LMFDB - Embedded newform 74.4.f.b.7.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,4,Mod(7,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("74.7");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	74.f (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.36614134042$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			7.1
Character	$\chi$	$=$	74.7
Dual form			74.4.f.b.53.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.87939 + 0.684040i) q^{2} +(-6.73393 - 2.45095i) q^{3} +(3.06418 - 2.57115i) q^{4} +(-2.75980 - 15.6516i) q^{5} +14.3322 q^{6} +(5.01435 + 28.4378i) q^{7} +(-4.00000 + 6.92820i) q^{8} +(18.6555 + 15.6538i) q^{9} +O(q^{10})$	\(q+(-1.87939 + 0.684040i) q^{2} +(-6.73393 - 2.45095i) q^{3} +(3.06418 - 2.57115i) q^{4} +(-2.75980 - 15.6516i) q^{5} +14.3322 q^{6} +(5.01435 + 28.4378i) q^{7} +(-4.00000 + 6.92820i) q^{8} +(18.6555 + 15.6538i) q^{9} +(15.8931 + 27.5276i) q^{10} +(-0.433038 + 0.750044i) q^{11} +(-26.9357 + 9.80380i) q^{12} +(-52.8199 + 44.3212i) q^{13} +(-28.8765 - 50.0155i) q^{14} +(-19.7770 + 112.161i) q^{15} +(2.77837 - 15.7569i) q^{16} +(47.0412 + 39.4723i) q^{17} +(-45.7687 - 16.6584i) q^{18} +(98.8344 + 35.9728i) q^{19} +(-48.6991 - 40.8634i) q^{20} +(35.9333 - 203.788i) q^{21} +(0.300785 - 1.70584i) q^{22} +(30.1411 + 52.2060i) q^{23} +(43.9164 - 36.8503i) q^{24} +(-119.895 + 43.6381i) q^{25} +(68.9515 - 119.427i) q^{26} +(9.48428 + 16.4273i) q^{27} +(88.4826 + 74.2457i) q^{28} +(15.3095 - 26.5167i) q^{29} +(-39.5540 - 224.322i) q^{30} -322.240 q^{31} +(5.55674 + 31.5138i) q^{32} +(4.75437 - 3.98939i) q^{33} +(-115.409 - 42.0055i) q^{34} +(431.258 - 156.965i) q^{35} +97.4121 q^{36} +(-167.535 - 150.283i) q^{37} -210.355 q^{38} +(464.315 - 168.997i) q^{39} +(119.477 + 43.4860i) q^{40} +(-342.179 + 287.123i) q^{41} +(71.8666 + 407.576i) q^{42} +174.447 q^{43} +(0.601570 + 3.41167i) q^{44} +(193.522 - 335.190i) q^{45} +(-92.3578 - 77.4974i) q^{46} +(60.9935 + 105.644i) q^{47} +(-57.3288 + 99.2964i) q^{48} +(-461.249 + 167.881i) q^{49} +(195.478 - 164.025i) q^{50} +(-220.028 - 381.099i) q^{51} +(-47.8932 + 271.616i) q^{52} +(-42.6097 + 241.652i) q^{53} +(-29.0615 - 24.3855i) q^{54} +(12.9345 + 4.70777i) q^{55} +(-217.080 - 79.0107i) q^{56} +(-577.377 - 484.476i) q^{57} +(-10.6338 + 60.3075i) q^{58} +(25.1251 - 142.491i) q^{59} +(227.782 + 394.531i) q^{60} +(-95.3712 + 80.0259i) q^{61} +(605.614 - 220.425i) q^{62} +(-351.615 + 609.014i) q^{63} +(-32.0000 - 55.4256i) q^{64} +(839.470 + 704.399i) q^{65} +(-6.20639 + 10.7498i) q^{66} +(130.518 + 740.207i) q^{67} +245.632 q^{68} +(-75.0141 - 425.426i) q^{69} +(-703.130 + 589.996i) q^{70} +(206.389 + 75.1193i) q^{71} +(-183.075 + 66.6338i) q^{72} -377.863 q^{73} +(417.663 + 167.838i) q^{74} +914.317 q^{75} +(395.338 - 143.891i) q^{76} +(-23.5010 - 8.55366i) q^{77} +(-757.026 + 635.220i) q^{78} +(221.449 + 1255.90i) q^{79} -254.289 q^{80} +(-137.783 - 781.408i) q^{81} +(446.684 - 773.679i) q^{82} +(-767.770 - 644.235i) q^{83} +(-413.863 - 716.833i) q^{84} +(487.980 - 845.206i) q^{85} +(-327.852 + 119.328i) q^{86} +(-168.084 + 141.039i) q^{87} +(-3.46431 - 6.00035i) q^{88} +(168.268 - 954.295i) q^{89} +(-134.419 + 762.327i) q^{90} +(-1525.25 - 1279.84i) q^{91} +(226.587 + 82.4710i) q^{92} +(2169.95 + 789.796i) q^{93} +(-186.895 - 156.823i) q^{94} +(290.268 - 1646.19i) q^{95} +(39.8202 - 225.831i) q^{96} +(544.027 + 942.283i) q^{97} +(752.027 - 631.025i) q^{98} +(-19.8196 + 7.21374i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 6 q^{3} - 6 q^{5} - 36 q^{6} - 75 q^{7} - 120 q^{8} - 48 q^{9}+O(q^{10}) $ 30 * q + 6 * q^3 - 6 * q^5 - 36 * q^6 - 75 * q^7 - 120 * q^8 - 48 * q^9	\( 30 q + 6 q^{3} - 6 q^{5} - 36 q^{6} - 75 q^{7} - 120 q^{8} - 48 q^{9} + 54 q^{10} - 21 q^{11} + 24 q^{12} - 159 q^{13} + 6 q^{14} - 69 q^{15} - 171 q^{17} + 192 q^{18} - 45 q^{19} - 24 q^{20} + 579 q^{21} + 42 q^{22} + 459 q^{23} + 48 q^{24} - 204 q^{25} + 264 q^{26} + 435 q^{27} + 96 q^{28} + 273 q^{29} - 138 q^{30} - 258 q^{31} - 318 q^{33} - 558 q^{34} - 753 q^{35} + 1296 q^{36} - 891 q^{37} - 2556 q^{38} - 504 q^{39} + 96 q^{40} + 648 q^{41} + 1158 q^{42} - 216 q^{43} + 84 q^{44} + 1731 q^{45} - 6 q^{46} + 48 q^{47} + 144 q^{48} + 1731 q^{49} + 240 q^{50} + 972 q^{51} + 48 q^{52} - 135 q^{53} + 360 q^{54} + 765 q^{55} + 408 q^{56} - 405 q^{57} - 762 q^{58} + 1836 q^{59} + 108 q^{60} - 684 q^{61} - 204 q^{62} - 3264 q^{63} - 960 q^{64} - 1350 q^{65} + 252 q^{66} + 1095 q^{67} - 432 q^{68} - 5823 q^{69} - 1146 q^{70} + 4179 q^{71} + 768 q^{72} - 2658 q^{73} - 1692 q^{74} - 10416 q^{75} - 180 q^{76} + 267 q^{77} + 1530 q^{78} + 4866 q^{79} - 864 q^{80} - 2076 q^{81} + 1800 q^{82} - 186 q^{83} + 504 q^{84} + 753 q^{85} + 648 q^{86} - 525 q^{87} - 168 q^{88} + 687 q^{89} + 768 q^{90} + 3990 q^{91} + 132 q^{92} + 3753 q^{93} + 6210 q^{94} + 9000 q^{95} - 384 q^{96} + 7428 q^{97} - 1542 q^{98} + 6324 q^{99}+O(q^{100}) \) 30 * q + 6 * q^3 - 6 * q^5 - 36 * q^6 - 75 * q^7 - 120 * q^8 - 48 * q^9 + 54 * q^10 - 21 * q^11 + 24 * q^12 - 159 * q^13 + 6 * q^14 - 69 * q^15 - 171 * q^17 + 192 * q^18 - 45 * q^19 - 24 * q^20 + 579 * q^21 + 42 * q^22 + 459 * q^23 + 48 * q^24 - 204 * q^25 + 264 * q^26 + 435 * q^27 + 96 * q^28 + 273 * q^29 - 138 * q^30 - 258 * q^31 - 318 * q^33 - 558 * q^34 - 753 * q^35 + 1296 * q^36 - 891 * q^37 - 2556 * q^38 - 504 * q^39 + 96 * q^40 + 648 * q^41 + 1158 * q^42 - 216 * q^43 + 84 * q^44 + 1731 * q^45 - 6 * q^46 + 48 * q^47 + 144 * q^48 + 1731 * q^49 + 240 * q^50 + 972 * q^51 + 48 * q^52 - 135 * q^53 + 360 * q^54 + 765 * q^55 + 408 * q^56 - 405 * q^57 - 762 * q^58 + 1836 * q^59 + 108 * q^60 - 684 * q^61 - 204 * q^62 - 3264 * q^63 - 960 * q^64 - 1350 * q^65 + 252 * q^66 + 1095 * q^67 - 432 * q^68 - 5823 * q^69 - 1146 * q^70 + 4179 * q^71 + 768 * q^72 - 2658 * q^73 - 1692 * q^74 - 10416 * q^75 - 180 * q^76 + 267 * q^77 + 1530 * q^78 + 4866 * q^79 - 864 * q^80 - 2076 * q^81 + 1800 * q^82 - 186 * q^83 + 504 * q^84 + 753 * q^85 + 648 * q^86 - 525 * q^87 - 168 * q^88 + 687 * q^89 + 768 * q^90 + 3990 * q^91 + 132 * q^92 + 3753 * q^93 + 6210 * q^94 + 9000 * q^95 - 384 * q^96 + 7428 * q^97 - 1542 * q^98 + 6324 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.87939	+	0.684040i	−0.664463	+	0.241845i
$2$	−1.87939	+	0.684040i	−0.664463	+	0.241845i
$3$	−6.73393	−	2.45095i	−1.29595	−	0.471686i	−0.400272	−	0.916396i	$-0.631084\pi$
$3$	−6.73393	−	2.45095i	−1.29595	−	0.471686i	−0.895674	+	0.444711i	$0.853306\pi$
$4$	3.06418	−	2.57115i	0.383022	−	0.321394i
$5$	−2.75980	−	15.6516i	−0.246844	−	1.39992i	−0.816171	−	0.577811i	$-0.803907\pi$
$5$	−2.75980	−	15.6516i	−0.246844	−	1.39992i	0.569327	−	0.822111i	$-0.307204\pi$
$6$	14.3322			0.975183
$7$	5.01435	+	28.4378i	0.270749	+	1.53550i	0.752148	+	0.658994i	$0.229018\pi$
$7$	5.01435	+	28.4378i	0.270749	+	1.53550i	−0.481399	+	0.876502i	$0.659871\pi$
$8$	−4.00000	+	6.92820i	−0.176777	+	0.306186i
$9$	18.6555	+	15.6538i	0.690944	+	0.579771i
$10$	15.8931	+	27.5276i	0.502583	+	0.870498i
$11$	−0.433038	+	0.750044i	−0.0118696	+	0.0205588i	−0.871899	−	0.489685i	$-0.837112\pi$
$11$	−0.433038	+	0.750044i	−0.0118696	+	0.0205588i	0.860030	+	0.510244i	$0.170445\pi$
$12$	−26.9357	+	9.80380i	−0.647973	+	0.235843i
$13$	−52.8199	+	44.3212i	−1.12689	+	0.945575i	−0.998932	−	0.0462039i	$-0.985288\pi$
$13$	−52.8199	+	44.3212i	−1.12689	+	0.945575i	−0.127961	+	0.991779i	$0.540843\pi$
$14$	−28.8765	−	50.0155i	−0.551254	−	0.954801i
$15$	−19.7770	+	112.161i	−0.340427	+	1.93066i
$16$	2.77837	−	15.7569i	0.0434120	−	0.246202i
$17$	47.0412	+	39.4723i	0.671128	+	0.563143i	0.913399	−	0.407065i	$-0.133448\pi$
$17$	47.0412	+	39.4723i	0.671128	+	0.563143i	−0.242271	+	0.970209i	$0.577892\pi$
$18$	−45.7687	−	16.6584i	−0.599321	−	0.218135i
$19$	98.8344	+	35.9728i	1.19338	+	0.434354i	0.860908	−	0.508761i	$-0.169896\pi$
