LMFDB - Embedded newform 435.2.q.c.191.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [435,2,Mod(41,435)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [36,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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			191.18
Character	$\chi$	$=$	435.191
Dual form			435.2.q.c.41.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.93705 + 1.93705i) q^{2} +(-0.865476 - 1.50032i) q^{3} +5.50431i q^{4} -1.00000 q^{5} +(1.22972 - 4.58265i) q^{6} +1.59227 q^{7} +(-6.78801 + 6.78801i) q^{8} +(-1.50190 + 2.59698i) q^{9} +(-1.93705 - 1.93705i) q^{10} +(2.51227 + 2.51227i) q^{11} +(8.25821 - 4.76385i) q^{12} +5.42072i q^{13} +(3.08430 + 3.08430i) q^{14} +(0.865476 + 1.50032i) q^{15} -15.2888 q^{16} +(-1.58699 - 1.58699i) q^{17} +(-7.93972 + 2.12121i) q^{18} +(1.79172 - 1.79172i) q^{19} -5.50431i q^{20} +(-1.37807 - 2.38891i) q^{21} +9.73277i q^{22} -2.26767i q^{23} +(16.0590 + 4.30931i) q^{24} +1.00000 q^{25} +(-10.5002 + 10.5002i) q^{26} +(5.19615 + 0.00570619i) q^{27} +8.76433i q^{28} +(-1.83937 - 5.06130i) q^{29} +(-1.22972 + 4.58265i) q^{30} +(6.53520 - 6.53520i) q^{31} +(-16.0391 - 16.0391i) q^{32} +(1.59489 - 5.94351i) q^{33} -6.14814i q^{34} -1.59227 q^{35} +(-14.2946 - 8.26693i) q^{36} +(1.18750 + 1.18750i) q^{37} +6.94129 q^{38} +(8.13280 - 4.69151i) q^{39} +(6.78801 - 6.78801i) q^{40} +(6.56896 - 6.56896i) q^{41} +(1.95804 - 7.29681i) q^{42} +(0.586602 - 0.586602i) q^{43} +(-13.8283 + 13.8283i) q^{44} +(1.50190 - 2.59698i) q^{45} +(4.39258 - 4.39258i) q^{46} +(-2.90529 + 2.90529i) q^{47} +(13.2321 + 22.9380i) q^{48} -4.46468 q^{49} +(1.93705 + 1.93705i) q^{50} +(-1.00748 + 3.75448i) q^{51} -29.8373 q^{52} +3.69903i q^{53} +(10.0541 + 10.0762i) q^{54} +(-2.51227 - 2.51227i) q^{55} +(-10.8083 + 10.8083i) q^{56} +(-4.23884 - 1.13746i) q^{57} +(6.24102 - 13.3669i) q^{58} +12.1062i q^{59} +(-8.25821 + 4.76385i) q^{60} +(7.46553 - 7.46553i) q^{61} +25.3180 q^{62} +(-2.39143 + 4.13508i) q^{63} -31.5594i q^{64} -5.42072i q^{65} +(14.6022 - 8.42348i) q^{66} -1.85583i q^{67} +(8.73526 - 8.73526i) q^{68} +(-3.40222 + 1.96261i) q^{69} +(-3.08430 - 3.08430i) q^{70} -3.52616 q^{71} +(-7.43339 - 27.8232i) q^{72} +(6.40581 + 6.40581i) q^{73} +4.60050i q^{74} +(-0.865476 - 1.50032i) q^{75} +(9.86218 + 9.86218i) q^{76} +(4.00020 + 4.00020i) q^{77} +(24.8413 + 6.66595i) q^{78} +(-3.54465 + 3.54465i) q^{79} +15.2888 q^{80} +(-4.48858 - 7.80081i) q^{81} +25.4488 q^{82} -14.3942i q^{83} +(13.1493 - 7.58532i) q^{84} +(1.58699 + 1.58699i) q^{85} +2.27255 q^{86} +(-6.00161 + 7.14007i) q^{87} -34.1066 q^{88} +(3.15754 + 3.15754i) q^{89} +(7.93972 - 2.12121i) q^{90} +8.63124i q^{91} +12.4819 q^{92} +(-15.4609 - 4.14881i) q^{93} -11.2554 q^{94} +(-1.79172 + 1.79172i) q^{95} +(-10.1823 + 37.9452i) q^{96} +(-11.8364 - 11.8364i) q^{97} +(-8.64830 - 8.64830i) q^{98} +(-10.2975 + 2.75112i) 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} + 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}+ \cdots - 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

Character values

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

$n$	$31$	$146$	$262$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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 $

$2$	1.93705	+	1.93705i	1.36970	+	1.36970i	0.860863	+	0.508836i	$0.169924\pi$
$2$	1.93705	+	1.93705i	1.36970	+	1.36970i	0.508836	+	0.860863i	$0.330076\pi$
$3$	−0.865476	−	1.50032i	−0.499683	−	0.866208i
$3$	−0.865476	−	1.50032i	−0.499683	−	0.866208i
$4$			5.50431i			2.75215i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	1.22972	−	4.58265i	0.502030	−	1.87086i
$7$	1.59227			0.601821			0.300910	−	0.953652i	$-0.402710\pi$
$7$	1.59227			0.601821			0.300910	+	0.953652i	$0.402710\pi$
$8$	−6.78801	+	6.78801i	−2.39992	+	2.39992i
$9$	−1.50190	+	2.59698i	−0.500634	+	0.865659i
$10$	−1.93705	−	1.93705i	−0.612548	−	0.612548i
$11$	2.51227	+	2.51227i	0.757477	+	0.757477i	0.975863	−	0.218385i	$-0.0700790\pi$
$11$	2.51227	+	2.51227i	0.757477	+	0.757477i	−0.218385	+	0.975863i	$0.570079\pi$
$12$	8.25821	−	4.76385i	2.38394	−	1.37520i
$13$			5.42072i			1.50344i	0.659484	+	0.751719i	$0.270775\pi$
$13$			5.42072i			1.50344i	−0.659484	+	0.751719i	$0.729225\pi$
$14$	3.08430	+	3.08430i	0.824314	+	0.824314i
$15$	0.865476	+	1.50032i	0.223465	+	0.387380i
$16$	−15.2888			−3.82220
$17$	−1.58699	−	1.58699i	−0.384901	−	0.384901i	0.487963	−	0.872864i	$-0.337740\pi$
$17$	−1.58699	−	1.58699i	−0.384901	−	0.384901i	−0.872864	+	0.487963i	$0.837740\pi$
$18$	−7.93972	+	2.12121i	−1.87141	+	0.499975i
$19$	1.79172	−	1.79172i	0.411049	−	0.411049i	−0.471055	−	0.882104i	$-0.656127\pi$
$19$	1.79172	−	1.79172i	0.411049	−	0.411049i	0.882104	+	0.471055i	$0.156127\pi$
$20$		−	5.50431i		−	1.23080i
$21$	−1.37807	−	2.38891i	−0.300720	−	0.521302i
$22$			9.73277i			2.07503i
$23$		−	2.26767i		−	0.472841i	−0.971651	−	0.236421i	$-0.924026\pi$
$23$		−	2.26767i		−	0.472841i	0.971651	−	0.236421i	$-0.0759743\pi$
$24$	16.0590	+	4.30931i	3.27804	+	0.879633i
$25$	1.00000			0.200000
$26$	−10.5002	+	10.5002i	−2.05926	+	2.05926i
$27$	5.19615	+	0.00570619i	0.999999	+	0.00109816i
$28$			8.76433i			1.65630i
$29$	−1.83937	−	5.06130i	−0.341563	−	0.939859i
$29$	−1.83937	−	5.06130i	−0.341563	−	0.939859i
$30$	−1.22972	+	4.58265i	−0.224515	+	0.836674i
$31$	6.53520	−	6.53520i	1.17376	−	1.17376i	0.192451	−	0.981307i	$-0.438357\pi$
$31$	6.53520	−	6.53520i	1.17376	−	1.17376i	0.981307	−	0.192451i	$-0.0616435\pi$
$32$	−16.0391	−	16.0391i	−2.83534	−	2.83534i
$33$	1.59489	−	5.94351i	0.277635	−	1.03463i
$34$		−	6.14814i		−	1.05440i
$35$	−1.59227			−0.269142
$36$	−14.2946	−	8.26693i	−2.38243	−	1.37782i
$37$	1.18750	+	1.18750i	0.195224	+	0.195224i	0.797949	−	0.602725i	$-0.205918\pi$
$37$	1.18750	+	1.18750i	0.195224	+	0.195224i	−0.602725	+	0.797949i	$0.705918\pi$
$38$	6.94129			1.12603
$39$	8.13280	−	4.69151i	1.30229	−	0.751242i
$40$	6.78801	−	6.78801i	1.07328	−	1.07328i
$41$	6.56896	−	6.56896i	1.02590	−	1.02590i	0.0262439	−	0.999656i	$-0.491645\pi$
$41$	6.56896	−	6.56896i	1.02590	−	1.02590i	0.999656	−	0.0262439i	$-0.00835466\pi$
$42$	1.95804	−	7.29681i	0.302132	−	1.12592i
$43$	0.586602	−	0.586602i	0.0894560	−	0.0894560i	−0.660963	−	0.750419i	$-0.729852\pi$
$43$	0.586602	−	0.586602i	0.0894560	−	0.0894560i	0.750419	+	0.660963i	$0.229852\pi$
$44$	−13.8283	+	13.8283i	−2.08469	+	2.08469i
$45$	1.50190	−	2.59698i	0.223890	−	0.387135i
$46$	4.39258	−	4.39258i	0.647650	−	0.647650i
$47$	−2.90529	+	2.90529i	−0.423781	+	0.423781i	−0.886503	−	0.462722i	$-0.846873\pi$
$47$	−2.90529	+	2.90529i	−0.423781	+	0.423781i	0.462722	+	0.886503i	$0.346873\pi$
$48$	13.2321	+	22.9380i	1.90989	+	3.31082i
$49$	−4.46468			−0.637812
$50$	1.93705	+	1.93705i	0.273940	+	0.273940i
$51$	−1.00748	+	3.75448i	−0.141076	+	0.525733i
$52$	−29.8373			−4.13769
$53$			3.69903i			0.508100i	0.967191	+	0.254050i	$0.0817629\pi$
$53$			3.69903i			0.508100i	−0.967191	+	0.254050i	$0.918237\pi$
$54$	10.0541	+	10.0762i	1.36819	+	1.37120i
$55$	−2.51227	−	2.51227i	−0.338754	−	0.338754i
$56$	−10.8083	+	10.8083i	−1.44432	+	1.44432i
$57$	−4.23884	−	1.13746i	−0.561448	−	0.150660i
$58$	6.24102	−	13.3669i	0.819486	−	1.75516i
$59$			12.1062i			1.57609i	0.615617	+	0.788045i	$0.288907\pi$
$59$			12.1062i			1.57609i	−0.615617	+	0.788045i	$0.711093\pi$
$60$	−8.25821	+	4.76385i	−1.06613	+	0.615010i
$61$	7.46553	−	7.46553i	0.955863	−	0.955863i	−0.0432030	−	0.999066i	$-0.513756\pi$
$61$	7.46553	−	7.46553i	0.955863	−	0.955863i	0.999066	+	0.0432030i	$0.0137562\pi$
$62$	25.3180			3.21539
$63$	−2.39143	+	4.13508i	−0.301292	+	0.520972i
$64$		−	31.5594i		−	3.94493i
$65$		−	5.42072i		−	0.672358i
$66$	14.6022	−	8.42348i	1.79741	−	1.03686i
$67$		−	1.85583i		−	0.226725i	−0.993554	−	0.113363i	$-0.963838\pi$
$67$		−	1.85583i		−	0.226725i	0.993554	−	0.113363i	$-0.0361622\pi$
$68$	8.73526	−	8.73526i	1.05931	−	1.05931i
$69$	−3.40222	+	1.96261i	−0.409579	+	0.236271i
$70$	−3.08430	−	3.08430i	−0.368644	−	0.368644i
$71$	−3.52616			−0.418478			−0.209239	−	0.977864i	$-0.567099\pi$
$71$	−3.52616			−0.418478			−0.209239	+	0.977864i	$0.567099\pi$
$72$	−7.43339	−	27.8232i	−0.876033	−	3.27900i
$73$	6.40581	+	6.40581i	0.749743	+	0.749743i	0.974431	−	0.224688i	$-0.0721362\pi$
$73$	6.40581	+	6.40581i	0.749743	+	0.749743i	−0.224688	+	0.974431i	$0.572136\pi$
