LMFDB - Embedded newform 76.6.f.a.31.18

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			31.18
Character	$\chi$	$=$	76.31
Dual form			76.6.f.a.27.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.50677 + 5.07111i) q^{2} +(-2.01363 - 3.48771i) q^{3} +(-19.4322 - 25.4242i) q^{4} +(54.6845 + 94.7163i) q^{5} +(22.7343 - 1.46846i) q^{6} -177.092i q^{7} +(177.641 - 34.8105i) q^{8} +(113.391 - 196.398i) q^{9} +O(q^{10})$	\(q+(-2.50677 + 5.07111i) q^{2} +(-2.01363 - 3.48771i) q^{3} +(-19.4322 - 25.4242i) q^{4} +(54.6845 + 94.7163i) q^{5} +(22.7343 - 1.46846i) q^{6} -177.092i q^{7} +(177.641 - 34.8105i) q^{8} +(113.391 - 196.398i) q^{9} +(-617.397 + 39.8792i) q^{10} +61.3620i q^{11} +(-49.5428 + 118.969i) q^{12} +(252.490 + 145.775i) q^{13} +(898.054 + 443.929i) q^{14} +(220.229 - 381.447i) q^{15} +(-268.776 + 988.097i) q^{16} +(269.971 + 467.603i) q^{17} +(711.713 + 1067.34i) q^{18} +(1472.04 + 556.059i) q^{19} +(1345.44 - 3230.86i) q^{20} +(-617.647 + 356.598i) q^{21} +(-311.173 - 153.820i) q^{22} +(2540.20 + 1466.59i) q^{23} +(-479.112 - 549.464i) q^{24} +(-4418.28 + 7652.69i) q^{25} +(-1372.18 + 914.980i) q^{26} -1891.93 q^{27} +(-4502.42 + 3441.30i) q^{28} +(3743.38 + 2161.24i) q^{29} +(1382.30 + 2073.00i) q^{30} -5976.45 q^{31} +(-4336.99 - 3839.92i) q^{32} +(214.013 - 123.560i) q^{33} +(-3048.02 + 196.879i) q^{34} +(16773.5 - 9684.20i) q^{35} +(-7196.69 + 933.598i) q^{36} +2104.57i q^{37} +(-6509.89 + 6070.95i) q^{38} -1174.15i q^{39} +(13011.3 + 14921.9i) q^{40} +(8334.82 - 4812.11i) q^{41} +(-260.053 - 4026.06i) q^{42} +(16202.5 - 9354.53i) q^{43} +(1560.08 - 1192.40i) q^{44} +24802.8 q^{45} +(-13804.9 + 9205.25i) q^{46} +(-1389.93 - 802.479i) q^{47} +(3987.41 - 1052.25i) q^{48} -14554.7 q^{49} +(-27732.0 - 41589.1i) q^{50} +(1087.24 - 1883.16i) q^{51} +(-1200.24 - 9252.09i) q^{52} +(-17327.4 - 10004.0i) q^{53} +(4742.63 - 9594.19i) q^{54} +(-5811.98 + 3355.55i) q^{55} +(-6164.68 - 31458.8i) q^{56} +(-1024.77 - 6253.74i) q^{57} +(-20343.6 + 13565.3i) q^{58} +(17573.1 + 30437.5i) q^{59} +(-13977.5 + 1813.25i) q^{60} +(6467.16 - 11201.4i) q^{61} +(14981.6 - 30307.2i) q^{62} +(-34780.6 - 20080.6i) q^{63} +(30344.5 - 12367.5i) q^{64} +31886.6i q^{65} +(90.1076 + 1395.02i) q^{66} +(2566.32 - 4445.01i) q^{67} +(6642.28 - 15950.4i) q^{68} -11812.7i q^{69} +(7062.29 + 109336. i) q^{70} +(19654.5 + 34042.5i) q^{71} +(13306.1 - 38835.5i) q^{72} +(25575.8 + 44298.5i) q^{73} +(-10672.5 - 5275.68i) q^{74} +35587.1 q^{75} +(-14467.7 - 48230.8i) q^{76} +10866.7 q^{77} +(5954.24 + 2943.32i) q^{78} +(-43513.7 - 75368.0i) q^{79} +(-108287. + 28576.1i) q^{80} +(-23744.3 - 41126.3i) q^{81} +(3509.28 + 54329.6i) q^{82} -32951.6i q^{83} +(21068.5 + 8773.64i) q^{84} +(-29526.4 + 51141.3i) q^{85} +(6821.88 + 105614. i) q^{86} -17407.8i q^{87} +(2136.04 + 10900.4i) q^{88} +(-41492.7 - 23955.8i) q^{89} +(-62174.9 + 125778. i) q^{90} +(25815.7 - 44714.0i) q^{91} +(-12075.1 - 93081.6i) q^{92} +(12034.4 + 20844.1i) q^{93} +(7553.70 - 5036.88i) q^{94} +(27829.8 + 169834. i) q^{95} +(-4659.44 + 22858.3i) q^{96} +(77714.5 - 44868.5i) q^{97} +(36485.2 - 73808.3i) q^{98} +(12051.4 + 6957.88i) 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 $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−2.50677	+	5.07111i	−0.443138	+	0.896453i
$2$	−2.50677	+	5.07111i	−0.443138	+	0.896453i
$3$	−2.01363	−	3.48771i	−0.129174	−	0.223737i	0.794183	−	0.607679i	$-0.207899\pi$
$3$	−2.01363	−	3.48771i	−0.129174	−	0.223737i	−0.923357	+	0.383943i	$0.874566\pi$
$4$	−19.4322	−	25.4242i	−0.607258	−	0.794505i
$5$	54.6845	+	94.7163i	0.978225	+	1.69434i	0.668852	+	0.743395i	$0.266786\pi$
$5$	54.6845	+	94.7163i	0.978225	+	1.69434i	0.309373	+	0.950941i	$0.399881\pi$
$6$	22.7343	−	1.46846i	0.257812	−	0.0166527i
$7$		−	177.092i		−	1.36601i	−0.730413	−	0.683006i	$-0.760672\pi$
$7$		−	177.092i		−	1.36601i	0.730413	−	0.683006i	$-0.239328\pi$
$8$	177.641	−	34.8105i	0.981336	−	0.192303i
$9$	113.391	−	196.398i	0.466628	−	0.808223i
$10$	−617.397	+	39.8792i	−1.95238	+	0.126109i
$11$			61.3620i			0.152904i	0.997073	+	0.0764518i	$0.0243591\pi$
$11$			61.3620i			0.152904i	−0.997073	+	0.0764518i	$0.975641\pi$
$12$	−49.5428	+	118.969i	−0.0993178	+	0.238496i
$13$	252.490	+	145.775i	0.414368	+	0.239235i	0.692665	−	0.721260i	$-0.256437\pi$
$13$	252.490	+	145.775i	0.414368	+	0.239235i	−0.278297	+	0.960495i	$0.589770\pi$
$14$	898.054	+	443.929i	1.22457	+	0.605332i
$15$	220.229	−	381.447i	0.252723	−	0.437730i
$16$	−268.776	+	988.097i	−0.262476	+	0.964938i
$17$	269.971	+	467.603i	0.226566	+	0.392424i	0.956788	−	0.290786i	$-0.0939168\pi$
$17$	269.971	+	467.603i	0.226566	+	0.392424i	−0.730222	+	0.683210i	$0.760583\pi$
$18$	711.713	+	1067.34i	0.517754	+	0.776465i
$19$	1472.04	+	556.059i	0.935481	+	0.353376i
$19$	1472.04	+	556.059i	0.935481	+	0.353376i
$20$	1345.44	−	3230.86i	0.752124	−	1.80610i
$21$	−617.647	+	356.598i	−0.305627	+	0.176454i
$22$	−311.173	−	153.820i	−0.137071	−	0.0677574i
$23$	2540.20	+	1466.59i	1.00126	+	0.578080i	0.908622	−	0.417619i	$-0.137135\pi$
$23$	2540.20	+	1466.59i	1.00126	+	0.578080i	0.0926422	+	0.995699i	$0.470469\pi$
$24$	−479.112	−	549.464i	−0.169789	−	0.194720i
$25$	−4418.28	+	7652.69i	−1.41385	+	2.44886i
$26$	−1372.18	+	914.980i	−0.398085	+	0.265447i
$27$	−1891.93			−0.499455
$28$	−4502.42	+	3441.30i	−1.08530	+	0.829521i
$29$	3743.38	+	2161.24i	0.826549	+	0.477208i	0.852670	−	0.522451i	$-0.174982\pi$
$29$	3743.38	+	2161.24i	0.826549	+	0.477208i	−0.0261207	+	0.999659i	$0.508315\pi$
$30$	1382.30	+	2073.00i	0.280413	+	0.420530i
$31$	−5976.45			−1.11696			−0.558482	−	0.829516i	$-0.688616\pi$
$31$	−5976.45			−1.11696			−0.558482	+	0.829516i	$0.688616\pi$
$32$	−4336.99	−	3839.92i	−0.748709	−	0.662899i
$33$	214.013	−	123.560i	0.0342102	−	0.0197513i
$34$	−3048.02	+	196.879i	−0.452190	+	0.0292080i
$35$	16773.5	−	9684.20i	2.31448	−	1.33627i
$36$	−7196.69	+	933.598i	−0.925501	+	0.120061i
$37$			2104.57i			0.252732i	0.991984	+	0.126366i	$0.0403313\pi$
$37$			2104.57i			0.252732i	−0.991984	+	0.126366i	$0.959669\pi$
$38$	−6509.89	+	6070.95i	−0.731332	+	0.682021i
$39$		−	1174.15i		−	0.123612i
$40$	13011.3	+	14921.9i	1.28579	+	1.47460i
$41$	8334.82	−	4812.11i	0.774349	−	0.447071i	−0.0600749	−	0.998194i	$-0.519134\pi$
$41$	8334.82	−	4812.11i	0.774349	−	0.447071i	0.834424	+	0.551123i	$0.185801\pi$
$42$	−260.053	−	4026.06i	−0.0227477	−	0.352174i
$43$	16202.5	−	9354.53i	1.33632	−	0.771526i	0.350063	−	0.936726i	$-0.386160\pi$
$43$	16202.5	−	9354.53i	1.33632	−	0.771526i	0.986260	+	0.165200i	$0.0528269\pi$
$44$	1560.08	−	1192.40i	0.121483	−	0.0928519i
$45$	24802.8			1.82587
$46$	−13804.9	+	9205.25i	−0.961920	+	0.641418i
$47$	−1389.93	−	802.479i	−0.0917804	−	0.0529894i	0.453407	−	0.891303i	$-0.350208\pi$
$47$	−1389.93	−	802.479i	−0.0917804	−	0.0529894i	−0.545188	+	0.838314i	$0.683542\pi$
$48$	3987.41	−	1052.25i	0.249797	−	0.0659198i
$49$	−14554.7			−0.865989
$50$	−27732.0	−	41589.1i	−1.56876	−	2.35263i
$51$	1087.24	−	1883.16i	0.0585331	−	0.101382i
$52$	−1200.24	−	9252.09i	−0.0615543	−	0.474495i
$53$	−17327.4	−	10004.0i	−0.847312	−	0.489196i	0.0124308	−	0.999923i	$-0.496043\pi$
$53$	−17327.4	−	10004.0i	−0.847312	−	0.489196i	−0.859743	+	0.510727i	$0.829376\pi$
$54$	4742.63	−	9594.19i	0.221327	−	0.447738i
$55$	−5811.98	+	3355.55i	−0.259070	+	0.149574i
$56$	−6164.68	−	31458.8i	−0.262688	−	1.34052i
$57$	−1024.77	−	6253.74i	−0.0417771	−	0.254949i
$58$	−20343.6	+	13565.3i	−0.794070	+	0.529494i
$59$	17573.1	+	30437.5i	0.657230	+	1.13836i	0.981330	+	0.192333i	$0.0616055\pi$
$59$	17573.1	+	30437.5i	0.657230	+	1.13836i	−0.324099	+	0.946023i	$0.605061\pi$
$60$	−13977.5	+	1813.25i	−0.501247	+	0.0650247i
$61$	6467.16	−	11201.4i	0.222530	−	0.385433i	−0.733045	−	0.680180i	$-0.761902\pi$
$61$	6467.16	−	11201.4i	0.222530	−	0.385433i	0.955576	+	0.294746i	$0.0952351\pi$
$62$	14981.6	−	30307.2i	0.494969	−	1.00131i
$63$	−34780.6	−	20080.6i	−1.10404	−	0.637419i
$64$	30344.5	−	12367.5i	0.926039	−	0.377427i
$65$			31886.6i			0.936104i
$66$	90.1076	+	1395.02i	0.00254625	+	0.0394204i
$67$	2566.32	−	4445.01i	0.0698433	−	0.120972i	−0.828989	−	0.559265i	$-0.811083\pi$
$67$	2566.32	−	4445.01i	0.0698433	−	0.120972i	0.898832	+	0.438293i	$0.144417\pi$
$68$	6642.28	−	15950.4i	0.174199	−	0.418310i
$69$		−	11812.7i		−	0.298693i
$70$	7062.29	+	109336.i	0.172266	+	2.66698i
$71$	19654.5	+	34042.5i	0.462717	+	0.801449i	0.999095	−	0.0425285i	$-0.0135413\pi$
$71$	19654.5	+	34042.5i	0.462717	+	0.801449i	−0.536378	+	0.843978i	$0.680208\pi$
$72$	13306.1	−	38835.5i	0.302495	−	0.882872i
$73$	25575.8	+	44298.5i	0.561722	+	0.972931i	0.997346	+	0.0728028i	$0.0231944\pi$
$73$	25575.8	+	44298.5i	0.561722	+	0.972931i	−0.435624	+	0.900129i	$0.643472\pi$
$74$	−10672.5	−	5275.68i	−0.226562	−	0.111995i
$75$	35587.1			0.730533
$76$	−14467.7	−	48230.8i	−0.287319	−	0.957835i
$77$	10866.7			0.208868
$78$	5954.24	+	2943.32i	0.110813	+	0.0547773i
$79$	−43513.7	−	75368.0i	−0.784438	−	1.35869i	−0.929334	−	0.369240i	$-0.879618\pi$
$79$	−43513.7	−	75368.0i	−0.784438	−	1.35869i	0.144896	−	0.989447i	$-0.453715\pi$
$80$	−108287.	+	28576.1i	−1.89169	+	0.499204i
