LMFDB - Embedded newform 930.2.bf.a.377.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(377,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 8]))

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

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

chi := DirichletCharacter("930.377");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bf (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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$64$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			377.3
Character	$\chi$	$=$	930.377
Dual form			930.2.bf.a.893.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-1.65429 - 0.513158i) q^{3} -1.00000i q^{4} +(1.83992 - 1.27071i) q^{5} +(1.53262 - 0.806900i) q^{6} +(3.00096 - 0.804106i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.47334 + 1.69782i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.65429 - 0.513158i) q^{3} -1.00000i q^{4} +(1.83992 - 1.27071i) q^{5} +(1.53262 - 0.806900i) q^{6} +(3.00096 - 0.804106i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.47334 + 1.69782i) q^{9} +(-0.402493 + 2.19955i) q^{10} +(-0.524341 + 0.302728i) q^{11} +(-0.513158 + 1.65429i) q^{12} +(1.46925 + 0.393685i) q^{13} +(-1.55341 + 2.69059i) q^{14} +(-3.69583 + 1.15795i) q^{15} -1.00000 q^{16} +(1.78011 + 6.64345i) q^{17} +(-2.94946 + 0.548371i) q^{18} +(2.98734 + 1.72474i) q^{19} +(-1.27071 - 1.83992i) q^{20} +(-5.37709 - 0.209747i) q^{21} +(0.156704 - 0.584826i) q^{22} +(-1.23007 - 1.23007i) q^{23} +(-0.806900 - 1.53262i) q^{24} +(1.77060 - 4.67600i) q^{25} +(-1.31729 + 0.760541i) q^{26} +(-3.22036 - 4.07790i) q^{27} +(-0.804106 - 3.00096i) q^{28} +1.17381 q^{29} +(1.79455 - 3.43214i) q^{30} +(-2.34408 - 5.05028i) q^{31} +(0.707107 - 0.707107i) q^{32} +(1.02276 - 0.231730i) q^{33} +(-5.95636 - 3.43890i) q^{34} +(4.49975 - 5.29284i) q^{35} +(1.69782 - 2.47334i) q^{36} +(-2.05653 + 0.551046i) q^{37} +(-3.33194 + 0.892791i) q^{38} +(-2.22854 - 1.40523i) q^{39} +(2.19955 + 0.402493i) q^{40} +(7.05436 - 4.07284i) q^{41} +(3.95049 - 3.65386i) q^{42} +(3.03539 + 11.3282i) q^{43} +(0.302728 + 0.524341i) q^{44} +(6.70818 - 0.0190325i) q^{45} +1.73959 q^{46} +(-8.52574 + 8.52574i) q^{47} +(1.65429 + 0.513158i) q^{48} +(2.29702 - 1.32619i) q^{49} +(2.05443 + 4.55844i) q^{50} +(0.464333 - 11.9037i) q^{51} +(0.393685 - 1.46925i) q^{52} +(-1.79554 + 6.70105i) q^{53} +(5.16065 + 0.606374i) q^{54} +(-0.580065 + 1.22328i) q^{55} +(2.69059 + 1.55341i) q^{56} +(-4.05685 - 4.38619i) q^{57} +(-0.830012 + 0.830012i) q^{58} +(4.85652 - 8.41174i) q^{59} +(1.15795 + 3.69583i) q^{60} +9.77332 q^{61} +(5.22860 + 1.91357i) q^{62} +(8.78763 + 3.10628i) q^{63} +1.00000i q^{64} +(3.20356 - 1.14264i) q^{65} +(-0.559341 + 0.887057i) q^{66} +(1.18586 - 4.42570i) q^{67} +(6.64345 - 1.78011i) q^{68} +(1.40367 + 2.66612i) q^{69} +(0.560801 + 6.92440i) q^{70} +(6.96683 - 4.02230i) q^{71} +(0.548371 + 2.94946i) q^{72} +(5.78136 + 1.54911i) q^{73} +(1.06454 - 1.84384i) q^{74} +(-5.32861 + 6.82685i) q^{75} +(1.72474 - 2.98734i) q^{76} +(-1.33010 + 1.33010i) q^{77} +(2.56946 - 0.582172i) q^{78} +(0.229542 + 0.132526i) q^{79} +(-1.83992 + 1.27071i) q^{80} +(3.23479 + 8.39858i) q^{81} +(-2.10826 + 7.86811i) q^{82} +(4.61888 - 17.2379i) q^{83} +(-0.209747 + 5.37709i) q^{84} +(11.7171 + 9.96142i) q^{85} +(-10.1566 - 5.86392i) q^{86} +(-1.94183 - 0.602353i) q^{87} +(-0.584826 - 0.156704i) q^{88} -9.19075 q^{89} +(-4.72994 + 4.75686i) q^{90} +4.72574 q^{91} +(-1.23007 + 1.23007i) q^{92} +(1.28618 + 9.55750i) q^{93} -12.0572i q^{94} +(7.68810 - 0.622652i) q^{95} +(-1.53262 + 0.806900i) q^{96} +(10.5328 + 10.5328i) q^{97} +(-0.686485 + 2.56200i) q^{98} +(-1.81085 - 0.141489i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q + 8 q^{3} - 4 q^{7}+O(q^{10}) $ 256 * q + 8 * q^3 - 4 * q^7	$ 256 q + 8 q^{3} - 4 q^{7} - 8 q^{10} - 8 q^{12} + 8 q^{15} - 256 q^{16} - 4 q^{22} - 16 q^{25} - 40 q^{27} - 4 q^{28} - 48 q^{30} + 32 q^{31} - 8 q^{33} + 8 q^{37} - 12 q^{42} - 40 q^{45} + 16 q^{46} - 8 q^{48} - 16 q^{51} + 20 q^{55} + 40 q^{57} + 56 q^{58} - 8 q^{60} - 32 q^{61} + 56 q^{63} + 32 q^{66} - 24 q^{67} + 24 q^{70} + 8 q^{73} - 4 q^{75} + 16 q^{76} - 88 q^{78} - 48 q^{81} + 64 q^{85} - 20 q^{87} - 4 q^{88} - 8 q^{90} - 68 q^{93} + 152 q^{97}+O(q^{100}) $ 256 * q + 8 * q^3 - 4 * q^7 - 8 * q^10 - 8 * q^12 + 8 * q^15 - 256 * q^16 - 4 * q^22 - 16 * q^25 - 40 * q^27 - 4 * q^28 - 48 * q^30 + 32 * q^31 - 8 * q^33 + 8 * q^37 - 12 * q^42 - 40 * q^45 + 16 * q^46 - 8 * q^48 - 16 * q^51 + 20 * q^55 + 40 * q^57 + 56 * q^58 - 8 * q^60 - 32 * q^61 + 56 * q^63 + 32 * q^66 - 24 * q^67 + 24 * q^70 + 8 * q^73 - 4 * q^75 + 16 * q^76 - 88 * q^78 - 48 * q^81 + 64 * q^85 - 20 * q^87 - 4 * q^88 - 8 * q^90 - 68 * q^93 + 152 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

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
$3$	−1.65429	−	0.513158i	−0.955104	−	0.296272i
$3$	−1.65429	−	0.513158i	−0.955104	−	0.296272i
$4$		−	1.00000i		−	0.500000i
$5$	1.83992	−	1.27071i	0.822837	−	0.568278i
$5$	1.83992	−	1.27071i	0.822837	−	0.568278i
$6$	1.53262	−	0.806900i	0.625688	−	0.329416i
$7$	3.00096	−	0.804106i	1.13426	−	0.303923i	0.357618	−	0.933868i	$-0.383589\pi$
$7$	3.00096	−	0.804106i	1.13426	−	0.303923i	0.776640	+	0.629945i	$0.216922\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	2.47334	+	1.69782i	0.824446	+	0.565941i
$10$	−0.402493	+	2.19955i	−0.127279	+	0.695557i
$11$	−0.524341	+	0.302728i	−0.158095	+	0.0912760i	−0.576960	−	0.816772i	$-0.695761\pi$
$11$	−0.524341	+	0.302728i	−0.158095	+	0.0912760i	0.418866	+	0.908048i	$0.362428\pi$
$12$	−0.513158	+	1.65429i	−0.148136	+	0.477552i
$13$	1.46925	+	0.393685i	0.407497	+	0.109189i	0.456744	−	0.889598i	$-0.349015\pi$
$13$	1.46925	+	0.393685i	0.407497	+	0.109189i	−0.0492470	+	0.998787i	$0.515682\pi$
$14$	−1.55341	+	2.69059i	−0.415167	+	0.719091i
$15$	−3.69583	+	1.15795i	−0.954259	+	0.298981i
$16$	−1.00000			−0.250000
$17$	1.78011	+	6.64345i	0.431740	+	1.61127i	0.748750	+	0.662852i	$0.230654\pi$
$17$	1.78011	+	6.64345i	0.431740	+	1.61127i	−0.317011	+	0.948422i	$0.602679\pi$
$18$	−2.94946	+	0.548371i	−0.695193	+	0.129252i
$19$	2.98734	+	1.72474i	0.685342	+	0.395682i	0.801865	−	0.597506i	$-0.203841\pi$
$19$	2.98734	+	1.72474i	0.685342	+	0.395682i	−0.116523	+	0.993188i	$0.537175\pi$
$20$	−1.27071	−	1.83992i	−0.284139	−	0.411418i
$21$	−5.37709	−	0.209747i	−1.17338	−	0.0457706i
$22$	0.156704	−	0.584826i	0.0334093	−	0.124685i
$23$	−1.23007	−	1.23007i	−0.256488	−	0.256488i	0.567136	−	0.823624i	$-0.308051\pi$
$23$	−1.23007	−	1.23007i	−0.256488	−	0.256488i	−0.823624	+	0.567136i	$0.808051\pi$
$24$	−0.806900	−	1.53262i	−0.164708	−	0.312844i
$25$	1.77060	−	4.67600i	0.354120	−	0.935200i
$26$	−1.31729	+	0.760541i	−0.258343	+	0.149154i
$27$	−3.22036	−	4.07790i	−0.619758	−	0.784793i
$28$	−0.804106	−	3.00096i	−0.151962	−	0.567129i
$29$	1.17381			0.217972			0.108986	−	0.994043i	$-0.465240\pi$
$29$	1.17381			0.217972			0.108986	+	0.994043i	$0.465240\pi$
$30$	1.79455	−	3.43214i	0.327639	−	0.626620i
$31$	−2.34408	−	5.05028i	−0.421008	−	0.907057i
$31$	−2.34408	−	5.05028i	−0.421008	−	0.907057i
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	1.02276	−	0.231730i	0.178039	−	0.0403390i
$34$	−5.95636	−	3.43890i	−1.02151	−	0.589767i
$35$	4.49975	−	5.29284i	0.760596	−	0.894653i
$36$	1.69782	−	2.47334i	0.282971	−	0.412223i
$37$	−2.05653	+	0.551046i	−0.338092	+	0.0905914i	−0.423871	−	0.905723i	$-0.639329\pi$
$37$	−2.05653	+	0.551046i	−0.338092	+	0.0905914i	0.0857787	+	0.996314i	$0.472662\pi$
$38$	−3.33194	+	0.892791i	−0.540512	+	0.144830i
$39$	−2.22854	−	1.40523i	−0.356852	−	0.225016i
$40$	2.19955	+	0.402493i	0.347779	+	0.0636397i
$41$	7.05436	−	4.07284i	1.10171	−	0.636070i	0.165037	−	0.986287i	$-0.447226\pi$
$41$	7.05436	−	4.07284i	1.10171	−	0.636070i	0.936669	+	0.350217i	$0.113892\pi$
$42$	3.95049	−	3.65386i	0.609574	−	0.563804i
$43$	3.03539	+	11.3282i	0.462892	+	1.72754i	0.663784	+	0.747924i	$0.268949\pi$
$43$	3.03539	+	11.3282i	0.462892	+	1.72754i	−0.200892	+	0.979613i	$0.564384\pi$
$44$	0.302728	+	0.524341i	0.0456380	+	0.0790473i
$45$	6.70818	−	0.0190325i	0.999996	−	0.00283720i
$46$	1.73959			0.256488
$47$	−8.52574	+	8.52574i	−1.24361	+	1.24361i	−0.285113	+	0.958494i	$0.592031\pi$
$47$	−8.52574	+	8.52574i	−1.24361	+	1.24361i	−0.958494	+	0.285113i	$0.907969\pi$
$48$	1.65429	+	0.513158i	0.238776	+	0.0740680i
$49$	2.29702	−	1.32619i	0.328146	−	0.189455i
$50$	2.05443	+	4.55844i	0.290540	+	0.644660i
$51$	0.464333	−	11.9037i	0.0650196	−	1.66685i
$52$	0.393685	−	1.46925i	0.0545943	−	0.203749i
$53$	−1.79554	+	6.70105i	−0.246636	+	0.920460i	0.725917	+	0.687782i	$0.241415\pi$
$53$	−1.79554	+	6.70105i	−0.246636	+	0.920460i	−0.972554	+	0.232678i	$0.925251\pi$
$54$	5.16065	+	0.606374i	0.702276	+	0.0825171i
$55$	−0.580065	+	1.22328i	−0.0782159	+	0.164947i
$56$	2.69059	+	1.55341i	0.359545	+	0.207584i
$57$	−4.05685	−	4.38619i	−0.537343	−	0.580965i
$58$	−0.830012	+	0.830012i	−0.108986	+	0.108986i
$59$	4.85652	−	8.41174i	0.632265	−	1.09511i	−0.354823	−	0.934934i	$-0.615459\pi$
$59$	4.85652	−	8.41174i	0.632265	−	1.09511i	0.987088	−	0.160181i	$-0.0512079\pi$
$60$	1.15795	+	3.69583i	0.149490	+	0.477130i
$61$	9.77332			1.25135			0.625673	−	0.780086i	$-0.284825\pi$
$61$	9.77332			1.25135			0.625673	+	0.780086i	$0.284825\pi$
$62$	5.22860	+	1.91357i	0.664033	+	0.243024i
$63$	8.78763	+	3.10628i	1.10714	+	0.391355i
$64$			1.00000i			0.125000i
$65$	3.20356	−	1.14264i	0.397353	−	0.141727i
