LMFDB - Embedded newform 117.3.p.a.107.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,3,Mod(35,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("117.35");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	117.p (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:	$3.18801909302$
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} - 32 x^{18} + 690 x^{16} - 7984 x^{14} + 66147 x^{12} - 315440 x^{10} + 1074610 x^{8} + \cdots + 1327104 $ x^20 - 32x^18 + 690x^16 - 7984x^14 + 66147x^12 - 315440x^10 + 1074610x^8 - 2130504x^6 + 3043521x^4 - 2471040*x^2 + 1327104
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			107.2
Root			$-2.68869 - 1.55231i$ of defining polynomial
Character	$\chi$	$=$	117.107
Dual form			117.3.p.a.35.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.68869 + 1.55231i) q^{2} +(2.81935 - 4.88326i) q^{4} +1.11552i q^{5} +(3.02043 - 5.23153i) q^{7} +5.08757i q^{8} +(-1.73164 - 2.99928i) q^{10} +(6.97549 - 4.02730i) q^{11} +(11.3646 + 6.31242i) q^{13} +18.7546i q^{14} +(3.37991 + 5.85418i) q^{16} +(10.8335 + 6.25475i) q^{17} +(-11.9460 + 20.6910i) q^{19} +(5.44737 + 3.14504i) q^{20} +(-12.5033 + 21.6563i) q^{22} +(4.66601 - 2.69392i) q^{23} +23.7556 q^{25} +(-40.3546 + 0.669252i) q^{26} +(-17.0313 - 29.4991i) q^{28} +(48.6098 - 28.0649i) q^{29} +5.07777 q^{31} +(-35.7989 - 20.6685i) q^{32} -38.8373 q^{34} +(5.83588 + 3.36935i) q^{35} +(-23.1859 - 40.1592i) q^{37} -74.1754i q^{38} -5.67528 q^{40} +(-43.4982 + 25.1137i) q^{41} +(26.0986 - 45.2041i) q^{43} -45.4175i q^{44} +(-8.36361 + 14.4862i) q^{46} -31.5408i q^{47} +(6.25403 + 10.8323i) q^{49} +(-63.8714 + 36.8762i) q^{50} +(62.8659 - 37.6992i) q^{52} +53.8374i q^{53} +(4.49254 + 7.78130i) q^{55} +(26.6158 + 15.3666i) q^{56} +(-87.1310 + 150.915i) q^{58} +(47.3544 + 27.3401i) q^{59} +(-24.9071 + 43.1404i) q^{61} +(-13.6525 + 7.88229i) q^{62} +101.297 q^{64} +(-7.04163 + 12.6774i) q^{65} +(-57.4929 - 99.5806i) q^{67} +(61.0872 - 35.2687i) q^{68} -20.9211 q^{70} +(55.9889 + 32.3252i) q^{71} +23.1540 q^{73} +(124.679 + 71.9837i) q^{74} +(67.3597 + 116.670i) q^{76} -48.6567i q^{77} -80.7964 q^{79} +(-6.53046 + 3.77036i) q^{80} +(77.9687 - 135.046i) q^{82} -53.2055i q^{83} +(-6.97730 + 12.0850i) q^{85} +162.053i q^{86} +(20.4892 + 35.4883i) q^{88} +(-127.780 + 73.7737i) q^{89} +(67.3495 - 40.3879i) q^{91} -30.3804i q^{92} +(48.9611 + 84.8032i) q^{94} +(-23.0812 - 13.3259i) q^{95} +(13.6694 - 23.6760i) q^{97} +(-33.6303 - 19.4164i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 24 q^{4} - 6 q^{7} + 12 q^{10} - 2 q^{13} - 104 q^{16} - 92 q^{19} + 44 q^{22} - 116 q^{25} + 76 q^{28} - 156 q^{31} + 80 q^{34} + 148 q^{37} + 328 q^{40} + 186 q^{43} + 164 q^{46} + 8 q^{49} + 392 q^{52}+ \cdots - 14 q^{97}+O(q^{100}) $ 20 * q + 24 * q^4 - 6 * q^7 + 12 * q^10 - 2 * q^13 - 104 * q^16 - 92 * q^19 + 44 * q^22 - 116 * q^25 + 76 * q^28 - 156 * q^31 + 80 * q^34 + 148 * q^37 + 328 * q^40 + 186 * q^43 + 164 * q^46 + 8 * q^49 + 392 * q^52 - 208 * q^55 - 236 * q^58 + 210 * q^61 - 1568 * q^64 - 158 * q^67 - 1048 * q^70 + 156 * q^73 + 764 * q^76 - 132 * q^79 + 648 * q^82 + 44 * q^85 + 372 * q^88 + 834 * q^91 - 220 * q^94 - 14 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	−2.68869	+	1.55231i	−1.34434	+	0.776157i	−0.987441	−	0.157986i	$-0.949500\pi$
$2$	−2.68869	+	1.55231i	−1.34434	+	0.776157i	−0.356901	+	0.934142i	$0.616167\pi$
$3$		0			0
$3$		0			0
$4$	2.81935	−	4.88326i	0.704838	−	1.22082i
$5$			1.11552i			0.223104i	0.993759	+	0.111552i	$0.0355822\pi$
$5$			1.11552i			0.223104i	−0.993759	+	0.111552i	$0.964418\pi$
$6$		0			0
$7$	3.02043	−	5.23153i	0.431490	−	0.747362i	−0.565512	−	0.824740i	$-0.691321\pi$
$7$	3.02043	−	5.23153i	0.431490	−	0.747362i	0.997002	+	0.0773779i	$0.0246548\pi$
$8$			5.08757i			0.635946i
$9$		0			0
$10$	−1.73164	−	2.99928i	−0.173164	−	0.299928i
$11$	6.97549	−	4.02730i	0.634136	−	0.366118i	−0.148216	−	0.988955i	$-0.547353\pi$
$11$	6.97549	−	4.02730i	0.634136	−	0.366118i	0.782352	+	0.622837i	$0.214020\pi$
$12$		0			0
$13$	11.3646	+	6.31242i	0.874197	+	0.485571i
$13$	11.3646	+	6.31242i	0.874197	+	0.485571i
$14$			18.7546i			1.33961i
$15$		0			0
$16$	3.37991	+	5.85418i	0.211245	+	0.365886i
$17$	10.8335	+	6.25475i	0.637267	+	0.367926i	0.783561	−	0.621315i	$-0.213401\pi$
$17$	10.8335	+	6.25475i	0.637267	+	0.367926i	−0.146294	+	0.989241i	$0.546734\pi$
$18$		0			0
$19$	−11.9460	+	20.6910i	−0.628734	+	1.08900i	0.359072	+	0.933310i	$0.383093\pi$
$19$	−11.9460	+	20.6910i	−0.628734	+	1.08900i	−0.987806	+	0.155690i	$0.950240\pi$
$20$	5.44737	+	3.14504i	0.272369	+	0.157252i
$21$		0			0
$22$	−12.5033	+	21.6563i	−0.568330	+	0.984377i
$23$	4.66601	−	2.69392i	0.202870	−	0.117127i	−0.395124	−	0.918628i	$-0.629298\pi$
$23$	4.66601	−	2.69392i	0.202870	−	0.117127i	0.597993	+	0.801501i	$0.295965\pi$
$24$		0			0
$25$	23.7556			0.950225
$26$	−40.3546	+	0.669252i	−1.55210	+	0.0257405i
$27$		0			0
$28$	−17.0313	−	29.4991i	−0.608261	−	1.05354i
$29$	48.6098	−	28.0649i	1.67620	−	0.967755i	0.712153	−	0.702024i	$-0.247720\pi$
$29$	48.6098	−	28.0649i	1.67620	−	0.967755i	0.964047	−	0.265730i	$-0.0856130\pi$
$30$		0			0
$31$	5.07777			0.163799			0.0818995	−	0.996641i	$-0.473901\pi$
$31$	5.07777			0.163799			0.0818995	+	0.996641i	$0.473901\pi$
$32$	−35.7989	−	20.6685i	−1.11872	−	0.645891i
$33$		0			0
$34$	−38.8373			−1.14227
$35$	5.83588	+	3.36935i	0.166739	+	0.0962670i
$36$		0			0
$37$	−23.1859	−	40.1592i	−0.626647	−	1.08538i	−0.988220	−	0.153041i	$-0.951093\pi$
$37$	−23.1859	−	40.1592i	−0.626647	−	1.08538i	0.361573	−	0.932344i	$-0.382240\pi$
$38$		−	74.1754i		−	1.95199i
$39$		0			0
$40$	−5.67528			−0.141882
$41$	−43.4982	+	25.1137i	−1.06093	+	0.612530i	−0.925690	−	0.378283i	$-0.876515\pi$
$41$	−43.4982	+	25.1137i	−1.06093	+	0.612530i	−0.135243	+	0.990813i	$0.543181\pi$
$42$		0			0
$43$	26.0986	−	45.2041i	0.606944	−	1.05126i	−0.384797	−	0.923001i	$-0.625729\pi$
$43$	26.0986	−	45.2041i	0.606944	−	1.05126i	0.991741	−	0.128257i	$-0.0409381\pi$
$44$		−	45.4175i		−	1.03222i
$45$		0			0
$46$	−8.36361	+	14.4862i	−0.181818	+	0.314917i
$47$		−	31.5408i		−	0.671080i	−0.942026	−	0.335540i	$-0.891081\pi$
$47$		−	31.5408i		−	0.671080i	0.942026	−	0.335540i	$-0.108919\pi$
$48$		0			0
$49$	6.25403	+	10.8323i	0.127633	+	0.221067i
$50$	−63.8714	+	36.8762i	−1.27743	+	0.737523i
$51$		0			0
$52$	62.8659	−	37.6992i	1.20896	−	0.724985i
$53$			53.8374i			1.01580i	0.861416	+	0.507900i	$0.169578\pi$
$53$			53.8374i			1.01580i	−0.861416	+	0.507900i	$0.830422\pi$
$54$		0			0
$55$	4.49254	+	7.78130i	0.0816825	+	0.141478i
$56$	26.6158	+	15.3666i	0.475282	+	0.274404i
$57$		0			0
$58$	−87.1310	+	150.915i	−1.50226	+	2.60199i
$59$	47.3544	+	27.3401i	0.802617	+	0.463391i	0.844385	−	0.535736i	$-0.179966\pi$
$59$	47.3544	+	27.3401i	0.802617	+	0.463391i	−0.0417683	+	0.999127i	$0.513299\pi$
$60$		0			0
$61$	−24.9071	+	43.1404i	−0.408314	+	0.707220i	−0.994701	−	0.102811i	$-0.967216\pi$
$61$	−24.9071	+	43.1404i	−0.408314	+	0.707220i	0.586387	+	0.810031i	$0.300550\pi$
$62$	−13.6525	+	7.88229i	−0.220202	+	0.127134i
$63$		0			0
$64$	101.297			1.58276
$65$	−7.04163	+	12.6774i	−0.108333	+	0.195037i
$66$		0			0
