LMFDB - Embedded newform 162.4.e.a.127.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,4,Mod(19,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, 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("162.19");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	162.e (of order $9$, degree $6$, not 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:	$9.55830942093$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			127.3
Character	$\chi$	$=$	162.127
Dual form			162.4.e.a.37.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.53209 - 1.28558i) q^{2} +(0.694593 + 3.93923i) q^{4} +(-1.07676 - 0.391909i) q^{5} +(0.470326 - 2.66735i) q^{7} +(4.00000 - 6.92820i) q^{8} +O(q^{10})$	\(q+(-1.53209 - 1.28558i) q^{2} +(0.694593 + 3.93923i) q^{4} +(-1.07676 - 0.391909i) q^{5} +(0.470326 - 2.66735i) q^{7} +(4.00000 - 6.92820i) q^{8} +(1.14586 + 1.98470i) q^{10} +(-11.5929 + 4.21946i) q^{11} +(32.4873 - 27.2601i) q^{13} +(-4.14966 + 3.48198i) q^{14} +(-15.0351 + 5.47232i) q^{16} +(-21.7389 - 37.6528i) q^{17} +(65.6659 - 113.737i) q^{19} +(0.795909 - 4.51383i) q^{20} +(23.1858 + 8.43893i) q^{22} +(4.11546 + 23.3399i) q^{23} +(-94.7497 - 79.5045i) q^{25} -84.8184 q^{26} +10.8340 q^{28} +(-134.085 - 112.511i) q^{29} +(-33.0436 - 187.400i) q^{31} +(30.0702 + 10.9446i) q^{32} +(-15.0997 + 85.6344i) q^{34} +(-1.55179 + 2.68777i) q^{35} +(-26.4028 - 45.7310i) q^{37} +(-246.823 + 89.8362i) q^{38} +(-7.02227 + 5.89238i) q^{40} +(179.171 - 150.342i) q^{41} +(-365.375 + 132.985i) q^{43} +(-24.6738 - 42.7362i) q^{44} +(23.7000 - 41.0496i) q^{46} +(89.7800 - 509.168i) q^{47} +(315.421 + 114.804i) q^{49} +(42.9560 + 243.616i) q^{50} +(129.949 + 109.040i) q^{52} -97.4224 q^{53} +14.1364 q^{55} +(-16.5986 - 13.9279i) q^{56} +(60.7894 + 344.754i) q^{58} +(677.161 + 246.466i) q^{59} +(-86.3009 + 489.437i) q^{61} +(-190.291 + 329.593i) q^{62} +(-32.0000 - 55.4256i) q^{64} +(-45.6646 + 16.6205i) q^{65} +(106.104 - 89.0315i) q^{67} +(133.223 - 111.788i) q^{68} +(5.83281 - 2.12297i) q^{70} +(488.539 + 846.174i) q^{71} +(209.614 - 363.061i) q^{73} +(-18.3392 + 104.007i) q^{74} +(493.646 + 179.672i) q^{76} +(5.80236 + 32.9068i) q^{77} +(-203.671 - 170.901i) q^{79} +18.3338 q^{80} -467.781 q^{82} +(466.701 + 391.608i) q^{83} +(8.65108 + 49.0627i) q^{85} +(730.749 + 265.971i) q^{86} +(-17.1382 + 97.1957i) q^{88} +(-532.975 + 923.140i) q^{89} +(-57.4326 - 99.4763i) q^{91} +(-89.0828 + 32.4235i) q^{92} +(-792.125 + 664.671i) q^{94} +(-115.281 + 96.7321i) q^{95} +(-829.931 + 302.070i) q^{97} +(-335.664 - 581.387i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{5} - 33 q^{7} + 96 q^{8}+O(q^{10}) $ 24 * q + 12 * q^5 - 33 * q^7 + 96 * q^8	$ 24 q + 12 q^{5} - 33 q^{7} + 96 q^{8} + 30 q^{10} + 12 q^{11} + 60 q^{13} + 66 q^{14} - 102 q^{17} + 171 q^{19} - 96 q^{20} - 24 q^{22} + 708 q^{23} + 864 q^{25} + 468 q^{26} - 336 q^{28} + 381 q^{29} + 909 q^{31} - 48 q^{34} - 624 q^{35} + 555 q^{37} - 66 q^{38} - 96 q^{40} - 618 q^{41} - 1161 q^{43} - 132 q^{44} + 348 q^{46} + 378 q^{47} + 579 q^{49} - 36 q^{50} + 240 q^{52} + 1794 q^{53} - 3906 q^{55} + 264 q^{56} + 444 q^{58} - 1038 q^{59} + 324 q^{61} - 744 q^{62} - 768 q^{64} - 5718 q^{65} - 576 q^{67} - 1056 q^{68} - 1038 q^{70} - 120 q^{71} + 3036 q^{73} + 1110 q^{74} + 132 q^{76} + 3804 q^{77} - 2991 q^{79} + 480 q^{80} - 3408 q^{82} - 513 q^{83} - 2925 q^{85} + 2322 q^{86} + 480 q^{88} - 1065 q^{89} + 2859 q^{91} - 1884 q^{92} - 828 q^{94} - 6357 q^{95} - 2055 q^{97} - 1356 q^{98}+O(q^{100}) $ 24 * q + 12 * q^5 - 33 * q^7 + 96 * q^8 + 30 * q^10 + 12 * q^11 + 60 * q^13 + 66 * q^14 - 102 * q^17 + 171 * q^19 - 96 * q^20 - 24 * q^22 + 708 * q^23 + 864 * q^25 + 468 * q^26 - 336 * q^28 + 381 * q^29 + 909 * q^31 - 48 * q^34 - 624 * q^35 + 555 * q^37 - 66 * q^38 - 96 * q^40 - 618 * q^41 - 1161 * q^43 - 132 * q^44 + 348 * q^46 + 378 * q^47 + 579 * q^49 - 36 * q^50 + 240 * q^52 + 1794 * q^53 - 3906 * q^55 + 264 * q^56 + 444 * q^58 - 1038 * q^59 + 324 * q^61 - 744 * q^62 - 768 * q^64 - 5718 * q^65 - 576 * q^67 - 1056 * q^68 - 1038 * q^70 - 120 * q^71 + 3036 * q^73 + 1110 * q^74 + 132 * q^76 + 3804 * q^77 - 2991 * q^79 + 480 * q^80 - 3408 * q^82 - 513 * q^83 - 2925 * q^85 + 2322 * q^86 + 480 * q^88 - 1065 * q^89 + 2859 * q^91 - 1884 * q^92 - 828 * q^94 - 6357 * q^95 - 2055 * q^97 - 1356 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{2}{9}\right)$

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 $

$2$	−1.53209	−	1.28558i	−0.541675	−	0.454519i
$2$	−1.53209	−	1.28558i	−0.541675	−	0.454519i
$3$		0			0
$3$		0			0
$4$	0.694593	+	3.93923i	0.0868241	+	0.492404i
$5$	−1.07676	−	0.391909i	−0.0963084	−	0.0350534i	0.293417	−	0.955985i	$-0.405208\pi$
$5$	−1.07676	−	0.391909i	−0.0963084	−	0.0350534i	−0.389725	+	0.920931i	$0.627430\pi$
$6$		0			0
$7$	0.470326	−	2.66735i	0.0253952	−	0.144023i	−0.969474	−	0.245195i	$-0.921148\pi$
$7$	0.470326	−	2.66735i	0.0253952	−	0.144023i	0.994869	+	0.101172i	$0.0322591\pi$
$8$	4.00000	−	6.92820i	0.176777	−	0.306186i
$9$		0			0
$10$	1.14586	+	1.98470i	0.0362354	+	0.0627616i
$11$	−11.5929	+	4.21946i	−0.317762	+	0.115656i	−0.495977	−	0.868336i	$-0.665190\pi$
$11$	−11.5929	+	4.21946i	−0.317762	+	0.115656i	0.178215	+	0.983992i	$0.442968\pi$
$12$		0			0
$13$	32.4873	−	27.2601i	0.693105	−	0.581584i	−0.226698	−	0.973965i	$-0.572793\pi$
$13$	32.4873	−	27.2601i	0.693105	−	0.581584i	0.919803	+	0.392381i	$0.128348\pi$
$14$	−4.14966	+	3.48198i	−0.0792174	+	0.0664713i
$15$		0			0
$16$	−15.0351	+	5.47232i	−0.234923	+	0.0855050i
$17$	−21.7389	−	37.6528i	−0.310144	−	0.537185i	0.668249	−	0.743937i	$-0.267044\pi$
$17$	−21.7389	−	37.6528i	−0.310144	−	0.537185i	−0.978393	+	0.206752i	$0.933711\pi$
$18$		0			0
$19$	65.6659	−	113.737i	0.792884	−	1.37331i	−0.131291	−	0.991344i	$-0.541912\pi$
$19$	65.6659	−	113.737i	0.792884	−	1.37331i	0.924174	−	0.381971i	$-0.124754\pi$
$20$	0.795909	−	4.51383i	0.00889854	−	0.0504661i
$21$		0			0
$22$	23.1858	+	8.43893i	0.224692	+	0.0817811i
$23$	4.11546	+	23.3399i	0.0373101	+	0.211596i	0.997763	−	0.0668452i	$-0.0212934\pi$
$23$	4.11546	+	23.3399i	0.0373101	+	0.211596i	−0.960453	+	0.278441i	$0.910182\pi$
$24$		0			0
$25$	−94.7497	−	79.5045i	−0.757998	−	0.636036i
$26$	−84.8184			−0.639779
$27$		0			0
$28$	10.8340			0.0731226
$29$	−134.085	−	112.511i	−0.858588	−	0.720441i	0.103076	−	0.994674i	$-0.467132\pi$
$29$	−134.085	−	112.511i	−0.858588	−	0.720441i	−0.961663	+	0.274233i	$0.911576\pi$
$30$		0			0
$31$	−33.0436	−	187.400i	−0.191445	−	1.08574i	−0.917391	−	0.397988i	$-0.869709\pi$
$31$	−33.0436	−	187.400i	−0.191445	−	1.08574i	0.725945	−	0.687753i	$-0.241403\pi$
$32$	30.0702	+	10.9446i	0.166116	+	0.0604612i
$33$		0			0
$34$	−15.0997	+	85.6344i	−0.0761638	+	0.431946i
$35$	−1.55179	+	2.68777i	−0.00749428	+	0.0129805i
$36$		0			0
$37$	−26.4028	−	45.7310i	−0.117313	−	0.203193i	0.801389	−	0.598144i	$-0.204095\pi$
$37$	−26.4028	−	45.7310i	−0.117313	−	0.203193i	−0.918702	+	0.394951i	$0.870762\pi$
$38$	−246.823	+	89.8362i	−1.05368	+	0.383509i
$39$		0			0
$40$	−7.02227	+	5.89238i	−0.0277579	+	0.0232917i
$41$	179.171	−	150.342i	0.682482	−	0.572670i	−0.234248	−	0.972177i	$-0.575263\pi$
$41$	179.171	−	150.342i	0.682482	−	0.572670i	0.916730	+	0.399506i	$0.130818\pi$
$42$		0			0
$43$	−365.375	+	132.985i	−1.29579	+	0.471630i	−0.895624	−	0.444811i	$-0.853271\pi$
$43$	−365.375	+	132.985i	−1.29579	+	0.471630i	−0.400169	+	0.916441i	$0.631049\pi$
$44$	−24.6738	−	42.7362i	−0.0845389	−	0.146426i
$45$		0			0
$46$	23.7000	−	41.0496i	0.0759646	−	0.131575i
$47$	89.7800	−	509.168i	0.278633	−	1.58021i	−0.448546	−	0.893760i	$-0.648058\pi$
$47$	89.7800	−	509.168i	0.278633	−	1.58021i	0.727179	−	0.686448i	$-0.240831\pi$
$48$		0			0
$49$	315.421	+	114.804i	0.919595	+	0.334705i
$50$	42.9560	+	243.616i	0.121498	+	0.689050i
$51$		0			0
$52$	129.949	+	109.040i	0.346553	+	0.290792i
$53$	−97.4224			−0.252491			−0.126245	−	0.991999i	$-0.540293\pi$