$81$	−23744.3	−	41126.3i	−0.402111	−	0.696477i
$82$	3509.28	+	54329.6i	0.0576346	+	0.892282i
$83$		−	32951.6i		−	0.525026i	−0.964928	−	0.262513i	$-0.915449\pi$
$83$		−	32951.6i		−	0.525026i	0.964928	−	0.262513i	$-0.0845513\pi$
$84$	21068.5	+	8773.64i	0.325788	+	0.135669i
$85$	−29526.4	+	51141.3i	−0.443265	+	0.767758i
$86$	6821.88	+	105614.i	0.0994621	+	1.53984i
$87$		−	17407.8i		−	0.246572i
$88$	2136.04	+	10900.4i	0.0294038	+	0.150050i
$89$	−41492.7	−	23955.8i	−0.555261	−	0.320580i	0.195980	−	0.980608i	$-0.437211\pi$
$89$	−41492.7	−	23955.8i	−0.555261	−	0.320580i	−0.751241	+	0.660028i	$0.770544\pi$
$90$	−62174.9	+	125778.i	−0.809112	+	1.63681i
$91$	25815.7	−	44714.0i	0.326798	−	0.566031i
$92$	−12075.1	−	93081.6i	−0.148738	−	1.14655i
$93$	12034.4	+	20844.1i	0.144283	+	0.249906i
$94$	7553.70	−	5036.88i	0.0881739	−	0.0587952i
$95$	27829.8	+	169834.i	0.316374	+	1.93070i
$96$	−4659.44	+	22858.3i	−0.0516007	+	0.253143i
$97$	77714.5	−	44868.5i	0.838635	−	0.484186i	−0.0181653	−	0.999835i	$-0.505783\pi$
$97$	77714.5	−	44868.5i	0.838635	−	0.484186i	0.856800	+	0.515649i	$0.172449\pi$
$98$	36485.2	−	73808.3i	0.383753	−	0.776319i
$99$	12051.4	+	6957.88i	0.123580	+	0.0713491i
$100$	280420.	−	36377.8i	2.80420	−	0.363778i
$101$	−16924.1	+	29313.3i	−0.165083	+	0.285931i	−0.936685	−	0.350174i	$-0.886122\pi$
$101$	−16924.1	+	29313.3i	−0.165083	+	0.285931i	0.771602	+	0.636106i	$0.219456\pi$
$102$	6824.24	+	10234.2i	0.0649462	+	0.0973985i
$103$	−207497.			−1.92716			−0.963581	−	0.267417i	$-0.913830\pi$
$103$	−207497.			−1.92716			−0.963581	+	0.267417i	$0.913830\pi$
$104$	49927.0	+	17106.3i	0.452639	+	0.155086i
$105$	−67551.4	−	39000.8i	−0.597944	−	0.345223i
$106$	94166.9	−	62791.4i	0.814018	−	0.542795i
$107$	−23059.0			−0.194706			−0.0973532	−	0.995250i	$-0.531038\pi$
$107$	−23059.0			−0.194706			−0.0973532	+	0.995250i	$0.531038\pi$
$108$	36764.5	+	48100.8i	0.303298	+	0.396819i
$109$	70405.5	−	40648.6i	0.567597	−	0.327702i	−0.188592	−	0.982056i	$-0.560392\pi$
$109$	70405.5	−	40648.6i	0.567597	−	0.327702i	0.756189	+	0.654353i	$0.227059\pi$
$110$	−2447.07	−	37884.8i	−0.0192825	−	0.298526i
$111$	7340.15	−	4237.84i	0.0565454	−	0.0326465i
$112$	174984.	+	47598.1i	1.31812	+	0.358546i
$113$			64217.9i			0.473107i	0.971618	+	0.236554i	$0.0760179\pi$
$113$			64217.9i			0.473107i	−0.971618	+	0.236554i	$0.923982\pi$
$114$	34282.2	+	10480.0i	0.247063	+	0.0755262i
$115$			320798.i			2.26197i
$116$	−17794.5	−	137170.i	−0.122784	−	0.946486i
$117$	57260.0	−	33059.1i	0.386711	−	0.223268i
$118$	−198403.	+	12815.3i	−1.31173	+	0.0847276i
$119$	82808.9	−	47809.8i	0.536056	−	0.309492i
$120$	25843.2	−	75426.8i	0.163830	−	0.478159i
$121$	157286.			0.976620
$122$	40592.1	+	60875.0i	0.246912	+	0.370288i
$123$	−33566.5	−	19379.6i	−0.200052	−	0.115500i
$124$	116136.	+	151946.i	0.678285	+	0.887434i
$125$	−624667.			−3.57580
$126$	189018.	−	126039.i	1.06066	−	0.707258i
$127$	−10299.4	+	17839.1i	−0.0566636	+	0.0981442i	−0.892966	−	0.450125i	$-0.851380\pi$
$127$	−10299.4	+	17839.1i	−0.0566636	+	0.0981442i	0.836302	+	0.548269i	$0.184713\pi$
$128$	−13349.4	+	184882.i	−0.0720171	+	0.997403i
$129$	−65251.8	−	37673.1i	−0.345238	−	0.199323i
$130$	−161700.	−	79932.1i	−0.839174	−	0.414823i
$131$	−62079.5	+	35841.6i	−0.316060	+	0.182477i	−0.649635	−	0.760246i	$-0.725078\pi$
$131$	−62079.5	+	35841.6i	−0.316060	+	0.182477i	0.333575	+	0.942724i	$0.391745\pi$
$132$	−7300.17	−	3040.04i	−0.0364669	−	0.0151861i
$133$	98473.8	−	260687.i	0.482716	−	1.27788i
$134$	16107.9	+	24156.7i	0.0774957	+	0.116219i
$135$	−103459.	−	179197.i	−0.488579	−	0.846244i
$136$	64235.3	+	73667.6i	0.297801	+	0.341530i
$137$	164184.	−	284376.i	0.747361	−	1.29447i	−0.201722	−	0.979443i	$-0.564654\pi$
$137$	164184.	−	284376.i	0.747361	−	1.29447i	0.949083	−	0.315025i	$-0.102013\pi$
$138$	59903.2	+	29611.6i	0.267764	+	0.132362i
$139$	−288464.	−	166545.i	−1.26635	−	0.731129i	−0.292056	−	0.956401i	$-0.594339\pi$
$139$	−288464.	−	166545.i	−1.26635	−	0.731129i	−0.974296	+	0.225272i	$0.927673\pi$
$140$	−572160.	−	238267.i	−2.46716	−	1.02741i
$141$			6463.59i			0.0273795i
$142$	−221902.	+	14333.2i	−0.923509	+	0.0596516i
$143$	−8945.06	+	15493.3i	−0.0365800	+	0.0633583i
$144$	163584.	+	164828.i	0.657407	+	0.662407i
$145$			472745.i			1.86727i
$146$	−288755.	+	18651.4i	−1.12111	+	0.0724150i
$147$	29307.8	+	50762.5i	0.111864	+	0.193754i
$148$	53507.0	−	40896.6i	0.200797	−	0.153473i
$149$	−1980.69	−	3430.66i	−0.00730890	−	0.0126594i	0.862348	−	0.506316i	$-0.168993\pi$
$149$	−1980.69	−	3430.66i	−0.00730890	−	0.0126594i	−0.869657	+	0.493657i	$0.835660\pi$
$150$	−89208.7	+	180466.i	−0.323727	+	0.654889i
$151$	275213.			0.982260			0.491130	−	0.871086i	$-0.336584\pi$
$151$	275213.			0.982260			0.491130	+	0.871086i	$0.336584\pi$
$152$	280851.	+	47536.3i	0.985976	+	0.166885i
$153$	122449.			0.422888
$154$	−27240.4	+	55106.4i	−0.0925575	+	0.187241i
$155$	−326819.	−	566067.i	−1.09264	−	1.89251i
$156$	−29851.8	+	22816.4i	−0.0982107	+	0.0750646i
$157$	206589.	+	357822.i	0.668894	+	1.15856i	0.978214	+	0.207600i	$0.0665654\pi$
$157$	206589.	+	357822.i	0.668894	+	1.15856i	−0.309320	+	0.950958i	$0.600101\pi$
$158$	491278.	−	31732.8i	1.56561	−	0.101127i
$159$			80577.2i			0.252767i
$160$	126537.	−	620767.i	0.390767	−	1.91703i
$161$	259721.	−	449850.i	0.789665	−	1.36774i
$162$	268077.	−	17315.7i	0.802550	−	0.0518386i
$163$			58659.1i			0.172928i	0.996255	+	0.0864642i	$0.0275568\pi$
$163$			58659.1i			0.172928i	−0.996255	+	0.0864642i	$0.972443\pi$
$164$	−284308.	−	118396.i	−0.825429	−	0.343737i
$165$	23406.4	+	13513.7i	0.0669305	+	0.0386424i
$166$	167101.	+	82601.9i	0.470662	+	0.232659i
$167$	−296161.	+	512966.i	−0.821744	+	1.42330i	0.0826383	+	0.996580i	$0.473665\pi$
$167$	−296161.	+	512966.i	−0.821744	+	1.42330i	−0.904382	+	0.426723i	$0.859668\pi$
$168$	−97305.8	+	84847.0i	−0.265990	+	0.231933i
$169$	−143146.	−	247936.i	−0.385533	−	0.667763i
$170$	−185327.	−	277931.i	−0.491831	−	0.737589i
$171$	276124.	−	226054.i	0.722128	−	0.591183i
$172$	−552682.	−	230156.i	−1.42447	−	0.593200i
$173$	−39293.7	+	22686.2i	−0.0998176	+	0.0576297i	−0.549078	−	0.835771i	$-0.685021\pi$
$173$	−39293.7	+	22686.2i	−0.0998176	+	0.0576297i	0.449260	+	0.893401i	$0.351688\pi$
$174$	88276.6	+	43637.2i	0.221041	+	0.109266i
$175$	1.35523e6	+	782444.i	3.34517	+	1.93134i
$176$	−60631.6	−	16492.6i	−0.147543	−	0.0401336i
$177$	70771.4	−	122580.i	0.169795	−	0.294093i
$178$	225495.	−	150362.i	0.533442	−	0.355704i
$179$	−345370.			−0.805660			−0.402830	−	0.915275i	$-0.631973\pi$
$179$	−345370.			−0.805660			−0.402830	+	0.915275i	$0.631973\pi$
$180$	−481974.	−	630591.i	−1.10877	−	1.45066i
$181$	−553203.	−	319392.i	−1.25513	−	0.724648i	−0.283004	−	0.959119i	$-0.591331\pi$
$181$	−553203.	−	319392.i	−1.25513	−	0.724648i	−0.972123	+	0.234470i	$0.924664\pi$
$182$	162036.	+	243002.i	0.362604	+	0.543789i
$183$	−52089.9			−0.114981
$184$	502296.	+	172100.i	1.09374	+	0.374745i
$185$	−199337.	+	115088.i	−0.428213	+	0.247229i
$186$	−135870.	+	8776.18i	−0.287967	+	0.0186004i
$187$	−28693.1	+	16566.0i	−0.0600030	+	0.0346428i
$188$	6607.19	+	50931.9i	0.0136340	+	0.105098i
$189$			335047.i			0.682261i
$190$	−931008.	−	284606.i	−1.87098	−	0.571952i
$191$		−	571829.i		−	1.13418i	−0.823655	−	0.567091i	$-0.808069\pi$
$191$		−	571829.i		−	1.13418i	0.823655	−	0.567091i	$-0.191931\pi$
$192$	−104237.	−	80929.0i	−0.204065	−	0.158435i
$193$	−595146.	+	343607.i	−1.15009	+	0.664002i	−0.948908	−	0.315553i	$-0.897810\pi$
$193$	−595146.	+	343607.i	−1.15009	+	0.664002i	−0.201177	+	0.979555i	$0.564477\pi$
$194$	32720.8	+	506573.i	0.0624193	+	0.966358i
$195$	111211.	−	64207.7i	0.209441	−	0.120921i
$196$	282830.	+	370041.i	0.525879	+	0.688033i
$197$	833534.			1.53023			0.765117	−	0.643891i	$-0.222681\pi$
$197$	833534.			1.53023			0.765117	+	0.643891i	$0.222681\pi$
$198$	−65494.2	+	43672.1i	−0.118724	+	0.0791665i
$199$	−425483.	−	245653.i	−0.761640	−	0.439733i	0.0682444	−	0.997669i	$-0.478260\pi$
$199$	−425483.	−	245653.i	−0.761640	−	0.439733i	−0.829884	+	0.557936i	$0.811594\pi$
$200$	−518473.	+	1.51323e6i	−0.916539	+	2.67504i
$201$	−20670.5			−0.0360879
$202$	−106226.	−	159305.i	−0.183170	−	0.274696i
$203$	382739.	−	662923.i	0.651872	−	1.12908i
$204$	−69005.4	+	8951.78i	−0.116093	+	0.0150603i
$205$	911570.	+	526295.i	1.51498	+	0.874671i
$206$	520146.	−	1.05224e6i	0.853999	−	1.72761i
$207$	576070.	−	332594.i	0.934436	−	0.539497i
$208$	−211903.	+	210304.i	−0.339609	+	0.337046i
$209$	−34120.9	+	90327.3i	−0.0540325	+	0.143039i
$210$	367113.	−	244794.i	0.574449	−	0.383048i
$211$	−169744.	−	294006.i	−0.262476	−	0.454621i	0.704423	−	0.709780i	$-0.251206\pi$
$211$	−169744.	−	294006.i	−0.262476	−	0.454621i	−0.966899	+	0.255159i	$0.917872\pi$
$212$	82367.4	+	634934.i	0.125868	+	0.970262i
$213$	79153.7	−	137098.i	0.119542	−	0.207054i
$214$	57803.4	−	116934.i	0.0862818	−	0.174545i
$215$	1.77205e6	+	1.02309e6i	2.61445	+	1.50945i
$216$	−336084.	+	65859.1i	−0.490133	+	0.0960465i
$217$			1.05838e6i			1.52579i
$218$	29643.4	+	458930.i	0.0422461	+	0.654042i
$219$	103000.	−	178402.i	0.145120	−	0.251356i
