LMFDB - Embedded newform 930.2.v.b.401.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(401,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 3]))

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

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

chi := DirichletCharacter("930.401");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.v (of order $10$, 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:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			401.1
Character	$\chi$	$=$	930.401
Dual form			930.2.v.b.821.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.587785 + 0.809017i) q^{2} +(-1.71066 + 0.271374i) q^{3} +(-0.309017 - 0.951057i) q^{4} +1.00000i q^{5} +(0.785954 - 1.54346i) q^{6} +(0.226704 + 0.697724i) q^{7} +(0.951057 + 0.309017i) q^{8} +(2.85271 - 0.928458i) q^{9} +O(q^{10})$	\(q+(-0.587785 + 0.809017i) q^{2} +(-1.71066 + 0.271374i) q^{3} +(-0.309017 - 0.951057i) q^{4} +1.00000i q^{5} +(0.785954 - 1.54346i) q^{6} +(0.226704 + 0.697724i) q^{7} +(0.951057 + 0.309017i) q^{8} +(2.85271 - 0.928458i) q^{9} +(-0.809017 - 0.587785i) q^{10} +(-0.278880 - 0.858303i) q^{11} +(0.786715 + 1.54307i) q^{12} +(-1.34625 - 1.85295i) q^{13} +(-0.697724 - 0.226704i) q^{14} +(-0.271374 - 1.71066i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-0.168446 + 0.518424i) q^{17} +(-0.925643 + 2.85363i) q^{18} +(-5.91722 - 4.29911i) q^{19} +(0.951057 - 0.309017i) q^{20} +(-0.577158 - 1.13205i) q^{21} +(0.858303 + 0.278880i) q^{22} +(-1.57277 + 4.84049i) q^{23} +(-1.71079 - 0.270530i) q^{24} -1.00000 q^{25} +2.29037 q^{26} +(-4.62806 + 2.36243i) q^{27} +(0.593520 - 0.431217i) q^{28} +(-2.18866 - 1.59015i) q^{29} +(1.54346 + 0.785954i) q^{30} +(5.56072 - 0.280036i) q^{31} -1.00000i q^{32} +(0.709989 + 1.39258i) q^{33} +(-0.320403 - 0.440997i) q^{34} +(-0.697724 + 0.226704i) q^{35} +(-1.76455 - 2.42618i) q^{36} -3.45745i q^{37} +(6.95611 - 2.26018i) q^{38} +(2.80581 + 2.80443i) q^{39} +(-0.309017 + 0.951057i) q^{40} +(5.09391 - 7.01117i) q^{41} +(1.25509 + 0.198469i) q^{42} +(1.02523 - 1.41110i) q^{43} +(-0.730116 + 0.530460i) q^{44} +(0.928458 + 2.85271i) q^{45} +(-2.99158 - 4.11756i) q^{46} +(-0.871603 - 1.19966i) q^{47} +(1.22444 - 1.22505i) q^{48} +(5.22769 - 3.79814i) q^{49} +(0.587785 - 0.809017i) q^{50} +(0.147467 - 0.932558i) q^{51} +(-1.34625 + 1.85295i) q^{52} +(1.52164 - 4.68312i) q^{53} +(0.809059 - 5.13278i) q^{54} +(0.858303 - 0.278880i) q^{55} +0.733631i q^{56} +(11.2890 + 5.74854i) q^{57} +(2.57292 - 0.835994i) q^{58} +(-5.64150 - 7.76486i) q^{59} +(-1.54307 + 0.786715i) q^{60} -6.50632i q^{61} +(-3.04195 + 4.66332i) q^{62} +(1.29453 + 1.77992i) q^{63} +(0.809017 + 0.587785i) q^{64} +(1.85295 - 1.34625i) q^{65} +(-1.54395 - 0.244147i) q^{66} +11.4373 q^{67} +0.545103 q^{68} +(1.37689 - 8.70723i) q^{69} +(0.226704 - 0.697724i) q^{70} +(-2.22717 - 0.723652i) q^{71} +(3.00000 - 0.00147998i) q^{72} +(10.1559 - 3.29984i) q^{73} +(2.79714 + 2.03224i) q^{74} +(1.71066 - 0.271374i) q^{75} +(-2.26018 + 6.95611i) q^{76} +(0.535636 - 0.389162i) q^{77} +(-3.91804 + 0.621548i) q^{78} +(-6.36431 - 2.06789i) q^{79} +(-0.587785 - 0.809017i) q^{80} +(7.27593 - 5.29725i) q^{81} +(2.67803 + 8.24212i) q^{82} +(-2.02341 - 1.47009i) q^{83} +(-0.898289 + 0.898732i) q^{84} +(-0.518424 - 0.168446i) q^{85} +(0.538994 + 1.65885i) q^{86} +(4.17558 + 2.12627i) q^{87} -0.902473i q^{88} +(-0.0750353 - 0.230935i) q^{89} +(-2.85363 - 0.925643i) q^{90} +(0.987647 - 1.35938i) q^{91} +5.08959 q^{92} +(-9.43650 + 1.98808i) q^{93} +1.48286 q^{94} +(4.29911 - 5.91722i) q^{95} +(0.271374 + 1.71066i) q^{96} +(3.20868 + 9.87531i) q^{97} +6.46179i q^{98} +(-1.59246 - 2.18956i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 20 q^{4} + 12 q^{7} + 8 q^{9}+O(q^{10}) $ 80 * q + 20 * q^4 + 12 * q^7 + 8 * q^9	$ 80 q + 20 q^{4} + 12 q^{7} + 8 q^{9} - 20 q^{10} + 10 q^{13} - 20 q^{16} - 4 q^{18} - 12 q^{19} - 30 q^{21} - 10 q^{22} - 80 q^{25} + 60 q^{27} + 18 q^{28} + 8 q^{31} - 20 q^{33} + 10 q^{34} - 8 q^{36} - 46 q^{39} + 20 q^{40} + 50 q^{43} - 16 q^{45} - 10 q^{46} - 8 q^{49} - 20 q^{51} + 10 q^{52} - 10 q^{55} + 10 q^{58} + 44 q^{63} + 20 q^{64} - 10 q^{66} - 132 q^{67} - 16 q^{69} + 12 q^{70} + 4 q^{72} - 20 q^{73} - 18 q^{76} + 48 q^{78} - 120 q^{79} + 48 q^{81} - 20 q^{82} + 20 q^{84} - 136 q^{87} - 12 q^{90} - 110 q^{91} - 20 q^{93} - 28 q^{94} + 22 q^{97}+O(q^{100}) $ 80 * q + 20 * q^4 + 12 * q^7 + 8 * q^9 - 20 * q^10 + 10 * q^13 - 20 * q^16 - 4 * q^18 - 12 * q^19 - 30 * q^21 - 10 * q^22 - 80 * q^25 + 60 * q^27 + 18 * q^28 + 8 * q^31 - 20 * q^33 + 10 * q^34 - 8 * q^36 - 46 * q^39 + 20 * q^40 + 50 * q^43 - 16 * q^45 - 10 * q^46 - 8 * q^49 - 20 * q^51 + 10 * q^52 - 10 * q^55 + 10 * q^58 + 44 * q^63 + 20 * q^64 - 10 * q^66 - 132 * q^67 - 16 * q^69 + 12 * q^70 + 4 * q^72 - 20 * q^73 - 18 * q^76 + 48 * q^78 - 120 * q^79 + 48 * q^81 - 20 * q^82 + 20 * q^84 - 136 * q^87 - 12 * q^90 - 110 * q^91 - 20 * q^93 - 28 * q^94 + 22 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{10}\right)$

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 $

$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i
$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i
$3$	−1.71066	+	0.271374i	−0.987650	+	0.156678i
$3$	−1.71066	+	0.271374i	−0.987650	+	0.156678i
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	0.785954	−	1.54346i	0.320864	−	0.630116i
$7$	0.226704	+	0.697724i	0.0856862	+	0.263715i	0.984715	−	0.174175i	$-0.0557259\pi$
$7$	0.226704	+	0.697724i	0.0856862	+	0.263715i	−0.899029	+	0.437890i	$0.855726\pi$
$8$	0.951057	+	0.309017i	0.336249	+	0.109254i
$9$	2.85271	−	0.928458i	0.950904	−	0.309486i
$10$	−0.809017	−	0.587785i	−0.255834	−	0.185874i
$11$	−0.278880	−	0.858303i	−0.0840854	−	0.258788i	0.900171	−	0.435538i	$-0.143442\pi$
$11$	−0.278880	−	0.858303i	−0.0840854	−	0.258788i	−0.984256	+	0.176750i	$0.943442\pi$
$12$	0.786715	+	1.54307i	0.227105	+	0.445447i
$13$	−1.34625	−	1.85295i	−0.373382	−	0.513916i	0.580435	−	0.814307i	$-0.302883\pi$
$13$	−1.34625	−	1.85295i	−0.373382	−	0.513916i	−0.953816	+	0.300391i	$0.902883\pi$
$14$	−0.697724	−	0.226704i	−0.186475	−	0.0605893i
$15$	−0.271374	−	1.71066i	−0.0700686	−	0.441690i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−0.168446	+	0.518424i	−0.0408542	+	0.125736i	−0.969403	−	0.245473i	$-0.921057\pi$
$17$	−0.168446	+	0.518424i	−0.0408542	+	0.125736i	0.928549	+	0.371209i	$0.121057\pi$
$18$	−0.925643	+	2.85363i	−0.218176	+	0.672606i
$19$	−5.91722	−	4.29911i	−1.35750	−	0.986284i	−0.998599	−	0.0529099i	$-0.983150\pi$
$19$	−5.91722	−	4.29911i	−1.35750	−	0.986284i	−0.358905	−	0.933374i	$-0.616850\pi$
$20$	0.951057	−	0.309017i	0.212663	−	0.0690983i
$21$	−0.577158	−	1.13205i	−0.125946	−	0.247033i
$22$	0.858303	+	0.278880i	0.182991	+	0.0594573i
$23$	−1.57277	+	4.84049i	−0.327945	+	1.00931i	0.642149	+	0.766580i	$0.278043\pi$
$23$	−1.57277	+	4.84049i	−0.327945	+	1.00931i	−0.970094	+	0.242731i	$0.921957\pi$
$24$	−1.71079	−	0.270530i	−0.349214	−	0.0552218i
$25$	−1.00000			−0.200000
$26$	2.29037			0.449179
$27$	−4.62806	+	2.36243i	−0.890670	+	0.454650i
$28$	0.593520	−	0.431217i	0.112165	−	0.0814924i
$29$	−2.18866	−	1.59015i	−0.406424	−	0.295284i	0.365729	−	0.930722i	$-0.380820\pi$
$29$	−2.18866	−	1.59015i	−0.406424	−	0.295284i	−0.772152	+	0.635437i	$0.780820\pi$
$30$	1.54346	+	0.785954i	0.281796	+	0.143495i
$31$	5.56072	−	0.280036i	0.998734	−	0.0502959i
$31$	5.56072	−	0.280036i	0.998734	−	0.0502959i
$32$		−	1.00000i		−	0.176777i
$33$	0.709989	+	1.39258i	0.123593	+	0.242418i
$34$	−0.320403	−	0.440997i	−0.0549487	−	0.0756304i
$35$	−0.697724	+	0.226704i	−0.117937	+	0.0383200i
$36$	−1.76455	−	2.42618i	−0.294092	−	0.404363i
$37$		−	3.45745i		−	0.568401i	−0.958765	−	0.284201i	$-0.908272\pi$
$37$		−	3.45745i		−	0.568401i	0.958765	−	0.284201i	$-0.0917282\pi$
$38$	6.95611	−	2.26018i	1.12843	−	0.366649i
$39$	2.80581	+	2.80443i	0.449289	+	0.449068i
$40$	−0.309017	+	0.951057i	−0.0488599	+	0.150375i
$41$	5.09391	−	7.01117i	0.795535	−	1.09496i	−0.197861	−	0.980230i	$-0.563400\pi$
$41$	5.09391	−	7.01117i	0.795535	−	1.09496i	0.993397	−	0.114730i	$-0.0366004\pi$
$42$	1.25509	+	0.198469i	0.193665	+	0.0306245i
$43$	1.02523	−	1.41110i	0.156346	−	0.215191i	−0.723657	−	0.690159i	$-0.757540\pi$
$43$	1.02523	−	1.41110i	0.156346	−	0.215191i	0.880003	+	0.474968i	$0.157540\pi$
$44$	−0.730116	+	0.530460i	−0.110069	+	0.0799699i
$45$	0.928458	+	2.85271i	0.138406	+	0.425257i
$46$	−2.99158	−	4.11756i	−0.441085	−	0.607102i
$47$	−0.871603	−	1.19966i	−0.127136	−	0.174988i	0.740704	−	0.671832i	$-0.234492\pi$
$47$	−0.871603	−	1.19966i	−0.127136	−	0.174988i	−0.867840	+	0.496844i	$0.834492\pi$
$48$	1.22444	−	1.22505i	0.176733	−	0.176820i
$49$	5.22769	−	3.79814i	0.746814	−	0.542592i
$50$	0.587785	−	0.809017i	0.0831254	−	0.114412i
$51$	0.147467	−	0.932558i	0.0206495	−	0.130584i
$52$	−1.34625	+	1.85295i	−0.186691	+	0.256958i
$53$	1.52164	−	4.68312i	0.209013	−	0.643276i	−0.790512	−	0.612447i	$-0.790185\pi$
$53$	1.52164	−	4.68312i	0.209013	−	0.643276i	0.999525	−	0.0308289i	$-0.00981471\pi$
$54$	0.809059	−	5.13278i	0.110099	−	0.698483i
$55$	0.858303	−	0.278880i	0.115734	−	0.0376041i
$56$			0.733631i			0.0980355i
$57$	11.2890	+	5.74854i	1.49527	+	0.761412i
$58$	2.57292	−	0.835994i	0.337841	−	0.109771i
$59$	−5.64150	−	7.76486i	−0.734461	−	1.01090i	−0.998918	−	0.0465017i	$-0.985193\pi$
$59$	−5.64150	−	7.76486i	−0.734461	−	1.01090i	0.264457	−	0.964397i	$-0.414807\pi$