$53$	−97.4224			−0.252491			−0.126245	+	0.991999i	$0.540293\pi$
$54$		0			0
$55$	14.1364			0.0346573
$56$	−16.5986	−	13.9279i	−0.0396087	−	0.0332356i
$57$		0			0
$58$	60.7894	+	344.754i	0.137621	+	0.780490i
$59$	677.161	+	246.466i	1.49422	+	0.543851i	0.954556	−	0.298032i	$-0.0963301\pi$
$59$	677.161	+	246.466i	1.49422	+	0.543851i	0.539661	+	0.841882i	$0.318552\pi$
$60$		0			0
$61$	−86.3009	+	489.437i	−0.181143	+	1.02731i	0.749669	+	0.661813i	$0.230213\pi$
$61$	−86.3009	+	489.437i	−0.181143	+	1.02731i	−0.930812	+	0.365499i	$0.880899\pi$
$62$	−190.291	+	329.593i	−0.389789	+	0.675134i
$63$		0			0
$64$	−32.0000	−	55.4256i	−0.0625000	−	0.108253i
$65$	−45.6646	+	16.6205i	−0.0871384	+	0.0317158i
$66$		0			0
$67$	106.104	−	89.0315i	0.193472	−	0.162342i	−0.540906	−	0.841083i	$-0.681918\pi$
$67$	106.104	−	89.0315i	0.193472	−	0.162342i	0.734378	+	0.678741i	$0.237474\pi$
$68$	133.223	−	111.788i	0.237584	−	0.199357i
$69$		0			0
$70$	5.83281	−	2.12297i	0.00995934	−	0.00362490i
$71$	488.539	+	846.174i	0.816604	+	1.41440i	0.908170	+	0.418601i	$0.137480\pi$
$71$	488.539	+	846.174i	0.816604	+	1.41440i	−0.0915657	+	0.995799i	$0.529187\pi$
$72$		0			0
$73$	209.614	−	363.061i	0.336074	−	0.582097i	−0.647616	−	0.761966i	$-0.724234\pi$
$73$	209.614	−	363.061i	0.336074	−	0.582097i	0.983691	+	0.179869i	$0.0575674\pi$
$74$	−18.3392	+	104.007i	−0.0288093	+	0.163386i
$75$		0			0
$76$	493.646	+	179.672i	0.745067	+	0.271182i
$77$	5.80236	+	32.9068i	0.00858753	+	0.0487023i
$78$		0			0
$79$	−203.671	−	170.901i	−0.290061	−	0.243390i	0.486132	−	0.873885i	$-0.338407\pi$
$79$	−203.671	−	170.901i	−0.290061	−	0.243390i	−0.776193	+	0.630495i	$0.782852\pi$
$80$	18.3338			0.0256223
$81$		0			0
$82$	−467.781			−0.629973
$83$	466.701	+	391.608i	0.617194	+	0.517887i	0.896920	−	0.442193i	$-0.145799\pi$
$83$	466.701	+	391.608i	0.617194	+	0.517887i	−0.279726	+	0.960080i	$0.590244\pi$
$84$		0			0
$85$	8.65108	+	49.0627i	0.0110393	+	0.0626070i
$86$	730.749	+	265.971i	0.916264	+	0.333493i
$87$		0			0
$88$	−17.1382	+	97.1957i	−0.0207607	+	0.117740i
$89$	−532.975	+	923.140i	−0.634778	+	1.09947i	0.351784	+	0.936081i	$0.385575\pi$
$89$	−532.975	+	923.140i	−0.634778	+	1.09947i	−0.986562	+	0.163387i	$0.947758\pi$
$90$		0			0
$91$	−57.4326	−	99.4763i	−0.0661602	−	0.114593i
$92$	−89.0828	+	32.4235i	−0.100951	+	0.0367433i
$93$		0			0
$94$	−792.125	+	664.671i	−0.869164	+	0.729315i
$95$	−115.281	+	96.7321i	−0.124501	+	0.104468i
$96$		0			0
$97$	−829.931	+	302.070i	−0.868729	+	0.316192i	−0.737653	−	0.675181i	$-0.764066\pi$
$97$	−829.931	+	302.070i	−0.868729	+	0.316192i	−0.131077	+	0.991372i	$0.541843\pi$
$98$	−335.664	−	581.387i	−0.345992	−	0.599275i
$99$		0			0
$100$	247.374	−	428.464i	0.247374	−	0.428464i
$101$	326.683	−	1852.71i	0.321843	−	1.82526i	−0.209146	−	0.977885i	$-0.567068\pi$
$101$	326.683	−	1852.71i	0.321843	−	1.82526i	0.530989	−	0.847379i	$-0.321821\pi$
$102$		0			0
$103$	1768.06	+	643.521i	1.69138	+	0.615612i	0.994798	−	0.101866i	$-0.0324813\pi$
$103$	1768.06	+	643.521i	1.69138	+	0.615612i	0.696581	+	0.717478i	$0.254703\pi$
$104$	−58.9143	−	334.119i	−0.0555483	−	0.315030i
$105$		0			0
$106$	149.260	+	125.244i	0.136768	+	0.114762i
$107$	−539.428			−0.487369			−0.243684	−	0.969855i	$-0.578356\pi$
$107$	−539.428			−0.487369			−0.243684	+	0.969855i	$0.578356\pi$
$108$		0			0
$109$	−172.844			−0.151885			−0.0759424	−	0.997112i	$-0.524197\pi$
$109$	−172.844			−0.151885			−0.0759424	+	0.997112i	$0.524197\pi$
$110$	−21.6582	−	18.1734i	−0.0187730	−	0.0157524i
$111$		0			0
$112$	7.52521	+	42.6776i	0.00634880	+	0.0360058i
$113$	−1681.98	−	612.192i	−1.40025	−	0.509648i	−0.471994	−	0.881602i	$-0.656466\pi$
$113$	−1681.98	−	612.192i	−1.40025	−	0.509648i	−0.928251	+	0.371954i	$0.878688\pi$
$114$		0			0
$115$	4.71576	−	26.7444i	0.00382388	−	0.0216863i
$116$	350.072	−	606.343i	0.280202	−	0.485323i
$117$		0			0
$118$	−720.619	−	1248.15i	−0.562190	−	0.973741i
$119$	−110.658	+	40.2761i	−0.0852434	+	0.0310261i
$120$		0			0
$121$	−903.014	+	757.719i	−0.678448	+	0.569285i
$122$	761.429	−	638.915i	0.565053	−	0.474136i
$123$		0			0
$124$	715.258	−	260.333i	0.518001	−	0.188537i
$125$	142.481	+	246.784i	0.101951	+	0.176584i
$126$		0			0
$127$	−76.0764	+	131.768i	−0.0531550	+	0.0920672i	−0.891379	−	0.453260i	$-0.850261\pi$
$127$	−76.0764	+	131.768i	−0.0531550	+	0.0920672i	0.838224	+	0.545327i	$0.183594\pi$
$128$	−22.2270	+	126.055i	−0.0153485	+	0.0870455i
$129$		0			0
$130$	91.3291	+	33.2411i	0.0616161	+	0.0224264i
$131$	−109.547	−	621.274i	−0.0730626	−	0.414359i	−0.999300	−	0.0374173i	$-0.988087\pi$
$131$	−109.547	−	621.274i	−0.0730626	−	0.414359i	0.926237	−	0.376941i	$-0.123024\pi$
$132$		0			0
$133$	−272.491	−	228.647i	−0.177654	−	0.149069i
$134$	−277.017			−0.178587
$135$		0			0
$136$	−347.822			−0.219305
$137$	−250.924	−	210.551i	−0.156481	−	0.131303i	0.561186	−	0.827690i	$-0.310345\pi$
$137$	−250.924	−	210.551i	−0.156481	−	0.131303i	−0.717667	+	0.696387i	$0.754790\pi$
$138$		0			0
$139$	−421.104	−	2388.20i	−0.256961	−	1.45730i	−0.790988	−	0.611832i	$-0.790433\pi$
$139$	−421.104	−	2388.20i	−0.256961	−	1.45730i	0.534027	−	0.845468i	$-0.320678\pi$
$140$	−11.6656	−	4.24594i	−0.00704232	−	0.00256319i
$141$		0			0
$142$	339.336	−	1924.47i	0.200538	−	1.13731i
$143$	−261.599	+	453.102i	−0.152979	+	0.264967i
$144$		0			0
$145$	100.284	+	173.697i	0.0574353	+	0.0994809i
$146$	−787.889	+	286.768i	−0.446618	+	0.162555i
$147$		0			0
$148$	161.806	−	135.771i	0.0898673	−	0.0754077i
$149$	−1226.24	+	1028.93i	−0.674209	+	0.565728i	−0.914308	−	0.405020i	$-0.867265\pi$
$149$	−1226.24	+	1028.93i	−0.674209	+	0.565728i	0.240099	+	0.970748i	$0.422820\pi$
$150$		0			0
$151$	556.461	−	202.535i	0.299895	−	0.109153i	−0.187690	−	0.982228i	$-0.560100\pi$
$151$	556.461	−	202.535i	0.299895	−	0.109153i	0.487585	+	0.873075i	$0.337878\pi$
$152$	−525.327	−	909.893i	−0.280327	−	0.485540i
$153$		0			0
$154$	33.4144	−	57.8755i	0.0174845	−	0.0302840i
$155$	−37.8635	+	214.735i	−0.0196211	+	0.111277i
$156$		0			0
$157$	−94.3245	−	34.3313i	−0.0479485	−	0.0174518i	0.317935	−	0.948113i	$-0.397011\pi$
$157$	−94.3245	−	34.3313i	−0.0479485	−	0.0174518i	−0.365883	+	0.930661i	$0.619233\pi$
$158$	92.3371	+	523.670i	0.0464933	+	0.263677i
$159$		0			0
$160$	−28.0891	−	23.5695i	−0.0138790	−	0.0116458i
$161$	64.1913			0.0314223
$162$		0			0
$163$	2711.32			1.30287			0.651433	−	0.758706i	$-0.274168\pi$
$163$	2711.32			1.30287			0.651433	+	0.758706i	$0.274168\pi$
$164$	716.683	+	601.368i	0.341241	+	0.286335i
$165$		0			0
$166$	−211.585	−	1199.96i	−0.0989288	−	0.561053i
$167$	−1002.02	−	364.706i	−0.464304	−	0.168993i	0.0992664	−	0.995061i	$-0.468350\pi$
$167$	−1002.02	−	364.706i	−0.464304	−	0.168993i	−0.563570	+	0.826068i	$0.690573\pi$
$168$		0			0
$169$	−69.1916	+	392.405i	−0.0314937	+	0.178610i
$170$	49.8196	−	86.2900i	0.0224764	−	0.0389303i
$171$		0			0
$172$	−777.647	−	1346.92i	−0.344739	−	0.597105i
$173$	−709.872	+	258.372i	−0.311969	+	0.113547i	−0.493260	−	0.869882i	$-0.664195\pi$
$173$	−709.872	+	258.372i	−0.311969	+	0.113547i	0.181291	+	0.983430i	$0.441972\pi$
$174$		0			0
$175$	−256.630	+	215.338i	−0.110854	+	0.0930172i
$176$	151.210	−	126.880i	0.0647605	−	0.0543405i
$177$		0			0
$178$	2003.33	−	729.153i	0.843573	−	0.307035i
$179$	699.224	+	1211.09i	0.291969	+	0.505705i	0.974275	−	0.225361i	$-0.0723562\pi$
$179$	699.224	+	1211.09i	0.291969	+	0.505705i	−0.682306	+	0.731067i	$0.739023\pi$
$180$		0			0
$181$	−1821.76	+	3155.39i	−0.748125	+	1.29579i	0.200595	+	0.979674i	$0.435712\pi$
$181$	−1821.76	+	3155.39i	−0.748125	+	1.29579i	−0.948720	+	0.316116i	$0.897621\pi$
$182$	−39.8923	+	226.240i	−0.0162473	+	0.0921432i
$183$		0			0
$184$	178.166	+	64.8470i	0.0713834	+	0.0259814i
$185$	10.5071	+	59.5889i	0.00417567	+	0.0236814i
$186$		0			0
$187$	410.891	+	344.778i	0.160681	+	0.134827i
$188$	2068.09			0.802292
$189$		0			0
$190$	300.977			0.114922
$191$	1751.69	+	1469.85i	0.663603	+	0.556829i	0.911164	−	0.412043i	$-0.135185\pi$
