LMFDB - Embedded newform 378.3.s.e.107.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,3,Mod(53,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("378.53");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	378.s (of order $6$, degree $2$, 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:	$10.2997539928$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			107.7
Character	$\chi$	$=$	378.107
Dual form			378.3.s.e.53.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22474 + 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(-5.31178 - 3.06676i) q^{5} +(5.10682 + 4.78753i) q^{7} +2.82843i q^{8} +O(q^{10})$	\(q+(1.22474 + 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(-5.31178 - 3.06676i) q^{5} +(5.10682 + 4.78753i) q^{7} +2.82843i q^{8} +(-4.33705 - 7.51200i) q^{10} +(8.42297 - 4.86301i) q^{11} +21.0999 q^{13} +(2.86925 + 9.47457i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(-2.48336 + 1.43377i) q^{17} +(-18.4925 + 32.0300i) q^{19} -12.2670i q^{20} +13.7547 q^{22} +(38.2847 + 22.1037i) q^{23} +(6.31004 + 10.9293i) q^{25} +(25.8420 + 14.9199i) q^{26} +(-3.18543 + 13.6328i) q^{28} +7.81103i q^{29} +(11.1852 + 19.3734i) q^{31} +(-4.89898 + 2.82843i) q^{32} -4.05532 q^{34} +(-12.4441 - 41.0917i) q^{35} +(11.9333 - 20.6691i) q^{37} +(-45.2972 + 26.1524i) q^{38} +(8.67411 - 15.0240i) q^{40} -49.9383i q^{41} +58.0697 q^{43} +(16.8459 + 9.72601i) q^{44} +(31.2593 + 54.1428i) q^{46} +(-58.3505 - 33.6887i) q^{47} +(3.15914 + 48.8981i) q^{49} +17.8475i q^{50} +(21.0999 + 36.5461i) q^{52} +(28.4314 - 16.4149i) q^{53} -59.6547 q^{55} +(-13.5412 + 14.4443i) q^{56} +(-5.52323 + 9.56652i) q^{58} +(-61.5206 + 35.5189i) q^{59} +(23.3278 - 40.4050i) q^{61} +31.6366i q^{62} -8.00000 q^{64} +(-112.078 - 64.7084i) q^{65} +(-9.40879 - 16.2965i) q^{67} +(-4.96673 - 2.86754i) q^{68} +(13.8154 - 59.1262i) q^{70} +27.6586i q^{71} +(-43.8876 - 76.0156i) q^{73} +(29.2305 - 16.8762i) q^{74} -73.9701 q^{76} +(66.2964 + 15.4907i) q^{77} +(-39.8584 + 69.0367i) q^{79} +(21.2471 - 12.2670i) q^{80} +(35.3117 - 61.1616i) q^{82} -93.3124i q^{83} +17.5881 q^{85} +(71.1205 + 41.0615i) q^{86} +(13.7547 + 23.8238i) q^{88} +(-15.2947 - 8.83038i) q^{89} +(107.753 + 101.016i) q^{91} +88.4148i q^{92} +(-47.6430 - 82.5201i) q^{94} +(196.457 - 113.424i) q^{95} +17.2922 q^{97} +(-30.7070 + 62.1215i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{4} + 8 q^{7}+O(q^{10}) $ 24 * q + 24 * q^4 + 8 * q^7	$ 24 q + 24 q^{4} + 8 q^{7} + 8 q^{10} - 16 q^{13} - 48 q^{16} - 36 q^{19} + 64 q^{22} + 128 q^{25} + 32 q^{28} + 176 q^{31} + 16 q^{34} - 72 q^{37} - 16 q^{40} + 216 q^{43} + 64 q^{46} - 24 q^{49} - 16 q^{52} + 448 q^{55} + 104 q^{58} - 268 q^{61} - 192 q^{64} - 248 q^{67} - 80 q^{70} - 116 q^{73} - 144 q^{76} + 152 q^{79} + 240 q^{82} - 536 q^{85} + 64 q^{88} + 428 q^{91} + 144 q^{94} + 16 q^{97}+O(q^{100}) $ 24 * q + 24 * q^4 + 8 * q^7 + 8 * q^10 - 16 * q^13 - 48 * q^16 - 36 * q^19 + 64 * q^22 + 128 * q^25 + 32 * q^28 + 176 * q^31 + 16 * q^34 - 72 * q^37 - 16 * q^40 + 216 * q^43 + 64 * q^46 - 24 * q^49 - 16 * q^52 + 448 * q^55 + 104 * q^58 - 268 * q^61 - 192 * q^64 - 248 * q^67 - 80 * q^70 - 116 * q^73 - 144 * q^76 + 152 * q^79 + 240 * q^82 - 536 * q^85 + 64 * q^88 + 428 * q^91 + 144 * q^94 + 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.22474	+	0.707107i	0.612372	+	0.353553i
$2$	1.22474	+	0.707107i	0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	1.00000	+	1.73205i	0.250000	+	0.433013i
$5$	−5.31178	−	3.06676i	−1.06236	−	0.613352i	−0.136274	−	0.990671i	$-0.543513\pi$
$5$	−5.31178	−	3.06676i	−1.06236	−	0.613352i	−0.926083	+	0.377319i	$0.876846\pi$
$6$		0			0
$7$	5.10682	+	4.78753i	0.729545	+	0.683933i
$7$	5.10682	+	4.78753i	0.729545	+	0.683933i
$8$			2.82843i			0.353553i
$9$		0			0
$10$	−4.33705	−	7.51200i	−0.433705	−	0.751200i
$11$	8.42297	−	4.86301i	0.765725	−	0.442092i	−0.0656225	−	0.997845i	$-0.520903\pi$
$11$	8.42297	−	4.86301i	0.765725	−	0.442092i	0.831347	+	0.555753i	$0.187570\pi$
$12$		0			0
$13$	21.0999			1.62307			0.811535	−	0.584304i	$-0.198632\pi$
$13$	21.0999			1.62307			0.811535	+	0.584304i	$0.198632\pi$
$14$	2.86925	+	9.47457i	0.204947	+	0.676755i
$15$		0			0
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	−2.48336	+	1.43377i	−0.146080	+	0.0843395i	−0.571259	−	0.820770i	$-0.693545\pi$
$17$	−2.48336	+	1.43377i	−0.146080	+	0.0843395i	0.425178	+	0.905110i	$0.360211\pi$
$18$		0			0
$19$	−18.4925	+	32.0300i	−0.973291	+	1.68579i	−0.287827	+	0.957683i	$0.592933\pi$
$19$	−18.4925	+	32.0300i	−0.973291	+	1.68579i	−0.685464	+	0.728106i	$0.740401\pi$
$20$		−	12.2670i		−	0.613352i
$21$		0			0
$22$	13.7547			0.625212
$23$	38.2847	+	22.1037i	1.66455	+	0.961030i	0.970498	+	0.241108i	$0.0775108\pi$
$23$	38.2847	+	22.1037i	1.66455	+	0.961030i	0.694055	+	0.719922i	$0.255822\pi$
$24$		0			0
$25$	6.31004	+	10.9293i	0.252402	+	0.437172i
$26$	25.8420	+	14.9199i	0.993923	+	0.573842i
$27$		0			0
$28$	−3.18543	+	13.6328i	−0.113765	+	0.486885i
$29$			7.81103i			0.269346i	0.990890	+	0.134673i	$0.0429984\pi$
$29$			7.81103i			0.269346i	−0.990890	+	0.134673i	$0.957002\pi$
$30$		0			0
$31$	11.1852	+	19.3734i	0.360814	+	0.624949i	0.988095	−	0.153845i	$-0.0491655\pi$
$31$	11.1852	+	19.3734i	0.360814	+	0.624949i	−0.627281	+	0.778793i	$0.715832\pi$
$32$	−4.89898	+	2.82843i	−0.153093	+	0.0883883i
$33$		0			0
$34$	−4.05532			−0.119274
$35$	−12.4441	−	41.0917i	−0.355546	−	1.17405i
$36$		0			0
$37$	11.9333	−	20.6691i	0.322522	−	0.558624i	−0.658486	−	0.752593i	$-0.728803\pi$
$37$	11.9333	−	20.6691i	0.322522	−	0.558624i	0.981008	+	0.193969i	$0.0621361\pi$
$38$	−45.2972	+	26.1524i	−1.19203	+	0.688220i
$39$		0			0
$40$	8.67411	−	15.0240i	0.216853	−	0.375600i
$41$		−	49.9383i		−	1.21801i	−0.793168	−	0.609003i	$-0.791570\pi$
$41$		−	49.9383i		−	1.21801i	0.793168	−	0.609003i	$-0.208430\pi$
$42$		0			0
$43$	58.0697			1.35046			0.675229	−	0.737608i	$-0.264045\pi$
$43$	58.0697			1.35046			0.675229	+	0.737608i	$0.264045\pi$
$44$	16.8459	+	9.72601i	0.382862	+	0.221046i
$45$		0			0
$46$	31.2593	+	54.1428i	0.679551	+	1.17702i
$47$	−58.3505	−	33.6887i	−1.24150	−	0.716780i	−0.272101	−	0.962269i	$-0.587718\pi$
$47$	−58.3505	−	33.6887i	−1.24150	−	0.716780i	−0.969400	+	0.245488i	$0.921052\pi$
$48$		0			0
$49$	3.15914	+	48.8981i	0.0644723	+	0.997919i
$50$			17.8475i			0.356950i
$51$		0			0
$52$	21.0999	+	36.5461i	0.405767	+	0.702810i
$53$	28.4314	−	16.4149i	0.536442	−	0.309715i	−0.207194	−	0.978300i	$-0.566433\pi$
$53$	28.4314	−	16.4149i	0.536442	−	0.309715i	0.743636	+	0.668585i	$0.233100\pi$
$54$		0			0
$55$	−59.6547			−1.08463
$56$	−13.5412	+	14.4443i	−0.241807	+	0.257933i
$57$		0			0
$58$	−5.52323	+	9.56652i	−0.0952281	+	0.164940i
$59$	−61.5206	+	35.5189i	−1.04272	+	0.602015i	−0.920603	−	0.390500i	$-0.872302\pi$
$59$	−61.5206	+	35.5189i	−1.04272	+	0.602015i	−0.122118	+	0.992516i	$0.538969\pi$
$60$		0			0
$61$	23.3278	−	40.4050i	0.382423	−	0.662377i	−0.608985	−	0.793182i	$-0.708423\pi$
$61$	23.3278	−	40.4050i	0.382423	−	0.662377i	0.991408	+	0.130805i	$0.0417563\pi$
$62$			31.6366i			0.510268i
$63$		0			0
$64$	−8.00000			−0.125000
$65$	−112.078	−	64.7084i	−1.72428	−	0.995513i
$66$		0			0
$67$	−9.40879	−	16.2965i	−0.140430	−	0.243231i	0.787229	−	0.616661i	$-0.211515\pi$
