LMFDB - Embedded newform 115.4.g.a.6.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,4,Mod(6,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 18]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("115.6");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	115.g (of order $11$, degree $10$, 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:	$6.78521965066$
Analytic rank:	$0$
Dimension:	$110$
Relative dimension:	$11$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			6.5
Character	$\chi$	$=$	115.6
Dual form			115.4.g.a.96.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.743310 + 1.62762i) q^{2} +(9.31398 + 2.73483i) q^{3} +(3.14224 + 3.62634i) q^{4} +(4.20627 - 2.70320i) q^{5} +(-11.3745 + 13.1268i) q^{6} +(-1.18121 + 8.21547i) q^{7} +(-21.9727 + 6.45176i) q^{8} +(56.5571 + 36.3470i) q^{9} +O(q^{10})$	\(q+(-0.743310 + 1.62762i) q^{2} +(9.31398 + 2.73483i) q^{3} +(3.14224 + 3.62634i) q^{4} +(4.20627 - 2.70320i) q^{5} +(-11.3745 + 13.1268i) q^{6} +(-1.18121 + 8.21547i) q^{7} +(-21.9727 + 6.45176i) q^{8} +(56.5571 + 36.3470i) q^{9} +(1.27323 + 8.85554i) q^{10} +(-12.5186 - 27.4119i) q^{11} +(19.3493 + 42.3691i) q^{12} +(-11.2741 - 78.4134i) q^{13} +(-12.4937 - 8.02920i) q^{14} +(46.5699 - 13.6742i) q^{15} +(0.368500 - 2.56297i) q^{16} +(-8.15688 + 9.41354i) q^{17} +(-101.199 + 65.0365i) q^{18} +(-73.8957 - 85.2802i) q^{19} +(23.0198 + 6.75923i) q^{20} +(-33.4697 + 73.2883i) q^{21} +53.9215 q^{22} +(92.4421 + 60.1786i) q^{23} -222.298 q^{24} +(10.3854 - 22.7408i) q^{25} +(136.008 + 39.9354i) q^{26} +(255.734 + 295.132i) q^{27} +(-33.5037 + 21.5315i) q^{28} +(-137.124 + 158.250i) q^{29} +(-12.3595 + 85.9624i) q^{30} +(66.4084 - 19.4993i) q^{31} +(-150.222 - 96.5419i) q^{32} +(-41.6311 - 289.550i) q^{33} +(-9.25860 - 20.2735i) q^{34} +(17.2396 + 37.7495i) q^{35} +(45.9093 + 319.306i) q^{36} +(56.4601 + 36.2847i) q^{37} +(193.731 - 56.8847i) q^{38} +(109.440 - 761.173i) q^{39} +(-74.9826 + 86.5345i) q^{40} +(-212.484 + 136.555i) q^{41} +(-94.4074 - 108.952i) q^{42} +(-100.522 - 29.5158i) q^{43} +(60.0685 - 131.532i) q^{44} +336.148 q^{45} +(-166.661 + 105.729i) q^{46} -50.7819 q^{47} +(10.4415 - 22.8637i) q^{48} +(263.007 + 77.2259i) q^{49} +(29.2939 + 33.8069i) q^{50} +(-101.717 + 65.3698i) q^{51} +(248.927 - 287.277i) q^{52} +(89.7864 - 624.478i) q^{53} +(-670.454 + 196.863i) q^{54} +(-126.757 - 81.4615i) q^{55} +(-27.0500 - 188.137i) q^{56} +(-455.036 - 996.390i) q^{57} +(-155.645 - 340.815i) q^{58} +(4.07708 + 28.3567i) q^{59} +(195.921 + 125.911i) q^{60} +(817.001 - 239.893i) q^{61} +(-17.6246 + 122.582i) q^{62} +(-365.414 + 421.710i) q^{63} +(286.222 - 183.944i) q^{64} +(-259.389 - 299.351i) q^{65} +(502.224 + 147.466i) q^{66} +(98.5586 - 215.813i) q^{67} -59.7675 q^{68} +(696.425 + 813.316i) q^{69} -74.2563 q^{70} +(-398.456 + 872.496i) q^{71} +(-1477.21 - 433.749i) q^{72} +(-82.8202 - 95.5796i) q^{73} +(-101.025 + 64.9249i) q^{74} +(158.921 - 183.405i) q^{75} +(77.0568 - 535.941i) q^{76} +(239.989 - 70.4671i) q^{77} +(1157.56 + 743.916i) q^{78} +(75.1633 + 522.772i) q^{79} +(-5.37823 - 11.7767i) q^{80} +(820.700 + 1797.08i) q^{81} +(-64.3186 - 447.346i) q^{82} +(299.599 + 192.540i) q^{83} +(-370.938 + 108.917i) q^{84} +(-8.86329 + 61.6456i) q^{85} +(122.759 - 141.672i) q^{86} +(-1709.96 + 1098.92i) q^{87} +(451.923 + 521.547i) q^{88} +(-1365.69 - 401.002i) q^{89} +(-249.862 + 547.122i) q^{90} +657.520 q^{91} +(72.2471 + 524.322i) q^{92} +671.854 q^{93} +(37.7467 - 82.6538i) q^{94} +(-541.355 - 158.956i) q^{95} +(-1135.14 - 1310.02i) q^{96} +(-427.054 + 274.451i) q^{97} +(-321.191 + 370.674i) q^{98} +(288.326 - 2005.35i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 110 q - 2 q^{2} + 6 q^{3} - 40 q^{4} - 55 q^{5} - 3 q^{6} - 10 q^{7} + 243 q^{8} - 233 q^{9}+O(q^{10}) $ 110 * q - 2 * q^2 + 6 * q^3 - 40 * q^4 - 55 * q^5 - 3 * q^6 - 10 * q^7 + 243 * q^8 - 233 * q^9	\( 110 q - 2 q^{2} + 6 q^{3} - 40 q^{4} - 55 q^{5} - 3 q^{6} - 10 q^{7} + 243 q^{8} - 233 q^{9} - 10 q^{10} + 2 q^{11} - 57 q^{12} + 34 q^{13} - 154 q^{14} + 30 q^{15} + 16 q^{16} + 252 q^{17} - 33 q^{18} - 160 q^{19} - 200 q^{20} - 684 q^{21} - 704 q^{22} + 127 q^{23} - 3090 q^{24} - 275 q^{25} - 567 q^{26} + 384 q^{27} - 188 q^{28} + 340 q^{29} - 15 q^{30} + 582 q^{31} - 1364 q^{32} + 1760 q^{33} + 1819 q^{34} + 665 q^{35} + 2794 q^{36} + 312 q^{37} + 3123 q^{38} - 1560 q^{39} - 1205 q^{40} + 1324 q^{41} + 1454 q^{42} - 1740 q^{43} - 369 q^{44} + 3730 q^{45} - 4322 q^{46} - 2858 q^{47} - 2686 q^{48} + 2015 q^{49} - 325 q^{50} - 1426 q^{51} + 1717 q^{52} + 882 q^{53} + 2541 q^{54} + 450 q^{55} + 7755 q^{56} + 3688 q^{57} + 6622 q^{58} + 2605 q^{59} + 1530 q^{60} - 104 q^{61} - 9360 q^{62} - 7618 q^{63} + 3483 q^{64} + 170 q^{65} - 1766 q^{66} - 166 q^{67} - 5018 q^{68} - 1194 q^{69} - 770 q^{70} - 1222 q^{71} + 3303 q^{72} - 922 q^{73} + 1245 q^{74} + 150 q^{75} + 1360 q^{76} - 3093 q^{77} - 1600 q^{78} + 2448 q^{79} + 2115 q^{80} - 1371 q^{81} + 6609 q^{82} + 6704 q^{83} + 3894 q^{84} - 720 q^{85} - 5074 q^{86} - 6324 q^{87} + 1918 q^{88} - 5380 q^{89} - 165 q^{90} + 7828 q^{91} - 16225 q^{92} - 24948 q^{93} - 16490 q^{94} + 685 q^{95} + 675 q^{96} - 4400 q^{97} + 8790 q^{98} - 3626 q^{99}+O(q^{100}) \) 110 * q - 2 * q^2 + 6 * q^3 - 40 * q^4 - 55 * q^5 - 3 * q^6 - 10 * q^7 + 243 * q^8 - 233 * q^9 - 10 * q^10 + 2 * q^11 - 57 * q^12 + 34 * q^13 - 154 * q^14 + 30 * q^15 + 16 * q^16 + 252 * q^17 - 33 * q^18 - 160 * q^19 - 200 * q^20 - 684 * q^21 - 704 * q^22 + 127 * q^23 - 3090 * q^24 - 275 * q^25 - 567 * q^26 + 384 * q^27 - 188 * q^28 + 340 * q^29 - 15 * q^30 + 582 * q^31 - 1364 * q^32 + 1760 * q^33 + 1819 * q^34 + 665 * q^35 + 2794 * q^36 + 312 * q^37 + 3123 * q^38 - 1560 * q^39 - 1205 * q^40 + 1324 * q^41 + 1454 * q^42 - 1740 * q^43 - 369 * q^44 + 3730 * q^45 - 4322 * q^46 - 2858 * q^47 - 2686 * q^48 + 2015 * q^49 - 325 * q^50 - 1426 * q^51 + 1717 * q^52 + 882 * q^53 + 2541 * q^54 + 450 * q^55 + 7755 * q^56 + 3688 * q^57 + 6622 * q^58 + 2605 * q^59 + 1530 * q^60 - 104 * q^61 - 9360 * q^62 - 7618 * q^63 + 3483 * q^64 + 170 * q^65 - 1766 * q^66 - 166 * q^67 - 5018 * q^68 - 1194 * q^69 - 770 * q^70 - 1222 * q^71 + 3303 * q^72 - 922 * q^73 + 1245 * q^74 + 150 * q^75 + 1360 * q^76 - 3093 * q^77 - 1600 * q^78 + 2448 * q^79 + 2115 * q^80 - 1371 * q^81 + 6609 * q^82 + 6704 * q^83 + 3894 * q^84 - 720 * q^85 - 5074 * q^86 - 6324 * q^87 + 1918 * q^88 - 5380 * q^89 - 165 * q^90 + 7828 * q^91 - 16225 * q^92 - 24948 * q^93 - 16490 * q^94 + 685 * q^95 + 675 * q^96 - 4400 * q^97 + 8790 * q^98 - 3626 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$e\left(\frac{9}{11}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.743310	+	1.62762i	−0.262800	+	0.575452i	−0.994328	−	0.106360i	$-0.966080\pi$
$2$	−0.743310	+	1.62762i	−0.262800	+	0.575452i	0.731528	+	0.681812i	$0.238808\pi$
$3$	9.31398	+	2.73483i	1.79248	+	0.526319i	0.996839	−	0.0794537i	$-0.0253176\pi$
$3$	9.31398	+	2.73483i	1.79248	+	0.526319i	0.795638	+	0.605772i	$0.207136\pi$
$4$	3.14224	+	3.62634i	0.392780	+	0.453292i
$5$	4.20627	−	2.70320i	0.376220	−	0.241782i
$5$	4.20627	−	2.70320i	0.376220	−	0.241782i
$6$	−11.3745	+	13.1268i	−0.773934	+	0.893167i
$7$	−1.18121	+	8.21547i	−0.0637791	+	0.443594i	0.932762	+	0.360493i	$0.117391\pi$
$7$	−1.18121	+	8.21547i	−0.0637791	+	0.443594i	−0.996541	+	0.0831009i	$0.973518\pi$
$8$	−21.9727	+	6.45176i	−0.971065	+	0.285130i
$9$	56.5571	+	36.3470i	2.09471	+	1.34619i
$10$	1.27323	+	8.85554i	0.0402632	+	0.280037i
$11$	−12.5186	−	27.4119i	−0.343137	−	0.751364i	0.656860	−	0.754013i	$-0.271884\pi$
$11$	−12.5186	−	27.4119i	−0.343137	−	0.751364i	−0.999996	+	0.00264838i	$0.999157\pi$
$12$	19.3493	+	42.3691i	0.465473	+	1.01924i
$13$	−11.2741	−	78.4134i	−0.240530	−	1.67292i	−0.649492	−	0.760368i	$-0.725018\pi$
$13$	−11.2741	−	78.4134i	−0.240530	−	1.67292i	0.408963	−	0.912551i	$-0.365891\pi$
$14$	−12.4937	−	8.02920i	−0.238505	−	0.153278i
$15$	46.5699	−	13.6742i	0.801620	−	0.235377i