$191$	1751.69	+	1469.85i	0.663603	+	0.556829i	−0.247561	+	0.968872i	$0.579629\pi$
$192$		0			0
$193$	−831.797	−	4717.35i	−0.310228	−	1.75939i	−0.597812	−	0.801636i	$-0.703963\pi$
$193$	−831.797	−	4717.35i	−0.310228	−	1.75939i	0.287584	−	0.957756i	$-0.407148\pi$
$194$	1659.86	+	604.141i	0.614284	+	0.223581i
$195$		0			0
$196$	−233.150	+	1322.26i	−0.0849671	+	0.481873i
$197$	1999.64	−	3463.47i	0.723189	−	1.25260i	−0.236527	−	0.971625i	$-0.576009\pi$
$197$	1999.64	−	3463.47i	0.723189	−	1.25260i	0.959715	−	0.280974i	$-0.0906576\pi$
$198$		0			0
$199$	2626.97	+	4550.04i	0.935782	+	1.62082i	0.773233	+	0.634122i	$0.218638\pi$
$199$	2626.97	+	4550.04i	0.935782	+	1.62082i	0.162549	+	0.986700i	$0.448028\pi$
$200$	−929.822	+	338.428i	−0.328742	+	0.119652i
$201$		0			0
$202$	−2882.31	+	2418.54i	−1.00395	+	0.842416i
$203$	−363.170	+	304.736i	−0.125564	+	0.105361i
$204$		0			0
$205$	−251.844	+	91.6638i	−0.0858028	+	0.0312297i
$206$	−1881.53	−	3258.91i	−0.636371	−	1.10223i
$207$		0			0
$208$	−339.274	+	587.639i	−0.113098	+	0.195892i
$209$	−281.349	+	1595.61i	−0.0931164	+	0.528089i
$210$		0			0
$211$	1787.38	+	650.553i	0.583168	+	0.212256i	0.616722	−	0.787181i	$-0.288460\pi$
$211$	1787.38	+	650.553i	0.583168	+	0.212256i	−0.0335542	+	0.999437i	$0.510683\pi$
$212$	−67.6689	−	383.770i	−0.0219223	−	0.124327i
$213$		0			0
$214$	826.451	+	693.475i	0.263996	+	0.221519i
$215$	445.539			0.141328
$216$		0			0
$217$	−515.402			−0.161234
$218$	264.812	+	222.204i	0.0822722	+	0.0690346i
$219$		0			0
$220$	9.81904	+	55.6865i	0.00300909	+	0.0170654i
$221$	−1732.66	−	630.636i	−0.527381	−	0.191951i
$222$		0			0
$223$	128.866	−	730.836i	0.0386974	−	0.219464i	−0.959327	−	0.282299i	$-0.908903\pi$
$223$	128.866	−	730.836i	0.0386974	−	0.219464i	0.998024	+	0.0628349i	$0.0200142\pi$
$224$	43.3360	−	75.0601i	0.0129264	−	0.0223891i
$225$		0			0
$226$	1789.93	+	3100.25i	0.526834	+	0.912502i
$227$	1690.72	−	615.371i	0.494347	−	0.179928i	−0.0828025	−	0.996566i	$-0.526387\pi$
$227$	1690.72	−	615.371i	0.494347	−	0.179928i	0.577150	+	0.816638i	$0.304165\pi$
$228$		0			0
$229$	−5198.62	+	4362.16i	−1.50015	+	1.25878i	−0.619515	+	0.784984i	$0.712671\pi$
$229$	−5198.62	+	4362.16i	−1.50015	+	1.25878i	−0.880636	+	0.473793i	$0.842885\pi$
$230$	−41.6069	+	34.9123i	−0.0119282	+	0.0100089i
$231$		0			0
$232$	−1315.84	+	478.927i	−0.372367	+	0.135531i
$233$	980.266	+	1697.87i	0.275620	+	0.477387i	0.970291	−	0.241940i	$-0.0777837\pi$
$233$	980.266	+	1697.87i	0.275620	+	0.477387i	−0.694672	+	0.719327i	$0.744450\pi$
$234$		0			0
$235$	−296.219	+	513.066i	−0.0822264	+	0.142420i
$236$	−500.537	+	2838.69i	−0.138060	+	0.782978i
$237$		0			0
$238$	221.315	+	80.5521i	0.0602762	+	0.0219387i
$239$	361.176	+	2048.33i	0.0977511	+	0.554374i	0.993870	+	0.110559i	$0.0352641\pi$
$239$	361.176	+	2048.33i	0.0977511	+	0.554374i	−0.896118	+	0.443815i	$0.853625\pi$
$240$		0			0
$241$	−327.511	−	274.815i	−0.0875388	−	0.0734538i	0.597968	−	0.801520i	$-0.295975\pi$
$241$	−327.511	−	274.815i	−0.0875388	−	0.0734538i	−0.685507	+	0.728066i	$0.740419\pi$
$242$	2357.60			0.626250
$243$		0			0
$244$	−1987.95			−0.521580
$245$	−294.640	−	247.233i	−0.0768322	−	0.0644698i
$246$		0			0
$247$	−967.164	−	5485.06i	−0.249147	−	1.41298i
$248$	−1430.52	−	520.666i	−0.366282	−	0.133316i
$249$		0			0
$250$	98.9661	−	561.265i	0.0250367	−	0.141990i
$251$	3149.13	−	5454.45i	0.791917	−	1.37164i	−0.132862	−	0.991135i	$-0.542417\pi$
$251$	3149.13	−	5454.45i	0.791917	−	1.37164i	0.924779	−	0.380505i	$-0.124250\pi$
$252$		0			0
$253$	−146.192	−	253.212i	−0.0363281	−	0.0629221i
$254$	285.954	−	104.079i	0.0706391	−	0.0257105i
$255$		0			0
$256$	196.107	−	164.554i	0.0478778	−	0.0401742i
$257$	−2218.91	+	1861.88i	−0.538566	+	0.451911i	−0.871047	−	0.491199i	$-0.836559\pi$
$257$	−2218.91	+	1861.88i	−0.538566	+	0.451911i	0.332481	+	0.943110i	$0.392114\pi$
$258$		0			0
$259$	−134.399	+	48.9171i	−0.0322437	+	0.0117358i
$260$	−97.1904	−	168.339i	−0.0231827	−	0.0401536i
$261$		0			0
$262$	−630.859	+	1092.68i	−0.148758	+	0.257656i
$263$	−1030.83	+	5846.14i	−0.241688	+	1.37068i	0.586374	+	0.810041i	$0.300555\pi$
$263$	−1030.83	+	5846.14i	−0.241688	+	1.37068i	−0.828061	+	0.560638i	$0.810556\pi$
$264$		0			0
$265$	104.901	+	38.1807i	0.0243170	+	0.00885065i
$266$	123.537	+	700.616i	0.0284758	+	0.161494i
$267$		0			0
$268$	424.415	+	356.126i	0.0967360	+	0.0811711i
$269$	903.714			0.204834			0.102417	−	0.994742i	$-0.467342\pi$
$269$	903.714			0.204834			0.102417	+	0.994742i	$0.467342\pi$
$270$		0			0
$271$	762.435			0.170903			0.0854513	−	0.996342i	$-0.472767\pi$
$271$	762.435			0.170903			0.0854513	+	0.996342i	$0.472767\pi$
$272$	532.894	+	447.151i	0.118792	+	0.0996783i
$273$		0			0
$274$	113.760	+	645.164i	0.0250821	+	0.142247i
$275$	1433.89	+	521.893i	0.314424	+	0.114441i
$276$		0			0
$277$	207.955	−	1179.37i	0.0451077	−	0.255818i	−0.953912	−	0.300086i	$-0.902984\pi$
$277$	207.955	−	1179.37i	0.0451077	−	0.255818i	0.999020	+	0.0442681i	$0.0140956\pi$
$278$	−2425.04	+	4200.30i	−0.523181	+	0.906177i
$279$		0			0
$280$	12.4143	+	21.5022i	0.00264963	+	0.00458929i
$281$	4434.64	−	1614.08i	0.941454	−	0.342661i	0.174714	−	0.984619i	$-0.444100\pi$
$281$	4434.64	−	1614.08i	0.941454	−	0.342661i	0.766740	+	0.641958i	$0.221878\pi$
$282$		0			0
$283$	861.354	−	722.762i	0.180926	−	0.151815i	−0.547827	−	0.836592i	$-0.684545\pi$
$283$	861.354	−	722.762i	0.180926	−	0.151815i	0.728753	+	0.684777i	$0.240100\pi$
$284$	−2993.94	+	2512.21i	−0.625555	+	0.524903i
$285$		0			0
$286$	983.290	−	357.888i	0.203298	−	0.0739943i
$287$	−316.746	−	548.621i	−0.0651461	−	0.112836i
$288$		0			0
$289$	1511.34	−	2617.72i	0.307621	−	0.532816i
$290$	69.6564	−	395.041i	0.0141047	−	0.0799918i
$291$		0			0
$292$	1575.78	+	573.536i	0.315806	+	0.114944i
$293$	−796.503	−	4517.19i	−0.158813	−	0.900673i	−0.955217	−	0.295908i	$-0.904378\pi$
$293$	−796.503	−	4517.19i	−0.158813	−	0.900673i	0.796404	−	0.604766i	$-0.206733\pi$
$294$		0			0
$295$	−632.548	−	530.771i	−0.124842	−	0.104755i
$296$	−422.445			−0.0829532
$297$		0			0
$298$	3201.47			0.622337
$299$	769.949	+	646.064i	0.148921	+	0.124959i
$300$		0			0
$301$	182.874	+	1037.13i	0.0350188	+	0.198602i
$302$	−1112.92	−	405.071i	−0.212058	−	0.0771828i
$303$		0			0
$304$	−364.888	+	2069.38i	−0.0688414	+	0.390419i
$305$	284.740	−	493.184i	0.0534563	−	0.0925890i
$306$		0			0
$307$	−900.322	−	1559.40i	−0.167375	−	0.289902i	0.770121	−	0.637898i	$-0.220196\pi$
$307$	−900.322	−	1559.40i	−0.167375	−	0.289902i	−0.937496	+	0.347996i	$0.886862\pi$
$308$	−125.597	+	45.7136i	−0.0232356	+	0.00845707i
$309$		0			0
$310$	334.068	−	280.316i	0.0612057	−	0.0513577i
$311$	4619.29	−	3876.04i	0.842237	−	0.706721i	−0.115829	−	0.993269i	$-0.536952\pi$
$311$	4619.29	−	3876.04i	0.842237	−	0.706721i	0.958066	+	0.286548i	$0.0925079\pi$
$312$		0			0
$313$	5054.21	−	1839.58i	0.912718	−	0.332202i	0.157381	−	0.987538i	$-0.449695\pi$
$313$	5054.21	−	1839.58i	0.912718	−	0.332202i	0.755338	+	0.655336i	$0.227473\pi$
$314$	100.378	+	173.860i	0.0180403	+	0.0312467i
$315$		0			0
$316$	531.748	−	921.015i	0.0946620	−	0.163959i
$317$	946.602	−	5368.45i	0.167718	−	0.951173i	−0.778501	−	0.627644i	$-0.784019\pi$
$317$	946.602	−	5368.45i	0.167718	−	0.951173i	0.946218	−	0.323529i	$-0.104869\pi$
$318$		0			0
$319$	2029.17	+	738.558i	0.356150	+	0.129628i
$320$	12.7345	+	72.2212i	0.00222463	+	0.0126165i
$321$		0			0
$322$	−98.3469	−	82.5228i	−0.0170207	−	0.0142820i
$323$	−5710.01			−0.983632
$324$		0			0
$325$	−5245.47			−0.895281
$326$	−4153.99	−	3485.61i	−0.705730	−	0.592178i
$327$		0			0
$328$	−324.918	−	1842.70i	−0.0546969	−	0.310201i
$329$	−1315.90	−	478.950i	−0.220511	−	0.0802594i
$330$		0			0
$331$	852.014	−	4832.01i	0.141483	−	0.802391i	−0.828641	−	0.559781i	$-0.810885\pi$
$331$	852.014	−	4832.01i	0.141483	−	0.802391i	0.970124	−	0.242610i	$-0.0780035\pi$
$332$	−1218.47	+	2110.45i	−0.201422	+	0.348874i
$333$		0			0
$334$	1066.33	+	1846.94i	0.174691	+	0.302574i