$67$	−9.40879	−	16.2965i	−0.140430	−	0.243231i	−0.927659	+	0.373430i	$0.878182\pi$
$68$	−4.96673	−	2.86754i	−0.0730401	−	0.0421697i
$69$		0			0
$70$	13.8154	−	59.1262i	0.197362	−	0.844659i
$71$			27.6586i			0.389557i	0.980847	+	0.194779i	$0.0623988\pi$
$71$			27.6586i			0.389557i	−0.980847	+	0.194779i	$0.937601\pi$
$72$		0			0
$73$	−43.8876	−	76.0156i	−0.601201	−	1.04131i	−0.992640	−	0.121106i	$-0.961356\pi$
$73$	−43.8876	−	76.0156i	−0.601201	−	1.04131i	0.391439	−	0.920204i	$-0.371977\pi$
$74$	29.2305	−	16.8762i	0.395007	−	0.228057i
$75$		0			0
$76$	−73.9701			−0.973291
$77$	66.2964	+	15.4907i	0.860992	+	0.201179i
$78$		0			0
$79$	−39.8584	+	69.0367i	−0.504536	+	0.873883i	0.495450	+	0.868637i	$0.335003\pi$
$79$	−39.8584	+	69.0367i	−0.504536	+	0.873883i	−0.999986	+	0.00524619i	$0.998330\pi$
$80$	21.2471	−	12.2670i	0.265589	−	0.153338i
$81$		0			0
$82$	35.3117	−	61.1616i	0.430630	−	0.745874i
$83$		−	93.3124i		−	1.12425i	−0.827054	−	0.562123i	$-0.809985\pi$
$83$		−	93.3124i		−	1.12425i	0.827054	−	0.562123i	$-0.190015\pi$
$84$		0			0
$85$	17.5881			0.206919
$86$	71.1205	+	41.0615i	0.826983	+	0.477459i
$87$		0			0
$88$	13.7547	+	23.8238i	0.156303	+	0.270725i
$89$	−15.2947	−	8.83038i	−0.171850	−	0.0992178i	0.411608	−	0.911361i	$-0.364967\pi$
$89$	−15.2947	−	8.83038i	−0.171850	−	0.0992178i	−0.583458	+	0.812143i	$0.698301\pi$
$90$		0			0
$91$	107.753	+	101.016i	1.18410	+	1.11007i
$92$			88.4148i			0.961030i
$93$		0			0
$94$	−47.6430	−	82.5201i	−0.506840	−	0.877873i
$95$	196.457	−	113.424i	2.06796	−	1.19394i
$96$		0			0
$97$	17.2922			0.178271			0.0891353	−	0.996020i	$-0.471590\pi$
$97$	17.2922			0.178271			0.0891353	+	0.996020i	$0.471590\pi$
$98$	−30.7070	+	62.1215i	−0.313337	+	0.633893i
$99$		0			0
$100$	−12.6201	+	21.8586i	−0.126201	+	0.218586i
$101$	−45.3275	+	26.1698i	−0.448787	+	0.259107i	−0.707318	−	0.706896i	$-0.750095\pi$
$101$	−45.3275	+	26.1698i	−0.448787	+	0.259107i	0.258531	+	0.966003i	$0.416762\pi$
$102$		0			0
$103$	12.2845	−	21.2774i	0.119267	−	0.206576i	−0.800210	−	0.599719i	$-0.795279\pi$
$103$	12.2845	−	21.2774i	0.119267	−	0.206576i	0.919477	+	0.393143i	$0.128612\pi$
$104$			59.6795i			0.573842i
$105$		0			0
$106$	46.4283			0.438003
$107$	−7.15249	−	4.12949i	−0.0668457	−	0.0385934i	0.466205	−	0.884677i	$-0.345621\pi$
$107$	−7.15249	−	4.12949i	−0.0668457	−	0.0385934i	−0.533050	+	0.846084i	$0.678954\pi$
$108$		0			0
$109$	−72.7815	−	126.061i	−0.667720	−	1.15652i	−0.978540	−	0.206056i	$-0.933937\pi$
$109$	−72.7815	−	126.061i	−0.667720	−	1.15652i	0.310820	−	0.950469i	$-0.399396\pi$
$110$	−73.0618	−	42.1822i	−0.664198	−	0.383475i
$111$		0			0
$112$	−26.7981	+	8.11547i	−0.239269	+	0.0724596i
$113$			55.4871i			0.491036i	0.969392	+	0.245518i	$0.0789581\pi$
$113$			55.4871i			0.491036i	−0.969392	+	0.245518i	$0.921042\pi$
$114$		0			0
$115$	−135.573	−	234.820i	−1.17890	−	2.04191i
$116$	−13.5291	+	7.81103i	−0.116630	+	0.0673365i
$117$		0			0
$118$	−100.463			−0.851378
$119$	−19.5463	−	4.56717i	−0.164255	−	0.0383796i
$120$		0			0
$121$	−13.2023	+	22.8671i	−0.109110	+	0.188984i
$122$	57.1413	−	32.9905i	0.468371	−	0.270414i
$123$		0			0
$124$	−22.3705	+	38.7468i	−0.180407	+	0.312474i
$125$			75.9325i			0.607460i
$126$		0			0
$127$	−71.7198			−0.564723			−0.282362	−	0.959308i	$-0.591118\pi$
$127$	−71.7198			−0.564723			−0.282362	+	0.959308i	$0.591118\pi$
$128$	−9.79796	−	5.65685i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	−91.5114	−	158.502i	−0.703934	−	1.21925i
$131$	95.8544	+	55.3415i	0.731713	+	0.422455i	0.819048	−	0.573724i	$-0.194502\pi$
$131$	95.8544	+	55.3415i	0.731713	+	0.422455i	−0.0873357	+	0.996179i	$0.527835\pi$
$132$		0			0
$133$	−247.782	+	75.0378i	−1.86303	+	0.564194i
$134$		−	26.6121i		−	0.198598i
$135$		0			0
$136$	−4.05532	−	7.02402i	−0.0298185	−	0.0516472i
$137$	−179.598	+	103.691i	−1.31093	+	0.756868i	−0.982251	−	0.187573i	$-0.939938\pi$
$137$	−179.598	+	103.691i	−1.31093	+	0.756868i	−0.328683	+	0.944440i	$0.606605\pi$
$138$		0			0
$139$	77.0171			0.554080			0.277040	−	0.960858i	$-0.410647\pi$
$139$	77.0171			0.554080			0.277040	+	0.960858i	$0.410647\pi$
$140$	58.7288	−	62.6455i	0.419491	−	0.447468i
$141$		0			0
$142$	−19.5576	+	33.8747i	−0.137729	+	0.238554i
$143$	177.724	−	102.609i	1.24282	−	0.717545i
$144$		0			0
$145$	23.9546	−	41.4905i	0.165204	−	0.286141i
$146$		−	124.133i		−	0.850226i
$147$		0			0
$148$	47.7332			0.322522
$149$	−92.8956	−	53.6333i	−0.623461	−	0.359955i	0.154754	−	0.987953i	$-0.450541\pi$
$149$	−92.8956	−	53.6333i	−0.623461	−	0.359955i	−0.778215	+	0.627998i	$0.783875\pi$
$150$		0			0
$151$	−89.6185	−	155.224i	−0.593500	−	1.02797i	−0.993757	−	0.111569i	$-0.964412\pi$
$151$	−89.6185	−	155.224i	−0.593500	−	1.02797i	0.400257	−	0.916403i	$-0.368921\pi$
$152$	−90.5945	−	52.3048i	−0.596016	−	0.344110i
$153$		0			0
$154$	70.2425	+	65.8508i	0.456120	+	0.427603i
$155$		−	137.210i		−	0.885225i
$156$		0			0
$157$	43.9884	+	76.1902i	0.280181	+	0.485288i	0.971429	−	0.237330i	$-0.0762722\pi$
$157$	43.9884	+	76.1902i	0.280181	+	0.485288i	−0.691248	+	0.722617i	$0.742939\pi$
$158$	−97.6327	+	56.3683i	−0.617928	+	0.356761i
$159$		0			0
$160$	34.6964			0.216853
$161$	89.6910	+	296.169i	0.557087	+	1.83956i
$162$		0			0
$163$	85.8957	−	148.776i	0.526967	−	0.912734i	−0.472539	−	0.881310i	$-0.656662\pi$
$163$	85.8957	−	148.776i	0.526967	−	0.912734i	0.999506	−	0.0314243i	$-0.0100043\pi$
$164$	86.4956	−	49.9383i	0.527412	−	0.304502i
$165$		0			0
$166$	65.9818	−	114.284i	0.397481	−	0.688457i
$167$			57.4621i			0.344084i	0.985090	+	0.172042i	$0.0550365\pi$
$167$			57.4621i			0.344084i	−0.985090	+	0.172042i	$0.944963\pi$
$168$		0			0
$169$	276.206			1.63435
$170$	21.5410	+	12.4367i	0.126712	+	0.0731570i
$171$		0			0
$172$	58.0697	+	100.580i	0.337614	+	0.584765i
$173$	−20.2643	−	11.6996i	−0.117135	−	0.0676279i	0.440288	−	0.897857i	$-0.354876\pi$
$173$	−20.2643	−	11.6996i	−0.117135	−	0.0676279i	−0.557423	+	0.830229i	$0.688210\pi$
$174$		0			0
$175$	−20.1002	+	86.0234i	−0.114858	+	0.491563i
$176$			38.9041i			0.221046i
$177$		0			0
$178$	−12.4880	−	21.6299i	−0.0701576	−	0.121516i
$179$	301.229	−	173.915i	1.68284	−	0.971590i	0.723087	−	0.690757i	$-0.242722\pi$
$179$	301.229	−	173.915i	1.68284	−	0.971590i	0.959756	−	0.280834i	$-0.0906110\pi$
$180$		0			0
$181$	−122.648			−0.677614			−0.338807	−	0.940856i	$-0.610023\pi$
$181$	−122.648			−0.677614			−0.338807	+	0.940856i	$0.610023\pi$
$182$	60.5410	+	199.912i	0.332643	+	1.09842i
$183$		0			0
$184$	−62.5187	+	108.286i	−0.339775	+	0.588508i
$185$	−126.774	+	73.1932i	−0.685266	+	0.395639i
$186$		0			0
$187$	−13.9449	+	24.1532i	−0.0745715	+	0.129162i
$188$		−	134.755i		−	0.716780i
$189$		0			0
$190$	320.812			1.68849
$191$	−99.0232	−	57.1711i	−0.518446	−	0.299325i	0.217853	−	0.975982i	$-0.430095\pi$
$191$	−99.0232	−	57.1711i	−0.518446	−	0.299325i	−0.736299	+	0.676657i	$0.763428\pi$
$192$		0			0
$193$	26.8925	+	46.5792i	0.139340	+	0.241343i	0.927247	−	0.374451i	$-0.122169\pi$
$193$	26.8925	+	46.5792i	0.139340	+	0.241343i	−0.787907	+	0.615794i	$0.788835\pi$
$194$	21.1786	+	12.2275i	0.109168	+	0.0630281i
$195$		0			0
$196$	−81.5348	+	54.3699i	−0.415994	+	0.277397i
$197$			64.1428i			0.325598i	0.986659	+	0.162799i	$0.0520522\pi$
$197$			64.1428i			0.325598i	−0.986659	+	0.162799i	$0.947948\pi$
