LMFDB - Embedded newform 76.5.l.a.43.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,5,Mod(23,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 2]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("76.23");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	76.l (of order $18$, degree $6$, 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:	$7.85611719437$
Analytic rank:	$0$
Dimension:	$228$
Relative dimension:	$38$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			43.7
Character	$\chi$	$=$	76.43
Dual form			76.5.l.a.23.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.53287 - 1.87585i) q^{2} +(3.32006 + 0.585416i) q^{3} +(8.96237 + 13.2543i) q^{4} +(31.7438 + 26.6362i) q^{5} +(-10.6312 - 8.29614i) q^{6} +(-51.6354 + 29.8117i) q^{7} +(-6.79985 - 63.6377i) q^{8} +(-65.4350 - 23.8164i) q^{9} +O(q^{10})$	\(q+(-3.53287 - 1.87585i) q^{2} +(3.32006 + 0.585416i) q^{3} +(8.96237 + 13.2543i) q^{4} +(31.7438 + 26.6362i) q^{5} +(-10.6312 - 8.29614i) q^{6} +(-51.6354 + 29.8117i) q^{7} +(-6.79985 - 63.6377i) q^{8} +(-65.4350 - 23.8164i) q^{9} +(-62.1812 - 153.649i) q^{10} +(-66.2459 - 38.2471i) q^{11} +(21.9963 + 49.2517i) q^{12} +(47.6602 + 270.294i) q^{13} +(238.344 - 8.46066i) q^{14} +(89.7981 + 107.017i) q^{15} +(-95.3519 + 237.579i) q^{16} +(-219.584 + 79.9221i) q^{17} +(186.497 + 206.887i) q^{18} +(-65.3930 - 355.028i) q^{19} +(-68.5442 + 659.465i) q^{20} +(-188.885 + 68.7485i) q^{21} +(162.292 + 259.389i) q^{22} +(424.356 + 505.727i) q^{23} +(14.6787 - 215.262i) q^{24} +(189.651 + 1075.56i) q^{25} +(338.654 - 1044.32i) q^{26} +(-439.794 - 253.915i) q^{27} +(-857.908 - 417.207i) q^{28} +(770.112 + 280.298i) q^{29} +(-116.497 - 546.526i) q^{30} +(-956.138 + 552.027i) q^{31} +(782.530 - 660.472i) q^{32} +(-197.550 - 165.764i) q^{33} +(925.685 + 129.553i) q^{34} +(-2433.18 - 429.035i) q^{35} +(-270.783 - 1080.75i) q^{36} +1009.86 q^{37} +(-434.954 + 1376.94i) q^{38} +925.294i q^{39} +(1479.22 - 2201.23i) q^{40} +(-198.738 + 1127.10i) q^{41} +(796.269 + 111.440i) q^{42} +(1941.94 - 2314.31i) q^{43} +(-86.7825 - 1220.83i) q^{44} +(-1442.78 - 2498.96i) q^{45} +(-550.525 - 2582.70i) q^{46} +(-580.185 + 1594.05i) q^{47} +(-455.657 + 732.958i) q^{48} +(576.977 - 999.354i) q^{49} +(1347.59 - 4155.59i) q^{50} +(-775.821 + 136.798i) q^{51} +(-3155.41 + 3054.18i) q^{52} +(990.107 - 830.798i) q^{53} +(1077.43 + 1722.04i) q^{54} +(-1084.14 - 2978.65i) q^{55} +(2248.26 + 3083.25i) q^{56} +(-9.26962 - 1217.00i) q^{57} +(-2194.91 - 2434.87i) q^{58} +(1220.87 + 3354.30i) q^{59} +(-613.633 + 2149.34i) q^{60} +(-20.3696 + 17.0922i) q^{61} +(4413.43 - 156.667i) q^{62} +(4088.77 - 720.961i) q^{63} +(-4003.52 + 865.454i) q^{64} +(-5686.70 + 9849.65i) q^{65} +(386.970 + 956.198i) q^{66} +(746.531 - 2051.08i) q^{67} +(-3027.31 - 2194.14i) q^{68} +(1112.83 + 1927.47i) q^{69} +(7791.29 + 6080.00i) q^{70} +(-3890.82 + 4636.90i) q^{71} +(-1070.67 + 4326.08i) q^{72} +(1670.93 - 9476.31i) q^{73} +(-3567.70 - 1894.34i) q^{74} +3681.97i q^{75} +(4119.56 - 4048.63i) q^{76} +4560.84 q^{77} +(1735.71 - 3268.95i) q^{78} +(5574.82 + 982.992i) q^{79} +(-9355.05 + 5001.86i) q^{80} +(3009.29 + 2525.10i) q^{81} +(2816.39 - 3609.10i) q^{82} +(3635.44 - 2098.92i) q^{83} +(-2604.07 - 1887.39i) q^{84} +(-9099.26 - 3311.86i) q^{85} +(-11201.9 + 4533.38i) q^{86} +(2392.73 + 1381.44i) q^{87} +(-1983.50 + 4475.81i) q^{88} +(-47.9543 - 271.962i) q^{89} +(409.465 + 11535.0i) q^{90} +(-10518.9 - 12535.9i) q^{91} +(-2899.82 + 10157.0i) q^{92} +(-3497.60 + 1273.02i) q^{93} +(5039.91 - 4543.22i) q^{94} +(7380.78 - 13011.8i) q^{95} +(2984.70 - 1734.70i) q^{96} +(12941.3 - 4710.26i) q^{97} +(-3913.02 + 2448.27i) q^{98} +(3423.89 + 4080.44i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 228 q - 6 q^{2} - 48 q^{4} - 12 q^{5} - 60 q^{6} - 3 q^{8} - 180 q^{9}+O(q^{10}) $ 228 * q - 6 * q^2 - 48 * q^4 - 12 * q^5 - 60 * q^6 - 3 * q^8 - 180 * q^9	$ 228 q - 6 q^{2} - 48 q^{4} - 12 q^{5} - 60 q^{6} - 3 q^{8} - 180 q^{9} - 453 q^{10} - 3 q^{12} + 516 q^{13} + 81 q^{14} - 720 q^{16} - 12 q^{17} - 12 q^{18} - 1182 q^{20} - 930 q^{21} - 54 q^{22} - 2664 q^{24} - 12 q^{25} - 3099 q^{26} - 4824 q^{28} - 12 q^{29} + 5814 q^{30} + 7419 q^{32} + 1542 q^{33} + 6912 q^{34} + 8547 q^{36} - 24 q^{37} - 1536 q^{38} - 6942 q^{40} + 6396 q^{41} - 18855 q^{42} - 1143 q^{44} - 6 q^{45} - 1488 q^{46} + 6093 q^{48} + 26748 q^{49} + 8070 q^{50} - 12591 q^{52} + 2436 q^{53} - 7365 q^{54} - 14418 q^{56} - 12 q^{57} + 8268 q^{58} + 34632 q^{60} - 31068 q^{61} + 27396 q^{62} + 4575 q^{64} + 3594 q^{65} - 29556 q^{66} - 22782 q^{68} + 29370 q^{69} - 71541 q^{70} - 30174 q^{72} - 6348 q^{73} - 417 q^{74} + 43194 q^{76} - 50436 q^{77} + 45537 q^{78} + 30081 q^{80} - 41994 q^{81} + 72219 q^{82} + 13779 q^{84} - 59244 q^{85} + 19200 q^{86} - 22395 q^{88} + 1860 q^{89} + 45594 q^{90} - 64140 q^{92} + 59118 q^{93} - 55590 q^{94} - 98646 q^{96} - 5556 q^{97} - 52215 q^{98}+O(q^{100}) $ 228 * q - 6 * q^2 - 48 * q^4 - 12 * q^5 - 60 * q^6 - 3 * q^8 - 180 * q^9 - 453 * q^10 - 3 * q^12 + 516 * q^13 + 81 * q^14 - 720 * q^16 - 12 * q^17 - 12 * q^18 - 1182 * q^20 - 930 * q^21 - 54 * q^22 - 2664 * q^24 - 12 * q^25 - 3099 * q^26 - 4824 * q^28 - 12 * q^29 + 5814 * q^30 + 7419 * q^32 + 1542 * q^33 + 6912 * q^34 + 8547 * q^36 - 24 * q^37 - 1536 * q^38 - 6942 * q^40 + 6396 * q^41 - 18855 * q^42 - 1143 * q^44 - 6 * q^45 - 1488 * q^46 + 6093 * q^48 + 26748 * q^49 + 8070 * q^50 - 12591 * q^52 + 2436 * q^53 - 7365 * q^54 - 14418 * q^56 - 12 * q^57 + 8268 * q^58 + 34632 * q^60 - 31068 * q^61 + 27396 * q^62 + 4575 * q^64 + 3594 * q^65 - 29556 * q^66 - 22782 * q^68 + 29370 * q^69 - 71541 * q^70 - 30174 * q^72 - 6348 * q^73 - 417 * q^74 + 43194 * q^76 - 50436 * q^77 + 45537 * q^78 + 30081 * q^80 - 41994 * q^81 + 72219 * q^82 + 13779 * q^84 - 59244 * q^85 + 19200 * q^86 - 22395 * q^88 + 1860 * q^89 + 45594 * q^90 - 64140 * q^92 + 59118 * q^93 - 55590 * q^94 - 98646 * q^96 - 5556 * q^97 - 52215 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$-1$

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 $

$2$	−3.53287	−	1.87585i	−0.883218	−	0.468963i
$2$	−3.53287	−	1.87585i	−0.883218	−	0.468963i
$3$	3.32006	+	0.585416i	0.368896	+	0.0650463i	0.355023	−	0.934857i	$-0.384473\pi$
$3$	3.32006	+	0.585416i	0.368896	+	0.0650463i	0.0138726	+	0.999904i	$0.495584\pi$
$4$	8.96237	+	13.2543i	0.560148	+	0.828393i
$5$	31.7438	+	26.6362i	1.26975	+	1.06545i	0.994571	+	0.104056i	$0.0331822\pi$
$5$	31.7438	+	26.6362i	1.26975	+	1.06545i	0.275181	+	0.961392i	$0.411262\pi$
$6$	−10.6312	−	8.29614i	−0.295311	−	0.230448i
$7$	−51.6354	+	29.8117i	−1.05378	+	0.608402i	−0.923706	−	0.383101i	$-0.874856\pi$
$7$	−51.6354	+	29.8117i	−1.05378	+	0.608402i	−0.130078	+	0.991504i	$0.541523\pi$
$8$	−6.79985	−	63.6377i	−0.106248	−	0.994340i
$9$	−65.4350	−	23.8164i	−0.807840	−	0.294030i
$10$	−62.1812	−	153.649i	−0.621812	−	1.53649i
$11$	−66.2459	−	38.2471i	−0.547487	−	0.316092i	0.200621	−	0.979669i	$-0.435704\pi$
$11$	−66.2459	−	38.2471i	−0.547487	−	0.316092i	−0.748108	+	0.663577i	$0.769037\pi$
$12$	21.9963	+	49.2517i	0.152752	+	0.342026i
$13$	47.6602	+	270.294i	0.282013	+	1.59937i	0.715765	+	0.698341i	$0.246078\pi$
$13$	47.6602	+	270.294i	0.282013	+	1.59937i	−0.433752	+	0.901032i	$0.642811\pi$
$14$	238.344	−	8.46066i	1.21604	−	0.0431666i
$15$	89.7981	+	107.017i	0.399103	+	0.475632i
$16$	−95.3519	+	237.579i	−0.372468	+	0.928045i
$17$	−219.584	+	79.9221i	−0.759807	+	0.276547i	−0.692727	−	0.721200i	$-0.743591\pi$
$17$	−219.584	+	79.9221i	−0.759807	+	0.276547i	−0.0670806	+	0.997748i	$0.521368\pi$
$18$	186.497	+	206.887i	0.575610	+	0.638539i
$19$	−65.3930	−	355.028i	−0.181144	−	0.983457i
$19$	−65.3930	−	355.028i	−0.181144	−	0.983457i
$20$	−68.5442	+	659.465i	−0.171361	+	1.64866i
$21$	−188.885	+	68.7485i	−0.428311	+	0.155892i
$22$	162.292	+	259.389i	0.335315	+	0.535929i
$23$	424.356	+	505.727i	0.802184	+	0.956006i	0.999705	−	0.0242926i	$-0.00773335\pi$
$23$	424.356	+	505.727i	0.802184	+	0.956006i	−0.197521	+	0.980299i	$0.563289\pi$
$24$	14.6787	−	215.262i	0.0254838	−	0.373719i
$25$	189.651	+	1075.56i	0.303442	+	1.72090i
$26$	338.654	−	1044.32i	0.500968	−	1.54485i
$27$	−439.794	−	253.915i	−0.603285	−	0.348306i
$28$	−857.908	−	417.207i	−1.09427	−	0.532151i
$29$	770.112	+	280.298i	0.915709	+	0.333291i	0.756530	−	0.653959i	$-0.226893\pi$
$29$	770.112	+	280.298i	0.915709	+	0.333291i	0.159179	+	0.987250i	$0.449115\pi$
$30$	−116.497	−	546.526i	−0.129441	−	0.607251i
$31$	−956.138	+	552.027i	−0.994941	+	0.574430i	−0.906748	−	0.421674i	$-0.861443\pi$
$31$	−956.138	+	552.027i	−0.994941	+	0.574430i	−0.0881936	+	0.996103i	$0.528109\pi$
$32$	782.530	−	660.472i	0.764189	−	0.644992i
$33$	−197.550	−	165.764i	−0.181405	−	0.152217i
$34$	925.685	+	129.553i	0.800766	+	0.112070i
$35$	−2433.18	−	429.035i	−1.98627	−	0.350232i
$36$	−270.783	−	1080.75i	−0.208938	−	0.833908i
$37$	1009.86			0.737662			0.368831	−	0.929497i	$-0.379758\pi$
$37$	1009.86			0.737662			0.368831	+	0.929497i	$0.379758\pi$
$38$	−434.954	+	1376.94i	−0.301215	+	0.953556i
$39$			925.294i			0.608346i
$40$	1479.22	−	2201.23i	0.924510	−	1.37577i
$41$	−198.738	+	1127.10i	−0.118226	+	0.670494i	0.866876	+	0.498524i	$0.166124\pi$
$41$	−198.738	+	1127.10i	−0.118226	+	0.670494i	−0.985102	+	0.171970i	$0.944987\pi$
$42$	796.269	+	111.440i	0.451399	+	0.0631748i
$43$	1941.94	−	2314.31i	1.05026	−	1.25166i	0.0833580	−	0.996520i	$-0.473436\pi$
$43$	1941.94	−	2314.31i	1.05026	−	1.25166i	0.966905	−	0.255135i	$-0.0821201\pi$
$44$	−86.7825	−	1220.83i	−0.0448257	−	0.630592i
$45$	−1442.78	−	2498.96i	−0.712483	−	1.23406i
$46$	−550.525	−	2582.70i	−0.260172	−	1.22056i
$47$	−580.185	+	1594.05i	−0.262646	+	0.721615i	0.736341	+	0.676611i	$0.236552\pi$
$47$	−580.185	+	1594.05i	−0.262646	+	0.721615i	−0.998987	+	0.0450035i	$0.985670\pi$
