LMFDB - Embedded newform 960.2.cn.a.611.25

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [960,2,Mod(11,960)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(960, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([8, 5, 8, 0]))

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

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

chi := DirichletCharacter("960.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 960 = 2^{6} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	960.cn (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:	$7.66563859404$
Analytic rank:	$0$
Dimension:	$1024$
Relative dimension:	$128$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			611.25
Character	$\chi$	$=$	960.611
Dual form			960.2.cn.a.11.25

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.14053 - 0.836178i) q^{2} +(-1.69151 - 0.372539i) q^{3} +(0.601612 + 1.90737i) q^{4} +(0.831470 + 0.555570i) q^{5} +(1.61771 + 1.83930i) q^{6} +(1.37816 + 3.32718i) q^{7} +(0.908746 - 2.67847i) q^{8} +(2.72243 + 1.26031i) q^{9} +O(q^{10})$	\(q+(-1.14053 - 0.836178i) q^{2} +(-1.69151 - 0.372539i) q^{3} +(0.601612 + 1.90737i) q^{4} +(0.831470 + 0.555570i) q^{5} +(1.61771 + 1.83930i) q^{6} +(1.37816 + 3.32718i) q^{7} +(0.908746 - 2.67847i) q^{8} +(2.72243 + 1.26031i) q^{9} +(-0.483759 - 1.32890i) q^{10} +(0.927897 + 4.66486i) q^{11} +(-0.307063 - 3.45047i) q^{12} +(-0.139558 - 0.208863i) q^{13} +(1.21028 - 4.94713i) q^{14} +(-1.19947 - 1.24951i) q^{15} +(-3.27613 + 2.29499i) q^{16} +(-0.486157 + 0.486157i) q^{17} +(-2.05116 - 3.71386i) q^{18} +(2.52528 + 3.77936i) q^{19} +(-0.559456 + 1.92016i) q^{20} +(-1.09167 - 6.14138i) q^{21} +(2.84236 - 6.09629i) q^{22} +(0.746279 - 1.80168i) q^{23} +(-2.53499 + 4.19211i) q^{24} +(0.382683 + 0.923880i) q^{25} +(-0.0154771 + 0.354910i) q^{26} +(-4.13551 - 3.14604i) q^{27} +(-5.51704 + 4.63034i) q^{28} +(-5.44222 - 1.08252i) q^{29} +(0.323217 + 2.42807i) q^{30} -5.21038 q^{31} +(5.65554 + 0.121920i) q^{32} +(0.168292 - 8.23634i) q^{33} +(0.960991 - 0.147962i) q^{34} +(-0.702581 + 3.53211i) q^{35} +(-0.766033 + 5.95090i) q^{36} +(-7.41579 - 4.95507i) q^{37} +(0.280055 - 6.42205i) q^{38} +(0.158254 + 0.405286i) q^{39} +(2.24367 - 1.72219i) q^{40} +(-0.503535 - 0.208571i) q^{41} +(-3.89021 + 7.91726i) q^{42} +(-1.25617 - 6.31521i) q^{43} +(-8.33937 + 4.57628i) q^{44} +(1.56343 + 2.56041i) q^{45} +(-2.35768 + 1.43084i) q^{46} +(7.39004 + 7.39004i) q^{47} +(6.39658 - 2.66152i) q^{48} +(-4.22104 + 4.22104i) q^{49} +(0.336067 - 1.37370i) q^{50} +(1.00345 - 0.641229i) q^{51} +(0.314420 - 0.391844i) q^{52} +(-6.90392 + 1.37328i) q^{53} +(2.08601 + 7.04617i) q^{54} +(-1.82014 + 4.39420i) q^{55} +(10.1641 - 0.667800i) q^{56} +(-2.86359 - 7.33359i) q^{57} +(5.30182 + 5.78532i) q^{58} +(-6.02530 + 9.01749i) q^{59} +(1.66166 - 3.03955i) q^{60} +(12.7023 + 2.52665i) q^{61} +(5.94259 + 4.35681i) q^{62} +(-0.441326 + 10.7949i) q^{63} +(-6.34836 - 4.86809i) q^{64} -0.251198i q^{65} +(-7.07899 + 9.25306i) q^{66} +(-0.654549 + 3.29064i) q^{67} +(-1.21976 - 0.634804i) q^{68} +(-1.93354 + 2.76954i) q^{69} +(3.75479 - 3.44099i) q^{70} +(9.82712 - 4.07053i) q^{71} +(5.84969 - 6.14663i) q^{72} +(-3.16403 - 1.31058i) q^{73} +(4.31460 + 11.8523i) q^{74} +(-0.303132 - 1.70532i) q^{75} +(-5.68939 + 7.09036i) q^{76} +(-14.2420 + 9.51621i) q^{77} +(0.158398 - 0.594569i) q^{78} +(6.49247 + 6.49247i) q^{79} +(-3.99903 + 0.0880990i) q^{80} +(5.82324 + 6.86221i) q^{81} +(0.399894 + 0.658927i) q^{82} +(0.476554 - 0.318424i) q^{83} +(11.0571 - 5.77696i) q^{84} +(-0.674320 + 0.134131i) q^{85} +(-3.84794 + 8.25307i) q^{86} +(8.80230 + 3.85855i) q^{87} +(13.3379 + 1.75383i) q^{88} +(-6.88885 + 2.85346i) q^{89} +(0.357826 - 4.22752i) q^{90} +(0.502592 - 0.752182i) q^{91} +(3.88544 + 0.339521i) q^{92} +(8.81343 + 1.94107i) q^{93} +(-2.24916 - 14.6079i) q^{94} +4.54539i q^{95} +(-9.52100 - 2.31314i) q^{96} -18.0967i q^{97} +(8.34375 - 1.28467i) q^{98} +(-3.35303 + 13.8692i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1024 q+O(q^{10}) $ 1024 * q	$ 1024 q + 80 q^{24} + 80 q^{42} - 96 q^{52} - 288 q^{58} - 96 q^{64} + 256 q^{67} - 112 q^{76} - 48 q^{78} + 32 q^{79} - 112 q^{84} - 160 q^{88} - 144 q^{90} - 16 q^{94} - 272 q^{96}+O(q^{100}) $ 1024 * q + 80 * q^24 + 80 * q^42 - 96 * q^52 - 288 * q^58 - 96 * q^64 + 256 * q^67 - 112 * q^76 - 48 * q^78 + 32 * q^79 - 112 * q^84 - 160 * q^88 - 144 * q^90 - 16 * q^94 - 272 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/960\mathbb{Z}\right)^\times$.

$n$	$511$	$577$	$641$	$901$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{11}{16}\right)$

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 $

$2$	−1.14053	−	0.836178i	−0.806476	−	0.591267i
$2$	−1.14053	−	0.836178i	−0.806476	−	0.591267i
$3$	−1.69151	−	0.372539i	−0.976595	−	0.215086i
$3$	−1.69151	−	0.372539i	−0.976595	−	0.215086i
$4$	0.601612	+	1.90737i	0.300806	+	0.953685i
$5$	0.831470	+	0.555570i	0.371845	+	0.248459i
$5$	0.831470	+	0.555570i	0.371845	+	0.248459i
$6$	1.61771	+	1.83930i	0.660427	+	0.750890i
$7$	1.37816	+	3.32718i	0.520896	+	1.25756i	0.937347	+	0.348397i	$0.113274\pi$
$7$	1.37816	+	3.32718i	0.520896	+	1.25756i	−0.416451	+	0.909158i	$0.636726\pi$
$8$	0.908746	−	2.67847i	0.321290	−	0.946981i
$9$	2.72243	+	1.26031i	0.907476	+	0.420103i
$10$	−0.483759	−	1.32890i	−0.152978	−	0.420235i
$11$	0.927897	+	4.66486i	0.279772	+	1.40651i	0.823534	+	0.567267i	$0.191999\pi$
$11$	0.927897	+	4.66486i	0.279772	+	1.40651i	−0.543762	+	0.839239i	$0.683001\pi$
$12$	−0.307063	−	3.45047i	−0.0886415	−	0.996064i
$13$	−0.139558	−	0.208863i	−0.0387065	−	0.0579283i	0.811612	−	0.584197i	$-0.198591\pi$
$13$	−0.139558	−	0.208863i	−0.0387065	−	0.0579283i	−0.850318	+	0.526269i	$0.823591\pi$
$14$	1.21028	−	4.94713i	0.323461	−	1.32218i
$15$	−1.19947	−	1.24951i	−0.309702	−	0.322622i
$16$	−3.27613	+	2.29499i	−0.819032	+	0.573748i
$17$	−0.486157	+	0.486157i	−0.117911	+	0.117911i	−0.763600	−	0.645690i	$-0.776570\pi$
$17$	−0.486157	+	0.486157i	−0.117911	+	0.117911i	0.645690	+	0.763600i	$0.276570\pi$
$18$	−2.05116	−	3.71386i	−0.483464	−	0.875364i
$19$	2.52528	+	3.77936i	0.579340	+	0.867044i	0.999177	−	0.0405558i	$-0.0129129\pi$
$19$	2.52528	+	3.77936i	0.579340	+	0.867044i	−0.419837	+	0.907599i	$0.637913\pi$
$20$	−0.559456	+	1.92016i	−0.125098	+	0.429360i
$21$	−1.09167	−	6.14138i	−0.238223	−	1.34016i
$22$	2.84236	−	6.09629i	0.605993	−	1.29973i
$23$	0.746279	−	1.80168i	0.155610	−	0.375676i	−0.826778	−	0.562528i	$-0.809829\pi$
$23$	0.746279	−	1.80168i	0.155610	−	0.375676i	0.982388	+	0.186853i	$0.0598287\pi$
$24$	−2.53499	+	4.19211i	−0.517453	+	0.855712i
$25$	0.382683	+	0.923880i	0.0765367	+	0.184776i
$26$	−0.0154771	+	0.354910i	−0.00303530	+	0.0696036i
$27$	−4.13551	−	3.14604i	−0.795879	−	0.605456i
$28$	−5.51704	+	4.63034i	−1.04262	+	0.875051i
$29$	−5.44222	−	1.08252i	−1.01059	−	0.201020i	−0.338091	−	0.941113i	$-0.609781\pi$
$29$	−5.44222	−	1.08252i	−1.01059	−	0.201020i	−0.672504	+	0.740094i	$0.734781\pi$
$30$	0.323217	+	2.42807i	0.0590111	+	0.443303i
$31$	−5.21038			−0.935812			−0.467906	−	0.883778i	$-0.654991\pi$
$31$	−5.21038			−0.935812			−0.467906	+	0.883778i	$0.654991\pi$
$32$	5.65554	+	0.121920i	0.999768	+	0.0215525i
$33$	0.168292	−	8.23634i	0.0292959	−	1.43376i
$34$	0.960991	−	0.147962i	0.164809	−	0.0253753i
$35$	−0.702581	+	3.53211i	−0.118758	+	0.597036i
$36$	−0.766033	+	5.95090i	−0.127672	+	0.991816i
$37$	−7.41579	−	4.95507i	−1.21915	−	0.814609i	−0.231736	−	0.972779i	$-0.574441\pi$
$37$	−7.41579	−	4.95507i	−1.21915	−	0.814609i	−0.987412	+	0.158170i	$0.949441\pi$
$38$	0.280055	−	6.42205i	0.0454309	−	1.04179i
$39$	0.158254	+	0.405286i	0.0253410	+	0.0648977i
$40$	2.24367	−	1.72219i	0.354756	−	0.272302i
$41$	−0.503535	−	0.208571i	−0.0786390	−	0.0325733i	0.343017	−	0.939329i	$-0.388551\pi$
$41$	−0.503535	−	0.208571i	−0.0786390	−	0.0325733i	−0.421656	+	0.906756i	$0.638551\pi$
$42$	−3.89021	+	7.91726i	−0.600272	+	1.22166i
$43$	−1.25617	−	6.31521i	−0.191565	−	0.963061i	−0.950223	−	0.311572i	$-0.899145\pi$
$43$	−1.25617	−	6.31521i	−0.191565	−	0.963061i	0.758658	−	0.651489i	$-0.225855\pi$
$44$	−8.33937	+	4.57628i	−1.25721	+	0.689900i
$45$	1.56343	+	2.56041i	0.233062	+	0.381683i
$46$	−2.35768	+	1.43084i	−0.347620	+	0.210966i
$47$	7.39004	+	7.39004i	1.07795	+	1.07795i	0.996693	+	0.0812549i	$0.0258928\pi$
$47$	7.39004	+	7.39004i	1.07795	+	1.07795i	0.0812549	+	0.996693i	$0.474107\pi$
$48$	6.39658	−	2.66152i	0.923267	−	0.384158i
$49$	−4.22104	+	4.22104i	−0.603005	+	0.603005i
$50$	0.336067	−	1.37370i	0.0475270	−	0.194271i
$51$	1.00345	−	0.641229i	0.140512	−	0.0897900i
$52$	0.314420	−	0.391844i	0.0436022	−	0.0543390i
$53$	−6.90392	+	1.37328i	−0.948326	+	0.188634i	−0.644940	−	0.764234i	$-0.723117\pi$
$53$	−6.90392	+	1.37328i	−0.948326	+	0.188634i	−0.303387	+	0.952867i	$0.598117\pi$
$54$	2.08601	+	7.04617i	0.283871	+	0.958863i
$55$	−1.82014	+	4.39420i	−0.245427	+	0.592513i
$56$	10.1641	−	0.667800i	1.35824	−	0.0892385i
$57$	−2.86359	−	7.33359i	−0.379292	−	0.971358i
$58$	5.30182	+	5.78532i	0.696164	+	0.759649i
$59$	−6.02530	+	9.01749i	−0.784427	+	1.17398i	0.196672	+	0.980469i	$0.436987\pi$
$59$	−6.02530	+	9.01749i	−0.784427	+	1.17398i	−0.981099	+	0.193508i	$0.938013\pi$
$60$	1.66166	−	3.03955i	0.214520	−	0.392405i
$61$	12.7023	+	2.52665i	1.62637	+	0.323504i	0.922254	−	0.386585i	$-0.126345\pi$
$61$	12.7023	+	2.52665i	1.62637	+	0.323504i	0.704112	+	0.710089i	$0.251345\pi$
$62$	5.94259	+	4.35681i	0.754710	+	0.553315i
