LMFDB - Embedded newform 456.3.w.a.145.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [456,3,Mod(145,456)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(456, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))

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

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

chi := DirichletCharacter("456.145");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 456 = 2^{3} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	456.w (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:	$12.4251000548$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 154 x^{18} - 24 x^{17} + 16374 x^{16} - 4328 x^{15} + 911836 x^{14} - 590088 x^{13} + \cdots + 338560000 $ x^20 + 154x^18 - 24x^17 + 16374x^16 - 4328x^15 + 911836x^14 - 590088x^13 + 36808708x^12 - 29040960x^11 + 727387008x^10 - 1003792064x^9 + 10261479936x^8 - 7069668864x^7 + 36940887936x^6 + 52280031232x^5 + 60574204416x^4 + 32700144640x^3 + 13448832000x^2 + 2490624000x + 338560000
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{18} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.7
Root			$-0.328356 + 0.568730i$ of defining polynomial
Character	$\chi$	$=$	456.145
Dual form			456.3.w.a.217.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 + 0.866025i) q^{3} +(0.328356 + 0.568730i) q^{5} -2.26614 q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.50000 + 0.866025i) q^{3} +(0.328356 + 0.568730i) q^{5} -2.26614 q^{7} +(1.50000 - 2.59808i) q^{9} +1.81331 q^{11} +(-9.14187 - 5.27806i) q^{13} +(-0.985069 - 0.568730i) q^{15} +(-9.38434 - 16.2542i) q^{17} +(13.5109 + 13.3588i) q^{19} +(3.39920 - 1.96253i) q^{21} +(0.434002 - 0.751713i) q^{23} +(12.2844 - 21.2771i) q^{25} +5.19615i q^{27} +(-5.65206 - 3.26322i) q^{29} -25.1462i q^{31} +(-2.71996 + 1.57037i) q^{33} +(-0.744100 - 1.28882i) q^{35} -60.4853i q^{37} +18.2837 q^{39} +(49.3980 - 28.5199i) q^{41} +(-20.0700 - 34.7623i) q^{43} +1.97014 q^{45} +(-7.05974 + 12.2278i) q^{47} -43.8646 q^{49} +(28.1530 + 16.2542i) q^{51} +(9.28807 + 5.36247i) q^{53} +(0.595411 + 1.03128i) q^{55} +(-31.8353 - 8.33740i) q^{57} +(54.3347 - 31.3701i) q^{59} +(36.5507 - 63.3077i) q^{61} +(-3.39920 + 5.88759i) q^{63} -6.93234i q^{65} +(26.6801 + 15.4038i) q^{67} +1.50343i q^{69} +(-53.9165 + 31.1287i) q^{71} +(-59.4362 - 102.946i) q^{73} +42.5543i q^{75} -4.10920 q^{77} +(6.11453 - 3.53023i) q^{79} +(-4.50000 - 7.79423i) q^{81} -9.32225 q^{83} +(6.16281 - 10.6743i) q^{85} +11.3041 q^{87} +(25.1100 + 14.4972i) q^{89} +(20.7167 + 11.9608i) q^{91} +(21.7772 + 37.7193i) q^{93} +(-3.16115 + 12.0705i) q^{95} +(-14.3430 + 8.28096i) q^{97} +(2.71996 - 4.71111i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 30 q^{3} + 20 q^{7} + 30 q^{9}+O(q^{10}) $ 20 * q - 30 * q^3 + 20 * q^7 + 30 * q^9	$ 20 q - 30 q^{3} + 20 q^{7} + 30 q^{9} - 8 q^{11} + 18 q^{13} + 8 q^{17} + 28 q^{19} - 30 q^{21} - 8 q^{23} - 58 q^{25} + 108 q^{29} + 12 q^{33} + 20 q^{35} - 36 q^{39} - 36 q^{41} - 2 q^{43} + 296 q^{49} - 24 q^{51} - 72 q^{53} + 216 q^{55} - 30 q^{57} + 72 q^{59} - 26 q^{61} + 30 q^{63} + 138 q^{67} - 204 q^{71} + 218 q^{73} - 8 q^{77} - 78 q^{79} - 90 q^{81} - 112 q^{83} + 224 q^{85} - 216 q^{87} - 432 q^{89} - 330 q^{91} - 126 q^{93} + 220 q^{95} + 132 q^{97} - 12 q^{99}+O(q^{100}) $ 20 * q - 30 * q^3 + 20 * q^7 + 30 * q^9 - 8 * q^11 + 18 * q^13 + 8 * q^17 + 28 * q^19 - 30 * q^21 - 8 * q^23 - 58 * q^25 + 108 * q^29 + 12 * q^33 + 20 * q^35 - 36 * q^39 - 36 * q^41 - 2 * q^43 + 296 * q^49 - 24 * q^51 - 72 * q^53 + 216 * q^55 - 30 * q^57 + 72 * q^59 - 26 * q^61 + 30 * q^63 + 138 * q^67 - 204 * q^71 + 218 * q^73 - 8 * q^77 - 78 * q^79 - 90 * q^81 - 112 * q^83 + 224 * q^85 - 216 * q^87 - 432 * q^89 - 330 * q^91 - 126 * q^93 + 220 * q^95 + 132 * q^97 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/456\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$343$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−1.50000	+	0.866025i	−0.500000	+	0.288675i
$3$	−1.50000	+	0.866025i	−0.500000	+	0.288675i
$4$		0			0
$5$	0.328356	+	0.568730i	0.0656712	+	0.113746i	0.896992	−	0.442048i	$-0.145748\pi$
$5$	0.328356	+	0.568730i	0.0656712	+	0.113746i	−0.831320	+	0.555794i	$0.812414\pi$
$6$		0			0
$7$	−2.26614			−0.323734			−0.161867	−	0.986813i	$-0.551751\pi$
$7$	−2.26614			−0.323734			−0.161867	+	0.986813i	$0.551751\pi$
$8$		0			0
$9$	1.50000	−	2.59808i	0.166667	−	0.288675i
$10$		0			0
$11$	1.81331			0.164846			0.0824231	−	0.996597i	$-0.473734\pi$
$11$	1.81331			0.164846			0.0824231	+	0.996597i	$0.473734\pi$
$12$		0			0
$13$	−9.14187	−	5.27806i	−0.703221	−	0.406005i	0.105325	−	0.994438i	$-0.466412\pi$
$13$	−9.14187	−	5.27806i	−0.703221	−	0.406005i	−0.808546	+	0.588433i	$0.799745\pi$
$14$		0			0
$15$	−0.985069	−	0.568730i	−0.0656712	−	0.0379153i
$16$		0			0
$17$	−9.38434	−	16.2542i	−0.552020	−	0.956126i	−0.998129	−	0.0611478i	$-0.980524\pi$
$17$	−9.38434	−	16.2542i	−0.552020	−	0.956126i	0.446109	−	0.894979i	$-0.352809\pi$
$18$		0			0
$19$	13.5109	+	13.3588i	0.711098	+	0.703093i
$19$	13.5109	+	13.3588i	0.711098	+	0.703093i
$20$		0			0
$21$	3.39920	−	1.96253i	0.161867	−	0.0934538i
$22$		0			0
$23$	0.434002	−	0.751713i	0.0188696	−	0.0326832i	−0.856436	−	0.516253i	$-0.827327\pi$
$23$	0.434002	−	0.751713i	0.0188696	−	0.0326832i	0.875306	+	0.483569i	$0.160660\pi$
$24$		0			0
$25$	12.2844	−	21.2771i	0.491375	−	0.851086i
$26$		0			0
$27$			5.19615i			0.192450i
$28$		0			0
$29$	−5.65206	−	3.26322i	−0.194899	−	0.112525i	0.399375	−	0.916788i	$-0.369227\pi$
$29$	−5.65206	−	3.26322i	−0.194899	−	0.112525i	−0.594274	+	0.804263i	$0.702560\pi$
$30$		0			0
$31$		−	25.1462i		−	0.811167i	−0.914058	−	0.405584i	$-0.867068\pi$
$31$		−	25.1462i		−	0.811167i	0.914058	−	0.405584i	$-0.132932\pi$
$32$		0			0
$33$	−2.71996	+	1.57037i	−0.0824231	+	0.0475870i
$34$		0			0
$35$	−0.744100	−	1.28882i	−0.0212600	−	0.0368234i
$36$		0			0
$37$		−	60.4853i		−	1.63474i	−0.576114	−	0.817369i	$-0.695432\pi$
$37$		−	60.4853i		−	1.63474i	0.576114	−	0.817369i	$-0.304568\pi$
$38$		0			0
$39$	18.2837			0.468814
$40$		0			0
$41$	49.3980	−	28.5199i	1.20483	−	0.695608i	0.243204	−	0.969975i	$-0.421802\pi$
$41$	49.3980	−	28.5199i	1.20483	−	0.695608i	0.961625	+	0.274367i	$0.0884684\pi$
$42$		0			0
$43$	−20.0700	−	34.7623i	−0.466745	−	0.808426i	0.532533	−	0.846409i	$-0.321240\pi$
$43$	−20.0700	−	34.7623i	−0.466745	−	0.808426i	−0.999278	+	0.0379828i	$0.987907\pi$
$44$		0			0
$45$	1.97014			0.0437808
$46$		0			0
$47$	−7.05974	+	12.2278i	−0.150207	+	0.260167i	−0.931304	−	0.364244i	$-0.881327\pi$
$47$	−7.05974	+	12.2278i	−0.150207	+	0.260167i	0.781096	+	0.624411i	$0.214661\pi$
$48$		0			0
$49$	−43.8646			−0.895197
$50$		0			0
