LMFDB - Embedded newform 192.2.r.a.13.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [192,2,Mod(13,192)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(192, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 15, 0]))

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

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

chi := DirichletCharacter("192.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 192 = 2^{6} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	192.r (of order $16$, degree $8$, 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:	$1.53312771881$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			13.7
Character	$\chi$	$=$	192.13
Dual form			192.2.r.a.133.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.643008 - 1.25958i) q^{2} +(0.831470 - 0.555570i) q^{3} +(-1.17308 + 1.61984i) q^{4} +(1.10082 - 0.218966i) q^{5} +(-1.23443 - 0.690066i) q^{6} +(-0.899420 - 2.17139i) q^{7} +(2.79462 + 0.436020i) q^{8} +(0.382683 - 0.923880i) q^{9} +O(q^{10})$	\(q+(-0.643008 - 1.25958i) q^{2} +(0.831470 - 0.555570i) q^{3} +(-1.17308 + 1.61984i) q^{4} +(1.10082 - 0.218966i) q^{5} +(-1.23443 - 0.690066i) q^{6} +(-0.899420 - 2.17139i) q^{7} +(2.79462 + 0.436020i) q^{8} +(0.382683 - 0.923880i) q^{9} +(-0.983641 - 1.24577i) q^{10} +(2.85504 - 4.27287i) q^{11} +(-0.0754472 + 1.99858i) q^{12} +(-2.75860 - 0.548720i) q^{13} +(-2.15671 + 2.52911i) q^{14} +(0.793646 - 0.793646i) q^{15} +(-1.24776 - 3.80041i) q^{16} +(2.30407 + 2.30407i) q^{17} +(-1.40977 + 0.112042i) q^{18} +(-0.562614 + 2.82845i) q^{19} +(-0.936659 + 2.04001i) q^{20} +(-1.95420 - 1.30576i) q^{21} +(-7.21784 - 0.848662i) q^{22} +(0.814910 + 0.337547i) q^{23} +(2.56588 - 1.19007i) q^{24} +(-3.45554 + 1.43133i) q^{25} +(1.08265 + 3.82751i) q^{26} +(-0.195090 - 0.980785i) q^{27} +(4.57240 + 1.09030i) q^{28} +(1.52765 + 2.28630i) q^{29} +(-1.50998 - 0.489340i) q^{30} -3.24135i q^{31} +(-3.98460 + 4.01534i) q^{32} -5.13894i q^{33} +(1.42063 - 4.38370i) q^{34} +(-1.46556 - 2.19337i) q^{35} +(1.04762 + 1.70367i) q^{36} +(1.56493 + 7.86745i) q^{37} +(3.92443 - 1.11006i) q^{38} +(-2.59855 + 1.07635i) q^{39} +(3.17184 - 0.131948i) q^{40} +(4.45205 + 1.84410i) q^{41} +(-0.388136 + 3.30108i) q^{42} +(9.42323 + 6.29640i) q^{43} +(3.57217 + 9.63714i) q^{44} +(0.218966 - 1.10082i) q^{45} +(-0.0988266 - 1.24349i) q^{46} +(-3.29361 - 3.29361i) q^{47} +(-3.14887 - 2.46671i) q^{48} +(1.04376 - 1.04376i) q^{49} +(4.02482 + 3.43217i) q^{50} +(3.19584 + 0.635693i) q^{51} +(4.12490 - 3.82480i) q^{52} +(-7.30356 + 10.9305i) q^{53} +(-1.10993 + 0.876384i) q^{54} +(2.20727 - 5.32882i) q^{55} +(-1.56676 - 6.46038i) q^{56} +(1.10361 + 2.66434i) q^{57} +(1.89748 - 3.39431i) q^{58} +(11.9601 - 2.37900i) q^{59} +(0.354567 + 2.21659i) q^{60} +(-2.93711 + 1.96252i) q^{61} +(-4.08274 + 2.08421i) q^{62} -2.35030 q^{63} +(7.61977 + 2.43702i) q^{64} -3.15687 q^{65} +(-6.47291 + 3.30438i) q^{66} +(-8.01120 + 5.35291i) q^{67} +(-6.43510 + 1.02936i) q^{68} +(0.865104 - 0.172080i) q^{69} +(-1.82035 + 3.25634i) q^{70} +(-5.44734 - 13.1510i) q^{71} +(1.47228 - 2.41503i) q^{72} +(-3.71675 + 8.97304i) q^{73} +(8.90342 - 7.02999i) q^{74} +(-2.07797 + 3.10991i) q^{75} +(-3.92165 - 4.22935i) q^{76} +(-11.8460 - 2.35631i) q^{77} +(3.02664 + 2.58097i) q^{78} +(-4.99132 + 4.99132i) q^{79} +(-2.20572 - 3.91034i) q^{80} +(-0.707107 - 0.707107i) q^{81} +(-0.539913 - 6.79348i) q^{82} +(-0.535891 + 2.69411i) q^{83} +(4.40755 - 1.63373i) q^{84} +(3.04088 + 2.03185i) q^{85} +(1.87161 - 15.9179i) q^{86} +(2.54040 + 1.05227i) q^{87} +(9.84181 - 10.6962i) q^{88} +(7.33117 - 3.03667i) q^{89} +(-1.52737 + 0.432029i) q^{90} +(1.28966 + 6.48354i) q^{91} +(-1.50273 + 0.924054i) q^{92} +(-1.80080 - 2.69509i) q^{93} +(-2.03074 + 6.26638i) q^{94} +3.23681i q^{95} +(-1.08227 + 5.55236i) q^{96} -17.2593i q^{97} +(-1.98584 - 0.643553i) q^{98} +(-2.85504 - 4.27287i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q - 16 q^{22} - 80 q^{26} - 80 q^{28} - 80 q^{32} - 80 q^{34} - 80 q^{38} - 80 q^{40} - 16 q^{44} + 48 q^{50} - 32 q^{51} + 48 q^{52} + 16 q^{54} - 64 q^{55} + 112 q^{56} - 128 q^{59} + 96 q^{60} + 96 q^{62} - 32 q^{63} + 96 q^{64} + 96 q^{66} - 32 q^{67} + 96 q^{68} + 96 q^{70} - 128 q^{71} + 112 q^{74} - 64 q^{75} + 16 q^{76} + 48 q^{78} - 32 q^{79} + 48 q^{80} - 80 q^{82} - 80 q^{88} - 96 q^{94}+O(q^{100}) $ 128 * q - 16 * q^22 - 80 * q^26 - 80 * q^28 - 80 * q^32 - 80 * q^34 - 80 * q^38 - 80 * q^40 - 16 * q^44 + 48 * q^50 - 32 * q^51 + 48 * q^52 + 16 * q^54 - 64 * q^55 + 112 * q^56 - 128 * q^59 + 96 * q^60 + 96 * q^62 - 32 * q^63 + 96 * q^64 + 96 * q^66 - 32 * q^67 + 96 * q^68 + 96 * q^70 - 128 * q^71 + 112 * q^74 - 64 * q^75 + 16 * q^76 + 48 * q^78 - 32 * q^79 + 48 * q^80 - 80 * q^82 - 80 * q^88 - 96 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$133$
$\chi(n)$	$1$	$1$	$e\left(\frac{15}{16}\right)$

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 $

$2$	−0.643008	−	1.25958i	−0.454675	−	0.890657i
$2$	−0.643008	−	1.25958i	−0.454675	−	0.890657i
$3$	0.831470	−	0.555570i	0.480049	−	0.320759i
$3$	0.831470	−	0.555570i	0.480049	−	0.320759i
$4$	−1.17308	+	1.61984i	−0.586541	+	0.809920i
$5$	1.10082	−	0.218966i	0.492301	−	0.0979247i	0.0573042	−	0.998357i	$-0.481750\pi$
$5$	1.10082	−	0.218966i	0.492301	−	0.0979247i	0.434997	+	0.900432i	$0.356750\pi$
$6$	−1.23443	−	0.690066i	−0.503953	−	0.281718i
$7$	−0.899420	−	2.17139i	−0.339949	−	0.820709i	−0.997720	−	0.0674912i	$-0.978501\pi$
$7$	−0.899420	−	2.17139i	−0.339949	−	0.820709i	0.657771	−	0.753218i	$-0.271499\pi$
$8$	2.79462	+	0.436020i	0.988046	+	0.154156i
$9$	0.382683	−	0.923880i	0.127561	−	0.307960i
$10$	−0.983641	−	1.24577i	−0.311054	−	0.393947i
$11$	2.85504	−	4.27287i	0.860828	−	1.28832i	−0.0953232	−	0.995446i	$-0.530388\pi$
$11$	2.85504	−	4.27287i	0.860828	−	1.28832i	0.956151	−	0.292874i	$-0.0946115\pi$
$12$	−0.0754472	+	1.99858i	−0.0217797	+	0.576939i
$13$	−2.75860	−	0.548720i	−0.765098	−	0.152188i	−0.202911	−	0.979197i	$-0.565040\pi$
$13$	−2.75860	−	0.548720i	−0.765098	−	0.152188i	−0.562188	+	0.827010i	$0.690040\pi$
$14$	−2.15671	+	2.52911i	−0.576404	+	0.675934i
$15$	0.793646	−	0.793646i	0.204918	−	0.204918i
$16$	−1.24776	−	3.80041i	−0.311940	−	0.950102i
$17$	2.30407	+	2.30407i	0.558820	+	0.558820i	0.928971	−	0.370151i	$-0.120694\pi$
$17$	2.30407	+	2.30407i	0.558820	+	0.558820i	−0.370151	+	0.928971i	$0.620694\pi$
$18$	−1.40977	+	0.112042i	−0.332286	+	0.0264085i
$19$	−0.562614	+	2.82845i	−0.129073	+	0.648891i	0.861031	+	0.508553i	$0.169819\pi$
$19$	−0.562614	+	2.82845i	−0.129073	+	0.648891i	−0.990104	+	0.140339i	$0.955181\pi$
$20$	−0.936659	+	2.04001i	−0.209443	+	0.456161i
$21$	−1.95420	−	1.30576i	−0.426442	−	0.284939i
$22$	−7.21784	−	0.848662i	−1.53885	−	0.180935i
$23$	0.814910	+	0.337547i	0.169921	+	0.0703834i	0.466022	−	0.884773i	$-0.345687\pi$
$23$	0.814910	+	0.337547i	0.169921	+	0.0703834i	−0.296102	+	0.955156i	$0.595687\pi$
$24$	2.56588	−	1.19007i	0.523758	−	0.242922i
$25$	−3.45554	+	1.43133i	−0.691109	+	0.286267i
$26$	1.08265	+	3.82751i	0.212324	+	0.750636i
$27$	−0.195090	−	0.980785i	−0.0375451	−	0.188752i
$28$	4.57240	+	1.09030i	0.864102	+	0.206048i
$29$	1.52765	+	2.28630i	0.283678	+	0.424555i	0.945755	−	0.324882i	$-0.105325\pi$
$29$	1.52765	+	2.28630i	0.283678	+	0.424555i	−0.662076	+	0.749436i	$0.730325\pi$
$30$	−1.50998	−	0.489340i	−0.275683	−	0.0893408i
$31$		−	3.24135i		−	0.582164i	−0.956698	−	0.291082i	$-0.905985\pi$
$31$		−	3.24135i		−	0.582164i	0.956698	−	0.291082i	$-0.0940152\pi$
$32$	−3.98460	+	4.01534i	−0.704384	+	0.709819i
$33$		−	5.13894i		−	0.894575i
$34$	1.42063	−	4.38370i	0.243636	−	0.751799i
$35$	−1.46556	−	2.19337i	−0.247725	−	0.370746i
$36$	1.04762	+	1.70367i	0.174603	+	0.283945i
$37$	1.56493	+	7.86745i	0.257273	+	1.29340i	0.866009	+	0.500028i	$0.166677\pi$
$37$	1.56493	+	7.86745i	0.257273	+	1.29340i	−0.608736	+	0.793373i	$0.708323\pi$
$38$	3.92443	−	1.11006i	0.636626	−	0.180075i
$39$	−2.59855	+	1.07635i	−0.416100	+	0.172354i
$40$	3.17184	−	0.131948i	0.501512	−	0.0208628i
$41$	4.45205	+	1.84410i	0.695293	+	0.288000i	0.702204	−	0.711976i	$-0.252200\pi$
$41$	4.45205	+	1.84410i	0.695293	+	0.288000i	−0.00691036	+	0.999976i	$0.502200\pi$
$42$	−0.388136	+	3.30108i	−0.0598907	+	0.509368i
$43$	9.42323	+	6.29640i	1.43703	+	0.960192i	0.998097	+	0.0616715i	$0.0196431\pi$
$43$	9.42323	+	6.29640i	1.43703	+	0.960192i	0.438932	+	0.898520i	$0.355357\pi$
$44$	3.57217	+	9.63714i	0.538525	+	1.45285i
$45$	0.218966	−	1.10082i	0.0326416	−	0.164100i
$46$	−0.0988266	−	1.24349i	−0.0145712	−	0.183343i
$47$	−3.29361	−	3.29361i	−0.480422	−	0.480422i	0.424844	−	0.905266i	$-0.360329\pi$
$47$	−3.29361	−	3.29361i	−0.480422	−	0.480422i	−0.905266	+	0.424844i	$0.860329\pi$
$48$	−3.14887	−	2.46671i	−0.454500	−	0.356038i
$49$	1.04376	−	1.04376i	0.149108	−	0.149108i
$50$	4.02482	+	3.43217i	0.569195	+	0.485383i
$51$	3.19584	+	0.635693i	0.447508	+	0.0890148i
$52$	4.12490	−	3.82480i	0.572021	−	0.530404i
$53$	−7.30356	+	10.9305i	−1.00322	+	1.50143i	−0.144159	+	0.989554i	$0.546048\pi$
$53$	−7.30356	+	10.9305i	−1.00322	+	1.50143i	−0.859062	+	0.511872i	$0.828952\pi$
$54$	−1.10993	+	0.876384i	−0.151043	+	0.119261i
$55$	2.20727	−	5.32882i	0.297628	−	0.718538i
$56$	−1.56676	−	6.46038i	−0.209368	−	0.863304i
$57$	1.10361	+	2.66434i	0.146176	+	0.352901i
$58$	1.89748	−	3.39431i	0.249151	−	0.445695i
$59$	11.9601	−	2.37900i	1.55707	−	0.309720i	0.659880	−	0.751371i	$-0.270607\pi$
$59$	11.9601	−	2.37900i	1.55707	−	0.309720i	0.897187	+	0.441652i	$0.145607\pi$
