LMFDB - Embedded newform 76.6.f.a.27.6

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			27.6
Character	$\chi$	$=$	76.27
Dual form			76.6.f.a.31.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.16544 - 2.30614i) q^{2} +(-14.1896 + 24.5772i) q^{3} +(21.3634 + 23.8244i) q^{4} +(24.5038 - 42.4418i) q^{5} +(129.974 - 94.2285i) q^{6} -6.61611i q^{7} +(-55.4091 - 172.331i) q^{8} +(-281.192 - 487.038i) q^{9} +O(q^{10})$	\(q+(-5.16544 - 2.30614i) q^{2} +(-14.1896 + 24.5772i) q^{3} +(21.3634 + 23.8244i) q^{4} +(24.5038 - 42.4418i) q^{5} +(129.974 - 94.2285i) q^{6} -6.61611i q^{7} +(-55.4091 - 172.331i) q^{8} +(-281.192 - 487.038i) q^{9} +(-224.449 + 162.721i) q^{10} +102.400i q^{11} +(-888.677 + 186.993i) q^{12} +(718.961 - 415.092i) q^{13} +(-15.2577 + 34.1751i) q^{14} +(695.399 + 1204.47i) q^{15} +(-111.206 + 1017.94i) 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} +(236.150 - 528.943i) q^{22} +(-1774.70 + 1024.62i) q^{23} +(5021.63 + 1083.51i) q^{24} +(361.630 + 626.361i) q^{25} +(-4671.01 + 486.109i) q^{26} +9063.87 q^{27} +(157.625 - 141.343i) q^{28} +(-1344.24 + 776.096i) q^{29} +(-814.373 - 7825.29i) q^{30} +9082.58 q^{31} +(2921.95 - 5001.67i) q^{32} +(-2516.71 - 1453.02i) q^{33} +(406.342 - 294.590i) q^{34} +(-280.799 - 162.120i) q^{35} +(5596.18 - 17104.0i) q^{36} +13310.4i q^{37} +(-8614.53 + 2241.67i) q^{38} +23560.0i q^{39} +(-8671.75 - 1871.09i) q^{40} +(4422.70 + 2553.45i) q^{41} +(-623.426 - 859.922i) q^{42} +(-6152.55 - 3552.18i) q^{43} +(-2439.63 + 2187.63i) q^{44} -27561.0 q^{45} +(11530.0 - 1199.92i) q^{46} +(-12584.9 + 7265.91i) q^{47} +(-23440.2 - 17177.4i) q^{48} +16763.2 q^{49} +(-423.500 - 4069.40i) q^{50} +(-1258.95 - 2180.56i) q^{51} +(25248.8 + 8261.02i) q^{52} +(20292.1 - 11715.7i) q^{53} +(-46818.8 - 20902.5i) 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} +(-13839.6 + 42299.1i) q^{60} +(-21243.9 - 36795.5i) q^{61} +(-46915.5 - 20945.7i) q^{62} +(-3222.30 + 1860.39i) q^{63} +(-26627.7 + 19097.4i) q^{64} -40685.3i q^{65} +(9649.04 + 13309.4i) q^{66} +(26113.8 + 45230.5i) q^{67} +(-2778.30 + 584.604i) q^{68} -58156.1i q^{69} +(1076.58 + 1484.98i) q^{70} +(35903.7 - 62187.0i) q^{71} +(-68351.0 + 75444.3i) q^{72} +(28690.5 - 49693.4i) q^{73} +(30695.6 - 68753.8i) q^{74} -20525.6 q^{75} +(49667.4 + 8287.08i) q^{76} +677.492 q^{77} +(54332.7 - 121698. i) q^{78} +(-29171.1 + 50525.8i) q^{79} +(40478.4 + 29663.3i) q^{80} +(-60283.4 + 104414. i) q^{81} +(-16956.6 - 23389.0i) q^{82} +57869.7i q^{83} +(1237.17 + 5879.58i) q^{84} +(2174.05 + 3765.57i) q^{85} +(23588.8 + 32537.2i) q^{86} -44050.1i q^{87} +(17646.7 - 5673.91i) q^{88} +(92288.0 - 53282.5i) q^{89} +(142365. + 63559.6i) q^{90} +(-2746.30 - 4756.72i) q^{91} +(-62324.7 - 20391.7i) 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} +(-86589.4 - 38658.3i) 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 $

$2$	−5.16544	−	2.30614i	−0.913129	−	0.407672i
$2$	−5.16544	−	2.30614i	−0.913129	−	0.407672i
$3$	−14.1896	+	24.5772i	−0.910266	+	1.57663i	−0.0965771	+	0.995326i	$0.530789\pi$
$3$	−14.1896	+	24.5772i	−0.910266	+	1.57663i	−0.813689	+	0.581301i	$0.802544\pi$
$4$	21.3634	+	23.8244i	0.667608	+	0.744513i
$5$	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	$0.0222343\pi$
$6$	129.974	−	94.2285i	1.47394	−	1.06857i
$7$		−	6.61611i		−	0.0510338i	−0.999674	−	0.0255169i	$-0.991877\pi$
$7$		−	6.61611i		−	0.0510338i	0.999674	−	0.0255169i	$-0.00812316\pi$
$8$	−55.4091	−	172.331i	−0.306095	−	0.952001i
$9$	−281.192	−	487.038i	−1.15717	−	2.00427i
$10$	−224.449	+	162.721i	−0.709771	+	0.514570i
$11$			102.400i			0.255164i	0.991828	+	0.127582i	$0.0407217\pi$
$11$			102.400i			0.255164i	−0.991828	+	0.127582i	$0.959278\pi$
$12$	−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	$0.0947838\pi$
$14$	−15.2577	+	34.1751i	−0.0208050	+	0.0466004i
$15$	695.399	+	1204.47i	0.798006	+	1.38219i
$16$	−111.206	+	1017.94i	−0.108600	+	0.994086i
$17$	−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
$22$	236.150	−	528.943i	0.104023	−	0.232998i
$23$	−1774.70	+	1024.62i	−0.699528	+	0.403872i	−0.807171	−	0.590317i	$-0.799003\pi$
$23$	−1774.70	+	1024.62i	−0.699528	+	0.403872i	0.107644	+	0.994190i	$0.465669\pi$
$24$	5021.63	+	1083.51i	1.77958	+	0.383977i
$25$	361.630	+	626.361i	0.115722	+	0.200436i
$26$	−4671.01	+	486.109i	−1.35512	+	0.141026i
$27$	9063.87			2.39279
$28$	157.625	−	141.343i	0.0379953	−	0.0340705i
$29$	−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	$-0.177361\pi$
$31$	9082.58			1.69748			0.848741	+	0.528809i	$0.177361\pi$
$32$	2921.95	−	5001.67i	0.504426	−	0.863455i
$33$	−2516.71	−	1453.02i	−0.402299	−	0.232267i
$34$	406.342	−	294.590i	0.0602830	−	0.0437039i
$35$	−280.799	−	162.120i	−0.0387459	−	0.0223700i
$36$	5596.18	−	17104.0i	0.719674	−	2.19959i
$37$			13310.4i			1.59840i	0.601064	+	0.799201i	$0.294743\pi$
$37$			13310.4i			1.59840i	−0.601064	+	0.799201i	$0.705257\pi$
$38$	−8614.53	+	2241.67i	−0.967771	+	0.251833i
$39$			23560.0i			2.48036i
$40$	−8671.75	−	1871.09i	−0.856953	−	0.184903i
$41$	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	$0.590428\pi$
$42$	−623.426	−	859.922i	−0.0545333	−	0.0752205i
$43$	−6152.55	−	3552.18i	−0.507439	−	0.292970i	0.224341	−	0.974511i	$-0.427977\pi$
$43$	−6152.55	−	3552.18i	−0.507439	−	0.292970i	−0.731780	+	0.681540i	$0.761310\pi$
$44$	−2439.63	+	2187.63i	−0.189973	+	0.170350i
$45$	−27561.0			−2.02892
$46$	11530.0	−	1199.92i	0.803406	−	0.0836100i
$47$	−12584.9	+	7265.91i	−0.831010	+	0.479784i	−0.854198	−	0.519947i	$-0.825952\pi$
$47$	−12584.9	+	7265.91i	−0.831010	+	0.479784i	0.0231886	+	0.999731i	$0.492618\pi$
$48$	−23440.2	−	17177.4i	−1.46845	−	1.07610i
$49$	16763.2			0.997396
$50$	−423.500	−	4069.40i	−0.0239568	−	0.230200i
$51$	−1258.95	−	2180.56i	−0.0677770	−	0.117393i
$52$	25248.8	+	8261.02i	1.29489	+	0.423668i
$53$	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	$0.139153\pi$
$54$	−46818.8	−	20902.5i	−2.18492	−	0.975472i
$55$	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	−0.652560	−	0.757737i	$-0.726305\pi$
$59$	8821.95	−	15280.1i	0.329940	−	0.571472i	0.982500	+	0.186265i	$0.0596383\pi$
$60$	−13839.6	+	42299.1i	−0.496301	+	1.51688i
$61$	−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	$-0.427606\pi$
$62$	−46915.5	−	20945.7i	−1.55002	−	0.692015i
$63$	−3222.30	+	1860.39i	−0.102286	+	0.0590546i
$64$	−26627.7	+	19097.4i	−0.812612	+	0.582805i
$65$		−	40685.3i		−	1.19441i
$66$	9649.04	+	13309.4i	0.272662	+	0.376096i
$67$	26113.8	+	45230.5i	0.710696	+	1.23096i	0.964596	+	0.263731i	$0.0849531\pi$
$67$	26113.8	+	45230.5i	0.710696	+	1.23096i	−0.253901	+	0.967230i	$0.581714\pi$
$68$	−2778.30	+	584.604i	−0.0728630	+	0.0153317i
$69$		−	58156.1i		−	1.47053i
$70$	1076.58	+	1484.98i	0.0262604	+	0.0362223i
$71$	35903.7	−	62187.0i	0.845265	−	1.46404i	−0.0401258	−	0.999195i	$-0.512776\pi$
$71$	35903.7	−	62187.0i	0.845265	−	1.46404i	0.885391	−	0.464847i	$-0.153891\pi$
$72$	−68351.0	+	75444.3i	−1.55387	+	1.71512i
$73$	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	$-0.0503320\pi$
