LMFDB - Embedded newform 930.2.bf.a.377.4

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			377.4
Character	$\chi$	$=$	930.377
Dual form			930.2.bf.a.893.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-1.64704 - 0.535974i) q^{3} -1.00000i q^{4} +(-0.601583 + 2.15362i) q^{5} +(1.54362 - 0.785641i) q^{6} +(-4.77476 + 1.27939i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.42546 + 1.76554i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.64704 - 0.535974i) q^{3} -1.00000i q^{4} +(-0.601583 + 2.15362i) q^{5} +(1.54362 - 0.785641i) q^{6} +(-4.77476 + 1.27939i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.42546 + 1.76554i) q^{9} +(-1.09746 - 1.94823i) q^{10} +(-4.69648 + 2.71151i) q^{11} +(-0.535974 + 1.64704i) q^{12} +(-3.13598 - 0.840283i) q^{13} +(2.47160 - 4.28093i) q^{14} +(2.14512 - 3.22467i) q^{15} -1.00000 q^{16} +(-0.636212 - 2.37438i) q^{17} +(-2.96349 + 0.466638i) q^{18} +(6.16217 + 3.55773i) q^{19} +(2.15362 + 0.601583i) q^{20} +(8.54993 + 0.451939i) q^{21} +(1.40358 - 5.23824i) q^{22} +(3.46253 + 3.46253i) q^{23} +(-0.785641 - 1.54362i) q^{24} +(-4.27620 - 2.59117i) q^{25} +(2.81164 - 1.62330i) q^{26} +(-3.04855 - 4.20789i) q^{27} +(1.27939 + 4.77476i) q^{28} -1.53068 q^{29} +(0.763357 + 3.79701i) q^{30} +(-5.30670 + 1.68490i) q^{31} +(0.707107 - 0.707107i) q^{32} +(9.18857 - 1.94877i) q^{33} +(2.12881 + 1.22907i) q^{34} +(0.117083 - 11.0527i) q^{35} +(1.76554 - 2.42546i) q^{36} +(-0.363051 + 0.0972792i) q^{37} +(-6.87301 + 1.84162i) q^{38} +(4.71470 + 3.06478i) q^{39} +(-1.94823 + 1.09746i) q^{40} +(3.91686 - 2.26140i) q^{41} +(-6.36528 + 5.72615i) q^{42} +(-1.15590 - 4.31389i) q^{43} +(2.71151 + 4.69648i) q^{44} +(-5.26142 + 4.16142i) q^{45} -4.89676 q^{46} +(-7.74617 + 7.74617i) q^{47} +(1.64704 + 0.535974i) q^{48} +(15.0993 - 8.71760i) q^{49} +(4.85596 - 1.19149i) q^{50} +(-0.224738 + 4.25168i) q^{51} +(-0.840283 + 3.13598i) q^{52} +(1.72063 - 6.42148i) q^{53} +(5.13108 + 0.819781i) q^{54} +(-3.01426 - 11.7456i) q^{55} +(-4.28093 - 2.47160i) q^{56} +(-8.24248 - 9.16248i) q^{57} +(1.08236 - 1.08236i) q^{58} +(1.98970 - 3.44626i) q^{59} +(-3.22467 - 2.14512i) q^{60} +7.97074 q^{61} +(2.56100 - 4.94381i) q^{62} +(-13.8398 - 5.32690i) q^{63} +1.00000i q^{64} +(3.69620 - 6.24822i) q^{65} +(-5.11931 + 7.87529i) q^{66} +(3.31584 - 12.3749i) q^{67} +(-2.37438 + 0.636212i) q^{68} +(-3.84709 - 7.55875i) q^{69} +(7.73265 + 7.89823i) q^{70} +(-6.67494 + 3.85378i) q^{71} +(0.466638 + 2.96349i) q^{72} +(9.43484 + 2.52806i) q^{73} +(0.187929 - 0.325503i) q^{74} +(5.65425 + 6.55968i) q^{75} +(3.55773 - 6.16217i) q^{76} +(18.9555 - 18.9555i) q^{77} +(-5.50092 + 1.16667i) q^{78} +(3.41094 + 1.96931i) q^{79} +(0.601583 - 2.15362i) q^{80} +(2.76575 + 8.56450i) q^{81} +(-1.17059 + 4.36869i) q^{82} +(-0.798015 + 2.97823i) q^{83} +(0.451939 - 8.54993i) q^{84} +(5.49625 + 0.0582228i) q^{85} +(3.86773 + 2.23303i) q^{86} +(2.52109 + 0.820406i) q^{87} +(-5.23824 - 1.40358i) q^{88} -12.5784 q^{89} +(0.777820 - 6.66296i) q^{90} +16.0486 q^{91} +(3.46253 - 3.46253i) q^{92} +(9.64340 + 0.0691608i) q^{93} -10.9547i q^{94} +(-11.3691 + 11.1307i) q^{95} +(-1.54362 + 0.785641i) q^{96} +(4.96468 + 4.96468i) q^{97} +(-4.51256 + 16.8411i) q^{98} +(-16.1784 - 1.71513i) 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
$3$	−1.64704	−	0.535974i	−0.950917	−	0.309445i
$3$	−1.64704	−	0.535974i	−0.950917	−	0.309445i
$4$		−	1.00000i		−	0.500000i
$5$	−0.601583	+	2.15362i	−0.269036	+	0.963130i
$5$	−0.601583	+	2.15362i	−0.269036	+	0.963130i
$6$	1.54362	−	0.785641i	0.630181	−	0.320736i
$7$	−4.77476	+	1.27939i	−1.80469	+	0.483565i	−0.994695	−	0.102871i	$-0.967197\pi$
$7$	−4.77476	+	1.27939i	−1.80469	+	0.483565i	−0.809996	+	0.586436i	$0.800531\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	2.42546	+	1.76554i	0.808488	+	0.588513i
$10$	−1.09746	−	1.94823i	−0.347047	−	0.616083i
$11$	−4.69648	+	2.71151i	−1.41604	+	0.817552i	−0.995948	−	0.0899294i	$-0.971336\pi$
$11$	−4.69648	+	2.71151i	−1.41604	+	0.817552i	−0.420093	+	0.907481i	$0.638003\pi$
$12$	−0.535974	+	1.64704i	−0.154722	+	0.475459i
$13$	−3.13598	−	0.840283i	−0.869764	−	0.233052i	−0.203778	−	0.979017i	$-0.565322\pi$
$13$	−3.13598	−	0.840283i	−0.869764	−	0.233052i	−0.665986	+	0.745965i	$0.731989\pi$
$14$	2.47160	−	4.28093i	0.660563	−	1.14413i
$15$	2.14512	−	3.22467i	0.553867	−	0.832605i
$16$	−1.00000			−0.250000
$17$	−0.636212	−	2.37438i	−0.154304	−	0.575871i	−0.999164	−	0.0408832i	$-0.986983\pi$
$17$	−0.636212	−	2.37438i	−0.154304	−	0.575871i	0.844860	−	0.534988i	$-0.179684\pi$
$18$	−2.96349	+	0.466638i	−0.698500	+	0.109988i
$19$	6.16217	+	3.55773i	1.41370	+	0.816200i	0.995735	−	0.0922636i	$-0.0294102\pi$
$19$	6.16217	+	3.55773i	1.41370	+	0.816200i	0.417965	+	0.908463i	$0.362744\pi$
$20$	2.15362	+	0.601583i	0.481565	+	0.134518i
$21$	8.54993	+	0.451939i	1.86575	+	0.0986211i
$22$	1.40358	−	5.23824i	0.299245	−	1.11680i
$23$	3.46253	+	3.46253i	0.721988	+	0.721988i	0.969010	−	0.247022i	$-0.0794520\pi$
$23$	3.46253	+	3.46253i	0.721988	+	0.721988i	−0.247022	+	0.969010i	$0.579452\pi$
$24$	−0.785641	−	1.54362i	−0.160368	−	0.315091i
$25$	−4.27620	−	2.59117i	−0.855239	−	0.518234i
$26$	2.81164	−	1.62330i	0.551408	−	0.318356i
$27$	−3.04855	−	4.20789i	−0.586693	−	0.809809i
$28$	1.27939	+	4.77476i	0.241783	+	0.902345i
$29$	−1.53068			−0.284240			−0.142120	−	0.989849i	$-0.545392\pi$
$29$	−1.53068			−0.284240			−0.142120	+	0.989849i	$0.545392\pi$
$30$	0.763357	+	3.79701i	0.139369	+	0.693236i
$31$	−5.30670	+	1.68490i	−0.953112	+	0.302617i
$31$	−5.30670	+	1.68490i	−0.953112	+	0.302617i
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	9.18857	−	1.94877i	1.59953	−	0.339238i
$34$	2.12881	+	1.22907i	0.365088	+	0.210783i
$35$	0.117083	−	11.0527i	0.0197907	−	1.86825i
$36$	1.76554	−	2.42546i	0.294256	−	0.404244i
$37$	−0.363051	+	0.0972792i	−0.0596852	+	0.0159926i	−0.288538	−	0.957468i	$-0.593169\pi$
$37$	−0.363051	+	0.0972792i	−0.0596852	+	0.0159926i	0.228853	+	0.973461i	$0.426503\pi$
$38$	−6.87301	+	1.84162i	−1.11495	+	0.298750i
$39$	4.71470	+	3.06478i	0.754957	+	0.490757i
$40$	−1.94823	+	1.09746i	−0.308042	+	0.173523i
$41$	3.91686	−	2.26140i	0.611711	−	0.353171i	−0.161924	−	0.986803i	$-0.551770\pi$
$41$	3.91686	−	2.26140i	0.611711	−	0.353171i	0.773635	+	0.633632i	$0.218437\pi$
$42$	−6.36528	+	5.72615i	−0.982185	+	0.883564i
$43$	−1.15590	−	4.31389i	−0.176273	−	0.657862i	−0.996331	−	0.0855808i	$-0.972725\pi$
$43$	−1.15590	−	4.31389i	−0.176273	−	0.657862i	0.820058	−	0.572281i	$-0.193941\pi$
$44$	2.71151	+	4.69648i	0.408776	+	0.708021i
$45$	−5.26142	+	4.16142i	−0.784327	+	0.620348i
$46$	−4.89676			−0.721988
$47$	−7.74617	+	7.74617i	−1.12990	+	1.12990i	−0.139701	+	0.990194i	$0.544614\pi$
$47$	−7.74617	+	7.74617i	−1.12990	+	1.12990i	−0.990194	+	0.139701i	$0.955386\pi$
$48$	1.64704	+	0.535974i	0.237729	+	0.0773612i
$49$	15.0993	−	8.71760i	2.15705	−	1.24537i
$50$	4.85596	−	1.19149i	0.686736	−	0.168503i
$51$	−0.224738	+	4.25168i	−0.0314697	+	0.595354i
$52$	−0.840283	+	3.13598i	−0.116526	+	0.434882i
$53$	1.72063	−	6.42148i	0.236347	−	0.882058i	−0.741191	−	0.671295i	$-0.765739\pi$
$53$	1.72063	−	6.42148i	0.236347	−	0.882058i	0.977537	−	0.210763i	$-0.0675948\pi$
$54$	5.13108	+	0.819781i	0.698251	+	0.111558i
$55$	−3.01426	−	11.7456i	−0.406442	−	1.58378i
$56$	−4.28093	−	2.47160i	−0.572064	−	0.330281i
$57$	−8.24248	−	9.16248i	−1.09174	−	1.21360i
$58$	1.08236	−	1.08236i	0.142120	−	0.142120i
$59$	1.98970	−	3.44626i	0.259037	−	0.448665i	−0.706947	−	0.707266i	$-0.749928\pi$
$59$	1.98970	−	3.44626i	0.259037	−	0.448665i	0.965984	+	0.258601i	$0.0832615\pi$
$60$	−3.22467	−	2.14512i	−0.416303	−	0.276933i
$61$	7.97074			1.02055			0.510275	−	0.860012i	$-0.329544\pi$
$61$	7.97074			1.02055			0.510275	+	0.860012i	$0.329544\pi$
$62$	2.56100	−	4.94381i	0.325248	−	0.627865i
$63$	−13.8398	−	5.32690i	−1.74365	−	0.671126i
$64$			1.00000i			0.125000i
$65$	3.69620	−	6.24822i	0.458458	−	0.774996i
$66$	−5.11931	+	7.87529i	−0.630144	+	0.969382i
$67$	3.31584	−	12.3749i	0.405094	−	1.51183i	−0.398788	−	0.917043i	$-0.630569\pi$
$67$	3.31584	−	12.3749i	0.405094	−	1.51183i	0.803882	−	0.594789i	$-0.202764\pi$
$68$	−2.37438	+	0.636212i	−0.287936	+	0.0771521i
$69$	−3.84709	−	7.55875i	−0.463136	−	0.909966i
$70$	7.73265	+	7.89823i	0.924229	+	0.944019i
$71$	−6.67494	+	3.85378i	−0.792169	+	0.457359i	−0.840726	−	0.541461i	$-0.817871\pi$
$71$	−6.67494	+	3.85378i	−0.792169	+	0.457359i	0.0485563	+	0.998820i	$0.484538\pi$
$72$	0.466638	+	2.96349i	0.0549938	+	0.349250i
$73$	9.43484	+	2.52806i	1.10426	+	0.295887i	0.764500	−	0.644624i	$-0.222986\pi$
$73$	9.43484	+	2.52806i	1.10426	+	0.295887i	0.339765	+	0.940510i	$0.389653\pi$
$74$	0.187929	−	0.325503i	0.0218463	−	0.0378389i
$75$	5.65425	+	6.55968i	0.652897	+	0.757447i
$76$	3.55773	−	6.16217i	0.408100	−	0.706850i
$77$	18.9555	−	18.9555i	2.16018	−	2.16018i
$78$	−5.50092	+	1.16667i	−0.622857	+	0.132100i
$79$	3.41094	+	1.96931i	0.383760	+	0.221564i	0.679453	−	0.733719i	$-0.262217\pi$
$79$	3.41094	+	1.96931i	0.383760	+	0.221564i	−0.295693	+	0.955283i	$0.595550\pi$
$80$	0.601583	−	2.15362i	0.0672590	−	0.240783i