$60$	0.354567	+	2.21659i	0.0457744	+	0.286161i
$61$	−2.93711	+	1.96252i	−0.376059	+	0.251274i	−0.729207	−	0.684293i	$-0.760111\pi$
$61$	−2.93711	+	1.96252i	−0.376059	+	0.251274i	0.353149	+	0.935567i	$0.385111\pi$
$62$	−4.08274	+	2.08421i	−0.518509	+	0.264696i
$63$	−2.35030			−0.296110
$64$	7.61977	+	2.43702i	0.952472	+	0.304627i
$65$	−3.15687			−0.391562
$66$	−6.47291	+	3.30438i	−0.796760	+	0.406741i
$67$	−8.01120	+	5.35291i	−0.978724	+	0.653962i	−0.938518	−	0.345229i	$-0.887801\pi$
$67$	−8.01120	+	5.35291i	−0.978724	+	0.653962i	−0.0402053	+	0.999191i	$0.512801\pi$
$68$	−6.43510	+	1.02936i	−0.780370	+	0.124829i
$69$	0.865104	−	0.172080i	0.104146	−	0.0207160i
$70$	−1.82035	+	3.25634i	−0.217574	+	0.389207i
$71$	−5.44734	−	13.1510i	−0.646481	−	1.56074i	−0.817785	−	0.575524i	$-0.804798\pi$
$71$	−5.44734	−	13.1510i	−0.646481	−	1.56074i	0.171304	−	0.985218i	$-0.445202\pi$
$72$	1.47228	−	2.41503i	0.173510	−	0.284614i
$73$	−3.71675	+	8.97304i	−0.435013	+	1.05021i	0.542635	+	0.839968i	$0.317427\pi$
$73$	−3.71675	+	8.97304i	−0.435013	+	1.05021i	−0.977649	+	0.210246i	$0.932573\pi$
$74$	8.90342	−	7.02999i	1.03500	−	0.817220i
$75$	−2.07797	+	3.10991i	−0.239944	+	0.359101i
$76$	−3.92165	−	4.22935i	−0.449844	−	0.485140i
$77$	−11.8460	−	2.35631i	−1.34997	−	0.268526i
$78$	3.02664	+	2.58097i	0.342699	+	0.292238i
$79$	−4.99132	+	4.99132i	−0.561567	+	0.561567i	−0.929752	−	0.368185i	$-0.879979\pi$
$79$	−4.99132	+	4.99132i	−0.561567	+	0.561567i	0.368185	+	0.929752i	$0.379979\pi$
$80$	−2.20572	−	3.91034i	−0.246607	−	0.437189i
$81$	−0.707107	−	0.707107i	−0.0785674	−	0.0785674i
$82$	−0.539913	−	6.79348i	−0.0596234	−	0.750214i
$83$	−0.535891	+	2.69411i	−0.0588217	+	0.295717i	−0.998987	−	0.0450023i	$-0.985670\pi$
$83$	−0.535891	+	2.69411i	−0.0588217	+	0.295717i	0.940165	+	0.340719i	$0.110670\pi$
$84$	4.40755	−	1.63373i	0.480903	−	0.178255i
$85$	3.04088	+	2.03185i	0.329830	+	0.220385i
$86$	1.87161	−	15.9179i	0.201820	−	1.71648i
$87$	2.54040	+	1.05227i	0.272359	+	0.112815i
$88$	9.84181	−	10.6962i	1.04914	−	1.14022i
$89$	7.33117	−	3.03667i	0.777103	−	0.321886i	0.0413570	−	0.999144i	$-0.486832\pi$
$89$	7.33117	−	3.03667i	0.777103	−	0.321886i	0.735746	+	0.677258i	$0.236832\pi$
$90$	−1.52737	+	0.432029i	−0.160998	+	0.0455399i
$91$	1.28966	+	6.48354i	0.135193	+	0.679659i
$92$	−1.50273	+	0.924054i	−0.156670	+	0.0963393i
$93$	−1.80080	−	2.69509i	−0.186734	−	0.279467i
$94$	−2.03074	+	6.26638i	−0.209455	+	0.646327i
$95$			3.23681i			0.332089i
$96$	−1.08227	+	5.55236i	−0.110458	+	0.566685i
$97$		−	17.2593i		−	1.75242i	−0.481929	−	0.876210i	$-0.660064\pi$
$97$		−	17.2593i		−	1.75242i	0.481929	−	0.876210i	$-0.339936\pi$
$98$	−1.98584	−	0.643553i	−0.200600	−	0.0650086i
$99$	−2.85504	−	4.27287i	−0.286943	−	0.429440i
$100$	1.73510	−	7.27649i	0.173510	−	0.727649i
$101$	0.500457	+	2.51597i	0.0497973	+	0.250348i	0.997663	−	0.0683209i	$-0.0217642\pi$
$101$	0.500457	+	2.51597i	0.0497973	+	0.250348i	−0.947866	+	0.318669i	$0.896764\pi$
$102$	−1.25425	−	4.43417i	−0.124189	−	0.439049i
$103$	−11.3461	+	4.69970i	−1.11796	+	0.463075i	−0.863672	−	0.504053i	$-0.831841\pi$
$103$	−11.3461	+	4.69970i	−1.11796	+	0.463075i	−0.254289	+	0.967128i	$0.581841\pi$
$104$	−7.46998	−	2.73627i	−0.732492	−	0.268313i
$105$	−2.43714	−	1.00950i	−0.237840	−	0.0985167i
$106$	18.4641	+	2.17099i	1.79340	+	0.210865i
$107$	−10.8795	−	7.26942i	−1.05176	−	0.702761i	−0.0955411	−	0.995425i	$-0.530458\pi$
$107$	−10.8795	−	7.26942i	−1.05176	−	0.702761i	−0.956215	+	0.292664i	$0.905458\pi$
$108$	1.81757	+	0.834526i	0.174896	+	0.0803023i
$109$	1.37249	−	6.89995i	0.131460	−	0.660896i	−0.857711	−	0.514132i	$-0.828114\pi$
$109$	1.37249	−	6.89995i	0.131460	−	0.660896i	0.989172	−	0.146764i	$-0.0468858\pi$
$110$	−8.13136	+	0.646241i	−0.775295	+	0.0616167i
$111$	5.67212	+	5.67212i	0.538373	+	0.538373i
$112$	−7.12992	+	6.12754i	−0.673714	+	0.578998i
$113$	5.40400	−	5.40400i	0.508366	−	0.508366i	−0.405659	−	0.914025i	$-0.632958\pi$
$113$	5.40400	−	5.40400i	0.508366	−	0.508366i	0.914025	+	0.405659i	$0.132958\pi$
$114$	2.64632	−	3.10328i	0.247851	−	0.290648i
$115$	0.970980	+	0.193140i	0.0905443	+	0.0180104i
$116$	−5.49550	−	0.207458i	−0.510244	−	0.0192620i
$117$	−1.56262	+	2.33863i	−0.144464	+	0.216206i
$118$	−10.6870	−	13.5349i	−0.983814	−	1.24599i
$119$	2.93072	−	7.07538i	0.268659	−	0.648599i
$120$	2.56398	−	1.87189i	0.234058	−	0.170879i
$121$	−5.89666	−	14.2358i	−0.536060	−	1.29416i
$122$	4.36053	+	2.43761i	0.394784	+	0.220691i
$123$	4.72627	−	0.940113i	0.426153	−	0.0847672i
$124$	5.25047	+	3.80237i	0.471506	+	0.341463i
$125$	−8.15666	+	5.45010i	−0.729553	+	0.487472i
$126$	1.51126	+	2.96039i	0.134634	+	0.263732i
$127$	10.6369			0.943874			0.471937	−	0.881632i	$-0.343555\pi$
$127$	10.6369			0.943874			0.471937	+	0.881632i	$0.343555\pi$
$128$	−1.82995	−	11.1647i	−0.161747	−	0.986832i
$129$	11.3332			0.997834
$130$	2.02989	+	3.97633i	0.178033	+	0.348747i
$131$	−8.36414	+	5.58874i	−0.730778	+	0.488290i	−0.864440	−	0.502737i	$-0.832326\pi$
$131$	−8.36414	+	5.58874i	−0.730778	+	0.488290i	0.133662	+	0.991027i	$0.457326\pi$
$132$	8.32426	+	6.02840i	0.724534	+	0.524705i
$133$	6.64771	−	1.32231i	0.576429	−	0.114659i
$134$	11.8937	+	6.64878i	1.02746	+	0.574367i
$135$	−0.429518	−	1.03695i	−0.0369670	−	0.0892463i
$136$	5.43438	+	7.44363i	0.465994	+	0.638286i
$137$	−1.30777	+	3.15723i	−0.111730	+	0.269741i	−0.969847	−	0.243714i	$-0.921634\pi$
$137$	−1.30777	+	3.15723i	−0.111730	+	0.269741i	0.858117	+	0.513454i	$0.171634\pi$
$138$	−0.773017	−	0.979019i	−0.0658036	−	0.0833396i
$139$	−9.85523	+	14.7494i	−0.835910	+	1.25103i	0.129835	+	0.991536i	$0.458555\pi$
$139$	−9.85523	+	14.7494i	−0.835910	+	1.25103i	−0.965745	+	0.259492i	$0.916445\pi$
$140$	5.27212	+	0.199025i	0.445576	+	0.0168207i
$141$	−4.56836	−	0.908704i	−0.384726	−	0.0765267i
$142$	−13.0621	+	15.3176i	−1.09615	+	1.28542i
$143$	−10.2205	+	10.2205i	−0.854684	+	0.854684i
$144$	−3.98862	−	0.301574i	−0.332385	−	0.0251312i
$145$	2.18229	+	2.18229i	0.181230	+	0.181230i
$146$	13.6922	−	1.08819i	1.13317	−	0.0900589i
$147$	0.287973	−	1.44774i	0.0237516	−	0.119407i
$148$	−14.5798	−	6.69422i	−1.19845	−	0.550262i
$149$	11.9841	+	8.00750i	0.981773	+	0.656000i	0.939300	−	0.343098i	$-0.111476\pi$
$149$	11.9841	+	8.00750i	0.981773	+	0.656000i	0.0424734	+	0.999098i	$0.486476\pi$
$150$	5.25333	+	0.617678i	0.428932	+	0.0504332i
$151$	4.12805	+	1.70989i	0.335936	+	0.139149i	0.544274	−	0.838908i	$-0.316805\pi$
$151$	4.12805	+	1.70989i	0.335936	+	0.139149i	−0.208338	+	0.978057i	$0.566805\pi$
$152$	−2.80555	+	7.65913i	−0.227560	+	0.621238i
$153$	3.01042	−	1.24696i	0.243378	−	0.100810i
$154$	4.64909	+	16.4361i	0.374635	+	1.32446i
$155$	−0.709747	−	3.56814i	−0.0570082	−	0.286600i
$156$	1.30479	−	5.47188i	0.104467	−	0.438101i
$157$	8.53816	+	12.7783i	0.681420	+	1.01982i	0.997471	+	0.0710744i	$0.0226428\pi$
$157$	8.53816	+	12.7783i	0.681420	+	1.01982i	−0.316051	+	0.948742i	$0.602357\pi$
$158$	9.49642	+	3.07751i	0.755495	+	0.244833i
$159$			13.1461i			1.04255i
$160$	−3.50709	+	5.29266i	−0.277260	+	0.418421i
$161$		−	2.07309i		−	0.163382i
$162$	−0.435982	+	1.34533i	−0.0342540	+	0.105699i
$163$	0.621330	+	0.929886i	0.0486663	+	0.0728343i	0.855005	−	0.518620i	$-0.173554\pi$
$163$	0.621330	+	0.929886i	0.0486663	+	0.0728343i	−0.806339	+	0.591454i	$0.798554\pi$
$164$	−8.20976	+	5.04832i	−0.641075	+	0.394208i
$165$	−1.12526	−	5.65704i	−0.0876010	−	0.440400i
$166$	3.73803	−	1.05733i	0.290127	−	0.0820651i
$167$	5.86233	−	2.42826i	0.453640	−	0.187904i	−0.144151	−	0.989556i	$-0.546045\pi$
$167$	5.86233	−	2.42826i	0.453640	−	0.187904i	0.597791	+	0.801652i	$0.296045\pi$
$168$	−4.89191	−	4.50116i	−0.377419	−	0.347272i
$169$	−4.70164	−	1.94748i	−0.361665	−	0.149807i
$170$	0.603969	−	5.13673i	0.0463223	−	0.393969i
$171$	2.39785	+	1.60219i	0.183368	+	0.122522i
$172$	−21.2534	+	7.87792i	−1.62055	+	0.600686i
$173$	4.10805	−	20.6526i	0.312329	−	1.57019i	−0.431686	−	0.902024i	$-0.642081\pi$
$173$	4.10805	−	20.6526i	0.312329	−	1.57019i	0.744015	−	0.668162i	$-0.232919\pi$
$174$	−0.308081	−	3.87645i	−0.0233556	−	0.293873i
$175$	6.21597	+	6.21597i	0.469883	+	0.469883i
$176$	−19.8011	−	5.51881i	−1.49256	−	0.415996i
$177$	8.62272	−	8.62272i	0.648123	−	0.648123i
$178$	−8.53893	−	7.28159i	−0.640020	−	0.545778i
$179$	5.09852	+	1.01416i	0.381081	+	0.0758018i	0.381914	−	0.924198i	$-0.375265\pi$
$179$	5.09852	+	1.01416i	0.381081	+	0.0758018i	−0.000832665		1.00000i	$0.500265\pi$
$180$	1.52628	+	1.64604i	0.113762	+	0.122689i
$181$	13.5006	−	20.2051i	1.00349	−	1.50183i	0.144723	−	0.989472i	$-0.453771\pi$
$181$	13.5006	−	20.2051i	1.00349	−	1.50183i	0.858770	−	0.512361i	$-0.171229\pi$
$182$	7.33727	−	5.79339i	0.543875	−	0.429435i
$183$	−1.35180	+	3.26355i	−0.0999283	+	0.241248i
$184$	2.13019	+	1.29863i	0.157039	+	0.0957364i
$185$	3.44542	+	8.31797i	0.253312	+	0.611549i
$186$	−2.23675	+	4.00121i	−0.164006	+	0.293383i
$187$	16.4233	−	3.26679i	1.20099	−	0.238891i
$188$	9.19878	−	1.47144i	0.670890	−	0.107316i
$189$	−1.95420	+	1.30576i	−0.142147	+	0.0949798i
$190$	4.07701	−	2.08129i	0.295778	−	0.150993i
$191$	−16.2783			−1.17785			−0.588927	−	0.808186i	$-0.700449\pi$
$191$	−16.2783			−1.17785			−0.588927	+	0.808186i	$0.700449\pi$
$192$	7.68954	−	2.20701i	0.554945	−	0.159277i
$193$	−10.3258			−0.743267			−0.371634	−	0.928380i	$-0.621202\pi$
$193$	−10.3258			−0.743267			−0.371634	+	0.928380i	$0.621202\pi$
$194$	−21.7395	+	11.0979i	−1.56081	+	0.796782i
$195$	−2.62484	+	1.75386i	−0.187969	+	0.125597i
$196$	0.466307	+	2.91514i	0.0333077	+	0.208224i