$19$	98.8344	+	35.9728i	1.19338	+	0.434354i	0.332469	+	0.943114i	$0.392118\pi$
$20$	−48.6991	−	40.8634i	−0.544473	−	0.456867i
$21$	35.9333	−	203.788i	0.373395	−	2.11763i
$22$	0.300785	−	1.70584i	0.00291489	−	0.0165312i
$23$	30.1411	+	52.2060i	0.273255	+	0.473291i	0.969693	−	0.244325i	$-0.0785665\pi$
$23$	30.1411	+	52.2060i	0.273255	+	0.473291i	−0.696439	+	0.717616i	$0.745233\pi$
$24$	43.9164	−	36.8503i	0.373517	−	0.313418i
$25$	−119.895	+	43.6381i	−0.959157	+	0.349105i
$26$	68.9515	−	119.427i	0.520096	−	0.900833i
$27$	9.48428	+	16.4273i	0.0676019	+	0.117090i
$28$	88.4826	+	74.2457i	0.597202	+	0.501112i
$29$	15.3095	−	26.5167i	0.0980308	−	0.169794i	−0.812839	−	0.582489i	$-0.802079\pi$
$29$	15.3095	−	26.5167i	0.0980308	−	0.169794i	0.910869	+	0.412695i	$0.135412\pi$
$30$	−39.5540	−	224.322i	−0.240718	−	1.36518i
$31$	−322.240			−1.86697			−0.933485	−	0.358616i	$-0.883249\pi$
$31$	−322.240			−1.86697			−0.933485	+	0.358616i	$0.883249\pi$
$32$	5.55674	+	31.5138i	0.0306970	+	0.174091i
$33$	4.75437	−	3.98939i	0.0250797	−	0.0210444i
$34$	−115.409	−	42.0055i	−0.582133	−	0.211879i
$35$	431.258	−	156.965i	2.08274	−	0.758056i
$36$	97.4121			0.450982
$37$	−167.535	−	150.283i	−0.744396	−	0.667739i
$37$	−167.535	−	150.283i	−0.744396	−	0.667739i
$38$	−210.355			−0.898001
$39$	464.315	−	168.997i	1.90641	−	0.693875i
$40$	119.477	+	43.4860i	0.472273	+	0.171893i
$41$	−342.179	+	287.123i	−1.30340	+	1.09368i	−0.313855	+	0.949471i	$0.601620\pi$
$41$	−342.179	+	287.123i	−1.30340	+	1.09368i	−0.989547	+	0.144213i	$0.953935\pi$
$42$	71.8666	+	407.576i	0.264030	+	1.49739i
$43$	174.447			0.618671			0.309336	−	0.950953i	$-0.399893\pi$
$43$	174.447			0.618671			0.309336	+	0.950953i	$0.399893\pi$
$44$	0.601570	+	3.41167i	0.00206114	+	0.0116893i
$45$	193.522	−	335.190i	0.641079	−	1.11038i
$46$	−92.3578	−	77.4974i	−0.296031	−	0.248399i
$47$	60.9935	+	105.644i	0.189294	+	0.327867i	0.945015	−	0.327027i	$-0.106047\pi$
$47$	60.9935	+	105.644i	0.189294	+	0.327867i	−0.755721	+	0.654894i	$0.772713\pi$
$48$	−57.3288	+	99.2964i	−0.172390	+	0.298588i
$49$	−461.249	+	167.881i	−1.34475	+	0.489448i
$50$	195.478	−	164.025i	0.552895	−	0.463934i
$51$	−220.028	−	381.099i	−0.604119	−	1.04636i
$52$	−47.8932	+	271.616i	−0.127723	+	0.724353i
$53$	−42.6097	+	241.652i	−0.110432	+	0.626291i	0.878479	+	0.477781i	$0.158559\pi$
$53$	−42.6097	+	241.652i	−0.110432	+	0.626291i	−0.988911	+	0.148510i	$0.952552\pi$
$54$	−29.0615	−	24.3855i	−0.0732365	−	0.0614527i
$55$	12.9345	+	4.70777i	0.0317107	+	0.0115417i
$56$	−217.080	−	79.0107i	−0.518010	−	0.188540i
$57$	−577.377	−	484.476i	−1.34167	−	1.12580i
$58$	−10.6338	+	60.3075i	−0.0240740	+	0.136530i
$59$	25.1251	−	142.491i	0.0554408	−	0.314420i	−0.944458	−	0.328631i	$-0.893413\pi$
$59$	25.1251	−	142.491i	0.0554408	−	0.314420i	0.999899	+	0.0142112i	$0.00452371\pi$
$60$	227.782	+	394.531i	0.490110	+	0.848895i
$61$	−95.3712	+	80.0259i	−0.200181	+	0.167972i	−0.737368	−	0.675492i	$-0.763931\pi$
$61$	−95.3712	+	80.0259i	−0.200181	+	0.167972i	0.537187	+	0.843463i	$0.319487\pi$
$62$	605.614	−	220.425i	1.24053	−	0.451517i
$63$	−351.615	+	609.014i	−0.703163	+	1.21791i
$64$	−32.0000	−	55.4256i	−0.0625000	−	0.108253i
$65$	839.470	+	704.399i	1.60190	+	1.34415i
$66$	−6.20639	+	10.7498i	−0.0115751	+	0.0200486i
$67$	130.518	+	740.207i	0.237990	+	1.34971i	0.836224	+	0.548389i	$0.184759\pi$
$67$	130.518	+	740.207i	0.237990	+	1.34971i	−0.598233	+	0.801322i	$0.704130\pi$
$68$	245.632			0.438048
$69$	−75.0141	−	425.426i	−0.130879	−	0.742250i
$70$	−703.130	+	589.996i	−1.20057	+	1.00740i
$71$	206.389	+	75.1193i	0.344983	+	0.125564i	0.508700	−	0.860944i	$-0.330126\pi$
$71$	206.389	+	75.1193i	0.344983	+	0.125564i	−0.163717	+	0.986507i	$0.552348\pi$
$72$	−183.075	+	66.6338i	−0.299661	+	0.109068i
$73$	−377.863			−0.605830			−0.302915	−	0.953018i	$-0.597960\pi$
$73$	−377.863			−0.605830			−0.302915	+	0.953018i	$0.597960\pi$
$74$	417.663	+	167.838i	0.656113	+	0.263659i
$75$	914.317			1.40768
$76$	395.338	−	143.891i	0.596688	−	0.217177i
$77$	−23.5010	−	8.55366i	−0.0347816	−	0.0126595i
$78$	−757.026	+	635.220i	−1.09893	+	0.922109i
$79$	221.449	+	1255.90i	0.315380	+	1.78861i	0.570083	+	0.821587i	$0.306911\pi$
$79$	221.449	+	1255.90i	0.315380	+	1.78861i	−0.254703	+	0.967019i	$0.581978\pi$
$80$	−254.289			−0.355380
$81$	−137.783	−	781.408i	−0.189003	−	1.07189i
$82$	446.684	−	773.679i	0.601560	−	1.04193i
$83$	−767.770	−	644.235i	−1.01535	−	0.851976i	−0.0263100	−	0.999654i	$-0.508376\pi$
$83$	−767.770	−	644.235i	−1.01535	−	0.851976i	−0.989036	+	0.147678i	$0.952820\pi$
$84$	−413.863	−	716.833i	−0.537574	−	0.931105i
$85$	487.980	−	845.206i	0.622693	−	1.07854i
$86$	−327.852	+	119.328i	−0.411084	+	0.149622i
$87$	−168.084	+	141.039i	−0.207132	+	0.173805i
$88$	−3.46431	−	6.00035i	−0.00419655	−	0.00726863i
$89$	168.268	−	954.295i	0.200409	−	1.13657i	−0.704094	−	0.710106i	$-0.748647\pi$
$89$	168.268	−	954.295i	0.200409	−	1.13657i	0.904503	−	0.426467i	$-0.140242\pi$
$90$	−134.419	+	762.327i	−0.157433	+	0.892849i
$91$	−1525.25	−	1279.84i	−1.75703	−	1.47432i
$92$	226.587	+	82.4710i	0.256775	+	0.0934586i
$93$	2169.95	+	789.796i	2.41949	+	0.880623i
$94$	−186.895	−	156.823i	−0.205072	−	0.172075i
$95$	290.268	−	1646.19i	0.313483	−	1.77785i
$96$	39.8202	−	225.831i	0.0423347	−	0.240092i
$97$	544.027	+	942.283i	0.569460	+	0.986333i	0.996619	+	0.0821571i	$0.0261809\pi$
$97$	544.027	+	942.283i	0.569460	+	0.986333i	−0.427160	+	0.904176i	$0.640486\pi$
$98$	752.027	−	631.025i	0.775165	−	0.650441i
$99$	−19.8196	+	7.21374i	−0.0201206	+	0.00732332i
$100$	−255.178	+	441.982i	−0.255178	+	0.441982i
$101$	−747.409	−	1294.55i	−0.736336	−	1.27537i	−0.954135	−	0.299378i	$-0.903221\pi$
$101$	−747.409	−	1294.55i	−0.736336	−	1.27537i	0.217798	−	0.975994i	$-0.430112\pi$
$102$	674.205	+	565.725i	0.654473	+	0.549168i
$103$	−349.807	+	605.883i	−0.334636	+	0.579606i	−0.983415	−	0.181371i	$-0.941947\pi$
$103$	−349.807	+	605.883i	−0.334636	+	0.579606i	0.648779	+	0.760977i	$0.275280\pi$
$104$	−95.7864	−	543.232i	−0.0903137	−	0.512195i
$105$	−3288.78			−3.05668
$106$	−85.2194	−	483.303i	−0.0780872	−	0.442854i
$107$	−1260.61	+	1057.77i	−1.13895	+	0.955690i	−0.999404	−	0.0345263i	$-0.989008\pi$
$107$	−1260.61	+	1057.77i	−1.13895	+	0.955690i	−0.139543	+	0.990216i	$0.544563\pi$
$108$	71.2985	+	25.9505i	0.0635250	+	0.0231212i
$109$	1483.07	−	539.793i	1.30323	−	0.474338i	0.405184	−	0.914235i	$-0.367207\pi$
$109$	1483.07	−	539.793i	1.30323	−	0.474338i	0.898048	+	0.439897i	$0.144985\pi$
$110$	−27.5292			−0.0238619
$111$	759.836	+	1422.61i	0.649734	+	1.21647i
$112$	462.024			0.389796
$113$	711.549	−	258.983i	0.592362	−	0.215602i	−0.0284061	−	0.999596i	$-0.509043\pi$
$113$	711.549	−	258.983i	0.592362	−	0.215602i	0.620768	+	0.783994i	$0.286821\pi$
$114$	1416.51	+	515.569i	1.16376	+	0.423574i
$115$	733.923	−	615.835i	0.595119	−	0.499364i
$116$	−21.2677	−	120.615i	−0.0170229	−	0.0965415i
$117$	−1679.18			−1.32684
$118$	50.2502	+	284.983i	0.0392026	+	0.222329i
$119$	−886.623	+	1535.68i	−0.682996	+	1.18298i
$120$	−697.966	−	585.663i	−0.530961	−	0.445529i
$121$	665.125	+	1152.03i	0.499718	+	0.865537i
$122$	124.498	−	215.637i	0.0923897	−	0.160024i
$123$	3007.94	−	1094.80i	2.20501	−	0.802559i
$124$	−987.402	+	828.529i	−0.715091	+	0.600033i
$125$	20.5750	+	35.6369i	0.0147223	+	0.0254997i
$126$	244.229	−	1385.09i	0.172680	−	0.979315i
$127$	153.989	−	873.315i	0.107593	−	0.610191i	−0.882560	−	0.470200i	$-0.844182\pi$
$127$	153.989	−	873.315i	0.107593	−	0.610191i	0.990153	−	0.139990i	$-0.0447072\pi$
$128$	98.0537	+	82.2768i	0.0677094	+	0.0568149i
$129$	−1174.71	−	427.560i	−0.801764	−	0.291818i
$130$	−2059.52	−	749.605i	−1.38948	−	0.505729i
$131$	1134.45	+	951.918i	0.756622	+	0.634882i	0.937245	−	0.348671i	$-0.113367\pi$
$131$	1134.45	+	951.918i	0.756622	+	0.634882i	−0.180623	+	0.983552i	$0.557811\pi$
$132$	4.31091	−	24.4484i	0.00284255	−	0.0161209i