$74$			4.60050i			0.534798i
$75$	−0.865476	−	1.50032i	−0.0999366	−	0.173242i
$76$	9.86218	+	9.86218i	1.13127	+	1.13127i
$77$	4.00020	+	4.00020i	0.455865	+	0.455865i
$78$	24.8413	+	6.66595i	2.81272	+	0.754770i
$79$	−3.54465	+	3.54465i	−0.398804	+	0.398804i	−0.877811	−	0.479007i	$-0.840997\pi$
$79$	−3.54465	+	3.54465i	−0.398804	+	0.398804i	0.479007	+	0.877811i	$0.340997\pi$
$80$	15.2888			1.70934
$81$	−4.48858	−	7.80081i	−0.498731	−	0.866757i
$82$	25.4488			2.81035
$83$		−	14.3942i		−	1.57997i	−0.613127	−	0.789984i	$-0.710089\pi$
$83$		−	14.3942i		−	1.57997i	0.613127	−	0.789984i	$-0.289911\pi$
$84$	13.1493	−	7.58532i	1.43470	−	0.827626i
$85$	1.58699	+	1.58699i	0.172133	+	0.172133i
$86$	2.27255			0.245056
$87$	−6.00161	+	7.14007i	−0.643441	+	0.765496i
$88$	−34.1066			−3.63578
$89$	3.15754	+	3.15754i	0.334699	+	0.334699i	0.854368	−	0.519669i	$-0.173945\pi$
$89$	3.15754	+	3.15754i	0.334699	+	0.334699i	−0.519669	+	0.854368i	$0.673945\pi$
$90$	7.93972	−	2.12121i	0.836920	−	0.223596i
$91$			8.63124i			0.904800i
$92$	12.4819			1.30133
$93$	−15.4609	−	4.14881i	−1.60322	−	0.430212i
$94$	−11.2554			−1.16090
$95$	−1.79172	+	1.79172i	−0.183827	+	0.183827i
$96$	−10.1823	+	37.9452i	−1.03922	+	3.87276i
$97$	−11.8364	−	11.8364i	−1.20180	−	1.20180i	−0.973618	−	0.228184i	$-0.926721\pi$
$97$	−11.8364	−	11.8364i	−1.20180	−	1.20180i	−0.228184	−	0.973618i	$-0.573279\pi$
$98$	−8.64830	−	8.64830i	−0.873611	−	0.873611i
$99$	−10.2975	+	2.75112i	−1.03494	+	0.276498i
$100$			5.50431i			0.550431i
$101$	9.76773	+	9.76773i	0.971926	+	0.971926i	0.999617	−	0.0276909i	$-0.00881542\pi$
$101$	9.76773	+	9.76773i	0.971926	+	0.971926i	−0.0276909	+	0.999617i	$0.508815\pi$
$102$	−9.22415	+	5.32107i	−0.913327	+	0.526864i
$103$	6.84057			0.674022			0.337011	−	0.941501i	$-0.390584\pi$
$103$	6.84057			0.674022			0.337011	+	0.941501i	$0.390584\pi$
$104$	−36.7959	−	36.7959i	−3.60814	−	3.60814i
$105$	1.37807	+	2.38891i	0.134486	+	0.233133i
$106$	−7.16519	+	7.16519i	−0.695945	+	0.695945i
$107$		−	0.164280i		−	0.0158815i	−0.999968	−	0.00794076i	$-0.997472\pi$
$107$		−	0.164280i		−	0.0158815i	0.999968	−	0.00794076i	$-0.00252765\pi$
$108$	−0.0314086	+	28.6012i	−0.00302229	+	2.75215i
$109$		−	14.6990i		−	1.40791i	−0.710245	−	0.703954i	$-0.751416\pi$
$109$		−	14.6990i		−	1.40791i	0.710245	−	0.703954i	$-0.248584\pi$
$110$		−	9.73277i		−	0.927983i
$111$	0.753875	−	2.80939i	0.0715547	−	0.266655i
$112$	−24.3438			−2.30028
$113$	−7.66400	+	7.66400i	−0.720968	+	0.720968i	−0.968802	−	0.247834i	$-0.920281\pi$
$113$	−7.66400	+	7.66400i	−0.720968	+	0.720968i	0.247834	+	0.968802i	$0.420281\pi$
$114$	−6.00752	−	10.4141i	−0.562656	−	0.975374i
$115$			2.26767i			0.211461i
$116$	27.8589	−	10.1245i	2.58664	−	0.940033i
$117$	−14.0775	−	8.14139i	−1.30146	−	0.752672i
$118$	−23.4503	+	23.4503i	−2.15877	+	2.15877i
$119$	−2.52691	−	2.52691i	−0.231641	−	0.231641i
$120$	−16.0590	−	4.30931i	−1.46598	−	0.393384i
$121$			1.62298i			0.147543i
$122$	28.9222			2.61849
$123$	−15.5408	−	4.17024i	−1.40127	−	0.376018i
$124$	35.9718	+	35.9718i	3.23036	+	3.23036i
$125$	−1.00000			−0.0894427
$126$	−12.6422	+	3.37754i	−1.12625	+	0.300895i
$127$	−13.8555	+	13.8555i	−1.22948	+	1.22948i	−0.265314	+	0.964162i	$0.585475\pi$
$127$	−13.8555	+	13.8555i	−1.22948	+	1.22948i	−0.964162	+	0.265314i	$0.914525\pi$
$128$	29.0539	−	29.0539i	2.56802	−	2.56802i
$129$	−1.38778	−	0.372399i	−0.122187	−	0.0327879i
$130$	10.5002	−	10.5002i	0.920928	−	0.920928i
$131$	4.43515	−	4.43515i	0.387501	−	0.387501i	−0.486294	−	0.873795i	$-0.661652\pi$
$131$	4.43515	−	4.43515i	0.387501	−	0.387501i	0.873795	+	0.486294i	$0.161652\pi$
$132$	32.7149	+	8.77876i	2.84747	+	0.764093i
$133$	2.85290	−	2.85290i	0.247378	−	0.247378i
$134$	3.59483	−	3.59483i	0.310546	−	0.310546i
$135$	−5.19615	−	0.00570619i	−0.447213	−	0.000491110i
$136$	21.5450			1.84747
$137$	−4.07631	−	4.07631i	−0.348262	−	0.348262i	0.511200	−	0.859462i	$-0.329201\pi$
$137$	−4.07631	−	4.07631i	−0.348262	−	0.348262i	−0.859462	+	0.511200i	$0.829201\pi$
$138$	−10.3919	−	2.78859i	−0.884620	−	0.237380i
$139$	13.7092			1.16280			0.581398	−	0.813620i	$-0.302506\pi$
$139$	13.7092			1.16280			0.581398	+	0.813620i	$0.302506\pi$
$140$		−	8.76433i		−	0.740721i
$141$	6.87333	+	1.84440i	0.578838	+	0.155326i
$142$	−6.83034	−	6.83034i	−0.573190	−	0.573190i
$143$	−13.6183	+	13.6183i	−1.13882	+	1.13882i
$144$	22.9623	−	39.7046i	1.91352	−	3.30872i
$145$	1.83937	+	5.06130i	0.152752	+	0.420318i
$146$			24.8167i			2.05385i
$147$	3.86408	+	6.69844i	0.318704	+	0.552478i
$148$	−6.53639	+	6.53639i	−0.537288	+	0.537288i
$149$	19.9073			1.63087			0.815436	−	0.578847i	$-0.196497\pi$
$149$	19.9073			1.63087			0.815436	+	0.578847i	$0.196497\pi$
$150$	1.22972	−	4.58265i	0.100406	−	0.374172i
$151$			7.19222i			0.585295i	0.956220	+	0.292647i	$0.0945362\pi$
$151$			7.19222i			0.585295i	−0.956220	+	0.292647i	$0.905464\pi$
$152$			24.3244i			1.97297i
$153$	6.50487	−	1.73787i	0.525887	−	0.140498i
$154$			15.4972i			1.24880i
$155$	−6.53520	+	6.53520i	−0.524920	+	0.524920i
$156$	25.8235	+	44.7654i	2.06753	+	3.58410i
$157$	−7.33987	−	7.33987i	−0.585785	−	0.585785i	0.350702	−	0.936487i	$-0.385943\pi$
$157$	−7.33987	−	7.33987i	−0.585785	−	0.585785i	−0.936487	+	0.350702i	$0.885943\pi$
$158$	−13.7323			−1.09248
$159$	5.54971	−	3.20142i	0.440121	−	0.253889i
$160$	16.0391	+	16.0391i	1.26800	+	1.26800i
$161$		−	3.61073i		−	0.284565i
$162$	6.41594	−	23.8051i	0.504084	−	1.87031i
$163$	−2.83532	−	2.83532i	−0.222079	−	0.222079i	0.587294	−	0.809374i	$-0.300193\pi$
$163$	−2.83532	−	2.83532i	−0.222079	−	0.222079i	−0.809374	+	0.587294i	$0.800193\pi$
$164$	36.1576	+	36.1576i	2.82343	+	2.82343i
$165$	−1.59489	+	5.94351i	−0.124162	+	0.462701i
$166$	27.8823	−	27.8823i	2.16408	−	2.16408i
$167$	−9.25131			−0.715888			−0.357944	−	0.933743i	$-0.616522\pi$
$167$	−9.25131			−0.715888			−0.357944	+	0.933743i	$0.616522\pi$
$168$	25.5703	+	6.86157i	1.97279	+	0.529382i
$169$	−16.3842			−1.26032
$170$			6.14814i			0.471541i
$171$	1.96207	+	7.34404i	0.150043	+	0.561613i
$172$	3.22884	+	3.22884i	0.246197	+	0.246197i
$173$	1.09012			0.0828805			0.0414402	−	0.999141i	$-0.486805\pi$
$173$	1.09012			0.0828805			0.0414402	+	0.999141i	$0.486805\pi$
$174$	−25.4561	+	2.20525i	−1.92982	+	0.167179i
$175$	1.59227			0.120364
$176$	−38.4095	−	38.4095i	−2.89523	−	2.89523i
$177$	18.1631	−	10.4776i	1.36522	−	0.787546i
$178$			12.2326i			0.916874i
$179$	0.592168			0.0442607			0.0221303	−	0.999755i	$-0.492955\pi$
$179$	0.592168			0.0442607			0.0221303	+	0.999755i	$0.492955\pi$
$180$	14.2946	+	8.26693i	1.06545	+	0.616181i
$181$	−9.12023			−0.677902			−0.338951	−	0.940804i	$-0.610072\pi$
$181$	−9.12023			−0.677902			−0.338951	+	0.940804i	$0.610072\pi$
$182$	−16.7191	+	16.7191i	−1.23930	+	1.23930i
$183$	−17.6619	−	4.73942i	−1.30561	−	0.350348i
$184$	15.3929	+	15.3929i	1.13478	+	1.13478i
$185$	−1.18750	−	1.18750i	−0.0873070	−	0.0873070i
$186$	−21.9121	−	37.9850i	−1.60668	−	2.78520i
$187$		−	7.97387i		−	0.583107i
$188$	−15.9916	−	15.9916i	−1.16631	−	1.16631i
$189$	8.27366	+	0.00908578i	0.601820	+	0.000660893i
$190$	−6.94129			−0.503574
$191$	15.0126	+	15.0126i	1.08628	+	1.08628i	0.995909	+	0.0903669i	$0.0288040\pi$
$191$	15.0126	+	15.0126i	1.08628	+	1.08628i	0.0903669	+	0.995909i	$0.471196\pi$
$192$	−47.3491	+	27.3139i	−3.41713	+	1.97121i
$193$	2.01301	−	2.01301i	0.144900	−	0.144900i	−0.630935	−	0.775835i	$-0.717329\pi$
$193$	2.01301	−	2.01301i	0.144900	−	0.144900i	0.775835	+	0.630935i	$0.217329\pi$
$194$		−	45.8553i		−	3.29222i
$195$	−8.13280	+	4.69151i	−0.582402	+	0.335966i
$196$		−	24.5750i		−	1.75536i
$197$			4.71783i			0.336131i	0.985776	+	0.168066i	$0.0537521\pi$
$197$			4.71783i			0.336131i	−0.985776	+	0.168066i	$0.946248\pi$
$198$	−25.2758	−	14.6177i	−1.79627	−	1.03883i
$199$	−18.5631			−1.31591			−0.657953	−	0.753059i	$-0.728577\pi$
$199$	−18.5631			−1.31591			−0.657953	+	0.753059i	$0.728577\pi$
$200$	−6.78801	+	6.78801i	−0.479985	+	0.479985i
$201$	−2.78433	+	1.60617i	−0.196391	+	0.113291i
$202$			37.8411i			2.66249i
$203$	−2.92877	−	8.05894i	−0.205560	−	0.565627i
$204$	−20.6658	−	5.54550i	−1.44690	−	0.388263i
$205$	−6.56896	+	6.56896i	−0.458796	+	0.458796i
$206$	13.2505	+	13.2505i	0.923207	+	0.923207i
$207$	5.88908	+	3.40581i	0.409319	+	0.236720i
$208$		−	82.8763i		−	5.74644i
$209$	9.00256			0.622720