$63$	−0.441326	+	10.7949i	−0.0556019	+	1.36003i
$64$	−6.34836	−	4.86809i	−0.793545	−	0.608512i
$65$		−	0.251198i		−	0.0311573i
$66$	−7.07899	+	9.25306i	−0.871363	+	1.13897i
$67$	−0.654549	+	3.29064i	−0.0799659	+	0.402016i	0.919983	+	0.391957i	$0.128202\pi$
$67$	−0.654549	+	3.29064i	−0.0799659	+	0.402016i	−0.999949	+	0.0100587i	$0.996798\pi$
$68$	−1.21976	−	0.634804i	−0.147918	−	0.0769814i
$69$	−1.93354	+	2.76954i	−0.232770	+	0.333414i
$70$	3.75479	−	3.44099i	0.448783	−	0.411277i
$71$	9.82712	−	4.07053i	1.16626	−	0.483083i	0.286308	−	0.958137i	$-0.407572\pi$
$71$	9.82712	−	4.07053i	1.16626	−	0.483083i	0.879956	+	0.475055i	$0.157572\pi$
$72$	5.84969	−	6.14663i	0.689393	−	0.724387i
$73$	−3.16403	−	1.31058i	−0.370321	−	0.153392i	0.189759	−	0.981831i	$-0.439229\pi$
$73$	−3.16403	−	1.31058i	−0.370321	−	0.153392i	−0.560080	+	0.828439i	$0.689229\pi$
$74$	4.31460	+	11.8523i	0.501562	+	1.37780i
$75$	−0.303132	−	1.70532i	−0.0350027	−	0.196913i
$76$	−5.68939	+	7.09036i	−0.652618	+	0.813320i
$77$	−14.2420	+	9.51621i	−1.62303	+	1.08447i
$78$	0.158398	−	0.594569i	0.0179350	−	0.0673217i
$79$	6.49247	+	6.49247i	0.730460	+	0.730460i	0.970711	−	0.240251i	$-0.0772296\pi$
$79$	6.49247	+	6.49247i	0.730460	+	0.730460i	−0.240251	+	0.970711i	$0.577230\pi$
$80$	−3.99903	+	0.0880990i	−0.447105	+	0.00984977i
$81$	5.82324	+	6.86221i	0.647026	+	0.762468i
$82$	0.399894	+	0.658927i	0.0441609	+	0.0727663i
$83$	0.476554	−	0.318424i	0.0523086	−	0.0349515i	−0.529141	−	0.848534i	$-0.677486\pi$
$83$	0.476554	−	0.318424i	0.0523086	−	0.0349515i	0.581450	+	0.813582i	$0.302486\pi$
$84$	11.0571	−	5.77696i	1.20643	−	0.630318i
$85$	−0.674320	+	0.134131i	−0.0731402	+	0.0145485i
$86$	−3.84794	+	8.25307i	−0.414934	+	0.889951i
$87$	8.80230	+	3.85855i	0.943706	+	0.413679i
$88$	13.3379	+	1.75383i	1.42182	+	0.186959i
$89$	−6.88885	+	2.85346i	−0.730217	+	0.302466i	−0.716641	−	0.697442i	$-0.754321\pi$
$89$	−6.88885	+	2.85346i	−0.730217	+	0.302466i	−0.0135758	+	0.999908i	$0.504321\pi$
$90$	0.357826	−	4.22752i	0.0377182	−	0.445620i
$91$	0.502592	−	0.752182i	0.0526860	−	0.0788501i
$92$	3.88544	+	0.339521i	0.405085	+	0.0353975i
$93$	8.81343	+	1.94107i	0.913910	+	0.201280i
$94$	−2.24916	−	14.6079i	−0.231983	−	1.50669i
$95$			4.54539i			0.466347i
$96$	−9.52100	−	2.31314i	−0.971733	−	0.236084i
$97$		−	18.0967i		−	1.83744i	−0.394913	−	0.918718i	$-0.629225\pi$
$97$		−	18.0967i		−	1.83744i	0.394913	−	0.918718i	$-0.370775\pi$
$98$	8.34375	−	1.28467i	0.842846	−	0.129772i
$99$	−3.35303	+	13.8692i	−0.336992	+	1.39390i
$100$	−1.53195	+	1.28574i	−0.153195	+	0.128574i
$101$	3.88327	−	5.81173i	0.386400	−	0.578289i	−0.586375	−	0.810040i	$-0.699445\pi$
$101$	3.88327	−	5.81173i	0.386400	−	0.578289i	0.972775	+	0.231751i	$0.0744455\pi$
$102$	−1.68065	−	0.107727i	−0.166409	−	0.0106665i
$103$	6.13023	−	2.53923i	0.604030	−	0.250197i	−0.0596437	−	0.998220i	$-0.518996\pi$
$103$	6.13023	−	2.53923i	0.604030	−	0.250197i	0.663673	+	0.748022i	$0.268996\pi$
$104$	−0.686257	+	0.183998i	−0.0672930	+	0.0180425i
$105$	2.50428	−	5.71287i	0.244392	−	0.557520i
$106$	9.02242	+	4.20665i	0.876335	+	0.408586i
$107$	−14.6310	+	2.91028i	−1.41443	+	0.281348i	−0.842386	−	0.538875i	$-0.818850\pi$
$107$	−14.6310	+	2.91028i	−1.41443	+	0.281348i	−0.572045	+	0.820222i	$0.693850\pi$
$108$	3.51270	−	9.78064i	0.338009	−	0.941143i
$109$	−7.77267	+	5.19353i	−0.744487	+	0.497450i	−0.869027	−	0.494764i	$-0.835254\pi$
$109$	−7.77267	+	5.19353i	−0.744487	+	0.497450i	0.124540	+	0.992215i	$0.460254\pi$
$110$	5.75025	−	3.48975i	0.548265	−	0.332735i
$111$	10.6979	+	11.1442i	1.01540	+	1.05776i
$112$	−12.1509	−	7.73738i	−1.14815	−	0.731114i
$113$	13.1503	+	13.1503i	1.23708	+	1.23708i	0.961190	+	0.275887i	$0.0889716\pi$
$113$	13.1503	+	13.1503i	1.23708	+	1.23708i	0.275887	+	0.961190i	$0.411028\pi$
$114$	−2.86618	+	10.7586i	−0.268443	+	1.00764i
$115$	1.62147	−	1.08343i	0.151203	−	0.101030i
$116$	−1.20933	−	11.0316i	−0.112283	−	1.02426i
$117$	−0.116704	−	0.744502i	−0.0107893	−	0.0688293i
$118$	14.4123	−	5.24649i	1.32676	−	0.482978i
$119$	−2.28754	−	0.947529i	−0.209698	−	0.0868598i
$120$	−4.43678	+	2.07725i	−0.405021	+	0.189626i
$121$	−10.7372	+	4.44750i	−0.976110	+	0.404318i
$122$	−12.3746	−	13.5031i	−1.12035	−	1.22252i
$123$	0.774035	+	0.540387i	0.0697924	+	0.0487251i
$124$	−3.13463	−	9.93813i	−0.281498	−	0.892470i
$125$	−0.195090	+	0.980785i	−0.0174494	+	0.0877241i
$126$	9.52982	−	11.9429i	0.848984	−	1.06396i
$127$			8.36607i			0.742369i	0.928559	+	0.371184i	$0.121048\pi$
$127$			8.36607i			0.742369i	−0.928559	+	0.371184i	$0.878952\pi$
$128$	3.16989	+	10.8606i	0.280182	+	0.959947i
$129$	−0.227831	+	11.1502i	−0.0200594	+	0.981724i
$130$	−0.210046	+	0.286498i	−0.0184223	+	0.0251276i
$131$	0.0989137	+	0.0196752i	0.00864213	+	0.00171903i	0.199409	−	0.979916i	$-0.436098\pi$
$131$	0.0989137	+	0.0196752i	0.00864213	+	0.00171903i	−0.190767	+	0.981635i	$0.561098\pi$
$132$	15.8110	−	4.63408i	1.37617	−	0.403345i
$133$	−9.09434	+	13.6106i	−0.788579	+	1.18019i
$134$	3.49810	−	3.20575i	0.302189	−	0.276935i
$135$	−1.69070	−	4.91340i	−0.145512	−	0.422878i
$136$	0.860362	+	1.74395i	0.0737755	+	0.149542i
$137$	−3.14266	+	7.58705i	−0.268496	+	0.648206i	−0.999413	−	0.0342603i	$-0.989092\pi$
$137$	−3.14266	+	7.58705i	−0.268496	+	0.648206i	0.730917	+	0.682466i	$0.239092\pi$
$138$	4.52108	−	1.54196i	0.384860	−	0.131260i
$139$	−14.3363	+	2.85167i	−1.21599	+	0.241876i	−0.761079	−	0.648660i	$-0.775330\pi$
$139$	−14.3363	+	2.85167i	−1.21599	+	0.241876i	−0.454914	+	0.890536i	$0.650330\pi$
$140$	−7.15973	+	0.784879i	−0.605108	+	0.0663343i
$141$	−9.74727	−	15.2534i	−0.820868	−	1.28457i
$142$	−14.6118	−	3.57467i	−1.22619	−	0.299980i
$143$	0.844822	−	0.844822i	0.0706476	−	0.0706476i
$144$	−11.8114	+	2.11902i	−0.984285	+	0.176585i
$145$	−3.92362	−	3.92362i	−0.325839	−	0.325839i
$146$	2.51278	+	4.14045i	0.207959	+	0.342666i
$147$	8.71244	−	5.56743i	0.718590	−	0.459194i
$148$	4.98973	−	17.1257i	0.410153	−	1.40772i
$149$	1.04975	+	5.27746i	0.0859990	+	0.432346i	0.999665	+	0.0258805i	$0.00823893\pi$
$149$	1.04975	+	5.27746i	0.0859990	+	0.432346i	−0.913666	+	0.406466i	$0.866761\pi$
$150$	−1.08022	+	2.19844i	−0.0881995	+	0.179502i
$151$	3.55098	+	1.47086i	0.288975	+	0.119697i	0.522462	−	0.852663i	$-0.325014\pi$
$151$	3.55098	+	1.47086i	0.288975	+	0.119697i	−0.233487	+	0.972360i	$0.575014\pi$
$152$	12.4177	−	3.32941i	1.00721	−	0.270051i
$153$	−1.93624	+	0.710820i	−0.156536	+	0.0574664i
$154$	24.2007	+	1.05535i	1.95015	+	0.0850427i
$155$	−4.33227	−	2.89473i	−0.347977	−	0.232511i
$156$	−0.677823	+	0.545675i	−0.0542693	+	0.0436889i
$157$	−0.236001	+	1.18646i	−0.0188349	+	0.0946895i	−0.989059	−	0.147518i	$-0.952872\pi$
$157$	−0.236001	+	1.18646i	−0.0188349	+	0.0946895i	0.970224	+	0.242208i	$0.0778715\pi$
$158$	−1.97599	−	12.8337i	−0.157201	−	1.02100i
$159$	12.1897	+	0.249070i	0.966703	+	0.0197525i
$160$	4.63467	+	3.24342i	0.366403	+	0.256415i
$161$	7.02300			0.553490
$162$	−0.903542	−	12.6958i	−0.0709890	−	0.997477i
$163$	−3.13357	−	0.623306i	−0.245440	−	0.0488211i	0.0708370	−	0.997488i	$-0.477433\pi$
$163$	−3.13357	−	0.623306i	−0.245440	−	0.0488211i	−0.316277	+	0.948667i	$0.602433\pi$
$164$	0.0948897	−	1.08591i	0.00740964	−	0.0847951i
$165$	4.71579	−	6.75477i	0.367124	−	0.525858i
$166$	−0.809783	−	0.0353133i	−0.0628513	−	0.00274084i
$167$	−1.48251	−	3.57910i	−0.114720	−	0.276959i	0.856082	−	0.516840i	$-0.172892\pi$
$167$	−1.48251	−	3.57910i	−0.114720	−	0.276959i	−0.970802	+	0.239880i	$0.922892\pi$
$168$	−17.4415	−	2.65695i	−1.34564	−	0.204988i
$169$	4.95074	−	11.9521i	0.380826	−	0.919395i
$170$	0.881238	+	0.410872i	0.0675879	+	0.0315124i
$171$	2.11175	+	13.4717i	0.161489	+	1.03020i
$172$	11.2897	−	6.19530i	0.860834	−	0.472387i
$173$	−5.13394	−	7.68349i	−0.390326	−	0.584165i	0.583316	−	0.812245i	$-0.301755\pi$
$173$	−5.13394	−	7.68349i	−0.390326	−	0.584165i	−0.973642	+	0.228081i	$0.926755\pi$
$174$	−6.81284	−	11.7611i	−0.516480	−	0.891605i
$175$	−2.54651	+	2.54651i	−0.192498	+	0.192498i
$176$	−13.7457	−	13.1531i	−1.03612	−	0.991455i
$177$	13.5512	−	13.0085i	1.01857	−	0.977782i
$178$	10.2429	+	2.50586i	0.767740	+	0.187822i
$179$	2.24086	+	3.35368i	0.167490	+	0.250666i	0.905714	−	0.423889i	$-0.139335\pi$
$179$	2.24086	+	3.35368i	0.167490	+	0.250666i	−0.738224	+	0.674555i	$0.764335\pi$
$180$	−3.94308	+	4.52241i	−0.293899	+	0.337080i
$181$	−3.96322	−	19.9244i	−0.294584	−	1.48097i	−0.790425	−	0.612559i	$-0.790140\pi$
$181$	−3.96322	−	19.9244i	−0.294584	−	1.48097i	0.495841	−	0.868413i	$-0.334860\pi$
$182$	−1.20218	+	0.437629i	−0.0891115	+	0.0324392i
$183$	−20.5449	−	9.00597i	−1.51872	−	0.665741i
$184$	−4.14755	−	3.63615i	−0.305762	−	0.268061i
$185$	−3.41311	−	8.23998i	−0.250937	−	0.605815i
$186$	−8.42888	−	9.58344i	−0.618036	−	0.702692i
$187$	−2.71896	−	1.81675i	−0.198830	−	0.132854i
$188$	−9.64961	+	18.5415i	−0.703770	+	1.35228i
$189$	4.76804	−	18.0953i	0.346824	−	1.31624i
$190$	3.80076	−	5.18415i	0.275736	−	0.376098i
$191$	−18.1096			−1.31037			−0.655183	−	0.755471i	$-0.727408\pi$
$191$	−18.1096			−1.31037			−0.655183	+	0.755471i	$0.727408\pi$
$192$	8.92477	+	10.5995i	0.644090	+	0.764950i
$193$	2.74514			0.197599			0.0987997	−	0.995107i	$-0.468500\pi$
$193$	2.74514			0.197599			0.0987997	+	0.995107i	$0.468500\pi$
$194$	−15.1320	+	20.6398i	−1.08642	+	1.48185i
$195$	−0.0935811	+	0.424904i	−0.00670148	+	0.0304280i
$196$	−10.5905	−	5.51165i	−0.756465	−	0.393690i
$197$	9.65971	+	6.45441i	0.688226	+	0.459858i	0.849871	−	0.526991i	$-0.176680\pi$