$51$	28.1530	+	16.2542i	0.552020	+	0.318709i
$52$		0			0
$53$	9.28807	+	5.36247i	0.175247	+	0.101179i	0.585057	−	0.810992i	$-0.301072\pi$
$53$	9.28807	+	5.36247i	0.175247	+	0.101179i	−0.409811	+	0.912171i	$0.634405\pi$
$54$		0			0
$55$	0.595411	+	1.03128i	0.0108257	+	0.0187506i
$56$		0			0
$57$	−31.8353	−	8.33740i	−0.558514	−	0.146270i
$58$		0			0
$59$	54.3347	−	31.3701i	0.920926	−	0.531697i	0.0369959	−	0.999315i	$-0.488221\pi$
$59$	54.3347	−	31.3701i	0.920926	−	0.531697i	0.883930	+	0.467618i	$0.154888\pi$
$60$		0			0
$61$	36.5507	−	63.3077i	0.599192	−	1.03783i	−0.393749	−	0.919218i	$-0.628822\pi$
$61$	36.5507	−	63.3077i	0.599192	−	1.03783i	0.992941	−	0.118613i	$-0.0378448\pi$
$62$		0			0
$63$	−3.39920	+	5.88759i	−0.0539556	+	0.0934538i
$64$		0			0
$65$		−	6.93234i		−	0.106651i
$66$		0			0
$67$	26.6801	+	15.4038i	0.398211	+	0.229907i	0.685712	−	0.727873i	$-0.259491\pi$
$67$	26.6801	+	15.4038i	0.398211	+	0.229907i	−0.287501	+	0.957780i	$0.592824\pi$
$68$		0			0
$69$			1.50343i			0.0217888i
$70$		0			0
$71$	−53.9165	+	31.1287i	−0.759388	+	0.438433i	−0.829076	−	0.559136i	$-0.811133\pi$
$71$	−53.9165	+	31.1287i	−0.759388	+	0.438433i	0.0696883	+	0.997569i	$0.477800\pi$
$72$		0			0
$73$	−59.4362	−	102.946i	−0.814194	−	1.41023i	−0.909905	−	0.414816i	$-0.863846\pi$
$73$	−59.4362	−	102.946i	−0.814194	−	1.41023i	0.0957112	−	0.995409i	$-0.469487\pi$
$74$		0			0
$75$			42.5543i			0.567390i
$76$		0			0
$77$	−4.10920			−0.0533662
$78$		0			0
$79$	6.11453	−	3.53023i	0.0773991	−	0.0446864i	−0.460801	−	0.887503i	$-0.652438\pi$
$79$	6.11453	−	3.53023i	0.0773991	−	0.0446864i	0.538200	+	0.842817i	$0.319104\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−9.32225			−0.112316			−0.0561581	−	0.998422i	$-0.517885\pi$
$83$	−9.32225			−0.112316			−0.0561581	+	0.998422i	$0.517885\pi$
$84$		0			0
$85$	6.16281	−	10.6743i	0.0725037	−	0.125580i
$86$		0			0
$87$	11.3041			0.129932
$88$		0			0
$89$	25.1100	+	14.4972i	0.282134	+	0.162890i	0.634389	−	0.773014i	$-0.281252\pi$
$89$	25.1100	+	14.4972i	0.282134	+	0.162890i	−0.352255	+	0.935904i	$0.614585\pi$
$90$		0			0
$91$	20.7167	+	11.9608i	0.227656	+	0.131437i
$92$		0			0
$93$	21.7772	+	37.7193i	0.234164	+	0.405584i
$94$		0			0
$95$	−3.16115	+	12.0705i	−0.0332753	+	0.127058i
$96$		0			0
$97$	−14.3430	+	8.28096i	−0.147866	+	0.0853707i	−0.572108	−	0.820178i	$-0.693874\pi$
$97$	−14.3430	+	8.28096i	−0.147866	+	0.0853707i	0.424241	+	0.905549i	$0.360541\pi$
$98$		0			0
$99$	2.71996	−	4.71111i	0.0274744	−	0.0475870i
$100$		0			0
$101$	−50.9885	+	88.3146i	−0.504836	+	0.874402i	0.495148	+	0.868809i	$0.335114\pi$
$101$	−50.9885	+	88.3146i	−0.504836	+	0.874402i	−0.999984	+	0.00559362i	$0.998219\pi$
$102$		0			0
$103$		−	6.57220i		−	0.0638077i	−0.999491	−	0.0319039i	$-0.989843\pi$
$103$		−	6.57220i		−	0.0638077i	0.999491	−	0.0319039i	$-0.0101570\pi$
$104$		0			0
$105$	2.23230	+	1.28882i	0.0212600	+	0.0122745i
$106$		0			0
$107$			124.686i			1.16529i	0.812726	+	0.582646i	$0.197983\pi$
$107$			124.686i			1.16529i	−0.812726	+	0.582646i	$0.802017\pi$
$108$		0			0
$109$	−48.1594	+	27.8049i	−0.441830	+	0.255091i	−0.704373	−	0.709830i	$-0.748772\pi$
$109$	−48.1594	+	27.8049i	−0.441830	+	0.255091i	0.262544	+	0.964920i	$0.415439\pi$
$110$		0			0
$111$	52.3818	+	90.7280i	0.471908	+	0.817369i
$112$		0			0
$113$			17.9099i			0.158494i	0.996855	+	0.0792472i	$0.0252517\pi$
$113$			17.9099i			0.158494i	−0.996855	+	0.0792472i	$0.974748\pi$
$114$		0			0
$115$	0.570028			0.00495677
$116$		0			0
$117$	−27.4256	+	15.8342i	−0.234407	+	0.135335i
$118$		0			0
$119$	21.2662	+	36.8341i	0.178707	+	0.309530i
$120$		0			0
$121$	−117.712			−0.972826
$122$		0			0
$123$	−49.3980	+	85.5598i	−0.401610	+	0.695608i
$124$		0			0
$125$	32.5524			0.260419
$126$		0			0
$127$	−99.6825	−	57.5517i	−0.784901	−	0.453163i	0.0532631	−	0.998581i	$-0.483038\pi$
$127$	−99.6825	−	57.5517i	−0.784901	−	0.453163i	−0.838165	+	0.545417i	$0.816371\pi$
$128$		0			0
$129$	60.2101	+	34.7623i	0.466745	+	0.269475i
$130$		0			0
$131$	36.1976	+	62.6960i	0.276317	+	0.478596i	0.970467	−	0.241235i	$-0.0775526\pi$
$131$	36.1976	+	62.6960i	0.276317	+	0.478596i	−0.694149	+	0.719831i	$0.744219\pi$
$132$		0			0
$133$	−30.6174	−	30.2728i	−0.230206	−	0.227615i
$134$		0			0
$135$	−2.95521	+	1.70619i	−0.0218904	+	0.0126384i
$136$		0			0
$137$	−28.5309	+	49.4170i	−0.208255	+	0.360708i	−0.951165	−	0.308683i	$-0.900112\pi$
$137$	−28.5309	+	49.4170i	−0.208255	+	0.360708i	0.742910	+	0.669391i	$0.233445\pi$
$138$		0			0
$139$	−12.7951	+	22.1617i	−0.0920509	+	0.159437i	−0.908374	−	0.418159i	$-0.862676\pi$
$139$	−12.7951	+	22.1617i	−0.0920509	+	0.159437i	0.816323	+	0.577596i	$0.196009\pi$
$140$		0			0
$141$		−	24.4557i		−	0.173444i
$142$		0			0
$143$	−16.5770	−	9.57075i	−0.115923	−	0.0669283i
$144$		0			0
$145$		−	4.28599i		−	0.0295586i
$146$		0			0
$147$	65.7969	−	37.9879i	0.447598	−	0.258421i
$148$		0			0
$149$	143.387	+	248.354i	0.962329	+	1.66680i	0.716627	+	0.697457i	$0.245685\pi$
$149$	143.387	+	248.354i	0.962329	+	1.66680i	0.245702	+	0.969346i	$0.420982\pi$
$150$		0			0
$151$			71.6434i			0.474460i	0.971454	+	0.237230i	$0.0762395\pi$
$151$			71.6434i			0.474460i	−0.971454	+	0.237230i	$0.923761\pi$
$152$		0			0
$153$	−56.3060			−0.368013
$154$		0			0
$155$	14.3014	−	8.25691i	0.0922670	−	0.0532704i
$156$		0			0
$157$	−47.9356	−	83.0269i	−0.305322	−	0.528834i	0.672011	−	0.740542i	$-0.265431\pi$
$157$	−47.9356	−	83.0269i	−0.305322	−	0.528834i	−0.977333	+	0.211708i	$0.932098\pi$
$158$		0			0
$159$	−18.5761			−0.116831
$160$		0			0
$161$	−0.983506	+	1.70348i	−0.00610873	+	0.0105806i
$162$		0			0
$163$	154.298			0.946616			0.473308	−	0.880897i	$-0.343060\pi$
$163$	154.298			0.946616			0.473308	+	0.880897i	$0.343060\pi$
$164$		0			0
$165$	−1.78623	−	1.03128i	−0.0108257	−	0.00625019i
$166$		0			0
$167$	−110.732	−	63.9312i	−0.663067	−	0.382822i	0.130378	−	0.991464i	$-0.458381\pi$
$167$	−110.732	−	63.9312i	−0.663067	−	0.382822i	−0.793444	+	0.608643i	$0.791714\pi$
$168$		0			0
$169$	−28.7842	−	49.8556i	−0.170320	−	0.295004i
$170$		0			0
$171$	54.9734	−	15.0641i	0.321482	−	0.0880942i
$172$		0			0
$173$	79.4727	−	45.8836i	0.459380	−	0.265223i	−0.252404	−	0.967622i	$-0.581221\pi$
$173$	79.4727	−	45.8836i	0.459380	−	0.265223i	0.711783	+	0.702399i	$0.247888\pi$
$174$		0			0
$175$	−27.8380	+	48.2169i	−0.159074	+	0.275525i
$176$		0			0
$177$	−54.3347	+	94.1104i	−0.306975	+	0.531697i
$178$		0			0
$179$			50.0605i			0.279668i	0.990175	+	0.139834i	$0.0446569\pi$
$179$			50.0605i			0.279668i	−0.990175	+	0.139834i	$0.955343\pi$
$180$		0			0
$181$	43.6725	+	25.2144i	0.241285	+	0.139306i	0.615767	−	0.787928i	$-0.288846\pi$
$181$	43.6725	+	25.2144i	0.241285	+	0.139306i	−0.374482	+	0.927234i	$0.622180\pi$
$182$		0			0
