LMFDB - Embedded newform 192.2.r.a.181.2

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			181.2
Character	$\chi$	$=$	192.181
Dual form			192.2.r.a.157.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38576 - 0.282266i) q^{2} +(-0.980785 + 0.195090i) q^{3} +(1.84065 + 0.782304i) q^{4} +(2.00072 + 2.99429i) q^{5} +(1.41420 + 0.00649411i) q^{6} +(-3.93986 - 1.63194i) q^{7} +(-2.32988 - 1.60364i) q^{8} +(0.923880 - 0.382683i) q^{9} +O(q^{10})$	\(q+(-1.38576 - 0.282266i) q^{2} +(-0.980785 + 0.195090i) q^{3} +(1.84065 + 0.782304i) q^{4} +(2.00072 + 2.99429i) q^{5} +(1.41420 + 0.00649411i) q^{6} +(-3.93986 - 1.63194i) q^{7} +(-2.32988 - 1.60364i) q^{8} +(0.923880 - 0.382683i) q^{9} +(-1.92733 - 4.71410i) q^{10} +(-0.787083 + 3.95693i) q^{11} +(-1.95790 - 0.408179i) q^{12} +(-0.507984 + 0.760252i) q^{13} +(4.99905 + 3.37356i) q^{14} +(-2.54643 - 2.54643i) q^{15} +(2.77600 + 2.87990i) q^{16} +(-3.70628 + 3.70628i) q^{17} +(-1.38829 + 0.269527i) q^{18} +(1.20422 + 0.804632i) q^{19} +(1.34018 + 7.07662i) q^{20} +(4.18253 + 0.831957i) q^{21} +(2.20761 - 5.26119i) q^{22} +(2.69871 + 6.51527i) q^{23} +(2.59797 + 1.11829i) q^{24} +(-3.04947 + 7.36208i) q^{25} +(0.918536 - 0.910139i) q^{26} +(-0.831470 + 0.555570i) q^{27} +(-5.97523 - 6.08601i) q^{28} +(-1.13604 - 5.71125i) q^{29} +(2.80997 + 4.24751i) q^{30} -2.46811i q^{31} +(-3.03397 - 4.77442i) q^{32} -4.03446i q^{33} +(6.18216 - 4.08985i) q^{34} +(-2.99605 - 15.0621i) q^{35} +(1.99992 + 0.0183679i) q^{36} +(-3.29940 + 2.20459i) q^{37} +(-1.44163 - 1.45493i) q^{38} +(0.349906 - 0.844747i) q^{39} +(0.140316 - 10.1848i) q^{40} +(0.457544 + 1.10461i) q^{41} +(-5.56114 - 2.33348i) q^{42} +(6.68723 + 1.33017i) q^{43} +(-4.54427 + 6.66760i) q^{44} +(2.99429 + 2.00072i) q^{45} +(-1.90073 - 9.79034i) q^{46} +(2.46296 - 2.46296i) q^{47} +(-3.28450 - 2.28299i) q^{48} +(7.90949 + 7.90949i) q^{49} +(6.30390 - 9.34130i) q^{50} +(2.91200 - 4.35812i) q^{51} +(-1.52977 + 1.00196i) q^{52} +(1.69490 - 8.52084i) q^{53} +(1.30903 - 0.535191i) q^{54} +(-13.4229 + 5.55996i) q^{55} +(6.56235 + 10.1203i) q^{56} +(-1.33805 - 0.554240i) q^{57} +(-0.0378162 + 8.23508i) q^{58} +(3.49136 + 5.22519i) q^{59} +(-2.69501 - 6.67919i) q^{60} +(8.64534 - 1.71967i) q^{61} +(-0.696662 + 3.42020i) q^{62} -4.26447 q^{63} +(2.85669 + 7.47257i) q^{64} -3.29275 q^{65} +(-1.13879 + 5.59078i) q^{66} +(0.326267 - 0.0648985i) q^{67} +(-9.72141 + 3.92253i) q^{68} +(-3.91792 - 5.86359i) q^{69} +(-0.0997315 + 21.7182i) q^{70} +(-10.0335 - 4.15601i) q^{71} +(-2.76622 - 0.589961i) q^{72} +(12.5504 - 5.19854i) q^{73} +(5.19445 - 2.12372i) q^{74} +(1.55461 - 7.81554i) q^{75} +(1.58708 + 2.42311i) q^{76} +(9.55848 - 14.3053i) q^{77} +(-0.723328 + 1.07185i) q^{78} +(-3.74185 - 3.74185i) q^{79} +(-3.06926 + 14.0740i) q^{80} +(0.707107 - 0.707107i) q^{81} +(-0.322252 - 1.65987i) q^{82} +(4.11429 + 2.74908i) q^{83} +(7.04774 + 4.80335i) q^{84} +(-18.5129 - 3.68244i) q^{85} +(-8.89143 - 3.73088i) q^{86} +(2.22842 + 5.37988i) q^{87} +(8.17930 - 7.95699i) q^{88} +(-2.28974 + 5.52793i) q^{89} +(-3.58463 - 3.61770i) q^{90} +(3.24207 - 2.16628i) q^{91} +(-0.129532 + 14.1036i) q^{92} +(0.481504 + 2.42068i) q^{93} +(-4.10828 + 2.71786i) q^{94} +5.21562i q^{95} +(3.90711 + 4.09078i) q^{96} -0.186301i q^{97} +(-8.72806 - 13.1932i) q^{98} +(0.787083 + 3.95693i) 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 $\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$133$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{16}\right)$

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 $

$2$	−1.38576	−	0.282266i	−0.979879	−	0.199592i
$2$	−1.38576	−	0.282266i	−0.979879	−	0.199592i
$3$	−0.980785	+	0.195090i	−0.566257	+	0.112635i
$3$	−0.980785	+	0.195090i	−0.566257	+	0.112635i
$4$	1.84065	+	0.782304i	0.920326	+	0.391152i
$5$	2.00072	+	2.99429i	0.894750	+	1.33909i	0.940379	+	0.340129i	$0.110471\pi$
$5$	2.00072	+	2.99429i	0.894750	+	1.33909i	−0.0456293	+	0.998958i	$0.514529\pi$
$6$	1.41420	+	0.00649411i	0.577344	+	0.00265121i
$7$	−3.93986	−	1.63194i	−1.48913	−	0.616816i	−0.517999	−	0.855381i	$-0.673323\pi$
$7$	−3.93986	−	1.63194i	−1.48913	−	0.616816i	−0.971127	+	0.238565i	$0.923323\pi$
$8$	−2.32988	−	1.60364i	−0.823737	−	0.566972i
$9$	0.923880	−	0.382683i	0.307960	−	0.127561i
$10$	−1.92733	−	4.71410i	−0.609475	−	1.49073i
$11$	−0.787083	+	3.95693i	−0.237315	+	1.19306i	0.659861	+	0.751387i	$0.270615\pi$
$11$	−0.787083	+	3.95693i	−0.237315	+	1.19306i	−0.897176	+	0.441673i	$0.854385\pi$
$12$	−1.95790	−	0.408179i	−0.565198	−	0.117831i
$13$	−0.507984	+	0.760252i	−0.140889	+	0.210856i	−0.895203	−	0.445658i	$-0.852970\pi$
$13$	−0.507984	+	0.760252i	−0.140889	+	0.210856i	0.754314	+	0.656514i	$0.227970\pi$
$14$	4.99905	+	3.37356i	1.33605	+	0.901623i
$15$	−2.54643	−	2.54643i	−0.657487	−	0.657487i
$16$	2.77600	+	2.87990i	0.694000	+	0.719975i
$17$	−3.70628	+	3.70628i	−0.898904	+	0.898904i	−0.995339	−	0.0964348i	$-0.969256\pi$
$17$	−3.70628	+	3.70628i	−0.898904	+	0.898904i	0.0964348	+	0.995339i	$0.469256\pi$
$18$	−1.38829	+	0.269527i	−0.327224	+	0.0635282i
$19$	1.20422	+	0.804632i	0.276266	+	0.184595i	0.685983	−	0.727618i	$-0.259372\pi$
$19$	1.20422	+	0.804632i	0.276266	+	0.184595i	−0.409717	+	0.912213i	$0.634372\pi$
$20$	1.34018	+	7.07662i	0.299674	+	1.58238i
$21$	4.18253	+	0.831957i	0.912703	+	0.181548i
$22$	2.20761	−	5.26119i	0.470665	−	1.12169i
$23$	2.69871	+	6.51527i	0.562720	+	1.35853i	0.907582	+	0.419874i	$0.137926\pi$
$23$	2.69871	+	6.51527i	0.562720	+	1.35853i	−0.344862	+	0.938653i	$0.612074\pi$
$24$	2.59797	+	1.11829i	0.530308	+	0.228269i
$25$	−3.04947	+	7.36208i	−0.609895	+	1.47242i
$26$	0.918536	−	0.910139i	0.180140	−	0.178493i
$27$	−0.831470	+	0.555570i	−0.160016	+	0.106920i
$28$	−5.97523	−	6.08601i	−1.12921	−	1.15015i
$29$	−1.13604	−	5.71125i	−0.210957	−	1.06055i	−0.930552	−	0.366159i	$-0.880673\pi$
$29$	−1.13604	−	5.71125i	−0.210957	−	1.06055i	0.719595	−	0.694394i	$-0.244327\pi$
$30$	2.80997	+	4.24751i	0.513028	+	0.775486i
$31$		−	2.46811i		−	0.443285i	−0.975128	−	0.221642i	$-0.928858\pi$
$31$		−	2.46811i		−	0.443285i	0.975128	−	0.221642i	$-0.0711418\pi$
$32$	−3.03397	−	4.77442i	−0.536335	−	0.844005i
$33$		−	4.03446i		−	0.702308i
$34$	6.18216	−	4.08985i	1.06023	−	0.701403i
$35$	−2.99605	−	15.0621i	−0.506424	−	2.54597i
$36$	1.99992	+	0.0183679i	0.333319	+	0.00306132i
$37$	−3.29940	+	2.20459i	−0.542418	+	0.362432i	−0.796394	−	0.604778i	$-0.793262\pi$
$37$	−3.29940	+	2.20459i	−0.542418	+	0.362432i	0.253976	+	0.967211i	$0.418262\pi$
$38$	−1.44163	−	1.45493i	−0.233864	−	0.236022i
$39$	0.349906	−	0.844747i	0.0560297	−	0.135268i
$40$	0.140316	−	10.1848i	0.0221859	−	1.61035i
$41$	0.457544	+	1.10461i	0.0714563	+	0.172511i	0.955572	−	0.294757i	$-0.0952386\pi$
$41$	0.457544	+	1.10461i	0.0714563	+	0.172511i	−0.884116	+	0.467267i	$0.845239\pi$
$42$	−5.56114	−	2.33348i	−0.858103	−	0.360063i
$43$	6.68723	+	1.33017i	1.01979	+	0.202850i	0.676550	−	0.736397i	$-0.263474\pi$
$43$	6.68723	+	1.33017i	1.01979	+	0.202850i	0.343244	+	0.939246i	$0.388474\pi$
$44$	−4.54427	+	6.66760i	−0.685075	+	1.00518i
$45$	2.99429	+	2.00072i	0.446362	+	0.298250i
$46$	−1.90073	−	9.79034i	−0.280247	−	1.44351i
$47$	2.46296	−	2.46296i	0.359260	−	0.359260i	−0.504280	−	0.863540i	$-0.668242\pi$
$47$	2.46296	−	2.46296i	0.359260	−	0.359260i	0.863540	+	0.504280i	$0.168242\pi$
$48$	−3.28450	−	2.28299i	−0.474077	−	0.329522i
$49$	7.90949	+	7.90949i	1.12993	+	1.12993i
$50$	6.30390	−	9.34130i	0.891505	−	1.32106i
$51$	2.91200	−	4.35812i	0.407762	−	0.610259i
$52$	−1.52977	+	1.00196i	−0.212141	+	0.138947i
$53$	1.69490	−	8.52084i	0.232812	−	1.17043i	−0.670655	−	0.741770i	$-0.733987\pi$
$53$	1.69490	−	8.52084i	0.232812	−	1.17043i	0.903467	−	0.428657i	$-0.141013\pi$
$54$	1.30903	−	0.535191i	0.178137	−	0.0728302i
$55$	−13.4229	+	5.55996i	−1.80995	+	0.749706i
$56$	6.56235	+	10.1203i	0.876931	+	1.35239i
$57$	−1.33805	−	0.554240i	−0.177230	−	0.0734109i
$58$	−0.0378162	+	8.23508i	−0.00496551	+	1.08132i
$59$	3.49136	+	5.22519i	0.454537	+	0.680262i	0.985986	−	0.166828i	$-0.0533524\pi$
$59$	3.49136	+	5.22519i	0.454537	+	0.680262i	−0.531449	+	0.847090i	$0.678352\pi$
$60$	−2.69501	−	6.67919i	−0.347925	−	0.862279i
$61$	8.64534	−	1.71967i	1.10692	−	0.220181i	0.392401	−	0.919794i	$-0.371645\pi$
$61$	8.64534	−	1.71967i	1.10692	−	0.220181i	0.714521	+	0.699614i	$0.246645\pi$
$62$	−0.696662	+	3.42020i	−0.0884762	+	0.434366i
$63$	−4.26447			−0.537273
$64$	2.85669	+	7.47257i	0.357086	+	0.934071i
$65$	−3.29275			−0.408415
$66$	−1.13879	+	5.59078i	−0.140175	+	0.688177i
$67$	0.326267	−	0.0648985i	0.0398598	−	0.00792861i	−0.175120	−	0.984547i	$-0.556031\pi$
$67$	0.326267	−	0.0648985i	0.0398598	−	0.00792861i	0.214980	+	0.976618i	$0.431031\pi$
$68$	−9.72141	+	3.92253i	−1.17889	+	0.475677i
$69$	−3.91792	−	5.86359i	−0.471662	−	0.705893i
$70$	−0.0997315	+	21.7182i	−0.0119202	+	2.59582i
$71$	−10.0335	−	4.15601i	−1.19076	−	0.493228i	−0.302755	−	0.953068i	$-0.597906\pi$
$71$	−10.0335	−	4.15601i	−1.19076	−	0.493228i	−0.888001	+	0.459841i	$0.847906\pi$
$72$	−2.76622	−	0.589961i	−0.326002	−	0.0695276i
$73$	12.5504	−	5.19854i	1.46891	−	0.608443i	0.502301	−	0.864693i	$-0.332487\pi$
$73$	12.5504	−	5.19854i	1.46891	−	0.608443i	0.966611	+	0.256249i	$0.0824868\pi$