$66$	−0.559341	+	0.887057i	−0.0688501	+	0.109189i
$67$	1.18586	−	4.42570i	0.144876	−	0.540685i	−0.854885	−	0.518818i	$-0.826372\pi$
$67$	1.18586	−	4.42570i	0.144876	−	0.540685i	0.999761	−	0.0218674i	$-0.00696115\pi$
$68$	6.64345	−	1.78011i	0.805637	−	0.215870i
$69$	1.40367	+	2.66612i	0.168982	+	0.320963i
$70$	0.560801	+	6.92440i	0.0670286	+	0.827625i
$71$	6.96683	−	4.02230i	0.826810	−	0.477359i	−0.0259490	−	0.999663i	$-0.508261\pi$
$71$	6.96683	−	4.02230i	0.826810	−	0.477359i	0.852759	+	0.522304i	$0.174927\pi$
$72$	0.548371	+	2.94946i	0.0646261	+	0.347597i
$73$	5.78136	+	1.54911i	0.676657	+	0.181310i	0.580752	−	0.814081i	$-0.302759\pi$
$73$	5.78136	+	1.54911i	0.676657	+	0.181310i	0.0959054	+	0.995390i	$0.469425\pi$
$74$	1.06454	−	1.84384i	0.123750	−	0.214342i
$75$	−5.32861	+	6.82685i	−0.615295	+	0.788297i
$76$	1.72474	−	2.98734i	0.197841	−	0.342671i
$77$	−1.33010	+	1.33010i	−0.151579	+	0.151579i
$78$	2.56946	−	0.582172i	0.290934	−	0.0659180i
$79$	0.229542	+	0.132526i	0.0258255	+	0.0149104i	0.512857	−	0.858474i	$-0.328587\pi$
$79$	0.229542	+	0.132526i	0.0258255	+	0.0149104i	−0.487032	+	0.873384i	$0.661920\pi$
$80$	−1.83992	+	1.27071i	−0.205709	+	0.142069i
$81$	3.23479	+	8.39858i	0.359421	+	0.933175i
$82$	−2.10826	+	7.86811i	−0.232818	+	0.868888i
$83$	4.61888	−	17.2379i	0.506988	−	1.89210i	0.0585643	−	0.998284i	$-0.481348\pi$
$83$	4.61888	−	17.2379i	0.506988	−	1.89210i	0.448424	−	0.893821i	$-0.351986\pi$
$84$	−0.209747	+	5.37709i	−0.0228853	+	0.586689i
$85$	11.7171	+	9.96142i	1.27090	+	1.08047i
$86$	−10.1566	−	5.86392i	−1.09521	−	0.632323i
$87$	−1.94183	−	0.602353i	−0.208186	−	0.0645790i
$88$	−0.584826	−	0.156704i	−0.0623427	−	0.0167047i
$89$	−9.19075			−0.974218			−0.487109	−	0.873341i	$-0.661949\pi$
$89$	−9.19075			−0.974218			−0.487109	+	0.873341i	$0.661949\pi$
$90$	−4.72994	+	4.75686i	−0.498579	+	0.501417i
$91$	4.72574			0.495392
$92$	−1.23007	+	1.23007i	−0.128244	+	0.128244i
$93$	1.28618	+	9.55750i	0.133371	+	0.991066i
$94$		−	12.0572i		−	1.24361i
$95$	7.68810	−	0.622652i	0.788782	−	0.0638828i
$96$	−1.53262	+	0.806900i	−0.156422	+	0.0823539i
$97$	10.5328	+	10.5328i	1.06945	+	1.06945i	0.997401	+	0.0720453i	$0.0229526\pi$
$97$	10.5328	+	10.5328i	1.06945	+	1.06945i	0.0720453	+	0.997401i	$0.477047\pi$
$98$	−0.686485	+	2.56200i	−0.0693454	+	0.258801i
$99$	−1.81085	−	0.141489i	−0.181997	−	0.0142202i
$100$	−4.67600	−	1.77060i	−0.467600	−	0.177060i
$101$		−	2.05829i		−	0.204807i	−0.994743	−	0.102404i	$-0.967347\pi$
$101$		−	2.05829i		−	0.204807i	0.994743	−	0.102404i	$-0.0326533\pi$
$102$	8.08883	+	8.74549i	0.800913	+	0.865933i
$103$	−0.139301	−	0.0373257i	−0.0137258	−	0.00367781i	0.251950	−	0.967740i	$-0.418928\pi$
$103$	−0.139301	−	0.0373257i	−0.0137258	−	0.00367781i	−0.265675	+	0.964063i	$0.585595\pi$
$104$	0.760541	+	1.31729i	0.0745771	+	0.129171i
$105$	−10.1599	+	6.44680i	−0.991509	+	0.629143i
$106$	−3.46872	−	6.00800i	−0.336912	−	0.583548i
$107$	−1.79627	−	6.70376i	−0.173652	−	0.648076i	−0.996777	−	0.0802174i	$-0.974439\pi$
$107$	−1.79627	−	6.70376i	−0.173652	−	0.648076i	0.823126	−	0.567859i	$-0.192228\pi$
$108$	−4.07790	+	3.22036i	−0.392396	+	0.309879i
$109$		−	8.73992i		−	0.837133i	−0.908186	−	0.418566i	$-0.862533\pi$
$109$		−	8.73992i		−	0.837133i	0.908186	−	0.418566i	$-0.137467\pi$
$110$	−0.454821	−	1.27516i	−0.0433655	−	0.121581i
$111$	3.68487	+	0.143738i	0.349752	+	0.0136430i
$112$	−3.00096	+	0.804106i	−0.283564	+	0.0759809i
$113$	0.628802	−	2.34672i	0.0591527	−	0.220761i	−0.930022	−	0.367504i	$-0.880212\pi$
$113$	0.628802	−	2.34672i	0.0591527	−	0.220761i	0.989175	+	0.146743i	$0.0468791\pi$
$114$	5.97013	+	0.232880i	0.559154	+	0.0218112i
$115$	−3.82630	−	0.700170i	−0.356804	−	0.0652912i
$116$		−	1.17381i		−	0.108986i
$117$	2.96555	+	3.46824i	0.274165	+	0.320639i
$118$	2.51392	+	9.38207i	0.231425	+	0.863690i
$119$	10.6841	+	18.5054i	0.979408	+	1.69638i
$120$	−3.43214	−	1.79455i	−0.313310	−	0.163820i
$121$	−5.31671	+	9.20881i	−0.483337	+	0.837165i
$122$	−6.91078	+	6.91078i	−0.625673	+	0.625673i
$123$	−13.7600	+	3.11764i	−1.24069	+	0.281108i
$124$	−5.05028	+	2.34408i	−0.453528	+	0.210504i
$125$	−2.68407	−	10.8534i	−0.240070	−	0.970756i
$126$	−8.41026	+	4.01732i	−0.749246	+	0.357891i
$127$	−12.1081	+	3.24437i	−1.07442	+	0.287891i	−0.752309	−	0.658810i	$-0.771060\pi$
$127$	−12.1081	+	3.24437i	−1.07442	+	0.287891i	−0.322114	+	0.946701i	$0.604393\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	0.791766	−	20.2978i	0.0697111	−	1.78712i
$130$	−1.45729	+	3.07323i	−0.127813	+	0.269540i
$131$	−11.9327	−	6.88934i	−1.04256	−	0.601925i	−0.122006	−	0.992529i	$-0.538933\pi$
$131$	−11.9327	−	6.88934i	−1.04256	−	0.601925i	−0.920558	+	0.390605i	$0.872266\pi$
$132$	−0.231730	−	1.02276i	−0.0201695	−	0.0890196i
$133$	10.3518	+	2.77375i	0.897612	+	0.240514i
$134$	2.29091	+	3.96798i	0.197905	+	0.342781i
$135$	−11.1070	−	3.41087i	−0.955940	−	0.293561i
$136$	−3.43890	+	5.95636i	−0.294884	+	0.510753i
$137$	−5.47725	−	1.46763i	−0.467953	−	0.125388i	0.0171345	−	0.999853i	$-0.494546\pi$
$137$	−5.47725	−	1.46763i	−0.467953	−	0.125388i	−0.485088	+	0.874466i	$0.661212\pi$
$138$	−2.87777	−	0.892683i	−0.244972	−	0.0759902i
$139$		−	12.3379i		−	1.04648i	−0.852184	−	0.523242i	$-0.824723\pi$
$139$		−	12.3379i		−	1.04648i	0.852184	−	0.523242i	$-0.175277\pi$
$140$	−5.29284	−	4.49975i	−0.447327	−	0.380298i
$141$	18.4791	−	9.72897i	1.55622	−	0.819327i
$142$	−2.08210	+	7.77049i	−0.174726	+	0.652085i
$143$	−0.889568	+	0.238359i	−0.0743894	+	0.0199326i
$144$	−2.47334	−	1.69782i	−0.206111	−	0.141485i
$145$	2.15972	−	1.49158i	0.179355	−	0.123869i
$146$	−5.18343	+	2.99265i	−0.428983	+	0.247674i
$147$	−4.48048	+	1.01516i	−0.369544	+	0.0837288i
$148$	0.551046	+	2.05653i	0.0452957	+	0.169046i
$149$	2.72304	−	4.71645i	0.223080	−	0.386387i	−0.732661	−	0.680593i	$-0.761722\pi$
$149$	2.72304	−	4.71645i	0.223080	−	0.386387i	0.955742	+	0.294207i	$0.0950554\pi$
$150$	−1.05941	−	8.59521i	−0.0865008	−	0.701796i
$151$	13.6207			1.10844			0.554219	−	0.832371i	$-0.313017\pi$
$151$	13.6207			1.10844			0.554219	+	0.832371i	$0.313017\pi$
$152$	0.892791	+	3.33194i	0.0724149	+	0.270256i
$153$	−6.87660	+	19.4538i	−0.555940	+	1.57275i
$154$		−	1.88105i		−	0.151579i
$155$	−10.7303	−	6.31346i	−0.861882	−	0.507110i
$156$	−1.40523	+	2.22854i	−0.112508	+	0.178426i
$157$	−10.4860	−	10.4860i	−0.836871	−	0.836871i	0.151575	−	0.988446i	$-0.451565\pi$
$157$	−10.4860	−	10.4860i	−0.836871	−	0.836871i	−0.988446	+	0.151575i	$0.951565\pi$
$158$	−0.256021	+	0.0686006i	−0.0203679	+	0.00545757i
$159$	6.40904	−	10.1641i	0.508270	−	0.806063i
$160$	0.402493	−	2.19955i	0.0318198	−	0.173889i
$161$	−4.68051	−	2.70230i	−0.368876	−	0.212971i
$162$	−8.22604	−	3.65135i	−0.646298	−	0.286877i
$163$	6.20797	−	6.20797i	0.486245	−	0.486245i	−0.420874	−	0.907119i	$-0.638276\pi$
$163$	6.20797	−	6.20797i	0.486245	−	0.486245i	0.907119	+	0.420874i	$0.138276\pi$
$164$	−4.07284	−	7.05436i	−0.318035	−	0.550853i
$165$	1.58733	−	1.72599i	0.123573	−	0.134368i
$166$	8.92299	+	15.4551i	0.692558	+	1.19955i
$167$	−1.55828	−	5.81558i	−0.120583	−	0.450023i	0.879060	−	0.476710i	$-0.158171\pi$
$167$	−1.55828	−	5.81558i	−0.120583	−	0.450023i	−0.999644	+	0.0266870i	$0.991504\pi$
$168$	−3.65386	−	3.95049i	−0.281902	−	0.304787i
$169$	−9.25462	−	5.34316i	−0.711894	−	0.411012i
$170$	−15.3291	+	1.24149i	−1.17569	+	0.0952177i
$171$	4.46039	+	9.33783i	0.341094	+	0.714082i
$172$	11.3282	−	3.03539i	0.863769	−	0.231446i
$173$	1.05712	−	3.94521i	0.0803711	−	0.299949i	−0.914026	−	0.405655i	$-0.867044\pi$
$173$	1.05712	−	3.94521i	0.0803711	−	0.299949i	0.994397	+	0.105706i	$0.0337102\pi$
$174$	1.79901	−	0.947152i	0.136382	−	0.0718034i
$175$	1.55351	−	15.4563i	0.117435	−	1.16838i
$176$	0.524341	−	0.302728i	0.0395237	−	0.0228190i
$177$	−12.3506	+	11.4233i	−0.928330	+	0.858626i
$178$	6.49884	−	6.49884i	0.487109	−	0.487109i
$179$	−1.73940	+	3.01273i	−0.130009	+	0.225182i	−0.923680	−	0.383165i	$-0.874834\pi$
$179$	−1.73940	+	3.01273i	−0.130009	+	0.225182i	0.793671	+	0.608347i	$0.208167\pi$
$180$	−0.0190325	−	6.70818i	−0.00141860	−	0.499998i
$181$	7.78822	+	13.4896i	0.578894	+	1.00267i	0.995607	+	0.0936352i	$0.0298487\pi$
$181$	7.78822	+	13.4896i	0.578894	+	1.00267i	−0.416713	+	0.909038i	$0.636818\pi$
$182$	−3.34160	+	3.34160i	−0.247696	+	0.247696i
$183$	−16.1679	−	5.01526i	−1.19516	−	0.370739i
$184$		−	1.73959i		−	0.128244i
$185$	−3.08363	+	3.62713i	−0.226713	+	0.266672i
$186$	−7.66764	−	5.84870i	−0.562219	−	0.428848i
$187$	−2.94454	−	2.94454i	−0.215326	−	0.215326i
$188$	8.52574	+	8.52574i	0.621803	+	0.621803i
$189$	−12.9432	−	9.64813i	−0.941483	−	0.701798i
$190$	−4.99602	+	5.87659i	−0.362450	+	0.426332i
$191$	−16.9972	+	9.81335i	−1.22988	+	0.710069i	−0.967004	−	0.254762i	$-0.918003\pi$
$191$	−16.9972	+	9.81335i	−1.22988	+	0.710069i	−0.262872	+	0.964831i	$0.584670\pi$
$192$	0.513158	−	1.65429i	0.0370340	−	0.119388i
$193$	4.05776	+	15.1438i	0.292084	+	1.09007i	0.943506	+	0.331356i	$0.107506\pi$
$193$	4.05776	+	15.1438i	0.292084	+	1.09007i	−0.651422	+	0.758715i	$0.725827\pi$
$194$	−14.8957			−1.06945
$195$	−5.88597	+	0.246324i	−0.421503	+	0.0176396i
$196$	−1.32619	−	2.29702i	−0.0947276	−	0.164073i
$197$	7.85843	+	2.10566i	0.559890	+	0.150022i	0.527656	−	0.849458i	$-0.323071\pi$
$197$	7.85843	+	2.10566i	0.559890	+	0.150022i	0.0322340	+	0.999480i	$0.489738\pi$
$198$	1.38051	−	1.18042i	0.0981087	−	0.0838885i
$199$	−9.33362	+	5.38877i	−0.661643	+	0.382000i	−0.792903	−	0.609348i	$-0.791431\pi$
