LMFDB - Embedded newform 216.3.p.b.19.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,3,Mod(19,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("216.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	216.p (of order $6$, degree $2$, 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:	$5.88557371018$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.19
Character	$\chi$	$=$	216.19
Dual form			216.3.p.b.91.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.95218 + 0.434750i) q^{2} +(3.62198 + 1.69742i) q^{4} +(0.0166003 - 0.00958419i) q^{5} +(4.07208 + 2.35102i) q^{7} +(6.33280 + 4.88832i) q^{8} +O(q^{10})$	\(q+(1.95218 + 0.434750i) q^{2} +(3.62198 + 1.69742i) q^{4} +(0.0166003 - 0.00958419i) q^{5} +(4.07208 + 2.35102i) q^{7} +(6.33280 + 4.88832i) q^{8} +(0.0365734 - 0.0114930i) q^{10} +(-2.84945 + 4.93540i) q^{11} +(10.0617 - 5.80910i) q^{13} +(6.92732 + 6.35994i) q^{14} +(10.2375 + 12.2960i) q^{16} +0.376814 q^{17} -15.0519 q^{19} +(0.0763944 - 0.00653612i) q^{20} +(-7.70830 + 8.39597i) q^{22} +(39.1821 - 22.6218i) q^{23} +(-12.4998 + 21.6503i) q^{25} +(22.1676 - 6.96608i) q^{26} +(10.7584 + 15.4274i) q^{28} +(-32.0010 - 18.4758i) q^{29} +(-26.3839 + 15.2328i) q^{31} +(14.6398 + 28.4548i) q^{32} +(0.735607 + 0.163820i) q^{34} +0.0901304 q^{35} -53.4253i q^{37} +(-29.3840 - 6.54383i) q^{38} +(0.151977 + 0.0204528i) q^{40} +(-29.0192 - 50.2628i) q^{41} +(-23.0516 + 39.9265i) q^{43} +(-18.6981 + 13.0392i) q^{44} +(86.3252 - 27.1273i) q^{46} +(34.2487 + 19.7735i) q^{47} +(-13.4454 - 23.2882i) q^{49} +(-33.8143 + 36.8309i) q^{50} +(46.3036 - 3.96163i) q^{52} +0.989874i q^{53} +0.109239i q^{55} +(14.2952 + 34.7942i) q^{56} +(-54.4392 - 49.9804i) q^{58} +(-29.4331 - 50.9797i) q^{59} +(-75.1051 - 43.3619i) q^{61} +(-58.1285 + 18.2666i) q^{62} +(16.2087 + 61.9135i) q^{64} +(0.111351 - 0.192866i) q^{65} +(-34.1445 - 59.1400i) q^{67} +(1.36481 + 0.639610i) q^{68} +(0.175950 + 0.0391842i) q^{70} +42.3565i q^{71} +26.6644 q^{73} +(23.2267 - 104.296i) q^{74} +(-54.5179 - 25.5494i) q^{76} +(-23.2064 + 13.3982i) q^{77} +(121.208 + 69.9797i) q^{79} +(0.287794 + 0.106000i) q^{80} +(-34.7989 - 110.738i) q^{82} +(-40.9931 + 71.0021i) q^{83} +(0.00625522 - 0.00361145i) q^{85} +(-62.3588 + 67.9219i) q^{86} +(-42.1708 + 17.3259i) q^{88} +42.6370 q^{89} +54.6292 q^{91} +(180.316 - 15.4274i) q^{92} +(58.2629 + 53.4909i) q^{94} +(-0.249867 + 0.144261i) q^{95} +(55.9278 - 96.8698i) q^{97} +(-16.1233 - 51.3080i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 5 q^{2} + 7 q^{4} - 46 q^{8}+O(q^{10}) $ 40 * q + 5 * q^2 + 7 * q^4 - 46 * q^8	$ 40 q + 5 q^{2} + 7 q^{4} - 46 q^{8} - 12 q^{10} + 16 q^{11} - 6 q^{14} + 31 q^{16} + 4 q^{17} - 76 q^{19} + 12 q^{20} + 35 q^{22} + 118 q^{25} + 72 q^{26} - 36 q^{28} + 5 q^{32} + 5 q^{34} + 108 q^{35} + 169 q^{38} - 6 q^{40} - 20 q^{41} - 16 q^{43} - 362 q^{44} - 96 q^{46} + 166 q^{49} - 73 q^{50} - 24 q^{52} - 186 q^{56} + 36 q^{58} + 64 q^{59} - 384 q^{62} - 518 q^{64} + 102 q^{65} - 64 q^{67} + 295 q^{68} - 6 q^{70} - 292 q^{73} - 318 q^{74} + 197 q^{76} + 720 q^{80} + 386 q^{82} - 554 q^{83} + 295 q^{86} + 59 q^{88} + 688 q^{89} - 204 q^{91} + 378 q^{92} - 66 q^{94} + 92 q^{97} + 614 q^{98}+O(q^{100}) $ 40 * q + 5 * q^2 + 7 * q^4 - 46 * q^8 - 12 * q^10 + 16 * q^11 - 6 * q^14 + 31 * q^16 + 4 * q^17 - 76 * q^19 + 12 * q^20 + 35 * q^22 + 118 * q^25 + 72 * q^26 - 36 * q^28 + 5 * q^32 + 5 * q^34 + 108 * q^35 + 169 * q^38 - 6 * q^40 - 20 * q^41 - 16 * q^43 - 362 * q^44 - 96 * q^46 + 166 * q^49 - 73 * q^50 - 24 * q^52 - 186 * q^56 + 36 * q^58 + 64 * q^59 - 384 * q^62 - 518 * q^64 + 102 * q^65 - 64 * q^67 + 295 * q^68 - 6 * q^70 - 292 * q^73 - 318 * q^74 + 197 * q^76 + 720 * q^80 + 386 * q^82 - 554 * q^83 + 295 * q^86 + 59 * q^88 + 688 * q^89 - 204 * q^91 + 378 * q^92 - 66 * q^94 + 92 * q^97 + 614 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.95218	+	0.434750i	0.976088	+	0.217375i
$2$	1.95218	+	0.434750i	0.976088	+	0.217375i
$3$		0			0
$3$		0			0
$4$	3.62198	+	1.69742i	0.905496	+	0.424355i
$5$	0.0166003	−	0.00958419i	0.00332006	−	0.00191684i	−0.498339	−	0.866982i	$-0.666057\pi$
$5$	0.0166003	−	0.00958419i	0.00332006	−	0.00191684i	0.501659	+	0.865065i	$0.332723\pi$
$6$		0			0
$7$	4.07208	+	2.35102i	0.581726	+	0.335860i	0.761819	−	0.647790i	$-0.224306\pi$
$7$	4.07208	+	2.35102i	0.581726	+	0.335860i	−0.180093	+	0.983650i	$0.557640\pi$
$8$	6.33280	+	4.88832i	0.791600	+	0.611040i
$9$		0			0
$10$	0.0365734	−	0.0114930i	0.00365734	−	0.00114930i
$11$	−2.84945	+	4.93540i	−0.259041	+	0.448673i	−0.965985	−	0.258597i	$-0.916740\pi$
$11$	−2.84945	+	4.93540i	−0.259041	+	0.448673i	0.706944	+	0.707269i	$0.250073\pi$
$12$		0			0
$13$	10.0617	−	5.80910i	0.773974	−	0.446854i	−0.0603167	−	0.998179i	$-0.519211\pi$
$13$	10.0617	−	5.80910i	0.773974	−	0.446854i	0.834290	+	0.551325i	$0.185878\pi$
$14$	6.92732	+	6.35994i	0.494809	+	0.454282i
$15$		0			0
$16$	10.2375	+	12.2960i	0.639846	+	0.768503i
$17$	0.376814			0.0221655			0.0110828	−	0.999939i	$-0.496472\pi$
$17$	0.376814			0.0221655			0.0110828	+	0.999939i	$0.496472\pi$
$18$		0			0
$19$	−15.0519			−0.792207			−0.396103	−	0.918206i	$-0.629638\pi$
$19$	−15.0519			−0.792207			−0.396103	+	0.918206i	$0.629638\pi$
$20$	0.0763944	−	0.00653612i	0.00381972	−	0.000326806i
$21$		0			0
$22$	−7.70830	+	8.39597i	−0.350377	+	0.381635i
$23$	39.1821	−	22.6218i	1.70357	−	0.983556i	0.761484	−	0.648184i	$-0.224471\pi$
$23$	39.1821	−	22.6218i	1.70357	−	0.983556i	0.942086	−	0.335372i	$-0.108862\pi$
$24$		0			0
$25$	−12.4998	+	21.6503i	−0.499993	+	0.866013i
$26$	22.1676	−	6.96608i	0.852601	−	0.267926i
$27$		0			0
$28$	10.7584	+	15.4274i	0.384227	+	0.550978i
$29$	−32.0010	−	18.4758i	−1.10348	−	0.637096i	−0.166349	−	0.986067i	$-0.553198\pi$
$29$	−32.0010	−	18.4758i	−1.10348	−	0.637096i	−0.937134	+	0.348971i	$0.886531\pi$
$30$		0			0
$31$	−26.3839	+	15.2328i	−0.851094	+	0.491379i	−0.861020	−	0.508571i	$-0.830174\pi$
$31$	−26.3839	+	15.2328i	−0.851094	+	0.491379i	0.00992571	+	0.999951i	$0.496840\pi$
$32$	14.6398	+	28.4548i	0.457493	+	0.889213i
$33$		0			0
$34$	0.735607	+	0.163820i	0.0216355	+	0.00481823i
$35$	0.0901304			0.00257515
$36$		0			0
$37$		−	53.4253i		−	1.44393i	−0.691931	−	0.721964i	$-0.743240\pi$
$37$		−	53.4253i		−	1.44393i	0.691931	−	0.721964i	$-0.256760\pi$
$38$	−29.3840	−	6.54383i	−0.773264	−	0.172206i
$39$		0			0
$40$	0.151977	+	0.0204528i	0.00379942	+	0.000511321i
$41$	−29.0192	−	50.2628i	−0.707786	−	1.22592i	−0.965677	−	0.259747i	$-0.916361\pi$
$41$	−29.0192	−	50.2628i	−0.707786	−	1.22592i	0.257891	−	0.966174i	$-0.416973\pi$
$42$		0			0
$43$	−23.0516	+	39.9265i	−0.536083	+	0.928524i	0.463027	+	0.886344i	$0.346763\pi$
$43$	−23.0516	+	39.9265i	−0.536083	+	0.928524i	−0.999110	+	0.0421794i	$0.986570\pi$
$44$	−18.6981	+	13.0392i	−0.424957	+	0.296346i
$45$		0			0
$46$	86.3252	−	27.1273i	1.87663	−	0.589724i
$47$	34.2487	+	19.7735i	0.728695	+	0.420712i	0.817944	−	0.575297i	$-0.195114\pi$
$47$	34.2487	+	19.7735i	0.728695	+	0.420712i	−0.0892497	+	0.996009i	$0.528447\pi$
$48$		0			0
$49$	−13.4454	−	23.2882i	−0.274396	−	0.475268i
$50$	−33.8143	+	36.8309i	−0.676287	+	0.736619i
$51$		0			0
$52$	46.3036	−	3.96163i	0.890455	−	0.0761852i
$53$			0.989874i			0.0186769i	0.999956	+	0.00933844i	$0.00297256\pi$
$53$			0.989874i			0.0186769i	−0.999956	+	0.00933844i	$0.997027\pi$
$54$		0			0
$55$			0.109239i			0.00198616i
$56$	14.2952	+	34.7942i	0.255271	+	0.621325i
$57$		0			0
$58$	−54.4392	−	49.9804i	−0.938608	−	0.861732i
$59$	−29.4331	−	50.9797i	−0.498866	−	0.864062i	0.501133	−	0.865370i	$-0.332917\pi$
$59$	−29.4331	−	50.9797i	−0.498866	−	0.864062i	−0.999999	+	0.00130851i	$0.999583\pi$
$60$		0			0
$61$	−75.1051	−	43.3619i	−1.23123	−	0.710851i	−0.263944	−	0.964538i	$-0.585023\pi$
$61$	−75.1051	−	43.3619i	−1.23123	−	0.710851i	−0.967286	+	0.253687i	$0.918357\pi$
