LMFDB - Embedded newform 45.4.l.a.23.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,4,Mod(2,45)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(45, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("45.2");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	45.l (of order $12$, degree $4$, 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:	$2.65508595026$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			23.4
Character	$\chi$	$=$	45.23
Dual form			45.4.l.a.2.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.771317 + 2.87860i) q^{2} +(0.414910 - 5.17956i) q^{3} +(-0.763180 - 0.440622i) q^{4} +(1.89424 + 11.0187i) q^{5} +(14.5898 + 5.18944i) q^{6} +(31.3140 + 8.39055i) q^{7} +(-15.0012 + 15.0012i) q^{8} +(-26.6557 - 4.29810i) q^{9} +O(q^{10})$	\(q+(-0.771317 + 2.87860i) q^{2} +(0.414910 - 5.17956i) q^{3} +(-0.763180 - 0.440622i) q^{4} +(1.89424 + 11.0187i) q^{5} +(14.5898 + 5.18944i) q^{6} +(31.3140 + 8.39055i) q^{7} +(-15.0012 + 15.0012i) q^{8} +(-26.6557 - 4.29810i) q^{9} +(-33.1795 - 3.04617i) q^{10} +(15.0191 - 8.67129i) q^{11} +(-2.59888 + 3.77012i) q^{12} +(-8.49586 + 2.27646i) q^{13} +(-48.3060 + 83.6685i) q^{14} +(57.8580 - 5.23955i) q^{15} +(-35.1367 - 60.8585i) q^{16} +(23.2549 + 23.2549i) q^{17} +(32.9325 - 73.4158i) q^{18} -145.204i q^{19} +(3.40944 - 9.24389i) q^{20} +(56.4519 - 158.711i) q^{21} +(13.3766 + 49.9223i) q^{22} +(-3.00990 - 11.2331i) q^{23} +(71.4755 + 83.9238i) q^{24} +(-117.824 + 41.7441i) q^{25} -26.2120i q^{26} +(-33.3220 + 136.281i) q^{27} +(-20.2011 - 20.2011i) q^{28} +(-110.651 - 191.653i) q^{29} +(-29.5443 + 170.591i) q^{30} +(-34.8793 + 60.4127i) q^{31} +(38.3524 - 10.2765i) q^{32} +(-38.6819 - 81.3902i) q^{33} +(-84.8784 + 49.0046i) q^{34} +(-33.1369 + 360.933i) q^{35} +(18.4492 + 15.0253i) q^{36} +(56.4980 - 56.4980i) q^{37} +(417.984 + 111.998i) q^{38} +(8.26604 + 44.9494i) q^{39} +(-193.710 - 136.878i) q^{40} +(-141.694 - 81.8068i) q^{41} +(413.323 + 284.919i) q^{42} +(-28.8478 + 107.661i) q^{43} -15.2830 q^{44} +(-3.13270 - 301.853i) q^{45} +34.6571 q^{46} +(49.8826 - 186.165i) q^{47} +(-329.799 + 156.742i) q^{48} +(613.116 + 353.983i) q^{49} +(-29.2849 - 371.365i) q^{50} +(130.099 - 110.801i) q^{51} +(7.48693 + 2.00612i) q^{52} +(367.732 - 367.732i) q^{53} +(-366.597 - 201.037i) q^{54} +(123.996 + 149.066i) q^{55} +(-595.615 + 343.879i) q^{56} +(-752.093 - 60.2466i) q^{57} +(637.039 - 170.694i) q^{58} +(-210.017 + 363.760i) q^{59} +(-46.4647 - 21.4948i) q^{60} +(226.039 + 391.511i) q^{61} +(-147.001 - 147.001i) q^{62} +(-798.632 - 358.247i) q^{63} -443.859i q^{64} +(-41.1768 - 89.3013i) q^{65} +(264.126 - 48.5718i) q^{66} +(60.3981 + 225.409i) q^{67} +(-7.50105 - 27.9943i) q^{68} +(-59.4313 + 10.9292i) q^{69} +(-1013.42 - 373.782i) q^{70} -434.936i q^{71} +(464.344 - 335.391i) q^{72} +(226.275 + 226.275i) q^{73} +(119.057 + 206.213i) q^{74} +(167.330 + 627.595i) q^{75} +(-63.9801 + 110.817i) q^{76} +(543.065 - 145.514i) q^{77} +(-135.767 - 10.8756i) q^{78} +(138.839 - 80.1586i) q^{79} +(604.025 - 502.441i) q^{80} +(692.053 + 229.138i) q^{81} +(344.779 - 344.779i) q^{82} +(-146.319 - 39.2062i) q^{83} +(-113.015 + 96.2513i) q^{84} +(-212.189 + 300.289i) q^{85} +(-287.663 - 166.082i) q^{86} +(-1038.59 + 493.605i) q^{87} +(-95.2250 + 355.384i) q^{88} -125.629 q^{89} +(871.329 + 223.807i) q^{90} -285.140 q^{91} +(-2.65245 + 9.89909i) q^{92} +(298.439 + 205.725i) q^{93} +(497.417 + 287.184i) q^{94} +(1599.96 - 275.051i) q^{95} +(-37.3150 - 202.913i) q^{96} +(-983.843 - 263.620i) q^{97} +(-1491.88 + 1491.88i) q^{98} +(-437.615 + 166.586i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 6 q^{2} - 6 q^{5} - 24 q^{6} - 2 q^{7}+O(q^{10}) $ 64 * q - 6 * q^2 - 6 * q^5 - 24 * q^6 - 2 * q^7	$ 64 q - 6 q^{2} - 6 q^{5} - 24 q^{6} - 2 q^{7} - 8 q^{10} - 36 q^{11} - 138 q^{12} - 2 q^{13} - 96 q^{15} + 316 q^{16} - 480 q^{18} + 378 q^{20} + 480 q^{21} - 34 q^{22} + 306 q^{23} - 146 q^{25} + 180 q^{27} - 232 q^{28} - 1170 q^{30} - 4 q^{31} - 1770 q^{32} - 294 q^{33} - 216 q^{36} + 136 q^{37} + 114 q^{38} + 126 q^{40} + 1992 q^{41} + 1698 q^{42} - 2 q^{43} + 1134 q^{45} - 952 q^{46} + 3462 q^{47} + 4326 q^{48} + 666 q^{50} - 2496 q^{51} - 242 q^{52} + 284 q^{55} - 7128 q^{56} - 2544 q^{57} + 534 q^{58} + 1818 q^{60} + 32 q^{61} - 4038 q^{63} - 2094 q^{65} + 2892 q^{66} + 610 q^{67} - 2694 q^{68} + 498 q^{70} - 1854 q^{72} - 8 q^{73} - 6408 q^{75} + 1368 q^{76} - 6486 q^{77} + 1434 q^{78} + 3012 q^{81} - 3784 q^{82} + 2814 q^{83} - 1658 q^{85} + 12480 q^{86} + 4830 q^{87} - 1338 q^{88} + 13914 q^{90} + 992 q^{91} + 13152 q^{92} + 8310 q^{93} + 4284 q^{95} - 7932 q^{96} + 358 q^{97}+O(q^{100}) $ 64 * q - 6 * q^2 - 6 * q^5 - 24 * q^6 - 2 * q^7 - 8 * q^10 - 36 * q^11 - 138 * q^12 - 2 * q^13 - 96 * q^15 + 316 * q^16 - 480 * q^18 + 378 * q^20 + 480 * q^21 - 34 * q^22 + 306 * q^23 - 146 * q^25 + 180 * q^27 - 232 * q^28 - 1170 * q^30 - 4 * q^31 - 1770 * q^32 - 294 * q^33 - 216 * q^36 + 136 * q^37 + 114 * q^38 + 126 * q^40 + 1992 * q^41 + 1698 * q^42 - 2 * q^43 + 1134 * q^45 - 952 * q^46 + 3462 * q^47 + 4326 * q^48 + 666 * q^50 - 2496 * q^51 - 242 * q^52 + 284 * q^55 - 7128 * q^56 - 2544 * q^57 + 534 * q^58 + 1818 * q^60 + 32 * q^61 - 4038 * q^63 - 2094 * q^65 + 2892 * q^66 + 610 * q^67 - 2694 * q^68 + 498 * q^70 - 1854 * q^72 - 8 * q^73 - 6408 * q^75 + 1368 * q^76 - 6486 * q^77 + 1434 * q^78 + 3012 * q^81 - 3784 * q^82 + 2814 * q^83 - 1658 * q^85 + 12480 * q^86 + 4830 * q^87 - 1338 * q^88 + 13914 * q^90 + 992 * q^91 + 13152 * q^92 + 8310 * q^93 + 4284 * q^95 - 7932 * q^96 + 358 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.771317	+	2.87860i	−0.272702	+	1.01774i	0.684664	+	0.728859i	$0.259949\pi$
$2$	−0.771317	+	2.87860i	−0.272702	+	1.01774i	−0.957366	+	0.288878i	$0.906718\pi$
$3$	0.414910	−	5.17956i	0.0798495	−	0.996807i
$3$	0.414910	−	5.17956i	0.0798495	−	0.996807i
$4$	−0.763180	−	0.440622i	−0.0953974	−	0.0550777i
$5$	1.89424	+	11.0187i	0.169426	+	0.985543i
$5$	1.89424	+	11.0187i	0.169426	+	0.985543i
$6$	14.5898	+	5.18944i	0.992712	+	0.353097i
$7$	31.3140	+	8.39055i	1.69080	+	0.453047i	0.970595	−	0.240719i	$-0.0773832\pi$
$7$	31.3140	+	8.39055i	1.69080	+	0.453047i	0.720200	+	0.693766i	$0.244050\pi$
$8$	−15.0012	+	15.0012i	−0.662966	+	0.662966i
$9$	−26.6557	−	4.29810i	−0.987248	−	0.159189i
$10$	−33.1795	−	3.04617i	−1.04923	−	0.0963285i
$11$	15.0191	−	8.67129i	0.411676	−	0.237681i	−0.279834	−	0.960048i	$-0.590279\pi$
$11$	15.0191	−	8.67129i	0.411676	−	0.237681i	0.691509	+	0.722367i	$0.256946\pi$
$12$	−2.59888	+	3.77012i	−0.0625193	+	0.0906949i
$13$	−8.49586	+	2.27646i	−0.181256	+	0.0485674i	−0.348305	−	0.937381i	$-0.613243\pi$
$13$	−8.49586	+	2.27646i	−0.181256	+	0.0485674i	0.167049	+	0.985949i	$0.446576\pi$
$14$	−48.3060	+	83.6685i	−0.922166	+	1.59724i
$15$	57.8580	−	5.23955i	0.995925	−	0.0901897i
$16$	−35.1367	−	60.8585i	−0.549011	−	0.950914i
$17$	23.2549	+	23.2549i	0.331773	+	0.331773i	0.853260	−	0.521486i	$-0.174622\pi$
$17$	23.2549	+	23.2549i	0.331773	+	0.331773i	−0.521486	+	0.853260i	$0.674622\pi$
$18$	32.9325	−	73.4158i	0.431237	−	0.961348i
$19$		−	145.204i		−	1.75327i	−0.481158	−	0.876634i	$-0.659784\pi$
$19$		−	145.204i		−	1.75327i	0.481158	−	0.876634i	$-0.340216\pi$
$20$	3.40944	−	9.24389i	0.0381187	−	0.103350i
$21$	56.4519	−	158.711i	0.586610	−	1.64922i
$22$	13.3766	+	49.9223i	0.129632	+	0.483794i
$23$	−3.00990	−	11.2331i	−0.0272873	−	0.101837i	0.950939	−	0.309378i	$-0.100121\pi$
$23$	−3.00990	−	11.2331i	−0.0272873	−	0.101837i	−0.978226	+	0.207540i	$0.933454\pi$
$24$	71.4755	+	83.9238i	0.607911	+	0.713786i
$25$	−117.824	+	41.7441i	−0.942590	+	0.333953i
$26$		−	26.2120i		−	0.197715i
$27$	−33.3220	+	136.281i	−0.237512	+	0.971385i
$28$	−20.2011	−	20.2011i	−0.136345	−	0.136345i
$29$	−110.651	−	191.653i	−0.708531	−	1.22721i	−0.965402	−	0.260766i	$-0.916025\pi$
$29$	−110.651	−	191.653i	−0.708531	−	1.22721i	0.256872	−	0.966446i	$-0.417308\pi$
$30$	−29.5443	+	170.591i	−0.179801	+	1.03818i
$31$	−34.8793	+	60.4127i	−0.202081	+	0.350014i	−0.949199	−	0.314677i	$-0.898104\pi$
$31$	−34.8793	+	60.4127i	−0.202081	+	0.350014i	0.747118	+	0.664691i	$0.231437\pi$
$32$	38.3524	−	10.2765i	0.211869	−	0.0567702i
$33$	−38.6819	−	81.3902i	−0.204050	−	0.429340i
$34$	−84.8784	+	49.0046i	−0.428133	+	0.247183i
$35$	−33.1369	+	360.933i	−0.160033	+	1.74311i
$36$	18.4492	+	15.0253i	0.0854132	+	0.0695616i
$37$	56.4980	−	56.4980i	0.251033	−	0.251033i	−0.570361	−	0.821394i	$-0.693197\pi$
$37$	56.4980	−	56.4980i	0.251033	−	0.251033i	0.821394	+	0.570361i	$0.193197\pi$
$38$	417.984	+	111.998i	1.78437	+	0.478119i
$39$	8.26604	+	44.9494i	0.0339391	+	0.184555i
$40$	−193.710	−	136.878i	−0.765705	−	0.541058i
$41$	−141.694	−	81.8068i	−0.539727	−	0.311612i	0.205241	−	0.978711i	$-0.434202\pi$
$41$	−141.694	−	81.8068i	−0.539727	−	0.311612i	−0.744968	+	0.667100i	$0.767535\pi$
$42$	413.323	+	284.919i	1.51850	+	1.04676i
$43$	−28.8478	+	107.661i	−0.102308	+	0.381819i	−0.998026	−	0.0628041i	$-0.979996\pi$
$43$	−28.8478	+	107.661i	−0.102308	+	0.381819i	0.895718	+	0.444623i	$0.146662\pi$
$44$	−15.2830			−0.0523637
$45$	−3.13270	−	301.853i	−0.0103777	−	0.999946i
$46$	34.6571			0.111085
$47$	49.8826	−	186.165i	0.154811	−	0.577764i	−0.844310	−	0.535855i	$-0.819989\pi$
$47$	49.8826	−	186.165i	0.154811	−	0.577764i	0.999121	−	0.0419088i	$-0.0133439\pi$
$48$	−329.799	+	156.742i	−0.991716	+	0.471328i
$49$	613.116	+	353.983i	1.78751	+	1.03202i
$50$	−29.2849	−	371.365i	−0.0828301	−	1.05038i
$51$	130.099	−	110.801i	0.357206	−	0.304222i
$52$	7.48693	+	2.00612i	0.0199663	+	0.00534997i
$53$	367.732	−	367.732i	0.953054	−	0.953054i	−0.0458925	−	0.998946i	$-0.514613\pi$