$198$		0			0
$199$	−174.040	−	301.447i	−0.874574	−	1.51481i	−0.857216	−	0.514957i	$-0.827808\pi$
$199$	−174.040	−	301.447i	−0.874574	−	1.51481i	−0.0173584	−	0.999849i	$-0.505526\pi$
$200$	−30.9127	+	17.8475i	−0.154564	+	0.0892374i
$201$		0			0
$202$	−74.0195			−0.366433
$203$	−37.3955	+	39.8895i	−0.184214	+	0.196500i
$204$		0			0
$205$	−153.149	+	265.261i	−0.747067	+	1.29396i
$206$	30.0907	−	17.3729i	0.146071	−	0.0843344i
$207$		0			0
$208$	−42.1998	+	73.0922i	−0.202884	+	0.351405i
$209$			359.717i			1.72113i
$210$		0			0
$211$	264.009			1.25123			0.625614	−	0.780133i	$-0.284848\pi$
$211$	264.009			1.25123			0.625614	+	0.780133i	$0.284848\pi$
$212$	56.8629	+	32.8298i	0.268221	+	0.154858i
$213$		0			0
$214$	−5.83999	−	10.1152i	−0.0272897	−	0.0472671i
$215$	−308.454	−	178.086i	−1.43467	−	0.828306i
$216$		0			0
$217$	−35.6298	+	152.486i	−0.164192	+	0.702701i
$218$		−	205.857i		−	0.944299i
$219$		0			0
$220$	−59.6547	−	103.325i	−0.271158	−	0.469659i
$221$	−52.3988	+	30.2524i	−0.237098	+	0.136889i
$222$		0			0
$223$	38.3767			0.172093			0.0860463	−	0.996291i	$-0.472577\pi$
$223$	38.3767			0.172093			0.0860463	+	0.996291i	$0.472577\pi$
$224$	−38.5594	−	9.00975i	−0.172140	−	0.0402221i
$225$		0			0
$226$	−39.2353	+	67.9575i	−0.173607	+	0.300697i
$227$	114.887	−	66.3298i	0.506109	−	0.292202i	−0.225124	−	0.974330i	$-0.572279\pi$
$227$	114.887	−	66.3298i	0.506109	−	0.292202i	0.731233	+	0.682128i	$0.238945\pi$
$228$		0			0
$229$	136.270	−	236.027i	0.595068	−	1.03069i	−0.398470	−	0.917182i	$-0.630459\pi$
$229$	136.270	−	236.027i	0.595068	−	1.03069i	0.993537	−	0.113506i	$-0.0362081\pi$
$230$		−	383.460i		−	1.66722i
$231$		0			0
$232$	−22.0929			−0.0952281
$233$	−184.457	−	106.496i	−0.791661	−	0.457066i	0.0488859	−	0.998804i	$-0.484433\pi$
$233$	−184.457	−	106.496i	−0.791661	−	0.457066i	−0.840547	+	0.541739i	$0.817766\pi$
$234$		0			0
$235$	206.630	+	357.894i	0.879278	+	1.52295i
$236$	−123.041	−	71.0378i	−0.521361	−	0.301008i
$237$		0			0
$238$	−20.7098	−	19.4149i	−0.0870158	−	0.0815754i
$239$			220.129i			0.921040i	0.887649	+	0.460520i	$0.152337\pi$
$239$			220.129i			0.921040i	−0.887649	+	0.460520i	$0.847663\pi$
$240$		0			0
$241$	27.3447	+	47.3625i	0.113464	+	0.196525i	0.917165	−	0.398509i	$-0.130472\pi$
$241$	27.3447	+	47.3625i	0.113464	+	0.196525i	−0.803701	+	0.595033i	$0.797139\pi$
$242$	−32.3390	+	18.6709i	−0.133632	+	0.0771525i
$243$		0			0
$244$	93.3113			0.382423
$245$	133.178	−	269.424i	0.543583	−	1.09969i
$246$		0			0
$247$	−390.190	+	675.830i	−1.57972	+	2.73615i
$248$	−54.7963	+	31.6366i	−0.220953	+	0.127567i
$249$		0			0
$250$	−53.6924	+	92.9980i	−0.214770	+	0.371992i
$251$			409.511i			1.63152i	0.578391	+	0.815759i	$0.303681\pi$
$251$			409.511i			1.63152i	−0.578391	+	0.815759i	$0.696319\pi$
$252$		0			0
$253$	429.962			1.69945
$254$	−87.8385	−	50.7136i	−0.345821	−	0.199660i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	−19.5089	−	11.2635i	−0.0759100	−	0.0438267i	0.461565	−	0.887107i	$-0.347288\pi$
$257$	−19.5089	−	11.2635i	−0.0759100	−	0.0438267i	−0.537475	+	0.843280i	$0.680622\pi$
$258$		0			0
$259$	159.895	−	48.4222i	0.617355	−	0.186958i
$260$		−	258.833i		−	0.995513i
$261$		0			0
$262$	78.2648	+	135.559i	0.298720	+	0.517399i
$263$	−23.1206	+	13.3487i	−0.0879110	+	0.0507554i	−0.543311	−	0.839531i	$-0.682830\pi$
$263$	−23.1206	+	13.3487i	−0.0879110	+	0.0507554i	0.455400	+	0.890287i	$0.349496\pi$
$264$		0			0
$265$	−201.362			−0.759858
$266$	−356.530	−	83.3065i	−1.34034	−	0.313182i
$267$		0			0
$268$	18.8176	−	32.5930i	0.0702149	−	0.121616i
$269$	−342.020	+	197.466i	−1.27145	+	0.734073i	−0.975261	−	0.221056i	$-0.929050\pi$
$269$	−342.020	+	197.466i	−1.27145	+	0.734073i	−0.296190	+	0.955129i	$0.595716\pi$
$270$		0			0
$271$	196.369	−	340.122i	0.724610	−	1.25506i	−0.234524	−	0.972110i	$-0.575353\pi$
$271$	196.369	−	340.122i	0.724610	−	1.25506i	0.959134	−	0.282951i	$-0.0913135\pi$
$272$		−	11.4702i		−	0.0421697i
$273$		0			0
$274$	−293.282			−1.07037
$275$	106.299	+	61.3715i	0.386540	+	0.223169i
$276$		0			0
$277$	8.53772	+	14.7878i	0.0308221	+	0.0533854i	0.881025	−	0.473070i	$-0.156854\pi$
$277$	8.53772	+	14.7878i	0.0308221	+	0.0533854i	−0.850203	+	0.526455i	$0.823521\pi$
$278$	94.3263	+	54.4593i	0.339303	+	0.195897i
$279$		0			0
$280$	116.225	−	35.1972i	0.415089	−	0.125704i
$281$			218.154i			0.776348i	0.921586	+	0.388174i	$0.126894\pi$
$281$			218.154i			0.776348i	−0.921586	+	0.388174i	$0.873106\pi$
$282$		0			0
$283$	41.7348	+	72.2868i	0.147473	+	0.255430i	0.930293	−	0.366818i	$-0.119553\pi$
$283$	41.7348	+	72.2868i	0.147473	+	0.255430i	−0.782820	+	0.622248i	$0.786219\pi$
$284$	−47.9060	+	27.6586i	−0.168683	+	0.0973893i
$285$		0			0
$286$	290.222			1.01476
$287$	239.081	−	255.026i	0.833034	−	0.888591i
$288$		0			0
$289$	−140.389	+	243.160i	−0.485774	+	0.841385i
$290$	58.6764	−	33.8769i	0.202333	−	0.116817i
$291$		0			0
$292$	87.7753	−	152.031i	0.300600	−	0.520655i
$293$		−	256.811i		−	0.876488i	−0.898856	−	0.438244i	$-0.855601\pi$
$293$		−	256.811i		−	0.876488i	0.898856	−	0.438244i	$-0.144399\pi$
$294$		0			0
$295$	435.712			1.47699
$296$	58.4610	+	33.7525i	0.197503	+	0.114029i
$297$		0			0
$298$	−75.8490	−	131.374i	−0.254527	−	0.440853i
$299$	807.804	+	466.386i	2.70169	+	1.55982i
$300$		0			0
$301$	296.551	+	278.010i	0.985220	+	0.923622i
$302$		−	253.479i		−	0.839336i
$303$		0			0
$304$	−73.9701	−	128.120i	−0.243323	−	0.421447i
$305$	−247.825	+	143.082i	−0.812540	+	0.469120i
$306$		0			0
$307$	−54.1606			−0.176419			−0.0882094	−	0.996102i	$-0.528114\pi$
$307$	−54.1606			−0.176419			−0.0882094	+	0.996102i	$0.528114\pi$
$308$	39.4656	+	130.319i	0.128135	+	0.423115i
$309$		0			0
$310$	97.0220	−	168.047i	0.312974	−	0.542087i
$311$	−126.461	+	73.0125i	−0.406628	+	0.234767i	−0.689340	−	0.724438i	$-0.742099\pi$
$311$	−126.461	+	73.0125i	−0.406628	+	0.234767i	0.282712	+	0.959205i	$0.408766\pi$
$312$		0			0
$313$	−138.340	+	239.612i	−0.441981	+	0.765533i	−0.997836	−	0.0657459i	$-0.979057\pi$
$313$	−138.340	+	239.612i	−0.441981	+	0.765533i	0.555856	+	0.831279i	$0.312391\pi$
$314$			124.418i			0.396236i
$315$		0			0
$316$	−159.434			−0.504536
$317$	314.677	+	181.679i	0.992671	+	0.573119i	0.906072	−	0.423124i	$-0.139067\pi$
$317$	314.677	+	181.679i	0.992671	+	0.573119i	0.0865993	+	0.996243i	$0.472400\pi$
$318$		0			0
$319$	37.9851	+	65.7921i	0.119076	+	0.206245i
$320$	42.4943	+	24.5341i	0.132795	+	0.0766690i
$321$		0			0
$322$	−99.5743	+	426.152i	−0.309237	+	1.32345i
$323$		−	106.056i		−	0.328347i
$324$		0			0
$325$	133.141	+	230.607i	0.409665	+	0.709561i
$326$	210.401	−	121.475i	0.645401	−	0.372622i
$327$		0			0
$328$	141.247			0.430630
$329$	−136.700	−	451.397i	−0.415501	−	1.37203i
$330$		0			0
$331$	163.868	−	283.828i	0.495071	−	0.857488i	−0.504913	−	0.863170i	$-0.668475\pi$
$331$	163.868	−	283.828i	0.495071	−	0.857488i	0.999984	+	0.00568236i	$0.00180876\pi$
$332$	161.622	−	93.3124i	0.486813	−	0.281061i
$333$		0			0
$334$	−40.6318	+	70.3764i	−0.121652	+	0.210708i
$335$			115.418i			0.344531i
$336$		0			0
$337$	274.511			0.814571			0.407286	−	0.913301i	$-0.366475\pi$
$337$	274.511			0.814571			0.407286	+	0.913301i	$0.366475\pi$
$338$	338.282	+	195.307i	1.00083	+	0.577832i
$339$		0			0
$340$	17.5881	+	30.4635i	0.0517298	+	0.0895986i