$183$			126.615i			0.691887i
$184$		0			0
$185$	34.3998	−	19.8607i	0.185945	−	0.107355i
$186$		0			0
$187$	−17.0167	−	29.4738i	−0.0909984	−	0.157614i
$188$		0			0
$189$		−	11.7752i		−	0.0623026i
$190$		0			0
$191$	−291.816			−1.52783			−0.763916	−	0.645315i	$-0.776726\pi$
$191$	−291.816			−1.52783			−0.763916	+	0.645315i	$0.776726\pi$
$192$		0			0
$193$	167.552	−	96.7359i	0.868143	−	0.501222i	0.00141211	−	0.999999i	$-0.499551\pi$
$193$	167.552	−	96.7359i	0.868143	−	0.501222i	0.866731	+	0.498777i	$0.166217\pi$
$194$		0			0
$195$	6.00358	+	10.3985i	0.0307876	+	0.0533257i
$196$		0			0
$197$	1.09208			0.00554356			0.00277178	−	0.999996i	$-0.499118\pi$
$197$	1.09208			0.00554356			0.00277178	+	0.999996i	$0.499118\pi$
$198$		0			0
$199$	−37.7176	+	65.3288i	−0.189536	+	0.328286i	−0.945096	−	0.326794i	$-0.894032\pi$
$199$	−37.7176	+	65.3288i	−0.189536	+	0.328286i	0.755560	+	0.655080i	$0.227365\pi$
$200$		0			0
$201$	−53.3602			−0.265474
$202$		0			0
$203$	12.8083	+	7.39489i	0.0630952	+	0.0364280i
$204$		0			0
$205$	32.4403	+	18.7294i	0.158245	+	0.0913629i
$206$		0			0
$207$	−1.30200	−	2.25514i	−0.00628988	−	0.0108944i
$208$		0			0
$209$	24.4994	+	24.2235i	0.117222	+	0.115902i
$210$		0			0
$211$	174.258	−	100.608i	0.825867	−	0.476815i	−0.0265683	−	0.999647i	$-0.508458\pi$
$211$	174.258	−	100.608i	0.825867	−	0.476815i	0.852436	+	0.522832i	$0.175125\pi$
$212$		0			0
$213$	53.9165	−	93.3861i	0.253129	−	0.438433i
$214$		0			0
$215$	13.1802	−	22.8289i	0.0613035	−	0.106181i
$216$		0			0
$217$			56.9846i			0.262602i
$218$		0			0
$219$	178.308	+	102.946i	0.814194	+	0.470075i
$220$		0			0
$221$			198.124i			0.896491i
$222$		0			0
$223$	−98.6819	+	56.9740i	−0.442520	+	0.255489i	−0.704666	−	0.709539i	$-0.748903\pi$
$223$	−98.6819	+	56.9740i	−0.442520	+	0.255489i	0.262146	+	0.965028i	$0.415570\pi$
$224$		0			0
$225$	−36.8531	−	63.8314i	−0.163792	−	0.283695i
$226$		0			0
$227$		−	157.439i		−	0.693566i	−0.937945	−	0.346783i	$-0.887274\pi$
$227$		−	157.439i		−	0.693566i	0.937945	−	0.346783i	$-0.112726\pi$
$228$		0			0
$229$	−160.467			−0.700730			−0.350365	−	0.936613i	$-0.613942\pi$
$229$	−160.467			−0.700730			−0.350365	+	0.936613i	$0.613942\pi$
$230$		0			0
$231$	6.16380	−	3.55867i	0.0266831	−	0.0154055i
$232$		0			0
$233$	115.942	+	200.818i	0.497606	+	0.861879i	0.999996	−	0.00276216i	$-0.000879225\pi$
$233$	115.942	+	200.818i	0.497606	+	0.861879i	−0.502390	+	0.864641i	$0.667546\pi$
$234$		0			0
$235$	−9.27244			−0.0394572
$236$		0			0
$237$	−6.11453	+	10.5907i	−0.0257997	+	0.0446864i
$238$		0			0
$239$	−54.0752			−0.226256			−0.113128	−	0.993580i	$-0.536087\pi$
$239$	−54.0752			−0.226256			−0.113128	+	0.993580i	$0.536087\pi$
$240$		0			0
$241$	−247.270	−	142.762i	−1.02602	−	0.592371i	−0.110176	−	0.993912i	$-0.535142\pi$
$241$	−247.270	−	142.762i	−1.02602	−	0.592371i	−0.915841	+	0.401541i	$0.868475\pi$
$242$		0			0
$243$	13.5000	+	7.79423i	0.0555556	+	0.0320750i
$244$		0			0
$245$	−14.4032	−	24.9471i	−0.0587887	−	0.101825i
$246$		0			0
$247$	−53.0062	−	193.435i	−0.214600	−	0.783139i
$248$		0			0
$249$	13.9834	−	8.07331i	0.0561581	−	0.0324229i
$250$		0			0
$251$	97.1774	−	168.316i	0.387161	−	0.670583i	−0.604905	−	0.796297i	$-0.706789\pi$
$251$	97.1774	−	168.316i	0.387161	−	0.670583i	0.992066	+	0.125715i	$0.0401224\pi$
$252$		0			0
$253$	0.786978	−	1.36309i	0.00311059	−	0.00538769i
$254$		0			0
$255$			21.3486i			0.0837200i
$256$		0			0
$257$	105.437	+	60.8741i	0.410261	+	0.236864i	0.690902	−	0.722948i	$-0.257214\pi$
$257$	105.437	+	60.8741i	0.410261	+	0.236864i	−0.280641	+	0.959813i	$0.590547\pi$
$258$		0			0
$259$			137.068i			0.529220i
$260$		0			0
$261$	−16.9562	+	9.78965i	−0.0649662	+	0.0375082i
$262$		0			0
$263$	−253.074	−	438.337i	−0.962259	−	1.66668i	−0.716805	−	0.697274i	$-0.754396\pi$
$263$	−253.074	−	438.337i	−0.962259	−	1.66668i	−0.245455	−	0.969408i	$-0.578937\pi$
$264$		0			0
$265$			7.04321i			0.0265781i
$266$		0			0
$267$	−50.2199			−0.188090
$268$		0			0
$269$	143.295	−	82.7317i	0.532697	−	0.307553i	−0.209417	−	0.977826i	$-0.567157\pi$
$269$	143.295	−	82.7317i	0.532697	−	0.307553i	0.742114	+	0.670274i	$0.233823\pi$
$270$		0			0
$271$	−201.600	−	349.181i	−0.743910	−	1.28849i	−0.950702	−	0.310105i	$-0.899636\pi$
$271$	−201.600	−	349.181i	−0.743910	−	1.28849i	0.206792	−	0.978385i	$-0.433698\pi$
$272$		0			0
$273$	−41.4334			−0.151771
$274$		0			0
$275$	22.2753	−	38.5820i	0.0810012	−	0.140298i
$276$		0			0
$277$	182.277			0.658041			0.329020	−	0.944323i	$-0.393282\pi$
$277$	182.277			0.658041			0.329020	+	0.944323i	$0.393282\pi$
$278$		0			0
$279$	−65.3317	−	37.7193i	−0.234164	−	0.135195i
$280$		0			0
$281$	373.811	+	215.820i	1.33029	+	0.768042i	0.985344	−	0.170581i	$-0.0545643\pi$
$281$	373.811	+	215.820i	1.33029	+	0.768042i	0.344945	+	0.938623i	$0.387898\pi$
$282$		0			0
$283$	75.1512	+	130.166i	0.265552	+	0.459949i	0.967708	−	0.252074i	$-0.0811125\pi$
$283$	75.1512	+	130.166i	0.265552	+	0.459949i	−0.702156	+	0.712023i	$0.747779\pi$
$284$		0			0
$285$	−5.71160	−	20.8433i	−0.0200407	−	0.0731345i
$286$		0			0
$287$	−111.942	+	64.6300i	−0.390043	+	0.225192i
$288$		0			0
$289$	−31.6316	+	54.7875i	−0.109452	+	0.189576i
$290$		0			0
$291$	14.3430	−	24.8429i	0.0492888	−	0.0853707i
$292$		0			0
$293$		−	79.0796i		−	0.269896i	−0.990853	−	0.134948i	$-0.956913\pi$
$293$		−	79.0796i		−	0.269896i	0.990853	−	0.134948i	$-0.0430868\pi$
$294$		0			0
$295$	35.6822	+	20.6012i	0.120957	+	0.0698344i
$296$		0			0
$297$			9.42222i			0.0317247i
$298$		0			0
$299$	−7.93517	+	4.58137i	−0.0265390	+	0.0153223i
$300$		0			0
$301$	45.4814	+	78.7761i	0.151101	+	0.261715i
$302$		0			0
$303$		−	176.629i		−	0.582935i
$304$		0			0
$305$	48.0066			0.157399
$306$		0			0
$307$	463.571	−	267.643i	1.51000	−	0.871801i	0.510071	−	0.860132i	$-0.329619\pi$
$307$	463.571	−	267.643i	1.51000	−	0.871801i	0.999932	−	0.0116689i	$-0.00371440\pi$
$308$		0			0
$309$	5.69169	+	9.85830i	0.0184197	+	0.0319039i
$310$		0			0
$311$	−167.577			−0.538834			−0.269417	−	0.963024i	$-0.586831\pi$
$311$	−167.577			−0.538834			−0.269417	+	0.963024i	$0.586831\pi$
$312$		0			0
$313$	−80.2751	+	139.041i	−0.256470	+	0.444219i	−0.965294	−	0.261167i	$-0.915893\pi$
$313$	−80.2751	+	139.041i	−0.256470	+	0.444219i	0.708824	+	0.705386i	$0.249226\pi$
$314$		0			0
$315$	−4.46460			−0.0141733
$316$		0			0
$317$	−343.946	−	198.577i	−1.08500	−	0.626427i	−0.152761	−	0.988263i	$-0.548816\pi$
$317$	−343.946	−	198.577i	−1.08500	−	0.626427i	−0.932242	+	0.361837i	$0.882150\pi$
$318$		0			0
$319$	−10.2489	−	5.91722i	−0.0321283	−	0.0185493i
$320$		0			0
$321$	−107.981	−	187.029i	−0.336391	−	0.582646i
$322$		0			0
$323$	90.3449	−	344.971i	0.279705	−	1.06802i
$324$		0			0
$325$	−224.604	+	129.675i	−0.691090	+	0.399001i
