LMFDB - Embedded newform 847.2.n.f.753.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(9,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([10, 18]))

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

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

chi := DirichletCharacter("847.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.n (of order $15$, degree $8$, 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:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			753.3
Character	$\chi$	$=$	847.753
Dual form			847.2.n.f.9.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.02517 - 1.13856i) q^{2} +(2.63045 - 1.17115i) q^{3} +(-0.0363024 - 0.345394i) q^{4} +(-2.29600 + 0.488030i) q^{5} +(1.36322 - 4.19556i) q^{6} +(2.64186 + 0.143384i) q^{7} +(2.04850 + 1.48832i) q^{8} +(3.54028 - 3.93187i) q^{9} +(-1.79813 + 3.11446i) q^{10} +(-0.500000 - 0.866025i) q^{12} +(0.0571040 + 0.175748i) q^{13} +(2.87160 - 2.86094i) q^{14} +(-5.46796 + 3.97271i) q^{15} +(4.47403 - 0.950983i) q^{16} +(2.62384 + 2.91407i) q^{17} +(-0.847315 - 8.06166i) q^{18} +(0.0808338 - 0.769082i) q^{19} +(0.251913 + 0.775308i) q^{20} +(7.11721 - 2.71686i) q^{21} +(-4.17752 - 7.23567i) q^{23} +(7.13154 + 1.51585i) q^{24} +(0.465726 - 0.207354i) q^{25} +(0.258642 + 0.115155i) q^{26} +(2.03836 - 6.27342i) q^{27} +(-0.0463820 - 0.917688i) q^{28} +(-6.60987 + 4.80235i) q^{29} +(-1.08240 + 10.2983i) q^{30} +(-2.59474 - 0.551528i) q^{31} +(0.971782 - 1.68317i) q^{32} +6.00774 q^{34} +(-6.13570 + 0.960100i) q^{35} +(-1.48657 - 1.08005i) q^{36} +(-6.23307 - 2.77514i) q^{37} +(-0.792781 - 0.880472i) q^{38} +(0.356037 + 0.395419i) q^{39} +(-5.42971 - 2.41746i) q^{40} +(0.344659 + 0.250409i) q^{41} +(4.20302 - 10.8886i) q^{42} -1.18479 q^{43} +(-6.20961 + 10.7554i) q^{45} +(-12.5209 - 2.66141i) q^{46} +(0.802783 - 7.63797i) q^{47} +(10.6550 - 7.74128i) q^{48} +(6.95888 + 0.757600i) q^{49} +(0.241361 - 0.742831i) q^{50} +(10.3147 + 4.59241i) q^{51} +(0.0586293 - 0.0261035i) q^{52} +(-6.41115 - 1.36273i) q^{53} +(-5.05303 - 8.75211i) q^{54} +(5.19846 + 4.22567i) q^{56} +(-0.688082 - 2.11770i) q^{57} +(-1.30844 + 12.4490i) q^{58} +(-0.0213649 - 0.203273i) q^{59} +(1.57065 + 1.74438i) q^{60} +(14.2631 - 3.03171i) q^{61} +(-3.28799 + 2.38886i) q^{62} +(9.91669 - 9.87986i) q^{63} +(1.90671 + 5.86825i) q^{64} +(-0.216881 - 0.375650i) q^{65} +(-1.87939 + 3.25519i) q^{67} +(0.911252 - 1.01205i) q^{68} +(-19.4628 - 14.1406i) q^{69} +(-5.19698 + 7.97015i) q^{70} +(-3.07962 + 9.47809i) q^{71} +(13.1042 - 2.78538i) q^{72} +(0.0126077 + 0.119954i) q^{73} +(-9.54962 + 4.25177i) q^{74} +(0.982224 - 1.09087i) q^{75} -0.268571 q^{76} +0.815207 q^{78} +(-0.219271 + 0.243526i) q^{79} +(-9.80826 + 4.36692i) q^{80} +(-0.326193 - 3.10352i) q^{81} +(0.638441 - 0.135705i) q^{82} +(-1.03676 + 3.19083i) q^{83} +(-1.19676 - 2.35961i) q^{84} +(-7.44651 - 5.41021i) q^{85} +(-1.21461 + 1.34896i) q^{86} +(-11.7626 + 20.3735i) q^{87} +(2.32635 + 4.02936i) q^{89} +(5.87977 + 18.0961i) q^{90} +(0.125662 + 0.472490i) q^{91} +(-2.34750 + 1.70556i) q^{92} +(-7.47124 + 1.58806i) q^{93} +(-7.87333 - 8.74422i) q^{94} +(0.189741 + 1.80526i) q^{95} +(0.584969 - 5.56561i) q^{96} +(4.05449 + 12.4784i) q^{97} +(7.99660 - 7.14647i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{3} + 6 q^{5} - 6 q^{6} + 6 q^{8} + 12 q^{10} - 12 q^{12} + 6 q^{13} + 12 q^{14} - 18 q^{15} - 6 q^{16} + 3 q^{17} + 12 q^{18} - 9 q^{19} - 12 q^{20} + 48 q^{21} - 6 q^{24} + 3 q^{25} + 9 q^{26}+ \cdots + 24 q^{98}+O(q^{100}) $ 24 * q + 3 * q^3 + 6 * q^5 - 6 * q^6 + 6 * q^8 + 12 * q^10 - 12 * q^12 + 6 * q^13 + 12 * q^14 - 18 * q^15 - 6 * q^16 + 3 * q^17 + 12 * q^18 - 9 * q^19 - 12 * q^20 + 48 * q^21 - 6 * q^24 + 3 * q^25 + 9 * q^26 - 12 * q^27 + 3 * q^28 - 6 * q^29 + 6 * q^30 + 9 * q^31 - 36 * q^32 - 48 * q^34 - 15 * q^35 - 6 * q^36 - 3 * q^39 - 3 * q^40 + 18 * q^41 + 18 * q^42 - 12 * q^45 + 24 * q^46 - 3 * q^47 + 36 * q^48 + 30 * q^50 + 18 * q^51 - 9 * q^52 + 9 * q^53 - 72 * q^54 + 12 * q^56 + 15 * q^58 + 6 * q^60 - 12 * q^61 - 6 * q^62 + 6 * q^63 + 6 * q^64 + 60 * q^65 + 21 * q^68 - 42 * q^69 - 45 * q^70 + 18 * q^71 - 12 * q^72 - 6 * q^73 - 18 * q^74 + 9 * q^75 + 72 * q^76 + 48 * q^78 + 3 * q^79 - 27 * q^80 + 15 * q^81 - 3 * q^82 - 30 * q^83 - 54 * q^85 - 9 * q^86 - 96 * q^87 + 60 * q^89 - 72 * q^90 - 9 * q^91 + 6 * q^92 + 6 * q^93 - 9 * q^95 - 3 * q^96 - 90 * q^97 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	1.02517	−	1.13856i	0.724903	−	0.805086i	−0.262227	−	0.965006i	$-0.584457\pi$
$2$	1.02517	−	1.13856i	0.724903	−	0.805086i	0.987130	+	0.159920i	$0.0511236\pi$
$3$	2.63045	−	1.17115i	1.51869	−	0.676165i	0.533215	−	0.845980i	$-0.320984\pi$
$3$	2.63045	−	1.17115i	1.51869	−	0.676165i	0.985476	+	0.169815i	$0.0543171\pi$
$4$	−0.0363024	−	0.345394i	−0.0181512	−	0.172697i
$5$	−2.29600	+	0.488030i	−1.02680	+	0.218254i	−0.690372	−	0.723454i	$-0.742553\pi$
$5$	−2.29600	+	0.488030i	−1.02680	+	0.218254i	−0.336431	+	0.941708i	$0.609220\pi$
$6$	1.36322	−	4.19556i	0.556532	−	1.71283i
$7$	2.64186	+	0.143384i	0.998530	+	0.0541939i
$7$	2.64186	+	0.143384i	0.998530	+	0.0541939i
$8$	2.04850	+	1.48832i	0.724255	+	0.526202i
$9$	3.54028	−	3.93187i	1.18009	−	1.31062i
$10$	−1.79813	+	3.11446i	−0.568620	+	0.984878i
$11$		0			0
$11$		0			0
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	0.0571040	+	0.175748i	0.0158378	+	0.0487438i	0.958663	−	0.284544i	$-0.0918421\pi$
$13$	0.0571040	+	0.175748i	0.0158378	+	0.0487438i	−0.942825	+	0.333287i	$0.891842\pi$
$14$	2.87160	−	2.86094i	0.767468	−	0.764618i
$15$	−5.46796	+	3.97271i	−1.41182	+	1.02575i
$16$	4.47403	−	0.950983i	1.11851	−	0.237746i
$17$	2.62384	+	2.91407i	0.636376	+	0.706767i	0.971934	−	0.235252i	$-0.0755917\pi$
$17$	2.62384	+	2.91407i	0.636376	+	0.706767i	−0.335559	+	0.942019i	$0.608925\pi$
$18$	−0.847315	−	8.06166i	−0.199714	−	1.90015i
$19$	0.0808338	−	0.769082i	0.0185445	−	0.176440i	−0.981329	−	0.192336i	$-0.938394\pi$
$19$	0.0808338	−	0.769082i	0.0185445	−	0.176440i	0.999874	+	0.0158966i	$0.00506027\pi$
$20$	0.251913	+	0.775308i	0.0563295	+	0.173364i
$21$	7.11721	−	2.71686i	1.55310	−	0.592867i
$22$		0			0
$23$	−4.17752	−	7.23567i	−0.871073	−	1.50874i	−0.860888	−	0.508794i	$-0.830091\pi$
$23$	−4.17752	−	7.23567i	−0.871073	−	1.50874i	−0.0101847	−	0.999948i	$-0.503242\pi$
$24$	7.13154	+	1.51585i	1.45572	+	0.309423i
$25$	0.465726	−	0.207354i	0.0931451	−	0.0414709i
$26$	0.258642	+	0.115155i	0.0507238	+	0.0225837i
$27$	2.03836	−	6.27342i	0.392282	−	1.20732i
$28$	−0.0463820	−	0.917688i	−0.00876538	−	0.173427i
$29$	−6.60987	+	4.80235i	−1.22742	+	0.891774i	−0.996694	−	0.0812446i	$-0.974111\pi$
$29$	−6.60987	+	4.80235i	−1.22742	+	0.891774i	−0.230727	+	0.973018i	$0.574111\pi$
$30$	−1.08240	+	10.2983i	−0.197618	+	1.88021i
$31$	−2.59474	−	0.551528i	−0.466028	−	0.0990574i	−0.0310880	−	0.999517i	$-0.509897\pi$
$31$	−2.59474	−	0.551528i	−0.466028	−	0.0990574i	−0.434940	+	0.900459i	$0.643231\pi$
$32$	0.971782	−	1.68317i	0.171788	−	0.297546i
$33$		0			0
$34$	6.00774			1.03032
$35$	−6.13570	+	0.960100i	−1.03712	+	0.162287i
$36$	−1.48657	−	1.08005i	−0.247761	−	0.180009i
$37$	−6.23307	−	2.77514i	−1.02471	−	0.456231i	−0.175609	−	0.984460i	$-0.556189\pi$
$37$	−6.23307	−	2.77514i	−1.02471	−	0.456231i	−0.849102	+	0.528229i	$0.822856\pi$
$38$	−0.792781	−	0.880472i	−0.128606	−	0.142831i
$39$	0.356037	+	0.395419i	0.0570115	+	0.0633177i
$40$	−5.42971	−	2.41746i	−0.858513	−	0.382235i
$41$	0.344659	+	0.250409i	0.0538267	+	0.0391074i	0.614373	−	0.789016i	$-0.289409\pi$
$41$	0.344659	+	0.250409i	0.0538267	+	0.0391074i	−0.560547	+	0.828123i	$0.689409\pi$
$42$	4.20302	−	10.8886i	0.648540	−	1.68015i
$43$	−1.18479			−0.180679			−0.0903396	−	0.995911i	$-0.528795\pi$
$43$	−1.18479			−0.180679			−0.0903396	+	0.995911i	$0.528795\pi$
$44$		0			0
$45$	−6.20961	+	10.7554i	−0.925674	+	1.60331i
$46$	−12.5209	−	2.66141i	−1.84611	−	0.392403i
$47$	0.802783	−	7.63797i	0.117098	−	1.11411i	−0.765321	−	0.643649i	$-0.777420\pi$
$47$	0.802783	−	7.63797i	0.117098	−	1.11411i	0.882419	−	0.470464i	$-0.155914\pi$
$48$	10.6550	−	7.74128i	1.53791	−	1.11736i
$49$	6.95888	+	0.757600i	0.994126	+	0.108229i
$50$	0.241361	−	0.742831i	0.0341335	−	0.105052i
$51$	10.3147	+	4.59241i	1.44435	+	0.643065i
$52$	0.0586293	−	0.0261035i	0.00813042	−	0.00361990i
$53$	−6.41115	−	1.36273i	−0.880639	−	0.187186i	−0.254665	−	0.967029i	$-0.581965\pi$
$53$	−6.41115	−	1.36273i	−0.880639	−	0.187186i	−0.625974	+	0.779844i	$0.715298\pi$
$54$	−5.05303	−	8.75211i	−0.687631	−	1.19101i
$55$		0			0
$56$	5.19846	+	4.22567i	0.694674	+	0.564679i
$57$	−0.688082	−	2.11770i	−0.0911387	−	0.280496i
$58$	−1.30844	+	12.4490i	−0.171806	+	1.63463i
$59$	−0.0213649	−	0.203273i	−0.00278147	−	0.0264639i	0.993043	−	0.117751i	$-0.0375685\pi$
$59$	−0.0213649	−	0.203273i	−0.00278147	−	0.0264639i	−0.995825	+	0.0912873i	$0.970902\pi$
$60$	1.57065	+	1.74438i	0.202770	+	0.225199i
$61$	14.2631	−	3.03171i	1.82620	−	0.388171i	0.838547	−	0.544830i	$-0.183406\pi$
$61$	14.2631	−	3.03171i	1.82620	−	0.388171i	0.987653	+	0.156659i	$0.0500724\pi$
$62$	−3.28799	+	2.38886i	−0.417575	+	0.303386i
$63$	9.91669	−	9.87986i	1.24939	−	1.24475i
$64$	1.90671	+	5.86825i	0.238339	+	0.733531i
$65$	−0.216881	−	0.375650i	−0.0269008	−	0.0465936i
$66$		0			0
$67$	−1.87939	+	3.25519i	−0.229603	+	0.397685i	−0.957691	−	0.287800i	$-0.907076\pi$