$74$	5.19445	−	2.12372i	0.603843	−	0.246877i
$75$	1.55461	−	7.81554i	0.179511	−	0.902461i
$76$	1.58708	+	2.42311i	0.182050	+	0.277950i
$77$	9.55848	−	14.3053i	1.08929	−	1.63024i
$78$	−0.723328	+	1.07185i	−0.0819007	+	0.121363i
$79$	−3.74185	−	3.74185i	−0.420992	−	0.420992i	0.464553	−	0.885545i	$-0.346215\pi$
$79$	−3.74185	−	3.74185i	−0.420992	−	0.420992i	−0.885545	+	0.464553i	$0.846215\pi$
$80$	−3.06926	+	14.0740i	−0.343153	+	1.57352i
$81$	0.707107	−	0.707107i	0.0785674	−	0.0785674i
$82$	−0.322252	−	1.65987i	−0.0355868	−	0.183302i
$83$	4.11429	+	2.74908i	0.451602	+	0.301751i	0.760492	−	0.649347i	$-0.224958\pi$
$83$	4.11429	+	2.74908i	0.451602	+	0.301751i	−0.308891	+	0.951098i	$0.599958\pi$
$84$	7.04774	+	4.80335i	0.768971	+	0.524089i
$85$	−18.5129	−	3.68244i	−2.00801	−	0.399417i
$86$	−8.89143	−	3.73088i	−0.958787	−	0.402311i
$87$	2.22842	+	5.37988i	0.238912	+	0.576784i
$88$	8.17930	−	7.95699i	0.871916	−	0.848218i
$89$	−2.28974	+	5.52793i	−0.242712	+	0.585959i	−0.997550	−	0.0699521i	$-0.977715\pi$
$89$	−2.28974	+	5.52793i	−0.242712	+	0.585959i	0.754838	+	0.655911i	$0.227715\pi$
$90$	−3.58463	−	3.61770i	−0.377853	−	0.381339i
$91$	3.24207	−	2.16628i	0.339862	−	0.227088i
$92$	−0.129532	+	14.1036i	−0.0135046	+	1.47040i
$93$	0.481504	+	2.42068i	0.0499296	+	0.251013i
$94$	−4.10828	+	2.71786i	−0.423737	+	0.280326i
$95$			5.21562i			0.535111i
$96$	3.90711	+	4.09078i	0.398768	+	0.417513i
$97$		−	0.186301i		−	0.0189160i	−0.999955	−	0.00945798i	$-0.996989\pi$
$97$		−	0.186301i		−	0.0189160i	0.999955	−	0.00945798i	$-0.00301061\pi$
$98$	−8.72806	−	13.1932i	−0.881668	−	1.33272i
$99$	0.787083	+	3.95693i	0.0791048	+	0.397687i
$100$	−11.3724	+	11.1654i	−1.13724	+	1.11654i
$101$	−8.59008	+	5.73971i	−0.854745	+	0.571122i	−0.903936	−	0.427667i	$-0.859335\pi$
$101$	−8.59008	+	5.73971i	−0.854745	+	0.571122i	0.0491917	+	0.998789i	$0.484335\pi$
$102$	−5.26548	+	5.21734i	−0.521360	+	0.516594i
$103$	1.74997	−	4.22480i	0.172430	−	0.416282i	−0.813913	−	0.580986i	$-0.802667\pi$
$103$	1.74997	−	4.22480i	0.172430	−	0.416282i	0.986343	+	0.164704i	$0.0526670\pi$
$104$	2.40271	−	0.956674i	0.235605	−	0.0938096i
$105$	5.87695	+	14.1882i	0.573532	+	1.38463i
$106$	−4.75386	+	11.3294i	−0.461736	+	1.10041i
$107$	16.6536	+	3.31261i	1.60996	+	0.320242i	0.916434	−	0.400186i	$-0.131054\pi$
$107$	16.6536	+	3.31261i	1.60996	+	0.320242i	0.693530	+	0.720427i	$0.256054\pi$
$108$	−1.96507	+	0.372149i	−0.189089	+	0.0358101i
$109$	8.24468	+	5.50892i	0.789697	+	0.527659i	0.883778	−	0.467906i	$-0.154991\pi$
$109$	8.24468	+	5.50892i	0.789697	+	0.527659i	−0.0940813	+	0.995565i	$0.529991\pi$
$110$	20.1703	−	3.91593i	1.92317	−	0.373369i
$111$	2.80591	−	2.80591i	0.266325	−	0.266325i
$112$	−6.23721	−	15.8767i	−0.589361	−	1.50020i
$113$	0.0137915	+	0.0137915i	0.00129740	+	0.00129740i	0.707755	−	0.706458i	$-0.249708\pi$
$113$	0.0137915	+	0.0137915i	0.00129740	+	0.00129740i	−0.706458	+	0.707755i	$0.749708\pi$
$114$	1.69778	+	1.14573i	0.159011	+	0.107307i
$115$	−14.1092	+	21.1160i	−1.31569	+	1.96907i
$116$	2.37689	−	11.4012i	0.220688	−	1.05857i
$117$	−0.178380	+	0.896778i	−0.0164913	+	0.0829072i
$118$	−3.36329	−	8.22635i	−0.309616	−	0.757297i
$119$	20.6506	−	8.55377i	1.89304	−	0.784123i
$120$	1.84933	+	10.0164i	0.168820	+	0.914372i
$121$	−4.87515	−	2.01935i	−0.443196	−	0.183578i
$122$	−12.4658	−	0.0572437i	−1.12860	−	0.00518260i
$123$	−0.664250	−	0.994121i	−0.0598934	−	0.0896369i
$124$	1.93081	−	4.54292i	0.173392	−	0.407967i
$125$	−10.4853	+	2.08566i	−0.937835	+	0.186547i
$126$	5.90953	+	1.20371i	0.526462	+	0.107235i
$127$	2.66259			0.236267			0.118134	−	0.992998i	$-0.462309\pi$
$127$	2.66259			0.236267			0.118134	+	0.992998i	$0.462309\pi$
$128$	−1.84943	−	11.1615i	−0.163468	−	0.986549i
$129$	−6.81824			−0.600313
$130$	4.56295	+	0.929431i	0.400198	+	0.0815164i
$131$	2.06604	−	0.410961i	0.180511	−	0.0359058i	−0.104007	−	0.994577i	$-0.533166\pi$
$131$	2.06604	−	0.410961i	0.180511	−	0.0359058i	0.284518	+	0.958671i	$0.408166\pi$
$132$	3.15617	−	7.42603i	0.274709	−	0.646353i
$133$	−3.43133	−	5.13535i	−0.297534	−	0.445291i
$134$	−0.470445	−	0.00216032i	−0.0406403	−	0.000186623i
$135$	−3.32708	−	1.37812i	−0.286349	−	0.118610i
$136$	14.5787	−	2.69166i	1.25011	−	0.230808i
$137$	−13.0962	+	5.42463i	−1.11889	+	0.463457i	−0.863989	−	0.503511i	$-0.832041\pi$
$137$	−13.0962	+	5.42463i	−1.11889	+	0.463457i	−0.254896	+	0.966968i	$0.582041\pi$
$138$	3.77420	+	9.23141i	0.321282	+	0.785830i
$139$	−2.62933	+	13.2185i	−0.223016	+	1.12118i	0.693277	+	0.720671i	$0.256166\pi$
$139$	−2.62933	+	13.2185i	−0.223016	+	1.12118i	−0.916293	+	0.400508i	$0.868834\pi$
$140$	6.26850	−	30.0680i	0.529785	−	2.54121i
$141$	−1.93514	+	2.89614i	−0.162968	+	0.243899i
$142$	12.7309	+	8.59134i	1.06835	+	0.720969i
$143$	−2.60844	−	2.60844i	−0.218129	−	0.218129i
$144$	3.66678	+	1.59835i	0.305565	+	0.133196i
$145$	14.8283	−	14.8283i	1.23142	−	1.23142i
$146$	−18.8592	+	3.66138i	−1.56080	+	0.303018i
$147$	−9.30058	−	6.21445i	−0.767099	−	0.512559i
$148$	−7.79771	+	1.47675i	−0.640968	+	0.121388i
$149$	−10.4120	−	2.07108i	−0.852984	−	0.169669i	−0.250813	−	0.968036i	$-0.580698\pi$
$149$	−10.4120	−	2.07108i	−0.852984	−	0.169669i	−0.602172	+	0.798367i	$0.705698\pi$
$150$	−4.36037	+	10.3916i	−0.356023	+	0.848474i
$151$	−5.53145	−	13.3541i	−0.450143	−	1.08674i	−0.972267	−	0.233872i	$-0.924860\pi$
$151$	−5.53145	−	13.3541i	−0.450143	−	1.08674i	0.522125	−	0.852869i	$-0.325140\pi$
$152$	−1.51534	−	3.80582i	−0.122911	−	0.308693i
$153$	−2.00582	+	4.84249i	−0.162161	+	0.391492i
$154$	−17.2836	+	17.1256i	−1.39276	+	1.38002i
$155$	7.39023	−	4.93799i	0.593597	−	0.396629i
$156$	1.30490	−	1.28115i	0.104476	−	0.102574i
$157$	−1.55492	−	7.81711i	−0.124096	−	0.623873i	−0.991906	−	0.126977i	$-0.959473\pi$
$157$	−1.55492	−	7.81711i	−0.124096	−	0.623873i	0.867810	−	0.496897i	$-0.165527\pi$
$158$	4.12911	+	6.24150i	0.328494	+	0.496547i
$159$			8.68777i			0.688985i
$160$	8.22586	−	18.6369i	0.650312	−	1.47337i
$161$		−	30.0734i		−	2.37011i
$162$	−1.17947	+	0.780287i	−0.0926680	+	0.0613051i
$163$	1.45059	+	7.29259i	0.113619	+	0.571200i	0.995091	+	0.0989642i	$0.0315529\pi$
$163$	1.45059	+	7.29259i	0.113619	+	0.571200i	−0.881472	+	0.472236i	$0.843447\pi$
$164$	−0.0219611	+	2.39114i	−0.00171487	+	0.186716i
$165$	12.0803	−	8.07182i	0.940452	−	0.628390i
$166$	−4.92544	−	4.97088i	−0.382288	−	0.385815i
$167$	−7.29027	+	17.6003i	−0.564138	+	1.36195i	0.342292	+	0.939594i	$0.388797\pi$
$167$	−7.29027	+	17.6003i	−0.564138	+	1.36195i	−0.906430	+	0.422356i	$0.861203\pi$
$168$	−8.41064	−	8.64562i	−0.648895	−	0.667024i
$169$	4.65495	+	11.2380i	0.358073	+	0.864465i
$170$	24.6150	+	10.3285i	1.88788	+	0.792163i
$171$	1.42047	+	0.282549i	0.108626	+	0.0216071i
$172$	11.2683	+	7.67984i	0.859198	+	0.585582i
$173$	15.1191	+	10.1023i	1.14948	+	0.768061i	0.976213	−	0.216813i	$-0.0695663\pi$
$173$	15.1191	+	10.1023i	1.14948	+	0.768061i	0.173271	+	0.984874i	$0.444566\pi$
$174$	−1.56950	−	8.08423i	−0.118983	−	0.612864i
$175$	24.0290	−	24.0290i	1.81642	−	1.81642i
$176$	−13.5805	+	8.71773i	−1.02367	+	0.657123i
$177$	−4.44366	−	4.44366i	−0.334006	−	0.334006i
$178$	4.73337	−	7.01405i	0.354781	−	0.525726i
$179$	7.52202	−	11.2575i	0.562223	−	0.841425i	−0.436066	−	0.899915i	$-0.643628\pi$
$179$	7.52202	−	11.2575i	0.562223	−	0.841425i	0.998288	+	0.0584895i	$0.0186284\pi$
$180$	3.94627	+	6.02508i	0.294138	+	0.449083i
$181$	−3.75633	+	18.8844i	−0.279206	+	1.40366i	0.545505	+	0.838108i	$0.316338\pi$
$181$	−3.75633	+	18.8844i	−0.279206	+	1.40366i	−0.824711	+	0.565555i	$0.808662\pi$
$182$	−5.10420	+	2.08682i	−0.378348	+	0.154685i
$183$	−8.14373	+	3.37324i	−0.602002	+	0.249357i
$184$	4.16045	−	19.5076i	0.306713	−	1.43812i
$185$	−13.2024	−	5.46860i	−0.970657	−	0.402059i
$186$	0.0160282	−	3.49039i	0.00117524	−	0.255928i
$187$	−11.7483	−	17.5826i	−0.859124	−	1.28577i
$188$	6.46024	−	2.60667i	0.471161	−	0.190111i
$189$	4.18253	−	0.831957i	0.304234	−	0.0605160i
$190$	1.47219	−	7.22759i	0.106804	−	0.524344i
$191$	−2.64758			−0.191572			−0.0957860	−	0.995402i	$-0.530536\pi$
$191$	−2.64758			−0.191572			−0.0957860	+	0.995402i	$0.530536\pi$
$192$	−4.25963	−	6.77167i	−0.307412	−	0.488704i
$193$	−20.0210			−1.44114			−0.720570	−	0.693382i	$-0.756120\pi$
$193$	−20.0210			−1.44114			−0.720570	+	0.693382i	$0.756120\pi$
$194$	−0.0525863	+	0.258168i	−0.00377548	+	0.0185354i
$195$	3.22948	−	0.642384i	0.231268	−	0.0460020i
$196$	8.37099	+	20.7463i	0.597928	+	1.48188i
$197$	−7.08646	−	10.6056i	−0.504889	−	0.755620i	0.488232	−	0.872714i	$-0.337642\pi$
$197$	−7.08646	−	10.6056i	−0.504889	−	0.755620i	−0.993121	+	0.117094i	$0.962642\pi$
$198$	0.0262002	−	5.70552i	0.00186197	−	0.405474i
$199$	16.2036	+	6.71174i	1.14864	+	0.475783i	0.874078	−	0.485786i	$-0.161467\pi$
$199$	16.2036	+	6.71174i	1.14864	+	0.475783i	0.274564	+	0.961569i	$0.411467\pi$
$200$	18.9110	−	12.2625i	1.33721	−	0.867091i
$201$	−0.307336	+	0.127303i	−0.0216778	+	0.00897926i
$202$	13.5239	−	5.52916i	0.951538	−	0.389030i
$203$	−4.84461	+	24.3555i	−0.340025	+	1.70942i
$204$	8.76936	−	5.74371i	0.613978	−	0.402140i
$205$	−2.39210	+	3.58003i	−0.167072	+	0.250040i
$206$	−3.61755	+	5.36060i	−0.252047	+	0.373491i
$207$	4.98657	+	4.98657i	0.346591	+	0.346591i
$208$	−3.59961	+	0.647516i	−0.249588	+	0.0448971i