$74$	30695.6	−	68753.8i	0.651623	−	1.45955i
$75$	−20525.6			−0.421349
$76$	49667.4	+	8287.08i	0.986364	+	0.164576i
$77$	677.492			0.0130220
$78$	54332.7	−	121698.i	1.01117	−	2.26489i
$79$	−29171.1	+	50525.8i	−0.525878	+	0.910848i	0.473667	+	0.880704i	$0.342930\pi$
$79$	−29171.1	+	50525.8i	−0.525878	+	0.910848i	−0.999546	+	0.0301438i	$0.990403\pi$
$80$	40478.4	+	29663.3i	0.707128	+	0.518196i
$81$	−60283.4	+	104414.i	−1.02091	+	1.76826i
$82$	−16956.6	−	23389.0i	−0.278486	−	0.384129i
$83$			57869.7i			0.922054i	0.887386	+	0.461027i	$0.152519\pi$
$83$			57869.7i			0.922054i	−0.887386	+	0.461027i	$0.847481\pi$
$84$	1237.17	+	5879.58i	0.0191307	+	0.0909176i
$85$	2174.05	+	3765.57i	0.0326379	+	0.0565305i
$86$	23588.8	+	32537.2i	0.343922	+	0.474388i
$87$		−	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	$0.0806542\pi$
$90$	142365.	+	63559.6i	1.85266	+	0.827132i
$91$	−2746.30	−	4756.72i	−0.0347651	−	0.0602150i
$92$	−62324.7	−	20391.7i	−0.767699	−	0.251179i
$93$	−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	$0.452142\pi$
$98$	−86589.4	−	38658.3i	−0.910750	−	0.406610i
$99$	49872.9	−	28794.1i	0.511419	−	0.295268i
$100$	−7197.03	+	21996.9i	−0.0719703	+	0.219969i
$101$	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	$-0.470782\pi$
$103$	19738.5			0.183325			0.0916623	+	0.995790i	$0.470782\pi$
$104$	−111370.	−	100899.i	−1.00968	−	0.914753i
$105$	7968.89	−	4600.84i	0.0705382	−	0.0407252i
$106$	−131836.	+	13720.0i	−1.13964	+	0.118602i
$107$	105744.			0.892891			0.446445	−	0.894811i	$-0.352690\pi$
$107$	105744.			0.892891			0.446445	+	0.894811i	$0.352690\pi$
$108$	193635.	+	215941.i	1.59744	+	1.78146i
$109$	−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	$0.747950\pi$
$110$	−16662.7	−	22983.7i	−0.131300	−	0.181108i
$111$	−327131.	−	188869.i	−2.52008	−	1.45497i
$112$	6734.83	+	735.752i	0.0507319	+	0.00554225i
$113$		−	4202.08i		−	0.0309576i	−0.999880	−	0.0154788i	$-0.995073\pi$
$113$		−	4202.08i		−	0.0309576i	0.999880	−	0.0154788i	$-0.00492726\pi$
$114$	67143.1	−	243529.i	0.483881	−	1.75505i
$115$			100428.i			0.708129i
$116$	−47207.6	−	15445.6i	−0.325737	−	0.106576i
$117$	−404332.	−	233441.i	−2.73069	−	1.57657i
$118$	−80807.1	+	58583.5i	−0.534250	+	0.387321i
$119$	508.358	+	293.501i	0.00329081	+	0.00189995i
$120$	169035.	−	186577.i	1.07158	−	1.18278i
$121$	150565.			0.934891
$122$	24878.4	+	239056.i	0.151329	+	1.45412i
$123$	−125513.	+	72464.9i	−0.748042	+	0.431882i
$124$	194035.	+	216387.i	1.13325	+	1.26380i
$125$	188594.			1.07957
$126$	20934.9	−	2178.68i	0.117475	−	0.0122255i
$127$	38925.4	+	67420.8i	0.214153	+	0.370924i	0.953010	−	0.302938i	$-0.0979676\pi$
$127$	38925.4	+	67420.8i	0.214153	+	0.370924i	−0.738857	+	0.673862i	$0.764634\pi$
$128$	181585.	−	37239.1i	0.979612	−	0.200897i
$129$	174605.	−	100808.i	0.923809	−	0.533362i
$130$	−93826.0	+	210157.i	−0.486928	+	1.09065i
$131$	−314648.	−	181662.i	−1.60194	−	0.924881i	−0.991099	−	0.133129i	$-0.957497\pi$
$131$	−314648.	−	181662.i	−1.60194	−	0.924881i	−0.610843	−	0.791752i	$-0.709169\pi$
$132$	−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
$136$	15699.3	+	3387.41i	0.0727835	+	0.0157044i
$137$	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	$0.732011\pi$
$138$	−134116.	+	300402.i	−0.599491	+	1.34278i
$139$	277800.	−	160388.i	1.21954	−	0.704101i	0.254720	−	0.967015i	$-0.418017\pi$
$139$	277800.	−	160388.i	1.21954	−	0.704101i	0.964819	+	0.262914i	$0.0846835\pi$
$140$	−2136.44	−	10153.3i	−0.00921235	−	0.0437812i
$141$		−	412403.i		−	1.74692i
$142$	−328870.	+	238424.i	−1.36868	+	0.992268i
$143$	42505.6	+	73621.9i	0.173823	+	0.301070i
$144$	527048.	−	232076.i	2.11809	−	0.932660i
$145$			76069.1i			0.300461i
$146$	−262799.	+	190524.i	−1.02033	+	0.739719i
$147$	−237864.	+	411993.i	−0.907895	+	1.57252i
$148$	−317112.	+	284355.i	−1.19003	+	1.06710i
$149$	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	$0.127886\pi$
$150$	106024.	+	47334.8i	0.384746	+	0.171772i
$151$	−215525.			−0.769230			−0.384615	−	0.923077i	$-0.625666\pi$
$151$	−215525.			−0.769230			−0.384615	+	0.923077i	$0.625666\pi$
$152$	−237443.	−	157346.i	−0.833584	−	0.552392i
$153$	49896.4			0.172322
$154$	−3499.54	−	1562.39i	−0.0118908	−	0.00530870i
$155$	222558.	−	385481.i	0.744069	−	1.28877i
$156$	−561304.	+	503324.i	−1.84666	+	1.65591i
$157$	−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	$0.988230\pi$
$158$	267201.	−	193715.i	0.851521	−	0.617335i
$159$			664964.i			2.08596i
$160$	−140681.	−	246572.i	−0.434445	−	0.761455i
$161$	6779.01	+	11741.6i	0.0206111	+	0.0356995i
$162$	552183.	−	400322.i	1.65309	−	1.19845i
$163$			16950.9i			0.0499717i	0.999688	+	0.0249859i	$0.00795408\pi$
$163$			16950.9i			0.0499717i	−0.999688	+	0.0249859i	$0.992046\pi$
$164$	33649.7	+	159919.i	0.0976948	+	0.464290i
$165$	−123338.	+	71209.2i	−0.352685	+	0.203623i
$166$	133456.	−	298922.i	0.375895	−	0.841954i
$167$	100621.	+	174280.i	0.279187	+	0.483566i	0.971183	−	0.238335i	$-0.0766017\pi$
$167$	100621.	+	174280.i	0.279187	+	0.483566i	−0.691996	+	0.721902i	$0.743268\pi$
$168$	7168.62	−	33223.7i	0.0195958	−	0.0908185i
$169$	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	$0.880707\pi$
$174$	−101586.	+	227538.i	−0.254366	+	0.569745i
$175$	4144.07	−	2392.58i	0.0102290	−	0.00590570i
$176$	−104238.	−	11387.6i	−0.253655	−	0.0277108i
$177$	250360.	+	433637.i	0.600665	+	1.04038i
$178$	−599585.	+	62398.4i	−1.41841	+	0.147613i
$179$	−759487.			−1.77169			−0.885845	−	0.463982i	$-0.846420\pi$
$179$	−759487.			−1.77169			−0.885845	+	0.463982i	$0.846420\pi$
$180$	−588799.	−	656626.i	−1.35452	−	1.51056i
$181$	−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
$184$	274908.	+	249061.i	0.598609	+	0.542328i
$185$	564916.	+	326154.i	1.21354	+	0.700638i
$186$	1.18050e6	−	855839.i	2.50198	−	1.81388i
$187$	−7868.09	−	4542.64i	−0.0164538	−	0.00949958i
$188$	−441964.	−	144604.i	−0.911994	−	0.298390i
$189$		−	59967.5i		−	0.122113i
$190$	−115948.	+	420545.i	−0.233012	+	0.845140i
$191$		−	31022.2i		−	0.0615303i	−0.999527	−	0.0307651i	$-0.990206\pi$
$191$		−	31022.2i		−	0.0615303i	0.999527	−	0.0307651i	$-0.00979439\pi$
$192$	−91522.3	−	925417.i	−0.179174	−	1.81169i
$193$	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	$0.658871\pi$
$194$	−384042.	−	529728.i	−0.732612	−	1.01053i
$195$	999930.	+	577310.i	1.88314	+	1.08723i
$196$	358120.	+	399374.i	0.665869	+	0.742574i
$197$	−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	0.195523	−	0.980699i	$-0.437360\pi$
$199$	638300.	−	368523.i	1.14259	−	0.659677i	0.947072	+	0.321022i	$0.104026\pi$
$200$	87903.6	−	97026.0i	0.155393	−	0.171519i
$201$	−1.48218e6			−2.58769
$202$	−33096.4	−	318023.i	−0.0570693	−	0.548377i
$203$	5134.73	+	8893.62i	0.00874536	+	0.0151474i
$204$	25055.2	−	76578.1i	0.0421524	−	0.128834i
$205$	216746.	−	125138.i	0.360218	−	0.207972i
$206$	−101958.	−	45519.7i	−0.167399	−	0.0747362i
$207$	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	−0.880661	−	0.473748i	$-0.842901\pi$
$211$	−19435.2	+	33662.8i	−0.0300527	+	0.0520528i	0.850608	+	0.525801i	$0.176234\pi$