$197$	16.8611	−	3.35388i	1.20130	−	0.238954i	0.446427	−	0.894820i	$-0.352696\pi$
$197$	16.8611	−	3.35388i	1.20130	−	0.238954i	0.754877	+	0.655866i	$0.227696\pi$
$198$	−3.54621	+	6.34365i	−0.252018	+	0.450823i
$199$	−7.04678	−	17.0124i	−0.499533	−	1.20598i	−0.949736	−	0.313053i	$-0.898648\pi$
$199$	−7.04678	−	17.0124i	−0.499533	−	1.20598i	0.450203	−	0.892926i	$-0.351352\pi$
$200$	−10.2810	+	2.49334i	−0.726977	+	0.176306i
$201$	−3.68715	+	8.90157i	−0.260072	+	0.627868i
$202$	2.84726	−	2.24815i	0.200333	−	0.158179i
$203$	3.59044	−	5.37348i	0.252000	−	0.377144i
$204$	−4.77870	+	4.43103i	−0.334576	+	0.310234i
$205$	5.30469	+	1.05517i	0.370496	+	0.0736962i
$206$	13.2153	+	11.2693i	0.920750	+	0.785172i
$207$	0.623705	−	0.623705i	0.0433505	−	0.0433505i
$208$	1.35671	+	11.1685i	0.0940709	+	0.774395i
$209$	10.4793	+	10.4793i	0.724871	+	0.724871i
$210$	0.295559	+	3.71888i	0.0203955	+	0.256627i
$211$	−1.79805	+	9.03940i	−0.123783	+	0.622298i	0.868230	+	0.496162i	$0.165258\pi$
$211$	−1.79805	+	9.03940i	−0.123783	+	0.622298i	−0.992013	+	0.126136i	$0.959742\pi$
$212$	−9.13806	−	24.6530i	−0.627605	−	1.69318i
$213$	−11.8356	−	7.90832i	−0.810964	−	0.541869i
$214$	−2.16084	+	18.3778i	−0.147712	+	1.25628i
$215$	11.7520	+	4.86782i	0.801477	+	0.331983i
$216$	−0.117561	−	2.82598i	−0.00799898	−	0.192284i
$217$	−7.03825	+	2.91534i	−0.477787	+	0.197906i
$218$	−9.57356	+	2.70797i	−0.648403	+	0.183407i
$219$	1.89478	+	9.52572i	0.128038	+	0.643689i
$220$	6.04252	+	9.82656i	0.407387	+	0.662506i
$221$	−5.09173	−	7.62031i	−0.342507	−	0.512598i
$222$	3.49727	−	10.7917i	0.234721	−	0.724291i
$223$		−	21.8970i		−	1.46633i	−0.680050	−	0.733166i	$-0.738042\pi$
$223$		−	21.8970i		−	1.46633i	0.680050	−	0.733166i	$-0.261958\pi$
$224$	12.3027	+	5.04064i	0.822010	+	0.336792i
$225$			3.74025i			0.249350i
$226$	−10.2816	−	3.33195i	−0.683921	−	0.221638i
$227$	−9.75700	−	14.6024i	−0.647595	−	0.969194i	−0.999451	−	0.0331402i	$-0.989449\pi$
$227$	−9.75700	−	14.6024i	−0.647595	−	0.969194i	0.351856	−	0.936054i	$-0.385551\pi$
$228$	−5.61043	−	1.33783i	−0.371560	−	0.0885997i
$229$	−1.26054	−	6.33717i	−0.0832990	−	0.418772i	−0.999823	−	0.0187935i	$-0.994017\pi$
$229$	−1.26054	−	6.33717i	−0.0832990	−	0.418772i	0.916524	−	0.399979i	$-0.130983\pi$
$230$	−0.381073	−	1.34722i	−0.0251272	−	0.0888329i
$231$	−11.1587	+	4.62207i	−0.734186	+	0.304110i
$232$	3.27234	+	7.05541i	0.214840	+	0.463211i
$233$	−9.09184	−	3.76596i	−0.595626	−	0.246717i	0.0644427	−	0.997921i	$-0.479473\pi$
$233$	−9.09184	−	3.76596i	−0.595626	−	0.246717i	−0.660069	+	0.751205i	$0.729473\pi$
$234$	3.95047	+	0.464490i	0.258250	+	0.0303647i
$235$	−4.34685	−	2.90447i	−0.283557	−	0.189467i
$236$	−10.1765	+	22.1641i	−0.662435	+	1.44276i
$237$	−1.37710	+	6.92316i	−0.0894524	+	0.449707i
$238$	−10.7965	+	0.858052i	−0.699832	+	0.0556193i
$239$	18.5979	+	18.5979i	1.20300	+	1.20300i	0.973251	+	0.229746i	$0.0737895\pi$
$239$	18.5979	+	18.5979i	1.20300	+	1.20300i	0.229746	+	0.973251i	$0.426211\pi$
$240$	−4.00646	−	2.02590i	−0.258616	−	0.130771i
$241$	4.77013	−	4.77013i	0.307271	−	0.307271i	−0.536579	−	0.843850i	$-0.680284\pi$
$241$	4.77013	−	4.77013i	0.307271	−	0.307271i	0.843850	+	0.536579i	$0.180284\pi$
$242$	−14.1395	+	16.5811i	−0.908923	+	1.06587i
$243$	−0.980785	−	0.195090i	−0.0629174	−	0.0125150i
$244$	0.266513	−	7.05984i	0.0170617	−	0.451960i
$245$	0.920441	−	1.37754i	0.0588048	−	0.0880077i
$246$	−4.22318	−	5.34861i	−0.269260	−	0.341015i
$247$	3.10406	−	7.49386i	0.197506	−	0.476823i
$248$	1.41329	−	9.05834i	0.0897443	−	0.575205i
$249$	1.05119	+	2.53779i	0.0666164	+	0.160826i
$250$	12.1096	+	6.76950i	0.765880	+	0.428141i
$251$	9.01248	−	1.79269i	0.568863	−	0.113154i	0.0977249	−	0.995213i	$-0.468843\pi$
$251$	9.01248	−	1.79269i	0.568863	−	0.113154i	0.471138	+	0.882060i	$0.343843\pi$
$252$	2.75709	−	3.80711i	0.173680	−	0.239825i
$253$	3.76890	−	2.51830i	0.236949	−	0.158324i
$254$	−6.83962	−	13.3980i	−0.429156	−	0.840668i
$255$	3.65724			0.229025
$256$	−12.8862	+	9.48398i	−0.805387	+	0.592749i
$257$	−13.9513			−0.870260			−0.435130	−	0.900368i	$-0.643298\pi$
$257$	−13.9513			−0.870260			−0.435130	+	0.900368i	$0.643298\pi$
$258$	−7.28735	−	14.2751i	−0.453691	−	0.888728i
$259$	15.6758	−	10.4742i	0.974046	−	0.650837i
$260$	3.70327	−	5.11362i	0.229667	−	0.317133i
$261$	2.69687	−	0.536441i	0.166932	−	0.0332049i
$262$	12.4177	+	6.94169i	0.767166	+	0.428859i
$263$	8.37970	+	20.2304i	0.516714	+	1.24746i	0.939911	+	0.341421i	$0.110908\pi$
$263$	8.37970	+	20.2304i	0.516714	+	1.24746i	−0.423196	+	0.906038i	$0.639092\pi$
$264$	2.24068	−	14.3614i	0.137905	−	0.883882i
$265$	−5.64647	+	13.6318i	−0.346860	+	0.837394i
$266$	−5.94008	−	7.52306i	−0.364210	−	0.461268i
$267$	4.40856	−	6.59788i	0.269800	−	0.403784i
$268$	0.726933	−	19.2563i	0.0444045	−	1.17626i
$269$	−15.0982	−	3.00321i	−0.920551	−	0.183109i	−0.288002	−	0.957630i	$-0.592991\pi$
$269$	−15.0982	−	3.00321i	−0.920551	−	0.183109i	−0.632549	+	0.774521i	$0.717991\pi$
$270$	−1.02994	+	1.20778i	−0.0626799	+	0.0735030i
$271$	−4.11471	+	4.11471i	−0.249951	+	0.249951i	−0.820950	−	0.571000i	$-0.806556\pi$
$271$	−4.11471	+	4.11471i	−0.249951	+	0.249951i	0.571000	+	0.820950i	$0.306556\pi$
$272$	5.88149	−	11.6314i	0.356618	−	0.705254i
$273$	4.67437	+	4.67437i	0.282906	+	0.282906i
$274$	4.81769	−	0.382887i	0.291047	−	0.0231310i
$275$	−3.74982	+	18.8516i	−0.226123	+	1.13680i
$276$	−0.736096	+	1.60319i	−0.0443078	+	0.0965009i
$277$	−8.81737	−	5.89158i	−0.529785	−	0.353991i	0.261730	−	0.965141i	$-0.415707\pi$
$277$	−8.81737	−	5.89158i	−0.529785	−	0.353991i	−0.791514	+	0.611150i	$0.790707\pi$
$278$	24.9150	+	2.92947i	1.49430	+	0.175698i
$279$	−2.99462	−	1.24041i	−0.179283	−	0.0742615i
$280$	−3.13933	−	6.76863i	−0.187611	−	0.404503i
$281$	5.40709	−	2.23969i	0.322560	−	0.133609i	−0.215528	−	0.976498i	$-0.569147\pi$
$281$	5.40709	−	2.23969i	0.322560	−	0.133609i	0.538087	+	0.842889i	$0.319147\pi$
$282$	1.79291	+	6.33852i	0.106766	+	0.377454i
$283$	−3.84399	−	19.3250i	−0.228501	−	1.14875i	−0.909254	−	0.416241i	$-0.863347\pi$
$283$	−3.84399	−	19.3250i	−0.228501	−	1.14875i	0.680753	−	0.732513i	$-0.261653\pi$
$284$	27.6928	+	6.60343i	1.64326	+	0.391842i
$285$	1.79827	+	2.69131i	0.106520	+	0.159419i
$286$	19.4455	+	6.30170i	1.14983	+	0.372627i
$287$		−	11.3258i		−	0.668539i
$288$	2.18485	+	5.21789i	0.128744	+	0.307467i
$289$		−	6.38248i		−	0.375440i
$290$	1.34554	−	4.15200i	0.0790128	−	0.243814i
$291$	−9.58877	−	14.3506i	−0.562104	−	0.841248i
$292$	−10.1748	−	16.5466i	−0.595436	−	0.968319i
$293$	4.45109	+	22.3772i	0.260036	+	1.30729i	0.861243	+	0.508194i	$0.169687\pi$
$293$	4.45109	+	22.3772i	0.260036	+	1.30729i	−0.601207	+	0.799093i	$0.705313\pi$
$294$	−2.00871	+	0.568181i	−0.117150	+	0.0331370i
$295$	12.6449	−	5.23770i	0.736216	−	0.304951i
$296$	0.943022	+	22.6689i	0.0548120	+	1.31760i
$297$	−4.74776	−	1.96659i	−0.275493	−	0.114113i
$298$	2.38023	−	20.2438i	0.137883	−	1.17269i
$299$	−2.06279	−	1.37832i	−0.119294	−	0.0797100i
$300$	−2.59992	−	7.01416i	−0.150106	−	0.404963i
$301$	5.19651	−	26.1246i	0.299522	−	1.50580i
$302$	−0.500621	−	6.29908i	−0.0288075	−	0.362471i
$303$	1.81391	+	1.81391i	0.104206	+	0.104206i
$304$	11.4513	−	1.39106i	0.656776	−	0.0797830i
$305$	−2.80350	+	2.80350i	−0.160528	+	0.160528i
$306$	−3.50636	−	2.99006i	−0.200445	−	0.170930i
$307$	−22.0815	−	4.39228i	−1.26026	−	0.250680i	−0.480628	−	0.876924i	$-0.659591\pi$
$307$	−22.0815	−	4.39228i	−1.26026	−	0.250680i	−0.779627	+	0.626244i	$0.784591\pi$
$308$	17.7131	−	16.4244i	1.00930	−	0.935868i
$309$	−6.82290	+	10.2112i	−0.388141	+	0.580894i
$310$	−4.03798	+	3.18832i	−0.229342	+	0.181085i
$311$	−2.08804	+	5.04097i	−0.118402	+	0.285847i	−0.971958	−	0.235153i	$-0.924441\pi$
$311$	−2.08804	+	5.04097i	−0.118402	+	0.285847i	0.853557	+	0.521000i	$0.174441\pi$
$312$	−7.73125	+	1.87498i	−0.437696	+	0.106150i
$313$	−3.53449	−	8.53301i	−0.199781	−	0.482314i	0.791960	−	0.610574i	$-0.209061\pi$
$313$	−3.53449	−	8.53301i	−0.199781	−	0.482314i	−0.991741	+	0.128259i	$0.959061\pi$
$314$	10.6051	−	18.9710i	0.598482	−	1.07060i
$315$	−2.58725	+	0.514636i	−0.145775	+	0.0289965i
$316$	−2.22991	−	13.9404i	−0.125442	−	0.784206i
$317$	−0.332653	+	0.222271i	−0.0186836	+	0.0124840i	−0.564877	−	0.825175i	$-0.691076\pi$
$317$	−0.332653	+	0.222271i	−0.0186836	+	0.0124840i	0.546193	+	0.837659i	$0.316076\pi$
$318$	16.5585	−	8.45302i	0.928555	−	0.474022i
$319$	14.1306			0.791161
$320$	8.92161	+	1.01424i	0.498733	+	0.0566978i
$321$	−13.0846			−0.730311
$322$	−2.61122	+	1.33301i	−0.145517	+	0.0742858i
$323$	−7.81327	+	5.22066i	−0.434742	+	0.290485i
$324$	1.97489	−	0.315905i	0.109716	−	0.0175503i
$325$	10.3179	−	2.05235i	0.572332	−	0.113844i
$326$	0.771745	−	1.38054i	0.0427430	−	0.0764609i
$327$	−2.69223	−	6.49962i	−0.148881	−	0.359430i
$328$	11.6377	+	7.09473i	0.642585	+	0.391741i
$329$	−4.18938	+	10.1140i	−0.230968	+	0.557606i
$330$	−6.40195	+	5.05487i	−0.352416	+	0.278262i
$331$	−11.7805	+	17.6308i	−0.647517	+	0.969078i	0.351936	+	0.936024i	$0.385523\pi$
$331$	−11.7805	+	17.6308i	−0.647517	+	0.969078i	−0.999454	+	0.0330542i	$0.989477\pi$
$332$	−3.73538	−	4.02847i	−0.205005	−	0.221091i
$333$	7.86745	+	1.56493i	0.431134	+	0.0857578i
$334$	−6.82810	−	5.82268i	−0.373617	−	0.318603i
$335$	−7.64677	+	7.64677i	−0.417788	+	0.417788i
$336$	−2.52403	+	9.05603i	−0.137697	+	0.494047i
$337$	16.3796	+	16.3796i	0.892255	+	0.892255i	0.994735	−	0.102480i	$-0.0326778\pi$
$337$	16.3796	+	16.3796i	0.892255	+	0.892255i	−0.102480	+	0.994735i	$0.532678\pi$
$338$	0.570182	+	7.17434i	0.0310138	+	0.390233i