$67$	−1.87939	+	3.25519i	−0.229603	+	0.397685i	0.728087	+	0.685485i	$0.240410\pi$
$68$	0.911252	−	1.01205i	0.110505	−	0.122729i
$69$	−19.4628	−	14.1406i	−2.34305	−	1.70232i
$70$	−5.19698	+	7.97015i	−0.621158	+	0.952615i
$71$	−3.07962	+	9.47809i	−0.365483	+	1.12484i	0.584194	+	0.811614i	$0.301411\pi$
$71$	−3.07962	+	9.47809i	−0.365483	+	1.12484i	−0.949678	+	0.313228i	$0.898589\pi$
$72$	13.1042	−	2.78538i	1.54434	−	0.328260i
$73$	0.0126077	+	0.119954i	0.00147562	+	0.0140396i	0.995235	−	0.0975061i	$-0.0310865\pi$
$73$	0.0126077	+	0.119954i	0.00147562	+	0.0140396i	−0.993759	+	0.111546i	$0.964420\pi$
$74$	−9.54962	+	4.25177i	−1.11012	+	0.494258i
$75$	0.982224	−	1.09087i	0.113417	−	0.125963i
$76$	−0.268571			−0.0308072
$77$		0			0
$78$	0.815207			0.0923041
$79$	−0.219271	+	0.243526i	−0.0246700	+	0.0273988i	−0.755354	−	0.655318i	$-0.772535\pi$
$79$	−0.219271	+	0.243526i	−0.0246700	+	0.0273988i	0.730684	+	0.682716i	$0.239201\pi$
$80$	−9.80826	+	4.36692i	−1.09660	+	0.488237i
$81$	−0.326193	−	3.10352i	−0.0362437	−	0.344836i
$82$	0.638441	−	0.135705i	0.0705040	−	0.0149861i
$83$	−1.03676	+	3.19083i	−0.113800	+	0.350239i	−0.991695	−	0.128614i	$-0.958947\pi$
$83$	−1.03676	+	3.19083i	−0.113800	+	0.350239i	0.877895	+	0.478853i	$0.158947\pi$
$84$	−1.19676	−	2.35961i	−0.130577	−	0.257455i
$85$	−7.44651	−	5.41021i	−0.807687	−	0.586819i
$86$	−1.21461	+	1.34896i	−0.130975	+	0.145462i
$87$	−11.7626	+	20.3735i	−1.26109	+	2.18427i
$88$		0			0
$89$	2.32635	+	4.02936i	0.246593	+	0.427111i	0.962578	−	0.271004i	$-0.0873557\pi$
$89$	2.32635	+	4.02936i	0.246593	+	0.427111i	−0.715985	+	0.698115i	$0.754022\pi$
$90$	5.87977	+	18.0961i	0.619782	+	1.90749i
$91$	0.125662	+	0.472490i	0.0131729	+	0.0495304i
$92$	−2.34750	+	1.70556i	−0.244744	+	0.177817i
$93$	−7.47124	+	1.58806i	−0.774732	+	0.164674i
$94$	−7.87333	−	8.74422i	−0.812072	−	0.901898i
$95$	0.189741	+	1.80526i	0.0194670	+	0.185216i
$96$	0.584969	−	5.56561i	0.0597032	−	0.568038i
$97$	4.05449	+	12.4784i	0.411671	+	1.26699i	0.915194	+	0.403012i	$0.132037\pi$
$97$	4.05449	+	12.4784i	0.411671	+	1.26699i	−0.503523	+	0.863982i	$0.667963\pi$
$98$	7.99660	−	7.14647i	0.807778	−	0.721902i
$99$		0			0
$100$	−0.0885259	−	0.153331i	−0.00885259	−	0.0153331i
$101$	−5.77271	−	1.22703i	−0.574406	−	0.122094i	−0.0884555	−	0.996080i	$-0.528193\pi$
$101$	−5.77271	−	1.22703i	−0.574406	−	0.122094i	−0.485950	+	0.873986i	$0.661526\pi$
$102$	15.8031	−	7.03597i	1.56474	−	0.696665i
$103$	0.841626	+	0.374716i	0.0829279	+	0.0369219i	0.447781	−	0.894143i	$-0.352214\pi$
$103$	0.841626	+	0.374716i	0.0829279	+	0.0369219i	−0.364854	+	0.931065i	$0.618881\pi$
$104$	−0.144592	+	0.445010i	−0.0141785	+	0.0436368i
$105$	−15.0152	+	9.71133i	−1.46534	+	0.947729i
$106$	−8.12406	+	5.90247i	−0.789078	+	0.573299i
$107$	−1.08159	+	10.2906i	−0.104561	+	0.994831i	0.808911	+	0.587930i	$0.200057\pi$
$107$	−1.08159	+	10.2906i	−0.104561	+	0.994831i	−0.913472	+	0.406901i	$0.866610\pi$
$108$	−2.24080	−	0.476296i	−0.215621	−	0.0458316i
$109$	0.237826	−	0.411927i	0.0227796	−	0.0394554i	−0.854411	−	0.519598i	$-0.826082\pi$
$109$	0.237826	−	0.411927i	0.0227796	−	0.0394554i	0.877190	+	0.480143i	$0.159415\pi$
$110$		0			0
$111$	−19.6459			−1.86471
$112$	11.9561	−	1.87087i	1.12975	−	0.176780i
$113$	2.54266	+	1.84735i	0.239194	+	0.173784i	0.700924	−	0.713236i	$-0.252771\pi$
$113$	2.54266	+	1.84735i	0.239194	+	0.173784i	−0.461730	+	0.887020i	$0.652771\pi$
$114$	−3.11654	−	1.38757i	−0.291890	−	0.129958i
$115$	13.1228	+	14.5744i	1.22371	+	1.35907i
$116$	1.89866	+	2.10867i	0.176286	+	0.195785i
$117$	0.893184	+	0.397671i	0.0825749	+	0.0367647i
$118$	−0.253342	−	0.184064i	−0.0233220	−	0.0169444i
$119$	6.51401	+	8.07480i	0.597138	+	0.740216i
$120$	−17.1138			−1.56227
$121$		0			0
$122$	11.1702	−	19.3474i	1.01131	−	1.75163i
$123$	1.19988	+	0.255041i	0.108189	+	0.0229963i
$124$	−0.0962994	+	0.916227i	−0.00864794	+	0.0822797i
$125$	8.52690	−	6.19516i	0.762669	−	0.554112i
$126$	−1.08258	−	21.4193i	−0.0964438	−	1.90818i
$127$	0.137705	−	0.423812i	0.0122193	−	0.0376072i	−0.944761	−	0.327760i	$-0.893706\pi$
$127$	0.137705	−	0.423812i	0.0122193	−	0.0376072i	0.956980	+	0.290153i	$0.0937062\pi$
$128$	12.1871	+	5.42607i	1.07720	+	0.479601i
$129$	−3.11654	+	1.38757i	−0.274396	+	0.122169i
$130$	−0.650041	−	0.138170i	−0.0570124	−	0.0121184i
$131$	−6.04323	−	10.4672i	−0.528000	−	0.914522i	−0.999467	−	0.0326389i	$-0.989609\pi$
$131$	−6.04323	−	10.4672i	−0.528000	−	0.914522i	0.471467	−	0.881883i	$-0.343724\pi$
$132$		0			0
$133$	0.323826	−	2.02022i	0.0280792	−	0.175175i
$134$	1.77956	+	5.47692i	0.153730	+	0.473133i
$135$	−1.61846	+	15.3986i	−0.139294	+	1.32530i
$136$	1.03786	+	9.87462i	0.0889962	+	0.846742i
$137$	−10.9391	−	12.1491i	−0.934590	−	1.03797i	−0.999197	−	0.0400571i	$-0.987246\pi$
$137$	−10.9391	−	12.1491i	−0.934590	−	1.03797i	0.0646069	−	0.997911i	$-0.479421\pi$
$138$	−36.0526	+	7.66322i	−3.06900	+	0.652336i
$139$	−16.7707	+	12.1846i	−1.42247	+	1.03348i	−0.431111	+	0.902299i	$0.641878\pi$
$139$	−16.7707	+	12.1846i	−1.42247	+	1.03348i	−0.991358	+	0.131185i	$0.958122\pi$
$140$	0.554353	+	2.08438i	0.0468514	+	0.176162i
$141$	−6.83354	−	21.0315i	−0.575488	−	1.77117i
$142$	7.63429	+	13.2230i	0.640655	+	1.10965i
$143$		0			0
$144$	12.1001	−	20.9581i	1.00834	−	1.74650i
$145$	12.8326	−	14.2520i	1.06569	−	1.18357i
$146$	0.149500	+	0.108618i	0.0123727	+	0.00898932i
$147$	19.1923	−	6.15708i	1.58295	−	0.507827i
$148$	−0.732242	+	2.25361i	−0.0601899	+	0.185246i
$149$	−0.698586	+	0.148489i	−0.0572304	+	0.0121647i	−0.236438	−	0.971647i	$-0.575980\pi$
$149$	−0.698586	+	0.148489i	−0.0572304	+	0.0121647i	0.179207	+	0.983811i	$0.442647\pi$
$150$	−0.235081	−	2.23665i	−0.0191943	−	0.182622i
$151$	8.71968	−	3.88225i	0.709598	−	0.315933i	−0.0200094	−	0.999800i	$-0.506370\pi$
$151$	8.71968	−	3.88225i	0.709598	−	0.315933i	0.729607	+	0.683866i	$0.239703\pi$
$152$	1.31023	−	1.45516i	0.106274	−	0.118029i
$153$	20.7469			1.67729
$154$		0			0
$155$	6.22668			0.500139
$156$	0.123650	−	0.137328i	0.00989995	−	0.0109950i
$157$	8.44228	−	3.75875i	0.673768	−	0.299981i	−0.0411871	−	0.999151i	$-0.513114\pi$
$157$	8.44228	−	3.75875i	0.673768	−	0.299981i	0.714955	+	0.699171i	$0.246447\pi$
$158$	0.0524795	+	0.499309i	0.00417504	+	0.0397229i
$159$	−18.4602	+	3.92383i	−1.46399	+	0.311180i
$160$	−1.40977	+	4.33883i	−0.111452	+	0.343015i
$161$	−9.99896	−	19.7146i	−0.788028	−	1.55373i
$162$	−3.86796	−	2.81024i	−0.303895	−	0.220793i
$163$	−5.89059	+	6.54216i	−0.461387	+	0.512422i	−0.928275	−	0.371895i	$-0.878708\pi$
$163$	−5.89059	+	6.54216i	−0.461387	+	0.512422i	0.466888	+	0.884316i	$0.345375\pi$
$164$	0.0739780	−	0.128134i	0.00577671	−	0.0100056i
$165$		0			0
$166$	2.57011	+	4.45156i	0.199479	+	0.345508i
$167$	−2.59030	−	7.97212i	−0.200443	−	0.616901i	−0.999870	−	0.0161370i	$-0.994863\pi$
$167$	−2.59030	−	7.97212i	−0.200443	−	0.616901i	0.799427	−	0.600764i	$-0.205137\pi$
$168$	18.6232	+	5.02723i	1.43681	+	0.387859i
$169$	10.4896	−	7.62114i	0.806892	−	0.586241i
$170$	−13.7938	+	2.93196i	−1.05794	+	0.224871i
$171$	−2.73776	−	3.04059i	−0.209362	−	0.232520i
$172$	0.0430108	+	0.409220i	0.00327954	+	0.0312027i
$173$	0.569223	−	5.41579i	0.0432772	−	0.411755i	−0.951340	−	0.308142i	$-0.900293\pi$
$173$	0.569223	−	5.41579i	0.0432772	−	0.411755i	0.994618	−	0.103613i	$-0.0330404\pi$
$174$	11.1378	+	34.2788i	0.844358	+	2.59867i
$175$	1.26011	−	0.481025i	0.0952557	−	0.0363620i
$176$		0			0
$177$	−0.294263	−	0.509678i	−0.0221182	−	0.0383098i
$178$	6.97258	+	1.48207i	0.522617	+	0.111086i
$179$	−9.21906	+	4.10459i	−0.689065	+	0.306792i	−0.721235	−	0.692691i	$-0.756425\pi$
$179$	−9.21906	+	4.10459i	−0.689065	+	0.306792i	0.0321696	+	0.999482i	$0.489758\pi$
$180$	3.94026	+	1.75432i	0.293689	+	0.130759i
$181$	6.14307	−	18.9064i	0.456611	−	1.40530i	−0.412623	−	0.910902i	$-0.635387\pi$
$181$	6.14307	−	18.9064i	0.456611	−	1.40530i	0.869234	−	0.494401i	$-0.164613\pi$
$182$	0.666785	+	0.341308i	0.0494254	+	0.0252994i
$183$	33.9677	−	24.6790i	2.51096	−	1.82432i
$184$	2.21137	−	21.0398i	0.163025	−	1.55107i
$185$	15.6655	+	3.32981i	1.15175	+	0.244812i
$186$	−5.85117	+	10.1345i	−0.429028	+	0.743099i
$187$		0			0
$188$	−2.66725			−0.194529
$189$	6.28457	−	16.2813i	0.457135	−	1.18429i
$190$	2.24992	+	1.63467i	0.163227	+	0.118591i
$191$	−23.1904	−	10.3250i	−1.67800	−	0.747093i	−0.999927	−	0.0120984i	$-0.996149\pi$
$191$	−23.1904	−	10.3250i	−1.67800	−	0.747093i	−0.678073	−	0.734995i	$-0.737184\pi$
$192$	11.8881	+	13.2031i	0.857951	+	0.952851i
$193$	5.17334	+	5.74557i	0.372385	+	0.413575i	0.899987	−	0.435916i	$-0.143576\pi$
$193$	5.17334	+	5.74557i	0.372385	+	0.413575i	−0.527602	+	0.849491i	$0.676909\pi$
$194$	18.3640	+	8.17620i	1.31846	+	0.587017i
$195$	−1.01044	−	0.734126i	−0.0723590	−	0.0525719i
$196$	0.00904656	−	2.43106i	0.000646183	−	0.173647i
$197$	5.37464			0.382927			0.191464	−	0.981500i	$-0.438677\pi$
$197$	5.37464			0.382927			0.191464	+	0.981500i	$0.438677\pi$
$198$		0			0
$199$	−4.39053	+	7.60462i	−0.311236	+	0.539077i	−0.978630	−	0.205628i	$-0.934076\pi$
$199$	−4.39053	+	7.60462i	−0.311236	+	0.539077i	0.667394	+	0.744705i	$0.267410\pi$
$200$	1.26265	+	0.268385i	0.0892829	+	0.0189777i
$201$	−1.13131	+	10.7637i	−0.0797962	+	0.759210i
$202$	−7.31504	+	5.31469i	−0.514685	+	0.373940i
$203$	−18.1509	+	11.7394i	−1.27395	+	0.823945i
$204$	1.21174	−	3.72935i	0.0848388	−	0.261107i