$341$	188.426	+	108.788i	0.552569	+	0.319026i
$342$		0			0
$343$	−217.968	+	264.838i	−0.635474	+	0.772122i
$344$			164.246i			0.477459i
$345$		0			0
$346$	−16.5458	−	28.6581i	−0.0478201	−	0.0828269i
$347$	204.888	−	118.292i	0.590455	−	0.340899i	−0.174822	−	0.984600i	$-0.555935\pi$
$347$	204.888	−	118.292i	0.590455	−	0.340899i	0.765277	+	0.643701i	$0.222602\pi$
$348$		0			0
$349$	−350.018			−1.00292			−0.501459	−	0.865181i	$-0.667203\pi$
$349$	−350.018			−1.00292			−0.501459	+	0.865181i	$0.667203\pi$
$350$	−85.4453	+	91.1438i	−0.244130	+	0.260411i
$351$		0			0
$352$	−27.5093	+	47.6475i	−0.0781515	+	0.135362i
$353$	23.0061	−	13.2826i	0.0651730	−	0.0376276i	−0.467059	−	0.884226i	$-0.654687\pi$
$353$	23.0061	−	13.2826i	0.0651730	−	0.0376276i	0.532232	+	0.846598i	$0.321353\pi$
$354$		0			0
$355$	84.8222	−	146.916i	0.238936	−	0.413849i
$356$		−	35.3215i		−	0.0992178i
$357$		0			0
$358$	491.905			1.37404
$359$	−470.674	−	271.744i	−1.31107	−	0.756947i	−0.328797	−	0.944401i	$-0.606643\pi$
$359$	−470.674	−	271.744i	−1.31107	−	0.756947i	−0.982273	+	0.187453i	$0.939977\pi$
$360$		0			0
$361$	−503.447	−	871.996i	−1.39459	−	2.41550i
$362$	−150.213	−	86.7253i	−0.414952	−	0.239573i
$363$		0			0
$364$	−67.2122	+	287.651i	−0.184649	+	0.790249i
$365$			538.372i			1.47499i
$366$		0			0
$367$	−245.967	−	426.027i	−0.670210	−	1.16084i	−0.977844	−	0.209333i	$-0.932871\pi$
$367$	−245.967	−	426.027i	−0.670210	−	1.16084i	0.307634	−	0.951505i	$-0.400463\pi$
$368$	−153.139	+	88.4148i	−0.416138	+	0.240258i
$369$		0			0
$370$	−207.022			−0.559518
$371$	223.781	+	52.2885i	0.603183	+	0.140939i
$372$		0			0
$373$	275.398	−	477.004i	0.738333	−	1.27883i	−0.214913	−	0.976633i	$-0.568947\pi$
$373$	275.398	−	477.004i	0.738333	−	1.27883i	0.953246	−	0.302197i	$-0.0977199\pi$
$374$	−34.1578	+	19.7210i	−0.0913311	+	0.0527300i
$375$		0			0
$376$	95.2860	−	165.040i	0.253420	−	0.438937i
$377$			164.812i			0.437167i
$378$		0			0
$379$	−637.775			−1.68278			−0.841391	−	0.540426i	$-0.818263\pi$
$379$	−637.775			−1.68278			−0.841391	+	0.540426i	$0.818263\pi$
$380$	392.913	+	226.849i	1.03398	+	0.596970i
$381$		0			0
$382$	−80.8521	−	140.040i	−0.211655	−	0.366597i
$383$	−158.309	−	91.4000i	−0.413341	−	0.238642i	0.278883	−	0.960325i	$-0.410036\pi$
$383$	−158.309	−	91.4000i	−0.413341	−	0.238642i	−0.692224	+	0.721683i	$0.743369\pi$
$384$		0			0
$385$	−304.646	−	285.599i	−0.791287	−	0.741815i
$386$			76.0636i			0.197056i
$387$		0			0
$388$	17.2922	+	29.9510i	0.0445676	+	0.0771934i
$389$	210.951	−	121.793i	0.542292	−	0.313092i	−0.203716	−	0.979030i	$-0.565302\pi$
$389$	210.951	−	121.793i	0.542292	−	0.313092i	0.746007	+	0.665938i	$0.231968\pi$
$390$		0			0
$391$	−126.767			−0.324211
$392$	−138.305	+	8.93541i	−0.352818	+	0.0227944i
$393$		0			0
$394$	−45.3558	+	78.5585i	−0.115116	+	0.199387i
$395$	423.438	−	244.472i	1.07200	−	0.618917i
$396$		0			0
$397$	41.6018	−	72.0564i	0.104790	−	0.181502i	−0.808862	−	0.587998i	$-0.799916\pi$
$397$	41.6018	−	72.0564i	0.104790	−	0.181502i	0.913653	+	0.406496i	$0.133249\pi$
$398$		−	492.260i		−	1.23683i
$399$		0			0
$400$	−50.4803			−0.126201
$401$	136.176	+	78.6211i	0.339591	+	0.196063i	0.660091	−	0.751186i	$-0.270518\pi$
$401$	136.176	+	78.6211i	0.339591	+	0.196063i	−0.320500	+	0.947248i	$0.603851\pi$
$402$		0			0
$403$	236.007	+	408.777i	0.585627	+	1.01433i
$404$	−90.6550	−	52.3397i	−0.224394	−	0.129554i
$405$		0			0
$406$	−74.0061	+	22.4118i	−0.182281	+	0.0552015i
$407$		−	232.127i		−	0.570337i
$408$		0			0
$409$	−211.212	−	365.831i	−0.516412	−	0.894451i	−0.999818	−	0.0190553i	$-0.993934\pi$
$409$	−211.212	−	365.831i	−0.516412	−	0.894451i	0.483407	−	0.875396i	$-0.339399\pi$
$410$	−375.136	+	216.585i	−0.914966	+	0.528256i
$411$		0			0
$412$	49.1379			0.119267
$413$	−484.222	−	113.143i	−1.17245	−	0.273954i
$414$		0			0
$415$	−286.167	+	495.655i	−0.689559	+	1.19435i
$416$	−103.368	+	59.6795i	−0.248481	+	0.143460i
$417$		0			0
$418$	−254.358	+	440.562i	−0.608513	+	1.05398i
$419$		−	648.968i		−	1.54885i	−0.632665	−	0.774425i	$-0.718039\pi$
$419$		−	648.968i		−	1.54885i	0.632665	−	0.774425i	$-0.281961\pi$
$420$		0			0
$421$	−36.6250			−0.0869952			−0.0434976	−	0.999054i	$-0.513850\pi$
$421$	−36.6250			−0.0869952			−0.0434976	+	0.999054i	$0.513850\pi$
$422$	323.344	+	186.683i	0.766218	+	0.442376i
$423$		0			0
$424$	46.4283	+	80.4163i	0.109501	+	0.189661i
$425$	−31.3403	−	18.0943i	−0.0737418	−	0.0425748i
$426$		0			0
$427$	312.571	−	94.6582i	0.732016	−	0.221682i
$428$		−	16.5180i		−	0.0385934i
$429$		0			0
$430$	−251.851	−	436.219i	−0.585701	−	1.01446i
$431$	−379.544	+	219.130i	−0.880613	+	0.508422i	−0.870861	−	0.491530i	$-0.836438\pi$
$431$	−379.544	+	219.130i	−0.880613	+	0.508422i	−0.00975258	+	0.999952i	$0.503104\pi$
$432$		0			0
$433$	−22.0578			−0.0509418			−0.0254709	−	0.999676i	$-0.508109\pi$
$433$	−22.0578			−0.0509418			−0.0254709	+	0.999676i	$0.508109\pi$
$434$	−151.461	+	161.562i	−0.348989	+	0.372264i
$435$		0			0
$436$	145.563	−	252.122i	0.333860	−	0.578262i
$437$	−1415.96	+	817.506i	−3.24019	+	1.87072i
$438$		0			0
$439$	−124.308	+	215.308i	−0.283162	+	0.490452i	−0.972162	−	0.234310i	$-0.924717\pi$
$439$	−124.308	+	215.308i	−0.283162	+	0.490452i	0.689000	+	0.724762i	$0.258050\pi$
$440$		−	168.729i		−	0.383475i
$441$		0			0
$442$	−85.5668			−0.193590
$443$	−316.168	−	182.540i	−0.713698	−	0.412054i	0.0987307	−	0.995114i	$-0.468522\pi$
$443$	−316.168	−	182.540i	−0.713698	−	0.412054i	−0.812429	+	0.583060i	$0.801855\pi$
$444$		0			0
$445$	54.1613	+	93.8102i	0.121711	+	0.210809i
$446$	47.0016	+	27.1364i	0.105385	+	0.0608439i
$447$		0			0
$448$	−40.8545	−	38.3002i	−0.0911931	−	0.0854916i
$449$		−	877.108i		−	1.95347i	−0.214449	−	0.976735i	$-0.568796\pi$
$449$		−	877.108i		−	1.95347i	0.214449	−	0.976735i	$-0.431204\pi$
$450$		0			0
$451$	−242.850	−	420.629i	−0.538470	−	0.932658i
$452$	−96.1064	+	55.4871i	−0.212625	+	0.122759i
$453$		0			0
$454$	187.609			0.413236
$455$	−262.569	−	867.031i	−0.577076	−	1.90556i
$456$		0			0
$457$	259.830	−	450.039i	0.568556	−	0.984767i	−0.428153	−	0.903706i	$-0.640836\pi$
$457$	259.830	−	450.039i	0.568556	−	0.984767i	0.996709	−	0.0810613i	$-0.0258309\pi$
$458$	333.793	−	192.716i	0.728806	−	0.420776i
$459$		0			0
$460$	271.147	−	469.640i	0.589450	−	1.02096i
$461$			731.608i			1.58700i	0.608569	+	0.793501i	$0.291744\pi$
$461$			731.608i			1.58700i	−0.608569	+	0.793501i	$0.708256\pi$
$462$		0			0
$463$	−193.383			−0.417674			−0.208837	−	0.977950i	$-0.566968\pi$
$463$	−193.383			−0.417674			−0.208837	+	0.977950i	$0.566968\pi$
$464$	−27.0582	−	15.6221i	−0.0583151	−	0.0336682i
$465$		0			0
$466$	−150.609	−	260.862i	−0.323194	−	0.559789i
$467$	588.738	+	339.908i	1.26068	+	0.727855i	0.973206	−	0.229933i	$-0.0738508\pi$
$467$	588.738	+	339.908i	1.26068	+	0.727855i	0.287475	+	0.957788i	$0.407184\pi$
$468$		0			0
$469$	29.9710	−	128.268i	0.0639041	−	0.273493i
$470$			584.439i			1.24349i
$471$		0			0
$472$	−100.463	−	174.006i	−0.212845	−	0.368658i
$473$	489.119	−	282.393i	1.03408	−	0.597026i
$474$		0			0
$475$	−466.754			−0.982640
$476$	−11.6357	−	38.4224i	−0.0244448	−	0.0807193i
$477$		0			0
$478$	−155.654	+	269.601i	−0.325637	+	0.564019i
$479$	645.119	−	372.460i	1.34680	−	0.777578i	0.359008	−	0.933334i	$-0.383115\pi$
