LMFDB - Embedded newform 1216.2.n.f.639.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1216,2,Mod(255,1216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1216, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1216.255");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1216 = 2^{6} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1216.n (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.70980888579$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 6 x^{14} - 9 x^{13} + 12 x^{12} - 9 x^{11} + 3 x^{10} + 6 x^{9} - 10 x^{8} + \cdots + 256 $ x^16 - 3x^15 + 6x^14 - 9x^13 + 12x^12 - 9x^11 + 3x^10 + 6x^9 - 10x^8 + 12x^7 + 12x^6 - 72x^5 + 192x^4 - 288x^3 + 384x^2 - 384*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 76)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			639.4
Root			$1.16486 + 0.801943i$ of defining polynomial
Character	$\chi$	$=$	1216.639
Dual form			1216.2.n.f.255.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.305055 - 0.528371i) q^{3} +(-1.59295 - 2.75907i) q^{5} -2.36291i q^{7} +(1.31388 - 2.27571i) q^{9} -5.46750i q^{11} +(2.31924 + 1.33901i) q^{13} +(-0.971875 + 1.68334i) q^{15} +(-0.552780 - 0.957443i) q^{17} +(1.37952 + 4.13484i) q^{19} +(-1.24849 + 0.720818i) q^{21} +(-2.46168 - 1.42125i) q^{23} +(-2.57499 + 4.46001i) q^{25} -3.43356 q^{27} +(5.63736 + 3.25473i) q^{29} -1.01504 q^{31} +(-2.88887 + 1.66789i) q^{33} +(-6.51945 + 3.76400i) q^{35} +0.450315i q^{37} -1.63389i q^{39} +(0.336089 - 0.194041i) q^{41} +(-4.96197 + 2.86479i) q^{43} -8.37180 q^{45} +(-2.91563 - 1.68334i) q^{47} +1.41665 q^{49} +(-0.337257 + 0.584146i) q^{51} +(3.53036 + 2.03825i) q^{53} +(-15.0852 + 8.70946i) q^{55} +(1.76390 - 1.99025i) q^{57} +(-6.82450 - 11.8204i) q^{59} +(6.77885 - 11.7413i) q^{61} +(-5.37731 - 3.10459i) q^{63} -8.53193i q^{65} +(-4.27064 + 7.39696i) q^{67} +1.73424i q^{69} +(-1.07447 - 1.86103i) q^{71} +(3.91944 + 6.78867i) q^{73} +3.14205 q^{75} -12.9192 q^{77} +(5.57208 + 9.65112i) q^{79} +(-2.89422 - 5.01294i) q^{81} -4.14868i q^{83} +(-1.76110 + 3.05032i) q^{85} -3.97149i q^{87} +(4.19126 + 2.41982i) q^{89} +(3.16397 - 5.48016i) q^{91} +(0.309642 + 0.536316i) q^{93} +(9.21082 - 10.3928i) q^{95} +(-0.641491 + 0.370365i) q^{97} +(-12.4425 - 7.18366i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{5} - 4 q^{9} + 18 q^{13} + 2 q^{17} - 2 q^{25} + 6 q^{29} + 18 q^{33} - 48 q^{41} - 24 q^{45} + 16 q^{49} - 6 q^{53} - 26 q^{57} + 26 q^{61} + 16 q^{73} - 80 q^{77} + 12 q^{81} - 14 q^{85} + 18 q^{89}+ \cdots - 12 q^{97}+O(q^{100}) $ 16 * q + 2 * q^5 - 4 * q^9 + 18 * q^13 + 2 * q^17 - 2 * q^25 + 6 * q^29 + 18 * q^33 - 48 * q^41 - 24 * q^45 + 16 * q^49 - 6 * q^53 - 26 * q^57 + 26 * q^61 + 16 * q^73 - 80 * q^77 + 12 * q^81 - 14 * q^85 + 18 * q^89 + 20 * q^93 - 12 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times$.

$n$	$191$	$705$	$837$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

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
$3$	−0.305055	−	0.528371i	−0.176124	−	0.305055i	0.764426	−	0.644712i	$-0.223023\pi$
$3$	−0.305055	−	0.528371i	−0.176124	−	0.305055i	−0.940550	+	0.339657i	$0.889689\pi$
$4$		0			0
$5$	−1.59295	−	2.75907i	−0.712389	−	1.23389i	−0.963958	−	0.266055i	$-0.914280\pi$
$5$	−1.59295	−	2.75907i	−0.712389	−	1.23389i	0.251569	−	0.967839i	$-0.419054\pi$
$6$		0			0
$7$		−	2.36291i		−	0.893097i	−0.894759	−	0.446548i	$-0.852653\pi$
$7$		−	2.36291i		−	0.893097i	0.894759	−	0.446548i	$-0.147347\pi$
$8$		0			0
$9$	1.31388	−	2.27571i	0.437961	−	0.758571i
$10$		0			0
$11$		−	5.46750i		−	1.64851i	−0.566216	−	0.824257i	$-0.691593\pi$
$11$		−	5.46750i		−	1.64851i	0.566216	−	0.824257i	$-0.308407\pi$
$12$		0			0
$13$	2.31924	+	1.33901i	0.643241	+	0.371375i	0.785862	−	0.618402i	$-0.212220\pi$
$13$	2.31924	+	1.33901i	0.643241	+	0.371375i	−0.142621	+	0.989777i	$0.545553\pi$
$14$		0			0
$15$	−0.971875	+	1.68334i	−0.250937	+	0.434636i
$16$		0			0
$17$	−0.552780	−	0.957443i	−0.134069	−	0.232214i	0.791173	−	0.611593i	$-0.209471\pi$
$17$	−0.552780	−	0.957443i	−0.134069	−	0.232214i	−0.925241	+	0.379379i	$0.876138\pi$
$18$		0			0
$19$	1.37952	+	4.13484i	0.316484	+	0.948598i
$19$	1.37952	+	4.13484i	0.316484	+	0.948598i
$20$		0			0
$21$	−1.24849	+	0.720818i	−0.272444	+	0.157295i
$22$		0			0
$23$	−2.46168	−	1.42125i	−0.513296	−	0.296352i	0.220891	−	0.975298i	$-0.429103\pi$
$23$	−2.46168	−	1.42125i	−0.513296	−	0.296352i	−0.734187	+	0.678947i	$0.762437\pi$
$24$		0			0
$25$	−2.57499	+	4.46001i	−0.514997	+	0.892001i
$26$		0			0
$27$	−3.43356			−0.660788
$28$		0			0
$29$	5.63736	+	3.25473i	1.04683	+	0.604389i	0.921761	−	0.387759i	$-0.126751\pi$
$29$	5.63736	+	3.25473i	1.04683	+	0.604389i	0.125071	+	0.992148i	$0.460084\pi$
$30$		0			0
$31$	−1.01504			−0.182306			−0.0911531	−	0.995837i	$-0.529055\pi$
$31$	−1.01504			−0.182306			−0.0911531	+	0.995837i	$0.529055\pi$
$32$		0			0
$33$	−2.88887	+	1.66789i	−0.502887	+	0.290342i
$34$		0			0
$35$	−6.51945	+	3.76400i	−1.10199	+	0.636233i
$36$		0			0
$37$			0.450315i			0.0740314i	0.999315	+	0.0370157i	$0.0117851\pi$
$37$			0.450315i			0.0740314i	−0.999315	+	0.0370157i	$0.988215\pi$
$38$		0			0
$39$		−	1.63389i		−	0.261632i
$40$		0			0
$41$	0.336089	−	0.194041i	0.0524882	−	0.0303041i	−0.473526	−	0.880780i	$-0.657019\pi$
$41$	0.336089	−	0.194041i	0.0524882	−	0.0303041i	0.526014	+	0.850476i	$0.323686\pi$
$42$		0			0
$43$	−4.96197	+	2.86479i	−0.756693	+	0.436877i	−0.828107	−	0.560570i	$-0.810582\pi$
$43$	−4.96197	+	2.86479i	−0.756693	+	0.436877i	0.0714141	+	0.997447i	$0.477249\pi$
$44$		0			0
$45$	−8.37180			−1.24799
$46$		0			0
$47$	−2.91563	−	1.68334i	−0.425288	−	0.245540i	0.272049	−	0.962283i	$-0.412299\pi$
$47$	−2.91563	−	1.68334i	−0.425288	−	0.245540i	−0.697337	+	0.716743i	$0.745632\pi$
$48$		0			0
$49$	1.41665			0.202378
$50$		0			0
$51$	−0.337257	+	0.584146i	−0.0472254	+	0.0817967i
$52$		0			0
$53$	3.53036	+	2.03825i	0.484932	+	0.279976i	0.722470	−	0.691403i	$-0.243007\pi$
$53$	3.53036	+	2.03825i	0.484932	+	0.279976i	−0.237537	+	0.971378i	$0.576340\pi$
$54$		0			0
$55$	−15.0852	+	8.70946i	−2.03409	+	1.17438i
$56$		0			0
$57$	1.76390	−	1.99025i	0.233634	−	0.263616i
$58$		0			0
$59$	−6.82450	−	11.8204i	−0.888474	−	1.53888i	−0.841679	−	0.539978i	$-0.818433\pi$
$59$	−6.82450	−	11.8204i	−0.888474	−	1.53888i	−0.0467951	−	0.998905i	$-0.514901\pi$
$60$		0			0
$61$	6.77885	−	11.7413i	0.867943	−	1.50332i	0.00384839	−	0.999993i	$-0.498775\pi$
$61$	6.77885	−	11.7413i	0.867943	−	1.50332i	0.864095	−	0.503329i	$-0.167892\pi$
$62$		0			0
$63$	−5.37731	−	3.10459i	−0.677477	−	0.391142i
