LMFDB - Embedded newform 630.2.cd.a.23.38

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(23,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 9, 4]))

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

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

chi := DirichletCharacter("630.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.cd (of order $12$, degree $4$, 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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			23.38
Character	$\chi$	$=$	630.23
Dual form			630.2.cd.a.137.38

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(0.300646 + 1.70576i) q^{3} +1.00000i q^{4} +(2.15534 + 0.595421i) q^{5} +(-0.993564 + 1.41874i) q^{6} +(-2.63287 + 0.260796i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.81922 + 1.02566i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(0.300646 + 1.70576i) q^{3} +1.00000i q^{4} +(2.15534 + 0.595421i) q^{5} +(-0.993564 + 1.41874i) q^{6} +(-2.63287 + 0.260796i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.81922 + 1.02566i) q^{9} +(1.10303 + 1.94508i) q^{10} +(-0.920878 - 0.531669i) q^{11} +(-1.70576 + 0.300646i) q^{12} +(-5.82989 + 1.56211i) q^{13} +(-2.04613 - 1.67731i) q^{14} +(-0.367651 + 3.85549i) q^{15} -1.00000 q^{16} +(-0.372689 + 1.39089i) q^{17} +(-2.71874 - 1.26824i) q^{18} +(1.99067 + 1.14931i) q^{19} +(-0.595421 + 2.15534i) q^{20} +(-1.23642 - 4.41263i) q^{21} +(-0.275212 - 1.02711i) q^{22} +(8.59548 + 2.30315i) q^{23} +(-1.41874 - 0.993564i) q^{24} +(4.29095 + 2.56667i) q^{25} +(-5.22693 - 3.01777i) q^{26} +(-2.59712 - 4.50055i) q^{27} +(-0.260796 - 2.63287i) q^{28} +(1.36331 + 2.36131i) q^{29} +(-2.98621 + 2.46628i) q^{30} +7.68165 q^{31} +(-0.707107 - 0.707107i) q^{32} +(0.630040 - 1.73064i) q^{33} +(-1.24704 + 0.719980i) q^{34} +(-5.83000 - 1.00556i) q^{35} +(-1.02566 - 2.81922i) q^{36} +(0.681326 + 2.54274i) q^{37} +(0.594929 + 2.22030i) q^{38} +(-4.41732 - 9.47474i) q^{39} +(-1.94508 + 1.10303i) q^{40} +(-0.580119 - 0.334932i) q^{41} +(2.24592 - 3.99448i) q^{42} +(-0.513911 + 1.91794i) q^{43} +(0.531669 - 0.920878i) q^{44} +(-6.68707 + 0.532017i) q^{45} +(4.44935 + 7.70650i) q^{46} +(-1.10538 - 1.10538i) q^{47} +(-0.300646 - 1.70576i) q^{48} +(6.86397 - 1.37328i) q^{49} +(1.21925 + 4.84906i) q^{50} +(-2.48458 - 0.217550i) q^{51} +(-1.56211 - 5.82989i) q^{52} +(-6.65595 - 1.78346i) q^{53} +(1.34593 - 5.01881i) q^{54} +(-1.66823 - 1.69424i) q^{55} +(1.67731 - 2.04613i) q^{56} +(-1.36196 + 3.74114i) q^{57} +(-0.705699 + 2.63370i) q^{58} +8.10168 q^{59} +(-3.85549 - 0.367651i) q^{60} +1.52352 q^{61} +(5.43175 + 5.43175i) q^{62} +(7.15515 - 3.43567i) q^{63} -1.00000i q^{64} +(-13.4955 - 0.104360i) q^{65} +(1.66925 - 0.778241i) q^{66} +(10.4539 - 10.4539i) q^{67} +(-1.39089 - 0.372689i) q^{68} +(-1.34442 + 15.3542i) q^{69} +(-3.41139 - 4.83347i) q^{70} -1.27742i q^{71} +(1.26824 - 2.71874i) q^{72} +(-2.63231 + 9.82391i) q^{73} +(-1.31622 + 2.27976i) q^{74} +(-3.08805 + 8.09098i) q^{75} +(-1.14931 + 1.99067i) q^{76} +(2.56321 + 1.15965i) q^{77} +(3.57613 - 9.82317i) q^{78} -14.4771i q^{79} +(-2.15534 - 0.595421i) q^{80} +(6.89604 - 5.78313i) q^{81} +(-0.173373 - 0.647038i) q^{82} +(-9.19959 - 2.46502i) q^{83} +(4.41263 - 1.23642i) q^{84} +(-1.63144 + 2.77594i) q^{85} +(-1.71958 + 0.992800i) q^{86} +(-3.61796 + 3.03539i) q^{87} +(1.02711 - 0.275212i) q^{88} +(-3.87841 + 6.71760i) q^{89} +(-5.10467 - 4.35228i) q^{90} +(14.9419 - 5.63325i) q^{91} +(-2.30315 + 8.59548i) q^{92} +(2.30946 + 13.1030i) q^{93} -1.56324i q^{94} +(3.60624 + 3.66244i) q^{95} +(0.993564 - 1.41874i) q^{96} +(0.457480 + 0.122581i) q^{97} +(5.82462 + 3.88250i) q^{98} +(3.14147 + 0.554386i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 8 q^{6}+O(q^{10}) $ 192 * q + 8 * q^6	$ 192 q + 8 q^{6} + 24 q^{11} + 12 q^{15} - 192 q^{16} - 36 q^{17} - 8 q^{18} + 24 q^{23} + 36 q^{27} - 12 q^{30} + 40 q^{33} + 12 q^{41} - 4 q^{42} + 8 q^{45} - 12 q^{46} - 48 q^{50} + 24 q^{51} - 12 q^{56} - 48 q^{57} - 12 q^{58} - 16 q^{60} - 24 q^{61} - 52 q^{63} - 36 q^{68} + 8 q^{72} + 8 q^{75} + 96 q^{77} - 16 q^{78} + 16 q^{81} + 76 q^{87} - 20 q^{90} - 24 q^{92} - 8 q^{96}+O(q^{100}) $ 192 * q + 8 * q^6 + 24 * q^11 + 12 * q^15 - 192 * q^16 - 36 * q^17 - 8 * q^18 + 24 * q^23 + 36 * q^27 - 12 * q^30 + 40 * q^33 + 12 * q^41 - 4 * q^42 + 8 * q^45 - 12 * q^46 - 48 * q^50 + 24 * q^51 - 12 * q^56 - 48 * q^57 - 12 * q^58 - 16 * q^60 - 24 * q^61 - 52 * q^63 - 36 * q^68 + 8 * q^72 + 8 * q^75 + 96 * q^77 - 16 * q^78 + 16 * q^81 + 76 * q^87 - 20 * q^90 - 24 * q^92 - 8 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	0.300646	+	1.70576i	0.173578	+	0.984820i
$3$	0.300646	+	1.70576i	0.173578	+	0.984820i
$4$			1.00000i			0.500000i
$5$	2.15534	+	0.595421i	0.963896	+	0.266281i
$5$	2.15534	+	0.595421i	0.963896	+	0.266281i
$6$	−0.993564	+	1.41874i	−0.405621	+	0.579199i
$7$	−2.63287	+	0.260796i	−0.995130	+	0.0985718i
$7$	−2.63287	+	0.260796i	−0.995130	+	0.0985718i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−2.81922	+	1.02566i	−0.939741	+	0.341887i
$10$	1.10303	+	1.94508i	0.348808	+	0.615088i
$11$	−0.920878	−	0.531669i	−0.277655	−	0.160304i	0.354706	−	0.934978i	$-0.384581\pi$
$11$	−0.920878	−	0.531669i	−0.277655	−	0.160304i	−0.632361	+	0.774674i	$0.717914\pi$
$12$	−1.70576	+	0.300646i	−0.492410	+	0.0867892i
$13$	−5.82989	+	1.56211i	−1.61692	+	0.433252i	−0.950095	−	0.311962i	$-0.899014\pi$
$13$	−5.82989	+	1.56211i	−1.61692	+	0.433252i	−0.666825	+	0.745214i	$0.732347\pi$
$14$	−2.04613	−	1.67731i	−0.546851	−	0.448279i
$15$	−0.367651	+	3.85549i	−0.0949270	+	0.995484i
$16$	−1.00000			−0.250000
$17$	−0.372689	+	1.39089i	−0.0903904	+	0.337342i	−0.996280	−	0.0861717i	$-0.972537\pi$
$17$	−0.372689	+	1.39089i	−0.0903904	+	0.337342i	0.905890	+	0.423513i	$0.139203\pi$
$18$	−2.71874	−	1.26824i	−0.640814	−	0.298927i
$19$	1.99067	+	1.14931i	0.456691	+	0.263671i	0.710652	−	0.703544i	$-0.248400\pi$
$19$	1.99067	+	1.14931i	0.456691	+	0.263671i	−0.253961	+	0.967214i	$0.581733\pi$
$20$	−0.595421	+	2.15534i	−0.133140	+	0.481948i
$21$	−1.23642	−	4.41263i	−0.269808	−	0.962914i
$22$	−0.275212	−	1.02711i	−0.0586754	−	0.218980i
$23$	8.59548	+	2.30315i	1.79228	+	0.480240i	0.992731	−	0.120357i	$-0.0384041\pi$
$23$	8.59548	+	2.30315i	1.79228	+	0.480240i	0.799551	+	0.600598i	$0.205071\pi$
$24$	−1.41874	−	0.993564i	−0.289600	−	0.202810i
$25$	4.29095	+	2.56667i	0.858189	+	0.513333i
$26$	−5.22693	−	3.01777i	−1.02509	−	0.591834i
$27$	−2.59712	−	4.50055i	−0.499816	−	0.866132i
$28$	−0.260796	−	2.63287i	−0.0492859	−	0.497565i
$29$	1.36331	+	2.36131i	0.253159	+	0.438485i	0.964394	−	0.264470i	$-0.0851970\pi$
$29$	1.36331	+	2.36131i	0.253159	+	0.438485i	−0.711235	+	0.702955i	$0.751864\pi$
$30$	−2.98621	+	2.46628i	−0.545206	+	0.450279i
$31$	7.68165			1.37967			0.689833	−	0.723969i	$-0.257684\pi$
$31$	7.68165			1.37967			0.689833	+	0.723969i	$0.257684\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	0.630040	−	1.73064i	0.109676	−	0.301266i
$34$	−1.24704	+	0.719980i	−0.213866	+	0.123476i
$35$	−5.83000	−	1.00556i	−0.985449	−	0.169971i
$36$	−1.02566	−	2.81922i	−0.170943	−	0.469871i
$37$	0.681326	+	2.54274i	0.112009	+	0.418025i	0.999046	−	0.0436748i	$-0.0139065\pi$
$37$	0.681326	+	2.54274i	0.112009	+	0.418025i	−0.887036	+	0.461699i	$0.847240\pi$
$38$	0.594929	+	2.22030i	0.0965102	+	0.360181i
$39$	−4.41732	−	9.47474i	−0.707338	−	1.51717i
$40$	−1.94508	+	1.10303i	−0.307544	+	0.174404i
$41$	−0.580119	−	0.334932i	−0.0905993	−	0.0523075i	0.454016	−	0.890994i	$-0.349991\pi$
$41$	−0.580119	−	0.334932i	−0.0905993	−	0.0523075i	−0.544615	+	0.838686i	$0.683324\pi$
$42$	2.24592	−	3.99448i	0.346553	−	0.616361i
$43$	−0.513911	+	1.91794i	−0.0783707	+	0.292483i	−0.993976	−	0.109594i	$-0.965045\pi$
$43$	−0.513911	+	1.91794i	−0.0783707	+	0.292483i	0.915606	+	0.402077i	$0.131712\pi$
$44$	0.531669	−	0.920878i	0.0801521	−	0.138828i
$45$	−6.68707	+	0.532017i	−0.996850	+	0.0793084i
$46$	4.44935	+	7.70650i	0.656021	+	1.13626i
$47$	−1.10538	−	1.10538i	−0.161236	−	0.161236i	0.621878	−	0.783114i	$-0.286370\pi$
$47$	−1.10538	−	1.10538i	−0.161236	−	0.161236i	−0.783114	+	0.621878i	$0.786370\pi$
$48$	−0.300646	−	1.70576i	−0.0433946	−	0.246205i
$49$	6.86397	−	1.37328i	0.980567	−	0.196183i
$50$	1.21925	+	4.84906i	0.172428	+	0.685761i
$51$	−2.48458	−	0.217550i	−0.347910	−	0.0304631i
$52$	−1.56211	−	5.82989i	−0.216626	−	0.808460i
$53$	−6.65595	−	1.78346i	−0.914264	−	0.244976i	−0.229132	−	0.973395i	$-0.573589\pi$
$53$	−6.65595	−	1.78346i	−0.914264	−	0.244976i	−0.685132	+	0.728419i	$0.740256\pi$
$54$	1.34593	−	5.01881i	0.183158	−	0.682974i
$55$	−1.66823	−	1.69424i	−0.224945	−	0.228451i
$56$	1.67731	−	2.04613i	0.224140	−	0.273425i
$57$	−1.36196	+	3.74114i	−0.180396	+	0.495526i
$58$	−0.705699	+	2.63370i	−0.0926628	+	0.345822i
$59$	8.10168			1.05475			0.527375	−	0.849633i	$-0.323176\pi$
$59$	8.10168			1.05475			0.527375	+	0.849633i	$0.323176\pi$
$60$	−3.85549	−	0.367651i	−0.497742	−	0.0474635i
$61$	1.52352			0.195067			0.0975335	−	0.995232i	$-0.468905\pi$
$61$	1.52352			0.195067			0.0975335	+	0.995232i	$0.468905\pi$
$62$	5.43175	+	5.43175i	0.689833	+	0.689833i
$63$	7.15515	−	3.43567i	0.901464	−	0.432854i
$64$		−	1.00000i		−	0.125000i
$65$	−13.4955	−	0.104360i	−1.67391	−	0.0129442i
$66$	1.66925	−	0.778241i	0.205471	−	0.0957949i
$67$	10.4539	−	10.4539i	1.27715	−	1.27715i	0.334898	−	0.942254i	$-0.391298\pi$