$81$	2.76575	+	8.56450i	0.307306	+	0.951611i
$82$	−1.17059	+	4.36869i	−0.129270	+	0.482441i
$83$	−0.798015	+	2.97823i	−0.0875936	+	0.326904i	−0.995793	−	0.0916347i	$-0.970791\pi$
$83$	−0.798015	+	2.97823i	−0.0875936	+	0.326904i	0.908199	+	0.418538i	$0.137457\pi$
$84$	0.451939	−	8.54993i	0.0493105	−	0.932874i
$85$	5.49625	+	0.0582228i	0.596152	+	0.00631514i
$86$	3.86773	+	2.23303i	0.417068	+	0.240794i
$87$	2.52109	+	0.820406i	0.270289	+	0.0879567i
$88$	−5.23824	−	1.40358i	−0.558398	−	0.149622i
$89$	−12.5784			−1.33331			−0.666655	−	0.745367i	$-0.732274\pi$
$89$	−12.5784			−1.33331			−0.666655	+	0.745367i	$0.732274\pi$
$90$	0.777820	−	6.66296i	0.0819894	−	0.702337i
$91$	16.0486			1.68235
$92$	3.46253	−	3.46253i	0.360994	−	0.360994i
$93$	9.64340	+	0.0691608i	0.999974	+	0.00717165i
$94$		−	10.9547i		−	1.12990i
$95$	−11.3691	+	11.1307i	−1.16644	+	1.14199i
$96$	−1.54362	+	0.785641i	−0.157545	+	0.0801841i
$97$	4.96468	+	4.96468i	0.504087	+	0.504087i	0.912705	−	0.408618i	$-0.133989\pi$
$97$	4.96468	+	4.96468i	0.504087	+	0.504087i	−0.408618	+	0.912705i	$0.633989\pi$
$98$	−4.51256	+	16.8411i	−0.455838	+	1.70121i
$99$	−16.1784	−	1.71513i	−1.62599	−	0.172377i
$100$	−2.59117	+	4.27620i	−0.259117	+	0.427620i
$101$		−	6.34123i		−	0.630976i	−0.948930	−	0.315488i	$-0.897832\pi$
$101$		−	6.34123i		−	0.630976i	0.948930	−	0.315488i	$-0.102168\pi$
$102$	−2.84748	−	3.16531i	−0.281942	−	0.313412i
$103$	−6.26471	−	1.67862i	−0.617280	−	0.165400i	−0.0633890	−	0.997989i	$-0.520191\pi$
$103$	−6.26471	−	1.67862i	−0.617280	−	0.165400i	−0.553891	+	0.832589i	$0.686858\pi$
$104$	−1.62330	−	2.81164i	−0.159178	−	0.275704i
$105$	−6.11680	+	18.1415i	−0.596939	+	1.77043i
$106$	3.32400	+	5.75734i	0.322856	+	0.559202i
$107$	1.31434	+	4.90518i	0.127062	+	0.474201i	0.999905	−	0.0138000i	$-0.00439282\pi$
$107$	1.31434	+	4.90518i	0.127062	+	0.474201i	−0.872843	+	0.488001i	$0.837726\pi$
$108$	−4.20789	+	3.04855i	−0.404905	+	0.293347i
$109$		−	6.95750i		−	0.666408i	−0.942855	−	0.333204i	$-0.891870\pi$
$109$		−	6.95750i		−	0.666408i	0.942855	−	0.333204i	$-0.108130\pi$
$110$	10.4368	+	6.17402i	0.995113	+	0.588670i
$111$	0.650098	+	0.0343633i	0.0617046	+	0.00326162i
$112$	4.77476	−	1.27939i	0.451173	−	0.120891i
$113$	−1.85267	+	6.91427i	−0.174285	+	0.650439i	0.822388	+	0.568928i	$0.192642\pi$
$113$	−1.85267	+	6.91427i	−0.174285	+	0.650439i	−0.996672	+	0.0815119i	$0.974025\pi$
$114$	12.3072	+	0.650541i	1.15267	+	0.0609288i
$115$	−9.54000	+	5.37399i	−0.889609	+	0.501127i
$116$			1.53068i			0.142120i
$117$	−6.12265	−	7.57476i	−0.566039	−	0.700287i
$118$	1.02994	+	3.84381i	0.0948141	+	0.353851i
$119$	6.07553	+	10.5231i	0.556943	+	0.964653i
$120$	3.79701	−	0.763357i	0.346618	−	0.0696847i
$121$	9.20460	−	15.9428i	0.836782	−	1.44935i
$122$	−5.63617	+	5.63617i	−0.510275	+	0.510275i
$123$	−7.66327	+	1.62528i	−0.690974	+	0.146546i
$124$	1.68490	+	5.30670i	0.151309	+	0.476556i
$125$	8.15289	−	7.65052i	0.729217	−	0.684283i
$126$	13.5529	−	6.01955i	1.20739	−	0.536264i
$127$	4.69034	−	1.25677i	0.416200	−	0.111520i	−0.0446412	−	0.999003i	$-0.514214\pi$
$127$	4.69034	−	1.25677i	0.416200	−	0.111520i	0.460841	+	0.887483i	$0.347548\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−0.408316	+	7.72467i	−0.0359502	+	0.680119i
$130$	1.80455	+	7.03177i	0.158269	+	0.616727i
$131$	−0.817118	−	0.471763i	−0.0713920	−	0.0412182i	0.463879	−	0.885899i	$-0.346457\pi$
$131$	−0.817118	−	0.471763i	−0.0713920	−	0.0412182i	−0.535271	+	0.844680i	$0.679791\pi$
$132$	−1.94877	−	9.18857i	−0.169619	−	0.799763i
$133$	−33.9746	−	9.10348i	−2.94598	−	0.789372i
$134$	6.40571	+	11.0950i	0.553369	+	0.958463i
$135$	10.8962	−	4.03403i	0.937793	−	0.347194i
$136$	1.22907	−	2.12881i	0.105392	−	0.182544i
$137$	−1.11609	−	0.299056i	−0.0953542	−	0.0255501i	0.210826	−	0.977524i	$-0.432385\pi$
$137$	−1.11609	−	0.299056i	−0.0953542	−	0.0255501i	−0.306181	+	0.951973i	$0.599051\pi$
$138$	8.06515	+	2.62454i	0.686551	+	0.223415i
$139$		−	13.9941i		−	1.18697i	−0.804846	−	0.593483i	$-0.797752\pi$
$139$		−	13.9941i		−	1.18697i	0.804846	−	0.593483i	$-0.202248\pi$
$140$	−11.0527	−	0.117083i	−0.934124	−	0.00989534i
$141$	16.9100	−	8.60649i	1.42408	−	0.724797i
$142$	1.99486	−	7.44493i	0.167405	−	0.624764i
$143$	17.0065	−	4.55687i	1.42215	−	0.381065i
$144$	−2.42546	−	1.76554i	−0.202122	−	0.147128i
$145$	0.920832	−	3.29651i	0.0764710	−	0.273761i
$146$	−8.45905	+	4.88383i	−0.700076	+	0.404189i
$147$	−29.5416	+	6.26537i	−2.43655	+	0.516759i
$148$	0.0972792	+	0.363051i	0.00799630	+	0.0298426i
$149$	−5.58764	+	9.67808i	−0.457758	+	0.792860i	−0.998842	−	0.0481088i	$-0.984681\pi$
$149$	−5.58764	+	9.67808i	−0.457758	+	0.792860i	0.541084	+	0.840968i	$0.318014\pi$
$150$	−8.63656	−	0.640232i	−0.705172	−	0.0522747i
$151$	−12.7956			−1.04129			−0.520646	−	0.853773i	$-0.674309\pi$
$151$	−12.7956			−1.04129			−0.520646	+	0.853773i	$0.674309\pi$
$152$	1.84162	+	6.87301i	0.149375	+	0.557475i
$153$	2.64894	−	6.88222i	0.214154	−	0.556395i
$154$			26.8071i			2.16018i
$155$	−0.436219	−	12.4423i	−0.0350379	−	0.999386i
$156$	3.06478	−	4.71470i	0.245379	−	0.377478i
$157$	14.5095	+	14.5095i	1.15799	+	1.15799i	0.984908	+	0.173078i	$0.0553712\pi$
$157$	14.5095	+	14.5095i	1.15799	+	1.15799i	0.173078	+	0.984908i	$0.444629\pi$
$158$	−3.80441	+	1.01939i	−0.302662	+	0.0810981i
$159$	−6.27568	+	9.65420i	−0.497694	+	0.765628i
$160$	1.09746	+	1.94823i	0.0867617	+	0.154021i
$161$	−20.9627	−	12.1028i	−1.65209	−	0.953836i
$162$	−8.01170	−	4.10033i	−0.629458	−	0.322153i
$163$	−11.4457	+	11.4457i	−0.896496	+	0.896496i	−0.995124	−	0.0986282i	$-0.968555\pi$
$163$	−11.4457	+	11.4457i	−0.896496	+	0.896496i	0.0986282	+	0.995124i	$0.468555\pi$
$164$	−2.26140	−	3.91686i	−0.176586	−	0.305855i
$165$	−1.33077	+	20.9611i	−0.103600	+	1.63182i
$166$	−1.54165	−	2.67021i	−0.119655	−	0.207249i
$167$	−2.03847	−	7.60769i	−0.157742	−	0.588700i	−0.998855	−	0.0478413i	$-0.984766\pi$
$167$	−2.03847	−	7.60769i	−0.157742	−	0.588700i	0.841113	−	0.540859i	$-0.181901\pi$
$168$	5.72615	+	6.36528i	0.441782	+	0.491092i
$169$	−2.13005	−	1.22978i	−0.163850	−	0.0945988i
$170$	−3.92761	+	3.84527i	−0.301234	+	0.294919i
$171$	8.66482	+	19.5087i	0.662615	+	1.49187i
$172$	−4.31389	+	1.15590i	−0.328931	+	0.0881367i
$173$	−2.82879	+	10.5572i	−0.215069	+	0.802648i	0.771074	+	0.636746i	$0.219720\pi$
$173$	−2.82879	+	10.5572i	−0.215069	+	0.802648i	−0.986142	+	0.165902i	$0.946947\pi$
$174$	−2.36279	+	1.20257i	−0.179123	+	0.0911663i
$175$	23.7329	+	6.90127i	1.79404	+	0.521687i
$176$	4.69648	−	2.71151i	0.354010	−	0.204388i
$177$	−5.12422	+	4.60970i	−0.385160	+	0.346486i
$178$	8.89429	−	8.89429i	0.666655	−	0.666655i
$179$	6.72567	−	11.6492i	0.502700	−	0.870702i	−0.497295	−	0.867581i	$-0.665673\pi$
$179$	6.72567	−	11.6492i	0.502700	−	0.870702i	0.999995	−	0.00312043i	$-0.000993266\pi$
$180$	4.16142	+	5.26142i	0.310174	+	0.392163i
$181$	2.80510	+	4.85858i	0.208502	+	0.361135i	0.951243	−	0.308443i	$-0.0998080\pi$
$181$	2.80510	+	4.85858i	0.208502	+	0.361135i	−0.742741	+	0.669579i	$0.766475\pi$
$182$	−11.3481	+	11.3481i	−0.841175	+	0.841175i
$183$	−13.1281	−	4.27211i	−0.970458	−	0.315803i
$184$			4.89676i			0.360994i
$185$	0.00890248	−	0.840397i	0.000654523	−	0.0617872i
$186$	−6.86782	+	6.77001i	−0.503573	+	0.496401i
$187$	9.42611	+	9.42611i	0.689305	+	0.689305i
$188$	7.74617	+	7.74617i	0.564948	+	0.564948i
$189$	19.9396	+	16.1914i	1.45040	+	1.17775i
$190$	0.168535	−	15.9098i	0.0122268	−	1.15422i
$191$	16.5201	−	9.53788i	1.19535	−	0.690137i	0.235837	−	0.971793i	$-0.424217\pi$
$191$	16.5201	−	9.53788i	1.19535	−	0.690137i	0.959515	+	0.281656i	$0.0908837\pi$
$192$	0.535974	−	1.64704i	0.0386806	−	0.118865i
$193$	4.98267	+	18.5956i	0.358660	+	1.33854i	0.875815	+	0.482647i	$0.160324\pi$
$193$	4.98267	+	18.5956i	0.358660	+	1.33854i	−0.517155	+	0.855892i	$0.673009\pi$
$194$	−7.02112			−0.504087
$195$	−9.43667	+	8.30998i	−0.675774	+	0.595090i
$196$	−8.71760	−	15.0993i	−0.622686	−	1.07852i
$197$	−21.6846	−	5.81038i	−1.54497	−	0.413972i	−0.617099	−	0.786885i	$-0.711692\pi$
$197$	−21.6846	−	5.81038i	−1.54497	−	0.413972i	−0.927866	+	0.372913i	$0.878359\pi$
$198$	12.6526	−	10.2271i	0.899185	−	0.726807i
$199$	2.56290	−	1.47969i	0.181679	−	0.104892i	−0.406402	−	0.913694i	$-0.633217\pi$
$199$	2.56290	−	1.47969i	0.181679	−	0.104892i	0.588081	+	0.808802i	$0.299884\pi$
$200$	−1.19149	−	4.85596i	−0.0842514	−	0.343368i
$201$	−12.0939	+	18.6047i	−0.853040	+	1.31227i
$202$	4.48393	+	4.48393i	0.315488	+	0.315488i
$203$	7.30864	−	1.95834i	0.512966	−	0.137449i
$204$	4.25168	+	0.224738i	0.297677	+	0.0157348i
$205$	2.51389	+	9.79587i	0.175578	+	0.684173i
$206$	5.61678	−	3.24285i	0.391340	−	0.225940i
$207$	2.28502	+	14.5115i	0.158820	+	1.00862i
$208$	3.13598	+	0.840283i	0.217441	+	0.0582631i
$209$	−38.5873			−2.66914
$210$	−8.50272	−	17.1532i	−0.586743	−	1.18368i
$211$	−7.02674	+	12.1707i	−0.483741	+	0.837864i	−0.999826	−	0.0186735i	$-0.994056\pi$
$211$	−7.02674	+	12.1707i	−0.483741	+	0.837864i	0.516085	+	0.856538i	$0.327389\pi$
$212$	−6.42148	−	1.72063i	−0.441029	−	0.118173i
$213$	13.0594	−	2.76972i	0.894815	−	0.189778i