$67$	−57.4929	−	99.5806i	−0.858103	−	1.48628i	−0.873736	−	0.486400i	$-0.838310\pi$
$67$	−57.4929	−	99.5806i	−0.858103	−	1.48628i	0.0156329	−	0.999878i	$-0.495024\pi$
$68$	61.0872	−	35.2687i	0.898341	−	0.518657i
$69$		0			0
$70$	−20.9211			−0.298873
$71$	55.9889	+	32.3252i	0.788576	+	0.455285i	0.839461	−	0.543420i	$-0.182871\pi$
$71$	55.9889	+	32.3252i	0.788576	+	0.455285i	−0.0508847	+	0.998705i	$0.516204\pi$
$72$		0			0
$73$	23.1540			0.317179			0.158589	−	0.987345i	$-0.449305\pi$
$73$	23.1540			0.317179			0.158589	+	0.987345i	$0.449305\pi$
$74$	124.679	+	71.9837i	1.68486	+	0.972752i
$75$		0			0
$76$	67.3597	+	116.670i	0.886312	+	1.53514i
$77$		−	48.6567i		−	0.631905i
$78$		0			0
$79$	−80.7964			−1.02274			−0.511370	−	0.859361i	$-0.670862\pi$
$79$	−80.7964			−1.02274			−0.511370	+	0.859361i	$0.670862\pi$
$80$	−6.53046	+	3.77036i	−0.0816307	+	0.0471295i
$81$		0			0
$82$	77.9687	−	135.046i	0.950838	−	1.64690i
$83$		−	53.2055i		−	0.641031i	−0.947243	−	0.320515i	$-0.896144\pi$
$83$		−	53.2055i		−	0.641031i	0.947243	−	0.320515i	$-0.103856\pi$
$84$		0			0
$85$	−6.97730	+	12.0850i	−0.0820859	+	0.142177i
$86$			162.053i			1.88433i
$87$		0			0
$88$	20.4892	+	35.4883i	0.232831	+	0.403276i
$89$	−127.780	+	73.7737i	−1.43573	+	0.828918i	−0.997549	−	0.0699700i	$-0.977710\pi$
$89$	−127.780	+	73.7737i	−1.43573	+	0.828918i	−0.438179	+	0.898888i	$0.644376\pi$
$90$		0			0
$91$	67.3495	−	40.3879i	0.740104	−	0.443823i
$92$		−	30.3804i		−	0.330222i
$93$		0			0
$94$	48.9611	+	84.8032i	0.520863	+	0.902162i
$95$	−23.0812	−	13.3259i	−0.242960	−	0.140273i
$96$		0			0
$97$	13.6694	−	23.6760i	0.140921	−	0.244083i	−0.786923	−	0.617052i	$-0.788327\pi$
$97$	13.6694	−	23.6760i	0.140921	−	0.244083i	0.927844	+	0.372969i	$0.121660\pi$
$98$	−33.6303	−	19.4164i	−0.343166	−	0.198127i
$99$		0			0
$100$	66.9755	−	116.005i	0.669755	−	1.16005i
$101$	−112.681	+	65.0566i	−1.11566	+	0.644125i	−0.940289	−	0.340378i	$-0.889445\pi$
$101$	−112.681	+	65.0566i	−1.11566	+	0.644125i	−0.175368	+	0.984503i	$0.556112\pi$
$102$		0			0
$103$	−45.0788			−0.437658			−0.218829	−	0.975763i	$-0.570224\pi$
$103$	−45.0788			−0.437658			−0.218829	+	0.975763i	$0.570224\pi$
$104$	−32.1149	+	57.8180i	−0.308797	+	0.555942i
$105$		0			0
$106$	−83.5725	−	144.752i	−0.788420	−	1.36558i
$107$	−1.49273	+	0.861830i	−0.0139508	+	0.00805449i	−0.506959	−	0.861970i	$-0.669231\pi$
$107$	−1.49273	+	0.861830i	−0.0139508	+	0.00805449i	0.493008	+	0.870025i	$0.335897\pi$
$108$		0			0
$109$	51.4209			0.471751			0.235875	−	0.971783i	$-0.424204\pi$
$109$	51.4209			0.471751			0.235875	+	0.971783i	$0.424204\pi$
$110$	−24.1580	−	13.9476i	−0.219618	−	0.126797i
$111$		0			0
$112$	40.8351			0.364599
$113$	48.6041	+	28.0616i	0.430125	+	0.248333i	0.699400	−	0.714731i	$-0.253451\pi$
$113$	48.6041	+	28.0616i	0.430125	+	0.248333i	−0.269275	+	0.963063i	$0.586784\pi$
$114$		0			0
$115$	3.00512	+	5.20502i	0.0261315	+	0.0452611i
$116$		−	316.499i		−	2.72844i
$117$		0			0
$118$	−169.761			−1.43866
$119$	65.4439	−	37.7840i	0.549949	−	0.317513i
$120$		0			0
$121$	−28.0617	+	48.6042i	−0.231915	+	0.401688i
$122$		−	154.655i		−	1.26766i
$123$		0			0
$124$	14.3160	−	24.7961i	0.115452	−	0.199968i
$125$			54.3879i			0.435103i
$126$		0			0
$127$	−43.8145	−	75.8890i	−0.344996	−	0.597551i	0.640357	−	0.768078i	$-0.278786\pi$
$127$	−43.8145	−	75.8890i	−0.344996	−	0.597551i	−0.985353	+	0.170526i	$0.945453\pi$
$128$	−129.159	+	74.5701i	−1.00906	+	0.582579i
$129$		0			0
$130$	−0.746564	−	45.0163i	−0.00574280	−	0.346280i
$131$		−	238.427i		−	1.82005i	−0.414552	−	0.910026i	$-0.636062\pi$
$131$		−	238.427i		−	1.82005i	0.414552	−	0.910026i	$-0.363938\pi$
$132$		0			0
$133$	72.1638	+	124.991i	0.542585	+	0.939784i
$134$	309.161	+	178.494i	2.30717	+	1.33204i
$135$		0			0
$136$	−31.8215	+	55.1164i	−0.233981	+	0.405268i
$137$	−110.979	−	64.0740i	−0.810068	−	0.467693i	0.0369112	−	0.999319i	$-0.488248\pi$
$137$	−110.979	−	64.0740i	−0.810068	−	0.467693i	−0.846980	+	0.531625i	$0.821581\pi$
$138$		0			0
$139$	−131.585	+	227.911i	−0.946651	+	1.63965i	−0.194241	+	0.980954i	$0.562224\pi$
$139$	−131.585	+	227.911i	−0.946651	+	1.63965i	−0.752411	+	0.658694i	$0.771109\pi$
$140$	32.9068	−	18.9988i	0.235049	−	0.135705i
$141$		0			0
$142$	−200.715			−1.41349
$143$	104.695	−	1.73630i	0.732136	−	0.0121420i
$144$		0			0
$145$	31.3069	+	54.2252i	0.215910	+	0.373967i
$146$	−62.2539	+	35.9423i	−0.426397	+	0.246180i
$147$		0			0
$148$	−261.477			−1.76674
$149$	−17.5133	−	10.1113i	−0.117539	−	0.0678610i	0.440078	−	0.897960i	$-0.354951\pi$
$149$	−17.5133	−	10.1113i	−0.117539	−	0.0678610i	−0.557617	+	0.830099i	$0.688284\pi$
$150$		0			0
$151$	103.283			0.683994			0.341997	−	0.939701i	$-0.388897\pi$
$151$	103.283			0.683994			0.341997	+	0.939701i	$0.388897\pi$
$152$	−105.267	−	60.7758i	−0.692545	−	0.399841i
$153$		0			0
$154$	75.5304	+	130.823i	0.490457	+	0.849497i
$155$			5.66435i			0.0365442i
$156$		0			0
$157$	163.877			1.04380			0.521901	−	0.853006i	$-0.325223\pi$
$157$	163.877			1.04380			0.521901	+	0.853006i	$0.325223\pi$
$158$	217.236	−	125.421i	1.37491	−	0.793806i
$159$		0			0
$160$	23.0561	−	39.9344i	0.144101	−	0.249590i
$161$		−	32.5472i		−	0.202156i
$162$		0			0
$163$	−110.733	+	191.795i	−0.679344	+	1.17666i	0.295835	+	0.955239i	$0.404402\pi$
$163$	−110.733	+	191.795i	−0.679344	+	1.17666i	−0.975179	+	0.221419i	$0.928931\pi$
$164$			283.218i			1.72694i
$165$		0			0
$166$	82.5917	+	143.053i	0.497540	+	0.861765i
$167$	−134.363	+	77.5747i	−0.804571	+	0.464519i	−0.845067	−	0.534660i	$-0.820440\pi$
$167$	−134.363	+	77.5747i	−0.804571	+	0.464519i	0.0404960	+	0.999180i	$0.487106\pi$
$168$		0			0
$169$	89.3067	+	143.476i	0.528442	+	0.848969i
$170$		−	43.3238i		−	0.254846i
$171$		0			0
$172$	−147.162	−	254.892i	−0.855594	−	1.48193i
$173$	−118.525	−	68.4304i	−0.685115	−	0.395551i	0.116665	−	0.993171i	$-0.462780\pi$
$173$	−118.525	−	68.4304i	−0.685115	−	0.395551i	−0.801779	+	0.597620i	$0.796113\pi$
$174$		0			0
$175$	71.7521	−	124.278i	0.410012	−	0.710162i
$176$	47.1531	+	27.2239i	0.267915	+	0.154681i
$177$		0			0
$178$	229.040	−	396.708i	1.28674	−	2.22870i
$179$	89.3566	−	51.5900i	0.499199	−	0.288213i	−0.229184	−	0.973383i	$-0.573606\pi$
$179$	89.3566	−	51.5900i	0.499199	−	0.288213i	0.728383	+	0.685171i	$0.240272\pi$
$180$		0			0
$181$	−300.340			−1.65934			−0.829668	−	0.558257i	$-0.811470\pi$
$181$	−300.340			−1.65934			−0.829668	+	0.558257i	$0.811470\pi$
$182$	−118.387	+	213.138i	−0.650478	+	1.17109i
$183$		0			0
$184$	13.7055	+	23.7386i	0.0744864	+	0.129014i
$185$	44.7984	−	25.8644i	0.242154	−	0.139807i
$186$		0			0
$187$	100.759			0.538819
$188$	−154.022	−	88.9245i	−0.819265	−	0.473003i
$189$		0			0
$190$	82.7442			0.435496
$191$	36.4642	+	21.0526i	0.190912	+	0.110223i	0.592409	−	0.805637i	$-0.298177\pi$
$191$	36.4642	+	21.0526i	0.190912	+	0.110223i	−0.401497	+	0.915860i	$0.631510\pi$
$192$		0			0
$193$	43.3600	+	75.1017i	0.224663	+	0.389128i	0.956218	−	0.292654i	$-0.0945385\pi$
$193$	43.3600	+	75.1017i	0.224663	+	0.389128i	−0.731555	+	0.681782i	$0.761205\pi$
$194$			84.8765i			0.437508i
$195$		0			0
$196$	70.5293			0.359843
$197$	−57.8728	+	33.4129i	−0.293771	+	0.169609i	−0.639641	−	0.768674i	$-0.720917\pi$