$67$	10.4539	−	10.4539i	1.27715	−	1.27715i	0.942254	−	0.334898i	$-0.108702\pi$
$68$	−1.39089	−	0.372689i	−0.168671	−	0.0451952i
$69$	−1.34442	+	15.3542i	−0.161849	+	1.84843i
$70$	−3.41139	−	4.83347i	−0.407739	−	0.577710i
$71$		−	1.27742i		−	0.151602i	−0.997123	−	0.0758011i	$-0.975849\pi$
$71$		−	1.27742i		−	0.151602i	0.997123	−	0.0758011i	$-0.0241514\pi$
$72$	1.26824	−	2.71874i	0.149464	−	0.320407i
$73$	−2.63231	+	9.82391i	−0.308089	+	1.14980i	0.622165	+	0.782886i	$0.286253\pi$
$73$	−2.63231	+	9.82391i	−0.308089	+	1.14980i	−0.930254	+	0.366916i	$0.880414\pi$
$74$	−1.31622	+	2.27976i	−0.153008	+	0.265017i
$75$	−3.08805	+	8.09098i	−0.356578	+	0.934266i
$76$	−1.14931	+	1.99067i	−0.131835	+	0.228345i
$77$	2.56321	+	1.15965i	0.292104	+	0.132155i
$78$	3.57613	−	9.82317i	0.404917	−	1.11225i
$79$		−	14.4771i		−	1.62880i	−0.580305	−	0.814399i	$-0.697067\pi$
$79$		−	14.4771i		−	1.62880i	0.580305	−	0.814399i	$-0.302933\pi$
$80$	−2.15534	−	0.595421i	−0.240974	−	0.0665701i
$81$	6.89604	−	5.78313i	0.766227	−	0.642570i
$82$	−0.173373	−	0.647038i	−0.0191459	−	0.0714534i
$83$	−9.19959	−	2.46502i	−1.00979	−	0.270571i	−0.284246	−	0.958751i	$-0.591743\pi$
$83$	−9.19959	−	2.46502i	−1.00979	−	0.270571i	−0.725540	+	0.688180i	$0.758410\pi$
$84$	4.41263	−	1.23642i	0.481457	−	0.134904i
$85$	−1.63144	+	2.77594i	−0.176954	+	0.301093i
$86$	−1.71958	+	0.992800i	−0.185427	+	0.107056i
$87$	−3.61796	+	3.03539i	−0.387886	+	0.325428i
$88$	1.02711	−	0.275212i	0.109490	−	0.0293377i
$89$	−3.87841	+	6.71760i	−0.411111	+	0.712064i	−0.995011	−	0.0997606i	$-0.968192\pi$
$89$	−3.87841	+	6.71760i	−0.411111	+	0.712064i	0.583901	+	0.811825i	$0.301526\pi$
$90$	−5.10467	−	4.35228i	−0.538079	−	0.458771i
$91$	14.9419	−	5.63325i	1.56634	−	0.590525i
$92$	−2.30315	+	8.59548i	−0.240120	+	0.896141i
$93$	2.30946	+	13.1030i	0.239480	+	1.35872i
$94$		−	1.56324i		−	0.161236i
$95$	3.60624	+	3.66244i	0.369992	+	0.375759i
$96$	0.993564	−	1.41874i	0.101405	−	0.144800i
$97$	0.457480	+	0.122581i	0.0464501	+	0.0124463i	0.281969	−	0.959423i	$-0.409012\pi$
$97$	0.457480	+	0.122581i	0.0464501	+	0.0124463i	−0.235519	+	0.971870i	$0.575679\pi$
$98$	5.82462	+	3.88250i	0.588375	+	0.392192i
$99$	3.14147	+	0.554386i	0.315730	+	0.0557179i
$100$	−2.56667	+	4.29095i	−0.256667	+	0.429095i
$101$	−5.18916	−	2.99597i	−0.516341	−	0.298110i	0.219095	−	0.975703i	$-0.429689\pi$
$101$	−5.18916	−	2.99597i	−0.516341	−	0.298110i	−0.735436	+	0.677594i	$0.763023\pi$
$102$	−1.60303	−	1.91069i	−0.158724	−	0.189187i
$103$	−4.67198	+	17.4361i	−0.460344	+	1.71803i	0.211538	+	0.977370i	$0.432153\pi$
$103$	−4.67198	+	17.4361i	−0.460344	+	1.71803i	−0.671882	+	0.740658i	$0.734514\pi$
$104$	3.01777	−	5.22693i	0.295917	−	0.512543i
$105$	−0.0375235	−	10.2469i	−0.00366192	−	0.999993i
$106$	−3.44537	−	5.96756i	−0.334644	−	0.579620i
$107$	−2.38247	+	0.638382i	−0.230323	+	0.0617147i	−0.372134	−	0.928179i	$-0.621374\pi$
$107$	−2.38247	+	0.638382i	−0.230323	+	0.0617147i	0.141812	+	0.989894i	$0.454707\pi$
$108$	4.50055	−	2.59712i	0.433066	−	0.249908i
$109$	14.2932	−	8.25216i	1.36904	−	0.790413i	0.378231	−	0.925711i	$-0.376532\pi$
$109$	14.2932	−	8.25216i	1.36904	−	0.790413i	0.990805	+	0.135298i	$0.0431991\pi$
$110$	0.0183860	−	2.37763i	0.00175304	−	0.226698i
$111$	−4.13247	+	1.92665i	−0.392237	+	0.182869i
$112$	2.63287	−	0.260796i	0.248782	−	0.0246429i
$113$	1.97602	+	7.37460i	0.185888	+	0.693744i	0.994439	+	0.105317i	$0.0335859\pi$
$113$	1.97602	+	7.37460i	0.185888	+	0.693744i	−0.808550	+	0.588427i	$0.799747\pi$
$114$	−3.60844	+	1.68233i	−0.337961	+	0.157565i
$115$	17.1548	+	10.0820i	1.59969	+	0.940151i
$116$	−2.36131	+	1.36331i	−0.219242	+	0.126580i
$117$	14.8336	−	10.3834i	1.37136	−	0.959949i
$118$	5.72876	+	5.72876i	0.527375	+	0.527375i
$119$	0.618500	−	3.75924i	0.0566978	−	0.344609i
$120$	−2.46628	−	2.98621i	−0.225139	−	0.272603i
$121$	−4.93466	−	8.54707i	−0.448605	−	0.777007i
$122$	1.07729	+	1.07729i	0.0975335	+	0.0975335i
$123$	0.396902	−	1.09024i	0.0357874	−	0.0983035i
$124$			7.68165i			0.689833i
$125$	7.72018	+	8.08695i	0.690514	+	0.723319i
$126$	7.48884	+	2.63007i	0.667159	+	0.234305i
$127$	11.9378	−	11.9378i	1.05931	−	1.05931i	0.0611858	−	0.998126i	$-0.480512\pi$
$127$	11.9378	−	11.9378i	1.05931	−	1.05931i	0.998126	−	0.0611858i	$-0.0194882\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	−3.42605	−	0.299986i	−0.301647	−	0.0264123i
$130$	−9.46895	−	9.61654i	−0.830482	−	0.843426i
$131$	5.12320	−	2.95788i	0.447616	−	0.258431i	−0.259207	−	0.965822i	$-0.583461\pi$
$131$	5.12320	−	2.95788i	0.447616	−	0.258431i	0.706823	+	0.707391i	$0.250128\pi$
$132$	1.73064	+	0.630040i	0.150633	+	0.0548380i
$133$	−5.54090	−	2.50683i	−0.480457	−	0.217370i
$134$	14.7841			1.27715
$135$	−2.91794	−	11.2466i	−0.251136	−	0.967952i
$136$	−0.719980	−	1.24704i	−0.0617378	−	0.106933i
$137$	−4.09853	+	1.09820i	−0.350161	+	0.0938254i	−0.429612	−	0.903013i	$-0.641350\pi$
$137$	−4.09853	+	1.09820i	−0.350161	+	0.0938254i	0.0794514	+	0.996839i	$0.474683\pi$
$138$	−11.8077	+	9.90645i	−1.00514	+	0.843293i
$139$	16.5661	+	9.56443i	1.40512	+	0.811244i	0.994912	−	0.100749i	$-0.0321239\pi$
$139$	16.5661	+	9.56443i	1.40512	+	0.811244i	0.410205	+	0.911993i	$0.365457\pi$
$140$	1.00556	−	5.83000i	0.0849854	−	0.492725i
$141$	1.55318	−	2.21783i	0.130801	−	0.186775i
$142$	0.903274	−	0.903274i	0.0758011	−	0.0758011i
$143$	6.19914	+	1.66106i	0.518398	+	0.138904i
$144$	2.81922	−	1.02566i	0.234935	−	0.0854717i
$145$	1.53240	+	5.90117i	0.127259	+	0.490065i
$146$	−8.80788	+	5.08523i	−0.728945	+	0.420857i
$147$	4.40612	+	11.2954i	0.363411	+	0.931629i
$148$	−2.54274	+	0.681326i	−0.209012	+	0.0560047i
$149$	−7.89278	−	13.6707i	−0.646602	−	1.11995i	−0.983929	−	0.178560i	$-0.942856\pi$
$149$	−7.89278	−	13.6707i	−0.646602	−	1.11995i	0.337327	−	0.941388i	$-0.390477\pi$
$150$	−7.90477	+	3.53760i	−0.645422	+	0.288844i
$151$	−9.15200	+	15.8517i	−0.744780	+	1.29000i	0.205518	+	0.978653i	$0.434112\pi$
$151$	−9.15200	+	15.8517i	−0.744780	+	1.29000i	−0.950298	+	0.311343i	$0.899221\pi$
$152$	−2.22030	+	0.594929i	−0.180090	+	0.0482551i
$153$	−0.375892	−	4.30350i	−0.0303891	−	0.347917i
$154$	0.992462	+	2.63246i	0.0799749	+	0.212129i
$155$	16.5565	+	4.57382i	1.32985	+	0.367378i
$156$	9.47474	−	4.41732i	0.758586	−	0.353669i
$157$	1.34314	−	1.34314i	0.107194	−	0.107194i	−0.651476	−	0.758670i	$-0.725850\pi$
$157$	1.34314	−	1.34314i	0.107194	−	0.107194i	0.758670	+	0.651476i	$0.225850\pi$
$158$	10.2368	−	10.2368i	0.814399	−	0.814399i
$159$	1.04106	−	11.8896i	0.0825612	−	0.942908i
$160$	−1.10303	−	1.94508i	−0.0872019	−	0.153772i
$161$	−23.2314	−	3.82222i	−1.83089	−	0.301233i
$162$	8.96553	+	0.786946i	0.704399	+	0.0618283i
$163$	6.82534	−	1.82884i	0.534602	−	0.143246i	0.0185894	−	0.999827i	$-0.494082\pi$
$163$	6.82534	−	1.82884i	0.534602	−	0.143246i	0.516013	+	0.856581i	$0.327416\pi$
$164$	0.334932	−	0.580119i	0.0261538	−	0.0452996i
$165$	2.38841	−	3.35497i	0.185937	−	0.261184i
$166$	−4.76206	−	8.24813i	−0.369607	−	0.640179i
$167$	−2.66520	+	0.714139i	−0.206240	+	0.0552617i	−0.360460	−	0.932775i	$-0.617380\pi$
$167$	−2.66520	+	0.714139i	−0.206240	+	0.0552617i	0.154220	+	0.988037i	$0.450713\pi$
$168$	3.99448	+	2.24592i	0.308181	+	0.173276i
$169$	20.2891	−	11.7139i	1.56070	−	0.901069i
$170$	−3.11649	+	0.809284i	−0.239024	+	0.0620692i
$171$	−6.79095	−	1.19842i	−0.519317	−	0.0916455i
$172$	−1.91794	−	0.513911i	−0.146242	−	0.0391853i
$173$	−8.05396	+	8.05396i	−0.612331	+	0.612331i	−0.943553	−	0.331222i	$-0.892539\pi$
$173$	−8.05396	+	8.05396i	−0.612331	+	0.612331i	0.331222	+	0.943553i	$0.392539\pi$
$174$	−4.70463	−	0.411938i	−0.356657	−	0.0312289i
$175$	−11.9669	−	5.63863i	−0.904610	−	0.426240i
$176$	0.920878	+	0.531669i	0.0694138	+	0.0400761i
$177$	2.43574	+	13.8195i	0.183082	+	1.03874i
$178$	−7.49251	+	2.00761i	−0.561587	+	0.150477i
$179$	−8.36582	−	14.4900i	−0.625291	−	1.08304i	−0.988485	−	0.151322i	$-0.951647\pi$
$179$	−8.36582	−	14.4900i	−0.625291	−	1.08304i	0.363194	−	0.931714i	$-0.381686\pi$
$180$	−0.532017	−	6.68707i	−0.0396542	−	0.498425i
$181$	−16.8133			−1.24972			−0.624860	−	0.780737i	$-0.714844\pi$
$181$	−16.8133			−1.24972			−0.624860	+	0.780737i	$0.714844\pi$
$182$	14.5488	+	6.58222i	1.07843	+	0.487907i
$183$	0.458042	+	2.59876i	0.0338594	+	0.192106i
$184$	−7.70650	+	4.44935i	−0.568131	+	0.328010i
$185$	−0.0455171	+	5.88615i	−0.00334648	+	0.432758i
$186$	−7.63221	+	10.8983i	−0.559621	+	0.799101i
$187$	1.08270	−	1.08270i	0.0791746	−	0.0791746i
$188$	1.10538	−	1.10538i	0.0806179	−	0.0806179i
$189$	8.01159	+	11.1720i	0.582758	+	0.812646i
$190$	−0.0397452	+	5.13973i	−0.00288342	+	0.372875i
$191$			22.7609i			1.64692i	0.567371	+	0.823462i	$0.307960\pi$
$191$			22.7609i			1.64692i	−0.567371	+	0.823462i	$0.692040\pi$
$192$	1.70576	−	0.300646i	0.123103	−	0.0216973i
$193$	1.08939	+	1.08939i	0.0784158	+	0.0784158i	0.745227	−	0.666811i	$-0.232341\pi$
$193$	1.08939	+	1.08939i	0.0784158	+	0.0784158i	−0.666811	+	0.745227i	$0.732341\pi$
$194$	0.236809	+	0.410165i	0.0170019	+	0.0294482i
$195$	−3.87936	−	23.0514i	−0.277807	−	1.65075i
$196$	1.37328	+	6.86397i	0.0980917	+	0.490284i
$197$	−3.78826	−	3.78826i	−0.269902	−	0.269902i	0.559158	−	0.829061i	$-0.311124\pi$
$197$	−3.78826	−	3.78826i	−0.269902	−	0.269902i	−0.829061	+	0.559158i	$0.811124\pi$
$198$	1.82935	+	2.61337i	0.130006	+	0.185724i
$199$	−17.7428	+	10.2438i	−1.25776	+	0.726165i	−0.972638	−	0.232327i	$-0.925366\pi$
$199$	−17.7428	+	10.2438i	−1.25776	+	0.726165i	−0.285118	+	0.958493i	$0.592033\pi$