$53$	367.732	−	367.732i	0.953054	−	0.953054i	0.998946	+	0.0458925i	$0.0146132\pi$
$54$	−366.597	−	201.037i	−0.923844	−	0.506623i
$55$	123.996	+	149.066i	0.303993	+	0.365455i
$56$	−595.615	+	343.879i	−1.42129	+	0.820584i
$57$	−752.093	−	60.2466i	−1.74767	−	0.139997i
$58$	637.039	−	170.694i	1.44220	−	0.386435i
$59$	−210.017	+	363.760i	−0.463422	+	0.802671i	−0.999129	−	0.0417334i	$-0.986712\pi$
$59$	−210.017	+	363.760i	−0.463422	+	0.802671i	0.535707	+	0.844404i	$0.320045\pi$
$60$	−46.4647	−	21.4948i	−0.0999761	−	0.0462494i
$61$	226.039	+	391.511i	0.474448	+	0.821768i	0.999572	−	0.0292577i	$-0.00931436\pi$
$61$	226.039	+	391.511i	0.474448	+	0.821768i	−0.525124	+	0.851026i	$0.675981\pi$
$62$	−147.001	−	147.001i	−0.301115	−	0.301115i
$63$	−798.632	−	358.247i	−1.59711	−	0.716426i
$64$		−	443.859i		−	0.866913i
$65$	−41.1768	−	89.3013i	−0.0785747	−	0.170407i
$66$	264.126	−	48.5718i	0.492600	−	0.0905876i
$67$	60.3981	+	225.409i	0.110131	+	0.411016i	0.998877	−	0.0473854i	$-0.0150889\pi$
$67$	60.3981	+	225.409i	0.110131	+	0.411016i	−0.888745	+	0.458401i	$0.848422\pi$
$68$	−7.50105	−	27.9943i	−0.0133770	−	0.0499236i
$69$	−59.4313	+	10.9292i	−0.103691	+	0.0190685i
$70$	−1013.42	−	373.782i	−1.73039	−	0.638221i
$71$		−	434.936i		−	0.727005i	−0.931593	−	0.363502i	$-0.881581\pi$
$71$		−	434.936i		−	0.727005i	0.931593	−	0.363502i	$-0.118419\pi$
$72$	464.344	−	335.391i	0.760048	−	0.548975i
$73$	226.275	+	226.275i	0.362788	+	0.362788i	0.864838	−	0.502050i	$-0.167421\pi$
$73$	226.275	+	226.275i	0.362788	+	0.362788i	−0.502050	+	0.864838i	$0.667421\pi$
$74$	119.057	+	206.213i	0.187028	+	0.323943i
$75$	167.330	+	627.595i	0.257621	+	0.966246i
$76$	−63.9801	+	110.817i	−0.0965660	+	0.167257i
$77$	543.065	−	145.514i	0.803740	−	0.215362i
$78$	−135.767	−	10.8756i	−0.197084	−	0.0157875i
$79$	138.839	−	80.1586i	0.197729	−	0.114159i	−0.397867	−	0.917443i	$-0.630249\pi$
$79$	138.839	−	80.1586i	0.197729	−	0.114159i	0.595596	+	0.803284i	$0.296916\pi$
$80$	604.025	−	502.441i	0.844150	−	0.702183i
$81$	692.053	+	229.138i	0.949318	+	0.314318i
$82$	344.779	−	344.779i	0.464323	−	0.464323i
$83$	−146.319	−	39.2062i	−0.193502	−	0.0518486i	0.160767	−	0.986992i	$-0.448603\pi$
$83$	−146.319	−	39.2062i	−0.193502	−	0.0518486i	−0.354268	+	0.935144i	$0.615270\pi$
$84$	−113.015	+	96.2513i	−0.146796	+	0.125022i
$85$	−212.189	+	300.289i	−0.270766	+	0.383188i
$86$	−287.663	−	166.082i	−0.360692	−	0.208245i
$87$	−1038.59	+	493.605i	−1.27987	+	0.608276i
$88$	−95.2250	+	355.384i	−0.115352	+	0.430501i
$89$	−125.629			−0.149625			−0.0748124	−	0.997198i	$-0.523836\pi$
$89$	−125.629			−0.149625			−0.0748124	+	0.997198i	$0.523836\pi$
$90$	871.329	+	223.807i	1.02051	+	0.262125i
$91$	−285.140			−0.328470
$92$	−2.65245	+	9.89909i	−0.00300584	+	0.0112180i
$93$	298.439	+	205.725i	0.332760	+	0.229384i
$94$	497.417	+	287.184i	0.545794	+	0.315114i
$95$	1599.96	−	275.051i	1.72792	−	0.297049i
$96$	−37.3150	−	202.913i	−0.0396713	−	0.215726i
$97$	−983.843	−	263.620i	−1.02984	−	0.275944i	−0.295941	−	0.955206i	$-0.595633\pi$
$97$	−983.843	−	263.620i	−1.02984	−	0.275944i	−0.733895	+	0.679263i	$0.762300\pi$
$98$	−1491.88	+	1491.88i	−1.53778	+	1.53778i
$99$	−437.615	+	166.586i	−0.444262	+	0.169116i
$100$	108.314	+	20.0575i	0.108314	+	0.0200575i
$101$	−98.3353	+	56.7739i	−0.0968785	+	0.0559328i	−0.547656	−	0.836703i	$-0.684480\pi$
$101$	−98.3353	+	56.7739i	−0.0968785	+	0.0559328i	0.450778	+	0.892636i	$0.351147\pi$
$102$	218.605	+	459.965i	0.212207	+	0.446503i
$103$	−953.687	+	255.540i	−0.912326	+	0.244457i	−0.684302	−	0.729199i	$-0.739893\pi$
$103$	−953.687	+	255.540i	−0.912326	+	0.244457i	−0.228024	+	0.973656i	$0.573226\pi$
$104$	93.2985	−	161.598i	0.0879680	−	0.152365i
$105$	1855.73	+	321.389i	1.72476	+	0.298709i
$106$	774.913	+	1342.19i	0.710059	+	1.22986i
$107$	−54.7470	−	54.7470i	−0.0494634	−	0.0494634i	0.681942	−	0.731406i	$-0.261135\pi$
$107$	−54.7470	−	54.7470i	−0.0494634	−	0.0494634i	−0.731406	+	0.681942i	$0.761135\pi$
$108$	85.4793	−	89.3248i	0.0761597	−	0.0795860i
$109$		−	1089.23i		−	0.957147i	−0.878048	−	0.478573i	$-0.841154\pi$
$109$		−	1089.23i		−	0.957147i	0.878048	−	0.478573i	$-0.158846\pi$
$110$	−524.740	+	241.958i	−0.454837	+	0.209725i
$111$	−269.193	−	316.077i	−0.230187	−	0.270276i
$112$	−589.632	−	2200.54i	−0.497455	−	1.85653i
$113$	335.761	+	1253.08i	0.279520	+	1.04318i	0.952751	+	0.303751i	$0.0982391\pi$
$113$	335.761	+	1253.08i	0.279520	+	1.04318i	−0.673232	+	0.739432i	$0.735094\pi$
$114$	753.528	−	2118.50i	0.619073	−	1.74049i
$115$	118.073	−	54.4433i	0.0957420	−	0.0441467i
$116$			195.021i			0.156097i
$117$	236.248	−	24.1645i	0.186676	−	0.0190941i
$118$	−885.129	−	885.129i	−0.690532	−	0.690532i
$119$	533.082	+	923.325i	0.410652	+	0.711269i
$120$	−789.340	+	946.539i	−0.600471	+	0.720056i
$121$	−515.117	+	892.210i	−0.387015	+	0.670330i
$122$	−1301.35	+	348.696i	−0.965727	+	0.258766i
$123$	−482.513	+	699.968i	−0.353714	+	0.513122i
$124$	53.2383	−	30.7371i	0.0385560	−	0.0222603i
$125$	−683.152	−	1219.19i	−0.488824	−	0.872383i
$126$	1647.25	−	2022.62i	1.16467	−	1.43007i
$127$	−1888.92	+	1888.92i	−1.31980	+	1.31980i	−0.405869	+	0.913931i	$0.633031\pi$
$127$	−1888.92	+	1888.92i	−1.31980	+	1.31980i	−0.913931	+	0.405869i	$0.866969\pi$
$128$	1584.51	+	424.568i	1.09416	+	0.293179i
$129$	545.670	+	194.089i	0.372430	+	0.132469i
$130$	288.823	−	49.6518i	0.194857	−	0.0334981i
$131$	−581.255	−	335.588i	−0.387668	−	0.223820i	0.293481	−	0.955965i	$-0.405186\pi$
$131$	−581.255	−	335.588i	−0.387668	−	0.223820i	−0.681149	+	0.732145i	$0.738519\pi$
$132$	−6.34109	+	79.1594i	−0.00418122	+	0.0521965i
$133$	1218.34	−	4546.91i	0.794313	−	2.96442i
$134$	−695.447			−0.448339
$135$	−1564.77	−	109.016i	−0.997582	−	0.0695006i
$136$	−697.703			−0.439908
$137$	457.464	−	1707.28i	0.285283	−	1.06469i	−0.663349	−	0.748310i	$-0.730866\pi$
$137$	457.464	−	1707.28i	0.285283	−	1.06469i	0.948632	−	0.316381i	$-0.102468\pi$
$138$	14.3796	−	179.509i	0.00887008	−	0.110730i
$139$	450.428	+	260.055i	0.274855	+	0.158687i	0.631092	−	0.775708i	$-0.282607\pi$
$139$	450.428	+	260.055i	0.274855	+	0.158687i	−0.356237	+	0.934396i	$0.615940\pi$
$140$	184.324	−	260.856i	0.111273	−	0.157474i
$141$	−943.554	−	335.612i	−0.563557	−	0.200451i
$142$	1252.00	+	335.473i	0.739900	+	0.198256i
$143$	−107.860	+	107.860i	−0.0630752	+	0.0630752i
$144$	675.017	+	1773.25i	0.390635	+	1.02618i
$145$	1902.17	−	1582.27i	1.08943	−	0.906209i
$146$	−825.886	+	476.825i	−0.468156	+	0.270290i
$147$	2087.86	−	3028.80i	1.17146	−	1.69940i
$148$	−68.0124	+	18.2239i	−0.0377742	+	0.0101216i
$149$	−1068.70	+	1851.04i	−0.587590	+	1.01774i	0.406957	+	0.913447i	$0.366590\pi$
$149$	−1068.70	+	1851.04i	−0.587590	+	1.01774i	−0.994547	+	0.104289i	$0.966743\pi$
$150$	−1935.66	−	2.40020i	−1.05364	−	0.00130650i
$151$	1014.78	+	1757.66i	0.546900	+	0.947258i	0.998485	+	0.0550300i	$0.0175254\pi$
$151$	1014.78	+	1757.66i	0.546900	+	0.947258i	−0.451585	+	0.892228i	$0.649141\pi$
$152$	2178.23	+	2178.23i	1.16236	+	1.16236i
$153$	−519.924	−	719.828i	−0.274728	−	0.380357i
$154$			1675.50i			0.876726i
$155$	−731.739	−	269.888i	−0.379192	−	0.139858i
$156$	13.4972	−	37.9466i	0.00692719	−	0.0194754i
$157$	−63.1332	−	235.616i	−0.0320929	−	0.119772i	0.948021	−	0.318207i	$-0.103081\pi$
$157$	−63.1332	−	235.616i	−0.0320929	−	0.119772i	−0.980114	+	0.198435i	$0.936414\pi$
$158$	123.655	+	461.489i	0.0622627	+	0.232367i
$159$	−1752.11	−	2057.27i	−0.873910	−	1.02611i
$160$	185.882	+	403.128i	0.0918456	+	0.199188i
$161$		−	377.007i		−	0.184549i
$162$	−1193.39	+	1815.40i	−0.578774	+	0.880441i
$163$	1746.22	+	1746.22i	0.839108	+	0.839108i	0.988742	−	0.149633i	$-0.0478093\pi$
$163$	1746.22	+	1746.22i	0.839108	+	0.839108i	−0.149633	+	0.988742i	$0.547809\pi$
$164$	72.0918	+	124.867i	0.0343257	+	0.0594539i
$165$	823.542	−	580.397i	0.388562	−	0.273841i
$166$	225.717	−	390.954i	0.105537	−	0.182795i
$167$	40.3002	−	10.7984i	0.0186738	−	0.00500363i	−0.249470	−	0.968383i	$-0.580256\pi$
$167$	40.3002	−	10.7984i	0.0186738	−	0.00500363i	0.268144	+	0.963379i	$0.413590\pi$
$168$	1534.01	+	3227.71i	0.704475	+	1.48228i
$169$	−1835.66	+	1059.82i	−0.835530	+	0.482394i
$170$	−700.747	−	842.424i	−0.316146	−	0.380064i
$171$	−624.102	+	3870.51i	−0.279101	+	1.73091i
$172$	69.4540	−	69.4540i	0.0307896	−	0.0307896i
$173$	−2271.35	−	608.606i	−0.998193	−	0.267465i	−0.277505	−	0.960724i	$-0.589507\pi$
$173$	−2271.35	−	608.606i	−0.998193	−	0.267465i	−0.720688	+	0.693259i	$0.756174\pi$
$174$	−619.807	−	3370.41i	−0.270043	−	1.46845i
$175$	−4039.78	+	318.567i	−1.74502	+	0.137608i
$176$	−1055.44	−	609.361i	−0.452029	−	0.260979i
$177$	1796.98	+	1238.72i	0.763104	+	0.526035i
$178$	96.8996	−	361.634i	0.0408030	−	0.152279i
$179$	3861.04			1.61222			0.806111	−	0.591764i	$-0.201568\pi$
$179$	3861.04			1.61222			0.806111	+	0.591764i	$0.201568\pi$
$180$	−130.612	+	231.748i	−0.0540848	+	0.0959639i
$181$	1336.19			0.548721			0.274360	−	0.961627i	$-0.411534\pi$
$181$	1336.19			0.548721			0.274360	+	0.961627i	$0.411534\pi$
$182$	219.933	−	820.803i	0.0895744	−	0.334296i
$183$	2121.64	−	1008.34i	0.857028	−	0.407315i
$184$	213.662	+	123.358i	0.0856053	+	0.0494242i
$185$	729.556	+	515.515i	0.289935	+	0.204872i
$186$	−822.391	+	700.407i	−0.324197	+	0.276109i
$187$	550.918	+	147.618i	0.215439	+	0.0577267i
$188$	−120.098	+	120.098i	−0.0465905	+	0.0465905i
$189$	−2186.92	+	3987.92i	−0.841667	+	1.53481i
$190$	−442.317	+	4817.79i	−0.168890	+	1.83958i
$191$	1813.42	−	1046.98i	0.686986	−	0.396632i	−0.115496	−	0.993308i	$-0.536846\pi$
$191$	1813.42	−	1046.98i	0.686986	−	0.396632i	0.802482	+	0.596676i	$0.203512\pi$
$192$	−2299.00	−	184.162i	−0.864145	−	0.0692225i
$193$	2372.73	−	635.771i	0.884937	−	0.237118i	0.212401	−	0.977183i	$-0.431872\pi$