$60$	−1.54307	+	0.786715i	−0.199210	+	0.101565i
$61$		−	6.50632i		−	0.833048i	−0.909125	−	0.416524i	$-0.863248\pi$
$61$		−	6.50632i		−	0.833048i	0.909125	−	0.416524i	$-0.136752\pi$
$62$	−3.04195	+	4.66332i	−0.386329	+	0.592242i
$63$	1.29453	+	1.77992i	0.163095	+	0.224249i
$64$	0.809017	+	0.587785i	0.101127	+	0.0734732i
$65$	1.85295	−	1.34625i	0.229830	−	0.166981i
$66$	−1.54395	−	0.244147i	−0.190047	−	0.0300524i
$67$	11.4373			1.39729			0.698644	−	0.715470i	$-0.253787\pi$
$67$	11.4373			1.39729			0.698644	+	0.715470i	$0.253787\pi$
$68$	0.545103			0.0661034
$69$	1.37689	−	8.70723i	0.165758	−	1.04823i
$70$	0.226704	−	0.697724i	0.0270963	−	0.0833940i
$71$	−2.22717	−	0.723652i	−0.264317	−	0.0858817i	0.173861	−	0.984770i	$-0.444376\pi$
$71$	−2.22717	−	0.723652i	−0.264317	−	0.0858817i	−0.438177	+	0.898889i	$0.644376\pi$
$72$	3.00000	−	0.00147998i	0.353553	−	0.000174418i
$73$	10.1559	−	3.29984i	1.18865	−	0.386217i	0.353078	−	0.935594i	$-0.385135\pi$
$73$	10.1559	−	3.29984i	1.18865	−	0.386217i	0.835574	+	0.549377i	$0.185135\pi$
$74$	2.79714	+	2.03224i	0.325160	+	0.236243i
$75$	1.71066	−	0.271374i	0.197530	−	0.0313356i
$76$	−2.26018	+	6.95611i	−0.259260	+	0.797921i
$77$	0.535636	−	0.389162i	0.0610413	−	0.0443491i
$78$	−3.91804	+	0.621548i	−0.443631	+	0.0703765i
$79$	−6.36431	−	2.06789i	−0.716041	−	0.232656i	−0.0717353	−	0.997424i	$-0.522854\pi$
$79$	−6.36431	−	2.06789i	−0.716041	−	0.232656i	−0.644306	+	0.764768i	$0.722854\pi$
$80$	−0.587785	−	0.809017i	−0.0657164	−	0.0904508i
$81$	7.27593	−	5.29725i	0.808437	−	0.588583i
$82$	2.67803	+	8.24212i	0.295739	+	0.910190i
$83$	−2.02341	−	1.47009i	−0.222098	−	0.161363i	0.471173	−	0.882041i	$-0.343831\pi$
$83$	−2.02341	−	1.47009i	−0.222098	−	0.161363i	−0.693270	+	0.720678i	$0.743831\pi$
$84$	−0.898289	+	0.898732i	−0.0980113	+	0.0980597i
$85$	−0.518424	−	0.168446i	−0.0562309	−	0.0182705i
$86$	0.538994	+	1.65885i	0.0581212	+	0.178879i
$87$	4.17558	+	2.12627i	0.447669	+	0.227960i
$88$		−	0.902473i		−	0.0962040i
$89$	−0.0750353	−	0.230935i	−0.00795373	−	0.0244791i	0.947001	−	0.321231i	$-0.104097\pi$
$89$	−0.0750353	−	0.230935i	−0.00795373	−	0.0244791i	−0.954955	+	0.296752i	$0.904097\pi$
$90$	−2.85363	−	0.925643i	−0.300799	−	0.0975714i
$91$	0.987647	−	1.35938i	0.103534	−	0.142502i
$92$	5.08959			0.530626
$93$	−9.43650	+	1.98808i	−0.978519	+	0.206155i
$94$	1.48286			0.152945
$95$	4.29911	−	5.91722i	0.441080	−	0.607094i
$96$	0.271374	+	1.71066i	0.0276970	+	0.174593i
$97$	3.20868	+	9.87531i	0.325792	+	1.00269i	0.971082	+	0.238747i	$0.0767368\pi$
$97$	3.20868	+	9.87531i	0.325792	+	1.00269i	−0.645289	+	0.763938i	$0.723263\pi$
$98$			6.46179i			0.652739i
$99$	−1.59246	−	2.18956i	−0.160048	−	0.220059i
$100$	0.309017	+	0.951057i	0.0309017	+	0.0951057i
$101$	4.81109	+	1.56322i	0.478721	+	0.155546i	0.538431	−	0.842670i	$-0.319017\pi$
$101$	4.81109	+	1.56322i	0.478721	+	0.155546i	−0.0597095	+	0.998216i	$0.519017\pi$
$102$	0.667777	+	0.667447i	0.0661197	+	0.0660871i
$103$	−12.9021	−	9.37393i	−1.27128	−	0.923641i	−0.272029	−	0.962289i	$-0.587695\pi$
$103$	−12.9021	−	9.37393i	−1.27128	−	0.923641i	−0.999253	+	0.0386483i	$0.987695\pi$
$104$	−0.707764	−	2.17827i	−0.0694019	−	0.213597i
$105$	1.13205	−	0.577158i	0.110476	−	0.0563249i
$106$	2.89433	+	3.98370i	0.281122	+	0.386931i
$107$	2.16903	+	0.704761i	0.209688	+	0.0681318i	0.411978	−	0.911194i	$-0.364838\pi$
$107$	2.16903	+	0.704761i	0.209688	+	0.0681318i	−0.202290	+	0.979326i	$0.564838\pi$
$108$	3.67695	+	3.67151i	0.353815	+	0.353292i
$109$	7.63407	−	5.54648i	0.731211	−	0.531256i	−0.158735	−	0.987321i	$-0.550742\pi$
$109$	7.63407	−	5.54648i	0.731211	−	0.531256i	0.889946	+	0.456065i	$0.150742\pi$
$110$	−0.278880	+	0.858303i	−0.0265901	+	0.0818360i
$111$	0.938263	+	5.91452i	0.0890560	+	0.561381i
$112$	−0.593520	−	0.431217i	−0.0560823	−	0.0407462i
$113$	−17.2707	+	5.61160i	−1.62469	+	0.527895i	−0.973043	−	0.230625i	$-0.925923\pi$
$113$	−17.2707	+	5.61160i	−1.62469	+	0.527895i	−0.651650	+	0.758520i	$0.725923\pi$
$114$	−11.2862	+	5.75410i	−1.05705	+	0.538921i
$115$	−4.84049	−	1.57277i	−0.451378	−	0.146661i
$116$	−0.835994	+	2.57292i	−0.0776201	+	0.238890i
$117$	−5.56084	−	4.03600i	−0.514100	−	0.373128i
$118$	9.59790			0.883558
$119$	−0.399904			−0.0366592
$120$	0.270530	−	1.71079i	0.0246959	−	0.156173i
$121$	8.24028	−	5.98691i	0.749116	−	0.544265i
$122$	5.26372	+	3.82432i	0.476555	+	0.346237i
$123$	−6.81130	+	13.3761i	−0.614154	+	1.20608i
$124$	−1.98469	−	5.20202i	−0.178230	−	0.467155i
$125$		−	1.00000i		−	0.0894427i
$126$	−2.20089	+	0.00108576i	−0.196071	+	9.67273e-5i
$127$	8.19545	+	11.2801i	0.727229	+	1.00094i	0.999253	+	0.0386543i	$0.0123071\pi$
$127$	8.19545	+	11.2801i	0.727229	+	1.00094i	−0.272024	+	0.962291i	$0.587693\pi$
$128$	−0.951057	+	0.309017i	−0.0840623	+	0.0273135i
$129$	−1.37088	+	2.69214i	−0.120699	+	0.237030i
$130$			2.29037i			0.200879i
$131$	7.47416	−	2.42850i	0.653021	−	0.212179i	0.0362752	−	0.999342i	$-0.488451\pi$
$131$	7.47416	−	2.42850i	0.653021	−	0.212179i	0.616746	+	0.787163i	$0.288451\pi$
$132$	1.10503	−	1.10557i	0.0961802	−	0.0962277i
$133$	1.65814	−	5.10322i	0.143779	−	0.442505i
$134$	−6.72267	+	9.25296i	−0.580750	+	0.799334i
$135$	−2.36243	−	4.62806i	−0.203326	−	0.398320i
$136$	−0.320403	+	0.440997i	−0.0274744	+	0.0378152i
$137$	−3.70775	+	2.69384i	−0.316775	+	0.230150i	−0.734798	−	0.678286i	$-0.762723\pi$
$137$	−3.70775	+	2.69384i	−0.316775	+	0.230150i	0.418023	+	0.908436i	$0.362723\pi$
$138$	6.23498	+	6.23191i	0.530757	+	0.530495i
$139$	−10.2059	−	14.0472i	−0.865652	−	1.19147i	−0.980192	−	0.198049i	$-0.936539\pi$
$139$	−10.2059	−	14.0472i	−0.865652	−	1.19147i	0.114540	−	0.993419i	$-0.463461\pi$
$140$	0.431217	+	0.593520i	0.0364445	+	0.0501616i
$141$	1.81657	+	1.81568i	0.152983	+	0.152908i
$142$	1.89455	−	1.37647i	0.158987	−	0.115511i
$143$	−1.21495	+	1.67224i	−0.101599	+	0.139839i
$144$	−1.76216	+	2.42792i	−0.146847	+	0.202327i
$145$	1.59015	−	2.18866i	0.132055	−	0.181758i
$146$	−3.29984	+	10.1559i	−0.273096	+	0.840504i
$147$	−7.91209	+	7.91599i	−0.652578	+	0.652900i
$148$	−3.28823	+	1.06841i	−0.270291	+	0.0878228i
$149$			7.90077i			0.647256i	0.946184	+	0.323628i	$0.104903\pi$
$149$			7.90077i			0.647256i	−0.946184	+	0.323628i	$0.895097\pi$
$150$	−0.785954	+	1.54346i	−0.0641729	+	0.126023i
$151$	−10.2595	+	3.33352i	−0.834909	+	0.271278i	−0.695112	−	0.718902i	$-0.744645\pi$
$151$	−10.2595	+	3.33352i	−0.834909	+	0.271278i	−0.139797	+	0.990180i	$0.544645\pi$
$152$	−4.29911	−	5.91722i	−0.348704	−	0.479950i
$153$	0.000806743		1.63531i	6.52213e−5		0.132207i
$154$			0.662082i			0.0533521i
$155$	0.280036	+	5.56072i	0.0224930	+	0.446648i
$156$	1.80013	−	3.53510i	0.144125	−	0.283035i
$157$	7.49182	+	5.44313i	0.597912	+	0.434409i	0.845137	−	0.534549i	$-0.179519\pi$
$157$	7.49182	+	5.44313i	0.597912	+	0.434409i	−0.247225	+	0.968958i	$0.579519\pi$
$158$	5.41381	−	3.93336i	0.430699	−	0.312922i
$159$	−1.33213	+	8.42416i	−0.105644	+	0.668079i
$160$	1.00000			0.0790569
$161$	−3.73388			−0.294271
$162$	0.00887990	+	9.00000i	0.000697671	+	0.707106i
$163$	2.79930	−	8.61537i	0.219258	−	0.674808i	−0.779565	−	0.626321i	$-0.784560\pi$
$163$	2.79930	−	8.61537i	0.219258	−	0.674808i	0.998824	−	0.0484873i	$-0.0154400\pi$
$164$	−8.24212	−	2.67803i	−0.643602	−	0.209119i
$165$	−1.39258	+	0.709989i	−0.108412	+	0.0552726i
$166$	2.37866	−	0.772872i	0.184619	−	0.0599865i
$167$	−12.6056	−	9.15852i	−0.975452	−	0.708708i	−0.0187647	−	0.999824i	$-0.505973\pi$
$167$	−12.6056	−	9.15852i	−0.975452	−	0.708708i	−0.956688	+	0.291116i	$0.905973\pi$
$168$	−0.199089	−	1.25499i	−0.0153600	−	0.0968247i
$169$	2.39618	−	7.37468i	0.184322	−	0.567283i
$170$	0.440997	−	0.320403i	0.0338230	−	0.0245738i
$171$	−20.8717	−	6.77024i	−1.59610	−	0.517733i
$172$	−1.65885	−	0.538994i	−0.126486	−	0.0410979i
$173$	−7.60870	−	10.4725i	−0.578479	−	0.796207i	0.415049	−	0.909799i	$-0.363764\pi$
$173$	−7.60870	−	10.4725i	−0.578479	−	0.796207i	−0.993528	+	0.113592i	$0.963764\pi$
$174$	−4.17453	+	2.12833i	−0.316470	+	0.161348i
$175$	−0.226704	−	0.697724i	−0.0171372	−	0.0527430i
$176$	0.730116	+	0.530460i	0.0550346	+	0.0399850i
$177$	11.7579	+	11.7521i	0.883776	+	0.883340i
$178$	0.230935	+	0.0750353i	0.0173093	+	0.00562413i
$179$	4.01886	+	12.3688i	0.300384	+	0.924487i	0.981360	+	0.192181i	$0.0615560\pi$
$179$	4.01886	+	12.3688i	0.300384	+	0.924487i	−0.680975	+	0.732306i	$0.738444\pi$
$180$	2.42618	−	1.76455i	0.180837	−	0.131522i
$181$			12.3861i			0.920651i	0.887750	+	0.460325i	$0.152267\pi$
$181$			12.3861i			0.920651i	−0.887750	+	0.460325i	$0.847733\pi$
$182$	0.519237	+	1.59805i	0.0384884	+	0.118455i
$183$	1.76565	+	11.1301i	0.130520	+	0.822760i
$184$	−2.99158	+	4.11756i	−0.220543	+	0.303551i
$185$	3.45745			0.254197
$186$	3.93824	−	8.80285i	0.288766	−	0.645457i
$187$	0.491941			0.0359743
$188$	−0.871603	+	1.19966i	−0.0635682	+	0.0874941i
$189$	−2.69752	−	2.69354i	−0.196216	−	0.195926i
$190$	2.26018	+	6.95611i	0.163971	+	0.504649i
$191$			7.20910i			0.521632i	0.965389	+	0.260816i	$0.0839916\pi$
$191$			7.20910i			0.521632i	−0.965389	+	0.260816i	$0.916008\pi$
$192$	−1.54346	−	0.785954i	−0.111390	−	0.0567213i
$193$	−6.15801	−	18.9524i	−0.443263	−	1.36422i	−0.884377	−	0.466773i	$-0.845417\pi$
$193$	−6.15801	−	18.9524i	−0.443263	−	1.36422i	0.441114	−	0.897451i	$-0.354583\pi$
$194$	−9.87531	−	3.20868i	−0.709006	−	0.230370i
$195$	−2.80443	+	2.80581i	−0.200829	+	0.200928i