$200$	−4.84906	+	1.21925i	−0.342881	+	0.0862140i
$201$	20.9748	+	14.6890i	1.47945	+	1.03608i
$202$	−1.55083	−	5.78776i	−0.109116	−	0.407225i
$203$	−4.20522	−	5.86148i	−0.295149	−	0.411395i
$204$	0.217550	−	2.48458i	0.0152315	−	0.173955i
$205$	−1.05092	−	1.06731i	−0.0733998	−	0.0745438i
$206$	−15.6328	+	9.02558i	−1.08919	+	0.628842i
$207$	−26.5948	+	2.32294i	−1.84847	+	0.161456i
$208$	5.82989	−	1.56211i	0.404230	−	0.108313i
$209$	−1.22211	−	2.11675i	−0.0845350	−	0.146419i
$210$	7.21911	−	7.27217i	0.498166	−	0.501828i
$211$	9.45709	−	16.3802i	0.651053	−	1.12766i	−0.331815	−	0.943345i	$-0.607661\pi$
$211$	9.45709	−	16.3802i	0.651053	−	1.12766i	0.982868	−	0.184312i	$-0.0590058\pi$
$212$	1.78346	−	6.65595i	0.122488	−	0.457132i
$213$	2.17897	−	0.384053i	0.149301	−	0.0263149i
$214$	−2.13607	−	1.23326i	−0.146019	−	0.0843039i
$215$	−2.24963	+	3.82782i	−0.153424	+	0.261055i
$216$	5.01881	+	1.34593i	0.341487	+	0.0915790i
$217$	−20.2248	+	2.00335i	−1.37295	+	0.135996i
$218$	15.9419	+	4.27163i	1.07972	+	0.289311i
$219$	−17.5486	−	1.53656i	−1.18583	−	0.103831i
$220$	1.69424	−	1.66823i	0.114225	−	0.112472i
$221$		−	8.69094i		−	0.584616i
$222$	−4.28444	−	1.55975i	−0.287553	−	0.104684i
$223$	1.91332	−	7.14063i	0.128126	−	0.478172i	−0.871806	−	0.489851i	$-0.837051\pi$
$223$	1.91332	−	7.14063i	0.128126	−	0.478172i	0.999932	+	0.0116795i	$0.00371778\pi$
$224$	2.04613	+	1.67731i	0.136713	+	0.112070i
$225$	−14.7297	−	2.83495i	−0.981978	−	0.188997i
$226$	−3.81738	+	6.61189i	−0.253928	+	0.439816i
$227$	23.1889	−	6.21344i	1.53910	−	0.412400i	0.613125	−	0.789986i	$-0.289912\pi$
$227$	23.1889	−	6.21344i	1.53910	−	0.412400i	0.925975	+	0.377586i	$0.123246\pi$
$228$	−3.74114	−	1.36196i	−0.247763	−	0.0901982i
$229$	3.03627	−	1.75299i	0.200642	−	0.115841i	−0.396313	−	0.918116i	$-0.629710\pi$
$229$	3.03627	−	1.75299i	0.200642	−	0.115841i	0.596955	+	0.802275i	$0.296377\pi$
$230$	5.00123	+	19.2593i	0.329771	+	1.26992i
$231$	−1.20747	+	4.72085i	−0.0794455	+	0.310609i
$232$	−2.63370	−	0.705699i	−0.172911	−	0.0463314i
$233$	−3.28038	−	12.2425i	−0.214905	−	0.802035i	−0.986200	−	0.165558i	$-0.947058\pi$
$233$	−3.28038	−	12.2425i	−0.214905	−	0.802035i	0.771295	−	0.636477i	$-0.219609\pi$
$234$	17.8311	+	3.14671i	1.16566	+	0.205707i
$235$	−1.72429	−	3.04062i	−0.112480	−	0.198348i
$236$			8.10168i			0.527375i
$237$	24.6944	−	4.35248i	1.60407	−	0.282724i
$238$	3.09553	−	2.22084i	0.200653	−	0.143955i
$239$	2.02058	−	3.49975i	0.130700	−	0.226380i	−0.793246	−	0.608901i	$-0.791611\pi$
$239$	2.02058	−	3.49975i	0.130700	−	0.226380i	0.923947	+	0.382521i	$0.124944\pi$
$240$	0.367651	−	3.85549i	0.0237318	−	0.248871i
$241$	7.91935	−	13.7167i	0.510130	−	0.883571i	−0.489801	−	0.871834i	$-0.662931\pi$
$241$	7.91935	−	13.7167i	0.510130	−	0.883571i	0.999931	−	0.0117367i	$-0.00373600\pi$
$242$	2.55437	−	9.53302i	0.164201	−	0.612806i
$243$	11.9379	+	10.0243i	0.765816	+	0.643059i
$244$			1.52352i			0.0975335i
$245$	15.6118	+	1.12707i	0.997404	+	0.0720056i
$246$	1.05157	−	0.490263i	0.0670454	−	0.0312580i
$247$	−13.4007	−	3.59072i	−0.852669	−	0.228472i
$248$	−5.43175	+	5.43175i	−0.344916	+	0.344916i
$249$	1.43891	−	16.4334i	0.0911872	−	1.04142i
$250$	−0.259342	+	11.1773i	−0.0164022	+	0.706917i
$251$		−	10.5488i		−	0.665836i	−0.942956	−	0.332918i	$-0.891967\pi$
$251$		−	10.5488i		−	0.665836i	0.942956	−	0.332918i	$-0.108033\pi$
$252$	3.43567	+	7.15515i	0.216427	+	0.450732i
$253$	−6.69087	−	6.69087i	−0.420652	−	0.420652i
$254$	16.8827			1.05931
$255$	−5.22557	−	1.94826i	−0.327238	−	0.122005i
$256$	1.00000			0.0625000
$257$	−1.13556	+	4.23798i	−0.0708346	+	0.264358i	−0.992257	−	0.124205i	$-0.960362\pi$
$257$	−1.13556	+	4.23798i	−0.0708346	+	0.264358i	0.921422	+	0.388563i	$0.127029\pi$
$258$	−2.21046	−	2.63471i	−0.137617	−	0.164030i
$259$	−2.45698	−	6.51702i	−0.152669	−	0.404948i
$260$	0.104360	−	13.4955i	0.00647210	−	0.836954i
$261$	−6.26537	−	5.25878i	−0.387817	−	0.325510i
$262$	5.71419	+	1.53111i	0.353024	+	0.0945924i
$263$	−0.727801	−	2.71619i	−0.0448781	−	0.167487i	0.939850	−	0.341588i	$-0.110965\pi$
$263$	−0.727801	−	2.71619i	−0.0448781	−	0.167487i	−0.984728	+	0.174101i	$0.944298\pi$
$264$	0.778241	+	1.66925i	0.0478974	+	0.102735i
$265$	−13.2839	−	7.80704i	−0.816023	−	0.479582i
$266$	−2.14541	−	5.69061i	−0.131544	−	0.348914i
$267$	−12.6246	−	4.59601i	−0.772615	−	0.281271i
$268$	10.4539	+	10.4539i	0.638576	+	0.638576i
$269$	−0.818317	−	1.41737i	−0.0498936	−	0.0864183i	0.840000	−	0.542586i	$-0.182555\pi$
$269$	−0.818317	−	1.41737i	−0.0498936	−	0.0864183i	−0.889894	+	0.456168i	$0.849222\pi$
$270$	5.88924	−	10.0158i	0.358408	−	0.609544i
$271$	−1.81683	+	3.14683i	−0.110364	+	0.191157i	−0.915917	−	0.401367i	$-0.868535\pi$
$271$	−1.81683	+	3.14683i	−0.110364	+	0.191157i	0.805553	+	0.592524i	$0.201868\pi$
$272$	0.372689	−	1.39089i	0.0225976	−	0.0843354i
$273$	14.1012	+	23.7937i	0.853443	+	1.44006i
$274$	−3.67464	−	2.12156i	−0.221993	−	0.128168i
$275$	−2.58682	−	4.64495i	−0.155991	−	0.280101i
$276$	−15.3542	−	1.34442i	−0.924217	−	0.0809246i
$277$	−0.297670	−	1.11092i	−0.0178852	−	0.0667486i	0.956406	−	0.292039i	$-0.0943336\pi$
$277$	−0.297670	−	1.11092i	−0.0178852	−	0.0667486i	−0.974292	+	0.225290i	$0.927667\pi$
$278$	4.95091	+	18.4771i	0.296936	+	1.10818i
$279$	−21.6563	+	7.87876i	−1.29653	+	0.471689i
$280$	4.83347	−	3.41139i	0.288855	−	0.203870i
$281$	−22.3933	+	12.9288i	−1.33587	+	0.771268i	−0.986193	−	0.165601i	$-0.947044\pi$
$281$	−22.3933	+	12.9288i	−1.33587	+	0.771268i	−0.349682	+	0.936868i	$0.613710\pi$
$282$	2.66651	−	0.469982i	0.158788	−	0.0279870i
$283$	5.25090	+	5.25090i	0.312134	+	0.312134i	0.845736	−	0.533602i	$-0.179162\pi$
$283$	5.25090	+	5.25090i	0.312134	+	0.312134i	−0.533602	+	0.845736i	$0.679162\pi$
$284$	1.27742			0.0758011
$285$	−5.16304	+	7.25247i	−0.305832	+	0.429599i
$286$	3.20891	+	5.55800i	0.189747	+	0.328651i
$287$	1.61472	+	0.730537i	0.0953141	+	0.0431223i
$288$	2.71874	+	1.26824i	0.160203	+	0.0747318i
$289$	12.9267	+	7.46326i	0.760397	+	0.439015i
$290$	−3.08918	+	5.25633i	−0.181403	+	0.308662i
$291$	−0.0715545	+	0.817204i	−0.00419460	+	0.0479054i
$292$	−9.82391	−	2.63231i	−0.574901	−	0.154044i
$293$	6.83404	+	25.5050i	0.399249	+	1.49002i	0.814421	+	0.580275i	$0.197055\pi$
$293$	6.83404	+	25.5050i	0.399249	+	1.49002i	−0.415172	+	0.909743i	$0.636278\pi$
$294$	−4.87146	+	11.1027i	−0.284109	+	0.647520i
$295$	17.4619	+	4.82392i	1.01667	+	0.280859i
$296$	−2.27976	−	1.31622i	−0.132509	−	0.0765038i
$297$	−0.00117586	+	5.52527i	−6.82301e−5	+	0.320608i
$298$	4.08561	−	15.2477i	0.236673	−	0.883275i
$299$	−53.7085			−3.10604
$300$	−8.09098	−	3.08805i	−0.467133	−	0.178289i
$301$	0.852867	−	5.18371i	0.0491584	−	0.298784i
$302$	−17.6803	+	4.73743i	−1.01739	+	0.272608i
$303$	3.55029	−	9.75219i	0.203959	−	0.560249i
$304$	−1.99067	−	1.14931i	−0.114173	−	0.0659177i
$305$	3.28370	+	0.907138i	0.188024	+	0.0519426i
$306$	2.77724	−	3.30883i	0.158764	−	0.189153i
$307$	4.70855	−	4.70855i	0.268731	−	0.268731i	−0.559858	−	0.828589i	$-0.689144\pi$
$307$	4.70855	−	4.70855i	0.268731	−	0.268731i	0.828589	+	0.559858i	$0.189144\pi$
$308$	−1.15965	+	2.56321i	−0.0660773	+	0.146052i
$309$	−31.1463	−	2.72718i	−1.77185	−	0.155144i
$310$	8.47306	+	14.9414i	0.481238	+	0.848615i
$311$		−	29.1318i		−	1.65191i	−0.563736	−	0.825955i	$-0.690636\pi$
$311$		−	29.1318i		−	1.65191i	0.563736	−	0.825955i	$-0.309364\pi$
$312$	9.82317	+	3.57613i	0.556127	+	0.202459i
$313$	7.10961	+	7.10961i	0.401859	+	0.401859i	0.878888	−	0.477029i	$-0.158286\pi$
$313$	7.10961	+	7.10961i	0.401859	+	0.401859i	−0.477029	+	0.878888i	$0.658286\pi$
$314$	1.89948			0.107194
$315$	17.4674	−	3.14469i	0.984178	−	0.177183i
$316$	14.4771			0.814399
$317$	13.7534	+	13.7534i	0.772468	+	0.772468i	0.978537	−	0.206070i	$-0.0660674\pi$
$317$	13.7534	+	13.7534i	0.772468	+	0.772468i	−0.206070	+	0.978537i	$0.566067\pi$
$318$	9.14337	−	7.67109i	0.512735	−	0.430174i
$319$		−	2.89931i		−	0.162330i
$320$	0.595421	−	2.15534i	0.0332851	−	0.120487i
$321$	−1.80521	−	3.87200i	−0.100757	−	0.216114i
$322$	−13.7244	−	19.1298i	−0.764829	−	1.06606i
$323$	−2.34048	+	2.34048i	−0.130228	+	0.130228i
$324$	5.78313	+	6.89604i	0.321285	+	0.383113i
$325$	−29.0252	−	8.26043i	−1.61003	−	0.458206i
$326$	6.11943	+	3.53306i	0.338924	+	0.195678i
$327$	18.3734	+	21.8997i	1.01605	+	1.21106i
$328$	0.647038	−	0.173373i	0.0357267	−	0.00957294i
$329$	3.19859	+	2.62203i	0.176344	+	0.144557i
$330$	4.06118	−	0.683463i	0.223561	−	0.0376234i
$331$	−18.8983			−1.03874			−0.519371	−	0.854549i	$-0.673834\pi$
$331$	−18.8983			−1.03874			−0.519371	+	0.854549i	$0.673834\pi$
$332$	2.46502	−	9.19959i	0.135286	−	0.504893i
$333$	−4.52880	−	6.46976i	−0.248177	−	0.354540i
$334$	−2.38955	−	1.37961i	−0.130751	−	0.0754889i
$335$	28.7563	−	16.3073i	1.57112	−	0.890961i
$336$	1.23642	+	4.41263i	0.0674521	+	0.240729i
$337$	6.36015	+	23.7364i	0.346459	+	1.29300i	0.890898	+	0.454203i	$0.150076\pi$
$337$	6.36015	+	23.7364i	0.346459	+	1.29300i	−0.544439	+	0.838801i	$0.683257\pi$
$338$	22.6295	+	6.06356i	1.23088	+	0.329814i
$339$	−11.9852	+	5.58776i	−0.650947	+	0.303485i
$340$	−2.77594	−	1.63144i	−0.150546	−	0.0884772i
$341$	−7.07386	−	4.08410i	−0.383071	−	0.221166i
$342$	−3.95451	−	5.64934i	−0.213836	−	0.305481i
$343$	−17.7138	+	5.40577i	−0.956454	+	0.291884i
$344$	−0.992800	−	1.71958i	−0.0535282	−	0.0927135i
$345$	−12.0399	+	32.2931i	−0.648208	+	1.73860i
$346$	−11.3900			−0.612331
$347$	−18.7550	−	18.7550i	−1.00682	−	1.00682i	−0.999977	−	0.00684687i	$-0.997821\pi$