$16$	0.368500	−	2.56297i	0.00575781	−	0.0400464i
$17$	−8.15688	+	9.41354i	−0.116373	+	0.134301i	−0.810947	−	0.585120i	$-0.801047\pi$
$17$	−8.15688	+	9.41354i	−0.116373	+	0.134301i	0.694574	+	0.719421i	$0.255593\pi$
$18$	−101.199	+	65.0365i	−1.32515	+	0.851625i
$19$	−73.8957	−	85.2802i	−0.892254	−	1.02972i	−0.999371	−	0.0354699i	$-0.988707\pi$
$19$	−73.8957	−	85.2802i	−0.892254	−	1.02972i	0.107116	−	0.994246i	$-0.465838\pi$
$20$	23.0198	+	6.75923i	0.257370	+	0.0755705i
$21$	−33.4697	+	73.2883i	−0.347794	+	0.761563i
$22$	53.9215			0.522550
$23$	92.4421	+	60.1786i	0.838065	+	0.545570i
$23$	92.4421	+	60.1786i	0.838065	+	0.545570i
$24$	−222.298			−1.89068
$25$	10.3854	−	22.7408i	0.0830830	−	0.181926i
$26$	136.008	+	39.9354i	1.02590	+	0.301230i
$27$	255.734	+	295.132i	1.82281	+	2.10364i
$28$	−33.5037	+	21.5315i	−0.226129	+	0.145324i
$29$	−137.124	+	158.250i	−0.878046	+	1.01332i	0.121738	+	0.992562i	$0.461153\pi$
$29$	−137.124	+	158.250i	−0.878046	+	1.01332i	−0.999785	+	0.0207574i	$0.993392\pi$
$30$	−12.3595	+	85.9624i	−0.0752177	+	0.523150i
$31$	66.4084	−	19.4993i	0.384752	−	0.112973i	−0.0836359	−	0.996496i	$-0.526653\pi$
$31$	66.4084	−	19.4993i	0.384752	−	0.112973i	0.468388	+	0.883523i	$0.344835\pi$
$32$	−150.222	−	96.5419i	−0.829868	−	0.533324i
$33$	−41.6311	−	289.550i	−0.219607	−	1.52740i
$34$	−9.25860	−	20.2735i	−0.0467011	−	0.102261i
$35$	17.2396	+	37.7495i	0.0832579	+	0.182309i
$36$	45.9093	+	319.306i	0.212543	+	1.47827i
$37$	56.4601	+	36.2847i	0.250864	+	0.161221i	0.660030	−	0.751240i	$-0.270544\pi$
$37$	56.4601	+	36.2847i	0.250864	+	0.161221i	−0.409165	+	0.912460i	$0.634180\pi$
$38$	193.731	−	56.8847i	0.827036	−	0.242840i
$39$	109.440	−	761.173i	0.449345	−	3.12526i
$40$	−74.9826	+	86.5345i	−0.296395	+	0.342058i
$41$	−212.484	+	136.555i	−0.809374	+	0.520153i	−0.878663	−	0.477443i	$-0.841564\pi$
$41$	−212.484	+	136.555i	−0.809374	+	0.520153i	0.0692882	+	0.997597i	$0.477927\pi$
$42$	−94.4074	−	108.952i	−0.346842	−	0.400277i
$43$	−100.522	−	29.5158i	−0.356498	−	0.104677i	0.0985793	−	0.995129i	$-0.468570\pi$
$43$	−100.522	−	29.5158i	−0.356498	−	0.104677i	−0.455077	+	0.890452i	$0.650388\pi$
$44$	60.0685	−	131.532i	0.205810	−	0.450662i
$45$	336.148			1.11355
$46$	−166.661	+	105.729i	−0.534193	+	0.338890i
$47$	−50.7819			−0.157602			−0.0788011	−	0.996890i	$-0.525109\pi$
$47$	−50.7819			−0.157602			−0.0788011	+	0.996890i	$0.525109\pi$
$48$	10.4415	−	22.8637i	0.0313979	−	0.0687519i
$49$	263.007	+	77.2259i	0.766785	+	0.225149i
$50$	29.2939	+	33.8069i	0.0828556	+	0.0956205i
$51$	−101.717	+	65.3698i	−0.279280	+	0.179482i
$52$	248.927	−	287.277i	0.663846	−	0.766120i
$53$	89.7864	−	624.478i	0.232700	−	1.61846i	−0.453641	−	0.891185i	$-0.649875\pi$
$53$	89.7864	−	624.478i	0.232700	−	1.61846i	0.686341	−	0.727280i	$-0.259216\pi$
$54$	−670.454	+	196.863i	−1.68958	+	0.496105i
$55$	−126.757	−	81.4615i	−0.310761	−	0.199714i
$56$	−27.0500	−	188.137i	−0.0645483	−	0.448944i
$57$	−455.036	−	996.390i	−1.05739	−	2.31535i
$58$	−155.645	−	340.815i	−0.352366	−	0.771574i
$59$	4.07708	+	28.3567i	0.00899644	+	0.0625716i	0.993825	−	0.110958i	$-0.0353919\pi$
$59$	4.07708	+	28.3567i	0.00899644	+	0.0625716i	−0.984829	+	0.173530i	$0.944483\pi$
$60$	195.921	+	125.911i	0.421555	+	0.270917i
$61$	817.001	−	239.893i	1.71486	−	0.503527i	0.730984	−	0.682395i	$-0.239061\pi$
$61$	817.001	−	239.893i	1.71486	−	0.503527i	0.983873	+	0.178867i	$0.0572433\pi$
$62$	−17.6246	+	122.582i	−0.0361021	+	0.251095i
$63$	−365.414	+	421.710i	−0.730758	+	0.843340i
$64$	286.222	−	183.944i	0.559027	−	0.359265i
$65$	−259.389	−	299.351i	−0.494974	−	0.571230i
$66$	502.224	+	147.466i	0.936659	+	0.275028i
$67$	98.5586	−	215.813i	0.179714	−	0.393519i	−0.798240	−	0.602340i	$-0.794235\pi$
$67$	98.5586	−	215.813i	0.179714	−	0.393519i	0.977954	+	0.208821i	$0.0669625\pi$
$68$	−59.7675			−0.106586
$69$	696.425	+	813.316i	1.21507	+	1.41901i
$70$	−74.2563			−0.126790
$71$	−398.456	+	872.496i	−0.666028	+	1.45840i	0.210768	+	0.977536i	$0.432403\pi$
$71$	−398.456	+	872.496i	−0.666028	+	1.45840i	−0.876796	+	0.480862i	$0.840324\pi$
$72$	−1477.21	−	433.749i	−2.41794	−	0.709970i
$73$	−82.8202	−	95.5796i	−0.132786	−	0.153243i	0.685462	−	0.728108i	$-0.259600\pi$
$73$	−82.8202	−	95.5796i	−0.132786	−	0.153243i	−0.818248	+	0.574865i	$0.805055\pi$
$74$	−101.025	+	64.9249i	−0.158702	+	0.101991i
$75$	158.921	−	183.405i	0.244676	−	0.282371i
$76$	77.0568	−	535.941i	0.116303	−	0.808904i
$77$	239.989	−	70.4671i	0.355185	−	0.104292i
$78$	1157.56	+	743.916i	1.68035	+	1.07990i
$79$	75.1633	+	522.772i	0.107045	+	0.744512i	0.970677	+	0.240389i	$0.0772751\pi$
$79$	75.1633	+	522.772i	0.107045	+	0.744512i	−0.863632	+	0.504123i	$0.831816\pi$
$80$	−5.37823	−	11.7767i	−0.00751630	−	0.0164584i
$81$	820.700	+	1797.08i	1.12579	+	2.46513i
$82$	−64.3186	−	447.346i	−0.0866195	−	0.602452i
$83$	299.599	+	192.540i	0.396207	+	0.254627i	0.723540	−	0.690282i	$-0.242514\pi$
$83$	299.599	+	192.540i	0.396207	+	0.254627i	−0.327333	+	0.944909i	$0.606150\pi$
$84$	−370.938	+	108.917i	−0.481817	+	0.141474i
$85$	−8.86329	+	61.6456i	−0.0113101	+	0.0786635i
$86$	122.759	−	141.672i	0.153924	−	0.177638i
$87$	−1709.96	+	1098.92i	−2.10721	+	1.35422i
$88$	451.923	+	521.547i	0.547445	+	0.631785i
$89$	−1365.69	−	401.002i	−1.62655	−	0.477597i	−0.663779	−	0.747929i	$-0.731048\pi$
$89$	−1365.69	−	401.002i	−1.62655	−	0.477597i	−0.962767	+	0.270332i	$0.912867\pi$
$90$	−249.862	+	547.122i	−0.292642	+	0.640797i
$91$	657.520			0.757437
$92$	72.2471	+	524.322i	0.0818726	+	0.594178i
$93$	671.854			0.749118
$94$	37.7467	−	82.6538i	0.0414178	−	0.0906924i
$95$	−541.355	−	158.956i	−0.584651	−	0.171669i
$96$	−1135.14	−	1310.02i	−1.20682	−	1.39275i
$97$	−427.054	+	274.451i	−0.447019	+	0.287281i	−0.744719	−	0.667378i	$-0.767417\pi$
$97$	−427.054	+	274.451i	−0.447019	+	0.287281i	0.297701	+	0.954659i	$0.403780\pi$
$98$	−321.191	+	370.674i	−0.331073	+	0.382079i
$99$	288.326	−	2005.35i	0.292706	−	2.03581i
$100$	115.099	−	33.7962i	0.115099	−	0.0337962i
$101$	920.388	+	591.498i	0.906753	+	0.582735i	0.908786	−	0.417263i	$-0.137011\pi$
$101$	920.388	+	591.498i	0.906753	+	0.582735i	−0.00203267	+	0.999998i	$0.500647\pi$
$102$	−30.7898	−	214.148i	−0.0298887	−	0.207880i
$103$	−468.102	−	1025.00i	−0.447800	−	0.980546i	−0.990100	−	0.140361i	$-0.955174\pi$
$103$	−468.102	−	1025.00i	−0.447800	−	0.980546i	0.542300	−	0.840185i	$-0.317554\pi$
$104$	753.628	+	1650.21i	0.710570	+	1.55593i
$105$	57.3310	+	398.746i	0.0532850	+	0.370606i
$106$	949.675	+	610.319i	0.870195	+	0.559240i
$107$	−611.943	+	179.683i	−0.552885	+	0.162342i	−0.546229	−	0.837636i	$-0.683937\pi$
$107$	−611.943	+	179.683i	−0.552885	+	0.162342i	−0.00665652	+	0.999978i	$0.502119\pi$
$108$	−266.673	+	1854.75i	−0.237599	+	1.65253i
$109$	−52.9450	+	61.1017i	−0.0465248	+	0.0536925i	−0.778535	−	0.627601i	$-0.784037\pi$
$109$	−52.9450	+	61.1017i	−0.0465248	+	0.0536925i	0.732010	+	0.681294i	$0.238582\pi$
$110$	226.808	−	145.761i	0.196594	−	0.126343i
$111$	426.635	+	492.364i	0.364815	+	0.421019i
$112$	20.6207	+	6.05480i	0.0173971	+	0.00510825i
$113$	406.198	−	889.449i	0.338158	−	0.740463i	−0.661799	−	0.749681i	$-0.730207\pi$
$113$	406.198	−	889.449i	0.338158	−	0.740463i	0.999958	+	0.00921807i	$0.00293425\pi$
$114$	1959.98			1.61025
$115$	551.511	+	3.23767i	0.447206	+	0.00262535i
$116$	−1004.75			−0.804209
$117$	2212.46	−	4844.61i	1.74822	−	3.82807i
$118$	−49.1845	−	14.4419i	−0.0383712	−	0.0112668i
$119$	−67.7017	−	78.1319i	−0.0521530	−	0.0601877i
$120$	−935.044	+	600.916i	−0.711312	+	0.457132i
$121$	276.921	−	319.584i	0.208055	−	0.240109i
$122$	−216.830	+	1508.08i	−0.160909	+	1.11914i
$123$	−2352.52	+	690.763i	−1.72455	+	0.506374i
$124$	279.382	+	179.548i	0.202333	+	0.130031i
$125$	−17.7894	−	123.728i	−0.0127290	−	0.0885323i
$126$	−414.769	−	908.217i	−0.293258	−	0.642146i
$127$	−360.648	−	789.710i	−0.251987	−	0.551775i	0.740792	−	0.671735i	$-0.234451\pi$
$127$	−360.648	−	789.710i	−0.251987	−	0.551775i	−0.992779	+	0.119960i	$0.961723\pi$