$193$	2372.73	−	635.771i	0.884937	−	0.237118i	0.672536	+	0.740064i	$0.265205\pi$
$194$	1517.71	−	2628.75i	0.561676	−	0.972852i
$195$	−479.626	+	176.226i	−0.176137	+	0.0647169i
$196$	−311.945	−	540.305i	−0.113683	−	0.196904i
$197$	1820.36	+	1820.36i	0.658351	+	0.658351i	0.954990	−	0.296639i	$-0.0958657\pi$
$197$	1820.36	+	1820.36i	0.658351	+	0.658351i	−0.296639	+	0.954990i	$0.595866\pi$
$198$	−141.992	−	1388.21i	−0.0509645	−	0.498261i
$199$		−	185.331i		−	0.0660189i	−0.999455	−	0.0330095i	$-0.989491\pi$
$199$		−	185.331i		−	0.0660189i	0.999455	−	0.0330095i	$-0.0105092\pi$
$200$	1141.29	−	2393.71i	0.403505	−	0.846304i
$201$	1192.58	−	219.311i	0.418498	−	0.0769603i
$202$	−87.5814	−	326.858i	−0.0305060	−	0.113850i
$203$	−1856.85	−	6929.85i	−0.641996	−	2.39596i
$204$	−148.110	+	27.2370i	−0.0508324	+	0.00934791i
$205$	633.004	−	1716.24i	0.215663	−	0.584719i
$206$		−	2942.38i		−	0.995172i
$207$	31.9500	+	312.363i	0.0107279	+	0.104883i
$208$	437.058	+	437.058i	0.145695	+	0.145695i
$209$	−1259.11	−	2180.84i	−0.416719	−	0.721778i
$210$	−2356.50	+	5093.99i	−0.774353	+	1.67390i
$211$	2573.74	−	4457.84i	0.839732	−	1.45446i	−0.0503871	−	0.998730i	$-0.516046\pi$
$211$	2573.74	−	4457.84i	0.839732	−	1.45446i	0.890119	−	0.455728i	$-0.150621\pi$
$212$	−442.676	+	118.615i	−0.143411	+	0.0384268i
$213$	−2252.77	−	180.459i	−0.724684	−	0.0580510i
$214$	199.822	−	115.367i	0.0638296	−	0.0368520i
$215$	−1240.93	−	113.929i	−0.393633	−	0.0361390i
$216$	−1544.52	−	2544.26i	−0.486532	−	0.801457i
$217$	−1599.10	+	1599.10i	−0.500250	+	0.500250i
$218$	3135.44	+	840.139i	0.974124	+	0.261016i
$219$	1265.89	−	1078.12i	0.390598	−	0.332661i
$220$	−28.9497	−	168.399i	−0.00887177	−	0.0516067i
$221$	−250.509	−	144.632i	−0.0762492	−	0.0440225i
$222$	1117.49	−	531.104i	0.337843	−	0.160565i
$223$	−1164.32	+	4345.30i	−0.349635	+	1.30485i	0.537469	+	0.843284i	$0.319381\pi$
$223$	−1164.32	+	4345.30i	−0.349635	+	1.30485i	−0.887103	+	0.461571i	$0.847286\pi$
$224$	1287.19			0.383947
$225$	3320.09	−	606.299i	0.983732	−	0.179644i
$226$	−3866.08			−1.13791
$227$	−1205.41	+	4498.66i	−0.352450	+	1.31536i	0.531214	+	0.847238i	$0.321736\pi$
$227$	−1205.41	+	4498.66i	−0.352450	+	1.31536i	−0.883663	+	0.468123i	$0.844931\pi$
$228$	547.436	+	377.368i	0.159012	+	0.109613i
$229$	−3532.61	−	2039.55i	−1.01939	−	0.588547i	−0.105466	−	0.994423i	$-0.533633\pi$
$229$	−3532.61	−	2039.55i	−1.01939	−	0.588547i	−0.913928	+	0.405875i	$0.866967\pi$
$230$	65.6488	+	381.877i	0.0188207	+	0.109479i
$231$	−528.375	−	2873.21i	−0.150496	−	0.818370i
$232$	4534.93	+	1215.13i	1.28333	+	0.343867i
$233$	−2530.52	+	2530.52i	−0.711500	+	0.711500i	−0.966849	−	0.255349i	$-0.917810\pi$
$233$	−2530.52	+	2530.52i	−0.711500	+	0.711500i	0.255349	+	0.966849i	$0.417810\pi$
$234$	−112.662	+	698.700i	−0.0314741	+	0.195194i
$235$	2145.78	+	197.002i	0.595640	+	0.0546851i
$236$	320.562	−	185.076i	0.0884186	−	0.0510485i
$237$	−357.581	−	752.383i	−0.0980058	−	0.206213i
$238$	−3069.05	+	822.351i	−0.835871	+	0.223971i
$239$	−3482.36	+	6031.62i	−0.942490	+	1.63244i	−0.181790	+	0.983337i	$0.558189\pi$
$239$	−3482.36	+	6031.62i	−0.942490	+	1.63244i	−0.760700	+	0.649103i	$0.775144\pi$
$240$	−2351.81	−	3337.05i	−0.632536	−	0.897524i
$241$	−2601.64	−	4506.16i	−0.695378	−	1.20443i	−0.970053	−	0.242893i	$-0.921904\pi$
$241$	−2601.64	−	4506.16i	−0.695378	−	1.20443i	0.274675	−	0.961537i	$-0.411430\pi$
$242$	−2170.99	−	2170.99i	−0.576680	−	0.576680i
$243$	1473.97	−	3489.46i	0.389117	−	0.921188i
$244$		−	398.391i		−	0.104526i
$245$	−2739.05	+	7426.28i	−0.714250	+	1.93652i
$246$	−1642.75	−	1928.86i	−0.425765	−	0.499917i
$247$	330.551	+	1233.63i	0.0851517	+	0.317790i
$248$	−383.032	−	1429.49i	−0.0980747	−	0.366020i
$249$	−263.780	+	741.603i	−0.0671341	+	0.188744i
$250$	4036.49	−	1026.13i	1.02116	−	0.259594i
$251$			653.428i			0.164319i	0.996619	+	0.0821593i	$0.0261816\pi$
$251$			653.428i			0.164319i	−0.996619	+	0.0821593i	$0.973818\pi$
$252$	451.648	+	625.301i	0.112901	+	0.156311i
$253$	−142.611	−	142.611i	−0.0354383	−	0.0354383i
$254$	−3980.48	−	6894.40i	−0.983298	−	1.70312i
$255$	1467.33	+	1223.64i	0.360344	+	0.300498i
$256$	−668.884	+	1158.54i	−0.163302	+	0.282847i
$257$	30.6904	−	8.22348i	0.00744909	−	0.00199598i	−0.255093	−	0.966917i	$-0.582106\pi$
$257$	30.6904	−	8.22348i	0.00744909	−	0.00199598i	0.262542	+	0.964921i	$0.415439\pi$
$258$	−979.587	+	1421.06i	−0.236382	+	0.342912i
$259$	2243.23	−	1295.13i	0.538175	−	0.310716i
$260$	−7.92278	+	86.2963i	−0.00188981	+	0.0205841i
$261$	2125.74	+	5584.24i	0.504137	+	1.32435i
$262$	1414.35	−	1414.35i	0.333508	−	0.333508i
$263$	6775.73	+	1815.55i	1.58863	+	0.425672i	0.941583	−	0.336780i	$-0.109338\pi$
$263$	6775.73	+	1815.55i	1.58863	+	0.425672i	0.647045	+	0.762452i	$0.276005\pi$
$264$	1801.23	+	640.676i	0.419916	+	0.149359i
$265$	4748.50	+	3355.36i	1.10075	+	0.777804i
$266$	12149.0	+	7014.23i	2.80039	+	1.61680i
$267$	−52.1246	+	650.701i	−0.0119475	+	0.149147i
$268$	53.2255	−	198.640i	0.0121316	−	0.0452757i
$269$	−1104.05			−0.250241			−0.125121	−	0.992142i	$-0.539932\pi$
$269$	−1104.05			−0.250241			−0.125121	+	0.992142i	$0.539932\pi$
$270$	1520.74	−	4420.24i	0.342776	−	0.996323i
$271$	3956.84			0.886940			0.443470	−	0.896289i	$-0.353747\pi$
$271$	3956.84			0.886940			0.443470	+	0.896289i	$0.353747\pi$
$272$	598.159	−	2232.36i	0.133341	−	0.497635i
$273$	−118.307	+	1476.90i	−0.0262282	+	0.327421i
$274$	4561.71	+	2633.71i	1.00578	+	0.580686i
$275$	−1407.63	+	1648.64i	−0.308667	+	0.361516i
$276$	50.1724	+	17.8458i	0.0109421	+	0.00389199i
$277$	−1089.65	−	291.971i	−0.236357	−	0.0633315i	0.138696	−	0.990335i	$-0.455709\pi$
$277$	−1089.65	−	291.971i	−0.236357	−	0.0633315i	−0.375053	+	0.927003i	$0.622375\pi$
$278$	−1096.02	+	1096.02i	−0.236455	+	0.236455i
$279$	1189.39	−	1460.43i	0.255222	−	0.313382i
$280$	−4917.34	−	5911.52i	−1.04953	−	1.26172i
$281$	−4252.77	+	2455.34i	−0.902844	+	0.521257i	−0.878122	−	0.478437i	$-0.841203\pi$
$281$	−4252.77	+	2455.34i	−0.902844	+	0.521257i	−0.0247222	+	0.999694i	$0.507870\pi$
$282$	1693.87	−	2457.25i	0.357690	−	0.518890i
$283$	−6556.15	+	1756.71i	−1.37711	+	0.368996i	−0.870071	−	0.492926i	$-0.835927\pi$
$283$	−6556.15	+	1756.71i	−1.37711	+	0.368996i	−0.507040	+	0.861922i	$0.669260\pi$
$284$	−191.642	+	331.934i	−0.0400418	+	0.0693544i
$285$	−760.803	−	8401.21i	−0.158127	−	1.74612i
$286$	−227.292	−	393.681i	−0.0469932	−	0.0813947i
$287$	−3750.58	−	3750.58i	−0.771394	−	0.771394i
$288$	−1066.48	+	109.085i	−0.218205	+	0.0223190i
$289$		−	3831.42i		−	0.779853i
$290$	3087.53	+	6696.01i	0.625194	+	1.35587i
$291$	−1773.64	+	4986.49i	−0.357294	+	1.00451i
$292$	−72.9869	−	272.391i	−0.0146275	−	0.0545906i
$293$	−144.468	−	539.160i	−0.0288051	−	0.107502i	0.950027	−	0.312169i	$-0.101056\pi$
$293$	−144.468	−	539.160i	−0.0288051	−	0.107502i	−0.978832	+	0.204667i	$0.934389\pi$
$294$	7108.29	+	8346.29i	1.41008	+	1.65566i
$295$	−4405.99	−	1625.07i	−0.869582	−	0.320729i
$296$			1695.08i			0.332852i
$297$	681.269	+	2335.77i	0.133102	+	0.456348i
$298$	−4504.08	−	4504.08i	−0.875551	−	0.875551i
$299$	51.1434	+	88.5829i	0.00989196	+	0.0171334i
$300$	148.829	−	552.697i	0.0286422	−	0.106367i
$301$	−1806.68	+	3129.26i	−0.345964	+	0.599227i
$302$	−5842.30	+	1565.44i	−1.11320	+	0.298281i
$303$	253.264	+	532.889i	0.0480185	+	0.101035i
$304$	−8836.90	+	5101.99i	−1.66721	+	0.962563i
$305$	−3885.77	+	3232.27i	−0.729504	+	0.606818i
$306$	2473.12	−	941.435i	0.462022	−	0.175877i
$307$	1975.51	−	1975.51i	0.367257	−	0.367257i	−0.499219	−	0.866476i	$-0.666380\pi$
$307$	1975.51	−	1975.51i	0.367257	−	0.367257i	0.866476	+	0.499219i	$0.166380\pi$
$308$	−478.573	−	128.233i	−0.0885364	−	0.0237233i
$309$	927.889	+	5045.71i	0.170828	+	0.928933i
$310$	1341.30	−	1898.21i	0.245745	−	0.347778i
$311$	2070.74	+	1195.54i	0.377558	+	0.217983i	0.676755	−	0.736208i	$-0.263385\pi$
$311$	2070.74	+	1195.54i	0.377558	+	0.217983i	−0.299197	+	0.954191i	$0.596719\pi$
$312$	−798.295	−	550.294i	−0.144854	−	0.0998534i
$313$	−1343.71	+	5014.78i	−0.242654	+	0.905597i	0.731894	+	0.681418i	$0.238637\pi$
$313$	−1343.71	+	5014.78i	−0.242654	+	0.905597i	−0.974548	+	0.224179i	$0.928030\pi$
$314$	726.940			0.130648
$315$	2434.62	−	9478.50i	0.435476	−	1.69541i
$316$	−141.279			−0.0251504
$317$	2143.43	−	7999.38i	0.379769	−	1.41732i	−0.466481	−	0.884531i	$-0.654478\pi$
$317$	2143.43	−	7999.38i	0.379769	−	1.41732i	0.846250	−	0.532786i	$-0.178855\pi$
$318$	7273.47	−	3456.82i	1.28263	−	0.609588i
$319$	−3323.76	−	1918.97i	−0.583370	−	0.336809i
$320$	4890.75	−	840.775i	0.854380	−	0.146877i
$321$	−306.280	+	260.850i	−0.0532551	+	0.0453559i
$322$	1085.25	+	290.792i	0.187822	+	0.0503268i
$323$	3376.71	−	3376.71i	0.581687	−	0.581687i
$324$	−427.197	−	479.807i	−0.0732506	−	0.0822714i
$325$	905.986	−	622.873i	0.154631	−	0.106310i
$326$	−6373.56	+	3679.78i	−1.08282	+	0.625165i
$327$	−5641.72	−	451.931i	−0.954091	−	0.0764277i
$328$	3352.77	−	898.373i	0.564409	−	0.151233i
$329$	3124.05	−	5411.01i	0.523508	−	0.906743i
$330$	1035.52	+	2818.31i	0.172737	+	0.470131i
$331$	−3824.32	−	6623.91i	−0.635056	−	1.09995i	−0.986503	−	0.163741i	$-0.947644\pi$
$331$	−3824.32	−	6623.91i	−0.635056	−	1.09995i	0.351447	−	0.936208i	$-0.385690\pi$
$332$	94.3929	+	94.3929i	0.0156039	+	0.0156039i
$333$	−1748.83	+	1263.16i	−0.287794	+	0.207870i
$334$			124.337i			0.0203695i
$335$	−2369.31	+	1092.49i	−0.386415	+	0.178176i
$336$	−11642.5	+	2141.01i	−1.89032	+	0.347624i
$337$	393.402	+	1468.20i	0.0635904	+	0.237323i	0.990405	−	0.138197i	$-0.0441308\pi$
$337$	393.402	+	1468.20i	0.0635904	+	0.237323i	−0.926814	+	0.375520i	$0.877464\pi$
$338$	−1634.91	−	6101.58i	−0.263099	−	0.981900i
$339$	6629.70	−	1219.18i	1.06217	−	0.195330i
$340$	294.252	−	135.680i	0.0469355	−	0.0216419i