$209$	−4.13169	+	4.13169i	−0.285795	+	0.285795i
$210$	−4.13919	−	21.3203i	−0.285631	−	1.47124i
$211$	−4.81268	−	3.21573i	−0.331319	−	0.221380i	0.378773	−	0.925490i	$-0.376346\pi$
$211$	−4.81268	−	3.21573i	−0.331319	−	0.221380i	−0.710091	+	0.704110i	$0.751346\pi$
$212$	9.78561	−	14.3580i	0.672078	−	0.986109i
$213$	10.6515	+	2.11872i	0.729829	+	0.145172i
$214$	−22.1428	−	9.29121i	−1.51365	−	0.635134i
$215$	9.39636	+	22.6848i	0.640827	+	1.54709i
$216$	2.82816	+	0.0389636i	0.192432	+	0.00265114i
$217$	−4.02781	+	9.72399i	−0.273425	+	0.660107i
$218$	−9.87015	−	9.96122i	−0.668491	−	0.674659i
$219$	−11.2951	+	7.54711i	−0.763249	+	0.509987i
$220$	−29.0566	−	0.266866i	−1.95899	−	0.0179921i
$221$	−0.934975	−	4.70044i	−0.0628932	−	0.316186i
$222$	−4.68033	+	3.09630i	−0.314123	+	0.207810i
$223$			11.0608i			0.740687i	0.928895	+	0.370344i	$0.120760\pi$
$223$			11.0608i			0.740687i	−0.928895	+	0.370344i	$0.879240\pi$
$224$	4.16183	+	23.7618i	0.278074	+	1.58765i
$225$			7.96866i			0.531244i
$226$	−0.0152188	−	0.0230046i	−0.00101234	−	0.00153024i
$227$	1.44779	+	7.27852i	0.0960930	+	0.483092i	0.998623	+	0.0524646i	$0.0167077\pi$
$227$	1.44779	+	7.27852i	0.0960930	+	0.483092i	−0.902530	+	0.430627i	$0.858292\pi$
$228$	−2.02931	−	2.06693i	−0.134394	−	0.136886i
$229$	23.6508	−	15.8029i	1.56289	−	1.04429i	0.591644	−	0.806199i	$-0.298479\pi$
$229$	23.6508	−	15.8029i	1.56289	−	1.04429i	0.971243	−	0.238088i	$-0.0765208\pi$
$230$	25.5123	−	25.2791i	1.68223	−	1.66685i
$231$	−6.58400	+	15.8952i	−0.433195	+	1.04583i
$232$	−6.51195	+	15.1283i	−0.427530	+	0.993224i
$233$	−0.454136	−	1.09638i	−0.0297514	−	0.0718263i	0.908306	−	0.418307i	$-0.137377\pi$
$233$	−0.454136	−	1.09638i	−0.0297514	−	0.0718263i	−0.938057	+	0.346481i	$0.887377\pi$
$234$	0.500322	−	1.19237i	0.0327071	−	0.0779475i
$235$	12.3025	+	2.44712i	0.802528	+	0.159633i
$236$	2.33869	+	12.3491i	0.152236	+	0.803856i
$237$	4.39996	+	2.93996i	0.285808	+	0.190971i
$238$	−31.0312	+	6.02449i	−2.01146	+	0.390510i
$239$	−12.5377	+	12.5377i	−0.810996	+	0.810996i	−0.984783	−	0.173787i	$-0.944400\pi$
$239$	−12.5377	+	12.5377i	−0.810996	+	0.810996i	0.173787	+	0.984783i	$0.444400\pi$
$240$	0.264575	−	14.4024i	0.0170783	−	0.929670i
$241$	−16.7220	−	16.7220i	−1.07716	−	1.07716i	−0.996763	−	0.0803930i	$-0.974382\pi$
$241$	−16.7220	−	16.7220i	−1.07716	−	1.07716i	−0.0803930	−	0.996763i	$-0.525618\pi$
$242$	6.18579	+	4.17443i	0.397638	+	0.268342i
$243$	−0.555570	+	0.831470i	−0.0356398	+	0.0533388i
$244$	17.2584	+	3.59798i	1.10485	+	0.230337i
$245$	−7.85863	+	39.5080i	−0.502069	+	2.52407i
$246$	0.639884	+	1.56511i	0.0407975	+	0.0997876i
$247$	−1.22345	+	0.506768i	−0.0778460	+	0.0322449i
$248$	−3.95795	+	5.75039i	−0.251330	+	0.365150i
$249$	−4.57155	−	1.89360i	−0.289710	−	0.120002i
$250$	15.1188	+	0.0694268i	0.956198	+	0.00439094i
$251$	−4.26066	−	6.37653i	−0.268931	−	0.402483i	0.672283	−	0.740294i	$-0.265314\pi$
$251$	−4.26066	−	6.37653i	−0.268931	−	0.402483i	−0.941214	+	0.337811i	$0.890314\pi$
$252$	−7.84941	−	3.33611i	−0.494466	−	0.210155i
$253$	−27.9046	+	5.55057i	−1.75435	+	0.348961i
$254$	−3.68971	−	0.751559i	−0.231513	−	0.0471570i
$255$	18.8756			1.18204
$256$	−0.587650	+	15.9892i	−0.0367281	+	0.999325i
$257$	19.4102			1.21078			0.605389	−	0.795930i	$-0.293018\pi$
$257$	19.4102			1.21078			0.605389	+	0.795930i	$0.293018\pi$
$258$	9.44844	+	1.92456i	0.588234	+	0.119818i
$259$	16.5969	−	3.30134i	1.03128	−	0.205135i
$260$	−6.06081	−	2.57593i	−0.375875	−	0.159753i
$261$	−3.23517	−	4.84177i	−0.200252	−	0.299698i
$262$	−2.97903	−	0.0136800i	−0.184045	−	0.000845150i
$263$	−6.67555	−	2.76510i	−0.411632	−	0.170504i	0.167251	−	0.985914i	$-0.446511\pi$
$263$	−6.67555	−	2.76510i	−0.411632	−	0.170504i	−0.578883	+	0.815411i	$0.696511\pi$
$264$	−6.46980	+	9.39980i	−0.398189	+	0.578518i
$265$	28.9049	−	11.9728i	1.77561	−	0.735483i
$266$	3.30546	+	8.08490i	0.202671	+	0.495717i
$267$	1.16730	−	5.86842i	0.0714376	−	0.359141i
$268$	0.651314	+	0.135784i	0.0397853	+	0.00829435i
$269$	−2.91731	+	4.36606i	−0.177871	+	0.266203i	−0.909683	−	0.415304i	$-0.863675\pi$
$269$	−2.91731	+	4.36606i	−0.177871	+	0.266203i	0.731811	+	0.681507i	$0.238675\pi$
$270$	4.22153	+	2.84886i	0.256914	+	0.173376i
$271$	−15.6337	−	15.6337i	−0.949681	−	0.949681i	0.0491118	−	0.998793i	$-0.484361\pi$
$271$	−15.6337	−	15.6337i	−0.949681	−	0.949681i	−0.998793	+	0.0491118i	$0.984361\pi$
$272$	−20.9623	−	0.385084i	−1.27103	−	0.0233491i
$273$	−2.75716	+	2.75716i	−0.166871	+	0.166871i
$274$	19.6794	−	3.82061i	1.18887	−	0.230812i
$275$	−26.7311	−	17.8611i	−1.61194	−	1.07707i
$276$	−2.62442	−	13.8578i	−0.157972	−	0.834143i
$277$	−4.52942	−	0.900957i	−0.272146	−	0.0541333i	0.0571304	−	0.998367i	$-0.481805\pi$
$277$	−4.52942	−	0.900957i	−0.272146	−	0.0541333i	−0.329277	+	0.944233i	$0.606805\pi$
$278$	7.37474	−	17.5755i	0.442308	−	1.05411i
$279$	−0.944503	−	2.28023i	−0.0565459	−	0.136514i
$280$	−17.1738	+	39.8976i	−1.02633	+	2.38434i
$281$	4.41675	−	10.6630i	0.263482	−	0.636101i	−0.735668	−	0.677343i	$-0.763131\pi$
$281$	4.41675	−	10.6630i	0.263482	−	0.636101i	0.999149	+	0.0412420i	$0.0131315\pi$
$282$	3.49911	−	3.46712i	0.208369	−	0.206464i
$283$	3.12791	−	2.09000i	0.185935	−	0.124238i	−0.459119	−	0.888375i	$-0.651835\pi$
$283$	3.12791	−	2.09000i	0.185935	−	0.124238i	0.645054	+	0.764137i	$0.276835\pi$
$284$	−15.2169	−	15.4990i	−0.902957	−	0.919697i
$285$	−1.01752	−	5.11540i	−0.0602725	−	0.303010i
$286$	2.87840	+	4.35094i	0.170203	+	0.257277i
$287$		−	5.09868i		−	0.300966i
$288$	−4.63011	−	3.24994i	−0.272832	−	0.191504i
$289$		−	10.4730i		−	0.616058i
$290$	−24.7339	+	16.3629i	−1.45242	+	0.960861i
$291$	0.0363454	+	0.182721i	0.00213061	+	0.0107113i
$292$	27.1677	+	0.249518i	1.58987	+	0.0146019i
$293$	4.31206	−	2.88123i	0.251913	−	0.168323i	−0.423202	−	0.906035i	$-0.639094\pi$
$293$	4.31206	−	2.88123i	0.251913	−	0.168323i	0.675115	+	0.737712i	$0.264094\pi$
$294$	11.1342	+	11.2370i	0.649361	+	0.655353i
$295$	−8.66050	+	20.9083i	−0.504234	+	1.21733i
$296$	11.2226	+	0.154614i	0.652299	+	0.00898673i
$297$	−1.54392	−	3.72735i	−0.0895873	−	0.216283i
$298$	13.8439	+	5.80896i	0.801957	+	0.336504i
$299$	−6.32415	−	1.25795i	−0.365735	−	0.0727492i
$300$	8.97562	−	13.1695i	0.518208	−	0.760342i
$301$	−24.1760	−	16.1539i	−1.39348	−	0.931094i
$302$	3.89584	+	20.0669i	0.224181	+	1.15472i
$303$	7.30526	−	7.30526i	0.419676	−	0.419676i
$304$	1.02565	+	5.70168i	0.0588248	+	0.327014i
$305$	22.4461	+	22.4461i	1.28526	+	1.28526i
$306$	4.14645	−	6.14434i	0.237037	−	0.351248i
$307$	3.61857	−	5.41558i	0.206523	−	0.309083i	−0.713720	−	0.700431i	$-0.752991\pi$
$307$	3.61857	−	5.41558i	0.206523	−	0.309083i	0.920243	+	0.391348i	$0.127991\pi$
$308$	28.7849	−	18.8534i	1.64017	−	1.07427i
$309$	−0.892127	+	4.48503i	−0.0507513	+	0.255144i
$310$	−11.6349	+	4.75685i	−0.660817	+	0.270171i
$311$	10.8463	−	4.49269i	0.615038	−	0.254757i	−0.0533428	−	0.998576i	$-0.516988\pi$
$311$	10.8463	−	4.49269i	0.615038	−	0.254757i	0.668381	+	0.743819i	$0.266988\pi$
$312$	−2.16991	+	1.40704i	−0.122847	+	0.0796578i
$313$	24.1427	+	10.0002i	1.36463	+	0.565246i	0.940326	−	0.340276i	$-0.110520\pi$
$313$	24.1427	+	10.0002i	1.36463	+	0.565246i	0.424300	+	0.905522i	$0.360520\pi$
$314$	−0.0517598	+	11.2715i	−0.00292097	+	0.636089i
$315$	−8.53201	−	12.7691i	−0.480725	−	0.719455i
$316$	−3.96018	−	9.81472i	−0.222778	−	0.552121i
$317$	10.2616	−	2.04116i	0.576350	−	0.114643i	0.101696	−	0.994816i	$-0.467573\pi$
$317$	10.2616	−	2.04116i	0.576350	−	0.114643i	0.474654	+	0.880172i	$0.342573\pi$
$318$	2.45226	−	12.0391i	0.137516	−	0.675122i
$319$	23.4932			1.31537
$320$	−16.6596	+	23.5043i	−0.931300	+	1.31393i
$321$	−16.9799			−0.947724
$322$	−8.48868	+	41.6744i	−0.473056	+	2.32242i
$323$	−7.44535	+	1.48097i	−0.414271	+	0.0824035i
$324$	1.85471	−	0.748365i	0.103039	−	0.0415758i
$325$	−4.04795	−	6.05819i	−0.224540	−	0.336048i
$326$	0.0482868	−	10.5152i	0.00267436	−	0.582384i
$327$	−9.16100	−	3.79461i	−0.506604	−	0.209842i
$328$	0.705369	−	3.30734i	0.0389475	−	0.182617i
$329$	−13.7231	+	5.68430i	−0.756580	+	0.313386i
$330$	−19.0188	+	7.77572i	−1.04695	+	0.428040i
$331$	−3.24628	+	16.3201i	−0.178432	+	0.897036i	0.783006	+	0.622014i	$0.213685\pi$
$331$	−3.24628	+	16.3201i	−0.178432	+	0.897036i	−0.961438	+	0.275022i	$0.911315\pi$
$332$	5.42236	+	8.27872i	0.297590	+	0.454354i
$333$	−2.20459	+	3.29940i	−0.120811	+	0.180806i
$334$	15.0705	−	22.3319i	0.824621	−	1.22195i
$335$	0.847093	+	0.847093i	0.0462816	+	0.0462816i
$336$	9.21475	+	14.3548i	0.502706	+	0.783118i
$337$	−14.4576	+	14.4576i	−0.787553	+	0.787553i	−0.981093	−	0.193539i	$-0.938003\pi$
$337$	−14.4576	+	14.4576i	−0.787553	+	0.787553i	0.193539	+	0.981093i	$0.438003\pi$
$338$	−3.27852	−	16.8871i	−0.178328	−	0.918539i
$339$	−0.0162171	−	0.0108359i	−0.000880793	−	0.000588527i
$340$	−31.1950	−	21.2608i	−1.69179	−	1.15303i
$341$	9.76613	+	1.94260i	0.528866	+	0.105198i
$342$	−1.88868	−	0.792495i	−0.102128	−	0.0428532i
$343$	−6.83084	−	16.4911i	−0.368831	−	0.890436i
$344$	−13.4473	−	13.8230i	−0.725032	−	0.745289i
$345$	9.71861	−	23.4628i	0.523232	−	1.26319i
$346$	−18.0999	−	18.2669i	−0.973057	−	0.982035i
$347$	0.431532	−	0.288340i	0.0231658	−	0.0154789i	−0.543933	−	0.839128i	$-0.683066\pi$