$199$	−9.33362	+	5.38877i	−0.661643	+	0.382000i	0.131260	+	0.991348i	$0.458098\pi$
$200$	4.55844	−	2.05443i	0.322330	−	0.145270i
$201$	−4.23284	+	6.71285i	−0.298562	+	0.473488i
$202$	1.45543	+	1.45543i	0.102404	+	0.102404i
$203$	3.52258	−	0.943871i	0.247236	−	0.0662468i
$204$	−11.9037	−	0.464333i	−0.833423	−	0.0325098i
$205$	7.80406	−	16.4577i	0.545059	−	1.14946i
$206$	0.124894	−	0.0721077i	0.00870179	−	0.00502398i
$207$	−0.953938	−	5.13083i	−0.0663033	−	0.356617i
$208$	−1.46925	−	0.393685i	−0.101874	−	0.0272971i
$209$	−2.08851			−0.144465
$210$	2.62559	−	11.7427i	0.181183	−	0.810326i
$211$	9.30613	−	16.1187i	0.640660	−	1.10966i	−0.344625	−	0.938740i	$-0.611994\pi$
$211$	9.30613	−	16.1187i	0.640660	−	1.10966i	0.985286	−	0.170916i	$-0.0546727\pi$
$212$	6.70105	+	1.79554i	0.460230	+	0.123318i
$213$	−13.5892	+	3.07896i	−0.931118	+	0.210967i
$214$	6.01042	+	3.47012i	0.410864	+	0.237212i
$215$	19.9797	+	16.9859i	1.36261	+	1.15843i
$216$	0.606374	−	5.16065i	0.0412586	−	0.351138i
$217$	−11.0954	−	13.2708i	−0.753208	−	0.900882i
$218$	6.18006	+	6.18006i	0.418566	+	0.418566i
$219$	−8.76910	−	5.52943i	−0.592561	−	0.373644i
$220$	1.22328	+	0.580065i	0.0824735	+	0.0391080i
$221$			10.4617i			0.703731i
$222$	−2.70724	+	2.50396i	−0.181698	+	0.168055i
$223$	2.75660	+	10.2878i	0.184596	+	0.688921i	0.994717	+	0.102658i	$0.0327347\pi$
$223$	2.75660	+	10.2878i	0.184596	+	0.688921i	−0.810121	+	0.586263i	$0.800599\pi$
$224$	1.55341	−	2.69059i	0.103792	−	0.179773i
$225$	12.3183	−	8.55915i	0.821221	−	0.570610i
$226$	1.21475	+	2.10401i	0.0808041	+	0.139957i
$227$	−19.1018	−	5.11831i	−1.26783	−	0.339714i	−0.438631	−	0.898667i	$-0.644537\pi$
$227$	−19.1018	−	5.11831i	−1.26783	−	0.339714i	−0.829200	+	0.558953i	$0.811203\pi$
$228$	−4.38619	+	4.05685i	−0.290483	+	0.268671i
$229$	0.980323	+	0.565990i	0.0647815	+	0.0374016i	0.532041	−	0.846719i	$-0.321425\pi$
$229$	0.980323	+	0.565990i	0.0647815	+	0.0374016i	−0.467259	+	0.884120i	$0.654759\pi$
$230$	3.20070	−	2.21051i	0.211048	−	0.145756i
$231$	2.88292	−	1.51782i	0.189682	−	0.0998651i
$232$	0.830012	+	0.830012i	0.0544930	+	0.0544930i
$233$	12.8364	+	12.8364i	0.840938	+	0.840938i	0.988981	−	0.148043i	$-0.0472975\pi$
$233$	12.8364	+	12.8364i	0.840938	+	0.840938i	−0.148043	+	0.988981i	$0.547297\pi$
$234$	−4.54938	−	0.355461i	−0.297402	−	0.0232372i
$235$	−4.85294	+	26.5204i	−0.316571	+	1.73000i
$236$	−8.41174	−	4.85652i	−0.547557	−	0.316132i
$237$	−0.311722	−	0.337028i	−0.0202485	−	0.0218923i
$238$	−20.6401	−	5.53049i	−1.33790	−	0.358488i
$239$	5.09828	+	8.83048i	0.329780	+	0.571196i	0.982468	−	0.186431i	$-0.0596920\pi$
$239$	5.09828	+	8.83048i	0.329780	+	0.571196i	−0.652688	+	0.757627i	$0.726359\pi$
$240$	3.69583	−	1.15795i	0.238565	−	0.0747452i
$241$	−1.77740	+	3.07854i	−0.114492	+	0.198306i	−0.917577	−	0.397559i	$-0.869857\pi$
$241$	−1.77740	+	3.07854i	−0.114492	+	0.198306i	0.803084	+	0.595865i	$0.203191\pi$
$242$	−2.75213	−	10.2711i	−0.176914	−	0.660251i
$243$	−1.04148	−	15.5536i	−0.0668107	−	0.997766i
$244$		−	9.77332i		−	0.625673i
$245$	2.54114	−	5.35892i	0.162347	−	0.342369i
$246$	7.52525	−	11.9343i	0.479792	−	0.760901i
$247$	3.71014	+	3.71014i	0.236071	+	0.236071i
$248$	1.91357	−	5.22860i	0.121512	−	0.332016i
$249$	−16.4867	+	26.1462i	−1.04480	+	1.65695i
$250$	9.57242	+	5.77657i	0.605413	+	0.365343i
$251$	−4.43345	−	2.55966i	−0.279837	−	0.161564i	0.353513	−	0.935430i	$-0.384987\pi$
$251$	−4.43345	−	2.55966i	−0.279837	−	0.161564i	−0.633350	+	0.773866i	$0.718320\pi$
$252$	3.10628	−	8.78763i	0.195677	−	0.553568i
$253$	1.01735	+	0.272599i	0.0639605	+	0.0171382i
$254$	6.26763	−	10.8559i	0.393266	−	0.681157i
$255$	−14.2717	−	22.4918i	−0.893732	−	1.40849i
$256$	1.00000			0.0625000
$257$	19.5860	+	5.24805i	1.22174	+	0.327365i	0.811359	−	0.584549i	$-0.198728\pi$
$257$	19.5860	+	5.24805i	1.22174	+	0.327365i	0.410383	+	0.911913i	$0.365395\pi$
$258$	13.7928	+	14.9126i	0.858704	+	0.928415i
$259$	−5.72848	+	3.30734i	−0.355950	+	0.205508i
$260$	−1.14264	−	3.20356i	−0.0708636	−	0.198676i
$261$	2.90324	+	1.99293i	0.179706	+	0.123359i
$262$	13.3092	−	3.56619i	0.822244	−	0.220320i
$263$	−22.1635	−	22.1635i	−1.36666	−	1.36666i	−0.865151	−	0.501512i	$-0.832777\pi$
$263$	−22.1635	−	22.1635i	−1.36666	−	1.36666i	−0.501512	−	0.865151i	$-0.667223\pi$
$264$	0.887057	+	0.559341i	0.0545946	+	0.0344251i
$265$	5.21143	+	14.6110i	0.320136	+	0.897546i
$266$	−9.28114	+	5.35847i	−0.569063	+	0.328549i
$267$	15.2041	+	4.71631i	0.930479	+	0.288634i
$268$	−4.42570	−	1.18586i	−0.270343	−	0.0724381i
$269$	0.452756	+	0.784196i	0.0276050	+	0.0478133i	0.879498	−	0.475903i	$-0.157879\pi$
$269$	0.452756	+	0.784196i	0.0276050	+	0.0478133i	−0.851893	+	0.523716i	$0.824545\pi$
$270$	10.2657	−	5.44200i	0.624751	−	0.331190i
$271$	−12.9558			−0.787011			−0.393505	−	0.919322i	$-0.628738\pi$
$271$	−12.9558			−0.787011			−0.393505	+	0.919322i	$0.628738\pi$
$272$	−1.78011	−	6.64345i	−0.107935	−	0.402819i
$273$	−7.81773	−	2.42505i	−0.473150	−	0.146771i
$274$	4.91077	−	2.83523i	0.296670	−	0.171283i
$275$	0.487158	+	2.98783i	0.0293768	+	0.180173i
$276$	2.66612	−	1.40367i	0.160481	−	0.0844911i
$277$	4.87066	+	4.87066i	0.292650	+	0.292650i	0.838126	−	0.545477i	$-0.183651\pi$
$277$	4.87066	+	4.87066i	0.292650	+	0.292650i	−0.545477	+	0.838126i	$0.683651\pi$
$278$	8.72418	+	8.72418i	0.523242	+	0.523242i
$279$	2.77679	−	16.4709i	0.166242	−	0.986085i
$280$	6.92440	−	0.560801i	0.413812	−	0.0335143i
$281$		−	16.7235i		−	0.997639i	−0.866706	−	0.498819i	$-0.833767\pi$
$281$		−	16.7235i		−	0.997639i	0.866706	−	0.498819i	$-0.166233\pi$
$282$	−6.18726	+	19.9461i	−0.368446	+	1.18777i
$283$	−22.6680	+	22.6680i	−1.34747	+	1.34747i	−0.459079	+	0.888396i	$0.651820\pi$
$283$	−22.6680	+	22.6680i	−1.34747	+	1.34747i	−0.888396	+	0.459079i	$0.848180\pi$
$284$	−4.02230	−	6.96683i	−0.238680	−	0.413405i
$285$	−13.0378	−	2.91516i	−0.772295	−	0.172679i
$286$	0.460474	−	0.797565i	0.0272284	−	0.0471610i
$287$	17.8949	−	17.8949i	1.05630	−	1.05630i
$288$	2.94946	−	0.548371i	0.173798	−	0.0323131i
$289$	−26.2443	+	15.1521i	−1.54378	+	0.891302i
$290$	−0.472452	+	2.58186i	−0.0277433	+	0.151612i
$291$	−12.0193	−	22.8293i	−0.704585	−	1.33828i
$292$	1.54911	−	5.78136i	0.0906549	−	0.338329i
$293$	19.1703	−	5.13666i	1.11994	−	0.300087i	0.349081	−	0.937092i	$-0.386494\pi$
$293$	19.1703	−	5.13666i	1.11994	−	0.300087i	0.770859	+	0.637005i	$0.219827\pi$
$294$	2.45035	−	3.88600i	0.142907	−	0.226636i
$295$	−1.75326	−	21.6481i	−0.102079	−	1.26040i
$296$	−1.84384	−	1.06454i	−0.107171	−	0.0618751i
$297$	2.92306	+	1.16332i	0.169613	+	0.0675024i
$298$	1.40955	+	5.26051i	0.0816531	+	0.304733i
$299$	−1.32303	−	2.29155i	−0.0765125	−	0.132524i
$300$	6.82685	+	5.32861i	0.394148	+	0.307648i
$301$	18.2182	+	31.5548i	1.05008	+	1.81879i
$302$	−9.63130	+	9.63130i	−0.554219	+	0.554219i
$303$	−1.05623	+	3.40500i	−0.0606787	+	0.195612i
$304$	−2.98734	−	1.72474i	−0.171335	−	0.0989206i
$305$	17.9821	−	12.4190i	1.02965	−	0.711112i
$306$	−8.89343	−	18.6184i	−0.508403	−	1.06434i
$307$	−5.59386	+	1.49887i	−0.319259	+	0.0855451i	−0.414890	−	0.909872i	$-0.636180\pi$
$307$	−5.59386	+	1.49887i	−0.319259	+	0.0855451i	0.0956310	+	0.995417i	$0.469513\pi$
$308$	1.33010	+	1.33010i	0.0757896	+	0.0757896i
$309$	0.211291	+	0.133231i	0.0120199	+	0.00757925i
$310$	12.0518	−	3.12320i	0.684496	−	0.177386i
$311$			18.4397i			1.04562i	0.852449	+	0.522811i	$0.175117\pi$
$311$			18.4397i			1.04562i	−0.852449	+	0.522811i	$0.824883\pi$
$312$	−0.582172	−	2.56946i	−0.0329590	−	0.145467i
$313$	−1.61045	−	6.01029i	−0.0910281	−	0.339722i	0.905359	−	0.424647i	$-0.139602\pi$
$313$	−1.61045	−	6.01029i	−0.0910281	−	0.339722i	−0.996387	+	0.0849249i	$0.972935\pi$
$314$	14.8294			0.836871
$315$	20.1157	−	5.45120i	1.13339	−	0.307140i
$316$	0.132526	−	0.229542i	0.00745518	−	0.0129127i
$317$	−7.70317	−	28.7486i	−0.432653	−	1.61468i	−0.746620	−	0.665250i	$-0.768325\pi$
$317$	−7.70317	−	28.7486i	−0.432653	−	1.61468i	0.313967	−	0.949434i	$-0.398342\pi$
$318$	2.65521	+	11.7190i	0.148897	+	0.657166i
$319$	−0.615479	+	0.355347i	−0.0344602	+	0.0198956i
$320$	1.27071	+	1.83992i	0.0710347	+	0.102855i
$321$	−0.468547	+	12.0117i	−0.0261518	+	0.670428i
$322$	5.22043	−	1.39881i	0.290923	−	0.0779527i
$323$	−6.14045	+	22.9165i	−0.341664	+	1.27511i
$324$	8.39858	−	3.23479i	0.466588	−	0.179711i
$325$	4.44233	−	6.17316i	0.246416	−	0.342425i
$326$			8.77939i			0.486245i
$327$	−4.48497	+	14.4584i	−0.248019	+	0.799549i
$328$	7.86811	+	2.10826i	0.434444	+	0.116409i
$329$	−18.7298	+	32.4410i	−1.03261	+	1.78853i
$330$	0.0980477	+	2.34287i	0.00539735	+	0.128971i
$331$	−9.06716	−	15.7048i	−0.498376	−	0.863213i	0.501622	−	0.865087i	$-0.332737\pi$
$331$	−9.06716	−	15.7048i	−0.498376	−	0.863213i	−0.999998	+	0.00187384i	$0.999404\pi$
$332$	−17.2379	−	4.61888i	−0.946052	−	0.253494i
$333$	−6.02208	−	2.12871i	−0.330008	−	0.116652i
$334$	5.21411	+	3.01037i	0.285303	+	0.164720i
$335$	−3.44188	−	9.64982i	−0.188050	−	0.527226i
$336$	5.37709	+	0.209747i	0.293344	+	0.0114426i
$337$	−18.5113	−	18.5113i	−1.00837	−	1.00837i	−0.999965	−	0.00840756i	$-0.997324\pi$
$337$	−18.5113	−	18.5113i	−1.00837	−	1.00837i	−0.00840756	−	0.999965i	$-0.502676\pi$
$338$	10.3222	−	2.76582i	0.561453	−	0.150441i
$339$	−2.24446	+	3.55948i	−0.121902	+	0.193324i
$340$	9.96142	−	11.7171i	0.540234	−	0.635451i
$341$	2.75796	+	1.93845i	0.149352	+	0.104973i
$342$	−9.75681	−	3.44887i	−0.527588	−	0.186494i
$343$	−9.55112	+	9.55112i	−0.515712	+	0.515712i