$341$			1209.79i			0.192123i
$342$	−10660.3	−	4781.93i	−1.68550	−	0.756074i
$343$	8366.26	+	8366.26i	1.31701	+	1.31701i
$344$	−1182.30	−	2047.80i	−0.185306	−	0.320960i
$345$	−233.003	−	634.154i	−0.0363608	−	0.0989614i
$346$	3503.86	−	6068.86i	0.544418	−	0.942960i
$347$	3016.05	−	808.147i	0.466599	−	0.125025i	−0.0178568	−	0.999841i	$-0.505684\pi$
$347$	3016.05	−	808.147i	0.466599	−	0.125025i	0.484456	+	0.874816i	$0.339018\pi$
$348$	1010.12	+	80.9162i	0.155599	+	0.0124643i
$349$	10814.9	−	6243.98i	1.65876	−	0.957687i	0.685476	−	0.728096i	$-0.259594\pi$
$349$	10814.9	−	6243.98i	1.65876	−	0.957687i	0.973287	−	0.229591i	$-0.0737390\pi$
$350$	2198.93	−	11874.6i	0.335822	−	1.81350i
$351$	−27.1402	−	1233.69i	−0.00412716	−	0.187605i
$352$	486.909	−	486.909i	0.0737282	−	0.0737282i
$353$	−4859.23	−	1302.03i	−0.732665	−	0.196317i	−0.126849	−	0.991922i	$-0.540486\pi$
$353$	−4859.23	−	1302.03i	−0.732665	−	0.196317i	−0.605816	+	0.795605i	$0.707153\pi$
$354$	−4951.83	+	4217.33i	−0.743466	+	0.633188i
$355$	4792.43	−	823.871i	0.716495	−	0.123173i
$356$	95.8772	+	55.3548i	0.0142738	+	0.00824100i
$357$	5003.60	−	2378.03i	0.741788	−	0.352546i
$358$	−2978.09	+	11114.4i	−0.439656	+	1.64082i
$359$	6972.21			1.02501			0.512506	−	0.858684i	$-0.328717\pi$
$359$	6972.21			1.02501			0.512506	+	0.858684i	$0.328717\pi$
$360$	4575.15	+	4481.16i	0.669810	+	0.656050i
$361$	−14225.2			−2.07395
$362$	−1030.63	+	3846.36i	−0.149637	+	0.558454i
$363$	4407.53	+	3038.27i	0.637287	+	0.439305i
$364$	217.613	+	125.639i	0.0313352	+	0.0180914i
$365$	−2064.64	+	2921.88i	−0.296078	+	0.419009i
$366$	1266.15	+	6885.10i	0.180827	+	0.983305i
$367$	−9074.03	−	2431.38i	−1.29063	−	0.345823i	−0.452729	−	0.891648i	$-0.649550\pi$
$367$	−9074.03	−	2431.38i	−1.29063	−	0.345823i	−0.837899	+	0.545825i	$0.816216\pi$
$368$	−577.872	+	577.872i	−0.0818577	+	0.0818577i
$369$	3425.33	+	2789.63i	0.483240	+	0.393557i
$370$	−2046.68	+	1702.47i	−0.287572	+	0.239209i
$371$	14600.6	−	8429.67i	2.04320	−	1.17964i
$372$	−137.116	−	288.504i	−0.0191105	−	0.0402103i
$373$	−917.897	+	245.950i	−0.127418	+	0.0341415i	−0.321964	−	0.946752i	$-0.604343\pi$
$373$	−917.897	+	245.950i	−0.127418	+	0.0341415i	0.194547	+	0.980893i	$0.437676\pi$
$374$	−849.865	+	1472.01i	−0.117501	+	0.203518i
$375$	−6598.32	+	3032.57i	−0.908629	+	0.417604i
$376$	2044.39	+	3540.99i	0.280403	+	0.485672i
$377$	1376.37	+	1376.37i	0.188028	+	0.188028i
$378$	−9792.81	−	9371.22i	−1.33251	−	1.27514i
$379$		−	1292.12i		−	0.175123i	−0.996159	−	0.0875613i	$-0.972093\pi$
$379$		−	1292.12i		−	0.175123i	0.996159	−	0.0875613i	$-0.0279074\pi$
$380$	−1342.25	−	495.064i	−0.181200	−	0.0668323i
$381$	9000.05	+	10567.5i	1.21020	+	1.42097i
$382$	1615.10	+	6027.65i	0.216324	+	0.807334i
$383$	−1537.66	−	5738.62i	−0.205145	−	0.765613i	−0.989405	−	0.145180i	$-0.953624\pi$
$383$	−1537.66	−	5738.62i	−0.205145	−	0.765613i	0.784260	−	0.620432i	$-0.213043\pi$
$384$	2856.51	−	8030.91i	0.379611	−	1.06725i
$385$	2632.07	+	5708.23i	0.348422	+	0.755633i
$386$			7320.51i			0.965296i
$387$	1231.70	−	2745.80i	0.161785	−	0.360664i
$388$	634.692	+	634.692i	0.0830453	+	0.0830453i
$389$	3075.20	+	5326.40i	0.400820	+	0.694240i	0.993825	−	0.110959i	$-0.0353921\pi$
$389$	3075.20	+	5326.40i	0.400820	+	0.694240i	−0.593005	+	0.805198i	$0.702059\pi$
$390$	−137.339	−	1516.58i	−0.0178319	−	0.196910i
$391$	191.230	−	331.219i	0.0247338	−	0.0428401i
$392$	−14507.7	+	3887.31i	−1.86925	+	0.500865i
$393$	−1979.36	+	2871.41i	−0.254060	+	0.368558i
$394$	−6644.15	+	3836.00i	−0.849562	+	0.490495i
$395$	1146.24	+	1377.98i	0.146009	+	0.175529i
$396$	407.380	+	65.6881i	0.0516960	+	0.00833573i
$397$	9111.20	−	9111.20i	1.15183	−	1.15183i	0.165649	−	0.986185i	$-0.447028\pi$
$397$	9111.20	−	9111.20i	1.15183	−	1.15183i	0.986185	−	0.165649i	$-0.0529719\pi$
$398$	533.493	+	142.949i	0.0671899	+	0.0180035i
$399$	−23045.5	−	8197.04i	−2.89153	−	1.02848i
$400$	6680.42	+	5703.83i	0.835052	+	0.712979i
$401$	−3577.13	−	2065.26i	−0.445470	−	0.257192i	0.260445	−	0.965489i	$-0.416131\pi$
$401$	−3577.13	−	2065.26i	−0.445470	−	0.257192i	−0.705915	+	0.708297i	$0.749464\pi$
$402$	−288.548	+	3602.11i	−0.0357997	+	0.446908i
$403$	158.803	−	592.659i	0.0196291	−	0.0732567i
$404$	100.063			0.0123226
$405$	−1213.89	+	8059.57i	−0.148935	+	0.988847i
$406$	21380.5			2.61353
$407$	358.640	−	1338.46i	0.0436784	−	0.163010i
$408$	−289.484	+	3613.79i	−0.0351264	+	0.438504i
$409$	4525.80	+	2612.97i	0.547156	+	0.315900i	0.747974	−	0.663728i	$-0.231027\pi$
$409$	4525.80	+	2612.97i	0.547156	+	0.315900i	−0.200818	+	0.979628i	$0.564360\pi$
$410$	4452.12	+	3145.93i	0.536279	+	0.378942i
$411$	−8653.14	−	3077.83i	−1.03851	−	0.369387i
$412$	840.431	+	225.193i	0.100498	+	0.0269283i
$413$	−9628.62	+	9628.62i	−1.14720	+	1.14720i
$414$	−923.810	−	148.960i	−0.109669	−	0.0176835i
$415$	154.837	−	1686.52i	0.0183149	−	0.199489i
$416$	−302.443	+	174.615i	−0.0356454	+	0.0205799i
$417$	1533.86	−	2225.12i	0.180128	−	0.261306i
$418$	7248.92	−	1942.34i	0.848220	−	0.227280i
$419$	4683.53	−	8112.11i	0.546075	−	0.945829i	−0.452464	−	0.891783i	$-0.649455\pi$
$419$	4683.53	−	8112.11i	0.546075	−	0.945829i	0.998538	−	0.0540462i	$-0.0172118\pi$
$420$	−1274.64	−	1062.95i	−0.148086	−	0.123492i
$421$	1386.04	+	2400.70i	0.160455	+	0.277916i	0.935032	−	0.354563i	$-0.115370\pi$
$421$	1386.04	+	2400.70i	0.160455	+	0.277916i	−0.774577	+	0.632480i	$0.782037\pi$
$422$	10847.2	+	10847.2i	1.25126	+	1.25126i
$423$	−2129.81	+	4747.95i	−0.244811	+	0.545752i
$424$			11032.8i			1.26368i
$425$	−3710.73	−	1769.22i	−0.423522	−	0.201929i
$426$	2257.07	−	6345.64i	0.256703	−	0.721707i
$427$	3793.18	+	14156.4i	0.429895	+	1.60439i
$428$	17.6590	+	65.9045i	0.00199435	+	0.00744302i
$429$	513.918	+	603.422i	0.0578372	+	0.0679103i
$430$	1285.11	−	3484.27i	0.144124	−	0.390759i
$431$		−	14381.5i		−	1.60727i	−0.595125	−	0.803633i	$-0.702898\pi$
$431$		−	14381.5i		−	1.60727i	0.595125	−	0.803633i	$-0.297102\pi$
$432$	9464.71	−	2760.55i	1.05410	−	0.307447i
$433$	−7313.75	−	7313.75i	−0.811724	−	0.811724i	0.173168	−	0.984892i	$-0.444600\pi$
$433$	−7313.75	−	7313.75i	−0.811724	−	0.811724i	−0.984892	+	0.173168i	$0.944600\pi$
$434$	−3369.76	−	5836.59i	−0.372704	−	0.645542i
$435$	−7406.23	−	10508.9i	−0.816325	−	1.15831i
$436$	−479.937	+	831.275i	−0.0527175	+	0.0913093i
$437$	−1631.09	+	437.049i	−0.178548	+	0.0478419i
$438$	2127.08	+	4475.56i	0.232045	+	0.488244i
$439$	−1284.46	+	741.581i	−0.139644	+	0.0806235i	−0.568194	−	0.822894i	$-0.692358\pi$
$439$	−1284.46	+	741.581i	−0.139644	+	0.0806235i	0.428550	+	0.903518i	$0.359024\pi$
$440$	−4096.26	−	376.073i	−0.443821	−	0.0407468i
$441$	−14821.6	−	12070.9i	−1.60043	−	1.30341i
$442$	609.558	−	609.558i	0.0655967	−	0.0655967i
$443$	10486.7	+	2809.90i	1.12469	+	0.301359i	0.772779	−	0.634675i	$-0.218866\pi$
$443$	10486.7	+	2809.90i	1.12469	+	0.301359i	0.351909	+	0.936034i	$0.385533\pi$
$444$	66.1726	+	359.836i	0.00707300	+	0.0384618i
$445$	−237.971	−	1384.27i	−0.0253503	−	0.147462i
$446$	−11610.3	−	6703.21i	−1.23265	−	0.711673i
$447$	9144.14	+	6303.39i	0.967568	+	0.666980i
$448$	3724.22	−	13899.0i	0.392752	−	1.46577i
$449$	−3675.43			−0.386312			−0.193156	−	0.981168i	$-0.561872\pi$
$449$	−3675.43			−0.386312			−0.193156	+	0.981168i	$0.561872\pi$
$450$	−815.555	+	10024.9i	−0.0854348	+	1.05017i
$451$	−2837.48			−0.296257
$452$	295.887	−	1104.27i	0.0307907	−	0.114912i
$453$	9524.93	−	4526.86i	0.987903	−	0.469515i
$454$	−12020.1	−	6939.80i	−1.24258	−	0.717403i
$455$	−540.123	−	3141.87i	−0.0556513	−	0.323721i
$456$	12186.1	−	10378.5i	1.25146	−	1.06583i
$457$	−8560.02	−	2293.65i	−0.876195	−	0.234776i	−0.207430	−	0.978250i	$-0.566510\pi$
$457$	−8560.02	−	2293.65i	−0.876195	−	0.234776i	−0.668765	+	0.743474i	$0.733177\pi$
$458$	8595.81	−	8595.81i	0.876977	−	0.876977i
$459$	−3944.11	+	2394.31i	−0.401079	+	0.243479i
$460$	−114.100	−	10.4754i	−0.0115650	−	0.00106178i
$461$	615.619	−	355.428i	0.0621958	−	0.0359087i	−0.468580	−	0.883421i	$-0.655234\pi$
$461$	615.619	−	355.428i	0.0621958	−	0.0359087i	0.530775	+	0.847513i	$0.321901\pi$
$462$	8678.36	+	695.182i	0.873926	+	0.0700061i
$463$	4165.52	−	1116.15i	0.418117	−	0.112034i	−0.0436261	−	0.999048i	$-0.513891\pi$
$463$	4165.52	−	1116.15i	0.418117	−	0.112034i	0.461743	+	0.887014i	$0.347224\pi$
$464$	−7775.82	+	13468.1i	−0.777982	+	1.34750i
$465$	−1701.51	+	3678.11i	−0.169689	+	0.366813i
$466$	−5332.50	−	9236.16i	−0.530093	−	0.918148i
$467$	5693.93	+	5693.93i	0.564205	+	0.564205i	0.930499	−	0.366294i	$-0.119374\pi$
$467$	5693.93	+	5693.93i	0.564205	+	0.564205i	−0.366294	+	0.930499i	$0.619374\pi$
$468$	−190.947	−	85.6540i	−0.0188601	−	0.00846017i
$469$			7565.22i			0.744839i
$470$	−2222.17	+	6024.89i	−0.218087	+	0.591292i
$471$	−1246.58	+	229.243i	−0.121952	+	0.0224267i
$472$	−2306.33	−	8607.35i	−0.224910	−	0.839376i
$473$	500.295	+	1867.13i	0.0486334	+	0.181502i
$474$	2441.61	−	449.005i	0.236597	−	0.0435094i
$475$	6061.41	+	17108.5i	0.585509	+	1.65261i
$476$		−	939.550i		−	0.0904710i
$477$	−11382.7	+	8221.60i	−1.09262	+	0.789185i
$478$	−14676.6	−	14676.6i	−1.40438	−	1.40438i
$479$	578.158	+	1001.40i	0.0551497	+	0.0955222i	0.892282	−	0.451478i	$-0.149103\pi$
$479$	578.158	+	1001.40i	0.0551497	+	0.0955222i	−0.837133	+	0.547000i	$0.815770\pi$
$480$	2165.15	−	795.527i	0.205886	−	0.0756472i
$481$	−351.384	+	608.615i	−0.0333092	+	0.0576933i
$482$	14978.1	−	4013.37i	1.41542	−	0.379262i
$483$	−1952.73	−	156.424i	−0.183959	−	0.0147361i
$484$	786.254	−	453.944i	0.0738406	−	0.0426319i
$485$	1041.12	−	11340.0i	0.0974736	−	1.06170i
$486$	8907.83	+	6934.45i	0.831415	+	0.647229i
$487$	−11304.4	+	11304.4i	−1.05185	+	1.05185i	−0.0532673	+	0.998580i	$0.516964\pi$
