	0.889631	−	0.456681i	$-0.150962\pi$
$431$	190195.	+	329427.i	0.0493180	+	0.0854213i	−0.840313	+	0.542102i	$0.817629\pi$
$432$	7.48641e6	−	5.48617e6i	1.93003	−	1.41436i
$433$	−1.20601e6	+	696289.i	−0.309122	+	0.178472i	−0.646534	−	0.762886i	$-0.723782\pi$
$433$	−1.20601e6	+	696289.i	−0.309122	+	0.178472i	0.337411	+	0.941357i	$0.390449\pi$
$434$	−199523.	+	275212.i	−0.0508474	+	0.0701363i
$435$	1.86956e6	+	1.07939e6i	0.473715	+	0.273499i
$436$	412896.	−	1.96227e6i	0.104022	−	0.494359i
$437$	−1.17425e6	+	3.00321e6i	−0.294141	+	0.752285i
$438$	−953516.	+	9.16231e6i	−0.237489	+	2.28202i
$439$	−915447.	+	1.58560e6i	−0.226711	+	0.392674i	−0.956831	−	0.290644i	$-0.906131\pi$
$439$	−915447.	+	1.58560e6i	−0.226711	+	0.392674i	0.730121	+	0.683318i	$0.239464\pi$
$440$	−673223.	+	609926.i	−0.165778	+	0.150192i
$441$	−4.71368e6	−	8.16433e6i	−1.15415	−	1.99905i
$442$	244564.	−	337339.i	0.0595438	−	0.0821317i
$443$	5.39424e6	−	3.11437e6i	1.30593	−	0.753981i	0.324519	−	0.945879i	$-0.394798\pi$
$443$	5.39424e6	−	3.11437e6i	1.30593	−	0.753981i	0.981415	+	0.191898i	$0.0614644\pi$
$444$	−2.48895e6	+	1.18286e7i	−0.599182	+	2.84758i
$445$		−	5.22249e6i		−	1.25020i
$446$	−74482.7	+	33253.2i	−0.0177304	+	0.00791583i
$447$	−934665.	−	1.61889e6i	−0.221252	−	0.383219i
$448$	126350.	−	176172.i	0.0297427	−	0.0414706i
$449$			1.56977e6i			0.367468i	0.982976	+	0.183734i	$0.0588185\pi$
$449$			1.56977e6i			0.367468i	−0.982976	+	0.183734i	$0.941182\pi$
$450$	−2.10104e6	+	938020.i	−0.489105	+	0.218364i
$451$	261474.	−	452886.i	0.0605323	−	0.104845i
$452$	127800.	−	41814.1i	0.0294228	−	0.00962669i
$453$	3.05823e6	−	5.29700e6i	0.700203	−	1.21279i
$454$	−4.80118e6	−	3.48076e6i	−1.09322	−	0.792564i
$455$	269178.			0.0609553
$456$	7.98018e6	+	1.28956e6i	1.79722	+	0.290422i
$457$	−851569.			−0.190735			−0.0953673	−	0.995442i	$-0.530403\pi$
$457$	−851569.			−0.190735			−0.0953673	+	0.995442i	$0.530403\pi$
$458$	−4.96540e6	−	3.59982e6i	−1.10609	−	0.801894i
$459$	402087.	−	696436.i	0.0890817	−	0.154294i
$460$	3.05438e6	−	999347.i	0.673021	−	0.220202i
$461$	−443756.	+	768609.i	−0.0972506	+	0.168443i	−0.910546	−	0.413408i	$-0.864338\pi$
$461$	−443756.	+	768609.i	−0.0972506	+	0.168443i	0.813295	+	0.581851i	$0.197672\pi$
$462$	−99314.5	+	44339.5i	−0.0216475	+	0.00966465i
$463$			8.37376e6i			1.81538i	0.419640	+	0.907691i	$0.362156\pi$
$463$			8.37376e6i			1.81538i	−0.419640	+	0.907691i	$0.637844\pi$
$464$	640534.	−	1.45466e6i	0.138117	−	0.313666i
$465$	6.31602e6	+	1.09397e7i	1.35460	+	2.34624i
$466$	−3.91629e6	+	1.74845e6i	−0.835430	+	0.372982i
$467$		−	6.88767e6i		−	1.46144i	−0.682679	−	0.730718i	$-0.739185\pi$
$467$		−	6.88767e6i		−	1.46144i	0.682679	−	0.730718i	$-0.260815\pi$
$468$	3.07632e6	−	1.46201e7i	0.649258	−	3.08557i
$469$	299250.	−	172772.i	0.0628206	−	0.0362695i
$470$	−2.36464e6	+	3.26166e6i	−0.493764	+	0.681073i
$471$	4.66010e6	+	8.07153e6i	0.967928	+	1.67650i
$472$	2.14441e6	+	2.36695e6i	0.443049	+	0.489028i
$473$	363744.	−	630024.i	0.0747556	−	0.129480i
$474$	−969489.	+	9.31580e6i	−0.198197	+	1.90447i
$475$	−1.05995e6	−	414438.i	−0.215552	−	0.0842802i
$476$	3867.80	−	18381.5i	0.000782432	−	0.00371847i
$477$	−1.14119e7	−	6.58869e6i	−2.29649	−	1.32588i
$478$	1.07264e6	−	1.47955e6i	0.214726	−	0.296182i
$479$	982202.	−	567074.i	0.195597	−	0.112928i	−0.399003	−	0.916950i	$-0.630644\pi$
$479$	982202.	−	567074.i	0.195597	−	0.112928i	0.594600	+	0.804022i	$0.297310\pi$
$480$	−4.06384e6	−	6.95631e6i	−0.805070	−	1.37808i
$481$	5.52503e6	+	9.56963e6i	1.08886	+	1.88596i
$482$	4.69373e6	+	488473.i	0.920239	+	0.0957687i
$483$	384767.			0.0750464
$484$	1.49825e6	+	4.57921e6i	0.290717	+	0.888541i
$485$	4.90898e6	−	2.83420e6i	0.947625	−	0.547112i
$486$	713824.	−	6.85912e6i	0.137088	−	1.31728i
$487$	−7.04972e6			−1.34694			−0.673472	−	0.739212i	$-0.735198\pi$
$487$	−7.04972e6			−1.34694			−0.673472	+	0.739212i	$0.735198\pi$
$488$	−7.51809e6	+	1.62217e6i	−1.42909	+	0.308351i
$489$	−416606.	−	240528.i	−0.0787868	−	0.0454876i
$490$	−4.24353e6	+	1.89455e6i	−0.798431	+	0.356464i
$491$	−2.17000e6	−	1.25285e6i	−0.406216	−	0.234529i	0.282947	−	0.959136i	$-0.408688\pi$
$491$	−2.17000e6	−	1.25285e6i	−0.406216	−	0.234529i	−0.689163	+	0.724607i	$0.742021\pi$
$492$	3.45287e6	+	3.09620e6i	0.643084	+	0.576656i
$493$		−	137715.i		−	0.0255191i
$494$	6.21838e6	−	3.99264e6i	1.14646	−	0.736110i
$495$			2.82226e6i			0.517707i
$496$	7.50187e6	−	5.49750e6i	1.36919	−	1.00337i
$497$	−411436.	−	237543.i	−0.0747156	−	0.0431370i
$498$	3.78737e6	+	8.48320e6i	0.684329	+	1.53280i
$499$	4.86409e6	+	2.80828e6i	0.874480	+	0.504882i	0.868835	−	0.495103i	$-0.164870\pi$
$499$	4.86409e6	+	2.80828e6i	0.874480	+	0.504882i	0.00564591	+	0.999984i	$0.498203\pi$
$500$	1.87666e6	+	5.73580e6i	0.335708	+	1.02605i
$501$	−5.71108e6			−1.01654
$502$	9.73406e6	+	1.01302e6i	1.72399	+	0.179415i
$503$	8.92000e6	−	5.14996e6i	1.57197	−	0.907578i	0.576044	−	0.817419i	$-0.304596\pi$
$503$	8.92000e6	−	5.14996e6i	1.57197	−	0.907578i	0.995927	−	0.0901595i	$-0.0287377\pi$
$504$	−142058.	−	658383.i	−0.0249109	−	0.115452i
$505$	2.77003e6			0.483344
$506$	−122872.	+	1.18068e6i	−0.0213343	+	0.205001i
$507$	−4.51107e6	−	7.81341e6i	−0.779399	−	1.34996i
$508$	1.66316e6	−	1.85475e6i	0.285940	−	0.318879i
$509$	−2.57452e6	+	1.48640e6i	−0.440454	+	0.254296i	−0.703790	−	0.710408i	$-0.748511\pi$