$220$	198252.	+	82558.9i	0.276160	+	0.115002i
$221$			157420.i			0.216810i
$222$	3090.48	+	47845.9i	0.00420866	+	0.0651572i
$223$	−75210.3	−	130268.i	−0.101278	−	0.175419i	0.810933	−	0.585138i	$-0.198960\pi$
$223$	−75210.3	−	130268.i	−0.101278	−	0.175419i	−0.912211	+	0.409720i	$0.865626\pi$
$224$	−680020.	+	768047.i	−0.905528	+	1.02275i
$225$	1.00198e6	+	1.73549e6i	1.31948	+	2.28541i
$226$	−325656.	−	160979.i	−0.424119	−	0.209652i
$227$	−1.30617e6			−1.68243			−0.841213	−	0.540703i	$-0.818158\pi$
$227$	−1.30617e6			−1.68243			−0.841213	+	0.540703i	$0.818158\pi$
$228$	−139083.	+	147578.i	−0.177189	+	0.188012i
$229$	−375776.			−0.473522			−0.236761	−	0.971568i	$-0.576086\pi$
$229$	−375776.			−0.473522			−0.236761	+	0.971568i	$0.576086\pi$
$230$	−1.62680e6	−	804166.i	−2.02775	−	1.00237i
$231$	−21881.6	−	37900.0i	−0.0269805	−	0.0467315i
$232$	740210.	+	253615.i	0.902890	+	0.309354i
$233$	−158635.	−	274764.i	−0.191430	−	0.331566i	0.754295	−	0.656536i	$-0.227979\pi$
$233$	−158635.	−	274764.i	−0.191430	−	0.331566i	−0.945724	+	0.324970i	$0.894646\pi$
$234$	24108.6	+	373243.i	0.0287828	+	0.445607i
$235$		−	175533.i		−	0.207342i
$236$	432363.	−	1.03825e6i	0.505322	−	1.21345i
$237$	−175241.	+	303527.i	−0.202659	+	0.351015i
$238$	34865.7	+	539781.i	0.0398985	+	0.617696i
$239$		−	672989.i		−	0.762102i	−0.924554	−	0.381051i	$-0.875562\pi$
$239$		−	672989.i		−	0.762102i	0.924554	−	0.381051i	$-0.124438\pi$
$240$	317715.	+	320131.i	0.356048	+	0.358756i
$241$	−1.00505e6	−	580265.i	−1.11466	−	0.643552i	−0.174631	−	0.984634i	$-0.555873\pi$
$241$	−1.00505e6	−	580265.i	−1.11466	−	0.643552i	−0.940033	+	0.341082i	$0.889207\pi$
$242$	−394279.	+	797613.i	−0.432778	+	0.875495i
$243$	−325494.	+	563772.i	−0.353612	+	0.612474i
$244$	−410459.	+	53247.1i	−0.441362	+	0.0572561i
$245$	−795915.	−	1.37857e6i	−0.847133	−	1.46728i
$246$	182420.	−	121639.i	0.192191	−	0.128155i
$247$	290615.	+	354986.i	0.303093	+	0.370228i
$248$	−1.06166e6	+	208044.i	−1.09612	+	0.214795i
$249$	−114926.	+	66352.3i	−0.117468	+	0.0678200i
$250$	1.56590e6	−	3.16775e6i	1.58457	−	3.20554i
$251$	50440.9	+	29122.1i	0.0505357	+	0.0291768i	0.525055	−	0.851068i	$-0.324045\pi$
$251$	50440.9	+	29122.1i	0.0505357	+	0.0291768i	−0.474519	+	0.880245i	$0.657378\pi$
$252$	165333.	+	1.27448e6i	0.164005	+	1.26425i
$253$	−89992.7	+	155872.i	−0.0883906	+	0.153097i
$254$	−64645.9	−	96948.1i	−0.0628719	−	0.0942877i
$255$	237821.			0.229034
$256$	−904095.	−	531153.i	−0.862212	−	0.506547i
$257$	220465.	+	127285.i	0.208212	+	0.120211i	0.600480	−	0.799640i	$-0.294976\pi$
$257$	220465.	+	127285.i	0.208212	+	0.120211i	−0.392268	+	0.919851i	$0.628309\pi$
$258$	354615.	−	236461.i	0.331672	−	0.221162i
$259$	372704.			0.345235
$260$	810689.	−	619627.i	0.743740	−	0.568456i
$261$	848927.	−	490128.i	0.771382	−	0.445357i
$262$	−26137.8	−	404658.i	−0.0235243	−	0.364196i
$263$	−1.47513e6	+	851669.i	−1.31505	+	0.759244i	−0.982928	−	0.183992i	$-0.941098\pi$
$263$	−1.47513e6	+	851669.i	−1.31505	+	0.759244i	−0.332122	+	0.943236i	$0.607765\pi$
$264$	33716.2	−	29399.3i	0.0297734	−	0.0259613i
$265$		−	2.18825e6i		−	1.91418i
$266$	1.07512e6	+	1.15285e6i	0.931649	+	0.999009i
$267$			192953.i			0.165643i
$268$	−162880.	+	21129.8i	−0.138526	+	0.0179704i
$269$	−322613.	+	186261.i	−0.271832	+	0.156942i	−0.629720	−	0.776822i	$-0.716830\pi$
$269$	−322613.	+	186261.i	−0.271832	+	0.156942i	0.357888	+	0.933765i	$0.383497\pi$
$270$	1.16807e6	−	75448.6i	0.975126	−	0.0629857i
$271$	−312244.	+	180274.i	−0.258268	+	0.149111i	−0.623544	−	0.781788i	$-0.714308\pi$
$271$	−312244.	+	180274.i	−0.258268	+	0.149111i	0.365276	+	0.930899i	$0.380975\pi$
$272$	−534599.	+	141077.i	−0.438133	+	0.115620i
$273$	−207933.			−0.168856
$274$	1.03053e6	+	1.54546e6i	0.829246	+	1.24360i
$275$	−469584.	−	271115.i	−0.374440	−	0.216183i
$276$	−300327.	+	229546.i	−0.237313	+	0.181383i
$277$	1.15217e6			0.902226			0.451113	−	0.892467i	$-0.351027\pi$
$277$	1.15217e6			0.902226			0.451113	+	0.892467i	$0.351027\pi$
$278$	1.56768e6	−	1.04534e6i	1.21659	−	0.811235i
$279$	−677674.	+	1.17377e6i	−0.521207	+	0.902757i
$280$	2.64255e6	−	2.30420e6i	2.01432	−	1.75641i
$281$	−1.60778e6	−	928253.i	−1.21468	−	0.701295i	−0.250904	−	0.968012i	$-0.580728\pi$
$281$	−1.60778e6	−	928253.i	−1.21468	−	0.701295i	−0.963775	+	0.266717i	$0.914061\pi$
$282$	−32777.5	−	16202.7i	−0.0245445	−	0.0121329i
$283$	893708.	−	515982.i	0.663330	−	0.382974i	−0.130215	−	0.991486i	$-0.541567\pi$
$283$	893708.	−	515982.i	0.663330	−	0.382974i	0.793544	+	0.608512i	$0.208233\pi$
$284$	483572.	−	1.16122e6i	0.355767	−	0.854317i
$285$	536292.	−	439045.i	0.391101	−	0.320182i
$286$	−56145.0	−	84199.4i	−0.0405878	−	0.0608687i
$287$	−852188.	−	1.47603e6i	−0.610704	−	1.05777i
$288$	−1.24593e6	+	416366.i	−0.885139	+	0.295797i
$289$	564160.	−	977154.i	0.397336	−	0.688206i
$290$	−2.39734e6	−	1.18506e6i	−1.67392	−	0.827458i
$291$	−312977.	−	180697.i	−0.216660	−	0.125089i
$292$	629259.	−	1.51106e6i	0.431889	−	1.03711i
$293$			573532.i			0.390291i	0.980774	+	0.195145i	$0.0625179\pi$
$293$			573532.i			0.390291i	−0.980774	+	0.195145i	$0.937482\pi$
$294$	−330890.	+	21373.0i	−0.223262	+	0.0144210i
$295$	−1.92195e6	+	3.32891e6i	−1.28584	+	2.22714i
$296$	73261.3	+	373858.i	0.0486010	+	0.248015i
$297$		−	116093.i		−	0.0763684i
$298$	22362.4	−	1444.44i	0.0145874	−	0.000942234i
$299$	427584.	+	740597.i	0.276594	+	0.479076i
$300$	−691538.	−	904773.i	−0.443622	−	0.580412i
$301$	−1.65661e6	−	2.86934e6i	−1.05391	−	1.82543i
$302$	−689894.	+	1.39563e6i	−0.435277	+	0.880550i
$303$	136315.			0.0852978
$304$	−945089.	+	1.30506e6i	−0.586528	+	0.809929i
$305$	1.41461e6			0.870738
$306$	−306950.	+	620950.i	−0.187398	+	0.379099i
$307$	−392332.	−	679539.i	−0.237579	−	0.411499i	0.722440	−	0.691433i	$-0.243020\pi$
$307$	−392332.	−	679539.i	−0.237579	−	0.411499i	−0.960019	+	0.279935i	$0.909687\pi$
$308$	−211165.	−	276278.i	−0.126837	−	0.165947i
$309$	417822.	+	723689.i	0.248940	+	0.431177i
$310$	3.68985e6	−	238336.i	2.18074	−	0.140859i
$311$			590840.i			0.346393i	0.984887	+	0.173196i	$0.0554095\pi$
$311$			590840.i			0.346393i	−0.984887	+	0.173196i	$0.944590\pi$
$312$	−40872.8	−	208577.i	−0.0237710	−	0.121305i
$313$	171100.	−	296353.i	0.0987161	−	0.170981i	−0.812437	−	0.583048i	$-0.801860\pi$
$313$	171100.	−	296353.i	0.0987161	−	0.170981i	0.911153	+	0.412067i	$0.135193\pi$
$314$	−2.33242e6	+	150657.i	−1.33501	+	0.0862312i
$315$		−	4.39239e6i		−	2.49416i
$316$	−1.07060e6	+	2.57087e6i	−0.603128	+	1.44831i
$317$	1.40964e6	+	813857.i	0.787881	+	0.454883i	0.839216	−	0.543798i	$-0.183014\pi$
$317$	1.40964e6	+	813857.i	0.787881	+	0.454883i	−0.0513352	+	0.998681i	$0.516348\pi$
$318$	−408616.	−	201988.i	−0.226593	−	0.112010i
$319$	−132618.	+	229701.i	−0.0729669	+	0.126382i
$320$	2.83078e6	+	2.19780e6i	1.54536	+	1.19981i
$321$	46432.2	+	80423.0i	0.0251511	+	0.0435630i
$322$	1.63018e6	+	2.44474e6i	0.876184	+	1.31399i
$323$	137392.	+	838450.i	0.0732751	+	0.447168i
$324$	−584197.	+	1.40285e6i	−0.309169	+	0.742420i
$325$	−2.23114e6	+	1.28815e6i	−1.17171	+	0.676486i
$326$	−297467.	−	147045.i	−0.155022	−	0.0766311i
$327$	−283541.	−	163703.i	−0.146638	−	0.0846615i
$328$	1.31309e6	−	1.14497e6i	0.673923	−	0.587636i
$329$	−142113.	+	246147.i	−0.0723842	+	0.125373i
$330$	−127204.	+	84820.6i	−0.0643005	+	0.0428762i
$331$	−1.63245e6			−0.818972			−0.409486	−	0.912316i	$-0.634292\pi$
$331$	−1.63245e6			−0.818972			−0.409486	+	0.912316i	$0.634292\pi$
$332$	−837766.	+	640323.i	−0.417136	+	0.318826i
$333$	413335.	+	238639.i	0.204264	+	0.117932i
$334$	−1.85890e6	−	2.78775e6i	−0.911779	−	1.36737i
$335$	561352.			0.273290
$336$	−186345.	−	706140.i	−0.0900472	−	0.341226i
$337$	−2.53284e6	+	1.46234e6i	−1.21488	+	0.701410i	−0.963818	−	0.266561i	$-0.914113\pi$
$337$	−2.53284e6	+	1.46234e6i	−1.21488	+	0.701410i	−0.251060	+	0.967971i	$0.580779\pi$
$338$	1.61614e6	−	104390.i	0.769462	−	0.0497014i
$339$	223973.	−	129311.i	0.105852	−	0.0611134i
$340$	1.87399e6	−	243105.i	0.879163	−	0.114050i
$341$		−	366727.i		−	0.170788i
$342$	454164.	+	1.96692e6i	0.209965	+	0.909330i
$343$		−	398868.i		−	0.183060i
$344$	2.55259e6	−	2.22576e6i	1.16301	−	1.01410i
$345$	1.11885e6	−	645969.i	0.506086	−	0.292189i
$346$	−16544.1	−	256131.i	−0.00742940	−	0.115020i
$347$	2.73564e6	−	1.57942e6i	1.21965	−	0.704164i	0.254806	−	0.966992i	$-0.417988\pi$
$347$	2.73564e6	−	1.57942e6i	1.21965	−	0.704164i	0.964843	+	0.262828i	$0.0846552\pi$
$348$	−442578.	+	338272.i	−0.195903	+	0.149733i
$349$	−1.02170e6			−0.449016			−0.224508	−	0.974472i	$-0.572077\pi$
$349$	−1.02170e6			−0.449016			−0.224508	+	0.974472i	$0.572077\pi$
$350$	−7.36510e6	+	4.91112e6i	−3.21373	+	2.14294i
$351$	−477694.	−	275797.i	−0.206958	−	0.119487i
$352$	235625.	−	266126.i	0.101360	−	0.114480i
$353$	−384733.			−0.164332			−0.0821661	−	0.996619i	$-0.526184\pi$
$353$	−384733.			−0.164332			−0.0821661	+	0.996619i	$0.526184\pi$
$354$	444207.	+	666167.i	0.188398	+	0.282537i
$355$	−2.14959e6	+	3.72319e6i	−0.905283	+	1.56800i
$356$	197240.	+	1.52043e6i	0.0824840	+	0.635832i
$357$	−333493.	−	192542.i	−0.138489	−	0.0799569i