$347$	0.431532	−	0.288340i	0.0231658	−	0.0154789i	0.567099	+	0.823649i	$0.308066\pi$
$348$	−0.106959	+	11.6458i	−0.00573361	+	0.624280i
$349$	5.20867	+	26.1857i	0.278814	+	1.40169i	0.825523	+	0.564368i	$0.190880\pi$
$349$	5.20867	+	26.1857i	0.278814	+	1.40169i	−0.546710	+	0.837322i	$0.684120\pi$
$350$	−40.0809	+	26.5158i	−2.14241	+	1.41733i
$351$		−	0.914347i		−	0.0488042i
$352$	21.2800	−	8.24735i	1.13423	−	0.439585i
$353$			2.11097i			0.112356i	0.998421	+	0.0561779i	$0.0178914\pi$
$353$			2.11097i			0.112356i	−0.998421	+	0.0561779i	$0.982109\pi$
$354$	4.90355	+	7.41213i	0.260621	+	0.393950i
$355$	−7.62992	−	38.3582i	−0.404954	−	2.03584i
$356$	−8.53914	+	8.38371i	−0.452573	+	0.444336i
$357$	−18.5851	+	12.4182i	−0.983627	+	0.657238i
$358$	−13.6013	+	13.4770i	−0.718852	+	0.712280i
$359$	10.4260	−	25.1705i	0.550261	−	1.32845i	−0.367022	−	0.930212i	$-0.619623\pi$
$359$	10.4260	−	25.1705i	0.550261	−	1.32845i	0.917283	−	0.398235i	$-0.130377\pi$
$360$	−3.76791	−	9.46320i	−0.198586	−	0.498754i
$361$	−6.46828	−	15.6158i	−0.340436	−	0.821885i
$362$	10.5358	−	25.1089i	0.553748	−	1.31969i
$363$	5.17544	+	1.02946i	0.271640	+	0.0540325i
$364$	7.66222	−	1.45109i	0.401609	−	0.0760576i
$365$	40.6758	+	27.1787i	2.12907	+	1.42260i
$366$	12.2374	−	2.37580i	0.639659	−	0.124185i
$367$	12.9194	−	12.9194i	0.674388	−	0.674388i	−0.284337	−	0.958725i	$-0.591773\pi$
$367$	12.9194	−	12.9194i	0.674388	−	0.674388i	0.958725	+	0.284337i	$0.0917733\pi$
$368$	−11.2717	+	25.8584i	−0.587578	+	1.34796i
$369$	0.845430	+	0.845430i	0.0440114	+	0.0440114i
$370$	16.7517	+	11.3047i	0.870879	+	0.587705i
$371$	−20.5832	+	30.8049i	−1.06863	+	1.59931i
$372$	−1.00743	+	4.83232i	−0.0522328	+	0.250544i
$373$	0.155651	−	0.782508i	0.00805928	−	0.0405167i	−0.976546	−	0.215307i	$-0.930925\pi$
$373$	0.155651	−	0.782508i	0.00805928	−	0.0405167i	0.984606	+	0.174790i	$0.0559248\pi$
$374$	11.3174	+	27.6815i	0.585208	+	1.43137i
$375$	9.87695	−	4.09117i	0.510044	−	0.211267i
$376$	−9.68810	+	1.78871i	−0.499626	+	0.0922456i
$377$	4.91908	+	2.03755i	0.253346	+	0.104939i
$378$	−6.03081	−	0.0276940i	−0.310191	−	0.00142442i
$379$	12.0719	+	18.0669i	0.620091	+	0.928032i	0.999995	+	0.00300629i	$0.000956933\pi$
$379$	12.0719	+	18.0669i	0.620091	+	0.928032i	−0.379904	+	0.925026i	$0.624043\pi$
$380$	−4.08020	+	9.60014i	−0.209310	+	0.492477i
$381$	−2.61143	+	0.519446i	−0.133788	+	0.0266120i
$382$	3.66890	+	0.747321i	0.187717	+	0.0382363i
$383$	5.38281			0.275049			0.137524	−	0.990498i	$-0.456085\pi$
$383$	5.38281			0.275049			0.137524	+	0.990498i	$0.456085\pi$
$384$	3.99140	+	10.5863i	0.203685	+	0.540227i
$385$	61.9580			3.15767
$386$	27.7442	+	5.65123i	1.41214	+	0.287640i
$387$	6.68723	−	1.33017i	0.339931	−	0.0676165i
$388$	0.145744	−	0.342915i	0.00739902	−	0.0174088i
$389$	13.8846	+	20.7797i	0.703975	+	1.05357i	0.995290	+	0.0969461i	$0.0309074\pi$
$389$	13.8846	+	20.7797i	0.703975	+	1.05357i	−0.291314	+	0.956627i	$0.594093\pi$
$390$	−4.65660	−	0.0213835i	−0.235796	−	0.00108280i
$391$	−34.1496	−	14.1452i	−1.72702	−	0.715354i
$392$	−5.74421	−	31.1121i	−0.290127	−	1.57140i
$393$	−1.94617	+	0.806129i	−0.0981711	+	0.0406638i
$394$	6.82651	+	16.6971i	0.343915	+	0.841188i
$395$	3.71779	−	18.6906i	0.187062	−	0.940426i
$396$	−1.64678	+	7.89908i	−0.0827538	+	0.396944i
$397$	−0.832645	+	1.24614i	−0.0417893	+	0.0625420i	−0.851776	−	0.523906i	$-0.824474\pi$
$397$	−0.832645	+	1.24614i	−0.0417893	+	0.0625420i	0.809987	+	0.586448i	$0.199474\pi$
$398$	−20.5598	−	13.8746i	−1.03057	−	0.695469i
$399$	4.36725	+	4.36725i	0.218636	+	0.218636i
$400$	−29.6674	+	11.6550i	−1.48337	+	0.582748i
$401$	3.25173	−	3.25173i	0.162384	−	0.162384i	−0.621238	−	0.783622i	$-0.713370\pi$
$401$	3.25173	−	3.25173i	0.162384	−	0.162384i	0.783622	+	0.621238i	$0.213370\pi$
$402$	0.461827	−	0.0896605i	0.0230339	−	0.00447186i
$403$	1.87638	+	1.25376i	0.0934693	+	0.0624542i
$404$	−20.3015	+	3.84475i	−1.01004	+	0.191283i
$405$	3.53201	+	0.702560i	0.175507	+	0.0349105i
$406$	13.5882	−	32.3833i	0.674370	−	1.60716i
$407$	−6.12651	−	14.7907i	−0.303680	−	0.733148i
$408$	−13.7735	+	5.48411i	−0.681888	+	0.271504i
$409$	0.640222	−	1.54563i	0.0316569	−	0.0764266i	−0.907260	−	0.420569i	$-0.861830\pi$
$409$	0.640222	−	1.54563i	0.0316569	−	0.0764266i	0.938917	+	0.344143i	$0.111830\pi$
$410$	4.32539	−	4.28585i	0.213616	−	0.211663i
$411$	11.7863	−	7.87534i	0.581374	−	0.388462i
$412$	6.52617	−	6.40738i	0.321521	−	0.315669i
$413$	−5.22826	−	26.2842i	−0.257266	−	1.29336i
$414$	−5.50264	−	8.31772i	−0.270440	−	0.408794i
$415$			17.8195i			0.874726i
$416$	5.17097	+	0.118747i	0.253527	+	0.00582207i
$417$		−	13.4775i		−	0.659995i
$418$	6.89177	−	4.55929i	0.337087	−	0.223002i
$419$	−5.97809	−	30.0539i	−0.292049	−	1.46823i	−0.796421	−	0.604742i	$-0.793276\pi$
$419$	−5.97809	−	30.0539i	−0.292049	−	1.46823i	0.504372	−	0.863486i	$-0.331724\pi$
$420$	−0.282080	+	30.7131i	−0.0137641	+	1.49865i
$421$	22.9020	−	15.3026i	1.11617	−	0.745804i	0.146259	−	0.989246i	$-0.453277\pi$
$421$	22.9020	−	15.3026i	1.11617	−	0.745804i	0.969915	+	0.243442i	$0.0782766\pi$
$422$	5.76152	+	5.81468i	0.280466	+	0.283054i
$423$	1.33294	−	3.21801i	0.0648100	−	0.156465i
$424$	−17.6132	+	17.1345i	−0.855375	+	0.832126i
$425$	−15.9837	−	38.5881i	−0.775324	−	1.87180i
$426$	−14.1624	−	5.94258i	−0.686169	−	0.287919i
$427$	−36.8678	−	7.33346i	−1.78416	−	0.354891i
$428$	28.0620	+	19.1255i	1.35643	+	0.924468i
$429$	3.06720	+	2.04944i	0.148086	+	0.0989479i
$430$	−6.61794	−	34.0880i	−0.319145	−	1.64387i
$431$	−18.3036	+	18.3036i	−0.881653	+	0.881653i	−0.993703	−	0.112049i	$-0.964259\pi$
$431$	−18.3036	+	18.3036i	−0.881653	+	0.881653i	0.112049	+	0.993703i	$0.464259\pi$
$432$	−3.90815	−	0.852287i	−0.188031	−	0.0410057i
$433$	−18.8526	−	18.8526i	−0.905997	−	0.905997i	0.0899493	−	0.995946i	$-0.471329\pi$
$433$	−18.8526	−	18.8526i	−0.905997	−	0.905997i	−0.995946	+	0.0899493i	$0.971329\pi$
$434$	8.32631	−	12.3382i	0.399676	−	0.592252i
$435$	−11.6505	+	17.4362i	−0.558598	+	0.836001i
$436$	10.8659	+	16.5898i	0.520384	+	0.794510i
$437$	−1.99256	+	10.0173i	−0.0953170	+	0.479191i
$438$	17.7825	−	7.27027i	0.849681	−	0.347387i
$439$	25.2770	−	10.4701i	1.20641	−	0.499710i	0.313343	−	0.949640i	$-0.398551\pi$
$439$	25.2770	−	10.4701i	1.20641	−	0.499710i	0.893064	+	0.449930i	$0.148551\pi$
$440$	40.1900	+	8.57148i	1.91598	+	0.408629i
$441$	10.3342	+	4.28059i	0.492107	+	0.203837i
$442$	−0.0311232	+	6.77758i	−0.00148038	+	0.322377i
$443$	−8.71304	−	13.0400i	−0.413969	−	0.619549i	0.564625	−	0.825347i	$-0.309021\pi$
$443$	−8.71304	−	13.0400i	−0.413969	−	0.619549i	−0.978594	+	0.205799i	$0.934021\pi$
$444$	7.35978	−	2.96963i	0.349280	−	0.140932i
$445$	−21.1333	+	4.20368i	−1.00182	+	0.199274i
$446$	3.12209	−	15.3276i	0.147835	−	0.725784i
$447$	10.6160			0.502119
$448$	0.939848	−	34.1028i	0.0444037	−	1.61121i
$449$	−28.0321			−1.32292			−0.661459	−	0.749981i	$-0.730062\pi$
$449$	−28.0321			−1.32292			−0.661459	+	0.749981i	$0.730062\pi$
$450$	2.24928	−	11.0426i	0.106032	−	0.520555i
$451$	−4.73099	+	0.941052i	−0.222773	+	0.0443124i
$452$	0.0145962	+	0.0361746i	0.000686549	+	0.00170151i
$453$	8.03042	+	12.0184i	0.377302	+	0.564672i
$454$	0.0481935	−	10.4949i	0.00226183	−	0.492551i
$455$	12.9730	+	5.37358i	0.608182	+	0.251917i
$456$	2.22871	+	3.43707i	0.104369	+	0.160955i
$457$	15.0947	−	6.25242i	0.706099	−	0.292476i	−0.000590259	−	1.00000i	$-0.500188\pi$
$457$	15.0947	−	6.25242i	0.706099	−	0.292476i	0.706689	+	0.707524i	$0.250188\pi$
$458$	−37.2349	+	15.2233i	−1.73987	+	0.711336i
$459$	1.02256	−	5.14076i	0.0477290	−	0.239950i
$460$	−42.4893	+	27.8294i	−1.98107	+	1.29755i
$461$	13.0217	−	19.4883i	0.606480	−	0.907661i	−0.393452	−	0.919345i	$-0.628719\pi$
$461$	13.0217	−	19.4883i	0.606480	−	0.907661i	0.999932	+	0.0116839i	$0.00371920\pi$
$462$	13.6105	−	20.1684i	0.633218	−	0.938321i
$463$	−2.32339	−	2.32339i	−0.107977	−	0.107977i	0.651054	−	0.759031i	$-0.274327\pi$
$463$	−2.32339	−	2.32339i	−0.107977	−	0.107977i	−0.759031	+	0.651054i	$0.774327\pi$
$464$	13.2942	−	19.1261i	0.617168	−	0.887908i
$465$	−6.28487	+	6.28487i	−0.291454	+	0.291454i
$466$	0.319852	+	1.64751i	0.0148169	+	0.0763193i
$467$	−13.6604	−	9.12758i	−0.632128	−	0.422374i	0.197802	−	0.980242i	$-0.436620\pi$
$467$	−13.6604	−	9.12758i	−0.632128	−	0.422374i	−0.829930	+	0.557868i	$0.811620\pi$
$468$	−1.02989	+	1.51111i	−0.0476067	+	0.0698510i
$469$	−1.39135	−	0.276758i	−0.0642468	−	0.0127795i
$470$	−16.3576	−	6.86370i	−0.754519	−	0.316599i
$471$	3.05009	+	7.36356i	0.140541	+	0.339295i
$472$	0.244858	−	17.7730i	0.0112705	−	0.818067i
$473$	−10.5268	+	25.4140i	−0.484024	+	1.16854i
$474$	−5.26743	−	5.31603i	−0.241941	−	0.244173i
$475$	−9.59599	+	6.41184i	−0.440294	+	0.294195i
$476$	44.7023	+	0.410562i	2.04893	+	0.0188181i
$477$	−1.69490	−	8.52084i	−0.0776041	−	0.390142i
$478$	20.9132	−	13.8353i	0.956546	−	0.632810i
$479$		−	10.9910i		−	0.502189i	−0.967963	−	0.251095i	$-0.919209\pi$
$479$		−	10.9910i		−	0.502189i	0.967963	−	0.251095i	$-0.0807906\pi$
$480$	−4.43194	+	19.8835i	−0.202289	+	0.907555i
$481$		−	3.62827i		−	0.165435i
$482$	18.4526	+	27.8926i	0.840491	+	1.27047i
$483$	5.86702	+	29.4955i	0.266959	+	1.34209i
$484$	−7.39371	−	7.53078i	−0.336078	−	0.342308i
$485$	0.557838	−	0.372735i	0.0253301	−	0.0169250i