$197$	9.65971	+	6.45441i	0.688226	+	0.459858i	−0.161645	+	0.986849i	$0.551680\pi$
$198$	15.4213	−	13.0145i	1.09595	−	0.924898i
$199$	7.68085	+	18.5432i	0.544481	+	1.31449i	0.921533	+	0.388301i	$0.126938\pi$
$199$	7.68085	+	18.5432i	0.544481	+	1.31449i	−0.377052	+	0.926192i	$0.623062\pi$
$200$	2.82234	−	0.185432i	0.199570	−	0.0131120i
$201$	2.33307	−	5.32232i	0.164562	−	0.375407i
$202$	−9.28863	+	3.38134i	−0.653546	+	0.237910i
$203$	−3.89851	−	19.5991i	−0.273622	−	1.37559i
$204$	1.82675	+	1.52819i	0.127898	+	0.106995i
$205$	−0.302798	−	0.453170i	−0.0211484	−	0.0316508i
$206$	−9.11495	−	2.22991i	−0.635069	−	0.155365i
$207$	4.30236	−	3.96440i	0.299035	−	0.275545i
$208$	0.936550	+	0.363978i	0.0649381	+	0.0252373i
$209$	−15.2869	+	15.2869i	−1.05742	+	1.05742i
$210$	−7.63318	+	4.42168i	−0.526739	+	0.305125i
$211$	4.80197	+	7.18666i	0.330581	+	0.494750i	0.959109	−	0.283037i	$-0.0913420\pi$
$211$	4.80197	+	7.18666i	0.330581	+	0.494750i	−0.628527	+	0.777787i	$0.716342\pi$
$212$	−6.77282	−	12.3422i	−0.465160	−	0.847663i
$213$	−18.1391	+	3.22436i	−1.24287	+	0.220929i
$214$	19.1206	+	8.91485i	1.30706	+	0.609407i
$215$	2.46407	−	5.94880i	0.168048	−	0.405705i
$216$	−12.1847	+	8.21786i	−0.829063	+	0.559155i
$217$	−7.18075	−	17.3359i	−0.487461	−	1.17684i
$218$	13.2077	+	0.575965i	0.894537	+	0.0390093i
$219$	4.86374	+	3.39559i	0.328661	+	0.229453i
$220$	−9.47638	−	0.828073i	−0.638897	−	0.0558287i
$221$	0.169388	+	0.0336933i	0.0113943	+	0.00226646i
$222$	−2.88274	−	21.6557i	−0.193477	−	1.45344i
$223$	−26.9976			−1.80789			−0.903945	−	0.427648i	$-0.859342\pi$
$223$	−26.9976			−1.80789			−0.903945	+	0.427648i	$0.859342\pi$
$224$	7.38860	+	18.9850i	0.493672	+	1.26849i
$225$	−0.122546	+	2.99750i	−0.00816973	+	0.199833i
$226$	−4.00230	−	25.9943i	−0.266229	−	1.72912i
$227$	−0.862522	+	4.33619i	−0.0572476	+	0.287803i	−0.998795	−	0.0490775i	$-0.984372\pi$
$227$	−0.862522	+	4.33619i	−0.0572476	+	0.287803i	0.941547	+	0.336881i	$0.109372\pi$
$228$	12.2651	−	9.87391i	0.812277	−	0.653916i
$229$	4.15863	+	2.77871i	0.274810	+	0.183622i	0.685337	−	0.728226i	$-0.259655\pi$
$229$	4.15863	+	2.77871i	0.274810	+	0.183622i	−0.410526	+	0.911849i	$0.634655\pi$
$230$	−2.75527	−	0.120153i	−0.181677	−	0.00792264i
$231$	27.6357	−	10.7911i	1.81830	−	0.710001i
$232$	−7.84510	+	13.5931i	−0.515056	+	0.892428i
$233$	20.6318	+	8.54598i	1.35164	+	0.559866i	0.936747	−	0.350006i	$-0.113821\pi$
$233$	20.6318	+	8.54598i	1.35164	+	0.559866i	0.414889	+	0.909872i	$0.363821\pi$
$234$	−0.489432	+	0.946712i	−0.0319952	+	0.0618885i
$235$	2.03891	+	10.2503i	0.133004	+	0.668655i
$236$	−20.8246	−	6.06744i	−1.35557	−	0.394957i
$237$	−8.56340	−	13.4008i	−0.556252	−	0.870476i
$238$	1.81670	+	2.99347i	0.117759	+	0.194038i
$239$	−14.8170	−	14.8170i	−0.958432	−	0.958432i	0.0407380	−	0.999170i	$-0.487029\pi$
$239$	−14.8170	−	14.8170i	−0.958432	−	0.958432i	−0.999170	+	0.0407380i	$0.987029\pi$
$240$	6.79723	+	1.34078i	0.438759	+	0.0865467i
$241$	−0.339227	+	0.339227i	−0.0218515	+	0.0218515i	−0.717948	−	0.696097i	$-0.754919\pi$
$241$	−0.339227	+	0.339227i	−0.0218515	+	0.0218515i	0.696097	+	0.717948i	$0.254919\pi$
$242$	15.9650	+	3.90572i	1.02627	+	0.251069i
$243$	−7.29364	−	13.7769i	−0.467887	−	0.883788i
$244$	2.82261	+	25.7481i	0.180699	+	1.64835i
$245$	−5.85474	+	1.16458i	−0.374046	+	0.0744024i
$246$	−0.430949	−	1.26356i	−0.0274763	−	0.0805616i
$247$	0.436945	−	1.05488i	0.0278022	−	0.0671204i
$248$	−4.73492	+	13.9558i	−0.300667	+	0.886196i
$249$	−0.924723	+	0.361082i	−0.0586019	+	0.0228826i
$250$	1.04262	−	0.955484i	0.0659409	−	0.0604301i
$251$	11.8551	−	17.7425i	0.748289	−	1.11989i	−0.240511	−	0.970646i	$-0.577315\pi$
$251$	11.8551	−	17.7425i	0.748289	−	1.11989i	0.988800	−	0.149247i	$-0.0476850\pi$
$252$	−20.8554	+	5.65258i	−1.31377	+	0.356079i
$253$	9.09704	+	1.80951i	0.571926	+	0.113763i
$254$	6.99553	−	9.54175i	0.438938	−	0.598702i
$255$	1.19059	+	0.0243271i	0.0745576	+	0.00152342i
$256$	5.46601	−	15.0374i	0.341626	−	0.939836i
$257$			21.0595i			1.31365i	0.754041	+	0.656827i	$0.228102\pi$
$257$			21.0595i			1.31365i	−0.754041	+	0.656827i	$0.771898\pi$
$258$	9.58343	−	12.5267i	0.596639	−	0.779876i
$259$	6.26624	−	31.5025i	0.389365	−	1.95747i
$260$	0.479128	−	0.151124i	0.0297142	−	0.00937229i
$261$	−13.4517	−	9.80598i	−0.832642	−	0.606975i
$262$	−0.0963620	−	0.105150i	−0.00595326	−	0.00649616i
$263$	26.2197	−	10.8606i	1.61678	−	0.669690i	0.623117	−	0.782129i	$-0.285866\pi$
$263$	26.2197	−	10.8606i	1.61678	−	0.669690i	0.993659	+	0.112439i	$0.0358662\pi$
$264$	−21.9078	−	7.93551i	−1.34833	−	0.488397i
$265$	−6.50335	−	2.69378i	−0.399498	−	0.165477i
$266$	21.7533	−	7.91884i	1.33378	−	0.485535i
$267$	12.7156	−	2.26029i	0.778182	−	0.138327i
$268$	−6.67026	+	0.731221i	−0.407451	+	0.0446664i
$269$	6.37759	−	4.26137i	0.388848	−	0.259820i	−0.345744	−	0.938329i	$-0.612373\pi$
$269$	6.37759	−	4.26137i	0.388848	−	0.259820i	0.734592	+	0.678509i	$0.237373\pi$
$270$	−2.18019	+	7.01761i	−0.132682	+	0.427078i
$271$	−3.09452	−	3.09452i	−0.187979	−	0.187979i	0.606843	−	0.794822i	$-0.292436\pi$
$271$	−3.09452	−	3.09452i	−0.187979	−	0.187979i	−0.794822	+	0.606843i	$0.792436\pi$
$272$	0.476985	−	2.70844i	0.0289215	−	0.164223i
$273$	−1.13036	+	1.08509i	−0.0684124	+	0.0656727i
$274$	9.92842	−	6.02543i	0.599798	−	0.364009i
$275$	−3.95467	+	2.64243i	−0.238476	+	0.159344i
$276$	−6.44578	−	2.02178i	−0.387990	−	0.121697i
$277$	13.4747	−	2.68029i	0.809617	−	0.161043i	0.227111	−	0.973869i	$-0.427072\pi$
$277$	13.4747	−	2.68029i	0.809617	−	0.161043i	0.582506	+	0.812826i	$0.302072\pi$
$278$	18.7355	+	8.73532i	1.12368	+	0.523909i
$279$	−14.1849	−	6.56670i	−0.849227	−	0.393138i
$280$	8.82218	+	5.09163i	0.527226	+	0.304283i
$281$	23.6299	−	9.78784i	1.40964	−	0.583894i	0.457408	−	0.889257i	$-0.348778\pi$
$281$	23.6299	−	9.78784i	1.40964	−	0.583894i	0.952236	+	0.305363i	$0.0987778\pi$
$282$	−1.63755	+	25.5474i	−0.0975145	+	1.52133i
$283$	−16.8464	+	25.2124i	−1.00141	+	1.49872i	−0.140430	+	0.990091i	$0.544848\pi$
$283$	−16.8464	+	25.2124i	−1.00141	+	1.49872i	−0.860984	+	0.508631i	$0.830152\pi$
$284$	13.6761	+	16.2951i	0.811528	+	0.966935i
$285$	1.69334	−	7.68859i	0.100305	−	0.455433i
$286$	−1.66997	+	0.257122i	−0.0987472	+	0.0152039i
$287$		−	1.96280i		−	0.115860i
$288$	15.2431	+	7.45965i	0.898211	+	0.439564i
$289$			16.5273i			0.972194i
$290$	1.19416	+	7.75585i	0.0701233	+	0.455439i
$291$	−6.74171	+	30.6107i	−0.395206	+	1.79443i
$292$	0.596251	−	6.82343i	0.0348930	−	0.399311i
$293$	12.8463	−	19.2259i	0.750492	−	1.12319i	−0.237904	−	0.971289i	$-0.576460\pi$
$293$	12.8463	−	19.2259i	0.750492	−	1.12319i	0.988396	−	0.151901i	$-0.0485396\pi$
$294$	−14.5921	−	0.935333i	−0.851031	−	0.0545497i
$295$	−10.0197	+	4.15030i	−0.583370	+	0.241640i
$296$	−20.0111	+	15.3600i	−1.16312	+	0.892784i
$297$	10.8385	−	22.2107i	0.628914	−	1.28880i
$298$	3.21562	−	6.89687i	0.186276	−	0.399525i
$299$	−0.480454	+	0.0955682i	−0.0277854	+	0.00552685i
$300$	3.07031	−	1.60413i	0.177264	−	0.0926142i
$301$	19.2806	−	12.8829i	1.11132	−	0.742558i
$302$	−2.82009	−	4.64682i	−0.162278	−	0.267394i
$303$	−8.73370	+	8.38394i	−0.501738	+	0.481645i
$304$	−16.9467	−	6.58613i	−0.971963	−	0.377741i
$305$	9.15787	+	9.15787i	0.524378	+	0.524378i
$306$	2.80271	+	0.808329i	0.160220	+	0.0462091i
$307$	−16.2942	+	10.8875i	−0.929961	+	0.621380i	−0.925556	−	0.378610i	$-0.876402\pi$
$307$	−16.2942	+	10.8875i	−0.929961	+	0.621380i	−0.00440451	+	0.999990i	$0.501402\pi$
$308$	−26.7191	−	21.4397i	−1.52246	−	1.22164i
$309$	−11.3153	+	2.01138i	−0.643706	+	0.114423i
$310$	2.52057	+	6.92408i	0.143159	+	0.393261i
$311$	6.30458	+	2.61144i	0.357500	+	0.148081i	0.554203	−	0.832382i	$-0.313023\pi$
$311$	6.30458	+	2.61144i	0.357500	+	0.148081i	−0.196702	+	0.980463i	$0.563023\pi$
$312$	1.22936	−	0.0555769i	0.0695987	−	0.00314642i
$313$	−18.6809	+	7.73790i	−1.05591	+	0.437372i	−0.841998	−	0.539481i	$-0.818620\pi$
$313$	−18.6809	+	7.73790i	−1.05591	+	0.437372i	−0.213911	+	0.976853i	$0.568620\pi$
$314$	1.26125	−	1.15585i	0.0711767	−	0.0652283i
$315$	−6.36428	+	8.73046i	−0.358587	+	0.491906i
$316$	−8.47760	+	16.2895i	−0.476903	+	0.916356i
$317$	−2.96686	+	14.9154i	−0.166635	+	0.837733i	0.803525	+	0.595270i	$0.202955\pi$
$317$	−2.96686	+	14.9154i	−0.166635	+	0.837733i	−0.970161	+	0.242462i	$0.922045\pi$
$318$	−13.6944	−	10.4768i	−0.767944	−	0.587510i
$319$		−	26.3916i		−	1.47765i
$320$	−2.57390	−	7.57463i	−0.143885	−	0.423435i
$321$	25.8327	+	0.527836i	1.44184	+	0.0294609i
$322$	−8.00993	−	5.87248i	−0.446376	−	0.327260i
$323$	−3.06505	−	0.609676i	−0.170544	−	0.0339233i
$324$	−9.58545	+	15.2355i	−0.532525	+	0.846414i
$325$	0.139558	−	0.208863i	0.00774129	−	0.0115857i
$326$	3.05273	+	3.33112i	0.169075	+	0.184494i
$327$	15.0824	−	5.88930i	0.834057	−	0.325679i
$328$	−1.01624	+	1.15916i	−0.0561123	+	0.0640041i
$329$	−14.4033	+	34.7727i	−0.794080	+	1.91708i
$330$	−11.0267	+	3.76076i	−0.606999	+	0.207023i
$331$	19.9918	−	3.97661i	1.09885	−	0.218575i	0.387818	−	0.921736i	$-0.373229\pi$
$331$	19.9918	−	3.97661i	1.09885	−	0.218575i	0.711030	+	0.703161i	$0.248229\pi$
$332$	0.894052	+	0.717399i	0.0490675	+	0.0393724i
$333$	−13.9440	−	22.8360i	−0.764128	−	1.25141i
$334$	−1.30192	+	5.32172i	−0.0712379	+	0.291191i
$335$	−2.37242	+	2.37242i	−0.129619	+	0.129619i
$336$	17.6709	+	17.6146i	0.964026	+	0.960953i
$337$	25.4554	+	25.4554i	1.38665	+	1.38665i	0.832260	+	0.554385i	$0.187047\pi$
$337$	25.4554	+	25.4554i	1.38665	+	1.38665i	0.554385	+	0.832260i	$0.312953\pi$
$338$	−15.6406	+	9.49206i	−0.850735	+	0.516300i