$344$	−5.86392	+	10.1566i	−0.316161	+	0.547607i
$345$	5.97050	+	3.12178i	0.321441	+	0.168071i
$346$	2.04219	+	3.53718i	0.109789	+	0.190160i
$347$	5.14372	+	19.1966i	0.276129	+	1.03053i	0.955081	+	0.296345i	$0.0957679\pi$
$347$	5.14372	+	19.1966i	0.276129	+	1.03053i	−0.678952	+	0.734183i	$0.737565\pi$
$348$	−0.602353	+	1.94183i	−0.0322895	+	0.104093i
$349$			11.7379i			0.628313i	0.949371	+	0.314156i	$0.101722\pi$
$349$			11.7379i			0.628313i	−0.949371	+	0.314156i	$0.898278\pi$
$350$	9.83073	+	12.0277i	0.525474	+	0.642909i
$351$	−3.12611	−	7.25927i	−0.166859	−	0.387471i
$352$	−0.156704	+	0.584826i	−0.00835233	+	0.0311713i
$353$	2.85647	−	0.765388i	0.152034	−	0.0407375i	−0.181999	−	0.983299i	$-0.558257\pi$
$353$	2.85647	−	0.765388i	0.152034	−	0.0407375i	0.334033	+	0.942561i	$0.391590\pi$
$354$	0.655744	−	16.8107i	0.0348524	−	0.893478i
$355$	7.70723	−	16.2535i	0.409057	−	0.862647i
$356$			9.19075i			0.487109i
$357$	−8.17836	−	36.0958i	−0.432845	−	1.91039i
$358$	−0.900379	−	3.36026i	−0.0475865	−	0.177595i
$359$	12.4571	+	21.5763i	0.657459	+	1.13875i	0.981271	+	0.192631i	$0.0617021\pi$
$359$	12.4571	+	21.5763i	0.657459	+	1.13875i	−0.323812	+	0.946121i	$0.604965\pi$
$360$	4.75686	+	4.72994i	0.250708	+	0.249290i
$361$	−3.55055	−	6.14973i	−0.186871	−	0.323670i
$362$	−15.0457	−	4.03148i	−0.790784	−	0.211890i
$363$	13.5210	−	12.5057i	0.709666	−	0.656380i
$364$		−	4.72574i		−	0.247696i
$365$	12.6057	−	4.49618i	0.659813	−	0.235341i
$366$	14.9787	−	7.88609i	0.782951	−	0.412213i
$367$	−4.44658	+	16.5948i	−0.232109	+	0.866244i	0.747321	+	0.664463i	$0.231340\pi$
$367$	−4.44658	+	16.5948i	−0.232109	+	0.866244i	−0.979431	+	0.201781i	$0.935327\pi$
$368$	1.23007	+	1.23007i	0.0641220	+	0.0641220i
$369$	24.3628	+	1.90356i	1.26827	+	0.0990953i
$370$	−0.384312	−	4.74523i	−0.0199794	−	0.246693i
$371$			21.5534i			1.11900i
$372$	9.55750	−	1.28618i	0.495533	−	0.0666855i
$373$	−13.5755	+	13.5755i	−0.702912	+	0.702912i	−0.965035	−	0.262122i	$-0.915578\pi$
$373$	−13.5755	+	13.5755i	−0.702912	+	0.702912i	0.262122	+	0.965035i	$0.415578\pi$
$374$	4.16421			0.215326
$375$	−1.12928	+	19.3320i	−0.0583158	+	0.998298i
$376$	−12.0572			−0.621803
$377$	1.72463	+	0.462113i	0.0888229	+	0.0238000i
$378$	15.9745	−	2.33000i	0.821640	−	0.119842i
$379$	2.89244	+	1.66995i	0.148575	+	0.0857796i	0.572444	−	0.819944i	$-0.305995\pi$
$379$	2.89244	+	1.66995i	0.148575	+	0.0857796i	−0.423870	+	0.905723i	$0.639329\pi$
$380$	−0.622652	−	7.68810i	−0.0319414	−	0.394391i
$381$	21.6952	+	0.846277i	1.11148	+	0.0433561i
$382$	5.07976	−	18.9579i	0.259903	−	0.969972i
$383$	−3.01678	+	11.2588i	−0.154150	+	0.575297i	0.845026	+	0.534725i	$0.179585\pi$
$383$	−3.01678	+	11.2588i	−0.154150	+	0.575297i	−0.999177	+	0.0405722i	$0.987082\pi$
$384$	0.806900	+	1.53262i	0.0411770	+	0.0782110i
$385$	−0.757108	+	4.13745i	−0.0385858	+	0.210864i
$386$	−13.5775	−	7.83898i	−0.691077	−	0.398994i
$387$	−11.7258	+	33.1721i	−0.596055	+	1.68623i
$388$	10.5328	−	10.5328i	0.534723	−	0.534723i
$389$	−11.2469	+	19.4801i	−0.570238	+	0.987681i	0.426303	+	0.904580i	$0.359816\pi$
$389$	−11.2469	+	19.4801i	−0.570238	+	0.987681i	−0.996541	+	0.0831010i	$0.973518\pi$
$390$	3.98783	−	4.33619i	0.201932	−	0.219571i
$391$	5.98227	−	10.3616i	0.302536	−	0.524008i
$392$	2.56200	+	0.686485i	0.129400	+	0.0346727i
$393$	16.2048	+	17.5203i	0.817423	+	0.883783i
$394$	−7.04567	+	4.06782i	−0.354956	+	0.204934i
$395$	0.590741	−	0.0478436i	0.0297234	−	0.00240727i
$396$	−0.141489	+	1.81085i	−0.00711008	+	0.0909986i
$397$	9.78032	−	2.62063i	0.490860	−	0.131526i	−0.00489473	−	0.999988i	$-0.501558\pi$
$397$	9.78032	−	2.62063i	0.490860	−	0.131526i	0.495755	+	0.868462i	$0.334891\pi$
$398$	2.78943	−	10.4103i	0.139822	−	0.521821i
$399$	−15.7014	−	9.90067i	−0.786054	−	0.495653i
$400$	−1.77060	+	4.67600i	−0.0885301	+	0.233800i
$401$		−	1.43860i		−	0.0718402i	−0.999355	−	0.0359201i	$-0.988564\pi$
$401$		−	1.43860i		−	0.0718402i	0.999355	−	0.0359201i	$-0.0114362\pi$
$402$	−1.75363	−	7.73977i	−0.0874630	−	0.386025i
$403$	−1.45582	−	8.34296i	−0.0725196	−	0.415592i
$404$	−2.05829			−0.102404
$405$	16.6239	+	11.3422i	0.826048	+	0.563600i
$406$	−1.82342	+	3.15826i	−0.0904948	+	0.156742i
$407$	0.911506	−	0.911506i	0.0451817	−	0.0451817i
$408$	8.74549	−	8.08883i	0.432966	−	0.400457i
$409$	11.2048	+	6.46912i	0.554044	+	0.319877i	0.750751	−	0.660585i	$-0.229692\pi$
$409$	11.2048	+	6.46912i	0.554044	+	0.319877i	−0.196708	+	0.980462i	$0.563025\pi$
$410$	6.11906	+	17.1557i	0.302199	+	0.847258i
$411$	8.30783	+	5.23857i	0.409795	+	0.258400i
$412$	−0.0373257	+	0.139301i	−0.00183891	+	0.00686289i
$413$	7.81031	−	29.1485i	0.384320	−	1.43430i
$414$	4.30258	+	2.95351i	0.211460	+	0.145157i
$415$	−13.4060	−	37.5856i	−0.658073	−	1.84500i
$416$	1.31729	−	0.760541i	0.0645857	−	0.0372886i
$417$	−6.33127	+	20.4104i	−0.310044	+	0.999500i
$418$	1.47680	−	1.47680i	0.0722326	−	0.0722326i
$419$	−18.9241			−0.924503			−0.462252	−	0.886749i	$-0.652958\pi$
$419$	−18.9241			−0.924503			−0.462252	+	0.886749i	$0.652958\pi$
$420$	6.44680	+	10.1599i	0.314572	+	0.495754i
$421$	−1.20707	−	2.09070i	−0.0588288	−	0.101895i	0.835111	−	0.550081i	$-0.185403\pi$
$421$	−1.20707	−	2.09070i	−0.0588288	−	0.101895i	−0.893940	+	0.448187i	$0.852070\pi$
$422$	4.81721	+	17.9781i	0.234498	+	0.875158i
$423$	−35.5622	+	6.61183i	−1.72909	+	0.321478i
$424$	−6.00800	+	3.46872i	−0.291774	+	0.168456i
$425$	34.2166	+	3.43913i	1.65975	+	0.166822i
$426$	7.43188	−	11.7862i	0.360076	−	0.571042i
$427$	29.3294	−	7.85878i	1.41935	−	0.380313i
$428$	−6.70376	+	1.79627i	−0.324038	+	0.0868258i
$429$	1.59392	+	0.0621748i	0.0769550	+	0.00300183i
$430$	−26.1387	+	2.11695i	−1.26052	+	0.102088i
$431$	25.6104	+	14.7862i	1.23361	+	0.712226i	0.967781	−	0.251794i	$-0.0810204\pi$
$431$	25.6104	+	14.7862i	1.23361	+	0.712226i	0.265831	+	0.964020i	$0.414354\pi$
$432$	3.22036	+	4.07790i	0.154940	+	0.196198i
$433$	−16.7210	+	16.7210i	−0.803561	+	0.803561i	−0.983650	−	0.180089i	$-0.942361\pi$
$433$	−16.7210	+	16.7210i	−0.803561	+	0.803561i	0.180089	+	0.983650i	$0.442361\pi$
$434$	17.2296	+	1.53822i	0.827045	+	0.0738369i
$435$	−4.33822	+	1.35922i	−0.208002	+	0.0651694i
$436$	−8.73992			−0.418566
$437$	−1.55309	−	5.79619i	−0.0742942	−	0.277270i
$438$	10.1106	−	2.29079i	0.483102	−	0.109458i
$439$	−11.5847	+	6.68842i	−0.552907	+	0.319221i	−0.750294	−	0.661105i	$-0.770088\pi$
$439$	−11.5847	+	6.68842i	−0.552907	+	0.319221i	0.197387	+	0.980326i	$0.436755\pi$
$440$	−1.27516	+	0.454821i	−0.0607907	+	0.0216827i
$441$	7.93294	+	0.619832i	0.377759	+	0.0295158i
$442$	−7.39754	−	7.39754i	−0.351865	−	0.351865i
$443$	−2.71529	+	10.1336i	−0.129007	+	0.481462i	−0.999951	−	0.00992151i	$-0.996842\pi$
$443$	−2.71529	+	10.1336i	−0.129007	+	0.481462i	0.870944	+	0.491383i	$0.163509\pi$
$444$	0.143738	−	3.68487i	0.00682149	−	0.174876i
$445$	−16.9102	+	11.6788i	−0.801622	+	0.553626i
$446$	−9.22377	−	5.32535i	−0.436758	−	0.252162i
$447$	−6.92498	+	6.40501i	−0.327540	+	0.302947i
$448$	0.804106	+	3.00096i	0.0379904	+	0.141782i
$449$	−38.5539			−1.81947			−0.909735	−	0.415190i	$-0.863715\pi$
$449$	−38.5539			−1.81947			−0.909735	+	0.415190i	$0.863715\pi$
$450$	−2.65813	+	14.7626i	−0.125305	+	0.695916i
$451$	−2.46592	+	4.27111i	−0.116116	+	0.201119i
$452$	−2.34672	−	0.628802i	−0.110380	−	0.0295764i
$453$	−22.5326	−	6.98958i	−1.05867	−	0.328399i
$454$	17.1262	−	9.88782i	0.803773	−	0.464058i
$455$	8.69497	−	6.00503i	0.407626	−	0.281520i
$456$	0.232880	−	5.97013i	0.0109056	−	0.279577i
$457$	−25.4484	−	25.4484i	−1.19043	−	1.19043i	−0.976948	−	0.213480i	$-0.931520\pi$
$457$	−25.4484	−	25.4484i	−1.19043	−	1.19043i	−0.213480	−	0.976948i	$-0.568480\pi$
$458$	−1.09341	+	0.292978i	−0.0510916	+	0.0136900i
$459$	21.3588	−	28.6534i	0.996942	−	1.33743i
$460$	−0.700170	+	3.82630i	−0.0326456	+	0.178402i
$461$			14.5175i			0.676146i	0.941120	+	0.338073i	$0.109775\pi$
$461$			14.5175i			0.676146i	−0.941120	+	0.338073i	$0.890225\pi$
$462$	−0.965276	+	3.11180i	−0.0449087	+	0.144774i
$463$	19.1679	−	19.1679i	0.890809	−	0.890809i	−0.103791	−	0.994599i	$-0.533097\pi$
$463$	19.1679	−	19.1679i	0.890809	−	0.890809i	0.994599	+	0.103791i	$0.0330972\pi$
$464$	−1.17381			−0.0544930
$465$	14.5113	+	15.9507i	0.672944	+	0.739694i
$466$	−18.1533			−0.840938
$467$	−6.25230	+	6.25230i	−0.289322	+	0.289322i	−0.836812	−	0.547490i	$-0.815583\pi$
$467$	−6.25230	+	6.25230i	−0.289322	+	0.289322i	0.547490	+	0.836812i	$0.315583\pi$
$468$	3.46824	−	2.96555i	0.160320	−	0.137082i
$469$		−	14.2349i		−	0.657308i
$470$	−15.3212	−	22.1843i	−0.706714	−	1.02329i
$471$	11.9658	+	22.7278i	0.551357	+	1.04724i
$472$	9.38207	−	2.51392i	0.431845	−	0.115712i
$473$	−5.02095	−	5.02095i	−0.230863	−	0.230863i
$474$	0.458735	+	0.0178941i	0.0210704	+	0.000821904i
$475$	13.3543	−	10.9150i	0.612736	−	0.500813i
$476$	18.5054	−	10.6841i	0.848192	−	0.489704i
$477$	−15.8182	+	13.5254i	−0.724264	+	0.619287i
$478$	−9.84912	−	2.63906i	−0.450488	−	0.120708i
$479$	−13.9592	+	24.1780i	−0.637811	+	1.10472i	0.348101	+	0.937457i	$0.386827\pi$
$479$	−13.9592	+	24.1780i	−0.637811	+	1.10472i	−0.985912	+	0.167264i	$0.946507\pi$
$480$	−1.79455	+	3.43214i	−0.0819098	+	0.156655i
$481$	−3.23850			−0.147663
$482$	−0.920048	−	3.43367i	−0.0419071	−	0.156399i
$483$	6.35621	+	6.87222i	0.289218	+	0.312697i
$484$	9.20881	+	5.31671i	0.418582	+	0.241669i
$485$	32.7637	+	5.99540i	1.48772	+	0.272237i
$486$	11.7345	+	10.2616i	0.532288	+	0.465477i
$487$	−2.47049	+	9.22000i	−0.111949	+	0.417798i	−0.999041	−	0.0437947i	$-0.986055\pi$