$212$	712628.	+	233161.i	1.08899	+	0.356300i
$213$	1.01892e6	+	1.76482e6i	1.53883	+	2.66533i
$214$	−546216.	−	243861.i	−0.815324	−	0.364006i
$215$	−301522.	+	174084.i	−0.444859	+	0.256839i
$216$	−502221.	−	1.56198e6i	−0.732420	−	2.27794i
$217$		−	60091.4i		−	0.0866289i
$218$	208064.	+	286993.i	0.296521	+	0.409006i
$219$	814215.	+	1.41026e6i	1.14717	+	1.98696i
$220$	33066.6	+	157147.i	0.0460609	+	0.218902i
$221$			73656.5i			0.101445i
$222$	1.25422e6	+	1.73000e6i	1.70801	+	2.35594i
$223$	−7209.72	+	12487.6i	−0.00970859	+	0.0168158i	−0.870839	−	0.491569i	$-0.836424\pi$
$223$	−7209.72	+	12487.6i	−0.00970859	+	0.0168158i	0.861130	+	0.508384i	$0.169757\pi$
$224$	−33091.6	−	19331.9i	−0.0440653	−	0.0257428i
$225$	203375.	−	352255.i	0.267818	−	0.463875i
$226$	−9690.57	+	21705.6i	−0.0126205	+	0.0282683i
$227$	−1.04832e6			−1.35029			−0.675147	−	0.737683i	$-0.735920\pi$
$227$	−1.04832e6			−1.35029			−0.675147	+	0.737683i	$0.735920\pi$
$228$	−908435.	+	1.10309e6i	−1.15733	+	1.40532i
$229$	1.08418e6			1.36619			0.683094	−	0.730330i	$-0.260634\pi$
$229$	1.08418e6			1.36619			0.683094	+	0.730330i	$0.260634\pi$
$230$	231602.	−	518757.i	0.288684	−	0.646613i
$231$	−9613.37	+	16650.8i	−0.0118535	+	0.0205308i
$232$	208228.	+	188650.i	0.253991	+	0.230111i
$233$	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	$0.0154279\pi$
$234$	1.55020e6	+	2.13827e6i	1.85075	+	2.55283i
$235$			712169.i			0.841228i
$236$	552506.	−	116257.i	0.645739	−	0.135875i
$237$	−827855.	−	1.43389e6i	−0.957378	−	1.65823i
$238$	−1949.04	−	2688.40i	−0.00223038	−	0.00307647i
$239$		−	323053.i		−	0.365830i	−0.983129	−	0.182915i	$-0.941447\pi$
$239$		−	323053.i		−	0.365830i	0.983129	−	0.182915i	$-0.0585533\pi$
$240$	−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	$0.486418\pi$
$242$	−777735.	−	347224.i	−0.853676	−	0.381129i
$243$	−609540.	−	1.05576e6i	−0.662196	−	1.14696i
$244$	422789.	−	1.29220e6i	0.454620	−	1.38949i
$245$	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
$250$	−974169.	−	434923.i	−0.985790	−	0.440112i
$251$	1.49827e6	−	865024.i	1.50108	−	0.866650i	0.501083	−	0.865399i	$-0.332935\pi$
$251$	1.49827e6	−	865024.i	1.50108	−	0.866650i	0.999999	−	0.00125049i	$-0.000398043\pi$
$252$	−113162.	−	37024.9i	−0.112254	−	0.0367276i
$253$	−104922.	−	181730.i	−0.103054	−	0.178495i
$254$	−45585.0	−	438025.i	−0.0443341	−	0.426005i
$255$	−123396.			−0.118837
$256$	−1.02384e6	−	226403.i	−0.976412	−	0.215915i
$257$	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
$260$	969304.	−	869179.i	0.889256	−	0.797399i
$261$	755976.	+	436463.i	0.686921	+	0.396594i
$262$	1.20636e6	+	1.66399e6i	1.08573	+	1.49760i
$263$	−471561.	−	272256.i	−0.420386	−	0.242710i	0.274856	−	0.961485i	$-0.411370\pi$
$263$	−471561.	−	272256.i	−0.420386	−	0.242710i	−0.695243	+	0.718775i	$0.744703\pi$
$264$	−110952.	+	514217.i	−0.0979771	+	0.454085i
$265$		−	1.14831e6i		−	1.00449i
$266$	14831.1	+	56994.6i	0.0128520	+	0.0493890i
$267$			3.02424e6i			2.59620i
$268$	−519709.	+	1.58843e6i	−0.442001	+	1.35092i
$269$	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	$0.645453\pi$
$270$	−2.03438e6	+	1.47488e6i	−1.69833	+	1.23126i
$271$	−246302.	−	142203.i	−0.203725	−	0.117621i	0.394667	−	0.918824i	$-0.370860\pi$
$271$	−246302.	−	142203.i	−0.203725	−	0.117621i	−0.598392	+	0.801203i	$0.704193\pi$
$272$	−73281.9	−	53702.3i	−0.0600585	−	0.0440119i
$273$	155876.			0.126582
$274$	−80516.4	−	773680.i	−0.0647900	−	0.622566i
$275$	−64139.6	+	37031.0i	−0.0511440	+	0.0295280i
$276$	1.38554e6	−	1.24241e6i	1.09483	−	0.981734i
$277$	−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
$280$	−12379.3	+	57373.2i	−0.00943631	+	0.0437335i
$281$	−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	$0.520357\pi$
$282$	−951058.	+	2.13024e6i	−0.712171	+	1.59516i
$283$	−1.93396e6	−	1.11657e6i	−1.43543	−	0.828743i	−0.437898	−	0.899025i	$-0.644277\pi$
$283$	−1.93396e6	−	1.11657e6i	−1.43543	−	0.828743i	−0.997527	+	0.0702817i	$0.977610\pi$
$284$	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
$288$	−3.25763e6	−	16673.6i	−2.31430	−	0.0118453i
$289$	705993.	+	1.22282e6i	0.497228	+	0.861224i
$290$	175426.	−	392930.i	0.122489	−	0.274360i
$291$	−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	$0.854220\pi$
$294$	2.17878e6	−	1.57957e6i	1.47010	−	1.06579i
$295$	−432342.	−	748838.i	−0.289249	−	0.500995i
$296$	2.29378e6	−	737515.i	1.52168	−	0.489262i
$297$			928144.i			0.610554i
$298$	−301675.	+	218708.i	−0.196788	+	0.142667i
$299$	−850626.	+	1.47333e6i	−0.550251	+	0.953062i
$300$	−438497.	−	489010.i	−0.281296	−	0.313700i
$301$	−23501.6	+	40705.9i	−0.0149514	+	0.0258965i
$302$	1.11328e6	+	497031.i	0.702406	+	0.313593i
$303$	−1.60407e6			−1.00373
$304$	863632.	+	1.36034e6i	0.535975	+	0.844234i
$305$	−2.08222e6			−1.28167
$306$	−257737.	−	115068.i	−0.157352	−	0.0702508i
$307$	1.07731e6	−	1.86595e6i	0.652369	−	1.12994i	−0.330177	−	0.943919i	$-0.607109\pi$
$307$	1.07731e6	−	1.86595e6i	0.652369	−	1.12994i	0.982546	−	0.186017i	$-0.0595581\pi$
$308$	14473.6	+	16140.9i	0.00869359	+	0.00969505i
$309$	−280082.	+	485116.i	−0.166874	+	0.289034i
$310$	−2.03858e6	+	1.47793e6i	−1.20482	+	0.873473i
$311$			1.05752e6i			0.619993i	0.950738	+	0.309997i	$0.100328\pi$
$311$			1.05752e6i			0.619993i	−0.950738	+	0.309997i	$0.899672\pi$
$312$	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	$0.877845\pi$
$314$	1.50411e6	−	1.09045e6i	0.860905	−	0.624139i
$315$			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	$0.360896\pi$
$318$	1.53350e6	−	3.43483e6i	0.850385	−	1.90475i
$319$	−79472.5	−	137650.i	−0.0437260	−	0.0757357i
$320$	158048.	+	1.59808e6i	0.0862807	+	0.872418i
$321$	−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
$326$	39091.2	−	87558.9i	0.0203721	−	0.0456306i
$327$	1.54010e6	−	889175.i	0.796487	−	0.459852i
$328$	194979.	−	903650.i	0.100070	−	0.463784i
$329$	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	$-0.343941\pi$
$331$	1.87715e6			0.941737			0.470869	+	0.882203i	$0.343941\pi$
$332$	−1.37871e6	+	1.23630e6i	−0.686481	+	0.615570i
$333$	6.48266e6	−	3.74276e6i	3.20363	−	1.84962i
$334$	−117835.	−	1.13228e6i	−0.0577975	−	0.555375i
$335$	2.55955e6			1.24610
$336$	−113647.	+	155083.i	−0.0549176	+	0.0749404i
$337$	−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	$0.770863\pi$
$338$	−1.45601e6	+	1.05558e6i	−0.693222	+	0.502572i
$339$	103275.	+	59625.9i	0.0488086	+	0.0281797i
$340$	−43267.2	+	132241.i	−0.0202984	+	0.0620396i
$341$			930060.i			0.433137i
$342$	3.51411e6	+	3.56526e6i	1.62462	+	1.64826i
$343$		−	222104.i		−	0.101935i
$344$	−271242.	+	1.25710e6i	−0.123583	+	0.572759i
$345$	−2.46825e6	−	1.42504e6i	−1.11645	−	0.644585i
$346$	1.62830e6	+	2.24600e6i	0.731216	+	1.00860i
$347$	−824436.	−	475988.i	−0.367564	−	0.212213i	0.304830	−	0.952407i	$-0.401400\pi$
$347$	−824436.	−	475988.i	−0.367564	−	0.212213i	−0.672394	+	0.740194i	$0.734734\pi$
$348$	1.04947e6	−	941061.i	0.464537	−	0.416553i
$349$	−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
$352$	512173.	+	299209.i	0.220323	+	0.128712i