$62$	−58.1285	+	18.2666i	−0.937557	+	0.294623i
$63$		0			0
$64$	16.2087	+	61.9135i	0.253261	+	0.967398i
$65$	0.111351	−	0.192866i	0.00171309	−	0.00296716i
$66$		0			0
$67$	−34.1445	−	59.1400i	−0.509620	−	0.882687i	−0.999938	−	0.0111436i	$-0.996453\pi$
$67$	−34.1445	−	59.1400i	−0.509620	−	0.882687i	0.490318	−	0.871543i	$-0.336881\pi$
$68$	1.36481	+	0.639610i	0.0200708	+	0.00940603i
$69$		0			0
$70$	0.175950	+	0.0391842i	0.00251358	+	0.000559775i
$71$			42.3565i			0.596571i	0.954477	+	0.298285i	$0.0964147\pi$
$71$			42.3565i			0.596571i	−0.954477	+	0.298285i	$0.903585\pi$
$72$		0			0
$73$	26.6644			0.365266			0.182633	−	0.983181i	$-0.441538\pi$
$73$	26.6644			0.365266			0.182633	+	0.983181i	$0.441538\pi$
$74$	23.2267	−	104.296i	0.313874	−	1.40940i
$75$		0			0
$76$	−54.5179	−	25.5494i	−0.717340	−	0.336177i
$77$	−23.2064	+	13.3982i	−0.301382	+	0.174003i
$78$		0			0
$79$	121.208	+	69.9797i	1.53428	+	0.885819i	0.999157	+	0.0410462i	$0.0130691\pi$
$79$	121.208	+	69.9797i	1.53428	+	0.885819i	0.535126	+	0.844772i	$0.320264\pi$
$80$	0.287794	+	0.106000i	0.00359742	+	0.00132499i
$81$		0			0
$82$	−34.7989	−	110.738i	−0.424377	−	1.35046i
$83$	−40.9931	+	71.0021i	−0.493892	+	0.855447i	−0.999975	−	0.00703820i	$-0.997760\pi$
$83$	−40.9931	+	71.0021i	−0.493892	+	0.855447i	0.506083	+	0.862485i	$0.331093\pi$
$84$		0			0
$85$	0.00625522	−	0.00361145i	7.35908e−5	−	4.24877e-5i
$86$	−62.3588	+	67.9219i	−0.725103	+	0.789790i
$87$		0			0
$88$	−42.1708	+	17.3259i	−0.479214	+	0.196885i
$89$	42.6370			0.479068			0.239534	−	0.970888i	$-0.423005\pi$
$89$	42.6370			0.479068			0.239534	+	0.970888i	$0.423005\pi$
$90$		0			0
$91$	54.6292			0.600321
$92$	180.316	−	15.4274i	1.95995	−	0.167689i
$93$		0			0
$94$	58.2629	+	53.4909i	0.619818	+	0.569052i
$95$	−0.249867	+	0.144261i	−0.00263017	+	0.00151853i
$96$		0			0
$97$	55.9278	−	96.8698i	0.576576	−	0.998658i	−0.419293	−	0.907851i	$-0.637722\pi$
$97$	55.9278	−	96.8698i	0.576576	−	0.998658i	0.995868	−	0.0908072i	$-0.0289447\pi$
$98$	−16.1233	−	51.3080i	−0.164523	−	0.523551i
$99$		0			0
$100$	−82.0238	+	57.1997i	−0.820238	+	0.571997i
$101$	−92.9636	−	53.6726i	−0.920432	−	0.531412i	−0.0366592	−	0.999328i	$-0.511672\pi$
$101$	−92.9636	−	53.6726i	−0.920432	−	0.531412i	−0.883773	+	0.467916i	$0.845005\pi$
$102$		0			0
$103$	−44.0704	+	25.4441i	−0.427868	+	0.247030i	−0.698438	−	0.715671i	$-0.746121\pi$
$103$	−44.0704	+	25.4441i	−0.427868	+	0.247030i	0.270570	+	0.962700i	$0.412788\pi$
$104$	92.1152	+	12.3967i	0.885723	+	0.119199i
$105$		0			0
$106$	−0.430348	+	1.93241i	−0.00405989	+	0.0182303i
$107$	49.7181			0.464656			0.232328	−	0.972638i	$-0.425366\pi$
$107$	49.7181			0.464656			0.232328	+	0.972638i	$0.425366\pi$
$108$		0			0
$109$			40.3370i			0.370064i	0.982732	+	0.185032i	$0.0592389\pi$
$109$			40.3370i			0.370064i	−0.982732	+	0.185032i	$0.940761\pi$
$110$	−0.0474916	+	0.213253i	−0.000431742	+	0.00193867i
$111$		0			0
$112$	12.7799	+	74.1392i	0.114106	+	0.661957i
$113$	12.9411	+	22.4146i	0.114523	+	0.198360i	0.917589	−	0.397530i	$-0.130133\pi$
$113$	12.9411	+	22.4146i	0.114523	+	0.198360i	−0.803066	+	0.595890i	$0.796799\pi$
$114$		0			0
$115$	0.433623	−	0.751057i	0.00377063	−	0.00653093i
$116$	−84.5460	−	121.238i	−0.728845	−	1.04516i
$117$		0			0
$118$	−35.2952	−	112.317i	−0.299112	−	0.951842i
$119$	1.53442	+	0.885896i	0.0128943	+	0.00744450i
$120$		0			0
$121$	44.2612	+	76.6627i	0.365795	+	0.633576i
$122$	−127.767	−	117.302i	−1.04727	−	0.961492i
$123$		0			0
$124$	−121.419	+	10.3883i	−0.979182	+	0.0837765i
$125$			0.958412i			0.00766729i
$126$		0			0
$127$			38.2335i			0.301051i	0.988606	+	0.150526i	$0.0480966\pi$
$127$			38.2335i			0.301051i	−0.988606	+	0.150526i	$0.951903\pi$
$128$	4.72531	+	127.913i	0.0369165	+	0.999318i
$129$		0			0
$130$	0.301225	−	0.328098i	0.00231712	−	0.00252383i
$131$	61.9020	+	107.217i	0.472534	+	0.818453i	0.999506	−	0.0314294i	$-0.0100059\pi$
$131$	61.9020	+	107.217i	0.472534	+	0.818453i	−0.526972	+	0.849883i	$0.676673\pi$
$132$		0			0
$133$	−61.2927	−	35.3874i	−0.460848	−	0.266070i
$134$	−40.9450	−	130.296i	−0.305559	−	0.972359i
$135$		0			0
$136$	2.38628	+	1.84198i	0.0175462	+	0.0135440i
$137$	−56.1949	+	97.3324i	−0.410182	+	0.710456i	−0.994909	−	0.100774i	$-0.967868\pi$
$137$	−56.1949	+	97.3324i	−0.410182	+	0.710456i	0.584728	+	0.811230i	$0.301201\pi$
$138$		0			0
$139$	56.1874	+	97.3194i	0.404226	+	0.700140i	0.994231	−	0.107260i	$-0.0342077\pi$
$139$	56.1874	+	97.3194i	0.404226	+	0.700140i	−0.590005	+	0.807399i	$0.700874\pi$
$140$	0.326451	+	0.152989i	0.00233179	+	0.00109278i
$141$		0			0
$142$	−18.4145	+	82.6874i	−0.129680	+	0.582306i
$143$			66.2111i			0.463014i
$144$		0			0
$145$	−0.708302			−0.00488484
$146$	52.0536	+	11.5924i	0.356532	+	0.0793997i
$147$		0			0
$148$	90.6851	−	193.506i	0.612737	−	1.30747i
$149$	0.193825	−	0.111905i	0.00130084	−	0.000751040i	−0.499349	−	0.866401i	$-0.666428\pi$
$149$	0.193825	−	0.111905i	0.00130084	−	0.000751040i	0.500650	+	0.865650i	$0.333094\pi$
$150$		0			0
$151$	106.870	+	61.7013i	0.707747	+	0.408618i	0.810226	−	0.586117i	$-0.199344\pi$
$151$	106.870	+	61.7013i	0.707747	+	0.408618i	−0.102479	+	0.994735i	$0.532677\pi$
$152$	−95.3209	−	73.5786i	−0.627111	−	0.484070i
$153$		0			0
$154$	−51.1279	+	16.0667i	−0.332000	+	0.104329i
$155$	−0.291987	+	0.505737i	−0.00188379	+	0.00326282i
$156$		0			0
$157$	169.459	−	97.8372i	1.07936	−	0.623167i	0.148634	−	0.988892i	$-0.452512\pi$
$157$	169.459	−	97.8372i	1.07936	−	0.623167i	0.930723	+	0.365726i	$0.119179\pi$
$158$	206.196	+	189.308i	1.30504	+	1.19815i
$159$		0			0
$160$	0.515741	+	0.332048i	0.00322338	+	0.00207530i
$161$	212.737			1.32135
$162$		0			0
$163$	36.1007			0.221477			0.110738	−	0.993850i	$-0.464678\pi$
$163$	36.1007			0.221477			0.110738	+	0.993850i	$0.464678\pi$
$164$	−19.7902	−	231.309i	−0.120672	−	1.41042i
$165$		0			0
$166$	−110.894	+	120.787i	−0.668035	+	0.727631i
$167$	89.8711	−	51.8871i	0.538150	−	0.310701i	−0.206179	−	0.978514i	$-0.566103\pi$
$167$	89.8711	−	51.8871i	0.538150	−	0.310701i	0.744329	+	0.667813i	$0.232770\pi$
$168$		0			0
$169$	−17.0087	+	29.4600i	−0.100643	+	0.174319i
$170$	0.0137814	−	0.00433073i	8.10669e−5	−	2.54749e-5i
$171$		0			0
$172$	−151.265	+	105.485i	−0.879445	+	0.613285i
$173$	53.5978	+	30.9447i	0.309814	+	0.178871i	0.646843	−	0.762623i	$-0.276089\pi$
$173$	53.5978	+	30.9447i	0.309814	+	0.178871i	−0.337029	+	0.941494i	$0.609422\pi$
$174$		0			0
$175$	−101.801	+	58.7746i	−0.581718	+	0.335855i
$176$	−89.8573	+	15.4893i	−0.510553	+	0.0880076i
$177$		0			0
$178$	83.2350	+	18.5365i	0.467612	+	0.104137i
$179$	235.967			1.31825			0.659125	−	0.752033i	$-0.270927\pi$
$179$	235.967			1.31825			0.659125	+	0.752033i	$0.270927\pi$
$180$		0			0
$181$			274.398i			1.51601i	0.652250	+	0.758004i	$0.273825\pi$
$181$			274.398i			1.51601i	−0.652250	+	0.758004i	$0.726175\pi$
$182$	106.646	+	23.7501i	0.585966	+	0.130495i
$183$		0			0
$184$	358.715	+	48.2753i	1.94954	+	0.262366i
$185$	−0.512038	−	0.886876i	−0.00276777	−	0.00479392i
$186$		0			0
$187$	−1.07371	+	1.85973i	−0.00574178	+	0.00994506i
$188$	90.4842	+	129.753i	0.481299	+	0.690178i
$189$		0			0
$190$	−0.550501	+	0.172992i	−0.00289737	+	0.000910486i
$191$	−75.3616	−	43.5100i	−0.394563	−	0.227801i	0.289572	−	0.957156i	$-0.406487\pi$
$191$	−75.3616	−	43.5100i	−0.394563	−	0.227801i	−0.684135	+	0.729355i	$0.739820\pi$
$192$		0			0
$193$	51.8130	+	89.7428i	0.268461	+	0.464989i	0.968465	−	0.249151i	$-0.0801515\pi$
$193$	51.8130	+	89.7428i	0.268461	+	0.464989i	−0.700003	+	0.714140i	$0.746818\pi$
$194$	151.295	−	164.792i	0.779872	−	0.849445i
$195$		0			0
$196$	−9.16937	−	107.172i	−0.0467825	−	0.546795i
$197$			200.158i			1.01603i	0.861349	+	0.508014i	$0.169620\pi$
$197$			200.158i			1.01603i	−0.861349	+	0.508014i	$0.830380\pi$
$198$		0			0
$199$		−	178.871i		−	0.898847i	−0.893319	−	0.449424i	$-0.851629\pi$