$339$	−17.3449	−	27.1429i	−0.942046	−	1.47420i
$340$	−0.661515	−	1.20548i	−0.0358757	−	0.0653765i
$341$	−4.83470	−	24.3057i	−0.261814	−	1.31623i
$342$	8.85620	−	17.1306i	0.478889	−	0.926318i
$343$	3.42884	+	1.42027i	0.185140	+	0.0766874i
$344$	−18.0566	−	2.37431i	−0.973548	−	0.128014i
$345$	−3.14635	+	1.22857i	−0.169394	+	0.0661442i
$346$	−0.569356	+	13.0561i	−0.0306088	+	0.701902i
$347$	−13.8790	−	9.27364i	−0.745063	−	0.497835i	0.124156	−	0.992263i	$-0.460378\pi$
$347$	−13.8790	−	9.27364i	−0.745063	−	0.497835i	−0.869219	+	0.494428i	$0.835378\pi$
$348$	−2.06411	+	19.1106i	−0.110648	+	1.02444i
$349$	6.50023	−	32.6789i	0.347949	−	1.74926i	−0.269830	−	0.962908i	$-0.586968\pi$
$349$	6.50023	−	32.6789i	0.347949	−	1.74926i	0.617779	−	0.786351i	$-0.288032\pi$
$350$	5.03371	−	0.775032i	0.269063	−	0.0414272i
$351$	−0.0799495	+	1.30281i	−0.00426739	+	0.0695390i
$352$	4.67902	+	26.4954i	0.249393	+	1.41221i
$353$	−14.6444			−0.779440			−0.389720	−	0.920933i	$-0.627428\pi$
$353$	−14.6444			−0.779440			−0.389720	+	0.920933i	$0.627428\pi$
$354$	−26.3330	+	3.50537i	−1.39958	+	0.186308i
$355$	10.4324	+	2.07514i	0.553695	+	0.110137i
$356$	−9.58701	−	11.4229i	−0.508111	−	0.605414i
$357$	3.51640	+	2.45495i	0.186108	+	0.129930i
$358$	0.248512	−	5.69873i	0.0131343	−	0.301187i
$359$	2.38095	+	5.74813i	0.125662	+	0.303375i	0.974173	−	0.225803i	$-0.0725006\pi$
$359$	2.38095	+	5.74813i	0.125662	+	0.303375i	−0.848511	+	0.529178i	$0.822501\pi$
$360$	8.27873	−	1.86082i	0.436327	−	0.0980739i
$361$	−0.635480	+	1.53418i	−0.0334463	+	0.0807465i
$362$	−12.1402	+	26.0384i	−0.638076	+	1.36855i
$363$	19.8190	−	3.52296i	1.04023	−	0.184908i
$364$	1.73706	+	0.506108i	0.0910465	+	0.0265273i
$365$	−1.90267	−	2.84755i	−0.0995903	−	0.149047i
$366$	15.9014	+	27.4507i	0.831180	+	1.43487i
$367$	−11.1466	+	11.1466i	−0.581846	+	0.581846i	−0.935410	−	0.353564i	$-0.884970\pi$
$367$	−11.1466	+	11.1466i	−0.581846	+	0.581846i	0.353564	+	0.935410i	$0.384970\pi$
$368$	1.68993	+	7.61523i	0.0880938	+	0.396971i
$369$	−1.10797	−	1.20243i	−0.0576789	−	0.0625960i
$370$	−2.99734	+	12.2519i	−0.155824	+	0.636946i
$371$	−14.0839	−	21.0780i	−0.731197	−	1.09431i
$372$	1.59992	+	17.9782i	0.0829518	+	0.932128i
$373$	3.77189	+	18.9626i	0.195301	+	0.981845i	0.946729	+	0.322030i	$0.104365\pi$
$373$	3.77189	+	18.9626i	0.195301	+	0.981845i	−0.751428	+	0.659815i	$0.770635\pi$
$374$	1.58192	+	4.34559i	0.0817993	+	0.224705i
$375$	0.695379	−	1.58633i	0.0359092	−	0.0819178i
$376$	26.5096	−	13.0783i	1.36713	−	0.674462i
$377$	0.533406	+	1.28776i	0.0274718	+	0.0663228i
$378$	−20.5690	+	16.6513i	−1.05796	+	0.856451i
$379$	19.4836	+	13.0185i	1.00080	+	0.668715i	0.944094	−	0.329676i	$-0.106939\pi$
$379$	19.4836	+	13.0185i	1.00080	+	0.668715i	0.0567086	+	0.998391i	$0.481939\pi$
$380$	−8.66975	+	2.73456i	−0.444749	+	0.140280i
$381$	3.11669	−	14.1513i	0.159673	−	0.724994i
$382$	20.6545	+	15.1429i	1.05678	+	0.774776i
$383$	18.8043			0.960856			0.480428	−	0.877034i	$-0.340481\pi$
$383$	18.8043			0.960856			0.480428	+	0.877034i	$0.340481\pi$
$384$	−1.31593	−	19.5517i	−0.0671532	−	0.997743i
$385$	−17.1287			−0.872960
$386$	−3.13091	−	2.29543i	−0.159359	−	0.116834i
$387$	4.53928	−	18.7759i	0.230745	−	0.954432i
$388$	34.5170	−	10.8872i	1.75234	−	0.552712i
$389$	29.2920	+	19.5723i	1.48517	+	0.992356i	0.992514	+	0.122129i	$0.0389721\pi$
$389$	29.2920	+	19.5723i	1.48517	+	0.992356i	0.492651	+	0.870227i	$0.336028\pi$
$390$	0.462028	−	0.406365i	0.0233957	−	0.0205771i
$391$	0.513090	+	1.23871i	0.0259481	+	0.0626442i
$392$	7.47005	+	15.1418i	0.377294	+	0.764774i
$393$	−0.159984	−	0.0701300i	−0.00807013	−	0.00353759i
$394$	−5.62014	−	15.4387i	−0.283139	−	0.777790i
$395$	1.79127	+	9.00532i	0.0901285	+	0.453107i
$396$	−28.4709	+	1.94839i	−1.43072	+	0.0979104i
$397$	−0.216339	−	0.323775i	−0.0108578	−	0.0162498i	0.826001	−	0.563669i	$-0.190610\pi$
$397$	−0.216339	−	0.323775i	−0.0108578	−	0.0162498i	−0.836859	+	0.547419i	$0.815610\pi$
$398$	6.74520	−	27.5716i	0.338106	−	1.38204i
$399$	20.4537	−	19.6346i	1.02396	−	0.982958i
$400$	−3.37402	−	2.14849i	−0.168701	−	0.107425i
$401$	3.56888	−	3.56888i	0.178221	−	0.178221i	−0.612359	−	0.790580i	$-0.709779\pi$
$401$	3.56888	−	3.56888i	0.178221	−	0.178221i	0.790580	+	0.612359i	$0.209779\pi$
$402$	−7.11134	+	4.11939i	−0.354681	+	0.205457i
$403$	0.727151	+	1.08826i	0.0362220	+	0.0542100i
$404$	13.4213	+	3.91044i	0.667737	+	0.194552i
$405$	1.02941	+	8.94094i	0.0511517	+	0.444279i
$406$	−11.9420	+	25.6132i	−0.592672	+	1.27116i
$407$	16.2336	−	39.1914i	0.804670	−	1.94264i
$408$	−0.805624	−	3.27043i	−0.0398843	−	0.161911i
$409$	2.67838	+	6.46618i	0.132437	+	0.319732i	0.976162	−	0.217045i	$-0.0696417\pi$
$409$	2.67838	+	6.46618i	0.132437	+	0.319732i	−0.843724	+	0.536777i	$0.819642\pi$
$410$	−0.0335805	+	0.770047i	−0.00165842	+	0.0380299i
$411$	8.14232	−	11.6628i	0.401631	−	0.575285i
$412$	8.53127	+	10.1650i	0.420305	+	0.500794i
$413$	−38.3066	−	7.61966i	−1.88495	−	0.374939i
$414$	−8.22191	+	0.923964i	−0.404085	+	0.0454104i
$415$	0.573147			0.0281347
$416$	−0.763812	−	1.19825i	−0.0374490	−	0.0587491i
$417$	25.3125	+	0.517206i	1.23956	+	0.0253277i
$418$	30.2178	−	4.65259i	1.47800	−	0.227566i
$419$	0.559845	−	2.81453i	0.0273502	−	0.137499i	−0.964698	−	0.263360i	$-0.915169\pi$
$419$	0.559845	−	2.81453i	0.0273502	−	0.137499i	0.992048	+	0.125861i	$0.0401693\pi$
$420$	12.4032	+	1.33965i	0.605213	+	0.0653682i
$421$	1.09941	+	0.734600i	0.0535818	+	0.0358022i	0.582073	−	0.813137i	$-0.302242\pi$
$421$	1.09941	+	0.734600i	0.0535818	+	0.0358022i	−0.528491	+	0.848939i	$0.677242\pi$
$422$	0.532541	−	12.2119i	0.0259237	−	0.594466i
$423$	10.8051	+	29.4326i	0.525363	+	1.43106i
$424$	−2.59564	+	19.7399i	−0.126056	+	0.958653i
$425$	−0.635195	−	0.263107i	−0.0308115	−	0.0127625i
$426$	23.3843	+	11.4901i	1.13297	+	0.556696i
$427$	9.09925	+	45.7450i	0.440344	+	2.21376i
$428$	−14.3532	−	26.1559i	−0.693786	−	1.26429i
$429$	−1.74376	+	1.11430i	−0.0841894	+	0.0537988i
$430$	−7.78461	+	4.72437i	−0.375407	+	0.227830i
$431$	11.8797	+	11.8797i	0.572224	+	0.572224i	0.932749	−	0.360526i	$-0.117403\pi$
$431$	11.8797	+	11.8797i	0.572224	+	0.572224i	−0.360526	+	0.932749i	$0.617403\pi$
$432$	20.7686	+	0.815867i	0.999229	+	0.0392534i
$433$	−20.4326	+	20.4326i	−0.981928	+	0.981928i	−0.999840	−	0.0179118i	$-0.994298\pi$
$433$	−20.4326	+	20.4326i	−0.981928	+	0.981928i	0.0179118	+	0.999840i	$0.494298\pi$
$434$	−6.30602	+	25.7764i	−0.302699	+	1.23731i
$435$	5.17515	+	8.09856i	0.248130	+	0.388296i
$436$	−14.5821	−	11.7009i	−0.698357	−	0.560370i
$437$	8.69375	−	1.72929i	0.415878	−	0.0827233i
$438$	−2.70792	−	7.93973i	−0.129390	−	0.379375i
$439$	10.3600	−	25.0112i	0.494454	−	1.19372i	−0.457977	−	0.888964i	$-0.651426\pi$
$439$	10.3600	−	25.0112i	0.494454	−	1.19372i	0.952431	−	0.304754i	$-0.0985742\pi$
$440$	10.1157	+	8.86838i	0.482245	+	0.422784i
$441$	−16.8113	+	6.17166i	−0.800537	+	0.293888i
$442$	−0.165018	−	0.180067i	−0.00784910	−	0.00856489i
$443$	−19.0185	+	28.4631i	−0.903594	+	1.35232i	0.0320900	+	0.999485i	$0.489784\pi$
$443$	−19.0185	+	28.4631i	−0.903594	+	1.35232i	−0.935684	+	0.352839i	$0.885216\pi$
$444$	−14.8202	+	27.1094i	−0.703335	+	1.28656i
$445$	−7.31317	−	1.45468i	−0.346677	−	0.0689584i
$446$	30.7915	+	22.5748i	1.45802	+	1.06895i
$447$	0.190393	−	9.31796i	0.00900526	−	0.440724i
$448$	7.44794	−	27.8311i	0.351882	−	1.31490i
$449$		−	35.9065i		−	1.69453i	−0.531167	−	0.847267i	$-0.678246\pi$
$449$		−	35.9065i		−	1.69453i	0.531167	−	0.847267i	$-0.321754\pi$
$450$	2.64621	−	3.31626i	0.124743	−	0.156330i
$451$	0.505725	−	2.54245i	0.0238137	−	0.119719i
$452$	−17.1711	+	32.9939i	−0.807662	+	1.55190i
$453$	−5.45857	−	3.81086i	−0.256466	−	0.179050i
$454$	4.60956	−	4.22433i	0.216337	−	0.198258i
$455$	0.835780	−	0.346192i	0.0391820	−	0.0162297i
$456$	−22.2451	+	1.00566i	−1.04172	+	0.0470941i
$457$	−7.79936	−	3.23060i	−0.364839	−	0.151121i	0.192730	−	0.981252i	$-0.438266\pi$
$457$	−7.79936	−	3.23060i	−0.364839	−	0.151121i	−0.557569	+	0.830131i	$0.688266\pi$
$458$	−2.41954	−	6.64656i	−0.113058	−	0.310573i
$459$	3.53998	−	0.481036i	0.165232	−	0.0224528i
$460$	3.04200	+	2.44093i	0.141834	+	0.113809i
$461$	15.4423	−	10.3182i	0.719222	−	0.480569i	−0.141310	−	0.989965i	$-0.545131\pi$
$461$	15.4423	−	10.3182i	0.719222	−	0.480569i	0.860532	+	0.509397i	$0.170131\pi$
$462$	−40.5426	−	10.8008i	−1.88621	−	0.502501i
$463$	9.57473	+	9.57473i	0.444975	+	0.444975i	0.893680	−	0.448705i	$-0.148114\pi$
$463$	9.57473	+	9.57473i	0.444975	+	0.444975i	−0.448705	+	0.893680i	$0.648114\pi$
$464$	20.3138	−	8.94337i	0.943044	−	0.415186i
$465$	6.24969	+	6.51042i	0.289823	+	0.301913i
$466$	−16.3852	−	26.9988i	−0.759031	−	1.25070i
$467$	24.3210	−	16.2508i	1.12544	−	0.751995i	0.153717	−	0.988115i	$-0.450876\pi$
$467$	24.3210	−	16.2508i	1.12544	−	0.751995i	0.971724	+	0.236120i	$0.0758757\pi$
$468$	1.34983	−	0.670500i	0.0623960	−	0.0309939i
$469$	−11.8506	+	2.35724i	−0.547211	+	0.108847i
$470$	6.24563	−	13.3956i	0.288089	−	0.617894i
$471$	0.841200	−	1.91899i	0.0387605	−	0.0884222i
$472$	18.6776	+	24.3332i	0.859705	+	1.12002i
$473$	28.2940	−	11.7197i	1.30096	−	0.538874i
$474$	−1.43866	+	22.4445i	−0.0660797	+	1.03091i
$475$	−2.52528	+	3.77936i	−0.115868	+	0.173409i
$476$	0.431079	−	4.93322i	0.0197585	−	0.226114i
$477$	−20.5262	−	4.96243i	−0.939829	−	0.227214i
$478$	4.50956	+	29.2889i	0.206263	+	1.33964i
$479$		−	35.6712i		−	1.62986i	−0.579559	−	0.814930i	$-0.696775\pi$
$479$		−	35.6712i		−	1.62986i	0.579559	−	0.814930i	$-0.303225\pi$