$196$	−5.22769	−	3.79814i	−0.373407	−	0.271296i
$197$	−3.86477	−	11.8945i	−0.275353	−	0.847450i	−0.989126	−	0.147072i	$-0.953015\pi$
$197$	−3.86477	−	11.8945i	−0.275353	−	0.847450i	0.713772	−	0.700378i	$-0.246985\pi$
$198$	2.70742	−	0.00133565i	0.192408	−	9.49202e-5i
$199$	−3.38757	−	4.66259i	−0.240139	−	0.330522i	0.671889	−	0.740652i	$-0.265483\pi$
$199$	−3.38757	−	4.66259i	−0.240139	−	0.330522i	−0.912027	+	0.410130i	$0.865483\pi$
$200$	−0.951057	−	0.309017i	−0.0672499	−	0.0218508i
$201$	−19.5653	+	3.10379i	−1.38003	+	0.218924i
$202$	−4.09255	+	2.97342i	−0.287951	+	0.209209i
$203$	0.613310	−	1.88758i	0.0430460	−	0.132482i
$204$	−0.932485	+	0.147927i	−0.0652870	+	0.0103570i
$205$	7.01117	+	5.09391i	0.489681	+	0.355774i
$206$	15.1673	−	4.92817i	1.05676	−	0.343362i
$207$	0.00753250	+	15.2688i	0.000523545	+	1.06125i
$208$	2.17827	+	0.707764i	0.151036	+	0.0490746i
$209$	−2.03975	+	6.27770i	−0.141092	+	0.434238i
$210$	−0.198469	+	1.25509i	−0.0136957	+	0.0866095i
$211$	−23.5053			−1.61817			−0.809085	−	0.587691i	$-0.800037\pi$
$211$	−23.5053			−1.61817			−0.809085	+	0.587691i	$0.800037\pi$
$212$	−4.92412			−0.338190
$213$	4.00631	+	0.633525i	0.274508	+	0.0434084i
$214$	−1.84509	+	1.34053i	−0.126128	+	0.0916370i
$215$	1.41110	+	1.02523i	0.0962365	+	0.0699199i
$216$	−5.13158	+	0.816655i	−0.349160	+	0.0555663i
$217$	1.45603	+	3.81636i	0.0988415	+	0.259072i
$218$			9.43623i			0.639102i
$219$	−16.4777	+	8.40093i	−1.11346	+	0.567683i
$220$	−0.530460	−	0.730116i	−0.0357636	−	0.0492244i
$221$	1.18738	−	0.385804i	0.0798720	−	0.0259520i
$222$	−5.33644	−	2.71740i	−0.358159	−	0.182380i
$223$			18.7282i			1.25413i	0.778966	+	0.627066i	$0.215745\pi$
$223$			18.7282i			1.25413i	−0.778966	+	0.627066i	$0.784255\pi$
$224$	0.697724	−	0.226704i	0.0466187	−	0.0151473i
$225$	−2.85271	+	0.928458i	−0.190181	+	0.0618972i
$226$	5.61160	−	17.2707i	0.373278	−	1.14883i
$227$	8.05499	−	11.0867i	0.534629	−	0.735853i	−0.453198	−	0.891410i	$-0.649717\pi$
$227$	8.05499	−	11.0867i	0.534629	−	0.735853i	0.987827	+	0.155557i	$0.0497171\pi$
$228$	1.97868	−	12.5129i	0.131042	−	0.828687i
$229$	2.46612	−	3.39432i	0.162966	−	0.224303i	−0.719723	−	0.694262i	$-0.755731\pi$
$229$	2.46612	−	3.39432i	0.162966	−	0.224303i	0.882689	+	0.469958i	$0.155731\pi$
$230$	4.11756	−	2.99158i	0.271504	−	0.197259i
$231$	−0.810681	+	0.811082i	−0.0533389	+	0.0533652i
$232$	−1.59015	−	2.18866i	−0.104399	−	0.143693i
$233$	−11.7562	−	16.1811i	−0.770178	−	1.06006i	−0.996299	−	0.0859592i	$-0.972605\pi$
$233$	−11.7562	−	16.1811i	−0.770178	−	1.06006i	0.226121	−	0.974099i	$-0.427395\pi$
$234$	6.53377	−	2.12651i	0.427126	−	0.139015i
$235$	1.19966	−	0.871603i	0.0782571	−	0.0568571i
$236$	−5.64150	+	7.76486i	−0.367231	+	0.505450i
$237$	11.4483	+	1.81035i	0.743650	+	0.117595i
$238$	0.235058	−	0.323529i	0.0152365	−	0.0209713i
$239$	−2.48607	+	7.65133i	−0.160810	+	0.494923i	−0.998703	−	0.0509115i	$-0.983787\pi$
$239$	−2.48607	+	7.65133i	−0.160810	+	0.494923i	0.837893	+	0.545835i	$0.183787\pi$
$240$	1.22505	+	1.22444i	0.0790764	+	0.0790374i
$241$	16.7872	−	5.45449i	1.08136	−	0.351355i	0.286457	−	0.958093i	$-0.407522\pi$
$241$	16.7872	−	5.45449i	1.08136	−	0.351355i	0.794902	+	0.606738i	$0.207522\pi$
$242$			10.1855i			0.654751i
$243$	−11.0091	+	11.0363i	−0.706234	+	0.707978i
$244$	−6.18787	+	2.01056i	−0.396138	+	0.128713i
$245$	3.79814	+	5.22769i	0.242654	+	0.333985i
$246$	−6.81789	−	13.3727i	−0.434693	−	0.852613i
$247$			16.7520i			1.06590i
$248$	5.37509	+	1.45203i	0.341319	+	0.0922038i
$249$	3.86030	+	1.96572i	0.244637	+	0.124573i
$250$	0.809017	+	0.587785i	0.0511667	+	0.0371748i
$251$	2.45483	−	1.78354i	0.154947	−	0.112576i	−0.507610	−	0.861587i	$-0.669471\pi$
$251$	2.45483	−	1.78354i	0.154947	−	0.112576i	0.662558	+	0.749011i	$0.269471\pi$
$252$	1.29277	−	1.78120i	0.0814371	−	0.112205i
$253$	4.59322			0.288773
$254$	−13.9429			−0.874858
$255$	0.932558	+	0.147467i	0.0583991	+	0.00923474i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−6.07393	−	1.97354i	−0.378882	−	0.123106i	0.113384	−	0.993551i	$-0.463831\pi$
$257$	−6.07393	−	1.97354i	−0.378882	−	0.123106i	−0.492265	+	0.870445i	$0.663831\pi$
$258$	−1.37221	−	2.69146i	−0.0854298	−	0.167563i
$259$	2.41235	−	0.783819i	0.149896	−	0.0487041i
$260$	−1.85295	−	1.34625i	−0.114915	−	0.0834906i
$261$	−7.72001	−	2.50417i	−0.477856	−	0.155004i
$262$	−2.42850	+	7.47416i	−0.150033	+	0.461755i
$263$	−12.4214	+	9.02465i	−0.765934	+	0.556484i	−0.900725	−	0.434390i	$-0.856964\pi$
$263$	−12.4214	+	9.02465i	−0.765934	+	0.556484i	0.134791	+	0.990874i	$0.456964\pi$
$264$	0.244908	+	1.54382i	0.0150731	+	0.0950158i
$265$	4.68312	+	1.52164i	0.287682	+	0.0934735i
$266$	3.15396	+	4.34105i	0.193382	+	0.266167i
$267$	0.191030	+	0.374688i	0.0116908	+	0.0229306i
$268$	−3.53432	−	10.8775i	−0.215893	−	0.664450i
$269$	−25.1114	−	18.2445i	−1.53107	−	1.11239i	−0.955640	−	0.294537i	$-0.904835\pi$
$269$	−25.1114	−	18.2445i	−1.53107	−	1.11239i	−0.575430	−	0.817851i	$-0.695165\pi$
$270$	5.13278	+	0.809059i	0.312371	+	0.0492378i
$271$	−2.00228	−	0.650580i	−0.121630	−	0.0395199i	0.247570	−	0.968870i	$-0.420368\pi$
$271$	−2.00228	−	0.650580i	−0.121630	−	0.0395199i	−0.369199	+	0.929350i	$0.620368\pi$
$272$	−0.168446	−	0.518424i	−0.0102135	−	0.0314340i
$273$	−1.32063	+	2.59346i	−0.0799280	+	0.156963i
$274$		−	4.58303i		−	0.276871i
$275$	0.278880	+	0.858303i	0.0168171	+	0.0517576i
$276$	−8.70655	+	1.38118i	−0.524073	+	0.0831375i
$277$	−8.37141	+	11.5223i	−0.502989	+	0.692305i	−0.982717	−	0.185112i	$-0.940735\pi$
$277$	−8.37141	+	11.5223i	−0.502989	+	0.692305i	0.479728	+	0.877417i	$0.340735\pi$
$278$	17.3633			1.04138
$279$	15.6031	−	5.96176i	0.934135	−	0.356921i
$280$	−0.733631			−0.0438428
$281$	−5.98852	+	8.24249i	−0.357245	+	0.491705i	−0.949379	−	0.314134i	$-0.898286\pi$
$281$	−5.98852	+	8.24249i	−0.357245	+	0.491705i	0.592134	+	0.805840i	$0.298286\pi$
$282$	−2.53667	+	0.402410i	−0.151056	+	0.0239632i
$283$	−5.07601	−	15.6223i	−0.301737	−	0.928652i	−0.980875	−	0.194641i	$-0.937646\pi$
$283$	−5.07601	−	15.6223i	−0.301737	−	0.928652i	0.679137	−	0.734011i	$-0.262354\pi$
$284$			2.34179i			0.138960i
$285$	−5.74854	+	11.2890i	−0.340514	+	0.668704i
$286$	−0.638738	−	1.96583i	−0.0377694	−	0.116242i
$287$	6.04667	+	1.96468i	0.356924	+	0.115972i
$288$	−0.928458	−	2.85271i	−0.0547099	−	0.168098i
$289$	13.5129	+	9.81770i	0.794876	+	0.577512i
$290$	0.835994	+	2.57292i	0.0490912	+	0.151087i
$291$	−8.16887	−	16.0225i	−0.478868	−	0.939258i
$292$	−6.27666	−	8.63908i	−0.367314	−	0.505564i
$293$	14.8465	+	4.82392i	0.867341	+	0.281816i	0.708691	−	0.705519i	$-0.249286\pi$
$293$	14.8465	+	4.82392i	0.867341	+	0.281816i	0.158650	+	0.987335i	$0.449286\pi$
$294$	−1.75356	−	11.0539i	−0.102270	−	0.644677i
$295$	7.76486	−	5.64150i	0.452088	−	0.328461i
$296$	1.06841	−	3.28823i	0.0621001	−	0.191125i
$297$	3.31835	+	3.31344i	0.192550	+	0.192266i
$298$	−6.39185	−	4.64395i	−0.370270	−	0.269017i
$299$	11.0865	−	3.60222i	0.641149	−	0.208322i
$300$	−0.786715	−	1.54307i	−0.0454210	−	0.0890895i
$301$	1.21699	+	0.395422i	0.0701459	+	0.0227918i
$302$	3.33352	−	10.2595i	0.191823	−	0.590370i
$303$	−8.65435	−	1.36853i	−0.497179	−	0.0786198i
$304$	7.31409			0.419492
$305$	6.50632			0.372551
$306$	−1.32347	−	0.960557i	−0.0756575	−	0.0549114i
$307$	16.5505	−	12.0247i	0.944589	−	0.686284i	−0.00493215	−	0.999988i	$-0.501570\pi$
$307$	16.5505	−	12.0247i	0.944589	−	0.686284i	0.949521	+	0.313704i	$0.101570\pi$
$308$	−0.535636	−	0.389162i	−0.0305207	−	0.0221746i
$309$	24.6150	+	12.5343i	1.40030	+	0.713051i
$310$	−4.66332	−	3.04195i	−0.264859	−	0.172771i
$311$		−	21.0767i		−	1.19515i	−0.801813	−	0.597575i	$-0.796131\pi$
$311$		−	21.0767i		−	1.19515i	0.801813	−	0.597575i	$-0.203869\pi$
$312$	1.80187	+	3.53421i	0.102011	+	0.200085i
$313$	1.20003	+	1.65170i	0.0678296	+	0.0933594i	0.841584	−	0.540126i	$-0.181624\pi$
$313$	1.20003	+	1.65170i	0.0678296	+	0.0933594i	−0.773754	+	0.633486i	$0.781624\pi$
$314$	−8.80716	+	2.86162i	−0.497017	+	0.161491i
$315$	−1.77992	+	1.29453i	−0.100287	+	0.0729385i
$316$			6.69184i			0.376445i
$317$	17.7221	−	5.75827i	0.995374	−	0.323417i	0.234358	−	0.972150i	$-0.424701\pi$
$317$	17.7221	−	5.75827i	0.995374	−	0.323417i	0.761015	+	0.648734i	$0.224701\pi$
$318$	−6.03228	−	6.02931i	−0.338274	−	0.338107i
$319$	−0.754462	+	2.32199i	−0.0422418	+	0.130007i
$320$	−0.587785	+	0.809017i	−0.0328582	+	0.0452254i
$321$	−3.90173	−	0.616986i	−0.217773	−	0.0344368i
$322$	2.19472	−	3.02077i	0.122307	−	0.168341i
$323$	3.22549	−	2.34346i	0.179471	−	0.130394i
$324$	−7.28637	−	5.28288i	−0.404798	−	0.293493i
$325$	1.34625	+	1.85295i	0.0746763	+	0.102783i
$326$	5.32459	+	7.32867i	0.294902	+	0.405898i
$327$	−11.5541	+	11.5598i	−0.638945	+	0.639260i
$328$	7.01117	−	5.09391i	0.387127	−	0.281264i
$329$	0.639435	−	0.880106i	0.0352532	−	0.0485218i
$330$	0.244147	−	1.54395i	0.0134398	−	0.0849914i
$331$	−15.8654	+	21.8369i	−0.872043	+	1.20026i	0.106519	+	0.994311i	$0.466029\pi$
$331$	−15.8654	+	21.8369i	−0.872043	+	1.20026i	−0.978562	+	0.205953i	$0.933971\pi$
$332$	−0.772872	+	2.37866i	−0.0424169	+	0.130546i
$333$	−3.21010	−	9.86311i	−0.175912	−	0.540495i
$334$	14.8188	−	4.81492i	0.810849	−	0.263461i
$335$			11.4373i			0.624886i
$336$	1.13233	+	0.576600i	0.0617737	+	0.0314561i
$337$	−10.7586	+	3.49567i	−0.586057	+	0.190422i	−0.587012	−	0.809578i	$-0.699696\pi$
$337$	−10.7586	+	3.49567i	−0.586057	+	0.190422i	0.000955107		1.00000i	$0.499696\pi$