$199$		−	178.871i		−	0.898847i	0.893319	−	0.449424i	$-0.148371\pi$
$200$	−184.992	+	76.0040i	−0.924962	+	0.380020i
$201$		0			0
$202$	−158.147	−	145.194i	−0.782907	−	0.718784i
$203$	−86.8738	−	150.470i	−0.427950	−	0.741231i
$204$		0			0
$205$	−0.963456	−	0.556251i	−0.00469978	−	0.00271342i
$206$	−97.0951	+	30.5117i	−0.471335	+	0.148115i
$207$		0			0
$208$	174.436	+	64.2477i	0.838633	+	0.308883i
$209$	42.8898	−	74.2873i	0.205214	−	0.355442i
$210$		0			0
$211$	−95.3087	−	165.079i	−0.451700	−	0.782367i	0.546792	−	0.837269i	$-0.315849\pi$
$211$	−95.3087	−	165.079i	−0.451700	−	0.782367i	−0.998492	+	0.0549013i	$0.982516\pi$
$212$	−1.68023	+	3.58531i	−0.00792562	+	0.0169118i
$213$		0			0
$214$	97.0586	+	21.6150i	0.453545	+	0.101005i
$215$			0.883723i			0.00411034i
$216$		0			0
$217$	−143.250			−0.660139
$218$	−17.5365	+	78.7450i	−0.0804428	+	0.361216i
$219$		0			0
$220$	−0.185424	+	0.395661i	−0.000842836	+	0.00179846i
$221$	3.79137	−	2.18895i	0.0171555	−	0.00990474i
$222$		0			0
$223$	−188.439	−	108.795i	−0.845018	−	0.487871i	0.0139487	−	0.999903i	$-0.495560\pi$
$223$	−188.439	−	108.795i	−0.845018	−	0.487871i	−0.858967	+	0.512031i	$0.828893\pi$
$224$	−7.28342	+	150.289i	−0.0325153	+	0.670932i
$225$		0			0
$226$	15.5185	+	49.3835i	0.0686661	+	0.218511i
$227$	−68.5871	+	118.796i	−0.302146	+	0.523332i	−0.976622	−	0.214965i	$-0.931036\pi$
$227$	−68.5871	+	118.796i	−0.302146	+	0.523332i	0.674476	+	0.738297i	$0.264370\pi$
$228$		0			0
$229$	222.151	−	128.259i	0.970090	−	0.560082i	0.0708262	−	0.997489i	$-0.477436\pi$
$229$	222.151	−	128.259i	0.970090	−	0.560082i	0.899264	+	0.437407i	$0.144103\pi$
$230$	1.17303	−	1.27768i	0.00510013	−	0.00555512i
$231$		0			0
$232$	−112.340	−	273.435i	−0.484226	−	1.17860i
$233$	−305.481			−1.31108			−0.655538	−	0.755162i	$-0.727558\pi$
$233$	−305.481			−1.31108			−0.655538	+	0.755162i	$0.727558\pi$
$234$		0			0
$235$	0.758051			0.00322575
$236$	−20.0725	−	234.608i	−0.0850529	−	0.994101i
$237$		0			0
$238$	2.61031	+	2.39651i	0.0109677	+	0.0100694i
$239$	−68.4669	+	39.5294i	−0.286472	+	0.165395i	−0.636350	−	0.771401i	$-0.719557\pi$
$239$	−68.4669	+	39.5294i	−0.286472	+	0.165395i	0.349878	+	0.936795i	$0.386223\pi$
$240$		0			0
$241$	111.403	−	192.956i	0.462254	−	0.800647i	−0.536819	−	0.843697i	$-0.680374\pi$
$241$	111.403	−	192.956i	0.462254	−	0.800647i	0.999073	+	0.0430503i	$0.0137076\pi$
$242$	53.0766	+	168.902i	0.219325	+	0.697941i
$243$		0			0
$244$	−198.426	−	284.541i	−0.813221	−	1.16615i
$245$	−0.446396	−	0.257727i	−0.00182202	−	0.00105195i
$246$		0			0
$247$	−151.447	+	87.4382i	−0.613147	+	0.354001i
$248$	−241.547	−	32.5070i	−0.973978	−	0.131077i
$249$		0			0
$250$	−0.416670	+	1.87099i	−0.00166668	+	0.00748395i
$251$	−393.373			−1.56722			−0.783611	−	0.621252i	$-0.786624\pi$
$251$	−393.373			−1.56722			−0.783611	+	0.621252i	$0.786624\pi$
$252$		0			0
$253$			257.839i			1.01913i
$254$	−16.6220	+	74.6386i	−0.0654411	+	0.293853i
$255$		0			0
$256$	−46.3855	+	251.763i	−0.181193	+	0.983448i
$257$	−89.6613	−	155.298i	−0.348877	−	0.604272i	0.637173	−	0.770720i	$-0.280103\pi$
$257$	−89.6613	−	155.298i	−0.348877	−	0.604272i	−0.986050	+	0.166448i	$0.946770\pi$
$258$		0			0
$259$	125.604	−	217.552i	0.484957	−	0.839970i
$260$	0.730685	−	0.509547i	0.00281033	−	0.00195980i
$261$		0			0
$262$	74.2308	+	236.219i	0.283324	+	0.901600i
$263$	−241.721	−	139.558i	−0.919092	−	0.530638i	−0.0357465	−	0.999361i	$-0.511381\pi$
$263$	−241.721	−	139.558i	−0.919092	−	0.530638i	−0.883345	+	0.468723i	$0.844714\pi$
$264$		0			0
$265$	0.00948714	+	0.0164322i	3.58005e−5	+	6.20083e-5i
$266$	−104.270	−	95.7294i	−0.391991	−	0.359885i
$267$		0			0
$268$	−23.2855	−	272.162i	−0.0868863	−	1.01553i
$269$		−	112.462i		−	0.418076i	−0.977908	−	0.209038i	$-0.932967\pi$
$269$		−	112.462i		−	0.418076i	0.977908	−	0.209038i	$-0.0670332\pi$
$270$		0			0
$271$		−	500.279i		−	1.84605i	−0.384740	−	0.923025i	$-0.625709\pi$
$271$		−	500.279i		−	1.84605i	0.384740	−	0.923025i	$-0.374291\pi$
$272$	3.85764	+	4.63332i	0.0141825	+	0.0170343i
$273$		0			0
$274$	−152.018	+	165.579i	−0.554809	+	0.604304i
$275$	−71.2353	−	123.383i	−0.259037	−	0.448666i
$276$		0			0
$277$	−222.630	−	128.535i	−0.803718	−	0.464027i	0.0410514	−	0.999157i	$-0.486929\pi$
$277$	−222.630	−	128.535i	−0.803718	−	0.464027i	−0.844770	+	0.535130i	$0.820263\pi$
$278$	67.3780	+	214.412i	0.242367	+	0.771267i
$279$		0			0
$280$	0.570778	+	0.440586i	0.00203849	+	0.00157352i
$281$	−139.228	+	241.150i	−0.495474	+	0.858187i	−0.999986	−	0.00521797i	$-0.998339\pi$
$281$	−139.228	+	241.150i	−0.495474	+	0.858187i	0.504512	+	0.863405i	$0.331672\pi$
$282$		0			0
$283$	93.9509	+	162.728i	0.331982	+	0.575009i	0.982900	−	0.184138i	$-0.0589494\pi$
$283$	93.9509	+	162.728i	0.331982	+	0.575009i	−0.650919	+	0.759148i	$0.725616\pi$
$284$	−71.8967	+	153.415i	−0.253158	+	0.540192i
$285$		0			0
$286$	−28.7853	+	129.256i	−0.100648	+	0.451943i
$287$		−	272.899i		−	0.950868i
$288$		0			0
$289$	−288.858			−0.999509
$290$	−1.38273	−	0.307934i	−0.00476803	−	0.00106184i
$291$		0			0
$292$	96.5781	+	45.2607i	0.330747	+	0.155002i
$293$	442.987	−	255.759i	1.51190	−	0.872897i	0.511999	−	0.858986i	$-0.328905\pi$
$293$	442.987	−	255.759i	1.51190	−	0.872897i	0.999903	−	0.0139109i	$-0.00442813\pi$
$294$		0			0
$295$	−0.977197	−	0.564185i	−0.00331253	−	0.00191249i
$296$	261.160	−	338.332i	0.882297	−	1.14301i
$297$		0			0
$298$	0.427031	−	0.134193i	0.00143299	−	0.000450311i
$299$	262.825	−	455.225i	0.879012	−	1.52249i
$300$		0			0
$301$	−187.736	+	108.389i	−0.623708	+	0.360098i
$302$	181.804	+	166.914i	0.602000	+	0.552694i
$303$		0			0
$304$	−154.095	−	185.079i	−0.506891	−	0.608813i
$305$	−1.66236			−0.00545035
$306$		0			0
$307$	−195.885			−0.638061			−0.319031	−	0.947744i	$-0.603357\pi$
$307$	−195.885			−0.638061			−0.319031	+	0.947744i	$0.603357\pi$
$308$	−106.796	+	9.13719i	−0.346740	+	0.0296662i
$309$		0			0
$310$	−0.789880	+	0.860346i	−0.00254800	+	0.00277531i
$311$	−395.492	+	228.338i	−1.27168	+	0.734205i	−0.975304	−	0.220867i	$-0.929111\pi$
$311$	−395.492	+	228.338i	−1.27168	+	0.734205i	−0.296376	+	0.955071i	$0.595778\pi$
$312$		0			0
$313$	−185.314	+	320.973i	−0.592058	+	1.02547i	0.401897	+	0.915685i	$0.368351\pi$
$313$	−185.314	+	320.973i	−0.592058	+	1.02547i	−0.993955	+	0.109789i	$0.964982\pi$
$314$	373.348	−	117.323i	1.18901	−	0.373640i
$315$		0			0
$316$	320.230	+	459.207i	1.01339	+	1.45319i
$317$	435.393	+	251.374i	1.37348	+	0.792979i	0.991364	−	0.131136i	$-0.0418624\pi$
$317$	435.393	+	251.374i	1.37348	+	0.792979i	0.382115	+	0.924115i	$0.375196\pi$
$318$		0			0
$319$	182.371	−	105.292i	0.571695	−	0.330068i
$320$	0.862459	+	0.872435i	0.00269519	+	0.00272636i
$321$		0			0
$322$	415.300	+	92.4875i	1.28975	+	0.287228i
$323$	−5.67177			−0.0175597
$324$		0			0
$325$			290.451i			0.893695i
$326$	70.4750	+	15.6948i	0.216181	+	0.0481436i
$327$		0			0
$328$	61.9275	−	460.159i	0.188803	−	1.40292i
$329$	92.9756	+	161.038i	0.282601	+	0.489479i
$330$		0			0
$331$	−187.810	+	325.297i	−0.567402	+	0.982769i	0.429420	+	0.903105i	$0.358718\pi$
$331$	−187.810	+	325.297i	−0.567402	+	0.982769i	−0.996822	+	0.0796642i	$0.974615\pi$
$332$	−268.996	+	187.586i	−0.810230	+	0.565018i
$333$		0			0
$334$	198.002	−	62.2213i	0.592821	−	0.186291i
$335$	−1.13362	−	0.654495i	−0.00338394	−	0.00195372i
$336$		0			0
$337$	−161.252	−	279.296i	−0.478492	−	0.828772i	0.521204	−	0.853432i	$-0.325483\pi$
$337$	−161.252	−	279.296i	−0.478492	−	0.828772i	−0.999696	+	0.0246599i	$0.992150\pi$
$338$	−46.0117	+	50.1165i	−0.136129	+	0.148274i
$339$		0			0
$340$	0.0287864	−	0.00246290i	8.46660e−5	−	7.24382e-6i
$341$		−	173.620i		−	0.509150i
$342$		0			0
$343$		−	356.842i		−	1.04035i
$344$	−341.155	+	140.163i	−0.991729	+	0.407451i
$345$		0			0
$346$	91.1791	+	83.7111i	0.263523	+	0.241940i
$347$	42.4458	+	73.5183i	0.122322	+	0.211868i	0.920683	−	0.390311i	$-0.127633\pi$