$214$	−4.39786	−	2.53911i	−0.300632	−	0.173570i
$215$	9.98586	+	0.105782i	0.681030	+	0.00721427i
$216$	0.819781	−	5.13108i	0.0557790	−	0.349126i
$217$	23.1826	−	14.8344i	1.57374	−	1.00702i
$218$	4.91970	+	4.91970i	0.333204	+	0.333204i
$219$	−14.1846	−	9.22064i	−0.958504	−	0.623073i
$220$	−11.7456	+	3.01426i	−0.791891	+	0.203221i
$221$			7.98059i			0.536833i
$222$	−0.483987	+	0.435390i	−0.0324831	+	0.0292215i
$223$	2.27130	+	8.47660i	0.152097	+	0.567635i	0.999336	+	0.0364234i	$0.0115965\pi$
$223$	2.27130	+	8.47660i	0.152097	+	0.567635i	−0.847239	+	0.531212i	$0.821737\pi$
$224$	−2.47160	+	4.28093i	−0.165141	+	0.286032i
$225$	−5.79695	−	13.8346i	−0.386463	−	0.922305i
$226$	−3.57909	−	6.19916i	−0.238077	−	0.412362i
$227$	6.20161	+	1.66172i	0.411616	+	0.110292i	0.458684	−	0.888600i	$-0.348321\pi$
$227$	6.20161	+	1.66172i	0.411616	+	0.110292i	−0.0470681	+	0.998892i	$0.514988\pi$
$228$	−9.16248	+	8.24248i	−0.606800	+	0.545871i
$229$	−11.2643	−	6.50345i	−0.744366	−	0.429760i	0.0792886	−	0.996852i	$-0.474735\pi$
$229$	−11.2643	−	6.50345i	−0.744366	−	0.429760i	−0.823655	+	0.567092i	$0.808068\pi$
$230$	2.94581	−	10.5458i	0.194241	−	0.695368i
$231$	−41.3800	+	21.0607i	−2.72260	+	1.38569i
$232$	−1.08236	−	1.08236i	−0.0710601	−	0.0710601i
$233$	−6.28446	−	6.28446i	−0.411708	−	0.411708i	0.470625	−	0.882333i	$-0.344028\pi$
$233$	−6.28446	−	6.28446i	−0.411708	−	0.411708i	−0.882333	+	0.470625i	$0.844028\pi$
$234$	9.68553	+	1.02680i	0.633163	+	0.0671240i
$235$	−12.0224	−	21.3423i	−0.784253	−	1.39222i
$236$	−3.44626	−	1.98970i	−0.224333	−	0.129518i
$237$	−4.56244	−	5.07169i	−0.296363	−	0.329442i
$238$	−11.7370	−	3.14492i	−0.760798	−	0.203855i
$239$	−3.89851	−	6.75242i	−0.252174	−	0.436778i	0.711950	−	0.702230i	$-0.247812\pi$
$239$	−3.89851	−	6.75242i	−0.252174	−	0.436778i	−0.964124	+	0.265452i	$0.914479\pi$
$240$	−2.14512	+	3.22467i	−0.138467	+	0.208151i
$241$	−9.89698	+	17.1421i	−0.637521	+	1.10422i	0.348454	+	0.937326i	$0.386707\pi$
$241$	−9.89698	+	17.1421i	−0.637521	+	1.10422i	−0.985975	+	0.166893i	$0.946627\pi$
$242$	4.76465	+	17.7819i	0.306283	+	1.14306i
$243$	0.0350512	−	15.5884i	0.00224854	−	0.999997i
$244$		−	7.97074i		−	0.510275i
$245$	9.69094	+	37.7626i	0.619131	+	2.41257i
$246$	4.26950	−	6.56799i	0.272214	−	0.418760i
$247$	−16.3349	−	16.3349i	−1.03937	−	1.03937i
$248$	−4.94381	−	2.56100i	−0.313932	−	0.162624i
$249$	2.91062	−	4.47755i	0.184453	−	0.283753i
$250$	−0.355233	+	11.1747i	−0.0224669	+	0.706750i
$251$	−2.65154	−	1.53087i	−0.167364	−	0.0966276i	0.413978	−	0.910287i	$-0.364139\pi$
$251$	−2.65154	−	1.53087i	−0.167364	−	0.0966276i	−0.581342	+	0.813659i	$0.697472\pi$
$252$	−5.32690	+	13.8398i	−0.335563	+	0.871827i
$253$	−25.6504	−	6.87300i	−1.61263	−	0.432102i
$254$	−2.42790	+	4.20524i	−0.152340	+	0.263860i
$255$	−9.02133	−	3.04174i	−0.564937	−	0.190481i
$256$	1.00000			0.0625000
$257$	2.31021	+	0.619019i	0.144107	+	0.0386134i	0.330151	−	0.943928i	$-0.392900\pi$
$257$	2.31021	+	0.619019i	0.144107	+	0.0386134i	−0.186044	+	0.982541i	$0.559567\pi$
$258$	−5.17344	−	5.75089i	−0.322084	−	0.358035i
$259$	1.60902	−	0.928971i	0.0999799	−	0.0577234i
$260$	−6.24822	−	3.69620i	−0.387498	−	0.229229i
$261$	−3.71261	−	2.70248i	−0.229805	−	0.167279i
$262$	0.911377	−	0.244203i	0.0563051	−	0.0150869i
$263$	5.38068	+	5.38068i	0.331787	+	0.331787i	0.853265	−	0.521478i	$-0.174619\pi$
$263$	5.38068	+	5.38068i	0.331787	+	0.331787i	−0.521478	+	0.853265i	$0.674619\pi$
$264$	7.87529	+	5.11931i	0.484691	+	0.315072i
$265$	12.7943	+	7.56864i	0.785950	+	0.464938i
$266$	30.4608	−	17.5866i	1.86767	−	1.07830i
$267$	20.7171	+	6.74170i	1.26787	+	0.412586i
$268$	−12.3749	−	3.31584i	−0.755916	−	0.202547i
$269$	−5.61797	−	9.73061i	−0.342534	−	0.593286i	0.642369	−	0.766396i	$-0.277952\pi$
$269$	−5.61797	−	9.73061i	−0.342534	−	0.593286i	−0.984902	+	0.173110i	$0.944618\pi$
$270$	−4.85227	+	10.5572i	−0.295300	+	0.642494i
$271$	10.9344			0.664220			0.332110	−	0.943241i	$-0.392239\pi$
$271$	10.9344			0.664220			0.332110	+	0.943241i	$0.392239\pi$
$272$	0.636212	+	2.37438i	0.0385760	+	0.143968i
$273$	−26.4326	−	8.60163i	−1.59978	−	0.520594i
$274$	1.00066	−	0.577732i	0.0604521	−	0.0349021i
$275$	27.1090	+	0.574406i	1.63474	+	0.0346380i
$276$	−7.55875	+	3.84709i	−0.454983	+	0.231568i
$277$	−14.1752	−	14.1752i	−0.851707	−	0.851707i	0.138637	−	0.990343i	$-0.455728\pi$
$277$	−14.1752	−	14.1752i	−0.851707	−	0.851707i	−0.990343	+	0.138637i	$0.955728\pi$
$278$	9.89534	+	9.89534i	0.593483	+	0.593483i
$279$	−15.8460	−	5.28252i	−0.948674	−	0.316256i
$280$	7.89823	−	7.73265i	0.472010	−	0.462114i
$281$			8.19366i			0.488793i	0.969675	+	0.244397i	$0.0785898\pi$
$281$			8.19366i			0.488793i	−0.969675	+	0.244397i	$0.921410\pi$
$282$	−5.87145	+	18.0429i	−0.349640	+	1.07444i
$283$	13.3225	−	13.3225i	0.791939	−	0.791939i	−0.189870	−	0.981809i	$-0.560807\pi$
$283$	13.3225	−	13.3225i	0.791939	−	0.791939i	0.981809	+	0.189870i	$0.0608068\pi$
$284$	3.85378	+	6.67494i	0.228680	+	0.396085i
$285$	24.6911	−	12.2392i	1.46257	−	0.724988i
$286$	−8.80320	+	15.2476i	−0.520544	+	0.901609i
$287$	−15.8089	+	15.8089i	−0.933167	+	0.933167i
$288$	2.96349	−	0.466638i	0.174625	−	0.0274969i
$289$	9.48953	−	5.47878i	0.558208	−	0.322281i
$290$	1.67986	+	2.98211i	0.0986448	+	0.175116i
$291$	−5.51608	−	10.8380i	−0.323358	−	0.635332i
$292$	2.52806	−	9.43484i	0.147943	−	0.552132i
$293$	−8.95550	+	2.39962i	−0.523186	+	0.140187i	−0.510740	−	0.859735i	$-0.670628\pi$
$293$	−8.95550	+	2.39962i	−0.523186	+	0.140187i	−0.0124460	+	0.999923i	$0.503962\pi$
$294$	16.4588	−	25.3193i	0.959894	−	1.47665i
$295$	6.22498	+	6.35828i	0.362433	+	0.370193i
$296$	−0.325503	−	0.187929i	−0.0189195	−	0.0109232i
$297$	25.7272	+	11.4961i	1.49284	+	0.667071i
$298$	−2.89238	−	10.7945i	−0.167551	−	0.625309i
$299$	−7.94892	−	13.7679i	−0.459698	−	0.796220i
$300$	6.55968	−	5.65425i	0.378723	−	0.326449i
$301$	11.0383	+	19.1189i	0.636238	+	1.10200i
$302$	9.04786	−	9.04786i	0.520646	−	0.520646i
$303$	−3.39873	+	10.4442i	−0.195252	+	0.600006i
$304$	−6.16217	−	3.55773i	−0.353425	−	0.204050i
$305$	−4.79506	+	17.1660i	−0.274565	+	0.982921i
$306$	2.99338	+	6.73955i	0.171120	+	0.385275i
$307$	−6.26027	+	1.67744i	−0.357293	+	0.0957363i	−0.433000	−	0.901394i	$-0.642545\pi$
$307$	−6.26027	+	1.67744i	−0.357293	+	0.0957363i	0.0757076	+	0.997130i	$0.475878\pi$
$308$	−18.9555	−	18.9555i	−1.08009	−	1.08009i
$309$	9.41851	+	6.12248i	0.535800	+	0.348295i
$310$	9.10646	+	8.48955i	0.517212	+	0.482174i
$311$			17.9267i			1.01653i	0.861202	+	0.508264i	$0.169712\pi$
$311$			17.9267i			1.01653i	−0.861202	+	0.508264i	$0.830288\pi$
$312$	1.16667	+	5.50092i	0.0660498	+	0.311429i
$313$	−5.44812	−	20.3326i	−0.307946	−	1.14927i	−0.930380	−	0.366597i	$-0.880523\pi$
$313$	−5.44812	−	20.3326i	−0.307946	−	1.14927i	0.622434	−	0.782672i	$-0.286144\pi$
$314$	−20.5196			−1.15799
$315$	19.7980	−	26.6012i	1.11549	−	1.49881i
$316$	1.96931	−	3.41094i	0.110782	−	0.191880i
$317$	−6.18989	−	23.1010i	−0.347659	−	1.29748i	−0.889475	−	0.456984i	$-0.848930\pi$
$317$	−6.18989	−	23.1010i	−0.347659	−	1.29748i	0.541816	−	0.840497i	$-0.317737\pi$
$318$	−2.38897	−	11.2641i	−0.133967	−	0.631661i
$319$	7.18881	−	4.15046i	0.402496	−	0.232381i
$320$	−2.15362	−	0.601583i	−0.120391	−	0.0336295i
$321$	0.464282	−	8.78346i	0.0259137	−	0.490245i
$322$	23.3809	−	6.26488i	1.30296	−	0.349128i
$323$	4.52695	−	16.8948i	0.251886	−	0.940052i
$324$	8.56450	−	2.76575i	0.475805	−	0.153653i
$325$	11.2327	+	11.7191i	0.623080	+	0.650056i
$326$		−	16.1867i		−	0.896496i
$327$	−3.72904	+	11.4593i	−0.206216	+	0.633699i
$328$	4.36869	+	1.17059i	0.241221	+	0.0646349i
$329$	27.0757	−	46.8965i	1.49273	−	2.58549i
$330$	−13.8807	−	15.7627i	−0.764109	−	0.867709i
$331$	−2.25600	−	3.90750i	−0.124001	−	0.214776i	0.797341	−	0.603529i	$-0.206239\pi$
$331$	−2.25600	−	3.90750i	−0.124001	−	0.214776i	−0.921342	+	0.388753i	$0.872906\pi$
$332$	2.97823	+	0.798015i	0.163452	+	0.0437968i
$333$	−1.05232	−	0.405033i	−0.0576666	−	0.0221957i
$334$	6.82087	+	3.93803i	0.373221	+	0.215479i
$335$	24.6561	+	14.5856i	1.34711	+	0.796896i
$336$	−8.54993	−	0.451939i	−0.466437	−	0.0246553i
$337$	22.0985	+	22.0985i	1.20378	+	1.20378i	0.973006	+	0.230778i	$0.0741270\pi$
$337$	22.0985	+	22.0985i	1.20378	+	1.20378i	0.230778	+	0.973006i	$0.425873\pi$
$338$	2.37576	−	0.636583i	0.129224	−	0.0346256i
$339$	6.75729	−	10.3951i	0.367005	−	0.564583i
$340$	0.0582228	−	5.49625i	0.00315757	−	0.298076i
$341$	20.3542	−	22.3023i	1.10224	−	1.20774i
$342$	−19.9217	−	7.66778i	−1.07724	−	0.414626i
$343$	−36.4749	+	36.4749i	−1.96946	+	1.96946i
$344$	2.23303	−	3.86773i	0.120397	−	0.208534i
$345$	18.5930	−	3.73798i	1.00102	−	0.201246i
$346$	−5.46480	−	9.46531i	−0.293789	−	0.508858i
$347$	−5.39474	−	20.1334i	−0.289605	−	1.08082i	−0.945408	−	0.325888i	$-0.894337\pi$
$347$	−5.39474	−	20.1334i	−0.289605	−	1.08082i	0.655804	−	0.754932i	$-0.272330\pi$
$348$	0.820406	−	2.52109i	0.0439784	−	0.135145i
$349$			12.5475i			0.671650i	0.941924	+	0.335825i	$0.109015\pi$
$349$			12.5475i			0.671650i	−0.941924	+	0.335825i	$0.890985\pi$
$350$	−21.6617	+	11.9018i	−1.15786	+	0.636177i
$351$	6.02436	+	15.7575i	0.321556	+	0.841073i