$509$	−2.57452e6	+	1.48640e6i	−0.440454	+	0.254296i	0.263336	+	0.964704i	$0.415177\pi$
$510$	−565140.	−	409715.i	−0.0962124	−	0.0697520i
$511$	328777.	+	189819.i	0.0556992	+	0.0321579i
$512$	−4.76647e6	+	3.53059e6i	−0.803568	+	0.595214i
$513$	1.11395e7	−	8.90681e6i	1.86885	−	1.49427i
$514$	−6.43996e6	−	670203.i	−1.07517	−	0.111892i
$515$	−483667.	+	837737.i	−0.0803579	+	0.139184i
$516$	4.80340e6	+	4.30722e6i	0.794189	+	0.712153i
$517$	−744032.	−	1.28870e6i	−0.122424	−	0.212044i
$518$	403318.	+	292398.i	0.0660425	+	0.0478795i
$519$	−1.20528e7	+	6.95866e6i	−1.96412	+	1.13399i
$520$	−7.01132e6	−	2.25434e6i	−1.13708	−	0.365603i
$521$		−	329207.i		−	0.0531343i	−0.999647	−	0.0265671i	$-0.991542\pi$
$521$		−	329207.i		−	0.0531343i	0.999647	−	0.0265671i	$-0.00845758\pi$
$522$	−2.01309e6	−	4.50905e6i	−0.323360	−	0.724283i
$523$	1.48549e6	+	2.57294e6i	0.237473	+	0.411315i	0.959989	−	0.280039i	$-0.0903475\pi$
$523$	1.48549e6	+	2.57294e6i	0.237473	+	0.411315i	−0.722515	+	0.691355i	$0.757014\pi$
$524$	−2.39397e6	+	1.13772e7i	−0.380882	+	1.81012i
$525$			135799.i			0.0215030i
$526$	−1.25572e6	−	2.81264e6i	−0.197892	−	0.443251i
$527$	402918.	−	697874.i	0.0631960	−	0.109459i
$528$	2.95820e6	−	323171.i	0.461787	−	0.0504484i
$529$	−1.11847e6	+	1.93725e6i	−0.173774	+	0.300985i
$530$	−3.81277e6	+	5.25914e6i	−0.589591	+	0.813252i
$531$	9.92263e6			1.52718
$532$	182604.	−	278645.i	0.0279725	−	0.0426847i
$533$	4.23966e6			0.646418
$534$	−1.00415e7	+	1.38507e7i	−1.52386	+	2.10193i
$535$	−2.59114e6	+	4.48799e6i	−0.391387	+	0.677902i
$536$	−9.24154e6	+	1.99403e6i	−1.38942	+	0.299792i
$537$	1.07768e7	−	1.86660e7i	1.61271	−	2.79329i
$538$	−364539.	−	816517.i	−0.0542986	−	0.121621i
$539$		−	1.71656e6i		−	0.254500i
$540$	−1.39097e7	−	2.92686e6i	−2.05274	−	0.431934i
$541$	−6.08899e6	−	1.05464e7i	−0.894442	−	1.54922i	−0.834494	−	0.551017i	$-0.814240\pi$
$541$	−6.08899e6	−	1.05464e7i	−0.894442	−	1.54922i	−0.0599482	−	0.998201i	$-0.519094\pi$
$542$	−655878.	−	1.46908e6i	−0.0959014	−	0.214806i
$543$			4.99057e6i			0.726358i
$544$	−254688.	+	446394.i	−0.0368987	+	0.0646727i
$545$	−2.65956e6	+	1.53550e6i	−0.383547	+	0.221441i
$546$	−713894.	−	517559.i	−0.102483	−	0.0742982i
$547$	−1.11581e6	−	1.93264e6i	−0.159449	−	0.276173i	0.775221	−	0.631690i	$-0.217638\pi$
$547$	−1.11581e6	−	1.93264e6i	−0.159449	−	0.276173i	−0.934670	+	0.355516i	$0.884305\pi$
$548$	−2.93763e6	+	3.27603e6i	−0.417874	+	0.466012i
$549$	−1.19472e7	+	2.06932e7i	−1.69175	+	2.93019i
$550$	−416708.	−	43366.5i	−0.0587388	−	0.00611291i
$551$	889427.	−	2.27477e6i	0.124805	−	0.319197i
$552$	−1.00221e7	−	3.22238e6i	−1.39994	−	0.450120i
$553$	334284.	+	192999.i	0.0464840	+	0.0268375i
$554$	4.66755e6	+	3.38388e6i	0.646122	+	0.468425i
$555$	1.60319e7	−	9.25602e6i	2.20929	−	1.27553i
$556$	−7.64231e6	−	6.85288e6i	−1.04843	−	0.940127i
$557$	−4.73228e6	−	8.19656e6i	−0.646298	−	1.11942i	−0.984000	−	0.178168i	$-0.942983\pi$
$557$	−4.73228e6	−	8.19656e6i	−0.646298	−	1.11942i	0.337702	−	0.941253i	$-0.390350\pi$
$558$	2.99089e6	−	2.87394e7i	0.406645	−	3.90744i
$559$	5.89793e6			0.798307
$560$	−330057.	+	36057.4i	−0.0444753	+	0.00485875i
$561$	223291.	−	128917.i	0.0299546	−	0.0172943i
$562$	8.25650e6	+	859249.i	1.10269	+	0.114757i
$563$	−9.76622e6			−1.29854			−0.649270	−	0.760558i	$-0.724926\pi$
$563$	−9.76622e6			−1.29854			−0.649270	+	0.760558i	$0.724926\pi$
$564$	1.25426e7	−	4.10375e6i	1.66031	−	0.543229i
$565$	−178344.	−	102967.i	−0.0235037	−	0.0135699i
$566$	−5.14993e6	−	1.15351e7i	−0.675710	−	1.51350i
$567$	−690814.	−	398842.i	−0.0902409	−	0.0521006i
$568$	8.72733e6	+	9.63302e6i	1.13504	+	1.25283i
$569$		−	630739.i		−	0.0816713i	−0.999166	−	0.0408356i	$-0.986998\pi$
$569$		−	630739.i		−	0.0816713i	0.999166	−	0.0408356i	$-0.0130020\pi$
$570$	−6.68882e6	−	1.04176e7i	−0.862308	−	1.34301i
$571$			8.05237e6i			1.03356i	0.856120	+	0.516778i	$0.172869\pi$
$571$			8.05237e6i			1.03356i	−0.856120	+	0.516778i	$0.827131\pi$
$572$	1.81613e6	−	2.02534e6i	0.232091	−	0.258826i
$573$	762437.	+	440193.i	0.0970102	+	0.0560089i
$574$	174528.	−	77919.2i	0.0221099	−	0.00987108i
$575$	1.28357e6	+	741068.i	0.161901	+	0.0934735i
$576$	−1.81367e6	+	1.83387e7i	−0.227773	+	2.30310i
$577$	1.16889e7			1.46162			0.730811	−	0.682580i	$-0.239142\pi$
$577$	1.16889e7			1.46162			0.730811	+	0.682580i	$0.239142\pi$
$578$	826778.	−	7.94449e6i	0.102936	−	0.989114i
$579$	622914.	−	359640.i	0.0772204	−	0.0445832i
$580$	−2.31353e6	+	756951.i	−0.285565	+	0.0934324i
$581$	382872.			0.0470559
$582$	−1.84686e7	−	1.92202e6i	−2.26010	−	0.235207i
$583$	−1.19969e6	−	2.07792e6i	−0.146183	−	0.253197i
$584$	−6.97397e6	−	7.69771e6i	−0.846152	−	0.933963i
$585$	−1.98153e7	+	1.14404e7i	−2.39393	+	1.38213i
$586$	4.31458e6	−	5.95132e6i	0.519033	−	0.715927i
$587$	4.17618e6	+	2.41112e6i	0.500247	+	0.288818i	0.728816	−	0.684710i	$-0.240071\pi$
$587$	4.17618e6	+	2.41112e6i	0.500247	+	0.288818i	−0.228569	+	0.973528i	$0.573405\pi$
$588$	1.48971e7	+	3.13461e6i	1.77688	+	0.373887i
$589$	1.11625e7	−	8.92520e6i	1.32579	−	1.06006i
$590$	506310.	−	4.86512e6i	0.0598806	−	0.575391i
$591$	−6.73736e6	+	1.16695e7i	−0.793453	+	1.37430i
$592$	−8.05649e6	−	1.09939e7i	−0.944804	−	1.28928i
$593$	3.85797e6	+	6.68220e6i	0.450528	+	0.780338i	0.998419	−	0.0562120i	$-0.0179023\pi$
$593$	3.85797e6	+	6.68220e6i	0.450528	+	0.780338i	−0.547890	+	0.836550i	$0.684569\pi$