$339$	1.49096	−	7.49556i	0.0809779	−	0.407103i
$340$	−6.85848	+	2.54221i	−0.371953	+	0.137871i
$341$	−13.8499	−	9.25420i	−0.750013	−	0.501143i
$342$	0.476251	−	4.05050i	0.0257527	−	0.219026i
$343$	−18.4049	−	7.62357i	−0.993773	−	0.411634i
$344$	23.5890	+	21.7047i	1.27183	+	1.17024i
$345$	0.914643	−	0.378858i	0.0492427	−	0.0203970i
$346$	−28.6551	+	8.10535i	−1.54051	+	0.435746i
$347$	−4.65714	−	23.4130i	−0.250008	−	1.25688i	−0.878002	−	0.478657i	$-0.841124\pi$
$347$	−4.65714	−	23.4130i	−0.250008	−	1.25688i	0.627994	−	0.778218i	$-0.283876\pi$
$348$	−4.68460	+	2.88064i	−0.251121	+	0.154419i
$349$	12.5737	+	18.8179i	0.673057	+	1.00730i	0.998101	+	0.0616020i	$0.0196210\pi$
$349$	12.5737	+	18.8179i	0.673057	+	1.00730i	−0.325044	+	0.945699i	$0.605379\pi$
$350$	3.83259	−	11.8264i	0.204861	−	0.632149i
$351$			2.81265i			0.150128i
$352$	5.78086	+	28.4897i	0.308121	+	1.51850i
$353$			20.2428i			1.07741i	0.842493	+	0.538707i	$0.181087\pi$
$353$			20.2428i			1.07741i	−0.842493	+	0.538707i	$0.818913\pi$
$354$	−16.4055	−	5.31652i	−0.871941	−	0.282570i
$355$	−8.87617	−	13.2841i	−0.471098	−	0.705048i
$356$	−3.68114	+	15.4376i	−0.195100	+	0.818190i
$357$	−1.49407	−	7.51118i	−0.0790744	−	0.397534i
$358$	−2.00098	−	7.07411i	−0.105755	−	0.373878i
$359$	−12.1555	+	5.03499i	−0.641545	+	0.265736i	−0.679649	−	0.733537i	$-0.737868\pi$
$359$	−12.1555	+	5.03499i	−0.641545	+	0.265736i	0.0381047	+	0.999274i	$0.487868\pi$
$360$	1.09191	−	2.98089i	0.0575485	−	0.157107i
$361$	9.87010	+	4.08833i	0.519479	+	0.215175i
$362$	−34.1309	−	4.01306i	−1.79388	−	0.210922i
$363$	−12.8119	−	8.56063i	−0.672450	−	0.449317i
$364$	−12.0152	−	5.51668i	−0.629765	−	0.289153i
$365$	−2.12668	+	10.6915i	−0.111315	+	0.559620i
$366$	4.97992	−	0.395780i	0.260304	−	0.0206877i
$367$	12.0748	+	12.0748i	0.630298	+	0.630298i	0.948143	−	0.317845i	$-0.102959\pi$
$367$	12.0748	+	12.0748i	0.630298	+	0.630298i	−0.317845	+	0.948143i	$0.602959\pi$
$368$	0.266004	−	3.51817i	0.0138664	−	0.183397i
$369$	3.40745	−	3.40745i	0.177385	−	0.177385i
$370$	8.26171	−	9.68829i	0.429506	−	0.503670i
$371$	30.3035	+	6.02774i	1.57328	+	0.312945i
$372$	6.47809	+	0.244551i	0.335873	+	0.0126794i
$373$	−20.4698	+	30.6353i	−1.05989	+	1.58623i	−0.280330	+	0.959904i	$0.590444\pi$
$373$	−20.4698	+	30.6353i	−1.05989	+	1.58623i	−0.779558	+	0.626330i	$0.784556\pi$
$374$	−14.6751	−	18.5858i	−0.758829	−	0.961050i
$375$	−3.75410	+	9.06319i	−0.193861	+	0.468021i
$376$	−7.76829	−	10.6405i	−0.400619	−	0.548739i
$377$	−2.95965	−	7.14524i	−0.152430	−	0.367998i
$378$	2.90127	+	1.62186i	0.149225	+	0.0834195i
$379$	−11.8829	+	2.36365i	−0.610382	+	0.121413i	−0.490596	−	0.871387i	$-0.663221\pi$
$379$	−11.8829	+	2.36365i	−0.610382	+	0.121413i	−0.119786	+	0.992800i	$0.538221\pi$
$380$	−5.24311	−	3.79704i	−0.268966	−	0.194784i
$381$	8.84427	−	5.90955i	0.453106	−	0.302756i
$382$	10.4671	+	20.5038i	0.535541	+	1.04906i
$383$	−3.53211			−0.180482			−0.0902412	−	0.995920i	$-0.528764\pi$
$383$	−3.53211			−0.180482			−0.0902412	+	0.995920i	$0.528764\pi$
$384$	−7.72434	−	8.26647i	−0.394181	−	0.421846i
$385$	−13.5562			−0.690889
$386$	6.63957	+	13.0062i	0.337945	+	0.661996i
$387$	9.42323	−	6.29640i	0.479010	−	0.320064i
$388$	27.9574	+	20.2466i	1.41932	+	1.02787i
$389$	18.4685	−	3.67362i	0.936392	−	0.186260i	0.296770	−	0.954949i	$-0.404091\pi$
$389$	18.4685	−	3.67362i	0.936392	−	0.186260i	0.639623	+	0.768689i	$0.279091\pi$
$390$	3.89692	+	2.17845i	0.197328	+	0.110310i
$391$	1.09988	+	2.65535i	0.0556234	+	0.134287i
$392$	3.37201	−	2.46181i	0.170312	−	0.124340i
$393$	−3.84959	+	9.29373i	−0.194186	+	0.468807i
$394$	−15.0663	−	19.0813i	−0.759029	−	0.961303i
$395$	−4.40160	+	6.58747i	−0.221469	+	0.331451i
$396$	10.2706	+	0.387719i	0.516115	+	0.0194836i
$397$	−2.60521	−	0.518209i	−0.130752	−	0.0260081i	0.129281	−	0.991608i	$-0.458733\pi$
$397$	−2.60521	−	0.518209i	−0.130752	−	0.0260081i	−0.260032	+	0.965600i	$0.583733\pi$
$398$	−16.8974	+	19.8151i	−0.846989	+	0.993242i
$399$	4.79273	−	4.79273i	0.239937	−	0.239937i
$400$	9.75133	+	11.3465i	0.487567	+	0.567326i
$401$	0.662573	+	0.662573i	0.0330873	+	0.0330873i	0.723457	−	0.690370i	$-0.242552\pi$
$401$	0.662573	+	0.662573i	0.0330873	+	0.0330873i	−0.690370	+	0.723457i	$0.742552\pi$
$402$	13.5831	−	1.07952i	0.677463	−	0.0538415i
$403$	−1.77859	+	8.94160i	−0.0885981	+	0.445413i
$404$	−4.66254	−	2.14078i	−0.231970	−	0.106508i
$405$	−0.933229	−	0.623564i	−0.0463725	−	0.0309851i
$406$	−9.07701	−	1.06726i	−0.450484	−	0.0529673i
$407$	38.0846	+	15.7752i	1.88778	+	0.781945i
$408$	8.65398	+	3.16997i	0.428436	+	0.156937i
$409$	−18.7149	+	7.75195i	−0.925391	+	0.383309i	−0.793928	−	0.608012i	$-0.791967\pi$
$409$	−18.7149	+	7.75195i	−0.925391	+	0.383309i	−0.131463	+	0.991321i	$0.541967\pi$
$410$	−2.08189	−	7.36016i	−0.102817	−	0.363493i
$411$	0.666695	+	3.35170i	0.0328856	+	0.165327i
$412$	5.69711	−	23.8919i	0.280677	−	1.17707i
$413$	−15.9229	−	23.8302i	−0.783513	−	1.17261i
$414$	−1.18665	−	0.384559i	−0.0583209	−	0.0189001i
$415$			3.08307i			0.151342i
$416$	13.1952	−	8.89031i	0.646949	−	0.435883i
$417$			17.7390i			0.868680i
$418$	6.46126	−	19.9378i	0.316031	−	0.975192i
$419$	3.63817	+	5.44491i	0.177736	+	0.266001i	0.909632	−	0.415416i	$-0.136364\pi$
$419$	3.63817	+	5.44491i	0.177736	+	0.266001i	−0.731895	+	0.681417i	$0.761364\pi$
$420$	4.49418	−	2.76355i	0.219294	−	0.134847i
$421$	−2.59589	−	13.0504i	−0.126516	−	0.636039i	−0.991053	−	0.133470i	$-0.957388\pi$
$421$	−2.59589	−	13.0504i	−0.126516	−	0.636039i	0.864537	−	0.502569i	$-0.167612\pi$
$422$	12.5420	−	3.54762i	0.610535	−	0.172695i
$423$	−4.30330	+	1.78249i	−0.209234	+	0.0866675i
$424$	−25.1766	+	27.3622i	−1.22268	+	1.32883i
$425$	−11.2597	−	4.66393i	−0.546177	−	0.226234i
$426$	−2.35075	+	19.9930i	−0.113894	+	0.968665i
$427$	6.90309	+	4.61250i	0.334064	+	0.223214i
$428$	24.5378	−	9.09534i	1.18608	−	0.439640i
$429$	−2.81984	+	14.1763i	−0.136143	+	0.684438i
$430$	−1.42519	−	17.9326i	−0.0687290	−	0.864786i
$431$	−15.5516	−	15.5516i	−0.749094	−	0.749094i	0.225215	−	0.974309i	$-0.427692\pi$
$431$	−15.5516	−	15.5516i	−0.749094	−	0.749094i	−0.974309	+	0.225215i	$0.927692\pi$
$432$	−3.48396	+	1.96521i	−0.167622	+	0.0945510i
$433$	−27.0589	+	27.0589i	−1.30037	+	1.30037i	−0.372222	+	0.928144i	$0.621404\pi$
$433$	−27.0589	+	27.0589i	−1.30037	+	1.30037i	−0.928144	+	0.372222i	$0.878596\pi$
$434$	8.19775	+	6.99065i	0.393504	+	0.335562i
$435$	3.02693	+	0.602093i	0.145130	+	0.0288682i
$436$	9.56678	+	10.3174i	0.458166	+	0.494115i
$437$	−1.41322	+	2.11503i	−0.0676033	+	0.101175i
$438$	10.7800	−	8.51175i	0.515091	−	0.406707i
$439$	7.57195	−	18.2803i	0.361389	−	0.872471i	−0.633708	−	0.773572i	$-0.718468\pi$
$439$	7.57195	−	18.2803i	0.361389	−	0.872471i	0.995098	−	0.0988987i	$-0.0315320\pi$
$440$	8.49194	−	13.9296i	0.404837	−	0.664067i
$441$	−0.564879	−	1.36374i	−0.0268990	−	0.0649399i
$442$	−6.32437	+	11.3134i	−0.300820	+	0.538122i
$443$	−10.6886	+	2.12609i	−0.507829	+	0.101014i	−0.442354	−	0.896841i	$-0.645856\pi$
$443$	−10.6886	+	2.12609i	−0.507829	+	0.101014i	−0.0654755	+	0.997854i	$0.520856\pi$
$444$	−15.8418	+	2.53406i	−0.751817	+	0.120261i
$445$	7.40536	−	4.94810i	0.351048	−	0.234563i
$446$	−27.5810	+	14.0800i	−1.30600	+	0.666705i
$447$	14.4131			0.681717
$448$	−1.56165	−	18.7374i	−0.0737811	−	0.885260i
$449$	−15.2267			−0.718593			−0.359296	−	0.933224i	$-0.616983\pi$
$449$	−15.2267			−0.718593			−0.359296	+	0.933224i	$0.616983\pi$
$450$	4.71115	−	2.40501i	0.222086	−	0.113373i
$451$	20.5904	−	13.7581i	0.969564	−	0.647842i
$452$	2.41428	+	15.0929i	0.113558	+	0.709912i
$453$	4.38231	−	0.871696i	0.205899	−	0.0409559i
$454$	−12.1190	+	21.6792i	−0.568775	+	1.01745i
$455$	2.83935	+	6.85480i	0.133111	+	0.321358i
$456$	1.92245	+	7.92702i	0.0900271	+	0.371217i
$457$	−14.0232	+	33.8549i	−0.655976	+	1.58367i	0.147988	+	0.988989i	$0.452720\pi$
$457$	−14.0232	+	33.8549i	−0.655976	+	1.58367i	−0.803964	+	0.594678i	$0.797280\pi$
$458$	−7.17164	+	5.66261i	−0.335109	+	0.264596i
$459$	1.81030	−	2.70930i	0.0844975	−	0.126460i
$460$	−1.45189	+	1.34626i	−0.0676949	+	0.0627698i
$461$	25.9716	+	5.16606i	1.20962	+	0.240608i	0.758389	−	0.651802i	$-0.225987\pi$
$461$	25.9716	+	5.16606i	1.20962	+	0.240608i	0.451227	+	0.892409i	$0.350987\pi$
$462$	12.9970	+	11.0832i	0.604674	+	0.515637i
$463$	−6.92681	+	6.92681i	−0.321916	+	0.321916i	−0.849502	−	0.527586i	$-0.823097\pi$
$463$	−6.92681	+	6.92681i	−0.321916	+	0.321916i	0.527586	+	0.849502i	$0.323097\pi$
$464$	6.78272	−	8.65846i	0.314880	−	0.401959i
$465$	−2.57248	−	2.57248i	−0.119296	−	0.119296i
$466$	1.10259	+	13.8734i	0.0510767	+	0.642675i
$467$	1.28868	−	6.47864i	0.0596331	−	0.299796i	−0.939446	−	0.342696i	$-0.888660\pi$
$467$	1.28868	−	6.47864i	0.0596331	−	0.299796i	0.999079	+	0.0429004i	$0.0136598\pi$
$468$	−1.95512	−	5.27460i	−0.0903755	−	0.243818i
$469$	18.8287	+	12.5809i	0.869429	+	0.580934i
$470$	−0.863356	+	7.34281i	−0.0398236	+	0.338698i
$471$	14.1984	+	5.88119i	0.654230	+	0.270991i
$472$	34.4611	−	1.43358i	1.58620	−	0.0659857i
$473$	53.8074	−	22.2878i	2.47407	−	1.02479i
$474$	9.60575	−	2.71708i	0.441207	−	0.124799i
$475$	−2.10432	−	10.5791i	−0.0965528	−	0.485404i
$476$	8.02301	+	13.0473i	0.367734	+	0.598022i
$477$	7.30356	+	10.9305i	0.334407	+	0.500475i
$478$	11.4669	−	35.3841i	0.524485	−	1.61843i
$479$		−	8.56249i		−	0.391230i	−0.980681	−	0.195615i	$-0.937330\pi$
$479$		−	8.56249i		−	0.391230i	0.980681	−	0.195615i	$-0.0626703\pi$
$480$	0.0244019	+	6.34912i	0.00111379	+	0.289796i
$481$		−	22.5619i		−	1.02873i
$482$	−9.07559	−	2.94113i	−0.413382	−	0.133965i