$128$	−116.665	−	811.426i	−0.0805615	−	0.560317i
$129$	−855.536	−	549.820i	−0.583921	−	0.375263i
$130$	680.038	−	199.677i	0.458794	−	0.134714i
$131$	−235.895	+	1640.69i	−0.157330	+	1.09426i	0.746197	+	0.665726i	$0.231878\pi$
$131$	−235.895	+	1640.69i	−0.157330	+	1.09426i	−0.903527	+	0.428531i	$0.859031\pi$
$132$	919.193	−	1060.81i	0.606102	−	0.699479i
$133$	787.903	−	506.354i	0.513683	−	0.330124i
$134$	278.003	+	320.832i	0.179222	+	0.206834i
$135$	1873.49	+	550.105i	1.19440	+	0.350708i
$136$	118.495	−	259.467i	0.0747120	−	0.163596i
$137$	−1543.90			−0.962805			−0.481403	−	0.876500i	$-0.659873\pi$
$137$	−1543.90			−0.962805			−0.481403	+	0.876500i	$0.659873\pi$
$138$	−1841.43	+	528.971i	−1.13589	+	0.326297i
$139$	−550.248			−0.335766			−0.167883	−	0.985807i	$-0.553693\pi$
$139$	−550.248			−0.335766			−0.167883	+	0.985807i	$0.553693\pi$
$140$	−82.7214	+	181.135i	−0.0499374	+	0.109348i
$141$	−472.982	−	138.880i	−0.282498	−	0.0829489i
$142$	−1123.92	−	1297.07i	−0.664205	−	0.766534i
$143$	−2008.32	+	1290.67i	−1.17444	+	0.754765i
$144$	113.998	−	131.560i	0.0659709	−	0.0761345i
$145$	−149.000	+	1036.32i	−0.0853363	+	0.593527i
$146$	217.129	−	63.7547i	0.123080	−	0.0361396i
$147$	2238.45	+	1438.56i	1.25595	+	0.807147i
$148$	45.8306	+	318.758i	0.0254544	+	0.177039i
$149$	561.263	+	1228.99i	0.308593	+	0.675725i	0.998855	−	0.0478343i	$-0.0152319\pi$
$149$	561.263	+	1228.99i	0.308593	+	0.675725i	−0.690262	+	0.723560i	$0.742505\pi$
$150$	180.386	+	394.991i	0.0981899	+	0.215006i
$151$	425.981	+	2962.76i	0.229575	+	1.59673i	0.699904	+	0.714237i	$0.253226\pi$
$151$	425.981	+	2962.76i	0.229575	+	1.59673i	−0.470329	+	0.882491i	$0.655865\pi$
$152$	2173.89	+	1397.08i	1.16004	+	0.745513i
$153$	−803.484	+	235.924i	−0.424561	+	0.124662i
$154$	−63.6924	+	442.990i	−0.0333278	+	0.231800i
$155$	226.621	−	261.535i	0.117436	−	0.135529i
$156$	3104.16	−	1994.92i	1.59315	−	1.02386i
$157$	2478.89	+	2860.80i	1.26011	+	1.45424i	0.836091	+	0.548590i	$0.184835\pi$
$157$	2478.89	+	2860.80i	1.26011	+	1.45424i	0.424018	+	0.905654i	$0.360619\pi$
$158$	−906.746	−	266.245i	−0.456562	−	0.134059i
$159$	2544.11	−	5570.83i	1.26894	−	2.77859i
$160$	−892.847			−0.441161
$161$	−603.589	+	688.371i	−0.295462	+	0.336964i
$162$	−3535.01			−1.71442
$163$	355.352	−	778.113i	0.170757	−	0.373905i	−0.804835	−	0.593499i	$-0.797746\pi$
$163$	355.352	−	778.113i	0.170757	−	0.373905i	0.975591	+	0.219594i	$0.0704733\pi$
$164$	−1162.87	−	341.449i	−0.553688	−	0.162577i
$165$	−957.825	−	1105.39i	−0.451919	−	0.521542i
$166$	−536.078	+	344.516i	−0.250649	+	0.161082i
$167$	928.967	−	1072.09i	0.430453	−	0.496769i	−0.498540	−	0.866867i	$-0.666130\pi$
$167$	928.967	−	1072.09i	0.430453	−	0.496769i	0.928993	+	0.370098i	$0.120676\pi$
$168$	262.579	−	1826.28i	0.120586	−	0.838694i
$169$	−3913.54	+	1149.12i	−1.78131	+	0.523040i
$170$	−93.7475	−	60.2479i	−0.0422948	−	0.0271812i
$171$	−1079.64	−	7509.09i	−0.482821	−	3.35810i
$172$	−208.829	−	457.272i	−0.0925759	−	0.202713i
$173$	−4.16782	−	9.12625i	−0.00183164	−	0.00401073i	0.908714	−	0.417419i	$-0.137065\pi$
$173$	−4.16782	−	9.12625i	−0.00183164	−	0.00401073i	−0.910546	+	0.413409i	$0.864338\pi$
$174$	−517.604	−	3600.01i	−0.225514	−	1.56848i
$175$	174.559	+	112.182i	0.0754024	+	0.0484582i
$176$	−74.8691	+	21.9835i	−0.0320652	+	0.00941518i
$177$	−39.5770	+	275.264i	−0.0168067	+	0.116893i
$178$	1667.81	−	1924.76i	0.702290	−	0.810486i
$179$	−3221.93	+	2070.61i	−1.34535	+	0.864607i	−0.997341	−	0.0728827i	$-0.976780\pi$
$179$	−3221.93	+	2070.61i	−1.34535	+	0.864607i	−0.348014	+	0.937489i	$0.613144\pi$
$180$	1056.26	+	1218.99i	0.437382	+	0.504766i
$181$	−3996.79	−	1173.56i	−1.64132	−	0.481936i	−0.674690	−	0.738102i	$-0.735722\pi$
$181$	−3996.79	−	1173.56i	−1.64132	−	0.481936i	−0.966633	+	0.256166i	$0.917541\pi$
$182$	−488.741	+	1070.19i	−0.199054	+	0.435868i
$183$	8265.60			3.33886
$184$	−2419.46	−	725.872i	−0.969374	−	0.290826i
$185$	335.571			0.133360
$186$	−499.396	+	1093.52i	−0.196868	+	0.431081i
$187$	360.156	+	105.751i	0.140841	+	0.0413546i
$188$	−159.569	−	184.152i	−0.0619030	−	0.0714398i
$189$	−2726.72	+	1752.36i	−1.04942	+	0.674420i
$190$	661.115	−	762.968i	0.252433	−	0.291324i
$191$	−251.148	+	1746.77i	−0.0951436	+	0.661738i	0.885312	+	0.464997i	$0.153945\pi$
$191$	−251.148	+	1746.77i	−0.0951436	+	0.661738i	−0.980456	+	0.196741i	$0.936964\pi$
$192$	3168.92	−	930.478i	1.19113	−	0.349747i
$193$	−2593.21	−	1666.55i	−0.967167	−	0.621560i	−0.0411940	−	0.999151i	$-0.513116\pi$
$193$	−2593.21	−	1666.55i	−0.967167	−	0.621560i	−0.925972	+	0.377591i	$0.876753\pi$
$194$	−129.269	−	899.086i	−0.0478401	−	0.332735i
$195$	−1597.27	−	3497.54i	−0.586580	−	1.28443i
$196$	546.385	+	1196.42i	0.199120	+	0.436012i
$197$	158.061	+	1099.34i	0.0571642	+	0.397586i	0.998236	+	0.0593777i	$0.0189116\pi$
$197$	158.061	+	1099.34i	0.0571642	+	0.397586i	−0.941071	+	0.338208i	$0.890179\pi$
$198$	3049.64	+	1959.89i	1.09459	+	0.703450i
$199$	2929.22	−	860.096i	1.04345	−	0.306385i	0.285283	−	0.958443i	$-0.407913\pi$
$199$	2929.22	−	860.096i	1.04345	−	0.306385i	0.758169	+	0.652059i	$0.226094\pi$
$200$	−81.4764	+	566.681i	−0.0288062	+	0.200352i
$201$	1508.19	−	1740.54i	0.529250	−	0.610787i
$202$	−1646.87	+	1058.38i	−0.573630	+	0.368650i
$203$	−1138.13	−	1313.47i	−0.393501	−	0.454124i
$204$	−556.674	−	163.454i	−0.191054	−	0.0560984i
$205$	−524.627	+	1148.77i	−0.178739	+	0.391384i
$206$	2016.26			0.681939
$207$	3040.94	+	6763.52i	1.02106	+	2.27100i
$208$	−205.126			−0.0683794
$209$	−1412.62	+	3093.21i	−0.467527	+	1.02374i
$210$	−691.622	−	203.079i	−0.227269	−	0.0667322i
$211$	374.164	+	431.808i	0.122078	+	0.140886i	0.813499	−	0.581567i	$-0.197560\pi$
$211$	374.164	+	431.808i	0.122078	+	0.140886i	−0.691420	+	0.722453i	$0.743015\pi$
$212$	2546.70	−	1636.66i	0.825038	−	0.530220i
$213$	−6097.34	+	7036.70i	−1.96142	+	2.26360i
$214$	162.408	−	1129.57i	0.0518784	−	0.360822i
$215$	−502.609	+	147.579i	−0.159431	+	0.0468131i
$216$	−7523.28	−	4834.92i	−2.36988	−	1.52303i
$217$	81.7536	+	568.609i	0.0255751	+	0.177879i
$218$	−60.0961	−	131.592i	−0.0186707	−	0.0408832i
$219$	−509.992	−	1116.73i	−0.157361	−	0.344572i
$220$	−102.893	−	715.634i	−0.0315319	−	0.219309i
$221$	830.109	+	533.479i	0.252666	+	0.162379i
$222$	−1118.50	+	328.423i	−0.338149	+	0.0992896i
$223$	416.613	−	2897.60i	0.125105	−	0.870125i	−0.826530	−	0.562893i	$-0.809688\pi$
$223$	416.613	−	2897.60i	0.125105	−	0.870125i	0.951635	−	0.307232i	$-0.0994027\pi$
$224$	970.580	−	1120.11i	0.289507	−	0.334109i
$225$	1413.93	−	908.676i	0.418942	−	0.269237i
$226$	1145.76	+	1322.27i	0.337233	+	0.389187i
$227$	6278.49	+	1843.53i	1.83576	+	0.539029i	0.999950	−	0.00998500i	$-0.00317838\pi$
$227$	6278.49	+	1843.53i	1.83576	+	0.539029i	0.835813	+	0.549014i	$0.184997\pi$
$228$	2183.42	−	4781.01i	0.634211	−	1.38873i
$229$	−742.751			−0.214334			−0.107167	−	0.994241i	$-0.534178\pi$
$229$	−742.751			−0.214334			−0.107167	+	0.994241i	$0.534178\pi$
$230$	−415.214	+	895.245i	−0.119036	+	0.256655i
$231$	2427.97			0.691552
$232$	1992.00	−	4361.87i	0.563712	−	1.23436i
$233$	−2135.89	−	627.153i	−0.600543	−	0.176335i	−0.0326903	−	0.999466i	$-0.510407\pi$
$233$	−2135.89	−	627.153i	−0.600543	−	0.176335i	−0.567853	+	0.823130i	$0.692226\pi$
$234$	6240.66	+	7202.10i	1.74344	+	2.01204i
$235$	−213.602	+	137.274i	−0.0592931	+	0.0381053i
$236$	−90.0198	+	103.888i	−0.0248296	+	0.0286549i
$237$	−729.625	+	5074.65i	−0.199976	+	1.39086i
$238$	177.493	−	52.1165i	0.0483409	−	0.0141942i
$239$	4589.25	+	2949.33i	1.24207	+	0.798228i	0.985726	−	0.168359i	$-0.0538466\pi$
$239$	4589.25	+	2949.33i	1.24207	+	0.798228i	0.256341	+	0.966586i	$0.417483\pi$
$240$	−17.8855	−	124.396i	−0.00481043	−	0.0334573i
$241$	−314.772	−	689.254i	−0.0841338	−	0.184227i	0.862889	−	0.505393i	$-0.168653\pi$
$241$	−314.772	−	689.254i	−0.0841338	−	0.184227i	−0.947023	+	0.321166i	$0.895925\pi$
$242$	314.324	+	688.274i	0.0834939	+	0.182826i
$243$	1228.71	+	8545.86i	0.324369	+	2.25604i
$244$	3437.15	+	2208.92i	0.901807	+	0.579556i