$480$	−6.63131	−	7.21289i	−0.302676	−	0.329222i
$481$			2.24041i			0.102154i
$482$	0.670553	−	0.103244i	0.0305428	−	0.00470263i
$483$	−11.8795	−	2.61634i	−0.540535	−	0.119048i
$484$	−14.9427	−	17.8042i	−0.679212	−	0.809280i
$485$	10.0540	−	15.0468i	0.456527	−	0.683241i
$486$	−3.20134	+	21.8117i	−0.145216	+	0.989400i
$487$	23.5333	−	9.74780i	1.06639	−	0.441715i	0.220678	−	0.975347i	$-0.429173\pi$
$487$	23.5333	−	9.74780i	1.06639	−	0.441715i	0.845717	+	0.533632i	$0.179173\pi$
$488$	18.3107	−	31.7267i	0.828888	−	1.43620i
$489$	5.06827	+	2.22171i	0.229195	+	0.100469i
$490$	7.65130	+	3.56737i	0.345651	+	0.161157i
$491$	−20.6746	+	4.11243i	−0.933032	+	0.185592i	−0.638123	−	0.769934i	$-0.720289\pi$
$491$	−20.6746	+	4.11243i	−0.933032	+	0.185592i	−0.294908	+	0.955526i	$0.595289\pi$
$492$	−0.565050	+	1.80148i	−0.0254744	+	0.0812168i
$493$	3.17205	−	2.11950i	0.142862	−	0.0954574i
$494$	−1.38042	+	0.837756i	−0.0621078	+	0.0376924i
$495$	−10.4932	+	9.66895i	−0.471636	+	0.434587i
$496$	17.0699	−	11.9578i	0.766460	−	0.536921i
$497$	27.0867	+	27.0867i	1.21501	+	1.21501i
$498$	1.35660	+	0.361409i	0.0607908	+	0.0161951i
$499$	−28.7465	+	19.2078i	−1.28687	+	0.859860i	−0.995314	−	0.0966941i	$-0.969173\pi$
$499$	−28.7465	+	19.2078i	−1.28687	+	0.859860i	−0.291557	+	0.956554i	$0.594173\pi$
$500$	−1.98809	+	0.217942i	−0.0889101	+	0.00974668i
$501$	1.17433	+	6.60639i	0.0524653	+	0.295152i
$502$	−28.3570	+	10.3228i	−1.26563	+	0.460728i
$503$	22.8662	+	9.47151i	1.01956	+	0.422314i	0.828932	−	0.559349i	$-0.188949\pi$
$503$	22.8662	+	9.47151i	1.01956	+	0.422314i	0.190624	+	0.981663i	$0.438949\pi$
$504$	28.5128	+	10.9919i	1.27006	+	0.489619i
$505$	6.45765	−	2.67485i	0.287362	−	0.119029i
$506$	−8.86236	−	9.67054i	−0.393980	−	0.429908i
$507$	−12.8269	+	18.3728i	−0.569661	+	0.815967i
$508$	−15.9572	+	5.03313i	−0.707986	+	0.223309i
$509$	−3.62169	+	18.2074i	−0.160528	+	0.807031i	0.813668	+	0.581330i	$0.197467\pi$
$509$	−3.62169	+	18.2074i	−0.160528	+	0.807031i	−0.974197	+	0.225701i	$0.927533\pi$
$510$	−1.33756	−	1.02329i	−0.0592281	−	0.0453121i
$511$		−	12.3335i		−	0.545601i
$512$	−18.8081	+	12.5800i	−0.831207	+	0.555963i
$513$	1.44668	−	23.5742i	0.0638723	−	1.04083i
$514$	17.6095	−	24.0189i	0.776721	−	1.05943i
$515$	6.50782	+	1.29449i	0.286769	+	0.0570419i
$516$	−21.4047	+	6.27356i	−0.942290	+	0.276178i
$517$	−27.6163	+	41.3307i	−1.21456	+	1.81772i
$518$	−33.4886	+	30.6899i	−1.47140	+	1.34843i
$519$	5.82173	+	14.9093i	0.255545	+	0.654446i
$520$	−0.672825	−	0.228275i	−0.0295053	−	0.0100105i
$521$	7.62966	−	18.4196i	0.334261	−	0.806979i	−0.663983	−	0.747748i	$-0.731135\pi$
$521$	7.62966	−	18.4196i	0.334261	−	0.806979i	0.998244	−	0.0592307i	$-0.0188648\pi$
$522$	7.14255	+	22.4321i	0.312621	+	0.981824i
$523$	1.57942	−	0.314166i	0.0690631	−	0.0137375i	−0.160438	−	0.987046i	$-0.551291\pi$
$523$	1.57942	−	0.314166i	0.0690631	−	0.0137375i	0.229501	+	0.973308i	$0.426291\pi$
$524$	0.0219798	+	0.200502i	0.000960193	+	0.00875897i
$525$	5.25613	−	3.35878i	0.229396	−	0.146589i
$526$	−38.9857	−	9.53756i	−1.69986	−	0.415858i
$527$	2.53307	−	2.53307i	0.110342	−	0.110342i
$528$	18.3510	+	27.3695i	0.798625	+	1.19111i
$529$	13.5743	+	13.5743i	0.590189	+	0.590189i
$530$	5.16478	+	8.51029i	0.224344	+	0.369663i
$531$	−27.7683	+	16.9557i	−1.20504	+	0.735817i
$532$	−31.4318	−	9.15795i	−1.36274	−	0.397048i
$533$	0.0267095	+	0.134278i	0.00115692	+	0.00581622i
$534$	−16.3925	−	8.05459i	−0.709374	−	0.348556i
$535$	−13.7821	−	5.70873i	−0.595852	−	0.246810i
$536$	8.21905	+	4.74355i	0.355009	+	0.204890i
$537$	−2.54106	−	6.50760i	−0.109655	−	0.280824i
$538$	−10.8371	−	0.472588i	−0.467220	−	0.0203747i
$539$	−23.6072	−	15.7738i	−1.01683	−	0.679427i
$540$	8.35453	−	6.18076i	0.359522	−	0.265977i
$541$	−1.78372	+	8.96738i	−0.0766882	+	0.385538i	0.923311	+	0.384054i	$0.125472\pi$
$541$	−1.78372	+	8.96738i	−0.0766882	+	0.385538i	−0.999999	+	0.00148381i	$0.999528\pi$
$542$	0.941818	+	6.11696i	0.0404546	+	0.262746i
$543$	−0.718806	+	35.1789i	−0.0308469	+	1.50967i
$544$	−2.80876	+	2.69021i	−0.120424	+	0.115342i
$545$	−9.34811			−0.400429
$546$	2.19654	−	0.292396i	0.0940030	−	0.0125134i
$547$	12.9369	+	2.57331i	0.553142	+	0.110027i	0.463744	−	0.885969i	$-0.346506\pi$
$547$	12.9369	+	2.57331i	0.553142	+	0.110027i	0.0893977	+	0.995996i	$0.471506\pi$
$548$	−16.3620	−	1.42976i	−0.698949	−	0.0610762i
$549$	31.3968	+	22.8875i	1.33998	+	0.976814i
$550$	6.71996	+	0.293046i	0.286540	+	0.0124955i
$551$	−9.65191	−	23.3018i	−0.411185	−	0.992689i
$552$	5.66103	+	7.69572i	0.240949	+	0.327552i
$553$	−12.6539	+	30.5493i	−0.538100	+	1.29909i
$554$	−17.6095	−	8.21032i	−0.748156	−	0.348823i
$555$	2.70360	+	15.2096i	0.114762	+	0.645609i
$556$	−14.0641	−	25.6291i	−0.596451	−	1.08692i
$557$	−3.10550	−	4.64771i	−0.131584	−	0.196930i	0.759827	−	0.650126i	$-0.225284\pi$
$557$	−3.10550	−	4.64771i	−0.131584	−	0.196930i	−0.891411	+	0.453196i	$0.850284\pi$
$558$	10.6874	+	19.3506i	0.452432	+	0.819176i
$559$	−1.14371	+	1.14371i	−0.0483737	+	0.0483737i
$560$	−5.80443	−	13.1841i	−0.245282	−	0.557129i
$561$	3.92234	+	4.08597i	0.165601	+	0.172510i
$562$	−35.1350	−	8.59553i	−1.48208	−	0.362580i
$563$	−1.80597	−	2.70282i	−0.0761125	−	0.113910i	0.791460	−	0.611220i	$-0.209321\pi$
$563$	−1.80597	−	2.70282i	−0.0761125	−	0.113910i	−0.867573	+	0.497310i	$0.834321\pi$
$564$	23.2299	−	27.7683i	0.978154	−	1.16926i
$565$	3.62816	+	18.2400i	0.152638	+	0.767363i
$566$	40.2959	−	14.6689i	1.69376	−	0.616579i
$567$	−14.8064	+	28.8322i	−0.621811	+	1.21084i
$568$	−1.97241	−	30.0207i	−0.0827603	−	1.25964i
$569$	8.97545	+	21.6686i	0.376270	+	0.908397i	0.992658	+	0.120954i	$0.0385954\pi$
$569$	8.97545	+	21.6686i	0.376270	+	0.908397i	−0.616388	+	0.787443i	$0.711405\pi$
$570$	−8.36033	+	7.35312i	−0.350176	+	0.307988i
$571$	20.7739	+	13.8807i	0.869360	+	0.580888i	0.908284	−	0.418355i	$-0.137393\pi$
$571$	20.7739	+	13.8807i	0.869360	+	0.580888i	−0.0389240	+	0.999242i	$0.512393\pi$
$572$	2.11964	+	1.10313i	0.0886268	+	0.0461244i
$573$	30.6326	+	6.74654i	1.27970	+	0.281841i
$574$	−1.64125	+	2.23863i	−0.0685044	+	0.0934384i
$575$	1.95012			0.0813257
$576$	−11.1477	−	21.2539i	−0.464486	−	0.885581i
$577$	−7.19662			−0.299599			−0.149800	−	0.988716i	$-0.547863\pi$
$577$	−7.19662			−0.299599			−0.149800	+	0.988716i	$0.547863\pi$
$578$	13.8198	−	18.8499i	0.574827	−	0.784051i
$579$	−4.64344	−	1.02267i	−0.192975	−	0.0425008i
$580$	5.12330	−	9.84430i	0.212734	−	0.408762i
$581$	1.71622	+	1.14674i	0.0712008	+	0.0475749i
$582$	33.2851	−	29.2751i	1.37971	−	1.21349i
$583$	−12.8123	−	30.9315i	−0.530630	−	1.28105i
$584$	−6.38565	+	7.28375i	−0.264240	+	0.301404i
$585$	0.316587	−	0.683869i	0.0130893	−	0.0282745i
$586$	−30.7279	+	11.1859i	−1.26936	+	0.462084i
$587$	−6.41616	−	32.2562i	−0.264823	−	1.33136i	−0.852698	−	0.522404i	$-0.825035\pi$
$587$	−6.41616	−	32.2562i	−0.264823	−	1.33136i	0.587875	−	0.808952i	$-0.299965\pi$
$588$	15.8607	+	13.2684i	0.654083	+	0.547180i
$589$	−13.1577	−	19.6919i	−0.542153	−	0.811390i
$590$	14.8981	+	3.64472i	0.613347	+	0.150051i
$591$	−13.9350	−	14.5163i	−0.573209	−	0.597123i
$592$	35.6669	−	0.785746i	1.46590	−	0.0322940i
$593$	−0.154684	+	0.154684i	−0.00635211	+	0.00635211i	−0.710276	−	0.703924i	$-0.751430\pi$
$593$	−0.154684	+	0.154684i	−0.00635211	+	0.00635211i	0.703924	+	0.710276i	$0.251430\pi$
$594$	−30.9338	+	16.2691i	−1.26923	+	0.667528i
$595$	−1.37560	−	2.05873i	−0.0563940	−	0.0843996i
$596$	−9.43452	+	5.17725i	−0.386453	+	0.212068i
$597$	−6.08418	−	34.2275i	−0.249009	−	1.40084i
$598$	0.627884	+	0.292747i	0.0256761	+	0.0119713i
$599$	−2.64509	+	6.38581i	−0.108075	+	0.260917i	−0.968660	−	0.248390i	$-0.920098\pi$
$599$	−2.64509	+	6.38581i	−0.108075	+	0.260917i	0.860585	+	0.509308i	$0.170098\pi$
$600$	−4.84311	−	0.737772i	−0.197719	−	0.0301194i
$601$	−11.0011	−	26.5589i	−0.448743	−	1.08336i	−0.972793	−	0.231674i	$-0.925580\pi$
$601$	−11.0011	−	26.5589i	−0.448743	−	1.08336i	0.524050	−	0.851687i	$-0.324420\pi$
$602$	−32.7625	−	1.42872i	−1.33530	−	0.0582303i
$603$	−5.92919	+	8.13360i	−0.241455	+	0.331226i
$604$	−0.669172	+	7.65792i	−0.0272282	+	0.311597i
$605$	−11.3986	−	2.26731i	−0.463417	−	0.0921794i
$606$	16.9715	−	2.25919i	0.689420	−	0.0917734i
$607$	−42.8692			−1.74001			−0.870004	−	0.493045i	$-0.835884\pi$
$607$	−42.8692			−1.74001			−0.870004	+	0.493045i	$0.835884\pi$
$608$	13.8211	+	21.6822i	0.560518	+	0.879328i
$609$	−0.707069	+	34.6045i	−0.0286519	+	1.40225i
$610$	−2.78720	−	18.1024i	−0.112850	−	0.732945i
$611$	0.512169	−	2.57485i	0.0207202	−	0.104167i
$612$	−2.52066	−	3.26549i	−0.101892	−	0.131999i
$613$	−22.1210	−	14.7808i	−0.893459	−	0.596990i	0.0218415	−	0.999761i	$-0.493047\pi$
$613$	−22.1210	−	14.7808i	−0.893459	−	0.596990i	−0.915301	+	0.402771i	$0.868047\pi$
$614$	27.6879	+	1.20742i	1.11739	+	0.0487276i
$615$	0.343364	+	0.879347i	0.0138458	+	0.0354587i
$616$	12.5465	+	46.7946i	0.505511	+	1.88541i
$617$	−39.1627	−	16.2217i	−1.57663	−	0.653061i	−0.588755	−	0.808312i	$-0.700382\pi$
$617$	−39.1627	−	16.2217i	−1.57663	−	0.653061i	−0.987875	+	0.155250i	$0.950382\pi$
$618$	14.5873	+	7.16759i	0.586788	+	0.288323i
$619$	7.07947	+	35.5909i	0.284548	+	1.43052i	0.813351	+	0.581774i	$0.197641\pi$
$619$	7.07947	+	35.5909i	0.284548	+	1.43052i	−0.528803	+	0.848745i	$0.677359\pi$
$620$	2.91498	−	10.0048i	0.117068	−	0.401801i
$621$	−8.75440	+	5.10303i	−0.351302	+	0.204777i
$622$	−5.00693	−	8.25018i	−0.200759	−	0.330802i
$623$	−18.9879	−	18.9879i	−0.760735	−	0.760735i