$133$	−527.396	+	2991.01i	−0.343842	+	1.95003i
$134$	−751.625	−	1301.85i	−0.484556	−	0.839276i
$135$	230.938	−	193.780i	0.147230	−	0.123540i
$136$	−461.637	+	168.022i	−0.291066	+	0.105940i
$137$	343.767	−	595.423i	0.214380	−	0.371317i	−0.738701	−	0.674034i	$-0.764560\pi$
$137$	343.767	−	595.423i	0.214380	−	0.371317i	0.953081	+	0.302717i	$0.0978936\pi$
$138$	431.989	+	748.226i	0.266473	+	0.461545i
$139$	−217.984	−	182.910i	−0.133015	−	0.111613i	0.573853	−	0.818958i	$-0.305448\pi$
$139$	−217.984	−	182.910i	−0.133015	−	0.111613i	−0.706868	+	0.707345i	$0.749893\pi$
$140$	917.871	−	1589.80i	0.554102	−	0.959732i
$141$	−151.798	−	860.890i	−0.0906646	−	0.514185i
$142$	−439.268			−0.259596
$143$	−10.3698	−	58.8100i	−0.00606410	−	0.0343912i
$144$	298.488	−	250.461i	0.172736	−	0.144943i
$145$	−457.281	−	166.437i	−0.261897	−	0.0953228i
$146$	710.151	−	258.474i	0.402551	−	0.146517i
$147$	3517.48			1.97359
$148$	−899.758	−	29.7344i	−0.499727	−	0.0165145i
$149$	522.815			0.287454			0.143727	−	0.989617i	$-0.454091\pi$
$149$	522.815			0.287454			0.143727	+	0.989617i	$0.454091\pi$
$150$	−1718.35	+	625.430i	−0.935353	+	0.340441i
$151$	−1253.14	−	456.107i	−0.675360	−	0.245811i	−0.0185060	−	0.999829i	$-0.505891\pi$
$151$	−1253.14	−	456.107i	−0.675360	−	0.245811i	−0.656854	+	0.754018i	$0.728113\pi$
$152$	−644.564	+	540.854i	−0.343954	+	0.288612i
$153$	259.686	+	1472.75i	0.137218	+	0.778201i
$154$	50.0185			0.0261727
$155$	889.319	+	5043.58i	0.460851	+	2.61361i
$156$	988.227	−	1711.66i	0.507189	−	0.878477i
$157$	−937.081	−	786.304i	−0.476352	−	0.399707i	0.372753	−	0.927930i	$-0.378414\pi$
$157$	−937.081	−	786.304i	−0.476352	−	0.399707i	−0.849105	+	0.528224i	$0.822858\pi$
$158$	−1275.28	−	2208.84i	−0.642123	−	1.11219i
$159$	879.207	−	1522.83i	0.438526	−	0.759550i
$160$	477.907	−	173.944i	0.236137	−	0.0859467i
$161$	−1333.48	+	1118.93i	−0.652753	+	0.547725i
$162$	793.462	+	1374.32i	0.384816	+	0.666522i
$163$	−501.432	+	2843.76i	−0.240952	+	1.36651i	0.588756	+	0.808311i	$0.299618\pi$
$163$	−501.432	+	2843.76i	−0.240952	+	1.36651i	−0.829708	+	0.558197i	$0.811493\pi$
$164$	−310.263	+	1759.59i	−0.147729	+	0.837810i
$165$	−75.5615	−	63.4036i	−0.0356512	−	0.0299149i
$166$	1883.62	+	685.581i	0.880705	+	0.320551i
$167$	−2540.06	−	924.507i	−1.17698	−	0.428386i	−0.321847	−	0.946792i	$-0.604304\pi$
$167$	−2540.06	−	924.507i	−1.17698	−	0.428386i	−0.855135	+	0.518405i	$0.826526\pi$
$168$	1268.15	+	1064.11i	0.582381	+	0.488676i
$169$	444.072	−	2518.46i	0.202126	−	1.14632i
$170$	−338.947	+	1922.27i	−0.152918	+	0.867242i
$171$	1280.69	+	2218.23i	0.572731	+	0.991999i
$172$	534.535	−	448.528i	0.236965	−	0.198837i
$173$	−1152.23	+	419.377i	−0.506372	+	0.184304i	−0.582558	−	0.812789i	$-0.697948\pi$
$173$	−1152.23	+	419.377i	−0.506372	+	0.184304i	0.0761856	+	0.997094i	$0.475726\pi$
$174$	219.418	−	380.043i	0.0955980	−	0.165581i
$175$	−1842.16	−	3190.72i	−0.795739	−	1.37826i
$176$	10.6152	+	8.90725i	0.00454633	+	0.00381483i
$177$	−518.430	+	897.947i	−0.220156	+	0.381321i
$178$	336.536	+	1908.59i	0.141710	+	0.803679i
$179$	−773.588			−0.323021			−0.161510	−	0.986871i	$-0.551637\pi$
$179$	−773.588			−0.323021			−0.161510	+	0.986871i	$0.551637\pi$
$180$	−268.838	−	1524.65i	−0.111322	−	0.631339i
$181$	285.724	−	239.751i	0.117335	−	0.0984560i	−0.582232	−	0.813023i	$-0.697821\pi$
$181$	285.724	−	239.751i	0.117335	−	0.0984560i	0.699567	+	0.714567i	$0.253376\pi$
$182$	3742.00	+	1361.98i	1.52404	+	0.554705i
$183$	838.363	−	305.139i	0.338653	−	0.123260i
$184$	−482.258			−0.193220
$185$	−1889.80	+	3036.95i	−0.751032	+	1.20692i
$186$	−4618.42			−1.82064
$187$	−49.9766	+	18.1900i	−0.0195436	+	0.00711329i
$188$	458.521	+	166.888i	0.177878	+	0.0647423i
$189$	−419.597	+	352.084i	−0.161488	+	0.135504i
$190$	580.537	+	3292.39i	0.221666	+	1.25713i
$191$	1913.11			0.724752			0.362376	−	0.932032i	$-0.381966\pi$
$191$	1913.11			0.724752			0.362376	+	0.932032i	$0.381966\pi$
$192$	79.6404	+	451.663i	0.0299351	+	0.169771i
$193$	−799.138	+	1384.15i	−0.298048	+	0.516234i	−0.975689	−	0.219159i	$-0.929669\pi$
$193$	−799.138	+	1384.15i	−0.298048	+	0.516234i	0.677642	+	0.735392i	$0.263002\pi$
$194$	−1667.00	−	1398.78i	−0.616925	−	0.517661i
$195$	−3926.49	−	6800.87i	−1.44196	−	2.49754i
$196$	−981.701	+	1700.36i	−0.357763	+	0.619663i
$197$	3829.69	−	1393.89i	1.38505	−	0.504115i	0.461342	−	0.887223i	$-0.347368\pi$
$197$	3829.69	−	1393.89i	1.38505	−	0.504115i	0.923704	+	0.383107i	$0.125146\pi$
$198$	32.3142	−	27.1148i	0.0115983	−	0.00973215i
$199$	−558.999	−	968.214i	−0.199127	−	0.344899i	0.749118	−	0.662436i	$-0.230477\pi$
$199$	−558.999	−	968.214i	−0.199127	−	0.344899i	−0.948246	+	0.317537i	$0.897144\pi$
$200$	177.245	−	1005.21i	0.0626656	−	0.355394i
$201$	935.308	−	5304.40i	0.328217	−	1.86141i
$202$	2290.19	+	1921.70i	0.797710	+	0.669358i
$203$	830.844	+	302.403i	0.287260	+	0.104554i
$204$	−1654.07	−	602.032i	−0.567686	−	0.206621i
$205$	5438.28	+	4563.26i	1.85281	+	1.55469i
$206$	242.973	−	1377.97i	0.0821783	−	0.466056i
$207$	−254.925	+	1445.75i	−0.0855967	+	0.485443i
$208$	551.612	+	955.420i	0.183882	+	0.318493i
$209$	−69.7802	+	58.5526i	−0.0230947	+	0.0193788i
$210$	6180.88	−	2249.66i	2.03105	−	0.739243i
$211$	1848.88	−	3202.35i	0.603231	−	1.04483i	−0.389097	−	0.921197i	$-0.627213\pi$
$211$	1848.88	−	3202.35i	0.603231	−	1.04483i	0.992328	−	0.123631i	$-0.0394538\pi$
$212$	490.759	+	850.020i	0.158988	+	0.275375i
$213$	−1205.69	−	1011.70i	−0.387853	−	0.325447i
$214$	1645.60	−	2850.27i	0.525659	−	0.910469i
$215$	−481.438	−	2730.37i	−0.152715	−	0.866091i
$216$	−151.748			−0.0478017
$217$	−1615.83	−	9163.80i	−0.505481	−	2.86672i
$218$	−2418.02	+	2028.96i	−0.751233	+	0.630360i
$219$	2544.51	+	926.125i	0.785123	+	0.285761i
$220$	51.7380	−	18.8311i	0.0158553	−	0.00577087i
$221$	−4234.17			−1.28878
$222$	−2401.15	−	2153.88i	−0.725922	−	0.651167i
$223$	−2543.94			−0.763922			−0.381961	−	0.924178i	$-0.624751\pi$
$223$	−2543.94			−0.763922			−0.381961	+	0.924178i	$0.624751\pi$
$224$	−868.320	+	316.043i	−0.259005	+	0.0942700i
$225$	−2919.80	−	1062.72i	−0.865125	−	0.314880i
$226$	−1160.12	+	973.456i	−0.341460	+	0.286519i
$227$	−733.420	−	4159.43i	−0.214444	−	1.21617i	−0.881868	−	0.471496i	$-0.843714\pi$
$227$	−733.420	−	4159.43i	−0.214444	−	1.21617i	0.667424	−	0.744678i	$-0.267397\pi$
$228$	−3014.85			−0.875715
$229$	88.4186	+	501.447i	0.0255147	+	0.144701i	0.994904	−	0.100828i	$-0.0321493\pi$
$229$	88.4186	+	501.447i	0.0255147	+	0.144701i	−0.969389	+	0.245529i	$0.921038\pi$
$230$	−958.069	+	1659.42i	−0.274666	+	0.475736i
$231$	137.289	+	115.200i	0.0391038	+	0.0328120i
$232$	122.476	+	212.134i	0.0346591	+	0.0600314i
$233$	−499.953	+	865.944i	−0.140571	+	0.243476i	−0.927712	−	0.373297i	$-0.878227\pi$
$233$	−499.953	+	865.944i	−0.140571	+	0.243476i	0.787141	+	0.616773i	$0.211560\pi$
$234$	3155.82	−	1148.62i	0.881634	−	0.320889i
$235$	1485.16	−	1246.20i	0.412262	−	0.345928i
$236$	−289.379	−	501.219i	−0.0798177	−	0.138248i
$237$	1586.93	−	8999.91i	0.434945	−	2.46670i
$238$	615.842	−	3492.61i	0.167727	−	0.951229i
$239$	1290.09	+	1082.51i	0.349158	+	0.292978i	0.800452	−	0.599397i	$-0.204593\pi$
$239$	1290.09	+	1082.51i	0.349158	+	0.292978i	−0.451294	+	0.892375i	$0.649037\pi$
$240$	1712.36	+	623.250i	0.460553	+	0.167627i
$241$	5348.84	+	1946.82i	1.42966	+	0.520355i	0.936835	−	0.349771i	$-0.113741\pi$
$241$	5348.84	+	1946.82i	1.42966	+	0.520355i	0.492829	+	0.870126i	$0.335963\pi$
$242$	−2038.06	−	1710.14i	−0.541370	−	0.454263i
$243$	−898.435	+	5095.28i	−0.237179	+	1.34511i
$244$	−86.4756	+	490.427i	−0.0226886	+	0.128674i
$245$	3900.56	+	6755.96i	1.01713	+	1.76173i
$246$	−4904.19	+	4115.10i	−1.27105	+	1.06654i
$247$	−6814.78	+	2480.38i	−1.75552	+	0.638958i
$248$	1288.96	−	2232.55i	0.330037	−	0.571641i
$249$	3591.12	+	6220.00i	0.913968	+	1.58304i
$250$	−63.0454	−	52.9014i	−0.0159494	−	0.0133831i