$48$	−455.657	+	732.958i	−0.197768	+	0.318124i
$49$	576.977	−	999.354i	0.240307	−	0.416224i
$50$	1347.59	−	4155.59i	0.539034	−	1.66224i
$51$	−775.821	+	136.798i	−0.298278	+	0.0525945i
$52$	−3155.41	+	3054.18i	−1.16694	+	1.12950i
$53$	990.107	−	830.798i	0.352477	−	0.295763i	−0.449307	−	0.893377i	$-0.648329\pi$
$53$	990.107	−	830.798i	0.352477	−	0.295763i	0.801784	+	0.597614i	$0.203885\pi$
$54$	1077.43	+	1722.04i	0.369489	+	0.590548i
$55$	−1084.14	−	2978.65i	−0.358393	−	0.984677i
$56$	2248.26	+	3083.25i	0.716921	+	0.983178i
$57$	−9.26962	−	1217.00i	−0.00285307	−	0.374576i
$58$	−2194.91	−	2434.87i	−0.652470	−	0.723802i
$59$	1220.87	+	3354.30i	0.350723	+	0.963603i	0.982139	+	0.188158i	$0.0602519\pi$
$59$	1220.87	+	3354.30i	0.350723	+	0.963603i	−0.631416	+	0.775444i	$0.717526\pi$
$60$	−613.633	+	2149.34i	−0.170454	+	0.597038i
$61$	−20.3696	+	17.0922i	−0.00547424	+	0.00459343i	−0.645521	−	0.763743i	$-0.723360\pi$
$61$	−20.3696	+	17.0922i	−0.00547424	+	0.00459343i	0.640046	+	0.768336i	$0.278915\pi$
$62$	4413.43	−	156.667i	1.14814	−	0.0407562i
$63$	4088.77	−	720.961i	1.03018	−	0.181648i
$64$	−4003.52	+	865.454i	−0.977423	+	0.211292i
$65$	−5686.70	+	9849.65i	−1.34596	+	2.33128i
$66$	386.970	+	956.198i	0.0888361	+	0.219513i
$67$	746.531	−	2051.08i	0.166302	−	0.456912i	−0.828348	−	0.560214i	$-0.810719\pi$
$67$	746.531	−	2051.08i	0.166302	−	0.456912i	0.994650	+	0.103302i	$0.0329409\pi$
$68$	−3027.31	−	2194.14i	−0.654694	−	0.474511i
$69$	1112.83	+	1927.47i	0.233738	+	0.404846i
$70$	7791.29	+	6080.00i	1.59006	+	1.24082i
$71$	−3890.82	+	4636.90i	−0.771835	+	0.919837i	−0.998534	−	0.0541279i	$-0.982762\pi$
$71$	−3890.82	+	4636.90i	−0.771835	+	0.919837i	0.226699	+	0.973965i	$0.427207\pi$
$72$	−1070.67	+	4326.08i	−0.206534	+	0.834507i
$73$	1670.93	−	9476.31i	0.313554	−	1.77825i	−0.266661	−	0.963790i	$-0.585920\pi$
$73$	1670.93	−	9476.31i	0.313554	−	1.77825i	0.580215	−	0.814463i	$-0.302968\pi$
$74$	−3567.70	−	1894.34i	−0.651516	−	0.345936i
$75$			3681.97i			0.654572i
$76$	4119.56	−	4048.63i	0.713221	−	0.700940i
$77$	4560.84			0.769243
$78$	1735.71	−	3268.95i	0.285292	−	0.537302i
$79$	5574.82	+	982.992i	0.893258	+	0.157506i	0.601392	−	0.798954i	$-0.294613\pi$
$79$	5574.82	+	982.992i	0.893258	+	0.157506i	0.291866	+	0.956459i	$0.405724\pi$
$80$	−9355.05	+	5001.86i	−1.46173	+	0.781541i
$81$	3009.29	+	2525.10i	0.458664	+	0.384865i
$82$	2816.39	−	3609.10i	0.418856	−	0.536749i
$83$	3635.44	−	2098.92i	0.527716	−	0.304677i	−0.212370	−	0.977189i	$-0.568118\pi$
$83$	3635.44	−	2098.92i	0.527716	−	0.304677i	0.740086	+	0.672512i	$0.234785\pi$
$84$	−2604.07	−	1887.39i	−0.369057	−	0.267487i
$85$	−9099.26	−	3311.86i	−1.25941	−	0.458389i
$86$	−11201.9	+	4533.38i	−1.51459	+	0.612950i
$87$	2392.73	+	1381.44i	0.316122	+	0.182513i
$88$	−1983.50	+	4475.81i	−0.256133	+	0.577972i
$89$	−47.9543	−	271.962i	−0.00605407	−	0.0343343i	0.981631	−	0.190789i	$-0.0611046\pi$
$89$	−47.9543	−	271.962i	−0.00605407	−	0.0343343i	−0.987685	+	0.156455i	$0.949994\pi$
$90$	409.465	+	11535.0i	0.0505512	+	1.42407i
$91$	−10518.9	−	12535.9i	−1.27024	−	1.51382i
$92$	−2899.82	+	10157.0i	−0.342606	+	1.20003i
$93$	−3497.60	+	1273.02i	−0.404394	+	0.147187i
$94$	5039.91	−	4543.22i	0.570384	−	0.514172i
$95$	7380.78	−	13011.8i	0.817814	−	1.44175i
$96$	2984.70	−	1734.70i	0.323860	−	0.188227i
$97$	12941.3	−	4710.26i	1.37542	−	0.500612i	0.454633	−	0.890679i	$-0.349770\pi$
$97$	12941.3	−	4710.26i	1.37542	−	0.500612i	0.920787	+	0.390067i	$0.127548\pi$
$98$	−3913.02	+	2448.27i	−0.407437	+	0.254921i
$99$	3423.89	+	4080.44i	0.349341	+	0.416329i
$100$	−12556.1	+	12153.3i	−1.25561	+	1.21533i
$101$	−604.527	−	3428.44i	−0.0592616	−	0.336089i	0.940734	−	0.339146i	$-0.110138\pi$
$101$	−604.527	−	3428.44i	−0.0592616	−	0.336089i	−0.999995	+	0.00305697i	$0.999027\pi$
$102$	2997.49	+	972.034i	0.288109	+	0.0934289i
$103$	2251.42	+	1299.86i	0.212218	+	0.122524i	0.602342	−	0.798238i	$-0.294234\pi$
$103$	2251.42	+	1299.86i	0.212218	+	0.122524i	−0.390124	+	0.920762i	$0.627568\pi$
$104$	16876.8	−	4870.94i	1.56036	−	0.450346i
$105$	−7827.13	−	2848.84i	−0.709944	−	0.258398i
$106$	−5056.37	+	1077.81i	−0.450015	+	0.0959248i
$107$	3448.72	−	1991.12i	0.301224	−	0.173912i	−0.341768	−	0.939784i	$-0.611026\pi$
$107$	3448.72	−	1991.12i	0.301224	−	0.173912i	0.642993	+	0.765872i	$0.277693\pi$
$108$	−576.133	−	8104.84i	−0.0493941	−	0.694860i
$109$	−1891.56	−	1587.20i	−0.159209	−	0.133592i	0.559703	−	0.828693i	$-0.310915\pi$
$109$	−1891.56	−	1587.20i	−0.159209	−	0.133592i	−0.718912	+	0.695101i	$0.755360\pi$
$110$	−1757.37	+	12556.9i	−0.145237	+	1.03776i
$111$	3352.79	+	591.188i	0.272120	+	0.0479821i
$112$	−2159.12	−	15110.1i	−0.172124	−	1.20457i
$113$	−5364.85			−0.420146			−0.210073	−	0.977686i	$-0.567370\pi$
$113$	−5364.85			−0.420146			−0.210073	+	0.977686i	$0.567370\pi$
$114$	−2250.16	+	4316.88i	−0.173142	+	0.332170i
$115$			27356.9i			2.06858i
$116$	3186.88	+	12719.4i	0.236837	+	0.945259i
$117$	3318.79	−	18821.8i	0.242442	−	1.37496i
$118$	1979.01	−	14140.5i	0.142129	−	1.01555i
$119$	8955.71	−	10673.0i	0.632421	−	0.753689i
$120$	6199.72	−	6442.25i	0.430536	−	0.447379i
$121$	−4394.82	−	7612.05i	−0.300172	−	0.519914i
$122$	104.026	−	22.1740i	0.00698909	−	0.00148979i
$123$	−1319.65	+	3625.70i	−0.0872263	+	0.239652i
$124$	−15886.0	−	7725.46i	−1.03317	−	0.502436i
$125$	−9679.17	+	16764.8i	−0.619467	+	1.07295i
$126$	−15797.5	−	5122.86i	−0.995057	−	0.322680i
$127$	−25972.7	+	4579.69i	−1.61031	+	0.283941i	−0.905146	−	0.425101i	$-0.860238\pi$
$127$	−25972.7	+	4579.69i	−1.61031	+	0.283941i	−0.705166	+	0.709043i	$0.749127\pi$
$128$	15767.4	+	4452.48i	0.962366	+	0.271758i
$129$	7802.19	−	6546.81i	0.468853	−	0.393415i
$130$	38566.9	−	24130.2i	2.28206	−	1.42782i
$131$	9908.05	+	27222.2i	0.577359	+	1.58628i	0.792615	+	0.609723i	$0.208719\pi$
$131$	9908.05	+	27222.2i	0.577359	+	1.58628i	−0.215256	+	0.976558i	$0.569059\pi$
$132$	426.568	−	4104.02i	0.0244817	−	0.235538i
$133$	13960.6	+	16382.5i	0.789224	+	0.926142i
$134$	−6484.92	+	5845.82i	−0.361156	+	0.325563i
$135$	−7197.40	−	19774.7i	−0.394919	−	1.08503i
$136$	6579.20	+	13430.4i	0.355710	+	0.726124i
$137$	5161.54	−	4331.04i	0.275003	−	0.230755i	−0.494846	−	0.868981i	$-0.664776\pi$
$137$	5161.54	−	4331.04i	0.275003	−	0.230755i	0.769850	+	0.638225i	$0.220331\pi$
$138$	−315.823	−	8897.00i	−0.0165839	−	0.467181i
$139$	−3248.30	+	572.763i	−0.168123	+	0.0296446i	−0.257076	−	0.966391i	$-0.582759\pi$
$139$	−3248.30	+	572.763i	−0.168123	+	0.0296446i	0.0889531	+	0.996036i	$0.471648\pi$
$140$	−16120.5	−	36095.2i	−0.822473	−	1.84159i
$141$	−2859.43	+	4952.68i	−0.143827	+	0.249116i
$142$	22443.9	−	9082.97i	1.11307	−	0.450455i
$143$	7180.67	−	19728.7i	0.351150	−	0.964778i
$144$	11897.6	−	13275.1i	0.573767	−	0.640195i
$145$	16980.2	+	29410.6i	0.807620	+	1.39884i
$146$	−23679.3	+	30344.2i	−1.11087	+	1.42354i
$147$	2500.64	−	2980.14i	0.115722	−	0.137912i
$148$	9050.73	+	13385.0i	0.413200	+	0.611073i
$149$	2113.97	−	11988.9i	0.0952195	−	0.540016i	−0.899460	−	0.437002i	$-0.856040\pi$
$149$	2113.97	−	11988.9i	0.0952195	−	0.540016i	0.994680	−	0.103014i	$-0.0328487\pi$
$150$	6906.82	−	13007.9i	0.306970	−	0.578130i
$151$			1447.84i			0.0634990i	0.999496	+	0.0317495i	$0.0101079\pi$
$151$			1447.84i			0.0634990i	−0.999496	+	0.0317495i	$0.989892\pi$
$152$	−22148.5	+	6575.60i	−0.958644	+	0.284609i
$153$	16272.0			0.695115
$154$	−16112.9	−	8555.46i	−0.679410	−	0.360746i
$155$	−45055.4	−	7944.48i	−1.87535	−	0.330676i
$156$	−12264.1	+	8292.83i	−0.503949	+	0.340764i
$157$	2870.46	+	2408.60i	0.116453	+	0.0977160i	0.699155	−	0.714970i	$-0.253560\pi$
$157$	2870.46	+	2408.60i	0.116453	+	0.0977160i	−0.582701	+	0.812686i	$0.698004\pi$
$158$	−17851.2	−	13930.3i	−0.715077	−	0.558016i
$159$	3773.58	−	2178.68i	0.149265	−	0.0861784i
$160$	42432.9	−	122.263i	1.65754	−	0.00477588i
$161$	−36988.4	−	13462.7i	−1.42697	−	0.519373i
$162$	−5894.74	−	14565.8i	−0.224613	−	0.555016i
$163$	3335.65	+	1925.84i	0.125547	+	0.0724845i	0.561458	−	0.827505i	$-0.310241\pi$
$163$	3335.65	+	1925.84i	0.125547	+	0.0724845i	−0.435911	+	0.899990i	$0.643574\pi$
$164$	−16720.1	+	7467.36i	−0.621657	+	0.277638i
$165$	−1855.66	−	10524.0i	−0.0681601	−	0.386555i
$166$	−16780.8	+	595.680i	−0.608970	+	0.0216171i
$167$	−5140.77	−	6126.53i	−0.184330	−	0.219676i	0.665964	−	0.745984i	$-0.268020\pi$
$167$	−5140.77	−	6126.53i	−0.184330	−	0.219676i	−0.850294	+	0.526308i	$0.823576\pi$
$168$	5659.39	+	11552.7i	0.200517	+	0.409323i
$169$	−43948.9	+	15996.1i	−1.53877	+	0.560067i
$170$	25934.0	+	28769.2i	0.897369	+	0.995476i
$171$	−4176.49	+	24788.7i	−0.142830	+	0.847737i
$172$	48078.9	+	4997.28i	1.62516	+	0.168918i
$173$	−2378.42	+	865.676i	−0.0794689	+	0.0289243i	−0.381449	−	0.924390i	$-0.624575\pi$
$173$	−2378.42	+	865.676i	−0.0794689	+	0.0289243i	0.301980	+	0.953314i	$0.402352\pi$
$174$	−5861.82	−	9368.85i	−0.193613	−	0.309448i
$175$	−41857.2	−	49883.4i	−1.36676	−	1.62885i
$176$	15403.4	−	12091.7i	0.497269	−	0.390358i
$177$	2089.69	+	11851.2i	0.0667014	+	0.378282i
$178$	−340.744	+	1050.76i	−0.0107545	+	0.0331638i
$179$	37271.5	+	21518.7i	1.16324	+	0.671599i	0.952079	−	0.305851i	$-0.0989411\pi$
$179$	37271.5	+	21518.7i	1.16324	+	0.671599i	0.211164	+	0.977451i	$0.432274\pi$
$180$	20191.3	−	41519.6i	0.623187	−	1.28147i
$181$	18336.5	+	6673.93i	0.559705	+	0.203716i	0.606353	−	0.795196i	$-0.292632\pi$
$181$	18336.5	+	6673.93i	0.559705	+	0.203716i	−0.0466484	+	0.998911i	$0.514854\pi$
$182$	13646.4	+	64019.7i	0.411978	+	1.93273i
$183$	−77.6345	+	44.8223i	−0.00231821	+	0.00133842i
$184$	29297.8	−	30443.9i	0.865365	−	0.899217i
$185$	32056.8	+	26898.8i	0.936648	+	0.785941i
$186$	14744.6	+	2063.55i	0.426194	+	0.0596472i
$187$	17603.3	+	3103.94i	0.503399	+	0.0887627i
$188$	−26327.8	+	6596.49i	−0.744901	+	0.186637i
$189$	30278.6			0.847642
$190$	−50483.4	+	32123.6i	−1.39843	+	0.889851i