$205$	−0.913545	−	0.406737i	−0.0638048	−	0.0284077i
$206$	1.28945	−	0.574098i	0.0898399	−	0.0399993i
$207$	−43.2393	−	9.19080i	−3.00534	−	0.638805i
$208$	0.422618	+	0.731997i	0.0293033	+	0.0507548i
$209$		0			0
$210$	−4.33615	+	27.0515i	−0.299223	+	1.86673i
$211$	−1.31061	−	4.03365i	−0.0902263	−	0.277688i	0.895754	−	0.444550i	$-0.146636\pi$
$211$	−1.31061	−	4.03365i	−0.0902263	−	0.277688i	−0.985980	+	0.166862i	$0.946636\pi$
$212$	−0.237939	+	2.26384i	−0.0163417	+	0.155481i
$213$	2.99950	+	28.5383i	0.205522	+	1.95541i
$214$	10.6077	+	11.7811i	0.725128	+	0.805337i
$215$	2.72029	−	0.578215i	0.185522	−	0.0394339i
$216$	13.5125	−	9.81739i	0.919407	−	0.667988i
$217$	−6.77586	−	1.82910i	−0.459975	−	0.124168i
$218$	−0.225193	−	0.693074i	−0.0152520	−	0.0469409i
$219$	0.173648	+	0.300767i	0.0117341	+	0.0203240i
$220$		0			0
$221$	−0.362311	+	0.627541i	−0.0243717	+	0.0422130i
$222$	−20.1403	+	22.3681i	−1.35173	+	1.50125i
$223$	14.5907	+	10.6008i	0.977065	+	0.709879i	0.957051	−	0.289921i	$-0.0936289\pi$
$223$	14.5907	+	10.6008i	0.977065	+	0.709879i	0.0200140	+	0.999800i	$0.493629\pi$
$224$	2.80865	−	4.30738i	0.187661	−	0.287799i
$225$	0.833506	−	2.56527i	0.0555670	−	0.171018i
$226$	4.70998	−	1.00114i	0.313303	−	0.0665947i
$227$	1.90297	+	18.1056i	0.126305	+	1.20171i	0.855646	+	0.517561i	$0.173160\pi$
$227$	1.90297	+	18.1056i	0.126305	+	1.20171i	−0.729342	+	0.684150i	$0.760173\pi$
$228$	−0.706462	+	0.314537i	−0.0467866	+	0.0208307i
$229$	12.8749	−	14.2990i	0.850797	−	0.944906i	−0.148232	−	0.988953i	$-0.547358\pi$
$229$	12.8749	−	14.2990i	0.850797	−	0.944906i	0.999029	+	0.0440467i	$0.0140250\pi$
$230$	30.0469			1.98124
$231$		0			0
$232$	−20.6878			−1.35822
$233$	−6.23965	+	6.92983i	−0.408773	+	0.453988i	−0.912015	−	0.410157i	$-0.865474\pi$
$233$	−6.23965	+	6.92983i	−0.408773	+	0.453988i	0.503242	+	0.864146i	$0.332140\pi$
$234$	1.36844	−	0.609267i	0.0894575	−	0.0398291i
$235$	1.88437	+	17.9286i	0.122923	+	1.16953i
$236$	−0.0694337	+	0.0147586i	−0.00451975	+	0.000960702i
$237$	−0.291577	+	0.897382i	−0.0189400	+	0.0582912i
$238$	15.8716	+	0.861412i	1.02880	+	0.0558370i
$239$	9.05277	+	6.57723i	0.585575	+	0.425445i	0.840730	−	0.541455i	$-0.182126\pi$
$239$	9.05277	+	6.57723i	0.585575	+	0.425445i	−0.255154	+	0.966900i	$0.582126\pi$
$240$	−20.6858	+	22.9739i	−1.33526	+	1.48296i
$241$	10.1022	−	17.4975i	0.650740	−	1.12711i	−0.332204	−	0.943208i	$-0.607792\pi$
$241$	10.1022	−	17.4975i	0.650740	−	1.12711i	0.982944	−	0.183907i	$-0.0588744\pi$
$242$		0			0
$243$	5.40167	+	9.35597i	0.346518	+	0.600186i
$244$	−1.56492	−	4.81632i	−0.100184	−	0.308333i
$245$	−16.3473	+	1.65669i	−1.04439	+	0.105842i
$246$	1.52045	−	1.10467i	0.0969406	−	0.0704315i
$247$	0.139781	−	0.0297113i	0.00889403	−	0.00189048i
$248$	−4.49447	−	4.99162i	−0.285399	−	0.316968i
$249$	1.00979	+	9.60752i	0.0639929	+	0.608852i
$250$	1.68792	−	16.0595i	0.106753	−	1.01569i
$251$	−1.82078	−	5.60379i	−0.114927	−	0.353708i	0.877005	−	0.480481i	$-0.159538\pi$
$251$	−1.82078	−	5.60379i	−0.114927	−	0.353708i	−0.991932	+	0.126773i	$0.959538\pi$
$252$	−3.77244	−	3.06650i	−0.237641	−	0.193171i
$253$		0			0
$254$	−0.341367	−	0.591264i	−0.0214192	−	0.0370992i
$255$	−25.9238	−	5.51028i	−1.62341	−	0.345067i
$256$	7.39819	−	3.29389i	0.462387	−	0.205868i
$257$	−2.49990	−	1.11303i	−0.155940	−	0.0694287i	0.327283	−	0.944926i	$-0.393867\pi$
$257$	−2.49990	−	1.11303i	−0.155940	−	0.0694287i	−0.483222	+	0.875498i	$0.660534\pi$
$258$	−1.61513	+	4.97087i	−0.100554	+	0.309473i
$259$	−16.0690	−	8.22527i	−0.998480	−	0.511093i
$260$	−0.121874	+	0.0885465i	−0.00755829	+	0.00549142i
$261$	−4.51852	+	42.9908i	−0.279689	+	2.66106i
$262$	−18.1129	−	3.85001i	−1.11902	−	0.237855i
$263$	3.09879	−	5.36727i	0.191080	−	0.330960i	−0.754529	−	0.656267i	$-0.772134\pi$
$263$	3.09879	−	5.36727i	0.191080	−	0.330960i	0.945608	+	0.325307i	$0.105468\pi$
$264$		0			0
$265$	15.3851			0.945097
$266$	−1.96817	−	2.43976i	−0.120676	−	0.149591i
$267$	10.8383	+	7.87452i	0.663296	+	0.481913i
$268$	1.19255	+	0.530957i	0.0728465	+	0.0324334i
$269$	−2.81667	−	3.12823i	−0.171735	−	0.190731i	0.651133	−	0.758964i	$-0.274294\pi$
$269$	−2.81667	−	3.12823i	−0.171735	−	0.190731i	−0.822868	+	0.568232i	$0.807627\pi$
$270$	15.8731	+	17.6288i	0.966004	+	1.07286i
$271$	−23.3701	−	10.4050i	−1.41963	−	0.632060i	−0.453769	−	0.891119i	$-0.649921\pi$
$271$	−23.3701	−	10.4050i	−1.41963	−	0.632060i	−0.965861	+	0.259059i	$0.916587\pi$
$272$	14.5104	+	10.5424i	0.879821	+	0.639228i
$273$	0.883904	+	1.09569i	0.0534963	+	0.0663144i
$274$	−25.0469			−1.51314
$275$		0			0
$276$	−4.17752	+	7.23567i	−0.251457	+	0.435536i
$277$	−15.0221	−	3.19305i	−0.902592	−	0.191852i	−0.266836	−	0.963742i	$-0.585978\pi$
$277$	−15.0221	−	3.19305i	−0.902592	−	0.191852i	−0.635756	+	0.771890i	$0.719312\pi$
$278$	−3.31979	+	31.5857i	−0.199108	+	1.89439i
$279$	−11.3546	+	8.24961i	−0.679783	+	0.493891i
$280$	−13.9979	−	7.16514i	−0.836537	−	0.428199i
$281$	−5.94982	+	18.3117i	−0.354937	+	1.09238i	0.601110	+	0.799166i	$0.294725\pi$
$281$	−5.94982	+	18.3117i	−0.354937	+	1.09238i	−0.956046	+	0.293216i	$0.905275\pi$
$282$	−30.9512	−	13.7804i	−1.84312	−	0.820609i
$283$	24.7252	−	11.0084i	1.46976	−	0.654380i	0.493258	−	0.869883i	$-0.335806\pi$
$283$	24.7252	−	11.0084i	1.46976	−	0.654380i	0.976503	+	0.215503i	$0.0691392\pi$
$284$	3.38547	+	0.719604i	0.200891	+	0.0427006i
$285$	2.61334	+	4.52644i	0.154801	+	0.268123i
$286$		0			0
$287$	0.874638	+	0.710966i	0.0516282	+	0.0419670i
$288$	−3.17766	−	9.77983i	−0.187245	−	0.576282i
$289$	0.169713	−	1.61471i	0.00998313	−	0.0949831i
$290$	−3.07129	−	29.2214i	−0.180353	−	1.71594i
$291$	25.2793	+	28.0755i	1.48190	+	1.64581i
$292$	0.0409737	−	0.00870923i	0.00239780	−	0.000509669i
$293$	3.26445	−	2.37176i	0.190711	−	0.138560i	−0.488333	−	0.872658i	$-0.662395\pi$
$293$	3.26445	−	2.37176i	0.190711	−	0.138560i	0.679044	+	0.734098i	$0.262395\pi$
$294$	12.6650	−	28.1636i	0.738641	−	1.64254i
$295$	0.148257	+	0.456289i	0.00863187	+	0.0265662i
$296$	−8.63816	−	14.9617i	−0.502083	−	0.869633i
$297$		0			0
$298$	−0.547104	+	0.947611i	−0.0316929	+	0.0548936i
$299$	1.03310	−	1.14738i	0.0597459	−	0.0663545i
$300$	−0.412437	−	0.299653i	−0.0238121	−	0.0173005i
$301$	−3.13006	−	0.169880i	−0.180414	−	0.00979171i
$302$	4.51894	−	13.9079i	0.260036	−	0.800308i
$303$	−16.6219	+	3.53308i	−0.954900	+	0.202970i
$304$	−0.369732	−	3.51776i	−0.0212056	−	0.201758i
$305$	−31.2685	+	13.9216i	−1.79043	+	0.797150i
$306$	21.2691	−	23.6217i	1.21587	−	1.35036i
$307$	−2.92902			−0.167168			−0.0835839	−	0.996501i	$-0.526637\pi$
$307$	−2.92902			−0.167168			−0.0835839	+	0.996501i	$0.526637\pi$
$308$		0			0
$309$	2.65270			0.150907
$310$	6.38339	−	7.08948i	0.362552	−	0.402655i
$311$	14.2729	−	6.35469i	0.809341	−	0.360342i	0.0400154	−	0.999199i	$-0.487259\pi$
$311$	14.2729	−	6.35469i	0.809341	−	0.360342i	0.769325	+	0.638857i	$0.220593\pi$
$312$	0.140831	+	1.33992i	0.00797298	+	0.0758578i
$313$	21.4957	−	4.56906i	1.21501	−	0.258258i	0.444555	−	0.895752i	$-0.353362\pi$
$313$	21.4957	−	4.56906i	1.21501	−	0.258258i	0.770456	+	0.637493i	$0.220029\pi$
$314$	4.37518	−	13.4654i	0.246906	−	0.759898i
$315$	−17.9471	+	27.5238i	−1.01120	+	1.55079i
$316$	0.0920723	+	0.0668944i	0.00517947	+	0.00376311i
$317$	−2.01533	+	2.23825i	−0.113192	+	0.125713i	−0.797078	−	0.603877i	$-0.793622\pi$
$317$	−2.01533	+	2.23825i	−0.113192	+	0.125713i	0.683886	+	0.729589i	$0.260289\pi$
$318$	−14.4572	+	25.0407i	−0.810721	+	1.40421i
$319$		0			0
$320$	−7.24170	−	12.5430i	−0.404823	−	0.701174i
$321$	9.20681	+	28.3356i	0.513874	+	1.58154i
$322$	−32.6970	−	8.82637i	−1.82213	−	0.491874i
$323$	2.45326	−	1.78240i	0.136503	−	0.0991752i
$324$	−1.06009	+	0.225330i	−0.0588942	+	0.0125183i
$325$	0.0630370	+	0.0700096i	0.00349666	+	0.00388344i
$326$	1.40983	+	13.4136i	0.0780832	+	0.742912i
$327$	0.143161	−	1.36208i	0.00791680	−	0.0753233i
$328$	0.333345	+	1.02593i	0.0184059	+	0.0566475i
$329$	3.21600	−	20.0634i	0.177304	−	1.10613i
$330$		0			0
$331$	−13.7344	−	23.7887i	−0.754912	−	1.30755i	−0.945418	−	0.325860i	$-0.894346\pi$
$331$	−13.7344	−	23.7887i	−0.754912	−	1.30755i	0.190506	−	0.981686i	$-0.438987\pi$
$332$	1.13973	+	0.242257i	0.0625508	+	0.0132956i
$333$	−32.9783	+	14.6829i	−1.80720	+	0.804618i
$334$	−11.7323	−	5.22354i	−0.641960	−	0.285819i
$335$	2.72644	−	8.39112i	0.148961	−	0.458456i
$336$	29.2589	−	18.9236i	1.59620	−	1.03237i
$337$	13.9492	−	10.1347i	0.759862	−	0.552072i	−0.139006	−	0.990291i	$-0.544391\pi$
$337$	13.9492	−	10.1347i	0.759862	−	0.552072i	0.898868	+	0.438220i	$0.144391\pi$
$338$	2.07644	−	19.7560i	0.112943	−	1.07459i
$339$	8.85187	+	1.88152i	0.480768	+	0.102190i
$340$	−1.59833	+	2.76838i	−0.0866814	+	0.150137i
$341$		0			0
$342$	−6.26857			−0.338965
$343$	18.2758	+	2.99927i	0.986800	+	0.161945i
$344$	−2.42705	−	1.76336i	−0.130858	−	0.0950738i
$345$	51.5877	+	22.9683i	2.77739	+	1.23657i
$346$	−5.58268	−	6.20019i	−0.300126	−	0.333324i
$347$	7.64888	+	8.49494i	0.410613	+	0.456032i	0.912606	−	0.408839i	$-0.134066\pi$
$347$	7.64888	+	8.49494i	0.410613	+	0.456032i	−0.501993	+	0.864872i	$0.667400\pi$
$348$	7.46389	+	3.32314i	0.400106	+	0.178139i
$349$	22.9121	+	16.6466i	1.22646	+	0.891072i	0.996619	−	0.0821572i	$-0.0261810\pi$
$349$	22.9121	+	16.6466i	1.22646	+	0.891072i	0.229836	+	0.973229i	$0.426181\pi$
$350$	0.744151	−	1.92785i	0.0397766	−	0.103048i