$210$	−1.95804	+	7.29681i	−0.135117	+	0.503528i
$211$	0.489150	+	0.489150i	0.0336745	+	0.0336745i	0.723744	−	0.690069i	$-0.242420\pi$
$211$	0.489150	+	0.489150i	0.0336745	+	0.0336745i	−0.690069	+	0.723744i	$0.742420\pi$
$212$	−20.3606			−1.39837
$213$	3.05181	+	5.29036i	0.209106	+	0.362489i
$214$	0.318218	−	0.318218i	0.0217529	−	0.0217529i
$215$	−0.586602	+	0.586602i	−0.0400060	+	0.0400060i
$216$	−35.3103	+	35.2328i	−2.40256	+	2.39729i
$217$	10.4058	−	10.4058i	0.706391	−	0.706391i
$218$	28.4727	−	28.4727i	1.92841	−	1.92841i
$219$	4.06667	−	15.1548i	0.274800	−	1.02407i
$220$	13.8283	−	13.8283i	0.932303	−	0.932303i
$221$	8.60261	−	8.60261i	0.578674	−	0.578674i
$222$	6.90221	−	3.98163i	0.463246	−	0.267229i
$223$	−19.4176			−1.30030			−0.650151	−	0.759805i	$-0.725294\pi$
$223$	−19.4176			−1.30030			−0.650151	+	0.759805i	$0.725294\pi$
$224$	−25.5385	−	25.5385i	−1.70637	−	1.70637i
$225$	−1.50190	+	2.59698i	−0.100127	+	0.173132i
$226$	−29.6911			−1.97502
$227$			18.2628i			1.21215i	0.795409	+	0.606073i	$0.207256\pi$
$227$			18.2628i			1.21215i	−0.795409	+	0.606073i	$0.792744\pi$
$228$	6.26091	−	23.3319i	0.414639	−	1.54519i
$229$	−18.1241	−	18.1241i	−1.19768	−	1.19768i	−0.974861	−	0.222816i	$-0.928475\pi$
$229$	−18.1241	−	18.1241i	−1.19768	−	1.19768i	−0.222816	−	0.974861i	$-0.571525\pi$
$230$	−4.39258	+	4.39258i	−0.289638	+	0.289638i
$231$	2.53949	−	9.46365i	0.167086	−	0.622663i
$232$	46.8418	+	21.8705i	3.07532	+	1.43587i
$233$			0.0786482i			0.00515241i	0.999997	+	0.00257621i	$0.000820033\pi$
$233$			0.0786482i			0.00515241i	−0.999997	+	0.00257621i	$0.999180\pi$
$234$	−11.4985	−	43.0390i	−0.751681	−	2.81355i
$235$	2.90529	−	2.90529i	0.189521	−	0.189521i
$236$	−66.6361			−4.33764
$237$	8.38590	+	2.25029i	0.544723	+	0.146172i
$238$		−	9.78948i		−	0.634558i
$239$			19.5678i			1.26574i	0.774259	+	0.632869i	$0.218123\pi$
$239$			19.5678i			1.26574i	−0.774259	+	0.632869i	$0.781877\pi$
$240$	−13.2321	−	22.9380i	−0.854127	−	1.48064i
$241$		−	3.03156i		−	0.195280i	−0.995222	−	0.0976399i	$-0.968871\pi$
$241$		−	3.03156i		−	0.195280i	0.995222	−	0.0976399i	$-0.0311293\pi$
$242$	−3.14379	+	3.14379i	−0.202090	+	0.202090i
$243$	−7.81892	+	13.4857i	−0.501584	+	0.865109i
$244$	41.0926	+	41.0926i	2.63068	+	2.63068i
$245$	4.46468			0.285238
$246$	−22.0253	−	38.1812i	−1.40428	−	2.43435i
$247$	9.71241	+	9.71241i	0.617986	+	0.617986i
$248$			88.7221i			5.63386i
$249$	−21.5959	+	12.4578i	−1.36858	+	0.789484i
$250$	−1.93705	−	1.93705i	−0.122510	−	0.122510i
$251$	−2.96374	−	2.96374i	−0.187070	−	0.187070i	0.607358	−	0.794428i	$-0.292229\pi$
$251$	−2.96374	−	2.96374i	−0.187070	−	0.187070i	−0.794428	+	0.607358i	$0.792229\pi$
$252$	−22.7608	−	13.1632i	−1.43379	−	0.829201i
$253$	5.69698	−	5.69698i	0.358166	−	0.358166i
$254$	−53.6775			−3.36802
$255$	1.00748	−	3.75448i	0.0630911	−	0.235115i
$256$	49.4387			3.08992
$257$		−	19.6791i		−	1.22755i	−0.789481	−	0.613775i	$-0.789650\pi$
$257$		−	19.6791i		−	1.22755i	0.789481	−	0.613775i	$-0.210350\pi$
$258$	−1.96684	−	3.40955i	−0.122450	−	0.212269i
$259$	1.89082	+	1.89082i	0.117490	+	0.117490i
$260$	29.8373			1.85043
$261$	15.9066	+	2.82476i	0.984595	+	0.174848i
$262$	17.1822			1.06152
$263$	−1.93126	−	1.93126i	−0.119087	−	0.119087i	0.645052	−	0.764139i	$-0.276836\pi$
$263$	−1.93126	−	1.93126i	−0.119087	−	0.119087i	−0.764139	+	0.645052i	$0.776836\pi$
$264$	29.5185	+	51.1707i	1.81674	+	3.14934i
$265$		−	3.69903i		−	0.227229i
$266$	11.0524			0.677666
$267$	2.00454	−	7.47010i	0.122676	−	0.457162i
$268$	10.2150			0.623983
$269$	9.63194	−	9.63194i	0.587270	−	0.587270i	−0.349621	−	0.936891i	$-0.613690\pi$
$269$	9.63194	−	9.63194i	0.587270	−	0.587270i	0.936891	+	0.349621i	$0.113690\pi$
$270$	−10.0541	−	10.0762i	−0.611875	−	0.613221i
$271$	−3.05787	−	3.05787i	−0.185752	−	0.185752i	0.608105	−	0.793857i	$-0.291930\pi$
$271$	−3.05787	−	3.05787i	−0.185752	−	0.185752i	−0.793857	+	0.608105i	$0.791930\pi$
$272$	24.2631	+	24.2631i	1.47117	+	1.47117i
$273$	12.9496	−	7.47013i	0.783745	−	0.452113i
$274$		−	15.7920i		−	0.954029i
$275$	2.51227	+	2.51227i	0.151495	+	0.151495i
$276$	−10.8028	−	18.7269i	−0.650253	−	1.12722i
$277$	−7.70541			−0.462973			−0.231487	−	0.972838i	$-0.574359\pi$
$277$	−7.70541			−0.462973			−0.231487	+	0.972838i	$0.574359\pi$
$278$	26.5553	+	26.5553i	1.59268	+	1.59268i
$279$	7.15654	+	26.7870i	0.428451	+	1.60370i
$280$	10.8083	−	10.8083i	0.645921	−	0.645921i
$281$		−	11.9105i		−	0.710522i	−0.934767	−	0.355261i	$-0.884392\pi$
$281$		−	11.9105i		−	0.710522i	0.934767	−	0.355261i	$-0.115608\pi$
$282$	9.74127	+	16.8866i	0.580084	+	1.00559i
$283$		−	0.222685i		−	0.0132372i	−0.999978	−	0.00661862i	$-0.997893\pi$
$283$		−	0.222685i		−	0.0132372i	0.999978	−	0.00661862i	$-0.00210679\pi$
$284$		−	19.4091i		−	1.15172i
$285$	4.23884	+	1.13746i	0.251087	+	0.0673771i
$286$	−52.7586			−3.11968
$287$	10.4595	−	10.4595i	0.617408	−	0.617408i
$288$	65.7423	−	17.5640i	3.87390	−	1.03497i
$289$		−	11.9629i		−	0.703703i
$290$	−6.24102	+	13.3669i	−0.366485	+	0.784933i
$291$	−7.51422	+	28.0024i	−0.440491	+	1.64153i
$292$	−35.2595	+	35.2595i	−2.06341	+	2.06341i
$293$	0.391762	+	0.391762i	0.0228870	+	0.0228870i	0.718458	−	0.695571i	$-0.244848\pi$
$293$	0.391762	+	0.391762i	0.0228870	+	0.0228870i	−0.695571	+	0.718458i	$0.744848\pi$
$294$	−5.49030	+	20.4601i	−0.320201	+	1.19326i
$295$		−	12.1062i		−	0.704849i
$296$	−16.1216			−0.937048
$297$	13.0398	+	13.0685i	0.756645	+	0.758309i
$298$	38.5615	+	38.5615i	2.23381	+	2.23381i
$299$	12.2924			0.710887
$300$	8.25821	−	4.76385i	0.476788	−	0.275041i
$301$	0.934028	−	0.934028i	0.0538365	−	0.0538365i
$302$	−13.9317	+	13.9317i	−0.801678	+	0.801678i
$303$	6.20095	−	23.1084i	0.356235	−	1.32754i
$304$	−27.3932	+	27.3932i	−1.57111	+	1.57111i
$305$	−7.46553	+	7.46553i	−0.427475	+	0.427475i
$306$	15.9666	+	9.23390i	0.912748	+	0.527867i
$307$	12.5167	−	12.5167i	0.714367	−	0.714367i	−0.253079	−	0.967446i	$-0.581443\pi$
$307$	12.5167	−	12.5167i	0.714367	−	0.714367i	0.967446	+	0.253079i	$0.0814431\pi$
$308$	−22.0183	+	22.0183i	−1.25461	+	1.25461i
$309$	−5.92035	−	10.2630i	−0.336797	−	0.583843i
$310$	−25.3180			−1.43797
$311$	−7.23981	−	7.23981i	−0.410532	−	0.410532i	0.471392	−	0.881924i	$-0.343752\pi$
$311$	−7.23981	−	7.23981i	−0.410532	−	0.410532i	−0.881924	+	0.471392i	$0.843752\pi$
$312$	−23.3595	+	87.0515i	−1.32247	+	4.92832i
$313$	6.37435			0.360300			0.180150	−	0.983639i	$-0.442342\pi$
$313$	6.37435			0.360300			0.180150	+	0.983639i	$0.442342\pi$
$314$		−	28.4353i		−	1.60470i
$315$	2.39143	−	4.13508i	0.134742	−	0.232986i
$316$	−19.5108	−	19.5108i	−1.09757	−	1.09757i
$317$	−3.85301	+	3.85301i	−0.216407	+	0.216407i	−0.806982	−	0.590576i	$-0.798901\pi$
$317$	−3.85301	+	3.85301i	−0.216407	+	0.216407i	0.590576	+	0.806982i	$0.298901\pi$
$318$	16.9514	+	4.54876i	0.950585	+	0.255082i
$319$	8.09433	−	17.3363i	0.453196	−	0.970648i
$320$			31.5594i			1.76422i
$321$	−0.246472	+	0.142180i	−0.0137567	+	0.00793572i
$322$	6.99416	−	6.99416i	0.389769	−	0.389769i
$323$	−5.68687			−0.316426
$324$	42.9381	−	24.7065i	2.38545	−	1.37259i
$325$			5.42072i			0.300688i
$326$		−	10.9843i		−	0.608364i
$327$	−22.0532	+	12.7216i	−1.21954	+	0.703508i
$328$			89.1804i			4.92416i
$329$	−4.62601	+	4.62601i	−0.255040	+	0.255040i
$330$	−14.6022	+	8.42348i	−0.803826	+	0.463697i
$331$	15.1637	+	15.1637i	0.833470	+	0.833470i	0.987990	−	0.154520i	$-0.0493831\pi$
$331$	15.1637	+	15.1637i	0.833470	+	0.833470i	−0.154520	+	0.987990i	$0.549383\pi$
$332$	79.2301			4.34832
$333$	−4.86743	+	1.30041i	−0.266734	+	0.0712618i
$334$	−17.9202	−	17.9202i	−0.980551	−	0.980551i
$335$			1.85583i			0.101395i
$336$	21.0690	+	36.5235i	1.14941	+	1.99252i
$337$	6.16123	+	6.16123i	0.335624	+	0.335624i	0.854717	−	0.519094i	$-0.173730\pi$
$337$	6.16123	+	6.16123i	0.335624	+	0.335624i	−0.519094	+	0.854717i	$0.673730\pi$
$338$	−31.7370	−	31.7370i	−1.72627	−	1.72627i
$339$	18.1314	+	4.86542i	0.984765	+	0.264253i
$340$	−8.73526	+	8.73526i	−0.473736	+	0.473736i
$341$	32.8364			1.77819
$342$	−10.4251	+	18.0264i	−0.563727	+	0.974755i
$343$	−18.2548			−0.985669
$344$			7.96373i			0.429375i
$345$	3.40222	−	1.96261i	0.183169	−	0.105663i
$346$	2.11162	+	2.11162i	0.113521	+	0.113521i
$347$	−12.2488			−0.657552			−0.328776	−	0.944408i	$-0.606636\pi$
$347$	−12.2488			−0.657552			−0.328776	+	0.944408i	$0.606636\pi$
$348$	−39.3012	−	33.0347i	−2.10676	−	1.77085i