$335$	−149.140	+	54.2827i	−0.0243236	+	0.00885308i
$336$		0			0
$337$	−3509.74	+	2945.02i	−0.567322	+	0.476040i	−0.880756	−	0.473570i	$-0.842965\pi$
$337$	−3509.74	+	2945.02i	−0.567322	+	0.476040i	0.313434	+	0.949610i	$0.398521\pi$
$338$	610.474	−	512.249i	0.0982409	−	0.0824339i
$339$		0			0
$340$	−187.260	+	68.1572i	−0.0298695	+	0.0108716i
$341$	1173.80	+	2033.07i	0.186407	+	0.322866i
$342$		0			0
$343$	919.080	−	1591.89i	0.144681	−	0.250595i
$344$	−540.148	+	3063.33i	−0.0846594	+	0.480127i
$345$		0			0
$346$	1419.74	+	516.745i	0.220595	+	0.0802901i
$347$	−625.223	−	3545.82i	−0.0967254	−	0.548557i	−0.994205	−	0.107501i	$-0.965715\pi$
$347$	−625.223	−	3545.82i	−0.0967254	−	0.548557i	0.897480	−	0.441056i	$-0.145396\pi$
$348$		0			0
$349$	3825.13	+	3209.67i	0.586689	+	0.492291i	0.887136	−	0.461508i	$-0.152691\pi$
$349$	3825.13	+	3209.67i	0.586689	+	0.492291i	−0.300447	+	0.953799i	$0.597136\pi$
$350$	670.012			0.102325
$351$		0			0
$352$	−394.780			−0.0597780
$353$	−8485.65	−	7120.30i	−1.27945	−	1.07358i	−0.993320	−	0.115394i	$-0.963187\pi$
$353$	−8485.65	−	7120.30i	−1.27945	−	1.07358i	−0.286129	−	0.958191i	$-0.592369\pi$
$354$		0			0
$355$	−194.416	−	1102.59i	−0.0290663	−	0.164843i
$356$	−4006.66	−	1458.31i	−0.596496	−	0.217107i
$357$		0			0
$358$	485.676	−	2754.41i	0.0717005	−	0.406634i
$359$	−1966.12	+	3405.41i	−0.289046	+	0.500643i	−0.973582	−	0.228336i	$-0.926671\pi$
$359$	−1966.12	+	3405.41i	−0.289046	+	0.500643i	0.684536	+	0.728979i	$0.260005\pi$
$360$		0			0
$361$	−5194.52	−	8997.17i	−0.757329	−	1.31173i
$362$	6847.59	−	2492.32i	0.994203	−	0.361860i
$363$		0			0
$364$	351.968	−	295.336i	0.0506816	−	0.0425270i
$365$	−367.990	+	308.781i	−0.0527712	+	0.0442803i
$366$		0			0
$367$	−1576.24	+	573.703i	−0.224193	+	0.0815996i	−0.451674	−	0.892183i	$-0.649173\pi$
$367$	−1576.24	+	573.703i	−0.224193	+	0.0815996i	0.227481	+	0.973782i	$0.426951\pi$
$368$	−189.600	−	328.396i	−0.0268575	−	0.0465186i
$369$		0			0
$370$	60.5081	−	104.803i	0.00850181	−	0.0147256i
$371$	−45.8203	+	259.860i	−0.00641205	+	0.0363646i
$372$		0			0
$373$	6858.92	+	2496.44i	0.952122	+	0.346544i	0.770942	−	0.636906i	$-0.219786\pi$
$373$	6858.92	+	2496.44i	0.952122	+	0.346544i	0.181180	+	0.983450i	$0.442008\pi$
$374$	−186.283	−	1056.46i	−0.0257552	−	0.146065i
$375$		0			0
$376$	−3168.50	−	2658.69i	−0.434582	−	0.364658i
$377$	−7423.14			−1.01409
$378$		0			0
$379$	−6835.79			−0.926467			−0.463234	−	0.886236i	$-0.653311\pi$
$379$	−6835.79			−0.926467			−0.463234	+	0.886236i	$0.653311\pi$
$380$	−461.123	−	386.928i	−0.0622503	−	0.0522342i
$381$		0			0
$382$	−794.154	−	4503.87i	−0.106368	−	0.603241i
$383$	7091.15	+	2580.97i	0.946060	+	0.344338i	0.768556	−	0.639783i	$-0.220976\pi$
$383$	7091.15	+	2580.97i	0.946060	+	0.344338i	0.177504	+	0.984120i	$0.443198\pi$
$384$		0			0
$385$	6.64871	−	37.7067i	0.000880129	−	0.00499146i
$386$	−4790.13	+	8296.74i	−0.631635	+	1.09402i
$387$		0			0
$388$	−1766.39	−	3059.48i	−0.231121	−	0.400313i
$389$	−3563.87	+	1297.14i	−0.464512	+	0.169069i	−0.563665	−	0.826004i	$-0.690609\pi$
$389$	−3563.87	+	1297.14i	−0.464512	+	0.169069i	0.0991525	+	0.995072i	$0.468387\pi$
$390$		0			0
$391$	789.348	−	662.342i	0.102095	−	0.0856677i
$392$	2057.07	−	1726.09i	0.265045	−	0.222399i
$393$		0			0
$394$	−7516.17	+	2735.66i	−0.961064	+	0.349799i
$395$	152.328	+	263.840i	0.0194037	+	0.0336081i
$396$		0			0
$397$	4699.16	−	8139.18i	0.594066	−	1.02895i	−0.399612	−	0.916684i	$-0.630855\pi$
$397$	4699.16	−	8139.18i	0.594066	−	1.02895i	0.993678	−	0.112268i	$-0.0358114\pi$
$398$	1824.67	−	10348.2i	0.229805	−	1.30329i
$399$		0			0
$400$	1859.64	+	676.855i	0.232456	+	0.0846069i
$401$	1740.64	+	9871.68i	0.216767	+	1.22935i	0.877814	+	0.479003i	$0.159002\pi$
$401$	1740.64	+	9871.68i	0.216767	+	1.22935i	−0.661046	+	0.750345i	$0.729887\pi$
$402$		0			0
$403$	−6182.03	−	5187.34i	−0.764142	−	0.641191i
$404$	7525.17			0.926710
$405$		0			0
$406$	948.170			0.115904
$407$	499.045	+	418.749i	0.0607783	+	0.0509990i
$408$		0			0
$409$	2037.57	+	11555.6i	0.246336	+	1.39704i	0.817369	+	0.576114i	$0.195432\pi$
$409$	2037.57	+	11555.6i	0.246336	+	1.39704i	−0.571033	+	0.820927i	$0.693457\pi$
$410$	503.689	+	183.328i	0.0606717	+	0.0220827i
$411$		0			0
$412$	−1306.90	+	7411.78i	−0.156277	+	0.886292i
$413$	975.898	−	1690.31i	0.116273	−	0.201391i
$414$		0			0
$415$	−349.050	−	604.573i	−0.0412872	−	0.0715116i
$416$	1275.25	−	464.154i	0.150299	−	0.0547044i
$417$		0			0
$418$	2482.33	−	2082.92i	0.290466	−	0.243730i
$419$	5327.63	−	4470.42i	0.621174	−	0.521227i	−0.276998	−	0.960870i	$-0.589340\pi$
$419$	5327.63	−	4470.42i	0.621174	−	0.521227i	0.898172	+	0.439643i	$0.144895\pi$
$420$		0			0
$421$	1470.40	−	535.182i	0.170221	−	0.0619553i	−0.255504	−	0.966808i	$-0.582241\pi$
$421$	1470.40	−	535.182i	0.170221	−	0.0619553i	0.425725	+	0.904853i	$0.360019\pi$
$422$	−1902.09	−	3294.52i	−0.219413	−	0.380035i
$423$		0			0
$424$	−389.690	+	674.962i	−0.0446345	+	0.0773091i
$425$	−933.815	+	5295.93i	−0.106580	+	0.604448i
$426$		0			0
$427$	1264.91	+	460.390i	0.143357	+	0.0521776i
$428$	−374.683	−	2124.93i	−0.0423153	−	0.239982i
$429$		0			0
$430$	−682.606	−	572.774i	−0.0765539	−	0.0642363i
$431$	−12992.9			−1.45208			−0.726040	−	0.687653i	$-0.758641\pi$
$431$	−12992.9			−1.45208			−0.726040	+	0.687653i	$0.758641\pi$
$432$		0			0
$433$	3840.16			0.426204			0.213102	−	0.977030i	$-0.431643\pi$
$433$	3840.16			0.426204			0.213102	+	0.977030i	$0.431643\pi$
$434$	789.641	+	662.588i	0.0873364	+	0.0732839i
$435$		0			0
$436$	−120.056	−	680.872i	−0.0131873	−	0.0747887i
$437$	2924.85	+	1064.56i	0.320171	+	0.116533i
$438$		0			0
$439$	−2383.98	+	13520.2i	−0.259183	+	1.46990i	0.525920	+	0.850534i	$0.323721\pi$
$439$	−2383.98	+	13520.2i	−0.259183	+	1.46990i	−0.785103	+	0.619366i	$0.787390\pi$
$440$	56.5456	−	97.9399i	0.00612660	−	0.0106116i
$441$		0			0
$442$	1843.86	+	3193.65i	0.198424	+	0.343680i
$443$	−2037.95	+	741.752i	−0.218568	+	0.0795523i	−0.448983	−	0.893540i	$-0.648214\pi$
$443$	−2037.95	+	741.752i	−0.218568	+	0.0795523i	0.230415	+	0.973092i	$0.425992\pi$
$444$		0			0
$445$	935.673	−	785.123i	0.0996745	−	0.0836369i
$446$	−1136.98	+	954.039i	−0.120712	+	0.101289i
$447$		0			0
$448$	−162.890	+	59.2871i	−0.0171782	+	0.00625235i
$449$	7281.56	+	12612.0i	0.765341	+	1.32561i	0.940066	+	0.340992i	$0.110763\pi$
$449$	7281.56	+	12612.0i	0.765341	+	1.32561i	−0.174725	+	0.984617i	$0.555904\pi$
$450$		0			0
$451$	−1442.74	+	2498.90i	−0.150634	+	0.260906i
$452$	1243.27	−	7050.95i	0.129377	−	0.733736i
$453$		0			0
$454$	−3381.43	−	1230.74i	−0.349556	−	0.127228i
$455$	22.8556	+	129.620i	0.00235492	+	0.0133554i
$456$		0			0
$457$	8446.37	+	7087.34i	0.864561	+	0.725453i	0.962946	−	0.269696i	$-0.0869231\pi$
$457$	8446.37	+	7087.34i	0.864561	+	0.725453i	−0.0983847	+	0.995148i	$0.531368\pi$
$458$	13572.6			1.38473
$459$		0			0
$460$	108.628			0.0110104
$461$	−3111.60	−	2610.94i	−0.314364	−	0.263783i	0.471929	−	0.881637i	$-0.343558\pi$
$461$	−3111.60	−	2610.94i	−0.314364	−	0.263783i	−0.786293	+	0.617854i	$0.788002\pi$
$462$		0			0
$463$	3039.94	+	17240.4i	0.305136	+	1.73051i	0.622862	+	0.782332i	$0.285970\pi$
$463$	3039.94	+	17240.4i	0.305136	+	1.73051i	−0.317725	+	0.948183i	$0.602919\pi$
$464$	2631.68	+	957.854i	0.263303	+	0.0958346i
$465$		0			0
$466$	680.885	−	3861.49i	0.0676854	−	0.383863i
$467$	647.020	−	1120.67i	0.0641124	−	0.111046i	−0.832188	−	0.554494i	$-0.812912\pi$
$467$	647.020	−	1120.67i	0.0641124	−	0.111046i	0.896300	+	0.443448i	$0.146245\pi$
$468$		0			0
$469$	−187.575	−	324.889i	−0.0184678	−	0.0319872i
$470$	1113.42	−	405.251i	0.109273	−	0.0397720i
$471$		0			0
$472$	4416.21	−	3705.64i	0.430662	−	0.361369i
$473$	3674.62	−	3083.37i	0.357207	−	0.299732i
$474$		0			0
$475$	−15264.4	+	5555.79i	−1.47448	+	0.536667i
$476$	−235.519	−	407.930i	−0.0226785	−	0.0392804i
$477$		0			0
$478$	2079.93	−	3602.54i	0.199024	−	0.344720i
$479$	−1784.01	+	10117.6i	−0.170174	+	0.965104i	0.773394	+	0.633925i	$0.218557\pi$