$251$	−1899.13	+	3289.38i	−0.477577	+	0.827187i	−0.999670	−	0.0257014i	$-0.991818\pi$
$251$	−1899.13	+	3289.38i	−0.477577	+	0.827187i	0.522093	+	0.852889i	$0.325151\pi$
$252$	488.458	+	2770.18i	0.122103	+	0.692480i
$253$	−52.2090			−0.0129737
$254$	307.978	+	1746.63i	0.0760798	+	0.431470i
$255$	−5357.58	+	4495.55i	−1.31571	+	1.10401i
$256$	−240.561	−	87.5572i	−0.0587308	−	0.0213763i
$257$	1654.63	−	602.234i	0.401606	−	0.146173i	−0.133317	−	0.991073i	$-0.542563\pi$
$257$	1654.63	−	602.234i	0.401606	−	0.146173i	0.534923	+	0.844901i	$0.320341\pi$
$258$	2500.20			0.603317
$259$	3433.63	−	5517.90i	0.823765	−	1.32381i
$260$	4383.40			1.04556
$261$	700.694	−	255.032i	0.166176	−	0.0604830i
$262$	−2783.22	−	1013.01i	−0.656290	−	0.238870i
$263$	666.581	−	559.328i	0.156286	−	0.131139i	−0.561292	−	0.827618i	$-0.689695\pi$
$263$	666.581	−	559.328i	0.156286	−	0.131139i	0.717577	+	0.696479i	$0.245251\pi$
$264$	8.62183	+	48.8968i	0.00200999	+	0.0113992i
$265$	3899.83			0.904018
$266$	−1054.79	−	5982.02i	−0.243133	−	1.37888i
$267$	−3472.03	+	6013.74i	−0.795824	+	1.37841i
$268$	2303.11	+	1932.54i	0.524944	+	0.440481i
$269$	1774.89	+	3074.20i	0.402294	+	0.696793i	0.994002	−	0.109359i	$-0.0348797\pi$
$269$	1774.89	+	3074.20i	0.402294	+	0.696793i	−0.591709	+	0.806152i	$0.701546\pi$
$270$	−301.468	+	522.158i	−0.0679510	+	0.117695i
$271$	5176.50	−	1884.09i	1.16033	−	0.422326i	0.311116	−	0.950372i	$-0.399297\pi$
$271$	5176.50	−	1884.09i	1.16033	−	0.422326i	0.849216	+	0.528046i	$0.177075\pi$
$272$	752.660	−	631.557i	0.167782	−	0.140786i
$273$	7134.13	+	12356.7i	1.58160	+	2.73941i
$274$	−238.778	+	1354.18i	−0.0526465	+	0.298573i
$275$	19.1885	−	108.823i	0.00420767	−	0.0238629i
$276$	−1323.69	−	1110.71i	−0.288684	−	0.242235i
$277$	−4243.42	−	1544.48i	−0.920443	−	0.335014i	−0.162028	−	0.986786i	$-0.551804\pi$
$277$	−4243.42	−	1544.48i	−0.920443	−	0.335014i	−0.758415	+	0.651772i	$0.774026\pi$
$278$	534.793	+	194.649i	0.115377	+	0.0419937i
$279$	−6011.55	−	5044.29i	−1.28997	−	1.08242i
$280$	−637.546	+	3615.70i	−0.136074	+	0.771713i
$281$	253.385	−	1437.02i	0.0537925	−	0.305072i	−0.946027	−	0.324089i	$-0.894942\pi$
$281$	253.385	−	1437.02i	0.0537925	−	0.305072i	0.999819	+	0.0190165i	$0.00605350\pi$
$282$	874.171	+	1514.11i	0.184596	+	0.319730i
$283$	−57.3757	+	48.1439i	−0.0120517	+	0.0101126i	−0.648794	−	0.760964i	$-0.724726\pi$
$283$	−57.3757	+	48.1439i	−0.0120517	+	0.0101126i	0.636742	+	0.771077i	$0.280282\pi$
$284$	825.554	−	300.477i	0.172492	−	0.0627818i
$285$	−5989.39	+	10373.9i	−1.24485	+	2.15613i
$286$	59.7173	+	103.433i	0.0123467	+	0.0213851i
$287$	−9880.94	−	8291.09i	−2.03224	−	1.70525i
$288$	−389.648	+	674.891i	−0.0797231	+	0.138084i
$289$	−198.317	−	1124.71i	−0.0403657	−	0.228925i
$290$	973.256			0.197074
$291$	−1353.95	−	7678.65i	−0.272750	−	1.54684i
$292$	−1157.84	+	971.544i	−0.232046	+	0.194710i
$293$	−6142.13	−	2235.55i	−1.22466	−	0.445742i	−0.352898	−	0.935662i	$-0.614804\pi$
$293$	−6142.13	−	2235.55i	−1.22466	−	0.445742i	−0.871767	+	0.489920i	$0.837026\pi$
$294$	−6610.71	+	2406.10i	−1.31138	+	0.477302i
$295$	−2299.56			−0.453849
$296$	1711.33	−	559.588i	0.336044	−	0.109883i
$297$	−16.4282			−0.00320964
$298$	−982.570	+	357.626i	−0.191003	+	0.0695192i
$299$	−3905.88	−	1421.62i	−0.755461	−	0.274965i
$300$	2801.63	−	2350.85i	0.539174	−	0.452421i
$301$	874.736	+	4960.87i	0.167505	+	0.949966i
$302$	2667.13			0.508200
$303$	1860.12	+	10549.3i	0.352677	+	2.00013i
$304$	841.419	−	1457.38i	0.158746	−	0.274956i
$305$	1515.74	+	1271.86i	0.284561	+	0.238775i
$306$	−1495.47	−	2590.23i	−0.279380	−	0.483900i
$307$	2786.88	−	4827.03i	0.518097	−	0.897371i	−0.481682	−	0.876346i	$-0.659974\pi$
$307$	2786.88	−	4827.03i	0.518097	−	0.897371i	0.999779	−	0.0210247i	$-0.00669286\pi$
$308$	−94.0039	+	34.2146i	−0.0173908	+	0.00632974i
$309$	3840.56	−	3222.61i	0.707061	−	0.593295i
$310$	−5121.38	−	8870.50i	−0.938307	−	1.62520i
$311$	−1063.93	+	6033.85i	−0.193987	+	1.10015i	0.719867	+	0.694112i	$0.244203\pi$
$311$	−1063.93	+	6033.85i	−0.193987	+	1.10015i	−0.913854	+	0.406043i	$0.866908\pi$
$312$	−686.415	+	3892.85i	−0.124553	+	0.706376i
$313$	5069.05	+	4253.44i	0.915398	+	0.768110i	0.973138	−	0.230221i	$-0.0739450\pi$
$313$	5069.05	+	4253.44i	0.915398	+	0.768110i	−0.0577400	+	0.998332i	$0.518389\pi$
$314$	2299.00	+	836.768i	0.413185	+	0.150387i
$315$	10502.4	+	3822.57i	1.87856	+	0.683739i
$316$	3907.67	+	3278.92i	0.695644	+	0.583715i
$317$	1220.80	−	6923.49i	0.216299	−	1.22669i	−0.662339	−	0.749204i	$-0.730436\pi$
$317$	1220.80	−	6923.49i	0.216299	−	1.22669i	0.878638	−	0.477489i	$-0.158453\pi$
$318$	−610.691	+	3463.40i	−0.107691	+	0.610748i
$319$	13.2592	+	22.9655i	0.00232718	+	0.00403079i
$320$	−779.186	+	653.815i	−0.136118	+	0.114217i
$321$	11081.4	−	4033.29i	1.92680	−	0.701297i
$322$	1740.74	−	3015.05i	0.301266	−	0.521808i
$323$	3229.36	+	5593.42i	0.556305	+	0.963549i
$324$	−2431.31	−	2040.11i	−0.416891	−	0.349813i
$325$	4398.73	−	7618.83i	0.750762	−	1.30036i
$326$	−1002.86	−	5687.53i	−0.170379	−	0.966267i
$327$	−11309.9			−1.91266
$328$	−620.526	−	3519.18i	−0.104460	−	0.592421i
$329$	−2698.43	+	2264.25i	−0.452186	+	0.379429i
$330$	185.380	+	67.4727i	0.0309237	+	0.0112553i
$331$	−2152.09	+	783.296i	−0.357370	+	0.130072i	−0.514465	−	0.857511i	$-0.672009\pi$
$331$	−2152.09	+	783.296i	−0.357370	+	0.130072i	0.157095	+	0.987584i	$0.449787\pi$
$332$	−4009.01			−0.662720
$333$	−772.956	−	5426.17i	−0.127200	−	0.892949i
$334$	5406.16			0.885664
$335$	11225.2	−	4085.64i	1.83074	−	0.666336i
$336$	−3111.24	−	1132.40i	−0.505154	−	0.183861i
$337$	718.011	−	602.483i	0.116061	−	0.0973867i	−0.582910	−	0.812537i	$-0.698086\pi$
$337$	718.011	−	602.483i	0.116061	−	0.0973867i	0.698971	+	0.715150i	$0.253642\pi$
$338$	888.144	+	5036.91i	0.142925	+	0.810568i
$339$	−5426.28			−0.869365
$340$	−677.895	−	3844.53i	−0.108129	−	0.613233i
$341$	139.542	−	241.695i	0.0221603	−	0.0383827i
$342$	−3924.27	−	3292.85i	−0.620469	−	0.520635i
$343$	−2134.70	−	3697.41i	−0.336044	−	0.582045i
$344$	−697.786	+	1208.60i	−0.109367	+	0.189429i
$345$	−6451.57	+	2348.18i	−1.00679	+	0.366440i
$346$	1878.61	−	1576.34i	0.291893	−	0.244927i
$347$	6298.07	+	10908.6i	0.974346	+	1.68762i	0.682078	+	0.731280i	$0.261077\pi$
$347$	6298.07	+	10908.6i	0.974346	+	1.68762i	0.292268	+	0.956337i	$0.405590\pi$
$348$	−152.406	+	864.339i	−0.0234765	+	0.133142i
$349$	−1748.75	+	9917.68i	−0.268220	+	1.52115i	0.491488	+	0.870884i	$0.336453\pi$
$349$	−1748.75	+	9917.68i	−0.268220	+	1.52115i	−0.759708	+	0.650265i	$0.774658\pi$
$350$	5644.71	+	4736.48i	0.862065	+	0.723358i
$351$	−1229.03	−	447.332i	−0.186897	−	0.0680251i
$352$	−26.0431	−	9.47890i	−0.00394347	−	0.00143530i
$353$	−2066.63	−	1734.11i	−0.311602	−	0.261465i	0.473552	−	0.880766i	$-0.342972\pi$
$353$	−2066.63	−	1734.11i	−0.311602	−	0.261465i	−0.785154	+	0.619301i	$0.787416\pi$
$354$	360.098	−	2042.22i	0.0540649	−	0.306617i
$355$	606.146	−	3437.63i	0.0906222	−	0.513944i
$356$	−1938.03	−	3356.77i	−0.288527	−	0.499743i
$357$	9734.32	−	8168.07i	1.44312	−	1.21092i
$358$	1453.87	−	529.166i	0.214635	−	0.0781209i
$359$	−188.511	+	326.510i	−0.0277137	+	0.0480015i	−0.879550	−	0.475807i	$-0.842156\pi$
$359$	−188.511	+	326.510i	−0.0277137	+	0.0480015i	0.851836	+	0.523809i	$0.175489\pi$
$360$	1548.18	+	2681.52i	0.226656	+	0.392579i
$361$	3219.90	+	2701.81i	0.469441	+	0.393908i
$362$	−372.986	+	646.031i	−0.0541539	+	0.0937973i
$363$	−1655.34	−	9387.88i	−0.239346	−	1.35740i
$364$	−7964.30			−1.14682
$365$	1042.83	+	5914.17i	0.149545	+	0.848114i
$366$	−1366.88	+	1146.95i	−0.195213	+	0.163803i
$367$	−3679.44	−	1339.21i	−0.523339	−	0.190480i	0.0668229	−	0.997765i	$-0.478714\pi$
$367$	−3679.44	−	1339.21i	−0.523339	−	0.190480i	−0.590162	+	0.807285i	$0.700936\pi$
$368$	906.349	−	329.884i	0.128388	−	0.0467293i
$369$	−10878.1			−1.53466
$370$	1474.27	−	7000.29i	0.207145	−	0.983589i