$347$	−18.7550	−	18.7550i	−1.00682	−	1.00682i	−0.00684687	−	0.999977i	$-0.502179\pi$
$348$	−3.03539	−	3.61796i	−0.162714	−	0.193943i
$349$	−16.8403	+	9.72273i	−0.901439	+	0.520446i	−0.877667	−	0.479272i	$-0.840901\pi$
$349$	−16.8403	+	9.72273i	−0.901439	+	0.520446i	−0.0237719	+	0.999717i	$0.507568\pi$
$350$	−4.47474	−	12.4490i	−0.239185	−	0.665425i
$351$	22.1713	+	22.1807i	1.18342	+	1.18392i
$352$	0.275212	+	1.02711i	0.0146689	+	0.0547449i
$353$	0.660510	+	2.46506i	0.0351554	+	0.131202i	0.981273	−	0.192621i	$-0.0616986\pi$
$353$	0.660510	+	2.46506i	0.0351554	+	0.131202i	−0.946118	+	0.323822i	$0.895032\pi$
$354$	−8.04954	+	11.4942i	−0.427828	+	0.610910i
$355$	0.760605	−	2.75328i	0.0403687	−	0.146129i
$356$	−6.71760	−	3.87841i	−0.356032	−	0.205555i
$357$	6.59830	−	0.0751888i	0.349219	−	0.00397941i
$358$	4.33047	−	16.1615i	0.228872	−	0.854163i
$359$	−8.37289	+	14.5023i	−0.441904	+	0.765400i	−0.997831	−	0.0658311i	$-0.979030\pi$
$359$	−8.37289	+	14.5023i	−0.441904	+	0.765400i	0.555927	+	0.831231i	$0.312363\pi$
$360$	4.35228	−	5.10467i	0.229385	−	0.269040i
$361$	−6.85816	−	11.8787i	−0.360956	−	0.625193i
$362$	−11.8888	−	11.8888i	−0.624860	−	0.624860i
$363$	13.0957	−	10.9870i	0.687344	−	0.576667i
$364$	5.63325	+	14.9419i	0.295263	+	0.783169i
$365$	−11.5229	+	19.6065i	−0.603135	+	1.02625i
$366$	−1.51372	+	2.16149i	−0.0791233	+	0.112983i
$367$	−1.75180	−	6.53781i	−0.0914433	−	0.341271i	0.905013	−	0.425384i	$-0.139861\pi$
$367$	−1.75180	−	6.53781i	−0.0914433	−	0.341271i	−0.996456	+	0.0841131i	$0.973194\pi$
$368$	−8.59548	−	2.30315i	−0.448070	−	0.120060i
$369$	1.97901	+	0.349242i	0.103023	+	0.0181808i
$370$	−4.19432	+	4.12995i	−0.218052	+	0.214706i
$371$	17.9893	+	2.95975i	0.933960	+	0.153663i
$372$	−13.1030	+	2.30946i	−0.679361	+	0.119740i
$373$	3.83005	−	14.2939i	0.198312	−	0.740112i	−0.793072	−	0.609128i	$-0.791520\pi$
$373$	3.83005	−	14.2939i	0.198312	−	0.740112i	0.991384	−	0.130984i	$-0.0418136\pi$
$374$	1.53116			0.0791746
$375$	−11.4733	+	15.6001i	−0.592480	+	0.805585i
$376$	1.56324			0.0806179
$377$	−11.6366	−	11.6366i	−0.599313	−	0.599313i
$378$	−2.23477	+	13.5649i	−0.114944	+	0.697702i
$379$			18.3985i			0.945067i	0.881313	+	0.472534i	$0.156660\pi$
$379$			18.3985i			0.945067i	−0.881313	+	0.472534i	$0.843340\pi$
$380$	−3.66244	+	3.60624i	−0.187879	+	0.184996i
$381$	23.9521	+	16.7740i	1.22711	+	0.859358i
$382$	−16.0944	+	16.0944i	−0.823462	+	0.823462i
$383$	−16.0449	−	4.29921i	−0.819855	−	0.219679i	−0.175572	−	0.984467i	$-0.556177\pi$
$383$	−16.0449	−	4.29921i	−0.819855	−	0.219679i	−0.644283	+	0.764787i	$0.722844\pi$
$384$	1.41874	+	0.993564i	0.0723999	+	0.0507026i
$385$	4.83409	+	4.02563i	0.246368	+	0.205165i
$386$			1.54063i			0.0784158i
$387$	−0.518327	−	5.93420i	−0.0263481	−	0.301653i
$388$	−0.122581	+	0.457480i	−0.00622313	+	0.0232250i
$389$	10.2046	−	17.6749i	0.517393	−	0.896152i	−0.482403	−	0.875950i	$-0.660236\pi$
$389$	10.2046	−	17.6749i	0.517393	−	0.896152i	0.999796	−	0.0202019i	$-0.00643091\pi$
$390$	13.5567	−	19.0429i	0.686470	−	0.964276i
$391$	−6.40688	+	11.0970i	−0.324010	+	0.561202i
$392$	−3.88250	+	5.82462i	−0.196096	+	0.294188i
$393$	6.58570	+	7.84966i	0.332205	+	0.395963i
$394$		−	5.35741i		−	0.269902i
$395$	8.61996	−	31.2030i	0.433717	−	1.56999i
$396$	−0.554386	+	3.14147i	−0.0278589	+	0.157865i
$397$	−0.197620	−	0.737528i	−0.00991826	−	0.0370154i	0.960789	−	0.277279i	$-0.0894327\pi$
$397$	−0.197620	−	0.737528i	−0.00991826	−	0.0370154i	−0.970708	+	0.240264i	$0.922766\pi$
$398$	−19.7895	−	5.30259i	−0.991960	−	0.265795i
$399$	2.61019	−	10.2051i	0.130673	−	0.510895i
$400$	−4.29095	−	2.56667i	−0.214547	−	0.128333i
$401$	21.5472	−	12.4403i	1.07602	−	0.621238i	0.146197	−	0.989256i	$-0.453297\pi$
$401$	21.5472	−	12.4403i	1.07602	−	0.621238i	0.929819	+	0.368018i	$0.119963\pi$
$402$	4.44479	+	25.2181i	0.221686	+	1.25777i
$403$	−44.7832	+	11.9996i	−2.23081	+	0.597743i
$404$	2.99597	−	5.18916i	0.149055	−	0.258171i
$405$	18.3067	−	8.35854i	0.909667	−	0.415339i
$406$	1.17115	−	7.11823i	0.0581232	−	0.353272i
$407$	0.724480	−	2.70380i	0.0359112	−	0.134022i
$408$	1.91069	−	1.60303i	0.0945934	−	0.0793619i
$409$		−	16.0133i		−	0.791807i	−0.918292	−	0.395903i	$-0.870431\pi$
$409$		−	16.0133i		−	0.791807i	0.918292	−	0.395903i	$-0.129569\pi$
$410$	0.0115825	−	1.49781i	0.000572018	−	0.0739718i
$411$	−3.10547	−	6.66093i	−0.153181	−	0.328560i
$412$	−17.4361	−	4.67198i	−0.859014	−	0.230172i
$413$	−21.3307	+	2.11289i	−1.04961	+	0.103969i
$414$	−20.4480	−	17.1628i	−1.00496	−	0.843507i
$415$	−18.3605	−	10.7906i	−0.901281	−	0.529689i
$416$	5.22693	+	3.01777i	0.256272	+	0.147958i
$417$	−11.3341	+	31.1332i	−0.555032	+	1.52460i
$418$	0.632610	−	2.36093i	0.0309420	−	0.115477i
$419$	8.38194	−	14.5179i	0.409485	−	0.709248i	−0.585347	−	0.810783i	$-0.699042\pi$
$419$	8.38194	−	14.5179i	0.409485	−	0.709248i	0.994832	+	0.101534i	$0.0323752\pi$
$420$	10.2469	−	0.0375235i	0.499997	−	0.00183096i
$421$	5.23727	+	9.07122i	0.255249	+	0.442104i	0.964963	−	0.262386i	$-0.0845092\pi$
$421$	5.23727	+	9.07122i	0.255249	+	0.442104i	−0.709714	+	0.704490i	$0.751176\pi$
$422$	18.2697	−	4.89535i	0.889355	−	0.238302i
$423$	4.25004	+	1.98256i	0.206644	+	0.0963955i
$424$	5.96756	−	3.44537i	0.289810	−	0.167322i
$425$	−5.16915	+	5.01169i	−0.250741	+	0.243103i
$426$	1.81233	+	1.26920i	0.0878079	+	0.0614930i
$427$	−4.01123	+	0.397329i	−0.194117	+	0.0192281i
$428$	−0.638382	−	2.38247i	−0.0308574	−	0.115161i
$429$	−0.969609	+	11.0736i	−0.0468131	+	0.534640i
$430$	−4.29741	+	1.11594i	−0.207239	+	0.0538155i
$431$	9.93195	−	5.73421i	0.478405	−	0.276207i	−0.241346	−	0.970439i	$-0.577589\pi$
$431$	9.93195	−	5.73421i	0.478405	−	0.276207i	0.719752	+	0.694232i	$0.244256\pi$
$432$	2.59712	+	4.50055i	0.124954	+	0.216533i
$433$	−16.8219	−	16.8219i	−0.808411	−	0.808411i	0.175983	−	0.984393i	$-0.443690\pi$
$433$	−16.8219	−	16.8219i	−0.808411	−	0.808411i	−0.984393	+	0.175983i	$0.943690\pi$
$434$	−15.7176	−	12.8845i	−0.754471	−	0.618475i
$435$	−9.60525	+	4.38808i	−0.460537	+	0.210392i
$436$	8.25216	+	14.2932i	0.395207	+	0.684518i
$437$	14.4637	+	14.4637i	0.691894	+	0.691894i
$438$	−11.3222	−	13.4953i	−0.540997	−	0.644828i
$439$			36.1468i			1.72519i	0.505892	+	0.862597i	$0.331163\pi$
$439$			36.1468i			1.72519i	−0.505892	+	0.862597i	$0.668837\pi$
$440$	2.37763	+	0.0183860i	0.113349	+	0.000876518i
$441$	−17.9425	+	10.9117i	−0.854407	+	0.519605i
$442$	6.14542	−	6.14542i	0.292308	−	0.292308i
$443$	28.2687	−	28.2687i	1.34309	−	1.34309i	0.450116	−	0.892970i	$-0.351382\pi$
$443$	28.2687	−	28.2687i	1.34309	−	1.34309i	0.892970	−	0.450116i	$-0.148618\pi$
$444$	−1.92665	−	4.13247i	−0.0914346	−	0.196118i
$445$	−12.3591	+	12.1694i	−0.585876	+	0.576885i
$446$	6.40211	−	3.69626i	0.303149	−	0.175023i
$447$	20.9460	−	17.5732i	0.990711	−	0.831185i
$448$	0.260796	+	2.63287i	0.0123215	+	0.124391i
$449$	20.4371			0.964488			0.482244	−	0.876037i	$-0.339822\pi$
$449$	20.4371			0.964488			0.482244	+	0.876037i	$0.339822\pi$
$450$	−8.41083	−	12.4201i	−0.396491	−	0.585487i
$451$	0.356146	+	0.616862i	0.0167702	+	0.0290469i
$452$	−7.37460	+	1.97602i	−0.346872	+	0.0929441i
$453$	−29.7907	−	10.8453i	−1.39969	−	0.509558i
$454$	20.7906	+	12.0034i	0.975750	+	0.563350i
$455$	35.5590	−	3.24481i	1.66703	−	0.152119i
$456$	−1.68233	−	3.60844i	−0.0787824	−	0.168981i
$457$	12.4034	−	12.4034i	0.580206	−	0.580206i	−0.354754	−	0.934960i	$-0.615435\pi$
$457$	12.4034	−	12.4034i	0.580206	−	0.580206i	0.934960	+	0.354754i	$0.115435\pi$
$458$	3.38652	+	0.907415i	0.158242	+	0.0424007i
$459$	7.22771	−	1.93501i	0.337361	−	0.0903186i
$460$	−10.0820	+	17.1548i	−0.470076	+	0.799847i
$461$	−28.3736	+	16.3815i	−1.32149	+	0.762964i	−0.983967	−	0.178353i	$-0.942923\pi$
$461$	−28.3736	+	16.3815i	−1.32149	+	0.762964i	−0.337525	+	0.941316i	$0.609590\pi$
$462$	−4.19196	+	2.48434i	−0.195027	+	0.115582i
$463$	−25.2416	+	6.76347i	−1.17308	+	0.314325i	−0.792178	−	0.610291i	$-0.791053\pi$
$463$	−25.2416	+	6.76347i	−1.17308	+	0.314325i	−0.380900	+	0.924616i	$0.624386\pi$
$464$	−1.36331	−	2.36131i	−0.0632898	−	0.109621i
$465$	−2.82416	+	29.6166i	−0.130967	+	1.37343i
$466$	6.33720	−	10.9764i	0.293565	−	0.508470i
$467$	−11.8032	+	3.16265i	−0.546185	+	0.146350i	−0.521352	−	0.853342i	$-0.674572\pi$
$467$	−11.8032	+	3.16265i	−0.546185	+	0.146350i	−0.0248332	+	0.999692i	$0.507905\pi$
$468$	10.3834	+	14.8336i	0.479974	+	0.685681i
$469$	−24.7975	+	30.2502i	−1.14504	+	1.39682i
$470$	0.930785	−	3.36930i	0.0429339	−	0.155414i
$471$	2.69487	+	1.88726i	0.124173	+	0.0869601i
$472$	−5.72876	+	5.72876i	−0.263687	+	0.263687i
$473$	1.49296	−	1.49296i	0.0686464	−	0.0686464i
$474$	20.5393	+	14.3839i	0.943399	+	0.660675i
$475$	5.59195	+	10.0410i	0.256576	+	0.460714i
$476$	3.75924	+	0.618500i	0.172304	+	0.0283489i
$477$	20.5938	−	1.79878i	0.942926	−	0.0823605i
$478$	3.90346	−	1.04593i	0.178540	−	0.0478397i
$479$	12.4545	−	21.5718i	0.569059	−	0.985640i	−0.427600	−	0.903968i	$-0.640641\pi$
$479$	12.4545	−	21.5718i	0.569059	−	0.985640i	0.996659	−	0.0816716i	$-0.0260259\pi$
$480$	2.98621	−	2.46628i	0.136301	−	0.112570i
$481$	−7.94411	−	13.7596i	−0.362220	−	0.627384i
$482$	15.2990	−	4.09935i	0.696850	−	0.186720i
$483$	−0.464654	−	40.7763i	−0.0211425	−	1.85539i
$484$	8.54707	−	4.93466i	0.388503	−	0.224303i
$485$	0.913036	+	0.536598i	0.0414588	+	0.0243656i
$486$	1.35312	+	15.5296i	0.0613786	+	0.704438i
$487$	13.7978	+	3.69711i	0.625238	+	0.167532i	0.557508	−	0.830172i	$-0.311758\pi$