$245$	1315.04	−	386.130i	0.342917	−	0.100689i
$246$	624.353	−	4342.47i	0.161818	−	1.12547i
$247$	−5853.99	+	6755.87i	−1.50802	+	1.74035i
$248$	−1333.37	+	856.903i	−0.341407	+	0.219409i
$249$	2263.89	+	2612.67i	0.576178	+	0.664944i
$250$	214.605	+	63.0137i	0.0542913	+	0.0159413i
$251$	−1095.68	+	2399.21i	−0.275533	+	0.603333i	−0.995920	−	0.0902394i	$-0.971237\pi$
$251$	−1095.68	+	2399.21i	−0.275533	+	0.603333i	0.720387	+	0.693572i	$0.243964\pi$
$252$	−2677.48			−0.669307
$253$	492.366	−	3287.37i	0.122351	−	0.816897i
$254$	1553.42			0.383742
$255$	−251.143	+	549.926i	−0.0616752	+	0.135050i
$256$	4019.02	+	1180.09i	0.981206	+	0.288108i
$257$	−1908.18	−	2202.16i	−0.463148	−	0.534501i	0.475345	−	0.879799i	$-0.342323\pi$
$257$	−1908.18	−	2202.16i	−0.463148	−	0.534501i	−0.938493	+	0.345298i	$0.887778\pi$
$258$	1530.83	−	983.804i	0.369400	−	0.237399i
$259$	−364.787	+	420.986i	−0.0875164	+	0.100999i
$260$	270.485	−	1881.27i	0.0645184	−	0.448736i
$261$	−13507.3	+	3966.09i	−3.20337	+	0.940594i
$262$	−2495.08	−	1603.49i	−0.588345	−	0.378107i
$263$	766.109	+	5328.40i	0.179621	+	1.24929i	0.857642	+	0.514248i	$0.171929\pi$
$263$	766.109	+	5328.40i	0.179621	+	1.24929i	−0.678021	+	0.735043i	$0.737162\pi$
$264$	2782.86	+	6093.61i	0.648762	+	1.42059i
$265$	−1310.43	−	2869.43i	−0.303769	−	0.665162i
$266$	238.497	+	1658.79i	0.0549745	+	0.382356i
$267$	−11623.3	−	7469.85i	−2.66418	−	1.71216i
$268$	1092.31	−	320.730i	0.248967	−	0.0731034i
$269$	608.954	−	4235.37i	0.138024	−	0.959981i	−0.796641	−	0.604453i	$-0.793392\pi$
$269$	608.954	−	4235.37i	0.138024	−	0.959981i	0.934666	−	0.355528i	$-0.115699\pi$
$270$	−2287.95	+	2640.43i	−0.515704	+	0.595154i
$271$	2747.82	−	1765.92i	0.615935	−	0.395837i	−0.195144	−	0.980775i	$-0.562517\pi$
$271$	2747.82	−	1765.92i	0.615935	−	0.395837i	0.811078	+	0.584937i	$0.198881\pi$
$272$	21.1208	+	24.3747i	0.00470823	+	0.00543358i
$273$	6124.13	+	1798.21i	1.35769	+	0.398653i
$274$	1147.60	−	2512.89i	0.253025	−	0.554048i
$275$	−753.380			−0.165202
$276$	−761.024	+	5081.11i	−0.165972	+	1.10814i
$277$	1245.44			0.270148			0.135074	−	0.990835i	$-0.456873\pi$
$277$	1245.44			0.270148			0.135074	+	0.990835i	$0.456873\pi$
$278$	409.005	−	895.596i	0.0882392	−	0.193217i
$279$	4464.61	+	1310.93i	0.958026	+	0.281302i
$280$	−622.352	−	718.232i	−0.132831	−	0.153295i
$281$	1262.82	−	811.567i	0.268092	−	0.172292i	−0.399688	−	0.916651i	$-0.630881\pi$
$281$	1262.82	−	811.567i	0.268092	−	0.172292i	0.667779	+	0.744359i	$0.267245\pi$
$282$	577.616	−	666.605i	0.121974	−	0.140765i
$283$	747.678	−	5200.22i	0.157049	−	1.09230i	−0.746986	−	0.664840i	$-0.768500\pi$
$283$	747.678	−	5200.22i	0.157049	−	1.09230i	0.904035	−	0.427459i	$-0.140591\pi$
$284$	−4416.01	+	1296.66i	−0.922683	+	0.270924i
$285$	−4607.45	−	2961.03i	−0.957620	−	0.615425i
$286$	−607.918	−	4228.17i	−0.125689	−	0.874184i
$287$	−870.875	−	1906.95i	−0.179115	−	0.392208i
$288$	−4987.12	−	10920.3i	−1.02038	−	2.23431i
$289$	677.113	+	4709.42i	0.137821	+	0.958564i
$290$	−1575.98	−	1012.82i	−0.319120	−	0.205086i
$291$	−4728.15	+	1388.31i	−0.952472	+	0.279671i
$292$	86.3630	−	600.668i	0.0173083	−	0.120382i
$293$	−1136.74	+	1311.87i	−0.226652	+	0.261570i	−0.857673	−	0.514196i	$-0.828091\pi$
$293$	−1136.74	+	1311.87i	−0.226652	+	0.261570i	0.631021	+	0.775765i	$0.282636\pi$
$294$	−4005.30	+	2574.05i	−0.794536	+	0.510617i
$295$	93.8032	+	108.255i	0.0185133	+	0.0213655i
$296$	−1474.68	−	433.005i	−0.289574	−	0.0850267i
$297$	4888.72	−	10704.8i	0.955125	−	2.09143i
$298$	−2417.53			−0.469946
$299$	3676.60	−	7927.15i	0.711115	−	1.53324i
$300$	1164.46			0.224100
$301$	361.223	−	790.969i	0.0691713	−	0.151464i
$302$	−5138.89	−	1508.91i	−0.979172	−	0.287511i
$303$	6954.83	+	8026.31i	1.31863	+	1.52178i
$304$	−245.801	+	157.967i	−0.0463739	+	0.0298027i
$305$	2788.05	−	3217.58i	0.523420	−	0.604059i
$306$	213.242	−	1483.13i	0.0398374	−	0.277075i
$307$	6879.55	−	2020.02i	1.27895	−	0.375533i	0.429433	−	0.903099i	$-0.358714\pi$
$307$	6879.55	−	2020.02i	1.27895	−	0.375533i	0.849514	+	0.527566i	$0.176895\pi$
$308$	1009.64	+	648.856i	0.186784	+	0.120039i
$309$	−1556.69	−	10827.0i	−0.286592	−	1.99329i
$310$	257.230	+	563.255i	0.0471280	+	0.103196i
$311$	−1753.88	−	3840.47i	−0.319787	−	0.700235i	0.679659	−	0.733528i	$-0.262128\pi$
$311$	−1753.88	−	3840.47i	−0.319787	−	0.700235i	−0.999446	+	0.0332932i	$0.989400\pi$
$312$	2506.22	+	17431.1i	0.454765	+	3.16296i
$313$	−5964.26	−	3833.00i	−1.07706	−	0.692185i	−0.123184	−	0.992384i	$-0.539311\pi$
$313$	−5964.26	−	3833.00i	−1.07706	−	0.692185i	−0.953877	+	0.300199i	$0.902947\pi$
$314$	−6498.88	+	1908.24i	−1.16800	+	0.342957i
$315$	−397.060	+	2761.61i	−0.0710215	+	0.493966i
$316$	−1659.57	+	1915.24i	−0.295437	+	0.340952i
$317$	3904.34	−	2509.17i	0.691765	−	0.444570i	−0.146948	−	0.989144i	$-0.546945\pi$
$317$	3904.34	−	2509.17i	0.691765	−	0.444570i	0.838713	+	0.544574i	$0.183309\pi$
$318$	7176.14	+	8281.71i	1.26547	+	1.46042i
$319$	6054.54	+	1777.77i	1.06266	+	0.312026i
$320$	706.688	−	1547.43i	0.123453	−	0.270325i
$321$	−6191.02			−1.07648
$322$	−671.755	−	1494.09i	−0.116259	−	0.258579i
$323$	1405.55			0.242126
$324$	−3937.99	+	8623.00i	−0.675239	+	1.47857i
$325$	−1900.27	−	557.969i	−0.324332	−	0.0952325i
$326$	1002.34	+	1156.76i	0.170289	+	0.196524i
$327$	−660.231	+	424.305i	−0.111654	+	0.0717557i
$328$	3787.81	−	4371.37i	0.637644	−	0.735880i
$329$	59.9839	−	417.197i	0.0100517	−	0.0699113i
$330$	2511.12	−	737.331i	0.418886	−	0.122996i
$331$	1622.83	+	1042.93i	0.269483	+	0.173186i	0.668403	−	0.743800i	$-0.266978\pi$
$331$	1622.83	+	1042.93i	0.269483	+	0.173186i	−0.398919	+	0.916986i	$0.630615\pi$
$332$	243.194	+	1691.45i	0.0402019	+	0.279610i
$333$	1874.38	+	4104.31i	0.308454	+	0.675420i
$334$	1054.44	+	2308.90i	0.172744	+	0.378256i
$335$	−168.823	−	1174.19i	−0.0275337	−	0.191501i
$336$	175.502	+	112.789i	0.0284954	+	0.0183129i
$337$	−8308.14	+	2439.49i	−1.34295	+	0.394325i	−0.872720	−	0.488221i	$-0.837646\pi$
$337$	−8308.14	+	2439.49i	−1.34295	+	0.394325i	−0.470227	+	0.882546i	$0.655828\pi$
$338$	1038.64	−	7223.93i	0.167144	−	1.16251i
$339$	6215.81	−	7173.43i	0.995860	−	1.14928i
$340$	−251.398	+	161.564i	−0.0401000	+	0.0257707i
$341$	−1365.85	−	1576.28i	−0.216906	−	0.250323i
$342$	13024.5	+	3824.33i	2.05931	+	0.604667i
$343$	−2127.75	+	4659.13i	−0.334950	+	0.733438i
$344$	2399.16			0.376029
$345$	5127.91	+	1538.45i	0.800224	+	0.240079i
$346$	17.9521			0.00278933
$347$	−190.241	+	416.570i	−0.0294314	+	0.0644458i	−0.923777	−	0.382931i	$-0.874915\pi$
$347$	−190.241	+	416.570i	−0.0294314	+	0.0644458i	0.894345	+	0.447377i	$0.147642\pi$
$348$	−9358.18	−	2747.81i	−1.44153	−	0.423270i
$349$	−1482.15	−	1710.49i	−0.227328	−	0.262351i	0.630614	−	0.776096i	$-0.282803\pi$
$349$	−1482.15	−	1710.49i	−0.227328	−	0.262351i	−0.857943	+	0.513746i	$0.828258\pi$
$350$	−312.342	+	200.730i	−0.0477011	+	0.0306556i
$351$	20259.1	−	23380.3i	3.08078	−	3.55541i
$352$	−765.828	+	5326.45i	−0.115962	+	0.806536i
$353$	−3785.22	+	1111.44i	−0.570728	+	0.167581i	−0.554348	−	0.832285i	$-0.687032\pi$
$353$	−3785.22	+	1111.44i	−0.570728	+	0.167581i	−0.0163801	+	0.999866i	$0.505214\pi$
$354$	−418.608	−	269.023i	−0.0628496	−	0.0403910i
$355$	682.524	+	4747.06i	0.102041	+	0.709712i
$356$	−2837.15	−	6212.49i	−0.422384	−	0.924891i
$357$	−416.895	−	912.872i	−0.0618050	−	0.135334i
$358$	−975.276	−	6783.19i	−0.143980	−	1.00140i
$359$	−4249.79	−	2731.17i	−0.624778	−	0.401520i	0.189595	−	0.981862i	$-0.439283\pi$
$359$	−4249.79	−	2731.17i	−0.624778	−	0.401520i	−0.814373	+	0.580342i	$0.802919\pi$
$360$	−7386.07	+	2168.75i	−1.08133	+	0.317508i
$361$	−835.997	+	5814.49i	−0.121883	+	0.847716i
$362$	4880.98	−	5632.95i	0.708670	−	0.817849i
$363$	3453.25	−	2219.27i	0.499308	−	0.320886i
$364$	2066.08	+	2384.39i	0.297506	+	0.343340i
$365$	−606.735	−	178.153i	−0.0870081	−	0.0255479i
$366$	−6143.91	+	13453.3i	−0.877451	+	1.92135i
$367$	−1994.55			−0.283691			−0.141845	−	0.989889i	$-0.545304\pi$