$353$	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
$356$	3.24102e6	+	1.06041e6i	1.35536	+	0.443455i
$357$	−14426.8	+	8329.34i	−0.00599102	+	0.00345892i
$358$	3.92308e6	+	1.75148e6i	1.61778	+	0.722267i
$359$	2.07901e6	+	1.20031e6i	0.851373	+	0.491540i	0.861114	−	0.508412i	$-0.169767\pi$
$359$	2.07901e6	+	1.20031e6i	0.851373	+	0.491540i	−0.00974107	+	0.999953i	$0.503101\pi$
$360$	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
$364$	54655.8	−	167049.i	0.0216214	−	0.0660831i
$365$	−1.40605e6	−	2.43535e6i	−0.552419	−	0.956818i
$366$	−6.22834e6	−	2.78068e6i	−2.43035	−	1.08505i
$367$	−1.40886e6	+	813405.i	−0.546012	+	0.315240i	−0.747512	−	0.664248i	$-0.768752\pi$
$367$	−1.40886e6	+	813405.i	−0.546012	+	0.315240i	0.201500	+	0.979489i	$0.435418\pi$
$368$	−845651.	−	1.92049e6i	−0.325515	−	0.739251i
$369$		−	2.87203e6i		−	1.09805i
$370$	−2.16588e6	−	2.98750e6i	−0.822489	−	1.13450i
$371$	−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	$0.950654\pi$
$374$	30166.1	+	41609.6i	0.0111517	+	0.0153821i
$375$	−2.67608e6	+	4.63510e6i	−0.982699	+	1.70208i
$376$	1.94946e6	+	1.76617e6i	0.711122	+	0.644263i
$377$	−644302.	+	1.11596e6i	−0.233473	+	0.404387i
$378$	−138293.	+	309758.i	−0.0497820	+	0.111505i
$379$	−1.60971e6			−0.575637			−0.287819	−	0.957685i	$-0.592930\pi$
$379$	−1.60971e6			−0.575637			−0.287819	+	0.957685i	$0.592930\pi$
$380$	1.56876e6	−	1.90491e6i	0.557310	−	0.676729i
$381$	−2.20935e6			−0.779744
$382$	−71541.4	+	160243.i	−0.0250841	+	0.0561850i
$383$	759653.	−	1.31576e6i	0.264617	−	0.458330i	−0.702846	−	0.711342i	$-0.748088\pi$
$383$	759653.	−	1.31576e6i	0.264617	−	0.458330i	0.967463	+	0.253012i	$0.0814211\pi$
$384$	−1.66139e6	+	4.99125e6i	−0.574967	+	1.72735i
$385$	16601.1	−	28754.0i	0.00570802	−	0.00988658i
$386$	−84154.5	−	116078.i	−0.0287481	−	0.0396537i
$387$			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	$0.823043\pi$
$390$	−3.83372e6	−	5.28803e6i	−1.27632	−	1.76049i
$391$		−	181815.i		−	0.0601435i
$392$	−928835.	−	2.88882e6i	−0.305298	−	0.949522i
$393$	8.92948e6	−	5.15544e6i	2.91638	−	1.68378i
$394$	2.45259e6	+	1.09497e6i	0.795949	+	0.355356i
$395$	1.42960e6	+	2.47615e6i	0.461024	+	0.798516i
$396$	1.75146e6	+	573051.i	0.561258	+	0.183635i
$397$	−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	$0.801772\pi$
$402$	7.65612e6	+	3.41812e6i	2.36289	+	1.05493i
$403$	6.53002e6	−	3.77011e6i	2.00287	−	1.15636i
$404$	−562447.	+	1.71905e6i	−0.171446	+	0.524005i
$405$	2.95434e6	+	5.11707e6i	0.895001	+	1.55019i
$406$	−6013.21	−	57780.8i	−0.00181047	−	0.0173968i
$407$	−1.36299e6			−0.407855
$408$	−306021.	+	337778.i	−0.0910123	+	0.100457i
$409$	−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
$412$	421682.	+	470258.i	0.122389	+	0.136488i
$413$	−101095.	−	58367.0i	−0.0291644	−	0.0168381i
$414$	−3.82655e6	−	5.27815e6i	−1.09725	−	1.51349i
$415$	2.45609e6	+	1.41803e6i	0.700043	+	0.404170i
$416$	24613.3	−	4.80888e6i	0.00697328	−	1.36242i
$417$			9.10339e6i			2.56368i
$418$	−229548.	−	882131.i	−0.0642589	−	0.246941i
$419$			627746.i			0.174682i	0.996178	+	0.0873411i	$0.0278370\pi$
$419$			627746.i			0.174682i	−0.996178	+	0.0873411i	$0.972163\pi$
$420$	279855.	+	91564.3i	0.0774123	+	0.0253281i
$421$	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	$0.614070\pi$
$422$	178022.	−	129063.i	0.0486624	−	0.0352793i
$423$	7.07755e6	+	4.08623e6i	1.92323	+	1.11038i
$424$	−3.14333e6	−	2.84780e6i	−0.849133	−	0.769298i
$425$	−64169.8			−0.0172329
$426$	−1.19324e6	−	1.14658e7i	−0.318570	−	3.06113i
$427$	−243443.	+	140552.i	−0.0646141	+	0.0373050i
$428$	2.25907e6	+	2.51930e6i	0.596101	+	0.664769i
$429$	−2.41256e6			−0.632899
$430$	1.95895e6	−	203867.i	0.510919	−	0.0531711i
$431$	−190195.	−	329427.i	−0.0493180	−	0.0854213i	0.840313	−	0.542102i	$-0.182371\pi$
$431$	−190195.	−	329427.i	−0.0493180	−	0.0854213i	−0.889631	+	0.456681i	$0.849038\pi$
$432$	−1.00796e6	+	9.22651e6i	−0.259856	+	2.37864i
$433$	−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	$0.390449\pi$
$434$	−138579.	+	310398.i	−0.0353161	+	0.0791033i
$435$	−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	−0.730121	−	0.683318i	$-0.760536\pi$
$439$	915447.	−	1.58560e6i	0.226711	−	0.392674i	0.956831	+	0.290644i	$0.0938695\pi$
$440$	191600.	−	887991.i	0.0471807	−	0.218664i
$441$	−4.71368e6	−	8.16433e6i	−1.15415	−	1.99905i
$442$	169862.	−	380468.i	0.0413562	−	0.0926323i
$443$	−5.39424e6	+	3.11437e6i	−1.30593	+	0.753981i	−0.981415	−	0.191898i	$-0.938536\pi$
$443$	−5.39424e6	+	3.11437e6i	−1.30593	+	0.753981i	−0.324519	+	0.945879i	$0.605202\pi$
$444$	−2.48895e6	−	1.18286e7i	−0.599182	−	2.84758i
$445$		−	5.22249e6i		−	1.25020i
$446$	66039.5	−	47877.3i	0.0157205	−	0.0113970i
$447$	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	$0.941182\pi$
$450$	−1.86287e6	+	1.35054e6i	−0.433661	+	0.314396i
$451$	−261474.	+	452886.i	−0.0605323	+	0.104845i
$452$	100112.	−	89770.8i	0.0230484	−	0.0206676i
$453$	3.05823e6	−	5.29700e6i	0.700203	−	1.21279i
$454$	5.41502e6	+	2.41757e6i	1.23299	+	0.550476i
$455$	−269178.			−0.0609553
$456$	7.23635e6	−	3.60298e6i	1.62970	−	0.811428i
$457$	−851569.			−0.190735			−0.0953673	−	0.995442i	$-0.530403\pi$
$457$	−851569.			−0.190735			−0.0953673	+	0.995442i	$0.530403\pi$
$458$	−5.60024e6	−	2.50026e6i	−1.24751	−	0.556956i
$459$	−402087.	+	696436.i	−0.0890817	+	0.154294i
$460$	−2.39265e6	+	2.14550e6i	−0.527211	+	0.472752i
$461$	−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	$0.197672\pi$
$462$	88056.4	−	63839.1i	0.0191936	−	0.0139150i
$463$		−	8.37376e6i		−	1.81538i	−0.419640	−	0.907691i	$-0.637844\pi$
$463$		−	8.37376e6i		−	1.81538i	0.419640	−	0.907691i	$-0.362156\pi$
$464$	−640534.	−	1.45466e6i	−0.138117	−	0.313666i
$465$	6.31602e6	+	1.09397e7i	1.35460	+	2.34624i
$466$	−3.47235e6	+	2.51738e6i	−0.740727	+	0.537012i
$467$			6.88767e6i			1.46144i	0.682679	+	0.730718i	$0.260815\pi$
$467$			6.88767e6i			1.46144i	−0.682679	+	0.730718i	$0.739185\pi$
$468$	−3.07632e6	−	1.46201e7i	−0.649258	−	3.08557i
$469$	299250.	−	172772.i	0.0628206	−	0.0362695i
$470$	1.64236e6	−	3.67866e6i	0.342945	−	0.768149i
$471$	−4.66010e6	−	8.07153e6i	−0.967928	−	1.67650i
$472$	−3.12204e6	−	673637.i	−0.645035	−	0.139178i
$473$	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
$478$	−745005.	+	1.66871e6i	−0.149138	+	0.334050i
$479$	−982202.	+	567074.i	−0.195597	+	0.112928i	−0.594600	−	0.804022i	$-0.702690\pi$
$479$	−982202.	+	567074.i	−0.195597	+	0.112928i	0.399003	+	0.916950i	$0.369356\pi$
$480$	8.05626e6	+	41234.4i	1.59599	+	0.00816878i
$481$	5.52503e6	+	9.56963e6i	1.08886	+	1.88596i
$482$	4.69373e6	−	488473.i	0.920239	−	0.0957687i
$483$	−384767.			−0.0750464
$484$	3.21659e6	+	3.58713e6i	0.624141	+	0.696039i
$485$	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	$-0.264802\pi$
$487$	7.04972e6			1.34694			0.673472	+	0.739212i	$0.264802\pi$
$488$	−5.16388e6	+	5.69978e6i	−0.981583	+	1.08345i
$489$	−416606.	−	240528.i	−0.0787868	−	0.0454876i
$490$	−3.76250e6	+	2.72773e6i	−0.707923	+	0.513229i
$491$	2.17000e6	+	1.25285e6i	0.406216	+	0.234529i	0.689163	−	0.724607i	$-0.257979\pi$
