LMFDB - Embedded newform 435.2.q.c.41.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [435,2,Mod(41,435)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(435, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 1]))

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

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

chi := DirichletCharacter("435.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 435 = 3 \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	435.q (of order $4$, degree $2$, 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:	$3.47349248793$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			41.8
Character	$\chi$	$=$	435.41
Dual form			435.2.q.c.191.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.398500 + 0.398500i) q^{2} +(1.60347 + 0.654884i) q^{3} +1.68239i q^{4} -1.00000 q^{5} +(-0.899957 + 0.378013i) q^{6} -4.31678 q^{7} +(-1.46744 - 1.46744i) q^{8} +(2.14225 + 2.10018i) q^{9} +O(q^{10})$	\(q+(-0.398500 + 0.398500i) q^{2} +(1.60347 + 0.654884i) q^{3} +1.68239i q^{4} -1.00000 q^{5} +(-0.899957 + 0.378013i) q^{6} -4.31678 q^{7} +(-1.46744 - 1.46744i) q^{8} +(2.14225 + 2.10018i) q^{9} +(0.398500 - 0.398500i) q^{10} +(0.656522 - 0.656522i) q^{11} +(-1.10177 + 2.69768i) q^{12} +2.82252i q^{13} +(1.72024 - 1.72024i) q^{14} +(-1.60347 - 0.654884i) q^{15} -2.19524 q^{16} +(-4.74898 + 4.74898i) q^{17} +(-1.69061 + 0.0167668i) q^{18} +(1.21009 + 1.21009i) q^{19} -1.68239i q^{20} +(-6.92184 - 2.82699i) q^{21} +0.523249i q^{22} +1.96103i q^{23} +(-1.39199 - 3.31400i) q^{24} +1.00000 q^{25} +(-1.12477 - 1.12477i) q^{26} +(2.05967 + 4.77051i) q^{27} -7.26253i q^{28} +(1.25489 - 5.23691i) q^{29} +(0.899957 - 0.378013i) q^{30} +(2.91893 + 2.91893i) q^{31} +(3.80968 - 3.80968i) q^{32} +(1.48266 - 0.622769i) q^{33} -3.78494i q^{34} +4.31678 q^{35} +(-3.53333 + 3.60412i) q^{36} +(3.89885 - 3.89885i) q^{37} -0.964443 q^{38} +(-1.84842 + 4.52583i) q^{39} +(1.46744 + 1.46744i) q^{40} +(-2.91236 - 2.91236i) q^{41} +(3.88491 - 1.63180i) q^{42} +(4.82538 + 4.82538i) q^{43} +(1.10453 + 1.10453i) q^{44} +(-2.14225 - 2.10018i) q^{45} +(-0.781470 - 0.781470i) q^{46} +(-6.22784 - 6.22784i) q^{47} +(-3.52001 - 1.43763i) q^{48} +11.6346 q^{49} +(-0.398500 + 0.398500i) q^{50} +(-10.7249 + 4.50483i) q^{51} -4.74859 q^{52} +7.97602i q^{53} +(-2.72183 - 1.08027i) q^{54} +(-0.656522 + 0.656522i) q^{55} +(6.33460 + 6.33460i) q^{56} +(1.14788 + 2.73282i) q^{57} +(1.58684 + 2.58699i) q^{58} +7.91809i q^{59} +(1.10177 - 2.69768i) q^{60} +(2.74726 + 2.74726i) q^{61} -2.32639 q^{62} +(-9.24764 - 9.06601i) q^{63} -1.35417i q^{64} -2.82252i q^{65} +(-0.342667 + 0.839015i) q^{66} +9.91992i q^{67} +(-7.98966 - 7.98966i) q^{68} +(-1.28425 + 3.14445i) q^{69} +(-1.72024 + 1.72024i) q^{70} +5.70361 q^{71} +(-0.0617419 - 6.22550i) q^{72} +(6.98527 - 6.98527i) q^{73} +3.10738i q^{74} +(1.60347 + 0.654884i) q^{75} +(-2.03585 + 2.03585i) q^{76} +(-2.83406 + 2.83406i) q^{77} +(-1.06695 - 2.54014i) q^{78} +(3.13992 + 3.13992i) q^{79} +2.19524 q^{80} +(0.178499 + 8.99823i) q^{81} +2.32116 q^{82} +13.0602i q^{83} +(4.75611 - 11.6453i) q^{84} +(4.74898 - 4.74898i) q^{85} -3.84584 q^{86} +(5.44175 - 7.57544i) q^{87} -1.92681 q^{88} +(10.5737 - 10.5737i) q^{89} +(1.69061 - 0.0167668i) q^{90} -12.1842i q^{91} -3.29922 q^{92} +(2.76886 + 6.59198i) q^{93} +4.96359 q^{94} +(-1.21009 - 1.21009i) q^{95} +(8.60361 - 3.61382i) q^{96} +(8.43681 - 8.43681i) q^{97} +(-4.63639 + 4.63639i) q^{98} +(2.78525 - 0.0276229i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 4 q^{2} + 6 q^{3} - 36 q^{5} + 8 q^{6} + 8 q^{7} + 4 q^{8}+O(q^{10}) $ 36 * q - 4 * q^2 + 6 * q^3 - 36 * q^5 + 8 * q^6 + 8 * q^7 + 4 * q^8	$ 36 q - 4 q^{2} + 6 q^{3} - 36 q^{5} + 8 q^{6} + 8 q^{7} + 4 q^{8} + 4 q^{10} - 12 q^{11} + 10 q^{12} + 28 q^{14} - 6 q^{15} - 60 q^{16} - 20 q^{17} - 28 q^{18} + 16 q^{19} + 12 q^{21} + 24 q^{24} + 36 q^{25} + 4 q^{26} + 30 q^{27} - 28 q^{29} - 8 q^{30} - 8 q^{31} - 16 q^{32} - 8 q^{33} - 8 q^{35} - 28 q^{36} - 4 q^{37} + 24 q^{38} - 40 q^{39} - 4 q^{40} + 48 q^{41} - 8 q^{42} + 4 q^{43} + 16 q^{44} + 20 q^{46} - 20 q^{47} - 14 q^{48} + 28 q^{49} - 4 q^{50} - 44 q^{52} - 24 q^{54} + 12 q^{55} - 84 q^{56} + 28 q^{57} - 64 q^{58} - 10 q^{60} + 20 q^{61} + 8 q^{62} + 32 q^{63} + 40 q^{66} + 60 q^{68} + 36 q^{69} - 28 q^{70} - 16 q^{71} - 132 q^{72} + 8 q^{73} + 6 q^{75} + 16 q^{76} + 32 q^{77} + 48 q^{78} + 12 q^{79} + 60 q^{80} - 60 q^{81} + 56 q^{82} + 44 q^{84} + 20 q^{85} + 8 q^{86} + 22 q^{87} - 24 q^{88} + 20 q^{89} + 28 q^{90} - 16 q^{92} + 24 q^{93} + 52 q^{94} - 16 q^{95} - 8 q^{96} + 4 q^{97} - 8 q^{98} - 48 q^{99}+O(q^{100}) $ 36 * q - 4 * q^2 + 6 * q^3 - 36 * q^5 + 8 * q^6 + 8 * q^7 + 4 * q^8 + 4 * q^10 - 12 * q^11 + 10 * q^12 + 28 * q^14 - 6 * q^15 - 60 * q^16 - 20 * q^17 - 28 * q^18 + 16 * q^19 + 12 * q^21 + 24 * q^24 + 36 * q^25 + 4 * q^26 + 30 * q^27 - 28 * q^29 - 8 * q^30 - 8 * q^31 - 16 * q^32 - 8 * q^33 - 8 * q^35 - 28 * q^36 - 4 * q^37 + 24 * q^38 - 40 * q^39 - 4 * q^40 + 48 * q^41 - 8 * q^42 + 4 * q^43 + 16 * q^44 + 20 * q^46 - 20 * q^47 - 14 * q^48 + 28 * q^49 - 4 * q^50 - 44 * q^52 - 24 * q^54 + 12 * q^55 - 84 * q^56 + 28 * q^57 - 64 * q^58 - 10 * q^60 + 20 * q^61 + 8 * q^62 + 32 * q^63 + 40 * q^66 + 60 * q^68 + 36 * q^69 - 28 * q^70 - 16 * q^71 - 132 * q^72 + 8 * q^73 + 6 * q^75 + 16 * q^76 + 32 * q^77 + 48 * q^78 + 12 * q^79 + 60 * q^80 - 60 * q^81 + 56 * q^82 + 44 * q^84 + 20 * q^85 + 8 * q^86 + 22 * q^87 - 24 * q^88 + 20 * q^89 + 28 * q^90 - 16 * q^92 + 24 * q^93 + 52 * q^94 - 16 * q^95 - 8 * q^96 + 4 * q^97 - 8 * q^98 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/435\mathbb{Z}\right)^\times$.

$n$	$31$	$146$	$262$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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 $

$2$	−0.398500	+	0.398500i	−0.281782	+	0.281782i	−0.833820	−	0.552037i	$-0.813851\pi$
$2$	−0.398500	+	0.398500i	−0.281782	+	0.281782i	0.552037	+	0.833820i	$0.313851\pi$
$3$	1.60347	+	0.654884i	0.925766	+	0.378098i
$3$	1.60347	+	0.654884i	0.925766	+	0.378098i
$4$			1.68239i			0.841197i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−0.899957	+	0.378013i	−0.367406	+	0.154323i
$7$	−4.31678			−1.63159			−0.815795	−	0.578342i	$-0.803700\pi$
$7$	−4.31678			−1.63159			−0.815795	+	0.578342i	$0.803700\pi$
$8$	−1.46744	−	1.46744i	−0.518817	−	0.518817i
$9$	2.14225	+	2.10018i	0.714084	+	0.700060i
$10$	0.398500	−	0.398500i	0.126017	−	0.126017i
$11$	0.656522	−	0.656522i	0.197949	−	0.197949i	−0.601171	−	0.799120i	$-0.705299\pi$
$11$	0.656522	−	0.656522i	0.197949	−	0.197949i	0.799120	+	0.601171i	$0.205299\pi$
$12$	−1.10177	+	2.69768i	−0.318055	+	0.778752i
$13$			2.82252i			0.782825i	0.920215	+	0.391413i	$0.128013\pi$
$13$			2.82252i			0.782825i	−0.920215	+	0.391413i	$0.871987\pi$
$14$	1.72024	−	1.72024i	0.459753	−	0.459753i
$15$	−1.60347	−	0.654884i	−0.414015	−	0.169090i
$16$	−2.19524			−0.548810
$17$	−4.74898	+	4.74898i	−1.15180	+	1.15180i	−0.165606	+	0.986192i	$0.552958\pi$
$17$	−4.74898	+	4.74898i	−1.15180	+	1.15180i	−0.986192	+	0.165606i	$0.947042\pi$
$18$	−1.69061	+	0.0167668i	−0.398481	+	0.00395197i
$19$	1.21009	+	1.21009i	0.277614	+	0.277614i	0.832156	−	0.554542i	$-0.187107\pi$
$19$	1.21009	+	1.21009i	0.277614	+	0.277614i	−0.554542	+	0.832156i	$0.687107\pi$
$20$		−	1.68239i		−	0.376195i
$21$	−6.92184	−	2.82699i	−1.51047	−	0.616900i
$22$			0.523249i			0.111557i
$23$			1.96103i			0.408902i	0.978877	+	0.204451i	$0.0655410\pi$
$23$			1.96103i			0.408902i	−0.978877	+	0.204451i	$0.934459\pi$
$24$	−1.39199	−	3.31400i	−0.284140	−	0.676466i
$25$	1.00000			0.200000
$26$	−1.12477	−	1.12477i	−0.220586	−	0.220586i
$27$	2.05967	+	4.77051i	0.396384	+	0.918085i
$28$		−	7.26253i		−	1.37249i
$29$	1.25489	−	5.23691i	0.233027	−	0.972470i
$29$	1.25489	−	5.23691i	0.233027	−	0.972470i
$30$	0.899957	−	0.378013i	0.164309	−	0.0690155i
$31$	2.91893	+	2.91893i	0.524255	+	0.524255i	0.918854	−	0.394599i	$-0.129116\pi$
$31$	2.91893	+	2.91893i	0.524255	+	0.524255i	−0.394599	+	0.918854i	$0.629116\pi$
$32$	3.80968	−	3.80968i	0.673462	−	0.673462i
$33$	1.48266	−	0.622769i	0.258098	−	0.108410i
$34$		−	3.78494i		−	0.649113i
$35$	4.31678			0.729669
$36$	−3.53333	+	3.60412i	−0.588888	+	0.600686i
$37$	3.89885	−	3.89885i	0.640966	−	0.640966i	−0.309827	−	0.950793i	$-0.600271\pi$
$37$	3.89885	−	3.89885i	0.640966	−	0.640966i	0.950793	+	0.309827i	$0.100271\pi$
$38$	−0.964443			−0.156453
$39$	−1.84842	+	4.52583i	−0.295984	+	0.724713i
$40$	1.46744	+	1.46744i	0.232022	+	0.232022i
$41$	−2.91236	−	2.91236i	−0.454835	−	0.454835i	0.442121	−	0.896956i	$-0.354226\pi$
$41$	−2.91236	−	2.91236i	−0.454835	−	0.454835i	−0.896956	+	0.442121i	$0.854226\pi$
$42$	3.88491	−	1.63180i	0.599455	−	0.251792i
$43$	4.82538	+	4.82538i	0.735864	+	0.735864i	0.971775	−	0.235911i	$-0.0758073\pi$
$43$	4.82538	+	4.82538i	0.735864	+	0.735864i	−0.235911	+	0.971775i	$0.575807\pi$
$44$	1.10453	+	1.10453i	0.166514	+	0.166514i