$197$	−57.8728	+	33.4129i	−0.293771	+	0.169609i	0.345870	+	0.938282i	$0.387584\pi$
$198$		0			0
$199$	112.545	−	194.933i	0.565551	−	0.979563i	−0.431447	−	0.902138i	$-0.641997\pi$
$199$	112.545	−	194.933i	0.565551	−	0.979563i	0.996998	−	0.0774251i	$-0.0246699\pi$
$200$			120.858i			0.604291i
$201$		0			0
$202$	201.976	−	349.833i	0.999883	−	1.73185i
$203$		−	339.072i		−	1.67030i
$204$		0			0
$205$	−28.0149	−	48.5231i	−0.136658	−	0.236698i
$206$	121.203	−	69.9764i	0.588362	−	0.339691i
$207$		0			0
$208$	1.45719	+	87.8657i	0.00700572	+	0.422431i
$209$			192.440i			0.920765i
$210$		0			0
$211$	−177.438	−	307.332i	−0.840939	−	1.45655i	−0.889102	−	0.457709i	$-0.848670\pi$
$211$	−177.438	−	307.332i	−0.840939	−	1.45655i	0.0481632	−	0.998839i	$-0.484663\pi$
$212$	262.902	+	151.787i	1.24010	+	0.715975i
$213$		0			0
$214$	2.67566	−	4.63438i	0.0125031	−	0.0216560i
$215$	50.4260	+	29.1135i	0.234540	+	0.135412i
$216$		0			0
$217$	15.3370	−	26.5645i	0.0706776	−	0.122417i
$218$	−138.255	+	79.8213i	−0.634195	+	0.366153i
$219$		0			0
$220$	50.6642			0.230292
$221$	83.6359	+	139.468i	0.378443	+	0.631079i
$222$		0			0
$223$	135.201	+	234.175i	0.606281	+	1.05011i	0.991848	+	0.127430i	$0.0406728\pi$
$223$	135.201	+	234.175i	0.606281	+	1.05011i	−0.385566	+	0.922680i	$0.625994\pi$
$224$	−216.256	+	124.855i	−0.965428	+	0.557390i
$225$		0			0
$226$	−174.242			−0.770981
$227$	−347.799	−	200.802i	−1.53215	−	0.884589i	−0.999262	−	0.0384055i	$-0.987772\pi$
$227$	−347.799	−	200.802i	−1.53215	−	0.884589i	−0.532891	−	0.846184i	$-0.678895\pi$
$228$		0			0
$229$	306.258			1.33737			0.668686	−	0.743545i	$-0.266857\pi$
$229$	306.258			1.33737			0.668686	+	0.743545i	$0.266857\pi$
$230$	−16.1596	−	9.32978i	−0.0702593	−	0.0405642i
$231$		0			0
$232$	142.782	+	247.306i	0.615440	+	1.06597i
$233$			360.011i			1.54511i	0.634946	+	0.772556i	$0.281022\pi$
$233$			360.011i			1.54511i	−0.634946	+	0.772556i	$0.718978\pi$
$234$		0			0
$235$	35.1843			0.149721
$236$	267.018	−	154.163i	1.13143	−	0.653232i
$237$		0			0
$238$	−117.305	+	203.179i	−0.492880	+	0.853692i
$239$			279.768i			1.17058i	0.810825	+	0.585289i	$0.199019\pi$
$239$			279.768i			1.17058i	−0.810825	+	0.585289i	$0.800981\pi$
$240$		0			0
$241$	−44.0179	+	76.2412i	−0.182647	+	0.316353i	−0.942781	−	0.333413i	$-0.891800\pi$
$241$	−44.0179	+	76.2412i	−0.182647	+	0.316353i	0.760134	+	0.649766i	$0.225133\pi$
$242$		−	174.242i		−	0.720008i
$243$		0			0
$244$	140.444	+	243.256i	0.575590	+	0.996951i
$245$	−12.0837	+	6.97650i	−0.0493210	+	0.0284755i
$246$		0			0
$247$	−266.371	+	159.736i	−1.07842	+	0.646706i
$248$			25.8335i			0.104167i
$249$		0			0
$250$	−84.4270	−	146.232i	−0.337708	−	0.584927i
$251$	206.190	+	119.044i	0.821473	+	0.474278i	0.850924	−	0.525289i	$-0.176043\pi$
$251$	206.190	+	119.044i	0.821473	+	0.474278i	−0.0294512	+	0.999566i	$0.509376\pi$
$252$		0			0
$253$	21.6985	−	37.5828i	0.0857647	−	0.148549i
$254$	235.607	+	136.028i	0.927586	+	0.535542i
$255$		0			0
$256$	28.9190	−	50.0892i	0.112965	−	0.195661i
$257$	−70.5091	+	40.7085i	−0.274355	+	0.158399i	−0.630865	−	0.775893i	$-0.717300\pi$
$257$	−70.5091	+	40.7085i	−0.274355	+	0.158399i	0.356510	+	0.934291i	$0.383966\pi$
$258$		0			0
$259$	−280.126			−1.08157
$260$	42.0542	+	70.1282i	0.161747	+	0.269724i
$261$		0			0
$262$	370.113	+	641.055i	1.41265	+	2.44677i
$263$	370.192	−	213.730i	1.40757	−	0.812663i	0.412420	−	0.910994i	$-0.364684\pi$
$263$	370.192	−	213.730i	1.40757	−	0.812663i	0.995154	+	0.0983308i	$0.0313503\pi$
$264$		0			0
$265$	−60.0567			−0.226629
$266$	−388.051	−	224.042i	−1.45884	−	0.842262i
$267$		0			0
$268$	−648.371			−2.41930
$269$	−57.4246	−	33.1541i	−0.213474	−	0.123250i	0.389451	−	0.921047i	$-0.372665\pi$
$269$	−57.4246	−	33.1541i	−0.213474	−	0.123250i	−0.602925	+	0.797798i	$0.705998\pi$
$270$		0			0
$271$	−144.004	−	249.421i	−0.531378	−	0.920375i	−0.999329	−	0.0366200i	$-0.988341\pi$
$271$	−144.004	−	249.421i	−0.531378	−	0.920375i	0.467951	−	0.883755i	$-0.344992\pi$
$272$			84.5621i			0.310890i
$273$		0			0
$274$	397.852			1.45201
$275$	165.707	−	95.6711i	0.602571	−	0.347895i
$276$		0			0
$277$	17.5929	−	30.4717i	0.0635121	−	0.110006i	−0.832521	−	0.553994i	$-0.813103\pi$
$277$	17.5929	−	30.4717i	0.0635121	−	0.110006i	0.896033	+	0.443987i	$0.146437\pi$
$278$		−	817.042i		−	2.93900i
$279$		0			0
$280$	−17.1418	+	29.6904i	−0.0612206	+	0.106037i
$281$		−	346.978i		−	1.23480i	−0.786650	−	0.617399i	$-0.788187\pi$
$281$		−	346.978i		−	1.23480i	0.786650	−	0.617399i	$-0.211813\pi$
$282$		0			0
$283$	−193.944	−	335.921i	−0.685315	−	1.18700i	−0.973338	−	0.229377i	$-0.926331\pi$
$283$	−193.944	−	335.921i	−0.685315	−	1.18700i	0.288023	−	0.957624i	$-0.407002\pi$
$284$	315.705	−	182.272i	1.11164	−	0.641804i
$285$		0			0
$286$	−278.798	+	167.189i	−0.974818	+	0.584575i
$287$			303.417i			1.05720i
$288$		0			0
$289$	−66.2562	−	114.759i	−0.229260	−	0.397090i
$290$	−168.349	−	97.1963i	−0.580514	−	0.335160i
$291$		0			0
$292$	65.2794	−	113.067i	0.223560	−	0.387217i
$293$	−185.957	−	107.362i	−0.634665	−	0.366424i	0.147891	−	0.989004i	$-0.452751\pi$
$293$	−185.957	−	107.362i	−0.634665	−	0.366424i	−0.782557	+	0.622580i	$0.786085\pi$
$294$		0			0
$295$	−30.4984	+	52.8248i	−0.103384	+	0.179067i
$296$	204.313	−	117.960i	0.690246	−	0.398514i
$297$		0			0
$298$	62.7836			0.210683
$299$	70.0323	−	1.16144i	0.234222	−	0.00388440i
$300$		0			0
$301$	−157.658	−	273.071i	−0.523780	−	0.907214i
$302$	−277.696	+	160.328i	−0.919522	+	0.530886i
$303$		0			0
$304$	−161.505			−0.531267
$305$	−48.1240	−	27.7844i	−0.157784	−	0.0910964i
$306$		0			0
$307$	−7.29485			−0.0237617			−0.0118809	−	0.999929i	$-0.503782\pi$
$307$	−7.29485			−0.0237617			−0.0118809	+	0.999929i	$0.503782\pi$
$308$	−237.603	−	137.180i	−0.771440	−	0.445391i
$309$		0			0
$310$	−8.79285	−	15.2297i	−0.0283640	−	0.0491279i
$311$			80.3011i			0.258203i	0.991631	+	0.129101i	$0.0412093\pi$
$311$			80.3011i			0.258203i	−0.991631	+	0.129101i	$0.958791\pi$
$312$		0			0
$313$	250.123			0.799115			0.399558	−	0.916708i	$-0.369164\pi$
$313$	250.123			0.799115			0.399558	+	0.916708i	$0.369164\pi$
$314$	−440.614	+	254.388i	−1.40323	+	0.810154i
$315$		0			0
$316$	−227.793	+	394.550i	−0.720865	+	1.24858i
$317$			386.141i			1.21811i	0.793128	+	0.609055i	$0.208451\pi$
$317$			386.141i			1.21811i	−0.793128	+	0.609055i	$0.791549\pi$
$318$		0			0
$319$	226.052	−	391.533i	0.708626	−	1.22738i
$320$			112.998i			0.353120i
$321$		0			0
$322$	50.5234	+	87.5091i	0.156905	+	0.271767i
$323$	−258.834	+	149.438i	−0.801344	+	0.462656i
$324$		0			0
$325$	269.972	+	149.955i	0.830684	+	0.461401i
$326$		−	687.570i		−	2.10911i
$327$		0			0
$328$	−127.768	−	221.300i	−0.389536	−	0.674696i
$329$	−165.007	−	95.2666i	−0.501540	−	0.289564i
$330$		0			0
$331$	62.7935	−	108.762i	0.189709	−	0.328585i	−0.755444	−	0.655213i	$-0.772579\pi$
$331$	62.7935	−	108.762i	0.189709	−	0.328585i	0.945153	+	0.326628i	$0.105912\pi$
$332$	−259.817	−	150.005i	−0.782580	−	0.451823i
$333$		0			0
$334$	240.841	−	417.148i	0.721079	−	1.24895i
$335$	111.084	−	64.1345i	0.331595	−	0.191446i
$336$		0			0
$337$	−264.510			−0.784896			−0.392448	−	0.919774i	$-0.628372\pi$
$337$	−264.510			−0.784896			−0.392448	+	0.919774i	$0.628372\pi$