$371$	−7085.69			−0.991566
$372$	8679.78	−	3159.18i	1.20975	−	0.440312i
$373$	−8917.62	−	3245.75i	−1.23790	−	0.450559i	−0.361604	−	0.932332i	$-0.617771\pi$
$373$	−8917.62	−	3245.75i	−1.23790	−	0.450559i	−0.876296	+	0.481773i	$0.839993\pi$
$374$	81.4826	−	68.3720i	0.0112657	−	0.00945303i
$375$	−51.2062	−	290.405i	−0.00705140	−	0.0399905i
$376$	−975.895			−0.133851
$377$	366.609	+	2079.14i	0.0500831	+	0.284036i
$378$	547.745	−	948.722i	0.0745316	−	0.129093i
$379$	2254.87	+	1892.06i	0.305607	+	0.256435i	0.782674	−	0.622432i	$-0.213855\pi$
$379$	2254.87	+	1892.06i	0.305607	+	0.256435i	−0.477066	+	0.878867i	$0.658300\pi$
$380$	−3343.18	−	5790.56i	−0.451320	−	0.781708i
$381$	−3177.41	+	5503.43i	−0.427253	+	0.740024i
$382$	−3595.47	+	1308.64i	−0.481571	+	0.175278i
$383$	−713.388	+	598.604i	−0.0951761	+	0.0798622i	−0.689134	−	0.724634i	$-0.742009\pi$
$383$	−713.388	+	598.604i	−0.0951761	+	0.0798622i	0.593958	+	0.804496i	$0.297564\pi$
$384$	−458.631	−	794.371i	−0.0609489	−	0.105567i
$385$	−69.0205	+	391.435i	−0.00913665	+	0.0518165i
$386$	555.075	−	3147.99i	0.0731932	−	0.415100i
$387$	3254.39	+	2730.75i	0.427467	+	0.358688i
$388$	4089.75	+	1488.55i	0.535117	+	0.194767i
$389$	−12022.7	−	4375.90i	−1.56703	−	0.570352i	−0.594697	−	0.803950i	$-0.702728\pi$
$389$	−12022.7	−	4375.90i	−1.56703	−	0.570352i	−0.972333	+	0.233598i	$0.924950\pi$
$390$	12031.4	+	10095.6i	1.56214	+	1.31079i
$391$	−642.813	+	3645.57i	−0.0831418	+	0.471520i
$392$	681.882	−	3867.15i	0.0878578	−	0.498266i
$393$	−5306.22	−	9190.64i	−0.681077	−	1.17966i
$394$	−6243.98	+	5239.32i	−0.798394	+	0.669932i
$395$	19045.7	−	6932.07i	2.42606	−	0.883014i
$396$	−42.1831	+	73.0633i	−0.00535299	+	0.00927164i
$397$	2812.58	+	4871.54i	0.355566	+	0.615858i	0.987215	−	0.159397i	$-0.0509549\pi$
$397$	2812.58	+	4871.54i	0.355566	+	0.615858i	−0.631649	+	0.775255i	$0.717622\pi$
$398$	1712.87	+	1437.27i	0.215725	+	0.181015i
$399$	10882.3	−	18848.6i	1.36540	−	2.36494i
$400$	354.490	+	2010.41i	0.0443113	+	0.251302i
$401$	1086.88			0.135352			0.0676760	−	0.997707i	$-0.478442\pi$
$401$	1086.88			0.135352			0.0676760	+	0.997707i	$0.478442\pi$
$402$	1870.62	+	10608.8i	0.232084	+	1.31622i
$403$	17020.7	−	14282.1i	2.10388	−	1.76536i
$404$	−5618.68	−	2045.03i	−0.691930	−	0.251842i
$405$	−11850.0	+	4313.06i	−1.45391	+	0.529179i
$406$	−1768.33			−0.216160
$407$	185.268	−	60.5808i	0.0225636	−	0.00737808i
$408$	3520.45			0.427177
$409$	8357.12	−	3041.74i	1.01035	−	0.367737i	0.216782	−	0.976220i	$-0.430444\pi$
$409$	8357.12	−	3041.74i	1.01035	−	0.367737i	0.793567	+	0.608483i	$0.208222\pi$
$410$	−13342.1	−	4856.12i	−1.60712	−	0.584943i
$411$	−3774.26	+	3166.98i	−0.452970	+	0.380087i
$412$	485.946	+	2755.94i	0.0581088	+	0.329552i
$413$	4178.12			0.497801
$414$	−509.850	−	2891.50i	−0.0605260	−	0.343260i
$415$	−7964.42	+	13794.8i	−0.942068	+	1.63171i
$416$	−1690.24	−	1418.28i	−0.199208	−	0.167156i
$417$	1019.58	+	1765.97i	0.119734	+	0.207386i
$418$	91.0916	−	157.775i	0.0106589	−	0.0184618i
$419$	3635.58	−	1323.24i	0.423890	−	0.154283i	−0.121262	−	0.992621i	$-0.538694\pi$
$419$	3635.58	−	1323.24i	0.423890	−	0.154283i	0.545152	+	0.838337i	$0.316472\pi$
$420$	−10077.4	+	8455.94i	−1.17078	+	0.982399i
$421$	−967.573	−	1675.89i	−0.112011	−	0.194009i	0.804570	−	0.593858i	$-0.202396\pi$
$421$	−967.573	−	1675.89i	−0.112011	−	0.194009i	−0.916581	+	0.399849i	$0.869063\pi$
$422$	−1284.22	+	7283.15i	−0.148139	+	0.840138i
$423$	−515.865	+	2925.62i	−0.0592960	+	0.336285i
$424$	−1503.77	−	1261.82i	−0.172240	−	0.144526i
$425$	−7362.48	−	2679.73i	−0.840313	−	0.305849i
$426$	2958.00	+	1076.62i	0.336422	+	0.122448i
$427$	−2753.98	−	2310.87i	−0.312118	−	0.261898i
$428$	−1143.02	+	6482.41i	−0.129089	+	0.732101i
$429$	−74.3110	+	421.439i	−0.00836310	+	0.0474295i
$430$	2772.49	+	4802.09i	0.310933	+	0.538552i
$431$	6702.44	−	5624.01i	0.749061	−	0.628536i	−0.186194	−	0.982513i	$-0.559615\pi$
$431$	6702.44	−	5624.01i	0.749061	−	0.628536i	0.935254	+	0.353977i	$0.115171\pi$
$432$	285.194	−	103.802i	0.0317625	−	0.0115606i
$433$	1039.09	−	1799.75i	0.115324	−	0.199748i	−0.802585	−	0.596538i	$-0.796543\pi$
$433$	1039.09	−	1799.75i	0.115324	−	0.199748i	0.917909	+	0.396790i	$0.129876\pi$
$434$	9305.17	+	16117.0i	1.02918	+	1.78258i
$435$	2671.37	+	2241.54i	0.294442	+	0.247066i
$436$	3156.50	−	5467.22i	0.346718	−	0.600533i
$437$	1100.99	+	6244.00i	0.120520	+	0.683504i
$438$	−5415.62			−0.590795
$439$	2232.65	+	12662.0i	0.242730	+	1.37659i	0.825705	+	0.564102i	$0.190778\pi$
$439$	2232.65	+	12662.0i	0.242730	+	1.37659i	−0.582974	+	0.812491i	$0.698111\pi$
$440$	−84.3544	+	70.7817i	−0.00913963	+	0.00766906i
$441$	−11232.8	−	4088.40i	−1.21291	−	0.441465i
$442$	7957.64	−	2896.34i	0.856349	−	0.311686i
$443$	−1335.45			−0.143226			−0.0716129	−	0.997433i	$-0.522815\pi$
$443$	−1335.45			−0.143226			−0.0716129	+	0.997433i	$0.522815\pi$
$444$	5986.03	+	2405.49i	0.639830	+	0.257116i
$445$	−15400.6			−1.64058
$446$	4781.04	−	1740.15i	0.507598	−	0.184750i
$447$	−3520.60	−	1281.39i	−0.372525	−	0.135588i
$448$	1415.72	−	1187.93i	0.149300	−	0.125278i
$449$	826.151	+	4685.33i	0.0868340	+	0.492460i	0.996946	+	0.0780972i	$0.0248845\pi$
$449$	826.151	+	4685.33i	0.0868340	+	0.492460i	−0.910112	+	0.414363i	$0.864004\pi$
$450$	6214.36			0.650995
$451$	−67.1779	−	380.985i	−0.00701393	−	0.0397780i
$452$	1514.43	−	2623.07i	0.157595	−	0.272962i
$453$	7320.69	+	6142.79i	0.759285	+	0.637115i
$454$	4223.60	+	7315.49i	0.436615	+	0.756240i
$455$	−15822.1	+	27404.7i	−1.63023	+	2.82364i
$456$	5666.06	−	2062.28i	0.581880	−	0.211787i
$457$	12654.0	−	10617.9i	1.29525	−	1.08684i	0.304302	−	0.952576i	$-0.401577\pi$
$457$	12654.0	−	10617.9i	1.29525	−	1.08684i	0.990945	−	0.134266i	$-0.0428675\pi$
$458$	−509.182	−	881.929i	−0.0519487	−	0.0899778i
$459$	−202.269	+	1147.12i	−0.0205689	+	0.116652i
$460$	665.468	−	3774.06i	0.0674513	−	0.382535i
$461$	−13086.2	−	10980.6i	−1.32209	−	1.10937i	−0.985856	−	0.167592i	$-0.946401\pi$
$461$	−13086.2	−	10980.6i	−1.32209	−	1.10937i	−0.336238	−	0.941777i	$-0.609155\pi$
$462$	−336.821	−	122.593i	−0.0339185	−	0.0123453i
$463$	5539.47	+	2016.20i	0.556028	+	0.202378i	0.604723	−	0.796436i	$-0.293284\pi$
$463$	5539.47	+	2016.20i	0.556028	+	0.202378i	−0.0486947	+	0.998814i	$0.515506\pi$
$464$	−375.287	−	314.903i	−0.0375480	−	0.0315065i
$465$	6372.95	−	36142.8i	0.635567	−	3.60448i
$466$	347.264	−	1969.43i	0.0345208	−	0.195777i
$467$	4892.45	+	8473.97i	0.484787	+	0.839676i	0.999847	−	0.0174782i	$-0.00556378\pi$
$467$	4892.45	+	8473.97i	0.484787	+	0.839676i	−0.515060	+	0.857154i	$0.672230\pi$
$468$	−5145.30	+	4317.42i	−0.508208	+	0.426437i
$469$	−20395.4	+	7423.30i	−2.00804	+	0.730866i
$470$	−1938.74	+	3358.00i	−0.190272	+	0.329560i
$471$	4383.05	+	7591.66i	0.428790	+	0.742686i
$472$	886.709	+	744.037i	0.0864705	+	0.0725574i
$473$	−75.5420	+	130.843i	−0.00734340	+	0.0127191i
$474$	3173.86	+	17999.8i	0.307553	+	1.74422i
$475$	−13419.5			−1.29627
$476$	1231.68	+	6985.22i	0.118601	+	0.672620i
$477$	−4577.68	+	3841.13i	−0.439408	+	0.368707i
$478$	−3165.05	−	1151.98i	−0.302858	−	0.110231i
$479$	−11903.1	+	4332.39i	−1.13542	+	0.413261i	−0.840259	−	0.542186i	$-0.817597\pi$
$479$	−11903.1	+	4332.39i	−1.13542	+	0.413261i	−0.295165	+	0.955446i	$0.595375\pi$
$480$	−3644.52			−0.346560
$481$	15509.9	+	512.557i	1.47025	+	0.0485875i
$482$	−11384.2			−1.07580
$483$	11722.0	−	4266.46i	1.10429	−	0.401927i
$484$	5000.10	+	1819.89i	0.469582	+	0.170914i
$485$	13246.8	−	11115.4i	1.24022	−	1.04067i
$486$	−1796.87	−	10190.6i	−0.167711	−	0.951137i
$487$	−1999.26			−0.186027			−0.0930133	−	0.995665i	$-0.529650\pi$
$487$	−1999.26			−0.186027			−0.0930133	+	0.995665i	$0.529650\pi$
$488$	−172.951	−	980.854i	−0.0160433	−	0.0909861i
$489$	10346.5	−	17920.7i	0.956823	−	1.65727i
$490$	−11952.0	−	10028.9i	−1.10191	−	0.924613i
$491$	−6013.98	−	10416.5i	−0.552764	−	0.957415i	−0.998074	−	0.0620383i	$-0.980240\pi$