$358$	865761.	−	1.75141e6i	0.357018	−	0.722236i
$359$	−942762.	+	544304.i	−0.386070	+	0.222897i	−0.680456	−	0.732789i	$-0.738218\pi$
$359$	−942762.	+	544304.i	−0.386070	+	0.222897i	0.294386	+	0.955687i	$0.404885\pi$
$360$	4.40599e6	−	863399.i	1.79179	−	0.351120i
$361$	1.85770e6	+	1.63708e6i	0.750251	+	0.661153i
$362$	3.00642e6	−	2.00471e6i	1.20581	−	0.804044i
$363$	−316715.	−	548567.i	−0.126154	−	0.218506i
$364$	−1.63847e6	+	212553.i	−0.648166	+	0.0840839i
$365$	−2.79719e6	+	4.84488e6i	−1.09898	+	1.90349i
$366$	130577.	−	264153.i	0.0509524	−	0.103075i
$367$	2.60609e6	+	1.50463e6i	1.01001	+	0.583127i	0.911193	−	0.411979i	$-0.135162\pi$
$367$	2.60609e6	+	1.50463e6i	1.01001	+	0.583127i	0.0988127	+	0.995106i	$0.468496\pi$
$368$	−2.13188e6	+	2.11578e6i	−0.820620	+	0.814426i
$369$		−	2.18259e6i		−	0.834462i
$370$	−83928.6	−	1.29936e6i	−0.0318717	−	0.493429i
$371$	−1.77163e6	+	3.06855e6i	−0.668248	+	1.15744i
$372$	296090.	−	711012.i	0.110934	−	0.266391i
$373$		−	1.47256e6i		−	0.548027i	−0.961726	−	0.274014i	$-0.911649\pi$
$373$		−	1.47256e6i		−	0.548027i	0.961726	−	0.274014i	$-0.0883514\pi$
$374$	−12080.9	−	187033.i	−0.00446601	−	0.0691414i
$375$	1.25785e6	+	2.17866e6i	0.461903	+	0.800039i
$376$	−274844.	−	94168.6i	−0.100257	−	0.0343508i
$377$	630110.	+	1.09138e6i	0.228330	+	0.395479i
$378$	−1.69906e6	−	839883.i	−0.611615	−	0.302336i
$379$	2.47021e6			0.883357			0.441679	−	0.897173i	$-0.354383\pi$
$379$	2.47021e6			0.883357			0.441679	+	0.897173i	$0.354383\pi$
$380$	3.77709e6	−	4.00780e6i	1.34183	−	1.42379i
$381$	82957.0			0.0292779
$382$	2.89981e6	+	1.43344e6i	1.01674	+	0.502599i
$383$	1.72934e6	+	2.99530e6i	0.602396	+	1.04338i	0.992457	+	0.122592i	$0.0391206\pi$
$383$	1.72934e6	+	2.99530e6i	0.602396	+	1.04338i	−0.390061	+	0.920789i	$0.627546\pi$
$384$	671697.	−	325726.i	0.232459	−	0.112726i
$385$	594242.	+	1.02926e6i	0.204320	+	0.353893i
$386$	−250579.	−	3.87939e6i	−0.0856005	−	1.32524i
$387$		−	4.24286e6i		−	1.44006i
$388$	−2.65091e6	−	1.10393e6i	−0.893955	−	0.372274i
$389$	−777923.	+	1.34740e6i	−0.260653	+	0.451464i	−0.966416	−	0.256984i	$-0.917271\pi$
$389$	−777923.	+	1.34740e6i	−0.260653	+	0.451464i	0.705763	+	0.708448i	$0.250604\pi$
$390$	46824.1	+	724917.i	0.0155886	+	0.241339i
$391$			1.58374e6i			0.523893i
$392$	−2.58550e6	+	506656.i	−0.849826	+	0.166532i
$393$	250010.	+	144344.i	0.0816538	+	0.0471429i
$394$	−2.08948e6	+	4.22694e6i	−0.678105	+	1.37178i
$395$	4.75905e6	−	8.24292e6i	1.53471	−	2.65820i
$396$	−57287.5	−	441604.i	−0.0183578	−	0.141512i
$397$	958527.	+	1.66022e6i	0.305231	+	0.528675i	0.977313	−	0.211802i	$-0.0679331\pi$
$397$	958527.	+	1.66022e6i	0.305231	+	0.528675i	−0.672082	+	0.740477i	$0.734600\pi$
$398$	2.31232e6	−	1.54188e6i	0.731712	−	0.487912i
$399$	−1.10749e6	+	181479.i	−0.348263	+	0.0570681i
$400$	−6.37407e6	−	6.42255e6i	−1.99190	−	2.00705i
$401$	1.73728e6	−	1.00302e6i	0.539520	−	0.311492i	−0.205364	−	0.978686i	$-0.565838\pi$
$401$	1.73728e6	−	1.00302e6i	0.539520	−	0.311492i	0.744885	+	0.667193i	$0.232505\pi$
$402$	51816.2	−	104822.i	0.0159919	−	0.0323511i
$403$	−1.50900e6	−	871219.i	−0.462834	−	0.267217i
$404$	1.07414e6	−	139344.i	0.327422	−	0.0424751i
$405$	2.59688e6	−	4.49794e6i	0.786711	−	1.36262i
$406$	2.40232e6	+	3.60270e6i	0.723295	+	1.08471i
$407$	−129141.			−0.0386436
$408$	127585.	−	372374.i	0.0379445	−	0.110746i
$409$	5.69490e6	+	3.28795e6i	1.68336	+	0.971890i	0.959399	+	0.282052i	$0.0910149\pi$
$409$	5.69490e6	+	3.28795e6i	1.68336	+	0.971890i	0.723963	+	0.689838i	$0.242318\pi$
$410$	−4.95399e6	+	3.30337e6i	−1.45545	+	0.970505i
$411$	−1.32243e6			−0.386160
$412$	4.03213e6	+	5.27543e6i	1.17028	+	1.53114i
$413$	5.39024e6	−	3.11206e6i	1.55501	−	0.897785i
$414$	242547.	+	3.75505e6i	0.0695498	+	1.07675i
$415$	3.12105e6	−	1.80194e6i	0.889571	−	0.513594i
$416$	−535281.	−	1.60177e6i	−0.151652	−	0.453801i
$417$			1.34144e6i			0.377773i
$418$	−372526.	−	399460.i	−0.104284	−	0.111823i
$419$		−	5.78950e6i		−	1.61104i	−0.592569	−	0.805520i	$-0.701886\pi$
$419$		−	5.78950e6i		−	1.61104i	0.592569	−	0.805520i	$-0.298114\pi$
$420$	321112.	+	2.47531e6i	0.0888246	+	0.684709i
$421$	−4.26798e6	+	2.46412e6i	−1.17359	+	0.677574i	−0.954523	−	0.298136i	$-0.903635\pi$
$421$	−4.26798e6	+	2.46412e6i	−1.17359	+	0.677574i	−0.219068	+	0.975709i	$0.570302\pi$
$422$	1.91644e6	−	123788.i	0.523860	−	0.0338373i
$423$	−315211.	+	181987.i	−0.0856546	+	0.0494527i
$424$	−3.42629e6	−	1.17394e6i	−0.925572	−	0.317125i
$425$	−4.77123e6			−1.28132
$426$	496820.	+	745070.i	0.132640	+	0.198917i
$427$	−1.98369e6	−	1.14528e6i	−0.526507	−	0.303979i
$428$	448087.	+	586255.i	0.118237	+	0.154695i
$429$	72048.2			0.0189008
$430$	−9.63034e6	+	6.42160e6i	−2.51172	+	1.67484i
$431$	616672.	−	1.06811e6i	0.159905	−	0.276963i	−0.774930	−	0.632048i	$-0.782215\pi$
$431$	616672.	−	1.06811e6i	0.159905	−	0.276963i	0.934834	+	0.355085i	$0.115548\pi$
$432$	508506.	−	1.86941e6i	0.131095	−	0.481943i
$433$	−3.34659e6	−	1.93216e6i	−0.857794	−	0.495248i	0.00547864	−	0.999985i	$-0.498256\pi$
$433$	−3.34659e6	−	1.93216e6i	−0.857794	−	0.495248i	−0.863273	+	0.504737i	$0.831589\pi$
$434$	−5.36718e6	−	2.65312e6i	−1.36780	−	0.676134i
$435$	1.64880e6	−	951934.i	0.417777	−	0.241203i
$436$	−2.40159e6	−	1.00011e6i	−0.605039	−	0.251959i
$437$	2.92377e6	+	3.57137e6i	0.732385	+	0.894606i
$438$	646497.	+	969537.i	0.161020	+	0.241479i
$439$	1.84789e6	+	3.20063e6i	0.457629	+	0.792637i	0.998835	−	0.0482528i	$-0.0153653\pi$
$439$	1.84789e6	+	3.20063e6i	0.457629	+	0.792637i	−0.541206	+	0.840890i	$0.682032\pi$
$440$	−915636.	+	798400.i	−0.225471	+	0.196602i
$441$	−1.65036e6	+	2.85851e6i	−0.404095	+	0.699913i
$442$	−798295.	−	394616.i	−0.194360	−	0.0960769i
$443$	479466.	+	276820.i	0.116078	+	0.0670174i	0.556915	−	0.830570i	$-0.311985\pi$
$443$	479466.	+	276820.i	0.116078	+	0.0670174i	−0.440837	+	0.897587i	$0.645318\pi$
$444$	−250379.	−	104266.i	−0.0602754	−	0.0251008i
$445$		−	5.24005e6i		−	1.25440i
$446$	849137.	−	54847.8i	0.202135	−	0.0130564i
$447$	−7976.77	+	13816.2i	−0.00188825	+	0.00327054i
$448$	−2.19020e6	−	5.37377e6i	−0.515570	−	1.26498i
$449$		−	6.58290e6i		−	1.54100i	−0.637443	−	0.770498i	$-0.720008\pi$
$449$		−	6.58290e6i		−	1.54100i	0.637443	−	0.770498i	$-0.279992\pi$
$450$	−1.13126e7	+	730705.i	−2.63348	+	0.170103i
$451$	295281.	+	511441.i	0.0683587	+	0.118401i
$452$	1.63269e6	−	1.24790e6i	0.375886	−	0.287298i
$453$	−554177.	−	959863.i	−0.126883	−	0.219768i
$454$	3.27427e6	−	6.62374e6i	0.745547	−	1.50822i
$455$	5.64686e6			1.27873
$456$	−399737.	−	1.07525e6i	−0.0900247	−	0.242156i
$457$	−2.13565e6			−0.478344			−0.239172	−	0.970977i	$-0.576876\pi$
$457$	−2.13565e6			−0.478344			−0.239172	+	0.970977i	$0.576876\pi$
$458$	941982.	−	1.90560e6i	0.209835	−	0.424490i
$459$	−510766.	−	884673.i	−0.113159	−	0.195998i
$460$	8.15602e6	−	6.23382e6i	1.79715	−	1.37360i
$461$	−2008.12	−	3478.17i	−0.000440086	−	0.000762252i	0.865805	−	0.500381i	$-0.166807\pi$
$461$	−2008.12	−	3478.17i	−0.000440086	−	0.000762252i	−0.866245	+	0.499619i	$0.833473\pi$
$462$	247047.	−	15957.4i	0.0538487	−	0.00347821i
$463$			3.03840e6i			0.658708i	0.944207	+	0.329354i	$0.106831\pi$
$463$			3.03840e6i			0.658708i	−0.944207	+	0.329354i	$0.893169\pi$
$464$	−3.14164e6	+	3.11793e6i	−0.677426	+	0.672313i
$465$	−1.31619e6	+	2.27970e6i	−0.282283	+	0.488929i
$466$	1.79102e6	−	115686.i	0.382063	−	0.0246783i
$467$			1.68405e6i			0.357325i	0.983910	+	0.178663i	$0.0571771\pi$
$467$			1.68405e6i			0.357325i	−0.983910	+	0.178663i	$0.942823\pi$
$468$	−1.95319e6	−	813375.i	−0.412221	−	0.171663i
$469$	−787176.	−	454476.i	−0.165249	−	0.0954068i
$470$	890144.	+	440019.i	0.185873	+	0.0918813i
$471$	831987.	−	1.44104e6i	0.172808	−	0.299312i
$472$	4.18124e6	+	4.79520e6i	0.863873	+	0.990722i
$473$	574013.	+	994219.i	0.117969	+	0.204329i
$474$	−1.09993e6	−	1.64954e6i	−0.224863	−	0.337222i
$475$	−1.07592e7	+	8.80822e6i	−2.18800	+	1.79124i
$476$	−2.82469e6	−	1.17630e6i	−0.571417	−	0.237958i
$477$	−3.92953e6	+	2.26871e6i	−0.790759	+	0.456545i
$478$	3.41280e6	+	1.68703e6i	0.683189	+	0.337716i
$479$	−2.91226e6	−	1.68139e6i	−0.579951	−	0.334835i	0.181163	−	0.983453i	$-0.442014\pi$
$479$	−2.91226e6	−	1.68139e6i	−0.579951	−	0.334835i	−0.761114	+	0.648618i	$0.775347\pi$
$480$	−2.41985e6	+	808671.i	−0.479387	+	0.160202i
$481$	−306795.	+	531384.i	−0.0604624	+	0.104724i
$482$	5.46200e6	−	3.64212e6i	1.07086	−	0.714062i
$483$	−2.09193e6			−0.408018
$484$	−3.05641e6	−	3.99886e6i	−0.593060	−	0.775930i
$485$	8.49955e6	+	4.90722e6i	1.64075	+	0.947286i
$486$	−2.04301e6	−	3.06386e6i	−0.392356	−	0.588408i
$487$	6.83855e6			1.30660			0.653299	−	0.757100i	$-0.273385\pi$
$487$	6.83855e6			1.30660			0.653299	+	0.757100i	$0.273385\pi$
$488$	758902.	−	2.21496e6i	0.144257	−	0.421033i
$489$	204586.	−	118118.i	0.0386904	−	0.0223379i
$490$	8.98602e6	−	580428.i	1.69074	−	0.109209i
$491$	−126727.	+	73165.8i	−0.0237228	+	0.0136963i	−0.511814	−	0.859096i	$-0.671026\pi$
$491$	−126727.	+	73165.8i	−0.0237228	+	0.0136963i	0.488092	+	0.872792i	$0.337693\pi$
$492$	159562.	+	1.22999e6i	0.0297177	+	0.229081i
$493$			2.33389e6i			0.432477i
$494$	−2.52868e6	+	583875.i	−0.466204	+	0.107647i