$486$	1.00458	−	0.995397i	0.0455687	−	0.0451521i
$487$	9.45014	−	22.8147i	0.428227	−	1.03383i	−0.551623	−	0.834094i	$-0.685991\pi$
$487$	9.45014	−	22.8147i	0.428227	−	1.03383i	0.979849	−	0.199737i	$-0.0640089\pi$
$488$	−22.9003	−	9.85738i	−1.03665	−	0.446223i
$489$	−2.84543	−	6.86947i	−0.128675	−	0.310648i
$490$	22.0419	−	52.5303i	0.995752	−	2.37308i
$491$	−8.69167	−	1.72888i	−0.392249	−	0.0780233i	−0.00497467	−	0.999988i	$-0.501583\pi$
$491$	−8.69167	−	1.72888i	−0.392249	−	0.0780233i	−0.387275	+	0.921964i	$0.626583\pi$
$492$	−0.444949	−	2.34948i	−0.0200598	−	0.105923i
$493$	25.3780	+	16.9570i	1.14297	+	0.763706i
$494$	1.83844	−	0.356921i	0.0827155	−	0.0160586i
$495$	−10.2735	+	10.2735i	−0.461758	+	0.461758i
$496$	7.10790	−	6.85146i	0.319154	−	0.307640i
$497$	32.7482	+	32.7482i	1.46896	+	1.46896i
$498$	5.80057	+	3.91446i	0.259930	+	0.175411i
$499$	−14.4306	+	21.5969i	−0.646002	+	0.966810i	0.353506	+	0.935432i	$0.384989\pi$
$499$	−14.4306	+	21.5969i	−0.646002	+	0.966810i	−0.999508	+	0.0313774i	$0.990011\pi$
$500$	−20.9314	−	4.36374i	−0.936082	−	0.195152i
$501$	3.71655	−	18.6843i	0.166043	−	0.834755i
$502$	4.10437	+	10.0390i	0.183187	+	0.448061i
$503$	32.1398	−	13.3127i	1.43304	−	0.593585i	0.474942	−	0.880017i	$-0.342469\pi$
$503$	32.1398	−	13.3127i	1.43304	−	0.593585i	0.958101	+	0.286432i	$0.0924692\pi$
$504$	9.93571	+	6.83867i	0.442572	+	0.304618i
$505$	−34.3727	−	14.2376i	−1.52956	−	0.633566i
$506$	40.2358	+	0.184766i	1.78870	+	0.00821384i
$507$	−6.75794	−	10.1140i	−0.300131	−	0.449177i
$508$	4.90091	+	2.08296i	0.217443	+	0.0924164i
$509$	2.06009	−	0.409778i	0.0913120	−	0.0181631i	−0.149223	−	0.988804i	$-0.547677\pi$
$509$	2.06009	−	0.409778i	0.0913120	−	0.0181631i	0.240535	+	0.970641i	$0.422677\pi$
$510$	−26.1570	−	5.32793i	−1.15825	−	0.235925i
$511$	−57.9305			−2.56269
$512$	5.32755	−	21.9913i	0.235447	−	0.971887i
$513$	−1.44830			−0.0639440
$514$	−26.8979	−	5.47885i	−1.18642	−	0.241662i
$515$	16.1515	−	3.21273i	0.711719	−	0.141570i
$516$	−12.5500	−	5.33394i	−0.552484	−	0.234814i
$517$	7.80722	+	11.6843i	0.343361	+	0.513876i
$518$	−23.9312	−	0.109894i	−1.05148	−	0.00482846i
$519$	−16.7995	−	6.95856i	−0.737414	−	0.305447i
$520$	7.67171	+	5.28038i	0.336427	+	0.231560i
$521$	37.9511	−	15.7199i	1.66267	−	0.688700i	0.664393	−	0.747383i	$-0.268690\pi$
$521$	37.9511	−	15.7199i	1.66267	−	0.688700i	0.998277	+	0.0586829i	$0.0186901\pi$
$522$	3.11649	+	7.62270i	0.136405	+	0.333636i
$523$	0.702666	−	3.53254i	0.0307254	−	0.154467i	−0.962377	−	0.271718i	$-0.912408\pi$
$523$	0.702666	−	3.53254i	0.0307254	−	0.154467i	0.993102	+	0.117251i	$0.0374082\pi$
$524$	4.12436	+	0.859836i	0.180173	+	0.0375621i
$525$	−18.8794	+	28.2551i	−0.823967	+	1.23315i
$526$	8.47021	+	5.71605i	0.369319	+	0.249231i
$527$	9.14749	+	9.14749i	0.398471	+	0.398471i
$528$	11.6188	−	11.1996i	0.505645	−	0.487402i
$529$	−18.9022	+	18.9022i	−0.821835	+	0.821835i
$530$	−43.4347	+	8.43254i	−1.88668	+	0.366286i
$531$	5.22519	+	3.49136i	0.226754	+	0.151512i
$532$	−2.29848	−	12.1367i	−0.0996517	−	0.526194i
$533$	−1.07221	−	0.213275i	−0.0464424	−	0.00923796i
$534$	−3.27405	+	7.80272i	−0.141682	+	0.337657i
$535$	23.4003	+	56.4933i	1.01168	+	2.44242i
$536$	−0.864236	−	0.372008i	−0.0373293	−	0.0160683i
$537$	−5.18126	+	12.5087i	−0.223588	+	0.539789i
$538$	5.27508	−	5.22685i	0.227425	−	0.225346i
$539$	−37.5228	+	25.0719i	−1.61622	+	1.07992i
$540$	−5.04588	−	5.13943i	−0.217140	−	0.221166i
$541$	5.44456	+	27.3716i	0.234080	+	1.17680i	0.901722	+	0.432316i	$0.142304\pi$
$541$	5.44456	+	27.3716i	0.234080	+	1.17680i	−0.667642	+	0.744482i	$0.732696\pi$
$542$	17.2517	+	26.0774i	0.741024	+	1.12012i
$543$		−	19.2543i		−	0.826282i
$544$	28.9400	+	6.45058i	1.24079	+	0.276566i
$545$			35.7088i			1.52960i
$546$	4.59900	−	3.04250i	0.196819	−	0.130207i
$547$	6.57952	+	33.0775i	0.281320	+	1.41429i	0.820281	+	0.571961i	$0.193817\pi$
$547$	6.57952	+	33.0775i	0.281320	+	1.41429i	−0.538961	+	0.842331i	$0.681183\pi$
$548$	−28.3493	−	0.260370i	−1.21102	−	0.0111224i
$549$	7.32917	−	4.89719i	0.312801	−	0.209007i
$550$	32.0012	+	32.2965i	1.36454	+	1.37713i
$551$	3.22742	−	7.79168i	0.137493	−	0.331937i
$552$	−0.274774	+	19.9444i	−0.0116952	+	0.848889i
$553$	8.63588	+	20.8489i	0.367235	+	0.886584i
$554$	6.02237	+	2.52701i	0.255866	+	0.107362i
$555$	14.0156	+	2.78787i	0.594927	+	0.118338i
$556$	−15.1806	+	22.2737i	−0.643800	+	0.944617i
$557$	−32.4174	−	21.6606i	−1.37357	−	0.917791i	−0.373619	−	0.927582i	$-0.621883\pi$
$557$	−32.4174	−	21.6606i	−1.37357	−	0.917791i	−0.999952	+	0.00979179i	$0.996883\pi$
$558$	0.665222	+	3.42645i	0.0281611	+	0.145053i
$559$	−4.40828	+	4.40828i	−0.186450	+	0.186450i
$560$	35.0604	−	50.4408i	1.48157	−	2.13151i
$561$	14.9528	+	14.9528i	0.631308	+	0.631308i
$562$	−9.13035	+	13.5296i	−0.385141	+	0.570713i
$563$	9.23380	−	13.8194i	0.389158	−	0.582416i	−0.584227	−	0.811590i	$-0.698602\pi$
$563$	9.23380	−	13.8194i	0.389158	−	0.582416i	0.973386	+	0.229174i	$0.0736024\pi$
$564$	−5.82757	+	3.81691i	−0.245385	+	0.160721i
$565$	−0.0137028	+	0.0688888i	−0.000576483	+	0.00289817i
$566$	−4.92446	+	2.01333i	−0.206990	+	0.0846267i
$567$	−3.93986	+	1.63194i	−0.165458	+	0.0685351i
$568$	16.7121	+	25.7731i	0.701225	+	1.08142i
$569$	−41.8582	−	17.3382i	−1.75479	−	0.726857i	−0.997254	−	0.0740609i	$-0.976404\pi$
$569$	−41.8582	−	17.3382i	−1.75479	−	0.726857i	−0.757534	−	0.652796i	$-0.773596\pi$
$570$	−0.0338708	+	7.37592i	−0.00141869	+	0.308943i
$571$	6.11301	+	9.14877i	0.255822	+	0.382864i	0.937043	−	0.349213i	$-0.113551\pi$
$571$	6.11301	+	9.14877i	0.255822	+	0.382864i	−0.681222	+	0.732077i	$0.738551\pi$
$572$	−2.76064	−	6.84183i	−0.115428	−	0.286071i
$573$	2.59671	−	0.516517i	0.108479	−	0.0215778i
$574$	−1.43918	+	7.06554i	−0.0600704	+	0.294910i
$575$	−56.1956			−2.34352
$576$	5.49887	+	5.81055i	0.229119	+	0.242106i
$577$	−15.5979			−0.649351			−0.324675	−	0.945826i	$-0.605255\pi$
$577$	−15.5979			−0.649351			−0.324675	+	0.945826i	$0.605255\pi$
$578$	−2.95617	+	14.5130i	−0.122960	+	0.603663i
$579$	19.6363	−	3.90589i	0.816055	−	0.162323i
$580$	38.8939	−	15.6935i	1.61498	−	0.651635i
$581$	−11.7234	−	17.5453i	−0.486367	−	0.727900i
$582$	0.00120986	−	0.263466i	5.01502e−5	−	0.0109210i
$583$	32.3824	+	13.4132i	1.34114	+	0.555518i
$584$	−37.5775	−	8.01430i	−1.55497	−	0.331634i
$585$	−3.04210	+	1.26008i	−0.125776	+	0.0520979i
$586$	−6.78874	+	2.77554i	−0.280440	+	0.114656i
$587$	2.33564	−	11.7421i	0.0964022	−	0.484647i	−0.902177	−	0.431365i	$-0.858032\pi$
$587$	2.33564	−	11.7421i	0.0964022	−	0.484647i	0.998580	−	0.0532814i	$-0.0169680\pi$
$588$	−12.2575	−	18.7145i	−0.505492	−	0.771774i
$589$	1.98592	−	2.97214i	0.0818283	−	0.122465i
$590$	17.9031	−	26.5293i	0.737057	−	1.09219i
$591$	9.01935	+	9.01935i	0.371007	+	0.371007i
$592$	−15.5081	−	3.38201i	−0.637380	−	0.139000i
$593$	1.27547	−	1.27547i	0.0523774	−	0.0523774i	−0.680433	−	0.732810i	$-0.738208\pi$
$593$	1.27547	−	1.27547i	0.0523774	−	0.0523774i	0.732810	+	0.680433i	$0.238208\pi$
$594$	1.08740	+	5.60100i	0.0446164	+	0.229812i
$595$	66.9286	+	44.7203i	2.74381	+	1.83335i
$596$	−17.5447	−	11.9575i	−0.718657	−	0.489798i
$597$	−17.2016	−	3.42162i	−0.704016	−	0.140037i
$598$	8.40866	+	3.52831i	0.343856	+	0.144283i
$599$	−5.48447	−	13.2407i	−0.224089	−	0.540999i	0.771348	−	0.636413i	$-0.219583\pi$
$599$	−5.48447	−	13.2407i	−0.224089	−	0.540999i	−0.995438	+	0.0954137i	$0.969583\pi$
$600$	−16.1553	+	15.7163i	−0.659539	+	0.641613i
$601$	−11.4101	+	27.5465i	−0.465429	+	1.12365i	0.500708	+	0.865616i	$0.333073\pi$
$601$	−11.4101	+	27.5465i	−0.465429	+	1.12365i	−0.966137	+	0.258029i	$0.916927\pi$
$602$	28.9424	+	29.2094i	1.17960	+	1.19049i
$603$	0.276595	−	0.184815i	0.0112638	−	0.00752626i
$604$	0.265497	−	28.9075i	0.0108029	−	1.17623i
$605$	−3.70729	−	18.6378i	−0.150723	−	0.757734i
$606$	−12.1853	+	8.06130i	−0.494996	+	0.327468i
$607$			36.8155i			1.49430i	0.664658	+	0.747148i	$0.268577\pi$
$607$			36.8155i			1.49430i	−0.664658	+	0.747148i	$0.731423\pi$
$608$	0.188093	−	8.19066i	0.00762816	−	0.332175i
$609$		−	24.8326i		−	1.00627i
$610$	−24.7691	−	37.4406i	−1.00287	−	1.51593i
$611$	0.621326	+	3.12362i	0.0251362	+	0.126368i
$612$	−7.48032	+	7.34417i	−0.302374	+	0.296870i
$613$	−35.4697	+	23.7001i	−1.43261	+	0.957239i	−0.434202	+	0.900815i	$0.642970\pi$
$613$	−35.4697	+	23.7001i	−1.43261	+	0.957239i	−0.998407	+	0.0564236i	$0.982030\pi$
$614$	−6.54310	+	6.48328i	−0.264058	+	0.261644i
$615$	1.64771	−	3.97792i	0.0664420	−	0.160405i
$616$	−45.2106	+	18.0013i	−1.82159	+	0.725291i
$617$	6.16351	+	14.8800i	0.248134	+	0.599048i	0.998046	−	0.0624900i	$-0.0199042\pi$
$617$	6.16351	+	14.8800i	0.248134	+	0.599048i	−0.749912	+	0.661538i	$0.769904\pi$
$618$	2.50224	−	5.96334i	0.100655	−	0.239881i
$619$	−30.5691	−	6.08056i	−1.22867	−	0.244399i	−0.462260	−	0.886745i	$-0.652961\pi$
$619$	−30.5691	−	6.08056i	−1.22867	−	0.244399i	−0.766415	+	0.642346i	$0.777961\pi$
$620$	17.4658	−	3.30772i	0.701445	−	0.132841i
$621$	−5.86359	−	3.91792i	−0.235298	−	0.157221i
$622$	−16.2985	+	3.16424i	−0.653511	+	0.126874i
$623$	18.0425	−	18.0425i	0.722858	−	0.722858i
$624$	3.40412	−	1.33732i	0.136274	−	0.0535358i
$625$	0.950204	+	0.950204i	0.0380082	+	0.0380082i
$626$	−30.6332	−	20.6726i	−1.22435	−	0.826241i