$338$	4.55781	+	6.27328i	0.247912	+	0.341221i
$339$	28.0215	−	14.2864i	1.52192	−	0.775929i
$340$			0.545103i			0.0295624i
$341$	−1.79113	−	4.69468i	−0.0969949	−	0.254231i
$342$	17.7453	−	12.9061i	0.959556	−	0.697882i
$343$	7.98983	+	5.80495i	0.431410	+	0.313438i
$344$	1.41110	−	1.02523i	0.0760817	−	0.0552766i
$345$	8.70723	+	1.37689i	0.468782	+	0.0741292i
$346$	12.9447			0.695911
$347$	−8.06724			−0.433072			−0.216536	−	0.976275i	$-0.569476\pi$
$347$	−8.06724			−0.433072			−0.216536	+	0.976275i	$0.569476\pi$
$348$	0.731875	−	4.62826i	0.0392326	−	0.248101i
$349$	−0.191838	+	0.590417i	−0.0102689	+	0.0316043i	−0.956060	−	0.293172i	$-0.905289\pi$
$349$	−0.191838	+	0.590417i	−0.0102689	+	0.0316043i	0.945791	+	0.324776i	$0.105289\pi$
$350$	0.697724	+	0.226704i	0.0372949	+	0.0121179i
$351$	10.6080	+	5.39515i	0.566211	+	0.287972i
$352$	−0.858303	+	0.278880i	−0.0457477	+	0.0148643i
$353$	−3.72279	−	2.70477i	−0.198144	−	0.143960i	0.484289	−	0.874908i	$-0.339078\pi$
$353$	−3.72279	−	2.70477i	−0.198144	−	0.143960i	−0.682433	+	0.730948i	$0.739078\pi$
$354$	−16.4187	+	2.60462i	−0.872646	+	0.138434i
$355$	0.723652	−	2.22717i	0.0384075	−	0.118206i
$356$	−0.196445	+	0.142726i	−0.0104116	+	0.00756444i
$357$	0.684100	−	0.108524i	0.0362064	−	0.00574369i
$358$	−12.3688	−	4.01886i	−0.653711	−	0.212404i
$359$	7.23843	+	9.96284i	0.382030	+	0.525819i	0.956121	−	0.292973i	$-0.0946445\pi$
$359$	7.23843	+	9.96284i	0.382030	+	0.525819i	−0.574091	+	0.818791i	$0.694645\pi$
$360$	0.00147998	+	3.00000i	7.80020e−5	+	0.158114i
$361$	10.6598	+	32.8075i	0.561043	+	1.72671i
$362$	−10.0206	−	7.28036i	−0.526669	−	0.382647i
$363$	−12.4716	+	12.4778i	−0.654590	+	0.654913i
$364$	−1.59805	−	0.519237i	−0.0837604	−	0.0272154i
$365$	3.29984	+	10.1559i	0.172721	+	0.531582i
$366$	−10.0423	−	5.11366i	−0.524917	−	0.267296i
$367$			14.7052i			0.767604i	0.923415	+	0.383802i	$0.125386\pi$
$367$			14.7052i			0.767604i	−0.923415	+	0.383802i	$0.874614\pi$
$368$	−1.57277	−	4.84049i	−0.0819863	−	0.252328i
$369$	8.02188	−	24.7303i	0.417603	−	1.28741i
$370$	−2.03224	+	2.79714i	−0.105651	+	0.145416i
$371$	3.61249			0.187551
$372$	4.80682	+	8.36029i	0.249222	+	0.433461i
$373$	−14.8411			−0.768444			−0.384222	−	0.923241i	$-0.625530\pi$
$373$	−14.8411			−0.768444			−0.384222	+	0.923241i	$0.625530\pi$
$374$	−0.289156	+	0.397988i	−0.0149519	+	0.0205795i
$375$	0.271374	+	1.71066i	0.0140137	+	0.0883381i
$376$	−0.458229	−	1.41028i	−0.0236314	−	0.0727298i
$377$			6.19621i			0.319121i
$378$	3.76468	−	0.599123i	0.193634	−	0.0308156i
$379$	5.35027	+	16.4664i	0.274825	+	0.845824i	0.989266	+	0.146128i	$0.0466812\pi$
$379$	5.35027	+	16.4664i	0.274825	+	0.845824i	−0.714441	+	0.699696i	$0.753319\pi$
$380$	−6.95611	−	2.26018i	−0.356841	−	0.115945i
$381$	−17.0808	−	17.0723i	−0.875074	−	0.874642i
$382$	−5.83228	−	4.23740i	−0.298405	−	0.216804i
$383$	−9.29863	−	28.6183i	−0.475138	−	1.46232i	−0.845772	−	0.533545i	$-0.820859\pi$
$383$	−9.29863	−	28.6183i	−0.475138	−	1.46232i	0.370634	−	0.928779i	$-0.379141\pi$
$384$	1.54307	−	0.786715i	0.0787447	−	0.0401469i
$385$	0.389162	+	0.535636i	0.0198335	+	0.0272985i
$386$	18.9524	+	6.15801i	0.964652	+	0.313434i
$387$	1.61453	−	4.97736i	0.0820710	−	0.253013i
$388$	8.40044	−	6.10328i	0.426468	−	0.309847i
$389$	4.42203	−	13.6096i	0.224206	−	0.690034i	−0.774166	−	0.632983i	$-0.781830\pi$
$389$	4.42203	−	13.6096i	0.224206	−	0.690034i	0.998371	−	0.0570510i	$-0.0181698\pi$
$390$	−0.621548	−	3.91804i	−0.0314733	−	0.198398i
$391$	−2.24450	−	1.63072i	−0.113509	−	0.0824691i
$392$	6.14552	−	1.99680i	0.310396	−	0.100854i
$393$	−12.1267	+	6.18264i	−0.611712	+	0.311873i
$394$	11.8945	+	3.86477i	0.599238	+	0.194704i
$395$	2.06789	−	6.36431i	0.104047	−	0.320223i
$396$	−1.59030	+	2.19113i	−0.0799156	+	0.110109i
$397$	−23.5488			−1.18188			−0.590940	−	0.806715i	$-0.701243\pi$
$397$	−23.5488			−1.18188			−0.590940	+	0.806715i	$0.701243\pi$
$398$	5.76328			0.288887
$399$	−1.45162	+	9.17984i	−0.0726720	+	0.459567i
$400$	0.809017	−	0.587785i	0.0404508	−	0.0293893i
$401$	22.5289	+	16.3682i	1.12504	+	0.817390i	0.984966	−	0.172751i	$-0.0552656\pi$
$401$	22.5289	+	16.3682i	1.12504	+	0.817390i	0.140075	+	0.990141i	$0.455266\pi$
$402$	8.98918	−	17.6530i	0.448340	−	0.880453i
$403$	−8.00499	−	9.92673i	−0.398757	−	0.494486i
$404$		−	5.05868i		−	0.251679i
$405$	5.29725	+	7.27593i	0.263222	+	0.361544i
$406$	1.16659	+	1.60567i	0.0578967	+	0.0796879i
$407$	−2.96754	+	0.964212i	−0.147095	+	0.0477942i
$408$	0.428426	−	0.841346i	0.0212102	−	0.0416528i
$409$		−	6.22702i		−	0.307906i	−0.988078	−	0.153953i	$-0.950800\pi$
$409$		−	6.22702i		−	0.307906i	0.988078	−	0.153953i	$-0.0492005\pi$
$410$	−8.24212	+	2.67803i	−0.407049	+	0.132258i
$411$	5.61166	−	5.61443i	0.276803	−	0.276939i
$412$	−4.92817	+	15.1673i	−0.242793	+	0.747241i
$413$	4.13878	−	5.69654i	0.203656	−	0.280308i
$414$	−12.3571	−	8.96866i	−0.607319	−	0.440786i
$415$	1.47009	−	2.02341i	0.0721639	−	0.0993251i
$416$	−1.85295	+	1.34625i	−0.0908483	+	0.0660052i
$417$	21.2708	+	21.2604i	1.04164	+	1.04112i
$418$	−3.87983	−	5.34013i	−0.189769	−	0.261195i
$419$	7.81251	+	10.7530i	0.381666	+	0.525318i	0.956025	−	0.293285i	$-0.0947486\pi$
$419$	7.81251	+	10.7530i	0.381666	+	0.525318i	−0.574359	+	0.818604i	$0.694749\pi$
$420$	−0.898732	−	0.898289i	−0.0438536	−	0.0438320i
$421$	−0.419752	+	0.304968i	−0.0204575	+	0.0148632i	−0.597967	−	0.801521i	$-0.704025\pi$
$421$	−0.419752	+	0.304968i	−0.0204575	+	0.0148632i	0.577510	+	0.816384i	$0.304025\pi$
$422$	13.8161	−	19.0162i	0.672555	−	0.925693i
$423$	−3.60027	−	2.61303i	−0.175051	−	0.127050i
$424$	2.89433	−	3.98370i	0.140561	−	0.193466i
$425$	0.168446	−	0.518424i	0.00817083	−	0.0251472i
$426$	−2.86738	+	2.86880i	−0.138925	+	0.138994i
$427$	4.53961	−	1.47501i	0.219687	−	0.0713807i
$428$		−	2.28065i		−	0.110240i
$429$	1.62457	−	3.19033i	0.0784348	−	0.154031i
$430$	−1.65885	+	0.538994i	−0.0799970	+	0.0259926i
$431$	4.30962	+	5.93168i	0.207587	+	0.285719i	0.900097	−	0.435689i	$-0.143495\pi$
$431$	4.30962	+	5.93168i	0.207587	+	0.285719i	−0.692510	+	0.721408i	$0.743495\pi$
$432$	2.35558	−	4.63155i	0.113333	−	0.222836i
$433$			14.4701i			0.695390i	0.937608	+	0.347695i	$0.113035\pi$
$433$			14.4701i			0.695390i	−0.937608	+	0.347695i	$0.886965\pi$
$434$	−3.94333	−	1.06525i	−0.189286	−	0.0511337i
$435$	−2.12627	+	4.17558i	−0.101947	+	0.200204i
$436$	−7.63407	−	5.54648i	−0.365606	−	0.265628i
$437$	30.1162	−	21.8807i	1.44065	−	1.04670i
$438$	2.88886	−	18.2687i	0.138035	−	0.872912i
$439$	−8.03054			−0.383277			−0.191638	−	0.981466i	$-0.561380\pi$
$439$	−8.03054			−0.383277			−0.191638	+	0.981466i	$0.561380\pi$
$440$	0.902473			0.0430237
$441$	11.3867	−	15.6887i	0.542223	−	0.747081i
$442$	−0.385804	+	1.18738i	−0.0183508	+	0.0564780i
$443$	16.6487	+	5.40950i	0.791005	+	0.257013i	0.676532	−	0.736413i	$-0.263482\pi$
$443$	16.6487	+	5.40950i	0.791005	+	0.257013i	0.114473	+	0.993426i	$0.463482\pi$
$444$	5.33510	−	2.72003i	0.253193	−	0.129087i
$445$	0.230935	−	0.0750353i	0.0109474	−	0.00355701i
$446$	−15.1514	−	11.0082i	−0.717441	−	0.521251i
$447$	−2.14407	−	13.5155i	−0.101411	−	0.639262i
$448$	−0.226704	+	0.697724i	−0.0107108	+	0.0329644i
$449$	−21.7229	+	15.7826i	−1.02517	+	0.744827i	−0.967336	−	0.253499i	$-0.918419\pi$
$449$	−21.7229	+	15.7826i	−1.02517	+	0.744827i	−0.0578311	+	0.998326i	$0.518419\pi$
$450$	0.925643	−	2.85363i	0.0436352	−	0.134521i
$451$	−7.43829	−	2.41685i	−0.350256	−	0.113805i
$452$	10.6739	+	14.6913i	0.502058	+	0.691023i
$453$	16.6459	−	8.48670i	0.782094	−	0.398740i
$454$	4.23476	+	13.0333i	0.198747	+	0.611681i
$455$	1.35938	+	0.987647i	0.0637287	+	0.0463016i
$456$	8.96010	+	8.95568i	0.419595	+	0.419388i
$457$	32.0591	+	10.4166i	1.49966	+	0.487269i	0.939919	−	0.341398i	$-0.110900\pi$
$457$	32.0591	+	10.4166i	1.49966	+	0.487269i	0.559742	+	0.828667i	$0.310900\pi$
$458$	1.29652	+	3.99026i	0.0605822	+	0.186453i
$459$	−0.445161	−	2.79724i	−0.0207783	−	0.130564i
$460$			5.08959i			0.237303i
$461$	10.3197	+	31.7606i	0.480634	+	1.47924i	0.838206	+	0.545354i	$0.183605\pi$
$461$	10.3197	+	31.7606i	0.480634	+	1.47924i	−0.357572	+	0.933886i	$0.616395\pi$
$462$	−0.179672	−	1.13260i	−0.00835910	−	0.0526932i
$463$	−15.7389	+	21.6627i	−0.731449	+	1.00675i	0.267617	+	0.963525i	$0.413764\pi$
$463$	−15.7389	+	21.6627i	−0.731449	+	1.00675i	−0.999065	+	0.0432271i	$0.986236\pi$
$464$	2.70533			0.125592
$465$	−1.98808	−	9.43650i	−0.0921951	−	0.437607i
$466$	20.0009			0.926525
$467$	−3.18023	+	4.37721i	−0.147164	+	0.202553i	−0.876235	−	0.481885i	$-0.839952\pi$
$467$	−3.18023	+	4.37721i	−0.147164	+	0.202553i	0.729071	+	0.684438i	$0.239952\pi$
$468$	−2.12007	+	6.53586i	−0.0980001	+	0.302120i
$469$	2.59288	+	7.98007i	0.119728	+	0.368486i
$470$			1.48286i			0.0683992i
$471$	−14.2931	−	7.27825i	−0.658590	−	0.335364i
$472$	−2.96591	−	9.12815i	−0.136517	−	0.420157i
$473$	−1.49707	−	0.486428i	−0.0688354	−	0.0223660i
$474$	−8.19377	+	8.19781i	−0.376352	+	0.376538i
$475$	5.91722	+	4.29911i	0.271501	+	0.197257i
$476$	0.123577	+	0.380331i	0.00566415	+	0.0174325i
$477$	−0.00728762	−	14.7724i	−0.000333677	−	0.676380i
$478$	−4.72878	−	6.50861i	−0.216289	−	0.297697i
$479$	27.1889	+	8.83420i	1.24229	+	0.403645i	0.855153	−	0.518376i	$-0.173463\pi$
$479$	27.1889	+	8.83420i	1.24229	+	0.403645i	0.387139	+	0.922021i	$0.373463\pi$
$480$	−1.71066	+	0.271374i	−0.0780806	+	0.0123865i
$481$	−6.40648	+	4.65458i	−0.292110	+	0.212231i