$483$	−1.15175	−	1.72371i	−0.0524062	−	0.0784315i
$484$	29.9770	+	7.14812i	1.36259	+	0.324914i
$485$	−3.77921	−	18.9994i	−0.171605	−	0.862718i
$486$	0.384921	+	1.36082i	0.0174604	+	0.0617281i
$487$	8.34116	−	3.45502i	0.377974	−	0.156562i	−0.185604	−	0.982625i	$-0.559424\pi$
$487$	8.34116	−	3.45502i	0.377974	−	0.156562i	0.563578	+	0.826063i	$0.309424\pi$
$488$	−9.06380	+	4.20384i	−0.410299	+	0.190299i
$489$	1.03323	+	0.427979i	0.0467244	+	0.0193539i
$490$	−2.32697	−	0.273601i	−0.105122	−	0.0123601i
$491$	−11.2721	−	7.53178i	−0.508703	−	0.339904i	0.274586	−	0.961563i	$-0.411459\pi$
$491$	−11.2721	−	7.53178i	−0.508703	−	0.339904i	−0.783289	+	0.621658i	$0.786459\pi$
$492$	−4.02147	+	8.75863i	−0.181302	+	0.394869i
$493$	−1.74797	+	8.78763i	−0.0787245	+	0.395775i
$494$	−11.4350	+	0.908802i	−0.514487	+	0.0408889i
$495$	−4.07850	−	4.07850i	−0.183315	−	0.183315i
$496$	−12.3185	+	4.04442i	−0.553115	+	0.181600i
$497$	−23.6566	+	23.6566i	−1.06115	+	1.06115i
$498$	2.52063	−	2.95588i	0.112952	−	0.132456i
$499$	−7.22643	−	1.43743i	−0.323499	−	0.0643480i	0.0306693	−	0.999530i	$-0.490236\pi$
$499$	−7.22643	−	1.43743i	−0.323499	−	0.0643480i	−0.354169	+	0.935182i	$0.615236\pi$
$500$	0.740132	−	19.6059i	0.0330997	−	0.876802i
$501$	3.52528	−	5.27595i	0.157498	−	0.235712i
$502$	−8.05314	−	10.1992i	−0.359429	−	0.455213i
$503$	0.247896	−	0.598473i	0.0110531	−	0.0266846i	−0.918257	−	0.395986i	$-0.870403\pi$
$503$	0.247896	−	0.598473i	0.0110531	−	0.0266846i	0.929310	+	0.369301i	$0.120403\pi$
$504$	−6.56818	−	1.02478i	−0.292570	−	0.0456472i
$505$	1.10182	+	2.66004i	0.0490306	+	0.118370i
$506$	−5.59543	−	3.12794i	−0.248747	−	0.139054i
$507$	−4.99124	+	0.992819i	−0.221669	+	0.0440926i
$508$	−12.4780	+	17.2301i	−0.553620	+	0.764462i
$509$	−14.6415	+	9.78316i	−0.648975	+	0.433631i	−0.836004	−	0.548723i	$-0.815114\pi$
$509$	−14.6415	+	9.78316i	−0.648975	+	0.433631i	0.187029	+	0.982354i	$0.440114\pi$
$510$	−2.35163	−	4.60658i	−0.104132	−	0.203983i
$511$	22.8269			1.00980
$512$	20.2318	+	10.1329i	0.894126	+	0.447816i
$513$	2.88387			0.127326
$514$	8.97081	+	17.5728i	0.395686	+	0.775103i
$515$	−11.4609	+	7.65792i	−0.505027	+	0.337448i
$516$	−13.2948	+	18.3580i	−0.585270	+	0.808166i
$517$	−23.4766	+	4.66978i	−1.03250	+	0.205377i
$518$	−23.2728	−	13.0099i	−1.02255	−	0.571622i
$519$	−8.05824	−	19.4543i	−0.353717	−	0.853949i
$520$	−8.82225	−	1.37646i	−0.386881	−	0.0603617i
$521$	14.7297	−	35.5605i	0.645318	−	1.55794i	−0.174093	−	0.984729i	$-0.555699\pi$
$521$	14.7297	−	35.5605i	0.645318	−	1.55794i	0.819411	−	0.573206i	$-0.194301\pi$
$522$	−2.40980	−	3.05199i	−0.105474	−	0.133582i
$523$	−13.0998	+	19.6052i	−0.572812	+	0.857274i	−0.998875	−	0.0474196i	$-0.984900\pi$
$523$	−13.0998	+	19.6052i	−0.572812	+	0.857274i	0.426063	+	0.904694i	$0.359900\pi$
$524$	0.758959	−	20.1046i	0.0331553	−	0.878274i
$525$	8.62180	+	1.71498i	0.376286	+	0.0748480i
$526$	20.0936	−	23.5632i	0.876121	−	1.02740i
$527$	7.46831	−	7.46831i	0.325325	−	0.325325i
$528$	−19.5301	+	6.41216i	−0.849937	+	0.279053i
$529$	−15.7133	−	15.7133i	−0.683188	−	0.683188i
$530$	20.8010	−	1.65317i	0.903539	−	0.0718090i
$531$	2.37900	−	11.9601i	0.103240	−	0.519022i
$532$	−5.65637	+	12.3194i	−0.245235	+	0.534114i
$533$	−11.2695	−	7.53006i	−0.488138	−	0.326163i
$534$	−11.1453	−	1.31045i	−0.482304	−	0.0567086i
$535$	−13.5681	−	5.62007i	−0.586598	−	0.242977i
$536$	−24.7222	+	11.4663i	−1.06784	+	0.495269i
$537$	4.80270	−	1.98934i	0.207252	−	0.0858465i
$538$	5.92545	+	20.9484i	0.255464	+	0.903151i
$539$	−1.47987	−	7.43983i	−0.0637427	−	0.320456i
$540$	2.18355	+	0.520675i	0.0939650	+	0.0224063i
$541$	16.5249	+	24.7313i	0.710463	+	1.06328i	0.994527	+	0.104477i	$0.0333169\pi$
$541$	16.5249	+	24.7313i	0.710463	+	1.06328i	−0.284065	+	0.958805i	$0.591683\pi$
$542$	7.82859	+	2.53701i	0.336267	+	0.108974i
$543$		−	24.3005i		−	1.04283i
$544$	−18.4325	+	0.0708424i	−0.790285	+	0.00303734i
$545$		−	7.89613i		−	0.338233i
$546$	2.88208	−	8.89340i	0.123342	−	0.380602i
$547$	−0.124948	−	0.186997i	−0.00534237	−	0.00799542i	0.828789	−	0.559562i	$-0.189030\pi$
$547$	−0.124948	−	0.186997i	−0.00534237	−	0.00799542i	−0.834131	+	0.551566i	$0.814030\pi$
$548$	−3.58009	−	5.82207i	−0.152934	−	0.248706i
$549$	0.689144	+	3.46456i	0.0294120	+	0.147864i
$550$	26.1563	−	7.39854i	1.11531	−	0.315475i
$551$	−7.32616	+	3.03460i	−0.312105	+	0.129278i
$552$	2.49267	−	0.103695i	0.106095	−	0.00441354i
$553$	15.3274	+	6.34882i	0.651787	+	0.269979i
$554$	−1.75127	+	14.8945i	−0.0744045	+	0.632807i
$555$	7.48597	+	5.00197i	0.317762	+	0.212322i
$556$	−12.3307	−	33.2661i	−0.522937	−	1.41080i
$557$	5.08629	−	25.5705i	0.215513	−	1.08346i	−0.709844	−	0.704359i	$-0.751235\pi$
$557$	5.08629	−	25.5705i	0.215513	−	1.08346i	0.925357	−	0.379097i	$-0.123765\pi$
$558$	0.363166	+	4.56955i	0.0153740	+	0.193445i
$559$	−22.5400	−	22.5400i	−0.953339	−	0.953339i
$560$	−6.50702	+	8.30652i	−0.274972	+	0.351014i
$561$	11.8405	−	11.8405i	0.499906	−	0.499906i
$562$	−6.29787	−	5.37052i	−0.265659	−	0.226542i
$563$	−5.97284	−	1.18807i	−0.251725	−	0.0500712i	0.0676147	−	0.997712i	$-0.478461\pi$
$563$	−5.97284	−	1.18807i	−0.251725	−	0.0500712i	−0.319340	+	0.947640i	$0.603461\pi$
$564$	6.83102	−	6.33403i	0.287638	−	0.266711i
$565$	4.76553	−	7.13212i	0.200487	−	0.300050i
$566$	−21.8697	+	17.2680i	−0.919252	+	0.725826i
$567$	−0.899420	+	2.17139i	−0.0377721	+	0.0911899i
$568$	−9.48911	−	39.1273i	−0.398154	−	1.64174i
$569$	−4.41747	−	10.6647i	−0.185190	−	0.447089i	0.803832	−	0.594856i	$-0.202791\pi$
$569$	−4.41747	−	10.6647i	−0.185190	−	0.447089i	−0.989022	+	0.147768i	$0.952791\pi$
$570$	2.23361	−	3.99560i	0.0935556	−	0.167357i
$571$	16.7687	−	3.33550i	0.701748	−	0.139586i	0.168695	−	0.985668i	$-0.446045\pi$
$571$	16.7687	−	3.33550i	0.701748	−	0.139586i	0.533053	+	0.846082i	$0.321045\pi$
$572$	−4.56610	−	28.5452i	−0.190918	−	1.19353i
$573$	−13.5349	+	9.04372i	−0.565428	+	0.377807i
$574$	−14.2657	+	7.28256i	−0.595439	+	0.303968i
$575$	−3.29910			−0.137582
$576$	5.16747	−	6.10714i	0.215311	−	0.254464i
$577$	40.3595			1.68019			0.840095	−	0.542439i	$-0.182499\pi$
$577$	40.3595			1.68019			0.840095	+	0.542439i	$0.182499\pi$
$578$	−8.03925	+	4.10399i	−0.334389	+	0.170703i
$579$	−8.58559	+	5.73671i	−0.356805	+	0.238409i
$580$	−6.09497	+	0.974956i	−0.253080	+	0.0404828i
$581$	6.33196	−	1.25950i	0.262694	−	0.0522530i
$582$	−11.9101	+	21.3054i	−0.493689	+	0.883136i
$583$	25.8529	+	62.4144i	1.07072	+	2.58494i
$584$	−14.2993	+	23.4556i	−0.591710	+	0.970600i
$585$	−1.20808	+	2.91657i	−0.0499480	+	0.120585i
$586$	25.3237	−	19.9952i	1.04611	−	0.825994i
$587$	11.0998	−	16.6120i	0.458136	−	0.685649i	−0.528436	−	0.848973i	$-0.677221\pi$
$587$	11.0998	−	16.6120i	0.458136	−	0.685649i	0.986573	+	0.163324i	$0.0522215\pi$
$588$	2.00728	+	2.16478i	0.0827790	+	0.0892741i
$589$	9.16801	+	1.82363i	0.377761	+	0.0751414i
$590$	−14.7281	−	12.5594i	−0.606346	−	0.517063i
$591$	12.1562	−	12.1562i	0.500038	−	0.500038i
$592$	27.9469	−	15.7641i	1.14861	−	0.647899i
$593$	−28.5859	−	28.5859i	−1.17388	−	1.17388i	−0.981276	−	0.192604i	$-0.938307\pi$
$593$	−28.5859	−	28.5859i	−1.17388	−	1.17388i	−0.192604	−	0.981276i	$-0.561693\pi$
$594$	0.575775	+	7.24472i	0.0236243	+	0.297254i
$595$	1.67692	−	8.43044i	0.0687469	−	0.345614i
$596$	−27.0291	+	10.0188i	−1.10716	+	0.410387i
$597$	−15.3108	−	10.2303i	−0.626629	−	0.418700i
$598$	−0.409705	+	3.48452i	−0.0167541	+	0.142493i
$599$	27.9944	+	11.5957i	1.14382	+	0.473787i	0.872457	−	0.488690i	$-0.162525\pi$
$599$	27.9944	+	11.5957i	1.14382	+	0.473787i	0.271365	+	0.962477i	$0.412525\pi$
$600$	−7.16312	+	7.78496i	−0.292433	+	0.317820i
$601$	7.39208	−	3.06190i	0.301529	−	0.124897i	−0.226789	−	0.973944i	$-0.572823\pi$
$601$	7.39208	−	3.06190i	0.301529	−	0.124897i	0.528318	+	0.849046i	$0.322823\pi$
$602$	−36.2474	+	10.2529i	−1.47734	+	0.417878i
$603$	1.87969	+	9.44985i	0.0765470	+	0.384828i
$604$	−7.61229	+	4.68093i	−0.309740	+	0.190464i
$605$	−9.60832	−	14.3799i	−0.390634	−	0.584625i
$606$	1.11841	−	3.45113i	0.0454322	−	0.140192i
$607$		−	39.2584i		−	1.59345i	−0.604341	−	0.796726i	$-0.706564\pi$
$607$		−	39.2584i		−	1.59345i	0.604341	−	0.796726i	$-0.293436\pi$
$608$	−9.11542	−	13.5293i	−0.369679	−	0.548687i
$609$		−	6.46263i		−	0.261879i
$610$	5.33391	+	1.72856i	0.215964	+	0.0699874i
$611$	7.27848	+	10.8930i	0.294456	+	0.440684i
$612$	−1.51160	+	6.33917i	−0.0611027	+	0.256246i
$613$	1.15228	+	5.79291i	0.0465402	+	0.233974i	0.997053	−	0.0767108i	$-0.0244418\pi$
$613$	1.15228	+	5.79291i	0.0465402	+	0.233974i	−0.950513	+	0.310684i	$0.899442\pi$
$614$	8.66613	+	30.6376i	0.349737	+	1.23643i
$615$	4.99691	−	2.06979i	0.201495	−	0.0834619i
$616$	−32.0776	−	11.7501i	−1.29244	−	0.473424i
$617$	10.3440	+	4.28464i	0.416435	+	0.172493i	0.581055	−	0.813864i	$-0.302640\pi$
$617$	10.3440	+	4.28464i	0.416435	+	0.172493i	−0.164621	+	0.986357i	$0.552640\pi$
$618$	17.2490	+	2.02811i	0.693856	+	0.0815825i
$619$	7.87296	+	5.26054i	0.316441	+	0.211439i	0.703639	−	0.710557i	$-0.251557\pi$
$619$	7.87296	+	5.26054i	0.316441	+	0.211439i	−0.387198	+	0.921996i	$0.626557\pi$
$620$	6.61240	+	3.03604i	0.265560	+	0.121930i
$621$	0.172080	−	0.865104i	0.00690533	−	0.0347154i
$622$	7.69213	−	0.611333i	0.308426	−	0.0245122i
$623$	−13.1876	−	13.1876i	−0.528350	−	0.528350i
$624$	7.33294	+	8.53250i	0.293552	+	0.341574i
$625$	5.43818	−	5.43818i	0.217527	−	0.217527i
$626$	−8.47530	+	9.93876i	−0.338741	+	0.397233i
$627$	14.5353	+	2.89124i	0.580482	+	0.115465i
$628$	−30.7147	−	1.15949i	−1.22565	−	0.0462689i