$347$	42.4458	+	73.5183i	0.122322	+	0.211868i	−0.798361	+	0.602179i	$0.794299\pi$
$348$		0			0
$349$	35.4597	+	20.4727i	0.101604	+	0.0586610i	0.549941	−	0.835204i	$-0.314650\pi$
$349$	35.4597	+	20.4727i	0.101604	+	0.0586610i	−0.448337	+	0.893865i	$0.647984\pi$
$350$	−224.285	+	70.4806i	−0.640814	+	0.201373i
$351$		0			0
$352$	−182.151	−	8.82757i	−0.517475	−	0.0250783i
$353$	272.714	−	472.355i	0.772561	−	1.33812i	−0.163593	−	0.986528i	$-0.552309\pi$
$353$	272.714	−	472.355i	0.772561	−	1.33812i	0.936155	−	0.351588i	$-0.114358\pi$
$354$		0			0
$355$	0.405953	+	0.703131i	0.00114353	+	0.00198065i
$356$	154.431	+	72.3729i	0.433794	+	0.203295i
$357$		0			0
$358$	460.649	+	102.587i	1.28673	+	0.286555i
$359$			24.1503i			0.0672710i	0.999434	+	0.0336355i	$0.0107085\pi$
$359$			24.1503i			0.0672710i	−0.999434	+	0.0336355i	$0.989291\pi$
$360$		0			0
$361$	−134.439			−0.372408
$362$	−119.294	+	535.672i	−0.329543	+	1.47976i
$363$		0			0
$364$	197.866	+	92.7286i	0.543588	+	0.254749i
$365$	0.442637	−	0.255557i	0.00121270	−	0.000700155i
$366$		0			0
$367$	227.281	+	131.221i	0.619295	+	0.357550i	0.776595	−	0.630001i	$-0.216945\pi$
$367$	227.281	+	131.221i	0.619295	+	0.357550i	−0.157299	+	0.987551i	$0.550279\pi$
$368$	679.287	+	250.193i	1.84589	+	0.679873i
$369$		0			0
$370$	−0.614019	−	1.95395i	−0.00165951	−	0.00528094i
$371$	−2.32721	+	4.03085i	−0.00627281	+	0.0108648i
$372$		0			0
$373$	97.0579	−	56.0364i	0.260209	−	0.150232i	−0.364221	−	0.931313i	$-0.618665\pi$
$373$	97.0579	−	56.0364i	0.260209	−	0.150232i	0.624430	+	0.781081i	$0.285331\pi$
$374$	−2.90459	+	3.16372i	−0.00776629	+	0.00845913i
$375$		0			0
$376$	120.231	+	292.640i	0.319763	+	0.778297i
$377$	−429.311			−1.13876
$378$		0			0
$379$	305.554			0.806210			0.403105	−	0.915154i	$-0.367931\pi$
$379$	305.554			0.806210			0.403105	+	0.915154i	$0.367931\pi$
$380$	−1.14988	+	0.0983813i	−0.00302601	+	0.000258898i
$381$		0			0
$382$	−128.203	−	117.703i	−0.335610	−	0.308122i
$383$	50.9660	−	29.4252i	0.133070	−	0.0768283i	−0.431987	−	0.901880i	$-0.642187\pi$
$383$	50.9660	−	29.4252i	0.133070	−	0.0768283i	0.565057	+	0.825052i	$0.308854\pi$
$384$		0			0
$385$	−0.256823	+	0.444830i	−0.000667071	+	0.00115540i
$386$	62.1325	+	197.719i	0.160965	+	0.512227i
$387$		0			0
$388$	366.998	−	255.928i	0.945872	−	0.659609i
$389$	417.667	+	241.140i	1.07369	+	0.619897i	0.929188	−	0.369607i	$-0.120508\pi$
$389$	417.667	+	241.140i	1.07369	+	0.619897i	0.144505	+	0.989504i	$0.453841\pi$
$390$		0			0
$391$	14.7643	−	8.52420i	0.0377605	−	0.0218010i
$392$	28.6928	−	213.205i	0.0731958	−	0.543889i
$393$		0			0
$394$	−87.0185	+	390.743i	−0.220859	+	0.991733i
$395$	2.68279			0.00679188
$396$		0			0
$397$		−	74.8863i		−	0.188631i	−0.995542	−	0.0943153i	$-0.969934\pi$
$397$		−	74.8863i		−	0.188631i	0.995542	−	0.0943153i	$-0.0300662\pi$
$398$	77.7640	−	349.187i	0.195387	−	0.877354i
$399$		0			0
$400$	−394.181	+	67.9477i	−0.985452	+	0.169869i
$401$	299.864	+	519.380i	0.747791	+	1.29521i	0.948879	+	0.315639i	$0.102219\pi$
$401$	299.864	+	519.380i	0.747791	+	1.29521i	−0.201088	+	0.979573i	$0.564448\pi$
$402$		0			0
$403$	−176.977	+	306.534i	−0.439150	+	0.760629i
$404$	−245.608	−	352.199i	−0.607941	−	0.871781i
$405$		0			0
$406$	−104.176	−	331.512i	−0.256592	−	0.816533i
$407$	263.675	+	152.233i	0.647851	+	0.374037i
$408$		0			0
$409$	274.176	+	474.886i	0.670356	+	1.16109i	0.977803	+	0.209526i	$0.0671921\pi$
$409$	274.176	+	474.886i	0.670356	+	1.16109i	−0.307447	+	0.951565i	$0.599475\pi$
$410$	−1.63900	−	1.50476i	−0.00399757	−	0.00367015i
$411$		0			0
$412$	−202.812	+	17.3521i	−0.492261	+	0.0421167i
$413$		−	276.791i		−	0.670197i
$414$		0			0
$415$			1.57154i			0.00378685i
$416$	312.597	+	201.259i	0.751436	+	0.483795i
$417$		0			0
$418$	116.025	−	126.376i	0.277571	−	0.302334i
$419$	134.464	+	232.899i	0.320917	+	0.555845i	0.980677	−	0.195631i	$-0.0626756\pi$
$419$	134.464	+	232.899i	0.320917	+	0.555845i	−0.659761	+	0.751476i	$0.729342\pi$
$420$		0			0
$421$	235.498	+	135.965i	0.559378	+	0.322957i	0.752896	−	0.658140i	$-0.228656\pi$
$421$	235.498	+	135.965i	0.559378	+	0.322957i	−0.193518	+	0.981097i	$0.561990\pi$
$422$	−114.291	−	363.700i	−0.270832	−	0.861848i
$423$		0			0
$424$	−4.83882	+	6.26867i	−0.0114123	+	0.0147846i
$425$	−4.71010	+	8.15813i	−0.0110826	+	0.0191956i
$426$		0			0
$427$	−203.889	−	353.147i	−0.477493	−	0.827042i
$428$	180.078	+	84.3925i	0.420744	+	0.197179i
$429$		0			0
$430$	−0.384199	+	1.72518i	−0.000893486	+	0.00401205i
$431$		−	140.920i		−	0.326960i	−0.986547	−	0.163480i	$-0.947728\pi$
$431$		−	140.920i		−	0.326960i	0.986547	−	0.163480i	$-0.0522719\pi$
$432$		0			0
$433$	649.144			1.49918			0.749589	−	0.661903i	$-0.230251\pi$
$433$	649.144			1.49918			0.749589	+	0.661903i	$0.230251\pi$
$434$	−279.649	−	62.2780i	−0.644353	−	0.143498i
$435$		0			0
$436$	−68.4688	+	146.100i	−0.157039	+	0.335092i
$437$	−589.766	+	340.502i	−1.34958	+	0.779180i
$438$		0			0
$439$	135.712	+	78.3535i	0.309140	+	0.178482i	0.646541	−	0.762879i	$-0.276215\pi$
$439$	135.712	+	78.3535i	0.309140	+	0.178482i	−0.337402	+	0.941361i	$0.609548\pi$
$440$	−0.533994	+	0.691787i	−0.00121362	+	0.00157224i
$441$		0			0
$442$	8.35307	−	2.62491i	0.0188983	−	0.00593872i
$443$	−6.92104	+	11.9876i	−0.0156231	+	0.0270600i	−0.873731	−	0.486409i	$-0.838307\pi$
$443$	−6.92104	+	11.9876i	−0.0156231	+	0.0270600i	0.858108	+	0.513469i	$0.171640\pi$
$444$		0			0
$445$	0.707787	−	0.408641i	0.00159053	−	0.000918295i
$446$	−320.567	−	294.312i	−0.718761	−	0.659891i
$447$		0			0
$448$	−79.5566	+	290.224i	−0.177582	+	0.647821i
$449$	682.313			1.51963			0.759814	−	0.650140i	$-0.225290\pi$
$449$	682.313			1.51963			0.759814	+	0.650140i	$0.225290\pi$
$450$		0			0
$451$	330.756			0.733383
$452$	8.82544	+	103.152i	0.0195253	+	0.228212i
$453$		0			0
$454$	−185.541	+	202.093i	−0.408680	+	0.445139i
$455$	0.906861	−	0.523577i	0.00199310	−	0.00115072i
$456$		0			0
$457$	−140.879	+	244.010i	−0.308270	+	0.533938i	−0.977984	−	0.208680i	$-0.933083\pi$
$457$	−140.879	+	244.010i	−0.308270	+	0.533938i	0.669714	+	0.742619i	$0.266417\pi$
$458$	489.438	−	153.804i	1.06864	−	0.335816i
$459$		0			0
$460$	2.84543	−	1.98428i	0.00618573	−	0.00431365i
$461$	−556.528	−	321.312i	−1.20722	−	0.696989i	−0.245069	−	0.969506i	$-0.578811\pi$
$461$	−556.528	−	321.312i	−1.20722	−	0.696989i	−0.962151	+	0.272517i	$0.912144\pi$
$462$		0			0
$463$	−528.367	+	305.053i	−1.14118	+	0.658861i	−0.946723	−	0.322050i	$-0.895628\pi$
$463$	−528.367	+	305.053i	−1.14118	+	0.658861i	−0.194458	+	0.980911i	$0.562295\pi$
$464$	−100.432	−	582.632i	−0.216449	−	1.25567i
$465$		0			0
$466$	−596.352	−	132.808i	−1.27973	−	0.284995i
$467$	−289.260			−0.619400			−0.309700	−	0.950834i	$-0.600229\pi$
$467$	−289.260			−0.619400			−0.309700	+	0.950834i	$0.600229\pi$
$468$		0			0
$469$		−	321.098i		−	0.684643i
$470$	1.47985	+	0.329563i	0.00314861	+	0.000701197i
$471$		0			0
$472$	62.8108	−	466.722i	0.133074	−	0.988819i
$473$	−131.369	−	227.538i	−0.277736	−	0.481052i
$474$		0			0
$475$	188.146	−	325.879i	0.396098	−	0.686061i
$476$	4.05390	+	5.81325i	0.00851659	+	0.0122127i
$477$		0			0
$478$	−150.845	+	47.4023i	−0.315575	+	0.0991680i
$479$	115.068	+	66.4346i	0.240226	+	0.138694i	0.615281	−	0.788308i	$-0.289043\pi$
$479$	115.068	+	66.4346i	0.240226	+	0.138694i	−0.375055	+	0.927003i	$0.622376\pi$
$480$		0			0
$481$	−310.353	−	537.547i	−0.645224	−	1.11756i
$482$	301.366	−	328.251i	0.625241	−	0.681020i
$483$		0			0
$484$	30.1848	+	352.801i	0.0623653	+	0.728927i
$485$		−	2.14409i		−	0.00442081i
$486$		0			0
$487$			800.882i			1.64452i	0.569111	+	0.822261i	$0.307287\pi$
$487$			800.882i			1.64452i	−0.569111	+	0.822261i	$0.692713\pi$
$488$	−263.658	−	641.740i	−0.540283	−	1.31504i
$489$		0			0
$490$	−0.759397	−	0.697199i	−0.00154979	−	0.00142286i
$491$	416.975	+	722.222i	0.849236	+	1.47092i	0.881891	+	0.471454i	$0.156270\pi$