$624$	−1.44859	−	0.964575i	−0.0579900	−	0.0386139i
$625$	−0.707107	+	0.707107i	−0.0282843	+	0.0282843i
$626$	27.7764	+	6.79530i	1.11017	+	0.271595i
$627$	31.5530	−	20.1631i	1.26011	−	0.805235i
$628$	−2.40499	+	0.263645i	−0.0959697	+	0.0105206i
$629$	6.01419	−	1.19630i	0.239801	−	0.0476994i
$630$	14.5589	−	4.63566i	0.580039	−	0.184689i
$631$	−5.46067	+	13.1832i	−0.217386	+	0.524816i	−0.994523	−	0.104515i	$-0.966671\pi$
$631$	−5.46067	+	13.1832i	−0.217386	+	0.524816i	0.777137	+	0.629331i	$0.216671\pi$
$632$	23.2899	−	11.4899i	0.926422	−	0.457042i
$633$	−5.44528	−	13.9452i	−0.216431	−	0.554274i
$634$	15.8557	−	14.5306i	0.629711	−	0.577085i
$635$	−4.64794	+	6.95613i	−0.184448	+	0.276046i
$636$	6.85838	+	23.4001i	0.271952	+	0.927873i
$637$	1.47070	+	0.292540i	0.0582712	+	0.0115909i
$638$	−22.0681	+	30.1004i	−0.873685	+	1.19169i
$639$	31.8838	+	1.30350i	1.26130	+	0.0515655i
$640$	−3.39813	+	10.7913i	−0.134323	+	0.426565i
$641$			3.78160i			0.149364i	0.997207	+	0.0746821i	$0.0237942\pi$
$641$			3.78160i			0.149364i	−0.997207	+	0.0746821i	$0.976206\pi$
$642$	−29.0216	−	22.2027i	−1.14539	−	0.876272i
$643$	6.09619	−	30.6476i	0.240410	−	1.20862i	−0.652289	−	0.757971i	$-0.726191\pi$
$643$	6.09619	−	30.6476i	0.240410	−	1.20862i	0.892699	−	0.450654i	$-0.148809\pi$
$644$	4.22512	+	13.3955i	0.166493	+	0.527855i
$645$	−6.38418	+	9.14451i	−0.251377	+	0.360065i
$646$	2.98598	+	3.25828i	0.117482	+	0.128195i
$647$	8.13178	−	3.36829i	0.319693	−	0.132421i	−0.217066	−	0.976157i	$-0.569649\pi$
$647$	8.13178	−	3.36829i	0.319693	−	0.132421i	0.536759	+	0.843736i	$0.319649\pi$
$648$	23.6720	−	9.36134i	0.929925	−	0.367748i
$649$	−47.6562	−	19.7398i	−1.87067	−	0.774856i
$650$	−0.333817	+	0.121519i	−0.0130934	+	0.00476638i
$651$	5.68804	+	31.9990i	0.222932	+	1.25414i
$652$	−0.696318	−	6.35187i	−0.0272699	−	0.248758i
$653$	10.5494	−	7.04890i	0.412831	−	0.275845i	−0.331763	−	0.943363i	$-0.607643\pi$
$653$	10.5494	−	7.04890i	0.412831	−	0.275845i	0.744594	+	0.667518i	$0.232643\pi$
$654$	−22.1264	−	5.89463i	−0.865210	−	0.230498i
$655$	0.0713128	+	0.0713128i	0.00278642	+	0.00278642i
$656$	2.12831	−	0.472305i	0.0830967	−	0.0184404i
$657$	−6.96209	−	7.55562i	−0.271617	−	0.294773i
$658$	45.5035	−	27.6155i	1.77391	−	1.07656i
$659$	−15.9442	+	10.6536i	−0.621099	+	0.415005i	−0.825914	−	0.563796i	$-0.809341\pi$
$659$	−15.9442	+	10.6536i	−0.621099	+	0.415005i	0.204816	+	0.978801i	$0.434341\pi$
$660$	15.7209	+	4.93102i	0.611936	+	0.191940i
$661$	35.4548	−	7.05239i	1.37903	−	0.274306i	0.550774	−	0.834655i	$-0.314333\pi$
$661$	35.4548	−	7.05239i	1.37903	−	0.274306i	0.828257	+	0.560348i	$0.189333\pi$
$662$	−26.1264	−	12.1813i	−1.01543	−	0.473438i
$663$	−0.273969	−	0.120096i	−0.0106401	−	0.00466415i
$664$	−0.419819	−	1.56580i	−0.0162922	−	0.0607649i
$665$	−15.1233	+	6.26429i	−0.586458	+	0.242919i
$666$	−3.19141	+	37.7048i	−0.123665	+	1.46103i
$667$	−6.01178	+	8.99726i	−0.232777	+	0.348375i
$668$	5.93478	−	4.98093i	0.229624	−	0.192718i
$669$	45.6667	+	10.0577i	1.76558	+	0.388851i
$670$	4.68958	−	0.722047i	0.181174	−	0.0278951i
$671$			61.5990i			2.37800i
$672$	−5.42525	−	34.8659i	−0.209284	−	1.34498i
$673$		−	4.03040i		−	0.155360i	−0.996978	−	0.0776802i	$-0.975249\pi$
$673$		−	4.03040i		−	0.155360i	0.996978	−	0.0776802i	$-0.0247513\pi$
$674$	−7.74737	−	50.3179i	−0.298418	−	1.93817i
$675$	1.32397	−	5.02465i	0.0509598	−	0.193399i
$676$	25.7756	+	2.25234i	0.991368	+	0.0866286i
$677$	−2.96826	+	4.44231i	−0.114079	+	0.170732i	−0.884116	−	0.467268i	$-0.845238\pi$
$677$	−2.96826	+	4.44231i	−0.114079	+	0.170732i	0.770036	+	0.638000i	$0.220238\pi$
$678$	−2.91396	+	45.4607i	−0.111910	+	1.74591i
$679$	60.2108	−	24.9401i	2.31068	−	0.957114i
$680$	−0.253522	+	1.92803i	−0.00972211	+	0.0739367i
$681$	3.07437	−	7.01340i	0.117810	−	0.268754i
$682$	−14.8098	+	31.7640i	−0.567095	+	1.21631i
$683$	32.6198	−	6.48847i	1.24816	−	0.248275i	0.473581	−	0.880751i	$-0.342961\pi$
$683$	32.6198	−	6.48847i	1.24816	−	0.248275i	0.774580	+	0.632476i	$0.217961\pi$
$684$	−24.4250	+	12.1326i	−0.933914	+	0.463902i
$685$	−6.82817	+	4.56244i	−0.260891	+	0.174322i
$686$	−2.72309	−	4.48698i	−0.103968	−	0.171314i
$687$	−5.99920	−	6.24948i	−0.228884	−	0.238432i
$688$	18.6088	+	17.8065i	0.709452	+	0.678868i
$689$	1.25032	+	1.25032i	0.0476336	+	0.0476336i
$690$	4.61581	+	1.22969i	0.175721	+	0.0468134i
$691$	−18.6031	+	12.4302i	−0.707695	+	0.472866i	−0.856597	−	0.515985i	$-0.827426\pi$
$691$	−18.6031	+	12.4302i	−0.707695	+	0.472866i	0.148903	+	0.988852i	$0.452426\pi$
$692$	11.5666	−	14.4148i	0.439697	−	0.547969i
$693$	−50.7662	+	7.95785i	−1.92845	+	0.302294i
$694$	8.07496	+	22.1822i	0.306521	+	0.842023i
$695$	−13.5045	−	5.59376i	−0.512256	−	0.212183i
$696$	18.3340	−	20.0702i	0.694950	−	0.760760i
$697$	0.346196	−	0.143399i	0.0131131	−	0.00543163i
$698$	−34.7391	+	31.8358i	−1.31489	+	1.20500i
$699$	−31.7153	−	22.1418i	−1.19958	−	0.837480i
$700$	−6.38915	−	3.32513i	−0.241487	−	0.125678i
$701$	−6.30005	+	31.6725i	−0.237950	+	1.19625i	0.658318	+	0.752740i	$0.271268\pi$
$701$	−6.30005	+	31.6725i	−0.237950	+	1.19625i	−0.896268	+	0.443514i	$0.853732\pi$
$702$	1.18057	−	1.41904i	0.0445577	−	0.0535583i
$703$		−	40.5399i		−	1.52899i
$704$	16.8183	−	34.1313i	0.633864	−	1.28637i
$705$	0.369795	−	18.0981i	0.0139273	−	0.681612i
$706$	16.7023	+	12.2453i	0.628600	+	0.460858i
$707$	24.6884	+	4.91084i	0.928504	+	0.184691i
$708$	32.9647	+	18.0211i	1.23889	+	0.677276i
$709$	23.3163	−	34.8953i	0.875663	−	1.31052i	−0.0740035	−	0.997258i	$-0.523578\pi$
$709$	23.3163	−	34.8953i	0.875663	−	1.31052i	0.949666	−	0.313264i	$-0.101422\pi$
$710$	−10.1633	−	11.0901i	−0.381421	−	0.416204i
$711$	9.49277	+	25.8578i	0.356007	+	0.969744i
$712$	1.38267	+	21.0446i	0.0518176	+	0.788681i
$713$	−3.88840	+	9.38743i	−0.145622	+	0.351562i
$714$	−1.95778	−	5.74029i	−0.0732681	−	0.214825i
$715$	1.17180	−	0.233086i	0.0438229	−	0.00871692i
$716$	−5.04859	+	6.29176i	−0.188675	+	0.235134i
$717$	19.5432	+	30.5830i	0.729855	+	1.14214i
$718$	2.09091	−	8.54681i	0.0780322	−	0.318964i
$719$	31.3283	−	31.3283i	1.16835	−	1.16835i	0.185754	−	0.982596i	$-0.440527\pi$
$719$	31.3283	−	31.3283i	1.16835	−	1.16835i	0.982596	−	0.185754i	$-0.0594727\pi$
$720$	−10.9981	−	4.80017i	−0.409875	−	0.178892i
$721$	16.8969	+	16.8969i	0.629274	+	0.629274i
$722$	2.00763	−	1.21841i	0.0747164	−	0.0453444i
$723$	0.700183	−	0.447432i	0.0260401	−	0.0166402i
$724$	35.6190	−	19.5461i	1.32377	−	0.726425i
$725$	−1.08252	−	5.44222i	−0.0402040	−	0.202119i
$726$	−25.5499	−	12.5542i	−0.948248	−	0.465929i
$727$	−14.2273	−	5.89314i	−0.527662	−	0.218565i	0.102917	−	0.994690i	$-0.467182\pi$
$727$	−14.2273	−	5.89314i	−0.527662	−	0.218565i	−0.630579	+	0.776125i	$0.717182\pi$
$728$	−1.55797	−	2.02972i	−0.0577421	−	0.0752264i
$729$	7.20484	+	26.0210i	0.266846	+	0.963739i
$730$	−0.211007	+	4.83868i	−0.00780972	+	0.179088i
$731$	3.68089	+	2.45949i	0.136143	+	0.0909675i
$732$	4.81770	−	44.6048i	0.178067	−	1.64864i
$733$	3.36356	−	16.9098i	0.124236	−	0.624577i	−0.867622	−	0.497225i	$-0.834352\pi$
$733$	3.36356	−	16.9098i	0.124236	−	0.624577i	0.991858	−	0.127352i	$-0.0406477\pi$
$734$	22.0335	−	3.39246i	0.813271	−	0.125218i
$735$	10.3372	+	0.211219i	0.381294	+	0.00779093i
$736$	4.44027	−	10.0985i	0.163671	−	0.372235i
$737$	−15.9577			−0.587810
$738$	0.258231	+	2.29787i	0.00950561	+	0.0845858i
$739$	−2.78592	−	0.554154i	−0.102482	−	0.0203849i	0.143583	−	0.989638i	$-0.454138\pi$
$739$	−2.78592	−	0.554154i	−0.102482	−	0.0203849i	−0.246065	+	0.969253i	$0.579138\pi$
$740$	13.6633	−	11.4673i	0.502274	−	0.421548i
$741$	−1.13208	+	1.62156i	−0.0415881	+	0.0595696i
$742$	−1.56191	+	35.8167i	−0.0573394	+	1.31487i
$743$	4.09888	+	9.89557i	0.150373	+	0.363033i	0.981059	−	0.193708i	$-0.0620514\pi$
$743$	4.09888	+	9.89557i	0.150373	+	0.363033i	−0.830686	+	0.556741i	$0.812051\pi$
$744$	13.2083	−	21.8425i	0.484238	−	0.800786i
$745$	−2.05916	+	4.97126i	−0.0754418	+	0.182133i
$746$	11.5541	−	24.7813i	0.423027	−	0.907309i
$747$	1.69870	−	0.266279i	0.0621521	−	0.00974264i
$748$	1.82946	−	6.27904i	0.0668916	−	0.229584i
$749$	−29.8469	−	44.6691i	−1.09058	−	1.63217i
$750$	−2.11956	+	1.22780i	−0.0773952	+	0.0448328i
$751$	14.1884	−	14.1884i	0.517743	−	0.517743i	−0.399145	−	0.916888i	$-0.630693\pi$
$751$	14.1884	−	14.1884i	0.517743	−	0.517743i	0.916888	+	0.399145i	$0.130693\pi$
$752$	−41.1708	−	7.25061i	−1.50134	−	0.264403i
$753$	−26.6629	+	25.5951i	−0.971649	+	0.932737i
$754$	0.468429	−	1.91475i	0.0170592	−	0.0697309i
$755$	2.13536	+	3.19580i	0.0777138	+	0.116307i
$756$	37.3830	−	1.79194i	1.35961	−	0.0651723i
$757$	3.94395	+	19.8276i	0.143345	+	0.720645i	0.983872	+	0.178875i	$0.0572456\pi$
$757$	3.94395	+	19.8276i	0.143345	+	0.720645i	−0.840527	+	0.541770i	$0.817754\pi$
$758$	−11.3358	−	31.1397i	−0.411734	−	1.13104i
$759$	−14.7136	−	6.44982i	−0.534071	−	0.234114i
$760$	12.1747	+	4.13061i	0.441622	+	0.149833i
$761$	2.82043	+	6.80912i	0.102241	+	0.246830i	0.966720	−	0.255838i	$-0.0823515\pi$
$761$	2.82043	+	6.80912i	0.102241	+	0.246830i	−0.864479	+	0.502669i	$0.832351\pi$
$762$	−15.3877	+	13.5339i	−0.557437	+	0.490280i
$763$	−27.9918	−	18.7035i	−1.01337	−	0.677113i
$764$	−10.8950	−	34.5417i	−0.394166	−	1.24968i
$765$	−2.00483	−	0.484691i	−0.0724849	−	0.0175240i
$766$	−21.4469	−	15.7238i	−0.774907	−	0.568123i
$767$	2.72430			0.0983689
$768$	−14.8478	+	23.3996i	−0.535775	+	0.844361i
$769$	32.8578			1.18488			0.592442	−	0.805613i	$-0.298164\pi$
$769$	32.8578			1.18488			0.592442	+	0.805613i	$0.298164\pi$
$770$	19.5358	+	14.3227i	0.704021	+	0.516153i