$351$	1.21894			0.0650622
$352$		0			0
$353$	−8.21806	+	14.2341i	−0.437403	+	0.757605i	−0.997488	−	0.0708303i	$-0.977435\pi$
$353$	−8.21806	+	14.2341i	−0.437403	+	0.757605i	0.560085	+	0.828435i	$0.310768\pi$
$354$	−0.881970	−	0.187469i	−0.0468762	−	0.00996384i
$355$	2.44521	−	23.2647i	0.129778	−	1.23476i
$356$	1.30726	−	0.949783i	0.0692848	−	0.0503384i
$357$	26.5916	+	13.6115i	1.40738	+	0.720395i
$358$	−4.77774	+	14.7044i	−0.252512	+	0.777151i
$359$	−22.7136	−	10.1127i	−1.19878	−	0.533729i	−0.292438	−	0.956284i	$-0.594467\pi$
$359$	−22.7136	−	10.1127i	−1.19878	−	0.533729i	−0.906337	+	0.422555i	$0.861133\pi$
$360$	−28.7279	+	12.7905i	−1.51409	+	0.674117i
$361$	17.9999	+	3.82599i	0.947361	+	0.201368i
$362$	−15.2285	−	26.3765i	−0.800392	−	1.38632i
$363$		0			0
$364$	0.158633	−	0.0605553i	0.00831465	−	0.00317396i
$365$	−0.0874885	−	0.269262i	−0.00457935	−	0.0140938i
$366$	6.72399	−	63.9745i	0.351469	−	3.34400i
$367$	−0.449326	−	4.27505i	−0.0234546	−	0.223156i	−0.999970	−	0.00770943i	$-0.997546\pi$
$367$	−0.449326	−	4.27505i	−0.0234546	−	0.223156i	0.976516	−	0.215446i	$-0.0691207\pi$
$368$	−25.5713	−	28.3998i	−1.33300	−	1.48044i
$369$	2.20477	−	0.468638i	0.114776	−	0.0243963i
$370$	19.8510	−	14.4226i	1.03200	−	0.749794i
$371$	−16.7420	−	4.51940i	−0.869201	−	0.234636i
$372$	0.819731	+	2.52287i	0.0425010	+	0.130805i
$373$	−1.36484	−	2.36397i	−0.0706686	−	0.122402i	0.828526	−	0.559951i	$-0.189180\pi$
$373$	−1.36484	−	2.36397i	−0.0706686	−	0.122402i	−0.899195	+	0.437549i	$0.855847\pi$
$374$		0			0
$375$	15.1741	−	26.2823i	0.783588	−	1.35721i
$376$	13.0123	−	14.4516i	0.671057	−	0.745285i
$377$	−1.22145	−	0.887438i	−0.0629081	−	0.0457054i
$378$	−12.0945	−	23.8464i	−0.622075	−	1.22653i
$379$	−5.08593	+	15.6529i	−0.261247	+	0.804035i	0.731288	+	0.682069i	$0.238920\pi$
$379$	−5.08593	+	15.6529i	−0.261247	+	0.804035i	−0.992534	+	0.121965i	$0.961080\pi$
$380$	0.616639	−	0.131071i	0.0316329	−	0.00672378i
$381$	−0.134122	−	1.27609i	−0.00687130	−	0.0653760i
$382$	−35.5298	+	15.8189i	−1.81786	+	0.809364i
$383$	−5.25922	+	5.84096i	−0.268734	+	0.298459i	−0.862374	−	0.506271i	$-0.831023\pi$
$383$	−5.25922	+	5.84096i	−0.268734	+	0.298459i	0.593641	+	0.804730i	$0.297690\pi$
$384$	38.4124			1.96022
$385$		0			0
$386$	11.8452			0.602907
$387$	−4.19449	+	4.65846i	−0.213218	+	0.236803i
$388$	4.16279	−	1.85339i	0.211334	−	0.0940918i
$389$	−1.00799	−	9.59038i	−0.0511071	−	0.486252i	−0.989900	−	0.141769i	$-0.954721\pi$
$389$	−1.00799	−	9.59038i	−0.0511071	−	0.486252i	0.938793	−	0.344483i	$-0.111946\pi$
$390$	−1.87172	+	0.397846i	−0.0947781	+	0.0201457i
$391$	10.1241	−	31.1589i	0.512000	−	1.57577i
$392$	13.1277	+	11.9090i	0.663051	+	0.601496i
$393$	−28.1551	−	20.4559i	−1.42024	−	1.03186i
$394$	5.50990	−	6.11937i	0.277585	−	0.308289i
$395$	0.384600	−	0.666146i	0.0193513	−	0.0335175i
$396$		0			0
$397$	4.71688	+	8.16988i	0.236733	+	0.410034i	0.959775	−	0.280770i	$-0.0905898\pi$
$397$	4.71688	+	8.16988i	0.236733	+	0.410034i	−0.723042	+	0.690805i	$0.757257\pi$
$398$	4.15732	+	12.7949i	0.208388	+	0.641351i
$399$	−1.51418	−	5.69333i	−0.0758036	−	0.285023i
$400$	1.88648	−	1.37061i	0.0943239	−	0.0685303i
$401$	17.8217	−	3.78812i	0.889975	−	0.189170i	0.259836	−	0.965653i	$-0.416331\pi$
$401$	17.8217	−	3.78812i	0.889975	−	0.189170i	0.630138	+	0.776483i	$0.282998\pi$
$402$	11.0953	+	12.3226i	0.553385	+	0.614596i
$403$	−0.0512398	−	0.487514i	−0.00255244	−	0.0242848i
$404$	−0.214245	+	2.03840i	−0.0106591	+	0.101414i
$405$	2.26355	+	6.96650i	0.112477	+	0.346168i
$406$	−5.24170	+	32.7009i	−0.260141	+	1.62292i
$407$		0			0
$408$	14.2947	+	24.7592i	0.707695	+	1.22576i
$409$	6.27137	+	1.33302i	0.310099	+	0.0659136i	0.360333	−	0.932824i	$-0.382663\pi$
$409$	6.27137	+	1.33302i	0.310099	+	0.0659136i	−0.0502334	+	0.998738i	$0.515997\pi$
$410$	−1.39963	+	0.623157i	−0.0691229	+	0.0307755i
$411$	−43.0032	−	19.1463i	−2.12119	−	0.944415i
$412$	0.0988716	−	0.304295i	0.00487105	−	0.0149916i
$413$	−0.0272970	−	0.540083i	−0.00134320	−	0.0265758i
$414$	−54.7919	+	39.8086i	−2.69287	+	1.95649i
$415$	0.823190	−	7.83212i	0.0404088	−	0.384464i
$416$	0.351308	+	0.0746727i	0.0172243	+	0.00366113i
$417$	−29.8444	+	51.6919i	−1.46148	+	2.53137i
$418$		0			0
$419$	1.62092			0.0791871			0.0395935	−	0.999216i	$-0.487394\pi$
$419$	1.62092			0.0791871			0.0395935	+	0.999216i	$0.487394\pi$
$420$	3.89932	+	4.83362i	0.190267	+	0.235857i
$421$	−25.2000	−	18.3089i	−1.22817	−	0.892319i	−0.231420	−	0.972854i	$-0.574337\pi$
$421$	−25.2000	−	18.3089i	−1.22817	−	0.892319i	−0.996752	+	0.0805348i	$0.974337\pi$
$422$	−5.93616	−	2.64295i	−0.288968	−	0.128657i
$423$	−27.1895	−	30.1970i	−1.32200	−	1.46823i
$424$	−11.1051	−	12.3334i	−0.539310	−	0.598964i
$425$	1.82624	+	0.813094i	0.0885856	+	0.0394408i
$426$	35.5677	+	25.8414i	1.72326	+	1.25202i
$427$	38.1158	−	5.96427i	1.84455	−	0.288631i
$428$	3.59358			0.173702
$429$		0			0
$430$	2.13041	−	3.68999i	0.102738	−	0.177947i
$431$	33.4605	+	7.11225i	1.61173	+	0.342585i	0.923707	−	0.383099i	$-0.125143\pi$
$431$	33.4605	+	7.11225i	1.61173	+	0.342585i	0.688028	+	0.725684i	$0.258477\pi$
$432$	3.15375	−	30.0059i	0.151735	−	1.44366i
$433$	16.5832	−	12.0484i	0.796937	−	0.579009i	−0.113077	−	0.993586i	$-0.536071\pi$
$433$	16.5832	−	12.0484i	0.796937	−	0.579009i	0.910014	+	0.414578i	$0.136071\pi$
$434$	−9.02894	+	5.83961i	−0.433403	+	0.280310i
$435$	17.0642	−	52.5181i	0.818164	−	2.51805i
$436$	−0.150911	−	0.0671897i	−0.00722730	−	0.00321780i
$437$	−5.90251	+	2.62797i	−0.282355	+	0.125713i
$438$	0.520461	+	0.110628i	0.0248686	+	0.00528599i
$439$	15.6609	+	27.1255i	0.747455	+	1.29463i	0.949039	+	0.315158i	$0.102058\pi$
$439$	15.6609	+	27.1255i	0.747455	+	1.29463i	−0.201585	+	0.979471i	$0.564609\pi$
$440$		0			0
$441$	27.6152	−	24.6793i	1.31501	−	1.17521i
$442$	0.343066	+	1.05585i	0.0163180	+	0.0502216i
$443$	3.07291	−	29.2368i	0.145999	−	1.38908i	−0.638819	−	0.769357i	$-0.720577\pi$
$443$	3.07291	−	29.2368i	0.145999	−	1.38908i	0.784818	−	0.619726i	$-0.212756\pi$
$444$	0.713192	+	6.78557i	0.0338466	+	0.322029i
$445$	−7.30776	−	8.11609i	−0.346421	−	0.384739i
$446$	27.0275	−	5.74488i	1.27979	−	0.272028i
$447$	−1.66369	+	1.20874i	−0.0786900	+	0.0571716i
$448$	4.19586	+	15.7765i	0.198236	+	0.745370i
$449$	−2.13245	−	6.56299i	−0.100636	−	0.309727i	0.888045	−	0.459756i	$-0.152063\pi$
$449$	−2.13245	−	6.56299i	−0.100636	−	0.309727i	−0.988682	+	0.150029i	$0.952063\pi$
$450$	−2.06624	−	3.57883i	−0.0974034	−	0.168708i
$451$		0			0
$452$	0.545759	−	0.945283i	0.0256704	−	0.0444624i
$453$	18.3900	−	20.4241i	0.864037	−	0.959610i
$454$	22.5652	+	16.3946i	1.05904	+	0.769437i
$455$	−0.519109	−	1.02351i	−0.0243362	−	0.0479830i
$456$	1.74229	−	5.36220i	0.0815900	−	0.251108i
$457$	12.1042	−	2.57283i	0.566212	−	0.120352i	0.0840929	−	0.996458i	$-0.473201\pi$
$457$	12.1042	−	2.57283i	0.566212	−	0.120352i	0.482119	+	0.876106i	$0.339867\pi$
$458$	−3.08142	−	29.3178i	−0.143985	−	1.36993i
$459$	23.6296	−	10.5206i	1.10293	−	0.491058i
$460$	4.55751	−	5.06163i	0.212495	−	0.235999i
$461$	−20.0942			−0.935881			−0.467940	−	0.883760i	$-0.655004\pi$
$461$	−20.0942			−0.935881			−0.467940	+	0.883760i	$0.655004\pi$
$462$		0			0
$463$	8.69190			0.403947			0.201974	−	0.979391i	$-0.435265\pi$
$463$	8.69190			0.403947			0.201974	+	0.979391i	$0.435265\pi$
$464$	−25.0058	+	27.7717i	−1.16086	+	1.28927i
$465$	16.3790	−	7.29239i	0.759557	−	0.338176i
$466$	1.49337	+	14.2085i	0.0691791	+	0.658195i
$467$	−4.66498	+	0.991572i	−0.215870	+	0.0458845i	−0.314577	−	0.949232i	$-0.601863\pi$
$467$	−4.66498	+	0.991572i	−0.215870	+	0.0458845i	0.0987072	+	0.995117i	$0.468529\pi$
$468$	0.104928	−	0.322937i	0.00485032	−	0.0149277i
$469$	−5.43182	+	8.33030i	−0.250818	+	0.384657i
$470$	22.3446	+	16.2343i	1.03068	+	0.748834i
$471$	17.8049	−	19.7744i	0.820408	−	0.911156i
$472$	0.258770	−	0.448204i	0.0119109	−	0.0206302i
$473$		0			0
$474$	0.722811	+	1.25195i	0.0331998	+	0.0575038i
$475$	−0.121826	−	0.374942i	−0.00558977	−	0.0172035i
$476$	2.55251	−	2.54303i	0.116994	−	0.116560i
$477$	−28.0553	+	20.3834i	−1.28457	+	0.933291i
$478$	16.7692	−	3.56440i	0.767005	−	0.163032i
$479$	26.5070	+	29.4390i	1.21114	+	1.34510i	0.921699	+	0.387906i	$0.126802\pi$
$479$	26.5070	+	29.4390i	1.21114	+	1.34510i	0.289438	+	0.957197i	$0.406532\pi$
$480$	1.37310	+	13.0641i	0.0626730	+	0.596293i
$481$	0.131793	−	1.25392i	0.00600923	−	0.0571740i
$482$	−9.56560	−	29.4399i	−0.435701	−	1.34095i
$483$	−49.3906	−	40.1481i	−2.24735	−	1.82680i
$484$		0			0
$485$	−15.3990	−	26.6718i	−0.699232	−	1.21111i
$486$	16.1900	+	3.44129i	0.734393	+	0.156100i
$487$	4.70996	−	2.09701i	0.213429	−	0.0950246i	−0.297238	−	0.954804i	$-0.596065\pi$
$487$	4.70996	−	2.09701i	0.213429	−	0.0950246i	0.510666	+	0.859779i	$0.329399\pi$
$488$	33.7301	+	15.0176i	1.52689	+	0.679815i
$489$	−7.83303	+	24.1076i	−0.354222	+	1.09018i
$490$	−14.8725	+	20.3109i	−0.671872	+	0.917552i
$491$	8.24593	−	5.99102i	0.372134	−	0.270371i	−0.385961	−	0.922515i	$-0.626130\pi$
$491$	8.24593	−	5.99102i	0.372134	−	0.270371i	0.758095	+	0.652144i	$0.226130\pi$
$492$	0.0445314	−	0.423688i	0.00200763	−	0.0191013i
$493$	−31.3377	−	6.66103i	−1.41138	−	0.299998i
$494$	0.109470	−	0.189608i	0.00492531	−	0.00853088i
$495$		0			0
$496$	−12.1334			−0.544806
$497$	−9.49493	+	24.5982i	−0.425906	+	1.10338i
$498$	11.9740	+	8.69961i	0.536567	+	0.389839i