$491$	2.17000e6	+	1.25285e6i	0.406216	+	0.234529i	−0.282947	+	0.959136i	$0.591312\pi$
$492$	−4.40782e6	−	1.44217e6i	−0.820940	−	0.268599i
$493$		−	137715.i		−	0.0255191i
$494$	−5.26301e6	+	5.18750e6i	−0.970324	+	0.956402i
$495$		−	2.82226e6i		−	0.517707i
$496$	−1.01004e6	+	9.24556e6i	−0.184346	+	1.68744i
$497$	−411436.	−	237543.i	−0.0747156	−	0.0431370i
$498$	5.45298e6	+	7.52156e6i	0.985282	+	1.35905i
$499$	−4.86409e6	−	2.80828e6i	−0.874480	−	0.504882i	−0.00564591	−	0.999984i	$-0.501797\pi$
$499$	−4.86409e6	−	2.80828e6i	−0.874480	−	0.504882i	−0.868835	+	0.495103i	$0.835130\pi$
$500$	4.02901e6	+	4.49314e6i	0.720732	+	0.803757i
$501$	−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	$0.695404\pi$
$503$	−8.92000e6	+	5.14996e6i	−1.57197	+	0.907578i	−0.995927	+	0.0901595i	$0.971262\pi$
$504$	499148.	+	452218.i	0.0875291	+	0.0792996i
$505$	2.77003e6			0.483344
$506$	122872.	+	1.18068e6i	0.0213343	+	0.205001i
$507$	4.51107e6	+	7.81341e6i	0.779399	+	1.34996i
$508$	−774680.	+	2.36772e6i	−0.133187	+	0.407071i
$509$	−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	$0.415177\pi$
$510$	637394.	+	284568.i	0.108513	+	0.0484464i
$511$	−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
$516$	6.13186e6	+	2.00625e6i	1.01384	+	0.331712i
$517$	−744032.	−	1.28870e6i	−0.122424	−	0.212044i
$518$	−454883.	−	203085.i	−0.0744861	−	0.0332548i
$519$	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	$-0.00845758\pi$
$522$	−2.89840e6	−	3.99791e6i	−0.465567	−	0.642180i
$523$	−1.48549e6	−	2.57294e6i	−0.237473	−	0.411315i	0.722515	−	0.691355i	$-0.242986\pi$
$523$	−1.48549e6	−	2.57294e6i	−0.237473	−	0.411315i	−0.959989	+	0.280039i	$0.909652\pi$
$524$	−2.39397e6	−	1.13772e7i	−0.380882	−	1.81012i
$525$			135799.i			0.0215030i
$526$	1.80796e6	+	2.49380e6i	0.284921	+	0.393005i
$527$	−402918.	+	697874.i	−0.0631960	+	0.109459i
$528$	1.75897e6	−	2.40029e6i	0.274583	−	0.374695i
$529$	−1.11847e6	+	1.93725e6i	−0.173774	+	0.300985i
$530$	−2.64817e6	+	5.93153e6i	−0.409502	+	0.917227i
$531$	−9.92263e6			−1.52718
$532$	54828.2	−	328605.i	0.00839895	−	0.0503379i
$533$	4.23966e6			0.646418
$534$	6.97431e6	−	1.56215e7i	1.05840	−	2.37066i
$535$	2.59114e6	−	4.48799e6i	0.391387	−	0.677902i
$536$	6.34765e6	−	7.00639e6i	0.954336	−	1.05337i
$537$	1.07768e7	−	1.86660e7i	1.61271	−	2.79329i
$538$	−524855.	−	723959.i	−0.0781779	−	0.107835i
$539$			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	$-0.519094\pi$
$542$	944319.	+	1.30255e6i	0.138077	+	0.190456i
$543$		−	4.99057e6i		−	0.726358i
$544$	254688.	+	446394.i	0.0368987	+	0.0646727i
$545$	−2.65956e6	+	1.53550e6i	−0.383547	+	0.221441i
$546$	−805166.	−	359471.i	−0.115586	−	0.0516039i
$547$	1.11581e6	+	1.93264e6i	0.159449	+	0.276173i	0.934670	−	0.355516i	$-0.115695\pi$
$547$	1.11581e6	+	1.93264e6i	0.159449	+	0.276173i	−0.775221	+	0.631690i	$0.782362\pi$
$548$	−1.36831e6	+	4.18208e6i	−0.194641	+	0.594895i
$549$	−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
$554$	5.26430e6	+	2.35028e6i	0.728729	+	0.325345i
$555$	−1.60319e7	+	9.25602e6i	−2.20929	+	1.27553i
$556$	9.75592e6	+	3.19199e6i	1.33839	+	0.437899i
$557$	−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
$560$	196255.	−	267809.i	0.0264455	−	0.0360874i
$561$	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	$-0.275074\pi$
$563$	9.76622e6			1.29854			0.649270	+	0.760558i	$0.275074\pi$
$564$	9.82525e6	−	8.81034e6i	1.30061	−	1.16626i
$565$	−178344.	−	102967.i	−0.0235037	−	0.0135699i
$566$	7.41476e6	+	1.02275e7i	0.972873	+	1.34193i
$567$	690814.	+	398842.i	0.0902409	+	0.0521006i
$568$	−1.27061e7	−	2.74158e6i	−1.65250	−	0.356557i
$569$		−	630739.i		−	0.0816713i	−0.999166	−	0.0408356i	$-0.986998\pi$
$569$		−	630739.i		−	0.0816713i	0.999166	−	0.0408356i	$-0.0130020\pi$
$570$	−8.69056e6	−	8.81706e6i	−1.12037	−	1.13668i
$571$		−	8.05237e6i		−	1.03356i	−0.856120	−	0.516778i	$-0.827131\pi$
$571$		−	8.05237e6i		−	1.03356i	0.856120	−	0.516778i	$-0.172869\pi$
$572$	−845932.	+	2.58549e6i	−0.108105	+	0.330410i
$573$	762437.	+	440193.i	0.0970102	+	0.0560089i
$574$	−154744.	+	112186.i	−0.0196035	+	0.0142122i
$575$	−1.28357e6	−	741068.i	−0.161901	−	0.0934735i
$576$	1.67886e7	+	7.59867e6i	2.10843	+	0.954292i
$577$	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
$580$	−1.81230e6	+	1.62510e6i	−0.223697	+	0.200590i
$581$	382872.			0.0470559
$582$	1.84686e7	−	1.92202e6i	2.26010	−	0.235207i
$583$	1.19969e6	+	2.07792e6i	0.146183	+	0.253197i
$584$	−1.01534e7	−	2.19078e6i	−1.23191	−	0.265807i
$585$	−1.98153e7	+	1.14404e7i	−2.39393	+	1.38213i
$586$	2.99670e6	−	6.71220e6i	0.360495	−	0.807459i
$587$	−4.17618e6	−	2.41112e6i	−0.500247	−	0.288818i	0.228569	−	0.973528i	$-0.426595\pi$
$587$	−4.17618e6	−	2.41112e6i	−0.500247	−	0.288818i	−0.728816	+	0.684710i	$0.759929\pi$
$588$	−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
$592$	−1.35492e7	−	1.48019e6i	−1.58895	−	0.173586i
$593$	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	$0.684569\pi$
$594$	2.14043e6	−	4.79427e6i	0.248906	−	0.557515i
$595$	24913.4	−	14383.8i	0.00288497	−	0.00166564i
$596$	2.06266e6	−	434019.i	0.237854	−	0.0500488i
$597$			2.09168e7i			2.40193i
$598$	7.79155e6	−	5.64871e6i	0.890986	−	0.645947i
$599$	2.68875e6	+	4.65706e6i	0.306185	+	0.530328i	0.977524	−	0.210822i	$-0.0676140\pi$
$599$	2.68875e6	+	4.65706e6i	0.306185	+	0.530328i	−0.671339	+	0.741150i	$0.734281\pi$
$600$	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	$0.812025\pi$
$602$	215270.	−	156066.i	0.0242098	−	0.0175516i
$603$	1.46860e7	−	2.54369e7i	1.64479	−	2.84886i
$604$	−4.60436e6	−	5.13477e6i	−0.513544	−	0.572702i
$605$	3.68942e6	−	6.39025e6i	0.409797	−	0.709790i
$606$	8.28572e6	+	3.69921e6i	0.916534	+	0.409192i
$607$	1.67126e7			1.84108			0.920540	−	0.390649i	$-0.127749\pi$
$607$	1.67126e7			1.84108			0.920540	+	0.390649i	$0.127749\pi$
$608$	−1.32391e6	−	9.01839e6i	−0.145244	−	0.989396i
$609$	−291440.			−0.0318424
$610$	1.07556e7	+	4.80189e6i	1.17033	+	0.522502i
$611$	−6.03205e6	+	1.04478e7i	−0.653675	+	1.13220i
$612$	1.06596e6	+	1.18875e6i	0.115043	+	0.128296i
$613$	−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	$0.301869\pi$
$614$	−9.86790e6	+	7.15402e6i	−1.05634	+	0.765825i
$615$			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	$0.764678\pi$
$618$	2.56549e6	−	1.85993e6i	0.270209	−	0.195896i
$619$		−	1.39528e7i		−	1.46364i	−0.681499	−	0.731819i	$-0.738672\pi$
$619$		−	1.39528e7i		−	1.46364i	0.681499	−	0.731819i	$-0.261328\pi$
$620$	1.39385e7	−	2.93290e6i	1.45625	−	0.306421i
$621$	−1.60856e7	+	9.28704e6i	−1.67382	+	0.966381i
$622$	2.43879e6	−	5.46255e6i	0.252754	−	0.566134i
$623$	−352523.	−	610588.i	−0.0363888	−	0.0630272i
$624$	−2.39828e7	−	2.62002e6i	−2.46569	−	0.269366i
$625$	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
$630$	420517.	−	941901.i	0.0422116	−	0.0945483i
$631$	−4.43389e6	+	2.55991e6i	−0.443314	+	0.255947i	−0.705002	−	0.709205i	$-0.749054\pi$
$631$	−4.43389e6	+	2.55991e6i	−0.443314	+	0.255947i	0.261688	+	0.965152i	$0.415721\pi$
$632$	1.03235e7	+	2.22748e6i	1.02810	+	0.221831i