$45$	−2.14225	−	2.10018i	−0.319348	−	0.313076i
$46$	−0.781470	−	0.781470i	−0.115221	−	0.115221i
$47$	−6.22784	−	6.22784i	−0.908423	−	0.908423i	0.0877216	−	0.996145i	$-0.472041\pi$
$47$	−6.22784	−	6.22784i	−0.908423	−	0.908423i	−0.996145	+	0.0877216i	$0.972041\pi$
$48$	−3.52001	−	1.43763i	−0.508070	−	0.207504i
$49$	11.6346			1.66208
$50$	−0.398500	+	0.398500i	−0.0563565	+	0.0563565i
$51$	−10.7249	+	4.50483i	−1.50179	+	0.630803i
$52$	−4.74859			−0.658511
$53$			7.97602i			1.09559i	0.836612	+	0.547795i	$0.184533\pi$
$53$			7.97602i			1.09559i	−0.836612	+	0.547795i	$0.815467\pi$
$54$	−2.72183	−	1.08027i	−0.370394	−	0.147006i
$55$	−0.656522	+	0.656522i	−0.0885254	+	0.0885254i
$56$	6.33460	+	6.33460i	0.846496	+	0.846496i
$57$	1.14788	+	2.73282i	0.152040	+	0.361970i
$58$	1.58684	+	2.58699i	0.208362	+	0.339688i
$59$			7.91809i			1.03085i	0.856935	+	0.515424i	$0.172365\pi$
$59$			7.91809i			1.03085i	−0.856935	+	0.515424i	$0.827635\pi$
$60$	1.10177	−	2.69768i	0.142238	−	0.348268i
$61$	2.74726	+	2.74726i	0.351751	+	0.351751i	0.860761	−	0.509010i	$-0.169988\pi$
$61$	2.74726	+	2.74726i	0.351751	+	0.351751i	−0.509010	+	0.860761i	$0.669988\pi$
$62$	−2.32639			−0.295452
$63$	−9.24764	−	9.06601i	−1.16509	−	1.14221i
$64$		−	1.35417i		−	0.169271i
$65$		−	2.82252i		−	0.350090i
$66$	−0.342667	+	0.839015i	−0.0421794	+	0.103276i
$67$			9.91992i			1.21191i	0.795498	+	0.605956i	$0.207209\pi$
$67$			9.91992i			1.21191i	−0.795498	+	0.605956i	$0.792791\pi$
$68$	−7.98966	−	7.98966i	−0.968889	−	0.968889i
$69$	−1.28425	+	3.14445i	−0.154605	+	0.378548i
$70$	−1.72024	+	1.72024i	−0.205608	+	0.205608i
$71$	5.70361			0.676894			0.338447	−	0.940985i	$-0.390098\pi$
$71$	5.70361			0.676894			0.338447	+	0.940985i	$0.390098\pi$
$72$	−0.0617419	−	6.22550i	−0.00727635	−	0.733682i
$73$	6.98527	−	6.98527i	0.817564	−	0.817564i	−0.168191	−	0.985754i	$-0.553792\pi$
$73$	6.98527	−	6.98527i	0.817564	−	0.817564i	0.985754	+	0.168191i	$0.0537925\pi$
$74$			3.10738i			0.361226i
$75$	1.60347	+	0.654884i	0.185153	+	0.0756195i
$76$	−2.03585	+	2.03585i	−0.233528	+	0.233528i
$77$	−2.83406	+	2.83406i	−0.322971	+	0.322971i
$78$	−1.06695	−	2.54014i	−0.120808	−	0.287615i
$79$	3.13992	+	3.13992i	0.353268	+	0.353268i	0.861324	−	0.508056i	$-0.169636\pi$
$79$	3.13992	+	3.13992i	0.353268	+	0.353268i	−0.508056	+	0.861324i	$0.669636\pi$
$80$	2.19524			0.245435
$81$	0.178499	+	8.99823i	0.0198332	+	0.999803i
$82$	2.32116			0.256329
$83$			13.0602i			1.43355i	0.697305	+	0.716774i	$0.254382\pi$
$83$			13.0602i			1.43355i	−0.697305	+	0.716774i	$0.745618\pi$
$84$	4.75611	−	11.6453i	0.518935	−	1.27060i
$85$	4.74898	−	4.74898i	0.515100	−	0.515100i
$86$	−3.84584			−0.414707
$87$	5.44175	−	7.57544i	0.583417	−	0.812173i
$88$	−1.92681			−0.205398
$89$	10.5737	−	10.5737i	1.12081	−	1.12081i	0.129195	−	0.991619i	$-0.458761\pi$
$89$	10.5737	−	10.5737i	1.12081	−	1.12081i	0.991619	−	0.129195i	$-0.0412392\pi$
$90$	1.69061	−	0.0167668i	0.178206	−	0.00176737i
$91$		−	12.1842i		−	1.27725i
$92$	−3.29922			−0.343968
$93$	2.76886	+	6.59198i	0.287118	+	0.683557i
$94$	4.96359			0.511955
$95$	−1.21009	−	1.21009i	−0.124153	−	0.124153i
$96$	8.60361	−	3.61382i	0.878103	−	0.368834i
$97$	8.43681	−	8.43681i	0.856628	−	0.856628i	−0.134311	−	0.990939i	$-0.542882\pi$
$97$	8.43681	−	8.43681i	0.856628	−	0.856628i	0.990939	+	0.134311i	$0.0428822\pi$
$98$	−4.63639	+	4.63639i	−0.468346	+	0.468346i
$99$	2.78525	−	0.0276229i	0.279928	−	0.00277621i
$100$			1.68239i			0.168239i
$101$	−5.85042	+	5.85042i	−0.582138	+	0.582138i	−0.935490	−	0.353352i	$-0.885042\pi$
$101$	−5.85042	+	5.85042i	−0.582138	+	0.582138i	0.353352	+	0.935490i	$0.385042\pi$
$102$	2.47870	−	6.06906i	0.245428	−	0.600926i
$103$	−13.1281			−1.29355			−0.646776	−	0.762680i	$-0.723883\pi$
$103$	−13.1281			−1.29355			−0.646776	+	0.762680i	$0.723883\pi$
$104$	4.14186	−	4.14186i	0.406143	−	0.406143i
$105$	6.92184	+	2.82699i	0.675503	+	0.275886i
$106$	−3.17845	−	3.17845i	−0.308718	−	0.308718i
$107$		−	5.63620i		−	0.544872i	−0.962174	−	0.272436i	$-0.912171\pi$
$107$		−	5.63620i		−	0.544872i	0.962174	−	0.272436i	$-0.0878293\pi$
$108$	−8.02588	+	3.46518i	−0.772290	+	0.333437i
$109$			0.0680903i			0.00652187i	0.999995	+	0.00326093i	$0.00103799\pi$
$109$			0.0680903i			0.00652187i	−0.999995	+	0.00326093i	$0.998962\pi$
$110$		−	0.523249i		−	0.0498898i
$111$	8.80499	−	3.69840i	0.835732	−	0.351037i
$112$	9.47637			0.895433
$113$	10.1422	+	10.1422i	0.954100	+	0.954100i	0.998992	−	0.0448920i	$-0.0142944\pi$
$113$	10.1422	+	10.1422i	0.954100	+	0.954100i	−0.0448920	+	0.998992i	$0.514294\pi$
$114$	−1.54646	−	0.631598i	−0.144839	−	0.0591546i
$115$		−	1.96103i		−	0.182867i
$116$	8.81055	+	2.11122i	0.818039	+	0.196022i
$117$	−5.92779	+	6.04655i	−0.548024	+	0.559003i
$118$	−3.15536	−	3.15536i	−0.290475	−	0.290475i
$119$	20.5003	−	20.5003i	1.87926	−	1.87926i
$120$	1.39199	+	3.31400i	0.127071	+	0.302525i
$121$			10.1380i			0.921633i
$122$	−2.18957			−0.198234
$123$	−2.76264	−	6.57716i	−0.249099	−	0.593042i
$124$	−4.91079	+	4.91079i	−0.441002	+	0.441002i
$125$	−1.00000			−0.0894427
$126$	7.29800	−	0.0723785i	0.650157	−	0.00644799i
$127$	−11.0227	−	11.0227i	−0.978104	−	0.978104i	0.0216610	−	0.999765i	$-0.493105\pi$
$127$	−11.0227	−	11.0227i	−0.978104	−	0.978104i	−0.999765	+	0.0216610i	$0.993105\pi$
$128$	8.15899	+	8.15899i	0.721160	+	0.721160i
$129$	4.57731	+	10.8974i	0.403009	+	0.959466i
$130$	1.12477	+	1.12477i	0.0986492	+	0.0986492i
$131$	−6.82538	−	6.82538i	−0.596336	−	0.596336i	0.342999	−	0.939336i	$-0.388557\pi$
$131$	−6.82538	−	6.82538i	−0.596336	−	0.596336i	−0.939336	+	0.342999i	$0.888557\pi$
$132$	1.04774	+	2.49442i	0.0911944	+	0.217111i
$133$	−5.22369	−	5.22369i	−0.452952	−	0.452952i
$134$	−3.95309	−	3.95309i	−0.341495	−	0.341495i
$135$	−2.05967	−	4.77051i	−0.177268	−	0.410580i
$136$	13.9377			1.19514
$137$	−13.6340	+	13.6340i	−1.16483	+	1.16483i	−0.181428	+	0.983404i	$0.558072\pi$
$137$	−13.6340	+	13.6340i	−1.16483	+	1.16483i	−0.983404	+	0.181428i	$0.941928\pi$
$138$	−0.741294	−	1.76484i	−0.0631031	−	0.150233i
$139$	−2.76749			−0.234735			−0.117368	−	0.993089i	$-0.537446\pi$
$139$	−2.76749			−0.234735			−0.117368	+	0.993089i	$0.537446\pi$
$140$			7.26253i			0.613796i
$141$	−5.90766	−	14.0647i	−0.497515	−	1.18446i
$142$	−2.27289	+	2.27289i	−0.190737	+	0.190737i
$143$	1.85304	+	1.85304i	0.154959	+	0.154959i
$144$	−4.70276	−	4.61040i	−0.391897	−	0.384200i
$145$	−1.25489	+	5.23691i	−0.104213	+	0.434902i
$146$			5.56726i			0.460750i
$147$	18.6558	+	7.61931i	1.53870	+	0.628430i
$148$	6.55940	+	6.55940i	0.539179	+	0.539179i
$149$	8.11024			0.664416			0.332208	−	0.943206i	$-0.392206\pi$
$149$	8.11024			0.664416			0.332208	+	0.943206i	$0.392206\pi$
$150$	−0.899957	+	0.378013i	−0.0734811	+	0.0308647i
$151$		−	12.6219i		−	1.02715i	−0.858044	−	0.513577i	$-0.828320\pi$
$151$		−	12.6219i		−	1.02715i	0.858044	−	0.513577i	$-0.171680\pi$
$152$		−	3.55146i		−	0.288061i
$153$	−20.1472	+	0.199812i	−1.62881	+	0.0161538i
$154$		−	2.25875i		−	0.182015i
$155$	−2.91893	−	2.91893i	−0.234454	−	0.234454i
$156$	−7.61423	−	3.10977i	−0.609627	−	0.248981i
$157$	7.95829	−	7.95829i	0.635141	−	0.635141i	−0.314212	−	0.949353i	$-0.601740\pi$
$157$	7.95829	−	7.95829i	0.635141	−	0.635141i	0.949353	+	0.314212i	$0.101740\pi$
$158$	−2.50252			−0.199090
$159$	−5.22337	+	12.7893i	−0.414240	+	1.01426i
$160$	−3.80968	+	3.80968i	−0.301181	+	0.301181i
$161$		−	8.46532i		−	0.667161i
$162$	−3.65693	−	3.51467i	−0.287316	−	0.276138i
$163$	7.60375	−	7.60375i	0.595571	−	0.595571i	−0.343560	−	0.939131i	$-0.611633\pi$
$163$	7.60375	−	7.60375i	0.595571	−	0.595571i	0.939131	+	0.343560i	$0.111633\pi$
$164$	4.89975	−	4.89975i	0.382606	−	0.382606i
$165$	−1.48266	+	0.622769i	−0.115425	+	0.0484825i
$166$	−5.20452	−	5.20452i	−0.403949	−	0.403949i
$167$	3.24817			0.251351			0.125676	−	0.992071i	$-0.459890\pi$
$167$	3.24817			0.251351			0.125676	+	0.992071i	$0.459890\pi$
$168$	6.00893	+	14.3058i	0.463599	+	1.10372i
$169$	5.03340			0.387185
$170$			3.78494i			0.290292i
$171$	0.0509141	+	5.13372i	0.00389350	+	0.392586i
$172$	−8.11820	+	8.11820i	−0.619007	+	0.619007i
$173$	−15.3533			−1.16729			−0.583647	−	0.812008i	$-0.698375\pi$
$173$	−15.3533			−1.16729			−0.583647	+	0.812008i	$0.698375\pi$
$174$	0.850275	+	5.18736i	0.0644592	+	0.393253i
$175$	−4.31678			−0.326318
$176$	−1.44122	+	1.44122i	−0.108636	+	0.108636i
$177$	−5.18543	+	12.6964i	−0.389761	+	0.954323i
$178$			8.42728i			0.631651i
$179$	4.39983			0.328859			0.164429	−	0.986389i	$-0.447422\pi$
$179$	4.39983			0.328859			0.164429	+	0.986389i	$0.447422\pi$
$180$	3.53333	−	3.60412i	0.263359	−	0.268635i
$181$	21.7145			1.61403			0.807014	−	0.590532i	$-0.201082\pi$
$181$	21.7145			1.61403			0.807014	+	0.590532i	$0.201082\pi$
$182$	4.85540	+	4.85540i	0.359906	+	0.359906i
$183$	2.60602	+	6.20430i	0.192643	+	0.458635i
$184$	2.87768	−	2.87768i	0.212145	−	0.212145i
$185$	−3.89885	+	3.89885i	−0.286649	+	0.286649i