$191$			46644.6i			1.27860i	0.768958	+	0.639299i	$0.220776\pi$
$191$			46644.6i			1.27860i	−0.768958	+	0.639299i	$0.779224\pi$
$192$	−13798.6	+	529.631i	−0.374311	+	0.0143672i
$193$	−12701.6	+	72034.6i	−0.340993	+	1.93387i	0.0162820	+	0.999867i	$0.494817\pi$
$193$	−12701.6	+	72034.6i	−0.340993	+	1.93387i	−0.357275	+	0.933999i	$0.616294\pi$
$194$	−54555.8	−	7635.26i	−1.44956	−	0.202871i
$195$	−24646.3	+	29372.4i	−0.648161	+	0.772449i
$196$	18416.8	−	1309.16i	0.479404	−	0.0340785i
$197$	15759.2	+	27295.6i	0.406069	+	0.703333i	0.994445	−	0.105255i	$-0.0335658\pi$
$197$	15759.2	+	27295.6i	0.406069	+	0.703333i	−0.588376	+	0.808588i	$0.700232\pi$
$198$	−4441.88	−	20838.4i	−0.113302	−	0.531537i
$199$	4842.02	−	13303.3i	0.122270	−	0.335935i	−0.863424	−	0.504479i	$-0.831685\pi$
$199$	4842.02	−	13303.3i	0.122270	−	0.335935i	0.985694	+	0.168545i	$0.0539067\pi$
$200$	67156.9	−	19382.6i	1.67892	−	0.484566i
$201$	3679.27	−	6372.67i	0.0910687	−	0.157736i
$202$	−4295.53	+	13246.3i	−0.105272	+	0.324631i
$203$	−48121.2	+	8485.06i	−1.16773	+	0.205903i
$204$	−8766.36	−	9056.91i	−0.210649	−	0.217631i
$205$	−36330.4	+	30484.8i	−0.864495	+	0.725398i
$206$	−5515.63	−	8815.55i	−0.129975	−	0.207738i
$207$	−15723.1	−	43198.9i	−0.366942	−	1.00817i
$208$	−68760.8	−	14450.0i	−1.58933	−	0.333996i
$209$	−9246.76	+	26020.2i	−0.211688	+	0.595687i
$210$	22308.2	+	24747.1i	0.505856	+	0.561159i
$211$	6928.60	+	19036.2i	0.155625	+	0.427577i	0.992863	−	0.119262i	$-0.0380530\pi$
$211$	6928.60	+	19036.2i	0.155625	+	0.427577i	−0.837237	+	0.546840i	$0.815831\pi$
$212$	19885.3	+	5677.23i	0.442447	+	0.126318i
$213$	−15632.3	+	13117.0i	−0.344559	+	0.289119i
$214$	−15918.9	+	565.085i	−0.347605	+	0.0123392i
$215$	123289.	−	21739.2i	2.66715	−	0.470290i
$216$	−13168.1	+	29714.1i	−0.282237	+	0.636877i
$217$	32913.7	−	57008.3i	0.698969	−	1.21065i
$218$	3705.27	+	9155.67i	0.0779663	+	0.192654i
$219$	11095.2	−	30483.8i	0.231338	−	0.635595i
$220$	29763.4	−	41065.2i	0.614946	−	0.848455i
$221$	−32067.9	−	55543.2i	−0.656578	−	1.13723i
$222$	−10736.0	−	8377.93i	−0.217840	−	0.169993i
$223$	−12218.2	+	14561.1i	−0.245697	+	0.292810i	−0.874772	−	0.484534i	$-0.838989\pi$
$223$	−12218.2	+	14561.1i	−0.245697	+	0.292810i	0.629076	+	0.777344i	$0.283434\pi$
$224$	−20716.4	+	57432.3i	−0.412875	+	1.14462i
$225$	13206.3	−	74896.4i	0.260864	−	1.47944i
$226$	18953.3	+	10063.6i	0.371081	+	0.197033i
$227$		−	3600.63i		−	0.0698758i	−0.999389	−	0.0349379i	$-0.988877\pi$
$227$		−	3600.63i		−	0.0698758i	0.999389	−	0.0349379i	$-0.0111233\pi$
$228$	16047.3	−	11030.0i	0.308698	−	0.212181i
$229$	−1792.58			−0.0341828			−0.0170914	−	0.999854i	$-0.505441\pi$
$229$	−1792.58			−0.0341828			−0.0170914	+	0.999854i	$0.505441\pi$
$230$	51317.5	−	96648.5i	0.970085	−	1.82700i
$231$	15142.3	+	2669.99i	0.283771	+	0.0500364i
$232$	12600.9	−	50914.1i	0.234112	−	0.945937i
$233$	−69462.4	−	58285.9i	−1.27949	−	1.07362i	−0.993314	−	0.115446i	$-0.963170\pi$
$233$	−69462.4	−	58285.9i	−1.27949	−	1.07362i	−0.286179	−	0.958176i	$-0.592385\pi$
$234$	−47031.7	+	60269.4i	−0.858933	+	1.10069i
$235$	−60876.7	+	35147.2i	−1.10234	+	0.636436i
$236$	−33517.0	+	46244.2i	−0.601785	+	0.830296i
$237$	17933.3	+	6527.19i	0.319274	+	0.116206i
$238$	−51660.3	+	20906.8i	−0.912017	+	0.369090i
$239$	−1201.15	−	693.481i	−0.0210281	−	0.0121406i	0.489449	−	0.872032i	$-0.337198\pi$
$239$	−1201.15	−	693.481i	−0.0210281	−	0.0121406i	−0.510477	+	0.859891i	$0.670531\pi$
$240$	−33987.5	+	11129.9i	−0.590061	+	0.193227i
$241$	−9395.14	−	53282.5i	−0.161759	−	0.917382i	−0.952343	−	0.305029i	$-0.901334\pi$
$241$	−9395.14	−	53282.5i	−0.161759	−	0.917382i	0.790584	−	0.612354i	$-0.209777\pi$
$242$	1247.26	+	35136.4i	0.0212975	+	0.599967i
$243$	34953.4	+	41655.9i	0.591939	+	0.705446i
$244$	−409.105	−	116.799i	−0.00687155	−	0.00196182i
$245$	44934.4	−	16354.8i	0.748596	−	0.272467i
$246$	11463.4	−	10333.7i	0.189428	−	0.170759i
$247$	92845.3	−	34596.0i	1.52183	−	0.567064i
$248$	41631.3	+	57092.8i	0.676888	+	0.928278i
$249$	13298.6	−	4840.30i	0.214490	−	0.0780681i
$250$	65643.6	−	41071.3i	1.05030	−	0.657140i
$251$	−28694.3	−	34196.6i	−0.455458	−	0.542794i	0.488628	−	0.872492i	$-0.337498\pi$
$251$	−28694.3	−	34196.6i	−0.455458	−	0.542794i	−0.944086	+	0.329698i	$0.893053\pi$
$252$	46200.9	+	47732.2i	0.727527	+	0.751641i
$253$	−8769.22	−	49732.7i	−0.137000	−	0.776964i
$254$	100349.	+	32541.5i	1.55541	+	0.504394i
$255$	−28271.3	−	16322.4i	−0.434776	−	0.251018i
$256$	−47352.0	−	45307.3i	−0.722535	−	0.691335i
$257$	30735.8	+	11186.9i	0.465348	+	0.169373i	0.564044	−	0.825745i	$-0.309245\pi$
$257$	30735.8	+	11186.9i	0.465348	+	0.169373i	−0.0986958	+	0.995118i	$0.531467\pi$
$258$	−39845.0	+	8493.31i	−0.598596	+	0.127596i
$259$	−52144.5	+	30105.6i	−0.777336	+	0.448795i
$260$	−181516.	+	12903.1i	−2.68515	+	0.190874i
$261$	−43716.6	−	36682.6i	−0.641749	−	0.538491i
$262$	16060.8	−	114758.i	0.233973	−	1.67179i
$263$	50641.3	+	8929.42i	0.732138	+	0.129096i	0.527275	−	0.849695i	$-0.323214\pi$
$263$	50641.3	+	8929.42i	0.732138	+	0.129096i	0.204863	+	0.978791i	$0.434325\pi$
$264$	−9205.54	+	13698.8i	−0.132081	+	0.196551i
$265$	53559.1			0.762678
$266$	−18589.8	−	84065.4i	−0.262731	−	1.18810i
$267$		−	931.005i		−	0.0130596i
$268$	33876.3	−	8487.78i	0.471657	−	0.118175i
$269$	2439.14	−	13833.1i	0.0337080	−	0.191167i	−0.963304	−	0.268412i	$-0.913501\pi$
$269$	2439.14	−	13833.1i	0.0337080	−	0.191167i	0.997012	+	0.0772446i	$0.0246123\pi$
$270$	−11666.9	+	83362.7i	−0.160040	+	1.14352i
$271$	14125.1	−	16833.6i	0.192333	−	0.229213i	−0.661257	−	0.750160i	$-0.729977\pi$
$271$	14125.1	−	16833.6i	0.192333	−	0.229213i	0.853589	+	0.520947i	$0.174421\pi$
$272$	1949.92	−	59789.4i	0.0263560	−	0.808140i
$273$	−27584.6	−	47778.0i	−0.370119	−	0.641065i
$274$	−26359.4	+	5618.75i	−0.351104	+	0.0748408i
$275$	28573.6	−	78505.4i	0.377833	−	1.03809i
$276$	−15573.7	+	32024.4i	−0.204443	+	0.420400i
$277$	1905.29	−	3300.06i	0.0248314	−	0.0430093i	−0.853343	−	0.521350i	$-0.825428\pi$
$277$	1905.29	−	3300.06i	0.0248314	−	0.0430093i	0.878174	+	0.478341i	$0.158762\pi$
$278$	12550.2	+	4069.83i	0.162391	+	0.0526607i
$279$	75712.2	−	13350.1i	0.972652	−	0.171505i
$280$	−10757.6	+	157759.i	−0.137214	+	2.01223i
$281$	22067.4	−	18516.7i	0.279472	−	0.234504i	−0.492267	−	0.870444i	$-0.663832\pi$
$281$	22067.4	−	18516.7i	0.279472	−	0.234504i	0.771739	+	0.635940i	$0.219387\pi$
$282$	19392.5	−	12133.3i	0.243857	−	0.152574i
$283$	−34620.1	−	95118.0i	−0.432271	−	1.18765i	−0.944415	−	0.328755i	$-0.893371\pi$
$283$	−34620.1	−	95118.0i	−0.432271	−	1.18765i	0.512145	−	0.858899i	$-0.328851\pi$
$284$	−96329.7	−	10012.4i	−1.19433	−	0.124137i
$285$	32121.9	−	38879.0i	0.395468	−	0.478658i
$286$	−62376.6	+	56229.2i	−0.762587	+	0.687433i
$287$	−23338.9	−	64123.0i	−0.283345	−	0.778485i
$288$	−66934.9	+	24580.9i	−0.806989	+	0.296356i
$289$	−22151.1	+	18587.0i	−0.265216	+	0.222543i
$290$	−4819.04	−	135756.i	−0.0573013	−	1.61422i
$291$	45723.5	−	8062.28i	0.539950	−	0.0952077i
$292$	140577.	−	62783.2i	1.64873	−	0.736339i
$293$	7825.00	−	13553.3i	0.0911484	−	0.157874i	−0.816846	−	0.576856i	$-0.804280\pi$
$293$	7825.00	−	13553.3i	0.0911484	−	0.157874i	0.907995	+	0.418982i	$0.137613\pi$
$294$	−14424.7	+	5837.64i	−0.166883	+	0.0675372i
$295$	−50591.0	+	138998.i	−0.581338	+	1.59721i
$296$	−6866.89	−	64265.1i	−0.0783748	−	0.733486i
$297$	19423.0	+	33641.7i	0.220193	+	0.381386i
$298$	−29957.8	+	38389.8i	−0.337347	+	0.432298i
$299$	−116470.	+	138804.i	−1.30278	+	1.55260i
$300$	−48801.8	+	32999.1i	−0.542243	+	0.366657i
$301$	−31279.1	+	177393.i	−0.345241	+	1.95796i
$302$	2715.93	−	5115.04i	0.0297787	−	0.0560835i
$303$		−	11736.5i		−	0.127837i
$304$	90582.7	+	18316.5i	0.980162	+	0.198197i
$305$	−1101.88			−0.0118450
$306$	−57486.7	−	30523.8i	−0.613938	−	0.325983i
$307$	154702.	+	27278.1i	1.64142	+	0.289426i	0.916686	−	0.399607i	$-0.130854\pi$
$307$	154702.	+	27278.1i	1.64142	+	0.289426i	0.724730	+	0.689033i	$0.241965\pi$
$308$	40876.0	+	60450.7i	0.430890	+	0.637236i
$309$	6713.89	+	5633.62i	0.0703165	+	0.0590025i
$310$	144272.	+	112584.i	1.50127	+	1.17153i
$311$	−96272.3	+	55582.8i	−0.995361	+	0.574672i	−0.906872	−	0.421405i	$-0.861537\pi$
$311$	−96272.3	+	55582.8i	−0.995361	+	0.574672i	−0.0884884	+	0.996077i	$0.528204\pi$
$312$	58883.6	−	6291.86i	0.604903	−	0.0646353i
$313$	66493.3	+	24201.6i	0.678718	+	0.247033i	0.658297	−	0.752758i	$-0.271277\pi$
$313$	66493.3	+	24201.6i	0.678718	+	0.247033i	0.0204210	+	0.999791i	$0.493499\pi$
$314$	−5622.79	−	13893.8i	−0.0570286	−	0.140917i
$315$	148997.	+	86023.4i	1.50161	+	0.866952i
$316$	36934.8	+	82700.2i	0.369880	+	0.828195i
$317$	25845.3	+	146576.i	0.257195	+	1.45863i	0.790375	+	0.612624i	$0.209886\pi$
$317$	25845.3	+	146576.i	0.257195	+	1.45863i	−0.533180	+	0.846002i	$0.679003\pi$
$318$	−17418.4	+	618.315i	−0.172248	+	0.00611443i
$319$	−40296.2	−	48023.1i	−0.395988	−	0.471920i
$320$	−150140.	−	79165.9i	−1.46621	−	0.773105i
$321$	12615.6	−	4591.70i	0.122433	−	0.0445618i
$322$	105421.	+	116947.i	1.01675	+	1.12791i
$323$	42733.9	+	72732.2i	0.409607	+	0.697142i
$324$	−6497.95	+	62516.9i	−0.0618994	+	0.595535i
$325$	−281680.	+	102523.i	−2.66679	+	0.970634i
$326$	−8171.84	−	13060.9i	−0.0768927	−	0.122896i
$327$	−5350.91	−	6376.97i	−0.0500417	−	0.0596374i
$328$	73077.5	+	4983.14i	0.679260	+	0.0463186i
$329$	−17563.1	−	99605.6i	−0.162260	−	0.920220i
$330$	−13185.6	+	40660.8i	−0.121080	+	0.373377i
$331$	−105892.	−	61136.8i	−0.966512	−	0.558016i	−0.0683409	−	0.997662i	$-0.521771\pi$
$331$	−105892.	−	61136.8i	−0.966512	−	0.558016i	−0.898171	+	0.439646i	$0.855104\pi$
$332$	60401.8	+	29373.8i	0.547991	+	0.266492i
$333$	−66080.1	−	24051.2i	−0.595912	−	0.216894i
$334$	6669.23	+	31287.6i	0.0597837	+	0.280465i
$335$	78330.7	−	45224.3i	0.697979	−	0.402978i
$336$	1677.31	−	51430.5i	0.0148571	−	0.455557i