$594$	3.08174e6	−	4.25080e6i	0.358369	−	0.494316i
$595$	−24913.4	+	14383.8i	−0.00288497	+	0.00166564i
$596$	2.06266e6	+	434019.i	0.237854	+	0.0500488i
$597$			2.09168e7i			2.40193i
$598$	−8.78770e6	+	3.92332e6i	−1.00490	+	0.448643i
$599$	−2.68875e6	−	4.65706e6i	−0.306185	−	0.530328i	0.671339	−	0.741150i	$-0.265719\pi$
$599$	−2.68875e6	−	4.65706e6i	−0.306185	−	0.530328i	−0.977524	+	0.210822i	$0.932386\pi$
$600$	1.13730e6	−	3.53719e6i	0.128973	−	0.401125i
$601$			9.86104e6i			1.11362i	0.830640	+	0.556810i	$0.187975\pi$
$601$			9.86104e6i			1.11362i	−0.830640	+	0.556810i	$0.812025\pi$
$602$	242792.	−	108396.i	0.0273051	−	0.0121905i
$603$	−1.46860e7	+	2.54369e7i	−1.64479	+	2.84886i
$604$	2.14466e6	+	6.55488e6i	0.239202	+	0.731093i
$605$	3.68942e6	−	6.39025e6i	0.409797	−	0.709790i
$606$	−7.34647e6	−	5.32604e6i	−0.812638	−	0.589146i
$607$	−1.67126e7			−1.84108			−0.920540	−	0.390649i	$-0.872251\pi$
$607$	−1.67126e7			−1.84108			−0.920540	+	0.390649i	$0.872251\pi$
$608$	−7.08993e6	+	5.72861e6i	−0.777827	+	0.628478i
$609$	−291440.			−0.0318424
$610$	9.53635e6	+	6.91366e6i	1.03767	+	0.752287i
$611$	6.03205e6	−	1.04478e7i	0.653675	−	1.13220i
$612$	496511.	+	1.51752e6i	0.0535858	+	0.163779i
$613$	−3.83396e6	+	6.64062e6i	−0.412094	+	0.713768i	−0.995119	−	0.0986865i	$-0.968536\pi$
$613$	−3.83396e6	+	6.64062e6i	−0.412094	+	0.713768i	0.583024	+	0.812455i	$0.301869\pi$
$614$	1.11295e7	−	4.96884e6i	1.19139	−	0.531905i
$615$		−	7.10266e6i		−	0.757239i
$616$	37539.2	−	116753.i	0.00398597	−	0.0123970i
$617$	2.02379e6	+	3.50531e6i	0.214019	+	0.370693i	0.952969	−	0.303068i	$-0.0980111\pi$
$617$	2.02379e6	+	3.50531e6i	0.214019	+	0.370693i	−0.738949	+	0.673761i	$0.764678\pi$
$618$	2.89349e6	−	1.29182e6i	0.304755	−	0.136060i
$619$			1.39528e7i			1.46364i	0.681499	+	0.731819i	$0.261328\pi$
$619$			1.39528e7i			1.46364i	−0.681499	+	0.731819i	$0.738672\pi$
$620$	−1.39385e7	−	2.93290e6i	−1.45625	−	0.306421i
$621$	−1.60856e7	+	9.28704e6i	−1.67382	+	0.966381i
$622$	−3.51131e6	+	4.84332e6i	−0.363909	+	0.501958i
$623$	352523.	+	610588.i	0.0363888	+	0.0630272i
$624$	1.42604e7	+	1.94597e7i	1.46612	+	2.00067i
$625$	3.49117e6	−	6.04688e6i	0.357496	−	0.619200i
$626$	−282918.	+	2.71855e6i	−0.0288552	+	0.277269i
$627$	4.52090e6	−	687328.i	0.459257	−	0.0698225i
$628$	−1.02841e7	−	2.16396e6i	−1.04056	−	0.218952i
$629$	−1.02272e6	−	590469.i	−0.103070	−	0.0595073i
$630$	−605451.	+	835129.i	−0.0607754	+	0.0838305i
$631$	4.43389e6	−	2.55991e6i	0.443314	−	0.255947i	−0.261688	−	0.965152i	$-0.584279\pi$
$631$	4.43389e6	−	2.55991e6i	0.443314	−	0.255947i	0.705002	+	0.709205i	$0.250946\pi$
$632$	−7.09080e6	−	7.82666e6i	−0.706159	−	0.779442i
$633$	−551558.	−	955326.i	−0.0547119	−	0.0947638i
$634$	1.74115e6	+	181201.i	0.172034	+	0.0179034i
$635$	−3.81528e6			−0.375484
$636$	2.02239e7	−	6.61694e6i	1.98254	−	0.648656i
$637$	1.20521e7	−	6.95829e6i	1.17683	−	0.679444i
$638$	93069.2	−	894299.i	0.00905220	−	0.0869823i
$639$	4.03832e7			3.91245
$640$	8.89902e6	+	1.82500e6i	0.858800	+	0.176122i
$641$	1.34925e7	+	7.78992e6i	1.29703	+	0.748838i	0.979889	−	0.199542i	$-0.0639454\pi$
$641$	1.34925e7	+	7.78992e6i	1.29703	+	0.748838i	0.317136	+	0.948380i	$0.397279\pi$
$642$	1.55012e7	−	6.92061e6i	1.48432	−	0.662685i
$643$	1.64399e7	+	9.49160e6i	1.56810	+	0.905341i	0.996391	+	0.0848818i	$0.0270513\pi$
$643$	1.64399e7	+	9.49160e6i	1.56810	+	0.905341i	0.571705	+	0.820459i	$0.306282\pi$
$644$	−289646.	+	323012.i	−0.0275203	+	0.0306905i
$645$		−	9.88073e6i		−	0.935168i
$646$	−362183.	+	701816.i	−0.0341465	+	0.0661671i
$647$		−	1.00942e7i		−	0.948009i	−0.880522	−	0.474005i	$-0.842808\pi$
$647$		−	1.00942e7i		−	0.948009i	0.880522	−	0.474005i	$-0.157192\pi$
$648$	1.46535e7	+	1.61742e7i	1.37089	+	1.51316i
$649$	1.56468e6	+	903371.i	0.145819	+	0.0841888i
$650$	−1.38470e6	−	3.10153e6i	−0.128550	−	0.287934i
$651$	−1.47688e6	−	852675.i	−0.136581	−	0.0788553i
$652$	515537.	−	168676.i	0.0474942	−	0.0155394i
$653$	4.89706e6			0.449420			0.224710	−	0.974426i	$-0.427856\pi$
$653$	4.89706e6			0.449420			0.224710	+	0.974426i	$0.427856\pi$
$654$	1.00058e7	+	1.04130e6i	0.914763	+	0.0951989i
$655$	1.54201e7	−	8.90281e6i	1.40438	−	0.810819i
$656$	−5.19853e6	+	567918.i	−0.471651	+	0.0515259i
$657$	−3.22701e7			−2.91667
$658$	56296.5	−	540952.i	0.00506894	−	0.0487073i
$659$	−7.84698e6	−	1.35914e7i	−0.703864	−	1.21913i	−0.967100	−	0.254397i	$-0.918123\pi$
$659$	−7.84698e6	−	1.35914e7i	−0.703864	−	1.21913i	0.263236	−	0.964732i	$-0.415210\pi$
$660$	−3.39304e6	−	3.04255e6i	−0.303200	−	0.271880i
$661$	−45158.0	+	26072.0i	−0.00402005	+	0.00232098i	−0.502009	−	0.864863i	$-0.667405\pi$
$661$	−45158.0	+	26072.0i	−0.00402005	+	0.00232098i	0.497989	+	0.867184i	$0.334072\pi$
$662$	8.59716e6	+	6.23277e6i	0.762448	+	0.552759i
$663$	1.81027e6	+	1.04516e6i	0.159941	+	0.0923419i
$664$	−9.97272e6	−	3.20651e6i	−0.877796	−	0.282236i
$665$	−504415.	+	76687.8i	−0.0442317	+	0.00672469i
$666$	−4.21171e7	−	4.38310e6i	−3.67936	−	0.382909i
$667$	−1.59041e6	+	2.75467e6i	−0.138419	+	0.239748i
$668$	4.29920e6	−	4.79445e6i	0.372775	−	0.415717i
$669$	−204607.	−	354389.i	−0.0176748	−	0.0306136i
$670$	1.17225e7	+	8.49855e6i	1.00886	+	0.731405i
$671$	−3.76787e6	+	2.17538e6i	−0.323065	+	0.186522i
$672$	944681.	+	538984.i	0.0806979	+	0.0460418i
$673$		−	5.74746e6i		−	0.489146i	−0.969631	−	0.244573i	$-0.921352\pi$