$487$	−2.47049	+	9.22000i	−0.111949	+	0.417798i	0.887092	+	0.461593i	$0.152722\pi$
$488$	6.91078	+	6.91078i	0.312836	+	0.312836i
$489$	−13.4554	+	7.08409i	−0.608476	+	0.320354i
$490$	1.99247	+	5.58618i	0.0900107	+	0.252358i
$491$	24.1750	−	13.9575i	1.09100	−	0.629891i	0.157160	−	0.987573i	$-0.449766\pi$
$491$	24.1750	−	13.9575i	1.09100	−	0.629891i	0.933844	+	0.357682i	$0.116433\pi$
$492$	3.11764	+	13.7600i	0.140554	+	0.620346i
$493$	2.08952	+	7.79818i	0.0941071	+	0.351213i
$494$	−5.24694			−0.236071
$495$	−3.51161	+	2.04073i	−0.157835	+	0.0917242i
$496$	2.34408	+	5.05028i	0.105252	+	0.226764i
$497$	17.6728	−	17.6728i	0.792735	−	0.792735i
$498$	−6.83030	−	30.1460i	−0.306073	−	1.35088i
$499$	0.843617	+	0.487063i	0.0377655	+	0.0218039i	0.518764	−	0.854918i	$-0.326392\pi$
$499$	0.843617	+	0.487063i	0.0377655	+	0.0218039i	−0.480998	+	0.876721i	$0.659726\pi$
$500$	−10.8534	+	2.68407i	−0.485378	+	0.120035i
$501$	−0.406470	+	10.4203i	−0.0181597	+	0.465544i
$502$	4.94487	−	1.32498i	0.220701	−	0.0591365i
$503$	31.7720	−	8.51327i	1.41664	−	0.379588i	0.532351	−	0.846524i	$-0.321309\pi$
$503$	31.7720	−	8.51327i	1.41664	−	0.379588i	0.884291	+	0.466936i	$0.154642\pi$
$504$	4.01732	+	8.41026i	0.178946	+	0.374623i
$505$	−2.61548	−	3.78708i	−0.116387	−	0.168523i
$506$	−0.912135	+	0.526621i	−0.0405494	+	0.0234112i
$507$	12.5679	+	13.5882i	0.558161	+	0.603473i
$508$	3.24437	+	12.1081i	0.143945	+	0.537212i
$509$	7.51993	+	13.0249i	0.333315	+	0.577318i	0.983160	−	0.182749i	$-0.0584994\pi$
$509$	7.51993	+	13.0249i	0.333315	+	0.577318i	−0.649845	+	0.760067i	$0.725166\pi$
$510$	25.9958	+	5.81246i	1.15111	+	0.257380i
$511$	18.5953			0.822608
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−2.58698	−	17.7363i	−0.114218	−	0.783079i
$514$	−17.5603	+	10.1385i	−0.774553	+	0.447188i
$515$	−0.303733	+	0.108335i	−0.0133841	+	0.00477382i
$516$	−20.2978	−	0.791766i	−0.893560	−	0.0348556i
$517$	1.88941	−	7.05137i	0.0830961	−	0.310119i
$518$	1.71201	−	6.38929i	0.0752212	−	0.280729i
$519$	−3.77329	+	5.98405i	−0.165629	+	0.262671i
$520$	3.07323	+	1.45729i	0.134770	+	0.0639064i
$521$	−14.8902	−	8.59688i	−0.652353	−	0.376636i	0.137004	−	0.990570i	$-0.456253\pi$
$521$	−14.8902	−	8.59688i	−0.652353	−	0.376636i	−0.789357	+	0.613934i	$0.789586\pi$
$522$	−3.46211	+	0.643686i	−0.151533	+	0.0281734i
$523$	−18.6692	+	18.6692i	−0.816345	+	0.816345i	−0.985576	−	0.169231i	$-0.945872\pi$
$523$	−18.6692	+	18.6692i	−0.816345	+	0.816345i	0.169231	+	0.985576i	$0.445872\pi$
$524$	−6.88934	+	11.9327i	−0.300962	+	0.521282i
$525$	−10.5015	+	24.7719i	−0.458322	+	1.08113i
$526$	31.3440			1.36666
$527$	29.3786	−	24.5628i	1.27975	−	1.06997i
$528$	−1.02276	+	0.231730i	−0.0445098	+	0.0100847i
$529$		−	19.9738i		−	0.868428i
$530$	−14.0166	−	6.64650i	−0.608841	−	0.288705i
$531$	26.2934	−	12.5595i	1.14104	−	0.545038i
$532$	2.77375	−	10.3518i	0.120257	−	0.448806i
$533$	11.9680	−	3.20683i	0.518393	−	0.138903i
$534$	−14.0859	+	7.41602i	−0.609556	+	0.320923i
$535$	−11.8235	−	10.0518i	−0.511174	−	0.434579i
$536$	3.96798	−	2.29091i	0.171390	−	0.0989523i
$537$	4.42347	−	4.09133i	0.190887	−	0.176554i
$538$	−0.874657	−	0.234364i	−0.0377091	−	0.0101041i
$539$	−0.802948	+	1.39075i	−0.0345854	+	0.0599037i
$540$	−3.41087	+	11.1070i	−0.146781	+	0.477970i
$541$	4.72570	−	8.18515i	0.203174	−	0.351907i	−0.746376	−	0.665525i	$-0.768208\pi$
$541$	4.72570	−	8.18515i	0.203174	−	0.351907i	0.949549	+	0.313618i	$0.101541\pi$
$542$	9.16115	−	9.16115i	0.393505	−	0.393505i
$543$	−5.96166	−	26.3123i	−0.255839	−	1.12917i
$544$	5.95636	+	3.43890i	0.255377	+	0.147442i
$545$	−11.1059	−	16.0808i	−0.475724	−	0.688824i
$546$	7.24274	−	3.81320i	0.309961	−	0.163190i
$547$	5.66056	−	21.1255i	0.242028	−	0.903261i	−0.732826	−	0.680416i	$-0.761799\pi$
$547$	5.66056	−	21.1255i	0.242028	−	0.903261i	0.974854	−	0.222845i	$-0.0715343\pi$
$548$	−1.46763	+	5.47725i	−0.0626938	+	0.233977i
$549$	24.1727	+	16.5934i	1.03167	+	0.708188i
$550$	−2.45719	−	1.76824i	−0.104775	−	0.0753980i
$551$	3.50658	+	2.02452i	0.149385	+	0.0862476i
$552$	−0.892683	+	2.87777i	−0.0379951	+	0.122486i
$553$	0.795412	+	0.213130i	0.0338244	+	0.00906321i
$554$	−6.88815			−0.292650
$555$	6.96251	−	4.41793i	0.295542	−	0.187531i
$556$	−12.3379			−0.523242
$557$	−23.0760	+	23.0760i	−0.977763	+	0.977763i	−0.999758	−	0.0219946i	$-0.992998\pi$
$557$	−23.0760	+	23.0760i	−0.977763	+	0.977763i	0.0219946	+	0.999758i	$0.492998\pi$
$558$	9.68317	+	13.6101i	0.409921	+	0.576164i
$559$			17.8390i			0.754509i
$560$	−4.49975	+	5.29284i	−0.190149	+	0.223663i
$561$	3.36011	+	6.38214i	0.141864	+	0.269454i
$562$	11.8253	+	11.8253i	0.498819	+	0.498819i
$563$	−7.30718	+	27.2708i	−0.307961	+	1.14933i	0.622405	+	0.782695i	$0.286155\pi$
$563$	−7.30718	+	27.2708i	−0.307961	+	1.14933i	−0.930366	+	0.366631i	$0.880511\pi$
$564$	−9.72897	−	18.4791i	−0.409664	−	0.778110i
$565$	−1.82505	−	5.11680i	−0.0767806	−	0.215265i
$566$		−	32.0574i		−	1.34747i
$567$	16.4608	+	22.6027i	0.691290	+	0.949225i
$568$	7.77049	+	2.08210i	0.326042	+	0.0873628i
$569$	−11.4442	−	19.8219i	−0.479764	−	0.830976i	0.519966	−	0.854187i	$-0.325944\pi$
$569$	−11.4442	−	19.8219i	−0.479764	−	0.830976i	−0.999731	+	0.0232107i	$0.992611\pi$
$570$	11.2805	−	7.15781i	0.472487	−	0.299808i
$571$	−3.78375	−	6.55365i	−0.158345	−	0.274262i	0.775927	−	0.630823i	$-0.217282\pi$
$571$	−3.78375	−	6.55365i	−0.158345	−	0.274262i	−0.934272	+	0.356561i	$0.883949\pi$
$572$	0.238359	+	0.889568i	0.00996629	+	0.0371947i
$573$	33.1541	−	7.51184i	1.38503	−	0.313812i
$574$			25.3072i			1.05630i
$575$	−7.92979	+	3.57385i	−0.330695	+	0.149040i
$576$	−1.69782	+	2.47334i	−0.0707426	+	0.103056i
$577$	−26.9834	+	7.23017i	−1.12333	+	0.300996i	−0.772231	−	0.635342i	$-0.780859\pi$
$577$	−26.9834	+	7.23017i	−1.12333	+	0.300996i	−0.351101	+	0.936338i	$0.614193\pi$
$578$	7.84332	−	29.2717i	0.326239	−	1.21754i
$579$	1.05845	−	27.1344i	0.0439875	−	1.12767i
$580$	−1.49158	−	2.15972i	−0.0619343	−	0.0896776i
$581$		−	55.4444i		−	2.30022i
$582$	24.6417	+	7.64384i	1.02143	+	0.316847i
$583$	−1.08712	−	4.05719i	−0.0450240	−	0.168032i
$584$	2.99265	+	5.18343i	0.123837	+	0.214492i
$585$	9.86349	+	2.61294i	0.407805	+	0.108032i
$586$	−9.92327	+	17.1876i	−0.409927	+	0.710014i
$587$	21.8218	−	21.8218i	0.900681	−	0.900681i	−0.0948138	−	0.995495i	$-0.530226\pi$
$587$	21.8218	−	21.8218i	0.900681	−	0.900681i	0.995495	+	0.0948138i	$0.0302256\pi$
$588$	1.01516	+	4.48048i	0.0418644	+	0.184772i
$589$	1.70787	−	19.1298i	0.0703716	−	0.788230i
$590$	16.5473	+	14.0678i	0.681241	+	0.579162i
$591$	−11.9196	−	7.51598i	−0.490305	−	0.309166i
$592$	2.05653	−	0.551046i	0.0845230	−	0.0226479i
$593$	14.9012	+	14.9012i	0.611921	+	0.611921i	0.943446	−	0.331526i	$-0.107563\pi$
$593$	14.9012	+	14.9012i	0.611921	+	0.611921i	−0.331526	+	0.943446i	$0.607563\pi$
$594$	−2.88950	+	1.24433i	−0.118558	+	0.0510554i
$595$	43.1728	+	20.4720i	1.76991	+	0.839271i
$596$	−4.71645	−	2.72304i	−0.193193	−	0.111540i
$597$	18.2058	−	4.12495i	0.745113	−	0.168823i
$598$	2.55589	+	0.684848i	0.104518	+	0.0280055i
$599$	13.4439	+	23.2855i	0.549302	+	0.951418i	0.998323	+	0.0578971i	$0.0184395\pi$
$599$	13.4439	+	23.2855i	0.549302	+	0.951418i	−0.449021	+	0.893521i	$0.648227\pi$
$600$	−8.59521	+	1.05941i	−0.350898	+	0.0432504i
$601$	−16.7975	+	29.0941i	−0.685185	+	1.18677i	0.288194	+	0.957572i	$0.406945\pi$
$601$	−16.7975	+	29.0941i	−0.685185	+	1.18677i	−0.973379	+	0.229203i	$0.926388\pi$
$602$	−35.1948	−	9.43042i	−1.43443	−	0.384355i
$603$	10.4471	−	8.93287i	0.425439	−	0.363774i
$604$		−	13.6207i		−	0.554219i
$605$	1.91940	+	23.6995i	0.0780346	+	0.963520i
$606$	−1.66083	−	3.15456i	−0.0674667	−	0.128145i
$607$	−4.29967	+	16.0466i	−0.174518	+	0.651311i	0.822115	+	0.569321i	$0.192794\pi$
$607$	−4.29967	+	16.0466i	−0.174518	+	0.651311i	−0.996633	+	0.0819893i	$0.973873\pi$
$608$	3.33194	−	0.892791i	0.135128	−	0.0362074i
$609$	−6.31171	−	0.246204i	−0.255763	−	0.00997670i
$610$	−3.93369	+	21.4969i	−0.159270	+	0.870382i
$611$	−15.8829	+	9.17000i	−0.642554	+	0.370979i
$612$	19.4538	+	6.87660i	0.786374	+	0.277970i
$613$	−8.95107	−	33.4058i	−0.361530	−	1.34925i	−0.872064	−	0.489392i	$-0.837219\pi$
$613$	−8.95107	−	33.4058i	−0.361530	−	1.34925i	0.510534	−	0.859858i	$-0.329448\pi$
$614$	2.89560	−	5.01532i	0.116857	−	0.202402i
$615$	−21.3556	+	23.2211i	−0.861140	+	0.936365i
$616$	−1.88105			−0.0757896
$617$	−8.27243	−	30.8731i	−0.333036	−	1.24291i	−0.905983	−	0.423314i	$-0.860867\pi$
$617$	−8.27243	−	30.8731i	−0.333036	−	1.24291i	0.572948	−	0.819592i	$-0.305800\pi$
$618$	−0.243614	+	0.0551964i	−0.00979958	+	0.00222033i
$619$			24.3390i			0.978267i	0.872209	+	0.489134i	$0.162687\pi$
$619$			24.3390i			0.978267i	−0.872209	+	0.489134i	$0.837313\pi$
$620$	−6.31346	+	10.7303i	−0.253555	+	0.430941i
$621$	−1.05484	+	8.97739i	−0.0423293	+	0.360250i
$622$	−13.0389	−	13.0389i	−0.522811	−	0.522811i
$623$	−27.5811	+	7.39034i	−1.10501	+	0.296088i
$624$	2.22854	+	1.40523i	0.0892131	+	0.0562541i
$625$	−18.7299	−	16.5587i	−0.749198	−	0.662347i
$626$	5.38868	+	3.11115i	0.215375	+	0.124347i
$627$	3.45499	+	1.07174i	0.137979	+	0.0428010i
$628$	−10.4860	+	10.4860i	−0.418435	+	0.418435i
$629$	−7.32170	−	12.6816i	−0.291935	−	0.505647i
$630$	−10.3694	+	18.0785i	−0.413125	+	0.720266i
$631$	−13.6606	−	23.6609i	−0.543820	−	0.941924i	−0.998680	−	0.0513609i	$-0.983644\pi$
$631$	−13.6606	−	23.6609i	−0.543820	−	0.941924i	0.454860	−	0.890563i	$-0.349689\pi$
$632$	0.0686006	+	0.256021i	0.00272878	+	0.0101840i