$338$	−462.837	−	247.129i	−1.36934	−	0.731152i
$339$		0			0
$340$	39.3429	+	68.1439i	0.115714	+	0.200423i
$341$	35.4199	−	20.4497i	0.103871	−	0.0599698i
$342$		0			0
$343$	371.561			1.08327
$344$	229.979	+	132.778i	0.668543	+	0.385983i
$345$		0			0
$346$	424.901			1.22804
$347$	−69.3047	−	40.0131i	−0.199725	−	0.115311i	0.396802	−	0.917904i	$-0.370120\pi$
$347$	−69.3047	−	40.0131i	−0.199725	−	0.115311i	−0.596527	+	0.802593i	$0.703453\pi$
$348$		0			0
$349$	−58.5745	−	101.454i	−0.167835	−	0.290699i	0.769823	−	0.638257i	$-0.220344\pi$
$349$	−58.5745	−	101.454i	−0.167835	−	0.290699i	−0.937658	+	0.347558i	$0.887011\pi$
$350$			445.527i			1.27293i
$351$		0			0
$352$	−332.953			−0.945890
$353$	264.477	−	152.696i	0.749226	−	0.432566i	−0.0761883	−	0.997093i	$-0.524275\pi$
$353$	264.477	−	152.696i	0.749226	−	0.432566i	0.825414	+	0.564528i	$0.190942\pi$
$354$		0			0
$355$	−36.0594	+	62.4568i	−0.101576	+	0.175935i
$356$			831.976i			2.33701i
$357$		0			0
$358$	−160.168	+	277.419i	−0.447396	+	0.774913i
$359$		−	123.190i		−	0.343148i	−0.985171	−	0.171574i	$-0.945115\pi$
$359$		−	123.190i		−	0.343148i	0.985171	−	0.171574i	$-0.0548853\pi$
$360$		0			0
$361$	−104.912	−	181.712i	−0.290614	−	0.503358i
$362$	807.519	−	466.222i	2.23072	−	1.28790i
$363$		0			0
$364$	−7.34274	−	442.753i	−0.0201724	−	1.21635i
$365$			25.8288i			0.0707638i
$366$		0			0
$367$	206.300	+	357.322i	0.562126	+	0.973631i	0.997311	+	0.0732896i	$0.0233497\pi$
$367$	206.300	+	357.322i	0.562126	+	0.973631i	−0.435185	+	0.900341i	$0.643317\pi$
$368$	31.5414	+	18.2104i	0.0857103	+	0.0494849i
$369$		0			0
$370$	−80.2992	+	139.082i	−0.217025	+	0.375898i
$371$	281.652	+	162.612i	0.759171	+	0.438307i
$372$		0			0
$373$	−241.436	+	418.179i	−0.647281	+	1.12112i	0.336489	+	0.941687i	$0.390761\pi$
$373$	−241.436	+	418.179i	−0.647281	+	1.12112i	−0.983770	+	0.179436i	$0.942573\pi$
$374$	−270.909	+	156.410i	−0.724357	+	0.418208i
$375$		0			0
$376$	160.466			0.426771
$377$	729.587	−	12.0997i	1.93524	−	0.0320946i
$378$		0			0
$379$	33.6590	+	58.2991i	0.0888100	+	0.153823i	0.907008	−	0.421113i	$-0.138360\pi$
$379$	33.6590	+	58.2991i	0.0888100	+	0.153823i	−0.818198	+	0.574936i	$0.805027\pi$
$380$	−130.148	+	75.1411i	−0.342495	+	0.197740i
$381$		0			0
$382$	−130.721			−0.342202
$383$	574.563	+	331.724i	1.50016	+	0.866120i	1.00000		0.000189998i	$6.04782e-5\pi$
$383$	574.563	+	331.724i	1.50016	+	0.866120i	0.500165	+	0.865930i	$0.333273\pi$
$384$		0			0
$385$	54.2775			0.140981
$386$	−233.163	−	134.617i	−0.604049	−	0.348748i
$387$		0			0
$388$	−77.0775	−	133.502i	−0.198653	−	0.344078i
$389$		−	144.019i		−	0.370230i	−0.982717	−	0.185115i	$-0.940734\pi$
$389$		−	144.019i		−	0.370230i	0.982717	−	0.185115i	$-0.0592657\pi$
$390$		0			0
$391$	67.3992			0.172376
$392$	−55.1101	+	31.8178i	−0.140587	+	0.0811679i
$393$		0			0
$394$	103.735	−	179.674i	0.263286	−	0.456024i
$395$		−	90.1300i		−	0.228177i
$396$		0			0
$397$	−208.061	+	360.372i	−0.524082	+	0.907737i	0.475524	+	0.879702i	$0.342258\pi$
$397$	−208.061	+	360.372i	−0.524082	+	0.907737i	−0.999607	+	0.0280350i	$0.991075\pi$
$398$			698.818i			1.75583i
$399$		0			0
$400$	80.2919	+	139.070i	0.200730	+	0.347674i
$401$	−150.244	+	86.7436i	−0.374674	+	0.216318i	−0.675498	−	0.737361i	$-0.736071\pi$
$401$	−150.244	+	86.7436i	−0.374674	+	0.216318i	0.300824	+	0.953680i	$0.402738\pi$
$402$		0			0
$403$	57.7066	+	32.0530i	0.143193	+	0.0795360i
$404$			733.670i			1.81601i
$405$		0			0
$406$	526.346	+	911.657i	1.29642	+	2.24546i
$407$	−323.467	−	186.754i	−0.794759	−	0.458854i
$408$		0			0
$409$	172.368	−	298.549i	0.421437	−	0.729950i	−0.574644	−	0.818404i	$-0.694859\pi$
$409$	172.368	−	298.549i	0.421437	−	0.729950i	0.996080	+	0.0884541i	$0.0281927\pi$
$410$	150.646	+	86.9757i	0.367430	+	0.212136i
$411$		0			0
$412$	−127.093	+	220.131i	−0.308478	+	0.534300i
$413$	286.061	−	165.157i	0.692642	−	0.399897i
$414$		0			0
$415$	59.3518			0.143016
$416$	−276.371	−	460.866i	−0.664352	−	1.10785i
$417$		0			0
$418$	−298.727	−	517.410i	−0.714658	−	1.23782i
$419$	22.9084	−	13.2261i	0.0546739	−	0.0315660i	−0.472414	−	0.881377i	$-0.656617\pi$
$419$	22.9084	−	13.2261i	0.0546739	−	0.0315660i	0.527088	+	0.849811i	$0.323284\pi$
$420$		0			0
$421$	755.443			1.79440			0.897200	−	0.441624i	$-0.145597\pi$
$421$	755.443			1.79440			0.897200	+	0.441624i	$0.145597\pi$
$422$	954.150	+	550.879i	2.26102	+	1.30540i
$423$		0			0
$424$	−273.901			−0.645994
$425$	257.358	+	148.585i	0.605547	+	0.349613i
$426$		0			0
$427$	150.460	+	260.605i	0.352366	+	0.610316i
$428$			9.71921i			0.0227084i
$429$		0			0
$430$	−180.773			−0.420402
$431$	−710.453	+	410.180i	−1.64838	+	0.951694i	−0.670667	+	0.741759i	$0.733992\pi$
$431$	−710.453	+	410.180i	−1.64838	+	0.951694i	−0.977715	+	0.209935i	$0.932675\pi$
$432$		0			0
$433$	−66.9125	+	115.896i	−0.154532	+	0.267658i	−0.932889	−	0.360165i	$-0.882720\pi$
$433$	−66.9125	+	115.896i	−0.154532	+	0.267658i	0.778356	+	0.627823i	$0.216054\pi$
$434$			95.2315i			0.219427i
$435$		0			0
$436$	144.974	−	251.102i	0.332508	−	0.575921i
$437$			128.726i			0.294567i
$438$		0			0
$439$	103.467	+	179.210i	0.235688	+	0.408224i	0.959472	−	0.281803i	$-0.0909323\pi$
$439$	103.467	+	179.210i	0.235688	+	0.408224i	−0.723784	+	0.690026i	$0.757599\pi$
$440$	−39.5879	+	22.8561i	−0.0899725	+	0.0519456i
$441$		0			0
$442$	−441.369	−	245.158i	−0.998573	−	0.554655i
$443$		−	453.412i		−	1.02350i	−0.859133	−	0.511752i	$-0.828997\pi$
$443$		−	453.412i		−	1.02350i	0.859133	−	0.511752i	$-0.171003\pi$
$444$		0			0
$445$	−82.2960	−	142.541i	−0.184935	−	0.320317i
$446$	−727.024	−	419.748i	−1.63010	−	0.941138i
$447$		0			0
$448$	305.959	−	529.937i	0.682945	−	1.18289i
$449$	−570.588	−	329.429i	−1.27080	−	0.733695i	−0.295659	−	0.955294i	$-0.595539\pi$
$449$	−570.588	−	329.429i	−1.27080	−	0.733695i	−0.975138	+	0.221599i	$0.928872\pi$
$450$		0			0
$451$	−202.281	+	350.361i	−0.448517	+	0.776854i
$452$	274.064	−	158.231i	0.606337	−	0.350069i
$453$		0			0
$454$	1246.83			2.74632
$455$	45.0535	+	75.1297i	0.0990187	+	0.165120i
$456$		0			0
$457$	−110.001	−	190.527i	−0.240702	−	0.416909i	0.720212	−	0.693754i	$-0.244044\pi$
$457$	−110.001	−	190.527i	−0.240702	−	0.416909i	−0.960915	+	0.276845i	$0.910711\pi$
$458$	−823.432	+	475.409i	−1.79789	+	1.03801i
$459$		0			0
$460$	33.8900			0.0736739
$461$	289.797	+	167.314i	0.628627	+	0.362938i	0.780220	−	0.625505i	$-0.215107\pi$
$461$	289.797	+	167.314i	0.628627	+	0.362938i	−0.151593	+	0.988443i	$0.548440\pi$
$462$		0			0
$463$	304.853			0.658431			0.329215	−	0.944255i	$-0.393216\pi$
$463$	304.853			0.658431			0.329215	+	0.944255i	$0.393216\pi$
$464$	328.594	+	189.714i	0.708176	+	0.408866i
$465$		0			0
$466$	−558.850	−	967.957i	−1.19925	−	2.07716i
$467$		−	740.663i		−	1.58600i	−0.609221	−	0.793001i	$-0.708518\pi$
$467$		−	740.663i		−	1.58600i	0.609221	−	0.793001i	$-0.291482\pi$
$468$		0			0
$469$	−694.613			−1.48105
$470$	−94.5996	+	54.6171i	−0.201276	+	0.116207i
$471$		0			0
$472$	−139.094	+	240.919i	−0.294692	+	0.510421i
$473$		−	420.428i		−	0.888853i
$474$		0			0
$475$	−283.783	+	491.527i	−0.597439	+	1.03479i
$476$		−	426.106i		−	0.895181i
$477$		0			0
$478$	−434.288	−	752.209i	−0.908552	−	1.57366i