$495$			1.52195e6i			0.279182i
$496$	1.60633e6	−	5.90532e6i	0.293177	−	1.07780i
$497$	6.02867e6	−	3.48065e6i	1.09479	−	0.632077i
$498$	−48388.0	−	749129.i	−0.00874308	−	0.135358i
$499$	−7.67261e6	+	4.42978e6i	−1.37940	+	0.796400i	−0.992088	−	0.125547i	$-0.959931\pi$
$499$	−7.67261e6	+	4.42978e6i	−1.37940	+	0.796400i	−0.387317	+	0.921947i	$0.626598\pi$
$500$	1.21387e7	+	1.58816e7i	2.17143	+	2.84099i
$501$	2.38544e6			0.424593
$502$	−274125.	+	182789.i	−0.0485500	+	0.0323736i
$503$	6.90915e6	+	3.98900e6i	1.21760	+	0.702982i	0.964404	−	0.264433i	$-0.0851850\pi$
$503$	6.90915e6	+	3.98900e6i	1.21760	+	0.702982i	0.253196	+	0.967415i	$0.418518\pi$
$504$	−6.87747e6	−	2.35640e6i	−1.20601	−	0.413212i
$505$	−3.70193e6			−0.645952
$506$	−564853.	−	847097.i	−0.0980751	−	0.147081i
$507$	−576485.	+	998501.i	−0.0996020	+	0.172516i
$508$	653686.	−	84800.0i	0.112385	−	0.0145793i
$509$	−5.80531e6	−	3.35170e6i	−0.993187	−	0.573417i	−0.0869614	−	0.996212i	$-0.527716\pi$
$509$	−5.80531e6	−	3.35170e6i	−0.993187	−	0.573417i	−0.906225	+	0.422795i	$0.861049\pi$
$510$	−596162.	+	1.20602e6i	−0.101494	+	0.205318i
$511$	7.84493e6	−	4.52927e6i	1.32904	−	0.767319i
$512$	4.95989e6	−	3.25328e6i	0.836175	−	0.548463i
$513$	−2.78500e6	−	1.05203e6i	−0.467230	−	0.176495i
$514$	−1.19813e6	+	798925.i	−0.200031	+	0.133382i
$515$	−1.13468e7	−	1.96533e7i	−1.88520	−	3.26526i
$516$	310181.	+	2.39105e6i	0.0512850	+	0.395333i
$517$	49241.7	−	85289.2i	0.00810228	−	0.0140336i
$518$	−934282.	+	1.89002e6i	−0.152987	+	0.309487i
$519$	158246.	+	91363.3i	0.0257878	+	0.0148886i
$520$	1.10999e6	+	5.66435e6i	0.180015	+	0.918632i
$521$		−	3.34161e6i		−	0.539339i	−0.962953	−	0.269670i	$-0.913086\pi$
$521$		−	3.34161e6i		−	0.539339i	0.962953	−	0.269670i	$-0.0869145\pi$
$522$	357431.	+	5.53364e6i	0.0574137	+	0.888862i
$523$	−3.20091e6	+	5.54413e6i	−0.511704	+	0.886297i	0.488204	+	0.872730i	$0.337652\pi$
$523$	−3.20091e6	+	5.54413e6i	−0.511704	+	0.886297i	−0.999908	+	0.0135678i	$0.995681\pi$
$524$	2.11759e6	+	881836.i	0.336909	+	0.140301i
$525$		−	6.30221e6i		−	0.997917i
$526$	−621088.	−	9.61550e6i	−0.0978788	−	1.51533i
$527$	−1.61347e6	−	2.79461e6i	−0.253066	−	0.438323i
$528$	64568.2	+	244676.i	0.0100794	+	0.0381949i
$529$	1.08358e6	+	1.87682e6i	0.168354	+	0.291597i
$530$	1.10968e7	+	5.48543e6i	1.71597	+	0.848244i
$531$	7.97048e6			1.22673
$532$	−8.54131e6	+	2.56211e6i	−1.30841	+	0.392482i
$533$	2.80595e6			0.427820
$534$	−978485.	−	483688.i	−0.148491	−	0.0734027i
$535$	−1.26097e6	−	2.18406e6i	−0.190467	−	0.329898i
$536$	301151.	−	878949.i	0.0452764	−	0.132145i
$537$	695447.	+	1.20455e6i	0.104071	+	0.180256i
$538$	−135832.	−	2.10292e6i	−0.0202324	−	0.313232i
$539$		−	893105.i		−	0.132413i
$540$	−2.54548e6	+	6.11256e6i	−0.375652	+	0.902067i
$541$	2.09132e6	−	3.62228e6i	0.307205	−	0.532094i	−0.670545	−	0.741869i	$-0.733940\pi$
$541$	2.09132e6	−	3.62228e6i	0.307205	−	0.532094i	0.977750	+	0.209775i	$0.0672730\pi$
$542$	−131467.	−	2.03533e6i	−0.0192228	−	0.297602i
$543$			2.57255e6i			0.374424i
$544$	624699.	−	3.06466e6i	0.0905052	−	0.444001i
$545$	7.70017e6	+	4.44569e6i	1.11048	+	0.641133i
$546$	521239.	−	1.05445e6i	0.0748265	−	0.151372i
$547$	−239528.	+	414875.i	−0.0342286	+	0.0592856i	−0.882632	−	0.470064i	$-0.844231\pi$
$547$	−239528.	+	414875.i	−0.0342286	+	0.0592856i	0.848404	+	0.529350i	$0.177564\pi$
$548$	−1.04205e7	+	1.35181e6i	−1.48230	+	0.192293i
$549$	−1.46663e6	−	2.54028e6i	−0.207677	−	0.359708i
$550$	2.55199e6	−	1.70169e6i	0.359726	−	0.239869i
$551$	4.30862e6	+	5.26297e6i	0.604587	+	0.738502i
$552$	−411205.	−	2.09841e6i	−0.0574395	−	0.293118i
$553$	−1.33471e7	+	7.70595e6i	−1.85598	+	1.07155i
$554$	−2.88821e6	+	5.84275e6i	−0.399811	+	0.808804i
$555$	802784.	+	463487.i	0.110628	+	0.0638713i
$556$	1.37124e6	+	1.05703e7i	0.188116	+	1.45011i
$557$	1.93826e6	−	3.35717e6i	0.264712	−	0.458495i	−0.702776	−	0.711411i	$-0.748056\pi$
$557$	1.93826e6	−	3.35717e6i	0.264712	−	0.458495i	0.967488	+	0.252916i	$0.0813897\pi$
$558$	−4.25352e6	−	6.37891e6i	−0.578313	−	0.867283i
$559$	5.45463e6			0.738305
$560$	5.06061e6	+	1.91767e7i	0.681919	+	2.58407i
$561$	115555.	+	66715.4i	0.0155017	+	0.00894992i
$562$	8.73761e6	−	5.82632e6i	1.16695	−	0.778132i
$563$	−6.98110e6			−0.928224			−0.464112	−	0.885777i	$-0.653626\pi$
$563$	−6.98110e6			−0.928224			−0.464112	+	0.885777i	$0.653626\pi$
$564$	164331.	−	125602.i	0.0217532	−	0.0166264i
$565$	−6.08248e6	+	3.51172e6i	−0.801603	+	0.462806i
$566$	376285.	+	5.82553e6i	0.0493714	+	0.764354i
$567$	−7.28314e6	+	4.20493e6i	−0.951396	+	0.549289i
$568$	4.67647e6	+	5.36316e6i	0.608201	+	0.697509i
$569$			1.45003e6i			0.187757i	0.995584	+	0.0938787i	$0.0299266\pi$
$569$			1.45003e6i			0.187757i	−0.995584	+	0.0938787i	$0.970073\pi$
$570$	882083.	+	3.82018e6i	0.113716	+	0.492489i
$571$		−	2.09836e6i		−	0.269334i	−0.990891	−	0.134667i	$-0.957004\pi$
$571$		−	2.09836e6i		−	0.269334i	0.990891	−	0.134667i	$-0.0429964\pi$
$572$	567727.	−	73648.9i	0.0725520	−	0.00941187i
$573$	−1.99437e6	+	1.15145e6i	−0.253758	+	0.146507i
$574$	9.62135e6	−	621466.i	1.21887	−	0.0787295i
$575$	−2.24467e7	+	1.29596e7i	−2.83128	+	1.63464i
$576$	1.01181e6	−	7.36196e6i	0.127070	−	0.924565i
$577$	9.52681e6			1.19126			0.595632	−	0.803257i	$-0.296902\pi$
$577$	9.52681e6			1.19126			0.595632	+	0.803257i	$0.296902\pi$
$578$	3.54103e6	+	5.31041e6i	0.440870	+	0.661163i
$579$	2.39681e6	+	1.38380e6i	0.297123	+	0.171544i
$580$	1.20191e7	−	9.18649e6i	1.48355	−	1.13391i
$581$	−5.83547e6			−0.717192
$582$	1.70089e6	−	1.13417e6i	0.208147	−	0.138794i
$583$	613864.	−	1.06324e6i	0.0747999	−	0.129557i
$584$	6.08535e6	+	6.97892e6i	0.738336	+	0.846752i
$585$	6.26246e6	+	3.61563e6i	0.756581	+	0.436812i
$586$	−2.90844e6	−	1.43771e6i	−0.349878	−	0.172953i
$587$	6.05280e6	−	3.49458e6i	0.725038	−	0.418601i	−0.0915661	−	0.995799i	$-0.529187\pi$
$587$	6.05280e6	−	3.49458e6i	0.725038	−	0.418601i	0.816604	+	0.577198i	$0.195854\pi$
$588$	721079.	−	1.73155e6i	0.0860082	−	0.206535i
$589$	−8.79757e6	−	3.32326e6i	−1.04490	−	0.394708i
$590$	−1.20634e7	−	1.80912e7i	−1.42672	−	2.13962i
$591$	−1.67843e6	−	2.90713e6i	−0.197667	−	0.342370i
$592$	−2.07952e6	−	565659.i	−0.243871	−	0.0663362i
$593$	−13576.3	+	23514.8i	−0.00158542	+	0.00274602i	−0.866817	−	0.498626i	$-0.833838\pi$
$593$	−13576.3	+	23514.8i	−0.00158542	+	0.00274602i	0.865232	+	0.501372i	$0.167171\pi$
$594$	588719.	+	291017.i	0.0684608	+	0.0338418i
$595$	9.05672e6	+	5.22890e6i	1.04877	+	0.605506i
$596$	−48732.4	+	117023.i	−0.00561956	+	0.0134945i
$597$			1.97862e6i			0.227209i
$598$	−4.82750e6	+	311820.i	−0.552038	+	0.0356575i
$599$	−670686.	+	1.16166e6i	−0.0763752	+	0.132286i	−0.901683	−	0.432397i	$-0.857668\pi$
$599$	−670686.	+	1.16166e6i	−0.0763752	+	0.132286i	0.825308	+	0.564682i	$0.191001\pi$
$600$	6.32173e6	−	1.23881e6i	0.716898	−	0.140484i
$601$		−	1.09584e6i		−	0.123754i	−0.998084	−	0.0618771i	$-0.980291\pi$
$601$		−	1.09584e6i		−	0.123754i	0.998084	−	0.0618771i	$-0.0197087\pi$
$602$	1.87035e7	−	1.20810e6i	2.10345	−	0.135866i
$603$	−581994.	−	1.00804e6i	−0.0651816	−	0.112898i
$604$	−5.34800e6	−	6.99706e6i	−0.596485	−	0.780410i
$605$	8.60108e6	+	1.48975e7i	0.955355	+	1.65472i
$606$	−341710.	+	691269.i	−0.0377987	+	0.0764655i
$607$	−7.00239e6			−0.771391			−0.385695	−	0.922626i	$-0.626038\pi$
$607$	−7.00239e6			−0.771391			−0.385695	+	0.922626i	$0.626038\pi$
$608$	−4.24899e6	−	8.06413e6i	−0.466151	−	0.884705i
$609$	−3.08278e6			−0.336821
$610$	−3.54610e6	+	7.17365e6i	−0.385857	+	0.780576i
$611$	−233963.	−	405236.i	−0.0253539	−	0.0439142i
$612$	−2.37945e6	−	3.11315e6i	−0.256802	−	0.335987i
$613$	1.08004e6	+	1.87068e6i	0.116088	+	0.201071i	0.918214	−	0.396084i	$-0.129631\pi$
$613$	1.08004e6	+	1.87068e6i	0.116088	+	0.201071i	−0.802126	+	0.597155i	$0.796298\pi$
$614$	4.42950e6	−	286112.i	0.474170	−	0.0306277i
$615$		−	4.23906e6i		−	0.451941i
$616$	1.93038e6	−	378277.i	0.204970	−	0.0401660i
$617$	930657.	−	1.61195e6i	0.0984185	−	0.170466i	−0.812612	−	0.582806i	$-0.801955\pi$
$617$	930657.	−	1.61195e6i	0.0984185	−	0.170466i	0.911030	+	0.412340i	$0.135288\pi$
$618$	−4.71728e6	+	304700.i	−0.496845	+	0.0320924i
$619$			6.22804e6i			0.653318i	0.945142	+	0.326659i	$0.105923\pi$
$619$			6.22804e6i			0.653318i	−0.945142	+	0.326659i	$0.894077\pi$
$620$	−8.04096e6	+	1.93091e7i	−0.840096	+	2.01735i
$621$	−4.80589e6	−	2.77468e6i	−0.500086	−	0.288725i
$622$	−2.99621e6	−	1.48110e6i	−0.310525	−	0.153500i
$623$	−4.24240e6	+	7.34805e6i	−0.437916	+	0.758493i
$624$	1.16017e6	+	315583.i	0.119278	+	0.0324453i
$625$	−2.03525e7	−	3.52515e7i	−2.08409	−	3.60976i
$626$	1.07393e6	+	1.61055e6i	0.109532	+	0.164263i
$627$	383742.	−	62881.9i	0.0389826	−	0.00638788i
$628$	5.08284e6	−	1.22056e7i	0.514290	−	1.23498i
$629$	−984106.	+	568174.i	−0.0991780	+	0.0572604i
$630$	2.22743e7	+	1.10107e7i	2.23590	+	1.10526i
$631$	−3.43366e6	−	1.98242e6i	−0.343308	−	0.198209i	0.318426	−	0.947948i	$-0.396846\pi$
$631$	−3.43366e6	−	1.98242e6i	−0.343308	−	0.198209i	−0.661734	+	0.749739i	$0.730179\pi$
$632$	−1.03534e7	−	1.18737e7i	−1.03108	−	1.18248i
$633$	−683605.	+	1.18404e6i	−0.0678103	+	0.117451i