$479$	645.119	−	372.460i	1.34680	−	0.777578i	0.987795	+	0.155757i	$0.0497816\pi$
$480$		0			0
$481$	251.792	−	436.116i	0.523475	−	0.906686i
$482$			77.3426i			0.160462i
$483$		0			0
$484$	−52.8093			−0.109110
$485$	−91.8527	−	53.0312i	−0.189387	−	0.109343i
$486$		0			0
$487$	−76.9759	−	133.326i	−0.158061	−	0.273770i	0.776108	−	0.630600i	$-0.217191\pi$
$487$	−76.9759	−	133.326i	−0.158061	−	0.273770i	−0.934170	+	0.356829i	$0.883858\pi$
$488$	114.283	+	65.9811i	0.234186	+	0.135207i
$489$		0			0
$490$	353.621	−	235.805i	0.721675	−	0.481235i
$491$		−	231.266i		−	0.471010i	−0.971873	−	0.235505i	$-0.924326\pi$
$491$		−	231.266i		−	0.471010i	0.971873	−	0.235505i	$-0.0756745\pi$
$492$		0			0
$493$	−11.1992	−	19.3976i	−0.0227165	−	0.0393461i
$494$	−955.768	+	551.813i	−1.93475	+	1.11703i
$495$		0			0
$496$	−89.4819			−0.180407
$497$	−132.416	+	141.247i	−0.266431	+	0.284199i
$498$		0			0
$499$	−207.935	+	360.154i	−0.416704	+	0.721752i	−0.995606	−	0.0936449i	$-0.970148\pi$
$499$	−207.935	+	360.154i	−0.416704	+	0.721752i	0.578902	+	0.815397i	$0.303482\pi$
$500$	−131.519	+	75.9325i	−0.263038	+	0.151865i
$501$		0			0
$502$	−289.568	+	501.547i	−0.576829	+	0.999097i
$503$			35.5917i			0.0707589i	0.999374	+	0.0353794i	$0.0112640\pi$
$503$			35.5917i			0.0707589i	−0.999374	+	0.0353794i	$0.988736\pi$
$504$		0			0
$505$	321.026			0.635696
$506$	526.593	+	304.029i	1.04070	+	0.600847i
$507$		0			0
$508$	−71.7198	−	124.222i	−0.141181	−	0.244532i
$509$	−27.1437	−	15.6714i	−0.0533276	−	0.0307887i	0.473099	−	0.881009i	$-0.343135\pi$
$509$	−27.1437	−	15.6714i	−0.0533276	−	0.0307887i	−0.526427	+	0.850220i	$0.676469\pi$
$510$		0			0
$511$	139.801	−	598.311i	0.273583	−	1.17086i
$512$		−	22.6274i		−	0.0441942i
$513$		0			0
$514$	−15.9289	−	27.5897i	−0.0309901	−	0.0536765i
$515$	−130.505	+	75.3471i	−0.253408	+	0.146305i
$516$		0			0
$517$	−655.313			−1.26753
$518$	230.070	+	53.7580i	0.444151	+	0.103780i
$519$		0			0
$520$	183.023	−	317.005i	0.351967	−	0.609625i
$521$	684.192	−	395.018i	1.31323	−	0.758193i	0.330599	−	0.943771i	$-0.392749\pi$
$521$	684.192	−	395.018i	1.31323	−	0.758193i	0.982629	+	0.185579i	$0.0594159\pi$
$522$		0			0
$523$	−210.978	+	365.424i	−0.403399	+	0.698707i	−0.994134	−	0.108159i	$-0.965505\pi$
$523$	−210.978	+	365.424i	−0.403399	+	0.698707i	0.590735	+	0.806866i	$0.298838\pi$
$524$			221.366i			0.422455i
$525$		0			0
$526$	−37.7558			−0.0717790
$527$	−55.5541	−	32.0741i	−0.105416	−	0.0608618i
$528$		0			0
$529$	712.647	+	1234.34i	1.34716	+	2.33335i
$530$	−246.617	−	142.385i	−0.465316	−	0.268650i
$531$		0			0
$532$	−377.752	−	354.134i	−0.710060	−	0.665665i
$533$		−	1053.69i		−	1.97691i
$534$		0			0
$535$	25.3283	+	43.8700i	0.0473427	+	0.0819999i
$536$	46.0935	−	26.6121i	0.0859953	−	0.0496494i
$537$		0			0
$538$	−558.517			−1.03814
$539$	264.401	+	396.504i	0.490540	+	0.735629i
$540$		0			0
$541$	197.868	−	342.718i	0.365745	−	0.633489i	−0.623150	−	0.782102i	$-0.714148\pi$
$541$	197.868	−	342.718i	0.365745	−	0.633489i	0.988895	+	0.148613i	$0.0474809\pi$
$542$	481.005	−	277.708i	0.887463	−	0.512377i
$543$		0			0
$544$	8.11063	−	14.0480i	0.0149093	−	0.0258236i
$545$			892.813i			1.63819i
$546$		0			0
$547$	121.599			0.222302			0.111151	−	0.993804i	$-0.464546\pi$
$547$	121.599			0.222302			0.111151	+	0.993804i	$0.464546\pi$
$548$	−359.196	−	207.382i	−0.655467	−	0.378434i
$549$		0			0
$550$	86.7924	+	150.329i	0.157804	+	0.273325i
$551$	−250.187	−	144.446i	−0.454060	−	0.262152i
$552$		0			0
$553$	−534.065	+	161.735i	−0.965759	+	0.292468i
$554$			24.1483i			0.0435890i
$555$		0			0
$556$	77.0171	+	133.398i	0.138520	+	0.239924i
$557$	−45.0429	+	26.0055i	−0.0808670	+	0.0466886i	−0.539888	−	0.841737i	$-0.681534\pi$
$557$	−45.0429	+	26.0055i	−0.0808670	+	0.0466886i	0.459021	+	0.888425i	$0.348200\pi$
$558$		0			0
$559$	1225.26			2.19189
$560$	167.234	+	39.0758i	0.298632	+	0.0697781i
$561$		0			0
$562$	−154.258	+	267.183i	−0.274481	+	0.475414i
$563$	−225.978	+	130.468i	−0.401382	+	0.231738i	−0.687080	−	0.726582i	$-0.741108\pi$
$563$	−225.978	+	130.468i	−0.401382	+	0.231738i	0.285698	+	0.958320i	$0.407775\pi$
$564$		0			0
$565$	170.166	−	294.735i	0.301178	−	0.521656i
$566$			118.044i			0.208558i
$567$		0			0
$568$	−78.2302			−0.137729
$569$	−886.831	−	512.012i	−1.55858	−	0.899846i	−0.997393	−	0.0721561i	$-0.977012\pi$
$569$	−886.831	−	512.012i	−1.55858	−	0.899846i	−0.561186	−	0.827690i	$-0.689655\pi$
$570$		0			0
$571$	−296.232	−	513.090i	−0.518796	−	0.898581i	−0.999761	−	0.0218412i	$-0.993047\pi$
$571$	−296.232	−	513.090i	−0.518796	−	0.898581i	0.480966	−	0.876739i	$-0.340286\pi$
$572$	355.448	+	205.218i	0.621412	+	0.358773i
$573$		0			0
$574$	473.143	−	143.286i	0.824292	−	0.249626i
$575$			557.901i			0.970262i
$576$		0			0
$577$	462.892	+	801.752i	0.802239	+	1.38952i	0.918140	+	0.396257i	$0.129691\pi$
$577$	462.892	+	801.752i	0.802239	+	1.38952i	−0.115901	+	0.993261i	$0.536976\pi$
$578$	−343.880	+	198.539i	−0.594949	+	0.343494i
$579$		0			0
$580$	95.8182			0.165204
$581$	446.736	−	476.529i	0.768908	−	0.820188i
$582$		0			0
$583$	159.652	−	276.525i	0.273845	−	0.474313i
$584$	215.005	−	124.133i	0.368159	−	0.212557i
$585$		0			0
$586$	181.593	−	314.528i	0.309885	−	0.536737i
$587$		−	96.6603i		−	0.164668i	−0.996605	−	0.0823341i	$-0.973763\pi$
$587$		−	96.6603i		−	0.164668i	0.996605	−	0.0823341i	$-0.0262375\pi$
$588$		0			0
$589$	−827.373			−1.40471
$590$	533.636	+	308.095i	0.904468	+	0.522195i
$591$		0			0
$592$	47.7332	+	82.6764i	0.0806304	+	0.139656i
$593$	−271.601	−	156.809i	−0.458012	−	0.264433i	0.253196	−	0.967415i	$-0.418518\pi$
$593$	−271.601	−	156.809i	−0.458012	−	0.264433i	−0.711208	+	0.702982i	$0.751852\pi$
$594$		0			0
$595$	89.8194	+	84.2037i	0.150957	+	0.141519i
$596$		−	214.533i		−	0.359955i
$597$		0			0
$598$	659.569	+	1142.41i	1.10296	+	1.91038i
$599$	10.3122	−	5.95375i	0.0172157	−	0.00993949i	−0.491367	−	0.870952i	$-0.663503\pi$
$599$	10.3122	−	5.95375i	0.0172157	−	0.00993949i	0.508583	+	0.861013i	$0.330169\pi$
$600$		0			0
$601$	−107.981			−0.179668			−0.0898341	−	0.995957i	$-0.528634\pi$
$601$	−107.981			−0.179668			−0.0898341	+	0.995957i	$0.528634\pi$
$602$	166.617	+	550.185i	0.276772	+	0.913928i
$603$		0			0
$604$	179.237	−	310.448i	0.296750	−	0.513986i
$605$	140.256	−	80.9768i	0.231828	−	0.133846i
$606$		0			0
$607$	−229.573	+	397.632i	−0.378209	+	0.655077i	−0.990802	−	0.135322i	$-0.956793\pi$
$607$	−229.573	+	397.632i	−0.378209	+	0.655077i	0.612593	+	0.790399i	$0.290127\pi$
$608$		−	209.219i		−	0.344110i
$609$		0			0
$610$	−404.696			−0.663436
$611$	−1231.19	−	710.828i	−2.01504	−	1.16338i
$612$		0			0
$613$	−56.7368	−	98.2711i	−0.0925560	−	0.160312i	0.816030	−	0.578010i	$-0.196170\pi$
$613$	−56.7368	−	98.2711i	−0.0925560	−	0.160312i	−0.908586	+	0.417698i	$0.862837\pi$
$614$	−66.3329	−	38.2973i	−0.108034	−	0.0623735i
$615$		0			0
$616$	−43.8145	+	187.514i	−0.0711274	+	0.304407i
$617$		−	278.593i		−	0.451528i	−0.974182	−	0.225764i	$-0.927512\pi$
$617$		−	278.593i		−	0.451528i	0.974182	−	0.225764i	$-0.0724878\pi$
$618$		0			0
$619$	189.205	+	327.713i	0.305663	+	0.529424i	0.977409	−	0.211358i	$-0.0677885\pi$
$619$	189.205	+	327.713i	0.305663	+	0.529424i	−0.671746	+	0.740782i	$0.734455\pi$
$620$	237.654	−	137.210i	0.383313	−	0.221306i
$621$		0			0