$367$	−1994.55			−0.283691			−0.141845	+	0.989889i	$0.545304\pi$
$368$	188.301	−	214.751i	0.0266736	−	0.0304202i
$369$	−16980.8			−2.39563
$370$	−249.433	+	546.183i	−0.0350471	+	0.0767424i
$371$	5024.32	+	1475.27i	0.703099	+	0.206449i
$372$	2111.13	+	2436.37i	0.294239	+	0.339570i
$373$	−8605.42	+	5530.37i	−1.19456	+	0.767699i	−0.978007	−	0.208572i	$-0.933119\pi$
$373$	−8605.42	+	5530.37i	−1.19456	+	0.767699i	−0.216556	+	0.976270i	$0.569482\pi$
$374$	−439.831	+	507.592i	−0.0608105	+	0.0701790i
$375$	172.685	−	1201.05i	0.0237797	−	0.165392i
$376$	1115.81	−	327.633i	0.153042	−	0.0449372i
$377$	13954.9	+	8968.25i	1.90640	+	1.22517i
$378$	−825.377	−	5740.63i	−0.112309	−	0.781127i
$379$	−586.080	−	1283.34i	−0.0794325	−	0.173933i	0.865749	−	0.500479i	$-0.166843\pi$
$379$	−586.080	−	1283.34i	−0.0794325	−	0.173933i	−0.945181	+	0.326546i	$0.894115\pi$
$380$	−1124.64	−	2462.61i	−0.151823	−	0.332446i
$381$	−1199.35	−	8341.66i	−0.161272	−	1.12167i
$382$	−2656.40	−	1707.17i	−0.355794	−	0.228655i
$383$	−830.896	+	243.973i	−0.110853	+	0.0325495i	−0.336689	−	0.941616i	$-0.609307\pi$
$383$	−830.896	+	243.973i	−0.110853	+	0.0325495i	0.225835	+	0.974165i	$0.427489\pi$
$384$	1132.49	−	7876.67i	0.150501	−	1.04676i
$385$	818.971	−	945.142i	0.108412	−	0.125114i
$386$	4640.08	−	2982.00i	0.611849	−	0.393212i
$387$	−4612.40	−	5323.00i	−0.605844	−	0.699181i
$388$	−2337.16	−	686.252i	−0.305802	−	0.0897917i
$389$	2319.67	−	5079.37i	0.302344	−	0.662041i	−0.696092	−	0.717953i	$-0.745079\pi$
$389$	2319.67	−	5079.37i	0.302344	−	0.662041i	0.998436	+	0.0559116i	$0.0178065\pi$
$390$	6879.94			0.893281
$391$	−1320.53	+	379.337i	−0.170798	+	0.0490637i
$392$	−6277.22			−0.808795
$393$	−6684.13	+	14636.2i	−0.857939	+	1.87862i
$394$	−1906.79	−	559.884i	−0.243814	−	0.0715903i
$395$	1729.32	+	1995.74i	0.220282	+	0.254219i
$396$	8178.08	−	5255.73i	1.03779	−	0.666946i
$397$	−1449.63	+	1672.96i	−0.183261	+	0.211495i	−0.839945	−	0.542671i	$-0.817413\pi$
$397$	−1449.63	+	1672.96i	−0.183261	+	0.211495i	0.656684	+	0.754166i	$0.271959\pi$
$398$	−777.407	+	5406.98i	−0.0979092	+	0.680974i
$399$	8723.30	−	2561.39i	1.09451	−	0.321379i
$400$	−54.4570	−	34.9974i	−0.00680713	−	0.00437468i
$401$	−915.842	−	6369.82i	−0.114052	−	0.793252i	−0.963908	−	0.266236i	$-0.914220\pi$
$401$	−915.842	−	6369.82i	−0.114052	−	0.793252i	0.849856	−	0.527016i	$-0.176689\pi$
$402$	1711.89	+	3748.52i	0.212391	+	0.465072i
$403$	−2277.70	−	4987.47i	−0.281539	−	0.616485i
$404$	747.110	+	5196.27i	0.0920053	+	0.639911i
$405$	8309.97	+	5340.49i	1.01957	+	0.655237i
$406$	2983.81	−	876.125i	0.364739	−	0.107097i
$407$	287.832	−	2001.91i	0.0350547	−	0.243811i
$408$	1813.26	−	2092.61i	0.220023	−	0.253920i
$409$	12709.6	−	8167.97i	1.53655	−	0.987482i	0.548020	−	0.836465i	$-0.315382\pi$
$409$	12709.6	−	8167.97i	1.53655	−	0.987482i	0.988531	−	0.151016i	$-0.0482546\pi$
$410$	−1479.81	−	1707.79i	−0.178250	−	0.205711i
$411$	−14379.9	−	4222.31i	−1.72581	−	0.506742i
$412$	2246.11	−	4918.29i	0.268587	−	0.588123i
$413$	−237.779			−0.0283302
$414$	−13268.8	−	77.8953i	−1.57519	−	0.00924722i
$415$	1780.67			0.210625
$416$	−5876.55	+	12867.8i	−0.692600	+	1.51658i
$417$	−5125.00	−	1504.84i	−0.601852	−	0.176720i
$418$	−3984.56	−	4598.43i	−0.466247	−	0.538078i
$419$	790.765	−	508.194i	0.0921991	−	0.0592528i	−0.493729	−	0.869616i	$-0.664366\pi$
$419$	790.765	−	508.194i	0.0921991	−	0.0592528i	0.585928	+	0.810363i	$0.300730\pi$
$420$	−1265.84	+	1460.86i	−0.147063	+	0.169720i
$421$	−1846.00	+	12839.2i	−0.213702	+	1.48633i	0.546949	+	0.837166i	$0.315789\pi$
$421$	−1846.00	+	12839.2i	−0.213702	+	1.48633i	−0.760651	+	0.649162i	$0.775120\pi$
$422$	−980.941	+	288.030i	−0.113155	+	0.0332253i
$423$	−2872.08	−	1845.77i	−0.330130	−	0.212162i
$424$	2056.14	+	14300.7i	0.235507	+	1.63798i
$425$	129.359	+	283.257i	0.0147643	+	0.0323294i
$426$	−6920.89	−	15154.6i	−0.787131	−	1.72358i
$427$	1005.79	+	6995.41i	0.113989	+	0.792814i
$428$	−2574.46	−	1654.50i	−0.290751	−	0.186854i
$429$	−22235.3	+	6528.86i	−2.50240	+	0.734771i
$430$	133.391	−	927.754i	0.0149597	−	0.104047i
$431$	−4147.08	+	4785.99i	−0.463475	+	0.534879i	−0.938585	−	0.345047i	$-0.887863\pi$
$431$	−4147.08	+	4785.99i	−0.463475	+	0.534879i	0.475110	+	0.879926i	$0.342408\pi$
$432$	850.654	−	546.682i	0.0947386	−	0.0608848i
$433$	6045.75	+	6977.17i	0.670994	+	0.774368i	0.984532	−	0.175208i	$-0.0560597\pi$
$433$	6045.75	+	6977.17i	0.670994	+	0.774368i	−0.313538	+	0.949576i	$0.601514\pi$
$434$	−986.249	−	289.589i	−0.109082	−	0.0320293i
$435$	−4221.93	+	9244.74i	−0.465348	+	1.01897i
$436$	−387.941			−0.0426124
$437$	−1699.03	−	12330.4i	−0.185985	−	1.34976i
$438$	2196.69			0.239639
$439$	1688.64	−	3697.61i	0.183586	−	0.401998i	−0.795354	−	0.606145i	$-0.792715\pi$
$439$	1688.64	−	3697.61i	0.183586	−	0.401998i	0.978940	+	0.204147i	$0.0654422\pi$
$440$	3310.76	+	972.125i	0.358714	+	0.105328i
$441$	12068.0	+	13927.2i	1.30310	+	1.50386i
$442$	−1485.33	+	954.564i	−0.159842	+	0.102724i
$443$	8840.90	−	10202.9i	0.948180	−	1.09426i	−0.0472610	−	0.998883i	$-0.515049\pi$
$443$	8840.90	−	10202.9i	0.948180	−	1.09426i	0.995441	−	0.0953759i	$-0.0304053\pi$
$444$	−444.886	+	3094.25i	−0.0475526	+	0.330736i
$445$	−6828.44	+	2005.01i	−0.727413	+	0.213588i
$446$	4406.53	+	2831.91i	0.467837	+	0.300661i
$447$	1866.50	+	12981.8i	0.197500	+	1.37364i
$448$	1173.10	+	2568.72i	0.123713	+	0.270894i
$449$	−3716.11	−	8137.15i	−0.390589	−	0.855270i	−0.998138	−	0.0609881i	$-0.980575\pi$
$449$	−3716.11	−	8137.15i	−0.390589	−	0.855270i	0.607550	−	0.794281i	$-0.292152\pi$
$450$	427.995	+	2976.77i	0.0448353	+	0.311836i
$451$	6403.23	+	4115.11i	0.668551	+	0.429651i
$452$	4501.81	−	1321.85i	0.468468	−	0.137555i
$453$	−4135.07	+	28760.1i	−0.428880	+	2.98293i
$454$	−7667.45	+	8848.70i	−0.792623	+	0.914736i
$455$	2765.70	−	1777.41i	0.284963	−	0.183135i
$456$	16426.8	+	18957.6i	1.68697	+	1.94686i
$457$	8368.76	+	2457.29i	0.856617	+	0.251525i	0.680414	−	0.732828i	$-0.261800\pi$
$457$	8368.76	+	2457.29i	0.856617	+	0.251525i	0.176204	+	0.984354i	$0.443618\pi$
$458$	552.095	−	1208.92i	0.0563269	−	0.123339i
$459$	−4864.23			−0.494646
$460$	1721.24	+	2010.14i	0.174463	+	0.203746i
$461$	1056.63			0.106751			0.0533754	−	0.998575i	$-0.483002\pi$
$461$	1056.63			0.106751			0.0533754	+	0.998575i	$0.483002\pi$
$462$	−1804.73	+	3951.82i	−0.181740	+	0.397955i
$463$	8973.51	+	2634.86i	0.900722	+	0.264476i	0.699131	−	0.714994i	$-0.253571\pi$
$463$	8973.51	+	2634.86i	0.900722	+	0.264476i	0.201591	+	0.979470i	$0.435389\pi$
$464$	355.060	+	409.761i	0.0355242	+	0.0409971i
$465$	2826.00	−	1816.16i	0.281833	−	0.181123i
$466$	2608.39	−	3010.25i	0.259295	−	0.299242i
$467$	223.237	−	1552.65i	0.0221203	−	0.153850i	−0.975768	−	0.218809i	$-0.929783\pi$
$467$	223.237	−	1552.65i	0.0221203	−	0.153850i	0.997888	+	0.0649594i	$0.0206918\pi$
$468$	24520.3	−	7199.81i	2.42190	−	0.711135i
$469$	1656.59	+	1064.62i	0.163101	+	0.104818i
$470$	−64.6572	−	449.701i	−0.00634556	−	0.0441344i
$471$	15264.6	+	33424.7i	1.49332	+	3.26992i
$472$	−272.535	−	596.769i	−0.0265772	−	0.0581960i
$473$	449.306	+	3124.99i	0.0436768	+	0.303778i
$474$	−7717.28	−	4959.59i	−0.747819	−	0.480594i
$475$	−2706.77	+	794.780i	−0.261464	+	0.0767727i
$476$	70.5978	−	491.018i	0.00679799	−	0.0472811i
$477$	27776.0	−	32055.2i	2.66619	−	3.07695i
$478$	−8211.64	+	5277.30i	−0.785757	+	0.504975i
$479$	−5395.23	−	6226.43i	−0.514644	−	0.593931i	0.437638	−	0.899151i	$-0.355815\pi$
$479$	−5395.23	−	6226.43i	−0.514644	−	0.593931i	−0.952282	+	0.305220i	$0.901270\pi$
$480$	−8315.96	−	2441.79i	−0.790771	−	0.232191i
$481$	2208.67	−	4836.30i	0.209369	−	0.458454i
$482$	1355.82			0.128124
$483$	−7504.39	+	4760.77i	−0.706960	+	0.448493i
$484$	2029.08			0.190559
$485$	−1054.41	+	2308.83i	−0.0987179	+	0.216162i
$486$	−14822.8	−	4352.35i	−1.38349	−	0.406228i
$487$	757.744	+	874.483i	0.0705065	+	0.0813688i	0.789907	−	0.613227i	$-0.210129\pi$
$487$	757.744	+	874.483i	0.0705065	+	0.0813688i	−0.719400	+	0.694596i	$0.755583\pi$