$499$	5.38061	+	2.39560i	0.240869	+	0.107242i	0.523621	−	0.851951i	$-0.324581\pi$
$499$	5.38061	+	2.39560i	0.240869	+	0.107242i	−0.282752	+	0.959193i	$0.591247\pi$
$500$	−2.44932	−	2.72024i	−0.109537	−	0.121653i
$501$	−16.1502	−	17.9366i	−0.721538	−	0.801349i
$502$	−8.24689	−	3.67175i	−0.368077	−	0.163878i
$503$	−10.3836	−	7.54411i	−0.462981	−	0.336375i	0.331719	−	0.943378i	$-0.392372\pi$
$503$	−10.3836	−	7.54411i	−0.462981	−	0.336375i	−0.794699	+	0.607003i	$0.792372\pi$
$504$	35.0188	−	5.47966i	1.55986	−	0.244084i
$505$	13.8530			0.616449
$506$		0			0
$507$	18.6668	−	32.3319i	0.829024	−	1.43591i
$508$	−0.151381	−	0.0321770i	−0.00671645	−	0.00142763i
$509$	−3.36718	+	32.0366i	−0.149248	+	1.42000i	0.621778	+	0.783193i	$0.286411\pi$
$509$	−3.36718	+	32.0366i	−0.149248	+	1.42000i	−0.771026	+	0.636804i	$0.780256\pi$
$510$	−32.8501	+	23.8670i	−1.45463	+	1.05685i
$511$	0.0161083	+	0.318710i	0.000712590	+	0.0140989i
$512$	−4.41079	+	13.5750i	−0.194931	+	0.599937i
$513$	−4.66001	−	2.07477i	−0.205744	−	0.0916033i
$514$	−3.83007	+	1.70526i	−0.168937	+	0.0752157i
$515$	−2.11525	−	0.449610i	−0.0932090	−	0.0198122i
$516$	0.592396	+	1.02606i	0.0260788	+	0.0451698i
$517$		0			0
$518$	−25.8384	+	9.86332i	−1.13528	+	0.433370i
$519$	−4.84540	−	14.9126i	−0.212689	−	0.654591i
$520$	0.114806	−	1.09231i	0.00503459	−	0.0479009i
$521$	−1.93670	−	18.4265i	−0.0848484	−	0.807278i	−0.951352	−	0.308107i	$-0.900304\pi$
$521$	−1.93670	−	18.4265i	−0.0848484	−	0.807278i	0.866503	−	0.499171i	$-0.166362\pi$
$522$	44.3155	+	49.2174i	1.93964	+	2.15419i
$523$	−36.4283	+	7.74308i	−1.59290	+	0.338581i	−0.917148	−	0.398548i	$-0.869514\pi$
$523$	−36.4283	+	7.74308i	−1.59290	+	0.338581i	−0.675752	+	0.737129i	$0.736181\pi$
$524$	−3.39592	+	2.46728i	−0.148351	+	0.107784i
$525$	2.75132	−	2.74110i	0.120077	−	0.119631i
$526$	−2.93419	−	9.03052i	−0.127937	−	0.393749i
$527$	−5.20099	−	9.00838i	−0.226559	−	0.392411i
$528$		0			0
$529$	−23.4033	+	40.5357i	−1.01754	+	1.76242i
$530$	15.7723	−	17.5169i	0.685104	−	0.760885i
$531$	−0.874882	−	0.635639i	−0.0379667	−	0.0275844i
$532$	−0.709527	−	0.0385086i	−0.0307619	−	0.00166956i
$533$	−0.0243276	+	0.0748726i	−0.00105374	+	0.00324309i
$534$	20.0768	−	4.26745i	0.868806	−	0.184670i
$535$	−2.53881	−	24.1551i	−0.109762	−	1.04432i
$536$	−8.69471	+	3.87113i	−0.375554	+	0.167207i
$537$	−19.4432	+	21.5938i	−0.839035	+	0.931843i
$538$	−6.44924			−0.278047
$539$		0			0
$540$	5.37733			0.231403
$541$	−24.1935	+	26.8696i	−1.04016	+	1.15521i	−0.0524971	+	0.998621i	$0.516718\pi$
$541$	−24.1935	+	26.8696i	−1.04016	+	1.15521i	−0.987663	+	0.156594i	$0.949949\pi$
$542$	−35.8050	+	15.9414i	−1.53796	+	0.684743i
$543$	−5.98325	−	56.9268i	−0.256766	−	2.44296i
$544$	7.45470	−	1.58455i	0.319618	−	0.0679368i
$545$	−0.345016	+	1.06185i	−0.0147789	+	0.0454847i
$546$	2.15367	+	0.116887i	0.0921684	+	0.00500232i
$547$	10.3538	+	7.52246i	0.442696	+	0.321637i	0.786705	−	0.617329i	$-0.211785\pi$
$547$	10.3538	+	7.52246i	0.442696	+	0.321637i	−0.344010	+	0.938966i	$0.611785\pi$
$548$	−3.79911	+	4.21934i	−0.162290	+	0.180241i
$549$	38.5749	−	66.8137i	1.64634	−	2.85154i
$550$		0			0
$551$	3.15910	+	5.47172i	0.134582	+	0.233103i
$552$	−18.8239	−	57.9340i	−0.801198	−	2.46583i
$553$	−0.614203	+	0.611921i	−0.0261186	+	0.0260215i
$554$	−19.0357	+	13.8302i	−0.808749	+	0.587590i
$555$	45.1070	−	9.58779i	1.91469	−	0.406979i
$556$	4.81730	+	5.35015i	0.204299	+	0.226897i
$557$	−3.20471	−	30.4907i	−0.135788	−	1.29193i	−0.824069	−	0.566490i	$-0.808301\pi$
$557$	−3.20471	−	30.4907i	−0.135788	−	1.29193i	0.688281	−	0.725444i	$-0.258366\pi$
$558$	−2.24767	+	21.3852i	−0.0951517	+	0.905308i
$559$	−0.0676564	−	0.208225i	−0.00286156	−	0.00880698i
$560$	−26.5382	+	10.1305i	−1.12145	+	0.428090i
$561$		0			0
$562$	14.7494	+	25.5468i	0.622167	+	1.07763i
$563$	−14.1878	−	3.01571i	−0.597944	−	0.127097i	−0.101010	−	0.994885i	$-0.532207\pi$
$563$	−14.1878	−	3.01571i	−0.597944	−	0.127097i	−0.496934	+	0.867789i	$0.665541\pi$
$564$	−7.01607	+	3.12376i	−0.295430	+	0.131534i
$565$	−6.73952	−	3.00063i	−0.283534	−	0.126237i
$566$	12.8137	−	39.4367i	0.538602	−	1.65765i
$567$	−0.416763	−	8.24585i	−0.0175024	−	0.346293i
$568$	−20.4151	+	14.8324i	−0.856598	+	0.622355i
$569$	1.98657	−	18.9009i	0.0832813	−	0.792369i	−0.870561	−	0.492061i	$-0.836244\pi$
$569$	1.98657	−	18.9009i	0.0832813	−	0.792369i	0.953842	−	0.300308i	$-0.0970895\pi$
$570$	7.83275	+	1.66490i	0.328078	+	0.0697351i
$571$	−10.5005	+	18.1873i	−0.439431	+	0.761117i	−0.997646	−	0.0685799i	$-0.978153\pi$
$571$	−10.5005	+	18.1873i	−0.439431	+	0.761117i	0.558215	+	0.829696i	$0.311487\pi$
$572$		0			0
$573$	−73.0934			−3.05352
$574$	1.70613	−	0.266971i	0.0712125	−	0.0111432i
$575$	−3.44593	−	2.50361i	−0.143705	−	0.104408i
$576$	29.8235	+	13.2783i	1.24265	+	0.553262i
$577$	−3.47110	−	3.85505i	−0.144504	−	0.160488i	0.666548	−	0.745462i	$-0.267771\pi$
$577$	−3.47110	−	3.85505i	−0.144504	−	0.160488i	−0.811052	+	0.584974i	$0.801105\pi$
$578$	−1.66447	−	1.84858i	−0.0692328	−	0.0768908i
$579$	20.3371	+	9.05467i	0.845182	+	0.376299i
$580$	−5.38841	−	3.91491i	−0.223742	−	0.162558i
$581$	−3.19650	+	8.28108i	−0.132613	+	0.343557i
$582$	57.8813			2.39926
$583$		0			0
$584$	−0.152704	+	0.264490i	−0.00631892	+	0.0109447i
$585$	−2.24483	−	0.477153i	−0.0928122	−	0.0197278i
$586$	0.646206	−	6.14824i	0.0266945	−	0.253981i
$587$	−6.74568	+	4.90103i	−0.278424	+	0.202287i	−0.718230	−	0.695806i	$-0.755047\pi$
$587$	−6.74568	+	4.90103i	−0.278424	+	0.202287i	0.439806	+	0.898093i	$0.355047\pi$
$588$	−2.82334	−	6.40537i	−0.116433	−	0.264153i
$589$	−0.633913	+	1.95098i	−0.0261199	+	0.0803888i
$590$	0.671503	+	0.298972i	0.0276453	+	0.0123085i
$591$	14.1377	−	6.29451i	0.581548	−	0.258922i
$592$	−30.5260	−	6.48851i	−1.25461	−	0.266676i
$593$	3.05097	+	5.28444i	0.125288	+	0.217006i	0.921846	−	0.387557i	$-0.126681\pi$
$593$	3.05097	+	5.28444i	0.125288	+	0.217006i	−0.796557	+	0.604563i	$0.793348\pi$
$594$		0			0
$595$	−18.8969	−	15.3607i	−0.774698	−	0.629729i
$596$	0.0766475	+	0.235897i	0.00313961	+	0.00966271i
$597$	−2.64290	+	25.1455i	−0.108167	+	1.02914i
$598$	−0.247259	−	2.35251i	−0.0101112	−	0.0962012i
$599$	−9.26765	−	10.2928i	−0.378666	−	0.420551i	0.523442	−	0.852061i	$-0.324648\pi$
$599$	−9.26765	−	10.2928i	−0.378666	−	0.420551i	−0.902108	+	0.431510i	$0.857981\pi$
$600$	3.63566	−	0.772783i	0.148425	−	0.0315487i
$601$	25.2976	−	18.3798i	1.03191	−	0.749726i	0.0632191	−	0.998000i	$-0.479863\pi$
$601$	25.2976	−	18.3798i	1.03191	−	0.749726i	0.968690	+	0.248274i	$0.0798633\pi$
$602$	−3.40225	+	3.38962i	−0.138666	+	0.138151i
$603$	6.14546	+	18.9138i	0.250262	+	0.770229i
$604$	−1.65745	−	2.87079i	−0.0674407	−	0.116811i
$605$		0			0
$606$	−13.0175	+	22.5470i	−0.528801	+	0.915911i
$607$	−25.2906	+	28.0881i	−1.02651	+	1.14006i	−0.0364652	+	0.999335i	$0.511610\pi$
$607$	−25.2906	+	28.0881i	−1.02651	+	1.14006i	−0.990049	+	0.140724i	$0.955057\pi$
$608$	−1.21595	−	0.883437i	−0.0493132	−	0.0358281i
$609$	−33.9965	+	52.1374i	−1.37761	+	2.11271i
$610$	−16.2048	+	49.8732i	−0.656112	+	2.01931i
$611$	1.38820	−	0.295071i	0.0561606	−	0.0119373i
$612$	−0.753162	−	7.16586i	−0.0304448	−	0.289663i
$613$	−19.3072	+	8.59611i	−0.779810	+	0.347194i	−0.757735	−	0.652563i	$-0.773694\pi$
$613$	−19.3072	+	8.59611i	−0.779810	+	0.347194i	−0.0220750	+	0.999756i	$0.507027\pi$
$614$	−3.00273	+	3.33487i	−0.121180	+	0.134584i
$615$	−2.87939			−0.116108
$616$		0			0
$617$	23.7743			0.957115			0.478558	−	0.878056i	$-0.341160\pi$
$617$	23.7743			0.957115			0.478558	+	0.878056i	$0.341160\pi$
$618$	2.71947	−	3.02027i	0.109393	−	0.121493i
$619$	12.3347	−	5.49178i	0.495775	−	0.220733i	−0.143589	−	0.989637i	$-0.545864\pi$
$619$	12.3347	−	5.49178i	0.495775	−	0.220733i	0.639364	+	0.768904i	$0.279198\pi$
$620$	−0.226043	−	2.15066i	−0.00907811	−	0.0863725i
$621$	−53.9077	+	11.4584i	−2.16324	+	0.459811i
$622$	7.39686	−	22.7652i	0.296587	−	0.912802i
$623$	5.56816	+	10.9786i	0.223084	+	0.439847i
$624$	1.96896	+	1.43053i	0.0788213	+	0.0572670i
$625$	−18.2600	+	20.2798i	−0.730399	+	0.811190i
$626$	16.8346	−	29.1583i	0.672844	−	1.16540i
$627$		0			0
$628$	−1.60472	−	2.77946i	−0.0640354	−	0.110913i
$629$	−8.26764	−	25.4452i	−0.329652	−	1.01457i
$630$	12.9389	+	48.6504i	0.515497	+	1.93828i
$631$	30.9331	−	22.4742i	1.23143	−	0.894683i	0.234429	−	0.972133i	$-0.424678\pi$
$631$	30.9331	−	22.4742i	1.23143	−	0.894683i	0.996996	+	0.0774503i	$0.0246779\pi$
$632$	−0.811623	+	0.172516i	−0.0322846	+	0.00686231i
$633$	−8.17151	−	9.07538i	−0.324788	−	0.360714i
$634$	0.482340	+	4.58916i	0.0191562	+	0.182259i
$635$	−0.109338	+	1.04028i	−0.00433893	+	0.0412822i
$636$	2.02541	+	6.23358i	0.0803129	+	0.247178i
$637$	0.264233	+	1.26627i	0.0104693	+	0.0501715i
$638$		0			0
$639$	26.3640	+	45.6637i	1.04294	+	1.80643i
$640$	−30.6298	−	6.51056i	−1.21075	−	0.257353i
$641$	35.2220	−	15.6819i	1.39119	−	0.619396i	0.431923	−	0.901910i	$-0.357835\pi$
$641$	35.2220	−	15.6819i	1.39119	−	0.619396i	0.959263	+	0.282514i	$0.0911684\pi$
$642$	41.7005	+	18.5662i	1.64579	+	0.732751i
$643$	5.95250	−	18.3199i	0.234744	−	0.722467i	−0.762412	−	0.647092i	$-0.775985\pi$
$643$	5.95250	−	18.3199i	0.234744	−	0.722467i	0.997155	−	0.0753745i	$-0.0240152\pi$
$644$	−6.44633	+	4.16927i	−0.254021	+	0.164292i
$645$	6.47840	−	4.70683i	0.255087	−	0.185331i
$646$	0.485628	−	4.62045i	0.0191068	−	0.181789i