$673$		−	5.74746e6i		−	0.489146i	0.969631	−	0.244573i	$-0.0786478\pi$
$674$	3.09177e6	+	6.92514e6i	0.262154	+	0.587190i
$675$	−3.27776e6	−	5.67725e6i	−0.276897	−	0.479600i
$676$	9.95522e6	+	2.09476e6i	0.837885	+	0.176306i
$677$		−	1.35922e7i		−	1.13977i	−0.821724	−	0.569885i	$-0.806988\pi$
$677$		−	1.35922e7i		−	1.13977i	0.821724	−	0.569885i	$-0.193012\pi$
$678$	275011.	+	615988.i	0.0229761	+	0.0514633i
$679$	−382622.	+	662721.i	−0.0318490	+	0.0551641i
$680$	769385.	−	166009.i	0.0638074	−	0.0137676i
$681$	1.48752e7	−	2.57647e7i	1.22913	−	2.12891i
$682$	3.08811e6	−	4.25958e6i	0.254233	−	0.350676i
$683$	−1.91109e7			−1.56758			−0.783791	−	0.621025i	$-0.786716\pi$
$683$	−1.91109e7			−1.56758			−0.783791	+	0.621025i	$0.786716\pi$
$684$	−1.59953e6	+	2.82730e7i	−0.130723	+	2.31064i
$685$	6.73890e6			0.548735
$686$	737459.	−	1.01721e6i	0.0598312	−	0.0825281i
$687$	1.53841e7	−	2.66460e7i	1.24359	−	2.15397i
$688$	−7.23183e6	+	790048.i	−0.582475	+	0.0636330i
$689$	9.72616e6	−	1.68462e7i	0.780537	−	1.35193i
$690$	6.57270e6	+	1.47219e7i	0.525558	+	1.17718i
$691$			5.89087e6i			0.469336i	0.972076	+	0.234668i	$0.0754004\pi$
$691$			5.89087e6i			0.469336i	−0.972076	+	0.234668i	$0.924600\pi$
$692$	3.23131e6	−	1.53567e7i	0.256516	−	1.21908i
$693$	−190505.	−	329965.i	−0.0150686	−	0.0260996i
$694$	−2.19539e6	−	4.91737e6i	−0.173027	−	0.387556i
$695$			1.57205e7i			1.23453i
$696$	7.59117e6	+	2.44077e6i	0.593999	+	0.190987i
$697$	−392395.	+	226550.i	−0.0305944	+	0.0176637i
$698$	255151.	+	184979.i	0.0198225	+	0.0143709i
$699$	−1.07582e7	−	1.86337e7i	−0.832810	−	1.44247i
$700$	−114004.	−	102228.i	−0.00879375	−	0.00788539i
$701$	960411.	−	1.66348e6i	0.0738180	−	0.127856i	−0.826754	−	0.562564i	$-0.809815\pi$
$701$	960411.	−	1.66348e6i	0.0738180	−	0.127856i	0.900572	+	0.434708i	$0.143148\pi$
$702$	4.23374e7	+	4.40603e6i	3.24251	+	0.337446i
$703$	−1.30797e7	−	1.63585e7i	−0.998183	−	1.24841i
$704$	−1.95558e6	+	2.72668e6i	−0.148711	+	0.207350i
$705$	−1.75031e7	−	1.01054e7i	−1.32630	−	0.765741i
$706$	−2.94583e6	−	2.13567e6i	−0.222432	−	0.161258i
$707$	−323859.	+	186980.i	−0.0243673	+	0.0140684i
$708$	−1.06971e7	+	1.19294e7i	−0.802018	+	0.894407i
$709$	−6.72328e6	−	1.16451e7i	−0.502303	−	0.870014i	−0.999996	−	0.00266079i	$-0.999153\pi$
$709$	−6.72328e6	−	1.16451e7i	−0.502303	−	0.870014i	0.497694	−	0.867353i	$-0.334180\pi$
$710$	2.06059e6	−	1.98001e7i	0.153407	−	1.47408i
$711$	−3.28107e7			−2.43412
$712$	−4.06861e6	−	1.88564e7i	−0.300778	−	1.39399i
$713$	−1.61188e7	+	9.30622e6i	−1.18744	+	0.685566i
$714$	93729.6	+	9754.38i	0.00688067	+	0.000716068i
$715$	−4.16619e6			−0.304771
$716$	7.55752e6	+	2.30986e7i	0.550931	+	1.68385i
$717$	7.93973e6	+	4.58401e6i	0.576777	+	0.333002i
$718$	5.53619e6	+	1.24003e7i	0.400774	+	0.897679i
$719$	1.06260e7	+	6.13494e6i	0.766565	+	0.442576i	0.831648	−	0.555303i	$-0.187398\pi$
$719$	1.06260e7	+	6.13494e6i	0.766565	+	0.442576i	−0.0650830	+	0.997880i	$0.520731\pi$
$720$	2.27644e7	−	1.66821e7i	1.63653	−	1.19928i
$721$		−	130592.i		−	0.00935574i
$722$	−1.05152e7	+	9.25341e6i	−0.750711	+	0.660631i
$723$			2.36746e7i			1.68437i
$724$	−4.18959e6	−	3.75682e6i	−0.297047	−	0.266363i
$725$	−972232.	−	561318.i	−0.0686950	−	0.0396611i
$726$	−2.20715e7	+	9.85397e6i	−1.55414	+	0.693857i
$727$	9.24656e6	+	5.33850e6i	0.648850	+	0.374614i	0.788015	−	0.615655i	$-0.211109\pi$
$727$	9.24656e6	+	5.33850e6i	0.648850	+	0.374614i	−0.139166	+	0.990269i	$0.544442\pi$
$728$	971899.	−	209705.i	0.0679661	−	0.0146649i
$729$	5.29888e6			0.369288
$730$	−1.64661e6	+	1.58222e7i	−0.114362	+	1.09890i
$731$	−545874.	+	315160.i	−0.0377832	+	0.0218141i
$732$	−1.19984e7	−	3.66718e7i	−0.827650	−	2.52961i
$733$	−3.05745e6			−0.210184			−0.105092	−	0.994463i	$-0.533514\pi$
$733$	−3.05745e6			−0.210184			−0.105092	+	0.994463i	$0.533514\pi$
$734$	−9.15320e6	−	952568.i	−0.627094	−	0.0652613i
$735$	−1.16571e7	−	2.01908e7i	−0.795928	−	1.37859i
$736$	1.02496e7	−	5.98779e6i	0.697451	−	0.407448i
$737$	−4.63162e6	+	2.67407e6i	−0.314097	+	0.181344i
$738$	−9.53608e6	+	1.31536e7i	−0.644509	+	0.889003i
$739$	−4.58356e6	−	2.64632e6i	−0.308739	−	0.178251i	0.337623	−	0.941281i	$-0.390377\pi$
$739$	−4.58356e6	−	2.64632e6i	−0.308739	−	0.178251i	−0.646362	+	0.763031i	$0.723710\pi$
$740$	−4.29811e6	+	2.04266e7i	−0.288535	+	1.37125i
$741$	2.31518e7	+	2.89554e7i	1.54896	+	1.93724i
$742$	90773.3	−	872238.i	0.00605269	−	0.0581601i
$743$	−3.49316e6	+	6.05034e6i	−0.232138	+	0.402075i	−0.958437	−	0.285304i	$-0.907906\pi$
$743$	−3.49316e6	+	6.05034e6i	−0.232138	+	0.402075i	0.726299	+	0.687379i	$0.241239\pi$
$744$	3.13273e7	+	3.45784e7i	2.07487	+	2.29019i
$745$	−1.61405e6	−	2.79562e6i	−0.106543	−	0.184539i
$746$	2.75513e6	−	3.80029e6i	0.181257	−	0.250017i
$747$	−2.81848e7	+	1.62725e7i	−1.84805	+	1.06697i
$748$	−59863.6	+	284499.i	−0.00391209	+	0.0185920i
$749$		−	699617.i		−	0.0455676i
$750$	−2.76462e7	+	1.23428e7i	−1.79466	+	0.801237i
$751$	3.02318e6	+	5.23630e6i	0.195598	+	0.338785i	0.947096	−	0.320950i	$-0.104002\pi$
$751$	3.02318e6	+	5.23630e6i	0.195598	+	0.338785i	−0.751499	+	0.659735i	$0.770669\pi$
$752$	−5.99677e6	+	1.36188e7i	−0.386699	+	0.878199i
$753$			4.90975e7i			3.15553i
$754$	6.65621e6	−	2.97170e6i	0.426382	−	0.190361i
$755$	5.28119e6	−	9.14728e6i	0.337182	−	0.584016i
$756$	1.82382e6	−	596727.i	0.116059	−	0.0379727i