$488$	−16404.0	+	10542.2i	−1.52167	+	0.977916i
$489$	5437.75	−	6275.50i	0.502871	−	0.580344i
$490$	−349.007	+	2427.40i	−0.0321766	+	0.223793i
$491$	−1301.37	+	382.117i	−0.119613	+	0.0351216i	−0.340991	−	0.940066i	$-0.610763\pi$
$491$	−1301.37	+	382.117i	−0.119613	+	0.0351216i	0.221378	+	0.975188i	$0.428944\pi$
$492$	−9897.13	−	6360.50i	−0.906905	−	0.582832i
$493$	−371.185	−	2581.65i	−0.0339094	−	0.235845i
$494$	−6644.67	−	14549.8i	−0.605178	−	1.32515i
$495$	−4208.10	−	9214.46i	−0.382101	−	0.836685i
$496$	−25.5046	−	177.388i	−0.00230885	−	0.0160584i
$497$	−6697.31	−	4304.10i	−0.604457	−	0.388461i
$498$	−5935.21	+	1742.74i	−0.534063	+	0.156815i
$499$	−1914.11	+	13312.9i	−0.171718	+	1.19432i	0.703536	+	0.710659i	$0.251603\pi$
$499$	−1914.11	+	13312.9i	−0.171718	+	1.19432i	−0.875254	+	0.483664i	$0.839306\pi$
$500$	392.780	−	453.292i	0.0351313	−	0.0405437i
$501$	11584.4	−	7444.81i	1.03304	−	0.663892i
$502$	−3090.57	−	3566.71i	−0.274779	−	0.317112i
$503$	10022.7	+	2942.92i	0.888447	+	0.260872i	0.693943	−	0.720030i	$-0.255872\pi$
$503$	10022.7	+	2942.92i	0.888447	+	0.260872i	0.194504	+	0.980902i	$0.437690\pi$
$504$	5308.35	−	11623.7i	0.469152	−	1.02730i
$505$	5470.34			0.482033
$506$	4984.61	+	3244.92i	0.437931	+	0.285088i
$507$	−39593.3			−3.46825
$508$	1730.51	−	3789.29i	0.151140	−	0.330950i
$509$	6892.18	+	2023.73i	0.600178	+	0.176228i	0.567688	−	0.823244i	$-0.307838\pi$
$509$	6892.18	+	2023.73i	0.600178	+	0.176228i	0.0324902	+	0.999472i	$0.489656\pi$
$510$	−708.395	−	817.531i	−0.0615064	−	0.0709822i
$511$	883.059	−	567.507i	0.0764466	−	0.0491293i
$512$	−613.438	+	707.945i	−0.0529500	+	0.0611075i
$513$	6271.32	−	43618.0i	0.539738	−	3.75396i
$514$	5002.65	−	1468.91i	0.429295	−	0.126052i
$515$	−4739.74	−	3046.05i	−0.405550	−	0.260631i
$516$	−694.468	−	4830.13i	−0.0592485	−	0.412083i
$517$	635.718	+	1392.03i	0.0540790	+	0.118417i
$518$	−414.057	−	906.658i	−0.0351209	−	0.0769040i
$519$	−13.8602	−	96.4000i	−0.00117225	−	0.00815316i
$520$	7630.83	+	4904.03i	0.643527	+	0.413570i
$521$	−5650.00	+	1658.99i	−0.475107	+	0.139504i	−0.510515	−	0.859869i	$-0.670545\pi$
$521$	−5650.00	+	1658.99i	−0.475107	+	0.139504i	0.0354076	+	0.999373i	$0.488727\pi$
$522$	3584.79	−	24932.8i	0.300579	−	2.09057i
$523$	10827.0	−	12495.0i	0.905220	−	1.04468i	−0.0935751	−	0.995612i	$-0.529830\pi$
$523$	10827.0	−	12495.0i	0.905220	−	1.04468i	0.998795	−	0.0490677i	$-0.0156250\pi$
$524$	−6690.93	+	4300.00i	−0.557814	+	0.358486i
$525$	1319.04	+	1522.25i	0.109653	+	0.126546i
$526$	−9242.09	−	2713.72i	−0.766111	−	0.224950i
$527$	−358.128	+	784.191i	−0.0296021	+	0.0648196i
$528$	−757.451			−0.0624315
$529$	4924.07	+	11126.1i	0.404707	+	0.914447i
$530$	5644.41			0.462599
$531$	−800.094	+	1751.96i	−0.0653882	+	0.143180i
$532$	4311.99	+	1266.11i	0.351407	+	0.103182i
$533$	13103.3	+	15122.0i	1.06485	+	1.22891i
$534$	20797.8	−	13366.0i	1.68541	−	1.08315i
$535$	−2088.28	+	2410.00i	−0.168755	+	0.194754i
$536$	−773.221	+	5377.87i	−0.0623098	+	0.433374i
$537$	−35671.8	+	10474.2i	−2.86657	+	0.841702i
$538$	6440.94	+	4139.34i	0.516150	+	0.331709i
$539$	−1175.57	−	8176.30i	−0.0939436	−	0.653392i
$540$	3892.08	+	8522.46i	0.310164	+	0.679164i
$541$	−8766.00	−	19194.9i	−0.696635	−	1.52542i	−0.844004	−	0.536337i	$-0.819808\pi$
$541$	−8766.00	−	19194.9i	−0.696635	−	1.52542i	0.147369	−	0.989082i	$-0.452920\pi$
$542$	831.764	+	5785.05i	0.0659176	+	0.458467i
$543$	−34016.6	−	21861.1i	−2.68838	−	1.72772i
$544$	2134.14	−	626.641i	0.168200	−	0.0493879i
$545$	−57.5302	+	400.131i	−0.00452169	+	0.0314491i
$546$	−7478.93	+	8631.14i	−0.586206	+	0.676518i
$547$	−16333.6	+	10497.0i	−1.27674	+	0.820508i	−0.990482	−	0.137645i	$-0.956047\pi$
$547$	−16333.6	+	10497.0i	−1.27674	+	0.820508i	−0.286254	+	0.958154i	$0.592410\pi$
$548$	−4851.31	−	5598.71i	−0.378171	−	0.436432i
$549$	54926.6	+	16127.9i	4.26997	+	1.25378i
$550$	559.995	−	1226.22i	0.0434150	−	0.0950656i
$551$	23628.5			1.82687
$552$	−20549.7	−	13377.6i	−1.58451	−	1.03150i
$553$	−4383.60			−0.337088
$554$	−925.747	+	2027.10i	−0.0709950	+	0.155457i
$555$	3125.50	+	917.730i	0.239045	+	0.0701901i
$556$	−1729.01	−	1995.38i	−0.131882	−	0.152200i
$557$	12876.4	−	8275.17i	0.979517	−	0.629497i	0.0501840	−	0.998740i	$-0.484019\pi$
$557$	12876.4	−	8275.17i	0.979517	−	0.629497i	0.929333	+	0.369243i	$0.120383\pi$
$558$	−5452.29	+	6292.27i	−0.413645	+	0.477371i
$559$	−1181.14	+	8215.01i	−0.0893683	+	0.621571i
$560$	103.104	−	30.2740i	0.00778023	−	0.00228448i
$561$	3065.27	+	1969.93i	0.230688	+	0.148254i
$562$	382.256	+	2658.65i	0.0286913	+	0.199552i
$563$	−2266.66	−	4963.29i	−0.169677	−	0.371541i	0.805622	−	0.592430i	$-0.201831\pi$
$563$	−2266.66	−	4963.29i	−0.169677	−	0.371541i	−0.975299	+	0.220889i	$0.929104\pi$
$564$	−982.596	−	2151.59i	−0.0733595	−	0.160635i
$565$	−695.786	−	4839.29i	−0.0518087	−	0.360337i
$566$	7908.23	+	5082.31i	0.587293	+	0.377430i
$567$	−15733.3	+	4619.71i	−1.16532	+	0.342169i
$568$	3126.00	−	21741.8i	0.230923	−	1.60610i
$569$	−4675.53	+	5395.85i	−0.344479	+	0.397550i	−0.901380	−	0.433029i	$-0.857445\pi$
$569$	−4675.53	+	5395.85i	−0.344479	+	0.397550i	0.556901	+	0.830579i	$0.311990\pi$
$570$	8244.20	−	5298.23i	0.605810	−	0.389330i
$571$	−13190.1	−	15222.2i	−0.966708	−	1.11564i	−0.993250	−	0.115992i	$-0.962995\pi$
$571$	−13190.1	−	15222.2i	−0.966708	−	1.11564i	0.0265426	−	0.999648i	$-0.491550\pi$
$572$	−10991.1	−	3227.26i	−0.803425	−	0.235907i
$573$	−7116.31	+	15582.6i	−0.518828	+	1.13607i
$574$	3751.13			0.272768
$575$	2328.56	−	1477.23i	0.168883	−	0.107139i
$576$	22873.7			1.65464
$577$	2545.75	−	5574.42i	0.183676	−	0.402194i	−0.795287	−	0.606233i	$-0.792680\pi$
$577$	2545.75	−	5574.42i	0.183676	−	0.402194i	0.978963	+	0.204039i	$0.0654070\pi$
$578$	−8168.47	−	2398.48i	−0.587826	−	0.172601i
$579$	−19595.3	−	22614.2i	−1.40648	−	1.62317i
$580$	−4226.23	+	2716.03i	−0.302560	+	0.194443i
$581$	−1935.70	+	2233.91i	−0.138221	+	0.159515i
$582$	1254.84	−	8727.60i	0.0893724	−	0.621599i
$583$	−18242.1	+	5356.38i	−1.29590	+	0.380512i
$584$	2436.44	+	1565.80i	0.172638	+	0.110948i
$585$	−3789.78	−	26358.5i	−0.267843	−	1.86289i
$586$	−1290.27	−	2825.30i	−0.0909568	−	0.199168i
$587$	3580.29	+	7839.75i	0.251745	+	0.551245i	0.992742	−	0.120263i	$-0.0383739\pi$
$587$	3580.29	+	7839.75i	0.251745	+	0.551245i	−0.740997	+	0.671509i	$0.765647\pi$
$588$	1817.02	+	12637.7i	0.127437	+	0.886341i
$589$	−6570.20	−	4222.41i	−0.459627	−	0.295384i
$590$	−245.923	+	72.2094i	−0.0171601	+	0.00503867i
$591$	−1534.32	+	10671.5i	−0.106791	+	0.742750i
$592$	113.802	−	131.335i	0.00790074	−	0.00911794i
$593$	10843.6	−	6968.77i	0.750917	−	0.482585i	−0.108350	−	0.994113i	$-0.534557\pi$
$593$	10843.6	−	6968.77i	0.750917	−	0.482585i	0.859267	+	0.511528i	$0.170920\pi$
$594$	13789.5	+	15914.0i	0.952511	+	1.09926i
$595$	−495.978	−	145.632i	−0.0341733	−	0.0100342i
$596$	−2693.13	+	5897.12i	−0.185092	+	0.405294i
$597$	29634.9			2.03162
$598$	10169.6	+	11876.5i	0.695425	+	0.812148i
$599$	19807.4			1.35110			0.675549	−	0.737315i	$-0.263907\pi$
$599$	19807.4			1.35110			0.675549	+	0.737315i	$0.263907\pi$
$600$	−2308.65	+	5055.23i	−0.157083	+	0.343965i
$601$	−14499.3	−	4257.37i	−0.984090	−	0.288955i	−0.250178	−	0.968200i	$-0.580489\pi$
$601$	−14499.3	−	4257.37i	−0.984090	−	0.288955i	−0.733912	+	0.679245i	$0.762307\pi$
$602$	1018.90	+	1175.87i	0.0689820	+	0.0796095i
$603$	13418.4	−	8623.45i	0.906199	−	0.582378i
$604$	−9405.44	+	10854.5i	−0.633612	+	0.731228i
$605$	300.904	−	2092.83i	0.0202206	−	0.140638i
$606$	−18233.4	+	5353.81i	−1.22225	+	0.358884i
$607$	11913.8	+	7656.51i	0.796647	+	0.511974i	0.874520	−	0.484990i	$-0.161177\pi$
$607$	11913.8	+	7656.51i	0.796647	+	0.511974i	−0.0778733	+	0.996963i	$0.524813\pi$
$608$	2867.66	+	19945.0i	0.191281	+	1.33039i
$609$	−7008.37	−	15346.2i	−0.466327	−	1.02111i
$610$	3164.62	+	6929.54i	0.210052	+	0.459949i
$611$	572.522	+	3981.98i	0.0379080	+	0.263656i
$612$	−3380.28	−	2172.37i	−0.223267	−	0.143485i
$613$	22026.3	−	6467.50i	1.45128	−	0.426134i	0.541314	−	0.840820i	$-0.317927\pi$