$771$	7.84548	−	35.6224i	0.282548	−	1.28291i
$772$	1.65151	+	5.23600i	0.0594391	+	0.188448i
$773$	−5.42511	−	3.62494i	−0.195128	−	0.130380i	0.454169	−	0.890916i	$-0.349936\pi$
$773$	−5.42511	−	3.62494i	−0.195128	−	0.130380i	−0.649296	+	0.760536i	$0.724936\pi$
$774$	−20.8772	+	17.6188i	−0.750414	+	0.633295i
$775$	−1.99393	−	4.81377i	−0.0716240	−	0.172916i
$776$	−48.4713	−	16.4453i	−1.74002	−	0.590351i
$777$	−22.3354	+	50.9525i	−0.801277	+	1.82791i
$778$	−17.0425	−	46.8162i	−0.611002	−	1.67844i
$779$	−0.483305	−	2.42974i	−0.0173162	−	0.0870545i
$780$	−0.866750	+	0.0771337i	−0.0310346	+	0.00276183i
$781$	28.1070	+	42.0651i	1.00575	+	1.50521i
$782$	0.450587	−	1.84182i	0.0161130	−	0.0658632i
$783$	19.1007	+	21.5982i	0.682602	+	0.771858i
$784$	4.14140	−	23.5159i	0.147907	−	0.839853i
$785$	−0.855387	+	0.855387i	−0.0305301	+	0.0305301i
$786$	0.123825	+	0.213760i	0.00441670	+	0.00762458i
$787$	3.69584	+	5.53121i	0.131742	+	0.197166i	0.891476	−	0.453068i	$-0.149671\pi$
$787$	3.69584	+	5.53121i	0.131742	+	0.197166i	−0.759733	+	0.650235i	$0.774671\pi$
$788$	−6.49956	+	22.3077i	−0.231537	+	0.794679i
$789$	−48.3969	+	8.60289i	−1.72298	+	0.306271i
$790$	5.48706	−	11.7686i	0.195221	−	0.418710i
$791$	−25.6302	+	61.8767i	−0.911304	+	2.20008i
$792$	34.1011	+	21.5845i	1.21173	+	0.766973i
$793$	−1.24499	−	3.00567i	−0.0442108	−	0.106734i
$794$	−0.0239921	+	0.550173i	−0.000851449	+	0.0195249i
$795$	9.99696	+	6.97931i	0.354556	+	0.247531i
$796$	−30.7479	+	25.8060i	−1.08983	+	0.914671i
$797$	43.4347	+	8.63970i	1.53854	+	0.306034i	0.890289	−	0.455396i	$-0.150502\pi$
$797$	43.4347	+	8.63970i	1.53854	+	0.306034i	0.648247	+	0.761430i	$0.275502\pi$
$798$	−39.7460	+	5.29086i	−1.40699	+	0.187294i
$799$	−7.18545			−0.254203
$800$	2.05164	+	5.27169i	0.0725365	+	0.186383i
$801$	−22.3507	−	0.913757i	−0.789721	−	0.0322860i
$802$	−7.05463	+	1.08619i	−0.249108	+	0.0383547i
$803$	3.17779	−	15.9758i	0.112142	−	0.563774i
$804$	11.5552	+	1.24806i	0.407522	+	0.0440158i
$805$	5.83941	+	3.90177i	0.205812	+	0.137519i
$806$	0.0806414	−	1.84922i	0.00284047	−	0.0651359i
$807$	−12.3753	+	4.83226i	−0.435631	+	0.170103i
$808$	−12.0376	−	15.6826i	−0.423482	−	0.551712i
$809$	−51.7784	−	21.4473i	−1.82043	−	0.754047i	−0.975789	−	0.218713i	$-0.929814\pi$
$809$	−51.7784	−	21.4473i	−1.82043	−	0.754047i	−0.844641	−	0.535334i	$-0.820186\pi$
$810$	6.30215	−	11.0582i	0.221435	−	0.388544i
$811$	−7.41402	−	37.2728i	−0.260341	−	1.30882i	−0.860708	−	0.509099i	$-0.829979\pi$
$811$	−7.41402	−	37.2728i	−0.260341	−	1.30882i	0.600366	−	0.799725i	$-0.295021\pi$
$812$	35.0374	−	19.2270i	1.22957	−	0.674734i
$813$	4.08159	+	6.38725i	0.143147	+	0.224010i
$814$	−51.2859	+	31.1247i	−1.79757	+	1.09092i
$815$	−2.25918	−	2.25918i	−0.0791356	−	0.0791356i
$816$	−1.81583	+	4.40367i	−0.0635667	+	0.154159i
$817$	20.6952	−	20.6952i	0.724035	−	0.724035i
$818$	2.35211	−	9.61447i	0.0822397	−	0.336162i
$819$	2.31625	−	1.41434i	0.0809365	−	0.0494211i
$820$	0.682196	−	0.850181i	0.0238233	−	0.0296896i
$821$	−10.9632	+	2.18071i	−0.382617	+	0.0761072i	−0.382652	−	0.923893i	$-0.624989\pi$
$821$	−10.9632	+	2.18071i	−0.382617	+	0.0761072i	3.45614e−5		1.00000i	$0.499989\pi$
$822$	−19.0388	+	6.49336i	−0.664053	+	0.226482i
$823$	10.6178	−	25.6337i	0.370115	−	0.893536i	−0.623616	−	0.781731i	$-0.714337\pi$
$823$	10.6178	−	25.6337i	0.370115	−	0.893536i	0.993730	−	0.111805i	$-0.0356630\pi$
$824$	−1.23040	−	18.7271i	−0.0428631	−	0.652391i
$825$	7.67379	−	2.99643i	0.267167	−	0.104322i
$826$	37.3184	+	40.7216i	1.29847	+	1.41689i
$827$	4.63551	−	6.93754i	0.161193	−	0.241242i	−0.742078	−	0.670314i	$-0.766159\pi$
$827$	4.63551	−	6.93754i	0.161193	−	0.241242i	0.903270	+	0.429072i	$0.141159\pi$
$828$	10.1499	+	5.82118i	0.352734	+	0.202300i
$829$	37.3514	+	7.42965i	1.29727	+	0.258042i	0.794968	−	0.606652i	$-0.207488\pi$
$829$	37.3514	+	7.42965i	1.29727	+	0.258042i	0.502299	+	0.864694i	$0.332488\pi$
$830$	−0.653691	−	0.479253i	−0.0226899	−	0.0166351i
$831$	−23.7912	−	0.486121i	−0.825306	−	0.0168634i
$832$	−0.130802	+	2.00532i	−0.00453473	+	0.0695220i
$833$		−	4.10418i		−	0.142201i
$834$	−28.4371	−	21.7556i	−0.984696	−	0.753335i
$835$	0.755779	−	3.79956i	0.0261548	−	0.131489i
$836$	−38.3547	−	19.9611i	−1.32652	−	0.690368i
$837$	21.5476	+	16.3921i	0.744793	+	0.566593i
$838$	−2.99197	+	2.74192i	−0.103356	+	0.0947181i
$839$	23.6386	−	9.79145i	0.816097	−	0.338038i	0.0647131	−	0.997904i	$-0.479387\pi$
$839$	23.6386	−	9.79145i	0.816097	−	0.338038i	0.751384	+	0.659866i	$0.229387\pi$
$840$	−13.0260	−	11.8992i	−0.449439	−	0.410560i
$841$	1.65339	+	0.684856i	0.0570134	+	0.0236157i
$842$	−0.639649	−	1.75713i	−0.0220437	−	0.0605548i
$843$	−43.6167	+	7.75318i	−1.50224	+	0.267034i
$844$	−10.8187	+	13.4827i	−0.372395	+	0.464094i
$845$	10.7566	−	7.18736i	0.370040	−	0.247253i
$846$	12.2874	−	42.6037i	0.422448	−	1.46475i
$847$	−29.5952	−	29.5952i	−1.01690	−	1.01690i
$848$	19.4665	−	20.3435i	0.668481	−	0.698598i
$849$	37.8885	−	36.3712i	1.30033	−	1.24825i
$850$	0.504455	+	0.831217i	0.0173027	+	0.0285105i
$851$	−14.4617	+	9.66299i	−0.495740	+	0.331243i
$852$	−17.0628	−	32.6582i	−0.584561	−	1.11885i
$853$	25.9913	−	5.17000i	0.889927	−	0.177017i	0.271106	−	0.962550i	$-0.412611\pi$
$853$	25.9913	−	5.17000i	0.889927	−	0.177017i	0.618821	+	0.785532i	$0.287611\pi$
$854$	27.8730	−	59.7821i	0.953796	−	2.04570i
$855$	−5.72860	+	12.3745i	−0.195914	+	0.423199i
$856$	−5.50076	+	41.8333i	−0.188012	+	1.42983i
$857$	23.0823	−	9.56099i	0.788476	−	0.326597i	0.0481451	−	0.998840i	$-0.484669\pi$
$857$	23.0823	−	9.56099i	0.788476	−	0.326597i	0.740331	+	0.672243i	$0.234669\pi$
$858$	2.92056	+	0.187203i	0.0997062	+	0.00639100i
$859$	8.79619	−	13.1644i	0.300122	−	0.449165i	−0.650504	−	0.759503i	$-0.725442\pi$
$859$	8.79619	−	13.1644i	0.300122	−	0.449165i	0.950626	+	0.310338i	$0.100442\pi$
$860$	12.8290	+	1.12103i	0.437465	+	0.0382269i
$861$	−0.731219	+	3.32009i	−0.0249199	+	0.113149i
$862$	−3.61558	−	23.4826i	−0.123147	−	0.799822i
$863$			16.5445i			0.563180i	0.959535	+	0.281590i	$0.0908618\pi$
$863$			16.5445i			0.563180i	−0.959535	+	0.281590i	$0.909138\pi$
$864$	−23.0050	−	18.2968i	−0.782645	−	0.622469i
$865$		−	9.24085i		−	0.314198i
$866$	40.3893	−	6.21867i	1.37248	−	0.211319i
$867$	6.15707	−	27.9561i	0.209105	−	0.949440i
$868$	28.7459	−	24.1258i	0.975700	−	0.818884i
$869$	−24.2621	+	36.3108i	−0.823035	+	1.23176i
$870$	0.869429	−	13.5640i	0.0294764	−	0.459862i
$871$	0.778642	−	0.322524i	0.0263833	−	0.0109283i
$872$	6.84731	+	25.5384i	0.231879	+	0.864841i
$873$	22.8074	−	49.2668i	0.771913	−	1.66743i
$874$	−11.3615	−	5.29721i	−0.384307	−	0.179181i
$875$	−3.53211	+	0.702581i	−0.119407	+	0.0237516i
$876$	−3.55056	+	11.3198i	−0.119962	+	0.382460i
$877$	21.7615	−	14.5406i	0.734835	−	0.491001i	−0.130968	−	0.991387i	$-0.541808\pi$
$877$	21.7615	−	14.5406i	0.734835	−	0.491001i	0.865803	+	0.500386i	$0.166808\pi$
$878$	−32.7296	+	19.8632i	−1.10457	+	0.670350i
$879$	−28.8922	+	27.7351i	−0.974509	+	0.935482i
$880$	−4.12166	−	18.5731i	−0.138941	−	0.626101i
$881$	4.06232	+	4.06232i	0.136863	+	0.136863i	0.772219	−	0.635356i	$-0.219147\pi$
$881$	4.06232	+	4.06232i	0.136863	+	0.136863i	−0.635356	+	0.772219i	$0.719147\pi$
$882$	24.3344	+	7.01828i	0.819380	+	0.236318i
$883$	16.4951	−	11.0216i	0.555103	−	0.370908i	−0.246152	−	0.969231i	$-0.579166\pi$
$883$	16.4951	−	11.0216i	0.555103	−	0.370908i	0.801255	+	0.598323i	$0.204166\pi$
$884$	0.0376400	+	0.343356i	0.00126597	+	0.0115483i
$885$	18.4946	−	3.28755i	0.621689	−	0.110510i
$886$	45.4913	−	16.5602i	1.52831	−	0.556351i
$887$	−36.5268	−	15.1299i	−1.22645	−	0.508012i	−0.326994	−	0.945026i	$-0.606036\pi$
$887$	−36.5268	−	15.1299i	−1.22645	−	0.508012i	−0.899454	+	0.437015i	$0.856036\pi$
$888$	39.5712	−	18.5268i	1.32792	−	0.621718i
$889$	−27.8354	+	11.5298i	−0.933570	+	0.386697i
$890$	7.12451	+	7.77422i	0.238814	+	0.260592i
$891$	−26.6078	+	33.5320i	−0.891396	+	1.12336i
$892$	−16.2421	−	51.4944i	−0.543824	−	1.72416i
$893$	−9.26763	+	46.5915i	−0.310130	+	1.55913i
$894$	−8.00862	+	10.4682i	−0.267848	+	0.350109i
$895$			4.03344i			0.134823i
$896$	−31.7664	+	25.5144i	−1.06124	+	0.852377i
$897$	0.848297	+	0.0173331i	0.0283238	+	0.000578736i
$898$	−30.0243	+	40.9524i	−1.00192	+	1.36660i
$899$	28.3560	+	5.64037i	0.945727	+	0.188117i
$900$	−5.79106	+	1.56959i	−0.193035	+	0.0523196i
$901$	2.68876	−	4.02402i	0.0895757	−	0.134060i
$902$	−2.70274	+	2.47686i	−0.0899913	+	0.0824705i
$903$	−37.4128	+	14.6088i	−1.24502	+	0.486151i
$904$	47.1730	−	23.2724i	1.56895	−	0.774027i
$905$	7.77413	−	18.7684i	0.258421	−	0.623883i
$906$	3.03910	+	8.91074i	0.100967	+	0.296040i
$907$	51.0016	−	10.1448i	1.69348	−	0.336854i	0.748289	−	0.663373i	$-0.230876\pi$
$907$	51.0016	−	10.1448i	1.69348	−	0.336854i	0.945191	+	0.326518i	$0.105876\pi$
$908$	−8.78963	+	0.963554i	−0.291694	+	0.0319767i
$909$	17.8965	−	10.9279i	0.593590	−	0.362455i
$910$	−1.24271	−	0.304020i	−0.0411954	−	0.0100782i
$911$	14.2206	−	14.2206i	0.471151	−	0.471151i	−0.431136	−	0.902287i	$-0.641887\pi$
$911$	14.2206	−	14.2206i	0.471151	−	0.471151i	0.902287	+	0.431136i	$0.141887\pi$
$912$	26.2120	+	17.4539i	0.867967	+	0.577955i
$913$	1.92759	+	1.92759i	0.0637940	+	0.0637940i
$914$	6.19404	+	10.2062i	0.204881	+	0.337593i
$915$	−12.0790	−	18.9023i	−0.399319	−	0.624891i
$916$	−2.79815	+	9.60376i	−0.0924534	+	0.317317i
$917$	0.0708564	+	0.356219i	0.00233988	+	0.0117634i
$918$	−4.43968	−	2.41142i	−0.146531	−	0.0795887i
$919$	−30.2164	−	12.5160i	−0.996746	−	0.412866i	−0.176143	−	0.984365i	$-0.556362\pi$