$479$	−1784.01	+	10117.6i	−0.170174	+	0.965104i	−0.943568	+	0.331179i	$0.892554\pi$
$480$		0			0
$481$	−2104.39	−	765.936i	−0.199484	−	0.0726064i
$482$	148.482	+	842.081i	0.0140314	+	0.0795762i
$483$		0			0
$484$	−3612.06	−	3030.88i	−0.339224	−	0.284643i
$485$	1012.02			0.0947495
$486$		0			0
$487$	6611.63			0.615198			0.307599	−	0.951516i	$-0.400474\pi$
$487$	6611.63			0.615198			0.307599	+	0.951516i	$0.400474\pi$
$488$	3045.72	+	2555.66i	0.282527	+	0.237068i
$489$		0			0
$490$	133.579	+	757.564i	0.0123153	+	0.0698434i
$491$	17016.2	+	6193.39i	1.56401	+	0.569254i	0.971652	−	0.236417i	$-0.0759733\pi$
$491$	17016.2	+	6193.39i	1.56401	+	0.569254i	0.592362	+	0.805672i	$0.298195\pi$
$492$		0			0
$493$	−1321.49	+	7494.55i	−0.120724	+	0.684661i
$494$	−5569.68	+	9646.96i	−0.507270	+	0.878618i
$495$		0			0
$496$	1522.32	+	2636.74i	0.137811	+	0.238696i
$497$	2486.82	−	905.127i	0.224445	−	0.0816911i
$498$		0			0
$499$	3443.74	−	2889.64i	0.308944	−	0.259234i	−0.475112	−	0.879926i	$-0.657592\pi$
$499$	3443.74	−	2889.64i	0.308944	−	0.259234i	0.784055	+	0.620691i	$0.213148\pi$
$500$	−873.173	+	732.679i	−0.0780990	+	0.0655328i
$501$		0			0
$502$	−11836.8	+	4308.26i	−1.05240	+	0.383042i
$503$	−5953.92	−	10312.5i	−0.527778	−	0.914138i	−0.999476	−	0.0323780i	$-0.989692\pi$
$503$	−5953.92	−	10312.5i	−0.527778	−	0.914138i	0.471698	−	0.881760i	$-0.343641\pi$
$504$		0			0
$505$	−1077.85	+	1866.90i	−0.0949779	+	0.164506i
$506$	−101.544	+	575.884i	−0.00892129	+	0.0505952i
$507$		0			0
$508$	−571.907	−	208.157i	−0.0499494	−	0.0181801i
$509$	3399.48	+	19279.4i	0.296030	+	1.67887i	0.662986	+	0.748632i	$0.269289\pi$
$509$	3399.48	+	19279.4i	0.296030	+	1.67887i	−0.366956	+	0.930238i	$0.619600\pi$
$510$		0			0
$511$	−869.825	−	729.870i	−0.0753010	−	0.0631850i
$512$	−512.000			−0.0441942
$513$		0			0
$514$	5793.15			0.497130
$515$	−1651.58	−	1385.84i	−0.141315	−	0.118577i
$516$		0			0
$517$	1107.61	+	6281.54i	0.0942214	+	0.534356i
$518$	268.797	+	97.8342i	0.0227998	+	0.00829843i
$519$		0			0
$520$	−67.5078	+	382.856i	−0.00569310	+	0.0322872i
$521$	7049.83	−	12210.7i	0.592819	−	1.02679i	−0.401032	−	0.916064i	$-0.631348\pi$
$521$	7049.83	−	12210.7i	0.592819	−	1.02679i	0.993851	−	0.110729i	$-0.0353184\pi$
$522$		0			0
$523$	−171.009	−	296.197i	−0.0142977	−	0.0247644i	0.858788	−	0.512331i	$-0.171218\pi$
$523$	−171.009	−	296.197i	−0.0142977	−	0.0247644i	−0.873086	+	0.487567i	$0.837885\pi$
$524$	2371.25	−	863.065i	0.197688	−	0.0719526i
$525$		0			0
$526$	9094.98	−	7631.59i	0.753916	−	0.632611i
$527$	−6337.79	+	5318.04i	−0.523868	+	0.439577i
$528$		0			0
$529$	10905.4	−	3969.25i	0.896312	−	0.326231i
$530$	−111.633	−	193.354i	−0.00914910	−	0.0158467i
$531$		0			0
$532$	711.424	−	1232.22i	0.0579777	−	0.100420i
$533$	1722.44	−	9768.43i	0.139976	−	0.793842i
$534$		0			0
$535$	580.834	+	211.406i	0.0469377	+	0.0170839i
$536$	−192.414	−	1091.23i	−0.0155056	−	0.0879368i
$537$		0			0
$538$	−1384.57	−	1161.79i	−0.110954	−	0.0931012i
$539$	−4141.05			−0.330923
$540$		0			0
$541$	1438.72			0.114335			0.0571675	−	0.998365i	$-0.481793\pi$
$541$	1438.72			0.114335			0.0571675	+	0.998365i	$0.481793\pi$
$542$	−1168.12	−	980.167i	−0.0925737	−	0.0776786i
$543$		0			0
$544$	−241.594	−	1370.15i	−0.0190409	−	0.107987i
$545$	186.111	+	67.7390i	0.0146278	+	0.00532408i
$546$		0			0
$547$	719.189	−	4078.72i	0.0562162	−	0.318818i	−0.943712	−	0.330767i	$-0.892692\pi$
$547$	719.189	−	4078.72i	0.0562162	−	0.318818i	0.999929	+	0.0119491i	$0.00380360\pi$
$548$	655.117	−	1134.70i	0.0510679	−	0.0884522i
$549$		0			0
$550$	−1525.91	−	2642.96i	−0.118300	−	0.204902i
$551$	−21601.5	+	7862.29i	−1.67015	+	0.607885i
$552$		0			0
$553$	−551.644	+	462.884i	−0.0424200	+	0.0355946i
$554$	−1834.78	+	1539.56i	−0.140708	+	0.118068i
$555$		0			0
$556$	9115.18	−	3317.65i	0.695269	−	0.253057i
$557$	7247.84	+	12553.6i	0.551348	+	0.954963i	0.998178	+	0.0603438i	$0.0192197\pi$
$557$	7247.84	+	12553.6i	0.551348	+	0.954963i	−0.446830	+	0.894619i	$0.647447\pi$
$558$		0			0
$559$	−8244.85	+	14280.5i	−0.623828	+	1.08050i
$560$	8.62288	−	48.9028i	0.000650684	−	0.00369021i
$561$		0			0
$562$	−8869.28	−	3228.15i	−0.665708	−	0.242298i
$563$	−3967.44	−	22500.5i	−0.296994	−	1.68434i	−0.658986	−	0.752155i	$-0.729014\pi$
$563$	−3967.44	−	22500.5i	−0.296994	−	1.68434i	0.361992	−	0.932181i	$-0.382097\pi$
$564$		0			0
$565$	1571.17	+	1318.37i	0.116991	+	0.0981667i
$566$	−2248.84			−0.167006
$567$		0			0
$568$	7816.62			0.577427
$569$	8207.70	+	6887.08i	0.604718	+	0.507419i	0.892958	−	0.450139i	$-0.148626\pi$
$569$	8207.70	+	6887.08i	0.604718	+	0.507419i	−0.288240	+	0.957558i	$0.593070\pi$
$570$		0			0
$571$	−2821.15	−	15999.5i	−0.206762	−	1.17261i	−0.894642	−	0.446783i	$-0.852570\pi$
$571$	−2821.15	−	15999.5i	−0.206762	−	1.17261i	0.687880	−	0.725824i	$-0.258541\pi$
$572$	−1966.58	−	715.776i	−0.143753	−	0.0523219i
$573$		0			0
$574$	−220.010	+	1247.74i	−0.0159983	+	0.0907309i
$575$	1465.69	−	2538.65i	0.106302	−	0.184120i
$576$		0			0
$577$	−9474.79	−	16410.8i	−0.683606	−	1.18404i	−0.973873	−	0.227094i	$-0.927077\pi$
$577$	−9474.79	−	16410.8i	−0.683606	−	1.18404i	0.290267	−	0.956946i	$-0.406256\pi$
$578$	−5680.80	+	2067.64i	−0.408806	+	0.148793i
$579$		0			0
$580$	−614.575	+	515.690i	−0.0439980	+	0.0369187i
$581$	1264.06	−	1060.67i	0.0902616	−	0.0757385i
$582$		0			0
$583$	1129.41	−	411.070i	0.0802320	−	0.0292021i
$584$	−1676.91	−	2904.49i	−0.118820	−	0.205802i
$585$		0			0
$586$	−4586.88	+	7944.71i	−0.323348	+	0.560056i
$587$	681.011	−	3862.20i	0.0478847	−	0.271568i	−0.951460	−	0.307774i	$-0.900416\pi$
$587$	681.011	−	3862.20i	0.0478847	−	0.271568i	0.999344	+	0.0362059i	$0.0115272\pi$
$588$		0			0
$589$	−23484.0	−	8547.49i	−1.64286	−	0.597951i
$590$	286.774	+	1626.38i	0.0200107	+	0.113486i
$591$		0			0
$592$	647.224	+	543.085i	0.0449337	+	0.0377038i
$593$	6323.05			0.437870			0.218935	−	0.975740i	$-0.429742\pi$
$593$	6323.05			0.437870			0.218935	+	0.975740i	$0.429742\pi$
$594$		0			0
$595$	134.936			0.00929722
$596$	−4904.94	−	4115.74i	−0.337104	−	0.282864i
$597$		0			0
$598$	−349.067	−	1979.66i	−0.0238702	−	0.135375i
$599$	−9257.69	−	3369.52i	−0.631484	−	0.229841i	0.00639294	−	0.999980i	$-0.497965\pi$
$599$	−9257.69	−	3369.52i	−0.631484	−	0.229841i	−0.637877	+	0.770138i	$0.720187\pi$
$600$		0			0
$601$	3450.22	−	19567.2i	0.234172	−	1.32806i	−0.610178	−	0.792265i	$-0.708902\pi$
$601$	3450.22	−	19567.2i	0.234172	−	1.32806i	0.844350	−	0.535792i	$-0.179987\pi$
$602$	1053.13	−	1824.07i	0.0712995	−	0.123494i
$603$		0			0
$604$	1184.35	+	2051.35i	0.0797855	+	0.138192i
$605$	1269.29	−	461.983i	0.0852956	−	0.0310451i
$606$		0			0
$607$	13887.2	−	11652.8i	0.928607	−	0.779194i	−0.0469599	−	0.998897i	$-0.514953\pi$
$607$	13887.2	−	11652.8i	0.928607	−	0.779194i	0.975567	+	0.219703i	$0.0705088\pi$
$608$	3219.39	−	2701.39i	0.214743	−	0.180191i
$609$		0			0
$610$	−1070.27	+	389.547i	−0.0710395	+	0.0258563i
$611$	−10963.3	−	18988.9i	−0.725902	−	1.25730i
$612$		0			0
$613$	6233.42	−	10796.6i	0.410710	−	0.711371i	−0.584257	−	0.811568i	$-0.698614\pi$
$613$	6233.42	−	10796.6i	0.410710	−	0.711371i	0.994968	+	0.100198i	$0.0319475\pi$
$614$	−625.357	+	3546.58i	−0.0411032	+	0.233108i
$615$		0			0
$616$	251.194	+	91.4273i	0.0164300	+	0.00598005i
$617$	−789.207	−	4475.81i	−0.0514948	−	0.292041i	0.948175	−	0.317749i	$-0.102927\pi$
$617$	−789.207	−	4475.81i	−0.0514948	−	0.292041i	−0.999669	+	0.0257081i	$0.991816\pi$
$618$		0			0
$619$	−10101.9	−	8476.50i	−0.655945	−	0.550403i	0.252924	−	0.967486i	$-0.418608\pi$
$619$	−10101.9	−	8476.50i	−0.655945	−	0.550403i	−0.908868	+	0.417083i	$0.863052\pi$
$620$	−872.189			−0.0564967
$621$		0			0
$622$	−12060.1			−0.777438
$623$	2211.67	+	1855.81i	0.142229	+	0.119344i
$624$		0			0
$625$	2628.05	+	14904.4i	0.168195	+	0.953883i
$626$	−10108.4	−	3679.16i	−0.645389	−	0.234903i
$627$		0			0
$628$	69.7218	−	395.412i	0.00443026	−	0.0251253i
$629$	−1147.93	+	1988.28i	−0.0727681	+	0.126038i