$482$	−5.45449	+	16.7872i	−0.248445	+	0.764636i
$483$	6.38739	−	1.01328i	0.290636	−	0.0461058i
$484$	−8.24028	−	5.98691i	−0.374558	−	0.272132i
$485$	−9.87531	+	3.20868i	−0.448415	+	0.145699i
$486$	−2.45756	−	15.3935i	−0.111477	−	0.698264i
$487$	−27.1703	−	8.82818i	−1.23121	−	0.400043i	−0.380055	−	0.924964i	$-0.624095\pi$
$487$	−27.1703	−	8.82818i	−1.23121	−	0.400043i	−0.851151	+	0.524921i	$0.824095\pi$
$488$	2.01056	−	6.18787i	0.0910139	−	0.280112i
$489$	−2.45067	+	15.4976i	−0.110823	+	0.700827i
$490$	−6.46179			−0.291914
$491$	8.92945			0.402980			0.201490	−	0.979491i	$-0.435422\pi$
$491$	8.92945			0.402980			0.201490	+	0.979491i	$0.435422\pi$
$492$	14.8262	+	2.34449i	0.668417	+	0.105698i
$493$	1.19304	−	0.866798i	0.0537320	−	0.0390386i
$494$	−13.5526	−	9.84656i	−0.609762	−	0.443018i
$495$	2.18956	−	1.59246i	0.0984136	−	0.0715758i
$496$	−4.33411	+	3.49506i	−0.194607	+	0.156933i
$497$		−	1.71801i		−	0.0770632i
$498$	−3.85933	+	1.96763i	−0.172941	+	0.0881715i
$499$	−15.7882	−	21.7305i	−0.706775	−	0.972792i	−0.999860	−	0.0167057i	$-0.994682\pi$
$499$	−15.7882	−	21.7305i	−0.706775	−	0.972792i	0.293086	−	0.956086i	$-0.405318\pi$
$500$	−0.951057	+	0.309017i	−0.0425325	+	0.0138197i
$501$	24.0493	+	12.2463i	1.07444	+	0.547123i
$502$			3.03433i			0.135429i
$503$	17.9520	−	5.83296i	0.800440	−	0.260079i	0.119897	−	0.992786i	$-0.461744\pi$
$503$	17.9520	−	5.83296i	0.800440	−	0.260079i	0.680544	+	0.732708i	$0.261744\pi$
$504$	0.681146	+	2.09284i	0.0303406	+	0.0932224i
$505$	−1.56322	+	4.81109i	−0.0695622	+	0.214091i
$506$	−2.69983	+	3.71599i	−0.120022	+	0.165196i
$507$	−2.09775	+	13.2658i	−0.0931642	+	0.589156i
$508$	8.19545	−	11.2801i	0.363615	−	0.500472i
$509$	25.6676	−	18.6486i	1.13770	−	0.826586i	0.150901	−	0.988549i	$-0.451782\pi$
$509$	25.6676	−	18.6486i	1.13770	−	0.826586i	0.986797	+	0.161963i	$0.0517824\pi$
$510$	−0.667447	+	0.667777i	−0.0295551	+	0.0295696i
$511$	4.60475	+	6.33790i	0.203702	+	0.280372i
$512$	0.587785	+	0.809017i	0.0259767	+	0.0357538i
$513$	37.5416	+	5.91753i	1.65750	+	0.261265i
$514$	5.16680	−	3.75390i	0.227898	−	0.165577i
$515$	9.37393	−	12.9021i	0.413065	−	0.568535i
$516$	2.98400	+	0.471865i	0.131363	+	0.0207727i
$517$	−0.786599	+	1.08266i	−0.0345946	+	0.0476153i
$518$	−0.783819	+	2.41235i	−0.0344390	+	0.105992i
$519$	15.8579	+	15.8500i	0.696082	+	0.695739i
$520$	2.17827	−	0.707764i	0.0955236	−	0.0310375i
$521$		−	2.38988i		−	0.104702i	−0.998629	−	0.0523512i	$-0.983328\pi$
$521$		−	2.38988i		−	0.104702i	0.998629	−	0.0523512i	$-0.0166715\pi$
$522$	6.56362	−	4.77370i	0.287282	−	0.208939i
$523$	−6.98117	+	2.26832i	−0.305265	+	0.0991867i	−0.457644	−	0.889135i	$-0.651307\pi$
$523$	−6.98117	+	2.26832i	−0.305265	+	0.0991867i	0.152379	+	0.988322i	$0.451307\pi$
$524$	−4.61929	−	6.35790i	−0.201795	−	0.277746i
$525$	0.577158	+	1.13205i	0.0251893	+	0.0494066i
$526$		−	15.3537i		−	0.669451i
$527$	−0.791504	+	2.92998i	−0.0344784	+	0.127632i
$528$	−1.39293	−	0.709302i	−0.0606197	−	0.0308684i
$529$	−2.34931	−	1.70687i	−0.102144	−	0.0742118i
$530$	−3.98370	+	2.89433i	−0.173041	+	0.125722i
$531$	−23.3029	−	16.9130i	−1.01126	−	0.733962i
$532$	−5.36584			−0.232639
$533$	−19.8490			−0.859755
$534$	−0.415414	−	0.0656900i	−0.0179767	−	0.00284269i
$535$	−0.704761	+	2.16903i	−0.0304695	+	0.0937754i
$536$	10.8775	+	3.53432i	0.469837	+	0.152659i
$537$	−10.2315	−	20.0682i	−0.441521	−	0.866006i
$538$	29.5202	−	9.59171i	1.27271	−	0.413528i
$539$	−4.71785	−	3.42772i	−0.203212	−	0.147642i
$540$	−3.67151	+	3.67695i	−0.157997	+	0.158231i
$541$	2.34135	−	7.20594i	0.100663	−	0.309807i	−0.888025	−	0.459794i	$-0.847923\pi$
$541$	2.34135	−	7.20594i	0.100663	−	0.309807i	0.988688	+	0.149987i	$0.0479231\pi$
$542$	1.70324	−	1.23748i	0.0731604	−	0.0531542i
$543$	−3.36127	−	21.1884i	−0.144246	−	0.909281i
$544$	0.518424	+	0.168446i	0.0222272	+	0.00722206i
$545$	5.54648	+	7.63407i	0.237585	+	0.327008i
$546$	−1.32191	−	2.59281i	−0.0565724	−	0.110962i
$547$	−2.67411	−	8.23006i	−0.114337	−	0.351892i	0.877472	−	0.479629i	$-0.159229\pi$
$547$	−2.67411	−	8.23006i	−0.114337	−	0.351892i	−0.991808	+	0.127737i	$0.959229\pi$
$548$	3.70775	+	2.69384i	0.158387	+	0.115075i
$549$	−6.04084	−	18.5606i	−0.257817	−	0.792149i
$550$	−0.858303	−	0.278880i	−0.0365982	−	0.0118915i
$551$	6.11453	+	18.8186i	0.260488	+	0.801699i
$552$	4.00018	−	7.85559i	0.170259	−	0.334356i
$553$		−	4.90934i		−	0.208766i
$554$	−4.40111	−	13.5452i	−0.186985	−	0.575481i
$555$	−5.91452	+	0.938263i	−0.251057	+	0.0398271i
$556$	−10.2059	+	14.0472i	−0.432826	+	0.595734i
$557$	−21.0438			−0.891654			−0.445827	−	0.895119i	$-0.647090\pi$
$557$	−21.0438			−0.891654			−0.445827	+	0.895119i	$0.647090\pi$
$558$	−4.34812	+	16.1274i	−0.184071	+	0.682728i
$559$	−3.99491			−0.168967
$560$	0.431217	−	0.593520i	0.0182223	−	0.0250808i
$561$	−0.841543	+	0.133500i	−0.0355300	+	0.00563638i
$562$	−3.14835	−	9.68962i	−0.132805	−	0.408732i
$563$		−	22.7028i		−	0.956807i	−0.878140	−	0.478404i	$-0.841216\pi$
$563$		−	22.7028i		−	0.956807i	0.878140	−	0.478404i	$-0.158784\pi$
$564$	1.16546	−	2.28874i	0.0490747	−	0.0963733i
$565$	−5.61160	−	17.2707i	−0.236082	−	0.726585i
$566$	15.6223	+	5.07601i	0.656656	+	0.213361i
$567$	5.34550	+	3.87568i	0.224490	+	0.162763i
$568$	−1.89455	−	1.37647i	−0.0794934	−	0.0577553i
$569$	−10.5416	−	32.4436i	−0.441926	−	1.36011i	−0.885820	−	0.464028i	$-0.846404\pi$
$569$	−10.5416	−	32.4436i	−0.441926	−	1.36011i	0.443895	−	0.896079i	$-0.353596\pi$
$570$	−5.75410	−	11.2862i	−0.241013	−	0.472726i
$571$	−13.8574	−	19.0730i	−0.579913	−	0.798182i	0.413773	−	0.910380i	$-0.364211\pi$
$571$	−13.8574	−	19.0730i	−0.579913	−	0.798182i	−0.993686	+	0.112199i	$0.964211\pi$
$572$	1.96583	+	0.638738i	0.0821956	+	0.0267070i
$573$	−1.95636	−	12.3323i	−0.0817283	−	0.515190i
$574$	−5.14361	+	3.73705i	−0.214690	+	0.155981i
$575$	1.57277	−	4.84049i	0.0655890	−	0.201862i
$576$	2.85363	+	0.925643i	0.118901	+	0.0385685i
$577$	−6.50585	−	4.72678i	−0.270842	−	0.196778i	0.444071	−	0.895992i	$-0.353534\pi$
$577$	−6.50585	−	4.72678i	−0.270842	−	0.196778i	−0.714913	+	0.699213i	$0.753534\pi$
$578$	−15.8854	+	5.16147i	−0.660744	+	0.214689i
$579$	15.6775	+	30.7500i	0.651533	+	1.27793i
$580$	−2.57292	−	0.835994i	−0.106835	−	0.0347127i
$581$	0.567003	−	1.74505i	0.0235232	−	0.0723971i
$582$	17.7640	+	2.80906i	0.736343	+	0.116439i
$583$	−4.44389			−0.184047
$584$	10.6785			0.441879
$585$	4.03600	−	5.56084i	0.166868	−	0.229912i
$586$	−12.6292	+	9.17564i	−0.521707	+	0.379042i
$587$	−27.4457	−	19.9405i	−1.13281	−	0.823032i	−0.146705	−	0.989180i	$-0.546867\pi$
$587$	−27.4457	−	19.9405i	−1.13281	−	0.823032i	−0.986101	+	0.166149i	$0.946867\pi$
$588$	9.97352	+	5.07867i	0.411301	+	0.209441i
$589$	−34.1079	−	22.2491i	−1.40539	−	0.916759i
$590$			9.59790i			0.395139i
$591$	9.83917	+	19.2987i	0.404729	+	0.793842i
$592$	2.03224	+	2.79714i	0.0835245	+	0.114962i
$593$	−7.68655	+	2.49751i	−0.315649	+	0.102560i	−0.462557	−	0.886590i	$-0.653068\pi$
$593$	−7.68655	+	2.49751i	−0.315649	+	0.102560i	0.146908	+	0.989150i	$0.453068\pi$
$594$	−4.63111	+	0.737009i	−0.190017	+	0.0302399i
$595$		−	0.399904i		−	0.0163945i
$596$	7.51408	−	2.44147i	0.307789	−	0.100007i
$597$	7.06029	+	7.05681i	0.288958	+	0.288816i
$598$	−3.60222	+	11.0865i	−0.147306	+	0.453361i
$599$	22.7309	−	31.2864i	0.928759	−	1.27833i	−0.0315831	−	0.999501i	$-0.510055\pi$
$599$	22.7309	−	31.2864i	0.928759	−	1.27833i	0.960342	−	0.278826i	$-0.0899451\pi$
$600$	1.71079	+	0.270530i	0.0698428	+	0.0110444i
$601$	−10.1208	+	13.9301i	−0.412836	+	0.568219i	−0.963907	−	0.266239i	$-0.914219\pi$
$601$	−10.1208	+	13.9301i	−0.412836	+	0.568219i	0.551072	+	0.834458i	$0.314219\pi$
$602$	−1.03523	+	0.752138i	−0.0421928	+	0.0306549i
$603$	32.6273	−	10.6190i	1.32869	−	0.432441i
$604$	6.34074	+	8.72728i	0.258001	+	0.355108i
$605$	5.98691	+	8.24028i	0.243403	+	0.335015i
$606$	6.19406	−	6.19712i	0.251616	−	0.251741i
$607$	−3.97859	+	2.89062i	−0.161486	+	0.117326i	−0.665594	−	0.746314i	$-0.731822\pi$
$607$	−3.97859	+	2.89062i	−0.161486	+	0.117326i	0.504108	+	0.863641i	$0.331822\pi$
$608$	−4.29911	+	5.91722i	−0.174352	+	0.239975i
$609$	−0.536926	+	3.39544i	−0.0217573	+	0.137590i
$610$	−3.82432	+	5.26372i	−0.154842	+	0.213122i
$611$	−1.04951	+	3.23007i	−0.0424588	+	0.130675i
$612$	1.55502	−	0.506105i	0.0628580	−	0.0204581i
$613$	−11.9781	+	3.89191i	−0.483789	+	0.157193i	−0.540749	−	0.841184i	$-0.681859\pi$
$613$	−11.9781	+	3.89191i	−0.483789	+	0.157193i	0.0569602	+	0.998376i	$0.481859\pi$
$614$			20.4576i			0.825601i
$615$	−13.3761	−	6.81130i	−0.539376	−	0.274658i
$616$	0.629677	−	0.204595i	0.0253704	−	0.00824335i
$617$	−20.3426	−	27.9991i	−0.818961	−	1.12720i	−0.989879	−	0.141917i	$-0.954673\pi$
$617$	−20.3426	−	27.9991i	−0.818961	−	1.12720i	0.170918	−	0.985285i	$-0.445327\pi$
$618$	−24.6088	+	12.5464i	−0.989910	+	0.504692i
$619$			14.7174i			0.591543i	0.955259	+	0.295772i	$0.0955768\pi$
$619$			14.7174i			0.591543i	−0.955259	+	0.295772i	$0.904423\pi$
$620$	5.20202	−	1.98469i	0.208918	−	0.0797069i
$621$	−4.15644	−	26.1176i	−0.166792	−	1.04806i
$622$	17.0514	+	12.3886i	0.683699	+	0.496736i
$623$	0.144118	−	0.104708i	0.00577397	−	0.00419503i
$624$	−3.91835	−	0.619615i	−0.156860	−	0.0248045i
$625$	1.00000			0.0400000
$626$	−2.04161			−0.0815991
$627$	1.78571	−	11.2926i	0.0713144	−	0.450981i
$628$	2.86162	−	8.80716i	0.114191	−	0.351444i
$629$	1.79242	+	0.582394i	0.0714686	+	0.0232216i