$337$	10521.3	+	8828.43i	0.0926425	+	0.0777363i	0.687933	−	0.725775i	$-0.258518\pi$
$337$	10521.3	+	8828.43i	0.0926425	+	0.0777363i	−0.595290	+	0.803511i	$0.702963\pi$
$338$	185272.	+	25929.4i	1.62172	+	0.226965i
$339$	−17811.6	−	3140.67i	−0.154990	−	0.0273289i
$340$	−37654.6	−	150286.i	−0.325732	−	1.30005i
$341$	84453.7			0.726289
$342$	61254.9	−	79740.7i	0.523707	−	0.681754i
$343$		−	74353.2i		−	0.631991i
$344$	−160482.	−	107844.i	−1.35616	−	0.911333i
$345$	−16015.2	+	90826.7i	−0.134553	+	0.763089i
$346$	10026.5	+	1403.25i	0.0837528	+	0.0117215i
$347$	−2917.94	+	3477.46i	−0.0242336	+	0.0288804i	−0.778025	−	0.628233i	$-0.783778\pi$
$347$	−2917.94	+	3477.46i	−0.0242336	+	0.0288804i	0.753792	+	0.657114i	$0.228223\pi$
$348$	3134.49	+	44094.9i	0.0258826	+	0.364107i
$349$	−18323.1	−	31736.6i	−0.150435	−	0.260561i	0.780952	−	0.624591i	$-0.214734\pi$
$349$	−18323.1	−	31736.6i	−0.150435	−	0.260561i	−0.931387	+	0.364029i	$0.881401\pi$
$350$	54302.1	+	254749.i	0.443283	+	2.07959i
$351$	47671.2	−	130976.i	0.386938	−	1.06310i
$352$	−77100.5	+	13824.1i	−0.622260	+	0.111571i
$353$	−42192.4	+	73079.3i	−0.338598	+	0.586469i	−0.984169	−	0.177231i	$-0.943286\pi$
$353$	−42192.4	+	73079.3i	−0.338598	+	0.586469i	0.645571	+	0.763700i	$0.276619\pi$
$354$	14848.5	−	45788.7i	0.118488	−	0.365386i
$355$	−247019.	+	43556.1i	−1.96008	+	0.345615i
$356$	3174.88	−	3073.03i	0.0250511	−	0.0242475i
$357$	35981.7	−	30192.2i	0.282322	−	0.236896i
$358$	−91309.5	−	145939.i	−0.712443	−	1.13869i
$359$	−48202.5	−	132435.i	−0.374008	−	1.02758i	−0.973797	−	0.227420i	$-0.926971\pi$
$359$	−48202.5	−	132435.i	−0.374008	−	1.02758i	0.599789	−	0.800158i	$-0.295251\pi$
$360$	−149218.	+	108808.i	−1.15137	+	0.839565i
$361$	−121769.	+	46432.7i	−0.934374	+	0.356295i
$362$	−52261.1	−	57974.7i	−0.398806	−	0.442406i
$363$	−10134.9	−	27845.3i	−0.0769138	−	0.211319i
$364$	71880.5	−	251772.i	0.542510	−	1.90022i
$365$	305455.	−	256307.i	2.29277	−	1.92387i
$366$	358.353	−	12.7207i	0.00267515	−	9.49619e-5i
$367$	−76097.3	+	13418.0i	−0.564986	+	0.0996222i	−0.448843	−	0.893610i	$-0.648164\pi$
$367$	−76097.3	+	13418.0i	−0.564986	+	0.0996222i	−0.116142	+	0.993233i	$0.537053\pi$
$368$	−160614.	+	52596.1i	−1.18600	+	0.388381i
$369$	39847.9	−	69018.6i	0.292653	−	0.506890i
$370$	−62794.3	−	155164.i	−0.458687	−	1.13341i
$371$	−26357.0	+	72415.4i	−0.191491	+	0.526118i
$372$	−48219.8	−	34948.9i	−0.348449	−	0.252550i
$373$	88081.7	+	152562.i	0.633094	+	1.09655i	0.986916	+	0.161238i	$0.0515486\pi$
$373$	88081.7	+	152562.i	0.633094	+	1.09655i	−0.353822	+	0.935313i	$0.615118\pi$
$374$	−56367.8	−	43987.1i	−0.402984	−	0.314472i
$375$	−41949.8	+	49993.9i	−0.298310	+	0.355512i
$376$	105387.	+	26082.4i	0.745436	+	0.184490i
$377$	−39059.2	+	221516.i	−0.274815	+	1.55855i
$378$	−106970.	−	56798.2i	−0.748653	−	0.397512i
$379$			53659.2i			0.373564i	0.982401	+	0.186782i	$0.0598059\pi$
$379$			53659.2i			0.373564i	−0.982401	+	0.186782i	$0.940194\pi$
$380$	238611.	−	18789.3i	1.65243	−	0.130120i
$381$	−88912.0			−0.612506
$382$	87498.2	−	164789.i	0.599615	−	1.12928i
$383$	139515.	+	24600.2i	0.951093	+	0.167703i	0.627607	−	0.778530i	$-0.284034\pi$
$383$	139515.	+	24600.2i	0.951093	+	0.167703i	0.323485	+	0.946233i	$0.395145\pi$
$384$	49742.2	+	24013.0i	0.337336	+	0.162849i
$385$	144779.	+	121484.i	0.976749	+	0.819589i
$386$	179999.	−	230663.i	1.20808	−	1.54811i
$387$	−182189.	+	105187.i	−1.21647	+	0.702328i
$388$	178416.	+	129313.i	1.18514	+	0.858971i
$389$	−113800.	−	41420.0i	−0.752047	−	0.273723i	−0.0625800	−	0.998040i	$-0.519933\pi$
$389$	−113800.	−	41420.0i	−0.752047	−	0.273723i	−0.689467	+	0.724317i	$0.742155\pi$
$390$	142171.	−	57535.9i	0.934718	−	0.378277i
$391$	−133601.	−	77134.3i	−0.873886	−	0.504538i
$392$	−67520.0	−	29922.1i	−0.439400	−	0.194724i
$393$	16959.1	+	96179.6i	0.109804	+	0.622727i
$394$	−4472.50	−	125994.i	−0.0288110	−	0.811628i
$395$	150783.	+	179696.i	0.966402	+	1.15171i
$396$	−23397.1	+	81951.6i	−0.149201	+	0.522597i
$397$	201707.	−	73415.2i	1.27979	−	0.465806i	0.389428	−	0.921057i	$-0.372673\pi$
$397$	201707.	−	73415.2i	1.27979	−	0.465806i	0.890363	+	0.455251i	$0.150450\pi$
$398$	−42061.3	+	37916.1i	−0.265532	+	0.239363i
$399$	36759.4	+	62563.8i	0.230899	+	0.392986i
$400$	−273616.	−	57500.0i	−1.71010	−	0.359375i
$401$	127737.	−	46492.6i	0.794381	−	0.289131i	0.0872250	−	0.996189i	$-0.472200\pi$
$401$	127737.	−	46492.6i	0.794381	−	0.289131i	0.707156	+	0.707058i	$0.249978\pi$
$402$	−24952.6	+	15612.1i	−0.154406	+	0.0966071i
$403$	−194779.	−	232129.i	−1.19931	−	1.42929i
$404$	40023.6	−	38739.5i	0.245218	−	0.237351i
$405$	28267.4	+	160312.i	0.172336	+	0.977365i
$406$	185923.	+	60291.5i	1.12793	+	0.365767i
$407$	−66899.0	−	38624.1i	−0.403860	−	0.233169i
$408$	13981.0	+	48441.3i	0.0839881	+	0.291002i
$409$	−201715.	−	73418.4i	−1.20585	−	0.438893i	−0.340586	−	0.940213i	$-0.610625\pi$
$409$	−201715.	−	73418.4i	−1.20585	−	0.438893i	−0.865261	+	0.501321i	$0.832848\pi$
$410$	185536.	−	39548.6i	1.10372	−	0.235268i
$411$	19672.1	−	11357.7i	0.116457	−	0.0672367i
$412$	2949.37	+	41490.7i	0.0173754	+	0.244431i
$413$	−163037.	−	136805.i	−0.955844	−	0.802049i
$414$	−25486.9	+	182110.i	−0.148702	+	1.06251i
$415$	171310.	+	30206.5i	0.994686	+	0.175390i
$416$	215817.	+	180035.i	1.24709	+	1.04033i
$417$	−11119.9			−0.0639480
$418$	81477.7	−	74580.6i	0.466322	−	0.426848i
$419$			269807.i			1.53683i	0.639953	+	0.768414i	$0.278954\pi$
$419$			269807.i			1.53683i	−0.639953	+	0.768414i	$0.721046\pi$
$420$	−32390.3	−	129275.i	−0.183618	−	0.732854i
$421$	−4461.90	+	25304.7i	−0.0251742	+	0.142770i	−0.994804	−	0.101806i	$-0.967538\pi$
$421$	−4461.90	+	25304.7i	−0.0251742	+	0.142770i	0.969630	+	0.244576i	$0.0786489\pi$
$422$	11231.2	−	80249.3i	0.0630666	−	0.450626i
$423$	75928.9	−	90488.5i	0.424352	−	0.505723i
$424$	−59602.7	−	57358.9i	−0.331539	−	0.319057i
$425$	−127606.	−	221020.i	−0.706468	−	1.22364i
$426$	79832.4	−	17017.0i	0.439906	−	0.0937700i
$427$	542.248	−	1489.81i	0.00297401	−	0.00817102i
$428$	57299.5	+	27865.1i	0.312797	+	0.152116i
$429$	35389.8	−	61296.9i	0.192293	−	0.333061i
$430$	−476343.	−	154470.i	−2.57622	−	0.835424i
$431$	40041.1	−	7060.32i	0.215551	−	0.0380075i	−0.0648294	−	0.997896i	$-0.520650\pi$
$431$	40041.1	−	7060.32i	0.215551	−	0.0380075i	0.280381	+	0.959889i	$0.409539\pi$
$432$	102260.	−	80274.8i	0.547948	−	0.430142i
$433$	42542.0	−	35697.0i	0.226904	−	0.190395i	−0.522247	−	0.852794i	$-0.674906\pi$
$433$	42542.0	−	35697.0i	0.226904	−	0.190395i	0.749151	+	0.662399i	$0.230462\pi$
$434$	−223219.	+	139662.i	−1.18509	+	0.741477i
$435$	39157.9	+	107585.i	0.206938	+	0.568558i
$436$	4084.43	−	39296.3i	0.0214861	−	0.206718i
$437$	151797.	−	183729.i	0.794880	−	0.962088i
$438$	−96380.8	+	86882.3i	−0.502392	+	0.452880i
$439$	5879.45	+	16153.7i	0.0305076	+	0.0838189i	0.954011	−	0.299770i	$-0.0969101\pi$
$439$	5879.45	+	16153.7i	0.0305076	+	0.0838189i	−0.923504	+	0.383589i	$0.874688\pi$
$440$	−182182.	+	89246.5i	−0.941025	+	0.460984i
$441$	−61555.5	+	51651.2i	−0.316512	+	0.265585i
$442$	9100.97	+	256382.i	0.0465847	+	1.31233i
$443$	−35237.7	+	6213.36i	−0.179556	+	0.0316606i	−0.262703	−	0.964877i	$-0.584614\pi$
$443$	−35237.7	+	6213.36i	−0.179556	+	0.0316606i	0.0831470	+	0.996537i	$0.473503\pi$
$444$	22213.2	+	49737.3i	0.112680	+	0.252299i
$445$	5721.79	−	9910.44i	0.0288943	−	0.0500464i
$446$	70480.0	−	28523.0i	0.354321	−	0.143392i
$447$	14037.0	−	38566.4i	0.0702521	−	0.193016i
$448$	180923.	−	164040.i	0.901442	−	0.817323i
$449$	1615.37	+	2797.90i	0.00801269	+	0.0138784i	0.870004	−	0.493045i	$-0.164116\pi$
$449$	1615.37	+	2797.90i	0.00801269	+	0.0138784i	−0.861991	+	0.506923i	$0.830783\pi$
$450$	−187150.	+	239826.i	−0.924200	+	1.18433i
$451$	56273.9	−	67064.6i	0.276665	−	0.329716i
$452$	−48081.7	−	71107.2i	−0.235344	−	0.348046i
$453$	−847.590	+	4806.92i	−0.00413037	+	0.0234245i
$454$	−6754.25	+	12720.6i	−0.0327691	+	0.0617156i
$455$		−	678121.i		−	3.27555i
$456$	−77383.9	+	8865.29i	−0.372152	+	0.0426347i
$457$	184239.			0.882162			0.441081	−	0.897467i	$-0.354595\pi$
$457$	184239.			0.882162			0.441081	+	0.897467i	$0.354595\pi$
$458$	6332.96	+	3362.61i	0.0301909	+	0.0160305i
$459$	116865.	+	20606.5i	0.554703	+	0.0978091i
$460$	−362596.	+	245183.i	−1.71359	+	1.15871i
$461$	−281594.	−	236286.i	−1.32502	−	1.11182i	−0.985214	−	0.171327i	$-0.945194\pi$
$461$	−281594.	−	236286.i	−1.32502	−	1.11182i	−0.339805	−	0.940496i	$-0.610361\pi$
$462$	−48487.2	−	37837.4i	−0.227166	−	0.177271i
$463$	−166665.	+	96223.8i	−0.777466	+	0.448870i	−0.835531	−	0.549443i	$-0.814840\pi$
$463$	−166665.	+	96223.8i	−0.777466	+	0.448870i	0.0580658	+	0.998313i	$0.481507\pi$
$464$	−140025.	+	156236.i	−0.650382	+	0.725679i
$465$	−144936.	−	52752.3i	−0.670301	−	0.243970i
$466$	136066.	+	336218.i	0.626583	+	1.54828i
$467$	360785.	+	208299.i	1.65430	+	0.955112i	0.975274	+	0.221000i	$0.0709322\pi$
$467$	360785.	+	208299.i	1.65430	+	0.955112i	0.679029	+	0.734112i	$0.262401\pi$
$468$	279214.	−	124700.i	1.27481	−	0.569342i
$469$	22598.7	+	128164.i	0.102740	+	0.582665i
$470$	281000.	−	9974.88i	1.27207	−	0.0451556i
$471$	8120.07	+	9677.12i	0.0366031	+	0.0436219i
$472$	205158.	−	100502.i	0.920885	−	0.451118i
$473$	−217161.	+	79040.1i	−0.970643	+	0.353285i
$474$	−51112.0	−	56699.9i	−0.227492	−	0.252363i
$475$	369454.	−	137666.i	1.63747	−	0.610153i
$476$	221727.	+	23046.1i	0.978600	+	0.101715i
$477$	−84574.3	+	30782.5i	−0.371708	+	0.135290i
$478$	2942.62	+	4703.15i	0.0128789	+	0.0205842i
$479$	−153131.	−	182494.i	−0.667408	−	0.795386i	0.321021	−	0.947072i	$-0.395974\pi$
$479$	−153131.	−	182494.i	−0.667408	−	0.795386i	−0.988429	+	0.151686i	$0.951530\pi$
$480$	140952.	+	24435.0i	0.611769	+	0.106055i
$481$	48130.0	+	272959.i	0.208030	+	1.17980i
$482$	−66758.2	+	205864.i	−0.287349	+	0.886108i
$483$	−114922.	−	66350.5i	−0.492618	−	0.284413i