$630$		0			0
$631$	12557.7	+	21750.6i	0.792257	+	1.37223i	0.924567	+	0.381021i	$0.124427\pi$
$631$	12557.7	+	21750.6i	0.792257	+	1.37223i	−0.132310	+	0.991208i	$0.542239\pi$
$632$	−1998.72	+	727.475i	−0.125799	+	0.0457870i
$633$		0			0
$634$	−8351.82	+	7008.01i	−0.523175	+	0.438996i
$635$	133.557	−	112.068i	0.00834654	−	0.00700358i
$636$		0			0
$637$	13376.8	−	4868.74i	0.832035	−	0.302836i
$638$	−2159.40	−	3740.19i	−0.133999	−	0.232093i
$639$		0			0
$640$	73.3353	−	127.021i	0.00452943	−	0.00784520i
$641$	2301.36	−	13051.7i	0.141807	−	0.804228i	−0.828068	−	0.560627i	$-0.810560\pi$
$641$	2301.36	−	13051.7i	0.141807	−	0.804228i	0.969875	−	0.243601i	$-0.0783288\pi$
$642$		0			0
$643$	−26622.2	−	9689.68i	−1.63278	−	0.594283i	−0.647023	−	0.762471i	$-0.723986\pi$
$643$	−26622.2	−	9689.68i	−1.63278	−	0.594283i	−0.985755	+	0.168188i	$0.946208\pi$
$644$	44.5868	+	252.865i	0.00272821	+	0.0154725i
$645$		0			0
$646$	8748.24	+	7340.64i	0.532809	+	0.447080i
$647$	−20473.5			−1.24405			−0.622023	−	0.782999i	$-0.713689\pi$
$647$	−20473.5			−1.24405			−0.622023	+	0.782999i	$0.713689\pi$
$648$		0			0
$649$	−8890.20			−0.537705
$650$	8036.52	+	6743.44i	0.484951	+	0.406923i
$651$		0			0
$652$	1883.26	+	10680.5i	0.113120	+	0.641536i
$653$	−29600.7	−	10773.8i	−1.77391	−	0.645651i	−0.999922	−	0.0124521i	$-0.996036\pi$
$653$	−29600.7	−	10773.8i	−1.77391	−	0.645651i	−0.773989	−	0.633199i	$-0.781742\pi$
$654$		0			0
$655$	−125.527	+	711.896i	−0.00748813	+	0.0424673i
$656$	−1871.13	+	3240.88i	−0.111365	+	0.192889i
$657$		0			0
$658$	1400.35	+	2425.49i	0.0829658	+	0.143701i
$659$	−272.330	+	99.1200i	−0.0160978	+	0.00585913i	−0.350057	−	0.936729i	$-0.613838\pi$
$659$	−272.330	+	99.1200i	−0.0160978	+	0.00585913i	0.333959	+	0.942588i	$0.391615\pi$
$660$		0			0
$661$	16679.7	−	13995.9i	0.981488	−	0.823566i	−0.00282495	−	0.999996i	$-0.500899\pi$
$661$	16679.7	−	13995.9i	0.981488	−	0.823566i	0.984313	+	0.176430i	$0.0564548\pi$
$662$	−7517.27	+	6307.74i	−0.441340	+	0.370328i
$663$		0			0
$664$	4579.95	−	1666.96i	0.267675	−	0.0974258i
$665$	203.799	+	352.990i	0.0118842	+	0.0205840i
$666$		0			0
$667$	2074.18	−	3592.58i	0.120408	−	0.208553i
$668$	740.664	−	4200.52i	0.0428999	−	0.243298i
$669$		0			0
$670$	298.281	+	108.565i	0.0171994	+	0.00626007i
$671$	−1064.68	−	6038.13i	−0.0612544	−	0.347391i
$672$		0			0
$673$	10857.5	+	9110.52i	0.621881	+	0.521820i	0.898394	−	0.439190i	$-0.144735\pi$
$673$	10857.5	+	9110.52i	0.621881	+	0.521820i	−0.276513	+	0.961010i	$0.589179\pi$
$674$	9163.27			0.523674
$675$		0			0
$676$	−1593.83			−0.0906824
$677$	21293.9	+	17867.7i	1.20885	+	1.01435i	0.999332	+	0.0365415i	$0.0116341\pi$
$677$	21293.9	+	17867.7i	1.20885	+	1.01435i	0.209519	+	0.977805i	$0.432810\pi$
$678$		0			0
$679$	415.389	+	2355.79i	0.0234774	+	0.133147i
$680$	374.521	+	136.314i	0.0211209	+	0.00768738i
$681$		0			0
$682$	815.310	−	4623.85i	0.0457769	−	0.259614i
$683$	13772.7	−	23855.1i	0.771595	−	1.33644i	−0.165093	−	0.986278i	$-0.552793\pi$
$683$	13772.7	−	23855.1i	0.771595	−	1.33644i	0.936688	−	0.350164i	$-0.113874\pi$
$684$		0			0
$685$	187.669	+	325.052i	0.0104678	+	0.0181308i
$686$	−3454.61	+	1257.38i	−0.192271	+	0.0699808i
$687$		0			0
$688$	4765.70	−	3998.90i	0.264085	−	0.221594i
$689$	−3165.00	+	2655.75i	−0.175003	+	0.146845i
$690$		0			0
$691$	10321.0	−	3756.53i	0.568204	−	0.206809i	−0.0419120	−	0.999121i	$-0.513345\pi$
$691$	10321.0	−	3756.53i	0.568204	−	0.206809i	0.610116	+	0.792312i	$0.291123\pi$
$692$	−1510.86	−	2616.89i	−0.0829976	−	0.143756i
$693$		0			0
$694$	−3600.52	+	6236.28i	−0.196936	+	0.341103i
$695$	−482.529	+	2736.56i	−0.0263358	+	0.149358i
$696$		0			0
$697$	−9555.77	−	3478.01i	−0.519298	−	0.189009i
$698$	−1734.17	−	9834.98i	−0.0940393	−	0.533323i
$699$		0			0
$700$	−1026.52	−	861.351i	−0.0554268	−	0.0465086i
$701$	29101.9			1.56799			0.783997	−	0.620765i	$-0.213178\pi$
$701$	29101.9			1.56799			0.783997	+	0.620765i	$0.213178\pi$
$702$		0			0
$703$	−6935.06			−0.372064
$704$	604.838	+	507.520i	0.0323803	+	0.0271703i
$705$		0			0
$706$	3847.08	+	21817.9i	0.205080	+	1.16307i
$707$	−4788.18	−	1742.76i	−0.254707	−	0.0927059i
$708$		0			0
$709$	4673.58	−	26505.2i	0.247560	−	1.40398i	−0.566911	−	0.823779i	$-0.691862\pi$
$709$	4673.58	−	26505.2i	0.247560	−	1.40398i	0.814471	−	0.580204i	$-0.197027\pi$
$710$	−1119.60	+	1939.20i	−0.0591800	+	0.102503i
$711$		0			0
$712$	4263.80	+	7385.12i	0.224428	+	0.388721i
$713$	4237.90	−	1542.47i	0.222596	−	0.0810182i
$714$		0			0
$715$	459.254	−	385.360i	0.0240212	−	0.0201561i
$716$	−4285.09	+	3595.62i	−0.223661	+	0.187674i
$717$		0			0
$718$	7390.18	−	2689.80i	0.384121	−	0.139809i
$719$	16557.9	+	28679.1i	0.858839	+	1.48755i	0.873037	+	0.487654i	$0.162147\pi$
$719$	16557.9	+	28679.1i	0.858839	+	1.48755i	−0.0141975	+	0.999899i	$0.504519\pi$
$720$		0			0
$721$	2548.06	−	4413.37i	0.131615	−	0.227965i
$722$	−3608.07	+	20462.4i	−0.185981	+	1.05475i
$723$		0			0
$724$	−13695.2	−	4984.64i	−0.703008	−	0.255874i
$725$	3759.43	+	21320.8i	0.192582	+	1.09218i
$726$		0			0
$727$	−1984.23	−	1664.97i	−0.101226	−	0.0849385i	0.590770	−	0.806840i	$-0.298824\pi$
$727$	−1984.23	−	1664.97i	−0.101226	−	0.0849385i	−0.691996	+	0.721901i	$0.743268\pi$
$728$	−918.922			−0.0467823
$729$		0			0
$730$	960.755			0.0487111
$731$	12950.1	+	10866.4i	0.655235	+	0.549808i
$732$		0			0
$733$	524.717	+	2975.82i	0.0264405	+	0.149951i	0.995170	−	0.0981685i	$-0.0312984\pi$
$733$	524.717	+	2975.82i	0.0264405	+	0.149951i	−0.968729	+	0.248120i	$0.920187\pi$
$734$	3152.47	+	1147.41i	0.158528	+	0.0576996i
$735$		0			0
$736$	−131.695	+	746.877i	−0.00659556	+	0.0374053i
$737$	−854.382	+	1479.83i	−0.0427022	+	0.0739624i
$738$		0			0
$739$	5728.66	+	9922.32i	0.285158	+	0.493909i	0.972648	−	0.232286i	$-0.0746205\pi$
$739$	5728.66	+	9922.32i	0.285158	+	0.493909i	−0.687489	+	0.726195i	$0.741287\pi$
$740$	−227.436	+	82.7800i	−0.0112983	+	0.00411224i
$741$		0			0
$742$	404.270	−	339.223i	0.0200016	−	0.0167834i
$743$	−4427.23	+	3714.89i	−0.218599	+	0.183427i	−0.745511	−	0.666494i	$-0.767794\pi$
$743$	−4427.23	+	3714.89i	−0.218599	+	0.183427i	0.526911	+	0.849920i	$0.323350\pi$
$744$		0			0
$745$	1723.61	−	627.343i	0.0847627	−	0.0308511i
$746$	−7299.11	−	12642.4i	−0.358230	−	0.620472i
$747$		0			0
$748$	−1072.76	+	1858.07i	−0.0524384	+	0.0908260i
$749$	−253.707	+	1438.84i	−0.0123768	+	0.0701925i
$750$		0			0
$751$	−4419.24	−	1608.47i	−0.214728	−	0.0781544i	0.232417	−	0.972616i	$-0.425337\pi$
$751$	−4419.24	−	1608.47i	−0.214728	−	0.0781544i	−0.447144	+	0.894462i	$0.647559\pi$
$752$	1436.48	+	8146.69i	0.0696583	+	0.395052i
$753$		0			0
$754$	11372.9	+	9543.01i	0.549307	+	0.460923i
$755$	−678.551			−0.0327086
$756$		0			0
$757$	9623.47			0.462049			0.231024	−	0.972948i	$-0.425792\pi$
$757$	9623.47			0.462049			0.231024	+	0.972948i	$0.425792\pi$
$758$	10473.0	+	8787.92i	0.501844	+	0.421097i
$759$		0			0
$760$	209.056	+	1185.62i	0.00997799	+	0.0565880i
$761$	−4096.07	−	1490.85i	−0.195115	−	0.0710160i	0.242614	−	0.970123i	$-0.421995\pi$
$761$	−4096.07	−	1490.85i	−0.195115	−	0.0710160i	−0.437729	+	0.899107i	$0.644217\pi$
$762$		0			0
$763$	−81.2929	+	461.035i	−0.00385715	+	0.0218750i
$764$	−4573.35	+	7921.27i	−0.216568	+	0.375107i
$765$		0			0
$766$	−7546.25	−	13070.5i	−0.355949	−	0.616522i
$767$	28717.9	−	10452.4i	1.35194	−	0.492068i
$768$		0			0
$769$	−11282.2	+	9466.87i	−0.529058	+	0.443932i	−0.867776	−	0.496956i	$-0.834451\pi$
$769$	−11282.2	+	9466.87i	−0.529058	+	0.443932i	0.338718	+	0.940888i	$0.390007\pi$
$770$	−58.6613	+	49.2226i	−0.00274546	+	0.00230372i
$771$		0			0
$772$	18005.0	−	6553.28i	0.839396	−	0.305515i
$773$	4980.86	+	8627.10i	0.231758	+	0.401417i	0.958326	−	0.285678i	$-0.0922188\pi$
$773$	4980.86	+	8627.10i	0.231758	+	0.401417i	−0.726567	+	0.687095i	$0.758886\pi$
$774$		0			0
$775$	−11768.2	+	20383.2i	−0.545455	+	0.944755i
$776$	−1226.92	+	6958.21i	−0.0567576	+	0.321888i
$777$		0			0