$491$	416.975	+	722.222i	0.849236	+	1.47092i	−0.0326547	+	0.999467i	$0.510396\pi$
$492$		0			0
$493$	−12.0584	−	6.96193i	−0.0244593	−	0.0141216i
$494$	−333.666	+	104.853i	−0.675437	+	0.212253i
$495$		0			0
$496$	−457.409	−	168.472i	−0.922196	−	0.339661i
$497$	−99.5810	+	172.479i	−0.200364	+	0.347041i
$498$		0			0
$499$	−62.9732	−	109.073i	−0.126199	−	0.218583i	0.796002	−	0.605294i	$-0.206944\pi$
$499$	−62.9732	−	109.073i	−0.126199	−	0.218583i	−0.922201	+	0.386711i	$0.873611\pi$
$500$	−1.62683	+	3.47135i	−0.00325365	+	0.00694270i
$501$		0			0
$502$	−767.933	−	171.019i	−1.52975	−	0.340675i
$503$		−	321.537i		−	0.639239i	−0.947546	−	0.319619i	$-0.896445\pi$
$503$		−	321.537i		−	0.639239i	0.947546	−	0.319619i	$-0.103555\pi$
$504$		0			0
$505$	−2.05763			−0.00407452
$506$	−112.096	+	503.347i	−0.221533	+	0.994757i
$507$		0			0
$508$	−64.8983	+	138.481i	−0.127753	+	0.272601i
$509$	−473.601	+	273.434i	−0.930455	+	0.537198i	−0.886955	−	0.461855i	$-0.847184\pi$
$509$	−473.601	+	273.434i	−0.930455	+	0.537198i	−0.0434992	+	0.999053i	$0.513851\pi$
$510$		0			0
$511$	108.580	+	62.6885i	0.212485	+	0.122678i
$512$	−200.006	+	471.319i	−0.390638	+	0.920545i
$513$		0			0
$514$	−107.519	−	342.149i	−0.209181	−	0.665660i
$515$	−0.487722	+	0.844758i	−0.000947032	+	0.00164031i
$516$		0			0
$517$	−195.180	+	112.687i	−0.377524	+	0.217964i
$518$	339.782	−	370.094i	0.655950	−	0.714468i
$519$		0			0
$520$	1.64795	−	0.677060i	0.00316914	−	0.00130204i
$521$	−774.144			−1.48588			−0.742940	−	0.669358i	$-0.766569\pi$
$521$	−774.144			−1.48588			−0.742940	+	0.669358i	$0.766569\pi$
$522$		0			0
$523$	126.448			0.241774			0.120887	−	0.992666i	$-0.461426\pi$
$523$	126.448			0.241774			0.120887	+	0.992666i	$0.461426\pi$
$524$	42.2153	+	493.413i	0.0805635	+	0.941629i
$525$		0			0
$526$	−411.209	−	377.530i	−0.781767	−	0.717737i
$527$	−9.94182	+	5.73991i	−0.0188649	+	0.0108917i
$528$		0			0
$529$	758.991	−	1314.61i	1.43477	−	2.48509i
$530$	0.0113767	+	0.0362031i	2.14654e−5	+	6.83077e-5i
$531$		0			0
$532$	−161.934	−	232.212i	−0.304387	−	0.436489i
$533$	−583.963	−	337.151i	−1.09562	−	0.632554i
$534$		0			0
$535$	0.825336	−	0.476508i	0.00154268	−	0.000890669i
$536$	72.8650	−	541.431i	0.135942	−	1.01013i
$537$		0			0
$538$	48.8930	−	219.546i	0.0908792	−	0.408079i
$539$	153.248			0.284320
$540$		0			0
$541$		−	323.091i		−	0.597210i	−0.954377	−	0.298605i	$-0.903479\pi$
$541$		−	323.091i		−	0.597210i	0.954377	−	0.298605i	$-0.0965213\pi$
$542$	217.497	−	976.634i	0.401285	−	1.80191i
$543$		0			0
$544$	5.51647	+	10.7222i	0.0101406	+	0.0197099i
$545$	0.386598	+	0.669607i	0.000709353	+	0.00122864i
$546$		0			0
$547$	42.9079	−	74.3187i	0.0784423	−	0.135866i	−0.824136	−	0.566392i	$-0.808339\pi$
$547$	42.9079	−	74.3187i	0.0784423	−	0.135866i	0.902578	+	0.430526i	$0.141672\pi$
$548$	−368.751	+	257.150i	−0.672903	+	0.469252i
$549$		0			0
$550$	−85.4230	−	271.835i	−0.155315	−	0.494246i
$551$	481.677	+	278.096i	0.874187	+	0.504712i
$552$		0			0
$553$	329.047	+	569.926i	0.595022	+	1.03061i
$554$	−378.732	−	347.712i	−0.683632	−	0.627640i
$555$		0			0
$556$	38.3181	+	447.863i	0.0689174	+	0.805509i
$557$			666.623i			1.19681i	0.801194	+	0.598405i	$0.204199\pi$
$557$			666.623i			1.19681i	−0.801194	+	0.598405i	$0.795801\pi$
$558$		0			0
$559$			535.636i			0.958204i
$560$	0.922714	+	1.10825i	0.00164770	+	0.00197901i
$561$		0			0
$562$	−376.638	+	410.239i	−0.670175	+	0.729962i
$563$	−234.690	−	406.495i	−0.416856	−	0.722016i	0.578765	−	0.815494i	$-0.303535\pi$
$563$	−234.690	−	406.495i	−0.416856	−	0.722016i	−0.995621	+	0.0934780i	$0.970202\pi$
$564$		0			0
$565$	0.429652	+	0.248060i	0.000760446	+	0.000439044i
$566$	112.663	+	358.518i	0.199051	+	0.633424i
$567$		0			0
$568$	−207.052	+	268.235i	−0.364528	+	0.472245i
$569$	129.732	−	224.702i	0.228000	−	0.394907i	−0.729215	−	0.684284i	$-0.760115\pi$
$569$	129.732	−	224.702i	0.228000	−	0.394907i	0.957215	+	0.289377i	$0.0934481\pi$
$570$		0			0
$571$	38.3743	+	66.4663i	0.0672055	+	0.116403i	0.897670	−	0.440668i	$-0.145258\pi$
$571$	38.3743	+	66.4663i	0.0672055	+	0.116403i	−0.830465	+	0.557071i	$0.811925\pi$
$572$	−112.388	+	239.815i	−0.196482	+	0.419258i
$573$		0			0
$574$	118.643	−	532.747i	0.206695	−	0.928131i
$575$			1131.07i			1.96708i
$576$		0			0
$577$	289.811			0.502272			0.251136	−	0.967952i	$-0.419196\pi$
$577$	289.811			0.502272			0.251136	+	0.967952i	$0.419196\pi$
$578$	−563.902	−	125.581i	−0.975609	−	0.217268i
$579$		0			0
$580$	−2.56546	−	1.20228i	−0.00442320	−	0.00207290i
$581$	−333.854	+	192.751i	−0.574620	+	0.331757i
$582$		0			0
$583$	−4.88542	−	2.82060i	−0.00837980	−	0.00483808i
$584$	168.860	+	130.344i	0.289144	+	0.223192i
$585$		0			0
$586$	975.981	−	306.697i	1.66550	−	0.523375i
$587$	−136.875	+	237.074i	−0.233177	+	0.403874i	−0.958741	−	0.284280i	$-0.908245\pi$
$587$	−136.875	+	237.074i	−0.233177	+	0.403874i	0.725565	+	0.688154i	$0.241579\pi$
$588$		0			0
$589$	397.129	−	229.282i	0.674243	−	0.389274i
$590$	−1.66238	−	1.52623i	−0.00281760	−	0.00258682i
$591$		0			0
$592$	656.920	−	546.944i	1.10966	−	0.923892i
$593$	461.865			0.778861			0.389431	−	0.921056i	$-0.372672\pi$
$593$	461.865			0.778861			0.389431	+	0.921056i	$0.372672\pi$
$594$		0			0
$595$	0.0339624			5.70796e−5
$596$	0.891980	−	0.0763157i	0.00149661	−	0.000128047i
$597$		0			0
$598$	710.989	−	774.417i	1.18895	−	1.29501i
$599$	551.557	−	318.442i	0.920797	−	0.531622i	0.0369077	−	0.999319i	$-0.488249\pi$
$599$	551.557	−	318.442i	0.920797	−	0.531622i	0.883889	+	0.467696i	$0.154916\pi$
$600$		0			0
$601$	−456.737	+	791.092i	−0.759962	+	1.31629i	0.182908	+	0.983130i	$0.441449\pi$
$601$	−456.737	+	791.092i	−0.759962	+	1.31629i	−0.942869	+	0.333162i	$0.891884\pi$
$602$	−413.616	+	129.977i	−0.687070	+	0.215909i
$603$		0			0
$604$	282.348	+	404.884i	0.467464	+	0.670338i
$605$	1.46950	+	0.848416i	0.00242892	+	0.00140234i
$606$		0			0
$607$	108.688	−	62.7511i	0.179058	−	0.103379i	−0.407792	−	0.913075i	$-0.633701\pi$
$607$	108.688	−	62.7511i	0.179058	−	0.103379i	0.586850	+	0.809696i	$0.300368\pi$
$608$	−220.357	−	428.300i	−0.362429	−	0.704441i
$609$		0			0
$610$	−3.24521	−	0.722709i	−0.00532002	−	0.00118477i
$611$	459.464			0.751987
$612$		0			0
$613$		−	929.305i		−	1.51600i	−0.652257	−	0.757998i	$-0.726178\pi$
$613$		−	929.305i		−	1.51600i	0.652257	−	0.757998i	$-0.273822\pi$
$614$	−382.402	−	85.1610i	−0.622804	−	0.138699i
$615$		0			0
$616$	−212.457	−	28.5921i	−0.344897	−	0.0464157i
$617$	−9.42520	−	16.3249i	−0.0152759	−	0.0264585i	0.858286	−	0.513171i	$-0.171529\pi$
$617$	−9.42520	−	16.3249i	−0.0152759	−	0.0264585i	−0.873562	+	0.486712i	$0.838196\pi$
$618$		0			0
$619$	158.239	−	274.079i	0.255637	−	0.442777i	−0.709431	−	0.704775i	$-0.751048\pi$
$619$	158.239	−	274.079i	0.255637	−	0.442777i	0.965068	+	0.261998i	$0.0843814\pi$
$620$	−1.91602	+	1.33615i	−0.00309036	+	0.00215507i
$621$		0			0
$622$	−871.341	+	273.815i	−1.40087	+	0.440217i
$623$	173.622	+	100.240i	0.278686	+	0.160900i
$624$		0			0
$625$	−312.486	−	541.242i	−0.499978	−	0.865987i
$626$	−501.309	+	546.031i	−0.800813	+	0.872255i
$627$		0			0
$628$	779.848	−	66.7220i	1.24180	−	0.106245i
$629$		−	20.1314i		−	0.0320054i
$630$		0			0
$631$			254.226i			0.402893i	0.979499	+	0.201447i	$0.0645643\pi$
$631$			254.226i			0.402893i	−0.979499	+	0.201447i	$0.935436\pi$
$632$	425.505	+	1035.67i	0.673268	+	1.63872i
$633$		0			0
$634$	740.679	+	680.014i	1.16826	+	1.07258i
$635$	0.366437	+	0.634688i	0.000577066	+	0.000999508i
$636$		0			0
$637$	−270.566	−	156.212i	−0.424751	−	0.245230i
$638$	401.796	−	126.262i	0.629774	−	0.197904i
$639$		0			0
$640$	1.30438	+	2.07810i	0.00203810	+	0.00324703i
$641$	509.350	−	882.221i	0.794618	−	1.37632i	−0.128463	−	0.991714i	$-0.541004\pi$
$641$	509.350	−	882.221i	0.794618	−	1.37632i	0.923081	−	0.384605i	$-0.125662\pi$
$642$		0			0
$643$	302.348	+	523.683i	0.470215	+	0.814436i	0.999420	−	0.0340578i	$-0.0108430\pi$