$757$	306749.	−	531305.i	0.0194556	−	0.0336980i	−0.856134	−	0.516754i	$-0.827140\pi$
$757$	306749.	−	531305.i	0.0194556	−	0.0336980i	0.875589	+	0.483056i	$0.160473\pi$
$758$	−7.37229e6	−	5.34476e6i	−0.466046	−	0.337874i
$759$	−5.95521e6			−0.375226
$760$	1.37808e7	+	2.22691e6i	0.865447	+	0.139852i
$761$	1.56491e7			0.979553			0.489777	−	0.871848i	$-0.337078\pi$
$761$	1.56491e7			0.979553			0.489777	+	0.871848i	$0.337078\pi$
$762$	1.01186e7	+	7.33577e6i	0.631295	+	0.457676i
$763$	207295.	−	359045.i	0.0128907	−	0.0223274i
$764$	−943493.	+	308696.i	−0.0584797	+	0.0191337i
$765$	1.22265e6	−	2.11769e6i	0.0755351	−	0.130831i
$766$	7.84787e6	−	3.50373e6i	0.483259	−	0.215754i
$767$			1.46477e7i			0.899043i
$768$	−2.00923e7	−	2.19506e7i	−1.22921	−	1.34290i
$769$	9.03760e6	+	1.56536e7i	0.551109	+	0.954549i	0.998195	+	0.0600576i	$0.0191284\pi$
$769$	9.03760e6	+	1.56536e7i	0.551109	+	0.954549i	−0.447086	+	0.894491i	$0.647538\pi$
$770$	−171504.	+	76569.0i	−0.0104243	+	0.00465400i
$771$		−	3.24825e7i		−	1.96794i
$772$	−167002.	+	793668.i	−0.0100850	+	0.0479287i
$773$	−1.41973e7	+	8.19683e6i	−0.854590	+	0.493398i	−0.862197	−	0.506573i	$-0.830912\pi$
$773$	−1.41973e7	+	8.19683e6i	−0.854590	+	0.493398i	0.00760666	+	0.999971i	$0.497579\pi$
$774$	−1.32659e7	+	1.82984e7i	−0.795950	+	1.09789i
$775$	−3.28453e6	−	5.68898e6i	−0.196435	−	0.340236i
$776$	1.55164e7	−	1.40576e7i	0.924990	−	0.838022i
$777$	−1.24958e6	+	2.16434e6i	−0.0742526	+	0.128609i
$778$	112976.	−	1.08558e6i	0.00669170	−	0.0643004i
$779$	−7.94472e6	+	1.20786e6i	−0.469067	+	0.0713138i
$780$	7.60788e6	−	3.61561e7i	0.447741	−	2.12787i
$781$	6.36797e6	+	3.67655e6i	0.373571	+	0.215682i
$782$	603687.	−	832695.i	0.0353016	−	0.0486933i
$783$	1.21840e7	−	7.03443e6i	0.710207	−	0.410038i
$784$	−1.38458e7	+	1.01464e7i	−0.804503	+	0.589553i
$785$	8.04743e6	+	1.39386e7i	0.466104	+	0.807316i
$786$	−5.80138e7	−	6.03746e6i	−3.34946	−	0.348576i
$787$	1.71571e7			0.987430			0.493715	−	0.869624i	$-0.335639\pi$
$787$	1.71571e7			0.987430			0.493715	+	0.869624i	$0.335639\pi$
$788$	−4.72474e6	−	1.44406e7i	−0.271058	−	0.828456i
$789$	1.33826e7	−	7.72642e6i	0.765326	−	0.441861i
$790$	−1.67419e6	+	1.60872e7i	−0.0954414	+	0.917094i
$791$	27801.4			0.00157988
$792$	2.19870e6	+	1.01901e7i	0.124553	+	0.577251i
$793$	−3.05470e7	−	1.76363e7i	−1.72499	−	0.995923i
$794$	2.57229e7	−	1.14841e7i	1.44800	−	0.646468i
$795$	−2.82223e7	−	1.62941e7i	−1.58370	−	0.914352i
$796$	−1.75597e7	−	1.57458e7i	−0.982277	−	0.880811i
$797$			2.77536e7i			1.54765i	0.633396	+	0.773827i	$0.281660\pi$
$797$			2.77536e7i			1.54765i	−0.633396	+	0.773827i	$0.718340\pi$
$798$	1.48522e6	+	766470.i	0.0825626	+	0.0426077i
$799$			1.28931e6i			0.0714480i
$800$	2.11333e6	+	3.61750e6i	0.116746	+	0.199841i
$801$	−5.19013e7	−	2.99652e7i	−2.85823	−	1.65020i
$802$	6.11615e6	+	1.36993e7i	0.335770	+	0.752080i
$803$	−5.08862e6	−	2.93792e6i	−0.278491	−	0.160787i
$804$	−1.47490e7	−	4.50784e7i	−0.804676	−	2.45940i
$805$	664446.			0.0361385
$806$	4.24248e7	+	4.41512e6i	2.30029	+	0.239390i
$807$	3.88499e6	−	2.24300e6i	0.209994	−	0.121240i
$808$	1.00015e7	−	2.15801e6i	0.538936	−	0.116285i
$809$	−1.85990e7			−0.999124			−0.499562	−	0.866278i	$-0.666506\pi$
$809$	−1.85990e7			−0.999124			−0.499562	+	0.866278i	$0.666506\pi$
$810$	3.45979e6	−	3.32450e7i	0.185284	−	1.78039i
$811$	−1.46988e7	−	2.54591e7i	−0.784749	−	1.35922i	−0.929149	−	0.369705i	$-0.879459\pi$
$811$	−1.46988e7	−	2.54591e7i	−0.784749	−	1.35922i	0.144400	−	0.989519i	$-0.453875\pi$
$812$	219391.	−	244664.i	0.0116769	−	0.0130221i
$813$	6.98988e6	−	4.03561e6i	0.370888	−	0.214133i
$814$	−6.24234e6	−	4.52557e6i	−0.330207	−	0.239393i
$815$	−719428.	−	415362.i	−0.0379396	−	0.0219045i
$816$	−2.35969e6	−	1.03905e6i	−0.124060	−	0.0546273i
$817$	−1.10521e7	+	1.68029e6i	−0.579284	+	0.0880705i
$818$	1.76174e7	+	1.83343e6i	0.920571	+	0.0958033i
$819$	1.54447e6	−	2.67510e6i	0.0804581	−	0.139358i
$820$	5.96269e6	+	5.34676e6i	0.309676	+	0.277687i
$821$	−1.23615e7	−	2.14108e7i	−0.640051	−	1.10860i	−0.985421	−	0.170134i	$-0.945580\pi$
$821$	−1.23615e7	−	2.14108e7i	−0.640051	−	1.10860i	0.345370	−	0.938467i	$-0.387753\pi$
$822$	−1.78724e7	−	1.29571e7i	−0.922577	−	0.668850i
$823$	1.90904e7	−	1.10219e7i	0.982463	−	0.567225i	0.0794502	−	0.996839i	$-0.474684\pi$
$823$	1.90904e7	−	1.10219e7i	0.982463	−	0.567225i	0.903013	+	0.429614i	$0.141350\pi$
$824$	−1.09369e6	+	3.40154e6i	−0.0561147	+	0.174525i
$825$		−	2.10183e6i		−	0.107513i
$826$	269205.	+	602982.i	0.0137288	+	0.0307506i
$827$	1.39128e7	+	2.40977e7i	0.707378	+	1.22522i	0.965826	+	0.259190i	$0.0834557\pi$
$827$	1.39128e7	+	2.40977e7i	0.707378	+	1.22522i	−0.258448	+	0.966025i	$0.583211\pi$
$828$	7.59366e6	−	3.60885e7i	0.384924	−	1.82933i
$829$			8.88778e6i			0.449166i	0.974455	+	0.224583i	$0.0721020\pi$
$829$			8.88778e6i			0.449166i	−0.974455	+	0.224583i	$0.927898\pi$
$830$	6.54033e6	+	1.46495e7i	0.329537	+	0.738119i
$831$	−1.44612e7	+	2.50476e7i	−0.726444	+	1.25824i
$832$	−2.70714e7	−	2.67732e6i	−1.35582	−	0.134089i
$833$	−743643.	+	1.28803e6i	−0.0371323	+	0.0643150i
$834$	3.02263e7	−	4.16926e7i	1.50477	−	2.07560i
$835$	−9.86233e6			−0.489512
$836$	−2.82625e6	+	4.31271e6i	−0.139860	+	0.213420i
$837$	8.23234e7			4.06171
$838$	−2.08432e6	+	2.87501e6i	−0.102531	+	0.141426i
$839$	−1.33580e7	+	2.31367e7i	−0.655144	+	1.13474i	0.326714	+	0.945123i	$0.394059\pi$