$186$	−3.73030	−	1.52351i	−0.273519	−	0.111710i
$187$			6.23562i			0.455994i
$188$	10.4777	−	10.4777i	0.764163	−	0.764163i
$189$	−8.89115	−	20.5932i	−0.646736	−	1.49794i
$190$	0.964443			0.0699680
$191$	−2.11790	+	2.11790i	−0.153246	+	0.153246i	−0.779566	−	0.626320i	$-0.784560\pi$
$191$	−2.11790	+	2.11790i	−0.153246	+	0.153246i	0.626320	+	0.779566i	$0.284560\pi$
$192$	0.886822	−	2.17137i	0.0640009	−	0.156705i
$193$	−7.58685	−	7.58685i	−0.546114	−	0.546114i	0.379201	−	0.925314i	$-0.376199\pi$
$193$	−7.58685	−	7.58685i	−0.546114	−	0.546114i	−0.925314	+	0.379201i	$0.876199\pi$
$194$			6.72414i			0.482765i
$195$	1.84842	−	4.52583i	0.132368	−	0.324101i
$196$			19.5740i			1.39814i
$197$		−	11.3571i		−	0.809161i	−0.914502	−	0.404580i	$-0.867418\pi$
$197$		−	11.3571i		−	0.809161i	0.914502	−	0.404580i	$-0.132582\pi$
$198$	−1.09892	+	1.12093i	−0.0780965	+	0.0796611i
$199$	−18.3425			−1.30027			−0.650133	−	0.759820i	$-0.725287\pi$
$199$	−18.3425			−1.30027			−0.650133	+	0.759820i	$0.725287\pi$
$200$	−1.46744	−	1.46744i	−0.103763	−	0.103763i
$201$	−6.49640	+	15.9063i	−0.458221	+	1.12195i
$202$		−	4.66279i		−	0.328073i
$203$	−5.41709	+	22.6066i	−0.380205	+	1.58667i
$204$	−7.57891	−	18.0435i	−0.530630	−	1.26330i
$205$	2.91236	+	2.91236i	0.203408	+	0.203408i
$206$	5.23156	−	5.23156i	0.364500	−	0.364500i
$207$	−4.11851	+	4.20102i	−0.286256	+	0.291991i
$208$		−	6.19611i		−	0.429623i
$209$	1.58890			0.109907
$210$	−3.88491	+	1.63180i	−0.268085	+	0.112605i
$211$	−3.09636	+	3.09636i	−0.213162	+	0.213162i	−0.805609	−	0.592447i	$-0.798162\pi$
$211$	−3.09636	+	3.09636i	−0.213162	+	0.213162i	0.592447	+	0.805609i	$0.298162\pi$
$212$	−13.4188			−0.921608
$213$	9.14558	+	3.73520i	0.626645	+	0.255932i
$214$	2.24603	+	2.24603i	0.153535	+	0.153535i
$215$	−4.82538	−	4.82538i	−0.329088	−	0.329088i
$216$	3.97798	−	10.0229i	0.270667	−	0.681969i
$217$	−12.6004	−	12.6004i	−0.855369	−	0.855369i
$218$	−0.0271340	−	0.0271340i	−0.00183775	−	0.00183775i
$219$	15.7752	−	6.62615i	1.06599	−	0.447754i
$220$	−1.10453	−	1.10453i	−0.0744673	−	0.0744673i
$221$	−13.4041	−	13.4041i	−0.901656	−	0.901656i
$222$	−2.03498	+	4.98261i	−0.136579	+	0.334411i
$223$	−27.3950			−1.83451			−0.917254	−	0.398303i	$-0.869599\pi$
$223$	−27.3950			−1.83451			−0.917254	+	0.398303i	$0.869599\pi$
$224$	−16.4455	+	16.4455i	−1.09881	+	1.09881i
$225$	2.14225	+	2.10018i	0.142817	+	0.140012i
$226$	−8.08336			−0.537697
$227$			4.72070i			0.313324i	0.987652	+	0.156662i	$0.0500733\pi$
$227$			4.72070i			0.313324i	−0.987652	+	0.156662i	$0.949927\pi$
$228$	−4.59767	+	1.93118i	−0.304488	+	0.127896i
$229$	−16.2982	+	16.2982i	−1.07701	+	1.07701i	−0.0802374	+	0.996776i	$0.525568\pi$
$229$	−16.2982	+	16.2982i	−1.07701	+	1.07701i	−0.996776	+	0.0802374i	$0.974432\pi$
$230$	0.781470	+	0.781470i	0.0515286	+	0.0515286i
$231$	−6.40032	+	2.68836i	−0.421110	+	0.176881i
$232$	−9.52631	+	5.84336i	−0.625433	+	0.383636i
$233$		−	19.9545i		−	1.30726i	−0.756813	−	0.653631i	$-0.773245\pi$
$233$		−	19.9545i		−	1.30726i	0.756813	−	0.653631i	$-0.226755\pi$
$234$	−0.0473245	−	4.77178i	−0.00309370	−	0.311941i
$235$	6.22784	+	6.22784i	0.406259	+	0.406259i
$236$	−13.3214			−0.867146
$237$	2.97849	+	7.09106i	0.193474	+	0.460614i
$238$			16.3388i			1.05909i
$239$		−	16.8894i		−	1.09248i	−0.837628	−	0.546241i	$-0.816058\pi$
$239$		−	16.8894i		−	1.09248i	0.837628	−	0.546241i	$-0.183942\pi$
$240$	3.52001	+	1.43763i	0.227216	+	0.0927985i
$241$			18.4770i			1.19021i	0.803648	+	0.595104i	$0.202889\pi$
$241$			18.4770i			1.19021i	−0.803648	+	0.595104i	$0.797111\pi$
$242$	−4.03998	−	4.03998i	−0.259700	−	0.259700i
$243$	−5.60658	+	14.5453i	−0.359662	+	0.933083i
$244$	−4.62198	+	4.62198i	−0.295892	+	0.295892i
$245$	−11.6346			−0.743307
$246$	3.72191	+	1.52009i	0.237300	+	0.0969173i
$247$	−3.41550	+	3.41550i	−0.217323	+	0.217323i
$248$		−	8.56668i		−	0.543985i
$249$	−8.55295	+	20.9418i	−0.542021	+	1.32713i
$250$	0.398500	−	0.398500i	0.0252034	−	0.0252034i
$251$	−9.71848	+	9.71848i	−0.613425	+	0.613425i	−0.943837	−	0.330412i	$-0.892812\pi$
$251$	−9.71848	+	9.71848i	−0.613425	+	0.613425i	0.330412	+	0.943837i	$0.392812\pi$
$252$	15.2526	−	15.5582i	0.960824	−	0.980073i
$253$	1.28746	+	1.28746i	0.0809417	+	0.0809417i
$254$	8.78508			0.551225
$255$	10.7249	−	4.50483i	0.671619	−	0.282104i
$256$	−3.79439			−0.237149
$257$			4.63017i			0.288822i	0.989518	+	0.144411i	$0.0461288\pi$
$257$			4.63017i			0.288822i	−0.989518	+	0.144411i	$0.953871\pi$
$258$	−6.16669	−	2.51858i	−0.383922	−	0.156800i
$259$	−16.8305	+	16.8305i	−1.04579	+	1.04579i
$260$	4.74859			0.294495
$261$	13.6867	−	8.58330i	0.847188	−	0.531293i
$262$	5.43984			0.336074
$263$	11.6315	−	11.6315i	0.717229	−	0.717229i	−0.250808	−	0.968037i	$-0.580696\pi$
$263$	11.6315	−	11.6315i	0.717229	−	0.717229i	0.968037	+	0.250808i	$0.0806962\pi$
$264$	−3.08958	−	1.26184i	−0.190151	−	0.0776606i
$265$		−	7.97602i		−	0.489963i
$266$	4.16329			0.255268
$267$	23.8793	−	10.0301i	1.46139	−	0.613834i
$268$	−16.6892			−1.01946
$269$	13.0452	+	13.0452i	0.795380	+	0.795380i	0.982363	−	0.186983i	$-0.0598709\pi$
$269$	13.0452	+	13.0452i	0.795380	+	0.795380i	−0.186983	+	0.982363i	$0.559871\pi$
$270$	2.72183	+	1.08027i	0.165645	+	0.0657431i
$271$	−12.4795	+	12.4795i	−0.758075	+	0.758075i	−0.975972	−	0.217897i	$-0.930080\pi$
$271$	−12.4795	+	12.4795i	−0.758075	+	0.758075i	0.217897	+	0.975972i	$0.430080\pi$
$272$	10.4252	−	10.4252i	0.632118	−	0.632118i
$273$	7.97923	−	19.5370i	0.482925	−	1.18243i
$274$		−	10.8663i		−	0.656459i
$275$	0.656522	−	0.656522i	0.0395898	−	0.0395898i
$276$	−5.29021	−	2.16061i	−0.318433	−	0.130053i
$277$	3.31802			0.199360			0.0996802	−	0.995020i	$-0.468218\pi$
$277$	3.31802			0.199360			0.0996802	+	0.995020i	$0.468218\pi$
$278$	1.10285	−	1.10285i	0.0661443	−	0.0661443i
$279$	0.122813	+	12.3833i	0.00735262	+	0.741372i
$280$	−6.33460	−	6.33460i	−0.378565	−	0.378565i
$281$			12.7931i			0.763171i	0.924334	+	0.381585i	$0.124622\pi$
$281$			12.7931i			0.763171i	−0.924334	+	0.381585i	$0.875378\pi$
$282$	7.95899	+	3.25058i	0.473951	+	0.193569i
$283$		−	13.3442i		−	0.793233i	−0.917984	−	0.396616i	$-0.870184\pi$
$283$		−	13.3442i		−	0.793233i	0.917984	−	0.396616i	$-0.129816\pi$
$284$			9.59572i			0.569401i
$285$	−1.14788	−	2.73282i	−0.0679944	−	0.161878i
$286$	−1.47688			−0.0873296
$287$	12.5720	+	12.5720i	0.742104	+	0.742104i
$288$	16.1623	−	0.160291i	0.952372	−	0.00944523i
$289$		−	28.1057i		−	1.65328i
$290$	−1.58684	−	2.58699i	−0.0931823	−	0.151913i
$291$	19.0533	−	8.00306i	1.11693	−	0.469148i
$292$	11.7520	+	11.7520i	0.687732	+	0.687732i
$293$	23.7072	−	23.7072i	1.38499	−	1.38499i	0.549490	−	0.835500i	$-0.314822\pi$
$293$	23.7072	−	23.7072i	1.38499	−	1.38499i	0.835500	−	0.549490i	$-0.185178\pi$
$294$	−10.4706	+	4.39803i	−0.610659	+	0.256498i
$295$		−	7.91809i		−	0.461009i
$296$	−11.4426			−0.665088
$297$	4.48416	+	1.77972i	0.260198	+	0.103270i
$298$	−3.23193	+	3.23193i	−0.187221	+	0.187221i
$299$	−5.53503			−0.320099
$300$	−1.10177	+	2.69768i	−0.0636109	+	0.155750i
$301$	−20.8301	−	20.8301i	−1.20063	−	1.20063i
$302$	5.02982	+	5.02982i	0.289434	+	0.289434i
$303$	−13.2123	+	5.54964i	−0.759028	+	0.318819i
$304$	−2.65644	−	2.65644i	−0.152357	−	0.152357i
$305$	−2.74726	−	2.74726i	−0.157308	−	0.157308i
$306$	7.94906	−	8.10831i	0.454418	−	0.463521i
$307$	1.47714	+	1.47714i	0.0843046	+	0.0843046i	0.748002	−	0.663697i	$-0.231014\pi$
$307$	1.47714	+	1.47714i	0.0843046	+	0.0843046i	−0.663697	+	0.748002i	$0.731014\pi$
$308$	−4.76801	−	4.76801i	−0.271682	−	0.271682i
$309$	−21.0506	−	8.59740i	−1.19753	−	0.489089i
$310$	2.32639			0.132130
$311$	10.8110	−	10.8110i	0.613034	−	0.613034i	−0.330702	−	0.943735i	$-0.607285\pi$
$311$	10.8110	−	10.8110i	0.613034	−	0.613034i	0.943735	+	0.330702i	$0.107285\pi$
$312$	9.35381	−	3.92893i	0.529555	−	0.222432i
$313$	34.5425			1.95246			0.976228	−	0.216746i	$-0.0695443\pi$
$313$	34.5425			1.95246			0.976228	+	0.216746i	$0.0695443\pi$
$314$			6.34277i			0.357943i
$315$	9.24764	+	9.06601i	0.521045	+	0.510812i
$316$	−5.28258	+	5.28258i	−0.297168	+	0.297168i
$317$	6.92109	+	6.92109i	0.388727	+	0.388727i	0.874233	−	0.485506i	$-0.161365\pi$
$317$	6.92109	+	6.92109i	0.388727	+	0.388727i	−0.485506	+	0.874233i	$0.661365\pi$
$318$	−3.01504	−	7.17807i	−0.169075	−	0.402526i
$319$	−2.61428	−	4.26201i	−0.146372	−	0.238627i
$320$			1.35417i			0.0757002i
$321$	3.69106	−	9.03750i	0.206015	−	0.504424i
$322$	3.37343	+	3.37343i	0.187994	+	0.187994i
$323$	−11.4934			−0.639510
$324$	−15.1386	+	0.300306i	−0.841032	+	0.0166836i
$325$			2.82252i			0.156565i
$326$			6.06019i			0.335643i
$327$	−0.0445913	+	0.109181i	−0.00246590	+	0.00603772i
$328$			8.54742i			0.471952i
$329$	26.8842	+	26.8842i	1.48217	+	1.48217i
$330$	0.342667	−	0.839015i	0.0188632	−	0.0461863i
$331$	8.20372	−	8.20372i	0.450917	−	0.450917i	−0.444741	−	0.895659i	$-0.646704\pi$
$331$	8.20372	−	8.20372i	0.450917	−	0.450917i	0.895659	+	0.444741i	$0.146704\pi$
$332$	−21.9725			−1.20590