$633$	−23.6665	+	21.8894i	−0.940657	+	0.870027i
$634$	25.7753	+	14.8814i	1.02367	+	0.591015i
$635$	−18.1553	+	21.3553i	−0.720473	+	0.847458i
$636$	−10.1641	−	6.40904i	−0.403032	−	0.254135i
$637$	3.89700	−	1.04420i	0.154405	−	0.0413727i
$638$	0.183941	−	0.686477i	0.00728229	−	0.0271779i
$639$	24.0605	+	1.87994i	0.951817	+	0.0743693i
$640$	−2.19955	−	0.402493i	−0.0869447	−	0.0159099i
$641$	10.9386	−	6.31540i	0.432048	−	0.249443i	−0.268170	−	0.963371i	$-0.586419\pi$
$641$	10.9386	−	6.31540i	0.432048	−	0.249443i	0.700219	+	0.713928i	$0.253086\pi$
$642$	−8.16225	−	8.82487i	−0.322138	−	0.348290i
$643$	11.5945	−	11.5945i	0.457241	−	0.457241i	−0.440508	−	0.897749i	$-0.645202\pi$
$643$	11.5945	−	11.5945i	0.457241	−	0.457241i	0.897749	+	0.440508i	$0.145202\pi$
$644$	−2.70230	+	4.68051i	−0.106485	+	0.184438i
$645$	−24.3358	−	38.3524i	−0.958220	−	1.51012i
$646$	−11.8624	−	20.5463i	−0.466721	−	0.808385i
$647$	−14.9469	+	14.9469i	−0.587623	+	0.587623i	−0.936987	−	0.349364i	$-0.886398\pi$
$647$	−14.9469	+	14.9469i	−0.587623	+	0.587623i	0.349364	+	0.936987i	$0.386398\pi$
$648$	−3.65135	+	8.22604i	−0.143439	+	0.323149i
$649$			5.88082i			0.230842i
$650$	1.22388	+	7.50628i	0.0480046	+	0.294421i
$651$	11.5450	+	27.6475i	0.452485	+	1.08359i
$652$	−6.20797	−	6.20797i	−0.243123	−	0.243123i
$653$	1.79103	+	1.79103i	0.0700883	+	0.0700883i	0.741282	−	0.671194i	$-0.234218\pi$
$653$	1.79103	+	1.79103i	0.0700883	+	0.0700883i	−0.671194	+	0.741282i	$0.734218\pi$
$654$	−7.05225	−	13.3949i	−0.275765	−	0.523784i
$655$	−30.7095	+	2.48714i	−1.19992	+	0.0971805i
$656$	−7.05436	+	4.07284i	−0.275426	+	0.159018i
$657$	11.6691	+	13.6472i	0.455256	+	0.532428i
$658$	−9.69528	−	36.1833i	−0.377961	−	1.41057i
$659$	21.4943			0.837299			0.418650	−	0.908148i	$-0.362504\pi$
$659$	21.4943			0.837299			0.418650	+	0.908148i	$0.362504\pi$
$660$	−1.72599	−	1.58733i	−0.0671841	−	0.0617867i
$661$	−24.6453	−	42.6870i	−0.958593	−	1.66033i	−0.725923	−	0.687776i	$-0.758587\pi$
$661$	−24.6453	−	42.6870i	−0.958593	−	1.66033i	−0.232670	−	0.972556i	$-0.574746\pi$
$662$	17.5164	+	4.69351i	0.680795	+	0.182418i
$663$	5.36851	−	17.3067i	0.208496	−	0.672136i
$664$	15.4551	−	8.92299i	0.599773	−	0.346279i
$665$	22.5710	−	8.05060i	0.875267	−	0.312189i
$666$	5.76347	−	2.75303i	0.223330	−	0.106678i
$667$	−1.44388	−	1.44388i	−0.0559071	−	0.0559071i
$668$	−5.81558	+	1.55828i	−0.225012	+	0.0602917i
$669$	0.719046	−	18.4335i	0.0277999	−	0.712681i
$670$	9.25723	+	4.38967i	0.357638	+	0.169588i
$671$	−5.12455	+	2.95866i	−0.197831	+	0.114218i
$672$	−3.95049	+	3.65386i	−0.152394	+	0.140951i
$673$	17.7503	+	4.75617i	0.684223	+	0.183337i	0.584153	−	0.811643i	$-0.301427\pi$
$673$	17.7503	+	4.75617i	0.684223	+	0.183337i	0.100070	+	0.994980i	$0.468093\pi$
$674$	26.1789			1.00837
$675$	−24.7702	+	7.83806i	−0.953407	+	0.301687i
$676$	−5.34316	+	9.25462i	−0.205506	+	0.355947i
$677$	6.34960	+	1.70137i	0.244035	+	0.0653889i	0.378763	−	0.925494i	$-0.376350\pi$
$677$	6.34960	+	1.70137i	0.244035	+	0.0653889i	−0.134728	+	0.990883i	$0.543016\pi$
$678$	−0.929858	−	4.10400i	−0.0357110	−	0.157613i
$679$	40.0782	+	23.1391i	1.53806	+	0.887998i
$680$	1.24149	+	15.3291i	0.0476089	+	0.587843i
$681$	28.9734	+	18.2694i	1.11026	+	0.700085i
$682$	−3.32086	+	0.579480i	−0.127162	+	0.0221894i
$683$	−6.72436	−	6.72436i	−0.257301	−	0.257301i	0.566655	−	0.823955i	$-0.308237\pi$
$683$	−6.72436	−	6.72436i	−0.257301	−	0.257301i	−0.823955	+	0.566655i	$0.808237\pi$
$684$	9.33783	−	4.46039i	0.357041	−	0.170547i
$685$	−11.9426	+	4.25968i	−0.456304	+	0.162754i
$686$		−	13.5073i		−	0.515712i
$687$	−1.33129	−	1.43937i	−0.0507920	−	0.0549154i
$688$	−3.03539	−	11.3282i	−0.115723	−	0.431884i
$689$	−5.27620	+	9.13865i	−0.201007	+	0.348155i
$690$	−6.42921	+	2.01435i	−0.244756	+	0.0766849i
$691$	−3.00833	−	5.21057i	−0.114442	−	0.198220i	0.803114	−	0.595825i	$-0.203175\pi$
$691$	−3.00833	−	5.21057i	−0.114442	−	0.198220i	−0.917557	+	0.397605i	$0.869841\pi$
$692$	−3.94521	−	1.05712i	−0.149974	−	0.0401855i
$693$	−5.54807	+	1.03151i	−0.210754	+	0.0391839i
$694$	−17.2112	−	9.93690i	−0.653329	−	0.377199i
$695$	−15.6778	−	22.7006i	−0.594693	−	0.861085i
$696$	−0.947152	−	1.79901i	−0.0359017	−	0.0681912i
$697$	39.6152	+	39.6152i	1.50053	+	1.50053i
$698$	−8.29992	−	8.29992i	−0.314156	−	0.314156i
$699$	−14.6479	−	27.8221i	−0.554036	−	1.05233i
$700$	−15.4563	−	1.55351i	−0.584192	−	0.0587173i
$701$	21.2051	+	12.2428i	0.800905	+	0.462403i	0.843788	−	0.536677i	$-0.180321\pi$
$701$	21.2051	+	12.2428i	0.800905	+	0.462403i	−0.0428825	+	0.999080i	$0.513654\pi$
$702$	7.34357	+	2.92259i	0.277165	+	0.110306i
$703$	−7.09397	−	1.90082i	−0.267554	−	0.0716909i
$704$	−0.302728	−	0.524341i	−0.0114095	−	0.0197618i
$705$	21.6373	−	41.3820i	0.814909	−	1.55854i
$706$	−1.47862	+	2.56104i	−0.0556484	+	0.0963859i
$707$	−1.65508	−	6.17685i	−0.0622457	−	0.232304i
$708$	11.4233	+	12.3506i	0.429313	+	0.464165i
$709$		−	28.2577i		−	1.06124i	−0.847610	−	0.530620i	$-0.821959\pi$
$709$		−	28.2577i		−	1.06124i	0.847610	−	0.530620i	$-0.178041\pi$
$710$	6.04313	+	16.9428i	0.226795	+	0.635852i
$711$	0.342729	+	0.717503i	0.0128533	+	0.0269085i
$712$	−6.49884	−	6.49884i	−0.243554	−	0.243554i
$713$	−3.32882	+	9.09559i	−0.124665	+	0.340633i
$714$	31.3066	+	19.7406i	1.17162	+	0.738775i
$715$	−1.33385	+	1.56894i	−0.0498831	+	0.0586751i
$716$	3.01273	+	1.73940i	0.112591	+	0.0650044i
$717$	−3.90259	−	17.2244i	−0.145745	−	0.643256i
$718$	−24.0652	−	6.44826i	−0.898106	−	0.240647i
$719$	−1.76274	+	3.05316i	−0.0657392	+	0.113864i	−0.897022	−	0.441987i	$-0.854274\pi$
$719$	−1.76274	+	3.05316i	−0.0657392	+	0.113864i	0.831282	+	0.555850i	$0.187607\pi$
$720$	−6.70818	+	0.0190325i	−0.249999	+	0.000709300i
$721$	−0.448052			−0.0166863
$722$	6.85913	+	1.83790i	0.255270	+	0.0683995i
$723$	4.52011	−	4.18071i	0.168105	−	0.155482i
$724$	13.4896	−	7.78822i	0.501337	−	0.289447i
$725$	2.07836	−	5.48876i	0.0771883	−	0.203847i
$726$	−0.717880	+	18.4036i	−0.0266430	+	0.683023i
$727$	5.29500	−	1.41879i	0.196381	−	0.0526200i	−0.159288	−	0.987232i	$-0.550920\pi$
$727$	5.29500	−	1.41879i	0.196381	−	0.0526200i	0.355669	+	0.934612i	$0.384253\pi$
$728$	3.34160	+	3.34160i	0.123848	+	0.123848i
$729$	−6.25857	+	26.2646i	−0.231799	+	0.972764i
$730$	−5.73430	+	12.0929i	−0.212236	+	0.447577i
$731$	−69.8552	+	40.3309i	−2.58369	+	1.49169i
$732$	−5.01526	+	16.1679i	−0.185369	+	0.597582i
$733$	42.2152	+	11.3115i	1.55925	+	0.417801i	0.932427	−	0.361358i	$-0.117687\pi$
$733$	42.2152	+	11.3115i	1.55925	+	0.417801i	0.626826	+	0.779159i	$0.284353\pi$
$734$	−8.59012	−	14.8785i	−0.317067	−	0.549177i
$735$	−6.95375	+	7.56119i	−0.256493	+	0.278899i
$736$	−1.73959			−0.0641220
$737$	0.717988	+	2.67957i	0.0264474	+	0.0987032i
$738$	−18.5731	+	15.8811i	−0.683685	+	0.584590i
$739$	38.4588	−	22.2042i	1.41473	−	0.816795i	0.418902	−	0.908031i	$-0.362415\pi$
$739$	38.4588	−	22.2042i	1.41473	−	0.816795i	0.995829	+	0.0912360i	$0.0290817\pi$
$740$	3.62713	+	3.08363i	0.133336	+	0.113357i
$741$	−4.23376	−	8.04154i	−0.155531	−	0.295413i
$742$	−15.2406	−	15.2406i	−0.559499	−	0.559499i
$743$	−20.9627	−	20.9627i	−0.769046	−	0.769046i	0.208893	−	0.977939i	$-0.433014\pi$
$743$	−20.9627	−	20.9627i	−0.769046	−	0.769046i	−0.977939	+	0.208893i	$0.933014\pi$
$744$	−5.84870	+	7.66764i	−0.214424	+	0.281109i
$745$	−0.983052	−	12.1381i	−0.0360162	−	0.444705i
$746$		−	19.1986i		−	0.702912i
$747$	40.6909	−	34.7931i	1.48880	−	1.27301i
$748$	−2.94454	+	2.94454i	−0.107663	+	0.107663i
$749$	−10.7811	−	18.6733i	−0.393931	−	0.682309i
$750$	−12.8712	−	14.4683i	−0.469991	−	0.528307i
$751$	14.2786	−	24.7313i	0.521034	−	0.902457i	−0.478667	−	0.877997i	$-0.658880\pi$
$751$	14.2786	−	24.7313i	0.521034	−	0.902457i	0.999701	−	0.0244605i	$-0.00778679\pi$
$752$	8.52574	−	8.52574i	0.310902	−	0.310902i
$753$	6.02070	+	6.50947i	0.219407	+	0.237218i
$754$	−1.54626	+	0.892734i	−0.0563115	+	0.0325114i
$755$	25.0610	−	17.3079i	0.912063	−	0.629901i
$756$	−9.64813	+	12.9432i	−0.350899	+	0.470741i
$757$	−7.32188	+	27.3256i	−0.266118	+	0.993167i	0.695444	+	0.718580i	$0.255208\pi$
$757$	−7.32188	+	27.3256i	−0.266118	+	0.993167i	−0.961562	+	0.274587i	$0.911459\pi$
$758$	−3.22610	+	0.864430i	−0.117177	+	0.0313975i
$759$	−1.54311	−	0.973022i	−0.0560114	−	0.0353185i
$760$	5.87659	+	4.99602i	0.213166	+	0.181225i
$761$	−37.6479	−	21.7360i	−1.36474	−	0.787931i	−0.374487	−	0.927232i	$-0.622181\pi$
$761$	−37.6479	−	21.7360i	−1.36474	−	0.787931i	−0.990250	+	0.139301i	$0.955514\pi$
$762$	−15.9392	+	14.7424i	−0.577418	+	0.534062i
$763$	−7.02783	−	26.2282i	−0.254424	−	0.949525i
$764$	9.81335	+	16.9972i	0.355034	+	0.614938i
$765$	12.0677	+	44.5316i	0.436309	+	1.61004i
$766$	−5.82798	−	10.0944i	−0.210573	−	0.364724i
$767$	10.4470	−	10.4470i	0.377220	−	0.377220i
$768$	−1.65429	−	0.513158i	−0.0596940	−	0.0185170i
$769$	27.9238	+	16.1218i	1.00696	+	0.581368i	0.910300	−	0.413949i	$-0.135851\pi$
$769$	27.9238	+	16.1218i	1.00696	+	0.581368i	0.0966592	+	0.995318i	$0.469184\pi$
$770$	−2.39026	−	3.46098i	−0.0861391	−	0.124725i
$771$	−29.7078	−	18.7325i	−1.06990	−	0.674635i
$772$	15.1438	−	4.05776i	0.545036	−	0.146042i
$773$	−29.1360	−	29.1360i	−1.04795	−	1.04795i	−0.998791	−	0.0491569i	$-0.984347\pi$
$773$	−29.1360	−	29.1360i	−1.04795	−	1.04795i	−0.0491569	−	0.998791i	$-0.515653\pi$
$774$	−15.1648	−	31.7476i	−0.545088	−	1.14114i
$775$	−27.7655	+	2.01887i	−0.997367	+	0.0725199i
$776$			14.8957i			0.534723i
$777$	11.1737	−	2.53167i	0.400856	−	0.0908233i
$778$	−5.82180	−	21.7273i	−0.208722	−	0.778960i