$487$	−11304.4	+	11304.4i	−1.05185	+	1.05185i	−0.998580	+	0.0532673i	$0.983036\pi$
$488$	−9263.99	−	2482.28i	−0.859347	−	0.230261i
$489$	9769.19	−	8320.14i	0.903431	−	0.769427i
$490$	−19264.6	−	13612.6i	−1.77609	−	1.25501i
$491$	11832.0	+	6831.20i	1.08752	+	0.627878i	0.932914	−	0.360099i	$-0.117257\pi$
$491$	11832.0	+	6831.20i	1.08752	+	0.627878i	0.154602	+	0.987977i	$0.450591\pi$
$492$	676.666	−	321.595i	0.0620050	−	0.0294688i
$493$	1883.70	−	7030.06i	0.172084	−	0.642227i
$494$	−3806.09			−0.346648
$495$	−2664.50	−	4506.40i	−0.241941	−	0.409187i
$496$	4902.17			0.443778
$497$	3649.35	−	13619.6i	0.329368	−	1.22922i
$498$	−1931.32	−	1331.33i	−0.173784	−	0.119796i
$499$	−10650.2	−	6148.91i	−0.955450	−	0.551629i	−0.0606800	−	0.998157i	$-0.519327\pi$
$499$	−10650.2	−	6148.91i	−0.955450	−	0.551629i	−0.894770	+	0.446528i	$0.852660\pi$
$500$	−15.8350	+	1231.47i	−0.00141632	+	0.110146i
$501$	−39.2100	−	213.218i	−0.00349656	−	0.0190137i
$502$	−1880.95	−	504.000i	−0.167233	−	0.0448100i
$503$	−10869.2	+	10869.2i	−0.963483	+	0.963483i	−0.999356	−	0.0358736i	$-0.988579\pi$
$503$	−10869.2	+	10869.2i	−0.963483	+	0.963483i	0.0358736	+	0.999356i	$0.488579\pi$
$504$	17354.6	−	6606.31i	1.53380	−	0.583866i
$505$	−811.845	−	975.984i	−0.0715379	−	0.0860014i
$506$	520.519	−	300.522i	0.0457310	−	0.0264028i
$507$	4727.76	+	9947.64i	0.414137	+	0.871381i
$508$	2273.89	−	609.286i	0.198597	−	0.0532140i
$509$	−3933.77	+	6813.50i	−0.342557	+	0.593326i	−0.984907	−	0.173086i	$-0.944626\pi$
$509$	−3933.77	+	6813.50i	−0.342557	+	0.593326i	0.642350	+	0.766412i	$0.277960\pi$
$510$	−4654.13	+	3280.03i	−0.404095	+	0.284789i
$511$	5187.01	+	8984.16i	0.449040	+	0.777761i
$512$	6460.49	+	6460.49i	0.557648	+	0.557648i
$513$	19788.6	+	4838.49i	1.70310	+	0.416422i
$514$			94.6883i			0.00812553i
$515$	−4622.23	−	10024.3i	−0.395494	−	0.857719i
$516$	−330.924	−	388.558i	−0.0282328	−	0.0331499i
$517$	−865.094	−	3228.57i	−0.0735914	−	0.274647i
$518$	1997.91	+	7456.30i	0.169465	+	0.632454i
$519$	−4094.71	+	11512.1i	−0.346316	+	0.973648i
$520$	1957.33	+	721.924i	0.165066	+	0.0608817i
$521$			5611.99i			0.471911i	0.971764	+	0.235956i	$0.0758220\pi$
$521$			5611.99i			0.471911i	−0.971764	+	0.235956i	$0.924178\pi$
$522$	−17714.4	+	1811.91i	−1.48532	+	0.151926i
$523$	4528.31	+	4528.31i	0.378603	+	0.378603i	0.870598	−	0.491995i	$-0.163732\pi$
$523$	4528.31	+	4528.31i	0.378603	+	0.378603i	−0.491995	+	0.870598i	$0.663732\pi$
$524$	295.734	+	512.227i	0.0246550	+	0.0427037i
$525$	−26.1099	+	21056.5i	−0.00217053	+	1.75044i
$526$	−10452.5	+	18104.2i	−0.866444	+	1.50072i
$527$	−2216.00	+	593.777i	−0.183170	+	0.0490803i
$528$	−3594.13	+	5213.90i	−0.296240	+	0.429746i
$529$	10419.8	−	6015.88i	0.856399	−	0.494442i
$530$	−13321.3	+	11081.0i	−1.09178	+	0.908163i
$531$	7161.64	−	8793.61i	0.585289	−	0.718664i
$532$	−2933.28	+	2933.28i	−0.239049	+	0.239049i
$533$	1390.04	+	372.460i	0.112963	+	0.0302683i
$534$	−1832.90	−	651.943i	−0.148534	−	0.0528321i
$535$	499.537	−	706.944i	0.0403680	−	0.0571287i
$536$	−4287.45	−	2475.36i	−0.345503	−	0.199476i
$537$	1601.98	−	19998.5i	0.128735	−	1.60707i
$538$	851.570	−	3178.10i	0.0682412	−	0.254680i
$539$	12278.0			0.981167
$540$	1146.16	+	772.668i	0.0913388	+	0.0615747i
$541$	−1601.81			−0.127296			−0.0636481	−	0.997972i	$-0.520274\pi$
$541$	−1601.81			−0.127296			−0.0636481	+	0.997972i	$0.520274\pi$
$542$	−3051.98	+	11390.1i	−0.241870	+	0.902672i
$543$	554.400	−	6920.89i	0.0438151	−	0.546969i
$544$	1130.86	+	652.903i	0.0891273	+	0.0514577i
$545$	12001.9	−	2063.25i	0.943309	−	0.162165i
$546$	−4160.14	−	1479.72i	−0.326076	−	0.115982i
$547$	16277.9	+	4361.65i	1.27238	+	0.340934i	0.830943	−	0.556357i	$-0.187801\pi$
$547$	16277.9	+	4361.65i	1.27238	+	0.340934i	0.441440	+	0.897291i	$0.354468\pi$
$548$	−1101.39	+	1101.39i	−0.0858560	+	0.0858560i
$549$	−4342.47	−	11407.5i	−0.337581	−	0.886816i
$550$	−3660.04	−	5323.63i	−0.283754	−	0.412728i
$551$	−27828.8	+	16067.0i	−2.15163	+	1.24224i
$552$	727.590	−	1055.49i	0.0561019	−	0.0813854i
$553$	5020.17	−	1345.15i	0.386039	−	0.103439i
$554$	1680.93	−	2911.46i	0.128910	−	0.223278i
$555$	2972.84	−	3564.89i	0.227369	−	0.272651i
$556$	−229.172	−	396.937i	−0.0174803	−	0.0302767i
$557$	−12036.2	−	12036.2i	−0.915600	−	0.915600i	0.0811057	−	0.996706i	$-0.474155\pi$
$557$	−12036.2	−	12036.2i	−0.915600	−	0.915600i	−0.996706	+	0.0811057i	$0.974155\pi$
$558$	3286.58	+	4550.23i	0.249341	+	0.345209i
$559$		−	980.348i		−	0.0741758i
$560$	23130.2	−	10665.3i	1.74541	−	0.804808i
$561$	993.178	−	2792.27i	0.0747451	−	0.210142i
$562$	−3787.69	−	14135.9i	−0.284296	−	1.06101i
$563$	4969.86	+	18547.8i	0.372033	+	1.38845i	0.857631	+	0.514265i	$0.171935\pi$
$563$	4969.86	+	18547.8i	0.372033	+	1.38845i	−0.485598	+	0.874182i	$0.661398\pi$
$564$	572.223	+	671.882i	0.0427215	+	0.0501620i
$565$	−13171.3	+	6073.28i	−0.980743	+	0.452221i
$566$		−	20227.5i		−	1.50216i
$567$	19748.3	+	12981.9i	1.46270	+	0.961533i
$568$	6524.55	+	6524.55i	0.481979	+	0.481979i
$569$	9856.25	+	17071.5i	0.726178	+	1.25778i	0.958487	+	0.285136i	$0.0920387\pi$
$569$	9856.25	+	17071.5i	0.726178	+	1.25778i	−0.232309	+	0.972642i	$0.574628\pi$
$570$	24770.5	+	4289.96i	1.82022	+	0.315239i
$571$	−4422.13	+	7659.35i	−0.324099	+	0.561355i	−0.981330	−	0.192334i	$-0.938394\pi$
$571$	−4422.13	+	7659.35i	−0.324099	+	0.561355i	0.657231	+	0.753689i	$0.271728\pi$
$572$	129.843	−	34.7912i	0.00949125	−	0.00254317i
$573$	−4670.48	−	9827.11i	−0.340510	−	0.716463i
$574$	13689.3	−	7903.52i	0.995436	−	0.574715i
$575$	823.553	+	1197.88i	0.0597296	+	0.0868783i
$576$	−1907.75	+	11831.4i	−0.138003	+	0.855858i
$577$	5344.50	−	5344.50i	0.385605	−	0.385605i	−0.487511	−	0.873117i	$-0.662095\pi$
$577$	5344.50	−	5344.50i	0.385605	−	0.385605i	0.873117	+	0.487511i	$0.162095\pi$
$578$	11029.1	+	2955.24i	0.793686	+	0.212667i
$579$	−2308.55	−	12553.5i	−0.165699	−	0.901045i
$580$	−2148.88	+	369.416i	−0.153840	+	0.0264469i
$581$	−4252.88	−	2455.40i	−0.303682	−	0.175331i
$582$	−12986.1	−	8951.76i	−0.924896	−	0.637565i
$583$	2334.30	−	8711.72i	0.165826	−	0.618872i
$584$	−6788.81			−0.481032
$585$	713.771	+	2557.37i	0.0504458	+	0.180742i
$586$	1663.46			0.117264
$587$	−4016.09	+	14988.2i	−0.282388	+	1.05389i	0.668339	+	0.743856i	$0.267005\pi$
$587$	−4016.09	+	14988.2i	−0.282388	+	1.05389i	−0.950727	+	0.310029i	$0.899661\pi$
$588$	−2927.97	+	1391.56i	−0.205353	+	0.0975970i
$589$	8772.16	+	5064.61i	0.613668	+	0.354302i
$590$	8076.33	−	11429.6i	0.563555	−	0.797543i
$591$	10183.9	−	8673.37i	0.708818	−	0.603680i
$592$	−5423.54	−	1453.23i	−0.376531	−	0.100891i
$593$	−7756.63	+	7756.63i	−0.537145	+	0.537145i	−0.922689	−	0.385545i	$-0.874014\pi$
$593$	−7756.63	+	7756.63i	−0.537145	+	0.537145i	0.385545	+	0.922689i	$0.374014\pi$
$594$	−7249.22	+	159.477i	−0.500739	+	0.0110159i
$595$	−9164.06	+	7622.87i	−0.631411	+	0.525222i
$596$	1631.21	−	941.781i	0.112109	−	0.0647263i
$597$	−959.933	−	76.8957i	−0.0658081	−	0.00527158i
$598$	−294.442	+	78.8955i	−0.0201348	+	0.00539511i
$599$	−3436.79	+	5952.70i	−0.234430	+	0.406045i	−0.959107	−	0.283044i	$-0.908656\pi$
$599$	−3436.79	+	5952.70i	−0.234430	+	0.406045i	0.724677	+	0.689089i	$0.241989\pi$
$600$	−11924.8	−	6904.53i	−0.811382	−	0.469794i
$601$	1499.90	+	2597.90i	0.101800	+	0.176323i	0.912426	−	0.409241i	$-0.134206\pi$
$601$	1499.90	+	2597.90i	0.101800	+	0.176323i	−0.810626	+	0.585564i	$0.800873\pi$
$602$	−7614.34	−	7614.34i	−0.515511	−	0.515511i
$603$	−641.124	−	6268.03i	−0.0432978	−	0.423306i
$604$		−	1788.54i		−	0.120488i
$605$	−10806.8	−	3985.87i	−0.726210	−	0.267849i
$606$	−1729.32	+	318.016i	−0.115922	+	0.0213177i
$607$	−2529.48	−	9440.13i	−0.169141	−	0.631241i	−0.997476	−	0.0710082i	$-0.977378\pi$
$607$	−2529.48	−	9440.13i	−0.169141	−	0.631241i	0.828335	−	0.560233i	$-0.189288\pi$
$608$	−1492.19	−	5568.93i	−0.0995333	−	0.371463i
$609$	−36664.0	+	6742.39i	−2.43957	+	0.448630i
$610$	−6307.24	−	13678.7i	−0.418644	−	0.907924i
$611$			1695.18i			0.112242i
$612$	79.6233	+	778.448i	0.00525912	+	0.0514165i
$613$	3413.76	+	3413.76i	0.224927	+	0.224927i	0.810570	−	0.585642i	$-0.199158\pi$
$613$	3413.76	+	3413.76i	0.224927	+	0.224927i	−0.585642	+	0.810570i	$0.699158\pi$
$614$	4162.94	+	7210.42i	0.273620	+	0.473923i
$615$	−8626.74	−	3990.77i	−0.565632	−	0.261664i
$616$	−5963.74	+	10329.5i	−0.390075	+	0.675629i
$617$	13266.8	−	3554.83i	0.865642	−	0.231948i	0.201440	−	0.979501i	$-0.435438\pi$
$617$	13266.8	−	3554.83i	0.865642	−	0.231948i	0.664202	+	0.747553i	$0.268771\pi$
$618$	−15240.2	−	1220.82i	−0.991994	−	0.0794639i
$619$	10576.7	−	6106.47i	0.686776	−	0.396510i	−0.115627	−	0.993293i	$-0.536888\pi$
$619$	10576.7	−	6106.47i	0.686776	−	0.396510i	0.802403	+	0.596782i	$0.203554\pi$
$620$	439.529	+	528.394i	0.0284709	+	0.0342271i
$621$	1631.16	−	35.8843i	0.105404	−	0.00231882i
$622$	−5038.67	+	5038.67i	−0.324811	+	0.324811i
$623$	−3933.93	−	1054.09i	−0.252985	−	0.0677871i
$624$	2445.11	−	2082.43i	0.156863	−	0.133596i
$625$	12139.9	−	9836.89i	0.776951	−	0.629561i
$626$	−13399.1	−	7735.97i	−0.855488	−	0.493916i
$627$	−11818.2	+	5616.77i	−0.752748	+	0.357754i
$628$	−55.6358	+	207.636i	−0.00353521	+	0.0131936i
$629$	2627.71			0.166572
$630$	25406.9	+	14319.2i	1.60672	+	0.905541i
$631$	8057.84			0.508364			0.254182	−	0.967156i	$-0.418194\pi$
$631$	8057.84			0.508364			0.254182	+	0.967156i	$0.418194\pi$
$632$	−880.273	+	3285.22i	−0.0554041	+	0.206771i
$633$	−22021.8	−	15180.4i	−1.38276	−	0.953188i
$634$	21373.7	+	12340.1i	1.33889	+	0.773011i
$635$	−24391.5	−	17235.4i	−1.52433	−	1.07711i
$636$	430.701	+	2342.08i	0.0268529	+	0.146021i
$637$	−6014.78	−	1611.66i	−0.374120	−	0.100245i
$638$	8087.63	−	8087.63i	0.501869	−	0.501869i
$639$	−1869.40	+	11593.5i	−0.115731	+	0.717734i