$634$	−7.66080e6	+	5.10829e6i	−0.756921	+	0.504722i
$635$	−2.25288e6			−0.221719
$636$	2.04861e6	−	1.56580e6i	0.200824	−	0.153494i
$637$	−3.67491e6	−	2.12171e6i	−0.358838	−	0.207175i
$638$	−832397.	−	1.24833e6i	−0.0809615	−	0.121416i
$639$	8.91452e6			0.863666
$640$	−1.82414e7	+	8.84580e6i	−1.76039	+	0.853664i
$641$	2.02946e6	−	1.17171e6i	0.195090	−	0.112636i	−0.399273	−	0.916832i	$-0.630737\pi$
$641$	2.02946e6	−	1.17171e6i	0.195090	−	0.112636i	0.594363	+	0.804197i	$0.297404\pi$
$642$	−524228.	+	33861.1i	−0.0501976	+	0.00324238i
$643$	−3.81707e6	+	2.20379e6i	−0.364085	+	0.210205i	−0.670871	−	0.741574i	$-0.734080\pi$
$643$	−3.81707e6	+	2.20379e6i	−0.364085	+	0.210205i	0.306786	+	0.951778i	$0.400746\pi$
$644$	−1.64840e7	+	2.13841e6i	−1.56621	+	0.203178i
$645$		−	8.24054e6i		−	0.779931i
$646$	−4.59628e6	−	1.40507e6i	−0.433336	−	0.132469i
$647$			2.24473e6i			0.210816i	0.994429	+	0.105408i	$0.0336149\pi$
$647$			2.24473e6i			0.210816i	−0.994429	+	0.105408i	$0.966385\pi$
$648$	−5.64957e6	−	6.47915e6i	−0.528540	−	0.606150i
$649$	−1.86770e6	+	1.07832e6i	−0.174059	+	0.100493i
$650$	−939397.	−	1.45435e7i	−0.0872099	−	1.35016i
$651$	3.69134e6	−	2.13119e6i	0.341375	−	0.197093i
$652$	1.49136e6	−	1.13988e6i	0.137392	−	0.105012i
$653$	−5.15559e6			−0.473146			−0.236573	−	0.971614i	$-0.576024\pi$
$653$	−5.15559e6			−0.473146			−0.236573	+	0.971614i	$0.576024\pi$
$654$	1.54092e6	−	1.02750e6i	0.140876	−	0.0939375i
$655$	−6.78957e6	−	3.91996e6i	−0.618356	−	0.357008i
$656$	2.51463e6	+	9.52899e6i	0.228147	+	0.864544i
$657$	1.16002e7			1.04846
$658$	−891993.	−	1.33770e6i	−0.0803150	−	0.120447i
$659$	9.66959e6	−	1.67482e7i	0.867351	−	1.50230i	0.00265631	−	0.999996i	$-0.499154\pi$
$659$	9.66959e6	−	1.67482e7i	0.867351	−	1.50230i	0.864694	−	0.502299i	$-0.167512\pi$
$660$	−111264.	−	857688.i	−0.00994252	−	0.0766425i
$661$	−5.15993e6	−	2.97909e6i	−0.459347	−	0.265204i	0.252423	−	0.967617i	$-0.418773\pi$
$661$	−5.15993e6	−	2.97909e6i	−0.459347	−	0.265204i	−0.711769	+	0.702413i	$0.752106\pi$
$662$	4.09216e6	−	8.27831e6i	0.362918	−	0.734171i
$663$	549036.	−	316986.i	0.0485084	−	0.0280064i
$664$	−1.14706e6	−	5.85354e6i	−0.100964	−	0.515227i
$665$	3.00763e7	−	4.92844e6i	2.63736	−	0.432171i
$666$	−2.24630e6	+	1.49785e6i	−0.196237	+	0.130853i
$667$	6.33929e6	+	1.09800e7i	0.551729	+	0.955623i
$668$	1.87968e7	−	2.43843e6i	1.62983	−	0.211431i
$669$	−302891.	+	524623.i	−0.0261651	+	0.0453192i
$670$	−1.40718e6	+	2.84668e6i	−0.121105	+	0.244992i
$671$	687343.	+	396838.i	0.0589342	+	0.0340257i
$672$	4.04803e6	+	825151.i	0.345797	+	0.0704872i
$673$			7.93595e6i			0.675400i	0.941254	+	0.337700i	$0.109649\pi$
$673$			7.93595e6i			0.675400i	−0.941254	+	0.337700i	$0.890351\pi$
$674$	−1.06642e6	−	1.65100e7i	−0.0904231	−	1.39990i
$675$	8.35908e6	−	1.44784e7i	0.706154	−	1.22309i
$676$	−3.52191e6	+	8.45730e6i	−0.296423	+	0.711812i
$677$			1.37549e6i			0.115341i	0.998336	+	0.0576707i	$0.0183673\pi$
$677$			1.37549e6i			0.115341i	−0.998336	+	0.0576707i	$0.981633\pi$
$678$	94301.3	+	1.45995e6i	0.00787850	+	0.121973i
$679$	−7.94586e6	−	1.37626e7i	−0.661404	−	1.14559i
$680$	−3.46484e6	+	1.01126e7i	−0.287350	+	0.838669i
$681$	2.63015e6	+	4.55555e6i	0.217327	+	0.376421i
$682$	1.85971e6	+	919300.i	0.153103	+	0.0756826i
$683$	1.35393e7			1.11057			0.555285	−	0.831660i	$-0.312609\pi$
$683$	1.35393e7			1.11057			0.555285	+	0.831660i	$0.312609\pi$
$684$	−1.11129e7	−	2.62750e6i	−0.908216	−	0.214734i
$685$	3.59133e7			2.92435
$686$	2.02270e6	+	999869.i	0.164105	+	0.0811209i
$687$	756674.	+	1.31060e6i	0.0611669	+	0.105944i
$688$	4.88833e6	+	1.85239e7i	0.393722	+	1.49198i
$689$	−2.91666e6	−	5.05181e6i	−0.234066	−	0.405414i
$690$	471079.	+	7.29310e6i	0.0376678	+	0.583163i
$691$			2.13347e7i			1.69977i	0.526966	+	0.849887i	$0.323330\pi$
$691$			2.13347e7i			1.69977i	−0.526966	+	0.849887i	$0.676670\pi$
$692$	1.34034e6	+	558164.i	0.106402	+	0.0443095i
$693$	1.23219e6	−	2.13421e6i	0.0974638	−	0.168812i
$694$	1.15181e6	+	1.78319e7i	0.0907781	+	1.40540i
$695$		−	3.64296e7i		−	2.86083i
$696$	−605973.	−	3.09233e6i	−0.0474166	−	0.241970i
$697$	4.50032e6	+	2.59826e6i	0.350882	+	0.202582i
$698$	2.56117e6	−	5.18117e6i	0.198976	−	0.402522i
$699$	−638864.	+	1.10655e6i	−0.0494556	+	0.0856597i
$700$	−6.44223e6	−	4.96603e7i	−0.496925	−	3.83057i
$701$	7.00091e6	+	1.21259e7i	0.538096	+	0.932010i	0.999007	+	0.0445630i	$0.0141895\pi$
$701$	7.00091e6	+	1.21259e7i	0.538096	+	0.932010i	−0.460911	+	0.887447i	$0.652477\pi$
$702$	2.59606e6	−	1.73108e6i	0.198826	−	0.132579i
$703$	−1.17027e6	+	3.09801e6i	−0.0893093	+	0.236426i
$704$	758897.	+	1.86200e6i	0.0577100	+	0.141595i
$705$	−612207.	+	353458.i	−0.0463901	+	0.0267833i
$706$	964436.	−	1.95102e6i	0.0728219	−	0.147316i
$707$	5.19117e6	+	2.99712e6i	0.390586	+	0.225505i
$708$	−4.49173e6	+	582694.i	−0.336768	+	0.0436875i
$709$	7.01897e6	−	1.21572e7i	0.524394	−	0.908277i	−0.475203	−	0.879876i	$-0.657625\pi$
$709$	7.01897e6	−	1.21572e7i	0.524394	−	0.908277i	0.999597	−	0.0284008i	$-0.00904146\pi$
$710$	−1.34922e7	−	2.02340e7i	−1.00447	−	1.50638i
$711$	−1.97362e7			−1.46416
$712$	−8.20472e6	−	2.81115e6i	−0.606546	−	0.207818i
$713$	−1.51814e7	−	8.76499e6i	−1.11838	−	0.645695i
$714$	1.81239e6	−	1.20852e6i	0.133048	−	0.0887174i
$715$	−1.95662e6			−0.143134
$716$	6.71131e6	+	8.78073e6i	0.489243	+	0.640101i
$717$	−2.34719e6	+	1.35515e6i	−0.170510	+	0.0984441i
$718$	−396938.	−	6.14529e6i	−0.0287351	−	0.444868i
$719$	−1.11491e7	+	6.43693e6i	−0.804299	+	0.464362i	−0.844972	−	0.534810i	$-0.820383\pi$
$719$	−1.11491e7	+	6.43693e6i	−0.804299	+	0.464362i	0.0406733	+	0.999172i	$0.487050\pi$
$720$	−6.66640e6	+	2.45076e7i	−0.479248	+	1.76185i
$721$			3.67461e7i			2.63253i
$722$	−1.29586e7	+	5.31679e6i	−0.925158	+	0.379583i
$723$			4.67375e6i			0.332522i
$724$	2.62970e6	+	2.02712e7i	0.186449	+	1.43725i
$725$	−3.30786e7	+	1.90979e7i	−2.33723	+	1.34940i
$726$	3.57577e6	−	230968.i	0.251784	−	0.0162633i
$727$	1.92785e7	−	1.11305e7i	1.35281	−	0.781046i	0.364169	−	0.931333i	$-0.381353\pi$
$727$	1.92785e7	−	1.11305e7i	1.35281	−	0.781046i	0.988642	+	0.150287i	$0.0480197\pi$
$728$	3.02939e6	−	8.84169e6i	0.211849	−	0.618311i
$729$	−8.91801e6			−0.621512
$730$	−1.75570e7	−	2.63299e7i	−1.21939	−	1.82870i
$731$	8.74842e6	+	5.05090e6i	0.605530	+	0.349603i
$732$	1.01222e6	+	1.32434e6i	0.0698230	+	0.0913528i
$733$	−2.32106e7			−1.59561			−0.797804	−	0.602917i	$-0.794005\pi$
$733$	−2.32106e7			−1.59561			−0.797804	+	0.602917i	$0.794005\pi$
$734$	−1.41630e7	+	9.44401e6i	−0.970319	+	0.647018i
$735$	−3.20536e6	+	5.55184e6i	−0.218856	+	0.379069i
$736$	−5.38525e6	−	1.61147e7i	−0.366447	−	1.09655i
$737$	272754.	+	157475.i	0.0184971	+	0.0106793i
$738$	1.10682e7	+	5.47125e6i	0.748057	+	0.369782i
$739$	1.66903e7	−	9.63613e6i	1.12422	−	0.649070i	0.181747	−	0.983345i	$-0.441825\pi$
$739$	1.66903e7	−	9.63613e6i	1.12422	−	0.649070i	0.942475	+	0.334275i	$0.108492\pi$
$740$	6.79958e6	+	2.83158e6i	0.456460	+	0.190086i
$741$	652897.	−	1.72839e6i	0.0436816	−	0.115637i
$742$	−1.11199e7	−	1.66762e7i	−0.741464	−	1.11196i
$743$	8.35960e6	+	1.44792e7i	0.555538	+	0.962219i	0.997861	+	0.0653639i	$0.0208208\pi$
$743$	8.35960e6	+	1.44792e7i	0.555538	+	0.962219i	−0.442324	+	0.896855i	$0.645846\pi$
$744$	2.86339e6	+	3.28385e6i	0.189648	+	0.217496i
$745$	216626.	−	375208.i	0.0142995	−	0.0247675i
$746$	7.46753e6	+	3.69138e6i	0.491281	+	0.242852i
$747$	−6.47163e6	−	3.73640e6i	−0.424338	−	0.244992i
$748$	978746.	+	407584.i	0.0639611	+	0.0266356i
$749$			4.08356e6i			0.265971i
$750$	−1.42013e7	+	917298.i	−0.921884	+	0.0595467i
$751$	−1.00966e7	+	1.74878e7i	−0.653242	+	1.13145i	0.329090	+	0.944299i	$0.393258\pi$
$751$	−1.00966e7	+	1.74878e7i	−0.653242	+	1.13145i	−0.982332	+	0.187149i	$0.940075\pi$
$752$	1.16651e6	−	1.15770e6i	0.0752217	−	0.0746539i
$753$		−	234564.i		−	0.0150756i
$754$	−7.11406e6	+	459514.i	−0.455711	+	0.0294354i
$755$	1.50499e7	+	2.60671e7i	0.960871	+	1.66428i
$756$	8.51828e6	−	6.51070e6i	0.542060	−	0.414308i
$757$	6.17824e6	+	1.07010e7i	0.391855	+	0.678713i	0.992694	−	0.120657i	$-0.0385002\pi$
$757$	6.17824e6	+	1.07010e7i	0.391855	+	0.678713i	−0.600839	+	0.799370i	$0.705167\pi$
$758$	−6.19225e6	+	1.25267e7i	−0.391449	+	0.791889i
$759$	724848.			0.0456712
$760$	1.08557e7	+	2.92006e7i	0.681748	+	1.83383i
$761$	9.76295e6			0.611110			0.305555	−	0.952174i	$-0.401158\pi$
$761$	9.76295e6			0.611110			0.305555	+	0.952174i	$0.401158\pi$
$762$	−207954.	+	420684.i	−0.0129742	+	0.0262463i
$763$	−7.19856e6	−	1.24683e7i	−0.447645	−	0.775344i
$764$	−1.45383e7	+	1.11119e7i	−0.901113	+	0.688740i
$765$	6.69604e6	+	1.15979e7i	0.413680	+	0.716514i
$766$	−1.95245e7	+	1.26113e6i	−1.20229	+	0.0776585i
$767$			1.02469e7i			0.628931i
$768$	−31995.7	+	4.22277e6i	−0.00195744	+	0.258342i
$769$	9.21316e6	−	1.59577e7i	0.561814	−	0.973091i	−0.435524	−	0.900177i	$-0.643437\pi$
$769$	9.21316e6	−	1.59577e7i	0.561814	−	0.973091i	0.997338	−	0.0729135i	$-0.0232297\pi$
$770$	−6.70910e6	+	433356.i	−0.407791	+	0.0263402i
$771$		−	1.02522e6i		−	0.0621129i
$772$	2.03009e7	+	8.45401e6i	1.22595	+	0.510528i