$487$	13.7978	+	3.69711i	0.625238	+	0.167532i	0.0677299	+	0.997704i	$0.478424\pi$
$488$	−1.07729	+	1.07729i	−0.0487668	+	0.0487668i
$489$	5.17158	+	11.0925i	0.233867	+	0.501622i
$490$	10.2423	+	11.8362i	0.462699	+	0.534705i
$491$	−17.5334	−	10.1229i	−0.791271	−	0.456841i	0.0491386	−	0.998792i	$-0.484352\pi$
$491$	−17.5334	−	10.1229i	−0.791271	−	0.456841i	−0.840410	+	0.541951i	$0.817686\pi$
$492$	1.09024	+	0.396902i	0.0491517	+	0.0178937i
$493$	−3.79243	+	1.01618i	−0.170802	+	0.0457664i
$494$	−6.93673	−	12.0148i	−0.312098	−	0.540570i
$495$	6.44084	+	3.06539i	0.289494	+	0.137779i
$496$	−7.68165			−0.344916
$497$	0.333147	+	3.36328i	0.0149437	+	0.150864i
$498$	12.6376	−	10.6027i	0.566305	−	0.475118i
$499$	18.6377	−	10.7605i	0.834338	−	0.481706i	−0.0209973	−	0.999780i	$-0.506684\pi$
$499$	18.6377	−	10.7605i	0.834338	−	0.481706i	0.855336	+	0.518074i	$0.173351\pi$
$500$	−8.08695	+	7.72018i	−0.361659	+	0.345257i
$501$	−2.01943	−	4.33149i	−0.0902215	−	0.193517i
$502$	7.45915	−	7.45915i	0.332918	−	0.332918i
$503$	17.0865	−	17.0865i	0.761849	−	0.761849i	−0.214807	−	0.976657i	$-0.568912\pi$
$503$	17.0865	−	17.0865i	0.761849	−	0.761849i	0.976657	+	0.214807i	$0.0689123\pi$
$504$	−2.63007	+	7.48884i	−0.117153	+	0.333579i
$505$	−9.40053	−	9.54705i	−0.418318	−	0.424838i
$506$		−	9.46232i		−	0.420652i
$507$	26.0809	+	31.0865i	1.15829	+	1.38060i
$508$	11.9378	+	11.9378i	0.529656	+	0.529656i
$509$	−3.48073	−	6.02880i	−0.154281	−	0.267222i	0.778516	−	0.627624i	$-0.215973\pi$
$509$	−3.48073	−	6.02880i	−0.154281	−	0.267222i	−0.932797	+	0.360403i	$0.882639\pi$
$510$	−2.31740	−	5.07266i	−0.102616	−	0.224621i
$511$	4.36848	−	26.5516i	0.193250	−	1.17457i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	0.00254186	−	11.9440i	0.000112226	−	0.527341i
$514$	−3.79967	+	2.19374i	−0.167596	+	0.0967618i
$515$	−20.4515	+	34.7988i	−0.901201	+	1.53342i
$516$	0.299986	−	3.42605i	0.0132061	−	0.150823i
$517$	0.430222	+	1.60561i	0.0189212	+	0.0706147i
$518$	2.87088	−	6.34558i	0.126139	−	0.278809i
$519$	−16.1595	−	11.3167i	−0.709324	−	0.496749i
$520$	9.61654	−	9.46895i	0.421713	−	0.415241i
$521$	32.7545	−	18.9108i	1.43500	−	0.828498i	0.437504	−	0.899216i	$-0.355863\pi$
$521$	32.7545	−	18.9108i	1.43500	−	0.828498i	0.997496	+	0.0707184i	$0.0225292\pi$
$522$	−0.711763	−	8.14880i	−0.0311530	−	0.356663i
$523$	22.2623	−	5.96516i	0.973461	−	0.260838i	0.263173	−	0.964749i	$-0.415231\pi$
$523$	22.2623	−	5.96516i	0.973461	−	0.260838i	0.710289	+	0.703911i	$0.248564\pi$
$524$	2.95788	+	5.12320i	0.129216	+	0.223808i
$525$	6.02034	−	22.1078i	0.262749	−	0.964864i
$526$	1.40600	−	2.43527i	0.0613046	−	0.106183i
$527$	−2.86287	+	10.6844i	−0.124708	+	0.465418i
$528$	−0.630040	+	1.73064i	−0.0274190	+	0.0753164i
$529$	48.6592	+	28.0934i	2.11562	+	1.22145i
$530$	−3.87272	−	14.9135i	−0.168220	−	0.647803i
$531$	−22.8405	+	8.30958i	−0.991191	+	0.360605i
$532$	2.50683	−	5.54090i	0.108685	−	0.240229i
$533$	3.90523	+	1.04640i	0.169154	+	0.0453247i
$534$	−5.67710	−	12.1768i	−0.245672	−	0.526943i
$535$	−5.51514	−	0.0426482i	−0.238440	−	0.00184384i
$536$			14.7841i			0.638576i
$537$	22.2013	−	18.6264i	0.958058	−	0.803790i
$538$	0.423592	−	1.58087i	0.0182623	−	0.0681560i
$539$	−7.05101	−	2.38473i	−0.303709	−	0.102718i
$540$	11.2466	−	2.91794i	0.483976	−	0.125568i
$541$	6.86834	−	11.8963i	0.295293	−	0.511462i	−0.679760	−	0.733435i	$-0.737916\pi$
$541$	6.86834	−	11.8963i	0.295293	−	0.511462i	0.975053	+	0.221972i	$0.0712494\pi$
$542$	−3.50984	+	0.940458i	−0.150760	+	0.0403961i
$543$	−5.05485	−	28.6794i	−0.216924	−	1.23075i
$544$	1.24704	−	0.719980i	0.0534665	−	0.0308689i
$545$	35.7201	−	9.27572i	1.53008	−	0.397328i
$546$	−6.85363	+	26.7957i	−0.293308	+	1.14675i
$547$	−1.20895	−	0.323937i	−0.0516910	−	0.0138506i	0.232881	−	0.972505i	$-0.425185\pi$
$547$	−1.20895	−	0.323937i	−0.0516910	−	0.0138506i	−0.284572	+	0.958655i	$0.591851\pi$
$548$	−1.09820	−	4.09853i	−0.0469127	−	0.175081i
$549$	−4.29515	+	1.56262i	−0.183313	+	0.0666909i
$550$	1.45532	−	5.11363i	0.0620549	−	0.218046i
$551$			6.26746i			0.267003i
$552$	−9.90645	−	11.8077i	−0.421646	−	0.502571i
$553$	3.77557	+	38.1162i	0.160554	+	1.62087i
$554$	0.575054	−	0.996022i	0.0244317	−	0.0423169i
$555$	−10.0540	+	1.69201i	−0.426770	+	0.0718217i
$556$	−9.56443	+	16.5661i	−0.405622	+	0.702558i
$557$	−3.45682	+	12.9010i	−0.146470	+	0.546634i	0.853216	+	0.521558i	$0.174649\pi$
$557$	−3.45682	+	12.9010i	−0.146470	+	0.546634i	−0.999686	+	0.0250751i	$0.992017\pi$
$558$	−20.8844	−	9.74218i	−0.884109	−	0.412419i
$559$		−	11.9842i		−	0.506877i
$560$	5.83000	+	1.00556i	0.246362	+	0.0424927i
$561$	2.17233	+	1.52131i	0.0917158	+	0.0642298i
$562$	−24.9765	−	6.69244i	−1.05357	−	0.282304i
$563$	−1.13158	+	1.13158i	−0.0476903	+	0.0476903i	−0.730550	−	0.682859i	$-0.760736\pi$
$563$	−1.13158	+	1.13158i	−0.0476903	+	0.0476903i	0.682859	+	0.730550i	$0.260736\pi$
$564$	2.21783	+	1.55318i	0.0933876	+	0.0654006i
$565$	−0.132011	+	17.0713i	−0.00555375	+	0.718196i
$566$			7.42590i			0.312134i
$567$	−16.6481	+	17.0247i	−0.699156	+	0.714969i
$568$	0.903274	+	0.903274i	0.0379005	+	0.0379005i
$569$	14.3253			0.600546			0.300273	−	0.953853i	$-0.402922\pi$
$569$	14.3253			0.600546			0.300273	+	0.953853i	$0.402922\pi$
$570$	−8.77909	+	1.47745i	−0.367716	+	0.0618834i
$571$	42.3929			1.77409			0.887044	−	0.461686i	$-0.152755\pi$
$571$	42.3929			1.77409			0.887044	+	0.461686i	$0.152755\pi$
$572$	−1.66106	+	6.19914i	−0.0694522	+	0.259199i
$573$	−38.8247	+	6.84300i	−1.62192	+	0.285870i
$574$	0.625214	+	1.65835i	0.0260959	+	0.0692182i
$575$	30.9713	+	31.9444i	1.29159	+	1.33218i
$576$	1.02566	+	2.81922i	0.0427359	+	0.117468i
$577$	−3.75747	−	1.00681i	−0.156425	−	0.0419141i	0.179756	−	0.983711i	$-0.442469\pi$
$577$	−3.75747	−	1.00681i	−0.156425	−	0.0419141i	−0.336182	+	0.941797i	$0.609136\pi$
$578$	3.86327	+	14.4179i	0.160691	+	0.599706i
$579$	−1.53071	+	2.18575i	−0.0636141	+	0.0908367i
$580$	−5.90117	+	1.53240i	−0.245033	+	0.0636296i
$581$	24.8642	+	4.09086i	1.03154	+	0.169717i
$582$	−0.628447	+	0.527254i	−0.0260500	+	0.0218554i
$583$	5.18110	+	5.18110i	0.214579	+	0.214579i
$584$	−5.08523	−	8.80788i	−0.210428	−	0.364473i
$585$	38.1538	−	13.5476i	1.57747	−	0.560123i
$586$	−13.2024	+	22.8672i	−0.545384	+	0.944633i
$587$	−9.57665	+	35.7406i	−0.395271	+	1.47517i	0.426048	+	0.904701i	$0.359906\pi$
$587$	−9.57665	+	35.7406i	−0.395271	+	1.47517i	−0.821318	+	0.570470i	$0.806761\pi$
$588$	−11.2954	+	4.40612i	−0.465815	+	0.181705i
$589$	15.2916	+	8.82863i	0.630081	+	0.363777i
$590$	8.93637	+	15.7584i	0.367905	+	0.648764i
$591$	5.32293	−	7.60078i	0.218956	−	0.312654i
$592$	−0.681326	−	2.54274i	−0.0280023	−	0.104506i
$593$	−6.27760	−	23.4283i	−0.257790	−	0.962086i	−0.966517	−	0.256603i	$-0.917397\pi$
$593$	−6.27760	−	23.4283i	−0.257790	−	0.962086i	0.708727	−	0.705483i	$-0.249270\pi$
$594$	−3.90779	+	3.90612i	−0.160338	+	0.160270i
$595$	3.57141	−	7.73415i	0.146413	−	0.317069i
$596$	13.6707	−	7.89278i	0.559974	−	0.323301i
$597$	−22.8078	−	27.1852i	−0.933461	−	1.11262i
$598$	−37.9776	−	37.9776i	−1.55302	−	1.55302i
$599$	−43.8960			−1.79354			−0.896770	−	0.442497i	$-0.854093\pi$
$599$	−43.8960			−1.79354			−0.896770	+	0.442497i	$0.854093\pi$
$600$	−3.53760	−	7.90477i	−0.144422	−	0.322711i
$601$	8.92883	+	15.4652i	0.364215	+	0.630838i	0.988650	−	0.150238i	$-0.0480041\pi$
$601$	8.92883	+	15.4652i	0.364215	+	0.630838i	−0.624435	+	0.781077i	$0.714671\pi$
$602$	4.26850	−	3.06237i	0.173971	−	0.124813i
$603$	−18.7498	+	40.1942i	−0.763551	+	1.63683i
$604$	−15.8517	−	9.15200i	−0.644998	−	0.372390i
$605$	−5.54673	−	21.3600i	−0.225507	−	0.868408i
$606$	9.40627	−	4.38540i	0.382104	−	0.178145i
$607$	−13.1484	−	3.52310i	−0.533677	−	0.142998i	−0.0180912	−	0.999836i	$-0.505759\pi$
$607$	−13.1484	−	3.52310i	−0.533677	−	0.142998i	−0.515586	+	0.856838i	$0.672426\pi$
$608$	−0.594929	−	2.22030i	−0.0241275	−	0.0900452i
$609$	8.73398	−	8.93533i	0.353919	−	0.362078i
$610$	1.68049	+	2.96337i	0.0680409	+	0.119983i
$611$	8.17094	+	4.71750i	0.330561	+	0.190849i
$612$	4.30350	−	0.375892i	0.173958	−	0.0151945i
$613$	5.13857	−	19.1774i	0.207545	−	0.774568i	−0.781114	−	0.624389i	$-0.785348\pi$
$613$	5.13857	−	19.1774i	0.207545	−	0.774568i	0.988659	−	0.150180i	$-0.0479852\pi$
$614$	6.65889			0.268731
$615$	1.50461	−	2.11351i	0.0606716	−	0.0852248i
$616$	−2.63246	+	0.992462i	−0.106065	+	0.0399874i
$617$	−25.5343	+	6.84189i	−1.02797	+	0.275444i	−0.733120	−	0.680099i	$-0.761937\pi$
$617$	−25.5343	+	6.84189i	−1.02797	+	0.275444i	−0.294851	+	0.955543i	$0.595270\pi$
$618$	−20.0954	−	23.9522i	−0.808355	−	0.963499i
$619$	−4.51970	−	2.60945i	−0.181662	−	0.104883i	0.406411	−	0.913690i	$-0.366780\pi$
$619$	−4.51970	−	2.60945i	−0.181662	−	0.104883i	−0.588073	+	0.808808i	$0.700113\pi$
$620$	−4.57382	+	16.5565i	−0.183689	+	0.664927i
$621$	−11.9580	−	44.6660i	−0.479859	−	1.79238i
$622$	20.5993	−	20.5993i	0.825955	−	0.825955i
$623$	8.45941	−	18.6980i	0.338919	−	0.749120i
$624$	4.41732	+	9.47474i	0.176834	+	0.379293i
$625$	11.8245	+	22.0269i	0.472978	+	0.881074i
$626$			10.0545i			0.401859i
$627$	3.24325	−	2.72102i	0.129523	−	0.108667i
$628$	1.34314	+	1.34314i	0.0535969	+	0.0535969i
$629$	−3.79061			−0.151142
$630$	14.5750	+	10.1277i	0.580681	+	0.403497i
$631$	−0.742517			−0.0295591			−0.0147796	−	0.999891i	$-0.504705\pi$
$631$	−0.742517			−0.0295591			−0.0147796	+	0.999891i	$0.504705\pi$
$632$	10.2368	+	10.2368i	0.407200	+	0.407200i