$643$	302.348	+	523.683i	0.470215	+	0.814436i	−0.529205	+	0.848494i	$0.677510\pi$
$644$	770.530	+	361.104i	1.19648	+	0.560720i
$645$		0			0
$646$	−11.0723	−	2.46580i	−0.0171398	−	0.00381703i
$647$		−	86.7767i		−	0.134122i	−0.997749	−	0.0670608i	$-0.978638\pi$
$647$		−	86.7767i		−	0.134122i	0.997749	−	0.0670608i	$-0.0213622\pi$
$648$		0			0
$649$	335.473			0.516908
$650$	−126.274	+	567.011i	−0.194267	+	0.872325i
$651$		0			0
$652$	130.756	+	61.2781i	0.200547	+	0.0939848i
$653$	346.903	−	200.285i	0.531245	−	0.306714i	−0.210278	−	0.977642i	$-0.567437\pi$
$653$	346.903	−	200.285i	0.531245	−	0.306714i	0.741523	+	0.670927i	$0.234104\pi$
$654$		0			0
$655$	2.05518	+	1.18656i	0.00313768	+	0.00181154i
$656$	320.948	−	871.389i	0.489250	−	1.32834i
$657$		0			0
$658$	111.493	+	354.797i	0.169443	+	0.539205i
$659$	−28.0360	+	48.5597i	−0.0425432	+	0.0736870i	−0.886513	−	0.462704i	$-0.846879\pi$
$659$	−28.0360	+	48.5597i	−0.0425432	+	0.0736870i	0.843970	+	0.536391i	$0.180213\pi$
$660$		0			0
$661$	−675.562	+	390.036i	−1.02203	+	0.590069i	−0.914691	−	0.404153i	$-0.867566\pi$
$661$	−675.562	+	390.036i	−1.02203	+	0.590069i	−0.107339	+	0.994222i	$0.534233\pi$
$662$	−508.061	+	553.386i	−0.767464	+	0.835930i
$663$		0			0
$664$	−606.682	+	249.255i	−0.913677	+	0.375384i
$665$	−1.35664			−0.00204006
$666$		0			0
$667$	−1671.82			−2.50648
$668$	413.586	−	35.3854i	0.619140	−	0.0529722i
$669$		0			0
$670$	−1.92848	−	1.77053i	−0.00287833	−	0.00264258i
$671$	428.017	−	247.116i	0.637879	−	0.368280i
$672$		0			0
$673$	−353.998	+	613.143i	−0.526001	+	0.911060i	0.473541	+	0.880772i	$0.342976\pi$
$673$	−353.998	+	613.143i	−0.526001	+	0.911060i	−0.999541	+	0.0302878i	$0.990358\pi$
$674$	−193.368	−	615.340i	−0.286896	−	0.912967i
$675$		0			0
$676$	−111.611	+	77.8326i	−0.165105	+	0.115137i
$677$	−503.417	−	290.648i	−0.743600	−	0.429318i	0.0797769	−	0.996813i	$-0.474579\pi$
$677$	−503.417	−	290.648i	−0.743600	−	0.429318i	−0.823377	+	0.567495i	$0.807913\pi$
$678$		0			0
$679$	455.486	−	262.975i	0.670818	−	0.387297i
$680$	0.0572670	+	0.00770690i	8.42161e−5	+	1.13337e-5i
$681$		0			0
$682$	75.4814	−	338.937i	0.110677	−	0.496976i
$683$	−558.887			−0.818282			−0.409141	−	0.912471i	$-0.634172\pi$
$683$	−558.887			−0.818282			−0.409141	+	0.912471i	$0.634172\pi$
$684$		0			0
$685$			2.15433i			0.00314501i
$686$	155.137	−	696.618i	0.226147	−	1.01548i
$687$		0			0
$688$	−726.930	+	125.306i	−1.05658	+	0.182131i
$689$	5.75028	+	9.95977i	0.00834583	+	0.0144554i
$690$		0			0
$691$	−158.856	+	275.147i	−0.229893	+	0.398187i	−0.957776	−	0.287515i	$-0.907171\pi$
$691$	−158.856	+	275.147i	−0.229893	+	0.398187i	0.727883	+	0.685701i	$0.240504\pi$
$692$	141.604	+	203.059i	0.204630	+	0.293438i
$693$		0			0
$694$	50.8996	+	161.974i	0.0733423	+	0.233392i
$695$	1.86545	+	1.07702i	0.00268411	+	0.00154967i
$696$		0			0
$697$	−10.9348	−	18.9397i	−0.0156884	−	0.0271732i
$698$	60.3232	+	55.3824i	0.0864229	+	0.0793445i
$699$		0			0
$700$	−468.485	+	40.0825i	−0.669265	+	0.0572607i
$701$		−	731.568i		−	1.04361i	−0.853066	−	0.521803i	$-0.825259\pi$
$701$		−	731.568i		−	1.04361i	0.853066	−	0.521803i	$-0.174741\pi$
$702$		0			0
$703$			804.154i			1.14389i
$704$	−351.754	−	96.4233i	−0.499650	−	0.136965i
$705$		0			0
$706$	737.743	−	803.557i	1.04496	−	1.13818i
$707$	−252.371	−	437.119i	−0.356960	−	0.618272i
$708$		0			0
$709$	−112.277	−	64.8230i	−0.158359	−	0.0914288i	0.418726	−	0.908113i	$-0.362477\pi$
$709$	−112.277	−	64.8230i	−0.158359	−	0.0914288i	−0.577085	+	0.816684i	$0.695810\pi$
$710$	0.486805	+	1.54912i	0.000685641	+	0.00218186i
$711$		0			0
$712$	270.012	+	208.423i	0.379230	+	0.292729i
$713$	−689.185	+	1193.70i	−0.966599	+	1.67420i
$714$		0			0
$715$	0.634579	+	1.09912i	0.000887523	+	0.00153724i
$716$	854.668	+	400.534i	1.19367	+	0.559405i
$717$		0			0
$718$	−10.4993	+	47.1456i	−0.0146230	+	0.0656624i
$719$		−	726.317i		−	1.01018i	−0.863068	−	0.505088i	$-0.831460\pi$
$719$		−	726.317i		−	1.01018i	0.863068	−	0.505088i	$-0.168540\pi$
$720$		0			0
$721$	−239.278			−0.331870
$722$	−262.449	−	58.4476i	−0.363503	−	0.0809523i
$723$		0			0
$724$	−465.767	+	993.864i	−0.643325	+	1.37274i
$725$	800.013	−	461.888i	1.10347	−	0.637087i
$726$		0			0
$727$	−498.049	−	287.549i	−0.685075	−	0.395528i	0.116690	−	0.993168i	$-0.462772\pi$
$727$	−498.049	−	287.549i	−0.685075	−	0.395528i	−0.801764	+	0.597640i	$0.796105\pi$
$728$	345.956	+	267.045i	0.475214	+	0.366820i
$729$		0			0
$730$	0.975209	−	0.306455i	0.00133590	−	0.000419801i
$731$	−8.68615	+	15.0449i	−0.0118826	+	0.0205812i
$732$		0			0
$733$	−113.103	+	65.3000i	−0.154301	+	0.0890859i	−0.575163	−	0.818039i	$-0.695061\pi$
$733$	−113.103	+	65.3000i	−0.154301	+	0.0890859i	0.420861	+	0.907125i	$0.361728\pi$
$734$	386.645	+	354.977i	0.526764	+	0.483620i
$735$		0			0
$736$	1217.32	+	783.742i	1.65396	+	1.06487i
$737$	389.173			0.528050
$738$		0			0
$739$	−61.7030			−0.0834953			−0.0417477	−	0.999128i	$-0.513293\pi$
$739$	−61.7030			−0.0834953			−0.0417477	+	0.999128i	$0.513293\pi$
$740$	−0.349194	−	4.08139i	−0.000471884	−	0.00551540i
$741$		0			0
$742$	−6.29554	+	6.85718i	−0.00848456	+	0.00924148i
$743$	−368.246	+	212.607i	−0.495620	+	0.286147i	−0.726903	−	0.686740i	$-0.759041\pi$
$743$	−368.246	+	212.607i	−0.495620	+	0.286147i	0.231283	+	0.972887i	$0.425708\pi$
$744$		0			0
$745$	0.00214503	−	0.00371531i	2.87924e−6	−	4.98699e-6i
$746$	213.836	−	67.1970i	0.286644	−	0.0900764i
$747$		0			0
$748$	−7.04570	+	4.91336i	−0.00941939	+	0.00656866i
$749$	202.456	+	116.888i	0.270302	+	0.156059i
$750$		0			0
$751$	1180.47	−	681.543i	1.57186	−	0.907514i	0.575920	−	0.817506i	$-0.304644\pi$
$751$	1180.47	−	681.543i	1.57186	−	0.907514i	0.995941	−	0.0900084i	$-0.0286894\pi$
$752$	107.487	+	623.555i	0.142934	+	0.829195i
$753$		0			0
$754$	−838.090	−	186.643i	−1.11153	−	0.247537i
$755$	2.36543			0.00313302
$756$		0			0
$757$			105.684i			0.139610i	0.997561	+	0.0698048i	$0.0222376\pi$
$757$			105.684i			0.139610i	−0.997561	+	0.0698048i	$0.977762\pi$
$758$	596.494	+	132.839i	0.786932	+	0.175250i
$759$		0			0
$760$	−2.28755	−	0.307854i	−0.00300993	−	0.000405072i
$761$	−452.651	−	784.015i	−0.594811	−	1.03024i	−0.993574	−	0.113189i	$-0.963894\pi$
$761$	−452.651	−	784.015i	−0.594811	−	1.03024i	0.398763	−	0.917054i	$-0.369440\pi$
$762$		0			0
$763$	−94.8331	+	164.256i	−0.124290	+	0.215276i
$764$	−199.104	−	285.513i	−0.260607	−	0.373708i
$765$		0			0
$766$	112.287	−	35.2858i	0.146589	−	0.0460650i
$767$	−592.292	−	341.960i	−0.772219	−	0.445841i
$768$		0			0
$769$	−16.2383	−	28.1255i	−0.0211161	−	0.0365741i	0.855274	−	0.518176i	$-0.173389\pi$
$769$	−16.2383	−	28.1255i	−0.0211161	−	0.0365741i	−0.876390	+	0.481601i	$0.840055\pi$
$770$	−0.694753	+	0.756732i	−0.000902276	+	0.000982769i
$771$		0			0
$772$	35.3349	+	412.995i	0.0457706	+	0.534968i
$773$		−	367.930i		−	0.475976i	−0.971268	−	0.237988i	$-0.923512\pi$
$773$		−	367.930i		−	0.475976i	0.971268	−	0.237988i	$-0.0764880\pi$
$774$		0			0
$775$		−	761.627i		−	0.982744i
$776$	827.710	−	340.064i	1.06664	−	0.438227i
$777$		0			0
$778$	710.524	+	652.329i	0.913269	+	0.838469i
$779$	436.795	+	756.552i	0.560713	+	0.971183i
$780$		0			0
$781$	−209.046	−	120.693i	−0.267665	−	0.154536i
$782$	32.5285	−	10.2219i	0.0415966	−	0.0130715i
$783$		0			0
$784$	148.704	−	403.739i	0.189674	−	0.514973i
$785$	1.87538	−	3.24825i	0.00238902	−	0.00413790i
$786$		0			0
$787$	563.311	+	975.684i	0.715770	+	1.23975i	0.962662	+	0.270707i	$0.0872576\pi$
$787$	563.311	+	975.684i	0.715770	+	1.23975i	−0.246891	+	0.969043i	$0.579409\pi$
$788$	−339.751	+	724.967i	−0.431156	+	0.920009i
$789$		0			0
$790$	5.23729	+	1.16635i	0.00662948	+	0.00147639i
$791$			121.699i			0.153855i
$792$		0			0
$793$	−1007.58			−1.27059
$794$	32.5568	−	146.191i	0.0410036	−	0.184120i
$795$		0			0
$796$	303.618	−	647.866i	0.381430	−	0.813903i