$633$	−551558.	−	955326.i	−0.0547119	−	0.0947638i
$634$	1.74115e6	−	181201.i	0.172034	−	0.0179034i
$635$	3.81528e6			0.375484
$636$	−1.58424e7	+	1.42059e7i	−1.55302	+	1.39260i
$637$	1.20521e7	−	6.95829e6i	1.17683	−	0.679444i
$638$	93069.2	+	894299.i	0.00905220	+	0.0869823i
$639$	−4.03832e7			−3.91245
$640$	2.86902e6	−	8.61928e6i	0.276875	−	0.831804i
$641$	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	$0.397279\pi$
$642$	1.37440e7	−	9.96415e6i	1.31606	−	0.954119i
$643$	−1.64399e7	−	9.49160e6i	−1.56810	−	0.905341i	−0.996391	−	0.0848818i	$-0.972949\pi$
$643$	−1.64399e7	−	9.49160e6i	−1.56810	−	0.905341i	−0.571705	−	0.820459i	$-0.693718\pi$
$644$	−134914.	+	412347.i	−0.0128186	+	0.0391785i
$645$		−	9.88073e6i		−	0.935168i
$646$	209912.	−	761354.i	0.0197904	−	0.0717803i
$647$			1.00942e7i			0.948009i	0.880522	+	0.474005i	$0.157192\pi$
$647$			1.00942e7i			0.948009i	−0.880522	+	0.474005i	$0.842808\pi$
$648$	2.13340e7	+	4.60320e6i	1.99588	+	0.430648i
$649$	1.56468e6	+	903371.i	0.145819	+	0.0841888i
$650$	−1.99365e6	−	2.74995e6i	−0.185083	−	0.255294i
$651$	1.47688e6	+	852675.i	0.136581	+	0.0788553i
$652$	−403846.	+	362130.i	−0.0372046	+	0.0333615i
$653$	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
$656$	−3.09109e6	+	4.21810e6i	−0.280448	+	0.382699i
$657$	−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	$0.0818770\pi$
$659$	7.84698e6	+	1.35914e7i	0.703864	+	1.21913i	−0.263236	+	0.964732i	$0.584790\pi$
$660$	−4.33144e6	−	1.41718e6i	−0.387055	−	0.126638i
$661$	−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	$0.334072\pi$
$662$	−9.69632e6	−	4.32898e6i	−0.859927	−	0.383920i
$663$	−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
$668$	−2.00252e6	+	6.12044e6i	−0.173634	+	0.530691i
$669$	−204607.	−	354389.i	−0.0176748	−	0.0306136i
$670$	−1.32212e7	−	5.90268e6i	−1.13785	−	0.507998i
$671$	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	$-0.0786478\pi$
$674$	4.45146e6	+	6.14012e6i	0.377444	+	0.520627i
$675$	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	$-0.193012\pi$
$678$	−395955.	−	546161.i	−0.0330805	−	0.0456296i
$679$	382622.	−	662721.i	0.0318490	−	0.0551641i
$680$	528460.	−	583302.i	0.0438268	−	0.0483750i
$681$	1.48752e7	−	2.57647e7i	1.22913	−	2.12891i
$682$	2.14485e6	−	4.80417e6i	0.176578	−	0.395510i
$683$	1.91109e7			1.56758			0.783791	−	0.621025i	$-0.213284\pi$
$683$	1.91109e7			1.56758			0.783791	+	0.621025i	$0.213284\pi$
$684$	−9.92993e6	−	2.65202e7i	−0.811533	−	2.16739i
$685$	6.73890e6			0.548735
$686$	−512203.	+	1.14727e6i	−0.0415558	+	0.0930794i
$687$	−1.53841e7	+	2.66460e7i	−1.24359	+	2.15397i
$688$	4.30012e6	−	5.86793e6i	0.346345	−	0.472622i
$689$	9.72616e6	−	1.68462e7i	0.780537	−	1.35193i
$690$	9.46323e6	+	1.30531e7i	0.756688	+	1.04374i
$691$		−	5.89087e6i		−	0.469336i	−0.972076	−	0.234668i	$-0.924600\pi$
$691$		−	5.89087e6i		−	0.469336i	0.972076	−	0.234668i	$-0.0754004\pi$
$692$	−3.23131e6	−	1.53567e7i	−0.256516	−	1.21908i
$693$	−190505.	−	329965.i	−0.0150686	−	0.0260996i
$694$	3.16088e6	+	4.35995e6i	0.249120	+	0.343623i
$695$		−	1.57205e7i		−	1.23453i
$696$	−7.59117e6	+	2.44077e6i	−0.593999	+	0.190987i
$697$	−392395.	+	226550.i	−0.0305944	+	0.0176637i
$698$	287772.	+	128477.i	0.0223568	+	0.00998132i
$699$	1.07582e7	+	1.86337e7i	0.832810	+	1.44247i
$700$	145534.	+	47616.3i	0.0112258	+	0.00367292i
$701$	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
$706$	−3.32246e6	−	1.48333e6i	−0.250870	−	0.112002i
$707$	323859.	−	186980.i	0.0243673	−	0.0140684i
$708$	−4.98259e6	+	1.52287e7i	−0.373570	+	1.14177i
$709$	−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
$712$	−1.42958e7	−	1.29517e7i	−1.05684	−	0.957475i
$713$	−1.61188e7	+	9.30622e6i	−1.18744	+	0.685566i
$714$	93729.6	−	9754.38i	0.00688067	−	0.000716068i
$715$	4.16619e6			0.304771
$716$	−1.62253e7	−	1.80943e7i	−1.18279	−	1.31905i
$717$	7.93973e6	+	4.58401e6i	0.576777	+	0.333002i
$718$	−7.97088e6	−	1.09946e7i	−0.577026	−	0.795920i
$719$	−1.06260e7	−	6.13494e6i	−0.766565	−	0.442576i	0.0650830	−	0.997880i	$-0.479269\pi$
$719$	−1.06260e7	−	6.13494e6i	−0.766565	−	0.442576i	−0.831648	+	0.555303i	$0.812602\pi$
$720$	3.06496e6	−	2.80556e7i	0.220340	−	2.01692i
$721$		−	130592.i		−	0.00935574i
$722$	−8.38447e6	+	1.12203e7i	−0.598595	+	0.801052i
$723$		−	2.36746e7i		−	1.68437i
$724$	−5.34829e6	−	1.74988e6i	−0.379200	−	0.124069i
$725$	−972232.	−	561318.i	−0.0686950	−	0.0396611i
$726$	1.95696e7	−	1.41875e7i	1.37797	−	0.999000i
$727$	−9.24656e6	−	5.33850e6i	−0.648850	−	0.374614i	0.139166	−	0.990269i	$-0.455558\pi$
$727$	−9.24656e6	−	5.33850e6i	−0.648850	−	0.374614i	−0.788015	+	0.615655i	$0.788891\pi$
$728$	−667559.	+	736836.i	−0.0466833	+	0.0515279i
$729$	5.29888e6			0.369288
$730$	1.64661e6	+	1.58222e7i	0.114362	+	1.09890i
$731$	545874.	−	315160.i	0.0377832	−	0.0218141i
$732$	2.57595e7	+	2.87268e7i	1.77688	+	1.98157i
$733$	−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
$736$	−60756.1	+	1.18703e7i	−0.00413423	+	0.807734i
$737$	−4.63162e6	+	2.67407e6i	−0.314097	+	0.181344i
$738$	−6.62330e6	+	1.48353e7i	−0.447645	+	1.00266i
$739$	4.58356e6	+	2.64632e6i	0.308739	+	0.178251i	0.646362	−	0.763031i	$-0.276290\pi$
$739$	4.58356e6	+	2.64632e6i	0.308739	+	0.178251i	−0.337623	+	0.941281i	$0.609623\pi$
$740$	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	−0.726299	−	0.687379i	$-0.758761\pi$
$743$	3.49316e6	−	6.05034e6i	0.232138	−	0.402075i	0.958437	+	0.285304i	$0.0920944\pi$
$744$	4.56094e7	+	9.84107e6i	3.02080	+	0.651793i
$745$	−1.61405e6	−	2.79562e6i	−0.106543	−	0.184539i
$746$	1.91358e6	−	4.28616e6i	0.125892	−	0.281982i
$747$	2.81848e7	−	1.62725e7i	1.84805	−	1.06697i
$748$	−59863.6	−	284499.i	−0.00391209	−	0.0185920i
$749$		−	699617.i		−	0.0455676i
$750$	2.45123e7	−	1.77709e7i	1.59122	−	1.15360i
$751$	−3.02318e6	−	5.23630e6i	−0.195598	−	0.338785i	0.751499	−	0.659735i	$-0.229331\pi$
$751$	−3.02318e6	−	5.23630e6i	−0.195598	−	0.338785i	−0.947096	+	0.320950i	$0.895998\pi$
$752$	−5.99677e6	−	1.36188e7i	−0.386699	−	0.878199i
$753$			4.90975e7i			3.15553i
$754$	5.90167e6	−	4.27859e6i	0.378048	−	0.274077i
$755$	−5.28119e6	+	9.14728e6i	−0.337182	+	0.584016i
$756$	1.42869e6	−	1.28111e6i	0.0909147	−	0.0815235i
$757$	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	$0.160473\pi$
$758$	8.31484e6	+	3.71221e6i	0.525631	+	0.234671i
$759$	5.95521e6			0.375226
$760$	−1.24963e7	+	6.22191e6i	−0.784779	+	0.390742i
$761$	1.56491e7			0.979553			0.489777	−	0.871848i	$-0.337078\pi$
$761$	1.56491e7			0.979553			0.489777	+	0.871848i	$0.337078\pi$
$762$	1.14123e7	+	5.09507e6i	0.712007	+	0.317879i
$763$	−207295.	+	359045.i	−0.0128907	+	0.0223274i
$764$	739085.	−	662741.i	0.0458101	−	0.0410781i
$765$	1.22265e6	−	2.11769e6i	0.0755351	−	0.130831i
$766$	−6.95825e6	+	5.04459e6i	−0.428478	+	0.310638i
$767$		−	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	$0.647538\pi$
$770$	−152063.	+	110242.i	−0.00924264	+	0.00670072i
$771$			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	$0.497579\pi$
$774$	9.21388e6	−	2.06378e7i	0.552828	−	1.23826i