$484$	61504.3	−	126472.i	0.262552	−	0.539889i
$485$	536270.	+	195186.i	2.27982	+	0.829786i
$486$	−45345.8	−	212732.i	−0.191984	−	0.900660i
$487$	−192225.	+	110981.i	−0.810499	+	0.467942i	−0.847129	−	0.531387i	$-0.821671\pi$
$487$	−192225.	+	110981.i	−0.810499	+	0.467942i	0.0366299	+	0.999329i	$0.488338\pi$
$488$	1226.22	+	1180.05i	0.00514906	+	0.00495521i
$489$	9947.15	+	8346.65i	0.0415988	+	0.0349056i
$490$	−189427.	−	26510.9i	−0.788950	−	0.110416i
$491$	99879.3	+	17611.4i	0.414298	+	0.0730518i	0.376912	−	0.926249i	$-0.376986\pi$
$491$	99879.3	+	17611.4i	0.414298	+	0.0730518i	0.0373855	+	0.999301i	$0.488097\pi$
$492$	−59883.2	+	15003.9i	−0.247386	+	0.0619831i
$493$	−191506.			−0.787933
$494$	−392908.	−	51940.6i	−1.61004	−	0.212840i
$495$			220728.i			0.900839i
$496$	−39980.6	−	279796.i	−0.162512	−	1.13731i
$497$	62670.2	−	355420.i	0.253716	−	1.43890i
$498$	−56062.0	−	7846.05i	−0.226053	−	0.0316368i
$499$	−155217.	+	184980.i	−0.623358	+	0.742889i	−0.981644	−	0.190723i	$-0.938917\pi$
$499$	−155217.	+	184980.i	−0.623358	+	0.742889i	0.358286	+	0.933612i	$0.383361\pi$
$500$	−308954.	+	21962.0i	−1.23582	+	0.0878480i
$501$	−13481.1	−	23350.0i	−0.0537094	−	0.0930273i
$502$	37225.7	+	174638.i	0.147719	+	0.692999i
$503$	−67597.8	+	185723.i	−0.267176	+	0.734059i	0.731462	+	0.681882i	$0.238838\pi$
$503$	−67597.8	+	185723.i	−0.267176	+	0.734059i	−0.998638	+	0.0521768i	$0.983384\pi$
$504$	−73683.3	−	255298.i	−0.290074	−	1.00505i
$505$	72130.8	−	124934.i	0.282838	−	0.489890i
$506$	−62310.6	+	192149.i	−0.243367	+	0.750477i
$507$	−155277.	+	27379.6i	−0.604077	+	0.106515i
$508$	−293477.	−	303205.i	−1.13723	−	1.17492i
$509$	−28947.8	+	24290.1i	−0.111733	+	0.0937549i	−0.696942	−	0.717127i	$-0.745457\pi$
$509$	−28947.8	+	24290.1i	−0.111733	+	0.0937549i	0.585210	+	0.810882i	$0.301012\pi$
$510$	69260.4	+	110698.i	0.266284	+	0.425597i
$511$	196226.	+	539127.i	0.751476	+	2.06466i
$512$	82298.9	+	248890.i	0.313945	+	0.949441i
$513$	−61387.6	+	172744.i	−0.233263	+	0.656398i
$514$	−87600.6	−	97177.6i	−0.331574	−	0.367824i
$515$	36845.3	+	101232.i	0.138921	+	0.381682i
$516$	156699.	+	44737.4i	0.588529	+	0.168024i
$517$	99402.5	−	83408.6i	0.371892	−	0.312054i
$518$	240693.	−	8544.07i	0.897025	−	0.0318424i
$519$	−8403.30	+	1481.73i	−0.0311972	+	0.00550090i
$520$	665478.	+	294913.i	2.46109	+	1.09065i
$521$	86697.7	−	150165.i	0.319398	−	0.553214i	−0.660964	−	0.750417i	$-0.729853\pi$
$521$	86697.7	−	150165.i	0.319398	−	0.553214i	0.980363	+	0.197203i	$0.0631859\pi$
$522$	85634.0	+	211601.i	0.314272	+	0.776561i
$523$	138211.	−	379731.i	0.505288	−	1.38827i	−0.380761	−	0.924674i	$-0.624338\pi$
$523$	138211.	−	379731.i	0.505288	−	1.38827i	0.886048	−	0.463593i	$-0.153440\pi$
$524$	−272010.	+	375299.i	−0.990656	+	1.36683i
$525$	−109766.	−	190120.i	−0.398243	−	0.689777i
$526$	−162159.	−	126542.i	−0.586097	−	0.457365i
$527$	165834.	−	197633.i	0.597107	−	0.711604i
$528$	58218.9	−	31127.9i	0.208832	−	0.111656i
$529$	−27088.5	+	153627.i	−0.0967997	+	0.548979i
$530$	−189217.	−	100469.i	−0.673611	−	0.357668i
$531$		−	248565.i		−	0.881559i
$532$	−92018.8	+	331864.i	−0.325127	+	1.17256i
$533$	−314121.			−1.10571
$534$	−1746.43	+	3289.12i	−0.00612446	+	0.0115345i
$535$	162511.	+	28655.1i	0.567774	+	0.100114i
$536$	−135602.	−	33560.6i	−0.471995	−	0.116815i
$537$	111146.	+	93262.8i	0.385431	+	0.323415i
$538$	−34565.9	+	44295.0i	−0.119422	+	0.153035i
$539$	−76444.7	+	44135.4i	−0.263130	+	0.151918i
$540$	197594.	−	272625.i	0.677619	−	0.934926i
$541$	1830.93	+	666.402i	0.00625570	+	0.00227689i	0.345146	−	0.938549i	$-0.387829\pi$
$541$	1830.93	+	666.402i	0.00625570	+	0.00227689i	−0.338890	+	0.940826i	$0.610052\pi$
$542$	−81479.6	+	32974.5i	−0.277364	+	0.112248i
$543$	56971.2	+	32892.4i	0.193222	+	0.111557i
$544$	−119045.	+	207571.i	−0.402266	+	0.701404i
$545$	−17768.1	−	100768.i	−0.0598202	−	0.339257i
$546$	7828.60	+	220538.i	0.0262603	+	0.739772i
$547$	−332768.	−	396578.i	−1.11216	−	1.32542i	−0.940318	−	0.340297i	$-0.889472\pi$
$547$	−332768.	−	396578.i	−1.11216	−	1.32542i	−0.171843	−	0.985124i	$-0.554972\pi$
$548$	103664.	+	29596.1i	0.345198	+	0.0985537i
$549$	1739.96	−	633.294i	0.00577291	−	0.00210117i
$550$	−248211.	+	223750.i	−0.820533	+	0.739668i
$551$	49153.6	−	291741.i	0.161902	−	0.960934i
$552$	115093.	−	83924.2i	0.377720	−	0.275429i
$553$	−317163.	+	115438.i	−1.03713	+	0.377484i
$554$	−12921.6	+	8084.64i	−0.0421013	+	0.0263415i
$555$	90683.4	+	108072.i	0.294403	+	0.350856i
$556$	−36704.0	−	37920.6i	−0.118731	−	0.122666i
$557$	58284.7	+	330549.i	0.187864	+	1.06543i	0.922220	+	0.386667i	$0.126374\pi$
$557$	58284.7	+	330549.i	0.187864	+	1.06543i	−0.734355	+	0.678765i	$0.762515\pi$
$558$	−292524.	−	94860.6i	−0.939493	−	0.304661i
$559$	718098.	+	414594.i	2.29805	+	1.32678i
$560$	333938.	−	537163.i	1.06485	−	1.71289i
$561$	56627.1	+	20610.6i	0.179928	+	0.0654884i
$562$	−112696.	+	24022.1i	−0.356808	+	0.0760569i
$563$	339376.	−	195939.i	1.07069	−	0.618164i	0.142321	−	0.989821i	$-0.454543\pi$
$563$	339376.	−	195939.i	1.07069	−	0.618164i	0.928370	+	0.371657i	$0.121210\pi$
$564$	−91271.5	+	6488.04i	−0.286931	+	0.0203965i
$565$	−170301.	−	142899.i	−0.533481	−	0.447644i
$566$	−56118.7	+	400982.i	−0.175176	+	1.25168i
$567$	−230664.	−	40672.2i	−0.717485	−	0.126512i
$568$	321539.	+	216073.i	0.996636	+	0.669735i
$569$	450807.			1.39241			0.696203	−	0.717845i	$-0.254871\pi$
$569$	450807.			1.39241			0.696203	+	0.717845i	$0.254871\pi$
$570$	−186414.	+	77098.6i	−0.573758	+	0.237300i
$571$		−	577692.i		−	1.77184i	−0.463841	−	0.885919i	$-0.653529\pi$
$571$		−	577692.i		−	1.77184i	0.463841	−	0.885919i	$-0.346471\pi$
$572$	325846.	−	81641.5i	0.995911	−	0.249528i
$573$	−27306.5	+	154863.i	−0.0831681	+	0.471670i
$574$	−37832.0	+	270319.i	−0.114825	+	0.820450i
$575$	−463463.	+	552334.i	−1.40178	+	1.67057i
$576$	282583.	+	38718.5i	0.851727	+	0.116701i
$577$	−318962.	−	552458.i	−0.958047	−	1.65939i	−0.727236	−	0.686388i	$-0.759195\pi$
$577$	−318962.	−	552458.i	−0.958047	−	1.65939i	−0.230811	−	0.972998i	$-0.574138\pi$
$578$	113123.	−	24113.3i	0.338608	−	0.0721772i
$579$	−84340.5	+	231724.i	−0.251582	+	0.691215i
$580$	−237633.	+	488649.i	−0.706401	+	1.45258i
$581$	−125145.	+	216757.i	−0.370732	+	0.642127i
$582$	−176659.	−	57287.4i	−0.521542	−	0.169127i
$583$	−97366.1	+	17168.3i	−0.286464	+	0.0505114i
$584$	−614413.	−	41896.7i	−1.80150	−	0.122844i
$585$	606692.	−	509075.i	1.77279	−	1.48755i
$586$	−53068.7	+	33203.5i	−0.154541	+	0.0966917i
$587$	−142731.	−	392150.i	−0.414230	−	1.13809i	−0.954919	−	0.296866i	$-0.904059\pi$
$587$	−142731.	−	392150.i	−0.414230	−	1.13809i	0.540689	−	0.841223i	$-0.318164\pi$
$588$	61911.3	+	6435.01i	0.179067	+	0.0186121i
$589$	258510.	+	303357.i	0.745154	+	0.874427i
$590$	439470.	−	396159.i	1.26248	−	1.13806i
$591$	36342.0	+	99848.9i	0.104048	+	0.285870i
$592$	−96292.0	+	239922.i	−0.274756	+	0.684583i
$593$	51386.5	−	43118.4i	0.146130	−	0.122618i	−0.566792	−	0.823861i	$-0.691816\pi$
$593$	51386.5	−	43118.4i	0.146130	−	0.122618i	0.712922	+	0.701243i	$0.247371\pi$
$594$	−5512.32	−	155287.i	−0.0156229	−	0.440110i
$595$	568577.	−	100255.i	1.60603	−	0.283187i
$596$	177850.	−	79429.9i	0.500683	−	0.223610i
$597$	23863.8	−	41333.3i	0.0669562	−	0.115972i
$598$	671850.	−	271895.i	1.87875	−	0.760325i
$599$	−71146.6	+	195474.i	−0.198290	+	0.544797i	−0.998490	−	0.0549365i	$-0.982504\pi$
$599$	−71146.6	+	195474.i	−0.198290	+	0.544797i	0.800200	+	0.599733i	$0.204727\pi$
$600$	234312.	−	25036.8i	0.650867	−	0.0695467i
$601$	255493.	+	442527.i	0.707344	+	1.22516i	0.965839	+	0.259143i	$0.0834400\pi$
$601$	255493.	+	442527.i	0.707344	+	1.22516i	−0.258495	+	0.966013i	$0.583227\pi$
$602$	443268.	−	568031.i	1.22313	−	1.56740i
$603$	−97698.6	+	116433.i	−0.268691	+	0.320214i
$604$	−19190.1	+	12976.1i	−0.0526021	+	0.0355688i
$605$	63248.0	−	358697.i	0.172797	−	0.979980i
$606$	−22016.0	+	41463.7i	−0.0599506	+	0.112908i
$607$			469911.i			1.27538i	0.770295	+	0.637688i	$0.220109\pi$
$607$			469911.i			1.27538i	−0.770295	+	0.637688i	$0.779891\pi$
$608$	−285658.	−	234630.i	−0.772750	−	0.634710i
$609$	−164733.			−0.444166
$610$	3892.80	+	2066.96i	0.0104617	+	0.00555486i
$611$	−458513.	−	80848.2i	−1.22820	−	0.216565i
$612$	145835.	+	215673.i	0.389367	+	0.575828i
$613$	−437186.	−	366843.i	−1.16344	−	0.976246i	−0.163498	−	0.986544i	$-0.552278\pi$
$613$	−437186.	−	366843.i	−1.16344	−	0.976246i	−0.999947	+	0.0102977i	$0.996722\pi$
$614$	−495372.	−	386568.i	−1.31400	−	1.02539i
$615$	−138466.	+	79943.1i	−0.366093	+	0.211364i
$616$	−31013.0	−	290242.i	−0.0817303	−	0.764889i
$617$	−462494.	−	168334.i	−1.21489	−	0.442182i	−0.346490	−	0.938054i	$-0.612626\pi$
$617$	−462494.	−	168334.i	−1.21489	−	0.442182i	−0.868396	+	0.495871i	$0.834849\pi$
$618$	−13151.5	−	32497.1i	−0.0344348	−	0.0850879i
$619$	−57654.1	−	33286.6i	−0.150470	−	0.0868736i	0.422875	−	0.906188i	$-0.361021\pi$
$619$	−57654.1	−	33286.6i	−0.150470	−	0.0868736i	−0.573344	+	0.819314i	$0.694354\pi$
$620$	−298505.	−	668378.i	−0.776547	−	1.73876i
$621$	−58217.3	−	330166.i	−0.150962	−	0.856150i
$622$	444383.	−	15774.6i	1.14862	−	0.0407734i
$623$	10583.8	+	12613.3i	0.0272688	+	0.0324977i
$624$	−219831.	−	88228.6i	−0.564572	−	0.226590i
$625$	−112372.	+	40900.2i	−0.287673	+	0.104705i
$626$	−189514.	−	210233.i	−0.483607	−	0.536477i
$627$	−45932.5	+	80975.5i	−0.116838	+	0.205977i
$628$	−6198.16	+	59632.6i	−0.0157161	+	0.151205i
$629$	−221749.	+	80710.1i	−0.560481	+	0.203998i
$630$	−365020.	−	583405.i	−0.919677	−	1.46990i
$631$	−332245.	−	395954.i	−0.834448	−	0.994457i	−0.999966	−	0.00824991i	$-0.997374\pi$
$631$	−332245.	−	395954.i	−0.834448	−	0.994457i	0.165518	−	0.986207i	$-0.447071\pi$
$632$	24647.4	−	361453.i	0.0617074	−	0.904937i
$633$	11859.3	+	67257.3i	0.0295972	+	0.167854i
$634$	183646.	−	566316.i	0.456882	−	1.40890i
$635$	−946458.	−	546438.i	−2.34722	−	1.35517i