$640$	−1676.75	+	18263.5i	−0.103562	+	1.12801i
$641$	21555.5	−	12445.1i	1.32823	−	0.766852i	0.343201	−	0.939262i	$-0.388489\pi$
$641$	21555.5	−	12445.1i	1.32823	−	0.766852i	0.985025	+	0.172410i	$0.0551555\pi$
$642$	−514.643	−	1082.86i	−0.0316376	−	0.0665684i
$643$	−10661.6	+	2856.76i	−0.653891	+	0.175210i	−0.570488	−	0.821306i	$-0.693246\pi$
$643$	−10661.6	+	2856.76i	−0.653891	+	0.175210i	−0.0834036	+	0.996516i	$0.526579\pi$
$644$	−166.118	+	287.724i	−0.0101645	+	0.0176055i
$645$	−1104.98	+	6380.22i	−0.0674550	+	0.389490i
$646$	7115.66	+	12324.7i	0.433377	+	0.750632i
$647$	−17868.7	−	17868.7i	−1.08577	−	1.08577i	−0.995959	−	0.0898058i	$-0.971375\pi$
$647$	−17868.7	−	17868.7i	−1.08577	−	1.08577i	−0.0898058	−	0.995959i	$-0.528625\pi$
$648$	−13819.0	+	6944.28i	−0.837747	+	0.420983i
$649$			7284.48i			0.440587i
$650$	1094.20	+	3088.40i	0.0660276	+	0.186365i
$651$	7619.17	+	8946.14i	0.458708	+	0.538597i
$652$	−563.257	−	2102.10i	−0.0338326	−	0.126265i
$653$	−6216.66	−	23200.9i	−0.372553	−	1.39039i	−0.856888	−	0.515503i	$-0.827605\pi$
$653$	−6216.66	−	23200.9i	−0.372553	−	1.39039i	0.484335	−	0.874882i	$-0.339061\pi$
$654$	5652.48	−	15891.6i	0.337966	−	0.950172i
$655$	2596.71	−	7040.36i	0.154903	−	0.419984i
$656$			11497.7i			0.684313i
$657$	−5058.98	−	7004.09i	−0.300410	−	0.415914i
$658$	13166.5	+	13166.5i	0.780065	+	0.780065i
$659$	−14654.5	−	25382.4i	−0.866250	−	1.50039i	−0.865801	−	0.500389i	$-0.833190\pi$
$659$	−14654.5	−	25382.4i	−0.866250	−	1.50039i	−0.000449468	−	1.00000i	$-0.500143\pi$
$660$	−884.246	+	80.0762i	−0.0521503	+	0.00472267i
$661$	5726.89	−	9919.27i	0.336990	−	0.583684i	−0.646875	−	0.762596i	$-0.723924\pi$
$661$	5726.89	−	9919.27i	0.336990	−	0.583684i	0.983865	+	0.178912i	$0.0572578\pi$
$662$	22017.3	−	5899.53i	1.29264	−	0.346362i
$663$	−853.067	+	1237.52i	−0.0499704	+	0.0724906i
$664$	2783.11	−	1606.83i	0.162659	−	0.0939111i
$665$	52408.9	+	4811.62i	3.05614	+	0.280581i
$666$	−2287.23	−	6008.47i	−0.133075	−	0.349585i
$667$	−1819.81	+	1819.81i	−0.105642	+	0.105642i
$668$	−35.5143	−	9.51603i	−0.00205702	−	0.000551177i
$669$	22023.6	+	7833.57i	1.27277	+	0.452710i
$670$	−1317.34	−	7662.93i	−0.0759602	−	0.441858i
$671$	6789.81	+	3920.10i	0.390637	+	0.225535i
$672$	534.069	−	6667.09i	0.0306580	−	0.382721i
$673$	−4683.57	+	17479.3i	−0.268259	+	1.00116i	0.691966	+	0.721930i	$0.256745\pi$
$673$	−4683.57	+	17479.3i	−0.268259	+	1.00116i	−0.960225	+	0.279227i	$0.909922\pi$
$674$	−4529.78			−0.258873
$675$	−1762.82	−	17448.2i	−0.100520	−	0.994935i
$676$	1867.92			0.106277
$677$	−992.214	+	3702.99i	−0.0563277	+	0.210218i	−0.988354	−	0.152173i	$-0.951373\pi$
$677$	−992.214	+	3702.99i	−0.0563277	+	0.210218i	0.932026	+	0.362391i	$0.118040\pi$
$678$	−1604.08	+	20024.6i	−0.0908616	+	1.13428i
$679$	−28596.1	−	16510.0i	−1.61623	−	0.933129i
$680$	−1321.62	−	7687.78i	−0.0745318	−	0.433549i
$681$	22801.0	+	8110.05i	1.28302	+	0.456355i
$682$	−3482.50	−	933.134i	−0.195531	−	0.0523923i
$683$	15444.0	−	15444.0i	0.865222	−	0.865222i	−0.126717	−	0.991939i	$-0.540444\pi$
$683$	15444.0	−	15444.0i	0.865222	−	0.865222i	0.991939	+	0.126717i	$0.0404440\pi$
$684$	2181.74	−	2678.90i	0.121960	−	0.149752i
$685$	19678.5	+	1806.67i	1.09763	+	0.100773i
$686$	−30536.1	+	17630.0i	−1.69953	+	0.981222i
$687$	−12029.7	+	17451.1i	−0.668066	+	0.969144i
$688$	7565.73	−	2027.23i	0.419245	−	0.112336i
$689$	−2287.07	+	3961.33i	−0.126459	+	0.219034i
$690$	2005.19	−	181.588i	0.110632	−	0.0100187i
$691$	10639.5	+	18428.2i	0.585741	+	1.01453i	0.994783	+	0.102017i	$0.0325297\pi$
$691$	10639.5	+	18428.2i	0.585741	+	1.01453i	−0.409042	+	0.912516i	$0.634137\pi$
$692$	1465.28	+	1465.28i	0.0804937	+	0.0804937i
$693$	−15101.2	+	1544.62i	−0.827774	+	0.0846687i
$694$			9305.32i			0.508970i
$695$	−2012.25	+	5455.74i	−0.109826	+	0.297767i
$696$	8175.43	−	22984.8i	0.445243	−	1.25177i
$697$	−1392.66	−	5197.48i	−0.0756826	−	0.282451i
$698$	9632.19	+	35947.8i	0.522326	+	1.94935i
$699$	12057.0	+	14156.9i	0.652416	+	0.766042i
$700$	3223.45	+	1536.89i	0.174050	+	0.0829845i
$701$		−	510.344i		−	0.0274970i	−0.999905	−	0.0137485i	$-0.995624\pi$
$701$		−	510.344i		−	0.0274970i	0.999905	−	0.0137485i	$-0.00437642\pi$
$702$	3572.21	+	873.437i	0.192058	+	0.0469598i
$703$	−8203.74	−	8203.74i	−0.440128	−	0.440128i
$704$	−3848.83	−	6666.37i	−0.206049	−	0.356887i
$705$	1910.69	−	11032.5i	0.102072	−	0.589371i
$706$	7496.01	−	12983.5i	0.399598	−	0.692124i
$707$	−3555.63	+	952.729i	−0.189142	+	0.0506804i
$708$	−825.610	−	1737.16i	−0.0438253	−	0.0922125i
$709$	−8375.17	+	4835.41i	−0.443634	+	0.256132i	−0.705138	−	0.709070i	$-0.749115\pi$
$709$	−8375.17	+	4835.41i	−0.443634	+	0.256132i	0.261504	+	0.965202i	$0.415782\pi$
$710$	−1324.89	+	14430.9i	−0.0700313	+	0.762793i
$711$	−4045.38	+	1539.94i	−0.213380	+	0.0812268i
$712$	1884.58	−	1884.58i	0.0991962	−	0.0991962i
$713$	783.604	+	209.966i	0.0411588	+	0.0110285i
$714$	2986.03	+	16237.6i	0.156512	+	0.851086i
$715$	−1392.80	−	984.170i	−0.0728498	−	0.0514767i
$716$	−2946.67	−	1701.26i	−0.153802	−	0.0887975i
$717$	29796.3	+	20539.7i	1.55197	+	1.06983i
$718$	−5377.79	+	20070.2i	−0.279523	+	1.04319i
$719$	−6320.54			−0.327839			−0.163920	−	0.986474i	$-0.552414\pi$
$719$	−6320.54			−0.327839			−0.163920	+	0.986474i	$0.552414\pi$
$720$	−18260.2	+	10796.8i	−0.945166	+	0.558849i
$721$	−32007.8			−1.65331
$722$	10972.2	−	40948.6i	0.565570	−	2.11073i
$723$	−24419.4	+	11605.7i	−1.25611	+	0.596984i
$724$	−1019.76	−	588.756i	−0.0523466	−	0.0302223i
$725$	21037.7	+	17962.3i	1.07768	+	0.920141i
$726$	−12145.6	+	10344.0i	−0.620887	+	0.528791i
$727$	−6302.81	−	1688.83i	−0.321538	−	0.0861558i	0.0944399	−	0.995531i	$-0.469894\pi$
$727$	−6302.81	−	1688.83i	−0.321538	−	0.0861558i	−0.415978	+	0.909375i	$0.636561\pi$
$728$	4277.44	−	4277.44i	0.217764	−	0.217764i
$729$	−17462.3	−	9082.34i	−0.887176	−	0.461431i
$730$	−6818.42	−	8196.97i	−0.345700	−	0.415594i
$731$	−3174.51	+	1832.80i	−0.160620	+	0.0927342i
$732$	−2063.49	−	165.296i	−0.104192	−	0.00834635i
$733$	−6569.29	+	1760.23i	−0.331026	+	0.0886982i	−0.420504	−	0.907291i	$-0.638147\pi$
$733$	−6569.29	+	1760.23i	−0.331026	+	0.0886982i	0.0894781	+	0.995989i	$0.471480\pi$
$734$	13997.9	−	24245.1i	0.703914	−	1.21921i
$735$	37328.4	+	17268.3i	1.87330	+	0.866599i
$736$	−230.874	−	399.885i	−0.0115627	−	0.0200271i
$737$	2861.71	+	2861.71i	0.143029	+	0.143029i
$738$	−10672.2	+	7708.44i	−0.532318	+	0.384487i
$739$			5975.83i			0.297462i	0.988878	+	0.148731i	$0.0475189\pi$
$739$			5975.83i			0.297462i	−0.988878	+	0.148731i	$0.952481\pi$
$740$	−329.635	−	714.888i	−0.0163752	−	0.0355133i
$741$	6526.83	−	1200.26i	0.323575	−	0.0595044i
$742$	13003.9	+	48531.2i	0.643380	+	2.40113i
$743$	−187.477	−	699.672i	−0.00925686	−	0.0345471i	0.961143	−	0.276051i	$-0.0890259\pi$
$743$	−187.477	−	699.672i	−0.00925686	−	0.0345471i	−0.970400	+	0.241504i	$0.922359\pi$
$744$	−7563.07	+	1390.82i	−0.372682	+	0.0685351i
$745$	−22420.4	−	8269.34i	−1.10258	−	0.406665i
$746$		−	2831.96i		−	0.138988i
$747$	3731.73	+	1673.96i	0.182780	+	0.0819908i
$748$	−355.406	−	355.406i	−0.0173729	−	0.0173729i
$749$	−1254.99	−	2173.70i	−0.0612233	−	0.106042i
$750$	−3640.15	−	21333.0i	−0.177226	−	1.03863i
$751$	10732.0	−	18588.3i	0.521459	−	0.903193i	−0.478230	−	0.878235i	$-0.658721\pi$
$751$	10732.0	−	18588.3i	0.521459	−	0.903193i	0.999688	−	0.0249581i	$-0.00794524\pi$
$752$	−13082.4	+	3505.42i	−0.634397	+	0.169986i
$753$	3384.47	+	271.114i	0.163794	+	0.0131208i
$754$	−5023.62	+	2900.39i	−0.242639	+	0.140087i
$755$	−17444.8	+	14511.0i	−0.840905	+	0.699483i
$756$	3426.18	−	2079.90i	0.164827	−	0.100060i
$757$	15108.9	−	15108.9i	0.725420	−	0.725420i	−0.244284	−	0.969704i	$-0.578553\pi$
$757$	15108.9	−	15108.9i	0.725420	−	0.725420i	0.969704	+	0.244284i	$0.0785530\pi$
$758$	3719.48	+	996.631i	0.178229	+	0.0477563i
$759$	−797.835	+	679.494i	−0.0381549	+	0.0324955i
$760$	−19875.2	+	28127.4i	−0.948619	+	1.34249i
$761$	−17720.2	−	10230.7i	−0.844094	−	0.487338i	0.0145596	−	0.999894i	$-0.495365\pi$
$761$	−17720.2	−	10230.7i	−0.844094	−	0.487338i	−0.858654	+	0.512556i	$0.828699\pi$
$762$	−37361.5	+	17756.6i	−1.77620	+	0.844165i
$763$	9139.21	−	34108.0i	0.433633	−	1.61834i
$764$	−1845.29			−0.0873823
$765$	6946.71	−	7092.41i	0.328312	−	0.335198i
$766$	17705.2			0.835136
$767$	956.191	−	3568.55i	0.0450144	−	0.167996i
$768$	5723.21	+	3945.22i	0.268904	+	0.185366i
$769$	35643.4	+	20578.7i	1.67144	+	0.965004i	0.966835	+	0.255401i	$0.0822076\pi$
$769$	35643.4	+	20578.7i	1.67144	+	0.965004i	0.704602	+	0.709603i	$0.251126\pi$
$770$	−18461.9	+	3173.80i	−0.864051	+	0.148540i
$771$	−29.8602	−	162.375i	−0.00139480	−	0.00758468i
$772$	−2090.95	−	560.269i	−0.0974807	−	0.0261199i
$773$	12436.1	−	12436.1i	0.578649	−	0.578649i	−0.355882	−	0.934531i	$-0.615820\pi$
$773$	12436.1	−	12436.1i	0.578649	−	0.578649i	0.934531	+	0.355882i	$0.115820\pi$
$774$	6954.02	+	5663.44i	0.322942	+	0.263008i
$775$	1587.73	−	8574.05i	0.0735911	−	0.397405i
$776$	18713.4	−	10804.2i	0.865687	−	0.499805i
$777$	−5777.46	−	12156.3i	−0.266750	−	0.561267i
$778$	−17704.5	+	4743.91i	−0.815858	+	0.218608i
$779$	−11878.7	+	20574.5i	−0.546339	+	0.946286i
$780$	443.690	+	76.8417i	0.0203675	+	0.00352740i
$781$	−3771.45	−	6532.35i	−0.172795	−	0.299290i
$782$	805.948	+	805.948i	0.0368550	+	0.0368550i
$783$	29805.9	−	8693.42i	1.36038	−	0.396779i
$784$		−	49751.1i		−	2.26636i
$785$	2476.60	−	1141.96i	0.112603	−	0.0519214i
$786$	−6738.90	−	7912.55i	−0.305812	−	0.359073i
$787$	−6289.08	−	23471.2i	−0.284856	−	1.06310i	−0.948945	−	0.315442i	$-0.897847\pi$
$787$	−6289.08	−	23471.2i	−0.284856	−	1.06310i	0.664089	−	0.747653i	$-0.268820\pi$
$788$	−587.170	−	2191.35i	−0.0265445	−	0.0990655i
$789$	12215.1	−	34342.0i	0.551164	−	1.54957i