$633$	30.7838	+	11.2069i	1.22355	+	0.445433i
$634$			19.4502i			0.772468i
$635$	32.8381	−	18.6220i	1.30314	−	0.738992i
$636$	11.8896	+	1.04106i	0.471454	+	0.0412806i
$637$	−37.8710	+	18.7284i	−1.50050	+	0.742046i
$638$	2.05012	−	2.05012i	0.0811651	−	0.0811651i
$639$	1.31020	+	3.60134i	0.0518308	+	0.142467i
$640$	1.94508	−	1.10303i	0.0768860	−	0.0436009i
$641$	33.9048	+	19.5749i	1.33916	+	0.773163i	0.986683	−	0.162658i	$-0.0520067\pi$
$641$	33.9048	+	19.5749i	1.33916	+	0.773163i	0.352475	+	0.935821i	$0.385340\pi$
$642$	1.46144	−	4.01439i	0.0576785	−	0.158435i
$643$	17.0799	−	4.57654i	0.673564	−	0.180481i	0.0942044	−	0.995553i	$-0.469969\pi$
$643$	17.0799	−	4.57654i	0.673564	−	0.180481i	0.579360	+	0.815072i	$0.303303\pi$
$644$	3.82222	−	23.2314i	0.150617	−	0.915446i
$645$	−7.20567	−	2.68651i	−0.283723	−	0.105781i
$646$	−3.30993			−0.130228
$647$	0.191784	−	0.715746i	0.00753979	−	0.0281389i	−0.962053	−	0.272861i	$-0.912030\pi$
$647$	0.191784	−	0.715746i	0.00753979	−	0.0281389i	0.969593	+	0.244722i	$0.0786967\pi$
$648$	−0.786946	+	8.96553i	−0.0309141	+	0.352199i
$649$	−7.46066	−	4.30741i	−0.292857	−	0.169081i
$650$	−14.6829	−	26.3649i	−0.575910	−	1.03412i
$651$	−9.49773	−	33.8963i	−0.372245	−	1.32850i
$652$	1.82884	+	6.82534i	0.0716231	+	0.267301i
$653$	−35.2884	−	9.45549i	−1.38094	−	0.370022i	−0.509478	−	0.860484i	$-0.670161\pi$
$653$	−35.2884	−	9.45549i	−1.38094	−	0.370022i	−0.871463	+	0.490462i	$0.836828\pi$
$654$	−2.49348	+	28.4774i	−0.0975028	+	1.11355i
$655$	12.8034	−	3.32476i	0.500270	−	0.129909i
$656$	0.580119	+	0.334932i	0.0226498	+	0.0130769i
$657$	−2.65493	−	30.3957i	−0.103579	−	1.18585i
$658$	0.407687	+	4.11580i	0.0158933	+	0.160450i
$659$	−14.1819	−	24.5638i	−0.552449	−	0.956870i	−0.998097	−	0.0616618i	$-0.980360\pi$
$659$	−14.1819	−	24.5638i	−0.552449	−	0.956870i	0.445648	−	0.895208i	$-0.352973\pi$
$660$	3.35497	+	2.38841i	0.130592	+	0.0929687i
$661$	26.7920			1.04209			0.521044	−	0.853530i	$-0.325543\pi$
$661$	26.7920			1.04209			0.521044	+	0.853530i	$0.325543\pi$
$662$	−13.3631	−	13.3631i	−0.519371	−	0.519371i
$663$	14.8246	−	2.61290i	0.575742	−	0.101477i
$664$	8.24813	−	4.76206i	0.320089	−	0.184804i
$665$	−10.4499	−	8.70223i	−0.405229	−	0.337458i
$666$	1.37246	−	7.77716i	0.0531818	−	0.301359i
$667$	6.27980	+	23.4365i	0.243155	+	0.907466i
$668$	−0.714139	−	2.66520i	−0.0276309	−	0.103120i
$669$	12.7554	+	1.11687i	0.493153	+	0.0431805i
$670$	31.8647	+	8.80278i	1.23104	+	0.340081i
$671$	−1.40298	−	0.810010i	−0.0541614	−	0.0312701i
$672$	−2.24592	+	3.99448i	−0.0866382	+	0.154090i
$673$	3.59852	−	13.4299i	0.138713	−	0.517683i	−0.861242	−	0.508195i	$-0.830313\pi$
$673$	3.59852	−	13.4299i	0.138713	−	0.517683i	0.999955	−	0.00948855i	$-0.00302035\pi$
$674$	−12.2869	+	21.2815i	−0.473272	+	0.819732i
$675$	0.407319	−	25.9776i	0.0156777	−	0.999877i
$676$	11.7139	+	20.2891i	0.450534	+	0.780349i
$677$	−18.3270	−	18.3270i	−0.704362	−	0.704362i	0.260982	−	0.965344i	$-0.415954\pi$
$677$	−18.3270	−	18.3270i	−0.704362	−	0.704362i	−0.965344	+	0.260982i	$0.915954\pi$
$678$	−12.4260	−	4.52368i	−0.477216	−	0.173731i
$679$	−1.23645	−	0.203431i	−0.0474507	−	0.00780698i
$680$	−0.809284	−	3.11649i	−0.0310346	−	0.119512i
$681$	17.5703	+	37.6866i	0.673295	+	1.44415i
$682$	−2.11408	−	7.88987i	−0.0809524	−	0.302119i
$683$	33.6390	+	9.01354i	1.28716	+	0.344894i	0.836581	−	0.547843i	$-0.184551\pi$
$683$	33.6390	+	9.01354i	1.28716	+	0.344894i	0.450579	+	0.892737i	$0.351218\pi$
$684$	1.19842	−	6.79095i	0.0458228	−	0.259658i
$685$	−9.48760	−	0.0733669i	−0.362503	−	0.00280320i
$686$	−16.3480	−	8.70307i	−0.624169	−	0.332285i
$687$	3.90303	+	4.65211i	0.148910	+	0.177489i
$688$	0.513911	−	1.91794i	0.0195927	−	0.0731209i
$689$	41.5894			1.58443
$690$	−31.3482	+	14.3211i	−1.19340	+	0.545196i
$691$	0.411218			0.0156435			0.00782173	−	0.999969i	$-0.497510\pi$
$691$	0.411218			0.0156435			0.00782173	+	0.999969i	$0.497510\pi$
$692$	−8.05396	−	8.05396i	−0.306166	−	0.306166i
$693$	−8.41566	−	0.640339i	−0.319684	−	0.0243245i
$694$		−	26.5236i		−	1.00682i
$695$	30.0106	+	30.4784i	1.13837	+	1.15611i
$696$	0.411938	−	4.70463i	0.0156145	−	0.178328i
$697$	0.682058	−	0.682058i	0.0258348	−	0.0258348i
$698$	−18.7829	−	5.03286i	−0.710942	−	0.190496i
$699$	19.8966	−	9.27621i	0.752558	−	0.350858i
$700$	5.63863	−	11.9669i	0.213120	−	0.452305i
$701$			3.08417i			0.116488i	0.998302	+	0.0582438i	$0.0185501\pi$
$701$			3.08417i			0.116488i	−0.998302	+	0.0582438i	$0.981450\pi$
$702$	−0.00667420	+	31.3616i	−0.000251902	+	1.18367i
$703$	−1.56612	+	5.84482i	−0.0590672	+	0.220442i
$704$	−0.531669	+	0.920878i	−0.0200380	+	0.0347069i
$705$	4.66816	−	3.85538i	0.175813	−	0.145202i
$706$	−1.27601	+	2.21011i	−0.0480232	+	0.0831786i
$707$	14.4437	+	6.53466i	0.543212	+	0.245761i
$708$	−13.8195	+	2.43574i	−0.519369	+	0.0915408i
$709$		−	23.1737i		−	0.870307i	−0.900356	−	0.435153i	$-0.856694\pi$
$709$		−	23.1737i		−	0.870307i	0.900356	−	0.435153i	$-0.143306\pi$
$710$	2.48469	−	1.40903i	0.0932487	−	0.0528800i
$711$	14.8486	+	40.8141i	0.556865	+	1.53065i
$712$	−2.00761	−	7.49251i	−0.0752385	−	0.280794i
$713$	66.0275	+	17.6920i	2.47275	+	0.662571i
$714$	4.71887	+	4.61253i	0.176599	+	0.172620i
$715$	12.3722	+	7.27123i	0.462694	+	0.271929i
$716$	14.4900	−	8.36582i	0.541518	−	0.312645i
$717$	6.57720	+	2.39443i	0.245630	+	0.0894218i
$718$	−16.1752	+	4.33412i	−0.603652	+	0.161748i
$719$	−7.72927	+	13.3875i	−0.288253	+	0.499269i	−0.973393	−	0.229143i	$-0.926408\pi$
$719$	−7.72927	+	13.3875i	−0.288253	+	0.499269i	0.685140	+	0.728412i	$0.259741\pi$
$720$	6.68707	−	0.532017i	0.249213	−	0.0198271i
$721$	7.75344	−	47.1253i	0.288753	−	1.75504i
$722$	3.55004	−	13.2489i	0.132119	−	0.493075i
$723$	25.7783	+	9.38461i	0.958706	+	0.349017i
$724$		−	16.8133i		−	0.624860i
$725$	−0.210834	+	13.6314i	−0.00783018	+	0.506258i
$726$	17.0290	+	1.49106i	0.632005	+	0.0553385i
$727$	−30.9185	−	8.28458i	−1.14670	−	0.307258i	−0.365060	−	0.930984i	$-0.618952\pi$
$727$	−30.9185	−	8.28458i	−1.14670	−	0.307258i	−0.781643	+	0.623726i	$0.785618\pi$
$728$	−6.58222	+	14.5488i	−0.243953	+	0.539216i
$729$	−13.5100	+	23.3769i	−0.500369	+	0.865813i
$730$	−22.0118	+	5.71598i	−0.814693	+	0.211558i
$731$	−2.47613	−	1.42959i	−0.0915828	−	0.0528754i
$732$	−2.59876	+	0.458042i	−0.0960530	+	0.0169297i
$733$	8.92857	−	33.3219i	0.329784	−	1.23077i	−0.579630	−	0.814880i	$-0.696803\pi$
$733$	8.92857	−	33.3219i	0.329784	−	1.23077i	0.909414	−	0.415892i	$-0.136531\pi$
$734$	3.38422	−	5.86164i	0.124914	−	0.216357i
$735$	2.77114	+	26.9689i	0.102215	+	0.994762i
$736$	−4.44935	−	7.70650i	−0.164005	−	0.284065i
$737$	−15.1848	+	4.06877i	−0.559341	+	0.149875i
$738$	1.15242	+	1.64632i	0.0424212	+	0.0606020i
$739$	−12.8962	+	7.44565i	−0.474396	+	0.273893i	−0.718078	−	0.695962i	$-0.754978\pi$
$739$	−12.8962	+	7.44565i	−0.474396	+	0.273893i	0.243682	+	0.969855i	$0.421645\pi$
$740$	−5.88615	−	0.0455171i	−0.216379	−	0.00167324i
$741$	2.09601	−	23.9380i	0.0769989	−	0.879383i
$742$	10.6275	+	14.8132i	0.390148	+	0.543811i
$743$	−5.54455	−	20.6925i	−0.203410	−	0.759135i	−0.989928	−	0.141569i	$-0.954785\pi$
$743$	−5.54455	−	20.6925i	−0.203410	−	0.759135i	0.786519	−	0.617566i	$-0.211881\pi$
$744$	−10.8983	−	7.63221i	−0.399550	−	0.279810i
$745$	−8.87177	−	34.1645i	−0.325037	−	1.25169i
$746$	12.8156	−	7.39908i	0.469212	−	0.270900i
$747$	28.4640	−	2.48621i	1.04144	−	0.0909655i
$748$	1.08270	+	1.08270i	0.0395873	+	0.0395873i
$749$	6.10625	−	2.30212i	0.223118	−	0.0841175i
$750$	−19.1438	+	2.91805i	−0.699033	+	0.106552i
$751$	5.00908	+	8.67598i	0.182784	+	0.316591i	0.942828	−	0.333281i	$-0.108156\pi$
$751$	5.00908	+	8.67598i	0.182784	+	0.316591i	−0.760044	+	0.649872i	$0.774822\pi$
$752$	1.10538	+	1.10538i	0.0403089	+	0.0403089i
$753$	17.9937	−	3.17147i	0.655729	−	0.115575i
$754$		−	16.4566i		−	0.599313i
$755$	−29.1641	+	28.7165i	−1.06139	+	1.04510i
$756$	−11.1720	+	8.01159i	−0.406323	+	0.291379i
$757$	32.2032	−	32.2032i	1.17044	−	1.17044i	0.188340	−	0.982104i	$-0.439689\pi$
$757$	32.2032	−	32.2032i	1.17044	−	1.17044i	0.982104	−	0.188340i	$-0.0603107\pi$
$758$	−13.0097	+	13.0097i	−0.472534	+	0.472534i
$759$	9.40143	−	13.4246i	0.341250	−	0.487282i
$760$	−5.13973	−	0.0397452i	−0.186438	−	0.00144171i
$761$	−10.2508	+	5.91833i	−0.371593	+	0.214539i	−0.674154	−	0.738591i	$-0.735492\pi$
$761$	−10.2508	+	5.91833i	−0.371593	+	0.214539i	0.302561	+	0.953130i	$0.402158\pi$
$762$	5.07571	+	28.7977i	0.183874	+	1.04323i
$763$	−35.4798	+	25.4544i	−1.28446	+	0.921512i
$764$	−22.7609			−0.823462
$765$	1.75222	−	9.49929i	0.0633516	−	0.343448i
$766$	−8.30544	−	14.3854i	−0.300088	−	0.519767i
$767$	−47.2319	+	12.6558i	−1.70545	+	0.456973i
$768$	0.300646	+	1.70576i	0.0108486	+	0.0615513i
$769$	−1.77019	−	1.02202i	−0.0638346	−	0.0368549i	0.467743	−	0.883865i	$-0.345067\pi$
$769$	−1.77019	−	1.02202i	−0.0638346	−	0.0368549i	−0.531578	+	0.847010i	$0.678401\pi$
$770$	0.571668	+	6.26476i	0.0206015	+	0.225766i
$771$	−7.57038	−	0.662864i	−0.272641	−	0.0238725i
$772$	−1.08939	+	1.08939i	−0.0392079	+	0.0392079i
$773$	−38.1591	−	10.2247i	−1.37249	−	0.367757i	−0.504102	−	0.863644i	$-0.668176\pi$
$773$	−38.1591	−	10.2247i	−1.37249	−	0.367757i	−0.868387	+	0.495887i	$0.834843\pi$
$774$	3.82960	−	4.56263i	0.137652	−	0.164000i
$775$	32.9616	+	19.7162i	1.18401	+	0.708228i
$776$	−0.410165	+	0.236809i	−0.0147241	+	0.00850095i
$777$	10.3778	−	6.15033i	0.372301	−	0.220642i
$778$	19.7138	−	5.28229i	0.706772	−	0.189379i
$779$	−0.769883	−	1.33348i	−0.0275839	−	0.0477767i