$636$	62697.0	+	30490.0i	0.155000	+	0.0753777i
$637$	297618.	+	108324.i	0.733467	+	0.266960i
$638$	52277.0	+	245249.i	0.128431	+	0.602512i
$639$	365030.	−	210750.i	0.893978	−	0.516138i
$640$	381920.	+	561322.i	0.932422	+	1.37042i
$641$	395902.	+	332201.i	0.963544	+	0.808510i	0.981526	−	0.191329i	$-0.0612796\pi$
$641$	395902.	+	332201.i	0.963544	+	0.808510i	−0.0179817	+	0.999838i	$0.505724\pi$
$642$	−53182.6	−	7443.07i	−0.129033	−	0.0180585i
$643$	−417196.	−	73562.9i	−1.00906	−	0.177925i	−0.355403	−	0.934713i	$-0.615656\pi$
$643$	−417196.	−	73562.9i	−1.00906	−	0.177925i	−0.653660	+	0.756788i	$0.726767\pi$
$644$	−153065.	−	610912.i	−0.369067	−	1.47301i
$645$	422053.			1.01449
$646$	−14538.5	−	337116.i	−0.0348382	−	0.807819i
$647$			406880.i			0.971981i	0.873964	+	0.485991i	$0.161541\pi$
$647$			406880.i			0.971981i	−0.873964	+	0.485991i	$0.838459\pi$
$648$	140229.	−	208675.i	0.333954	−	0.496959i
$649$	47414.9	−	268903.i	0.112571	−	0.638420i
$650$	1.18746e6	+	166189.i	2.81055	+	0.393346i
$651$	142649.	−	170003.i	0.336595	−	0.401138i
$652$	4369.72	+	61471.7i	0.0102792	+	0.144604i
$653$	325842.	+	564374.i	0.764153	+	1.32355i	0.940693	+	0.339258i	$0.110176\pi$
$653$	325842.	+	564374.i	0.764153	+	1.32355i	−0.176540	+	0.984293i	$0.556491\pi$
$654$	6941.84	+	32566.5i	0.0162300	+	0.0761405i
$655$	−410576.	+	1.12805e6i	−0.956998	+	2.62933i
$656$	−248826.	−	154687.i	−0.578213	−	0.359457i
$657$	−335029.	+	580287.i	−0.776161	+	1.34435i
$658$	−124797.	+	384840.i	−0.288238	+	0.888849i
$659$	469564.	−	82796.7i	1.08124	−	0.190652i	0.395478	−	0.918475i	$-0.370579\pi$
$659$	469564.	−	82796.7i	1.08124	−	0.190652i	0.685765	+	0.727823i	$0.259468\pi$
$660$	122857.	−	118915.i	0.282040	−	0.272992i
$661$	−33682.3	+	28262.8i	−0.0770901	+	0.0646863i	−0.680518	−	0.732731i	$-0.738245\pi$
$661$	−33682.3	+	28262.8i	−0.0770901	+	0.0646863i	0.603428	+	0.797417i	$0.293801\pi$
$662$	259419.	+	414626.i	0.591952	+	0.946108i
$663$	−73951.5	−	203180.i	−0.168236	−	0.462226i
$664$	−158291.	−	217079.i	−0.359021	−	0.492358i
$665$	6793.43	+	891901.i	0.0153619	+	2.01685i
$666$	188336.	+	208926.i	0.424605	+	0.471026i
$667$	185047.	+	508412.i	0.415940	+	1.14278i
$668$	35129.3	−	123045.i	0.0787257	−	0.275748i
$669$	−49089.7	+	41191.1i	−0.109683	+	0.0920347i
$670$	−361566.	+	12834.8i	−0.805450	+	0.0285916i
$671$	2003.13	−	353.206i	0.00444902	−	0.000784482i
$672$	−102402.	+	178551.i	−0.226761	+	0.395388i
$673$	267915.	−	464043.i	0.591517	−	1.02454i	−0.402511	−	0.915415i	$-0.631862\pi$
$673$	267915.	−	464043.i	0.591517	−	1.02454i	0.994028	−	0.109123i	$-0.0348042\pi$
$674$	−20609.6	−	50926.1i	−0.0453681	−	0.112104i
$675$	189695.	−	521183.i	0.416340	−	1.14389i
$676$	−605903.	−	439148.i	−1.32590	−	0.960987i
$677$	307740.	+	533021.i	0.671438	+	1.16296i	0.977496	+	0.210952i	$0.0676564\pi$
$677$	307740.	+	533021.i	0.671438	+	1.16296i	−0.306058	+	0.952013i	$0.599010\pi$
$678$	57034.7	+	44507.5i	0.124074	+	0.0968220i
$679$	−527810.	+	629019.i	−1.14482	+	1.36435i
$680$	−148886.	+	601577.i	−0.321985	+	1.30099i
$681$	2107.87	−	11954.3i	0.00454516	−	0.0257769i
$682$	−298364.	−	158422.i	−0.641472	−	0.340603i
$683$		−	18652.0i		−	0.0399838i	−0.999800	−	0.0199919i	$-0.993636\pi$
$683$		−	18652.0i		−	0.0399838i	0.999800	−	0.0199919i	$-0.00636405\pi$
$684$	−365987.	+	166809.i	−0.782265	+	0.356539i
$685$	279210.			0.595044
$686$	−139475.	+	262680.i	−0.296380	+	0.558186i
$687$	−5951.48	−	1049.41i	−0.0126099	−	0.00222346i
$688$	364665.	+	682038.i	0.770402	+	1.44089i
$689$	271749.	+	228024.i	0.572438	+	0.480333i
$690$	226957.	−	290837.i	0.476700	−	0.610874i
$691$	406712.	−	234815.i	0.851787	−	0.491779i	−0.00946644	−	0.999955i	$-0.503013\pi$
$691$	406712.	−	234815.i	0.851787	−	0.491779i	0.861253	+	0.508176i	$0.169680\pi$
$692$	−32790.2	−	23765.8i	−0.0684750	−	0.0496295i
$693$	−298439.	−	108623.i	−0.621425	−	0.226180i
$694$	16831.9	−	6811.82i	0.0349473	−	0.0141431i
$695$	−118370.	−	68340.7i	−0.245059	−	0.141485i
$696$	71641.6	−	161661.i	0.147893	−	0.333724i
$697$	−46440.5	−	263377.i	−0.0955942	−	0.542141i
$698$	5200.17	+	146493.i	0.0106735	+	0.300681i
$699$	−196498.	−	234177.i	−0.402164	−	0.479281i
$700$	286030.	−	1.00186e6i	0.583734	−	2.04461i
$701$	−789547.	+	287372.i	−1.60673	+	0.584801i	−0.980789	−	0.195072i	$-0.937506\pi$
$701$	−789547.	+	287372.i	−1.60673	+	0.584801i	−0.625938	+	0.779873i	$0.715284\pi$
$702$	−414107.	+	373296.i	−0.840307	+	0.757493i
$703$	−66037.7	−	358528.i	−0.133623	−	0.725458i
$704$	298318.	+	95790.3i	0.601914	+	0.193275i
$705$	−222690.	+	81052.5i	−0.448046	+	0.163075i
$706$	286146.	−	179033.i	0.574088	−	0.359190i
$707$	133423.	+	159007.i	0.266926	+	0.318110i
$708$	−138351.	+	133912.i	−0.276004	+	0.267149i
$709$	−133037.	−	754488.i	−0.264654	−	1.50093i	−0.770018	−	0.638022i	$-0.779753\pi$
$709$	−133037.	−	754488.i	−0.264654	−	1.50093i	0.505364	−	0.862906i	$-0.331358\pi$
$710$	954391.	+	309492.i	1.89326	+	0.613950i
$711$	−341377.	−	197094.i	−0.675298	−	0.389883i
$712$	−16981.0	+	4901.00i	−0.0334968	+	0.00966774i
$713$	−684918.	−	249290.i	−1.34728	−	0.490371i
$714$	−183755.	+	39168.9i	−0.360447	+	0.0768326i
$715$	753441.	−	434999.i	1.47379	−	0.850896i
$716$	48825.9	+	686865.i	0.0952410	+	1.33982i
$717$	−3581.90	−	3005.57i	−0.00696747	−	0.00584640i
$718$	−78135.5	+	558297.i	−0.151565	+	1.08297i
$719$	505235.	+	89086.5i	0.977317	+	0.172327i	0.639422	−	0.768856i	$-0.279174\pi$
$719$	505235.	+	89086.5i	0.977317	+	0.172327i	0.337895	+	0.941184i	$0.390285\pi$
$720$	731274.	−	104493.i	1.41064	−	0.201569i
$721$	−155004.			−0.298176
$722$	517293.	+	64378.9i	0.992344	+	0.123501i
$723$		−	182401.i		−	0.348940i
$724$	75880.1	+	302851.i	0.144761	+	0.577766i
$725$	−155426.	+	881464.i	−0.295697	+	1.67698i
$726$	−16428.5	+	117385.i	−0.0311690	+	0.222710i
$727$	655488.	−	781180.i	1.24021	−	1.47803i	0.418404	−	0.908261i	$-0.362590\pi$
$727$	655488.	−	781180.i	1.24021	−	1.47803i	0.821808	−	0.569765i	$-0.192966\pi$
$728$	−726231.	+	754640.i	−1.37029	+	1.42389i
$729$	−67436.8	−	116804.i	−0.126894	−	0.219787i
$730$	−1.55993e6	+	332512.i	−2.92724	+	0.623967i
$731$	−241454.	+	663390.i	−0.451856	+	1.24146i
$732$	−1289.88	−	627.276i	−0.00240728	−	0.00117067i
$733$	−115246.	+	199613.i	−0.214496	+	0.371518i	−0.953117	−	0.302603i	$-0.902144\pi$
$733$	−115246.	+	199613.i	−0.214496	+	0.371518i	0.738621	+	0.674121i	$0.235478\pi$
$734$	294012.	+	95343.1i	0.545725	+	0.176969i
$735$	158760.	−	27993.6i	0.293877	−	0.0518184i
$736$	666089.	+	115472.i	1.22964	+	0.213167i
$737$	−127902.	+	107323.i	−0.235474	+	0.197586i
$738$	−270246.	+	169085.i	−0.496189	+	0.310451i
$739$	258871.	+	711243.i	0.474018	+	1.30235i	0.914498	+	0.404591i	$0.132586\pi$
$739$	258871.	+	711243.i	0.474018	+	1.30235i	−0.440480	+	0.897762i	$0.645192\pi$
$740$	−69220.0	+	665966.i	−0.126406	+	1.21615i
$741$	328505.	−	60507.8i	0.598282	−	0.110198i
$742$	228957.	−	206392.i	0.415858	−	0.374874i
$743$	101615.	+	279185.i	0.184069	+	0.505726i	0.997066	−	0.0765419i	$-0.0243879\pi$
$743$	101615.	+	279185.i	0.184069	+	0.505726i	−0.812997	+	0.582267i	$0.802166\pi$
$744$	104796.	+	213923.i	0.189320	+	0.386467i
$745$	386444.	−	324265.i	0.696265	−	0.584236i
$746$	−24997.9	−	704210.i	−0.0449185	−	1.26539i
$747$	−287873.	+	50759.9i	−0.515894	+	0.0909660i
$748$	116627.	+	261138.i	0.208447	+	0.466732i
$749$	−118717.	+	205624.i	−0.211617	+	0.366531i
$750$	241985.	−	97930.3i	0.430195	−	0.174098i
$751$	−117557.	+	322984.i	−0.208433	+	0.572666i	−0.999223	−	0.0394225i	$-0.987448\pi$
$751$	−117557.	+	322984.i	−0.208433	+	0.572666i	0.790789	+	0.612089i	$0.209670\pi$
$752$	−323391.	−	289836.i	−0.571863	−	0.512526i
$753$	−75247.7	−	130333.i	−0.132710	−	0.229860i
$754$	553521.	−	709317.i	0.973625	−	1.24766i
$755$	−38565.0	+	45960.0i	−0.0676549	+	0.0806280i
$756$	271368.	+	401321.i	0.474805	+	0.702180i
$757$	64616.6	−	366459.i	0.112759	−	0.639490i	−0.875076	−	0.483986i	$-0.839189\pi$
$757$	64616.6	−	366459.i	0.112759	−	0.639490i	0.987835	−	0.155504i	$-0.0497002\pi$
$758$	100657.	−	189571.i	0.175188	−	0.329939i
$759$		−	170249.i		−	0.295530i
$760$	−878227.	−	381218.i	−1.52048	−	0.660003i
$761$	−507063.			−0.875574			−0.437787	−	0.899079i	$-0.644238\pi$
$761$	−507063.			−0.875574			−0.437787	+	0.899079i	$0.644238\pi$
$762$	314115.	+	166786.i	0.540977	+	0.287243i
$763$	144989.	+	25565.4i	0.249049	+	0.0439141i
$764$	−618240.	+	418046.i	−1.05918	+	0.716205i
$765$	516534.	+	433423.i	0.882624	+	0.740610i
$766$	−446742.	−	348618.i	−0.761376	−	0.594146i
$767$	−848461.	+	489859.i	−1.44225	+	0.832685i
$768$	−130688.	−	178144.i	−0.221571	−	0.302029i
$769$	987248.	+	359329.i	1.66945	+	0.607631i	0.991805	−	0.127758i	$-0.0407781\pi$
$769$	987248.	+	359329.i	1.66945	+	0.607631i	0.677646	+	0.735389i	$0.263000\pi$
$770$	−283599.	−	700769.i	−0.478325	−	1.18193i
$771$	95495.7	+	55134.5i	0.160648	+	0.0927501i
$772$	−1.06860e6	+	477249.i	−1.79301	+	0.800776i
$773$	−21922.6	−	124329.i	−0.0366888	−	0.208073i	0.960953	−	0.276713i	$-0.0892450\pi$
$773$	−21922.6	−	124329.i	−0.0366888	−	0.208073i	−0.997641	+	0.0686402i	$0.978134\pi$
$774$	840966.	−	29852.4i	1.40377	−	0.0498307i
$775$	−775073.	−	923697.i	−1.29044	−	1.53789i
$776$	−387749.	−	791528.i	−0.643913	−	1.31445i
$777$	−190747.	+	69426.3i	−0.315948	+	0.114996i
$778$	324345.	+	359804.i	0.535856	+	0.594439i
$779$	413148.	−	3146.87i	0.680818	−	0.00518565i
$780$	−610199.	−	63423.6i	−1.00296	−	0.104246i
$781$	435099.	−	158363.i	0.713322	−	0.259628i
$782$	327301.	+	523121.i	0.535222	+	0.855437i
$783$	−267519.	−	318817.i	−0.436346	−	0.520017i
$784$	182410.	+	232368.i	0.296768	+	0.378046i
$785$	26963.3	+	152916.i	0.0437556	+	0.248150i
$786$	120504.	−	371603.i	0.195055	−	0.601498i
$787$	−243297.	−	140468.i	−0.392814	−	0.226792i	0.290564	−	0.956855i	$-0.406157\pi$
$787$	−243297.	−	140468.i	−0.392814	−	0.226792i	−0.683379	+	0.730064i	$0.739490\pi$