$622$	−206.511			−0.332011
$623$	−35.8314	−	118.319i	−0.0575142	−	0.189918i
$624$		0			0
$625$	390.618	−	676.570i	0.624988	−	1.08251i
$626$	−338.862	+	195.642i	−0.541313	+	0.312527i
$627$		0			0
$628$	−87.9768	+	152.380i	−0.140090	+	0.242644i
$629$			68.4385i			0.108805i
$630$		0			0
$631$	643.779			1.02025			0.510126	−	0.860100i	$-0.329599\pi$
$631$	643.779			1.02025			0.510126	+	0.860100i	$0.329599\pi$
$632$	−195.265	−	112.737i	−0.308964	−	0.178381i
$633$		0			0
$634$	256.932	+	445.020i	0.405256	+	0.701924i
$635$	380.960	+	219.948i	0.599937	+	0.346374i
$636$		0			0
$637$	66.6576	+	1031.74i	0.104643	+	1.61969i
$638$			107.438i			0.168398i
$639$		0			0
$640$	34.6964	+	60.0960i	0.0542132	+	0.0939000i
$641$	238.102	−	137.468i	0.371454	−	0.214459i	−0.302639	−	0.953105i	$-0.597868\pi$
$641$	238.102	−	137.468i	0.371454	−	0.214459i	0.674094	+	0.738646i	$0.264534\pi$
$642$		0			0
$643$	293.154			0.455917			0.227958	−	0.973671i	$-0.426795\pi$
$643$	293.154			0.455917			0.227958	+	0.973671i	$0.426795\pi$
$644$	−423.288	+	451.518i	−0.657280	+	0.701115i
$645$		0			0
$646$	74.9931	−	129.892i	0.116088	−	0.201071i
$647$	−329.450	+	190.208i	−0.509197	+	0.293985i	−0.732503	−	0.680763i	$-0.761648\pi$
$647$	−329.450	+	190.208i	−0.509197	+	0.293985i	0.223307	+	0.974748i	$0.428315\pi$
$648$		0			0
$649$	−345.457	+	598.350i	−0.532292	+	0.921956i
$650$			376.580i			0.579354i
$651$		0			0
$652$	343.583			0.526967
$653$	644.861	+	372.311i	0.987536	+	0.570154i	0.904537	−	0.426395i	$-0.140217\pi$
$653$	644.861	+	372.311i	0.987536	+	0.570154i	0.0829992	+	0.996550i	$0.473550\pi$
$654$		0			0
$655$	−339.439	−	587.925i	−0.518227	−	0.897595i
$656$	172.991	+	99.8765i	0.263706	+	0.152251i
$657$		0			0
$658$	151.763	−	649.507i	0.230643	−	0.987093i
$659$			967.075i			1.46749i	0.679426	+	0.733744i	$0.262229\pi$
$659$			967.075i			1.46749i	−0.679426	+	0.733744i	$0.737771\pi$
$660$		0			0
$661$	83.2377	+	144.172i	0.125927	+	0.218112i	0.922095	−	0.386964i	$-0.126476\pi$
$661$	83.2377	+	144.172i	0.125927	+	0.218112i	−0.796168	+	0.605076i	$0.793143\pi$
$662$	401.394	−	231.745i	0.606335	−	0.350068i
$663$		0			0
$664$	263.927			0.397481
$665$	1546.29	+	361.305i	2.32525	+	0.543315i
$666$		0			0
$667$	−172.653	+	299.043i	−0.258849	+	0.448340i
$668$	−99.5273	+	57.4621i	−0.148993	+	0.0860211i
$669$		0			0
$670$	−81.6129	+	141.358i	−0.121810	+	0.210982i
$671$		−	453.774i		−	0.676265i
$672$		0			0
$673$	−877.847			−1.30438			−0.652189	−	0.758056i	$-0.726149\pi$
$673$	−877.847			−1.30438			−0.652189	+	0.758056i	$0.726149\pi$
$674$	336.205	+	194.108i	0.498821	+	0.287994i
$675$		0			0
$676$	276.206	+	478.403i	0.408589	+	0.707696i
$677$	−357.978	−	206.679i	−0.528771	−	0.305286i	0.211745	−	0.977325i	$-0.432085\pi$
$677$	−357.978	−	206.679i	−0.528771	−	0.305286i	−0.740516	+	0.672039i	$0.765419\pi$
$678$		0			0
$679$	88.3083	+	82.7871i	0.130056	+	0.121925i
$680$			49.7467i			0.0731570i
$681$		0			0
$682$	153.849	+	266.475i	0.225585	+	0.390725i
$683$	914.285	−	527.863i	1.33863	−	0.772859i	0.352027	−	0.935990i	$-0.385493\pi$
$683$	914.285	−	527.863i	1.33863	−	0.772859i	0.986604	+	0.163131i	$0.0521592\pi$
$684$		0			0
$685$	1271.98			1.85691
$686$	−454.223	+	170.232i	−0.662133	+	0.248152i
$687$		0			0
$688$	−116.139	+	201.159i	−0.168807	+	0.292383i
$689$	599.901	−	346.353i	0.870683	−	0.502689i
$690$		0			0
$691$	106.864	−	185.094i	0.154652	−	0.267864i	−0.778281	−	0.627917i	$-0.783908\pi$
$691$	106.864	−	185.094i	0.154652	−	0.267864i	0.932932	+	0.360052i	$0.117241\pi$
$692$		−	46.7985i		−	0.0676279i
$693$		0			0
$694$	334.581			0.482105
$695$	−409.098	−	236.193i	−0.588631	−	0.339846i
$696$		0			0
$697$	71.6001	+	124.015i	0.102726	+	0.177927i
$698$	−428.683	−	247.500i	−0.614159	−	0.354585i
$699$		0			0
$700$	−169.097	+	51.2089i	−0.241567	+	0.0731556i
$701$		−	71.0240i		−	0.101318i	−0.998716	−	0.0506591i	$-0.983868\pi$
$701$		−	71.0240i		−	0.101318i	0.998716	−	0.0506591i	$-0.0161322\pi$
$702$		0			0
$703$	441.354	+	764.447i	0.627815	+	1.08741i
$704$	−67.3838	+	38.9041i	−0.0957156	+	0.0552614i
$705$		0			0
$706$	37.5687			0.0532135
$707$	−356.768	−	83.3621i	−0.504622	−	0.117910i
$708$		0			0
$709$	−538.530	+	932.761i	−0.759563	+	1.31560i	0.183511	+	0.983018i	$0.441254\pi$
$709$	−538.530	+	932.761i	−0.759563	+	1.31560i	−0.943074	+	0.332583i	$0.892080\pi$
$710$	207.771	−	119.957i	0.292635	−	0.168953i
$711$		0			0
$712$	24.9761	−	43.2599i	0.0350788	−	0.0607582i
$713$			988.940i			1.38701i
$714$		0			0
$715$	−1258.71			−1.76043
$716$	602.458	+	347.829i	0.841422	+	0.485795i
$717$		0			0
$718$	−384.304	−	665.634i	−0.535242	−	0.927067i
$719$	297.051	+	171.503i	0.413145	+	0.238529i	0.692140	−	0.721763i	$-0.256668\pi$
$719$	297.051	+	171.503i	0.413145	+	0.238529i	−0.278995	+	0.960292i	$0.590001\pi$
$720$		0			0
$721$	164.601	−	49.8472i	0.228295	−	0.0691362i
$722$		−	1423.96i		−	1.97225i
$723$		0			0
$724$	−122.648	−	212.433i	−0.169403	−	0.293415i
$725$	−85.3691	+	49.2879i	−0.117751	+	0.0679833i
$726$		0			0
$727$	1006.37			1.38428			0.692141	−	0.721763i	$-0.256668\pi$
$727$	1006.37			1.38428			0.692141	+	0.721763i	$0.256668\pi$
$728$	−285.718	+	304.772i	−0.392469	+	0.418643i
$729$		0			0
$730$	−380.686	+	659.368i	−0.521488	+	0.903244i
$731$	−144.208	+	83.2586i	−0.197275	+	0.113897i
$732$		0			0
$733$	33.2726	−	57.6299i	0.0453924	−	0.0786220i	−0.842437	−	0.538796i	$-0.818880\pi$
$733$	33.2726	−	57.6299i	0.0453924	−	0.0786220i	0.887829	+	0.460174i	$0.152213\pi$
$734$		−	695.700i		−	0.947820i
$735$		0			0
$736$	−250.075			−0.339775
$737$	−158.500	−	91.5100i	−0.215061	−	0.124166i
$738$		0			0
$739$	−133.274	−	230.838i	−0.180344	−	0.312365i	0.761654	−	0.647984i	$-0.224388\pi$
$739$	−133.274	−	230.838i	−0.180344	−	0.312365i	−0.941998	+	0.335619i	$0.891054\pi$
$740$	−253.549	−	146.386i	−0.342633	−	0.197819i
$741$		0			0
$742$	237.101	+	222.277i	0.319543	+	0.299565i
$743$			816.816i			1.09935i	0.835379	+	0.549674i	$0.185248\pi$
$743$			816.816i			1.09935i	−0.835379	+	0.549674i	$0.814752\pi$
$744$		0			0
$745$	328.961	+	569.777i	0.441559	+	0.764802i
$746$	674.585	−	389.472i	0.904269	−	0.522080i
$747$		0			0
$748$	−55.7795			−0.0745715
$749$	−16.7564	−	55.3313i	−0.0223717	−	0.0738736i
$750$		0			0
$751$	542.159	−	939.046i	0.721916	−	1.25039i	−0.238315	−	0.971188i	$-0.576595\pi$
$751$	542.159	−	939.046i	0.721916	−	1.25039i	0.960231	−	0.279207i	$-0.0900715\pi$
$752$	233.402	−	134.755i	0.310375	−	0.179195i
$753$		0			0
$754$	−116.540	+	201.853i	−0.154562	+	0.267709i
$755$			1099.35i			1.45610i
$756$		0			0
$757$	−1338.17			−1.76773			−0.883866	−	0.467741i	$-0.845068\pi$
$757$	−1338.17			−1.76773			−0.883866	+	0.467741i	$0.845068\pi$
$758$	−781.111	−	450.975i	−1.03049	−	0.594954i
$759$		0			0
$760$	320.812	+	555.663i	0.422121	+	0.731136i
$761$	606.681	+	350.267i	0.797215	+	0.460272i	0.842496	−	0.538702i	$-0.181085\pi$
$761$	606.681	+	350.267i	0.797215	+	0.460272i	−0.0452812	+	0.998974i	$0.514418\pi$
$762$		0			0
$763$	231.840	−	992.215i	0.303853	−	1.30041i
$764$		−	228.684i		−	0.299325i
$765$		0			0
$766$	−129.259	−	223.883i	−0.168746	−	0.292276i
$767$	−1298.08	+	749.446i	−1.69241	+	0.977113i
$768$		0			0
$769$	959.916			1.24827			0.624133	−	0.781318i	$-0.285452\pi$
$769$	959.916			1.24827			0.624133	+	0.781318i	$0.285452\pi$