$627$	3.24625	−	4.85836i	0.129643	−	0.194024i
$628$	3.25329	−	15.6050i	0.129821	−	0.622707i
$629$	4.05768	−	20.3993i	0.161790	−	0.813374i
$630$	8.21904	+	20.1031i	0.327454	+	0.800928i
$631$	8.96722	−	3.71434i	0.356979	−	0.147866i	−0.196984	−	0.980407i	$-0.563115\pi$
$631$	8.96722	−	3.71434i	0.356979	−	0.147866i	0.553963	+	0.832541i	$0.313115\pi$
$632$	2.71750	+	14.7187i	0.108096	+	0.585477i
$633$	5.34756	+	2.21503i	0.212547	+	0.0880397i
$634$	−14.7963	−	0.0679456i	−0.587635	−	0.00269847i
$635$	5.32711	+	7.97258i	0.211400	+	0.316382i
$636$	−6.79648	+	15.9912i	−0.269498	+	0.634091i
$637$	−10.0311	+	1.99531i	−0.397447	+	0.0790571i
$638$	−32.5559	−	6.63133i	−1.28890	−	0.262537i
$639$	−10.8602			−0.429622
$640$	29.7206	−	27.8688i	1.17481	−	1.10161i
$641$	43.2577			1.70857			0.854287	−	0.519801i	$-0.173994\pi$
$641$	43.2577			1.70857			0.854287	+	0.519801i	$0.173994\pi$
$642$	23.5300	+	4.79283i	0.928655	+	0.189158i
$643$	2.64504	−	0.526131i	0.104310	−	0.0207486i	−0.142659	−	0.989772i	$-0.545565\pi$
$643$	2.64504	−	0.526131i	0.104310	−	0.0207486i	0.246969	+	0.969023i	$0.420565\pi$
$644$	23.5265	−	55.3546i	0.927075	−	2.18128i
$645$	−13.6414	−	20.4158i	−0.537130	−	0.803871i
$646$	10.7355	+	0.0492982i	0.422382	+	0.00193961i
$647$	4.36955	+	1.80993i	0.171785	+	0.0711556i	0.466918	−	0.884300i	$-0.345364\pi$
$647$	4.36955	+	1.80993i	0.171785	+	0.0711556i	−0.295134	+	0.955456i	$0.595364\pi$
$648$	−2.78142	+	0.513531i	−0.109264	+	0.0201734i
$649$	−23.4237	+	9.70243i	−0.919462	+	0.380854i
$650$	3.89946	+	9.53778i	0.152950	+	0.374103i
$651$	2.05336	−	10.3229i	0.0804774	−	0.404587i
$652$	−3.03500	+	14.5579i	−0.118860	+	0.570132i
$653$	−14.5186	+	21.7286i	−0.568156	+	0.850305i	−0.998632	−	0.0522968i	$-0.983346\pi$
$653$	−14.5186	+	21.7286i	−0.568156	+	0.850305i	0.430476	+	0.902602i	$0.358346\pi$
$654$	11.6238	+	7.84425i	0.454528	+	0.306734i
$655$	5.36410	+	5.36410i	0.209593	+	0.209593i
$656$	−1.91102	+	4.38407i	−0.0746128	+	0.171169i
$657$	9.60565	−	9.60565i	0.374752	−	0.374752i
$658$	20.6214	−	4.00350i	0.803907	−	0.156073i
$659$	0.847864	+	0.566525i	0.0330281	+	0.0220687i	0.571975	−	0.820271i	$-0.306178\pi$
$659$	0.847864	+	0.566525i	0.0330281	+	0.0220687i	−0.538947	+	0.842340i	$0.681178\pi$
$660$	28.5503	−	5.40691i	1.11132	−	0.210464i
$661$	6.08991	+	1.21136i	0.236870	+	0.0471164i	0.312098	−	0.950050i	$-0.398968\pi$
$661$	6.08991	+	1.21136i	0.236870	+	0.0471164i	−0.0752276	+	0.997166i	$0.523968\pi$
$662$	9.10518	−	21.6995i	0.353883	−	0.843373i
$663$	1.83402	+	4.42771i	0.0712274	+	0.171958i
$664$	−5.17727	−	13.0029i	−0.200917	−	0.504609i
$665$	8.51159	−	20.5488i	0.330065	−	0.796848i
$666$	3.98634	−	3.94989i	0.154467	−	0.153055i
$667$	34.1445	−	22.8146i	1.32208	−	0.883386i
$668$	−27.1876	+	26.6928i	−1.05192	+	1.03277i
$669$	−2.15786	−	10.8483i	−0.0834276	−	0.419419i
$670$	−0.934761	−	1.41297i	−0.0361130	−	0.0545879i
$671$			35.5626i			1.37288i
$672$	−8.71755	−	22.4933i	−0.336287	−	0.867697i
$673$		−	6.82199i		−	0.262968i	−0.991318	−	0.131484i	$-0.958026\pi$
$673$		−	6.82199i		−	0.262968i	0.991318	−	0.131484i	$-0.0419743\pi$
$674$	24.1156	−	15.9538i	0.928897	−	0.614518i
$675$	−1.55461	−	7.81554i	−0.0598369	−	0.300820i
$676$	−0.223427	+	24.3269i	−0.00859335	+	0.935650i
$677$	−18.8825	+	12.6169i	−0.725714	+	0.484907i	−0.862732	−	0.505662i	$-0.831248\pi$
$677$	−18.8825	+	12.6169i	−0.725714	+	0.484907i	0.137018	+	0.990569i	$0.456248\pi$
$678$	0.0194144	+	0.0195935i	0.000745605	+	0.000752485i
$679$	−0.304032	+	0.733998i	−0.0116677	+	0.0281682i
$680$	37.2275	+	38.2676i	1.42761	+	1.46750i
$681$	−2.83994	−	6.85621i	−0.108827	−	0.262731i
$682$	−12.9852	−	5.44863i	−0.497228	−	0.208639i
$683$	36.1095	+	7.18262i	1.38169	+	0.274835i	0.829325	−	0.558767i	$-0.188725\pi$
$683$	36.1095	+	7.18262i	1.38169	+	0.274835i	0.552366	+	0.833602i	$0.313725\pi$
$684$	2.39355	+	1.63132i	0.0915198	+	0.0623749i
$685$	−42.4448	−	28.3607i	−1.62173	−	1.08361i
$686$	4.81102	+	24.7808i	0.183685	+	0.946135i
$687$	−20.1133	+	20.1133i	−0.767371	+	0.767371i
$688$	14.7330	+	22.9511i	0.561690	+	0.875004i
$689$	5.61700	+	5.61700i	0.213991	+	0.213991i
$690$	−20.0904	+	29.7705i	−0.764828	+	1.13334i
$691$	5.03225	−	7.53129i	0.191436	−	0.286504i	−0.723319	−	0.690514i	$-0.757384\pi$
$691$	5.03225	−	7.53129i	0.191436	−	0.286504i	0.914754	+	0.404011i	$0.132384\pi$
$692$	19.9260	+	30.4225i	0.757472	+	1.15649i
$693$	3.35649	−	16.8742i	0.127503	−	0.640999i
$694$	−0.679388	+	0.277763i	−0.0257892	+	0.0105438i
$695$	−44.8406	+	18.5736i	−1.70090	+	0.704536i
$696$	3.43543	−	16.1081i	0.130220	−	0.610575i
$697$	−5.78977	−	2.39820i	−0.219303	−	0.0908383i
$698$	0.173385	−	37.7573i	0.00656271	−	1.42914i
$699$	0.659303	+	0.986717i	0.0249371	+	0.0373211i
$700$	63.0270	−	25.4310i	2.38220	−	0.961202i
$701$	39.6170	−	7.88032i	1.49631	−	0.297636i	0.622009	−	0.783010i	$-0.286317\pi$
$701$	39.6170	−	7.88032i	1.49631	−	0.297636i	0.874306	+	0.485375i	$0.161317\pi$
$702$	−0.258089	+	1.26706i	−0.00974094	+	0.0478223i
$703$	−5.74708			−0.216755
$704$	−31.8169	+	5.42221i	−1.19915	+	0.204357i
$705$	−12.5435			−0.472417
$706$	0.595855	−	2.92530i	0.0224253	−	0.110095i
$707$	43.2105	−	8.59511i	1.62510	−	0.323252i
$708$	−4.70294	−	11.6555i	−0.176747	−	0.438042i
$709$	−10.3388	−	15.4731i	−0.388281	−	0.581104i	0.584911	−	0.811098i	$-0.301129\pi$
$709$	−10.3388	−	15.4731i	−0.388281	−	0.581104i	−0.973192	+	0.229994i	$0.926129\pi$
$710$	−0.253983	+	55.3089i	−0.00953180	+	2.07570i
$711$	−4.88897	−	2.02508i	−0.183351	−	0.0759463i
$712$	14.1996	−	9.20749i	0.532153	−	0.345065i
$713$	16.0804	−	6.66071i	0.602215	−	0.249445i
$714$	29.2597	−	11.9626i	1.09502	−	0.447690i
$715$	2.59167	−	13.0292i	0.0969229	−	0.487264i
$716$	22.6522	−	14.8366i	0.846553	−	0.554471i
$717$	9.85080	−	14.7428i	0.367885	−	0.550579i
$718$	−21.5526	+	31.9373i	−0.804337	+	1.19189i
$719$	−22.0403	−	22.0403i	−0.821965	−	0.821965i	0.164425	−	0.986390i	$-0.447423\pi$
$719$	−22.0403	−	22.0403i	−0.821965	−	0.821965i	−0.986390	+	0.164425i	$0.947423\pi$
$720$	2.55027	+	14.1773i	0.0950431	+	0.528355i
$721$	−13.7893	+	13.7893i	−0.513539	+	0.513539i
$722$	4.55566	+	23.4655i	0.169544	+	0.873296i
$723$	19.6629	+	13.1384i	0.731273	+	0.488621i
$724$	−21.6874	+	31.8209i	−0.806006	+	1.18262i
$725$	45.5110	+	9.05271i	1.69024	+	0.336209i
$726$	−6.88132	−	2.88743i	−0.255390	−	0.107163i
$727$	−13.7095	−	33.0977i	−0.508458	−	1.22753i	−0.944771	−	0.327732i	$-0.893716\pi$
$727$	−13.7095	−	33.0977i	−0.508458	−	1.22753i	0.436312	−	0.899795i	$-0.356284\pi$
$728$	−11.0276	−	0.151927i	−0.408709	−	0.00563079i
$729$	0.382683	−	0.923880i	0.0141735	−	0.0342178i
$730$	−48.6952	−	49.1445i	−1.80229	−	1.81892i
$731$	−29.7147	+	19.8548i	−1.09904	+	0.734355i
$732$	−17.6287	−	0.161908i	−0.651575	−	0.00598429i
$733$	5.88351	+	29.5784i	0.217312	+	1.09250i	0.923241	+	0.384220i	$0.125530\pi$
$733$	5.88351	+	29.5784i	0.217312	+	1.09250i	−0.705929	+	0.708282i	$0.749470\pi$
$734$	−21.5499	+	14.2565i	−0.795421	+	0.526216i
$735$		−	40.2820i		−	1.48582i
$736$	22.9188	−	32.6519i	0.844798	−	1.20356i
$737$			1.34210i			0.0494367i
$738$	−0.932926	−	1.41020i	−0.0343415	−	0.0519101i
$739$	−8.19891	−	41.2187i	−0.301602	−	1.51626i	−0.773041	−	0.634357i	$-0.781265\pi$
$739$	−8.19891	−	41.2187i	−0.301602	−	1.51626i	0.471439	−	0.881899i	$-0.343735\pi$
$740$	−20.0228	−	20.3940i	−0.736054	−	0.749700i
$741$	1.10107	−	0.735713i	0.0404489	−	0.0270271i
$742$	37.2185	−	36.8782i	1.36633	−	1.35384i
$743$	−4.17592	+	10.0816i	−0.153200	+	0.369857i	−0.981782	−	0.190010i	$-0.939148\pi$
$743$	−4.17592	+	10.0816i	−0.153200	+	0.369857i	0.828582	+	0.559867i	$0.189148\pi$
$744$	2.76005	−	6.41206i	0.101188	−	0.235077i
$745$	−14.6301	−	35.3202i	−0.536006	−	1.29403i
$746$	−0.436569	+	1.04043i	−0.0159839	+	0.0380929i
$747$	4.85313	+	0.965348i	0.177567	+	0.0353203i
$748$	−7.86964	−	41.5543i	−0.287743	−	1.51938i
$749$	−60.2068	−	40.2289i	−2.19991	−	1.46993i
$750$	−14.8419	+	2.88144i	−0.541948	+	0.105215i
$751$	9.56875	−	9.56875i	0.349169	−	0.349169i	−0.510631	−	0.859800i	$-0.670588\pi$
$751$	9.56875	−	9.56875i	0.349169	−	0.349169i	0.859800	+	0.510631i	$0.170588\pi$
$752$	13.9303	+	0.255902i	0.507984	+	0.00933180i
$753$	5.42279	+	5.42279i	0.197618	+	0.197618i
$754$	−6.24153	−	4.21204i	−0.227303	−	0.153393i
$755$	28.9192	−	43.2806i	1.05248	−	1.57514i
$756$	8.34943	+	1.74067i	0.303666	+	0.0633075i
$757$	5.47612	−	27.5303i	0.199033	−	1.00061i	−0.744069	−	0.668103i	$-0.767107\pi$
$757$	5.47612	−	27.5303i	0.199033	−	1.00061i	0.943102	−	0.332504i	$-0.107893\pi$
$758$	−11.6291	−	28.4438i	−0.422387	−	1.03312i
$759$	26.2856	−	10.8878i	0.954105	−	0.395203i
$760$	8.36396	−	12.1518i	0.303393	−	0.440791i
$761$	22.6499	+	9.38191i	0.821060	+	0.340094i	0.753357	−	0.657611i	$-0.228433\pi$
$761$	22.6499	+	9.38191i	0.821060	+	0.340094i	0.0677025	+	0.997706i	$0.478433\pi$
$762$	3.76544	+	0.0172912i	0.136407	+	0.000626394i
$763$	−23.4926	−	35.1592i	−0.850490	−	1.27285i
$764$	−4.87327	−	2.07121i	−0.176309	−	0.0749338i
$765$	−18.5129	+	3.68244i	−0.669335	+	0.133139i
$766$	−7.45928	−	1.51938i	−0.269515	−	0.0548976i
$767$	−5.74602			−0.207477
$768$	−2.54298	−	15.7966i	−0.0917619	−	0.570011i
$769$	−28.8978			−1.04208			−0.521040	−	0.853532i	$-0.674456\pi$
$769$	−28.8978			−1.04208			−0.521040	+	0.853532i	$0.674456\pi$