$629$	−14.5215	+	21.7329i	−0.579009	+	0.866548i
$630$	2.31185	+	2.92793i	0.0921062	+	0.116652i
$631$	−11.1515	+	26.9221i	−0.443934	+	1.07175i	0.530623	+	0.847608i	$0.321958\pi$
$631$	−11.1515	+	26.9221i	−0.443934	+	1.07175i	−0.974556	+	0.224143i	$0.928042\pi$
$632$	−16.1251	+	11.7725i	−0.641424	+	0.468285i
$633$	3.52700	+	8.51492i	0.140186	+	0.338438i
$634$	0.493867	+	0.276080i	0.0196140	+	0.0109645i
$635$	11.7093	−	2.32913i	0.464670	−	0.0924286i
$636$	−21.2945	−	15.4214i	−0.844382	−	0.611498i
$637$	−3.45205	+	2.30658i	−0.136775	+	0.0913902i
$638$	−9.08608	−	17.7986i	−0.359721	−	0.704653i
$639$	−14.2346			−0.563112
$640$	−4.45915	−	11.8896i	−0.176263	−	0.469979i
$641$	−14.4610			−0.571177			−0.285589	−	0.958352i	$-0.592189\pi$
$641$	−14.4610			−0.571177			−0.285589	+	0.958352i	$0.592189\pi$
$642$	8.41350	+	16.4811i	0.332055	+	0.650457i
$643$	17.9009	−	11.9610i	0.705944	−	0.471697i	−0.150052	−	0.988678i	$-0.547944\pi$
$643$	17.9009	−	11.9610i	0.705944	−	0.471697i	0.855997	+	0.516981i	$0.172944\pi$
$644$	3.35807	+	2.43190i	0.132326	+	0.0958303i
$645$	12.4758	−	2.48159i	0.491235	−	0.0977127i
$646$	11.5998	+	6.48451i	0.456389	+	0.255130i
$647$	−6.08613	−	14.6932i	−0.239270	−	0.577650i	0.757937	−	0.652327i	$-0.226207\pi$
$647$	−6.08613	−	14.6932i	−0.239270	−	0.577650i	−0.997208	+	0.0746777i	$0.976207\pi$
$648$	−1.66778	−	2.28441i	−0.0655166	−	0.0897399i
$649$	23.9813	−	57.8960i	0.941348	−	2.27261i
$650$	−9.21957	−	11.6765i	−0.361621	−	0.457990i
$651$	−4.23241	+	6.33425i	−0.165881	+	0.248259i
$652$	−2.23514	−	0.0843775i	−0.0875347	−	0.00330448i
$653$	4.67112	+	0.929144i	0.182795	+	0.0363602i	0.285639	−	0.958337i	$-0.407794\pi$
$653$	4.67112	+	0.929144i	0.182795	+	0.0363602i	−0.102844	+	0.994698i	$0.532794\pi$
$654$	−6.45566	+	7.57038i	−0.252436	+	0.296025i
$655$	−7.98365	+	7.98365i	−0.311947	+	0.311947i
$656$	1.45324	−	19.2206i	0.0567397	−	0.750438i
$657$	6.86766	+	6.86766i	0.267933	+	0.267933i
$658$	15.4333	−	1.22656i	0.601651	−	0.0478163i
$659$	−5.07329	+	25.5051i	−0.197627	+	0.993539i	0.746858	+	0.664984i	$0.231562\pi$
$659$	−5.07329	+	25.5051i	−0.197627	+	0.993539i	−0.944485	+	0.328555i	$0.893438\pi$
$660$	10.4835	+	4.81344i	0.408070	+	0.187363i
$661$	−18.4874	−	12.3529i	−0.719077	−	0.480472i	0.141406	−	0.989952i	$-0.454838\pi$
$661$	−18.4874	−	12.3529i	−0.719077	−	0.480472i	−0.860483	+	0.509480i	$0.829838\pi$
$662$	29.7824	+	3.50177i	1.15753	+	0.136100i
$663$	−8.46724	−	3.50725i	−0.328840	−	0.136210i
$664$	−2.67230	+	7.29534i	−0.103705	+	0.283114i
$665$	7.02838	−	2.91125i	0.272549	−	0.112893i
$666$	−3.08768	−	10.9159i	−0.119645	−	0.422984i
$667$	0.473169	+	2.37878i	0.0183212	+	0.0921068i
$668$	−2.94360	+	12.3446i	−0.113891	+	0.477626i
$669$	−12.1653	−	18.2067i	−0.470339	−	0.703912i
$670$	14.5486	+	4.71478i	0.562063	+	0.182148i
$671$			18.1530i			0.700788i
$672$	13.0298	−	2.64388i	0.502634	−	0.101990i
$673$			16.1507i			0.622564i	0.950318	+	0.311282i	$0.100758\pi$
$673$			16.1507i			0.622564i	−0.950318	+	0.311282i	$0.899242\pi$
$674$	10.0992	−	31.1637i	0.389007	−	1.20038i
$675$	2.07797	+	3.10991i	0.0799812	+	0.119700i
$676$	8.67003	−	5.33135i	0.333463	−	0.205052i
$677$	−4.62855	−	23.2693i	−0.177890	−	0.894311i	−0.961866	−	0.273521i	$-0.911812\pi$
$677$	−4.62855	−	23.2693i	−0.177890	−	0.894311i	0.783976	−	0.620791i	$-0.213188\pi$
$678$	−10.4000	+	2.94172i	−0.399408	+	0.112976i
$679$	−37.4768	+	15.5234i	−1.43823	+	0.595733i
$680$	7.61217	+	7.00414i	0.291914	+	0.268596i
$681$	−16.2253	−	6.72074i	−0.621755	−	0.257539i
$682$	−2.75081	+	23.3956i	−0.105334	+	0.895862i
$683$	10.3658	+	6.92618i	0.396635	+	0.265023i	0.737853	−	0.674961i	$-0.235840\pi$
$683$	10.3658	+	6.92618i	0.396635	+	0.265023i	−0.341219	+	0.939984i	$0.610840\pi$
$684$	−5.40816	+	2.00463i	−0.206786	+	0.0766488i
$685$	−0.748288	+	3.76190i	−0.0285906	+	0.143735i
$686$	2.23202	+	28.0845i	0.0852189	+	1.07227i
$687$	−4.56885	−	4.56885i	−0.174312	−	0.174312i
$688$	12.1710	−	43.6685i	0.464014	−	1.66485i
$689$	26.1454	−	26.1454i	0.996061	−	0.996061i
$690$	−1.06532	−	0.908457i	−0.0405562	−	0.0345844i
$691$	16.6634	+	3.31456i	0.633907	+	0.126092i	0.501576	−	0.865114i	$-0.332754\pi$
$691$	16.6634	+	3.31456i	0.633907	+	0.126092i	0.132331	+	0.991206i	$0.457754\pi$
$692$	28.6348	+	30.8815i	1.08853	+	1.17394i
$693$	−6.71020	+	10.0425i	−0.254900	+	0.381484i
$694$	−26.4960	+	20.9208i	−1.00577	+	0.794142i
$695$	−7.61920	+	18.3944i	−0.289013	+	0.697738i
$696$	6.64063	+	4.04835i	0.251712	+	0.153452i
$697$	6.00891	+	14.5068i	0.227604	+	0.549484i
$698$	15.6177	−	27.9377i	0.591138	−	1.05746i
$699$	−9.65185	+	1.91987i	−0.365066	+	0.0726162i
$700$	−17.3607	+	2.77703i	−0.656173	+	0.104962i
$701$	36.3684	−	24.3006i	1.37361	−	0.917820i	0.373662	−	0.927565i	$-0.378102\pi$
$701$	36.3684	−	24.3006i	1.37361	−	0.917820i	0.999953	+	0.00974462i	$0.00310186\pi$
$702$	3.54275	−	1.80855i	0.133713	−	0.0682595i
$703$	−23.1332			−0.872484
$704$	32.1679	−	25.6005i	1.21237	−	0.964856i
$705$	−5.22791			−0.196895
$706$	25.4974	−	13.0163i	0.959606	−	0.489873i
$707$	5.01303	−	3.34960i	0.188534	−	0.125975i
$708$	3.85226	+	24.0826i	0.144777	+	0.905078i
$709$	−40.5607	+	8.06803i	−1.52329	+	0.303001i	−0.884559	−	0.466429i	$-0.845540\pi$
$709$	−40.5607	+	8.06803i	−1.52329	+	0.303001i	−0.638731	+	0.769430i	$0.720540\pi$
$710$	−11.0250	+	19.7220i	−0.413760	+	0.740155i
$711$	2.70128	+	6.52147i	0.101306	+	0.244574i
$712$	21.8119	−	5.28979i	0.817434	−	0.198243i
$713$	1.09411	−	2.64141i	0.0409747	−	0.0989216i
$714$	−8.50024	+	6.71165i	−0.318113	+	0.251177i
$715$	−9.01300	+	13.4889i	−0.337067	+	0.504457i
$716$	−7.62376	+	7.06909i	−0.284913	+	0.264184i
$717$	25.7960	+	5.13114i	0.963369	+	0.191626i
$718$	14.1581	+	12.0733i	0.528375	+	0.450573i
$719$	−5.93274	+	5.93274i	−0.221254	+	0.221254i	−0.809026	−	0.587772i	$-0.800005\pi$
$719$	−5.93274	+	5.93274i	−0.221254	+	0.221254i	0.587772	+	0.809026i	$0.300005\pi$
$720$	−4.45678	+	0.541394i	−0.166094	+	0.0201766i
$721$	20.4098	+	20.4098i	0.760099	+	0.760099i
$722$	−1.19698	−	15.0610i	−0.0445469	−	0.560513i
$723$	1.31608	−	6.61636i	0.0489454	−	0.246065i
$724$	16.8917	+	45.5711i	0.627775	+	1.69364i
$725$	−8.55133	−	5.71382i	−0.317588	−	0.212206i
$726$	−2.54465	+	21.6421i	−0.0944408	+	0.803215i
$727$	−14.1268	−	5.85151i	−0.523934	−	0.217021i	0.105010	−	0.994471i	$-0.466513\pi$
$727$	−14.1268	−	5.85151i	−0.523934	−	0.217021i	−0.628944	+	0.777451i	$0.716513\pi$
$728$	0.777141	+	18.6813i	0.0288027	+	0.692376i
$729$	−0.923880	+	0.382683i	−0.0342178	+	0.0141735i
$730$	14.8343	−	4.19602i	0.549042	−	0.155302i
$731$	7.20444	+	36.2192i	0.266466	+	1.33961i
$732$	−3.70064	−	6.01811i	−0.136780	−	0.222436i
$733$	29.1094	+	43.5654i	1.07518	+	1.60912i	0.747406	+	0.664368i	$0.231299\pi$
$733$	29.1094	+	43.5654i	1.07518	+	1.60912i	0.327776	+	0.944755i	$0.393701\pi$
$734$	7.44496	−	22.9733i	0.274799	−	0.847960i
$735$		−	1.65675i		−	0.0611102i
$736$	−4.60246	+	1.92716i	−0.169649	+	0.0710359i
$737$			49.5136i			1.82386i
$738$	−6.48297	−	2.10094i	−0.238642	−	0.0773366i
$739$	15.8956	+	23.7895i	0.584730	+	0.875111i	0.999392	−	0.0348648i	$-0.0111001\pi$
$739$	15.8956	+	23.7895i	0.584730	+	0.875111i	−0.414662	+	0.909976i	$0.636100\pi$
$740$	−17.5155	−	4.17664i	−0.643883	−	0.153536i
$741$	−1.58243	−	7.95543i	−0.0581322	−	0.292250i
$742$	−11.8930	−	42.0455i	−0.436604	−	1.54354i
$743$	16.2982	−	6.75095i	0.597924	−	0.247668i	−0.0631313	−	0.998005i	$-0.520109\pi$
$743$	16.2982	−	6.75095i	0.597924	−	0.247668i	0.661056	+	0.750337i	$0.270109\pi$
$744$	−3.85743	−	8.31692i	−0.141420	−	0.304913i
$745$	14.9457	+	6.19069i	0.547566	+	0.226809i
$746$	51.7498	+	6.08466i	1.89470	+	0.222775i
$747$	2.28395	+	1.52609i	0.0835655	+	0.0558367i
$748$	−13.9741	+	30.4352i	−0.510945	+	1.11282i
$749$	−5.99956	+	30.1618i	−0.219219	+	1.10209i
$750$	13.8297	−	1.09912i	0.504990	−	0.0401342i
$751$	9.73589	+	9.73589i	0.355268	+	0.355268i	0.862065	−	0.506797i	$-0.169171\pi$
$751$	9.73589	+	9.73589i	0.355268	+	0.355268i	−0.506797	+	0.862065i	$0.669171\pi$
$752$	−8.40742	+	16.6267i	−0.306587	+	0.606312i
$753$	6.49764	−	6.49764i	0.236787	−	0.236787i
$754$	−7.09691	+	8.32237i	−0.258454	+	0.303083i
$755$	4.91864	+	0.978379i	0.179008	+	0.0356068i
$756$	0.177324	−	4.69725i	0.00644919	−	0.170837i
$757$	22.0131	−	32.9450i	0.800082	−	1.19741i	−0.176931	−	0.984223i	$-0.556617\pi$
$757$	22.0131	−	32.9450i	0.800082	−	1.19741i	0.977012	−	0.213183i	$-0.0683831\pi$
$758$	10.6180	+	13.4476i	0.385663	+	0.488438i
$759$	1.73463	−	4.18778i	0.0629632	−	0.152007i
$760$	−1.41131	+	9.04563i	−0.0511937	+	0.328120i
$761$	−14.5474	−	35.1206i	−0.527344	−	1.27312i	−0.933257	−	0.359210i	$-0.883046\pi$
$761$	−14.5474	−	35.1206i	−0.527344	−	1.27312i	0.405913	−	0.913912i	$-0.366954\pi$
$762$	−13.1305	−	7.34018i	−0.475667	−	0.265906i
$763$	−16.2170	+	3.22575i	−0.587093	+	0.116780i
$764$	19.0957	−	26.3682i	0.690859	−	0.953967i
$765$	3.04088	−	2.03185i	0.109943	−	0.0734618i
$766$	2.27118	+	4.44898i	0.0820609	+	0.160748i
$767$	−34.2984			−1.23844
$768$	−5.44546	+	15.0448i	−0.196496	+	0.542884i
$769$	4.52202			0.163068			0.0815340	−	0.996671i	$-0.474018\pi$
$769$	4.52202			0.163068			0.0815340	+	0.996671i	$0.474018\pi$
$770$	8.71675	+	17.0751i	0.314130	+	0.615345i
$771$	−11.6001	+	7.75094i	−0.417767	+	0.279143i
$772$	12.1130	−	16.7261i	0.435956	−	0.601987i
$773$	0.945190	−	0.188010i	0.0339961	−	0.00676225i	−0.178063	−	0.984019i	$-0.556983\pi$
$773$	0.945190	−	0.188010i	0.0339961	−	0.00676225i	0.212059	+	0.977257i	$0.431983\pi$
$774$	−13.9900	−	7.82067i	−0.502861	−	0.281108i