$64$		0			0
$65$		−	8.53193i		−	1.05826i
$66$		0			0
$67$	−4.27064	+	7.39696i	−0.521742	+	0.903683i	0.477939	+	0.878393i	$0.341384\pi$
$67$	−4.27064	+	7.39696i	−0.521742	+	0.903683i	−0.999680	+	0.0252897i	$0.991949\pi$
$68$		0			0
$69$			1.73424i			0.208778i
$70$		0			0
$71$	−1.07447	−	1.86103i	−0.127516	−	0.220864i	0.795198	−	0.606350i	$-0.207367\pi$
$71$	−1.07447	−	1.86103i	−0.127516	−	0.220864i	−0.922714	+	0.385486i	$0.874034\pi$
$72$		0			0
$73$	3.91944	+	6.78867i	0.458736	+	0.794554i	0.998894	−	0.0470092i	$-0.0149690\pi$
$73$	3.91944	+	6.78867i	0.458736	+	0.794554i	−0.540158	+	0.841563i	$0.681636\pi$
$74$		0			0
$75$	3.14205			0.362813
$76$		0			0
$77$	−12.9192			−1.47228
$78$		0			0
$79$	5.57208	+	9.65112i	0.626908	+	1.08584i	0.988169	+	0.153371i	$0.0490131\pi$
$79$	5.57208	+	9.65112i	0.626908	+	1.08584i	−0.361261	+	0.932465i	$0.617654\pi$
$80$		0			0
$81$	−2.89422	−	5.01294i	−0.321581	−	0.556994i
$82$		0			0
$83$		−	4.14868i		−	0.455376i	−0.973734	−	0.227688i	$-0.926883\pi$
$83$		−	4.14868i		−	0.455376i	0.973734	−	0.227688i	$-0.0731167\pi$
$84$		0			0
$85$	−1.76110	+	3.05032i	−0.191018	+	0.330854i
$86$		0			0
$87$		−	3.97149i		−	0.425788i
$88$		0			0
$89$	4.19126	+	2.41982i	0.444272	+	0.256501i	0.705408	−	0.708801i	$-0.250764\pi$
$89$	4.19126	+	2.41982i	0.444272	+	0.256501i	−0.261136	+	0.965302i	$0.584097\pi$
$90$		0			0
$91$	3.16397	−	5.48016i	0.331674	−	0.574477i
$92$		0			0
$93$	0.309642	+	0.536316i	0.0321084	+	0.0556134i
$94$		0			0
$95$	9.21082	−	10.3928i	0.945010	−	1.06628i
$96$		0			0
$97$	−0.641491	+	0.370365i	−0.0651335	+	0.0376048i	−0.532213	−	0.846610i	$-0.678639\pi$
$97$	−0.641491	+	0.370365i	−0.0651335	+	0.0376048i	0.467080	+	0.884215i	$0.345306\pi$
$98$		0			0
$99$	−12.4425	−	7.18366i	−1.25051	−	0.721985i
$100$		0			0
$101$	−2.69851	+	4.67396i	−0.268512	+	0.465076i	−0.968478	−	0.249100i	$-0.919865\pi$
$101$	−2.69851	+	4.67396i	−0.268512	+	0.465076i	0.699966	+	0.714176i	$0.253199\pi$
$102$		0			0
$103$	−7.54816			−0.743743			−0.371871	−	0.928284i	$-0.621284\pi$
$103$	−7.54816			−0.743743			−0.371871	+	0.928284i	$0.621284\pi$
$104$		0			0
$105$	3.97758	+	2.29646i	0.388172	+	0.224111i
$106$		0			0
$107$	18.4008			1.77887			0.889437	−	0.457058i	$-0.151097\pi$
$107$	18.4008			1.77887			0.889437	+	0.457058i	$0.151097\pi$
$108$		0			0
$109$	−4.23847	+	2.44708i	−0.405971	+	0.234388i	−0.689057	−	0.724707i	$-0.741975\pi$
$109$	−4.23847	+	2.44708i	−0.405971	+	0.234388i	0.283086	+	0.959095i	$0.408642\pi$
$110$		0			0
$111$	0.237933	−	0.137371i	0.0225836	−	0.0130387i
$112$		0			0
$113$			17.8362i			1.67789i	0.544220	+	0.838943i	$0.316826\pi$
$113$			17.8362i			1.67789i	−0.544220	+	0.838943i	$0.683174\pi$
$114$		0			0
$115$			9.05594i			0.844471i
$116$		0			0
$117$	6.09442	−	3.51861i	0.563429	−	0.325296i
$118$		0			0
$119$	−2.26235	+	1.30617i	−0.207390	+	0.119736i
$120$		0			0
$121$	−18.8936			−1.71760
$122$		0			0
$123$	−0.205051	−	0.118386i	−0.0184888	−	0.0106745i
$124$		0			0
$125$	0.477794			0.0427352
$126$		0			0
$127$	4.84855	−	8.39793i	0.430239	−	0.745196i	−0.566655	−	0.823955i	$-0.691763\pi$
$127$	4.84855	−	8.39793i	0.430239	−	0.745196i	0.996894	+	0.0787596i	$0.0250959\pi$
$128$		0			0
$129$	3.02735	+	1.74784i	0.266543	+	0.153889i
$130$		0			0
$131$	−6.81626	+	3.93537i	−0.595539	+	0.343835i	−0.767285	−	0.641307i	$-0.778393\pi$
$131$	−6.81626	+	3.93537i	−0.595539	+	0.343835i	0.171745	+	0.985141i	$0.445059\pi$
$132$		0			0
$133$	9.77027	−	3.25969i	0.847190	−	0.282651i
$134$		0			0
$135$	5.46949	+	9.47343i	0.470739	+	0.815343i
$136$		0			0
$137$	5.32438	−	9.22210i	0.454893	−	0.787897i	−0.543790	−	0.839222i	$-0.683011\pi$
$137$	5.32438	−	9.22210i	0.454893	−	0.787897i	0.998682	+	0.0513247i	$0.0163443\pi$
$138$		0			0
$139$	3.86571	+	2.23187i	0.327885	+	0.189305i	0.654902	−	0.755714i	$-0.272710\pi$
$139$	3.86571	+	2.23187i	0.327885	+	0.189305i	−0.327017	+	0.945019i	$0.606043\pi$
$140$		0			0
$141$			2.05404i			0.172982i
$142$		0			0
$143$	7.32106	−	12.6804i	0.612218	−	1.06039i
$144$		0			0
$145$		−	20.7385i		−	1.72224i
$146$		0			0
$147$	−0.432155	−	0.748514i	−0.0356435	−	0.0617364i
$148$		0			0
$149$	4.00960	+	6.94483i	0.328479	+	0.568942i	0.982210	−	0.187785i	$-0.0601307\pi$
$149$	4.00960	+	6.94483i	0.328479	+	0.568942i	−0.653731	+	0.756727i	$0.726797\pi$
$150$		0			0
$151$	5.53975			0.450818			0.225409	−	0.974264i	$-0.427628\pi$
$151$	5.53975			0.450818			0.225409	+	0.974264i	$0.427628\pi$
$152$		0			0
$153$	−2.90515			−0.234868
$154$		0			0
$155$	1.61691	+	2.80056i	0.129873	+	0.224947i
$156$		0			0
$157$	−1.42480	−	2.46782i	−0.113711	−	0.196954i	0.803553	−	0.595234i	$-0.202941\pi$
$157$	−1.42480	−	2.46782i	−0.113711	−	0.196954i	−0.917264	+	0.398280i	$0.869607\pi$
$158$		0			0
$159$		−	2.48712i		−	0.197241i
$160$		0			0
$161$	−3.35829	+	5.81674i	−0.264671	+	0.458423i
$162$		0			0
$163$		−	8.60401i		−	0.673918i	−0.941519	−	0.336959i	$-0.890602\pi$
$163$		−	8.60401i		−	0.673918i	0.941519	−	0.336959i	$-0.109398\pi$
$164$		0			0
$165$	9.20365	+	5.31373i	0.716503	+	0.413673i
$166$		0			0
$167$	−9.00563	+	15.5982i	−0.696877	+	1.20703i	0.272667	+	0.962108i	$0.412094\pi$
$167$	−9.00563	+	15.5982i	−0.696877	+	1.20703i	−0.969544	+	0.244918i	$0.921239\pi$
$168$		0			0
$169$	−2.91409	−	5.04735i	−0.224161	−	0.388257i
$170$		0			0
$171$	11.2222	+	2.29330i	0.858186	+	0.175373i
$172$		0			0
$173$	15.3081	−	8.83813i	1.16385	−	0.671951i	0.211629	−	0.977350i	$-0.432123\pi$
$173$	15.3081	−	8.83813i	1.16385	−	0.671951i	0.952224	+	0.305399i	$0.0987899\pi$
$174$		0			0
$175$	10.5386	+	6.08447i	0.796644	+	0.459942i
$176$		0			0
$177$	−4.16370	+	7.21173i	−0.312963	+	0.542067i
$178$		0			0
$179$	14.9607			1.11822			0.559108	−	0.829095i	$-0.311144\pi$
$179$	14.9607			1.11822			0.559108	+	0.829095i	$0.311144\pi$
$180$		0			0
$181$	−15.1591	−	8.75213i	−1.12677	−	0.650541i	−0.183649	−	0.982992i	$-0.558791\pi$
$181$	−15.1591	−	8.75213i	−1.12677	−	0.650541i	−0.943121	+	0.332451i	$0.892124\pi$
$182$		0			0
$183$	−8.27169			−0.611461
$184$		0			0
$185$	1.24245	−	0.717330i	0.0913469	−	0.0527392i
$186$		0			0
$187$	−5.23482	+	3.02233i	−0.382808	+	0.221014i
$188$		0			0
$189$			8.11319i			0.590148i
$190$		0			0
$191$		−	18.6529i		−	1.34967i	−0.737967	−	0.674837i	$-0.764214\pi$
$191$		−	18.6529i		−	1.34967i	0.737967	−	0.674837i	$-0.235786\pi$
$192$		0			0
$193$	−6.44722	+	3.72230i	−0.464081	+	0.267937i	−0.713759	−	0.700392i	$-0.753009\pi$
$193$	−6.44722	+	3.72230i	−0.464081	+	0.267937i	0.249678	+	0.968329i	$0.419675\pi$
$194$		0			0
$195$	−4.50802	+	2.60271i	−0.322826	+	0.186384i