$630$	−0.00108576	−	2.20089i	−4.32577e−5	−	0.0876856i
$631$	29.5074	−	9.58753i	1.17467	−	0.381674i	0.344286	−	0.938865i	$-0.388121\pi$
$631$	29.5074	−	9.58753i	1.17467	−	0.381674i	0.830384	+	0.557191i	$0.188121\pi$
$632$	−5.41381	−	3.93336i	−0.215350	−	0.156461i
$633$	40.2095	−	6.37873i	1.59819	−	0.253532i
$634$	−5.75827	+	17.7221i	−0.228690	+	0.703835i
$635$	−11.2801	+	8.19545i	−0.447636	+	0.325227i
$636$	8.42350	−	1.33628i	0.334013	−	0.0529870i
$637$	−14.0755	−	4.57342i	−0.557693	−	0.181205i
$638$	−1.43507	−	1.97521i	−0.0568150	−	0.0781992i
$639$	−7.02536	+	0.00346581i	−0.277919	+	0.000137105i
$640$	−0.309017	−	0.951057i	−0.0122150	−	0.0375938i
$641$	−6.97521	−	5.06778i	−0.275504	−	0.200165i	0.441450	−	0.897286i	$-0.354464\pi$
$641$	−6.97521	−	5.06778i	−0.275504	−	0.200165i	−0.716954	+	0.697120i	$0.754464\pi$
$642$	2.79253	−	2.79391i	0.110212	−	0.110267i
$643$	−8.36333	−	2.71741i	−0.329818	−	0.107164i	0.139427	−	0.990232i	$-0.455474\pi$
$643$	−8.36333	−	2.71741i	−0.329818	−	0.107164i	−0.469245	+	0.883068i	$0.655474\pi$
$644$	1.15383	+	3.55113i	0.0454673	+	0.139934i
$645$	−2.69214	−	1.37088i	−0.106003	−	0.0539782i
$646$			3.98693i			0.156864i
$647$	−7.12391	−	21.9251i	−0.280070	−	0.861966i	−0.987833	−	0.155517i	$-0.950296\pi$
$647$	−7.12391	−	21.9251i	−0.280070	−	0.861966i	0.707763	−	0.706450i	$-0.249704\pi$
$648$	8.55676	−	2.78960i	0.336141	−	0.109586i
$649$	−5.09131	+	7.00758i	−0.199851	+	0.275072i
$650$	−2.29037			−0.0898357
$651$	−3.52643	−	6.13337i	−0.138212	−	0.240386i
$652$	−9.05874			−0.354768
$653$	−18.0302	+	24.8165i	−0.705577	+	0.971144i	0.294304	+	0.955712i	$0.404912\pi$
$653$	−18.0302	+	24.8165i	−0.705577	+	0.971144i	−0.999881	+	0.0154318i	$0.995088\pi$
$654$	−2.56075	−	16.1422i	−0.100133	−	0.631209i
$655$	2.42850	+	7.47416i	0.0948895	+	0.292040i
$656$			8.66628i			0.338361i
$657$	25.9080	−	18.8428i	1.01077	−	0.735126i
$658$	0.336171	+	1.03463i	0.0131053	+	0.0403340i
$659$	28.8524	+	9.37471i	1.12393	+	0.365187i	0.811266	−	0.584677i	$-0.198779\pi$
$659$	28.8524	+	9.37471i	1.12393	+	0.365187i	0.312664	+	0.949864i	$0.398779\pi$
$660$	1.10557	+	1.10503i	0.0430343	+	0.0430131i
$661$	28.6114	+	20.7874i	1.11285	+	0.808535i	0.983111	−	0.183012i	$-0.0585848\pi$
$661$	28.6114	+	20.7874i	1.11285	+	0.808535i	0.129743	+	0.991548i	$0.458585\pi$
$662$	−8.34095	−	25.6708i	−0.324180	−	0.997724i
$663$	−1.92651	+	0.982204i	−0.0748194	+	0.0381457i
$664$	−1.47009	−	2.02341i	−0.0570506	−	0.0785234i
$665$	5.10322	+	1.65814i	0.197894	+	0.0642997i
$666$	9.86627	+	3.20037i	0.382310	+	0.124012i
$667$	11.1394	−	8.09323i	0.431318	−	0.313371i
$668$	−4.81492	+	14.8188i	−0.186295	+	0.573357i
$669$	−5.08235	−	32.0376i	−0.196495	−	1.23864i
$670$	−9.25296	−	6.72267i	−0.357473	−	0.259719i
$671$	−5.58439	+	1.81448i	−0.215583	+	0.0700472i
$672$	−1.13205	+	0.577158i	−0.0436696	+	0.0222644i
$673$	15.7847	+	5.12875i	0.608454	+	0.197699i	0.597007	−	0.802236i	$-0.296356\pi$
$673$	15.7847	+	5.12875i	0.608454	+	0.197699i	0.0114467	+	0.999934i	$0.496356\pi$
$674$	3.49567	−	10.7586i	0.134648	−	0.414405i
$675$	4.62806	−	2.36243i	0.178134	−	0.0909299i
$676$	−7.75420			−0.298239
$677$	−5.69070			−0.218711			−0.109356	−	0.994003i	$-0.534879\pi$
$677$	−5.69070			−0.218711			−0.109356	+	0.994003i	$0.534879\pi$
$678$	−4.91270	+	31.0672i	−0.188671	+	1.19313i
$679$	−6.16282	+	4.47755i	−0.236507	+	0.171833i
$680$	−0.440997	−	0.320403i	−0.0169115	−	0.0122869i
$681$	−10.7707	+	21.1516i	−0.412734	+	0.810530i
$682$	4.85088	+	1.31042i	0.185750	+	0.0501784i
$683$			42.3632i			1.62098i	0.585752	+	0.810491i	$0.300799\pi$
$683$			42.3632i			1.62098i	−0.585752	+	0.810491i	$0.699201\pi$
$684$	0.0108247	+	21.9423i	0.000413894	+	0.838983i
$685$	−2.69384	−	3.70775i	−0.102926	−	0.141666i
$686$	−9.39261	+	3.05185i	−0.358612	+	0.116520i
$687$	−3.29756	+	6.47577i	−0.125810	+	0.247066i
$688$			1.74422i			0.0664978i
$689$	−10.7261	+	3.48511i	−0.408631	+	0.132772i
$690$	−6.23191	+	6.23498i	−0.237245	+	0.237362i
$691$	−8.88370	+	27.3412i	−0.337952	+	1.04011i	0.627298	+	0.778779i	$0.284161\pi$
$691$	−8.88370	+	27.3412i	−0.337952	+	1.04011i	−0.965250	+	0.261329i	$0.915839\pi$
$692$	−7.60870	+	10.4725i	−0.289239	+	0.398104i
$693$	1.16669	−	1.60748i	0.0443190	−	0.0610632i
$694$	4.74180	−	6.52653i	0.179996	−	0.247744i
$695$	14.0472	−	10.2059i	0.532841	−	0.387131i
$696$	3.31416	+	3.31252i	0.125623	+	0.125561i
$697$	2.77671	+	3.82181i	0.105175	+	0.144761i
$698$	−0.364898	−	0.502239i	−0.0138116	−	0.0190100i
$699$	24.5021	+	24.4900i	0.926754	+	0.926296i
$700$	−0.593520	+	0.431217i	−0.0224329	+	0.0162985i
$701$	−23.6143	+	32.5023i	−0.891901	+	1.22760i	0.0810792	+	0.996708i	$0.474163\pi$
$701$	−23.6143	+	32.5023i	−0.891901	+	1.22760i	−0.972980	+	0.230889i	$0.925837\pi$
$702$	−10.6000	+	5.41084i	−0.400070	+	0.204219i
$703$	−14.8640	+	20.4585i	−0.560605	+	0.771607i
$704$	0.278880	−	0.858303i	0.0105107	−	0.0323485i
$705$	−1.81568	+	1.81657i	−0.0683824	+	0.0684161i
$706$	4.37640	−	1.42198i	0.164708	−	0.0535169i
$707$			3.71120i			0.139574i
$708$	7.54351	−	14.8140i	0.283502	−	0.556744i
$709$	−19.3080	+	6.27355i	−0.725127	+	0.235608i	−0.648245	−	0.761432i	$-0.724497\pi$
$709$	−19.3080	+	6.27355i	−0.725127	+	0.235608i	−0.0768824	+	0.997040i	$0.524497\pi$
$710$	1.37647	+	1.89455i	0.0516579	+	0.0711010i
$711$	−20.0755	+	0.00990380i	−0.752890	+	0.000371422i
$712$		−	0.242819i		−	0.00910004i
$713$	−7.39022	+	27.3570i	−0.276766	+	1.02453i
$714$	−0.314306	+	0.617237i	−0.0117626	+	0.0230995i
$715$	−1.67224	−	1.21495i	−0.0625381	−	0.0454366i
$716$	10.5215	−	7.64433i	0.393208	−	0.285682i
$717$	2.17644	−	13.7635i	0.0812806	−	0.514006i
$718$	−12.3147			−0.459582
$719$	40.9148			1.52586			0.762932	−	0.646479i	$-0.223759\pi$
$719$	40.9148			1.52586			0.762932	+	0.646479i	$0.223759\pi$
$720$	−2.42792	−	1.76216i	−0.0904833	−	0.0656718i
$721$	3.61545	−	11.1272i	0.134647	−	0.414399i
$722$	−32.8075	−	10.6598i	−1.22097	−	0.396717i
$723$	−27.2370	+	13.8864i	−1.01295	+	0.516441i
$724$	11.7799	−	3.82751i	0.437795	−	0.142248i
$725$	2.18866	+	1.59015i	0.0812848	+	0.0590568i
$726$	−2.76410	−	17.4240i	−0.102585	−	0.646665i
$727$	11.5488	−	35.5437i	0.428323	−	1.31824i	−0.471453	−	0.881891i	$-0.656270\pi$
$727$	11.5488	−	35.5437i	0.428323	−	1.31824i	0.899776	−	0.436352i	$-0.143730\pi$
$728$	1.35938	−	0.987647i	0.0503820	−	0.0366046i
$729$	15.8379	−	21.8669i	0.586587	−	0.809886i
$730$	−10.1559	−	3.29984i	−0.375885	−	0.122132i
$731$	0.558854	+	0.769197i	0.0206700	+	0.0284498i
$732$	10.0397	−	5.11862i	0.371079	−	0.189190i
$733$	1.45413	+	4.47535i	0.0537095	+	0.165301i	0.974313	−	0.225198i	$-0.0723027\pi$
$733$	1.45413	+	4.47535i	0.0537095	+	0.165301i	−0.920604	+	0.390498i	$0.872303\pi$
$734$	−11.8967	−	8.64349i	−0.439117	−	0.319037i
$735$	−7.91599	−	7.91209i	−0.291986	−	0.291842i
$736$	4.84049	+	1.57277i	0.178423	+	0.0579730i
$737$	−3.18963	−	9.81666i	−0.117491	−	0.361601i
$738$	15.2921	+	21.0260i	0.562910	+	0.773976i
$739$			20.7220i			0.762270i	0.924519	+	0.381135i	$0.124467\pi$
$739$			20.7220i			0.762270i	−0.924519	+	0.381135i	$0.875533\pi$
$740$	−1.06841	−	3.28823i	−0.0392756	−	0.120878i
$741$	−4.54606	−	28.6569i	−0.167004	−	1.05274i
$742$	−2.12337	+	2.92256i	−0.0779513	+	0.107291i
$743$	51.4735			1.88838			0.944191	−	0.329399i	$-0.106846\pi$
$743$	51.4735			1.88838			0.944191	+	0.329399i	$0.106846\pi$
$744$	−9.58900	−	1.02526i	−0.351550	−	0.0375879i
$745$	−7.90077			−0.289462
$746$	8.72339	−	12.0067i	0.319386	−	0.439597i
$747$	−7.13711	−	2.31510i	−0.261133	−	0.0847049i
$748$	−0.152018	−	0.467863i	−0.00555833	−	0.0171068i
$749$			1.67316i			0.0611358i
$750$	−1.54346	−	0.785954i	−0.0563593	−	0.0286990i
$751$	−0.998845	−	3.07413i	−0.0364484	−	0.112177i	0.931177	−	0.364567i	$-0.118783\pi$
$751$	−0.998845	−	3.07413i	−0.0364484	−	0.112177i	−0.967625	+	0.252391i	$0.918783\pi$
$752$	1.41028	+	0.458229i	0.0514278	+	0.0167099i
$753$	−3.71537	+	3.71720i	−0.135396	+	0.135462i
$754$	−5.01284	−	3.64204i	−0.182557	−	0.132635i
$755$	−3.33352	−	10.2595i	−0.121319	−	0.373383i
$756$	−1.72812	+	3.39785i	−0.0628512	+	0.123578i
$757$	10.9599	+	15.0850i	0.398345	+	0.548275i	0.960328	−	0.278874i	$-0.0899612\pi$
$757$	10.9599	+	15.0850i	0.398345	+	0.548275i	−0.561982	+	0.827149i	$0.689961\pi$
$758$	−16.4664	−	5.35027i	−0.598088	−	0.194331i
$759$	−7.85743	+	1.24648i	−0.285207	+	0.0452444i
$760$	5.91722	−	4.29911i	0.214640	−	0.155945i
$761$	−4.17740	+	12.8567i	−0.151431	+	0.466056i	−0.997782	−	0.0665697i	$-0.978795\pi$
$761$	−4.17740	+	12.8567i	−0.151431	+	0.466056i	0.846351	+	0.532625i	$0.178795\pi$
$762$	23.8516	−	3.78376i	0.864053	−	0.137071i
$763$	5.60059	+	4.06907i	0.202755	+	0.147310i
$764$	6.85626	−	2.22773i	0.248051	−	0.0805966i
$765$	−1.63531		0.000806743i	−0.0591247		2.91679e-5i
$766$	28.6183	+	9.29863i	1.03402	+	0.335973i
$767$	−6.79304	+	20.9068i	−0.245283	+	0.754902i
$768$	−0.270530	+	1.71079i	−0.00976193	+	0.0617329i
$769$	−10.4448			−0.376649			−0.188324	−	0.982107i	$-0.560306\pi$
$769$	−10.4448			−0.376649			−0.188324	+	0.982107i	$0.560306\pi$
$770$	−0.662082			−0.0238598
$771$	10.9260	+	1.72775i	0.393490	+	0.0622232i
$772$	−16.1219	+	11.7132i	−0.580239	+	0.421568i
$773$	−38.4668	−	27.9478i	−1.38355	−	1.00521i	−0.996538	−	0.0831383i	$-0.973506\pi$
$773$	−38.4668	−	27.9478i	−1.38355	−	1.00521i	−0.387016	−	0.922073i	$-0.626494\pi$
$774$	3.07777	+	4.23180i	0.110628	+	0.152109i
$775$	−5.56072	+	0.280036i	−0.199747	+	0.0100592i
$776$			10.3835i			0.372746i