$349$	13.4198			0.718344			0.359172	−	0.933271i	$-0.383059\pi$
$349$	13.4198			0.718344			0.359172	+	0.933271i	$0.383059\pi$
$350$	3.08430	+	3.08430i	0.164863	+	0.164863i
$351$	−0.0309316	+	28.1669i	−0.00165101	+	1.50344i
$352$		−	80.5890i		−	4.29541i
$353$	−23.6542			−1.25898			−0.629492	−	0.777007i	$-0.716737\pi$
$353$	−23.6542			−1.25898			−0.629492	+	0.777007i	$0.716737\pi$
$354$	55.4784	+	14.8872i	2.94865	+	0.791244i
$355$	3.52616			0.187149
$356$	−17.3801	+	17.3801i	−0.921143	+	0.921143i
$357$	−1.60418	+	5.97814i	−0.0849024	+	0.316397i
$358$	1.14706	+	1.14706i	0.0606239	+	0.0606239i
$359$	−15.8691	−	15.8691i	−0.837539	−	0.837539i	0.150996	−	0.988534i	$-0.451752\pi$
$359$	−15.8691	−	15.8691i	−0.837539	−	0.837539i	−0.988534	+	0.150996i	$0.951752\pi$
$360$	7.43339	+	27.8232i	0.391774	+	1.46641i
$361$			12.5795i			0.662078i
$362$	−17.6663	−	17.6663i	−0.928522	−	0.928522i
$363$	2.43498	−	1.40465i	0.127803	−	0.0737250i
$364$	−47.5090			−2.49015
$365$	−6.40581	−	6.40581i	−0.335295	−	0.335295i
$366$	−25.0315	−	43.3924i	−1.30842	−	2.26816i
$367$	15.2494	−	15.2494i	0.796010	−	0.796010i	−0.186454	−	0.982464i	$-0.559699\pi$
$367$	15.2494	−	15.2494i	0.796010	−	0.796010i	0.982464	+	0.186454i	$0.0596994\pi$
$368$			34.6699i			1.80729i
$369$	7.19351	+	26.9254i	0.374479	+	1.40168i
$370$		−	4.60050i		−	0.239169i
$371$			5.88984i			0.305785i
$372$	22.8363	−	85.1018i	1.18401	−	4.41232i
$373$	27.4763			1.42267			0.711334	−	0.702854i	$-0.248091\pi$
$373$	27.4763			1.42267			0.711334	+	0.702854i	$0.248091\pi$
$374$	15.4458	−	15.4458i	0.798682	−	0.798682i
$375$	0.865476	+	1.50032i	0.0446930	+	0.0774760i
$376$		−	39.4423i		−	2.03408i
$377$	27.4359	−	9.97072i	1.41302	−	0.513518i
$378$	16.0089	+	16.0441i	0.823408	+	0.825218i
$379$	17.2230	−	17.2230i	0.884684	−	0.884684i	−0.109322	−	0.994006i	$-0.534868\pi$
$379$	17.2230	−	17.2230i	0.884684	−	0.884684i	0.994006	+	0.109322i	$0.0348680\pi$
$380$	−9.86218	−	9.86218i	−0.505919	−	0.505919i
$381$	32.7792	+	8.79603i	1.67933	+	0.450634i
$382$			58.1603i			2.97574i
$383$	13.5536			0.692558			0.346279	−	0.938132i	$-0.387445\pi$
$383$	13.5536			0.692558			0.346279	+	0.938132i	$0.387445\pi$
$384$	−68.7355	−	18.4446i	−3.50764	−	0.941246i
$385$	−4.00020	−	4.00020i	−0.203869	−	0.203869i
$386$	7.79861			0.396939
$387$	0.642374	+	2.40441i	0.0326537	+	0.122223i
$388$	65.1511	−	65.1511i	3.30755	−	3.30755i
$389$	−13.9518	+	13.9518i	−0.707386	+	0.707386i	−0.965985	−	0.258599i	$-0.916739\pi$
$389$	−13.9518	+	13.9518i	−0.707386	+	0.707386i	0.258599	+	0.965985i	$0.416739\pi$
$390$	−24.8413	−	6.66595i	−1.25789	−	0.337544i
$391$	−3.59875	+	3.59875i	−0.181997	+	0.181997i
$392$	30.3063	−	30.3063i	1.53070	−	1.53070i
$393$	−10.4926	−	2.81561i	−0.529284	−	0.142029i
$394$	−9.13866	+	9.13866i	−0.460399	+	0.460399i
$395$	3.54465	−	3.54465i	0.178351	−	0.178351i
$396$	−15.1430	−	56.6805i	−0.760966	−	2.84830i
$397$	−5.38419			−0.270225			−0.135112	−	0.990830i	$-0.543140\pi$
$397$	−5.38419			−0.270225			−0.135112	+	0.990830i	$0.543140\pi$
$398$	−35.9577	−	35.9577i	−1.80240	−	1.80240i
$399$	−6.74937	−	1.81114i	−0.337891	−	0.0906702i
$400$	−15.2888			−0.764440
$401$		−	8.94942i		−	0.446913i	−0.974714	−	0.223456i	$-0.928266\pi$
$401$		−	8.94942i		−	0.446913i	0.974714	−	0.223456i	$-0.0717340\pi$
$402$	−8.50462	−	2.28214i	−0.424172	−	0.113823i
$403$	35.4255	+	35.4255i	1.76467	+	1.76467i
$404$	−53.7646	+	53.7646i	−2.67489	+	2.67489i
$405$	4.48858	+	7.80081i	0.223039	+	0.387625i
$406$	9.93737	−	21.2837i	0.493184	−	1.05629i
$407$			5.96665i			0.295756i
$408$	−18.6467	−	32.3243i	−0.923147	−	1.60029i
$409$	−20.5964	+	20.5964i	−1.01842	+	1.01842i	−0.0185969	+	0.999827i	$0.505920\pi$
$409$	−20.5964	+	20.5964i	−1.01842	+	1.01842i	−0.999827	+	0.0185969i	$0.994080\pi$
$410$	−25.4488			−1.25683
$411$	−2.58780	+	9.64370i	−0.127647	+	0.475688i
$412$			37.6526i			1.85501i
$413$			19.2763i			0.948524i
$414$	4.81020	+	18.0046i	0.236409	+	0.884880i
$415$			14.3942i			0.706584i
$416$	86.9435	−	86.9435i	4.26275	−	4.26275i
$417$	−11.8649	−	20.5681i	−0.581029	−	1.00722i
$418$	17.4384	+	17.4384i	0.852939	+	0.852939i
$419$	−13.7990			−0.674126			−0.337063	−	0.941482i	$-0.609434\pi$
$419$	−13.7990			−0.674126			−0.337063	+	0.941482i	$0.609434\pi$
$420$	−13.1493	+	7.58532i	−0.641619	+	0.370126i
$421$	13.4860	+	13.4860i	0.657266	+	0.657266i	0.954732	−	0.297467i	$-0.0961417\pi$
$421$	13.4860	+	13.4860i	0.657266	+	0.657266i	−0.297467	+	0.954732i	$0.596142\pi$
$422$			1.89501i			0.0922478i
$423$	−3.18152	−	11.9085i	−0.154691	−	0.579009i
$424$	−25.1090	−	25.1090i	−1.21940	−	1.21940i
$425$	−1.58699	−	1.58699i	−0.0769802	−	0.0769802i
$426$	−4.33618	+	16.1592i	−0.210089	+	0.782915i
$427$	11.8871	−	11.8871i	0.575258	−	0.575258i
$428$	0.904246			0.0437084
$429$	32.2181	+	8.64545i	1.55550	+	0.417406i
$430$	−2.27255			−0.109592
$431$			8.11323i			0.390800i	0.980724	+	0.195400i	$0.0626006\pi$
$431$			8.11323i			0.390800i	−0.980724	+	0.195400i	$0.937399\pi$
$432$	−79.4428	−	0.0872407i	−3.82220	−	0.00419737i
$433$	−25.0939	−	25.0939i	−1.20594	−	1.20594i	−0.972331	−	0.233606i	$-0.924947\pi$
$433$	−25.0939	−	25.0939i	−1.20594	−	1.20594i	−0.233606	−	0.972331i	$-0.575053\pi$
$434$	40.3130			1.93509
$435$	6.00161	−	7.14007i	0.287755	−	0.342340i
$436$	80.9078			3.87478
$437$	−4.06302	−	4.06302i	−0.194361	−	0.194361i
$438$	37.2329	−	21.4783i	1.77906	−	1.02627i
$439$		−	18.9770i		−	0.905724i	−0.891581	−	0.452862i	$-0.850403\pi$
$439$		−	18.9770i		−	0.905724i	0.891581	−	0.452862i	$-0.149597\pi$
$440$	34.1066			1.62597
$441$	6.70552	−	11.5947i	0.319310	−	0.552128i
$442$	33.3273			1.58522
$443$	−28.6076	+	28.6076i	−1.35919	+	1.35919i	−0.484264	+	0.874922i	$0.660913\pi$
$443$	−28.6076	+	28.6076i	−1.35919	+	1.35919i	−0.874922	+	0.484264i	$0.839087\pi$
$444$	15.4637	+	4.14956i	0.733876	+	0.196930i
$445$	−3.15754	−	3.15754i	−0.149682	−	0.149682i
$446$	−37.6129	−	37.6129i	−1.78102	−	1.78102i
$447$	−17.2293	−	29.8673i	−0.814919	−	1.41268i
$448$		−	50.2510i		−	2.37414i
$449$	−9.47070	−	9.47070i	−0.446950	−	0.446950i	0.447389	−	0.894339i	$-0.352354\pi$
$449$	−9.47070	−	9.47070i	−0.446950	−	0.446950i	−0.894339	+	0.447389i	$0.852354\pi$
$450$	−7.93972	+	2.12121i	−0.374282	+	0.0999950i
$451$	33.0060			1.55419
$452$	−42.1850	−	42.1850i	−1.98422	−	1.98422i
$453$	10.7906	−	6.22470i	0.506987	−	0.292462i
$454$	−35.3759	+	35.3759i	−1.66028	+	1.66028i
$455$		−	8.63124i		−	0.404639i
$456$	36.4944	−	21.0522i	1.70900	−	0.985860i
$457$		−	6.85908i		−	0.320854i	−0.987048	−	0.160427i	$-0.948713\pi$
$457$		−	6.85908i		−	0.320854i	0.987048	−	0.160427i	$-0.0512871\pi$
$458$		−	70.2146i		−	3.28091i
$459$	−8.23716	−	8.25527i	−0.384478	−	0.385323i
$460$	−12.4819			−0.581973
$461$	−12.8682	+	12.8682i	−0.599332	+	0.599332i	−0.940135	−	0.340803i	$-0.889301\pi$
$461$	−12.8682	+	12.8682i	−0.599332	+	0.599332i	0.340803	+	0.940135i	$0.389301\pi$
$462$	23.2507	−	13.4124i	1.08172	−	0.624003i
$463$			21.1440i			0.982647i	0.870977	+	0.491324i	$0.163487\pi$
$463$			21.1440i			0.982647i	−0.870977	+	0.491324i	$0.836513\pi$
$464$	28.1218	+	77.3811i	1.30552	+	3.59233i
$465$	15.4609	+	4.14881i	0.716984	+	0.192397i
$466$	−0.152345	+	0.152345i	−0.00705726	+	0.00705726i
$467$	6.85345	+	6.85345i	0.317140	+	0.317140i	0.847667	−	0.530528i	$-0.178006\pi$
$467$	6.85345	+	6.85345i	0.317140	+	0.317140i	−0.530528	+	0.847667i	$0.678006\pi$
$468$	44.8127	−	77.4868i	2.07147	−	3.58183i
$469$		−	2.95497i		−	0.136448i
$470$	11.2554			0.519172
$471$	−4.65965	+	17.3646i	−0.214705	+	0.800119i
$472$	−82.1769	−	82.1769i	−3.78250	−	3.78250i
$473$	2.94740			0.135522
$474$	11.8850	+	20.6028i	0.545895	+	0.946318i
$475$	1.79172	−	1.79172i	0.0822097	−	0.0822097i
$476$	13.9089	−	13.9089i	0.637512	−	0.637512i
$477$	−9.60629	−	5.55557i	−0.439842	−	0.254372i
$478$	−37.9038	+	37.9038i	−1.73368	+	1.73368i
$479$	−4.28513	+	4.28513i	−0.195792	+	0.195792i	−0.798194	−	0.602401i	$-0.794211\pi$
$479$	−4.28513	+	4.28513i	−0.195792	+	0.195792i	0.602401	+	0.798194i	$0.294211\pi$
$480$	10.1823	−	37.9452i	0.464755	−	1.73195i
$481$	−6.43713	+	6.43713i	−0.293508	+	0.293508i
$482$	5.87227	−	5.87227i	0.267475	−	0.267475i
$483$	−5.41724	+	3.12500i	−0.246493	+	0.142193i
$484$	−8.93337			−0.406062
$485$	11.8364	+	11.8364i	0.537462	+	0.537462i
$486$	−41.2681	+	10.9768i	−1.87196	+	0.497920i