$196$		0			0
$197$	−14.1748			−1.00991			−0.504955	−	0.863146i	$-0.668491\pi$
$197$	−14.1748			−1.00991			−0.504955	+	0.863146i	$0.668491\pi$
$198$		0			0
$199$	5.81457	+	3.35704i	0.412184	+	0.237974i	0.691728	−	0.722159i	$-0.256850\pi$
$199$	5.81457	+	3.35704i	0.412184	+	0.237974i	−0.279544	+	0.960133i	$0.590183\pi$
$200$		0			0
$201$	5.21112			0.367564
$202$		0			0
$203$	7.69065	−	13.3206i	0.539778	−	0.934922i
$204$		0			0
$205$	−1.07075	−	0.618195i	−0.0747841	−	0.0431766i
$206$		0			0
$207$	−6.46872	+	3.73472i	−0.449607	+	0.259581i
$208$		0			0
$209$	22.6073	−	7.54254i	1.56378	−	0.521728i
$210$		0			0
$211$	3.81983	+	6.61614i	0.262968	+	0.455474i	0.967029	−	0.254665i	$-0.0819653\pi$
$211$	3.81983	+	6.61614i	0.262968	+	0.455474i	−0.704061	+	0.710139i	$0.748632\pi$
$212$		0			0
$213$	−0.655543	+	1.13543i	−0.0449171	+	0.0777986i
$214$		0			0
$215$	15.8083	+	9.12695i	1.07812	+	0.622453i
$216$		0			0
$217$			2.39845i			0.162817i
$218$		0			0
$219$	2.39129	−	4.14184i	0.161589	−	0.279880i
$220$		0			0
$221$		−	2.96072i		−	0.199160i
$222$		0			0
$223$	0.858455	+	1.48689i	0.0574864	+	0.0995693i	0.893336	−	0.449388i	$-0.148358\pi$
$223$	0.858455	+	1.48689i	0.0574864	+	0.0995693i	−0.835850	+	0.548958i	$0.815025\pi$
$224$		0			0
$225$	6.76646	+	11.7199i	0.451097	+	0.781323i
$226$		0			0
$227$	−17.2724			−1.14641			−0.573203	−	0.819413i	$-0.694299\pi$
$227$	−17.2724			−1.14641			−0.573203	+	0.819413i	$0.694299\pi$
$228$		0			0
$229$	−16.7940			−1.10978			−0.554891	−	0.831923i	$-0.687240\pi$
$229$	−16.7940			−1.10978			−0.554891	+	0.831923i	$0.687240\pi$
$230$		0			0
$231$	3.94108	+	6.82614i	0.259304	+	0.449127i
$232$		0			0
$233$	−1.66348	−	2.88123i	−0.108978	−	0.188756i	0.806378	−	0.591400i	$-0.201425\pi$
$233$	−1.66348	−	2.88123i	−0.108978	−	0.188756i	−0.915357	+	0.402644i	$0.868091\pi$
$234$		0			0
$235$			10.7259i			0.699680i
$236$		0			0
$237$	3.39958	−	5.88825i	0.220827	−	0.382483i
$238$		0			0
$239$			4.83178i			0.312542i	0.987714	+	0.156271i	$0.0499473\pi$
$239$			4.83178i			0.312542i	−0.987714	+	0.156271i	$0.950053\pi$
$240$		0			0
$241$	23.1768	+	13.3811i	1.49295	+	0.861954i	0.999967	−	0.00808705i	$-0.00257422\pi$
$241$	23.1768	+	13.3811i	1.49295	+	0.861954i	0.492980	+	0.870041i	$0.335908\pi$
$242$		0			0
$243$	−6.91613	+	11.9791i	−0.443670	+	0.768459i
$244$		0			0
$245$	−2.25665	−	3.90863i	−0.144172	−	0.249713i
$246$		0			0
$247$	−2.33717	+	11.4369i	−0.148710	+	0.727712i
$248$		0			0
$249$	−2.19204	+	1.26557i	−0.138915	+	0.0802025i
$250$		0			0
$251$	12.7393	+	7.35502i	0.804096	+	0.464245i	0.844901	−	0.534922i	$-0.179659\pi$
$251$	12.7393	+	7.35502i	0.804096	+	0.464245i	−0.0408056	+	0.999167i	$0.512992\pi$
$252$		0			0
$253$	−7.77070	+	13.4592i	−0.488540	+	0.846176i
$254$		0			0
$255$	2.14893			0.134571
$256$		0			0
$257$	−8.75454	−	5.05443i	−0.546093	−	0.315287i	0.201452	−	0.979498i	$-0.435434\pi$
$257$	−8.75454	−	5.05443i	−0.546093	−	0.315287i	−0.747545	+	0.664212i	$0.768767\pi$
$258$		0			0
$259$	1.06406			0.0661172
$260$		0			0
$261$	14.8137	−	8.55268i	0.916943	−	0.529397i
$262$		0			0
$263$	13.6702	−	7.89252i	0.842943	−	0.486673i	−0.0153204	−	0.999883i	$-0.504877\pi$
$263$	13.6702	−	7.89252i	0.842943	−	0.486673i	0.858264	+	0.513209i	$0.171543\pi$
$264$		0			0
$265$		−	12.9874i		−	0.797807i
$266$		0			0
$267$		−	2.95272i		−	0.180703i
$268$		0			0
$269$	0.0632774	−	0.0365332i	0.00385809	−	0.00222747i	−0.498070	−	0.867137i	$-0.665958\pi$
$269$	0.0632774	−	0.0365332i	0.00385809	−	0.00222747i	0.501928	+	0.864910i	$0.332624\pi$
$270$		0			0
$271$	6.48453	−	3.74384i	0.393907	−	0.227422i	−0.289945	−	0.957043i	$-0.593637\pi$
$271$	6.48453	−	3.74384i	0.393907	−	0.227422i	0.683852	+	0.729621i	$0.260304\pi$
$272$		0			0
$273$	−3.86074			−0.233663
$274$		0			0
$275$	24.3851	+	14.0787i	1.47048	+	0.848980i
$276$		0			0
$277$	19.0585			1.14511			0.572557	−	0.819865i	$-0.305952\pi$
$277$	19.0585			1.14511			0.572557	+	0.819865i	$0.305952\pi$
$278$		0			0
$279$	−1.33364	+	2.30993i	−0.0798430	+	0.138292i
$280$		0			0
$281$	−7.58314	−	4.37813i	−0.452372	−	0.261177i	0.256459	−	0.966555i	$-0.417444\pi$
$281$	−7.58314	−	4.37813i	−0.452372	−	0.261177i	−0.708832	+	0.705378i	$0.750777\pi$
$282$		0			0
$283$	17.9331	−	10.3537i	1.06601	−	0.615461i	0.138921	−	0.990303i	$-0.455637\pi$
$283$	17.9331	−	10.3537i	1.06601	−	0.615461i	0.927088	+	0.374843i	$0.122303\pi$
$284$		0			0
$285$	−8.30106	−	1.69635i	−0.491712	−	0.100483i
$286$		0			0
$287$	−0.458501	−	0.794148i	−0.0270645	−	0.0468771i
$288$		0			0
$289$	7.88887	−	13.6639i	0.464051	−	0.803760i
$290$		0			0
$291$	0.391380	+	0.225963i	0.0229431	+	0.0132462i
$292$		0			0
$293$		−	19.7950i		−	1.15643i	−0.815883	−	0.578217i	$-0.803749\pi$
$293$		−	19.7950i		−	1.15643i	0.815883	−	0.578217i	$-0.196251\pi$
$294$		0			0
$295$	−21.7422	+	37.6586i	−1.26588	+	2.19257i
$296$		0			0
$297$			18.7730i			1.08932i
$298$		0			0
$299$	−3.80615	−	6.59245i	−0.220115	−	0.381251i
$300$		0			0
$301$	6.76926	+	11.7247i	0.390173	+	0.675800i
$302$		0			0
$303$	3.29278			0.189165
$304$		0			0
$305$	−43.1935			−2.47325
$306$		0			0
$307$	−4.47582	−	7.75235i	−0.255449	−	0.442450i	0.709569	−	0.704636i	$-0.248890\pi$
$307$	−4.47582	−	7.75235i	−0.255449	−	0.442450i	−0.965017	+	0.262186i	$0.915556\pi$
$308$		0			0
$309$	2.30260	+	3.98823i	0.130991	+	0.226882i
$310$		0			0
$311$		−	0.249429i		−	0.0141438i	−0.999975	−	0.00707191i	$-0.997749\pi$
$311$		−	0.249429i		−	0.0141438i	0.999975	−	0.00707191i	$-0.00225108\pi$
$312$		0			0
$313$	11.8686	−	20.5570i	0.670852	−	1.16195i	−0.306811	−	0.951770i	$-0.599262\pi$
$313$	11.8686	−	20.5570i	0.670852	−	1.16195i	0.977663	−	0.210179i	$-0.0674046\pi$
$314$		0			0
$315$			19.7818i			1.11458i
$316$		0			0
$317$	14.6359	+	8.45005i	0.822035	+	0.474602i	0.851118	−	0.524975i	$-0.175925\pi$
$317$	14.6359	+	8.45005i	0.822035	+	0.474602i	−0.0290826	+	0.999577i	$0.509259\pi$
$318$		0			0
$319$	17.7953	−	30.8223i	0.996343	−	1.72572i
$320$		0			0
$321$	−5.61326	−	9.72245i	−0.313302	−	0.542654i
$322$		0			0
$323$	3.19630	−	3.60647i	0.177847	−	0.200669i
$324$		0			0
$325$	−11.9440	+	6.89588i	−0.662535	+	0.382515i
$326$		0			0
$327$	2.58593	+	1.49299i	0.143002	+	0.0825624i
$328$		0			0
$329$	−3.97758	+	6.88937i	−0.219291	+	0.379823i
$330$		0			0
$331$	−9.72419			−0.534490			−0.267245	−	0.963629i	$-0.586113\pi$
$331$	−9.72419			−0.534490			−0.267245	+	0.963629i	$0.586113\pi$
$332$		0			0
$333$	1.02479	+	0.591661i	0.0561580	+	0.0324228i
$334$		0			0
$335$	27.2117			1.48673
$336$		0			0