$333$	16.5406	−	0.164043i	0.906419	−	0.00898948i
$334$	−1.29440	+	1.29440i	−0.0708264	+	0.0708264i
$335$		−	9.91992i		−	0.541983i
$336$	15.1951	+	6.20593i	0.828961	+	0.338561i
$337$	−14.5049	+	14.5049i	−0.790130	+	0.790130i	−0.981515	−	0.191385i	$-0.938702\pi$
$337$	−14.5049	+	14.5049i	−0.790130	+	0.790130i	0.191385	+	0.981515i	$0.438702\pi$
$338$	−2.00581	+	2.00581i	−0.109102	+	0.109102i
$339$	9.62080	+	22.9048i	0.522530	+	1.24402i
$340$	7.98966	+	7.98966i	0.433300	+	0.433300i
$341$	3.83268			0.207551
$342$	−2.06608	−	2.02550i	−0.111721	−	0.109527i
$343$	−20.0065			−1.08025
$344$		−	14.1619i		−	0.763558i
$345$	1.28425	−	3.14445i	0.0691414	−	0.169292i
$346$	6.11832	−	6.11832i	0.328923	−	0.328923i
$347$	−25.1323			−1.34917			−0.674586	−	0.738196i	$-0.735678\pi$
$347$	−25.1323			−1.34917			−0.674586	+	0.738196i	$0.735678\pi$
$348$	12.7449	+	9.15518i	0.683197	+	0.490769i
$349$	−4.42340			−0.236779			−0.118390	−	0.992967i	$-0.537773\pi$
$349$	−4.42340			−0.236779			−0.118390	+	0.992967i	$0.537773\pi$
$350$	1.72024	−	1.72024i	0.0919506	−	0.0919506i
$351$	−13.4648	+	5.81346i	−0.718700	+	0.310300i
$352$		−	5.00227i		−	0.266622i
$353$	32.6674			1.73871			0.869354	−	0.494190i	$-0.164535\pi$
$353$	32.6674			1.73871			0.869354	+	0.494190i	$0.164535\pi$
$354$	−2.99314	−	7.12594i	−0.159084	−	0.378739i
$355$	−5.70361			−0.302716
$356$	17.7892	+	17.7892i	0.942826	+	0.942826i
$357$	46.2970	−	19.4464i	2.45030	−	1.02921i
$358$	−1.75334	+	1.75334i	−0.0926666	+	0.0926666i
$359$	−13.7847	+	13.7847i	−0.727531	+	0.727531i	−0.970127	−	0.242596i	$-0.922001\pi$
$359$	−13.7847	+	13.7847i	−0.727531	+	0.727531i	0.242596	+	0.970127i	$0.422001\pi$
$360$	0.0617419	+	6.22550i	0.00325408	+	0.328113i
$361$		−	16.0714i		−	0.845861i
$362$	−8.65325	+	8.65325i	−0.454805	+	0.454805i
$363$	−6.63919	+	16.2559i	−0.348467	+	0.853216i
$364$	20.4986			1.07442
$365$	−6.98527	+	6.98527i	−0.365626	+	0.365626i
$366$	−3.51092	−	1.43392i	−0.183519	−	0.0749519i
$367$	15.2488	+	15.2488i	0.795982	+	0.795982i	0.982459	−	0.186477i	$-0.0597070\pi$
$367$	15.2488	+	15.2488i	0.795982	+	0.795982i	−0.186477	+	0.982459i	$0.559707\pi$
$368$		−	4.30493i		−	0.224410i
$369$	−0.122537	−	12.3555i	−0.00637901	−	0.643202i
$370$		−	3.10738i		−	0.161545i
$371$		−	34.4307i		−	1.78755i
$372$	−11.0903	+	4.65832i	−0.575006	+	0.241523i
$373$	32.0655			1.66029			0.830144	−	0.557550i	$-0.188258\pi$
$373$	32.0655			1.66029			0.830144	+	0.557550i	$0.188258\pi$
$374$	−2.48490	−	2.48490i	−0.128491	−	0.128491i
$375$	−1.60347	−	0.654884i	−0.0828030	−	0.0338181i
$376$			18.2779i			0.942611i
$377$	14.7813	+	3.54195i	0.761274	+	0.182420i
$378$	11.7495	+	4.66329i	0.604331	+	0.239854i
$379$	12.2562	+	12.2562i	0.629558	+	0.629558i	0.947957	−	0.318399i	$-0.103145\pi$
$379$	12.2562	+	12.2562i	0.629558	+	0.629558i	−0.318399	+	0.947957i	$0.603145\pi$
$380$	2.03585	−	2.03585i	0.104437	−	0.104437i
$381$	−10.4560	−	24.8931i	−0.535677	−	1.27531i
$382$		−	1.68797i		−	0.0863638i
$383$	−26.9635			−1.37777			−0.688886	−	0.724870i	$-0.741900\pi$
$383$	−26.9635			−1.37777			−0.688886	+	0.724870i	$0.741900\pi$
$384$	7.73953	+	18.4259i	0.394956	+	0.940294i
$385$	2.83406	−	2.83406i	0.144437	−	0.144437i
$386$	6.04673			0.307770
$387$	0.203026	+	20.4714i	0.0103204	+	1.04062i
$388$	14.1940	+	14.1940i	0.720593	+	0.720593i
$389$	−8.03415	−	8.03415i	−0.407347	−	0.407347i	0.473465	−	0.880813i	$-0.343003\pi$
$389$	−8.03415	−	8.03415i	−0.407347	−	0.407347i	−0.880813	+	0.473465i	$0.843003\pi$
$390$	1.06695	+	2.54014i	0.0540270	+	0.128625i
$391$	−9.31288	−	9.31288i	−0.470973	−	0.470973i
$392$	−17.0730	−	17.0730i	−0.862317	−	0.862317i
$393$	−6.47448	−	15.4141i	−0.326594	−	0.777541i
$394$	4.52582	+	4.52582i	0.228007	+	0.228007i
$395$	−3.13992	−	3.13992i	−0.157986	−	0.157986i
$396$	0.0464727	+	4.68589i	0.00233534	+	0.235475i
$397$	−30.6452			−1.53804			−0.769019	−	0.639226i	$-0.779255\pi$
$397$	−30.6452			−1.53804			−0.769019	+	0.639226i	$0.779255\pi$
$398$	7.30950	−	7.30950i	0.366392	−	0.366392i
$399$	−4.95514	−	11.7970i	−0.248067	−	0.590587i
$400$	−2.19524			−0.109762
$401$			19.1654i			0.957077i	0.878067	+	0.478538i	$0.158833\pi$
$401$			19.1654i			0.957077i	−0.878067	+	0.478538i	$0.841167\pi$
$402$	−3.74986	−	8.92750i	−0.187026	−	0.445263i
$403$	−8.23872	+	8.23872i	−0.410400	+	0.410400i
$404$	−9.84271	−	9.84271i	−0.489693	−	0.489693i
$405$	−0.178499	−	8.99823i	−0.00886968	−	0.447126i
$406$	−6.85003	−	11.1675i	−0.339961	−	0.554231i
$407$		−	5.11935i		−	0.253757i
$408$	22.3487	+	9.12755i	1.10642	+	0.451881i
$409$	−7.17266	−	7.17266i	−0.354665	−	0.354665i	0.507177	−	0.861842i	$-0.330689\pi$
$409$	−7.17266	−	7.17266i	−0.354665	−	0.354665i	−0.861842	+	0.507177i	$0.830689\pi$
$410$	−2.32116			−0.114634
$411$	−30.7905	+	12.9331i	−1.51878	+	0.637942i
$412$		−	22.0867i		−	1.08813i
$413$		−	34.1806i		−	1.68192i
$414$	−0.0328801	−	3.31533i	−0.00161597	−	0.162940i
$415$		−	13.0602i		−	0.641102i
$416$	10.7529	+	10.7529i	0.527203	+	0.527203i
$417$	−4.43760	−	1.81239i	−0.217310	−	0.0887529i
$418$	−0.633178	+	0.633178i	−0.0309697	+	0.0309697i
$419$	−15.5420			−0.759279			−0.379639	−	0.925135i	$-0.623952\pi$
$419$	−15.5420			−0.759279			−0.379639	+	0.925135i	$0.623952\pi$
$420$	−4.75611	+	11.6453i	−0.232075	+	0.568231i
$421$	19.2805	−	19.2805i	0.939672	−	0.939672i	−0.0586090	−	0.998281i	$-0.518667\pi$
$421$	19.2805	−	19.2805i	0.939672	−	0.939672i	0.998281	+	0.0586090i	$0.0186665\pi$
$422$		−	2.46780i		−	0.120131i
$423$	−0.262034	−	26.4212i	−0.0127405	−	1.28464i
$424$	11.7043	−	11.7043i	0.568411	−	0.568411i
$425$	−4.74898	+	4.74898i	−0.230360	+	0.230360i
$426$	−5.13300	+	2.15604i	−0.248695	+	0.104460i
$427$	−11.8593	−	11.8593i	−0.573913	−	0.573913i
$428$	9.48232			0.458345
$429$	1.75778	+	4.18484i	0.0848663	+	0.202046i
$430$	3.84584			0.185463
$431$		−	3.74079i		−	0.180187i	−0.995933	−	0.0900937i	$-0.971283\pi$
$431$		−	3.74079i		−	0.180187i	0.995933	−	0.0900937i	$-0.0287167\pi$
$432$	−4.52148	−	10.4724i	−0.217540	−	0.503854i
$433$	20.5998	−	20.5998i	0.989962	−	0.989962i	−0.00998784	−	0.999950i	$-0.503179\pi$
$433$	20.5998	−	20.5998i	0.989962	−	0.989962i	0.999950	+	0.00998784i	$0.00317928\pi$
$434$	10.0425			0.482056
$435$	−5.44175	+	7.57544i	−0.260912	+	0.363215i
$436$	−0.114555			−0.00548618
$437$	−2.37302	+	2.37302i	−0.113517	+	0.113517i
$438$	−3.64591	+	8.92696i	−0.174208	+	0.426547i
$439$			5.20976i			0.248648i	0.992242	+	0.124324i	$0.0396763\pi$
$439$			5.20976i			0.248648i	−0.992242	+	0.124324i	$0.960324\pi$
$440$	1.92681			0.0918570
$441$	24.9242	+	24.4347i	1.18687	+	1.16356i
$442$	10.6831			0.508142
$443$	17.1342	+	17.1342i	0.814070	+	0.814070i	0.985241	−	0.171171i	$-0.0547552\pi$
$443$	17.1342	+	17.1342i	0.814070	+	0.814070i	−0.171171	+	0.985241i	$0.554755\pi$
$444$	6.22217	+	14.8135i	0.295291	+	0.703016i
$445$	−10.5737	+	10.5737i	−0.501243	+	0.501243i
$446$	10.9169	−	10.9169i	0.516932	−	0.516932i
$447$	13.0045	+	5.31127i	0.615094	+	0.251214i
$448$			5.84564i			0.276180i
$449$	−10.1699	+	10.1699i	−0.479946	+	0.479946i	−0.905114	−	0.425168i	$-0.860215\pi$
$449$	−10.1699	+	10.1699i	−0.479946	+	0.479946i	0.425168	+	0.905114i	$0.360215\pi$
$450$	−1.69061	+	0.0167668i	−0.0796962	+	0.000790393i
$451$	−3.82406			−0.180068
$452$	−17.0632	+	17.0632i	−0.802586	+	0.802586i
$453$	8.26586	−	20.2388i	0.388364	−	0.950903i
$454$	−1.88120	−	1.88120i	−0.0882891	−	0.0882891i
$455$			12.1842i			0.571203i
$456$	2.32579	−	5.69467i	0.108915	−	0.266677i
$457$		−	1.73517i		−	0.0811678i	−0.999176	−	0.0405839i	$-0.987078\pi$
$457$		−	1.73517i		−	0.0811678i	0.999176	−	0.0405839i	$-0.0129218\pi$
$458$		−	12.9897i		−	0.606967i
$459$	−32.4364	−	12.8737i	−1.51400	−	0.600894i
$460$	3.29922			0.153827
$461$	16.7396	+	16.7396i	0.779640	+	0.779640i	0.979769	−	0.200130i	$-0.0641363\pi$
$461$	16.7396	+	16.7396i	0.779640	+	0.779640i	−0.200130	+	0.979769i	$0.564136\pi$
$462$	1.47922	−	3.62184i	0.0688195	−	0.168503i
$463$		−	0.797061i		−	0.0370426i	−0.999828	−	0.0185213i	$-0.994104\pi$
$463$		−	0.797061i		−	0.0370426i	0.999828	−	0.0185213i	$-0.00589585\pi$
$464$	−2.75479	+	11.4963i	−0.127888	+	0.533702i
$465$	−2.76886	−	6.59198i	−0.128403	−	0.305696i
$466$	7.95188	+	7.95188i	0.368364	+	0.368364i
$467$	−9.03132	+	9.03132i	−0.417919	+	0.417919i	−0.884486	−	0.466567i	$-0.845491\pi$
$467$	−9.03132	+	9.03132i	−0.417919	+	0.417919i	0.466567	+	0.884486i	$0.345491\pi$
$468$	−10.1727	−	9.97288i	−0.470232	−	0.460997i
$469$		−	42.8221i		−	1.97734i
$470$	−4.96359			−0.228953
$471$	17.9727	−	7.54915i	0.828137	−	0.347846i
$472$	11.6193	−	11.6193i	0.534821	−	0.534821i
$473$	6.33594			0.291327
$474$	−4.01272	−	1.63886i	−0.184310	−	0.0752753i
$475$	1.21009	+	1.21009i	0.0555227	+	0.0555227i
$476$	34.4896	+	34.4896i	1.58083	+	1.58083i
$477$	−16.7511	+	17.0867i	−0.766979	+	0.782344i
$478$	6.73042	+	6.73042i	0.307842	+	0.307842i
$479$	−0.198959	−	0.198959i	−0.00909069	−	0.00909069i	0.702547	−	0.711638i	$-0.252046\pi$