$788$	−220545.	+	453510.i	−0.355177	+	0.730355i
$789$	162905.	+	59292.5i	0.261685	+	0.0952457i
$790$	−195614.	−	917690.i	−0.313433	−	1.47042i
$791$	277016.	−	159935.i	0.442743	−	0.255618i
$792$	236388.	−	245635.i	0.376855	−	0.391598i
$793$	−5590.73	−	4691.18i	−0.00889042	−	0.00745995i
$794$	−850320.	−	119005.i	−1.34878	−	0.188766i
$795$	177819.	+	31354.4i	0.281349	+	0.0496094i
$796$	219722.	−	55052.0i	0.346775	−	0.0868854i
$797$	835261.			1.31494			0.657469	−	0.753482i	$-0.271627\pi$
$797$	835261.			1.31494			0.657469	+	0.753482i	$0.271627\pi$
$798$	−12505.9	−	289985.i	−0.0196386	−	0.455375i
$799$		−	396397.i		−	0.620922i
$800$	858788.	+	716402.i	1.34186	+	1.11938i
$801$	−3339.27	+	18938.0i	−0.00520459	+	0.0295167i
$802$	−538492.	−	75363.8i	−0.837203	−	0.117169i
$803$	−473134.	+	563859.i	−0.733758	+	0.874458i
$804$	117440.	−	8348.24i	0.181679	−	0.0129147i
$805$	−815557.	−	1.41259e6i	−1.25853	−	2.17983i
$806$	252691.	+	1.18546e6i	0.388973	+	1.82480i
$807$	16196.2	−	44498.7i	0.0248695	−	0.0683283i
$808$	−214068.	+	61783.6i	−0.327890	+	0.0946348i
$809$	367353.	−	636275.i	0.561290	−	0.972182i	−0.436095	−	0.899901i	$-0.643639\pi$
$809$	367353.	−	636275.i	0.561290	−	0.972182i	0.997384	−	0.0722814i	$-0.0230280\pi$
$810$	200857.	−	619388.i	0.306138	−	0.944046i
$811$	1.03782e6	−	182996.i	1.57791	−	0.278228i	0.685026	−	0.728519i	$-0.259791\pi$
$811$	1.03782e6	−	182996.i	1.57791	−	0.278228i	0.892882	+	0.450291i	$0.148680\pi$
$812$	−543743.	−	561765.i	−0.824673	−	0.852006i
$813$	56750.9	−	47619.7i	0.0858602	−	0.0720453i
$814$	163892.	+	261947.i	0.247349	+	0.395334i
$815$	54589.2	+	149983.i	0.0821848	+	0.225801i
$816$	41475.6	−	197363.i	0.0622891	−	0.296405i
$817$	−948634.	−	538102.i	−1.42120	−	0.806159i
$818$	574913.	+	637766.i	0.859202	+	0.953135i
$819$	389743.	+	1.07081e6i	0.581046	+	1.59641i
$820$	−729661.	−	208317.i	−1.08516	−	0.309811i
$821$	500490.	−	419961.i	0.742522	−	0.623050i	−0.190992	−	0.981592i	$-0.561170\pi$
$821$	500490.	−	419961.i	0.742522	−	0.623050i	0.933514	+	0.358542i	$0.116726\pi$
$822$	−90804.3	+	3223.35i	−0.134389	+	0.00477050i
$823$	330313.	−	58243.1i	0.487670	−	0.0859894i	0.0755937	−	0.997139i	$-0.475915\pi$
$823$	330313.	−	58243.1i	0.487670	−	0.0859894i	0.412076	+	0.911149i	$0.364804\pi$
$824$	67410.6	−	152114.i	0.0992828	−	0.224034i
$825$	140824.	−	243915.i	0.206905	−	0.358369i
$826$	319365.	+	789147.i	0.468088	+	1.15664i
$827$	359439.	−	987549.i	0.525550	−	1.44394i	−0.338711	−	0.940891i	$-0.609991\pi$
$827$	359439.	−	987549.i	0.525550	−	1.44394i	0.864260	−	0.503045i	$-0.167787\pi$
$828$	431654.	−	595563.i	0.629615	−	0.868694i
$829$	−311982.	−	540368.i	−0.453963	−	0.786286i	0.544665	−	0.838654i	$-0.316657\pi$
$829$	−311982.	−	540368.i	−0.453963	−	0.786286i	−0.998628	+	0.0523672i	$0.983323\pi$
$830$	−548553.	−	428068.i	−0.796273	−	0.621378i
$831$	8257.58	−	9841.01i	0.0119578	−	0.0142507i
$832$	−424736.	−	1.04088e6i	−0.613581	−	1.50368i
$833$	−46824.6	+	265556.i	−0.0674814	+	0.382706i
$834$	39285.0	+	20859.2i	0.0564800	+	0.0299892i
$835$		−	331410.i		−	0.475327i
$836$	−427752.	+	110644.i	−0.612040	+	0.158312i
$837$	560673.			0.800310
$838$	506118.	−	953194.i	0.720715	−	1.35735i
$839$	9843.90	+	1735.75i	0.0139844	+	0.00246582i	0.180636	−	0.983550i	$-0.442184\pi$
$839$	9843.90	+	1735.75i	0.0139844	+	0.00246582i	−0.166652	+	0.986016i	$0.553296\pi$
$840$	−128071.	+	517473.i	−0.181506	+	0.733380i
$841$	−27303.7	−	22910.5i	−0.0386038	−	0.0323924i
$842$	63231.2	−	81028.4i	0.0891882	−	0.114291i
$843$	84105.0	−	48558.0i	0.118350	−	0.0683291i
$844$	−190214.	+	262443.i	−0.267028	+	0.368425i
$845$	−1.82118e6	−	662855.i	−2.55058	−	0.928336i
$846$	−437990.	+	177253.i	−0.611961	+	0.247658i
$847$	453857.	+	262034.i	0.632633	+	0.365251i
$848$	102972.	+	314447.i	0.143195	+	0.437276i
$849$	−59257.3	−	336065.i	−0.0822104	−	0.466238i
$850$	36215.0	+	1.02020e6i	0.0501245	+	1.41205i
$851$	428539.	+	510713.i	0.591741	+	0.705209i
$852$	−313959.	−	89634.9i	−0.432508	−	0.123480i
$853$	955679.	−	347839.i	1.31345	−	0.478057i	0.412098	−	0.911140i	$-0.364796\pi$
$853$	955679.	−	347839.i	1.31345	−	0.478057i	0.901354	+	0.433082i	$0.142574\pi$
$854$	−4710.36	+	4246.15i	−0.00645860	+	0.00582210i
$855$	−792854.	+	675641.i	−1.08458	+	0.924238i
$856$	−150161.	−	205929.i	−0.204932	−	0.281041i
$857$	124345.	−	45257.9i	0.169304	−	0.0616216i	−0.255978	−	0.966683i	$-0.582397\pi$
$857$	124345.	−	45257.9i	0.169304	−	0.0616216i	0.425281	+	0.905061i	$0.360175\pi$
$858$	−240012.	+	150168.i	−0.326030	+	0.203987i
$859$	−183890.	−	219152.i	−0.249214	−	0.297002i	0.626906	−	0.779095i	$-0.284321\pi$
$859$	−183890.	−	219152.i	−0.249214	−	0.297002i	−0.876120	+	0.482093i	$0.839877\pi$
$860$	1.39310e6	+	1.43927e6i	1.88358	+	1.94601i
$861$	−39947.8	−	226555.i	−0.0538874	−	0.305610i
$862$	−154704.	−	50167.8i	−0.208203	−	0.0675167i
$863$	106304.	+	61374.7i	0.142734	+	0.0824077i	0.569666	−	0.821876i	$-0.307072\pi$
$863$	106304.	+	61374.7i	0.142734	+	0.0824077i	−0.426932	+	0.904284i	$0.640406\pi$
$864$	−511856.	+	91775.5i	−0.685678	+	0.122942i
$865$	−98558.6	−	35872.4i	−0.131723	−	0.0479433i
$866$	−217258.	+	46310.4i	−0.289694	+	0.0617509i
$867$	−84424.1	+	48742.3i	−0.112313	+	0.0648437i
$868$	1.05059e6	−	74681.2i	1.39442	−	0.0991223i
$869$	−331713.	−	278340.i	−0.439261	−	0.368584i
$870$	63474.4	−	453540.i	0.0838610	−	0.599207i
$871$	589974.	+	104028.i	0.777673	+	0.137125i
$872$	−88143.8	+	131167.i	−0.115920	+	0.172501i
$873$	−958997.			−1.25831
$874$	−880929.	+	364342.i	−1.15324	+	0.476965i
$875$		−	1.15421e6i		−	1.50754i
$876$	503479.	−	126148.i	0.656105	−	0.164389i
$877$	−226320.	+	1.28352e6i	−0.294255	+	1.66880i	0.375962	+	0.926635i	$0.377312\pi$
$877$	−226320.	+	1.28352e6i	−0.294255	+	1.66880i	−0.670217	+	0.742165i	$0.733799\pi$
$878$	9530.50	−	68097.8i	0.0123631	−	0.0883373i
$879$	33913.8	−	40416.9i	0.0438934	−	0.0523101i
$880$	811040.	+	26450.5i	1.04731	+	0.0341562i
$881$	−205177.	−	355376.i	−0.264348	−	0.457864i	0.703045	−	0.711146i	$-0.251823\pi$
$881$	−205177.	−	355376.i	−0.264348	−	0.457864i	−0.967393	+	0.253281i	$0.918490\pi$
$882$	314358.	−	67008.1i	0.404098	−	0.0861371i
$883$	115459.	−	317220.i	0.148083	−	0.406855i	−0.843368	−	0.537337i	$-0.819430\pi$
$883$	115459.	−	317220.i	0.148083	−	0.406855i	0.991451	+	0.130482i	$0.0416526\pi$
$884$	448781.	−	922836.i	0.574289	−	1.18092i
$885$	−249337.	+	431864.i	−0.318346	+	0.551392i
$886$	136146.	+	44149.7i	0.173435	+	0.0562420i
$887$	781269.	−	137759.i	0.993009	−	0.175094i	0.346541	−	0.938035i	$-0.387356\pi$
$887$	781269.	−	137759.i	0.993009	−	0.175094i	0.646469	+	0.762941i	$0.276245\pi$
$888$	14823.4	−	217384.i	0.0187984	−	0.275678i
$889$	1.20458e6	−	1.01077e6i	1.52417	−	1.27893i
$890$	−38804.9	+	24279.1i	−0.0489899	+	0.0306515i
$891$	−102776.	−	282374.i	−0.129460	−	0.355688i
$892$	−302502.	−	31441.8i	−0.380188	−	0.0395164i
$893$	603871.	+	101743.i	0.757253	+	0.127585i
$894$	−121936.	+	109919.i	−0.152565	+	0.137530i
$895$	609962.	+	1.67586e6i	0.761477	+	2.09214i
$896$	−946892.	+	240148.i	−1.17946	+	0.299132i
$897$	−467947.	+	392654.i	−0.581583	+	0.488006i
$898$	−458.446	−	12914.8i	−0.000568507	−	0.0160153i
$899$	−891065.	+	157119.i	−1.10253	+	0.194406i
$900$	1.11106e6	−	496210.i	1.37168	−	0.612605i
$901$	−151013.	+	261562.i	−0.186022	+	0.322199i
$902$	−324612.	+	131369.i	−0.398980	+	0.161466i
$903$	−207697.	+	570644.i	−0.254716	+	0.699825i
$904$	36480.1	+	341407.i	0.0446395	+	0.417768i
$905$	404301.	+	700271.i	0.493638	+	0.855005i
$906$	12011.5	−	15392.3i	0.0146332	−	0.0187520i
$907$	818198.	−	975090.i	0.994589	−	1.18531i	0.0119214	−	0.999929i	$-0.496205\pi$
$907$	818198.	−	975090.i	0.994589	−	1.18531i	0.982668	−	0.185376i	$-0.0593503\pi$
$908$	47723.8	−	32270.2i	0.0578846	−	0.0391408i
$909$	−42095.9	+	238738.i	−0.0509463	+	0.288931i
$910$	−1.27205e6	+	2.39571e6i	−1.53611	+	2.89303i
$911$		−	939285.i		−	1.13178i	−0.824482	−	0.565888i	$-0.808533\pi$
$911$		−	939285.i		−	1.13178i	0.824482	−	0.565888i	$-0.191467\pi$
$912$	290017.	+	113841.i	0.348686	+	0.136870i
$913$	−321110.			−0.385223
$914$	−650892.	−	345604.i	−0.779142	−	0.413701i
$915$	−3658.31	−	645.059i	−0.00436957	−	0.000770473i
$916$	−16065.8	−	23759.4i	−0.0191474	−	0.0283168i
$917$	−1.32315e6	−	1.11025e6i	−1.57351	−	1.32033i
$918$	−374216.	−	292022.i	−0.444055	−	0.346522i
$919$	−486006.	+	280596.i	−0.575454	+	0.332239i	−0.759325	−	0.650712i	$-0.774471\pi$
$919$	−486006.	+	280596.i	−0.575454	+	0.332239i	0.183871	+	0.982950i	$0.441137\pi$
$920$	1.74093e6	−	186023.i	2.05687	−	0.219781i
$921$	497651.	+	181130.i	0.586685	+	0.213536i
$922$	551600.	+	1.36300e6i	0.648877	+	1.60337i
$923$	−1.43876e6	−	830670.i	−1.68883	−	0.975047i
$924$	100322.	+	224630.i	0.117504	+	0.263101i
$925$	191521.	+	1.08617e6i	0.223837	+	1.26944i
$926$	769306.	−	27308.6i	0.897175	−	0.0318477i
$927$	−116364.	−	138677.i	−0.135412	−	0.161378i
$928$	787764.	−	289296.i	0.914745	−	0.335928i
$929$	1.19192e6	−	433824.i	1.38107	−	0.502669i	0.458569	−	0.888659i	$-0.348362\pi$
$929$	1.19192e6	−	433824.i	1.38107	−	0.502669i	0.922503	+	0.385990i	$0.126140\pi$
$930$	413084.	+	458245.i	0.477609	+	0.529824i
$931$	−392529.	−	139492.i	−0.452868	−	0.160935i
$932$	149990.	−	1.44305e6i	0.172675	−	1.66131i
$933$	−352169.	+	128179.i	−0.404565	+	0.147249i
$934$	−883869.	−	1.41267e6i	−1.01320	−	1.61938i
$935$	476120.	+	567417.i	0.544619	+	0.649052i
$936$	−1.22034e6	−	83215.0i	−1.39293	−	0.0949838i
$937$	140484.	+	796724.i	0.160010	+	0.907463i	0.954061	+	0.299612i	$0.0968571\pi$
$937$	140484.	+	796724.i	0.160010	+	0.907463i	−0.794051	+	0.607851i	$0.792032\pi$
$938$	160578.	−	495178.i	0.182507	−	0.562802i
$939$	206594.	+	119277.i	0.234308	+	0.135278i
$940$	−1.01145e6	−	491875.i	−1.14469	−	0.556671i
$941$	−1.06239e6	−	386677.i	−1.19978	−	0.436685i	−0.336634	−	0.941635i	$-0.609289\pi$