$326$		0			0
$327$	48.1594	−	83.4146i	0.147277	−	0.255091i
$328$		0			0
$329$	15.9983	−	27.7099i	0.0486271	−	0.0842246i
$330$		0			0
$331$		−	90.2458i		−	0.272646i	−0.990664	−	0.136323i	$-0.956472\pi$
$331$		−	90.2458i		−	0.272646i	0.990664	−	0.136323i	$-0.0435285\pi$
$332$		0			0
$333$	−157.145	−	90.7280i	−0.471908	−	0.272456i
$334$		0			0
$335$			20.2317i			0.0603931i
$336$		0			0
$337$	171.964	−	99.2835i	0.510279	−	0.294610i	−0.222669	−	0.974894i	$-0.571477\pi$
$337$	171.964	−	99.2835i	0.510279	−	0.294610i	0.732948	+	0.680284i	$0.238144\pi$
$338$		0			0
$339$	−15.5104	−	26.8648i	−0.0457534	−	0.0792472i
$340$		0			0
$341$		−	45.5978i		−	0.133718i
$342$		0			0
$343$	210.444			0.613539
$344$		0			0
$345$	−0.855043	+	0.493659i	−0.00247838	+	0.00143090i
$346$		0			0
$347$	−239.116	−	414.161i	−0.689095	−	1.19355i	−0.972131	−	0.234438i	$-0.924675\pi$
$347$	−239.116	−	414.161i	−0.689095	−	1.19355i	0.283036	−	0.959109i	$-0.408658\pi$
$348$		0			0
$349$	363.494			1.04153			0.520766	−	0.853700i	$-0.325646\pi$
$349$	363.494			1.04153			0.520766	+	0.853700i	$0.325646\pi$
$350$		0			0
$351$	27.4256	−	47.5025i	0.0781356	−	0.135335i
$352$		0			0
$353$	260.228			0.737189			0.368595	−	0.929590i	$-0.379839\pi$
$353$	260.228			0.737189			0.368595	+	0.929590i	$0.379839\pi$
$354$		0			0
$355$	−35.4077	−	20.4426i	−0.0997399	−	0.0575848i
$356$		0			0
$357$	−63.7985	−	36.8341i	−0.178707	−	0.103177i
$358$		0			0
$359$	−314.641	−	544.974i	−0.876437	−	1.51803i	−0.855225	−	0.518258i	$-0.826581\pi$
$359$	−314.641	−	544.974i	−0.876437	−	1.51803i	−0.0212119	−	0.999775i	$-0.506752\pi$
$360$		0			0
$361$	4.08685	+	360.977i	0.0113209	+	0.999936i
$362$		0			0
$363$	176.568	−	101.942i	0.486413	−	0.280831i
$364$		0			0
$365$	39.0325	−	67.6062i	0.106938	−	0.185223i
$366$		0			0
$367$	−86.9136	+	150.539i	−0.236822	+	0.410188i	−0.959801	−	0.280683i	$-0.909439\pi$
$367$	−86.9136	+	150.539i	−0.236822	+	0.410188i	0.722979	+	0.690870i	$0.242772\pi$
$368$		0			0
$369$		−	171.120i		−	0.463739i
$370$		0			0
$371$	−21.0480	−	12.1521i	−0.0567332	−	0.0327550i
$372$		0			0
$373$			154.949i			0.415414i	0.978191	+	0.207707i	$0.0666000\pi$
$373$			154.949i			0.415414i	−0.978191	+	0.207707i	$0.933400\pi$
$374$		0			0
$375$	−48.8286	+	28.1912i	−0.130210	+	0.0751766i
$376$		0			0
$377$	34.4469	+	59.6638i	0.0913711	+	0.158259i
$378$		0			0
$379$			273.948i			0.722819i	0.932407	+	0.361409i	$0.117704\pi$
$379$			273.948i			0.722819i	−0.932407	+	0.361409i	$0.882296\pi$
$380$		0			0
$381$	199.365			0.523268
$382$		0			0
$383$	300.575	−	173.537i	0.784792	−	0.453100i	−0.0533339	−	0.998577i	$-0.516985\pi$
$383$	300.575	−	173.537i	0.784792	−	0.453100i	0.838126	+	0.545477i	$0.183651\pi$
$384$		0			0
$385$	−1.34928	−	2.33702i	−0.00350463	−	0.00607019i
$386$		0			0
$387$	−120.420			−0.311163
$388$		0			0
$389$	−353.091	+	611.572i	−0.907689	+	1.57216i	−0.0904228	+	0.995903i	$0.528822\pi$
$389$	−353.091	+	611.572i	−0.907689	+	1.57216i	−0.817266	+	0.576260i	$0.804511\pi$
$390$		0			0
$391$	−16.2913			−0.0416656
$392$		0			0
$393$	−108.593	−	62.6960i	−0.276317	−	0.159532i
$394$		0			0
$395$	4.01549	+	2.31834i	0.0101658	+	0.00586922i
$396$		0			0
$397$	−140.955	−	244.141i	−0.355050	−	0.614965i	0.632076	−	0.774906i	$-0.282203\pi$
$397$	−140.955	−	244.141i	−0.355050	−	0.614965i	−0.987127	+	0.159941i	$0.948870\pi$
$398$		0			0
$399$	72.1431	+	18.8937i	0.180810	+	0.0473525i
$400$		0			0
$401$	600.609	−	346.762i	1.49778	−	0.864743i	0.497782	−	0.867302i	$-0.334148\pi$
$401$	600.609	−	346.762i	1.49778	−	0.864743i	0.999997	+	0.00255898i	$0.000814550\pi$
$402$		0			0
$403$	−132.723	+	229.883i	−0.329338	+	0.570430i
$404$		0			0
$405$	2.95521	−	5.11857i	0.00729681	−	0.0126384i
$406$		0			0
$407$		−	109.679i		−	0.269480i
$408$		0			0
$409$	478.575	+	276.306i	1.17011	+	0.675564i	0.953706	−	0.300740i	$-0.0972337\pi$
$409$	478.575	+	276.306i	1.17011	+	0.675564i	0.216404	+	0.976304i	$0.430567\pi$
$410$		0			0
$411$		−	98.8341i		−	0.240472i
$412$		0			0
$413$	−123.130	+	71.0889i	−0.298135	+	0.172128i
$414$		0			0
$415$	−3.06102	−	5.30184i	−0.00737595	−	0.0127755i
$416$		0			0
$417$		−	44.3234i		−	0.106291i
$418$		0			0
$419$	719.822			1.71795			0.858976	−	0.512015i	$-0.171101\pi$
$419$	719.822			1.71795			0.858976	+	0.512015i	$0.171101\pi$
$420$		0			0
$421$	262.530	−	151.572i	0.623587	−	0.360028i	−0.154677	−	0.987965i	$-0.549434\pi$
$421$	262.530	−	151.572i	0.623587	−	0.360028i	0.778264	+	0.627937i	$0.216100\pi$
$422$		0			0
$423$	21.1792	+	36.6835i	0.0500691	+	0.0867222i
$424$		0			0
$425$	−461.123			−1.08499
$426$		0			0
$427$	−82.8289	+	143.464i	−0.193979	+	0.335981i
$428$		0			0
$429$	33.1540			0.0772821
$430$		0			0
$431$	−153.496	−	88.6212i	−0.356140	−	0.205618i	0.311246	−	0.950329i	$-0.399254\pi$
$431$	−153.496	−	88.6212i	−0.356140	−	0.205618i	−0.667386	+	0.744712i	$0.732587\pi$
$432$		0			0
$433$	234.420	+	135.343i	0.541387	+	0.312570i	0.745641	−	0.666348i	$-0.232144\pi$
$433$	234.420	+	135.343i	0.541387	+	0.312570i	−0.204254	+	0.978918i	$0.565477\pi$
$434$		0			0
$435$	3.71178	+	6.42899i	0.00853282	+	0.0147793i
$436$		0			0
$437$	15.9057	−	4.35856i	0.0363975	−	0.00997383i
$438$		0			0
$439$	109.727	−	63.3509i	0.249947	−	0.144307i	−0.369793	−	0.929114i	$-0.620571\pi$
$439$	109.727	−	63.3509i	0.249947	−	0.144307i	0.619740	+	0.784807i	$0.287238\pi$
$440$		0			0
$441$	−65.7969	+	113.964i	−0.149199	+	0.258421i
$442$		0			0
$443$	−212.450	+	367.974i	−0.479571	+	0.830642i	−0.999725	−	0.0234307i	$-0.992541\pi$
$443$	−212.450	+	367.974i	−0.479571	+	0.830642i	0.520154	+	0.854072i	$0.325874\pi$
$444$		0			0
$445$			19.0410i			0.0427888i
$446$		0			0
$447$	−430.161	−	248.354i	−0.962329	−	0.555601i
$448$		0			0
$449$			46.5643i			0.103707i	0.998655	+	0.0518534i	$0.0165129\pi$
$449$			46.5643i			0.103707i	−0.998655	+	0.0518534i	$0.983487\pi$
$450$		0			0
$451$	89.5737	−	51.7154i	0.198611	−	0.114668i
$452$		0			0
$453$	−62.0450	−	107.465i	−0.136965	−	0.237230i
$454$		0			0
$455$			15.7096i			0.0345266i
$456$		0			0
$457$	−613.609			−1.34269			−0.671345	−	0.741145i	$-0.734283\pi$
$457$	−613.609			−1.34269			−0.671345	+	0.741145i	$0.734283\pi$
$458$		0			0
$459$	84.4590	−	48.7625i	0.184007	−	0.106236i
$460$		0			0
$461$	−310.683	−	538.119i	−0.673933	−	1.16729i	−0.976780	−	0.214247i	$-0.931270\pi$
$461$	−310.683	−	538.119i	−0.673933	−	1.16729i	0.302847	−	0.953039i	$-0.402063\pi$
$462$		0			0
$463$	−627.019			−1.35425			−0.677126	−	0.735867i	$-0.736775\pi$
$463$	−627.019			−1.35425			−0.677126	+	0.735867i	$0.736775\pi$
$464$		0			0
$465$	−14.3014	+	24.7707i	−0.0307557	+	0.0532704i
$466$		0			0
$467$	−75.6962			−0.162090			−0.0810452	−	0.996710i	$-0.525826\pi$
$467$	−75.6962			−0.162090			−0.0810452	+	0.996710i	$0.525826\pi$