$491$	−6013.98	−	10416.5i	−0.552764	−	0.957415i	0.445310	−	0.895376i	$-0.353093\pi$
$492$	6401.96	−	11088.5i	0.586631	−	1.01608i
$493$	1766.85	−	643.082i	0.161410	−	0.0587483i
$494$	11110.9	−	9323.16i	1.01195	−	0.849128i
$495$	167.605	+	290.300i	0.0152187	+	0.0263596i
$496$	−895.303	+	5077.52i	−0.0810490	+	0.459652i
$497$	−1101.32	+	6245.90i	−0.0993984	+	0.563716i
$498$	−11003.8	−	9233.31i	−0.990148	−	0.830832i
$499$	5221.01	+	1900.29i	0.468386	+	0.170478i	0.565421	−	0.824802i	$-0.308714\pi$
$499$	5221.01	+	1900.29i	0.468386	+	0.170478i	−0.0970352	+	0.995281i	$0.530936\pi$
$500$	154.673	+	56.2965i	0.0138344	+	0.00503531i
$501$	14838.7	+	12451.1i	1.32324	+	1.11033i
$502$	1319.12	−	7481.10i	0.117281	−	0.665135i
$503$	464.742	−	2635.69i	0.0411965	−	0.233637i	−0.957256	−	0.289241i	$-0.906597\pi$
$503$	464.742	−	2635.69i	0.0411965	−	0.233637i	0.998453	+	0.0556037i	$0.0177083\pi$
$504$	−2812.92	−	4872.11i	−0.248606	−	0.430598i
$505$	−18199.1	+	15270.8i	−1.60366	+	1.34563i
$506$	98.1209	−	35.7131i	0.00862056	−	0.00313763i
$507$	−9162.96	+	15870.7i	−0.802646	+	1.39022i
$508$	−1773.58	−	3071.92i	−0.154901	−	0.268296i
$509$	10478.9	+	8792.82i	0.912511	+	0.765687i	0.972595	−	0.232506i	$-0.0746925\pi$
$509$	10478.9	+	8792.82i	0.912511	+	0.765687i	−0.0600844	+	0.998193i	$0.519137\pi$
$510$	6993.83	−	12113.7i	0.607239	−	1.05177i
$511$	−1894.74	−	10745.6i	−0.164028	−	0.930249i
$512$	512.000			0.0441942
$513$	346.439	+	1964.75i	0.0298161	+	0.169095i
$514$	−2697.73	+	2263.66i	−0.231501	+	0.194253i
$515$	10448.4	+	3802.92i	0.894006	+	0.325391i
$516$	−4698.85	+	1710.24i	−0.400882	+	0.145909i
$517$	−105.650			−0.00898739
$518$	−2678.64	+	12719.0i	−0.227206	+	1.07884i
$519$	8786.91			0.743165
$520$	−8238.10	+	2998.42i	−0.694739	+	0.252864i
$521$	−12099.4	−	4403.80i	−1.01743	−	0.370315i	−0.221150	−	0.975240i	$-0.570981\pi$
$521$	−12099.4	−	4403.80i	−1.01743	−	0.370315i	−0.796283	+	0.604925i	$0.793203\pi$
$522$	−1142.42	+	958.605i	−0.0957901	+	0.0803774i
$523$	−766.834	−	4348.93i	−0.0641134	−	0.363605i	−0.999938	−	0.0111389i	$-0.996454\pi$
$523$	−766.834	−	4348.93i	−0.0641134	−	0.363605i	0.935825	−	0.352466i	$-0.114657\pi$
$524$	5923.69			0.493850
$525$	4584.70	+	26001.1i	0.381129	+	2.16149i
$526$	−870.160	+	1507.16i	−0.0721308	+	0.124934i
$527$	−15158.6	−	12719.6i	−1.25298	−	1.05137i
$528$	−49.6511	−	85.9983i	−0.00409240	−	0.00708825i
$529$	4266.53	−	7389.84i	0.350664	−	0.607367i
$530$	−7329.28	+	2667.64i	−0.600686	+	0.218632i
$531$	2699.25	−	2264.94i	0.220598	−	0.185104i
$532$	6074.30	+	10521.0i	0.495027	+	0.857412i
$533$	5348.28	−	30331.6i	0.434633	−	2.46493i
$534$	2411.65	−	13677.1i	0.195435	−	1.10837i
$535$	20034.9	+	16811.2i	1.61903	+	1.35853i
$536$	−5650.38	−	2056.57i	−0.455334	−	0.165728i
$537$	5209.29	+	1896.03i	0.418617	+	0.152364i
$538$	−5438.58	−	4563.51i	−0.435825	−	0.365701i
$539$	73.8203	−	418.656i	0.00589919	−	0.0334560i
$540$	209.398	−	1187.55i	0.0166871	−	0.0946373i
$541$	12103.3	+	20963.5i	0.961848	+	1.66597i	0.717854	+	0.696194i	$0.245125\pi$
$541$	12103.3	+	20963.5i	0.961848	+	1.66597i	0.243995	+	0.969777i	$0.421542\pi$
$542$	−8439.84	+	7081.87i	−0.668860	+	0.561240i
$543$	−2511.66	+	914.171i	−0.198501	+	0.0722483i
$544$	−982.528	+	1701.79i	−0.0774366	+	0.134124i
$545$	−12541.6	−	21722.7i	−0.985731	−	1.70734i
$546$	−21860.2	−	18342.9i	−1.71343	−	1.43774i
$547$	−3332.58	+	5772.20i	−0.260495	+	0.451191i	−0.966374	−	0.257142i	$-0.917219\pi$
$547$	−3332.58	+	5772.20i	−0.260495	+	0.451191i	0.705878	+	0.708333i	$0.250552\pi$
$548$	−477.557	−	2708.36i	−0.0372267	−	0.211123i
$549$	−3031.91			−0.235699
$550$	38.3769	+	217.646i	0.00297527	+	0.0168736i
$551$	2466.98	−	2070.04i	0.190739	−	0.160049i
$552$	3247.49	+	1181.99i	0.250403	+	0.0911393i
$553$	−34604.6	+	12595.0i	−2.66101	+	0.968528i
$554$	9031.52			0.692622
$555$	20169.2	−	15818.8i	1.54259	−	1.20986i
$556$	−1138.23			−0.0868196
$557$	6234.80	−	2269.28i	0.474285	−	0.172626i	−0.0938074	−	0.995590i	$-0.529904\pi$
$557$	6234.80	−	2269.28i	0.474285	−	0.172626i	0.568093	+	0.822965i	$0.307682\pi$
$558$	14748.5	+	5368.02i	1.11892	+	0.407252i
$559$	−9214.25	+	7731.68i	−0.697176	+	0.585000i
$560$	−1275.09	−	7231.41i	−0.0962187	−	0.545684i
$561$	381.122			0.0286827
$562$	506.770	+	2874.04i	0.0380370	+	0.215719i
$563$	−5265.28	+	9119.72i	−0.394147	+	0.682683i	−0.992992	−	0.118182i	$-0.962293\pi$
$563$	−5265.28	+	9119.72i	−0.394147	+	0.682683i	0.598845	+	0.800865i	$0.295627\pi$
$564$	−2678.61	−	2247.62i	−0.199982	−	0.167805i
$565$	−6017.22	−	10422.1i	−0.448047	−	0.776040i
$566$	74.8987	−	129.728i	0.00556224	−	0.00963408i
$567$	21530.6	−	7836.50i	1.59471	−	0.580427i
$568$	−1346.00	+	1129.42i	−0.0994309	+	0.0834324i
$569$	6515.94	+	11285.9i	0.480075	+	0.831513i	0.999739	−	0.0228571i	$-0.00727629\pi$
$569$	6515.94	+	11285.9i	0.480075	+	0.831513i	−0.519664	+	0.854371i	$0.673943\pi$
$570$	4160.19	−	23593.6i	0.305704	−	1.73373i
$571$	2988.99	−	16951.4i	0.219064	−	1.24237i	−0.654650	−	0.755932i	$-0.727184\pi$
$571$	2988.99	−	16951.4i	0.219064	−	1.24237i	0.873714	−	0.486441i	$-0.161705\pi$
$572$	−182.984	−	153.542i	−0.0133758	−	0.0112236i
$573$	−12882.7	−	4688.94i	−0.939240	−	0.341855i
$574$	24241.5	+	8823.19i	1.76276	+	0.641591i
$575$	−5891.93	−	4943.91i	−0.427322	−	0.358566i
$576$	270.647	−	1534.91i	0.0195780	−	0.111033i
$577$	−2682.73	+	15214.5i	−0.193559	+	1.09773i	0.720898	+	0.693041i	$0.243730\pi$
$577$	−2682.73	+	15214.5i	−0.193559	+	1.09773i	−0.914457	+	0.404684i	$0.867381\pi$
$578$	1142.06	+	1978.11i	0.0821859	+	0.142350i
$579$	8773.82	−	7362.11i	0.629754	−	0.528426i
$580$	−1829.12	+	665.746i	−0.130949	+	0.0476614i
$581$	14470.8	−	25064.1i	1.03330	−	1.78973i
$582$	7797.11	+	13505.0i	0.555327	+	0.961855i
$583$	−162.798	−	136.604i	−0.0115650	−	0.00970419i
$584$	1511.45	−	2617.91i	0.107097	−	0.185497i
$585$	4634.19	+	26281.8i	0.327522	+	1.85747i
$586$	13072.6			0.921545
$587$	−492.159	−	2791.17i	−0.0346058	−	0.196259i	0.962604	−	0.270914i	$-0.0873257\pi$
$587$	−492.159	−	2791.17i	−0.0346058	−	0.196259i	−0.997209	+	0.0746544i	$0.976215\pi$
$588$	10778.2	−	9043.98i	0.755928	−	0.634299i
$589$	−31848.4	−	11591.9i	−2.22800	−	0.810926i
$590$	4321.76	−	1572.99i	0.301566	−	0.109761i
$591$	−29205.2			−2.03273
$592$	−2833.47	+	2222.30i	−0.196714	+	0.154284i
$593$	8176.35			0.566210			0.283105	−	0.959089i	$-0.408636\pi$
$593$	8176.35			0.566210			0.283105	+	0.959089i	$0.408636\pi$
$594$	30.8750	−	11.2376i	0.00213268	−	0.000776234i
$595$	26482.7	+	9638.91i	1.82468	+	0.664129i
$596$	1602.00	−	1344.24i	0.110101	−	0.0923859i
$597$	1391.21	+	7889.97i	0.0953745	+	0.540896i
$598$	8313.10			0.568475
$599$	2257.65	+	12803.8i	0.153998	+	0.873368i	0.959696	+	0.281041i	$0.0906795\pi$
$599$	2257.65	+	12803.8i	0.153998	+	0.873368i	−0.805698	+	0.592327i	$0.798209\pi$
$600$	−3657.27	+	6334.57i	−0.248846	+	0.431013i
$601$	13816.1	+	11593.1i	0.937723	+	0.786843i	0.977188	−	0.212378i	$-0.0681208\pi$
$601$	13816.1	+	11593.1i	0.937723	+	0.786843i	−0.0394646	+	0.999221i	$0.512565\pi$
$602$	−5037.40	−	8725.04i	−0.341045	−	0.590707i
$603$	−9152.17	+	15852.0i	−0.618085	+	1.07055i
$604$	−5012.57	+	1824.43i	−0.337680	+	0.122905i
$605$	16195.5	−	13589.6i	1.08833	−	0.913219i
$606$	−10712.0	−	18553.8i	−0.718062	−	1.24372i
$607$	572.018	−	3244.07i	0.0382496	−	0.216924i	−0.959692	−	0.281054i	$-0.909316\pi$
$607$	572.018	−	3244.07i	0.0382496	−	0.216924i	0.997942	+	0.0641297i	$0.0204272\pi$
$608$	−584.443	+	3314.54i	−0.0389841	+	0.221090i
$609$	−4853.67	−	4072.72i	−0.322957	−	0.270993i
$610$	−3718.66	−	1353.48i	−0.246826	−	0.0898375i
$611$	−7903.92	−	2876.79i	−0.523336	−	0.190479i
$612$	4582.38	+	3845.08i	0.302666	+	0.253967i
$613$	−1269.56	+	7200.06i	−0.0836496	+	0.474401i	0.913990	+	0.405736i	$0.132985\pi$
$613$	−1269.56	+	7200.06i	−0.0836496	+	0.474401i	−0.997640	+	0.0686644i	$0.978126\pi$