$337$	8.24404	−	4.75970i	0.449081	−	0.259277i	−0.258361	−	0.966049i	$-0.583182\pi$
$337$	8.24404	−	4.75970i	0.449081	−	0.259277i	0.707442	+	0.706771i	$0.249849\pi$
$338$		0			0
$339$	9.42411	−	5.44101i	0.511847	−	0.295515i
$340$		0			0
$341$			5.54972i			0.300534i
$342$		0			0
$343$		−	19.8878i		−	1.07384i
$344$		0			0
$345$	4.78489	−	2.76256i	0.257610	−	0.148731i
$346$		0			0
$347$	15.9269	−	9.19538i	0.854999	−	0.493634i	−0.00733524	−	0.999973i	$-0.502335\pi$
$347$	15.9269	−	9.19538i	0.854999	−	0.493634i	0.862334	+	0.506339i	$0.169002\pi$
$348$		0			0
$349$	−5.86074			−0.313718			−0.156859	−	0.987621i	$-0.550137\pi$
$349$	−5.86074			−0.313718			−0.156859	+	0.987621i	$0.550137\pi$
$350$		0			0
$351$	−7.96324	−	4.59758i	−0.425046	−	0.245401i
$352$		0			0
$353$	−12.9828			−0.691006			−0.345503	−	0.938418i	$-0.612292\pi$
$353$	−12.9828			−0.691006			−0.345503	+	0.938418i	$0.612292\pi$
$354$		0			0
$355$	−3.42315	+	5.92906i	−0.181682	+	0.314682i
$356$		0			0
$357$	1.38028	+	0.796908i	0.0730524	+	0.0421768i
$358$		0			0
$359$	29.5172	−	17.0418i	1.55786	−	0.899430i	0.560396	−	0.828225i	$-0.310649\pi$
$359$	29.5172	−	17.0418i	1.55786	−	0.899430i	0.997462	−	0.0712049i	$-0.0226844\pi$
$360$		0			0
$361$	−15.1938	+	11.4082i	−0.799676	+	0.600432i
$362$		0			0
$363$	5.76358	+	9.98282i	0.302510	+	0.523962i
$364$		0			0
$365$	12.4870	−	21.6281i	0.653597	−	1.13206i
$366$		0			0
$367$	11.3161	+	6.53337i	0.590697	+	0.341039i	0.765373	−	0.643587i	$-0.222554\pi$
$367$	11.3161	+	6.53337i	0.590697	+	0.341039i	−0.174676	+	0.984626i	$0.555888\pi$
$368$		0			0
$369$		−	1.01979i		−	0.0530880i
$370$		0			0
$371$	4.81621	−	8.34193i	0.250045	−	0.433091i
$372$		0			0
$373$		−	11.8954i		−	0.615922i	−0.951399	−	0.307961i	$-0.900353\pi$
$373$		−	11.8954i		−	0.615922i	0.951399	−	0.307961i	$-0.0996466\pi$
$374$		0			0
$375$	−0.145754	−	0.252453i	−0.00752668	−	0.0130366i
$376$		0			0
$377$	8.71626	+	15.0970i	0.448910	+	0.777535i
$378$		0			0
$379$	8.93709			0.459068			0.229534	−	0.973301i	$-0.426280\pi$
$379$	8.93709			0.459068			0.229534	+	0.973301i	$0.426280\pi$
$380$		0			0
$381$	−5.91630			−0.303101
$382$		0			0
$383$	−6.14400	−	10.6417i	−0.313944	−	0.543767i	0.665269	−	0.746604i	$-0.268317\pi$
$383$	−6.14400	−	10.6417i	−0.313944	−	0.543767i	−0.979212	+	0.202838i	$0.934984\pi$
$384$		0			0
$385$	20.5797	+	35.6451i	1.04884	+	1.81664i
$386$		0			0
$387$			15.0560i			0.765340i
$388$		0			0
$389$	3.61961	−	6.26935i	0.183522	−	0.317869i	−0.759556	−	0.650442i	$-0.774584\pi$
$389$	3.61961	−	6.26935i	0.183522	−	0.317869i	0.943077	+	0.332573i	$0.107917\pi$
$390$		0			0
$391$			3.14256i			0.158926i
$392$		0			0
$393$	4.15867	+	2.40101i	0.209777	+	0.121115i
$394$		0			0
$395$	17.7521	−	30.7475i	0.893205	−	1.54708i
$396$		0			0
$397$	14.7425	+	25.5347i	0.739904	+	1.28155i	0.952538	+	0.304420i	$0.0984627\pi$
$397$	14.7425	+	25.5347i	0.739904	+	1.28155i	−0.212633	+	0.977132i	$0.568204\pi$
$398$		0			0
$399$	−4.70279	−	4.16794i	−0.235434	−	0.208658i
$400$		0			0
$401$	3.17820	−	1.83494i	0.158712	−	0.0916323i	−0.418541	−	0.908198i	$-0.637458\pi$
$401$	3.17820	−	1.83494i	0.158712	−	0.0916323i	0.577252	+	0.816566i	$0.304125\pi$
$402$		0			0
$403$	−2.35412	−	1.35915i	−0.117267	−	0.0677040i
$404$		0			0
$405$	−9.22072	+	15.9707i	−0.458181	+	0.793593i
$406$		0			0
$407$	2.46210			0.122042
$408$		0			0
$409$	0.913849	+	0.527611i	0.0451869	+	0.0260887i	0.522423	−	0.852686i	$-0.325028\pi$
$409$	0.913849	+	0.527611i	0.0451869	+	0.0260887i	−0.477236	+	0.878775i	$0.658361\pi$
$410$		0			0
$411$	−6.49692			−0.320469
$412$		0			0
$413$	−27.9305	+	16.1257i	−1.37437	+	0.793494i
$414$		0			0
$415$	−11.4465	+	6.60864i	−0.561886	+	0.324405i
$416$		0			0
$417$		−	2.72337i		−	0.133364i
$418$		0			0
$419$		−	12.9932i		−	0.634757i	−0.948299	−	0.317379i	$-0.897197\pi$
$419$		−	12.9932i		−	0.634757i	0.948299	−	0.317379i	$-0.102803\pi$
$420$		0			0
$421$	−28.8014	+	16.6285i	−1.40369	+	0.810424i	−0.994770	−	0.102144i	$-0.967430\pi$
$421$	−28.8014	+	16.6285i	−1.40369	+	0.810424i	−0.408925	+	0.912568i	$0.634096\pi$
$422$		0			0
$423$	−7.66158	+	4.42342i	−0.372519	+	0.215074i
$424$		0			0
$425$	5.69360			0.276180
$426$		0			0
$427$	−27.7437	−	16.0178i	−1.34261	−	0.775157i
$428$		0			0
$429$	−8.93330			−0.431304
$430$		0			0
$431$	−4.67046	+	8.08948i	−0.224968	+	0.389656i	−0.956310	−	0.292355i	$-0.905561\pi$
$431$	−4.67046	+	8.08948i	−0.224968	+	0.389656i	0.731342	+	0.682011i	$0.238894\pi$
$432$		0			0
$433$	−11.4412	−	6.60558i	−0.549829	−	0.317444i	0.199224	−	0.979954i	$-0.436158\pi$
$433$	−11.4412	−	6.60558i	−0.549829	−	0.317444i	−0.749053	+	0.662510i	$0.769491\pi$
$434$		0			0
$435$	−10.9576	+	6.32639i	−0.525378	+	0.303327i
$436$		0			0
$437$	2.48071	−	12.1393i	0.118669	−	0.580702i
$438$		0			0
$439$	−9.90270	−	17.1520i	−0.472630	−	0.818619i	0.526879	−	0.849940i	$-0.323362\pi$
$439$	−9.90270	−	17.1520i	−0.472630	−	0.818619i	−0.999509	+	0.0313210i	$0.990029\pi$
$440$		0			0
$441$	1.86131	−	3.22388i	0.0886336	−	0.153518i
$442$		0			0
$443$	−8.86172	−	5.11632i	−0.421033	−	0.243084i	0.274486	−	0.961591i	$-0.411492\pi$
$443$	−8.86172	−	5.11632i	−0.421033	−	0.243084i	−0.695519	+	0.718508i	$0.744826\pi$
$444$		0			0
$445$		−	15.4186i		−	0.730914i
$446$		0			0
$447$	2.44630	−	4.23711i	0.115706	−	0.200408i
$448$		0			0
$449$		−	9.69618i		−	0.457591i	−0.973475	−	0.228795i	$-0.926521\pi$
$449$		−	9.69618i		−	0.457591i	0.973475	−	0.228795i	$-0.0734787\pi$
$450$		0			0
$451$	−1.06092	−	1.83757i	−0.0499567	−	0.0865276i
$452$		0			0
$453$	−1.68993	−	2.92704i	−0.0793997	−	0.137524i
$454$		0			0
$455$	−20.1602			−0.945125
$456$		0			0
$457$	−8.85003			−0.413987			−0.206993	−	0.978342i	$-0.566368\pi$
$457$	−8.85003			−0.413987			−0.206993	+	0.978342i	$0.566368\pi$
$458$		0			0
$459$	1.89800	+	3.28743i	0.0885911	+	0.153444i
$460$		0			0
$461$	4.85595	+	8.41075i	0.226164	+	0.391728i	0.956668	−	0.291181i	$-0.0940481\pi$
$461$	4.85595	+	8.41075i	0.226164	+	0.391728i	−0.730504	+	0.682909i	$0.760715\pi$
$462$		0			0
$463$			38.4094i			1.78504i	0.451013	+	0.892518i	$0.351063\pi$
$463$			38.4094i			1.78504i	−0.451013	+	0.892518i	$0.648937\pi$
$464$		0			0
$465$	0.986490	−	1.70865i	0.0457474	−	0.0792368i
$466$		0			0
$467$			21.7838i			1.00803i	0.863694	+	0.504016i	$0.168145\pi$
$467$			21.7838i			1.00803i	−0.863694	+	0.504016i	$0.831855\pi$
$468$		0			0
$469$	17.4784	+	10.0911i	0.807076	+	0.465966i
$470$		0			0
$471$	−0.869284	+	1.50564i	−0.0400545	+	0.0693764i
$472$		0			0
$473$	15.6633	+	27.1296i	0.720198	+	1.24742i
$474$		0			0
$475$	−21.9937	−	4.49448i	−1.00914	−	0.206221i
$476$		0			0