$468$		0			0
$469$	−60.4607	−	34.9070i	−0.128914	−	0.0744286i
$470$		0			0
$471$	143.807	+	83.0269i	0.305322	+	0.176278i
$472$		0			0
$473$	−36.3932	−	63.0348i	−0.0769411	−	0.133266i
$474$		0			0
$475$	450.209	−	123.369i	0.947808	−	0.259723i
$476$		0			0
$477$	27.8642	−	16.0874i	0.0584156	−	0.0337262i
$478$		0			0
$479$	−158.834	+	275.108i	−0.331595	+	0.574339i	−0.982825	−	0.184541i	$-0.940920\pi$
$479$	−158.834	+	275.108i	−0.331595	+	0.574339i	0.651230	+	0.758881i	$0.274253\pi$
$480$		0			0
$481$	−319.245	+	552.949i	−0.663711	+	1.14958i
$482$		0			0
$483$		−	3.40697i		−	0.00705376i
$484$		0			0
$485$	−9.41925	−	5.43821i	−0.0194211	−	0.0112128i
$486$		0			0
$487$			777.789i			1.59710i	0.601926	+	0.798552i	$0.294400\pi$
$487$			777.789i			1.59710i	−0.601926	+	0.798552i	$0.705600\pi$
$488$		0			0
$489$	−231.448	+	133.626i	−0.473308	+	0.273264i
$490$		0			0
$491$	207.858	+	360.021i	0.423337	+	0.733241i	0.996263	−	0.0863659i	$-0.0275254\pi$
$491$	207.858	+	360.021i	0.423337	+	0.733241i	−0.572927	+	0.819607i	$0.694192\pi$
$492$		0			0
$493$			122.493i			0.248464i
$494$		0			0
$495$	3.57247			0.00721710
$496$		0			0
$497$	122.182	−	70.5419i	0.245839	−	0.141935i
$498$		0			0
$499$	472.160	+	817.804i	0.946211	+	1.63889i	0.753307	+	0.657669i	$0.228457\pi$
$499$	472.160	+	817.804i	0.946211	+	1.63889i	0.192904	+	0.981218i	$0.438209\pi$
$500$		0			0
$501$	221.464			0.442044
$502$		0			0
$503$	−329.108	+	570.033i	−0.654291	+	1.13327i	0.327780	+	0.944754i	$0.393700\pi$
$503$	−329.108	+	570.033i	−0.654291	+	1.13327i	−0.982071	+	0.188511i	$0.939634\pi$
$504$		0			0
$505$	−66.9695			−0.132613
$506$		0			0
$507$	86.3525	+	49.8556i	0.170320	+	0.0983346i
$508$		0			0
$509$	470.886	+	271.866i	0.925120	+	0.534118i	0.885265	−	0.465087i	$-0.153977\pi$
$509$	470.886	+	271.866i	0.925120	+	0.534118i	0.0398553	+	0.999205i	$0.487310\pi$
$510$		0			0
$511$	134.690	+	233.291i	0.263582	+	0.456537i
$512$		0			0
$513$	−69.4142	+	70.2045i	−0.135310	+	0.136851i
$514$		0			0
$515$	3.73780	−	2.15802i	0.00725787	−	0.00419033i
$516$		0			0
$517$	−12.8015	+	22.1728i	−0.0247611	+	0.0428874i
$518$		0			0
$519$	−79.4727	+	137.651i	−0.153127	+	0.265223i
$520$		0			0
$521$		−	377.781i		−	0.725107i	−0.931963	−	0.362553i	$-0.881905\pi$
$521$		−	377.781i		−	0.725107i	0.931963	−	0.362553i	$-0.118095\pi$
$522$		0			0
$523$	330.661	+	190.907i	0.632239	+	0.365024i	0.781619	−	0.623756i	$-0.214394\pi$
$523$	330.661	+	190.907i	0.632239	+	0.365024i	−0.149379	+	0.988780i	$0.547728\pi$
$524$		0			0
$525$		−	96.4338i		−	0.183683i
$526$		0			0
$527$	−408.730	+	235.980i	−0.775578	+	0.447780i
$528$		0			0
$529$	264.123	+	457.475i	0.499288	+	0.864792i
$530$		0			0
$531$		−	188.221i		−	0.354465i
$532$		0			0
$533$	−602.120			−1.12968
$534$		0			0
$535$	−70.9128	+	40.9415i	−0.132547	+	0.0765262i
$536$		0			0
$537$	−43.3537	−	75.0908i	−0.0807331	−	0.139834i
$538$		0			0
$539$	−79.5401			−0.147570
$540$		0			0
$541$	−30.2609	+	52.4134i	−0.0559351	+	0.0968824i	−0.892637	−	0.450776i	$-0.851147\pi$
$541$	−30.2609	+	52.4134i	−0.0559351	+	0.0968824i	0.836702	+	0.547658i	$0.184481\pi$
$542$		0			0
$543$	−87.3451			−0.160857
$544$		0			0
$545$	−31.6269	−	18.2598i	−0.0580310	−	0.0335042i
$546$		0			0
$547$	−245.181	−	141.555i	−0.448228	−	0.258785i	0.258853	−	0.965917i	$-0.416655\pi$
$547$	−245.181	−	141.555i	−0.448228	−	0.258785i	−0.707082	+	0.707132i	$0.749989\pi$
$548$		0			0
$549$	−109.652	−	189.923i	−0.199731	−	0.345944i
$550$		0			0
$551$	−32.7716	−	119.593i	−0.0594766	−	0.217048i
$552$		0			0
$553$	−13.8563	+	7.99997i	−0.0250567	+	0.0144665i
$554$		0			0
$555$	−34.3998	+	59.5822i	−0.0619816	+	0.107355i
$556$		0			0
$557$	−360.781	+	624.891i	−0.647722	+	1.12189i	0.335944	+	0.941882i	$0.390945\pi$
$557$	−360.781	+	624.891i	−0.647722	+	1.12189i	−0.983666	+	0.180005i	$0.942389\pi$
$558$		0			0
$559$			423.724i			0.758003i
$560$		0			0
$561$	51.0501	+	29.4738i	0.0909984	+	0.0525379i
$562$		0			0
$563$			751.762i			1.33528i	0.744485	+	0.667639i	$0.232695\pi$
$563$			751.762i			1.33528i	−0.744485	+	0.667639i	$0.767305\pi$
$564$		0			0
$565$	−10.1859	+	5.88082i	−0.0180281	+	0.0104085i
$566$		0			0
$567$	10.1976	+	17.6628i	0.0179852	+	0.0311513i
$568$		0			0
$569$		−	238.054i		−	0.418373i	−0.977876	−	0.209187i	$-0.932918\pi$
$569$		−	238.054i		−	0.418373i	0.977876	−	0.209187i	$-0.0670816\pi$
$570$		0			0
$571$	−495.732			−0.868181			−0.434091	−	0.900869i	$-0.642930\pi$
$571$	−495.732			−0.868181			−0.434091	+	0.900869i	$0.642930\pi$
$572$		0			0
$573$	437.724	−	252.720i	0.763916	−	0.441047i
$574$		0			0
$575$	−10.6629	−	18.4686i	−0.0185441	−	0.0321193i
$576$		0			0
$577$	−157.556			−0.273061			−0.136530	−	0.990636i	$-0.543595\pi$
$577$	−157.556			−0.273061			−0.136530	+	0.990636i	$0.543595\pi$
$578$		0			0
$579$	−167.552	+	290.208i	−0.289381	+	0.501222i
$580$		0			0
$581$	21.1255			0.0363605
$582$		0			0
$583$	16.8421	+	9.72381i	0.0288887	+	0.0166789i
$584$		0			0
$585$	−18.0107	−	10.3985i	−0.0307876	−	0.0177752i
$586$		0			0
$587$	−321.681	−	557.168i	−0.548009	−	0.949179i	−0.998411	−	0.0563531i	$-0.982053\pi$
$587$	−321.681	−	557.168i	−0.548009	−	0.949179i	0.450402	−	0.892826i	$-0.351281\pi$
$588$		0			0
$589$	335.922	−	339.747i	0.570326	−	0.576819i
$590$		0			0
$591$	−1.63812	+	0.945770i	−0.00277178	+	0.00160029i
$592$		0			0
$593$	310.939	−	538.562i	0.524349	−	0.908199i	−0.475249	−	0.879851i	$-0.657642\pi$
$593$	310.939	−	538.562i	0.524349	−	0.908199i	0.999598	−	0.0283475i	$-0.00902449\pi$
$594$		0			0
$595$	−13.9658	+	24.1894i	−0.0234719	+	0.0406545i
$596$		0			0
$597$		−	130.658i		−	0.218857i
$598$		0			0
$599$	970.603	+	560.378i	1.62037	+	0.935523i	0.986820	+	0.161824i	$0.0517377\pi$
$599$	970.603	+	560.378i	1.62037	+	0.935523i	0.633553	+	0.773699i	$0.281596\pi$
$600$		0			0
$601$			428.686i			0.713288i	0.934240	+	0.356644i	$0.116079\pi$
$601$			428.686i			0.713288i	−0.934240	+	0.356644i	$0.883921\pi$
$602$		0			0
$603$	80.0403	−	46.2113i	0.132737	−	0.0766357i
$604$		0			0
$605$	−38.6514	−	66.9463i	−0.0638867	−	0.110655i
$606$		0			0
$607$			175.626i			0.289334i	0.989480	+	0.144667i	$0.0462111\pi$
$607$			175.626i			0.289334i	−0.989480	+	0.144667i	$0.953789\pi$
$608$		0			0
$609$	−25.6167			−0.0420635
$610$		0			0
$611$	129.078	−	74.5235i	0.211258	−	0.121970i
$612$		0			0
$613$	−141.913	−	245.801i	−0.231506	−	0.400980i	0.726746	−	0.686907i	$-0.241032\pi$
$613$	−141.913	−	245.801i	−0.231506	−	0.400980i	−0.958251	+	0.285927i	$0.907699\pi$
$614$		0			0
$615$	−64.8805			−0.105497
$616$		0			0
$617$	225.883	−	391.241i	0.366099	−	0.634102i	−0.622853	−	0.782339i	$-0.714026\pi$
$617$	225.883	−	391.241i	0.366099	−	0.634102i	0.988952	+	0.148237i	$0.0473598\pi$