$797$	297.816	−	171.944i	0.373672	−	0.215739i	−0.301390	−	0.953501i	$-0.597450\pi$
$797$	297.816	−	171.944i	0.373672	−	0.215739i	0.675061	+	0.737762i	$0.264117\pi$
$798$		0			0
$799$	12.9054	+	7.45091i	0.0161519	+	0.00932530i
$800$	−799.050	−	38.7242i	−0.998813	−	0.0484053i
$801$		0			0
$802$	359.587	+	1144.29i	0.448363	+	1.42679i
$803$	−75.9790	+	131.600i	−0.0946189	+	0.163885i
$804$		0			0
$805$	3.53150	−	2.03891i	0.00438696	−	0.00253281i
$806$	−478.756	+	521.467i	−0.593991	+	0.646981i
$807$		0			0
$808$	−326.351	−	794.334i	−0.403900	−	0.983086i
$809$	−273.136			−0.337622			−0.168811	−	0.985648i	$-0.553993\pi$
$809$	−273.136			−0.337622			−0.168811	+	0.985648i	$0.553993\pi$
$810$		0			0
$811$	615.310			0.758705			0.379352	−	0.925252i	$-0.376147\pi$
$811$	615.310			0.758705			0.379352	+	0.925252i	$0.376147\pi$
$812$	−59.2453	−	692.461i	−0.0729622	−	0.852784i
$813$		0			0
$814$	448.557	+	411.818i	0.551053	+	0.505919i
$815$	0.599283	−	0.345996i	0.000735317	−	0.000424535i
$816$		0			0
$817$	346.971	−	600.971i	0.424689	−	0.735583i
$818$	328.782	+	1046.26i	0.401935	+	1.27905i
$819$		0			0
$820$	−2.54543	−	3.65012i	−0.00310418	−	0.00445137i
$821$	1110.25	+	641.002i	1.35231	+	0.780757i	0.988573	−	0.150744i	$-0.0481668\pi$
$821$	1110.25	+	641.002i	1.35231	+	0.780757i	0.363739	+	0.931501i	$0.381500\pi$
$822$		0			0
$823$	241.117	−	139.209i	0.292973	−	0.169148i	−0.346309	−	0.938121i	$-0.612565\pi$
$823$	241.117	−	139.209i	0.292973	−	0.169148i	0.639282	+	0.768972i	$0.279232\pi$
$824$	−403.468	−	54.2981i	−0.489645	−	0.0658957i
$825$		0			0
$826$	120.335	−	540.345i	0.145684	−	0.654171i
$827$	−88.6450			−0.107189			−0.0535943	−	0.998563i	$-0.517068\pi$
$827$	−88.6450			−0.107189			−0.0535943	+	0.998563i	$0.517068\pi$
$828$		0			0
$829$		−	673.447i		−	0.812361i	−0.913793	−	0.406180i	$-0.866860\pi$
$829$		−	673.447i		−	0.812361i	0.913793	−	0.406180i	$-0.133140\pi$
$830$	−0.683228	+	3.06792i	−0.000823166	+	0.00369629i
$831$		0			0
$832$	522.748	+	528.794i	0.628303	+	0.635570i
$833$	−5.06642	−	8.77529i	−0.00608213	−	0.0105346i
$834$		0			0
$835$	0.994591	−	1.72268i	0.00119113	−	0.00206309i
$836$	281.443	−	196.265i	0.336654	−	0.234767i
$837$		0			0
$838$	161.245	+	513.118i	0.192416	+	0.612313i
$839$	29.6126	+	17.0968i	0.0352951	+	0.0203776i	0.517544	−	0.855657i	$-0.326846\pi$
$839$	29.6126	+	17.0968i	0.0352951	+	0.0203776i	−0.482249	+	0.876034i	$0.660180\pi$
$840$		0			0
$841$	262.209	+	454.160i	0.311783	+	0.540024i
$842$	400.623	+	367.810i	0.475800	+	0.436830i
$843$		0			0
$844$	−64.9976	−	759.694i	−0.0770114	−	0.900111i
$845$			0.652059i			0.000771667i
$846$		0			0
$847$			416.236i			0.491424i
$848$	−12.1715	+	10.1339i	−0.0143532	+	0.0119503i
$849$		0			0
$850$	−12.7417	+	13.8784i	−0.0149902	+	0.0163275i
$851$	−1208.58	−	2093.32i	−1.42018	−	2.45983i
$852$		0			0
$853$	1052.33	+	607.564i	1.23368	+	0.712267i	0.967796	−	0.251737i	$-0.0810018\pi$
$853$	1052.33	+	607.564i	1.23368	+	0.712267i	0.265887	+	0.964004i	$0.414335\pi$
$854$	−244.497	−	778.046i	−0.286297	−	0.911061i
$855$		0			0
$856$	314.855	+	243.038i	0.367821	+	0.283923i
$857$	−462.160	+	800.484i	−0.539276	+	0.934054i	0.459667	+	0.888091i	$0.347969\pi$
$857$	−462.160	+	800.484i	−0.539276	+	0.934054i	−0.998943	+	0.0459627i	$0.985364\pi$
$858$		0			0
$859$	−625.687	−	1083.72i	−0.728390	−	1.26161i	−0.957563	−	0.288223i	$-0.906936\pi$
$859$	−625.687	−	1083.72i	−0.728390	−	1.26161i	0.229174	−	0.973386i	$-0.426398\pi$
$860$	−1.50005	+	3.20083i	−0.00174424	+	0.00372190i
$861$		0			0
$862$	61.2649	−	275.100i	0.0710729	−	0.319142i
$863$			291.210i			0.337439i	0.985664	+	0.168719i	$0.0539632\pi$
$863$			291.210i			0.337439i	−0.985664	+	0.168719i	$0.946037\pi$
$864$		0			0
$865$	1.18632			0.00137147
$866$	1267.24	+	282.216i	1.46333	+	0.325884i
$867$		0			0
$868$	−518.849	−	243.155i	−0.597753	−	0.280133i
$869$	−690.755	+	398.808i	−0.794885	+	0.458927i
$870$		0			0
$871$	−687.101	−	396.698i	−0.788864	−	0.455451i
$872$	−197.180	+	255.446i	−0.226124	+	0.292943i
$873$		0			0
$874$	−1299.36	+	408.318i	−1.48668	+	0.467183i
$875$	−2.25324	+	3.90273i	−0.00257514	+	0.00446027i
$876$		0			0
$877$	−623.417	+	359.930i	−0.710851	+	0.410410i	−0.811376	−	0.584524i	$-0.801281\pi$
$877$	−623.417	+	359.930i	−0.710851	+	0.410410i	0.100525	+	0.994935i	$0.467948\pi$
$878$	230.870	+	211.961i	0.262950	+	0.241413i
$879$		0			0
$880$	−1.34321	+	1.11834i	−0.00152637	+	0.00127084i
$881$	−136.645			−0.155102			−0.0775512	−	0.996988i	$-0.524710\pi$
$881$	−136.645			−0.155102			−0.0775512	+	0.996988i	$0.524710\pi$
$882$		0			0
$883$	−795.629			−0.901052			−0.450526	−	0.892763i	$-0.648764\pi$
$883$	−795.629			−0.901052			−0.450526	+	0.892763i	$0.648764\pi$
$884$	17.4478	−	1.49280i	0.0197374	−	0.00168868i
$885$		0			0
$886$	−18.7227	+	20.3930i	−0.0211317	+	0.0230169i
$887$	92.9513	−	53.6654i	0.104793	−	0.0605022i	−0.446688	−	0.894690i	$-0.647396\pi$
$887$	92.9513	−	53.6654i	0.104793	−	0.0605022i	0.551480	+	0.834188i	$0.314063\pi$
$888$		0			0
$889$	−89.8877	+	155.690i	−0.101111	+	0.175129i
$890$	1.55938	−	0.490029i	0.00175212	−	0.000550594i
$891$		0			0
$892$	−497.852	−	713.915i	−0.558130	−	0.800353i
$893$	−515.508	−	297.629i	−0.577277	−	0.333291i
$894$		0			0
$895$	3.91712	−	2.26155i	0.00437667	−	0.00252687i
$896$	−281.483	+	531.981i	−0.314156	+	0.593729i
$897$		0			0
$898$	1332.00	+	296.636i	1.48329	+	0.330329i
$899$	1125.75			1.25222
$900$		0			0
$901$			0.372998i			0.000413982i
$902$	645.694	+	143.796i	0.715847	+	0.159419i
$903$		0			0
$904$	−27.6165	+	205.208i	−0.0305493	+	0.227000i
$905$	2.62988	+	4.55508i	0.00290594	+	0.00503324i
$906$		0			0
$907$	686.970	−	1189.87i	0.757409	−	1.31187i	−0.186759	−	0.982406i	$-0.559798\pi$
$907$	686.970	−	1189.87i	0.757409	−	1.31187i	0.944168	−	0.329465i	$-0.106868\pi$
$908$	−450.068	+	313.857i	−0.495670	+	0.345658i
$909$		0			0
$910$	1.99798	−	0.627856i	0.00219558	−	0.000689951i
$911$	166.832	+	96.3207i	0.183131	+	0.105731i	0.588763	−	0.808306i	$-0.299615\pi$
$911$	166.832	+	96.3207i	0.183131	+	0.105731i	−0.405632	+	0.914037i	$0.632949\pi$
$912$		0			0
$913$	−233.616	−	404.634i	−0.255877	−	0.443192i
$914$	−381.104	+	415.103i	−0.416963	+	0.454161i
$915$		0			0
$916$	1022.33	−	87.4685i	1.11609	−	0.0954897i
$917$			582.131i			0.634821i
$918$		0			0
$919$			818.741i			0.890905i	0.895306	+	0.445452i	$0.146957\pi$
$919$			818.741i			0.890905i	−0.895306	+	0.445452i	$0.853043\pi$
$920$	6.41745	−	2.63661i	0.00697549	−	0.00286588i
$921$		0			0
$922$	−946.751	−	869.208i	−1.02684	−	0.942742i
$923$	246.053	+	426.177i	0.266580	+	0.461730i
$924$		0			0
$925$	1156.67	+	667.807i	1.25046	+	0.721953i
$926$	−1164.09	+	365.809i	−1.25711	+	0.395042i
$927$		0			0
$928$	57.2377	−	1181.06i	0.0616786	−	1.27270i
$929$	657.748	−	1139.25i	0.708017	−	1.22632i	−0.257575	−	0.966258i	$-0.582923\pi$
$929$	657.748	−	1139.25i	0.708017	−	1.22632i	0.965592	−	0.260063i	$-0.0837434\pi$
$930$		0			0
$931$	202.380	+	350.532i	0.217379	+	0.376511i
$932$	−1106.45	−	518.528i	−1.18717	−	0.556361i
$933$		0			0
$934$	−564.686	−	125.756i	−0.604589	−	0.134642i
$935$			0.0411627i			4.40242e-5i
$936$		0			0
$937$	−521.572			−0.556640			−0.278320	−	0.960488i	$-0.589778\pi$
$937$	−521.572			−0.556640			−0.278320	+	0.960488i	$0.589778\pi$
$938$	139.597	−	626.839i	0.148824	−	0.668272i
$939$		0			0
$940$	2.74565	+	1.28673i	0.00292090	+	0.00136886i
$941$	340.545	−	196.614i	0.361896	−	0.208941i	−0.308016	−	0.951381i	$-0.599665\pi$
$941$	340.545	−	196.614i	0.361896	−	0.208941i	0.669912	+	0.742440i	$0.266332\pi$
$942$		0			0
$943$	−2274.07	−	1312.93i	−2.41153	−	1.39229i
$944$	325.525	−	883.817i	0.344836	−	0.936247i
$945$		0			0
$946$	−157.533	−	501.306i	−0.166526	−	0.529922i
$947$	−437.860	+	758.396i	−0.462366	+	0.800841i	−0.999078	−	0.0429244i	$-0.986333\pi$
$947$	−437.860	+	758.396i	−0.462366	+	0.800841i	0.536713	+	0.843765i	$0.319666\pi$