$773$	−7.40351e6	−	4.27442e6i	−0.445645	−	0.257293i	0.260344	−	0.965516i	$-0.416164\pi$
$773$	−7.40351e6	−	4.27442e6i	−0.445645	−	0.257293i	−0.705989	+	0.708223i	$0.749497\pi$
$774$	2.15160e7	+	1.06359e7i	1.29095	+	0.638146i
$775$	2.64057e7	−	4.57359e7i	1.57922	−	2.73529i
$776$	1.22434e7	−	1.06758e7i	0.729872	−	0.636421i
$777$	−750488.	−	1.29988e6i	−0.0445955	−	0.0772417i
$778$	−4.88275e6	−	7.32255e6i	−0.289211	−	0.433724i
$779$	1.49450e7	−	2.44896e6i	0.882373	−	0.144590i
$780$	−3.79351e6	−	1.57975e6i	−0.223257	−	0.0929718i
$781$	−2.08892e6	+	1.20604e6i	−0.122545	+	0.0707511i
$782$	−8.03133e6	−	3.97007e6i	−0.469646	−	0.232157i
$783$	−7.08221e6	−	4.08892e6i	−0.412824	−	0.238344i
$784$	3.91195e6	−	1.43814e7i	0.227302	−	0.835626i
$785$	−2.25944e7	+	3.91346e7i	−1.30866	+	2.26666i
$786$	−1.35870e6	+	905994.i	−0.0784453	+	0.0523081i
$787$	2.21755e7			1.27625			0.638126	−	0.769932i	$-0.279710\pi$
$787$	2.21755e7			1.27625			0.638126	+	0.769932i	$0.279710\pi$
$788$	−1.61974e7	−	2.11919e7i	−0.929246	−	1.21578i
$789$	5.94075e6	+	3.42989e6i	0.339742	+	0.196150i
$790$	2.98709e7	+	4.47967e7i	1.70287	+	2.55375i
$791$	1.13725e7			0.646270
$792$	2.38303e6	+	816487.i	0.134994	+	0.0462526i
$793$	3.26579e6	−	1.88550e6i	0.184419	−	0.106474i
$794$	−1.08219e7	+	699015.i	−0.609192	+	0.0393491i
$795$	−7.63198e6	+	4.40632e6i	−0.428271	+	0.247263i
$796$	2.02257e6	+	1.55911e7i	0.113141	+	0.872158i
$797$		−	1.80645e7i		−	1.00735i	−0.863894	−	0.503674i	$-0.831981\pi$
$797$		−	1.80645e7i		−	1.00735i	0.863894	−	0.503674i	$-0.168019\pi$
$798$	1.85592e6	−	6.07112e6i	0.103170	−	0.337491i
$799$		−	866584.i		−	0.0480224i
$800$	4.85477e7	−	1.62238e7i	2.68191	−	0.896244i
$801$	−9.40977e6	+	5.43274e6i	−0.518201	+	0.299183i
$802$	731459.	+	1.13242e7i	0.0401564	+	0.621689i
$803$	−2.71825e6	+	1.56938e6i	−0.148765	+	0.0858894i
$804$	401675.	+	525531.i	0.0219146	+	0.0286720i
$805$	5.68109e7			3.08988
$806$	8.20074e6	−	5.46833e6i	0.444647	−	0.296495i
$807$	1.29925e6	+	750120.i	0.0702276	+	0.0405459i
$808$	−1.98599e6	+	5.79638e6i	−0.107016	+	0.312340i
$809$	−2.67213e7			−1.43544			−0.717721	−	0.696331i	$-0.754815\pi$
$809$	−2.67213e7			−1.43544			−0.717721	+	0.696331i	$0.754815\pi$
$810$	1.62997e7	+	2.44444e7i	0.872907	+	1.30908i
$811$	−1.18737e7	+	2.05658e7i	−0.633918	+	1.09798i	0.352825	+	0.935689i	$0.385221\pi$
$811$	−1.18737e7	+	2.05658e7i	−0.633918	+	1.09798i	−0.986743	+	0.162290i	$0.948112\pi$
$812$	−2.42917e7	+	3.15127e6i	−1.29291	+	0.167724i
$813$	1.25749e6	+	726012.i	0.0667233	+	0.0385227i
$814$	323726.	−	654887.i	0.0171245	−	0.0346422i
$815$	−5.55597e6	+	3.20774e6i	−0.292999	+	0.169163i
$816$	1.56852e6	+	1.58045e6i	0.0824641	+	0.0830913i
$817$	2.90524e7	−	4.76067e6i	1.52274	−	0.249524i
$818$	−3.09493e7	+	2.06373e7i	−1.61722	+	1.07838i
$819$	−5.85451e6	−	1.01403e7i	−0.304986	−	0.528252i
$820$	−4.33324e6	−	3.34030e7i	−0.225049	−	1.73481i
$821$	4.68020e6	−	8.10634e6i	0.242330	−	0.419727i	−0.719048	−	0.694961i	$-0.755422\pi$
$821$	4.68020e6	−	8.10634e6i	0.242330	−	0.419727i	0.961377	+	0.275233i	$0.0887551\pi$
$822$	3.31502e6	−	6.70617e6i	0.171122	−	0.346174i
$823$	−3.96039e6	−	2.28653e6i	−0.203816	−	0.117673i	0.394618	−	0.918845i	$-0.370877\pi$
$823$	−3.96039e6	−	2.28653e6i	−0.203816	−	0.117673i	−0.598434	+	0.801172i	$0.704210\pi$
$824$	−3.68599e7	+	7.22307e6i	−1.89119	+	0.370599i
$825$			2.18370e6i			0.111701i
$826$	2.26950e6	+	3.51357e7i	0.115739	+	1.79184i
$827$	7.49273e6	−	1.29778e7i	0.380957	−	0.659838i	−0.610242	−	0.792215i	$-0.708928\pi$
$827$	7.49273e6	−	1.29778e7i	0.380957	−	0.659838i	0.991199	+	0.132377i	$0.0422611\pi$
$828$	−1.96503e7	−	8.18305e6i	−0.996076	−	0.414800i
$829$			5.06167e6i			0.255804i	0.991787	+	0.127902i	$0.0408243\pi$
$829$			5.06167e6i			0.255804i	−0.991787	+	0.127902i	$0.959176\pi$
$830$	1.31408e6	+	2.03442e7i	0.0662105	+	1.02505i
$831$	−2.32004e6	−	4.01842e6i	−0.116545	−	0.201861i
$832$	9.46455e6	+	1.30079e6i	0.474015	+	0.0651476i
$833$	−3.92934e6	−	6.80582e6i	−0.196204	−	0.339835i
$834$	−6.80258e6	−	3.36267e6i	−0.338656	−	0.167405i
$835$	−6.47816e7			−3.21540
$836$	2.95954e6	−	887766.i	0.146456	−	0.0439322i
$837$	1.13070e7			0.557873
$838$	2.93592e7	+	1.45129e7i	1.44422	+	0.713913i
$839$	−1.30260e7	−	2.25616e7i	−0.638859	−	1.10654i	−0.985683	−	0.168607i	$-0.946073\pi$
$839$	−1.30260e7	−	2.25616e7i	−0.638859	−	1.10654i	0.346824	−	0.937930i	$-0.387260\pi$
$840$	−1.33575e7	−	4.57663e6i	−0.653172	−	0.223794i
$841$	−913661.	−	1.58251e6i	−0.0445446	−	0.0771535i
$842$	−1.79698e6	−	2.78204e7i	−0.0873501	−	1.35233i
$843$			7.47664e6i			0.362358i
$844$	−4.17634e6	+	1.00288e7i	−0.201809	+	0.484611i
$845$	1.56557e7	−	2.71164e7i	0.754276	−	1.30644i
$846$	−132716.	−	2.05467e6i	−0.00637525	−	0.0986997i
$847$		−	2.78541e7i		−	1.33408i
$848$	1.45421e7	−	1.44323e7i	0.694444	−	0.689202i
$849$	−3.59919e6	−	2.07800e6i	−0.171371	−	0.0989408i
$850$	1.19604e7	−	2.41954e7i	0.567802	−	1.14864i
$851$	−3.08654e6	+	5.34605e6i	−0.146099	+	0.253051i
$852$	−5.02374e6	+	651709.i	−0.237098	+	0.0307578i
$853$	−1.77268e7	−	3.07038e7i	−0.834178	−	1.44484i	−0.894698	−	0.446671i	$-0.852609\pi$
$853$	−1.77268e7	−	3.07038e7i	−0.834178	−	1.44484i	0.0605207	−	0.998167i	$-0.480724\pi$
$854$	1.07805e7	−	7.18854e6i	0.505818	−	0.337284i
$855$	3.65107e7	+	1.37918e7i	1.70807	+	0.645218i
$856$	−4.09621e6	+	802695.i	−0.191072	+	0.0374426i
$857$	−2.63286e7	+	1.52008e7i	−1.22455	+	0.706993i	−0.965884	−	0.258975i	$-0.916615\pi$
$857$	−2.63286e7	+	1.52008e7i	−1.22455	+	0.706993i	−0.258663	+	0.965968i	$0.583282\pi$
$858$	−180608.	+	365364.i	−0.00837566	+	0.0169437i
$859$	−1.69942e7	−	9.81163e6i	−0.785812	−	0.453689i	0.0526738	−	0.998612i	$-0.483226\pi$
$859$	−1.69942e7	−	9.81163e6i	−0.785812	−	0.453689i	−0.838486	+	0.544923i	$0.816559\pi$
$860$	−8.42362e6	−	6.49340e7i	−0.388376	−	2.99382i
$861$	−3.43198e6	+	5.94437e6i	−0.157775	+	0.273274i
$862$	3.87063e6	+	5.80470e6i	0.177424	+	0.266080i
$863$	3.16833e6			0.144812			0.0724059	−	0.997375i	$-0.476932\pi$
$863$	3.16833e6			0.144812			0.0724059	+	0.997375i	$0.476932\pi$
$864$	8.20528e6	+	7.26487e6i	0.373946	+	0.331088i
$865$	−4.29750e6	−	2.48117e6i	−0.195288	−	0.112750i
$866$	1.81873e7	−	1.21275e7i	0.824088	−	0.549510i
$867$	−4.54404e6			−0.205303
$868$	2.69085e7	−	2.05668e7i	1.21225	−	0.926546i
$869$	4.62473e6	−	2.67009e6i	0.207748	−	0.119943i
$870$	694207.	+	1.07475e7i	0.0310950	+	0.481404i
$871$	1.29594e6	−	748213.i	0.0578816	−	0.0334180i
$872$	1.10919e7	−	9.67170e6i	0.493985	−	0.430736i
$873$		−	2.03507e7i		−	0.903739i
$874$	−2.54400e7	+	5.87413e6i	−1.12652	+	0.260115i
$875$			1.10624e8i			4.88459i
$876$	−6.53724e6	+	848050.i	−0.287829	+	0.0373389i
$877$	−2.54127e7	+	1.46721e7i	−1.11571	+	0.644157i	−0.940303	−	0.340338i	$-0.889458\pi$
$877$	−2.54127e7	+	1.46721e7i	−1.11571	+	0.644157i	−0.175410	+	0.984495i	$0.556125\pi$
$878$	−2.08630e7	+	1.34759e6i	−0.913356	+	0.0589958i
$879$	2.00031e6	−	1.15488e6i	0.0873224	−	0.0504156i
$880$	−1.75349e6	−	6.64469e6i	−0.0763301	−	0.289247i
$881$	−1.98402e7			−0.861206			−0.430603	−	0.902541i	$-0.641699\pi$
$881$	−1.98402e7			−0.861206			−0.430603	+	0.902541i	$0.641699\pi$
$882$	−1.03588e7	−	1.55348e7i	−0.448369	−	0.672410i
$883$	1.22889e7	+	7.09503e6i	0.530411	+	0.306233i	0.741184	−	0.671302i	$-0.234265\pi$
$883$	1.22889e7	+	7.09503e6i	0.530411	+	0.306233i	−0.210773	+	0.977535i	$0.567598\pi$
$884$	4.00228e6	−	3.05903e6i	0.172257	−	0.131660i
$885$	1.54804e7			0.664390
$886$	−2.60569e6	+	1.73750e6i	−0.111516	+	0.0743602i
$887$	3.89916e6	−	6.75355e6i	0.166404	−	0.288219i	−0.770749	−	0.637139i	$-0.780118\pi$
$887$	3.89916e6	−	6.75355e6i	0.166404	−	0.288219i	0.937153	+	0.348919i	$0.113451\pi$
$888$	1.15639e6	−	1.00833e6i	0.0492120	−	0.0429110i
$889$	3.15917e6	+	1.82395e6i	0.134066	+	0.0774031i
$890$	2.65729e7	+	1.31356e7i	1.12451	+	0.555871i
$891$	2.52359e6	−	1.45700e6i	0.106494	−	0.0614843i
$892$	−1.85045e6	+	4.44356e6i	−0.0778691	+	0.186990i
$893$	−1.59981e6	−	1.95417e6i	−0.0671336	−	0.0820036i
$894$	−50067.4	−	75085.0i	−0.00209513	−	0.00314202i
$895$	−1.88864e7	−	3.27121e7i	−0.788117	−	1.36506i
$896$	3.27413e7	+	2.36407e6i	1.36247	+	0.0983763i
$897$	1.72199e6	−	2.98258e6i	0.0714579	−	0.123769i
$898$	3.33826e7	+	1.65018e7i	1.38143	+	0.682873i
$899$	−2.23721e7	−	1.29166e7i	−0.923226	−	0.533025i
$900$	2.46525e7	−	5.91989e7i	1.01451	−	2.43617i
$901$		−	1.08031e7i		−	0.443341i
$902$	−3.33377e6	+	215336.i	−0.136433	+	0.00881254i
$903$	−6.67162e6	+	1.15556e7i	−0.272278	+	0.471599i
$904$	2.23546e6	+	1.14077e7i	0.0909799	+	0.464277i
$905$		−	6.98631e7i		−	2.83548i
$906$	6.25676e6	−	404139.i	0.253238	−	0.0163572i
$907$	2.02692e6	+	3.51073e6i	0.0818123	+	0.141703i	0.904028	−	0.427472i	$-0.140596\pi$
$907$	2.02692e6	+	3.51073e6i	0.0818123	+	0.141703i	−0.822216	+	0.569175i	$0.807263\pi$
$908$	2.53819e7	+	3.32084e7i	1.02167	+	1.33670i
$909$	3.83806e6	+	6.64771e6i	0.154064	+	0.266847i
$910$	−1.41554e7	+	2.86358e7i	−0.566654	+	1.14632i
$911$	−1.57962e7			−0.630603			−0.315301	−	0.948992i	$-0.602106\pi$
$911$	−1.57962e7			−0.630603			−0.315301	+	0.948992i	$0.602106\pi$
$912$	6.45474e6	+	668285.i	0.256975	+	0.0266057i
$913$	2.02198e6			0.0802784