$618$		0			0
$619$	680.497			1.09935			0.549674	−	0.835379i	$-0.314752\pi$
$619$	680.497			1.09935			0.549674	+	0.835379i	$0.314752\pi$
$620$		0			0
$621$	3.90601	+	2.25514i	0.00628988	+	0.00363146i
$622$		0			0
$623$	−56.9025	−	32.8527i	−0.0913363	−	0.0527331i
$624$		0			0
$625$	−296.420	−	513.415i	−0.474273	−	0.821464i
$626$		0			0
$627$	−57.7272	−	15.1183i	−0.0920690	−	0.0241121i
$628$		0			0
$629$	−983.138	+	567.615i	−1.56302	+	0.902408i
$630$		0			0
$631$	−146.304	+	253.406i	−0.231861	+	0.401595i	−0.958356	−	0.285577i	$-0.907815\pi$
$631$	−146.304	+	253.406i	−0.231861	+	0.401595i	0.726495	+	0.687172i	$0.241148\pi$
$632$		0			0
$633$	−174.258	+	301.824i	−0.275289	+	0.476815i
$634$		0			0
$635$		−	75.5899i		−	0.119039i
$636$		0			0
$637$	401.005	+	231.520i	0.629521	+	0.363454i
$638$		0			0
$639$			186.772i			0.292288i
$640$		0			0
$641$	279.493	−	161.366i	0.436027	−	0.251740i	−0.265884	−	0.964005i	$-0.585664\pi$
$641$	279.493	−	161.366i	0.436027	−	0.251740i	0.701911	+	0.712265i	$0.252330\pi$
$642$		0			0
$643$	249.132	+	431.509i	0.387452	+	0.671087i	0.992106	−	0.125401i	$-0.0400219\pi$
$643$	249.132	+	431.509i	0.387452	+	0.671087i	−0.604654	+	0.796488i	$0.706689\pi$
$644$		0			0
$645$			45.6577i			0.0707872i
$646$		0			0
$647$	613.998			0.948992			0.474496	−	0.880258i	$-0.342630\pi$
$647$	613.998			0.948992			0.474496	+	0.880258i	$0.342630\pi$
$648$		0			0
$649$	98.5254	−	56.8837i	0.151811	−	0.0876482i
$650$		0			0
$651$	−49.3501	−	85.4770i	−0.0758067	−	0.131301i
$652$		0			0
$653$	123.792			0.189575			0.0947873	−	0.995498i	$-0.469783\pi$
$653$	123.792			0.189575			0.0947873	+	0.995498i	$0.469783\pi$
$654$		0			0
$655$	−23.7714	+	41.1733i	−0.0362922	+	0.0628599i
$656$		0			0
$657$	−356.617			−0.542796
$658$		0			0
$659$	251.555	+	145.235i	0.381722	+	0.220387i	0.678567	−	0.734538i	$-0.262601\pi$
$659$	251.555	+	145.235i	0.381722	+	0.220387i	−0.296845	+	0.954926i	$0.595935\pi$
$660$		0			0
$661$	125.439	+	72.4222i	0.189771	+	0.109565i	0.591876	−	0.806029i	$-0.298388\pi$
$661$	125.439	+	72.4222i	0.189771	+	0.109565i	−0.402104	+	0.915594i	$0.631721\pi$
$662$		0			0
$663$	−171.581	−	297.187i	−0.258795	−	0.448245i
$664$		0			0
$665$	7.16359	−	27.3533i	0.0107723	−	0.0411328i
$666$		0			0
$667$	−4.90600	+	2.83248i	−0.00735533	+	0.00424660i
$668$		0			0
$669$	98.6819	−	170.922i	0.147507	−	0.255489i
$670$		0			0
$671$	66.2777	−	114.796i	0.0987745	−	0.171082i
$672$		0			0
$673$		−	780.307i		−	1.15945i	−0.814814	−	0.579723i	$-0.803161\pi$
$673$		−	780.307i		−	1.15945i	0.814814	−	0.579723i	$-0.196839\pi$
$674$		0			0
$675$	110.559	+	63.8314i	0.163792	+	0.0945651i
$676$		0			0
$677$		−	719.919i		−	1.06340i	−0.846934	−	0.531698i	$-0.821554\pi$
$677$		−	719.919i		−	1.06340i	0.846934	−	0.531698i	$-0.178446\pi$
$678$		0			0
$679$	32.5033	−	18.7658i	0.0478693	−	0.0276374i
$680$		0			0
$681$	136.347	+	236.159i	0.200215	+	0.346783i
$682$		0			0
$683$			762.545i			1.11646i	0.829685	+	0.558232i	$0.188520\pi$
$683$			762.545i			1.11646i	−0.829685	+	0.558232i	$0.811480\pi$
$684$		0			0
$685$	−37.4733			−0.0547055
$686$		0			0
$687$	240.701	−	138.969i	0.350365	−	0.202283i
$688$		0			0
$689$	−56.6069	−	98.0460i	−0.0821581	−	0.142302i
$690$		0			0
$691$	−838.857			−1.21398			−0.606988	−	0.794711i	$-0.707622\pi$
$691$	−838.857			−1.21398			−0.606988	+	0.794711i	$0.707622\pi$
$692$		0			0
$693$	−6.16380	+	10.6760i	−0.00889437	+	0.0154055i
$694$		0			0
$695$	−16.8054			−0.0241804
$696$		0			0
$697$	−927.135	−	535.281i	−1.33018	−	0.767979i
$698$		0			0
$699$	−347.827	−	200.818i	−0.497606	−	0.287293i
$700$		0			0
$701$	−419.431	−	726.476i	−0.598333	−	1.03634i	−0.993067	−	0.117548i	$-0.962497\pi$
$701$	−419.431	−	726.476i	−0.598333	−	1.03634i	0.394735	−	0.918795i	$-0.370837\pi$
$702$		0			0
$703$	808.009	−	817.209i	1.14937	−	1.16246i
$704$		0			0
$705$	13.9087	−	8.03017i	0.0197286	−	0.0113903i
$706$		0			0
$707$	115.547	−	200.133i	0.163432	−	0.283073i
$708$		0			0
$709$	−220.519	+	381.950i	−0.311028	+	0.538716i	−0.978585	−	0.205842i	$-0.934007\pi$
$709$	−220.519	+	381.950i	−0.311028	+	0.538716i	0.667557	+	0.744559i	$0.267340\pi$
$710$		0			0
$711$		−	21.1814i		−	0.0297909i
$712$		0			0
$713$	−18.9027	−	10.9135i	−0.0265115	−	0.0153064i
$714$		0			0
$715$		−	12.5705i		−	0.0175811i
$716$		0			0
$717$	81.1129	−	46.8305i	0.113128	−	0.0653145i
$718$		0			0
$719$	165.024	+	285.829i	0.229518	+	0.397537i	0.957665	−	0.287884i	$-0.0929516\pi$
$719$	165.024	+	285.829i	0.229518	+	0.397537i	−0.728147	+	0.685421i	$0.759618\pi$
$720$		0			0
$721$			14.8935i			0.0206567i
$722$		0			0
$723$	494.540			0.684012
$724$		0			0
$725$	−138.864	+	80.1731i	−0.191536	+	0.110584i
$726$		0			0
$727$	−566.437	−	981.098i	−0.779143	−	1.34952i	−0.932436	−	0.361335i	$-0.882321\pi$
$727$	−566.437	−	981.098i	−0.779143	−	1.34952i	0.153293	−	0.988181i	$-0.451012\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	−376.688	+	652.443i	−0.515305	+	0.892535i
$732$		0			0
$733$	1276.95			1.74209			0.871047	−	0.491200i	$-0.163442\pi$
$733$	1276.95			1.74209			0.871047	+	0.491200i	$0.163442\pi$
$734$		0			0
$735$	43.2097	+	24.9471i	0.0587887	+	0.0339417i
$736$		0			0
$737$	48.3792	+	27.9318i	0.0656435	+	0.0378993i
$738$		0			0
$739$	−216.933	−	375.740i	−0.293550	−	0.508444i	0.681097	−	0.732194i	$-0.261503\pi$
$739$	−216.933	−	375.740i	−0.293550	−	0.508444i	−0.974647	+	0.223750i	$0.928170\pi$
$740$		0			0
$741$	247.029	+	244.248i	0.333373	+	0.329620i
$742$		0			0
$743$	1075.19	−	620.759i	1.44709	−	0.835476i	0.448780	−	0.893642i	$-0.351859\pi$
$743$	1075.19	−	620.759i	1.44709	−	0.835476i	0.998307	+	0.0581665i	$0.0185254\pi$
$744$		0			0
$745$	−94.1640	+	163.097i	−0.126395	+	0.218922i
$746$		0			0
$747$	−13.9834	+	24.2199i	−0.0187194	+	0.0324229i
$748$		0			0
$749$		−	282.556i		−	0.377244i
$750$		0			0
$751$	136.939	+	79.0619i	0.182342	+	0.105275i	0.588393	−	0.808575i	$-0.299761\pi$
$751$	136.939	+	79.0619i	0.182342	+	0.105275i	−0.406050	+	0.913851i	$0.633094\pi$
$752$		0			0
$753$			336.633i			0.447055i
$754$		0			0
$755$	−40.7457	+	23.5246i	−0.0539679	+	0.0311584i
$756$		0			0
$757$	109.456	+	189.583i	0.144591	+	0.250440i	0.929220	−	0.369526i	$-0.120480\pi$
$757$	109.456	+	189.583i	0.144591	+	0.250440i	−0.784629	+	0.619965i	$0.787147\pi$
$758$		0			0
$759$			2.72617i			0.00359180i
$760$		0			0
$761$	416.836			0.547747			0.273874	−	0.961766i	$-0.411695\pi$
$761$	416.836			0.547747			0.273874	+	0.961766i	$0.411695\pi$
$762$		0			0
$763$	109.136	−	63.0096i	0.143035	−	0.0825814i
$764$		0			0
$765$	−18.4884	−	32.0229i	−0.0241679	−	0.0418600i
$766$		0			0
$767$	−662.294			−0.863486
$768$		0			0
$769$	506.164	−	876.702i	0.658211	−	1.14006i	−0.322867	−	0.946444i	$-0.604647\pi$