$780$	23.0514	−	3.87936i	0.825373	−	0.138903i
$781$	−0.679166	+	1.17635i	−0.0243025	+	0.0420931i
$782$	−12.3772	+	3.31645i	−0.442606	+	0.118596i
$783$	7.08655	−	12.2682i	0.253253	−	0.438431i
$784$	−6.86397	+	1.37328i	−0.245142	+	0.0490459i
$785$	3.69464	−	2.09518i	0.131867	−	0.0747801i
$786$	−0.893756	+	10.2073i	−0.0318792	+	0.364084i
$787$	6.98853	−	6.98853i	0.249114	−	0.249114i	−0.571493	−	0.820607i	$-0.693636\pi$
$787$	6.98853	−	6.98853i	0.249114	−	0.249114i	0.820607	+	0.571493i	$0.193636\pi$
$788$	3.78826	−	3.78826i	0.134951	−	0.134951i
$789$	4.41435	−	2.05806i	0.157155	−	0.0732690i
$790$	28.1591	−	15.9686i	1.00185	−	0.568137i
$791$	−7.12586	−	18.9010i	−0.253367	−	0.672042i
$792$	−2.61337	+	1.82935i	−0.0928619	+	0.0650030i
$793$	−8.88197	+	2.37992i	−0.315408	+	0.0845133i
$794$	0.381772	−	0.661249i	0.0135486	−	0.0234669i
$795$	9.32316	−	25.0063i	0.330659	−	0.886881i
$796$	−10.2438	−	17.7428i	−0.363083	−	0.628878i
$797$	−33.4328	+	8.95828i	−1.18425	+	0.317319i	−0.796610	−	0.604493i	$-0.793376\pi$
$797$	−33.4328	+	8.95828i	−1.18425	+	0.317319i	−0.387638	+	0.921812i	$0.626709\pi$
$798$	9.06179	−	5.37042i	0.320784	−	0.190111i
$799$	1.94942	−	1.12550i	0.0689657	−	0.0398173i
$800$	−1.21925	−	4.84906i	−0.0431070	−	0.171440i
$801$	4.04412	−	22.9164i	0.142892	−	0.809709i
$802$	24.0328	+	6.43956i	0.848627	+	0.227389i
$803$	7.64711	−	7.64711i	0.269861	−	0.269861i
$804$	−14.6890	+	20.9748i	−0.518040	+	0.739726i
$805$	−47.7957	−	22.0706i	−1.68458	−	0.777888i
$806$	−40.1515	−	23.1815i	−1.41428	−	0.816532i
$807$	2.17166	−	1.82198i	0.0764461	−	0.0641366i
$808$	5.78776	−	1.55083i	0.203613	−	0.0545579i
$809$	24.2689	+	42.0350i	0.853249	+	1.47787i	0.878260	+	0.478183i	$0.158705\pi$
$809$	24.2689	+	42.0350i	0.853249	+	1.47787i	−0.0250112	+	0.999687i	$0.507962\pi$
$810$	18.8552	+	7.03440i	0.662503	+	0.247164i
$811$	−23.1667			−0.813491			−0.406746	−	0.913541i	$-0.633336\pi$
$811$	−23.1667			−0.813491			−0.406746	+	0.913541i	$0.633336\pi$
$812$	5.86148	−	4.20522i	0.205698	−	0.147574i
$813$	−5.91396	−	2.15298i	−0.207412	−	0.0755083i
$814$	2.42416	−	1.39959i	0.0849667	−	0.0490556i
$815$	15.7998	+	0.122179i	0.553444	+	0.00427974i
$816$	2.48458	+	0.217550i	0.0869776	+	0.00761577i
$817$	−3.22734	+	3.22734i	−0.112910	+	0.112910i
$818$	11.3231	−	11.3231i	0.395903	−	0.395903i
$819$	−36.3468	+	31.2067i	−1.27006	+	1.09045i
$820$	1.06731	−	1.05092i	0.0372719	−	0.0366999i
$821$			5.06265i			0.176688i	0.996090	+	0.0883439i	$0.0281574\pi$
$821$			5.06265i			0.176688i	−0.996090	+	0.0883439i	$0.971843\pi$
$822$	2.51409	−	6.90589i	0.0876890	−	0.240871i
$823$	19.8302	+	19.8302i	0.691238	+	0.691238i	0.962504	−	0.271266i	$-0.0874423\pi$
$823$	19.8302	+	19.8302i	0.691238	+	0.691238i	−0.271266	+	0.962504i	$0.587442\pi$
$824$	−9.02558	−	15.6328i	−0.314421	−	0.544593i
$825$	7.14544	−	5.80898i	0.248772	−	0.202243i
$826$	−16.5771	−	13.5890i	−0.576791	−	0.472822i
$827$	30.1951	+	30.1951i	1.04999	+	1.04999i	0.998683	+	0.0513028i	$0.0163374\pi$
$827$	30.1951	+	30.1951i	1.04999	+	1.04999i	0.0513028	+	0.998683i	$0.483663\pi$
$828$	−2.32294	−	26.5948i	−0.0807279	−	0.924234i
$829$	17.9310	−	10.3525i	0.622770	−	0.359556i	−0.155177	−	0.987887i	$-0.549595\pi$
$829$	17.9310	−	10.3525i	0.622770	−	0.359556i	0.777947	+	0.628330i	$0.216261\pi$
$830$	−5.35273	−	20.6129i	−0.185796	−	0.715485i
$831$	1.80547	−	0.841746i	0.0626309	−	0.0291999i
$832$	1.56211	+	5.82989i	0.0541565	+	0.202115i
$833$	−0.648034	+	10.0589i	−0.0224530	+	0.348519i
$834$	−30.0289	+	14.0001i	−1.03982	+	0.484785i
$835$	−6.16962	−	0.0477092i	−0.213508	−	0.00165104i
$836$	2.11675	−	1.22211i	0.0732095	−	0.0422675i
$837$	−19.9502	−	34.5717i	−0.689578	−	1.19497i
$838$	16.1927	−	4.33881i	0.559366	−	0.149882i
$839$	26.0191	+	45.0663i	0.898278	+	1.55586i	0.829694	+	0.558218i	$0.188515\pi$
$839$	26.0191	+	45.0663i	0.898278	+	1.55586i	0.0685836	+	0.997645i	$0.478152\pi$
$840$	7.27217	+	7.21911i	0.250914	+	0.249083i
$841$	10.7828	−	18.6764i	0.371821	−	0.644012i
$842$	−2.71101	+	10.1176i	−0.0934276	+	0.348677i
$843$	−28.7859	−	34.3106i	−0.991439	−	1.18172i
$844$	16.3802	+	9.45709i	0.563828	+	0.325527i
$845$	50.7044	−	13.1668i	1.74429	−	0.452953i
$846$	1.60335	+	4.40712i	0.0551244	+	0.151520i
$847$	15.2213	+	21.2164i	0.523011	+	0.729003i
$848$	6.65595	+	1.78346i	0.228566	+	0.0612441i
$849$	−7.37811	+	10.5354i	−0.253216	+	0.361575i
$850$	−7.19894	−	0.111344i	−0.246922	−	0.00381908i
$851$			23.4253i			0.803010i
$852$	0.384053	+	2.17897i	0.0131574	+	0.0746504i
$853$	−3.02845	+	11.3023i	−0.103692	+	0.386984i	−0.998194	−	0.0600809i	$-0.980864\pi$
$853$	−3.02845	+	11.3023i	−0.103692	+	0.386984i	0.894501	+	0.447065i	$0.147531\pi$
$854$	−3.11732	−	2.55541i	−0.106673	−	0.0874445i
$855$	−13.9232	−	6.62647i	−0.476164	−	0.226621i
$856$	1.23326	−	2.13607i	0.0421520	−	0.0730093i
$857$	−55.2422	+	14.8021i	−1.88704	+	0.505630i	−0.888096	+	0.459658i	$0.847972\pi$
$857$	−55.2422	+	14.8021i	−1.88704	+	0.505630i	−0.998943	+	0.0459723i	$0.985361\pi$
$858$	−8.51585	+	7.14462i	−0.290726	+	0.243913i
$859$	8.61609	−	4.97450i	0.293977	−	0.169728i	−0.345757	−	0.938324i	$-0.612378\pi$
$859$	8.61609	−	4.97450i	0.293977	−	0.169728i	0.639734	+	0.768596i	$0.279045\pi$
$860$	−3.82782	−	2.24963i	−0.130527	−	0.0767119i
$861$	−0.760659	+	2.97396i	−0.0259232	+	0.101352i
$862$	11.0776	+	2.96825i	0.377306	+	0.101099i
$863$	−5.36091	−	20.0072i	−0.182488	−	0.681053i	−0.995154	−	0.0983245i	$-0.968652\pi$
$863$	−5.36091	−	20.0072i	−0.182488	−	0.681053i	0.812667	−	0.582729i	$-0.198015\pi$
$864$	−1.34593	+	5.01881i	−0.0457895	+	0.170743i
$865$	−22.1545	+	12.5635i	−0.753275	+	0.427171i
$866$		−	23.7898i		−	0.808411i
$867$	−8.84414	+	24.2937i	−0.300363	+	0.825057i
$868$	−2.00335	−	20.2248i	−0.0679980	−	0.686473i
$869$	−7.69702	+	13.3316i	−0.261103	+	0.452244i
$870$	−9.89478	−	3.68910i	−0.335464	−	0.125072i
$871$	−44.6151	+	77.2756i	−1.51172	+	2.61838i
$872$	−4.27163	+	15.9419i	−0.144656	+	0.539862i
$873$	−1.41547	+	0.123635i	−0.0479062	+	0.00418440i
$874$			20.4548i			0.691894i
$875$	−22.4353	−	19.2785i	−0.758450	−	0.651731i
$876$	1.53656	−	17.5486i	0.0519155	−	0.592913i
$877$	−39.2231	−	10.5098i	−1.32447	−	0.354890i	−0.473819	−	0.880622i	$-0.657125\pi$
$877$	−39.2231	−	10.5098i	−1.32447	−	0.354890i	−0.850650	+	0.525732i	$0.823791\pi$
$878$	−25.5597	+	25.5597i	−0.862597	+	0.862597i
$879$	−41.4507	+	19.3252i	−1.39810	+	0.651823i
$880$	1.66823	+	1.69424i	0.0562362	+	0.0571127i
$881$			42.0460i			1.41657i	0.705928	+	0.708284i	$0.250530\pi$
$881$			42.0460i			1.41657i	−0.705928	+	0.708284i	$0.749470\pi$
$882$	−20.4030	−	4.97156i	−0.687006	−	0.167401i
$883$	−13.3727	−	13.3727i	−0.450026	−	0.450026i	0.445337	−	0.895363i	$-0.353084\pi$
$883$	−13.3727	−	13.3727i	−0.450026	−	0.450026i	−0.895363	+	0.445337i	$0.853084\pi$
$884$	8.69094			0.292308
$885$	−2.97859	+	31.2360i	−0.100124	+	1.04999i
$886$	39.9780			1.34309
$887$	−6.84709	+	25.5537i	−0.229903	+	0.858008i	0.750478	+	0.660895i	$0.229823\pi$
$887$	−6.84709	+	25.5537i	−0.229903	+	0.858008i	−0.980381	+	0.197113i	$0.936843\pi$
$888$	1.55975	−	4.28444i	0.0523419	−	0.143776i
$889$	−28.3174	+	34.5441i	−0.949735	+	1.15857i
$890$	−17.3443	−	0.134122i	−0.581381	−	0.00449577i
$891$	−9.42512	+	1.65915i	−0.315754	+	0.0555835i
$892$	7.14063	+	1.91332i	0.239086	+	0.0640629i
$893$	−0.930015	−	3.47086i	−0.0311218	−	0.116148i
$894$	27.2372	+	2.38489i	0.910948	+	0.0797627i
$895$	−9.40348	−	36.2121i	−0.314324	−	1.21044i
$896$	−1.67731	+	2.04613i	−0.0560349	+	0.0683564i
$897$	−16.1473	−	91.6137i	−0.539141	−	3.05889i
$898$	14.4512	+	14.4512i	0.482244	+	0.482244i
$899$	10.4724	+	18.1388i	0.349275	+	0.604962i
$900$	2.83495	−	14.7297i	0.0944984	−	0.490989i
$901$	4.96120	−	8.59304i	0.165281	−	0.286276i
$902$	−0.184354	+	0.688020i	−0.00613833	+	0.0229086i
$903$	9.09857	−	0.103680i	0.302781	−	0.00345025i
$904$	−6.61189	−	3.81738i	−0.219908	−	0.126964i
$905$	−36.2383	−	10.0110i	−1.20460	−	0.332776i
$906$	−13.3964	−	28.7341i	−0.445066	−	0.954625i
$907$	1.60466	+	5.98869i	0.0532820	+	0.198851i	0.987436	−	0.158019i	$-0.0505106\pi$
$907$	1.60466	+	5.98869i	0.0532820	+	0.198851i	−0.934154	+	0.356870i	$0.883844\pi$
$908$	6.21344	+	23.1889i	0.206200	+	0.769550i
$909$	17.7023	+	3.12398i	0.587147	+	0.103616i
$910$	27.4384	+	22.8496i	0.909576	+	0.757457i
$911$	2.61631	−	1.51052i	0.0866821	−	0.0500459i	−0.456032	−	0.889963i	$-0.650730\pi$
$911$	2.61631	−	1.51052i	0.0866821	−	0.0500459i	0.542714	+	0.839917i	$0.317397\pi$
$912$	1.36196	−	3.74114i	0.0450991	−	0.123881i
$913$	7.16112	+	7.16112i	0.236999	+	0.236999i
$914$	17.5410			0.580206
$915$	−0.560124	+	5.87393i	−0.0185171	+	0.194186i
$916$	1.75299	+	3.03627i	0.0579205	+	0.100321i
$917$	−12.7173	+	9.12381i	−0.419962	+	0.301295i
$918$	6.47902	+	3.74251i	0.213840	+	0.123521i
$919$	20.6682	+	11.9328i	0.681781	+	0.393627i	0.800526	−	0.599298i	$-0.204554\pi$
$919$	20.6682	+	11.9328i	0.681781	+	0.393627i	−0.118745	+	0.992925i	$0.537887\pi$
$920$	−19.2593	+	5.00123i	−0.634961	+	0.164886i
$921$	9.44726	+	6.61604i	0.311298	+	0.218006i
$922$	−31.6467	−	8.47970i	−1.04223	−	0.279264i
$923$	1.99548	+	7.44723i	0.0656820	+	0.245129i
$924$	−4.72085	−	1.20747i	−0.155305	−	0.0397228i
$925$	−3.60284	+	12.6595i	−0.118461	+	0.416242i
$926$	−22.6310	−	13.0660i	−0.743702	−	0.429376i
$927$	−4.71213	−	53.9481i	−0.154767	−	1.77189i
$928$	0.705699	−	2.63370i	0.0231657	−	0.0864555i
$929$	−36.6595			−1.20276			−0.601380	−	0.798963i	$-0.705382\pi$