$352$	−1.40358	+	5.23824i	−0.0748112	+	0.279199i
$353$	11.0986	−	2.97387i	0.590720	−	0.158283i	0.0489378	−	0.998802i	$-0.484416\pi$
$353$	11.0986	−	2.97387i	0.590720	−	0.158283i	0.541782	+	0.840519i	$0.317750\pi$
$354$	0.363822	−	6.88292i	0.0193369	−	0.365823i
$355$	−4.28406	−	16.6937i	−0.227374	−	0.886008i
$356$			12.5784i			0.666655i
$357$	−4.36650	−	20.5883i	−0.231100	−	1.08965i
$358$	3.48146	+	12.9930i	0.184001	+	0.686701i
$359$	−0.528303	−	0.915048i	−0.0278828	−	0.0482944i	0.851747	−	0.523953i	$-0.175543\pi$
$359$	−0.528303	−	0.915048i	−0.0278828	−	0.0482944i	−0.879630	+	0.475658i	$0.842210\pi$
$360$	−6.66296	−	0.777820i	−0.351169	−	0.0409947i
$361$	15.8149	+	27.3922i	0.832364	+	1.44170i
$362$	−5.41904	−	1.45203i	−0.284818	−	0.0763169i
$363$	−23.7053	+	21.3250i	−1.24420	+	1.11927i
$364$		−	16.0486i		−	0.841175i
$365$	−11.1203	+	18.7983i	−0.582065	+	0.983946i
$366$	12.3038	−	6.26214i	0.643131	−	0.327327i
$367$	0.588658	−	2.19690i	0.0307277	−	0.114677i	−0.948859	−	0.315701i	$-0.897760\pi$
$367$	0.588658	−	2.19690i	0.0307277	−	0.114677i	0.979586	+	0.201024i	$0.0644269\pi$
$368$	−3.46253	−	3.46253i	−0.180497	−	0.180497i
$369$	13.4928	+	1.43042i	0.702407	+	0.0744647i
$370$	0.587956	+	0.600546i	0.0305664	+	0.0312209i
$371$			32.8624i			1.70613i
$372$	0.0691608	−	9.64340i	0.00358582	−	0.499987i
$373$	−7.36989	+	7.36989i	−0.381598	+	0.381598i	−0.871678	−	0.490079i	$-0.836968\pi$
$373$	−7.36989	+	7.36989i	−0.381598	+	0.381598i	0.490079	+	0.871678i	$0.336968\pi$
$374$	−13.3305			−0.689305
$375$	−17.5286	+	8.23095i	−0.905173	+	0.425044i
$376$	−10.9547			−0.564948
$377$	4.80018	+	1.28621i	0.247222	+	0.0662430i
$378$	−25.5485	+	2.65041i	−1.31407	+	0.136322i
$379$	−15.9819	−	9.22714i	−0.820934	−	0.473966i	0.0298046	−	0.999556i	$-0.490512\pi$
$379$	−15.9819	−	9.22714i	−0.820934	−	0.473966i	−0.850738	+	0.525589i	$0.823845\pi$
$380$	11.1307	+	11.3691i	0.570995	+	0.583221i
$381$	−8.39875	−	0.443948i	−0.430281	−	0.0227441i
$382$	−4.93717	+	18.4258i	−0.252608	+	0.942744i
$383$	−5.63205	+	21.0191i	−0.287784	+	1.07402i	0.658997	+	0.752146i	$0.270981\pi$
$383$	−5.63205	+	21.0191i	−0.287784	+	1.07402i	−0.946781	+	0.321879i	$0.895686\pi$
$384$	0.785641	+	1.54362i	0.0400920	+	0.0787726i
$385$	29.4197	+	52.2262i	1.49937	+	2.66170i
$386$	−16.6723	−	9.62577i	−0.848599	−	0.489939i
$387$	4.81273	−	12.5040i	0.244645	−	0.635612i
$388$	4.96468	−	4.96468i	0.252044	−	0.252044i
$389$	15.3809	−	26.6405i	0.779842	−	1.35073i	−0.152191	−	0.988351i	$-0.548633\pi$
$389$	15.3809	−	26.6405i	0.779842	−	1.35073i	0.932033	−	0.362375i	$-0.118034\pi$
$390$	0.796690	−	12.5488i	0.0403420	−	0.635432i
$391$	6.01845	−	10.4243i	0.304366	−	0.527178i
$392$	16.8411	+	4.51256i	0.850605	+	0.227919i
$393$	1.09297	+	1.21497i	0.0551331	+	0.0612869i
$394$	19.4419	−	11.2248i	0.979469	−	0.565497i
$395$	−6.29311	+	6.16118i	−0.316640	+	0.310002i
$396$	−1.71513	+	16.1784i	−0.0861887	+	0.812996i
$397$	2.99218	−	0.801753i	0.150173	−	0.0402388i	−0.182949	−	0.983122i	$-0.558564\pi$
$397$	2.99218	−	0.801753i	0.150173	−	0.0402388i	0.333123	+	0.942884i	$0.391898\pi$
$398$	−0.765943	+	2.85854i	−0.0383933	+	0.143286i
$399$	51.0783	+	33.2033i	2.55711	+	1.66224i
$400$	4.27620	+	2.59117i	0.213810	+	0.129558i
$401$		−	9.82965i		−	0.490869i	−0.969413	−	0.245435i	$-0.921069\pi$
$401$		−	9.82965i		−	0.490869i	0.969413	−	0.245435i	$-0.0789307\pi$
$402$	−4.60381	−	21.7072i	−0.229617	−	1.08266i
$403$	18.0575	−	0.824679i	0.899508	−	0.0410802i
$404$	−6.34123			−0.315488
$405$	−20.1085	+	0.804132i	−0.999201	+	0.0399576i
$406$	−3.78323	+	6.55275i	−0.187759	+	0.325207i
$407$	1.44129	−	1.44129i	0.0714420	−	0.0714420i
$408$	−3.16531	+	2.84748i	−0.156706	+	0.140971i
$409$	−24.6866	−	14.2528i	−1.22067	−	0.704755i	−0.255610	−	0.966780i	$-0.582276\pi$
$409$	−24.6866	−	14.2528i	−1.22067	−	0.704755i	−0.965061	+	0.262025i	$0.915610\pi$
$410$	−8.70431	−	5.14914i	−0.429875	−	0.254298i
$411$	1.67796	+	1.09075i	0.0827676	+	0.0538029i
$412$	−1.67862	+	6.26471i	−0.0826998	+	0.308640i
$413$	−5.09122	+	19.0007i	−0.250523	+	0.934963i
$414$	−11.8769	−	8.64542i	−0.583719	−	0.424899i
$415$	−5.93392	−	3.51028i	−0.291285	−	0.172313i
$416$	−2.81164	+	1.62330i	−0.137852	+	0.0795889i
$417$	−7.50049	+	23.0488i	−0.367300	+	1.12871i
$418$	27.2854	−	27.2854i	1.33457	−	1.33457i
$419$	−0.972131			−0.0474917			−0.0237459	−	0.999718i	$-0.507559\pi$
$419$	−0.972131			−0.0474917			−0.0237459	+	0.999718i	$0.507559\pi$
$420$	18.1415	+	6.11680i	0.885213	+	0.298469i
$421$	−2.46419	−	4.26810i	−0.120097	−	0.208015i	0.799709	−	0.600388i	$-0.204987\pi$
$421$	−2.46419	−	4.26810i	−0.120097	−	0.208015i	−0.919806	+	0.392374i	$0.871654\pi$
$422$	−3.63731	−	13.5746i	−0.177062	−	0.660803i
$423$	−32.4642	+	5.11190i	−1.57846	+	0.248549i
$424$	5.75734	−	3.32400i	0.279601	−	0.161428i
$425$	−3.43184	+	11.8018i	−0.166469	+	0.572473i
$426$	−7.27590	+	11.1929i	−0.352518	+	0.542297i
$427$	−38.0584	+	10.1977i	−1.84178	+	0.493502i
$428$	4.90518	−	1.31434i	0.237101	−	0.0635309i
$429$	−30.4527	−	1.60969i	−1.47027	−	0.0777166i
$430$	−7.13587	+	6.98627i	−0.344122	+	0.336908i
$431$	−20.8507	−	12.0381i	−1.00434	−	0.579856i	−0.0948111	−	0.995495i	$-0.530225\pi$
$431$	−20.8507	−	12.0381i	−1.00434	−	0.579856i	−0.909530	+	0.415639i	$0.863558\pi$
$432$	3.04855	+	4.20789i	0.146673	+	0.202452i
$433$	13.3188	−	13.3188i	0.640060	−	0.640060i	−0.310510	−	0.950570i	$-0.600500\pi$
$433$	13.3188	−	13.3188i	0.640060	−	0.640060i	0.950570	+	0.310510i	$0.100500\pi$
$434$	−5.90309	+	26.8821i	−0.283358	+	1.29038i
$435$	−3.28349	+	4.93594i	−0.157431	+	0.236660i
$436$	−6.95750			−0.333204
$437$	9.01796	+	33.6555i	0.431388	+	1.60996i
$438$	16.5500	−	3.51003i	0.790788	−	0.167716i
$439$	20.1238	−	11.6185i	0.960458	−	0.554521i	0.0641439	−	0.997941i	$-0.479568\pi$
$439$	20.1238	−	11.6185i	0.960458	−	0.554521i	0.896314	+	0.443420i	$0.146235\pi$
$440$	6.17402	−	10.4368i	0.294335	−	0.497556i
$441$	52.0141	+	5.51421i	2.47686	+	0.262581i
$442$	−5.64313	−	5.64313i	−0.268416	−	0.268416i
$443$	10.8376	−	40.4464i	0.514910	−	1.92167i	0.158408	−	0.987374i	$-0.449364\pi$
$443$	10.8376	−	40.4464i	0.514910	−	1.92167i	0.356502	−	0.934295i	$-0.383969\pi$
$444$	0.0343633	−	0.650098i	0.00163081	−	0.0308523i
$445$	7.56696	−	27.0892i	0.358709	−	1.28415i
$446$	−7.59991	−	4.38781i	−0.359866	−	0.207769i
$447$	14.3903	−	12.9453i	0.680636	−	0.612293i
$448$	−1.27939	−	4.77476i	−0.0604457	−	0.225586i
$449$	31.8388			1.50256			0.751282	−	0.659981i	$-0.229436\pi$
$449$	31.8388			1.50256			0.751282	+	0.659981i	$0.229436\pi$
$450$	13.8816	+	5.68345i	0.654384	+	0.267921i
$451$	−12.2636	+	21.2412i	−0.577472	+	1.00021i
$452$	6.91427	+	1.85267i	0.325220	+	0.0871424i
$453$	21.0748	+	6.85811i	0.990182	+	0.322222i
$454$	−5.56021	+	3.21019i	−0.260954	+	0.150662i
$455$	−9.65457	+	34.5627i	−0.452613	+	1.62032i
$456$	0.650541	−	12.3072i	0.0304644	−	0.576336i
$457$	8.13264	+	8.13264i	0.380429	+	0.380429i	0.871257	−	0.490828i	$-0.163306\pi$
$457$	8.13264	+	8.13264i	0.380429	+	0.380429i	−0.490828	+	0.871257i	$0.663306\pi$
$458$	12.5637	−	3.36643i	0.587063	−	0.157303i
$459$	−8.05160	+	9.91552i	−0.375816	+	0.462817i
$460$	5.37399	+	9.54000i	0.250564	+	0.444805i
$461$		−	5.70422i		−	0.265672i	−0.991138	−	0.132836i	$-0.957592\pi$
$461$		−	5.70422i		−	0.265672i	0.991138	−	0.132836i	$-0.0424084\pi$
$462$	14.3679	−	44.1523i	0.668455	−	2.05415i
$463$	6.00369	−	6.00369i	0.279015	−	0.279015i	−0.553701	−	0.832716i	$-0.686785\pi$
$463$	6.00369	−	6.00369i	0.279015	−	0.279015i	0.832716	+	0.553701i	$0.186785\pi$
$464$	1.53068			0.0710601
$465$	−5.95026	+	20.7267i	−0.275936	+	0.961176i
$466$	8.88756			0.411708
$467$	26.3394	−	26.3394i	1.21884	−	1.21884i	0.250803	−	0.968038i	$-0.419305\pi$
$467$	26.3394	−	26.3394i	1.21884	−	1.21884i	0.968038	−	0.250803i	$-0.0806945\pi$
$468$	−7.57476	+	6.12265i	−0.350144	+	0.283020i
$469$			63.3294i			2.92428i
$470$	23.5924	+	6.59019i	1.08824	+	0.303983i
$471$	−16.1210	−	31.6744i	−0.742816	−	1.45948i
$472$	3.84381	−	1.02994i	0.176926	−	0.0474071i
$473$	17.1258	+	17.1258i	0.787446	+	0.787446i
$474$	6.81236	+	0.360093i	0.312902	+	0.0165396i
$475$	−17.1320	−	31.1808i	−0.786069	−	1.43067i
$476$	10.5231	−	6.07553i	0.482326	−	0.278471i
$477$	15.5107	−	12.5372i	0.710185	−	0.574040i
$478$	7.53135	+	2.01802i	0.344476	+	0.0923020i
$479$	−5.14187	+	8.90598i	−0.234938	+	0.406925i	−0.959255	−	0.282543i	$-0.908822\pi$
$479$	−5.14187	+	8.90598i	−0.234938	+	0.406925i	0.724317	+	0.689467i	$0.242155\pi$
$480$	−0.763357	−	3.79701i	−0.0348423	−	0.173309i
$481$	1.22026			0.0556392
$482$	−5.12306	−	19.1195i	−0.233349	−	0.870870i
$483$	28.0396	+	31.1693i	1.27584	+	1.41825i
$484$	−15.9428	−	9.20460i	−0.724674	−	0.418391i
$485$	−13.6787	+	7.70539i	−0.621119	+	0.349884i
$486$	10.9979	+	11.0475i	0.498874	+	0.501123i
$487$	9.85354	−	36.7739i	0.446507	−	1.66639i	−0.265421	−	0.964133i	$-0.585511\pi$
$487$	9.85354	−	36.7739i	0.446507	−	1.66639i	0.711928	−	0.702253i	$-0.247822\pi$
$488$	5.63617	+	5.63617i	0.255137	+	0.255137i
$489$	24.9861	−	12.7169i	1.12991	−	0.575078i
$490$	−33.5547	−	19.8497i	−1.51585	−	0.896718i
$491$	28.3604	−	16.3739i	1.27989	−	0.738942i	0.303058	−	0.952972i	$-0.401992\pi$