$777$	−3.91399	+	1.99550i	−0.140414	+	0.0715880i
$778$	8.41120	+	11.5770i	0.301556	+	0.415056i
$779$	−60.2836	+	19.5873i	−2.15988	+	0.701789i
$780$	3.53510	+	1.80013i	0.126577	+	0.0644549i
$781$			2.11340i			0.0756234i
$782$	2.63856	−	0.857321i	0.0943548	−	0.0306577i
$783$	13.8859	+	2.18877i	0.496241	+	0.0782204i
$784$	−1.99680	+	6.14552i	−0.0713143	+	0.219483i
$785$	−5.44313	+	7.49182i	−0.194273	+	0.267395i
$786$	2.12605	−	13.4448i	0.0758335	−	0.479560i
$787$	27.7017	−	38.1281i	0.987458	−	1.35912i	0.0547440	−	0.998500i	$-0.482566\pi$
$787$	27.7017	−	38.1281i	0.987458	−	1.35912i	0.932713	−	0.360618i	$-0.117434\pi$
$788$	−10.1181	+	7.35122i	−0.360442	+	0.261876i
$789$	18.7997	−	18.8089i	0.669286	−	0.669616i
$790$	3.93336	+	5.41381i	0.139943	+	0.192615i
$791$	−7.83069	−	10.7780i	−0.278427	−	0.383222i
$792$	−0.837909	−	2.57450i	−0.0297738	−	0.0914807i
$793$	−12.0559	+	8.75910i	−0.428117	+	0.311045i
$794$	13.8416	−	19.0514i	0.491221	−	0.676108i
$795$	−8.42416	−	1.33213i	−0.298774	−	0.0472456i
$796$	−3.38757	+	4.66259i	−0.120069	+	0.165261i
$797$	−5.77247	+	17.7658i	−0.204471	+	0.629298i	0.795263	+	0.606264i	$0.207333\pi$
$797$	−5.77247	+	17.7658i	−0.204471	+	0.629298i	−0.999735	+	0.0230338i	$0.992667\pi$
$798$	−6.57340	−	6.57016i	−0.232696	−	0.232581i
$799$	0.768750	−	0.249782i	0.0271964	−	0.00883665i
$800$			1.00000i			0.0353553i
$801$	−0.428468	−	0.589124i	−0.0151392	−	0.0208157i
$802$	−26.4843	+	8.60528i	−0.935194	+	0.303863i
$803$	−5.66452	−	7.79654i	−0.199897	−	0.275134i
$804$	8.99789	+	17.6486i	0.317331	+	0.622418i
$805$		−	3.73388i		−	0.131602i
$806$	12.7361	−	0.641386i	0.448610	−	0.0225918i
$807$	47.9082	+	24.3956i	1.68645	+	0.858764i
$808$	4.09255	+	2.97342i	0.143976	+	0.104604i
$809$	22.8061	−	16.5696i	0.801820	−	0.582556i	−0.109628	−	0.993973i	$-0.534966\pi$
$809$	22.8061	−	16.5696i	0.801820	−	0.582556i	0.911447	+	0.411417i	$0.134966\pi$
$810$	−9.00000	+	0.00887990i	−0.316228	+	0.000312008i
$811$	−6.88683			−0.241829			−0.120915	−	0.992663i	$-0.538583\pi$
$811$	−6.88683			−0.241829			−0.120915	+	0.992663i	$0.538583\pi$
$812$	−1.98471			−0.0696498
$813$	3.60177	+	0.569553i	0.126320	+	0.0199751i
$814$	0.964212	−	2.96754i	0.0337956	−	0.104012i
$815$	8.61537	+	2.79930i	0.301783	+	0.0980554i
$816$	0.428841	+	0.841134i	0.0150124	+	0.0294456i
$817$	−12.1330	+	3.94225i	−0.424480	+	0.137922i
$818$	5.03776	+	3.66015i	0.176141	+	0.127974i
$819$	1.55535	−	4.79491i	0.0543482	−	0.167548i
$820$	2.67803	−	8.24212i	0.0935208	−	0.287827i
$821$	−29.1313	+	21.1651i	−1.01669	+	0.738668i	−0.965602	−	0.260026i	$-0.916269\pi$
$821$	−29.1313	+	21.1651i	−1.01669	+	0.738668i	−0.0510879	+	0.998694i	$0.516269\pi$
$822$	1.24372	+	7.84001i	0.0433796	+	0.273452i
$823$	45.1736	+	14.6778i	1.57465	+	0.511635i	0.960672	−	0.277687i	$-0.0895678\pi$
$823$	45.1736	+	14.6778i	1.57465	+	0.511635i	0.613979	+	0.789322i	$0.289568\pi$
$824$	−9.37393	−	12.9021i	−0.326556	−	0.449466i
$825$	−0.709989	−	1.39258i	−0.0247187	−	0.0484835i
$826$	2.17589	+	6.69669i	0.0757087	+	0.233008i
$827$	−25.1048	−	18.2397i	−0.872978	−	0.634256i	0.0584063	−	0.998293i	$-0.481398\pi$
$827$	−25.1048	−	18.2397i	−0.872978	−	0.634256i	−0.931384	+	0.364037i	$0.881398\pi$
$828$	14.5191	−	4.72547i	0.504575	−	0.164221i
$829$	19.7050	+	6.40254i	0.684383	+	0.222370i	0.630513	−	0.776178i	$-0.282844\pi$
$829$	19.7050	+	6.40254i	0.684383	+	0.222370i	0.0538697	+	0.998548i	$0.482844\pi$
$830$	0.772872	+	2.37866i	0.0268268	+	0.0825643i
$831$	11.1938	−	21.9824i	0.388308	−	0.762562i
$832$		−	2.29037i		−	0.0794043i
$833$	1.08846	+	3.34994i	0.0377130	+	0.116069i
$834$	−29.7027	+	4.71195i	−1.02852	+	0.163162i
$835$	9.15852	−	12.6056i	0.316944	−	0.436236i
$836$	6.60077			0.228292
$837$	−25.0738	+	14.4328i	−0.866676	+	0.498871i
$838$	−13.2914			−0.459145
$839$	−9.55125	+	13.1462i	−0.329746	+	0.453856i	−0.941411	−	0.337260i	$-0.890500\pi$
$839$	−9.55125	+	13.1462i	−0.329746	+	0.453856i	0.611666	+	0.791116i	$0.290500\pi$
$840$	1.25499	−	0.199089i	0.0433013	−	0.00686921i
$841$	−6.69985	−	20.6200i	−0.231029	−	0.711035i
$842$		−	0.518842i		−	0.0178805i
$843$	8.00751	−	15.7252i	0.275793	−	0.541605i
$844$	7.26353	+	22.3549i	0.250021	+	0.769486i
$845$	7.37468	+	2.39618i	0.253697	+	0.0824311i
$846$	4.23017	−	1.37677i	0.145436	−	0.0473345i
$847$	6.04532	+	4.39218i	0.207720	+	0.150917i
$848$	1.52164	+	4.68312i	0.0522533	+	0.160819i
$849$	12.9228	+	25.3470i	0.443510	+	0.869907i
$850$	0.320403	+	0.440997i	0.0109897	+	0.0151261i
$851$	16.7357	+	5.43777i	0.573694	+	0.186404i
$852$	−0.635501	−	4.00600i	−0.0217719	−	0.137243i
$853$	−39.0877	+	28.3988i	−1.33834	+	0.972358i	−0.338832	+	0.940847i	$0.610032\pi$
$853$	−39.0877	+	28.3988i	−1.33834	+	0.972358i	−0.999503	+	0.0315112i	$0.989968\pi$
$854$	−1.47501	+	4.53961i	−0.0504738	+	0.155342i
$855$	6.77024	−	20.8717i	0.231537	−	0.713796i
$856$	1.84509	+	1.34053i	0.0630638	+	0.0458185i
$857$	−47.9642	+	15.5845i	−1.63843	+	0.532357i	−0.976186	−	0.216935i	$-0.930394\pi$
$857$	−47.9642	+	15.5845i	−1.63843	+	0.532357i	−0.662240	+	0.749292i	$0.730394\pi$
$858$	1.62614	+	3.18953i	0.0555155	+	0.108889i
$859$	−10.5759	−	3.43632i	−0.360846	−	0.117246i	0.122983	−	0.992409i	$-0.460754\pi$
$859$	−10.5759	−	3.43632i	−0.360846	−	0.117246i	−0.483828	+	0.875163i	$0.660754\pi$
$860$	0.538994	−	1.65885i	0.0183795	−	0.0565664i
$861$	−10.8770	−	1.71999i	−0.370686	−	0.0586172i
$862$	−7.33196			−0.249728
$863$	−41.2476			−1.40408			−0.702042	−	0.712136i	$-0.747728\pi$
$863$	−41.2476			−1.40408			−0.702042	+	0.712136i	$0.747728\pi$
$864$	2.36243	+	4.62806i	0.0803715	+	0.157450i
$865$	10.4725	−	7.60870i	0.356075	−	0.258703i
$866$	−11.7066	−	8.50533i	−0.397806	−	0.289023i
$867$	−25.7802	−	13.1277i	−0.875543	−	0.445839i
$868$	3.17964	−	2.56408i	0.107924	−	0.0870307i
$869$			6.03920i			0.204866i
$870$	−2.12833	−	4.17453i	−0.0721570	−	0.141530i
$871$	−15.3974	−	21.1927i	−0.521721	−	0.718088i
$872$	8.97439	−	2.91596i	0.303911	−	0.0987467i
$873$	18.3223	+	25.1923i	0.620115	+	0.852630i
$874$			37.2257i			1.25918i
$875$	0.697724	−	0.226704i	0.0235874	−	0.00766400i
$876$	13.0817	+	13.0752i	0.441988	+	0.441770i
$877$	6.63121	−	20.4088i	0.223920	−	0.689155i	−0.774480	−	0.632599i	$-0.781988\pi$
$877$	6.63121	−	20.4088i	0.223920	−	0.689155i	0.998399	−	0.0565557i	$-0.0180118\pi$
$878$	4.72024	−	6.49685i	0.159300	−	0.219258i
$879$	−26.7064	−	4.22312i	−0.900784	−	0.142442i
$880$	−0.530460	+	0.730116i	−0.0178818	+	0.0246122i
$881$	−36.3465	+	26.4073i	−1.22455	+	0.889684i	−0.996469	−	0.0839589i	$-0.973244\pi$
$881$	−36.3465	+	26.4073i	−1.22455	+	0.889684i	−0.228076	+	0.973643i	$0.573244\pi$
$882$	5.99950	+	18.4336i	0.202014	+	0.620692i
$883$	19.0772	+	26.2575i	0.641998	+	0.883634i	0.998720	−	0.0505762i	$-0.0161058\pi$
$883$	19.0772	+	26.2575i	0.641998	+	0.883634i	−0.356722	+	0.934210i	$0.616106\pi$
$884$	−0.733843	−	1.01005i	−0.0246818	−	0.0339716i
$885$	−11.7521	+	11.7579i	−0.395042	+	0.395237i
$886$	−14.1623	+	10.2895i	−0.475790	+	0.345682i
$887$	6.01274	−	8.27582i	0.201888	−	0.277875i	−0.696053	−	0.717990i	$-0.745062\pi$
$887$	6.01274	−	8.27582i	0.201888	−	0.277875i	0.897941	+	0.440115i	$0.145062\pi$
$888$	−0.935346	+	5.91498i	−0.0313881	+	0.198494i
$889$	−6.01244	+	8.27541i	−0.201651	+	0.277548i
$890$	−0.0750353	+	0.230935i	−0.00251519	+	0.00774096i
$891$	−6.57575	−	4.76766i	−0.220296	−	0.159723i
$892$	17.8116	−	5.78733i	0.596376	−	0.193774i
$893$			10.8458i			0.362940i
$894$	12.1945	+	6.20964i	0.407846	+	0.207681i
$895$	−12.3688	+	4.01886i	−0.413443	+	0.134336i
$896$	−0.431217	−	0.593520i	−0.0144060	−	0.0198281i
$897$	−17.9877	+	9.17077i	−0.600591	+	0.306203i
$898$		−	26.8510i		−	0.896029i
$899$	−12.6158	−	8.22950i	−0.420761	−	0.274469i
$900$	1.76455	+	2.42618i	0.0588184	+	0.0808727i
$901$	2.17153	+	1.57771i	0.0723440	+	0.0525610i
$902$	6.32739	−	4.59712i	0.210679	−	0.153067i
$903$	−2.18915	−	0.346175i	−0.0728505	−	0.0115200i
$904$	−18.1595			−0.603976
$905$	−12.3861			−0.411728
$906$	−2.91835	+	18.4552i	−0.0969557	+	0.613133i
$907$	10.0207	−	30.8404i	0.332730	−	1.02404i	−0.635099	−	0.772431i	$-0.719041\pi$
$907$	10.0207	−	30.8404i	0.332730	−	1.02404i	0.967829	−	0.251608i	$-0.0809593\pi$
$908$	−13.0333	−	4.23476i	−0.432524	−	0.140535i
$909$	15.1760	−	0.00748675i	0.503357	−	0.000248320i
$910$	−1.59805	+	0.519237i	−0.0529747	+	0.0172125i
$911$	−10.4372	−	7.58304i	−0.345798	−	0.251237i	0.401306	−	0.915944i	$-0.368556\pi$
$911$	−10.4372	−	7.58304i	−0.345798	−	0.251237i	−0.747104	+	0.664707i	$0.768556\pi$
$912$	−12.5119	+	1.98486i	−0.414311	+	0.0657252i
$913$	−0.697496	+	2.14667i	−0.0230838	+	0.0710445i
$914$	−27.2711	+	19.8136i	−0.902047	+	0.655376i
$915$	−11.1301	+	1.76565i	−0.367949	+	0.0583705i
$916$	−3.99026	−	1.29652i	−0.131842	−	0.0428381i
$917$	3.38885	+	4.66435i	0.111910	+	0.154030i
$918$	2.52467	+	1.28403i	0.0833266	+	0.0423794i
$919$	14.5328	+	44.7273i	0.479392	+	1.47542i	0.839941	+	0.542678i	$0.182590\pi$
$919$	14.5328	+	44.7273i	0.479392	+	1.47542i	−0.360548	+	0.932740i	$0.617410\pi$
$920$	−4.11756	−	2.99158i	−0.135752	−	0.0986296i
$921$	−25.0491	+	25.0615i	−0.825397	+	0.825804i
$922$	−31.7606	−	10.3197i	−1.04598	−	0.339860i
$923$	1.65743	+	5.10105i	0.0545550	+	0.167903i
$924$	1.02190	+	0.520366i	0.0336180	+	0.0171188i
$925$			3.45745i			0.113680i
$926$	−8.27443	−	25.4661i	−0.271915	−	0.836867i
$927$	−45.5093	−	14.7620i	−1.49472	−	0.484849i
$928$	−1.59015	+	2.18866i	−0.0521994	+	0.0718463i