$479$	−0.198959	−	0.198959i	−0.00909069	−	0.00909069i	−0.711638	+	0.702547i	$0.752046\pi$
$480$	−8.60361	+	3.61382i	−0.392699	+	0.164947i
$481$	11.0046	+	11.0046i	0.501765	+	0.501765i
$482$	−7.36310	−	7.36310i	−0.335380	−	0.335380i
$483$	5.54380	−	13.5739i	0.252252	−	0.617634i
$484$	−17.0560			−0.775275
$485$	−8.43681	+	8.43681i	−0.383096	+	0.383096i
$486$	−3.56209	−	8.03054i	−0.161580	−	0.364273i
$487$	23.1549			1.04925			0.524624	−	0.851334i	$-0.324206\pi$
$487$	23.1549			1.04925			0.524624	+	0.851334i	$0.324206\pi$
$488$		−	8.06286i		−	0.364989i
$489$	17.1720	−	7.21283i	0.776544	−	0.326175i
$490$	4.63639	−	4.63639i	0.209451	−	0.209451i
$491$	−0.0398597	−	0.0398597i	−0.00179884	−	0.00179884i	0.706207	−	0.708006i	$-0.250405\pi$
$491$	−0.0398597	−	0.0398597i	−0.00179884	−	0.00179884i	−0.708006	+	0.706207i	$0.750405\pi$
$492$	11.0654	−	4.64784i	0.498866	−	0.209541i
$493$	18.9106	+	30.8295i	0.851689	+	1.38849i
$494$		−	2.72216i		−	0.122476i
$495$	−2.78525	+	0.0276229i	−0.125188	+	0.00124156i
$496$	−6.40775	−	6.40775i	−0.287716	−	0.287716i
$497$	−24.6212			−1.10441
$498$	−4.93695	−	11.7537i	−0.221230	−	0.526694i
$499$		−	21.1013i		−	0.944622i	−0.881432	−	0.472311i	$-0.843420\pi$
$499$		−	21.1013i		−	0.944622i	0.881432	−	0.472311i	$-0.156580\pi$
$500$		−	1.68239i		−	0.0752390i
$501$	5.20836	+	2.12718i	0.232692	+	0.0950353i
$502$		−	7.74564i		−	0.345705i
$503$	−1.27517	−	1.27517i	−0.0568571	−	0.0568571i	0.678107	−	0.734964i	$-0.262801\pi$
$503$	−1.27517	−	1.27517i	−0.0568571	−	0.0568571i	−0.734964	+	0.678107i	$0.762801\pi$
$504$	0.266526	+	26.8741i	0.0118720	+	1.19707i
$505$	5.85042	−	5.85042i	0.260340	−	0.260340i
$506$	−1.02610			−0.0456159
$507$	8.07092	+	3.29629i	0.358442	+	0.146394i
$508$	18.5445	−	18.5445i	0.822779	−	0.822779i
$509$			38.4978i			1.70639i	0.521595	+	0.853193i	$0.325337\pi$
$509$			38.4978i			1.70639i	−0.521595	+	0.853193i	$0.674663\pi$
$510$	−2.47870	+	6.06906i	−0.109759	+	0.268742i
$511$	−30.1539	+	30.1539i	−1.33393	+	1.33393i
$512$	−14.8059	+	14.8059i	−0.654335	+	0.654335i
$513$	−3.28036	+	8.26513i	−0.144831	+	0.364915i
$514$	−1.84513	−	1.84513i	−0.0813850	−	0.0813850i
$515$	13.1281			0.578494
$516$	−18.3338	+	7.70084i	−0.807100	+	0.339010i
$517$	−8.17742			−0.359643
$518$		−	13.4139i		−	0.589373i
$519$	−24.6187	−	10.0547i	−1.08064	−	0.441351i
$520$	−4.14186	+	4.14186i	−0.181633	+	0.181633i
$521$	−19.9763			−0.875176			−0.437588	−	0.899176i	$-0.644167\pi$
$521$	−19.9763			−0.875176			−0.437588	+	0.899176i	$0.644167\pi$
$522$	−2.03373	+	8.87462i	−0.0890138	+	0.388432i
$523$	−18.8344			−0.823569			−0.411784	−	0.911281i	$-0.635094\pi$
$523$	−18.8344			−0.823569			−0.411784	+	0.911281i	$0.635094\pi$
$524$	11.4830	−	11.4830i	0.501636	−	0.501636i
$525$	−6.92184	−	2.82699i	−0.302094	−	0.123380i
$526$			9.27032i			0.404205i
$527$	−27.7239			−1.20767
$528$	−3.25480	+	1.36713i	−0.141647	+	0.0594967i
$529$	19.1544			0.832799
$530$	3.17845	+	3.17845i	0.138063	+	0.138063i
$531$	−16.6294	+	16.9626i	−0.721655	+	0.736112i
$532$	8.78831	−	8.78831i	0.381022	−	0.381022i
$533$	8.22020	−	8.22020i	0.356056	−	0.356056i
$534$	−5.51889	+	13.5129i	−0.238826	+	0.584761i
$535$			5.63620i			0.243674i
$536$	14.5569	−	14.5569i	0.628760	−	0.628760i
$537$	7.05501	+	2.88138i	0.304446	+	0.124341i
$538$	−10.3970			−0.448248
$539$	7.63836	−	7.63836i	0.329007	−	0.329007i
$540$	8.02588	−	3.46518i	0.345379	−	0.149118i
$541$	−10.1470	−	10.1470i	−0.436255	−	0.436255i	0.454494	−	0.890750i	$-0.349820\pi$
$541$	−10.1470	−	10.1470i	−0.436255	−	0.436255i	−0.890750	+	0.454494i	$0.849820\pi$
$542$		−	9.94616i		−	0.427224i
$543$	34.8187	+	14.2205i	1.49421	+	0.610260i
$544$			36.1842i			1.55138i
$545$		−	0.0680903i		−	0.00291667i
$546$	4.60578	+	10.9652i	0.197109	+	0.469269i
$547$	−11.0199			−0.471178			−0.235589	−	0.971853i	$-0.575702\pi$
$547$	−11.0199			−0.471178			−0.235589	+	0.971853i	$0.575702\pi$
$548$	−22.9378	−	22.9378i	−0.979854	−	0.979854i
$549$	0.115590	+	11.6551i	0.00493327	+	0.497426i
$550$			0.523249i			0.0223114i
$551$	7.85567	−	4.81860i	0.334663	−	0.205279i
$552$	6.49883	−	2.72974i	0.276609	−	0.116185i
$553$	−13.5543	−	13.5543i	−0.576389	−	0.576389i
$554$	−1.32223	+	1.32223i	−0.0561763	+	0.0561763i
$555$	−8.80499	+	3.69840i	−0.373751	+	0.156988i
$556$		−	4.65601i		−	0.197459i
$557$	36.5613			1.54915			0.774577	−	0.632480i	$-0.217963\pi$
$557$	36.5613			1.54915			0.774577	+	0.632480i	$0.217963\pi$
$558$	−4.98371	−	4.88583i	−0.210977	−	0.206834i
$559$	−13.6197	+	13.6197i	−0.576053	+	0.576053i
$560$	−9.47637			−0.400450
$561$	−4.08361	+	9.99865i	−0.172410	+	0.422144i
$562$	−5.09805	−	5.09805i	−0.215048	−	0.215048i
$563$	25.7361	+	25.7361i	1.08465	+	1.08465i	0.996069	+	0.0885779i	$0.0282322\pi$
$563$	25.7361	+	25.7361i	1.08465	+	1.08465i	0.0885779	+	0.996069i	$0.471768\pi$
$564$	23.6623	−	9.93901i	0.996365	−	0.418508i
$565$	−10.1422	−	10.1422i	−0.426686	−	0.426686i
$566$	5.31769	+	5.31769i	0.223519	+	0.223519i
$567$	−0.770541	−	38.8434i	−0.0323597	−	1.63127i
$568$	−8.36968	−	8.36968i	−0.351184	−	0.351184i
$569$	−19.2581	−	19.2581i	−0.807340	−	0.807340i	0.176891	−	0.984231i	$-0.443396\pi$
$569$	−19.2581	−	19.2581i	−0.807340	−	0.807340i	−0.984231	+	0.176891i	$0.943396\pi$
$570$	1.54646	+	0.631598i	0.0647740	+	0.0264547i
$571$	33.9675			1.42150			0.710749	−	0.703446i	$-0.248356\pi$
$571$	33.9675			1.42150			0.710749	+	0.703446i	$0.248356\pi$
$572$	−3.11755	+	3.11755i	−0.130351	+	0.130351i
$573$	−4.78297	+	2.00901i	−0.199811	+	0.0839277i
$574$	−10.0199			−0.418223
$575$			1.96103i			0.0817805i
$576$	2.84399	−	2.90097i	0.118500	−	0.120874i
$577$	20.2055	−	20.2055i	0.841166	−	0.841166i	−0.147844	−	0.989011i	$-0.547233\pi$
$577$	20.2055	−	20.2055i	0.841166	−	0.841166i	0.989011	+	0.147844i	$0.0472335\pi$
$578$	11.2001	+	11.2001i	0.465864	+	0.465864i
$579$	−7.19680	−	17.1338i	−0.299089	−	0.712057i
$580$	−8.81055	−	2.11122i	−0.365838	−	0.0876637i
$581$		−	56.3782i		−	2.33896i
$582$	−4.40354	+	10.7820i	−0.182532	+	0.446928i
$583$	5.23643	+	5.23643i	0.216871	+	0.216871i
$584$	−20.5009			−0.848332
$585$	5.92779	−	6.04655i	0.245084	−	0.249994i
$586$			18.8947i			0.780532i
$587$		−	36.9368i		−	1.52454i	−0.647257	−	0.762272i	$-0.724084\pi$
$587$		−	36.9368i		−	1.52454i	0.647257	−	0.762272i	$-0.275916\pi$
$588$	−12.8187	+	31.3863i	−0.528634	+	1.29435i
$589$			7.06433i			0.291081i
$590$	3.15536	+	3.15536i	0.129904	+	0.129904i
$591$	7.43760	−	18.2108i	0.305942	−	0.749093i
$592$	−8.55891	+	8.55891i	−0.351769	+	0.351769i
$593$	30.7125			1.26121			0.630606	−	0.776103i	$-0.282806\pi$
$593$	30.7125			1.26121			0.630606	+	0.776103i	$0.282806\pi$
$594$	−2.49616	+	1.07772i	−0.102419	+	0.0442194i
$595$	−20.5003	+	20.5003i	−0.840431	+	0.840431i
$596$			13.6446i			0.558905i
$597$	−29.4117	−	12.0122i	−1.20374	−	0.491628i
$598$	2.20571	−	2.20571i	0.0901983	−	0.0901983i
$599$	−4.07455	+	4.07455i	−0.166482	+	0.166482i	−0.785431	−	0.618949i	$-0.787559\pi$
$599$	−4.07455	+	4.07455i	−0.166482	+	0.166482i	0.618949	+	0.785431i	$0.287559\pi$
$600$	−1.39199	−	3.31400i	−0.0568279	−	0.135293i
$601$	2.77137	+	2.77137i	0.113047	+	0.113047i	0.761367	−	0.648321i	$-0.224528\pi$
$601$	2.77137	+	2.77137i	0.113047	+	0.113047i	−0.648321	+	0.761367i	$0.724528\pi$
$602$	16.6016			0.676632
$603$	−20.8336	+	21.2510i	−0.848410	+	0.865407i
$604$	21.2350			0.864039
$605$		−	10.1380i		−	0.412167i
$606$	3.05359	−	7.47665i	0.124043	−	0.303718i
$607$	−31.3196	+	31.3196i	−1.27123	+	1.27123i	−0.325779	+	0.945446i	$0.605627\pi$
$607$	−31.3196	+	31.3196i	−1.27123	+	1.27123i	−0.945446	+	0.325779i	$0.894373\pi$
$608$	9.22010			0.373925
$609$	−23.4909	+	32.7015i	−0.951898	+	1.32513i
$610$	2.18957			0.0886531
$611$	17.5782	−	17.5782i	0.711137	−	0.711137i
$612$	−0.336162	−	33.8956i	−0.0135886	−	1.37015i
$613$		−	20.2537i		−	0.818039i	−0.912526	−	0.409020i	$-0.865871\pi$
$613$		−	20.2537i		−	0.818039i	0.912526	−	0.409020i	$-0.134129\pi$
$614$	−1.17728			−0.0475111
$615$	2.76264	+	6.57716i	0.111400	+	0.265217i
$616$	8.31760			0.335126
$617$	−12.2176	−	12.2176i	−0.491862	−	0.491862i	0.417031	−	0.908892i	$-0.363071\pi$
$617$	−12.2176	−	12.2176i	−0.491862	−	0.491862i	−0.908892	+	0.417031i	$0.863071\pi$
$618$	11.8147	−	4.96261i	0.475259	−	0.199625i
$619$	21.7267	−	21.7267i	0.873272	−	0.873272i	−0.119556	−	0.992827i	$-0.538147\pi$
$619$	21.7267	−	21.7267i	0.873272	−	0.873272i	0.992827	+	0.119556i	$0.0381470\pi$
$620$	4.91079	−	4.91079i	0.197222	−	0.197222i
$621$	−9.35509	+	4.03907i	−0.375407	+	0.162082i
$622$			8.61635i			0.345484i
$623$	−45.6445	+	45.6445i	−1.82871	+	1.82871i
$624$	4.05773	−	9.93529i	0.162439	−	0.397730i
$625$	1.00000			0.0400000
$626$	−13.7652	+	13.7652i	−0.550168	+	0.550168i
$627$	2.54776	+	1.04055i	0.101748	+	0.0415554i
$628$	13.3890	+	13.3890i	0.534279	+	0.534279i
$629$			37.0311i			1.47653i
$630$	−7.29800	+	0.0723785i	−0.290759	+	0.00288363i
$631$		−	2.58896i		−	0.103065i	−0.998671	−	0.0515324i	$-0.983589\pi$
$631$		−	2.58896i		−	0.103065i	0.998671	−	0.0515324i	$-0.0164105\pi$