$614$	−1935.75	+	10978.2i	−0.127232	+	0.721569i
$615$	−25436.7	−	44057.6i	−1.66781	−	2.88874i
$616$	153.265	−	128.605i	0.0100247	−	0.00841176i
$617$	−3766.37	+	1370.85i	−0.245751	+	0.0894460i	−0.461959	−	0.886901i	$-0.652853\pi$
$617$	−3766.37	+	1370.85i	−0.245751	+	0.0894460i	0.216208	+	0.976347i	$0.430631\pi$
$618$	−5013.50	+	8683.63i	−0.326331	+	0.565222i
$619$	−7871.83	−	13634.4i	−0.511140	−	0.885320i	−0.999917	−	0.0129113i	$-0.995890\pi$
$619$	−7871.83	−	13634.4i	−0.511140	−	0.885320i	0.488777	−	0.872409i	$-0.337443\pi$
$620$	15692.8	+	13167.9i	1.01652	+	0.852957i
$621$	−571.734	+	990.272i	−0.0369451	+	0.0639907i
$622$	−2127.86	−	12067.7i	−0.137169	−	0.777927i
$623$	27981.8			1.79946
$624$	−1372.83	−	7785.71i	−0.0880724	−	0.499484i
$625$	−11716.4	+	9831.21i	−0.749848	+	0.629197i
$626$	−12436.2	−	4526.41i	−0.794012	−	0.288997i
$627$	613.405	−	223.261i	0.0390702	−	0.0142204i
$628$	−4893.09			−0.310916
$629$	−1949.07	−	13682.5i	−0.123552	−	0.867340i
$630$	−22352.9			−1.41359
$631$	−14744.7	+	5366.61i	−0.930230	+	0.338576i	−0.762301	−	0.647223i	$-0.775930\pi$
$631$	−14744.7	+	5366.61i	−0.930230	+	0.338576i	−0.167930	+	0.985799i	$0.553708\pi$
$632$	−9586.93	−	3489.36i	−0.603398	−	0.219619i
$633$	−20299.0	+	17032.9i	−1.27459	+	1.06950i
$634$	2441.59	+	13847.0i	0.152947	+	0.867403i
$635$	−14093.8			−0.880778
$636$	−1221.38	−	6926.80i	−0.0761493	−	0.431864i
$637$	16922.4	−	29310.5i	1.05258	−	1.82312i
$638$	−40.6284	−	34.0913i	−0.00252115	−	0.00211550i
$639$	2674.38	+	4632.16i	0.165566	+	0.286769i
$640$	1017.16	−	1761.76i	0.0628228	−	0.108812i
$641$	486.966	−	177.241i	0.0300062	−	0.0109214i	−0.326973	−	0.945034i	$-0.606029\pi$
$641$	486.966	−	177.241i	0.0300062	−	0.0109214i	0.356980	+	0.934112i	$0.383807\pi$
$642$	−18067.2	+	15160.2i	−1.11068	+	0.931972i
$643$	−1016.80	−	1761.15i	−0.0623617	−	0.108014i	0.833159	−	0.553034i	$-0.186530\pi$
$643$	−1016.80	−	1761.15i	−0.0623617	−	0.108014i	−0.895521	+	0.445020i	$0.853197\pi$
$644$	−1209.10	+	6857.17i	−0.0739835	+	0.419581i
$645$	−3450.03	+	19566.1i	−0.210612	+	1.19444i
$646$	−9895.34	−	8303.18i	−0.602674	−	0.505703i
$647$	29310.3	+	10668.1i	1.78100	+	0.648230i	0.999711	+	0.0240587i	$0.00765885\pi$
$647$	29310.3	+	10668.1i	1.78100	+	0.648230i	0.781287	+	0.624172i	$0.214563\pi$
$648$	5964.88	+	2171.04i	0.361609	+	0.131615i
$649$	95.9947	+	80.5491i	0.00580604	+	0.00487185i
$650$	−3055.33	+	17327.6i	−0.184369	+	1.04561i
$651$	−11579.2	+	65668.7i	−0.697117	+	3.95355i
$652$	5775.27	+	10003.1i	0.346897	+	0.600843i
$653$	−5456.37	+	4578.44i	−0.326990	+	0.274377i	−0.791472	−	0.611205i	$-0.790685\pi$
$653$	−5456.37	+	4578.44i	−0.326990	+	0.274377i	0.464482	+	0.885582i	$0.346240\pi$
$654$	21255.7	−	7736.43i	1.27089	−	0.462566i
$655$	11768.2	−	20383.1i	0.702017	−	1.21593i
$656$	3573.47	+	6189.43i	0.212684	+	0.368379i
$657$	−7049.23	−	5915.00i	−0.418595	−	0.351242i
$658$	3522.55	−	6101.24i	0.208698	−	0.361476i
$659$	5271.32	+	29895.2i	0.311596	+	1.76715i	0.590705	+	0.806888i	$0.298850\pi$
$659$	5271.32	+	29895.2i	0.311596	+	1.76715i	−0.279109	+	0.960259i	$0.590039\pi$
$660$	−394.554			−0.0232697
$661$	1083.40	+	6144.27i	0.0637510	+	0.361550i	0.999949	+	0.0100774i	$0.00320778\pi$
$661$	1083.40	+	6144.27i	0.0637510	+	0.361550i	−0.936198	+	0.351472i	$0.885681\pi$
$662$	3508.80	−	2944.23i	0.206002	−	0.172856i
$663$	28512.6	+	10377.7i	1.67019	+	0.607901i
$664$	7534.47	−	2742.32i	0.440353	−	0.160275i
$665$	48269.6			2.81476
$666$	5164.40	+	9669.12i	0.300475	+	0.562569i
$667$	1845.78			0.107150
$668$	−10160.3	+	3698.03i	−0.588491	+	0.214193i
$669$	17130.7	+	6235.06i	0.990001	+	0.360331i
$670$	−18301.8	+	15357.0i	−1.05531	+	0.885511i
$671$	−18.7236	−	106.187i	−0.00107722	−	0.00610924i
$672$	6621.82			0.380122
$673$	2440.65	+	13841.6i	0.139792	+	0.792800i	0.971402	+	0.237440i	$0.0763084\pi$
$673$	2440.65	+	13841.6i	0.139792	+	0.792800i	−0.831610	+	0.555360i	$0.812580\pi$
$674$	−937.297	+	1623.45i	−0.0535657	+	0.0927786i
$675$	−1853.97	−	1555.66i	−0.105717	−	0.0887074i
$676$	−5114.62	−	8858.77i	−0.291000	−	0.504027i
$677$	−3556.92	+	6160.76i	−0.201925	+	0.349745i	−0.949149	−	0.314828i	$-0.898053\pi$
$677$	−3556.92	+	6160.76i	−0.201925	+	0.349745i	0.747223	+	0.664573i	$0.231387\pi$
$678$	10198.1	−	3711.79i	0.577661	−	0.210251i
$679$	−24068.5	+	20195.9i	−1.36033	+	1.14145i
$680$	3903.84	+	6761.65i	0.220155	+	0.381320i
$681$	−5255.77	+	29806.9i	−0.295744	+	1.67725i
$682$	−96.9251	+	549.690i	−0.00544202	+	0.0308632i
$683$	−8540.75	−	7166.54i	−0.478482	−	0.401494i	0.371395	−	0.928475i	$-0.378879\pi$
$683$	−8540.75	−	7166.54i	−0.478482	−	0.401494i	−0.849877	+	0.526981i	$0.823324\pi$
$684$	9627.66	+	3504.18i	0.538191	+	0.195886i
$685$	−10268.0	−	3737.26i	−0.572733	−	0.208458i
$686$	6541.10	+	5488.64i	0.364053	+	0.305477i
$687$	633.616	−	3593.42i	0.0351877	−	0.199560i
$688$	484.677	−	2748.74i	0.0268578	−	0.152318i
$689$	−8459.64	−	14652.5i	−0.467760	−	0.810184i
$690$	10518.7	−	8826.27i	0.580350	−	0.486972i
$691$	−8999.19	+	3275.44i	−0.495435	+	0.180323i	−0.577639	−	0.816292i	$-0.696026\pi$
$691$	−8999.19	+	3275.44i	−0.495435	+	0.180323i	0.0822049	+	0.996615i	$0.473804\pi$
$692$	−2452.35	+	4247.60i	−0.134718	+	0.233338i
$693$	−304.525	−	527.453i	−0.0166926	−	0.0289124i
$694$	−19298.4	−	16193.3i	−1.05556	−	0.885718i
$695$	−2261.24	+	3916.59i	−0.123416	+	0.213762i
$696$	−304.813	−	1728.68i	−0.0166004	−	0.0941456i
$697$	−27429.9			−1.49065
$698$	−3497.51	−	19835.4i	−0.189660	−	1.07561i
$699$	5489.03	−	4605.85i	0.297016	−	0.249226i
$700$	−13848.5	−	5040.45i	−0.747750	−	0.272159i
$701$	30573.6	−	11127.9i	1.64729	−	0.599563i	0.658996	−	0.752147i	$-0.270982\pi$
$701$	30573.6	−	11127.9i	1.64729	−	0.599563i	0.988291	+	0.152584i	$0.0487593\pi$
$702$	2615.82			0.140638
$703$	−11152.2	−	20879.8i	−0.598310	−	1.12019i
$704$	55.4289			0.00296741
$705$	−13055.4	+	4751.77i	−0.697438	+	0.253847i
$706$	5070.19	+	1845.40i	0.270282	+	0.0983746i
$707$	33066.4	−	27746.0i	1.75896	−	1.47595i
$708$	720.195	+	4084.43i	0.0382297	+	0.216811i
$709$	13428.6			0.711312			0.355656	−	0.934617i	$-0.384257\pi$
$709$	13428.6			0.711312			0.355656	+	0.934617i	$0.384257\pi$
$710$	1212.29	+	6875.25i	0.0640796	+	0.363413i
$711$	−15528.4	+	26896.0i	−0.819072	+	1.41868i
$712$	5938.48	+	4982.97i	0.312576	+	0.262282i
$713$	−9712.69	−	16822.9i	−0.510159	−	0.883621i
$714$	−12707.3	+	22009.6i	−0.666046	+	1.15363i
$715$	−891.852	+	324.608i	−0.0466481	+	0.0169785i
$716$	−2370.41	+	1989.01i	−0.123724	+	0.103817i
$717$	−6034.18	−	10451.5i	−0.314296	−	0.544377i
$718$	130.938	−	742.587i	0.00680580	−	0.0385976i
$719$	4894.38	−	27757.4i	0.253866	−	1.43975i	−0.545101	−	0.838370i	$-0.683509\pi$
$719$	4894.38	−	27757.4i	0.253866	−	1.43975i	0.798967	−	0.601375i	$-0.205380\pi$
$720$	−4743.88	−	3980.59i	−0.245547	−	0.206039i
$721$	−18984.0	−	6909.61i	−0.980584	−	0.356903i
$722$	−7899.57	−	2875.21i	−0.407191	−	0.148205i
$723$	−31247.2	−	26219.5i	−1.60732	−	1.34870i
$724$	259.073	−	1469.28i	0.0132989	−	0.0754217i
$725$	−678.381	+	3847.29i	−0.0347509	+	0.197082i
$726$	9532.71	+	16511.1i	0.487317	+	0.844057i
$727$	−11311.2	+	9491.23i	−0.577042	+	0.484196i	−0.883974	−	0.467536i	$-0.845142\pi$
$727$	−11311.2	+	9491.23i	−0.577042	+	0.484196i	0.306932	+	0.951731i	$0.400697\pi$
$728$	14968.0	−	5447.90i	0.762020	−	0.277353i
$729$	7826.53	−	13556.0i	0.397629	−	0.688714i
$730$	−6005.40	−	10401.7i	−0.304479	−	0.527374i
$731$	8206.18	+	6885.80i	0.415207	+	0.348400i
$732$	1784.33	−	3090.56i	0.0900968	−	0.156052i
$733$	−4172.26	−	23662.1i	−0.210240	−	1.19233i	−0.888978	−	0.457950i	$-0.848584\pi$
$733$	−4172.26	−	23662.1i	−0.210240	−	1.19233i	0.678738	−	0.734381i	$-0.262527\pi$
$734$	7831.16			0.393806
$735$	−9707.55	−	55054.3i	−0.487168	−	2.76287i
$736$	−1477.72	+	1239.96i	−0.0740077	+	0.0620998i
$737$	−611.707	−	222.643i	−0.0305733	−	0.0111278i