$948$		0			0
$949$	268.288	−	154.896i	0.282706	−	0.163220i
$950$	508.971	−	554.377i	0.535759	−	0.583554i
$951$		0			0
$952$	5.38661	+	13.1109i	0.00565820	+	0.0137720i
$953$	−71.0166			−0.0745190			−0.0372595	−	0.999306i	$-0.511863\pi$
$953$	−71.0166			−0.0745190			−0.0372595	+	0.999306i	$0.511863\pi$
$954$		0			0
$955$	−1.66803			−0.00174663
$956$	−315.084	+	26.9578i	−0.329586	+	0.0281986i
$957$		0			0
$958$	195.751	+	179.718i	0.204333	+	0.187597i
$959$	−457.661	+	264.231i	−0.477227	+	0.275527i
$960$		0			0
$961$	−16.4259	+	28.4504i	−0.0170925	+	0.0296050i
$962$	−372.165	−	1184.31i	−0.386866	−	1.23109i
$963$		0			0
$964$	731.028	−	509.786i	0.758327	−	0.528823i
$965$	1.72022	+	0.993171i	0.00178261	+	0.00102919i
$966$		0			0
$967$	−194.113	+	112.071i	−0.200737	+	0.115896i	−0.596999	−	0.802242i	$-0.703641\pi$
$967$	−194.113	+	112.071i	−0.200737	+	0.115896i	0.396262	+	0.918137i	$0.370307\pi$
$968$	−94.4542	+	701.852i	−0.0975767	+	0.725054i
$969$		0			0
$970$	0.932144	−	4.18564i	0.000960973	−	0.00431510i
$971$	−91.8845			−0.0946287			−0.0473144	−	0.998880i	$-0.515066\pi$
$971$	−91.8845			−0.0946287			−0.0473144	+	0.998880i	$0.515066\pi$
$972$		0			0
$973$			528.390i			0.543053i
$974$	−348.184	+	1563.46i	−0.357478	+	1.60520i
$975$		0			0
$976$	−235.711	−	1367.41i	−0.241507	−	1.40104i
$977$	−368.517	−	638.289i	−0.377192	−	0.653316i	0.613461	−	0.789725i	$-0.289777\pi$
$977$	−368.517	−	638.289i	−0.377192	−	0.653316i	−0.990653	+	0.136410i	$0.956444\pi$
$978$		0			0
$979$	−121.492	+	210.431i	−0.124098	+	0.214945i
$980$	−1.17937	−	1.69120i	−0.00120344	−	0.00172572i
$981$		0			0
$982$	500.022	+	1591.18i	0.509188	+	1.62035i
$983$	−1534.66	−	886.034i	−1.56120	−	0.901357i	−0.997136	−	0.0756241i	$-0.975905\pi$
$983$	−1534.66	−	886.034i	−1.56120	−	0.901357i	−0.564061	−	0.825733i	$-0.690762\pi$
$984$		0			0
$985$	1.91835	+	3.32267i	0.00194756	+	0.00337327i
$986$	−20.5134	−	18.8333i	−0.0208047	−	0.0191007i
$987$		0			0
$988$	−696.959	+	59.6302i	−0.705424	+	0.0603544i
$989$			2085.87i			2.10907i
$990$		0			0
$991$		−	1115.19i		−	1.12532i	−0.826689	−	0.562659i	$-0.809779\pi$
$991$		−	1115.19i		−	1.12532i	0.826689	−	0.562659i	$-0.190221\pi$
$992$	−819.700	−	527.745i	−0.826311	−	0.532002i
$993$		0			0
$994$	−269.385	+	293.417i	−0.271011	+	0.295188i
$995$	−1.71433	−	2.96930i	−0.00172294	−	0.00298423i
$996$		0			0
$997$	−193.012	−	111.435i	−0.193593	−	0.111771i	0.400071	−	0.916484i	$-0.368986\pi$
$997$	−193.012	−	111.435i	−0.193593	−	0.111771i	−0.593663	+	0.804714i	$0.702319\pi$
$998$	−75.5153	−	240.307i	−0.0756666	−	0.240788i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.3.p.b.19.19		40
3.2	odd	2		72.3.p.b.43.2	✓	40
4.3	odd	2		864.3.t.b.559.11		40
8.3	odd	2	inner	216.3.p.b.19.6		40
8.5	even	2		864.3.t.b.559.10		40
9.2	odd	6		648.3.b.f.163.12		20
9.4	even	3	inner	216.3.p.b.91.6		40
9.5	odd	6		72.3.p.b.67.15	yes	40
9.7	even	3		648.3.b.e.163.9		20
12.11	even	2		288.3.t.b.79.1		40
24.5	odd	2		288.3.t.b.79.2		40
24.11	even	2		72.3.p.b.43.15	yes	40
36.7	odd	6		2592.3.b.f.1135.11		20
36.11	even	6		2592.3.b.e.1135.10		20
36.23	even	6		288.3.t.b.175.2		40
36.31	odd	6		864.3.t.b.847.10		40
72.5	odd	6		288.3.t.b.175.1		40
72.11	even	6		648.3.b.f.163.11		20
72.13	even	6		864.3.t.b.847.11		40
72.29	odd	6		2592.3.b.e.1135.11		20
72.43	odd	6		648.3.b.e.163.10		20
72.59	even	6		72.3.p.b.67.2	yes	40
72.61	even	6		2592.3.b.f.1135.10		20
72.67	odd	6	inner	216.3.p.b.91.19		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.3.p.b.43.2	✓	40	3.2	odd	2
72.3.p.b.43.15	yes	40	24.11	even	2
72.3.p.b.67.2	yes	40	72.59	even	6
72.3.p.b.67.15	yes	40	9.5	odd	6
216.3.p.b.19.6		40	8.3	odd	2	inner
216.3.p.b.19.19		40	1.1	even	1	trivial
216.3.p.b.91.6		40	9.4	even	3	inner
216.3.p.b.91.19		40	72.67	odd	6	inner
288.3.t.b.79.1		40	12.11	even	2
288.3.t.b.79.2		40	24.5	odd	2
288.3.t.b.175.1		40	72.5	odd	6
288.3.t.b.175.2		40	36.23	even	6
648.3.b.e.163.9		20	9.7	even	3
648.3.b.e.163.10		20	72.43	odd	6
648.3.b.f.163.11		20	72.11	even	6
648.3.b.f.163.12		20	9.2	odd	6
864.3.t.b.559.10		40	8.5	even	2
864.3.t.b.559.11		40	4.3	odd	2
864.3.t.b.847.10		40	36.31	odd	6
864.3.t.b.847.11		40	72.13	even	6
2592.3.b.e.1135.10		20	36.11	even	6
2592.3.b.e.1135.11		20	72.29	odd	6
2592.3.b.f.1135.10		20	72.61	even	6
2592.3.b.f.1135.11		20	36.7	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	216.p (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.95218 + 0.434750i) q^{2} +(3.62198 + 1.69742i) q^{4} +(0.0166003 - 0.00958419i) q^{5} +(4.07208 + 2.35102i) q^{7} +(6.33280 + 4.88832i) q^{8} +O(q^{10})\)	\(q+(1.95218 + 0.434750i) q^{2} +(3.62198 + 1.69742i) q^{4} +(0.0166003 - 0.00958419i) q^{5} +(4.07208 + 2.35102i) q^{7} +(6.33280 + 4.88832i) q^{8} +(0.0365734 - 0.0114930i) q^{10} +(-2.84945 + 4.93540i) q^{11} +(10.0617 - 5.80910i) q^{13} +(6.92732 + 6.35994i) q^{14} +(10.2375 + 12.2960i) q^{16} +0.376814 q^{17} -15.0519 q^{19} +(0.0763944 - 0.00653612i) q^{20} +(-7.70830 + 8.39597i) q^{22} +(39.1821 - 22.6218i) q^{23} +(-12.4998 + 21.6503i) q^{25} +(22.1676 - 6.96608i) q^{26} +(10.7584 + 15.4274i) q^{28} +(-32.0010 - 18.4758i) q^{29} +(-26.3839 + 15.2328i) q^{31} +(14.6398 + 28.4548i) q^{32} +(0.735607 + 0.163820i) q^{34} +0.0901304 q^{35} -53.4253i q^{37} +(-29.3840 - 6.54383i) q^{38} +(0.151977 + 0.0204528i) q^{40} +(-29.0192 - 50.2628i) q^{41} +(-23.0516 + 39.9265i) q^{43} +(-18.6981 + 13.0392i) q^{44} +(86.3252 - 27.1273i) q^{46} +(34.2487 + 19.7735i) q^{47} +(-13.4454 - 23.2882i) q^{49} +(-33.8143 + 36.8309i) q^{50} +(46.3036 - 3.96163i) q^{52} +0.989874i q^{53} +0.109239i q^{55} +(14.2952 + 34.7942i) q^{56} +(-54.4392 - 49.9804i) q^{58} +(-29.4331 - 50.9797i) q^{59} +(-75.1051 - 43.3619i) q^{61} +(-58.1285 + 18.2666i) q^{62} +(16.2087 + 61.9135i) q^{64} +(0.111351 - 0.192866i) q^{65} +(-34.1445 - 59.1400i) q^{67} +(1.36481 + 0.639610i) q^{68} +(0.175950 + 0.0391842i) q^{70} +42.3565i q^{71} +26.6644 q^{73} +(23.2267 - 104.296i) q^{74} +(-54.5179 - 25.5494i) q^{76} +(-23.2064 + 13.3982i) q^{77} +(121.208 + 69.9797i) q^{79} +(0.287794 + 0.106000i) q^{80} +(-34.7989 - 110.738i) q^{82} +(-40.9931 + 71.0021i) q^{83} +(0.00625522 - 0.00361145i) q^{85} +(-62.3588 + 67.9219i) q^{86} +(-42.1708 + 17.3259i) q^{88} +42.6370 q^{89} +54.6292 q^{91} +(180.316 - 15.4274i) q^{92} +(58.2629 + 53.4909i) q^{94} +(-0.249867 + 0.144261i) q^{95} +(55.9278 - 96.8698i) q^{97} +(-16.1233 - 51.3080i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 5 q^{2} + 7 q^{4} - 46 q^{8}+O(q^{10}) \) 40 * q + 5 * q^2 + 7 * q^4 - 46 * q^8	\( 40 q + 5 q^{2} + 7 q^{4} - 46 q^{8} - 12 q^{10} + 16 q^{11} - 6 q^{14} + 31 q^{16} + 4 q^{17} - 76 q^{19} + 12 q^{20} + 35 q^{22} + 118 q^{25} + 72 q^{26} - 36 q^{28} + 5 q^{32} + 5 q^{34} + 108 q^{35} + 169 q^{38} - 6 q^{40} - 20 q^{41} - 16 q^{43} - 362 q^{44} - 96 q^{46} + 166 q^{49} - 73 q^{50} - 24 q^{52} - 186 q^{56} + 36 q^{58} + 64 q^{59} - 384 q^{62} - 518 q^{64} + 102 q^{65} - 64 q^{67} + 295 q^{68} - 6 q^{70} - 292 q^{73} - 318 q^{74} + 197 q^{76} + 720 q^{80} + 386 q^{82} - 554 q^{83} + 295 q^{86} + 59 q^{88} + 688 q^{89} - 204 q^{91} + 378 q^{92} - 66 q^{94} + 92 q^{97} + 614 q^{98}+O(q^{100}) \) 40 * q + 5 * q^2 + 7 * q^4 - 46 * q^8 - 12 * q^10 + 16 * q^11 - 6 * q^14 + 31 * q^16 + 4 * q^17 - 76 * q^19 + 12 * q^20 + 35 * q^22 + 118 * q^25 + 72 * q^26 - 36 * q^28 + 5 * q^32 + 5 * q^34 + 108 * q^35 + 169 * q^38 - 6 * q^40 - 20 * q^41 - 16 * q^43 - 362 * q^44 - 96 * q^46 + 166 * q^49 - 73 * q^50 - 24 * q^52 - 186 * q^56 + 36 * q^58 + 64 * q^59 - 384 * q^62 - 518 * q^64 + 102 * q^65 - 64 * q^67 + 295 * q^68 - 6 * q^70 - 292 * q^73 - 318 * q^74 + 197 * q^76 + 720 * q^80 + 386 * q^82 - 554 * q^83 + 295 * q^86 + 59 * q^88 + 688 * q^89 - 204 * q^91 + 378 * q^92 - 66 * q^94 + 92 * q^97 + 614 * q^98

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