$770$	−85.8588	−	17.4886i	−3.09414	−	0.630246i
$771$	−19.0373	+	3.78675i	−0.685611	+	0.136377i
$772$	−36.8516	−	15.6625i	−1.32632	−	0.563705i
$773$	23.8801	+	35.7390i	0.858906	+	1.28544i	0.956947	+	0.290261i	$0.0937422\pi$
$773$	23.8801	+	35.7390i	0.858906	+	1.28544i	−0.0980414	+	0.995182i	$0.531258\pi$
$774$	−9.64235	−	0.0442785i	−0.346587	−	0.00159156i
$775$	18.1704	+	7.52642i	0.652700	+	0.270357i
$776$	−0.298759	+	0.434058i	−0.0107248	+	0.0155818i
$777$	−15.6340	+	6.47580i	−0.560865	+	0.232318i
$778$	−13.3752	−	32.7148i	−0.479526	−	1.17288i
$779$	−0.337821	+	1.69834i	−0.0121037	+	0.0608494i
$780$	6.44689	+	1.34403i	0.230836	+	0.0481241i
$781$	24.3423	−	36.4308i	0.871034	−	1.30359i
$782$	43.3303	+	29.2411i	1.54949	+	1.04566i
$783$	4.11758	+	4.11758i	0.147150	+	0.147150i
$784$	−0.821799	+	44.7353i	−0.0293500	+	1.59769i
$785$	20.2957	−	20.2957i	0.724386	−	0.724386i
$786$	2.92446	−	0.567763i	0.104312	−	0.0202514i
$787$	33.6840	+	22.5070i	1.20071	+	0.802286i	0.984726	−	0.174111i	$-0.0557053\pi$
$787$	33.6840	+	22.5070i	1.20071	+	0.802286i	0.215980	+	0.976398i	$0.430705\pi$
$788$	−4.74687	−	25.0651i	−0.169100	−	0.892906i
$789$	7.08673	+	1.40964i	0.252294	+	0.0501844i
$790$	−10.4277	+	24.8513i	−0.371000	+	0.884168i
$791$	−0.0318297	−	0.0768436i	−0.00113173	−	0.00273224i
$792$	4.51168	−	10.4814i	0.160316	−	0.372440i
$793$	−3.08432	+	7.44620i	−0.109527	+	0.264422i
$794$	1.50559	−	1.49182i	0.0534313	−	0.0529428i
$795$	−26.0137	+	17.3818i	−0.922611	+	0.616469i
$796$	24.5745	+	25.0301i	0.871021	+	0.887169i
$797$	−2.99772	−	15.0706i	−0.106185	−	0.533827i	−0.996860	−	0.0791867i	$-0.974768\pi$
$797$	−2.99772	−	15.0706i	−0.106185	−	0.533827i	0.890675	−	0.454641i	$-0.150232\pi$
$798$	−4.81923	−	7.28469i	−0.170599	−	0.257875i
$799$			18.2568i			0.645880i
$800$	44.4016	−	7.77686i	1.56983	−	0.274953i
$801$			5.98338i			0.211412i
$802$	−5.42397	+	3.58826i	−0.191527	+	0.126706i
$803$	10.6921	+	53.7528i	0.377316	+	1.89689i
$804$	−0.665289	−	0.00611025i	−0.0234629	−	0.000215492i
$805$	90.0484	−	60.1684i	3.17379	−	2.12066i
$806$	−2.24632	−	2.26705i	−0.0791232	−	0.0798533i
$807$	2.00948	−	4.85131i	0.0707370	−	0.170774i
$808$	29.2183	+	0.402540i	1.02789	+	0.0141613i
$809$	11.9187	+	28.7743i	0.419039	+	1.01165i	0.982626	+	0.185594i	$0.0594209\pi$
$809$	11.9187	+	28.7743i	0.419039	+	1.01165i	−0.563587	+	0.826057i	$0.690579\pi$
$810$	−4.69620	−	1.97054i	−0.165008	−	0.0692378i
$811$	12.5013	+	2.48667i	0.438982	+	0.0873189i	0.409633	−	0.912250i	$-0.365657\pi$
$811$	12.5013	+	2.48667i	0.438982	+	0.0873189i	0.0293486	+	0.999569i	$0.490657\pi$
$812$	−27.9706	+	41.0400i	−0.981577	+	1.44022i
$813$	18.3833	+	12.2833i	0.644731	+	0.430796i
$814$	4.31495	+	22.2257i	0.151239	+	0.779009i
$815$	−18.9339	+	18.9339i	−0.663226	+	0.663226i
$816$	20.6347	−	3.71186i	0.722358	−	0.129941i
$817$	6.98258	+	6.98258i	0.244290	+	0.244290i
$818$	−1.32347	+	1.96116i	−0.0462741	+	0.0685704i
$819$	2.16628	−	3.24207i	0.0756961	−	0.113287i
$820$	−7.20370	+	4.71824i	−0.251564	+	0.164768i
$821$	−0.879705	+	4.42257i	−0.0307019	+	0.154349i	−0.993095	−	0.117311i	$-0.962573\pi$
$821$	−0.879705	+	4.42257i	−0.0307019	+	0.154349i	0.962393	+	0.271660i	$0.0875726\pi$
$822$	−18.5559	+	7.58646i	−0.647210	+	0.264608i
$823$	−44.9645	+	18.6249i	−1.56736	+	0.649223i	−0.986349	−	0.164671i	$-0.947344\pi$
$823$	−44.9645	+	18.6249i	−1.56736	+	0.649223i	−0.581014	+	0.813894i	$0.697344\pi$
$824$	−10.8523	+	7.03697i	−0.378057	+	0.245144i
$825$	29.7020	+	12.3030i	1.03409	+	0.428334i
$826$	−0.174037	+	37.8993i	−0.00605551	+	1.31869i
$827$	14.7002	+	22.0005i	0.511177	+	0.765031i	0.993846	−	0.110772i	$-0.0353324\pi$
$827$	14.7002	+	22.0005i	0.511177	+	0.765031i	−0.482668	+	0.875803i	$0.660332\pi$
$828$	5.27752	+	13.0796i	0.183407	+	0.454546i
$829$	15.3163	−	3.04659i	0.531956	−	0.105813i	0.0781983	−	0.996938i	$-0.475083\pi$
$829$	15.3163	−	3.04659i	0.531956	−	0.105813i	0.453757	+	0.891125i	$0.350083\pi$
$830$	5.02984	−	24.6935i	0.174588	−	0.857125i
$831$	4.61816			0.160202
$832$	−7.13219	−	1.62414i	−0.247264	−	0.0563070i
$833$	−58.6296			−2.03139
$834$	−3.80423	+	18.6765i	−0.131730	+	0.646715i
$835$	−67.2861	+	13.3840i	−2.32853	+	0.463174i
$836$	−10.8373	+	4.37277i	−0.374814	+	0.151235i
$837$	1.37121	+	2.05216i	0.0473958	+	0.0709329i
$838$	−0.198997	+	43.3348i	−0.00687424	+	1.49698i
$839$	−29.7793	−	12.3350i	−1.02810	−	0.425851i	−0.196071	−	0.980590i	$-0.562818\pi$
$839$	−29.7793	−	12.3350i	−1.02810	−	0.425851i	−0.832025	+	0.554738i	$0.812818\pi$
$840$	9.06017	−	42.4814i	0.312605	−	1.46575i
$841$	−4.53533	+	1.87860i	−0.156391	+	0.0647792i
$842$	−36.0560	+	14.7413i	−1.24257	+	0.508018i
$843$	−2.25164	+	11.3198i	−0.0775507	+	0.389874i
$844$	−6.34279	−	9.68402i	−0.218328	−	0.333338i
$845$	−24.3367	+	36.4225i	−0.837208	+	1.25297i
$846$	−2.75547	+	4.08314i	−0.0947352	+	0.140381i
$847$	15.9119	+	15.9119i	0.546741	+	0.546741i
$848$	29.2442	−	18.7727i	1.00425	−	0.644657i
$849$	−2.66007	+	2.66007i	−0.0912932	+	0.0912932i
$850$	11.2575	+	57.9854i	0.386128	+	1.98888i
$851$	−23.2676	−	15.5469i	−0.797604	−	0.532942i
$852$	17.9482	+	12.2325i	0.614896	+	0.419080i
$853$	1.67452	+	0.333082i	0.0573344	+	0.0114045i	0.223674	−	0.974664i	$-0.428195\pi$
$853$	1.67452	+	0.333082i	0.0573344	+	0.0114045i	−0.166340	+	0.986068i	$0.553195\pi$
$854$	49.0199	+	20.5689i	1.67743	+	0.703854i
$855$	1.99593	+	4.81860i	0.0682594	+	0.164793i
$856$	−33.4887	−	34.4243i	−1.14462	−	1.17660i
$857$	20.9746	−	50.6372i	0.716479	−	1.72973i	0.0333399	−	0.999444i	$-0.489386\pi$
$857$	20.9746	−	50.6372i	0.716479	−	1.72973i	0.683139	−	0.730289i	$-0.260614\pi$
$858$	−3.67191	−	3.70579i	−0.125357	−	0.126514i
$859$	41.9553	−	28.0336i	1.43150	−	0.956495i	0.433016	−	0.901386i	$-0.357449\pi$
$859$	41.9553	−	28.0336i	1.43150	−	0.956495i	0.998480	−	0.0551087i	$-0.0175506\pi$
$860$	−0.451004	+	49.1057i	−0.0153791	+	1.67449i
$861$	0.994704	+	5.00071i	0.0338994	+	0.170424i
$862$	30.5308	−	20.1979i	1.03988	−	0.687943i
$863$			1.64656i			0.0560497i	0.999607	+	0.0280248i	$0.00892175\pi$
$863$			1.64656i			0.0560497i	−0.999607	+	0.0280248i	$0.991078\pi$
$864$	5.17517	+	2.28420i	0.176063	+	0.0777100i
$865$			65.4828i			2.22648i
$866$	20.8037	+	31.4466i	0.706938	+	1.06860i
$867$	2.04318	+	10.2718i	0.0693900	+	0.348847i
$868$	−15.0209	+	14.7475i	−0.509843	+	0.500563i
$869$	17.7514	−	11.8611i	0.602176	−	0.402361i
$870$	21.0664	−	20.8738i	0.714218	−	0.707688i
$871$	−0.116399	+	0.281012i	−0.00394403	+	0.00952174i
$872$	−10.3748	−	26.0566i	−0.351335	−	0.882388i
$873$	−0.0712941	−	0.172119i	−0.00241294	−	0.00582536i
$874$	5.58874	−	13.3191i	0.189042	−	0.450525i
$875$	44.7143	+	8.89423i	1.51162	+	0.300680i
$876$	−26.6944	+	5.05544i	−0.901920	+	0.170807i
$877$	−16.8002	−	11.2255i	−0.567302	−	0.379059i	0.238591	−	0.971120i	$-0.423314\pi$
$877$	−16.8002	−	11.2255i	−0.567302	−	0.379059i	−0.805893	+	0.592061i	$0.798314\pi$
$878$	−37.9832	+	7.37417i	−1.28187	+	0.248866i
$879$	−3.66711	+	3.66711i	−0.123688	+	0.123688i
$880$	−53.2742	−	23.2223i	−1.79587	−	0.782823i
$881$	−26.2013	−	26.2013i	−0.882745	−	0.882745i	0.111067	−	0.993813i	$-0.464573\pi$
$881$	−26.2013	−	26.2013i	−0.882745	−	0.882745i	−0.993813	+	0.111067i	$0.964573\pi$
$882$	−13.1125	−	8.84886i	−0.441521	−	0.297957i
$883$	18.3228	−	27.4220i	0.616612	−	0.922825i	−0.383388	−	0.923587i	$-0.625243\pi$
$883$	18.3228	−	27.4220i	0.616612	−	0.922825i	1.00000		0.000762785i	$0.000242802\pi$
$884$	1.95621	−	9.38330i	0.0657944	−	0.315595i
$885$	4.41509	−	22.1961i	0.148411	−	0.746115i
$886$	8.39343	+	20.5297i	0.281983	+	0.689708i
$887$	9.72837	−	4.02962i	0.326647	−	0.135302i	−0.213333	−	0.976980i	$-0.568432\pi$
$887$	9.72837	−	4.02962i	0.326647	−	0.135302i	0.539980	+	0.841678i	$0.318432\pi$
$888$	−11.0371	+	2.03777i	−0.370381	+	0.0683832i
$889$	−10.4902	−	4.34520i	−0.351831	−	0.145733i
$890$	30.4723	+	0.139931i	1.02143	+	0.00469050i
$891$	2.24142	+	3.35453i	0.0750905	+	0.112381i
$892$	−8.65292	+	20.3591i	−0.289721	+	0.681674i
$893$	4.94772	−	0.984162i	0.165569	−	0.0329337i
$894$	−14.7112	−	2.99653i	−0.492016	−	0.100219i
$895$	48.7577			1.62979
$896$	−10.9285	+	46.9930i	−0.365094	+	1.56993i
$897$	6.44805			0.215294
$898$	38.8457	+	7.91251i	1.29630	+	0.264044i
$899$	−14.0960	+	2.80386i	−0.470127	+	0.0935141i
$900$	−6.23391	+	14.6675i	−0.207797	+	0.488917i
$901$	25.2988	+	37.8624i	0.842826	+	1.26138i
$902$	6.82163	+	0.0313255i	0.227135	+	0.00104302i
$903$	26.8629	+	11.1270i	0.893942	+	0.370283i
$904$	−0.0100160	−	0.0542492i	−0.000333127	−	0.00180430i
$905$	−64.0606	+	26.5348i	−2.12945	+	0.882046i
$906$	−7.73584	−	18.9213i	−0.257006	−	0.628617i
$907$	10.3715	−	52.1412i	0.344381	−	1.73132i	−0.288867	−	0.957369i	$-0.593278\pi$
$907$	10.3715	−	52.1412i	0.344381	−	1.73132i	0.633247	−	0.773949i	$-0.281722\pi$
$908$	−3.02914	+	14.5298i	−0.100526	+	0.482189i
$909$	−5.73971	+	8.59008i	−0.190374	+	0.284915i
$910$	−16.4606	−	11.1083i	−0.545664	−	0.368237i
$911$	−1.48370	−	1.48370i	−0.0491572	−	0.0491572i	0.682101	−	0.731258i	$-0.261066\pi$
$911$	−1.48370	−	1.48370i	−0.0491572	−	0.0491572i	−0.731258	+	0.682101i	$0.761066\pi$
$912$	−2.11828	−	5.39203i	−0.0701433	−	0.178548i
$913$	−14.1162	+	14.1162i	−0.467179	+	0.467179i
$914$	−22.6824	+	4.40363i	−0.750268	+	0.145659i