$775$	3.28453e6	+	5.68898e6i	0.196435	+	0.340236i
$776$	4.41600e6	−	2.04664e7i	0.263254	−	1.22008i
$777$	−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
$782$	−419292.	+	939156.i	−0.0245188	+	0.0549188i
$783$	−1.21840e7	+	7.03443e6i	−0.710207	+	0.410038i
$784$	−1.86417e6	+	1.70640e7i	−0.108317	+	0.991497i
$785$	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	$-0.664361\pi$
$787$	−1.71571e7			−0.987430			−0.493715	+	0.869624i	$0.664361\pi$
$788$	−1.01435e7	−	1.13120e7i	−0.581935	−	0.648971i
$789$	1.33826e7	−	7.72642e6i	0.765326	−	0.441861i
$790$	−1.67419e6	−	1.60872e7i	−0.0954414	−	0.917094i
$791$	−27801.4			−0.00157988
$792$	−7.72553e6	−	6.99917e6i	−0.437638	−	0.396491i
$793$	−3.05470e7	−	1.76363e7i	−1.72499	−	0.995923i
$794$	2.28070e7	−	1.65346e7i	1.28386	−	0.930771i
$795$	2.82223e7	+	1.62941e7i	1.58370	+	0.914352i
$796$	2.24161e7	+	7.33421e6i	1.25394	+	0.410271i
$797$			2.77536e7i			1.54765i	0.633396	+	0.773827i	$0.281660\pi$
$797$			2.77536e7i			1.54765i	−0.633396	+	0.773827i	$0.718340\pi$
$798$	−1.61122e6	−	444226.i	−0.0895667	−	0.0246943i
$799$		−	1.28931e6i		−	0.0714480i
$800$	4.18951e6	+	21443.2i	0.231440	+	0.00118458i
$801$	−5.19013e7	−	2.99652e7i	−2.85823	−	1.65020i
$802$	8.80590e6	+	1.21464e7i	0.483435	+	0.666825i
$803$	5.08862e6	+	2.93792e6i	0.278491	+	0.160787i
$804$	−3.16646e7	−	3.53122e7i	−1.72756	−	1.92657i
$805$	664446.			0.0361385
$806$	−4.24248e7	+	4.41512e6i	−2.30029	+	0.239390i
$807$	−3.88499e6	+	2.24300e6i	−0.209994	+	0.121240i
$808$	6.86965e6	−	7.58256e6i	0.370174	−	0.408590i
$809$	−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	$0.120541\pi$
$811$	1.46988e7	+	2.54591e7i	0.784749	+	1.35922i	−0.144400	+	0.989519i	$0.546125\pi$
$812$	−102190.	+	312330.i	−0.00543897	+	0.0166236i
$813$	6.98988e6	−	4.03561e6i	0.370888	−	0.214133i
$814$	7.04042e6	+	3.14324e6i	0.372424	+	0.166271i
$815$	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
$820$	7.61178e6	+	2.49046e6i	0.395322	+	0.129343i
$821$	−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	$-0.387753\pi$
$822$	2.01574e7	+	8.99938e6i	1.04053	+	0.464550i
$823$	−1.90904e7	+	1.10219e7i	−0.982463	+	0.567225i	−0.903013	−	0.429614i	$-0.858650\pi$
$823$	−1.90904e7	+	1.10219e7i	−0.982463	+	0.567225i	−0.0794502	+	0.996839i	$0.525316\pi$
$824$	−1.09369e6	−	3.40154e6i	−0.0561147	−	0.174525i
$825$		−	2.10183e6i		−	0.107513i
$826$	387595.	+	534629.i	0.0197664	+	0.0272648i
$827$	−1.39128e7	−	2.40977e7i	−0.707378	−	1.22522i	−0.965826	−	0.259190i	$-0.916544\pi$
$827$	−1.39128e7	−	2.40977e7i	−0.707378	−	1.22522i	0.258448	−	0.966025i	$-0.416789\pi$
$828$	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	$0.927898\pi$
$830$	−9.41663e6	−	1.29888e7i	−0.474461	−	0.654447i
$831$	1.44612e7	−	2.50476e7i	0.726444	−	1.25824i
$832$	−1.12171e7	+	2.47832e7i	−0.561787	+	1.24122i
$833$	−743643.	+	1.28803e6i	−0.0371323	+	0.0643150i
$834$	2.09937e7	−	4.70230e7i	1.04514	−	2.34097i
$835$	9.86233e6			0.489512
$836$	−848601.	+	5.08596e6i	−0.0419940	+	0.251685i
$837$	8.23234e7			4.06171
$838$	1.44767e6	−	3.24258e6i	0.0712130	−	0.159507i
$839$	1.33580e7	−	2.31367e7i	0.655144	−	1.13474i	−0.326714	−	0.945123i	$-0.605941\pi$
$839$	1.33580e7	−	2.31367e7i	0.655144	−	1.13474i	0.981858	−	0.189619i	$-0.0607254\pi$
$840$	−1.23441e6	−	1.11835e6i	−0.0603619	−	0.0546866i
$841$	−9.05093e6	+	1.56767e7i	−0.441269	+	0.764300i
$842$	−3.97232e6	−	5.47921e6i	−0.193092	−	0.266341i
$843$		−	4.16449e7i		−	2.01833i
$844$	−1.21720e6	+	256120.i	−0.0588174	+	0.0123762i
$845$	−7.79008e6	−	1.34928e7i	−0.375318	−	0.650071i
$846$	−2.71352e7	−	3.74290e7i	−1.30349	−	1.79797i
$847$		−	996155.i		−	0.0477110i
$848$	9.66927e6	+	2.19591e7i	0.461747	+	1.04864i
$849$	5.48843e7	−	3.16875e7i	2.61324	−	1.50875i
$850$	331465.	+	147985.i	0.0157359	+	0.00702537i
$851$	−1.36381e7	−	2.36219e7i	−0.645550	−	1.11813i
$852$	−2.02782e7	+	6.19779e7i	−0.957041	+	2.92508i
$853$	−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	$0.707583\pi$
$858$	1.24619e7	+	5.56369e6i	0.577918	+	0.258015i
$859$	−2.72180e7	+	1.57143e7i	−1.25856	+	0.726629i	−0.972794	−	0.231670i	$-0.925581\pi$
$859$	−2.72180e7	+	1.57143e7i	−1.25856	+	0.726629i	−0.285765	+	0.958300i	$0.592248\pi$
$860$	−1.05890e7	−	3.46455e6i	−0.488211	−	0.159735i
$861$	479436.	+	830407.i	0.0220406	+	0.0381754i
$862$	222735.	+	2.14025e6i	0.0102099	+	0.0981062i
$863$	−2.11706e7			−0.967622			−0.483811	−	0.875172i	$-0.660748\pi$
$863$	−2.11706e7			−0.967622			−0.483811	+	0.875172i	$0.660748\pi$
$864$	2.64841e7	−	4.53344e7i	1.20698	−	2.06606i
$865$	−2.08136e7	+	1.20168e7i	−0.945819	+	0.546069i
$866$	7.83529e6	−	815414.i	0.355026	−	0.0369474i
$867$	−4.00711e7			−1.81044
$868$	1.43164e6	−	1.28376e6i	0.0644963	−	0.0578341i
$869$	−5.17387e6	−	2.98713e6i	−0.232416	−	0.134185i
$870$	7.16788e6	+	9.88701e6i	0.321065	+	0.442860i
$871$	3.75497e7	+	2.16793e7i	1.67711	+	0.968278i
$872$	−2.39248e6	+	1.10882e7i	−0.106551	+	0.493820i
$873$		−	6.50474e7i		−	2.88865i
$874$	1.29913e7	−	1.28049e7i	0.575274	−	0.567020i
$875$		−	1.24776e6i		−	0.0550947i
$876$	−1.62042e7	+	4.95263e7i	−0.713458	+	2.18060i
$877$	−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	$0.769894\pi$
$878$	−8.38530e6	+	6.07917e6i	−0.367098	+	0.266139i
$879$	−3.19367e7	−	1.84386e7i	−1.39418	−	0.804928i
$880$	−3.03753e6	+	4.14500e6i	−0.132225	+	0.180434i
$881$	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	−0.438078	−	0.898937i	$-0.644341\pi$
$883$	2.81232e6	−	1.62369e6i	0.121384	−	0.0700813i	0.559463	+	0.828855i	$0.311007\pi$
$884$	−1.75482e6	+	1.57356e6i	−0.0755271	+	0.0677255i
$885$	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	$-0.992238\pi$
$887$	−1.22073e7	−	2.11437e7i	−0.520968	−	0.902342i	0.478735	−	0.877959i	$-0.341095\pi$
$888$	−1.44219e7	+	6.68398e7i	−0.613749	+	2.84448i
$889$	446063.	−	257535.i	0.0189296	−	0.0109290i
$890$	−1.20438e7	+	2.69764e7i	−0.509669	+	1.14159i
$891$	−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
$896$	−246378.	−	1.20138e6i	−0.0102525	−	0.0499933i
$897$	−2.41401e7	−	4.18120e7i	−1.00175	−	1.73508i
$898$	3.62010e6	−	8.10853e6i	0.149806	−	0.335545i
$899$	−1.22091e7	+	7.04895e6i	−0.503832	+	0.290888i
$900$	1.27371e7	−	2.68010e6i	0.524159	−	0.110292i
$901$			2.07890e6i			0.0853142i
$902$	2.39504e6	−	1.73636e6i	0.0980161	−	0.0710596i
$903$	−666958.	−	1.15521e6i	−0.0272194	−	0.0471455i
$904$	−724146.	+	232833.i	−0.0294717	+	0.00947597i
$905$			8.61810e6i			0.349776i
$906$	−2.80127e7	+	2.03086e7i	−1.13379	+	0.821978i
$907$	−4.48615e6	+	7.77024e6i	−0.181074	+	0.313629i	−0.942246	−	0.334920i	$-0.891291\pi$
$907$	−4.48615e6	+	7.77024e6i	−0.181074	+	0.313629i	0.761173	+	0.648549i	$0.224624\pi$
$908$	−2.23957e7	−	2.49756e7i	−0.901467	−	1.00531i
$909$	1.58937e7	−	2.75287e7i	0.637991	−	1.10503i
$910$	1.39042e6	+	620763.i	0.0556601	+	0.0248498i
$911$	−972973.			−0.0388423			−0.0194211	−	0.999811i	$-0.506182\pi$
$911$	−972973.			−0.0388423			−0.0194211	+	0.999811i	$0.506182\pi$
$912$	−4.56879e7	+	1.92293e6i	−1.81892	+	0.0765555i
$913$	−5.92588e6			−0.235275
$914$	4.39873e6	+	1.96384e6i	0.174165	+	0.0777571i