$491$	28.3604	−	16.3739i	1.27989	−	0.738942i	0.976827	+	0.214030i	$0.0686589\pi$
$492$	1.62528	+	7.66327i	0.0732731	+	0.345487i
$493$	0.973839	+	3.63442i	0.0438595	+	0.163686i
$494$	23.1011			1.03937
$495$	13.4264	−	33.8104i	0.603472	−	1.51967i
$496$	5.30670	−	1.68490i	0.238278	−	0.0756543i
$497$	26.9407	−	26.9407i	1.20846	−	1.20846i
$498$	1.10799	+	5.22422i	0.0496501	+	0.234103i
$499$	−14.2250	−	8.21278i	−0.636796	−	0.367655i	0.146583	−	0.989198i	$-0.453172\pi$
$499$	−14.2250	−	8.21278i	−0.636796	−	0.367655i	−0.783379	+	0.621544i	$0.786506\pi$
$500$	−7.65052	−	8.15289i	−0.342141	−	0.364608i
$501$	−0.720079	+	13.6227i	−0.0321708	+	0.608618i
$502$	2.95741	−	0.792436i	0.131996	−	0.0353682i
$503$	12.8144	−	3.43361i	0.571366	−	0.153097i	0.0384432	−	0.999261i	$-0.487760\pi$
$503$	12.8144	−	3.43361i	0.571366	−	0.153097i	0.532923	+	0.846164i	$0.321093\pi$
$504$	−6.01955	−	13.5529i	−0.268132	−	0.603695i
$505$	13.6566	+	3.81478i	0.607712	+	0.169755i
$506$	22.9975	−	13.2776i	1.02236	−	0.590262i
$507$	2.84914	+	3.16715i	0.126535	+	0.140658i
$508$	−1.25677	−	4.69034i	−0.0557602	−	0.208100i
$509$	5.11037	+	8.85142i	0.226513	+	0.392332i	0.956772	−	0.290838i	$-0.0939341\pi$
$509$	5.11037	+	8.85142i	0.226513	+	0.392332i	−0.730259	+	0.683170i	$0.760601\pi$
$510$	8.52988	−	4.22820i	0.377709	−	0.187228i
$511$	−48.2835			−2.13594
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−3.81512	−	36.7757i	−0.168442	−	1.62369i
$514$	−2.07128	+	1.19585i	−0.0913602	+	0.0527469i
$515$	7.38387	−	12.4820i	0.325372	−	0.550022i
$516$	7.72467	+	0.408316i	0.340059	+	0.0179751i
$517$	15.3759	−	57.3835i	0.676230	−	2.52373i
$518$	−0.480871	+	1.79463i	−0.0211282	+	0.0788517i
$519$	10.3175	−	15.8719i	0.452888	−	0.696700i
$520$	7.03177	−	1.80455i	0.308363	−	0.0791346i
$521$	−12.9480	−	7.47555i	−0.567263	−	0.327510i	0.188792	−	0.982017i	$-0.439543\pi$
$521$	−12.9480	−	7.47555i	−0.567263	−	0.327510i	−0.756056	+	0.654507i	$0.772876\pi$
$522$	4.53615	−	0.714275i	0.198542	−	0.0312630i
$523$	−4.53028	+	4.53028i	−0.198095	+	0.198095i	−0.799183	−	0.601088i	$-0.794734\pi$
$523$	−4.53028	+	4.53028i	−0.198095	+	0.198095i	0.601088	+	0.799183i	$0.294734\pi$
$524$	−0.471763	+	0.817118i	−0.0206091	+	0.0356960i
$525$	−35.3901	−	24.0869i	−1.54455	−	1.05124i
$526$	−7.60943			−0.331787
$527$	7.37678	+	11.5282i	0.321338	+	0.502175i
$528$	−9.18857	+	1.94877i	−0.399881	+	0.0848095i
$529$			0.978261i			0.0425331i
$530$	−14.3988	+	3.69513i	−0.625444	+	0.160506i
$531$	10.9105	−	4.84589i	0.473473	−	0.210294i
$532$	−9.10348	+	33.9746i	−0.394686	+	1.47299i
$533$	−14.1834	+	3.80043i	−0.614351	+	0.164615i
$534$	−19.4163	+	9.88212i	−0.840227	+	0.427641i
$535$	−11.3546	−	0.120281i	−0.490902	−	0.00520021i
$536$	11.0950	−	6.40571i	0.479232	−	0.276685i
$537$	−17.3211	+	15.5819i	−0.747460	+	0.672408i
$538$	10.8531	+	2.90807i	0.467910	+	0.125376i
$539$	−47.2758	+	81.8840i	−2.03631	+	3.52699i
$540$	−4.03403	−	10.8962i	−0.173597	−	0.468897i
$541$	0.764192	−	1.32362i	0.0328552	−	0.0569068i	−0.849130	−	0.528183i	$-0.822873\pi$
$541$	0.764192	−	1.32362i	0.0328552	−	0.0569068i	0.881985	+	0.471277i	$0.156207\pi$
$542$	−7.73182	+	7.73182i	−0.332110	+	0.332110i
$543$	−2.01604	−	9.50572i	−0.0865164	−	0.407930i
$544$	−2.12881	−	1.22907i	−0.0912719	−	0.0526959i
$545$	14.9839	+	4.18552i	0.641838	+	0.179288i
$546$	24.7730	−	12.6084i	1.06019	−	0.539591i
$547$	−6.05615	+	22.6018i	−0.258942	+	0.966385i	0.706913	+	0.707301i	$0.250087\pi$
$547$	−6.05615	+	22.6018i	−0.258942	+	0.966385i	−0.965855	+	0.259084i	$0.916579\pi$
$548$	−0.299056	+	1.11609i	−0.0127750	+	0.0476771i
$549$	19.3327	+	14.0726i	0.825102	+	0.600606i
$550$	−19.5752	+	18.7628i	−0.834687	+	0.800049i
$551$	−9.43233	−	5.44576i	−0.401831	−	0.231997i
$552$	2.62454	−	8.06515i	0.111708	−	0.343275i
$553$	−18.8059	−	5.03903i	−0.799709	−	0.214281i
$554$	20.0468			0.851707
$555$	−0.465094	+	1.37939i	−0.0197421	+	0.0585520i
$556$	−13.9941			−0.593483
$557$	27.8637	−	27.8637i	1.18062	−	1.18062i	0.201042	−	0.979583i	$-0.435567\pi$
$557$	27.8637	−	27.8637i	1.18062	−	1.18062i	0.979583	−	0.201042i	$-0.0644328\pi$
$558$	14.9401	−	7.46949i	0.632465	−	0.316209i
$559$			14.4995i			0.613265i
$560$	−0.117083	+	11.0527i	−0.00494767	+	0.467062i
$561$	−10.4730	−	20.5773i	−0.442171	−	0.868774i
$562$	−5.79380	−	5.79380i	−0.244397	−	0.244397i
$563$	−7.51308	+	28.0392i	−0.316638	+	1.18171i	0.605816	+	0.795605i	$0.292847\pi$
$563$	−7.51308	+	28.0392i	−0.316638	+	1.18171i	−0.922454	+	0.386106i	$0.873820\pi$
$564$	−8.60649	−	16.9100i	−0.362398	−	0.712038i
$565$	−13.7762	−	8.14947i	−0.579569	−	0.342851i
$566$			18.8408i			0.791939i
$567$	−24.1632	−	37.3550i	−1.01476	−	1.56876i
$568$	−7.44493	−	1.99486i	−0.312382	−	0.0837026i
$569$	−17.2889	−	29.9452i	−0.724787	−	1.25537i	−0.959062	−	0.283197i	$-0.908605\pi$
$569$	−17.2889	−	29.9452i	−0.724787	−	1.25537i	0.234275	−	0.972170i	$-0.424729\pi$
$570$	−8.80480	+	26.1137i	−0.368793	+	1.09378i
$571$	−10.9374	−	18.9441i	−0.457715	−	0.792785i	0.541125	−	0.840942i	$-0.317999\pi$
$571$	−10.9374	−	18.9441i	−0.457715	−	0.792785i	−0.998840	+	0.0481568i	$0.984665\pi$
$572$	−4.55687	−	17.0065i	−0.190532	−	0.711077i
$573$	−32.3213	+	6.85491i	−1.35024	+	0.286368i
$574$		−	22.3571i		−	0.933167i
$575$	−5.83446	−	23.7785i	−0.243314	−	0.991631i
$576$	−1.76554	+	2.42546i	−0.0735641	+	0.101061i
$577$	−21.0327	+	5.63568i	−0.875601	+	0.234617i	−0.668508	−	0.743705i	$-0.733067\pi$
$577$	−21.0327	+	5.63568i	−0.875601	+	0.234617i	−0.207093	+	0.978321i	$0.566400\pi$
$578$	−2.83603	+	10.5842i	−0.117963	+	0.440245i
$579$	1.76010	−	33.2982i	0.0731472	−	1.38382i
$580$	−3.29651	−	0.920832i	−0.136880	−	0.0382355i
$581$		−	15.2413i		−	0.632317i
$582$	11.5640	+	3.76314i	0.479345	+	0.155987i
$583$	9.33102	+	34.8238i	0.386451	+	1.44226i
$584$	4.88383	+	8.45905i	0.202094	+	0.350038i
$585$	19.9965	−	8.62904i	0.826753	−	0.356767i
$586$	4.63571	−	8.02928i	0.191499	−	0.331687i
$587$	4.98995	−	4.98995i	0.205957	−	0.205957i	−0.596589	−	0.802547i	$-0.703478\pi$
$587$	4.98995	−	4.98995i	0.205957	−	0.205957i	0.802547	+	0.596589i	$0.203478\pi$
$588$	6.26537	+	29.5416i	0.258379	+	1.21827i
$589$	−38.6953	−	8.49718i	−1.59441	−	0.350120i
$590$	−8.89771	−	0.0942550i	−0.366313	−	0.00388042i
$591$	32.6012	+	21.1923i	1.34103	+	0.871735i
$592$	0.363051	−	0.0972792i	0.0149213	−	0.00399815i
$593$	−3.20484	−	3.20484i	−0.131607	−	0.131607i	0.638235	−	0.769842i	$-0.279665\pi$
$593$	−3.20484	−	3.20484i	−0.131607	−	0.131607i	−0.769842	+	0.638235i	$0.779665\pi$
$594$	−26.3208	+	10.0629i	−1.07996	+	0.412886i
$595$	−26.3178	+	6.75387i	−1.07892	+	0.276882i
$596$	9.67808	+	5.58764i	0.396430	+	0.228879i
$597$	−5.01426	+	1.06346i	−0.205220	+	0.0435244i
$598$	15.3561	+	4.11466i	0.627959	+	0.168261i
$599$	−10.6701	−	18.4812i	−0.435968	−	0.755119i	0.561406	−	0.827541i	$-0.310261\pi$
$599$	−10.6701	−	18.4812i	−0.435968	−	0.755119i	−0.997374	+	0.0724213i	$0.976927\pi$
$600$	−0.640232	+	8.63656i	−0.0261374	+	0.352586i
$601$	−15.6078	+	27.0335i	−0.636656	+	1.10272i	0.349505	+	0.936934i	$0.386350\pi$
$601$	−15.6078	+	27.0335i	−0.636656	+	1.10272i	−0.986162	+	0.165787i	$0.946984\pi$
$602$	−21.3244	−	5.71385i	−0.869117	−	0.232879i
$603$	29.8908	−	24.1606i	1.21725	−	0.983895i
$604$			12.7956i			0.520646i
$605$	28.7975	+	29.4142i	1.17079	+	1.19586i
$606$	−4.98193	−	9.78846i	−0.202377	−	0.397629i
$607$	−5.93325	+	22.1432i	−0.240823	+	0.898764i	0.734614	+	0.678486i	$0.237363\pi$
$607$	−5.93325	+	22.1432i	−0.240823	+	0.898764i	−0.975437	+	0.220279i	$0.929303\pi$
$608$	6.87301	−	1.84162i	0.278737	−	0.0746875i
$609$	−13.0872	−	0.691774i	−0.530321	−	0.0280321i
$610$	−8.74756	−	15.5288i	−0.354178	−	0.628743i
$611$	30.8008	−	17.7828i	1.24607	−	0.719417i
$612$	−6.88222	−	2.64894i	−0.278197	−	0.107077i
$613$	0.621744	+	2.32038i	0.0251120	+	0.0937193i	0.977345	−	0.211655i	$-0.0678852\pi$
$613$	0.621744	+	2.32038i	0.0251120	+	0.0937193i	−0.952233	+	0.305374i	$0.901219\pi$
$614$	3.24056	−	5.61281i	0.130778	−	0.226515i
$615$	1.10986	−	17.4815i	0.0447538	−	0.704924i
$616$	26.8071			1.08009
$617$	−8.31793	−	31.0429i	−0.334867	−	1.24974i	−0.904013	−	0.427505i	$-0.859393\pi$
$617$	−8.31793	−	31.0429i	−0.334867	−	1.24974i	0.569146	−	0.822237i	$-0.307274\pi$
$618$	−10.9891	+	2.33065i	−0.442048	+	0.0937524i
$619$		−	17.4010i		−	0.699404i	−0.936861	−	0.349702i	$-0.886283\pi$
$619$		−	17.4010i		−	0.699404i	0.936861	−	0.349702i	$-0.113717\pi$
$620$	−12.4423	+	0.436219i	−0.499693	+	0.0175190i
$621$	4.01427	−	25.1257i	0.161087	−	1.00826i
$622$	−12.6761	−	12.6761i	−0.508264	−	0.508264i
$623$	60.0590	−	16.0927i	2.40621	−	0.644742i
$624$	−4.71470	−	3.06478i	−0.188739	−	0.122689i
$625$	11.5717	+	22.1607i	0.462868	+	0.886427i
$626$	18.2298	+	10.5250i	0.728607	+	0.420662i
$627$	63.5548	+	20.6818i	2.53813	+	0.825952i
$628$	14.5095	−	14.5095i	0.578993	−	0.578993i
$629$	0.461955	+	0.800130i	0.0184194	+	0.0319033i
$630$	4.81064	+	32.8092i	0.191660	+	1.30715i
$631$	−17.6182	−	30.5156i	−0.701370	−	1.21481i	−0.967986	−	0.251005i	$-0.919239\pi$
$631$	−17.6182	−	30.5156i	−0.701370	−	1.21481i	0.266616	−	0.963803i	$-0.414095\pi$