$487$	−24.4125			−1.10624			−0.553118	−	0.833103i	$-0.686562\pi$
$487$	−24.4125			−1.10624			−0.553118	+	0.833103i	$0.686562\pi$
$488$			101.352i			4.58800i
$489$	−1.79998	+	6.70778i	−0.0813977	+	0.303336i
$490$	8.64830	+	8.64830i	0.390691	+	0.390691i
$491$	0.830529	−	0.830529i	0.0374813	−	0.0374813i	−0.688118	−	0.725599i	$-0.741563\pi$
$491$	0.830529	−	0.830529i	0.0374813	−	0.0374813i	0.725599	+	0.688118i	$0.241563\pi$
$492$	22.9543	−	85.5414i	1.03486	−	3.85650i
$493$	−5.11315	+	10.9513i	−0.230285	+	0.493220i
$494$			37.6268i			1.69291i
$495$	10.2975	−	2.75112i	0.462837	−	0.123654i
$496$	−99.9154	+	99.9154i	−4.48633	+	4.48633i
$497$	−5.61459			−0.251849
$498$	−65.9637	−	17.7008i	−2.95590	−	0.793191i
$499$		−	21.7815i		−	0.975072i	−0.873103	−	0.487536i	$-0.837896\pi$
$499$		−	21.7815i		−	0.975072i	0.873103	−	0.487536i	$-0.162104\pi$
$500$		−	5.50431i		−	0.246160i
$501$	8.00679	+	13.8799i	0.357717	+	0.620108i
$502$		−	11.4818i		−	0.512458i
$503$	−3.19151	+	3.19151i	−0.142302	+	0.142302i	−0.774669	−	0.632367i	$-0.782084\pi$
$503$	−3.19151	+	3.19151i	−0.142302	+	0.142302i	0.632367	+	0.774669i	$0.282084\pi$
$504$	−11.8359	−	44.3020i	−0.527215	−	1.97337i
$505$	−9.76773	−	9.76773i	−0.434658	−	0.434658i
$506$	22.0707			0.981160
$507$	14.1802	+	24.5815i	0.629763	+	1.09170i
$508$	−76.2649	−	76.2649i	−3.38371	−	3.38371i
$509$		−	22.4492i		−	0.995045i	−0.867451	−	0.497522i	$-0.834243\pi$
$509$		−	22.4492i		−	0.995045i	0.867451	−	0.497522i	$-0.165757\pi$
$510$	9.22415	−	5.32107i	0.408452	−	0.235621i
$511$	10.1998	+	10.1998i	0.451211	+	0.451211i
$512$	37.6574	+	37.6574i	1.66424	+	1.66424i
$513$	9.32027	−	9.29982i	0.411500	−	0.410597i
$514$	38.1194	−	38.1194i	1.68137	−	1.68137i
$515$	−6.84057			−0.301432
$516$	2.04980	−	7.63877i	0.0902374	−	0.336278i
$517$	−14.5978			−0.642009
$518$			7.32523i			0.321852i
$519$	−0.943475	−	1.63553i	−0.0414140	−	0.0717918i
$520$	36.7959	+	36.7959i	1.61361	+	1.61361i
$521$	2.88860			0.126552			0.0632760	−	0.997996i	$-0.479845\pi$
$521$	2.88860			0.126552			0.0632760	+	0.997996i	$0.479845\pi$
$522$	25.3402	+	36.2836i	1.10911	+	1.58809i
$523$	1.75222			0.0766194			0.0383097	−	0.999266i	$-0.487803\pi$
$523$	1.75222			0.0766194			0.0383097	+	0.999266i	$0.487803\pi$
$524$	24.4124	+	24.4124i	1.06646	+	1.06646i
$525$	−1.37807	−	2.38891i	−0.0601439	−	0.104260i
$526$		−	7.48190i		−	0.326226i
$527$	−20.7426			−0.903560
$528$	−24.3839	+	90.8690i	−1.06117	+	3.95457i
$529$	17.8577			0.776421
$530$	7.16519	−	7.16519i	0.311236	−	0.311236i
$531$	−31.4395	−	18.1823i	−1.36436	−	0.789044i
$532$	15.7032	+	15.7032i	0.680821	+	0.680821i
$533$	35.6085	+	35.6085i	1.54238	+	1.54238i
$534$	18.3528	−	10.5870i	0.794204	−	0.458146i
$535$			0.164280i			0.00710243i
$536$	12.5974	+	12.5974i	0.544124	+	0.544124i
$537$	−0.512507	−	0.888439i	−0.0221163	−	0.0383390i
$538$	37.3151			1.60877
$539$	−11.2165	−	11.2165i	−0.483128	−	0.483128i
$540$	0.0314086	−	28.6012i	0.00135161	−	1.23080i
$541$	−13.5847	+	13.5847i	−0.584053	+	0.584053i	−0.936014	−	0.351962i	$-0.885515\pi$
$541$	−13.5847	+	13.5847i	−0.584053	+	0.584053i	0.351962	+	0.936014i	$0.385515\pi$
$542$		−	11.8465i		−	0.508849i
$543$	7.89335	+	13.6832i	0.338736	+	0.587204i
$544$			50.9077i			2.18265i
$545$			14.6990i			0.629636i
$546$	39.5540	+	10.6140i	1.69275	+	0.454236i
$547$	−2.68306			−0.114719			−0.0573596	−	0.998354i	$-0.518268\pi$
$547$	−2.68306			−0.114719			−0.0573596	+	0.998354i	$0.518268\pi$
$548$	22.4372	−	22.4372i	0.958471	−	0.958471i
$549$	8.17532	+	30.6003i	0.348914	+	1.30599i
$550$			9.73277i			0.415007i
$551$	−12.3641	−	5.77278i	−0.526727	−	0.245929i
$552$	9.77207	−	36.4165i	0.415927	−	1.54999i
$553$	−5.64403	+	5.64403i	−0.240008	+	0.240008i
$554$	−14.9258	−	14.9258i	−0.634134	−	0.634134i
$555$	−0.753875	+	2.80939i	−0.0320002	+	0.119252i
$556$			75.4594i			3.20019i
$557$	38.3013			1.62288			0.811439	−	0.584437i	$-0.198685\pi$
$557$	38.3013			1.62288			0.811439	+	0.584437i	$0.198685\pi$
$558$	−38.0251	+	65.7503i	−1.60973	+	2.78343i
$559$	3.17981	+	3.17981i	0.134492	+	0.134492i
$560$	24.3438			1.02872
$561$	−11.9633	+	6.90119i	−0.505092	+	0.291369i
$562$	23.0712	−	23.0712i	0.973202	−	0.973202i
$563$	29.4969	−	29.4969i	1.24315	−	1.24315i	0.284458	−	0.958688i	$-0.408186\pi$
$563$	29.4969	−	29.4969i	1.24315	−	1.24315i	0.958688	−	0.284458i	$-0.0918137\pi$
$564$	−10.1521	+	37.8329i	−0.427482	+	1.59305i
$565$	7.66400	−	7.66400i	0.322427	−	0.322427i
$566$	0.431351	−	0.431351i	0.0181310	−	0.0181310i
$567$	−7.14703	−	12.4210i	−0.300147	−	0.521632i
$568$	23.9356	−	23.9356i	1.00432	−	1.00432i
$569$	14.9735	−	14.9735i	0.627722	−	0.627722i	−0.319772	−	0.947495i	$-0.603606\pi$
$569$	14.9735	−	14.9735i	0.627722	−	0.627722i	0.947495	+	0.319772i	$0.103606\pi$
$570$	6.00752	+	10.4141i	0.251628	+	0.436200i
$571$	31.8904			1.33457			0.667286	−	0.744801i	$-0.267456\pi$
$571$	31.8904			1.33457			0.667286	+	0.744801i	$0.267456\pi$
$572$	−74.9593	−	74.9593i	−3.13421	−	3.13421i
$573$	9.53062	−	35.5168i	0.398148	−	1.48373i
$574$	40.5213			1.69133
$575$		−	2.26767i		−	0.0945682i
$576$	81.9591	+	47.3991i	3.41496	+	1.97496i
$577$	14.1141	+	14.1141i	0.587577	+	0.587577i	0.936974	−	0.349398i	$-0.113614\pi$
$577$	14.1141	+	14.1141i	0.587577	+	0.587577i	−0.349398	+	0.936974i	$0.613614\pi$
$578$	23.1728	−	23.1728i	0.963861	−	0.963861i
$579$	−4.76237	−	1.27794i	−0.197917	−	0.0531095i
$580$	−27.8589	+	10.1245i	−1.15678	+	0.420396i
$581$		−	22.9194i		−	0.950858i
$582$	−68.7974	+	39.6866i	−2.85175	+	1.64506i
$583$	−9.29295	+	9.29295i	−0.384875	+	0.384875i
$584$	−86.9654			−3.59865
$585$	14.0775	+	8.14139i	0.582033	+	0.336605i
$586$			1.51772i			0.0626965i
$587$		−	37.8614i		−	1.56271i	−0.624088	−	0.781354i	$-0.714529\pi$
$587$		−	37.8614i		−	1.56271i	0.624088	−	0.781354i	$-0.285471\pi$
$588$	−36.8703	+	21.2691i	−1.52050	+	0.877122i
$589$		−	23.4185i		−	0.964943i
$590$	23.4503	−	23.4503i	0.965432	−	0.965432i
$591$	7.07824	−	4.08317i	0.291160	−	0.167959i
$592$	−18.1555	−	18.1555i	−0.746186	−	0.746186i
$593$	−4.24731			−0.174416			−0.0872080	−	0.996190i	$-0.527794\pi$
$593$	−4.24731			−0.174416			−0.0872080	+	0.996190i	$0.527794\pi$
$594$	−0.0555370	+	50.5729i	−0.00227871	+	2.07503i
$595$	2.52691	+	2.52691i	0.103593	+	0.103593i
$596$			109.576i			4.48841i
$597$	16.0660	+	27.8506i	0.657536	+	1.13985i
$598$	23.8109	+	23.8109i	0.973702	+	0.973702i
$599$	33.2384	+	33.2384i	1.35809	+	1.35809i	0.876276	+	0.481809i	$0.160020\pi$
$599$	33.2384	+	33.2384i	1.35809	+	1.35809i	0.481809	+	0.876276i	$0.339980\pi$
$600$	16.0590	+	4.30931i	0.655607	+	0.175927i
$601$	−6.75296	+	6.75296i	−0.275459	+	0.275459i	−0.831293	−	0.555834i	$-0.812399\pi$
$601$	−6.75296	+	6.75296i	−0.275459	+	0.275459i	0.555834	+	0.831293i	$0.312399\pi$
$602$	3.61851			0.147480
$603$	4.81954	+	2.78727i	0.196267	+	0.113506i
$604$	−39.5882			−1.61082
$605$		−	1.62298i		−	0.0659834i
$606$	56.7737	−	32.7506i	2.30627	−	1.33040i
$607$	12.3361	+	12.3361i	0.500708	+	0.500708i	0.911658	−	0.410950i	$-0.134803\pi$
$607$	12.3361	+	12.3361i	0.500708	+	0.500708i	−0.410950	+	0.911658i	$0.634803\pi$
$608$	−57.4751			−2.33092
$609$	−9.55618	+	11.3689i	−0.387236	+	0.460691i
$610$	−28.9222			−1.17102
$611$	−15.7488	−	15.7488i	−0.637128	−	0.637128i
$612$	9.56577	+	35.8048i	0.386673	+	1.44732i
$613$			12.7794i			0.516155i	0.966124	+	0.258077i	$0.0830889\pi$
$613$			12.7794i			0.516155i	−0.966124	+	0.258077i	$0.916911\pi$
$614$	48.4910			1.95694
$615$	15.5408	+	4.17024i	0.626666	+	0.168160i
$616$	−54.3069			−2.18809
$617$	1.63094	−	1.63094i	0.0656592	−	0.0656592i	−0.673515	−	0.739174i	$-0.735216\pi$
$617$	1.63094	−	1.63094i	0.0656592	−	0.0656592i	0.739174	+	0.673515i	$0.235216\pi$
$618$	8.41197	−	31.3480i	0.338379	−	1.26100i
$619$	−7.67417	−	7.67417i	−0.308451	−	0.308451i	0.535857	−	0.844308i	$-0.319988\pi$
$619$	−7.67417	−	7.67417i	−0.308451	−	0.308451i	−0.844308	+	0.535857i	$0.819988\pi$
$620$	−35.9718	−	35.9718i	−1.44466	−	1.44466i
$621$	0.0129397	−	11.7831i	0.000519253	−	0.472841i
$622$		−	28.0477i		−	1.12461i
$623$	5.02766	+	5.02766i	0.201429	+	0.201429i
$624$	−124.341	+	71.7274i	−4.97761	+	2.87140i
$625$	1.00000			0.0400000
$626$	12.3474	+	12.3474i	0.493502	+	0.493502i
$627$	−7.79150	−	13.5067i	−0.311163	−	0.539405i
$628$	40.4009	−	40.4009i	1.61217	−	1.61217i
$629$		−	3.76910i		−	0.150284i
$630$	12.6422	−	3.37754i	0.503676	−	0.134564i