$769$	506.164	−	876.702i	0.658211	−	1.14006i	0.981078	−	0.193611i	$-0.0620199\pi$
$770$		0			0
$771$	−210.874			−0.273507
$772$		0			0
$773$	−795.342	−	459.191i	−1.02890	−	0.594038i	−0.112233	−	0.993682i	$-0.535800\pi$
$773$	−795.342	−	459.191i	−1.02890	−	0.594038i	−0.916670	+	0.399644i	$0.869134\pi$
$774$		0			0
$775$	−535.039	−	308.905i	−0.690373	−	0.398587i
$776$		0			0
$777$	−118.704	−	205.602i	−0.152773	−	0.264610i
$778$		0			0
$779$	1048.40	+	274.567i	1.34583	+	0.352461i
$780$		0			0
$781$	−97.7672	+	56.4459i	−0.125182	+	0.0722739i
$782$		0			0
$783$	16.9562	−	29.3690i	0.0216554	−	0.0375082i
$784$		0			0
$785$	31.4799	−	54.5248i	0.0401018	−	0.0694584i
$786$		0			0
$787$		−	535.460i		−	0.680382i	−0.940356	−	0.340191i	$-0.889508\pi$
$787$		−	535.460i		−	0.680382i	0.940356	−	0.340191i	$-0.110492\pi$
$788$		0			0
$789$	759.223	+	438.337i	0.962259	+	0.555561i
$790$		0			0
$791$		−	40.5862i		−	0.0513100i
$792$		0			0
$793$	−668.284	+	385.834i	−0.842728	+	0.486550i
$794$		0			0
$795$	−6.09959	−	10.5648i	−0.00767245	−	0.0132891i
$796$		0			0
$797$		−	769.746i		−	0.965804i	−0.875674	−	0.482902i	$-0.839583\pi$
$797$		−	769.746i		−	0.965804i	0.875674	−	0.482902i	$-0.160417\pi$
$798$		0			0
$799$	265.004			0.331669
$800$		0			0
$801$	75.3299	−	43.4917i	0.0940448	−	0.0542968i
$802$		0			0
$803$	−107.776	−	186.674i	−0.134217	−	0.232470i
$804$		0			0
$805$	−1.29176			−0.00160467
$806$		0			0
$807$	−143.295	+	248.195i	−0.177566	+	0.307553i
$808$		0			0
$809$	−530.804			−0.656123			−0.328062	−	0.944656i	$-0.606395\pi$
$809$	−530.804			−0.656123			−0.328062	+	0.944656i	$0.606395\pi$
$810$		0			0
$811$	−1285.26	−	742.048i	−1.58479	−	0.914979i	−0.994146	−	0.108046i	$-0.965541\pi$
$811$	−1285.26	−	742.048i	−1.58479	−	0.914979i	−0.590644	−	0.806933i	$-0.701126\pi$
$812$		0			0
$813$	604.799	+	349.181i	0.743910	+	0.429497i
$814$		0			0
$815$	50.6648	+	87.7541i	0.0621654	+	0.107674i
$816$		0			0
$817$	193.218	−	737.780i	0.236497	−	0.903036i
$818$		0			0
$819$	62.1501	−	35.8824i	0.0758854	−	0.0438124i
$820$		0			0
$821$	−596.069	+	1032.42i	−0.726027	+	1.25752i	0.232522	+	0.972591i	$0.425302\pi$
$821$	−596.069	+	1032.42i	−0.726027	+	1.25752i	−0.958550	+	0.284925i	$0.908031\pi$
$822$		0			0
$823$	−100.598	+	174.241i	−0.122233	+	0.211714i	−0.920648	−	0.390393i	$-0.872339\pi$
$823$	−100.598	+	174.241i	−0.122233	+	0.211714i	0.798415	+	0.602108i	$0.205672\pi$
$824$		0			0
$825$			77.1640i			0.0935321i
$826$		0			0
$827$	−442.888	−	255.701i	−0.535535	−	0.309191i	0.207732	−	0.978186i	$-0.433392\pi$
$827$	−442.888	−	255.701i	−0.535535	−	0.309191i	−0.743268	+	0.668994i	$0.766725\pi$
$828$		0			0
$829$		−	820.857i		−	0.990178i	−0.868842	−	0.495089i	$-0.835136\pi$
$829$		−	820.857i		−	0.990178i	0.868842	−	0.495089i	$-0.164864\pi$
$830$		0			0
$831$	−273.416	+	157.857i	−0.329020	+	0.189960i
$832$		0			0
$833$	411.641	+	712.982i	0.494166	+	0.855921i
$834$		0			0
$835$		−	83.9689i		−	0.100562i
$836$		0			0
$837$	130.663			0.156109
$838$		0			0
$839$	1129.39	−	652.054i	1.34611	−	0.777179i	0.358418	−	0.933561i	$-0.383316\pi$
$839$	1129.39	−	652.054i	1.34611	−	0.777179i	0.987697	+	0.156382i	$0.0499831\pi$
$840$		0			0
$841$	−399.203	−	691.440i	−0.474676	−	0.822164i
$842$		0			0
$843$	−747.622			−0.886859
$844$		0			0
$845$	18.9029	−	32.7408i	0.0223703	−	0.0387465i
$846$		0			0
$847$	266.751			0.314936
$848$		0			0
$849$	−225.453	−	130.166i	−0.265552	−	0.153316i
$850$		0			0
$851$	−45.4676	−	26.2507i	−0.0534284	−	0.0308469i
$852$		0			0
$853$	165.624	+	286.869i	0.194167	+	0.336306i	0.946627	−	0.322331i	$-0.104466\pi$
$853$	165.624	+	286.869i	0.194167	+	0.336306i	−0.752460	+	0.658637i	$0.771133\pi$
$854$		0			0
$855$	26.6183	+	26.3186i	0.0311325	+	0.0307820i
$856$		0			0
$857$	−471.747	+	272.363i	−0.550463	+	0.317810i	−0.749309	−	0.662221i	$-0.769614\pi$
$857$	−471.747	+	272.363i	−0.550463	+	0.317810i	0.198846	+	0.980031i	$0.436281\pi$
$858$		0			0
$859$	407.112	−	705.138i	0.473937	−	0.820882i	−0.525618	−	0.850721i	$-0.676166\pi$
$859$	407.112	−	705.138i	0.473937	−	0.820882i	0.999555	+	0.0298382i	$0.00949920\pi$
$860$		0			0
$861$	111.942	−	193.890i	0.130014	−	0.225192i
$862$		0			0
$863$			456.762i			0.529272i	0.964348	+	0.264636i	$0.0852518\pi$
$863$			456.762i			0.529272i	−0.964348	+	0.264636i	$0.914748\pi$
$864$		0			0
$865$	52.1907	+	30.1323i	0.0603361	+	0.0348351i
$866$		0			0
$867$		−	109.575i		−	0.126384i
$868$		0			0
$869$	11.0875	−	6.40138i	0.0127589	−	0.00736638i
$870$		0			0
$871$	−162.604	−	281.638i	−0.186687	−	0.323351i
$872$		0			0
$873$			49.6858i			0.0569138i
$874$		0			0
$875$	−73.7681			−0.0843064
$876$		0			0
$877$	597.540	−	344.990i	0.681345	−	0.393375i	−0.119017	−	0.992892i	$-0.537974\pi$
$877$	597.540	−	344.990i	0.681345	−	0.393375i	0.800362	+	0.599518i	$0.204641\pi$
$878$		0			0
$879$	68.4850	+	118.619i	0.0779124	+	0.134948i
$880$		0			0
$881$	668.163			0.758414			0.379207	−	0.925312i	$-0.376197\pi$
$881$	668.163			0.758414			0.379207	+	0.925312i	$0.376197\pi$
$882$		0			0
$883$	377.209	−	653.345i	0.427190	−	0.739915i	−0.569432	−	0.822039i	$-0.692837\pi$
$883$	377.209	−	653.345i	0.427190	−	0.739915i	0.996622	+	0.0821231i	$0.0261701\pi$
$884$		0			0
$885$	−71.3645			−0.0806378
$886$		0			0
$887$	−10.1179	−	5.84155i	−0.0114068	−	0.00658574i	0.494286	−	0.869299i	$-0.335430\pi$
$887$	−10.1179	−	5.84155i	−0.0114068	−	0.00658574i	−0.505693	+	0.862714i	$0.668763\pi$
$888$		0			0
$889$	225.894	+	130.420i	0.254099	+	0.146704i
$890$		0			0
$891$	−8.15988	−	14.1333i	−0.00915812	−	0.0158623i
$892$		0			0
$893$	−258.732	+	70.8991i	−0.289733	+	0.0793943i
$894$		0			0
$895$	−28.4709	+	16.4377i	−0.0318111	+	0.0183661i
$896$		0			0
$897$	7.93517	−	13.7441i	0.00884634	−	0.0153223i
$898$		0			0
$899$	−82.0575	+	142.128i	−0.0912764	+	0.158095i
$900$		0			0
$901$		−	201.293i		−	0.223411i
$902$		0			0
$903$	−136.444	−	78.7761i	−0.151101	−	0.0872382i
$904$		0			0
$905$			33.1172i			0.0365936i
$906$		0			0
$907$	−423.728	+	244.639i	−0.467175	+	0.269724i	−0.715056	−	0.699067i	$-0.753599\pi$
$907$	−423.728	+	244.639i	−0.467175	+	0.269724i	0.247881	+	0.968790i	$0.420266\pi$
$908$		0			0
$909$	152.965	+	264.944i	0.168279	+	0.291467i
$910$		0			0
$911$			790.248i			0.867452i	0.901045	+	0.433726i	$0.142801\pi$
$911$			790.248i			0.867452i	−0.901045	+	0.433726i	$0.857199\pi$
$912$		0			0
$913$	−16.9041			−0.0185149
$914$		0			0
$915$	−72.0099	+	41.5750i	−0.0786994	+	0.0454371i
$916$		0			0
$917$	−82.0286	−	142.078i	−0.0894532	−	0.154937i
$918$		0			0
$919$	728.027			0.792195			0.396098	−	0.918208i	$-0.370364\pi$
$919$	728.027			0.792195			0.396098	+	0.918208i	$0.370364\pi$
$920$		0			0
$921$	−463.571	+	802.929i	−0.503334	+	0.871801i
$922$		0			0
$923$	657.197			0.712023