$929$	−36.6595			−1.20276			−0.601380	+	0.798963i	$0.705382\pi$
$930$	−22.9391	+	18.9451i	−0.752201	+	0.621234i
$931$	15.2422	+	5.15510i	0.499544	+	0.168952i
$932$	12.2425	−	3.28038i	0.401018	−	0.107452i
$933$	49.6917	−	8.75836i	1.62683	−	0.286736i
$934$	−10.5824	−	6.10977i	−0.346268	−	0.199918i
$935$	2.97824	−	1.68891i	0.0973987	−	0.0552334i
$936$	−3.14671	+	17.8311i	−0.102854	+	0.582828i
$937$	21.8202	−	21.8202i	0.712836	−	0.712836i	−0.254292	−	0.967128i	$-0.581842\pi$
$937$	21.8202	−	21.8202i	0.712836	−	0.712836i	0.967128	+	0.254292i	$0.0818424\pi$
$938$	−38.9246	+	3.85564i	−1.27093	+	0.125891i
$939$	−9.98980	+	14.2648i	−0.326005	+	0.465513i
$940$	3.04062	−	1.72429i	0.0991742	−	0.0562402i
$941$			45.6926i			1.48954i	0.667323	+	0.744768i	$0.267440\pi$
$941$			45.6926i			1.48954i	−0.667323	+	0.744768i	$0.732560\pi$
$942$	0.571072	+	3.24005i	0.0186065	+	0.105567i
$943$	−4.21500	−	4.21500i	−0.137259	−	0.137259i
$944$	−8.10168			−0.263687
$945$	10.6156	+	28.8498i	0.345326	+	0.938483i
$946$	2.11136			0.0686464
$947$	−23.5647	−	23.5647i	−0.765751	−	0.765751i	0.211604	−	0.977355i	$-0.432131\pi$
$947$	−23.5647	−	23.5647i	−0.765751	−	0.765751i	−0.977355	+	0.211604i	$0.932131\pi$
$948$	4.35248	+	24.6944i	0.141362	+	0.802037i
$949$		−	61.3843i		−	1.99262i
$950$	−3.14597	+	11.0542i	−0.102069	+	0.358645i
$951$	−19.3251	+	27.5949i	−0.626658	+	0.894825i
$952$	2.22084	+	3.09553i	0.0719777	+	0.100327i
$953$	−38.0214	+	38.0214i	−1.23164	+	1.23164i	−0.268300	+	0.963336i	$0.586462\pi$
$953$	−38.0214	+	38.0214i	−1.23164	+	1.23164i	−0.963336	+	0.268300i	$0.913538\pi$
$954$	15.8340	+	13.2901i	0.512643	+	0.430283i
$955$	−13.5524	+	49.0575i	−0.438544	+	1.58746i
$956$	3.49975	+	2.02058i	0.113190	+	0.0653502i
$957$	4.94552	−	0.871667i	0.159866	−	0.0281770i
$958$	24.0602	−	6.44691i	0.777350	−	0.208290i
$959$	10.5045	−	3.96029i	0.339207	−	0.127884i
$960$	3.85549	+	0.367651i	0.124436	+	0.0118659i
$961$	28.0077			0.903476
$962$	4.11218	−	15.3468i	0.132582	−	0.494802i
$963$	6.06197	−	4.24335i	0.195344	−	0.136740i
$964$	13.7167	+	7.91935i	0.441785	+	0.255065i
$965$	1.69935	+	2.99664i	0.0547040	+	0.0964652i
$966$	28.5046	−	29.1618i	0.917122	−	0.938264i
$967$	−5.54768	−	20.7042i	−0.178401	−	0.665803i	−0.995947	−	0.0899397i	$-0.971333\pi$
$967$	−5.54768	−	20.7042i	−0.178401	−	0.665803i	0.817546	−	0.575864i	$-0.195334\pi$
$968$	9.53302	+	2.55437i	0.306403	+	0.0821004i
$969$	−4.69594	−	3.28863i	−0.150855	−	0.105646i
$970$	0.266182	+	1.02505i	0.00854659	+	0.0329122i
$971$	−8.79284	−	5.07655i	−0.282176	−	0.162914i	0.352232	−	0.935913i	$-0.385423\pi$
$971$	−8.79284	−	5.07655i	−0.282176	−	0.162914i	−0.634408	+	0.772998i	$0.718756\pi$
$972$	−10.0243	+	11.9379i	−0.321530	+	0.382908i
$973$	−46.1106	−	20.8615i	−1.47824	−	0.668789i
$974$	7.14226	+	12.3708i	0.228853	+	0.396385i
$975$	5.36398	−	51.9934i	0.171785	−	1.66512i
$976$	−1.52352			−0.0487668
$977$	35.6467	+	35.6467i	1.14044	+	1.14044i	0.988370	+	0.152070i	$0.0485938\pi$
$977$	35.6467	+	35.6467i	1.14044	+	1.14044i	0.152070	+	0.988370i	$0.451406\pi$
$978$	−4.18675	+	11.5005i	−0.133878	+	0.367745i
$979$	7.14308	−	4.12406i	0.228294	−	0.131806i
$980$	−1.12707	+	15.6118i	−0.0360028	+	0.498702i
$981$	−31.8317	+	37.9246i	−1.01631	+	1.21084i
$982$	−5.24001	−	19.5560i	−0.167215	−	0.624056i
$983$	−4.36983	−	16.3084i	−0.139376	−	0.520158i	−0.999941	−	0.0108182i	$-0.996556\pi$
$983$	−4.36983	−	16.3084i	−0.139376	−	0.520158i	0.860566	−	0.509340i	$-0.170110\pi$
$984$	0.490263	+	1.05157i	0.0156290	+	0.0335227i
$985$	−5.90936	−	10.4206i	−0.188288	−	0.332027i
$986$	−3.40020	−	1.96310i	−0.108284	−	0.0625180i
$987$	−3.51091	+	6.24432i	−0.111753	+	0.198759i
$988$	3.59072	−	13.4007i	0.114236	−	0.426334i
$989$	−8.83463	+	15.3020i	−0.280925	+	0.486576i
$990$	2.38680	+	6.72191i	0.0758575	+	0.213636i
$991$	−14.6352	−	25.3489i	−0.464902	−	0.805234i	0.534295	−	0.845298i	$-0.320577\pi$
$991$	−14.6352	−	25.3489i	−0.464902	−	0.805234i	−0.999197	+	0.0400639i	$0.987244\pi$
$992$	−5.43175	−	5.43175i	−0.172458	−	0.172458i
$993$	−5.68169	−	32.2359i	−0.180303	−	1.02297i
$994$	−2.14263	+	2.61377i	−0.0679601	+	0.0829038i
$995$	−44.3411	+	11.5144i	−1.40571	+	0.365032i
$996$	16.4334	+	1.43891i	0.520712	+	0.0455936i
$997$	−12.1691	−	45.4155i	−0.385398	−	1.43832i	−0.837539	−	0.546378i	$-0.816006\pi$
$997$	−12.1691	−	45.4155i	−0.385398	−	1.43832i	0.452141	−	0.891946i	$-0.350660\pi$
$998$	20.7877	+	5.57004i	0.658022	+	0.176316i
$999$	9.67427	−	9.67016i	0.306080	−	0.305950i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.cd.a.23.38	yes	192
5.2	odd	4	inner	630.2.cd.a.527.23	yes	192
7.4	even	3		630.2.bt.a.473.19	yes	192
9.2	odd	6		630.2.bt.a.443.7	yes	192
35.32	odd	12		630.2.bt.a.347.7	yes	192
45.2	even	12		630.2.bt.a.317.19	✓	192
63.11	odd	6	inner	630.2.cd.a.263.23	yes	192
315.137	even	12	inner	630.2.cd.a.137.38	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bt.a.317.19	✓	192	45.2	even	12
630.2.bt.a.347.7	yes	192	35.32	odd	12
630.2.bt.a.443.7	yes	192	9.2	odd	6
630.2.bt.a.473.19	yes	192	7.4	even	3
630.2.cd.a.23.38	yes	192	1.1	even	1	trivial
630.2.cd.a.137.38	yes	192	315.137	even	12	inner
630.2.cd.a.263.23	yes	192	63.11	odd	6	inner
630.2.cd.a.527.23	yes	192	5.2	odd	4	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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.cd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.300646 + 1.70576i) q^{3} +1.00000i q^{4} +(2.15534 + 0.595421i) q^{5} +(-0.993564 + 1.41874i) q^{6} +(-2.63287 + 0.260796i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.81922 + 1.02566i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.300646 + 1.70576i) q^{3} +1.00000i q^{4} +(2.15534 + 0.595421i) q^{5} +(-0.993564 + 1.41874i) q^{6} +(-2.63287 + 0.260796i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.81922 + 1.02566i) q^{9} +(1.10303 + 1.94508i) q^{10} +(-0.920878 - 0.531669i) q^{11} +(-1.70576 + 0.300646i) q^{12} +(-5.82989 + 1.56211i) q^{13} +(-2.04613 - 1.67731i) q^{14} +(-0.367651 + 3.85549i) q^{15} -1.00000 q^{16} +(-0.372689 + 1.39089i) q^{17} +(-2.71874 - 1.26824i) q^{18} +(1.99067 + 1.14931i) q^{19} +(-0.595421 + 2.15534i) q^{20} +(-1.23642 - 4.41263i) q^{21} +(-0.275212 - 1.02711i) q^{22} +(8.59548 + 2.30315i) q^{23} +(-1.41874 - 0.993564i) q^{24} +(4.29095 + 2.56667i) q^{25} +(-5.22693 - 3.01777i) q^{26} +(-2.59712 - 4.50055i) q^{27} +(-0.260796 - 2.63287i) q^{28} +(1.36331 + 2.36131i) q^{29} +(-2.98621 + 2.46628i) q^{30} +7.68165 q^{31} +(-0.707107 - 0.707107i) q^{32} +(0.630040 - 1.73064i) q^{33} +(-1.24704 + 0.719980i) q^{34} +(-5.83000 - 1.00556i) q^{35} +(-1.02566 - 2.81922i) q^{36} +(0.681326 + 2.54274i) q^{37} +(0.594929 + 2.22030i) q^{38} +(-4.41732 - 9.47474i) q^{39} +(-1.94508 + 1.10303i) q^{40} +(-0.580119 - 0.334932i) q^{41} +(2.24592 - 3.99448i) q^{42} +(-0.513911 + 1.91794i) q^{43} +(0.531669 - 0.920878i) q^{44} +(-6.68707 + 0.532017i) q^{45} +(4.44935 + 7.70650i) q^{46} +(-1.10538 - 1.10538i) q^{47} +(-0.300646 - 1.70576i) q^{48} +(6.86397 - 1.37328i) q^{49} +(1.21925 + 4.84906i) q^{50} +(-2.48458 - 0.217550i) q^{51} +(-1.56211 - 5.82989i) q^{52} +(-6.65595 - 1.78346i) q^{53} +(1.34593 - 5.01881i) q^{54} +(-1.66823 - 1.69424i) q^{55} +(1.67731 - 2.04613i) q^{56} +(-1.36196 + 3.74114i) q^{57} +(-0.705699 + 2.63370i) q^{58} +8.10168 q^{59} +(-3.85549 - 0.367651i) q^{60} +1.52352 q^{61} +(5.43175 + 5.43175i) q^{62} +(7.15515 - 3.43567i) q^{63} -1.00000i q^{64} +(-13.4955 - 0.104360i) q^{65} +(1.66925 - 0.778241i) q^{66} +(10.4539 - 10.4539i) q^{67} +(-1.39089 - 0.372689i) q^{68} +(-1.34442 + 15.3542i) q^{69} +(-3.41139 - 4.83347i) q^{70} -1.27742i q^{71} +(1.26824 - 2.71874i) q^{72} +(-2.63231 + 9.82391i) q^{73} +(-1.31622 + 2.27976i) q^{74} +(-3.08805 + 8.09098i) q^{75} +(-1.14931 + 1.99067i) q^{76} +(2.56321 + 1.15965i) q^{77} +(3.57613 - 9.82317i) q^{78} -14.4771i q^{79} +(-2.15534 - 0.595421i) q^{80} +(6.89604 - 5.78313i) q^{81} +(-0.173373 - 0.647038i) q^{82} +(-9.19959 - 2.46502i) q^{83} +(4.41263 - 1.23642i) q^{84} +(-1.63144 + 2.77594i) q^{85} +(-1.71958 + 0.992800i) q^{86} +(-3.61796 + 3.03539i) q^{87} +(1.02711 - 0.275212i) q^{88} +(-3.87841 + 6.71760i) q^{89} +(-5.10467 - 4.35228i) q^{90} +(14.9419 - 5.63325i) q^{91} +(-2.30315 + 8.59548i) q^{92} +(2.30946 + 13.1030i) q^{93} -1.56324i q^{94} +(3.60624 + 3.66244i) q^{95} +(0.993564 - 1.41874i) q^{96} +(0.457480 + 0.122581i) q^{97} +(5.82462 + 3.88250i) q^{98} +(3.14147 + 0.554386i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 8 q^{6}+O(q^{10}) \) 192 * q + 8 * q^6	\( 192 q + 8 q^{6} + 24 q^{11} + 12 q^{15} - 192 q^{16} - 36 q^{17} - 8 q^{18} + 24 q^{23} + 36 q^{27} - 12 q^{30} + 40 q^{33} + 12 q^{41} - 4 q^{42} + 8 q^{45} - 12 q^{46} - 48 q^{50} + 24 q^{51} - 12 q^{56} - 48 q^{57} - 12 q^{58} - 16 q^{60} - 24 q^{61} - 52 q^{63} - 36 q^{68} + 8 q^{72} + 8 q^{75} + 96 q^{77} - 16 q^{78} + 16 q^{81} + 76 q^{87} - 20 q^{90} - 24 q^{92} - 8 q^{96}+O(q^{100}) \) 192 * q + 8 * q^6 + 24 * q^11 + 12 * q^15 - 192 * q^16 - 36 * q^17 - 8 * q^18 + 24 * q^23 + 36 * q^27 - 12 * q^30 + 40 * q^33 + 12 * q^41 - 4 * q^42 + 8 * q^45 - 12 * q^46 - 48 * q^50 + 24 * q^51 - 12 * q^56 - 48 * q^57 - 12 * q^58 - 16 * q^60 - 24 * q^61 - 52 * q^63 - 36 * q^68 + 8 * q^72 + 8 * q^75 + 96 * q^77 - 16 * q^78 + 16 * q^81 + 76 * q^87 - 20 * q^90 - 24 * q^92 - 8 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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