$631$		−	5.67773i		−	0.226027i	−0.993593	−	0.113013i	$-0.963950\pi$
$631$		−	5.67773i		−	0.226027i	0.993593	−	0.113013i	$-0.0360503\pi$
$632$		−	48.1222i		−	1.91420i
$633$	0.310532	−	1.15723i	0.0123425	−	0.0459956i
$634$	−14.9269			−0.592824
$635$	13.8555	−	13.8555i	0.549838	−	0.549838i
$636$	17.6216	+	30.5473i	0.698742	+	1.21128i
$637$		−	24.2018i		−	0.958910i
$638$	49.2604	−	17.9022i	1.95024	−	0.708754i
$639$	5.29595	−	9.15736i	0.209504	−	0.362260i
$640$	−29.0539	+	29.0539i	−1.14846	+	1.14846i
$641$	−33.9073	−	33.9073i	−1.33926	−	1.33926i	−0.896780	−	0.442476i	$-0.854100\pi$
$641$	−33.9073	−	33.9073i	−1.33926	−	1.33926i	−0.442476	−	0.896780i	$-0.645900\pi$
$642$	−0.752837	−	0.202017i	−0.0297121	−	0.00797299i
$643$			14.0115i			0.552560i	0.961077	+	0.276280i	$0.0891018\pi$
$643$			14.0115i			0.552560i	−0.961077	+	0.276280i	$0.910898\pi$
$644$	19.8746			0.783168
$645$	1.38778	+	0.372399i	0.0546438	+	0.0146632i
$646$	−11.0157	−	11.0157i	−0.433408	−	0.433408i
$647$	−24.7453			−0.972838			−0.486419	−	0.873726i	$-0.661697\pi$
$647$	−24.7453			−0.972838			−0.486419	+	0.873726i	$0.661697\pi$
$648$	83.4205	+	22.4834i	3.27707	+	0.883233i
$649$	−30.4140	+	30.4140i	−1.19385	+	1.19385i
$650$	−10.5002	+	10.5002i	−0.411852	+	0.411852i
$651$	−24.6180	−	6.60602i	−0.964854	−	0.258910i
$652$	15.6065	−	15.6065i	0.611197	−	0.611197i
$653$	−4.91961	+	4.91961i	−0.192519	+	0.192519i	−0.796784	−	0.604265i	$-0.793467\pi$
$653$	−4.91961	+	4.91961i	−0.192519	+	0.192519i	0.604265	+	0.796784i	$0.293467\pi$
$654$	−67.3604	−	18.0756i	−2.63400	−	0.706812i
$655$	−4.43515	+	4.43515i	−0.173296	+	0.173296i
$656$	−100.431	+	100.431i	−3.92119	+	3.92119i
$657$	−26.2566	+	7.01484i	−1.02437	+	0.273675i
$658$	−17.9216			−0.698656
$659$	−8.18968	−	8.18968i	−0.319025	−	0.319025i	0.529368	−	0.848392i	$-0.322429\pi$
$659$	−8.18968	−	8.18968i	−0.319025	−	0.319025i	−0.848392	+	0.529368i	$0.822429\pi$
$660$	−32.7149	−	8.77876i	−1.27343	−	0.341713i
$661$	14.4412			0.561699			0.280849	−	0.959752i	$-0.409384\pi$
$661$	14.4412			0.561699			0.280849	+	0.959752i	$0.409384\pi$
$662$			58.7454i			2.28321i
$663$	−20.3520	−	5.46129i	−0.790406	−	0.212099i
$664$	97.7080	+	97.7080i	3.79181	+	3.79181i
$665$	−2.85290	+	2.85290i	−0.110631	+	0.110631i
$666$	−11.9474	−	6.90950i	−0.462952	−	0.267738i
$667$	−11.4773	+	4.17108i	−0.444404	+	0.161505i
$668$		−	50.9221i		−	1.97023i
$669$	16.8055	+	29.1326i	0.649738	+	1.12633i
$670$	−3.59483	+	3.59483i	−0.138880	+	0.138880i
$671$	37.5108			1.44809
$672$	−16.2129	+	60.4189i	−0.625426	+	2.33071i
$673$		−	17.7314i		−	0.683497i	−0.939792	−	0.341748i	$-0.888981\pi$
$673$		−	17.7314i		−	0.683497i	0.939792	−	0.341748i	$-0.111019\pi$
$674$			23.8692i			0.919407i
$675$	5.19615	+	0.00570619i	0.200000	+	0.000219631i
$676$		−	90.1838i		−	3.46861i
$677$	−10.4788	+	10.4788i	−0.402734	+	0.402734i	−0.879195	−	0.476461i	$-0.841919\pi$
$677$	−10.4788	+	10.4788i	−0.402734	+	0.402734i	0.476461	+	0.879195i	$0.341919\pi$
$678$	25.6969	+	44.5460i	0.986884	+	1.71078i
$679$	−18.8467	−	18.8467i	−0.723269	−	0.723269i
$680$	−21.5450			−0.826212
$681$	27.4000	−	15.8060i	1.04997	−	0.605688i
$682$	63.6056	+	63.6056i	2.43558	+	2.43558i
$683$		−	6.30348i		−	0.241196i	−0.992701	−	0.120598i	$-0.961519\pi$
$683$		−	6.30348i		−	0.241196i	0.992701	−	0.120598i	$-0.0384812\pi$
$684$	−40.4239	+	10.7998i	−1.54565	+	0.412942i
$685$	4.07631	+	4.07631i	0.155748	+	0.155748i
$686$	−35.3605	−	35.3605i	−1.35007	−	1.35007i
$687$	−11.5059	+	42.8779i	−0.438979	+	1.63590i
$688$	−8.96844	+	8.96844i	−0.341919	+	0.341919i
$689$	−20.0514			−0.763897
$690$	10.3919	+	2.78859i	0.395614	+	0.106160i
$691$	−49.7574			−1.89286			−0.946431	−	0.322906i	$-0.895340\pi$
$691$	−49.7574			−1.89286			−0.946431	+	0.322906i	$0.895340\pi$
$692$			6.00037i			0.228100i
$693$	−16.3963	+	4.38053i	−0.622846	+	0.166402i
$694$	−23.7266	−	23.7266i	−0.900649	−	0.900649i
$695$	−13.7092			−0.520018
$696$	−7.72786	−	89.2059i	−0.292924	−	3.38134i
$697$	−20.8497			−0.789739
$698$	25.9948	+	25.9948i	0.983916	+	0.983916i
$699$	0.117997	−	0.0680681i	0.00446306	−	0.00257457i
$700$			8.76433i			0.331261i
$701$	−36.3379			−1.37247			−0.686233	−	0.727382i	$-0.740737\pi$
$701$	−36.3379			−1.37247			−0.686233	+	0.727382i	$0.740737\pi$
$702$	−54.6205	+	54.5007i	−2.06152	+	2.05700i
$703$	4.25535			0.160493
$704$	79.2857	−	79.2857i	2.98819	−	2.98819i
$705$	−6.87333	−	1.84440i	−0.258864	−	0.0694641i
$706$	−45.8192	−	45.8192i	−1.72443	−	1.72443i
$707$	15.5528	+	15.5528i	0.584925	+	0.584925i
$708$	57.6720	+	99.9753i	2.16745	+	3.75730i
$709$			1.03361i			0.0388179i	0.999812	+	0.0194090i	$0.00617846\pi$
$709$			1.03361i			0.0388179i	−0.999812	+	0.0194090i	$0.993822\pi$
$710$	6.83034	+	6.83034i	0.256338	+	0.256338i
$711$	−3.88166	−	14.5291i	−0.145573	−	0.544883i
$712$	−42.8669			−1.60650
$713$	−14.8197	−	14.8197i	−0.555001	−	0.555001i
$714$	−14.6873	+	8.47256i	−0.549659	+	0.317078i
$715$	13.6183	−	13.6183i	0.509296	−	0.509296i
$716$			3.25947i			0.121812i
$717$	29.3580	−	16.9355i	1.09639	−	0.632468i
$718$		−	61.4784i		−	2.29435i
$719$		−	14.6154i		−	0.545062i	−0.962147	−	0.272531i	$-0.912139\pi$
$719$		−	14.6154i		−	0.545062i	0.962147	−	0.272531i	$-0.0878607\pi$
$720$	−22.9623	+	39.7046i	−0.855753	+	1.47970i
$721$	10.8920			0.405640
$722$	−24.3671	+	24.3671i	−0.906848	+	0.906848i
$723$	−4.54830	+	2.62374i	−0.169153	+	0.0975780i
$724$		−	50.2006i		−	1.86569i
$725$	−1.83937	−	5.06130i	−0.0683126	−	0.187972i
$726$	7.43755	+	1.99580i	0.276033	+	0.0740712i
$727$	16.2730	−	16.2730i	0.603534	−	0.603534i	−0.337715	−	0.941248i	$-0.609654\pi$
$727$	16.2730	−	16.2730i	0.603534	−	0.603534i	0.941248	+	0.337715i	$0.109654\pi$
$728$	−58.5890	−	58.5890i	−2.17145	−	2.17145i
$729$	26.9999	+	0.0593004i	0.999998	+	0.00219631i
$730$		−	24.8167i		−	0.918508i
$731$	−1.86186			−0.0688634
$732$	26.0872	−	97.2166i	0.964212	−	3.59323i
$733$	−21.9573	−	21.9573i	−0.811011	−	0.811011i	0.173774	−	0.984785i	$-0.444404\pi$
$733$	−21.9573	−	21.9573i	−0.811011	−	0.811011i	−0.984785	+	0.173774i	$0.944404\pi$
$734$	59.0775			2.18059
$735$	−3.86408	−	6.69844i	−0.142529	−	0.247076i
$736$	−36.3713	+	36.3713i	−1.34066	+	1.34066i
$737$	4.66234	−	4.66234i	0.171739	−	0.171739i
$738$	−38.2216	+	66.0899i	−1.40696	+	2.43280i
$739$	−0.212016	+	0.212016i	−0.00779913	+	0.00779913i	−0.710996	−	0.703196i	$-0.751755\pi$
$739$	−0.212016	+	0.212016i	−0.00779913	+	0.00779913i	0.703196	+	0.710996i	$0.251755\pi$
$740$	6.53639	−	6.53639i	0.240282	−	0.240282i
$741$	6.16583	−	22.9776i	0.226508	−	0.844102i
$742$	−11.4089	+	11.4089i	−0.418834	+	0.418834i
$743$	24.0461	−	24.0461i	0.882166	−	0.882166i	−0.111588	−	0.993755i	$-0.535594\pi$
$743$	24.0461	−	24.0461i	0.882166	−	0.882166i	0.993755	+	0.111588i	$0.0355938\pi$
$744$	133.111	−	76.7869i	4.88009	−	2.81514i
$745$	−19.9073			−0.729348
$746$	53.2229	+	53.2229i	1.94863	+	1.94863i
$747$	37.3814	+	21.6187i	1.36771	+	0.790986i
$748$	43.8906			1.60480
$749$		−	0.261577i		−	0.00955782i
$750$	−1.22972	+	4.58265i	−0.0449029	+	0.167335i
$751$	18.7224	+	18.7224i	0.683192	+	0.683192i	0.960718	−	0.277526i	$-0.0895146\pi$
$751$	18.7224	+	18.7224i	0.683192	+	0.683192i	−0.277526	+	0.960718i	$0.589515\pi$
$752$	44.4184	−	44.4184i	1.61977	−	1.61977i
$753$	−1.88150	+	7.01160i	−0.0685658	+	0.255517i
$754$	72.4584	+	33.8308i	2.63878	+	1.23205i
$755$		−	7.19222i		−	0.261752i
$756$	−0.0500109	+	45.5408i	−0.00181888	+	1.65630i
$757$	−32.8279	+	32.8279i	−1.19315	+	1.19315i	−0.216972	+	0.976178i	$0.569618\pi$
$757$	−32.8279	+	32.8279i	−1.19315	+	1.19315i	−0.976178	+	0.216972i	$0.930382\pi$
$758$	66.7234			2.42350
$759$	−13.4779	−	3.61668i	−0.489216	−	0.131277i
$760$		−	24.3244i		−	0.882340i
$761$		−	32.4308i		−	1.17561i	−0.809001	−	0.587807i	$-0.799991\pi$
$761$		−	32.4308i		−	1.17561i	0.809001	−	0.587807i	$-0.200009\pi$
$762$	46.4566	+	80.5332i	1.68294	+	2.91741i
$763$		−	23.4047i		−	0.847308i
$764$	−82.6341	+	82.6341i	−2.98960	+	2.98960i
$765$	−6.50487	+	1.73787i	−0.235184	+	0.0628328i
$766$	26.2540	+	26.2540i	0.948597	+	0.948597i
$767$	−65.6242			−2.36955
$768$	−42.7880	−	74.1737i	−1.54398	−	2.67651i
$769$	−20.6376	−	20.6376i	−0.744213	−	0.744213i	0.229173	−	0.973386i	$-0.426398\pi$
$769$	−20.6376	−	20.6376i	−0.744213	−	0.744213i	−0.973386	+	0.229173i	$0.926398\pi$
$770$		−	15.4972i		−	0.558479i
$771$	−29.5249	+	17.0318i	−1.06331	+	0.613385i