$919$	−30.2164	−	12.5160i	−0.996746	−	0.412866i	−0.820603	+	0.571499i	$0.806362\pi$
$920$	−1.42843	−	5.32761i	−0.0470938	−	0.175646i
$921$	31.6179	−	12.3460i	1.04184	−	0.406815i
$922$	−26.2403	−	1.14430i	−0.864179	−	0.0376855i
$923$	−2.22164	−	1.48445i	−0.0731261	−	0.0488613i
$924$	37.2085	+	46.2195i	1.22407	+	1.52051i
$925$	1.73999	−	8.74752i	0.0572105	−	0.287617i
$926$	−2.91407	−	18.9264i	−0.0957624	−	0.621961i
$927$	19.8893	+	0.813131i	0.653251	+	0.0267067i
$928$	−30.6467	−	6.78578i	−1.00603	−	0.222754i
$929$	−8.93520			−0.293154			−0.146577	−	0.989199i	$-0.546826\pi$
$929$	−8.93520			−0.293154			−0.146577	+	0.989199i	$0.546826\pi$
$930$	−1.68408	−	12.6512i	−0.0552233	−	0.414849i
$931$	−26.6121	−	5.29348i	−0.872177	−	0.173487i
$932$	−3.88801	+	44.4939i	−0.127356	+	1.45745i
$933$	−9.69142	−	6.76599i	−0.317283	−	0.221509i
$934$	−41.3273	−	1.80222i	−1.35227	−	0.0589703i
$935$	−1.25140	−	3.02114i	−0.0409251	−	0.0988020i
$936$	−2.10018	−	0.363975i	−0.0686465	−	0.0118969i
$937$	−10.3537	+	24.9961i	−0.338241	+	0.816586i	0.659644	+	0.751578i	$0.270707\pi$
$937$	−10.3537	+	24.9961i	−0.338241	+	0.816586i	−0.997885	+	0.0650077i	$0.979293\pi$
$938$	15.4870	+	7.22074i	0.505670	+	0.235766i
$939$	34.4817	−	6.12937i	1.12527	−	0.200024i
$940$	−18.3245	+	10.0556i	−0.597678	+	0.327979i
$941$	−21.5293	−	32.2209i	−0.701835	−	1.05037i	−0.995528	−	0.0944709i	$-0.969884\pi$
$941$	−21.5293	−	32.2209i	−0.701835	−	1.05037i	0.293692	−	0.955900i	$-0.405116\pi$
$942$	−2.56403	+	1.48527i	−0.0835405	+	0.0483926i
$943$	−0.751556	+	0.751556i	−0.0244740	+	0.0244740i
$944$	−0.955456	−	43.3705i	−0.0310974	−	1.41159i
$945$	14.0177	−	12.3967i	0.455996	−	0.403266i
$946$	−42.0699	−	10.2921i	−1.36781	−	0.334625i
$947$	−7.27269	−	10.8843i	−0.236331	−	0.353694i	0.694280	−	0.719705i	$-0.255723\pi$
$947$	−7.27269	−	10.8843i	−0.236331	−	0.353694i	−0.930610	+	0.366012i	$0.880723\pi$
$948$	20.4085	−	24.3957i	0.662836	−	0.792334i
$949$	0.167833	+	0.843752i	0.00544808	+	0.0273893i
$950$	6.04037	−	2.19888i	0.195976	−	0.0713409i
$951$	10.5751	−	24.1243i	0.342920	−	0.782285i
$952$	−4.61671	+	5.26603i	−0.149629	+	0.170673i
$953$	14.8510	+	35.8535i	0.481071	+	1.16141i	0.959101	+	0.283065i	$0.0913513\pi$
$953$	14.8510	+	35.8535i	0.481071	+	1.16141i	−0.478029	+	0.878344i	$0.658649\pi$
$954$	19.2612	+	22.8233i	0.623605	+	0.738933i
$955$	−15.0576	−	10.0612i	−0.487252	−	0.325571i
$956$	19.3474	−	37.1756i	0.625740	−	1.20234i
$957$	−9.83192	+	44.6418i	−0.317821	+	1.44306i
$958$	−29.8275	+	40.6841i	−0.963683	+	1.31444i
$959$	−29.5746			−0.955013
$960$	1.53194	+	13.7715i	0.0494431	+	0.444472i
$961$	−3.85192			−0.124256
$962$	1.87338	−	2.55525i	0.0604002	−	0.0823845i
$963$	−43.4997	−	10.5165i	−1.40176	−	0.338891i
$964$	−0.851115	−	0.442949i	−0.0274126	−	0.0142664i
$965$	2.28250	+	1.52512i	0.0734763	+	0.0490953i
$966$	11.3612	+	12.9174i	0.365540	+	0.415610i
$967$	−23.0081	−	55.5464i	−0.739889	−	1.78625i	−0.606336	−	0.795209i	$-0.707361\pi$
$967$	−23.0081	−	55.5464i	−0.739889	−	1.78625i	−0.133554	−	0.991042i	$-0.542639\pi$
$968$	2.15507	+	32.8009i	0.0692666	+	1.05426i
$969$	4.95744	+	2.17313i	0.159256	+	0.0698108i
$970$	−24.0487	+	8.75442i	−0.772156	+	0.281088i
$971$	5.75915	+	28.9532i	0.184820	+	0.929153i	0.956186	+	0.292761i	$0.0945740\pi$
$971$	5.75915	+	28.9532i	0.184820	+	0.929153i	−0.771366	+	0.636392i	$0.780426\pi$
$972$	21.8897	−	22.2000i	0.702113	−	0.712066i
$973$	−29.2458	−	43.7695i	−0.937578	−	1.40318i
$974$	−34.9913	−	8.56037i	−1.12119	−	0.274292i
$975$	−0.313874	+	0.301304i	−0.0100520	+	0.00964946i
$976$	−47.4131	+	20.8741i	−1.51766	+	0.668165i
$977$	−10.7219	+	10.7219i	−0.343023	+	0.343023i	−0.857502	−	0.514480i	$-0.827985\pi$
$977$	−10.7219	+	10.7219i	−0.343023	+	0.343023i	0.514480	+	0.857502i	$0.327985\pi$
$978$	−3.92276	−	6.77190i	−0.125436	−	0.216541i
$979$	−19.7031	−	29.4878i	−0.629714	−	0.942434i
$980$	−5.74357	−	10.4665i	−0.183472	−	0.334341i
$981$	−27.7060	+	4.34305i	−0.884585	+	0.138663i
$982$	27.0187	+	12.5973i	0.862202	+	0.401996i
$983$	17.6754	−	42.6723i	0.563759	−	1.36103i	−0.342980	−	0.939343i	$-0.611436\pi$
$983$	17.6754	−	42.6723i	0.563759	−	1.36103i	0.906739	−	0.421692i	$-0.138564\pi$
$984$	2.15081	−	1.58215i	0.0685654	−	0.0504372i
$985$	4.44588	+	10.7333i	0.141657	+	0.341991i
$986$	−5.39010	−	0.235053i	−0.171656	−	0.00748562i
$987$	37.3176	−	53.4526i	1.18783	−	1.70141i
$988$	2.27492	+	0.198789i	0.0723748	+	0.00632432i
$989$	−12.3154	−	2.44969i	−0.391608	−	0.0778957i
$990$	20.0528	−	2.25350i	0.637320	−	0.0716210i
$991$	−47.0294			−1.49394			−0.746968	−	0.664859i	$-0.768491\pi$
$991$	−47.0294			−1.49394			−0.746968	+	0.664859i	$0.768491\pi$
$992$	−29.4675	−	0.635248i	−0.935595	−	0.0201691i
$993$	−35.2978	−	0.721235i	−1.12014	−	0.0228877i
$994$	−8.24386	−	53.5425i	−0.261479	−	1.69827i
$995$	−3.91566	+	19.6854i	−0.124135	+	0.624068i
$996$	−1.24504	−	1.54656i	−0.0394507	−	0.0490046i
$997$	16.0354	+	10.7145i	0.507845	+	0.339331i	0.782952	−	0.622083i	$-0.213713\pi$
$997$	16.0354	+	10.7145i	0.507845	+	0.339331i	−0.275107	+	0.961414i	$0.588713\pi$
$998$	48.8474	+	2.13015i	1.54624	+	0.0674288i
$999$	15.0792	+	43.8221i	0.477084	+	1.38647i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	960.2.cn.a.611.25	yes	1024
3.2	odd	2	inner	960.2.cn.a.611.104	yes	1024
64.11	odd	16	inner	960.2.cn.a.11.104	yes	1024
192.11	even	16	inner	960.2.cn.a.11.25	✓	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
960.2.cn.a.11.25	✓	1024	192.11	even	16	inner
960.2.cn.a.11.104	yes	1024	64.11	odd	16	inner
960.2.cn.a.611.25	yes	1024	1.1	even	1	trivial
960.2.cn.a.611.104	yes	1024	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	960.cn (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.14053 - 0.836178i) q^{2} +(-1.69151 - 0.372539i) q^{3} +(0.601612 + 1.90737i) q^{4} +(0.831470 + 0.555570i) q^{5} +(1.61771 + 1.83930i) q^{6} +(1.37816 + 3.32718i) q^{7} +(0.908746 - 2.67847i) q^{8} +(2.72243 + 1.26031i) q^{9} +O(q^{10})\)	\(q+(-1.14053 - 0.836178i) q^{2} +(-1.69151 - 0.372539i) q^{3} +(0.601612 + 1.90737i) q^{4} +(0.831470 + 0.555570i) q^{5} +(1.61771 + 1.83930i) q^{6} +(1.37816 + 3.32718i) q^{7} +(0.908746 - 2.67847i) q^{8} +(2.72243 + 1.26031i) q^{9} +(-0.483759 - 1.32890i) q^{10} +(0.927897 + 4.66486i) q^{11} +(-0.307063 - 3.45047i) q^{12} +(-0.139558 - 0.208863i) q^{13} +(1.21028 - 4.94713i) q^{14} +(-1.19947 - 1.24951i) q^{15} +(-3.27613 + 2.29499i) q^{16} +(-0.486157 + 0.486157i) q^{17} +(-2.05116 - 3.71386i) q^{18} +(2.52528 + 3.77936i) q^{19} +(-0.559456 + 1.92016i) q^{20} +(-1.09167 - 6.14138i) q^{21} +(2.84236 - 6.09629i) q^{22} +(0.746279 - 1.80168i) q^{23} +(-2.53499 + 4.19211i) q^{24} +(0.382683 + 0.923880i) q^{25} +(-0.0154771 + 0.354910i) q^{26} +(-4.13551 - 3.14604i) q^{27} +(-5.51704 + 4.63034i) q^{28} +(-5.44222 - 1.08252i) q^{29} +(0.323217 + 2.42807i) q^{30} -5.21038 q^{31} +(5.65554 + 0.121920i) q^{32} +(0.168292 - 8.23634i) q^{33} +(0.960991 - 0.147962i) q^{34} +(-0.702581 + 3.53211i) q^{35} +(-0.766033 + 5.95090i) q^{36} +(-7.41579 - 4.95507i) q^{37} +(0.280055 - 6.42205i) q^{38} +(0.158254 + 0.405286i) q^{39} +(2.24367 - 1.72219i) q^{40} +(-0.503535 - 0.208571i) q^{41} +(-3.89021 + 7.91726i) q^{42} +(-1.25617 - 6.31521i) q^{43} +(-8.33937 + 4.57628i) q^{44} +(1.56343 + 2.56041i) q^{45} +(-2.35768 + 1.43084i) q^{46} +(7.39004 + 7.39004i) q^{47} +(6.39658 - 2.66152i) q^{48} +(-4.22104 + 4.22104i) q^{49} +(0.336067 - 1.37370i) q^{50} +(1.00345 - 0.641229i) q^{51} +(0.314420 - 0.391844i) q^{52} +(-6.90392 + 1.37328i) q^{53} +(2.08601 + 7.04617i) q^{54} +(-1.82014 + 4.39420i) q^{55} +(10.1641 - 0.667800i) q^{56} +(-2.86359 - 7.33359i) q^{57} +(5.30182 + 5.78532i) q^{58} +(-6.02530 + 9.01749i) q^{59} +(1.66166 - 3.03955i) q^{60} +(12.7023 + 2.52665i) q^{61} +(5.94259 + 4.35681i) q^{62} +(-0.441326 + 10.7949i) q^{63} +(-6.34836 - 4.86809i) q^{64} -0.251198i q^{65} +(-7.07899 + 9.25306i) q^{66} +(-0.654549 + 3.29064i) q^{67} +(-1.21976 - 0.634804i) q^{68} +(-1.93354 + 2.76954i) q^{69} +(3.75479 - 3.44099i) q^{70} +(9.82712 - 4.07053i) q^{71} +(5.84969 - 6.14663i) q^{72} +(-3.16403 - 1.31058i) q^{73} +(4.31460 + 11.8523i) q^{74} +(-0.303132 - 1.70532i) q^{75} +(-5.68939 + 7.09036i) q^{76} +(-14.2420 + 9.51621i) q^{77} +(0.158398 - 0.594569i) q^{78} +(6.49247 + 6.49247i) q^{79} +(-3.99903 + 0.0880990i) q^{80} +(5.82324 + 6.86221i) q^{81} +(0.399894 + 0.658927i) q^{82} +(0.476554 - 0.318424i) q^{83} +(11.0571 - 5.77696i) q^{84} +(-0.674320 + 0.134131i) q^{85} +(-3.84794 + 8.25307i) q^{86} +(8.80230 + 3.85855i) q^{87} +(13.3379 + 1.75383i) q^{88} +(-6.88885 + 2.85346i) q^{89} +(0.357826 - 4.22752i) q^{90} +(0.502592 - 0.752182i) q^{91} +(3.88544 + 0.339521i) q^{92} +(8.81343 + 1.94107i) q^{93} +(-2.24916 - 14.6079i) q^{94} +4.54539i q^{95} +(-9.52100 - 2.31314i) q^{96} -18.0967i q^{97} +(8.34375 - 1.28467i) q^{98} +(-3.35303 + 13.8692i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1024 q+O(q^{10}) \) 1024 * q	\( 1024 q + 80 q^{24} + 80 q^{42} - 96 q^{52} - 288 q^{58} - 96 q^{64} + 256 q^{67} - 112 q^{76} - 48 q^{78} + 32 q^{79} - 112 q^{84} - 160 q^{88} - 144 q^{90} - 16 q^{94} - 272 q^{96}+O(q^{100}) \) 1024 * q + 80 * q^24 + 80 * q^42 - 96 * q^52 - 288 * q^58 - 96 * q^64 + 256 * q^67 - 112 * q^76 - 48 * q^78 + 32 * q^79 - 112 * q^84 - 160 * q^88 - 144 * q^90 - 16 * q^94 - 272 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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