$632$		−	9.21526i		−	0.366563i
$633$	−6.99269	+	2.93718i	−0.277935	+	0.116742i
$634$	−5.51612			−0.219073
$635$	11.0227	+	11.0227i	0.437422	+	0.437422i
$636$	−21.5167	−	8.78777i	−0.853193	−	0.348458i
$637$			32.8388i			1.30112i
$638$	2.74021	+	0.656620i	0.108486	+	0.0259958i
$639$	12.2186	+	11.9786i	0.483359	+	0.473866i
$640$	−8.15899	−	8.15899i	−0.322512	−	0.322512i
$641$	10.4313	−	10.4313i	0.412011	−	0.412011i	−0.470427	−	0.882439i	$-0.655900\pi$
$641$	10.4313	−	10.4313i	0.412011	−	0.412011i	0.882439	+	0.470427i	$0.155900\pi$
$642$	2.13056	+	5.07234i	0.0840865	+	0.200189i
$643$			10.7250i			0.422951i	0.977383	+	0.211476i	$0.0678269\pi$
$643$			10.7250i			0.422951i	−0.977383	+	0.211476i	$0.932173\pi$
$644$	14.2420			0.561214
$645$	−4.57731	−	10.8974i	−0.180231	−	0.429086i
$646$	4.58012	−	4.58012i	0.180203	−	0.180203i
$647$	34.0405			1.33827			0.669136	−	0.743140i	$-0.266665\pi$
$647$	34.0405			1.33827			0.669136	+	0.743140i	$0.266665\pi$
$648$	12.9424	−	13.4663i	0.508425	−	0.529005i
$649$	5.19840	+	5.19840i	0.204055	+	0.204055i
$650$	−1.12477	−	1.12477i	−0.0441173	−	0.0441173i
$651$	−11.9526	−	28.4561i	−0.468458	−	1.11528i
$652$	12.7925	+	12.7925i	0.500993	+	0.500993i
$653$	6.40111	+	6.40111i	0.250495	+	0.250495i	0.821173	−	0.570679i	$-0.193320\pi$
$653$	6.40111	+	6.40111i	0.250495	+	0.250495i	−0.570679	+	0.821173i	$0.693320\pi$
$654$	−0.0257390	−	0.0612783i	−0.00100648	−	0.00239617i
$655$	6.82538	+	6.82538i	0.266690	+	0.266690i
$656$	6.39334	+	6.39334i	0.249618	+	0.249618i
$657$	29.6345	−	0.293903i	1.15615	−	0.0114662i
$658$	−21.4267			−0.835301
$659$	−5.18622	+	5.18622i	−0.202027	+	0.202027i	−0.800868	−	0.598841i	$-0.795628\pi$
$659$	−5.18622	+	5.18622i	−0.202027	+	0.202027i	0.598841	+	0.800868i	$0.295628\pi$
$660$	−1.04774	−	2.49442i	−0.0407834	−	0.0970952i
$661$	−10.1675			−0.395468			−0.197734	−	0.980256i	$-0.563358\pi$
$661$	−10.1675			−0.395468			−0.197734	+	0.980256i	$0.563358\pi$
$662$			6.53838i			0.254121i
$663$	−12.7150	−	30.2712i	−0.493809	−	1.17564i
$664$	19.1651	−	19.1651i	0.743749	−	0.743749i
$665$	5.22369	+	5.22369i	0.202566	+	0.202566i
$666$	−6.52606	+	6.65680i	−0.252880	+	0.257946i
$667$	10.2697	+	2.46087i	0.397645	+	0.0952854i
$668$			5.46471i			0.211436i
$669$	−43.9272	−	17.9406i	−1.69832	−	0.693623i
$670$	3.95309	+	3.95309i	0.152721	+	0.152721i
$671$	3.60728			0.139257
$672$	−37.1399	+	15.6001i	−1.43270	+	0.601785i
$673$			17.7732i			0.685106i	0.939498	+	0.342553i	$0.111292\pi$
$673$			17.7732i			0.685106i	−0.939498	+	0.342553i	$0.888708\pi$
$674$		−	11.5604i		−	0.445290i
$675$	2.05967	+	4.77051i	0.0792768	+	0.183617i
$676$			8.46816i			0.325699i
$677$	5.11287	+	5.11287i	0.196504	+	0.196504i	0.798499	−	0.601996i	$-0.205628\pi$
$677$	5.11287	+	5.11287i	0.196504	+	0.196504i	−0.601996	+	0.798499i	$0.705628\pi$
$678$	−12.9615	−	5.29366i	−0.497782	−	0.203302i
$679$	−36.4198	+	36.4198i	−1.39767	+	1.39767i
$680$	−13.9377			−0.534485
$681$	−3.09151	+	7.56951i	−0.118467	+	0.290064i
$682$	−1.52732	+	1.52732i	−0.0584843	+	0.0584843i
$683$		−	1.13129i		−	0.0432875i	−0.999766	−	0.0216437i	$-0.993110\pi$
$683$		−	1.13129i		−	0.0432875i	0.999766	−	0.0216437i	$-0.00688996\pi$
$684$	−8.63695	+	0.0856577i	−0.330242	+	0.00327520i
$685$	13.6340	−	13.6340i	0.520929	−	0.520929i
$686$	7.97260	−	7.97260i	0.304395	−	0.304395i
$687$	−36.8071	+	15.4603i	−1.40428	+	0.589846i
$688$	−10.5929	−	10.5929i	−0.403850	−	0.403850i
$689$	−22.5124			−0.857656
$690$	0.741294	+	1.76484i	0.0282206	+	0.0671863i
$691$	10.1309			0.385399			0.192700	−	0.981258i	$-0.438276\pi$
$691$	10.1309			0.385399			0.192700	+	0.981258i	$0.438276\pi$
$692$		−	25.8304i		−	0.981924i
$693$	−12.0233	+	0.119242i	−0.456728	+	0.00452963i
$694$	10.0152	−	10.0152i	0.380173	−	0.380173i
$695$	2.76749			0.104977
$696$	−19.1019	+	3.13105i	−0.724056	+	0.118682i
$697$	27.6615			1.04776
$698$	1.76273	−	1.76273i	0.0667202	−	0.0667202i
$699$	13.0679	−	31.9965i	0.494273	−	1.21022i
$700$		−	7.26253i		−	0.274498i
$701$	−26.8245			−1.01315			−0.506575	−	0.862196i	$-0.669089\pi$
$701$	−26.8245			−1.01315			−0.506575	+	0.862196i	$0.669089\pi$
$702$	3.04908	−	7.68241i	0.115080	−	0.289954i
$703$	9.43591			0.355882
$704$	−0.889040	−	0.889040i	−0.0335070	−	0.0335070i
$705$	5.90766	+	14.0647i	0.222495	+	0.529707i
$706$	−13.0180	+	13.0180i	−0.489937	+	0.489937i
$707$	25.2550	−	25.2550i	0.949810	−	0.949810i
$708$	−21.3604	−	8.72394i	−0.802774	−	0.327866i
$709$		−	24.8414i		−	0.932939i	−0.884537	−	0.466470i	$-0.845526\pi$
$709$		−	24.8414i		−	0.932939i	0.884537	−	0.466470i	$-0.154474\pi$
$710$	2.27289	−	2.27289i	0.0853001	−	0.0853001i
$711$	0.132111	+	13.3209i	0.00495455	+	0.499572i
$712$	−31.0326			−1.16299
$713$	−5.72409	+	5.72409i	−0.214369	+	0.214369i
$714$	−10.7000	+	26.1988i	−0.400438	+	0.980465i
$715$	−1.85304	−	1.85304i	−0.0692999	−	0.0692999i
$716$			7.40225i			0.276635i
$717$	11.0606	−	27.0816i	0.413065	−	1.01138i
$718$		−	10.9865i		−	0.410011i
$719$		−	2.99765i		−	0.111794i	−0.998437	−	0.0558968i	$-0.982198\pi$
$719$		−	2.99765i		−	0.111794i	0.998437	−	0.0558968i	$-0.0178018\pi$
$720$	4.70276	+	4.61040i	0.175262	+	0.171819i
$721$	56.6712			2.11055
$722$	6.40445	+	6.40445i	0.238349	+	0.238349i
$723$	−12.1003	+	29.6274i	−0.450015	+	1.10185i
$724$			36.5324i			1.35772i
$725$	1.25489	−	5.23691i	0.0466055	−	0.194494i
$726$	−3.83228	−	9.12372i	−0.142229	−	0.338613i
$727$	32.2381	+	32.2381i	1.19565	+	1.19565i	0.975457	+	0.220188i	$0.0706672\pi$
$727$	32.2381	+	32.2381i	1.19565	+	1.19565i	0.220188	+	0.975457i	$0.429333\pi$
$728$	−17.8795	+	17.8795i	−0.662659	+	0.662659i
$729$	−18.5155	+	19.6514i	−0.685759	+	0.727828i
$730$		−	5.56726i		−	0.206054i
$731$	−45.8313			−1.69513
$732$	−10.4381	+	4.38436i	−0.385803	+	0.162051i
$733$	−14.4826	+	14.4826i	−0.534926	+	0.534926i	−0.922034	−	0.387108i	$-0.873474\pi$
$733$	−14.4826	+	14.4826i	−0.534926	+	0.534926i	0.387108	+	0.922034i	$0.373474\pi$
$734$	−12.1533			−0.448588
$735$	−18.6558	−	7.61931i	−0.688128	−	0.281042i
$736$	7.47088	+	7.47088i	0.275380	+	0.275380i
$737$	6.51265	+	6.51265i	0.239896	+	0.239896i
$738$	4.97251	+	4.87484i	0.183040	+	0.179445i
$739$	0.0615536	+	0.0615536i	0.00226429	+	0.00226429i	0.708238	−	0.705974i	$-0.249490\pi$
$739$	0.0615536	+	0.0615536i	0.00226429	+	0.00226429i	−0.705974	+	0.708238i	$0.749490\pi$
$740$	−6.55940	−	6.55940i	−0.241128	−	0.241128i
$741$	−7.71342	+	3.23991i	−0.283359	+	0.119021i
$742$	13.7207	+	13.7207i	0.503701	+	0.503701i
$743$	−4.42982	−	4.42982i	−0.162514	−	0.162514i	0.621165	−	0.783680i	$-0.286660\pi$
$743$	−4.42982	−	4.42982i	−0.162514	−	0.162514i	−0.783680	+	0.621165i	$0.786660\pi$
$744$	5.61018	−	13.7364i	0.205679	−	0.503602i
$745$	−8.11024			−0.297136
$746$	−12.7781	+	12.7781i	−0.467840	+	0.467840i
$747$	−27.4289	+	27.9784i	−1.00357	+	1.02367i
$748$	−10.4908			−0.383581
$749$			24.3302i			0.889008i
$750$	0.899957	−	0.378013i	0.0328618	−	0.0138031i
$751$	16.2807	−	16.2807i	0.594092	−	0.594092i	−0.344642	−	0.938734i	$-0.612000\pi$
$751$	16.2807	−	16.2807i	0.594092	−	0.594092i	0.938734	+	0.344642i	$0.112000\pi$
$752$	13.6716	+	13.6716i	0.498552	+	0.498552i
$753$	−21.9478	+	9.21884i	−0.799822	+	0.335953i
$754$	−7.30181	+	4.47888i	−0.265916	+	0.163111i
$755$			12.6219i			0.459357i
$756$	34.6459	−	14.9584i	1.26006	−	0.544033i
$757$	11.3147	+	11.3147i	0.411239	+	0.411239i	0.882170	−	0.470931i	$-0.156082\pi$
$757$	11.3147	+	11.3147i	0.411239	+	0.411239i	−0.470931	+	0.882170i	$0.656082\pi$
$758$	−9.76819			−0.354797
$759$	1.22127	+	2.90754i	0.0443292	+	0.105537i
$760$			3.55146i			0.128825i
$761$		−	48.7815i		−	1.76833i	−0.467175	−	0.884165i	$-0.654728\pi$
$761$		−	48.7815i		−	1.76833i	0.467175	−	0.884165i	$-0.345272\pi$
$762$	14.0866	+	5.75321i	0.510305	+	0.208417i
$763$		−	0.293931i		−	0.0106410i
$764$	−3.56314	−	3.56314i	−0.128910	−	0.128910i
$765$	20.1472	−	0.199812i	0.728425	−	0.00722421i
$766$	10.7450	−	10.7450i	0.388232	−	0.388232i
$767$	−22.3489			−0.806973
$768$	−6.08420	−	2.48489i	−0.219545	−	0.0896656i
$769$	−32.6307	+	32.6307i	−1.17669	+	1.17669i	−0.196113	+	0.980581i	$0.562832\pi$
$769$	−32.6307	+	32.6307i	−1.17669	+	1.17669i	−0.980581	+	0.196113i	$0.937168\pi$
$770$			2.25875i			0.0813997i
$771$	−3.03223	+	7.42436i	−0.109203	+	0.267382i
$772$	12.7641	−	12.7641i	0.459389	−	0.459389i
$773$	7.58007	−	7.58007i	0.272636	−	0.272636i	−0.557524	−	0.830161i	$-0.688249\pi$
$773$	7.58007	−	7.58007i	0.272636	−	0.272636i	0.830161	+	0.557524i	$0.188249\pi$
$774$	−8.23875	−	8.07694i	−0.296136	−	0.290320i
$775$	2.91893	+	2.91893i	0.104851	+	0.104851i
$776$	−24.7610			−0.888866
$777$	−38.0092	+	15.9652i	−1.36357	+	0.572748i
$778$	6.40322			0.229567
$779$		−	7.04844i		−	0.252537i
$780$	7.61423	+	3.10977i	0.272633	+	0.111348i
$781$	3.74454	−	3.74454i	0.133990	−	0.133990i
$782$	7.42238			0.265424
$783$	27.5674	−	4.79986i	0.985178	−	0.171533i
$784$	−25.5407			−0.912169
$785$	−7.95829	+	7.95829i	−0.284044	+	0.284044i
$786$	8.72263	+	3.56246i	0.311126	+	0.127069i