$839$	−1.33580e7	+	2.31367e7i	−0.655144	+	1.13474i	−0.981858	+	0.189619i	$0.939275\pi$
$840$	−351316.	−	1.62821e6i	−0.0171791	−	0.0796182i
$841$	−9.05093e6	+	1.56767e7i	−0.441269	+	0.764300i
$842$	−2.75898e6	−	6.17973e6i	−0.134112	−	0.300393i
$843$			4.16449e7i			2.01833i
$844$	1.21720e6	+	256120.i	0.0588174	+	0.0123762i
$845$	−7.79008e6	−	1.34928e7i	−0.375318	−	0.650071i
$846$	1.88468e7	+	4.22143e7i	0.905341	+	2.02784i
$847$			996155.i			0.0477110i
$848$	−9.66927e6	+	2.19591e7i	−0.461747	+	1.04864i
$849$	5.48843e7	−	3.16875e7i	2.61324	−	1.50875i
$850$	293891.	+	213065.i	0.0139521	+	0.0101150i
$851$	1.36381e7	+	2.36219e7i	0.645550	+	1.11813i
$852$	−4.35353e7	+	4.85504e7i	−2.05467	+	2.29136i
$853$	−2.02579e7	+	3.50878e7i	−0.953285	+	1.65114i	−0.215039	+	0.976606i	$0.568988\pi$
$853$	−2.02579e7	+	3.50878e7i	−0.953285	+	1.65114i	−0.738246	+	0.674532i	$0.764346\pi$
$854$	−1.58162e6	−	164598.i	−0.0742092	−	0.00772291i
$855$	3.38727e7	−	2.70835e7i	1.58465	−	1.26704i
$856$	−5.85921e6	+	1.82230e7i	−0.273309	+	0.850033i
$857$	−4.77378e6	−	2.75614e6i	−0.222029	−	0.128189i	0.384860	−	0.922975i	$-0.374250\pi$
$857$	−4.77378e6	−	2.75614e6i	−0.222029	−	0.128189i	−0.606890	+	0.794786i	$0.707583\pi$
$858$	1.10493e7	+	8.01048e6i	0.512407	+	0.371484i
$859$	2.72180e7	−	1.57143e7i	1.25856	−	0.726629i	0.285765	−	0.958300i	$-0.407752\pi$
$859$	2.72180e7	−	1.57143e7i	1.25856	−	0.726629i	0.972794	+	0.231670i	$0.0744191\pi$
$860$	8.29488e6	+	7.43805e6i	0.382441	+	0.342936i
$861$	479436.	+	830407.i	0.0220406	+	0.0381754i
$862$	222735.	−	2.14025e6i	0.0102099	−	0.0981062i
$863$	2.11706e7			0.967622			0.483811	−	0.875172i	$-0.339252\pi$
$863$	2.11706e7			0.967622			0.483811	+	0.875172i	$0.339252\pi$
$864$	−5.25028e7	+	268726.i	−2.39276	+	0.0122469i
$865$	−2.08136e7	+	1.20168e7i	−0.945819	+	0.546069i
$866$	7.83529e6	+	815414.i	0.355026	+	0.0369474i
$867$	4.00711e7			1.81044
$868$	1.82759e6	−	597959.i	0.0823340	−	0.0269384i
$869$	−5.17387e6	−	2.98713e6i	−0.232416	−	0.134185i
$870$	−4.97846e6	−	1.11511e7i	−0.222996	−	0.499480i
$871$	−3.75497e7	−	2.16793e7i	−1.67711	−	0.968278i
$872$	−8.40640e6	+	7.61603e6i	−0.374385	+	0.339186i
$873$		−	6.50474e7i		−	2.88865i
$874$	1.53496e7	−	9.85551e6i	0.679701	−	0.436416i
$875$			1.24776e6i			0.0550947i
$876$	3.47889e7	−	3.87964e7i	1.53172	−	1.70817i
$877$	−1.25709e7	−	7.25782e6i	−0.551909	−	0.318645i	0.197982	−	0.980206i	$-0.436561\pi$
$877$	−1.25709e7	−	7.25782e6i	−0.551909	−	0.318645i	−0.749892	+	0.661561i	$0.769894\pi$
$878$	9.45737e6	−	4.22230e6i	0.414032	−	0.184847i
$879$	3.19367e7	+	1.84386e7i	1.39418	+	0.804928i
$880$	5.10844e6	−	558076.i	0.222373	−	0.0242933i
$881$	2.01946e7			0.876588			0.438294	−	0.898832i	$-0.355583\pi$
$881$	2.01946e7			0.876588			0.438294	+	0.898832i	$0.355583\pi$
$882$	−5.52012e6	+	5.30427e7i	−0.238934	+	2.29591i
$883$	−2.81232e6	+	1.62369e6i	−0.121384	+	0.0700813i	−0.559463	−	0.828855i	$-0.688993\pi$
$883$	−2.81232e6	+	1.62369e6i	−0.121384	+	0.0700813i	0.438078	+	0.898937i	$0.355659\pi$
$884$	−2.24015e6	+	732944.i	−0.0964156	+	0.0315457i
$885$	2.45391e7			1.05318
$886$	−3.50458e7	−	3.64719e6i	−1.49986	−	0.156090i
$887$	1.22073e7	+	2.11437e7i	0.520968	+	0.902342i	0.999703	+	0.0243829i	$0.00776207\pi$
$887$	1.22073e7	+	2.11437e7i	0.520968	+	0.902342i	−0.478735	+	0.877959i	$0.658905\pi$
$888$	5.06740e7	−	4.59096e7i	2.15652	−	1.95376i
$889$	446063.	−	257535.i	0.0189296	−	0.0109290i
$890$	−1.73404e7	+	2.39185e7i	−0.733811	+	1.01218i
$891$	1.06920e7	+	6.17305e6i	0.451197	+	0.260499i
$892$	451534.	+	95010.8i	0.0190011	+	0.00399817i
$893$	−8.32694e6	+	2.12967e7i	−0.349427	+	0.893683i
$894$	−1.09457e6	+	1.05177e7i	−0.0458037	+	0.440127i
$895$	1.86103e7	−	3.22340e7i	0.776597	−	1.34511i
$896$	−1.16362e6	+	387322.i	−0.0484217	+	0.0161177i
$897$	−2.41401e7	−	4.18120e7i	−1.00175	−	1.73508i
$898$	5.21214e6	−	7.18936e6i	0.215688	−	0.297509i
$899$	1.22091e7	−	7.04895e6i	0.503832	−	0.290888i
$900$	1.27371e7	+	2.68010e6i	0.524159	+	0.110292i
$901$			2.07890e6i			0.0853142i
$902$	−2.70125e6	+	1.20599e6i	−0.110547	+	0.0493546i
$903$	666958.	+	1.15521e6i	0.0272194	+	0.0471455i
$904$	−724146.	−	232833.i	−0.0294717	−	0.00947597i
$905$			8.61810e6i			0.349776i
$906$	−3.15941e7	+	1.41054e7i	−1.27875	+	0.570906i
$907$	4.48615e6	−	7.77024e6i	0.181074	−	0.313629i	−0.761173	−	0.648549i	$-0.775376\pi$
$907$	4.48615e6	−	7.77024e6i	0.181074	−	0.313629i	0.942246	+	0.334920i	$0.108709\pi$
$908$	1.04316e7	+	3.18830e7i	0.419892	+	1.28335i
$909$	1.58937e7	−	2.75287e7i	0.637991	−	1.10503i
$910$	−1.23281e6	−	893761.i	−0.0493506	−	0.0357782i
$911$	972973.			0.0388423			0.0194211	−	0.999811i	$-0.493818\pi$
$911$	972973.			0.0388423			0.0194211	+	0.999811i	$0.493818\pi$
$912$	−3.22666e7	−	3.24029e7i	−1.28459	−	1.29002i
$913$	−5.92588e6			−0.235275
$914$	3.90010e6	+	2.82749e6i	0.154422	+	0.111953i
$915$	−2.95460e7	+	5.11751e7i	−1.16666	+	2.02072i
$916$	1.07884e7	+	3.29736e7i	0.424835	+	1.29846i
$917$	−1.20190e6	+	2.08174e6i	−0.0472002	+	0.0817531i
$918$	−4.15391e6	+	1.85454e6i	−0.162686	+	0.0726322i
$919$		−	1.66882e7i		−	0.651809i	−0.945403	−	0.325905i	$-0.894331\pi$
$919$		−	1.66882e7i		−	0.651809i	0.945403	−	0.325905i	$-0.105669\pi$
$920$	−1.73069e7	−	5.56465e6i	−0.674139	−	0.216755i
$921$	3.05732e7	+	5.29543e7i	1.18766	+	2.05708i
$922$	4.58439e6	−	2.04673e6i	0.177605	−	0.0792926i