$915$	−26.3938	−	17.6358i	−0.872552	−	0.583021i
$916$	55.8956	−	10.5856i	1.84684	−	0.349759i
$917$	−8.81057	−	1.75253i	−0.290951	−	0.0578737i
$918$	−2.86808	+	6.83521i	−0.0946607	+	0.225596i
$919$	−7.67862	−	18.5378i	−0.253294	−	0.611507i	0.745172	−	0.666873i	$-0.232367\pi$
$919$	−7.67862	−	18.5378i	−0.253294	−	0.611507i	−0.998466	+	0.0553659i	$0.982367\pi$
$920$	66.7352	−	26.5716i	2.20019	−	0.876039i
$921$	−2.49252	+	6.01746i	−0.0821312	+	0.198282i
$922$	−23.5458	+	23.3305i	−0.775439	+	0.768350i
$923$	8.25647	−	5.51680i	0.271765	−	0.181588i
$924$	−24.5537	+	24.1068i	−0.807758	+	0.793056i
$925$	−6.16893	−	31.0133i	−0.202833	−	1.01971i
$926$	2.56384	+	3.87546i	0.0842530	+	0.127356i
$927$		−	4.57289i		−	0.150194i
$928$	−23.8212	+	22.7517i	−0.781969	+	0.746861i
$929$			30.2284i			0.991761i	0.868391	+	0.495881i	$0.165155\pi$
$929$			30.2284i			0.991761i	−0.868391	+	0.495881i	$0.834845\pi$
$930$	10.4833	−	6.93531i	0.343761	−	0.227418i
$931$	3.16051	+	15.8890i	0.103582	+	0.520740i
$932$	0.0217975	−	2.37333i	0.000714001	−	0.0777410i
$933$	−9.76143	+	6.52238i	−0.319575	+	0.213533i
$934$	16.3536	+	16.5045i	0.535106	+	0.540043i
$935$	29.1424	−	70.3559i	0.953058	−	2.30089i
$936$	1.85371	−	1.80333i	0.0605905	−	0.0589437i
$937$	−11.9287	−	28.7984i	−0.389693	−	0.940802i	−0.990004	−	0.141036i	$-0.954957\pi$
$937$	−11.9287	−	28.7984i	−0.389693	−	0.940802i	0.600311	−	0.799766i	$-0.295043\pi$
$938$	1.84996	+	0.776251i	0.0604034	+	0.0253455i
$939$	−25.6297	−	5.09807i	−0.836395	−	0.166369i
$940$	20.7303	+	14.1286i	0.676146	+	0.460825i
$941$	−4.25584	−	2.84366i	−0.138736	−	0.0927008i	0.484265	−	0.874921i	$-0.339087\pi$
$941$	−4.25584	−	2.84366i	−0.138736	−	0.0927008i	−0.623002	+	0.782221i	$0.714087\pi$
$942$	−2.14820	−	11.0650i	−0.0699922	−	0.360519i
$943$	−5.96204	+	5.96204i	−0.194151	+	0.194151i
$944$	−5.35601	+	24.5599i	−0.174323	+	0.799357i
$945$	10.8592	+	10.8592i	0.353250	+	0.353250i
$946$	21.7611	−	32.2463i	0.707515	−	1.04842i
$947$	−1.72719	+	2.58493i	−0.0561262	+	0.0839988i	−0.858471	−	0.512862i	$-0.828585\pi$
$947$	−1.72719	+	2.58493i	−0.0561262	+	0.0839988i	0.802345	+	0.596860i	$0.203585\pi$
$948$	5.79885	+	8.85354i	0.188338	+	0.287550i
$949$	−2.42320	+	12.1822i	−0.0786603	+	0.395452i
$950$	15.1076	−	6.17664i	0.490154	−	0.200397i
$951$	−9.66623	+	4.00388i	−0.313449	+	0.129835i
$952$	−61.8307	−	13.1869i	−2.00394	−	0.427389i
$953$	−38.2104	−	15.8273i	−1.23776	−	0.512696i	−0.334744	−	0.942309i	$-0.608650\pi$
$953$	−38.2104	−	15.8273i	−1.23776	−	0.512696i	−0.903013	+	0.429613i	$0.858650\pi$
$954$	−0.0564194	+	12.2862i	−0.00182664	+	0.397781i
$955$	−5.29706	−	7.92762i	−0.171409	−	0.256532i
$956$	−32.8858	+	13.2692i	−1.06360	+	0.429158i
$957$	−23.0418	+	4.58330i	−0.744836	+	0.148157i
$958$	−3.10237	+	15.2308i	−0.100233	+	0.492085i
$959$	60.4499			1.95203
$960$	11.7540	−	26.3028i	0.379360	−	0.848919i
$961$	24.9085			0.803498
$962$	−1.02414	+	5.02791i	−0.0330195	+	0.162106i
$963$	16.6536	−	3.31261i	0.536655	−	0.106747i
$964$	−17.6976	−	43.8610i	−0.570003	−	1.41267i
$965$	−40.0563	−	59.9486i	−1.28946	−	1.92981i
$966$	0.195300	−	42.5297i	0.00628367	−	1.36837i
$967$	−11.3633	−	4.70685i	−0.365420	−	0.151362i	0.192415	−	0.981314i	$-0.438368\pi$
$967$	−11.3633	−	4.70685i	−0.365420	−	0.151362i	−0.557835	+	0.829952i	$0.688368\pi$
$968$	8.12021	+	12.5228i	0.260994	+	0.402499i
$969$	7.01337	−	2.90503i	0.225302	−	0.0933231i
$970$	−0.878239	+	0.359063i	−0.0281986	+	0.0115288i
$971$	−5.26747	+	26.4814i	−0.169041	+	0.849827i	0.799441	+	0.600745i	$0.205129\pi$
$971$	−5.26747	+	26.4814i	−0.169041	+	0.849827i	−0.968482	+	0.249083i	$0.919871\pi$
$972$	−1.67307	+	1.09582i	−0.0536639	+	0.0351485i
$973$	31.9310	−	47.7881i	1.02366	−	1.53202i
$974$	−19.5354	+	28.9482i	−0.625955	+	0.927559i
$975$	5.15206	+	5.15206i	0.164998	+	0.164998i
$976$	28.9519	+	20.1239i	0.926729	+	0.644151i
$977$	−13.2125	+	13.2125i	−0.422705	+	0.422705i	−0.886134	−	0.463429i	$-0.846619\pi$
$977$	−13.2125	+	13.2125i	−0.422705	+	0.422705i	0.463429	+	0.886134i	$0.346619\pi$
$978$	2.00406	+	10.3226i	0.0640828	+	0.330080i
$979$	−20.0714	−	13.4113i	−0.641485	−	0.428627i
$980$	−45.3723	+	66.5726i	−1.44936	+	2.12658i
$981$	9.72526	+	1.93447i	0.310504	+	0.0617630i
$982$	11.5565	+	4.84917i	0.368784	+	0.154743i
$983$	−11.8702	−	28.6573i	−0.378601	−	0.914025i	−0.992229	−	0.124429i	$-0.960290\pi$
$983$	−11.8702	−	28.6573i	−0.378601	−	0.914025i	0.613627	−	0.789596i	$-0.289710\pi$
$984$	−0.0465856	+	3.38140i	−0.00148510	+	0.107795i
$985$	17.5783	−	42.4378i	0.560092	−	1.35218i
$986$	−30.3813	−	30.6617i	−0.967539	−	0.976466i
$987$	12.3505	−	8.25233i	0.393120	−	0.262675i
$988$	−2.64839	−	0.0243237i	−0.0842564	−	0.000773840i
$989$	9.38048	+	47.1589i	0.298282	+	1.49956i
$990$	17.1364	−	11.3367i	0.544631	−	0.360304i
$991$			10.9584i			0.348106i	0.984736	+	0.174053i	$0.0556864\pi$
$991$			10.9584i			0.348106i	−0.984736	+	0.174053i	$0.944314\pi$
$992$	−11.7838	+	7.48815i	−0.374135	+	0.237749i
$993$		−	16.6399i		−	0.528050i
$994$	−36.1374	−	54.6247i	−1.14621	−	1.73259i
$995$	12.3219	+	61.9466i	0.390632	+	1.96384i
$996$	−6.93327	−	7.06180i	−0.219689	−	0.223762i
$997$	−27.7306	+	18.5290i	−0.878237	+	0.586819i	−0.910891	−	0.412647i	$-0.864604\pi$
$997$	−27.7306	+	18.5290i	−0.878237	+	0.586819i	0.0326537	+	0.999467i	$0.489604\pi$
$998$	26.0934	−	25.8548i	0.825971	−	0.818420i
$999$	1.51855	−	3.66610i	0.0480447	−	0.115990i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.2.r.a.181.2	yes	128
3.2	odd	2		576.2.bd.b.181.15		128
4.3	odd	2		768.2.r.a.49.15		128
64.29	even	16	inner	192.2.r.a.157.2	✓	128
64.35	odd	16		768.2.r.a.721.15		128
192.29	odd	16		576.2.bd.b.541.15		128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
192.2.r.a.157.2	✓	128	64.29	even	16	inner
192.2.r.a.181.2	yes	128	1.1	even	1	trivial
576.2.bd.b.181.15		128	3.2	odd	2
576.2.bd.b.541.15		128	192.29	odd	16
768.2.r.a.49.15		128	4.3	odd	2
768.2.r.a.721.15		128	64.35	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)

\(f(q)\)	\(=\)	\(q+(-1.38576 - 0.282266i) q^{2} +(-0.980785 + 0.195090i) q^{3} +(1.84065 + 0.782304i) q^{4} +(2.00072 + 2.99429i) q^{5} +(1.41420 + 0.00649411i) q^{6} +(-3.93986 - 1.63194i) q^{7} +(-2.32988 - 1.60364i) q^{8} +(0.923880 - 0.382683i) q^{9} +O(q^{10})\)	\(q+(-1.38576 - 0.282266i) q^{2} +(-0.980785 + 0.195090i) q^{3} +(1.84065 + 0.782304i) q^{4} +(2.00072 + 2.99429i) q^{5} +(1.41420 + 0.00649411i) q^{6} +(-3.93986 - 1.63194i) q^{7} +(-2.32988 - 1.60364i) q^{8} +(0.923880 - 0.382683i) q^{9} +(-1.92733 - 4.71410i) q^{10} +(-0.787083 + 3.95693i) q^{11} +(-1.95790 - 0.408179i) q^{12} +(-0.507984 + 0.760252i) q^{13} +(4.99905 + 3.37356i) q^{14} +(-2.54643 - 2.54643i) q^{15} +(2.77600 + 2.87990i) q^{16} +(-3.70628 + 3.70628i) q^{17} +(-1.38829 + 0.269527i) q^{18} +(1.20422 + 0.804632i) q^{19} +(1.34018 + 7.07662i) q^{20} +(4.18253 + 0.831957i) q^{21} +(2.20761 - 5.26119i) q^{22} +(2.69871 + 6.51527i) q^{23} +(2.59797 + 1.11829i) q^{24} +(-3.04947 + 7.36208i) q^{25} +(0.918536 - 0.910139i) q^{26} +(-0.831470 + 0.555570i) q^{27} +(-5.97523 - 6.08601i) q^{28} +(-1.13604 - 5.71125i) q^{29} +(2.80997 + 4.24751i) q^{30} -2.46811i q^{31} +(-3.03397 - 4.77442i) q^{32} -4.03446i q^{33} +(6.18216 - 4.08985i) q^{34} +(-2.99605 - 15.0621i) q^{35} +(1.99992 + 0.0183679i) q^{36} +(-3.29940 + 2.20459i) q^{37} +(-1.44163 - 1.45493i) q^{38} +(0.349906 - 0.844747i) q^{39} +(0.140316 - 10.1848i) q^{40} +(0.457544 + 1.10461i) q^{41} +(-5.56114 - 2.33348i) q^{42} +(6.68723 + 1.33017i) q^{43} +(-4.54427 + 6.66760i) q^{44} +(2.99429 + 2.00072i) q^{45} +(-1.90073 - 9.79034i) q^{46} +(2.46296 - 2.46296i) q^{47} +(-3.28450 - 2.28299i) q^{48} +(7.90949 + 7.90949i) q^{49} +(6.30390 - 9.34130i) q^{50} +(2.91200 - 4.35812i) q^{51} +(-1.52977 + 1.00196i) q^{52} +(1.69490 - 8.52084i) q^{53} +(1.30903 - 0.535191i) q^{54} +(-13.4229 + 5.55996i) q^{55} +(6.56235 + 10.1203i) q^{56} +(-1.33805 - 0.554240i) q^{57} +(-0.0378162 + 8.23508i) q^{58} +(3.49136 + 5.22519i) q^{59} +(-2.69501 - 6.67919i) q^{60} +(8.64534 - 1.71967i) q^{61} +(-0.696662 + 3.42020i) q^{62} -4.26447 q^{63} +(2.85669 + 7.47257i) q^{64} -3.29275 q^{65} +(-1.13879 + 5.59078i) q^{66} +(0.326267 - 0.0648985i) q^{67} +(-9.72141 + 3.92253i) q^{68} +(-3.91792 - 5.86359i) q^{69} +(-0.0997315 + 21.7182i) q^{70} +(-10.0335 - 4.15601i) q^{71} +(-2.76622 - 0.589961i) q^{72} +(12.5504 - 5.19854i) q^{73} +(5.19445 - 2.12372i) q^{74} +(1.55461 - 7.81554i) q^{75} +(1.58708 + 2.42311i) q^{76} +(9.55848 - 14.3053i) q^{77} +(-0.723328 + 1.07185i) q^{78} +(-3.74185 - 3.74185i) q^{79} +(-3.06926 + 14.0740i) q^{80} +(0.707107 - 0.707107i) q^{81} +(-0.322252 - 1.65987i) q^{82} +(4.11429 + 2.74908i) q^{83} +(7.04774 + 4.80335i) q^{84} +(-18.5129 - 3.68244i) q^{85} +(-8.89143 - 3.73088i) q^{86} +(2.22842 + 5.37988i) q^{87} +(8.17930 - 7.95699i) q^{88} +(-2.28974 + 5.52793i) q^{89} +(-3.58463 - 3.61770i) q^{90} +(3.24207 - 2.16628i) q^{91} +(-0.129532 + 14.1036i) q^{92} +(0.481504 + 2.42068i) q^{93} +(-4.10828 + 2.71786i) q^{94} +5.21562i q^{95} +(3.90711 + 4.09078i) q^{96} -0.186301i q^{97} +(-8.72806 - 13.1932i) q^{98} +(0.787083 + 3.95693i) 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

Related objects

Downloads

Learn more