$647$	−38.9150	−	8.27163i	−1.52991	−	0.325191i	−0.635377	−	0.772202i	$-0.719155\pi$
$647$	−38.9150	−	8.27163i	−1.52991	−	0.325191i	−0.894529	+	0.447011i	$0.852489\pi$
$648$	3.95084	−	6.84305i	0.155204	−	0.268820i
$649$		0			0
$650$	0.144334			0.00566124
$651$	−19.9657	+	3.12419i	−0.782518	+	0.122447i
$652$	2.47346	+	1.79708i	0.0968684	+	0.0703790i
$653$	4.35442	+	1.93871i	0.170402	+	0.0758678i	0.490165	−	0.871630i	$-0.336937\pi$
$653$	4.35442	+	1.93871i	0.170402	+	0.0758678i	−0.319763	+	0.947498i	$0.603603\pi$
$654$	−1.40405	−	1.55936i	−0.0549029	−	0.0609758i
$655$	18.9836	+	21.0834i	0.741750	+	0.823797i
$656$	1.78015	+	0.792573i	0.0695031	+	0.0309448i
$657$	0.516279	+	0.375099i	0.0201420	+	0.0146340i
$658$	−19.5465	−	24.2299i	−0.762002	−	0.944582i
$659$	38.3550			1.49410			0.747050	−	0.664768i	$-0.231470\pi$
$659$	38.3550			1.49410			0.747050	+	0.664768i	$0.231470\pi$
$660$		0			0
$661$	5.18139	−	8.97443i	0.201533	−	0.349065i	−0.747490	−	0.664273i	$-0.768741\pi$
$661$	5.18139	−	8.97443i	0.201533	−	0.349065i	0.949022	+	0.315208i	$0.102074\pi$
$662$	−41.1651	−	8.74990i	−1.59993	−	0.340075i
$663$	−0.218095	+	2.07504i	−0.00847011	+	0.0805877i
$664$	−6.87280	+	4.99338i	−0.266717	+	0.193781i
$665$	0.242424	+	4.79647i	0.00940080	+	0.185999i
$666$	−17.0909	+	52.6003i	−0.662258	+	2.03822i
$667$	62.3611	+	27.7649i	2.41463	+	1.07506i
$668$	−2.65949	+	1.18408i	−0.102899	+	0.0458134i
$669$	50.7952	+	10.7968i	1.96385	+	0.417430i
$670$	−6.75877	−	11.7065i	−0.261114	−	0.452263i
$671$		0			0
$672$	2.34343	−	14.6197i	0.0903996	−	0.563967i
$673$	7.91603	+	24.3630i	0.305140	+	0.939126i	0.979625	+	0.200836i	$0.0643660\pi$
$673$	7.91603	+	24.3630i	0.305140	+	0.939126i	−0.674484	+	0.738289i	$0.735634\pi$
$674$	2.76128	−	26.2718i	0.106360	−	1.01195i
$675$	−0.351506	−	3.34436i	−0.0135295	−	0.128724i
$676$	−3.01309	−	3.34638i	−0.115888	−	0.128707i
$677$	40.9232	−	8.69850i	1.57281	−	0.334311i	0.662766	−	0.748827i	$-0.269382\pi$
$677$	40.9232	−	8.69850i	1.57281	−	0.334311i	0.910042	+	0.414516i	$0.136049\pi$
$678$	11.2169	−	8.14955i	0.430782	−	0.312981i
$679$	8.92221	+	33.5477i	0.342403	+	1.28744i
$680$	−7.20206	−	22.1656i	−0.276186	−	0.850014i
$681$	26.2101	+	45.3972i	1.00437	+	1.73962i
$682$		0			0
$683$	23.0214	−	39.8743i	0.880890	−	1.52575i	0.0305366	−	0.999534i	$-0.490278\pi$
$683$	23.0214	−	39.8743i	0.880890	−	1.52575i	0.850353	−	0.526212i	$-0.176388\pi$
$684$	−0.950814	+	1.05599i	−0.0363553	+	0.0403766i
$685$	31.0453	+	22.5558i	1.18618	+	0.861811i
$686$	22.1506	−	17.7334i	0.845714	−	0.677064i
$687$	17.1204	−	52.6913i	0.653186	−	2.01030i
$688$	−5.30079	+	1.12672i	−0.202091	+	0.0429557i
$689$	−0.126605	−	1.20456i	−0.00482326	−	0.0458903i
$690$	79.0370	−	35.1895i	3.00889	−	1.33964i
$691$	5.35304	−	5.94516i	0.203639	−	0.226164i	−0.632671	−	0.774421i	$-0.718041\pi$
$691$	5.35304	−	5.94516i	0.203639	−	0.226164i	0.836310	+	0.548256i	$0.184708\pi$
$692$	−1.89124			−0.0718943
$693$		0			0
$694$	17.5134			0.664800
$695$	32.5590	−	36.1605i	1.23503	−	1.37164i
$696$	−54.4182	+	24.2285i	−2.06272	+	0.918380i
$697$	0.174620	+	1.66140i	0.00661420	+	0.0629299i
$698$	42.4419	−	9.02131i	1.60645	−	0.341462i
$699$	−8.29720	+	25.5361i	−0.313829	+	0.965866i
$700$	−0.211888	−	0.417774i	−0.00800862	−	0.0157904i
$701$	−26.5474	−	19.2878i	−1.00268	−	0.728491i	−0.0400199	−	0.999199i	$-0.512742\pi$
$701$	−26.5474	−	19.2878i	−1.00268	−	0.728491i	−0.962661	+	0.270708i	$0.912742\pi$
$702$	1.24962	−	1.38784i	0.0471638	−	0.0523807i
$703$	−2.63816	+	4.56942i	−0.0994999	+	0.172339i
$704$		0			0
$705$	25.9538	+	44.9534i	0.977478	+	1.69304i
$706$	7.78154	+	23.9491i	0.292862	+	0.901337i
$707$	−15.0748	−	4.06935i	−0.566945	−	0.153044i
$708$	−0.165357	+	0.120139i	−0.00621451	+	0.00451510i
$709$	−7.24023	+	1.53896i	−0.271912	+	0.0577968i	−0.341850	−	0.939755i	$-0.611053\pi$
$709$	−7.24023	+	1.53896i	−0.271912	+	0.0577968i	0.0699373	+	0.997551i	$0.477720\pi$
$710$	−23.9815	−	26.6342i	−0.900011	−	0.999564i
$711$	0.181231	+	1.72430i	0.00679668	+	0.0646661i
$712$	−1.23146	+	11.7165i	−0.0461508	+	0.439095i
$713$	6.84888	+	21.0787i	0.256493	+	0.789403i
$714$	42.7584	−	16.3222i	1.60019	−	0.610842i
$715$		0			0
$716$	1.75237	+	3.03520i	0.0654893	+	0.113431i
$717$	31.5158	+	6.69889i	1.17698	+	0.250175i
$718$	−34.7992	+	15.4936i	−1.29869	+	0.578216i
$719$	−12.9148	−	5.75005i	−0.481641	−	0.214441i	0.151529	−	0.988453i	$-0.451580\pi$
$719$	−12.9148	−	5.75005i	−0.481641	−	0.214441i	−0.633171	+	0.774012i	$0.718247\pi$
$720$	−17.5538	+	54.0250i	−0.654191	+	2.01339i
$721$	2.16973	+	1.11062i	0.0808051	+	0.0413618i
$722$	22.8090	−	16.5717i	0.848863	−	0.616735i
$723$	6.08107	−	57.8575i	0.226158	−	2.15174i
$724$	−6.75317	−	1.43543i	−0.250980	−	0.0533473i
$725$	−2.08260	+	3.60716i	−0.0773457	+	0.133967i
$726$		0			0
$727$	15.2790			0.566667			0.283333	−	0.959021i	$-0.408560\pi$
$727$	15.2790			0.566667			0.283333	+	0.959021i	$0.408560\pi$
$728$	−0.445801	+	1.15492i	−0.0165225	+	0.0428043i
$729$	32.7400	+	23.7870i	1.21259	+	0.881000i
$730$	−0.396262	−	0.176427i	−0.0146663	−	0.00652987i
$731$	−3.10871	−	3.45257i	−0.114980	−	0.127698i
$732$	−9.75707	−	10.8363i	−0.360632	−	0.400522i
$733$	−1.22866	−	0.547033i	−0.0453815	−	0.0202051i	0.383920	−	0.923366i	$-0.374574\pi$
$733$	−1.22866	−	0.547033i	−0.0453815	−	0.0202051i	−0.429302	+	0.903161i	$0.641240\pi$
$734$	−5.32805	−	3.87106i	−0.196662	−	0.142883i
$735$	−41.0606	+	23.5031i	−1.51454	+	0.866924i
$736$	−16.2385			−0.598561
$737$		0			0
$738$	1.72668	−	2.99070i	0.0635600	−	0.110089i
$739$	−25.0930	−	5.33369i	−0.923063	−	0.196203i	−0.278219	−	0.960518i	$-0.589744\pi$
$739$	−25.0930	−	5.33369i	−0.923063	−	0.196203i	−0.644843	+	0.764315i	$0.723077\pi$
$740$	0.581400	−	5.53165i	0.0213727	−	0.203347i
$741$	0.332890	−	0.241858i	0.0122290	−	0.00888489i
$742$	−22.3090	+	14.4287i	−0.818988	+	0.529693i
$743$	1.87916	−	5.78346i	0.0689397	−	0.212175i	−0.910651	−	0.413176i	$-0.864420\pi$
$743$	1.87916	−	5.78346i	0.0689397	−	0.212175i	0.979591	+	0.201001i	$0.0644195\pi$
$744$	−17.6684	−	7.86649i	−0.647756	−	0.288399i
$745$	1.53149	−	0.681863i	0.0561094	−	0.0249815i
$746$	−4.09072	−	0.869508i	−0.149772	−	0.0318350i
$747$	8.87551	+	15.3728i	0.324738	+	0.562463i
$748$		0			0
$749$	−4.33291	+	27.0313i	−0.158321	+	0.987703i
$750$	−14.3681	−	44.2205i	−0.524649	−	1.61470i
$751$	−2.17532	+	20.6968i	−0.0793785	+	0.755236i	0.880354	+	0.474318i	$0.157305\pi$
$751$	−2.17532	+	20.6968i	−0.0793785	+	0.755236i	−0.959732	+	0.280917i	$0.909361\pi$
$752$	−3.67191	−	34.9359i	−0.133901	−	1.27398i
$753$	−11.3524	−	12.6081i	−0.413703	−	0.459464i
$754$	−2.26260	+	0.480931i	−0.0823990	+	0.0175145i
$755$	−18.1258	+	13.1691i	−0.659664	+	0.479274i
$756$	−5.85159	−	1.57960i	−0.212820	−	0.0574496i
$757$	−1.62358	−	4.99687i	−0.0590101	−	0.181614i	0.917206	−	0.398412i	$-0.130439\pi$
$757$	−1.62358	−	4.99687i	−0.0590101	−	0.181614i	−0.976216	+	0.216798i	$0.930439\pi$
$758$	12.6079	+	21.8375i	0.457939	+	0.793173i
$759$		0			0
$760$	−2.29813	+	3.98048i	−0.0833621	+	0.144387i
$761$	27.4219	−	30.4551i	0.994042	−	1.10400i	−0.000535969	−	1.00000i	$-0.500171\pi$
$761$	27.4219	−	30.4551i	0.994042	−	1.10400i	0.994578	−	0.103995i	$-0.0331627\pi$
$762$	−1.59041	−	1.15550i	−0.0576144	−	0.0418593i
$763$	0.687367	−	1.05415i	0.0248844	−	0.0381629i
$764$	−2.72434	+	8.38465i	−0.0985631	+	0.303346i
$765$	−47.6350	+	10.1251i	−1.72225	+	0.366075i
$766$	1.25872	+	11.9759i	0.0454794	+	0.432708i
$767$	0.0345049	−	0.0153626i	0.00124590	−	0.000554710i
$768$	15.6029	−	17.3288i	0.563022	−	0.625299i
$769$	−47.5580			−1.71499			−0.857493	−	0.514496i	$-0.827979\pi$
$769$	−47.5580			−1.71499			−0.857493	+	0.514496i	$0.827979\pi$
$770$		0			0
$771$	−7.87939			−0.283769
$772$	1.79668	−	1.99542i	0.0646640	−	0.0718166i
$773$	18.7212	−	8.33521i	0.673354	−	0.299797i	−0.0414303	−	0.999141i	$-0.513191\pi$
$773$	18.7212	−	8.33521i	0.673354	−	0.299797i	0.714784	+	0.699345i	$0.246525\pi$
$774$	1.00389	+	9.55140i	0.0360842	+	0.343318i
$775$	−1.32280	+	0.281169i	−0.0475163	+	0.0100999i
$776$	−10.2663	+	31.5965i	−0.368540	+	1.13425i
$777$	−51.9018	−	2.81690i	−1.86197	−	0.101056i
$778$	−11.9526	−	8.68409i	−0.428522	−	0.311340i
$779$	0.220446	−	0.244830i	0.00789828	−	0.00877193i
$780$	−0.216881	+	0.375650i	−0.00776560	+	0.0134504i
$781$		0			0
$782$	−25.0974	−	43.4701i	−0.897483	−	1.55449i
$783$	16.6539	+	51.2554i	0.595161	+	1.83172i
$784$	31.8547	−	3.22826i	1.13767	−	0.115295i
$785$	−17.5491	+	12.7502i	−0.626355	+	0.455073i
$786$	−52.1540	+	11.0857i	−1.86027	+	0.395413i
$787$	12.7942	+	14.2094i	0.456064	+	0.506510i	0.926692	−	0.375822i	$-0.122639\pi$
$787$	12.7942	+	14.2094i	0.456064	+	0.506510i	−0.470628	+	0.882331i	$0.655973\pi$
$788$	−0.195112	−	1.85637i	−0.00695058	−	0.0661303i
$789$	1.86534	−	17.7475i	0.0664077	−	0.631827i
$790$	−0.364171	−	1.12080i	−0.0129566	−	0.0398764i
$791$	6.45249	+	5.24503i	0.229424	+	0.186492i
$792$		0			0
$793$	1.34730	+	2.33359i	0.0478439	+	0.0828681i
$794$	14.1375	+	3.00502i	0.501722	+	0.106644i
$795$	40.4696	−	18.0182i	1.43531	−	0.639041i
$796$	2.78598	+	1.24040i	0.0987463	+	0.0439647i
$797$	−16.2278	+	49.9441i	−0.574819	+	1.76911i	0.0619750	+	0.998078i	$0.480260\pi$
$797$	−16.2278	+	49.9441i	−0.574819	+	1.76911i	−0.636794	+	0.771034i	$0.719740\pi$
$798$	−8.03451	−	4.11263i	−0.284419	−	0.145586i
$799$	24.3640	−	17.7015i	0.861936	−	0.626233i
$800$	0.103570	−	0.985401i	0.00366175	−	0.0348392i