$778$	7127.74	+	2594.28i	0.328460	+	0.119550i
$779$	−5334.00	−	30250.6i	−0.245328	−	1.39132i
$780$		0			0
$781$	−9233.98	−	7748.23i	−0.423070	−	0.354998i
$782$	−2060.84			−0.0942398
$783$		0			0
$784$	−5370.62			−0.244653
$785$	88.1101	+	73.9332i	0.00400610	+	0.00336151i
$786$		0			0
$787$	964.516	+	5470.04i	0.0436865	+	0.247759i	0.998829	−	0.0483896i	$-0.0154089\pi$
$787$	964.516	+	5470.04i	0.0436865	+	0.247759i	−0.955142	+	0.296148i	$0.904298\pi$
$788$	15032.3	+	5471.33i	0.679575	+	0.247345i
$789$		0			0
$790$	105.806	−	600.055i	0.00476507	−	0.0270240i
$791$	−2424.01	+	4198.51i	−0.108961	+	0.188726i
$792$		0			0
$793$	10538.4	+	18253.1i	0.471917	+	0.817384i
$794$	−17663.1	+	6428.83i	−0.789469	+	0.287343i
$795$		0			0
$796$	−16099.0	+	13508.6i	−0.716851	+	0.601509i
$797$	−13045.1	+	10946.1i	−0.579775	+	0.486489i	−0.884873	−	0.465832i	$-0.845755\pi$
$797$	−13045.1	+	10946.1i	−0.579775	+	0.486489i	0.305098	+	0.952321i	$0.401311\pi$
$798$		0			0
$799$	−21123.3	+	7688.26i	−0.935280	+	0.340414i
$800$	−1978.99	−	3427.71i	−0.0874599	−	0.151485i
$801$		0			0
$802$	10024.0	−	17362.0i	0.441345	−	0.764432i
$803$	−898.101	+	5093.38i	−0.0394686	+	0.223838i
$804$		0			0
$805$	−69.1187	−	25.1572i	−0.00302623	−	0.00110146i
$806$	2802.71	+	15894.9i	0.122483	+	0.694634i
$807$		0			0
$808$	−11529.2	−	9674.17i	−0.501976	−	0.421208i
$809$	14673.3			0.637681			0.318841	−	0.947808i	$-0.396707\pi$
$809$	14673.3			0.637681			0.318841	+	0.947808i	$0.396707\pi$
$810$		0			0
$811$	−3706.94			−0.160503			−0.0802517	−	0.996775i	$-0.525572\pi$
$811$	−3706.94			−0.160503			−0.0802517	+	0.996775i	$0.525572\pi$
$812$	−1452.68	−	1218.94i	−0.0627821	−	0.0526805i
$813$		0			0
$814$	−226.249	−	1283.12i	−0.00974203	−	0.0552498i
$815$	−2919.44	−	1062.59i	−0.125477	−	0.0456699i
$816$		0			0
$817$	−8867.32	+	50289.1i	−0.379717	+	2.15348i
$818$	11733.9	−	20323.7i	0.501548	−	0.868707i
$819$		0			0
$820$	−536.014	−	928.404i	−0.0228274	−	0.0395381i
$821$	−3289.42	+	1197.25i	−0.139831	+	0.0508944i	−0.410988	−	0.911641i	$-0.634816\pi$
$821$	−3289.42	+	1197.25i	−0.139831	+	0.0508944i	0.271157	+	0.962535i	$0.412594\pi$
$822$		0			0
$823$	12101.9	−	10154.7i	0.512572	−	0.430099i	−0.349461	−	0.936951i	$-0.613635\pi$
$823$	12101.9	−	10154.7i	0.512572	−	0.430099i	0.862033	+	0.506852i	$0.169191\pi$
$824$	11530.7	−	9675.39i	0.487488	−	0.409051i
$825$		0			0
$826$	−3668.18	+	1335.11i	−0.154518	+	0.0562401i
$827$	−4244.25	−	7351.25i	−0.178461	−	0.309103i	0.762893	−	0.646525i	$-0.223778\pi$
$827$	−4244.25	−	7351.25i	−0.178461	−	0.309103i	−0.941353	+	0.337422i	$0.890445\pi$
$828$		0			0
$829$	−13301.0	+	23038.0i	−0.557253	+	0.965190i	0.440471	+	0.897767i	$0.354811\pi$
$829$	−13301.0	+	23038.0i	−0.557253	+	0.965190i	−0.997724	+	0.0674238i	$0.978522\pi$
$830$	−242.448	+	1374.99i	−0.0101391	+	0.0575019i
$831$		0			0
$832$	−2550.50	−	928.308i	−0.106277	−	0.0386818i
$833$	−2534.20	−	14372.2i	−0.105408	−	0.597799i
$834$		0			0
$835$	936.006	+	785.402i	0.0387926	+	0.0325509i
$836$	−6480.90			−0.268118
$837$		0			0
$838$	−13909.5			−0.573382
$839$	6947.91	+	5829.99i	0.285898	+	0.239897i	0.774446	−	0.632640i	$-0.218029\pi$
$839$	6947.91	+	5829.99i	0.285898	+	0.239897i	−0.488548	+	0.872537i	$0.662473\pi$
$840$		0			0
$841$	1085.06	+	6153.70i	0.0444899	+	0.252315i
$842$	−2940.80	−	1070.36i	−0.120364	−	0.0438090i
$843$		0			0
$844$	−1321.18	+	7492.77i	−0.0538825	+	0.305583i
$845$	228.290	−	395.410i	0.00929398	−	0.0160976i
$846$		0			0
$847$	1596.39	+	2765.03i	0.0647611	+	0.112169i
$848$	1464.75	−	533.127i	0.0593159	−	0.0215892i
$849$		0			0
$850$	8239.00	−	6913.34i	0.332465	−	0.278971i
$851$	958.699	−	804.444i	0.0386178	−	0.0324042i
$852$		0			0
$853$	3254.69	−	1184.61i	0.130643	−	0.0475501i	−0.275871	−	0.961195i	$-0.588966\pi$
$853$	3254.69	−	1184.61i	0.130643	−	0.0475501i	0.406514	+	0.913644i	$0.366744\pi$
$854$	−1346.09	−	2331.50i	−0.0539370	−	0.0934217i
$855$		0			0
$856$	−2157.71	+	3737.26i	−0.0861554	+	0.149226i
$857$	4490.86	−	25468.9i	0.179002	−	1.01517i	−0.754420	−	0.656392i	$-0.772082\pi$
$857$	4490.86	−	25468.9i	0.179002	−	1.01517i	0.933422	−	0.358779i	$-0.116807\pi$
$858$		0			0
$859$	−12952.2	−	4714.21i	−0.514462	−	0.187249i	0.0717250	−	0.997424i	$-0.477150\pi$
$859$	−12952.2	−	4714.21i	−0.514462	−	0.187249i	−0.586188	+	0.810175i	$0.699372\pi$
$860$	309.468	+	1755.08i	0.0122707	+	0.0695905i
$861$		0			0
$862$	19906.3	+	16703.4i	0.786556	+	0.659998i
$863$	−5200.59			−0.205134			−0.102567	−	0.994726i	$-0.532706\pi$
$863$	−5200.59			−0.205134			−0.102567	+	0.994726i	$0.532706\pi$
$864$		0			0
$865$	865.621			0.0340254
$866$	−5883.47	−	4936.82i	−0.230864	−	0.193718i
$867$		0			0
$868$	−357.994	−	2030.29i	−0.0139990	−	0.0793922i
$869$	3082.25	+	1121.85i	0.120320	+	0.0437929i
$870$		0			0
$871$	1020.02	−	5784.80i	0.0396807	−	0.225041i
$872$	−691.376	+	1197.50i	−0.0268497	+	0.0465050i
$873$		0			0
$874$	−3112.56	−	5391.11i	−0.120462	−	0.208647i
$875$	725.272	−	263.977i	0.0280213	−	0.0101989i
$876$		0			0
$877$	9498.66	−	7970.32i	0.365732	−	0.306886i	−0.441338	−	0.897341i	$-0.645496\pi$
$877$	9498.66	−	7970.32i	0.365732	−	0.306886i	0.807070	+	0.590455i	$0.201052\pi$
$878$	21033.8	−	17649.4i	0.808491	−	0.678405i
$879$		0			0
$880$	−212.542	+	77.3589i	−0.00814180	+	0.00296337i
$881$	−3626.76	−	6281.73i	−0.138693	−	0.240224i	0.788309	−	0.615279i	$-0.210957\pi$
$881$	−3626.76	−	6281.73i	−0.138693	−	0.240224i	−0.927002	+	0.375056i	$0.877624\pi$
$882$		0			0
$883$	4708.17	−	8154.79i	0.179437	−	0.310793i	−0.762251	−	0.647282i	$-0.775906\pi$
$883$	4708.17	−	8154.79i	0.179437	−	0.310793i	0.941688	+	0.336488i	$0.109239\pi$
$884$	1280.73	−	7263.37i	0.0487280	−	0.276350i
$885$		0			0
$886$	4075.89	+	1483.50i	0.154551	+	0.0562520i
$887$	6496.36	+	36842.7i	0.245915	+	1.39465i	0.818359	+	0.574708i	$0.194884\pi$
$887$	6496.36	+	36842.7i	0.245915	+	1.39465i	−0.572444	+	0.819944i	$0.694005\pi$
$888$		0			0
$889$	315.691	+	264.896i	0.0119099	+	0.00999363i
$890$	−2442.87			−0.0920058
$891$		0			0
$892$	2968.44			0.111425
$893$	−52015.6	−	43646.2i	−1.94920	−	1.63557i
$894$		0			0
$895$	−278.259	−	1578.09i	−0.0103924	−	0.0589382i
$896$	325.780	+	118.574i	0.0121468	+	0.00442108i
$897$		0			0
$898$	5057.72	−	28683.7i	0.187949	−	1.06591i
$899$	−16653.9	+	28845.3i	−0.617839	+	1.07013i
$900$		0			0
$901$	2117.85	+	3668.23i	0.0783084	+	0.135634i
$902$	5422.93	−	1973.79i	0.200182	−	0.0728602i
$903$		0			0
$904$	−10969.3	+	9204.36i	−0.403578	+	0.338642i
$905$	3198.23	−	2683.63i	0.117473	−	0.0985712i
$906$		0			0
$907$	−39053.0	+	14214.1i	−1.42969	+	0.520366i	−0.936844	−	0.349748i	$-0.886267\pi$
$907$	−39053.0	+	14214.1i	−1.42969	+	0.520366i	−0.492851	+	0.870114i	$0.664045\pi$
$908$	3598.45	+	6232.69i	0.131518	+	0.227797i
$909$		0			0
$910$	131.620	−	227.973i	0.00479468	−	0.00830464i
$911$	−5322.57	+	30185.8i	−0.193573	+	1.09781i	0.720864	+	0.693076i	$0.243745\pi$
$911$	−5322.57	+	30185.8i	−0.193573	+	1.09781i	−0.914437	+	0.404729i	$0.867366\pi$
$912$		0			0
$913$	−7062.78	−	2570.64i	−0.256018	−	0.0931828i
$914$	−3829.27	−	21716.9i	−0.138579	−	0.785920i
$915$		0			0
$916$	−20794.5	−	17448.7i	−0.750076	−	0.629388i
$917$	−1708.68			−0.0615328
$918$		0			0
$919$	43830.0			1.57325			0.786625	−	0.617431i	$-0.211826\pi$
$919$	43830.0			1.57325			0.786625	+	0.617431i	$0.211826\pi$
$920$	−166.428	−	139.649i	−0.00596408	−	0.00500446i
$921$		0			0
$922$	1410.69	+	8000.40i	0.0503888	+	0.285769i
$923$	38938.1	+	14172.3i	1.38859	+	0.505404i
$924$		0			0
$925$	−1134.16	+	6432.15i	−0.0403146	+	0.228635i
$926$	17506.3	−	30321.9i	0.621268	−	1.07607i
$927$		0			0
$928$	−2800.58	−	4850.74i	−0.0990662	−	0.171588i
$929$	2096.34	−	763.004i	0.0740351	−	0.0269466i	−0.304737	−	0.952436i	$-0.598569\pi$
$929$	2096.34	−	763.004i	0.0740351	−	0.0269466i	0.378772	+	0.925490i	$0.376346\pi$
$930$		0			0
$931$	33769.8	−	28336.2i	1.18879	−	0.997511i
$932$	−6007.42	+	5040.82i	−0.211137	+	0.177165i
$933$		0			0