$772$	11.0802	+	11.0802i	0.398787	+	0.398787i
$773$	−6.76485	−	6.76485i	−0.243315	−	0.243315i	0.574905	−	0.818220i	$-0.305039\pi$
$773$	−6.76485	−	6.76485i	−0.243315	−	0.243315i	−0.818220	+	0.574905i	$0.805039\pi$
$774$	−3.41315	+	5.90177i	−0.122683	+	0.212135i
$775$	6.53520	−	6.53520i	0.234751	−	0.234751i
$776$	160.691			5.76847
$777$	1.20037	−	4.47330i	0.0430631	−	0.160479i
$778$	−54.0507			−1.93781
$779$		−	23.5395i		−	0.843389i
$780$	−25.8235	−	44.7654i	−0.924629	−	1.60286i
$781$	−8.85866	−	8.85866i	−0.316988	−	0.316988i
$782$	−13.9419			−0.498562
$783$	−9.52877	−	26.3097i	−0.340530	−	0.940233i
$784$	68.2596			2.43784
$785$	7.33987	+	7.33987i	0.261971	+	0.261971i
$786$	−14.8708	−	25.7787i	−0.530423	−	0.919497i
$787$		−	16.6517i		−	0.593569i	−0.954944	−	0.296785i	$-0.904086\pi$
$787$		−	16.6517i		−	0.593569i	0.954944	−	0.296785i	$-0.0959143\pi$
$788$	−25.9684			−0.925085
$789$	−1.22604	+	4.56897i	−0.0436483	+	0.162660i
$790$	13.7323			0.488573
$791$	−12.2031	+	12.2031i	−0.433894	+	0.433894i
$792$	51.2248	−	88.5741i	1.82019	−	3.14734i
$793$	40.4686	+	40.4686i	1.43708	+	1.43708i
$794$	−10.4294	−	10.4294i	−0.370127	−	0.370127i
$795$	−5.54971	+	3.20142i	−0.196828	+	0.113543i
$796$		−	102.177i		−	3.62157i
$797$	38.7670	+	38.7670i	1.37320	+	1.37320i	0.855659	+	0.517540i	$0.173152\pi$
$797$	38.7670	+	38.7670i	1.37320	+	1.37320i	0.517540	+	0.855659i	$0.326848\pi$
$798$	−9.56559	−	16.5821i	−0.338618	−	0.587000i
$799$	9.22133			0.326227
$800$	−16.0391	−	16.0391i	−0.567068	−	0.567068i
$801$	−12.9424	+	3.45775i	−0.457297	+	0.122174i
$802$	17.3355	−	17.3355i	0.612136	−	0.612136i
$803$			32.1862i			1.13583i
$804$	−8.84088	−	15.3258i	−0.311794	−	0.540499i
$805$			3.61073i			0.127262i
$806$			137.242i			4.83414i
$807$	−22.7872	−	6.11475i	−0.802147	−	0.215249i
$808$	−132.607			−4.66510
$809$	−7.51762	+	7.51762i	−0.264305	+	0.264305i	−0.826801	−	0.562495i	$-0.809841\pi$
$809$	−7.51762	+	7.51762i	−0.264305	+	0.264305i	0.562495	+	0.826801i	$0.309841\pi$
$810$	−6.41594	+	23.8051i	−0.225433	+	0.836427i
$811$		−	9.12308i		−	0.320355i	−0.987088	−	0.160177i	$-0.948793\pi$
$811$		−	9.12308i		−	0.320355i	0.987088	−	0.160177i	$-0.0512066\pi$
$812$	44.3589	−	16.1209i	1.55669	−	0.565732i
$813$	−1.94126	+	7.23428i	−0.0680829	+	0.253717i
$814$	−11.5577	+	11.5577i	−0.405097	+	0.405097i
$815$	2.83532	+	2.83532i	0.0993169	+	0.0993169i
$816$	15.4032	−	57.4015i	0.539220	−	2.00945i
$817$		−	2.10205i		−	0.0735416i
$818$	−79.7922			−2.78987
$819$	−22.4151	−	12.9633i	−0.783248	−	0.452973i
$820$	−36.1576	−	36.1576i	−1.26268	−	1.26268i
$821$	−12.3423			−0.430749			−0.215374	−	0.976532i	$-0.569097\pi$
$821$	−12.3423			−0.430749			−0.215374	+	0.976532i	$0.569097\pi$
$822$	−23.6930	+	13.6676i	−0.826388	+	0.476712i
$823$	−3.25062	+	3.25062i	−0.113310	+	0.113310i	−0.761488	−	0.648179i	$-0.775531\pi$
$823$	−3.25062	+	3.25062i	−0.113310	+	0.113310i	0.648179	+	0.761488i	$0.275531\pi$
$824$	−46.4339	+	46.4339i	−1.61760	+	1.61760i
$825$	1.59489	−	5.94351i	0.0555269	−	0.206926i
$826$	−37.3391	+	37.3391i	−1.29919	+	1.29919i
$827$	−1.52365	+	1.52365i	−0.0529824	+	0.0529824i	−0.733102	−	0.680119i	$-0.761928\pi$
$827$	−1.52365	+	1.52365i	−0.0529824	+	0.0529824i	0.680119	+	0.733102i	$0.261928\pi$
$828$	−18.7466	+	32.4153i	−0.651491	+	1.12651i
$829$	−15.0106	+	15.0106i	−0.521340	+	0.521340i	−0.917976	−	0.396636i	$-0.870178\pi$
$829$	−15.0106	+	15.0106i	−0.521340	+	0.521340i	0.396636	+	0.917976i	$0.370178\pi$
$830$	−27.8823	+	27.8823i	−0.967807	+	0.967807i
$831$	6.66885	+	11.5606i	0.231340	+	0.401031i
$832$	171.075			5.93095
$833$	7.08539	+	7.08539i	0.245494	+	0.245494i
$834$	16.8584	−	62.8243i	0.583758	−	2.17543i
$835$	9.25131			0.320155
$836$			49.5529i			1.71382i
$837$	33.9952	−	33.9206i	1.17505	−	1.17247i
$838$	−26.7294	−	26.7294i	−0.923351	−	0.923351i
$839$	−30.8748	+	30.8748i	−1.06592	+	1.06592i	−0.0682485	+	0.997668i	$0.521741\pi$
$839$	−30.8748	+	30.8748i	−1.06592	+	1.06592i	−0.997668	+	0.0682485i	$0.978259\pi$
$840$	−25.5703	−	6.86157i	−0.882259	−	0.236747i
$841$	−22.2334	+	18.6192i	−0.766670	+	0.642042i
$842$			52.2459i			1.80051i
$843$	−17.8696	+	10.3083i	−0.615460	+	0.355036i
$844$	−2.69243	+	2.69243i	−0.0926773	+	0.0926773i
$845$	16.3842			0.563634
$846$	16.9045	−	29.2300i	0.581188	−	1.00495i
$847$			2.58422i			0.0887947i
$848$		−	56.5537i		−	1.94206i
$849$	−0.334098	+	0.192728i	−0.0114662	+	0.00661442i
$850$		−	6.14814i		−	0.210879i
$851$	2.69286	−	2.69286i	0.0923101	−	0.0923101i
$852$	−29.1198	+	16.7981i	−0.997627	+	0.575493i
$853$	−1.23954	−	1.23954i	−0.0424412	−	0.0424412i	0.685568	−	0.728009i	$-0.259554\pi$
$853$	−1.23954	−	1.23954i	−0.0424412	−	0.0424412i	−0.728009	+	0.685568i	$0.759554\pi$
$854$	46.0519			1.57586
$855$	−1.96207	−	7.34404i	−0.0671013	−	0.251161i
$856$	1.11513	+	1.11513i	0.0381144	+	0.0381144i
$857$		−	12.5177i		−	0.427596i	−0.976878	−	0.213798i	$-0.931417\pi$
$857$		−	12.5177i		−	0.427596i	0.976878	−	0.213798i	$-0.0685834\pi$
$858$	45.6613	+	79.1546i	1.55885	+	2.70229i
$859$	23.1283	+	23.1283i	0.789126	+	0.789126i	0.981351	−	0.192225i	$-0.0615704\pi$
$859$	23.1283	+	23.1283i	0.789126	+	0.789126i	−0.192225	+	0.981351i	$0.561570\pi$
$860$	−3.22884	−	3.22884i	−0.110103	−	0.110103i
$861$	−24.7451	−	6.64015i	−0.843312	−	0.226296i
$862$	−15.7157	+	15.7157i	−0.535279	+	0.535279i
$863$	40.8550			1.39072			0.695359	−	0.718662i	$-0.255245\pi$
$863$	40.8550			1.39072			0.695359	+	0.718662i	$0.255245\pi$
$864$	−83.2500	−	83.4331i	−2.83222	−	2.83845i
$865$	−1.09012			−0.0370653
$866$		−	97.2163i		−	3.30354i
$867$	−17.9482	+	10.3536i	−0.609553	+	0.351628i
$868$	57.2767	+	57.2767i	1.94410	+	1.94410i
$869$	−17.8102			−0.604170
$870$	25.4561	−	2.20525i	0.863042	−	0.0747649i
$871$	10.0599			0.340867
$872$	99.7770	+	99.7770i	3.37887	+	3.37887i
$873$	48.5159	−	12.9617i	1.64201	−	0.438688i
$874$		−	15.7405i		−	0.532432i
$875$	−1.59227			−0.0538285
$876$	83.4168	+	22.3842i	2.81839	+	0.756292i
$877$	−18.6911			−0.631155			−0.315578	−	0.948900i	$-0.602198\pi$
$877$	−18.6911			−0.631155			−0.315578	+	0.948900i	$0.602198\pi$
$878$	36.7594	−	36.7594i	1.24057	−	1.24057i
$879$	0.248706	−	0.926827i	0.00838865	−	0.0312611i
$880$	38.4095	+	38.4095i	1.29479	+	1.29479i
$881$	−26.0499	−	26.0499i	−0.877645	−	0.877645i	0.115646	−	0.993291i	$-0.463106\pi$
$881$	−26.0499	−	26.0499i	−0.877645	−	0.877645i	−0.993291	+	0.115646i	$0.963106\pi$
$882$	35.4484	−	9.47055i	1.19361	−	0.318890i
$883$			33.5443i			1.12886i	0.825482	+	0.564428i	$0.190903\pi$
$883$			33.5443i			1.12886i	−0.825482	+	0.564428i	$0.809097\pi$
$884$	47.3514	+	47.3514i	1.59260	+	1.59260i
$885$	−18.1631	+	10.4776i	−0.610546	+	0.352201i
$886$	−110.828			−3.72335
$887$	3.00322	+	3.00322i	0.100838	+	0.100838i	0.755726	−	0.654888i	$-0.227284\pi$
$887$	3.00322	+	3.00322i	0.100838	+	0.100838i	−0.654888	+	0.755726i	$0.727284\pi$
$888$	13.9528	+	24.1875i	0.468227	+	0.811678i
$889$	−22.0616	+	22.0616i	−0.739924	+	0.739924i
$890$		−	12.2326i		−	0.410039i
$891$	8.32120	−	30.8742i	0.278771	−	1.03433i
$892$		−	106.881i		−	3.57863i
$893$			10.4109i			0.348389i
$894$	24.4804	−	91.2285i	0.818747	−	3.05114i
$895$	−0.592168			−0.0197940
$896$	46.2616	−	46.2616i	1.54549	−	1.54549i
$897$	−10.6388	−	18.4425i	−0.355218	−	0.615776i
$898$		−	36.6904i		−	1.22437i
$899$	−45.0973	−	21.0559i	−1.50408	−	0.702254i
$900$	−14.2946	−	8.26693i	−0.476485	−	0.275564i
$901$	5.87031	−	5.87031i	0.195568	−	0.195568i
$902$	63.9342	+	63.9342i	2.12877	+	2.12877i
$903$	−2.20972	−	0.592959i	−0.0735348	−	0.0197324i
$904$		−	104.047i		−	3.46054i
$905$	9.12023			0.303167
$906$	32.9595	+	8.84440i	1.09501	+	0.293835i
$907$	6.64964	+	6.64964i	0.220798	+	0.220798i	0.808834	−	0.588037i	$-0.200099\pi$
$907$	6.64964	+	6.64964i	0.220798	+	0.220798i	−0.588037	+	0.808834i	$0.700099\pi$
$908$	−100.524			−3.33601
$909$	−40.0367	+	10.6964i	−1.32794	+	0.354777i
$910$	16.7191	−	16.7191i	0.554234	−	0.554234i
$911$	−12.7040	+	12.7040i	−0.420903	+	0.420903i	−0.885514	−	0.464612i	$-0.846194\pi$
$911$	−12.7040	+	12.7040i	−0.420903	+	0.420903i	0.464612	+	0.885514i	$0.346194\pi$
$912$	64.8067	+	17.3903i	2.14596	+	0.575852i
$913$	36.1621	−	36.1621i	1.19679	−	1.19679i
$914$	13.2864	−	13.2864i	0.439474	−	0.439474i
$915$	17.6619	+	4.73942i	0.583884	+	0.156680i
$916$	99.7608	−	99.7608i	3.29619	−	3.29619i