$479$	−407.725	+	235.400i	−0.851200	+	0.491440i	−0.861056	−	0.508511i	$-0.830196\pi$
$479$	−407.725	+	235.400i	−0.851200	+	0.491440i	0.00985567	+	0.999951i	$0.496863\pi$
$480$		0			0
$481$	−9.99621	−	602.752i	−0.0207821	−	1.25312i
$482$		−	273.318i		−	0.567050i
$483$		0			0
$484$	158.231	+	274.065i	0.326924	+	0.566250i
$485$	26.4111	+	15.2484i	0.0544558	+	0.0314401i
$486$		0			0
$487$	−42.7761	+	74.0905i	−0.0878360	+	0.152136i	−0.906596	−	0.421999i	$-0.861328\pi$
$487$	−42.7761	+	74.0905i	−0.0878360	+	0.152136i	0.818760	+	0.574136i	$0.194662\pi$
$488$	−219.480	−	126.717i	−0.449754	−	0.259665i
$489$		0			0
$490$	21.6594	−	37.5152i	0.0442029	−	0.0765617i
$491$	−444.713	+	256.755i	−0.905730	+	0.522923i	−0.879055	−	0.476721i	$-0.841825\pi$
$491$	−444.713	+	256.755i	−0.905730	+	0.522923i	−0.0266752	+	0.999644i	$0.508492\pi$
$492$		0			0
$493$	702.155			1.42425
$494$	468.227	−	842.972i	0.947827	−	1.70642i
$495$		0			0
$496$	17.1624	+	29.7262i	0.0346017	+	0.0599318i
$497$	338.221	−	195.272i	0.680525	−	0.392901i
$498$		0			0
$499$	52.0404			0.104289			0.0521447	−	0.998640i	$-0.483394\pi$
$499$	52.0404			0.104289			0.0521447	+	0.998640i	$0.483394\pi$
$500$	265.590	+	153.339i	0.531180	+	0.306677i
$501$		0			0
$502$	−739.172			−1.47245
$503$	−251.465	−	145.184i	−0.499931	−	0.288635i	0.228754	−	0.973484i	$-0.426535\pi$
$503$	−251.465	−	145.184i	−0.499931	−	0.288635i	−0.728685	+	0.684849i	$0.759868\pi$
$504$		0			0
$505$	−72.5719	−	125.698i	−0.143707	−	0.248907i
$506$			134.731i			0.266267i
$507$		0			0
$508$	−494.114			−0.972666
$509$	215.641	−	124.500i	0.423655	−	0.244598i	−0.272985	−	0.962018i	$-0.588011\pi$
$509$	215.641	−	124.500i	0.423655	−	0.244598i	0.696640	+	0.717421i	$0.254677\pi$
$510$		0			0
$511$	69.9351	−	121.131i	0.136859	−	0.237047i
$512$		−	416.995i		−	0.814444i
$513$		0			0
$514$	126.385	−	218.905i	0.245884	−	0.425884i
$515$		−	50.2863i		−	0.0976432i
$516$		0			0
$517$	−127.024	−	220.012i	−0.245695	−	0.425556i
$518$	753.170	−	434.843i	1.45400	−	0.839465i
$519$		0			0
$520$	−64.4971	−	35.8248i	−0.124033	−	0.0688938i
$521$			164.653i			0.316033i	0.987436	+	0.158017i	$0.0505100\pi$
$521$			164.653i			0.316033i	−0.987436	+	0.158017i	$0.949490\pi$
$522$		0			0
$523$	78.0624	+	135.208i	0.149259	+	0.258524i	0.930954	−	0.365137i	$-0.118978\pi$
$523$	78.0624	+	135.208i	0.149259	+	0.258524i	−0.781695	+	0.623661i	$0.785645\pi$
$524$	−1164.30	−	672.209i	−2.22195	−	1.28284i
$525$		0			0
$526$	−663.553	+	1149.31i	−1.26151	+	2.18500i
$527$	55.0102	+	31.7602i	0.104384	+	0.0602660i
$528$		0			0
$529$	−249.986	+	432.988i	−0.472563	+	0.818502i
$530$	161.474	−	93.2268i	0.304667	−	0.175900i
$531$		0			0
$532$	813.820			1.52974
$533$	−652.867	+	10.8273i	−1.22489	+	0.0203140i
$534$		0			0
$535$	−0.961389	−	1.66517i	−0.00179699	−	0.00311247i
$536$	506.623	−	292.499i	0.945192	−	0.545707i
$537$		0			0
$538$	205.862			0.382644
$539$	87.2499	+	50.3738i	0.161874	+	0.0934578i
$540$		0			0
$541$	−563.218			−1.04107			−0.520534	−	0.853841i	$-0.674267\pi$
$541$	−563.218			−1.04107			−0.520534	+	0.853841i	$0.674267\pi$
$542$	774.361	+	447.077i	1.42871	+	0.824866i
$543$		0			0
$544$	−258.553	−	447.826i	−0.475281	−	0.823210i
$545$			57.3610i			0.105250i
$546$		0			0
$547$	−432.234			−0.790190			−0.395095	−	0.918640i	$-0.629288\pi$
$547$	−432.234			−0.790190			−0.395095	+	0.918640i	$0.629288\pi$
$548$	−625.780	+	361.294i	−1.14193	+	0.659296i
$549$		0			0
$550$	−297.023	+	514.459i	−0.540042	+	0.935380i
$551$			1341.05i			2.43384i
$552$		0			0
$553$	−244.040	+	422.689i	−0.441301	+	0.764356i
$554$			109.239i			0.197181i
$555$		0			0
$556$	741.966	+	1285.12i	1.33447	+	2.31137i
$557$	157.788	−	91.0992i	0.283283	−	0.163553i	−0.351626	−	0.936141i	$-0.614371\pi$
$557$	157.788	−	91.0992i	0.283283	−	0.163553i	0.634909	+	0.772587i	$0.281038\pi$
$558$		0			0
$559$	581.946	−	348.979i	1.04105	−	0.624292i
$560$			45.5524i			0.0813436i
$561$		0			0
$562$	538.619	+	932.915i	0.958396	+	1.65999i
$563$	−706.461	−	407.875i	−1.25481	−	0.724468i	−0.282753	−	0.959193i	$-0.591248\pi$
$563$	−706.461	−	407.875i	−1.25481	−	0.724468i	−0.972062	+	0.234725i	$0.924581\pi$
$564$		0			0
$565$	−31.3033	+	54.2189i	−0.0554040	+	0.0959626i
$566$	1042.91	+	602.124i	1.84260	+	1.06382i
$567$		0			0
$568$	−164.457	+	284.847i	−0.289536	+	0.501492i
$569$	−124.183	+	71.6970i	−0.218248	+	0.126005i	−0.605139	−	0.796120i	$-0.706882\pi$
$569$	−124.183	+	71.6970i	−0.218248	+	0.126005i	0.386891	+	0.922125i	$0.373549\pi$
$570$		0			0
$571$	−301.875			−0.528678			−0.264339	−	0.964430i	$-0.585154\pi$
$571$	−301.875			−0.528678			−0.264339	+	0.964430i	$0.585154\pi$
$572$	286.695	−	516.151i	0.501214	−	0.902361i
$573$		0			0
$574$	−470.998	−	815.792i	−0.820554	−	1.42124i
$575$	110.844	−	63.9957i	0.192772	−	0.111297i
$576$		0			0
$577$	−132.688			−0.229962			−0.114981	−	0.993368i	$-0.536681\pi$
$577$	−132.688			−0.229962			−0.114981	+	0.993368i	$0.536681\pi$
$578$	356.284	+	205.701i	0.616409	+	0.355884i
$579$		0			0
$580$	353.061			0.608726
$581$	−278.347	−	160.704i	−0.479082	−	0.276598i
$582$		0			0
$583$	216.820	+	375.543i	0.371903	+	0.644155i
$584$			117.798i			0.201708i
$585$		0			0
$586$	666.639			1.13761
$587$	−657.935	+	379.859i	−1.12084	+	0.647119i	−0.941616	−	0.336689i	$-0.890693\pi$
$587$	−657.935	+	379.859i	−1.12084	+	0.647119i	−0.179227	+	0.983808i	$0.557360\pi$
$588$		0			0
$589$	−60.6588	+	105.064i	−0.102986	+	0.178377i
$590$		−	189.372i		−	0.320970i
$591$		0			0
$592$	156.733	−	271.469i	0.264752	−	0.458563i
$593$		−	629.225i		−	1.06109i	−0.847657	−	0.530544i	$-0.821988\pi$
$593$		−	629.225i		−	1.06109i	0.847657	−	0.530544i	$-0.178012\pi$
$594$		0			0
$595$	42.1488	+	73.0039i	0.0708384	+	0.122696i
$596$	−98.7522	+	57.0146i	−0.165692	+	0.0956621i
$597$		0			0
$598$	−186.492	+	111.835i	−0.311859	+	0.187015i
$599$			503.343i			0.840305i	0.907453	+	0.420153i	$0.138023\pi$
$599$			503.343i			0.840305i	−0.907453	+	0.420153i	$0.861977\pi$
$600$		0			0
$601$	−264.955	−	458.915i	−0.440857	−	0.763586i	0.556896	−	0.830582i	$-0.311992\pi$
$601$	−264.955	−	458.915i	−0.440857	−	0.763586i	−0.997753	+	0.0669956i	$0.978659\pi$
$602$	847.784	+	489.469i	1.40828	+	0.813071i
$603$		0			0
$604$	291.191	−	504.358i	0.482105	−	0.835030i
$605$	−54.2190	−	31.3033i	−0.0896181	−	0.0517411i
$606$		0			0
$607$	−189.318	+	327.908i	−0.311891	+	0.540211i	−0.978772	−	0.204953i	$-0.934296\pi$
$607$	−189.318	+	327.908i	−0.311891	+	0.540211i	0.666881	+	0.745165i	$0.267629\pi$
$608$	855.304	−	493.810i	1.40675	−	0.812187i
$609$		0			0
$610$	172.520			0.282820
$611$	199.099	−	358.447i	0.325857	−	0.586656i
$612$		0			0
$613$	−303.520	−	525.712i	−0.495139	−	0.857605i	0.504846	−	0.863210i	$-0.331549\pi$
$613$	−303.520	−	525.712i	−0.495139	−	0.857605i	−0.999984	+	0.00560423i	$0.998216\pi$
$614$	19.6136	−	11.3239i	0.0319439	−	0.0184428i
$615$		0			0
$616$	247.544			0.401858
$617$	104.350	+	60.2467i	0.169125	+	0.0976445i	0.582173	−	0.813065i	$-0.302203\pi$
$617$	104.350	+	60.2467i	0.169125	+	0.0976445i	−0.413048	+	0.910709i	$0.635536\pi$
$618$		0			0
$619$	−805.505			−1.30130			−0.650650	−	0.759378i	$-0.725504\pi$
$619$	−805.505			−1.30130			−0.650650	+	0.759378i	$0.725504\pi$