$787$		−	14.9040i		−	0.531270i	−0.964074	−	0.265635i	$-0.914418\pi$
$787$		−	14.9040i		−	0.531270i	0.964074	−	0.265635i	$-0.0855817\pi$
$788$	19.1071			0.680664
$789$	26.2681	−	11.0335i	0.935169	−	0.392804i
$790$	2.50252			0.0890356
$791$	−43.7817	−	43.7817i	−1.55670	−	1.55670i
$792$	−4.12771	−	4.04664i	−0.146672	−	0.143791i
$793$	−7.75419	+	7.75419i	−0.275359	+	0.275359i
$794$	12.2121	−	12.2121i	0.433392	−	0.433392i
$795$	5.22337	−	12.7893i	0.185254	−	0.453591i
$796$		−	30.8594i		−	1.09378i
$797$	25.0328	−	25.0328i	0.886709	−	0.886709i	−0.107497	−	0.994205i	$-0.534284\pi$
$797$	25.0328	−	25.0328i	0.886709	−	0.886709i	0.994205	+	0.107497i	$0.0342835\pi$
$798$	6.67572	+	2.72647i	0.236318	+	0.0965160i
$799$	59.1518			2.09264
$800$	3.80968	−	3.80968i	0.134692	−	0.134692i
$801$	44.8584	−	0.444887i	1.58499	−	0.0157193i
$802$	−7.63744	−	7.63744i	−0.269687	−	0.269687i
$803$		−	9.17196i		−	0.323671i
$804$	−26.7607	−	10.9295i	−0.943778	−	0.385454i
$805$			8.46532i			0.298363i
$806$		−	6.56627i		−	0.231287i
$807$	12.3745	+	29.4607i	0.435604	+	1.03707i
$808$	17.1702			0.604046
$809$	−6.04263	−	6.04263i	−0.212448	−	0.212448i	0.592859	−	0.805306i	$-0.297999\pi$
$809$	−6.04263	−	6.04263i	−0.212448	−	0.212448i	−0.805306	+	0.592859i	$0.797999\pi$
$810$	3.65693	+	3.51467i	0.128491	+	0.123493i
$811$		−	30.6502i		−	1.07628i	−0.842857	−	0.538138i	$-0.819128\pi$
$811$		−	30.6502i		−	1.07628i	0.842857	−	0.538138i	$-0.180872\pi$
$812$	−38.0332	−	9.11368i	−1.33470	−	0.319827i
$813$	−28.1831	+	11.8379i	−0.988426	+	0.415173i
$814$	2.04007	+	2.04007i	0.0715043	+	0.0715043i
$815$	−7.60375	+	7.60375i	−0.266348	+	0.266348i
$816$	23.5438	−	9.88920i	0.824196	−	0.346191i
$817$			11.6783i			0.408572i
$818$	5.71662			0.199877
$819$	25.5890	−	26.1016i	0.894151	−	0.912064i
$820$	−4.89975	+	4.89975i	−0.171107	+	0.171107i
$821$	6.61455			0.230849			0.115425	−	0.993316i	$-0.463177\pi$
$821$	6.61455			0.230849			0.115425	+	0.993316i	$0.463177\pi$
$822$	7.11618	−	17.4239i	0.248205	−	0.607727i
$823$	21.7215	+	21.7215i	0.757165	+	0.757165i	0.975806	−	0.218640i	$-0.0701621\pi$
$823$	21.7215	+	21.7215i	0.757165	+	0.757165i	−0.218640	+	0.975806i	$0.570162\pi$
$824$	19.2647	+	19.2647i	0.671117	+	0.671117i
$825$	1.48266	−	0.622769i	0.0516196	−	0.0216821i
$826$	13.6210	+	13.6210i	0.473935	+	0.473935i
$827$	33.7286	+	33.7286i	1.17286	+	1.17286i	0.981525	+	0.191333i	$0.0612811\pi$
$827$	33.7286	+	33.7286i	1.17286	+	1.17286i	0.191333	+	0.981525i	$0.438719\pi$
$828$	−7.06777	−	6.92895i	−0.245622	−	0.240798i
$829$	−15.6335	−	15.6335i	−0.542973	−	0.542973i	0.381426	−	0.924399i	$-0.375433\pi$
$829$	−15.6335	−	15.6335i	−0.542973	−	0.542973i	−0.924399	+	0.381426i	$0.875433\pi$
$830$	5.20452	+	5.20452i	0.180651	+	0.180651i
$831$	5.32036	+	2.17292i	0.184561	+	0.0753777i
$832$	3.82216			0.132509
$833$	−55.2525	+	55.2525i	−1.91438	+	1.91438i
$834$	2.49062	−	1.04615i	0.0862431	−	0.0362251i
$835$	−3.24817			−0.112408
$836$			2.67316i			0.0924531i
$837$	−7.91273	+	19.9368i	−0.273504	+	0.689117i
$838$	6.19351	−	6.19351i	0.213951	−	0.213951i
$839$	23.4740	+	23.4740i	0.810411	+	0.810411i	0.984695	−	0.174284i	$-0.0557612\pi$
$839$	23.4740	+	23.4740i	0.810411	+	0.810411i	−0.174284	+	0.984695i	$0.555761\pi$
$840$	−6.00893	−	14.3058i	−0.207328	−	0.493597i
$841$	−25.8505	−	13.1435i	−0.891397	−	0.453224i
$842$			15.3665i			0.529566i
$843$	−8.37798	+	20.5133i	−0.288553	+	0.706517i
$844$	−5.20930	−	5.20930i	−0.179312	−	0.179312i
$845$	−5.03340			−0.173154
$846$	10.6333	+	10.4244i	0.365579	+	0.358399i
$847$		−	43.7633i		−	1.50373i
$848$		−	17.5093i		−	0.601271i
$849$	8.73893	−	21.3971i	0.299919	−	0.734348i
$850$		−	3.78494i		−	0.129823i
$851$	7.64574	+	7.64574i	0.262093	+	0.262093i
$852$	−6.28409	+	15.3865i	−0.215289	+	0.527132i
$853$	−11.5295	+	11.5295i	−0.394764	+	0.394764i	−0.876381	−	0.481618i	$-0.840049\pi$
$853$	−11.5295	+	11.5295i	−0.394764	+	0.394764i	0.481618	+	0.876381i	$0.340049\pi$
$854$	9.45189			0.323437
$855$	−0.0509141	−	5.13372i	−0.00174123	−	0.175570i
$856$	−8.27077	+	8.27077i	−0.282689	+	0.282689i
$857$			22.7875i			0.778407i	0.921152	+	0.389203i	$0.127250\pi$
$857$			22.7875i			0.778407i	−0.921152	+	0.389203i	$0.872750\pi$
$858$	−2.36813	−	0.967184i	−0.0808468	−	0.0330191i
$859$	2.48576	−	2.48576i	0.0848130	−	0.0848130i	−0.663428	−	0.748241i	$-0.730899\pi$
$859$	2.48576	−	2.48576i	0.0848130	−	0.0848130i	0.748241	+	0.663428i	$0.230899\pi$
$860$	8.11820	−	8.11820i	0.276828	−	0.276828i
$861$	11.9257	+	28.3921i	0.406427	+	0.967602i
$862$	1.49071	+	1.49071i	0.0507737	+	0.0507737i
$863$	5.22225			0.177768			0.0888838	−	0.996042i	$-0.471670\pi$
$863$	5.22225			0.177768			0.0888838	+	0.996042i	$0.471670\pi$
$864$	26.0208	+	10.3274i	0.885245	+	0.351346i
$865$	15.3533			0.522029
$866$			16.4180i			0.557908i
$867$	18.4060	−	45.0667i	0.625100	−	1.53055i
$868$	21.1988	−	21.1988i	0.719534	−	0.719534i
$869$	4.12285			0.139858
$870$	−0.850275	−	5.18736i	−0.0288270	−	0.175868i
$871$	−27.9991			−0.948715
$872$	0.0999182	−	0.0999182i	0.00338366	−	0.00338366i
$873$	35.7926	−	0.354976i	1.21140	−	0.0120141i
$874$		−	1.89130i		−	0.0639741i
$875$	4.31678			0.145934
$876$	11.1478	+	26.5402i	0.376649	+	0.896709i
$877$	8.79570			0.297010			0.148505	−	0.988912i	$-0.452554\pi$
$877$	8.79570			0.297010			0.148505	+	0.988912i	$0.452554\pi$
$878$	−2.07609	−	2.07609i	−0.0700647	−	0.0700647i
$879$	53.5394	−	22.4884i	1.80584	−	0.758515i
$880$	1.44122	−	1.44122i	0.0485836	−	0.0485836i
$881$	−20.8395	+	20.8395i	−0.702101	+	0.702101i	−0.964861	−	0.262760i	$-0.915367\pi$
$881$	−20.8395	+	20.8395i	−0.702101	+	0.702101i	0.262760	+	0.964861i	$0.415367\pi$
$882$	−19.6696	+	0.195075i	−0.662309	+	0.00656850i
$883$		−	17.1307i		−	0.576493i	−0.957556	−	0.288247i	$-0.906928\pi$
$883$		−	17.1307i		−	0.576493i	0.957556	−	0.288247i	$-0.0930723\pi$
$884$	22.5510	−	22.5510i	0.758471	−	0.758471i
$885$	5.18543	−	12.6964i	0.174306	−	0.426786i
$886$	−13.6560			−0.458781
$887$	−22.2119	+	22.2119i	−0.745803	+	0.745803i	−0.973688	−	0.227885i	$-0.926819\pi$
$887$	−22.2119	+	22.2119i	−0.745803	+	0.745803i	0.227885	+	0.973688i	$0.426819\pi$
$888$	−18.3479	−	7.49359i	−0.615716	−	0.251468i
$889$	47.5825	+	47.5825i	1.59586	+	1.59586i
$890$		−	8.42728i		−	0.282483i
$891$	6.02472	+	5.79035i	0.201836	+	0.193984i
$892$		−	46.0893i		−	1.54318i
$893$		−	15.0725i		−	0.504382i
$894$	−7.29886	+	3.06578i	−0.244110	+	0.102535i
$895$	−4.39983			−0.147070
$896$	−35.2206	−	35.2206i	−1.17664	−	1.17664i
$897$	−8.87527	−	3.62480i	−0.296337	−	0.121029i
$898$		−	8.10540i		−	0.270481i
$899$	18.9491	−	11.6232i	0.631988	−	0.387656i
$900$	−3.53333	+	3.60412i	−0.117778	+	0.120137i
$901$	−37.8780	−	37.8780i	−1.26190	−	1.26190i
$902$	1.52389	−	1.52389i	0.0507400	−	0.0507400i
$903$	−19.7592	−	47.0419i	−0.657546	−	1.56545i
$904$		−	29.7661i		−	0.990006i
$905$	−21.7145			−0.721815
$906$	4.77123	+	11.3591i	0.158514	+	0.377382i
$907$	15.7409	−	15.7409i	0.522666	−	0.522666i	−0.395709	−	0.918376i	$-0.629501\pi$
$907$	15.7409	−	15.7409i	0.522666	−	0.522666i	0.918376	+	0.395709i	$0.129501\pi$
$908$	−7.94208			−0.263567
$909$	−24.8200	+	0.246154i	−0.823227	+	0.00816442i
$910$	−4.85540	−	4.85540i	−0.160955	−	0.160955i
$911$	37.1320	+	37.1320i	1.23024	+	1.23024i	0.963872	+	0.266368i	$0.0858235\pi$
$911$	37.1320	+	37.1320i	1.23024	+	1.23024i	0.266368	+	0.963872i	$0.414176\pi$
$912$	−2.51987	−	5.99919i	−0.0834412	−	0.198653i
$913$	8.57434	+	8.57434i	0.283769	+	0.283769i
$914$	0.691466	+	0.691466i	0.0228717	+	0.0228717i
$915$	−2.60602	−	6.20430i	−0.0861525	−	0.205108i
$916$	−27.4199	−	27.4199i	−0.905981	−	0.905981i
$917$	29.4637	+	29.4637i	0.972976	+	0.972976i
$918$	18.0561	−	7.79575i	0.595940	−	0.257298i
$919$	35.9407			1.18557			0.592787	−	0.805359i	$-0.298028\pi$
$919$	35.9407			1.18557			0.592787	+	0.805359i	$0.298028\pi$
$920$	−2.87768	+	2.87768i	−0.0948743	+	0.0948743i
$921$	1.40119	+	3.33590i	0.0461709	+	0.109922i
$922$	−13.3415			−0.439378
$923$			16.0985i			0.529890i
$924$	−4.52288	−	10.7679i	−0.148792	−	0.354237i
$925$	3.89885	−	3.89885i	0.128193	−	0.128193i
$926$	0.317629	+	0.317629i	0.0104379	+	0.0104379i
$927$	−28.1238	−	27.5714i	−0.923706	−	0.905564i
$928$	−15.1702	−	24.7317i	−0.497987	−	0.811857i
$929$		−	36.6569i		−	1.20267i	−0.798996	−	0.601337i	$-0.794635\pi$
$929$		−	36.6569i		−	1.20267i	0.798996	−	0.601337i	$-0.205365\pi$
$930$	3.73030	+	1.52351i	0.122321	+	0.0499580i
$931$	14.0789	+	14.0789i	0.461417	+	0.461417i
$932$	33.5713			1.09967
$933$	24.4150	−	10.2552i	0.799312	−	0.335739i
$934$		−	7.19797i		−	0.235525i
$935$		−	6.23562i		−	0.203927i
$936$	17.5716	−	0.174268i	0.574345	−	0.00569611i
$937$		−	7.28282i		−	0.237919i	−0.992899	−	0.118960i	$-0.962044\pi$
$937$		−	7.28282i		−	0.237919i	0.992899	−	0.118960i	$-0.0379559\pi$
$938$	17.0646	+	17.0646i	0.557180	+	0.557180i
$939$	55.3879	+	22.6213i	1.80752	+	0.738219i
$940$	−10.4777	+	10.4777i	−0.341744	+	0.341744i