$801$	24.0789	+	5.11812i	0.850785	+	0.180840i
$802$	13.9572	−	24.1746i	0.492847	−	0.853636i
$803$		0			0
$804$	3.75877			0.132562
$805$	32.5790	+	40.3851i	1.14826	+	1.42339i
$806$	−0.607596	−	0.441444i	−0.0214016	−	0.0155492i
$807$	−11.0727	−	4.92990i	−0.389779	−	0.173541i
$808$	−9.99920	−	11.1052i	−0.351770	−	0.390681i
$809$	−27.2145	−	30.2248i	−0.956812	−	1.06265i	−0.997982	−	0.0634953i	$-0.979775\pi$
$809$	−27.2145	−	30.2248i	−0.956812	−	1.06265i	0.0411701	−	0.999152i	$-0.486891\pi$
$810$	10.2523	+	4.56463i	0.360230	+	0.160385i
$811$	−16.6373	−	12.0877i	−0.584214	−	0.424456i	0.256027	−	0.966670i	$-0.417586\pi$
$811$	−16.6373	−	12.0877i	−0.584214	−	0.424456i	−0.840241	+	0.542213i	$0.817586\pi$
$812$	4.71364	+	5.84306i	0.165416	+	0.205051i
$813$	−73.6596			−2.58336
$814$		0			0
$815$	10.3320	−	17.8956i	0.361915	−	0.626856i
$816$	50.5156	+	10.7374i	1.76840	+	0.375885i
$817$	−0.0957713	+	0.911203i	−0.00335061	+	0.0318789i
$818$	7.94693	−	5.77378i	0.277858	−	0.201876i
$819$	2.30265	+	1.17866i	0.0804611	+	0.0411857i
$820$	−0.107320	+	0.330298i	−0.00374779	+	0.0115345i
$821$	−5.81269	−	2.58797i	−0.202864	−	0.0903209i	0.302790	−	0.953057i	$-0.402082\pi$
$821$	−5.81269	−	2.58797i	−0.202864	−	0.0903209i	−0.505654	+	0.862736i	$0.668749\pi$
$822$	−65.8847	+	29.3338i	−2.29799	+	1.02313i
$823$	2.45404	+	0.521623i	0.0855425	+	0.0181826i	0.250484	−	0.968121i	$-0.419410\pi$
$823$	2.45404	+	0.521623i	0.0855425	+	0.0181826i	−0.164942	+	0.986303i	$0.552744\pi$
$824$	1.16637	+	2.02022i	0.0406326	+	0.0703777i
$825$		0			0
$826$	−0.642903	−	0.522597i	−0.0223695	−	0.0181835i
$827$	12.7514	+	39.2448i	0.443410	+	1.36468i	0.884218	+	0.467075i	$0.154692\pi$
$827$	12.7514	+	39.2448i	0.443410	+	1.36468i	−0.440808	+	0.897602i	$0.645308\pi$
$828$	−1.60476	+	15.2682i	−0.0557692	+	0.530608i
$829$	4.88962	+	46.5216i	0.169823	+	1.61576i	0.664913	+	0.746921i	$0.268469\pi$
$829$	4.88962	+	46.5216i	0.169823	+	1.61576i	−0.495090	+	0.868842i	$0.664865\pi$
$830$	−8.07347	−	8.96649i	−0.280234	−	0.311232i
$831$	−43.2545	+	9.19402i	−1.50048	+	0.318937i
$832$	−0.922453	+	0.670202i	−0.0319803	+	0.0232351i
$833$	16.0513	+	22.2665i	0.556145	+	0.771489i
$834$	28.2591	+	86.9726i	0.978533	+	3.01162i
$835$	9.83796	+	17.0399i	0.340457	+	0.589688i
$836$		0			0
$837$	−8.74897	+	15.1537i	−0.302409	+	0.523787i
$838$	1.66171	−	1.84552i	0.0574030	−	0.0637524i
$839$	−13.3843	−	9.72429i	−0.462079	−	0.335720i	0.332268	−	0.943185i	$-0.392186\pi$
$839$	−13.3843	−	9.72429i	−0.462079	−	0.335720i	−0.794346	+	0.607465i	$0.792186\pi$
$840$	−45.2123	−	2.45384i	−1.55997	−	0.0846655i
$841$	11.6663	−	35.9051i	0.402286	−	1.23811i
$842$	−46.6800	+	9.92214i	−1.60870	+	0.341940i
$843$	5.79503	+	55.1360i	0.199591	+	1.89899i
$844$	−1.34562	+	0.599108i	−0.0463181	+	0.0206222i
$845$	−20.3648	+	22.6174i	−0.700570	+	0.778062i
$846$	−62.2550			−2.14037
$847$		0			0
$848$	−29.9796			−1.02950
$849$	52.1459	−	57.9139i	1.78964	−	1.98760i
$850$	2.79796	−	1.24573i	0.0959692	−	0.0427282i
$851$	5.95875	+	56.6937i	0.204263	+	1.94344i
$852$	9.74807	−	2.07202i	0.333964	−	0.0709861i
$853$	−4.08405	+	12.5694i	−0.139835	+	0.430368i	−0.996311	−	0.0858193i	$-0.972649\pi$
$853$	−4.08405	+	12.5694i	−0.139835	+	0.430368i	0.856476	+	0.516187i	$0.172649\pi$
$854$	32.2844	−	49.5116i	1.10475	−	1.69425i
$855$	7.76981	+	5.64509i	0.265722	+	0.193058i
$856$	−17.5314	+	19.4706i	−0.599211	+	0.665491i
$857$	−25.3606	+	43.9258i	−0.866300	+	1.50048i	−0.000549663		1.00000i	$0.500175\pi$
$857$	−25.3606	+	43.9258i	−0.866300	+	1.50048i	−0.865750	+	0.500476i	$0.833158\pi$
$858$		0			0
$859$	−27.5562	−	47.7287i	−0.940205	−	1.62848i	−0.765079	−	0.643937i	$-0.777300\pi$
$859$	−27.5562	−	47.7287i	−0.940205	−	1.62848i	−0.175126	−	0.984546i	$-0.556033\pi$
$860$	−0.298465	−	0.918580i	−0.0101776	−	0.0313233i
$861$	3.13334	+	0.845827i	0.106784	+	0.0288257i
$862$	42.4004	−	30.8057i	1.44416	−	1.04924i
$863$	−10.2903	+	2.18728i	−0.350287	+	0.0744558i	−0.379695	−	0.925112i	$-0.623971\pi$
$863$	−10.2903	+	2.18728i	−0.350287	+	0.0744558i	0.0294080	+	0.999567i	$0.490638\pi$
$864$	−8.57843	−	9.52731i	−0.291844	−	0.324126i
$865$	1.33613	+	12.7125i	0.0454299	+	0.432237i
$866$	3.28268	−	31.2326i	0.111550	−	1.06133i
$867$	−1.44465	−	4.44618i	−0.0490630	−	0.151000i
$868$	−0.385782	+	2.40674i	−0.0130943	+	0.0816901i
$869$		0			0
$870$	−42.3016	−	73.2685i	−1.43416	−	2.48404i
$871$	−0.679414	−	0.144414i	−0.0230211	−	0.00489328i
$872$	1.10027	−	0.489871i	0.0372598	−	0.0165891i
$873$	63.4177	+	28.2354i	2.14636	+	0.955623i
$874$	−3.05895	+	9.41449i	−0.103471	+	0.318450i
$875$	23.4152	−	15.1441i	0.791578	−	0.511965i
$876$	0.0975794	−	0.0708956i	0.00329690	−	0.00239534i
$877$	−4.14493	+	39.4364i	−0.139964	+	1.33167i	0.668757	+	0.743481i	$0.266827\pi$
$877$	−4.14493	+	39.4364i	−0.139964	+	1.33167i	−0.808721	+	0.588192i	$0.799840\pi$
$878$	46.9392	+	9.97723i	1.58412	+	0.336715i
$879$	5.80928	−	10.0620i	0.195942	−	0.339382i
$880$		0			0
$881$	25.0077			0.842532			0.421266	−	0.906937i	$-0.361586\pi$
$881$	25.0077			0.842532			0.421266	+	0.906937i	$0.361586\pi$
$882$	0.211151	−	56.7421i	0.00710983	−	1.91061i
$883$	−41.2065	−	29.9383i	−1.38671	−	1.00750i	−0.996217	−	0.0868978i	$-0.972305\pi$
$883$	−41.2065	−	29.9383i	−1.38671	−	1.00750i	−0.390493	−	0.920606i	$-0.627695\pi$
$884$	0.229902	+	0.102359i	0.00773243	+	0.00344270i
$885$	0.924367	+	1.02661i	0.0310723	+	0.0345092i
$886$	−30.1377	−	33.4713i	−1.01250	−	1.12449i
$887$	−29.2664	−	13.0302i	−0.982668	−	0.437512i	−0.148434	−	0.988922i	$-0.547423\pi$
$887$	−29.2664	−	13.0302i	−0.982668	−	0.437512i	−0.834234	+	0.551410i	$0.814090\pi$
$888$	−40.2447	−	29.2395i	−1.35052	−	0.981212i
$889$	0.424565	−	1.09991i	0.0142395	−	0.0368898i
$890$	−16.7324			−0.560870
$891$		0			0
$892$	3.13176	−	5.42437i	0.104859	−	0.181621i
$893$	−5.80934	−	1.23481i	−0.194402	−	0.0413214i
$894$	−0.329332	+	3.13338i	−0.0110145	+	0.104796i
$895$	19.1638	−	13.9233i	0.640576	−	0.465406i
$896$	31.4188	+	16.0824i	1.04963	+	0.537274i
$897$	1.37377	−	4.22804i	0.0458689	−	0.141170i
$898$	−9.65850	−	4.30024i	−0.322308	−	0.143501i
$899$	19.7995	−	8.81530i	0.660350	−	0.294007i
$900$	−0.916286	−	0.194762i	−0.0305429	−	0.00649208i
$901$	−12.8508	−	22.2582i	−0.428121	−	0.741527i
$902$		0			0
$903$	−8.43242	+	3.21891i	−0.280613	+	0.107119i
$904$	2.45919	+	7.56861i	0.0817915	+	0.251728i
$905$	−4.87759	+	46.4072i	−0.162137	+	1.54263i
$906$	−4.40138	−	41.8763i	−0.146226	−	1.39125i
$907$	−11.0226	−	12.2418i	−0.365998	−	0.406482i	0.531814	−	0.846861i	$-0.321511\pi$
$907$	−11.0226	−	12.2418i	−0.365998	−	0.406482i	−0.897812	+	0.440379i	$0.854844\pi$
$908$	6.18448	−	1.31455i	0.205239	−	0.0436249i
$909$	−25.2615	+	18.3536i	−0.837871	+	0.608749i
$910$	−1.69751	−	0.458233i	−0.0562718	−	0.0151903i
$911$	−14.0287	−	43.1759i	−0.464792	−	1.43048i	−0.859244	−	0.511566i	$-0.829066\pi$
$911$	−14.0287	−	43.1759i	−0.464792	−	1.43048i	0.394452	−	0.918916i	$-0.370934\pi$
$912$	−5.09240	−	8.82029i	−0.168626	−	0.292069i
$913$		0			0
$914$	9.47952	−	16.4190i	0.313555	−	0.543093i
$915$	−65.9458	+	73.2403i	−2.18010	+	2.42125i
$916$	−5.40618	−	3.92782i	−0.178625	−	0.129779i
$917$	−14.4646	−	28.5194i	−0.477662	−	0.941793i
$918$	12.2459	−	37.6891i	0.404176	−	1.24393i
$919$	−12.0516	+	2.56166i	−0.397547	+	0.0845013i	−0.402347	−	0.915487i	$-0.631805\pi$
$919$	−12.0516	+	2.56166i	−0.397547	+	0.0845013i	0.00479987	+	0.999988i	$0.498472\pi$
$920$	5.19075	+	49.3867i	0.171134	+	1.62823i
$921$	−7.70463	+	3.43032i	−0.253876	+	0.113033i
$922$	−20.5999	+	22.8785i	−0.678423	+	0.753465i
$923$	−1.84161			−0.0606175
$924$		0			0
$925$	−3.47834			−0.114367
$926$	8.91066	−	9.89629i	0.292822	−	0.325212i
$927$	4.45292	−	1.98257i	0.146253	−	0.0651161i
$928$	1.65985	+	15.7924i	0.0544872	+	0.518411i
$929$	−5.80348	+	1.23357i	−0.190406	+	0.0404720i	−0.302128	−	0.953268i	$-0.597697\pi$
$929$	−5.80348	+	1.23357i	−0.190406	+	0.0404720i	0.111722	+	0.993740i	$0.464364\pi$
$930$	8.48834	−	26.1244i	0.278344	−	0.856654i
$931$	1.14517	−	5.29071i	0.0375314	−	0.173396i
$932$	2.62003	+	1.90357i	0.0858221	+	0.0623534i
$933$	30.1018	−	33.4314i	0.985488	−	1.09449i
$934$	−3.65342	+	6.32791i	−0.119544	+	0.207055i
$935$		0			0
$936$	1.23783	+	2.14398i	0.0404596	+	0.0700781i
$937$	13.9132	+	42.8205i	0.454525	+	1.39889i	0.871691	+	0.490055i	$0.163023\pi$
$937$	13.9132	+	42.8205i	0.454525	+	1.39889i	−0.417166	+	0.908830i	$0.636977\pi$
$938$	3.91605	+	14.7244i	0.127864	+	0.480769i
$939$	51.1924	−	37.1934i	1.67060	−	1.21376i
$940$	6.12402	−	1.30170i	0.199743	−	0.0424568i
$941$	4.05655	+	4.50526i	0.132240	+	0.146867i	0.805628	−	0.592422i	$-0.201828\pi$
$941$	4.05655	+	4.50526i	0.132240	+	0.146867i	−0.673388	+	0.739289i	$0.735162\pi$
$942$	−4.26136	−	40.5441i	−0.138843	−	1.32100i
$943$	0.372062	−	3.53993i	0.0121160	−	0.115276i
$944$	−0.288896	−	0.889132i	−0.00940278	−	0.0289388i
$945$	−6.48364	+	40.4489i	−0.210913	+	1.31580i
$946$		0			0
$947$	9.47131	+	16.4048i	0.307776	+	0.533084i	0.977876	−	0.209187i	$-0.0670818\pi$
$947$	9.47131	+	16.4048i	0.307776	+	0.533084i	−0.670099	+	0.742272i	$0.733748\pi$
$948$	0.320535	+	0.0681318i	0.0104105	+	0.00221282i
$949$	−0.0203617	+	0.00906563i	−0.000660970	+	0.000294283i
$950$	−0.551788	−	0.245672i	−0.0179024	−	0.00797065i
$951$	−2.67989	+	8.24785i	−0.0869014	+	0.267455i
$952$	1.32604	+	26.2362i	0.0429771	+	0.850321i