$632$	1.01939	+	3.80441i	0.0405491	+	0.151331i
$633$	18.0965	−	16.2794i	0.719270	−	0.647049i
$634$	20.7118	+	11.9579i	0.822570	+	0.474911i
$635$	−0.115013	+	10.8573i	−0.00456415	+	0.430858i
$636$	9.65420	+	6.27568i	0.382814	+	0.248847i
$637$	−54.6764	+	14.6505i	−2.16636	+	0.580474i
$638$	−2.14844	+	8.01808i	−0.0850575	+	0.317439i
$639$	−22.9938	−	2.43766i	−0.909621	−	0.0964323i
$640$	1.94823	−	1.09746i	0.0770104	−	0.0433809i
$641$	−28.0892	+	16.2173i	−1.10946	+	0.640546i	−0.938689	−	0.344766i	$-0.887958\pi$
$641$	−28.0892	+	16.2173i	−1.10946	+	0.640546i	−0.170769	+	0.985311i	$0.554625\pi$
$642$	5.88255	+	6.53914i	0.232166	+	0.258079i
$643$	18.4065	−	18.4065i	0.725882	−	0.725882i	−0.243915	−	0.969797i	$-0.578432\pi$
$643$	18.4065	−	18.4065i	0.725882	−	0.725882i	0.969797	+	0.243915i	$0.0784318\pi$
$644$	−12.1028	+	20.9627i	−0.476918	+	0.826046i
$645$	−16.3904	−	5.52639i	−0.645371	−	0.217601i
$646$	8.74539	+	15.1475i	0.344083	+	0.595969i
$647$	−27.1918	+	27.1918i	−1.06902	+	1.06902i	−0.0715863	+	0.997434i	$0.522806\pi$
$647$	−27.1918	+	27.1918i	−1.06902	+	1.06902i	−0.997434	+	0.0715863i	$0.977194\pi$
$648$	−4.10033	+	8.01170i	−0.161076	+	0.314729i
$649$			21.5804i			0.847104i
$650$	−16.2294	−	0.343880i	−0.636568	−	0.0134881i
$651$	−46.1334	+	12.0075i	−1.80811	+	0.470610i
$652$	11.4457	+	11.4457i	0.448248	+	0.448248i
$653$	−16.6488	−	16.6488i	−0.651518	−	0.651518i	0.301840	−	0.953359i	$-0.402399\pi$
$653$	−16.6488	−	16.6488i	−0.651518	−	0.651518i	−0.953359	+	0.301840i	$0.902399\pi$
$654$	−5.46610	−	10.7398i	−0.213741	−	0.419958i
$655$	1.50757	−	1.47596i	0.0589055	−	0.0576706i
$656$	−3.91686	+	2.26140i	−0.152928	+	0.0882929i
$657$	18.4205	+	22.7893i	0.718652	+	0.889095i
$658$	14.0154	+	52.3063i	0.546378	+	2.03911i
$659$	−39.2701			−1.52975			−0.764874	−	0.644180i	$-0.777199\pi$
$659$	−39.2701			−1.52975			−0.764874	+	0.644180i	$0.777199\pi$
$660$	20.9611	+	1.33077i	0.815909	+	0.0518000i
$661$	−3.10561	−	5.37907i	−0.120794	−	0.209222i	0.799287	−	0.600950i	$-0.205211\pi$
$661$	−3.10561	−	5.37907i	−0.120794	−	0.209222i	−0.920081	+	0.391728i	$0.871877\pi$
$662$	4.35825	+	1.16779i	0.169388	+	0.0453874i
$663$	4.27739	−	13.1443i	0.166120	−	0.510484i
$664$	−2.67021	+	1.54165i	−0.103624	+	0.0598275i
$665$	40.0440	−	67.6921i	1.55284	−	2.62499i
$666$	1.03050	−	0.457699i	0.0399312	−	0.0177355i
$667$	−5.30004	−	5.30004i	−0.205218	−	0.205218i
$668$	−7.60769	+	2.03847i	−0.294350	+	0.0788709i
$669$	0.802324	−	15.1786i	0.0310196	−	0.586840i
$670$	−27.7481	+	7.12092i	−1.07200	+	0.275105i
$671$	−37.4344	+	21.6128i	−1.44514	+	0.834352i
$672$	6.36528	−	5.72615i	0.245546	−	0.220891i
$673$	−18.1812	−	4.87163i	−0.700832	−	0.187787i	−0.109229	−	0.994017i	$-0.534838\pi$
$673$	−18.1812	−	4.87163i	−0.700832	−	0.187787i	−0.591603	+	0.806229i	$0.701505\pi$
$674$	−31.2521			−1.20378
$675$	2.13283	+	25.8931i	0.0820926	+	0.996625i
$676$	−1.22978	+	2.13005i	−0.0472994	+	0.0819250i
$677$	−34.3553	−	9.20549i	−1.32038	−	0.353796i	−0.471262	−	0.881993i	$-0.656201\pi$
$677$	−34.3553	−	9.20549i	−1.32038	−	0.353796i	−0.849121	+	0.528198i	$0.822868\pi$
$678$	2.57230	+	12.1285i	0.0987887	+	0.465794i
$679$	−30.0570	−	17.3534i	−1.15348	−	0.665962i
$680$	3.84527	+	3.92761i	0.147459	+	0.150617i
$681$	−9.32365	−	6.06081i	−0.357283	−	0.232251i
$682$	1.37752	+	30.1627i	0.0527479	+	1.15499i
$683$	−5.00862	−	5.00862i	−0.191650	−	0.191650i	0.604759	−	0.796409i	$-0.293269\pi$
$683$	−5.00862	−	5.00862i	−0.191650	−	0.191650i	−0.796409	+	0.604759i	$0.793269\pi$
$684$	19.5087	−	8.66482i	0.745934	−	0.331308i
$685$	1.31548	−	2.22374i	0.0502618	−	0.0849646i
$686$		−	51.5833i		−	1.96946i
$687$	15.0670	+	16.7488i	0.574844	+	0.639006i
$688$	1.15590	+	4.31389i	0.0440684	+	0.164465i
$689$	−10.7917	+	18.6918i	−0.411131	+	0.712101i
$690$	−10.5041	+	15.7904i	−0.399885	+	0.601131i
$691$	−0.0160103	−	0.0277307i	−0.000609062	−	0.00105493i	0.865721	−	0.500527i	$-0.166861\pi$
$691$	−0.0160103	−	0.0277307i	−0.000609062	−	0.00105493i	−0.866330	+	0.499472i	$0.833527\pi$
$692$	10.5572	+	2.82879i	0.401324	+	0.107534i
$693$	79.4424	−	12.5092i	3.01777	−	0.475185i
$694$	18.0512	+	10.4218i	0.685212	+	0.395608i
$695$	30.1381	+	8.41863i	1.14320	+	0.319337i
$696$	1.20257	+	2.36279i	0.0455831	+	0.0895615i
$697$	−7.86137	−	7.86137i	−0.297771	−	0.297771i
$698$	−8.87240	−	8.87240i	−0.335825	−	0.335825i
$699$	6.98243	+	13.7190i	0.264100	+	0.518902i
$700$	6.90127	−	23.7329i	0.260844	−	0.897021i
$701$	−21.4083	−	12.3601i	−0.808580	−	0.466834i	0.0378823	−	0.999282i	$-0.487939\pi$
$701$	−21.4083	−	12.3601i	−0.808580	−	0.466834i	−0.846463	+	0.532448i	$0.821272\pi$
$702$	−15.4021	−	6.88237i	−0.581315	−	0.259758i
$703$	−2.58328	−	0.692187i	−0.0974301	−	0.0261063i
$704$	−2.71151	−	4.69648i	−0.102194	−	0.177005i
$705$	8.36238	+	41.5953i	0.314946	+	1.56657i
$706$	−5.74507	+	9.95075i	−0.216219	+	0.374502i
$707$	8.11293	+	30.2779i	0.305118	+	1.13872i
$708$	4.60970	+	5.12422i	0.173243	+	0.192580i
$709$		−	3.69982i		−	0.138950i	−0.997584	−	0.0694749i	$-0.977868\pi$
$709$		−	3.69982i		−	0.138950i	0.997584	−	0.0694749i	$-0.0221324\pi$
$710$	14.8335	+	8.77493i	0.556691	+	0.329317i
$711$	4.79622	+	10.7986i	0.179872	+	0.404980i
$712$	−8.89429	−	8.89429i	−0.333327	−	0.333327i
$713$	−24.2087	−	12.5406i	−0.906621	−	0.469650i
$714$	17.6457	+	11.4705i	0.660374	+	0.429274i
$715$	−0.417021	+	39.3669i	−0.0155957	+	1.47224i
$716$	−11.6492	−	6.72567i	−0.435351	−	0.251350i
$717$	2.80187	+	13.2110i	0.104638	+	0.493374i
$718$	1.02060	+	0.273470i	0.0380886	+	0.0102058i
$719$	−12.6938	+	21.9863i	−0.473399	+	0.819951i	−0.999536	−	0.0304489i	$-0.990306\pi$
$719$	−12.6938	+	21.9863i	−0.473399	+	0.819951i	0.526138	+	0.850399i	$0.323640\pi$
$720$	5.26142	−	4.16142i	0.196082	−	0.155087i
$721$	32.0601			1.19398
$722$	−30.5521	−	8.18640i	−1.13703	−	0.304666i
$723$	25.4884	−	22.9291i	0.947924	−	0.852743i
$724$	4.85858	−	2.80510i	0.180568	−	0.104251i
$725$	6.54549	+	3.96625i	0.243094	+	0.147303i
$726$	1.68309	−	31.8412i	0.0624652	−	1.18174i
$727$	31.3982	−	8.41312i	1.16449	−	0.312025i	0.375735	−	0.926727i	$-0.377390\pi$
$727$	31.3982	−	8.41312i	1.16449	−	0.312025i	0.788760	+	0.614702i	$0.210724\pi$
$728$	11.3481	+	11.3481i	0.420588	+	0.420588i
$729$	−8.41272	+	25.6559i	−0.311582	+	0.950219i
$730$	−5.42912	−	21.1556i	−0.200941	−	0.783006i
$731$	−9.50740	+	5.48910i	−0.351644	+	0.203022i
$732$	−4.27211	+	13.1281i	−0.157902	+	0.485229i
$733$	39.9822	+	10.7132i	1.47678	+	0.395701i	0.905249	−	0.424881i	$-0.139684\pi$
$733$	39.9822	+	10.7132i	1.47678	+	0.395701i	0.571528	+	0.820583i	$0.306351\pi$
$734$	1.13720	+	1.96969i	0.0419748	+	0.0727025i
$735$	4.27846	−	67.3906i	0.157813	−	2.48574i
$736$	4.89676			0.180497
$737$	17.9819	+	67.1093i	0.662371	+	2.47200i
$738$	−10.5523	+	8.52939i	−0.388436	+	0.313971i
$739$	17.3264	−	10.0034i	0.637361	−	0.367981i	−0.146236	−	0.989250i	$-0.546716\pi$
$739$	17.3264	−	10.0034i	0.637361	−	0.367981i	0.783597	+	0.621269i	$0.213383\pi$
$740$	−0.840397	−	0.00890248i	−0.0308936	−	0.000327261i
$741$	18.1491	+	35.6593i	0.666726	+	1.30998i
$742$	−23.2372	−	23.2372i	−0.853065	−	0.853065i
$743$	4.28031	+	4.28031i	0.157029	+	0.157029i	0.781249	−	0.624220i	$-0.214583\pi$
$743$	4.28031	+	4.28031i	0.157029	+	0.157029i	−0.624220	+	0.781249i	$0.714583\pi$
$744$	6.77001	+	6.86782i	0.248201	+	0.251786i
$745$	−17.4815	−	17.8559i	−0.640473	−	0.654188i
$746$		−	10.4226i		−	0.381598i
$747$	−7.19374	+	5.81467i	−0.263205	+	0.212748i
$748$	9.42611	−	9.42611i	0.344653	−	0.344653i
$749$	−12.5513	−	21.7395i	−0.458615	−	0.794344i
$750$	6.57443	−	18.2147i	0.240064	−	0.665108i
$751$	5.28944	−	9.16158i	0.193014	−	0.334311i	−0.753233	−	0.657753i	$-0.771507\pi$
$751$	5.28944	−	9.16158i	0.193014	−	0.334311i	0.946248	+	0.323443i	$0.104840\pi$
$752$	7.74617	−	7.74617i	0.282474	−	0.282474i
$753$	3.54668	+	3.94256i	0.129248	+	0.143675i
$754$	−4.30373	+	2.48476i	−0.156733	+	0.0904896i
$755$	7.69762	−	27.5569i	0.280145	−	1.00290i
$756$	16.1914	−	19.9396i	0.588875	−	0.725198i
$757$	−4.12414	+	15.3915i	−0.149895	+	0.559414i	0.849594	+	0.527437i	$0.176847\pi$
$757$	−4.12414	+	15.3915i	−0.149895	+	0.559414i	−0.999489	+	0.0319769i	$0.989820\pi$
$758$	17.8255	−	4.77632i	0.647450	−	0.173484i
$759$	38.5634	+	25.0680i	1.39976	+	0.909912i
$760$	−15.9098	−	0.168535i	−0.577108	−	0.00611341i
$761$	−1.15193	−	0.665068i	−0.0417575	−	0.0241087i	0.478976	−	0.877828i	$-0.341008\pi$
$761$	−1.15193	−	0.665068i	−0.0417575	−	0.0241087i	−0.520733	+	0.853719i	$0.674341\pi$
$762$	6.25273	−	5.62490i	0.226513	−	0.203769i
$763$	8.90139	+	33.2204i	0.322252	+	1.20266i
$764$	−9.53788	−	16.5201i	−0.345068	−	0.597676i
$765$	13.2282	+	9.84506i	0.478265	+	0.355949i
$766$	−10.8803	−	18.8452i	−0.393120	−	0.680904i
$767$	−9.13549	+	9.13549i	−0.329864	+	0.329864i
$768$	−1.64704	−	0.535974i	−0.0594323	−	0.0193403i
$769$	−12.9646	−	7.48514i	−0.467517	−	0.269921i	0.247683	−	0.968841i	$-0.420331\pi$
$769$	−12.9646	−	7.48514i	−0.467517	−	0.269921i	−0.715200	+	0.698920i	$0.753664\pi$
$770$	−57.7324	−	16.1267i	−2.08053	−	0.581166i
$771$	−3.47323	−	2.25776i	−0.125085	−	0.0813113i
$772$	18.5956	−	4.98267i	0.669269	−	0.179330i