$924$		0			0
$925$	−1286.95	−	743.024i	−1.39130	−	0.803269i
$926$		0			0
$927$	−17.0751	−	9.85830i	−0.0184197	−	0.0106346i
$928$		0			0
$929$	−458.910	−	794.855i	−0.493982	−	0.855603i	0.505994	−	0.862537i	$-0.331126\pi$
$929$	−458.910	−	794.855i	−0.493982	−	0.855603i	−0.999976	+	0.00693470i	$0.997793\pi$
$930$		0			0
$931$	−592.649	−	585.977i	−0.636573	−	0.629406i
$932$		0			0
$933$	251.366	−	145.126i	0.269417	−	0.155548i
$934$		0			0
$935$	11.1751	−	19.3558i	0.0119520	−	0.0207014i
$936$		0			0
$937$	−522.961	+	905.796i	−0.558123	+	0.966698i	0.439530	+	0.898228i	$0.355145\pi$
$937$	−522.961	+	905.796i	−0.558123	+	0.966698i	−0.997653	+	0.0684699i	$0.978188\pi$
$938$		0			0
$939$		−	278.081i		−	0.296146i
$940$		0			0
$941$	1131.15	+	653.067i	1.20207	+	0.694014i	0.961015	−	0.276498i	$-0.0891739\pi$
$941$	1131.15	+	653.067i	1.20207	+	0.694014i	0.241053	+	0.970512i	$0.422507\pi$
$942$		0			0
$943$		−	49.5108i		−	0.0525035i
$944$		0			0
$945$	6.69690	−	3.86645i	0.00708666	−	0.00409149i
$946$		0			0
$947$	−444.009	−	769.047i	−0.468859	−	0.812087i	0.530508	−	0.847680i	$-0.322001\pi$
$947$	−444.009	−	769.047i	−0.468859	−	0.812087i	−0.999366	+	0.0355929i	$0.988668\pi$
$948$		0			0
$949$			1254.83i			1.32227i
$950$		0			0
$951$	687.892			0.723335
$952$		0			0
$953$	1071.22	−	618.470i	1.12405	−	0.648972i	0.181620	−	0.983369i	$-0.441866\pi$
$953$	1071.22	−	618.470i	1.12405	−	0.648972i	0.942432	+	0.334397i	$0.108533\pi$
$954$		0			0
$955$	−95.8196	−	165.964i	−0.100335	−	0.173785i
$956$		0			0
$957$	20.4978			0.0214188
$958$		0			0
$959$	64.6550	−	111.986i	0.0674192	−	0.116773i
$960$		0			0
$961$	328.670			0.342008
$962$		0			0
$963$	323.944	+	187.029i	0.336391	+	0.194215i
$964$		0			0
$965$	110.033	+	63.5277i	0.114024	+	0.0658318i
$966$		0			0
$967$	−812.688	−	1407.62i	−0.840422	−	1.45565i	−0.889539	−	0.456860i	$-0.848974\pi$
$967$	−812.688	−	1407.62i	−0.840422	−	1.45565i	0.0491170	−	0.998793i	$-0.484359\pi$
$968$		0			0
$969$	163.236	+	595.697i	0.168458	+	0.614754i
$970$		0			0
$971$	615.047	−	355.097i	0.633416	−	0.365703i	−0.148658	−	0.988889i	$-0.547495\pi$
$971$	615.047	−	355.097i	0.633416	−	0.365703i	0.782074	+	0.623186i	$0.214162\pi$
$972$		0			0
$973$	28.9954	−	50.2215i	0.0298000	−	0.0516151i
$974$		0			0
$975$	224.604	−	389.026i	0.230363	−	0.399001i
$976$		0			0
$977$		−	526.491i		−	0.538885i	−0.963016	−	0.269443i	$-0.913161\pi$
$977$		−	526.491i		−	0.538885i	0.963016	−	0.269443i	$-0.0868394\pi$
$978$		0			0
$979$	45.5321	+	26.2880i	0.0465088	+	0.0268518i
$980$		0			0
$981$			166.829i			0.170060i
$982$		0			0
$983$	−1323.98	+	764.399i	−1.34687	+	0.777618i	−0.987806	−	0.155693i	$-0.950239\pi$
$983$	−1323.98	+	764.399i	−1.34687	+	0.777618i	−0.359069	+	0.933311i	$0.616906\pi$
$984$		0			0
$985$	0.358592	+	0.621099i	0.000364053	+	0.000630557i
$986$		0			0
$987$			55.4198i			0.0561498i
$988$		0			0
$989$	−34.8417			−0.0352292
$990$		0			0
$991$	629.893	−	363.669i	0.635614	−	0.366972i	−0.147309	−	0.989090i	$-0.547061\pi$
$991$	629.893	−	363.669i	0.635614	−	0.366972i	0.782923	+	0.622119i	$0.213728\pi$
$992$		0			0
$993$	78.1551	+	135.369i	0.0787061	+	0.136323i
$994$		0			0
$995$	−49.5393			−0.0497882
$996$		0			0
$997$	38.2032	−	66.1698i	0.0383181	−	0.0663689i	−0.846230	−	0.532817i	$-0.821133\pi$
$997$	38.2032	−	66.1698i	0.0383181	−	0.0663689i	0.884548	+	0.466448i	$0.154467\pi$
$998$		0			0
$999$	314.291			0.314606

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	456.3.w.a.145.7	✓	20
3.2	odd	2		1368.3.bv.c.145.4		20
4.3	odd	2		912.3.be.j.145.7		20
19.8	odd	6	inner	456.3.w.a.217.7	yes	20
57.8	even	6		1368.3.bv.c.217.4		20
76.27	even	6		912.3.be.j.673.7		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.3.w.a.145.7	✓	20	1.1	even	1	trivial
456.3.w.a.217.7	yes	20	19.8	odd	6	inner
912.3.be.j.145.7		20	4.3	odd	2
912.3.be.j.673.7		20	76.27	even	6
1368.3.bv.c.145.4		20	3.2	odd	2
1368.3.bv.c.217.4		20	57.8	even	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:	\( N \)	\(=\)	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	456.w (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 + 0.866025i) q^{3} +(0.328356 + 0.568730i) q^{5} -2.26614 q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.50000 + 0.866025i) q^{3} +(0.328356 + 0.568730i) q^{5} -2.26614 q^{7} +(1.50000 - 2.59808i) q^{9} +1.81331 q^{11} +(-9.14187 - 5.27806i) q^{13} +(-0.985069 - 0.568730i) q^{15} +(-9.38434 - 16.2542i) q^{17} +(13.5109 + 13.3588i) q^{19} +(3.39920 - 1.96253i) q^{21} +(0.434002 - 0.751713i) q^{23} +(12.2844 - 21.2771i) q^{25} +5.19615i q^{27} +(-5.65206 - 3.26322i) q^{29} -25.1462i q^{31} +(-2.71996 + 1.57037i) q^{33} +(-0.744100 - 1.28882i) q^{35} -60.4853i q^{37} +18.2837 q^{39} +(49.3980 - 28.5199i) q^{41} +(-20.0700 - 34.7623i) q^{43} +1.97014 q^{45} +(-7.05974 + 12.2278i) q^{47} -43.8646 q^{49} +(28.1530 + 16.2542i) q^{51} +(9.28807 + 5.36247i) q^{53} +(0.595411 + 1.03128i) q^{55} +(-31.8353 - 8.33740i) q^{57} +(54.3347 - 31.3701i) q^{59} +(36.5507 - 63.3077i) q^{61} +(-3.39920 + 5.88759i) q^{63} -6.93234i q^{65} +(26.6801 + 15.4038i) q^{67} +1.50343i q^{69} +(-53.9165 + 31.1287i) q^{71} +(-59.4362 - 102.946i) q^{73} +42.5543i q^{75} -4.10920 q^{77} +(6.11453 - 3.53023i) q^{79} +(-4.50000 - 7.79423i) q^{81} -9.32225 q^{83} +(6.16281 - 10.6743i) q^{85} +11.3041 q^{87} +(25.1100 + 14.4972i) q^{89} +(20.7167 + 11.9608i) q^{91} +(21.7772 + 37.7193i) q^{93} +(-3.16115 + 12.0705i) q^{95} +(-14.3430 + 8.28096i) q^{97} +(2.71996 - 4.71111i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 30 q^{3} + 20 q^{7} + 30 q^{9}+O(q^{10}) \) 20 * q - 30 * q^3 + 20 * q^7 + 30 * q^9	\( 20 q - 30 q^{3} + 20 q^{7} + 30 q^{9} - 8 q^{11} + 18 q^{13} + 8 q^{17} + 28 q^{19} - 30 q^{21} - 8 q^{23} - 58 q^{25} + 108 q^{29} + 12 q^{33} + 20 q^{35} - 36 q^{39} - 36 q^{41} - 2 q^{43} + 296 q^{49} - 24 q^{51} - 72 q^{53} + 216 q^{55} - 30 q^{57} + 72 q^{59} - 26 q^{61} + 30 q^{63} + 138 q^{67} - 204 q^{71} + 218 q^{73} - 8 q^{77} - 78 q^{79} - 90 q^{81} - 112 q^{83} + 224 q^{85} - 216 q^{87} - 432 q^{89} - 330 q^{91} - 126 q^{93} + 220 q^{95} + 132 q^{97} - 12 q^{99}+O(q^{100}) \) 20 * q - 30 * q^3 + 20 * q^7 + 30 * q^9 - 8 * q^11 + 18 * q^13 + 8 * q^17 + 28 * q^19 - 30 * q^21 - 8 * q^23 - 58 * q^25 + 108 * q^29 + 12 * q^33 + 20 * q^35 - 36 * q^39 - 36 * q^41 - 2 * q^43 + 296 * q^49 - 24 * q^51 - 72 * q^53 + 216 * q^55 - 30 * q^57 + 72 * q^59 - 26 * q^61 + 30 * q^63 + 138 * q^67 - 204 * q^71 + 218 * q^73 - 8 * q^77 - 78 * q^79 - 90 * q^81 - 112 * q^83 + 224 * q^85 - 216 * q^87 - 432 * q^89 - 330 * q^91 - 126 * q^93 + 220 * q^95 + 132 * q^97 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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