$613$	22026.3	−	6467.50i	1.45128	−	0.426134i	0.909964	+	0.414687i	$0.136109\pi$
$614$	−1825.81	+	12698.8i	−0.120006	+	0.834662i
$615$	−8028.06	+	9264.88i	−0.526379	+	0.607473i
$616$	−4818.56	+	3096.70i	−0.315171	+	0.202548i
$617$	−12955.5	−	14951.5i	−0.845332	−	0.975565i	0.154591	−	0.987979i	$-0.450594\pi$
$617$	−12955.5	−	14951.5i	−0.845332	−	0.975565i	−0.999923	+	0.0124137i	$0.996048\pi$
$618$	18779.4	+	5514.13i	1.22236	+	0.358917i
$619$	−6176.22	+	13524.0i	−0.401039	+	0.878153i	0.596125	+	0.802892i	$0.296706\pi$
$619$	−6176.22	+	13524.0i	−0.401039	+	0.878153i	−0.997164	+	0.0752614i	$0.976021\pi$
$620$	1660.51			0.107561
$621$	5879.88	+	42672.3i	0.379954	+	2.75746i
$622$	7554.52			0.486991
$623$	4907.58	−	10746.1i	0.315599	−	0.691065i
$624$	−1910.54	−	560.984i	−0.122568	−	0.0359893i
$625$	−409.288	−	472.343i	−0.0261944	−	0.0302300i
$626$	10672.0	−	6858.46i	0.681371	−	0.437890i
$627$	−21616.6	+	24946.8i	−1.37685	+	1.58896i
$628$	−2584.93	+	17978.6i	−0.164252	+	1.14240i
$629$	−802.105	+	235.519i	−0.0508458	+	0.0149297i
$630$	−4199.72	−	2699.00i	−0.265589	−	0.170684i
$631$	−4243.74	−	29515.9i	−0.267735	−	1.86214i	−0.469811	−	0.882767i	$-0.655678\pi$
$631$	−4243.74	−	29515.9i	−0.267735	−	1.86214i	0.202076	−	0.979370i	$-0.435231\pi$
$632$	−5024.34	−	11001.8i	−0.316231	−	0.692448i
$633$	2304.03	+	5045.13i	0.144672	+	0.316787i
$634$	1181.84	+	8219.88i	0.0740329	+	0.514910i
$635$	−3651.73	−	2346.83i	−0.228212	−	0.146663i
$636$	28195.9	−	8279.07i	1.75793	−	0.516173i
$637$	3090.36	−	21494.0i	0.192221	−	1.33693i
$638$	−7393.95	+	8533.07i	−0.458823	+	0.529510i
$639$	−54248.2	+	34863.2i	−3.35841	+	2.15832i
$640$	−2684.18	−	3097.71i	−0.165783	−	0.191324i
$641$	−6117.12	−	1796.15i	−0.376929	−	0.110676i	0.0877798	−	0.996140i	$-0.472023\pi$
$641$	−6117.12	−	1796.15i	−0.376929	−	0.110676i	−0.464709	+	0.885464i	$0.653841\pi$
$642$	4601.85	−	10076.6i	0.282898	−	0.619461i
$643$	8521.40			0.522630			0.261315	−	0.965254i	$-0.415844\pi$
$643$	8521.40			0.522630			0.261315	+	0.965254i	$0.415844\pi$
$644$	−4392.89	−	25.7887i	−0.268795	−	0.00157798i
$645$	−5084.89			−0.310415
$646$	−1044.76	+	2287.70i	−0.0636307	+	0.139332i
$647$	26317.0	+	7727.36i	1.59911	+	0.469542i	0.955300	−	0.295639i	$-0.0955325\pi$
$647$	26317.0	+	7727.36i	1.59911	+	0.469542i	0.643815	+	0.765181i	$0.277351\pi$
$648$	−29627.4	−	34191.8i	−1.79610	−	2.07281i
$649$	726.272	−	466.747i	0.0439271	−	0.0282302i
$650$	2320.65	−	2678.18i	0.140036	−	0.161610i
$651$	−793.598	+	5519.60i	−0.0477781	+	0.332304i
$652$	3938.30	−	1156.39i	0.236558	−	0.0694597i
$653$	−16825.7	−	10813.2i	−1.00833	−	0.648015i	−0.0713708	−	0.997450i	$-0.522737\pi$
$653$	−16825.7	−	10813.2i	−1.00833	−	0.648015i	−0.936961	+	0.349435i	$0.886374\pi$
$654$	−199.852	−	1390.00i	−0.0119493	−	0.0831089i
$655$	3442.88	+	7538.85i	0.205381	+	0.449721i
$656$	271.686	+	594.910i	0.0161701	+	0.0354075i
$657$	−1210.03	−	8415.97i	−0.0718538	−	0.499754i
$658$	634.453	+	407.738i	0.0375890	+	0.0241570i
$659$	26578.0	−	7803.99i	1.57106	−	0.461306i	0.623752	−	0.781622i	$-0.285608\pi$
$659$	26578.0	−	7803.99i	1.57106	−	0.461306i	0.947311	+	0.320317i	$0.103789\pi$
$660$	998.799	−	6946.80i	0.0589063	−	0.409703i
$661$	−19643.1	+	22669.3i	−1.15587	+	1.33394i	−0.222533	+	0.974925i	$0.571433\pi$
$661$	−19643.1	+	22669.3i	−1.15587	+	1.33394i	−0.933332	+	0.359014i	$0.883113\pi$
$662$	−2903.77	+	1866.14i	−0.170481	+	0.109561i
$663$	6272.64	+	7239.02i	0.367435	+	0.424042i
$664$	−7825.21	−	2297.69i	−0.457345	−	0.134289i
$665$	1945.35	−	4259.72i	0.113440	−	0.248398i
$666$	−8073.52			−0.469733
$667$	−22199.3	+	6376.99i	−1.28870	+	0.370192i
$668$	6806.78			0.394255
$669$	11804.8	−	25848.9i	0.682211	−	1.49383i
$670$	2036.63	+	598.008i	0.117436	+	0.0344822i
$671$	−16803.7	−	19392.4i	−0.966763	−	1.11570i
$672$	12103.3	−	7778.30i	0.694783	−	0.446510i
$673$	2600.04	−	3000.61i	0.148922	−	0.171865i	−0.676387	−	0.736546i	$-0.736455\pi$
$673$	2600.04	−	3000.61i	0.148922	−	0.171865i	0.825309	+	0.564681i	$0.191001\pi$
$674$	2204.96	−	15335.8i	0.126011	−	0.876429i
$675$	9367.43	−	2750.53i	0.534152	−	0.156841i
$676$	−16464.4	−	10581.0i	−0.936754	−	0.602015i
$677$	2773.36	+	19289.2i	0.157443	+	1.09504i	0.903323	+	0.428960i	$0.141120\pi$
$677$	2773.36	+	19289.2i	0.157443	+	1.09504i	−0.745880	+	0.666080i	$0.767971\pi$
$678$	7055.36	+	15449.1i	0.399645	+	0.875101i
$679$	−1750.31	−	3832.63i	−0.0989257	−	0.216617i
$680$	−202.972	−	1411.70i	−0.0114465	−	0.0796122i
$681$	53436.0	+	34341.3i	3.00686	+	1.93239i
$682$	3580.84	−	1051.43i	0.201052	−	0.0590342i
$683$	975.162	−	6782.40i	0.0546318	−	0.379973i	−0.944101	−	0.329655i	$-0.893068\pi$
$683$	975.162	−	6782.40i	0.0546318	−	0.379973i	0.998733	−	0.0503176i	$-0.0160234\pi$
$684$	23838.0	−	27510.5i	1.33256	−	1.53785i
$685$	−6494.06	+	4173.48i	−0.362227	+	0.232789i
$686$	−6001.72	−	6926.35i	−0.334033	−	0.385495i
$687$	−6917.97	−	2031.30i	−0.384188	−	0.112808i
$688$	−112.690	+	246.758i	−0.00624460	+	0.0136738i
$689$	−49979.7			−2.76353
$690$	−6315.64	+	7202.76i	−0.348453	+	0.397398i
$691$	20685.6			1.13881			0.569404	−	0.822058i	$-0.307174\pi$
$691$	20685.6			1.13881			0.569404	+	0.822058i	$0.307174\pi$
$692$	19.9986	−	43.7908i	0.00109860	−	0.00240560i
$693$	16134.3	+	4737.47i	0.884406	+	0.259685i
$694$	−536.611	−	619.282i	−0.0293508	−	0.0338727i
$695$	−2314.49	+	1487.43i	−0.126322	+	0.0811820i
$696$	30482.4	−	35178.6i	1.66011	−	1.91586i
$697$	447.737	−	3114.08i	0.0243318	−	0.169231i
$698$	3885.73	−	1140.95i	0.210712	−	0.0618706i
$699$	−18178.4	−	11682.6i	−0.983651	−	0.632154i
$700$	141.696	+	985.514i	0.00765084	+	0.0532128i
$701$	1100.20	+	2409.10i	0.0592780	+	0.129801i	0.936953	−	0.349456i	$-0.113634\pi$
$701$	1100.20	+	2409.10i	0.0592780	+	0.129801i	−0.877675	+	0.479257i	$0.840906\pi$
$702$	22995.5	+	50353.1i	1.23634	+	2.70720i
$703$	−1077.79	−	7496.20i	−0.0578232	−	0.402169i
$704$	−8625.34	−	5543.17i	−0.461761	−	0.296756i
$705$	−2364.91	+	694.400i	−0.126337	+	0.0370959i
$706$	1004.59	−	6987.06i	0.0535526	−	0.372467i
$707$	−5946.60	+	6862.74i	−0.316329	+	0.365064i
$708$	−1122.56	+	721.426i	−0.0595881	+	0.0382950i
$709$	19184.8	+	22140.4i	1.01622	+	1.17278i	0.984874	+	0.173272i	$0.0554340\pi$
$709$	19184.8	+	22140.4i	1.01622	+	1.17278i	0.0313464	+	0.999509i	$0.490021\pi$
$710$	−8233.75	−	2417.65i	−0.435221	−	0.127793i
$711$	−14750.2	+	32298.5i	−0.778025	+	1.70364i
$712$	32595.0			1.71566
$713$	7312.37	+	2193.81i	0.384082	+	0.115230i
$714$	1795.69			0.0941206
$715$	−4958.60	+	10857.8i	−0.259358	+	0.567915i
$716$	−17632.8	−	5177.46i	−0.920348	−	0.270239i
$717$	34678.3	+	40020.9i	1.80625	+	2.08453i
$718$	7604.23	−	4886.94i	0.395247	−	0.254010i
$719$	9886.86	−	11410.0i	0.512820	−	0.591826i	−0.438998	−	0.898488i	$-0.644667\pi$
$719$	9886.86	−	11410.0i	0.512820	−	0.591826i	0.951819	+	0.306662i	$0.0992121\pi$
$720$	123.870	−	861.537i	0.00641163	−	0.0445939i
$721$	8973.78	−	2634.94i	0.463524	−	0.136103i
$722$	−8842.38	−	5682.66i	−0.455789	−	0.292918i
$723$	−1046.78	−	7280.55i	−0.0538456	−	0.374504i
$724$	−8303.14	−	18181.3i	−0.426221	−	0.933294i
$725$	2174.64	+	4761.80i	0.111399	+	0.243929i
$726$	1045.30	+	7270.20i	0.0534361	+	0.371656i
$727$	−10995.5	−	7066.41i	−0.560939	−	0.360493i	0.229240	−	0.973370i	$-0.426376\pi$
$727$	−10995.5	−	7066.41i	−0.560939	−	0.360493i	−0.790179	+	0.612877i	$0.790012\pi$
$728$	−14447.5	+	4242.16i	−0.735521	+	0.215968i
$729$	−4336.02	+	30157.7i	−0.220293	+	1.53217i
$730$	740.959	−	855.112i	0.0375673	−	0.0433550i
$731$	1097.79	−	705.508i	0.0555449	−	0.0356965i
$732$	25972.5	+	29973.9i	1.31144	+	1.51348i
$733$	−24299.8	−	7135.06i	−1.22447	−	0.359535i	−0.395307	−	0.918549i	$-0.629362\pi$
$733$	−24299.8	−	7135.06i	−1.22447	−	0.359535i	−0.829158	+	0.559014i	$0.811180\pi$
$734$	1482.57	−	3246.37i	0.0745539	−	0.163250i
$735$	13304.2			0.667665
$736$	−8077.08	−	17964.7i	−0.404518	−	0.899711i
$737$	−7149.67			−0.357343
$738$	12622.0	−	27638.4i	0.629570	−	1.37857i