$477$	9.27696	−	5.35605i	0.424763	−	0.245237i
$478$		0			0
$479$	−10.5544	−	6.09359i	−0.482243	−	0.278423i	0.239108	−	0.970993i	$-0.423145\pi$
$479$	−10.5544	−	6.09359i	−0.482243	−	0.278423i	−0.721351	+	0.692570i	$0.756478\pi$
$480$		0			0
$481$	−0.602978	+	1.04439i	−0.0274934	+	0.0476200i
$482$		0			0
$483$	4.09786			0.186459
$484$		0			0
$485$	2.04373	+	1.17995i	0.0928008	+	0.0535786i
$486$		0			0
$487$	−27.8697			−1.26290			−0.631448	−	0.775418i	$-0.717539\pi$
$487$	−27.8697			−1.26290			−0.631448	+	0.775418i	$0.717539\pi$
$488$		0			0
$489$	−4.54611	+	2.62470i	−0.205582	+	0.118693i
$490$		0			0
$491$	14.9996	−	8.66002i	0.676922	−	0.390821i	−0.121772	−	0.992558i	$-0.538858\pi$
$491$	14.9996	−	8.66002i	0.676922	−	0.390821i	0.798694	+	0.601737i	$0.205524\pi$
$492$		0			0
$493$		−	7.19660i		−	0.324119i
$494$		0			0
$495$			45.7729i			2.05734i
$496$		0			0
$497$	−4.39745	+	2.53887i	−0.197253	+	0.113884i
$498$		0			0
$499$	1.00693	−	0.581349i	0.0450762	−	0.0260248i	−0.477293	−	0.878744i	$-0.658382\pi$
$499$	1.00693	−	0.581349i	0.0450762	−	0.0260248i	0.522369	+	0.852720i	$0.325048\pi$
$500$		0			0
$501$	10.9889			0.490946
$502$		0			0
$503$	11.1928	+	6.46214i	0.499060	+	0.288133i	0.728325	−	0.685231i	$-0.240299\pi$
$503$	11.1928	+	6.46214i	0.499060	+	0.288133i	−0.229265	+	0.973364i	$0.573632\pi$
$504$		0			0
$505$	17.1944			0.765140
$506$		0			0
$507$	−1.77791	+	3.07944i	−0.0789599	+	0.136763i
$508$		0			0
$509$	−25.6884	−	14.8312i	−1.13862	−	0.657381i	−0.192530	−	0.981291i	$-0.561669\pi$
$509$	−25.6884	−	14.8312i	−1.13862	−	0.657381i	−0.946088	+	0.323910i	$0.895002\pi$
$510$		0			0
$511$	16.0410	−	9.26130i	0.709614	−	0.409696i
$512$		0			0
$513$	−4.73667	−	14.1972i	−0.209129	−	0.626822i
$514$		0			0
$515$	12.0239	+	20.8259i	0.529834	+	0.917700i
$516$		0			0
$517$	−9.20365	+	15.9412i	−0.404776	+	0.701093i
$518$		0			0
$519$	−9.33962	−	5.39223i	−0.409964	−	0.236693i
$520$		0			0
$521$		−	35.2430i		−	1.54402i	−0.635608	−	0.772012i	$-0.719251\pi$
$521$		−	35.2430i		−	1.54402i	0.635608	−	0.772012i	$-0.280749\pi$
$522$		0			0
$523$	−11.4242	+	19.7872i	−0.499543	+	0.865234i	−1.00000		0.000527203i	$-0.999832\pi$
$523$	−11.4242	+	19.7872i	−0.499543	+	0.865234i	0.500457	+	0.865762i	$0.333166\pi$
$524$		0			0
$525$		−	7.42439i		−	0.324027i
$526$		0			0
$527$	0.561093	+	0.971841i	0.0244416	+	0.0423341i
$528$		0			0
$529$	−7.46008	−	12.9212i	−0.324351	−	0.561793i
$530$		0			0
$531$	−35.8664			−1.55647
$532$		0			0
$533$	1.03929			0.0450168
$534$		0			0
$535$	−29.3116	−	50.7692i	−1.26725	−	2.19494i
$536$		0			0
$537$	−4.56384	−	7.90481i	−0.196944	−	0.341118i
$538$		0			0
$539$		−	7.74551i		−	0.333623i
$540$		0			0
$541$	18.2188	−	31.5560i	0.783289	−	1.35670i	−0.146727	−	0.989177i	$-0.546874\pi$
$541$	18.2188	−	31.5560i	0.783289	−	1.35670i	0.930016	−	0.367520i	$-0.119793\pi$
$542$		0			0
$543$			10.6795i			0.458302i
$544$		0			0
$545$	13.5033	+	7.79616i	0.578420	+	0.333951i
$546$		0			0
$547$	−14.8588	+	25.7362i	−0.635317	+	1.10040i	0.351131	+	0.936326i	$0.385797\pi$
$547$	−14.8588	+	25.7362i	−0.635317	+	1.10040i	−0.986448	+	0.164075i	$0.947536\pi$
$548$		0			0
$549$	−17.8132	−	30.8534i	−0.760250	−	1.31679i
$550$		0			0
$551$	−5.68094	+	27.7996i	−0.242016	+	1.18430i
$552$		0			0
$553$	22.8048	−	13.1663i	0.969757	−	0.559889i
$554$		0			0
$555$	−0.758033	−	0.437650i	−0.0321767	−	0.0185772i
$556$		0			0
$557$	2.98070	−	5.16273i	0.126296	−	0.218752i	−0.795943	−	0.605372i	$-0.793024\pi$
$557$	2.98070	−	5.16273i	0.126296	−	0.218752i	0.922239	+	0.386620i	$0.126358\pi$
$558$		0			0
$559$	−15.3440			−0.648982
$560$		0			0
$561$	3.19382	+	1.84395i	0.134843	+	0.0778517i
$562$		0			0
$563$	−35.3916			−1.49158			−0.745789	−	0.666182i	$-0.767927\pi$
$563$	−35.3916			−1.49158			−0.745789	+	0.666182i	$0.767927\pi$
$564$		0			0
$565$	49.2113	−	28.4121i	2.07033	−	1.19531i
$566$		0			0
$567$	−11.8451	+	6.83880i	−0.497449	+	0.287203i
$568$		0			0
$569$		−	30.2541i		−	1.26832i	−0.773203	−	0.634158i	$-0.781347\pi$
$569$		−	30.2541i		−	1.26832i	0.773203	−	0.634158i	$-0.218653\pi$
$570$		0			0
$571$		−	25.4945i		−	1.06691i	−0.845828	−	0.533456i	$-0.820893\pi$
$571$		−	25.4945i		−	1.06691i	0.845828	−	0.533456i	$-0.179107\pi$
$572$		0			0
$573$	−9.85562	+	5.69015i	−0.411725	+	0.237709i
$574$		0			0
$575$	12.6776	−	7.31941i	0.528692	−	0.305240i
$576$		0			0
$577$	−12.0785			−0.502836			−0.251418	−	0.967879i	$-0.580897\pi$
$577$	−12.0785			−0.502836			−0.251418	+	0.967879i	$0.580897\pi$
$578$		0			0
$579$	3.93351	+	2.27102i	0.163471	+	0.0943802i
$580$		0			0
$581$	−9.80296			−0.406695
$582$		0			0
$583$	11.1442	−	19.3022i	0.461544	−	0.799417i
$584$		0			0
$585$	−19.4162	−	11.2100i	−0.802762	−	0.463475i
$586$		0			0
$587$	−18.8754	+	10.8977i	−0.779070	+	0.449796i	−0.836101	−	0.548576i	$-0.815170\pi$
$587$	−18.8754	+	10.8977i	−0.779070	+	0.449796i	0.0570304	+	0.998372i	$0.481837\pi$
$588$		0			0
$589$	−1.40027	−	4.19702i	−0.0576970	−	0.172935i
$590$		0			0
$591$	4.32408	+	7.48953i	0.177869	+	0.308078i
$592$		0			0
$593$	−10.3212	+	17.8768i	−0.423839	+	0.734111i	−0.996311	−	0.0858135i	$-0.972651\pi$
$593$	−10.3212	+	17.8768i	−0.423839	+	0.734111i	0.572472	+	0.819924i	$0.305984\pi$
$594$		0			0
$595$	7.20764	+	4.16133i	0.295484	+	0.170598i
$596$		0			0
$597$		−	4.09633i		−	0.167652i
$598$		0			0
$599$	18.6426	−	32.2900i	0.761717	−	1.31933i	−0.180248	−	0.983621i	$-0.557690\pi$
$599$	18.6426	−	32.2900i	0.761717	−	1.31933i	0.941965	−	0.335711i	$-0.108977\pi$
$600$		0			0
$601$			32.9087i			1.34238i	0.741287	+	0.671188i	$0.234216\pi$
$601$			32.9087i			1.34238i	−0.741287	+	0.671188i	$0.765784\pi$
$602$		0			0
$603$	11.2222	+	19.4375i	0.457005	+	0.791556i
$604$		0			0
$605$	30.0965	+	52.1287i	1.22360	+	2.11933i
$606$		0			0
$607$	−43.4094			−1.76193			−0.880966	−	0.473180i	$-0.843106\pi$
$607$	−43.4094			−1.76193			−0.880966	+	0.473180i	$0.843106\pi$
$608$		0			0
$609$	−9.38428			−0.380270
$610$		0			0
$611$	−4.50802	−	7.80813i	−0.182375	−	0.315883i
$612$		0			0
$613$	23.0269	+	39.8838i	0.930048	+	1.61089i	0.783234	+	0.621727i	$0.213569\pi$
$613$	23.0269	+	39.8838i	0.930048	+	1.61089i	0.146814	+	0.989164i	$0.453098\pi$
$614$		0			0
$615$			0.754334i			0.0304177i
$616$		0			0
$617$	−4.97177	+	8.61136i	−0.200156	+	0.346680i	−0.948579	−	0.316542i	$-0.897478\pi$
$617$	−4.97177	+	8.61136i	−0.200156	+	0.346680i	0.748423	+	0.663222i	$0.230812\pi$
$618$		0			0
$619$		−	4.75114i		−	0.190964i	−0.995431	−	0.0954822i	$-0.969561\pi$
$619$		−	4.75114i		−	0.190964i	0.995431	−	0.0954822i	$-0.0304393\pi$
$620$		0			0