$917$	7.06194	−	7.06194i	0.233206	−	0.233206i
$918$	0.0350824	−	31.9466i	0.00115789	−	1.05440i
$919$	21.9571			0.724297			0.362148	−	0.932120i	$-0.382043\pi$
$919$	21.9571			0.724297			0.362148	+	0.932120i	$0.382043\pi$
$920$	−15.3929	−	15.3929i	−0.507490	−	0.507490i
$921$	−29.6120	−	7.94612i	−0.975748	−	0.261834i
$922$	−49.8526			−1.64181
$923$		−	19.1143i		−	0.629156i
$924$	52.0909	+	13.9781i	1.71366	+	0.459847i
$925$	1.18750	+	1.18750i	0.0390449	+	0.0390449i
$926$	−40.9570	+	40.9570i	−1.34593	+	1.34593i
$927$	−10.2739	+	17.7648i	−0.337438	+	0.583473i
$928$	−51.6767	+	110.680i	−1.69637	+	3.63326i
$929$		−	9.65009i		−	0.316609i	−0.987390	−	0.158305i	$-0.949397\pi$
$929$		−	9.65009i		−	0.316609i	0.987390	−	0.158305i	$-0.0506028\pi$
$930$	21.9121	+	37.9850i	0.718527	+	1.24558i
$931$	−7.99946	+	7.99946i	−0.262172	+	0.262172i
$932$	−0.432904			−0.0141802
$933$	−4.59613	+	17.1279i	−0.150470	+	0.560742i
$934$			26.5509i			0.868772i
$935$			7.97387i			0.260773i
$936$	150.822	−	40.2943i	4.92977	−	1.31706i
$937$			38.7601i			1.26624i	0.774055	+	0.633118i	$0.218225\pi$
$937$			38.7601i			1.26624i	−0.774055	+	0.633118i	$0.781775\pi$
$938$	5.72393	−	5.72393i	0.186893	−	0.186893i
$939$	−5.51685	−	9.56355i	−0.180036	−	0.312095i
$940$	15.9916	+	15.9916i	0.521590	+	0.521590i
$941$	−28.9810			−0.944754			−0.472377	−	0.881397i	$-0.656604\pi$
$941$	−28.9810			−0.944754			−0.472377	+	0.881397i	$0.656604\pi$
$942$	−42.6620	+	24.6101i	−1.39000	+	0.801841i
$943$	−14.8962	−	14.8962i	−0.485087	−	0.485087i
$944$		−	185.089i		−	6.02413i
$945$	−8.27366	−	0.00908578i	−0.269142	−	0.000295560i
$946$	5.70926	+	5.70926i	0.185624	+	0.185624i
$947$	−5.05298	−	5.05298i	−0.164200	−	0.164200i	0.620224	−	0.784424i	$-0.287042\pi$
$947$	−5.05298	−	5.05298i	−0.164200	−	0.164200i	−0.784424	+	0.620224i	$0.787042\pi$
$948$	−12.3863	+	46.1586i	−0.402287	+	1.49916i
$949$	−34.7241	+	34.7241i	−1.12719	+	1.12719i
$950$	6.94129			0.225205
$951$	9.11543	+	2.44605i	0.295588	+	0.0793185i
$952$	34.3054			1.11184
$953$		−	32.6549i		−	1.05780i	−0.848686	−	0.528898i	$-0.822606\pi$
$953$		−	32.6549i		−	1.05780i	0.848686	−	0.528898i	$-0.177394\pi$
$954$	−7.84643	−	29.3693i	−0.254037	−	0.950865i
$955$	−15.0126	−	15.0126i	−0.485797	−	0.485797i
$956$	−107.707			−3.48351
$957$	−33.0154	+	2.86011i	−1.06724	+	0.0924542i
$958$	−16.6010			−0.536353
$959$	−6.49057	−	6.49057i	−0.209591	−	0.209591i
$960$	47.3491	−	27.3139i	1.52819	−	0.881553i
$961$		−	54.4178i		−	1.75541i
$962$	−24.9380			−0.804035
$963$	0.426631	+	0.246732i	0.0137480	+	0.00795082i
$964$	16.6866			0.537440
$965$	−2.01301	+	2.01301i	−0.0648012	+	0.0648012i
$966$	−16.5467	−	4.44018i	−0.532382	−	0.142860i
$967$	30.3946	+	30.3946i	0.977425	+	0.977425i	0.999751	−	0.0223259i	$-0.00710716\pi$
$967$	30.3946	+	30.3946i	0.977425	+	0.977425i	−0.0223259	+	0.999751i	$0.507107\pi$
$968$	−11.0168	−	11.0168i	−0.354093	−	0.354093i
$969$	4.92185	+	8.53211i	0.158113	+	0.274091i
$970$			45.8553i			1.47232i
$971$	15.9498	+	15.9498i	0.511852	+	0.511852i	0.915094	−	0.403241i	$-0.132116\pi$
$971$	15.9498	+	15.9498i	0.511852	+	0.511852i	−0.403241	+	0.915094i	$0.632116\pi$
$972$	−74.2295	−	43.0378i	−2.38091	−	1.38044i
$973$	21.8286			0.699794
$974$	−47.2882	−	47.2882i	−1.51521	−	1.51521i
$975$	8.13280	−	4.69151i	0.260458	−	0.150248i
$976$	−114.139	+	114.139i	−3.65350	+	3.65350i
$977$		−	10.6066i		−	0.339334i	−0.985501	−	0.169667i	$-0.945731\pi$
$977$		−	10.6066i		−	0.339334i	0.985501	−	0.169667i	$-0.0542693\pi$
$978$	−16.4799	+	9.50665i	−0.526970	+	0.303989i
$979$			15.8652i			0.507054i
$980$			24.5750i			0.785019i
$981$	38.1730	+	22.0764i	1.21877	+	0.704847i
$982$	3.21755			0.102676
$983$	−35.3828	+	35.3828i	−1.12854	+	1.12854i	−0.138121	+	0.990415i	$0.544106\pi$
$983$	−35.3828	+	35.3828i	−1.12854	+	1.12854i	−0.990415	+	0.138121i	$0.955894\pi$
$984$	133.799	−	77.1835i	4.26535	−	2.46052i
$985$		−	4.71783i		−	0.150323i
$986$	−31.1175	+	11.3087i	−0.990984	+	0.360143i
$987$	10.9442	+	2.93678i	0.348357	+	0.0934786i
$988$	−53.4601	+	53.4601i	−1.70079	+	1.70079i
$989$	−1.33022	−	1.33022i	−0.0422985	−	0.0422985i
$990$	25.2758	+	14.6177i	0.803317	+	0.464580i
$991$			23.9380i			0.760416i	0.924901	+	0.380208i	$0.124148\pi$
$991$			23.9380i			0.760416i	−0.924901	+	0.380208i	$0.875852\pi$
$992$	−209.637			−6.65600
$993$	9.62650	−	35.8741i	0.305488	−	1.13843i
$994$	−10.8757	−	10.8757i	−0.344957	−	0.344957i
$995$	18.5631			0.588491
$996$	−68.5718	−	118.870i	−2.17278	−	3.76655i
$997$	5.24305	−	5.24305i	0.166049	−	0.166049i	−0.619191	−	0.785240i	$-0.712539\pi$
$997$	5.24305	−	5.24305i	0.166049	−	0.166049i	0.785240	+	0.619191i	$0.212539\pi$
$998$	42.1917	−	42.1917i	1.33556	−	1.33556i
$999$	6.16367	+	6.17722i	0.195010	+	0.195439i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	435.2.q.c.191.18	yes	36
3.2	odd	2		435.2.q.d.191.1	yes	36
29.12	odd	4		435.2.q.d.41.1	yes	36
87.41	even	4	inner	435.2.q.c.41.18	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
435.2.q.c.41.18	✓	36	87.41	even	4	inner
435.2.q.c.191.18	yes	36	1.1	even	1	trivial
435.2.q.d.41.1	yes	36	29.12	odd	4
435.2.q.d.191.1	yes	36	3.2	odd	2

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 $\F_{q}$
Belyi maps

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+(1.93705 + 1.93705i) q^{2} +(-0.865476 - 1.50032i) q^{3} +5.50431i q^{4} -1.00000 q^{5} +(1.22972 - 4.58265i) q^{6} +1.59227 q^{7} +(-6.78801 + 6.78801i) q^{8} +(-1.50190 + 2.59698i) q^{9} +(-1.93705 - 1.93705i) q^{10} +(2.51227 + 2.51227i) q^{11} +(8.25821 - 4.76385i) q^{12} +5.42072i q^{13} +(3.08430 + 3.08430i) q^{14} +(0.865476 + 1.50032i) q^{15} -15.2888 q^{16} +(-1.58699 - 1.58699i) q^{17} +(-7.93972 + 2.12121i) q^{18} +(1.79172 - 1.79172i) q^{19} -5.50431i q^{20} +(-1.37807 - 2.38891i) q^{21} +9.73277i q^{22} -2.26767i q^{23} +(16.0590 + 4.30931i) q^{24} +1.00000 q^{25} +(-10.5002 + 10.5002i) q^{26} +(5.19615 + 0.00570619i) q^{27} +8.76433i q^{28} +(-1.83937 - 5.06130i) q^{29} +(-1.22972 + 4.58265i) q^{30} +(6.53520 - 6.53520i) q^{31} +(-16.0391 - 16.0391i) q^{32} +(1.59489 - 5.94351i) q^{33} -6.14814i q^{34} -1.59227 q^{35} +(-14.2946 - 8.26693i) q^{36} +(1.18750 + 1.18750i) q^{37} +6.94129 q^{38} +(8.13280 - 4.69151i) q^{39} +(6.78801 - 6.78801i) q^{40} +(6.56896 - 6.56896i) q^{41} +(1.95804 - 7.29681i) q^{42} +(0.586602 - 0.586602i) q^{43} +(-13.8283 + 13.8283i) q^{44} +(1.50190 - 2.59698i) q^{45} +(4.39258 - 4.39258i) q^{46} +(-2.90529 + 2.90529i) q^{47} +(13.2321 + 22.9380i) q^{48} -4.46468 q^{49} +(1.93705 + 1.93705i) q^{50} +(-1.00748 + 3.75448i) q^{51} -29.8373 q^{52} +3.69903i q^{53} +(10.0541 + 10.0762i) q^{54} +(-2.51227 - 2.51227i) q^{55} +(-10.8083 + 10.8083i) q^{56} +(-4.23884 - 1.13746i) q^{57} +(6.24102 - 13.3669i) q^{58} +12.1062i q^{59} +(-8.25821 + 4.76385i) q^{60} +(7.46553 - 7.46553i) q^{61} +25.3180 q^{62} +(-2.39143 + 4.13508i) q^{63} -31.5594i q^{64} -5.42072i q^{65} +(14.6022 - 8.42348i) q^{66} -1.85583i q^{67} +(8.73526 - 8.73526i) q^{68} +(-3.40222 + 1.96261i) q^{69} +(-3.08430 - 3.08430i) q^{70} -3.52616 q^{71} +(-7.43339 - 27.8232i) q^{72} +(6.40581 + 6.40581i) q^{73} +4.60050i q^{74} +(-0.865476 - 1.50032i) q^{75} +(9.86218 + 9.86218i) q^{76} +(4.00020 + 4.00020i) q^{77} +(24.8413 + 6.66595i) q^{78} +(-3.54465 + 3.54465i) q^{79} +15.2888 q^{80} +(-4.48858 - 7.80081i) q^{81} +25.4488 q^{82} -14.3942i q^{83} +(13.1493 - 7.58532i) q^{84} +(1.58699 + 1.58699i) q^{85} +2.27255 q^{86} +(-6.00161 + 7.14007i) q^{87} -34.1066 q^{88} +(3.15754 + 3.15754i) q^{89} +(7.93972 - 2.12121i) q^{90} +8.63124i q^{91} +12.4819 q^{92} +(-15.4609 - 4.14881i) q^{93} -11.2554 q^{94} +(-1.79172 + 1.79172i) q^{95} +(-10.1823 + 37.9452i) q^{96} +(-11.8364 - 11.8364i) q^{97} +(-8.64830 - 8.64830i) q^{98} +(-10.2975 + 2.75112i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 4 q^{2} + 6 q^{3} - 36 q^{5} + 8 q^{6} + 8 q^{7} + 4 q^{8} + 4 q^{10} - 12 q^{11} + 10 q^{12} + 28 q^{14} - 6 q^{15} - 60 q^{16} - 20 q^{17} - 28 q^{18} + 16 q^{19} + 12 q^{21} + 24 q^{24} + 36 q^{25}+ \cdots - 48 q^{99}+O(q^{100}) \) 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

L-functions

Modular forms

Varieties

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Representations

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Database

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