$770$	−171.164	−	565.202i	−0.222292	−	0.734029i
$771$		0			0
$772$	−53.7851	+	93.1585i	−0.0696698	+	0.120672i
$773$	852.740	−	492.330i	1.10316	−	0.636908i	0.166108	−	0.986107i	$-0.446880\pi$
$773$	852.740	−	492.330i	1.10316	−	0.636908i	0.937048	+	0.349200i	$0.113546\pi$
$774$		0			0
$775$	−141.159	+	244.494i	−0.182140	+	0.315476i
$776$			48.9098i			0.0630281i
$777$		0			0
$778$	344.482			0.442779
$779$	1599.52	+	923.485i	2.05330	+	1.18547i
$780$		0			0
$781$	134.504	+	232.967i	0.172220	+	0.298294i
$782$	−155.257	−	89.6375i	−0.198538	−	0.114626i
$783$		0			0
$784$	−175.706	−	86.8525i	−0.224115	−	0.110781i
$785$		−	539.608i		−	0.687398i
$786$		0			0
$787$	551.228	+	954.755i	0.700417	+	1.21316i	0.968320	+	0.249711i	$0.0803357\pi$
$787$	551.228	+	954.755i	0.700417	+	1.21316i	−0.267904	+	0.963446i	$0.586331\pi$
$788$	−111.099	+	64.1428i	−0.140988	+	0.0813995i
$789$		0			0
$790$	691.472			0.875281
$791$	−265.646	+	283.362i	−0.335836	+	0.358233i
$792$		0			0
$793$	492.215	−	852.541i	0.620700	−	1.07508i
$794$	101.903	−	58.8338i	0.128342	−	0.0740980i
$795$		0			0
$796$	348.080	−	602.893i	0.437287	−	0.757403i
$797$		−	1065.24i		−	1.33657i	−0.743907	−	0.668283i	$-0.767030\pi$
$797$		−	1065.24i		−	1.33657i	0.743907	−	0.668283i	$-0.232970\pi$
$798$		0			0
$799$	193.207			0.241812
$800$	−61.8255	−	35.6950i	−0.0772819	−	0.0446187i
$801$		0			0
$802$	111.187	+	192.582i	0.138637	+	0.240127i
$803$	−739.329	−	426.852i	−0.920709	−	0.531571i
$804$		0			0
$805$	431.859	−	1848.25i	0.536471	−	2.29596i
$806$			667.530i			0.828201i
$807$		0			0
$808$	−74.0195	−	128.205i	−0.0916083	−	0.158670i
$809$	−979.969	+	565.786i	−1.21133	+	0.699364i	−0.963050	−	0.269323i	$-0.913200\pi$
$809$	−979.969	+	565.786i	−1.21133	+	0.699364i	−0.248284	+	0.968687i	$0.579867\pi$
$810$		0			0
$811$	953.794			1.17607			0.588036	−	0.808835i	$-0.299901\pi$
$811$	953.794			1.17607			0.588036	+	0.808835i	$0.299901\pi$
$812$	−106.486	−	24.8815i	−0.131141	−	0.0306422i
$813$		0			0
$814$	164.139	−	284.296i	0.201644	−	0.349258i
$815$	−912.519	+	526.843i	−1.11965	+	0.646433i
$816$		0			0
$817$	−1073.85	+	1859.97i	−1.31439	+	2.27659i
$818$		−	597.399i		−	0.730316i
$819$		0			0
$820$	−612.595			−0.747067
$821$	−708.809	−	409.231i	−0.863348	−	0.498454i	0.00178390	−	0.999998i	$-0.499432\pi$
$821$	−708.809	−	409.231i	−0.863348	−	0.498454i	−0.865132	+	0.501544i	$0.832766\pi$
$822$		0			0
$823$	436.869	+	756.680i	0.530825	+	0.919416i	0.999353	+	0.0359675i	$0.0114513\pi$
$823$	436.869	+	756.680i	0.530825	+	0.919416i	−0.468528	+	0.883449i	$0.655215\pi$
$824$	60.1814	+	34.7458i	0.0730357	+	0.0421672i
$825$		0			0
$826$	−513.044	−	480.968i	−0.621119	−	0.582285i
$827$			735.728i			0.889634i	0.895621	+	0.444817i	$0.146731\pi$
$827$			735.728i			0.889634i	−0.895621	+	0.444817i	$0.853269\pi$
$828$		0			0
$829$	40.0620	+	69.3894i	0.0483257	+	0.0837025i	0.889176	−	0.457565i	$-0.151278\pi$
$829$	40.0620	+	69.3894i	0.0483257	+	0.0837025i	−0.840851	+	0.541267i	$0.817945\pi$
$830$	−700.963	+	404.701i	−0.844533	+	0.487592i
$831$		0			0
$832$	−168.799			−0.202884
$833$	−77.9539	−	116.902i	−0.0935822	−	0.140339i
$834$		0			0
$835$	176.222	−	305.226i	0.211045	−	0.365540i
$836$	−623.048	+	359.717i	−0.745273	+	0.430284i
$837$		0			0
$838$	458.890	−	794.821i	0.547601	−	0.948473i
$839$		−	1101.64i		−	1.31304i	−0.754309	−	0.656519i	$-0.772028\pi$
$839$		−	1101.64i		−	1.31304i	0.754309	−	0.656519i	$-0.227972\pi$
$840$		0			0
$841$	779.988			0.927453
$842$	−44.8562	−	25.8978i	−0.0532734	−	0.0307574i
$843$		0			0
$844$	264.009	+	457.277i	0.312807	+	0.541798i
$845$	−1467.15	−	847.058i	−1.73627	−	1.00244i
$846$		0			0
$847$	−176.899	+	53.5716i	−0.208853	+	0.0632486i
$848$			131.319i			0.154858i
$849$		0			0
$850$	−25.5892	−	44.3218i	−0.0301050	−	0.0521433i
$851$	913.726	−	527.540i	1.07371	−	0.619906i
$852$		0			0
$853$	−492.703			−0.577612			−0.288806	−	0.957388i	$-0.593258\pi$
$853$	−492.703			−0.577612			−0.288806	+	0.957388i	$0.593258\pi$
$854$	449.753	+	105.089i	0.526643	+	0.123055i
$855$		0			0
$856$	11.6800	−	20.2303i	0.0136448	−	0.0236335i
$857$	−880.407	+	508.303i	−1.02731	+	0.593120i	−0.916214	−	0.400690i	$-0.868771\pi$
$857$	−880.407	+	508.303i	−1.02731	+	0.593120i	−0.111099	+	0.993809i	$0.535437\pi$
$858$		0			0
$859$	−355.084	+	615.023i	−0.413369	+	0.715976i	−0.995256	−	0.0972939i	$-0.968981\pi$
$859$	−355.084	+	615.023i	−0.413369	+	0.715976i	0.581887	+	0.813270i	$0.302315\pi$
$860$		−	712.343i		−	0.828306i
$861$		0			0
$862$	−619.793			−0.719018
$863$	−998.565	−	576.522i	−1.15709	−	0.668043i	−0.206481	−	0.978451i	$-0.566201\pi$
$863$	−998.565	−	576.522i	−1.15709	−	0.668043i	−0.950604	+	0.310407i	$0.899535\pi$
$864$		0			0
$865$	71.7599	+	124.292i	0.0829594	+	0.143690i
$866$	−27.0152	−	15.5972i	−0.0311953	−	0.0180106i
$867$		0			0
$868$	−299.743	+	90.7735i	−0.345326	+	0.104578i
$869$			775.326i			0.892205i
$870$		0			0
$871$	−198.525	−	343.855i	−0.227927	−	0.394781i
$872$	356.555	−	205.857i	0.408893	−	0.236075i
$873$		0			0
$874$	−2312.26			−2.64560
$875$	−363.529	+	387.773i	−0.415462	+	0.443170i
$876$		0			0
$877$	−307.336	+	532.322i	−0.350441	+	0.606981i	−0.986327	−	0.164802i	$-0.947301\pi$
$877$	−307.336	+	532.322i	−0.350441	+	0.606981i	0.635886	+	0.771783i	$0.280635\pi$
$878$	−304.492	+	175.798i	−0.346802	+	0.200226i
$879$		0			0
$880$	119.309	−	206.650i	0.135579	−	0.234830i
$881$		−	515.117i		−	0.584696i	−0.956312	−	0.292348i	$-0.905563\pi$
$881$		−	515.117i		−	0.584696i	0.956312	−	0.292348i	$-0.0944365\pi$
$882$		0			0
$883$	−1647.52			−1.86582			−0.932909	−	0.360111i	$-0.882739\pi$
$883$	−1647.52			−1.86582			−0.932909	+	0.360111i	$0.882739\pi$
$884$	−104.798	−	60.5049i	−0.118549	−	0.0684444i
$885$		0			0
$886$	−258.150	−	447.129i	−0.291366	−	0.504661i
$887$	16.7923	+	9.69504i	0.0189316	+	0.0109301i	0.509436	−	0.860509i	$-0.329854\pi$
$887$	16.7923	+	9.69504i	0.0189316	+	0.0109301i	−0.490504	+	0.871439i	$0.663187\pi$
$888$		0			0
$889$	−366.260	−	343.361i	−0.411991	−	0.386232i
$890$			153.191i			0.172125i
$891$		0			0
$892$	38.3767	+	66.4703i	0.0430232	+	0.0745183i
$893$	2158.10	−	1245.98i	2.41668	−	1.39527i
$894$		0			0
$895$	−2133.42			−2.38371
$896$	−22.9540	−	75.7965i	−0.0256183	−	0.0845943i
$897$		0			0
$898$	620.209	−	1074.23i	0.690656	−	1.19625i
$899$	−151.326	+	87.3682i	−0.168327	+	0.0971838i
$900$		0			0
$901$	−47.0704	+	81.5284i	−0.0522424	+	0.0904865i
$902$		−	686.884i		−	0.761512i
$903$		0			0
$904$	−156.941			−0.173607
$905$	651.480	+	376.132i	0.719867	+	0.415616i
$906$		0			0
$907$	−493.066	−	854.016i	−0.543623	−	0.941583i	−0.998692	−	0.0511270i	$-0.983719\pi$
$907$	−493.066	−	854.016i	−0.543623	−	0.941583i	0.455069	−	0.890456i	$-0.349615\pi$
$908$	229.773	+	132.660i	0.253054	+	0.146101i
$909$		0			0
$910$	291.503	−	1247.56i	0.320333	−	1.37094i
$911$			1011.86i			1.11071i	0.831613	+	0.555355i	$0.187418\pi$
$911$			1011.86i			1.11071i	−0.831613	+	0.555355i	$0.812582\pi$
$912$		0			0
$913$	−453.779	−	785.968i	−0.497020	−	0.860863i
$914$	636.451	−	367.455i	0.696336	−	0.402030i
$915$		0			0
$916$	545.082			0.595068
$917$	224.561	+	741.525i	0.244887	+	0.808642i
$918$		0			0
$919$	321.508	−	556.868i	0.349845	−	0.605950i	−0.636376	−	0.771379i	$-0.719567\pi$
$919$	321.508	−	556.868i	0.349845	−	0.605950i	0.986222	+	0.165429i	$0.0529008\pi$