$779$	28.0983			1.00673
$780$	0.246324	+	5.88597i	0.00881982	+	0.210752i
$781$	−2.43533	+	4.21811i	−0.0871428	+	0.150936i
$782$	3.09665	+	11.5569i	0.110736	+	0.413272i
$783$	−3.78010	−	4.78670i	−0.135090	−	0.171063i
$784$	−2.29702	+	1.32619i	−0.0820365	+	0.0473638i
$785$	−32.6179	−	5.96872i	−1.16418	−	0.213033i
$786$	−23.8472	−	0.930222i	−0.850603	−	0.0331799i
$787$	12.3258	−	3.30268i	0.439366	−	0.117728i	−0.0323535	−	0.999476i	$-0.510300\pi$
$787$	12.3258	−	3.30268i	0.439366	−	0.117728i	0.471719	+	0.881749i	$0.343634\pi$
$788$	2.10566	−	7.85843i	0.0750110	−	0.279945i
$789$	25.2915	+	48.0383i	0.900400	+	1.71021i
$790$	−0.383886	+	0.451547i	−0.0136581	+	0.0160653i
$791$		−	7.54805i		−	0.268378i
$792$	−1.18042	−	1.38051i	−0.0419443	−	0.0490544i
$793$	14.3595	+	3.84761i	0.509919	+	0.136633i
$794$	−5.06267	+	8.76880i	−0.179667	+	0.311193i
$795$	−1.12345	−	26.8451i	−0.0398447	−	0.952097i
$796$	5.38877	+	9.33362i	0.191000	+	0.330821i
$797$	−48.8214	−	13.0817i	−1.72934	−	0.463376i	−0.749312	−	0.662217i	$-0.769616\pi$
$797$	−48.8214	−	13.0817i	−1.72934	−	0.463376i	−0.980032	+	0.198841i	$0.936282\pi$
$798$	18.1034	−	4.10175i	0.640854	−	0.145201i
$799$	−71.8171	−	41.4636i	−2.54071	−	1.46688i
$800$	−2.05443	−	4.55844i	−0.0726349	−	0.161165i
$801$	−22.7318	−	15.6043i	−0.803190	−	0.551350i
$802$	1.01724	+	1.01724i	0.0359201	+	0.0359201i
$803$	−3.50036	+	0.937919i	−0.123525	+	0.0330984i
$804$	6.71285	+	4.23284i	0.236744	+	0.149281i
$805$	−12.0456	+	0.975562i	−0.424551	+	0.0343840i
$806$	6.92878	+	4.86994i	0.244056	+	0.171536i
$807$	−0.346571	−	1.52962i	−0.0121999	−	0.0538452i
$808$	1.45543	−	1.45543i	0.0512018	−	0.0512018i
$809$	12.8191	−	22.2033i	0.450696	−	0.780628i	−0.547734	−	0.836653i	$-0.684509\pi$
$809$	12.8191	−	22.2033i	0.450696	−	0.780628i	0.998429	+	0.0560250i	$0.0178426\pi$
$810$	−19.7750	+	3.73470i	−0.694824	+	0.131224i
$811$	−4.29199	−	7.43394i	−0.150712	−	0.261041i	0.780777	−	0.624809i	$-0.214823\pi$
$811$	−4.29199	−	7.43394i	−0.150712	−	0.261041i	−0.931489	+	0.363768i	$0.881490\pi$
$812$	−0.943871	−	3.52258i	−0.0331234	−	0.123618i
$813$	21.4327	+	6.64839i	0.751677	+	0.233169i
$814$			1.28906i			0.0451817i
$815$	3.53364	−	19.3107i	0.123778	−	0.676423i
$816$	−0.464333	+	11.9037i	−0.0162549	+	0.416712i
$817$	−10.4705	+	39.0765i	−0.366317	+	1.36711i
$818$	−12.4974	+	3.34866i	−0.436961	+	0.117083i
$819$	11.6883	+	8.02346i	0.408424	+	0.280363i
$820$	−16.4577	−	7.80406i	−0.574728	−	0.272530i
$821$			39.4719i			1.37758i	0.724962	+	0.688789i	$0.241857\pi$
$821$			39.4719i			1.37758i	−0.724962	+	0.688789i	$0.758143\pi$
$822$	−9.57875	+	2.17029i	−0.334097	+	0.0756976i
$823$	8.47455	+	31.6275i	0.295404	+	1.10246i	0.940896	+	0.338696i	$0.109986\pi$
$823$	8.47455	+	31.6275i	0.295404	+	1.10246i	−0.645491	+	0.763768i	$0.723347\pi$
$824$	−0.0721077	−	0.124894i	−0.00251199	−	0.00435090i
$825$	0.727328	−	5.19272i	0.0253223	−	0.180787i
$826$	15.0884	+	26.1338i	0.524991	+	0.909311i
$827$	−32.0064	−	8.57609i	−1.11297	−	0.298220i	−0.344936	−	0.938626i	$-0.612099\pi$
$827$	−32.0064	−	8.57609i	−1.11297	−	0.298220i	−0.768036	+	0.640406i	$0.778766\pi$
$828$	−5.13083	+	0.953938i	−0.178309	+	0.0331516i
$829$			32.5146i			1.12928i	0.825338	+	0.564639i	$0.190984\pi$
$829$			32.5146i			1.12928i	−0.825338	+	0.564639i	$0.809016\pi$
$830$	36.0565	+	17.0976i	1.25154	+	0.593465i
$831$	−5.55805	−	10.5569i	−0.192807	−	0.366215i
$832$	−0.393685	+	1.46925i	−0.0136486	+	0.0509371i
$833$	12.8994	+	12.8994i	0.446938	+	0.446938i
$834$	−9.95542	−	18.9092i	−0.344728	−	0.654772i
$835$	−10.2570	−	8.72008i	−0.354959	−	0.301771i
$836$			2.08851i			0.0722326i
$837$	−13.0458	+	25.8226i	−0.450928	+	0.892560i
$838$	13.3814	−	13.3814i	0.462252	−	0.462252i
$839$	25.9290			0.895167			0.447584	−	0.894242i	$-0.352285\pi$
$839$	25.9290			0.895167			0.447584	+	0.894242i	$0.352285\pi$
$840$	−11.7427	−	2.62559i	−0.405163	−	0.0905914i
$841$	−27.6222			−0.952488
$842$	2.33187	+	0.624824i	0.0803617	+	0.0215329i
$843$	−8.58179	+	27.6654i	−0.295573	+	0.952849i
$844$	−16.1187	−	9.30613i	−0.554828	−	0.320330i
$845$	−23.8173	+	1.92895i	−0.819341	+	0.0663577i
$846$	20.4710	−	29.8216i	0.703808	−	1.02529i
$847$	−8.55040	+	31.9105i	−0.293795	+	1.09646i
$848$	1.79554	−	6.70105i	0.0616591	−	0.230115i
$849$	49.1317	−	25.8672i	1.68620	−	0.887758i
$850$	−26.6267	+	21.7630i	−0.913287	+	0.746465i
$851$	3.20751	+	1.85186i	0.109952	+	0.0634809i
$852$	3.07896	+	13.5892i	0.105483	+	0.465559i
$853$	−11.0363	+	11.0363i	−0.377875	+	0.377875i	−0.870335	−	0.492460i	$-0.836098\pi$
$853$	−11.0363	+	11.0363i	−0.377875	+	0.377875i	0.492460	+	0.870335i	$0.336098\pi$
$854$	−15.1820	+	26.2960i	−0.519517	+	0.899831i
$855$	20.0724	+	11.5130i	0.686462	+	0.393736i
$856$	3.47012	−	6.01042i	0.118606	−	0.205432i
$857$	−30.7855	−	8.24894i	−1.05161	−	0.281778i	−0.308694	−	0.951161i	$-0.599892\pi$
$857$	−30.7855	−	8.24894i	−1.05161	−	0.281778i	−0.742917	+	0.669383i	$0.766558\pi$
$858$	−1.17103	+	1.08311i	−0.0399784	+	0.0369766i
$859$	−13.5699	+	7.83457i	−0.462998	+	0.267312i	−0.713304	−	0.700855i	$-0.752802\pi$
$859$	−13.5699	+	7.83457i	−0.462998	+	0.267312i	0.250306	+	0.968167i	$0.419469\pi$
$860$	16.9859	−	19.9797i	0.579215	−	0.681303i
$861$	−38.7862	+	20.4204i	−1.32183	+	0.695925i
$862$	−28.5647	+	7.65390i	−0.972919	+	0.260693i
$863$	3.96938	−	14.8139i	0.135119	−	0.504272i	−0.864878	−	0.501982i	$-0.832604\pi$
$863$	3.96938	−	14.8139i	0.135119	−	0.504272i	0.999997	−	0.00228987i	$-0.000728889\pi$
$864$	−5.16065	−	0.606374i	−0.175569	−	0.0206293i
$865$	−3.06820	−	8.60216i	−0.104322	−	0.292482i
$866$		−	23.6471i		−	0.803561i
$867$	51.1910	−	11.5985i	1.73854	−	0.393907i
$868$	−13.2708	+	11.0954i	−0.450441	+	0.376604i
$869$	−0.160478			−0.00544383
$870$	2.10647	−	4.02869i	0.0714161	−	0.136586i
$871$	3.48466	−	6.03561i	0.118073	−	0.204509i
$872$	6.18006	−	6.18006i	0.209283	−	0.209283i
$873$	8.16835	+	43.9341i	0.276457	+	1.48694i
$874$	5.19673	+	3.00033i	0.175782	+	0.101488i
$875$	−16.7821	−	30.4123i	−0.567337	−	1.02812i
$876$	−5.52943	+	8.76910i	−0.186822	+	0.296280i
$877$	4.39400	−	16.3986i	0.148375	−	0.553743i	−0.851207	−	0.524830i	$-0.824129\pi$
$877$	4.39400	−	16.3986i	0.148375	−	0.553743i	0.999582	−	0.0289127i	$-0.00920448\pi$
$878$	3.46218	−	12.9210i	0.116843	−	0.436064i
$879$	−34.3491	−	1.33987i	−1.15857	−	0.0451928i
$880$	0.580065	−	1.22328i	0.0195540	−	0.0412367i
$881$	20.2131	−	11.6700i	0.680995	−	0.393173i	−0.119235	−	0.992866i	$-0.538044\pi$
$881$	20.2131	−	11.6700i	0.680995	−	0.393173i	0.800230	+	0.599693i	$0.204711\pi$
$882$	−6.04772	+	5.17115i	−0.203637	+	0.174122i
$883$	28.3804	−	28.3804i	0.955078	−	0.955078i	−0.0439557	−	0.999033i	$-0.513996\pi$
$883$	28.3804	−	28.3804i	0.955078	−	0.955078i	0.999033	+	0.0439557i	$0.0139960\pi$
$884$	10.4617			0.351865
$885$	−8.20852	+	36.7119i	−0.275926	+	1.23406i
$886$	−5.24553	−	9.08553i	−0.176227	−	0.305234i
$887$	13.3080	+	49.6661i	0.446838	+	1.66762i	0.711036	+	0.703155i	$0.248226\pi$
$887$	13.3080	+	49.6661i	0.446838	+	1.66762i	−0.264198	+	0.964468i	$0.585107\pi$
$888$	2.50396	+	2.70724i	0.0840274	+	0.0908489i
$889$	−33.7273	+	19.4725i	−1.13118	+	0.653085i
$890$	3.69921	−	20.2155i	0.123998	−	0.677624i
$891$	−4.23862	−	3.42445i	−0.141999	−	0.114723i
$892$	10.2878	−	2.75660i	0.344460	−	0.0922979i
$893$	−40.1739	+	10.7646i	−1.34437	+	0.360223i
$894$	0.367674	−	9.42573i	0.0122969	−	0.315244i
$895$	0.627945	+	7.75344i	0.0209899	+	0.259169i
$896$	−2.69059	−	1.55341i	−0.0898863	−	0.0518959i
$897$	1.01274	+	4.46980i	0.0338143	+	0.149242i
$898$	27.2617	−	27.2617i	0.909735	−	0.909735i
$899$	−2.75151	−	5.92809i	−0.0917680	−	0.197713i
$900$	−8.55915	−	12.3183i	−0.285305	−	0.410611i
$901$	−47.7144			−1.58960
$902$	−1.27646	−	4.76380i	−0.0425013	−	0.158617i
$903$	−13.9455	−	61.5496i	−0.464077	−	2.04824i
$904$	2.10401	−	1.21475i	0.0699784	−	0.0404021i
$905$	31.4710	+	14.9232i	1.04613	+	0.496064i
$906$	20.8753	−	10.9906i	0.693536	−	0.365137i
$907$	−40.2602	−	40.2602i	−1.33682	−	1.33682i	−0.899122	−	0.437697i	$-0.855794\pi$
$907$	−40.2602	−	40.2602i	−1.33682	−	1.33682i	−0.437697	−	0.899122i	$-0.644206\pi$
$908$	−5.11831	+	19.1018i	−0.169857	+	0.633916i
$909$	3.49461	−	5.09084i	0.115909	−	0.168852i
$910$	−1.90207	+	10.3945i	−0.0630531	+	0.344573i
$911$	32.3586	+	18.6822i	1.07209	+	0.618970i	0.928751	−	0.370704i	$-0.120884\pi$
$911$	32.3586	+	18.6822i	1.07209	+	0.618970i	0.143336	+	0.989674i	$0.454217\pi$
$912$	4.05685	+	4.38619i	0.134336	+	0.145241i
$913$	2.79653	+	10.4368i	0.0925516	+	0.345407i
$914$	35.9895			1.19043
$915$	−36.1205	+	11.3170i	−1.19411	+	0.374128i
$916$	0.565990	−	0.980323i	0.0187008	−	0.0323908i
$917$	−41.3493	−	11.0795i	−1.36548	−	0.365878i
$918$	5.15809	+	35.3640i	0.170242	+	1.16718i
$919$	−37.9843	+	21.9302i	−1.25299	+	0.723412i	−0.971701	−	0.236213i	$-0.924094\pi$
$919$	−37.9843	+	21.9302i	−1.25299	+	0.723412i	−0.281284	+	0.959624i	$0.590760\pi$
$920$	−2.21051	−	3.20070i	−0.0728782	−	0.105524i
$921$	10.0230	+	0.390973i	0.330270	+	0.0128830i
$922$	−10.2654	−	10.2654i	−0.338073	−	0.338073i
$923$	11.8195	−	3.16704i	0.389045	−	0.104244i
$924$	−1.51782	−	2.88292i	−0.0499326	−	0.0948412i
$925$	−1.06461	+	10.5920i	−0.0350041	+	0.348264i
$926$			27.1075i			0.890809i
$927$	−0.281167	−	0.328828i	−0.00923473	−	0.0108001i
$928$	0.830012	−	0.830012i	0.0272465	−	0.0272465i
$929$	−47.1441			−1.54675			−0.773373	−	0.633951i	$-0.781432\pi$
$929$	−47.1441			−1.54675			−0.773373	+	0.633951i	$0.781432\pi$