$790$	−4850.77	+	2236.69i	−0.218459	+	0.100732i
$791$			42056.1i			1.89044i
$792$	4065.77	−	9063.74i	0.182413	−	0.406649i
$793$	−2811.66	−	2811.66i	−0.125908	−	0.125908i
$794$	19199.8	+	33255.1i	0.858157	+	1.48637i
$795$	19349.5	−	23203.0i	0.863214	−	1.03513i
$796$	−81.6609	+	141.441i	−0.00363617	+	0.00629804i
$797$	−32080.4	+	8595.91i	−1.42578	+	0.382036i	−0.887530	−	0.460750i	$-0.847581\pi$
$797$	−32080.4	+	8595.91i	−1.42578	+	0.382036i	−0.538249	+	0.842786i	$0.680914\pi$
$798$	41371.4	−	60016.2i	1.83525	−	2.66234i
$799$	5489.25	−	3169.22i	0.243049	−	0.140324i
$800$	−4089.84	+	2811.80i	−0.180747	+	0.124265i
$801$	3348.72	+	539.965i	0.147717	+	0.0238186i
$802$	8704.14	−	8704.14i	0.383234	−	0.383234i
$803$	5360.56	+	1436.36i	0.235579	+	0.0631232i
$804$	−1006.78	−	358.102i	−0.0441624	−	0.0157081i
$805$	4154.13	−	714.142i	0.181881	−	0.0312673i
$806$	1583.54	+	914.256i	0.0692032	+	0.0399545i
$807$	−458.080	+	5718.47i	−0.0199816	+	0.249442i
$808$	623.470	−	2326.82i	0.0271456	−	0.101309i
$809$	−21561.9			−0.937054			−0.468527	−	0.883449i	$-0.655215\pi$
$809$	−21561.9			−0.937054			−0.468527	+	0.883449i	$0.655215\pi$
$810$	−22263.9	−	9710.78i	−0.965772	−	0.421237i
$811$	−34494.6			−1.49355			−0.746775	−	0.665077i	$-0.768399\pi$
$811$	−34494.6			−1.49355			−0.746775	+	0.665077i	$0.768399\pi$
$812$	−1636.34	+	6106.89i	−0.0707193	+	0.263928i
$813$	1641.73	−	20494.7i	0.0708217	−	0.884108i
$814$	3576.26	+	2064.76i	0.153990	+	0.0889063i
$815$	−15933.3	+	22548.9i	−0.684811	+	0.969144i
$816$	−11314.5	−	4024.43i	−0.485399	−	0.172651i
$817$	15632.9	+	4188.82i	0.669431	+	0.179373i
$818$	−11012.5	+	11012.5i	−0.470714	+	0.470714i
$819$	7600.60	+	1225.56i	0.324282	+	0.0522888i
$820$	−1239.31	+	1030.88i	−0.0527787	+	0.0439025i
$821$	20162.0	−	11640.5i	0.857073	−	0.494831i	−0.00595789	−	0.999982i	$-0.501896\pi$
$821$	20162.0	−	11640.5i	0.857073	−	0.494831i	0.863031	+	0.505151i	$0.168563\pi$
$822$	15534.1	−	22534.9i	0.659143	−	0.956199i
$823$	14166.9	−	3796.00i	0.600031	−	0.160778i	0.0539975	−	0.998541i	$-0.482804\pi$
$823$	14166.9	−	3796.00i	0.600031	−	0.160778i	0.546034	+	0.837763i	$0.316137\pi$
$824$	10473.0	−	18139.9i	0.442774	−	0.766907i
$825$	7955.21	+	7974.96i	0.335715	+	0.336548i
$826$	−20290.2	−	35143.6i	−0.854705	−	1.48039i
$827$	13463.5	+	13463.5i	0.566109	+	0.566109i	0.931036	−	0.364927i	$-0.118906\pi$
$827$	13463.5	+	13463.5i	0.566109	+	0.566109i	−0.364927	+	0.931036i	$0.618906\pi$
$828$	113.250	−	252.467i	0.00475329	−	0.0105964i
$829$		−	40270.0i		−	1.68713i	−0.537024	−	0.843567i	$-0.680452\pi$
$829$		−	40270.0i		−	1.68713i	0.537024	−	0.843567i	$-0.319548\pi$
$830$	4735.37	+	1746.55i	0.198033	+	0.0730407i
$831$	−1964.39	+	5522.77i	−0.0820023	+	0.230545i
$832$	1010.43	+	3770.97i	0.0421037	+	0.157133i
$833$	6026.12	+	22489.8i	0.250652	+	0.935445i
$834$	5222.13	+	6131.62i	0.216820	+	0.254581i
$835$	195.323	+	423.601i	0.00809511	+	0.0175561i
$836$			2219.16i			0.0918077i
$837$	−7070.88	−	6766.47i	−0.292002	−	0.279431i
$838$	19739.0	+	19739.0i	0.813690	+	0.813690i
$839$	6626.11	+	11476.8i	0.272656	+	0.472255i	0.969541	−	0.244928i	$-0.0787645\pi$
$839$	6626.11	+	11476.8i	0.272656	+	0.472255i	−0.696885	+	0.717183i	$0.745431\pi$
$840$	−32659.3	+	23016.9i	−1.34149	+	0.945426i
$841$	−12292.8	+	21291.8i	−0.504031	+	0.873008i
$842$	−7979.71	+	2138.16i	−0.326602	+	0.0875128i
$843$	10953.1	+	23046.2i	0.447501	+	0.941583i
$844$	−3928.45	+	2268.09i	−0.160217	+	0.0925011i
$845$	−15155.0	−	18219.1i	−0.616980	−	0.741721i
$846$	−12024.7	−	9793.04i	−0.488672	−	0.397981i
$847$	−23616.5	+	23616.5i	−0.958055	+	0.958055i
$848$	−35300.5	−	9458.74i	−1.42951	−	0.383036i
$849$	6378.80	+	34686.8i	0.257856	+	1.40218i
$850$	7955.04	−	9317.07i	0.321006	−	0.375968i
$851$	−804.701	−	464.594i	−0.0324146	−	0.0187146i
$852$	1639.76	+	1130.34i	0.0659356	+	0.0454518i
$853$	−8302.39	+	30985.0i	−0.333257	+	1.24373i	0.572489	+	0.819913i	$0.305978\pi$
$853$	−8302.39	+	30985.0i	−0.333257	+	1.24373i	−0.905746	+	0.423821i	$0.860689\pi$
$854$	−43676.2			−1.75008
$855$	−43830.3	+	454.881i	−1.75317	+	0.0181948i
$856$	1642.54			0.0655851
$857$	−11664.3	+	43531.9i	−0.464931	+	1.73515i	0.192186	+	0.981359i	$0.438442\pi$
$857$	−11664.3	+	43531.9i	−0.464931	+	1.73515i	−0.657117	+	0.753788i	$0.728224\pi$
$858$	−2133.40	+	1013.93i	−0.0848871	+	0.0403439i
$859$	14333.6	+	8275.49i	0.569331	+	0.328703i	0.756882	−	0.653551i	$-0.226722\pi$
$859$	14333.6	+	8275.49i	0.569331	+	0.328703i	−0.187551	+	0.982255i	$0.560055\pi$
$860$	896.856	+	633.731i	0.0355611	+	0.0251280i
$861$	−20982.5	+	17870.2i	−0.830526	+	0.707335i
$862$	41398.5	+	11092.7i	1.63577	+	0.438304i
$863$	15700.9	−	15700.9i	0.619310	−	0.619310i	−0.326045	−	0.945354i	$-0.605716\pi$
$863$	15700.9	−	15700.9i	0.619310	−	0.619310i	0.945354	+	0.326045i	$0.105716\pi$
$864$	122.517	+	5569.16i	0.00482422	+	0.219290i
$865$	2403.57	−	26180.1i	0.0944786	−	1.02908i
$866$	26694.6	−	15412.1i	1.04748	−	0.604763i
$867$	−19845.1	−	1589.69i	−0.777363	−	0.0622709i
$868$	1925.00	−	515.803i	0.0752752	−	0.0201699i
$869$	1390.16	−	2407.82i	0.0542668	−	0.0939929i
$870$	35963.5	−	13213.8i	1.40147	−	0.514932i
$871$	−1026.27	−	1777.55i	−0.0399240	−	0.0691503i
$872$	16339.7	+	16339.7i	0.634555	+	0.634555i
$873$	25091.9	+	11255.6i	0.972776	+	0.436363i
$874$		−	5032.35i		−	0.194762i
$875$	−11162.5	−	43909.8i	−0.431270	−	1.69648i
$876$	−1441.15	+	265.022i	−0.0555843	+	0.0102218i
$877$	−3643.66	−	13598.3i	−0.140294	−	0.523583i	−0.999920	−	0.0126598i	$-0.995970\pi$
$877$	−3643.66	−	13598.3i	−0.140294	−	0.523583i	0.859626	−	0.510924i	$-0.170697\pi$
$878$	−1143.99	−	4269.42i	−0.0439724	−	0.164107i
$879$	−2852.56	+	524.576i	−0.109459	+	0.0201291i
$880$	4715.10	−	12783.9i	0.180621	−	0.489710i
$881$		−	7520.39i		−	0.287592i	−0.989607	−	0.143796i	$-0.954069\pi$
$881$		−	7520.39i		−	0.287592i	0.989607	−	0.143796i	$-0.0459309\pi$
$882$	46179.4	−	33354.9i	1.76297	−	1.27338i
$883$	−23246.2	−	23246.2i	−0.885953	−	0.885953i	0.108179	−	0.994131i	$-0.465498\pi$
$883$	−23246.2	−	23246.2i	−0.885953	−	0.885953i	−0.994131	+	0.108179i	$0.965498\pi$
$884$	127.456	+	220.760i	0.00484932	+	0.00839927i
$885$	−10245.2	+	22146.8i	−0.389141	+	0.841196i
$886$	−16177.1	+	28019.6i	−0.613409	+	1.06246i
$887$	40787.4	−	10928.9i	1.54397	−	0.413707i	0.616427	−	0.787412i	$-0.288579\pi$
$887$	40787.4	−	10928.9i	1.54397	−	0.413707i	0.927548	+	0.373705i	$0.121913\pi$
$888$	8779.75	+	703.304i	0.331790	+	0.0265781i
$889$	−74998.7	+	43300.5i	−2.82944	+	1.63358i
$890$	4168.29	+	382.687i	0.156990	+	0.0144131i
$891$	12380.9	−	2559.54i	0.465519	−	0.0962378i
$892$	2803.22	−	2803.22i	0.105223	−	0.105223i
$893$	−27031.8	−	7243.16i	−1.01297	−	0.271426i
$894$	−25197.9	+	21460.4i	−0.942668	+	0.802843i
$895$	7313.73	+	42543.7i	0.273152	+	1.58891i
$896$	46055.0	+	26589.8i	1.71717	+	0.991411i
$897$	480.040	−	228.146i	0.0178685	−	0.00849229i
$898$	2834.92	−	10580.1i	0.105348	−	0.393165i
$899$	15437.7			0.572721
$900$	−2800.98	−	1000.19i	−0.103740	−	0.0370441i
$901$	17103.1			0.632395
$902$	2188.60	−	8167.96i	0.0807898	−	0.301512i
$903$	15458.6	+	10656.2i	0.569689	+	0.392707i
$904$	−23834.5	−	13760.8i	−0.876906	−	0.506282i
$905$	2531.07	+	14723.1i	0.0929674	+	0.540788i
$906$	5684.26	+	30910.1i	0.208440	+	1.13346i
$907$	9936.50	+	2662.48i	0.363767	+	0.0974709i	0.436072	−	0.899912i	$-0.356369\pi$
$907$	9936.50	+	2662.48i	0.363767	+	0.0974709i	−0.0723059	+	0.997382i	$0.523036\pi$
$908$	2902.16	−	2902.16i	0.106070	−	0.106070i
$909$	2865.22	−	1090.69i	0.104547	−	0.0397976i
$910$	9460.79	+	868.586i	0.344640	+	0.0316410i
$911$	12942.9	−	7472.60i	0.470711	−	0.271765i	−0.245826	−	0.969314i	$-0.579059\pi$
$911$	12942.9	−	7472.60i	0.470711	−	0.271765i	0.716537	+	0.697549i	$0.245726\pi$
$912$	22759.5	+	47888.1i	0.826364	+	1.73874i
$913$	−2537.56	+	679.936i	−0.0919834	+	0.0246469i
$914$	13205.0	−	22871.7i	0.477880	−	0.827712i
$915$	15129.5	+	21467.7i	0.546629	+	0.775629i
$916$	1797.34	+	3113.09i	0.0648317	+	0.112292i
$917$	−15385.6	−	15385.6i	−0.554065	−	0.554065i
$918$	−3850.10	−	13200.3i	−0.138423	−	0.474591i
$919$			26923.8i			0.966413i	0.875506	+	0.483207i	$0.160528\pi$
$919$			26923.8i			0.966413i	−0.875506	+	0.483207i	$0.839472\pi$
$920$	−954.517	+	2587.95i	−0.0342060	+	0.0927414i
$921$	−9412.59	−	11051.9i	−0.336759	−	0.395410i
$922$	548.296	+	2046.27i	0.0195848	+	0.0730913i
$923$	990.113	+	3695.15i	0.0353087	+	0.131774i
$924$	−862.756	+	2425.59i	−0.0307171	+	0.0863594i
$925$	−4298.35	+	9015.27i	−0.152788	+	0.320454i
$926$			12851.7i			0.456085i
$927$	26519.5	−	2712.54i	0.939607	−	0.0961075i
$928$	−6213.26	−	6213.26i	−0.219785	−	0.219785i
$929$	15434.9	+	26734.1i	0.545106	+	0.944151i	0.998600	+	0.0528918i	$0.0168438\pi$
$929$	15434.9	+	26734.1i	0.545106	+	0.944151i	−0.453494	+	0.891259i	$0.649823\pi$
$930$	−9275.38	−	7734.95i	−0.327045	−	0.272730i
$931$	51399.7	−	89027.0i	1.80941	−	3.13399i
$932$	3046.24	−	816.237i	0.107063	−	0.0286875i
$933$	7051.54	−	10229.5i	0.247435	−	0.358947i
$934$	−20782.4	+	11998.7i	−0.728073	+	0.420353i
$935$	−582.990	+	6350.03i	−0.0203912	+	0.222105i
$936$	−3181.50	+	3906.50i	−0.111101	+	0.136419i
$937$	2293.85	−	2293.85i	0.0799753	−	0.0799753i	−0.665988	−	0.745963i	$-0.731990\pi$
$937$	2293.85	−	2293.85i	0.0799753	−	0.0799753i	0.745963	+	0.665988i	$0.231990\pi$
$938$	−21777.2	−	5835.18i	−0.758050	−	0.203119i
$939$	25416.8	+	9040.48i	0.883330	+	0.314191i
$940$	−1550.81	−	1095.83i	−0.0538106	−	0.0380233i
$941$	−43555.5	−	25146.8i	−1.50889	−	0.871160i	−0.999946	−	0.0103625i	$-0.996701\pi$
$941$	−43555.5	−	25146.8i	−1.50889	−	0.871160i	−0.508947	−	0.860798i	$-0.669965\pi$
$942$	301.615	−	3765.23i	0.0104322	−	0.130231i
$943$	−492.460	+	1837.89i	−0.0170061	+	0.0634675i