$923$			5.96133e7i			2.30324i
$924$	602072.	+	126686.i	0.0231989	+	0.00488147i
$925$	−8.33710e6	+	4.81343e6i	−0.320376	+	0.184969i
$926$	2.78036e7	−	3.83509e7i	1.06555	−	1.46977i
$927$	5.55030e6	+	9.61340e6i	0.212137	+	0.367433i
$928$	−7.76354e6	+	4.53542e6i	−0.295931	+	0.172881i
$929$	−8.53583e6	+	1.47845e7i	−0.324494	+	0.562040i	−0.981410	−	0.191924i	$-0.938527\pi$
$929$	−8.53583e6	+	1.47845e7i	−0.324494	+	0.562040i	0.656916	+	0.753964i	$0.271861\pi$
$930$	7.39661e6	−	7.10738e7i	0.280431	−	2.69465i
$931$	−2.06021e7	+	1.64728e7i	−0.779000	+	0.622862i
$932$	2.37416e7	+	4.99565e6i	0.895304	+	0.188388i
$933$	−2.59908e7	−	1.50058e7i	−0.977498	−	0.564359i
$934$	−2.28693e7	+	3.15448e7i	−0.857800	+	1.18321i
$935$	385596.	−	222624.i	0.0144246	−	0.00832804i
$936$	−6.26327e7	+	5.67440e7i	−2.33674	+	2.11704i
$937$	1.11254e7	+	1.92698e7i	0.413968	+	0.717013i	0.995319	−	0.0966390i	$-0.0308092\pi$
$937$	1.11254e7	+	1.92698e7i	0.413968	+	0.717013i	−0.581352	+	0.813652i	$0.697476\pi$
$938$	−1.94419e6	−	202331.i	−0.0721493	−	0.00750853i
$939$	−1.37121e7			−0.507503
$940$	2.16596e7	−	7.08667e6i	0.799521	−	0.261591i
$941$	2.93578e7	−	1.69498e7i	1.08081	−	0.624007i	0.149697	−	0.988732i	$-0.452170\pi$
$941$	2.93578e7	−	1.69498e7i	1.08081	−	0.624007i	0.931115	+	0.364725i	$0.118837\pi$
$942$	5.45738e6	−	5.24398e7i	0.200381	−	1.92546i
$943$	1.04653e7			0.383240
$944$	−1.96211e6	−	1.79605e7i	−0.0716627	−	0.655976i
$945$	−2.54513e6	−	1.46943e6i	−0.0927108	−	0.0535266i
$946$	−3.75780e6	+	1.67769e6i	−0.136523	+	0.0609514i
$947$	−2.07481e7	−	1.19789e7i	−0.751800	−	0.434052i	0.0745437	−	0.997218i	$-0.476250\pi$
$947$	−2.07481e7	−	1.19789e7i	−0.751800	−	0.434052i	−0.826344	+	0.563166i	$0.809583\pi$
$948$	3.53717e7	−	3.94463e7i	1.27831	−	1.42556i
$949$		−	4.76368e7i		−	1.71703i
$950$	3.47840e6	+	5.41747e6i	0.125046	+	0.194755i
$951$			8.78218e6i			0.314884i
$952$	−78746.9	+	71343.1i	−0.00281605	+	0.00255129i
$953$	−3.58119e7	−	2.06760e7i	−1.27731	−	0.737454i	−0.300955	−	0.953638i	$-0.597305\pi$
$953$	−3.58119e7	−	2.06760e7i	−1.27731	−	0.737454i	−0.976353	+	0.216184i	$0.930639\pi$
$954$	3.03889e7	+	6.80669e7i	1.08104	+	2.42139i
$955$	1.31664e6	+	760160.i	0.0467151	+	0.0269710i
$956$	−9.82517e6	+	3.21465e6i	−0.347693	+	0.113760i
$957$	4.51074e6			0.159209
$958$	−6.38125e6	−	664093.i	−0.224643	−	0.0233784i
$959$	−787878.	+	454882.i	−0.0276638	+	0.0159717i
$960$	−4.48528e6	+	4.53524e7i	−0.157077	+	1.58826i
$961$	5.38642e7			1.88145
$962$	6.47029e6	−	6.21728e7i	0.225417	−	2.16602i
$963$	2.97345e7	+	5.15016e7i	1.03322	+	1.78960i
$964$	−1.98749e7	−	1.78219e7i	−0.688830	−	0.617676i
$965$	1.07570e6	−	621054.i	0.0371853	−	0.0214690i
$966$	−1.76219e6	−	1.27755e6i	−0.0607590	−	0.0440490i
$967$	−2.63851e7	−	1.52335e7i	−0.907388	−	0.523881i	−0.0277981	−	0.999614i	$-0.508850\pi$
$967$	−2.63851e7	−	1.52335e7i	−0.907388	−	0.523881i	−0.879590	+	0.475733i	$0.842183\pi$
$968$	8.34268e6	−	2.59470e7i	0.286165	−	0.890017i
$969$	−3.69003e6	−	1.44279e6i	−0.126247	−	0.0493621i
$970$	−3.18931e7	−	3.31909e6i	−1.08835	−	0.113263i
$971$	1.16226e7	−	2.01310e7i	0.395600	−	0.685199i	−0.597578	−	0.801811i	$-0.703870\pi$
$971$	1.16226e7	−	2.01310e7i	0.395600	−	0.685199i	0.993178	+	0.116612i	$0.0372033\pi$
$972$	−2.60438e7	+	2.90439e7i	−0.884175	+	0.986028i
$973$	−1.06114e6	−	1.83796e6i	−0.0359329	−	0.0622376i
$974$	3.22870e7	+	2.34074e7i	1.09051	+	0.790598i
$975$	1.47571e7	−	8.52001e6i	0.497152	−	0.287031i
$976$	3.98182e7	+	1.75332e7i	1.33800	+	0.589164i
$977$			1.75549e7i			0.588386i	0.955746	+	0.294193i	$0.0950509\pi$
$977$			1.75549e7i			0.588386i	−0.955746	+	0.294193i	$0.904949\pi$
$978$	1.10938e6	+	2.48486e6i	0.0370880	+	0.0830720i
$979$	−5.45615e6	−	9.45033e6i	−0.181941	−	0.315130i
$980$	2.57255e7	+	5.41309e6i	0.855653	+	0.180045i
$981$			3.52410e7i			1.16917i
$982$	5.77851e6	+	1.29431e7i	0.191222	+	0.428310i
$983$	1.16265e7	−	2.01377e7i	0.383764	−	0.664699i	−0.607833	−	0.794065i	$-0.707961\pi$
$983$	1.16265e7	−	2.01377e7i	0.383764	−	0.664699i	0.991597	+	0.129366i	$0.0412942\pi$
$984$	−5.53337e6	−	2.56449e7i	−0.182180	−	0.844333i
$985$	−1.16346e7	+	2.01517e7i	−0.382086	+	0.661792i
$986$	−457260.	+	630721.i	−0.0149786	+	0.0206607i
$987$	2.72850e6			0.0891520
$988$	−4.17364e7	−	2.36121e6i	−1.36026	−	0.0769561i
$989$	1.45586e7			0.473291
$990$	9.37084e6	−	1.29257e7i	0.303872	−	0.419145i
$991$	1.64931e7	−	2.85668e7i	0.533479	−	0.924013i	−0.465756	−	0.884913i	$-0.654218\pi$
$991$	1.64931e7	−	2.85668e7i	0.533479	−	0.924013i	0.999235	−	0.0390997i	$-0.0124490\pi$
$992$	−5.26113e7	+	269281.i	−1.69746	+	0.00868812i
$993$	−2.66361e7	+	4.61351e7i	−0.857231	+	1.48477i
$994$	1.09561e6	+	2.45402e6i	0.0351715	+	0.0787793i
$995$			3.61208e7i			1.15664i
$996$	1.08213e7	−	5.14275e7i	0.345644	−	1.64266i
$997$	−9.18677e6	−	1.59120e7i	−0.292701	−	0.506974i	0.681746	−	0.731589i	$-0.261221\pi$
$997$	−9.18677e6	−	1.59120e7i	−0.292701	−	0.506974i	−0.974448	+	0.224615i	$0.927888\pi$
$998$	−1.29526e7	−	2.90120e7i	−0.411652	−	0.922044i
$999$		−	1.20643e8i		−	3.82463i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.6.f.a.27.11	yes	96
4.3	odd	2	inner	76.6.f.a.27.6	✓	96
19.12	odd	6	inner	76.6.f.a.31.6	yes	96
76.31	even	6	inner	76.6.f.a.31.11	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.6.f.a.27.6	✓	96	4.3	odd	2	inner