$930$	−21.5398	−	1.01780i	−0.706319	−	0.0333750i
$931$	9.14930			0.299856
$932$	12.8364	−	12.8364i	0.420469	−	0.420469i
$933$	9.46250	−	30.5046i	0.309788	−	0.998677i
$934$		−	8.84209i		−	0.289322i
$935$	−9.15938	−	1.67607i	−0.299544	−	0.0548132i
$936$	−0.355461	+	4.54938i	−0.0116186	+	0.148701i
$937$	47.9042	−	12.8359i	1.56496	−	0.419331i	0.630733	−	0.776000i	$-0.282754\pi$
$937$	47.9042	−	12.8359i	1.56496	−	0.419331i	0.934231	+	0.356669i	$0.116088\pi$
$938$	10.0656	+	10.0656i	0.328654	+	0.328654i
$939$	−0.420079	+	10.7692i	−0.0137088	+	0.351438i
$940$	26.5204	+	4.85294i	0.865000	+	0.158285i
$941$	−2.31464	+	1.33636i	−0.0754551	+	0.0435640i	−0.537253	−	0.843421i	$-0.680538\pi$
$941$	−2.31464	+	1.33636i	−0.0754551	+	0.0435640i	0.461798	+	0.886985i	$0.347205\pi$
$942$	−24.5321	−	7.60982i	−0.799298	−	0.247941i
$943$	−13.6873	−	3.66749i	−0.445718	−	0.119430i
$944$	−4.85652	+	8.41174i	−0.158066	+	0.273779i
$945$	−36.0745	−	1.30468i	−1.17350	−	0.0424413i
$946$	7.10069			0.230863
$947$	−4.99052	−	18.6249i	−0.162170	−	0.605227i	−0.998384	−	0.0568237i	$-0.981903\pi$
$947$	−4.99052	−	18.6249i	−0.162170	−	0.605227i	0.836214	−	0.548403i	$-0.184764\pi$
$948$	−0.337028	+	0.311722i	−0.0109462	+	0.0101242i
$949$	7.88441	+	4.55207i	0.255939	+	0.147766i
$950$	−1.72485	+	17.1609i	−0.0559615	+	0.556774i
$951$	−2.00934	+	51.5115i	−0.0651572	+	1.67037i
$952$	−5.53049	+	20.6401i	−0.179244	+	0.668948i
$953$	−20.0579	−	20.0579i	−0.649740	−	0.649740i	0.303190	−	0.952930i	$-0.401948\pi$
$953$	−20.0579	−	20.0579i	−0.649740	−	0.649740i	−0.952930	+	0.303190i	$0.901948\pi$
$954$	1.62121	−	20.7491i	0.0524885	−	0.671776i
$955$	−18.8036	+	39.6543i	−0.608470	+	1.28318i
$956$	8.83048	−	5.09828i	0.285598	−	0.164890i
$957$	1.20053	−	0.272008i	0.0388076	−	0.00879276i
$958$	−7.22580	−	26.9671i	−0.233455	−	0.871266i
$959$	−17.6172			−0.568888
$960$	−1.15795	−	3.69583i	−0.0373726	−	0.119282i
$961$	−20.0106	+	23.6765i	−0.645504	+	0.763757i
$962$	2.28997	−	2.28997i	0.0738315	−	0.0738315i
$963$	6.93902	−	19.6304i	0.223607	−	0.632580i
$964$	3.07854	+	1.77740i	0.0991532	+	0.0572461i
$965$	26.7092	+	22.7071i	0.859801	+	0.730966i
$966$	−9.35391	−	0.364873i	−0.300957	−	0.0117396i
$967$	17.1317	−	4.59043i	0.550919	−	0.147618i	0.0273881	−	0.999625i	$-0.491281\pi$
$967$	17.1317	−	4.59043i	0.550919	−	0.147618i	0.523531	+	0.852007i	$0.324614\pi$
$968$	−10.2711	+	2.75213i	−0.330126	+	0.0884569i
$969$	21.9178	−	34.7594i	0.704102	−	1.11663i
$970$	−27.4068	+	18.9280i	−0.879980	+	0.607743i
$971$	−4.45923	+	2.57454i	−0.143103	+	0.0826208i	−0.569842	−	0.821754i	$-0.692996\pi$
$971$	−4.45923	+	2.57454i	−0.143103	+	0.0826208i	0.426739	+	0.904375i	$0.359662\pi$
$972$	−15.5536	+	1.04148i	−0.498883	+	0.0334054i
$973$	−9.92094	−	37.0255i	−0.318051	−	1.18698i
$974$	−4.77262	−	8.26643i	−0.152925	−	0.264873i
$975$	−10.5167	+	7.93257i	−0.336804	+	0.254045i
$976$	−9.77332			−0.312836
$977$	31.3330	−	31.3330i	1.00243	−	1.00243i	0.00243572	−	0.999997i	$-0.499225\pi$
$977$	31.3330	−	31.3330i	1.00243	−	1.00243i	0.999997	−	0.00243572i	$-0.000775316\pi$
$978$	4.50522	−	14.5236i	0.144061	−	0.464415i
$979$	4.81908	−	2.78230i	0.154019	−	0.0889227i
$980$	−5.35892	−	2.54114i	−0.171184	−	0.0811737i
$981$	14.8388	−	21.6168i	0.473768	−	0.690171i
$982$	−7.22491	+	26.9637i	−0.230556	+	0.860448i
$983$	1.30184	−	4.85855i	0.0415224	−	0.154964i	−0.942052	−	0.335467i	$-0.891106\pi$
$983$	1.30184	−	4.85855i	0.0415224	−	0.154964i	0.983574	+	0.180503i	$0.0577726\pi$
$984$	−11.9343	−	7.52525i	−0.380450	−	0.239896i
$985$	17.1345	−	6.11152i	0.545952	−	0.194729i
$986$	−6.99166	−	4.03664i	−0.222660	−	0.128553i
$987$	47.6319	−	44.0554i	1.51614	−	1.40230i
$988$	3.71014	−	3.71014i	0.118035	−	0.118035i
$989$	10.2008	−	17.6683i	0.324366	−	0.561819i
$990$	1.04006	−	3.92610i	0.0330554	−	0.124780i
$991$	31.0386			0.985973			0.492986	−	0.870037i	$-0.335905\pi$
$991$	31.0386			0.985973			0.492986	+	0.870037i	$0.335905\pi$
$992$	−5.22860	−	1.91357i	−0.166008	−	0.0607560i
$993$	6.94066	+	30.6331i	0.220255	+	0.972113i
$994$			24.9932i			0.792735i
$995$	−10.3256	+	21.7752i	−0.327342	+	0.690320i
$996$	26.1462	+	16.4867i	0.828475	+	0.522402i
$997$	−4.81323	+	17.9632i	−0.152436	+	0.568901i	0.846875	+	0.531792i	$0.178481\pi$
$997$	−4.81323	+	17.9632i	−0.152436	+	0.568901i	−0.999311	+	0.0371083i	$0.988185\pi$
$998$	−0.940933	+	0.252122i	−0.0297847	+	0.00798079i
$999$	8.86989	+	6.61177i	0.280631	+	0.209187i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bf.a.377.3	✓	256
3.2	odd	2	inner	930.2.bf.a.377.57	yes	256
5.3	odd	4	inner	930.2.bf.a.563.50	yes	256
15.8	even	4	inner	930.2.bf.a.563.24	yes	256
31.25	even	3	inner	930.2.bf.a.707.24	yes	256
93.56	odd	6	inner	930.2.bf.a.707.50	yes	256
155.118	odd	12	inner	930.2.bf.a.893.57	yes	256
465.428	even	12	inner	930.2.bf.a.893.3	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bf.a.377.3	✓	256	1.1	even	1	trivial
930.2.bf.a.377.57	yes	256	3.2	odd	2	inner
930.2.bf.a.563.24	yes	256	15.8	even	4	inner
930.2.bf.a.563.50	yes	256	5.3	odd	4	inner
930.2.bf.a.707.24	yes	256	31.25	even	3	inner
930.2.bf.a.707.50	yes	256	93.56	odd	6	inner
930.2.bf.a.893.3	yes	256	465.428	even	12	inner
930.2.bf.a.893.57	yes	256	155.118	odd	12	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bf (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.65429 - 0.513158i) q^{3} -1.00000i q^{4} +(1.83992 - 1.27071i) q^{5} +(1.53262 - 0.806900i) q^{6} +(3.00096 - 0.804106i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.47334 + 1.69782i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.65429 - 0.513158i) q^{3} -1.00000i q^{4} +(1.83992 - 1.27071i) q^{5} +(1.53262 - 0.806900i) q^{6} +(3.00096 - 0.804106i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.47334 + 1.69782i) q^{9} +(-0.402493 + 2.19955i) q^{10} +(-0.524341 + 0.302728i) q^{11} +(-0.513158 + 1.65429i) q^{12} +(1.46925 + 0.393685i) q^{13} +(-1.55341 + 2.69059i) q^{14} +(-3.69583 + 1.15795i) q^{15} -1.00000 q^{16} +(1.78011 + 6.64345i) q^{17} +(-2.94946 + 0.548371i) q^{18} +(2.98734 + 1.72474i) q^{19} +(-1.27071 - 1.83992i) q^{20} +(-5.37709 - 0.209747i) q^{21} +(0.156704 - 0.584826i) q^{22} +(-1.23007 - 1.23007i) q^{23} +(-0.806900 - 1.53262i) q^{24} +(1.77060 - 4.67600i) q^{25} +(-1.31729 + 0.760541i) q^{26} +(-3.22036 - 4.07790i) q^{27} +(-0.804106 - 3.00096i) q^{28} +1.17381 q^{29} +(1.79455 - 3.43214i) q^{30} +(-2.34408 - 5.05028i) q^{31} +(0.707107 - 0.707107i) q^{32} +(1.02276 - 0.231730i) q^{33} +(-5.95636 - 3.43890i) q^{34} +(4.49975 - 5.29284i) q^{35} +(1.69782 - 2.47334i) q^{36} +(-2.05653 + 0.551046i) q^{37} +(-3.33194 + 0.892791i) q^{38} +(-2.22854 - 1.40523i) q^{39} +(2.19955 + 0.402493i) q^{40} +(7.05436 - 4.07284i) q^{41} +(3.95049 - 3.65386i) q^{42} +(3.03539 + 11.3282i) q^{43} +(0.302728 + 0.524341i) q^{44} +(6.70818 - 0.0190325i) q^{45} +1.73959 q^{46} +(-8.52574 + 8.52574i) q^{47} +(1.65429 + 0.513158i) q^{48} +(2.29702 - 1.32619i) q^{49} +(2.05443 + 4.55844i) q^{50} +(0.464333 - 11.9037i) q^{51} +(0.393685 - 1.46925i) q^{52} +(-1.79554 + 6.70105i) q^{53} +(5.16065 + 0.606374i) q^{54} +(-0.580065 + 1.22328i) q^{55} +(2.69059 + 1.55341i) q^{56} +(-4.05685 - 4.38619i) q^{57} +(-0.830012 + 0.830012i) q^{58} +(4.85652 - 8.41174i) q^{59} +(1.15795 + 3.69583i) q^{60} +9.77332 q^{61} +(5.22860 + 1.91357i) q^{62} +(8.78763 + 3.10628i) q^{63} +1.00000i q^{64} +(3.20356 - 1.14264i) q^{65} +(-0.559341 + 0.887057i) q^{66} +(1.18586 - 4.42570i) q^{67} +(6.64345 - 1.78011i) q^{68} +(1.40367 + 2.66612i) q^{69} +(0.560801 + 6.92440i) q^{70} +(6.96683 - 4.02230i) q^{71} +(0.548371 + 2.94946i) q^{72} +(5.78136 + 1.54911i) q^{73} +(1.06454 - 1.84384i) q^{74} +(-5.32861 + 6.82685i) q^{75} +(1.72474 - 2.98734i) q^{76} +(-1.33010 + 1.33010i) q^{77} +(2.56946 - 0.582172i) q^{78} +(0.229542 + 0.132526i) q^{79} +(-1.83992 + 1.27071i) q^{80} +(3.23479 + 8.39858i) q^{81} +(-2.10826 + 7.86811i) q^{82} +(4.61888 - 17.2379i) q^{83} +(-0.209747 + 5.37709i) q^{84} +(11.7171 + 9.96142i) q^{85} +(-10.1566 - 5.86392i) q^{86} +(-1.94183 - 0.602353i) q^{87} +(-0.584826 - 0.156704i) q^{88} -9.19075 q^{89} +(-4.72994 + 4.75686i) q^{90} +4.72574 q^{91} +(-1.23007 + 1.23007i) q^{92} +(1.28618 + 9.55750i) q^{93} -12.0572i q^{94} +(7.68810 - 0.622652i) q^{95} +(-1.53262 + 0.806900i) q^{96} +(10.5328 + 10.5328i) q^{97} +(-0.686485 + 2.56200i) q^{98} +(-1.81085 - 0.141489i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q + 8 q^{3} - 4 q^{7}+O(q^{10}) \) 256 * q + 8 * q^3 - 4 * q^7	\( 256 q + 8 q^{3} - 4 q^{7} - 8 q^{10} - 8 q^{12} + 8 q^{15} - 256 q^{16} - 4 q^{22} - 16 q^{25} - 40 q^{27} - 4 q^{28} - 48 q^{30} + 32 q^{31} - 8 q^{33} + 8 q^{37} - 12 q^{42} - 40 q^{45} + 16 q^{46} - 8 q^{48} - 16 q^{51} + 20 q^{55} + 40 q^{57} + 56 q^{58} - 8 q^{60} - 32 q^{61} + 56 q^{63} + 32 q^{66} - 24 q^{67} + 24 q^{70} + 8 q^{73} - 4 q^{75} + 16 q^{76} - 88 q^{78} - 48 q^{81} + 64 q^{85} - 20 q^{87} - 4 q^{88} - 8 q^{90} - 68 q^{93} + 152 q^{97}+O(q^{100}) \) 256 * q + 8 * q^3 - 4 * q^7 - 8 * q^10 - 8 * q^12 + 8 * q^15 - 256 * q^16 - 4 * q^22 - 16 * q^25 - 40 * q^27 - 4 * q^28 - 48 * q^30 + 32 * q^31 - 8 * q^33 + 8 * q^37 - 12 * q^42 - 40 * q^45 + 16 * q^46 - 8 * q^48 - 16 * q^51 + 20 * q^55 + 40 * q^57 + 56 * q^58 - 8 * q^60 - 32 * q^61 + 56 * q^63 + 32 * q^66 - 24 * q^67 + 24 * q^70 + 8 * q^73 - 4 * q^75 + 16 * q^76 - 88 * q^78 - 48 * q^81 + 64 * q^85 - 20 * q^87 - 4 * q^88 - 8 * q^90 - 68 * q^93 + 152 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more