$773$	−3.41918	−	3.41918i	−0.122979	−	0.122979i	0.642938	−	0.765918i	$-0.277715\pi$
$773$	−3.41918	−	3.41918i	−0.122979	−	0.122979i	−0.765918	+	0.642938i	$0.777715\pi$
$774$	5.43853	+	12.2448i	0.195484	+	0.440129i
$775$	27.0584	+	6.54560i	0.971965	+	0.235125i
$776$			7.02112i			0.252044i
$777$	−3.14803	+	0.667654i	−0.112935	+	0.0239520i
$778$	7.96173	+	29.7136i	0.285442	+	1.06528i
$779$	32.1818			1.15303
$780$	8.30998	+	9.43667i	0.297545	+	0.337887i
$781$	20.8991	−	36.1984i	0.747830	−	1.29528i
$782$	3.11538	+	11.6268i	0.111406	+	0.415772i
$783$	4.66636	+	6.44094i	0.166762	+	0.230181i
$784$	−15.0993	+	8.71760i	−0.539262	+	0.311343i
$785$	−39.9767	+	22.5194i	−1.42683	+	0.803751i
$786$	−1.63196	−	0.0862633i	−0.0582100	−	0.00307691i
$787$	−7.57221	+	2.02897i	−0.269920	+	0.0723249i	−0.391240	−	0.920289i	$-0.627954\pi$
$787$	−7.57221	+	2.02897i	−0.269920	+	0.0723249i	0.121320	+	0.992613i	$0.461287\pi$
$788$	−5.81038	+	21.6846i	−0.206986	+	0.772483i
$789$	−5.97828	−	11.7461i	−0.212832	−	0.418172i
$790$	0.0932889	−	8.80651i	0.00331907	−	0.313321i
$791$		−	35.3843i		−	1.25812i
$792$	−10.2271	−	12.6526i	−0.363404	−	0.449592i
$793$	−24.9961	−	6.69768i	−0.887637	−	0.237841i
$794$	−1.54887	+	2.68272i	−0.0549672	+	0.0952061i
$795$	−17.0162	−	19.3233i	−0.603501	−	0.685326i
$796$	−1.47969	−	2.56290i	−0.0524462	−	0.0908394i
$797$	17.2531	+	4.62295i	0.611136	+	0.163753i	0.551095	−	0.834443i	$-0.314210\pi$
$797$	17.2531	+	4.62295i	0.611136	+	0.163753i	0.0600410	+	0.998196i	$0.480877\pi$
$798$	−59.5961	+	12.6395i	−2.10968	+	0.447434i
$799$	23.3205	+	13.4641i	0.825021	+	0.476326i
$800$	−4.85596	+	1.19149i	−0.171684	+	0.0421257i
$801$	−30.5085	−	22.2077i	−1.07796	−	0.784670i
$802$	6.95061	+	6.95061i	0.245435	+	0.245435i
$803$	−51.1654	+	13.7097i	−1.80559	+	0.483806i
$804$	18.6047	+	12.0939i	0.656137	+	0.426520i
$805$	38.6758	−	37.8649i	1.36314	−	1.33456i
$806$	−12.1854	+	13.3517i	−0.429214	+	0.470294i
$807$	4.03765	+	19.0378i	0.142132	+	0.670161i
$808$	4.48393	−	4.48393i	0.157744	−	0.157744i
$809$	−15.4104	+	26.6916i	−0.541800	+	0.938425i	0.457001	+	0.889466i	$0.348924\pi$
$809$	−15.4104	+	26.6916i	−0.541800	+	0.938425i	−0.998801	+	0.0489589i	$0.984410\pi$
$810$	13.6503	−	14.7875i	0.479622	−	0.519580i
$811$	0.435604	+	0.754489i	0.0152961	+	0.0264937i	0.873572	−	0.486695i	$-0.161798\pi$
$811$	0.435604	+	0.754489i	0.0152961	+	0.0264937i	−0.858276	+	0.513188i	$0.828464\pi$
$812$	−1.95834	−	7.30864i	−0.0687244	−	0.256483i
$813$	−18.0094	−	5.86058i	−0.631619	−	0.205539i
$814$			2.03829i			0.0714420i
$815$	−17.7642	−	31.5353i	−0.622253	−	1.10463i
$816$	0.224738	−	4.25168i	0.00786742	−	0.148839i
$817$	8.22478	−	30.6953i	0.287749	−	1.07389i
$818$	27.5343	−	7.37779i	0.962713	−	0.257958i
$819$	38.9253	+	28.3344i	1.36016	+	0.990084i
$820$	9.79587	−	2.51389i	0.342087	−	0.0877888i
$821$			24.8102i			0.865882i	0.901422	+	0.432941i	$0.142524\pi$
$821$			24.8102i			0.865882i	−0.901422	+	0.432941i	$0.857476\pi$
$822$	−1.95778	+	0.415218i	−0.0682853	+	0.0144824i
$823$	−10.3089	−	38.4735i	−0.359347	−	1.34110i	−0.874925	−	0.484259i	$-0.839089\pi$
$823$	−10.3089	−	38.4735i	−0.359347	−	1.34110i	0.515577	−	0.856843i	$-0.327578\pi$
$824$	−3.24285	−	5.61678i	−0.112970	−	0.195670i
$825$	−44.3417	−	15.4758i	−1.54378	−	0.538798i
$826$	−9.83548	−	17.0356i	−0.342220	−	0.592743i
$827$	7.52778	+	2.01706i	0.261767	+	0.0701401i	0.387315	−	0.921947i	$-0.373402\pi$
$827$	7.52778	+	2.01706i	0.261767	+	0.0701401i	−0.125549	+	0.992087i	$0.540069\pi$
$828$	14.5115	−	2.28502i	0.504309	−	0.0794098i
$829$			27.7480i			0.963727i	0.876246	+	0.481864i	$0.160040\pi$
$829$			27.7480i			0.963727i	−0.876246	+	0.481864i	$0.839960\pi$
$830$	6.67806	−	1.71377i	0.231799	−	0.0594860i
$831$	15.7496	+	30.9447i	0.546347	+	1.07346i
$832$	0.840283	−	3.13598i	0.0291316	−	0.108720i
$833$	−30.3053	−	30.3053i	−1.05001	−	1.05001i
$834$	−10.9944	−	21.6016i	−0.380703	−	0.748004i
$835$	17.6104	+	0.186550i	0.609433	+	0.00645583i
$836$			38.5873i			1.33457i
$837$	23.2676	+	17.1935i	0.804247	+	0.594296i
$838$	0.687400	−	0.687400i	0.0237459	−	0.0237459i
$839$	−10.3219			−0.356352			−0.178176	−	0.983999i	$-0.557020\pi$
$839$	−10.3219			−0.356352			−0.178176	+	0.983999i	$0.557020\pi$
$840$	−17.1532	+	8.50272i	−0.591841	+	0.293372i
$841$	−26.6570			−0.919207
$842$	4.76045	+	1.27556i	0.164056	+	0.0439587i
$843$	4.39159	−	13.4953i	0.151254	−	0.464802i
$844$	12.1707	+	7.02674i	0.418932	+	0.241871i
$845$	3.92989	−	3.84751i	0.135192	−	0.132358i
$846$	19.3410	−	26.5703i	0.664958	−	0.913507i
$847$	−23.5526	+	87.8995i	−0.809277	+	3.02026i
$848$	−1.72063	+	6.42148i	−0.0590867	+	0.220514i
$849$	−29.0831	+	14.8021i	−0.998130	+	0.508007i
$850$	−5.91848	−	10.7718i	−0.203002	−	0.369471i
$851$	−1.59391	−	0.920244i	−0.0546385	−	0.0315455i
$852$	−2.76972	−	13.0594i	−0.0948891	−	0.447408i
$853$	−18.5652	+	18.5652i	−0.635659	+	0.635659i	−0.949482	−	0.313822i	$-0.898390\pi$
$853$	−18.5652	+	18.5652i	−0.635659	+	0.635659i	0.313822	+	0.949482i	$0.398390\pi$
$854$	19.7005	−	34.1222i	0.674136	−	1.16764i
$855$	−47.2270	+	6.92465i	−1.61513	+	0.236818i
$856$	−2.53911	+	4.39786i	−0.0867848	+	0.150316i
$857$	33.7281	+	9.03741i	1.15213	+	0.308712i	0.783818	−	0.620990i	$-0.213269\pi$
$857$	33.7281	+	9.03741i	1.15213	+	0.308712i	0.368311	+	0.929703i	$0.379936\pi$
$858$	22.6715	−	20.3951i	0.773993	−	0.696276i
$859$	26.3845	−	15.2331i	0.900227	−	0.519746i	0.0229534	−	0.999737i	$-0.492693\pi$
$859$	26.3845	−	15.2331i	0.900227	−	0.519746i	0.877274	+	0.479990i	$0.159360\pi$
$860$	0.105782	−	9.98586i	0.00360714	−	0.340515i
$861$	34.5109	−	17.5646i	1.17613	−	0.598601i
$862$	23.2559	−	6.23140i	0.792099	−	0.212242i
$863$	11.2079	−	41.8285i	0.381522	−	1.42386i	−0.462056	−	0.886851i	$-0.652888\pi$
$863$	11.2079	−	41.8285i	0.381522	−	1.42386i	0.843577	−	0.537008i	$-0.180445\pi$
$864$	−5.13108	−	0.819781i	−0.174563	−	0.0278895i
$865$	−21.0345	−	12.4432i	−0.715193	−	0.423080i
$866$			18.8356i			0.640060i
$867$	−18.5661	+	3.93762i	−0.630538	+	0.133729i
$868$	−14.8344	−	23.1826i	−0.503511	−	0.786869i
$869$	−21.3592			−0.724561
$870$	−1.16846	−	5.81201i	−0.0396144	−	0.197046i
$871$	−20.7968	+	36.0211i	−0.704673	+	1.22053i
$872$	4.91970	−	4.91970i	0.166602	−	0.166602i
$873$	3.27632	+	20.8070i	0.110887	+	0.704210i
$874$	−30.1747	−	17.4214i	−1.02067	−	0.589286i
$875$	−29.1401	+	46.9601i	−0.985115	+	1.58754i
$876$	−9.22064	+	14.1846i	−0.311536	+	0.479252i
$877$	−1.84071	+	6.86963i	−0.0621565	+	0.231971i	−0.990015	−	0.140961i	$-0.954981\pi$
$877$	−1.84071	+	6.86963i	−0.0621565	+	0.231971i	0.927859	+	0.372932i	$0.121647\pi$
$878$	−6.01418	+	22.4452i	−0.202969	+	0.757489i
$879$	16.0362	+	0.847652i	0.540887	+	0.0285906i
$880$	3.01426	+	11.7456i	0.101611	+	0.395946i
$881$	28.7829	−	16.6178i	0.969719	−	0.559868i	0.0705687	−	0.997507i	$-0.477519\pi$
$881$	28.7829	−	16.6178i	0.969719	−	0.559868i	0.899151	+	0.437639i	$0.144185\pi$
$882$	−40.6787	+	32.8804i	−1.36972	+	1.10714i
$883$	17.9279	−	17.9279i	0.603320	−	0.603320i	−0.337872	−	0.941192i	$-0.609707\pi$
$883$	17.9279	−	17.9279i	0.603320	−	0.603320i	0.941192	+	0.337872i	$0.109707\pi$
$884$	7.98059			0.268416
$885$	−6.84491	−	13.8088i	−0.230089	−	0.464176i
$886$	20.9366	+	36.2633i	0.703379	+	1.21829i
$887$	−3.52942	−	13.1720i	−0.118506	−	0.442272i	0.881019	−	0.473081i	$-0.156858\pi$
$887$	−3.52942	−	13.1720i	−0.118506	−	0.442272i	−0.999525	+	0.0308093i	$0.990192\pi$
$888$	0.435390	+	0.483987i	0.0146107	+	0.0162415i
$889$	−20.7873	+	12.0016i	−0.697185	+	0.402520i
$890$	13.8043	+	24.5056i	0.462721	+	0.821430i
$891$	−36.2120	−	32.7236i	−1.21315	−	1.09628i
$892$	8.47660	−	2.27130i	0.283818	−	0.0760487i
$893$	−75.2920	+	20.1744i	−2.51955	+	0.675112i
$894$	−1.02172	+	19.3292i	−0.0341713	+	0.646465i
$895$	21.0419	+	21.4925i	0.703355	+	0.718416i
$896$	4.28093	+	2.47160i	0.143016	+	0.0825703i
$897$	5.71291	+	26.9367i	0.190749	+	0.899391i
$898$	−22.5134	+	22.5134i	−0.751282	+	0.751282i
$899$	8.12288	−	2.57905i	0.270913	−	0.0860160i
$900$	−13.8346	+	5.79695i	−0.461152	+	0.193232i
$901$	−16.3417			−0.544421
$902$	−6.34812	−	23.6915i	−0.211369	−	0.788841i
$903$	−7.93328	−	37.4058i	−0.264003	−	1.24479i
$904$	−6.19916	+	3.57909i	−0.206181	+	0.119039i
$905$	−12.1511	+	3.11830i	−0.403915	+	0.103656i
$906$	−19.7516	+	10.0527i	−0.656202	+	0.333980i
$907$	14.2594	+	14.2594i	0.473474	+	0.473474i	0.903037	−	0.429563i	$-0.141332\pi$
$907$	14.2594	+	14.2594i	0.473474	+	0.473474i	−0.429563	+	0.903037i	$0.641332\pi$
$908$	1.66172	−	6.20161i	0.0551460	−	0.205808i
$909$	11.1957	−	15.3804i	0.371337	−	0.510137i
$910$	−17.6127	−	31.2663i	−0.583855	−	1.03647i
$911$	30.3486	+	17.5218i	1.00550	+	0.580523i	0.909870	−	0.414894i	$-0.136182\pi$
$911$	30.3486	+	17.5218i	1.00550	+	0.580523i	0.0956256	+	0.995417i	$0.469515\pi$
$912$	8.24248	+	9.16248i	0.272936	+	0.303400i
$913$	−4.32766	−	16.1510i	−0.143225	−	0.534521i
$914$	−11.5013			−0.380429
$915$	17.0982	−	25.7030i	0.565248	−	0.849715i
$916$	−6.50345	+	11.2643i	−0.214880	+	0.372183i
$917$	4.50512	+	1.20714i	0.148772	+	0.0398634i
$918$	−1.31799	−	12.7047i	−0.0435001	−	0.419317i