$953$	−10.1103	+	7.34556i	−0.327504	+	0.237946i	−0.739371	−	0.673298i	$-0.764877\pi$
$953$	−10.1103	+	7.34556i	−0.327504	+	0.237946i	0.411867	+	0.911244i	$0.364877\pi$
$954$	−5.55362	+	52.8392i	−0.179805	+	1.71073i
$955$	58.2842	+	12.3887i	1.88603	+	0.400888i
$956$	1.94310	−	3.36554i	0.0628442	−	0.108849i
$957$		0			0
$958$	60.6923			1.96088
$959$	−27.1576	−	33.6648i	−0.876965	−	1.08709i
$960$	−33.7387	−	24.5126i	−1.08891	−	0.791140i
$961$	−21.8914	−	9.74670i	−0.706175	−	0.314410i
$962$	−1.29256	−	1.43554i	−0.0416739	−	0.0462835i
$963$	36.6323	+	40.6843i	1.18046	+	1.31103i
$964$	−6.41027	−	2.85404i	−0.206461	−	0.0919223i
$965$	−14.6820	−	10.6671i	−0.472630	−	0.343386i
$966$	−96.3448	+	15.0758i	−3.09984	+	0.485056i
$967$	18.5294			0.595865			0.297933	−	0.954587i	$-0.403703\pi$
$967$	18.5294			0.595865			0.297933	+	0.954587i	$0.403703\pi$
$968$		0			0
$969$	4.36571	−	7.56164i	0.140247	−	0.242915i
$970$	−46.1541	−	9.81036i	−1.48192	−	0.314992i
$971$	−4.33520	+	41.2467i	−0.139123	+	1.32367i	0.672765	+	0.739856i	$0.265107\pi$
$971$	−4.33520	+	41.2467i	−0.139123	+	1.32367i	−0.811888	+	0.583813i	$0.801560\pi$
$972$	3.03540	−	2.20535i	0.0973606	−	0.0707366i
$973$	−46.0529	+	29.7854i	−1.47639	+	0.954876i
$974$	2.44092	−	7.51238i	0.0782121	−	0.240712i
$975$	0.247807	+	0.110331i	0.00793619	+	0.00353342i
$976$	60.9302	−	27.1279i	1.95033	−	0.868343i
$977$	21.7462	+	4.62230i	0.695724	+	0.147881i	0.542181	−	0.840261i	$-0.317599\pi$
$977$	21.7462	+	4.62230i	0.695724	+	0.147881i	0.153542	+	0.988142i	$0.450932\pi$
$978$	19.4179	+	33.6327i	0.620915	+	1.07546i
$979$		0			0
$980$	1.16566	+	5.58613i	0.0372356	+	0.178442i
$981$	−0.777674	−	2.39344i	−0.0248292	−	0.0764165i
$982$	1.63230	−	15.5303i	0.0520889	−	0.495592i
$983$	−3.70160	−	35.2184i	−0.118063	−	1.12329i	−0.879779	−	0.475382i	$-0.842310\pi$
$983$	−3.70160	−	35.2184i	−0.118063	−	1.12329i	0.761716	−	0.647911i	$-0.224357\pi$
$984$	2.07836	+	2.30826i	0.0662558	+	0.0735846i
$985$	−12.3402	+	2.62299i	−0.393191	+	0.0835753i
$986$	−39.7104	+	28.8513i	−1.26464	+	0.918812i
$987$	−15.0377	−	56.5421i	−0.478656	−	1.79976i
$988$	−0.0153365	−	0.0472008i	−0.000487918	−	0.00150166i
$989$	4.94949	+	8.57277i	0.157385	+	0.272598i
$990$		0			0
$991$	−22.7863	+	39.4670i	−0.723830	+	1.25371i	0.235624	+	0.971844i	$0.424287\pi$
$991$	−22.7863	+	39.4670i	−0.723830	+	1.25371i	−0.959454	+	0.281866i	$0.909047\pi$
$992$	−3.44983	+	3.83143i	−0.109532	+	0.121648i
$993$	−63.9879	−	46.4899i	−2.03059	−	1.47531i
$994$	18.2728	+	36.0279i	0.579577	+	1.14274i
$995$	6.36938	−	19.6029i	0.201923	−	0.621455i
$996$	3.28172	−	0.697551i	0.103985	−	0.0221028i
$997$	2.38708	+	22.7116i	0.0755997	+	0.719283i	0.965017	+	0.262187i	$0.0844437\pi$
$997$	2.38708	+	22.7116i	0.0755997	+	0.719283i	−0.889417	+	0.457096i	$0.848890\pi$
$998$	8.24358	−	3.67028i	0.260946	−	0.116181i
$999$	−30.1149	+	33.4460i	−0.952793	+	1.05818i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.n.f.753.3		24
7.2	even	3	inner	847.2.n.f.632.1		24
11.2	odd	10		847.2.n.g.130.3		24
11.3	even	5		847.2.e.c.606.1		6
11.4	even	5	inner	847.2.n.f.487.3		24
11.5	even	5	inner	847.2.n.f.81.1		24
11.6	odd	10		847.2.n.g.81.3		24
11.7	odd	10		847.2.n.g.487.1		24
11.8	odd	10		77.2.e.a.67.3	yes	6
11.9	even	5	inner	847.2.n.f.130.1		24
11.10	odd	2		847.2.n.g.753.1		24
33.8	even	10		693.2.i.h.298.1		6
44.19	even	10		1232.2.q.m.529.3		6
77.2	odd	30		847.2.n.g.9.1		24
77.3	odd	30		5929.2.a.u.1.3		3
77.9	even	15	inner	847.2.n.f.9.3		24
77.16	even	15	inner	847.2.n.f.807.3		24
77.19	even	30		539.2.e.m.177.3		6
77.25	even	15		5929.2.a.x.1.3		3
77.30	odd	30		77.2.e.a.23.3	✓	6
77.37	even	15	inner	847.2.n.f.366.1		24
77.41	even	10		539.2.e.m.67.3		6
77.51	odd	30		847.2.n.g.366.3		24
77.52	even	30		539.2.a.g.1.1		3
77.58	even	15		847.2.e.c.485.1		6
77.65	odd	6		847.2.n.g.632.3		24
77.72	odd	30		847.2.n.g.807.1		24
77.74	odd	30		539.2.a.j.1.1		3
231.74	even	30		4851.2.a.bj.1.3		3
231.107	even	30		693.2.i.h.100.1		6
231.206	odd	30		4851.2.a.bk.1.3		3
308.107	even	30		1232.2.q.m.177.3		6
308.151	even	30		8624.2.a.ch.1.1		3
308.283	odd	30		8624.2.a.co.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.e.a.23.3	✓	6	77.30	odd	30
77.2.e.a.67.3	yes	6	11.8	odd	10
539.2.a.g.1.1		3	77.52	even	30
539.2.a.j.1.1		3	77.74	odd	30
539.2.e.m.67.3		6	77.41	even	10
539.2.e.m.177.3		6	77.19	even	30
693.2.i.h.100.1		6	231.107	even	30
693.2.i.h.298.1		6	33.8	even	10
847.2.e.c.485.1		6	77.58	even	15
847.2.e.c.606.1		6	11.3	even	5
847.2.n.f.9.3		24	77.9	even	15	inner
847.2.n.f.81.1		24	11.5	even	5	inner
847.2.n.f.130.1		24	11.9	even	5	inner
847.2.n.f.366.1		24	77.37	even	15	inner
847.2.n.f.487.3		24	11.4	even	5	inner
847.2.n.f.632.1		24	7.2	even	3	inner
847.2.n.f.753.3		24	1.1	even	1	trivial
847.2.n.f.807.3		24	77.16	even	15	inner
847.2.n.g.9.1		24	77.2	odd	30
847.2.n.g.81.3		24	11.6	odd	10
847.2.n.g.130.3		24	11.2	odd	10
847.2.n.g.366.3		24	77.51	odd	30
847.2.n.g.487.1		24	11.7	odd	10
847.2.n.g.632.3		24	77.65	odd	6
847.2.n.g.753.1		24	11.10	odd	2
847.2.n.g.807.1		24	77.72	odd	30
1232.2.q.m.177.3		6	308.107	even	30
1232.2.q.m.529.3		6	44.19	even	10
4851.2.a.bj.1.3		3	231.74	even	30
4851.2.a.bk.1.3		3	231.206	odd	30
5929.2.a.u.1.3		3	77.3	odd	30
5929.2.a.x.1.3		3	77.25	even	15
8624.2.a.ch.1.1		3	308.151	even	30
8624.2.a.co.1.3		3	308.283	odd	30

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:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.n (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.02517 - 1.13856i) q^{2} +(2.63045 - 1.17115i) q^{3} +(-0.0363024 - 0.345394i) q^{4} +(-2.29600 + 0.488030i) q^{5} +(1.36322 - 4.19556i) q^{6} +(2.64186 + 0.143384i) q^{7} +(2.04850 + 1.48832i) q^{8} +(3.54028 - 3.93187i) q^{9} +(-1.79813 + 3.11446i) q^{10} +(-0.500000 - 0.866025i) q^{12} +(0.0571040 + 0.175748i) q^{13} +(2.87160 - 2.86094i) q^{14} +(-5.46796 + 3.97271i) q^{15} +(4.47403 - 0.950983i) q^{16} +(2.62384 + 2.91407i) q^{17} +(-0.847315 - 8.06166i) q^{18} +(0.0808338 - 0.769082i) q^{19} +(0.251913 + 0.775308i) q^{20} +(7.11721 - 2.71686i) q^{21} +(-4.17752 - 7.23567i) q^{23} +(7.13154 + 1.51585i) q^{24} +(0.465726 - 0.207354i) q^{25} +(0.258642 + 0.115155i) q^{26} +(2.03836 - 6.27342i) q^{27} +(-0.0463820 - 0.917688i) q^{28} +(-6.60987 + 4.80235i) q^{29} +(-1.08240 + 10.2983i) q^{30} +(-2.59474 - 0.551528i) q^{31} +(0.971782 - 1.68317i) q^{32} +6.00774 q^{34} +(-6.13570 + 0.960100i) q^{35} +(-1.48657 - 1.08005i) q^{36} +(-6.23307 - 2.77514i) q^{37} +(-0.792781 - 0.880472i) q^{38} +(0.356037 + 0.395419i) q^{39} +(-5.42971 - 2.41746i) q^{40} +(0.344659 + 0.250409i) q^{41} +(4.20302 - 10.8886i) q^{42} -1.18479 q^{43} +(-6.20961 + 10.7554i) q^{45} +(-12.5209 - 2.66141i) q^{46} +(0.802783 - 7.63797i) q^{47} +(10.6550 - 7.74128i) q^{48} +(6.95888 + 0.757600i) q^{49} +(0.241361 - 0.742831i) q^{50} +(10.3147 + 4.59241i) q^{51} +(0.0586293 - 0.0261035i) q^{52} +(-6.41115 - 1.36273i) q^{53} +(-5.05303 - 8.75211i) q^{54} +(5.19846 + 4.22567i) q^{56} +(-0.688082 - 2.11770i) q^{57} +(-1.30844 + 12.4490i) q^{58} +(-0.0213649 - 0.203273i) q^{59} +(1.57065 + 1.74438i) q^{60} +(14.2631 - 3.03171i) q^{61} +(-3.28799 + 2.38886i) q^{62} +(9.91669 - 9.87986i) q^{63} +(1.90671 + 5.86825i) q^{64} +(-0.216881 - 0.375650i) q^{65} +(-1.87939 + 3.25519i) q^{67} +(0.911252 - 1.01205i) q^{68} +(-19.4628 - 14.1406i) q^{69} +(-5.19698 + 7.97015i) q^{70} +(-3.07962 + 9.47809i) q^{71} +(13.1042 - 2.78538i) q^{72} +(0.0126077 + 0.119954i) q^{73} +(-9.54962 + 4.25177i) q^{74} +(0.982224 - 1.09087i) q^{75} -0.268571 q^{76} +0.815207 q^{78} +(-0.219271 + 0.243526i) q^{79} +(-9.80826 + 4.36692i) q^{80} +(-0.326193 - 3.10352i) q^{81} +(0.638441 - 0.135705i) q^{82} +(-1.03676 + 3.19083i) q^{83} +(-1.19676 - 2.35961i) q^{84} +(-7.44651 - 5.41021i) q^{85} +(-1.21461 + 1.34896i) q^{86} +(-11.7626 + 20.3735i) q^{87} +(2.32635 + 4.02936i) q^{89} +(5.87977 + 18.0961i) q^{90} +(0.125662 + 0.472490i) q^{91} +(-2.34750 + 1.70556i) q^{92} +(-7.47124 + 1.58806i) q^{93} +(-7.87333 - 8.74422i) q^{94} +(0.189741 + 1.80526i) q^{95} +(0.584969 - 5.56561i) q^{96} +(4.05449 + 12.4784i) q^{97} +(7.99660 - 7.14647i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{3} + 6 q^{5} - 6 q^{6} + 6 q^{8} + 12 q^{10} - 12 q^{12} + 6 q^{13} + 12 q^{14} - 18 q^{15} - 6 q^{16} + 3 q^{17} + 12 q^{18} - 9 q^{19} - 12 q^{20} + 48 q^{21} - 6 q^{24} + 3 q^{25} + 9 q^{26}+ \cdots + 24 q^{98}+O(q^{100}) \) 24 * q + 3 * q^3 + 6 * q^5 - 6 * q^6 + 6 * q^8 + 12 * q^10 - 12 * q^12 + 6 * q^13 + 12 * q^14 - 18 * q^15 - 6 * q^16 + 3 * q^17 + 12 * q^18 - 9 * q^19 - 12 * q^20 + 48 * q^21 - 6 * q^24 + 3 * q^25 + 9 * q^26 - 12 * q^27 + 3 * q^28 - 6 * q^29 + 6 * q^30 + 9 * q^31 - 36 * q^32 - 48 * q^34 - 15 * q^35 - 6 * q^36 - 3 * q^39 - 3 * q^40 + 18 * q^41 + 18 * q^42 - 12 * q^45 + 24 * q^46 - 3 * q^47 + 36 * q^48 + 30 * q^50 + 18 * q^51 - 9 * q^52 + 9 * q^53 - 72 * q^54 + 12 * q^56 + 15 * q^58 + 6 * q^60 - 12 * q^61 - 6 * q^62 + 6 * q^63 + 6 * q^64 + 60 * q^65 + 21 * q^68 - 42 * q^69 - 45 * q^70 + 18 * q^71 - 12 * q^72 - 6 * q^73 - 18 * q^74 + 9 * q^75 + 72 * q^76 + 48 * q^78 + 3 * q^79 - 27 * q^80 + 15 * q^81 - 3 * q^82 - 30 * q^83 - 54 * q^85 - 9 * q^86 - 96 * q^87 + 60 * q^89 - 72 * q^90 - 9 * q^91 + 6 * q^92 + 6 * q^93 - 9 * q^95 - 3 * q^96 - 90 * q^97 + 24 * q^98

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