$944$	29517.2			1.01769
$945$	−48084.3	−	16543.0i	−1.65522	−	0.569463i
$946$	−5760.59			−0.197984
$947$	−12074.1	+	45061.0i	−0.414313	+	1.54624i	0.371896	+	0.928274i	$0.378708\pi$
$947$	−12074.1	+	45061.0i	−0.414313	+	1.54624i	−0.786209	+	0.617961i	$0.787959\pi$
$948$	−58.6179	+	731.761i	−0.00200825	+	0.0250701i
$949$	−2437.51	−	1407.30i	−0.0833772	−	0.0481379i
$950$	−53923.7	+	4252.28i	−1.84159	+	0.145223i
$951$	−40543.9	−	14421.0i	−1.38247	−	0.491729i
$952$	−21847.8	−	5854.11i	−0.743795	−	0.199299i
$953$	19475.8	−	19475.8i	0.661997	−	0.661997i	−0.293854	−	0.955850i	$-0.594938\pi$
$953$	19475.8	−	19475.8i	0.661997	−	0.661997i	0.955850	+	0.293854i	$0.0949379\pi$
$954$	−14887.0	−	39107.7i	−0.505224	−	1.32721i
$955$	14971.4	+	17998.3i	0.507291	+	0.609855i
$956$	5315.33	−	3068.81i	0.179822	−	0.103820i
$957$	−11318.5	+	16419.4i	−0.382315	+	0.554613i
$958$	−3328.57	+	891.887i	−0.112256	+	0.0300789i
$959$	28650.0	−	49623.3i	0.964710	−	1.67093i
$960$	−2325.62	−	25680.8i	−0.0781866	−	0.863380i
$961$	12462.4	+	21585.5i	0.418327	+	0.724563i
$962$	−1480.93	−	1480.93i	−0.0496331	−	0.0496331i
$963$	1224.01	+	1694.63i	0.0409586	+	0.0567067i
$964$			4585.35i			0.153199i
$965$	11499.9	+	24940.1i	0.383621	+	0.831970i
$966$	1956.46	−	5500.48i	0.0651636	−	0.183204i
$967$	838.365	+	3128.82i	0.0278800	+	0.104050i	0.978464	−	0.206418i	$-0.0661808\pi$
$967$	838.365	+	3128.82i	0.0278800	+	0.104050i	−0.950584	+	0.310468i	$0.899514\pi$
$968$	−5656.84	−	21111.6i	−0.187828	−	0.700984i
$969$	−16088.8	−	18890.9i	−0.533382	−	0.626277i
$970$	31840.3	+	11743.7i	1.05395	+	0.388730i
$971$		−	2493.85i		−	0.0824218i	−0.999150	−	0.0412109i	$-0.986878\pi$
$971$		−	2493.85i		−	0.0824218i	0.999150	−	0.0412109i	$-0.0131216\pi$
$972$	−2662.44	+	2013.62i	−0.0878577	+	0.0664473i
$973$	11922.7	+	11922.7i	0.392830	+	0.392830i
$974$	−23821.4	−	41260.0i	−0.783664	−	1.35735i
$975$	−2850.31	−	4951.04i	−0.0936235	−	0.162626i
$976$	15884.5	−	27512.8i	0.520954	−	0.902319i
$977$	50513.8	−	13535.1i	1.65413	−	0.443222i	0.693362	−	0.720590i	$-0.256129\pi$
$977$	50513.8	−	13535.1i	1.65413	−	0.443222i	0.960764	+	0.277368i	$0.0894622\pi$
$978$	16415.2	+	34539.0i	0.536707	+	1.12928i
$979$	−1886.83	+	1089.36i	−0.0615969	+	0.0355630i
$980$	5362.56	−	4460.70i	0.174797	−	0.145400i
$981$	−4681.61	+	29034.1i	−0.152367	+	0.944941i
$982$	−28790.5	+	28790.5i	−0.935582	+	0.935582i
$983$	−27885.8	−	7471.98i	−0.904801	−	0.242441i	−0.223724	−	0.974653i	$-0.571821\pi$
$983$	−27885.8	−	7471.98i	−0.904801	−	0.242441i	−0.681077	+	0.732212i	$0.738488\pi$
$984$	−3262.08	−	17738.6i	−0.105682	−	0.574682i
$985$	−16609.8	+	23506.2i	−0.537292	+	0.760375i
$986$	18783.8	+	10844.8i	0.606691	+	0.350273i
$987$	−26730.4	−	18426.3i	−0.862046	−	0.594240i
$988$	291.296	−	1087.13i	0.00937992	−	0.0350064i
$989$	1296.20			0.0416752
$990$	15027.3	−	4194.17i	0.482422	−	0.134646i
$991$	33344.3			1.06884			0.534418	−	0.845220i	$-0.320531\pi$
$991$	33344.3			1.06884			0.534418	+	0.845220i	$0.320531\pi$
$992$	−716.874	+	2675.41i	−0.0229443	+	0.0856294i
$993$	−35895.7	+	17060.0i	−1.14715	+	0.545198i
$994$	36390.4	+	21010.0i	1.16120	+	0.670419i
$995$	2042.11	−	351.061i	0.0650645	−	0.0111853i
$996$	528.078	−	449.749i	0.0168000	−	0.0143081i
$997$	−19265.6	−	5162.21i	−0.611984	−	0.163981i	−0.0605030	−	0.998168i	$-0.519270\pi$
$997$	−19265.6	−	5162.21i	−0.611984	−	0.163981i	−0.551481	+	0.834187i	$0.685937\pi$
$998$	25914.9	−	25914.9i	0.821966	−	0.821966i
$999$	5817.01	+	9582.26i	0.184226	+	0.303473i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.4.l.a.23.4	yes	64
3.2	odd	2		135.4.m.a.98.13		64
5.2	odd	4	inner	45.4.l.a.32.4	yes	64
5.3	odd	4		225.4.p.b.32.13		64
5.4	even	2		225.4.p.b.68.13		64
9.2	odd	6	inner	45.4.l.a.38.4	yes	64
9.7	even	3		135.4.m.a.8.13		64
15.2	even	4		135.4.m.a.17.13		64
45.2	even	12	inner	45.4.l.a.2.4	✓	64
45.7	odd	12		135.4.m.a.62.13		64
45.29	odd	6		225.4.p.b.218.13		64
45.38	even	12		225.4.p.b.182.13		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.l.a.2.4	✓	64	45.2	even	12	inner
45.4.l.a.23.4	yes	64	1.1	even	1	trivial
45.4.l.a.32.4	yes	64	5.2	odd	4	inner
45.4.l.a.38.4	yes	64	9.2	odd	6	inner
135.4.m.a.8.13		64	9.7	even	3
135.4.m.a.17.13		64	15.2	even	4
135.4.m.a.62.13		64	45.7	odd	12
135.4.m.a.98.13		64	3.2	odd	2
225.4.p.b.32.13		64	5.3	odd	4
225.4.p.b.68.13		64	5.4	even	2
225.4.p.b.182.13		64	45.38	even	12
225.4.p.b.218.13		64	45.29	odd	6

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:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	45.l (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.771317 + 2.87860i) q^{2} +(0.414910 - 5.17956i) q^{3} +(-0.763180 - 0.440622i) q^{4} +(1.89424 + 11.0187i) q^{5} +(14.5898 + 5.18944i) q^{6} +(31.3140 + 8.39055i) q^{7} +(-15.0012 + 15.0012i) q^{8} +(-26.6557 - 4.29810i) q^{9} +O(q^{10})\)	\(q+(-0.771317 + 2.87860i) q^{2} +(0.414910 - 5.17956i) q^{3} +(-0.763180 - 0.440622i) q^{4} +(1.89424 + 11.0187i) q^{5} +(14.5898 + 5.18944i) q^{6} +(31.3140 + 8.39055i) q^{7} +(-15.0012 + 15.0012i) q^{8} +(-26.6557 - 4.29810i) q^{9} +(-33.1795 - 3.04617i) q^{10} +(15.0191 - 8.67129i) q^{11} +(-2.59888 + 3.77012i) q^{12} +(-8.49586 + 2.27646i) q^{13} +(-48.3060 + 83.6685i) q^{14} +(57.8580 - 5.23955i) q^{15} +(-35.1367 - 60.8585i) q^{16} +(23.2549 + 23.2549i) q^{17} +(32.9325 - 73.4158i) q^{18} -145.204i q^{19} +(3.40944 - 9.24389i) q^{20} +(56.4519 - 158.711i) q^{21} +(13.3766 + 49.9223i) q^{22} +(-3.00990 - 11.2331i) q^{23} +(71.4755 + 83.9238i) q^{24} +(-117.824 + 41.7441i) q^{25} -26.2120i q^{26} +(-33.3220 + 136.281i) q^{27} +(-20.2011 - 20.2011i) q^{28} +(-110.651 - 191.653i) q^{29} +(-29.5443 + 170.591i) q^{30} +(-34.8793 + 60.4127i) q^{31} +(38.3524 - 10.2765i) q^{32} +(-38.6819 - 81.3902i) q^{33} +(-84.8784 + 49.0046i) q^{34} +(-33.1369 + 360.933i) q^{35} +(18.4492 + 15.0253i) q^{36} +(56.4980 - 56.4980i) q^{37} +(417.984 + 111.998i) q^{38} +(8.26604 + 44.9494i) q^{39} +(-193.710 - 136.878i) q^{40} +(-141.694 - 81.8068i) q^{41} +(413.323 + 284.919i) q^{42} +(-28.8478 + 107.661i) q^{43} -15.2830 q^{44} +(-3.13270 - 301.853i) q^{45} +34.6571 q^{46} +(49.8826 - 186.165i) q^{47} +(-329.799 + 156.742i) q^{48} +(613.116 + 353.983i) q^{49} +(-29.2849 - 371.365i) q^{50} +(130.099 - 110.801i) q^{51} +(7.48693 + 2.00612i) q^{52} +(367.732 - 367.732i) q^{53} +(-366.597 - 201.037i) q^{54} +(123.996 + 149.066i) q^{55} +(-595.615 + 343.879i) q^{56} +(-752.093 - 60.2466i) q^{57} +(637.039 - 170.694i) q^{58} +(-210.017 + 363.760i) q^{59} +(-46.4647 - 21.4948i) q^{60} +(226.039 + 391.511i) q^{61} +(-147.001 - 147.001i) q^{62} +(-798.632 - 358.247i) q^{63} -443.859i q^{64} +(-41.1768 - 89.3013i) q^{65} +(264.126 - 48.5718i) q^{66} +(60.3981 + 225.409i) q^{67} +(-7.50105 - 27.9943i) q^{68} +(-59.4313 + 10.9292i) q^{69} +(-1013.42 - 373.782i) q^{70} -434.936i q^{71} +(464.344 - 335.391i) q^{72} +(226.275 + 226.275i) q^{73} +(119.057 + 206.213i) q^{74} +(167.330 + 627.595i) q^{75} +(-63.9801 + 110.817i) q^{76} +(543.065 - 145.514i) q^{77} +(-135.767 - 10.8756i) q^{78} +(138.839 - 80.1586i) q^{79} +(604.025 - 502.441i) q^{80} +(692.053 + 229.138i) q^{81} +(344.779 - 344.779i) q^{82} +(-146.319 - 39.2062i) q^{83} +(-113.015 + 96.2513i) q^{84} +(-212.189 + 300.289i) q^{85} +(-287.663 - 166.082i) q^{86} +(-1038.59 + 493.605i) q^{87} +(-95.2250 + 355.384i) q^{88} -125.629 q^{89} +(871.329 + 223.807i) q^{90} -285.140 q^{91} +(-2.65245 + 9.89909i) q^{92} +(298.439 + 205.725i) q^{93} +(497.417 + 287.184i) q^{94} +(1599.96 - 275.051i) q^{95} +(-37.3150 - 202.913i) q^{96} +(-983.843 - 263.620i) q^{97} +(-1491.88 + 1491.88i) q^{98} +(-437.615 + 166.586i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 6 q^{2} - 6 q^{5} - 24 q^{6} - 2 q^{7}+O(q^{10}) \) 64 * q - 6 * q^2 - 6 * q^5 - 24 * q^6 - 2 * q^7	\( 64 q - 6 q^{2} - 6 q^{5} - 24 q^{6} - 2 q^{7} - 8 q^{10} - 36 q^{11} - 138 q^{12} - 2 q^{13} - 96 q^{15} + 316 q^{16} - 480 q^{18} + 378 q^{20} + 480 q^{21} - 34 q^{22} + 306 q^{23} - 146 q^{25} + 180 q^{27} - 232 q^{28} - 1170 q^{30} - 4 q^{31} - 1770 q^{32} - 294 q^{33} - 216 q^{36} + 136 q^{37} + 114 q^{38} + 126 q^{40} + 1992 q^{41} + 1698 q^{42} - 2 q^{43} + 1134 q^{45} - 952 q^{46} + 3462 q^{47} + 4326 q^{48} + 666 q^{50} - 2496 q^{51} - 242 q^{52} + 284 q^{55} - 7128 q^{56} - 2544 q^{57} + 534 q^{58} + 1818 q^{60} + 32 q^{61} - 4038 q^{63} - 2094 q^{65} + 2892 q^{66} + 610 q^{67} - 2694 q^{68} + 498 q^{70} - 1854 q^{72} - 8 q^{73} - 6408 q^{75} + 1368 q^{76} - 6486 q^{77} + 1434 q^{78} + 3012 q^{81} - 3784 q^{82} + 2814 q^{83} - 1658 q^{85} + 12480 q^{86} + 4830 q^{87} - 1338 q^{88} + 13914 q^{90} + 992 q^{91} + 13152 q^{92} + 8310 q^{93} + 4284 q^{95} - 7932 q^{96} + 358 q^{97}+O(q^{100}) \) 64 * q - 6 * q^2 - 6 * q^5 - 24 * q^6 - 2 * q^7 - 8 * q^10 - 36 * q^11 - 138 * q^12 - 2 * q^13 - 96 * q^15 + 316 * q^16 - 480 * q^18 + 378 * q^20 + 480 * q^21 - 34 * q^22 + 306 * q^23 - 146 * q^25 + 180 * q^27 - 232 * q^28 - 1170 * q^30 - 4 * q^31 - 1770 * q^32 - 294 * q^33 - 216 * q^36 + 136 * q^37 + 114 * q^38 + 126 * q^40 + 1992 * q^41 + 1698 * q^42 - 2 * q^43 + 1134 * q^45 - 952 * q^46 + 3462 * q^47 + 4326 * q^48 + 666 * q^50 - 2496 * q^51 - 242 * q^52 + 284 * q^55 - 7128 * q^56 - 2544 * q^57 + 534 * q^58 + 1818 * q^60 + 32 * q^61 - 4038 * q^63 - 2094 * q^65 + 2892 * q^66 + 610 * q^67 - 2694 * q^68 + 498 * q^70 - 1854 * q^72 - 8 * q^73 - 6408 * q^75 + 1368 * q^76 - 6486 * q^77 + 1434 * q^78 + 3012 * q^81 - 3784 * q^82 + 2814 * q^83 - 1658 * q^85 + 12480 * q^86 + 4830 * q^87 - 1338 * q^88 + 13914 * q^90 + 992 * q^91 + 13152 * q^92 + 8310 * q^93 + 4284 * q^95 - 7932 * q^96 + 358 * q^97

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