$739$	−1078.42	−	316.652i	−0.0536809	−	0.0157621i	0.254782	−	0.966999i	$-0.417996\pi$
$739$	−1078.42	−	316.652i	−0.0536809	−	0.0157621i	−0.308463	+	0.951236i	$0.599815\pi$
$740$	1054.44	+	1216.89i	0.0523813	+	0.0604512i
$741$	−73000.2	+	46914.4i	−3.61907	+	2.32583i
$742$	−6135.82	+	7081.12i	−0.303576	+	0.350345i
$743$	−1432.00	+	9959.77i	−0.0707065	+	0.491774i	0.923441	+	0.383741i	$0.125364\pi$
$743$	−1432.00	+	9959.77i	−0.0707065	+	0.491774i	−0.994147	+	0.108033i	$0.965545\pi$
$744$	−14762.4	+	4334.64i	−0.727443	+	0.213596i
$745$	5683.04	+	3652.27i	0.279477	+	0.179609i
$746$	−2604.85	−	18117.2i	−0.127843	−	0.889164i
$747$	9946.16	+	21779.0i	0.487163	+	1.06674i
$748$	748.206	+	1638.34i	0.0365737	+	0.0800852i
$749$	−753.346	−	5239.64i	−0.0367512	−	0.255610i
$750$	1826.50	+	1173.82i	0.0889256	+	0.0571490i
$751$	9486.27	−	2785.42i	0.460931	−	0.135341i	−0.0430193	−	0.999074i	$-0.513698\pi$
$751$	9486.27	−	2785.42i	0.460931	−	0.135341i	0.503950	+	0.863733i	$0.331880\pi$
$752$	−18.7131	+	130.153i	−0.000907443	+	0.00631140i
$753$	−16766.6	+	19349.7i	−0.811431	+	0.936442i
$754$	−24969.7	+	16047.1i	−1.20603	+	0.775066i
$755$	9800.73	+	11310.6i	0.472431	+	0.545214i
$756$	−14922.7	−	4381.69i	−0.717900	−	0.210794i
$757$	13305.4	−	29134.7i	0.638827	−	1.39884i	−0.262175	−	0.965020i	$-0.584440\pi$
$757$	13305.4	−	29134.7i	0.638827	−	1.39884i	0.901002	−	0.433815i	$-0.142833\pi$
$758$	2524.43			0.120965
$759$	13576.3	−	29271.9i	0.649260	−	1.39987i
$760$	12920.6			0.616682
$761$	−7298.12	+	15980.7i	−0.347643	+	0.761233i	0.652351	+	0.757917i	$0.273783\pi$
$761$	−7298.12	+	15980.7i	−0.347643	+	0.761233i	−0.999995	+	0.00331594i	$0.998945\pi$
$762$	14468.6	+	4248.35i	0.687849	+	0.201971i
$763$	−439.441	−	507.141i	−0.0208504	−	0.0240626i
$764$	−7123.55	+	4578.03i	−0.337331	+	0.216790i

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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	115.g (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.743310 + 1.62762i) q^{2} +(9.31398 + 2.73483i) q^{3} +(3.14224 + 3.62634i) q^{4} +(4.20627 - 2.70320i) q^{5} +(-11.3745 + 13.1268i) q^{6} +(-1.18121 + 8.21547i) q^{7} +(-21.9727 + 6.45176i) q^{8} +(56.5571 + 36.3470i) q^{9} +O(q^{10})\)	\(q+(-0.743310 + 1.62762i) q^{2} +(9.31398 + 2.73483i) q^{3} +(3.14224 + 3.62634i) q^{4} +(4.20627 - 2.70320i) q^{5} +(-11.3745 + 13.1268i) q^{6} +(-1.18121 + 8.21547i) q^{7} +(-21.9727 + 6.45176i) q^{8} +(56.5571 + 36.3470i) q^{9} +(1.27323 + 8.85554i) q^{10} +(-12.5186 - 27.4119i) q^{11} +(19.3493 + 42.3691i) q^{12} +(-11.2741 - 78.4134i) q^{13} +(-12.4937 - 8.02920i) q^{14} +(46.5699 - 13.6742i) q^{15} +(0.368500 - 2.56297i) q^{16} +(-8.15688 + 9.41354i) q^{17} +(-101.199 + 65.0365i) q^{18} +(-73.8957 - 85.2802i) q^{19} +(23.0198 + 6.75923i) q^{20} +(-33.4697 + 73.2883i) q^{21} +53.9215 q^{22} +(92.4421 + 60.1786i) q^{23} -222.298 q^{24} +(10.3854 - 22.7408i) q^{25} +(136.008 + 39.9354i) q^{26} +(255.734 + 295.132i) q^{27} +(-33.5037 + 21.5315i) q^{28} +(-137.124 + 158.250i) q^{29} +(-12.3595 + 85.9624i) q^{30} +(66.4084 - 19.4993i) q^{31} +(-150.222 - 96.5419i) q^{32} +(-41.6311 - 289.550i) q^{33} +(-9.25860 - 20.2735i) q^{34} +(17.2396 + 37.7495i) q^{35} +(45.9093 + 319.306i) q^{36} +(56.4601 + 36.2847i) q^{37} +(193.731 - 56.8847i) q^{38} +(109.440 - 761.173i) q^{39} +(-74.9826 + 86.5345i) q^{40} +(-212.484 + 136.555i) q^{41} +(-94.4074 - 108.952i) q^{42} +(-100.522 - 29.5158i) q^{43} +(60.0685 - 131.532i) q^{44} +336.148 q^{45} +(-166.661 + 105.729i) q^{46} -50.7819 q^{47} +(10.4415 - 22.8637i) q^{48} +(263.007 + 77.2259i) q^{49} +(29.2939 + 33.8069i) q^{50} +(-101.717 + 65.3698i) q^{51} +(248.927 - 287.277i) q^{52} +(89.7864 - 624.478i) q^{53} +(-670.454 + 196.863i) q^{54} +(-126.757 - 81.4615i) q^{55} +(-27.0500 - 188.137i) q^{56} +(-455.036 - 996.390i) q^{57} +(-155.645 - 340.815i) q^{58} +(4.07708 + 28.3567i) q^{59} +(195.921 + 125.911i) q^{60} +(817.001 - 239.893i) q^{61} +(-17.6246 + 122.582i) q^{62} +(-365.414 + 421.710i) q^{63} +(286.222 - 183.944i) q^{64} +(-259.389 - 299.351i) q^{65} +(502.224 + 147.466i) q^{66} +(98.5586 - 215.813i) q^{67} -59.7675 q^{68} +(696.425 + 813.316i) q^{69} -74.2563 q^{70} +(-398.456 + 872.496i) q^{71} +(-1477.21 - 433.749i) q^{72} +(-82.8202 - 95.5796i) q^{73} +(-101.025 + 64.9249i) q^{74} +(158.921 - 183.405i) q^{75} +(77.0568 - 535.941i) q^{76} +(239.989 - 70.4671i) q^{77} +(1157.56 + 743.916i) q^{78} +(75.1633 + 522.772i) q^{79} +(-5.37823 - 11.7767i) q^{80} +(820.700 + 1797.08i) q^{81} +(-64.3186 - 447.346i) q^{82} +(299.599 + 192.540i) q^{83} +(-370.938 + 108.917i) q^{84} +(-8.86329 + 61.6456i) q^{85} +(122.759 - 141.672i) q^{86} +(-1709.96 + 1098.92i) q^{87} +(451.923 + 521.547i) q^{88} +(-1365.69 - 401.002i) q^{89} +(-249.862 + 547.122i) q^{90} +657.520 q^{91} +(72.2471 + 524.322i) q^{92} +671.854 q^{93} +(37.7467 - 82.6538i) q^{94} +(-541.355 - 158.956i) q^{95} +(-1135.14 - 1310.02i) q^{96} +(-427.054 + 274.451i) q^{97} +(-321.191 + 370.674i) q^{98} +(288.326 - 2005.35i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 110 q - 2 q^{2} + 6 q^{3} - 40 q^{4} - 55 q^{5} - 3 q^{6} - 10 q^{7} + 243 q^{8} - 233 q^{9}+O(q^{10}) \) 110 * q - 2 * q^2 + 6 * q^3 - 40 * q^4 - 55 * q^5 - 3 * q^6 - 10 * q^7 + 243 * q^8 - 233 * q^9	\( 110 q - 2 q^{2} + 6 q^{3} - 40 q^{4} - 55 q^{5} - 3 q^{6} - 10 q^{7} + 243 q^{8} - 233 q^{9} - 10 q^{10} + 2 q^{11} - 57 q^{12} + 34 q^{13} - 154 q^{14} + 30 q^{15} + 16 q^{16} + 252 q^{17} - 33 q^{18} - 160 q^{19} - 200 q^{20} - 684 q^{21} - 704 q^{22} + 127 q^{23} - 3090 q^{24} - 275 q^{25} - 567 q^{26} + 384 q^{27} - 188 q^{28} + 340 q^{29} - 15 q^{30} + 582 q^{31} - 1364 q^{32} + 1760 q^{33} + 1819 q^{34} + 665 q^{35} + 2794 q^{36} + 312 q^{37} + 3123 q^{38} - 1560 q^{39} - 1205 q^{40} + 1324 q^{41} + 1454 q^{42} - 1740 q^{43} - 369 q^{44} + 3730 q^{45} - 4322 q^{46} - 2858 q^{47} - 2686 q^{48} + 2015 q^{49} - 325 q^{50} - 1426 q^{51} + 1717 q^{52} + 882 q^{53} + 2541 q^{54} + 450 q^{55} + 7755 q^{56} + 3688 q^{57} + 6622 q^{58} + 2605 q^{59} + 1530 q^{60} - 104 q^{61} - 9360 q^{62} - 7618 q^{63} + 3483 q^{64} + 170 q^{65} - 1766 q^{66} - 166 q^{67} - 5018 q^{68} - 1194 q^{69} - 770 q^{70} - 1222 q^{71} + 3303 q^{72} - 922 q^{73} + 1245 q^{74} + 150 q^{75} + 1360 q^{76} - 3093 q^{77} - 1600 q^{78} + 2448 q^{79} + 2115 q^{80} - 1371 q^{81} + 6609 q^{82} + 6704 q^{83} + 3894 q^{84} - 720 q^{85} - 5074 q^{86} - 6324 q^{87} + 1918 q^{88} - 5380 q^{89} - 165 q^{90} + 7828 q^{91} - 16225 q^{92} - 24948 q^{93} - 16490 q^{94} + 685 q^{95} + 675 q^{96} - 4400 q^{97} + 8790 q^{98} - 3626 q^{99}+O(q^{100}) \) 110 * q - 2 * q^2 + 6 * q^3 - 40 * q^4 - 55 * q^5 - 3 * q^6 - 10 * q^7 + 243 * q^8 - 233 * q^9 - 10 * q^10 + 2 * q^11 - 57 * q^12 + 34 * q^13 - 154 * q^14 + 30 * q^15 + 16 * q^16 + 252 * q^17 - 33 * q^18 - 160 * q^19 - 200 * q^20 - 684 * q^21 - 704 * q^22 + 127 * q^23 - 3090 * q^24 - 275 * q^25 - 567 * q^26 + 384 * q^27 - 188 * q^28 + 340 * q^29 - 15 * q^30 + 582 * q^31 - 1364 * q^32 + 1760 * q^33 + 1819 * q^34 + 665 * q^35 + 2794 * q^36 + 312 * q^37 + 3123 * q^38 - 1560 * q^39 - 1205 * q^40 + 1324 * q^41 + 1454 * q^42 - 1740 * q^43 - 369 * q^44 + 3730 * q^45 - 4322 * q^46 - 2858 * q^47 - 2686 * q^48 + 2015 * q^49 - 325 * q^50 - 1426 * q^51 + 1717 * q^52 + 882 * q^53 + 2541 * q^54 + 450 * q^55 + 7755 * q^56 + 3688 * q^57 + 6622 * q^58 + 2605 * q^59 + 1530 * q^60 - 104 * q^61 - 9360 * q^62 - 7618 * q^63 + 3483 * q^64 + 170 * q^65 - 1766 * q^66 - 166 * q^67 - 5018 * q^68 - 1194 * q^69 - 770 * q^70 - 1222 * q^71 + 3303 * q^72 - 922 * q^73 + 1245 * q^74 + 150 * q^75 + 1360 * q^76 - 3093 * q^77 - 1600 * q^78 + 2448 * q^79 + 2115 * q^80 - 1371 * q^81 + 6609 * q^82 + 6704 * q^83 + 3894 * q^84 - 720 * q^85 - 5074 * q^86 - 6324 * q^87 + 1918 * q^88 - 5380 * q^89 - 165 * q^90 + 7828 * q^91 - 16225 * q^92 - 24948 * q^93 - 16490 * q^94 + 685 * q^95 + 675 * q^96 - 4400 * q^97 + 8790 * q^98 - 3626 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more