$915$	2.95460e7	−	5.11751e7i	1.16666	−	2.02072i
$916$	2.31617e7	+	2.58298e7i	0.912078	+	1.01715i
$917$	−1.20190e6	+	2.08174e6i	−0.0472002	+	0.0817531i
$918$	3.68303e6	−	2.67012e6i	0.144244	−	0.104574i
$919$			1.66882e7i			0.651809i	0.945403	+	0.325905i	$0.105669\pi$
$919$			1.66882e7i			0.651809i	−0.945403	+	0.325905i	$0.894331\pi$
$920$	1.73069e7	−	5.56465e6i	0.674139	−	0.216755i
$921$	3.05732e7	+	5.29543e7i	1.18766	+	2.05708i
$922$	4.06471e6	−	2.94684e6i	0.157472	−	0.114164i
$923$		−	5.96133e7i		−	2.30324i
$924$	−602072.	+	126686.i	−0.0231989	+	0.00488147i
$925$	−8.33710e6	+	4.81343e6i	−0.320376	+	0.184969i
$926$	−1.93110e7	+	4.32541e7i	−0.740080	+	1.65768i
$927$	−5.55030e6	−	9.61340e6i	−0.212137	−	0.367433i
$928$	−46019.4	+	8.99113e6i	−0.00175417	+	0.342724i
$929$	−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
$934$	1.58839e7	−	3.55778e7i	0.595786	−	1.33448i
$935$	−385596.	+	222624.i	−0.0144246	+	0.00832804i
$936$	−1.78254e7	+	8.26135e7i	−0.665042	+	3.08220i
$937$	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
$940$	−1.69670e7	+	1.52144e7i	−0.626305	+	0.561610i
$941$	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
$944$	1.45732e7	+	1.06795e7i	0.532261	+	0.390050i
$945$	−2.54513e6	−	1.46943e6i	−0.0927108	−	0.0535266i
$946$	−3.33182e6	+	2.41550e6i	−0.121047	+	0.0877566i
$947$	2.07481e7	+	1.19789e7i	0.751800	+	0.434052i	0.826344	−	0.563166i	$-0.190417\pi$
$947$	2.07481e7	+	1.19789e7i	0.751800	+	0.434052i	−0.0745437	+	0.997218i	$0.523750\pi$
$948$	1.64757e7	−	5.03559e7i	0.595419	−	1.81983i
$949$		−	4.76368e7i		−	1.71703i
$950$	−4.51937e6	−	4.58515e6i	−0.162468	−	0.164833i
$951$		−	8.78218e6i		−	0.314884i
$952$	22411.5	−	103868.i	0.000801454	−	0.00371442i
$953$	−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	$0.930639\pi$
$954$	4.37532e7	+	6.03510e7i	1.55647	+	2.14691i
$955$	−1.31664e6	−	760160.i	−0.0467151	−	0.0269710i
$956$	7.69655e6	−	6.90153e6i	0.272365	−	0.244231i
$957$	4.51074e6			0.159209
$958$	6.38125e6	−	664093.i	0.224643	−	0.0233784i
$959$	787878.	−	454882.i	0.0276638	−	0.0159717i
$960$	−4.15190e7	−	1.87919e7i	−1.45402	−	0.658099i
$961$	5.38642e7			1.88145
$962$	−6.47029e6	−	6.21728e7i	−0.225417	−	2.16602i
$963$	−2.97345e7	−	5.15016e7i	−1.03322	−	1.78960i
$964$	−2.53716e7	−	8.30121e6i	−0.879338	−	0.287706i
$965$	1.07570e6	−	621054.i	0.0371853	−	0.0214690i
$966$	1.98749e6	+	887326.i	0.0685270	+	0.0305943i
$967$	2.63851e7	+	1.52335e7i	0.907388	+	0.523881i	0.879590	−	0.475733i	$-0.157817\pi$
$967$	2.63851e7	+	1.52335e7i	0.907388	+	0.523881i	0.0277981	+	0.999614i	$0.491150\pi$
$968$	−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	−0.993178	−	0.116612i	$-0.962797\pi$
$971$	−1.16226e7	+	2.01310e7i	−0.395600	+	0.685199i	0.597578	+	0.801811i	$0.296130\pi$
$972$	1.21309e7	−	3.70765e7i	0.411838	−	1.25873i
$973$	−1.06114e6	−	1.83796e6i	−0.0359329	−	0.0622376i
$974$	−3.64149e7	−	1.62576e7i	−1.22993	−	0.549111i
$975$	−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	$0.904949\pi$
$978$	1.59726e6	+	2.20318e6i	0.0533985	+	0.0736551i
$979$	5.45615e6	+	9.45033e6i	0.181941	+	0.315130i
$980$	2.57255e7	−	5.41309e6i	0.855653	−	0.180045i
$981$			3.52410e7i			1.16917i
$982$	−8.31977e6	−	1.14759e7i	−0.275317	−	0.379758i
$983$	−1.16265e7	+	2.01377e7i	−0.383764	+	0.664699i	−0.991597	−	0.129366i	$-0.958706\pi$
$983$	−1.16265e7	+	2.01377e7i	−0.383764	+	0.664699i	0.607833	+	0.794065i	$0.292039\pi$
$984$	1.94425e7	+	1.76145e7i	0.640124	+	0.579939i
$985$	−1.16346e7	+	2.01517e7i	−0.382086	+	0.661792i
$986$	−317590.	+	711359.i	−0.0104034	+	0.0233022i
$987$	−2.72850e6			−0.0891520
$988$	3.91488e7	−	1.46585e7i	1.27593	−	0.477745i
$989$	1.45586e7			0.473291
$990$	−6.50853e6	+	1.45782e7i	−0.211055	+	0.472733i
$991$	−1.64931e7	+	2.85668e7i	−0.533479	+	0.924013i	0.465756	+	0.884913i	$0.345782\pi$
$991$	−1.64931e7	+	2.85668e7i	−0.533479	+	0.924013i	−0.999235	+	0.0390997i	$0.987551\pi$
$992$	2.65388e7	−	4.54280e7i	0.856254	−	1.46570i
$993$	−2.66361e7	+	4.61351e7i	−0.857231	+	1.48477i
$994$	1.57744e6	+	2.17584e6i	0.0506392	+	0.0698491i
$995$		−	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	$0.927888\pi$
$998$	1.86488e7	+	2.57233e7i	0.592687	+	0.817523i
$999$			1.20643e8i			3.82463i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-5.16544 - 2.30614i) q^{2} +(-14.1896 + 24.5772i) q^{3} +(21.3634 + 23.8244i) q^{4} +(24.5038 - 42.4418i) q^{5} +(129.974 - 94.2285i) q^{6} -6.61611i q^{7} +(-55.4091 - 172.331i) q^{8} +(-281.192 - 487.038i) q^{9} +O(q^{10})\)	\(q+(-5.16544 - 2.30614i) q^{2} +(-14.1896 + 24.5772i) q^{3} +(21.3634 + 23.8244i) q^{4} +(24.5038 - 42.4418i) q^{5} +(129.974 - 94.2285i) q^{6} -6.61611i q^{7} +(-55.4091 - 172.331i) q^{8} +(-281.192 - 487.038i) q^{9} +(-224.449 + 162.721i) q^{10} +102.400i q^{11} +(-888.677 + 186.993i) q^{12} +(718.961 - 415.092i) q^{13} +(-15.2577 + 34.1751i) q^{14} +(695.399 + 1204.47i) q^{15} +(-111.206 + 1017.94i) 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} +(236.150 - 528.943i) q^{22} +(-1774.70 + 1024.62i) q^{23} +(5021.63 + 1083.51i) q^{24} +(361.630 + 626.361i) q^{25} +(-4671.01 + 486.109i) q^{26} +9063.87 q^{27} +(157.625 - 141.343i) q^{28} +(-1344.24 + 776.096i) q^{29} +(-814.373 - 7825.29i) q^{30} +9082.58 q^{31} +(2921.95 - 5001.67i) q^{32} +(-2516.71 - 1453.02i) q^{33} +(406.342 - 294.590i) q^{34} +(-280.799 - 162.120i) q^{35} +(5596.18 - 17104.0i) q^{36} +13310.4i q^{37} +(-8614.53 + 2241.67i) q^{38} +23560.0i q^{39} +(-8671.75 - 1871.09i) q^{40} +(4422.70 + 2553.45i) q^{41} +(-623.426 - 859.922i) q^{42} +(-6152.55 - 3552.18i) q^{43} +(-2439.63 + 2187.63i) q^{44} -27561.0 q^{45} +(11530.0 - 1199.92i) q^{46} +(-12584.9 + 7265.91i) q^{47} +(-23440.2 - 17177.4i) q^{48} +16763.2 q^{49} +(-423.500 - 4069.40i) q^{50} +(-1258.95 - 2180.56i) q^{51} +(25248.8 + 8261.02i) q^{52} +(20292.1 - 11715.7i) q^{53} +(-46818.8 - 20902.5i) 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} +(-13839.6 + 42299.1i) q^{60} +(-21243.9 - 36795.5i) q^{61} +(-46915.5 - 20945.7i) q^{62} +(-3222.30 + 1860.39i) q^{63} +(-26627.7 + 19097.4i) q^{64} -40685.3i q^{65} +(9649.04 + 13309.4i) q^{66} +(26113.8 + 45230.5i) q^{67} +(-2778.30 + 584.604i) q^{68} -58156.1i q^{69} +(1076.58 + 1484.98i) q^{70} +(35903.7 - 62187.0i) q^{71} +(-68351.0 + 75444.3i) q^{72} +(28690.5 - 49693.4i) q^{73} +(30695.6 - 68753.8i) q^{74} -20525.6 q^{75} +(49667.4 + 8287.08i) q^{76} +677.492 q^{77} +(54332.7 - 121698. i) q^{78} +(-29171.1 + 50525.8i) q^{79} +(40478.4 + 29663.3i) q^{80} +(-60283.4 + 104414. i) q^{81} +(-16956.6 - 23389.0i) q^{82} +57869.7i q^{83} +(1237.17 + 5879.58i) q^{84} +(2174.05 + 3765.57i) q^{85} +(23588.8 + 32537.2i) q^{86} -44050.1i q^{87} +(17646.7 - 5673.91i) q^{88} +(92288.0 - 53282.5i) q^{89} +(142365. + 63559.6i) q^{90} +(-2746.30 - 4756.72i) q^{91} +(-62324.7 - 20391.7i) 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} +(-86589.4 - 38658.3i) 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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more