$941$	−1.06239e6	−	386677.i	−1.19978	−	0.436685i	−0.863149	+	0.504950i	$0.831511\pi$
$942$	−10534.3	−	49420.1i	−0.0118715	−	0.0556931i
$943$	−654341.	+	377784.i	−0.735836	+	0.424835i
$944$	−913325.	−	29786.4i	−1.02490	−	0.0334252i
$945$	961159.	+	806508.i	1.07630	+	0.903119i
$946$	915469.	+	128123.i	1.02297	+	0.143167i
$947$	1.12230e6	+	197892.i	1.25144	+	0.220662i	0.759810	−	0.650145i	$-0.225292\pi$
$947$	1.12230e6	+	197892.i	1.25144	+	0.220662i	0.491626	+	0.870807i	$0.336403\pi$
$948$	74211.7	+	296192.i	0.0825763	+	0.329577i
$949$	2.64103e6			2.93252
$950$	−1.56347e6	−	206684.i	−1.73238	−	0.229013i
$951$			501771.i			0.554810i
$952$	−740103.	−	497346.i	−0.816617	−	0.548763i
$953$	−98829.4	+	560489.i	−0.108818	+	0.617137i	0.880809	+	0.473472i	$0.157000\pi$
$953$	−98829.4	+	560489.i	−0.108818	+	0.617137i	−0.989626	+	0.143664i	$0.954111\pi$
$954$	356533.	+	49898.0i	0.391745	+	0.0548260i
$955$	−1.24243e6	+	1.48068e6i	−1.36228	+	1.62350i
$956$	−1573.51	−	22135.5i	−0.00172168	−	0.0242200i
$957$	−105672.	−	183030.i	−0.115382	−	0.199847i
$958$	198660.	+	931979.i	0.216460	+	1.01549i
$959$	−137402.	+	377510.i	−0.149402	+	0.410479i
$960$	−452127.	−	350730.i	−0.490590	−	0.380566i
$961$	147707.	−	255835.i	0.159939	−	0.277022i
$962$	341993.	−	1.05461e6i	0.369545	−	1.13958i
$963$	−273088.	+	48152.8i	−0.294476	+	0.0519241i
$964$	622018.	−	602063.i	0.669343	−	0.647870i
$965$	−2.32193e6	+	1.94833e6i	−2.49341	+	2.09222i
$966$	281543.	+	449985.i	0.301710	+	0.482218i
$967$	−106407.	−	292351.i	−0.113793	−	0.312645i	0.869702	−	0.493577i	$-0.164311\pi$
$967$	−106407.	−	292351.i	−0.113793	−	0.312645i	−0.983496	+	0.180932i	$0.942089\pi$
$968$	−454530.	+	331437.i	−0.485078	+	0.353713i
$969$	99300.4	+	266492.i	0.105756	+	0.283816i
$970$	−1.52843e6	−	1.69553e6i	−1.62444	−	1.80203i
$971$	−102816.	−	282485.i	−0.109049	−	0.299610i	0.873150	−	0.487451i	$-0.162073\pi$
$971$	−102816.	−	282485.i	−0.109049	−	0.299610i	−0.982199	+	0.187841i	$0.939851\pi$
$972$	−238853.	+	836618.i	−0.252812	+	0.885512i
$973$	150652.	−	126412.i	0.159129	−	0.133525i
$974$	887292.	−	31496.9i	0.935295	−	0.0332009i
$975$	−995214.	+	175483.i	−1.04691	+	0.184598i
$976$	−2118.46	−	6469.18i	−0.00222393	−	0.00679125i
$977$	336990.	−	583684.i	0.353044	−	0.611489i	−0.633738	−	0.773548i	$-0.718480\pi$
$977$	336990.	−	583684.i	0.353044	−	0.611489i	0.986781	+	0.162059i	$0.0518134\pi$
$978$	−19484.9	−	48147.0i	−0.0203714	−	0.0503375i
$979$	−7224.99	+	19850.5i	−0.00753827	+	0.0207112i
$980$	619490.	+	448996.i	0.645034	+	0.467509i
$981$	85972.5	+	148909.i	0.0893350	+	0.154733i
$982$	−319824.	−	249577.i	−0.331656	−	0.258811i
$983$	878154.	−	1.04654e6i	0.908791	−	1.08305i	−0.0874278	−	0.996171i	$-0.527865\pi$
$983$	878154.	−	1.04654e6i	0.908791	−	1.08305i	0.996218	−	0.0868836i	$-0.0276908\pi$
$984$	239705.	+	59325.1i	0.247563	+	0.0612701i
$985$	−226797.	+	1.28623e6i	−0.233758	+	1.32570i
$986$	676567.	+	359237.i	0.695917	+	0.369511i
$987$		−	340978.i		−	0.350020i
$988$	1.29066e6	+	920535.i	1.32220	+	0.943032i
$989$	1.99448e6			2.03909
$990$	414053.	−	779804.i	0.422460	−	0.795637i
$991$	187692.	+	33095.2i	0.191117	+	0.0336991i	0.268387	−	0.963311i	$-0.413509\pi$
$991$	187692.	+	33095.2i	0.191117	+	0.0336991i	−0.0772703	+	0.997010i	$0.524620\pi$
$992$	−383609.	+	1.06348e6i	−0.389821	+	1.08070i
$993$	−315778.	−	264969.i	−0.320245	−	0.268718i
$994$	−888121.	+	1.13809e6i	−0.898875	+	1.15187i
$995$	508055.	−	293326.i	0.513174	−	0.296281i
$996$	183342.	+	132883.i	0.184817	+	0.133952i
$997$	365729.	+	133115.i	0.367934	+	0.133917i	0.519369	−	0.854550i	$-0.326167\pi$
$997$	365729.	+	133115.i	0.367934	+	0.133917i	−0.151435	+	0.988467i	$0.548389\pi$
$998$	895356.	−	362348.i	0.898948	−	0.363801i
$999$	−444130.	−	256419.i	−0.445020	−	0.256932i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.5.l.a.43.7	yes	228
4.3	odd	2	inner	76.5.l.a.43.14	yes	228
19.4	even	9	inner	76.5.l.a.23.14	yes	228
76.23	odd	18	inner	76.5.l.a.23.7	✓	228

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.5.l.a.23.7	✓	228	76.23	odd	18	inner
76.5.l.a.23.14	yes	228	19.4	even	9	inner
76.5.l.a.43.7	yes	228	1.1	even	1	trivial
76.5.l.a.43.14	yes	228	4.3	odd	2	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:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	76.l (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.53287 - 1.87585i) q^{2} +(3.32006 + 0.585416i) q^{3} +(8.96237 + 13.2543i) q^{4} +(31.7438 + 26.6362i) q^{5} +(-10.6312 - 8.29614i) q^{6} +(-51.6354 + 29.8117i) q^{7} +(-6.79985 - 63.6377i) q^{8} +(-65.4350 - 23.8164i) q^{9} +O(q^{10})\)	\(q+(-3.53287 - 1.87585i) q^{2} +(3.32006 + 0.585416i) q^{3} +(8.96237 + 13.2543i) q^{4} +(31.7438 + 26.6362i) q^{5} +(-10.6312 - 8.29614i) q^{6} +(-51.6354 + 29.8117i) q^{7} +(-6.79985 - 63.6377i) q^{8} +(-65.4350 - 23.8164i) q^{9} +(-62.1812 - 153.649i) q^{10} +(-66.2459 - 38.2471i) q^{11} +(21.9963 + 49.2517i) q^{12} +(47.6602 + 270.294i) q^{13} +(238.344 - 8.46066i) q^{14} +(89.7981 + 107.017i) q^{15} +(-95.3519 + 237.579i) q^{16} +(-219.584 + 79.9221i) q^{17} +(186.497 + 206.887i) q^{18} +(-65.3930 - 355.028i) q^{19} +(-68.5442 + 659.465i) q^{20} +(-188.885 + 68.7485i) q^{21} +(162.292 + 259.389i) q^{22} +(424.356 + 505.727i) q^{23} +(14.6787 - 215.262i) q^{24} +(189.651 + 1075.56i) q^{25} +(338.654 - 1044.32i) q^{26} +(-439.794 - 253.915i) q^{27} +(-857.908 - 417.207i) q^{28} +(770.112 + 280.298i) q^{29} +(-116.497 - 546.526i) q^{30} +(-956.138 + 552.027i) q^{31} +(782.530 - 660.472i) q^{32} +(-197.550 - 165.764i) q^{33} +(925.685 + 129.553i) q^{34} +(-2433.18 - 429.035i) q^{35} +(-270.783 - 1080.75i) q^{36} +1009.86 q^{37} +(-434.954 + 1376.94i) q^{38} +925.294i q^{39} +(1479.22 - 2201.23i) q^{40} +(-198.738 + 1127.10i) q^{41} +(796.269 + 111.440i) q^{42} +(1941.94 - 2314.31i) q^{43} +(-86.7825 - 1220.83i) q^{44} +(-1442.78 - 2498.96i) q^{45} +(-550.525 - 2582.70i) q^{46} +(-580.185 + 1594.05i) q^{47} +(-455.657 + 732.958i) q^{48} +(576.977 - 999.354i) q^{49} +(1347.59 - 4155.59i) q^{50} +(-775.821 + 136.798i) q^{51} +(-3155.41 + 3054.18i) q^{52} +(990.107 - 830.798i) q^{53} +(1077.43 + 1722.04i) q^{54} +(-1084.14 - 2978.65i) q^{55} +(2248.26 + 3083.25i) q^{56} +(-9.26962 - 1217.00i) q^{57} +(-2194.91 - 2434.87i) q^{58} +(1220.87 + 3354.30i) q^{59} +(-613.633 + 2149.34i) q^{60} +(-20.3696 + 17.0922i) q^{61} +(4413.43 - 156.667i) q^{62} +(4088.77 - 720.961i) q^{63} +(-4003.52 + 865.454i) q^{64} +(-5686.70 + 9849.65i) q^{65} +(386.970 + 956.198i) q^{66} +(746.531 - 2051.08i) q^{67} +(-3027.31 - 2194.14i) q^{68} +(1112.83 + 1927.47i) q^{69} +(7791.29 + 6080.00i) q^{70} +(-3890.82 + 4636.90i) q^{71} +(-1070.67 + 4326.08i) q^{72} +(1670.93 - 9476.31i) q^{73} +(-3567.70 - 1894.34i) q^{74} +3681.97i q^{75} +(4119.56 - 4048.63i) q^{76} +4560.84 q^{77} +(1735.71 - 3268.95i) q^{78} +(5574.82 + 982.992i) q^{79} +(-9355.05 + 5001.86i) q^{80} +(3009.29 + 2525.10i) q^{81} +(2816.39 - 3609.10i) q^{82} +(3635.44 - 2098.92i) q^{83} +(-2604.07 - 1887.39i) q^{84} +(-9099.26 - 3311.86i) q^{85} +(-11201.9 + 4533.38i) q^{86} +(2392.73 + 1381.44i) q^{87} +(-1983.50 + 4475.81i) q^{88} +(-47.9543 - 271.962i) q^{89} +(409.465 + 11535.0i) q^{90} +(-10518.9 - 12535.9i) q^{91} +(-2899.82 + 10157.0i) q^{92} +(-3497.60 + 1273.02i) q^{93} +(5039.91 - 4543.22i) q^{94} +(7380.78 - 13011.8i) q^{95} +(2984.70 - 1734.70i) q^{96} +(12941.3 - 4710.26i) q^{97} +(-3913.02 + 2448.27i) q^{98} +(3423.89 + 4080.44i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 228 q - 6 q^{2} - 48 q^{4} - 12 q^{5} - 60 q^{6} - 3 q^{8} - 180 q^{9}+O(q^{10}) \) 228 * q - 6 * q^2 - 48 * q^4 - 12 * q^5 - 60 * q^6 - 3 * q^8 - 180 * q^9	\( 228 q - 6 q^{2} - 48 q^{4} - 12 q^{5} - 60 q^{6} - 3 q^{8} - 180 q^{9} - 453 q^{10} - 3 q^{12} + 516 q^{13} + 81 q^{14} - 720 q^{16} - 12 q^{17} - 12 q^{18} - 1182 q^{20} - 930 q^{21} - 54 q^{22} - 2664 q^{24} - 12 q^{25} - 3099 q^{26} - 4824 q^{28} - 12 q^{29} + 5814 q^{30} + 7419 q^{32} + 1542 q^{33} + 6912 q^{34} + 8547 q^{36} - 24 q^{37} - 1536 q^{38} - 6942 q^{40} + 6396 q^{41} - 18855 q^{42} - 1143 q^{44} - 6 q^{45} - 1488 q^{46} + 6093 q^{48} + 26748 q^{49} + 8070 q^{50} - 12591 q^{52} + 2436 q^{53} - 7365 q^{54} - 14418 q^{56} - 12 q^{57} + 8268 q^{58} + 34632 q^{60} - 31068 q^{61} + 27396 q^{62} + 4575 q^{64} + 3594 q^{65} - 29556 q^{66} - 22782 q^{68} + 29370 q^{69} - 71541 q^{70} - 30174 q^{72} - 6348 q^{73} - 417 q^{74} + 43194 q^{76} - 50436 q^{77} + 45537 q^{78} + 30081 q^{80} - 41994 q^{81} + 72219 q^{82} + 13779 q^{84} - 59244 q^{85} + 19200 q^{86} - 22395 q^{88} + 1860 q^{89} + 45594 q^{90} - 64140 q^{92} + 59118 q^{93} - 55590 q^{94} - 98646 q^{96} - 5556 q^{97} - 52215 q^{98}+O(q^{100}) \) 228 * q - 6 * q^2 - 48 * q^4 - 12 * q^5 - 60 * q^6 - 3 * q^8 - 180 * q^9 - 453 * q^10 - 3 * q^12 + 516 * q^13 + 81 * q^14 - 720 * q^16 - 12 * q^17 - 12 * q^18 - 1182 * q^20 - 930 * q^21 - 54 * q^22 - 2664 * q^24 - 12 * q^25 - 3099 * q^26 - 4824 * q^28 - 12 * q^29 + 5814 * q^30 + 7419 * q^32 + 1542 * q^33 + 6912 * q^34 + 8547 * q^36 - 24 * q^37 - 1536 * q^38 - 6942 * q^40 + 6396 * q^41 - 18855 * q^42 - 1143 * q^44 - 6 * q^45 - 1488 * q^46 + 6093 * q^48 + 26748 * q^49 + 8070 * q^50 - 12591 * q^52 + 2436 * q^53 - 7365 * q^54 - 14418 * q^56 - 12 * q^57 + 8268 * q^58 + 34632 * q^60 - 31068 * q^61 + 27396 * q^62 + 4575 * q^64 + 3594 * q^65 - 29556 * q^66 - 22782 * q^68 + 29370 * q^69 - 71541 * q^70 - 30174 * q^72 - 6348 * q^73 - 417 * q^74 + 43194 * q^76 - 50436 * q^77 + 45537 * q^78 + 30081 * q^80 - 41994 * q^81 + 72219 * q^82 + 13779 * q^84 - 59244 * q^85 + 19200 * q^86 - 22395 * q^88 + 1860 * q^89 + 45594 * q^90 - 64140 * q^92 + 59118 * q^93 - 55590 * q^94 - 98646 * q^96 - 5556 * q^97 - 52215 * q^98

Introduction

L-functions

Modular forms

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