$775$	4.63945	+	11.2006i	0.166654	+	0.402338i
$776$	7.52542	−	48.2332i	0.270147	−	1.73147i
$777$	7.21477	−	17.4180i	0.258829	−	0.624868i
$778$	−16.5026	−	20.9004i	−0.591648	−	0.749317i
$779$	−7.72073	+	11.5549i	−0.276624	+	0.413997i
$780$	0.238177	−	6.30925i	0.00852811	−	0.225907i
$781$	−71.7452	−	14.2710i	−2.56724	−	0.510657i
$782$	2.63739	−	3.09280i	0.0943129	−	0.110598i
$783$	1.94434	−	1.94434i	0.0694849	−	0.0694849i
$784$	−5.26907	−	2.66435i	−0.188181	−	0.0951554i
$785$	12.1970	+	12.1970i	0.435329	+	0.435329i
$786$	14.1815	−	1.12708i	0.505838	−	0.0402015i
$787$	0.997819	−	5.01637i	0.0355684	−	0.178814i	−0.958917	−	0.283685i	$-0.908443\pi$
$787$	0.997819	−	5.01637i	0.0355684	−	0.178814i	0.994486	+	0.104871i	$0.0334429\pi$
$788$	−14.3467	+	31.2467i	−0.511080	+	1.11312i
$789$	18.2069	+	12.1654i	0.648182	+	0.433101i
$790$	11.1277	+	1.30838i	0.395906	+	0.0465500i
$791$	−16.5947	−	6.87374i	−0.590039	−	0.244402i
$792$	−6.11569	−	13.1859i	−0.217312	−	0.468541i
$793$	9.17920	−	3.80215i	0.325963	−	0.135018i
$794$	1.02245	+	3.61468i	0.0362852	+	0.128280i
$795$	2.87855	+	14.4714i	0.102091	+	0.513249i
$796$	35.8239	+	8.54232i	1.26974	+	0.302775i
$797$	15.0187	+	22.4771i	0.531991	+	0.796181i	0.995972	−	0.0896641i	$-0.0285794\pi$
$797$	15.0187	+	22.4771i	0.531991	+	0.796181i	−0.463981	+	0.885845i	$0.653579\pi$
$798$	−9.11859	−	2.95506i	−0.322794	−	0.104608i
$799$		−	15.1774i		−	0.536939i
$800$	8.02165	−	19.5785i	0.283608	−	0.692204i
$801$		−	7.93520i		−	0.280377i
$802$	0.408524	−	1.26060i	0.0144255	−	0.0445134i
$803$	27.7292	+	41.4996i	0.978541	+	1.46449i
$804$	−10.0938	−	16.4149i	−0.355980	−	0.578907i
$805$	−0.453936	−	2.28209i	−0.0159992	−	0.0804332i
$806$	12.4063	−	3.50924i	0.436993	−	0.123608i
$807$	−14.2222	+	5.89101i	−0.500644	+	0.207373i
$808$	0.301573	+	7.24938i	0.0106093	+	0.255032i
$809$	−7.24881	−	3.00256i	−0.254855	−	0.105564i	0.251599	−	0.967832i	$-0.419044\pi$
$809$	−7.24881	−	3.00256i	−0.254855	−	0.105564i	−0.506453	+	0.862267i	$0.669044\pi$
$810$	−0.185354	+	1.57643i	−0.00651269	+	0.0553902i
$811$	−27.9633	−	18.6845i	−0.981924	−	0.656100i	−0.0425854	−	0.999093i	$-0.513559\pi$
$811$	−27.9633	−	18.6845i	−0.981924	−	0.656100i	−0.939338	+	0.342992i	$0.888559\pi$
$812$	4.49229	+	12.1195i	0.157648	+	0.425310i
$813$	−1.13525	+	5.70726i	−0.0398148	+	0.200162i
$814$	−4.61863	−	58.1141i	−0.161883	−	2.03690i
$815$	0.887585	+	0.887585i	0.0310907	+	0.0310907i
$816$	−1.57175	−	12.9387i	−0.0550223	−	0.452945i
$817$	−23.1107	+	23.1107i	−0.808541	+	0.808541i
$818$	21.7980	+	18.5883i	0.762150	+	0.649925i
$819$	6.48354	+	1.28966i	0.226553	+	0.0450642i
$820$	−7.93204	+	7.35495i	−0.276999	+	0.256846i
$821$	−0.243998	+	0.365168i	−0.00851558	+	0.0127445i	−0.835703	−	0.549182i	$-0.814939\pi$
$821$	−0.243998	+	0.365168i	−0.00851558	+	0.0127445i	0.827187	+	0.561926i	$0.189939\pi$
$822$	3.79304	−	2.99492i	0.132298	−	0.104460i
$823$	−9.52365	+	22.9921i	−0.331974	+	0.801455i	0.666462	+	0.745539i	$0.267808\pi$
$823$	−9.52365	+	22.9921i	−0.331974	+	0.801455i	−0.998435	+	0.0559161i	$0.982192\pi$
$824$	−33.7571	+	8.18674i	−1.17598	+	0.285198i
$825$	7.35554	+	17.7578i	0.256087	+	0.618248i
$826$	−19.7776	+	35.3791i	−0.688149	+	1.23100i
$827$	−50.5251	+	10.0501i	−1.75693	+	0.349475i	−0.965223	−	0.261428i	$-0.915807\pi$
$827$	−50.5251	+	10.0501i	−1.75693	+	0.349475i	−0.791705	+	0.610903i	$0.790807\pi$
$828$	0.278645	+	1.74196i	0.00968359	+	0.0605373i
$829$	−32.7044	+	21.8524i	−1.13587	+	0.758964i	−0.973708	−	0.227800i	$-0.926847\pi$
$829$	−32.7044	+	21.8524i	−1.13587	+	0.758964i	−0.162162	+	0.986764i	$0.551847\pi$
$830$	3.88337	−	1.98244i	0.134794	−	0.0688113i
$831$	−10.6046			−0.367868
$832$	−19.6827	−	10.9039i	−0.682374	−	0.378024i
$833$	4.80980			0.166650
$834$	22.3436	−	11.4063i	0.773696	−	0.394967i
$835$	5.92165	−	3.95672i	0.204927	−	0.136928i
$836$	−29.2680	+	4.68172i	−1.01225	+	0.161921i
$837$	−3.17907	+	0.632356i	−0.109885	+	0.0218574i
$838$	4.51893	−	8.08369i	0.156104	−	0.279246i
$839$	−19.4130	−	46.8670i	−0.670210	−	1.61803i	−0.781253	−	0.624215i	$-0.785419\pi$
$839$	−19.4130	−	46.8670i	−0.670210	−	1.61803i	0.111043	−	0.993816i	$-0.464581\pi$
$840$	−6.37071	−	3.88379i	−0.219810	−	0.134004i
$841$	8.20439	−	19.8072i	0.282910	−	0.683006i
$842$	−14.7689	+	11.6613i	−0.508969	+	0.401874i
$843$	3.25152	−	4.86625i	0.111988	−	0.167603i
$844$	−12.5331	−	13.5165i	−0.431408	−	0.465257i
$845$	−5.60209	−	1.11432i	−0.192718	−	0.0383339i
$846$	5.01224	+	4.27420i	0.172324	+	0.146950i
$847$	−25.6079	+	25.6079i	−0.879899	+	0.879899i
$848$	50.6536	+	14.1178i	1.73945	+	0.484808i
$849$	−13.9326	−	13.9326i	−0.478165	−	0.478165i
$850$	1.36550	+	17.1815i	0.0468363	+	0.589319i
$851$	−1.38035	+	6.93951i	−0.0473179	+	0.237883i
$852$	26.6944	−	9.89472i	0.914534	−	0.338987i
$853$	−17.3242	−	11.5757i	−0.593171	−	0.396344i	0.222439	−	0.974947i	$-0.428598\pi$
$853$	−17.3242	−	11.5757i	−0.593171	−	0.396344i	−0.815610	+	0.578603i	$0.803598\pi$
$854$	1.37107	−	11.6609i	0.0469169	−	0.399027i
$855$	2.99042	+	1.23867i	0.102270	+	0.0423617i
$856$	−27.2343	−	25.0589i	−0.930849	−	0.856496i
$857$	−21.8298	+	9.04220i	−0.745692	+	0.308876i	−0.722982	−	0.690867i	$-0.757229\pi$
$857$	−21.8298	+	9.04220i	−0.745692	+	0.308876i	−0.0227092	+	0.999742i	$0.507229\pi$
$858$	19.6694	−	5.56366i	0.671501	−	0.189940i
$859$	−7.64312	−	38.4246i	−0.260780	−	1.31103i	−0.859938	−	0.510398i	$-0.829498\pi$
$859$	−7.64312	−	38.4246i	−0.260780	−	1.31103i	0.599158	−	0.800631i	$-0.295502\pi$
$860$	−21.6711	+	13.3259i	−0.738978	+	0.454411i
$861$	−6.29226	−	9.41703i	−0.214440	−	0.320931i
$862$	−9.58867	+	29.5883i	−0.326592	+	1.00778i
$863$			3.30235i			0.112413i	0.998419	+	0.0562067i	$0.0179006\pi$
$863$			3.30235i			0.112413i	−0.998419	+	0.0562067i	$0.982099\pi$
$864$	4.71555	+	3.12468i	0.160426	+	0.106304i
$865$		−	23.6343i		−	0.803589i
$866$	51.4818	+	16.6837i	1.74942	+	0.566936i
$867$	−3.54592	−	5.30684i	−0.120426	−	0.180230i
$868$	3.53406	−	14.8208i	0.119954	−	0.503049i
$869$	7.07685	+	35.5777i	0.240066	+	1.20689i
$870$	−1.18795	−	4.19981i	−0.0402754	−	0.142387i
$871$	25.0370	−	10.3706i	0.848345	−	0.351396i
$872$	6.84409	−	18.6843i	0.231770	−	0.632730i
$873$	−15.9455	−	6.60486i	−0.539675	−	0.223541i
$874$	3.57275	+	0.420079i	0.120850	+	0.0142094i
$875$	19.1706	+	12.8094i	0.648084	+	0.433036i
$876$	−17.6529	−	8.10521i	−0.596435	−	0.273850i
$877$	2.04191	−	10.2654i	0.0689504	−	0.346637i	−0.930875	−	0.365339i	$-0.880953\pi$
$877$	2.04191	−	10.2654i	0.0689504	−	0.346637i	0.999825	+	0.0187015i	$0.00595322\pi$
$878$	−27.8943	+	2.21690i	−0.941387	+	0.0748169i
$879$	16.1330	+	16.1330i	0.544154	+	0.544154i
$880$	−23.0058	−	1.73944i	−0.775526	−	0.0586365i
$881$	−0.695566	+	0.695566i	−0.0234342	+	0.0234342i	−0.718727	−	0.695293i	$-0.755275\pi$
$881$	−0.695566	+	0.695566i	−0.0234342	+	0.0234342i	0.695293	+	0.718727i	$0.255275\pi$
$882$	−1.35451	+	1.58840i	−0.0456089	+	0.0534843i
$883$	11.5281	+	2.29308i	0.387951	+	0.0771683i	0.385212	−	0.922828i	$-0.374128\pi$
$883$	11.5281	+	2.29308i	0.387951	+	0.0771683i	0.00273878	+	0.999996i	$0.499128\pi$
$884$	18.3167	+	0.691465i	0.616057	+	0.0232565i
$885$	7.60396	−	11.3801i	0.255604	−	0.382539i
$886$	9.55081	+	12.0960i	0.320866	+	0.406373i
$887$	−0.936854	+	2.26177i	−0.0314565	+	0.0759427i	−0.938827	−	0.344389i	$-0.888086\pi$
$887$	−0.936854	+	2.26177i	−0.0314565	+	0.0759427i	0.907371	+	0.420331i	$0.138086\pi$
$888$	13.3782	+	18.3246i	0.448944	+	0.614932i
$889$	−9.56706	−	23.0969i	−0.320869	−	0.774646i
$890$	−10.9942	−	6.14597i	−0.368528	−	0.206013i
$891$	−5.04020	+	1.00256i	−0.168853	+	0.0335870i
$892$	35.4696	+	25.6870i	1.18761	+	0.860064i
$893$	11.1688	−	7.46278i	0.373751	−	0.249732i
$894$	−9.26775	−	18.1545i	−0.309960	−	0.607176i
$895$	5.83461			0.195030
$896$	−22.5971	+	14.0153i	−0.754917	+	0.468219i
$897$	−2.48090			−0.0828349
$898$	9.79089	+	19.1793i	0.326726	+	0.640020i
$899$	7.41069	−	4.95167i	0.247160	−	0.165147i
$900$	−6.05861	−	4.38762i	−0.201954	−	0.146254i
$901$	−42.0127	+	8.35685i	−1.39965	+	0.278407i
$902$	−30.5692	−	17.0887i	−1.01784	−	0.568991i
$903$	−10.1933	−	24.6089i	−0.339213	−	0.818932i
$904$	17.4584	−	12.7459i	0.580657	−	0.423921i
$905$	10.4375	−	25.1983i	0.346954	−	0.837621i
$906$	−3.91583	−	4.95937i	−0.130095	−	0.164764i
$907$	4.80524	−	7.19155i	0.159555	−	0.238792i	−0.743075	−	0.669208i	$-0.766633\pi$
$907$	4.80524	−	7.19155i	0.159555	−	0.238792i	0.902630	+	0.430417i	$0.141633\pi$
$908$	35.0993	+	1.32502i	1.16481	+	0.0439722i
$909$	2.51597	+	0.500457i	0.0834494	+	0.0165991i
$910$	6.80845	−	7.98408i	0.225698	−	0.264670i
$911$	32.7068	−	32.7068i	1.08363	−	1.08363i	0.0874577	−	0.996168i	$-0.472126\pi$
$911$	32.7068	−	32.7068i	1.08363	−	1.08363i	0.996168	−	0.0874577i	$-0.0278743\pi$
$912$	8.74856	−	7.51862i	0.289694	−	0.248966i
$913$	9.98159	+	9.98159i	0.330342	+	0.330342i
$914$	51.6600	−	4.10569i	1.70876	−	0.135804i
$915$	−0.773485	+	3.88857i	−0.0255706	+	0.128552i
$916$	11.7439	+	5.39215i	0.388030	+	0.178162i
$917$	19.6582	+	13.1352i	0.649171	+	0.433762i
$918$	−4.57662	−	0.538112i	−0.151051	−	0.0177603i
$919$	−40.2874	−	16.6876i	−1.32896	−	0.550473i	−0.398601	−	0.917124i	$-0.630504\pi$
$919$	−40.2874	−	16.6876i	−1.32896	−	0.550473i	−0.930359	+	0.366651i	$0.880504\pi$
$920$	2.62930	+	0.963119i	0.0866856	+	0.0317531i
$921$	−20.8003	+	8.61576i	−0.685393	+	0.283899i
$922$	−10.1928	−	36.0351i	−0.335684	−	1.18675i
$923$	7.81080	+	39.2676i	0.257096	+	1.29251i
$924$	5.60301	−	23.4973i	0.184326	−	0.773004i
$925$	−16.6686	−	24.9464i	−0.548061	−	0.820232i
$926$	13.1789	+	4.27088i	0.433084	+	0.140350i