$621$	8.45232	+	4.87995i	0.339180	+	0.195826i
$622$		0			0
$623$	5.71783	−	9.90358i	0.229080	−	0.396778i
$624$		0			0
$625$	12.1138	+	20.9818i	0.484553	+	0.839270i
$626$		0			0
$627$	−10.8817	−	9.64413i	−0.434574	−	0.385149i
$628$		0			0
$629$	0.431151	−	0.248925i	0.0171911	−	0.00992530i
$630$		0			0
$631$	−17.8068	−	10.2807i	−0.708876	−	0.409270i	0.101769	−	0.994808i	$-0.467550\pi$
$631$	−17.8068	−	10.2807i	−0.708876	−	0.409270i	−0.810645	+	0.585538i	$0.800883\pi$
$632$		0			0
$633$	2.33052	−	4.03657i	0.0926297	−	0.160439i
$634$		0			0
$635$	−30.8940			−1.22599
$636$		0			0
$637$	3.28554	+	1.89691i	0.130178	+	0.0751582i
$638$		0			0
$639$	−5.64689			−0.223388
$640$		0			0
$641$	33.0540	−	19.0838i	1.30556	−	0.753763i	0.324205	−	0.945987i	$-0.394903\pi$
$641$	33.0540	−	19.0838i	1.30556	−	0.753763i	0.981351	+	0.192223i	$0.0615698\pi$
$642$		0			0
$643$	18.5705	−	10.7217i	0.732350	−	0.422822i	−0.0869313	−	0.996214i	$-0.527706\pi$
$643$	18.5705	−	10.7217i	0.732350	−	0.422822i	0.819281	+	0.573392i	$0.194373\pi$
$644$		0			0
$645$		−	11.1369i		−	0.438515i
$646$		0			0
$647$			23.8222i			0.936547i	0.883583	+	0.468274i	$0.155124\pi$
$647$			23.8222i			0.936547i	−0.883583	+	0.468274i	$0.844876\pi$
$648$		0			0
$649$	−64.6280	+	37.3130i	−2.53687	+	1.46466i
$650$		0			0
$651$	1.26727	−	0.731658i	0.0496682	−	0.0286759i
$652$		0			0
$653$	−16.6726			−0.652450			−0.326225	−	0.945292i	$-0.605777\pi$
$653$	−16.6726			−0.652450			−0.326225	+	0.945292i	$0.605777\pi$
$654$		0			0
$655$	21.7159	+	12.5377i	0.848512	+	0.489888i
$656$		0			0
$657$	20.5988			0.803634
$658$		0			0
$659$	7.26163	−	12.5775i	0.282873	−	0.489950i	−0.689218	−	0.724554i	$-0.742046\pi$
$659$	7.26163	−	12.5775i	0.282873	−	0.489950i	0.972091	+	0.234604i	$0.0753792\pi$
$660$		0			0
$661$	−19.7070	−	11.3778i	−0.766513	−	0.442547i	0.0651162	−	0.997878i	$-0.479258\pi$
$661$	−19.7070	−	11.3778i	−0.766513	−	0.442547i	−0.831629	+	0.555331i	$0.812592\pi$
$662$		0			0
$663$	−1.56436	+	0.903182i	−0.0607546	+	0.0350767i
$664$		0			0
$665$	−24.5573	−	21.7644i	−0.952290	−	0.843985i
$666$		0			0
$667$	−9.25159	−	16.0242i	−0.358223	−	0.620461i
$668$		0			0
$669$	0.523752	−	0.907165i	0.0202494	−	0.0350730i
$670$		0			0
$671$	−64.1957	−	37.0634i	−2.47825	−	1.43082i
$672$		0			0
$673$		−	11.1598i		−	0.430180i	−0.976594	−	0.215090i	$-0.930996\pi$
$673$		−	11.1598i		−	0.430180i	0.976594	−	0.215090i	$-0.0690044\pi$
$674$		0			0
$675$	8.84136	−	15.3137i	0.340304	−	0.589424i
$676$		0			0
$677$			36.0612i			1.38594i	0.720965	+	0.692972i	$0.243699\pi$
$677$			36.0612i			1.38594i	−0.720965	+	0.692972i	$0.756301\pi$
$678$		0			0
$679$	0.875139	+	1.51579i	0.0335848	+	0.0581705i
$680$		0			0
$681$	5.26902	+	9.12621i	0.201909	+	0.349717i
$682$		0			0
$683$	15.5917			0.596598			0.298299	−	0.954472i	$-0.403581\pi$
$683$	15.5917			0.596598			0.298299	+	0.954472i	$0.403581\pi$
$684$		0			0
$685$	−33.9259			−1.29624
$686$		0			0
$687$	5.12311	+	8.87348i	0.195459	+	0.338544i
$688$		0			0
$689$	5.45850	+	9.45440i	0.207952	+	0.360184i
$690$		0			0
$691$		−	22.9437i		−	0.872818i	−0.899748	−	0.436409i	$-0.856250\pi$
$691$		−	22.9437i		−	0.872818i	0.899748	−	0.436409i	$-0.143750\pi$
$692$		0			0
$693$	−16.9744	+	29.4004i	−0.644802	+	1.11683i
$694$		0			0
$695$		−	14.2210i		−	0.539435i
$696$		0			0
$697$	−0.371566	−	0.214524i	−0.0140741	−	0.00812567i
$698$		0			0
$699$	−1.01491	+	1.75787i	−0.0383873	+	0.0664887i
$700$		0			0
$701$	9.13435	+	15.8212i	0.345000	+	0.597557i	0.985354	−	0.170523i	$-0.0545457\pi$
$701$	9.13435	+	15.8212i	0.345000	+	0.597557i	−0.640354	+	0.768080i	$0.721212\pi$
$702$		0			0
$703$	−1.86198	+	0.621220i	−0.0702260	+	0.0234297i
$704$		0			0
$705$	5.66725	−	3.27199i	0.213441	−	0.123230i
$706$		0			0
$707$	11.0442	+	6.37634i	0.415358	+	0.239807i
$708$		0			0
$709$	17.4758	−	30.2690i	0.656318	−	1.13678i	−0.325244	−	0.945630i	$-0.605446\pi$
$709$	17.4758	−	30.2690i	0.656318	−	1.13678i	0.981562	−	0.191146i	$-0.0612204\pi$
$710$		0			0
$711$	29.2842			1.09824
$712$		0			0
$713$	2.49870	+	1.44262i	0.0935770	+	0.0540267i
$714$		0			0
$715$	−46.6483			−1.74455
$716$		0			0
$717$	2.55297	−	1.47396i	0.0953425	−	0.0550460i
$718$		0			0
$719$	3.07635	−	1.77613i	0.114728	−	0.0662385i	−0.441538	−	0.897243i	$-0.645567\pi$
$719$	3.07635	−	1.77613i	0.114728	−	0.0662385i	0.556266	+	0.831004i	$0.312234\pi$
$720$		0			0
$721$			17.8356i			0.664234i
$722$		0			0
$723$		−	16.3279i		−	0.607241i
$724$		0			0
$725$	−29.0323	+	16.7618i	−1.07823	+	0.622517i
$726$		0			0
$727$	−6.15483	+	3.55349i	−0.228270	+	0.131792i	−0.609774	−	0.792576i	$-0.708740\pi$
$727$	−6.15483	+	3.55349i	−0.228270	+	0.131792i	0.381504	+	0.924367i	$0.375406\pi$
$728$		0			0
$729$	−8.92615			−0.330598
$730$		0			0
$731$	5.48575	+	3.16720i	0.202898	+	0.117143i
$732$		0			0
$733$	15.8748			0.586350			0.293175	−	0.956059i	$-0.405288\pi$
$733$	15.8748			0.586350			0.293175	+	0.956059i	$0.405288\pi$
$734$		0			0
$735$	−1.37680	+	2.38469i	−0.0507842	+	0.0879607i
$736$		0			0
$737$	40.4429	+	23.3497i	1.48973	+	0.860098i
$738$		0			0
$739$	16.0186	−	9.24836i	0.589255	−	0.340206i	−0.175548	−	0.984471i	$-0.556170\pi$
$739$	16.0186	−	9.24836i	0.589255	−	0.340206i	0.764803	+	0.644264i	$0.222836\pi$
$740$		0			0
$741$	6.75588	−	2.25399i	0.248184	−	0.0828023i
$742$		0			0
$743$	−7.00831	−	12.1387i	−0.257110	−	0.445328i	0.708357	−	0.705855i	$-0.249437\pi$
$743$	−7.00831	−	12.1387i	−0.257110	−	0.445328i	−0.965466	+	0.260527i	$0.916104\pi$
$744$		0			0
$745$	12.7742	−	22.1255i	0.468010	−	0.810617i
$746$		0			0
$747$	−9.44119	−	5.45087i	−0.345435	−	0.199437i
$748$		0			0
$749$		−	43.4795i		−	1.58871i
$750$		0			0
$751$	−10.3122	+	17.8612i	−0.376297	+	0.651765i	−0.990520	−	0.137367i	$-0.956136\pi$
$751$	−10.3122	+	17.8612i	−0.376297	+	0.651765i	0.614223	+	0.789132i	$0.289469\pi$
$752$		0			0
$753$		−	8.97475i		−	0.327058i
$754$		0			0
$755$	−8.82454	−	15.2846i	−0.321158	−	0.556262i
$756$		0			0
$757$	−12.5598	−	21.7543i	−0.456495	−	0.790672i	0.542278	−	0.840199i	$-0.317562\pi$
$757$	−12.5598	−	21.7543i	−0.456495	−	0.790672i	−0.998773	+	0.0495268i	$0.984229\pi$
$758$		0			0
$759$	9.48196			0.344173
$760$		0			0
$761$	7.58718			0.275035			0.137518	−	0.990499i	$-0.456088\pi$
$761$	7.58718			0.275035			0.137518	+	0.990499i	$0.456088\pi$
$762$		0			0
$763$	5.78224	+	10.0151i	0.209331	+	0.362572i
$764$		0			0
$765$	4.62777	+	8.01553i	0.167317	+	0.289802i
$766$		0			0
$767$		−	36.5524i		−	1.31983i
$768$		0			0
$769$	−10.2413	+	17.7384i	−0.369309	+	0.639663i	−0.989458	−	0.144822i	$-0.953739\pi$