$620$	27.6605	+	15.9698i	0.0446137	+	0.0257578i
$621$		0			0
$622$	−124.652	−	215.904i	−0.200406	−	0.347113i
$623$			891.312i			1.43068i
$624$		0			0
$625$	533.220			0.853151
$626$	−672.502	+	388.269i	−1.07429	+	0.620239i
$627$		0			0
$628$	462.027	−	800.254i	0.735712	−	1.27429i
$629$		−	580.089i		−	0.922240i
$630$		0			0
$631$	339.183	−	587.483i	0.537533	−	0.931035i	−0.461503	−	0.887139i	$-0.652690\pi$
$631$	339.183	−	587.483i	0.537533	−	0.931035i	0.999036	−	0.0438961i	$-0.0139770\pi$
$632$		−	411.057i		−	0.650407i
$633$		0			0
$634$	−599.412	−	1038.21i	−0.945444	−	1.63756i
$635$	84.6557	−	48.8760i	0.133316	−	0.0769700i
$636$		0			0
$637$	2.69632	+	162.583i	0.00423284	+	0.255232i
$638$			1403.61i			2.20002i
$639$		0			0
$640$	−83.1844	−	144.080i	−0.129976	−	0.225124i
$641$	128.742	+	74.3289i	0.200845	+	0.115958i	0.597049	−	0.802204i	$-0.296340\pi$
$641$	128.742	+	74.3289i	0.200845	+	0.115958i	−0.396205	+	0.918162i	$0.629673\pi$
$642$		0			0
$643$	−142.221	+	246.333i	−0.221183	+	0.383100i	−0.955167	−	0.296066i	$-0.904325\pi$
$643$	−142.221	+	246.333i	−0.221183	+	0.383100i	0.733985	+	0.679166i	$0.237658\pi$
$644$	−158.936	−	91.7619i	−0.246795	−	0.142487i
$645$		0			0
$646$	463.949	−	803.583i	0.718187	−	1.24394i
$647$	−258.536	+	149.266i	−0.399592	+	0.230704i	−0.686308	−	0.727311i	$-0.740770\pi$
$647$	−258.536	+	149.266i	−0.399592	+	0.230704i	0.286716	+	0.958016i	$0.407436\pi$
$648$		0			0
$649$	440.427			0.678624
$650$	−958.648	+	15.8985i	−1.47484	+	0.0244592i
$651$		0			0
$652$	624.391	+	1081.48i	0.957655	+	1.65871i
$653$	840.205	−	485.093i	1.28668	−	0.742868i	0.308623	−	0.951184i	$-0.400132\pi$
$653$	840.205	−	485.093i	1.28668	−	0.742868i	0.978061	+	0.208317i	$0.0667984\pi$
$654$		0			0
$655$	265.970			0.406061
$656$	−294.041	−	169.764i	−0.448233	−	0.258787i
$657$		0			0
$658$	591.534			0.898988
$659$	−668.610	−	386.022i	−1.01458	−	0.585769i	−0.102052	−	0.994779i	$-0.532541\pi$
$659$	−668.610	−	386.022i	−1.01458	−	0.585769i	−0.912530	+	0.409010i	$0.865874\pi$
$660$		0			0
$661$	−245.612	−	425.412i	−0.371576	−	0.643588i	0.618232	−	0.785995i	$-0.287849\pi$
$661$	−245.612	−	425.412i	−0.371576	−	0.643588i	−0.989808	+	0.142407i	$0.954516\pi$
$662$			389.901i			0.588974i
$663$		0			0
$664$	270.687			0.407661
$665$	−139.430	+	80.5001i	−0.209670	+	0.121053i
$666$		0			0
$667$	151.209	−	261.902i	0.226700	−	0.392656i
$668$			874.842i			1.30964i
$669$		0			0
$670$	−199.114	+	344.875i	−0.297184	+	0.514739i
$671$			401.234i			0.597965i
$672$		0			0
$673$	−34.5009	−	59.7573i	−0.0512644	−	0.0887925i	0.839255	−	0.543739i	$-0.182992\pi$
$673$	−34.5009	−	59.7573i	−0.0512644	−	0.0887925i	−0.890519	+	0.454946i	$0.849658\pi$
$674$	711.184	−	410.602i	1.05517	−	0.609202i
$675$		0			0
$676$	952.417	−	31.5990i	1.40890	−	0.0467441i
$677$			188.294i			0.278129i	0.990283	+	0.139065i	$0.0444096\pi$
$677$			188.294i			0.278129i	−0.990283	+	0.139065i	$0.955590\pi$
$678$		0			0
$679$	−82.5747	−	143.024i	−0.121612	−	0.210638i
$680$	−61.4834	−	35.4975i	−0.0904168	−	0.0522022i
$681$		0			0
$682$	−63.4887	+	109.966i	−0.0930920	+	0.161240i
$683$	−863.397	−	498.483i	−1.26412	−	0.729843i	−0.290255	−	0.956949i	$-0.593740\pi$
$683$	−863.397	−	498.483i	−1.26412	−	0.729843i	−0.973870	+	0.227107i	$0.927073\pi$
$684$		0			0
$685$	71.4758	−	123.800i	0.104344	−	0.180729i
$686$	−999.012	+	576.780i	−1.45628	+	0.840787i
$687$		0			0
$688$	352.844			0.512854
$689$	−339.844	+	611.839i	−0.493243	+	0.888010i
$690$		0			0
$691$	79.7989	+	138.216i	0.115483	+	0.200023i	0.917973	−	0.396643i	$-0.129825\pi$
$691$	79.7989	+	138.216i	0.115483	+	0.200023i	−0.802490	+	0.596666i	$0.796492\pi$
$692$	−668.327	+	385.859i	−0.965790	+	0.557599i
$693$		0			0
$694$	248.451			0.357999
$695$	−254.239	−	146.785i	−0.365812	−	0.211202i
$696$		0			0
$697$	−628.320			−0.901464
$698$	314.977	+	181.852i	0.451256	+	0.260533i
$699$		0			0
$700$	−404.589	−	700.769i	−0.577984	−	1.00110i
$701$		−	238.018i		−	0.339541i	−0.985484	−	0.169771i	$-0.945697\pi$
$701$		−	238.018i		−	0.339541i	0.985484	−	0.169771i	$-0.0543027\pi$
$702$		0			0
$703$	1107.91			1.57598
$704$	706.594	−	407.952i	1.00368	−	0.579478i
$705$		0			0
$706$	−474.063	+	821.101i	−0.671477	+	1.16303i
$707$			785.995i			1.11173i
$708$		0			0
$709$	25.6161	−	44.3684i	0.0361299	−	0.0625789i	−0.847395	−	0.530963i	$-0.821830\pi$
$709$	25.6161	−	44.3684i	0.0361299	−	0.0625789i	0.883525	+	0.468384i	$0.155164\pi$
$710$		−	223.902i		−	0.315355i
$711$		0			0
$712$	−375.329	−	650.088i	−0.527147	−	0.913045i
$713$	23.6929	−	13.6791i	0.0332299	−	0.0191853i
$714$		0			0
$715$	1.93688	+	116.790i	0.00270892	+	0.163342i
$716$		−	581.802i		−	0.812573i
$717$		0			0
$718$	191.230	+	331.220i	0.266337	+	0.461309i
$719$	1030.21	+	594.790i	1.43283	+	0.827246i	0.997336	−	0.0729446i	$-0.0232396\pi$
$719$	1030.21	+	594.790i	1.43283	+	0.827246i	0.435496	+	0.900191i	$0.356573\pi$
$720$		0			0
$721$	−136.157	+	235.831i	−0.188845	+	0.327089i
$722$	564.149	+	325.711i	0.781369	+	0.451124i
$723$		0			0
$724$	−846.764	+	1466.64i	−1.16956	+	2.02574i
$725$	1154.76	−	666.699i	1.59277	−	0.919584i
$726$		0			0
$727$	−0.404850			−0.000556877			−0.000278439	−	1.00000i	$-0.500089\pi$
$727$	−0.404850			−0.000556877			−0.000278439		1.00000i	$0.500089\pi$
$728$	205.476	+	342.645i	0.282247	+	0.470666i
$729$		0			0
$730$	−40.0944	−	69.4455i	−0.0549238	−	0.0951308i
$731$	565.480	−	326.480i	0.773571	−	0.446622i
$732$		0			0
$733$	−559.319			−0.763055			−0.381527	−	0.924358i	$-0.624602\pi$
$733$	−559.319			−0.763055			−0.381527	+	0.924358i	$0.624602\pi$
$734$	−1109.35	−	640.485i	−1.51138	−	0.872596i
$735$		0			0
$736$	−222.717			−0.302605
$737$	−802.083	−	463.083i	−1.08831	−	0.628335i
$738$		0			0
$739$	209.810	+	363.402i	0.283911	+	0.491748i	0.972344	−	0.233551i	$-0.0750347\pi$
$739$	209.810	+	363.402i	0.283911	+	0.491748i	−0.688434	+	0.725299i	$0.741701\pi$
$740$		−	291.683i		−	0.394166i
$741$		0			0
$742$	−1009.70			−1.36078
$743$	729.497	−	421.175i	0.981827	−	0.566858i	0.0790056	−	0.996874i	$-0.474825\pi$
$743$	729.497	−	421.175i	0.981827	−	0.566858i	0.902821	+	0.430016i	$0.141492\pi$
$744$		0			0
$745$	11.2793	−	19.5364i	0.0151401	−	0.0262234i
$746$		−	1499.14i		−	2.00956i
$747$		0			0
$748$	284.075	−	492.033i	0.379780	−	0.657798i
$749$			10.4124i			0.0139017i
$750$		0			0
$751$	416.741	+	721.816i	0.554915	+	0.961140i	0.997910	+	0.0646165i	$0.0205824\pi$
$751$	416.741	+	721.816i	0.554915	+	0.961140i	−0.442996	+	0.896524i	$0.646084\pi$
$752$	184.645	−	106.605i	0.245539	−	0.141762i
$753$		0			0
$754$	−1942.85	+	1165.08i	−2.57672	+	1.54520i
$755$			115.214i			0.152602i
$756$		0			0
$757$	−376.168	−	651.541i	−0.496919	−	0.860689i	0.503075	−	0.864243i	$-0.332202\pi$
$757$	−376.168	−	651.541i	−0.496919	−	0.860689i	−0.999994	+	0.00355402i	$0.998869\pi$
$758$	−180.997	−	104.499i	−0.238782	−	0.137861i
$759$		0			0
$760$	67.7966	−	117.427i	0.0892061	−	0.154510i
$761$	974.738	+	562.765i	1.28086	+	0.739508i	0.977007	−	0.213209i	$-0.0683917\pi$
$761$	974.738	+	562.765i	1.28086	+	0.739508i	0.303858	+	0.952717i	$0.401725\pi$
$762$		0			0
$763$	155.313	−	269.010i	0.203556	−	0.352569i