$927$			12.2809i			0.403358i
$928$	−15.2674	−	2.97591i	−0.501176	−	0.0976891i
$929$		−	24.6196i		−	0.807743i	−0.914816	−	0.403872i	$-0.867664\pi$
$929$		−	24.6196i		−	0.807743i	0.914816	−	0.403872i	$-0.132336\pi$
$930$	−1.58612	+	4.89438i	−0.0520110	+	0.160493i
$931$	2.36499	+	3.53946i	0.0775094	+	0.116001i
$932$	16.7657	−	10.3095i	0.549180	−	0.337700i
$933$	1.06447	+	5.35146i	0.0348493	+	0.175199i
$934$	−8.98900	+	2.54262i	−0.294129	+	0.0831971i
$935$	17.3637	−	7.19228i	0.567854	−	0.235213i
$936$	−5.38662	+	5.85424i	−0.176067	+	0.191352i
$937$	−2.75903	−	1.14283i	−0.0901335	−	0.0373345i	0.337161	−	0.941447i	$-0.390533\pi$
$937$	−2.75903	−	1.14283i	−0.0901335	−	0.0373345i	−0.427295	+	0.904112i	$0.640533\pi$
$938$	3.73969	−	31.8059i	0.122105	−	1.03850i
$939$	−7.67951	−	5.13128i	−0.250611	−	0.167453i
$940$	9.80399	−	3.63402i	0.319771	−	0.118529i
$941$	−6.30860	+	31.7155i	−0.205654	+	1.03389i	0.730663	+	0.682739i	$0.239211\pi$
$941$	−6.30860	+	31.7155i	−0.205654	+	1.03389i	−0.936317	+	0.351156i	$0.885789\pi$
$942$	−1.72189	−	21.6657i	−0.0561021	−	0.705907i
$943$	3.00555	+	3.00555i	0.0978742	+	0.0978742i
$944$	−23.9644	−	42.4847i	−0.779976	−	1.38276i
$945$	−1.86530	+	1.86530i	−0.0606784	+	0.0606784i
$946$	−62.6718	−	53.4435i	−2.03764	−	1.73760i
$947$	16.7723	+	3.33622i	0.545026	+	0.108412i	0.459922	−	0.887960i	$-0.347878\pi$
$947$	16.7723	+	3.33622i	0.545026	+	0.108412i	0.0851047	+	0.996372i	$0.472878\pi$
$948$	−9.59895	−	10.3521i	−0.311759	−	0.336221i
$949$	15.1767	−	22.7136i	0.492657	−	0.737314i
$950$	−11.9722	+	9.45302i	−0.388428	+	0.306696i
$951$	−0.153103	+	0.369624i	−0.00496471	+	0.0119859i
$952$	11.2752	−	18.4951i	0.365433	−	0.599431i
$953$	16.8500	+	40.6796i	0.545826	+	1.31774i	0.920558	+	0.390607i	$0.127735\pi$
$953$	16.8500	+	40.6796i	0.545826	+	1.31774i	−0.374732	+	0.927133i	$0.622265\pi$
$954$	9.07165	−	16.2278i	0.293706	−	0.525396i
$955$	−17.9194	+	3.56439i	−0.579859	+	0.115341i
$956$	−51.9424	+	8.30874i	−1.67994	+	0.268724i
$957$	11.7491	−	7.85053i	0.379796	−	0.253772i
$958$	−10.7851	+	5.50575i	−0.348452	+	0.177883i
$959$	8.03182			0.259361
$960$	7.98153	−	4.11327i	0.257603	−	0.132755i
$961$	20.4936			0.661085
$962$	−28.4185	+	14.5075i	−0.916249	+	0.467739i
$963$	−10.8795	+	7.26942i	−0.350585	+	0.234254i
$964$	2.13109	+	13.3226i	0.0686379	+	0.429092i
$965$	−11.3668	+	2.26100i	−0.365911	+	0.0727842i
$966$	−1.43057	+	2.55907i	−0.0460277	+	0.0823368i
$967$	8.11299	+	19.5865i	0.260896	+	0.629859i	0.998994	−	0.0448343i	$-0.0142760\pi$
$967$	8.11299	+	19.5865i	0.260896	+	0.629859i	−0.738098	+	0.674693i	$0.764276\pi$
$968$	−10.2718	−	42.3547i	−0.330149	−	1.36133i
$969$	−3.59605	+	8.68164i	−0.115522	+	0.278894i
$970$	−21.5012	+	16.9770i	−0.690361	+	0.545098i
$971$	16.3196	−	24.4241i	0.523722	−	0.783806i	−0.471456	−	0.881890i	$-0.656271\pi$
$971$	16.3196	−	24.4241i	0.523722	−	0.783806i	0.995178	+	0.0980838i	$0.0312713\pi$
$972$	1.46656	−	1.35986i	0.0470398	−	0.0436175i
$973$	40.8907	+	8.13367i	1.31090	+	0.260754i
$974$	−9.71531	−	8.28475i	−0.311299	−	0.265461i
$975$	7.43877	−	7.43877i	0.238231	−	0.238231i
$976$	11.1232	+	8.71348i	0.356044	+	0.278912i
$977$	−1.63856	−	1.63856i	−0.0524223	−	0.0524223i	0.680410	−	0.732832i	$-0.261802\pi$
$977$	−1.63856	−	1.63856i	−0.0524223	−	0.0524223i	−0.732832	+	0.680410i	$0.761802\pi$
$978$	−0.125303	−	1.57663i	−0.00400676	−	0.0504152i
$979$	7.95550	−	39.9950i	0.254259	−	1.27825i
$980$	1.15164	+	3.10693i	0.0367877	+	0.0992473i
$981$	−5.84950	−	3.90851i	−0.186760	−	0.124789i
$982$	−2.23882	+	19.0411i	−0.0714437	+	0.607626i
$983$	−38.2444	−	15.8413i	−1.21981	−	0.505260i	−0.322458	−	0.946584i	$-0.604509\pi$
$983$	−38.2444	−	15.8413i	−1.21981	−	0.505260i	−0.897348	+	0.441324i	$0.854509\pi$
$984$	13.6180	−	0.566508i	0.434127	−	0.0180596i
$985$	17.8266	−	7.38403i	0.568003	−	0.235275i
$986$	12.1927	−	3.44881i	0.388294	−	0.109832i
$987$	2.13573	+	10.7370i	0.0679809	+	0.341763i
$988$	8.49753	+	13.8190i	0.270342	+	0.439640i
$989$	5.55376	+	8.31178i	0.176599	+	0.264299i
$990$	−2.51469	+	7.75970i	−0.0799220	+	0.246620i
$991$			37.4986i			1.19118i	0.803288	+	0.595591i	$0.203082\pi$
$991$			37.4986i			1.19118i	−0.803288	+	0.595591i	$0.796918\pi$
$992$	13.0151	+	12.9155i	0.413231	+	0.410067i
$993$			21.2044i			0.672902i
$994$	45.0088	+	14.5860i	1.42759	+	0.462640i
$995$	−11.4824	−	17.1846i	−0.364016	−	0.544788i
$996$	−5.34395	−	1.27428i	−0.169329	−	0.0403772i
$997$	−1.99642	−	10.0367i	−0.0632271	−	0.317864i	0.936209	−	0.351444i	$-0.114309\pi$
$997$	−1.99642	−	10.0367i	−0.0632271	−	0.317864i	−0.999436	+	0.0335797i	$0.989309\pi$
$998$	2.83610	+	10.0265i	0.0897751	+	0.317385i
$999$	7.41098	−	3.06973i	0.234473	−	0.0971219i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.2.r.a.13.7	✓	128
3.2	odd	2		576.2.bd.b.397.10		128
4.3	odd	2		768.2.r.a.145.5		128
64.5	even	16	inner	192.2.r.a.133.7	yes	128
64.59	odd	16		768.2.r.a.625.5		128
192.5	odd	16		576.2.bd.b.325.10		128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
192.2.r.a.13.7	✓	128	1.1	even	1	trivial
192.2.r.a.133.7	yes	128	64.5	even	16	inner
576.2.bd.b.325.10		128	192.5	odd	16
576.2.bd.b.397.10		128	3.2	odd	2
768.2.r.a.145.5		128	4.3	odd	2
768.2.r.a.625.5		128	64.59	odd	16

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:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	192.r (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.643008 - 1.25958i) q^{2} +(0.831470 - 0.555570i) q^{3} +(-1.17308 + 1.61984i) q^{4} +(1.10082 - 0.218966i) q^{5} +(-1.23443 - 0.690066i) q^{6} +(-0.899420 - 2.17139i) q^{7} +(2.79462 + 0.436020i) q^{8} +(0.382683 - 0.923880i) q^{9} +O(q^{10})\)	\(q+(-0.643008 - 1.25958i) q^{2} +(0.831470 - 0.555570i) q^{3} +(-1.17308 + 1.61984i) q^{4} +(1.10082 - 0.218966i) q^{5} +(-1.23443 - 0.690066i) q^{6} +(-0.899420 - 2.17139i) q^{7} +(2.79462 + 0.436020i) q^{8} +(0.382683 - 0.923880i) q^{9} +(-0.983641 - 1.24577i) q^{10} +(2.85504 - 4.27287i) q^{11} +(-0.0754472 + 1.99858i) q^{12} +(-2.75860 - 0.548720i) q^{13} +(-2.15671 + 2.52911i) q^{14} +(0.793646 - 0.793646i) q^{15} +(-1.24776 - 3.80041i) q^{16} +(2.30407 + 2.30407i) q^{17} +(-1.40977 + 0.112042i) q^{18} +(-0.562614 + 2.82845i) q^{19} +(-0.936659 + 2.04001i) q^{20} +(-1.95420 - 1.30576i) q^{21} +(-7.21784 - 0.848662i) q^{22} +(0.814910 + 0.337547i) q^{23} +(2.56588 - 1.19007i) q^{24} +(-3.45554 + 1.43133i) q^{25} +(1.08265 + 3.82751i) q^{26} +(-0.195090 - 0.980785i) q^{27} +(4.57240 + 1.09030i) q^{28} +(1.52765 + 2.28630i) q^{29} +(-1.50998 - 0.489340i) q^{30} -3.24135i q^{31} +(-3.98460 + 4.01534i) q^{32} -5.13894i q^{33} +(1.42063 - 4.38370i) q^{34} +(-1.46556 - 2.19337i) q^{35} +(1.04762 + 1.70367i) q^{36} +(1.56493 + 7.86745i) q^{37} +(3.92443 - 1.11006i) q^{38} +(-2.59855 + 1.07635i) q^{39} +(3.17184 - 0.131948i) q^{40} +(4.45205 + 1.84410i) q^{41} +(-0.388136 + 3.30108i) q^{42} +(9.42323 + 6.29640i) q^{43} +(3.57217 + 9.63714i) q^{44} +(0.218966 - 1.10082i) q^{45} +(-0.0988266 - 1.24349i) q^{46} +(-3.29361 - 3.29361i) q^{47} +(-3.14887 - 2.46671i) q^{48} +(1.04376 - 1.04376i) q^{49} +(4.02482 + 3.43217i) q^{50} +(3.19584 + 0.635693i) q^{51} +(4.12490 - 3.82480i) q^{52} +(-7.30356 + 10.9305i) q^{53} +(-1.10993 + 0.876384i) q^{54} +(2.20727 - 5.32882i) q^{55} +(-1.56676 - 6.46038i) q^{56} +(1.10361 + 2.66434i) q^{57} +(1.89748 - 3.39431i) q^{58} +(11.9601 - 2.37900i) q^{59} +(0.354567 + 2.21659i) q^{60} +(-2.93711 + 1.96252i) q^{61} +(-4.08274 + 2.08421i) q^{62} -2.35030 q^{63} +(7.61977 + 2.43702i) q^{64} -3.15687 q^{65} +(-6.47291 + 3.30438i) q^{66} +(-8.01120 + 5.35291i) q^{67} +(-6.43510 + 1.02936i) q^{68} +(0.865104 - 0.172080i) q^{69} +(-1.82035 + 3.25634i) q^{70} +(-5.44734 - 13.1510i) q^{71} +(1.47228 - 2.41503i) q^{72} +(-3.71675 + 8.97304i) q^{73} +(8.90342 - 7.02999i) q^{74} +(-2.07797 + 3.10991i) q^{75} +(-3.92165 - 4.22935i) q^{76} +(-11.8460 - 2.35631i) q^{77} +(3.02664 + 2.58097i) q^{78} +(-4.99132 + 4.99132i) q^{79} +(-2.20572 - 3.91034i) q^{80} +(-0.707107 - 0.707107i) q^{81} +(-0.539913 - 6.79348i) q^{82} +(-0.535891 + 2.69411i) q^{83} +(4.40755 - 1.63373i) q^{84} +(3.04088 + 2.03185i) q^{85} +(1.87161 - 15.9179i) q^{86} +(2.54040 + 1.05227i) q^{87} +(9.84181 - 10.6962i) q^{88} +(7.33117 - 3.03667i) q^{89} +(-1.52737 + 0.432029i) q^{90} +(1.28966 + 6.48354i) q^{91} +(-1.50273 + 0.924054i) q^{92} +(-1.80080 - 2.69509i) q^{93} +(-2.03074 + 6.26638i) q^{94} +3.23681i q^{95} +(-1.08227 + 5.55236i) q^{96} -17.2593i q^{97} +(-1.98584 - 0.643553i) q^{98} +(-2.85504 - 4.27287i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q - 16 q^{22} - 80 q^{26} - 80 q^{28} - 80 q^{32} - 80 q^{34} - 80 q^{38} - 80 q^{40} - 16 q^{44} + 48 q^{50} - 32 q^{51} + 48 q^{52} + 16 q^{54} - 64 q^{55} + 112 q^{56} - 128 q^{59} + 96 q^{60} + 96 q^{62} - 32 q^{63} + 96 q^{64} + 96 q^{66} - 32 q^{67} + 96 q^{68} + 96 q^{70} - 128 q^{71} + 112 q^{74} - 64 q^{75} + 16 q^{76} + 48 q^{78} - 32 q^{79} + 48 q^{80} - 80 q^{82} - 80 q^{88} - 96 q^{94}+O(q^{100}) \) 128 * q - 16 * q^22 - 80 * q^26 - 80 * q^28 - 80 * q^32 - 80 * q^34 - 80 * q^38 - 80 * q^40 - 16 * q^44 + 48 * q^50 - 32 * q^51 + 48 * q^52 + 16 * q^54 - 64 * q^55 + 112 * q^56 - 128 * q^59 + 96 * q^60 + 96 * q^62 - 32 * q^63 + 96 * q^64 + 96 * q^66 - 32 * q^67 + 96 * q^68 + 96 * q^70 - 128 * q^71 + 112 * q^74 - 64 * q^75 + 16 * q^76 + 48 * q^78 - 32 * q^79 + 48 * q^80 - 80 * q^82 - 80 * q^88 - 96 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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