$769$	−10.2413	+	17.7384i	−0.369309	+	0.639663i	0.620148	+	0.784485i	$0.287072\pi$
$770$		0			0
$771$			6.16752i			0.222118i
$772$		0			0
$773$	−16.5528	−	9.55676i	−0.595363	−	0.343733i	0.171852	−	0.985123i	$-0.445025\pi$
$773$	−16.5528	−	9.55676i	−0.595363	−	0.343733i	−0.767215	+	0.641390i	$0.778358\pi$
$774$		0			0
$775$	2.61371	−	4.52707i	0.0938872	−	0.162617i
$776$		0			0
$777$	−0.324595	−	0.562216i	−0.0116448	−	0.0201694i
$778$		0			0
$779$	1.26597	+	1.12199i	0.0453581	+	0.0401995i
$780$		0			0
$781$	−10.1752	+	5.87465i	−0.364097	+	0.210211i
$782$		0			0
$783$	−19.3562	−	11.1753i	−0.691734	−	0.399373i
$784$		0			0
$785$	−4.53927	+	7.86225i	−0.162014	+	0.280616i
$786$		0			0
$787$	−15.1750			−0.540931			−0.270465	−	0.962730i	$-0.587178\pi$
$787$	−15.1750			−0.540931			−0.270465	+	0.962730i	$0.587178\pi$
$788$		0			0
$789$	−8.34035	−	4.81530i	−0.296924	−	0.171429i
$790$		0			0
$791$	42.1453			1.49851
$792$		0			0
$793$	31.4436	−	18.1539i	1.11659	−	0.644666i
$794$		0			0
$795$	−6.86214	+	3.96186i	−0.243375	+	0.140513i
$796$		0			0
$797$		−	46.7518i		−	1.65603i	−0.560704	−	0.828017i	$-0.689469\pi$
$797$		−	46.7518i		−	1.65603i	0.560704	−	0.828017i	$-0.310531\pi$
$798$		0			0
$799$			3.72206i			0.131677i
$800$		0			0
$801$	11.0136	−	6.35873i	0.389148	−	0.224675i
$802$		0			0
$803$	37.1171	−	21.4296i	1.30983	−	0.756233i
$804$		0			0
$805$	21.3984			0.754194
$806$		0			0
$807$	−0.0386062	−	0.0222893i	−0.00135900	−	0.000784620i
$808$		0			0
$809$	29.0772			1.02230			0.511151	−	0.859491i	$-0.329219\pi$
$809$	29.0772			1.02230			0.511151	+	0.859491i	$0.329219\pi$
$810$		0			0
$811$	−23.7677	+	41.1669i	−0.834597	+	1.44556i	0.0597609	+	0.998213i	$0.480966\pi$
$811$	−23.7677	+	41.1669i	−0.834597	+	1.44556i	−0.894358	+	0.447352i	$0.852367\pi$
$812$		0			0
$813$	−3.95627	−	2.28416i	−0.138753	−	0.0801088i
$814$		0			0
$815$	−23.7391	+	13.7058i	−0.831544	+	0.480092i
$816$		0			0
$817$	−18.6906	−	16.5649i	−0.653902	−	0.579533i
$818$		0			0
$819$	−8.31417	−	14.4006i	−0.290521	−	0.503197i
$820$		0			0
$821$	−18.3351	+	31.7574i	−0.639900	+	1.10834i	0.345554	+	0.938399i	$0.387691\pi$
$821$	−18.3351	+	31.7574i	−0.639900	+	1.10834i	−0.985454	+	0.169940i	$0.945642\pi$
$822$		0			0
$823$	39.9324	+	23.0550i	1.39196	+	0.803647i	0.993532	−	0.113554i	$-0.0362236\pi$
$823$	39.9324	+	23.0550i	1.39196	+	0.803647i	0.398425	+	0.917201i	$0.369557\pi$
$824$		0			0
$825$		−	17.1792i		−	0.598102i
$826$		0			0
$827$	−3.93836	+	6.82143i	−0.136950	+	0.237205i	−0.926341	−	0.376687i	$-0.877063\pi$
$827$	−3.93836	+	6.82143i	−0.136950	+	0.237205i	0.789391	+	0.613891i	$0.210397\pi$
$828$		0			0
$829$		−	2.15631i		−	0.0748918i	−0.999299	−	0.0374459i	$-0.988078\pi$
$829$		−	2.15631i		−	0.0748918i	0.999299	−	0.0374459i	$-0.0119222\pi$
$830$		0			0
$831$	−5.81389	−	10.0699i	−0.201682	−	0.349323i
$832$		0			0
$833$	−0.783093	−	1.35636i	−0.0271326	−	0.0469950i
$834$		0			0
$835$	57.3821			1.98579
$836$		0			0
$837$	3.48519			0.120466
$838$		0			0
$839$	16.4564	+	28.5033i	0.568137	+	0.984043i	0.996750	+	0.0805545i	$0.0256691\pi$
$839$	16.4564	+	28.5033i	0.568137	+	0.984043i	−0.428613	+	0.903488i	$0.640998\pi$
$840$		0			0
$841$	6.68657	+	11.5815i	0.230571	+	0.399361i
$842$		0			0
$843$			5.34228i			0.183998i
$844$		0			0
$845$	−9.28399	+	16.0803i	−0.319379	+	0.553181i
$846$		0			0
$847$			44.6439i			1.53398i
$848$		0			0
$849$	−10.9411	−	6.31687i	−0.375499	−	0.216794i
$850$		0			0
$851$	0.640011	−	1.10853i	0.0219393	−	0.0380000i
$852$		0			0
$853$	−2.93070	−	5.07612i	−0.100345	−	0.173803i	0.811482	−	0.584378i	$-0.198661\pi$
$853$	−2.93070	−	5.07612i	−0.100345	−	0.173803i	−0.911827	+	0.410575i	$0.865328\pi$
$854$		0			0
$855$	−11.5491	−	34.6161i	−0.394970	−	1.18385i
$856$		0			0
$857$	1.57854	−	0.911371i	0.0539219	−	0.0311318i	−0.472797	−	0.881172i	$-0.656755\pi$
$857$	1.57854	−	0.911371i	0.0539219	−	0.0311318i	0.526719	+	0.850040i	$0.323422\pi$
$858$		0			0
$859$	36.6465	+	21.1578i	1.25036	+	0.721896i	0.971181	−	0.238342i	$-0.0766041\pi$
$859$	36.6465	+	21.1578i	1.25036	+	0.721896i	0.279180	+	0.960239i	$0.409937\pi$
$860$		0			0
$861$	−0.279736	+	0.484518i	−0.00953339	+	0.0165123i
$862$		0			0
$863$	32.8925			1.11967			0.559836	−	0.828603i	$-0.310864\pi$
$863$	32.8925			1.11967			0.559836	+	0.828603i	$0.310864\pi$
$864$		0			0
$865$	−48.7701	−	28.1574i	−1.65823	−	0.957381i
$866$		0			0
$867$	−9.62616			−0.326921
$868$		0			0
$869$	52.7675	−	30.4654i	1.79002	−	1.03347i
$870$		0			0
$871$	−19.8093	+	11.4369i	−0.671211	+	0.387524i
$872$		0			0
$873$			1.94646i			0.0658778i
$874$		0			0
$875$		−	1.12899i		−	0.0381667i
$876$		0			0
$877$	−37.4930	+	21.6466i	−1.26605	+	0.730954i	−0.974238	−	0.225522i	$-0.927591\pi$
$877$	−37.4930	+	21.6466i	−1.26605	+	0.730954i	−0.291811	+	0.956476i	$0.594258\pi$
$878$		0			0
$879$	−10.4591	+	6.03855i	−0.352776	+	0.203675i
$880$		0			0
$881$	−10.1569			−0.342193			−0.171097	−	0.985254i	$-0.554731\pi$
$881$	−10.1569			−0.342193			−0.171097	+	0.985254i	$0.554731\pi$
$882$		0			0
$883$	−31.8465	−	18.3866i	−1.07172	−	0.618757i	−0.143068	−	0.989713i	$-0.545697\pi$
$883$	−31.8465	−	18.3866i	−1.07172	−	0.618757i	−0.928651	+	0.370956i	$0.879030\pi$
$884$		0			0
$885$	26.5303			0.891805
$886$		0			0
$887$	−19.3619	+	33.5357i	−0.650108	+	1.12602i	0.332989	+	0.942931i	$0.391943\pi$
$887$	−19.3619	+	33.5357i	−0.650108	+	1.12602i	−0.983096	+	0.183089i	$0.941390\pi$
$888$		0			0
$889$	−19.8436	−	11.4567i	−0.665532	−	0.384245i
$890$		0			0
$891$	−27.4083	+	15.8242i	−0.918212	+	0.530130i
$892$		0			0
$893$	2.93817	−	14.3779i	0.0983220	−	0.481137i
$894$		0			0
$895$	−23.8317	−	41.2777i	−0.796606	−	1.37976i
$896$		0			0
$897$	−2.32217	+	4.02212i	−0.0775350	+	0.134295i
$898$		0			0
$899$	−5.72214	−	3.30368i	−0.190844	−	0.110184i
$900$		0			0
$901$		−	4.50682i		−	0.150144i
$902$		0			0
$903$	4.12999	−	7.15335i	0.137438	−	0.238049i
$904$		0			0
$905$			55.7669i			1.85375i
$906$		0			0
$907$	27.5458	+	47.7107i	0.914643	+	1.58421i	0.807423	+	0.589973i	$0.200862\pi$
$907$	27.5458	+	47.7107i	0.914643	+	1.58421i	0.107220	+	0.994235i	$0.465805\pi$
$908$		0			0
$909$	7.09105	+	12.2821i	0.235195	+	0.407370i
$910$		0			0
$911$	3.72616			0.123453			0.0617266	−	0.998093i	$-0.480339\pi$
$911$	3.72616			0.123453			0.0617266	+	0.998093i	$0.480339\pi$
$912$		0			0
$913$	−22.6829			−0.750694
$914$		0			0
$915$	13.1764	+	22.8222i	0.435598	+	0.754479i
$916$		0			0
$917$	9.29893	+	16.1062i	0.307078	+	0.531874i
$918$		0			0
$919$		−	17.4986i		−	0.577224i	−0.957446	−	0.288612i	$-0.906806\pi$