$920$	664.172	−	383.460i	0.721926	−	0.416804i
$921$		0			0
$922$	−517.325	+	896.033i	−0.561090	+	0.971836i
$923$			583.593i			0.632278i
$924$		0			0
$925$	301.198			0.325620
$926$	−236.845	−	136.743i	−0.255772	−	0.147670i
$927$		0			0
$928$	−22.0929	−	38.2661i	−0.0238070	−	0.0412350i
$929$	−219.777	−	126.888i	−0.236574	−	0.136586i	0.377027	−	0.926202i	$-0.376946\pi$
$929$	−219.777	−	126.888i	−0.236574	−	0.136586i	−0.613601	+	0.789616i	$0.710280\pi$
$930$		0			0
$931$	−1624.62	−	803.061i	−1.74503	−	0.862579i
$932$		−	425.985i		−	0.457066i
$933$		0			0
$934$	480.703	+	832.602i	0.514671	+	0.891436i
$935$	148.144	−	85.5312i	0.158443	−	0.0914772i
$936$		0			0
$937$	−801.763			−0.855670			−0.427835	−	0.903857i	$-0.640724\pi$
$937$	−801.763			−0.855670			−0.427835	+	0.903857i	$0.640724\pi$
$938$	127.406	−	135.903i	0.135827	−	0.144886i
$939$		0			0
$940$	−413.260	+	715.788i	−0.439639	+	0.761477i
$941$	−1276.20	+	736.812i	−1.35621	+	0.783009i	−0.989111	−	0.147172i	$-0.952983\pi$
$941$	−1276.20	+	736.812i	−1.35621	+	0.783009i	−0.367101	+	0.930181i	$0.619650\pi$
$942$		0			0
$943$	1103.82	−	1911.87i	1.17054	−	2.02744i
$944$		−	284.151i		−	0.301008i
$945$		0			0
$946$	798.729			0.844322
$947$	1069.62	+	617.548i	1.12949	+	0.652109i	0.943806	−	0.330501i	$-0.107218\pi$
$947$	1069.62	+	617.548i	1.12949	+	0.652109i	0.185681	+	0.982610i	$0.440551\pi$
$948$		0			0
$949$	−926.025	−	1603.92i	−0.975790	−	1.69012i
$950$	−571.655	−	330.045i	−0.601742	−	0.347416i
$951$		0			0
$952$	12.9179	−	55.2853i	0.0135692	−	0.0580728i
$953$		−	245.118i		−	0.257207i	−0.991696	−	0.128603i	$-0.958951\pi$
$953$		−	245.118i		−	0.257207i	0.991696	−	0.128603i	$-0.0410494\pi$
$954$		0			0
$955$	350.660	+	607.361i	0.367183	+	0.635980i
$956$	−381.274	+	220.129i	−0.398822	+	0.230260i
$957$		0			0
$958$	1053.47			1.09966
$959$	−1413.60	−	330.300i	−1.47403	−	0.344421i
$960$		0			0
$961$	230.281	−	398.858i	0.239626	−	0.415045i
$962$	616.761	−	356.087i	0.641124	−	0.370153i
$963$		0			0
$964$	−54.6895	+	94.7249i	−0.0567318	+	0.0982624i
$965$		−	329.892i		−	0.341857i
$966$		0			0
$967$	130.329			0.134777			0.0673883	−	0.997727i	$-0.478533\pi$
$967$	130.329			0.134777			0.0673883	+	0.997727i	$0.478533\pi$
$968$	−64.6779	−	37.3418i	−0.0668161	−	0.0385763i
$969$		0			0
$970$	−74.9974	−	129.899i	−0.0773169	−	0.133917i
$971$	1273.08	+	735.011i	1.31110	+	0.756963i	0.982278	−	0.187429i	$-0.0600155\pi$
$971$	1273.08	+	735.011i	1.31110	+	0.756963i	0.328821	+	0.944392i	$0.393349\pi$
$972$		0			0
$973$	393.312	+	368.722i	0.404226	+	0.378953i
$974$		−	217.721i		−	0.223533i
$975$		0			0
$976$	93.3113	+	161.620i	0.0956058	+	0.165594i
$977$	1193.53	−	689.085i	1.22163	−	0.705307i	0.256363	−	0.966581i	$-0.417476\pi$
$977$	1193.53	−	689.085i	1.22163	−	0.705307i	0.965265	+	0.261274i	$0.0841425\pi$
$978$		0			0
$979$	−171.769			−0.175453
$980$	599.834	−	38.7534i	0.612076	−	0.0395442i
$981$		0			0
$982$	163.530	−	283.242i	0.166527	−	0.288434i
$983$	−1201.25	+	693.543i	−1.22203	+	0.705537i	−0.965349	−	0.260961i	$-0.915961\pi$
$983$	−1201.25	+	693.543i	−1.22203	+	0.705537i	−0.256676	+	0.966498i	$0.582627\pi$
$984$		0			0
$985$	196.711	−	340.713i	0.199706	−	0.345901i
$986$		−	31.6762i		−	0.0321260i
$987$		0			0
$988$	−1560.76			−1.57972
$989$	2223.18	+	1283.55i	2.24791	+	1.29783i
$990$		0			0
$991$	255.321	+	442.228i	0.257639	+	0.446245i	0.965609	−	0.259998i	$-0.0837220\pi$
$991$	255.321	+	442.228i	0.257639	+	0.446245i	−0.707970	+	0.706243i	$0.750389\pi$
$992$	−109.593	−	63.2733i	−0.110476	−	0.0637835i
$993$		0			0
$994$	−262.053	+	79.3594i	−0.263635	+	0.0798384i
$995$			2134.96i			2.14569i
$996$		0			0
$997$	625.854	+	1084.01i	0.627737	+	1.08727i	0.988005	+	0.154424i	$0.0493521\pi$
$997$	625.854	+	1084.01i	0.627737	+	1.08727i	−0.360267	+	0.932849i	$0.617315\pi$
$998$	−509.335	+	294.065i	−0.510356	+	0.294654i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.3.s.e.107.7	yes	24
3.2	odd	2	inner	378.3.s.e.107.6	yes	24
7.4	even	3	inner	378.3.s.e.53.6	✓	24
21.11	odd	6	inner	378.3.s.e.53.7	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.3.s.e.53.6	✓	24	7.4	even	3	inner
378.3.s.e.53.7	yes	24	21.11	odd	6	inner
378.3.s.e.107.6	yes	24	3.2	odd	2	inner
378.3.s.e.107.7	yes	24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	378.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 + 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(-5.31178 - 3.06676i) q^{5} +(5.10682 + 4.78753i) q^{7} +2.82843i q^{8} +O(q^{10})\)	\(q+(1.22474 + 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(-5.31178 - 3.06676i) q^{5} +(5.10682 + 4.78753i) q^{7} +2.82843i q^{8} +(-4.33705 - 7.51200i) q^{10} +(8.42297 - 4.86301i) q^{11} +21.0999 q^{13} +(2.86925 + 9.47457i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(-2.48336 + 1.43377i) q^{17} +(-18.4925 + 32.0300i) q^{19} -12.2670i q^{20} +13.7547 q^{22} +(38.2847 + 22.1037i) q^{23} +(6.31004 + 10.9293i) q^{25} +(25.8420 + 14.9199i) q^{26} +(-3.18543 + 13.6328i) q^{28} +7.81103i q^{29} +(11.1852 + 19.3734i) q^{31} +(-4.89898 + 2.82843i) q^{32} -4.05532 q^{34} +(-12.4441 - 41.0917i) q^{35} +(11.9333 - 20.6691i) q^{37} +(-45.2972 + 26.1524i) q^{38} +(8.67411 - 15.0240i) q^{40} -49.9383i q^{41} +58.0697 q^{43} +(16.8459 + 9.72601i) q^{44} +(31.2593 + 54.1428i) q^{46} +(-58.3505 - 33.6887i) q^{47} +(3.15914 + 48.8981i) q^{49} +17.8475i q^{50} +(21.0999 + 36.5461i) q^{52} +(28.4314 - 16.4149i) q^{53} -59.6547 q^{55} +(-13.5412 + 14.4443i) q^{56} +(-5.52323 + 9.56652i) q^{58} +(-61.5206 + 35.5189i) q^{59} +(23.3278 - 40.4050i) q^{61} +31.6366i q^{62} -8.00000 q^{64} +(-112.078 - 64.7084i) q^{65} +(-9.40879 - 16.2965i) q^{67} +(-4.96673 - 2.86754i) q^{68} +(13.8154 - 59.1262i) q^{70} +27.6586i q^{71} +(-43.8876 - 76.0156i) q^{73} +(29.2305 - 16.8762i) q^{74} -73.9701 q^{76} +(66.2964 + 15.4907i) q^{77} +(-39.8584 + 69.0367i) q^{79} +(21.2471 - 12.2670i) q^{80} +(35.3117 - 61.1616i) q^{82} -93.3124i q^{83} +17.5881 q^{85} +(71.1205 + 41.0615i) q^{86} +(13.7547 + 23.8238i) q^{88} +(-15.2947 - 8.83038i) q^{89} +(107.753 + 101.016i) q^{91} +88.4148i q^{92} +(-47.6430 - 82.5201i) q^{94} +(196.457 - 113.424i) q^{95} +17.2922 q^{97} +(-30.7070 + 62.1215i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{4} + 8 q^{7}+O(q^{10}) \) 24 * q + 24 * q^4 + 8 * q^7	\( 24 q + 24 q^{4} + 8 q^{7} + 8 q^{10} - 16 q^{13} - 48 q^{16} - 36 q^{19} + 64 q^{22} + 128 q^{25} + 32 q^{28} + 176 q^{31} + 16 q^{34} - 72 q^{37} - 16 q^{40} + 216 q^{43} + 64 q^{46} - 24 q^{49} - 16 q^{52} + 448 q^{55} + 104 q^{58} - 268 q^{61} - 192 q^{64} - 248 q^{67} - 80 q^{70} - 116 q^{73} - 144 q^{76} + 152 q^{79} + 240 q^{82} - 536 q^{85} + 64 q^{88} + 428 q^{91} + 144 q^{94} + 16 q^{97}+O(q^{100}) \) 24 * q + 24 * q^4 + 8 * q^7 + 8 * q^10 - 16 * q^13 - 48 * q^16 - 36 * q^19 + 64 * q^22 + 128 * q^25 + 32 * q^28 + 176 * q^31 + 16 * q^34 - 72 * q^37 - 16 * q^40 + 216 * q^43 + 64 * q^46 - 24 * q^49 - 16 * q^52 + 448 * q^55 + 104 * q^58 - 268 * q^61 - 192 * q^64 - 248 * q^67 - 80 * q^70 - 116 * q^73 - 144 * q^76 + 152 * q^79 + 240 * q^82 - 536 * q^85 + 64 * q^88 + 428 * q^91 + 144 * q^94 + 16 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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