$738$	20444.1	−	7441.05i	1.01973	−	0.371150i
$739$	−1782.19			−0.0887128			−0.0443564	−	0.999016i	$-0.514124\pi$
$739$	−1782.19			−0.0887128			−0.0443564	+	0.999016i	$0.514124\pi$
$740$	2017.76	+	14164.7i	0.100236	+	0.703656i
$741$	51969.5			2.57645
$742$	13316.7	−	4846.90i	0.658859	−	0.239805i
$743$	−20667.0	−	7522.16i	−1.02045	−	0.371415i	−0.223015	−	0.974815i	$-0.571590\pi$
$743$	−20667.0	−	7522.16i	−1.02045	−	0.371415i	−0.797439	+	0.603400i	$0.793812\pi$
$744$	−14151.6	+	11874.6i	−0.697345	+	0.585142i
$745$	−1442.86	−	8182.89i	−0.0709563	−	0.402413i
$746$	18979.9			0.931504
$747$	−4238.38	−	24037.1i	−0.207596	−	1.17734i
$748$	−106.368	+	184.235i	−0.00519946	+	0.00900574i
$749$	−36401.8	−	30544.8i	−1.77583	−	1.49009i
$750$	294.885	+	510.755i	0.0143569	+	0.0248669i
$751$	10585.4	−	18334.5i	0.514339	−	0.890861i	−0.485523	−	0.874224i	$-0.661371\pi$
$751$	10585.4	−	18334.5i	0.514339	−	0.890861i	0.999862	−	0.0166370i	$-0.00529598\pi$
$752$	1834.08	−	667.552i	0.0889390	−	0.0323712i
$753$	20850.7	−	17495.8i	1.00909	−	0.846724i
$754$	−2111.22	−	3656.74i	−0.101971	−	0.176619i
$755$	−3680.38	+	20872.5i	−0.177408	+	1.00613i
$756$	−380.460	+	2157.69i	−0.0183032	+	0.103802i
$757$	13840.6	+	11613.6i	0.664524	+	0.557602i	0.911439	−	0.411435i	$-0.134972\pi$
$757$	13840.6	+	11613.6i	0.664524	+	0.557602i	−0.246915	+	0.969037i	$0.579417\pi$
$758$	−5532.03	−	2013.49i	−0.265082	−	0.0964820i
$759$	351.572	+	127.962i	0.0168133	+	0.00611952i
$760$	10244.1	+	8595.82i	0.488937	+	0.410267i
$761$	2397.12	−	13594.7i	0.114186	−	0.647580i	−0.872964	−	0.487784i	$-0.837805\pi$
$761$	2397.12	−	13594.7i	0.114186	−	0.647580i	0.987150	−	0.159796i	$-0.0510836\pi$
$762$	2207.00	−	12516.5i	0.104923	−	0.595048i
$763$	22787.1	+	39468.5i	1.08119	+	1.87268i
$764$	5862.11	−	4918.89i	0.277596	−	0.232931i
$765$	22334.2	−	8128.99i	1.05555	−	0.384189i
$766$	931.262	−	1612.99i	0.0439267	−

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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	74.f (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.87939 + 0.684040i) q^{2} +(-6.73393 - 2.45095i) q^{3} +(3.06418 - 2.57115i) q^{4} +(-2.75980 - 15.6516i) q^{5} +14.3322 q^{6} +(5.01435 + 28.4378i) q^{7} +(-4.00000 + 6.92820i) q^{8} +(18.6555 + 15.6538i) q^{9} +O(q^{10})\)	\(q+(-1.87939 + 0.684040i) q^{2} +(-6.73393 - 2.45095i) q^{3} +(3.06418 - 2.57115i) q^{4} +(-2.75980 - 15.6516i) q^{5} +14.3322 q^{6} +(5.01435 + 28.4378i) q^{7} +(-4.00000 + 6.92820i) q^{8} +(18.6555 + 15.6538i) q^{9} +(15.8931 + 27.5276i) q^{10} +(-0.433038 + 0.750044i) q^{11} +(-26.9357 + 9.80380i) q^{12} +(-52.8199 + 44.3212i) q^{13} +(-28.8765 - 50.0155i) q^{14} +(-19.7770 + 112.161i) q^{15} +(2.77837 - 15.7569i) q^{16} +(47.0412 + 39.4723i) q^{17} +(-45.7687 - 16.6584i) q^{18} +(98.8344 + 35.9728i) q^{19} +(-48.6991 - 40.8634i) q^{20} +(35.9333 - 203.788i) q^{21} +(0.300785 - 1.70584i) q^{22} +(30.1411 + 52.2060i) q^{23} +(43.9164 - 36.8503i) q^{24} +(-119.895 + 43.6381i) q^{25} +(68.9515 - 119.427i) q^{26} +(9.48428 + 16.4273i) q^{27} +(88.4826 + 74.2457i) q^{28} +(15.3095 - 26.5167i) q^{29} +(-39.5540 - 224.322i) q^{30} -322.240 q^{31} +(5.55674 + 31.5138i) q^{32} +(4.75437 - 3.98939i) q^{33} +(-115.409 - 42.0055i) q^{34} +(431.258 - 156.965i) q^{35} +97.4121 q^{36} +(-167.535 - 150.283i) q^{37} -210.355 q^{38} +(464.315 - 168.997i) q^{39} +(119.477 + 43.4860i) q^{40} +(-342.179 + 287.123i) q^{41} +(71.8666 + 407.576i) q^{42} +174.447 q^{43} +(0.601570 + 3.41167i) q^{44} +(193.522 - 335.190i) q^{45} +(-92.3578 - 77.4974i) q^{46} +(60.9935 + 105.644i) q^{47} +(-57.3288 + 99.2964i) q^{48} +(-461.249 + 167.881i) q^{49} +(195.478 - 164.025i) q^{50} +(-220.028 - 381.099i) q^{51} +(-47.8932 + 271.616i) q^{52} +(-42.6097 + 241.652i) q^{53} +(-29.0615 - 24.3855i) q^{54} +(12.9345 + 4.70777i) q^{55} +(-217.080 - 79.0107i) q^{56} +(-577.377 - 484.476i) q^{57} +(-10.6338 + 60.3075i) q^{58} +(25.1251 - 142.491i) q^{59} +(227.782 + 394.531i) q^{60} +(-95.3712 + 80.0259i) q^{61} +(605.614 - 220.425i) q^{62} +(-351.615 + 609.014i) q^{63} +(-32.0000 - 55.4256i) q^{64} +(839.470 + 704.399i) q^{65} +(-6.20639 + 10.7498i) q^{66} +(130.518 + 740.207i) q^{67} +245.632 q^{68} +(-75.0141 - 425.426i) q^{69} +(-703.130 + 589.996i) q^{70} +(206.389 + 75.1193i) q^{71} +(-183.075 + 66.6338i) q^{72} -377.863 q^{73} +(417.663 + 167.838i) q^{74} +914.317 q^{75} +(395.338 - 143.891i) q^{76} +(-23.5010 - 8.55366i) q^{77} +(-757.026 + 635.220i) q^{78} +(221.449 + 1255.90i) q^{79} -254.289 q^{80} +(-137.783 - 781.408i) q^{81} +(446.684 - 773.679i) q^{82} +(-767.770 - 644.235i) q^{83} +(-413.863 - 716.833i) q^{84} +(487.980 - 845.206i) q^{85} +(-327.852 + 119.328i) q^{86} +(-168.084 + 141.039i) q^{87} +(-3.46431 - 6.00035i) q^{88} +(168.268 - 954.295i) q^{89} +(-134.419 + 762.327i) q^{90} +(-1525.25 - 1279.84i) q^{91} +(226.587 + 82.4710i) q^{92} +(2169.95 + 789.796i) q^{93} +(-186.895 - 156.823i) q^{94} +(290.268 - 1646.19i) q^{95} +(39.8202 - 225.831i) q^{96} +(544.027 + 942.283i) q^{97} +(752.027 - 631.025i) q^{98} +(-19.8196 + 7.21374i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 6 q^{3} - 6 q^{5} - 36 q^{6} - 75 q^{7} - 120 q^{8} - 48 q^{9}+O(q^{10}) \) 30 * q + 6 * q^3 - 6 * q^5 - 36 * q^6 - 75 * q^7 - 120 * q^8 - 48 * q^9	\( 30 q + 6 q^{3} - 6 q^{5} - 36 q^{6} - 75 q^{7} - 120 q^{8} - 48 q^{9} + 54 q^{10} - 21 q^{11} + 24 q^{12} - 159 q^{13} + 6 q^{14} - 69 q^{15} - 171 q^{17} + 192 q^{18} - 45 q^{19} - 24 q^{20} + 579 q^{21} + 42 q^{22} + 459 q^{23} + 48 q^{24} - 204 q^{25} + 264 q^{26} + 435 q^{27} + 96 q^{28} + 273 q^{29} - 138 q^{30} - 258 q^{31} - 318 q^{33} - 558 q^{34} - 753 q^{35} + 1296 q^{36} - 891 q^{37} - 2556 q^{38} - 504 q^{39} + 96 q^{40} + 648 q^{41} + 1158 q^{42} - 216 q^{43} + 84 q^{44} + 1731 q^{45} - 6 q^{46} + 48 q^{47} + 144 q^{48} + 1731 q^{49} + 240 q^{50} + 972 q^{51} + 48 q^{52} - 135 q^{53} + 360 q^{54} + 765 q^{55} + 408 q^{56} - 405 q^{57} - 762 q^{58} + 1836 q^{59} + 108 q^{60} - 684 q^{61} - 204 q^{62} - 3264 q^{63} - 960 q^{64} - 1350 q^{65} + 252 q^{66} + 1095 q^{67} - 432 q^{68} - 5823 q^{69} - 1146 q^{70} + 4179 q^{71} + 768 q^{72} - 2658 q^{73} - 1692 q^{74} - 10416 q^{75} - 180 q^{76} + 267 q^{77} + 1530 q^{78} + 4866 q^{79} - 864 q^{80} - 2076 q^{81} + 1800 q^{82} - 186 q^{83} + 504 q^{84} + 753 q^{85} + 648 q^{86} - 525 q^{87} - 168 q^{88} + 687 q^{89} + 768 q^{90} + 3990 q^{91} + 132 q^{92} + 3753 q^{93} + 6210 q^{94} + 9000 q^{95} - 384 q^{96} + 7428 q^{97} - 1542 q^{98} + 6324 q^{99}+O(q^{100}) \) 30 * q + 6 * q^3 - 6 * q^5 - 36 * q^6 - 75 * q^7 - 120 * q^8 - 48 * q^9 + 54 * q^10 - 21 * q^11 + 24 * q^12 - 159 * q^13 + 6 * q^14 - 69 * q^15 - 171 * q^17 + 192 * q^18 - 45 * q^19 - 24 * q^20 + 579 * q^21 + 42 * q^22 + 459 * q^23 + 48 * q^24 - 204 * q^25 + 264 * q^26 + 435 * q^27 + 96 * q^28 + 273 * q^29 - 138 * q^30 - 258 * q^31 - 318 * q^33 - 558 * q^34 - 753 * q^35 + 1296 * q^36 - 891 * q^37 - 2556 * q^38 - 504 * q^39 + 96 * q^40 + 648 * q^41 + 1158 * q^42 - 216 * q^43 + 84 * q^44 + 1731 * q^45 - 6 * q^46 + 48 * q^47 + 144 * q^48 + 1731 * q^49 + 240 * q^50 + 972 * q^51 + 48 * q^52 - 135 * q^53 + 360 * q^54 + 765 * q^55 + 408 * q^56 - 405 * q^57 - 762 * q^58 + 1836 * q^59 + 108 * q^60 - 684 * q^61 - 204 * q^62 - 3264 * q^63 - 960 * q^64 - 1350 * q^65 + 252 * q^66 + 1095 * q^67 - 432 * q^68 - 5823 * q^69 - 1146 * q^70 + 4179 * q^71 + 768 * q^72 - 2658 * q^73 - 1692 * q^74 - 10416 * q^75 - 180 * q^76 + 267 * q^77 + 1530 * q^78 + 4866 * q^79 - 864 * q^80 - 2076 * q^81 + 1800 * q^82 - 186 * q^83 + 504 * q^84 + 753 * q^85 + 648 * q^86 - 525 * q^87 - 168 * q^88 + 687 * q^89 + 768 * q^90 + 3990 * q^91 + 132 * q^92 + 3753 * q^93 + 6210 * q^94 + 9000 * q^95 - 384 * q^96 + 7428 * q^97 - 1542 * q^98 + 6324 * q^99

Introduction

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