$919$		−	17.4986i		−	0.577224i	0.957446	−	0.288612i	$-0.0931938\pi$
$920$		0			0
$921$	−2.73074	+	4.72979i	−0.0899811	+	0.155852i
$922$		0			0
$923$		−	5.75490i		−	0.189425i
$924$		0			0
$925$	−2.00841	−	1.15956i	−0.0660361	−	0.0381259i
$926$		0			0
$927$	−9.91740	+	17.1774i	−0.325730	+	0.564181i
$928$		0			0
$929$	−7.98584	−	13.8319i	−0.262007	−	0.453810i	0.704768	−	0.709438i	$-0.251051\pi$
$929$	−7.98584	−	13.8319i	−0.262007	−	0.453810i	−0.966775	+	0.255628i	$0.917718\pi$
$930$		0			0
$931$	1.95429	+	5.85761i	0.0640494	+	0.191975i
$932$		0			0
$933$	−0.131791	+	0.0760896i	−0.00431464	+	0.00249106i
$934$		0			0
$935$	16.6776	+	9.62883i	0.545417	+	0.314897i
$936$		0			0
$937$	0.674194	−	1.16774i	0.0220249	−	0.0381483i	−0.854803	−	0.518953i	$-0.826322\pi$
$937$	0.674194	−	1.16774i	0.0220249	−	0.0381483i	0.876828	+	0.480805i	$0.159655\pi$
$938$		0			0
$939$	−14.4823			−0.472611
$940$		0			0
$941$	41.2979	+	23.8434i	1.34627	+	0.777271i	0.987719	−	0.156238i	$-0.0499367\pi$
$941$	41.2979	+	23.8434i	1.34627	+	0.777271i	0.358553	+	0.933509i	$0.383270\pi$
$942$		0			0
$943$	−1.10312			−0.0359227
$944$		0			0
$945$	22.3849	−	12.9239i	0.728180	−	0.420415i
$946$		0			0
$947$	−22.7091	+	13.1111i	−0.737946	+	0.426053i	−0.821322	−	0.570465i	$-0.806763\pi$
$947$	−22.7091	+	13.1111i	−0.737946	+	0.426053i	0.0833759	+	0.996518i	$0.473430\pi$
$948$		0			0
$949$			20.9927i			0.681453i
$950$		0			0
$951$		−	10.3109i		−	0.334355i
$952$		0			0
$953$	−23.7784	+	13.7285i	−0.770257	+	0.444708i	−0.832966	−	0.553324i	$-0.813359\pi$
$953$	−23.7784	+	13.7285i	−0.770257	+	0.444708i	0.0627090	+	0.998032i	$0.480026\pi$
$954$		0			0
$955$	−51.4646	+	29.7131i	−1.66535	+	0.961493i
$956$		0			0
$957$	−21.7141			−0.701918
$958$		0			0
$959$	−21.7910	−	12.5810i	−0.703668	−	0.406263i
$960$		0			0
$961$	−29.9697			−0.966764
$962$		0			0
$963$	24.1765	−	41.8749i	0.779077	−	1.34940i
$964$		0			0
$965$	20.5402	+	11.8589i	0.661213	+	0.381751i
$966$		0			0
$967$	14.9005	−	8.60278i	0.479166	−	0.276647i	−0.240903	−	0.970549i	$-0.577443\pi$
$967$	14.9005	−	8.60278i	0.479166	−	0.276647i	0.720069	+	0.693902i	$0.244110\pi$
$968$		0			0
$969$	−2.88060	−	0.588661i	−0.0925383	−	0.0189105i
$970$		0			0
$971$	−6.50590	−	11.2685i	−0.208784	−	0.361625i	0.742548	−	0.669793i	$-0.233617\pi$
$971$	−6.50590	−	11.2685i	−0.208784	−	0.361625i	−0.951332	+	0.308168i	$0.900284\pi$
$972$		0			0
$973$	5.27371	−	9.13434i	0.169067	−	0.292833i
$974$		0			0
$975$	7.28716	+	4.20725i	0.233376	+	0.134740i
$976$		0			0
$977$		−	38.1644i		−	1.22099i	−0.792021	−	0.610494i	$-0.790971\pi$
$977$		−	38.1644i		−	1.22099i	0.792021	−	0.610494i	$-0.209029\pi$
$978$		0			0
$979$	13.2304	−	22.9157i	0.422845	−	0.732389i
$980$		0			0
$981$			12.8607i			0.410611i
$982$		0			0
$983$	11.7428	+	20.3391i	0.374536	+	0.648715i	0.990257	−	0.139249i	$-0.0444688\pi$
$983$	11.7428	+	20.3391i	0.374536	+	0.648715i	−0.615722	+	0.787964i	$0.711135\pi$
$984$		0			0
$985$	22.5797	+	39.1092i	0.719449	+	1.24612i
$986$		0			0
$987$	4.85352			0.154489
$988$		0			0
$989$	16.2864			0.517877
$990$		0			0
$991$	13.8156	+	23.9293i	0.438866	+	0.760139i	0.997602	−	0.0692069i	$-0.0220469\pi$
$991$	13.8156	+	23.9293i	0.438866	+	0.760139i	−0.558736	+	0.829346i	$0.688714\pi$
$992$		0			0
$993$	2.96641	+	5.13798i	0.0941363	+	0.163049i
$994$		0			0
$995$		−	21.3904i		−	0.678122i
$996$		0			0
$997$	−11.8340	+	20.4970i	−0.374786	+	0.649148i	−0.990295	−	0.138982i	$-0.955617\pi$
$997$	−11.8340	+	20.4970i	−0.374786	+	0.649148i	0.615509	+	0.788130i	$0.288950\pi$
$998$		0			0
$999$		−	1.54618i		−	0.0489191i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1216.2.n.f.639.4		16
4.3	odd	2	inner	1216.2.n.f.639.5		16
8.3	odd	2		76.2.f.a.31.5	yes	16
8.5	even	2		76.2.f.a.31.2	yes	16
19.8	odd	6	inner	1216.2.n.f.255.5		16
24.5	odd	2		684.2.r.a.487.7		16
24.11	even	2		684.2.r.a.487.4		16
76.27	even	6	inner	1216.2.n.f.255.4		16
152.27	even	6		76.2.f.a.27.2	✓	16
152.141	odd	6		76.2.f.a.27.5	yes	16
456.179	odd	6		684.2.r.a.559.7		16
456.293	even	6		684.2.r.a.559.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.2.f.a.27.2	✓	16	152.27	even	6
76.2.f.a.27.5	yes	16	152.141	odd	6
76.2.f.a.31.2	yes	16	8.5	even	2
76.2.f.a.31.5	yes	16	8.3	odd	2
684.2.r.a.487.4		16	24.11	even	2
684.2.r.a.487.7		16	24.5	odd	2
684.2.r.a.559.4		16	456.293	even	6
684.2.r.a.559.7		16	456.179	odd	6
1216.2.n.f.255.4		16	76.27	even	6	inner
1216.2.n.f.255.5		16	19.8	odd	6	inner
1216.2.n.f.639.4		16	1.1	even	1	trivial
1216.2.n.f.639.5		16	4.3	odd	2	inner

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:	\( N \)	\(=\)	\( 1216 = 2^{6} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1216.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.305055 - 0.528371i) q^{3} +(-1.59295 - 2.75907i) q^{5} -2.36291i q^{7} +(1.31388 - 2.27571i) q^{9} -5.46750i q^{11} +(2.31924 + 1.33901i) q^{13} +(-0.971875 + 1.68334i) q^{15} +(-0.552780 - 0.957443i) q^{17} +(1.37952 + 4.13484i) q^{19} +(-1.24849 + 0.720818i) q^{21} +(-2.46168 - 1.42125i) q^{23} +(-2.57499 + 4.46001i) q^{25} -3.43356 q^{27} +(5.63736 + 3.25473i) q^{29} -1.01504 q^{31} +(-2.88887 + 1.66789i) q^{33} +(-6.51945 + 3.76400i) q^{35} +0.450315i q^{37} -1.63389i q^{39} +(0.336089 - 0.194041i) q^{41} +(-4.96197 + 2.86479i) q^{43} -8.37180 q^{45} +(-2.91563 - 1.68334i) q^{47} +1.41665 q^{49} +(-0.337257 + 0.584146i) q^{51} +(3.53036 + 2.03825i) q^{53} +(-15.0852 + 8.70946i) q^{55} +(1.76390 - 1.99025i) q^{57} +(-6.82450 - 11.8204i) q^{59} +(6.77885 - 11.7413i) q^{61} +(-5.37731 - 3.10459i) q^{63} -8.53193i q^{65} +(-4.27064 + 7.39696i) q^{67} +1.73424i q^{69} +(-1.07447 - 1.86103i) q^{71} +(3.91944 + 6.78867i) q^{73} +3.14205 q^{75} -12.9192 q^{77} +(5.57208 + 9.65112i) q^{79} +(-2.89422 - 5.01294i) q^{81} -4.14868i q^{83} +(-1.76110 + 3.05032i) q^{85} -3.97149i q^{87} +(4.19126 + 2.41982i) q^{89} +(3.16397 - 5.48016i) q^{91} +(0.309642 + 0.536316i) q^{93} +(9.21082 - 10.3928i) q^{95} +(-0.641491 + 0.370365i) q^{97} +(-12.4425 - 7.18366i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{5} - 4 q^{9} + 18 q^{13} + 2 q^{17} - 2 q^{25} + 6 q^{29} + 18 q^{33} - 48 q^{41} - 24 q^{45} + 16 q^{49} - 6 q^{53} - 26 q^{57} + 26 q^{61} + 16 q^{73} - 80 q^{77} + 12 q^{81} - 14 q^{85} + 18 q^{89}+ \cdots - 12 q^{97}+O(q^{100}) \) 16 * q + 2 * q^5 - 4 * q^9 + 18 * q^13 + 2 * q^17 - 2 * q^25 + 6 * q^29 + 18 * q^33 - 48 * q^41 - 24 * q^45 + 16 * q^49 - 6 * q^53 - 26 * q^57 + 26 * q^61 + 16 * q^73 - 80 * q^77 + 12 * q^81 - 14 * q^85 + 18 * q^89 + 20 * q^93 - 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more