$764$	205.611	−	118.709i	0.269124	−	0.155379i
$765$		0			0
$766$	−2059.76			−2.68898
$767$	365.580	+	609.629i	0.476637	+	0.794823i
$768$		0			0
$769$	746.826	+	1293.54i	0.971166	+	1.68211i	0.692048	+	0.721851i	$0.256708\pi$
$769$	746.826	+	1293.54i	0.971166	+	1.68211i	0.279117	+	0.960257i	$0.409958\pi$
$770$	−145.935	+	84.2557i	−0.189526	+	0.109423i
$771$		0			0
$772$	488.989			0.633405
$773$	653.621	+	377.368i	0.845564	+	0.488187i	0.859152	−	0.511721i	$-0.170992\pi$
$773$	653.621	+	377.368i	0.845564	+	0.488187i	−0.0135876	+	0.999908i	$0.504325\pi$
$774$		0			0
$775$	120.626			0.155646
$776$	120.453	+	69.5438i	0.155223	+	0.0896183i
$777$		0			0
$778$	223.563	+	387.223i	0.287356	+	0.497715i
$779$		−	1200.03i		−	1.54047i
$780$		0			0
$781$	520.734			0.666753
$782$	−181.215	+	104.625i	−0.231733	+	0.133791i
$783$		0			0
$784$	−42.2762	+	73.2245i	−0.0539237	+	0.0933986i
$785$			182.808i			0.232876i
$786$		0			0
$787$	147.007	−	254.623i	0.186794	−	0.323536i	−0.757386	−	0.652968i	$-0.773524\pi$
$787$	147.007	−	254.623i	0.186794	−	0.323536i	0.944179	+	0.329431i	$0.106857\pi$
$788$			376.811i			0.478187i
$789$		0			0
$790$	139.910	+	242.331i	0.177101	+	0.306748i
$791$	293.611	−	169.516i	0.371189	−	0.214306i
$792$		0			0
$793$	−555.379	+	333.048i	−0.700352	+	0.419985i
$794$		−	1291.90i		−	1.62708i
$795$		0			0
$796$	−634.606	−	1099.17i	−0.797244	−	1.38087i
$797$	−686.295	−	396.232i	−0.861097	−	0.497155i	0.00328220	−	0.999995i	$-0.498955\pi$
$797$	−686.295	−	396.232i	−0.861097	−	0.497155i	−0.864380	+	0.502840i	$0.832289\pi$
$798$		0			0
$799$	197.280	−	341.698i	0.246908	−	0.427657i
$800$	−850.425	−	490.993i	−1.06303	−	0.613741i
$801$		0			0
$802$	269.306	−	466.452i	0.335793	−	0.581611i
$803$	161.511	−	93.2483i	0.201134	−	0.116125i
$804$		0			0
$805$	36.3070			0.0451019
$806$	−204.911	+	3.39831i	−0.254232	+	0.00421626i
$807$		0			0
$808$	−330.980	−	573.274i	−0.409628	−	0.709497i
$809$	−303.661	+	175.319i	−0.375353	+	0.216710i	−0.675795	−	0.737090i	$-0.736199\pi$
$809$	−303.661	+	175.319i	−0.375353	+	0.216710i	0.300441	+	0.953800i	$0.402866\pi$
$810$		0			0
$811$	−276.945			−0.341485			−0.170743	−	0.985316i	$-0.554617\pi$
$811$	−276.945			−0.341485			−0.170743	+	0.985316i	$0.554617\pi$
$812$	−1655.78	−	955.963i	−2.03913	−	1.17729i
$813$		0			0
$814$	1159.60			1.42457
$815$	−213.951	−	123.525i	−0.262517	−	0.151564i
$816$		0			0
$817$	623.545	+	1080.01i	0.763213	+	1.32192i
$818$			1070.27i			1.30840i
$819$		0			0
$820$	−315.935			−0.385287
$821$	976.609	−	563.845i	1.18954	−	0.686779i	0.231334	−	0.972874i	$-0.425691\pi$
$821$	976.609	−	563.845i	1.18954	−	0.686779i	0.958201	+	0.286096i	$0.0923575\pi$
$822$		0			0
$823$	−434.072	+	751.835i	−0.527426	+	0.913529i	0.472063	+	0.881565i	$0.343510\pi$
$823$	−434.072	+	751.835i	−0.527426	+	0.913529i	−0.999489	+	0.0319643i	$0.989824\pi$
$824$		−	229.341i		−	0.278327i
$825$		0			0
$826$	−512.752	+	888.113i	−0.620765	+	1.07520i
$827$		−	173.580i		−	0.209891i	−0.994478	−	0.104946i	$-0.966533\pi$
$827$		−	173.580i		−	0.209891i	0.994478	−	0.104946i	$-0.0334669\pi$
$828$		0			0
$829$	−159.773	−	276.735i	−0.192730	−	0.333818i	0.753424	−	0.657535i	$-0.228401\pi$
$829$	−159.773	−	276.735i	−0.192730	−	0.333818i	−0.946154	+	0.323717i	$0.895067\pi$
$830$	−159.578	+	92.1326i	−0.192263	+	0.111003i
$831$		0			0
$832$	1151.19	+	639.427i	1.38364	+	0.768542i
$833$			156.470i			0.187839i
$834$		0			0
$835$	−86.5361	−	149.885i	−0.103636	−	0.179503i
$836$	939.734	+	542.556i	1.12408	+	0.648990i
$837$		0			0
$838$	−41.0622	+	71.1219i	−0.0490003	+	0.0848710i
$839$	298.945	+	172.596i	0.356311	+	0.205717i	0.667462	−	0.744644i	$-0.267381\pi$
$839$	298.945	+	172.596i	0.356311	+	0.205717i	−0.311150	+	0.950361i	$0.600714\pi$
$840$		0			0
$841$	1154.78	−	2000.13i	1.37310	−	2.37828i
$842$	−2031.15	+	1172.68i	−2.41229	+	1.39274i
$843$		0			0
$844$	−2001.04			−2.37090
$845$	−160.050	+	99.6234i	−0.189408	+	0.117897i
$846$		0			0
$847$	169.516	+	293.611i	0.200137	+	0.346648i
$848$	−315.174	+	181.966i	−0.371667	+	0.214582i
$849$		0			0
$850$	−922.605			−1.08542
$851$	−216.371	−	124.922i	−0.254255	−	0.146794i
$852$		0			0
$853$	671.330			0.787022			0.393511	−	0.919320i	$-0.371260\pi$
$853$	671.330			0.787022			0.393511	+	0.919320i	$0.371260\pi$
$854$	−809.081	−	467.123i	−0.947402	−	0.546983i
$855$		0			0
$856$	−4.38462	−	7.59438i	−0.00512222	−	0.00887194i
$857$			56.0776i			0.0654348i	0.999465	+	0.0327174i	$0.0104161\pi$
$857$			56.0776i			0.0654348i	−0.999465	+	0.0327174i	$0.989584\pi$
$858$		0			0
$859$	−929.971			−1.08262			−0.541310	−	0.840823i	$-0.682072\pi$
$859$	−929.971			−1.08262			−0.541310	+	0.840823i	$0.682072\pi$
$860$	284.338	−	164.162i	0.330625	−	0.190886i
$861$		0			0
$862$	1273.46	−	2205.69i	1.47733	−	2.55881i
$863$		−	2.59692i		−	0.00300918i	−0.999999	−	0.00150459i	$-0.999521\pi$
$863$		−	2.59692i		−	0.00300918i	0.999999	−	0.00150459i	$-0.000478926\pi$
$864$		0			0
$865$	76.3354	−	132.217i	0.0882490	−	0.152852i
$866$		−	415.477i		−	0.479765i
$867$		0			0
$868$	−86.4810	−	149.790i	−0.0996325	−	0.172569i
$869$	−563.595	+	325.391i	−0.648555	+	0.374444i
$870$		0			0
$871$	−24.7871	−	1494.61i	−0.0284582	−	1.71597i
$872$			261.607i			0.300008i
$873$		0			0
$874$	−199.823	−	346.103i	−0.228630	−	0.395999i
$875$	284.532	+	164.275i	0.325179	+	0.187742i
$876$		0			0
$877$	350.928	−	607.826i	0.400146	−	0.693074i	−0.593597	−	0.804763i	$-0.702293\pi$
$877$	350.928	−	607.826i	0.400146	−	0.693074i	0.993743	+	0.111689i	$0.0356260\pi$
$878$	−556.381	−	321.227i	−0.633691	−	0.365862i
$879$		0			0
$880$	−30.3688	+	52.6002i	−0.0345100	+	0.0597730i
$881$	1308.98	−	755.738i	1.48579	−	0.857819i	0.485917	−	0.874005i	$-0.338486\pi$
$881$	1308.98	−	755.738i	1.48579	−	0.857819i	0.999869	+	0.0161862i	$0.00515244\pi$
$882$		0			0
$883$	200.173			0.226696			0.113348	−	0.993555i	$-0.463842\pi$
$883$	200.173			0.226696			0.113348	+	0.993555i	$0.463842\pi$
$884$	916.860	−	15.2055i	1.03717	−	0.0172008i
$885$		0			0
$886$	703.838	+	1219.08i	0.794399	+	1.37594i
$887$	−1321.28	+	762.841i	−1.48961	+	0.860024i	−0.999929	−	0.0118806i	$-0.996218\pi$
$887$	−1321.28	+	762.841i	−1.48961	+	0.860024i	−0.489676	+	0.871905i	$0.662885\pi$
$888$		0			0
$889$	−529.354			−0.595449
$890$	442.536	+	255.498i	0.497232	+	0.287077i
$891$		0			0
$892$	1524.71			1.70932
$893$	652.610	+	376.784i	0.730806	+	0.421931i
$894$		0			0
$895$	57.5497	+	99.6790i	0.0643014	+	0.111373i
$896$			900.934i			1.00551i
$897$		0			0
$898$	2045.51			2.27785
$899$	246.829	−	142.507i	0.274560	−	0.158517i
$900$		0			0
$901$	−336.740	+	583.250i	−0.373740	+	0.647336i
$902$		−	1256.01i		−	1.39248i
$903$		0			0
$904$	−142.765	+	247.277i	−0.157926	+	0.273536i
$905$		−	335.035i		−	0.370204i
$906$		0			0
$907$	252.352	+	437.087i	0.278227	+	0.481904i	0.970944	−	0.239306i	$-0.0769198\pi$
$907$	252.352	+	437.087i	0.278227	+	0.481904i	−0.692717	+	0.721210i	$0.743586\pi$
$908$	−1961.14	+	1132.26i	−2.15984	+	1.24698i
$909$		0			0
$910$	−237.759	−	132.063i	−0.261274	−	0.145124i
$911$		−	1079.70i		−	1.18518i	−0.805504	−	0.592591i	$-0.798105\pi$
$911$		−	1079.70i		−	1.18518i	0.805504	−	0.592591i	$-0.201895\pi$
$912$		0			0
$913$	−214.275	−	371.135i	−0.234693	−	0.406500i