$929$	1.35663			0.0445096			0.0222548	−	0.999752i	$-0.492915\pi$
$929$	1.35663			0.0445096			0.0222548	+	0.999752i	$0.492915\pi$
$930$	8.80285	+	3.93824i	0.288657	+	0.129140i
$931$	−47.2621			−1.54895
$932$	−11.7562	+	16.1811i	−0.385089	+	0.530029i
$933$	5.71968	+	36.0550i	0.187254	+	1.18039i
$934$	−1.67195	−	5.14572i	−0.0547078	−	0.168373i
$935$			0.491941i			0.0160882i
$936$	−4.04148	−	5.55685i	−0.132100	−	0.181631i
$937$	−12.2107	−	37.5807i	−0.398907	−	1.22771i	−0.925877	−	0.377825i	$-0.876672\pi$
$937$	−12.2107	−	37.5807i	−0.398907	−	1.22771i	0.526970	−	0.849884i	$-0.323328\pi$
$938$	−7.98007	−	2.59288i	−0.260559	−	0.0846606i
$939$	−2.50107	−	2.49983i	−0.0816192	−	0.0815790i
$940$	−1.19966	−	0.871603i	−0.0391286	−	0.0284286i
$941$	−2.97058	−	9.14250i	−0.0968381	−	0.298037i	0.890890	−	0.454219i	$-0.150082\pi$
$941$	−2.97058	−	9.14250i	−0.0968381	−	0.298037i	−0.987728	+	0.156182i	$0.950082\pi$
$942$	14.2895	−	7.28530i	0.465577	−	0.237368i
$943$	25.9259	+	35.6840i	0.844264	+	1.16203i
$944$	9.12815	+	2.96591i	0.297096	+	0.0965323i
$945$	2.69354	−	2.69752i	0.0876207	−	0.0877505i
$946$	1.27348	−	0.925240i	0.0414045	−	0.0300822i
$947$	−15.8631	+	48.8214i	−0.515480	+	1.58648i	0.266927	+	0.963717i	$0.413992\pi$
$947$	−15.8631	+	48.8214i	−0.515480	+	1.58648i	−0.782407	+	0.622767i	$0.786008\pi$
$948$	−1.81599	−	11.4475i	−0.0589807	−	0.371796i
$949$	−19.7867	−	14.3759i	−0.642304	−	0.466661i
$950$	−6.95611	+	2.26018i	−0.225686	+	0.0733298i
$951$	−28.7539	+	14.6598i	−0.932408	+	0.475375i
$952$	−0.380331	−	0.123577i	−0.0123266	−	0.00400516i
$953$	16.8664	−	51.9094i	0.546356	−	1.68151i	−0.171387	−	0.985204i	$-0.554825\pi$
$953$	16.8664	−	51.9094i	0.546356	−	1.68151i	0.717743	−	0.696308i	$-0.245175\pi$
$954$	11.9554	+	8.67708i	0.387070	+	0.280931i
$955$	−7.20910			−0.233281
$956$	8.04508			0.260197
$957$	0.660497	−	4.17688i	0.0213508	−	0.135019i
$958$	−23.1282	+	16.8036i	−0.747239	+	0.542901i
$959$	−2.72012	−	1.97628i	−0.0878372	−	0.0638175i
$960$	0.785954	−	1.54346i	0.0253666	−	0.0498150i
$961$	30.8432	−	3.11440i	0.994941	−	0.100464i
$962$		−	7.91884i		−	0.255314i
$963$	6.84196	−	0.00337533i	0.220479	−	0.000108768i
$964$	−10.3751	−	14.2800i	−0.334158	−	0.459929i
$965$	18.9524	−	6.15801i	0.610100	−	0.198233i
$966$	−2.93466	+	5.76310i	−0.0944210	+	0.185425i
$967$		−	34.5986i		−	1.11262i	−0.830976	−	0.556309i	$-0.812217\pi$
$967$		−	34.5986i		−	1.11262i	0.830976	−	0.556309i	$-0.187783\pi$
$968$	9.68703	−	3.14751i	0.311353	−	0.101165i
$969$	−4.88177	+	4.88418i	−0.156825	+	0.156902i
$970$	3.20868	−	9.87531i	0.103025	−	0.317077i
$971$	19.4965	−	26.8346i	0.625671	−	0.861163i	−0.372079	−	0.928201i	$-0.621355\pi$
$971$	19.4965	−	26.8346i	0.625671	−	0.861163i	0.997750	+	0.0670382i	$0.0213549\pi$
$972$	13.8981	+	7.05988i	0.445783	+	0.226446i
$973$	7.48735	−	10.3055i	0.240033	−	0.330378i
$974$	23.1125	−	16.7922i	0.740571	−	0.538057i
$975$	−2.80581	−	2.80443i	−0.0898579	−	0.0898136i
$976$	3.82432	+	5.26372i	0.122413	+	0.168488i
$977$	−3.32083	−	4.57073i	−0.106243	−	0.146230i	0.752585	−	0.658495i	$-0.228807\pi$
$977$	−3.32083	−	4.57073i	−0.106243	−	0.146230i	−0.858828	+	0.512265i	$0.828807\pi$
$978$	−11.0974	−	11.0919i	−0.354855	−	0.354680i
$979$	−0.177286	+	0.128806i	−0.00566610	+	0.00411666i
$980$	3.79814	−	5.22769i	0.121327	−	0.166993i
$981$	16.6281	−	22.9104i	0.530895	−	0.731473i
$982$	−5.24860	+	7.22408i	−0.167490	+	0.230530i
$983$	−7.23975	+	22.2816i	−0.230912	+	0.710674i	0.766725	+	0.641975i	$0.221885\pi$
$983$	−7.23975	+	22.2816i	−0.230912	+	0.710674i	−0.997637	+	0.0686990i	$0.978115\pi$
$984$	−10.6114	+	10.6166i	−0.338278	+	0.338445i
$985$	11.8945	−	3.86477i	0.378991	−	0.123142i
$986$			1.47468i			0.0469635i
$987$	−0.855017	+	1.67909i	−0.0272155	+	0.0534460i
$988$	15.9321	−	5.17665i	0.506867	−	0.164691i
$989$	5.21798	+	7.18194i	0.165922	+	0.228372i
$990$	0.00133565	+	2.70742i	4.24496e−5	+	0.0860474i
$991$			15.2586i			0.484706i	0.970188	+	0.242353i	$0.0779191\pi$
$991$			15.2586i			0.484706i	−0.970188	+	0.242353i	$0.922081\pi$
$992$	−0.280036	−	5.56072i	−0.00889114	−	0.176553i
$993$	21.2144	−	41.6609i	0.673218	−	1.32207i
$994$	1.38990	+	1.00982i	0.0440849	+	0.0320295i
$995$	4.66259	−	3.38757i	0.147814	−	0.107393i
$996$	0.676615	−	4.27881i	0.0214394	−	0.135579i
$997$	11.4778			0.363507			0.181754	−	0.983344i	$-0.441823\pi$
$997$	11.4778			0.363507			0.181754	+	0.983344i	$0.441823\pi$
$998$	26.8604			0.850251
$999$	8.16798	+	16.0013i	0.258423	+	0.506258i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.v.b.401.1	✓	80
3.2	odd	2	inner	930.2.v.b.401.17	yes	80
31.15	odd	10	inner	930.2.v.b.821.17	yes	80
93.77	even	10	inner	930.2.v.b.821.1	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.v.b.401.1	✓	80	1.1	even	1	trivial
930.2.v.b.401.17	yes	80	3.2	odd	2	inner
930.2.v.b.821.1	yes	80	93.77	even	10	inner
930.2.v.b.821.17	yes	80	31.15	odd	10	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.v (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.587785 + 0.809017i) q^{2} +(-1.71066 + 0.271374i) q^{3} +(-0.309017 - 0.951057i) q^{4} +1.00000i q^{5} +(0.785954 - 1.54346i) q^{6} +(0.226704 + 0.697724i) q^{7} +(0.951057 + 0.309017i) q^{8} +(2.85271 - 0.928458i) q^{9} +O(q^{10})\)	\(q+(-0.587785 + 0.809017i) q^{2} +(-1.71066 + 0.271374i) q^{3} +(-0.309017 - 0.951057i) q^{4} +1.00000i q^{5} +(0.785954 - 1.54346i) q^{6} +(0.226704 + 0.697724i) q^{7} +(0.951057 + 0.309017i) q^{8} +(2.85271 - 0.928458i) q^{9} +(-0.809017 - 0.587785i) q^{10} +(-0.278880 - 0.858303i) q^{11} +(0.786715 + 1.54307i) q^{12} +(-1.34625 - 1.85295i) q^{13} +(-0.697724 - 0.226704i) q^{14} +(-0.271374 - 1.71066i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-0.168446 + 0.518424i) q^{17} +(-0.925643 + 2.85363i) q^{18} +(-5.91722 - 4.29911i) q^{19} +(0.951057 - 0.309017i) q^{20} +(-0.577158 - 1.13205i) q^{21} +(0.858303 + 0.278880i) q^{22} +(-1.57277 + 4.84049i) q^{23} +(-1.71079 - 0.270530i) q^{24} -1.00000 q^{25} +2.29037 q^{26} +(-4.62806 + 2.36243i) q^{27} +(0.593520 - 0.431217i) q^{28} +(-2.18866 - 1.59015i) q^{29} +(1.54346 + 0.785954i) q^{30} +(5.56072 - 0.280036i) q^{31} -1.00000i q^{32} +(0.709989 + 1.39258i) q^{33} +(-0.320403 - 0.440997i) q^{34} +(-0.697724 + 0.226704i) q^{35} +(-1.76455 - 2.42618i) q^{36} -3.45745i q^{37} +(6.95611 - 2.26018i) q^{38} +(2.80581 + 2.80443i) q^{39} +(-0.309017 + 0.951057i) q^{40} +(5.09391 - 7.01117i) q^{41} +(1.25509 + 0.198469i) q^{42} +(1.02523 - 1.41110i) q^{43} +(-0.730116 + 0.530460i) q^{44} +(0.928458 + 2.85271i) q^{45} +(-2.99158 - 4.11756i) q^{46} +(-0.871603 - 1.19966i) q^{47} +(1.22444 - 1.22505i) q^{48} +(5.22769 - 3.79814i) q^{49} +(0.587785 - 0.809017i) q^{50} +(0.147467 - 0.932558i) q^{51} +(-1.34625 + 1.85295i) q^{52} +(1.52164 - 4.68312i) q^{53} +(0.809059 - 5.13278i) q^{54} +(0.858303 - 0.278880i) q^{55} +0.733631i q^{56} +(11.2890 + 5.74854i) q^{57} +(2.57292 - 0.835994i) q^{58} +(-5.64150 - 7.76486i) q^{59} +(-1.54307 + 0.786715i) q^{60} -6.50632i q^{61} +(-3.04195 + 4.66332i) q^{62} +(1.29453 + 1.77992i) q^{63} +(0.809017 + 0.587785i) q^{64} +(1.85295 - 1.34625i) q^{65} +(-1.54395 - 0.244147i) q^{66} +11.4373 q^{67} +0.545103 q^{68} +(1.37689 - 8.70723i) q^{69} +(0.226704 - 0.697724i) q^{70} +(-2.22717 - 0.723652i) q^{71} +(3.00000 - 0.00147998i) q^{72} +(10.1559 - 3.29984i) q^{73} +(2.79714 + 2.03224i) q^{74} +(1.71066 - 0.271374i) q^{75} +(-2.26018 + 6.95611i) q^{76} +(0.535636 - 0.389162i) q^{77} +(-3.91804 + 0.621548i) q^{78} +(-6.36431 - 2.06789i) q^{79} +(-0.587785 - 0.809017i) q^{80} +(7.27593 - 5.29725i) q^{81} +(2.67803 + 8.24212i) q^{82} +(-2.02341 - 1.47009i) q^{83} +(-0.898289 + 0.898732i) q^{84} +(-0.518424 - 0.168446i) q^{85} +(0.538994 + 1.65885i) q^{86} +(4.17558 + 2.12627i) q^{87} -0.902473i q^{88} +(-0.0750353 - 0.230935i) q^{89} +(-2.85363 - 0.925643i) q^{90} +(0.987647 - 1.35938i) q^{91} +5.08959 q^{92} +(-9.43650 + 1.98808i) q^{93} +1.48286 q^{94} +(4.29911 - 5.91722i) q^{95} +(0.271374 + 1.71066i) q^{96} +(3.20868 + 9.87531i) q^{97} +6.46179i q^{98} +(-1.59246 - 2.18956i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 20 q^{4} + 12 q^{7} + 8 q^{9}+O(q^{10}) \) 80 * q + 20 * q^4 + 12 * q^7 + 8 * q^9	\( 80 q + 20 q^{4} + 12 q^{7} + 8 q^{9} - 20 q^{10} + 10 q^{13} - 20 q^{16} - 4 q^{18} - 12 q^{19} - 30 q^{21} - 10 q^{22} - 80 q^{25} + 60 q^{27} + 18 q^{28} + 8 q^{31} - 20 q^{33} + 10 q^{34} - 8 q^{36} - 46 q^{39} + 20 q^{40} + 50 q^{43} - 16 q^{45} - 10 q^{46} - 8 q^{49} - 20 q^{51} + 10 q^{52} - 10 q^{55} + 10 q^{58} + 44 q^{63} + 20 q^{64} - 10 q^{66} - 132 q^{67} - 16 q^{69} + 12 q^{70} + 4 q^{72} - 20 q^{73} - 18 q^{76} + 48 q^{78} - 120 q^{79} + 48 q^{81} - 20 q^{82} + 20 q^{84} - 136 q^{87} - 12 q^{90} - 110 q^{91} - 20 q^{93} - 28 q^{94} + 22 q^{97}+O(q^{100}) \) 80 * q + 20 * q^4 + 12 * q^7 + 8 * q^9 - 20 * q^10 + 10 * q^13 - 20 * q^16 - 4 * q^18 - 12 * q^19 - 30 * q^21 - 10 * q^22 - 80 * q^25 + 60 * q^27 + 18 * q^28 + 8 * q^31 - 20 * q^33 + 10 * q^34 - 8 * q^36 - 46 * q^39 + 20 * q^40 + 50 * q^43 - 16 * q^45 - 10 * q^46 - 8 * q^49 - 20 * q^51 + 10 * q^52 - 10 * q^55 + 10 * q^58 + 44 * q^63 + 20 * q^64 - 10 * q^66 - 132 * q^67 - 16 * q^69 + 12 * q^70 + 4 * q^72 - 20 * q^73 - 18 * q^76 + 48 * q^78 - 120 * q^79 + 48 * q^81 - 20 * q^82 + 20 * q^84 - 136 * q^87 - 12 * q^90 - 110 * q^91 - 20 * q^93 - 28 * q^94 + 22 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more