$941$	7.31481			0.238456			0.119228	−	0.992867i	$-0.461958\pi$
$941$	7.31481			0.238456			0.119228	+	0.992867i	$0.461958\pi$
$942$	−4.15378	+	10.1705i	−0.135337	+	0.331371i
$943$	5.71122	−	5.71122i	0.185983	−	0.185983i
$944$		−	17.3821i		−	0.565740i
$945$	8.89115	+	20.5932i	0.289229	+	0.669898i
$946$	−2.52487	+	2.52487i	−0.0820908	+	0.0820908i
$947$	−3.66380	+	3.66380i	−0.119058	+	0.119058i	−0.764125	−	0.645068i	$-0.776829\pi$
$947$	−3.66380	+	3.66380i	−0.119058	+	0.119058i	0.645068	+	0.764125i	$0.276829\pi$
$948$	−11.9300	+	5.01100i	−0.387467	+	0.162750i
$949$	19.7160	+	19.7160i	0.640009	+	0.640009i
$950$	−0.964443			−0.0312907
$951$	6.56527	+	15.6303i	0.212894	+	0.506847i
$952$	−60.1658			−1.94999
$953$			11.3439i			0.367466i	0.982976	+	0.183733i	$0.0588182\pi$
$953$			11.3439i			0.367466i	−0.982976	+	0.183733i	$0.941182\pi$
$954$	−0.133732	−	13.4843i	−0.00432974	−	0.436572i
$955$	2.11790	−	2.11790i	0.0685335	−	0.0685335i
$956$	28.4146			0.918993
$957$	−1.40081	−	8.54607i	−0.0452818	−	0.276255i
$958$	0.158571			0.00512319
$959$	58.8550	−	58.8550i	1.90053	−	1.90053i
$960$	−0.886822	+	2.17137i	−0.0286221	+	0.0700807i
$961$		−	13.9597i		−	0.450314i
$962$	−8.77064			−0.282777
$963$	11.8370	−	12.0742i	0.381443	−	0.389085i
$964$	−31.0856			−1.00120
$965$	7.58685	+	7.58685i	0.244229	+	0.244229i
$966$	3.20000	+	7.61842i	0.102958	+	0.245119i
$967$	6.47831	−	6.47831i	0.208329	−	0.208329i	−0.595228	−	0.803557i	$-0.702938\pi$
$967$	6.47831	−	6.47831i	0.208329	−	0.208329i	0.803557	+	0.595228i	$0.202938\pi$
$968$	14.8768	−	14.8768i	0.478159	−	0.478159i
$969$	−18.4294	−	7.52684i	−0.592036	−	0.241797i
$970$		−	6.72414i		−	0.215899i
$971$	7.39989	−	7.39989i	0.237474	−	0.237474i	−0.578330	−	0.815803i	$-0.696295\pi$
$971$	7.39989	−	7.39989i	0.237474	−	0.237474i	0.815803	+	0.578330i	$0.196295\pi$
$972$	−24.4710	−	9.43248i	−0.784907	−	0.302547i
$973$	11.9466			0.382992
$974$	−9.22722	+	9.22722i	−0.295659	+	0.295659i
$975$	−1.84842	+	4.52583i	−0.0591969	+	0.144943i
$976$	−6.03090	−	6.03090i	−0.193045	−	0.193045i
$977$		−	35.7246i		−	1.14293i	−0.820626	−	0.571465i	$-0.806375\pi$
$977$		−	35.7246i		−	1.14293i	0.820626	−	0.571465i	$-0.193625\pi$
$978$	−3.96872	+	9.71736i	−0.126906	+	0.310727i
$979$		−	13.8838i		−	0.443728i
$980$		−	19.5740i		−	0.625267i
$981$	−0.143002	+	0.145867i	−0.00456570	+	0.00465716i
$982$	0.0317682			0.00101376
$983$	−6.33950	−	6.33950i	−0.202199	−	0.202199i	0.598743	−	0.800941i	$-0.295667\pi$
$983$	−6.33950	−	6.33950i	−0.202199	−	0.202199i	−0.800941	+	0.598743i	$0.795667\pi$
$984$	−5.59757	+	13.7056i	−0.178444	+	0.436917i
$985$			11.3571i			0.361868i
$986$	−19.8214	−	4.74969i	−0.631243	−	0.151261i
$987$	25.5021	+	60.7141i	0.811740	+	1.93255i
$988$	−5.74622	−	5.74622i	−0.182812	−	0.182812i
$989$	−9.46270	+	9.46270i	−0.300896	+	0.300896i
$990$	1.09892	−	1.12093i	0.0349258	−	0.0356255i
$991$			30.9403i			0.982850i	0.870920	+	0.491425i	$0.163524\pi$
$991$			30.9403i			0.982850i	−0.870920	+	0.491425i	$0.836476\pi$
$992$	22.2403			0.706131
$993$	18.5269	−	7.78196i	0.587935	−	0.246953i
$994$	9.81157	−	9.81157i	0.311204	−	0.311204i
$995$	18.3425			0.581497
$996$	−35.2323	−	14.3894i	−1.11638	−	0.455947i
$997$	30.9046	+	30.9046i	0.978759	+	0.978759i	0.999779	−	0.0210196i	$-0.00669124\pi$
$997$	30.9046	+	30.9046i	0.978759	+	0.978759i	−0.0210196	+	0.999779i	$0.506691\pi$
$998$	8.40886	+	8.40886i	0.266178	+	0.266178i
$999$	26.6298	+	10.5691i	0.842530	+	0.334393i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	435.2.q.c.41.8	✓	36
3.2	odd	2		435.2.q.d.41.11	yes	36
29.17	odd	4		435.2.q.d.191.11	yes	36
87.17	even	4	inner	435.2.q.c.191.8	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
435.2.q.c.41.8	✓	36	1.1	even	1	trivial
435.2.q.c.191.8	yes	36	87.17	even	4	inner
435.2.q.d.41.11	yes	36	3.2	odd	2
435.2.q.d.191.11	yes	36	29.17	odd	4

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:	\( N \)	\(=\)	\( 435 = 3 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	435.q (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.398500 + 0.398500i) q^{2} +(1.60347 + 0.654884i) q^{3} +1.68239i q^{4} -1.00000 q^{5} +(-0.899957 + 0.378013i) q^{6} -4.31678 q^{7} +(-1.46744 - 1.46744i) q^{8} +(2.14225 + 2.10018i) q^{9} +O(q^{10})\)	\(q+(-0.398500 + 0.398500i) q^{2} +(1.60347 + 0.654884i) q^{3} +1.68239i q^{4} -1.00000 q^{5} +(-0.899957 + 0.378013i) q^{6} -4.31678 q^{7} +(-1.46744 - 1.46744i) q^{8} +(2.14225 + 2.10018i) q^{9} +(0.398500 - 0.398500i) q^{10} +(0.656522 - 0.656522i) q^{11} +(-1.10177 + 2.69768i) q^{12} +2.82252i q^{13} +(1.72024 - 1.72024i) q^{14} +(-1.60347 - 0.654884i) q^{15} -2.19524 q^{16} +(-4.74898 + 4.74898i) q^{17} +(-1.69061 + 0.0167668i) q^{18} +(1.21009 + 1.21009i) q^{19} -1.68239i q^{20} +(-6.92184 - 2.82699i) q^{21} +0.523249i q^{22} +1.96103i q^{23} +(-1.39199 - 3.31400i) q^{24} +1.00000 q^{25} +(-1.12477 - 1.12477i) q^{26} +(2.05967 + 4.77051i) q^{27} -7.26253i q^{28} +(1.25489 - 5.23691i) q^{29} +(0.899957 - 0.378013i) q^{30} +(2.91893 + 2.91893i) q^{31} +(3.80968 - 3.80968i) q^{32} +(1.48266 - 0.622769i) q^{33} -3.78494i q^{34} +4.31678 q^{35} +(-3.53333 + 3.60412i) q^{36} +(3.89885 - 3.89885i) q^{37} -0.964443 q^{38} +(-1.84842 + 4.52583i) q^{39} +(1.46744 + 1.46744i) q^{40} +(-2.91236 - 2.91236i) q^{41} +(3.88491 - 1.63180i) q^{42} +(4.82538 + 4.82538i) q^{43} +(1.10453 + 1.10453i) q^{44} +(-2.14225 - 2.10018i) q^{45} +(-0.781470 - 0.781470i) q^{46} +(-6.22784 - 6.22784i) q^{47} +(-3.52001 - 1.43763i) q^{48} +11.6346 q^{49} +(-0.398500 + 0.398500i) q^{50} +(-10.7249 + 4.50483i) q^{51} -4.74859 q^{52} +7.97602i q^{53} +(-2.72183 - 1.08027i) q^{54} +(-0.656522 + 0.656522i) q^{55} +(6.33460 + 6.33460i) q^{56} +(1.14788 + 2.73282i) q^{57} +(1.58684 + 2.58699i) q^{58} +7.91809i q^{59} +(1.10177 - 2.69768i) q^{60} +(2.74726 + 2.74726i) q^{61} -2.32639 q^{62} +(-9.24764 - 9.06601i) q^{63} -1.35417i q^{64} -2.82252i q^{65} +(-0.342667 + 0.839015i) q^{66} +9.91992i q^{67} +(-7.98966 - 7.98966i) q^{68} +(-1.28425 + 3.14445i) q^{69} +(-1.72024 + 1.72024i) q^{70} +5.70361 q^{71} +(-0.0617419 - 6.22550i) q^{72} +(6.98527 - 6.98527i) q^{73} +3.10738i q^{74} +(1.60347 + 0.654884i) q^{75} +(-2.03585 + 2.03585i) q^{76} +(-2.83406 + 2.83406i) q^{77} +(-1.06695 - 2.54014i) q^{78} +(3.13992 + 3.13992i) q^{79} +2.19524 q^{80} +(0.178499 + 8.99823i) q^{81} +2.32116 q^{82} +13.0602i q^{83} +(4.75611 - 11.6453i) q^{84} +(4.74898 - 4.74898i) q^{85} -3.84584 q^{86} +(5.44175 - 7.57544i) q^{87} -1.92681 q^{88} +(10.5737 - 10.5737i) q^{89} +(1.69061 - 0.0167668i) q^{90} -12.1842i q^{91} -3.29922 q^{92} +(2.76886 + 6.59198i) q^{93} +4.96359 q^{94} +(-1.21009 - 1.21009i) q^{95} +(8.60361 - 3.61382i) q^{96} +(8.43681 - 8.43681i) q^{97} +(-4.63639 + 4.63639i) q^{98} +(2.78525 - 0.0276229i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 4 q^{2} + 6 q^{3} - 36 q^{5} + 8 q^{6} + 8 q^{7} + 4 q^{8}+O(q^{10}) \) 36 * q - 4 * q^2 + 6 * q^3 - 36 * q^5 + 8 * q^6 + 8 * q^7 + 4 * q^8	\( 36 q - 4 q^{2} + 6 q^{3} - 36 q^{5} + 8 q^{6} + 8 q^{7} + 4 q^{8} + 4 q^{10} - 12 q^{11} + 10 q^{12} + 28 q^{14} - 6 q^{15} - 60 q^{16} - 20 q^{17} - 28 q^{18} + 16 q^{19} + 12 q^{21} + 24 q^{24} + 36 q^{25} + 4 q^{26} + 30 q^{27} - 28 q^{29} - 8 q^{30} - 8 q^{31} - 16 q^{32} - 8 q^{33} - 8 q^{35} - 28 q^{36} - 4 q^{37} + 24 q^{38} - 40 q^{39} - 4 q^{40} + 48 q^{41} - 8 q^{42} + 4 q^{43} + 16 q^{44} + 20 q^{46} - 20 q^{47} - 14 q^{48} + 28 q^{49} - 4 q^{50} - 44 q^{52} - 24 q^{54} + 12 q^{55} - 84 q^{56} + 28 q^{57} - 64 q^{58} - 10 q^{60} + 20 q^{61} + 8 q^{62} + 32 q^{63} + 40 q^{66} + 60 q^{68} + 36 q^{69} - 28 q^{70} - 16 q^{71} - 132 q^{72} + 8 q^{73} + 6 q^{75} + 16 q^{76} + 32 q^{77} + 48 q^{78} + 12 q^{79} + 60 q^{80} - 60 q^{81} + 56 q^{82} + 44 q^{84} + 20 q^{85} + 8 q^{86} + 22 q^{87} - 24 q^{88} + 20 q^{89} + 28 q^{90} - 16 q^{92} + 24 q^{93} + 52 q^{94} - 16 q^{95} - 8 q^{96} + 4 q^{97} - 8 q^{98} - 48 q^{99}+O(q^{100}) \) 36 * q - 4 * q^2 + 6 * q^3 - 36 * q^5 + 8 * q^6 + 8 * q^7 + 4 * q^8 + 4 * q^10 - 12 * q^11 + 10 * q^12 + 28 * q^14 - 6 * q^15 - 60 * q^16 - 20 * q^17 - 28 * q^18 + 16 * q^19 + 12 * q^21 + 24 * q^24 + 36 * q^25 + 4 * q^26 + 30 * q^27 - 28 * q^29 - 8 * q^30 - 8 * q^31 - 16 * q^32 - 8 * q^33 - 8 * q^35 - 28 * q^36 - 4 * q^37 + 24 * q^38 - 40 * q^39 - 4 * q^40 + 48 * q^41 - 8 * q^42 + 4 * q^43 + 16 * q^44 + 20 * q^46 - 20 * q^47 - 14 * q^48 + 28 * q^49 - 4 * q^50 - 44 * q^52 - 24 * q^54 + 12 * q^55 - 84 * q^56 + 28 * q^57 - 64 * q^58 - 10 * q^60 + 20 * q^61 + 8 * q^62 + 32 * q^63 + 40 * q^66 + 60 * q^68 + 36 * q^69 - 28 * q^70 - 16 * q^71 - 132 * q^72 + 8 * q^73 + 6 * q^75 + 16 * q^76 + 32 * q^77 + 48 * q^78 + 12 * q^79 + 60 * q^80 - 60 * q^81 + 56 * q^82 + 44 * q^84 + 20 * q^85 + 8 * q^86 + 22 * q^87 - 24 * q^88 + 20 * q^89 + 28 * q^90 - 16 * q^92 + 24 * q^93 + 52 * q^94 - 16 * q^95 - 8 * q^96 + 4 * q^97 - 8 * q^98 - 48 * q^99

Introduction

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