$914$	5.35358e6	−	1.08301e7i	0.211972	−	0.428813i
$915$	−2.84851e6	−	4.93376e6i	−0.112477	−	0.194816i
$916$	7.30217e6	+	9.55378e6i	0.287550	+	0.376215i
$917$	6.34727e6	+	1.09938e7i	0.249266	+	0.431742i
$918$	5.76665e6	−	372481.i	0.225848	−	0.0145881i
$919$			1.25713e7i			0.491012i	0.969395	+	0.245506i	$0.0789542\pi$
$919$			1.25713e7i			0.491012i	−0.969395	+	0.245506i	$0.921046\pi$
$920$	1.11671e7	+	5.69868e7i	0.434983	+	2.21975i
$921$	−1.58002e6	+	2.73668e6i	−0.0613783	+	0.106310i
$922$	22672.1	−	1464.44i	0.000878343	−	5.67342e-5i
$923$			1.14605e7i			0.442793i
$924$	−538368.	+	1.29280e6i	−0.0207443	+	0.0498142i
$925$	−1.61056e7	−	9.29860e6i	−0.618905	−	0.357325i
$926$	−1.54081e7	−	7.61657e6i	−0.590501	−	0.291898i
$927$	−2.35282e7	+	4.07520e7i	−0.899268	+	1.55758i
$928$	−7.93599e6	−	2.37475e7i	−0.302504	−	0.905208i
$929$	6.00665e6	+	1.04038e7i	0.228346	+	0.395507i	0.957318	−	0.289037i	$-0.0933350\pi$
$929$	6.00665e6	+	1.04038e7i	0.228346	+	0.395507i	−0.728972	+	0.684543i	$0.760002\pi$
$930$	−8.26124e6	−	1.23892e7i	−0.313212	−	0.469717i
$931$	−2.14251e7	−	8.09326e6i	−0.810117	−	0.306020i
$932$	−3.90301e6	+	9.37244e6i	−0.147184	+	0.353438i
$933$	2.06068e6	−	1.18973e6i	0.0775008	−	0.0447451i
$934$	−8.54002e6	−	4.22153e6i	−0.320326	−	0.158344i
$935$	−3.13813e6	−	1.81180e6i	−0.117393	−	0.0677769i
$936$	9.02090e6	−	7.86589e6i	0.336558	−	0.293466i
$937$	−324149.	+	561442.i	−0.0120613	+	0.0208908i	−0.871993	−	0.489518i	$-0.837173\pi$
$937$	−324149.	+	561442.i	−0.0120613	+	0.0208908i	0.859932	+	0.510409i	$0.170506\pi$
$938$	4.27797e6	−	2.85259e6i	0.158756	−	0.105860i
$939$	−1.37813e6			−0.0510064
$940$	−4.46277e6	+	3.41099e6i	−0.164735	+	0.125910i
$941$	−1.47141e7	−	8.49518e6i	−0.541700	−	0.312751i	0.204067	−	0.978957i	$-0.434584\pi$
$941$	−1.47141e7	−	8.49518e6i	−0.541700	−	0.312751i	−0.745768	+	0.666206i	$0.767917\pi$
$942$	5.22209e6	+	7.83145e6i	0.191742	+	0.287551i
$943$	2.82295e7			1.03377
$944$	−3.47984e7	+	9.18304e6i	−1.27095	+	0.335395i
$945$	−3.17344e7	+	1.83218e7i	−1.15598	+	0.667405i
$946$	−6.48071e6	+	418604.i	−0.235448	+	0.0152081i
$947$	−2.79671e7	+	1.61468e7i	−1.01338	+	0.585074i	−0.912179	−	0.409792i	$-0.865601\pi$
$947$	−2.79671e7	+	1.61468e7i	−1.01338	+	0.585074i	−0.101200	+	0.994866i	$0.532268\pi$
$948$	1.11222e7	−	1.44284e6i	0.401950	−	0.0521433i
$949$			1.49133e7i			0.537535i
$950$	−1.76966e7	−	7.66413e7i	−0.636180	−	2.75521i
$951$		−	6.55523e6i		−	0.235037i
$952$	1.30460e7	−	1.13756e7i	0.466534	−	0.406800i
$953$	3.91360e7	−	2.25952e7i	1.39587	−	0.805905i	0.401911	−	0.915679i	$-0.368346\pi$
$953$	3.91360e7	−	2.25952e7i	1.39587	−	0.805905i	0.993957	+	0.109774i	$0.0350127\pi$
$954$	−1.65448e6	−	2.56142e7i	−0.0588560	−	0.911191i
$955$	5.41615e7	−	3.12702e7i	1.92169	−	1.10949i
$956$	−1.71102e7	+	1.30777e7i	−0.605494	+	0.462792i
$957$	1.06817e6			0.0377018
$958$	1.58269e7	−	1.05535e7i	0.557162	−	0.371521i
$959$	−5.03608e7	−	2.90758e7i	−1.76826	−	1.02090i
$960$	1.96516e6	−	1.42985e7i	0.0688207	−	0.500740i
$961$	7.08886e6			0.247610
$962$	−1.92564e6	−	2.88784e6i	−0.0670869	−	0.100609i
$963$	−2.61467e6	+	4.52874e6i	−0.0908555	+	0.157366i
$964$	4.77759e6	+	3.68283e7i	0.165583	+	1.27641i
$965$	−6.50904e7	−	3.75800e7i	−2.25008	−	1.29909i
$966$	5.24398e6	−	1.06084e7i	0.180808	−	0.365769i
$967$	−1.29473e7	+	7.47511e6i	−0.445258	+	0.257070i	−0.705825	−	0.708386i	$-0.749424\pi$
$967$	−1.29473e7	+	7.47511e6i	−0.445258	+	0.257070i	0.260567	+	0.965456i	$0.416090\pi$
$968$	2.79403e7	−	5.47520e6i	0.958392	−	0.187807i
$969$	2.64761e6	−	2.16751e6i	0.0905826	−	0.0741570i
$970$	−4.61914e7	+	3.08009e7i	−1.57628	+	1.05108i
$971$	−1.61857e6	−	2.80345e6i	−0.0550915	−	0.0954213i	0.837164	−	0.546951i	$-0.184212\pi$
$971$	−1.61857e6	−	2.80345e6i	−0.0550915	−	0.0954213i	−0.892256	+	0.451530i	$0.850878\pi$
$972$	2.06585e7	−	2.67995e6i	0.701348	−	0.0909830i
$973$	−2.94938e7	+	5.10847e7i	−0.998731	+	1.72985i
$974$	−1.71427e7	+	3.46790e7i	−0.579003	+	1.17130i
$975$	8.98540e6	+	5.18772e6i	0.302709	+	0.174769i
$976$	9.32989e6	+	9.40085e6i	0.313511	+	0.315895i
$977$		−	4.57877e7i		−	1.53466i	−0.641253	−	0.767330i	$-0.721585\pi$
$977$		−	4.57877e7i		−	1.53466i	0.641253	−	0.767330i	$-0.278415\pi$
$978$	86138.5	+	1.33357e6i	0.00287972	+	0.0445830i
$979$	1.46998e6	−	2.54608e6i	0.0490179	−	0.0849014i
$980$	−1.95825e7	+	4.70241e7i	−0.651331	+	1.56407i
$981$		−	1.84367e7i		−	0.611660i
$982$	−53356.9	−	826056.i	−0.00176568	−	0.0273357i
$983$	1.20067e7	+	2.07963e7i	0.396316	+	0.686439i	0.993268	−	0.115837i	$-0.0369552\pi$
$983$	1.20067e7	+	2.07963e7i	0.396316	+	0.686439i	−0.596952	+	0.802277i	$0.703622\pi$
$984$	−6.63739e6	−	2.27414e6i	−0.218529	−	0.0748738i
$985$	4.55814e7	+	7.89493e7i	1.49691	+	2.59273i
$986$	−1.18354e7	−	5.85051e6i	−0.387695	−	0.191647i
$987$	1.14465e6			0.0374008
$988$	3.37791e6	−	1.42868e7i	0.110092	−	0.465633i
$989$	5.48769e7			1.78402
$990$	−7.71797e6	−	3.81518e6i	−0.250274	−	0.123716i
$991$	−8.51586e6	−	1.47499e7i	−0.275451	−	0.477095i	0.694798	−	0.719205i	$-0.255494\pi$
$991$	−8.51586e6	−	1.47499e7i	−0.275451	−	0.477095i	−0.970249	+	0.242110i	$0.922160\pi$
$992$	2.59198e7	+	2.29491e7i	0.836281	+	0.740434i
$993$	3.28715e6	+	5.69350e6i	0.105790	+	0.183234i
$994$	2.53830e6	+	3.92972e7i	0.0814849	+	1.26152i
$995$		−	5.37336e7i		−	1.72063i
$996$	3.92021e6	+	1.63251e6i	0.125216	+	0.0521444i
$997$	−1.97560e7	+	3.42184e7i	−0.629450	+	1.09024i	0.358212	+	0.933640i	$0.383387\pi$
$997$	−1.97560e7	+	3.42184e7i	−0.629450	+	1.09024i	−0.987662	+	0.156600i	$0.949947\pi$
$998$	−3.23046e6	−	5.00130e7i	−0.102669	−	1.58949i
$999$		−	3.98171e6i		−	0.126228i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.6.f.a.31.18	yes	96
4.3	odd	2	inner	76.6.f.a.31.2	yes	96
19.8	odd	6	inner	76.6.f.a.27.2	✓	96
76.27	even	6	inner	76.6.f.a.27.18	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.6.f.a.27.2	✓	96	19.8	odd	6	inner
76.6.f.a.27.18	yes	96	76.27	even	6	inner
76.6.f.a.31.2	yes	96	4.3	odd	2	inner
76.6.f.a.31.18	yes	96	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(-2.50677 + 5.07111i) q^{2} +(-2.01363 - 3.48771i) q^{3} +(-19.4322 - 25.4242i) q^{4} +(54.6845 + 94.7163i) q^{5} +(22.7343 - 1.46846i) q^{6} -177.092i q^{7} +(177.641 - 34.8105i) q^{8} +(113.391 - 196.398i) q^{9} +O(q^{10})\)	\(q+(-2.50677 + 5.07111i) q^{2} +(-2.01363 - 3.48771i) q^{3} +(-19.4322 - 25.4242i) q^{4} +(54.6845 + 94.7163i) q^{5} +(22.7343 - 1.46846i) q^{6} -177.092i q^{7} +(177.641 - 34.8105i) q^{8} +(113.391 - 196.398i) q^{9} +(-617.397 + 39.8792i) q^{10} +61.3620i q^{11} +(-49.5428 + 118.969i) q^{12} +(252.490 + 145.775i) q^{13} +(898.054 + 443.929i) q^{14} +(220.229 - 381.447i) q^{15} +(-268.776 + 988.097i) q^{16} +(269.971 + 467.603i) q^{17} +(711.713 + 1067.34i) q^{18} +(1472.04 + 556.059i) q^{19} +(1345.44 - 3230.86i) q^{20} +(-617.647 + 356.598i) q^{21} +(-311.173 - 153.820i) q^{22} +(2540.20 + 1466.59i) q^{23} +(-479.112 - 549.464i) q^{24} +(-4418.28 + 7652.69i) q^{25} +(-1372.18 + 914.980i) q^{26} -1891.93 q^{27} +(-4502.42 + 3441.30i) q^{28} +(3743.38 + 2161.24i) q^{29} +(1382.30 + 2073.00i) q^{30} -5976.45 q^{31} +(-4336.99 - 3839.92i) q^{32} +(214.013 - 123.560i) q^{33} +(-3048.02 + 196.879i) q^{34} +(16773.5 - 9684.20i) q^{35} +(-7196.69 + 933.598i) q^{36} +2104.57i q^{37} +(-6509.89 + 6070.95i) q^{38} -1174.15i q^{39} +(13011.3 + 14921.9i) q^{40} +(8334.82 - 4812.11i) q^{41} +(-260.053 - 4026.06i) q^{42} +(16202.5 - 9354.53i) q^{43} +(1560.08 - 1192.40i) q^{44} +24802.8 q^{45} +(-13804.9 + 9205.25i) q^{46} +(-1389.93 - 802.479i) q^{47} +(3987.41 - 1052.25i) q^{48} -14554.7 q^{49} +(-27732.0 - 41589.1i) q^{50} +(1087.24 - 1883.16i) q^{51} +(-1200.24 - 9252.09i) q^{52} +(-17327.4 - 10004.0i) q^{53} +(4742.63 - 9594.19i) q^{54} +(-5811.98 + 3355.55i) q^{55} +(-6164.68 - 31458.8i) q^{56} +(-1024.77 - 6253.74i) q^{57} +(-20343.6 + 13565.3i) q^{58} +(17573.1 + 30437.5i) q^{59} +(-13977.5 + 1813.25i) q^{60} +(6467.16 - 11201.4i) q^{61} +(14981.6 - 30307.2i) q^{62} +(-34780.6 - 20080.6i) q^{63} +(30344.5 - 12367.5i) q^{64} +31886.6i q^{65} +(90.1076 + 1395.02i) q^{66} +(2566.32 - 4445.01i) q^{67} +(6642.28 - 15950.4i) q^{68} -11812.7i q^{69} +(7062.29 + 109336. i) q^{70} +(19654.5 + 34042.5i) q^{71} +(13306.1 - 38835.5i) q^{72} +(25575.8 + 44298.5i) q^{73} +(-10672.5 - 5275.68i) q^{74} +35587.1 q^{75} +(-14467.7 - 48230.8i) q^{76} +10866.7 q^{77} +(5954.24 + 2943.32i) q^{78} +(-43513.7 - 75368.0i) q^{79} +(-108287. + 28576.1i) q^{80} +(-23744.3 - 41126.3i) q^{81} +(3509.28 + 54329.6i) q^{82} -32951.6i q^{83} +(21068.5 + 8773.64i) q^{84} +(-29526.4 + 51141.3i) q^{85} +(6821.88 + 105614. i) q^{86} -17407.8i q^{87} +(2136.04 + 10900.4i) q^{88} +(-41492.7 - 23955.8i) q^{89} +(-62174.9 + 125778. i) q^{90} +(25815.7 - 44714.0i) q^{91} +(-12075.1 - 93081.6i) q^{92} +(12034.4 + 20844.1i) q^{93} +(7553.70 - 5036.88i) q^{94} +(27829.8 + 169834. i) q^{95} +(-4659.44 + 22858.3i) q^{96} +(77714.5 - 44868.5i) q^{97} +(36485.2 - 73808.3i) q^{98} +(12051.4 + 6957.88i) 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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