$934$	−2432.00	+	885.175i	−0.0852007	+	0.0310105i
$935$	−307.309	−	532.275i	−0.0107488	−	0.0186174i
$936$		0			0
$937$	19637.5	−	34013.2i	0.684664	−	1.18587i	−0.288878	−	0.957366i	$-0.593282\pi$
$937$	19637.5	−	34013.2i	0.684664	−	1.18587i	0.973542	−	0.228508i	$-0.0733846\pi$
$938$	−130.288	+	738.901i	−0.00453525	+	0.0257207i
$939$		0			0
$940$	−2226.84	−	810.503i	−0.0772675	−	0.0281231i
$941$	1950.00	+	11059.0i	0.0675540	+	0.383118i	0.999775	+	0.0212275i	$0.00675742\pi$
$941$	1950.00	+	11059.0i	0.0675540	+	0.383118i	−0.932221	+	0.361890i	$0.882131\pi$
$942$		0			0
$943$	4246.34	+	3563.10i	0.146638	+	0.123044i
$944$	−11529.9			−0.397528
$945$		0			0
$946$	−9593.74			−0.329725
$947$	−20255.8	−	16996.6i	−0.695063	−	0.583227i	0.225301	−	0.974289i	$-0.427663\pi$
$947$	−20255.8	−	16996.6i	−0.695063	−	0.583227i	−0.920364	+	0.391062i	$0.872108\pi$
$948$		0			0
$949$	−3087.31	−	17509.0i	−0.105604	−	0.598910i
$950$	30528.8	+	11111.6i	1.04262	+	0.379481i
$951$		0			0
$952$	−163.590	+	927.762i	−0.00556929	+	0.0315850i
$953$	−21946.0	+	38011.6i	−0.745962	+	1.29204i	0.203783	+	0.979016i	$0.434676\pi$
$953$	−21946.0	+	38011.6i	−0.745962	+	1.29204i	−0.949744	+	0.313027i	$0.898657\pi$
$954$		0			0
$955$	−1310.11	−	2269.18i	−0.0443918	−	0.0768889i
$956$	−7817.97	+	2845.51i	−0.264489	+	0.0962661i
$957$		0			0
$958$	15740.2	−	13207.6i	0.530837	−	0.445426i
$959$	−679.628	+	570.276i	−0.0228846	+	0.0192025i
$960$		0			0
$961$	−6032.34	+	2195.59i	−0.202489	+	0.0736999i
$962$	2239.45	+	3878.84i	0.0750547	+	0.129999i
$963$		0			0
$964$	855.071	−	1481.03i	0.0285684	−	0.0494820i
$965$	−953.127	+	5405.45i	−0.0317951	+	0.180319i
$966$		0			0
$967$	34085.8	+	12406.2i	1.13353	+	0.412572i	0.839573	−	0.543246i	$-0.182805\pi$
$967$	34085.8	+	12406.2i	1.13353	+	0.412572i	0.293959	+	0.955818i	$0.405027\pi$
$968$	1637.57	+	9287.14i	0.0543736	+	0.308368i
$969$		0			0
$970$	−1550.51	−	1301.03i	−0.0513235	−	0.0430655i
$971$	4513.30			0.149164			0.0745822	−	0.997215i	$-0.476238\pi$
$971$	4513.30			0.149164			0.0745822	+	0.997215i	$0.476238\pi$
$972$		0			0
$973$	−6568.23			−0.216411
$974$	−10129.6	−	8499.75i	−0.333238	−	0.279620i
$975$		0			0
$976$	−1380.82	−	7830.99i	−0.0452857	−	0.256828i
$977$	−45028.4	−	16389.0i	−1.47450	−	0.536674i	−0.525181	−	0.850991i	$-0.676002\pi$
$977$	−45028.4	−	16389.0i	−1.47450	−	0.536674i	−0.949318	+	0.314317i	$0.898225\pi$
$978$		0			0
$979$	2283.56	−	12950.7i	0.0745484	−	0.422785i
$980$	769.251	−	1332.38i	0.0250743	−	0.0434300i
$981$		0			0
$982$	−18108.3	−	31364.4i	−0.588450	−	1.01923i
$983$	−27199.4	+	9899.76i	−0.882528	+	0.321214i	−0.743229	−	0.669037i	$-0.766707\pi$
$983$	−27199.4	+	9899.76i	−0.882528	+	0.321214i	−0.139298	+	0.990250i	$0.544485\pi$
$984$		0			0
$985$	−3510.49	+	2945.65i	−0.113557	+	0.0952856i
$986$	11659.5	−	9783.45i	0.376585	−	0.315992i
$987$		0			0
$988$	20935.1	−	7619.77i	0.674125	−	0.245361i
$989$	−4607.55	−	7980.52i	−0.148141	−	0.256588i
$990$		0			0
$991$	6259.39	−	10841.6i	0.200642	−	0.347522i	−0.748094	−	0.663593i	$-0.769031\pi$
$991$	6259.39	−	10841.6i	0.200642	−	0.347522i	0.948735	+	0.316072i	$0.102364\pi$
$992$	1057.40	−	5996.79i	0.0338431	−	0.191934i
$993$		0			0
$994$	−4973.63	−	1810.25i	−0.158706	−	0.0577644i
$995$	−1045.41	−	5928.83i	−0.0333084	−	0.188901i
$996$		0			0
$997$	−1285.78	−	1078.90i	−0.0408437	−	0.0342719i	0.622137	−	0.782908i	$-0.286265\pi$
$997$	−1285.78	−	1078.90i	−0.0408437	−	0.0342719i	−0.662981	+	0.748636i	$0.730709\pi$
$998$	−8990.96			−0.285174
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.4.e.a.127.3		24
3.2	odd	2		54.4.e.a.43.3	✓	24
27.5	odd	18		54.4.e.a.49.3	yes	24
27.7	even	9		1458.4.a.e.1.7		12
27.20	odd	18		1458.4.a.h.1.6		12
27.22	even	9	inner	162.4.e.a.37.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.4.e.a.43.3	✓	24	3.2	odd	2
54.4.e.a.49.3	yes	24	27.5	odd	18
162.4.e.a.37.3		24	27.22	even	9	inner
162.4.e.a.127.3		24	1.1	even	1	trivial
1458.4.a.e.1.7		12	27.7	even	9
1458.4.a.h.1.6		12	27.20	odd	18

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	162.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.53209 - 1.28558i) q^{2} +(0.694593 + 3.93923i) q^{4} +(-1.07676 - 0.391909i) q^{5} +(0.470326 - 2.66735i) q^{7} +(4.00000 - 6.92820i) q^{8} +O(q^{10})\)	\(q+(-1.53209 - 1.28558i) q^{2} +(0.694593 + 3.93923i) q^{4} +(-1.07676 - 0.391909i) q^{5} +(0.470326 - 2.66735i) q^{7} +(4.00000 - 6.92820i) q^{8} +(1.14586 + 1.98470i) q^{10} +(-11.5929 + 4.21946i) q^{11} +(32.4873 - 27.2601i) q^{13} +(-4.14966 + 3.48198i) q^{14} +(-15.0351 + 5.47232i) q^{16} +(-21.7389 - 37.6528i) q^{17} +(65.6659 - 113.737i) q^{19} +(0.795909 - 4.51383i) q^{20} +(23.1858 + 8.43893i) q^{22} +(4.11546 + 23.3399i) q^{23} +(-94.7497 - 79.5045i) q^{25} -84.8184 q^{26} +10.8340 q^{28} +(-134.085 - 112.511i) q^{29} +(-33.0436 - 187.400i) q^{31} +(30.0702 + 10.9446i) q^{32} +(-15.0997 + 85.6344i) q^{34} +(-1.55179 + 2.68777i) q^{35} +(-26.4028 - 45.7310i) q^{37} +(-246.823 + 89.8362i) q^{38} +(-7.02227 + 5.89238i) q^{40} +(179.171 - 150.342i) q^{41} +(-365.375 + 132.985i) q^{43} +(-24.6738 - 42.7362i) q^{44} +(23.7000 - 41.0496i) q^{46} +(89.7800 - 509.168i) q^{47} +(315.421 + 114.804i) q^{49} +(42.9560 + 243.616i) q^{50} +(129.949 + 109.040i) q^{52} -97.4224 q^{53} +14.1364 q^{55} +(-16.5986 - 13.9279i) q^{56} +(60.7894 + 344.754i) q^{58} +(677.161 + 246.466i) q^{59} +(-86.3009 + 489.437i) q^{61} +(-190.291 + 329.593i) q^{62} +(-32.0000 - 55.4256i) q^{64} +(-45.6646 + 16.6205i) q^{65} +(106.104 - 89.0315i) q^{67} +(133.223 - 111.788i) q^{68} +(5.83281 - 2.12297i) q^{70} +(488.539 + 846.174i) q^{71} +(209.614 - 363.061i) q^{73} +(-18.3392 + 104.007i) q^{74} +(493.646 + 179.672i) q^{76} +(5.80236 + 32.9068i) q^{77} +(-203.671 - 170.901i) q^{79} +18.3338 q^{80} -467.781 q^{82} +(466.701 + 391.608i) q^{83} +(8.65108 + 49.0627i) q^{85} +(730.749 + 265.971i) q^{86} +(-17.1382 + 97.1957i) q^{88} +(-532.975 + 923.140i) q^{89} +(-57.4326 - 99.4763i) q^{91} +(-89.0828 + 32.4235i) q^{92} +(-792.125 + 664.671i) q^{94} +(-115.281 + 96.7321i) q^{95} +(-829.931 + 302.070i) q^{97} +(-335.664 - 581.387i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{5} - 33 q^{7} + 96 q^{8}+O(q^{10}) \) 24 * q + 12 * q^5 - 33 * q^7 + 96 * q^8	\( 24 q + 12 q^{5} - 33 q^{7} + 96 q^{8} + 30 q^{10} + 12 q^{11} + 60 q^{13} + 66 q^{14} - 102 q^{17} + 171 q^{19} - 96 q^{20} - 24 q^{22} + 708 q^{23} + 864 q^{25} + 468 q^{26} - 336 q^{28} + 381 q^{29} + 909 q^{31} - 48 q^{34} - 624 q^{35} + 555 q^{37} - 66 q^{38} - 96 q^{40} - 618 q^{41} - 1161 q^{43} - 132 q^{44} + 348 q^{46} + 378 q^{47} + 579 q^{49} - 36 q^{50} + 240 q^{52} + 1794 q^{53} - 3906 q^{55} + 264 q^{56} + 444 q^{58} - 1038 q^{59} + 324 q^{61} - 744 q^{62} - 768 q^{64} - 5718 q^{65} - 576 q^{67} - 1056 q^{68} - 1038 q^{70} - 120 q^{71} + 3036 q^{73} + 1110 q^{74} + 132 q^{76} + 3804 q^{77} - 2991 q^{79} + 480 q^{80} - 3408 q^{82} - 513 q^{83} - 2925 q^{85} + 2322 q^{86} + 480 q^{88} - 1065 q^{89} + 2859 q^{91} - 1884 q^{92} - 828 q^{94} - 6357 q^{95} - 2055 q^{97} - 1356 q^{98}+O(q^{100}) \) 24 * q + 12 * q^5 - 33 * q^7 + 96 * q^8 + 30 * q^10 + 12 * q^11 + 60 * q^13 + 66 * q^14 - 102 * q^17 + 171 * q^19 - 96 * q^20 - 24 * q^22 + 708 * q^23 + 864 * q^25 + 468 * q^26 - 336 * q^28 + 381 * q^29 + 909 * q^31 - 48 * q^34 - 624 * q^35 + 555 * q^37 - 66 * q^38 - 96 * q^40 - 618 * q^41 - 1161 * q^43 - 132 * q^44 + 348 * q^46 + 378 * q^47 + 579 * q^49 - 36 * q^50 + 240 * q^52 + 1794 * q^53 - 3906 * q^55 + 264 * q^56 + 444 * q^58 - 1038 * q^59 + 324 * q^61 - 744 * q^62 - 768 * q^64 - 5718 * q^65 - 576 * q^67 - 1056 * q^68 - 1038 * q^70 - 120 * q^71 + 3036 * q^73 + 1110 * q^74 + 132 * q^76 + 3804 * q^77 - 2991 * q^79 + 480 * q^80 - 3408 * q^82 - 513 * q^83 - 2925 * q^85 + 2322 * q^86 + 480 * q^88 - 1065 * q^89 + 2859 * q^91 - 1884 * q^92 - 828 * q^94 - 6357 * q^95 - 2055 * q^97 - 1356 * q^98

Introduction

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