76.6.f.a.27.11	yes	96	1.1	even	1	trivial
76.6.f.a.31.6	yes	96	19.12	odd	6	inner
76.6.f.a.31.11	yes	96	76.31	even	6	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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	76.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.57989 - 3.32033i) q^{2} +(14.1896 - 24.5772i) q^{3} +(9.95083 + 30.4135i) q^{4} +(24.5038 - 42.4418i) q^{5} +(-146.591 + 65.4465i) q^{6} +6.61611i q^{7} +(55.4091 - 172.331i) q^{8} +(-281.192 - 487.038i) q^{9} +O(q^{10})\)	\(q+(-4.57989 - 3.32033i) q^{2} +(14.1896 - 24.5772i) q^{3} +(9.95083 + 30.4135i) q^{4} +(24.5038 - 42.4418i) q^{5} +(-146.591 + 65.4465i) q^{6} +6.61611i q^{7} +(55.4091 - 172.331i) q^{8} +(-281.192 - 487.038i) q^{9} +(-253.145 + 113.018i) q^{10} -102.400i q^{11} +(888.677 + 186.993i) q^{12} +(718.961 - 415.092i) q^{13} +(21.9677 - 30.3011i) q^{14} +(-695.399 - 1204.47i) q^{15} +(-825.962 + 605.279i) q^{16} +(-44.3616 + 76.8365i) q^{17} +(-329.300 + 3164.23i) q^{18} +(-1229.01 + 982.672i) q^{19} +(1534.64 + 322.915i) q^{20} +(162.605 + 93.8802i) q^{21} +(-340.003 + 468.983i) q^{22} +(1774.70 - 1024.62i) q^{23} +(-3449.16 - 3807.11i) q^{24} +(361.630 + 626.361i) q^{25} +(-4671.01 - 486.109i) q^{26} -9063.87 q^{27} +(-201.219 + 65.8358i) q^{28} +(-1344.24 + 776.096i) q^{29} +(-814.373 + 7825.29i) q^{30} -9082.58 q^{31} +(5792.54 - 29.6480i) q^{32} +(-2516.71 - 1453.02i) q^{33} +(458.294 - 204.608i) q^{34} +(280.799 + 162.120i) q^{35} +(12014.4 - 13398.5i) q^{36} +13310.4i q^{37} +(8891.51 - 419.830i) q^{38} -23560.0i q^{39} +(-5956.29 - 6574.41i) q^{40} +(4422.70 + 2553.45i) q^{41} +(-433.001 - 969.864i) q^{42} +(6152.55 + 3552.18i) q^{43} +(3114.36 - 1018.97i) q^{44} -27561.0 q^{45} +(-11530.0 - 1199.92i) q^{46} +(12584.9 - 7265.91i) q^{47} +(3155.95 + 28888.5i) q^{48} +16763.2 q^{49} +(423.500 - 4069.40i) q^{50} +(1258.95 + 2180.56i) q^{51} +(19778.7 + 17735.6i) q^{52} +(20292.1 - 11715.7i) q^{53} +(41511.5 + 30095.0i) q^{54} +(-4346.06 - 2509.20i) q^{55} +(1140.16 + 366.593i) q^{56} +(6712.16 + 44149.2i) q^{57} +(8733.35 + 908.875i) q^{58} +(-8821.95 + 15280.1i) q^{59} +(29712.3 - 33135.0i) q^{60} +(-21243.9 - 36795.5i) q^{61} +(41597.3 + 30157.2i) q^{62} +(3222.30 - 1860.39i) q^{63} +(-26627.7 - 19097.4i) q^{64} -40685.3i q^{65} +(6701.75 + 15011.0i) q^{66} +(-26113.8 - 45230.5i) q^{67} +(-2778.30 - 584.604i) q^{68} -58156.1i q^{69} +(-747.741 - 1674.84i) q^{70} +(-35903.7 + 62187.0i) q^{71} +(-99512.2 + 21471.6i) q^{72} +(28690.5 - 49693.4i) q^{73} +(44194.8 - 60960.1i) q^{74} +20525.6 q^{75} +(-42116.1 - 27600.0i) q^{76} +677.492 q^{77} +(-78227.1 + 107902. i) q^{78} +(29171.1 - 50525.8i) q^{79} +(5449.94 + 49886.9i) q^{80} +(-60283.4 + 104414. i) q^{81} +(-11777.2 - 26379.3i) q^{82} -57869.7i q^{83} +(-1237.17 + 5879.58i) q^{84} +(2174.05 + 3765.57i) q^{85} +(-16383.6 - 36697.1i) q^{86} +44050.1i q^{87} +(-17646.7 - 5673.91i) q^{88} +(92288.0 - 53282.5i) q^{89} +(126227. + 91511.7i) q^{90} +(2746.30 + 4756.72i) q^{91} +(48822.1 + 43778.9i) q^{92} +(-128879. + 223224. i) q^{93} +(-81762.8 - 8509.01i) q^{94} +(11591.1 + 76240.4i) q^{95} +(81465.4 - 142785. i) q^{96} +(100168. + 57831.9i) q^{97} +(-76773.8 - 55659.4i) q^{98} +(-49872.9 + 28794.1i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 3 q^{2} - 11 q^{4} - 2 q^{5} - 27 q^{6} - 3588 q^{9}+O(q^{10}) \) 96 * q - 3 * q^2 - 11 * q^4 - 2 * q^5 - 27 * q^6 - 3588 * q^9	\( 96 q - 3 q^{2} - 11 q^{4} - 2 q^{5} - 27 q^{6} - 3588 q^{9} + 648 q^{10} - 354 q^{13} + 2154 q^{14} - 611 q^{16} - 1006 q^{17} + 10524 q^{20} + 7824 q^{21} + 93 q^{22} - 5311 q^{24} - 25002 q^{25} - 13428 q^{26} + 1556 q^{28} - 6 q^{29} - 12656 q^{30} - 30453 q^{32} + 8586 q^{33} + 30102 q^{34} - 2306 q^{36} + 29846 q^{38} - 1392 q^{40} + 29064 q^{41} + 18616 q^{42} + 9155 q^{44} + 13464 q^{45} + 38217 q^{48} - 116224 q^{49} + 36858 q^{52} + 26262 q^{53} - 26355 q^{54} + 53974 q^{57} - 112740 q^{58} - 108810 q^{60} - 77370 q^{61} - 106848 q^{62} + 337966 q^{64} + 166855 q^{66} + 175796 q^{68} + 148122 q^{70} - 259842 q^{72} - 52040 q^{73} + 103690 q^{74} - 194709 q^{76} + 197584 q^{77} + 253206 q^{78} - 171934 q^{80} - 313100 q^{81} + 63919 q^{82} - 161762 q^{85} - 38442 q^{86} + 10482 q^{89} - 372450 q^{90} + 64544 q^{92} + 94012 q^{93} + 537614 q^{96} + 177180 q^{97} - 509397 q^{98}+O(q^{100}) \) 96 * q - 3 * q^2 - 11 * q^4 - 2 * q^5 - 27 * q^6 - 3588 * q^9 + 648 * q^10 - 354 * q^13 + 2154 * q^14 - 611 * q^16 - 1006 * q^17 + 10524 * q^20 + 7824 * q^21 + 93 * q^22 - 5311 * q^24 - 25002 * q^25 - 13428 * q^26 + 1556 * q^28 - 6 * q^29 - 12656 * q^30 - 30453 * q^32 + 8586 * q^33 + 30102 * q^34 - 2306 * q^36 + 29846 * q^38 - 1392 * q^40 + 29064 * q^41 + 18616 * q^42 + 9155 * q^44 + 13464 * q^45 + 38217 * q^48 - 116224 * q^49 + 36858 * q^52 + 26262 * q^53 - 26355 * q^54 + 53974 * q^57 - 112740 * q^58 - 108810 * q^60 - 77370 * q^61 - 106848 * q^62 + 337966 * q^64 + 166855 * q^66 + 175796 * q^68 + 148122 * q^70 - 259842 * q^72 - 52040 * q^73 + 103690 * q^74 - 194709 * q^76 + 197584 * q^77 + 253206 * q^78 - 171934 * q^80 - 313100 * q^81 + 63919 * q^82 - 161762 * q^85 - 38442 * q^86 + 10482 * q^89 - 372450 * q^90 + 64544 * q^92 + 94012 * q^93 + 537614 * q^96 + 177180 * q^97 - 509397 * q^98

Introduction

L-functions

Modular forms

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