$919$	−39.9512	+	23.0659i	−1.31787	+	0.760872i	−0.983386	−	0.181529i	$-0.941895\pi$
$919$	−39.9512	+	23.0659i	−1.31787	+	0.760872i	−0.334484	+	0.942401i	$0.608562\pi$
$920$	−10.5458	−	2.94581i	−0.347684	−	0.0971204i
$921$	11.2100	+	0.592545i	0.369381	+	0.0195250i
$922$	4.03349	+	4.03349i	0.132836	+	0.132836i
$923$	24.1707	−	6.47653i	0.795589	−	0.213177i
$924$	21.0607	+	41.3800i	0.692847	+	1.36130i
$925$	1.80454	+	0.524741i	0.0593331	+	0.0172534i
$926$			8.49049i			0.279015i
$927$	−12.2311	−	15.1320i	−0.401724	−	0.497001i
$928$	−1.08236	+	1.08236i	−0.0355301	+	0.0355301i
$929$	−26.2805			−0.862235			−0.431118	−	0.902296i	$-0.641881\pi$
$929$	−26.2805			−0.862235			−0.431118	+	0.902296i	$0.641881\pi$
$930$	−10.4485	−	18.8634i	−0.342620	−	0.618556i
$931$	124.060			4.06589
$932$	−6.28446	+	6.28446i	−0.205854	+	0.205854i
$933$	9.60822	−	29.5259i	0.314559	−	0.966633i
$934$			37.2495i			1.21884i
$935$	−25.9709	+	14.6297i	−0.849339	+	0.478443i
$936$	1.02680	−	9.68553i	0.0335620	−	0.316582i
$937$	−39.7334	+	10.6465i	−1.29804	+	0.347807i	−0.840707	−	0.541491i	$-0.817860\pi$
$937$	−39.7334	+	10.6465i	−1.29804	+	0.347807i	−0.457328	+	0.889298i	$0.651194\pi$
$938$	−44.7806	−	44.7806i	−1.46214	−	1.46214i
$939$	−1.92452	+	36.4087i	−0.0628042	+	1.18815i
$940$	−21.3423	+	12.0224i	−0.696109	+	0.392127i
$941$	3.47117	−	2.00408i	0.113157	−	0.0653311i	−0.442353	−	0.896841i	$-0.645856\pi$
$941$	3.47117	−	2.00408i	0.113157	−	0.0653311i	0.555510	+	0.831510i	$0.312523\pi$
$942$	33.7965	+	10.9979i	1.10115	+	0.358333i
$943$	21.3924	+	5.73208i	0.696633	+	0.186662i
$944$	−1.98970	+	3.44626i	−0.0647592	+	0.112166i
$945$	−46.8655	+	33.2020i	−1.52454	+	1.08006i
$946$	−24.2196			−0.787446
$947$	−7.36420	−	27.4836i	−0.239304	−	0.893097i	−0.976161	−	0.217047i	$-0.930357\pi$
$947$	−7.36420	−	27.4836i	−0.239304	−	0.893097i	0.736857	−	0.676049i	$-0.236309\pi$
$948$	−5.07169	+	4.56244i	−0.164721	+	0.148181i
$949$	−27.4632	−	15.8559i	−0.891492	−	0.514703i
$950$	34.1623	+	9.93401i	1.10837	+	0.322302i
$951$	−2.18654	+	41.3658i	−0.0709035	+	1.34138i
$952$	−3.14492	+	11.7370i	−0.101928	+	0.380399i
$953$	31.0411	+	31.0411i	1.00552	+	1.00552i	0.999985	+	0.00553553i	$0.00176202\pi$
$953$	31.0411	+	31.0411i	1.00552	+	1.00552i	0.00553553	+	0.999985i	$0.498238\pi$
$954$	−2.10256	+	19.8329i	−0.0680727	+	0.642113i
$955$	10.6028	+	41.3159i	0.343099	+	1.33695i
$956$	−6.75242	+	3.89851i	−0.218389	+	0.126087i
$957$	−14.0648	+	2.98295i	−0.454650	+	0.0964251i
$958$	−2.66163	−	9.93333i	−0.0859933	−	0.320931i
$959$	5.71169			0.184440
$960$	3.22467	+	2.14512i	0.104076	+	0.0692333i
$961$	25.3222	−	17.8825i	0.816846	−	0.576856i
$962$	−0.862856	+	0.862856i	−0.0278196	+	0.0278196i
$963$	−5.47239	+	14.2178i	−0.176345	+	0.458163i
$964$	17.1421	+	9.89698i	0.552109	+	0.318760i
$965$	−43.0454	−	0.455987i	−1.38568	−	0.0146787i
$966$	−41.8670	−	2.21304i	−1.34705	−	0.0712032i
$967$	−21.9645	+	5.88538i	−0.706332	+	0.189261i	−0.594065	−	0.804417i	$-0.702478\pi$
$967$	−21.9645	+	5.88538i	−0.706332	+	0.189261i	−0.112267	+	0.993678i	$0.535811\pi$
$968$	17.7819	−	4.76465i	0.571532	−	0.153142i
$969$	−16.5112	+	25.4000i	−0.530417	+	0.815967i
$970$	4.22379	−	15.1209i	0.135618	−	0.485501i
$971$	−20.7099	+	11.9569i	−0.664612	+	0.383714i	−0.794032	−	0.607876i	$-0.792022\pi$
$971$	−20.7099	+	11.9569i	−0.664612	+	0.383714i	0.129420	+	0.991590i	$0.458689\pi$
$972$	−15.5884	−	0.0350512i	−0.499999	−	0.00112427i
$973$	17.9040	+	66.8186i	0.573976	+	2.14211i
$974$	19.0356	+	32.9706i	0.609939	+	1.05645i
$975$	−12.2196	−	25.3222i	−0.391341	−	0.810959i
$976$	−7.97074			−0.255137
$977$	29.1881	−	29.1881i	0.933811	−	0.933811i	−0.0641301	−	0.997942i	$-0.520427\pi$
$977$	29.1881	−	29.1881i	0.933811	−	0.933811i	0.997942	+	0.0641301i	$0.0204273\pi$
$978$	−8.67563	+	26.6600i	−0.277416	+	0.852494i
$979$	59.0743	−	34.1065i	1.88802	−	1.09005i
$980$	37.7626	−	9.69094i	1.20628	−	0.309566i
$981$	12.2837	−	16.8752i	0.392190	−	0.538783i
$982$	−8.47574	+	31.6319i	−0.270472	+	1.00941i
$983$	3.71235	−	13.8547i	0.118406	−	0.441896i	−0.881113	−	0.472905i	$-0.843205\pi$
$983$	3.71235	−	13.8547i	0.118406	−	0.441896i	0.999519	+	0.0310091i	$0.00987210\pi$
$984$	−6.56799	−	4.26950i	−0.209380	−	0.136107i
$985$	25.5585	−	43.2051i	0.814361	−	1.37663i
$986$	−3.25853	−	1.88131i	−0.103773	−	0.0599132i
$987$	−69.7300	+	62.7284i	−2.21953	+	1.99667i
$988$	−16.3349	+	16.3349i	−0.519684	+	0.519684i
$989$	10.9346	−	18.9393i	0.347701	−	0.602235i
$990$	14.4137	+	33.4015i	0.458097	+	1.06157i
$991$	38.6200			1.22681			0.613403	−	0.789770i	$-0.289800\pi$
$991$	38.6200			1.22681			0.613403	+	0.789770i	$0.289800\pi$
$992$	−2.56100	+	4.94381i	−0.0813119	+	0.156966i
$993$	1.62139	+	7.64495i	0.0514533	+	0.242605i
$994$			38.1000i			1.20846i
$995$	1.64490	+	6.40967i	0.0521468	+	0.203200i
$996$	−4.47755	−	2.91062i	−0.141876	−	0.0922264i
$997$	4.84366	−	18.0768i	0.153400	−	0.572497i	−0.845837	−	0.533442i	$-0.820898\pi$
$997$	4.84366	−	18.0768i	0.153400	−	0.572497i	0.999237	−	0.0390554i	$-0.0124349\pi$
$998$	15.8659	−	4.25125i	0.502225	−	0.134571i
$999$	1.51612	+	1.23112i	0.0479679	+	0.0389509i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bf.a.377.4	✓	256
3.2	odd	2	inner	930.2.bf.a.377.56	yes	256
5.3	odd	4	inner	930.2.bf.a.563.51	yes	256
15.8	even	4	inner	930.2.bf.a.563.25	yes	256
31.25	even	3	inner	930.2.bf.a.707.25	yes	256
93.56	odd	6	inner	930.2.bf.a.707.51	yes	256
155.118	odd	12	inner	930.2.bf.a.893.56	yes	256
465.428	even	12	inner	930.2.bf.a.893.4	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bf.a.377.4	✓	256	1.1	even	1	trivial
930.2.bf.a.377.56	yes	256	3.2	odd	2	inner
930.2.bf.a.563.25	yes	256	15.8	even	4	inner
930.2.bf.a.563.51	yes	256	5.3	odd	4	inner
930.2.bf.a.707.25	yes	256	31.25	even	3	inner
930.2.bf.a.707.51	yes	256	93.56	odd	6	inner
930.2.bf.a.893.4	yes	256	465.428	even	12	inner
930.2.bf.a.893.56	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)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.64704 - 0.535974i) q^{3} -1.00000i q^{4} +(-0.601583 + 2.15362i) q^{5} +(1.54362 - 0.785641i) q^{6} +(-4.77476 + 1.27939i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.42546 + 1.76554i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.64704 - 0.535974i) q^{3} -1.00000i q^{4} +(-0.601583 + 2.15362i) q^{5} +(1.54362 - 0.785641i) q^{6} +(-4.77476 + 1.27939i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.42546 + 1.76554i) q^{9} +(-1.09746 - 1.94823i) q^{10} +(-4.69648 + 2.71151i) q^{11} +(-0.535974 + 1.64704i) q^{12} +(-3.13598 - 0.840283i) q^{13} +(2.47160 - 4.28093i) q^{14} +(2.14512 - 3.22467i) q^{15} -1.00000 q^{16} +(-0.636212 - 2.37438i) q^{17} +(-2.96349 + 0.466638i) q^{18} +(6.16217 + 3.55773i) q^{19} +(2.15362 + 0.601583i) q^{20} +(8.54993 + 0.451939i) q^{21} +(1.40358 - 5.23824i) q^{22} +(3.46253 + 3.46253i) q^{23} +(-0.785641 - 1.54362i) q^{24} +(-4.27620 - 2.59117i) q^{25} +(2.81164 - 1.62330i) q^{26} +(-3.04855 - 4.20789i) q^{27} +(1.27939 + 4.77476i) q^{28} -1.53068 q^{29} +(0.763357 + 3.79701i) q^{30} +(-5.30670 + 1.68490i) q^{31} +(0.707107 - 0.707107i) q^{32} +(9.18857 - 1.94877i) q^{33} +(2.12881 + 1.22907i) q^{34} +(0.117083 - 11.0527i) q^{35} +(1.76554 - 2.42546i) q^{36} +(-0.363051 + 0.0972792i) q^{37} +(-6.87301 + 1.84162i) q^{38} +(4.71470 + 3.06478i) q^{39} +(-1.94823 + 1.09746i) q^{40} +(3.91686 - 2.26140i) q^{41} +(-6.36528 + 5.72615i) q^{42} +(-1.15590 - 4.31389i) q^{43} +(2.71151 + 4.69648i) q^{44} +(-5.26142 + 4.16142i) q^{45} -4.89676 q^{46} +(-7.74617 + 7.74617i) q^{47} +(1.64704 + 0.535974i) q^{48} +(15.0993 - 8.71760i) q^{49} +(4.85596 - 1.19149i) q^{50} +(-0.224738 + 4.25168i) q^{51} +(-0.840283 + 3.13598i) q^{52} +(1.72063 - 6.42148i) q^{53} +(5.13108 + 0.819781i) q^{54} +(-3.01426 - 11.7456i) q^{55} +(-4.28093 - 2.47160i) q^{56} +(-8.24248 - 9.16248i) q^{57} +(1.08236 - 1.08236i) q^{58} +(1.98970 - 3.44626i) q^{59} +(-3.22467 - 2.14512i) q^{60} +7.97074 q^{61} +(2.56100 - 4.94381i) q^{62} +(-13.8398 - 5.32690i) q^{63} +1.00000i q^{64} +(3.69620 - 6.24822i) q^{65} +(-5.11931 + 7.87529i) q^{66} +(3.31584 - 12.3749i) q^{67} +(-2.37438 + 0.636212i) q^{68} +(-3.84709 - 7.55875i) q^{69} +(7.73265 + 7.89823i) q^{70} +(-6.67494 + 3.85378i) q^{71} +(0.466638 + 2.96349i) q^{72} +(9.43484 + 2.52806i) q^{73} +(0.187929 - 0.325503i) q^{74} +(5.65425 + 6.55968i) q^{75} +(3.55773 - 6.16217i) q^{76} +(18.9555 - 18.9555i) q^{77} +(-5.50092 + 1.16667i) q^{78} +(3.41094 + 1.96931i) q^{79} +(0.601583 - 2.15362i) q^{80} +(2.76575 + 8.56450i) q^{81} +(-1.17059 + 4.36869i) q^{82} +(-0.798015 + 2.97823i) q^{83} +(0.451939 - 8.54993i) q^{84} +(5.49625 + 0.0582228i) q^{85} +(3.86773 + 2.23303i) q^{86} +(2.52109 + 0.820406i) q^{87} +(-5.23824 - 1.40358i) q^{88} -12.5784 q^{89} +(0.777820 - 6.66296i) q^{90} +16.0486 q^{91} +(3.46253 - 3.46253i) q^{92} +(9.64340 + 0.0691608i) q^{93} -10.9547i q^{94} +(-11.3691 + 11.1307i) q^{95} +(-1.54362 + 0.785641i) q^{96} +(4.96468 + 4.96468i) q^{97} +(-4.51256 + 16.8411i) q^{98} +(-16.1784 - 1.71513i) 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

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