$914$	591.516	+	341.512i	0.647173	+	0.373645i
$915$		0			0
$916$	863.450	−	1495.54i	0.942631	−	1.63268i
$917$	−1247.34	−	720.151i	−1.36024	−	0.785333i
$918$		0			0
$919$	193.794	−	335.660i	0.210874	−	0.365245i	−0.741114	−	0.671379i	$-0.765702\pi$
$919$	193.794	−	335.660i	0.210874	−	0.365245i	0.951988	+	0.306134i	$0.0990356\pi$
$920$	−26.4809	+	15.2887i	−0.0287836	+	0.0166182i
$921$		0			0
$922$	−1038.90			−1.12679
$923$	432.239	+	720.788i	0.468298	+	0.780918i
$924$		0			0
$925$	−550.796	−	954.007i	−0.595455	−	1.03136i
$926$	−819.655	+	473.228i	−0.885156	+	0.511045i
$927$		0			0
$928$	−2320.24			−2.50025
$929$	552.771	+	319.143i	0.595018	+	0.343534i	0.767079	−	0.641553i	$-0.221709\pi$
$929$	552.771	+	319.143i	0.595018	+	0.343534i	−0.172061	+	0.985086i	$0.555043\pi$
$930$		0			0
$931$	−298.842			−0.320990
$932$	1758.03	+	1015.00i	1.88630	+	1.08905i
$933$		0			0
$934$	1149.74	+	1991.41i	1.23099	+	2.13213i
$935$			112.399i			0.120213i
$936$		0			0
$937$	−563.143			−0.601006			−0.300503	−	0.953781i	$-0.597155\pi$
$937$	−563.143			−0.601006			−0.300503	+	0.953781i	$0.597155\pi$
$938$	1867.59	−	1078.26i	1.99104	−	1.14953i
$939$		0			0
$940$	99.1971	−	171.814i	0.105529	−	0.182781i
$941$			1382.05i			1.46871i	0.678766	+	0.734354i	$0.262515\pi$
$941$			1382.05i			1.46871i	−0.678766	+	0.734354i	$0.737485\pi$
$942$		0			0
$943$	−135.309	+	234.362i	−0.143487	+	0.248528i
$944$			369.628i			0.391556i
$945$		0			0
$946$	652.635	+	1130.40i	0.689889	+	1.19492i
$947$	736.141	−	425.011i	0.777341	−	0.448798i	−0.0581464	−	0.998308i	$-0.518519\pi$
$947$	736.141	−	425.011i	0.777341	−	0.448798i	0.835487	+	0.549510i	$0.185186\pi$
$948$		0			0
$949$	263.136	+	146.158i	0.277277	+	0.154013i
$950$		−	1762.08i		−	1.85482i
$951$		0			0
$952$	192.229	+	332.950i	0.201921	+	0.349737i
$953$	1202.46	+	694.239i	1.26176	+	0.728478i	0.973415	−	0.229049i	$-0.0735615\pi$
$953$	1202.46	+	694.239i	1.26176	+	0.728478i	0.288346	+	0.957526i	$0.406895\pi$
$954$		0			0
$955$	−23.4846	+	40.6765i	−0.0245912	+	0.0425932i
$956$	1366.18	+	788.765i	1.42906	+	0.825068i
$957$		0			0
$958$	730.829	−	1265.83i	0.762870	−	1.32133i
$959$	−670.410	+	387.062i	−0.699072	+	0.403610i
$960$		0			0
$961$	−935.216			−0.973170
$962$	962.536	+	1605.09i	1.00056	+	1.66849i
$963$		0			0
$964$	248.204	+	429.901i	0.257473	+	0.445956i
$965$	−83.7775	+	48.3689i	−0.0868160	+	0.0501233i
$966$		0			0
$967$	1422.40			1.47094			0.735468	−	0.677559i	$-0.236962\pi$
$967$	1422.40			1.47094			0.735468	+	0.677559i	$0.236962\pi$
$968$	−247.277	−	142.766i	−0.255452	−	0.147485i
$969$		0			0
$970$	−94.6815			−0.0976098
$971$	−576.305	−	332.730i	−0.593517	−	0.342667i	0.172970	−	0.984927i	$-0.444664\pi$
$971$	−576.305	−	332.730i	−0.593517	−	0.342667i	−0.766487	+	0.642260i	$0.777997\pi$
$972$		0			0
$973$	794.883	+	1376.78i	0.816940	+	1.41498i
$974$		−	265.608i		−	0.272698i
$975$		0			0
$976$	−336.736			−0.345016
$977$	−213.789	+	123.431i	−0.218821	+	0.126337i	−0.605404	−	0.795918i	$-0.706989\pi$
$977$	−213.789	+	123.431i	−0.218821	+	0.126337i	0.386583	+	0.922255i	$0.373655\pi$
$978$		0			0
$979$	−594.218	+	1029.22i	−0.606964	+	1.05129i
$980$			78.6768i			0.0802825i
$981$		0			0
$982$	797.130	−	1380.67i	0.811741	−	1.40598i
$983$			1946.29i			1.97995i	0.141245	+	0.989975i	$0.454889\pi$
$983$			1946.29i			1.97995i	−0.141245	+	0.989975i	$0.545111\pi$
$984$		0			0
$985$	−37.2728	−	64.5583i	−0.0378404	−	0.0655414i
$986$	−1887.87	+	1089.97i	−1.91468	+	1.10544i
$987$		0			0
$988$	29.0409	+	1751.11i	0.0293937	+	1.77238i
$989$		−	281.230i		−	0.284358i
$990$		0			0
$991$	−268.271	−	464.660i	−0.270708	−	0.468880i	0.698335	−	0.715771i	$-0.253924\pi$
$991$	−268.271	−	464.660i	−0.270708	−	0.468880i	−0.969043	+	0.246891i	$0.920591\pi$
$992$	−181.779	−	104.950i	−0.183244	−	0.105796i
$993$		0			0
$994$	−606.247	+	1050.05i	−0.609906	+	1.05639i
$995$	217.452	+	125.546i	0.218544	+	0.126177i
$996$		0			0
$997$	306.414	−	530.725i	0.307336	−	0.532322i	−0.670442	−	0.741962i	$-0.733896\pi$
$997$	306.414	−	530.725i	0.307336	−	0.532322i	0.977779	+	0.209639i	$0.0672290\pi$
$998$	−139.920	+	80.7829i	−0.140201	+	0.0809448i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.3.p.a.107.2	yes	20
3.2	odd	2	inner	117.3.p.a.107.9	yes	20
13.9	even	3	inner	117.3.p.a.35.9	yes	20
39.35	odd	6	inner	117.3.p.a.35.2	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.3.p.a.35.2	✓	20	39.35	odd	6	inner
117.3.p.a.35.9	yes	20	13.9	even	3	inner
117.3.p.a.107.2	yes	20	1.1	even	1	trivial
117.3.p.a.107.9	yes	20	3.2	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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	117.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.68869 + 1.55231i) q^{2} +(2.81935 - 4.88326i) q^{4} +1.11552i q^{5} +(3.02043 - 5.23153i) q^{7} +5.08757i q^{8} +(-1.73164 - 2.99928i) q^{10} +(6.97549 - 4.02730i) q^{11} +(11.3646 + 6.31242i) q^{13} +18.7546i q^{14} +(3.37991 + 5.85418i) q^{16} +(10.8335 + 6.25475i) q^{17} +(-11.9460 + 20.6910i) q^{19} +(5.44737 + 3.14504i) q^{20} +(-12.5033 + 21.6563i) q^{22} +(4.66601 - 2.69392i) q^{23} +23.7556 q^{25} +(-40.3546 + 0.669252i) q^{26} +(-17.0313 - 29.4991i) q^{28} +(48.6098 - 28.0649i) q^{29} +5.07777 q^{31} +(-35.7989 - 20.6685i) q^{32} -38.8373 q^{34} +(5.83588 + 3.36935i) q^{35} +(-23.1859 - 40.1592i) q^{37} -74.1754i q^{38} -5.67528 q^{40} +(-43.4982 + 25.1137i) q^{41} +(26.0986 - 45.2041i) q^{43} -45.4175i q^{44} +(-8.36361 + 14.4862i) q^{46} -31.5408i q^{47} +(6.25403 + 10.8323i) q^{49} +(-63.8714 + 36.8762i) q^{50} +(62.8659 - 37.6992i) q^{52} +53.8374i q^{53} +(4.49254 + 7.78130i) q^{55} +(26.6158 + 15.3666i) q^{56} +(-87.1310 + 150.915i) q^{58} +(47.3544 + 27.3401i) q^{59} +(-24.9071 + 43.1404i) q^{61} +(-13.6525 + 7.88229i) q^{62} +101.297 q^{64} +(-7.04163 + 12.6774i) q^{65} +(-57.4929 - 99.5806i) q^{67} +(61.0872 - 35.2687i) q^{68} -20.9211 q^{70} +(55.9889 + 32.3252i) q^{71} +23.1540 q^{73} +(124.679 + 71.9837i) q^{74} +(67.3597 + 116.670i) q^{76} -48.6567i q^{77} -80.7964 q^{79} +(-6.53046 + 3.77036i) q^{80} +(77.9687 - 135.046i) q^{82} -53.2055i q^{83} +(-6.97730 + 12.0850i) q^{85} +162.053i q^{86} +(20.4892 + 35.4883i) q^{88} +(-127.780 + 73.7737i) q^{89} +(67.3495 - 40.3879i) q^{91} -30.3804i q^{92} +(48.9611 + 84.8032i) q^{94} +(-23.0812 - 13.3259i) q^{95} +(13.6694 - 23.6760i) q^{97} +(-33.6303 - 19.4164i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 24 q^{4} - 6 q^{7} + 12 q^{10} - 2 q^{13} - 104 q^{16} - 92 q^{19} + 44 q^{22} - 116 q^{25} + 76 q^{28} - 156 q^{31} + 80 q^{34} + 148 q^{37} + 328 q^{40} + 186 q^{43} + 164 q^{46} + 8 q^{49} + 392 q^{52}+ \cdots - 14 q^{97}+O(q^{100}) \) 20 * q + 24 * q^4 - 6 * q^7 + 12 * q^10 - 2 * q^13 - 104 * q^16 - 92 * q^19 + 44 * q^22 - 116 * q^25 + 76 * q^28 - 156 * q^31 + 80 * q^34 + 148 * q^37 + 328 * q^40 + 186 * q^43 + 164 * q^46 + 8 * q^49 + 392 * q^52 - 208 * q^55 - 236 * q^58 + 210 * q^61 - 1568 * q^64 - 158 * q^67 - 1048 * q^70 + 156 * q^73 + 764 * q^76 - 132 * q^79 + 648 * q^82 + 44 * q^85 + 372 * q^88 + 834 * q^91 - 220 * q^94 - 14 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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